LMFDB - Embedded newform 552.2.q.d.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.1
Character	$\chi$	$=$	552.169
Dual form			552.2.q.d.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(-2.35936 - 2.72285i) q^{5} +(1.95097 + 1.25381i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(-2.35936 - 2.72285i) q^{5} +(1.95097 + 1.25381i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.449660 - 3.12745i) q^{11} +(0.778312 - 0.500191i) q^{13} +(-1.49668 + 3.27726i) q^{15} +(-2.42180 + 0.711106i) q^{17} +(-4.25024 - 1.24798i) q^{19} +(0.330046 - 2.29552i) q^{21} +(-2.77223 - 3.91340i) q^{23} +(-1.13574 + 7.89928i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-9.66659 + 2.83837i) q^{29} +(0.151729 - 0.332241i) q^{31} +(-2.65804 + 1.70822i) q^{33} +(-1.18911 - 8.27041i) q^{35} +(-4.54638 + 5.24681i) q^{37} +(-0.778312 - 0.500191i) q^{39} +(4.45994 + 5.14705i) q^{41} +(-3.30753 - 7.24249i) q^{43} +3.60285 q^{45} +0.649844 q^{47} +(-0.673659 - 1.47511i) q^{49} +(1.65290 + 1.90755i) q^{51} +(4.44535 + 2.85685i) q^{53} +(-7.45467 + 8.60315i) q^{55} +(0.630409 + 4.38459i) q^{57} +(11.5867 - 7.44634i) q^{59} +(4.28731 - 9.38791i) q^{61} +(-2.22519 + 0.653373i) q^{63} +(-3.19826 - 0.939095i) q^{65} +(0.809005 - 5.62675i) q^{67} +(-2.40813 + 4.14740i) q^{69} +(0.930627 - 6.47265i) q^{71} +(6.41603 + 1.88392i) q^{73} +(7.65724 - 2.24837i) q^{75} +(3.04397 - 6.66537i) q^{77} +(-0.637245 + 0.409532i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(5.06491 - 5.84522i) q^{83} +(7.65015 + 4.91645i) q^{85} +(6.59752 + 7.61394i) q^{87} +(-6.23218 - 13.6466i) q^{89} +2.14561 q^{91} -0.365248 q^{93} +(6.62980 + 14.5172i) q^{95} +(-1.28908 - 1.48768i) q^{97} +(2.65804 + 1.70822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$	$1$	$1$

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
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$		0			0
$5$	−2.35936	−	2.72285i	−1.05514	−	1.21770i	−0.975299	−	0.220888i	$-0.929105\pi$
$5$	−2.35936	−	2.72285i	−1.05514	−	1.21770i	−0.0798400	−	0.996808i	$-0.525441\pi$
$6$		0			0
$7$	1.95097	+	1.25381i	0.737399	+	0.473897i	0.854650	−	0.519205i	$-0.173772\pi$
$7$	1.95097	+	1.25381i	0.737399	+	0.473897i	−0.117251	+	0.993102i	$0.537408\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	−0.449660	−	3.12745i	−0.135578	−	0.942962i	−0.938106	−	0.346349i	$-0.887421\pi$
$11$	−0.449660	−	3.12745i	−0.135578	−	0.942962i	0.802528	−	0.596614i	$-0.203488\pi$
$12$		0			0
$13$	0.778312	−	0.500191i	0.215865	−	0.138728i	−0.428240	−	0.903665i	$-0.640866\pi$
$13$	0.778312	−	0.500191i	0.215865	−	0.138728i	0.644105	+	0.764937i	$0.277230\pi$
$14$		0			0
$15$	−1.49668	+	3.27726i	−0.386440	+	0.846186i
$16$		0			0
$17$	−2.42180	+	0.711106i	−0.587374	+	0.172468i	−0.561897	−	0.827207i	$-0.689928\pi$
$17$	−2.42180	+	0.711106i	−0.587374	+	0.172468i	−0.0254763	+	0.999675i	$0.508110\pi$
$18$		0			0
$19$	−4.25024	−	1.24798i	−0.975073	−	0.286307i	−0.244884	−	0.969552i	$-0.578750\pi$
$19$	−4.25024	−	1.24798i	−0.975073	−	0.286307i	−0.730189	+	0.683245i	$0.760568\pi$
$20$		0			0
$21$	0.330046	−	2.29552i	0.0720220	−	0.500924i
$22$		0			0
$23$	−2.77223	−	3.91340i	−0.578051	−	0.816001i
$23$	−2.77223	−	3.91340i	−0.578051	−	0.816001i
$24$		0			0
$25$	−1.13574	+	7.89928i	−0.227149	+	1.57986i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	−9.66659	+	2.83837i	−1.79504	+	0.527072i	−0.997130	−	0.0757042i	$-0.975880\pi$
$29$	−9.66659	+	2.83837i	−1.79504	+	0.527072i	−0.797911	+	0.602776i	$0.794061\pi$
$30$		0			0
$31$	0.151729	−	0.332241i	0.0272514	−	0.0596723i	−0.895517	−	0.445028i	$-0.853194\pi$
$31$	0.151729	−	0.332241i	0.0272514	−	0.0596723i	0.922768	+	0.385355i	$0.125921\pi$
$32$		0			0
$33$	−2.65804	+	1.70822i	−0.462705	+	0.297362i
$34$		0			0
$35$	−1.18911	−	8.27041i	−0.200996	−	1.39795i
$36$		0			0
$37$	−4.54638	+	5.24681i	−0.747421	+	0.862570i	−0.994316	−	0.106473i	$-0.966044\pi$
$37$	−4.54638	+	5.24681i	−0.747421	+	0.862570i	0.246895	+	0.969042i	$0.420590\pi$
$38$		0			0
$39$	−0.778312	−	0.500191i	−0.124630	−	0.0800946i
$40$		0			0
$41$	4.45994	+	5.14705i	0.696526	+	0.803834i	0.988279	−	0.152660i	$-0.0487840\pi$
$41$	4.45994	+	5.14705i	0.696526	+	0.803834i	−0.291753	+	0.956494i	$0.594239\pi$
$42$		0			0
$43$	−3.30753	−	7.24249i	−0.504394	−	1.10447i	−0.975016	−	0.222134i	$-0.928698\pi$
$43$	−3.30753	−	7.24249i	−0.504394	−	1.10447i	0.470622	−	0.882335i	$-0.344029\pi$
$44$		0			0
$45$	3.60285			0.537081
$46$		0			0
$47$	0.649844			0.0947895			0.0473947	−	0.998876i	$-0.484908\pi$
$47$	0.649844			0.0947895			0.0473947	+	0.998876i	$0.484908\pi$
$48$		0			0
$49$	−0.673659	−	1.47511i	−0.0962370	−	0.210730i
$50$		0			0
$51$	1.65290	+	1.90755i	0.231452	+	0.267110i
$52$		0			0
$53$	4.44535	+	2.85685i	0.610615	+	0.392419i	0.809088	−	0.587688i	$-0.199962\pi$
$53$	4.44535	+	2.85685i	0.610615	+	0.392419i	−0.198472	+	0.980106i	$0.563598\pi$
$54$		0			0
$55$	−7.45467	+	8.60315i	−1.00519	+	1.16005i
$56$		0			0
$57$	0.630409	+	4.38459i	0.0834997	+	0.580753i
$58$		0			0
$59$	11.5867	−	7.44634i	1.50846	−	0.969431i	0.514768	−	0.857330i	$-0.327878\pi$
$59$	11.5867	−	7.44634i	1.50846	−	0.969431i	0.993697	−	0.112102i	$-0.0357582\pi$
$60$		0			0
$61$	4.28731	−	9.38791i	0.548934	−	1.20200i	−0.408343	−	0.912828i	$-0.633893\pi$
$61$	4.28731	−	9.38791i	0.548934	−	1.20200i	0.957278	−	0.289170i	$-0.0933793\pi$
$62$		0			0
$63$	−2.22519	+	0.653373i	−0.280347	+	0.0823173i
$64$		0			0
$65$	−3.19826	−	0.939095i	−0.396696	−	0.116480i
$66$		0			0
$67$	0.809005	−	5.62675i	0.0988357	−	0.687417i	−0.878812	−	0.477168i	$-0.841663\pi$
$67$	0.809005	−	5.62675i	0.0988357	−	0.687417i	0.977648	−	0.210249i	$-0.0674275\pi$
$68$		0			0
$69$	−2.40813	+	4.14740i	−0.289905	+	0.499288i
$70$		0			0
$71$	0.930627	−	6.47265i	0.110445	−	0.768162i	−0.857043	−	0.515245i	$-0.827701\pi$
$71$	0.930627	−	6.47265i	0.110445	−	0.768162i	0.967488	−	0.252917i	$-0.0813900\pi$
$72$		0			0
$73$	6.41603	+	1.88392i	0.750939	+	0.220496i	0.634735	−	0.772730i	$-0.281109\pi$
$73$	6.41603	+	1.88392i	0.750939	+	0.220496i	0.116204	+	0.993225i	$0.462927\pi$
$74$		0			0
$75$	7.65724	−	2.24837i	0.884182	−	0.259619i
$76$		0			0
$77$	3.04397	−	6.66537i	0.346893	−	0.759589i
$78$		0			0
$79$	−0.637245	+	0.409532i	−0.0716956	+	0.0460760i	−0.575998	−	0.817451i	$-0.695386\pi$
$79$	−0.637245	+	0.409532i	−0.0716956	+	0.0460760i	0.504302	+	0.863527i	$0.331750\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	5.06491	−	5.84522i	0.555946	−	0.641596i	−0.406312	−	0.913734i	$-0.633185\pi$
$83$	5.06491	−	5.84522i	0.555946	−	0.641596i	0.962258	+	0.272138i	$0.0877309\pi$
$84$		0			0
