LMFDB - Embedded newform 725.2.p.a.399.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(149,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("725.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.p (of order $14$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			399.4
Character	$\chi$	$=$	725.399
Dual form			725.2.p.a.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.504621 + 2.21089i) q^{2} +(-2.55926 - 1.23248i) q^{3} +(-2.83146 + 1.36356i) q^{4} +(1.43341 - 6.28018i) q^{6} +(0.677709 - 1.40728i) q^{7} +(-1.61565 - 2.02596i) q^{8} +(3.16036 + 3.96297i) q^{9} +(3.10613 + 2.47705i) q^{11} +8.92699 q^{12} +(-0.316631 - 0.252504i) q^{13} +(3.45332 + 0.788198i) q^{14} +(-0.254963 + 0.319714i) q^{16} -5.16843 q^{17} +(-7.16690 + 8.98701i) q^{18} +(1.49728 + 3.10914i) q^{19} +(-3.46887 + 2.76633i) q^{21} +(-3.90908 + 8.11728i) q^{22} +(-0.224414 - 0.0512209i) q^{23} +(1.63793 + 7.17623i) q^{24} +(0.398481 - 0.827455i) q^{26} +(-1.30768 - 5.72931i) q^{27} +4.90874i q^{28} +(-5.00751 - 1.98113i) q^{29} +(-4.21005 + 0.960917i) q^{31} +(-5.50488 - 2.65101i) q^{32} +(-4.89649 - 10.1677i) q^{33} +(-2.60810 - 11.4268i) q^{34} +(-14.3522 - 6.91164i) q^{36} +(3.34857 + 4.19898i) q^{37} +(-6.11841 + 4.87927i) q^{38} +(0.499135 + 1.03647i) q^{39} -1.46294i q^{41} +(-7.86653 - 6.27335i) q^{42} +(-1.44264 + 6.32061i) q^{43} +(-12.1725 - 2.77829i) q^{44} -0.522001i q^{46} +(-5.96928 + 7.48524i) q^{47} +(1.04656 - 0.503996i) q^{48} +(2.84329 + 3.56537i) q^{49} +(13.2274 + 6.36997i) q^{51} +(1.24083 + 0.283211i) q^{52} +(-1.74395 + 0.398044i) q^{53} +(12.0070 - 5.78226i) q^{54} +(-3.94604 + 0.900657i) q^{56} -9.80247i q^{57} +(1.85317 - 12.0708i) q^{58} +1.05216 q^{59} +(1.38382 - 2.87352i) q^{61} +(-4.24897 - 8.82307i) q^{62} +(7.71880 - 1.76177i) q^{63} +(2.90123 - 12.7111i) q^{64} +(20.0087 - 15.9564i) q^{66} +(-8.50052 + 6.77893i) q^{67} +(14.6342 - 7.04745i) q^{68} +(0.511205 + 0.407672i) q^{69} +(-8.38773 + 10.5179i) q^{71} +(2.92279 - 12.8056i) q^{72} +(-1.56113 + 6.83974i) q^{73} +(-7.59372 + 9.52223i) q^{74} +(-8.47898 - 6.76176i) q^{76} +(5.59095 - 2.69246i) q^{77} +(-2.03964 + 1.62656i) q^{78} +(-3.74078 + 2.98318i) q^{79} +(-0.330785 + 1.44926i) q^{81} +(3.23440 - 0.738232i) q^{82} +(-3.65480 - 7.58927i) q^{83} +(6.04990 - 12.5628i) q^{84} -14.7022 q^{86} +(10.3738 + 11.2419i) q^{87} -10.2950i q^{88} +(-1.10427 + 0.252043i) q^{89} +(-0.569927 + 0.274462i) q^{91} +(0.705260 - 0.160971i) q^{92} +(11.9589 + 2.72955i) q^{93} +(-19.5613 - 9.42022i) q^{94} +(10.8211 + 13.5693i) q^{96} +(15.5085 - 7.46850i) q^{97} +(-6.44786 + 8.08536i) q^{98} +20.1379i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{4} - 6 q^{6} + 6 q^{9} + 14 q^{11} + 14 q^{14} + 18 q^{16} + 14 q^{19} - 14 q^{21} + 50 q^{24} - 42 q^{26} + 30 q^{29} - 42 q^{31} + 26 q^{34} - 80 q^{36} - 42 q^{39} - 84 q^{44} - 26 q^{49}+ \cdots + 60 q^{96}+O(q^{100}) $ 24 * q + 2 * q^4 - 6 * q^6 + 6 * q^9 + 14 * q^11 + 14 * q^14 + 18 * q^16 + 14 * q^19 - 14 * q^21 + 50 * q^24 - 42 * q^26 + 30 * q^29 - 42 * q^31 + 26 * q^34 - 80 * q^36 - 42 * q^39 - 84 * q^44 - 26 * q^49 + 40 * q^51 + 76 * q^54 - 42 * q^56 - 88 * q^59 - 14 * q^61 + 52 * q^64 + 42 * q^66 - 42 * q^69 - 42 * q^71 + 14 * q^76 - 98 * q^79 + 2 * q^81 - 42 * q^84 - 88 * q^86 - 14 * q^89 - 6 * q^91 - 132 * q^94 + 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.504621	+	2.21089i	0.356821	+	1.56334i	0.761060	+	0.648682i	$0.224679\pi$
$2$	0.504621	+	2.21089i	0.356821	+	1.56334i	−0.404239	+	0.914654i	$0.632463\pi$
$3$	−2.55926	−	1.23248i	−1.47759	−	0.711571i	−0.490457	−	0.871465i	$-0.663170\pi$
$3$	−2.55926	−	1.23248i	−1.47759	−	0.711571i	−0.987134	+	0.159895i	$0.948885\pi$
$4$	−2.83146	+	1.36356i	−1.41573	+	0.681779i
$5$		0			0
$5$		0			0
$6$	1.43341	−	6.28018i	0.585188	−	2.56387i
$7$	0.677709	−	1.40728i	0.256150	−	0.531901i	−0.732747	−	0.680501i	$-0.761762\pi$
$7$	0.677709	−	1.40728i	0.256150	−	0.531901i	0.988897	+	0.148600i	$0.0474766\pi$
$8$	−1.61565	−	2.02596i	−0.571220	−	0.716287i
$9$	3.16036	+	3.96297i	1.05345	+	1.32099i
$10$		0			0
$11$	3.10613	+	2.47705i	0.936533	+	0.746860i	0.967555	−	0.252659i	$-0.0813051\pi$
$11$	3.10613	+	2.47705i	0.936533	+	0.746860i	−0.0310229	+	0.999519i	$0.509876\pi$
$12$	8.92699			2.57700
$13$	−0.316631	−	0.252504i	−0.0878175	−	0.0700321i	0.578597	−	0.815614i	$-0.303600\pi$
$13$	−0.316631	−	0.252504i	−0.0878175	−	0.0700321i	−0.666415	+	0.745581i	$0.732172\pi$
$14$	3.45332	+	0.788198i	0.922939	+	0.210655i
$15$		0			0
$16$	−0.254963	+	0.319714i	−0.0637408	+	0.0799285i
$17$	−5.16843			−1.25353			−0.626764	−	0.779209i	$-0.715621\pi$
$17$	−5.16843			−1.25353			−0.626764	+	0.779209i	$0.715621\pi$
$18$	−7.16690	+	8.98701i	−1.68926	+	2.11826i
$19$	1.49728	+	3.10914i	0.343500	+	0.713286i	0.999126	−	0.0418005i	$-0.0133094\pi$
$19$	1.49728	+	3.10914i	0.343500	+	0.713286i	−0.655626	+	0.755086i	$0.727595\pi$
$20$		0			0
$21$	−3.46887	+	2.76633i	−0.756970	+	0.603663i
$22$	−3.90908	+	8.11728i	−0.833418	+	1.73061i
$23$	−0.224414	−	0.0512209i	−0.0467935	−	0.0106803i	0.199060	−	0.979987i	$-0.436211\pi$
$23$	−0.224414	−	0.0512209i	−0.0467935	−	0.0106803i	−0.245854	+	0.969307i	$0.579068\pi$
$24$	1.63793	+	7.17623i	0.334341	+	1.46484i
$25$		0			0
$26$	0.398481	−	0.827455i	0.0781486	−	0.162277i
$27$	−1.30768	−	5.72931i	−0.251663	−	1.10261i
$28$			4.90874i			0.927664i
$29$	−5.00751	−	1.98113i	−0.929870	−	0.367887i
$29$	−5.00751	−	1.98113i	−0.929870	−	0.367887i
$30$		0			0
$31$	−4.21005	+	0.960917i	−0.756148	+	0.172586i	−0.583182	−	0.812342i	$-0.698192\pi$
$31$	−4.21005	+	0.960917i	−0.756148	+	0.172586i	−0.172967	+	0.984928i	$0.555335\pi$
$32$	−5.50488	−	2.65101i	−0.973135	−	0.468637i
$33$	−4.89649	−	10.1677i	−0.852369	−	1.76996i
$34$	−2.60810	−	11.4268i	−0.447285	−	1.95968i
$35$		0			0
$36$	−14.3522	−	6.91164i	−2.39203	−	1.15194i
$37$	3.34857	+	4.19898i	0.550502	+	0.690308i	0.976770	−	0.214289i	$-0.0687434\pi$
$37$	3.34857	+	4.19898i	0.550502	+	0.690308i	−0.426268	+	0.904597i	$0.640172\pi$
$38$	−6.11841	+	4.87927i	−0.992536	+	0.791521i
$39$	0.499135	+	1.03647i	0.0799256	+	0.165967i
$40$		0			0
$41$		−	1.46294i		−	0.228473i	−0.993454	−	0.114237i	$-0.963558\pi$
$41$		−	1.46294i		−	0.228473i	0.993454	−	0.114237i	$-0.0364422\pi$
$42$	−7.86653	−	6.27335i	−1.21383	−	0.967998i
$43$	−1.44264	+	6.32061i	−0.220000	+	0.963884i	0.737476	+	0.675373i	$0.236017\pi$
$43$	−1.44264	+	6.32061i	−0.220000	+	0.963884i	−0.957477	+	0.288511i	$0.906840\pi$
$44$	−12.1725	−	2.77829i	−1.83507	−	0.418842i
$45$		0			0
$46$		−	0.522001i		−	0.0769648i
$47$	−5.96928	+	7.48524i	−0.870709	+	1.09184i	0.124319	+	0.992242i	$0.460325\pi$
$47$	−5.96928	+	7.48524i	−0.870709	+	1.09184i	−0.995028	+	0.0995928i	$0.968246\pi$
$48$	1.04656	−	0.503996i	0.151058	−	0.0727455i
$49$	2.84329	+	3.56537i	0.406184	+	0.509339i
$50$		0			0
$51$	13.2274	+	6.36997i	1.85220	+	0.891974i
$52$	1.24083	+	0.283211i	0.172072	+	0.0392743i
$53$	−1.74395	+	0.398044i	−0.239549	+	0.0546756i	−0.340610	−	0.940205i	$-0.610634\pi$
$53$	−1.74395	+	0.398044i	−0.239549	+	0.0546756i	0.101061	+	0.994880i	$0.467776\pi$
$54$	12.0070	−	5.78226i	1.63394	−	0.786866i
$55$		0			0
$56$	−3.94604	+	0.900657i	−0.527311	+	0.120355i
$57$		−	9.80247i		−	1.29837i
$58$	1.85317	−	12.0708i	0.243333	−	1.58497i
$59$	1.05216			0.136980			0.0684900	−	0.997652i	$-0.478182\pi$
$59$	1.05216			0.136980			0.0684900	+	0.997652i	$0.478182\pi$
$60$		0			0
$61$	1.38382	−	2.87352i	0.177179	−	0.367917i	−0.793399	−	0.608702i	$-0.791691\pi$
$61$	1.38382	−	2.87352i	0.177179	−	0.367917i	0.970578	+	0.240785i	$0.0774049\pi$
$62$	−4.24897	−	8.82307i	−0.539619	−	1.12053i
$63$	7.71880	−	1.76177i	0.972478	−	0.221962i
$64$	2.90123	−	12.7111i	0.362653	−	1.58889i
$65$		0			0
$66$	20.0087	−	15.9564i	2.46290	−	1.96410i
$67$	−8.50052	+	6.77893i	−1.03850	+	0.828179i	−0.985373	−	0.170409i	$-0.945491\pi$
$67$	−8.50052	+	6.77893i	−1.03850	+	0.828179i	−0.0531298	+	0.998588i	$0.516920\pi$
$68$	14.6342	−	7.04745i	1.77465	−	0.854628i
$69$	0.511205	+	0.407672i	0.0615418	+	0.0490780i
$70$		0			0
$71$	−8.38773	+	10.5179i	−0.995440	+	1.24824i	−0.0268346	+	0.999640i	$0.508543\pi$
$71$	−8.38773	+	10.5179i	−0.995440	+	1.24824i	−0.968606	+	0.248603i	$0.920029\pi$
$72$	2.92279	−	12.8056i	0.344454	−	1.50915i
$73$	−1.56113	+	6.83974i	−0.182716	+	0.800531i	0.797615	+	0.603167i	$0.206095\pi$
$73$	−1.56113	+	6.83974i	−0.182716	+	0.800531i	−0.980330	+	0.197363i	$0.936762\pi$
$74$	−7.59372	+	9.52223i	−0.882752	+	1.10694i
