LMFDB - Embedded newform 578.2.d.h.399.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [578,2,Mod(155,578)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("578.155"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(578, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 578 = 2 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	578.d (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-24,0,-96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(18)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.61535323683$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			399.6
Character	$\chi$	$=$	578.399
Dual form			578.2.d.h.423.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(1.23480 - 2.98107i) q^{3} -1.00000i q^{4} +(1.09461 + 0.453400i) q^{5} +(-1.23480 - 2.98107i) q^{6} +(1.03531 - 0.428841i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-5.24070 - 5.24070i) q^{9} +(1.09461 - 0.453400i) q^{10} +(1.30551 + 3.15179i) q^{11} +(-2.98107 - 1.23480i) q^{12} +0.347296i q^{13} +(0.428841 - 1.03531i) q^{14} +(2.70323 - 2.70323i) q^{15} -1.00000 q^{16} -7.41147 q^{18} +(-0.245576 + 0.245576i) q^{19} +(0.453400 - 1.09461i) q^{20} -3.61587i q^{21} +(3.15179 + 1.30551i) q^{22} +(-0.157464 - 0.380153i) q^{23} +(-2.98107 + 1.23480i) q^{24} +(-2.54294 - 2.54294i) q^{25} +(0.245576 + 0.245576i) q^{26} +(-13.1509 + 5.44728i) q^{27} +(-0.428841 - 1.03531i) q^{28} +(8.11264 + 3.36037i) q^{29} -3.82295i q^{30} +(-3.33581 + 8.05335i) q^{31} +(-0.707107 + 0.707107i) q^{32} +11.0077 q^{33} +1.32770 q^{35} +(-5.24070 + 5.24070i) q^{36} +(-0.182024 + 0.439445i) q^{37} +0.347296i q^{38} +(1.03531 + 0.428841i) q^{39} +(-0.453400 - 1.09461i) q^{40} +(2.43734 - 1.00958i) q^{41} +(-2.55680 - 2.55680i) q^{42} +(6.59925 + 6.59925i) q^{43} +(3.15179 - 1.30551i) q^{44} +(-3.36037 - 8.11264i) q^{45} +(-0.380153 - 0.157464i) q^{46} -7.86484i q^{47} +(-1.23480 + 2.98107i) q^{48} +(-4.06178 + 4.06178i) q^{49} -3.59627 q^{50} +0.347296 q^{52} +(-5.95328 + 5.95328i) q^{53} +(-5.44728 + 13.1509i) q^{54} +4.04189i q^{55} +(-1.03531 - 0.428841i) q^{56} +(0.428841 + 1.03531i) q^{57} +(8.11264 - 3.36037i) q^{58} +(-4.53360 - 4.53360i) q^{59} +(-2.70323 - 2.70323i) q^{60} +(5.26827 - 2.18219i) q^{61} +(3.33581 + 8.05335i) q^{62} +(-7.67320 - 3.17834i) q^{63} +1.00000i q^{64} +(-0.157464 + 0.380153i) q^{65} +(7.78365 - 7.78365i) q^{66} -7.31315 q^{67} -1.32770 q^{69} +(0.938823 - 0.938823i) q^{70} +(2.90697 - 7.01804i) q^{71} +7.41147i q^{72} +(8.35362 + 3.46018i) q^{73} +(0.182024 + 0.439445i) q^{74} +(-10.7207 + 4.44066i) q^{75} +(0.245576 + 0.245576i) q^{76} +(2.70323 + 2.70323i) q^{77} +(1.03531 - 0.428841i) q^{78} +(-5.08062 - 12.2657i) q^{79} +(-1.09461 - 0.453400i) q^{80} +23.6955i q^{81} +(1.00958 - 2.43734i) q^{82} +(-5.47242 + 5.47242i) q^{83} -3.61587 q^{84} +9.33275 q^{86} +(20.0349 - 20.0349i) q^{87} +(1.30551 - 3.15179i) q^{88} -7.18479i q^{89} +(-8.11264 - 3.36037i) q^{90} +(0.148935 + 0.359560i) q^{91} +(-0.380153 + 0.157464i) q^{92} +(19.8885 + 19.8885i) q^{93} +(-5.56128 - 5.56128i) q^{94} +(-0.380153 + 0.157464i) q^{95} +(1.23480 + 2.98107i) q^{96} +(-0.204759 - 0.0848138i) q^{97} +5.74422i q^{98} +(9.67579 - 23.3594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{16} - 96 q^{18} + 72 q^{33} + 24 q^{50} + 72 q^{86}+O(q^{100}) $ 24 * q - 24 * q^16 - 96 * q^18 + 72 * q^33 + 24 * q^50 + 72 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/578\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.23480	−	2.98107i	0.712911	−	1.72112i	0.0203141	−	0.999794i	$-0.493533\pi$
$3$	1.23480	−	2.98107i	0.712911	−	1.72112i	0.692597	−	0.721325i	$-0.256467\pi$
$4$		−	1.00000i		−	0.500000i
$5$	1.09461	+	0.453400i	0.489522	+	0.202767i	0.613771	−	0.789484i	$-0.289652\pi$
$5$	1.09461	+	0.453400i	0.489522	+	0.202767i	−0.124248	+	0.992251i	$0.539652\pi$
$6$	−1.23480	−	2.98107i	−0.504104	−	1.21701i
$7$	1.03531	−	0.428841i	0.391312	−	0.162087i	−0.178348	−	0.983968i	$-0.557075\pi$
$7$	1.03531	−	0.428841i	0.391312	−	0.162087i	0.569659	+	0.821881i	$0.307075\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−5.24070	−	5.24070i	−1.74690	−	1.74690i
$10$	1.09461	−	0.453400i	0.346145	−	0.143378i
$11$	1.30551	+	3.15179i	0.393627	+	0.950301i	0.989143	+	0.146957i	$0.0469479\pi$
$11$	1.30551	+	3.15179i	0.393627	+	0.950301i	−0.595515	+	0.803344i	$0.703052\pi$
$12$	−2.98107	−	1.23480i	−0.860559	−	0.356455i
$13$			0.347296i			0.0963227i	0.998840	+	0.0481613i	$0.0153362\pi$
$13$			0.347296i			0.0963227i	−0.998840	+	0.0481613i	$0.984664\pi$
$14$	0.428841	−	1.03531i	0.114612	−	0.276699i
$15$	2.70323	−	2.70323i	0.697972	−	0.697972i
$16$	−1.00000			−0.250000
$17$		0			0
$17$		0			0
$18$	−7.41147			−1.74690
$19$	−0.245576	+	0.245576i	−0.0563389	+	0.0563389i	−0.734715	−	0.678376i	$-0.762684\pi$
$19$	−0.245576	+	0.245576i	−0.0563389	+	0.0563389i	0.678376	+	0.734715i	$0.262684\pi$
$20$	0.453400	−	1.09461i	0.101383	−	0.244761i
$21$		−	3.61587i		−	0.789047i
$22$	3.15179	+	1.30551i	0.671964	+	0.278337i
$23$	−0.157464	−	0.380153i	−0.0328336	−	0.0792673i	0.906612	−	0.421965i	$-0.138659\pi$
$23$	−0.157464	−	0.380153i	−0.0328336	−	0.0792673i	−0.939446	+	0.342697i	$0.888659\pi$
$24$	−2.98107	+	1.23480i	−0.608507	+	0.252052i
$25$	−2.54294	−	2.54294i	−0.508589	−	0.508589i
$26$	0.245576	+	0.245576i	0.0481613	+	0.0481613i
$27$	−13.1509	+	5.44728i	−2.53089	+	1.04833i
$28$	−0.428841	−	1.03531i	−0.0810433	−	0.195656i
$29$	8.11264	+	3.36037i	1.50648	+	0.624004i	0.974828	−	0.222959i	$-0.0715715\pi$
$29$	8.11264	+	3.36037i	1.50648	+	0.624004i	0.531652	+	0.846963i	$0.321572\pi$
$30$		−	3.82295i		−	0.697972i
$31$	−3.33581	+	8.05335i	−0.599128	+	1.44642i	0.275343	+	0.961346i	$0.411209\pi$
$31$	−3.33581	+	8.05335i	−0.599128	+	1.44642i	−0.874471	+	0.485078i	$0.838791\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	11.0077			1.91620
$34$		0			0
$35$	1.32770			0.224422
$36$	−5.24070	+	5.24070i	−0.873451	+	0.873451i
$37$	−0.182024	+	0.439445i	−0.0299246	+	0.0722443i	−0.938135	−	0.346269i	$-0.887449\pi$
$37$	−0.182024	+	0.439445i	−0.0299246	+	0.0722443i	0.908211	+	0.418513i	$0.137449\pi$
$38$			0.347296i			0.0563389i
$39$	1.03531	+	0.428841i	0.165783	+	0.0686695i
$40$	−0.453400	−	1.09461i	−0.0716889	−	0.173072i
$41$	2.43734	−	1.00958i	0.380648	−	0.157670i	−0.184151	−	0.982898i	$-0.558954\pi$
$41$	2.43734	−	1.00958i	0.380648	−	0.157670i	0.564799	+	0.825228i	$0.308954\pi$
$42$	−2.55680	−	2.55680i	−0.394523	−	0.394523i
$43$	6.59925	+	6.59925i	1.00638	+	1.00638i	0.999980	+	0.00639660i	$0.00203612\pi$
$43$	6.59925	+	6.59925i	1.00638	+	1.00638i	0.00639660	+	0.999980i	$0.497964\pi$
$44$	3.15179	−	1.30551i	0.475150	−	0.196814i
$45$	−3.36037	−	8.11264i	−0.500934	−	1.20936i
$46$	−0.380153	−	0.157464i	−0.0560504	−	0.0232168i
$47$		−	7.86484i		−	1.14720i	−0.819134	−	0.573602i	$-0.805546\pi$
$47$		−	7.86484i		−	1.14720i	0.819134	−	0.573602i	$-0.194454\pi$
$48$	−1.23480	+	2.98107i	−0.178228	+	0.430280i
$49$	−4.06178	+	4.06178i	−0.580254	+	0.580254i
$50$	−3.59627			−0.508589
$51$		0			0
$52$	0.347296			0.0481613
$53$	−5.95328	+	5.95328i	−0.817746	+	0.817746i	−0.985781	−	0.168035i	$-0.946258\pi$
$53$	−5.95328	+	5.95328i	−0.817746	+	0.817746i	0.168035	+	0.985781i	$0.446258\pi$
$54$	−5.44728	+	13.1509i	−0.741281	+	1.78961i
$55$			4.04189i			0.545008i
$56$	−1.03531	−	0.428841i	−0.138350	−	0.0573062i
$57$	0.428841	+	1.03531i	0.0568013	+	0.137131i
$58$	8.11264	−	3.36037i	1.06524	−	0.441238i
$59$	−4.53360	−	4.53360i	−0.590224	−	0.590224i	0.347468	−	0.937692i	$-0.387042\pi$
$59$	−4.53360	−	4.53360i	−0.590224	−	0.590224i	−0.937692	+	0.347468i	$0.887042\pi$
$60$	−2.70323	−	2.70323i	−0.348986	−	0.348986i
$61$	5.26827	−	2.18219i	0.674533	−	0.279401i	−0.0190066	−	0.999819i	$-0.506050\pi$
$61$	5.26827	−	2.18219i	0.674533	−	0.279401i	0.693539	+	0.720419i	$0.256050\pi$
$62$	3.33581	+	8.05335i	0.423648	+	1.02278i
$63$	−7.67320	−	3.17834i	−0.966732	−	0.400433i
$64$			1.00000i			0.125000i
$65$	−0.157464	+	0.380153i	−0.0195310	+	0.0471521i
$66$	7.78365	−	7.78365i	0.958101	−	0.958101i
$67$	−7.31315			−0.893443			−0.446722	−	0.894673i	$-0.647409\pi$
$67$	−7.31315			−0.893443			−0.446722	+	0.894673i	$0.647409\pi$
$68$		0			0
$69$	−1.32770			−0.159836
$70$	0.938823	−	0.938823i	0.112211	−	0.112211i
$71$	2.90697	−	7.01804i	0.344993	−	0.832888i	−0.652202	−	0.758045i	$-0.726155\pi$
$71$	2.90697	−	7.01804i	0.344993	−	0.832888i	0.997195	−	0.0748424i	$-0.0238454\pi$
$72$			7.41147i			0.873451i
$73$	8.35362	+	3.46018i	0.977717	+	0.404984i	0.813579	−	0.581454i	$-0.197516\pi$