$85$	7.65015	+	4.91645i	0.829775	+	0.533264i
$86$		0			0
$87$	6.59752	+	7.61394i	0.707328	+	0.816300i
$88$		0			0
$89$	−6.23218	−	13.6466i	−0.660609	−	1.44653i	−0.881953	−	0.471337i	$-0.843772\pi$
$89$	−6.23218	−	13.6466i	−0.660609	−	1.44653i	0.221344	−	0.975196i	$-0.428956\pi$
$90$		0			0
$91$	2.14561			0.224921
$92$		0			0
$93$	−0.365248			−0.0378744
$94$		0			0
$95$	6.62980	+	14.5172i	0.680203	+	1.48944i
$96$		0			0
$97$	−1.28908	−	1.48768i	−0.130887	−	0.151051i	0.686523	−	0.727108i	$-0.259136\pi$
$97$	−1.28908	−	1.48768i	−0.130887	−	0.151051i	−0.817410	+	0.576057i	$0.804591\pi$
$98$		0			0
$99$	2.65804	+	1.70822i	0.267143	+	0.171682i
$100$		0			0
$101$	−12.7755	+	14.7437i	−1.27121	+	1.46706i	−0.453687	+	0.891161i	$0.649892\pi$
$101$	−12.7755	+	14.7437i	−1.27121	+	1.46706i	−0.817524	+	0.575895i	$0.804654\pi$
$102$		0			0
$103$	2.12270	+	14.7637i	0.209156	+	1.45471i	0.775921	+	0.630830i	$0.217286\pi$
$103$	2.12270	+	14.7637i	0.209156	+	1.45471i	−0.566765	+	0.823879i	$0.691805\pi$
$104$		0			0
$105$	−7.02906	+	4.51730i	−0.685966	+	0.440843i
$106$		0			0
$107$	−2.36917	+	5.18776i	−0.229036	+	0.501519i	−0.988904	−	0.148559i	$-0.952537\pi$
$107$	−2.36917	+	5.18776i	−0.229036	+	0.501519i	0.759867	+	0.650078i	$0.225264\pi$
$108$		0			0
$109$	1.55295	−	0.455988i	0.148746	−	0.0436757i	−0.206512	−	0.978444i	$-0.566211\pi$
$109$	1.55295	−	0.455988i	0.148746	−	0.0436757i	0.355258	+	0.934768i	$0.384393\pi$
$110$		0			0
$111$	6.66130	+	1.95593i	0.632262	+	0.185649i
$112$		0			0
$113$	2.17966	−	15.1599i	0.205046	−	1.42612i	−0.583983	−	0.811766i	$-0.698506\pi$
$113$	2.17966	−	15.1599i	0.205046	−	1.42612i	0.789028	−	0.614357i	$-0.210584\pi$
$114$		0			0
$115$	−4.11490	+	16.7815i	−0.383716	+	1.56488i
$116$		0			0
$117$	−0.131667	+	0.915764i	−0.0121726	+	0.0846624i
$118$		0			0
$119$	−5.61647	−	1.64914i	−0.514861	−	0.151177i
$120$		0			0
$121$	0.975656	−	0.286478i	0.0886960	−	0.0260435i
$122$		0			0
$123$	2.82919	−	6.19507i	0.255100	−	0.558590i
$124$		0			0
$125$	9.03364	−	5.80557i	0.807993	−	0.519266i
$126$		0			0
$127$	−2.98754	−	20.7788i	−0.265101	−	1.84382i	−0.492869	−	0.870104i	$-0.664052\pi$
$127$	−2.98754	−	20.7788i	−0.265101	−	1.84382i	0.227768	−	0.973716i	$-0.426857\pi$
$128$		0			0
$129$	−5.21400	+	6.01727i	−0.459067	+	0.529791i
$130$		0			0
$131$	3.96527	+	2.54832i	0.346447	+	0.222648i	0.702279	−	0.711902i	$-0.252166\pi$
$131$	3.96527	+	2.54832i	0.346447	+	0.222648i	−0.355832	+	0.934550i	$0.615802\pi$
$132$		0			0
$133$	−6.72737	−	7.76380i	−0.583337	−	0.673207i
$134$		0			0
$135$	−1.49668	−	3.27726i	−0.128813	−	0.282062i
$136$		0			0
$137$	7.52633			0.643017			0.321509	−	0.946907i	$-0.395810\pi$
$137$	7.52633			0.643017			0.321509	+	0.946907i	$0.395810\pi$
$138$		0			0
$139$	10.4173			0.883587			0.441794	−	0.897117i	$-0.354342\pi$
$139$	10.4173			0.883587			0.441794	+	0.897117i	$0.354342\pi$
$140$		0			0
$141$	−0.269955	−	0.591119i	−0.0227343	−	0.0497812i
$142$		0			0
$143$	−1.91430	−	2.20922i	−0.160082	−	0.184744i
$144$		0			0
$145$	30.5354	+	19.6239i	2.53583	+	1.62968i
$146$		0			0
$147$	−1.06196	+	1.22556i	−0.0875887	+	0.101083i
$148$		0			0
$149$	−0.240065	−	1.66969i	−0.0196669	−	0.136786i	0.977622	−	0.210368i	$-0.0674662\pi$
$149$	−0.240065	−	1.66969i	−0.0196669	−	0.136786i	−0.997289	+	0.0735816i	$0.976557\pi$
$150$		0			0
$151$	−1.57531	+	1.01239i	−0.128197	+	0.0823872i	−0.603168	−	0.797614i	$-0.706095\pi$
$151$	−1.57531	+	1.01239i	−0.128197	+	0.0823872i	0.474971	+	0.880002i	$0.342459\pi$
$152$		0			0
$153$	1.04853	−	2.29595i	0.0847683	−	0.185617i
$154$		0			0
$155$	−1.26263	+	0.370741i	−0.101417	+	0.0297786i
$156$		0			0
$157$	10.8175	+	3.17629i	0.863328	+	0.253496i	0.683275	−	0.730161i	$-0.260555\pi$
$157$	10.8175	+	3.17629i	0.863328	+	0.253496i	0.180053	+	0.983657i	$0.442373\pi$
$158$		0			0
$159$	0.752019	−	5.23041i	0.0596390	−	0.414798i
$160$		0			0
$161$	−0.501876	−	11.1108i	−0.0395534	−	0.875655i
$162$		0			0
$163$	1.74485	−	12.1357i	0.136668	−	0.950543i	−0.799919	−	0.600108i	$-0.795124\pi$
$163$	1.74485	−	12.1357i	0.136668	−	0.950543i	0.936587	−	0.350436i	$-0.113967\pi$
$164$		0			0
$165$	10.9225	+	3.20713i	0.850314	+	0.249675i
$166$		0			0
$167$	5.46427	−	1.60445i	0.422838	−	0.124156i	−0.0633893	−	0.997989i	$-0.520191\pi$
$167$	5.46427	−	1.60445i	0.422838	−	0.124156i	0.486227	+	0.873832i	$0.338373\pi$
$168$		0			0
$169$	−5.04482	+	11.0466i	−0.388063	+	0.849739i
$170$		0			0
$171$	3.72648	−	2.39486i	0.284971	−	0.183140i
$172$		0			0
$173$	−1.82675	−	12.7053i	−0.138885	−	0.965969i	−0.933429	−	0.358762i	$-0.883199\pi$
$173$	−1.82675	−	12.7053i	−0.138885	−	0.965969i	0.794544	−	0.607207i	$-0.207710\pi$
$174$		0			0
$175$	−12.1200	+	13.9873i	−0.916188	+	1.05734i
$176$		0			0
$177$	−11.5867	−	7.44634i	−0.870912	−	0.559701i
$178$		0			0
$179$	13.6590	+	15.7634i	1.02092	+	1.17821i	0.983868	+	0.178895i	$0.0572524\pi$
$179$	13.6590	+	15.7634i	1.02092	+	1.17821i	0.0370556	+	0.999313i	$0.488202\pi$
$180$		0			0
$181$	5.03591	+	11.0271i	0.374316	+	0.819638i	0.999241	+	0.0389533i	$0.0124024\pi$
$181$	5.03591	+	11.0271i	0.374316	+	0.819638i	−0.624925	+	0.780685i	$0.714870\pi$
$182$		0			0
$183$	−10.3206			−0.762918
$184$		0			0
$185$	25.0128			1.83898
$186$		0			0
$187$	3.31294	+	7.25432i	0.242266	+	0.530488i
$188$		0			0
$189$	1.51870	+	1.75268i	0.110470	+	0.127489i
$190$		0			0
$191$	−15.2906	−	9.82665i	−1.10639	−	0.711031i	−0.145883	−	0.989302i	$-0.546602\pi$
$191$	−15.2906	−	9.82665i	−1.10639	−	0.711031i	−0.960503	+	0.278271i	$0.910239\pi$
$192$		0			0
$193$	7.62762	−	8.80275i	0.549048	−	0.633636i	−0.411613	−	0.911359i	$-0.635034\pi$
$193$	7.62762	−	8.80275i	0.549048	−	0.633636i	0.960661	+	0.277723i	$0.0895798\pi$
$194$		0			0
$195$	0.474376	+	3.29936i	0.0339708	+	0.236272i
$196$		0			0
$197$	−17.8475	+	11.4699i	−1.27158	+	0.817198i	−0.989825	−	0.142287i	$-0.954554\pi$
$197$	−17.8475	+	11.4699i	−1.27158	+	0.817198i	−0.281759	+	0.959485i	$0.590918\pi$
$198$		0			0
$199$	0.864646	−	1.89331i	0.0612931	−	0.134213i	−0.876507	−	0.481390i	$-0.840132\pi$
$199$	0.864646	−	1.89331i	0.0612931	−	0.134213i	0.937800	+	0.347176i	$0.112859\pi$
$200$		0			0
$201$	−5.45435	+	1.60154i	−0.384720	+	0.112964i
$202$		0			0
$203$	−22.4180	−	6.58253i	−1.57344	−	0.462003i
$204$		0			0
$205$	3.49202	−	24.2875i	0.243893	−	1.69631i
$206$		0			0
$207$	4.77298	+	0.467618i	0.331745	+	0.0325017i
$208$		0			0
$209$	−1.99185	+	13.8536i	−0.137779	+	0.958274i
$210$		0			0
$211$	5.23622	+	1.53749i	0.360476	+	0.105845i	0.456955	−	0.889490i	$-0.348940\pi$
$211$	5.23622	+	1.53749i	0.360476	+	0.105845i	−0.0964791	+	0.995335i	$0.530758\pi$
$212$		0			0
