LMFDB - Embedded newform 875.2.bb.b.143.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			143.15
Character	$\chi$	$=$	875.143
Dual form			875.2.bb.b.257.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0947490 + 1.80792i) q^{2} +(1.64111 + 1.32895i) q^{3} +(-1.27055 + 0.133540i) q^{4} +(-2.24713 + 3.09291i) q^{6} +(2.61446 - 0.405696i) q^{7} +(0.204604 + 1.29182i) q^{8} +(0.303414 + 1.42745i) q^{9} +(-2.23088 - 0.474189i) q^{11} +(-2.26258 - 1.46934i) q^{12} +(2.14873 + 4.21711i) q^{13} +(0.981183 + 4.68830i) q^{14} +(-4.81539 + 1.02354i) q^{16} +(-3.47011 - 1.33205i) q^{17} +(-2.55197 + 0.683798i) q^{18} +(0.216377 - 2.05869i) q^{19} +(4.82977 + 2.80869i) q^{21} +(0.645921 - 4.07818i) q^{22} +(1.58250 - 0.0829354i) q^{23} +(-1.38098 + 2.39193i) q^{24} +(-7.42061 + 4.28429i) q^{26} +(1.47703 - 2.89883i) q^{27} +(-3.26763 + 0.864593i) q^{28} +(6.19928 + 8.53257i) q^{29} +(1.38755 + 3.11648i) q^{31} +(-1.62970 - 6.08214i) q^{32} +(-3.03095 - 3.74292i) q^{33} +(2.07945 - 6.39988i) q^{34} +(-0.576126 - 1.77313i) q^{36} +(-1.17298 + 1.80623i) q^{37} +(3.74244 + 0.196133i) q^{38} +(-2.07801 + 9.77629i) q^{39} +(-4.99913 - 1.62432i) q^{41} +(-4.62026 + 8.99795i) q^{42} +(-6.27631 - 6.27631i) q^{43} +(2.89777 + 0.304568i) q^{44} +(0.299881 + 2.85318i) q^{46} +(2.30438 + 6.00311i) q^{47} +(-9.26282 - 4.71964i) q^{48} +(6.67082 - 2.12135i) q^{49} +(-3.92461 - 6.79762i) q^{51} +(-3.29322 - 5.07112i) q^{52} +(2.55248 - 3.15205i) q^{53} +(5.38080 + 2.39569i) q^{54} +(1.05902 + 3.29441i) q^{56} +(3.09098 - 3.09098i) q^{57} +(-14.8388 + 12.0162i) q^{58} +(-8.50113 - 9.44146i) q^{59} +(-0.722763 - 0.650779i) q^{61} +(-5.50288 + 2.80386i) q^{62} +(1.37238 + 3.60892i) q^{63} +(1.47757 - 0.480090i) q^{64} +(6.47971 - 5.83436i) q^{66} +(3.67699 - 9.57888i) q^{67} +(4.58683 + 1.22904i) q^{68} +(2.70728 + 1.96695i) q^{69} +(-1.86024 + 1.35154i) q^{71} +(-1.78193 + 0.684019i) q^{72} +(6.58242 - 4.27467i) q^{73} +(-3.37666 - 1.94951i) q^{74} +2.64456i q^{76} +(-6.02493 - 0.334689i) q^{77} +(-17.8716 - 2.83059i) q^{78} +(4.69941 - 10.5550i) q^{79} +(10.2759 - 4.57511i) q^{81} +(2.46297 - 9.19193i) q^{82} +(5.73970 - 0.909079i) q^{83} +(-6.51154 - 2.92361i) q^{84} +(10.7524 - 11.9417i) q^{86} +(-1.16562 + 22.2414i) q^{87} +(0.156119 - 2.97892i) q^{88} +(4.47423 - 4.96914i) q^{89} +(7.32863 + 10.1538i) q^{91} +(-1.99958 + 0.316702i) q^{92} +(-1.86452 + 6.95847i) q^{93} +(-10.6348 + 4.73492i) q^{94} +(5.40831 - 12.1473i) q^{96} +(-2.86204 - 0.453302i) q^{97} +(4.46729 + 11.8593i) q^{98} -3.32835i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) $ 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.0947490	+	1.80792i	0.0669977	+	1.27839i	0.800760	+	0.598986i	$0.204429\pi$
$2$	0.0947490	+	1.80792i	0.0669977	+	1.27839i	−0.733762	+	0.679407i	$0.762237\pi$
$3$	1.64111	+	1.32895i	0.947496	+	0.767267i	0.972616	−	0.232417i	$-0.0746635\pi$
$3$	1.64111	+	1.32895i	0.947496	+	0.767267i	−0.0251203	+	0.999684i	$0.507997\pi$
$4$	−1.27055	+	0.133540i	−0.635276	+	0.0667702i
$5$		0			0
$5$		0			0
$6$	−2.24713	+	3.09291i	−0.917388	+	1.26268i
$7$	2.61446	−	0.405696i	0.988174	−	0.153339i
$7$	2.61446	−	0.405696i	0.988174	−	0.153339i
$8$	0.204604	+	1.29182i	0.0723385	+	0.456728i
$9$	0.303414	+	1.42745i	0.101138	+	0.475817i
$10$		0			0
$11$	−2.23088	−	0.474189i	−0.672636	−	0.142973i	−0.141083	−	0.989998i	$-0.545058\pi$
$11$	−2.23088	−	0.474189i	−0.672636	−	0.142973i	−0.531554	+	0.847025i	$0.678392\pi$
$12$	−2.26258	−	1.46934i	−0.653152	−	0.424162i
$13$	2.14873	+	4.21711i	0.595949	+	1.16962i	0.970204	+	0.242290i	$0.0778987\pi$
$13$	2.14873	+	4.21711i	0.595949	+	1.16962i	−0.374254	+	0.927326i	$0.622101\pi$
$14$	0.981183	+	4.68830i	0.262232	+	1.25300i
$15$		0			0
$16$	−4.81539	+	1.02354i	−1.20385	+	0.255886i
$17$	−3.47011	−	1.33205i	−0.841625	−	0.323069i	−0.100915	−	0.994895i	$-0.532177\pi$
$17$	−3.47011	−	1.33205i	−0.841625	−	0.323069i	−0.740709	+	0.671826i	$0.765510\pi$
$18$	−2.55197	+	0.683798i	−0.601505	+	0.161173i
$19$	0.216377	−	2.05869i	0.0496402	−	0.472295i	−0.941259	−	0.337686i	$-0.890356\pi$
$19$	0.216377	−	2.05869i	0.0496402	−	0.472295i	0.990899	−	0.134608i	$-0.0429777\pi$
$20$		0			0
$21$	4.82977	+	2.80869i	1.05394	+	0.612905i
$22$	0.645921	−	4.07818i	0.137711	−	0.869472i
$23$	1.58250	−	0.0829354i	0.329975	−	0.0172932i	0.113371	−	0.993553i	$-0.463835\pi$
$23$	1.58250	−	0.0829354i	0.329975	−	0.0172932i	0.216604	+	0.976260i	$0.430502\pi$
$24$	−1.38098	+	2.39193i	−0.281892	+	0.488251i
$25$		0			0
$26$	−7.42061	+	4.28429i	−1.45530	+	0.840219i
$27$	1.47703	−	2.89883i	0.284254	−	0.557880i
$28$	−3.26763	+	0.864593i	−0.617524	+	0.163393i
$29$	6.19928	+	8.53257i	1.15118	+	1.58446i	0.739543	+	0.673109i	$0.235042\pi$
$29$	6.19928	+	8.53257i	1.15118	+	1.58446i	0.411633	+	0.911350i	$0.364958\pi$
$30$		0			0
$31$	1.38755	+	3.11648i	0.249211	+	0.559737i	0.994225	−	0.107312i	$-0.0342242\pi$
$31$	1.38755	+	3.11648i	0.249211	+	0.559737i	−0.745015	+	0.667048i	$0.767558\pi$
$32$	−1.62970	−	6.08214i	−0.288094	−	1.07518i
$33$	−3.03095	−	3.74292i	−0.527621	−	0.651558i
$34$	2.07945	−	6.39988i	0.356622	−	1.09757i
$35$		0			0
$36$	−0.576126	−	1.77313i	−0.0960209	−	0.295522i
$37$	−1.17298	+	1.80623i	−0.192837	+	0.296942i	−0.921842	−	0.387565i	$-0.873316\pi$
$37$	−1.17298	+	1.80623i	−0.192837	+	0.296942i	0.729006	+	0.684508i	$0.239983\pi$
$38$	3.74244	+	0.196133i	0.607104	+	0.0318170i
$39$	−2.07801	+	9.77629i	−0.332749	+	1.56546i
$40$		0			0
$41$	−4.99913	−	1.62432i	−0.780733	−	0.253676i	−0.108580	−	0.994088i	$-0.534630\pi$
$41$	−4.99913	−	1.62432i	−0.780733	−	0.253676i	−0.672153	+	0.740412i	$0.734630\pi$
$42$	−4.62026	+	8.99795i	−0.712922	+	1.38841i
$43$	−6.27631	−	6.27631i	−0.957128	−	0.957128i	0.0419898	−	0.999118i	$-0.486630\pi$
$43$	−6.27631	−	6.27631i	−0.957128	−	0.957128i	−0.999118	+	0.0419898i	$0.986630\pi$
$44$	2.89777	+	0.304568i	0.436856	+	0.0459154i
$45$		0			0
$46$	0.299881	+	2.85318i	0.0442151	+	0.420678i
$47$	2.30438	+	6.00311i	0.336128	+	0.875644i	0.992615	+	0.121306i	$0.0387084\pi$
$47$	2.30438	+	6.00311i	0.336128	+	0.875644i	−0.656487	+	0.754337i	$0.727958\pi$
$48$	−9.26282	−	4.71964i	−1.33697	−	0.681221i
$49$	6.67082	−	2.12135i	0.952975	−	0.303050i
$50$		0			0
$51$	−3.92461	−	6.79762i	−0.549555	−	0.951858i
$52$	−3.29322	−	5.07112i	−0.456688	−	0.703237i
$53$	2.55248	−	3.15205i	0.350610	−	0.432968i	−0.571080	−	0.820894i	$-0.693475\pi$
$53$	2.55248	−	3.15205i	0.350610	−	0.432968i	0.921690	+	0.387927i	$0.126809\pi$
$54$	5.38080	+	2.39569i	0.732234	+	0.326011i
$55$		0			0
$56$	1.05902	+	3.29441i	0.141517	+	0.440234i
$57$	3.09098	−	3.09098i	0.409410	−	0.409410i
$58$	−14.8388	+	12.0162i	−1.94843	+	1.57781i
$59$	−8.50113	−	9.44146i	−1.10675	−	1.22917i	−0.971165	−	0.238408i	$-0.923375\pi$
$59$	−8.50113	−	9.44146i	−1.10675	−	1.22917i	−0.135587	−	0.990765i	$-0.543292\pi$
$60$		0			0
$61$	−0.722763	−	0.650779i	−0.0925403	−	0.0833237i	0.621562	−	0.783365i	$-0.286498\pi$
$61$	−0.722763	−	0.650779i	−0.0925403	−	0.0833237i	−0.714103	+	0.700041i	$0.753165\pi$
$62$	−5.50288	+	2.80386i	−0.698866	+	0.356090i
$63$	1.37238	+	3.60892i	0.172903	+	0.454682i
$64$	1.47757	−	0.480090i	0.184696	−	0.0600113i
$65$		0			0
$66$	6.47971	−	5.83436i	0.797597	−	0.718160i
$67$	3.67699	−	9.57888i	0.449216	−	1.17025i	−0.502856	−	0.864370i	$-0.667717\pi$
$67$	3.67699	−	9.57888i	0.449216	−	1.17025i	0.952071	−	0.305876i	$-0.0989494\pi$
$68$	4.58683	+	1.22904i	0.556235	+	0.149043i
$69$	2.70728	+	1.96695i	0.325918	+	0.236793i
$70$		0			0
$71$	−1.86024	+	1.35154i	−0.220770	+	0.160399i	−0.692673	−	0.721252i	$-0.743567\pi$
$71$	−1.86024	+	1.35154i	−0.220770	+	0.160399i	0.471903	+	0.881650i	$0.343567\pi$
$72$	−1.78193	+	0.684019i	−0.210003	+	0.0806125i
$73$	6.58242	−	4.27467i	0.770414	−	0.500312i	−0.0985840	−	0.995129i	$-0.531431\pi$
$73$	6.58242	−	4.27467i	0.770414	−	0.500312i	0.868998	+	0.494816i	$0.164765\pi$
$74$	−3.37666	−	1.94951i	−0.392528	−	0.226626i
$75$		0			0
$76$			2.64456i			0.303352i
$77$	−6.02493	−	0.334689i	−0.686605	−	0.0381414i
$78$	−17.8716	−	2.83059i	−2.02356	−	0.320501i
$79$	4.69941	−	10.5550i	0.528725	−	1.18754i	−0.429904	−	0.902875i	$-0.641453\pi$
$79$	4.69941	−	10.5550i	0.528725	−	1.18754i	0.958628	−	0.284660i	$-0.0918808\pi$
$80$		0			0
$81$	10.2759	−	4.57511i	1.14176	−	0.508346i
$82$	2.46297	−	9.19193i	0.271990	−	1.01508i
