LMFDB - Embedded newform 343.2.e.d.197.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(50,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

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

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

chi := DirichletCharacter("343.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.e (of order $7$, 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:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			197.7
Character	$\chi$	$=$	343.197
Dual form			343.2.e.d.148.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.82128 + 0.877084i) q^{2} +(-0.311651 - 1.36543i) q^{3} +(1.30082 + 1.63117i) q^{4} +(-0.506263 - 2.21809i) q^{5} +(0.629993 - 2.76018i) q^{6} +(0.0388416 + 0.170176i) q^{8} +(0.935630 - 0.450576i) q^{9} +(1.02340 - 4.48380i) q^{10} +(-1.71915 - 0.827900i) q^{11} +(1.82185 - 2.28453i) q^{12} +(4.29166 + 2.06676i) q^{13} +(-2.87087 + 1.38254i) q^{15} +(0.849996 - 3.72407i) q^{16} +(-2.52418 + 3.16523i) q^{17} +2.09924 q^{18} -0.437865 q^{19} +(2.95953 - 3.71113i) q^{20} +(-2.40493 - 3.01568i) q^{22} +(4.25574 + 5.33653i) q^{23} +(0.220259 - 0.106071i) q^{24} +(-0.158755 + 0.0764522i) q^{25} +(6.00361 + 7.52829i) q^{26} +(-3.52650 - 4.42209i) q^{27} +(-5.30231 + 6.64889i) q^{29} -6.44126 q^{30} +0.818801 q^{31} +(5.03207 - 6.31002i) q^{32} +(-0.594665 + 2.60540i) q^{33} +(-7.37342 + 3.55085i) q^{34} +(1.95205 + 0.940059i) q^{36} +(-2.32255 + 2.91238i) q^{37} +(-0.797477 - 0.384045i) q^{38} +(1.48451 - 6.50407i) q^{39} +(0.357801 - 0.172308i) q^{40} +(2.40243 + 10.5257i) q^{41} +(1.79724 - 7.87423i) q^{43} +(-0.885854 - 3.88118i) q^{44} +(-1.47309 - 1.84720i) q^{45} +(3.07032 + 13.4520i) q^{46} +(-1.38455 - 0.666763i) q^{47} -5.34987 q^{48} -0.356192 q^{50} +(5.10856 + 2.46015i) q^{51} +(2.21143 + 9.68892i) q^{52} +(-0.515954 - 0.646986i) q^{53} +(-2.54421 - 11.1469i) q^{54} +(-0.966009 + 4.23236i) q^{55} +(0.136461 + 0.597875i) q^{57} +(-15.4886 + 7.45894i) q^{58} +(-0.679632 + 2.97766i) q^{59} +(-5.98963 - 2.88445i) q^{60} +(-0.0363546 + 0.0455872i) q^{61} +(1.49127 + 0.718157i) q^{62} +(7.81612 - 3.76404i) q^{64} +(2.41153 - 10.5656i) q^{65} +(-3.36821 + 4.22360i) q^{66} -12.1294 q^{67} -8.44654 q^{68} +(5.96036 - 7.47405i) q^{69} +(3.05705 + 3.83342i) q^{71} +(0.113019 + 0.141721i) q^{72} +(9.76551 - 4.70282i) q^{73} +(-6.78442 + 3.26720i) q^{74} +(0.153866 + 0.192942i) q^{75} +(-0.569583 - 0.714235i) q^{76} +(8.40834 - 10.5437i) q^{78} +2.45993 q^{79} -8.69063 q^{80} +(-2.99659 + 3.75761i) q^{81} +(-4.85644 + 21.2774i) q^{82} +(-4.16137 + 2.00401i) q^{83} +(8.29864 + 3.99642i) q^{85} +(10.1796 - 12.7649i) q^{86} +(10.7311 + 5.16781i) q^{87} +(0.0741142 - 0.324716i) q^{88} +(3.66390 - 1.76444i) q^{89} +(-1.06277 - 4.65630i) q^{90} +(-3.16886 + 13.8837i) q^{92} +(-0.255180 - 1.11802i) q^{93} +(-1.93685 - 2.42873i) q^{94} +(0.221675 + 0.971223i) q^{95} +(-10.1841 - 4.90443i) q^{96} +4.05436 q^{97} -1.98152 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 5 q^{2} + 7 q^{3} - 3 q^{4} + 7 q^{5} - 20 q^{8} + 9 q^{9} + 7 q^{10} + 6 q^{11} + 42 q^{12} - 14 q^{13} - 12 q^{15} - 15 q^{16} - 7 q^{17} - 4 q^{18} - 42 q^{19} + 14 q^{20} - 20 q^{22} + 12 q^{23}+ \cdots - 16 q^{99}+O(q^{100}) $ 48 * q + 5 * q^2 + 7 * q^3 - 3 * q^4 + 7 * q^5 - 20 * q^8 + 9 * q^9 + 7 * q^10 + 6 * q^11 + 42 * q^12 - 14 * q^13 - 12 * q^15 - 15 * q^16 - 7 * q^17 - 4 * q^18 - 42 * q^19 + 14 * q^20 - 20 * q^22 + 12 * q^23 + 49 * q^24 - 13 * q^25 + 21 * q^26 + 7 * q^27 + 12 * q^29 - 22 * q^30 - 70 * q^31 + 15 * q^32 + 7 * q^33 + 70 * q^34 - 12 * q^36 - 9 * q^37 - 7 * q^38 - 28 * q^39 - 63 * q^40 - 42 * q^41 - 30 * q^43 + 37 * q^44 + 28 * q^45 + 9 * q^46 + 21 * q^47 - 84 * q^48 + 40 * q^50 - q^51 + 77 * q^52 + 20 * q^53 + 7 * q^54 - 7 * q^55 - 12 * q^57 + 31 * q^58 - 7 * q^59 + 35 * q^60 + 7 * q^61 - 28 * q^62 - 32 * q^64 - 49 * q^65 - 119 * q^66 - 22 * q^67 - 154 * q^68 + 70 * q^69 + 19 * q^71 - 46 * q^72 + 28 * q^73 - 47 * q^74 + 7 * q^75 + 119 * q^76 + 28 * q^78 - 30 * q^79 - 140 * q^80 + 61 * q^81 + 112 * q^82 - 26 * q^85 + 24 * q^86 + 77 * q^87 + 28 * q^88 + 28 * q^89 - 182 * q^90 - 38 * q^92 + 34 * q^93 - 28 * q^94 - 67 * q^95 - 28 * q^96 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{7}\right)$

Coefficient data

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

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

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

$2$	1.82128	+	0.877084i	1.28784	+	0.620192i	0.947393	−	0.320071i	$-0.103707\pi$
$2$	1.82128	+	0.877084i	1.28784	+	0.620192i	0.340448	+	0.940263i	$0.389421\pi$
$3$	−0.311651	−	1.36543i	−0.179932	−	0.788332i	−0.981659	−	0.190643i	$-0.938943\pi$
$3$	−0.311651	−	1.36543i	−0.179932	−	0.788332i	0.801728	−	0.597689i	$-0.203914\pi$
$4$	1.30082	+	1.63117i	0.650409	+	0.815587i
$5$	−0.506263	−	2.21809i	−0.226408	−	0.991958i	−0.952543	−	0.304405i	$-0.901542\pi$
$5$	−0.506263	−	2.21809i	−0.226408	−	0.991958i	0.726135	−	0.687552i	$-0.241315\pi$
$6$	0.629993	−	2.76018i	0.257194	−	1.12684i
$7$		0			0
$7$		0			0
$8$	0.0388416	+	0.170176i	0.0137326	+	0.0601663i
$9$	0.935630	−	0.450576i	0.311877	−	0.150192i
$10$	1.02340	−	4.48380i	0.323627	−	1.41790i
$11$	−1.71915	−	0.827900i	−0.518344	−	0.249621i	0.156373	−	0.987698i	$-0.450020\pi$
$11$	−1.71915	−	0.827900i	−0.518344	−	0.249621i	−0.674717	+	0.738077i	$0.735734\pi$
$12$	1.82185	−	2.28453i	0.525924	−	0.659488i
$13$	4.29166	+	2.06676i	1.19029	+	0.573215i	0.920894	−	0.389814i	$-0.127461\pi$
$13$	4.29166	+	2.06676i	1.19029	+	0.573215i	0.269399	+	0.963029i	$0.413175\pi$
$14$		0			0
$15$	−2.87087	+	1.38254i	−0.741254	+	0.356969i
$16$	0.849996	−	3.72407i	0.212499	−	0.931018i
$17$	−2.52418	+	3.16523i	−0.612204	+	0.767680i	−0.987224	−	0.159337i	$-0.949064\pi$
$17$	−2.52418	+	3.16523i	−0.612204	+	0.767680i	0.375020	+	0.927017i	$0.377636\pi$
$18$	2.09924			0.494796
$19$	−0.437865			−0.100453			−0.0502266	−	0.998738i	$-0.515994\pi$
$19$	−0.437865			−0.100453			−0.0502266	+	0.998738i	$0.515994\pi$
$20$	2.95953	−	3.71113i	0.661770	−	0.829833i
$21$		0			0
$22$	−2.40493	−	3.01568i	−0.512732	−	0.642945i
$23$	4.25574	+	5.33653i	0.887383	+	1.11274i	0.992974	+	0.118333i	$0.0377551\pi$
$23$	4.25574	+	5.33653i	0.887383	+	1.11274i	−0.105591	+	0.994410i	$0.533673\pi$
$24$	0.220259	−	0.106071i	0.0449601	−	0.0216517i
$25$	−0.158755	+	0.0764522i	−0.0317509	+	0.0152904i
$26$	6.00361	+	7.52829i	1.17741	+	1.47642i
$27$	−3.52650	−	4.42209i	−0.678675	−	0.851031i
$28$		0			0
$29$	−5.30231	+	6.64889i	−0.984615	+	1.23467i	−0.0125582	+	0.999921i	$0.503997\pi$
$29$	−5.30231	+	6.64889i	−0.984615	+	1.23467i	−0.972057	+	0.234747i	$0.924574\pi$
$30$	−6.44126			−1.17601
$31$	0.818801			0.147061			0.0735305	−	0.997293i	$-0.476573\pi$
$31$	0.818801			0.147061			0.0735305	+	0.997293i	$0.476573\pi$
$32$	5.03207	−	6.31002i	0.889553	−	1.11546i
$33$	−0.594665	+	2.60540i	−0.103518	+	0.453542i
$34$	−7.37342	+	3.55085i	−1.26453	+	0.608966i
$35$		0			0
$36$	1.95205	+	0.940059i	0.325342	+	0.156676i
$37$	−2.32255	+	2.91238i	−0.381824	+	0.478792i	−0.935190	−	0.354146i	$-0.884772\pi$
$37$	−2.32255	+	2.91238i	−0.381824	+	0.478792i	0.553366	+	0.832938i	$0.313343\pi$
$38$	−0.797477	−	0.384045i	−0.129368	−	0.0623003i
$39$	1.48451	−	6.50407i	0.237712	−	1.04149i
$40$	0.357801	−	0.172308i	0.0565733	−	0.0272443i
$41$	2.40243	+	10.5257i	0.375196	+	1.64384i	0.711937	+	0.702243i	$0.247818\pi$
$41$	2.40243	+	10.5257i	0.375196	+	1.64384i	−0.336741	+	0.941597i	$0.609325\pi$
$42$		0			0
$43$	1.79724	−	7.87423i	0.274077	−	1.20081i	−0.631075	−	0.775722i	$-0.717386\pi$
$43$	1.79724	−	7.87423i	0.274077	−	1.20081i	0.905152	−	0.425088i	$-0.139757\pi$
$44$	−0.885854	−	3.88118i	−0.133548	−	0.585110i
$45$	−1.47309	−	1.84720i	−0.219595	−	0.275364i
$46$	3.07032	+	13.4520i	0.452695	+	1.98338i
$47$	−1.38455	−	0.666763i	−0.201957	−	0.0972574i	0.330171	−	0.943921i	$-0.392893\pi$
$47$	−1.38455	−	0.666763i	−0.201957	−	0.0972574i	−0.532129	+	0.846664i	$0.678608\pi$
$48$	−5.34987			−0.772187
$49$		0			0
$50$	−0.356192			−0.0503732
$51$	5.10856	+	2.46015i	0.715342	+	0.344490i
$52$	2.21143	+	9.68892i	0.306670	+	1.34361i
$53$	−0.515954	−	0.646986i	−0.0708718	−	0.0888704i	0.745132	−	0.666917i	$-0.232387\pi$
$53$	−0.515954	−	0.646986i	−0.0708718	−	0.0888704i	−0.816004	+	0.578047i	$0.803815\pi$
$54$	−2.54421	−	11.1469i	−0.346223	−	1.51690i
$55$	−0.966009	+	4.23236i	−0.130257	+	0.570691i
$56$		0			0
$57$	0.136461	+	0.597875i	0.0180747	+	0.0791905i
$58$	−15.4886	+	7.45894i	−2.03376	+	0.979407i
$59$	−0.679632	+	2.97766i	−0.0884805	+	0.387659i	−0.999706	−	0.0242495i	$-0.992280\pi$
$59$	−0.679632	+	2.97766i	−0.0884805	+	0.387659i	0.911225	+	0.411908i	$0.135138\pi$
$60$	−5.98963	−	2.88445i	−0.773258	−	0.372381i
