LMFDB - Embedded newform 484.2.i.a.89.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,2,Mod(45,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([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("484.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.i (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:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$110$
Relative dimension:	$11$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			89.9
Character	$\chi$	$=$	484.89
Dual form			484.2.i.a.397.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.44940 q^{3} +(1.47314 + 3.22572i) q^{5} +(3.83701 - 2.46590i) q^{7} -0.899249 q^{9} +(-0.184859 - 3.31147i) q^{11} +(1.30309 + 0.382621i) q^{13} +(2.13516 + 4.67535i) q^{15} +(-3.33111 + 3.84431i) q^{17} +(-3.52424 - 4.06719i) q^{19} +(5.56135 - 3.57406i) q^{21} +(4.38409 + 2.81749i) q^{23} +(-4.96085 + 5.72512i) q^{25} -5.65156 q^{27} +(3.62486 + 4.18331i) q^{29} +(-4.07013 + 1.19510i) q^{31} +(-0.267934 - 4.79963i) q^{33} +(13.6067 + 8.74453i) q^{35} +(-4.26569 + 1.25252i) q^{37} +(1.88869 + 0.554570i) q^{39} +(0.690733 - 4.80415i) q^{41} +(3.18409 - 6.97218i) q^{43} +(-1.32472 - 2.90073i) q^{45} +(-0.0505224 - 0.351391i) q^{47} +(5.73410 - 12.5559i) q^{49} +(-4.82810 + 5.57193i) q^{51} +(-3.72070 + 2.39115i) q^{53} +(10.4096 - 5.47455i) q^{55} +(-5.10802 - 5.89497i) q^{57} +(0.0680064 + 0.472995i) q^{59} +(-0.756971 - 5.26485i) q^{61} +(-3.45043 + 2.21746i) q^{63} +(0.685399 + 4.76705i) q^{65} +(-1.89237 + 13.1618i) q^{67} +(6.35429 + 4.08366i) q^{69} +(-8.42091 - 9.71825i) q^{71} +(5.19725 + 3.34007i) q^{73} +(-7.19024 + 8.29797i) q^{75} +(-8.87505 - 12.2503i) q^{77} +(1.66502 + 3.64589i) q^{79} -5.49360 q^{81} +(-13.5870 + 8.73186i) q^{83} +(-17.3079 - 5.08205i) q^{85} +(5.25385 + 6.06327i) q^{87} +(7.25282 - 8.37020i) q^{89} +(5.94347 - 1.74516i) q^{91} +(-5.89924 + 1.73217i) q^{93} +(7.92793 - 17.3597i) q^{95} +(-1.13825 + 2.49242i) q^{97} +(0.166234 + 2.97784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 2 q^{3} + 2 q^{5} - 2 q^{7} + 112 q^{9} - 10 q^{11} - 29 q^{13} - 18 q^{15} - 6 q^{17} - 8 q^{19} - 2 q^{21} + 4 q^{23} - 17 q^{25} + 4 q^{27} - 28 q^{31} + q^{33} + 6 q^{35} - 31 q^{37} + 4 q^{39}+ \cdots - 57 q^{99}+O(q^{100}) $ 110 * q - 2 * q^3 + 2 * q^5 - 2 * q^7 + 112 * q^9 - 10 * q^11 - 29 * q^13 - 18 * q^15 - 6 * q^17 - 8 * q^19 - 2 * q^21 + 4 * q^23 - 17 * q^25 + 4 * q^27 - 28 * q^31 + q^33 + 6 * q^35 - 31 * q^37 + 4 * q^39 + 10 * q^43 - 8 * q^45 + 2 * q^47 - 49 * q^49 + 115 * q^51 + 72 * q^53 + 41 * q^55 + 3 * q^57 - 6 * q^59 + 4 * q^61 - 51 * q^63 - 45 * q^65 - 51 * q^67 + 4 * q^69 + 26 * q^71 - 18 * q^73 + 46 * q^77 - 24 * q^79 + 110 * q^81 - 6 * q^83 - 92 * q^85 - 7 * q^89 - 91 * q^91 - 37 * q^93 - 64 * q^95 - 31 * q^97 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$

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
$3$	1.44940			0.836810			0.418405	−	0.908261i	$-0.362589\pi$
$3$	1.44940			0.836810			0.418405	+	0.908261i	$0.362589\pi$
$4$		0			0
$5$	1.47314	+	3.22572i	0.658807	+	1.44259i	0.883629	+	0.468187i	$0.155093\pi$
$5$	1.47314	+	3.22572i	0.658807	+	1.44259i	−0.224822	+	0.974400i	$0.572180\pi$
$6$		0			0
$7$	3.83701	−	2.46590i	1.45025	−	0.932022i	0.451035	−	0.892506i	$-0.351055\pi$
$7$	3.83701	−	2.46590i	1.45025	−	0.932022i	0.999219	−	0.0395153i	$-0.0125814\pi$
$8$		0			0
$9$	−0.899249			−0.299750
$10$		0			0
$11$	−0.184859	−	3.31147i	−0.0557370	−	0.998445i
$11$	−0.184859	−	3.31147i	−0.0557370	−	0.998445i
$12$		0			0
$13$	1.30309	+	0.382621i	0.361412	+	0.106120i	0.457397	−	0.889263i	$-0.348782\pi$
$13$	1.30309	+	0.382621i	0.361412	+	0.106120i	−0.0959852	+	0.995383i	$0.530600\pi$
$14$		0			0
$15$	2.13516	+	4.67535i	0.551296	+	1.20717i
$16$		0			0
$17$	−3.33111	+	3.84431i	−0.807913	+	0.932382i	−0.998787	−	0.0492330i	$-0.984322\pi$
$17$	−3.33111	+	3.84431i	−0.807913	+	0.932382i	0.190874	+	0.981615i	$0.438868\pi$
$18$		0			0
$19$	−3.52424	−	4.06719i	−0.808516	−	0.933077i	0.190300	−	0.981726i	$-0.439054\pi$
$19$	−3.52424	−	4.06719i	−0.808516	−	0.933077i	−0.998816	+	0.0486489i	$0.984508\pi$
$20$		0			0
$21$	5.56135	−	3.57406i	1.21359	−	0.779925i
$22$		0			0
$23$	4.38409	+	2.81749i	0.914147	+	0.587487i	0.910954	−	0.412508i	$-0.135347\pi$
$23$	4.38409	+	2.81749i	0.914147	+	0.587487i	0.00319311	+	0.999995i	$0.498984\pi$
$24$		0			0
$25$	−4.96085	+	5.72512i	−0.992169	+	1.14502i
$26$		0			0
$27$	−5.65156			−1.08764
$28$		0			0
$29$	3.62486	+	4.18331i	0.673119	+	0.776821i	0.984861	−	0.173346i	$-0.0554580\pi$
$29$	3.62486	+	4.18331i	0.673119	+	0.776821i	−0.311742	+	0.950167i	$0.600913\pi$
$30$		0			0
$31$	−4.07013	+	1.19510i	−0.731017	+	0.214646i	−0.625999	−	0.779824i	$-0.715308\pi$
$31$	−4.07013	+	1.19510i	−0.731017	+	0.214646i	−0.105019	+	0.994470i	$0.533490\pi$
$32$		0			0
$33$	−0.267934	−	4.79963i	−0.0466412	−	0.835509i
$34$		0			0
$35$	13.6067	+	8.74453i	2.29996	+	1.47809i
$36$		0			0
$37$	−4.26569	+	1.25252i	−0.701275	+	0.205913i	−0.612884	−	0.790173i	$-0.709991\pi$
$37$	−4.26569	+	1.25252i	−0.701275	+	0.205913i	−0.0883911	+	0.996086i	$0.528173\pi$
$38$		0			0
$39$	1.88869	+	0.554570i	0.302433	+	0.0888022i
$40$		0			0
$41$	0.690733	−	4.80415i	0.107874	−	0.750283i	−0.862041	−	0.506839i	$-0.830814\pi$
$41$	0.690733	−	4.80415i	0.107874	−	0.750283i	0.969915	−	0.243444i	$-0.0782771\pi$
$42$		0			0
$43$	3.18409	−	6.97218i	0.485569	−	1.06325i	−0.495326	−	0.868707i	$-0.664951\pi$
$43$	3.18409	−	6.97218i	0.485569	−	1.06325i	0.980895	−	0.194540i	$-0.0623213\pi$
$44$		0			0
$45$	−1.32472	−	2.90073i	−0.197477	−	0.432415i
$46$		0			0
$47$	−0.0505224	−	0.351391i	−0.00736946	−	0.0512557i	0.985805	−	0.167895i	$-0.0536969\pi$
$47$	−0.0505224	−	0.351391i	−0.00736946	−	0.0512557i	−0.993174	+	0.116639i	$0.962788\pi$
$48$		0			0
$49$	5.73410	−	12.5559i	0.819157	−	1.79370i
$50$		0			0
$51$	−4.82810	+	5.57193i	−0.676070	+	0.780226i
$52$		0			0
$53$	−3.72070	+	2.39115i	−0.511078	+	0.328450i	−0.770634	−	0.637278i	$-0.780060\pi$
$53$	−3.72070	+	2.39115i	−0.511078	+	0.328450i	0.259556	+	0.965728i	$0.416424\pi$
$54$		0			0
$55$	10.4096	−	5.47455i	1.40362	−	0.738189i
$56$		0			0
$57$	−5.10802	−	5.89497i	−0.676574	−	0.780808i
$58$		0			0
$59$	0.0680064	+	0.472995i	0.00885368	+	0.0615787i	0.993769	−	0.111457i	$-0.0355516\pi$
$59$	0.0680064	+	0.472995i	0.00885368	+	0.0615787i	−0.984916	+	0.173035i	$0.944643\pi$
$60$		0			0
$61$	−0.756971	−	5.26485i	−0.0969202	−	0.674095i	−0.979129	−	0.203237i	$-0.934854\pi$
$61$	−0.756971	−	5.26485i	−0.0969202	−	0.674095i	0.882209	−	0.470858i	$-0.156055\pi$
$62$		0			0
$63$	−3.45043	+	2.21746i	−0.434713	+	0.279373i
$64$		0			0
$65$	0.685399	+	4.76705i	0.0850133	+	0.591280i
$66$		0			0
$67$	−1.89237	+	13.1618i	−0.231190	+	1.60796i	0.461778	+	0.886996i	$0.347212\pi$
$67$	−1.89237	+	13.1618i	−0.231190	+	1.60796i	−0.692968	+	0.720968i	$0.743697\pi$