$73$	8.35362	+	3.46018i	0.977717	+	0.404984i	0.164137	+	0.986437i	$0.447516\pi$
$74$	0.182024	+	0.439445i	0.0211599	+	0.0510845i
$75$	−10.7207	+	4.44066i	−1.23792	+	0.512763i
$76$	0.245576	+	0.245576i	0.0281695	+	0.0281695i
$77$	2.70323	+	2.70323i	0.308062	+	0.308062i
$78$	1.03531	−	0.428841i	0.117226	−	0.0485566i
$79$	−5.08062	−	12.2657i	−0.571615	−	1.38000i	−0.900180	−	0.435519i	$-0.856565\pi$
$79$	−5.08062	−	12.2657i	−0.571615	−	1.38000i	0.328565	−	0.944481i	$-0.393435\pi$
$80$	−1.09461	−	0.453400i	−0.122381	−	0.0506917i
$81$			23.6955i			2.63284i
$82$	1.00958	−	2.43734i	0.111489	−	0.269159i
$83$	−5.47242	+	5.47242i	−0.600676	+	0.600676i	−0.940492	−	0.339816i	$-0.889635\pi$
$83$	−5.47242	+	5.47242i	−0.600676	+	0.600676i	0.339816	+	0.940492i	$0.389635\pi$
$84$	−3.61587			−0.394523
$85$		0			0
$86$	9.33275			1.00638
$87$	20.0349	−	20.0349i	2.14797	−	2.14797i
$88$	1.30551	−	3.15179i	0.139168	−	0.335982i
$89$		−	7.18479i		−	0.761586i	−0.924660	−	0.380793i	$-0.875651\pi$
$89$		−	7.18479i		−	0.761586i	0.924660	−	0.380793i	$-0.124349\pi$
$90$	−8.11264	−	3.36037i	−0.855147	−	0.354214i
$91$	0.148935	+	0.359560i	0.0156126	+	0.0376922i
$92$	−0.380153	+	0.157464i	−0.0396336	+	0.0164168i
$93$	19.8885	+	19.8885i	2.06234	+	2.06234i
$94$	−5.56128	−	5.56128i	−0.573602	−	0.573602i
$95$	−0.380153	+	0.157464i	−0.0390028	+	0.0161555i
$96$	1.23480	+	2.98107i	0.126026	+	0.304254i
$97$	−0.204759	−	0.0848138i	−0.0207901	−	0.00861154i	0.372264	−	0.928127i	$-0.378582\pi$
$97$	−0.204759	−	0.0848138i	−0.0207901	−	0.00861154i	−0.393054	+	0.919515i	$0.628582\pi$
$98$			5.74422i			0.580254i
$99$	9.67579	−	23.3594i	0.972453	−	2.34771i
$100$	−2.54294	+	2.54294i	−0.254294	+	0.254294i
$101$	4.86484			0.484069			0.242035	−	0.970268i	$-0.422185\pi$
$101$	4.86484			0.484069			0.242035	+	0.970268i	$0.422185\pi$
$102$		0			0
$103$	12.3969			1.22151			0.610753	−	0.791821i	$-0.290867\pi$
$103$	12.3969			1.22151			0.610753	+	0.791821i	$0.290867\pi$
$104$	0.245576	−	0.245576i	0.0240807	−	0.0240807i
$105$	1.63944	−	3.95795i	0.159993	−	0.386256i
$106$			8.41921i			0.817746i
$107$	−8.18289	−	3.38946i	−0.791070	−	0.327672i	−0.0496962	−	0.998764i	$-0.515825\pi$
$107$	−8.18289	−	3.38946i	−0.791070	−	0.327672i	−0.741374	+	0.671093i	$0.765825\pi$
$108$	5.44728	+	13.1509i	0.524165	+	1.26545i
$109$	10.9688	−	4.54344i	1.05062	−	0.435183i	0.210509	−	0.977592i	$-0.432488\pi$
$109$	10.9688	−	4.54344i	1.05062	−	0.435183i	0.840114	+	0.542409i	$0.182488\pi$
$110$	2.85805	+	2.85805i	0.272504	+	0.272504i
$111$	1.08525	+	1.08525i	0.103008	+	0.103008i
$112$	−1.03531	+	0.428841i	−0.0978279	+	0.0405216i
$113$	4.15779	+	10.0378i	0.391132	+	0.944277i	0.989694	+	0.143200i	$0.0457392\pi$
$113$	4.15779	+	10.0378i	0.391132	+	0.944277i	−0.598561	+	0.801077i	$0.704261\pi$
$114$	1.03531	+	0.428841i	0.0969660	+	0.0401646i
$115$		−	0.487511i		−	0.0454607i
$116$	3.36037	−	8.11264i	0.312002	−	0.753240i
$117$	1.82008	−	1.82008i	0.168266	−	0.168266i
$118$	−6.41147			−0.590224
$119$		0			0
$120$	−3.82295			−0.348986
$121$	−0.451244	+	0.451244i	−0.0410222	+	0.0410222i
$122$	2.18219	−	5.26827i	0.197566	−	0.476967i
$123$		−	8.51249i		−	0.767545i
$124$	8.05335	+	3.33581i	0.723212	+	0.299564i
$125$	−3.89755	−	9.40952i	−0.348608	−	0.841613i
$126$	−7.67320	+	3.17834i	−0.683583	+	0.283149i
$127$	−4.63274	−	4.63274i	−0.411090	−	0.411090i	0.471028	−	0.882118i	$-0.343883\pi$
$127$	−4.63274	−	4.63274i	−0.411090	−	0.411090i	−0.882118	+	0.471028i	$0.843883\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	27.8215	−	11.5241i	2.44955	−	1.01464i
$130$	0.157464	+	0.380153i	0.0138105	+	0.0333416i
$131$	−0.0458520	−	0.0189925i	−0.00400611	−	0.00165938i	0.380679	−	0.924707i	$-0.375690\pi$
$131$	−0.0458520	−	0.0189925i	−0.00400611	−	0.00165938i	−0.384686	+	0.923048i	$0.625690\pi$
$132$		−	11.0077i		−	0.958101i
$133$	−0.148935	+	0.359560i	−0.0129143	+	0.0311778i
$134$	−5.17118	+	5.17118i	−0.446722	+	0.446722i
$135$	−16.8648			−1.45149
$136$		0			0
$137$	−8.13341			−0.694884			−0.347442	−	0.937701i	$-0.612950\pi$
$137$	−8.13341			−0.694884			−0.347442	+	0.937701i	$0.612950\pi$
$138$	−0.938823	+	0.938823i	−0.0799179	+	0.0799179i
$139$	−5.88658	+	14.2115i	−0.499293	+	1.20540i	0.450572	+	0.892740i	$0.351220\pi$
$139$	−5.88658	+	14.2115i	−0.499293	+	1.20540i	−0.949865	+	0.312660i	$0.898780\pi$
$140$		−	1.32770i		−	0.112211i
$141$	−23.4456	−	9.71148i	−1.97448	−	0.817854i
$142$	−2.90697	−	7.01804i	−0.243947	−	0.588940i
$143$	−1.09461	+	0.453400i	−0.0915355	+	0.0379153i
$144$	5.24070	+	5.24070i	0.436725	+	0.436725i
$145$	7.35655	+	7.35655i	0.610928	+	0.610928i
$146$	8.35362	−	3.46018i	0.691350	−	0.286367i
$147$	7.09295	+	17.1239i	0.585017	+	1.41236i
$148$	0.439445	+	0.182024i	0.0361222	+	0.0149623i
$149$		−	16.1088i		−	1.31968i	−0.751406	−	0.659840i	$-0.770624\pi$
$149$		−	16.1088i		−	1.31968i	0.751406	−	0.659840i	$-0.229376\pi$
$150$	−4.44066	+	10.7207i	−0.362578	+	0.875342i
$151$	−1.91084	+	1.91084i	−0.155502	+	0.155502i	−0.780570	−	0.625068i	$-0.785071\pi$
$151$	−1.91084	+	1.91084i	−0.155502	+	0.155502i	0.625068	+	0.780570i	$0.285071\pi$
$152$	0.347296			0.0281695
$153$		0			0
$154$	3.82295			0.308062
$155$	−7.30278	+	7.30278i	−0.586574	+	0.586574i
$156$	0.428841	−	1.03531i	0.0343347	−	0.0828914i
$157$			23.5594i			1.88025i	0.340834	+	0.940124i	$0.389291\pi$
$157$			23.5594i			1.88025i	−0.340834	+	0.940124i	$0.610709\pi$
$158$	−12.2657	−	5.08062i	−0.975808	−	0.404193i
$159$	10.3960	+	25.0982i	0.824459	+	1.99042i
$160$	−1.09461	+	0.453400i	−0.0865362	+	0.0358445i
$161$	−0.326050	−	0.326050i	−0.0256963	−	0.0256963i
$162$	16.7553	+	16.7553i	1.31642	+	1.31642i
$163$	−1.73166	+	0.717276i	−0.135634	+	0.0561814i	−0.449468	−	0.893296i	$-0.648386\pi$
$163$	−1.73166	+	0.717276i	−0.135634	+	0.0561814i	0.313834	+	0.949478i	$0.398386\pi$
$164$	−1.00958	−	2.43734i	−0.0788348	−	0.190324i
$165$	12.0491	+	4.99091i	0.938024	+	0.388542i
$166$			7.73917i			0.600676i
$167$	−3.38946	+	8.18289i	−0.262285	+	0.633211i	−0.999079	−	0.0429057i	$-0.986339\pi$
$167$	−3.38946	+	8.18289i	−0.262285	+	0.633211i	0.736795	+	0.676117i	$0.236339\pi$
$168$	−2.55680	+	2.55680i	−0.197262	+	0.197262i
$169$	12.8794			0.990722
$170$		0			0
$171$	2.57398			0.196837
$172$	6.59925	−	6.59925i	0.503188	−	0.503188i
$173$	−2.45356	+	5.92343i	−0.186541	+	0.450350i	−0.989289	−	0.145968i	$-0.953370\pi$
$173$	−2.45356	+	5.92343i	−0.186541	+	0.450350i	0.802748	+	0.596318i	$0.203370\pi$
$174$		−	28.3337i		−	2.14797i
$175$	−3.72326	−	1.54223i	−0.281452	−	0.116581i
$176$	−1.30551	−	3.15179i	−0.0984069	−	0.237575i
$177$	−19.1130	+	7.91687i	−1.43662	+	0.595069i
$178$	−5.08042	−	5.08042i	−0.380793	−	0.380793i
$179$	0.891541	+	0.891541i	0.0666369	+	0.0666369i	0.739640	−	0.673003i	$-0.234996\pi$
$179$	0.891541	+	0.891541i	0.0666369	+	0.0666369i	−0.673003	+	0.739640i	$0.734996\pi$
$180$	−8.11264	+	3.36037i	−0.604681	+	0.250467i
$181$	−5.86305	−	14.1547i	−0.435797	−	1.05211i	−0.977386	−	0.211464i	$-0.932177\pi$
$181$	−5.86305	−	14.1547i	−0.435797	−	1.05211i	0.541589	−	0.840644i	$-0.317823\pi$
$182$	0.359560	+	0.148935i	0.0266524	+	0.0110398i
$183$		−	18.3996i		−	1.36014i
$184$	−0.157464	+	0.380153i	−0.0116084	+	0.0280252i
$185$	−0.398489	+	0.398489i	−0.0292975	+	0.0292975i
$186$	28.1266			2.06234
$187$		0			0
$188$	−7.86484			−0.573602
$189$	−11.2793	+	11.2793i	−0.820447	+	0.820447i
$190$	−0.157464	+	0.380153i	−0.0114237	+	0.0275792i
$191$		−	10.3601i		−	0.749630i	−0.927100	−	0.374815i	$-0.877706\pi$
$191$		−	10.3601i		−	0.749630i	0.927100	−	0.374815i	$-0.122294\pi$
$192$	2.98107	+	1.23480i	0.215140	+	0.0891138i
$193$	5.83746	+	14.0929i	0.420190	+	1.01443i	0.982291	+	0.187360i	$0.0599929\pi$
$193$	5.83746	+	14.0929i	0.420190	+	1.01443i	−0.562102	+	0.827068i	$0.690007\pi$
$194$	−0.204759	+	0.0848138i	−0.0147008	+	0.00608928i
$195$	0.938823	+	0.938823i	0.0672305	+	0.0672305i
$196$	4.06178	+	4.06178i	0.290127	+	0.290127i
$197$	−19.6252	+	8.12902i	−1.39824	+	0.579169i	−0.949294	−	0.314391i	$-0.898200\pi$
$197$	−19.6252	+	8.12902i	−1.39824	+	0.579169i	−0.448944	+	0.893560i	$0.648200\pi$
$198$	−9.67579	−	23.3594i	−0.687628	−	1.66008i
$199$	−12.0878	−	5.00695i	−0.856884	−	0.354933i	−0.0893958	−	0.995996i	$-0.528494\pi$
$199$	−12.0878	−	5.00695i	−0.856884	−	0.354933i	−0.767488	+	0.641063i	$0.778494\pi$
$200$			3.59627i			0.254294i
$201$	−9.03026	+	21.8010i	−0.636945	+	1.53772i
$202$	3.43996	−	3.43996i	0.242035	−	0.242035i
$203$	9.84018			0.690646
$204$		0			0
$205$	3.12567			0.218306
$206$	8.76595	−	8.76595i	0.610753	−	0.610753i
$207$	−1.16704	+	2.81749i	−0.0811151	+	0.195829i
$208$		−	0.347296i		−	0.0240807i