$75$		0			0
$76$	−8.47898	−	6.76176i	−0.972605	−	0.775627i
$77$	5.59095	−	2.69246i	0.637148	−	0.306834i
$78$	−2.03964	+	1.62656i	−0.230943	+	0.184171i
$79$	−3.74078	+	2.98318i	−0.420871	+	0.335634i	−0.810916	−	0.585162i	$-0.801031\pi$
$79$	−3.74078	+	2.98318i	−0.420871	+	0.335634i	0.390045	+	0.920796i	$0.372459\pi$
$80$		0			0
$81$	−0.330785	+	1.44926i	−0.0367539	+	0.161029i
$82$	3.23440	−	0.738232i	0.357180	−	0.0815241i
$83$	−3.65480	−	7.58927i	−0.401166	−	0.833030i	−0.999495	−	0.0317796i	$-0.989883\pi$
$83$	−3.65480	−	7.58927i	−0.401166	−	0.833030i	0.598329	−	0.801251i	$-0.295832\pi$
$84$	6.04990	−	12.5628i	0.660099	−	1.37071i
$85$		0			0
$86$	−14.7022			−1.58537
$87$	10.3738	+	11.2419i	1.11219	+	1.20526i
$88$		−	10.2950i		−	1.09745i
$89$	−1.10427	+	0.252043i	−0.117053	+	0.0267165i	−0.280646	−	0.959811i	$-0.590549\pi$
$89$	−1.10427	+	0.252043i	−0.117053	+	0.0267165i	0.163593	+	0.986528i	$0.447692\pi$
$90$		0			0
$91$	−0.569927	+	0.274462i	−0.0597446	+	0.0287715i
$92$	0.705260	−	0.160971i	0.0735284	−	0.0167824i
$93$	11.9589	+	2.72955i	1.24009	+	0.283041i
$94$	−19.5613	−	9.42022i	−2.01759	−	0.971621i
$95$		0			0
$96$	10.8211	+	13.5693i	1.10443	+	1.38491i
$97$	15.5085	−	7.46850i	1.57465	−	0.758311i	0.576383	−	0.817180i	$-0.304464\pi$
$97$	15.5085	−	7.46850i	1.57465	−	0.758311i	0.998266	+	0.0588689i	$0.0187494\pi$
$98$	−6.44786	+	8.08536i	−0.651332	+	0.816745i
$99$			20.1379i			2.02393i
$100$		0			0
$101$	−6.08315	−	1.38844i	−0.605296	−	0.138155i	−0.0911203	−	0.995840i	$-0.529045\pi$
$101$	−6.08315	−	1.38844i	−0.605296	−	0.138155i	−0.514175	+	0.857685i	$0.671902\pi$
$102$	−7.40848	+	32.4587i	−0.733549	+	3.21389i
$103$	10.3284	+	8.23659i	1.01768	+	0.811576i	0.982208	−	0.187795i	$-0.0601340\pi$
$103$	10.3284	+	8.23659i	1.01768	+	0.811576i	0.0354755	+	0.999371i	$0.488705\pi$
$104$			1.04944i			0.102906i
$105$		0			0
$106$	−1.76006	−	3.65481i	−0.170953	−	0.354987i
$107$	7.24619	−	5.77864i	0.700516	−	0.558642i	−0.207164	−	0.978306i	$-0.566423\pi$
$107$	7.24619	−	5.77864i	0.700516	−	0.558642i	0.907680	+	0.419664i	$0.137852\pi$
$108$	11.5149	+	14.4392i	1.10802	+	1.38941i
$109$	5.18545	+	2.49718i	0.496676	+	0.239187i	0.665414	−	0.746474i	$-0.268255\pi$
$109$	5.18545	+	2.49718i	0.496676	+	0.239187i	−0.168738	+	0.985661i	$0.553969\pi$
$110$		0			0
$111$	−3.39474	−	14.8733i	−0.322215	−	1.41171i
$112$	0.277135	+	0.575477i	0.0261868	+	0.0543775i
$113$	7.26385	+	3.49809i	0.683326	+	0.329072i	0.743139	−	0.669137i	$-0.233336\pi$
$113$	7.26385	+	3.49809i	0.683326	+	0.329072i	−0.0598131	+	0.998210i	$0.519050\pi$
$114$	21.6722	−	4.94654i	2.02979	−	0.463286i
$115$		0			0
$116$	16.8799	−	1.21853i	1.56726	−	0.113138i
$117$		−	2.05280i		−	0.189782i
$118$	0.530944	+	2.32622i	0.0488774	+	0.214146i
$119$	−3.50269	+	7.27341i	−0.321091	+	0.666753i
$120$		0			0
$121$	1.06450	+	4.66388i	0.0967727	+	0.423989i
$122$	7.05135	+	1.60942i	0.638399	+	0.145710i
$123$	−1.80304	+	3.74405i	−0.162575	+	0.337590i
$124$	10.6103	−	8.46144i	0.952834	−	0.759860i
$125$		0			0
$126$	7.79014	+	16.1764i	0.694001	+	1.44111i
$127$	−10.9570	+	13.7396i	−0.972277	+	1.21920i	0.00340252	+	0.999994i	$0.498917\pi$
$127$	−10.9570	+	13.7396i	−0.972277	+	1.21920i	−0.975679	+	0.219202i	$0.929654\pi$
$128$	17.3469			1.53327
$129$	11.4821	−	14.3981i	1.01094	−	1.26768i
$130$		0			0
$131$	−3.26398	−	0.744983i	−0.285176	−	0.0650895i	0.0775403	−	0.996989i	$-0.475293\pi$
$131$	−3.26398	−	0.744983i	−0.285176	−	0.0650895i	−0.362716	+	0.931900i	$0.618150\pi$
$132$	27.7284	+	22.1126i	2.41345	+	1.92466i
$133$	5.39014			0.467385
$134$	−19.2770	−	15.3729i	−1.66528	−	1.32802i
$135$		0			0
$136$	8.35039	+	10.4711i	0.716040	+	0.897885i
$137$	3.44204	+	4.31618i	0.294073	+	0.368756i	0.906816	−	0.421526i	$-0.138505\pi$
$137$	3.44204	+	4.31618i	0.294073	+	0.368756i	−0.612743	+	0.790282i	$0.709934\pi$
$138$	−0.643354	+	1.33594i	−0.0547659	+	0.113723i
$139$	−0.132958	+	0.582528i	−0.0112774	+	0.0494094i	−0.980254	−	0.197745i	$-0.936638\pi$
$139$	−0.132958	+	0.582528i	−0.0112774	+	0.0494094i	0.968976	+	0.247154i	$0.0794954\pi$
$140$		0			0
$141$	24.5024	−	11.7997i	2.06347	−	0.993715i
$142$	−27.4865	−	13.2368i	−2.30662	−	1.11081i
$143$	−0.358028	−	1.56862i	−0.0299398	−	0.131175i
$144$	−2.07279			−0.172733
$145$		0			0
$146$	−15.9097			−1.31669
$147$	−2.88249	−	12.6290i	−0.237744	−	1.04162i
$148$	−15.2069	−	7.32325i	−1.25000	−	0.601968i
$149$	−4.60312	+	2.21675i	−0.377102	+	0.181603i	−0.612827	−	0.790217i	$-0.709968\pi$
$149$	−4.60312	+	2.21675i	−0.377102	+	0.181603i	0.235725	+	0.971820i	$0.424254\pi$
$150$		0			0
$151$	−1.73572	+	7.60469i	−0.141251	+	0.618861i	0.853894	+	0.520446i	$0.174234\pi$
$151$	−1.73572	+	7.60469i	−0.141251	+	0.618861i	−0.995145	+	0.0984149i	$0.968623\pi$
$152$	3.87992	−	8.05673i	0.314703	−	0.653487i
$153$	−16.3341	−	20.4823i	−1.32053	−	1.65590i
$154$	8.77405	+	11.0023i	0.707033	+	0.886591i
$155$		0			0
$156$	−2.82656	−	2.25411i	−0.226306	−	0.180473i
$157$	18.8577			1.50501			0.752504	−	0.658588i	$-0.228846\pi$
$157$	18.8577			1.50501			0.752504	+	0.658588i	$0.228846\pi$
$158$	−8.48315	−	6.76509i	−0.674884	−	0.538202i
$159$	4.95380	+	1.13067i	0.392862	+	0.0896681i
$160$		0			0
$161$	−0.224169	+	0.281099i	−0.0176670	+	0.0221537i
$162$	−3.37109			−0.264858
$163$	1.41033	−	1.76850i	0.110466	−	0.138520i	−0.723525	−	0.690298i	$-0.757479\pi$
$163$	1.41033	−	1.76850i	0.110466	−	0.138520i	0.833991	+	0.551779i	$0.186051\pi$
$164$	1.99481	+	4.14226i	0.155768	+	0.323456i
$165$		0			0
$166$	14.9347	−	11.9101i	1.15916	−	0.924400i
$167$	5.09159	−	10.5728i	0.393999	−	0.818147i	−0.605748	−	0.795656i	$-0.707126\pi$
$167$	5.09159	−	10.5728i	0.393999	−	0.818147i	0.999747	−	0.0224905i	$-0.00715956\pi$
$168$	11.2090	+	2.55838i	0.864792	+	0.197383i
$169$	−2.85628	−	12.5142i	−0.219714	−	0.962628i
$170$		0			0
$171$	−7.58947	+	15.7597i	−0.580381	+	1.20517i
$172$	−4.53375	−	19.8636i	−0.345695	−	1.51459i
$173$		−	19.2889i		−	1.46651i	−0.679954	−	0.733254i	$-0.738000\pi$
$173$		−	19.2889i		−	1.46651i	0.679954	−	0.733254i	$-0.262000\pi$
$174$	−19.6197	+	28.6083i	−1.48737	+	2.16879i
$175$		0			0
$176$	−1.58390	+	0.361514i	−0.119391	+	0.0272501i
$177$	−2.69276	−	1.29677i	−0.202401	−	0.0974710i
$178$	−1.11448	−	2.31424i	−0.0835337	−	0.173460i
$179$	−0.202580	−	0.887562i	−0.0151416	−	0.0663395i	0.966793	−	0.255562i	$-0.0822604\pi$
$179$	−0.202580	−	0.887562i	−0.0151416	−	0.0663395i	−0.981934	+	0.189222i	$0.939403\pi$
$180$		0			0
$181$	−4.74107	−	2.28318i	−0.352401	−	0.169707i	0.249305	−	0.968425i	$-0.419798\pi$
$181$	−4.74107	−	2.28318i	−0.352401	−	0.169707i	−0.601706	+	0.798718i	$0.705512\pi$
$182$	−0.894404	−	1.12155i	−0.0662976	−	0.0831346i
$183$	−7.08310	+	5.64858i	−0.523598	+	0.417555i
$184$	0.258803	+	0.537409i	0.0190792	+	0.0396183i
$185$		0			0
$186$			27.8173i			2.03966i
$187$	−16.0538	−	12.8025i	−1.17397	−	0.936210i
$188$	6.69520	−	29.3336i	0.488298	−	2.13937i
$189$	−8.94895	−	2.04254i	−0.650940	−	0.148573i
$190$		0			0
$191$			10.3088i			0.745920i	0.927847	+	0.372960i	$0.121657\pi$
$191$			10.3088i			0.745920i	−0.927847	+	0.372960i	$0.878343\pi$
$192$	−23.0911	+	28.9554i	−1.66646	+	2.08967i
$193$	2.44160	−	1.17581i	0.175750	−	0.0846368i	−0.343940	−	0.938992i	$-0.611762\pi$
$193$	2.44160	−	1.17581i	0.175750	−	0.0846368i	0.519690	+	0.854355i	$0.326047\pi$
$194$	24.3379	+	30.5188i	1.74736	+	2.19112i
$195$		0			0
$196$	−12.9122	−	6.21820i	−0.922302	−	0.444157i
$197$	−14.4081	−	3.28855i	−1.02653	−	0.234300i	−0.324080	−	0.946030i	$-0.605055\pi$
$197$	−14.4081	−	3.28855i	−1.02653	−	0.234300i	−0.702453	+	0.711730i	$0.747912\pi$
$198$	−44.5226	+	10.1620i	−3.16409	+	0.722182i
$199$	13.5173	−	6.50959i	0.958216	−	0.461453i	0.111657	−	0.993747i	$-0.464384\pi$
$199$	13.5173	−	6.50959i	0.958216	−	0.461453i	0.846560	+	0.532294i	$0.178670\pi$
$200$		0			0
$201$	30.1099	−	6.87240i	2.12379	−	0.484741i
$202$		−	14.1498i		−	0.995577i
$203$	−6.18163	+	5.70432i	−0.433866	+	0.400365i
$204$	−46.1385			−3.23034
$205$		0			0
$206$	−12.9983	+	26.9912i	−0.905634	+	1.88057i
$207$	−0.506241	−	1.05122i	−0.0351862	−	0.0730649i
$208$	0.161458	−	0.0368518i	0.0111951	−	0.00255521i
$209$	−3.05076	+	13.3662i	−0.211025	+	0.924562i
$210$		0			0
$211$	9.36088	−	7.46505i	0.644430	−	0.513916i	−0.245863	−	0.969305i	$-0.579071\pi$
$211$	9.36088	−	7.46505i	0.644430	−	0.513916i	0.890293	+	0.455389i	$0.150500\pi$
$212$	4.39515	−	3.50501i	0.301860	−	0.240725i
$213$	34.4294	−	16.5803i	2.35907	−	1.13607i