$83$	5.73970	−	0.909079i	0.630014	−	0.0997844i	0.166742	−	0.986001i	$-0.446675\pi$
$83$	5.73970	−	0.909079i	0.630014	−	0.0997844i	0.463272	+	0.886216i	$0.346675\pi$
$84$	−6.51154	−	2.92361i	−0.710468	−	0.318992i
$85$		0			0
$86$	10.7524	−	11.9417i	1.15946	−	1.28771i
$87$	−1.16562	+	22.2414i	−0.124968	+	2.38453i
$88$	0.156119	−	2.97892i	0.0166423	−	0.317554i
$89$	4.47423	−	4.96914i	0.474268	−	0.526728i	−0.457779	−	0.889066i	$-0.651355\pi$
$89$	4.47423	−	4.96914i	0.474268	−	0.526728i	0.932047	+	0.362338i	$0.118022\pi$
$90$		0			0
$91$	7.32863	+	10.1538i	0.768249	+	1.06440i
$92$	−1.99958	+	0.316702i	−0.208470	+	0.0330184i
$93$	−1.86452	+	6.95847i	−0.193341	+	0.721559i
$94$	−10.6348	+	4.73492i	−1.09690	+	0.488370i
$95$		0			0
$96$	5.40831	−	12.1473i	0.551983	−	1.23977i
$97$	−2.86204	−	0.453302i	−0.290596	−	0.0460259i	0.00943453	−	0.999955i	$-0.496997\pi$
$97$	−2.86204	−	0.453302i	−0.290596	−	0.0460259i	−0.300030	+	0.953930i	$0.596997\pi$
$98$	4.46729	+	11.8593i	0.451264	+	1.19797i
$99$		−	3.32835i		−	0.334512i
$100$		0			0
$101$	−3.29920	−	1.90480i	−0.328283	−	0.189534i	0.326796	−	0.945095i	$-0.394031\pi$
$101$	−3.29920	−	1.90480i	−0.328283	−	0.189534i	−0.655079	+	0.755561i	$0.727364\pi$
$102$	11.9177	−	7.73945i	1.18003	−	0.766319i
$103$	15.9945	−	6.13972i	1.57599	−	0.604965i	0.595817	−	0.803120i	$-0.296828\pi$
$103$	15.9945	−	6.13972i	1.57599	−	0.604965i	0.980171	+	0.198155i	$0.0634950\pi$
$104$	−5.00811	+	3.63861i	−0.491086	+	0.356795i
$105$		0			0
$106$	5.94050	+	4.31603i	0.576992	+	0.419210i
$107$	6.17530	+	1.65467i	0.596988	+	0.159963i	0.544645	−	0.838667i	$-0.316664\pi$
$107$	6.17530	+	1.65467i	0.596988	+	0.159963i	0.0523433	+	0.998629i	$0.483331\pi$
$108$	−1.48953	+	3.88036i	−0.143330	+	0.373387i
$109$	6.87193	−	6.18751i	0.658211	−	0.592656i	−0.270832	−	0.962627i	$-0.587299\pi$
$109$	6.87193	−	6.18751i	0.658211	−	0.592656i	0.929044	+	0.369970i	$0.120632\pi$
$110$		0			0
$111$	−4.32537	+	1.40540i	−0.410546	+	0.133394i
$112$	−12.1744	+	4.62959i	−1.15037	+	0.437455i
$113$	−1.40652	+	0.716658i	−0.132314	+	0.0674175i	−0.518894	−	0.854838i	$-0.673656\pi$
$113$	−1.40652	+	0.716658i	−0.132314	+	0.0674175i	0.386580	+	0.922256i	$0.373656\pi$
$114$	5.88111	+	5.29537i	0.550816	+	0.495957i
$115$		0			0
$116$	−9.01594	−	10.0132i	−0.837109	−	0.929704i
$117$	−5.36777	+	4.34673i	−0.496250	+	0.401856i
$118$	16.2639	−	16.2639i	1.49722	−	1.49722i
$119$	−9.61287	−	2.07478i	−0.881210	−	0.190195i
$120$		0			0
$121$	−5.29702	−	2.35839i	−0.481547	−	0.214399i
$122$	1.10807	−	1.36836i	0.100320	−	0.123885i
$123$	−6.04550	−	9.30926i	−0.545105	−	0.839387i
$124$	−2.17913	−	3.77436i	−0.195691	−	0.338947i
$125$		0			0
$126$	−6.39461	+	2.82309i	−0.569677	+	0.251501i
$127$	−11.3459	−	5.78103i	−1.00679	−	0.512984i	−0.128801	−	0.991670i	$-0.541113\pi$
$127$	−11.3459	−	5.78103i	−1.00679	−	0.512984i	−0.877986	+	0.478687i	$0.841113\pi$
$128$	−3.50510	−	9.13111i	−0.309810	−	0.807083i
$129$	−1.95925	−	18.6410i	−0.172502	−	1.64125i
$130$		0			0
$131$	−14.2509	−	1.49783i	−1.24511	−	0.130866i	−0.541040	−	0.840997i	$-0.681969\pi$
$131$	−14.2509	−	1.49783i	−1.24511	−	0.130866i	−0.704070	+	0.710131i	$0.748636\pi$
$132$	4.35081	+	4.35081i	0.378690	+	0.378690i
$133$	−0.269491	−	5.47014i	−0.0233679	−	0.474321i
$134$	17.6662	+	5.74011i	1.52613	+	0.495870i
$135$		0			0
$136$	1.01077	−	4.75530i	0.0866728	−	0.407764i
$137$	−2.38153	−	0.124811i	−0.203468	−	0.0106633i	−0.0496701	−	0.998766i	$-0.515817\pi$
$137$	−2.38153	−	0.124811i	−0.203468	−	0.0106633i	−0.153797	+	0.988102i	$0.549150\pi$
$138$	−3.29958	+	5.08091i	−0.280879	+	0.432516i
$139$	6.04915	+	18.6174i	0.513082	+	1.57910i	0.786745	+	0.617278i	$0.211765\pi$
$139$	6.04915	+	18.6174i	0.513082	+	1.57910i	−0.273663	+	0.961826i	$0.588235\pi$
$140$		0			0
$141$	−4.19607	+	12.9142i	−0.353373	+	1.08757i
$142$	−2.61974	−	3.23511i	−0.219843	−	0.271484i
$143$	−2.79385	−	10.4268i	−0.233633	−	0.871931i
$144$	−2.92211	−	6.56317i	−0.243509	−	0.546931i
$145$		0			0
$146$	8.35194	+	11.4955i	0.691211	+	0.951371i
$147$	13.7667	+	5.38379i	1.13546	+	0.444047i
$148$	1.24913	−	2.45155i	0.102678	−	0.201516i
$149$	−20.6257	+	11.9082i	−1.68972	+	0.975561i	−0.734995	+	0.678072i	$0.762816\pi$
$149$	−20.6257	+	11.9082i	−1.68972	+	0.975561i	−0.954725	+	0.297488i	$0.903851\pi$
$150$		0			0
$151$	4.22319	−	7.31478i	0.343678	−	0.595268i	−0.641434	−	0.767178i	$-0.721660\pi$
$151$	4.22319	−	7.31478i	0.343678	−	0.595268i	0.985113	+	0.171910i	$0.0549937\pi$
$152$	2.70372	−	0.141696i	0.219301	−	0.0114931i
$153$	0.848556	−	5.35757i	0.0686017	−	0.433134i
$154$	0.0342342	−	10.9243i	0.00275867	−	0.880306i
$155$		0			0
$156$	1.33470	−	12.6988i	0.106861	−	1.01672i
$157$	15.7673	−	4.22483i	1.25837	−	0.337178i	0.432803	−	0.901489i	$-0.357525\pi$
$157$	15.7673	−	4.22483i	1.25837	−	0.337178i	0.825562	+	0.564311i	$0.190858\pi$
$158$	19.5279	+	7.49607i	1.55356	+	0.596355i
$159$	8.37781	−	1.78076i	0.664403	−	0.141223i
$160$		0			0
$161$	4.10375	−	0.858846i	0.323421	−	0.0676865i
$162$	9.24507	+	18.1445i	0.726361	+	1.42556i
$163$	8.46854	+	5.49953i	0.663307	+	0.430757i	0.831897	−	0.554929i	$-0.187255\pi$
$163$	8.46854	+	5.49953i	0.663307	+	0.430757i	−0.168590	+	0.985686i	$0.553921\pi$
$164$	6.56857	+	1.39619i	0.512919	+	0.109024i
$165$		0			0
$166$	2.18737	+	10.2908i	0.169773	+	0.798719i
$167$	3.25176	+	20.5308i	0.251628	+	1.58872i	0.712773	+	0.701394i	$0.247439\pi$
$167$	3.25176	+	20.5308i	0.251628	+	1.58872i	−0.461145	+	0.887325i	$0.652561\pi$
$168$	−2.64013	+	6.81387i	−0.203690	+	0.525701i
$169$	−5.52581	+	7.60562i	−0.425062	+	0.585048i
$170$		0			0
$171$	3.00432	−	0.315767i	0.229746	−	0.0241473i
$172$	8.81252	+	7.13623i	0.671948	+	0.544133i
$173$	0.825101	+	15.7439i	0.0627313	+	1.19698i	0.830783	+	0.556596i	$0.187893\pi$
$173$	0.825101	+	15.7439i	0.0627313	+	1.19698i	−0.768052	+	0.640388i	$0.778774\pi$
$174$	−40.3211			−3.05673
$175$		0			0
$176$	11.2279			0.846336
$177$	−1.40411	−	26.7920i	−0.105539	−	2.01381i
$178$	9.40773	+	7.61823i	0.705139	+	0.571011i
$179$	−15.9352	+	1.67486i	−1.19105	+	0.125185i	−0.679243	−	0.733914i	$-0.737692\pi$
$179$	−15.9352	+	1.67486i	−1.19105	+	0.125185i	−0.511810	+	0.859098i	$0.671025\pi$
$180$		0			0
$181$	−5.00248	+	6.88532i	−0.371831	+	0.511782i	−0.953397	−	0.301717i	$-0.902440\pi$
$181$	−5.00248	+	6.88532i	−0.371831	+	0.511782i	0.581566	+	0.813499i	$0.302440\pi$
$182$	−17.6628	+	14.2116i	−1.30925	+	1.05344i
$183$	−0.321285	−	2.02851i	−0.0237501	−	0.149952i
$184$	0.430925	+	2.02734i	0.0317682	+	0.149458i
$185$		0			0
$186$	−12.7570	−	2.71159i	−0.935389	−	0.198823i
$187$	7.10976	+	4.61713i	0.519917	+	0.337638i
$188$	−3.72949	−	7.31954i	−0.272001	−	0.533832i
$189$	2.68559	−	8.17810i	0.195348	−	0.594869i
$190$		0			0
$191$	−11.8260	+	2.51369i	−0.855699	+	0.181884i	−0.614817	−	0.788670i	$-0.710770\pi$
$191$	−11.8260	+	2.51369i	−0.855699	+	0.181884i	−0.240882	+	0.970554i	$0.577437\pi$
$192$	3.06286	+	1.17572i	0.221043	+	0.0848505i
$193$	−8.48275	+	2.27295i	−0.610602	+	0.163610i	−0.550852	−	0.834603i	$-0.685697\pi$
$193$	−8.48275	+	2.27295i	−0.610602	+	0.163610i	−0.0597499	+	0.998213i	$0.519030\pi$
$194$	0.548359	−	5.21728i	0.0393699	−	0.374579i
$195$		0			0
$196$	−8.19234	+	3.58611i	−0.585167	+	0.256151i
$197$	1.54234	−	9.73798i	0.109887	−	0.693802i	−0.869820	−	0.493369i	$-0.835765\pi$
$197$	1.54234	−	9.73798i	0.109887	−	0.693802i	0.979707	−	0.200433i	$-0.0642348\pi$
$198$	6.01739	−	0.315358i	0.427637	−	0.0224115i
$199$	2.51334	−	4.35324i	0.178166	−	0.308593i	−0.763086	−	0.646297i	$-0.776317\pi$
$199$	2.51334	−	4.35324i	0.178166	−	0.308593i	0.941252	+	0.337704i	$0.109650\pi$
$200$		0			0
$201$	18.7642	−	10.8335i	1.32352	−	0.764136i
$202$	3.13112	−	6.14517i	0.220305	−	0.432373i
$203$	19.6694	+	19.7931i	1.38052	+	1.38920i
$204$	5.89418	+	8.11264i	0.412675	+	0.567998i
$205$		0			0
$206$	12.6156	+	28.3351i	0.878970	+	1.97420i
$207$	0.598540	+	2.23378i	0.0416014	+	0.155259i
$208$	−14.6633	−	18.1077i	−1.01672	−	1.25554i
$209$	−1.45892	+	4.49008i	−0.100915	+	0.310585i
$210$		0			0
$211$	5.17345	+	15.9222i	0.356155	+	1.09613i	0.955337	+	0.295519i	$0.0954927\pi$
$211$	5.17345	+	15.9222i	0.356155	+	1.09613i	−0.599182	+	0.800613i	$0.704507\pi$
$212$	−2.82213	+	4.34570i	−0.193825	+	0.298464i
$213$	−4.84899	−	0.254125i	−0.332247	−	0.0174123i
$214$	−2.40640	+	11.3212i	−0.164498	+	0.773902i
$215$		0			0