$213$	−6.27433	+	1.84231i	−0.429910	+	0.126233i
$214$		0			0
$215$	−11.9165	+	26.0936i	−0.812701	+	1.77957i
$216$		0			0
$217$	0.712589	−	0.457953i	0.0483737	−	0.0310879i
$218$		0			0
$219$	−0.951644	−	6.61883i	−0.0643062	−	0.447259i
$220$		0			0
$221$	−1.52923	+	1.76483i	−0.102867	+	0.118715i
$222$		0			0
$223$	−14.2625	−	9.16593i	−0.955085	−	0.613796i	−0.0324514	−	0.999473i	$-0.510331\pi$
$223$	−14.2625	−	9.16593i	−0.955085	−	0.613796i	−0.922634	+	0.385677i	$0.873968\pi$
$224$		0			0
$225$	−5.22612	−	6.03126i	−0.348408	−	0.402084i
$226$		0			0
$227$	0.563241	+	1.23333i	0.0373836	+	0.0818587i	0.927403	−	0.374065i	$-0.122036\pi$
$227$	0.563241	+	1.23333i	0.0373836	+	0.0818587i	−0.890019	+	0.455924i	$0.849309\pi$
$228$		0			0
$229$	−11.8996			−0.786350			−0.393175	−	0.919464i	$-0.628623\pi$
$229$	−11.8996			−0.786350			−0.393175	+	0.919464i	$0.628623\pi$
$230$		0			0
$231$	−7.32754			−0.482117
$232$		0			0
$233$	0.377580	+	0.826784i	0.0247361	+	0.0541644i	0.921597	−	0.388149i	$-0.126885\pi$
$233$	0.377580	+	0.826784i	0.0247361	+	0.0541644i	−0.896861	+	0.442313i	$0.854158\pi$
$234$		0			0
$235$	−1.53322	−	1.76943i	−0.100016	−	0.115425i
$236$		0			0
$237$	0.637245	+	0.409532i	0.0413935	+	0.0266020i
$238$		0			0
$239$	−10.7299	+	12.3830i	−0.694063	+	0.800991i	−0.987938	−	0.154853i	$-0.950510\pi$
$239$	−10.7299	+	12.3830i	−0.694063	+	0.800991i	0.293875	+	0.955844i	$0.405055\pi$
$240$		0			0
$241$	−2.47303	−	17.2003i	−0.159302	−	1.10797i	−0.899924	−	0.436046i	$-0.856378\pi$
$241$	−2.47303	−	17.2003i	−0.159302	−	1.10797i	0.740623	−	0.671921i	$-0.234531\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	−2.42709	+	5.31459i	−0.155061	+	0.339536i
$246$		0			0
$247$	−3.93225	+	1.15461i	−0.250203	+	0.0734662i
$248$		0			0
$249$	−7.42104	−	2.17901i	−0.470289	−	0.138089i
$250$		0			0
$251$	0.238973	−	1.66210i	0.0150839	−	0.104911i	−0.980889	−	0.194570i	$-0.937669\pi$
$251$	0.238973	−	1.66210i	0.0150839	−	0.104911i	0.995972	+	0.0896595i	$0.0285779\pi$
$252$		0			0
$253$	−10.9924	+	10.4297i	−0.691087	+	0.655712i
$254$		0			0
$255$	1.29418	−	9.00119i	0.0810444	−	0.563676i
$256$		0			0
$257$	−15.2072	−	4.46523i	−0.948598	−	0.278534i	−0.229395	−	0.973333i	$-0.573675\pi$
$257$	−15.2072	−	4.46523i	−0.948598	−	0.278534i	−0.719203	+	0.694800i	$0.755493\pi$
$258$		0			0
$259$	−15.4484	+	4.53606i	−0.959916	+	0.281857i
$260$		0			0
$261$	4.18518	−	9.16426i	0.259056	−	0.567253i
$262$		0			0
$263$	17.9557	−	11.5394i	1.10720	−	0.711551i	0.146515	−	0.989208i	$-0.453194\pi$
$263$	17.9557	−	11.5394i	1.10720	−	0.711551i	0.960680	+	0.277657i	$0.0895580\pi$
$264$		0			0
$265$	−2.70941	−	18.8444i	−0.166438	−	1.15760i
$266$		0			0
$267$	−9.82441	+	11.3380i	−0.601244	+	0.693873i
$268$		0			0
$269$	14.4164	+	9.26488i	0.878985	+	0.564890i	0.900489	−	0.434879i	$-0.143209\pi$
$269$	14.4164	+	9.26488i	0.878985	+	0.564890i	−0.0215034	+	0.999769i	$0.506845\pi$
$270$		0			0
$271$	12.1783	+	14.0545i	0.739779	+	0.853750i	0.993536	−	0.113518i	$-0.0362119\pi$
$271$	12.1783	+	14.0545i	0.739779	+	0.853750i	−0.253757	+	0.967268i	$0.581666\pi$
$272$		0			0
$273$	−0.891319	−	1.95172i	−0.0539451	−	0.118123i
$274$		0			0
$275$	25.2153			1.52054
$276$		0			0
$277$	−12.5575			−0.754508			−0.377254	−	0.926110i	$-0.623132\pi$
$277$	−12.5575			−0.754508			−0.377254	+	0.926110i	$0.623132\pi$
$278$		0			0
$279$	0.151729	+	0.332241i	0.00908380	+	0.0198908i
$280$		0			0
$281$	−3.03728	−	3.50520i	−0.181189	−	0.209103i	0.657888	−	0.753115i	$-0.271450\pi$
$281$	−3.03728	−	3.50520i	−0.181189	−	0.209103i	−0.839077	+	0.544012i	$0.816904\pi$
$282$		0			0
$283$	−20.5957	−	13.2361i	−1.22429	−	0.786803i	−0.241298	−	0.970451i	$-0.577573\pi$
$283$	−20.5957	−	13.2361i	−1.22429	−	0.786803i	−0.982992	+	0.183648i	$0.941209\pi$
$284$		0			0
$285$	10.4512	−	12.0613i	0.619077	−	0.714453i
$286$		0			0
$287$	2.24778	+	15.6337i	0.132683	+	0.922827i
$288$		0			0
$289$	−8.94185	+	5.74658i	−0.525991	+	0.338034i
$290$		0			0
$291$	−0.817739	+	1.79060i	−0.0479367	+	0.104967i
$292$		0			0
$293$	23.7738	−	6.98061i	1.38888	−	0.407812i	0.500029	−	0.866009i	$-0.333323\pi$
$293$	23.7738	−	6.98061i	1.38888	−	0.407812i	0.888851	+	0.458197i	$0.151505\pi$
$294$		0			0
$295$	−47.6126	−	13.9803i	−2.77211	−	0.813966i
$296$		0			0
$297$	0.449660	−	3.12745i	0.0260919	−	0.181473i
$298$		0			0
$299$	−4.11511	−	1.65920i	−0.237983	−	0.0959541i
$300$		0			0
$301$	2.62783	−	18.2769i	0.151465	−	1.05346i
$302$		0			0
$303$	18.7185	+	5.49625i	1.07535	+	0.315751i
$304$		0			0
$305$	−35.6772	+	10.4758i	−2.04287	+	0.599841i
$306$		0			0
$307$	3.70711	−	8.11744i	0.211576	−	0.463287i	−0.773855	−	0.633363i	$-0.781674\pi$
$307$	3.70711	−	8.11744i	0.211576	−	0.463287i	0.985431	+	0.170076i	$0.0544014\pi$
$308$		0			0
$309$	12.5477	−	8.06393i	0.713815	−	0.458741i
$310$		0			0
$311$	2.16255	+	15.0409i	0.122627	+	0.852889i	0.954561	+	0.298015i	$0.0963245\pi$
$311$	2.16255	+	15.0409i	0.122627	+	0.852889i	−0.831934	+	0.554874i	$0.812766\pi$
$312$		0			0
$313$	10.7084	−	12.3582i	0.605276	−	0.698526i	−0.367566	−	0.929998i	$-0.619809\pi$
$313$	10.7084	−	12.3582i	0.605276	−	0.698526i	0.972842	+	0.231472i	$0.0743541\pi$
$314$		0			0
$315$	7.02906	+	4.51730i	0.396043	+	0.254521i
$316$		0			0
$317$	−0.641103	−	0.739873i	−0.0360080	−	0.0415554i	0.737460	−	0.675391i	$-0.236025\pi$
$317$	−0.641103	−	0.739873i	−0.0360080	−	0.0415554i	−0.773468	+	0.633835i	$0.781480\pi$
$318$		0			0
$319$	13.2235	+	28.9555i	0.740376	+	1.62120i
$320$		0			0
$321$	5.70314			0.318318
$322$		0			0
$323$	11.1807			0.622111
$324$		0			0
$325$	3.06718	+	6.71619i	0.170137	+	0.372547i
$326$		0			0
$327$	−1.05990	−	1.22319i	−0.0586126	−	0.0676425i
$328$		0			0
$329$	1.26783	+	0.814784i	0.0698976	+	0.0449205i
$330$		0			0
$331$	13.4773	−	15.5537i	0.740782	−	0.854908i	−0.252859	−	0.967503i	$-0.581371\pi$
$331$	13.4773	−	15.5537i	0.740782	−	0.854908i	0.993641	+	0.112595i	$0.0359164\pi$
$332$		0			0
$333$	−0.988024	−	6.87185i	−0.0541434	−	0.376575i
$334$		0			0
$335$	−17.2295	+	11.0728i	−0.941350	+	0.604969i
$336$		0			0
$337$	13.3055	−	29.1350i	0.724797	−	1.58708i	−0.0822612	−	0.996611i	$-0.526214\pi$
$337$	13.3055	−	29.1350i	0.724797	−	1.58708i	0.807058	−	0.590472i	$-0.201059\pi$
$338$		0			0
$339$	−14.6954	+	4.31496i	−0.798144	+	0.234356i
$340$		0			0
$341$	−1.10729	−	0.325131i	−0.0599634	−	0.0176068i
$342$		0			0
$343$	2.84554	−	19.7912i	0.153645	−	1.06862i
$344$		0			0
$345$	16.9744	−	3.22825i	0.913871	−	0.173803i
$346$		0			0
$347$	4.80157	−	33.3956i	0.257762	−	1.79277i	−0.290928	−	0.956745i	$-0.593964\pi$
$347$	4.80157	−	33.3956i	0.257762	−	1.79277i	0.548690	−	0.836026i	$-0.315127\pi$
