LMFDB - Embedded newform 352.2.m.e.225.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(97,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("352.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} + \cdots + 25 $ x^12 - 2x^11 + 11x^10 - 11x^9 + 39x^8 - 43x^7 + 99x^6 + 36x^5 + 431x^4 - 350x^3 + 510x^2 - 175*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			225.2
Root			$0.289142 - 0.889888i$ of defining polynomial
Character	$\chi$	$=$	352.225
Dual form			352.2.m.e.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0520331 - 0.0378043i) q^{3} +(0.714760 - 2.19980i) q^{5} +(1.31923 - 0.958478i) q^{7} +(-0.925773 - 2.84924i) q^{9} +(-1.79704 + 2.78759i) q^{11} +(-0.357360 - 1.09984i) q^{13} +(-0.120353 + 0.0874418i) q^{15} +(1.03847 - 3.19609i) q^{17} +(-4.72044 - 3.42960i) q^{19} -0.104878 q^{21} +7.86209 q^{23} +(-0.283172 - 0.205736i) q^{25} +(-0.119167 + 0.366759i) q^{27} +(4.79497 - 3.48375i) q^{29} +(1.11571 + 3.43382i) q^{31} +(0.198888 - 0.0771113i) q^{33} +(-1.16553 - 3.58713i) q^{35} +(0.293146 - 0.212983i) q^{37} +(-0.0229842 + 0.0707380i) q^{39} +(3.56752 + 2.59196i) q^{41} -5.15478 q^{43} -6.92946 q^{45} +(-0.937266 - 0.680964i) q^{47} +(-1.34143 + 4.12849i) q^{49} +(-0.174861 + 0.127044i) q^{51} +(1.89864 + 5.84340i) q^{53} +(4.84770 + 5.94559i) q^{55} +(0.115966 + 0.356906i) q^{57} +(-6.57117 + 4.77424i) q^{59} +(-2.72739 + 8.39403i) q^{61} +(-3.95224 - 2.87147i) q^{63} -2.67486 q^{65} +12.6763 q^{67} +(-0.409089 - 0.297221i) q^{69} +(4.63749 - 14.2727i) q^{71} +(-10.5190 + 7.64250i) q^{73} +(0.00695661 + 0.0214102i) q^{75} +(0.301134 + 5.39990i) q^{77} +(-0.641623 - 1.97471i) q^{79} +(-7.25105 + 5.26819i) q^{81} +(-2.76546 + 8.51121i) q^{83} +(-6.28851 - 4.56887i) q^{85} -0.381198 q^{87} +13.9653 q^{89} +(-1.52562 - 1.10842i) q^{91} +(0.0717589 - 0.220851i) q^{93} +(-10.9184 + 7.93270i) q^{95} +(0.00246842 + 0.00759703i) q^{97} +(9.60615 + 2.53951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} - q^{9} + 11 q^{11} - 2 q^{13} - 4 q^{15} + 12 q^{17} - 5 q^{19} + 24 q^{21} + 12 q^{23} + 13 q^{25} - 3 q^{27} - 16 q^{31} - 7 q^{33} + 28 q^{35} - 4 q^{37} - 46 q^{39} - 4 q^{41} + 22 q^{43}+ \cdots + 65 q^{99}+O(q^{100}) $ 12 * q - 6 * q^7 - q^9 + 11 * q^11 - 2 * q^13 - 4 * q^15 + 12 * q^17 - 5 * q^19 + 24 * q^21 + 12 * q^23 + 13 * q^25 - 3 * q^27 - 16 * q^31 - 7 * q^33 + 28 * q^35 - 4 * q^37 - 46 * q^39 - 4 * q^41 + 22 * q^43 + 28 * q^45 + 24 * q^47 - 5 * q^49 - 17 * q^51 - 14 * q^53 + 46 * q^55 - 37 * q^57 - 31 * q^59 - 14 * q^61 - 58 * q^63 - 52 * q^65 + 62 * q^67 - 18 * q^69 - 6 * q^71 - 8 * q^73 - 53 * q^75 - 46 * q^77 + 4 * q^79 - 22 * q^81 - 41 * q^83 - 36 * q^85 + 76 * q^87 - 2 * q^89 + 22 * q^91 + 8 * q^93 - 16 * q^95 + 3 * q^97 + 65 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	−0.0520331	−	0.0378043i	−0.0300414	−	0.0218263i	0.572663	−	0.819791i	$-0.305910\pi$
$3$	−0.0520331	−	0.0378043i	−0.0300414	−	0.0218263i	−0.602705	+	0.797964i	$0.705910\pi$
$4$		0			0
$5$	0.714760	−	2.19980i	0.319650	−	0.983782i	−0.654148	−	0.756367i	$-0.726972\pi$
$5$	0.714760	−	2.19980i	0.319650	−	0.983782i	0.973798	−	0.227415i	$-0.0730275\pi$
$6$		0			0
$7$	1.31923	−	0.958478i	0.498623	−	0.362271i	−0.309868	−	0.950780i	$-0.600285\pi$
$7$	1.31923	−	0.958478i	0.498623	−	0.362271i	0.808491	+	0.588509i	$0.200285\pi$
$8$		0			0
$9$	−0.925773	−	2.84924i	−0.308591	−	0.949745i
$10$		0			0
$11$	−1.79704	+	2.78759i	−0.541827	+	0.840490i
$11$	−1.79704	+	2.78759i	−0.541827	+	0.840490i
$12$		0			0
$13$	−0.357360	−	1.09984i	−0.0991139	−	0.305041i	0.889190	−	0.457538i	$-0.151269\pi$
$13$	−0.357360	−	1.09984i	−0.0991139	−	0.305041i	−0.988304	+	0.152497i	$0.951269\pi$
$14$		0			0
$15$	−0.120353	+	0.0874418i	−0.0310751	+	0.0225774i
$16$		0			0
$17$	1.03847	−	3.19609i	0.251866	−	0.775165i	−0.742565	−	0.669774i	$-0.766391\pi$
$17$	1.03847	−	3.19609i	0.251866	−	0.775165i	0.994431	−	0.105390i	$-0.0336092\pi$
$18$		0			0
$19$	−4.72044	−	3.42960i	−1.08294	−	0.786804i	−0.104749	−	0.994499i	$-0.533404\pi$
$19$	−4.72044	−	3.42960i	−1.08294	−	0.786804i	−0.978194	+	0.207695i	$0.933404\pi$
$20$		0			0
$21$	−0.104878			−0.0228863
$22$		0			0
$23$	7.86209			1.63936			0.819680	−	0.572822i	$-0.194152\pi$
$23$	7.86209			1.63936			0.819680	+	0.572822i	$0.194152\pi$
$24$		0			0
$25$	−0.283172	−	0.205736i	−0.0566344	−	0.0411473i
$26$		0			0
$27$	−0.119167	+	0.366759i	−0.0229337	+	0.0705828i
$28$		0			0
$29$	4.79497	−	3.48375i	0.890403	−	0.646916i	−0.0455797	−	0.998961i	$-0.514513\pi$
$29$	4.79497	−	3.48375i	0.890403	−	0.646916i	0.935983	+	0.352045i	$0.114513\pi$
$30$		0			0
$31$	1.11571	+	3.43382i	0.200388	+	0.616732i	0.999871	+	0.0160430i	$0.00510687\pi$
$31$	1.11571	+	3.43382i	0.200388	+	0.616732i	−0.799483	+	0.600689i	$0.794893\pi$
$32$		0			0
$33$	0.198888	−	0.0771113i	0.0346220	−	0.0134234i
$34$		0			0
$35$	−1.16553	−	3.58713i	−0.197011	−	0.606336i
$36$		0			0
$37$	0.293146	−	0.212983i	0.0481929	−	0.0350142i	−0.563428	−	0.826165i	$-0.690518\pi$
$37$	0.293146	−	0.212983i	0.0481929	−	0.0350142i	0.611621	+	0.791151i	$0.290518\pi$
$38$		0			0
$39$	−0.0229842	+	0.0707380i	−0.00368041	+	0.0113271i
$40$		0			0
$41$	3.56752	+	2.59196i	0.557153	+	0.404795i	0.830416	−	0.557144i	$-0.188103\pi$
$41$	3.56752	+	2.59196i	0.557153	+	0.404795i	−0.273263	+	0.961939i	$0.588103\pi$
$42$		0			0
$43$	−5.15478			−0.786097			−0.393049	−	0.919518i	$-0.628580\pi$
$43$	−5.15478			−0.786097			−0.393049	+	0.919518i	$0.628580\pi$
$44$		0			0
$45$	−6.92946			−1.03298
$46$		0			0
$47$	−0.937266	−	0.680964i	−0.136714	−	0.0993288i	0.517326	−	0.855788i	$-0.326927\pi$
$47$	−0.937266	−	0.680964i	−0.136714	−	0.0993288i	−0.654040	+	0.756460i	$0.726927\pi$
$48$		0			0
$49$	−1.34143	+	4.12849i	−0.191632	+	0.589784i
$50$		0			0
$51$	−0.174861	+	0.127044i	−0.0244854	+	0.0177897i
$52$		0			0
$53$	1.89864	+	5.84340i	0.260798	+	0.802653i	0.992632	+	0.121170i	$0.0386646\pi$
$53$	1.89864	+	5.84340i	0.260798	+	0.802653i	−0.731834	+	0.681483i	$0.761335\pi$
$54$		0			0
$55$	4.84770	+	5.94559i	0.653664	+	0.801703i
$56$		0			0
$57$	0.115966	+	0.356906i	0.0153600	+	0.0472733i
$58$		0			0
$59$	−6.57117	+	4.77424i	−0.855494	+	0.621553i	−0.926655	−	0.375912i	$-0.877329\pi$
$59$	−6.57117	+	4.77424i	−0.855494	+	0.621553i	0.0711616	+	0.997465i	$0.477329\pi$
$60$		0			0
$61$	−2.72739	+	8.39403i	−0.349206	+	1.07475i	0.610087	+	0.792334i	$0.291134\pi$
$61$	−2.72739	+	8.39403i	−0.349206	+	1.07475i	−0.959293	+	0.282411i	$0.908866\pi$
$62$		0			0
$63$	−3.95224	−	2.87147i	−0.497935	−	0.361771i
$64$		0			0
$65$	−2.67486			−0.331776
$66$		0			0
$67$	12.6763			1.54865			0.774326	−	0.632787i	$-0.218089\pi$
$67$	12.6763			1.54865			0.774326	+	0.632787i	$0.218089\pi$
$68$		0			0
$69$	−0.409089	−	0.297221i	−0.0492486	−	0.0357812i
$70$		0			0
$71$	4.63749	−	14.2727i	0.550368	−	1.69386i	−0.157503	−	0.987518i	$-0.550344\pi$