$61$	−0.0363546	+	0.0455872i	−0.00465473	+	0.00583685i	−0.784153	−	0.620567i	$-0.786902\pi$
$61$	−0.0363546	+	0.0455872i	−0.00465473	+	0.00583685i	0.779499	+	0.626404i	$0.215474\pi$
$62$	1.49127	+	0.718157i	0.189391	+	0.0912060i
$63$		0			0
$64$	7.81612	−	3.76404i	0.977015	−	0.470506i
$65$	2.41153	−	10.5656i	0.299113	−	1.31050i
$66$	−3.36821	+	4.22360i	−0.414598	+	0.519889i
$67$	−12.1294			−1.48184			−0.740918	−	0.671595i	$-0.765610\pi$
$67$	−12.1294			−1.48184			−0.740918	+	0.671595i	$0.765610\pi$
$68$	−8.44654			−1.02429
$69$	5.96036	−	7.47405i	0.717543	−	0.899770i
$70$		0			0
$71$	3.05705	+	3.83342i	0.362805	+	0.454944i	0.929411	−	0.369045i	$-0.120315\pi$
$71$	3.05705	+	3.83342i	0.362805	+	0.454944i	−0.566606	+	0.823989i	$0.691744\pi$
$72$	0.113019	+	0.141721i	0.0133194	+	0.0167020i
$73$	9.76551	−	4.70282i	1.14297	−	0.550424i	0.236053	−	0.971740i	$-0.424146\pi$
$73$	9.76551	−	4.70282i	1.14297	−	0.550424i	0.906914	+	0.421316i	$0.138432\pi$
$74$	−6.78442	+	3.26720i	−0.788672	+	0.379805i
$75$	0.153866	+	0.192942i	0.0177669	+	0.0222790i
$76$	−0.569583	−	0.714235i	−0.0653357	−	0.0819283i
$77$		0			0
$78$	8.40834	−	10.5437i	0.952057	−	1.19384i
$79$	2.45993			0.276764			0.138382	−	0.990379i	$-0.455810\pi$
$79$	2.45993			0.276764			0.138382	+	0.990379i	$0.455810\pi$
$80$	−8.69063			−0.971642
$81$	−2.99659	+	3.75761i	−0.332955	+	0.417512i
$82$	−4.85644	+	21.2774i	−0.536304	+	2.34970i
$83$	−4.16137	+	2.00401i	−0.456769	+	0.219968i	−0.648097	−	0.761558i	$-0.724435\pi$
$83$	−4.16137	+	2.00401i	−0.456769	+	0.219968i	0.191328	+	0.981526i	$0.438721\pi$
$84$		0			0
$85$	8.29864	+	3.99642i	0.900114	+	0.433472i
$86$	10.1796	−	12.7649i	1.09770	−	1.37647i
$87$	10.7311	+	5.16781i	1.15049	+	0.554048i
$88$	0.0741142	−	0.324716i	0.00790060	−	0.0346148i
$89$	3.66390	−	1.76444i	0.388372	−	0.187030i	−0.229500	−	0.973309i	$-0.573709\pi$
$89$	3.66390	−	1.76444i	0.388372	−	0.187030i	0.617872	+	0.786278i	$0.287995\pi$
$90$	−1.06277	−	4.65630i	−0.112026	−	0.490817i
$91$		0			0
$92$	−3.16886	+	13.8837i	−0.330377	+	1.44748i
$93$	−0.255180	−	1.11802i	−0.0264609	−	0.115933i
$94$	−1.93685	−	2.42873i	−0.199771	−	0.250504i
$95$	0.221675	+	0.971223i	0.0227434	+	0.0996454i
$96$	−10.1841	−	4.90443i	−1.03941	−	0.500556i
$97$	4.05436			0.411658			0.205829	−	0.978588i	$-0.434011\pi$
$97$	4.05436			0.411658			0.205829	+	0.978588i	$0.434011\pi$
$98$		0			0
$99$	−1.98152			−0.199151
$100$	−0.331218	−	0.159506i	−0.0331218	−	0.0159506i
$101$	0.799905	+	3.50461i	0.0795935	+	0.348722i	0.999006	−	0.0445723i	$-0.0141925\pi$
$101$	0.799905	+	3.50461i	0.0795935	+	0.348722i	−0.919413	+	0.393294i	$0.871335\pi$
$102$	7.14638	+	8.96128i	0.707597	+	0.887298i
$103$	−3.05292	−	13.3757i	−0.300814	−	1.31795i	−0.868903	−	0.494983i	$-0.835174\pi$
$103$	−3.05292	−	13.3757i	−0.300814	−	1.31795i	0.568089	−	0.822967i	$-0.307683\pi$
$104$	−0.185017	+	0.810614i	−0.0181425	+	0.0794873i
$105$		0			0
$106$	−0.372238	−	1.63088i	−0.0361549	−	0.158405i
$107$	−2.74438	+	1.32162i	−0.265309	+	0.127766i	−0.561809	−	0.827267i	$-0.689895\pi$
$107$	−2.74438	+	1.32162i	−0.265309	+	0.127766i	0.296501	+	0.955033i	$0.404180\pi$
$108$	2.62586	−	11.5047i	0.252674	−	1.10704i
$109$	−2.98017	−	1.43518i	−0.285449	−	0.137465i	0.285681	−	0.958325i	$-0.407780\pi$
$109$	−2.98017	−	1.43518i	−0.285449	−	0.137465i	−0.571130	+	0.820860i	$0.693495\pi$
$110$	−5.47151	+	6.86106i	−0.521688	+	0.654176i
$111$	4.70048	+	2.26363i	0.446150	+	0.214854i
$112$		0			0
$113$	2.55014	−	1.22808i	0.239897	−	0.115528i	−0.310073	−	0.950713i	$-0.600353\pi$
$113$	2.55014	−	1.22808i	0.239897	−	0.115528i	0.549970	+	0.835185i	$0.314639\pi$
$114$	−0.275852	+	1.20859i	−0.0258359	+	0.113195i
$115$	9.68235	−	12.1413i	0.902883	−	1.13218i
$116$	−17.7428			−1.64738
$117$	4.94664			0.457317
$118$	−3.84946	+	4.82707i	−0.354372	+	0.444368i
$119$		0			0
$120$	−0.346784	−	0.434853i	−0.0316569	−	0.0396964i
$121$	−4.58832	−	5.75357i	−0.417120	−	0.523052i
$122$	−0.106196	+	0.0511412i	−0.00961452	+	0.00463011i
$123$	13.6234	−	6.56070i	1.22838	−	0.591558i
$124$	1.06511	+	1.33561i	0.0956497	+	0.119941i
$125$	−6.84264	−	8.58040i	−0.612025	−	0.767455i
$126$		0			0
$127$	3.64167	−	4.56651i	0.323146	−	0.405212i	−0.593550	−	0.804797i	$-0.702274\pi$
$127$	3.64167	−	4.56651i	0.323146	−	0.405212i	0.916696	+	0.399585i	$0.130846\pi$
$128$	1.39512			0.123312
$129$	−11.3118			−0.995951
$130$	13.6590	−	17.1278i	1.19797	−	1.50221i
$131$	0.993091	−	4.35102i	0.0867668	−	0.380150i	−0.912836	−	0.408326i	$-0.866113\pi$
$131$	0.993091	−	4.35102i	0.0867668	−	0.380150i	0.999603	+	0.0281758i	$0.00896983\pi$
$132$	−5.02341	+	2.41915i	−0.437232	+	0.210560i
$133$		0			0
$134$	−22.0910	−	10.6385i	−1.90837	−	0.919023i
$135$	−8.02323	+	10.0608i	−0.690530	+	0.865897i
$136$	−0.636689	−	0.306613i	−0.0545956	−	0.0262919i
$137$	−0.969490	+	4.24762i	−0.0828292	+	0.362898i	−0.999308	−	0.0371839i	$-0.988161\pi$
$137$	−0.969490	+	4.24762i	−0.0828292	+	0.362898i	0.916479	+	0.400082i	$0.131018\pi$
$138$	17.4109	−	8.38463i	1.48211	−	0.713747i
$139$	−1.74312	−	7.63711i	−0.147849	−	0.647771i	−0.993480	−	0.114003i	$-0.963633\pi$
$139$	−1.74312	−	7.63711i	−0.147849	−	0.647771i	0.845631	−	0.533768i	$-0.179224\pi$
$140$		0			0
$141$	−0.478924	+	2.09830i	−0.0403327	+	0.176709i
$142$	2.20553	+	9.66304i	0.185084	+	0.810904i
$143$	−5.66695	−	7.10613i	−0.473894	−	0.594245i
$144$	−0.882696	−	3.86734i	−0.0735580	−	0.322279i
$145$	17.4322	+	8.39489i	1.44766	+	0.697158i
$146$	21.9105			1.81333
$147$		0			0
$148$	−7.77181			−0.638838
$149$	−6.05757	−	2.91717i	−0.496255	−	0.238984i	0.168978	−	0.985620i	$-0.445953\pi$
$149$	−6.05757	−	2.91717i	−0.496255	−	0.238984i	−0.665233	+	0.746636i	$0.731668\pi$
$150$	0.111008	+	0.486356i	0.00906373	+	0.0397108i
$151$	4.49692	+	5.63896i	0.365954	+	0.458892i	0.930383	−	0.366590i	$-0.119475\pi$
$151$	4.49692	+	5.63896i	0.365954	+	0.458892i	−0.564428	+	0.825482i	$0.690903\pi$
$152$	−0.0170074	−	0.0745142i	−0.00137948	−	0.00604390i
$153$	−0.935529	+	4.09882i	−0.0756330	+	0.331370i
$154$		0			0
$155$	−0.414529	−	1.81617i	−0.0332958	−	0.145878i
$156$	12.5404	−	6.03912i	1.00403	−	0.483516i
$157$	−5.43657	+	23.8192i	−0.433885	+	1.90098i	−1.72855e−5		1.00000i	$0.500006\pi$
$157$	−5.43657	+	23.8192i	−0.433885	+	1.90098i	−0.433868	+	0.900976i	$0.642852\pi$
$158$	4.48023	+	2.15756i	0.356428	+	0.171647i
$159$	−0.722618	+	0.906134i	−0.0573073	+	0.0718611i
$160$	−16.5437	−	7.96703i	−1.30790	−	0.629849i
$161$		0			0
$162$	−8.75338	+	4.21541i	−0.687731	+	0.331194i
$163$	−5.01679	+	21.9800i	−0.392945	+	1.72160i	0.261243	+	0.965273i	$0.415868\pi$
$163$	−5.01679	+	21.9800i	−0.392945	+	1.72160i	−0.654188	+	0.756332i	$0.726990\pi$
$164$	−14.0442	+	17.6108i	−1.09666	+	1.37517i
$165$	6.08006			0.473332
$166$	−9.33671			−0.724669
$167$	−6.55741	+	8.22273i	−0.507427	+	0.636294i	−0.967887	−	0.251387i	$-0.919113\pi$
$167$	−6.55741	+	8.22273i	−0.507427	+	0.636294i	0.460459	+	0.887681i	$0.347685\pi$
$168$		0			0
$169$	6.04151	+	7.57582i	0.464732	+	0.582755i
$170$	11.6090	+	14.5572i	0.890369	+	1.11649i
$171$	−0.409680	+	0.197292i	−0.0313290	+	0.0150873i
$172$	15.1821	−	7.31132i	1.15763	−	0.557483i
$173$	2.91877	+	3.66002i	0.221910	+	0.278266i	0.880307	−	0.474405i	$-0.157337\pi$
$173$	2.91877	+	3.66002i	0.221910	+	0.278266i	−0.658397	+	0.752671i	$0.728765\pi$
$174$	15.0117	+	18.8241i	1.13804	+	1.42705i
$175$		0			0
$176$	−4.54443	+	5.69854i	−0.342549	+	0.429543i
$177$	4.27760			0.321524
$178$	8.22056			0.616157
$179$	3.10413	−	3.89246i	0.232014	−	0.290936i	−0.652172	−	0.758071i	$-0.726142\pi$
$179$	3.10413	−	3.89246i	0.232014	−	0.290936i	0.884186	+	0.467134i	$0.154714\pi$
$180$	1.09688	−	4.80573i	0.0817564	−	0.358198i
$181$	19.9703	−	9.61720i	1.48438	−	0.714841i	0.496212	−	0.868201i	$-0.334724\pi$
$181$	19.9703	−	9.61720i	1.48438	−	0.714841i	0.988170	+	0.153360i	$0.0490095\pi$
$182$		0			0
$183$	0.0735762	+	0.0354324i	0.00543891	+	0.00261924i
$184$	−0.742850	+	0.931504i	−0.0547636	+	0.0686714i
$185$	7.63573	+	3.67717i	0.561390	+	0.270351i
$186$	0.515839	−	2.26004i	0.0378232	−	0.165714i
$187$	6.95995	−	3.35173i	0.508962	−	0.245103i
$188$	−0.713438	−	3.12578i	−0.0520328	−	0.227971i
$189$		0			0
$190$	−0.448110	+	1.96330i	−0.0325093	+	0.142433i
$191$	−2.90725	−	12.7375i	−0.210362	−	0.921654i	−0.964322	−	0.264734i	$-0.914716\pi$
$191$	−2.90725	−	12.7375i	−0.210362	−	0.921654i	0.753960	−	0.656920i	$-0.228141\pi$
$192$	−7.57544	−	9.49931i	−0.546711	−	0.685553i
$193$	2.39273	+	10.4832i	0.172232	+	0.754599i	0.985076	+	0.172118i	$0.0550610\pi$
$193$	2.39273	+	10.4832i	0.172232	+	0.754599i	−0.812844	+	0.582481i	$0.802082\pi$
$194$	7.38413	+	3.55601i	0.530150	+	0.255307i
$195$	−15.1781			−1.08693
$196$		0			0
$197$	−5.67753			−0.404507			−0.202254	−	0.979333i	$-0.564827\pi$
