LMFDB - Embedded newform 152.2.q.c.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(9,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.q (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 34 x^{15} + 204 x^{14} - 267 x^{13} + 1304 x^{12} - 972 x^{11} + \cdots + 1 $ x^18 - 3x^17 + 21x^16 - 34x^15 + 204x^14 - 267x^13 + 1304x^12 - 972x^11 + 4890x^10 - 2547x^9 + 12945x^8 - 2403x^7 + 14457x^6 - 6729x^5 + 8769x^4 - 686x^3 + 132x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.1
Root			$1.40179 - 2.42798i$ of defining polynomial
Character	$\chi$	$=$	152.73
Dual form			152.2.q.c.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.63451 + 0.958884i) q^{3} +(0.465881 - 2.64214i) q^{5} +(-0.731458 - 1.26692i) q^{7} +(3.72306 - 3.12402i) q^{9} +(2.54594 - 4.40970i) q^{11} +(-3.68269 - 1.34039i) q^{13} +(1.30614 + 7.40749i) q^{15} +(0.0943594 + 0.0791769i) q^{17} +(-1.78486 - 3.97672i) q^{19} +(3.14186 + 2.63634i) q^{21} +(1.23224 + 6.98836i) q^{23} +(-2.06542 - 0.751751i) q^{25} +(-2.60750 + 4.51632i) q^{27} +(-6.46506 + 5.42483i) q^{29} +(-3.09116 - 5.35404i) q^{31} +(-2.47892 + 14.0587i) q^{33} +(-3.68816 + 1.34238i) q^{35} +4.32850 q^{37} +10.9874 q^{39} +(9.35604 - 3.40532i) q^{41} +(-0.262249 + 1.48729i) q^{43} +(-6.51961 - 11.2923i) q^{45} +(2.06572 - 1.73334i) q^{47} +(2.42994 - 4.20878i) q^{49} +(-0.324512 - 0.118113i) q^{51} +(-1.04945 - 5.95173i) q^{53} +(-10.4650 - 8.78115i) q^{55} +(8.51545 + 8.76523i) q^{57} +(6.47790 + 5.43560i) q^{59} +(1.19119 + 6.75559i) q^{61} +(-6.68115 - 2.43174i) q^{63} +(-5.25719 + 9.10572i) q^{65} +(7.33630 - 6.15589i) q^{67} +(-9.94737 - 17.2294i) q^{69} +(-0.403285 + 2.28714i) q^{71} +(-11.1183 + 4.04674i) q^{73} +6.16221 q^{75} -7.44900 q^{77} +(2.80329 - 1.02032i) q^{79} +(0.00700815 - 0.0397452i) q^{81} +(1.93498 + 3.35148i) q^{83} +(0.253157 - 0.212424i) q^{85} +(11.8305 - 20.4910i) q^{87} +(8.22470 + 2.99355i) q^{89} +(0.995562 + 5.64611i) q^{91} +(13.2776 + 11.1412i) q^{93} +(-11.3386 + 2.86318i) q^{95} +(-9.50253 - 7.97357i) q^{97} +(-4.29730 - 24.3712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{7} - 6 q^{9} - 3 q^{11} + 3 q^{13} + 33 q^{15} + 9 q^{17} - 24 q^{19} - 15 q^{21} + 6 q^{23} + 6 q^{25} - 12 q^{27} - 3 q^{29} - 6 q^{31} - 45 q^{33} - 15 q^{35} + 48 q^{37} + 12 q^{39} - 18 q^{41}+ \cdots + 15 q^{99}+O(q^{100}) $ 18 * q - 9 * q^7 - 6 * q^9 - 3 * q^11 + 3 * q^13 + 33 * q^15 + 9 * q^17 - 24 * q^19 - 15 * q^21 + 6 * q^23 + 6 * q^25 - 12 * q^27 - 3 * q^29 - 6 * q^31 - 45 * q^33 - 15 * q^35 + 48 * q^37 + 12 * q^39 - 18 * q^41 - 39 * q^43 - 42 * q^45 - 27 * q^47 - 18 * q^49 + 48 * q^51 + 39 * q^53 - 27 * q^55 - 6 * q^57 + 9 * q^59 - 24 * q^61 + 3 * q^63 + 27 * q^65 + 39 * q^67 - 3 * q^69 + 12 * q^73 + 90 * q^75 + 60 * q^77 + 63 * q^79 - 6 * q^81 - 27 * q^83 - 30 * q^85 + 18 * q^87 + 66 * q^89 + 108 * q^91 + 60 * q^93 - 75 * q^95 - 81 * q^97 + 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{9}\right)$

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			0
$2$		0			0
$3$	−2.63451	+	0.958884i	−1.52104	+	0.553612i	−0.961407	−	0.275131i	$-0.911279\pi$
$3$	−2.63451	+	0.958884i	−1.52104	+	0.553612i	−0.559630	+	0.828743i	$0.689057\pi$
$4$		0			0
$5$	0.465881	−	2.64214i	0.208348	−	1.18160i	−0.683734	−	0.729731i	$-0.739645\pi$
$5$	0.465881	−	2.64214i	0.208348	−	1.18160i	0.892083	−	0.451872i	$-0.149244\pi$
$6$		0			0
$7$	−0.731458	−	1.26692i	−0.276465	−	0.478851i	0.694039	−	0.719938i	$-0.255830\pi$
$7$	−0.731458	−	1.26692i	−0.276465	−	0.478851i	−0.970504	+	0.241086i	$0.922496\pi$
$8$		0			0
$9$	3.72306	−	3.12402i	1.24102	−	1.04134i
$10$		0			0
$11$	2.54594	−	4.40970i	0.767631	−	1.32958i	−0.171214	−	0.985234i	$-0.554769\pi$
$11$	2.54594	−	4.40970i	0.767631	−	1.32958i	0.938844	−	0.344341i	$-0.111898\pi$
$12$		0			0
$13$	−3.68269	−	1.34039i	−1.02139	−	0.371757i	−0.223596	−	0.974682i	$-0.571779\pi$
$13$	−3.68269	−	1.34039i	−1.02139	−	0.371757i	−0.797798	+	0.602925i	$0.794002\pi$
$14$		0			0
$15$	1.30614	+	7.40749i	0.337244	+	1.91260i
$16$		0			0
$17$	0.0943594	+	0.0791769i	0.0228855	+	0.0192032i	0.654159	−	0.756357i	$-0.273023\pi$
$17$	0.0943594	+	0.0791769i	0.0228855	+	0.0192032i	−0.631273	+	0.775561i	$0.717467\pi$
$18$		0			0
$19$	−1.78486	−	3.97672i	−0.409475	−	0.912321i
$19$	−1.78486	−	3.97672i	−0.409475	−	0.912321i
$20$		0			0
$21$	3.14186	+	2.63634i	0.685611	+	0.575296i
$22$		0			0
$23$	1.23224	+	6.98836i	0.256939	+	1.45717i	0.791046	+	0.611757i	$0.209537\pi$
$23$	1.23224	+	6.98836i	0.256939	+	1.45717i	−0.534106	+	0.845417i	$0.679352\pi$
$24$		0			0
$25$	−2.06542	−	0.751751i	−0.413084	−	0.150350i
$26$		0			0
$27$	−2.60750	+	4.51632i	−0.501813	+	0.869165i
$28$		0			0
$29$	−6.46506	+	5.42483i	−1.20053	+	1.00737i	−0.200917	+	0.979608i	$0.564392\pi$
$29$	−6.46506	+	5.42483i	−1.20053	+	1.00737i	−0.999615	+	0.0277578i	$0.991163\pi$
$30$		0			0
$31$	−3.09116	−	5.35404i	−0.555188	−	0.961615i	−0.997889	−	0.0649450i	$-0.979313\pi$
$31$	−3.09116	−	5.35404i	−0.555188	−	0.961615i	0.442700	−	0.896670i	$-0.354021\pi$
$32$		0			0
$33$	−2.47892	+	14.0587i	−0.431525	+	2.44730i
$34$		0			0
$35$	−3.68816	+	1.34238i	−0.623413	+	0.226904i
$36$		0			0
$37$	4.32850			0.711601			0.355800	−	0.934562i	$-0.384208\pi$
$37$	4.32850			0.711601			0.355800	+	0.934562i	$0.384208\pi$
$38$		0			0
$39$	10.9874			1.75939
$40$		0			0
$41$	9.35604	−	3.40532i	1.46117	−	0.531822i	0.515481	−	0.856901i	$-0.327613\pi$
$41$	9.35604	−	3.40532i	1.46117	−	0.531822i	0.945687	+	0.325080i	$0.105391\pi$
$42$		0			0
$43$	−0.262249	+	1.48729i	−0.0399925	+	0.226809i	−0.998253	−	0.0590886i	$-0.981181\pi$
$43$	−0.262249	+	1.48729i	−0.0399925	+	0.226809i	0.958260	+	0.285897i	$0.0922917\pi$
$44$		0			0
$45$	−6.51961	−	11.2923i	−0.971886	−	1.68336i
$46$		0			0
$47$	2.06572	−	1.73334i	0.301316	−	0.252834i	−0.479576	−	0.877501i	$-0.659209\pi$
$47$	2.06572	−	1.73334i	0.301316	−	0.252834i	0.780892	+	0.624666i	$0.214765\pi$
$48$		0			0
$49$	2.42994	−	4.20878i	0.347134	−	0.601254i
$50$		0			0
$51$	−0.324512	−	0.118113i	−0.0454408	−	0.0165391i
$52$		0			0
$53$	−1.04945	−	5.95173i	−0.144153	−	0.817534i	−0.968043	−	0.250784i	$-0.919312\pi$
$53$	−1.04945	−	5.95173i	−0.144153	−	0.817534i	0.823890	−	0.566750i	$-0.191799\pi$
$54$		0			0
$55$	−10.4650	−	8.78115i	−1.41110	−	1.18405i
$56$		0			0
$57$	8.51545	+	8.76523i	1.12790	+	1.16098i
$58$		0			0
$59$	6.47790	+	5.43560i	0.843350	+	0.707655i	0.958315	−	0.285715i	$-0.0922310\pi$
$59$	6.47790	+	5.43560i	0.843350	+	0.707655i	−0.114964	+	0.993370i	$0.536675\pi$
$60$		0			0
$61$	1.19119	+	6.75559i	0.152517	+	0.864965i	0.961021	+	0.276475i	$0.0891663\pi$
$61$	1.19119	+	6.75559i	0.152517	+	0.864965i	−0.808504	+	0.588490i	$0.799723\pi$
$62$		0			0
$63$	−6.68115	−	2.43174i	−0.841746	−	0.306370i
$64$		0			0
$65$	−5.25719	+	9.10572i	−0.652074	+	1.12943i
$66$		0			0
$67$	7.33630	−	6.15589i	0.896272	−	0.752061i	−0.0731863	−	0.997318i	$-0.523317\pi$
