LMFDB - Embedded newform 578.2.d.h.423.6

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			423.6
Character	$\chi$	$=$	578.423
Dual form			578.2.d.h.399.6

$q$-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 $\left(\mathbb{Z}/578\mathbb{Z}\right)^\times$.

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

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	0.692597	+	0.721325i	$0.256467\pi$
$3$	1.23480	+	2.98107i	0.712911	+	1.72112i	0.0203141	+	0.999794i	$0.493533\pi$
$4$			1.00000i			0.500000i
$5$	1.09461	−	0.453400i	0.489522	−	0.202767i	−0.124248	−	0.992251i	$-0.539652\pi$
$5$	1.09461	−	0.453400i	0.489522	−	0.202767i	0.613771	+	0.789484i	$0.289652\pi$
$6$	−1.23480	+	2.98107i	−0.504104	+	1.21701i
$7$	1.03531	+	0.428841i	0.391312	+	0.162087i	0.569659	−	0.821881i	$-0.307075\pi$
$7$	1.03531	+	0.428841i	0.391312	+	0.162087i	−0.178348	+	0.983968i	$0.557075\pi$
$8$	−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	−0.595515	−	0.803344i	$-0.703052\pi$
$11$	1.30551	−	3.15179i	0.393627	−	0.950301i	0.989143	−	0.146957i	$-0.0469479\pi$
$12$	−2.98107	+	1.23480i	−0.860559	+	0.356455i
$13$		−	0.347296i		−	0.0963227i	−0.998840	−	0.0481613i	$-0.984664\pi$
$13$		−	0.347296i		−	0.0963227i	0.998840	−	0.0481613i	$-0.0153362\pi$
$14$	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	0.678376	−	0.734715i	$-0.262684\pi$
$19$	−0.245576	−	0.245576i	−0.0563389	−	0.0563389i	−0.734715	+	0.678376i	$0.762684\pi$
$20$	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	−0.939446	−	0.342697i	$-0.888659\pi$
$23$	−0.157464	+	0.380153i	−0.0328336	+	0.0792673i	0.906612	+	0.421965i	$0.138659\pi$
$24$	−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	0.531652	−	0.846963i	$-0.321572\pi$
$29$	8.11264	−	3.36037i	1.50648	−	0.624004i	0.974828	+	0.222959i	$0.0715715\pi$
$30$			3.82295i			0.697972i
$31$	−3.33581	−	8.05335i	−0.599128	−	1.44642i	−0.874471	−	0.485078i	$-0.838791\pi$
$31$	−3.33581	−	8.05335i	−0.599128	−	1.44642i	0.275343	−	0.961346i	$-0.411209\pi$
$32$	−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	0.908211	−	0.418513i	$-0.137449\pi$
$37$	−0.182024	−	0.439445i	−0.0299246	−	0.0722443i	−0.938135	+	0.346269i	$0.887449\pi$
$38$		−	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	0.564799	−	0.825228i	$-0.308954\pi$
$41$	2.43734	+	1.00958i	0.380648	+	0.157670i	−0.184151	+	0.982898i	$0.558954\pi$
$42$	−2.55680	+	2.55680i	−0.394523	+	0.394523i
$43$	6.59925	−	6.59925i	1.00638	−	1.00638i	0.00639660	−	0.999980i	$-0.497964\pi$
$43$	6.59925	−	6.59925i	1.00638	−	1.00638i	0.999980	−	0.00639660i	$-0.00203612\pi$
$44$	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	$0.194454\pi$
$47$			7.86484i			1.14720i	−0.819134	+	0.573602i	$0.805546\pi$
$48$	−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	0.168035	−	0.985781i	$-0.446258\pi$
$53$	−5.95328	−	5.95328i	−0.817746	−	0.817746i	−0.985781	+	0.168035i	$0.946258\pi$
$54$	−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	−0.937692	−	0.347468i	$-0.887042\pi$
$59$	−4.53360	+	4.53360i	−0.590224	+	0.590224i	0.347468	+	0.937692i	$0.387042\pi$
$60$	−2.70323	+	2.70323i	−0.348986	+	0.348986i
$61$	5.26827	+	2.18219i	0.674533	+	0.279401i	0.693539	−	0.720419i	$-0.256050\pi$
$61$	5.26827	+	2.18219i	0.674533	+	0.279401i	−0.0190066	+	0.999819i	$0.506050\pi$
$62$	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	0.997195	+	0.0748424i	$0.0238454\pi$
$71$	2.90697	+	7.01804i	0.344993	+	0.832888i	−0.652202	+	0.758045i	$0.726155\pi$
$72$		−	7.41147i		−	0.873451i
$73$	8.35362	−	3.46018i	0.977717	−	0.404984i	0.164137	−	0.986437i	$-0.447516\pi$
$73$	8.35362	−	3.46018i	0.977717	−	0.404984i	0.813579	+	0.581454i	$0.197516\pi$