$197$	−5.67753			−0.404507			−0.202254	+	0.979333i	$0.564827\pi$
$198$	−3.60891	−	1.73796i	−0.256474	−	0.123512i
$199$	−3.03115	−	13.2803i	−0.214873	−	0.941419i	−0.961203	−	0.275843i	$-0.911043\pi$
$199$	−3.03115	−	13.2803i	−0.214873	−	0.941419i	0.746330	−	0.665576i	$-0.231814\pi$
$200$	−0.0191766	−	0.0240467i	−0.00135599	−	0.00170036i
$201$	3.78012	+	16.5618i	0.266629	+	1.16818i
$202$	−1.61699	+	7.08448i	−0.113771	+	0.498462i
$203$		0			0
$204$	2.63237	+	11.5332i	0.184303	+	0.807483i
$205$	22.1307	−	10.6576i	1.54567	−	0.744357i
$206$	6.17140	−	27.0387i	0.429982	−	1.88387i
$207$	6.38631	+	3.07548i	0.443879	+	0.213761i
$208$	11.3446	−	14.2257i	0.786609	−	0.986377i
$209$	0.752757	+	0.362509i	0.0520693	+	0.0250753i
$210$		0			0
$211$	−14.5359	+	7.00014i	−1.00069	+	0.481909i	−0.861174	−	0.508310i	$-0.830270\pi$
$211$	−14.5359	+	7.00014i	−1.00069	+	0.481909i	−0.139521	+	0.990219i	$0.544556\pi$
$212$	0.384185	−	1.68322i	0.0263859	−	0.115604i
$213$	4.28154	−	5.36888i	0.293366	−	0.367870i
$214$	−6.15746			−0.420915
$215$	−18.3756			−1.25321
$216$	0.615559	−	0.771887i	0.0418835	−	0.0525202i
$217$		0			0
$218$	−4.16897	−	5.22772i	−0.282358	−	0.354066i
$219$	−9.46481	−	11.8685i	−0.639573	−	0.801999i
$220$	−8.16032	+	3.92980i	−0.550168	+	0.264947i
$221$	−17.3747	+	8.36721i	−1.16875	+	0.562839i
$222$	6.57551	+	8.24543i	0.441319	+	0.553397i
$223$	−4.65621	−	5.83871i	−0.311803	−	0.390989i	0.601094	−	0.799178i	$-0.294732\pi$
$223$	−4.65621	−	5.83871i	−0.311803	−	0.390989i	−0.912897	+	0.408190i	$0.866160\pi$
$224$		0			0
$225$	−0.114088	+	0.143062i	−0.00760588	+	0.00953747i
$226$	5.72165			0.380599
$227$	−9.62855			−0.639069			−0.319535	−	0.947575i	$-0.603527\pi$
$227$	−9.62855			−0.639069			−0.319535	+	0.947575i	$0.603527\pi$
$228$	−0.797727	+	1.00032i	−0.0528308	+	0.0662477i
$229$	3.10021	−	13.5829i	0.204868	−	0.897585i	−0.763054	−	0.646334i	$-0.776301\pi$
$229$	3.10021	−	13.5829i	0.204868	−	0.897585i	0.967922	−	0.251250i	$-0.0808417\pi$
$230$	28.2832	−	13.6205i	1.86494	−	0.898108i
$231$		0			0
$232$	−1.33743	−	0.644074i	−0.0878067	−	0.0422855i
$233$	−4.04280	+	5.06951i	−0.264852	+	0.332114i	−0.896419	−	0.443207i	$-0.853841\pi$
$233$	−4.04280	+	5.06951i	−0.264852	+	0.332114i	0.631567	+	0.775321i	$0.282412\pi$
$234$	9.00923	+	4.33862i	0.588952	+	0.283624i
$235$	−0.777992	+	3.40860i	−0.0507506	+	0.222353i
$236$	−5.74116	+	2.76480i	−0.373718	+	0.179973i
$237$	−0.766639	−	3.35886i	−0.0497985	−	0.218182i
$238$		0			0
$239$	3.80981	−	16.6919i	0.246436	−	1.07971i	−0.688596	−	0.725145i	$-0.741773\pi$
$239$	3.80981	−	16.6919i	0.246436	−	1.07971i	0.935032	−	0.354563i	$-0.115370\pi$
$240$	2.70844	+	11.8665i	0.174829	+	0.765977i
$241$	0.988878	+	1.24001i	0.0636992	+	0.0798763i	0.812660	−	0.582738i	$-0.198018\pi$
$241$	0.988878	+	1.24001i	0.0636992	+	0.0798763i	−0.748961	+	0.662614i	$0.769447\pi$
$242$	−3.31027	−	14.5032i	−0.212792	−	0.932303i
$243$	−9.22317	−	4.44164i	−0.591666	−	0.284932i
$244$	−0.121651			−0.00778793
$245$		0			0
$246$	30.5664			1.94884
$247$	−1.87917	−	0.904961i	−0.119569	−	0.0575813i
$248$	0.0318035	+	0.139340i	0.00201953	+	0.00884812i
$249$	4.03323	+	5.05751i	0.255595	+	0.320507i
$250$	−4.93666	−	21.6289i	−0.312222	−	1.36793i
$251$	3.72581	−	16.3239i	0.235171	−	1.03035i	−0.710109	−	0.704092i	$-0.751354\pi$
$251$	3.72581	−	16.3239i	0.235171	−	1.03035i	0.945280	−	0.326261i	$-0.105789\pi$
$252$		0			0
$253$	−2.89815	−	12.6976i	−0.182205	−	0.798293i
$254$	10.6377	−	5.12286i	0.667470	−	0.321437i
$255$	2.87055	−	12.5767i	0.179761	−	0.787584i
$256$	−13.0913	−	6.30445i	−0.818208	−	0.394028i
$257$	−18.2977	+	22.9446i	−1.14138	+	1.43125i	−0.255819	+	0.966725i	$0.582345\pi$
$257$	−18.2977	+	22.9446i	−1.14138	+	1.43125i	−0.885562	+	0.464522i	$0.846226\pi$
$258$	−20.6021	−	9.92143i	−1.28263	−	0.617681i
$259$		0			0
$260$	20.3713	−	9.81029i	1.26337	−	0.608408i
$261$	−1.96518	+	8.61000i	−0.121641	+	0.532945i
$262$	5.62491	−	7.05341i	0.347508	−	0.435761i
$263$	10.5462			0.650305			0.325153	−	0.945662i	$-0.394584\pi$
$263$	10.5462			0.650305			0.325153	+	0.945662i	$0.394584\pi$
$264$	−0.466474			−0.0287095
$265$	−1.17386	+	1.47198i	−0.0721098	+	0.0904228i
$266$		0			0
$267$	−3.55108	−	4.45291i	−0.217322	−	0.272514i
$268$	−15.7781	−	19.7851i	−0.963800	−	1.20857i
$269$	9.48960	−	4.56995i	0.578591	−	0.278635i	−0.121613	−	0.992578i	$-0.538807\pi$
$269$	9.48960	−	4.56995i	0.578591	−	0.278635i	0.700204	+	0.713943i	$0.253092\pi$
$270$	−23.4368	+	11.2865i	−1.42632	+	0.686877i
$271$	−15.4890	−	19.4226i	−0.940889	−	1.17984i	−0.983530	−	0.180747i	$-0.942149\pi$
$271$	−15.4890	−	19.4226i	−0.940889	−	1.17984i	0.0426411	−	0.999090i	$-0.486423\pi$
$272$	9.64199	+	12.0907i	0.584632	+	0.733105i
$273$		0			0
$274$	−5.49123	+	6.88579i	−0.331737	+	0.415986i
$275$	0.336218			0.0202747
$276$	19.9448			1.20054
$277$	8.21822	−	10.3053i	0.493785	−	0.619186i	−0.471030	−	0.882117i	$-0.656118\pi$
$277$	8.21822	−	10.3053i	0.493785	−	0.619186i	0.964815	+	0.262931i	$0.0846891\pi$
$278$	3.52367	−	15.4382i	0.211336	−	0.925922i
$279$	0.766095	−	0.368932i	0.0458649	−	0.0220874i
$280$		0			0
$281$	18.3370	+	8.83064i	1.09389	+	0.526792i	0.891734	−	0.452561i	$-0.149489\pi$
$281$	18.3370	+	8.83064i	1.09389	+	0.526792i	0.202161	+	0.979352i	$0.435204\pi$
$282$	−2.71264	+	3.40155i	−0.161536	+	0.202559i
$283$	−20.7675	−	10.0011i	−1.23450	−	0.594502i	−0.301184	−	0.953566i	$-0.597382\pi$
$283$	−20.7675	−	10.0011i	−1.23450	−	0.594502i	−0.933313	+	0.359064i	$0.883096\pi$
$284$	−2.27631	+	9.97316i	−0.135074	+	0.591798i
$285$	1.25705	−	0.605365i	0.0744614	−	0.0358587i
$286$	−4.08845	−	17.9127i	−0.241755	−	1.05920i
$287$		0			0
$288$	1.86502	−	8.17117i	0.109897	−	0.481491i
$289$	0.135702	+	0.594549i	0.00798247	+	0.0349735i
$290$	24.3859	+	30.5790i	1.43199	+	1.79566i
$291$	−1.26354	−	5.53595i	−0.0740702	−	0.324523i
$292$	20.3743	+	9.81173i	1.19231	+	0.574188i
$293$	−11.8715			−0.693539			−0.346769	−	0.937950i	$-0.612721\pi$
$293$	−11.8715			−0.693539			−0.346769	+	0.937950i	$0.612721\pi$
$294$		0			0
$295$	6.94878			0.404574
$296$	−0.585829	−	0.282120i	−0.0340506	−	0.0163979i
$297$	2.40154	+	10.5218i	0.139351	+	0.610539i
$298$	−8.47394	−	10.6260i	−0.490882	−	0.615547i
$299$	7.23489	+	31.6981i	0.418405	+	1.83315i
$300$	−0.114570	+	0.501965i	−0.00661472	+	0.0289810i
$301$		0			0
$302$	3.24433	+	14.2143i	0.186690	+	0.817943i
$303$	4.53602	−	2.18443i	0.260587	−	0.125492i
$304$	−0.372184	+	1.63064i	−0.0213462	+	0.0935238i
$305$	0.119521	+	0.0575585i	0.00684377	+	0.00329579i
$306$	−5.29887	+	6.64457i	−0.302916	+	0.379845i
$307$	13.2755	+	6.39317i	0.757676	+	0.364877i	0.772502	−	0.635013i	$-0.219005\pi$
$307$	13.2755	+	6.39317i	0.757676	+	0.364877i	−0.0148260	+	0.999890i	$0.504719\pi$
$308$		0			0
$309$	−17.3122	+	8.33711i	−0.984857	+	0.474282i
$310$	0.837959	−	3.67134i	0.0475929	−	0.208518i
$311$	−17.2291	+	21.6046i	−0.976972	+	1.22508i	−0.00263304	+	0.999997i	$0.500838\pi$
$311$	−17.2291	+	21.6046i	−0.976972	+	1.22508i	−0.974339	+	0.225087i	$0.927733\pi$
$312$	1.16450			0.0659268
$313$	−25.1189			−1.41980			−0.709901	−	0.704302i	$-0.751260\pi$
$313$	−25.1189			−1.41980			−0.709901	+	0.704302i	$0.751260\pi$
$314$	−30.7929	+	38.6131i	−1.73775	+	2.17906i
$315$		0			0
$316$	3.19992	+	4.01257i	0.180009	+	0.225725i
$317$	−13.6618	−	17.1313i	−0.767321	−	0.962190i	0.232625	−	0.972566i	$-0.425268\pi$
$317$	−13.6618	−	17.1313i	−0.767321	−	0.962190i	−0.999946	+	0.0103765i	$0.996697\pi$
$318$	−2.11085	+	1.01653i	−0.118370	+	0.0570042i
$319$	14.6201	−	7.04067i	0.818568	−	0.394202i
$320$	−12.3060	−	15.4312i	−0.687926	−	0.862631i
$321$	2.65987	+	3.33537i	0.148459	+	0.186162i
$322$		0			0
$323$	1.10525	−	1.38594i	0.0614979	−	0.0771160i
$324$	−10.0273			−0.557074
$325$	−0.839329			−0.0465576
$326$	−28.4153	+	35.6316i	−1.57378	+	1.97345i
$327$	−1.03086	+	4.51650i	−0.0570067	+	0.249763i
$328$	−1.69791	+	0.817671i	−0.0937515	+	0.0451483i
$329$		0			0
$330$	11.0735	+	5.33272i	0.609576	+	0.293556i
$331$	7.92486	−	9.93746i	0.435589	−	0.546212i	−0.514785	−	0.857319i	$-0.672128\pi$
$331$	7.92486	−	9.93746i	0.435589	−	0.546212i	0.950375	+	0.311107i	$0.100700\pi$
$332$	−8.68206	−	4.18106i	−0.476490	−	0.229465i
$333$	−0.860796	+	3.77139i	−0.0471713	+	0.206671i
$334$	−19.1549	+	9.22452i	−1.04811	+	0.504743i
$335$	6.14065	+	26.9039i	0.335500	+	1.46992i
$336$		0			0
$337$	−2.21226	+	9.69255i	−0.120509	+	0.527987i	0.878250	+	0.478201i	$0.158711\pi$
$337$	−2.21226	+	9.69255i	−0.120509	+	0.527987i	−0.998760	+	0.0497856i	$0.984146\pi$
$338$	4.35868	+	19.0966i	0.237081	+	1.03872i
$339$	−2.47161	−	3.09931i	−0.134240	−	0.168331i
$340$	4.27617	+	18.7351i	0.231908	+	1.01606i
$341$	−1.40764	−	0.677885i	−0.0762282	−	0.0367095i