$67$	7.33630	−	6.15589i	0.896272	−	0.752061i	0.969458	+	0.245257i	$0.0788723\pi$
$68$		0			0
$69$	−9.94737	−	17.2294i	−1.19752	−	2.07417i
$70$		0			0
$71$	−0.403285	+	2.28714i	−0.0478611	+	0.271434i	−0.999342	−	0.0362743i	$-0.988451\pi$
$71$	−0.403285	+	2.28714i	−0.0478611	+	0.271434i	0.951481	+	0.307708i	$0.0995621\pi$
$72$		0			0
$73$	−11.1183	+	4.04674i	−1.30130	+	0.473636i	−0.897421	−	0.441175i	$-0.854562\pi$
$73$	−11.1183	+	4.04674i	−1.30130	+	0.473636i	−0.403882	+	0.914811i	$0.632339\pi$
$74$		0			0
$75$	6.16221			0.711551
$76$		0			0
$77$	−7.44900			−0.848892
$78$		0			0
$79$	2.80329	−	1.02032i	0.315395	−	0.114794i	−0.179472	−	0.983763i	$-0.557439\pi$
$79$	2.80329	−	1.02032i	0.315395	−	0.114794i	0.494867	+	0.868969i	$0.335217\pi$
$80$		0			0
$81$	0.00700815	−	0.0397452i	0.000778684	−	0.00441613i
$82$		0			0
$83$	1.93498	+	3.35148i	0.212391	+	0.367873i	0.952462	−	0.304656i	$-0.0985415\pi$
$83$	1.93498	+	3.35148i	0.212391	+	0.367873i	−0.740071	+	0.672529i	$0.765208\pi$
$84$		0			0
$85$	0.253157	−	0.212424i	0.0274587	−	0.0230406i
$86$		0			0
$87$	11.8305	−	20.4910i	1.26836	−	2.19687i
$88$		0			0
$89$	8.22470	+	2.99355i	0.871817	+	0.317315i	0.738903	−	0.673812i	$-0.235344\pi$
$89$	8.22470	+	2.99355i	0.871817	+	0.317315i	0.132914	+	0.991128i	$0.457567\pi$
$90$		0			0
$91$	0.995562	+	5.64611i	0.104363	+	0.591873i
$92$		0			0
$93$	13.2776	+	11.1412i	1.37682	+	1.15529i
$94$		0			0
$95$	−11.3386	+	2.86318i	−1.16331	+	0.293756i
$96$		0			0
$97$	−9.50253	−	7.97357i	−0.964836	−	0.809594i	0.0168968	−	0.999857i	$-0.494621\pi$
$97$	−9.50253	−	7.97357i	−0.964836	−	0.809594i	−0.981733	+	0.190264i	$0.939066\pi$
$98$		0			0
$99$	−4.29730	−	24.3712i	−0.431894	−	2.44940i
$100$		0			0
$101$	0.137551	+	0.0500646i	0.0136869	+	0.00498161i	0.348855	−	0.937177i	$-0.386571\pi$
$101$	0.137551	+	0.0500646i	0.0136869	+	0.00498161i	−0.335168	+	0.942159i	$0.608793\pi$
$102$		0			0
$103$	1.51184	−	2.61859i	0.148966	−	0.258017i	−0.781879	−	0.623430i	$-0.785739\pi$
$103$	1.51184	−	2.61859i	0.148966	−	0.258017i	0.930846	+	0.365413i	$0.119072\pi$
$104$		0			0
$105$	8.42932	−	7.07304i	0.822617	−	0.690258i
$106$		0			0
$107$	3.44801	+	5.97212i	0.333331	+	0.577347i	0.983163	−	0.182731i	$-0.0584939\pi$
$107$	3.44801	+	5.97212i	0.333331	+	0.577347i	−0.649831	+	0.760078i	$0.725161\pi$
$108$		0			0
$109$	−0.872697	+	4.94931i	−0.0835892	+	0.474058i	0.914063	+	0.405572i	$0.132928\pi$
$109$	−0.872697	+	4.94931i	−0.0835892	+	0.474058i	−0.997652	+	0.0684855i	$0.978183\pi$
$110$		0			0
$111$	−11.4035	+	4.15053i	−1.08237	+	0.393951i
$112$		0			0
$113$	10.9474			1.02984			0.514921	−	0.857238i	$-0.327821\pi$
$113$	10.9474			1.02984			0.514921	+	0.857238i	$0.327821\pi$
$114$		0			0
$115$	19.0383			1.77533
$116$		0			0
$117$	−17.8983	+	6.51444i	−1.65470	+	0.602260i
$118$		0			0
$119$	0.0312911	−	0.177461i	0.00286845	−	0.0162678i
$120$		0			0
$121$	−7.46365	−	12.9274i	−0.678514	−	1.17522i
$122$		0			0
$123$	−21.3833	+	17.9427i	−1.92807	+	1.61784i
$124$		0			0
$125$	3.75879	−	6.51041i	0.336196	−	0.582309i
$126$		0			0
$127$	8.46669	+	3.08162i	0.751297	+	0.273450i	0.689152	−	0.724617i	$-0.257983\pi$
$127$	8.46669	+	3.08162i	0.751297	+	0.273450i	0.0621458	+	0.998067i	$0.480206\pi$
$128$		0			0
$129$	−0.735237	−	4.16974i	−0.0647340	−	0.367125i
$130$		0			0
$131$	10.8458	+	9.10069i	0.947600	+	0.795131i	0.978892	−	0.204379i	$-0.0655176\pi$
$131$	10.8458	+	9.10069i	0.947600	+	0.795131i	−0.0312917	+	0.999510i	$0.509962\pi$
$132$		0			0
$133$	−3.73264	+	5.17008i	−0.323661	+	0.448303i
$134$		0			0
$135$	10.7180	+	8.99345i	0.922456	+	0.774033i
$136$		0			0
$137$	−1.38005	−	7.82667i	−0.117906	−	0.668677i	−0.985270	−	0.171004i	$-0.945299\pi$
$137$	−1.38005	−	7.82667i	−0.117906	−	0.668677i	0.867365	−	0.497673i	$-0.165812\pi$
$138$		0			0
$139$	−10.7872	−	3.92623i	−0.914960	−	0.333018i	−0.158729	−	0.987322i	$-0.550739\pi$
$139$	−10.7872	−	3.92623i	−0.914960	−	0.333018i	−0.756232	+	0.654304i	$0.772962\pi$
$140$		0			0
$141$	−3.78009	+	6.54730i	−0.318341	+	0.551382i
$142$		0			0
$143$	−15.2866	+	12.8270i	−1.27833	+	1.07265i
$144$		0			0
$145$	11.3212	+	19.6090i	0.940178	+	1.62844i
$146$		0			0
$147$	−2.36597	+	13.4181i	−0.195142	+	1.10671i
$148$		0			0
$149$	17.3523	−	6.31573i	1.42156	−	0.517405i	0.487058	−	0.873369i	$-0.338070\pi$
$149$	17.3523	−	6.31573i	1.42156	−	0.517405i	0.934499	+	0.355965i	$0.115848\pi$
$150$		0			0
$151$	−11.0017			−0.895308			−0.447654	−	0.894207i	$-0.647740\pi$
$151$	−11.0017			−0.895308			−0.447654	+	0.894207i	$0.647740\pi$
$152$		0			0
$153$	0.598656			0.0483985
$154$		0			0
$155$	−15.5863	+	5.67294i	−1.25192	+	0.455661i
$156$		0			0
$157$	−1.36015	+	7.71378i	−0.108552	+	0.615627i	0.881190	+	0.472761i	$0.156743\pi$
$157$	−1.36015	+	7.71378i	−0.108552	+	0.615627i	−0.989742	+	0.142866i	$0.954368\pi$
$158$		0			0
$159$	8.47181	+	14.6736i	0.671859	+	1.16369i
$160$		0			0
$161$	7.95238	−	6.67284i	0.626735	−	0.525893i
$162$		0			0
$163$	−7.33460	+	12.7039i	−0.574490	+	0.995046i	0.421607	+	0.906779i	$0.361466\pi$
$163$	−7.33460	+	12.7039i	−0.574490	+	0.995046i	−0.996097	+	0.0882671i	$0.971867\pi$
$164$		0			0
$165$	35.9902	+	13.0994i	2.80183	+	1.01978i
$166$		0			0
$167$	−1.22566	−	6.95108i	−0.0948446	−	0.537890i	−0.994795	−	0.101898i	$-0.967508\pi$
$167$	−1.22566	−	6.95108i	−0.0948446	−	0.537890i	0.899950	−	0.435993i	$-0.143603\pi$
$168$		0			0
$169$	1.80695	+	1.51621i	0.138996	+	0.116632i
$170$		0			0
$171$	−19.0685	−	9.22962i	−1.45820	−	0.705807i
$172$		0			0
$173$	−7.99100	−	6.70525i	−0.607545	−	0.509791i	0.286316	−	0.958135i	$-0.407569\pi$
$173$	−7.99100	−	6.70525i	−0.607545	−	0.509791i	−0.893861	+	0.448345i	$0.852014\pi$
$174$		0			0
$175$	0.558356	+	3.16660i	0.0422078	+	0.239372i
$176$		0			0
$177$	−22.2782	−	8.10860i	−1.67453	−	0.609480i
$178$		0			0
$179$	6.73625	−	11.6675i	0.503491	−	0.872071i	−0.496501	−	0.868036i	$-0.665382\pi$
$179$	6.73625	−	11.6675i	0.503491	−	0.872071i	0.999992	−	0.00403536i	$-0.00128450\pi$
$180$		0			0
$181$	−0.0539381	+	0.0452594i	−0.00400919	+	0.00336411i	−0.644790	−	0.764360i	$-0.723055\pi$
$181$	−0.0539381	+	0.0452594i	−0.00400919	+	0.00336411i	0.640781	+	0.767724i	$0.278611\pi$
$182$		0			0
$183$	−9.61604	−	16.6555i	−0.710838	−	1.23121i
$184$		0			0
$185$	2.01657	−	11.4365i	0.148261	−	0.840829i
$186$		0			0
$187$	0.589380	−	0.214517i	0.0430998	−	0.0156870i
$188$		0			0
$189$	7.62909			0.554935
$190$		0			0
$191$	5.60628			0.405656			0.202828	−	0.979214i	$-0.434987\pi$
$191$	5.60628			0.405656			0.202828	+	0.979214i	$0.434987\pi$
$192$		0			0
$193$	17.9679	−	6.53977i	1.29336	−	0.470743i	0.398529	−	0.917156i	$-0.369521\pi$
$193$	17.9679	−	6.53977i	1.29336	−	0.470743i	0.894827	+	0.446412i	$0.147299\pi$
$194$		0			0
$195$	5.11880	−	29.0302i	0.366565	−	2.07889i
$196$		0			0
$197$	−6.96229	−	12.0590i	−0.496042	−	0.859170i	0.503947	−	0.863734i	$-0.331881\pi$