$348$		0			0
$349$	−7.92211	−	2.32614i	−0.424061	−	0.124515i	0.0627372	−	0.998030i	$-0.480017\pi$
$349$	−7.92211	−	2.32614i	−0.424061	−	0.124515i	−0.486798	+	0.873515i	$0.661835\pi$
$350$		0			0
$351$	0.887705	−	0.260654i	0.0473822	−	0.0139127i
$352$		0			0
$353$	−12.0828	+	26.4577i	−0.643103	+	1.40820i	0.254359	+	0.967110i	$0.418135\pi$
$353$	−12.0828	+	26.4577i	−0.643103	+	1.40820i	−0.897463	+	0.441090i	$0.854592\pi$
$354$		0			0
$355$	−19.8197	+	12.7374i	−1.05192	+	0.676030i
$356$		0			0
$357$	0.833051	+	5.79400i	0.0440897	+	0.306651i
$358$		0			0
$359$	15.3266	−	17.6878i	0.808907	−	0.933528i	−0.189928	−	0.981798i	$-0.560825\pi$
$359$	15.3266	−	17.6878i	0.808907	−	0.933528i	0.998834	+	0.0482699i	$0.0153708\pi$
$360$		0			0
$361$	0.523296	+	0.336302i	0.0275419	+	0.0177001i
$362$		0			0
$363$	−0.665892	−	0.768480i	−0.0349503	−	0.0403348i
$364$		0			0
$365$	−10.0081	−	21.9147i	−0.523849	−	1.14707i
$366$		0			0
$367$	13.8374			0.722308			0.361154	−	0.932506i	$-0.382383\pi$
$367$	13.8374			0.722308			0.361154	+	0.932506i	$0.382383\pi$
$368$		0			0
$369$	−6.81052			−0.354541
$370$		0			0
$371$	5.09079	+	11.1473i	0.264301	+	0.578738i
$372$		0			0
$373$	−20.4371	−	23.5857i	−1.05819	−	1.22122i	−0.974420	−	0.224736i	$-0.927848\pi$
$373$	−20.4371	−	23.5857i	−1.05819	−	1.22122i	−0.0837746	−	0.996485i	$-0.526698\pi$
$374$		0			0
$375$	−9.03364	−	5.80557i	−0.466495	−	0.299798i
$376$		0			0
$377$	−6.10390	+	7.04427i	−0.314367	+	0.362799i
$378$		0			0
$379$	4.21387	+	29.3081i	0.216452	+	1.50546i	0.750990	+	0.660313i	$0.229576\pi$
$379$	4.21387	+	29.3081i	0.216452	+	1.50546i	−0.534538	+	0.845144i	$0.679514\pi$
$380$		0			0
$381$	−17.6600	+	11.3494i	−0.904748	+	0.581446i
$382$		0			0
$383$	−8.57054	+	18.7669i	−0.437934	+	0.958942i	0.554039	+	0.832491i	$0.313086\pi$
$383$	−8.57054	+	18.7669i	−0.437934	+	0.958942i	−0.991973	+	0.126451i	$0.959641\pi$
$384$		0			0
$385$	−25.3306	+	7.43774i	−1.29097	+	0.379062i
$386$		0			0
$387$	7.63948	+	2.24315i	0.388337	+	0.114026i
$388$		0			0
$389$	−4.44340	+	30.9045i	−0.225289	+	1.56692i	0.492281	+	0.870436i	$0.336163\pi$
$389$	−4.44340	+	30.9045i	−0.225289	+	1.56692i	−0.717571	+	0.696486i	$0.754746\pi$
$390$		0			0
$391$	9.49665	+	7.50614i	0.480266	+	0.379602i
$392$		0			0
$393$	0.670805	−	4.66555i	0.0338376	−	0.235346i
$394$		0			0
$395$	2.61859	+	0.768886i	0.131755	+	0.0386869i
$396$		0			0
$397$	−1.05521	+	0.309838i	−0.0529596	+	0.0155503i	−0.308105	−	0.951352i	$-0.599695\pi$
$397$	−1.05521	+	0.309838i	−0.0529596	+	0.0155503i	0.255145	+	0.966903i	$0.417877\pi$
$398$		0			0
$399$	−4.26755	+	9.34463i	−0.213645	+	0.467817i
$400$		0			0
$401$	−10.7778	+	6.92645i	−0.538216	+	0.345890i	−0.781341	−	0.624105i	$-0.785464\pi$
$401$	−10.7778	+	6.92645i	−0.538216	+	0.345890i	0.243125	+	0.969995i	$0.421828\pi$
$402$		0			0
$403$	−0.0480911	−	0.334481i	−0.00239559	−	0.0166617i
$404$		0			0
$405$	−2.35936	+	2.72285i	−0.117238	+	0.135300i
$406$		0			0
$407$	18.4535	+	11.8593i	0.914704	+	0.587845i
$408$		0			0
$409$	9.62306	+	11.1056i	0.475830	+	0.549137i	0.942024	−	0.335546i	$-0.108921\pi$
$409$	9.62306	+	11.1056i	0.475830	+	0.549137i	−0.466194	+	0.884682i	$0.654375\pi$
$410$		0			0
$411$	−3.12655	−	6.84619i	−0.154221	−	0.337698i
$412$		0			0
$413$	31.9417			1.57175
$414$		0			0
$415$	−27.8656			−1.36787
$416$		0			0
$417$	−4.32752	−	9.47595i	−0.211920	−	0.464039i
$418$		0			0
$419$	5.75218	+	6.63837i	0.281012	+	0.324306i	0.878655	−	0.477457i	$-0.158441\pi$
$419$	5.75218	+	6.63837i	0.281012	+	0.324306i	−0.597643	+	0.801762i	$0.703896\pi$
$420$		0			0
$421$	−13.8674	−	8.91201i	−0.675854	−	0.434345i	0.157178	−	0.987570i	$-0.449760\pi$
$421$	−13.8674	−	8.91201i	−0.675854	−	0.434345i	−0.833032	+	0.553225i	$0.813397\pi$
$422$		0			0
$423$	−0.425557	+	0.491119i	−0.0206913	+	0.0238790i
$424$		0			0
$425$	−2.86667	−	19.9381i	−0.139054	−	0.967141i
$426$		0			0
$427$	20.1351	−	12.9401i	0.974407	−	0.626214i
$428$		0			0
$429$	−1.21435	+	2.65905i	−0.0586292	+	0.128380i
$430$		0			0
$431$	−20.3709	+	5.98142i	−0.981230	+	0.288115i	−0.732732	−	0.680517i	$-0.761755\pi$
$431$	−20.3709	+	5.98142i	−0.981230	+	0.288115i	−0.248498	+	0.968632i	$0.579937\pi$
$432$		0			0
$433$	31.5088	+	9.25181i	1.51421	+	0.444613i	0.930176	−	0.367113i	$-0.119654\pi$
$433$	31.5088	+	9.25181i	1.51421	+	0.444613i	0.584038	+	0.811726i	$0.301472\pi$
$434$		0			0
$435$	5.16568	−	35.9281i	0.247675	−	1.72262i
$436$		0			0
$437$	6.89881	+	20.0926i	0.330015	+	0.961160i
$438$		0			0
$439$	−0.760766	+	5.29125i	−0.0363094	+	0.252537i	−0.999889	−	0.0148834i	$-0.995262\pi$
$439$	−0.760766	+	5.29125i	−0.0363094	+	0.252537i	0.963580	+	0.267421i	$0.0861714\pi$
$440$		0			0
$441$	1.55596	+	0.456872i	0.0740935	+	0.0217558i
$442$		0			0
$443$	−25.0124	+	7.34431i	−1.18838	+	0.348939i	−0.815398	−	0.578901i	$-0.803482\pi$
$443$	−25.0124	+	7.34431i	−1.18838	+	0.348939i	−0.372978	+	0.927840i	$0.621663\pi$
$444$		0			0
$445$	−22.4536	+	49.1665i	−1.06440	+	2.33071i
$446$		0			0
$447$	−1.41908	+	0.911985i	−0.0671200	+	0.0431354i
$448$		0			0
$449$	2.00529	+	13.9471i	0.0946357	+	0.658206i	0.980826	+	0.194885i	$0.0624333\pi$
$449$	2.00529	+	13.9471i	0.0946357	+	0.658206i	−0.886190	+	0.463321i	$0.846658\pi$
$450$		0			0
$451$	14.0917	−	16.2627i	0.663552	−	0.765779i
$452$		0			0
$453$	1.57531	+	1.01239i	0.0740146	+	0.0475663i
$454$		0			0
$455$	−5.06228	−	5.84218i	−0.237323	−	0.273886i
$456$		0			0
$457$	9.12420	+	19.9792i	0.426812	+	0.934588i	0.993833	+	0.110885i	$0.0353685\pi$
$457$	9.12420	+	19.9792i	0.426812	+	0.934588i	−0.567021	+	0.823703i	$0.691904\pi$
$458$		0			0
$459$	−2.52404			−0.117812
$460$		0			0
$461$	37.2157			1.73331			0.866654	−	0.498910i	$-0.166266\pi$
$461$	37.2157			1.73331			0.866654	+	0.498910i	$0.166266\pi$
$462$		0			0
$463$	−0.828379	−	1.81390i	−0.0384981	−	0.0842990i	0.889406	−	0.457118i	$-0.151118\pi$
$463$	−0.828379	−	1.81390i	−0.0384981	−	0.0842990i	−0.927904	+	0.372819i	$0.878391\pi$
$464$		0			0
$465$	0.861752	+	0.994515i	0.0399628	+	0.0461195i
$466$		0			0
$467$	−20.4368	−	13.1339i	−0.945701	−	0.607765i	−0.0256949	−	0.999670i	$-0.508180\pi$
$467$	−20.4368	−	13.1339i	−0.945701	−	0.607765i	−0.920006	+	0.391905i	$0.871816\pi$
$468$		0			0
$469$	8.63325	−	9.96330i	0.398646	−	0.460062i
$470$		0			0
$471$	−1.60448	−	11.1594i	−0.0739305	−	0.514198i
$472$		0			0
$473$	−21.1633	+	13.6008i	−0.973088	+	0.625366i
$474$		0			0
$475$	14.6854	−	32.1565i	0.673811	−	1.47544i
$476$		0			0
$477$	−5.07015	+	1.48873i	−0.232146	+	0.0681643i
$478$		0			0
$479$	27.8805	+	8.18645i	1.27389	+	0.374048i	0.847647	−	0.530560i	$-0.178018\pi$