$342$	−0.919185			−0.0497038
$343$		0			0
$344$	1.40981			0.0760121
$345$	−19.5956	−	9.43674i	−1.05499	−	0.508057i
$346$	2.10576	+	9.22594i	0.113206	+	0.495990i
$347$	−10.4019	−	13.0436i	−0.558402	−	0.700215i	0.419859	−	0.907589i	$-0.362079\pi$
$347$	−10.4019	−	13.0436i	−0.558402	−	0.700215i	−0.978262	+	0.207375i	$0.933508\pi$
$348$	5.52957	+	24.2266i	0.296416	+	1.29868i
$349$	0.185225	−	0.811522i	0.00991484	−	0.0434398i	−0.969729	−	0.244186i	$-0.921479\pi$
$349$	0.185225	−	0.811522i	0.00991484	−	0.0434398i	0.979643	+	0.200746i	$0.0643365\pi$
$350$		0			0
$351$	−5.99516	−	26.2665i	−0.319998	−	1.40200i
$352$	−13.8750	+	6.68183i	−0.739538	+	0.356143i
$353$	−6.17738	+	27.0649i	−0.328789	+	1.44052i	0.492653	+	0.870226i	$0.336027\pi$
$353$	−6.17738	+	27.0649i	−0.328789	+	1.44052i	−0.821442	+	0.570292i	$0.806830\pi$
$354$	7.79072	+	3.75181i	0.414072	+	0.199407i
$355$	6.95518	−	8.72152i	0.369143	−	0.462890i
$356$	7.64417	+	3.68124i	0.405140	+	0.195105i
$357$		0			0
$358$	9.06752	−	4.36669i	0.479233	−	0.230787i
$359$	−5.67885	+	24.8807i	−0.299718	+	1.31315i	0.570829	+	0.821069i	$0.306622\pi$
$359$	−5.67885	+	24.8807i	−0.299718	+	1.31315i	−0.870548	+	0.492084i	$0.836235\pi$
$360$	0.257132	−	0.322433i	0.0135520	−	0.0169937i
$361$	−18.8083			−0.989909
$362$	44.8067			2.35499
$363$	−6.42616	+	8.05814i	−0.337286	+	0.422943i
$364$		0			0
$365$	−15.3752	−	19.2799i	−0.804774	−	1.00915i
$366$	0.102926	+	0.129065i	0.00538002	+	0.00674633i
$367$	−19.7673	+	9.51942i	−1.03184	+	0.496910i	−0.871626	−	0.490172i	$-0.836934\pi$
$367$	−19.7673	+	9.51942i	−1.03184	+	0.496910i	−0.160218	+	0.987082i	$0.551220\pi$
$368$	23.4910	−	11.3127i	1.22455	−	0.589713i
$369$	6.99042	+	8.76571i	0.363907	+	0.456324i
$370$	10.6816	+	13.3943i	0.555312	+	0.696339i
$371$		0			0
$372$	1.49174	−	1.87058i	0.0773429	−	0.0969849i
$373$	29.7677			1.54131			0.770657	−	0.637251i	$-0.219928\pi$
$373$	29.7677			1.54131			0.770657	+	0.637251i	$0.219928\pi$
$374$	15.6158			0.807473
$375$	−9.58344	+	12.0172i	−0.494887	+	0.620568i
$376$	0.0596891	−	0.261515i	0.00307823	−	0.0134866i
$377$	−36.4974	+	17.5762i	−1.87971	+	0.905220i
$378$		0			0
$379$	−6.35554	−	3.06067i	−0.326462	−	0.157216i	0.263473	−	0.964667i	$-0.415132\pi$
$379$	−6.35554	−	3.06067i	−0.326462	−	0.157216i	−0.589935	+	0.807451i	$0.700846\pi$
$380$	−1.29587	+	1.62497i	−0.0664769	+	0.0833594i
$381$	−7.37019	−	3.54929i	−0.377586	−	0.181836i
$382$	5.87693	−	25.7485i	0.300690	−	1.31741i
$383$	12.1253	−	5.83924i	0.619575	−	0.298371i	−0.0976421	−	0.995222i	$-0.531130\pi$
$383$	12.1253	−	5.83924i	0.619575	−	0.298371i	0.717217	+	0.696850i	$0.245416\pi$
$384$	−0.434790	−	1.90494i	−0.0221878	−	0.0972110i
$385$		0			0
$386$	−4.83683	+	21.1916i	−0.246188	+	1.07862i
$387$	−1.86638	−	8.17716i	−0.0948737	−	0.415669i
$388$	5.27398	+	6.61336i	0.267746	+	0.335743i
$389$	−2.65935	−	11.6514i	−0.134834	−	0.590748i	−0.996524	−	0.0833116i	$-0.973450\pi$
$389$	−2.65935	−	11.6514i	−0.134834	−	0.590748i	0.861689	−	0.507437i	$-0.169407\pi$
$390$	−27.6437	−	13.3125i	−1.39979	−	0.674105i
$391$	−27.6336			−1.39749
$392$		0			0
$393$	−6.25051			−0.315297
$394$	−10.3404	−	4.97967i	−0.520941	−	0.250872i
$395$	−1.24537	−	5.45633i	−0.0626615	−	0.274538i
$396$	−2.57760	−	3.23221i	−0.129529	−	0.162425i
$397$	1.14903	+	5.03422i	0.0576680	+	0.252660i	0.995542	−	0.0943149i	$-0.0300660\pi$
$397$	1.14903	+	5.03422i	0.0576680	+	0.252660i	−0.937874	+	0.346975i	$0.887209\pi$
$398$	6.12739	−	26.8459i	0.307138	−	1.34566i
$399$		0			0
$400$	0.149773	+	0.656198i	0.00748865	+	0.0328099i
$401$	−15.4835	+	7.45648i	−0.773211	+	0.372359i	−0.778514	−	0.627627i	$-0.784026\pi$
$401$	−15.4835	+	7.45648i	−0.773211	+	0.372359i	0.00530325	+	0.999986i	$0.498312\pi$
$402$	−7.64141	+	33.4792i	−0.381119	+	1.66979i
$403$	3.51402	+	1.69226i	0.175046	+	0.0842975i
$404$	−4.67610	+	5.86364i	−0.232645	+	0.291727i
$405$	9.85176	+	4.74436i	0.489538	+	0.235749i
$406$		0			0
$407$	6.40397	−	3.08399i	0.317433	−	0.152868i
$408$	−0.220235	+	0.964912i	−0.0109032	+	0.0477702i
$409$	13.5381	−	16.9762i	0.669416	−	0.839421i	−0.324916	−	0.945743i	$-0.605336\pi$
$409$	13.5381	−	16.9762i	0.669416	−	0.839421i	0.994332	+	0.106322i	$0.0339073\pi$
$410$	49.6538			2.45223
$411$	6.10197			0.300988
$412$	17.8468	−	22.3792i	0.879251	−	1.10255i
$413$		0			0
$414$	8.93382	+	11.2027i	0.439073	+	0.550581i
$415$	6.55181	+	8.21571i	0.321616	+	0.403293i
$416$	34.6372	−	16.6804i	1.69823	−	0.817824i
$417$	−9.88470	+	4.76022i	−0.484056	+	0.233109i
$418$	1.05303	+	1.32046i	0.0515056	+	0.0645859i
$419$	−6.50497	−	8.15697i	−0.317788	−	0.398494i	0.597122	−	0.802150i	$-0.296311\pi$
$419$	−6.50497	−	8.15697i	−0.317788	−	0.398494i	−0.914911	+	0.403656i	$0.867739\pi$
$420$		0			0
$421$	−6.92877	+	8.68841i	−0.337688	+	0.423447i	−0.921462	−	0.388469i	$-0.873004\pi$
$421$	−6.92877	+	8.68841i	−0.337688	+	0.423447i	0.583774	+	0.811916i	$0.301575\pi$
$422$	−32.6138			−1.58761
$423$	−1.59585			−0.0775930
$424$	0.0900611	−	0.112933i	0.00437376	−	0.00548452i
$425$	0.158737	−	0.695474i	0.00769989	−	0.0337354i
$426$	12.5069	−	6.02299i	0.605959	−	0.291815i
$427$		0			0
$428$	−5.72573	−	2.75736i	−0.276763	−	0.133282i
$429$	−7.93683	+	9.95246i	−0.383194	+	0.480510i
$430$	−33.4672	−	16.1169i	−1.61393	−	0.777228i
$431$	5.07718	−	22.2446i	0.244559	−	1.07148i	−0.692254	−	0.721654i	$-0.743382\pi$
$431$	5.07718	−	22.2446i	0.244559	−	1.07148i	0.936813	−	0.349830i	$-0.113761\pi$
$432$	−19.4657	+	9.37418i	−0.936544	+	0.451016i
$433$	−3.39696	−	14.8831i	−0.163247	−	0.715234i	−0.988594	−	0.150607i	$-0.951877\pi$
$433$	−3.39696	−	14.8831i	−0.163247	−	0.715234i	0.825346	−	0.564627i	$-0.190980\pi$
$434$		0			0
$435$	6.02990	−	26.4187i	0.289111	−	1.26668i
$436$	−1.53564	−	6.72808i	−0.0735438	−	0.322217i
$437$	−1.86344	−	2.33668i	−0.0891405	−	0.111779i
$438$	−6.82844	−	29.9173i	−0.326275	−	1.42951i
$439$	7.71705	+	3.71633i	0.368315	+	0.177371i	0.608881	−	0.793262i	$-0.291619\pi$
$439$	7.71705	+	3.71633i	0.368315	+	0.177371i	−0.240566	+	0.970633i	$0.577333\pi$
$440$	−0.757768			−0.0361252
$441$		0			0
$442$	−38.9830			−1.85423
$443$	6.98832	+	3.36540i	0.332025	+	0.159895i	0.592467	−	0.805595i	$-0.298154\pi$
$443$	6.98832	+	3.36540i	0.332025	+	0.159895i	−0.260442	+	0.965489i	$0.583868\pi$
$444$	2.42209	+	10.6119i	0.114947	+	0.503617i
$445$	−5.76857	−	7.23356i	−0.273457	−	0.342904i
$446$	−3.35925	−	14.7178i	−0.159065	−	0.696909i
$447$	−2.09535	+	9.18033i	−0.0991067	+	0.434215i
$448$		0			0
$449$	−0.364600	−	1.59742i	−0.0172065	−	0.0753867i	0.965596	−	0.260048i	$-0.0837384\pi$
$449$	−0.364600	−	1.59742i	−0.0172065	−	0.0753867i	−0.982802	+	0.184661i	$0.940881\pi$
$450$	−0.333264	+	0.160492i	−0.0157102	+	0.00756565i
$451$	4.58410	−	20.0843i	0.215857	−	0.945732i
$452$	5.32048	+	2.56221i	0.250254	+	0.120516i
$453$	6.29815	−	7.89763i	0.295913	−	0.371063i
$454$	−17.5363	−	8.44505i	−0.823020	−	0.396346i
$455$		0			0
$456$	−0.0964437	+	0.0464448i	−0.00451639	+	0.00217498i
$457$	4.04338	−	17.7152i	0.189141	−	0.828682i	−0.787929	−	0.615766i	$-0.788847\pi$
$457$	4.04338	−	17.7152i	0.189141	−	0.828682i	0.977070	−	0.212916i	$-0.0682962\pi$
$458$	17.5597	−	22.0192i	0.820512	−	1.02889i
$459$	22.8984			1.06881
$460$	32.3995			1.51063
$461$	19.4601	−	24.4021i	0.906345	−	1.13652i	−0.0838006	−	0.996483i	$-0.526706\pi$
$461$	19.4601	−	24.4021i	0.906345	−	1.13652i	0.990146	−	0.140039i	$-0.0447227\pi$
$462$		0			0
$463$	20.1031	+	25.2085i	0.934272	+	1.17154i	0.984953	+	0.172825i	$0.0552895\pi$
$463$	20.1031	+	25.2085i	0.934272	+	1.17154i	−0.0506807	+	0.998715i	$0.516139\pi$
$464$	20.2540	+	25.3977i	0.940269	+	1.17906i
$465$	−2.35067	+	1.13202i	−0.109010	+	0.0524962i
$466$	−11.8095	+	5.68714i	−0.547063	+	0.263451i
$467$	−12.9503	−	16.2392i	−0.599270	−	0.751461i	0.385994	−	0.922501i	$-0.373859\pi$
$467$	−12.9503	−	16.2392i	−0.599270	−	0.751461i	−0.985264	+	0.171040i	$0.945287\pi$
$468$	6.43467	+	8.06883i	0.297443	+	0.372982i
$469$		0			0
$470$	−4.40658	+	5.52567i	−0.203260	+	0.254880i
$471$	34.2177			1.57667
$472$	−0.533125			−0.0245391
$473$	−9.60881	+	12.0491i	−0.441813	+	0.554017i
$474$	1.54974	−	6.78985i	0.0711818	−	0.311868i
$475$	0.0695132	−	0.0334758i	0.00318948	−	0.00153597i
$476$		0			0
$477$	−0.774259	−	0.372864i	−0.0354509	−	0.0170722i
$478$	21.5789	−	27.0591i	0.986997	−	1.23766i
$479$	21.3691	+	10.2908i	0.976380	+	0.470200i	0.852858	−	0.522142i	$-0.174867\pi$
$479$	21.3691	+	10.2908i	0.976380	+	0.470200i	0.123521	+	0.992342i	$0.460581\pi$
$480$	−5.72257	+	25.0722i	−0.261199	+	1.14439i
$481$	−15.9868	+	7.69882i	−0.728933	+	0.351036i
$482$	0.713431	+	3.12575i	0.0324959	+	0.142374i
$483$		0			0
$484$	3.41651	−	14.9687i	0.155296	−	0.680395i
$485$	−2.05257	−	8.99291i	−0.0932025	−	0.408347i
$486$	−12.9023	−	16.1790i	−0.585260	−	0.733893i