$197$	−6.96229	−	12.0590i	−0.496042	−	0.859170i	−0.999990	+	0.00456395i	$0.998547\pi$
$198$		0			0
$199$	−3.56650	+	2.99265i	−0.252822	+	0.212143i	−0.760386	−	0.649471i	$-0.774990\pi$
$199$	−3.56650	+	2.99265i	−0.252822	+	0.212143i	0.507564	+	0.861614i	$0.330546\pi$
$200$		0			0
$201$	−13.4248	+	23.2524i	−0.946912	+	1.64010i
$202$		0			0
$203$	11.6018	+	4.22269i	0.814284	+	0.296375i
$204$		0			0
$205$	−4.63854	−	26.3065i	−0.323970	−	1.83732i
$206$		0			0
$207$	26.4195	+	22.1686i	1.83628	+	1.54082i
$208$		0			0
$209$	−22.0803	−	2.25378i	−1.52733	−	0.155897i
$210$		0			0
$211$	−7.81756	−	6.55971i	−0.538183	−	0.451589i	0.332733	−	0.943021i	$-0.392029\pi$
$211$	−7.81756	−	6.55971i	−0.538183	−	0.451589i	−0.870916	+	0.491432i	$0.836474\pi$
$212$		0			0
$213$	−1.13065	−	6.41221i	−0.0774706	−	0.439357i
$214$		0			0
$215$	3.80745	+	1.38580i	0.259666	+	0.0945106i
$216$		0			0
$217$	−4.52210	+	7.83251i	−0.306980	+	0.531705i
$218$		0			0
$219$	25.4110	−	21.3224i	1.71712	−	1.44083i
$220$		0			0
$221$	−0.241368	−	0.418062i	−0.0162362	−	0.0281219i
$222$		0			0
$223$	1.13148	−	6.41695i	0.0757696	−	0.429711i	−0.923200	−	0.384321i	$-0.874436\pi$
$223$	1.13148	−	6.41695i	0.0757696	−	0.429711i	0.998969	−	0.0453903i	$-0.0144532\pi$
$224$		0			0
$225$	−10.0382	+	3.65359i	−0.669211	+	0.243573i
$226$		0			0
$227$	−10.8291			−0.718749			−0.359375	−	0.933193i	$-0.617010\pi$
$227$	−10.8291			−0.718749			−0.359375	+	0.933193i	$0.617010\pi$
$228$		0			0
$229$	18.8721			1.24710			0.623552	−	0.781782i	$-0.285689\pi$
$229$	18.8721			1.24710			0.623552	+	0.781782i	$0.285689\pi$
$230$		0			0
$231$	19.6245	−	7.14272i	1.29120	−	0.469957i
$232$		0			0
$233$	0.756978	−	4.29304i	0.0495913	−	0.281246i	−0.949920	−	0.312492i	$-0.898836\pi$
$233$	0.756978	−	4.29304i	0.0495913	−	0.281246i	0.999512	+	0.0312456i	$0.00994740\pi$
$234$		0			0
$235$	−3.61737	−	6.26546i	−0.235971	−	0.408714i
$236$		0			0
$237$	−6.40695	+	5.37607i	−0.416176	+	0.349213i
$238$		0			0
$239$	1.62108	−	2.80779i	0.104859	−	0.181621i	−0.808822	−	0.588054i	$-0.799894\pi$
$239$	1.62108	−	2.80779i	0.104859	−	0.181621i	0.913681	+	0.406433i	$0.133228\pi$
$240$		0			0
$241$	−4.30613	−	1.56730i	−0.277382	−	0.100959i	0.199583	−	0.979881i	$-0.436041\pi$
$241$	−4.30613	−	1.56730i	−0.277382	−	0.100959i	−0.476965	+	0.878922i	$0.658263\pi$
$242$		0			0
$243$	−2.69707	−	15.2959i	−0.173017	−	0.981230i
$244$		0			0
$245$	−9.98814	−	8.38104i	−0.638119	−	0.535445i
$246$		0			0
$247$	1.24274	+	17.0374i	0.0790738	+	1.08406i
$248$		0			0
$249$	−8.31140	−	6.97410i	−0.526714	−	0.441965i
$250$		0			0
$251$	2.72340	+	15.4452i	0.171899	+	0.974889i	0.941662	+	0.336559i	$0.109263\pi$
$251$	2.72340	+	15.4452i	0.171899	+	0.974889i	−0.769763	+	0.638330i	$0.779626\pi$
$252$		0			0
$253$	33.9538	+	12.3582i	2.13466	+	0.776952i
$254$		0			0
$255$	−0.463255	+	0.802382i	−0.0290102	+	0.0502471i
$256$		0			0
$257$	−1.18195	+	0.991777i	−0.0737283	+	0.0618654i	−0.678907	−	0.734224i	$-0.737546\pi$
$257$	−1.18195	+	0.991777i	−0.0737283	+	0.0618654i	0.605179	+	0.796090i	$0.293102\pi$
$258$		0			0
$259$	−3.16611	−	5.48387i	−0.196733	−	0.340751i
$260$		0			0
$261$	−7.12255	+	40.3940i	−0.440875	+	2.50032i
$262$		0			0
$263$	−2.08326	+	0.758243i	−0.128459	+	0.0467553i	−0.405450	−	0.914117i	$-0.632885\pi$
$263$	−2.08326	+	0.758243i	−0.128459	+	0.0467553i	0.276991	+	0.960873i	$0.410663\pi$
$264$		0			0
$265$	−16.2143			−0.996034
$266$		0			0
$267$	−24.5385			−1.50173
$268$		0			0
$269$	−21.7316	+	7.90967i	−1.32500	+	0.482261i	−0.905057	−	0.425289i	$-0.860172\pi$
$269$	−21.7316	+	7.90967i	−1.32500	+	0.482261i	−0.419944	+	0.907550i	$0.637950\pi$
$270$		0			0
$271$	−0.107500	+	0.609664i	−0.00653017	+	0.0370344i	−0.987899	−	0.155100i	$-0.950430\pi$
$271$	−0.107500	+	0.609664i	−0.00653017	+	0.0370344i	0.981369	+	0.192135i	$0.0615410\pi$
$272$		0			0
$273$	−8.03678	−	13.9201i	−0.486408	−	0.842484i
$274$		0			0
$275$	−8.57343	+	7.19396i	−0.516997	+	0.433812i
$276$		0			0
$277$	−4.99063	+	8.64402i	−0.299858	+	0.519369i	−0.976103	−	0.217308i	$-0.930273\pi$
$277$	−4.99063	+	8.64402i	−0.299858	+	0.519369i	0.676245	+	0.736676i	$0.263606\pi$
$278$		0			0
$279$	−28.2347	−	10.2766i	−1.69037	−	0.615244i
$280$		0			0
$281$	0.394452	+	2.23705i	0.0235311	+	0.133451i	0.994310	−	0.106523i	$-0.0339719\pi$
$281$	0.394452	+	2.23705i	0.0235311	+	0.133451i	−0.970779	+	0.239975i	$0.922861\pi$
$282$		0			0
$283$	9.92729	+	8.32998i	0.590116	+	0.495166i	0.888252	−	0.459357i	$-0.151920\pi$
$283$	9.92729	+	8.32998i	0.590116	+	0.495166i	−0.298135	+	0.954524i	$0.596365\pi$
$284$		0			0
$285$	27.1262	−	18.4155i	1.60682	−	1.09084i
$286$		0			0
$287$	−11.1578	−	9.36252i	−0.658625	−	0.552652i
$288$		0			0
$289$	−2.94938	−	16.7268i	−0.173493	−	0.983929i
$290$		0			0
$291$	32.6803	+	11.8946i	1.91575	+	0.697277i
$292$		0			0
$293$	−6.69915	+	11.6033i	−0.391369	+	0.677871i	−0.992630	−	0.121182i	$-0.961332\pi$
$293$	−6.69915	+	11.6033i	−0.391369	+	0.677871i	0.601262	+	0.799052i	$0.294665\pi$
$294$		0			0
$295$	17.3796	−	14.5832i	1.01188	−	0.849066i
$296$		0			0
$297$	13.2771	+	22.9966i	0.770414	+	1.33440i
$298$		0			0
$299$	4.82918	−	27.3876i	0.279278	−	1.58387i
$300$		0			0
$301$	2.07610	−	0.755638i	0.119664	−	0.0435542i
$302$		0			0
$303$	−0.410387			−0.0235761
$304$		0			0
$305$	18.4042			1.05382
$306$		0			0
$307$	30.1328	−	10.9675i	1.71977	−	0.625946i	0.721952	−	0.691943i	$-0.243245\pi$
$307$	30.1328	−	10.9675i	1.71977	−	0.625946i	0.997820	+	0.0659970i	$0.0210228\pi$
$308$		0			0
$309$	−1.47205	+	8.34839i	−0.0837418	+	0.474923i
$310$		0			0
$311$	−1.72247	−	2.98341i	−0.0976723	−	0.169173i	0.813048	−	0.582196i	$-0.197806\pi$
$311$	−1.72247	−	2.98341i	−0.0976723	−	0.169173i	−0.910721	+	0.413023i	$0.864473\pi$
$312$		0			0
$313$	18.6501	−	15.6493i	1.05417	−	0.884552i	0.0606418	−	0.998160i	$-0.480685\pi$
$313$	18.6501	−	15.6493i	1.05417	−	0.884552i	0.993526	+	0.113608i	$0.0362408\pi$
$314$		0			0
$315$	−9.53763	+	16.5197i	−0.537385	+	0.930778i
$316$		0			0
$317$	16.8920	+	6.14817i	0.948748	+	0.345316i	0.769614	−	0.638509i	$-0.220448\pi$
$317$	16.8920	+	6.14817i	0.948748	+	0.345316i	0.179133	+	0.983825i	$0.442671\pi$
$318$		0			0
$319$	7.46221	+	42.3203i	0.417804	+	2.36948i
$320$		0			0
$321$	−14.8104	−	12.4274i	−0.826635	−	0.693629i
$322$		0			0
$323$	0.146446	−	0.516560i	0.00814846	−	0.0287422i
$324$		0			0
$325$	6.59865	+	5.53692i	0.366027	+	0.307133i
$326$		0			0
$327$	−2.44668	−	13.8758i	−0.135302	−	0.767335i
$328$		0			0
$329$	−3.70700	−	1.34924i	−0.204373	−	0.0743858i
$330$		0			0
$331$	−13.1916	+	22.8485i	−0.725076	+	1.25587i	0.233867	+	0.972269i	$0.424862\pi$
$331$	−13.1916	+	22.8485i	−0.725076	+	1.25587i	−0.958943	+	0.283600i	$0.908471\pi$
$332$		0			0
$333$	16.1153	−	13.5223i	0.883111	−	0.741018i
$334$		0			0
$335$	−12.8469	−	22.2515i	−0.701901	−	1.21573i
$336$		0			0