$71$	4.63749	−	14.2727i	0.550368	−	1.69386i	0.707872	−	0.706341i	$-0.249656\pi$
$72$		0			0
$73$	−10.5190	+	7.64250i	−1.23116	+	0.894487i	−0.996976	−	0.0777068i	$-0.975240\pi$
$73$	−10.5190	+	7.64250i	−1.23116	+	0.894487i	−0.234179	+	0.972193i	$0.575240\pi$
$74$		0			0
$75$	0.00695661	+	0.0214102i	0.000803280	+	0.00247224i
$76$		0			0
$77$	0.301134	+	5.39990i	0.0343174	+	0.615376i
$78$		0			0
$79$	−0.641623	−	1.97471i	−0.0721882	−	0.222172i	0.908453	−	0.417988i	$-0.137265\pi$
$79$	−0.641623	−	1.97471i	−0.0721882	−	0.222172i	−0.980641	+	0.195816i	$0.937265\pi$
$80$		0			0
$81$	−7.25105	+	5.26819i	−0.805672	+	0.585355i
$82$		0			0
$83$	−2.76546	+	8.51121i	−0.303549	+	0.934227i	0.676666	+	0.736290i	$0.263424\pi$
$83$	−2.76546	+	8.51121i	−0.303549	+	0.934227i	−0.980215	+	0.197937i	$0.936576\pi$
$84$		0			0
$85$	−6.28851	−	4.56887i	−0.682084	−	0.495563i
$86$		0			0
$87$	−0.381198			−0.0408687
$88$		0			0
$89$	13.9653			1.48032			0.740160	−	0.672431i	$-0.234750\pi$
$89$	13.9653			1.48032			0.740160	+	0.672431i	$0.234750\pi$
$90$		0			0
$91$	−1.52562	−	1.10842i	−0.159928	−	0.116195i
$92$		0			0
$93$	0.0717589	−	0.220851i	0.00744105	−	0.0229012i
$94$		0			0
$95$	−10.9184	+	7.93270i	−1.12021	+	0.813878i
$96$		0			0
$97$	0.00246842	+	0.00759703i	0.000250630	+	0.000771361i	0.951182	−	0.308631i	$-0.0998709\pi$
$97$	0.00246842	+	0.00759703i	0.000250630	+	0.000771361i	−0.950931	+	0.309403i	$0.899871\pi$
$98$		0			0
$99$	9.60615	+	2.53951i	0.965454	+	0.255230i
$100$		0			0
$101$	3.10740	+	9.56358i	0.309197	+	0.951612i	0.978077	+	0.208242i	$0.0667740\pi$
$101$	3.10740	+	9.56358i	0.309197	+	0.951612i	−0.668880	+	0.743370i	$0.733226\pi$
$102$		0			0
$103$	−3.94477	+	2.86604i	−0.388690	+	0.282400i	−0.764918	−	0.644127i	$-0.777221\pi$
$103$	−3.94477	+	2.86604i	−0.388690	+	0.282400i	0.376229	+	0.926527i	$0.377221\pi$
$104$		0			0
$105$	−0.0749628	+	0.230712i	−0.00731562	+	0.0225152i
$106$		0			0
$107$	−4.57351	−	3.32285i	−0.442138	−	0.321232i	0.344346	−	0.938843i	$-0.388101\pi$
$107$	−4.57351	−	3.32285i	−0.442138	−	0.321232i	−0.786484	+	0.617611i	$0.788101\pi$
$108$		0			0
$109$	8.01561			0.767756			0.383878	−	0.923384i	$-0.374588\pi$
$109$	8.01561			0.767756			0.383878	+	0.923384i	$0.374588\pi$
$110$		0			0
$111$	−0.0233050			−0.00221201
$112$		0			0
$113$	7.78627	+	5.65706i	0.732471	+	0.532171i	0.890344	−	0.455288i	$-0.150464\pi$
$113$	7.78627	+	5.65706i	0.732471	+	0.532171i	−0.157873	+	0.987459i	$0.550464\pi$
$114$		0			0
$115$	5.61951	−	17.2951i	0.524022	−	1.61277i
$116$		0			0
$117$	−2.80287	+	2.03641i	−0.259126	+	0.188266i
$118$		0			0
$119$	−1.69339	−	5.21173i	−0.155233	−	0.477759i
$120$		0			0
$121$	−4.54131	−	10.0188i	−0.412846	−	0.910801i
$122$		0			0
$123$	−0.0876423	−	0.269735i	−0.00790244	−	0.0243212i
$124$		0			0
$125$	8.70135	−	6.32190i	0.778272	−	0.565448i
$126$		0			0
$127$	−6.38611	+	19.6544i	−0.566676	+	1.74405i	0.0962444	+	0.995358i	$0.469317\pi$
$127$	−6.38611	+	19.6544i	−0.566676	+	1.74405i	−0.662920	+	0.748690i	$0.730683\pi$
$128$		0			0
$129$	0.268220	+	0.194873i	0.0236154	+	0.0171576i
$130$		0			0
$131$	17.9382			1.56727			0.783633	−	0.621224i	$-0.213364\pi$
$131$	17.9382			1.56727			0.783633	+	0.621224i	$0.213364\pi$
$132$		0			0
$133$	−9.51455			−0.825016
$134$		0			0
$135$	0.721622	+	0.524289i	0.0621073	+	0.0451236i
$136$		0			0
$137$	−1.37467	+	4.23081i	−0.117446	+	0.361463i	−0.992449	−	0.122655i	$-0.960859\pi$
$137$	−1.37467	+	4.23081i	−0.117446	+	0.361463i	0.875003	+	0.484117i	$0.160859\pi$
$138$		0			0
$139$	−4.46850	+	3.24655i	−0.379013	+	0.275369i	−0.760938	−	0.648824i	$-0.775261\pi$
$139$	−4.46850	+	3.24655i	−0.379013	+	0.275369i	0.381925	+	0.924193i	$0.375261\pi$
$140$		0			0
$141$	0.0230256	+	0.0708654i	0.00193910	+	0.00596794i
$142$		0			0
$143$	3.70810	+	0.980284i	0.310087	+	0.0819755i
$144$		0			0
$145$	−4.23632	−	13.0380i	−0.351807	−	1.08275i
$146$		0			0
$147$	0.225873	−	0.164106i	0.0186297	−	0.0135353i
$148$		0			0
$149$	3.74860	−	11.5370i	0.307097	−	0.945149i	−0.671789	−	0.740743i	$-0.734474\pi$
$149$	3.74860	−	11.5370i	0.307097	−	0.945149i	0.978886	−	0.204406i	$-0.0655262\pi$
$150$		0			0
$151$	−12.2528	−	8.90220i	−0.997121	−	0.724451i	−0.0356524	−	0.999364i	$-0.511351\pi$
$151$	−12.2528	−	8.90220i	−0.997121	−	0.724451i	−0.961469	+	0.274913i	$0.911351\pi$
$152$		0			0
$153$	−10.0678			−0.813933
$154$		0			0
$155$	8.35119			0.670784
$156$		0			0
$157$	−13.3128	−	9.67231i	−1.06248	−	0.771934i	−0.0879313	−	0.996127i	$-0.528026\pi$
$157$	−13.3128	−	9.67231i	−1.06248	−	0.771934i	−0.974545	+	0.224192i	$0.928026\pi$
$158$		0			0
$159$	0.122114	−	0.375827i	0.00968424	−	0.0298050i
$160$		0			0
$161$	10.3719	−	7.53564i	0.817422	−	0.593892i
$162$		0			0
$163$	−3.84634	−	11.8378i	−0.301268	−	0.927208i	−0.981043	−	0.193788i	$-0.937923\pi$
$163$	−3.84634	−	11.8378i	−0.301268	−	0.927208i	0.679775	−	0.733420i	$-0.262077\pi$
$164$		0			0
$165$	−0.0274724	−	0.492632i	−0.00213872	−	0.0383513i
$166$		0			0
$167$	−4.88568	−	15.0366i	−0.378065	−	1.16356i	−0.941387	−	0.337328i	$-0.890477\pi$
$167$	−4.88568	−	15.0366i	−0.378065	−	1.16356i	0.563322	−	0.826237i	$-0.309523\pi$
$168$		0			0
$169$	9.43527	−	6.85513i	0.725790	−	0.527318i
$170$		0			0
$171$	−5.40168	+	16.6247i	−0.413077	+	1.27132i
$172$		0			0
$173$	−0.670473	−	0.487127i	−0.0509751	−	0.0370356i	0.562006	−	0.827133i	$-0.310030\pi$
$173$	−0.670473	−	0.487127i	−0.0509751	−	0.0370356i	−0.612981	+	0.790098i	$0.710030\pi$
$174$		0			0
$175$	−0.570764			−0.0431457
$176$		0			0
$177$	0.522405			0.0392664
$178$		0			0
$179$	13.6719	+	9.93323i	1.02189	+	0.742444i	0.966669	−	0.256030i	$-0.0824146\pi$
$179$	13.6719	+	9.93323i	1.02189	+	0.742444i	0.0552180	+	0.998474i	$0.482415\pi$
$180$		0			0
$181$	3.47869	−	10.7063i	0.258569	−	0.795794i	−0.734536	−	0.678569i	$-0.762600\pi$
$181$	3.47869	−	10.7063i	0.258569	−	0.795794i	0.993105	−	0.117225i	$-0.0373997\pi$
$182$		0			0
$183$	0.459245	−	0.333661i	0.0339484	−	0.0246649i
$184$		0			0
$185$	−0.258992	−	0.797095i	−0.0190415	−	0.0586036i
$186$		0			0
$187$	7.04320	+	8.63832i	0.515050	+	0.631697i
$188$		0			0
$189$	0.194321	+	0.598059i	0.0141348	+	0.0435024i
$190$		0			0
$191$	−21.0000	+	15.2574i	−1.51951	+	1.10399i	−0.557778	+	0.829990i	$0.688346\pi$
$191$	−21.0000	+	15.2574i	−1.51951	+	1.10399i	−0.961730	+	0.273998i	$0.911654\pi$
$192$		0			0
$193$	0.194760	−	0.599410i	0.0140191	−	0.0431465i	−0.943802	−	0.330511i	$-0.892779\pi$
$193$	0.194760	−	0.599410i	0.0140191	−	0.0431465i	0.957821	+	0.287364i	$0.0927790\pi$
$194$		0			0
$195$	0.139182	+	0.101121i	0.00996700	+	0.00724145i
$196$		0			0
$197$	22.7866			1.62348			0.811741	−	0.584018i	$-0.198520\pi$
$197$	22.7866			1.62348			0.811741	+	0.584018i	$0.198520\pi$
$198$		0			0
$199$	17.6443			1.25077			0.625386	−	0.780316i	$-0.284942\pi$
$199$	17.6443			1.25077			0.625386	+	0.780316i	$0.284942\pi$
