LMFDB - Embedded newform 152.2.q.c.9.2

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			9.2
Root			$-0.0372770 - 0.0645657i$ of defining polynomial
Character	$\chi$	$=$	152.9
Dual form			152.2.q.c.17.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0571117 + 0.0479224i) q^{3} +(0.846087 + 0.307950i) q^{5} +(2.43770 - 4.22221i) q^{7} +(-0.519979 + 2.94895i) q^{9} +(0.751011 + 1.30079i) q^{11} +(3.17207 + 2.66168i) q^{13} +(-0.0630792 + 0.0229589i) q^{15} +(-0.653155 - 3.70423i) q^{17} +(-2.89658 - 3.25727i) q^{19} +(0.0631176 + 0.357958i) q^{21} +(-5.40609 + 1.96766i) q^{23} +(-3.20919 - 2.69283i) q^{25} +(-0.223455 - 0.387035i) q^{27} +(-1.28615 + 7.29412i) q^{29} +(-1.88138 + 3.25864i) q^{31} +(-0.105228 - 0.0383000i) q^{33} +(3.36274 - 2.82167i) q^{35} -3.40626 q^{37} -0.308716 q^{39} +(-1.68420 + 1.41321i) q^{41} +(-1.79265 - 0.652471i) q^{43} +(-1.34808 + 2.33494i) q^{45} +(-0.265978 + 1.50844i) q^{47} +(-8.38473 - 14.5228i) q^{49} +(0.214818 + 0.180254i) q^{51} +(9.33685 - 3.39833i) q^{53} +(0.234842 + 1.33185i) q^{55} +(0.321525 + 0.0472171i) q^{57} +(1.35529 + 7.68626i) q^{59} +(3.18704 - 1.15999i) q^{61} +(11.1835 + 9.38411i) q^{63} +(1.86418 + 3.22885i) q^{65} +(-0.445701 + 2.52769i) q^{67} +(0.214456 - 0.371449i) q^{69} +(-6.80954 - 2.47847i) q^{71} +(6.31681 - 5.30043i) q^{73} +0.312329 q^{75} +7.32295 q^{77} +(12.2907 - 10.3131i) q^{79} +(-8.41025 - 3.06108i) q^{81} +(-4.18215 + 7.24370i) q^{83} +(0.588092 - 3.33524i) q^{85} +(-0.276098 - 0.478215i) q^{87} +(-9.49361 - 7.96608i) q^{89} +(18.9707 - 6.90478i) q^{91} +(-0.0487133 - 0.276267i) q^{93} +(-1.44768 - 3.64794i) q^{95} +(1.91303 + 10.8493i) q^{97} +(-4.22647 + 1.53831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{9}\right)$

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
$3$	−0.0571117	+	0.0479224i	−0.0329734	+	0.0276680i	−0.659125	−	0.752033i	$-0.729073\pi$
$3$	−0.0571117	+	0.0479224i	−0.0329734	+	0.0276680i	0.626152	+	0.779701i	$0.284629\pi$
$4$		0			0
$5$	0.846087	+	0.307950i	0.378382	+	0.137720i	0.524207	−	0.851591i	$-0.324362\pi$
$5$	0.846087	+	0.307950i	0.378382	+	0.137720i	−0.145826	+	0.989310i	$0.546584\pi$
$6$		0			0
$7$	2.43770	−	4.22221i	0.921363	−	1.59585i	0.124054	−	0.992276i	$-0.460411\pi$
$7$	2.43770	−	4.22221i	0.921363	−	1.59585i	0.797309	−	0.603571i	$-0.206256\pi$
$8$		0			0
$9$	−0.519979	+	2.94895i	−0.173326	+	0.982983i
$10$		0			0
$11$	0.751011	+	1.30079i	0.226438	+	0.392203i	0.956750	−	0.290911i	$-0.0939585\pi$
$11$	0.751011	+	1.30079i	0.226438	+	0.392203i	−0.730312	+	0.683114i	$0.760625\pi$
$12$		0			0
$13$	3.17207	+	2.66168i	0.879773	+	0.738218i	0.966133	−	0.258046i	$-0.0830788\pi$
$13$	3.17207	+	2.66168i	0.879773	+	0.738218i	−0.0863590	+	0.996264i	$0.527523\pi$
$14$		0			0
$15$	−0.0630792	+	0.0229589i	−0.0162870	+	0.00592797i
$16$		0			0
$17$	−0.653155	−	3.70423i	−0.158413	−	0.898407i	−0.955599	−	0.294672i	$-0.904790\pi$
$17$	−0.653155	−	3.70423i	−0.158413	−	0.898407i	0.797185	−	0.603735i	$-0.206321\pi$
$18$		0			0
$19$	−2.89658	−	3.25727i	−0.664521	−	0.747269i
$19$	−2.89658	−	3.25727i	−0.664521	−	0.747269i
$20$		0			0
$21$	0.0631176	+	0.357958i	0.0137734	+	0.0781128i
$22$		0			0
$23$	−5.40609	+	1.96766i	−1.12725	+	0.410285i	−0.837292	−	0.546755i	$-0.815863\pi$
$23$	−5.40609	+	1.96766i	−1.12725	+	0.410285i	−0.289956	+	0.957040i	$0.593641\pi$
$24$		0			0
$25$	−3.20919	−	2.69283i	−0.641839	−	0.538566i
$26$		0			0
$27$	−0.223455	−	0.387035i	−0.0430039	−	0.0744849i
$28$		0			0
$29$	−1.28615	+	7.29412i	−0.238832	+	1.35448i	0.595559	+	0.803312i	$0.296931\pi$
$29$	−1.28615	+	7.29412i	−0.238832	+	1.35448i	−0.834391	+	0.551173i	$0.814180\pi$
$30$		0			0
$31$	−1.88138	+	3.25864i	−0.337905	+	0.585269i	−0.984039	−	0.177955i	$-0.943052\pi$
$31$	−1.88138	+	3.25864i	−0.337905	+	0.585269i	0.646133	+	0.763225i	$0.276385\pi$
$32$		0			0
$33$	−0.105228	−	0.0383000i	−0.0183179	−	0.00666718i
$34$		0			0
$35$	3.36274	−	2.82167i	0.568406	−	0.476949i
$36$		0			0
$37$	−3.40626			−0.559986			−0.279993	−	0.960002i	$-0.590332\pi$
$37$	−3.40626			−0.559986			−0.279993	+	0.960002i	$0.590332\pi$
$38$		0			0
$39$	−0.308716			−0.0494342
$40$		0			0
$41$	−1.68420	+	1.41321i	−0.263028	+	0.220707i	−0.764758	−	0.644317i	$-0.777142\pi$
$41$	−1.68420	+	1.41321i	−0.263028	+	0.220707i	0.501730	+	0.865024i	$0.332697\pi$
$42$		0			0
$43$	−1.79265	−	0.652471i	−0.273376	−	0.0995008i	0.201694	−	0.979449i	$-0.435355\pi$
$43$	−1.79265	−	0.652471i	−0.273376	−	0.0995008i	−0.475071	+	0.879948i	$0.657577\pi$
$44$		0			0
$45$	−1.34808	+	2.33494i	−0.200960	+	0.348072i
$46$		0			0
$47$	−0.265978	+	1.50844i	−0.0387969	+	0.220028i	−0.998042	−	0.0625471i	$-0.980078\pi$
$47$	−0.265978	+	1.50844i	−0.0387969	+	0.220028i	0.959245	+	0.282575i	$0.0911887\pi$
$48$		0			0
$49$	−8.38473	−	14.5228i	−1.19782	−	2.07468i
$50$		0			0
$51$	0.214818	+	0.180254i	0.0300805	+	0.0252406i
$52$		0			0
$53$	9.33685	−	3.39833i	1.28251	−	0.466797i	0.391252	−	0.920284i	$-0.372042\pi$
$53$	9.33685	−	3.39833i	1.28251	−	0.466797i	0.891263	+	0.453487i	$0.149820\pi$
$54$		0			0
$55$	0.234842	+	1.33185i	0.0316661	+	0.179587i
$56$		0			0
$57$	0.321525	+	0.0472171i	0.0425870	+	0.00625405i
$58$		0			0
$59$	1.35529	+	7.68626i	0.176444	+	1.00067i	0.936464	+	0.350765i	$0.114078\pi$
$59$	1.35529	+	7.68626i	0.176444	+	1.00067i	−0.760019	+	0.649901i	$0.774810\pi$
$60$		0			0
$61$	3.18704	−	1.15999i	0.408059	−	0.148521i	−0.129831	−	0.991536i	$-0.541444\pi$
$61$	3.18704	−	1.15999i	0.408059	−	0.148521i	0.537890	+	0.843015i	$0.319221\pi$
$62$		0			0
$63$	11.1835	+	9.38411i	1.40899	+	1.18229i
$64$		0			0
$65$	1.86418	+	3.22885i	0.231223	+	0.400490i
$66$		0			0
$67$	−0.445701	+	2.52769i	−0.0544510	+	0.308807i	−0.999854	−	0.0170971i	$-0.994558\pi$
$67$	−0.445701	+	2.52769i	−0.0544510	+	0.308807i	0.945403	+	0.325904i	$0.105669\pi$
$68$		0			0
$69$	0.214456	−	0.371449i	0.0258175	−	0.0447172i
$70$		0			0
$71$	−6.80954	−	2.47847i	−0.808144	−	0.294140i	−0.0952868	−	0.995450i	$-0.530377\pi$
$71$	−6.80954	−	2.47847i	−0.808144	−	0.294140i	−0.712857	+	0.701310i	$0.752599\pi$
$72$		0			0
$73$	6.31681	−	5.30043i	0.739327	−	0.620369i	−0.193330	−	0.981134i	$-0.561929\pi$
$73$	6.31681	−	5.30043i	0.739327	−	0.620369i	0.932657	+	0.360765i	$0.117484\pi$
$74$		0			0
$75$	0.312329			0.0360647
$76$		0			0
$77$	7.32295			0.834527
$78$		0			0
$79$	12.2907	−	10.3131i	1.38281	−	1.16031i	0.414647	−	0.909982i	$-0.363905\pi$
$79$	12.2907	−	10.3131i	1.38281	−	1.16031i	0.968160	−	0.250331i	$-0.0805393\pi$
$80$		0			0
$81$	−8.41025	−	3.06108i	−0.934473	−	0.340120i
$82$		0			0
$83$	−4.18215	+	7.24370i	−0.459051	+	0.795099i	−0.998911	−	0.0466555i	$-0.985144\pi$
$83$	−4.18215	+	7.24370i	−0.459051	+	0.795099i	0.539860	+	0.841755i	$0.318477\pi$