$337$	−3.31131	+	18.7794i	−0.180378	+	1.02298i	0.751373	+	0.659878i	$0.229392\pi$
$337$	−3.31131	+	18.7794i	−0.180378	+	1.02298i	−0.931751	+	0.363098i	$0.881719\pi$
$338$		0			0
$339$	−28.8410	+	10.4973i	−1.56643	+	0.570132i
$340$		0			0
$341$	−31.4797			−1.70472
$342$		0			0
$343$	−17.3500			−0.936812
$344$		0			0
$345$	−50.1567	+	18.2556i	−2.70035	+	0.982846i
$346$		0			0
$347$	−1.07931	+	6.12109i	−0.0579406	+	0.328598i	−0.999976	−	0.00691577i	$-0.997799\pi$
$347$	−1.07931	+	6.12109i	−0.0579406	+	0.328598i	0.942035	+	0.335513i	$0.108910\pi$
$348$		0			0
$349$	18.1788	+	31.4865i	0.973087	+	1.68544i	0.686109	+	0.727499i	$0.259317\pi$
$349$	18.1788	+	31.4865i	0.973087	+	1.68544i	0.286978	+	0.957937i	$0.407349\pi$
$350$		0			0
$351$	15.6562	−	13.1371i	0.835666	−	0.701207i
$352$		0			0
$353$	6.76616	−	11.7193i	0.360127	−	0.623757i	−0.627855	−	0.778330i	$-0.716067\pi$
$353$	6.76616	−	11.7193i	0.360127	−	0.623757i	0.987981	+	0.154573i	$0.0494002\pi$
$354$		0			0
$355$	5.85508	+	2.13107i	0.310755	+	0.113106i
$356$		0			0
$357$	0.0877273	+	0.497526i	0.00464302	+	0.0263319i
$358$		0			0
$359$	6.94608	+	5.82845i	0.366600	+	0.307614i	0.807415	−	0.589984i	$-0.200866\pi$
$359$	6.94608	+	5.82845i	0.366600	+	0.307614i	−0.440815	+	0.897598i	$0.645310\pi$
$360$		0			0
$361$	−12.6285	+	14.1958i	−0.664660	+	0.747146i
$362$		0			0
$363$	32.0590	+	26.9007i	1.68266	+	1.41192i
$364$		0			0
$365$	5.51226	+	31.2616i	0.288525	+	1.63630i
$366$		0			0
$367$	−26.3049	−	9.57418i	−1.37310	−	0.499768i	−0.453022	−	0.891499i	$-0.649654\pi$
$367$	−26.3049	−	9.57418i	−1.37310	−	0.499768i	−0.920080	+	0.391731i	$0.871876\pi$
$368$		0			0
$369$	24.1948	−	41.9067i	1.25953	−	2.18157i
$370$		0			0
$371$	−6.77275	+	5.68301i	−0.351624	+	0.295047i
$372$		0			0
$373$	−4.00524	−	6.93728i	−0.207383	−	0.359198i	0.743506	−	0.668729i	$-0.233161\pi$
$373$	−4.00524	−	6.93728i	−0.207383	−	0.359198i	−0.950889	+	0.309531i	$0.899828\pi$
$374$		0			0
$375$	−3.65984	+	20.7560i	−0.188993	+	1.07183i
$376$		0			0
$377$	31.0802	−	11.3123i	1.60071	−	0.582611i
$378$		0			0
$379$	1.40989			0.0724210			0.0362105	−	0.999344i	$-0.488471\pi$
$379$	1.40989			0.0724210			0.0362105	+	0.999344i	$0.488471\pi$
$380$		0			0
$381$	−25.2605			−1.29414
$382$		0			0
$383$	24.8931	−	9.06034i	1.27198	−	0.462962i	0.384206	−	0.923247i	$-0.374475\pi$
$383$	24.8931	−	9.06034i	1.27198	−	0.462962i	0.887771	+	0.460286i	$0.152253\pi$
$384$		0			0
$385$	−3.47035	+	19.6813i	−0.176865	+	1.00305i
$386$		0			0
$387$	3.66994	+	6.35653i	0.186554	+	0.323120i
$388$		0			0
$389$	−20.5618	+	17.2534i	−1.04252	+	0.874782i	−0.992288	−	0.123955i	$-0.960442\pi$
$389$	−20.5618	+	17.2534i	−1.04252	+	0.874782i	−0.0502367	+	0.998737i	$0.515998\pi$
$390$		0			0
$391$	−0.437044	+	0.756982i	−0.0221023	+	0.0382822i
$392$		0			0
$393$	−37.2998	−	13.5760i	−1.88153	−	0.684820i
$394$		0			0
$395$	−1.38982	−	7.88205i	−0.0699293	−	0.396589i
$396$		0			0
$397$	−28.1199	−	23.5954i	−1.41130	−	1.18422i	−0.955813	−	0.293974i	$-0.905022\pi$
$397$	−28.1199	−	23.5954i	−1.41130	−	1.18422i	−0.455483	−	0.890244i	$-0.650534\pi$
$398$		0			0
$399$	4.87617	−	17.1998i	0.244114	−	0.861067i
$400$		0			0
$401$	7.65288	+	6.42153i	0.382166	+	0.320676i	0.813552	−	0.581492i	$-0.197531\pi$
$401$	7.65288	+	6.42153i	0.382166	+	0.320676i	−0.431386	+	0.902168i	$0.641975\pi$
$402$		0			0
$403$	4.20727	+	23.8606i	0.209579	+	1.18858i
$404$		0			0
$405$	−0.101748	−	0.0370331i	−0.00505588	−	0.00184019i
$406$		0			0
$407$	11.0201	−	19.0874i	0.546247	−	0.946127i
$408$		0			0
$409$	−17.3137	+	14.5279i	−0.856109	+	0.718361i	−0.961126	−	0.276110i	$-0.910955\pi$
$409$	−17.3137	+	14.5279i	−0.856109	+	0.718361i	0.105017	+	0.994470i	$0.466510\pi$
$410$		0			0
$411$	11.1406	+	19.2961i	0.549527	+	0.951808i
$412$		0			0
$413$	2.14817	−	12.1829i	0.105705	−	0.599481i
$414$		0			0
$415$	9.75656	−	3.55110i	0.478931	−	0.174317i
$416$		0			0
$417$	32.1839			1.57605
$418$		0			0
$419$	25.7953			1.26018			0.630092	−	0.776520i	$-0.283017\pi$
$419$	25.7953			1.26018			0.630092	+	0.776520i	$0.283017\pi$
$420$		0			0
$421$	1.69142	−	0.615627i	0.0824349	−	0.0300038i	−0.300474	−	0.953790i	$-0.597145\pi$
$421$	1.69142	−	0.615627i	0.0824349	−	0.0300038i	0.382908	+	0.923786i	$0.374922\pi$
$422$		0			0
$423$	2.27580	−	12.9067i	0.110653	−	0.627545i
$424$		0			0
$425$	−0.135370	−	0.234468i	−0.00656642	−	0.0113734i
$426$		0			0
$427$	7.68750	−	6.45058i	0.372024	−	0.312165i
$428$		0			0
$429$	27.9732	−	48.4510i	1.35056	−	2.33923i
$430$		0			0
$431$	−30.0767	−	10.9470i	−1.44875	−	0.527300i	−0.506505	−	0.862237i	$-0.669063\pi$
$431$	−30.0767	−	10.9470i	−1.44875	−	0.527300i	−0.942241	+	0.334936i	$0.891285\pi$
$432$		0			0
$433$	4.30342	+	24.4059i	0.206809	+	1.17287i	0.894567	+	0.446933i	$0.147484\pi$
$433$	4.30342	+	24.4059i	0.206809	+	1.17287i	−0.687758	+	0.725940i	$0.741405\pi$
$434$		0			0
$435$	−48.6286	−	40.8043i	−2.33157	−	1.95642i
$436$		0			0
$437$	25.5914	−	17.3735i	1.22420	−	0.831088i
$438$		0			0
$439$	7.49608	+	6.28996i	0.357768	+	0.300203i	0.803901	−	0.594764i	$-0.202754\pi$
$439$	7.49608	+	6.28996i	0.357768	+	0.300203i	−0.446132	+	0.894967i	$0.647199\pi$
$440$		0			0
$441$	−4.10149	−	23.2607i	−0.195309	−	1.10765i
$442$		0			0
$443$	−21.4777	−	7.81725i	−1.02044	−	0.371409i	−0.223005	−	0.974817i	$-0.571587\pi$
$443$	−21.4777	−	7.81725i	−1.02044	−	0.371409i	−0.797432	+	0.603408i	$0.793809\pi$
$444$		0			0
$445$	11.7411	−	20.3362i	0.556582	−	0.964029i
$446$		0			0
$447$	−39.6589	+	33.2777i	−1.87580	+	1.57398i
$448$		0			0
$449$	8.35395	+	14.4695i	0.394247	+	0.682856i	0.993005	−	0.118074i	$-0.0376720\pi$
$449$	8.35395	+	14.4695i	0.394247	+	0.682856i	−0.598757	+	0.800930i	$0.704339\pi$
$450$		0			0
$451$	8.80349	−	49.9271i	0.414540	−	2.35097i
$452$		0			0
$453$	28.9842	−	10.5494i	1.36180	−	0.495653i
$454$		0			0
$455$	15.3817			0.721103
$456$		0			0
$457$	26.8638			1.25663			0.628317	−	0.777957i	$-0.283744\pi$
$457$	26.8638			1.25663			0.628317	+	0.777957i	$0.283744\pi$
$458$		0			0
$459$	−0.603630	+	0.219703i	−0.0281750	+	0.0102549i
$460$		0			0
$461$	1.49638	−	8.48640i	0.0696934	−	0.395251i	−0.929928	−	0.367741i	$-0.880131\pi$
$461$	1.49638	−	8.48640i	0.0696934	−	0.395251i	0.999622	−	0.0275097i	$-0.00875771\pi$
$462$		0			0
$463$	−2.61915	−	4.53651i	−0.121722	−	0.210829i	0.798725	−	0.601697i	$-0.205508\pi$
$463$	−2.61915	−	4.53651i	−0.121722	−	0.210829i	−0.920447	+	0.390867i	$0.872175\pi$
$464$		0			0
$465$	35.6225	−	29.8908i	1.65195	−	1.38615i
$466$		0			0
$467$	−1.56762	+	2.71519i	−0.0725407	+	0.125644i	−0.900014	−	0.435861i	$-0.856444\pi$
$467$	−1.56762	+	2.71519i	−0.0725407	+	0.125644i	0.827473	+	0.561505i	$0.189777\pi$
$468$		0			0
$469$	−13.1652	−	4.79175i	−0.607913	−	0.221262i
$470$		0			0
$471$	−3.81330	−	21.6263i	−0.175707	−	0.996486i
$472$		0			0
$473$	5.89082	+	4.94298i	0.270860	+	0.227279i
$474$		0			0
$475$	0.696986	+	9.55535i	0.0319799	+	0.438430i
$476$		0			0