$200$		0			0
$201$	−0.659586	−	0.479217i	−0.0465236	−	0.0338014i
$202$		0			0
$203$	2.98658	−	9.19175i	0.209617	−	0.645134i
$204$		0			0
$205$	8.25171	−	5.99522i	0.576325	−	0.418724i
$206$		0			0
$207$	−7.27851	−	22.4009i	−0.505891	−	1.55697i
$208$		0			0
$209$	18.0431	−	6.99552i	1.24807	−	0.483890i
$210$		0			0
$211$	−2.69949	−	8.30817i	−0.185840	−	0.571958i	0.814121	−	0.580695i	$-0.197219\pi$
$211$	−2.69949	−	8.30817i	−0.185840	−	0.571958i	−0.999962	+	0.00873682i	$0.997219\pi$
$212$		0			0
$213$	−0.780873	+	0.567337i	−0.0535045	+	0.0388733i
$214$		0			0
$215$	−3.68443	+	11.3395i	−0.251276	+	0.773349i
$216$		0			0
$217$	4.76313	+	3.46061i	0.323342	+	0.234922i
$218$		0			0
$219$	0.836256			0.0565089
$220$		0			0
$221$	−3.88630			−0.261421
$222$		0			0
$223$	6.66560	+	4.84284i	0.446361	+	0.324301i	0.788158	−	0.615474i	$-0.211035\pi$
$223$	6.66560	+	4.84284i	0.446361	+	0.324301i	−0.341796	+	0.939774i	$0.611035\pi$
$224$		0			0
$225$	−0.324039	+	0.997289i	−0.0216026	+	0.0664859i
$226$		0			0
$227$	−2.56318	+	1.86226i	−0.170124	+	0.123603i	−0.669589	−	0.742731i	$-0.733530\pi$
$227$	−2.56318	+	1.86226i	−0.170124	+	0.123603i	0.499465	+	0.866334i	$0.333530\pi$
$228$		0			0
$229$	−2.47730	−	7.62433i	−0.163704	−	0.503830i	0.835234	−	0.549894i	$-0.185332\pi$
$229$	−2.47730	−	7.62433i	−0.163704	−	0.503830i	−0.998938	+	0.0460643i	$0.985332\pi$
$230$		0			0
$231$	0.188470	−	0.292358i	0.0124004	−	0.0192357i
$232$		0			0
$233$	−5.67269	−	17.4588i	−0.371631	−	1.14376i	−0.945724	−	0.324971i	$-0.894645\pi$
$233$	−5.67269	−	17.4588i	−0.371631	−	1.14376i	0.574093	−	0.818790i	$-0.305355\pi$
$234$		0			0
$235$	−2.16791	+	1.57508i	−0.141419	+	0.102747i
$236$		0			0
$237$	−0.0412669	+	0.127007i	−0.00268058	+	0.00824996i
$238$		0			0
$239$	−12.0977	−	8.78948i	−0.782534	−	0.568544i	0.123204	−	0.992381i	$-0.460683\pi$
$239$	−12.0977	−	8.78948i	−0.782534	−	0.568544i	−0.905739	+	0.423837i	$0.860683\pi$
$240$		0			0
$241$	−24.4586			−1.57552			−0.787758	−	0.615984i	$-0.788758\pi$
$241$	−24.4586			−1.57552			−0.787758	+	0.615984i	$0.788758\pi$
$242$		0			0
$243$	1.73335			0.111195
$244$		0			0
$245$	8.12306	+	5.90175i	0.518963	+	0.377049i
$246$		0			0
$247$	−2.08512	+	6.41734i	−0.132673	+	0.408326i
$248$		0			0
$249$	0.465656	−	0.338319i	0.0295098	−	0.0214401i
$250$		0			0
$251$	2.19108	+	6.74344i	0.138300	+	0.425642i	0.996089	−	0.0883595i	$-0.0281624\pi$
$251$	2.19108	+	6.74344i	0.138300	+	0.425642i	−0.857789	+	0.514002i	$0.828162\pi$
$252$		0			0
$253$	−14.1285	+	21.9163i	−0.888250	+	1.37786i
$254$		0			0
$255$	0.154488	+	0.475465i	0.00967441	+	0.0297748i
$256$		0			0
$257$	−15.4384	+	11.2167i	−0.963023	+	0.699677i	−0.953851	−	0.300281i	$-0.902920\pi$
$257$	−15.4384	+	11.2167i	−0.963023	+	0.699677i	−0.00917198	+	0.999958i	$0.502920\pi$
$258$		0			0
$259$	0.182588	−	0.561947i	0.0113455	−	0.0349177i
$260$		0			0
$261$	−14.3651	−	10.4368i	−0.889176	−	0.646024i
$262$		0			0
$263$	16.3340			1.00720			0.503598	−	0.863938i	$-0.332009\pi$
$263$	16.3340			1.00720			0.503598	+	0.863938i	$0.332009\pi$
$264$		0			0
$265$	14.2114			0.873000
$266$		0			0
$267$	−0.726659	−	0.527949i	−0.0444708	−	0.0323099i
$268$		0			0
$269$	5.47241	−	16.8423i	0.333659	−	1.02690i	−0.633720	−	0.773562i	$-0.718473\pi$
$269$	5.47241	−	16.8423i	0.333659	−	1.02690i	0.967379	−	0.253333i	$-0.0815269\pi$
$270$		0			0
$271$	7.45427	−	5.41585i	0.452815	−	0.328989i	−0.337891	−	0.941185i	$-0.609714\pi$
$271$	7.45427	−	5.41585i	0.452815	−	0.328989i	0.790706	+	0.612196i	$0.209714\pi$
$272$		0			0
$273$	0.0374794	+	0.115350i	0.00226836	+	0.00698128i
$274$		0			0
$275$	1.08238	−	0.419651i	0.0652699	−	0.0253059i
$276$		0			0
$277$	9.18452	+	28.2671i	0.551845	+	1.69840i	0.704134	+	0.710067i	$0.251335\pi$
$277$	9.18452	+	28.2671i	0.551845	+	1.69840i	−0.152290	+	0.988336i	$0.548665\pi$
$278$		0			0
$279$	8.75085	−	6.35787i	0.523900	−	0.380636i
$280$		0			0
$281$	−4.47453	+	13.7712i	−0.266928	+	0.821520i	0.724315	+	0.689469i	$0.242156\pi$
$281$	−4.47453	+	13.7712i	−0.266928	+	0.821520i	−0.991243	+	0.132050i	$0.957844\pi$
$282$		0			0
$283$	−18.1000	−	13.1504i	−1.07594	−	0.781713i	−0.0989659	−	0.995091i	$-0.531553\pi$
$283$	−18.1000	−	13.1504i	−1.07594	−	0.781713i	−0.976970	+	0.213378i	$0.931553\pi$
$284$		0			0
$285$	0.868010			0.0514165
$286$		0			0
$287$	7.19072			0.424455
$288$		0			0
$289$	4.61674	+	3.35426i	0.271573	+	0.197309i
$290$		0			0
$291$	0.000158760	0	0.000488614i	9.30670e−6	0	2.86431e-5i
$292$		0			0
$293$	−18.8358	+	13.6850i	−1.10040	+	0.799487i	−0.981125	−	0.193374i	$-0.938057\pi$
$293$	−18.8358	+	13.6850i	−1.10040	+	0.799487i	−0.119274	+	0.992861i	$0.538057\pi$
$294$		0			0
$295$	5.80557	+	17.8677i	0.338014	+	1.04030i
$296$		0			0
$297$	−0.808225	−	0.991269i	−0.0468980	−	0.0575192i
$298$		0			0
$299$	−2.80960	−	8.64706i	−0.162483	−	0.500072i
$300$		0			0
$301$	−6.80036	+	4.94075i	−0.391966	+	0.284780i
$302$		0			0
$303$	0.199857	−	0.615096i	0.0114815	−	0.0353364i
$304$		0			0
$305$	16.5158	+	11.9994i	0.945692	+	0.687085i
$306$		0			0
$307$	−23.0645			−1.31636			−0.658179	−	0.752861i	$-0.728673\pi$
$307$	−23.0645			−1.31636			−0.658179	+	0.752861i	$0.728673\pi$
$308$		0			0
$309$	0.313608			0.0178405
$310$		0			0
$311$	2.11848	+	1.53917i	0.120128	+	0.0872780i	0.646227	−	0.763145i	$-0.276346\pi$
$311$	2.11848	+	1.53917i	0.120128	+	0.0872780i	−0.526099	+	0.850423i	$0.676346\pi$
$312$		0			0
$313$	−9.76216	+	30.0448i	−0.551790	+	1.69823i	0.152484	+	0.988306i	$0.451273\pi$
$313$	−9.76216	+	30.0448i	−0.551790	+	1.69823i	−0.704274	+	0.709928i	$0.748727\pi$
$314$		0			0
$315$	−9.14157	+	6.64174i	−0.515069	+	0.374220i
$316$		0			0
$317$	−3.53064	−	10.8662i	−0.198301	−	0.610307i	−0.999922	−	0.0124749i	$-0.996029\pi$
$317$	−3.53064	−	10.8662i	−0.198301	−	0.610307i	0.801621	−	0.597832i	$-0.203971\pi$
$318$		0			0
$319$	1.09452	+	19.6268i	0.0612814	+	1.09889i
$320$		0			0
$321$	0.112356	+	0.345796i	0.00627110	+	0.0193005i
$322$		0			0
$323$	−15.8633	+	11.5254i	−0.882660	+	0.641290i
$324$		0			0
$325$	−0.125083	+	0.384967i	−0.00693837	+	0.0213541i
$326$		0			0
$327$	−0.417077	−	0.303024i	−0.0230644	−	0.0167573i
$328$		0			0
$329$	−1.88916			−0.104153
$330$		0			0
$331$	19.5632			1.07529			0.537645	−	0.843171i	$-0.319314\pi$
$331$	19.5632			1.07529			0.537645	+	0.843171i	$0.319314\pi$
$332$		0			0
$333$	−0.878224	−	0.638067i	−0.0481264	−	0.0349659i
$334$		0			0
$335$	9.06048	−	27.8853i	0.495027	−	1.52354i
$336$		0			0
$337$	3.20368	−	2.32761i	0.174516	−	0.126793i	−0.497099	−	0.867694i	$-0.665601\pi$
$337$	3.20368	−	2.32761i	0.174516	−	0.126793i	0.671614	+	0.740901i	$0.265601\pi$
$338$		0			0
$339$	−0.191283	−	0.588709i	−0.0103891	−	0.0319743i
$340$		0			0
$341$	−11.5771	−	3.06054i	−0.626933	−	0.165738i
$342$		0			0
$343$	5.71472	+	17.5881i	0.308566	+	0.949669i
$344$		0			0
$345$	−0.946228	+	0.687475i	−0.0509432	+	0.0370124i