$216$	4.04697	+	1.31494i	0.275362	+	0.0894704i
$217$	4.89203	+	7.58500i	0.332093	+	0.514903i
$218$	11.8376	+	11.8376i	0.801746	+	0.801746i
$219$	16.4833	+	1.73246i	1.11384	+	0.117069i
$220$		0			0
$221$	−1.83891	−	17.4960i	−0.123698	−	1.17691i
$222$	−2.95067	−	7.68676i	−0.198036	−	0.515902i
$223$	9.48013	+	4.83037i	0.634836	+	0.323465i	0.741623	−	0.670817i	$-0.234056\pi$
$223$	9.48013	+	4.83037i	0.634836	+	0.323465i	−0.106787	+	0.994282i	$0.534056\pi$
$224$	−6.72830	−	15.2404i	−0.449553	−	1.01829i
$225$		0			0
$226$	−1.42893	−	2.47497i	−0.0950507	−	0.164633i
$227$	1.96131	+	3.02015i	0.130177	+	0.200455i	0.897748	−	0.440509i	$-0.145202\pi$
$227$	1.96131	+	3.02015i	0.130177	+	0.200455i	−0.767572	+	0.640963i	$0.778535\pi$
$228$	−3.51448	+	4.34002i	−0.232752	+	0.287425i
$229$	7.55461	+	3.36353i	0.499222	+	0.222268i	0.640871	−	0.767649i	$-0.278574\pi$
$229$	7.55461	+	3.36353i	0.499222	+	0.222268i	−0.141648	+	0.989917i	$0.545240\pi$
$230$		0			0
$231$	−9.44280	−	8.55607i	−0.621291	−	0.562948i
$232$	−9.75415	+	9.75415i	−0.640392	+	0.640392i
$233$	−3.05602	+	2.47471i	−0.200206	+	0.162124i	−0.724181	−	0.689610i	$-0.757782\pi$
$233$	−3.05602	+	2.47471i	−0.200206	+	0.162124i	0.523975	+	0.851734i	$0.324449\pi$
$234$	−8.36713	−	9.29264i	−0.546977	−	0.607479i
$235$		0			0
$236$	12.0619	+	10.8606i	0.785165	+	0.706966i
$237$	21.7393	−	11.0767i	1.41212	−	0.719512i
$238$	2.84023	−	17.5759i	0.184105	−	1.13927i
$239$	−13.0724	+	4.24747i	−0.845581	+	0.274746i	−0.699594	−	0.714541i	$-0.746636\pi$
$239$	−13.0724	+	4.24747i	−0.845581	+	0.274746i	−0.145987	+	0.989287i	$0.546636\pi$
$240$		0			0
$241$	7.90168	−	7.11470i	0.508992	−	0.458298i	−0.374174	−	0.927358i	$-0.622074\pi$
$241$	7.90168	−	7.11470i	0.508992	−	0.458298i	0.883166	+	0.469060i	$0.155407\pi$
$242$	3.76188	−	9.80004i	0.241823	−	0.629970i
$243$	13.5162	+	3.62166i	0.867065	+	0.232329i
$244$	1.00521	+	0.730330i	0.0643522	+	0.0467546i
$245$		0			0
$246$	16.2576	−	11.8118i	1.03655	−	0.753094i
$247$	9.14664	−	3.51107i	0.581987	−	0.223404i
$248$	−3.74204	+	2.43011i	−0.237620	+	0.154312i
$249$	10.6276	+	6.13585i	0.673497	+	0.388843i
$250$		0			0
$251$			7.76448i			0.490090i	0.969512	+	0.245045i	$0.0788027\pi$
$251$			7.76448i			0.490090i	−0.969512	+	0.245045i	$0.921197\pi$
$252$	−2.22561	−	4.40206i	−0.140200	−	0.277303i
$253$	−3.56970	−	0.565386i	−0.224425	−	0.0355455i
$254$	9.37662	−	21.0602i	0.588342	−	1.32144i
$255$		0			0
$256$	19.0148	−	8.46592i	1.18842	−	0.529120i
$257$	5.27589	−	19.6899i	0.329101	−	1.22822i	−0.581024	−	0.813887i	$-0.697348\pi$
$257$	5.27589	−	19.6899i	0.329101	−	1.22822i	0.910125	−	0.414335i	$-0.135986\pi$
$258$	33.5158	−	5.30838i	2.08660	−	0.330485i
$259$	−2.33393	+	5.19819i	−0.145023	+	0.323000i
$260$		0			0
$261$	−10.2989	+	11.4381i	−0.637485	+	0.707999i
$262$	1.35770	−	25.9065i	0.0838790	−	1.60051i
$263$	1.02582	−	19.5739i	0.0632549	−	1.20698i	−0.764025	−	0.645186i	$-0.776780\pi$
$263$	1.02582	−	19.5739i	0.0632549	−	1.20698i	0.827280	−	0.561789i	$-0.189887\pi$
$264$	4.21503	−	4.68127i	0.259417	−	0.288112i
$265$		0			0
$266$	9.86403	−	1.00551i	0.604803	−	0.0616517i
$267$	13.9464	−	2.20890i	0.853508	−	0.135182i
$268$	−3.39264	+	12.6615i	−0.207238	+	0.773424i
$269$	18.9392	−	8.43229i	1.15475	−	0.514126i	0.262169	−	0.965022i	$-0.415562\pi$
$269$	18.9392	−	8.43229i	1.15475	−	0.514126i	0.892576	+	0.450896i	$0.148896\pi$
$270$		0			0
$271$	−2.16651	+	4.86606i	−0.131606	+	0.295592i	−0.967314	−	0.253582i	$-0.918391\pi$
$271$	−2.16651	+	4.86606i	−0.131606	+	0.295592i	0.835708	+	0.549174i	$0.185058\pi$
$272$	18.0733	+	2.86253i	1.09586	+	0.173567i
$273$	−1.46669	+	26.4028i	−0.0887682	+	1.59797i
$274$		−	4.31743i		−	0.260826i
$275$		0			0
$276$	−3.70241	−	2.13758i	−0.222859	−	0.128667i
$277$	4.47434	−	2.90567i	0.268837	−	0.174585i	−0.403179	−	0.915121i	$-0.632095\pi$
$277$	4.47434	−	2.90567i	0.268837	−	0.174585i	0.672017	+	0.740536i	$0.265428\pi$
$278$	−33.0855	+	12.7004i	−1.98434	+	0.761716i
$279$	−4.02762	+	2.92624i	−0.241128	+	0.175189i
$280$		0			0
$281$	−19.3712	−	14.0740i	−1.15559	−	0.839582i	−0.166372	−	0.986063i	$-0.553205\pi$
$281$	−19.3712	−	14.0740i	−1.15559	−	0.839582i	−0.989214	+	0.146481i	$0.953205\pi$
$282$	−23.7453	−	6.36255i	−1.41401	−	0.378884i
$283$	−1.20959	+	3.15108i	−0.0719025	+	0.187312i	−0.964822	−	0.262904i	$-0.915320\pi$
$283$	−1.20959	+	3.15108i	−0.0719025	+	0.187312i	0.892920	+	0.450216i	$0.148653\pi$
$284$	2.18304	−	1.96562i	0.129540	−	0.116638i
$285$		0			0
$286$	18.5861	−	6.03898i	1.09902	−	0.357092i
$287$	−13.7290	−	2.21859i	−0.810398	−	0.130959i
$288$	8.18748	−	4.17173i	0.482452	−	0.245822i
$289$	−2.36618	−	2.13051i	−0.139187	−	0.125324i
$290$		0			0
$291$	−4.09451	−	4.54741i	−0.240024	−	0.266574i
$292$	−7.79246	+	6.31021i	−0.456019	+	0.369277i
$293$	−13.2445	+	13.2445i	−0.773751	+	0.773751i	−0.978760	−	0.205009i	$-0.934278\pi$
$293$	−13.2445	+	13.2445i	−0.773751	+	0.773751i	0.205009	+	0.978760i	$0.434278\pi$
$294$	−8.42907	+	25.3992i	−0.491593	+	1.48131i
$295$		0			0
$296$	−2.57332	−	1.14572i	−0.149571	−	0.0665934i
$297$	−4.66967	+	5.76656i	−0.270962	+	0.334610i
$298$	−23.4834	−	36.1613i	−1.36036	−	2.09477i
$299$	3.75011	+	6.49539i	0.216875	+	0.375638i
$300$		0			0
$301$	−18.9554	−	13.8629i	−1.09257	−	0.799044i
$302$	13.6247	+	6.94212i	0.784012	+	0.399474i
$303$	−2.88299	−	7.51044i	−0.165623	−	0.431464i
$304$	1.06521	+	10.1348i	0.0610942	+	0.581273i
$305$		0			0
$306$	9.76646	+	1.02650i	0.558311	+	0.0586809i
$307$	1.06555	+	1.06555i	0.0608142	+	0.0608142i	0.736860	−	0.676046i	$-0.236308\pi$
$307$	1.06555	+	1.06555i	0.0608142	+	0.0608142i	−0.676046	+	0.736860i	$0.736308\pi$
$308$	7.69968	−	0.379332i	0.438730	−	0.0216144i
$309$	34.4082	+	11.1799i	1.95741	+	0.636002i
$310$		0			0
$311$	1.04078	−	4.89649i	0.0590173	−	0.277655i	−0.938737	−	0.344634i	$-0.888003\pi$
$311$	1.04078	−	4.89649i	0.0590173	−	0.277655i	0.997754	+	0.0669796i	$0.0213363\pi$
$312$	−13.0544	−	0.684151i	−0.739059	−	0.0387324i
$313$	−18.4298	+	28.3794i	−1.04171	+	1.60410i	−0.275733	+	0.961234i	$0.588921\pi$
$313$	−18.4298	+	28.3794i	−1.04171	+	1.60410i	−0.765980	+	0.642864i	$0.777746\pi$
$314$	9.13208	+	28.1057i	0.515353	+	1.58609i
$315$		0			0
$316$	−4.56132	+	14.0383i	−0.256594	+	0.789715i
$317$	−8.47232	−	10.4624i	−0.475853	−	0.587629i	0.481538	−	0.876425i	$-0.340078\pi$
$317$	−8.47232	−	10.4624i	−0.475853	−	0.587629i	−0.957391	+	0.288796i	$0.906745\pi$
$318$	4.01326	+	14.9777i	0.225052	+	0.839907i
$319$	−9.78380	−	21.9748i	−0.547788	−	1.23035i
$320$		0			0
$321$	7.93539	+	10.9221i	0.442910	+	0.609613i
$322$	1.94155	+	7.33787i	0.108198	+	0.408923i
$323$	−3.49312	+	6.85563i	−0.194362	+	0.381458i
$324$	−12.4451	+	7.18516i	−0.691393	+	0.399176i
$325$		0			0
$326$	−9.14033	+	15.8315i	−0.506236	+	0.876826i
$327$	19.5005	−	1.02198i	1.07838	−	0.0565154i
$328$	1.07548	−	6.79032i	0.0593835	−	0.374933i
$329$	8.46015	+	14.7600i	0.466423	+	0.813747i
$330$		0			0
$331$	1.28920	−	12.2659i	0.0708609	−	0.674196i	−0.900218	−	0.435439i	$-0.856593\pi$
$331$	1.28920	−	12.2659i	0.0708609	−	0.674196i	0.971079	−	0.238758i	$-0.0767401\pi$
$332$	−7.17118	+	1.92151i	−0.393570	+	0.105457i
$333$	−2.93420	−	1.12634i	−0.160793	−	0.0617228i
$334$	−36.8099	+	7.82418i	−2.01415	+	0.428120i
$335$		0			0
$336$	−26.1320	−	8.58144i	−1.42562	−	0.468156i
$337$	−7.73487	−	15.1805i	−0.421345	−	0.826936i	−0.999936	−	0.0113182i	$-0.996397\pi$
$337$	−7.73487	−	15.1805i	−0.421345	−	0.826936i	0.578591	−	0.815618i	$-0.303603\pi$
$338$	−14.2739	−	9.26959i	−0.776398	−	0.504199i
$339$	−3.26065	−	0.693073i	−0.177094	−	0.0376426i
$340$		0			0
$341$	−1.61765	−	7.61046i	−0.0876008	−	0.412130i
$342$	0.855539	+	5.40166i	0.0462622	+	0.292088i
$343$	16.5800	−	8.25252i	0.895235	−	0.445594i
$344$	6.82371	−	9.39203i	0.367910	−	0.506384i
$345$		0			0
$346$	−28.3855	+	2.98343i	−1.52601	+	0.160390i
$347$	13.3971	+	10.8488i	0.719194	+	0.582392i	0.917494	−	0.397749i	$-0.130209\pi$
$347$	13.3971	+	10.8488i	0.719194	+	0.582392i	−0.198300	+	0.980141i	$0.563542\pi$
$348$	−1.48914	−	28.4145i	−0.0798263	−	1.52318i
$349$	−13.4664			−0.720839			−0.360419	−	0.932790i	$-0.617366\pi$
$349$	−13.4664			−0.720839			−0.360419	+	0.932790i	$0.617366\pi$
$350$		0			0
$351$	15.3984			0.821907
$352$	0.751597	+	14.3413i	0.0400602	+	0.764395i
$353$	6.92890	+	5.61091i	0.368788	+	0.298639i	0.795743	−	0.605634i	$-0.207080\pi$