$209$	−1.09461	−	0.453400i	−0.0757155	−	0.0313624i
$210$	−1.63944	−	3.95795i	−0.113132	−	0.273124i
$211$	9.19381	−	3.80820i	0.632928	−	0.262167i	−0.0430688	−	0.999072i	$-0.513713\pi$
$211$	9.19381	−	3.80820i	0.632928	−	0.262167i	0.675996	+	0.736905i	$0.263713\pi$
$212$	5.95328	+	5.95328i	0.408873	+	0.408873i
$213$	−17.3317	−	17.3317i	−1.18755	−	1.18755i
$214$	−8.18289	+	3.38946i	−0.559371	+	0.231699i
$215$	4.23147	+	10.2157i	0.288584	+	0.696703i
$216$	13.1509	+	5.44728i	0.894805	+	0.370640i
$217$			9.76827i			0.663113i
$218$	4.54344	−	10.9688i	0.307721	−	0.742903i
$219$	20.6301	−	20.6301i	1.39405	−	1.39405i
$220$	4.04189			0.272504
$221$		0			0
$222$	1.53478			0.103008
$223$	−13.9751	+	13.9751i	−0.935844	+	0.935844i	−0.998063	−	0.0622184i	$-0.980182\pi$
$223$	−13.9751	+	13.9751i	−0.935844	+	0.935844i	0.0622184	+	0.998063i	$0.480182\pi$
$224$	−0.428841	+	1.03531i	−0.0286531	+	0.0691748i
$225$			26.6536i			1.77691i
$226$	10.0378	+	4.15779i	0.667705	+	0.276572i
$227$	1.36020	+	3.28382i	0.0902797	+	0.217955i	0.962570	−	0.271035i	$-0.0873658\pi$
$227$	1.36020	+	3.28382i	0.0902797	+	0.217955i	−0.872290	+	0.488989i	$0.837366\pi$
$228$	1.03531	−	0.428841i	0.0685653	−	0.0284007i
$229$	−1.44383	−	1.44383i	−0.0954112	−	0.0954112i	0.657790	−	0.753201i	$-0.271491\pi$
$229$	−1.44383	−	1.44383i	−0.0954112	−	0.0954112i	−0.753201	+	0.657790i	$0.771491\pi$
$230$	−0.344723	−	0.344723i	−0.0227303	−	0.0227303i
$231$	11.3965	−	4.72057i	0.749832	−	0.310591i
$232$	−3.36037	−	8.11264i	−0.220619	−	0.532621i
$233$	3.61812	+	1.49867i	0.237031	+	0.0981813i	0.498037	−	0.867156i	$-0.334054\pi$
$233$	3.61812	+	1.49867i	0.237031	+	0.0981813i	−0.261006	+	0.965337i	$0.584054\pi$
$234$		−	2.57398i		−	0.168266i
$235$	3.56592	−	8.60889i	0.232615	−	0.561582i
$236$	−4.53360	+	4.53360i	−0.295112	+	0.295112i
$237$	−42.8384			−2.78266
$238$		0			0
$239$	−21.5544			−1.39424			−0.697118	−	0.716956i	$-0.745535\pi$
$239$	−21.5544			−1.39424			−0.697118	+	0.716956i	$0.745535\pi$
$240$	−2.70323	+	2.70323i	−0.174493	+	0.174493i
$241$	−9.64077	+	23.2749i	−0.621016	+	1.49927i	0.229495	+	0.973310i	$0.426292\pi$
$241$	−9.64077	+	23.2749i	−0.621016	+	1.49927i	−0.850512	+	0.525956i	$0.823708\pi$
$242$			0.638156i			0.0410222i
$243$	31.1852	+	12.9173i	2.00053	+	0.828648i
$244$	−2.18219	−	5.26827i	−0.139700	−	0.337266i
$245$	−6.28766	+	2.60443i	−0.401704	+	0.166391i
$246$	−6.01924	−	6.01924i	−0.383773	−	0.383773i
$247$	−0.0852875	−	0.0852875i	−0.00542671	−	0.00542671i
$248$	8.05335	−	3.33581i	0.511388	−	0.211824i
$249$	9.55631	+	23.0710i	0.605606	+	1.46206i
$250$	−9.40952	−	3.89755i	−0.595110	−	0.246503i
$251$			3.07604i			0.194158i	0.995277	+	0.0970789i	$0.0309499\pi$
$251$			3.07604i			0.194158i	−0.995277	+	0.0970789i	$0.969050\pi$
$252$	−3.17834	+	7.67320i	−0.200217	+	0.483366i
$253$	0.992589	−	0.992589i	0.0624036	−	0.0624036i
$254$	−6.55169			−0.411090
$255$		0			0
$256$	1.00000			0.0625000
$257$	17.6349	−	17.6349i	1.10003	−	1.10003i	0.105626	−	0.994406i	$-0.466315\pi$
$257$	17.6349	−	17.6349i	1.10003	−	1.10003i	0.994406	−	0.105626i	$-0.0336846\pi$
$258$	11.5241	−	27.8215i	0.717456	−	1.73209i
$259$			0.533023i			0.0331204i
$260$	0.380153	+	0.157464i	0.0235761	+	0.00976552i
$261$	−24.9053	−	60.1266i	−1.54160	−	3.72174i
$262$	−0.0458520	+	0.0189925i	−0.00283275	+	0.00117336i
$263$	−10.7778	−	10.7778i	−0.664590	−	0.664590i	0.291869	−	0.956458i	$-0.405723\pi$
$263$	−10.7778	−	10.7778i	−0.664590	−	0.664590i	−0.956458	+	0.291869i	$0.905723\pi$
$264$	−7.78365	−	7.78365i	−0.479050	−	0.479050i
$265$	−9.21572	+	3.81728i	−0.566117	+	0.234493i
$266$	0.148935	+	0.359560i	0.00913178	+	0.0220461i
$267$	−21.4183	−	8.87176i	−1.31078	−	0.542943i
$268$			7.31315i			0.446722i
$269$	1.44399	−	3.48609i	0.0880414	−	0.212551i	−0.873726	−	0.486418i	$-0.838303\pi$
$269$	1.44399	−	3.48609i	0.0880414	−	0.212551i	0.961767	+	0.273868i	$0.0883031\pi$
$270$	−11.9252	+	11.9252i	−0.725747	+	0.725747i
$271$	−4.72462			−0.287000			−0.143500	−	0.989650i	$-0.545836\pi$
$271$	−4.72462			−0.287000			−0.143500	+	0.989650i	$0.545836\pi$
$272$		0			0
$273$	1.25578			0.0760031
$274$	−5.75119	+	5.75119i	−0.347442	+	0.347442i
$275$	4.69498	−	11.3347i	0.283118	−	0.683507i
$276$			1.32770i			0.0799179i
$277$	16.8401	+	6.97541i	1.01182	+	0.419112i	0.826120	−	0.563494i	$-0.190543\pi$
$277$	16.8401	+	6.97541i	1.01182	+	0.419112i	0.185705	+	0.982606i	$0.440543\pi$
$278$	5.88658	+	14.2115i	0.353054	+	0.852347i
$279$	59.6872	−	24.7232i	3.57338	−	1.48014i
$280$	−0.938823	−	0.938823i	−0.0561054	−	0.0561054i
$281$	−17.9445	−	17.9445i	−1.07048	−	1.07048i	−0.997320	−	0.0731575i	$-0.976692\pi$
$281$	−17.9445	−	17.9445i	−1.07048	−	1.07048i	−0.0731575	−	0.997320i	$-0.523308\pi$
$282$	−23.4456	+	9.71148i	−1.39616	+	0.578310i
$283$	−4.99194	−	12.0516i	−0.296740	−	0.716394i	−0.999985	−	0.00544667i	$-0.998266\pi$
$283$	−4.99194	−	12.0516i	−0.296740	−	0.716394i	0.703245	−	0.710948i	$-0.251734\pi$
$284$	−7.01804	−	2.90697i	−0.416444	−	0.172497i
$285$			1.32770i			0.0786459i
$286$	−0.453400	+	1.09461i	−0.0268101	+	0.0647254i
$287$	2.09046	−	2.09046i	0.123396	−	0.123396i
$288$	7.41147			0.436725
$289$		0			0
$290$	10.4037			0.610928
$291$	−0.505671	+	0.505671i	−0.0296430	+	0.0296430i
$292$	3.46018	−	8.35362i	0.202492	−	0.488858i
$293$		−	3.80571i		−	0.222332i	−0.993802	−	0.111166i	$-0.964541\pi$
$293$		−	3.80571i		−	0.222332i	0.993802	−	0.111166i	$-0.0354585\pi$
$294$	17.1239	+	7.09295i	0.998686	+	0.413669i
$295$	−2.90697	−	7.01804i	−0.169250	−	0.408606i
$296$	0.439445	−	0.182024i	0.0255422	−	0.0105799i
$297$	−34.3374	−	34.3374i	−1.99246	−	1.99246i
$298$	−11.3906	−	11.3906i	−0.659840	−	0.659840i
$299$	0.132026	−	0.0546868i	0.00763524	−	0.00316262i
$300$	4.44066	+	10.7207i	0.256382	+	0.618960i
$301$	9.66232	+	4.00226i	0.556927	+	0.230687i
$302$			2.70233i			0.155502i
$303$	6.00709	−	14.5024i	0.345098	−	0.833141i
$304$	0.245576	−	0.245576i	0.0140847	−	0.0140847i
$305$	6.75608			0.386852
$306$		0			0
$307$	13.1070			0.748056			0.374028	−	0.927417i	$-0.377976\pi$
$307$	13.1070			0.748056			0.374028	+	0.927417i	$0.377976\pi$
$308$	2.70323	−	2.70323i	0.154031	−	0.154031i
$309$	15.3077	−	36.9560i	0.870824	−	2.10236i
$310$			10.3277i			0.586574i
$311$	9.54155	+	3.95224i	0.541051	+	0.224111i	0.636436	−	0.771330i	$-0.280408\pi$
$311$	9.54155	+	3.95224i	0.541051	+	0.224111i	−0.0953843	+	0.995441i	$0.530408\pi$
$312$	−0.428841	−	1.03531i	−0.0242783	−	0.0586131i
$313$	−20.0646	+	8.31105i	−1.13412	+	0.469768i	−0.869180	−	0.494496i	$-0.835353\pi$
$313$	−20.0646	+	8.31105i	−1.13412	+	0.469768i	−0.264941	+	0.964265i	$0.585353\pi$
$314$	16.6590	+	16.6590i	0.940124	+	0.940124i
$315$	−6.95806	−	6.95806i	−0.392042	−	0.392042i
$316$	−12.2657	+	5.08062i	−0.690000	+	0.285807i
$317$	−4.27956	−	10.3318i	−0.240364	−	0.580291i	0.756955	−	0.653467i	$-0.226686\pi$
$317$	−4.27956	−	10.3318i	−0.240364	−	0.580291i	−0.997319	+	0.0731767i	$0.976686\pi$
$318$	25.0982	+	10.3960i	1.40744	+	0.582980i
$319$			29.9564i			1.67723i
$320$	−0.453400	+	1.09461i	−0.0253459	+	0.0611903i
$321$	−20.2084	+	20.2084i	−1.12792	+	1.12792i
$322$	−0.461104			−0.0256963
$323$		0			0
$324$	23.6955			1.31642
$325$	0.883155	−	0.883155i	0.0489886	−	0.0489886i
$326$	−0.717276	+	1.73166i	−0.0397262	+	0.0959077i
$327$		−	38.3090i		−	2.11849i
$328$	−2.43734	−	1.00958i	−0.134579	−	0.0557446i
$329$	−3.37276	−	8.14257i	−0.185946	−	0.448914i
$330$	12.0491	−	4.99091i	0.663283	−	0.274741i
$331$	12.7878	+	12.7878i	0.702882	+	0.702882i	0.965028	−	0.262146i	$-0.0844302\pi$
$331$	12.7878	+	12.7878i	0.702882	+	0.702882i	−0.262146	+	0.965028i	$0.584430\pi$
$332$	5.47242	+	5.47242i	0.300338	+	0.300338i
$333$	3.25694	−	1.34907i	0.178479	−	0.0739284i
$334$	3.38946	+	8.18289i	0.185463	+	0.447748i
$335$	−8.00501	−	3.31578i	−0.437361	−	0.181161i
$336$			3.61587i			0.197262i
$337$	0.642925	−	1.55216i	0.0350224	−	0.0845515i	−0.905401	−	0.424558i	$-0.860429\pi$
$337$	0.642925	−	1.55216i	0.0350224	−	0.0845515i	0.940423	+	0.340007i	$0.110429\pi$
$338$	9.10710	−	9.10710i	0.495361	−	0.495361i
$339$	35.0574			1.90406
$340$		0			0
$341$	−29.7374			−1.61037
$342$	1.82008	−	1.82008i	0.0984185	−	0.0984185i
$343$	−5.46524	+	13.1943i	−0.295095	+	0.712423i
$344$		−	9.33275i		−	0.503188i
$345$	−1.45330	−	0.601978i	−0.0782432	−	0.0324094i
$346$	2.45356	+	5.92343i	0.131904	+	0.318446i
$347$	−20.7657	+	8.60142i	−1.11476	+	0.461748i	−0.862574	−	0.505931i	$-0.831149\pi$
$347$	−20.7657	+	8.60142i	−1.11476	+	0.461748i	−0.252185	+	0.967679i	$0.581149\pi$
$348$	−20.0349	−	20.0349i	−1.07399	−	1.07399i
$349$	14.9249	+	14.9249i	0.798912	+	0.798912i	0.982924	−	0.184012i	$-0.0589086\pi$