$346$		0			0
$347$	0.585635	−	1.80240i	0.0314385	−	0.0967578i	−0.934106	−	0.356996i	$-0.883801\pi$
$347$	0.585635	−	1.80240i	0.0314385	−	0.0967578i	0.965544	+	0.260238i	$0.0838010\pi$
$348$		0			0
$349$	22.2674	+	16.1782i	1.19195	+	0.866001i	0.993469	−	0.114104i	$-0.0363997\pi$
$349$	22.2674	+	16.1782i	1.19195	+	0.866001i	0.198479	+	0.980105i	$0.436400\pi$
$350$		0			0
$351$	0.445962			0.0238037
$352$		0			0
$353$	−17.3853			−0.925325			−0.462663	−	0.886534i	$-0.653106\pi$
$353$	−17.3853			−0.925325			−0.462663	+	0.886534i	$0.653106\pi$
$354$		0			0
$355$	−28.0825	−	20.4031i	−1.49046	−	1.08289i
$356$		0			0
$357$	−0.108913	+	0.335200i	−0.00576430	+	0.0177407i
$358$		0			0
$359$	0.780494	−	0.567062i	0.0411929	−	0.0299284i	−0.566998	−	0.823719i	$-0.691895\pi$
$359$	0.780494	−	0.567062i	0.0411929	−	0.0299284i	0.608191	+	0.793791i	$0.291895\pi$
$360$		0			0
$361$	4.64906	+	14.3083i	0.244688	+	0.753071i
$362$		0			0
$363$	−0.142455	+	0.692991i	−0.00747697	+	0.0363726i
$364$		0			0
$365$	9.29344	+	28.6023i	0.486441	+	1.49711i
$366$		0			0
$367$	16.8081	−	12.2118i	0.877378	−	0.637452i	−0.0551785	−	0.998477i	$-0.517573\pi$
$367$	16.8081	−	12.2118i	0.877378	−	0.637452i	0.932556	+	0.361024i	$0.117573\pi$
$368$		0			0
$369$	4.08238	−	12.5643i	0.212520	−	0.654070i
$370$		0			0
$371$	8.10551	+	5.88900i	0.420817	+	0.305742i
$372$		0			0
$373$	−2.62662			−0.136001			−0.0680006	−	0.997685i	$-0.521662\pi$
$373$	−2.62662			−0.136001			−0.0680006	+	0.997685i	$0.521662\pi$
$374$		0			0
$375$	−0.691753			−0.0357220
$376$		0			0
$377$	−5.54511	−	4.02876i	−0.285588	−	0.207491i
$378$		0			0
$379$	1.48316	−	4.56471i	0.0761850	−	0.234473i	−0.905711	−	0.423897i	$-0.860662\pi$
$379$	1.48316	−	4.56471i	0.0761850	−	0.234473i	0.981895	+	0.189424i	$0.0606619\pi$
$380$		0			0
$381$	1.07531	−	0.781259i	0.0550899	−	0.0400251i
$382$		0			0
$383$	5.29843	+	16.3069i	0.270737	+	0.833244i	0.990316	+	0.138833i	$0.0443351\pi$
$383$	5.29843	+	16.3069i	0.270737	+	0.833244i	−0.719578	+	0.694411i	$0.755665\pi$
$384$		0			0
$385$	12.0940	+	3.19720i	0.616365	+	0.162944i
$386$		0			0
$387$	4.77216	+	14.6872i	0.242582	+	0.746592i
$388$		0			0
$389$	12.5318	−	9.10485i	0.635385	−	0.461634i	−0.222877	−	0.974847i	$-0.571545\pi$
$389$	12.5318	−	9.10485i	0.635385	−	0.461634i	0.858262	+	0.513212i	$0.171545\pi$
$390$		0			0
$391$	8.16456	−	25.1279i	0.412899	−	1.27077i
$392$		0			0
$393$	−0.933380	−	0.678140i	−0.0470828	−	0.0342076i
$394$		0			0
$395$	−4.80258			−0.241644
$396$		0			0
$397$	−15.5364			−0.779750			−0.389875	−	0.920868i	$-0.627482\pi$
$397$	−15.5364			−0.779750			−0.389875	+	0.920868i	$0.627482\pi$
$398$		0			0
$399$	0.495072	+	0.359691i	0.0247846	+	0.0180071i
$400$		0			0
$401$	−5.79452	+	17.8337i	−0.289365	+	0.890572i	0.695692	+	0.718340i	$0.255098\pi$
$401$	−5.79452	+	17.8337i	−0.289365	+	0.890572i	−0.985056	+	0.172232i	$0.944902\pi$
$402$		0			0
$403$	3.37794	−	2.45422i	0.168267	−	0.122253i
$404$		0			0
$405$	6.40624	+	19.7164i	0.318329	+	0.979715i
$406$		0			0
$407$	0.0669147	+	1.19991i	0.00331684	+	0.0594772i
$408$		0			0
$409$	−11.3705	−	34.9949i	−0.562237	−	1.73039i	−0.676020	−	0.736883i	$-0.736297\pi$
$409$	−11.3705	−	34.9949i	−0.562237	−	1.73039i	0.113783	−	0.993506i	$-0.463703\pi$
$410$		0			0
$411$	0.231472	−	0.168174i	0.0114177	−	0.00829541i
$412$		0			0
$413$	−4.09290	+	12.5966i	−0.201398	+	0.619841i
$414$		0			0
$415$	16.7464	+	12.1669i	0.822047	+	0.597252i
$416$		0			0
$417$	0.355244			0.0173964
$418$		0			0
$419$	−18.6797			−0.912565			−0.456283	−	0.889835i	$-0.650819\pi$
$419$	−18.6797			−0.912565			−0.456283	+	0.889835i	$0.650819\pi$
$420$		0			0
$421$	1.46645	+	1.06544i	0.0714702	+	0.0519261i	0.622947	−	0.782264i	$-0.285935\pi$
$421$	1.46645	+	1.06544i	0.0714702	+	0.0519261i	−0.551476	+	0.834190i	$0.685935\pi$
$422$		0			0
$423$	−1.07253	+	3.30091i	−0.0521482	+	0.160496i
$424$		0			0
$425$	−0.951618	+	0.691391i	−0.0461602	+	0.0335374i
$426$		0			0
$427$	4.44744	+	13.6878i	0.215227	+	0.662400i
$428$		0			0
$429$	−0.155885	−	0.191189i	−0.00752620	−	0.00923071i
$430$		0			0
$431$	−6.13475	−	18.8808i	−0.295500	−	0.909457i	−0.983053	−	0.183322i	$-0.941315\pi$
$431$	−6.13475	−	18.8808i	−0.295500	−	0.909457i	0.687552	−	0.726135i	$-0.258685\pi$
$432$		0			0
$433$	−13.5039	+	9.81114i	−0.648955	+	0.471493i	−0.862915	−	0.505349i	$-0.831364\pi$
$433$	−13.5039	+	9.81114i	−0.648955	+	0.471493i	0.213960	+	0.976842i	$0.431364\pi$
$434$		0			0
$435$	−0.272465	+	0.838561i	−0.0130637	+	0.0402059i
$436$		0			0
$437$	−37.1125	−	26.9638i	−1.77533	−	1.28985i
$438$		0			0
$439$	−33.3999			−1.59409			−0.797044	−	0.603921i	$-0.793604\pi$
$439$	−33.3999			−1.59409			−0.797044	+	0.603921i	$0.793604\pi$
$440$		0			0
$441$	13.0049			0.619280
$442$		0			0
$443$	−7.35442	−	5.34330i	−0.349419	−	0.253868i	0.399206	−	0.916861i	$-0.369286\pi$
$443$	−7.35442	−	5.34330i	−0.349419	−	0.253868i	−0.748625	+	0.662993i	$0.769286\pi$
$444$		0			0
$445$	9.98184	−	30.7209i	0.473185	−	1.45631i
$446$		0			0
$447$	−0.631200	+	0.458594i	−0.0298547	+	0.0216907i
$448$		0			0
$449$	−1.58559	−	4.87996i	−0.0748288	−	0.230299i	0.906645	−	0.421893i	$-0.138634\pi$
$449$	−1.58559	−	4.87996i	−0.0748288	−	0.230299i	−0.981474	+	0.191594i	$0.938634\pi$
$450$		0			0
$451$	−13.6363	+	5.28694i	−0.642107	+	0.248952i
$452$		0			0
$453$	0.301012	+	0.926419i	0.0141428	+	0.0435270i
$454$		0			0
$455$	−3.52877	+	2.56380i	−0.165431	+	0.120193i
$456$		0			0
$457$	−1.15130	+	3.54335i	−0.0538557	+	0.165751i	−0.974367	−	0.224966i	$-0.927773\pi$
$457$	−1.15130	+	3.54335i	−0.0538557	+	0.165751i	0.920511	+	0.390717i	$0.127773\pi$
$458$		0			0
$459$	1.04844	+	0.761737i	0.0489370	+	0.0355548i
$460$		0			0
$461$	−0.439230			−0.0204570			−0.0102285	−	0.999948i	$-0.503256\pi$
$461$	−0.439230			−0.0204570			−0.0102285	+	0.999948i	$0.503256\pi$
$462$		0			0
$463$	26.8109			1.24601			0.623003	−	0.782219i	$-0.285912\pi$
$463$	26.8109			1.24601			0.623003	+	0.782219i	$0.285912\pi$
$464$		0			0
$465$	−0.434539	−	0.315711i	−0.0201513	−	0.0146407i
$466$		0			0
$467$	−5.23362	+	16.1074i	−0.242183	+	0.745362i	0.753904	+	0.656984i	$0.228168\pi$
$467$	−5.23362	+	16.1074i	−0.242183	+	0.745362i	−0.996087	+	0.0883778i	$0.971832\pi$
$468$		0			0
$469$	16.7229	−	12.1499i	0.772193	−	0.561031i
$470$		0			0
$471$	0.327052	+	1.00656i	0.0150697	+	0.0463799i
$472$		0			0
$473$	9.26334	−	14.3694i	0.425929	−	0.660707i
$474$		0			0
$475$	0.631102	+	1.94233i	0.0289570	+	0.0891203i
$476$		0			0
$477$	14.8915	−	10.8193i	0.681836	−	0.495383i
$478$		0			0
$479$	1.10066	−	3.38748i	0.0502903	−	0.154778i	−0.922758	−	0.385381i	$-0.874070\pi$
$479$	1.10066	−	3.38748i	0.0502903	−	0.154778i	0.973048	+	0.230603i	$0.0740700\pi$
$480$		0			0
$481$	−0.339006	−	0.246302i	−0.0154574	−	0.0112304i
$482$		0			0
$483$	−0.824563			−0.0375189
$484$		0			0
$485$	0.0184763			0.000838966