$74$	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	0.328565	+	0.944481i	$0.393435\pi$
$79$	−5.08062	+	12.2657i	−0.571615	+	1.38000i	−0.900180	+	0.435519i	$0.856565\pi$
$80$	−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	0.339816	−	0.940492i	$-0.389635\pi$
$83$	−5.47242	−	5.47242i	−0.600676	−	0.600676i	−0.940492	+	0.339816i	$0.889635\pi$
$84$	−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	$0.124349\pi$
$89$			7.18479i			0.761586i	−0.924660	+	0.380793i	$0.875651\pi$
$90$	−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	−0.393054	−	0.919515i	$-0.628582\pi$
$97$	−0.204759	+	0.0848138i	−0.0207901	+	0.00861154i	0.372264	+	0.928127i	$0.378582\pi$
$98$		−	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	−0.741374	−	0.671093i	$-0.765825\pi$
$107$	−8.18289	+	3.38946i	−0.791070	+	0.327672i	−0.0496962	+	0.998764i	$0.515825\pi$
$108$	5.44728	−	13.1509i	0.524165	−	1.26545i
$109$	10.9688	+	4.54344i	1.05062	+	0.435183i	0.840114	−	0.542409i	$-0.182488\pi$
$109$	10.9688	+	4.54344i	1.05062	+	0.435183i	0.210509	+	0.977592i	$0.432488\pi$
$110$	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	−0.598561	−	0.801077i	$-0.704261\pi$
$113$	4.15779	−	10.0378i	0.391132	−	0.944277i	0.989694	−	0.143200i	$-0.0457392\pi$
$114$	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	−0.882118	−	0.471028i	$-0.843883\pi$
$127$	−4.63274	+	4.63274i	−0.411090	+	0.411090i	0.471028	+	0.882118i	$0.343883\pi$
$128$	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	−0.384686	−	0.923048i	$-0.625690\pi$
$131$	−0.0458520	+	0.0189925i	−0.00400611	+	0.00165938i	0.380679	+	0.924707i	$0.375690\pi$
$132$			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	−0.949865	−	0.312660i	$-0.898780\pi$
$139$	−5.88658	−	14.2115i	−0.499293	−	1.20540i	0.450572	−	0.892740i	$-0.351220\pi$
$140$			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	$0.229376\pi$
$149$			16.1088i			1.31968i	−0.751406	+	0.659840i	$0.770624\pi$
$150$	−4.44066	−	10.7207i	−0.362578	−	0.875342i
$151$	−1.91084	−	1.91084i	−0.155502	−	0.155502i	0.625068	−	0.780570i	$-0.285071\pi$
$151$	−1.91084	−	1.91084i	−0.155502	−	0.155502i	−0.780570	+	0.625068i	$0.785071\pi$
$152$	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	$-0.610709\pi$
$157$		−	23.5594i		−	1.88025i	0.340834	−	0.940124i	$-0.389291\pi$
$158$	−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	0.313834	−	0.949478i	$-0.398386\pi$
$163$	−1.73166	−	0.717276i	−0.135634	−	0.0561814i	−0.449468	+	0.893296i	$0.648386\pi$
$164$	−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	0.736795	−	0.676117i	$-0.236339\pi$
$167$	−3.38946	−	8.18289i	−0.262285	−	0.633211i	−0.999079	+	0.0429057i	$0.986339\pi$
$168$	−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	0.802748	−	0.596318i	$-0.203370\pi$
$173$	−2.45356	−	5.92343i	−0.186541	−	0.450350i	−0.989289	+	0.145968i	$0.953370\pi$
$174$			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	−0.673003	−	0.739640i	$-0.734996\pi$
$179$	0.891541	−	0.891541i	0.0666369	−	0.0666369i	0.739640	+	0.673003i	$0.234996\pi$
$180$	−8.11264	−	3.36037i	−0.604681	−	0.250467i
$181$	−5.86305	+	14.1547i	−0.435797	+	1.05211i	0.541589	+	0.840644i	$0.317823\pi$
$181$	−5.86305	+	14.1547i	−0.435797	+	1.05211i	−0.977386	+	0.211464i	$0.932177\pi$
$182$	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	$0.122294\pi$
$191$			10.3601i			0.749630i	−0.927100	+	0.374815i	$0.877706\pi$
$192$	2.98107	−	1.23480i	0.215140	−	0.0891138i
$193$	5.83746	−	14.0929i	0.420190	−	1.01443i	−0.562102	−	0.827068i	$-0.690007\pi$
$193$	5.83746	−	14.0929i	0.420190	−	1.01443i	0.982291	−	0.187360i	$-0.0599929\pi$