$68$		0			0
$69$	6.35429	+	4.08366i	0.764967	+	0.491614i
$70$		0			0
$71$	−8.42091	−	9.71825i	−0.999378	−	1.15334i	−0.988163	−	0.153407i	$-0.950976\pi$
$71$	−8.42091	−	9.71825i	−0.999378	−	1.15334i	−0.0112149	−	0.999937i	$-0.503570\pi$
$72$		0			0
$73$	5.19725	+	3.34007i	0.608292	+	0.390926i	0.808216	−	0.588886i	$-0.200433\pi$
$73$	5.19725	+	3.34007i	0.608292	+	0.390926i	−0.199924	+	0.979811i	$0.564070\pi$
$74$		0			0
$75$	−7.19024	+	8.29797i	−0.830257	+	0.958167i
$76$		0			0
$77$	−8.87505	−	12.2503i	−1.01141	−	1.39605i
$78$		0			0
$79$	1.66502	+	3.64589i	0.187330	+	0.410195i	0.979873	−	0.199620i	$-0.0639709\pi$
$79$	1.66502	+	3.64589i	0.187330	+	0.410195i	−0.792544	+	0.609815i	$0.791244\pi$
$80$		0			0
$81$	−5.49360			−0.610400
$82$		0			0
$83$	−13.5870	+	8.73186i	−1.49137	+	0.958446i	−0.495409	+	0.868660i	$0.664982\pi$
$83$	−13.5870	+	8.73186i	−1.49137	+	0.958446i	−0.995961	+	0.0897860i	$0.971382\pi$
$84$		0			0
$85$	−17.3079	−	5.08205i	−1.87730	−	0.551225i
$86$		0			0
$87$	5.25385	+	6.06327i	0.563272	+	0.650051i
$88$		0			0
$89$	7.25282	−	8.37020i	0.768797	−	0.887239i	−0.227450	−	0.973790i	$-0.573039\pi$
$89$	7.25282	−	8.37020i	0.768797	−	0.887239i	0.996247	+	0.0865506i	$0.0275844\pi$
$90$		0			0
$91$	5.94347	−	1.74516i	0.623045	−	0.182942i
$92$		0			0
$93$	−5.89924	+	1.73217i	−0.611722	+	0.179618i
$94$		0			0
$95$	7.92793	−	17.3597i	0.813389	−	1.78107i
$96$		0			0
$97$	−1.13825	+	2.49242i	−0.115572	+	0.253067i	−0.958574	−	0.284843i	$-0.908059\pi$
$97$	−1.13825	+	2.49242i	−0.115572	+	0.253067i	0.843002	+	0.537910i	$0.180786\pi$
$98$		0			0
$99$	0.166234	+	2.97784i	0.0167071	+	0.299284i
$100$		0			0
$101$	0.698238	+	4.85635i	0.0694773	+	0.483225i	0.994619	+	0.103603i	$0.0330370\pi$
$101$	0.698238	+	4.85635i	0.0694773	+	0.483225i	−0.925142	+	0.379622i	$0.876054\pi$
$102$		0			0
$103$	2.19273	−	15.2508i	0.216056	−	1.50270i	−0.536346	−	0.843998i	$-0.680196\pi$
$103$	2.19273	−	15.2508i	0.216056	−	1.50270i	0.752402	−	0.658704i	$-0.228895\pi$
$104$		0			0
$105$	19.7216	+	12.6743i	1.92463	+	1.23688i
$106$		0			0
$107$	5.88608	+	12.8887i	0.569029	+	1.24600i	0.947313	+	0.320310i	$0.103787\pi$
$107$	5.88608	+	12.8887i	0.569029	+	1.24600i	−0.378284	+	0.925690i	$0.623486\pi$
$108$		0			0
$109$	−9.86896	−	2.89779i	−0.945275	−	0.277558i	−0.227457	−	0.973788i	$-0.573041\pi$
$109$	−9.86896	−	2.89779i	−0.945275	−	0.277558i	−0.717818	+	0.696230i	$0.754859\pi$
$110$		0			0
$111$	−6.18268	+	1.81540i	−0.586834	+	0.172310i
$112$		0			0
$113$	−0.327355	+	0.716807i	−0.0307949	+	0.0674315i	−0.924404	−	0.381414i	$-0.875437\pi$
$113$	−0.327355	+	0.716807i	−0.0307949	+	0.0674315i	0.893609	+	0.448845i	$0.148165\pi$
$114$		0			0
$115$	−2.63005	+	18.2924i	−0.245254	+	1.70578i
$116$		0			0
$117$	−1.17180	−	0.344072i	−0.108333	−	0.0318094i
$118$		0			0
$119$	−3.30184	+	22.9648i	−0.302680	+	2.10518i
$120$		0			0
$121$	−10.9317	+	1.22431i	−0.993787	+	0.111301i
$122$		0			0
$123$	1.00115	−	6.96313i	0.0902703	−	0.627844i
$124$		0			0
$125$	−8.76298	−	2.57304i	−0.783784	−	0.230140i
$126$		0			0
$127$	1.96077	−	13.6375i	0.173991	−	1.21013i	−0.696358	−	0.717695i	$-0.745197\pi$
$127$	1.96077	−	13.6375i	0.173991	−	1.21013i	0.870349	−	0.492436i	$-0.163893\pi$
$128$		0			0
$129$	4.61500	−	10.1055i	0.406328	−	0.889735i
$130$		0			0
$131$	3.18401	−	0.934910i	0.278188	−	0.0816834i	−0.139662	−	0.990199i	$-0.544602\pi$
$131$	3.18401	−	0.934910i	0.278188	−	0.0816834i	0.417851	+	0.908516i	$0.362784\pi$
$132$		0			0
$133$	−23.5518	−	6.91544i	−2.04220	−	0.599644i
$134$		0			0
$135$	−8.32553	−	18.2304i	−0.716547	−	1.56902i
$136$		0			0
$137$	−14.1265	−	9.07852i	−1.20690	−	0.775631i	−0.226767	−	0.973949i	$-0.572816\pi$
$137$	−14.1265	−	9.07852i	−1.20690	−	0.775631i	−0.980138	+	0.198318i	$0.936452\pi$
$138$		0			0
$139$	0.853423	−	5.93569i	0.0723864	−	0.503459i	−0.921084	−	0.389365i	$-0.872695\pi$
$139$	0.853423	−	5.93569i	0.0723864	−	0.503459i	0.993470	−	0.114094i	$-0.0363964\pi$
$140$		0			0
$141$	−0.0732271	−	0.509305i	−0.00616683	−	0.0428913i
$142$		0			0
$143$	1.02615	−	4.38587i	0.0858110	−	0.366765i
$144$		0			0
$145$	−8.15427	+	17.8554i	−0.677176	+	1.48281i
$146$		0			0
$147$	8.31099	−	18.1985i	0.685479	−	1.50099i
$148$		0			0
$149$	20.1697	−	5.92235i	1.65236	−	0.485178i	0.682920	−	0.730493i	$-0.260710\pi$
$149$	20.1697	−	5.92235i	1.65236	−	0.485178i	0.969443	+	0.245316i	$0.0788916\pi$
$150$		0			0
$151$	3.94665	−	1.15884i	0.321174	−	0.0943050i	−0.117172	−	0.993112i	$-0.537383\pi$
$151$	3.94665	−	1.15884i	0.321174	−	0.0943050i	0.438345	+	0.898807i	$0.355565\pi$
$152$		0			0
$153$	2.99550	−	3.45699i	0.242172	−	0.279481i
$154$		0			0
$155$	−9.85092	−	11.3686i	−0.791245	−	0.913146i
$156$		0			0
$157$	−13.4750	−	3.95662i	−1.07542	−	0.315772i	−0.304376	−	0.952552i	$-0.598448\pi$
$157$	−13.4750	−	3.95662i	−1.07542	−	0.315772i	−0.771046	+	0.636780i	$0.780266\pi$
$158$		0			0
$159$	−5.39278	+	3.46573i	−0.427675	+	0.274850i
$160$		0			0
$161$	23.7695			1.87330
$162$		0			0
$163$	−4.28267	−	9.37773i	−0.335444	−	0.734521i	0.664474	−	0.747312i	$-0.268656\pi$
$163$	−4.28267	−	9.37773i	−0.335444	−	0.734521i	−0.999918	+	0.0127908i	$0.995928\pi$
$164$		0			0
$165$	15.0876	−	7.93480i	1.17457	−	0.617723i
$166$		0			0
$167$	−5.29721	+	6.11330i	−0.409910	+	0.473062i	−0.922737	−	0.385431i	$-0.874053\pi$
$167$	−5.29721	+	6.11330i	−0.409910	+	0.473062i	0.512827	+	0.858492i	$0.328598\pi$
$168$		0			0
$169$	−9.38466	−	6.03115i	−0.721897	−	0.463935i
$170$		0			0
$171$	3.16917	+	3.65742i	0.242352	+	0.279690i
$172$		0			0
$173$	7.38772	+	4.74780i	0.561678	+	0.360969i	0.790464	−	0.612508i	$-0.209839\pi$
$173$	7.38772	+	4.74780i	0.561678	+	0.360969i	−0.228786	+	0.973477i	$0.573476\pi$
$174$		0			0
$175$	−4.91726	+	34.2003i	−0.371710	+	2.58530i
$176$		0			0
$177$	0.0985682	+	0.685557i	0.00740884	+	0.0515296i
$178$		0			0
$179$	13.9729	−	8.97986i	1.04439	−	0.671186i	0.0983183	−	0.995155i	$-0.468654\pi$
$179$	13.9729	−	8.97986i	1.04439	−	0.671186i	0.946068	+	0.323969i	$0.105017\pi$
$180$		0			0
$181$	1.91208	+	13.2988i	0.142124	+	0.988494i	0.928655	+	0.370944i	$0.120966\pi$
$181$	1.91208	+	13.2988i	0.142124	+	0.988494i	−0.786532	+	0.617550i	$0.788125\pi$
$182$		0			0
$183$	−1.09715	−	7.63086i	−0.0811038	−	0.564089i
$184$		0			0
$185$	−10.3242	−	11.9148i	−0.759053	−	0.875993i
$186$		0			0
$187$	13.3461	+	10.3202i	0.975963	+	0.754689i
$188$		0			0
$189$	−21.6851	+	13.9362i	−1.57736	+	1.01371i
$190$		0			0
$191$	0.436643	−	0.503913i	0.0315944	−	0.0364618i	−0.739732	−	0.672901i	$-0.765048\pi$
$191$	0.436643	−	0.503913i	0.0315944	−	0.0364618i	0.771327	+	0.636439i	$0.219593\pi$
$192$		0			0
$193$	−1.71521	+	3.75578i	−0.123463	+	0.270347i	−0.961264	−	0.275629i	$-0.911114\pi$
$193$	−1.71521	+	3.75578i	−0.123463	+	0.270347i	0.837801	+	0.545976i	$0.183841\pi$
$194$		0			0
$195$	0.993415	+	6.90935i	0.0711399	+	0.494789i