$486$		0			0
$487$	−14.5377	−	10.5623i	−0.658766	−	0.478622i	0.207480	−	0.978239i	$-0.433474\pi$
$487$	−14.5377	−	10.5623i	−0.658766	−	0.478622i	−0.866246	+	0.499618i	$0.833474\pi$
$488$		0			0
$489$	−0.247383	+	0.761366i	−0.0111870	+	0.0344302i
$490$		0			0
$491$	9.91237	−	7.20176i	0.447339	−	0.325011i	−0.341205	−	0.939989i	$-0.610835\pi$
$491$	9.91237	−	7.20176i	0.447339	−	0.325011i	0.788544	+	0.614978i	$0.210835\pi$
$492$		0			0
$493$	−6.15493	−	18.9429i	−0.277204	−	0.853146i
$494$		0			0
$495$	12.4525	−	19.3165i	0.559699	−	0.868212i
$496$		0			0
$497$	−7.56217	−	23.2740i	−0.339209	−	1.04398i
$498$		0			0
$499$	16.3463	−	11.8763i	0.731762	−	0.531656i	−0.158358	−	0.987382i	$-0.550620\pi$
$499$	16.3463	−	11.8763i	0.731762	−	0.531656i	0.890120	+	0.455725i	$0.150620\pi$
$500$		0			0
$501$	−0.314230	+	0.967100i	−0.0140388	+	0.0432068i
$502$		0			0
$503$	13.2493	+	9.62615i	0.590755	+	0.429209i	0.842586	−	0.538563i	$-0.181032\pi$
$503$	13.2493	+	9.62615i	0.590755	+	0.429209i	−0.251830	+	0.967771i	$0.581032\pi$
$504$		0			0
$505$	23.2590			1.03501
$506$		0			0
$507$	−0.750100			−0.0333131
$508$		0			0
$509$	−3.73628	−	2.71456i	−0.165608	−	0.120321i	0.501895	−	0.864929i	$-0.332637\pi$
$509$	−3.73628	−	2.71456i	−0.165608	−	0.120321i	−0.667502	+	0.744608i	$0.732637\pi$
$510$		0			0
$511$	−6.55183	+	20.1645i	−0.289836	+	0.892023i
$512$		0			0
$513$	1.82036	−	1.32257i	0.0803707	−	0.0583927i
$514$		0			0
$515$	3.48517	+	10.7263i	0.153575	+	0.472655i
$516$		0			0
$517$	3.58255	−	1.38900i	0.157560	−	0.0610879i
$518$		0			0
$519$	0.0164713	+	0.0506935i	0.000723011	+	0.00222520i
$520$		0			0
$521$	9.37691	−	6.81272i	0.410810	−	0.298471i	−0.363120	−	0.931742i	$-0.618288\pi$
$521$	9.37691	−	6.81272i	0.410810	−	0.298471i	0.773930	+	0.633272i	$0.218288\pi$
$522$		0			0
$523$	9.21116	−	28.3490i	0.402776	−	1.23962i	−0.519962	−	0.854189i	$-0.674054\pi$
$523$	9.21116	−	28.3490i	0.402776	−	1.23962i	0.922738	−	0.385428i	$-0.125946\pi$
$524$		0			0
$525$	0.0296986	+	0.0215773i	0.00129615	+	0.000941711i
$526$		0			0
$527$	12.1334			0.528540
$528$		0			0
$529$	38.8125			1.68750
$530$		0			0
$531$	19.6863	+	14.3030i	0.854314	+	0.620695i
$532$		0			0
$533$	1.57585	−	4.84997i	0.0682577	−	0.210076i
$534$		0			0
$535$	−10.5786	+	7.68578i	−0.457351	+	0.332285i
$536$		0			0
$537$	−0.335874	−	1.03371i	−0.0144940	−	0.0446081i
$538$		0			0
$539$	−9.09793	−	11.1584i	−0.391876	−	0.480626i
$540$		0			0
$541$	−0.747789	−	2.30146i	−0.0321500	−	0.0989474i	0.933694	−	0.358072i	$-0.116566\pi$
$541$	−0.747789	−	2.30146i	−0.0321500	−	0.0989474i	−0.965844	+	0.259125i	$0.916566\pi$
$542$		0			0
$543$	−0.585752	+	0.425574i	−0.0251370	+	0.0182631i
$544$		0			0
$545$	5.72923	−	17.6328i	0.245413	−	0.755305i
$546$		0			0
$547$	−10.8486	−	7.88196i	−0.463852	−	0.337008i	0.331189	−	0.943565i	$-0.392550\pi$
$547$	−10.8486	−	7.88196i	−0.463852	−	0.337008i	−0.795040	+	0.606556i	$0.792550\pi$
$548$		0			0
$549$	26.4415			1.12850
$550$		0			0
$551$	−34.5822			−1.47325
$552$		0			0
$553$	−2.73917	−	1.99012i	−0.116481	−	0.0846286i
$554$		0			0
$555$	−0.0166574	+	0.0512663i	−0.000707069	+	0.00217614i
$556$		0			0
$557$	−6.10060	+	4.43235i	−0.258491	+	0.187805i	−0.709481	−	0.704724i	$-0.751071\pi$
$557$	−6.10060	+	4.43235i	−0.258491	+	0.187805i	0.450991	+	0.892529i	$0.351071\pi$
$558$		0			0
$559$	1.84212	+	5.66945i	0.0779132	+	0.239792i
$560$		0			0
$561$	−0.0399145	−	0.715742i	−0.00168519	−	0.0302187i
$562$		0			0
$563$	0.379457	+	1.16785i	0.0159922	+	0.0492190i	0.958734	−	0.284304i	$-0.0917625\pi$
$563$	0.379457	+	1.16785i	0.0159922	+	0.0492190i	−0.942742	+	0.333523i	$0.891763\pi$
$564$		0			0
$565$	18.0097	−	13.0848i	0.757675	−	0.550483i
$566$		0			0
$567$	−4.51636	+	13.8999i	−0.189669	+	0.583743i
$568$		0			0
$569$	−10.8958	−	7.91626i	−0.456775	−	0.331867i	0.335490	−	0.942044i	$-0.391098\pi$
$569$	−10.8958	−	7.91626i	−0.456775	−	0.331867i	−0.792265	+	0.610177i	$0.791098\pi$
$570$		0			0
$571$	11.8746			0.496935			0.248467	−	0.968640i	$-0.420073\pi$
$571$	11.8746			0.496935			0.248467	+	0.968640i	$0.420073\pi$
$572$		0			0
$573$	1.66949			0.0697441
$574$		0			0
$575$	−2.22632	−	1.61752i	−0.0928441	−	0.0674552i
$576$		0			0
$577$	6.29752	−	19.3818i	0.262169	−	0.806874i	−0.730163	−	0.683273i	$-0.760556\pi$
$577$	6.29752	−	19.3818i	0.262169	−	0.806874i	0.992332	−	0.123601i	$-0.0394441\pi$
$578$		0			0
$579$	−0.0327943	+	0.0238264i	−0.00136288	+	0.000990192i
$580$		0			0
$581$	4.50953	+	13.8789i	0.187087	+	0.575794i
$582$		0			0
$583$	−19.7009	−	5.20819i	−0.815929	−	0.215701i
$584$		0			0
$585$	2.47632	+	7.62132i	0.102383	+	0.315103i
$586$		0			0
$587$	19.1775	−	13.9333i	0.791541	−	0.575088i	−0.116879	−	0.993146i	$-0.537289\pi$
$587$	19.1775	−	13.9333i	0.791541	−	0.575088i	0.908420	+	0.418058i	$0.137289\pi$
$588$		0			0
$589$	6.50995	−	20.0356i	0.268238	−	0.825551i
$590$		0			0
$591$	−1.18566	−	0.861433i	−0.0487716	−	0.0354346i
$592$		0			0
$593$	−40.7647			−1.67400			−0.837002	−	0.547199i	$-0.815694\pi$
$593$	−40.7647			−1.67400			−0.837002	+	0.547199i	$0.815694\pi$
$594$		0			0
$595$	−12.6752			−0.519631
$596$		0			0
$597$	−0.918089	−	0.667031i	−0.0375749	−	0.0272998i
$598$		0			0
$599$	−7.23216	+	22.2583i	−0.295498	+	0.909450i	0.687556	+	0.726132i	$0.258684\pi$
$599$	−7.23216	+	22.2583i	−0.295498	+	0.909450i	−0.983054	+	0.183318i	$0.941316\pi$
$600$		0			0
$601$	−26.1694	+	19.0132i	−1.06747	+	0.775563i	−0.975456	−	0.220195i	$-0.929331\pi$
$601$	−26.1694	+	19.0132i	−1.06747	+	0.775563i	−0.0920150	+	0.995758i	$0.529331\pi$
$602$		0			0
$603$	−11.7353	−	36.1176i	−0.477900	−	1.47082i
$604$		0			0
$605$	−25.2854	+	2.82895i	−1.02800	+	0.115013i
$606$		0			0
$607$	8.66071	+	26.6549i	0.351527	+	1.08189i	0.957996	+	0.286782i	$0.0925855\pi$
$607$	8.66071	+	26.6549i	0.351527	+	1.08189i	−0.606469	+	0.795107i	$0.707414\pi$
$608$		0			0
$609$	−0.502889	+	0.365370i	−0.0203781	+	0.0148055i
$610$		0			0
$611$	−0.414011	+	1.27419i	−0.0167491	+	0.0515484i
$612$		0			0
$613$	−1.91565	−	1.39180i	−0.0773722	−	0.0562142i	0.548427	−	0.836199i	$-0.315227\pi$
$613$	−1.91565	−	1.39180i	−0.0773722	−	0.0562142i	−0.625799	+	0.779984i	$0.715227\pi$
$614$		0			0
$615$	−0.656008			−0.0264528
$616$		0			0
$617$	−10.4196			−0.419477			−0.209738	−	0.977758i	$-0.567261\pi$
$617$	−10.4196			−0.419477			−0.209738	+	0.977758i	$0.567261\pi$
$618$		0			0
$619$	26.5852	+	19.3153i	1.06855	+	0.776347i	0.975651	−	0.219329i	$-0.0703868\pi$
$619$	26.5852	+	19.3153i	1.06855	+	0.776347i	0.0928986	+	0.995676i	$0.470387\pi$
$620$		0			0
$621$	−0.936903	+	2.88349i	−0.0375966	+	0.115710i
$622$		0			0
$623$	18.4235	−	13.3854i	0.738121	−	0.536277i
$624$		0			0
$625$	−8.22838	−	25.3243i	−0.329135	−	1.01297i
$626$		0			0
$627$	−1.20330	−	0.318108i	−0.0480552	−	0.0127040i
$628$		0			0
$629$	−0.376288	−	1.15810i	−0.0150036	−	0.0461763i
$630$		0			0