$214$	16.4325	+	13.1045i	1.12330	+	0.895805i
$215$		0			0
$216$	−9.49462	+	11.9059i	−0.646027	+	0.810093i
$217$	−1.50091	+	6.57594i	−0.101889	+	0.446404i
$218$	−2.90430	+	12.7246i	−0.196704	+	0.861818i
$219$	12.4251	−	15.5806i	0.839613	−	1.05284i
$220$		0			0
$221$	1.63648	+	1.30505i	0.110082	+	0.0877872i
$222$	31.1703	−	15.0108i	2.09201	−	1.00746i
$223$	−10.4541	+	8.33685i	−0.700057	+	0.558277i	−0.907542	−	0.419962i	$-0.862044\pi$
$223$	−10.4541	+	8.33685i	−0.700057	+	0.558277i	0.207485	+	0.978238i	$0.433472\pi$
$224$	−7.46142	+	5.95028i	−0.498537	+	0.397570i
$225$		0			0
$226$	−4.06839	+	17.8248i	−0.270625	+	1.18569i
$227$	2.06910	−	0.472258i	0.137331	−	0.0313448i	−0.153303	−	0.988179i	$-0.548991\pi$
$227$	2.06910	−	0.472258i	0.137331	−	0.0313448i	0.290634	+	0.956834i	$0.406134\pi$
$228$	13.3662	+	27.7553i	0.885200	+	1.83814i
$229$	11.8839	−	24.6772i	0.785312	−	1.63072i	0.00933352	−	0.999956i	$-0.497029\pi$
$229$	11.8839	−	24.6772i	0.785312	−	1.63072i	0.775978	−	0.630760i	$-0.217257\pi$
$230$		0			0
$231$	−17.6271			−1.15978
$232$	4.07669	+	13.3459i	0.267648	+	0.876198i
$233$			17.4774i			1.14498i	0.819910	+	0.572492i	$0.194023\pi$
$233$			17.4774i			1.14498i	−0.819910	+	0.572492i	$0.805977\pi$
$234$	4.53852	−	1.03589i	0.296692	−	0.0677181i
$235$		0			0
$236$	−2.97915	+	1.43468i	−0.193926	+	0.0933900i
$237$	13.2503	−	3.02431i	0.860703	−	0.196450i
$238$	−17.8482	−	4.07375i	−1.15693	−	0.264062i
$239$	15.5439	+	7.48555i	1.00545	+	0.484200i	0.862785	−	0.505571i	$-0.168718\pi$
$239$	15.5439	+	7.48555i	1.00545	+	0.484200i	0.142667	+	0.989771i	$0.454432\pi$
$240$		0			0
$241$	−13.7085	−	17.1899i	−0.883040	−	1.10730i	−0.993547	−	0.113422i	$-0.963819\pi$
$241$	−13.7085	−	17.1899i	−0.883040	−	1.10730i	0.110507	−	0.993875i	$-0.464753\pi$
$242$	−9.77415	+	4.70698i	−0.628306	+	0.302576i
$243$	−8.35934	+	10.4823i	−0.536252	+	0.672439i
$244$			10.0232i			0.641667i
$245$		0			0
$246$	−9.18755	−	2.09700i	−0.585777	−	0.133700i
$247$	0.310986	−	1.36252i	0.0197876	−	0.0866950i
$248$	8.74877	+	6.97691i	0.555548	+	0.443034i
$249$			23.9274i			1.51634i
$250$		0			0
$251$	−4.23936	−	8.80311i	−0.267586	−	0.555648i	0.723271	−	0.690564i	$-0.242638\pi$
$251$	−4.23936	−	8.80311i	−0.267586	−	0.555648i	−0.990857	+	0.134917i	$0.956923\pi$
$252$	−19.4532	+	15.5134i	−1.22544	+	0.977252i
$253$	−0.570180	−	0.714983i	−0.0358469	−	0.0449506i
$254$	−35.9060	−	17.2914i	−2.25294	−	1.08496i
$255$		0			0
$256$	2.95119	+	12.9300i	0.184449	+	0.808124i
$257$	−6.68278	−	13.8769i	−0.416861	−	0.865620i	−0.998633	−	0.0522684i	$-0.983355\pi$
$257$	−6.68278	−	13.8769i	−0.416861	−	0.865620i	0.581772	−	0.813352i	$-0.302359\pi$
$258$	37.6267	+	18.1201i	2.34254	+	1.12811i
$259$	8.17849	−	1.86669i	0.508187	−	0.115990i
$260$		0			0
$261$	−7.97437	−	26.1057i	−0.493601	−	1.61590i
$262$		−	7.59225i		−	0.469050i
$263$	6.89666	+	30.2162i	0.425266	+	1.86321i	0.500026	+	0.866010i	$0.333324\pi$
$263$	6.89666	+	30.2162i	0.425266	+	1.86321i	−0.0747599	+	0.997202i	$0.523819\pi$
$264$	−12.6883	+	26.3475i	−0.780911	+	1.62158i
$265$		0			0
$266$	2.71998	+	11.9170i	0.166773	+	0.730679i
$267$	3.13676	+	0.715945i	0.191967	+	0.0438151i
$268$	14.8254	−	30.7852i	0.905603	−	1.88050i
$269$	−10.8322	+	8.63841i	−0.660453	+	0.526693i	−0.895371	−	0.445322i	$-0.853089\pi$
$269$	−10.8322	+	8.63841i	−0.660453	+	0.526693i	0.234918	+	0.972015i	$0.424518\pi$
$270$		0			0
$271$	11.6447	+	24.1804i	0.707362	+	1.46885i	0.875565	+	0.483100i	$0.160489\pi$
$271$	11.6447	+	24.1804i	0.707362	+	1.46885i	−0.168203	+	0.985752i	$0.553796\pi$
$272$	1.31776	−	1.65242i	0.0799009	−	0.100193i
$273$	1.79686			0.108751
$274$	−7.80567	+	9.78800i	−0.471558	+	0.591315i
$275$		0			0
$276$	−2.00334	−	0.457249i	−0.120587	−	0.0275232i
$277$	17.6352	+	14.0636i	1.05960	+	0.845002i	0.988311	−	0.152454i	$-0.0487175\pi$
$277$	17.6352	+	14.0636i	1.05960	+	0.845002i	0.0712885	+	0.997456i	$0.477289\pi$
$278$	−1.35500			−0.0812675
$279$	−17.1134	−	13.6475i	−1.02455	−	0.817053i
$280$		0			0
$281$	−2.05756	−	2.58010i	−0.122744	−	0.153916i	0.716663	−	0.697420i	$-0.245669\pi$
$281$	−2.05756	−	2.58010i	−0.122744	−	0.153916i	−0.839406	+	0.543504i	$0.817097\pi$
$282$	38.4523	+	48.2176i	2.28980	+	2.87132i
$283$	7.66611	−	15.9189i	0.455703	−	0.946277i	−0.538885	−	0.842380i	$-0.681154\pi$
$283$	7.66611	−	15.9189i	0.455703	−	0.946277i	0.994588	−	0.103898i	$-0.0331315\pi$
$284$	9.40775	−	41.2180i	0.558247	−	2.44584i
$285$		0			0
$286$	3.28738	−	1.58312i	0.194387	−	0.0936118i
$287$	−2.05877	−	0.991449i	−0.121525	−	0.0585234i
$288$	−6.89155	−	30.1938i	−0.406088	−	1.77919i
$289$	9.71265			0.571332
$290$		0			0
$291$	−48.8951			−2.86628
$292$	−4.90611	−	21.4951i	−0.287109	−	1.25790i
$293$	−12.1939	−	5.87226i	−0.712374	−	0.343061i	0.0423508	−	0.999103i	$-0.486515\pi$
$293$	−12.1939	−	5.87226i	−0.712374	−	0.343061i	−0.754725	+	0.656042i	$0.772230\pi$
$294$	26.4668	−	12.7457i	1.54357	−	0.743346i
$295$		0			0
$296$	3.09685	−	13.5682i	0.180001	−	0.788635i
$297$	10.1300	−	21.0351i	0.587802	−	1.22058i
$298$	−7.22382	−	9.05838i	−0.418464	−	0.524738i
$299$	0.0581227	+	0.0728835i	0.00336132	+	0.00421496i
$300$		0			0
$301$	7.91716	+	6.31373i	0.456338	+	0.363917i
$302$	−17.6890			−1.01789
$303$	13.8572	+	11.0507i	0.796073	+	0.634847i
$304$	−1.37579	−	0.314014i	−0.0789068	−	0.0180100i
$305$		0			0
$306$	37.0416	−	46.4487i	2.11753	−	2.65530i
$307$	−6.51865			−0.372039			−0.186020	−	0.982546i	$-0.559559\pi$
$307$	−6.51865			−0.372039			−0.186020	+	0.982546i	$0.559559\pi$
$308$	−12.1592	+	15.2472i	−0.692835	+	0.868788i
$309$	−16.2816	−	33.8091i	−0.926227	−	1.92333i
$310$		0			0
$311$	19.1908	−	15.3042i	1.08821	−	0.867820i	0.0963761	−	0.995345i	$-0.469275\pi$
$311$	19.1908	−	15.3042i	1.08821	−	0.867820i	0.991835	+	0.127525i	$0.0407034\pi$
$312$	1.29341	−	2.68580i	0.0732251	−	0.152053i
$313$	−1.92496	−	0.439360i	−0.108805	−	0.0248341i	0.167772	−	0.985826i	$-0.446343\pi$
$313$	−1.92496	−	0.439360i	−0.108805	−	0.0248341i	−0.276577	+	0.960992i	$0.589200\pi$
$314$	9.51599	+	41.6923i	0.537019	+	2.35283i
$315$		0			0
$316$	6.52413	−	13.5475i	0.367011	−	0.762107i
$317$	6.60459	+	28.9366i	0.370951	+	1.62524i	0.724114	+	0.689680i	$0.242249\pi$
$317$	6.60459	+	28.9366i	0.370951	+	1.62524i	−0.353163	+	0.935562i	$0.614894\pi$
$318$			11.5229i			0.646170i
$319$	−10.6466	−	18.5575i	−0.596094	−	1.03902i
$320$		0			0
$321$	−25.6669	+	5.85831i	−1.43259	+	0.326979i
$322$	−0.734600	−	0.353765i	−0.0409377	−	0.0197145i
$323$	−7.73860	−	16.0694i	−0.430587	−	0.894123i
$324$	−1.03955	−	4.55457i	−0.0577529	−	0.253032i
$325$		0			0
$326$	4.62165	+	2.22567i	0.255969	+	0.123268i
$327$	−10.1932	−	12.7819i	−0.563686	−	0.706840i
$328$	−2.96387	+	2.36361i	−0.163652	+	0.130508i
$329$	6.48838	+	13.4733i	0.357716	+	0.742805i
$330$		0			0
$331$		−	28.3740i		−	1.55958i	−0.626044	−	0.779788i	$-0.715327\pi$
$331$		−	28.3740i		−	1.55958i	0.626044	−	0.779788i	$-0.284673\pi$
$332$	20.6968	+	16.5051i	1.13588	+	0.905838i
$333$	−6.05772	+	26.5406i	−0.331961	+	1.45442i
$334$	25.9446	+	5.92168i	1.41963	+	0.324020i
$335$		0			0
$336$		−	1.81436i		−	0.0989814i
$337$	−2.50472	+	3.14082i	−0.136441	+	0.171091i	−0.845358	−	0.534201i	$-0.820613\pi$
$337$	−2.50472	+	3.14082i	−0.136441	+	0.171091i	0.708917	+	0.705292i	$0.249184\pi$
$338$	26.2261	−	12.6298i	1.42651	−	0.686972i
$339$	−14.2788	−	17.9051i	−0.775518	−	0.972469i
$340$		0			0
$341$	−15.4572	−	7.44380i	−0.837055	−	0.403104i
$342$	−38.6728	−	8.82681i	−2.09118	−	0.477299i
$343$	17.6040	−	4.01799i	0.950525	−	0.216951i
$344$	15.1361	−	7.28918i	0.816086	−	0.393006i
$345$		0			0
$346$	42.6457	−	9.73360i	2.29265	−	0.523281i
$347$		−	3.55272i		−	0.190720i	−0.995443	−	0.0953601i	$-0.969600\pi$
$347$		−	3.55272i		−	0.190720i	0.995443	−	0.0953601i	$-0.0304003\pi$
$348$	−44.7020	−	17.6856i	−2.39628	−	0.948045i
$349$	−3.34203			−0.178895			−0.0894473	−	0.995992i	$-0.528510\pi$
$349$	−3.34203			−0.178895			−0.0894473	+	0.995992i	$0.528510\pi$
$350$		0			0
$351$	−1.03263	+	2.14427i	−0.0551175	+	0.114453i
$352$	−10.5322	−	21.8703i	−0.561366	−	1.16569i
$353$	−12.2016	+	2.78493i	−0.649424	+	0.148227i	−0.534528	−	0.845151i	$-0.679511\pi$
$353$	−12.2016	+	2.78493i	−0.649424	+	0.148227i	−0.114896	+	0.993378i	$0.536653\pi$
$354$	1.50818	−	6.60778i	0.0801590	−	0.351200i
$355$		0			0
$356$	2.78302	−	2.21939i	0.147500	−	0.117627i
$357$	17.9286	−	14.2976i	0.948883	−	0.756709i
$358$	1.86008	−	0.895765i	0.0983080	−	0.0473426i
$359$	14.3825	+	11.4697i	0.759080	+	0.605346i	0.924635	−	0.380855i	$-0.124370\pi$