$84$		0			0
$85$	0.588092	−	3.33524i	0.0637875	−	0.361757i
$86$		0			0
$87$	−0.276098	−	0.478215i	−0.0296008	−	0.0512700i
$88$		0			0
$89$	−9.49361	−	7.96608i	−1.00632	−	0.844403i	−0.0184730	−	0.999829i	$-0.505880\pi$
$89$	−9.49361	−	7.96608i	−1.00632	−	0.844403i	−0.987848	+	0.155426i	$0.950325\pi$
$90$		0			0
$91$	18.9707	−	6.90478i	1.98867	−	0.723818i
$92$		0			0
$93$	−0.0487133	−	0.276267i	−0.00505133	−	0.0286475i
$94$		0			0
$95$	−1.44768	−	3.64794i	−0.148529	−	0.374270i
$96$		0			0
$97$	1.91303	+	10.8493i	0.194239	+	1.10158i	0.913498	+	0.406843i	$0.133370\pi$
$97$	1.91303	+	10.8493i	0.194239	+	1.10158i	−0.719259	+	0.694742i	$0.755519\pi$
$98$		0			0
$99$	−4.22647	+	1.53831i	−0.424776	+	0.154606i
$100$		0			0
$101$	14.7030	+	12.3372i	1.46300	+	1.22760i	0.922351	+	0.386352i	$0.126265\pi$
$101$	14.7030	+	12.3372i	1.46300	+	1.22760i	0.540647	+	0.841249i	$0.318179\pi$
$102$		0			0
$103$	0.980290	+	1.69791i	0.0965908	+	0.167300i	0.910271	−	0.414012i	$-0.135873\pi$
$103$	0.980290	+	1.69791i	0.0965908	+	0.167300i	−0.813681	+	0.581312i	$0.802540\pi$
$104$		0			0
$105$	−0.0568303	+	0.322301i	−0.00554607	+	0.0314533i
$106$		0			0
$107$	−5.52414	+	9.56810i	−0.534039	+	0.924983i	0.465170	+	0.885221i	$0.345993\pi$
$107$	−5.52414	+	9.56810i	−0.534039	+	0.924983i	−0.999209	+	0.0397616i	$0.987340\pi$
$108$		0			0
$109$	−9.39024	−	3.41777i	−0.899422	−	0.327363i	−0.149401	−	0.988777i	$-0.547734\pi$
$109$	−9.39024	−	3.41777i	−0.899422	−	0.327363i	−0.750021	+	0.661414i	$0.769957\pi$
$110$		0			0
$111$	0.194537	−	0.163236i	0.0184647	−	0.0154937i
$112$		0			0
$113$	15.3630			1.44523			0.722617	−	0.691249i	$-0.242939\pi$
$113$	15.3630			1.44523			0.722617	+	0.691249i	$0.242939\pi$
$114$		0			0
$115$	−5.17996			−0.483034
$116$		0			0
$117$	−9.49857	+	7.97025i	−0.878143	+	0.736850i
$118$		0			0
$119$	−17.2322	−	6.27202i	−1.57968	−	0.574955i
$120$		0			0
$121$	4.37196	−	7.57246i	0.397451	−	0.688406i
$122$		0			0
$123$	0.0284630	−	0.161422i	0.00256643	−	0.0145549i
$124$		0			0
$125$	−4.13696	−	7.16543i	−0.370021	−	0.640896i
$126$		0			0
$127$	4.82452	+	4.04826i	0.428107	+	0.359225i	0.831237	−	0.555918i	$-0.187633\pi$
$127$	4.82452	+	4.04826i	0.428107	+	0.359225i	−0.403130	+	0.915143i	$0.632078\pi$
$128$		0			0
$129$	0.133649	−	0.0486443i	0.0117671	−	0.00428289i
$130$		0			0
$131$	−2.39308	−	13.5718i	−0.209084	−	1.18578i	−0.890882	−	0.454236i	$-0.849912\pi$
$131$	−2.39308	−	13.5718i	−0.209084	−	1.18578i	0.681797	−	0.731541i	$-0.261199\pi$
$132$		0			0
$133$	−20.8139	+	4.28975i	−1.80479	+	0.371969i
$134$		0			0
$135$	−0.0698745	−	0.396278i	−0.00601384	−	0.0341062i
$136$		0			0
$137$	−8.81317	+	3.20773i	−0.752960	+	0.274055i	−0.689851	−	0.723951i	$-0.742324\pi$
$137$	−8.81317	+	3.20773i	−0.752960	+	0.274055i	−0.0631094	+	0.998007i	$0.520102\pi$
$138$		0			0
$139$	−6.13672	−	5.14932i	−0.520510	−	0.436760i	0.344300	−	0.938860i	$-0.388116\pi$
$139$	−6.13672	−	5.14932i	−0.520510	−	0.436760i	−0.864809	+	0.502100i	$0.832561\pi$
$140$		0			0
$141$	−0.0570975	−	0.0988957i	−0.00480847	−	0.00832852i
$142$		0			0
$143$	−1.08003	+	6.12515i	−0.0903165	+	0.512210i
$144$		0			0
$145$	−3.33442	+	5.77539i	−0.276909	+	0.479620i
$146$		0			0
$147$	1.17483	+	0.427604i	0.0968985	+	0.0352682i
$148$		0			0
$149$	2.96174	−	2.48520i	0.242636	−	0.203595i	−0.513358	−	0.858175i	$-0.671599\pi$
$149$	2.96174	−	2.48520i	0.242636	−	0.203595i	0.755993	+	0.654579i	$0.227154\pi$
$150$		0			0
$151$	−6.96895			−0.567125			−0.283562	−	0.958954i	$-0.591516\pi$
$151$	−6.96895			−0.567125			−0.283562	+	0.958954i	$0.591516\pi$
$152$		0			0
$153$	11.2632			0.910576
$154$		0			0
$155$	−2.59531	+	2.17772i	−0.208460	+	0.174919i
$156$		0			0
$157$	9.88539	+	3.59799i	0.788940	+	0.287151i	0.704895	−	0.709311i	$-0.250994\pi$
$157$	9.88539	+	3.59799i	0.788940	+	0.287151i	0.0840448	+	0.996462i	$0.473216\pi$
$158$		0			0
$159$	−0.370387	+	0.641529i	−0.0293736	+	0.0508765i
$160$		0			0
$161$	−4.87054	+	27.6222i	−0.383853	+	2.17694i
$162$		0			0
$163$	−5.67049	−	9.82157i	−0.444147	−	0.769285i	0.553846	−	0.832619i	$-0.313160\pi$
$163$	−5.67049	−	9.82157i	−0.444147	−	0.769285i	−0.997992	+	0.0633346i	$0.979826\pi$
$164$		0			0
$165$	−0.0772379	−	0.0648103i	−0.00601296	−	0.00504547i
$166$		0			0
$167$	12.6635	−	4.60915i	0.979934	−	0.356667i	0.198119	−	0.980178i	$-0.436517\pi$
$167$	12.6635	−	4.60915i	0.979934	−	0.356667i	0.781815	+	0.623511i	$0.214294\pi$
$168$		0			0
$169$	0.720044	+	4.08357i	0.0553880	+	0.314121i
$170$		0			0
$171$	11.1117	−	6.84816i	0.849732	−	0.523692i
$172$		0			0
$173$	−2.08871	−	11.8457i	−0.158802	−	0.900609i	−0.955227	−	0.295872i	$-0.904390\pi$
$173$	−2.08871	−	11.8457i	−0.158802	−	0.900609i	0.796426	−	0.604736i	$-0.206721\pi$
$174$		0			0
$175$	−19.1928	+	6.98559i	−1.45084	+	0.528061i
$176$		0			0
$177$	−0.445747	−	0.374026i	−0.0335044	−	0.0281135i
$178$		0			0
$179$	−12.3965	−	21.4714i	−0.926558	−	1.60485i	−0.789036	−	0.614347i	$-0.789419\pi$
$179$	−12.3965	−	21.4714i	−0.926558	−	1.60485i	−0.137523	−	0.990499i	$-0.543914\pi$
$180$		0			0
$181$	−3.23698	+	18.3578i	−0.240603	+	1.36453i	0.589884	+	0.807488i	$0.299174\pi$
$181$	−3.23698	+	18.3578i	−0.240603	+	1.36453i	−0.830486	+	0.557039i	$0.811937\pi$
$182$		0			0
$183$	−0.126428	+	0.218980i	−0.00934582	+	0.0161874i
$184$		0			0
$185$	−2.88199	−	1.04896i	−0.211888	−	0.0771211i
$186$		0			0
$187$	4.32789	−	3.63153i	0.316487	−	0.265564i
$188$		0			0
$189$	−2.17886			−0.158489
$190$		0			0
$191$	2.40294			0.173870			0.0869352	−	0.996214i	$-0.472293\pi$
$191$	2.40294			0.173870			0.0869352	+	0.996214i	$0.472293\pi$
$192$		0			0
$193$	1.57700	−	1.32326i	0.113515	−	0.0952504i	−0.584263	−	0.811564i	$-0.698616\pi$
$193$	1.57700	−	1.32326i	0.113515	−	0.0952504i	0.697778	+	0.716314i	$0.254172\pi$
$194$		0			0
$195$	−0.261201	−	0.0950693i	−0.0187050	−	0.00680805i
$196$		0			0
$197$	10.9933	−	19.0410i	0.783242	−	1.35661i	−0.146802	−	0.989166i	$-0.546898\pi$
$197$	10.9933	−	19.0410i	0.783242	−	1.35661i	0.930044	−	0.367449i	$-0.119769\pi$
$198$		0			0
$199$	0.0440381	−	0.249753i	0.00312178	−	0.0177045i	−0.983207	−	0.182493i	$-0.941583\pi$
$199$	0.0440381	−	0.249753i	0.00312178	−	0.0177045i	0.986329	+	0.164789i	$0.0526943\pi$
$200$		0			0
$201$	−0.0956784	−	0.165720i	−0.00674864	−	0.0116890i
$202$		0			0
$203$	27.6621	+	23.2113i	1.94150	+	1.62911i
$204$		0			0
$205$	−1.86018	+	0.677050i	−0.129921	+	0.0472873i
$206$		0			0
$207$	−2.99146	−	16.9654i	−0.207921	−	1.17918i
$208$		0			0
$209$	2.06166	−	6.21409i	0.142608	−	0.429838i
$210$		0			0
$211$	2.92275	+	16.5758i	0.201211	+	1.14112i	0.903292	+	0.429025i	$0.141143\pi$
$211$	2.92275	+	16.5758i	0.201211	+	1.14112i	−0.702082	+	0.712096i	$0.747746\pi$
$212$		0			0
$213$	0.507678	−	0.184780i	0.0347855	−	0.0126609i