$479$	27.8805	+	8.18645i	1.27389	+	0.374048i	0.426244	+	0.904608i	$0.359836\pi$
$480$		0			0
$481$	−0.914101	+	6.35771i	−0.0416794	+	0.289887i
$482$		0			0
$483$	−9.89826	+	5.07212i	−0.450387	+	0.230789i
$484$		0			0
$485$	−1.00932	+	7.01997i	−0.0458308	+	0.318760i
$486$		0			0
$487$	33.3108	+	9.78095i	1.50946	+	0.443217i	0.928692	−	0.370853i	$-0.120935\pi$
$487$	33.3108	+	9.78095i	1.50946	+	0.443217i	0.580767	+	0.814070i	$0.302753\pi$
$488$		0			0
$489$	−11.7639	+	3.45419i	−0.531981	+	0.156204i
$490$		0			0
$491$	−15.8099	+	34.6187i	−0.713489	+	1.56232i	0.109322	+	0.994006i	$0.465132\pi$
$491$	−15.8099	+	34.6187i	−0.713489	+	1.56232i	−0.822811	+	0.568316i	$0.807595\pi$
$492$		0			0
$493$	21.3922	−	13.7479i	0.963456	−	0.619176i
$494$		0			0
$495$	−1.62006	−	11.2677i	−0.0728161	−	0.506447i
$496$		0			0
$497$	9.93113	−	11.4611i	0.445472	−	0.514102i
$498$		0			0
$499$	−4.35637	−	2.79967i	−0.195018	−	0.125330i	0.439488	−	0.898249i	$-0.355160\pi$
$499$	−4.35637	−	2.79967i	−0.195018	−	0.125330i	−0.634506	+	0.772918i	$0.718796\pi$
$500$		0			0
$501$	−3.72940	−	4.30396i	−0.166617	−	0.192287i
$502$		0			0
$503$	−11.2392	−	24.6105i	−0.501132	−	1.09733i	−0.976100	−	0.217323i	$-0.930267\pi$
$503$	−11.2392	−	24.6105i	−0.501132	−	1.09733i	0.474967	−	0.880003i	$-0.342460\pi$
$504$		0			0
$505$	70.2870			3.12773
$506$		0			0
$507$	12.1440			0.539336
$508$		0			0
$509$	16.2124	+	35.5003i	0.718604	+	1.57352i	0.815850	+	0.578263i	$0.196269\pi$
$509$	16.2124	+	35.5003i	0.718604	+	1.57352i	−0.0972465	+	0.995260i	$0.531004\pi$
$510$		0			0
$511$	10.1554	+	11.7200i	0.449249	+	0.518461i
$512$		0			0
$513$	−3.72648	−	2.39486i	−0.164528	−	0.105736i
$514$		0			0
$515$	35.1911	−	40.6127i	1.55070	−	1.78961i
$516$		0			0
$517$	−0.292209	−	2.03236i	−0.0128513	−	0.0893829i
$518$		0			0
$519$	−10.7983	+	6.93966i	−0.473994	+	0.304617i
$520$		0			0
$521$	13.8243	−	30.2710i	0.605655	−	1.32620i	−0.319852	−	0.947467i	$-0.603633\pi$
$521$	13.8243	−	30.2710i	0.605655	−	1.32620i	0.925507	−	0.378731i	$-0.123640\pi$
$522$		0			0
$523$	40.5200	−	11.8977i	1.77181	−	0.520252i	0.777705	−	0.628630i	$-0.216384\pi$
$523$	40.5200	−	11.8977i	1.77181	−	0.520252i	0.994110	+	0.108378i	$0.0345658\pi$
$524$		0			0
$525$	17.7581	+	5.21425i	0.775027	+	0.227569i
$526$		0			0
$527$	−0.131200	+	0.912518i	−0.00571518	+	0.0397499i
$528$		0			0
$529$	−7.62943	+	21.6977i	−0.331714	+	0.943380i
$530$		0			0
$531$	−1.96013	+	13.6330i	−0.0850623	+	0.591621i
$532$		0			0
$533$	6.04573	+	1.77519i	0.261870	+	0.0768919i
$534$		0			0
$535$	19.7152	−	5.78891i	0.852363	−	0.250276i
$536$		0			0
$537$	8.66469	−	18.9730i	0.373909	−	0.818746i
$538$		0			0
$539$	−4.31041	+	2.77013i	−0.185663	+	0.119318i
$540$		0			0
$541$	−2.96440	−	20.6179i	−0.127450	−	0.886431i	−0.948771	−	0.315965i	$-0.897672\pi$
$541$	−2.96440	−	20.6179i	−0.127450	−	0.886431i	0.821321	−	0.570466i	$-0.193237\pi$
$542$		0			0
$543$	7.93861	−	9.16165i	0.340679	−	0.393164i
$544$		0			0
$545$	−4.90556	−	3.15261i	−0.210131	−	0.135043i
$546$		0			0
$547$	−25.0431	−	28.9013i	−1.07077	−	1.23573i	−0.970584	−	0.240763i	$-0.922602\pi$
$547$	−25.0431	−	28.9013i	−1.07077	−	1.23573i	−0.100183	−	0.994969i	$-0.531943\pi$
$548$		0			0
$549$	4.28731	+	9.38791i	0.182978	+	0.400666i
$550$		0			0
$551$	44.6276			1.90120
$552$		0			0
$553$	−1.75672			−0.0747035
$554$		0			0
$555$	−10.3907	−	22.7525i	−0.441061	−	0.965789i
$556$		0			0
$557$	−17.1623	−	19.8063i	−0.727189	−	0.839220i	0.264963	−	0.964258i	$-0.414640\pi$
$557$	−17.1623	−	19.8063i	−0.727189	−	0.839220i	−0.992152	+	0.125038i	$0.960095\pi$
$558$		0			0
$559$	−6.19692	−	3.98252i	−0.262102	−	0.168442i
$560$		0			0
$561$	5.22252	−	6.02711i	0.220495	−	0.254465i
$562$		0			0
$563$	0.112532	+	0.782676i	0.00474265	+	0.0329859i	0.992055	−	0.125802i	$-0.0401504\pi$
$563$	0.112532	+	0.782676i	0.00474265	+	0.0329859i	−0.987313	+	0.158788i	$0.949241\pi$
$564$		0			0
$565$	−46.4207	+	29.8328i	−1.95293	+	1.25508i
$566$		0			0
$567$	0.963400	−	2.10955i	0.0404590	−	0.0885928i
$568$		0			0
$569$	−0.891075	+	0.261643i	−0.0373558	+	0.0109687i	−0.300357	−	0.953827i	$-0.597106\pi$
$569$	−0.891075	+	0.261643i	−0.0373558	+	0.0109687i	0.263001	+	0.964795i	$0.415288\pi$
$570$		0			0
$571$	−7.93998	−	2.33139i	−0.332278	−	0.0975655i	0.111338	−	0.993783i	$-0.464486\pi$
$571$	−7.93998	−	2.33139i	−0.332278	−	0.0975655i	−0.443616	+	0.896217i	$0.646305\pi$
$572$		0			0
$573$	−2.58670	+	17.9909i	−0.108061	+	0.751581i
$574$		0			0
$575$	34.0616	−	17.4540i	1.42047	−	0.727883i
$576$		0			0
$577$	−2.29790	+	15.9823i	−0.0956630	+	0.665351i	0.884410	+	0.466711i	$0.154561\pi$
$577$	−2.29790	+	15.9823i	−0.0956630	+	0.665351i	−0.980073	+	0.198639i	$0.936348\pi$
$578$		0			0
$579$	−11.1759	−	3.28154i	−0.464454	−	0.136376i
$580$		0			0
$581$	17.2103	−	5.05341i	0.714004	−	0.209651i
$582$		0			0
$583$	6.93577	−	15.1872i	0.287250	−	0.628991i
$584$		0			0
$585$	2.80414	−	1.80211i	0.115937	−	0.0745081i
$586$		0			0
$587$	−1.55857	−	10.8401i	−0.0643289	−	0.447418i	−0.996374	−	0.0850763i	$-0.972887\pi$
$587$	−1.55857	−	10.8401i	−0.0643289	−	0.447418i	0.932046	−	0.362341i	$-0.118022\pi$
$588$		0			0
$589$	−1.05952	+	1.22275i	−0.0436567	+	0.0503825i
$590$		0			0
$591$	17.8475	+	11.4699i	0.734150	+	0.471809i
$592$		0			0
$593$	27.1272	+	31.3064i	1.11398	+	1.28560i	0.954438	+	0.298410i	$0.0964562\pi$
$593$	27.1272	+	31.3064i	1.11398	+	1.28560i	0.159542	+	0.987191i	$0.448998\pi$
$594$		0			0
$595$	8.76092	+	19.1837i	0.359163	+	0.786456i
$596$		0			0
$597$	−2.08140			−0.0851862
$598$		0			0
$599$	−28.3244			−1.15731			−0.578653	−	0.815574i	$-0.696421\pi$
$599$	−28.3244			−1.15731			−0.578653	+	0.815574i	$0.696421\pi$
$600$		0			0
$601$	−5.49834	−	12.0397i	−0.224282	−	0.491109i	0.763721	−	0.645547i	$-0.223371\pi$
$601$	−5.49834	−	12.0397i	−0.224282	−	0.491109i	−0.988002	+	0.154438i	$0.950643\pi$
$602$		0			0
$603$	3.72263	+	4.29614i	0.151597	+	0.174952i
$604$		0			0
$605$	−3.08196	−	1.98066i	−0.125300	−	0.0805252i
$606$		0			0
$607$	−10.6163	+	12.2518i	−0.430901	+	0.497286i	−0.929127	−	0.369761i	$-0.879440\pi$
$607$	−10.6163	+	12.2518i	−0.430901	+	0.497286i	0.498226	+	0.867047i	$0.333985\pi$
$608$		0			0
$609$	3.32511	+	23.1267i	0.134740	+	0.937139i
$610$		0			0
$611$	0.505781	−	0.325046i	0.0204617	−	0.0131499i
$612$		0			0
$613$	−18.7006	+	40.9485i	−0.755308	+	1.65389i	0.00127684	+	0.999999i	$0.499594\pi$
$613$	−18.7006	+	40.9485i	−0.755308	+	1.65389i	−0.756585	+	0.653895i	$0.773134\pi$
$614$		0			0
$615$	−23.5433	+	6.91294i	−0.949358	+	0.278757i
$616$		0			0
$617$	−27.9202	−	8.19812i	−1.12403	−	0.330044i	−0.333669	−	0.942690i	$-0.608287\pi$