$477$	−22.5005	−	18.8802i	−1.03023	−	0.864464i
$478$		0			0
$479$	5.55924	+	31.5280i	0.254008	+	1.44055i	0.798606	+	0.601855i	$0.205571\pi$
$479$	5.55924	+	31.5280i	0.254008	+	1.44055i	−0.544597	+	0.838698i	$0.683317\pi$
$480$		0			0
$481$	−15.9405	−	5.80187i	−0.726824	−	0.264542i
$482$		0			0
$483$	−14.5522	+	25.2051i	−0.662146	+	1.14687i
$484$		0			0
$485$	−25.4944	+	21.3923i	−1.15764	+	0.971376i
$486$		0			0
$487$	2.76183	+	4.78363i	0.125150	+	0.216767i	0.921792	−	0.387685i	$-0.126725\pi$
$487$	2.76183	+	4.78363i	0.125150	+	0.216767i	−0.796641	+	0.604452i	$0.793392\pi$
$488$		0			0
$489$	7.14152	−	40.5016i	0.322951	−	1.83155i
$490$		0			0
$491$	24.4207	−	8.88840i	1.10209	−	0.401128i	0.274004	−	0.961729i	$-0.411652\pi$
$491$	24.4207	−	8.88840i	1.10209	−	0.401128i	0.828086	+	0.560601i	$0.189430\pi$
$492$		0			0
$493$	−1.03956			−0.0468195
$494$		0			0
$495$	−66.3942			−2.98420
$496$		0			0
$497$	3.19262	−	1.16202i	0.143208	−	0.0521236i
$498$		0			0
$499$	−3.07891	+	17.4614i	−0.137831	+	0.781679i	0.835015	+	0.550227i	$0.185459\pi$
$499$	−3.07891	+	17.4614i	−0.137831	+	0.781679i	−0.972846	+	0.231452i	$0.925652\pi$
$500$		0			0
$501$	9.89430	+	17.1374i	0.442045	+	0.765644i
$502$		0			0
$503$	−22.1391	+	18.5769i	−0.987132	+	0.828302i	−0.985150	−	0.171696i	$-0.945075\pi$
$503$	−22.1391	+	18.5769i	−0.987132	+	0.828302i	−0.00198219	+	0.999998i	$0.500631\pi$
$504$		0			0
$505$	0.196360	−	0.340106i	0.00873792	−	0.0151345i
$506$		0			0
$507$	−6.21432	−	2.26183i	−0.275987	−	0.100451i
$508$		0			0
$509$	6.01704	+	34.1243i	0.266701	+	1.51253i	0.764149	+	0.645040i	$0.223159\pi$
$509$	6.01704	+	34.1243i	0.266701	+	1.51253i	−0.497448	+	0.867494i	$0.665729\pi$
$510$		0			0
$511$	13.2595	+	11.1260i	0.586566	+	0.492187i
$512$		0			0
$513$	22.6141	+	2.30827i	0.998438	+	0.101913i
$514$		0			0
$515$	−6.21435	−	5.21446i	−0.273837	−	0.229777i
$516$		0			0
$517$	−2.38433	−	13.5222i	−0.104863	−	0.594706i
$518$		0			0
$519$	27.4819	+	10.0026i	1.20632	+	0.439066i
$520$		0			0
$521$	−13.9128	+	24.0977i	−0.609532	+	1.05574i	0.381785	+	0.924251i	$0.375309\pi$
$521$	−13.9128	+	24.0977i	−0.609532	+	1.05574i	−0.991317	+	0.131490i	$0.958024\pi$
$522$		0			0
$523$	−25.6416	+	21.5159i	−1.12123	+	0.940823i	−0.998666	−	0.0516379i	$-0.983556\pi$
$523$	−25.6416	+	21.5159i	−1.12123	+	0.940823i	−0.122563	+	0.992461i	$0.539111\pi$
$524$		0			0
$525$	−4.50739	−	7.80704i	−0.196719	−	0.340727i
$526$		0			0
$527$	0.132237	−	0.749953i	0.00576033	−	0.0326684i
$528$		0			0
$529$	−25.7059	+	9.35618i	−1.11765	+	0.406790i
$530$		0			0
$531$	41.0985			1.78352
$532$		0			0
$533$	−39.0198			−1.69013
$534$		0			0
$535$	17.3856	−	6.32783i	0.751644	−	0.273576i
$536$		0			0
$537$	−6.55892	+	37.1975i	−0.283038	+	1.60519i
$538$		0			0
$539$	−12.3730	−	21.4306i	−0.532942	−	0.923082i
$540$		0			0
$541$	28.9160	−	24.2634i	1.24320	−	1.04317i	0.245931	−	0.969287i	$-0.420906\pi$
$541$	28.9160	−	24.2634i	1.24320	−	1.04317i	0.997267	−	0.0738796i	$-0.0235381\pi$
$542$		0			0
$543$	0.0987020	−	0.170957i	0.00423571	−	0.00733646i
$544$		0			0
$545$	12.6702	+	4.61158i	0.542732	+	0.197538i
$546$		0			0
$547$	−0.551474	−	3.12757i	−0.0235793	−	0.133725i	0.970746	−	0.240110i	$-0.0771835\pi$
$547$	−0.551474	−	3.12757i	−0.0235793	−	0.133725i	−0.994325	+	0.106385i	$0.966072\pi$
$548$		0			0
$549$	25.5395	+	21.4302i	1.09000	+	0.914618i
$550$		0			0
$551$	33.1123	+	16.0271i	1.41063	+	0.682779i
$552$		0			0
$553$	−3.34315	−	2.80524i	−0.142165	−	0.119291i
$554$		0			0
$555$	5.65362	+	32.0633i	0.239983	+	1.36101i
$556$		0			0
$557$	−1.09576	−	0.398824i	−0.0464289	−	0.0168987i	0.318701	−	0.947855i	$-0.396753\pi$
$557$	−1.09576	−	0.398824i	−0.0464289	−	0.0168987i	−0.365130	+	0.930956i	$0.618976\pi$
$558$		0			0
$559$	2.95932	−	5.12569i	0.125166	−	0.216794i
$560$		0			0
$561$	−1.34703	+	1.13029i	−0.0568718	+	0.0477211i
$562$		0			0
$563$	−8.13224	−	14.0854i	−0.342733	−	0.593631i	0.642206	−	0.766532i	$-0.278019\pi$
$563$	−8.13224	−	14.0854i	−0.342733	−	0.593631i	−0.984939	+	0.172901i	$0.944686\pi$
$564$		0			0
$565$	5.10017	−	28.9245i	0.214566	−	1.21686i
$566$		0			0
$567$	−0.0554802	+	0.0201932i	−0.00232995	+	0.000848033i
$568$		0			0
$569$	−1.77172			−0.0742742			−0.0371371	−	0.999310i	$-0.511824\pi$
$569$	−1.77172			−0.0742742			−0.0371371	+	0.999310i	$0.511824\pi$
$570$		0			0
$571$	17.7171			0.741436			0.370718	−	0.928745i	$-0.379112\pi$
$571$	17.7171			0.741436			0.370718	+	0.928745i	$0.379112\pi$
$572$		0			0
$573$	−14.7698	+	5.37577i	−0.617018	+	0.224576i
$574$		0			0
$575$	2.70842	−	15.3602i	0.112949	−	0.640566i
$576$		0			0
$577$	−2.64778	−	4.58609i	−0.110229	−	0.190921i	0.805634	−	0.592414i	$-0.201825\pi$
$577$	−2.64778	−	4.58609i	−0.110229	−	0.190921i	−0.915862	+	0.401492i	$0.868492\pi$
$578$		0			0
$579$	−41.0657	+	34.4582i	−1.70663	+	1.43204i
$580$		0			0
$581$	2.83071	−	4.90293i	0.117438	−	0.203408i
$582$		0			0
$583$	−28.9172	−	10.5250i	−1.19763	−	0.435901i
$584$		0			0
$585$	8.87361	+	50.3248i	0.366879	+	2.08067i
$586$		0			0
$587$	−19.0477	−	15.9829i	−0.786183	−	0.659686i	0.158615	−	0.987341i	$-0.449297\pi$
$587$	−19.0477	−	15.9829i	−0.786183	−	0.659686i	−0.944797	+	0.327655i	$0.893742\pi$
$588$		0			0
$589$	−15.7742	+	21.8489i	−0.649965	+	0.900268i
$590$		0			0
$591$	29.9054	+	25.0936i	1.23015	+	1.03221i
$592$		0			0
$593$	3.38821	+	19.2155i	0.139137	+	0.789085i	0.971889	+	0.235439i	$0.0756527\pi$
$593$	3.38821	+	19.2155i	0.139137	+	0.789085i	−0.832752	+	0.553646i	$0.813236\pi$
$594$		0			0
$595$	−0.454298	−	0.165351i	−0.0186244	−	0.00677873i
$596$		0			0
$597$	6.52638	−	11.3040i	0.267107	−	0.462643i
$598$		0			0
$599$	8.75592	−	7.34709i	0.357757	−	0.300194i	−0.446139	−	0.894964i	$-0.647201\pi$
$599$	8.75592	−	7.34709i	0.357757	−	0.300194i	0.803896	+	0.594770i	$0.202757\pi$
$600$		0			0
$601$	4.31755	+	7.47822i	0.176117	+	0.305043i	0.940547	−	0.339663i	$-0.110313\pi$
$601$	4.31755	+	7.47822i	0.176117	+	0.305043i	−0.764430	+	0.644706i	$0.776980\pi$
$602$		0			0
$603$	8.08239	−	45.8375i	0.329140	−	1.86665i
$604$		0			0
$605$	−37.6333	+	13.6974i	−1.53001	+	0.556878i
$606$		0			0
$607$	8.95791			0.363591			0.181795	−	0.983336i	$-0.441809\pi$
$607$	8.95791			0.363591			0.181795	+	0.983336i	$0.441809\pi$
$608$		0			0
$609$	−34.6140			−1.40263
$610$		0			0
$611$	−9.93075	+	3.61450i	−0.401755	+	0.146227i
$612$		0			0
$613$	1.46237	−	8.29349i	0.0590644	−	0.334971i	−0.940929	−	0.338604i	$-0.890045\pi$
$613$	1.46237	−	8.29349i	0.0590644	−	0.334971i	0.999993	+	0.00363302i	$0.00115643\pi$
$614$		0			0
$615$	37.4452	+	64.8569i	1.50993	+	2.61528i
$616$		0			0
$617$	12.4542	−	10.4503i	0.501387	−	0.420713i	−0.356700	−	0.934219i	$-0.616098\pi$
$617$	12.4542	−	10.4503i	0.501387	−	0.420713i	0.858086	+	0.513506i	$0.171654\pi$
$618$		0			0
$619$	−0.853509	+	1.47832i	−0.0343054	+	0.0594187i	−0.882668	−	0.469996i	$-0.844255\pi$