$349$	14.9249	+	14.9249i	0.798912	+	0.798912i	−0.184012	+	0.982924i	$0.558909\pi$
$350$	−3.72326	+	1.54223i	−0.199017	+	0.0824354i
$351$	−1.89182	−	4.56726i	−0.100978	−	0.243782i
$352$	−3.15179	−	1.30551i	−0.167991	−	0.0695842i
$353$			3.86659i			0.205798i	0.994692	+	0.102899i	$0.0328118\pi$
$353$			3.86659i			0.205798i	−0.994692	+	0.102899i	$0.967188\pi$
$354$	−7.91687	+	19.1130i	−0.420777	+	1.01585i
$355$	6.36396	−	6.36396i	0.337764	−	0.337764i
$356$	−7.18479			−0.380793
$357$		0			0
$358$	1.26083			0.0666369
$359$	−25.7632	+	25.7632i	−1.35973	+	1.35973i	−0.485487	+	0.874244i	$0.661358\pi$
$359$	−25.7632	+	25.7632i	−1.35973	+	1.35973i	−0.874244	+	0.485487i	$0.838642\pi$
$360$	−3.36037	+	8.11264i	−0.177107	+	0.427574i
$361$			18.8794i			0.993652i
$362$	−14.1547	−	5.86305i	−0.743952	−	0.308155i
$363$	0.787993	+	1.90238i	0.0413589	+	0.0998493i
$364$	0.359560	−	0.148935i	0.0188461	−	0.00780631i
$365$	7.57507	+	7.57507i	0.396497	+	0.396497i
$366$	−13.0105	−	13.0105i	−0.680069	−	0.680069i
$367$	−12.7098	+	5.26458i	−0.663447	+	0.274809i	−0.688888	−	0.724867i	$-0.741901\pi$
$367$	−12.7098	+	5.26458i	−0.663447	+	0.274809i	0.0254410	+	0.999676i	$0.491901\pi$
$368$	0.157464	+	0.380153i	0.00820840	+	0.0198168i
$369$	−18.0643	−	7.48246i	−0.940388	−	0.389522i
$370$			0.563549i			0.0292975i
$371$	−3.61050	+	8.71652i	−0.187448	+	0.452539i
$372$	19.8885	−	19.8885i	1.03117	−	1.03117i
$373$	−22.7638			−1.17867			−0.589333	−	0.807890i	$-0.700609\pi$
$373$	−22.7638			−1.17867			−0.589333	+	0.807890i	$0.700609\pi$
$374$		0			0
$375$	−32.8631			−1.69704
$376$	−5.56128	+	5.56128i	−0.286801	+	0.286801i
$377$	−1.16704	+	2.81749i	−0.0601058	+	0.145108i
$378$			15.9513i			0.820447i
$379$	8.23970	+	3.41300i	0.423245	+	0.175314i	0.584131	−	0.811659i	$-0.301435\pi$
$379$	8.23970	+	3.41300i	0.423245	+	0.175314i	−0.160886	+	0.986973i	$0.551435\pi$
$380$	0.157464	+	0.380153i	0.00807775	+	0.0195014i
$381$	−19.5310	+	8.09001i	−1.00060	+	0.414464i
$382$	−7.32569	−	7.32569i	−0.374815	−	0.374815i
$383$	−13.7247	−	13.7247i	−0.701302	−	0.701302i	0.263388	−	0.964690i	$-0.415160\pi$
$383$	−13.7247	−	13.7247i	−0.701302	−	0.701302i	−0.964690	+	0.263388i	$0.915160\pi$
$384$	2.98107	−	1.23480i	0.152127	−	0.0630130i
$385$	1.73333	+	4.18462i	0.0883385	+	0.213268i
$386$	14.0929	+	5.83746i	0.717309	+	0.297119i
$387$		−	69.1694i		−	3.51608i
$388$	−0.0848138	+	0.204759i	−0.00430577	+	0.0103950i
$389$	25.2164	−	25.2164i	1.27852	−	1.27852i	0.337028	−	0.941495i	$-0.390578\pi$
$389$	25.2164	−	25.2164i	1.27852	−	1.27852i	0.941495	−	0.337028i	$-0.109422\pi$
$390$	1.32770			0.0672305
$391$		0			0
$392$	5.74422			0.290127
$393$	−0.113236	+	0.113236i	−0.00571200	+	0.00571200i
$394$	−8.12902	+	19.6252i	−0.409534	+	0.988703i
$395$		−	15.7297i		−	0.791446i
$396$	−23.3594	−	9.67579i	−1.17385	−	0.486227i
$397$	2.84932	+	6.87886i	0.143003	+	0.345240i	0.979111	−	0.203324i	$-0.0651746\pi$
$397$	2.84932	+	6.87886i	0.143003	+	0.345240i	−0.836108	+	0.548564i	$0.815175\pi$
$398$	−12.0878	+	5.00695i	−0.605908	+	0.250975i
$399$	0.887969	+	0.887969i	0.0444540	+	0.0444540i
$400$	2.54294	+	2.54294i	0.127147	+	0.127147i
$401$	−2.18921	+	0.906801i	−0.109324	+	0.0452835i	−0.436675	−	0.899619i	$-0.643844\pi$
$401$	−2.18921	+	0.906801i	−0.109324	+	0.0452835i	0.327351	+	0.944903i	$0.393844\pi$
$402$	9.03026	+	21.8010i	0.450388	+	1.08733i
$403$	−2.79690	−	1.15851i	−0.139323	−	0.0577097i
$404$		−	4.86484i		−	0.242035i
$405$	−10.7436	+	25.9373i	−0.533852	+	1.28883i
$406$	6.95806	−	6.95806i	0.345323	−	0.345323i
$407$	−1.62267			−0.0804330
$408$		0			0
$409$	−28.8357			−1.42584			−0.712918	−	0.701248i	$-0.752627\pi$
$409$	−28.8357			−1.42584			−0.712918	+	0.701248i	$0.752627\pi$
$410$	2.21018	−	2.21018i	0.109153	−	0.109153i
$411$	−10.0431	+	24.2462i	−0.495390	+	1.19598i
$412$		−	12.3969i		−	0.610753i
$413$	−6.63788	−	2.74950i	−0.326629	−	0.135294i
$414$	1.16704	+	2.81749i	0.0573570	+	0.138472i
$415$	−8.47134	+	3.50894i	−0.415842	+	0.172247i
$416$	−0.245576	−	0.245576i	−0.0120403	−	0.0120403i
$417$	35.0966	+	35.0966i	1.71869	+	1.71869i
$418$	−1.09461	+	0.453400i	−0.0535389	+	0.0221765i
$419$	−11.7407	−	28.3447i	−0.573573	−	1.38473i	−0.898494	−	0.438986i	$-0.855338\pi$
$419$	−11.7407	−	28.3447i	−0.573573	−	1.38473i	0.324921	−	0.945741i	$-0.394662\pi$
$420$	−3.95795	−	1.63944i	−0.193128	−	0.0799963i
$421$		−	6.20708i		−	0.302515i	−0.988494	−	0.151257i	$-0.951668\pi$
$421$		−	6.20708i		−	0.302515i	0.988494	−	0.151257i	$-0.0483322\pi$
$422$	3.80820	−	9.19381i	0.185380	−	0.447547i
$423$	−41.2173	+	41.2173i	−2.00405	+	2.00405i
$424$	8.41921			0.408873
$425$		0			0
$426$	−24.5107			−1.18755
$427$	4.51850	−	4.51850i	0.218665	−	0.218665i
$428$	−3.38946	+	8.18289i	−0.163836	+	0.395535i
$429$			3.82295i			0.184574i
$430$	10.2157	+	4.23147i	0.492644	+	0.204060i
$431$	3.34137	+	8.06679i	0.160948	+	0.388564i	0.983695	−	0.179845i	$-0.0575595\pi$
$431$	3.34137	+	8.06679i	0.160948	+	0.388564i	−0.822747	+	0.568408i	$0.807559\pi$
$432$	13.1509	−	5.44728i	0.632723	−	0.262082i
$433$	14.8390	+	14.8390i	0.713115	+	0.713115i	0.967186	−	0.254071i	$-0.0817697\pi$
$433$	14.8390	+	14.8390i	0.713115	+	0.713115i	−0.254071	+	0.967186i	$0.581770\pi$
$434$	6.90721	+	6.90721i	0.331557	+	0.331557i
$435$	31.0142	−	12.8465i	1.48702	−	0.615943i
$436$	−4.54344	−	10.9688i	−0.217591	−	0.525312i
$437$	0.132026	+	0.0546868i	0.00631564	+	0.00261602i
$438$		−	29.1753i		−	1.39405i
$439$	3.23986	−	7.82171i	0.154630	−	0.373310i	−0.827513	−	0.561447i	$-0.810245\pi$
$439$	3.23986	−	7.82171i	0.154630	−	0.373310i	0.982143	+	0.188137i	$0.0602449\pi$
$440$	2.85805	−	2.85805i	0.136252	−	0.136252i
$441$	42.5732			2.02729
$442$		0			0
$443$	23.9564			1.13820			0.569100	−	0.822268i	$-0.307292\pi$
$443$	23.9564			1.13820			0.569100	+	0.822268i	$0.307292\pi$
$444$	1.08525	−	1.08525i	0.0515038	−	0.0515038i
$445$	3.25759	−	7.86451i	0.154424	−	0.372814i
$446$			19.7638i			0.935844i
$447$	−48.0212	−	19.8911i	−2.27133	−	0.940814i
$448$	0.428841	+	1.03531i	0.0202608	+	0.0489139i
$449$	5.65938	−	2.34419i	0.267083	−	0.110629i	−0.245123	−	0.969492i	$-0.578828\pi$
$449$	5.65938	−	2.34419i	0.267083	−	0.110629i	0.512206	+	0.858863i	$0.328828\pi$
$450$	18.8470	+	18.8470i	0.888455	+	0.888455i
$451$	6.36396	+	6.36396i	0.299667	+	0.299667i
$452$	10.0378	−	4.15779i	0.472138	−	0.195566i
$453$	3.33683	+	8.05583i	0.156778	+	0.378496i
$454$	3.28382	+	1.36020i	0.154117	+	0.0638374i
$455$			0.461104i			0.0216169i
$456$	0.428841	−	1.03531i	0.0200823	−	0.0484830i
$457$	0.719065	−	0.719065i	0.0336365	−	0.0336365i	−0.690089	−	0.723725i	$-0.742428\pi$
$457$	0.719065	−	0.719065i	0.0336365	−	0.0336365i	0.723725	+	0.690089i	$0.242428\pi$
$458$	−2.04189			−0.0954112
$459$		0			0
$460$	−0.487511			−0.0227303
$461$	16.3227	−	16.3227i	0.760224	−	0.760224i	−0.216139	−	0.976363i	$-0.569346\pi$
$461$	16.3227	−	16.3227i	0.760224	−	0.760224i	0.976363	+	0.216139i	$0.0693464\pi$
$462$	4.72057	−	11.3965i	0.219621	−	0.530211i
$463$		−	19.3628i		−	0.899865i	−0.893063	−	0.449932i	$-0.851448\pi$
$463$		−	19.3628i		−	0.899865i	0.893063	−	0.449932i	$-0.148552\pi$
$464$	−8.11264	−	3.36037i	−0.376620	−	0.156001i
$465$	12.7526	+	30.7875i	0.591388	+	1.42774i
$466$	3.61812	−	1.49867i	0.167606	−	0.0694247i
$467$	−7.55865	−	7.55865i	−0.349772	−	0.349772i	0.510252	−	0.860025i	$-0.329552\pi$
$467$	−7.55865	−	7.55865i	−0.349772	−	0.349772i	−0.860025	+	0.510252i	$0.829552\pi$
$468$	−1.82008	−	1.82008i	−0.0841331	−	0.0841331i
$469$	−7.57140	+	3.13618i	−0.349615	+	0.144815i
$470$	−3.56592	−	8.60889i	−0.164484	−	0.397099i
$471$	70.2322	+	29.0911i	3.23613	+	1.34045i
$472$			6.41147i			0.295112i
$473$	−12.1840	+	29.4149i	−0.560223	+	1.35250i
$474$	−30.2913	+	30.2913i	−1.39133	+	1.39133i
$475$	1.24897			0.0573067
$476$		0			0
$477$	62.3988			2.85704
$478$	−15.2412	+	15.2412i	−0.697118	+	0.697118i
$479$	7.27691	−	17.5680i	0.332490	−	0.802703i	−0.665903	−	0.746039i	$-0.731953\pi$
$479$	7.27691	−	17.5680i	0.332490	−	0.802703i	0.998393	−	0.0566645i	$-0.0180465\pi$
$480$			3.82295i			0.174493i
$481$	−0.152618	−	0.0632163i	−0.00695877	−	0.00288242i
$482$	9.64077	+	23.2749i	0.439125	+	1.06014i
$483$	−1.37458	+	0.569370i	−0.0625456	+	0.0259072i
$484$	0.451244	+	0.451244i	0.0205111	+	0.0205111i
$485$	−0.185675	−	0.185675i	−0.00843108	−	0.00843108i
$486$	31.1852	−	12.9173i	1.41459	−	0.585943i
$487$	1.19820	+	2.89271i	0.0542956	+	0.131081i	0.948700	−	0.316179i	$-0.102400\pi$
$487$	1.19820	+	2.89271i	0.0542956	+	0.131081i	−0.894404	+	0.447260i	$0.852400\pi$
$488$	−5.26827	−	2.18219i	−0.238483	−	0.0987830i