$194$	−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	−0.448944	−	0.893560i	$-0.648200\pi$
$197$	−19.6252	−	8.12902i	−1.39824	−	0.579169i	−0.949294	+	0.314391i	$0.898200\pi$
$198$	−9.67579	+	23.3594i	−0.687628	+	1.66008i
$199$	−12.0878	+	5.00695i	−0.856884	+	0.354933i	−0.767488	−	0.641063i	$-0.778494\pi$
$199$	−12.0878	+	5.00695i	−0.856884	+	0.354933i	−0.0893958	+	0.995996i	$0.528494\pi$
$200$		−	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	0.675996	−	0.736905i	$-0.263713\pi$
$211$	9.19381	+	3.80820i	0.632928	+	0.262167i	−0.0430688	+	0.999072i	$0.513713\pi$
$212$	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	0.0622184	−	0.998063i	$-0.480182\pi$
$223$	−13.9751	−	13.9751i	−0.935844	−	0.935844i	−0.998063	+	0.0622184i	$0.980182\pi$
$224$	−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	−0.872290	−	0.488989i	$-0.837366\pi$
$227$	1.36020	−	3.28382i	0.0902797	−	0.217955i	0.962570	+	0.271035i	$0.0873658\pi$
$228$	1.03531	+	0.428841i	0.0685653	+	0.0284007i
$229$	−1.44383	+	1.44383i	−0.0954112	+	0.0954112i	−0.753201	−	0.657790i	$-0.771491\pi$
$229$	−1.44383	+	1.44383i	−0.0954112	+	0.0954112i	0.657790	+	0.753201i	$0.271491\pi$
$230$	−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	−0.261006	−	0.965337i	$-0.584054\pi$
$233$	3.61812	−	1.49867i	0.237031	−	0.0981813i	0.498037	+	0.867156i	$0.334054\pi$
$234$			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	−0.850512	−	0.525956i	$-0.823708\pi$
$241$	−9.64077	−	23.2749i	−0.621016	−	1.49927i	0.229495	−	0.973310i	$-0.426292\pi$
$242$		−	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	$-0.969050\pi$
$251$		−	3.07604i		−	0.194158i	0.995277	−	0.0970789i	$-0.0309499\pi$
$252$	−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	0.994406	+	0.105626i	$0.0336846\pi$
$257$	17.6349	+	17.6349i	1.10003	+	1.10003i	0.105626	+	0.994406i	$0.466315\pi$
$258$	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	−0.956458	−	0.291869i	$-0.905723\pi$
$263$	−10.7778	+	10.7778i	−0.664590	+	0.664590i	0.291869	+	0.956458i	$0.405723\pi$
$264$	−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	0.961767	−	0.273868i	$-0.0883031\pi$
$269$	1.44399	+	3.48609i	0.0880414	+	0.212551i	−0.873726	+	0.486418i	$0.838303\pi$
$270$	−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	0.185705	−	0.982606i	$-0.440543\pi$
$277$	16.8401	−	6.97541i	1.01182	−	0.419112i	0.826120	+	0.563494i	$0.190543\pi$
$278$	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	−0.0731575	+	0.997320i	$0.523308\pi$
$281$	−17.9445	+	17.9445i	−1.07048	+	1.07048i	−0.997320	+	0.0731575i	$0.976692\pi$
$282$	−23.4456	−	9.71148i	−1.39616	−	0.578310i
$283$	−4.99194	+	12.0516i	−0.296740	+	0.716394i	0.703245	+	0.710948i	$0.251734\pi$
$283$	−4.99194	+	12.0516i	−0.296740	+	0.716394i	−0.999985	+	0.00544667i	$0.998266\pi$
$284$	−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	$0.0354585\pi$
$293$			3.80571i			0.222332i	−0.993802	+	0.111166i	$0.964541\pi$
$294$	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	−0.0953843	−	0.995441i	$-0.530408\pi$
$311$	9.54155	−	3.95224i	0.541051	−	0.224111i	0.636436	+	0.771330i	$0.280408\pi$
$312$	−0.428841	+	1.03531i	−0.0242783	+	0.0586131i
$313$	−20.0646	−	8.31105i	−1.13412	−	0.469768i	−0.264941	−	0.964265i	$-0.585353\pi$
$313$	−20.0646	−	8.31105i	−1.13412	−	0.469768i	−0.869180	+	0.494496i	$0.835353\pi$
$314$	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	−0.997319	−	0.0731767i	$-0.976686\pi$
$317$	−4.27956	+	10.3318i	−0.240364	+	0.580291i	0.756955	+	0.653467i	$0.226686\pi$
$318$	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	−0.262146	−	0.965028i	$-0.584430\pi$