$359$	14.3825	+	11.4697i	0.759080	+	0.605346i	−0.165555	+	0.986201i	$0.552942\pi$
$360$		0			0
$361$	4.42141	−	5.54428i	0.232706	−	0.291804i
$362$	2.65541	−	11.6341i	0.139566	−	0.611476i
$363$	3.02378	−	13.2481i	0.158708	−	0.695343i
$364$	1.23948	−	1.55426i	0.0649663	−	0.0814652i
$365$		0			0
$366$	−16.0627	−	12.8096i	−0.839609	−	0.669566i
$367$	8.85669	−	4.26516i	0.462316	−	0.222639i	−0.188202	−	0.982130i	$-0.560266\pi$
$367$	8.85669	−	4.26516i	0.462316	−	0.222639i	0.650518	+	0.759491i	$0.274552\pi$
$368$	0.0735933	−	0.0586887i	0.00383631	−	0.00305936i
$369$	5.79760	−	4.62343i	0.301811	−	0.240686i
$370$		0			0
$371$	−0.621729	+	2.72397i	−0.0322786	+	0.141422i
$372$	−37.5831	+	8.57810i	−1.94859	+	0.444754i
$373$	−9.62338	−	19.9832i	−0.498280	−	1.03469i	−0.986771	−	0.162120i	$-0.948167\pi$
$373$	−9.62338	−	19.9832i	−0.498280	−	1.03469i	0.488491	−	0.872569i	$-0.337547\pi$
$374$	20.2038	−	41.9536i	1.04471	−	2.16937i
$375$		0			0
$376$	24.8091			1.27943
$377$	1.08528	+	1.89170i	0.0558950	+	0.0974277i
$378$		−	20.8159i		−	1.07065i
$379$	8.48209	−	1.93598i	0.435696	−	0.0994447i	0.000953214	−	1.00000i	$-0.499697\pi$
$379$	8.48209	−	1.93598i	0.435696	−	0.0994447i	0.434742	+	0.900555i	$0.356839\pi$
$380$		0			0
$381$	44.9757	−	21.6591i	2.30417	−	1.10963i
$382$	−22.7917	+	5.20205i	−1.16612	+	0.266160i
$383$	4.95869	+	1.13179i	0.253377	+	0.0578317i	0.347323	−	0.937746i	$-0.387091\pi$
$383$	4.95869	+	1.13179i	0.253377	+	0.0578317i	−0.0939456	+	0.995577i	$0.529948\pi$
$384$	−44.3954	−	21.3797i	−2.26554	−	1.09103i
$385$		0			0
$386$	3.83167	+	4.80477i	0.195027	+	0.244556i
$387$	−29.6076	+	14.2583i	−1.50504	+	0.724790i
$388$	−33.7279	+	42.2934i	−1.71227	+	2.14712i
$389$		−	29.8408i		−	1.51299i	−0.654000	−	0.756494i	$-0.726910\pi$
$389$		−	29.8408i		−	1.51299i	0.654000	−	0.756494i	$-0.273090\pi$
$390$		0			0
$391$	1.15987	+	0.264732i	0.0586569	+	0.0133881i
$392$	2.62955	−	11.5208i	0.132812	−	0.581888i
$393$	7.43522	+	5.92939i	0.375057	+	0.299098i
$394$		−	33.5142i		−	1.68842i
$395$		0			0
$396$	−27.4591	−	57.0195i	−1.37987	−	2.86534i
$397$	−2.28497	+	1.82220i	−0.114679	+	0.0914537i	−0.679150	−	0.733999i	$-0.737652\pi$
$397$	−2.28497	+	1.82220i	−0.114679	+	0.0914537i	0.564471	+	0.825453i	$0.309080\pi$
$398$	21.2131	+	26.6004i	1.06332	+	1.33336i
$399$	−13.7948	−	6.64322i	−0.690604	−	0.332577i
$400$		0			0
$401$	4.54850	+	19.9283i	0.227141	+	0.995171i	0.951958	+	0.306229i	$0.0990674\pi$
$401$	4.54850	+	19.9283i	0.227141	+	0.995171i	−0.724817	+	0.688942i	$0.758075\pi$
$402$	30.3882	+	63.1018i	1.51563	+	3.14723i
$403$	1.57567	+	0.758802i	0.0784896	+	0.0377986i
$404$	19.1174	−	4.36341i	0.951125	−	0.217088i
$405$		0			0
$406$	−15.7310	−	10.7884i	−0.780717	−	0.535419i
$407$			21.3372i			1.05764i
$408$	−8.46551	−	37.0898i	−0.419105	−	1.83622i
$409$	−14.5837	+	30.2833i	−0.721116	+	1.49741i	0.140625	+	0.990063i	$0.455089\pi$
$409$	−14.5837	+	30.2833i	−0.721116	+	1.49741i	−0.861741	+	0.507349i	$0.830626\pi$
$410$		0			0
$411$	−3.48949	−	15.2885i	−0.172124	−	0.754124i
$412$	−40.4754	−	9.23824i	−1.99408	−	0.455135i
$413$	0.713061	−	1.48069i	0.0350874	−	0.0728598i
$414$	2.06867	−	1.64971i	0.101670	−	0.0810789i
$415$		0			0
$416$	1.07362	+	2.22940i	0.0526387	+	0.109305i
$417$	1.05823	−	1.32698i	0.0518216	−	0.0649823i
$418$	−31.0907			−1.52070
$419$	−4.69488	+	5.88719i	−0.229360	+	0.287608i	−0.883173	−	0.469048i	$-0.844597\pi$
$419$	−4.69488	+	5.88719i	−0.229360	+	0.287608i	0.653813	+	0.756656i	$0.273168\pi$
$420$		0			0
$421$	19.8646	+	4.53398i	0.968144	+	0.220972i	0.677226	−	0.735775i	$-0.263182\pi$
$421$	19.8646	+	4.53398i	0.968144	+	0.220972i	0.290918	+	0.956748i	$0.406039\pi$
$422$	21.2281	+	16.9289i	1.03337	+	0.824084i
$423$	−48.5289			−2.35956
$424$	3.62403	+	2.89007i	0.175999	+	0.140354i
$425$		0			0
$426$	54.0312	+	67.7529i	2.61782	+	3.28264i
$427$	−3.10602	−	3.89482i	−0.150311	−	0.188484i
$428$	−12.6378	+	26.2426i	−0.610869	+	1.26848i
$429$	−1.01700	+	4.45578i	−0.0491013	+	0.215127i
$430$		0			0
$431$	−10.6631	+	5.13509i	−0.513625	+	0.247349i	−0.672697	−	0.739918i	$-0.734864\pi$
$431$	−10.6631	+	5.13509i	−0.513625	+	0.247349i	0.159072	+	0.987267i	$0.449150\pi$
$432$	2.16515	+	1.04268i	0.104171	+	0.0501660i
$433$	−3.80447	−	16.6685i	−0.182831	−	0.801037i	−0.980274	−	0.197642i	$-0.936672\pi$
$433$	−3.80447	−	16.6685i	−0.182831	−	0.801037i	0.797443	−	0.603394i	$-0.206186\pi$
$434$	−15.2961			−0.734235
$435$		0			0
$436$	−18.0874			−0.866230
$437$	−0.176758	−	0.774425i	−0.00845546	−	0.0370458i
$438$	40.7171	+	19.6083i	1.94554	+	0.936921i
$439$	−16.8940	+	8.13573i	−0.806308	+	0.388297i	−0.791176	−	0.611588i	$-0.790531\pi$
$439$	−16.8940	+	8.13573i	−0.806308	+	0.388297i	−0.0151314	+	0.999886i	$0.504817\pi$
$440$		0			0
$441$	−5.14363	+	22.5357i	−0.244935	+	1.07313i
$442$	−2.05952	+	4.27664i	−0.0979614	+	0.203419i
$443$	−2.12225	−	2.66122i	−0.100831	−	0.126438i	0.728856	−	0.684667i	$-0.240052\pi$
$443$	−2.12225	−	2.66122i	−0.100831	−	0.126438i	−0.829687	+	0.558229i	$0.811481\pi$
$444$	29.8927	+	37.4843i	1.41864	+	1.77892i
$445$		0			0
$446$	−23.7072	−	18.9059i	−1.12257	−	0.895219i
$447$	14.5127			0.686427
$448$	−15.9219	−	12.6973i	−0.752237	−	0.599889i
$449$	−0.135791	−	0.0309934i	−0.00640836	−	0.00146267i	0.219316	−	0.975654i	$-0.429618\pi$
$449$	−0.135791	−	0.0309934i	−0.00640836	−	0.00146267i	−0.225724	+	0.974191i	$0.572475\pi$
$450$		0			0
$451$	3.62379	−	4.54408i	0.170637	−	0.213973i
$452$	−25.3371			−1.19176
$453$	13.8148	−	17.3232i	0.649075	−	0.813914i
$454$	2.08822	+	4.33623i	0.0980050	+	0.203509i
$455$		0			0
$456$	−19.8595	+	15.8374i	−0.930005	+	0.741654i
$457$	13.9188	−	28.9026i	0.651093	−	1.35201i	−0.270073	−	0.962840i	$-0.587048\pi$
$457$	13.9188	−	28.9026i	0.651093	−	1.35201i	0.921166	−	0.389169i	$-0.127238\pi$
$458$	60.5555	+	13.8214i	2.82957	+	0.645831i
$459$	6.75864	+	29.6115i	0.315466	+	1.38215i
$460$		0			0
$461$	−0.314786	+	0.653661i	−0.0146611	+	0.0304440i	−0.908171	−	0.418600i	$-0.862521\pi$
$461$	−0.314786	+	0.653661i	−0.0146611	+	0.0304440i	0.893510	+	0.449044i	$0.148235\pi$
$462$	−8.89502	−	38.9716i	−0.413834	−	1.81312i
$463$			9.14813i			0.425150i	0.977145	+	0.212575i	$0.0681849\pi$
$463$			9.14813i			0.425150i	−0.977145	+	0.212575i	$0.931815\pi$
$464$	1.91013	−	1.09585i	0.0886753	−	0.0508737i
$465$		0			0
$466$	−38.6407	+	8.81948i	−1.78999	+	0.408554i
$467$	27.6274	+	13.3047i	1.27844	+	0.615667i	0.944990	−	0.327099i	$-0.106071\pi$
$467$	27.6274	+	13.3047i	1.27844	+	0.615667i	0.333455	+	0.942766i	$0.391785\pi$
$468$	2.79911	+	5.81242i	0.129389	+	0.268679i
$469$	3.77897	+	16.5567i	0.174496	+	0.764519i
$470$		0			0
$471$	−48.2618	−	23.2417i	−2.22379	−	1.07092i
$472$	−1.69993	−	2.13165i	−0.0782457	−	0.0981170i
$473$	−20.1375	+	16.0591i	−0.925924	+	0.738399i
$474$	13.3728	+	27.7689i	0.614234	+	1.27547i
$475$		0			0
$476$		−	25.3705i		−	1.16285i
$477$	−7.08894	−	5.65324i	−0.324580	−	0.258844i
$478$	−8.70595	+	38.1433i	−0.398201	+	1.74463i
$479$	5.16447	+	1.17876i	0.235971	+	0.0538588i	0.338871	−	0.940833i	$-0.389955\pi$
$479$	5.16447	+	1.17876i	0.235971	+	0.0538588i	−0.102900	+	0.994692i	$0.532812\pi$
$480$		0			0
$481$		−	2.17506i		−	0.0991740i
$482$	31.0873	−	38.9823i	1.41599	−	1.77559i
$483$	0.920156	−	0.443124i	0.0418686	−	0.0201628i
$484$	−9.37355	−	11.7541i	−0.426070	−	0.534275i
$485$		0			0
$486$	−27.3935	−	13.1920i	−1.24259	−	0.598401i
$487$	−3.39429	−	0.774725i	−0.153810	−	0.0351062i	0.144922	−	0.989443i	$-0.453707\pi$
$487$	−3.39429	−	0.774725i	−0.153810	−	0.0351062i	−0.298733	+	0.954337i	$0.596564\pi$
$488$	−8.05742	+	1.83905i	−0.364742	+	0.0832500i
$489$	−5.78905	+	2.78786i	−0.261790	+	0.126071i
$490$		0			0
$491$	5.70489	−	1.30210i	0.257458	−	0.0587631i	−0.0918437	−	0.995773i	$-0.529276\pi$
$491$	5.70489	−	1.30210i	0.257458	−	0.0587631i	0.349302	+	0.937010i	$0.386419\pi$
$492$		−	13.0597i		−	0.588776i
$493$	25.8809	+	10.2393i	1.16562	+	0.461157i
$494$	3.16931			0.142594
$495$		0			0
$496$	0.766191	−	1.59101i	0.0344030	−	0.0714385i
$497$	9.11713	+	18.9319i	0.408959	+	0.849213i
$498$	−52.9008	+	12.0743i	−2.37054	+	0.541061i
$499$	5.27783	−	23.1237i	0.236268	−	1.03516i	−0.708060	−	0.706152i	$-0.750429\pi$
$499$	5.27783	−	23.1237i	0.236268	−	1.03516i	0.944328	−	0.329005i	$-0.106713\pi$
$500$		0			0
$501$	−26.0614	+	20.7833i	−1.16434	+	0.928529i
$502$	17.3234	−	13.8150i	0.773183	−	0.616593i
$503$	−17.4212	+	8.38962i	−0.776774	+	0.374075i	−0.779887	−	0.625920i	$-0.784723\pi$