$196$		0			0
$197$	−0.941295	−	2.06115i	−0.0670645	−	0.146851i	0.873131	−	0.487485i	$-0.162086\pi$
$197$	−0.941295	−	2.06115i	−0.0670645	−	0.146851i	−0.940196	+	0.340634i	$0.889358\pi$
$198$		0			0
$199$	−1.89770	+	4.15539i	−0.134525	+	0.294568i	−0.964891	−	0.262650i	$-0.915404\pi$
$199$	−1.89770	+	4.15539i	−0.134525	+	0.294568i	0.830367	+	0.557217i	$0.188131\pi$
$200$		0			0
$201$	−2.74280	+	19.0766i	−0.193462	+	1.34556i
$202$		0			0
$203$	24.2242	+	7.11287i	1.70021	+	0.499226i
$204$		0			0
$205$	16.5144	−	4.84907i	1.15342	−	0.338674i
$206$		0			0
$207$	−3.94239	−	2.53362i	−0.274015	−	0.176099i
$208$		0			0
$209$	−12.8169	+	12.4223i	−0.886562	+	0.859266i
$210$		0			0
$211$	−7.90908	+	2.32231i	−0.544483	+	0.159875i	−0.542396	−	0.840123i	$-0.682483\pi$
$211$	−7.90908	+	2.32231i	−0.544483	+	0.159875i	−0.00208754	+	0.999998i	$0.500664\pi$
$212$		0			0
$213$	−12.2052	−	14.0856i	−0.836289	−	0.965129i
$214$		0			0
$215$	27.1809			1.85372
$216$		0			0
$217$	−12.6702	+	14.6221i	−0.860106	+	0.992615i
$218$		0			0
$219$	7.53288	+	4.84109i	0.509025	+	0.327130i
$220$		0			0
$221$	−5.81164	+	3.73492i	−0.390933	+	0.251238i
$222$		0			0
$223$	16.1732	+	18.6649i	1.08304	+	1.24989i	0.966489	+	0.256707i	$0.0826377\pi$
$223$	16.1732	+	18.6649i	1.08304	+	1.24989i	0.116549	+	0.993185i	$0.462817\pi$
$224$		0			0
$225$	4.46104	−	5.14831i	0.297402	−	0.343221i
$226$		0			0
$227$	3.31985	+	7.26946i	0.220346	+	0.482491i	0.987231	−	0.159293i	$-0.0509216\pi$
$227$	3.31985	+	7.26946i	0.220346	+	0.482491i	−0.766885	+	0.641785i	$0.778194\pi$
$228$		0			0
$229$	27.4617	+	8.06348i	1.81472	+	0.532850i	0.998962	−	0.0455457i	$-0.0145027\pi$
$229$	27.4617	+	8.06348i	1.81472	+	0.532850i	0.815757	+	0.578395i	$0.196321\pi$
$230$		0			0
$231$	−12.8635	−	17.7555i	−0.846354	−	1.16823i
$232$		0			0
$233$	23.8739			1.56403			0.782015	−	0.623260i	$-0.214192\pi$
$233$	23.8739			1.56403			0.782015	+	0.623260i	$0.214192\pi$
$234$		0			0
$235$	1.05906	−	0.680619i	0.0690857	−	0.0443987i
$236$		0			0
$237$	2.41328	+	5.28434i	0.156759	+	0.343255i
$238$		0			0
$239$	−7.45718			−0.482365			−0.241183	−	0.970480i	$-0.577535\pi$
$239$	−7.45718			−0.482365			−0.241183	+	0.970480i	$0.577535\pi$
$240$		0			0
$241$	4.33939			0.279525			0.139762	−	0.990185i	$-0.455366\pi$
$241$	4.33939			0.279525			0.139762	+	0.990185i	$0.455366\pi$
$242$		0			0
$243$	8.99227			0.576854
$244$		0			0
$245$	48.9491			3.12724
$246$		0			0
$247$	−3.03620	−	6.64835i	−0.193189	−	0.423025i
$248$		0			0
$249$	−19.6930	+	12.6559i	−1.24799	+	0.802037i
$250$		0			0
$251$	22.2961			1.40732			0.703660	−	0.710537i	$-0.251548\pi$
$251$	22.2961			1.40732			0.703660	+	0.710537i	$0.251548\pi$
$252$		0			0
$253$	8.51958	−	15.0386i	0.535622	−	0.945471i
$254$		0			0
$255$	−25.0860	−	7.36590i	−1.57094	−	0.461271i
$256$		0			0
$257$	−0.201844	−	0.441976i	−0.0125907	−	0.0275697i	0.903232	−	0.429152i	$-0.141188\pi$
$257$	−0.201844	−	0.441976i	−0.0125907	−	0.0275697i	−0.915823	+	0.401582i	$0.868460\pi$
$258$		0			0
$259$	−13.2789	+	15.3247i	−0.825112	+	0.952230i
$260$		0			0
$261$	−3.25965	−	3.76183i	−0.201767	−	0.232852i
$262$		0			0
$263$	0.0274060	−	0.0176128i	0.00168993	−	0.00108605i	−0.539796	−	0.841796i	$-0.681498\pi$
$263$	0.0274060	−	0.0176128i	0.00168993	−	0.00108605i	0.541486	+	0.840710i	$0.317862\pi$
$264$		0			0
$265$	−13.1943	−	8.47946i	−0.810520	−	0.520889i
$266$		0			0
$267$	10.5122	−	12.1317i	0.643337	−	0.742450i
$268$		0			0
$269$	−26.9612			−1.64386			−0.821928	−	0.569591i	$-0.807101\pi$
$269$	−26.9612			−1.64386			−0.821928	+	0.569591i	$0.807101\pi$
$270$		0			0
$271$	−15.0044	−	17.3160i	−0.911451	−	1.05187i	−0.998450	−	0.0556623i	$-0.982273\pi$
$271$	−15.0044	−	17.3160i	−0.911451	−	1.05187i	0.0869985	−	0.996208i	$-0.472272\pi$
$272$		0			0
$273$	8.61444	−	2.52943i	0.521370	−	0.153088i
$274$		0			0
$275$	19.8756	+	15.3694i	1.19855	+	0.926807i
$276$		0			0
$277$	13.3596	+	8.58568i	0.802699	+	0.515863i	0.876496	−	0.481410i	$-0.159875\pi$
$277$	13.3596	+	8.58568i	0.802699	+	0.515863i	−0.0737965	+	0.997273i	$0.523512\pi$
$278$		0			0
$279$	3.66006	−	1.07469i	0.219122	−	0.0643401i
$280$		0			0
$281$	14.1195	+	4.14586i	0.842299	+	0.247321i	0.674292	−	0.738465i	$-0.264449\pi$
$281$	14.1195	+	4.14586i	0.842299	+	0.247321i	0.168007	+	0.985786i	$0.446267\pi$
$282$		0			0
$283$	2.86294	−	19.9122i	0.170184	−	1.18366i	−0.708309	−	0.705902i	$-0.750542\pi$
$283$	2.86294	−	19.9122i	0.170184	−	1.18366i	0.878493	−	0.477755i	$-0.158549\pi$
$284$		0			0
$285$	11.4907	−	25.1612i	0.680651	−	1.49042i
$286$		0			0
$287$	−9.19620	−	20.1369i	−0.542835	−	1.18864i
$288$		0			0
$289$	−1.26304	−	8.78467i	−0.0742968	−	0.516745i
$290$		0			0
$291$	−1.64978	+	3.61251i	−0.0967116	+	0.211769i
$292$		0			0
$293$	3.48774	−	4.02507i	0.203756	−	0.235147i	−0.644670	−	0.764461i	$-0.723005\pi$
$293$	3.48774	−	4.02507i	0.203756	−	0.235147i	0.848426	+	0.529314i	$0.177551\pi$
$294$		0			0
$295$	−1.42557	+	0.916157i	−0.0829997	+	0.0533407i
$296$		0			0
$297$	1.04474	+	18.7150i	0.0606219	+	1.08595i
$298$		0			0
$299$	4.63483	+	5.34888i	0.268039	+	0.309334i
$300$		0			0
$301$	−4.97530	−	34.6040i	−0.286771	−	1.99454i
$302$		0			0
$303$	1.01202	+	7.03878i	0.0581392	+	0.404367i
$304$		0			0
$305$	15.8678	−	10.1976i	0.908589	−	0.583915i
$306$		0			0
$307$	3.87121	+	26.9249i	0.220942	+	1.53668i	0.734487	+	0.678622i	$0.237423\pi$
$307$	3.87121	+	26.9249i	0.220942	+	1.53668i	−0.513546	+	0.858062i	$0.671668\pi$
$308$		0			0
$309$	3.17813	−	22.1044i	0.180798	−	1.25748i
$310$		0			0
$311$	18.7454	+	12.0469i	1.06295	+	0.683118i	0.950559	−	0.310545i	$-0.100512\pi$
$311$	18.7454	+	12.0469i	1.06295	+	0.683118i	0.112394	+	0.993664i	$0.464148\pi$
$312$		0			0
$313$	23.1158	+	26.6771i	1.30658	+	1.50788i	0.705576	+	0.708634i	$0.250688\pi$
$313$	23.1158	+	26.6771i	1.30658	+	1.50788i	0.601007	+	0.799244i	$0.294766\pi$
$314$		0			0
$315$	−12.2359	−	7.86351i	−0.689412	−	0.443058i
$316$		0			0
$317$	−22.6845	+	26.1793i	−1.27409	+	1.47037i	−0.461949	+	0.886907i	$0.652850\pi$
$317$	−22.6845	+	26.1793i	−1.27409	+	1.47037i	−0.812137	+	0.583467i	$0.801696\pi$
$318$		0			0
$319$	13.1828	−	12.7769i	0.738095	−	0.715370i
$320$		0			0
$321$	8.53126	+	18.6809i	0.476169	+	1.04266i
$322$		0			0
$323$	27.3752			1.52319
$324$		0			0
$325$	−8.65497	+	5.56221i	−0.480091	+	0.308536i
$326$		0			0
$327$	−14.3040	−	4.20005i	−0.791015	−	0.232263i
$328$		0			0
$329$	−1.06035	−	1.22371i	−0.0584590	−	0.0674653i
$330$		0			0
$331$	−22.3237	+	25.7629i	−1.22702	+	1.41606i	−0.349212	+	0.937044i	$0.613551\pi$
$331$	−22.3237	+	25.7629i	−1.22702	+	1.41606i	−0.877808	+	0.479012i	$0.840995\pi$
$332$		0			0
$333$	3.83592	−	1.12633i	0.210207	−	0.0617223i
$334$		0			0
$335$	−45.2439	+	13.2848i	−2.47194	+	0.725826i
$336$		0			0
$337$	−2.43666	+	5.33554i	−0.132733	+	0.290646i	−0.964315	−	0.264757i	$-0.914708\pi$