$214$		0			0
$215$	−1.31581	−	1.10409i	−0.0897373	−	0.0752986i
$216$		0			0
$217$	9.17245	+	15.8872i	0.622667	+	1.07849i
$218$		0			0
$219$	−0.106754	+	0.605433i	−0.00721378	+	0.0409114i
$220$		0			0
$221$	7.78762	−	13.4885i	0.523852	−	0.907338i
$222$		0			0
$223$	24.3233	+	8.85297i	1.62881	+	0.592839i	0.985032	−	0.172372i	$-0.0551431\pi$
$223$	24.3233	+	8.85297i	1.62881	+	0.592839i	0.643780	+	0.765211i	$0.277365\pi$
$224$		0			0
$225$	9.60974	−	8.06353i	0.640649	−	0.537569i
$226$		0			0
$227$	−17.2212			−1.14301			−0.571506	−	0.820598i	$-0.693641\pi$
$227$	−17.2212			−1.14301			−0.571506	+	0.820598i	$0.693641\pi$
$228$		0			0
$229$	8.94376			0.591020			0.295510	−	0.955340i	$-0.404510\pi$
$229$	8.94376			0.591020			0.295510	+	0.955340i	$0.404510\pi$
$230$		0			0
$231$	−0.418226	+	0.350933i	−0.0275172	+	0.0230897i
$232$		0			0
$233$	6.30702	+	2.29557i	0.413187	+	0.150388i	0.540245	−	0.841508i	$-0.318331\pi$
$233$	6.30702	+	2.29557i	0.413187	+	0.150388i	−0.127059	+	0.991895i	$0.540554\pi$
$234$		0			0
$235$	−0.689565	+	1.19436i	−0.0449822	+	0.0779115i
$236$		0			0
$237$	−0.207712	+	1.17800i	−0.0134924	+	0.0765190i
$238$		0			0
$239$	7.37042	+	12.7659i	0.476753	+	0.825760i	0.999645	−	0.0266389i	$-0.00848041\pi$
$239$	7.37042	+	12.7659i	0.476753	+	0.825760i	−0.522892	+	0.852399i	$0.675147\pi$
$240$		0			0
$241$	1.71665	+	1.44044i	0.110579	+	0.0927868i	0.696401	−	0.717653i	$-0.254784\pi$
$241$	1.71665	+	1.44044i	0.110579	+	0.0927868i	−0.585822	+	0.810440i	$0.699228\pi$
$242$		0			0
$243$	1.88689	−	0.686772i	0.121044	−	0.0440565i
$244$		0			0
$245$	−2.62191	−	14.8696i	−0.167508	−	0.949984i
$246$		0			0
$247$	−0.518339	−	18.0421i	−0.0329811	−	1.14799i
$248$		0			0
$249$	−0.108286	−	0.614118i	−0.00686232	−	0.0389182i
$250$		0			0
$251$	9.84138	−	3.58197i	0.621182	−	0.226092i	−0.0122065	−	0.999925i	$-0.503886\pi$
$251$	9.84138	−	3.58197i	0.621182	−	0.226092i	0.633389	+	0.773834i	$0.281663\pi$
$252$		0			0
$253$	−6.61954	−	5.55445i	−0.416167	−	0.349206i
$254$		0			0
$255$	0.126246	+	0.218664i	0.00790580	+	0.0136932i
$256$		0			0
$257$	−0.465247	+	2.63855i	−0.0290213	+	0.164588i	−0.995874	−	0.0907468i	$-0.971075\pi$
$257$	−0.465247	+	2.63855i	−0.0290213	+	0.164588i	0.966853	+	0.255335i	$0.0821857\pi$
$258$		0			0
$259$	−8.30344	+	14.3820i	−0.515950	+	0.893652i
$260$		0			0
$261$	−20.8412	−	7.58559i	−1.29004	−	0.469536i
$262$		0			0
$263$	5.15900	−	4.32892i	0.318118	−	0.266932i	−0.469720	−	0.882816i	$-0.655645\pi$
$263$	5.15900	−	4.32892i	0.318118	−	0.266932i	0.787838	+	0.615883i	$0.211201\pi$
$264$		0			0
$265$	8.94630			0.549567
$266$		0			0
$267$	0.923950			0.0565448
$268$		0			0
$269$	−8.29577	+	6.96098i	−0.505802	+	0.424418i	−0.859649	−	0.510885i	$-0.829318\pi$
$269$	−8.29577	+	6.96098i	−0.505802	+	0.424418i	0.353847	+	0.935303i	$0.384873\pi$
$270$		0			0
$271$	9.24264	+	3.36405i	0.561450	+	0.204351i	0.607127	−	0.794605i	$-0.292322\pi$
$271$	9.24264	+	3.36405i	0.561450	+	0.204351i	−0.0456762	+	0.998956i	$0.514544\pi$
$272$		0			0
$273$	−0.752556	+	1.30347i	−0.0455468	+	0.0788894i
$274$		0			0
$275$	1.09267	−	6.19683i	0.0658904	−	0.373683i
$276$		0			0
$277$	−11.0574	−	19.1520i	−0.664375	−	1.15073i	−0.979454	−	0.201665i	$-0.935365\pi$
$277$	−11.0574	−	19.1520i	−0.664375	−	1.15073i	0.315080	−	0.949065i	$-0.397969\pi$
$278$		0			0
$279$	−8.63129	−	7.24251i	−0.516742	−	0.433598i
$280$		0			0
$281$	−10.4993	+	3.82144i	−0.626338	+	0.227968i	−0.635636	−	0.771989i	$-0.719262\pi$
$281$	−10.4993	+	3.82144i	−0.626338	+	0.227968i	0.00929888	+	0.999957i	$0.497040\pi$
$282$		0			0
$283$	5.06099	+	28.7023i	0.300844	+	1.70617i	0.642448	+	0.766329i	$0.277919\pi$
$283$	5.06099	+	28.7023i	0.300844	+	1.70617i	−0.341603	+	0.939844i	$0.610970\pi$
$284$		0			0
$285$	0.257497	+	0.138963i	0.0152528	+	0.00823148i
$286$		0			0
$287$	1.86132	+	10.5560i	0.109870	+	0.623104i
$288$		0			0
$289$	2.68010	−	0.975478i	0.157653	−	0.0573810i
$290$		0			0
$291$	−0.629183	−	0.527947i	−0.0368834	−	0.0309488i
$292$		0			0
$293$	6.96412	+	12.0622i	0.406848	+	0.704682i	0.994535	−	0.104407i	$-0.0332944\pi$
$293$	6.96412	+	12.0622i	0.406848	+	0.704682i	−0.587686	+	0.809089i	$0.699961\pi$
$294$		0			0
$295$	−1.22029	+	6.92061i	−0.0710480	+	0.402933i
$296$		0			0
$297$	0.335634	−	0.581335i	0.0194755	−	0.0337325i
$298$		0			0
$299$	−22.3858	−	8.14775i	−1.29460	−	0.471197i
$300$		0			0
$301$	−7.12480	+	5.97842i	−0.410667	+	0.344590i
$302$		0			0
$303$	−1.43094			−0.0822054
$304$		0			0
$305$	3.05373			0.174856
$306$		0			0
$307$	12.4177	−	10.4197i	0.708716	−	0.594684i	−0.215522	−	0.976499i	$-0.569145\pi$
$307$	12.4177	−	10.4197i	0.708716	−	0.594684i	0.924239	+	0.381815i	$0.124701\pi$
$308$		0			0
$309$	−0.137354	−	0.0499927i	−0.00781379	−	0.00284399i
$310$		0			0
$311$	0.795408	−	1.37769i	0.0451034	−	0.0781214i	−0.842592	−	0.538552i	$-0.818972\pi$
$311$	0.795408	−	1.37769i	0.0451034	−	0.0781214i	0.887696	+	0.460430i	$0.152305\pi$
$312$		0			0
$313$	1.35928	−	7.70884i	0.0768308	−	0.435729i	−0.921991	−	0.387210i	$-0.873439\pi$
$313$	1.35928	−	7.70884i	0.0768308	−	0.435729i	0.998822	−	0.0485189i	$-0.0154501\pi$
$314$		0			0
$315$	6.57241	+	11.3837i	0.370313	+	0.641401i
$316$		0			0
$317$	−18.4157	−	15.4526i	−1.03433	−	0.867904i	−0.0429677	−	0.999076i	$-0.513681\pi$
$317$	−18.4157	−	15.4526i	−1.03433	−	0.867904i	−0.991360	+	0.131173i	$0.958126\pi$
$318$		0			0
$319$	−10.4540	+	3.80496i	−0.585314	+	0.213037i
$320$		0			0
$321$	−0.143033	−	0.811180i	−0.00798332	−	0.0452757i
$322$		0			0
$323$	−10.1737	+	12.8571i	−0.566082	+	0.715388i
$324$		0			0
$325$	−3.01232	−	17.0837i	−0.167093	−	0.947633i
$326$		0			0
$327$	0.700080	−	0.254808i	0.0387145	−	0.0140909i
$328$		0			0
$329$	5.72057	+	4.80013i	0.315385	+	0.264640i
$330$		0			0
$331$	3.72375	+	6.44972i	0.204676	+	0.354509i	0.950029	−	0.312161i	$-0.101053\pi$
$331$	3.72375	+	6.44972i	0.204676	+	0.354509i	−0.745354	+	0.666669i	$0.767719\pi$
$332$		0			0
$333$	1.77119	−	10.0449i	0.0970604	−	0.550457i
$334$		0			0
$335$	−1.15551	+	2.00140i	−0.0631321	+	0.109348i
$336$		0			0
$337$	10.0217	+	3.64761i	0.545919	+	0.198698i	0.600232	−	0.799826i	$-0.295075\pi$
$337$	10.0217	+	3.64761i	0.545919	+	0.198698i	−0.0543134	+	0.998524i	$0.517297\pi$
$338$		0			0
$339$	−0.877409	+	0.736233i	−0.0476543	+	0.0399867i
$340$		0			0
$341$	−5.65174			−0.306059
$342$		0			0
$343$	−47.6299			−2.57177
$344$		0			0
$345$	0.295836	−	0.248236i	0.0159273	−	0.0133646i
$346$		0			0
$347$	−20.0551	−	7.29945i	−1.07661	−	0.391855i	−0.257967	−	0.966154i	$-0.583053\pi$
$347$	−20.0551	−	7.29945i	−1.07661	−	0.391855i	−0.818646	+	0.574299i	$0.805275\pi$
$348$		0			0
$349$	−12.0043	+	20.7921i	−0.642578	+	1.11298i	0.342277	+	0.939599i	$0.388802\pi$