$331$	12.7878	−	12.7878i	0.702882	−	0.702882i	0.965028	+	0.262146i	$0.0844302\pi$
$332$	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	0.940423	−	0.340007i	$-0.110429\pi$
$337$	0.642925	+	1.55216i	0.0350224	+	0.0845515i	−0.905401	+	0.424558i	$0.860429\pi$
$338$	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	−0.252185	−	0.967679i	$-0.581149\pi$
$347$	−20.7657	−	8.60142i	−1.11476	−	0.461748i	−0.862574	+	0.505931i	$0.831149\pi$
$348$	−20.0349	+	20.0349i	−1.07399	+	1.07399i
$349$	14.9249	−	14.9249i	0.798912	−	0.798912i	−0.184012	−	0.982924i	$-0.558909\pi$
$349$	14.9249	−	14.9249i	0.798912	−	0.798912i	0.982924	+	0.184012i	$0.0589086\pi$
$350$	−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	$-0.967188\pi$
$353$		−	3.86659i		−	0.205798i	0.994692	−	0.102899i	$-0.0328118\pi$
$354$	−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	−0.874244	−	0.485487i	$-0.838642\pi$
$359$	−25.7632	−	25.7632i	−1.35973	−	1.35973i	−0.485487	−	0.874244i	$-0.661358\pi$
$360$	−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	0.0254410	−	0.999676i	$-0.491901\pi$
$367$	−12.7098	−	5.26458i	−0.663447	−	0.274809i	−0.688888	+	0.724867i	$0.741901\pi$
$368$	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	−0.160886	−	0.986973i	$-0.551435\pi$
$379$	8.23970	−	3.41300i	0.423245	−	0.175314i	0.584131	+	0.811659i	$0.301435\pi$
$380$	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	−0.964690	−	0.263388i	$-0.915160\pi$
$383$	−13.7247	+	13.7247i	−0.701302	+	0.701302i	0.263388	+	0.964690i	$0.415160\pi$
$384$	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	0.941495	+	0.337028i	$0.109422\pi$
$389$	25.2164	+	25.2164i	1.27852	+	1.27852i	0.337028	+	0.941495i	$0.390578\pi$
$390$	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	−0.836108	−	0.548564i	$-0.815175\pi$
$397$	2.84932	−	6.87886i	0.143003	−	0.345240i	0.979111	+	0.203324i	$0.0651746\pi$
$398$	−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	0.327351	−	0.944903i	$-0.393844\pi$
$401$	−2.18921	−	0.906801i	−0.109324	−	0.0452835i	−0.436675	+	0.899619i	$0.643844\pi$
$402$	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	0.324921	+	0.945741i	$0.394662\pi$
$419$	−11.7407	+	28.3447i	−0.573573	+	1.38473i	−0.898494	+	0.438986i	$0.855338\pi$
$420$	−3.95795	+	1.63944i	−0.193128	+	0.0799963i
$421$			6.20708i			0.302515i	0.988494	+	0.151257i	$0.0483322\pi$
$421$			6.20708i			0.302515i	−0.988494	+	0.151257i	$0.951668\pi$
$422$	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	−0.822747	−	0.568408i	$-0.807559\pi$
$431$	3.34137	−	8.06679i	0.160948	−	0.388564i	0.983695	+	0.179845i	$0.0575595\pi$
$432$	13.1509	+	5.44728i	0.632723	+	0.262082i
$433$	14.8390	−	14.8390i	0.713115	−	0.713115i	−0.254071	−	0.967186i	$-0.581770\pi$
$433$	14.8390	−	14.8390i	0.713115	−	0.713115i	0.967186	+	0.254071i	$0.0817697\pi$
$434$	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	0.982143	−	0.188137i	$-0.0602449\pi$
$439$	3.23986	+	7.82171i	0.154630	+	0.373310i	−0.827513	+	0.561447i	$0.810245\pi$
$440$	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	0.512206	−	0.858863i	$-0.328828\pi$
$449$	5.65938	+	2.34419i	0.267083	+	0.110629i	−0.245123	+	0.969492i	$0.578828\pi$
$450$	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	0.723725	−	0.690089i	$-0.242428\pi$
$457$	0.719065	+	0.719065i	0.0336365	+	0.0336365i	−0.690089	+	0.723725i	$0.742428\pi$
$458$	−2.04189			−0.0954112
$459$		0			0
$460$	−0.487511			−0.0227303
$461$	16.3227	+	16.3227i	0.760224	+	0.760224i	0.976363	−	0.216139i	$-0.0693464\pi$
$461$	16.3227	+	16.3227i	0.760224	+	0.760224i	−0.216139	+	0.976363i	$0.569346\pi$
$462$	4.72057	+	11.3965i	0.219621	+	0.530211i