$353$	6.92890	+	5.61091i	0.368788	+	0.298639i	−0.426955	+	0.904273i	$0.640414\pi$
$354$	48.3048	−	5.07704i	2.56737	−	0.269841i
$355$		0			0
$356$	−5.02116	+	6.91104i	−0.266121	+	0.366284i
$357$	−13.0185	−	16.1799i	−0.689013	−	0.856333i
$358$	−4.53785	−	28.6509i	−0.239833	−	1.51425i
$359$	−4.52910	−	21.3077i	−0.239037	−	1.12458i	−0.919895	−	0.392164i	$-0.871726\pi$
$359$	−4.52910	−	21.3077i	−0.239037	−	1.12458i	0.680859	−	0.732415i	$-0.261607\pi$
$360$		0			0
$361$	14.3934	+	3.05942i	0.757549	+	0.161022i
$362$	−12.9221	−	8.39170i	−0.679170	−	0.441058i
$363$	−5.55883	−	10.9098i	−0.291763	−	0.572617i
$364$	−10.6673	−	11.9222i	−0.559120	−	0.624893i
$365$		0			0
$366$	3.63695	−	0.773057i	0.190106	−	0.0404083i
$367$	−11.0923	−	4.25793i	−0.579012	−	0.222262i	0.0511955	−	0.998689i	$-0.483697\pi$
$367$	−11.0923	−	4.25793i	−0.579012	−	0.222262i	−0.630207	+	0.776427i	$0.717030\pi$
$368$	−7.53547	+	2.01912i	−0.392814	+	0.105254i
$369$	0.801825	−	7.62886i	0.0417414	−	0.397142i
$370$		0			0
$371$	5.39459	−	9.27645i	0.280073	−	0.481609i
$372$	1.43973	−	9.09008i	0.0746464	−	0.471299i
$373$	19.9123	−	1.04356i	1.03102	−	0.0540334i	0.470686	−	0.882301i	$-0.344007\pi$
$373$	19.9123	−	1.04356i	1.03102	−	0.0540334i	0.560333	+	0.828267i	$0.310673\pi$
$374$	−7.67376	+	13.2913i	−0.396801	+	0.687279i
$375$		0			0
$376$	−7.28346	+	4.20511i	−0.375616	+	0.216862i
$377$	−22.6623	+	44.4772i	−1.16717	+	2.29069i
$378$	15.0398	+	4.08046i	0.773564	+	0.209876i
$379$	−11.9563	−	16.4564i	−0.614154	−	0.845311i	0.382757	−	0.923849i	$-0.374975\pi$
$379$	−11.9563	−	16.4564i	−0.614154	−	0.845311i	−0.996911	+	0.0785382i	$0.974975\pi$
$380$		0			0
$381$	−10.9372	−	24.5654i	−0.560331	−	1.25852i
$382$	−5.66505	−	21.1423i	−0.289849	−	1.08173i
$383$	6.92646	+	8.55346i	0.353925	+	0.437062i	0.922751	−	0.385397i	$-0.125935\pi$
$383$	6.92646	+	8.55346i	0.353925	+	0.437062i	−0.568826	+	0.822458i	$0.692602\pi$
$384$	6.38248	−	19.6432i	0.325704	−	1.00242i
$385$		0			0
$386$	−4.91303	−	15.1208i	−0.250067	−	0.769627i
$387$	7.05480	−	10.8634i	0.358616	−	0.552220i
$388$	3.69690	+	0.193746i	0.187682	+	0.00983598i
$389$	1.22745	−	5.77469i	0.0622341	−	0.292788i	−0.936013	−	0.351964i	$-0.885514\pi$
$389$	1.22745	−	5.77469i	0.0622341	−	0.292788i	0.998248	+	0.0591758i	$0.0188472\pi$
$390$		0			0
$391$	−5.60193	−	1.82018i	−0.283302	−	0.0920503i
$392$	4.10528	+	8.18347i	0.207348	+	0.413328i
$393$	−21.3968	−	21.3968i	−1.07933	−	1.07933i
$394$	17.7516	+	1.86577i	0.894313	+	0.0939961i
$395$		0			0
$396$	0.444469	+	4.22884i	0.0223354	+	0.212507i
$397$	6.10596	+	15.9066i	0.306450	+	0.798328i	0.997168	+	0.0752046i	$0.0239610\pi$
$397$	6.10596	+	15.9066i	0.306450	+	0.798328i	−0.690719	+	0.723124i	$0.742706\pi$
$398$	8.10845	+	4.13146i	0.406440	+	0.207091i
$399$	6.82725	−	9.33524i	0.341790	−	0.467347i
$400$		0			0
$401$	7.60244	+	13.1678i	0.379648	+	0.657569i	0.991011	−	0.133781i	$-0.0427119\pi$
$401$	7.60244	+	13.1678i	0.379648	+	0.657569i	−0.611363	+	0.791350i	$0.709379\pi$
$402$	21.3640	+	32.8976i	1.06554	+	1.64078i
$403$	−10.1611	+	12.5479i	−0.506160	+	0.625056i
$404$	4.44618	+	1.97956i	0.221205	+	0.0984870i
$405$		0			0
$406$	−33.9206	+	37.4361i	−1.68345	+	1.85792i
$407$	3.47327	−	3.47327i	0.172164	−	0.172164i
$408$	7.97832	−	6.46072i	0.394986	−	0.319853i
$409$	−7.61757	−	8.46017i	−0.376665	−	0.418328i	0.524770	−	0.851244i	$-0.324151\pi$
$409$	−7.61757	−	8.46017i	−0.376665	−	0.418328i	−0.901434	+	0.432916i	$0.857485\pi$
$410$		0			0
$411$	−3.74248	−	3.36975i	−0.184603	−	0.166217i
$412$	−19.5020	+	9.93675i	−0.960793	+	0.489549i
$413$	−26.0562	−	21.2355i	−1.28214	−	1.04493i
$414$	−3.98179	+	1.29376i	−0.195694	+	0.0635849i
$415$		0			0
$416$	22.1473	−	19.9415i	1.08586	−	0.977712i
$417$	−14.8141	+	38.5921i	−0.725451	+	1.88987i
$418$	−8.25594	−	2.21217i	−0.403811	−	0.108201i
$419$	11.5358	+	8.38127i	0.563562	+	0.409452i	0.832761	−	0.553633i	$-0.186759\pi$
$419$	11.5358	+	8.38127i	0.563562	+	0.409452i	−0.269199	+	0.963085i	$0.586759\pi$
$420$		0			0
$421$	−7.49291	+	5.44392i	−0.365182	+	0.265320i	−0.755210	−	0.655483i	$-0.772465\pi$
$421$	−7.49291	+	5.44392i	−0.365182	+	0.265320i	0.390028	+	0.920803i	$0.372465\pi$
$422$	−28.2960	+	10.8618i	−1.37743	+	0.528744i
$423$	−7.86997	+	5.11082i	−0.382651	+	0.248496i
$424$	4.59413	+	2.65242i	0.223111	+	0.128813i
$425$		0			0
$426$		−	8.79066i		−	0.425909i
$427$	−2.15365	−	1.40821i	−0.104223	−	0.0681483i
$428$	−8.06700	−	1.27769i	−0.389933	−	0.0617593i
$429$	9.27161	−	20.8244i	0.447638	−	1.00541i
$430$		0			0
$431$	7.32382	−	3.26078i	0.352776	−	0.157066i	−0.222695	−	0.974888i	$-0.571485\pi$
$431$	7.32382	−	3.26078i	0.352776	−	0.157066i	0.575471	+	0.817822i	$0.304819\pi$
$432$	−4.14538	+	15.4708i	−0.199445	+	0.744339i
$433$	−26.4096	+	4.18286i	−1.26916	+	0.201016i	−0.754456	−	0.656351i	$-0.772099\pi$
$433$	−26.4096	+	4.18286i	−1.26916	+	0.201016i	−0.514707	+	0.857366i	$0.672099\pi$
$434$	−13.2496	+	9.56307i	−0.635999	+	0.459042i
$435$		0			0
$436$	−7.90486	+	8.77923i	−0.378574	+	0.420449i
$437$	0.171678	−	3.27582i	0.00821249	−	0.156704i
$438$	−1.57038	+	29.9646i	−0.0750356	+	1.43176i
$439$	−11.7293	+	13.0267i	−0.559809	+	0.621731i	−0.954906	−	0.296909i	$-0.904044\pi$
$439$	−11.7293	+	13.0267i	−0.559809	+	0.621731i	0.395097	+	0.918639i	$0.370711\pi$
$440$		0			0
$441$	5.05215	+	8.87863i	0.240578	+	0.422792i
$442$	31.4572	−	4.98233i	1.49627	−	0.236985i
$443$	−3.98412	+	14.8689i	−0.189291	+	0.706445i	0.804380	+	0.594116i	$0.202498\pi$
$443$	−3.98412	+	14.8689i	−0.189291	+	0.706445i	−0.993671	+	0.112329i	$0.964169\pi$
$444$	5.30793	−	2.36324i	0.251903	−	0.112155i
$445$		0			0
$446$	−7.83468	+	17.5970i	−0.370983	+	0.833241i
$447$	−49.6744	−	7.86765i	−2.34952	−	0.372127i
$448$	3.66827	−	1.85462i	0.173310	−	0.0876226i
$449$		−	1.46011i		−	0.0689067i	−0.999406	−	0.0344533i	$-0.989031\pi$
$449$		−	1.46011i		−	0.0689067i	0.999406	−	0.0344533i	$-0.0109690\pi$
$450$		0			0
$451$	10.3822	+	5.99419i	0.488881	+	0.282255i
$452$	1.69135	−	1.09838i	0.0795546	−	0.0516633i
$453$	16.6517	−	6.39198i	0.782364	−	0.300321i
$454$	−5.27436	+	3.83205i	−0.247538	+	0.179847i
$455$		0			0
$456$	4.62542	+	3.36056i	0.216605	+	0.157373i
$457$	−38.5827	−	10.3382i	−1.80482	−	0.483600i	−0.810106	−	0.586283i	$-0.800591\pi$
$457$	−38.5827	−	10.3382i	−1.80482	−	0.483600i	−0.994714	+	0.102683i	$0.967257\pi$
$458$	−5.36519	+	13.9768i	−0.250699	+	0.653093i
$459$	−8.98683	+	8.09178i	−0.419469	+	0.377692i
$460$		0			0
$461$	−16.1060	+	5.23314i	−0.750130	+	0.243732i	−0.659037	−	0.752111i	$-0.729036\pi$
$461$	−16.1060	+	5.23314i	−0.750130	+	0.243732i	−0.0910926	+	0.995842i	$0.529036\pi$
$462$	14.5740	−	17.8825i	0.678043	−	0.831969i
$463$	11.4745	−	5.84654i	0.533265	−	0.271712i	−0.166554	−	0.986032i	$-0.553264\pi$
$463$	11.4745	−	5.84654i	0.533265	−	0.271712i	0.699819	+	0.714320i	$0.253264\pi$
$464$	−38.5854	−	34.7424i	−1.79128	−	1.61288i
$465$		0			0
$466$	−4.76364	−	5.29055i	−0.220671	−	0.245080i
$467$	5.10565	−	4.13448i	0.236261	−	0.191321i	−0.503877	−	0.863776i	$-0.668093\pi$
$467$	5.10565	−	4.13448i	0.236261	−	0.191321i	0.740138	+	0.672455i	$0.234760\pi$
$468$	6.23956	−	6.23956i	0.288424	−	0.288424i
$469$	5.72724	−	26.5354i	0.264459	−	1.22529i
$470$		0			0
$471$	31.4904	+	14.0204i	1.45100	+	0.646027i
$472$	10.4573	−	12.9137i	0.481336	−	0.594401i
$473$	11.0256	+	16.9779i	0.506955	+	0.780643i
$474$	22.0856	+	38.2534i	1.01443	+	1.75704i
$475$		0			0
$476$	12.4907	+	1.35242i	0.572511	+	0.0619879i
$477$	5.27386	+	2.68717i	0.241473	+	0.123037i
$478$	−8.91767	−	23.2313i	−0.407885	−	1.06258i
$479$	1.06015	+	10.0866i	0.0484393	+	0.460869i	0.991677	+	0.128751i	$0.0410967\pi$
$479$	1.06015	+	10.0866i	0.0484393	+	0.460869i	−0.943238	+	0.332118i	$0.892237\pi$
$480$		0			0
$481$	−10.1375	−	1.06549i	−0.462230	−	0.0485823i
$482$	13.6115	+	13.6115i	0.619986	+	0.619986i
$483$	7.87606	+	4.04419i	0.358373	+	0.184017i
$484$	7.04508	+	2.28908i	0.320231	+	0.104049i
$485$		0			0
$486$	−5.26702	+	24.7794i	−0.238917	+	1.12401i
$487$	−37.9617	−	1.98949i	−1.72021	−	0.0901523i	−0.833511	−	0.552502i	$-0.813673\pi$
$487$	−37.9617	−	1.98949i	−1.72021	−	0.0901523i	−0.886698	+	0.462350i	$0.847006\pi$
$488$	0.692809	−	1.06683i	0.0313620	−	0.0482932i
$489$	6.58923	+	20.2796i	0.297975	+	0.917074i
$490$		0			0
$491$	11.9197	−	36.6850i	0.537927	−	1.65557i	−0.199311	−	0.979936i	$-0.563870\pi$