$489$			6.04788i			0.273494i
$490$	−2.60443	+	6.28766i	−0.117656	+	0.284047i
$491$	23.6068	−	23.6068i	1.06536	−	1.06536i	0.0676513	−	0.997709i	$-0.478449\pi$
$491$	23.6068	−	23.6068i	1.06536	−	1.06536i	0.997709	−	0.0676513i	$-0.0215505\pi$
$492$	−8.51249			−0.383773
$493$		0			0
$494$	−0.120615			−0.00542671
$495$	21.1823	−	21.1823i	0.952075	−	0.952075i
$496$	3.33581	−	8.05335i	0.149782	−	0.361606i
$497$		−	8.51249i		−	0.381837i
$498$	23.0710	+	9.55631i	1.03383	+	0.428228i
$499$	−1.50424	−	3.63156i	−0.0673391	−	0.162571i	0.886627	−	0.462485i	$-0.153042\pi$
$499$	−1.50424	−	3.63156i	−0.0673391	−	0.162571i	−0.953966	+	0.299914i	$0.903042\pi$
$500$	−9.40952	+	3.89755i	−0.420807	+	0.174304i
$501$	20.2084	+	20.2084i	0.902846	+	0.902846i
$502$	2.17509	+	2.17509i	0.0970789	+	0.0970789i
$503$	−4.13877	+	1.71433i	−0.184539	+	0.0764384i	−0.473039	−	0.881041i	$-0.656843\pi$
$503$	−4.13877	+	1.71433i	−0.184539	+	0.0764384i	0.288501	+	0.957480i	$0.406843\pi$
$504$	3.17834	+	7.67320i	0.141575	+	0.341791i
$505$	5.32508	+	2.20572i	0.236963	+	0.0981532i
$506$		−	1.40373i		−	0.0624036i
$507$	15.9034	−	38.3943i	0.706296	−	1.70515i
$508$	−4.63274	+	4.63274i	−0.205545	+	0.205545i
$509$	2.58853			0.114734			0.0573672	−	0.998353i	$-0.481729\pi$
$509$	2.58853			0.114734			0.0573672	+	0.998353i	$0.481729\pi$
$510$		0			0
$511$	10.1325			0.448234
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	1.89182	−	4.56726i	0.0835259	−	0.201649i
$514$		−	24.9394i		−	1.10003i
$515$	13.5697	+	5.62077i	0.597954	+	0.247681i
$516$	−11.5241	−	27.8215i	−0.507318	−	1.22477i
$517$	24.7883	−	10.2677i	1.09019	−	0.451571i
$518$	0.376904	+	0.376904i	0.0165602	+	0.0165602i
$519$	14.6285	+	14.6285i	0.642119	+	0.642119i
$520$	0.380153	−	0.157464i	0.0166708	−	0.00690527i
$521$	14.6958	+	35.4788i	0.643835	+	1.55435i	0.821466	+	0.570257i	$0.193157\pi$
$521$	14.6958	+	35.4788i	0.643835	+	1.55435i	−0.177631	+	0.984097i	$0.556843\pi$
$522$	−60.1266	−	24.9053i	−2.63167	−	1.09007i
$523$			31.6614i			1.38446i	0.721679	+	0.692228i	$0.243371\pi$
$523$			31.6614i			1.38446i	−0.721679	+	0.692228i	$0.756629\pi$
$524$	−0.0189925	+	0.0458520i	−0.000829692	+	0.00200305i
$525$	−9.19495	+	9.19495i	−0.401300	+	0.401300i
$526$	−15.2422			−0.664590
$527$		0			0
$528$	−11.0077			−0.479050
$529$	16.1437	−	16.1437i	0.701902	−	0.701902i
$530$	−3.81728	+	9.21572i	−0.165812	+	0.400305i
$531$			47.5185i			2.06213i
$532$	0.359560	+	0.148935i	0.0155889	+	0.00645714i
$533$	0.350623	+	0.846479i	0.0151872	+	0.0366651i
$534$	−21.4183	+	8.87176i	−0.926862	+	0.383919i
$535$	−7.42025	−	7.42025i	−0.320805	−	0.320805i
$536$	5.17118	+	5.17118i	0.223361	+	0.223361i
$537$	3.75862	−	1.55687i	0.162196	−	0.0671839i
$538$	−1.44399	−	3.48609i	−0.0622547	−	0.150296i
$539$	−18.1046	−	7.49917i	−0.779820	−	0.323012i
$540$			16.8648i			0.725747i
$541$	14.5188	−	35.0515i	0.624212	−	1.50698i	−0.222502	−	0.974932i	$-0.571422\pi$
$541$	14.5188	−	35.0515i	0.624212	−	1.50698i	0.846714	−	0.532048i	$-0.178578\pi$
$542$	−3.34081	+	3.34081i	−0.143500	+	0.143500i
$543$	−49.4356			−2.12149
$544$		0			0
$545$	14.0665			0.602544
$546$	0.887969	−	0.887969i	0.0380016	−	0.0380016i
$547$	0.569603	−	1.37514i	0.0243545	−	0.0587969i	−0.911234	−	0.411888i	$-0.864869\pi$
$547$	0.569603	−	1.37514i	0.0243545	−	0.0587969i	0.935589	+	0.353091i	$0.114869\pi$
$548$			8.13341i			0.347442i
$549$	−39.0456	−	16.1732i	−1.66643	−	0.690257i
$550$	−4.69498	−	11.3347i	−0.200195	−	0.483312i
$551$	−2.81749	+	1.16704i	−0.120029	+	0.0497177i
$552$	0.938823	+	0.938823i	0.0399590	+	0.0399590i
$553$	−10.5201	−	10.5201i	−0.447359	−	0.447359i
$554$	16.8401	−	6.97541i	0.715468	−	0.296357i
$555$	0.695869	+	1.67998i	0.0295380	+	0.0713110i
$556$	14.2115	+	5.88658i	0.602700	+	0.249647i
$557$			23.3259i			0.988352i	0.869362	+	0.494176i	$0.164530\pi$
$557$			23.3259i			0.988352i	−0.869362	+	0.494176i	$0.835470\pi$
$558$	24.7232	−	59.6872i	1.04662	−	2.52676i
$559$	−2.29190	+	2.29190i	−0.0969368	+	0.0969368i
$560$	−1.32770			−0.0561054
$561$		0			0
$562$	−25.3773			−1.07048
$563$	3.09524	−	3.09524i	0.130449	−	0.130449i	−0.638868	−	0.769317i	$-0.720597\pi$
$563$	3.09524	−	3.09524i	0.130449	−	0.130449i	0.769317	+	0.638868i	$0.220597\pi$
$564$	−9.71148	+	23.4456i	−0.408927	+	0.987238i
$565$			12.8726i			0.541553i
$566$	−12.0516	−	4.99194i	−0.506567	−	0.209827i
$567$	10.1616	+	24.5323i	0.426747	+	1.03026i
$568$	−7.01804	+	2.90697i	−0.294470	+	0.121974i
$569$	3.32024	+	3.32024i	0.139192	+	0.139192i	0.773269	−	0.634078i	$-0.218620\pi$
$569$	3.32024	+	3.32024i	0.139192	+	0.139192i	−0.634078	+	0.773269i	$0.718620\pi$
$570$	0.938823	+	0.938823i	0.0393230	+	0.0393230i
$571$	12.4427	−	5.15395i	0.520712	−	0.215686i	−0.106818	−	0.994279i	$-0.534066\pi$
$571$	12.4427	−	5.15395i	0.520712	−	0.215686i	0.627530	+	0.778593i	$0.284066\pi$
$572$	0.453400	+	1.09461i	0.0189576	+	0.0457678i
$573$	−30.8841	−	12.7926i	−1.29020	−	0.534419i
$574$		−	2.95636i		−	0.123396i
$575$	−0.566284	+	1.36713i	−0.0236157	+	0.0570133i
$576$	5.24070	−	5.24070i	0.218363	−	0.218363i
$577$	−22.8066			−0.949453			−0.474727	−	0.880133i	$-0.657453\pi$
$577$	−22.8066			−0.949453			−0.474727	+	0.880133i	$0.657453\pi$
$578$		0			0
$579$	49.2199			2.04551
$580$	7.35655	−	7.35655i	0.305464	−	0.305464i
$581$	−3.31887	+	8.01246i	−0.137690	+	0.332413i
$582$			0.715127i			0.0296430i
$583$	−26.5356	−	10.9914i	−1.09899	−	0.455218i
$584$	−3.46018	−	8.35362i	−0.143183	−	0.345675i
$585$	2.81749	−	1.16704i	0.116489	−	0.0482513i
$586$	−2.69104	−	2.69104i	−0.111166	−	0.111166i
$587$	−27.2904	−	27.2904i	−1.12640	−	1.12640i	−0.990758	−	0.135639i	$-0.956691\pi$
$587$	−27.2904	−	27.2904i	−1.12640	−	1.12640i	−0.135639	−	0.990758i	$-0.543309\pi$
$588$	17.1239	−	7.09295i	0.706178	−	0.292508i
$589$	−1.15851	−	2.79690i	−0.0477357	−	0.115244i
$590$	−7.01804	−	2.90697i	−0.288928	−	0.119678i
$591$			68.5417i			2.81943i
$592$	0.182024	−	0.439445i	0.00748114	−	0.0180611i
$593$	1.62827	−	1.62827i	0.0668650	−	0.0668650i	−0.672884	−	0.739748i	$-0.734944\pi$
$593$	1.62827	−	1.62827i	0.0668650	−	0.0668650i	0.739748	+	0.672884i	$0.234944\pi$
$594$	−48.5604			−1.99246
$595$		0			0
$596$	−16.1088			−0.659840
$597$	−29.8521	+	29.8521i	−1.22176	+	1.22176i
$598$	0.0546868	−	0.132026i	0.00223631	−	0.00539893i
$599$			29.1830i			1.19239i	0.802841	+	0.596193i	$0.203321\pi$
$599$			29.1830i			1.19239i	−0.802841	+	0.596193i	$0.796679\pi$
$600$	10.7207	+	4.44066i	0.437671	+	0.181289i
$601$	5.37396	+	12.9739i	0.219208	+	0.529215i	0.994780	−	0.102044i	$-0.0325383\pi$
$601$	5.37396	+	12.9739i	0.219208	+	0.529215i	−0.775572	+	0.631260i	$0.782538\pi$
$602$	9.66232	−	4.00226i	0.393807	−	0.163120i
$603$	38.3260	+	38.3260i	1.56076	+	1.56076i
$604$	1.91084	+	1.91084i	0.0777509	+	0.0777509i
$605$	−0.698529	+	0.289340i	−0.0283992	+	0.0117633i
$606$	−6.00709	−	14.5024i	−0.244021	−	0.589120i
$607$	−9.48225	−	3.92768i	−0.384873	−	0.159420i	0.181854	−	0.983326i	$-0.441790\pi$
$607$	−9.48225	−	3.92768i	−0.384873	−	0.159420i	−0.566726	+	0.823906i	$0.691790\pi$
$608$		−	0.347296i		−	0.0140847i
$609$	12.1506	−	29.3342i	0.492369	−	1.18868i
$610$	4.77727	−	4.77727i	0.193426	−	0.193426i
$611$	2.73143			0.110502
$612$		0			0
$613$	2.66725			0.107729			0.0538646	−	0.998548i	$-0.482846\pi$
$613$	2.66725			0.107729			0.0538646	+	0.998548i	$0.482846\pi$
$614$	9.26805	−	9.26805i	0.374028	−	0.374028i
$615$	3.85957	−	9.31782i	0.155633	−	0.375731i
$616$		−	3.82295i		−	0.154031i
$617$	36.5435	+	15.1368i	1.47119	+	0.609385i	0.967129	−	0.254286i	$-0.0818405\pi$
$617$	36.5435	+	15.1368i	1.47119	+	0.609385i	0.504056	+	0.863671i	$0.331840\pi$
$618$	−15.3077	−	36.9560i	−0.615766	−	1.48659i
$619$	−20.6811	+	8.56639i	−0.831244	+	0.344312i	−0.757395	−	0.652957i	$-0.773528\pi$
$619$	−20.6811	+	8.56639i	−0.831244	+	0.344312i	−0.0738488	+	0.997269i	$0.523528\pi$
$620$	7.30278	+	7.30278i	0.293287	+	0.293287i
$621$	4.14159	+	4.14159i	0.166196	+	0.166196i
$622$	9.54155	−	3.95224i	0.382581	−	0.158470i
$623$	−3.08113	−	7.43851i	−0.123443	−	0.298018i
$624$	−1.03531	−	0.428841i	−0.0414457	−	0.0171674i
$625$			5.91447i			0.236579i
$626$	−8.31105	+	20.0646i	−0.332176	+	0.801944i
$627$	−2.70323	+	2.70323i	−0.107957	+	0.107957i
$628$	23.5594			0.940124
$629$		0			0
$630$	−9.84018			−0.392042
$631$	9.88016	−	9.88016i	0.393323	−	0.393323i	−0.482547	−	0.875870i	$-0.660288\pi$
$631$	9.88016	−	9.88016i	0.393323	−	0.393323i	0.875870	+	0.482547i	$0.160288\pi$
$632$	−5.08062	+	12.2657i	−0.202096	+	0.487904i
$633$		−	32.1097i		−	1.27625i
$634$	−10.3318	−	4.27956i	−0.410327	−	0.169963i
$635$	−2.97054	−	7.17152i	−0.117882	−	0.284593i