$337$	−2.43666	+	5.33554i	−0.132733	+	0.290646i	0.831582	+	0.555402i	$0.187436\pi$
$338$		0			0
$339$	−0.474467	+	1.03894i	−0.0257695	+	0.0564273i
$340$		0			0
$341$	4.70993	+	13.2572i	0.255057	+	0.717917i
$342$		0			0
$343$	−4.41607	−	30.7145i	−0.238446	−	1.65842i
$344$		0			0
$345$	−3.81199	+	26.5130i	−0.205231	+	1.42741i
$346$		0			0
$347$	−16.3123	−	10.4833i	−0.875691	−	0.562773i	0.0237972	−	0.999717i	$-0.492424\pi$
$347$	−16.3123	−	10.4833i	−0.875691	−	0.562773i	−0.899489	+	0.436944i	$0.856061\pi$
$348$		0			0
$349$	−8.13818	−	17.8201i	−0.435627	−	0.953889i	−0.992380	−	0.123212i	$-0.960681\pi$
$349$	−8.13818	−	17.8201i	−0.435627	−	0.953889i	0.556754	−	0.830677i	$-0.312047\pi$
$350$		0			0
$351$	−7.36448	−	2.16241i	−0.393087	−	0.115421i
$352$		0			0
$353$	15.8513	−	4.65435i	0.843678	−	0.247726i	0.168795	−	0.985651i	$-0.446012\pi$
$353$	15.8513	−	4.65435i	0.843678	−	0.247726i	0.674883	+	0.737925i	$0.264194\pi$
$354$		0			0
$355$	18.9432	−	41.4798i	1.00540	−	2.20152i
$356$		0			0
$357$	−4.78568	+	33.2851i	−0.253285	+	1.76164i
$358$		0			0
$359$	−29.4013	−	8.63301i	−1.55174	−	0.455633i	−0.610122	−	0.792308i	$-0.708879\pi$
$359$	−29.4013	−	8.63301i	−1.55174	−	0.455633i	−0.941621	+	0.336675i	$0.890698\pi$
$360$		0			0
$361$	−1.41778	+	9.86088i	−0.0746201	+	0.518994i
$362$		0			0
$363$	−15.8443	+	1.77451i	−0.831610	+	0.0931375i
$364$		0			0
$365$	−3.11787	+	21.6853i	−0.163197	+	1.13506i
$366$		0			0
$367$	9.19920	+	2.70113i	0.480195	+	0.140998i	0.512867	−	0.858468i	$-0.328584\pi$
$367$	9.19920	+	2.70113i	0.480195	+	0.140998i	−0.0326721	+	0.999466i	$0.510402\pi$
$368$		0			0
$369$	−0.621141	+	4.32013i	−0.0323353	+	0.224897i
$370$		0			0
$371$	−8.38005	+	18.3498i	−0.435071	+	0.952672i
$372$		0			0
$373$	34.2001	−	10.0421i	1.77082	−	0.519958i	0.776853	−	0.629681i	$-0.216815\pi$
$373$	34.2001	−	10.0421i	1.77082	−	0.519958i	0.993962	+	0.109723i	$0.0349964\pi$
$374$		0			0
$375$	−12.7010	−	3.72936i	−0.655878	−	0.192583i
$376$		0			0
$377$	3.12288	+	6.83816i	0.160837	+	0.352183i
$378$		0			0
$379$	−28.2626	−	18.1633i	−1.45175	−	0.932986i	−0.999148	−	0.0412750i	$-0.986858\pi$
$379$	−28.2626	−	18.1633i	−1.45175	−	0.932986i	−0.452606	−	0.891711i	$-0.649506\pi$
$380$		0			0
$381$	2.84194	−	19.7661i	0.145597	−	1.01265i
$382$		0			0
$383$	0.103796	+	0.721918i	0.00530374	+	0.0368883i	0.992301	−	0.123846i	$-0.0395229\pi$
$383$	0.103796	+	0.721918i	0.00530374	+	0.0368883i	−0.986998	+	0.160734i	$0.948614\pi$
$384$		0			0
$385$	26.4419	−	46.6748i	1.34760	−	2.37877i
$386$		0			0
$387$	−2.86329	+	6.26972i	−0.145549	+	0.318708i
$388$		0			0
$389$	−13.4466	+	29.4440i	−0.681772	+	1.49287i	0.178983	+	0.983852i	$0.442719\pi$
$389$	−13.4466	+	29.4440i	−0.681772	+	1.49287i	−0.860755	+	0.509020i	$0.830008\pi$
$390$		0			0
$391$	−25.4352	+	7.46845i	−1.28631	+	0.377696i
$392$		0			0
$393$	4.61489	−	1.35506i	0.232791	−	0.0683535i
$394$		0			0
$395$	−9.30783	+	10.7418i	−0.468328	+	0.540479i
$396$		0			0
$397$	23.0759	+	26.6310i	1.15815	+	1.33657i	0.931991	+	0.362482i	$0.118071\pi$
$397$	23.0759	+	26.6310i	1.15815	+	1.33657i	0.226157	+	0.974091i	$0.427384\pi$
$398$		0			0
$399$	−34.1359	−	10.0232i	−1.70893	−	0.501788i
$400$		0			0
$401$	−0.0330043	+	0.0212106i	−0.00164816	+	0.00105920i	−0.541465	−	0.840724i	$-0.682130\pi$
$401$	−0.0330043	+	0.0212106i	−0.00164816	+	0.00105920i	0.539816	+	0.841783i	$0.318494\pi$
$402$		0			0
$403$	−5.76101			−0.286976
$404$		0			0
$405$	−8.09284	−	17.7208i	−0.402136	−	0.880556i
$406$		0			0
$407$	4.93623	+	13.8942i	0.244680	+	0.688708i
$408$		0			0
$409$	−1.13268	+	1.30718i	−0.0560072	+	0.0646358i	−0.783062	−	0.621944i	$-0.786343\pi$
$409$	−1.13268	+	1.30718i	−0.0560072	+	0.0646358i	0.727055	+	0.686580i	$0.240889\pi$
$410$		0			0
$411$	−20.4748	−	13.1584i	−1.00995	−	0.649055i
$412$		0			0
$413$	1.42730	+	1.64719i	0.0702327	+	0.0810529i
$414$		0			0
$415$	−48.1821	−	30.9648i	−2.36517	−	1.52000i
$416$		0			0
$417$	1.23695	−	8.60317i	0.0605736	−	0.421299i
$418$		0			0
$419$	1.41271	+	9.82564i	0.0690156	+	0.480014i	0.994791	+	0.101939i	$0.0325047\pi$
$419$	1.41271	+	9.82564i	0.0690156	+	0.480014i	−0.925775	+	0.378075i	$0.876586\pi$
$420$		0			0
$421$	−17.6199	+	11.3237i	−0.858744	+	0.551881i	−0.894290	−	0.447487i	$-0.852319\pi$
$421$	−17.6199	+	11.3237i	−0.858744	+	0.551881i	0.0355469	+	0.999368i	$0.488683\pi$
$422$		0			0
$423$	0.0454323	+	0.315988i	0.00220899	+	0.0153639i
$424$		0			0
$425$	−5.48400	−	38.1420i	−0.266013	−	1.85016i
$426$		0			0
$427$	−15.8871	−	18.3347i	−0.768830	−	0.887277i
$428$		0			0
$429$	1.48730	−	6.35686i	0.0718075	−	0.306912i
$430$		0			0
$431$	20.2211	−	12.9953i	0.974017	−	0.625963i	0.0461737	−	0.998933i	$-0.485297\pi$
$431$	20.2211	−	12.9953i	0.974017	−	0.625963i	0.927843	+	0.372971i	$0.121661\pi$
$432$		0			0
$433$	10.3450	−	11.9388i	0.497150	−	0.573742i	−0.450612	−	0.892720i	$-0.648794\pi$
$433$	10.3450	−	11.9388i	0.497150	−	0.573742i	0.947762	+	0.318978i	$0.103340\pi$
$434$		0			0
$435$	−11.8188	+	25.8795i	−0.566667	+	1.24083i
$436$		0			0
$437$	−3.99135	−	27.7604i	−0.190932	−	1.32796i
$438$		0			0
$439$	−4.81018	−	10.5328i	−0.229577	−	0.502704i	0.759427	−	0.650593i	$-0.225480\pi$
$439$	−4.81018	−	10.5328i	−0.229577	−	0.502704i	−0.989004	+	0.147889i	$0.952752\pi$
$440$		0			0
$441$	−5.15638	+	11.2909i	−0.245542	+	0.537662i
$442$		0			0
$443$	−4.10905	+	28.5791i	−0.195227	+	1.35783i	0.622677	+	0.782479i	$0.286045\pi$
$443$	−4.10905	+	28.5791i	−0.195227	+	1.35783i	−0.817904	+	0.575354i	$0.804864\pi$
$444$		0			0
$445$	37.6843	+	11.0651i	1.78641	+	0.524537i
$446$		0			0
$447$	29.2338	−	8.58383i	1.38271	−	0.406001i
$448$		0			0
$449$	−7.10431	−	4.56566i	−0.335273	−	0.215467i	0.362161	−	0.932115i	$-0.382039\pi$
$449$	−7.10431	−	4.56566i	−0.335273	−	0.215467i	−0.697435	+	0.716648i	$0.745675\pi$
$450$		0			0
$451$	−16.0365	−	1.39925i	−0.755129	−	0.0658882i
$452$		0			0
$453$	5.72026	−	1.67962i	0.268761	−	0.0789154i
$454$		0			0
$455$	14.3849	+	16.6011i	0.674377	+	0.778272i
$456$		0			0
$457$	−24.4517			−1.14380			−0.571901	−	0.820322i	$-0.693794\pi$
$457$	−24.4517			−1.14380			−0.571901	+	0.820322i	$0.693794\pi$
$458$		0			0
$459$	18.8260	−	21.7263i	0.878721	−	1.01410i
$460$		0			0
$461$	24.2764	+	15.6015i	1.13067	+	0.726635i	0.965699	−	0.259665i	$-0.0836120\pi$
$461$	24.2764	+	15.6015i	1.13067	+	0.726635i	0.164967	+	0.986299i	$0.447248\pi$
$462$		0			0
$463$	11.4323	−	7.34712i	0.531306	−	0.341450i	−0.247324	−	0.968933i	$-0.579551\pi$
$463$	11.4323	−	7.34712i	0.531306	−	0.341450i	0.778630	+	0.627483i	$0.215915\pi$
$464$		0			0
$465$	−14.2779	−	16.4776i	−0.662122	−	0.764129i
$466$		0			0
$467$	3.20775	−	3.70194i	0.148437	−	0.171306i	−0.676662	−	0.736294i	$-0.736574\pi$
$467$	3.20775	−	3.70194i	0.148437	−	0.171306i	0.825099	+	0.564989i	$0.191119\pi$
$468$		0			0
$469$	25.1945	+	55.1682i	1.16337	+	2.54743i
$470$		0			0