$619$	−0.853509	+	1.47832i	−0.0343054	+	0.0594187i	0.848363	+	0.529415i	$0.177589\pi$
$620$		0			0
$621$	−34.7747	−	12.6570i	−1.39546	−	0.507906i
$622$		0			0
$623$	−2.22343	−	12.6097i	−0.0890799	−	0.505197i
$624$		0			0
$625$	−23.8690	−	20.0285i	−0.954760	−	0.801139i
$626$		0			0
$627$	60.3319	−	15.2348i	2.40942	−	0.608420i
$628$		0			0
$629$	0.408434	+	0.342717i	0.0162853	+	0.0136650i
$630$		0			0
$631$	−8.45638	−	47.9585i	−0.336643	−	1.90920i	−0.410371	−	0.911919i	$-0.634601\pi$
$631$	−8.45638	−	47.9585i	−0.336643	−	1.90920i	0.0737277	−	0.997278i	$-0.476510\pi$
$632$		0			0
$633$	26.8855	+	9.78551i	1.06860	+	0.388939i
$634$		0			0
$635$	12.0866	−	20.9346i	0.479641	−	0.830762i
$636$		0			0
$637$	−14.5901	+	12.2425i	−0.578081	+	0.485067i
$638$		0			0
$639$	5.64363	+	9.77505i	0.223258	+	0.386695i
$640$		0			0
$641$	−2.70651	+	15.3494i	−0.106901	+	0.606263i	0.883544	+	0.468349i	$0.155151\pi$
$641$	−2.70651	+	15.3494i	−0.106901	+	0.606263i	−0.990444	+	0.137914i	$0.955960\pi$
$642$		0			0
$643$	−20.5197	+	7.46857i	−0.809219	+	0.294532i	−0.713301	−	0.700858i	$-0.752801\pi$
$643$	−20.5197	+	7.46857i	−0.809219	+	0.294532i	−0.0959178	+	0.995389i	$0.530579\pi$
$644$		0			0
$645$	−11.3596			−0.447283
$646$		0			0
$647$	10.9347			0.429887			0.214944	−	0.976626i	$-0.431043\pi$
$647$	10.9347			0.429887			0.214944	+	0.976626i	$0.431043\pi$
$648$		0			0
$649$	40.4617	−	14.7269i	1.58826	−	0.578080i
$650$		0			0
$651$	4.40306	−	24.9710i	0.172570	−	0.978691i
$652$		0			0
$653$	20.2871	+	35.1383i	0.793896	+	1.37507i	0.923538	+	0.383508i	$0.125284\pi$
$653$	20.2871	+	35.1383i	0.793896	+	1.37507i	−0.129641	+	0.991561i	$0.541382\pi$
$654$		0			0
$655$	29.0982	−	24.4163i	1.13696	−	0.954023i
$656$		0			0
$657$	−28.7522	+	49.8002i	−1.12173	+	1.94289i
$658$		0			0
$659$	−21.1558	−	7.70009i	−0.824114	−	0.299953i	−0.104673	−	0.994507i	$-0.533380\pi$
$659$	−21.1558	−	7.70009i	−0.824114	−	0.299953i	−0.719441	+	0.694554i	$0.755602\pi$
$660$		0			0
$661$	−5.81544	−	32.9810i	−0.226195	−	1.28281i	−0.860388	−	0.509639i	$-0.829779\pi$
$661$	−5.81544	−	32.9810i	−0.226195	−	1.28281i	0.634194	−	0.773174i	$-0.281332\pi$
$662$		0			0
$663$	1.03676	+	0.869945i	0.0402644	+	0.0337859i
$664$		0			0
$665$	11.9211	+	12.2708i	0.462282	+	0.475842i
$666$		0			0
$667$	−45.8772	−	38.4955i	−1.77637	−	1.49055i
$668$		0			0
$669$	3.17221	+	17.9905i	0.122645	+	0.695553i
$670$		0			0
$671$	32.8229	+	11.9465i	1.26711	+	0.461191i
$672$		0			0
$673$	0.883145	−	1.52965i	0.0340427	−	0.0589637i	−0.848502	−	0.529192i	$-0.822495\pi$
$673$	0.883145	−	1.52965i	0.0340427	−	0.0589637i	0.882545	+	0.470228i	$0.155828\pi$
$674$		0			0
$675$	8.78071	−	7.36789i	0.337970	−	0.283590i
$676$		0			0
$677$	−4.98696	−	8.63767i	−0.191665	−	0.331973i	0.754137	−	0.656717i	$-0.228055\pi$
$677$	−4.98696	−	8.63767i	−0.191665	−	0.331973i	−0.945802	+	0.324744i	$0.894722\pi$
$678$		0			0
$679$	−3.15119	+	17.8713i	−0.120932	+	0.685837i
$680$		0			0
$681$	28.5293	−	10.3838i	1.09324	−	0.397908i
$682$		0			0
$683$	26.9258			1.03029			0.515144	−	0.857104i	$-0.327738\pi$
$683$	26.9258			1.03029			0.515144	+	0.857104i	$0.327738\pi$
$684$		0			0
$685$	−21.3221			−0.814676
$686$		0			0
$687$	−49.7188	+	18.0962i	−1.89689	+	0.690412i
$688$		0			0
$689$	−4.11283	+	23.3250i	−0.156686	+	0.888613i
$690$		0			0
$691$	−4.45054	−	7.70857i	−0.169307	−	0.293248i	0.768870	−	0.639406i	$-0.220820\pi$
$691$	−4.45054	−	7.70857i	−0.169307	−	0.293248i	−0.938176	+	0.346158i	$0.887486\pi$
$692$		0			0
$693$	−27.7331	+	23.2708i	−1.05349	+	0.883985i
$694$		0			0
$695$	−15.3992	+	26.6722i	−0.584126	+	1.01174i
$696$		0			0
$697$	1.15245	+	0.419458i	0.0436523	+	0.0158881i
$698$		0			0
$699$	2.12226	+	12.0359i	0.0802711	+	0.455240i
$700$		0			0
$701$	−20.6325	−	17.3127i	−0.779277	−	0.653891i	0.163789	−	0.986495i	$-0.447628\pi$
$701$	−20.6325	−	17.3127i	−0.779277	−	0.653891i	−0.943067	+	0.332604i	$0.892073\pi$
$702$		0			0
$703$	−7.72577	−	17.2132i	−0.291383	−	0.649208i
$704$		0			0
$705$	15.5378	+	13.0378i	0.585189	+	0.491032i
$706$		0			0
$707$	−0.0371850	−	0.210887i	−0.00139849	−	0.00793121i
$708$		0			0
$709$	−32.5792	−	11.8578i	−1.22354	−	0.445331i	−0.352157	−	0.935941i	$-0.614552\pi$
$709$	−32.5792	−	11.8578i	−1.22354	−	0.445331i	−0.871379	+	0.490610i	$0.836774\pi$
$710$		0			0
$711$	7.24935	−	12.5562i	0.271872	−	0.470896i
$712$		0			0
$713$	33.6070	−	28.1996i	1.25859	−	1.05608i
$714$		0			0
$715$	26.7690	+	46.3653i	1.00110	+	1.73396i
$716$		0			0
$717$	−1.57841	+	8.95159i	−0.0589467	+	0.334303i
$718$		0			0
$719$	18.0472	−	6.56864i	0.673047	−	0.244969i	0.0171876	−	0.999852i	$-0.494529\pi$
$719$	18.0472	−	6.56864i	0.673047	−	0.244969i	0.655859	+	0.754883i	$0.272307\pi$
$720$		0			0
$721$	−4.42340			−0.164736
$722$		0			0
$723$	12.8474			0.477800
$724$		0			0
$725$	17.4312	−	6.34443i	0.647378	−	0.235626i
$726$		0			0
$727$	−5.74663	+	32.5907i	−0.213131	+	1.20872i	0.670990	+	0.741466i	$0.265869\pi$
$727$	−5.74663	+	32.5907i	−0.213131	+	1.20872i	−0.884121	+	0.467258i	$0.845242\pi$
$728$		0			0
$729$	21.8330	+	37.8158i	0.808629	+	1.40059i
$730$		0			0
$731$	−0.142504	+	0.119575i	−0.00527071	+	0.00442265i
$732$		0			0
$733$	−5.25284	+	9.09818i	−0.194018	+	0.336049i	−0.946578	−	0.322474i	$-0.895485\pi$
$733$	−5.25284	+	9.09818i	−0.194018	+	0.336049i	0.752560	+	0.658523i	$0.228819\pi$
$734$		0			0
$735$	34.3503	+	12.5025i	1.26703	+	0.461161i
$736$		0			0
$737$	−8.46783	−	48.0234i	−0.311916	−	1.76897i
$738$		0			0
$739$	−41.1543	−	34.5325i	−1.51388	−	1.27030i	−0.855738	−	0.517409i	$-0.826897\pi$
$739$	−41.1543	−	34.5325i	−1.51388	−	1.27030i	−0.658146	−	0.752891i	$-0.728659\pi$
$740$		0			0
$741$	−19.6109	−	43.6936i	−0.720425	−	1.60512i
$742$		0			0
$743$	−19.8285	−	16.6381i	−0.727436	−	0.610391i	0.201995	−	0.979386i	$-0.435257\pi$
$743$	−19.8285	−	16.6381i	−0.727436	−	0.610391i	−0.929431	+	0.368995i	$0.879702\pi$
$744$		0			0
$745$	−8.60294	−	48.7897i	−0.315188	−	1.78752i
$746$		0			0
$747$	17.6741	+	6.43286i	0.646663	+	0.235366i
$748$		0			0
$749$	5.04414	−	8.73671i	0.184309	−	0.319232i
$750$		0			0
$751$	29.6103	−	24.8460i	1.08049	−	0.906642i	0.0845321	−	0.996421i	$-0.473060\pi$
$751$	29.6103	−	24.8460i	1.08049	−	0.906642i	0.995962	+	0.0897788i	$0.0286160\pi$
$752$		0			0
$753$	−21.9849	−	38.0790i	−0.801175	−	1.38768i
$754$		0			0
$755$	−5.12550	+	29.0681i	−0.186536	+	1.05790i
$756$		0			0
$757$	48.0462	−	17.4874i	1.74627	−	0.635589i	0.746705	−	0.665156i	$-0.231635\pi$
$757$	48.0462	−	17.4874i	1.74627	−	0.635589i	0.999563	+	0.0295665i	$0.00941269\pi$
$758$		0			0
$759$	−101.302			−3.67702
$760$		0			0
$761$	−12.3013			−0.445923			−0.222961	−	0.974827i	$-0.571572\pi$
$761$	−12.3013			−0.445923			−0.222961	+	0.974827i	$0.571572\pi$
$762$		0			0
$763$	6.90873	−	2.51457i	0.250113	−	0.0910336i
$764$		0			0
$765$	0.278903	−	1.58174i	0.0100837	−	0.0571878i
$766$		0			0
$767$	−16.5702	−	28.7005i	−0.598317	−	1.03631i