$463$			19.3628i			0.899865i	0.893063	+	0.449932i	$0.148552\pi$
$463$			19.3628i			0.899865i	−0.893063	+	0.449932i	$0.851448\pi$
$464$	−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	−0.860025	−	0.510252i	$-0.829552\pi$
$467$	−7.55865	+	7.55865i	−0.349772	+	0.349772i	0.510252	+	0.860025i	$0.329552\pi$
$468$	−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	0.998393	+	0.0566645i	$0.0180465\pi$
$479$	7.27691	+	17.5680i	0.332490	+	0.802703i	−0.665903	+	0.746039i	$0.731953\pi$
$480$		−	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	−0.894404	−	0.447260i	$-0.852400\pi$
$487$	1.19820	−	2.89271i	0.0542956	−	0.131081i	0.948700	+	0.316179i	$0.102400\pi$
$488$	−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	0.997709	+	0.0676513i	$0.0215505\pi$
$491$	23.6068	+	23.6068i	1.06536	+	1.06536i	0.0676513	+	0.997709i	$0.478449\pi$
$492$	−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	−0.953966	−	0.299914i	$-0.903042\pi$
$499$	−1.50424	+	3.63156i	−0.0673391	+	0.162571i	0.886627	+	0.462485i	$0.153042\pi$
$500$	−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	0.288501	−	0.957480i	$-0.406843\pi$
$503$	−4.13877	−	1.71433i	−0.184539	−	0.0764384i	−0.473039	+	0.881041i	$0.656843\pi$
$504$	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	−0.177631	−	0.984097i	$-0.556843\pi$
$521$	14.6958	−	35.4788i	0.643835	−	1.55435i	0.821466	−	0.570257i	$-0.193157\pi$
$522$	−60.1266	+	24.9053i	−2.63167	+	1.09007i
$523$		−	31.6614i		−	1.38446i	−0.721679	−	0.692228i	$-0.756629\pi$
$523$		−	31.6614i		−	1.38446i	0.721679	−	0.692228i	$-0.243371\pi$
$524$	−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	0.846714	+	0.532048i	$0.178578\pi$
$541$	14.5188	+	35.0515i	0.624212	+	1.50698i	−0.222502	+	0.974932i	$0.571422\pi$
$542$	−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	0.935589	−	0.353091i	$-0.114869\pi$
$547$	0.569603	+	1.37514i	0.0243545	+	0.0587969i	−0.911234	+	0.411888i	$0.864869\pi$
$548$		−	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	$-0.835470\pi$
$557$		−	23.3259i		−	0.988352i	0.869362	−	0.494176i	$-0.164530\pi$
$558$	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	0.769317	−	0.638868i	$-0.220597\pi$
$563$	3.09524	+	3.09524i	0.130449	+	0.130449i	−0.638868	+	0.769317i	$0.720597\pi$
$564$	−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	−0.634078	−	0.773269i	$-0.718620\pi$
$569$	3.32024	−	3.32024i	0.139192	−	0.139192i	0.773269	+	0.634078i	$0.218620\pi$
$570$	0.938823	−	0.938823i	0.0393230	−	0.0393230i
$571$	12.4427	+	5.15395i	0.520712	+	0.215686i	0.627530	−	0.778593i	$-0.284066\pi$
$571$	12.4427	+	5.15395i	0.520712	+	0.215686i	−0.106818	+	0.994279i	$0.534066\pi$
$572$	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	−0.135639	+	0.990758i	$0.543309\pi$
$587$	−27.2904	+	27.2904i	−1.12640	+	1.12640i	−0.990758	+	0.135639i	$0.956691\pi$
$588$	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	0.739748	−	0.672884i	$-0.234944\pi$
$593$	1.62827	+	1.62827i	0.0668650	+	0.0668650i	−0.672884	+	0.739748i	$0.734944\pi$
$594$	−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	$-0.796679\pi$
$599$		−	29.1830i		−	1.19239i	0.802841	−	0.596193i	$-0.203321\pi$
$600$	10.7207	−	4.44066i	0.437671	−	0.181289i
$601$	5.37396	−	12.9739i	0.219208	−	0.529215i	−0.775572	−	0.631260i	$-0.782538\pi$
$601$	5.37396	−	12.9739i	0.219208	−	0.529215i	0.994780	+	0.102044i	$0.0325383\pi$
$602$	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	−0.566726	−	0.823906i	$-0.691790\pi$
$607$	−9.48225	+	3.92768i	−0.384873	+	0.159420i	0.181854	+	0.983326i	$0.441790\pi$
$608$			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	0.504056	−	0.863671i	$-0.331840\pi$