$349$	−12.0043	+	20.7921i	−0.642578	+	1.11298i	−0.984855	+	0.173379i	$0.944532\pi$
$350$		0			0
$351$	0.321350	−	1.82247i	0.0171524	−	0.0972761i
$352$		0			0
$353$	−10.9493	−	18.9647i	−0.582771	−	1.00939i	−0.995149	−	0.0983765i	$-0.968635\pi$
$353$	−10.9493	−	18.9647i	−0.582771	−	1.00939i	0.412378	−	0.911013i	$-0.364698\pi$
$354$		0			0
$355$	−4.99822	−	4.19400i	−0.265278	−	0.222594i
$356$		0			0
$357$	1.28473	−	0.467604i	0.0679952	−	0.0247482i
$358$		0			0
$359$	3.15021	+	17.8657i	0.166262	+	0.942917i	0.947754	+	0.319002i	$0.103348\pi$
$359$	3.15021	+	17.8657i	0.166262	+	0.942917i	−0.781492	+	0.623915i	$0.785541\pi$
$360$		0			0
$361$	−2.21963	+	18.8699i	−0.116822	+	0.993153i
$362$		0			0
$363$	0.113200	+	0.641991i	0.00594148	+	0.0336958i
$364$		0			0
$365$	6.97684	−	2.53936i	0.365185	−	0.132916i
$366$		0			0
$367$	19.7837	+	16.6005i	1.03270	+	0.866540i	0.991170	−	0.132597i	$-0.0423317\pi$
$367$	19.7837	+	16.6005i	1.03270	+	0.866540i	0.0415319	+	0.999137i	$0.486776\pi$
$368$		0			0
$369$	−3.29174	−	5.70147i	−0.171361	−	0.296807i
$370$		0			0
$371$	8.41190	−	47.7063i	0.436724	−	2.47679i
$372$		0			0
$373$	−0.191644	+	0.331936i	−0.00992293	+	0.0171870i	−0.870944	−	0.491382i	$-0.836492\pi$
$373$	−0.191644	+	0.331936i	−0.00992293	+	0.0171870i	0.861021	+	0.508569i	$0.169825\pi$
$374$		0			0
$375$	0.579653	+	0.210977i	0.0299332	+	0.0108948i
$376$		0			0
$377$	−23.4944	+	19.7141i	−1.21002	+	1.01533i
$378$		0			0
$379$	12.1230			0.622718			0.311359	−	0.950292i	$-0.399216\pi$
$379$	12.1230			0.622718			0.311359	+	0.950292i	$0.399216\pi$
$380$		0			0
$381$	−0.469539			−0.0240552
$382$		0			0
$383$	18.0633	−	15.1569i	0.922990	−	0.774480i	−0.0515558	−	0.998670i	$-0.516418\pi$
$383$	18.0633	−	15.1569i	0.922990	−	0.774480i	0.974546	+	0.224190i	$0.0719735\pi$
$384$		0			0
$385$	6.19585	+	2.25510i	0.315770	+	0.114931i
$386$		0			0
$387$	2.85624	−	4.94716i	0.145191	−	0.251478i
$388$		0			0
$389$	2.87755	−	16.3194i	0.145898	−	0.827426i	−0.820745	−	0.571295i	$-0.806441\pi$
$389$	2.87755	−	16.3194i	0.145898	−	0.827426i	0.966642	−	0.256131i	$-0.0824478\pi$
$390$		0			0
$391$	10.8197	+	18.7402i	0.547174	+	0.947732i
$392$		0			0
$393$	0.787068	+	0.660428i	0.0397023	+	0.0333142i
$394$		0			0
$395$	13.5749	−	4.94085i	0.683027	−	0.248601i
$396$		0			0
$397$	2.56104	+	14.5244i	0.128535	+	0.728959i	0.979145	+	0.203162i	$0.0651218\pi$
$397$	2.56104	+	14.5244i	0.128535	+	0.728959i	−0.850610	+	0.525797i	$0.823767\pi$
$398$		0			0
$399$	0.983140	−	1.24245i	0.0492186	−	0.0622001i
$400$		0			0
$401$	2.43436	+	13.8060i	0.121566	+	0.689436i	0.983288	+	0.182056i	$0.0582751\pi$
$401$	2.43436	+	13.8060i	0.121566	+	0.689436i	−0.861722	+	0.507381i	$0.830614\pi$
$402$		0			0
$403$	−14.6413	+	5.32901i	−0.729336	+	0.265457i
$404$		0			0
$405$	−6.17314	−	5.17988i	−0.306746	−	0.257390i
$406$		0			0
$407$	−2.55814	−	4.43083i	−0.126802	−	0.219628i
$408$		0			0
$409$	−2.17011	+	12.3073i	−0.107305	+	0.608557i	0.882969	+	0.469430i	$0.155541\pi$
$409$	−2.17011	+	12.3073i	−0.107305	+	0.608557i	−0.990275	+	0.139127i	$0.955570\pi$
$410$		0			0
$411$	0.349613	−	0.605547i	0.0172451	−	0.0298694i
$412$		0			0
$413$	35.7568	+	13.0144i	1.75948	+	0.640398i
$414$		0			0
$415$	−5.76916	+	4.84090i	−0.283197	+	0.237631i
$416$		0			0
$417$	0.597246			0.0292473
$418$		0			0
$419$	23.0450			1.12582			0.562911	−	0.826517i	$-0.309681\pi$
$419$	23.0450			1.12582			0.562911	+	0.826517i	$0.309681\pi$
$420$		0			0
$421$	0.538028	−	0.451459i	0.0262219	−	0.0220028i	−0.629583	−	0.776934i	$-0.716774\pi$
$421$	0.538028	−	0.451459i	0.0262219	−	0.0220028i	0.655804	+	0.754931i	$0.272330\pi$
$422$		0			0
$423$	−4.31000	−	1.56871i	−0.209560	−	0.0762734i
$424$		0			0
$425$	−7.87876	+	13.6464i	−0.382176	+	0.661948i
$426$		0			0
$427$	2.87132	−	16.2841i	0.138953	−	0.788042i
$428$		0			0
$429$	−0.231849	−	0.401575i	−0.0111938	−	0.0193882i
$430$		0			0
$431$	−17.5441	−	14.7212i	−0.845069	−	0.709097i	0.113629	−	0.993523i	$-0.463753\pi$
$431$	−17.5441	−	14.7212i	−0.845069	−	0.709097i	−0.958698	+	0.284426i	$0.908197\pi$
$432$		0			0
$433$	−1.02276	+	0.372254i	−0.0491507	+	0.0178894i	−0.366478	−	0.930427i	$-0.619437\pi$
$433$	−1.02276	+	0.372254i	−0.0491507	+	0.0178894i	0.317328	+	0.948316i	$0.397214\pi$
$434$		0			0
$435$	−0.0863360	−	0.489636i	−0.00413949	−	0.0234762i
$436$		0			0
$437$	22.0684	+	11.9096i	1.05567	+	0.569715i
$438$		0			0
$439$	−6.02958	−	34.1954i	−0.287776	−	1.63206i	−0.695198	−	0.718819i	$-0.744683\pi$
$439$	−6.02958	−	34.1954i	−0.287776	−	1.63206i	0.407422	−	0.913240i	$-0.366428\pi$
$440$		0			0
$441$	47.1868	−	17.1746i	2.24699	−	0.817838i
$442$		0			0
$443$	−19.1005	−	16.0272i	−0.907490	−	0.761474i	0.0641500	−	0.997940i	$-0.479566\pi$
$443$	−19.1005	−	16.0272i	−0.907490	−	0.761474i	−0.971640	+	0.236466i	$0.924011\pi$
$444$		0			0
$445$	−5.57926	−	9.66356i	−0.264482	−	0.458097i
$446$		0			0
$447$	−0.0500535	+	0.283868i	−0.00236745	+	0.0134265i
$448$		0			0
$449$	15.4902	−	26.8298i	0.731028	−	1.26618i	−0.225416	−	0.974263i	$-0.572374\pi$
$449$	15.4902	−	26.8298i	0.731028	−	1.26618i	0.956444	−	0.291915i	$-0.0942925\pi$
$450$		0			0
$451$	−3.10315	−	1.12945i	−0.146121	−	0.0531839i
$452$		0			0
$453$	0.398008	−	0.333969i	0.0187001	−	0.0156912i
$454$		0			0
$455$	18.1772			0.852161
$456$		0			0
$457$	1.44629			0.0676548			0.0338274	−	0.999428i	$-0.489230\pi$
$457$	1.44629			0.0676548			0.0338274	+	0.999428i	$0.489230\pi$
$458$		0			0
$459$	−1.28771	+	1.08052i	−0.0601054	+	0.0504344i
$460$		0			0
$461$	−2.49659	−	0.908684i	−0.116278	−	0.0423217i	0.283226	−	0.959053i	$-0.408595\pi$
$461$	−2.49659	−	0.908684i	−0.116278	−	0.0423217i	−0.399504	+	0.916732i	$0.630818\pi$
$462$		0			0
$463$	−9.38621	+	16.2574i	−0.436214	+	0.755545i	−0.997394	−	0.0721489i	$-0.977014\pi$
$463$	−9.38621	+	16.2574i	−0.436214	+	0.755545i	0.561180	+	0.827694i	$0.310348\pi$
$464$		0			0
$465$	0.0438608	−	0.248747i	0.00203399	−	0.0115354i
$466$		0			0
$467$	16.9214	+	29.3088i	0.783031	+	1.35625i	0.930168	+	0.367133i	$0.119661\pi$
$467$	16.9214	+	29.3088i	0.783031	+	1.35625i	−0.147137	+	0.989116i	$0.547006\pi$
$468$		0			0
$469$	9.58599	+	8.04360i	0.442640	+	0.371419i
$470$		0			0
$471$	−0.736996	+	0.268244i	−0.0339590	+	0.0123601i
$472$		0			0
$473$	−0.497572	−	2.82187i	−0.0228784	−	0.129750i
$474$		0			0
$475$	0.524405	+	18.2532i	0.0240613	+	0.837515i
$476$		0			0
$477$	5.16655	+	29.3010i	0.236560	+	1.34160i
$478$		0			0
$479$	14.9720	−	5.44936i	0.684088	−	0.248988i	0.0234863	−	0.999724i	$-0.492523\pi$
$479$	14.9720	−	5.44936i	0.684088	−	0.248988i	0.660602	+	0.750736i	$0.270301\pi$
$480$		0			0
$481$	−10.8049	−	9.06639i	−0.492661	−	0.413392i
$482$		0			0
$483$	−1.04556	−	1.81096i	−0.0475745	−	0.0824015i
$484$		0			0