$503$	−17.4212	+	8.38962i	−0.776774	+	0.374075i	0.00311266	+	0.999995i	$0.499009\pi$
$504$	−16.0402	−	12.7916i	−0.714487	−	0.569784i
$505$		0			0
$506$	1.29302	−	1.62140i	0.0574819	−	0.0720801i
$507$	−8.11345	+	35.5473i	−0.360331	+	1.57871i
$508$	12.2895	−	53.8437i	0.545257	−	2.38893i
$509$	−24.2136	+	30.3629i	−1.07325	+	1.34581i	−0.138555	+	0.990355i	$0.544246\pi$
$509$	−24.2136	+	30.3629i	−1.07325	+	1.34581i	−0.934693	+	0.355456i	$0.884326\pi$
$510$		0			0
$511$	8.56742	+	6.83229i	0.379000	+	0.302243i
$512$	4.16055	−	2.00362i	0.183872	−	0.0885482i
$513$	15.8553	−	12.6441i	0.700027	−	0.558253i
$514$	27.3081	−	21.7775i	1.20451	−	0.960565i
$515$		0			0
$516$	−12.8784	+	56.4240i	−0.566941	+	2.48393i
$517$	−37.0827	+	8.46389i	−1.63090	+	0.372241i
$518$	8.25408	+	17.1398i	0.362663	+	0.753078i
$519$	−23.7731	+	49.3654i	−1.04352	+	2.16690i
$520$		0			0
$521$	33.3472			1.46097			0.730484	−	0.682930i	$-0.239294\pi$
$521$	33.3472			1.46097			0.730484	+	0.682930i	$0.239294\pi$
$522$	53.6928	−	30.8039i	2.35007	−	1.34825i
$523$			31.8103i			1.39097i	0.718542	+	0.695484i	$0.244810\pi$
$523$			31.8103i			1.39097i	−0.718542	+	0.695484i	$0.755190\pi$
$524$	10.2577	−	2.34124i	0.448108	−	0.102278i
$525$		0			0
$526$	−63.3246	+	30.4955i	−2.76108	+	1.32967i
$527$	21.7594	−	4.96643i	0.947853	−	0.216341i
$528$	4.49917	+	1.02691i	0.195801	+	0.0446903i
$529$	−20.6745	−	9.95634i	−0.898893	−	0.432884i
$530$		0			0
$531$	3.32522	+	4.16969i	0.144302	+	0.180949i
$532$	−15.2620	+	7.34977i	−0.661689	+	0.318653i
$533$	−0.369399	+	0.463212i	−0.0160005	+	0.0200640i
$534$			7.29632i			0.315742i
$535$		0			0
$536$	27.4678	+	6.26934i	1.18643	+	0.270794i
$537$	−0.575443	+	2.52118i	−0.0248322	+	0.108797i
$538$	−24.5648	−	19.5897i	−1.05906	−	0.844574i
$539$			18.1175i			0.780375i
$540$		0			0
$541$	16.8087	+	34.9037i	0.722664	+	1.50063i	0.860105	+	0.510117i	$0.170398\pi$
$541$	16.8087	+	34.9037i	0.722664	+	1.50063i	−0.137441	+	0.990510i	$0.543888\pi$
$542$	−47.5840	+	37.9470i	−2.04391	+	1.62996i
$543$	9.31969	+	11.6865i	0.399946	+	0.501517i
$544$	28.4516	+	13.7016i	1.21985	+	0.587450i
$545$		0			0
$546$	0.906735	+	3.97267i	0.0388047	+	0.170014i
$547$	2.59920	+	5.39730i	0.111134	+	0.230772i	0.949117	−	0.314925i	$-0.101979\pi$
$547$	2.59920	+	5.39730i	0.111134	+	0.230772i	−0.837983	+	0.545697i	$0.816265\pi$
$548$	−15.6313	−	7.52765i	−0.667737	−	0.321565i
$549$	15.7610	−	3.59735i	0.672665	−	0.153531i
$550$		0			0
$551$	−1.33803	−	18.5353i	−0.0570022	−	0.789632i
$552$		−	1.69434i		−	0.0721159i
$553$	1.66299	+	7.28605i	0.0707176	+	0.309834i
$554$	−22.1940	+	46.0864i	−0.942934	+	1.95802i
$555$		0			0
$556$	−0.417845	−	1.83070i	−0.0177206	−	0.0776389i
$557$	−1.83032	−	0.417760i	−0.0775533	−	0.0177010i	0.183568	−	0.983007i	$-0.441235\pi$
$557$	−1.83032	−	0.417760i	−0.0775533	−	0.0177010i	−0.261122	+	0.965306i	$0.584092\pi$
$558$	21.5373	−	44.7226i	0.911746	−	1.89326i
$559$	2.05277	−	1.63703i	0.0868227	−	0.0692388i
$560$		0			0
$561$	25.3071	+	52.5508i	1.06847	+	2.21870i
$562$	4.66602	−	5.85101i	0.196824	−	0.246810i
$563$	−26.4739			−1.11574			−0.557872	−	0.829927i	$-0.688382\pi$
$563$	−26.4739			−1.11574			−0.557872	+	0.829927i	$0.688382\pi$
$564$	−53.2877	+	66.8207i	−2.24382	+	2.81366i
$565$		0			0
$566$	39.0633	+	8.91595i	1.64195	+	0.374765i
$567$	1.81534	+	1.44769i	0.0762372	+	0.0607971i
$568$	34.8605			1.46271
$569$	9.99580	+	7.97139i	0.419046	+	0.334178i	0.810207	−	0.586144i	$-0.199355\pi$
$569$	9.99580	+	7.97139i	0.419046	+	0.334178i	−0.391161	+	0.920322i	$0.627926\pi$
$570$		0			0
$571$	−23.7265	−	29.7521i	−0.992924	−	1.24509i	−0.969431	−	0.245363i	$-0.921093\pi$
$571$	−23.7265	−	29.7521i	−0.992924	−	1.24509i	−0.0234924	−	0.999724i	$-0.507479\pi$
$572$	3.15264	+	3.95329i	0.131819	+	0.165295i
$573$	12.7054	−	26.3830i	0.530775	−	1.10216i
$574$	1.15309	−	5.05201i	0.0481290	−	0.210867i
$575$		0			0
$576$	59.5426	−	28.6742i	2.48094	−	1.19476i
$577$	−0.0921290	−	0.0443670i	−0.00383538	−	0.00184702i	0.431965	−	0.901890i	$-0.357820\pi$
$577$	−0.0921290	−	0.0443670i	−0.00383538	−	0.00184702i	−0.435800	+	0.900043i	$0.643535\pi$
$578$	4.90121	+	21.4736i	0.203863	+	0.893184i
$579$	−7.69786			−0.319912
$580$		0			0
$581$	−13.1571			−0.545848
$582$	−24.6735	−	108.102i	−1.02275	−	4.48096i
$583$	−6.40289	−	3.08347i	−0.265181	−	0.127704i
$584$	16.3793	−	7.88785i	0.677780	−	0.326402i
$585$		0			0
$586$	6.82964	−	29.9226i	0.282130	−	1.23609i
$587$	0.319039	−	0.662492i	0.0131682	−	0.0273440i	−0.894281	−	0.447506i	$-0.852312\pi$
$587$	0.319039	−	0.662492i	0.0131682	−	0.0273440i	0.907449	+	0.420162i	$0.138027\pi$
$588$	25.3820	+	31.8280i	1.04674	+	1.31257i
$589$	−9.29127	−	11.6509i	−0.382840	−	0.480066i
$590$		0			0
$591$	32.8210	+	26.1739i	1.35008	+	1.07665i
$592$	−2.19624			−0.0902647
$593$	−34.9913	−	27.9046i	−1.43692	−	1.14590i	−0.964356	−	0.264607i	$-0.914758\pi$
$593$	−34.9913	−	27.9046i	−1.43692	−	1.14590i	−0.472562	−	0.881297i	$-0.656671\pi$
$594$	51.6182	+	11.7815i	2.11792	+	0.483402i
$595$		0			0
$596$	10.0109	−	12.5532i	0.410061	−	0.514201i
$597$	−42.6173			−1.74421
$598$	−0.131808	+	0.165281i	−0.00539001	+	0.00675886i
$599$	−1.76159	−	3.65797i	−0.0719764	−	0.149461i	0.861876	−	0.507119i	$-0.169290\pi$
$599$	−1.76159	−	3.65797i	−0.0719764	−	0.149461i	−0.933853	+	0.357658i	$0.883575\pi$
$600$		0			0
$601$	−34.7392	+	27.7036i	−1.41704	+	1.13005i	−0.444921	+	0.895570i	$0.646768\pi$
$601$	−34.7392	+	27.7036i	−1.41704	+	1.13005i	−0.972120	+	0.234483i	$0.924660\pi$
$602$	−9.96379	+	20.6900i	−0.406094	+	0.843262i
$603$	−53.7294	−	12.2634i	−2.18803	−	0.499404i
$604$	−5.45481	−	23.8991i	−0.221953	−	0.972441i
$605$		0			0
$606$	−17.4393	+	36.2131i	−0.708423	+	1.47106i
$607$	2.15884	+	9.45849i	0.0876246	+	0.383908i	0.999656	−	0.0262110i	$-0.00834417\pi$
$607$	2.15884	+	9.45849i	0.0876246	+	0.383908i	−0.912032	+	0.410119i	$0.865487\pi$
$608$		−	21.0848i		−	0.855100i
$609$	22.8509	−	6.98013i	0.925964	−	0.282849i
$610$		0			0
$611$	3.78012	−	0.862787i	0.152927	−	0.0349046i
$612$	74.1781	+	35.7223i	2.99847	+	1.44399i
$613$	−0.774505	−	1.60828i	−0.0312820	−	0.0649576i	0.884742	−	0.466081i	$-0.154334\pi$
$613$	−0.774505	−	1.60828i	−0.0312820	−	0.0649576i	−0.916024	+	0.401123i	$0.868620\pi$
$614$	−3.28945	−	14.4120i	−0.132751	−	0.581622i
$615$		0			0
$616$	−14.4879	−	6.97699i	−0.583733	−	0.281111i
$617$	5.43065	+	6.80982i	0.218630	+	0.274153i	0.879036	−	0.476756i	$-0.158187\pi$
$617$	5.43065	+	6.80982i	0.218630	+	0.274153i	−0.660406	+	0.750909i	$0.729616\pi$
$618$	66.5321	−	53.0576i	2.67631	−	2.13429i
$619$	6.16293	+	12.7975i	0.247709	+	0.514373i	0.987336	−	0.158644i	$-0.0507122\pi$
$619$	6.16293	+	12.7975i	0.247709	+	0.514373i	−0.739627	+	0.673017i	$0.764998\pi$
$620$		0			0
$621$			1.35272i			0.0542826i
$622$	43.5199	+	34.7060i	1.74499	+	1.39158i
$623$	−0.393681	+	1.72483i	−0.0157725	+	0.0691038i
$624$	−0.458633	−	0.104680i	−0.0183600	−	0.00419056i
$625$		0			0
$626$		−	4.47759i		−	0.178961i
$627$	24.2813	−	30.4477i	0.969700	−	1.21597i
$628$	−53.3947	+	25.7135i	−2.13068	+	1.02608i
$629$	−17.3069	−	21.7021i	−0.690070	−	0.865320i
$630$		0			0
$631$	14.9293	+	7.18958i	0.594327	+	0.286213i	0.706768	−	0.707446i	$-0.250153\pi$
$631$	14.9293	+	7.18958i	0.594327	+	0.286213i	−0.112441	+	0.993658i	$0.535867\pi$
$632$	12.0876	+	2.75892i	0.480820	+	0.109744i
$633$	−33.1575	+	7.56798i	−1.31789	+	0.300800i
$634$	−60.6429	+	29.2041i	−2.40844	+	1.15984i
$635$		0			0
$636$	−15.5682	+	3.55334i	−0.617319	+	0.140899i
$637$		−	1.84685i		−	0.0731748i
$638$	35.6561	−	32.9029i	1.41164	−	1.30264i
$639$	−68.1903			−2.69757
$640$		0			0
$641$	3.16628	−	6.57486i	0.125061	−	0.259691i	−0.829033	−	0.559200i	$-0.811108\pi$
$641$	3.16628	−	6.57486i	0.125061	−	0.259691i	0.954094	+	0.299509i	$0.0968227\pi$
$642$	−25.9042	−	53.7906i	−1.02236	−	2.12294i
$643$	33.0214	−	7.53691i	1.30224	−	0.297227i	0.485499	−	0.874237i	$-0.338638\pi$
$643$	33.0214	−	7.53691i	1.30224	−	0.297227i	0.816737	+	0.577010i	$0.195781\pi$
$644$	0.251430	−	1.10159i	0.00990774	−	0.0434086i
$645$		0			0
$646$	31.6225	−	25.2181i	1.24417	−	0.992194i
$647$	−26.1482	+	20.8525i	−1.02799	+	0.819795i	−0.983807	−	0.179228i	$-0.942640\pi$
$647$	−26.1482	+	20.8525i	−1.02799	+	0.819795i	−0.0441829	+	0.999023i	$0.514068\pi$
$648$	3.47059	−	1.67135i	0.136338	−	0.0656568i
$649$	3.26815	+	2.60627i	0.128286	+	0.102305i
$650$		0			0
$651$	11.9459	−	14.9797i	0.468198	−	0.587101i
$652$	−1.58184	+	6.93051i	−0.0619497	+	0.271420i