$617$	−27.9202	−	8.19812i	−1.12403	−	0.330044i	−0.790357	+	0.612646i	$0.790105\pi$
$618$		0			0
$619$	−0.280180	+	1.94869i	−0.0112614	+	0.0783247i	−0.994677	−	0.103041i	$-0.967143\pi$
$619$	−0.280180	+	1.94869i	−0.0112614	+	0.0783247i	0.983416	+	0.181366i	$0.0580518\pi$
$620$		0			0
$621$	−1.55741	−	4.53591i	−0.0624966	−	0.182020i
$622$		0			0
$623$	4.95145	−	34.4381i	0.198376	−	1.37973i
$624$		0			0
$625$	1.16488	+	0.342041i	0.0465953	+	0.0136816i
$626$		0			0
$627$	13.4291	−	3.94315i	0.536308	−	0.157474i
$628$		0			0
$629$	7.27941	−	15.9397i	0.290249	−	0.635557i
$630$		0			0
$631$	9.89787	−	6.36098i	0.394028	−	0.253227i	−0.328592	−	0.944472i	$-0.606574\pi$
$631$	9.89787	−	6.36098i	0.394028	−	0.253227i	0.722620	+	0.691245i	$0.242938\pi$
$632$		0			0
$633$	−0.776652	−	5.40173i	−0.0308691	−	0.214699i
$634$		0			0
$635$	−49.5288	+	57.1593i	−1.96549	+	2.26830i
$636$		0			0
$637$	−1.26215	−	0.811136i	−0.0500083	−	0.0321384i
$638$		0			0
$639$	4.28227	+	4.94201i	0.169404	+	0.195503i
$640$		0			0
$641$	8.56271	+	18.7497i	0.338207	+	0.740570i	0.999958	−	0.00915378i	$-0.00291378\pi$
$641$	8.56271	+	18.7497i	0.338207	+	0.740570i	−0.661751	+	0.749723i	$0.730187\pi$
$642$		0			0
$643$	37.8318			1.49194			0.745971	−	0.665979i	$-0.231986\pi$
$643$	37.8318			1.49194			0.745971	+	0.665979i	$0.231986\pi$
$644$		0			0
$645$	28.6858			1.12950
$646$		0			0
$647$	3.05084	+	6.68040i	0.119941	+	0.262634i	0.960074	−	0.279747i	$-0.0902505\pi$
$647$	3.05084	+	6.68040i	0.119941	+	0.262634i	−0.840133	+	0.542380i	$0.817523\pi$
$648$		0			0
$649$	−28.4982	−	32.8886i	−1.11865	−	1.29099i
$650$		0			0
$651$	−0.712589	−	0.457953i	−0.0279286	−	0.0179486i
$652$		0			0
$653$	17.6830	−	20.4073i	0.691991	−	0.798600i	−0.295657	−	0.955294i	$-0.595538\pi$
$653$	17.6830	−	20.4073i	0.691991	−	0.798600i	0.987647	+	0.156695i	$0.0500839\pi$
$654$		0			0
$655$	−2.41681	−	16.8093i	−0.0944324	−	0.656792i
$656$		0			0
$657$	−5.62537	+	3.61521i	−0.219467	+	0.141043i
$658$		0			0
$659$	−6.28141	+	13.7544i	−0.244689	+	0.535795i	−0.991632	−	0.129093i	$-0.958793\pi$
$659$	−6.28141	+	13.7544i	−0.244689	+	0.535795i	0.746943	+	0.664888i	$0.231521\pi$
$660$		0			0
$661$	−33.0329	+	9.69935i	−1.28483	+	0.377261i	−0.851681	−	0.524060i	$-0.824417\pi$
$661$	−33.0329	+	9.69935i	−1.28483	+	0.377261i	−0.433151	+	0.901321i	$0.642598\pi$
$662$		0			0
$663$	2.24061	+	0.657901i	0.0870179	+	0.0255508i
$664$		0			0
$665$	−5.26735	+	36.6353i	−0.204259	+	1.42065i
$666$		0			0
$667$	37.9057	+	29.9606i	1.46772	+	1.16008i
$668$		0			0
$669$	−2.41278	+	16.7813i	−0.0932835	+	0.648801i
$670$		0			0
$671$	−31.2881	−	9.18701i	−1.20786	−	0.354661i
$672$		0			0
$673$	−10.4104	+	3.05678i	−0.401293	+	0.117830i	−0.476150	−	0.879364i	$-0.657968\pi$
$673$	−10.4104	+	3.05678i	−0.401293	+	0.117830i	0.0748573	+	0.997194i	$0.476150\pi$
$674$		0			0
$675$	−3.31522	+	7.25932i	−0.127603	+	0.279411i
$676$		0			0
$677$	23.7422	−	15.2582i	0.912486	−	0.586419i	0.00201750	−	0.999998i	$-0.499358\pi$
$677$	23.7422	−	15.2582i	0.912486	−	0.586419i	0.910468	+	0.413579i	$0.135721\pi$
$678$		0			0
$679$	−0.649691	−	4.51870i	−0.0249329	−	0.173412i
$680$		0			0
$681$	0.887894	−	1.02468i	0.0340242	−	0.0392660i
$682$		0			0
$683$	7.96663	+	5.11984i	0.304835	+	0.195905i	0.684111	−	0.729378i	$-0.260191\pi$
$683$	7.96663	+	5.11984i	0.304835	+	0.195905i	−0.379276	+	0.925284i	$0.623827\pi$
$684$		0			0
$685$	−17.7573	−	20.4931i	−0.678473	−	0.782999i
$686$		0			0
$687$	4.94328	+	10.8243i	0.188598	+	0.412972i
$688$		0			0
$689$	4.88884			0.186250
$690$		0			0
$691$	−34.5913			−1.31591			−0.657957	−	0.753055i	$-0.728579\pi$
$691$	−34.5913			−1.31591			−0.657957	+	0.753055i	$0.728579\pi$
$692$		0			0
$693$	3.04397	+	6.66537i	0.115631	+	0.253196i
$694$		0			0
$695$	−24.5783	−	28.3649i	−0.932308	−	1.07594i
$696$		0			0
$697$	−14.4612	−	9.29364i	−0.547757	−	0.352022i
$698$		0			0
$699$	0.595217	−	0.686917i	0.0225132	−	0.0259816i
$700$		0			0
$701$	−2.58557	−	17.9830i	−0.0976555	−	0.679209i	−0.978567	−	0.205928i	$-0.933979\pi$
$701$	−2.58557	−	17.9830i	−0.0976555	−	0.679209i	0.880912	−	0.473281i	$-0.156930\pi$
$702$		0			0
$703$	25.8712	−	16.6264i	0.975750	−	0.627076i
$704$		0			0
$705$	−0.972606	+	2.12971i	−0.0366305	+	0.0802095i
$706$		0			0
$707$	−43.4106	+	12.7465i	−1.63262	+	0.479381i
$708$		0			0
$709$	−43.9054	−	12.8918i	−1.64890	−	0.484161i	−0.680332	−	0.732904i	$-0.738165\pi$
$709$	−43.9054	−	12.8918i	−1.64890	−	0.484161i	−0.968570	+	0.248742i	$0.919983\pi$
$710$		0			0
$711$	0.107803	−	0.749784i	0.00404292	−	0.0281191i
$712$		0			0
$713$	−1.72082	+	0.327272i	−0.0644453	+	0.0122564i
$714$		0			0
$715$	−1.49884	+	10.4247i	−0.0560536	+	0.389861i
$716$		0			0
$717$	15.7214	+	4.61621i	0.587125	+	0.172396i
$718$		0			0
$719$	3.31304	−	0.972796i	0.123556	−	0.0362792i	−0.219370	−	0.975642i	$-0.570400\pi$
$719$	3.31304	−	0.972796i	0.123556	−	0.0362792i	0.342926	+	0.939363i	$0.388582\pi$
$720$		0			0
$721$	−14.3696	+	31.4650i	−0.535152	+	1.17182i
$722$		0			0
$723$	−14.6186	+	9.39480i	−0.543671	+	0.349396i
$724$		0			0
$725$	−11.4423	−	79.5827i	−0.424955	−	2.95563i
$726$		0			0
$727$	−12.4777	+	14.4000i	−0.462772	+	0.534067i	−0.938387	−	0.345586i	$-0.887680\pi$
$727$	−12.4777	+	14.4000i	−0.462772	+	0.534067i	0.475615	+	0.879653i	$0.342225\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	13.1604	+	15.1879i	0.486754	+	0.561744i
$732$		0			0
$733$	15.7691	+	34.5295i	0.582445	+	1.27538i	0.939901	+	0.341447i	$0.110917\pi$
$733$	15.7691	+	34.5295i	0.582445	+	1.27538i	−0.357456	+	0.933930i	$0.616356\pi$
$734$		0			0
$735$	5.84257			0.215506
$736$		0			0
$737$	−17.9612			−0.661608
$738$		0			0
$739$	9.76651	+	21.3857i	0.359267	+	0.786685i	0.999824	+	0.0187741i	$0.00597634\pi$
$739$	9.76651	+	21.3857i	0.359267	+	0.786685i	−0.640557	+	0.767911i	$0.721296\pi$
$740$		0			0
$741$	2.68379	+	3.09725i	0.0985913	+	0.113780i
$742$		0			0
$743$	−7.96596	−	5.11941i	−0.292243	−	0.187813i	0.386301	−	0.922373i	$-0.373752\pi$
$743$	−7.96596	−	5.11941i	−0.292243	−	0.187813i	−0.678544	+	0.734560i	$0.737389\pi$
$744$		0			0
$745$	−3.97991	+	4.59306i	−0.145813	+	0.168277i
$746$		0			0
$747$	1.10071	+	7.65561i	0.0402729	+	0.280104i
$748$		0			0
$749$	−11.1267	+	7.15068i	−0.406560	+	0.261280i
$750$		0			0
$751$	15.0293	−	32.9096i	0.548427	−	1.20089i	−0.409085	−	0.912496i	$-0.634152\pi$
$751$	15.0293	−	32.9096i	0.548427	−	1.20089i	0.957512	−	0.288392i	$-0.0931207\pi$
$752$		0			0
$753$	−1.61117	+	0.473082i	−0.0587143	+	0.0172401i
$754$		0			0
$755$	6.47332	+	1.90074i	0.235588	+	0.0691750i
$756$		0			0
$757$	1.41383	−	9.83338i	0.0513864	−	0.357400i	−0.947864	−	0.318676i	$-0.896762\pi$