$485$	−1.72247	+	9.76861i	−0.0782133	+	0.443570i
$486$		0			0
$487$	13.2382	−	22.9293i	0.599881	−	1.03902i	−0.392957	−	0.919557i	$-0.628548\pi$
$487$	13.2382	−	22.9293i	0.599881	−	1.03902i	0.992838	−	0.119467i	$-0.0381187\pi$
$488$		0			0
$489$	0.794524	+	0.289183i	0.0359296	+	0.0130773i
$490$		0			0
$491$	−10.6617	+	8.94624i	−0.481156	+	0.403738i	−0.850844	−	0.525418i	$-0.823909\pi$
$491$	−10.6617	+	8.94624i	−0.481156	+	0.403738i	0.369688	+	0.929156i	$0.379465\pi$
$492$		0			0
$493$	27.8591			1.25471
$494$		0			0
$495$	−4.04969			−0.182020
$496$		0			0
$497$	−27.0642	+	22.7096i	−1.21400	+	1.01866i
$498$		0			0
$499$	18.1464	+	6.60476i	0.812346	+	0.295670i	0.714592	−	0.699541i	$-0.246612\pi$
$499$	18.1464	+	6.60476i	0.812346	+	0.295670i	0.0977533	+	0.995211i	$0.468834\pi$
$500$		0			0
$501$	−0.502354	+	0.870103i	−0.0224435	+	0.0388733i
$502$		0			0
$503$	0.0372156	−	0.211060i	0.00165936	−	0.00941071i	−0.983967	−	0.178352i	$-0.942924\pi$
$503$	0.0372156	−	0.211060i	0.00165936	−	0.00941071i	0.985626	+	0.168941i	$0.0540347\pi$
$504$		0			0
$505$	8.64072	+	14.9662i	0.384507	+	0.665985i
$506$		0			0
$507$	−0.236817	−	0.198713i	−0.0105174	−	0.00882517i
$508$		0			0
$509$	−22.0843	+	8.03801i	−0.978867	+	0.356279i	−0.781400	−	0.624031i	$-0.785494\pi$
$509$	−22.0843	+	8.03801i	−0.978867	+	0.356279i	−0.197468	+	0.980309i	$0.563272\pi$
$510$		0			0
$511$	−6.98110	−	39.5918i	−0.308826	−	1.75144i
$512$		0			0
$513$	−0.613423	+	1.84893i	−0.0270833	+	0.0816323i
$514$		0			0
$515$	0.306538	+	1.73846i	0.0135077	+	0.0766057i
$516$		0			0
$517$	−2.16191	+	0.786872i	−0.0950808	+	0.0346066i
$518$		0			0
$519$	0.686962	+	0.576429i	0.0301543	+	0.0253024i
$520$		0			0
$521$	−5.47324	−	9.47994i	−0.239787	−	0.415324i	0.720866	−	0.693075i	$-0.243744\pi$
$521$	−5.47324	−	9.47994i	−0.239787	−	0.415324i	−0.960653	+	0.277751i	$0.910411\pi$
$522$		0			0
$523$	4.89094	−	27.7379i	0.213866	−	1.21289i	−0.668998	−	0.743264i	$-0.733277\pi$
$523$	4.89094	−	27.7379i	0.213866	−	1.21289i	0.882864	−	0.469629i	$-0.155612\pi$
$524$		0			0
$525$	0.761364	−	1.31872i	0.0332286	−	0.0575537i
$526$		0			0
$527$	13.2996	+	4.84065i	0.579338	+	0.210862i
$528$		0			0
$529$	7.73513	−	6.49055i	0.336310	−	0.282198i
$530$		0			0
$531$	−23.3711			−1.01422
$532$		0			0
$533$	−9.10393			−0.394335
$534$		0			0
$535$	−7.62041	+	6.39428i	−0.329459	+	0.276449i
$536$		0			0
$537$	1.73694	+	0.632196i	0.0749547	+	0.0272813i
$538$		0			0
$539$	12.5940	−	21.8135i	0.542464	−	0.939575i
$540$		0			0
$541$	−5.49172	+	31.1451i	−0.236108	+	1.33903i	0.604161	+	0.796863i	$0.293509\pi$
$541$	−5.49172	+	31.1451i	−0.236108	+	1.33903i	−0.840268	+	0.542171i	$0.817603\pi$
$542$		0			0
$543$	−0.694882	−	1.20357i	−0.0298202	−	0.0516502i
$544$		0			0
$545$	−6.89245	−	5.78346i	−0.295240	−	0.247736i
$546$		0			0
$547$	−36.8659	+	13.4181i	−1.57627	+	0.573716i	−0.974389	−	0.224868i	$-0.927805\pi$
$547$	−36.8659	+	13.4181i	−1.57627	+	0.573716i	−0.601883	+	0.798585i	$0.705583\pi$
$548$		0			0
$549$	1.76355	+	10.0016i	0.0752665	+	0.426858i
$550$		0			0
$551$	27.4844	−	16.9387i	1.17087	−	0.721612i
$552$		0			0
$553$	−13.5832	−	77.0340i	−0.577615	−	3.27582i
$554$		0			0
$555$	0.214864	−	0.0782042i	0.00912048	−	0.00331958i
$556$		0			0
$557$	−23.2983	−	19.5496i	−0.987180	−	0.828342i	−0.00202276	−	0.999998i	$-0.500644\pi$
$557$	−23.2983	−	19.5496i	−0.987180	−	0.828342i	−0.985157	+	0.171656i	$0.945088\pi$
$558$		0			0
$559$	−3.94973	−	6.84114i	−0.167056	−	0.289349i
$560$		0			0
$561$	−0.0731414	+	0.414806i	−0.00308803	+	0.0175131i
$562$		0			0
$563$	−16.7446	+	29.0025i	−0.705701	+	1.22231i	0.260736	+	0.965410i	$0.416035\pi$
$563$	−16.7446	+	29.0025i	−0.705701	+	1.22231i	−0.966438	+	0.256901i	$0.917299\pi$
$564$		0			0
$565$	12.9985	+	4.73105i	0.546849	+	0.199037i
$566$		0			0
$567$	−33.4262	+	28.0479i	−1.40377	+	1.17790i
$568$		0			0
$569$	−44.8839			−1.88163			−0.940816	−	0.338918i	$-0.889939\pi$
$569$	−44.8839			−1.88163			−0.940816	+	0.338918i	$0.889939\pi$
$570$		0			0
$571$	0.658444			0.0275550			0.0137775	−	0.999905i	$-0.495614\pi$
$571$	0.658444			0.0275550			0.0137775	+	0.999905i	$0.495614\pi$
$572$		0			0
$573$	−0.137236	+	0.115154i	−0.00573310	+	0.00481064i
$574$		0			0
$575$	22.6478	+	8.24311i	0.944477	+	0.343761i
$576$		0			0
$577$	1.77931	−	3.08185i	0.0740735	−	0.128299i	−0.826610	−	0.562776i	$-0.809733\pi$
$577$	1.77931	−	3.08185i	0.0740735	−	0.128299i	0.900683	+	0.434477i	$0.143067\pi$
$578$		0			0
$579$	−0.0266514	+	0.151147i	−0.00110759	+	0.00628147i
$580$		0			0
$581$	20.3896	+	35.3159i	0.845904	+	1.46515i
$582$		0			0
$583$	11.4326	+	9.59309i	0.473490	+	0.397305i
$584$		0			0
$585$	−10.4911	+	3.81843i	−0.433752	+	0.157873i
$586$		0			0
$587$	6.22859	+	35.3241i	0.257081	+	1.45798i	0.790673	+	0.612239i	$0.209731\pi$
$587$	6.22859	+	35.3241i	0.257081	+	1.45798i	−0.533591	+	0.845742i	$0.679158\pi$
$588$		0			0
$589$	16.0638	−	3.31077i	0.661899	−	0.136418i
$590$		0			0
$591$	0.284643	+	1.61429i	0.0117086	+	0.0664030i
$592$		0			0
$593$	−19.4440	+	7.07703i	−0.798469	+	0.290619i	−0.708852	−	0.705358i	$-0.750786\pi$
$593$	−19.4440	+	7.07703i	−0.798469	+	0.290619i	−0.0896168	+	0.995976i	$0.528564\pi$
$594$		0			0
$595$	−12.6485	−	10.6133i	−0.518537	−	0.435105i
$596$		0			0
$597$	0.00945365	+	0.0163742i	0.000386912	+	0.000670152i
$598$		0			0
$599$	−4.42673	+	25.1053i	−0.180871	+	1.02577i	0.750275	+	0.661126i	$0.229921\pi$
$599$	−4.42673	+	25.1053i	−0.180871	+	1.02577i	−0.931146	+	0.364646i	$0.881190\pi$
$600$		0			0
$601$	6.01475	−	10.4179i	0.245347	−	0.424953i	−0.716882	−	0.697194i	$-0.754431\pi$
$601$	6.01475	−	10.4179i	0.245347	−	0.424953i	0.962229	+	0.272241i	$0.0877648\pi$
$602$		0			0
$603$	−7.22229	−	2.62870i	−0.294114	−	0.107049i
$604$		0			0
$605$	6.03101	−	5.06061i	0.245195	−	0.205743i
$606$		0			0
$607$	−1.27655			−0.0518135			−0.0259067	−	0.999664i	$-0.508247\pi$
$607$	−1.27655			−0.0518135			−0.0259067	+	0.999664i	$0.508247\pi$
$608$		0			0
$609$	−2.69217			−0.109092
$610$		0			0
$611$	−4.85868	+	4.07692i	−0.196561	+	0.164934i
$612$		0			0
$613$	8.72020	+	3.17389i	0.352206	+	0.128192i	0.512063	−	0.858948i	$-0.328881\pi$
$613$	8.72020	+	3.17389i	0.352206	+	0.128192i	−0.159858	+	0.987140i	$0.551104\pi$
$614$		0			0
$615$	0.0737922	−	0.127812i	0.00297559	−	0.00515387i
$616$		0			0
$617$	6.07347	−	34.4443i	0.244509	−	1.38668i	−0.577123	−	0.816657i	$-0.695825\pi$
$617$	6.07347	−	34.4443i	0.244509	−	1.38668i	0.821631	−	0.570019i	$-0.193064\pi$
$618$		0			0
$619$	4.16416	+	7.21253i	0.167372	+	0.289896i	0.937495	−	0.347999i	$-0.113139\pi$
$619$	4.16416	+	7.21253i	0.167372	+	0.289896i	−0.770123	+	0.637895i	$0.779805\pi$
$620$		0			0
$621$	1.96957	+	1.65266i	0.0790361	+	0.0663191i
$622$		0			0
$623$	−56.7770	+	20.6652i	−2.27472	+	0.827932i