$631$	−16.7872	+	12.1966i	−0.668289	+	0.485540i	−0.869452	−	0.494017i	$-0.835528\pi$
$631$	−16.7872	+	12.1966i	−0.668289	+	0.485540i	0.201163	+	0.979558i	$0.435528\pi$
$632$		0			0
$633$	−0.173622	+	0.534352i	−0.00690084	+	0.0212386i
$634$		0			0
$635$	38.6713	+	28.0964i	1.53463	+	1.11497i
$636$		0			0
$637$	5.02006			0.198902
$638$		0			0
$639$	−44.9596			−1.77857
$640$		0			0
$641$	0.790786	+	0.574539i	0.0312342	+	0.0226929i	0.603293	−	0.797520i	$-0.293855\pi$
$641$	0.790786	+	0.574539i	0.0312342	+	0.0226929i	−0.572059	+	0.820213i	$0.693855\pi$
$642$		0			0
$643$	−11.8078	+	36.3406i	−0.465653	+	1.43313i	0.392506	+	0.919749i	$0.371608\pi$
$643$	−11.8078	+	36.3406i	−0.465653	+	1.43313i	−0.858159	+	0.513384i	$0.828392\pi$
$644$		0			0
$645$	0.620395	−	0.450743i	0.0244280	−	0.0177480i
$646$		0			0
$647$	−10.8077	−	33.2625i	−0.424893	−	1.30768i	−0.903097	−	0.429436i	$-0.858712\pi$
$647$	−10.8077	−	33.2625i	−0.424893	−	1.30768i	0.478205	−	0.878248i	$-0.341288\pi$
$648$		0			0
$649$	−1.49996	−	26.8972i	−0.0588787	−	1.05581i
$650$		0			0
$651$	−0.117014	−	0.360133i	−0.00458615	−	0.0141147i
$652$		0			0
$653$	−28.6326	+	20.8028i	−1.12048	+	0.814077i	−0.984282	−	0.176604i	$-0.943489\pi$
$653$	−28.6326	+	20.8028i	−1.12048	+	0.814077i	−0.136199	+	0.990681i	$0.543489\pi$
$654$		0			0
$655$	12.8215	−	39.4605i	0.500977	−	1.54185i
$656$		0			0
$657$	31.5135	+	22.8959i	1.22946	+	0.893253i
$658$		0			0
$659$	23.8852			0.930437			0.465219	−	0.885196i	$-0.345976\pi$
$659$	23.8852			0.930437			0.465219	+	0.885196i	$0.345976\pi$
$660$		0			0
$661$	−28.4658			−1.10719			−0.553596	−	0.832785i	$-0.686745\pi$
$661$	−28.4658			−1.10719			−0.553596	+	0.832785i	$0.686745\pi$
$662$		0			0
$663$	0.202216	+	0.146919i	0.00785343	+	0.00570585i
$664$		0			0
$665$	−6.80062	+	20.9301i	−0.263717	+	0.811636i
$666$		0			0
$667$	37.6985	−	27.3896i	1.45969	−	1.06053i
$668$		0			0
$669$	−0.163752	−	0.503976i	−0.00633101	−	0.0194849i
$670$		0			0
$671$	−18.4979	−	22.6872i	−0.714103	−	0.875831i
$672$		0			0
$673$	13.8277	+	42.5572i	0.533017	+	1.64046i	0.747895	+	0.663817i	$0.231065\pi$
$673$	13.8277	+	42.5572i	0.533017	+	1.64046i	−0.214878	+	0.976641i	$0.568935\pi$
$674$		0			0
$675$	0.109200	−	0.0793388i	0.00420313	−	0.00305375i
$676$		0			0
$677$	−1.82355	+	5.61231i	−0.0700847	+	0.215699i	−0.979964	−	0.199174i	$-0.936174\pi$
$677$	−1.82355	+	5.61231i	−0.0700847	+	0.215699i	0.909879	+	0.414873i	$0.136174\pi$
$678$		0			0
$679$	0.0105380	+	0.00765631i	0.000404412	+	0.000293822i
$680$		0			0
$681$	0.203772			0.00780856
$682$		0			0
$683$	−35.5174			−1.35904			−0.679518	−	0.733659i	$-0.737811\pi$
$683$	−35.5174			−1.35904			−0.679518	+	0.733659i	$0.737811\pi$
$684$		0			0
$685$	8.32440	+	6.04803i	0.318059	+	0.231083i
$686$		0			0
$687$	−0.159331	+	0.490371i	−0.00607886	+	0.0187088i
$688$		0			0
$689$	5.74832	−	4.17640i	0.218994	−	0.159108i
$690$		0			0
$691$	6.53766	+	20.1208i	0.248704	+	0.765433i	0.995005	+	0.0998241i	$0.0318280\pi$
$691$	6.53766	+	20.1208i	0.248704	+	0.765433i	−0.746301	+	0.665609i	$0.768172\pi$
$692$		0			0
$693$	15.1068	−	5.85708i	0.573860	−	0.222492i
$694$		0			0
$695$	3.94788	+	12.1503i	0.149752	+	0.460888i
$696$		0			0
$697$	11.9889	−	8.71043i	0.454111	−	0.329931i
$698$		0			0
$699$	−0.364848	+	1.12289i	−0.0137998	+	0.0424715i
$700$		0			0
$701$	15.6462	+	11.3677i	0.590951	+	0.429351i	0.842655	−	0.538453i	$-0.180991\pi$
$701$	15.6462	+	11.3677i	0.590951	+	0.429351i	−0.251705	+	0.967804i	$0.580991\pi$
$702$		0			0
$703$	−2.11422			−0.0797394
$704$		0			0
$705$	0.172348			0.00649099
$706$		0			0
$707$	13.2659	+	9.63821i	0.498914	+	0.362482i
$708$		0			0
$709$	−8.22899	+	25.3262i	−0.309046	+	0.951146i	0.669090	+	0.743181i	$0.266684\pi$
$709$	−8.22899	+	25.3262i	−0.309046	+	0.951146i	−0.978136	+	0.207965i	$0.933316\pi$
$710$		0			0
$711$	−5.03242	+	3.65627i	−0.188731	+	0.137121i
$712$		0			0
$713$	8.77185	+	26.9970i	0.328508	+	1.01104i
$714$		0			0
$715$	4.80683	−	7.45642i	0.179765	−	0.278854i
$716$		0			0
$717$	0.297200	+	0.914689i	0.0110992	+	0.0341597i
$718$		0			0
$719$	27.7036	−	20.1278i	1.03317	−	0.750641i	0.0642283	−	0.997935i	$-0.479541\pi$
$719$	27.7036	−	20.1278i	1.03317	−	0.750641i	0.968940	+	0.247294i	$0.0795414\pi$
$720$		0			0
$721$	−2.45703	+	7.56195i	−0.0915045	+	0.281622i
$722$		0			0
$723$	1.27266	+	0.924640i	0.0473307	+	0.0343877i
$724$		0			0
$725$	−2.07454			−0.0770463
$726$		0			0
$727$	−38.7547			−1.43733			−0.718666	−	0.695355i	$-0.755247\pi$
$727$	−38.7547			−1.43733			−0.718666	+	0.695355i	$0.755247\pi$
$728$		0			0
$729$	21.6630	+	15.7391i	0.802332	+	0.582928i
$730$		0			0
$731$	−5.35310	+	16.4751i	−0.197991	+	0.609355i
$732$		0			0
$733$	22.6174	−	16.4325i	0.835393	−	0.606949i	−0.0856869	−	0.996322i	$-0.527308\pi$
$733$	22.6174	−	16.4325i	0.835393	−	0.606949i	0.921080	+	0.389374i	$0.127308\pi$
$734$		0			0
$735$	−0.199557	−	0.614173i	−0.00736077	−	0.0226541i
$736$		0			0
$737$	−22.7797	+	35.3362i	−0.839102	+	1.30163i
$738$		0			0
$739$	−0.0121639	−	0.0374367i	−0.000447457	−	0.00137713i	0.950833	−	0.309705i	$-0.100230\pi$
$739$	−0.0121639	−	0.0374367i	−0.000447457	−	0.00137713i	−0.951280	+	0.308328i	$0.900230\pi$
$740$		0			0
$741$	0.351098	−	0.255088i	0.0128979	−	0.00937089i
$742$		0			0
$743$	−8.08821	+	24.8930i	−0.296728	+	0.913234i	0.685908	+	0.727688i	$0.259405\pi$
$743$	−8.08821	+	24.8930i	−0.296728	+	0.913234i	−0.982636	+	0.185546i	$0.940595\pi$
$744$		0			0
$745$	−22.6998	−	16.4924i	−0.831657	−	0.604234i
$746$		0			0
$747$	26.8106			0.980950
$748$		0			0
$749$	−9.21839			−0.336833
$750$		0			0
$751$	−15.6085	−	11.3402i	−0.569562	−	0.413811i	0.265384	−	0.964143i	$-0.414501\pi$
$751$	−15.6085	−	11.3402i	−0.569562	−	0.413811i	−0.834946	+	0.550332i	$0.814501\pi$
$752$		0			0
$753$	0.140922	−	0.433715i	0.00513550	−	0.0158054i
$754$		0			0
$755$	−28.3409	+	20.5909i	−1.03143	+	0.749379i
$756$		0			0
$757$	14.1487	+	43.5453i	0.514244	+	1.58268i	0.784653	+	0.619936i	$0.212841\pi$
$757$	14.1487	+	43.5453i	0.514244	+	1.58268i	−0.270408	+	0.962746i	$0.587159\pi$
$758$		0			0
$759$	1.56368	−	0.606256i	0.0567579	−	0.0220057i
$760$		0			0
$761$	−4.08236	−	12.5642i	−0.147985	−	0.455452i	0.849397	−	0.527754i	$-0.176966\pi$
$761$	−4.08236	−	12.5642i	−0.147985	−	0.455452i	−0.997383	+	0.0723016i	$0.976966\pi$
$762$		0			0
$763$	10.5744	−	7.68278i	0.382821	−	0.278135i
$764$		0			0
$765$	−7.19605	+	22.1472i	−0.260174	+	0.800733i
$766$		0			0
$767$	7.59918	+	5.52113i	0.274391	+	0.199356i
$768$		0			0
$769$	−3.36696			−0.121416			−0.0607078	−	0.998156i	$-0.519336\pi$
$769$	−3.36696			−0.121416			−0.0607078	+	0.998156i	$0.519336\pi$
$770$		0			0
$771$	1.22735			0.0442019
$772$		0			0
$773$	−39.0007	−	28.3357i	−1.40276	−	1.01916i	−0.994326	−	0.106374i	$-0.966076\pi$
$773$	−39.0007	−	28.3357i	−1.40276	−	1.01916i	−0.408432	−	0.912789i	$-0.633924\pi$
$774$		0			0