$757$	1.41383	−	9.83338i	0.0513864	−	0.357400i	0.999250	−	0.0387238i	$-0.0123293\pi$
$758$		0			0
$759$	14.0536	+	5.66639i	0.510115	+	0.205677i
$760$		0			0
$761$	1.86655	−	12.9821i	0.0676622	−	0.470601i	−0.927616	−	0.373536i	$-0.878145\pi$
$761$	1.86655	−	12.9821i	0.0676622	−	0.470601i	0.995278	−	0.0970654i	$-0.0309456\pi$
$762$		0			0
$763$	3.60149	+	1.05749i	0.130383	+	0.0382838i
$764$		0			0
$765$	−8.72539	+	2.56200i	−0.315467	+	0.0926295i
$766$		0			0
$767$	5.29350	−	11.5912i	0.191137	−	0.418532i
$768$		0			0
$769$	3.19706	−	2.05463i	0.115289	−	0.0740917i	−0.481726	−	0.876322i	$-0.659990\pi$
$769$	3.19706	−	2.05463i	0.115289	−	0.0740917i	0.597015	+	0.802230i	$0.296353\pi$
$770$		0			0
$771$	2.25557	+	15.6879i	0.0812325	+	0.564985i
$772$		0			0
$773$	1.32688	−	1.53131i	0.0477247	−	0.0550773i	−0.731385	−	0.681964i	$-0.761126\pi$
$773$	1.32688	−	1.53131i	0.0477247	−	0.0550773i	0.779110	+	0.626887i	$0.215671\pi$
$774$		0			0
$775$	2.45214	+	1.57589i	0.0880834	+	0.0566078i
$776$		0			0
$777$	10.5436	+	12.1680i	0.378251	+	0.436525i
$778$		0			0
$779$	−12.5324	−	27.4421i	−0.449020	−	0.983217i
$780$		0			0
$781$	−20.6614			−0.739322
$782$		0			0
$783$	−10.0747			−0.360040
$784$		0			0
$785$	−16.8738	−	36.9484i	−0.602250	−	1.31874i
$786$		0			0
$787$	−11.8425	−	13.6670i	−0.422141	−	0.487177i	0.504347	−	0.863501i	$-0.331733\pi$
$787$	−11.8425	−	13.6670i	−0.422141	−	0.487177i	−0.926488	+	0.376324i	$0.877188\pi$
$788$		0			0
$789$	−17.9557	−	11.5394i	−0.639239	−	0.410814i
$790$		0			0
$791$	23.2602	−	26.8437i	0.827036	−	0.954450i
$792$		0			0
$793$	−1.35888	−	9.45120i	−0.0482551	−	0.335622i
$794$		0			0
$795$	−16.0159	+	10.2928i	−0.568026	+	0.365048i
$796$		0			0
$797$	−17.0596	+	37.3553i	−0.604282	+	1.32319i	0.322135	+	0.946694i	$0.395600\pi$
$797$	−17.0596	+	37.3553i	−0.604282	+	1.32319i	−0.926417	+	0.376500i	$0.877128\pi$
$798$		0			0
$799$	−1.57379	+	0.462108i	−0.0556768	+	0.0163482i
$800$		0			0
$801$	14.3946	+	4.22663i	0.508608	+	0.149341i
$802$		0			0
$803$	3.00683	−	20.9129i	0.106109	−	0.738002i
$804$		0			0
$805$	−29.0690	+	27.5810i	−1.02455	+	0.972101i
$806$		0			0
$807$	2.43883	−	16.9624i	0.0858508	−	0.597105i
$808$		0			0
$809$	14.8109	+	4.34888i	0.520724	+	0.152898i	0.531524	−	0.847043i	$-0.321620\pi$
$809$	14.8109	+	4.34888i	0.520724	+	0.152898i	−0.0107997	+	0.999942i	$0.503438\pi$
$810$		0			0
$811$	−13.1728	+	3.86789i	−0.462560	+	0.135820i	−0.504706	−	0.863291i	$-0.668399\pi$
$811$	−13.1728	+	3.86789i	−0.462560	+	0.135820i	0.0421452	+	0.999111i	$0.486581\pi$
$812$		0			0
$813$	7.72538	−	16.9162i	0.270941	−	0.593278i
$814$		0			0
$815$	−37.1605	+	23.8816i	−1.30168	+	0.836536i
$816$		0			0
$817$	5.01931	+	34.9101i	0.175604	+	1.22135i
$818$		0			0
$819$	−1.40508	+	1.62155i	−0.0490974	+	0.0566614i
$820$		0			0
$821$	−21.2947	−	13.6853i	−0.743190	−	0.477619i	0.113444	−	0.993544i	$-0.463812\pi$
$821$	−21.2947	−	13.6853i	−0.743190	−	0.477619i	−0.856634	+	0.515925i	$0.827448\pi$
$822$		0			0
$823$	−1.19232	−	1.37601i	−0.0415616	−	0.0479647i	0.734588	−	0.678513i	$-0.237375\pi$
$823$	−1.19232	−	1.37601i	−0.0415616	−	0.0479647i	−0.776150	+	0.630549i	$0.782830\pi$
$824$		0			0
$825$	−10.4748	−	22.9367i	−0.364686	−	0.798552i
$826$		0			0
$827$	−26.0277			−0.905073			−0.452537	−	0.891746i	$-0.649481\pi$
$827$	−26.0277			−0.905073			−0.452537	+	0.891746i	$0.649481\pi$
$828$		0			0
$829$	21.7340			0.754854			0.377427	−	0.926039i	$-0.376809\pi$
$829$	21.7340			0.754854			0.377427	+	0.926039i	$0.376809\pi$
$830$		0			0
$831$	5.21658	+	11.4227i	0.180961	+	0.396250i
$832$		0			0
$833$	2.68043	+	3.09338i	0.0928713	+	0.107179i
$834$		0			0
$835$	−17.2609	−	11.0929i	−0.597337	−	0.383885i
$836$		0			0
$837$	0.239186	−	0.276036i	0.00826749	−	0.00954120i
$838$		0			0
$839$	0.926972	+	6.44723i	0.0320026	+	0.222583i	0.999546	−	0.0301208i	$-0.00958920\pi$
$839$	0.926972	+	6.44723i	0.0320026	+	0.222583i	−0.967544	+	0.252704i	$0.918680\pi$
$840$		0			0
$841$	60.9903	−	39.1961i	2.10311	−	1.35159i
$842$		0			0
$843$	−1.92672	+	4.21892i	−0.0663596	+	0.145307i
$844$		0			0
$845$	41.9808	−	12.3267i	1.44418	−	0.424051i
$846$		0			0
$847$	2.26267	+	0.664380i	0.0777462	+	0.0228284i
$848$		0			0
$849$	−3.48418	+	24.2330i	−0.119577	+	0.831675i
$850$		0			0
$851$	33.1365	+	3.24645i	1.13590	+	0.111287i
$852$		0			0
$853$	5.86856	−	40.8167i	0.200936	−	1.39754i	−0.600580	−	0.799565i	$-0.705064\pi$
$853$	5.86856	−	40.8167i	0.200936	−	1.39754i	0.801516	−	0.597974i	$-0.204027\pi$
$854$		0			0
$855$	−15.3130	−	4.49630i	−0.523693	−	0.153770i
$856$		0			0
$857$	−16.1418	+	4.73966i	−0.551394	+	0.161904i	−0.545549	−	0.838079i	$-0.683679\pi$
$857$	−16.1418	+	4.73966i	−0.551394	+	0.161904i	−0.00584493	+	0.999983i	$0.501861\pi$
$858$		0			0
$859$	−20.8099	+	45.5674i	−0.710026	+	1.55474i	0.117349	+	0.993091i	$0.462560\pi$
$859$	−20.8099	+	45.5674i	−0.710026	+	1.55474i	−0.827375	+	0.561650i	$0.810167\pi$
$860$		0			0
$861$	13.2871	−	8.53913i	0.452824	−	0.291013i
$862$		0			0
$863$	−4.17701	−	29.0517i	−0.142187	−	0.988932i	−0.928561	−	0.371181i	$-0.878953\pi$
$863$	−4.17701	−	29.0517i	−0.142187	−	0.988932i	0.786374	−	0.617751i	$-0.211956\pi$
$864$		0			0
$865$	−30.2848	+	34.9505i	−1.02971	+	1.18835i
$866$		0			0
$867$	8.94185	+	5.74658i	0.303681	+	0.195164i
$868$		0			0
$869$	1.56734	+	1.80880i	0.0531682	+	0.0613594i
$870$		0			0
$871$	−2.18479	−	4.78402i	−0.0740288	−	0.162100i
$872$		0			0
$873$	1.96849			0.0666232
$874$		0			0
$875$	24.9035			0.841891
$876$		0			0
$877$	6.05526	+	13.2592i	0.204472	+	0.447730i	0.983890	−	0.178773i	$-0.0572128\pi$
$877$	6.05526	+	13.2592i	0.204472	+	0.447730i	−0.779419	+	0.626503i	$0.784486\pi$
$878$		0			0
$879$	−16.2258	−	18.7255i	−0.547282	−	0.631597i
$880$		0			0
$881$	−20.1325	−	12.9384i	−0.678283	−	0.435906i	0.155620	−	0.987817i	$-0.450262\pi$
$881$	−20.1325	−	12.9384i	−0.678283	−	0.435906i	−0.833903	+	0.551911i	$0.813899\pi$
$882$		0			0
$883$	−31.1447	+	35.9429i	−1.04810	+	1.20958i	−0.0708529	+	0.997487i	$0.522572\pi$
$883$	−31.1447	+	35.9429i	−1.04810	+	1.20958i	−0.977250	+	0.212089i	$0.931973\pi$
$884$		0			0
$885$	7.06204	+	49.1176i	0.237388	+	1.65107i
$886$		0			0
$887$	−2.00383	+	1.28778i	−0.0672819	+	0.0432394i	−0.573849	−	0.818961i	$-0.694550\pi$
$887$	−2.00383	+	1.28778i	−0.0672819	+	0.0432394i	0.506567	+	0.862200i	$0.330914\pi$
$888$		0			0
$889$	20.2241	−	44.2847i	0.678296	−	1.48526i
$890$		0			0
$891$	−3.03163	+	0.890166i	−0.101563	+	0.0298217i
$892$		0			0
$893$	−2.76200	−	0.810995i	−0.0924267	−	0.0271389i
$894$		0			0
$895$	10.6947	−	74.3830i	0.357483	−	2.48635i
$896$		0			0
$897$	0.200216	+	4.43249i	0.00668502	+	0.147997i