$471$	−19.5306	−	5.73471i	−0.899923	−	0.264241i
$472$		0			0
$473$	−23.6768	−	9.25514i	−1.08866	−	0.425552i
$474$		0			0
$475$	40.7684			1.87058
$476$		0			0
$477$	3.34584	−	2.15024i	0.153196	−	0.0984528i
$478$		0			0
$479$	−2.35755	−	5.16232i	−0.107719	−	0.235872i	0.848095	−	0.529845i	$-0.177750\pi$
$479$	−2.35755	−	5.16232i	−0.107719	−	0.235872i	−0.955814	+	0.293972i	$0.905023\pi$
$480$		0			0
$481$	−6.03781			−0.275300
$482$		0			0
$483$	34.4514			1.56759
$484$		0			0
$485$	−9.71666			−0.441211
$486$		0			0
$487$	5.30022			0.240176			0.120088	−	0.992763i	$-0.461682\pi$
$487$	5.30022			0.240176			0.120088	+	0.992763i	$0.461682\pi$
$488$		0			0
$489$	−6.20728	−	13.5921i	−0.280703	−	0.614654i
$490$		0			0
$491$	13.7406	−	8.83053i	0.620104	−	0.398516i	−0.192530	−	0.981291i	$-0.561669\pi$
$491$	13.7406	−	8.83053i	0.620104	−	0.398516i	0.812634	+	0.582775i	$0.198033\pi$
$492$		0			0
$493$	−28.1567			−1.26811
$494$		0			0
$495$	−9.36079	+	4.92299i	−0.420736	+	0.221272i
$496$		0			0
$497$	−56.2753	−	16.5239i	−2.52429	−	0.741199i
$498$		0			0
$499$	2.13714	+	4.67968i	0.0956714	+	0.209491i	0.951417	−	0.307906i	$-0.0996283\pi$
$499$	2.13714	+	4.67968i	0.0956714	+	0.209491i	−0.855745	+	0.517397i	$0.826901\pi$
$500$		0			0
$501$	−7.67775	+	8.86060i	−0.343017	+	0.395862i
$502$		0			0
$503$	−3.53183	−	4.07595i	−0.157476	−	0.181738i	0.671529	−	0.740979i	$-0.265638\pi$
$503$	−3.53183	−	4.07595i	−0.157476	−	0.181738i	−0.829005	+	0.559241i	$0.811093\pi$
$504$		0			0
$505$	−14.6366	+	9.40640i	−0.651322	+	0.418579i
$506$		0			0
$507$	−13.6021	−	8.74153i	−0.604090	−	0.388225i
$508$		0			0
$509$	2.15954	−	2.49224i	0.0957199	−	0.110467i	−0.705869	−	0.708343i	$-0.749443\pi$
$509$	2.15954	−	2.49224i	0.0957199	−	0.110467i	0.801589	+	0.597876i	$0.203989\pi$
$510$		0			0
$511$	28.1782			1.24653
$512$		0			0
$513$	19.9174	+	22.9860i	0.879377	+	1.01485i
$514$		0			0
$515$	52.4249	−	15.3933i	2.31012	−	0.678312i
$516$		0			0
$517$	−1.15428	+	0.232261i	−0.0507653	+	0.0102148i
$518$		0			0
$519$	10.7077	+	6.88145i	0.470018	+	0.302062i
$520$		0			0
$521$	4.78055	−	1.40370i	0.209440	−	0.0614970i	−0.175330	−	0.984510i	$-0.556099\pi$
$521$	4.78055	−	1.40370i	0.209440	−	0.0614970i	0.384769	+	0.923013i	$0.374281\pi$
$522$		0			0
$523$	34.2462	+	10.0556i	1.49748	+	0.439701i	0.924921	−	0.380160i	$-0.124131\pi$
$523$	34.2462	+	10.0556i	1.49748	+	0.439701i	0.572562	+	0.819861i	$0.305949\pi$
$524$		0			0
$525$	−7.12706	+	49.5698i	−0.311050	+	2.16340i
$526$		0			0
$527$	8.96374	−	19.6278i	0.390466	−	0.855002i
$528$		0			0
$529$	1.72751	+	3.78272i	0.0751091	+	0.164466i
$530$		0			0
$531$	−0.0611547	−	0.425340i	−0.00265389	−	0.0184582i
$532$		0			0
$533$	2.73826	−	5.99595i	0.118607	−	0.259713i
$534$		0			0
$535$	−32.9044	+	37.9737i	−1.42258	+	1.64175i
$536$		0			0
$537$	20.2523	−	13.0154i	0.873952	−	0.561655i
$538$		0			0
$539$	−42.6386	−	16.6672i	−1.83657	−	0.717908i
$540$		0			0
$541$	−9.32545	−	10.7621i	−0.400933	−	0.462701i	0.519002	−	0.854773i	$-0.326304\pi$
$541$	−9.32545	−	10.7621i	−0.400933	−	0.462701i	−0.919934	+	0.392072i	$0.871758\pi$
$542$		0			0
$543$	2.77137	+	19.2753i	0.118931	+	0.827181i
$544$		0			0
$545$	−5.19088	−	36.1034i	−0.222353	−	1.54650i
$546$		0			0
$547$	27.9195	−	17.9428i	1.19375	−	0.767178i	0.215888	−	0.976418i	$-0.430735\pi$
$547$	27.9195	−	17.9428i	1.19375	−	0.767178i	0.977864	+	0.209240i	$0.0670990\pi$
$548$		0			0
$549$	0.680706	+	4.73441i	0.0290518	+	0.202060i
$550$		0			0
$551$	4.23944	−	29.4859i	0.180606	−	1.25614i
$552$		0			0
$553$	15.3791	+	9.88355i	0.653986	+	0.420291i
$554$		0			0
$555$	−14.9639	−	17.2693i	−0.635183	−	0.733040i
$556$		0			0
$557$	−21.1994	−	13.6240i	−0.898246	−	0.577268i	0.00802356	−	0.999968i	$-0.497446\pi$
$557$	−21.1994	−	13.6240i	−0.898246	−	0.577268i	−0.906270	+	0.422700i	$0.861082\pi$
$558$		0			0
$559$	6.81685	−	7.86706i	0.288322	−	0.332741i
$560$		0			0
$561$	19.3438	+	14.9581i	0.816695	+	0.631531i
$562$		0			0
$563$	7.71245	+	16.8879i	0.325041	+	0.711741i	0.999651	−	0.0264341i	$-0.00841520\pi$
$563$	7.71245	+	16.8879i	0.325041	+	0.711741i	−0.674609	+	0.738175i	$0.735688\pi$
$564$		0			0
$565$	−2.79446			−0.117564
$566$		0			0
$567$	−21.0790	+	13.5467i	−0.885236	+	0.568906i
$568$		0			0
$569$	−15.9645	−	4.68759i	−0.669265	−	0.196514i	−0.0705892	−	0.997505i	$-0.522488\pi$
$569$	−15.9645	−	4.68759i	−0.669265	−	0.196514i	−0.598676	+	0.800992i	$0.704306\pi$
$570$		0			0
$571$	−6.02932	−	6.95821i	−0.252319	−	0.291192i	0.615433	−	0.788189i	$-0.288981\pi$
$571$	−6.02932	−	6.95821i	−0.252319	−	0.291192i	−0.867752	+	0.496998i	$0.834436\pi$
$572$		0			0
$573$	0.632869	−	0.730369i	0.0264385	−	0.0305116i
$574$		0			0
$575$	−37.8793	+	11.1224i	−1.57968	+	0.463834i
$576$		0			0
$577$	1.97349	−	0.579470i	0.0821576	−	0.0241236i	−0.240395	−	0.970675i	$-0.577277\pi$
$577$	1.97349	−	0.579470i	0.0821576	−	0.0241236i	0.322553	+	0.946551i	$0.395459\pi$
$578$		0			0
$579$	−2.48601	+	5.44361i	−0.103315	+	0.226229i
$580$		0			0
$581$	−30.6017	+	67.0085i	−1.26957	+	2.77998i
$582$		0			0
$583$	8.60603	+	11.8790i	0.356425	+	0.491977i
$584$		0			0
$585$	−0.616344	−	4.28677i	−0.0254827	−	0.177236i
$586$		0			0
$587$	−0.868204	+	6.03849i	−0.0358346	+	0.249235i	−0.999863	−	0.0165649i	$-0.994727\pi$
$587$	−0.868204	+	6.03849i	−0.0358346	+	0.249235i	0.964028	+	0.265800i	$0.0856361\pi$
$588$		0			0
$589$	19.2048	+	12.3422i	0.791320	+	0.508551i
$590$		0			0
$591$	−1.36431	−	2.98742i	−0.0561202	−	0.122886i
$592$		0			0
$593$	−39.0564	−	11.4680i	−1.60386	−	0.470934i	−0.647240	−	0.762287i	$-0.724077\pi$
$593$	−39.0564	−	11.4680i	−1.60386	−	0.470934i	−0.956616	+	0.291352i	$0.905895\pi$
$594$		0			0
$595$	−78.9422	+	23.1795i	−3.23632	+	0.950268i
$596$		0			0
$597$	−2.75052	+	6.02280i	−0.112571	+	0.246497i
$598$		0			0
$599$	−2.59798	+	18.0693i	−0.106150	+	0.738293i	0.865335	+	0.501194i	$0.167106\pi$
$599$	−2.59798	+	18.0693i	−0.106150	+	0.738293i	−0.971486	+	0.237099i	$0.923803\pi$
$600$		0			0
$601$	4.26422	+	1.25209i	0.173941	+	0.0510737i	0.367543	−	0.930006i	$-0.380199\pi$
$601$	4.26422	+	1.25209i	0.173941	+	0.0510737i	−0.193602	+	0.981080i	$0.562017\pi$
$602$		0			0
$603$	1.70172	−	11.8357i	0.0692992	−	0.481987i
$604$		0			0
$605$	−20.0531	−	33.4589i	−0.815275	−	1.36030i
$606$		0			0
$607$	6.06568	−	42.1878i	0.246198	−	1.71235i	−0.373602	−	0.927589i	$-0.621878\pi$
$607$	6.06568	−	42.1878i	0.246198	−	1.71235i	0.619801	−	0.784759i	$-0.287213\pi$
$608$		0			0
$609$	35.1105	+	10.3094i	1.42275	+	0.417757i
$610$		0			0
$611$	0.0686145	−	0.477225i	0.00277585	−	0.0193064i
$612$		0			0
$613$	0.637691	−	1.39635i	0.0257561	−	0.0563980i	−0.896317	−	0.443414i	$-0.853767\pi$
$613$	0.637691	−	1.39635i	0.0257561	−	0.0563980i	0.922073	+	0.387016i	$0.126494\pi$
$614$		0			0
$615$	23.9359	−	7.02823i	0.965190	−	0.283405i
$616$		0			0
$617$	21.6285	+	6.35070i	0.870731	+	0.255670i	0.686426	−	0.727199i	$-0.259178\pi$