$491$	11.9197	−	36.6850i	0.537927	−	1.65557i	0.737238	−	0.675633i	$-0.236130\pi$
$492$	8.92429	+	11.0206i	0.402338	+	0.496846i
$493$	−10.1463	−	37.8667i	−0.456968	−	1.70543i
$494$	7.21436	+	16.2037i	0.324589	+	0.729040i
$495$		0			0
$496$	−9.87143	−	13.5869i	−0.443240	−	0.610068i
$497$	−4.31521	+	4.28825i	−0.193564	+	0.192354i
$498$	−10.0862	+	19.7952i	−0.451972	+	0.887044i
$499$	−2.65771	+	1.53443i	−0.118976	+	0.0686906i	−0.558307	−	0.829635i	$-0.688549\pi$
$499$	−2.65771	+	1.53443i	−0.118976	+	0.0686906i	0.439331	+	0.898325i	$0.355215\pi$
$500$		0			0
$501$	−21.9478	+	38.0147i	−0.980555	+	1.69837i
$502$	−14.0376	+	0.735677i	−0.626527	+	0.0328349i
$503$	−4.81016	+	30.3701i	−0.214474	+	1.35414i	0.611864	+	0.790963i	$0.290420\pi$
$503$	−4.81016	+	30.3701i	−0.214474	+	1.35414i	−0.826338	+	0.563174i	$0.809580\pi$
$504$	−4.38129	+	2.51126i	−0.195158	+	0.111861i
$505$		0			0
$506$	0.683945	−	6.50731i	0.0304051	−	0.289285i
$507$	−19.1759	+	5.13817i	−0.851632	+	0.228194i
$508$	15.1876	+	5.82996i	0.673839	+	0.258663i
$509$	−11.1394	+	2.36776i	−0.493747	+	0.104949i	−0.448054	−	0.894006i	$-0.647883\pi$
$509$	−11.1394	+	2.36776i	−0.493747	+	0.104949i	−0.0456925	+	0.998956i	$0.514549\pi$
$510$		0			0
$511$	15.4753	−	13.8464i	0.684585	−	0.612530i
$512$	8.22662	+	16.1456i	0.363569	+	0.713543i
$513$	−5.64818	−	3.66797i	−0.249373	−	0.161945i
$514$	36.0976	+	7.67278i	1.59220	+	0.338432i
$515$		0			0
$516$	4.97865	+	23.4227i	0.219173	+	1.03113i
$517$	−2.29419	−	14.4849i	−0.100898	−	0.637047i
$518$	−9.61905	−	3.72703i	−0.422637	−	0.163756i
$519$	−19.5687	+	26.9339i	−0.858969	+	1.18227i
$520$		0			0
$521$	−34.8820	+	3.66624i	−1.52821	+	0.160621i	−0.831009	−	0.556259i	$-0.812236\pi$
$521$	−34.8820	+	3.66624i	−1.52821	+	0.160621i	−0.697197	+	0.716880i	$0.745570\pi$
$522$	−21.6549	−	17.5358i	−0.947810	−	0.767521i
$523$	−1.09564	−	20.9061i	−0.0479091	−	0.914160i	−0.911839	−	0.410548i	$-0.865338\pi$
$523$	−1.09564	−	20.9061i	−0.0479091	−	0.914160i	0.863930	−	0.503612i	$-0.167996\pi$
$524$	18.3066			0.799726
$525$		0			0
$526$	35.4852			1.54723
$527$	−0.663629	−	12.6628i	−0.0289082	−	0.551600i
$528$	18.4263	+	14.9213i	0.801900	+	0.649366i
$529$	−20.3766	+	2.14166i	−0.885938	+	0.0931158i
$530$		0			0
$531$	10.8979	−	14.9996i	0.472927	−	0.650928i
$532$	1.07289	+	6.91410i	0.0465155	+	0.299764i
$533$	−3.89184	−	24.5721i	−0.168574	−	1.06434i
$534$	5.31492	+	25.0047i	0.229999	+	1.08206i
$535$		0			0
$536$	13.1265	+	2.79013i	0.566980	+	0.120515i
$537$	−28.3772	−	18.4284i	−1.22457	−	0.795244i
$538$	17.0394	+	33.4416i	0.734619	+	1.44177i
$539$	−15.8877	+	1.56926i	−0.684333	+	0.0675927i
$540$		0			0
$541$	−14.0929	+	2.99554i	−0.605901	+	0.128788i	−0.500639	−	0.865656i	$-0.666901\pi$
$541$	−14.0929	+	2.99554i	−0.605901	+	0.128788i	−0.105262	+	0.994445i	$0.533568\pi$
$542$	−9.00272	−	3.45582i	−0.386700	−	0.148440i
$543$	−17.3598	+	4.65155i	−0.744982	+	0.199617i
$544$	−2.44646	+	23.2765i	−0.104891	+	0.997972i
$545$		0			0
$546$	−47.8731	−	0.150023i	−2.04878	−	0.00642038i
$547$	6.04502	−	38.1667i	0.258466	−	1.63189i	−0.427328	−	0.904096i	$-0.640545\pi$
$547$	6.04502	−	38.1667i	0.258466	−	1.63189i	0.685795	−	0.727795i	$-0.259455\pi$
$548$	3.04252	−	0.159452i	0.129970	−	0.00681144i
$549$	0.709658	−	1.22916i	0.0302875	−	0.0524595i
$550$		0			0
$551$	18.9073	−	10.9161i	0.805476	−	0.465042i
$552$	−1.98703	+	3.89977i	−0.0845736	+	0.165985i
$553$	8.00429	−	29.5023i	0.340377	−	1.25456i
$554$	5.67716	+	7.81394i	0.241199	+	0.331983i
$555$		0			0
$556$	−10.1719	−	22.8465i	−0.431386	−	0.968908i
$557$	6.74079	+	25.1570i	0.285616	+	1.06593i	0.948388	+	0.317113i	$0.102713\pi$
$557$	6.74079	+	25.1570i	0.285616	+	1.06593i	−0.662772	+	0.748822i	$0.730620\pi$
$558$	−5.67202	−	7.00436i	−0.240116	−	0.296518i
$559$	12.9818	−	39.9540i	0.549073	−	1.68987i
$560$		0			0
$561$	5.53199	+	17.0257i	0.233561	+	0.718826i
$562$	23.6092	−	36.3550i	0.995894	−	1.53354i
$563$	−5.12594	−	0.268639i	−0.216032	−	0.0113218i	−0.0559873	−	0.998431i	$-0.517831\pi$
$563$	−5.12594	−	0.268639i	−0.216032	−	0.0113218i	−0.160045	+	0.987110i	$0.551164\pi$
$564$	3.60676	−	16.9685i	0.151872	−	0.714501i
$565$		0			0
$566$	−5.81151	−	1.88827i	−0.244276	−	0.0793701i
$567$	25.0098	−	16.1303i	1.05031	−	0.677411i
$568$	−2.12656	−	2.12656i	−0.0892287	−	0.0892287i
$569$	−8.90580	−	0.936038i	−0.373351	−	0.0392407i	−0.0840048	−	0.996465i	$-0.526771\pi$
$569$	−8.90580	−	0.936038i	−0.373351	−	0.0392407i	−0.289346	+	0.957225i	$0.593438\pi$
$570$		0			0
$571$	2.13250	+	20.2894i	0.0892423	+	0.849084i	0.943975	+	0.330016i	$0.107054\pi$
$571$	2.13250	+	20.2894i	0.0892423	+	0.849084i	−0.854733	+	0.519068i	$0.826279\pi$
$572$	4.94212	+	12.8747i	0.206641	+	0.538317i
$573$	−22.7483	−	11.5909i	−0.950325	−	0.484215i
$574$	2.71022	−	25.0312i	0.113122	−	1.04478i
$575$		0			0
$576$	1.13362	+	1.96349i	0.0472342	+	0.0818120i
$577$	−17.7297	−	27.3014i	−0.738097	−	1.13657i	−0.985831	−	0.167742i	$-0.946352\pi$
$577$	−17.7297	−	27.3014i	−0.738097	−	1.13657i	0.247733	−	0.968828i	$-0.420314\pi$
$578$	3.62760	−	4.47972i	0.150888	−	0.186332i
$579$	−16.9418	−	7.54295i	−0.704075	−	0.313474i
$580$		0			0
$581$	14.6374	−	4.70532i	0.607262	−	0.195210i
$582$	7.83340	−	7.83340i	0.324705	−	0.324705i
$583$	−7.18895	+	5.82150i	−0.297736	+	0.241102i
$584$	6.86890	+	7.62869i	0.284237	+	0.315677i
$585$		0			0
$586$	−25.1999	−	22.6901i	−1.04100	−	0.937318i
$587$	37.0069	−	18.8559i	1.52744	−	0.778268i	0.529877	−	0.848074i	$-0.322238\pi$
$587$	37.0069	−	18.8559i	1.52744	−	0.778268i	0.997561	+	0.0698062i	$0.0222381\pi$
$588$	−18.2103	−	5.00197i	−0.750979	−	0.206278i
$589$	6.71609	−	2.18219i	0.276732	−	0.0899155i
$590$		0			0
$591$	15.4724	−	13.9314i	0.636449	−	0.573062i
$592$	3.79960	−	9.89829i	0.156162	−	0.406817i
$593$	16.3610	+	4.38392i	0.671866	+	0.180026i	0.578595	−	0.815615i	$-0.303601\pi$
$593$	16.3610	+	4.38392i	0.671866	+	0.180026i	0.0932706	+	0.995641i	$0.470268\pi$
$594$	−10.8679	−	7.89600i	−0.445916	−	0.323977i
$595$		0			0
$596$	24.6157	−	17.8844i	1.00830	−	0.732573i
$597$	9.90990	−	3.80405i	0.405585	−	0.155690i
$598$	−11.3878	+	7.39533i	−0.465682	+	0.302418i
$599$	2.39394	+	1.38214i	0.0978138	+	0.0564728i	0.548109	−	0.836407i	$-0.315348\pi$
$599$	2.39394	+	1.38214i	0.0978138	+	0.0564728i	−0.450295	+	0.892880i	$0.648681\pi$
$600$		0			0
$601$			35.9435i			1.46616i	0.680140	+	0.733082i	$0.261919\pi$
$601$			35.9435i			1.46616i	−0.680140	+	0.733082i	$0.738081\pi$
$602$	23.2670	−	35.5834i	0.948292	−	1.45027i
$603$	14.7890	+	2.34235i	0.602256	+	0.0953880i
$604$	−4.38896	+	9.85777i	−0.178584	+	0.401107i
$605$		0			0
$606$	13.3051	−	5.92382i	0.540483	−	0.240639i
$607$	−3.86472	+	14.4233i	−0.156864	+	0.585425i	0.842074	+	0.539361i	$0.181334\pi$
$607$	−3.86472	+	14.4233i	−0.156864	+	0.585425i	−0.998939	+	0.0460635i	$0.985332\pi$
$608$	−12.8738	+	2.03902i	−0.522103	+	0.0826930i
$609$	5.97576	+	58.6222i	0.242150	+	2.37549i
$610$		0			0
$611$	−20.3643	+	22.6169i	−0.823852	+	0.914980i
$612$	−0.362682	+	6.92039i	−0.0146606	+	0.279740i
$613$	−2.52574	+	48.1939i	−0.102014	+	1.94654i	0.172625	+	0.984988i	$0.444775\pi$
$613$	−2.52574	+	48.1939i	−0.102014	+	1.94654i	−0.274639	+	0.961548i	$0.588558\pi$
$614$	−1.82547	+	2.02739i	−0.0736700	+	0.0818189i
$615$		0			0
$616$	−0.800369	−	7.85161i	−0.0322478	−	0.316350i
$617$	25.3234	−	4.01084i	1.01948	−	0.161470i	0.375750	−	0.926721i	$-0.377385\pi$
$617$	25.3234	−	4.01084i	1.01948	−	0.161470i	0.643732	+	0.765251i	$0.277385\pi$
$618$	−16.9522	+	63.2665i	−0.681917	+	2.54495i
$619$	1.31576	−	0.585813i	0.0528847	−	0.0235458i	−0.380124	−	0.924936i	$-0.624119\pi$
$619$	1.31576	−	0.585813i	0.0528847	−	0.0235458i	0.433009	+	0.901390i	$0.357452\pi$
$620$		0			0
$621$	2.09698	−	4.70990i	0.0841491	−	0.189002i
$622$	8.95108	+	1.41771i	0.358906	+	0.0568451i
$623$	9.68175	−	14.8068i	0.387891	−	0.593222i
$624$		−	49.2036i		−	1.96972i
$625$		0			0
$626$	−53.0539	−	30.6307i	−2.12046	−	1.22425i
$627$	−8.36131	+	5.42990i	−0.333919	+	0.216849i
$628$	−19.4689	+	7.47343i	−0.776896	+	0.298222i
$629$	6.47635	−	4.70534i	0.258229	−	0.187614i
$630$		0			0
$631$	−9.94266	−	7.22377i	−0.395811	−	0.287574i	0.372021	−	0.928224i	$-0.378665\pi$
$631$	−9.94266	−	7.22377i	−0.395811	−	0.287574i	−0.767833	+	0.640650i	$0.778665\pi$
$632$	14.5967	+	3.91119i	0.580627	+	0.155579i
$633$	−12.6696	+	33.0054i	−0.503571	+	1.31185i