$487$	5.27144	+	23.0957i	0.238872	+	1.04657i	0.942029	+	0.335531i	$0.108916\pi$
$487$	5.27144	+	23.0957i	0.238872	+	1.04657i	−0.703157	+	0.711034i	$0.748227\pi$
$488$	−0.00916993	−	0.00441600i	−0.000415103	−	0.000199903i
$489$	31.5756			1.42790
$490$		0			0
$491$	2.93971			0.132667			0.0663337	−	0.997797i	$-0.478870\pi$
$491$	2.93971			0.132667			0.0663337	+	0.997797i	$0.478870\pi$
$492$	28.4232	+	13.6879i	1.28142	+	0.617098i
$493$	−7.66123	−	33.5660i	−0.345044	−	1.51174i
$494$	−2.62878	−	3.29638i	−0.118274	−	0.148311i
$495$	1.00317	+	4.39519i	0.0450893	+	0.197549i
$496$	0.695977	−	3.04928i	0.0312503	−	0.136916i
$497$		0			0
$498$	2.90979	+	12.7486i	0.130391	+	0.571280i
$499$	1.83422	−	0.883314i	0.0821110	−	0.0395426i	−0.392378	−	0.919804i	$-0.628347\pi$
$499$	1.83422	−	0.883314i	0.0821110	−	0.0395426i	0.474489	+	0.880262i	$0.342633\pi$
$500$	5.09510	−	22.3231i	0.227860	−	0.998318i
$501$	13.2712	+	6.39107i	0.592913	+	0.285532i
$502$	21.1032	−	26.4625i	0.941880	−	1.18108i
$503$	7.22087	+	3.47739i	0.321963	+	0.155049i	0.587883	−	0.808946i	$-0.299961\pi$
$503$	7.22087	+	3.47739i	0.321963	+	0.155049i	−0.265920	+	0.963995i	$0.585676\pi$
$504$		0			0
$505$	7.36857	−	3.54851i	0.327897	−	0.157907i
$506$	5.85853	−	25.6679i	0.260443	−	1.14108i
$507$	8.46142	−	10.6103i	0.375785	−	0.471219i
$508$	12.1859			0.540663
$509$	16.9055			0.749324			0.374662	−	0.927161i	$-0.377759\pi$
$509$	16.9055			0.749324			0.374662	+	0.927161i	$0.377759\pi$
$510$	16.2589	−	20.3880i	0.719957	−	0.902798i
$511$		0			0
$512$	−20.0532	−	25.1459i	−0.886233	−	1.11130i
$513$	1.54413	+	1.93628i	0.0681751	+	0.0854889i
$514$	−53.4497	+	25.7400i	−2.35757	+	1.13534i
$515$	−28.1229	+	13.5433i	−1.23924	+	0.596789i
$516$	−14.7146	−	18.4516i	−0.647775	−	0.812285i
$517$	1.82824	+	2.29254i	0.0804057	+	0.100826i
$518$		0			0
$519$	4.08787	−	5.12603i	0.179438	−	0.225008i
$520$	1.89168			0.0829556
$521$	−9.50919			−0.416605			−0.208303	−	0.978064i	$-0.566794\pi$
$521$	−9.50919			−0.416605			−0.208303	+	0.978064i	$0.566794\pi$
$522$	−11.1308	+	13.9576i	−0.487183	+	0.610909i
$523$	−4.69293	+	20.5611i	−0.205207	+	0.899073i	0.762498	+	0.646990i	$0.223973\pi$
$523$	−4.69293	+	20.5611i	−0.205207	+	0.899073i	−0.967706	+	0.252082i	$0.918885\pi$
$524$	8.38909	−	4.03997i	0.366479	−	0.176487i
$525$		0			0
$526$	19.2076	+	9.24989i	0.837490	+	0.403314i
$527$	−2.06680	+	2.59169i	−0.0900314	+	0.112896i
$528$	9.19724	+	4.42916i	0.400258	+	0.192754i
$529$	−5.24923	+	22.9984i	−0.228227	+	0.999930i
$530$	−3.42898	+	1.65131i	−0.148945	+	0.0717284i
$531$	0.705778	+	3.09222i	0.0306282	+	0.134191i
$532$		0			0
$533$	−11.4437	+	50.1380i	−0.495681	+	2.17172i
$534$	−2.56194	−	11.2246i	−0.110866	−	0.485736i
$535$	4.32085	+	5.41817i	0.186806	+	0.234248i
$536$	−0.471124	−	2.06413i	−0.0203494	−	0.0891567i
$537$	−6.28229	−	3.02539i	−0.271101	−	0.130555i
$538$	21.2915			0.917941
$539$		0			0
$540$	−26.8477			−1.15534
$541$	19.7821	+	9.52654i	0.850497	+	0.409578i	0.807762	−	0.589509i	$-0.200679\pi$
$541$	19.7821	+	9.52654i	0.850497	+	0.409578i	0.0427350	+	0.999086i	$0.486393\pi$
$542$	−11.1746	−	48.9591i	−0.479990	−	2.10297i
$543$	−19.3554	−	24.2709i	−0.830619	−	1.04156i
$544$	7.27076	+	31.8553i	0.311731	+	1.36578i
$545$	−1.67459	+	7.33685i	−0.0717315	+	0.314276i
$546$		0			0
$547$	7.11554	+	31.1752i	0.304238	+	1.33296i	0.863661	+	0.504073i	$0.168166\pi$
$547$	7.11554	+	31.1752i	0.304238	+	1.33296i	−0.559423	+	0.828883i	$0.688977\pi$
$548$	−8.18973	+	3.94396i	−0.349848	+	0.168478i
$549$	−0.0134740	+	0.0590333i	−0.000575055	+	0.00251948i
$550$	0.612349	+	0.294892i	0.0261106	+	0.0125742i
$551$	2.32170	−	2.91132i	0.0989077	−	0.124026i
$552$	1.50341	+	0.724006i	0.0639896	+	0.0308158i
$553$		0			0
$554$	24.0063	−	11.5608i	1.01993	−	0.491173i
$555$	2.64125	−	11.5721i	0.112115	−	0.491206i
$556$	10.1900	−	12.7778i	0.432151	−	0.541900i
$557$	26.0094			1.10206			0.551028	−	0.834487i	$-0.314236\pi$
$557$	26.0094			1.10206			0.551028	+	0.834487i	$0.314236\pi$
$558$	1.71886			0.0727652
$559$	23.9873	−	30.0791i	1.01455	−	1.27221i
$560$		0			0
$561$	−6.74563	−	8.45876i	−0.284801	−	0.357129i
$562$	25.6517	+	32.1662i	1.08205	+	1.35685i
$563$	−7.78530	+	3.74920i	−0.328111	+	0.158010i	−0.590686	−	0.806902i	$-0.701143\pi$
$563$	−7.78530	+	3.74920i	−0.328111	+	0.158010i	0.262575	+	0.964912i	$0.415428\pi$
$564$	−4.04569	+	1.94830i	−0.170354	+	0.0820383i
$565$	−4.01503	−	5.03469i	−0.168914	−	0.211811i
$566$	−29.0516	−	36.4296i	−1.22113	−	1.53125i
$567$		0			0
$568$	−0.533616	+	0.669133i	−0.0223900	+	0.0280762i
$569$	−8.91670			−0.373808			−0.186904	−	0.982378i	$-0.559845\pi$
$569$	−8.91670			−0.373808			−0.186904	+	0.982378i	$0.559845\pi$
$570$	2.82041			0.118134
$571$	17.0403	−	21.3678i	0.713113	−	0.894215i	−0.284814	−	0.958583i	$-0.591932\pi$
$571$	17.0403	−	21.3678i	0.713113	−	0.894215i	0.997926	+	0.0643679i	$0.0205031\pi$
$572$	4.21967	−	18.4876i	0.176433	−	0.773004i
$573$	−16.4861	+	7.93931i	−0.688719	+	0.331669i
$574$		0			0
$575$	−1.08361	−	0.521838i	−0.0451896	−	0.0217621i
$576$	5.61701	−	7.04351i	0.234042	−	0.293480i
$577$	40.2279	+	19.3727i	1.67471	+	0.806498i	0.997497	+	0.0707114i	$0.0225269\pi$
$577$	40.2279	+	19.3727i	1.67471	+	0.806498i	0.677214	+	0.735787i	$0.263187\pi$
$578$	−0.274318	+	1.20187i	−0.0114101	+	0.0499910i
$579$	13.5684	−	6.53421i	0.563885	−	0.271553i
$580$	8.98255	+	39.3551i	0.372980	+	1.63413i
$581$		0			0
$582$	2.55422	−	11.1908i	0.105876	−	0.463872i
$583$	0.351364	+	1.53943i	0.0145520	+	0.0637565i
$584$	1.17962	+	1.47919i	0.0488129	+	0.0612094i
$585$	−2.50430	−	10.9721i	−0.103540	−	0.453639i
$586$	−21.6213	−	10.4123i	−0.893169	−	0.430127i
$587$	−2.64680			−0.109245			−0.0546226	−	0.998507i	$-0.517396\pi$
$587$	−2.64680			−0.109245			−0.0546226	+	0.998507i	$0.517396\pi$
$588$		0			0
$589$	−0.358525			−0.0147728
$590$	12.6557	+	6.09466i	0.521027	+	0.250913i
$591$	1.76941	+	7.75227i	0.0727836	+	0.318886i
$592$	8.87177	+	11.1248i	0.364627	+	0.457228i
$593$	−6.40384	−	28.0570i	−0.262974	−	1.15216i	−0.918007	−	0.396564i	$-0.870202\pi$
$593$	−6.40384	−	28.0570i	−0.262974	−	1.15216i	0.655033	−	0.755600i	$-0.272655\pi$
$594$	−4.85464	+	21.2696i	−0.199188	+	0.872702i
$595$		0			0
$596$	−3.12138	−	13.6757i	−0.127857	−	0.560177i
$597$	−17.1887	+	8.27766i	−0.703488	+	0.338782i
$598$	−14.6251	+	64.0769i	−0.598066	+	2.62030i
$599$	13.0269	+	6.27342i	0.532265	+	0.256325i	0.680656	−	0.732604i	$-0.261695\pi$
$599$	13.0269	+	6.27342i	0.532265	+	0.256325i	−0.148391	+	0.988929i	$0.547409\pi$
$600$	−0.0268577	+	0.0336785i	−0.00109646	+	0.00137492i
$601$	23.2856	+	11.2137i	0.949839	+	0.457418i	0.843630	−	0.536926i	$-0.180414\pi$
$601$	23.2856	+	11.2137i	0.949839	+	0.457418i	0.106209	+	0.994344i	$0.466129\pi$
$602$		0			0
$603$	−11.3486	+	5.46520i	−0.462151	+	0.222560i
$604$	−3.34845	+	14.6705i	−0.136247	+	0.596935i
$605$	−10.4390	+	13.0901i	−0.424406	+	0.532189i
$606$	10.1773			0.413424
$607$	26.0394			1.05691			0.528454	−	0.848962i	$-0.322772\pi$
$607$	26.0394			1.05691			0.528454	+	0.848962i	$0.322772\pi$
$608$	−2.20337	+	2.76294i	−0.0893585	+	0.112052i
$609$		0			0
$610$	0.167199	+	0.209661i	0.00676968	+	0.00848891i
$611$	−4.56398	−	5.72305i	−0.184639	−	0.231530i
$612$	−7.90284	+	3.80581i	−0.319453	+	0.153841i
$613$	19.2088	−	9.25046i	0.775835	−	0.373622i	−0.00369025	−	0.999993i	$-0.501175\pi$
$613$	19.2088	−	9.25046i	0.775835	−	0.373622i	0.779525	+	0.626371i	$0.215460\pi$
$614$	18.5712	+	23.2875i	0.749472	+	0.939809i
$615$	−21.4492	−	26.8965i	−0.864916	−	1.08457i
$616$		0			0
$617$	29.9571	−	37.5650i	1.20603	−	1.51231i	0.404294	−	0.914629i	$-0.367517\pi$
$617$	29.9571	−	37.5650i	1.20603	−	1.51231i	0.801733	−	0.597682i	$-0.203911\pi$
$618$	−38.8428			−1.56249
$619$	37.2547			1.49739			0.748696	−	0.662913i	$-0.230680\pi$
$619$	37.2547			1.49739			0.748696	+	0.662913i	$0.230680\pi$
$620$	2.42326	−	3.03867i	0.0973205	−	0.122036i
$621$	8.59074	−	37.6385i	0.344735	−	1.51038i
$622$	−50.3281	+	24.2367i	−2.01797	+	0.971804i
$623$		0			0
$624$	−22.9598	−	11.0569i	−0.919129	−	0.442629i
$625$	−16.1172	+	20.2103i	−0.644688	+	0.808413i
$626$	−45.7486	−	22.0313i	−1.82848	−	0.880550i
$627$	0.260383	−	1.14081i	0.0103987	−	0.0455597i
$628$	−45.9252	+	22.1164i	−1.83261	+	0.882540i
$629$	−3.35581	−	14.7028i	−0.133805	−	0.586238i
$630$		0			0
$631$	4.77509	−	20.9210i	0.190093	−	0.832854i	−0.786471	−	0.617627i	$-0.788094\pi$
$631$	4.77509	−	20.9210i	0.190093	−	0.832854i	0.976564	−	0.215226i	$-0.0690489\pi$
$632$	0.0955475	+	0.418621i	0.00380068	+	0.0166519i
$633$	14.0883	+	17.6662i	0.559961	+	0.702169i
$634$	−9.85634	−	43.1835i	−0.391445	−	1.71503i
$635$	−11.9726	−	5.76568i	−0.475116	−	0.228804i
$636$	−2.41806			−0.0958821
$637$		0			0
$638$	32.8026			1.29867