$653$	5.28615	−	23.1601i	0.206863	−	0.906326i	−0.759776	−	0.650184i	$-0.774692\pi$
$653$	5.28615	−	23.1601i	0.206863	−	0.906326i	0.966639	−	0.256141i	$-0.0824512\pi$
$654$	23.1156	−	28.9861i	0.903893	−	1.13345i
$655$		0			0
$656$	0.467723	+	0.372997i	0.0182615	+	0.0145631i
$657$	−32.0394	+	15.4294i	−1.24998	+	0.601956i
$658$	−26.5137	+	21.1440i	−1.03361	+	0.824278i
$659$	3.85540	−	3.07458i	0.150185	−	0.119769i	−0.545515	−	0.838101i	$-0.683666\pi$
$659$	3.85540	−	3.07458i	0.150185	−	0.119769i	0.695700	+	0.718333i	$0.255094\pi$
$660$		0			0
$661$	5.22326	−	22.8846i	0.203161	−	0.890107i	−0.765836	−	0.643036i	$-0.777675\pi$
$661$	5.22326	−	22.8846i	0.203161	−	0.890107i	0.968997	−	0.247071i	$-0.0794682\pi$
$662$	62.7318	−	14.3181i	2.43814	−	0.556489i
$663$	−2.57975	−	5.35690i	−0.100189	−	0.208045i
$664$	−9.47070	+	19.6661i	−0.367535	+	0.763193i
$665$		0			0
$666$	−61.7352			−2.39219
$667$	1.02228	+	0.701082i	0.0395827	+	0.0271460i
$668$			36.8790i			1.42689i
$669$	37.0297	−	8.45179i	1.43165	−	0.326765i
$670$		0			0
$671$	11.4162	−	5.49774i	0.440717	−	0.212238i
$672$	26.4293	−	6.03232i	1.01953	−	0.232702i
$673$	29.1789	+	6.65990i	1.12477	+	0.256720i	0.744150	−	0.668013i	$-0.232855\pi$
$673$	29.1789	+	6.65990i	1.12477	+	0.256720i	0.380616	+	0.924733i	$0.375712\pi$
$674$	−8.20794	−	3.95274i	−0.316158	−	0.152254i
$675$		0			0
$676$	25.1512	+	31.5386i	0.967353	+	1.21302i
$677$	−19.8360	+	9.55250i	−0.762358	+	0.367132i	−0.774318	−	0.632796i	$-0.781907\pi$
$677$	−19.8360	+	9.55250i	−0.762358	+	0.367132i	0.0119603	+	0.999928i	$0.496193\pi$
$678$	32.3807	−	40.6041i	1.24357	−	1.55939i
$679$		−	26.8862i		−	1.03180i
$680$		0			0
$681$	−5.87741	−	1.34148i	−0.225223	−	0.0514056i
$682$	8.65739	−	37.9305i	0.331508	−	1.45243i
$683$	−3.60979	−	2.87871i	−0.138125	−	0.110151i	0.551990	−	0.833851i	$-0.313869\pi$
$683$	−3.60979	−	2.87871i	−0.138125	−	0.110151i	−0.690115	+	0.723700i	$0.742440\pi$
$684$		−	54.9715i		−	2.10189i
$685$		0			0
$686$	17.7667	+	36.8929i	0.678335	+	1.40858i
$687$	−60.8282	+	48.5088i	−2.32074	+	1.85073i
$688$	−1.65297	−	2.07275i	−0.0630188	−	0.0790230i
$689$	0.652694	+	0.314321i	0.0248657	+	0.0119747i
$690$		0			0
$691$	7.95421	+	34.8497i	0.302592	+	1.32574i	0.866199	+	0.499700i	$0.166556\pi$
$691$	7.95421	+	34.8497i	0.302592	+	1.32574i	−0.563606	+	0.826044i	$0.690586\pi$
$692$	26.3015	+	54.6157i	0.999834	+	2.07618i
$693$	28.3396	+	13.6476i	1.07653	+	0.518430i
$694$	7.85468	−	1.79278i	0.298160	−	0.0680530i
$695$		0			0
$696$	6.01513	−	39.1800i	0.228003	−	1.48511i
$697$			7.56111i			0.286398i
$698$	−1.68646	−	7.38886i	−0.0638334	−	0.279672i
$699$	21.5405	−	44.7293i	0.814737	−	1.69182i
$700$		0			0
$701$	−0.811010	−	3.55327i	−0.0306314	−	0.134205i	0.957300	−	0.289096i	$-0.0933546\pi$
$701$	−0.811010	−	3.55327i	−0.0306314	−	0.134205i	−0.987932	+	0.154891i	$0.950497\pi$
$702$	−5.26183	−	1.20098i	−0.198595	−	0.0453280i
$703$	−8.04145	+	16.6982i	−0.303289	+	0.629786i
$704$	40.4976	−	32.2958i	1.52631	−	1.21719i
$705$		0			0
$706$	−12.3143	−	25.5710i	−0.463457	−	0.962377i
$707$	−6.07652	+	7.61972i	−0.228531	+	0.286569i
$708$	9.39266			0.352998
$709$	−13.0877	+	16.4114i	−0.491518	+	0.616344i	−0.964293	−	0.264839i	$-0.914681\pi$
$709$	−13.0877	+	16.4114i	−0.491518	+	0.616344i	0.472774	+	0.881184i	$0.343253\pi$
$710$		0			0
$711$	−23.6445	−	5.39670i	−0.886737	−	0.202392i
$712$	2.29475	+	1.83000i	0.0859994	+	0.0685822i
$713$	0.994013			0.0372261
$714$	40.6576	+	32.4233i	1.52157	+	1.21341i
$715$		0			0
$716$	1.78384	+	2.23686i	0.0666651	+	0.0835954i
$717$	−30.5552	−	38.3150i	−1.14110	−	1.43090i
$718$	−18.1005	+	37.5860i	−0.675503	+	1.40270i
$719$	5.39677	−	23.6448i	0.201266	−	0.881803i	−0.768902	−	0.639367i	$-0.779197\pi$
$719$	5.39677	−	23.6448i	0.201266	−	0.881803i	0.970167	−	0.242436i	$-0.0779463\pi$
$720$		0			0
$721$	18.5908	−	8.95286i	0.692357	−	0.333422i
$722$	14.4889	+	6.97750i	0.539222	+	0.259676i
$723$	13.8975	+	60.8888i	0.516852	+	2.26448i
$724$	16.5374			0.614607
$725$		0			0
$726$	30.8159			1.14368
$727$	6.88385	+	30.1601i	0.255308	+	1.11858i	0.926203	+	0.377025i	$0.123053\pi$
$727$	6.88385	+	30.1601i	0.255308	+	1.11858i	−0.670895	+	0.741552i	$0.734090\pi$
$728$	1.47686	+	0.711216i	0.0547359	+	0.0263594i
$729$	38.3309	−	18.4592i	1.41966	−	0.683673i
$730$		0			0
$731$	7.45617	−	32.6676i	0.275776	−	1.20826i
$732$	12.3533	−	25.6519i	0.456591	−	0.948122i
$733$	11.5408	+	14.4717i	0.426268	+	0.534523i	0.947866	−	0.318668i	$-0.103235\pi$
$733$	11.5408	+	14.4717i	0.426268	+	0.534523i	−0.521598	+	0.853191i	$0.674664\pi$
$734$	13.8991	+	17.4289i	0.513024	+	0.643312i
$735$		0			0
$736$	1.09958	+	0.876889i	0.0405312	+	0.0323225i
$737$	−43.1955			−1.59113
$738$	13.1475	+	10.4848i	0.483966	+	0.385950i
$739$	33.1954	+	7.57663i	1.22111	+	0.278711i	0.784037	−	0.620714i	$-0.213157\pi$
$739$	33.1954	+	7.57663i	1.22111	+	0.278711i	0.437075	+	0.899425i	$0.356014\pi$
$740$		0			0
$741$	−2.47517	+	3.10376i	−0.0909276	+	0.114020i
$742$	−6.33614			−0.232607
$743$	21.7142	−	27.2288i	0.796618	−	0.998927i	−0.203187	−	0.979140i	$-0.565130\pi$
$743$	21.7142	−	27.2288i	0.796618	−	0.998927i	0.999804	−	0.0197868i	$-0.00629873\pi$
$744$	−13.7915	−	28.6384i	−0.505622	−	1.04994i
$745$		0			0
$746$	39.3244	−	31.3602i	1.43977	−	1.14818i
$747$	18.5255	−	38.4687i	0.677814	−	1.40750i
$748$	62.9125	+	14.3594i	2.30031	+	0.525030i
$749$	−3.22135	−	14.1136i	−0.117705	−	0.515701i
$750$		0			0
$751$	−21.0818	+	43.7769i	−0.769287	+	1.59744i	0.0322376	+	0.999480i	$0.489737\pi$
$751$	−21.0818	+	43.7769i	−0.769287	+	1.59744i	−0.801525	+	0.597961i	$0.795978\pi$
$752$	−0.871188	−	3.81692i	−0.0317690	−	0.139189i
$753$			27.7544i			1.01143i
$754$	−3.63469	+	3.35404i	−0.132368	+	0.122147i
$755$		0			0
$756$	28.1237	−	6.41904i	1.02285	−	0.233458i
$757$	−27.1118	−	13.0563i	−0.985394	−	0.474541i	−0.129437	−	0.991588i	$-0.541317\pi$
$757$	−27.1118	−	13.0563i	−0.985394	−	0.474541i	−0.855957	+	0.517047i	$0.827031\pi$
$758$	8.56048	+	17.7760i	0.310931	+	0.645654i
$759$	0.578041	+	2.53256i	0.0209816	+	0.0919262i
$760$		0			0
$761$	8.85531	+	4.26449i	0.321005	+	0.154588i	0.587446	−	0.809263i	$-0.300133\pi$
$761$	8.85531	+	4.26449i	0.321005	+	0.154588i	−0.266441	+	0.963851i	$0.585848\pi$
$762$	70.5816	+	88.5066i	2.55690	+	3.20625i
$763$	7.02845	−	5.60500i	0.254447	−	0.202915i
$764$	−14.0567	−	29.1890i	−0.508552	−	1.05602i
$765$		0			0
$766$			11.5342i			0.416749i
$767$	−0.333147	−	0.265676i	−0.0120292	−	0.00959300i
$768$	8.38305	−	36.7285i	0.302497	−	1.32533i
$769$	29.2236	+	6.67010i	1.05383	+	0.240530i	0.714137	−	0.700006i	$-0.246819\pi$
$769$	29.2236	+	6.67010i	1.05383	+	0.240530i	0.339694	+	0.940536i	$0.389677\pi$
$770$		0			0
$771$			43.7511i			1.57566i
$772$	−5.30999	+	6.65852i	−0.191111	+	0.239645i
$773$	15.2398	−	7.33911i	0.548138	−	0.263969i	−0.139253	−	0.990257i	$-0.544470\pi$
$773$	15.2398	−	7.33911i	0.548138	−	0.263969i	0.687391	+	0.726287i	$0.258756\pi$
$774$	−46.4642	−	58.2642i	−1.67012	−	2.09426i
$775$		0			0
$776$	−40.1872	−	19.3532i	−1.44264	−	0.694738i
$777$	−23.2316	−	5.30245i	−0.833427	−	0.190224i
$778$	65.9747	−	15.0583i	2.36531	−	0.539866i
$779$	4.54849	−	2.19044i	0.162967	−	0.0784806i
$780$		0			0
$781$	−52.1067	+	11.8930i	−1.86452	+	0.425565i
$782$			2.69792i			0.0964776i
$783$	−4.80232	+	31.2802i	−0.171621	+	1.11786i
$784$	−1.86483			−0.0666012
$785$		0			0
$786$	−9.35726	+	19.4306i	−0.333763	+	0.693065i
$787$	8.67579	+	18.0155i	0.309259	+	0.642182i	0.996440	−	0.0843036i	$-0.0268665\pi$
$787$	8.67579	+	18.0155i	0.309259	+	0.642182i	−0.687181	+	0.726486i	$0.741152\pi$
$788$	45.2800	−	10.3349i	1.61303	−	0.368164i
$789$	19.5904	−	85.8312i	0.697437	−	3.05567i
$790$		0			0
$791$	9.84556	−	7.85157i	0.350068	−	0.279170i
$792$	40.7986	−	32.5358i	1.44972	−	1.15611i
$793$	−1.16374	+	0.560425i	−0.0413255	+	0.0199013i
$794$	−5.18173	−	4.13230i	−0.183893	−	0.146650i
$795$		0			0
$796$	−29.3975	+	36.8632i	−1.04197	+	1.30658i
$797$	8.96777	−	39.2904i	0.317655	−	1.39174i	−0.523999	−	0.851719i	$-0.675560\pi$
$797$	8.96777	−	39.2904i	0.317655	−	1.39174i	0.841654	−	0.540017i	$-0.181582\pi$
$798$	7.72629	−	33.8511i	0.273508	−	1.19832i
$799$	30.8518	−	38.6869i	1.09146	−	1.36865i
$800$		0			0
$801$	−4.48874	−	3.57965i	−0.158602	−	0.126481i
$802$	−41.7640	+	20.1125i	−1.47474	+	0.710196i
$803$	−21.7914	+	17.3781i	−0.769003	+	0.613260i
$804$	−75.8840	+	60.5155i	−2.67622	+	2.13422i
$805$		0			0
$806$	−0.882512	+	3.86654i	−0.0310851	+	0.136193i