$617$	21.6285	+	6.35070i	0.870731	+	0.255670i	0.184305	+	0.982869i	$0.440997\pi$
$618$		0			0
$619$	2.66550	+	5.83662i	0.107135	+	0.234594i	0.955605	−	0.294650i	$-0.0952030\pi$
$619$	2.66550	+	5.83662i	0.107135	+	0.234594i	−0.848470	+	0.529244i	$0.822476\pi$
$620$		0			0
$621$	−24.7770	−	15.9232i	−0.994266	−	0.638976i
$622$		0			0
$623$	7.18909	−	50.0012i	0.288025	−	2.00326i
$624$		0			0
$625$	0.781320	+	5.43420i	0.0312528	+	0.217368i
$626$		0			0
$627$	−18.5767	+	18.0048i	−0.741884	+	0.719042i
$628$		0			0
$629$	9.39442	−	20.5709i	0.374580	−	0.820216i
$630$		0			0
$631$	−6.48529	+	14.2008i	−0.258175	+	0.565325i	−0.993687	−	0.112187i	$-0.964214\pi$
$631$	−6.48529	+	14.2008i	−0.258175	+	0.565325i	0.735512	+	0.677512i	$0.236942\pi$
$632$		0			0
$633$	−11.4634	+	3.36596i	−0.455629	+	0.133785i
$634$		0			0
$635$	46.8792	−	13.7650i	1.86034	−	0.546247i
$636$		0			0
$637$	12.2762	−	14.1675i	0.486401	−	0.561336i
$638$		0			0
$639$	7.57249	+	8.73912i	0.299563	+	0.345714i
$640$		0			0
$641$	−36.0520	−	10.5858i	−1.42397	−	0.418115i	−0.523123	−	0.852257i	$-0.675233\pi$
$641$	−36.0520	−	10.5858i	−1.42397	−	0.418115i	−0.900844	+	0.434143i	$0.857051\pi$
$642$		0			0
$643$	−3.30844	+	2.12621i	−0.130472	+	0.0838493i	−0.604249	−	0.796796i	$-0.706527\pi$
$643$	−3.30844	+	2.12621i	−0.130472	+	0.0838493i	0.473777	+	0.880645i	$0.342890\pi$
$644$		0			0
$645$	39.3959			1.55121
$646$		0			0
$647$	13.4338	+	29.4160i	0.528139	+	1.15646i	0.966265	+	0.257549i	$0.0829149\pi$
$647$	13.4338	+	29.4160i	0.528139	+	1.15646i	−0.438126	+	0.898913i	$0.644358\pi$
$648$		0			0
$649$	1.55374	−	0.312638i	0.0609895	−	0.0122721i
$650$		0			0
$651$	−18.3641	+	21.1933i	−0.719745	+	0.830630i
$652$		0			0
$653$	−17.5810	−	11.2986i	−0.687999	−	0.442150i	0.149375	−	0.988781i	$-0.452274\pi$
$653$	−17.5810	−	11.2986i	−0.687999	−	0.442150i	−0.837374	+	0.546631i	$0.815910\pi$
$654$		0			0
$655$	7.70625	+	8.89348i	0.301108	+	0.347497i
$656$		0			0
$657$	−4.67362	−	3.00355i	−0.182335	−	0.117180i
$658$		0			0
$659$	−6.50750	+	45.2607i	−0.253496	+	1.76311i	0.323375	+	0.946271i	$0.395182\pi$
$659$	−6.50750	+	45.2607i	−0.253496	+	1.76311i	−0.576871	+	0.816835i	$0.695727\pi$
$660$		0			0
$661$	5.72854	+	39.8429i	0.222814	+	1.54971i	0.727320	+	0.686299i	$0.240766\pi$
$661$	5.72854	+	39.8429i	0.222814	+	1.54971i	−0.504505	+	0.863409i	$0.668325\pi$
$662$		0			0
$663$	−8.42338	+	5.41338i	−0.327137	+	0.210238i
$664$		0			0
$665$	−12.3878	−	86.1590i	−0.480378	−	3.34110i
$666$		0			0
$667$	4.10530	+	28.5530i	0.158958	+	1.10558i
$668$		0			0
$669$	23.4414	+	27.0528i	0.906297	+	1.04592i
$670$		0			0
$671$	−17.2945	+	3.47994i	−0.667645	+	0.134342i
$672$		0			0
$673$	14.6494	−	9.41463i	0.564695	−	0.362907i	−0.226934	−	0.973910i	$-0.572870\pi$
$673$	14.6494	−	9.41463i	0.564695	−	0.362907i	0.791628	+	0.611003i	$0.209234\pi$
$674$		0			0
$675$	28.0365	−	32.3559i	1.07913	−	1.24538i
$676$		0			0
$677$	1.20395	−	2.63628i	0.0462715	−	0.101320i	−0.885084	−	0.465430i	$-0.845900\pi$
$677$	1.20395	−	2.63628i	0.0462715	−	0.101320i	0.931356	+	0.364110i	$0.118627\pi$
$678$		0			0
$679$	1.77857	+	12.3703i	0.0682554	+	0.474727i
$680$		0			0
$681$	4.81178	+	10.5363i	0.184388	+	0.403753i
$682$		0			0
$683$	−3.72803	+	8.16324i	−0.142649	+	0.312358i	−0.967449	−	0.253067i	$-0.918561\pi$
$683$	−3.72803	+	8.16324i	−0.142649	+	0.312358i	0.824800	+	0.565425i	$0.191288\pi$
$684$		0			0
$685$	8.47457	−	58.9420i	0.323797	−	2.25206i
$686$		0			0
$687$	39.8029	+	11.6872i	1.51857	+	0.445894i
$688$		0			0
$689$	−5.76331	+	1.69226i	−0.219565	+	0.0644700i
$690$		0			0
$691$	−4.22282	−	2.71384i	−0.160644	−	0.103239i	0.457849	−	0.889030i	$-0.348620\pi$
$691$	−4.22282	−	2.71384i	−0.160644	−	0.103239i	−0.618493	+	0.785791i	$0.712256\pi$
$692$		0			0
$693$	7.98088	+	11.0161i	0.303169	+	0.418466i
$694$		0			0
$695$	20.4041	−	5.99118i	0.773971	−	0.227259i
$696$		0			0
$697$	16.1677	+	18.6586i	0.612397	+	0.706743i
$698$		0			0
$699$	34.6027			1.30880
$700$		0			0
$701$	−12.5357	+	14.4670i	−0.473468	+	0.546411i	−0.941373	−	0.337368i	$-0.890463\pi$
$701$	−12.5357	+	14.4670i	−0.473468	+	0.546411i	0.467905	+	0.883779i	$0.345009\pi$
$702$		0			0
$703$	20.1275	+	12.9352i	0.759125	+	0.487860i
$704$		0			0
$705$	1.53500	−	0.986487i	0.0578116	−	0.0371533i
$706$		0			0
$707$	14.6544	+	16.9121i	0.551136	+	0.636045i
$708$		0			0
$709$	21.0614	−	24.3062i	0.790979	−	0.912838i	−0.206872	−	0.978368i	$-0.566328\pi$
$709$	21.0614	−	24.3062i	0.790979	−	0.912838i	0.997851	+	0.0655300i	$0.0208738\pi$
$710$		0			0
$711$	−1.49727	−	3.27857i	−0.0561520	−	0.122956i
$712$		0			0
$713$	−21.2110	−	6.22812i	−0.794359	−	0.233245i
$714$		0			0
$715$	15.6592	−	3.15091i	0.585623	−	0.117837i
$716$		0			0
$717$	−10.8084			−0.403648
$718$		0			0
$719$	−2.60407	+	1.67353i	−0.0971153	+	0.0624122i	−0.588297	−	0.808645i	$-0.700201\pi$
$719$	−2.60407	+	1.67353i	−0.0971153	+	0.0624122i	0.491182	+	0.871057i	$0.336565\pi$
$720$		0			0
$721$	−29.1933	−	63.9244i	−1.08722	−	2.38067i
$722$		0			0
$723$	6.28950			0.233909
$724$		0			0
$725$	−41.9323			−1.55733
$726$		0			0
$727$	9.80831			0.363770			0.181885	−	0.983320i	$-0.441780\pi$
$727$	9.80831			0.363770			0.181885	+	0.983320i	$0.441780\pi$
$728$		0			0
$729$	29.5142			1.09312
$730$		0			0
$731$	16.1966	+	35.4657i	0.599055	+	1.31175i
$732$		0			0
$733$	25.9016	−	16.6459i	0.956697	−	0.614832i	0.0336148	−	0.999435i	$-0.489298\pi$
$733$	25.9016	−	16.6459i	0.956697	−	0.614832i	0.923082	+	0.384603i	$0.125662\pi$
$734$		0			0
$735$	70.9466			2.61690
$736$		0			0
$737$	43.9346	+	3.83347i	1.61835	+	0.141208i
$738$		0			0
$739$	−29.4391	−	8.64410i	−1.08294	−	0.317979i	−0.308883	−	0.951100i	$-0.599955\pi$
$739$	−29.4391	−	8.64410i	−1.08294	−	0.317979i	−0.774052	+	0.633122i	$0.781773\pi$
$740$		0			0
$741$	−4.40066	−	9.63610i	−0.161662	−	0.353991i
$742$		0			0
$743$	−0.0385046	+	0.0444367i	−0.00141260	+	0.00163023i	−0.756455	−	0.654045i	$-0.773071\pi$
$743$	−0.0385046	+	0.0444367i	−0.00141260	+	0.00163023i	0.755043	+	0.655675i	$0.227616\pi$
$744$		0			0
$745$	48.8166	+	56.3373i	1.78850	+	2.06404i
$746$		0			0
$747$	12.2181	−	7.85211i	0.447038	−	0.287294i
$748$		0			0
$749$	54.3672	+	34.9397i	1.98653	+	1.27667i
$750$		0			0
$751$	13.9887	−	16.1438i	0.510453	−	0.589095i	−0.440761	−	0.897624i	$-0.645291\pi$
$751$	13.9887	−	16.1438i	0.510453	−	0.589095i	0.951215	+	0.308530i	$0.0998369\pi$
$752$		0			0
$753$	32.3160			1.17766
$754$		0			0
$755$	9.55205	+	11.0237i	0.347635	+	0.401192i
$756$		0			0
$757$	−37.1405	+	10.9054i	−1.34989	+	0.396364i	−0.875189	−	0.483781i	$-0.839263\pi$
$757$	−37.1405	+	10.9054i	−1.34989	+	0.396364i	−0.474704	+	0.880145i	$0.657445\pi$
$758$		0			0
$759$	12.3483	−	21.7969i	0.448213	−	0.791179i
$760$		0			0
$761$	−5.71431	−	3.67237i	−0.207144	−	0.133123i	0.432956	−	0.901415i	$-0.357471\pi$