$617$	36.5435	−	15.1368i	1.47119	−	0.609385i	0.967129	+	0.254286i	$0.0818405\pi$
$618$	−15.3077	+	36.9560i	−0.615766	+	1.48659i
$619$	−20.6811	−	8.56639i	−0.831244	−	0.344312i	−0.0738488	−	0.997269i	$-0.523528\pi$
$619$	−20.6811	−	8.56639i	−0.831244	−	0.344312i	−0.757395	+	0.652957i	$0.773528\pi$
$620$	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	0.875870	−	0.482547i	$-0.160288\pi$
$631$	9.88016	+	9.88016i	0.393323	+	0.393323i	−0.482547	+	0.875870i	$0.660288\pi$
$632$	−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	0.114055	−	0.993474i	$-0.463616\pi$
$641$	22.7152	−	9.40895i	0.897197	−	0.371631i	0.783142	+	0.621843i	$0.213616\pi$
$642$		−	28.5790i		−	1.12792i
$643$	−11.3656	−	27.4389i	−0.448214	−	1.08208i	−0.972991	−	0.230844i	$-0.925851\pi$
$643$	−11.3656	−	27.4389i	−0.448214	−	1.08208i	0.524777	−	0.851240i	$-0.324149\pi$
$644$	−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	0.920599	−	0.390509i	$-0.127701\pi$
$653$	33.1032	+	13.7118i	1.29543	+	0.536585i	0.374831	+	0.927093i	$0.377701\pi$
$654$	−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	$0.187584\pi$
$659$			28.5354i			1.11158i	−0.831322	+	0.555790i	$0.812416\pi$
$660$	4.99091	+	12.0491i	0.194271	+	0.469012i
$661$	−31.9232	−	31.9232i	−1.24167	−	1.24167i	−0.959309	−	0.282359i	$-0.908883\pi$
$661$	−31.9232	−	31.9232i	−1.24167	−	1.24167i	−0.282359	−	0.959309i	$-0.591117\pi$
$662$	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	0.468426	−	0.883503i	$-0.344821\pi$
$673$	4.53789	+	1.87966i	0.174923	+	0.0724554i	−0.293503	+	0.955958i	$0.594821\pi$
$674$	−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	0.999728	−	0.0233035i	$-0.00741840\pi$
$677$	7.19004	+	17.3583i	0.276336	+	0.667133i	−0.723393	+	0.690437i	$0.757418\pi$
$678$	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	0.992990	+	0.118198i	$0.0377118\pi$
$683$	9.78516	+	23.6235i	0.374419	+	0.903927i	−0.618571	+	0.785729i	$0.712288\pi$
$684$			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	−0.261845	−	0.965110i	$-0.584331\pi$
$691$	15.9231	−	38.4418i	0.605743	−	1.46239i	0.867588	−	0.497283i	$-0.165669\pi$
$692$	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	$-0.995510\pi$
$701$		−	0.746911i		−	0.0282104i	0.999901	−	0.0141052i	$-0.00448998\pi$
$702$	−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	0.0153245	−	0.999883i	$-0.495122\pi$
$709$	19.5225	−	8.08650i	0.733184	−	0.303695i	0.717860	+	0.696188i	$0.245122\pi$
$710$			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	−0.322260	−	0.946651i	$-0.604442\pi$
$719$	3.19764	−	1.32451i	0.119252	−	0.0493958i	0.441512	+	0.897256i	$0.354442\pi$
$720$	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	$0.235319\pi$
$727$			36.3327i			1.34751i	−0.738956	+	0.673754i	$0.764681\pi$
$728$	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	0.611212	−	0.791467i	$-0.290682\pi$
$733$	−4.88022	−	4.88022i	−0.180255	−	0.180255i	−0.791467	+	0.611212i	$0.790682\pi$
$734$	−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	−0.998610	−	0.0527040i	$-0.983216\pi$
$739$	−25.7140	+	25.7140i	−0.945906	+	0.945906i	0.0527040	+	0.998610i	$0.483216\pi$
$740$	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	−0.996051	−	0.0887880i	$-0.971701\pi$
$743$	−44.6373	+	18.4894i	−1.63758	+	0.678309i	−0.641531	+	0.767097i	$0.721701\pi$
$744$			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	0.981686	−	0.190508i	$-0.0610136\pi$
$751$	4.18792	+	10.1105i	0.152819	+	0.368939i	−0.828866	+	0.559447i	$0.811014\pi$
$752$		−	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	−0.916221	−	0.400673i	$-0.868776\pi$