$807$	38.3692	−	8.75751i	1.35066	−	0.308279i
$808$	7.01532	+	14.5675i	0.246798	+	0.512482i
$809$	−21.7442	+	45.1522i	−0.764484	+	1.58747i	0.0440579	+	0.999029i	$0.485971\pi$
$809$	−21.7442	+	45.1522i	−0.764484	+	1.58747i	−0.808542	+	0.588439i	$0.799743\pi$
$810$		0			0
$811$	24.7764			0.870017			0.435009	−	0.900426i	$-0.356745\pi$
$811$	24.7764			0.870017			0.435009	+	0.900426i	$0.356745\pi$
$812$	9.72486	−	24.5805i	0.341276	−	0.862608i
$813$		−	76.2357i		−	2.67370i
$814$	−47.1741	+	10.7672i	−1.65345	+	0.377390i
$815$		0			0
$816$	−5.40906	+	2.60487i	−0.189355	+	0.0911885i
$817$	−21.8117	+	4.97838i	−0.763095	+	0.174171i
$818$	−74.3122	−	16.9613i	−2.59827	−	0.593037i
$819$	−2.88886	−	1.39120i	−0.100945	−	0.0486126i
$820$		0			0
$821$	22.1885	+	27.8235i	0.774384	+	0.971047i	0.999995	−	0.00317052i	$-0.00100921\pi$
$821$	22.1885	+	27.8235i	0.774384	+	0.971047i	−0.225611	+	0.974218i	$0.572438\pi$
$822$	32.0402	−	15.4298i	1.11753	−	0.538175i
$823$	−9.60419	+	12.0433i	−0.334781	+	0.419802i	−0.920519	−	0.390699i	$-0.872233\pi$
$823$	−9.60419	+	12.0433i	−0.334781	+	0.419802i	0.585738	+	0.810501i	$0.300805\pi$
$824$		−	34.2324i		−	1.19254i
$825$		0			0
$826$	3.63346	+	0.829313i	0.126424	+	0.0288555i
$827$	9.21841	−	40.3885i	0.320556	−	1.40445i	−0.516012	−	0.856581i	$-0.672584\pi$
$827$	9.21841	−	40.3885i	0.320556	−	1.40445i	0.836567	−	0.547864i	$-0.184559\pi$
$828$	2.86680	+	2.28620i	0.0996282	+	0.0794508i
$829$		−	4.64043i		−	0.161169i	−0.996748	−	0.0805844i	$-0.974321\pi$
$829$		−	4.64043i		−	0.161169i	0.996748	−	0.0805844i	$-0.0256787\pi$
$830$		0			0
$831$	−27.8001	−	57.7276i	−0.964376	−	2.00255i
$832$	−4.12823	+	3.29215i	−0.143120	+	0.114135i
$833$	−14.6953	−	18.4274i	−0.509163	−	0.638470i
$834$	3.46780	+	1.67000i	0.120080	+	0.0578275i
$835$		0			0
$836$	−9.58754	−	42.0058i	−0.331592	−	1.45280i
$837$	11.0108	+	22.8641i	0.380588	+	0.790300i
$838$	−15.3851	−	7.40906i	−0.531468	−	0.255942i
$839$	−34.5374	+	7.88295i	−1.19237	+	0.272150i	−0.772248	−	0.635321i	$-0.780868\pi$
$839$	−34.5374	+	7.88295i	−1.19237	+	0.272150i	−0.420117	+	0.907470i	$0.638011\pi$
$840$		0			0
$841$	21.1502	+	19.8411i	0.729318	+	0.684175i
$842$			46.2065i			1.59238i
$843$	2.08593	+	9.13904i	0.0718431	+	0.314765i
$844$	−16.3259	+	33.9011i	−0.561960	+	1.16692i
$845$		0			0
$846$	−24.4887	−	107.292i	−0.841939	−	3.68878i
$847$	7.28479	+	1.66271i	0.250308	+	0.0571313i
$848$	0.317382	−	0.659050i	0.0108989	−	0.0226319i
$849$	−39.2392	+	31.2922i	−1.34669	+	1.07395i
$850$		0			0
$851$	−0.536390	−	1.11383i	−0.0183872	−	0.0381814i
$852$	−74.8772	+	93.8930i	−2.56525	+	3.21672i
$853$	25.5045			0.873256			0.436628	−	0.899642i	$-0.356173\pi$
$853$	25.5045			0.873256			0.436628	+	0.899642i	$0.356173\pi$
$854$	7.04367	−	8.83248i	0.241029	−	0.302241i
$855$		0			0
$856$	−23.4147	−	5.34424i	−0.800296	−	0.182662i
$857$	27.9793	+	22.3127i	0.955754	+	0.762189i	0.971341	−	0.237690i	$-0.0763902\pi$
$857$	27.9793	+	22.3127i	0.955754	+	0.762189i	−0.0155868	+	0.999879i	$0.504962\pi$
$858$	−10.3644			−0.353836
$859$	−23.1233	−	18.4402i	−0.788956	−	0.629171i	0.143830	−	0.989602i	$-0.454058\pi$
$859$	−23.1233	−	18.4402i	−0.788956	−	0.629171i	−0.932786	+	0.360431i	$0.882630\pi$
$860$		0			0
$861$	4.04699	+	5.07476i	0.137921	+	0.172947i
$862$	−16.7340	−	20.9837i	−0.569961	−	0.714709i
$863$	17.4446	−	36.2241i	0.593822	−	1.23308i	−0.360068	−	0.932926i	$-0.617246\pi$
$863$	17.4446	−	36.2241i	0.593822	−	1.23308i	0.953890	−	0.300158i	$-0.0970393\pi$
$864$	−7.98986	+	35.0058i	−0.271820	+	1.19092i
$865$		0			0
$866$	34.9324	−	16.8225i	1.18705	−	0.571654i
$867$	−24.8572	−	11.9706i	−0.844196	−	0.406543i
$868$	−4.71689	−	20.6661i	−0.160102	−	0.701452i
$869$	−19.0088			−0.644831
$870$		0			0
$871$	4.40323			0.149198
$872$	−3.31869	−	14.5401i	−0.112385	−	0.492390i
$873$	78.6099	+	37.8565i	2.66054	+	1.28125i
$874$	1.62297	−	0.781583i	0.0548979	−	0.0264374i
$875$		0			0
$876$	−13.9362	+	61.0583i	−0.470859	+	2.06297i
$877$	22.6064	−	46.9427i	0.763364	−	1.58514i	−0.0467750	−	0.998905i	$-0.514894\pi$
$877$	22.6064	−	46.9427i	0.763364	−	1.58514i	0.810139	−	0.586237i	$-0.199391\pi$
$878$	−26.5123	−	33.2454i	−0.894747	−	1.12198i
$879$	23.9699	+	30.0573i	0.808485	+	1.01381i
$880$		0			0
$881$	35.3863	+	28.2196i	1.19219	+	0.950743i	0.999534	−	0.0305225i	$-0.00971713\pi$
$881$	35.3863	+	28.2196i	1.19219	+	0.950743i	0.192660	+	0.981266i	$0.438289\pi$
$882$	−52.4196			−1.76506
$883$	26.5025	+	21.1350i	0.891880	+	0.711251i	0.958063	−	0.286557i	$-0.0925107\pi$
$883$	26.5025	+	21.1350i	0.891880	+	0.711251i	−0.0661830	+	0.997808i	$0.521082\pi$
$884$	−6.41314	−	1.46376i	−0.215697	−	0.0492315i
$885$		0			0
$886$	4.81273	−	6.03497i	0.161687	−	0.202749i
$887$	−30.4108			−1.02110			−0.510548	−	0.859850i	$-0.670557\pi$
$887$	−30.4108			−1.02110			−0.510548	+	0.859850i	$0.670557\pi$
$888$	−24.6481	+	30.9078i	−0.827137	+	1.03720i
$889$	11.9098	+	24.7310i	0.399443	+	0.829452i
$890$		0			0
$891$	−4.61737	+	3.68223i	−0.154688	+	0.123359i
$892$	18.2325	−	37.8601i	0.610469	−	1.26765i
$893$	−32.2104	−	7.35181i	−1.07788	−	0.246019i
$894$	7.32341	+	32.0860i	0.244932	+	1.07312i
$895$		0			0
$896$	11.7562	−	24.4120i	0.392746	−	0.815546i
$897$	−0.0589240	−	0.258163i	−0.00196742	−	0.00861981i
$898$		−	0.315858i		−	0.0105403i
$899$	22.9856	+	3.52888i	0.766612	+	0.117695i
$900$		0			0
$901$	9.01346	−	2.05726i	0.300282	−	0.0685374i
$902$	11.8751	+	5.71875i	0.395398	+	0.190414i
$903$	−12.4806	−	25.9162i	−0.415328	−	0.862437i
$904$	−4.64886	−	20.3680i	−0.154619	−	0.677430i
$905$		0			0
$906$	45.2709	+	21.8013i	1.50402	+	0.724300i
$907$	9.90255	+	12.4174i	0.328809	+	0.412313i	0.918566	−	0.395267i	$-0.129348\pi$
$907$	9.90255	+	12.4174i	0.328809	+	0.412313i	−0.589757	+	0.807580i	$0.700777\pi$
$908$	−5.21460	+	4.15851i	−0.173053	+	0.138005i
$909$	−13.7226	−	28.4953i	−0.455150	−	0.945129i
$910$		0			0
$911$		−	24.9672i		−	0.827199i	−0.910459	−	0.413600i	$-0.864271\pi$
$911$		−	24.9672i		−	0.827199i	0.910459	−	0.413600i	$-0.135729\pi$
$912$	3.13399	+	2.49927i	0.103777	+	0.0827591i
$913$	7.44675	−	32.6264i	0.246452	−	1.07977i
$914$	70.9243	+	16.1880i	2.34597	+	0.535452i
$915$		0			0
$916$			86.0768i			2.84406i
$917$	−3.26043	+	4.08845i	−0.107669	+	0.135012i
$918$	−62.0573	+	29.8852i	−2.04819	+	0.986359i
$919$	−8.39456	−	10.5264i	−0.276911	−	0.347236i	0.623855	−	0.781540i	$-0.285566\pi$
$919$	−8.39456	−	10.5264i	−0.276911	−	0.347236i	−0.900766	+	0.434305i	$0.856994\pi$
$920$		0			0
$921$	16.6830	+	8.03409i	0.549722	+	0.264732i
$922$	−1.60402	−	0.366107i	−0.0528256	−	0.0120571i
$923$	5.31162	−	1.21234i	0.174834	−	0.0399048i
$924$	49.9104	−	24.0356i	1.64193	−	0.790712i
$925$		0			0
$926$	−20.2255	+	4.61634i	−0.664651	+	0.151702i
$927$			66.9616i			2.19931i
$928$	22.3137	+	24.1809i	0.732484	+	0.793776i
$929$	−7.53667			−0.247270			−0.123635	−	0.992328i	$-0.539455\pi$
$929$	−7.53667			−0.247270			−0.123635	+	0.992328i	$0.539455\pi$
$930$		0			0
$931$	−6.82803	+	14.1785i	−0.223780	+	0.464683i
$932$	−23.8315	−	49.4865i	−0.780625	−	1.62099i
$933$	−67.9764	+	15.5152i	−2.22545	+	0.507944i
$934$	−15.4738	+	67.7950i	−0.506317	+	2.21832i
$935$		0			0
$936$	−4.15891	+	3.31662i	−0.135938	+	0.108407i
$937$	28.5083	−	22.7346i	0.931326	−	0.742708i	−0.0351723	−	0.999381i	$-0.511198\pi$
$937$	28.5083	−	22.7346i	0.931326	−	0.742708i	0.966498	+	0.256674i	$0.0826266\pi$
$938$	−34.6982	+	16.7098i	−1.13294	+	0.545593i
$939$	4.38499	+	3.49691i	0.143099	+	0.114117i
$940$		0			0
$941$	21.9323	−	27.5023i	0.714973	−	0.896548i	−0.283068	−	0.959100i	$-0.591352\pi$
$941$	21.9323	−	27.5023i	0.714973	−	0.896548i	0.998042	+	0.0625515i	$0.0199238\pi$
$942$	27.0308	−	118.430i	0.880712	−	3.85865i
$943$	−0.0749333	+	0.328304i	−0.00244016	+	0.0106911i
$944$	−0.268263	+	0.336391i	−0.00873122	+	0.0109486i
$945$		0			0
$946$	−45.6668	−	36.4180i	−1.48476	−	1.18405i
$947$	−9.36711	+	4.51096i	−0.304390	+	0.146587i	−0.579843	−	0.814728i	$-0.696886\pi$
$947$	−9.36711	+	4.51096i	−0.304390	+	0.146587i	0.275453	+	0.961314i	$0.411172\pi$
$948$	−33.3940	+	26.6308i	−1.08459	+	0.864928i
$949$	2.22136	−	1.77148i	0.0721085	−	0.0575046i
$950$		0			0
$951$	18.7608	−	82.1964i	0.608361	−	2.66540i
$952$	20.3948	−	4.65498i	0.660999	−	0.150869i
$953$	−23.3495	−	48.4858i	−0.756366	−	1.57061i	−0.819818	−	0.572625i	$-0.805925\pi$
$953$	−23.3495	−	48.4858i	−0.756366	−	1.57061i	0.0634519	−	0.997985i	$-0.479789\pi$
$954$	8.92146	−	18.5256i	0.288843	−	0.599789i
$955$		0			0
$956$	−54.2189			−1.75356