$624$		0			0
$625$	2.34369	+	13.2917i	0.0937477	+	0.531669i
$626$		0			0
$627$	0.180049	+	0.453697i	0.00719047	+	0.0181189i
$628$		0			0
$629$	2.22482	+	12.6176i	0.0887093	+	0.503095i
$630$		0			0
$631$	−38.9932	+	14.1924i	−1.55230	+	0.564990i	−0.968955	−	0.247238i	$-0.920477\pi$
$631$	−38.9932	+	14.1924i	−1.55230	+	0.564990i	−0.583341	+	0.812227i	$0.698255\pi$
$632$		0			0
$633$	−0.961273	−	0.806604i	−0.0382072	−	0.0320596i
$634$		0			0
$635$	2.83530	+	4.91089i	0.112516	+	0.194883i
$636$		0			0
$637$	12.0581	−	68.3847i	0.477758	−	2.70950i
$638$		0			0
$639$	10.8497	−	18.7922i	0.429208	−	0.743409i
$640$		0			0
$641$	−41.8086	−	15.2171i	−1.65134	−	0.601039i	−0.662374	−	0.749174i	$-0.730451\pi$
$641$	−41.8086	−	15.2171i	−1.65134	−	0.601039i	−0.988967	+	0.148135i	$0.952673\pi$
$642$		0			0
$643$	30.4636	−	25.5620i	1.20137	−	1.00807i	0.201777	−	0.979431i	$-0.435328\pi$
$643$	30.4636	−	25.5620i	1.20137	−	1.00807i	0.999590	−	0.0286354i	$-0.00911619\pi$
$644$		0			0
$645$	0.128059			0.00504231
$646$		0			0
$647$	−2.21149			−0.0869428			−0.0434714	−	0.999055i	$-0.513842\pi$
$647$	−2.21149			−0.0869428			−0.0434714	+	0.999055i	$0.513842\pi$
$648$		0			0
$649$	−8.98036	+	7.53542i	−0.352510	+	0.295791i
$650$		0			0
$651$	−1.28520	−	0.467776i	−0.0503711	−	0.0183336i
$652$		0			0
$653$	9.53266	−	16.5110i	0.373042	−	0.646127i	−0.616990	−	0.786971i	$-0.711648\pi$
$653$	9.53266	−	16.5110i	0.373042	−	0.646127i	0.990032	+	0.140844i	$0.0449815\pi$
$654$		0			0
$655$	2.15470	−	12.2199i	0.0841910	−	0.477471i
$656$		0			0
$657$	12.3461	+	21.3841i	0.481667	+	0.834272i
$658$		0			0
$659$	21.8019	+	18.2939i	0.849280	+	0.712631i	0.959631	−	0.281262i	$-0.0907530\pi$
$659$	21.8019	+	18.2939i	0.849280	+	0.712631i	−0.110351	+	0.993893i	$0.535197\pi$
$660$		0			0
$661$	−31.6686	+	11.5264i	−1.23176	+	0.448326i	−0.874201	−	0.485564i	$-0.838614\pi$
$661$	−31.6686	+	11.5264i	−1.23176	+	0.448326i	−0.357563	+	0.933889i	$0.616392\pi$
$662$		0			0
$663$	0.201640	+	1.14355i	0.00783103	+	0.0444120i
$664$		0			0
$665$	−18.9314	−	2.78014i	−0.734127	−	0.107809i
$666$		0			0
$667$	−7.39928	−	41.9634i	−0.286501	−	1.62483i
$668$		0			0
$669$	−1.81340	+	0.660025i	−0.0701102	+	0.0255180i
$670$		0			0
$671$	3.90241	+	3.27451i	0.150651	+	0.126411i
$672$		0			0
$673$	−8.13873	−	14.0967i	−0.313725	−	0.543388i	0.665441	−	0.746451i	$-0.268244\pi$
$673$	−8.13873	−	14.0967i	−0.313725	−	0.543388i	−0.979166	+	0.203063i	$0.934910\pi$
$674$		0			0
$675$	−0.325111	+	1.84380i	−0.0125135	+	0.0709678i
$676$		0			0
$677$	−6.48501	+	11.2324i	−0.249239	+	0.431695i	−0.963315	−	0.268373i	$-0.913514\pi$
$677$	−6.48501	+	11.2324i	−0.249239	+	0.431695i	0.714076	+	0.700069i	$0.246847\pi$
$678$		0			0
$679$	50.4717	+	18.3702i	1.93692	+	0.704983i
$680$		0			0
$681$	0.983532	−	0.825281i	0.0376890	−	0.0316249i
$682$		0			0
$683$	4.22475			0.161656			0.0808278	−	0.996728i	$-0.474244\pi$
$683$	4.22475			0.161656			0.0808278	+	0.996728i	$0.474244\pi$
$684$		0			0
$685$	−8.44453			−0.322649
$686$		0			0
$687$	−0.510793	+	0.428606i	−0.0194880	+	0.0163524i
$688$		0			0
$689$	38.6624	+	14.0720i	1.47292	+	0.536099i
$690$		0			0
$691$	−8.89665	+	15.4095i	−0.338445	+	0.586203i	−0.984140	−	0.177391i	$-0.943234\pi$
$691$	−8.89665	+	15.4095i	−0.338445	+	0.586203i	0.645696	+	0.763595i	$0.276567\pi$
$692$		0			0
$693$	−3.80778	+	21.5950i	−0.144646	+	0.820326i
$694$		0			0
$695$	−3.60646	−	6.24658i	−0.136801	−	0.236946i
$696$		0			0
$697$	6.33490	+	5.31562i	0.239952	+	0.201343i
$698$		0			0
$699$	−0.470214	+	0.171144i	−0.0177851	+	0.00647325i
$700$		0			0
$701$	−0.689000	−	3.90751i	−0.0260232	−	0.147585i	0.969028	−	0.246952i	$-0.0794291\pi$
$701$	−0.689000	−	3.90751i	−0.0260232	−	0.147585i	−0.995051	+	0.0993677i	$0.968318\pi$
$702$		0			0
$703$	9.86652	+	11.0951i	0.372123	+	0.418460i
$704$		0			0
$705$	−0.0178544	−	0.101258i	−0.000672437	−	0.00381358i
$706$		0			0
$707$	87.9318	−	32.0046i	3.30702	−	1.20366i
$708$		0			0
$709$	0.284143	+	0.238424i	0.0106712	+	0.00895422i	0.648108	−	0.761549i	$-0.275561\pi$
$709$	0.284143	+	0.238424i	0.0106712	+	0.00895422i	−0.637436	+	0.770503i	$0.720005\pi$
$710$		0			0
$711$	24.0219	+	41.6071i	0.900891	+	1.56039i
$712$		0			0
$713$	3.75901	−	21.3184i	0.140776	−	0.798381i
$714$		0			0
$715$	−2.80004	+	4.84981i	−0.104716	+	0.181373i
$716$		0			0
$717$	−1.03271	−	0.375876i	−0.0385673	−	0.0140373i
$718$		0			0
$719$	−21.2652	+	17.8436i	−0.793059	+	0.665455i	−0.946501	−	0.322702i	$-0.895409\pi$
$719$	−21.2652	+	17.8436i	−0.793059	+	0.665455i	0.153442	+	0.988158i	$0.450964\pi$
$720$		0			0
$721$	9.55859			0.355981
$722$		0			0
$723$	−0.167070			−0.00621340
$724$		0			0
$725$	23.7694	−	19.9449i	0.882772	−	0.740734i
$726$		0			0
$727$	−6.60839	−	2.40526i	−0.245092	−	0.0892061i	0.216553	−	0.976271i	$-0.430518\pi$
$727$	−6.60839	−	2.40526i	−0.245092	−	0.0892061i	−0.461645	+	0.887065i	$0.652741\pi$
$728$		0			0
$729$	13.3502	−	23.1232i	0.494450	−	0.856413i
$730$		0			0
$731$	−1.24602	+	7.06654i	−0.0460858	+	0.261365i
$732$		0			0
$733$	−0.667519	−	1.15618i	−0.0246554	−	0.0427044i	0.853434	−	0.521200i	$-0.174516\pi$
$733$	−0.667519	−	1.15618i	−0.0246554	−	0.0427044i	−0.878090	+	0.478496i	$0.841182\pi$
$734$		0			0
$735$	0.862329	+	0.723580i	0.0318075	+	0.0266896i
$736$		0			0
$737$	−3.62272	+	1.31856i	−0.133445	+	0.0485699i
$738$		0			0
$739$	1.65784	+	9.40207i	0.0609846	+	0.345861i	0.999998	+	0.00198036i	$0.000630369\pi$
$739$	1.65784	+	9.40207i	0.0609846	+	0.345861i	−0.939013	+	0.343880i	$0.888259\pi$
$740$		0			0
$741$	0.894222	+	1.00557i	0.0328501	+	0.0369406i
$742$		0			0
$743$	−2.29396	−	13.0097i	−0.0841573	−	0.477280i	−0.997535	−	0.0701672i	$-0.977647\pi$
$743$	−2.29396	−	13.0097i	−0.0841573	−	0.477280i	0.913378	−	0.407113i	$-0.133464\pi$
$744$		0			0
$745$	3.27121	−	1.19062i	0.119848	−	0.0436211i
$746$		0			0
$747$	−19.1867	−	16.0995i	−0.702003	−	0.589051i
$748$		0			0
$749$	26.9324	+	46.6482i	0.984087	+	1.70449i
$750$		0			0
$751$	1.54348	−	8.75350i	0.0563223	−	0.319420i	−0.943610	−	0.331059i	$-0.892594\pi$
$751$	1.54348	−	8.75350i	0.0563223	−	0.319420i	0.999932	+	0.0116396i	$0.00370508\pi$
$752$		0			0
$753$	−0.390401	+	0.676195i	−0.0142270	+	0.0246419i
$754$		0			0
$755$	−5.89633	−	2.14609i	−0.214590	−	0.0781042i
$756$		0			0
$757$	15.4257	−	12.9437i	0.560656	−	0.470447i	−0.317874	−	0.948133i	$-0.602969\pi$
$757$	15.4257	−	12.9437i	0.560656	−	0.470447i	0.878530	+	0.477686i	$0.158524\pi$
$758$		0			0
$759$	0.644236			0.0233843
$760$		0			0
$761$	−17.1139			−0.620377			−0.310188	−	0.950675i	$-0.600392\pi$
$761$	−17.1139			−0.620377			−0.310188	+	0.950675i	$0.600392\pi$
$762$		0			0
$763$	−37.3211	+	31.3161i	−1.35111	+	1.13372i
$764$		0			0