$639$	4.58752	+	2.20923i	0.181479	+	0.0873959i
$640$	−0.706298	−	3.09449i	−0.0279189	−	0.122321i
$641$	18.5092	+	23.2098i	0.731070	+	0.916732i	0.998907	−	0.0467317i	$-0.0148806\pi$
$641$	18.5092	+	23.2098i	0.731070	+	0.916732i	−0.267838	+	0.963464i	$0.586309\pi$
$642$	1.91898	+	8.40759i	0.0757360	+	0.331821i
$643$	−4.65518	+	20.3957i	−0.183582	+	0.804326i	0.796324	+	0.604870i	$0.206775\pi$
$643$	−4.65518	+	20.3957i	−0.183582	+	0.804326i	−0.979907	+	0.199457i	$0.936082\pi$
$644$		0			0
$645$	5.72677	+	25.0906i	0.225491	+	0.987942i
$646$	3.22857	−	1.55480i	0.127026	−	0.0611726i
$647$	4.13192	−	18.1031i	0.162443	−	0.711707i	−0.826442	−	0.563022i	$-0.809639\pi$
$647$	4.13192	−	18.1031i	0.162443	−	0.711707i	0.988885	−	0.148685i	$-0.0475042\pi$
$648$	−0.755848	−	0.363997i	−0.0296925	−	0.0142992i
$649$	3.63360	−	4.55639i	0.142631	−	0.178854i
$650$	−1.52866	−	0.736162i	−0.0599588	−	0.0288747i
$651$		0			0
$652$	−42.3791	+	20.4087i	−1.65969	+	0.799266i
$653$	3.87369	−	16.9718i	0.151589	−	0.664156i	−0.840834	−	0.541293i	$-0.817935\pi$
$653$	3.87369	−	16.9718i	0.151589	−	0.664156i	0.992424	−	0.122863i	$-0.0392077\pi$
$654$	−5.83883	+	7.32167i	−0.228316	+	0.286300i
$655$	−10.1537			−0.396738
$656$	41.2406			1.61017
$657$	7.01793	−	8.80021i	0.273796	−	0.343329i
$658$		0			0
$659$	12.6442	+	15.8554i	0.492549	+	0.617637i	0.964531	−	0.263971i	$-0.0850324\pi$
$659$	12.6442	+	15.8554i	0.492549	+	0.617637i	−0.471981	+	0.881609i	$0.656461\pi$
$660$	7.90904	+	9.91762i	0.307859	+	0.386043i
$661$	6.99475	−	3.36849i	0.272064	−	0.131019i	−0.292878	−	0.956150i	$-0.594613\pi$
$661$	6.99475	−	3.36849i	0.272064	−	0.131019i	0.564942	+	0.825131i	$0.308899\pi$
$662$	23.1494	−	11.1482i	0.899727	−	0.433285i
$663$	16.8397	+	21.1163i	0.653999	+	0.820089i
$664$	−0.502668	−	0.630326i	−0.0195073	−	0.0244614i
$665$		0			0
$666$	−4.87558	+	6.11379i	−0.188925	+	0.236904i
$667$	−58.0472			−2.24760
$668$	−21.9427			−0.848988
$669$	−6.52124	+	8.17738i	−0.252126	+	0.316156i
$670$	−12.4132	+	54.3856i	−0.479562	+	2.10110i
$671$	0.100241	−	0.0482734i	0.00386975	−	0.00186357i
$672$		0			0
$673$	−36.1235	−	17.3962i	−1.39246	−	0.670572i	−0.420841	−	0.907134i	$-0.638265\pi$
$673$	−36.1235	−	17.3962i	−1.39246	−	0.670572i	−0.971616	+	0.236562i	$0.923979\pi$
$674$	−12.5303	+	15.7125i	−0.482650	+	0.605224i
$675$	0.897927	+	0.432419i	0.0345612	+	0.0166438i
$676$	−4.49857	+	19.7095i	−0.173022	+	0.758058i
$677$	−27.7627	+	13.3698i	−1.06701	+	0.513843i	−0.883141	−	0.469108i	$-0.844575\pi$
$677$	−27.7627	+	13.3698i	−1.06701	+	0.513843i	−0.183866	+	0.982951i	$0.558861\pi$
$678$	−1.78316	−	7.81253i	−0.0684818	−	0.300038i
$679$		0			0
$680$	−0.357762	+	1.56746i	−0.0137195	+	0.0601093i
$681$	3.00074	+	13.1471i	0.114989	+	0.503799i
$682$	−1.96916	−	2.46924i	−0.0754028	−	0.0945522i
$683$	−6.34504	−	27.7994i	−0.242786	−	1.06372i	−0.938468	−	0.345366i	$-0.887755\pi$
$683$	−6.34504	−	27.7994i	−0.242786	−	1.06372i	0.695682	−	0.718350i	$-0.255102\pi$
$684$	−0.854736	−	0.411619i	−0.0326817	−	0.0157387i
$685$	9.91239			0.378733
$686$		0			0
$687$	−19.5127			−0.744457
$688$	−27.7966	−	13.3861i	−1.05973	−	0.510341i
$689$	−0.877139	−	3.84300i	−0.0334163	−	0.146407i
$690$	−27.4123	−	34.3740i	−1.04357	−	1.30859i
$691$	3.12417	+	13.6879i	0.118849	+	0.520712i	0.998945	+	0.0459163i	$0.0146208\pi$
$691$	3.12417	+	13.6879i	0.118849	+	0.520712i	−0.880096	+	0.474795i	$0.842522\pi$
$692$	−2.17334	+	9.52204i	−0.0826181	+	0.361973i
$693$		0			0
$694$	−7.50449	−	32.8793i	−0.284867	−	1.24808i
$695$	−16.0573	+	7.73278i	−0.609087	+	0.293321i
$696$	−0.462626	+	2.02690i	−0.0175358	+	0.0768294i
$697$	−39.3804	−	18.9646i	−1.49164	−	0.718336i
$698$	1.04912	−	1.31555i	0.0397097	−	0.0497944i
$699$	8.18200	+	3.94024i	0.309472	+	0.149034i
$700$		0			0
$701$	26.9527	−	12.9797i	1.01799	−	0.490238i	0.150983	−	0.988536i	$-0.451756\pi$
$701$	26.9527	−	12.9797i	1.01799	−	0.490238i	0.867005	+	0.498299i	$0.166042\pi$
$702$	12.1191	−	53.0970i	0.457404	−	2.00402i
$703$	1.01696	−	1.27523i	0.0383555	−	0.0480962i
$704$	−16.5533			−0.623878
$705$	4.89668			0.184419
$706$	−34.9889	+	43.8747i	−1.31683	+	1.65125i
$707$		0			0
$708$	5.56438	+	6.97751i	0.209122	+	0.262231i
$709$	6.28366	+	7.87946i	0.235988	+	0.295919i	0.885697	−	0.464263i	$-0.153681\pi$
$709$	6.28366	+	7.87946i	0.235988	+	0.295919i	−0.649709	+	0.760183i	$0.725109\pi$
$710$	20.3169	−	9.78409i	0.762478	−	0.367190i
$711$	2.30158	−	1.10838i	0.0863161	−	0.0415677i
$712$	0.442577	+	0.554974i	0.0165863	+	0.0207985i
$713$	3.48460	+	4.36955i	0.130499	+	0.163641i
$714$		0			0
$715$	−12.8930	+	16.1674i	−0.482172	+	0.604625i
$716$	10.3872			0.388188
$717$	−23.9789			−0.895510
$718$	−32.1653	+	40.3340i	−1.20040	+	1.50525i
$719$	5.96757	−	26.1456i	0.222553	−	0.975067i	−0.732996	−	0.680233i	$-0.761879\pi$
$719$	5.96757	−	26.1456i	0.222553	−	0.975067i	0.955549	−	0.294834i	$-0.0952643\pi$
$720$	−8.13122	+	3.91579i	−0.303033	+	0.145933i
$721$		0			0
$722$	−34.2552	−	16.4964i	−1.27485	−	0.613934i
$723$	1.38497	−	1.73670i	0.0515075	−	0.0645884i
$724$	41.6651	+	20.0648i	1.54847	+	0.745704i
$725$	0.333444	−	1.46092i	0.0123838	−	0.0542570i
$726$	−18.7715	+	9.03989i	−0.696676	+	0.335502i
$727$	4.11406	+	18.0249i	0.152582	+	0.668506i	0.992129	+	0.125219i	$0.0399633\pi$
$727$	4.11406	+	18.0249i	0.152582	+	0.668506i	−0.839547	+	0.543287i	$0.817180\pi$
$728$		0			0
$729$	−6.39877	+	28.0348i	−0.236991	+	1.03833i
$730$	−11.0925	−	48.5994i	−0.410552	−	1.79875i
$731$	20.3872	+	25.5647i	0.754046	+	0.945544i
$732$	0.0379127	+	0.166107i	0.00140130	+	0.00613948i
$733$	46.9927	+	22.6305i	1.73572	+	0.835877i	0.984402	+	0.175931i	$0.0562936\pi$
$733$	46.9927	+	22.6305i	1.73572	+	0.835877i	0.751313	+	0.659946i	$0.229421\pi$
$734$	−44.3511			−1.63703
$735$		0			0
$736$	55.0888			2.03060
$737$	20.8522	+	10.0419i	0.768101	+	0.369898i
$738$	5.04327	+	22.0960i	0.185645	+	0.813366i
$739$	18.0413	+	22.6231i	0.663660	+	0.832203i	0.993736	−	0.111751i	$-0.0356459\pi$
$739$	18.0413	+	22.6231i	0.663660	+	0.832203i	−0.330076	+	0.943954i	$0.607075\pi$
$740$	3.93458	+	17.2385i	0.144638	+	0.633701i
$741$	−0.650017	+	2.84791i	−0.0238790	+	0.104621i
$742$		0			0
$743$	2.89866	+	12.6998i	0.106341	+	0.465912i	0.999858	+	0.0168809i	$0.00537360\pi$
$743$	2.89866	+	12.6998i	0.106341	+	0.465912i	−0.893516	+	0.449031i	$0.851769\pi$
$744$	0.180348	−	0.0868511i	0.00661188	−	0.00318411i
$745$	−3.40381	+	14.9131i	−0.124706	+	0.546372i
$746$	54.2154	+	26.1088i	1.98497	+	0.955910i
$747$	−2.99054	+	3.75002i	−0.109418	+	0.137206i
$748$	14.5209	+	6.99289i	0.530936	+	0.255685i
$749$		0			0
$750$	−27.9943	+	13.4813i	−1.02221	+	0.492269i
$751$	0.793314	−	3.47574i	0.0289485	−	0.126831i	−0.958389	−	0.285465i	$-0.907852\pi$
$751$	0.793314	−	3.47574i	0.0289485	−	0.126831i	0.987337	+	0.158634i	$0.0507090\pi$
$752$	−3.65994	+	4.58941i	−0.133464	+	0.167359i
$753$	−23.4503			−0.854575
$754$	−81.8878			−2.98218
$755$	10.2311	−	12.8294i	0.372347	−	0.466908i
$756$		0			0
$757$	2.92962	+	3.67362i	0.106479	+	0.133520i	0.832215	−	0.554453i	$-0.187072\pi$
$757$	2.92962	+	3.67362i	0.106479	+	0.133520i	−0.725737	+	0.687973i	$0.758501\pi$
$758$	−8.89077	−	11.1487i	−0.322927	−	0.404938i
$759$	−16.4345	+	7.91445i	−0.596535	+	0.287276i
$760$	−0.156669	+	0.0754477i	−0.00568297	+	0.00273678i
$761$	3.80315	+	4.76900i	0.137864	+	0.172876i	0.845971	−	0.533229i	$-0.179022\pi$
$761$	3.80315	+	4.76900i	0.137864	+	0.172876i	−0.708106	+	0.706106i	$0.750450\pi$
$762$	−10.3102	−	12.9285i	−0.373498	−	0.468352i
$763$		0			0
$764$	16.9953	−	21.3114i	0.614868	−	0.771020i
$765$	9.56515			0.345829
$766$	27.2051			0.982962
$767$	−9.07085	+	11.3745i	−0.327529	+	0.410709i
$768$	−4.52837	+	19.8401i	−0.163404	+	0.715918i
$769$	−7.74239	+	3.72854i	−0.279198	+	0.134455i	−0.568243	−	0.822861i	$-0.692377\pi$
$769$	−7.74239	+	3.72854i	−0.279198	+	0.134455i	0.289045	+	0.957316i	$0.406662\pi$
$770$		0			0
$771$	37.0318	+	17.8336i	1.33367	+	0.642261i
$772$	−13.9875	+	17.5397i	−0.503420	+	0.631268i
$773$	−41.0021	−	19.7456i	−1.47474	−	0.710199i	−0.488054	−	0.872813i	$-0.662293\pi$
$773$	−41.0021	−	19.7456i	−1.47474	−	0.710199i	−0.986690	+	0.162614i	$0.948008\pi$
$774$	3.77284	−	16.5299i	0.135612	−	0.594155i
$775$	−0.129988	+	0.0625991i	−0.00466932	+	0.00224863i
$776$	0.157478	+	0.689955i	0.00565312	+	0.0247679i
$777$		0			0
$778$	5.37580	−	23.5529i	0.192732	−	0.844413i
$779$	−1.05194	−	4.60885i	−0.0376896	−	0.165129i
$780$	−19.7440	−	24.7582i	−0.706948	−	0.886485i
$781$	−2.08185	−	9.12117i	−0.0744944	−	0.326381i
$782$	−50.3286	−	24.2370i	−1.79975	−	0.866712i
$783$	48.1006			1.71897
$784$		0			0
$785$	55.5853			1.98392
$786$	−11.3840	−	5.48222i	−0.406052	−	0.195544i
$787$	10.2282	+	44.8125i	0.364595	+	1.59739i	0.741375	+	0.671091i	$0.234174\pi$