$898$		0			0
$899$	−0.523684	+	3.64230i	−0.0174658	+	0.121478i
$900$		0			0
$901$	−12.7973	−	3.75762i	−0.426339	−	0.125184i
$902$		0			0
$903$	−17.7169	+	5.20216i	−0.589582	+	0.173117i
$904$		0			0
$905$	18.1436	−	39.7290i	0.603114	−	1.32064i
$906$		0			0
$907$	−9.40729	+	6.04570i	−0.312364	+	0.200744i	−0.687424	−	0.726257i	$-0.741258\pi$
$907$	−9.40729	+	6.04570i	−0.312364	+	0.200744i	0.375060	+	0.927001i	$0.377622\pi$
$908$		0			0
$909$	−2.77638	−	19.3102i	−0.0920869	−	0.640478i
$910$		0			0
$911$	2.06270	−	2.38049i	0.0683404	−	0.0788691i	−0.720550	−	0.693403i	$-0.756111\pi$
$911$	2.06270	−	2.38049i	0.0683404	−	0.0788691i	0.788890	+	0.614534i	$0.210656\pi$
$912$		0			0
$913$	−20.5581	−	13.2119i	−0.680375	−	0.437250i
$914$		0			0
$915$	24.3499	+	28.1013i	0.804984	+	0.929001i
$916$		0			0
$917$	4.54101	+	9.94342i	0.149957	+	0.328361i
$918$		0			0
$919$	32.6948			1.07850			0.539251	−	0.842145i	$-0.318708\pi$
$919$	32.6948			1.07850			0.539251	+	0.842145i	$0.318708\pi$
$920$		0			0
$921$	−8.92387			−0.294051
$922$		0			0
$923$	−2.51324	−	5.50323i	−0.0827244	−	0.181141i
$924$		0			0
$925$	−36.2824	−	41.8722i	−1.19296	−	1.37675i
$926$		0			0
$927$	−12.5477	−	8.06393i	−0.412121	−	0.264854i
$928$		0			0
$929$	−22.3893	+	25.8386i	−0.734569	+	0.847738i	−0.992978	−	0.118298i	$-0.962256\pi$
$929$	−22.3893	+	25.8386i	−0.734569	+	0.847738i	0.258409	+	0.966036i	$0.416802\pi$
$930$		0			0
$931$	1.02230	+	7.11028i	0.0335047	+	0.233030i
$932$		0			0
$933$	12.7833	−	8.21532i	0.418506	−	0.268958i
$934$		0			0
$935$	11.9360	−	26.1362i	0.390349	−	0.854745i
$936$		0			0
$937$	−18.2213	+	5.35026i	−0.595264	+	0.174785i	−0.565467	−	0.824771i	$-0.691304\pi$
$937$	−18.2213	+	5.35026i	−0.595264	+	0.174785i	−0.0297966	+	0.999556i	$0.509486\pi$
$938$		0			0
$939$	−15.6898	−	4.60695i	−0.512019	−	0.150342i
$940$		0			0
$941$	1.87888	−	13.0679i	0.0612497	−	0.426001i	−0.936007	−	0.351981i	$-0.885508\pi$
$941$	1.87888	−	13.0679i	0.0612497	−	0.426001i	0.997257	−	0.0740197i	$-0.0235828\pi$
$942$		0			0
$943$	7.77846	−	31.7224i	0.253301	−	1.03302i
$944$		0			0
$945$	1.18911	−	8.27041i	0.0386816	−	0.269036i
$946$		0			0
$947$	−29.9523	−	8.79479i	−0.973319	−	0.285792i	−0.243855	−	0.969812i	$-0.578412\pi$
$947$	−29.9523	−	8.79479i	−0.973319	−	0.285792i	−0.729464	+	0.684019i	$0.760230\pi$
$948$		0			0
$949$	5.93599	−	1.74296i	0.192690	−	0.0565790i
$950$		0			0
$951$	−0.406688	+	0.890523i	−0.0131878	+	0.0288772i
$952$		0			0
$953$	16.9098	−	10.8673i	0.547763	−	0.352026i	−0.237305	−	0.971435i	$-0.576264\pi$
$953$	16.9098	−	10.8673i	0.547763	−	0.352026i	0.785068	+	0.619409i	$0.212628\pi$
$954$		0			0
$955$	9.31950	+	64.8185i	0.301572	+	2.09748i
$956$		0			0
$957$	20.8456	−	24.0571i	0.673843	−	0.777656i
$958$		0			0
$959$	14.6837	+	9.43662i	0.474160	+	0.304724i
$960$		0			0
$961$	20.2133	+	23.3274i	0.652043	+	0.752497i
$962$		0			0
$963$	−2.36917	−	5.18776i	−0.0763454	−	0.167173i
$964$		0			0
$965$	−41.9649			−1.35090
$966$		0			0
$967$	36.3322			1.16836			0.584182	−	0.811623i	$-0.301415\pi$
$967$	36.3322			1.16836			0.584182	+	0.811623i	$0.301415\pi$
$968$		0			0
$969$	−4.64463	−	10.1703i	−0.149207	−	0.326718i
$970$		0			0
$971$	−18.0902	−	20.8772i	−0.580543	−	0.669982i	0.387178	−	0.922005i	$-0.373450\pi$
$971$	−18.0902	−	20.8772i	−0.580543	−	0.669982i	−0.967721	+	0.252023i	$0.918904\pi$
$972$		0			0
$973$	20.3240	+	13.0614i	0.651556	+	0.418730i
$974$		0			0
$975$	4.83511	−	5.58001i	0.154847	−	0.178703i
$976$		0			0
$977$	0.0118412	+	0.0823576i	0.000378834	+	0.00263485i	0.990010	−	0.140997i	$-0.0450309\pi$
$977$	0.0118412	+	0.0823576i	0.000378834	+	0.00263485i	−0.989631	+	0.143632i	$0.954122\pi$
$978$		0			0
$979$	−39.8766	+	25.6271i	−1.27446	+	0.819047i
$980$		0			0
$981$	−0.672354	+	1.47225i	−0.0214666	+	0.0470053i
$982$		0			0
$983$	−29.0577	+	8.53211i	−0.926797	+	0.272132i	−0.710095	−	0.704106i	$-0.751348\pi$
$983$	−29.0577	+	8.53211i	−0.926797	+	0.272132i	−0.216702	+	0.976238i	$0.569530\pi$
$984$		0			0
$985$	73.3397	+	21.5345i	2.33680	+	0.686146i
$986$		0			0
$987$	0.214478	−	1.49173i	0.00682692	−	0.0474823i
$988$		0			0
$989$	−19.1735	+	33.0216i	−0.609682	+	1.05002i
$990$		0			0
$991$	−6.16657	+	42.8895i	−0.195888	+	1.36243i	0.620174	+	0.784464i	$0.287062\pi$
$991$	−6.16657	+	42.8895i	−0.195888	+	1.36243i	−0.816062	+	0.577965i	$0.803847\pi$
$992$		0			0
$993$	−19.7468	−	5.79819i	−0.626646	−	0.184000i
$994$		0			0
$995$	−7.19522	+	2.11271i	−0.228104	+	0.0669773i
$996$		0			0
$997$	7.26098	−	15.8993i	0.229958	−	0.503537i	−0.759117	−	0.650954i	$-0.774369\pi$
$997$	7.26098	−	15.8993i	0.229958	−	0.503537i	0.989074	+	0.147418i	$0.0470961\pi$
$998$		0			0
$999$	−5.84042	+	3.75341i	−0.184783	+	0.118753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.d.169.1	yes	30
23.3	even	11	inner	552.2.q.d.49.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.d.49.1	✓	30	23.3	even	11	inner
552.2.q.d.169.1	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(-2.35936 - 2.72285i) q^{5} +(1.95097 + 1.25381i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(-2.35936 - 2.72285i) q^{5} +(1.95097 + 1.25381i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.449660 - 3.12745i) q^{11} +(0.778312 - 0.500191i) q^{13} +(-1.49668 + 3.27726i) q^{15} +(-2.42180 + 0.711106i) q^{17} +(-4.25024 - 1.24798i) q^{19} +(0.330046 - 2.29552i) q^{21} +(-2.77223 - 3.91340i) q^{23} +(-1.13574 + 7.89928i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-9.66659 + 2.83837i) q^{29} +(0.151729 - 0.332241i) q^{31} +(-2.65804 + 1.70822i) q^{33} +(-1.18911 - 8.27041i) q^{35} +(-4.54638 + 5.24681i) q^{37} +(-0.778312 - 0.500191i) q^{39} +(4.45994 + 5.14705i) q^{41} +(-3.30753 - 7.24249i) q^{43} +3.60285 q^{45} +0.649844 q^{47} +(-0.673659 - 1.47511i) q^{49} +(1.65290 + 1.90755i) q^{51} +(4.44535 + 2.85685i) q^{53} +(-7.45467 + 8.60315i) q^{55} +(0.630409 + 4.38459i) q^{57} +(11.5867 - 7.44634i) q^{59} +(4.28731 - 9.38791i) q^{61} +(-2.22519 + 0.653373i) q^{63} +(-3.19826 - 0.939095i) q^{65} +(0.809005 - 5.62675i) q^{67} +(-2.40813 + 4.14740i) q^{69} +(0.930627 - 6.47265i) q^{71} +(6.41603 + 1.88392i) q^{73} +(7.65724 - 2.24837i) q^{75} +(3.04397 - 6.66537i) q^{77} +(-0.637245 + 0.409532i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(5.06491 - 5.84522i) q^{83} +(7.65015 + 4.91645i) q^{85} +(6.59752 + 7.61394i) q^{87} +(-6.23218 - 13.6466i) q^{89} +2.14561 q^{91} -0.365248 q^{93} +(6.62980 + 14.5172i) q^{95} +(-1.28908 - 1.48768i) q^{97} +(2.65804 + 1.70822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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