$636$	25.0982	−	10.3960i	0.995209	−	0.412229i
$637$	−1.41064	−	1.41064i	−0.0558916	−	0.0558916i
$638$	21.1823	+	21.1823i	0.838617	+	0.838617i
$639$	−52.0140	+	21.5449i	−2.05764	+	0.852303i
$640$	0.453400	+	1.09461i	0.0179222	+	0.0432681i
$641$	22.7152	+	9.40895i	0.897197	+	0.371631i	0.783142	−	0.621843i	$-0.213616\pi$
$641$	22.7152	+	9.40895i	0.897197	+	0.371631i	0.114055	+	0.993474i	$0.463616\pi$
$642$			28.5790i			1.12792i
$643$	−11.3656	+	27.4389i	−0.448214	+	1.08208i	0.524777	+	0.851240i	$0.324149\pi$
$643$	−11.3656	+	27.4389i	−0.448214	+	1.08208i	−0.972991	+	0.230844i	$0.925851\pi$
$644$	−0.326050	+	0.326050i	−0.0128482	+	0.0128482i
$645$	35.6786			1.40484
$646$		0			0
$647$	16.3946			0.644537			0.322268	−	0.946648i	$-0.395555\pi$
$647$	16.3946			0.644537			0.322268	+	0.946648i	$0.395555\pi$
$648$	16.7553	−	16.7553i	0.658209	−	0.658209i
$649$	8.37027	−	20.2076i	0.328562	−	0.793219i
$650$		−	1.24897i		−	0.0489886i
$651$	29.1198	+	12.0618i	1.14130	+	0.472740i
$652$	0.717276	+	1.73166i	0.0280907	+	0.0678169i
$653$	33.1032	−	13.7118i	1.29543	−	0.536585i	0.374831	−	0.927093i	$-0.377701\pi$
$653$	33.1032	−	13.7118i	1.29543	−	0.536585i	0.920599	+	0.390509i	$0.127701\pi$
$654$	−27.0886	−	27.0886i	−1.05925	−	1.05925i
$655$	−0.0415786	−	0.0415786i	−0.00162461	−	0.00162461i
$656$	−2.43734	+	1.00958i	−0.0951621	+	0.0394174i
$657$	−25.6450	−	61.9126i	−1.00051	−	2.41544i
$658$	−8.14257	−	3.37276i	−0.317430	−	0.131484i
$659$		−	28.5354i		−	1.11158i	−0.831322	−	0.555790i	$-0.812416\pi$
$659$		−	28.5354i		−	1.11158i	0.831322	−	0.555790i	$-0.187584\pi$
$660$	4.99091	−	12.0491i	0.194271	−	0.469012i
$661$	−31.9232	+	31.9232i	−1.24167	+	1.24167i	−0.282359	+	0.959309i	$0.591117\pi$
$661$	−31.9232	+	31.9232i	−1.24167	+	1.24167i	−0.959309	+	0.282359i	$0.908883\pi$
$662$	18.0847			0.702882
$663$		0			0
$664$	7.73917			0.300338
$665$	−0.326050	+	0.326050i	−0.0126437	+	0.0126437i
$666$	1.34907	−	3.25694i	0.0522753	−	0.126204i
$667$		−	3.61318i		−	0.139903i
$668$	8.18289	+	3.38946i	0.316606	+	0.131142i
$669$	24.4043	+	58.9172i	0.943526	+	2.27787i
$670$	−8.00501	+	3.31578i	−0.309261	+	0.128100i
$671$	13.7556	+	13.7556i	0.531029	+	0.531029i
$672$	2.55680	+	2.55680i	0.0986309	+	0.0986309i
$673$	4.53789	−	1.87966i	0.174923	−	0.0724554i	−0.293503	−	0.955958i	$-0.594821\pi$
$673$	4.53789	−	1.87966i	0.174923	−	0.0724554i	0.468426	+	0.883503i	$0.344821\pi$
$674$	−0.642925	−	1.55216i	−0.0247646	−	0.0597869i
$675$	47.2941	+	19.5899i	1.82035	+	0.754014i
$676$		−	12.8794i		−	0.495361i
$677$	7.19004	−	17.3583i	0.276336	−	0.667133i	−0.723393	−	0.690437i	$-0.757418\pi$
$677$	7.19004	−	17.3583i	0.276336	−	0.667133i	0.999728	+	0.0233035i	$0.00741840\pi$
$678$	24.7893	−	24.7893i	0.952028	−	0.952028i
$679$	−0.248361			−0.00953122
$680$		0			0
$681$	11.4688			0.439487
$682$	−21.0275	+	21.0275i	−0.805186	+	0.805186i
$683$	9.78516	−	23.6235i	0.374419	−	0.903927i	−0.618571	−	0.785729i	$-0.712288\pi$
$683$	9.78516	−	23.6235i	0.374419	−	0.903927i	0.992990	−	0.118198i	$-0.0377118\pi$
$684$		−	2.57398i		−	0.0984185i
$685$	−8.90287	−	3.68769i	−0.340161	−	0.140899i
$686$	5.46524	+	13.1943i	0.208664	+	0.503759i
$687$	−6.08700	+	2.52132i	−0.232234	+	0.0961943i
$688$	−6.59925	−	6.59925i	−0.251594	−	0.251594i
$689$	−2.06755	−	2.06755i	−0.0787675	−	0.0787675i
$690$	−1.45330	+	0.601978i	−0.0553263	+	0.0229169i
$691$	15.9231	+	38.4418i	0.605743	+	1.46239i	0.867588	+	0.497283i	$0.165669\pi$
$691$	15.9231	+	38.4418i	0.605743	+	1.46239i	−0.261845	+	0.965110i	$0.584331\pi$
$692$	5.92343	+	2.45356i	0.225175	+	0.0932705i
$693$		−	28.3337i		−	1.07631i
$694$	−8.60142	+	20.7657i	−0.326505	+	0.788254i
$695$	−12.8870	+	12.8870i	−0.488831	+	0.488831i
$696$	−28.3337			−1.07399
$697$		0			0
$698$	21.1070			0.798912
$699$	8.93528	−	8.93528i	0.337964	−	0.337964i
$700$	−1.54223	+	3.72326i	−0.0582906	+	0.140726i
$701$			0.746911i			0.0282104i	0.999901	+	0.0141052i	$0.00448998\pi$
$701$			0.746911i			0.0282104i	−0.999901	+	0.0141052i	$0.995510\pi$
$702$	−4.56726	−	1.89182i	−0.172380	−	0.0714021i
$703$	−0.0632163	−	0.152618i	−0.00238425	−	0.00575608i
$704$	−3.15179	+	1.30551i	−0.118788	+	0.0492034i
$705$	−21.2605	−	21.2605i	−0.800716	−	0.800716i
$706$	2.73409	+	2.73409i	0.102899	+	0.102899i
$707$	5.03663	−	2.08624i	0.189422	−	0.0784611i
$708$	7.91687	+	19.1130i	0.297534	+	0.718311i
$709$	19.5225	+	8.08650i	0.733184	+	0.303695i	0.717860	−	0.696188i	$-0.245122\pi$
$709$	19.5225	+	8.08650i	0.733184	+	0.303695i	0.0153245	+	0.999883i	$0.495122\pi$
$710$		−	9.00000i		−	0.337764i
$711$	−37.6549	+	90.9070i	−1.41217	+	3.40928i
$712$	−5.08042	+	5.08042i	−0.190397	+	0.190397i
$713$	3.58677			0.134326
$714$		0			0
$715$	−1.40373			−0.0524967
$716$	0.891541	−	0.891541i	0.0333185	−	0.0333185i
$717$	−26.6153	+	64.2550i	−0.993966	+	2.39965i
$718$			36.4347i			1.35973i
$719$	3.19764	+	1.32451i	0.119252	+	0.0493958i	0.441512	−	0.897256i	$-0.354442\pi$
$719$	3.19764	+	1.32451i	0.119252	+	0.0493958i	−0.322260	+	0.946651i	$0.604442\pi$
$720$	3.36037	+	8.11264i	0.125233	+	0.302340i
$721$	12.8347	−	5.31631i	0.477989	−	0.197990i
$722$	13.3497	+	13.3497i	0.496826	+	0.496826i
$723$	57.4795	+	57.4795i	2.13769	+	2.13769i
$724$	−14.1547	+	5.86305i	−0.526054	+	0.217899i
$725$	−12.0848	−	29.1752i	−0.448817	−	1.08354i
$726$	1.90238	+	0.787993i	0.0706041	+	0.0292452i
$727$		−	36.3327i		−	1.34751i	−0.738956	−	0.673754i	$-0.764681\pi$
$727$		−	36.3327i		−	1.34751i	0.738956	−	0.673754i	$-0.235319\pi$
$728$	0.148935	−	0.359560i	0.00551989	−	0.0133262i
$729$	26.7491	−	26.7491i	0.990707	−	0.990707i
$730$	10.7128			0.396497
$731$		0			0
$732$	−18.3996			−0.680069
$733$	−4.88022	+	4.88022i	−0.180255	+	0.180255i	−0.791467	−	0.611212i	$-0.790682\pi$
$733$	−4.88022	+	4.88022i	−0.180255	+	0.180255i	0.611212	+	0.791467i	$0.290682\pi$
$734$	−5.26458	+	12.7098i	−0.194319	+	0.469128i
$735$			21.9599i			0.810002i
$736$	0.380153	+	0.157464i	0.0140126	+	0.00580421i
$737$	−9.54742	−	23.0495i	−0.351684	−	0.849040i
$738$	−18.0643	+	7.48246i	−0.664955	+	0.275433i
$739$	−25.7140	−	25.7140i	−0.945906	−	0.945906i	0.0527040	−	0.998610i	$-0.483216\pi$
$739$	−25.7140	−	25.7140i	−0.945906	−	0.945906i	−0.998610	+	0.0527040i	$0.983216\pi$
$740$	0.398489	+	0.398489i	0.0146488	+	0.0146488i
$741$	−0.359560	+	0.148935i	−0.0132088	+	0.00547126i
$742$	3.61050	+	8.71652i	0.132546	+	0.319994i
$743$	−44.6373	−	18.4894i	−1.63758	−	0.678309i	−0.641531	−	0.767097i	$-0.721701\pi$
$743$	−44.6373	−	18.4894i	−1.63758	−	0.678309i	−0.996051	+	0.0887880i	$0.971701\pi$
$744$		−	28.1266i		−	1.03117i
$745$	7.30372	−	17.6327i	0.267587	−	0.646013i
$746$	−16.0965	+	16.0965i	−0.589333	+	0.589333i
$747$	57.3587			2.09864
$748$		0			0
$749$	−9.92539			−0.362666
$750$	−23.2377	+	23.2377i	−0.848521	+	0.848521i
$751$	4.18792	−	10.1105i	0.152819	−	0.368939i	−0.828866	−	0.559447i	$-0.811014\pi$
$751$	4.18792	−	10.1105i	0.152819	−	0.368939i	0.981686	+	0.190508i	$0.0610136\pi$
$752$			7.86484i			0.286801i
$753$	9.16987	+	3.79828i	0.334169	+	0.138417i
$754$	1.16704	+	2.81749i	0.0425012	+	0.102607i
$755$	−2.95799	+	1.22524i	−0.107652	+	0.0445910i
$756$	11.2793	+	11.2793i	0.410223	+	0.410223i
$757$	−14.1846	−	14.1846i	−0.515548	−	0.515548i	0.400673	−	0.916221i	$-0.368776\pi$
$757$	−14.1846	−	14.1846i	−0.515548	−	0.515548i	−0.916221	+	0.400673i	$0.868776\pi$
$758$	8.23970	−	3.41300i	0.299279	−	0.123966i
$759$	−1.73333	−	4.18462i	−0.0629158	−	0.151892i
$760$	0.380153	+	0.157464i	0.0137896	+	0.00571183i
$761$		−	36.4671i		−	1.32193i	−0.750416	−	0.660965i	$-0.770147\pi$
$761$		−	36.4671i		−	1.32193i	0.750416	−	0.660965i	$-0.229853\pi$
$762$	−8.09001	+	19.5310i	−0.293070	+	0.707534i
$763$	9.40776	−	9.40776i	0.340584	−	0.340584i
$764$	−10.3601			−0.374815
$765$		0			0
$766$	−19.4097			−0.701302
$767$	1.57450	−	1.57450i	0.0568520	−	0.0568520i
$768$	1.23480	−	2.98107i	0.0445569	−	0.107570i
$769$		−	45.8120i		−	1.65202i	−0.563653	−	0.826012i	$-0.690604\pi$
$769$		−	45.8120i		−	1.65202i	0.563653	−	0.826012i	$-0.309396\pi$
$770$	4.18462	+	1.73333i	0.150803	+	0.0624648i
$771$	−30.7952	−	74.3461i	−1.10906	−	2.67751i
$772$	14.0929	−	5.83746i	0.507214	−	0.210095i
$773$	−29.8080	−	29.8080i	−1.07212	−	1.07212i	−0.997189	−	0.0749304i	$-0.976127\pi$
$773$	−29.8080	−	29.8080i	−1.07212	−	1.07212i	−0.0749304	−	0.997189i	$-0.523873\pi$
$774$	−48.9102	−	48.9102i	−1.75804	−	1.75804i
$775$	28.9620	−	11.9964i	1.04035	−	0.430925i
$776$	0.0848138	+	0.204759i	0.00304464	+	0.00735041i
$777$	1.58897	+	0.658175i	0.0570042	+	0.0236119i
$778$		−	35.6614i		−	1.27852i
$779$	−0.350623	+	0.846479i	−0.0125624	+	0.0303282i