$768$		0			0
$769$	−21.6923	+	18.2020i	−0.782246	+	0.656382i	−0.943813	−	0.330479i	$-0.892790\pi$
$769$	−21.6923	+	18.2020i	−0.782246	+	0.656382i	0.161567	+	0.986862i	$0.448345\pi$
$770$		0			0
$771$	2.16287	−	3.74621i	0.0778940	−	0.134916i
$772$		0			0
$773$	25.4219	+	9.25281i	0.914361	+	0.332800i	0.755993	−	0.654580i	$-0.227154\pi$
$773$	25.4219	+	9.25281i	0.914361	+	0.332800i	0.158368	+	0.987380i	$0.449377\pi$
$774$		0			0
$775$	2.35963	+	13.3821i	0.0847603	+	0.480700i
$776$		0			0
$777$	13.5996	+	11.4114i	0.487881	+	0.409381i
$778$		0			0
$779$	−30.2412	−	31.1283i	−1.08350	−	1.11529i
$780$		0			0
$781$	9.05888	+	7.60130i	0.324152	+	0.271996i
$782$		0			0
$783$	−7.64263	−	43.3435i	−0.273125	−	1.54897i
$784$		0			0
$785$	19.7473	+	7.18742i	0.704810	+	0.256530i
$786$		0			0
$787$	−2.23045	+	3.86326i	−0.0795071	+	0.137710i	−0.903037	−	0.429562i	$-0.858668\pi$
$787$	−2.23045	+	3.86326i	−0.0795071	+	0.137710i	0.823530	+	0.567272i	$0.192001\pi$
$788$		0			0
$789$	4.76129	−	3.99520i	0.169507	−	0.142233i
$790$		0			0
$791$	−8.00753	−	13.8695i	−0.284715	−	0.493141i
$792$		0			0
$793$	4.66833	−	26.4754i	0.165777	−	0.940169i
$794$		0			0
$795$	42.7167	−	15.5476i	1.51500	−	0.551416i
$796$		0			0
$797$	−12.6875			−0.449415			−0.224707	−	0.974426i	$-0.572143\pi$
$797$	−12.6875			−0.449415			−0.224707	+	0.974426i	$0.572143\pi$
$798$		0			0
$799$	0.332161			0.0117510
$800$		0			0
$801$	39.9730	−	14.5490i	1.41238	−	0.514063i
$802$		0			0
$803$	−10.4617	+	59.3313i	−0.369186	+	2.09376i
$804$		0			0
$805$	−13.9257	−	24.1201i	−0.490818	−	0.850121i
$806$		0			0
$807$	49.6678	−	41.6762i	1.74839	−	1.46707i
$808$		0			0
$809$	−4.94628	+	8.56721i	−0.173902	+	0.301207i	−0.939781	−	0.341778i	$-0.888971\pi$
$809$	−4.94628	+	8.56721i	−0.173902	+	0.301207i	0.765879	+	0.642985i	$0.222304\pi$
$810$		0			0
$811$	−8.24203	−	2.99985i	−0.289417	−	0.105339i	0.193232	−	0.981153i	$-0.438103\pi$
$811$	−8.24203	−	2.99985i	−0.289417	−	0.105339i	−0.482649	+	0.875814i	$0.660325\pi$
$812$		0			0
$813$	−0.301386	−	1.70925i	−0.0105701	−	0.0599459i
$814$		0			0
$815$	30.1485	+	25.2976i	1.05605	+	0.886135i
$816$		0			0
$817$	6.38259	−	1.61171i	0.223299	−	0.0563866i
$818$		0			0
$819$	21.3451	+	17.9107i	0.745858	+	0.625849i
$820$		0			0
$821$	3.73825	+	21.2006i	0.130466	+	0.739908i	0.977910	+	0.209024i	$0.0670287\pi$
$821$	3.73825	+	21.2006i	0.130466	+	0.739908i	−0.847445	+	0.530883i	$0.821860\pi$
$822$		0			0
$823$	−34.2122	−	12.4522i	−1.19256	−	0.434057i	−0.331939	−	0.943301i	$-0.607703\pi$
$823$	−34.2122	−	12.4522i	−1.19256	−	0.434057i	−0.860622	+	0.509244i	$0.829925\pi$
$824$		0			0
$825$	15.6886	−	27.1735i	0.546208	−	0.946060i
$826$		0			0
$827$	14.9279	−	12.5260i	0.519095	−	0.435572i	−0.345221	−	0.938521i	$-0.612196\pi$
$827$	14.9279	−	12.5260i	0.519095	−	0.435572i	0.864316	+	0.502949i	$0.167752\pi$
$828$		0			0
$829$	21.6104	+	37.4303i	0.750560	+	1.30001i	0.947552	+	0.319602i	$0.103549\pi$
$829$	21.6104	+	37.4303i	0.750560	+	1.30001i	−0.196992	+	0.980405i	$0.563117\pi$
$830$		0			0
$831$	4.85926	−	27.5582i	0.168566	−	0.955984i
$832$		0			0
$833$	0.562526	−	0.204743i	0.0194904	−	0.00709391i
$834$		0			0
$835$	−18.9368			−0.655334
$836$		0			0
$837$	32.2407			1.11440
$838$		0			0
$839$	−11.7088	+	4.26167i	−0.404234	+	0.147129i	−0.536132	−	0.844134i	$-0.680115\pi$
$839$	−11.7088	+	4.26167i	−0.404234	+	0.147129i	0.131898	+	0.991263i	$0.457893\pi$
$840$		0			0
$841$	7.33244	−	41.5843i	0.252843	−	1.43394i
$842$		0			0
$843$	−3.18426	−	5.51530i	−0.109672	−	0.189957i
$844$		0			0
$845$	4.84788	−	4.06786i	0.166772	−	0.139939i
$846$		0			0
$847$	−10.9187	+	18.9117i	−0.375171	+	0.649815i
$848$		0			0
$849$	−34.1411	−	12.4263i	−1.17172	−	0.426470i
$850$		0			0
$851$	5.33374	+	30.2491i	0.182838	+	1.03693i
$852$		0			0
$853$	16.8546	+	14.1427i	0.577090	+	0.484236i	0.883990	−	0.467506i	$-0.154847\pi$
$853$	16.8546	+	14.1427i	0.577090	+	0.484236i	−0.306900	+	0.951742i	$0.599292\pi$
$854$		0			0
$855$	−33.2696	+	46.0818i	−1.13780	+	1.57596i
$856$		0			0
$857$	−22.3475	−	18.7518i	−0.763376	−	0.640549i	0.175627	−	0.984457i	$-0.443805\pi$
$857$	−22.3475	−	18.7518i	−0.763376	−	0.640549i	−0.939003	+	0.343908i	$0.888249\pi$
$858$		0			0
$859$	5.26555	+	29.8624i	0.179658	+	1.01889i	0.932629	+	0.360837i	$0.117509\pi$
$859$	5.26555	+	29.8624i	0.179658	+	1.01889i	−0.752971	+	0.658054i	$0.771380\pi$
$860$		0			0
$861$	38.3730	+	13.9666i	1.30775	+	0.475981i
$862$		0			0
$863$	26.0836	−	45.1782i	0.887897	−	1.53788i	0.0455403	−	0.998963i	$-0.485499\pi$
$863$	26.0836	−	45.1782i	0.887897	−	1.53788i	0.842357	−	0.538920i	$-0.181168\pi$
$864$		0			0
$865$	−21.4391	+	17.9895i	−0.728951	+	0.611662i
$866$		0			0
$867$	23.8092	+	41.2388i	0.808604	+	1.40054i
$868$		0			0
$869$	2.63774	−	14.9594i	0.0894791	−	0.507461i
$870$		0			0
$871$	−35.2686	+	12.8367i	−1.19503	+	0.434955i
$872$		0			0
$873$	−60.2881			−2.04044
$874$		0			0
$875$	−10.9976			−0.371786
$876$		0			0
$877$	−25.5648	+	9.30484i	−0.863264	+	0.314202i	−0.735436	−	0.677594i	$-0.763023\pi$
$877$	−25.5648	+	9.30484i	−0.863264	+	0.314202i	−0.127828	+	0.991796i	$0.540800\pi$
$878$		0			0
$879$	6.52281	−	36.9927i	0.220009	−	1.24773i
$880$		0			0
$881$	21.7951	+	37.7502i	0.734294	+	1.27183i	0.955032	+	0.296502i	$0.0958201\pi$
$881$	21.7951	+	37.7502i	0.734294	+	1.27183i	−0.220738	+	0.975333i	$0.570847\pi$
$882$		0			0
$883$	−10.0387	+	8.42343i	−0.337828	+	0.283471i	−0.795880	−	0.605454i	$-0.792992\pi$
$883$	−10.0387	+	8.42343i	−0.337828	+	0.283471i	0.458053	+	0.888925i	$0.348547\pi$
$884$		0			0
$885$	−31.8031	+	55.0846i	−1.06905	+	1.85165i
$886$		0			0
$887$	30.8003	+	11.2104i	1.03417	+	0.376409i	0.802669	−	0.596425i	$-0.203413\pi$
$887$	30.8003	+	11.2104i	1.03417	+	0.376409i	0.231505	+	0.972834i	$0.425635\pi$
$888$		0			0
$889$	−2.28885	−	12.9807i	−0.0767656	−	0.435359i
$890$		0			0
$891$	−0.157422	−	0.132093i	−0.00527384	−	0.00442528i
$892$		0			0
$893$	−10.5800	−	5.12100i	−0.354048	−	0.171368i
$894$		0			0
$895$	−27.6890	−	23.2338i	−0.925541	−	0.776621i
$896$		0			0
$897$	13.5390	+	76.7836i	0.452055	+	2.56373i
$898$		0			0
$899$	49.0293	+	17.8452i	1.63522	+	0.595171i
$900$		0			0
$901$	0.372214	−	0.644694i	0.0124003	−	0.0214779i
$902$		0			0
$903$	−4.74494	+	3.98147i	−0.157902	+	0.132495i
$904$		0			0
$905$	0.0944532	+	0.163598i	0.00313973	+	0.00543817i
$906$		0			0
$907$	−0.185960	+	1.05463i	−0.00617470	+	0.0350185i	−0.987739	−	0.156111i	$-0.950104\pi$
$907$	−0.185960	+	1.05463i	−0.00617470	+	0.0350185i	0.981565	+	0.191130i	$0.0612152\pi$
$908$		0			0
$909$	0.668515	−	0.243319i	0.0221732	−	0.00807040i
$910$		0			0
$911$	−38.0199			−1.25966			−0.629828	−	0.776734i	$-0.716875\pi$
$911$	−38.0199			−1.25966			−0.629828	+	0.776734i	$0.716875\pi$
$912$		0			0
$913$	19.7054			0.652153
$914$		0			0
$915$	−48.4861	+	17.6475i	−1.60290	+	0.583408i
$916$		0			0
$917$	3.59663	−	20.3975i	0.118771	−	0.673585i