$787$	10.2282	+	44.8125i	0.364595	+	1.59739i	−0.376780	+	0.926303i	$0.622969\pi$
$788$	−7.38543	−	9.26103i	−0.263095	−	0.329911i
$789$	−3.28673	−	14.4001i	−0.117011	−	0.512657i
$790$	2.51748	−	11.0298i	0.0895681	−	0.392423i
$791$		0			0
$792$	−0.0769655	−	0.337208i	−0.00273485	−	0.0119822i
$793$	−0.250239	+	0.120509i	−0.00888626	+	0.00427940i
$794$	−2.32273	+	10.1765i	−0.0824305	+	0.361151i
$795$	2.37572	+	1.14409i	0.0842580	+	0.0405765i
$796$	17.7196	−	22.2196i	0.628054	−	0.787554i
$797$	−21.1004	−	10.1614i	−0.747415	−	0.359936i	0.0210922	−	0.999778i	$-0.493286\pi$
$797$	−21.1004	−	10.1614i	−0.747415	−	0.359936i	−0.768507	+	0.639842i	$0.779000\pi$
$798$		0			0
$799$	5.60531	−	2.69938i	0.198302	−	0.0954971i
$800$	−0.316450	+	1.38646i	−0.0111882	+	0.0490187i
$801$	2.63304	−	3.30173i	0.0930339	−	0.116661i
$802$	−34.7399			−1.22671
$803$	−20.6819			−0.729847
$804$	−22.0979	+	27.7099i	−0.779334	+	0.977254i
$805$		0			0
$806$	4.91576	+	6.16417i	0.173150	+	0.217124i
$807$	−9.19739	−	11.5332i	−0.323764	−	0.405987i
$808$	−0.565332	+	0.272249i	−0.0198883	+	0.00957770i
$809$	4.49685	−	2.16557i	0.158101	−	0.0761373i	−0.353160	−	0.935563i	$-0.614893\pi$
$809$	4.49685	−	2.16557i	0.158101	−	0.0761373i	0.511261	+	0.859426i	$0.329179\pi$
$810$	13.7817	+	17.2816i	0.484238	+	0.607215i
$811$	−0.433526	−	0.543624i	−0.0152231	−	0.0190892i	0.774162	−	0.632988i	$-0.218172\pi$
$811$	−0.433526	−	0.543624i	−0.0152231	−	0.0190892i	−0.789385	+	0.613899i	$0.789600\pi$
$812$		0			0
$813$	−21.6930	+	27.2022i	−0.760808	+	0.954023i
$814$	14.3684			0.503611
$815$	51.2933			1.79673
$816$	13.5041	−	16.9335i	0.472736	−	0.592793i
$817$	−0.786950	+	3.44785i	−0.0275319	+	0.120625i
$818$	39.5463	−	19.0445i	1.38270	−	0.665876i
$819$		0			0
$820$	46.1723	+	22.2354i	1.61241	+	0.776494i
$821$	7.49950	−	9.40408i	0.261734	−	0.328205i	−0.633548	−	0.773703i	$-0.718402\pi$
$821$	7.49950	−	9.40408i	0.261734	−	0.328205i	0.895283	+	0.445499i	$0.146974\pi$
$822$	11.1134	+	5.35194i	0.387625	+	0.186670i
$823$	−9.43991	+	41.3590i	−0.329055	+	1.44168i	0.491881	+	0.870662i	$0.336309\pi$
$823$	−9.43991	+	41.3590i	−0.329055	+	1.44168i	−0.820936	+	0.571020i	$0.806548\pi$
$824$	2.15765	−	1.03907i	0.0751653	−	0.0361977i
$825$	−0.104783	−	0.459083i	−0.00364806	−	0.0159832i
$826$		0			0
$827$	1.01662	−	4.45411i	0.0353514	−	0.154885i	−0.954172	−	0.299260i	$-0.903260\pi$
$827$	1.01662	−	4.45411i	0.0353514	−	0.154885i	0.989523	+	0.144375i	$0.0461173\pi$
$828$	3.29077	+	14.4178i	0.114362	+	0.501054i
$829$	−0.820089	−	1.02836i	−0.0284829	−	0.0357164i	0.767386	−	0.641185i	$-0.221557\pi$
$829$	−0.820089	−	1.02836i	−0.0284829	−	0.0357164i	−0.795869	+	0.605469i	$0.792986\pi$
$830$	4.72683	+	20.7096i	0.164071	+	0.718841i
$831$	−16.6324	−	8.00975i	−0.576972	−	0.277855i
$832$	41.3235			1.43263
$833$		0			0
$834$	−22.1779			−0.767960
$835$	21.5585	+	10.3820i	0.746062	+	0.359285i
$836$	0.387885	+	1.69944i	0.0134153	+	0.0587762i
$837$	−2.88750	−	3.62081i	−0.0998066	−	0.125154i
$838$	−4.69304	−	20.5616i	−0.162118	−	0.710287i
$839$	1.84273	−	8.07355i	0.0636183	−	0.278730i	−0.933106	−	0.359601i	$-0.882913\pi$
$839$	1.84273	−	8.07355i	0.0636183	−	0.278730i	0.996725	+	0.0808707i	$0.0257701\pi$
$840$		0			0
$841$	−9.64011	−	42.2361i	−0.332418	−	1.45642i
$842$	−20.2397	+	9.74694i	−0.697507	+	0.335902i
$843$	6.34289	−	27.7900i	0.218461	−	0.957139i
$844$	−30.3270	−	14.6047i	−1.04390	−	0.502715i
$845$	13.7452	−	17.2360i	0.472850	−	0.592935i
$846$	−2.90650	−	1.39970i	−0.0999276	−	0.0481226i
$847$		0			0
$848$	−2.84798	+	1.37152i	−0.0978002	+	0.0470981i
$849$	−7.18359	+	31.4734i	−0.246540	+	1.08016i
$850$	0.899095	−	1.12743i	0.0308387	−	0.0386705i
$851$	−25.4261			−0.871597
$852$	14.3271			0.490838
$853$	4.03596	−	5.06093i	0.138189	−	0.173283i	−0.707922	−	0.706291i	$-0.750367\pi$
$853$	4.03596	−	5.06093i	0.138189	−	0.173283i	0.846110	+	0.533008i	$0.178938\pi$
$854$		0			0
$855$	0.645016	+	0.808824i	0.0220591	+	0.0276612i
$856$	−0.331504	−	0.415693i	−0.0113306	−	0.0142081i
$857$	32.1436	−	15.4796i	1.09801	−	0.528772i	0.204975	−	0.978767i	$-0.434289\pi$
$857$	32.1436	−	15.4796i	1.09801	−	0.528772i	0.893031	+	0.449995i	$0.148574\pi$
$858$	−23.1844	+	11.1650i	−0.791501	+	0.381167i
$859$	−17.5300	−	21.9819i	−0.598116	−	0.750014i	0.386967	−	0.922094i	$-0.373523\pi$
$859$	−17.5300	−	21.9819i	−0.598116	−	0.750014i	−0.985083	+	0.172080i	$0.944951\pi$
$860$	−23.9033	−	29.9738i	−0.815096	−	1.02210i
$861$		0			0
$862$	28.7574	−	36.0606i	0.979480	−	1.22823i
$863$	46.4267			1.58038			0.790191	−	0.612861i	$-0.209981\pi$
$863$	46.4267			1.58038			0.790191	+	0.612861i	$0.209981\pi$
$864$	−45.6491			−1.55301
$865$	6.64057	−	8.32701i	0.225786	−	0.283127i
$866$	6.86686	−	30.0857i	0.233345	−	1.02235i
$867$	0.769525	−	0.370584i	0.0261344	−	0.0125857i
$868$		0			0
$869$	−4.22899	−	2.03657i	−0.143459	−	0.0690861i
$870$	34.1536	−	42.8272i	1.15791	−	1.45198i
$871$	−52.0551	−	25.0684i	−1.76382	−	0.849411i
$872$	0.128478	−	0.562899i	0.00435081	−	0.0190622i
$873$	3.79338	−	1.82680i	0.128386	−	0.0618277i
$874$	−1.34439	−	5.89015i	−0.0454746	−	0.199237i
$875$		0			0
$876$	7.04759	−	30.8775i	0.238116	−	1.04325i
$877$	7.06117	+	30.9370i	0.238439	+	1.04467i	0.942415	+	0.334445i	$0.108549\pi$
$877$	7.06117	+	30.9370i	0.238439	+	1.04467i	−0.703977	+	0.710223i	$0.748594\pi$
$878$	10.7954	+	13.5370i	0.364327	+	0.456851i
$879$	3.69975	+	16.2097i	0.124790	+	0.546739i
$880$	14.9405	+	7.19498i	0.503645	+	0.242543i
$881$	−39.5493			−1.33245			−0.666225	−	0.745750i	$-0.732091\pi$
$881$	−39.5493			−1.33245			−0.666225	+	0.745750i	$0.732091\pi$
$882$		0			0
$883$	−8.59085			−0.289105			−0.144553	−	0.989497i	$-0.546174\pi$
$883$	−8.59085			−0.289105			−0.144553	+	0.989497i	$0.546174\pi$
$884$	−36.2497	−	17.4569i	−1.21921	−	0.587140i
$885$	−2.16559	−	9.48808i	−0.0727956	−	0.318938i
$886$	9.77598	+	12.2587i	0.328430	+	0.411839i
$887$	−5.96973	−	26.1551i	−0.200444	−	0.878202i	−0.970667	−	0.240428i	$-0.922712\pi$
$887$	−5.96973	−	26.1551i	−0.200444	−	0.878202i	0.770223	−	0.637775i	$-0.220145\pi$
$888$	−0.202642	+	0.887832i	−0.00680022	+	0.0297937i
$889$		0			0
$890$	−4.16177	−	18.2339i	−0.139503	−	0.611201i
$891$	8.26252	−	3.97902i	0.276805	−	0.133302i
$892$	3.46706	−	15.1902i	0.116086	−	0.508605i
$893$	0.606246	+	0.291953i	0.0202872	+	0.00976982i
$894$	−11.8681	+	14.8822i	−0.396930	+	0.497735i
$895$	−10.2053	−	4.91462i	−0.341126	−	0.164278i
$896$		0			0
$897$	41.0269	−	19.7575i	1.36985	−	0.659684i
$898$	0.737028	−	3.22913i	0.0245949	−	0.107757i
$899$	−4.34154	+	5.44412i	−0.144798	+	0.181571i
$900$	−0.381767			−0.0127256
$901$	3.35022			0.111612
$902$	25.9645	−	32.5585i	0.864525	−	1.08408i
$903$		0			0
$904$	0.308042	+	0.386272i	0.0102453	+	0.0128472i
$905$	−31.4420	−	39.4270i	−1.04517	−	1.31060i
$906$	18.3976	−	8.85981i	0.611219	−	0.294348i
$907$	−25.9411	+	12.4926i	−0.861359	+	0.414809i	−0.811781	−	0.583962i	$-0.801502\pi$
$907$	−25.9411	+	12.4926i	−0.861359	+	0.414809i	−0.0495777	+	0.998770i	$0.515788\pi$
$908$	−12.5250	−	15.7058i	−0.415656	−	0.521216i
$909$	2.32751	+	2.91860i	0.0771986	+	0.0968040i
$910$		0			0
$911$	−31.1144	+	39.0162i	−1.03087	+	1.29266i	−0.0755295	+	0.997144i	$0.524065\pi$
$911$	−31.1144	+	39.0162i	−1.03087	+	1.29266i	−0.955336	+	0.295521i	$0.904507\pi$
$912$	2.34252			0.0775687
$913$	8.81314			0.291672
$914$	22.9019	−	28.7180i	0.757526	−	0.949908i
$915$	0.0413432	−	0.181136i	0.00136676	−	0.00598818i
$916$	26.1889	−	12.6119i	0.865306	−	0.416709i
$917$		0			0
$918$	41.7046	+	20.0839i	1.37646	+	0.662866i
$919$	19.4402	−	24.3773i	0.641274	−	0.804132i	−0.349888	−	0.936792i	$-0.613780\pi$
$919$	19.4402	−	24.3773i	0.641274	−	0.804132i	0.991162	+	0.132660i	$0.0423517\pi$
$920$	2.44223	+	1.17612i	0.0805180	+	0.0387754i
$921$	4.59210	−	20.1193i	0.151315	−	0.662953i
$922$	56.8450	−	27.3751i	1.87209	−	0.901551i
$923$	5.19709	+	22.7699i	0.171064	+	0.749481i
$924$		0			0
$925$	0.146057	−	0.639918i	0.00480233	−	0.0210404i
$926$	14.5035	+	63.5440i	0.476615	+	2.08819i
$927$	−8.88319	−	11.1392i	−0.291762	−	0.365858i
$928$	15.2730	+	66.9154i	0.501361	+	2.19660i
$929$	−3.70596	−	1.78470i	−0.121589	−	0.0585540i	0.372100	−	0.928192i	$-0.378638\pi$
$929$	−3.70596	−	1.78470i	−0.121589	−	0.0585540i	−0.493689	+	0.869638i	$0.664352\pi$
$930$	−5.27411			−0.172945
$931$		0			0
$932$	−13.5282			−0.443130
$933$	34.8690	+	16.7920i	1.14156	+	0.549747i
$934$	−9.34308	−	40.9347i	−0.305715	−	1.33943i
$935$	−10.9580	−	13.7409i	−0.358365	−	0.449375i
$936$	0.192135	+	0.841800i	0.00628014	+	0.0275151i
$937$	−11.7963	+	51.6829i	−0.385367	+	1.68841i	0.294970	+	0.955506i	$0.404690\pi$
$937$	−11.7963	+	51.6829i	−0.385367	+	1.68841i	−0.680338	+	0.732899i	$0.738167\pi$
$938$		0			0