$780$	0.938823	−	0.938823i	0.0336153	−	0.0336153i
$781$	25.9145			0.927293
$782$		0			0
$783$	−124.993			−4.46690
$784$	4.06178	−	4.06178i	0.145064	−	0.145064i
$785$	−10.6819	+	25.7883i	−0.381252	+	0.920423i
$786$			0.160140i			0.00571200i
$787$	−20.5235	−	8.50112i	−0.731584	−	0.303032i	−0.0143815	−	0.999897i	$-0.504578\pi$
$787$	−20.5235	−	8.50112i	−0.731584	−	0.303032i	−0.717203	+	0.696864i	$0.754578\pi$
$788$	8.12902	+	19.6252i	0.289584	+	0.699119i
$789$	−45.4379	+	18.8210i	−1.61763	+	0.670045i
$790$	−11.1226	−	11.1226i	−0.395723	−	0.395723i
$791$	8.60924	+	8.60924i	0.306109	+	0.306109i
$792$	−23.3594	+	9.67579i	−0.830041	+	0.343814i
$793$	0.757866	+	1.82965i	0.0269126	+	0.0649728i
$794$	6.87886	+	2.84932i	0.244122	+	0.101118i
$795$			32.1862i			1.14153i
$796$	−5.00695	+	12.0878i	−0.177466	+	0.428442i
$797$	4.01764	−	4.01764i	0.142312	−	0.142312i	−0.632361	−	0.774673i	$-0.717914\pi$
$797$	4.01764	−	4.01764i	0.142312	−	0.142312i	0.774673	+	0.632361i	$0.217914\pi$
$798$	1.25578			0.0444540
$799$		0			0
$800$	3.59627			0.127147
$801$	−37.6534	+	37.6534i	−1.33042	+	1.33042i
$802$	−0.906801	+	2.18921i	−0.0320203	+	0.0773037i
$803$			30.8462i			1.08854i
$804$	21.8010	+	9.03026i	0.768861	+	0.318473i
$805$	−0.209065	−	0.504727i	−0.00736856	−	0.0177893i
$806$	−2.79690	+	1.15851i	−0.0985165	+	0.0408069i
$807$	−8.60924	−	8.60924i	−0.303059	−	0.303059i
$808$	−3.43996	−	3.43996i	−0.121017	−	0.121017i
$809$	−16.5033	+	6.83591i	−0.580226	+	0.240338i	−0.653440	−	0.756979i	$-0.726675\pi$
$809$	−16.5033	+	6.83591i	−0.580226	+	0.240338i	0.0732132	+	0.997316i	$0.476675\pi$
$810$	10.7436	+	25.9373i	0.377490	+	0.911342i
$811$	−2.30780	−	0.955920i	−0.0810377	−	0.0335669i	0.341796	−	0.939774i	$-0.388965\pi$
$811$	−2.30780	−	0.955920i	−0.0810377	−	0.0335669i	−0.422834	+	0.906207i	$0.638965\pi$
$812$		−	9.84018i		−	0.345323i
$813$	−5.83395	+	14.0844i	−0.204606	+	0.493962i
$814$	−1.14740	+	1.14740i	−0.0402165	+	0.0402165i
$815$	−2.22070			−0.0777876
$816$		0			0
$817$	−3.24123			−0.113396
$818$	−20.3899	+	20.3899i	−0.712918	+	0.712918i
$819$	1.10383	−	2.66487i	0.0385708	−	0.0931182i
$820$		−	3.12567i		−	0.109153i
$821$	23.7555	+	9.83985i	0.829072	+	0.343413i	0.756535	−	0.653953i	$-0.226890\pi$
$821$	23.7555	+	9.83985i	0.829072	+	0.343413i	0.0725370	+	0.997366i	$0.476890\pi$
$822$	10.0431	+	24.2462i	0.350294	+	0.845684i
$823$	12.3157	−	5.10132i	0.429297	−	0.177821i	−0.157563	−	0.987509i	$-0.550364\pi$
$823$	12.3157	−	5.10132i	0.429297	−	0.177821i	0.586860	+	0.809688i	$0.300364\pi$
$824$	−8.76595	−	8.76595i	−0.305376	−	0.305376i
$825$	−27.9921	−	27.9921i	−0.974559	−	0.974559i
$826$	−6.63788	+	2.74950i	−0.230961	+	0.0956674i
$827$	4.31877	+	10.4264i	0.150178	+	0.362562i	0.981009	−	0.193963i	$-0.0621342\pi$
$827$	4.31877	+	10.4264i	0.150178	+	0.362562i	−0.830831	+	0.556525i	$0.812134\pi$
$828$	2.81749	+	1.16704i	0.0979146	+	0.0405575i
$829$		−	25.9786i		−	0.902276i	−0.892454	−	0.451138i	$-0.851018\pi$
$829$		−	25.9786i		−	0.902276i	0.892454	−	0.451138i	$-0.148982\pi$
$830$	−3.50894	+	8.47134i	−0.121797	+	0.294044i
$831$	41.5883	−	41.5883i	1.44268	−	1.44268i
$832$	−0.347296			−0.0120403
$833$		0			0
$834$	49.6340			1.71869
$835$	−7.42025	+	7.42025i	−0.256788	+	0.256788i
$836$	−0.453400	+	1.09461i	−0.0156812	+	0.0378577i
$837$		−	124.080i		−	4.28882i
$838$	−28.3447	−	11.7407i	−0.979150	−	0.405577i
$839$	−8.02625	−	19.3771i	−0.277097	−	0.668971i	0.722656	−	0.691208i	$-0.242921\pi$
$839$	−8.02625	−	19.3771i	−0.277097	−	0.668971i	−0.999753	+	0.0222371i	$0.992921\pi$
$840$	−3.95795	+	1.63944i	−0.136562	+	0.0565659i
$841$	34.0168	+	34.0168i	1.17299	+	1.17299i
$842$	−4.38907	−	4.38907i	−0.151257	−	0.151257i
$843$	−75.6515	+	31.3359i	−2.60557	+	1.07926i
$844$	−3.80820	−	9.19381i	−0.131084	−	0.316464i
$845$	14.0978	+	5.83952i	0.484981	+	0.200886i
$846$			58.2900i			2.00405i
$847$	−0.273667	+	0.660691i	−0.00940331	+	0.0227016i
$848$	5.95328	−	5.95328i	0.204437	−	0.204437i
$849$	−42.0907			−1.44455
$850$		0			0
$851$	0.195718			0.00670914
$852$	−17.3317	+	17.3317i	−0.593774	+	0.593774i
$853$	19.5035	−	47.0855i	0.667786	−	1.61218i	−0.117520	−	0.993071i	$-0.537494\pi$
$853$	19.5035	−	47.0855i	0.667786	−	1.61218i	0.785306	−	0.619108i	$-0.212506\pi$
$854$		−	6.39012i		−	0.218665i
$855$	2.81749	+	1.16704i	0.0963561	+	0.0399120i
$856$	3.38946	+	8.18289i	0.115849	+	0.279685i
$857$	36.0368	−	14.9269i	1.23099	−	0.509895i	0.330106	−	0.943944i	$-0.392916\pi$
$857$	36.0368	−	14.9269i	1.23099	−	0.509895i	0.900889	+	0.434049i	$0.142916\pi$
$858$	2.70323	+	2.70323i	0.0922868	+	0.0922868i
$859$	8.96199	+	8.96199i	0.305779	+	0.305779i	0.843270	−	0.537491i	$-0.180628\pi$
$859$	8.96199	+	8.96199i	0.305779	+	0.305779i	−0.537491	+	0.843270i	$0.680628\pi$
$860$	10.2157	−	4.23147i	0.348352	−	0.144292i
$861$	−3.65050	−	8.81309i	−0.124409	−	0.300349i
$862$	8.06679	+	3.34137i	0.274756	+	0.113808i
$863$			31.9905i			1.08897i	0.838771	+	0.544485i	$0.183275\pi$
$863$			31.9905i			1.08897i	−0.838771	+	0.544485i	$0.816725\pi$
$864$	5.44728	−	13.1509i	0.185320	−	0.447402i
$865$	−5.37137	+	5.37137i	−0.182632	+	0.182632i
$866$	20.9855			0.713115
$867$		0			0
$868$	9.76827			0.331557
$869$	32.0261	−	32.0261i	1.08641	−	1.08641i
$870$	12.8465	−	31.0142i	0.435537	−	1.05148i
$871$		−	2.53983i		−	0.0860588i
$872$	−10.9688	−	4.54344i	−0.371452	−	0.153860i
$873$	0.628595	+	1.51756i	0.0212747	+	0.0513617i
$874$	0.132026	−	0.0546868i	0.00446583	−	0.00184981i
$875$	−8.07037	−	8.07037i	−0.272828	−	0.272828i
$876$	−20.6301	−	20.6301i	−0.697025	−	0.697025i
$877$	26.4426	−	10.9529i	0.892903	−	0.369852i	0.111416	−	0.993774i	$-0.464462\pi$
$877$	26.4426	−	10.9529i	0.892903	−	0.369852i	0.781487	+	0.623922i	$0.214462\pi$
$878$	−3.23986	−	7.82171i	−0.109340	−	0.263970i
$879$	−11.3451	−	4.69928i	−0.382660	−	0.158503i
$880$		−	4.04189i		−	0.136252i
$881$	6.98757	−	16.8695i	0.235417	−	0.568347i	−0.761381	−	0.648305i	$-0.775478\pi$
$881$	6.98757	−	16.8695i	0.235417	−	0.568347i	0.996798	+	0.0799572i	$0.0254784\pi$
$882$	30.1038	−	30.1038i	1.01365	−	1.01365i
$883$	18.4688			0.621526			0.310763	−	0.950487i	$-0.399415\pi$
$883$	18.4688			0.621526			0.310763	+	0.950487i	$0.399415\pi$
$884$		0			0
$885$	−24.5107			−0.823919
$886$	16.9397	−	16.9397i	0.569100	−	0.569100i
$887$	16.6413	−	40.1756i	0.558759	−	1.34896i	−0.351989	−	0.936004i	$-0.614495\pi$
$887$	16.6413	−	40.1756i	0.558759	−	1.34896i	0.910749	−	0.412961i	$-0.135505\pi$
$888$		−	1.53478i		−	0.0515038i
$889$	−6.78305	−	2.80963i	−0.227496	−	0.0942320i
$890$	−3.25759	−	7.86451i	−0.109195	−	0.263619i
$891$	−74.6833	+	30.9349i	−2.50199	+	1.03636i
$892$	13.9751	+	13.9751i	0.467922	+	0.467922i
$893$	1.93141	+	1.93141i	0.0646322	+	0.0646322i
$894$	−48.0212	+	19.8911i	−1.60607	+	0.665256i
$895$	0.571661	+	1.38011i	0.0191085	+	0.0461320i
$896$	1.03531	+	0.428841i	0.0345874	+	0.0143266i
$897$		−	0.461104i		−	0.0153958i
$898$	2.34419	−	5.65938i	0.0782267	−	0.188856i
$899$	−54.1244	+	54.1244i	−1.80515	+	1.80515i
$900$	26.6536			0.888455
$901$		0			0
$902$	9.00000			0.299667
$903$	23.8620	−	23.8620i	0.794078	−	0.794078i
$904$	4.15779	−	10.0378i	0.138286	−	0.333852i
$905$		−	18.1521i		−	0.603395i
$906$	8.05583	+	3.33683i	0.267637	+	0.110859i
$907$	−10.1026	−	24.3898i	−0.335450	−	0.809849i	−0.998141	−	0.0609551i	$-0.980585\pi$
$907$	−10.1026	−	24.3898i	−0.335450	−	0.809849i	0.662690	−	0.748894i	$-0.269415\pi$
$908$	3.28382	−	1.36020i	0.108977	−	0.0451399i
$909$	−25.4952	−	25.4952i	−0.845621	−	0.845621i
$910$	0.326050	+	0.326050i	0.0108084	+	0.0108084i
$911$	2.45879	−	1.01847i	0.0814634	−	0.0337433i	−0.341580	−	0.939853i	$-0.610962\pi$
$911$	2.45879	−	1.01847i	0.0814634	−	0.0337433i	0.423043	+	0.906110i	$0.360962\pi$
$912$	−0.428841	−	1.03531i	−0.0142003	−	0.0342826i
$913$	−24.3922	−	10.1036i	−0.807266	−	0.334380i
$914$		−	1.01691i		−	0.0336365i
$915$	8.34239	−	20.1403i	0.275791	−	0.665818i
$916$	−1.44383	+	1.44383i	−0.0477056	+	0.0477056i
$917$	−0.0556159			−0.00183660
$918$		0			0
$919$	15.1088			0.498392			0.249196	−	0.968453i	$-0.419834\pi$
$919$	15.1088			0.498392			0.249196	+	0.968453i	$0.419834\pi$
$920$	−0.344723	+	0.344723i	−0.0113652	+	0.0113652i
$921$	16.1845	−	39.0728i	0.533297	−	1.28749i
$922$		−	23.0838i		−	0.760224i
$923$	2.43734	+	1.00958i	0.0802260	+	0.0332307i
$924$	−4.72057	−	11.3965i	−0.155295	−	0.374916i
$925$	1.58036	−	0.654607i	0.0519620	−	0.0215234i
$926$	−13.6916	−	13.6916i	−0.449932	−	0.449932i
$927$	−64.9686	−	64.9686i	−2.13385	−	2.13385i
$928$	−8.11264	+	3.36037i	−0.266310	+	0.110309i
$929$	−1.89079	−	4.56477i	−0.0620348	−	0.149765i	0.889822	−	0.456307i	$-0.150828\pi$