$634$	18.1125	−	16.3086i	0.719340	−	0.647696i
$635$		0			0
$636$	−10.4066	+	3.38132i	−0.412650	+	0.134078i
$637$	23.2797	+	23.5734i	0.922377	+	0.934012i
$638$	38.8016	−	19.7704i	1.53617	−	0.782718i
$639$	−2.49368	−	2.24532i	−0.0986487	−	0.0888236i
$640$		0			0
$641$	−12.3273	−	13.6908i	−0.486899	−	0.540756i	0.448764	−	0.893650i	$-0.351864\pi$
$641$	−12.3273	−	13.6908i	−0.486899	−	0.540756i	−0.935663	+	0.352894i	$0.885198\pi$
$642$	−18.9944	+	15.3814i	−0.749651	+	0.607055i
$643$	6.68684	−	6.68684i	0.263703	−	0.263703i	−0.562853	−	0.826557i	$-0.690296\pi$
$643$	6.68684	−	6.68684i	0.263703	−	0.263703i	0.826557	+	0.562853i	$0.190296\pi$
$644$	−5.09933	+	1.63922i	−0.200942	+	0.0645945i
$645$		0			0
$646$	−12.7254	−	5.66571i	−0.500674	−	0.222915i
$647$	−12.0946	+	14.9356i	−0.475488	+	0.587178i	−0.957300	−	0.289096i	$-0.906645\pi$
$647$	−12.0946	+	14.9356i	−0.475488	+	0.587178i	0.481812	+	0.876274i	$0.339979\pi$
$648$	8.01272	+	12.3385i	0.314769	+	0.484702i
$649$	14.4880	+	25.0939i	0.568703	+	0.985022i
$650$		0			0
$651$	−2.05168	+	18.9491i	−0.0804119	+	0.742673i
$652$	−11.4941	−	5.85655i	−0.450145	−	0.229360i
$653$	−10.9430	−	28.5075i	−0.428233	−	1.11558i	−0.962742	−	0.270421i	$-0.912837\pi$
$653$	−10.9430	−	28.5075i	−0.428233	−	1.11558i	0.534510	−	0.845162i	$-0.320496\pi$
$654$	3.69530	+	35.1584i	0.144498	+	1.37480i
$655$		0			0
$656$	25.7353	+	2.70489i	1.00480	+	0.105608i
$657$	8.09908	+	8.09908i	0.315975	+	0.315975i
$658$	−25.8834	+	16.6938i	−1.00904	+	0.650791i
$659$	38.5495	+	12.5255i	1.50168	+	0.487924i	0.940506	−	0.339777i	$-0.110352\pi$
$659$	38.5495	+	12.5255i	1.50168	+	0.487924i	0.561169	+	0.827701i	$0.310352\pi$
$660$		0			0
$661$	−3.84813	+	18.1040i	−0.149675	+	0.704165i	0.837747	+	0.546059i	$0.183872\pi$
$661$	−3.84813	+	18.1040i	−0.149675	+	0.704165i	−0.987422	+	0.158107i	$0.949461\pi$
$662$	22.2980	+	1.16859i	0.866635	+	0.0454184i
$663$	20.2334	−	31.1568i	0.785801	−	1.21003i
$664$	2.34873	+	7.22866i	0.0911485	+	0.280526i
$665$		0			0
$666$	1.75831	−	5.41152i	0.0681331	−	0.209692i
$667$	10.5180	+	12.9887i	0.407259	+	0.502924i
$668$	−6.87321	−	25.6512i	−0.265933	−	0.992474i
$669$	9.13865	+	20.5257i	0.353321	+	0.793571i
$670$		0			0
$671$	1.30381	+	1.79454i	0.0503329	+	0.0692773i
$672$	9.21172	−	33.9527i	0.355350	−	1.30975i
$673$	2.55105	−	5.00671i	0.0983356	−	0.192994i	−0.836598	−	0.547817i	$-0.815459\pi$
$673$	2.55105	−	5.00671i	0.0983356	−	0.192994i	0.934934	+	0.354823i	$0.115459\pi$
$674$	26.7123	−	15.4224i	1.02892	−	0.594047i
$675$		0			0
$676$	6.00516	−	10.4012i	0.230968	−	0.400048i
$677$	24.7924	−	1.29931i	0.952847	−	0.0499366i	0.430428	−	0.902625i	$-0.358363\pi$
$677$	24.7924	−	1.29931i	0.952847	−	0.0499366i	0.522420	+	0.852688i	$0.325029\pi$
$678$	0.944077	−	5.96067i	0.0362571	−	0.228918i
$679$	−7.66659	−	0.0240253i	−0.294217	−	0.000922005i
$680$		0			0
$681$	−0.794891	+	7.56288i	−0.0304603	+	0.289810i
$682$	13.6058	−	3.64567i	0.520994	−	0.139600i
$683$	−35.6764	−	13.6949i	−1.36512	−	0.524020i	−0.438063	−	0.898944i	$-0.644335\pi$
$683$	−35.6764	−	13.6949i	−1.36512	−	0.524020i	−0.927055	+	0.374925i	$0.877669\pi$
$684$	−3.77498	+	0.802397i	−0.144340	+	0.0306804i
$685$		0			0
$686$	16.4908	+	29.1934i	0.629623	+	1.11461i
$687$	7.92800	+	15.5596i	0.302472	+	0.593635i
$688$	36.6469	+	23.7988i	1.39715	+	0.907320i
$689$	18.7771	+	3.99120i	0.715352	+	0.152053i
$690$		0			0
$691$	−4.28899	−	20.1781i	−0.163161	−	0.767612i	−0.981284	−	0.192568i	$-0.938318\pi$
$691$	−4.28899	−	20.1781i	−0.163161	−	0.767612i	0.818123	−	0.575044i	$-0.195015\pi$
$692$	−3.15078	−	19.8932i	−0.119775	−	0.756226i
$693$	−1.35030	−	8.70185i	−0.0512936	−	0.330556i
$694$	−18.3443	+	25.2488i	−0.696341	+	0.958431i
$695$		0			0
$696$	−28.9704	+	3.04491i	−1.09812	+	0.115417i
$697$	15.1839	+	12.2956i	0.575129	+	0.465731i
$698$	−1.27593	−	24.3461i	−0.0482945	−	0.921515i
$699$	−8.30402			−0.314087
$700$		0			0
$701$	−16.8050			−0.634717			−0.317359	−	0.948306i	$-0.602796\pi$
$701$	−16.8050			−0.634717			−0.317359	+	0.948306i	$0.602796\pi$
$702$	1.45899	+	27.8391i	0.0550659	+	1.05072i
$703$	3.46465	+	2.80562i	0.130672	+	0.105816i
$704$	−3.52393	+	0.370380i	−0.132813	+	0.0139592i
$705$		0			0
$706$	−9.48757	+	13.0585i	−0.357069	+	0.491464i
$707$	−9.39841	−	3.64154i	−0.353464	−	0.136954i
$708$	5.36181	+	33.8531i	0.201509	+	1.27228i
$709$	−3.71391	−	17.4726i	−0.139479	−	0.656197i	−0.991219	−	0.132232i	$-0.957786\pi$
$709$	−3.71391	−	17.4726i	−0.139479	−	0.656197i	0.851740	−	0.523965i	$-0.175548\pi$
$710$		0			0
$711$	16.4927	+	3.50563i	0.618524	+	0.131471i
$712$	7.33469	+	4.76320i	0.274879	+	0.178508i
$713$	2.45426	+	4.81676i	0.0919129	+	0.180389i
$714$	28.0185	−	25.0694i	1.04857	−	0.938201i
$715$		0			0
$716$	20.0228	−	4.25599i	0.748289	−	0.159054i
$717$	−27.0978	−	10.4019i	−1.01199	−	0.388466i
$718$	38.0935	−	10.2071i	1.42164	−	0.380927i
$719$	4.03131	−	38.3553i	0.150342	−	1.43041i	−0.615882	−	0.787839i	$-0.711200\pi$
$719$	4.03131	−	38.3553i	0.150342	−	1.43041i	0.766224	−	0.642574i	$-0.222133\pi$
$720$		0			0
$721$	39.3262	−	22.5410i	1.46459	−	0.839470i
$722$	−4.16742	+	26.3121i	−0.155095	+	0.979233i
$723$	22.4226	−	1.17512i	0.833905	−	0.0437031i
$724$	5.43644	−	9.41619i	0.202044	−	0.349950i
$725$		0			0
$726$	19.1974	−	11.0836i	0.712482	−	0.411352i
$727$	−12.2509	+	24.0437i	−0.454359	+	0.891730i	0.544246	+	0.838926i	$0.316816\pi$
$727$	−12.2509	+	24.0437i	−0.454359	+	0.891730i	−0.998605	+	0.0528040i	$0.983184\pi$
$728$	−11.6174	+	11.5448i	−0.430568	+	0.427878i
$729$	−2.46622	−	3.39447i	−0.0913416	−	0.125721i
$730$		0			0
$731$	13.4191	+	30.1398i	0.496324	+	1.11476i
$732$	0.679097	+	2.53443i	0.0251002	+	0.0936751i
$733$	14.1650	+	17.4923i	0.523197	+	0.646094i	0.968420	−	0.249326i	$-0.0802089\pi$
$733$	14.1650	+	17.4923i	0.523197	+	0.646094i	−0.445223	+	0.895420i	$0.646876\pi$
$734$	6.64700	−	20.4574i	0.245345	−	0.755095i
$735$		0			0
$736$	−3.08344	−	9.48984i	−0.113657	−	0.349800i
$737$	−12.7451	+	19.6258i	−0.469473	+	0.722925i
$738$	13.8683	+	0.726809i	0.510500	+	0.0267542i
$739$	2.85454	−	13.4296i	0.105006	−	0.494015i	−0.893943	−	0.448181i	$-0.852072\pi$
$739$	2.85454	−	13.4296i	0.105006	−	0.494015i	0.998949	−	0.0458340i	$-0.0145945\pi$
$740$		0			0
$741$	19.6767	+	6.39334i	0.722840	+	0.234865i
$742$	17.2822	+	8.87405i	0.634450	+	0.325777i
$743$	16.3770	+	16.3770i	0.600813	+	0.600813i	0.940528	−	0.339715i	$-0.110331\pi$
$743$	16.3770	+	16.3770i	0.600813	+	0.600813i	−0.339715	+	0.940528i	$0.610331\pi$
$744$	−9.37058	−	0.984887i	−0.343542	−	0.0361077i
$745$		0			0
$746$	3.77334	+	35.9009i	0.138152	+	1.31443i
$747$	3.03917	+	7.91731i	0.111197	+	0.289679i
$748$	−9.64989	−	4.91686i	−0.352835	−	0.179778i
$749$	16.8164	+	1.82077i	0.614457	+	0.0665295i
$750$		0			0
$751$	−6.00270	−	10.3970i	−0.219042	−	0.379391i	0.735474	−	0.677553i	$-0.236960\pi$
$751$	−6.00270	−	10.3970i	−0.219042	−	0.379391i	−0.954515	+	0.298162i	$0.903626\pi$
$752$	−17.2409	−	26.5487i	−0.628711	−	0.968131i
$753$	−10.3186	+	12.7424i	−0.376030	+	0.464358i
$754$	−82.5584	−	36.7574i	−3.00660	−	1.33862i
$755$		0			0
$756$	−2.32007	+	10.7493i	−0.0843803	+	0.390950i
$757$	−31.8390	+	31.8390i	−1.15721	+	1.15721i	−0.172134	+	0.985073i	$0.555066\pi$
$757$	−31.8390	+	31.8390i	−1.15721	+	1.15721i	−0.985073	+	0.172134i	$0.944934\pi$
$758$	28.6191	−	23.1753i	1.03949	−	0.841764i
$759$	−5.10691	−	5.67180i	−0.185369	−	0.205873i
$760$		0			0
$761$	22.6106	+	20.3586i	0.819632	+	0.738000i	0.968005	−	0.250931i	$-0.0807368\pi$
$761$	22.6106	+	20.3586i	0.819632	+	0.738000i	−0.148373	+	0.988932i	$0.547404\pi$
$762$	43.3760	−	22.1012i	1.57135	−	0.800641i
$763$	15.4561	−	18.9649i	0.559550	−	0.686576i
$764$	14.6899	−	4.77302i	0.531460	−	0.172682i
$765$		0			0
$766$	−14.8077	+	13.3329i	−0.535024	+	0.481738i
$767$	21.5491	−	56.1373i	0.778093	−	2.02700i
$768$	42.4561	+	11.3761i	1.53200	+	0.410499i
$769$	−21.3880	−	15.5393i	−0.771270	−	0.560361i	0.131076	−	0.991372i	$-0.458157\pi$
$769$	−21.3880	−	15.5393i	−0.771270	−	0.560361i	−0.902346	+	0.431012i	$0.858157\pi$
$770$		0			0
$771$	34.8251	−	25.3019i	1.25420	−	0.911226i
$772$	10.4742	−	4.02068i	0.376976	−	0.144708i
$773$	−8.85013	+	5.74734i	−0.318317	+	0.206718i	−0.693900	−	0.720071i	$-0.744109\pi$
$773$	−8.85013	+	5.74734i	−0.318317	+	0.206718i	0.375583	+	0.926789i	$0.377442\pi$
$774$	20.3087	+	11.7252i	0.729980	+	0.421454i
$775$		0			0