$765$	9.52964	+	3.46851i	0.344545	+	0.125404i
$766$		0			0
$767$	−16.1593	+	27.9887i	−0.583478	+	1.01061i
$768$		0			0
$769$	8.82477	−	50.0477i	0.318229	−	1.80477i	−0.235283	−	0.971927i	$-0.575602\pi$
$769$	8.82477	−	50.0477i	0.318229	−	1.80477i	0.553512	−	0.832841i	$-0.313287\pi$
$770$		0			0
$771$	−0.0998744	−	0.172988i	−0.00359689	−	0.00622999i
$772$		0			0
$773$	−25.0406	−	21.0116i	−0.900649	−	0.755735i	0.0696678	−	0.997570i	$-0.477806\pi$
$773$	−25.0406	−	21.0116i	−0.900649	−	0.755735i	−0.970317	+	0.241836i	$0.922251\pi$
$774$		0			0
$775$	14.8127	−	5.39137i	0.532087	−	0.193664i
$776$		0			0
$777$	−0.214995	−	1.21930i	−0.00771291	−	0.0437421i
$778$		0			0
$779$	9.48165	+	1.39241i	0.339715	+	0.0498884i
$780$		0			0
$781$	−1.89007	−	10.7191i	−0.0676321	−	0.383561i
$782$		0			0
$783$	3.11048	−	1.13212i	0.111159	−	0.0404587i
$784$		0			0
$785$	7.25590	+	6.08842i	0.258974	+	0.217305i
$786$		0			0
$787$	−20.6795	−	35.8180i	−0.737145	−	1.27677i	−0.953776	−	0.300519i	$-0.902840\pi$
$787$	−20.6795	−	35.8180i	−0.737145	−	1.27677i	0.216631	−	0.976254i	$-0.430493\pi$
$788$		0			0
$789$	−0.0871872	+	0.494463i	−0.00310395	+	0.0176034i
$790$		0			0
$791$	37.4504	−	64.8660i	1.33158	−	2.30637i
$792$		0			0
$793$	13.1970	+	4.80333i	0.468641	+	0.170571i
$794$		0			0
$795$	−0.510938	+	0.428728i	−0.0181211	+	0.0152054i
$796$		0			0
$797$	18.7142			0.662893			0.331446	−	0.943474i	$-0.392463\pi$
$797$	18.7142			0.662893			0.331446	+	0.943474i	$0.392463\pi$
$798$		0			0
$799$	5.76132			0.203821
$800$		0			0
$801$	28.4281	−	23.8540i	1.00446	−	0.842839i
$802$		0			0
$803$	11.6387	+	4.23616i	0.410722	+	0.149491i
$804$		0			0
$805$	−12.6272	+	21.8709i	−0.445050	+	0.770848i
$806$		0			0
$807$	0.140199	−	0.795106i	0.00493523	−	0.0279891i
$808$		0			0
$809$	20.2960	+	35.1536i	0.713568	+	1.23594i	0.963509	+	0.267675i	$0.0862552\pi$
$809$	20.2960	+	35.1536i	0.713568	+	1.23594i	−0.249942	+	0.968261i	$0.580411\pi$
$810$		0			0
$811$	−20.2180	−	16.9649i	−0.709951	−	0.595720i	0.214634	−	0.976694i	$-0.431144\pi$
$811$	−20.2180	−	16.9649i	−0.709951	−	0.595720i	−0.924585	+	0.380975i	$0.875588\pi$
$812$		0			0
$813$	−0.689076	+	0.250803i	−0.0241669	+	0.00879605i
$814$		0			0
$815$	−1.77317	−	10.0561i	−0.0621113	−	0.352251i
$816$		0			0
$817$	3.06728	+	7.72908i	0.107311	+	0.270406i
$818$		0			0
$819$	10.4975	+	59.5341i	0.366811	+	2.08029i
$820$		0			0
$821$	16.5325	−	6.01732i	0.576987	−	0.210006i	−0.0370095	−	0.999315i	$-0.511783\pi$
$821$	16.5325	−	6.01732i	0.576987	−	0.210006i	0.613996	+	0.789309i	$0.289561\pi$
$822$		0			0
$823$	8.81502	+	7.39668i	0.307272	+	0.257832i	0.783364	−	0.621564i	$-0.213502\pi$
$823$	8.81502	+	7.39668i	0.307272	+	0.257832i	−0.476091	+	0.879396i	$0.657947\pi$
$824$		0			0
$825$	0.234563	+	0.406275i	0.00816643	+	0.0141447i
$826$		0			0
$827$	−4.16521	+	23.6221i	−0.144839	+	0.821421i	0.822658	+	0.568537i	$0.192490\pi$
$827$	−4.16521	+	23.6221i	−0.144839	+	0.821421i	−0.967497	+	0.252884i	$0.918621\pi$
$828$		0			0
$829$	−16.2682	+	28.1773i	−0.565017	+	0.978637i	0.432032	+	0.901858i	$0.357797\pi$
$829$	−16.2682	+	28.1773i	−0.565017	+	0.978637i	−0.997048	+	0.0767789i	$0.975536\pi$
$830$		0			0
$831$	1.54931	+	0.563904i	0.0537451	+	0.0195616i
$832$		0			0
$833$	−48.3191	+	40.5445i	−1.67416	+	1.40478i
$834$		0			0
$835$	12.1338			0.419909
$836$		0			0
$837$	1.68161			0.0581250
$838$		0			0
$839$	13.5516	−	11.3712i	0.467854	−	0.392576i	−0.378157	−	0.925742i	$-0.623442\pi$
$839$	13.5516	−	11.3712i	0.467854	−	0.392576i	0.846011	+	0.533165i	$0.178998\pi$
$840$		0			0
$841$	−24.2990	−	8.84411i	−0.837896	−	0.304969i
$842$		0			0
$843$	0.416502	−	0.721402i	0.0143451	−	0.0248464i
$844$		0			0
$845$	−0.648318	+	3.67679i	−0.0223028	+	0.126486i
$846$		0			0
$847$	−21.3150	−	36.9187i	−0.732394	−	1.26854i
$848$		0			0
$849$	−1.66452	−	1.39670i	−0.0571263	−	0.0479346i
$850$		0			0
$851$	18.4146	−	6.70236i	0.631243	−	0.229754i
$852$		0			0
$853$	5.85399	+	33.1996i	0.200437	+	1.13673i	0.904461	+	0.426557i	$0.140274\pi$
$853$	5.85399	+	33.1996i	0.200437	+	1.13673i	−0.704024	+	0.710176i	$0.748615\pi$
$854$		0			0
$855$	11.5103	−	2.37229i	0.393646	−	0.0811305i
$856$		0			0
$857$	6.00554	+	34.0591i	0.205145	+	1.16344i	0.897211	+	0.441602i	$0.145590\pi$
$857$	6.00554	+	34.0591i	0.205145	+	1.16344i	−0.692065	+	0.721835i	$0.743299\pi$
$858$		0			0
$859$	9.85335	−	3.58633i	0.336192	−	0.122364i	−0.168407	−	0.985717i	$-0.553862\pi$
$859$	9.85335	−	3.58633i	0.336192	−	0.122364i	0.504599	+	0.863354i	$0.331640\pi$
$860$		0			0
$861$	−0.612174	−	0.513675i	−0.0208628	−	0.0175060i
$862$		0			0
$863$	−13.9197	−	24.1097i	−0.473833	−	0.820703i	0.525718	−	0.850659i	$-0.323797\pi$
$863$	−13.9197	−	24.1097i	−0.473833	−	0.820703i	−0.999551	+	0.0299556i	$0.990463\pi$
$864$		0			0
$865$	1.88065	−	10.6657i	0.0639439	−	0.362644i
$866$		0			0
$867$	−0.106318	+	0.184148i	−0.00361075	+	0.00625400i
$868$		0			0
$869$	22.6456	+	8.24232i	0.768199	+	0.279601i
$870$		0			0
$871$	−8.14171	+	6.83171i	−0.275871	+	0.231484i
$872$		0			0
$873$	−32.9889			−1.11651
$874$		0			0
$875$	−40.3386			−1.36370
$876$		0			0
$877$	8.23733	−	6.91194i	0.278155	−	0.233400i	−0.493028	−	0.870014i	$-0.664110\pi$
$877$	8.23733	−	6.91194i	0.278155	−	0.233400i	0.771183	+	0.636614i	$0.219665\pi$
$878$		0			0
$879$	−0.975783	−	0.355156i	−0.0329123	−	0.0119791i
$880$		0			0
$881$	−8.16415	+	14.1407i	−0.275057	+	0.476413i	−0.970150	−	0.242507i	$-0.922030\pi$
$881$	−8.16415	+	14.1407i	−0.275057	+	0.476413i	0.695092	+	0.718921i	$0.255363\pi$
$882$		0			0
$883$	4.20203	−	23.8309i	0.141409	−	0.801973i	−0.828771	−	0.559588i	$-0.810959\pi$
$883$	4.20203	−	23.8309i	0.141409	−	0.801973i	0.970180	−	0.242385i	$-0.0779296\pi$
$884$		0			0
$885$	−0.261959	−	0.453727i	−0.00880566	−	0.0152519i
$886$		0			0
$887$	−25.0976	−	21.0594i	−0.842694	−	0.707104i	0.115474	−	0.993310i	$-0.463161\pi$
$887$	−25.0976	−	21.0594i	−0.842694	−	0.707104i	−0.958168	+	0.286206i	$0.907606\pi$
$888$		0			0
$889$	28.8533	−	10.5018i	0.967710	−	0.352218i
$890$		0			0
$891$	−2.33437	−	13.2389i	−0.0782044	−	0.443519i
$892$		0			0
$893$	5.68382	−	3.50295i	0.190202	−	0.117222i
$894$		0			0
$895$	−3.87640	−	21.9842i	−0.129574	−	0.734849i
$896$		0			0
$897$	1.66895	−	0.607448i	0.0557246	−	0.0202821i
$898$		0			0
$899$	−21.3492	−	17.9141i	−0.712036	−	0.597469i
$900$		0			0
$901$	−18.6866	−	32.3661i	−0.622541	−	1.07827i
$902$		0			0
$903$	0.120409	−	0.682875i	0.00400697	−	0.0227247i
$904$		0			0
$905$	−8.39207	+	14.5355i	−0.278962	+	0.483176i
$906$		0			0
$907$	−2.66758	−	0.970921i	−0.0885757	−	0.0322389i	0.297352	−	0.954768i	$-0.403896\pi$
$907$	−2.66758	−	0.970921i	−0.0885757	−	0.0322389i	−0.385928	+	0.922529i	$0.626119\pi$
$908$		0			0
$909$	−44.0271	+	36.9432i	−1.46029	+	1.22533i