$757$	−14.1846	+	14.1846i	−0.515548	+	0.515548i	0.400673	+	0.916221i	$0.368776\pi$
$758$	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	$0.229853\pi$
$761$			36.4671i			1.32193i	−0.750416	+	0.660965i	$0.770147\pi$
$762$	−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	$0.309396\pi$
$769$			45.8120i			1.65202i	−0.563653	+	0.826012i	$0.690604\pi$
$770$	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	−0.0749304	+	0.997189i	$0.523873\pi$
$773$	−29.8080	+	29.8080i	−1.07212	+	1.07212i	−0.997189	+	0.0749304i	$0.976127\pi$
$774$	−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	−0.717203	−	0.696864i	$-0.754578\pi$
$787$	−20.5235	+	8.50112i	−0.731584	+	0.303032i	−0.0143815	+	0.999897i	$0.504578\pi$
$788$	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	0.774673	−	0.632361i	$-0.217914\pi$
$797$	4.01764	+	4.01764i	0.142312	+	0.142312i	−0.632361	+	0.774673i	$0.717914\pi$
$798$	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	0.0732132	−	0.997316i	$-0.476675\pi$
$809$	−16.5033	−	6.83591i	−0.580226	−	0.240338i	−0.653440	+	0.756979i	$0.726675\pi$
$810$	10.7436	−	25.9373i	0.377490	−	0.911342i
$811$	−2.30780	+	0.955920i	−0.0810377	+	0.0335669i	−0.422834	−	0.906207i	$-0.638965\pi$
$811$	−2.30780	+	0.955920i	−0.0810377	+	0.0335669i	0.341796	+	0.939774i	$0.388965\pi$
$812$			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	0.0725370	−	0.997366i	$-0.476890\pi$
$821$	23.7555	−	9.83985i	0.829072	−	0.343413i	0.756535	+	0.653953i	$0.226890\pi$
$822$	10.0431	−	24.2462i	0.350294	−	0.845684i
$823$	12.3157	+	5.10132i	0.429297	+	0.177821i	0.586860	−	0.809688i	$-0.300364\pi$
$823$	12.3157	+	5.10132i	0.429297	+	0.177821i	−0.157563	+	0.987509i	$0.550364\pi$
$824$	−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	−0.830831	−	0.556525i	$-0.812134\pi$
$827$	4.31877	−	10.4264i	0.150178	−	0.362562i	0.981009	+	0.193963i	$0.0621342\pi$
$828$	2.81749	−	1.16704i	0.0979146	−	0.0405575i
$829$			25.9786i			0.902276i	0.892454	+	0.451138i	$0.148982\pi$
$829$			25.9786i			0.902276i	−0.892454	+	0.451138i	$0.851018\pi$
$830$	−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	−0.999753	−	0.0222371i	$-0.992921\pi$
$839$	−8.02625	+	19.3771i	−0.277097	+	0.668971i	0.722656	+	0.691208i	$0.242921\pi$
$840$	−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	0.785306	+	0.619108i	$0.212506\pi$
$853$	19.5035	+	47.0855i	0.667786	+	1.61218i	−0.117520	+	0.993071i	$0.537494\pi$
$854$			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	0.900889	−	0.434049i	$-0.142916\pi$
$857$	36.0368	+	14.9269i	1.23099	+	0.509895i	0.330106	+	0.943944i	$0.392916\pi$
$858$	2.70323	−	2.70323i	0.0922868	−	0.0922868i
$859$	8.96199	−	8.96199i	0.305779	−	0.305779i	−0.537491	−	0.843270i	$-0.680628\pi$
$859$	8.96199	−	8.96199i	0.305779	−	0.305779i	0.843270	+	0.537491i	$0.180628\pi$
$860$	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	$-0.816725\pi$
$863$		−	31.9905i		−	1.08897i	0.838771	−	0.544485i	$-0.183275\pi$
$864$	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	0.781487	−	0.623922i	$-0.214462\pi$
$877$	26.4426	+	10.9529i	0.892903	+	0.369852i	0.111416	+	0.993774i	$0.464462\pi$
$878$	−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	0.996798	−	0.0799572i	$-0.0254784\pi$
$881$	6.98757	+	16.8695i	0.235417	+	0.568347i	−0.761381	+	0.648305i	$0.775478\pi$
$882$	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	0.910749	+	0.412961i	$0.135505\pi$
$887$	16.6413	+	40.1756i	0.558759	+	1.34896i	−0.351989	+	0.936004i	$0.614495\pi$
$888$			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	0.662690	+	0.748894i	$0.269415\pi$
$907$	−10.1026	+	24.3898i	−0.335450	+	0.809849i	−0.998141	+	0.0609551i	$0.980585\pi$