$775$	0.390522	−	1.20190i	0.0140280	−	0.0431737i
$776$		0			0
$777$	−0.0307446	+	0.0223373i	−0.00110296	+	0.000801346i
$778$		0			0
$779$	−7.95089	−	24.4703i	−0.284870	−	0.876741i
$780$		0			0
$781$	31.4527	+	38.5760i	1.12547	+	1.38036i
$782$		0			0
$783$	0.706293	+	2.17375i	0.0252408	+	0.0776833i
$784$		0			0
$785$	−30.7926	+	22.3722i	−1.09904	+	0.798496i
$786$		0			0
$787$	7.98685	−	24.5810i	0.284700	−	0.876218i	−0.701788	−	0.712386i	$-0.747615\pi$
$787$	7.98685	−	24.5810i	0.284700	−	0.876218i	0.986488	−	0.163832i	$-0.0523855\pi$
$788$		0			0
$789$	−0.849908	−	0.617494i	−0.0302575	−	0.0219834i
$790$		0			0
$791$	15.6941			0.558017
$792$		0			0
$793$	10.2068			0.362453
$794$		0			0
$795$	−0.739464	−	0.537252i	−0.0262261	−	0.0190544i
$796$		0			0
$797$	0.0666498	−	0.205127i	0.00236086	−	0.00726597i	−0.949869	−	0.312648i	$-0.898784\pi$
$797$	0.0666498	−	0.205127i	0.00236086	−	0.00726597i	0.952230	+	0.305382i	$0.0987841\pi$
$798$		0			0
$799$	−3.14974	+	2.28842i	−0.111430	+	0.0809586i
$800$		0			0
$801$	−12.9287	−	39.7905i	−0.456813	−	1.40593i
$802$		0			0
$803$	−2.40111	−	43.0565i	−0.0847334	−	1.51943i
$804$		0			0
$805$	−9.16350	−	28.2024i	−0.322971	−	0.994003i
$806$		0			0
$807$	−0.921459	+	0.669479i	−0.0324369	+	0.0235668i
$808$		0			0
$809$	−7.30467	+	22.4815i	−0.256819	+	0.790406i	0.736647	+	0.676277i	$0.236408\pi$
$809$	−7.30467	+	22.4815i	−0.256819	+	0.790406i	−0.993466	+	0.114129i	$0.963592\pi$
$810$		0			0
$811$	30.6038	+	22.2350i	1.07465	+	0.780776i	0.976742	−	0.214420i	$-0.0687861\pi$
$811$	30.6038	+	22.2350i	1.07465	+	0.780776i	0.0979043	+	0.995196i	$0.468786\pi$
$812$		0			0
$813$	−0.592612			−0.0207838
$814$		0			0
$815$	−28.7901			−1.00847
$816$		0			0
$817$	24.3328	+	17.6788i	0.851298	+	0.618504i
$818$		0			0
$819$	−1.74579	+	5.37299i	−0.0610028	+	0.187747i
$820$		0			0
$821$	−21.6139	+	15.7034i	−0.754331	+	0.548053i	−0.897166	−	0.441693i	$-0.854378\pi$
$821$	−21.6139	+	15.7034i	−0.754331	+	0.548053i	0.142835	+	0.989746i	$0.454378\pi$
$822$		0			0
$823$	6.04233	+	18.5964i	0.210622	+	0.648229i	0.999435	+	0.0335960i	$0.0106960\pi$
$823$	6.04233	+	18.5964i	0.210622	+	0.648229i	−0.788813	+	0.614633i	$0.789304\pi$
$824$		0			0
$825$	−0.0721842	−	0.0190828i	−0.00251313	−	0.000664379i
$826$		0			0
$827$	8.27460	+	25.4666i	0.287736	+	0.885560i	0.985565	+	0.169296i	$0.0541494\pi$
$827$	8.27460	+	25.4666i	0.287736	+	0.885560i	−0.697829	+	0.716264i	$0.745851\pi$
$828$		0			0
$829$	−27.9174	+	20.2832i	−0.969612	+	0.704464i	−0.955363	−	0.295434i	$-0.904536\pi$
$829$	−27.9174	+	20.2832i	−0.969612	+	0.704464i	−0.0142486	+	0.999898i	$0.504536\pi$
$830$		0			0
$831$	0.590716	−	1.81804i	0.0204917	−	0.0630671i
$832$		0			0
$833$	11.8020	+	8.57463i	0.408914	+	0.297093i
$834$		0			0
$835$	−36.5696			−1.26554
$836$		0			0
$837$	−1.39234			−0.0481263
$838$		0			0
$839$	26.5571	+	19.2948i	0.916851	+	0.666132i	0.942738	−	0.333533i	$-0.108241\pi$
$839$	26.5571	+	19.2948i	0.916851	+	0.666132i	−0.0258869	+	0.999665i	$0.508241\pi$
$840$		0			0
$841$	1.89373	−	5.82831i	0.0653011	−	0.200976i
$842$		0			0
$843$	0.753433	−	0.547401i	0.0259496	−	0.0188535i
$844$		0			0
$845$	−8.33599	−	25.6555i	−0.286767	−	0.882577i
$846$		0			0
$847$	−15.5938	−	8.86439i	−0.535811	−	0.304584i
$848$		0			0
$849$	0.444659	+	1.36852i	0.0152606	+	0.0469674i
$850$		0			0
$851$	2.30474	−	1.67449i	0.0790054	−	0.0574008i
$852$		0			0
$853$	−9.36132	+	28.8112i	−0.320525	+	0.986476i	0.652895	+	0.757449i	$0.273554\pi$
$853$	−9.36132	+	28.8112i	−0.320525	+	0.986476i	−0.973420	+	0.229027i	$0.926446\pi$
$854$		0			0
$855$	32.7101	+	23.7653i	1.11866	+	0.812756i
$856$		0			0
$857$	−22.7328			−0.776538			−0.388269	−	0.921546i	$-0.626927\pi$
$857$	−22.7328			−0.776538			−0.388269	+	0.921546i	$0.626927\pi$
$858$		0			0
$859$	−18.4958			−0.631068			−0.315534	−	0.948914i	$-0.602184\pi$
$859$	−18.4958			−0.631068			−0.315534	+	0.948914i	$0.602184\pi$
$860$		0			0
$861$	−0.374156	−	0.271840i	−0.0127512	−	0.00926429i
$862$		0			0
$863$	−12.3132	+	37.8961i	−0.419146	+	1.29000i	0.489344	+	0.872091i	$0.337236\pi$
$863$	−12.3132	+	37.8961i	−0.419146	+	1.29000i	−0.908490	+	0.417908i	$0.862764\pi$
$864$		0			0
$865$	−1.55081	+	1.12673i	−0.0527292	+	0.0383100i
$866$		0			0
$867$	−0.113418	−	0.349065i	−0.00385188	−	0.0118549i
$868$		0			0
$869$	6.65770	+	1.76005i	0.225847	+	0.0597056i
$870$		0			0
$871$	−4.52999	−	13.9419i	−0.153493	−	0.472403i
$872$		0			0
$873$	0.0193605	−	0.0140662i	0.000655254	−	0.000476070i
$874$		0			0
$875$	5.41969	−	16.6801i	0.183219	−	0.563890i
$876$		0			0
$877$	−0.146583	−	0.106498i	−0.00494974	−	0.00359620i	0.585308	−	0.810811i	$-0.300974\pi$
$877$	−0.146583	−	0.106498i	−0.00494974	−	0.00359620i	−0.590257	+	0.807215i	$0.700974\pi$
$878$		0			0
$879$	1.49744			0.0505073
$880$		0			0
$881$	−2.32439			−0.0783108			−0.0391554	−	0.999233i	$-0.512467\pi$
$881$	−2.32439			−0.0783108			−0.0391554	+	0.999233i	$0.512467\pi$
$882$		0			0
$883$	−46.5566	−	33.8253i	−1.56675	−	1.13831i	−0.930184	−	0.367093i	$-0.880353\pi$
$883$	−46.5566	−	33.8253i	−1.56675	−	1.13831i	−0.636569	−	0.771220i	$-0.719647\pi$
$884$		0			0
$885$	0.373394	−	1.14919i	0.0125515	−	0.0386296i
$886$		0			0
$887$	−7.44033	+	5.40572i	−0.249822	+	0.181506i	−0.705648	−	0.708563i	$-0.749344\pi$
$887$	−7.44033	+	5.40572i	−0.249822	+	0.181506i	0.455826	+	0.890069i	$0.349344\pi$
$888$		0			0
$889$	10.4136	+	32.0497i	0.349260	+	1.07491i
$890$		0			0
$891$	−1.65516	−	29.6801i	−0.0554498	−	0.994320i
$892$		0			0
$893$	2.08887	+	6.42889i	0.0699015	+	0.215135i
$894$		0			0
$895$	31.6233	−	22.9757i	1.05705	−	0.767992i
$896$		0			0
$897$	−0.180704	+	0.556149i	−0.00603352	+	0.0185693i
$898$		0			0
$899$	17.3124	+	12.5782i	0.577400	+	0.419506i
$900$		0			0
$901$	20.6477			0.687874
$902$		0			0
$903$	0.540626			0.0179909
$904$		0			0
$905$	−21.0654	−	15.3049i	−0.700236	−	0.508751i
$906$		0			0
$907$	−6.60183	+	20.3183i	−0.219210	+	0.674659i	0.779618	+	0.626256i	$0.215413\pi$
$907$	−6.60183	+	20.3183i	−0.219210	+	0.674659i	−0.998828	+	0.0484035i	$0.984587\pi$
$908$		0			0
$909$	24.3722	−	17.7074i	0.808373	−	0.587318i
$910$		0			0
$911$	−2.43738	−	7.50147i	−0.0807538	−	0.248535i	0.902526	−	0.430635i	$-0.141710\pi$
$911$	−2.43738	−	7.50147i	−0.0807538	−	0.248535i	−0.983280	+	0.182100i	$0.941710\pi$
$912$		0			0
$913$	−18.7561	−	23.0039i	−0.620737	−	0.761319i
$914$		0			0
$915$	−0.405739	−	1.24874i	−0.0134133	−	0.0412820i
$916$		0			0
$917$	23.6646	−	17.1933i	0.781474	−	0.567774i
$918$		0			0
$919$	13.6579	−	42.0345i	0.450531	−	1.38659i	−0.425772	−	0.904831i	$-0.639997\pi$
$919$	13.6579	−	42.0345i	0.450531	−	1.38659i	0.876303	−	0.481761i	$-0.160003\pi$
$920$		0			0
$921$	1.20012	+	0.871936i	0.0395452	+	0.0287313i
$922$		0			0
$923$	−17.3550			−0.571246
$924$		0			0
$925$	−0.126829			−0.00417011
$926$		0			0
$927$	11.8180	+	8.58628i	0.388154	+	0.282010i