$918$		0			0
$919$	18.9095	+	32.7523i	0.623768	+	1.08040i	0.988778	+	0.149395i	$0.0477325\pi$
$919$	18.9095	+	32.7523i	0.623768	+	1.08040i	−0.365009	+	0.931004i	$0.618934\pi$
$920$		0			0
$921$	−68.8688	+	57.7878i	−2.26930	+	1.90417i
$922$		0			0
$923$	4.55083	−	7.88227i	0.149792	−	0.259448i
$924$		0			0
$925$	−8.94016	−	3.25395i	−0.293951	−	0.106989i
$926$		0			0
$927$	−2.55184	−	14.4722i	−0.0838134	−	0.475329i
$928$		0			0
$929$	11.3219	+	9.50017i	0.371458	+	0.311690i	0.809338	−	0.587343i	$-0.199826\pi$
$929$	11.3219	+	9.50017i	0.371458	+	0.311690i	−0.437880	+	0.899033i	$0.644271\pi$
$930$		0			0
$931$	−21.0742	−	2.15109i	−0.690680	−	0.0704992i
$932$		0			0
$933$	7.39861	+	6.20817i	0.242220	+	0.203246i
$934$		0			0
$935$	−0.292203	−	1.65717i	−0.00955607	−	0.0541952i
$936$		0			0
$937$	27.4882	+	10.0049i	0.898001	+	0.326846i	0.749451	−	0.662059i	$-0.230317\pi$
$937$	27.4882	+	10.0049i	0.898001	+	0.326846i	0.148549	+	0.988905i	$0.452540\pi$
$938$		0			0
$939$	−34.1281	+	59.1116i	−1.11373	+	1.92903i
$940$		0			0
$941$	−3.88121	+	3.25672i	−0.126524	+	0.106166i	−0.703854	−	0.710345i	$-0.748539\pi$
$941$	−3.88121	+	3.25672i	−0.126524	+	0.106166i	0.577330	+	0.816511i	$0.304095\pi$
$942$		0			0
$943$	35.3265	+	61.1872i	1.15039	+	1.99253i
$944$		0			0
$945$	3.55425	−	20.1572i	0.115620	−	0.655712i
$946$		0			0
$947$	15.9231	−	5.79554i	0.517432	−	0.188330i	−0.0700860	−	0.997541i	$-0.522327\pi$
$947$	15.9231	−	5.79554i	0.517432	−	0.188330i	0.587518	+	0.809211i	$0.300105\pi$
$948$		0			0
$949$	46.3695			1.50522
$950$		0			0
$951$	−50.3975			−1.63425
$952$		0			0
$953$	12.9760	−	4.72288i	0.420334	−	0.152989i	−0.123189	−	0.992383i	$-0.539312\pi$
$953$	12.9760	−	4.72288i	0.420334	−	0.152989i	0.543523	+	0.839394i	$0.317090\pi$
$954$		0			0
$955$	2.61186	−	14.8126i	0.0845178	−	0.479324i
$956$		0			0
$957$	−60.2396	−	104.338i	−1.94727	−	3.37277i
$958$		0			0
$959$	−8.90632	+	7.47329i	−0.287600	+	0.241325i
$960$		0			0
$961$	−3.61052	+	6.25360i	−0.116468	+	0.201729i
$962$		0			0
$963$	31.4942	+	11.4629i	1.01489	+	0.369388i
$964$		0			0
$965$	−8.90813	−	50.5205i	−0.286763	−	1.62631i
$966$		0			0
$967$	36.6756	+	30.7745i	1.17941	+	0.989640i	0.999983	+	0.00586825i	$0.00186793\pi$
$967$	36.6756	+	30.7745i	1.17941	+	0.989640i	0.179424	+	0.983772i	$0.442577\pi$
$968$		0			0
$969$	0.109508	+	1.50131i	0.00351792	+	0.0482290i
$970$		0			0
$971$	18.8315	+	15.8015i	0.604333	+	0.507095i	0.892835	−	0.450384i	$-0.148713\pi$
$971$	18.8315	+	15.8015i	0.604333	+	0.507095i	−0.288502	+	0.957479i	$0.593157\pi$
$972$		0			0
$973$	2.91617	+	16.5384i	0.0934882	+	0.530198i
$974$		0			0
$975$	−22.6935	−	8.25975i	−0.726773	−	0.264524i
$976$		0			0
$977$	−15.0455	+	26.0596i	−0.481348	+	0.833719i	−0.999771	−	0.0214050i	$-0.993186\pi$
$977$	−15.0455	+	26.0596i	−0.481348	+	0.833719i	0.518423	+	0.855124i	$0.326519\pi$
$978$		0			0
$979$	34.1403	−	28.6471i	1.09113	−	0.915565i
$980$		0			0
$981$	12.2126	+	21.1529i	0.389920	+	0.675361i
$982$		0			0
$983$	−3.63321	+	20.6049i	−0.115881	+	0.657196i	0.870429	+	0.492294i	$0.163842\pi$
$983$	−3.63321	+	20.6049i	−0.115881	+	0.657196i	−0.986310	+	0.164901i	$0.947269\pi$
$984$		0			0
$985$	−35.1053	+	12.7773i	−1.11855	+	0.407118i
$986$		0			0
$987$	11.0599			0.352040
$988$		0			0
$989$	−10.7168			−0.340776
$990$		0			0
$991$	−5.66225	+	2.06089i	−0.179867	+	0.0654663i	−0.430384	−	0.902646i	$-0.641622\pi$
$991$	−5.66225	+	2.06089i	−0.179867	+	0.0654663i	0.250517	+	0.968112i	$0.419400\pi$
$992$		0			0
$993$	12.8443	−	72.8439i	0.407603	−	2.31163i
$994$		0			0
$995$	6.24544	+	10.8174i	0.197994	+	0.342935i
$996$		0			0
$997$	16.4637	−	13.8147i	0.521411	−	0.437516i	−0.343712	−	0.939075i	$-0.611685\pi$
$997$	16.4637	−	13.8147i	0.521411	−	0.437516i	0.865123	+	0.501559i	$0.167240\pi$
$998$		0			0
$999$	−11.2865	+	19.5489i	−0.357090	+	0.618499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.q.c.73.1	yes	18
4.3	odd	2		304.2.u.f.225.3		18
19.5	even	9		2888.2.a.y.1.9		9
19.6	even	9	inner	152.2.q.c.25.1	✓	18
19.14	odd	18		2888.2.a.x.1.1		9
76.43	odd	18		5776.2.a.cd.1.1		9
76.63	odd	18		304.2.u.f.177.3		18
76.71	even	18		5776.2.a.ce.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.c.25.1	✓	18	19.6	even	9	inner
152.2.q.c.73.1	yes	18	1.1	even	1	trivial
304.2.u.f.177.3		18	76.63	odd	18
304.2.u.f.225.3		18	4.3	odd	2
2888.2.a.x.1.1		9	19.14	odd	18
2888.2.a.y.1.9		9	19.5	even	9
5776.2.a.cd.1.1		9	76.43	odd	18
5776.2.a.ce.1.9		9	76.71	even	18

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.63451 + 0.958884i) q^{3} +(0.465881 - 2.64214i) q^{5} +(-0.731458 - 1.26692i) q^{7} +(3.72306 - 3.12402i) q^{9} +(2.54594 - 4.40970i) q^{11} +(-3.68269 - 1.34039i) q^{13} +(1.30614 + 7.40749i) q^{15} +(0.0943594 + 0.0791769i) q^{17} +(-1.78486 - 3.97672i) q^{19} +(3.14186 + 2.63634i) q^{21} +(1.23224 + 6.98836i) q^{23} +(-2.06542 - 0.751751i) q^{25} +(-2.60750 + 4.51632i) q^{27} +(-6.46506 + 5.42483i) q^{29} +(-3.09116 - 5.35404i) q^{31} +(-2.47892 + 14.0587i) q^{33} +(-3.68816 + 1.34238i) q^{35} +4.32850 q^{37} +10.9874 q^{39} +(9.35604 - 3.40532i) q^{41} +(-0.262249 + 1.48729i) q^{43} +(-6.51961 - 11.2923i) q^{45} +(2.06572 - 1.73334i) q^{47} +(2.42994 - 4.20878i) q^{49} +(-0.324512 - 0.118113i) q^{51} +(-1.04945 - 5.95173i) q^{53} +(-10.4650 - 8.78115i) q^{55} +(8.51545 + 8.76523i) q^{57} +(6.47790 + 5.43560i) q^{59} +(1.19119 + 6.75559i) q^{61} +(-6.68115 - 2.43174i) q^{63} +(-5.25719 + 9.10572i) q^{65} +(7.33630 - 6.15589i) q^{67} +(-9.94737 - 17.2294i) q^{69} +(-0.403285 + 2.28714i) q^{71} +(-11.1183 + 4.04674i) q^{73} +6.16221 q^{75} -7.44900 q^{77} +(2.80329 - 1.02032i) q^{79} +(0.00700815 - 0.0397452i) q^{81} +(1.93498 + 3.35148i) q^{83} +(0.253157 - 0.212424i) q^{85} +(11.8305 - 20.4910i) q^{87} +(8.22470 + 2.99355i) q^{89} +(0.995562 + 5.64611i) q^{91} +(13.2776 + 11.1412i) q^{93} +(-11.3386 + 2.86318i) q^{95} +(-9.50253 - 7.97357i) q^{97} +(-4.29730 - 24.3712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{7} - 6 q^{9} - 3 q^{11} + 3 q^{13} + 33 q^{15} + 9 q^{17} - 24 q^{19} - 15 q^{21} + 6 q^{23} + 6 q^{25} - 12 q^{27} - 3 q^{29} - 6 q^{31} - 45 q^{33} - 15 q^{35} + 48 q^{37} + 12 q^{39} - 18 q^{41}+ \cdots + 15 q^{99}+O(q^{100}) \) 18 * q - 9 * q^7 - 6 * q^9 - 3 * q^11 + 3 * q^13 + 33 * q^15 + 9 * q^17 - 24 * q^19 - 15 * q^21 + 6 * q^23 + 6 * q^25 - 12 * q^27 - 3 * q^29 - 6 * q^31 - 45 * q^33 - 15 * q^35 + 48 * q^37 + 12 * q^39 - 18 * q^41 - 39 * q^43 - 42 * q^45 - 27 * q^47 - 18 * q^49 + 48 * q^51 + 39 * q^53 - 27 * q^55 - 6 * q^57 + 9 * q^59 - 24 * q^61 + 3 * q^63 + 27 * q^65 + 39 * q^67 - 3 * q^69 + 12 * q^73 + 90 * q^75 + 60 * q^77 + 63 * q^79 - 6 * q^81 - 27 * q^83 - 30 * q^85 + 18 * q^87 + 66 * q^89 + 108 * q^91 + 60 * q^93 - 75 * q^95 - 81 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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