$761$	−5.71431	−	3.67237i	−0.207144	−	0.133123i	−0.640100	+	0.768292i	$0.721107\pi$
$762$		0			0
$763$	−45.0130	+	13.2170i	−1.62958	+	0.478488i
$764$		0			0
$765$	15.5641	+	4.57002i	0.562720	+	0.165230i
$766$		0			0
$767$	−0.0923595	+	0.642374i	−0.00333491	+	0.0231948i
$768$		0			0
$769$	−16.3903	+	35.8898i	−0.591050	+	1.29422i	0.343755	+	0.939059i	$0.388301\pi$
$769$	−16.3903	+	35.8898i	−0.591050	+	1.29422i	−0.934805	+	0.355160i	$0.884426\pi$
$770$		0			0
$771$	−0.292552	−	0.640599i	−0.0105360	−	0.0230706i
$772$		0			0
$773$	2.80417	+	19.5034i	0.100859	+	0.701489i	0.976024	+	0.217664i	$0.0698438\pi$
$773$	2.80417	+	19.5034i	0.100859	+	0.701489i	−0.875165	+	0.483825i	$0.839247\pi$
$774$		0			0
$775$	13.3492	−	29.2307i	0.479518	−	1.05000i
$776$		0			0
$777$	−19.2464	+	22.2115i	−0.690461	+	0.796835i
$778$		0			0
$779$	−21.9737	+	14.1216i	−0.787290	+	0.505960i
$780$		0			0
$781$	−30.6250	+	29.6821i	−1.09585	+	1.06211i
$782$		0			0
$783$	−20.4861	−	23.6422i	−0.732113	−	0.844903i
$784$		0			0
$785$	−7.08759	−	49.2953i	−0.252967	−	1.75942i
$786$		0			0
$787$	−2.67718	−	18.6202i	−0.0954312	−	0.663738i	−0.980244	−	0.197792i	$-0.936623\pi$
$787$	−2.67718	−	18.6202i	−0.0954312	−	0.663738i	0.884813	−	0.465947i	$-0.154286\pi$
$788$		0			0
$789$	0.0397221	−	0.0255279i	0.00141415	−	0.000908816i
$790$		0			0
$791$	0.511508	+	3.55762i	0.0181871	+	0.126494i
$792$		0			0
$793$	1.02804	−	7.15020i	0.0365069	−	0.253911i
$794$		0			0
$795$	−19.1238	−	12.2901i	−0.678251	−	0.435885i
$796$		0			0
$797$	−1.39999	−	1.61568i	−0.0495903	−	0.0572303i	0.730412	−	0.683006i	$-0.239328\pi$
$797$	−1.39999	−	1.61568i	−0.0495903	−	0.0572303i	−0.780003	+	0.625776i	$0.784782\pi$
$798$		0			0
$799$	1.51915	+	0.976300i	0.0537437	+	0.0345390i
$800$		0			0
$801$	−6.52209	+	7.52689i	−0.230447	+	0.265950i
$802$		0			0
$803$	10.0998	−	17.8280i	0.356413	−	0.629135i
$804$		0			0
$805$	35.0157	+	76.6737i	1.23414	+	2.70239i
$806$		0			0
$807$	−39.0775			−1.37559
$808$		0			0
$809$	26.5814	−	17.0828i	0.934552	−	0.600600i	0.0177071	−	0.999843i	$-0.494363\pi$
$809$	26.5814	−	17.0828i	0.934552	−	0.600600i	0.916845	+	0.399243i	$0.130727\pi$
$810$		0			0
$811$	−2.26564	−	0.665251i	−0.0795573	−	0.0233601i	0.241712	−	0.970348i	$-0.422291\pi$
$811$	−2.26564	−	0.665251i	−0.0795573	−	0.0233601i	−0.321269	+	0.946988i	$0.604109\pi$
$812$		0			0
$813$	−21.7473	−	25.0977i	−0.762711	−	0.880216i
$814$		0			0
$815$	23.9410	−	27.6294i	0.838617	−	0.967815i
$816$		0			0
$817$	−39.5786	+	11.6213i	−1.38468	+	0.406579i
$818$		0			0
$819$	−5.34466	+	1.56933i	−0.186757	+	0.0548369i
$820$		0			0
$821$	−4.94937	+	10.8376i	−0.172734	+	0.378235i	−0.976123	−	0.217220i	$-0.930301\pi$
$821$	−4.94937	+	10.8376i	−0.172734	+	0.378235i	0.803389	+	0.595455i	$0.203028\pi$
$822$		0			0
$823$	−1.16077	+	2.54172i	−0.0404617	+	0.0885989i	−0.928784	−	0.370623i	$-0.879144\pi$
$823$	−1.16077	+	2.54172i	−0.0404617	+	0.0885989i	0.888322	+	0.459222i	$0.151872\pi$
$824$		0			0
$825$	28.8077	+	22.2763i	1.00295	+	0.775561i
$826$		0			0
$827$	−0.567066	−	3.94403i	−0.0197188	−	0.137147i	0.977584	−	0.210547i	$-0.0675244\pi$
$827$	−0.567066	−	3.94403i	−0.0197188	−	0.137147i	−0.997303	+	0.0733992i	$0.976615\pi$
$828$		0			0
$829$	0.0308833	−	0.214798i	0.00107262	−	0.00746024i	−0.989278	−	0.146044i	$-0.953346\pi$
$829$	0.0308833	−	0.214798i	0.00107262	−	0.00746024i	0.990351	+	0.138584i	$0.0442550\pi$
$830$		0			0
$831$	19.3633	+	12.4441i	0.671706	+	0.431679i
$832$		0			0
$833$	29.1679	+	63.8688i	1.01061	+	2.21292i
$834$		0			0
$835$	−27.5233	−	8.08158i	−0.952484	−	0.279675i
$836$		0			0
$837$	23.0026	−	6.75417i	0.795086	−	0.233458i
$838$		0			0
$839$	2.09598	−	4.58956i	0.0723613	−	0.158449i	−0.869995	−	0.493061i	$-0.835878\pi$
$839$	2.09598	−	4.58956i	0.0723613	−	0.158449i	0.942356	+	0.334612i	$0.108605\pi$
$840$		0			0
$841$	−0.233344	+	1.62294i	−0.00804635	+	0.0559636i
$842$		0			0
$843$	20.4648	+	6.00899i	0.704844	+	0.206961i
$844$		0			0
$845$	5.62993	−	39.1570i	0.193675	−	1.34704i
$846$		0			0
$847$	−38.9259	+	31.6540i	−1.33751	+	1.08764i
$848$		0			0
$849$	4.14954	−	28.8607i	0.142412	−	0.990496i
$850$		0			0
$851$	−22.2301	−	6.52736i	−0.762040	−	0.223755i
$852$		0			0
$853$	3.52201	−	24.4961i	0.120591	−	0.838730i	−0.836298	−	0.548276i	$-0.815284\pi$
$853$	3.52201	−	24.4961i	0.120591	−	0.838730i	0.956889	−	0.290455i	$-0.0938065\pi$
$854$		0			0
$855$	−7.12919	+	15.6107i	−0.243813	+	0.533876i
$856$		0			0
$857$	−40.2698	+	11.8243i	−1.37559	+	0.403909i	−0.884232	−	0.467049i	$-0.845317\pi$
$857$	−40.2698	+	11.8243i	−1.37559	+	0.403909i	−0.491357	+	0.870958i	$0.663499\pi$
$858$		0			0
$859$	32.4862	+	9.53881i	1.10842	+	0.325460i	0.784191	−	0.620520i	$-0.213078\pi$
$859$	32.4862	+	9.53881i	1.10842	+	0.325460i	0.324225	+	0.945980i	$0.394897\pi$
$860$		0			0
$861$	−13.3289	−	29.1863i	−0.454249	−	0.994667i
$862$		0			0
$863$	19.3819	+	12.4560i	0.659769	+	0.424008i	0.827224	−	0.561872i	$-0.189919\pi$
$863$	19.3819	+	12.4560i	0.659769	+	0.424008i	−0.167455	+	0.985880i	$0.553555\pi$
$864$		0			0
$865$	−4.43195	+	30.8249i	−0.150691	+	1.04808i
$866$		0			0
$867$	−1.83065	−	12.7325i	−0.0621722	−	0.432417i
$868$		0			0
$869$	11.7655	−	6.18765i	0.399116	−	0.209902i
$870$		0			0
$871$	−7.50189	+	16.4269i	−0.254192	+	0.556603i
$872$		0			0
$873$	1.02357	−	2.24131i	0.0346426	−	0.0758568i
$874$		0			0
$875$	−39.9685	+	11.7358i	−1.35118	+	0.396743i
$876$		0			0
$877$	4.27904	−	1.25644i	0.144493	−	0.0424270i	−0.208686	−	0.977983i	$-0.566919\pi$
$877$	4.27904	−	1.25644i	0.144493	−	0.0424270i	0.353179	+	0.935556i	$0.385101\pi$
$878$		0			0
$879$	5.05512	−	5.83392i	0.170505	−	0.196773i
$880$		0			0
$881$	−16.6032	−	19.1611i	−0.559376	−	0.645555i	0.403665	−	0.914907i	$-0.367736\pi$
$881$	−16.6032	−	19.1611i	−0.559376	−	0.645555i	−0.963042	+	0.269352i	$0.913191\pi$
$882$		0			0
$883$	−25.0574	−	7.35752i	−0.843249	−	0.247600i	−0.168550	−	0.985693i	$-0.553908\pi$
$883$	−25.0574	−	7.35752i	−0.843249	−	0.247600i	−0.674699	+	0.738093i	$0.735727\pi$
$884$		0			0
$885$	−2.06621	+	1.32787i	−0.0694550	+	0.0446360i
$886$		0			0
$887$	2.78739			0.0935913			0.0467957	−	0.998904i	$-0.485099\pi$
$887$	2.78739			0.0935913			0.0467957	+	0.998904i	$0.485099\pi$
$888$		0			0
$889$	−26.1051	−	57.1622i	−0.875537	−	1.91716i
$890$		0			0
$891$	1.01554	+	18.1919i	0.0340219	+	0.609452i
$892$		0			0
$893$	−1.25112	+	1.44387i	−0.0418672	+	0.0483173i
$894$		0			0
$895$	49.5506	+	31.8442i	1.65629	+	1.06444i
$896$		0			0
$897$	6.71771	+	7.75265i	0.224298	+	0.258853i
$898$		0			0
$899$	−19.7531	−	12.6945i	−0.658803	−	0.423387i
$900$		0			0
$901$	3.20176	−	22.2687i	0.106666	−	0.741879i
$902$		0			0
$903$	−7.21118	−	50.1549i	−0.239973	−	1.66905i
$904$		0			0
$905$	−40.0816	+	25.7588i	−1.33236	+	0.856253i
$906$		0			0
$907$	−0.00740593	−	0.0515094i	−0.000245910	−	0.00171034i	0.989698	−	0.143170i	$-0.0457296\pi$