$928$		0			0
$929$	11.5674	−	35.6009i	0.379515	−	1.16803i	−0.560866	−	0.827906i	$-0.689532\pi$
$929$	11.5674	−	35.6009i	0.379515	−	1.16803i	0.940382	−	0.340121i	$-0.110468\pi$
$930$		0			0
$931$	20.4912	−	14.8877i	0.671571	−	0.487925i
$932$		0			0
$933$	−0.0520441	−	0.160175i	−0.00170385	−	0.00524390i
$934$		0			0
$935$	24.0368	−	9.31935i	0.786088	−	0.304775i
$936$		0			0
$937$	12.0708	+	37.1502i	0.394337	+	1.21365i	0.929476	+	0.368882i	$0.120259\pi$
$937$	12.0708	+	37.1502i	0.394337	+	1.21365i	−0.535139	+	0.844764i	$0.679741\pi$
$938$		0			0
$939$	1.64378	−	1.19428i	0.0536427	−	0.0389737i
$940$		0			0
$941$	17.8264	−	54.8639i	0.581123	−	1.78851i	−0.0331893	−	0.999449i	$-0.510566\pi$
$941$	17.8264	−	54.8639i	0.581123	−	1.78851i	0.614312	−	0.789063i	$-0.289434\pi$
$942$		0			0
$943$	28.0482	+	20.3782i	0.913374	+	0.663605i
$944$		0			0
$945$	1.45451			0.0473151
$946$		0			0
$947$	−28.2809			−0.919007			−0.459503	−	0.888176i	$-0.651973\pi$
$947$	−28.2809			−0.919007			−0.459503	+	0.888176i	$0.651973\pi$
$948$		0			0
$949$	12.1646	+	8.83811i	0.394880	+	0.286897i
$950$		0			0
$951$	−0.227079	+	0.698876i	−0.00736353	+	0.0226626i
$952$		0			0
$953$	6.31132	−	4.58544i	0.204444	−	0.148537i	−0.480852	−	0.876802i	$-0.659673\pi$
$953$	6.31132	−	4.58544i	0.204444	−	0.148537i	0.685296	+	0.728264i	$0.259673\pi$
$954$		0			0
$955$	18.5533	+	57.1013i	0.600372	+	1.84776i
$956$		0			0
$957$	0.685027	−	1.06262i	0.0221438	−	0.0343497i
$958$		0			0
$959$	2.24163	+	6.89902i	0.0723859	+	0.222781i
$960$		0			0
$961$	14.5332	−	10.5590i	0.468814	−	0.340614i
$962$		0			0
$963$	−5.23355	+	16.1072i	−0.168649	+	0.519047i
$964$		0			0
$965$	−1.17938	−	0.856868i	−0.0379655	−	0.0275836i
$966$		0			0
$967$	−21.5958			−0.694475			−0.347237	−	0.937777i	$-0.612880\pi$
$967$	−21.5958			−0.694475			−0.347237	+	0.937777i	$0.612880\pi$
$968$		0			0
$969$	1.26113			0.0405133
$970$		0			0
$971$	−24.6230	−	17.8897i	−0.790190	−	0.574107i	0.117830	−	0.993034i	$-0.462406\pi$
$971$	−24.6230	−	17.8897i	−0.790190	−	0.574107i	−0.908020	+	0.418927i	$0.862406\pi$
$972$		0			0
$973$	−2.78324	+	8.56592i	−0.0892264	+	0.274611i
$974$		0			0
$975$	0.0210619	−	0.0153023i	0.000674520	−	0.000490067i
$976$		0			0
$977$	−9.02534	−	27.7772i	−0.288746	−	0.888670i	−0.985251	−	0.171117i	$-0.945262\pi$
$977$	−9.02534	−	27.7772i	−0.288746	−	0.888670i	0.696504	−	0.717553i	$-0.254738\pi$
$978$		0			0
$979$	−25.0962	+	38.9296i	−0.802078	+	1.24419i
$980$		0			0
$981$	−7.42063	−	22.8384i	−0.236922	−	0.729172i
$982$		0			0
$983$	4.38749	−	3.18770i	0.139939	−	0.101672i	−0.515613	−	0.856822i	$-0.672436\pi$
$983$	4.38749	−	3.18770i	0.139939	−	0.101672i	0.655552	+	0.755150i	$0.272436\pi$
$984$		0			0
$985$	16.2870	−	50.1262i	0.518946	−	1.59715i
$986$		0			0
$987$	0.0982990	+	0.0714184i	0.00312889	+	0.00227327i
$988$		0			0
$989$	−40.5274			−1.28870
$990$		0			0
$991$	27.9224			0.886985			0.443492	−	0.896278i	$-0.353739\pi$
$991$	27.9224			0.886985			0.443492	+	0.896278i	$0.353739\pi$
$992$		0			0
$993$	−1.01793	−	0.739572i	−0.0323032	−	0.0234696i
$994$		0			0
$995$	12.6114	−	38.8140i	0.399810	−	1.23049i
$996$		0			0
$997$	−10.3584	+	7.52580i	−0.328053	+	0.238344i	−0.739604	−	0.673042i	$-0.764987\pi$
$997$	−10.3584	+	7.52580i	−0.328053	+	0.238344i	0.411551	+	0.911387i	$0.364987\pi$
$998$		0			0
$999$	0.0431800	+	0.132894i	0.00136615	+	0.00420459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.m.e.225.2	yes	12
4.3	odd	2		352.2.m.f.225.2	yes	12
8.3	odd	2		704.2.m.n.577.2		12
8.5	even	2		704.2.m.m.577.2		12
11.3	even	5		3872.2.a.bq.1.3		6
11.8	odd	10		3872.2.a.bp.1.3		6
11.9	even	5	inner	352.2.m.e.97.2	✓	12
44.3	odd	10		3872.2.a.bn.1.4		6
44.19	even	10		3872.2.a.bo.1.4		6
44.31	odd	10		352.2.m.f.97.2	yes	12
88.3	odd	10		7744.2.a.dv.1.3		6
88.19	even	10		7744.2.a.dw.1.3		6
88.53	even	10		704.2.m.m.449.2		12
88.69	even	10		7744.2.a.du.1.4		6
88.75	odd	10		704.2.m.n.449.2		12
88.85	odd	10		7744.2.a.dt.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.m.e.97.2	✓	12	11.9	even	5	inner
352.2.m.e.225.2	yes	12	1.1	even	1	trivial
352.2.m.f.97.2	yes	12	44.31	odd	10
352.2.m.f.225.2	yes	12	4.3	odd	2
704.2.m.m.449.2		12	88.53	even	10
704.2.m.m.577.2		12	8.5	even	2
704.2.m.n.449.2		12	88.75	odd	10
704.2.m.n.577.2		12	8.3	odd	2
3872.2.a.bn.1.4		6	44.3	odd	10
3872.2.a.bo.1.4		6	44.19	even	10
3872.2.a.bp.1.3		6	11.8	odd	10
3872.2.a.bq.1.3		6	11.3	even	5
7744.2.a.dt.1.4		6	88.85	odd	10
7744.2.a.du.1.4		6	88.69	even	10
7744.2.a.dv.1.3		6	88.3	odd	10
7744.2.a.dw.1.3		6	88.19	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0520331 - 0.0378043i) q^{3} +(0.714760 - 2.19980i) q^{5} +(1.31923 - 0.958478i) q^{7} +(-0.925773 - 2.84924i) q^{9} +(-1.79704 + 2.78759i) q^{11} +(-0.357360 - 1.09984i) q^{13} +(-0.120353 + 0.0874418i) q^{15} +(1.03847 - 3.19609i) q^{17} +(-4.72044 - 3.42960i) q^{19} -0.104878 q^{21} +7.86209 q^{23} +(-0.283172 - 0.205736i) q^{25} +(-0.119167 + 0.366759i) q^{27} +(4.79497 - 3.48375i) q^{29} +(1.11571 + 3.43382i) q^{31} +(0.198888 - 0.0771113i) q^{33} +(-1.16553 - 3.58713i) q^{35} +(0.293146 - 0.212983i) q^{37} +(-0.0229842 + 0.0707380i) q^{39} +(3.56752 + 2.59196i) q^{41} -5.15478 q^{43} -6.92946 q^{45} +(-0.937266 - 0.680964i) q^{47} +(-1.34143 + 4.12849i) q^{49} +(-0.174861 + 0.127044i) q^{51} +(1.89864 + 5.84340i) q^{53} +(4.84770 + 5.94559i) q^{55} +(0.115966 + 0.356906i) q^{57} +(-6.57117 + 4.77424i) q^{59} +(-2.72739 + 8.39403i) q^{61} +(-3.95224 - 2.87147i) q^{63} -2.67486 q^{65} +12.6763 q^{67} +(-0.409089 - 0.297221i) q^{69} +(4.63749 - 14.2727i) q^{71} +(-10.5190 + 7.64250i) q^{73} +(0.00695661 + 0.0214102i) q^{75} +(0.301134 + 5.39990i) q^{77} +(-0.641623 - 1.97471i) q^{79} +(-7.25105 + 5.26819i) q^{81} +(-2.76546 + 8.51121i) q^{83} +(-6.28851 - 4.56887i) q^{85} -0.381198 q^{87} +13.9653 q^{89} +(-1.52562 - 1.10842i) q^{91} +(0.0717589 - 0.220851i) q^{93} +(-10.9184 + 7.93270i) q^{95} +(0.00246842 + 0.00759703i) q^{97} +(9.60615 + 2.53951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} - q^{9} + 11 q^{11} - 2 q^{13} - 4 q^{15} + 12 q^{17} - 5 q^{19} + 24 q^{21} + 12 q^{23} + 13 q^{25} - 3 q^{27} - 16 q^{31} - 7 q^{33} + 28 q^{35} - 4 q^{37} - 46 q^{39} - 4 q^{41} + 22 q^{43}+ \cdots + 65 q^{99}+O(q^{100}) \) 12 * q - 6 * q^7 - q^9 + 11 * q^11 - 2 * q^13 - 4 * q^15 + 12 * q^17 - 5 * q^19 + 24 * q^21 + 12 * q^23 + 13 * q^25 - 3 * q^27 - 16 * q^31 - 7 * q^33 + 28 * q^35 - 4 * q^37 - 46 * q^39 - 4 * q^41 + 22 * q^43 + 28 * q^45 + 24 * q^47 - 5 * q^49 - 17 * q^51 - 14 * q^53 + 46 * q^55 - 37 * q^57 - 31 * q^59 - 14 * q^61 - 58 * q^63 - 52 * q^65 + 62 * q^67 - 18 * q^69 - 6 * q^71 - 8 * q^73 - 53 * q^75 - 46 * q^77 + 4 * q^79 - 22 * q^81 - 41 * q^83 - 36 * q^85 + 76 * q^87 - 2 * q^89 + 22 * q^91 + 8 * q^93 - 16 * q^95 + 3 * q^97 + 65 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more