$929$	−1.89079	−	4.56477i	−0.0620348	−	0.149765i	−0.951857	+	0.306542i	$0.900828\pi$
$930$	30.7875	+	12.7526i	1.00956	+	0.418175i
$931$		−	1.99495i		−	0.0653818i
$932$	1.49867	−	3.61812i	0.0490907	−	0.118515i
$933$	23.5638	−	23.5638i	0.771443	−	0.771443i
$934$	−10.6895			−0.349772
$935$		0			0
$936$	−2.57398			−0.0841331
$937$	−2.41418	+	2.41418i	−0.0788677	+	0.0788677i	−0.745440	−	0.666572i	$-0.767761\pi$
$937$	−2.41418	+	2.41418i	−0.0788677	+	0.0788677i	0.666572	+	0.745440i	$0.267761\pi$
$938$	−3.13618	+	7.57140i	−0.102400	+	0.247215i
$939$			70.0765i			2.28686i
$940$	−8.60889	−	3.56592i	−0.280791	−	0.116308i
$941$	−10.8150	−	26.1096i	−0.352557	−	0.851149i	−0.996303	−	0.0859092i	$-0.972621\pi$
$941$	−10.8150	−	26.1096i	−0.352557	−	0.851149i	0.643746	−	0.765240i	$-0.277379\pi$
$942$	70.2322	−	29.0911i	2.28829	−	0.947840i
$943$	−0.767588	−	0.767588i	−0.0249961	−	0.0249961i
$944$	4.53360	+	4.53360i	0.147556	+	0.147556i
$945$	−17.4604	+	7.23233i	−0.567986	+	0.235268i
$946$	12.1840	+	29.4149i	0.396137	+	0.956360i
$947$	5.62098	+	2.32829i	0.182657	+	0.0756591i	0.472138	−	0.881525i	$-0.343483\pi$
$947$	5.62098	+	2.32829i	0.182657	+	0.0756591i	−0.289480	+	0.957184i	$0.593483\pi$
$948$			42.8384i			1.39133i
$949$	−1.20171	+	2.90118i	−0.0390091	+	0.0941763i
$950$	0.883155	−	0.883155i	0.0286533	−	0.0286533i
$951$	−36.0841			−1.17011
$952$		0			0
$953$	26.7110			0.865254			0.432627	−	0.901573i	$-0.357587\pi$
$953$	26.7110			0.865254			0.432627	+	0.901573i	$0.357587\pi$
$954$	44.1226	−	44.1226i	1.42852	−	1.42852i
$955$	4.69727	−	11.3402i	0.152000	−	0.366961i
$956$			21.5544i			0.697118i
$957$	89.3018	+	36.9900i	2.88672	+	1.19572i
$958$	−7.27691	−	17.5680i	−0.235106	−	0.567597i
$959$	−8.42062	+	3.48794i	−0.271916	+	0.112631i
$960$	2.70323	+	2.70323i	0.0872465	+	0.0872465i
$961$	−31.8085	−	31.8085i	−1.02608	−	1.02608i
$962$	−0.152618	+	0.0632163i	−0.00492059	+	0.00203818i
$963$	25.1209	+	60.6473i	0.809511	+	1.95433i
$964$	23.2749	+	9.64077i	0.749633	+	0.310508i
$965$			18.0729i			0.581786i
$966$	−0.569370	+	1.37458i	−0.0183192	+	0.0442264i
$967$	−19.1675	+	19.1675i	−0.616387	+	0.616387i	−0.944603	−	0.328216i	$-0.893553\pi$
$967$	−19.1675	+	19.1675i	−0.616387	+	0.616387i	0.328216	+	0.944603i	$0.393553\pi$
$968$	0.638156			0.0205111
$969$		0			0
$970$	−0.262585			−0.00843108
$971$	−35.4066	+	35.4066i	−1.13625	+	1.13625i	−0.147136	+	0.989116i	$0.547006\pi$
$971$	−35.4066	+	35.4066i	−1.13625	+	1.13625i	−0.989116	+	0.147136i	$0.952994\pi$
$972$	12.9173	−	31.1852i	0.414324	−	1.00027i
$973$			17.2377i			0.552616i
$974$	2.89271	+	1.19820i	0.0926883	+	0.0383928i
$975$	−1.54223	−	3.72326i	−0.0493907	−	0.119240i
$976$	−5.26827	+	2.18219i	−0.168633	+	0.0698502i
$977$	1.59317	+	1.59317i	0.0509702	+	0.0509702i	0.732132	−	0.681162i	$-0.238525\pi$
$977$	1.59317	+	1.59317i	0.0509702	+	0.0509702i	−0.681162	+	0.732132i	$0.738525\pi$
$978$	4.27649	+	4.27649i	0.136747	+	0.136747i
$979$	22.6450	−	9.37985i	0.723736	−	0.299781i
$980$	2.60443	+	6.28766i	0.0831956	+	0.200852i
$981$	−81.2952	−	33.6736i	−2.59556	−	1.07511i
$982$		−	33.3851i		−	1.06536i
$983$	−13.2809	+	32.0630i	−0.423595	+	1.02265i	0.557683	+	0.830054i	$0.311691\pi$
$983$	−13.2809	+	32.0630i	−0.423595	+	1.02265i	−0.981278	+	0.192596i	$0.938309\pi$
$984$	−6.01924	+	6.01924i	−0.191886	+	0.191886i
$985$	−25.1676			−0.801905
$986$		0			0
$987$	−28.4382			−0.905198
$988$	−0.0852875	+	0.0852875i	−0.00271336	+	0.00271336i
$989$	1.46957	−	3.54787i	0.0467298	−	0.112816i
$990$		−	29.9564i		−	0.952075i
$991$	−14.1538	−	5.86269i	−0.449610	−	0.186235i	0.146377	−	0.989229i	$-0.453239\pi$
$991$	−14.1538	−	5.86269i	−0.449610	−	0.186235i	−0.595987	+	0.802994i	$0.703239\pi$
$992$	−3.33581	−	8.05335i	−0.105912	−	0.255694i
$993$	53.9117	−	22.3310i	1.71084	−	0.708652i
$994$	−6.01924	−	6.01924i	−0.190919	−	0.190919i
$995$	−10.9613	−	10.9613i	−0.347495	−	0.347495i
$996$	23.0710	−	9.55631i	0.731032	−	0.302803i
$997$	20.1321	+	48.6031i	0.637589	+	1.53928i	0.829882	+	0.557939i	$0.188408\pi$
$997$	20.1321	+	48.6031i	0.637589	+	1.53928i	−0.192293	+	0.981337i	$0.561592\pi$
$998$	−3.63156	−	1.50424i	−0.114955	−	0.0476159i
$999$		−	6.77063i		−	0.214213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.2.d.h.399.6		24
17.2	even	8	inner	578.2.d.h.423.1		24
17.3	odd	16		578.2.c.g.327.6		12
17.4	even	4	inner	578.2.d.h.179.1		24
17.5	odd	16		578.2.c.g.251.6		12
17.6	odd	16		578.2.b.f.577.1		6
17.7	odd	16		578.2.a.e.1.1	✓	3
17.8	even	8	inner	578.2.d.h.155.1		24
17.9	even	8	inner	578.2.d.h.155.6		24
17.10	odd	16		578.2.a.f.1.3	yes	3
17.11	odd	16		578.2.b.f.577.6		6
17.12	odd	16		578.2.c.g.251.1		12
17.13	even	4	inner	578.2.d.h.179.6		24
17.14	odd	16		578.2.c.g.327.1		12
17.15	even	8	inner	578.2.d.h.423.6		24
17.16	even	2	inner	578.2.d.h.399.1		24
51.41	even	16		5202.2.a.bn.1.2		3
51.44	even	16		5202.2.a.bo.1.2		3
68.7	even	16		4624.2.a.bj.1.3		3
68.27	even	16		4624.2.a.ba.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
578.2.a.e.1.1	✓	3	17.7	odd	16
578.2.a.f.1.3	yes	3	17.10	odd	16
578.2.b.f.577.1		6	17.6	odd	16
578.2.b.f.577.6		6	17.11	odd	16
578.2.c.g.251.1		12	17.12	odd	16
578.2.c.g.251.6		12	17.5	odd	16
578.2.c.g.327.1		12	17.14	odd	16
578.2.c.g.327.6		12	17.3	odd	16
578.2.d.h.155.1		24	17.8	even	8	inner
578.2.d.h.155.6		24	17.9	even	8	inner
578.2.d.h.179.1		24	17.4	even	4	inner
578.2.d.h.179.6		24	17.13	even	4	inner
578.2.d.h.399.1		24	17.16	even	2	inner
578.2.d.h.399.6		24	1.1	even	1	trivial
578.2.d.h.423.1		24	17.2	even	8	inner
578.2.d.h.423.6		24	17.15	even	8	inner
4624.2.a.ba.1.1		3	68.27	even	16
4624.2.a.bj.1.3		3	68.7	even	16
5202.2.a.bn.1.2		3	51.41	even	16
5202.2.a.bo.1.2		3	51.44	even	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.d (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.23480 - 2.98107i) q^{3} -1.00000i q^{4} +(1.09461 + 0.453400i) q^{5} +(-1.23480 - 2.98107i) q^{6} +(1.03531 - 0.428841i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-5.24070 - 5.24070i) q^{9} +(1.09461 - 0.453400i) q^{10} +(1.30551 + 3.15179i) q^{11} +(-2.98107 - 1.23480i) q^{12} +0.347296i q^{13} +(0.428841 - 1.03531i) q^{14} +(2.70323 - 2.70323i) q^{15} -1.00000 q^{16} -7.41147 q^{18} +(-0.245576 + 0.245576i) q^{19} +(0.453400 - 1.09461i) q^{20} -3.61587i q^{21} +(3.15179 + 1.30551i) q^{22} +(-0.157464 - 0.380153i) q^{23} +(-2.98107 + 1.23480i) q^{24} +(-2.54294 - 2.54294i) q^{25} +(0.245576 + 0.245576i) q^{26} +(-13.1509 + 5.44728i) q^{27} +(-0.428841 - 1.03531i) q^{28} +(8.11264 + 3.36037i) q^{29} -3.82295i q^{30} +(-3.33581 + 8.05335i) q^{31} +(-0.707107 + 0.707107i) q^{32} +11.0077 q^{33} +1.32770 q^{35} +(-5.24070 + 5.24070i) q^{36} +(-0.182024 + 0.439445i) q^{37} +0.347296i q^{38} +(1.03531 + 0.428841i) q^{39} +(-0.453400 - 1.09461i) q^{40} +(2.43734 - 1.00958i) q^{41} +(-2.55680 - 2.55680i) q^{42} +(6.59925 + 6.59925i) q^{43} +(3.15179 - 1.30551i) q^{44} +(-3.36037 - 8.11264i) q^{45} +(-0.380153 - 0.157464i) q^{46} -7.86484i q^{47} +(-1.23480 + 2.98107i) q^{48} +(-4.06178 + 4.06178i) q^{49} -3.59627 q^{50} +0.347296 q^{52} +(-5.95328 + 5.95328i) q^{53} +(-5.44728 + 13.1509i) q^{54} +4.04189i q^{55} +(-1.03531 - 0.428841i) q^{56} +(0.428841 + 1.03531i) q^{57} +(8.11264 - 3.36037i) q^{58} +(-4.53360 - 4.53360i) q^{59} +(-2.70323 - 2.70323i) q^{60} +(5.26827 - 2.18219i) q^{61} +(3.33581 + 8.05335i) q^{62} +(-7.67320 - 3.17834i) q^{63} +1.00000i q^{64} +(-0.157464 + 0.380153i) q^{65} +(7.78365 - 7.78365i) q^{66} -7.31315 q^{67} -1.32770 q^{69} +(0.938823 - 0.938823i) q^{70} +(2.90697 - 7.01804i) q^{71} +7.41147i q^{72} +(8.35362 + 3.46018i) q^{73} +(0.182024 + 0.439445i) q^{74} +(-10.7207 + 4.44066i) q^{75} +(0.245576 + 0.245576i) q^{76} +(2.70323 + 2.70323i) q^{77} +(1.03531 - 0.428841i) q^{78} +(-5.08062 - 12.2657i) q^{79} +(-1.09461 - 0.453400i) q^{80} +23.6955i q^{81} +(1.00958 - 2.43734i) q^{82} +(-5.47242 + 5.47242i) q^{83} -3.61587 q^{84} +9.33275 q^{86} +(20.0349 - 20.0349i) q^{87} +(1.30551 - 3.15179i) q^{88} -7.18479i q^{89} +(-8.11264 - 3.36037i) q^{90} +(0.148935 + 0.359560i) q^{91} +(-0.380153 + 0.157464i) q^{92} +(19.8885 + 19.8885i) q^{93} +(-5.56128 - 5.56128i) q^{94} +(-0.380153 + 0.157464i) q^{95} +(1.23480 + 2.98107i) q^{96} +(-0.204759 - 0.0848138i) q^{97} +5.74422i q^{98} +(9.67579 - 23.3594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{16} - 96 q^{18} + 72 q^{33} + 24 q^{50} + 72 q^{86}+O(q^{100}) \) 24 * q - 24 * q^16 - 96 * q^18 + 72 * q^33 + 24 * q^50 + 72 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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