$907$	−0.00740593	−	0.0515094i	−0.000245910	−	0.00171034i	−0.989944	+	0.141460i	$0.954820\pi$
$908$		0			0
$909$	−0.627890	−	4.36707i	−0.0208258	−	0.144847i
$910$		0			0
$911$	−7.64070	−	8.81784i	−0.253148	−	0.292148i	0.614925	−	0.788586i	$-0.289186\pi$
$911$	−7.64070	−	8.81784i	−0.253148	−	0.292148i	−0.868072	+	0.496438i	$0.834641\pi$
$912$		0			0
$913$	31.4269	+	43.3789i	1.04008	+	1.43563i
$914$		0			0
$915$	22.9988	−	14.7804i	0.760316	−	0.488625i
$916$		0			0
$917$	9.91169	−	11.4387i	0.327313	−	0.377739i
$918$		0			0
$919$	21.5028	−	47.0845i	0.709311	−	1.55317i	−0.118994	−	0.992895i	$-0.537967\pi$
$919$	21.5028	−	47.0845i	0.709311	−	1.55317i	0.828304	−	0.560278i	$-0.189306\pi$
$920$		0			0
$921$	5.61093	+	39.0248i	0.184886	+	1.28591i
$922$		0			0
$923$	−7.25478	−	15.8857i	−0.238794	−	0.522886i
$924$		0			0
$925$	13.9906	−	30.6352i	0.460008	−	1.00728i
$926$		0			0
$927$	−1.97181	+	13.7142i	−0.0647627	+	0.450435i
$928$		0			0
$929$	−14.5006	−	4.25777i	−0.475750	−	0.139693i	0.0350622	−	0.999385i	$-0.488837\pi$
$929$	−14.5006	−	4.25777i	−0.475750	−	0.139693i	−0.510812	+	0.859692i	$0.670655\pi$
$930$		0			0
$931$	−71.2757	+	20.9284i	−2.33597	+	0.685901i
$932$		0			0
$933$	27.1695	+	17.4608i	0.889489	+	0.571640i
$934$		0			0
$935$	−13.6295	+	58.2539i	−0.445733	+	1.90511i
$936$		0			0
$937$	21.2548	−	6.24098i	0.694365	−	0.203884i	0.0845398	−	0.996420i	$-0.473058\pi$
$937$	21.2548	−	6.24098i	0.694365	−	0.203884i	0.609825	+	0.792536i	$0.291240\pi$
$938$		0			0
$939$	33.5040	+	38.6657i	1.09336	+	1.26181i
$940$		0			0
$941$	−3.66227			−0.119387			−0.0596933	−	0.998217i	$-0.519012\pi$
$941$	−3.66227			−0.119387			−0.0596933	+	0.998217i	$0.519012\pi$
$942$		0			0
$943$	16.5639	−	19.1157i	0.539394	−	0.622494i
$944$		0			0
$945$	−76.8993	−	49.4202i	−2.50154	−	1.60764i
$946$		0			0
$947$	14.0482	−	9.02824i	0.456506	−	0.293378i	−0.292107	−	0.956385i	$-0.594357\pi$
$947$	14.0482	−	9.02824i	0.456506	−	0.293378i	0.748613	+	0.663007i	$0.230720\pi$
$948$		0			0
$949$	5.49449	+	6.34098i	0.178359	+	0.205837i
$950$		0			0
$951$	−32.8788	+	37.9441i	−1.06617	+	1.23042i
$952$		0			0
$953$	6.03048	+	13.2049i	0.195346	+	0.427749i	0.981804	−	0.189895i	$-0.0608147\pi$
$953$	6.03048	+	13.2049i	0.195346	+	0.427749i	−0.786458	+	0.617644i	$0.788087\pi$
$954$		0			0
$955$	2.26872	+	0.666155i	0.0734140	+	0.0215563i
$956$		0			0
$957$	19.1071	−	18.5188i	0.617645	−	0.598629i
$958$		0			0
$959$	−76.5901			−2.47322
$960$		0			0
$961$	−10.9411	+	7.03145i	−0.352940	+	0.226821i
$962$		0			0
$963$	−5.29305	−	11.5902i	−0.170566	−	0.373488i
$964$		0			0
$965$	−14.6418			−0.471337
$966$		0			0
$967$	13.5906			0.437045			0.218522	−	0.975832i	$-0.429876\pi$
$967$	13.5906			0.437045			0.218522	+	0.975832i	$0.429876\pi$
$968$		0			0
$969$	39.6775			1.27462
$970$		0			0
$971$	24.6775			0.791937			0.395969	−	0.918264i	$-0.370409\pi$
$971$	24.6775			0.791937			0.395969	+	0.918264i	$0.370409\pi$
$972$		0			0
$973$	−11.3622	−	24.8798i	−0.364256	−	0.797608i
$974$		0			0
$975$	−12.5445	+	8.06185i	−0.401745	+	0.258186i
$976$		0			0
$977$	−30.4196			−0.973210			−0.486605	−	0.873622i	$-0.661765\pi$
$977$	−30.4196			−0.973210			−0.486605	+	0.873622i	$0.661765\pi$
$978$		0			0
$979$	−29.0584	−	22.4702i	−0.928710	−	0.718150i
$980$		0			0
$981$	8.87466	+	2.60583i	0.283346	+	0.0831979i
$982$		0			0
$983$	−4.00840	−	8.77718i	−0.127848	−	0.279949i	0.834874	−	0.550442i	$-0.185541\pi$
$983$	−4.00840	−	8.77718i	−0.127848	−	0.279949i	−0.962722	+	0.270493i	$0.912813\pi$
$984$		0			0
$985$	5.26204	−	6.07271i	0.167662	−	0.193493i
$986$		0			0
$987$	−1.53687	−	1.77364i	−0.0489190	−	0.0564556i
$988$		0			0
$989$	33.6034	−	21.5956i	1.06852	−	0.686699i
$990$		0			0
$991$	−5.33082	−	3.42591i	−0.169339	−	0.108828i	0.453226	−	0.891396i	$-0.350273\pi$
$991$	−5.33082	−	3.42591i	−0.169339	−	0.108828i	−0.622565	+	0.782568i	$0.713909\pi$
$992$		0			0
$993$	−32.3559	+	37.3406i	−1.02678	+	1.18497i
$994$		0			0
$995$	−16.1997			−0.513565
$996$		0			0
$997$	−19.9305	−	23.0010i	−0.631205	−	0.728449i	0.346589	−	0.938017i	$-0.387340\pi$
$997$	−19.9305	−	23.0010i	−0.631205	−	0.728449i	−0.977794	+	0.209568i	$0.932794\pi$
$998$		0			0
$999$	24.1078	−	7.07869i	0.762737	−	0.223960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.i.a.89.9	✓	110
121.34	even	11	inner	484.2.i.a.397.9	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
484.2.i.a.89.9	✓	110	1.1	even	1	trivial
484.2.i.a.397.9	yes	110	121.34	even	11	inner

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+1.44940 q^{3} +(1.47314 + 3.22572i) q^{5} +(3.83701 - 2.46590i) q^{7} -0.899249 q^{9} +(-0.184859 - 3.31147i) q^{11} +(1.30309 + 0.382621i) q^{13} +(2.13516 + 4.67535i) q^{15} +(-3.33111 + 3.84431i) q^{17} +(-3.52424 - 4.06719i) q^{19} +(5.56135 - 3.57406i) q^{21} +(4.38409 + 2.81749i) q^{23} +(-4.96085 + 5.72512i) q^{25} -5.65156 q^{27} +(3.62486 + 4.18331i) q^{29} +(-4.07013 + 1.19510i) q^{31} +(-0.267934 - 4.79963i) q^{33} +(13.6067 + 8.74453i) q^{35} +(-4.26569 + 1.25252i) q^{37} +(1.88869 + 0.554570i) q^{39} +(0.690733 - 4.80415i) q^{41} +(3.18409 - 6.97218i) q^{43} +(-1.32472 - 2.90073i) q^{45} +(-0.0505224 - 0.351391i) q^{47} +(5.73410 - 12.5559i) q^{49} +(-4.82810 + 5.57193i) q^{51} +(-3.72070 + 2.39115i) q^{53} +(10.4096 - 5.47455i) q^{55} +(-5.10802 - 5.89497i) q^{57} +(0.0680064 + 0.472995i) q^{59} +(-0.756971 - 5.26485i) q^{61} +(-3.45043 + 2.21746i) q^{63} +(0.685399 + 4.76705i) q^{65} +(-1.89237 + 13.1618i) q^{67} +(6.35429 + 4.08366i) q^{69} +(-8.42091 - 9.71825i) q^{71} +(5.19725 + 3.34007i) q^{73} +(-7.19024 + 8.29797i) q^{75} +(-8.87505 - 12.2503i) q^{77} +(1.66502 + 3.64589i) q^{79} -5.49360 q^{81} +(-13.5870 + 8.73186i) q^{83} +(-17.3079 - 5.08205i) q^{85} +(5.25385 + 6.06327i) q^{87} +(7.25282 - 8.37020i) q^{89} +(5.94347 - 1.74516i) q^{91} +(-5.89924 + 1.73217i) q^{93} +(7.92793 - 17.3597i) q^{95} +(-1.13825 + 2.49242i) q^{97} +(0.166234 + 2.97784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 2 q^{3} + 2 q^{5} - 2 q^{7} + 112 q^{9} - 10 q^{11} - 29 q^{13} - 18 q^{15} - 6 q^{17} - 8 q^{19} - 2 q^{21} + 4 q^{23} - 17 q^{25} + 4 q^{27} - 28 q^{31} + q^{33} + 6 q^{35} - 31 q^{37} + 4 q^{39}+ \cdots - 57 q^{99}+O(q^{100}) \) 110 * q - 2 * q^3 + 2 * q^5 - 2 * q^7 + 112 * q^9 - 10 * q^11 - 29 * q^13 - 18 * q^15 - 6 * q^17 - 8 * q^19 - 2 * q^21 + 4 * q^23 - 17 * q^25 + 4 * q^27 - 28 * q^31 + q^33 + 6 * q^35 - 31 * q^37 + 4 * q^39 + 10 * q^43 - 8 * q^45 + 2 * q^47 - 49 * q^49 + 115 * q^51 + 72 * q^53 + 41 * q^55 + 3 * q^57 - 6 * q^59 + 4 * q^61 - 51 * q^63 - 45 * q^65 - 51 * q^67 + 4 * q^69 + 26 * q^71 - 18 * q^73 + 46 * q^77 - 24 * q^79 + 110 * q^81 - 6 * q^83 - 92 * q^85 - 7 * q^89 - 91 * q^91 - 37 * q^93 - 64 * q^95 - 31 * q^97 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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