$939$	7.82831	+	34.2981i	0.255467	+	1.11928i
$940$	−6.57205	+	3.16493i	−0.214357	+	0.103229i
$941$	12.7510	−	55.8657i	0.415670	−	1.82117i	−0.140473	−	0.990084i	$-0.544862\pi$
$941$	12.7510	−	55.8657i	0.415670	−	1.82117i	0.556143	−	0.831086i	$-0.312281\pi$
$942$	62.3202	+	30.0118i	2.03050	+	0.977838i
$943$	−45.9467	+	57.6153i	−1.49623	+	1.87621i
$944$	10.5114	+	5.06200i	0.342115	+	0.164754i
$945$		0			0
$946$	−28.0684	+	13.5170i	−0.912582	+	0.439477i
$947$	−7.96791	+	34.9097i	−0.258922	+	1.13441i	0.663483	+	0.748191i	$0.269077\pi$
$947$	−7.96791	+	34.9097i	−0.258922	+	1.13441i	−0.922406	+	0.386222i	$0.873780\pi$
$948$	4.48163	−	5.61979i	0.145557	−	0.182522i
$949$	51.6299			1.67598
$950$	0.155964			0.00506015
$951$	−19.1339	+	23.9932i	−0.620460	+	0.778032i
$952$		0			0
$953$	−29.1457	−	36.5476i	−0.944123	−	1.18389i	−0.982806	−	0.184641i	$-0.940888\pi$
$953$	−29.1457	−	36.5476i	−0.944123	−	1.18389i	0.0386828	−	0.999252i	$-0.487684\pi$
$954$	−1.08311	−	1.35818i	−0.0350671	−	0.0439727i
$955$	−26.7810	+	12.8971i	−0.866614	+	0.417339i
$956$	32.1832	−	15.4986i	1.04088	−	0.501261i
$957$	−14.1699	−	17.7685i	−0.458048	−	0.574374i
$958$	29.8933	+	37.4850i	0.965808	+	1.21109i
$959$		0			0
$960$	−17.2351	+	21.6121i	−0.556260	+	0.697528i
$961$	−30.3296			−0.978373
$962$	−35.8689			−1.15646
$963$	−1.97223	+	2.47310i	−0.0635542	+	0.0796945i
$964$	−0.736328	+	3.22606i	−0.0237155	+	0.103904i
$965$	22.0413	−	10.6146i	0.709536	−	0.341695i
$966$		0			0
$967$	−39.2046	−	18.8800i	−1.26074	−	0.607139i	−0.320367	−	0.947294i	$-0.603806\pi$
$967$	−39.2046	−	18.8800i	−1.26074	−	0.607139i	−0.940369	+	0.340155i	$0.889520\pi$
$968$	0.800903	−	1.00430i	0.0257420	−	0.0322795i
$969$	−2.23686	−	1.07722i	−0.0718584	−	0.0346052i
$970$	4.14922	−	18.1789i	0.133223	−	0.583690i
$971$	15.4418	−	7.43640i	0.495552	−	0.238645i	−0.169378	−	0.985551i	$-0.554176\pi$
$971$	15.4418	−	7.43640i	0.495552	−	0.238645i	0.664930	+	0.746906i	$0.268461\pi$
$972$	−4.75257	−	20.8224i	−0.152439	−	0.667877i
$973$		0			0
$974$	−10.6561	+	46.6873i	−0.341442	+	1.49596i
$975$	0.261578	+	1.14605i	0.00837719	+	0.0367029i
$976$	0.138869	+	0.174136i	0.00444509	+	0.00557396i
$977$	−7.38313	−	32.3476i	−0.236207	−	1.03489i	−0.944381	−	0.328853i	$-0.893338\pi$
$977$	−7.38313	−	32.3476i	−0.236207	−	1.03489i	0.708174	−	0.706038i	$-0.249519\pi$
$978$	57.5082	+	27.6945i	1.83891	+	0.885572i
$979$	−7.75958			−0.247997
$980$		0			0
$981$	−3.43500			−0.109671
$982$	5.35405	+	2.57837i	0.170855	+	0.0822792i
$983$	13.4216	+	58.8037i	0.428082	+	1.87555i	0.480620	+	0.876929i	$0.340412\pi$
$983$	13.4216	+	58.8037i	0.428082	+	1.87555i	−0.0525387	+	0.998619i	$0.516731\pi$
$984$	1.64563	+	2.06355i	0.0524607	+	0.0657837i
$985$	2.87432	+	12.5932i	0.0915836	+	0.401254i
$986$	15.4870	−	67.8528i	0.493205	−	2.16087i
$987$		0			0
$988$	−0.968310	−	4.24244i	−0.0308060	−	0.134970i
$989$	49.6696	−	23.9196i	1.57940	−	0.760600i
$990$	−2.02789	+	8.88475i	−0.0644504	+	0.282376i
$991$	−40.4078	−	19.4594i	−1.28360	−	0.618147i	−0.337284	−	0.941403i	$-0.609508\pi$
$991$	−40.4078	−	19.4594i	−1.28360	−	0.618147i	−0.946312	+	0.323256i	$0.895223\pi$
$992$	4.12026	−	5.16665i	0.130819	−	0.164041i
$993$	−16.0387	−	7.72383i	−0.508973	−	0.245108i
$994$		0			0
$995$	−27.9224	+	13.4467i	−0.885199	+	0.426289i
$996$	−3.00318	+	13.1578i	−0.0951594	+	0.416920i
$997$	−0.719238	+	0.901896i	−0.0227785	+	0.0285633i	−0.793090	−	0.609104i	$-0.791529\pi$
$997$	−0.719238	+	0.901896i	−0.0227785	+	0.0285633i	0.770312	+	0.637667i	$0.220101\pi$
$998$	4.11538			0.130270
$999$	21.0693			0.666602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.e.d.197.7		48
7.2	even	3		49.2.g.a.32.1	yes	48
7.3	odd	6		343.2.g.h.30.1		48
7.4	even	3		343.2.g.i.30.1		48
7.5	odd	6		343.2.g.g.116.1		48
7.6	odd	2		343.2.e.c.197.7		48
21.2	odd	6		441.2.bb.d.424.4		48
28.23	odd	6		784.2.bg.c.81.1		48
49.4	even	21		49.2.g.a.23.1	✓	48
49.13	odd	14		2401.2.a.i.1.5		24
49.22	even	7	inner	343.2.e.d.148.7		48
49.23	even	21		343.2.g.i.263.1		48
49.26	odd	42		343.2.g.h.263.1		48
49.27	odd	14		343.2.e.c.148.7		48
49.36	even	7		2401.2.a.h.1.5		24
49.45	odd	42		343.2.g.g.275.1		48
147.53	odd	42		441.2.bb.d.415.4		48
196.151	odd	42		784.2.bg.c.513.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.23.1	✓	48	49.4	even	21
49.2.g.a.32.1	yes	48	7.2	even	3
343.2.e.c.148.7		48	49.27	odd	14
343.2.e.c.197.7		48	7.6	odd	2
343.2.e.d.148.7		48	49.22	even	7	inner
343.2.e.d.197.7		48	1.1	even	1	trivial
343.2.g.g.116.1		48	7.5	odd	6
343.2.g.g.275.1		48	49.45	odd	42
343.2.g.h.30.1		48	7.3	odd	6
343.2.g.h.263.1		48	49.26	odd	42
343.2.g.i.30.1		48	7.4	even	3
343.2.g.i.263.1		48	49.23	even	21
441.2.bb.d.415.4		48	147.53	odd	42
441.2.bb.d.424.4		48	21.2	odd	6
784.2.bg.c.81.1		48	28.23	odd	6
784.2.bg.c.513.1		48	196.151	odd	42
2401.2.a.h.1.5		24	49.36	even	7
2401.2.a.i.1.5		24	49.13	odd	14

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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.e (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.82128 + 0.877084i) q^{2} +(-0.311651 - 1.36543i) q^{3} +(1.30082 + 1.63117i) q^{4} +(-0.506263 - 2.21809i) q^{5} +(0.629993 - 2.76018i) q^{6} +(0.0388416 + 0.170176i) q^{8} +(0.935630 - 0.450576i) q^{9} +(1.02340 - 4.48380i) q^{10} +(-1.71915 - 0.827900i) q^{11} +(1.82185 - 2.28453i) q^{12} +(4.29166 + 2.06676i) q^{13} +(-2.87087 + 1.38254i) q^{15} +(0.849996 - 3.72407i) q^{16} +(-2.52418 + 3.16523i) q^{17} +2.09924 q^{18} -0.437865 q^{19} +(2.95953 - 3.71113i) q^{20} +(-2.40493 - 3.01568i) q^{22} +(4.25574 + 5.33653i) q^{23} +(0.220259 - 0.106071i) q^{24} +(-0.158755 + 0.0764522i) q^{25} +(6.00361 + 7.52829i) q^{26} +(-3.52650 - 4.42209i) q^{27} +(-5.30231 + 6.64889i) q^{29} -6.44126 q^{30} +0.818801 q^{31} +(5.03207 - 6.31002i) q^{32} +(-0.594665 + 2.60540i) q^{33} +(-7.37342 + 3.55085i) q^{34} +(1.95205 + 0.940059i) q^{36} +(-2.32255 + 2.91238i) q^{37} +(-0.797477 - 0.384045i) q^{38} +(1.48451 - 6.50407i) q^{39} +(0.357801 - 0.172308i) q^{40} +(2.40243 + 10.5257i) q^{41} +(1.79724 - 7.87423i) q^{43} +(-0.885854 - 3.88118i) q^{44} +(-1.47309 - 1.84720i) q^{45} +(3.07032 + 13.4520i) q^{46} +(-1.38455 - 0.666763i) q^{47} -5.34987 q^{48} -0.356192 q^{50} +(5.10856 + 2.46015i) q^{51} +(2.21143 + 9.68892i) q^{52} +(-0.515954 - 0.646986i) q^{53} +(-2.54421 - 11.1469i) q^{54} +(-0.966009 + 4.23236i) q^{55} +(0.136461 + 0.597875i) q^{57} +(-15.4886 + 7.45894i) q^{58} +(-0.679632 + 2.97766i) q^{59} +(-5.98963 - 2.88445i) q^{60} +(-0.0363546 + 0.0455872i) q^{61} +(1.49127 + 0.718157i) q^{62} +(7.81612 - 3.76404i) q^{64} +(2.41153 - 10.5656i) q^{65} +(-3.36821 + 4.22360i) q^{66} -12.1294 q^{67} -8.44654 q^{68} +(5.96036 - 7.47405i) q^{69} +(3.05705 + 3.83342i) q^{71} +(0.113019 + 0.141721i) q^{72} +(9.76551 - 4.70282i) q^{73} +(-6.78442 + 3.26720i) q^{74} +(0.153866 + 0.192942i) q^{75} +(-0.569583 - 0.714235i) q^{76} +(8.40834 - 10.5437i) q^{78} +2.45993 q^{79} -8.69063 q^{80} +(-2.99659 + 3.75761i) q^{81} +(-4.85644 + 21.2774i) q^{82} +(-4.16137 + 2.00401i) q^{83} +(8.29864 + 3.99642i) q^{85} +(10.1796 - 12.7649i) q^{86} +(10.7311 + 5.16781i) q^{87} +(0.0741142 - 0.324716i) q^{88} +(3.66390 - 1.76444i) q^{89} +(-1.06277 - 4.65630i) q^{90} +(-3.16886 + 13.8837i) q^{92} +(-0.255180 - 1.11802i) q^{93} +(-1.93685 - 2.42873i) q^{94} +(0.221675 + 0.971223i) q^{95} +(-10.1841 - 4.90443i) q^{96} +4.05436 q^{97} -1.98152 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 5 q^{2} + 7 q^{3} - 3 q^{4} + 7 q^{5} - 20 q^{8} + 9 q^{9} + 7 q^{10} + 6 q^{11} + 42 q^{12} - 14 q^{13} - 12 q^{15} - 15 q^{16} - 7 q^{17} - 4 q^{18} - 42 q^{19} + 14 q^{20} - 20 q^{22} + 12 q^{23}+ \cdots - 16 q^{99}+O(q^{100}) \) 48 * q + 5 * q^2 + 7 * q^3 - 3 * q^4 + 7 * q^5 - 20 * q^8 + 9 * q^9 + 7 * q^10 + 6 * q^11 + 42 * q^12 - 14 * q^13 - 12 * q^15 - 15 * q^16 - 7 * q^17 - 4 * q^18 - 42 * q^19 + 14 * q^20 - 20 * q^22 + 12 * q^23 + 49 * q^24 - 13 * q^25 + 21 * q^26 + 7 * q^27 + 12 * q^29 - 22 * q^30 - 70 * q^31 + 15 * q^32 + 7 * q^33 + 70 * q^34 - 12 * q^36 - 9 * q^37 - 7 * q^38 - 28 * q^39 - 63 * q^40 - 42 * q^41 - 30 * q^43 + 37 * q^44 + 28 * q^45 + 9 * q^46 + 21 * q^47 - 84 * q^48 + 40 * q^50 - q^51 + 77 * q^52 + 20 * q^53 + 7 * q^54 - 7 * q^55 - 12 * q^57 + 31 * q^58 - 7 * q^59 + 35 * q^60 + 7 * q^61 - 28 * q^62 - 32 * q^64 - 49 * q^65 - 119 * q^66 - 22 * q^67 - 154 * q^68 + 70 * q^69 + 19 * q^71 - 46 * q^72 + 28 * q^73 - 47 * q^74 + 7 * q^75 + 119 * q^76 + 28 * q^78 - 30 * q^79 - 140 * q^80 + 61 * q^81 + 112 * q^82 - 26 * q^85 + 24 * q^86 + 77 * q^87 + 28 * q^88 + 28 * q^89 - 182 * q^90 - 38 * q^92 + 34 * q^93 - 28 * q^94 - 67 * q^95 - 28 * q^96 - 16 * q^99

Introduction

L-functions

Modular forms

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