$908$	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	0.423043	−	0.906110i	$-0.360962\pi$
$911$	2.45879	+	1.01847i	0.0814634	+	0.0337433i	−0.341580	+	0.939853i	$0.610962\pi$
$912$	−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	−0.951857	−	0.306542i	$-0.900828\pi$
$929$	−1.89079	+	4.56477i	−0.0620348	+	0.149765i	0.889822	+	0.456307i	$0.150828\pi$
$930$	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	0.666572	−	0.745440i	$-0.267761\pi$
$937$	−2.41418	−	2.41418i	−0.0788677	−	0.0788677i	−0.745440	+	0.666572i	$0.767761\pi$
$938$	−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	0.643746	+	0.765240i	$0.277379\pi$
$941$	−10.8150	+	26.1096i	−0.352557	+	0.851149i	−0.996303	+	0.0859092i	$0.972621\pi$
$942$	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	−0.289480	−	0.957184i	$-0.593483\pi$
$947$	5.62098	−	2.32829i	0.182657	−	0.0756591i	0.472138	+	0.881525i	$0.343483\pi$
$948$		−	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	0.328216	−	0.944603i	$-0.393553\pi$
$967$	−19.1675	−	19.1675i	−0.616387	−	0.616387i	−0.944603	+	0.328216i	$0.893553\pi$
$968$	0.638156			0.0205111
$969$		0			0
$970$	−0.262585			−0.00843108
$971$	−35.4066	−	35.4066i	−1.13625	−	1.13625i	−0.989116	−	0.147136i	$-0.952994\pi$
$971$	−35.4066	−	35.4066i	−1.13625	−	1.13625i	−0.147136	−	0.989116i	$-0.547006\pi$
$972$	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	−0.681162	−	0.732132i	$-0.738525\pi$
$977$	1.59317	−	1.59317i	0.0509702	−	0.0509702i	0.732132	+	0.681162i	$0.238525\pi$
$978$	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	−0.981278	−	0.192596i	$-0.938309\pi$
$983$	−13.2809	−	32.0630i	−0.423595	−	1.02265i	0.557683	−	0.830054i	$-0.311691\pi$
$984$	−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	−0.595987	−	0.802994i	$-0.703239\pi$
$991$	−14.1538	+	5.86269i	−0.449610	+	0.186235i	0.146377	+	0.989229i	$0.453239\pi$
$992$	−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	−0.192293	−	0.981337i	$-0.561592\pi$
$997$	20.1321	−	48.6031i	0.637589	−	1.53928i	0.829882	−	0.557939i	$-0.188408\pi$
$998$	−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.423.6		24
17.2	even	8	inner	578.2.d.h.179.6		24
17.3	odd	16		578.2.b.f.577.6		6
17.4	even	4	inner	578.2.d.h.155.6		24
17.5	odd	16		578.2.a.e.1.1	✓	3
17.6	odd	16		578.2.c.g.251.6		12
17.7	odd	16		578.2.c.g.327.6		12
17.8	even	8	inner	578.2.d.h.399.6		24
17.9	even	8	inner	578.2.d.h.399.1		24
17.10	odd	16		578.2.c.g.327.1		12
17.11	odd	16		578.2.c.g.251.1		12
17.12	odd	16		578.2.a.f.1.3	yes	3
17.13	even	4	inner	578.2.d.h.155.1		24
17.14	odd	16		578.2.b.f.577.1		6
17.15	even	8	inner	578.2.d.h.179.1		24
17.16	even	2	inner	578.2.d.h.423.1		24
51.5	even	16		5202.2.a.bn.1.2		3
51.29	even	16		5202.2.a.bo.1.2		3
68.39	even	16		4624.2.a.bj.1.3		3
68.63	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	17.5	odd	16
578.2.a.f.1.3	yes	3	17.12	odd	16
578.2.b.f.577.1		6	17.14	odd	16
578.2.b.f.577.6		6	17.3	odd	16
578.2.c.g.251.1		12	17.11	odd	16
578.2.c.g.251.6		12	17.6	odd	16
578.2.c.g.327.1		12	17.10	odd	16
578.2.c.g.327.6		12	17.7	odd	16
578.2.d.h.155.1		24	17.13	even	4	inner
578.2.d.h.155.6		24	17.4	even	4	inner
578.2.d.h.179.1		24	17.15	even	8	inner
578.2.d.h.179.6		24	17.2	even	8	inner
578.2.d.h.399.1		24	17.9	even	8	inner
578.2.d.h.399.6		24	17.8	even	8	inner
578.2.d.h.423.1		24	17.16	even	2	inner
578.2.d.h.423.6		24	1.1	even	1	trivial
4624.2.a.ba.1.1		3	68.63	even	16
4624.2.a.bj.1.3		3	68.39	even	16
5202.2.a.bn.1.2		3	51.5	even	16
5202.2.a.bo.1.2		3	51.29	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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