$776$		−	3.78999i		−	0.136053i
$777$	−10.7384	+	5.42914i	−0.385236	+	0.194769i
$778$	10.5565	+	1.67198i	0.378468	+	0.0599434i
$779$	−4.42565	+	9.94018i	−0.158565	+	0.356144i
$780$		0			0
$781$	4.79086	−	2.13303i	0.171431	−	0.0763258i
$782$	2.75996	−	10.3003i	0.0986958	−	0.368338i
$783$	33.8910	−	5.36780i	1.21116	−	0.191830i
$784$	−29.9513	+	17.0430i	−1.06969	+	0.608678i
$785$		0			0
$786$	36.6564	−	40.7111i	1.30749	−	1.45212i
$787$	0.288705	−	5.50882i	0.0102912	−	0.196368i	−0.988646	−	0.150267i	$-0.951987\pi$
$787$	0.288705	−	5.50882i	0.0102912	−	0.196368i	0.998937	−	0.0461017i	$-0.0146798\pi$
$788$	−0.659215	+	12.5786i	−0.0234836	+	0.448093i
$789$	27.6961	−	30.7596i	0.986006	−	1.09507i
$790$		0			0
$791$	−3.38655	+	2.44429i	−0.120412	+	0.0869090i
$792$	4.29963	−	0.680995i	0.152781	−	0.0241981i
$793$	1.19139	−	4.44632i	0.0423074	−	0.157893i
$794$	−28.1793	+	12.5462i	−1.00005	+	0.445249i
$795$		0			0
$796$	−2.61200	+	5.86665i	−0.0925799	+	0.207938i
$797$	−9.27158	−	1.46847i	−0.328416	−	0.0520160i	−0.00995081	−	0.999950i	$-0.503167\pi$
$797$	−9.27158	−	1.46847i	−0.328416	−	0.0520160i	−0.318465	+	0.947934i	$0.603167\pi$
$798$	17.5242	+	11.4586i	0.620351	+	0.405630i
$799$		−	23.9010i		−	0.845556i
$800$		0			0
$801$	8.45075	+	4.87904i	0.298593	+	0.172393i
$802$	−23.0860	+	14.9922i	−0.815196	+	0.529394i
$803$	−16.7116	+	6.41498i	−0.589739	+	0.226380i
$804$	−22.3941	+	16.2703i	−0.789780	+	0.573809i
$805$		0			0
$806$	−23.6484	−	17.1815i	−0.832978	−	0.605194i
$807$	42.2874	+	11.3309i	1.48859	+	0.398866i
$808$	1.78562	−	4.65171i	0.0628180	−	0.163647i
$809$	−41.2878	+	37.1757i	−1.45160	+	1.30703i	−0.582080	+	0.813132i	$0.697761\pi$
$809$	−41.2878	+	37.1757i	−1.45160	+	1.30703i	−0.869521	+	0.493895i	$0.835573\pi$
$810$		0			0
$811$	−11.0355	+	3.58564i	−0.387508	+	0.125909i	−0.496290	−	0.868157i	$-0.665305\pi$
$811$	−11.0355	+	3.58564i	−0.387508	+	0.125909i	0.108782	+	0.994066i	$0.465305\pi$
$812$	−27.6342	−	22.5215i	−0.969769	−	0.790348i
$813$	−10.0222	+	5.10657i	−0.351494	+	0.179095i
$814$	6.60849	+	5.95031i	0.231627	+	0.208558i
$815$		0			0
$816$	25.8562	+	28.7162i	0.905147	+	1.00527i
$817$	−14.2790	+	11.5629i	−0.499559	+	0.404535i
$818$	14.5735	−	14.5735i	0.509552	−	0.509552i
$819$	−12.2704	+	13.5420i	−0.428762	+	0.473197i
$820$		0			0
$821$	−1.91514	−	0.852675i	−0.0668389	−	0.0297586i	0.373045	−	0.927813i	$-0.378314\pi$
$821$	−1.91514	−	0.852675i	−0.0668389	−	0.0297586i	−0.439884	+	0.898055i	$0.644980\pi$
$822$	5.73764	−	7.08539i	0.200123	−	0.247131i
$823$	5.74818	+	8.85143i	0.200369	+	0.308541i	0.924544	−	0.381075i	$-0.124446\pi$
$823$	5.74818	+	8.85143i	0.200369	+	0.308541i	−0.724175	+	0.689616i	$0.757779\pi$
$824$	11.2040	+	19.4058i	0.390309	+	0.676035i
$825$		0			0
$826$	35.9232	−	49.1196i	1.24993	−	1.70909i
$827$	9.99601	+	5.09322i	0.347595	+	0.177109i	0.619068	−	0.785337i	$-0.287511\pi$
$827$	9.99601	+	5.09322i	0.347595	+	0.177109i	−0.271472	+	0.962446i	$0.587511\pi$
$828$	−1.05878	−	2.75821i	−0.0367950	−	0.0958543i
$829$	3.30687	+	31.4628i	0.114852	+	1.09275i	0.888419	+	0.459033i	$0.151804\pi$
$829$	3.30687	+	31.4628i	0.114852	+	1.09275i	−0.773567	+	0.633715i	$0.781529\pi$
$830$		0			0
$831$	11.2044	+	1.17763i	0.388675	+	0.0408514i
$832$	5.19948	+	5.19948i	0.180260	+	0.180260i
$833$	−25.9742	−	1.52455i	−0.899953	−	0.0528224i
$834$	−71.1751	−	23.1262i	−2.46459	−	0.800795i
$835$		0			0
$836$	1.25402	−	5.89970i	0.0433712	−	0.204046i
$837$	11.0836	+	0.580866i	0.383105	+	0.0200777i
$838$	−14.0597	+	21.6500i	−0.485683	+	0.747886i
$839$	−1.19025	−	3.66323i	−0.0410922	−	0.126469i	0.928406	−	0.371568i	$-0.121180\pi$
$839$	−1.19025	−	3.66323i	−0.0410922	−	0.126469i	−0.969498	+	0.245099i	$0.921180\pi$
$840$		0			0
$841$	−25.4123	+	78.2109i	−0.876285	+	2.69693i
$842$	−10.5521	−	13.0308i	−0.363650	−	0.449070i
$843$	−13.0867	−	48.8401i	−0.450729	−	1.68214i
$844$	−8.69940	−	19.5392i	−0.299446	−	0.672566i
$845$		0			0
$846$	−9.98562	−	13.7440i	−0.343313	−	0.472529i
$847$	−14.8056	−	4.01693i	−0.508728	−	0.138023i
$848$	−9.06493	+	17.7909i	−0.311291	+	0.610943i
$849$	−6.17268	+	3.56380i	−0.211846	+	0.122309i
$850$		0			0
$851$	−1.70644	+	2.95564i	−0.0584961	+	0.101318i
$852$	6.19482	−	0.324657i	0.212231	−	0.0111226i
$853$	5.03998	−	31.8212i	0.172566	−	1.08954i	−0.737583	−	0.675256i	$-0.764033\pi$
$853$	5.03998	−	31.8212i	0.172566	−	1.08954i	0.910149	−	0.414281i	$-0.135967\pi$
$854$	2.34188	−	4.02706i	0.0801376	−	0.137803i
$855$		0			0
$856$	−0.874039	+	8.31593i	−0.0298740	+	0.284233i
$857$	2.15174	−	0.576556i	0.0735019	−	0.0196948i	−0.221881	−	0.975074i	$-0.571220\pi$
$857$	2.15174	−	0.576556i	0.0735019	−	0.0196948i	0.295383	+	0.955379i	$0.404553\pi$
$858$	38.5273	+	14.7892i	1.31530	+	0.504896i
$859$	42.4890	−	9.03132i	1.44971	−	0.308145i	0.585251	−	0.810852i	$-0.300996\pi$
$859$	42.4890	−	9.03132i	1.44971	−	0.308145i	0.864456	+	0.502708i	$0.167663\pi$
$860$		0			0
$861$	−19.5825	−	21.8861i	−0.667368	−	0.745875i
$862$	6.58914	+	12.9319i	0.224427	+	0.440463i
$863$	−34.6780	−	22.5201i	−1.18045	−	0.766595i	−0.203296	−	0.979117i	$-0.565165\pi$
$863$	−34.6780	−	22.5201i	−1.18045	−	0.766595i	−0.977156	+	0.212523i	$0.931832\pi$
$864$	−20.0382	−	4.25925i	−0.681713	−	0.144903i
$865$		0			0
$866$	−10.0646	−	47.3500i	−0.342008	−	1.60902i
$867$	−1.05182	−	6.64093i	−0.0357217	−	0.225538i
$868$	−7.22848	−	8.98385i	−0.245351	−	0.304932i
$869$	−15.4889	+	21.3187i	−0.525425	+	0.723186i
$870$		0			0
$871$	48.2961	−	5.07612i	1.63645	−	0.171998i
$872$	9.39918	+	7.61131i	0.318297	+	0.257751i
$873$	−0.221316	−	4.22296i	−0.00749041	−	0.142925i
$874$	5.93868			0.200879
$875$		0			0
$876$	−21.1742			−0.715410
$877$	2.25803	+	43.0858i	0.0762484	+	1.45491i	0.722283	+	0.691598i	$0.243093\pi$
$877$	2.25803	+	43.0858i	0.0762484	+	1.45491i	−0.646035	+	0.763308i	$0.723574\pi$
$878$	−24.6626	−	19.9714i	−0.832321	−	0.674001i
$879$	−39.3369	+	4.13447i	−1.32680	+	0.139452i
$880$		0			0
$881$	31.0502	−	42.7370i	1.04611	−	1.43985i	0.153974	−	0.988075i	$-0.450793\pi$
$881$	31.0502	−	42.7370i	1.04611	−	1.43985i	0.892134	−	0.451770i	$-0.149207\pi$
$882$	−15.5732	+	9.97512i	−0.524375	+	0.335880i
$883$	4.81230	+	30.3837i	0.161947	+	1.02249i	0.926051	+	0.377399i	$0.123181\pi$
$883$	4.81230	+	30.3837i	0.161947	+	1.02249i	−0.764104	+	0.645093i	$0.776819\pi$
$884$	4.67286	+	21.9841i	0.157165	+	0.739404i
$885$		0			0
$886$	−27.2594	−	5.79415i	−0.915796	−	0.194658i
$887$	19.5745	+	12.7118i	0.657247	+	0.426821i	0.829710	−	0.558195i	$-0.188506\pi$
$887$	19.5745	+	12.7118i	0.657247	+	0.426821i	−0.172463	+	0.985016i	$0.555173\pi$
$888$	−2.70051	−	5.30005i	−0.0906232	−	0.177858i
$889$	−32.0088	−	10.5113i	−1.07354	−	0.352538i
$890$		0			0
$891$	−25.0937	+	5.33384i	−0.840672	+	0.178690i
$892$	−12.6900	−	4.87125i	−0.424894	−	0.163102i
$893$	12.8571	−	3.44506i	0.430247	−	0.115284i
$894$	9.51748	−	90.5528i	0.318312	−	3.02854i
$895$		0			0
$896$	−12.8684	−	22.4509i	−0.429903	−	0.750033i
$897$	−2.47766	+	15.6433i	−0.0827267	+	0.522316i
$898$	2.63975	−	0.138344i	0.0880897	−	0.00461659i
$899$	−17.9898	+	31.1593i	−0.599994	+	1.03922i
$900$		0			0
$901$	−13.0561	+	7.53793i	−0.434961	+	0.251125i
$902$	−9.85331	+	19.3382i	−0.328079	+	0.643892i
$903$	−12.6849	−	47.9413i	−0.422129	−	1.59539i
$904$	−1.21357	−	1.67034i	−0.0403628	−	0.0555547i
$905$		0			0
$906$	13.1339	+	29.4992i	0.436345	+	0.980047i
$907$	6.35831	+	23.7295i	0.211124	+	0.787926i	0.987495	+	0.157650i	$0.0503917\pi$
$907$	6.35831	+	23.7295i	0.211124	+	0.787926i	−0.776371	+	0.630276i	$0.782942\pi$
$908$	−2.89526	−	3.57535i	−0.0960825	−	0.118652i
$909$	1.71798	−	5.28739i	0.0569817	−	0.175372i
$910$		0			0
$911$	−0.207879	−	0.639784i	−0.00688732	−	0.0211970i	0.947554	−	0.319596i	$-0.103547\pi$
$911$	−0.207879	−	0.639784i	−0.00688732	−	0.0211970i	−0.954441	+	0.298399i	$0.903547\pi$
$912$	−11.7205	+	18.0480i	−0.388105	+	0.597629i
$913$	−13.2357	−	0.693652i	−0.438037	−	0.0229565i
$914$	15.0349	−	70.7339i	0.497312	−	2.33967i
$915$		0			0
$916$	−10.0477	−	3.26469i	−0.331985	−	0.107868i
$917$	−37.8662	+	1.86551i	−1.25045	+	0.0616047i
$918$	−15.4808	−	15.4808i	−0.510942	−	0.510942i
$919$	−10.6826	−	1.12278i	−0.352386	−	0.0370372i	−0.0733178	−	0.997309i	$-0.523359\pi$
$919$	−10.6826	−	1.12278i	−0.352386	−	0.0370372i	−0.279068	+	0.960271i	$0.590025\pi$
$920$		0			0
$921$	0.332628	+	3.16475i	0.0109605	+	0.104282i