$910$		0			0
$911$	−24.6095			−0.815349			−0.407675	−	0.913127i	$-0.633660\pi$
$911$	−24.6095			−0.815349			−0.407675	+	0.913127i	$0.633660\pi$
$912$		0			0
$913$	−12.5634			−0.415787
$914$		0			0
$915$	−0.174404	+	0.146342i	−0.00576561	+	0.00483792i
$916$		0			0
$917$	−63.1368	−	22.9799i	−2.08496	−	0.758864i
$918$		0			0
$919$	−8.86763	+	15.3592i	−0.292516	+	0.506653i	−0.974404	−	0.224804i	$-0.927826\pi$
$919$	−8.86763	+	15.3592i	−0.292516	+	0.506653i	0.681888	+	0.731457i	$0.261159\pi$
$920$		0			0
$921$	−0.209860	+	1.19017i	−0.00691511	+	0.0392175i
$922$		0			0
$923$	−15.0034	−	25.9867i	−0.493844	−	0.855363i
$924$		0			0
$925$	10.9314	+	9.17250i	0.359421	+	0.301590i
$926$		0			0
$927$	−5.51678	+	2.00795i	−0.181195	+	0.0659496i
$928$		0			0
$929$	0.538315	+	3.05294i	0.0176615	+	0.100164i	0.992364	−	0.123342i	$-0.0393611\pi$
$929$	0.538315	+	3.05294i	0.0176615	+	0.100164i	−0.974703	+	0.223505i	$0.928250\pi$
$930$		0			0
$931$	−23.0176	+	69.3777i	−0.754370	+	2.27376i
$932$		0			0
$933$	0.0205950	+	0.116800i	0.000674249	+	0.00382385i
$934$		0			0
$935$	4.78010	−	1.73981i	0.156326	−	0.0568980i
$936$		0			0
$937$	22.2172	+	18.6424i	0.725803	+	0.609021i	0.928984	−	0.370120i	$-0.120684\pi$
$937$	22.2172	+	18.6424i	0.725803	+	0.609021i	−0.203181	+	0.979141i	$0.565128\pi$
$938$		0			0
$939$	0.291795	+	0.505404i	0.00952238	+	0.0164932i
$940$		0			0
$941$	0.900989	−	5.10976i	0.0293714	−	0.166574i	−0.966594	−	0.256313i	$-0.917492\pi$
$941$	0.900989	−	5.10976i	0.0293714	−	0.166574i	0.995965	+	0.0897393i	$0.0286034\pi$
$942$		0			0
$943$	6.32423	−	10.9539i	0.205945	−	0.356708i
$944$		0			0
$945$	−1.84350	−	0.670981i	−0.0599692	−	0.0218270i
$946$		0			0
$947$	4.67086	−	3.91932i	0.151783	−	0.127361i	−0.563734	−	0.825956i	$-0.690636\pi$
$947$	4.67086	−	3.91932i	0.151783	−	0.127361i	0.715517	+	0.698596i	$0.246191\pi$
$948$		0			0
$949$	34.1454			1.10841
$950$		0			0
$951$	1.79227			0.0581185
$952$		0			0
$953$	7.30332	−	6.12821i	0.236578	−	0.198512i	−0.516789	−	0.856113i	$-0.672873\pi$
$953$	7.30332	−	6.12821i	0.236578	−	0.198512i	0.753367	+	0.657600i	$0.228428\pi$
$954$		0			0
$955$	2.03309	+	0.739985i	0.0657893	+	0.0239454i
$956$		0			0
$957$	0.414705	−	0.718290i	0.0134055	−	0.0232190i
$958$		0			0
$959$	−7.94011	+	45.0306i	−0.256399	+	1.45411i
$960$		0			0
$961$	8.42084	+	14.5853i	0.271640	+	0.470494i
$962$		0			0
$963$	−25.3434	−	21.2656i	−0.816680	−	0.685275i
$964$		0			0
$965$	1.74178	−	0.633956i	0.0560699	−	0.0204078i
$966$		0			0
$967$	6.00694	+	34.0671i	0.193170	+	1.09552i	0.915001	+	0.403453i	$0.132190\pi$
$967$	6.00694	+	34.0671i	0.193170	+	1.09552i	−0.721830	+	0.692070i	$0.756699\pi$
$968$		0			0
$969$	−0.0351028	−	1.22184i	−0.00112766	−	0.0392512i
$970$		0			0
$971$	1.45826	+	8.27021i	0.0467978	+	0.265404i	0.999225	−	0.0393627i	$-0.0125328\pi$
$971$	1.45826	+	8.27021i	0.0467978	+	0.265404i	−0.952427	+	0.304766i	$0.901422\pi$
$972$		0			0
$973$	−36.7010	+	13.3581i	−1.17658	+	0.428240i
$974$		0			0
$975$	0.990730	+	0.831321i	0.0317288	+	0.0266236i
$976$		0			0
$977$	0.964414	+	1.67041i	0.0308543	+	0.0534413i	0.881040	−	0.473041i	$-0.156844\pi$
$977$	0.964414	+	1.67041i	0.0308543	+	0.0534413i	−0.850186	+	0.526483i	$0.823511\pi$
$978$		0			0
$979$	3.23239	−	18.3318i	0.103308	−	0.585887i
$980$		0			0
$981$	14.9616	−	25.9142i	0.477686	−	0.827376i
$982$		0			0
$983$	−18.0660	−	6.57550i	−0.576217	−	0.209726i	0.0374397	−	0.999299i	$-0.488080\pi$
$983$	−18.0660	−	6.57550i	−0.576217	−	0.209726i	−0.613656	+	0.789573i	$0.710302\pi$
$984$		0			0
$985$	15.1650	−	12.7249i	0.483197	−	0.405450i
$986$		0			0
$987$	−0.556745			−0.0177214
$988$		0			0
$989$	10.9751			0.348987
$990$		0			0
$991$	3.91263	−	3.28309i	0.124289	−	0.104291i	−0.578525	−	0.815665i	$-0.696371\pi$
$991$	3.91263	−	3.28309i	0.124289	−	0.104291i	0.702813	+	0.711374i	$0.251927\pi$
$992$		0			0
$993$	−0.521755	−	0.189903i	−0.0165574	−	0.00602640i
$994$		0			0
$995$	0.114172	−	0.197751i	0.00361948	−	0.00626913i
$996$		0			0
$997$	2.86243	−	16.2336i	0.0906540	−	0.514125i	−0.905339	−	0.424690i	$-0.860383\pi$
$997$	2.86243	−	16.2336i	0.0906540	−	0.514125i	0.995993	−	0.0894343i	$-0.0285059\pi$
$998$		0			0
$999$	0.761146	+	1.31834i	0.0240816	+	0.0417105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.q.c.9.2	✓	18
4.3	odd	2		304.2.u.f.161.2		18
19.6	even	9		2888.2.a.y.1.4		9
19.13	odd	18		2888.2.a.x.1.6		9
19.17	even	9	inner	152.2.q.c.17.2	yes	18
76.51	even	18		5776.2.a.ce.1.4		9
76.55	odd	18		304.2.u.f.17.2		18
76.63	odd	18		5776.2.a.cd.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.c.9.2	✓	18	1.1	even	1	trivial
152.2.q.c.17.2	yes	18	19.17	even	9	inner
304.2.u.f.17.2		18	76.55	odd	18
304.2.u.f.161.2		18	4.3	odd	2
2888.2.a.x.1.6		9	19.13	odd	18
2888.2.a.y.1.4		9	19.6	even	9
5776.2.a.cd.1.6		9	76.63	odd	18
5776.2.a.ce.1.4		9	76.51	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)

\(f(q)\)	\(=\)	\(q+(-0.0571117 + 0.0479224i) q^{3} +(0.846087 + 0.307950i) q^{5} +(2.43770 - 4.22221i) q^{7} +(-0.519979 + 2.94895i) q^{9} +(0.751011 + 1.30079i) q^{11} +(3.17207 + 2.66168i) q^{13} +(-0.0630792 + 0.0229589i) q^{15} +(-0.653155 - 3.70423i) q^{17} +(-2.89658 - 3.25727i) q^{19} +(0.0631176 + 0.357958i) q^{21} +(-5.40609 + 1.96766i) q^{23} +(-3.20919 - 2.69283i) q^{25} +(-0.223455 - 0.387035i) q^{27} +(-1.28615 + 7.29412i) q^{29} +(-1.88138 + 3.25864i) q^{31} +(-0.105228 - 0.0383000i) q^{33} +(3.36274 - 2.82167i) q^{35} -3.40626 q^{37} -0.308716 q^{39} +(-1.68420 + 1.41321i) q^{41} +(-1.79265 - 0.652471i) q^{43} +(-1.34808 + 2.33494i) q^{45} +(-0.265978 + 1.50844i) q^{47} +(-8.38473 - 14.5228i) q^{49} +(0.214818 + 0.180254i) q^{51} +(9.33685 - 3.39833i) q^{53} +(0.234842 + 1.33185i) q^{55} +(0.321525 + 0.0472171i) q^{57} +(1.35529 + 7.68626i) q^{59} +(3.18704 - 1.15999i) q^{61} +(11.1835 + 9.38411i) q^{63} +(1.86418 + 3.22885i) q^{65} +(-0.445701 + 2.52769i) q^{67} +(0.214456 - 0.371449i) q^{69} +(-6.80954 - 2.47847i) q^{71} +(6.31681 - 5.30043i) q^{73} +0.312329 q^{75} +7.32295 q^{77} +(12.2907 - 10.3131i) q^{79} +(-8.41025 - 3.06108i) q^{81} +(-4.18215 + 7.24370i) q^{83} +(0.588092 - 3.33524i) q^{85} +(-0.276098 - 0.478215i) q^{87} +(-9.49361 - 7.96608i) q^{89} +(18.9707 - 6.90478i) q^{91} +(-0.0487133 - 0.276267i) q^{93} +(-1.44768 - 3.64794i) q^{95} +(1.91303 + 10.8493i) q^{97} +(-4.22647 + 1.53831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{7} - 6 q^{9} - 3 q^{11} + 3 q^{13} + 33 q^{15} + 9 q^{17} - 24 q^{19} - 15 q^{21} + 6 q^{23} + 6 q^{25} - 12 q^{27} - 3 q^{29} - 6 q^{31} - 45 q^{33} - 15 q^{35} + 48 q^{37} + 12 q^{39} - 18 q^{41}+ \cdots + 15 q^{99}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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