$957$	4.37571	+	60.6152i	0.141446	+	1.95941i
$958$			12.0129i			0.388119i
$959$	8.40676	−	1.91879i	0.271468	−	0.0619609i
$960$		0			0
$961$	−11.1288	+	5.35937i	−0.358995	+	0.172883i
$962$	4.80881	−	1.09758i	0.155042	−	0.0353874i
$963$	45.8012	+	10.4538i	1.47592	+	0.336870i
$964$	62.2543	+	29.9801i	2.00508	+	0.965594i
$965$		0			0
$966$	1.44403	+	1.81075i	0.0464609	+	0.0582601i
$967$	10.7168	−	5.16092i	0.344628	−	0.165964i	−0.253561	−	0.967319i	$-0.581602\pi$
$967$	10.7168	−	5.16092i	0.344628	−	0.165964i	0.598188	+	0.801356i	$0.295887\pi$
$968$	7.72899	−	9.69185i	0.248419	−	0.311508i
$969$			50.6634i			1.62754i
$970$		0			0
$971$	−48.8341	−	11.1461i	−1.56716	−	0.357694i	−0.651183	−	0.758921i	$-0.725727\pi$
$971$	−48.8341	−	11.1461i	−1.56716	−	0.357694i	−0.915979	+	0.401226i	$0.868584\pi$
$972$	9.37591	−	41.0785i	0.300732	−	1.31759i
$973$	0.729672	+	0.581894i	0.0233922	+	0.0186547i
$974$		−	7.89535i		−	0.252983i
$975$		0			0
$976$	0.565883	+	1.17507i	0.0181135	+	0.0376130i
$977$	10.7983	−	8.61138i	0.345469	−	0.275502i	−0.435348	−	0.900262i	$-0.643375\pi$
$977$	10.7983	−	8.61138i	0.345469	−	0.275502i	0.780817	+	0.624760i	$0.214803\pi$
$978$	−9.08493	−	11.3921i	−0.290504	−	0.364281i
$979$	−4.05433	−	1.95246i	−0.129577	−	0.0624010i
$980$		0			0
$981$	6.49165	+	28.4418i	0.207262	+	0.908076i
$982$	5.75762	+	11.9558i	0.183733	+	0.381525i
$983$	10.5011	+	5.05705i	0.334932	+	0.161295i	0.593789	−	0.804621i	$-0.297631\pi$
$983$	10.5011	+	5.05705i	0.334932	+	0.161295i	−0.258857	+	0.965916i	$0.583346\pi$
$984$	10.4984	−	2.39619i	0.334677	−	0.0763879i
$985$		0			0
$986$	−9.57799	+	62.3869i	−0.305025	+	1.98680i
$987$		−	42.4784i		−	1.35210i
$988$	0.977329	+	4.28196i	0.0310930	+	0.136227i
$989$	0.647495	−	1.34454i	0.0205891	−	0.0427538i
$990$		0			0
$991$	1.54324	+	6.76136i	0.0490225	+	0.214782i	0.993506	−	0.113776i	$-0.0362946\pi$
$991$	1.54324	+	6.76136i	0.0490225	+	0.214782i	−0.944484	+	0.328558i	$0.893437\pi$
$992$	25.7233	+	5.87117i	0.816715	+	0.186410i
$993$	−34.9703	+	72.6165i	−1.10975	+	2.30442i
$994$	−37.2557	+	29.7104i	−1.18168	+	0.942358i
$995$		0			0
$996$	−32.6264	−	67.7493i	−1.03381	−	2.14672i
$997$	−14.9450	+	18.7405i	−0.473314	+	0.593516i	−0.959979	−	0.280072i	$-0.909642\pi$
$997$	−14.9450	+	18.7405i	−0.473314	+	0.593516i	0.486665	+	0.873588i	$0.338213\pi$
$998$	53.7872			1.70260
$999$	19.6784	−	24.6759i	0.622597	−	0.780712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.p.a.399.4		24
5.2	odd	4		29.2.e.a.22.1	yes	12
5.3	odd	4		725.2.q.a.51.2		12
5.4	even	2	inner	725.2.p.a.399.1		24
15.2	even	4		261.2.o.a.109.2		12
20.7	even	4		464.2.y.d.225.2		12
29.4	even	14	inner	725.2.p.a.149.1		24
145.2	even	28		841.2.a.k.1.2		12
145.4	even	14	inner	725.2.p.a.149.4		24
145.7	odd	28		841.2.e.e.63.2		12
145.12	even	4		841.2.d.m.645.1		24
145.17	even	4		841.2.d.m.645.4		24
145.22	odd	28		841.2.e.f.63.1		12
145.27	even	28		841.2.a.k.1.11		12
145.32	even	28		841.2.d.k.778.1		24
145.33	odd	28		725.2.q.a.526.2		12
145.37	even	28		841.2.d.l.190.1		24
145.42	odd	28		841.2.e.e.267.2		12
145.47	even	28		841.2.d.k.574.4		24
145.52	odd	28		841.2.e.h.270.2		12
145.57	odd	4		841.2.e.i.196.2		12
145.62	odd	28		29.2.e.a.4.1	✓	12
145.67	odd	28		841.2.e.h.651.2		12
145.72	even	28		841.2.d.l.571.4		24
145.77	even	28		841.2.d.m.605.4		24
145.82	odd	28		841.2.b.e.840.2		12
145.92	odd	28		841.2.b.e.840.11		12
145.97	even	28		841.2.d.m.605.1		24
145.102	even	28		841.2.d.l.571.1		24
145.107	odd	28		841.2.e.a.651.1		12
145.112	odd	28		841.2.e.i.236.2		12
145.122	odd	28		841.2.e.a.270.1		12
145.127	even	28		841.2.d.k.574.1		24
145.132	odd	28		841.2.e.f.267.1		12
145.137	even	28		841.2.d.l.190.4		24
145.142	even	28		841.2.d.k.778.4		24
435.2	odd	28		7569.2.a.bp.1.11		12
435.62	even	28		261.2.o.a.91.2		12
435.317	odd	28		7569.2.a.bp.1.2		12
580.207	even	28		464.2.y.d.33.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.4.1	✓	12	145.62	odd	28
29.2.e.a.22.1	yes	12	5.2	odd	4
261.2.o.a.91.2		12	435.62	even	28
261.2.o.a.109.2		12	15.2	even	4
464.2.y.d.33.2		12	580.207	even	28
464.2.y.d.225.2		12	20.7	even	4
725.2.p.a.149.1		24	29.4	even	14	inner
725.2.p.a.149.4		24	145.4	even	14	inner
725.2.p.a.399.1		24	5.4	even	2	inner
725.2.p.a.399.4		24	1.1	even	1	trivial
725.2.q.a.51.2		12	5.3	odd	4
725.2.q.a.526.2		12	145.33	odd	28
841.2.a.k.1.2		12	145.2	even	28
841.2.a.k.1.11		12	145.27	even	28
841.2.b.e.840.2		12	145.82	odd	28
841.2.b.e.840.11		12	145.92	odd	28
841.2.d.k.574.1		24	145.127	even	28
841.2.d.k.574.4		24	145.47	even	28
841.2.d.k.778.1		24	145.32	even	28
841.2.d.k.778.4		24	145.142	even	28
841.2.d.l.190.1		24	145.37	even	28
841.2.d.l.190.4		24	145.137	even	28
841.2.d.l.571.1		24	145.102	even	28
841.2.d.l.571.4		24	145.72	even	28
841.2.d.m.605.1		24	145.97	even	28
841.2.d.m.605.4		24	145.77	even	28
841.2.d.m.645.1		24	145.12	even	4
841.2.d.m.645.4		24	145.17	even	4
841.2.e.a.270.1		12	145.122	odd	28
841.2.e.a.651.1		12	145.107	odd	28
841.2.e.e.63.2		12	145.7	odd	28
841.2.e.e.267.2		12	145.42	odd	28
841.2.e.f.63.1		12	145.22	odd	28
841.2.e.f.267.1		12	145.132	odd	28
841.2.e.h.270.2		12	145.52	odd	28
841.2.e.h.651.2		12	145.67	odd	28
841.2.e.i.196.2		12	145.57	odd	4
841.2.e.i.236.2		12	145.112	odd	28
7569.2.a.bp.1.2		12	435.317	odd	28
7569.2.a.bp.1.11		12	435.2	odd	28

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.p (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.504621 + 2.21089i) q^{2} +(-2.55926 - 1.23248i) q^{3} +(-2.83146 + 1.36356i) q^{4} +(1.43341 - 6.28018i) q^{6} +(0.677709 - 1.40728i) q^{7} +(-1.61565 - 2.02596i) q^{8} +(3.16036 + 3.96297i) q^{9} +(3.10613 + 2.47705i) q^{11} +8.92699 q^{12} +(-0.316631 - 0.252504i) q^{13} +(3.45332 + 0.788198i) q^{14} +(-0.254963 + 0.319714i) q^{16} -5.16843 q^{17} +(-7.16690 + 8.98701i) q^{18} +(1.49728 + 3.10914i) q^{19} +(-3.46887 + 2.76633i) q^{21} +(-3.90908 + 8.11728i) q^{22} +(-0.224414 - 0.0512209i) q^{23} +(1.63793 + 7.17623i) q^{24} +(0.398481 - 0.827455i) q^{26} +(-1.30768 - 5.72931i) q^{27} +4.90874i q^{28} +(-5.00751 - 1.98113i) q^{29} +(-4.21005 + 0.960917i) q^{31} +(-5.50488 - 2.65101i) q^{32} +(-4.89649 - 10.1677i) q^{33} +(-2.60810 - 11.4268i) q^{34} +(-14.3522 - 6.91164i) q^{36} +(3.34857 + 4.19898i) q^{37} +(-6.11841 + 4.87927i) q^{38} +(0.499135 + 1.03647i) q^{39} -1.46294i q^{41} +(-7.86653 - 6.27335i) q^{42} +(-1.44264 + 6.32061i) q^{43} +(-12.1725 - 2.77829i) q^{44} -0.522001i q^{46} +(-5.96928 + 7.48524i) q^{47} +(1.04656 - 0.503996i) q^{48} +(2.84329 + 3.56537i) q^{49} +(13.2274 + 6.36997i) q^{51} +(1.24083 + 0.283211i) q^{52} +(-1.74395 + 0.398044i) q^{53} +(12.0070 - 5.78226i) q^{54} +(-3.94604 + 0.900657i) q^{56} -9.80247i q^{57} +(1.85317 - 12.0708i) q^{58} +1.05216 q^{59} +(1.38382 - 2.87352i) q^{61} +(-4.24897 - 8.82307i) q^{62} +(7.71880 - 1.76177i) q^{63} +(2.90123 - 12.7111i) q^{64} +(20.0087 - 15.9564i) q^{66} +(-8.50052 + 6.77893i) q^{67} +(14.6342 - 7.04745i) q^{68} +(0.511205 + 0.407672i) q^{69} +(-8.38773 + 10.5179i) q^{71} +(2.92279 - 12.8056i) q^{72} +(-1.56113 + 6.83974i) q^{73} +(-7.59372 + 9.52223i) q^{74} +(-8.47898 - 6.76176i) q^{76} +(5.59095 - 2.69246i) q^{77} +(-2.03964 + 1.62656i) q^{78} +(-3.74078 + 2.98318i) q^{79} +(-0.330785 + 1.44926i) q^{81} +(3.23440 - 0.738232i) q^{82} +(-3.65480 - 7.58927i) q^{83} +(6.04990 - 12.5628i) q^{84} -14.7022 q^{86} +(10.3738 + 11.2419i) q^{87} -10.2950i q^{88} +(-1.10427 + 0.252043i) q^{89} +(-0.569927 + 0.274462i) q^{91} +(0.705260 - 0.160971i) q^{92} +(11.9589 + 2.72955i) q^{93} +(-19.5613 - 9.42022i) q^{94} +(10.8211 + 13.5693i) q^{96} +(15.5085 - 7.46850i) q^{97} +(-6.44786 + 8.08536i) q^{98} +20.1379i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{4} - 6 q^{6} + 6 q^{9} + 14 q^{11} + 14 q^{14} + 18 q^{16} + 14 q^{19} - 14 q^{21} + 50 q^{24} - 42 q^{26} + 30 q^{29} - 42 q^{31} + 26 q^{34} - 80 q^{36} - 42 q^{39} - 84 q^{44} - 26 q^{49}+ \cdots + 60 q^{96}+O(q^{100}) \) 24 * q + 2 * q^4 - 6 * q^6 + 6 * q^9 + 14 * q^11 + 14 * q^14 + 18 * q^16 + 14 * q^19 - 14 * q^21 + 50 * q^24 - 42 * q^26 + 30 * q^29 - 42 * q^31 + 26 * q^34 - 80 * q^36 - 42 * q^39 - 84 * q^44 - 26 * q^49 + 40 * q^51 + 76 * q^54 - 42 * q^56 - 88 * q^59 - 14 * q^61 + 52 * q^64 + 42 * q^66 - 42 * q^69 - 42 * q^71 + 14 * q^76 - 98 * q^79 + 2 * q^81 - 42 * q^84 - 88 * q^86 - 14 * q^89 - 6 * q^91 - 132 * q^94 + 60 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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