$922$	−10.9871	−	28.6225i	−0.361842	−	0.942630i
$923$	−9.69676	−	4.94074i	−0.319173	−	0.162627i
$924$	13.1401	+	9.60993i	0.432279	+	0.316144i
$925$		0			0
$926$	11.6573	+	20.1910i	0.383082	+	0.663517i
$927$	13.6171	+	20.9685i	0.447245	+	0.688697i
$928$	41.7933	−	51.6104i	1.37193	−	1.69420i
$929$	23.4767	+	10.4525i	0.770246	+	0.342936i	0.753950	−	0.656931i	$-0.228146\pi$
$929$	23.4767	+	10.4525i	0.770246	+	0.342936i	0.0162961	+	0.999867i	$0.494813\pi$
$930$		0			0
$931$	−2.92379	−	14.1921i	−0.0958232	−	0.465128i
$932$	3.55235	−	3.55235i	0.116361	−	0.116361i
$933$	8.21521	−	6.65255i	0.268954	−	0.217795i
$934$	7.95855	+	8.83887i	0.260412	+	0.289217i
$935$		0			0
$936$	−6.71347	−	6.04483i	−0.219437	−	0.197582i
$937$	−6.12376	+	3.12021i	−0.200055	+	0.101933i	−0.551148	−	0.834408i	$-0.685810\pi$
$937$	−6.12376	+	3.12021i	−0.200055	+	0.101933i	0.351093	+	0.936340i	$0.385810\pi$
$938$	48.5164	+	7.84018i	1.58412	+	0.255991i
$939$	−67.9600	+	22.0815i	−2.21779	+	0.720604i
$940$		0			0
$941$	−21.3813	+	19.2518i	−0.697009	+	0.627590i	−0.939494	−	0.342565i	$-0.888704\pi$
$941$	−21.3813	+	19.2518i	−0.697009	+	0.627590i	0.242485	+	0.970155i	$0.422038\pi$
$942$	−22.3641	+	58.2605i	−0.728663	+	1.89823i
$943$	−8.04585	−	2.15588i	−0.262009	−	0.0702051i
$944$	50.5999	+	36.7630i	1.64689	+	1.19653i
$945$		0			0
$946$	−29.6499	+	21.5419i	−0.964003	+	0.700389i
$947$	−10.7253	+	4.11707i	−0.348526	+	0.133787i	−0.526333	−	0.850279i	$-0.676433\pi$
$947$	−10.7253	+	4.11707i	−0.348526	+	0.133787i	0.177806	+	0.984066i	$0.443100\pi$
$948$	−26.1417	+	16.9766i	−0.849044	+	0.551376i
$949$	32.1706	+	18.5737i	1.04430	+	0.602928i
$950$		0			0
$951$		−	28.4293i		−	0.921883i
$952$	0.713416	−	12.8426i	0.0231219	−	0.416231i
$953$	44.1290	+	6.98934i	1.42948	+	0.226407i	0.822705	−	0.568468i	$-0.192464\pi$
$953$	44.1290	+	6.98934i	1.42948	+	0.226407i	0.606773	+	0.794875i	$0.292464\pi$
$954$	−4.35848	+	9.78932i	−0.141111	+	0.316941i
$955$		0			0
$956$	16.0419	−	7.14231i	0.518832	−	0.230999i
$957$	13.1470	−	49.0652i	0.424982	−	1.58605i
$958$	−18.1353	+	2.87235i	−0.585926	+	0.0928015i
$959$	−6.27705	+	0.639863i	−0.202696	+	0.0206622i
$960$		0			0
$961$	12.9559	−	14.3890i	0.417932	−	0.464160i
$962$	0.965808	−	18.4287i	0.0311389	−	0.594165i
$963$	−0.488282	+	9.31698i	−0.0157347	+	0.300236i
$964$	−9.08939	+	10.0948i	−0.292750	+	0.325131i
$965$		0			0
$966$	−6.56533	+	14.6225i	−0.211236	+	0.470470i
$967$	−10.0191	+	1.58687i	−0.322192	+	0.0510302i	−0.315435	−	0.948947i	$-0.602151\pi$
$967$	−10.0191	+	1.58687i	−0.322192	+	0.0510302i	−0.00675621	+	0.999977i	$0.502151\pi$
$968$	1.96282	−	7.32534i	0.0630874	−	0.235445i
$969$	−14.8434	+	6.60869i	−0.476837	+	0.212302i
$970$		0			0
$971$	6.19581	−	13.9160i	0.198833	−	0.446586i	−0.786419	−	0.617693i	$-0.788068\pi$
$971$	6.19581	−	13.9160i	0.198833	−	0.446586i	0.985253	+	0.171106i	$0.0547342\pi$
$972$	−17.6567	−	2.79654i	−0.566338	−	0.0896992i
$973$	23.3683	+	46.2203i	0.749152	+	1.48175i
$974$		−	68.8202i		−	2.20514i
$975$		0			0
$976$	4.14648	+	2.39397i	0.132726	+	0.0766292i
$977$	−1.11728	+	0.725573i	−0.0357451	+	0.0232131i	−0.562388	−	0.826874i	$-0.690117\pi$
$977$	−1.11728	+	0.725573i	−0.0357451	+	0.0232131i	0.526643	+	0.850087i	$0.323451\pi$
$978$	−36.0395	+	13.8343i	−1.15242	+	0.442371i
$979$	−12.3378	+	8.96393i	−0.394318	+	0.286489i
$980$		0			0
$981$	10.9174	+	7.93196i	0.348566	+	0.253248i
$982$	67.4528	+	18.0739i	2.15251	+	0.576762i
$983$	4.53193	−	11.8061i	0.144546	−	0.376555i	−0.842125	−	0.539282i	$-0.818696\pi$
$983$	4.53193	−	11.8061i	0.144546	−	0.376555i	0.986671	+	0.162727i	$0.0520290\pi$
$984$	10.7890	−	9.71442i	0.343939	−	0.309684i
$985$		0			0
$986$	67.4985	−	21.9316i	2.14959	−	0.698445i
$987$	−5.73124	+	35.4659i	−0.182427	+	1.12889i
$988$	−11.1524	+	5.68244i	−0.354805	+	0.180782i
$989$	−10.4528	−	9.41175i	−0.332380	−	0.299276i
$990$		0			0
$991$	−2.57117	−	2.85557i	−0.0816758	−	0.0907102i	0.700922	−	0.713238i	$-0.252772\pi$
$991$	−2.57117	−	2.85557i	−0.0816758	−	0.0907102i	−0.782597	+	0.622528i	$0.786106\pi$
$992$	16.6936	−	13.5182i	0.530022	−	0.429203i
$993$	18.4165	−	18.4165i	0.584429	−	0.584429i
$994$	−8.16167	−	7.39525i	−0.258872	−	0.234563i
$995$		0			0
$996$	−14.3223	−	6.37670i	−0.453819	−	0.202053i
$997$	−22.4421	+	27.7136i	−0.710747	+	0.877700i	−0.996752	−	0.0805283i	$-0.974339\pi$
$997$	−22.4421	+	27.7136i	−0.710747	+	0.877700i	0.286005	+	0.958228i	$0.407673\pi$
$998$	−3.02595	−	4.65955i	−0.0957846	−	0.147495i
$999$	3.50343	+	6.06812i	0.110844	+	0.191987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.143.15		288
5.2	odd	4		175.2.x.a.17.4	yes	288
5.3	odd	4		875.2.bb.c.857.15		288
5.4	even	2		875.2.bb.a.143.4		288
7.5	odd	6	inner	875.2.bb.b.768.15		288
25.3	odd	20		875.2.bb.a.507.4		288
25.4	even	10		875.2.bb.c.493.4		288
25.21	even	5		175.2.x.a.3.15	✓	288
25.22	odd	20	inner	875.2.bb.b.507.15		288
35.12	even	12		175.2.x.a.117.15	yes	288
35.19	odd	6		875.2.bb.a.768.4		288
35.33	even	12		875.2.bb.c.607.4		288
175.47	even	60	inner	875.2.bb.b.257.15		288
175.54	odd	30		875.2.bb.c.243.15		288
175.96	odd	30		175.2.x.a.103.4	yes	288
175.103	even	60		875.2.bb.a.257.4		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.15	✓	288	25.21	even	5
175.2.x.a.17.4	yes	288	5.2	odd	4
175.2.x.a.103.4	yes	288	175.96	odd	30
175.2.x.a.117.15	yes	288	35.12	even	12
875.2.bb.a.143.4		288	5.4	even	2
875.2.bb.a.257.4		288	175.103	even	60
875.2.bb.a.507.4		288	25.3	odd	20
875.2.bb.a.768.4		288	35.19	odd	6
875.2.bb.b.143.15		288	1.1	even	1	trivial
875.2.bb.b.257.15		288	175.47	even	60	inner
875.2.bb.b.507.15		288	25.22	odd	20	inner
875.2.bb.b.768.15		288	7.5	odd	6	inner
875.2.bb.c.243.15		288	175.54	odd	30
875.2.bb.c.493.4		288	25.4	even	10
875.2.bb.c.607.4		288	35.33	even	12
875.2.bb.c.857.15		288	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0947490 + 1.80792i) q^{2} +(1.64111 + 1.32895i) q^{3} +(-1.27055 + 0.133540i) q^{4} +(-2.24713 + 3.09291i) q^{6} +(2.61446 - 0.405696i) q^{7} +(0.204604 + 1.29182i) q^{8} +(0.303414 + 1.42745i) q^{9} +(-2.23088 - 0.474189i) q^{11} +(-2.26258 - 1.46934i) q^{12} +(2.14873 + 4.21711i) q^{13} +(0.981183 + 4.68830i) q^{14} +(-4.81539 + 1.02354i) q^{16} +(-3.47011 - 1.33205i) q^{17} +(-2.55197 + 0.683798i) q^{18} +(0.216377 - 2.05869i) q^{19} +(4.82977 + 2.80869i) q^{21} +(0.645921 - 4.07818i) q^{22} +(1.58250 - 0.0829354i) q^{23} +(-1.38098 + 2.39193i) q^{24} +(-7.42061 + 4.28429i) q^{26} +(1.47703 - 2.89883i) q^{27} +(-3.26763 + 0.864593i) q^{28} +(6.19928 + 8.53257i) q^{29} +(1.38755 + 3.11648i) q^{31} +(-1.62970 - 6.08214i) q^{32} +(-3.03095 - 3.74292i) q^{33} +(2.07945 - 6.39988i) q^{34} +(-0.576126 - 1.77313i) q^{36} +(-1.17298 + 1.80623i) q^{37} +(3.74244 + 0.196133i) q^{38} +(-2.07801 + 9.77629i) q^{39} +(-4.99913 - 1.62432i) q^{41} +(-4.62026 + 8.99795i) q^{42} +(-6.27631 - 6.27631i) q^{43} +(2.89777 + 0.304568i) q^{44} +(0.299881 + 2.85318i) q^{46} +(2.30438 + 6.00311i) q^{47} +(-9.26282 - 4.71964i) q^{48} +(6.67082 - 2.12135i) q^{49} +(-3.92461 - 6.79762i) q^{51} +(-3.29322 - 5.07112i) q^{52} +(2.55248 - 3.15205i) q^{53} +(5.38080 + 2.39569i) q^{54} +(1.05902 + 3.29441i) q^{56} +(3.09098 - 3.09098i) q^{57} +(-14.8388 + 12.0162i) q^{58} +(-8.50113 - 9.44146i) q^{59} +(-0.722763 - 0.650779i) q^{61} +(-5.50288 + 2.80386i) q^{62} +(1.37238 + 3.60892i) q^{63} +(1.47757 - 0.480090i) q^{64} +(6.47971 - 5.83436i) q^{66} +(3.67699 - 9.57888i) q^{67} +(4.58683 + 1.22904i) q^{68} +(2.70728 + 1.96695i) q^{69} +(-1.86024 + 1.35154i) q^{71} +(-1.78193 + 0.684019i) q^{72} +(6.58242 - 4.27467i) q^{73} +(-3.37666 - 1.94951i) q^{74} +2.64456i q^{76} +(-6.02493 - 0.334689i) q^{77} +(-17.8716 - 2.83059i) q^{78} +(4.69941 - 10.5550i) q^{79} +(10.2759 - 4.57511i) q^{81} +(2.46297 - 9.19193i) q^{82} +(5.73970 - 0.909079i) q^{83} +(-6.51154 - 2.92361i) q^{84} +(10.7524 - 11.9417i) q^{86} +(-1.16562 + 22.2414i) q^{87} +(0.156119 - 2.97892i) q^{88} +(4.47423 - 4.96914i) q^{89} +(7.32863 + 10.1538i) q^{91} +(-1.99958 + 0.316702i) q^{92} +(-1.86452 + 6.95847i) q^{93} +(-10.6348 + 4.73492i) q^{94} +(5.40831 - 12.1473i) q^{96} +(-2.86204 - 0.453302i) q^{97} +(4.46729 + 11.8593i) q^{98} -3.32835i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) \) 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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