LMFDB - Embedded newform 760.2.cg.a.169.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,2,Mod(9,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 9, 8]))

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

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

chi := DirichletCharacter("760.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.cg (of order $18$, degree $6$, 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:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$30$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.18
Character	$\chi$	$=$	760.169
Dual form			760.2.cg.a.9.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.248287 - 0.295897i) q^{3} +(1.42231 - 1.72541i) q^{5} +(1.75773 - 1.01483i) q^{7} +(0.495036 + 2.80749i) q^{9} +O(q^{10})$	\(q+(0.248287 - 0.295897i) q^{3} +(1.42231 - 1.72541i) q^{5} +(1.75773 - 1.01483i) q^{7} +(0.495036 + 2.80749i) q^{9} +(-2.49808 + 4.32679i) q^{11} +(3.32037 + 3.95706i) q^{13} +(-0.157403 - 0.849254i) q^{15} +(2.75531 + 0.485835i) q^{17} +(2.11103 + 3.81360i) q^{19} +(0.136138 - 0.772075i) q^{21} +(2.36723 - 6.50391i) q^{23} +(-0.954078 - 4.90813i) q^{25} +(1.95719 + 1.12998i) q^{27} +(-0.923331 - 5.23647i) q^{29} +(-3.07542 - 5.32678i) q^{31} +(0.660045 + 1.81346i) q^{33} +(0.749044 - 4.47620i) q^{35} +0.614404i q^{37} +1.99529 q^{39} +(3.88992 + 3.26403i) q^{41} +(-1.00644 - 2.76516i) q^{43} +(5.54816 + 3.13897i) q^{45} +(-10.7185 + 1.88996i) q^{47} +(-1.44026 + 2.49460i) q^{49} +(0.827865 - 0.694661i) q^{51} +(4.43998 - 12.1987i) q^{53} +(3.91246 + 10.4642i) q^{55} +(1.65257 + 0.322219i) q^{57} +(0.214362 - 1.21571i) q^{59} +(11.9813 + 4.36085i) q^{61} +(3.71925 + 4.43243i) q^{63} +(11.5502 - 0.100835i) q^{65} +(-0.339144 + 0.0598002i) q^{67} +(-1.33673 - 2.31529i) q^{69} +(-12.3969 + 4.51209i) q^{71} +(-2.77452 + 3.30654i) q^{73} +(-1.68919 - 0.936316i) q^{75} +10.1404i q^{77} +(-1.12187 - 0.941358i) q^{79} +(-7.21632 + 2.62653i) q^{81} +(6.12427 - 3.53585i) q^{83} +(4.75717 - 4.06303i) q^{85} +(-1.77871 - 1.02694i) q^{87} +(-2.07556 + 1.74160i) q^{89} +(9.85205 + 3.58585i) q^{91} +(-2.33976 - 0.412563i) q^{93} +(9.58256 + 1.78172i) q^{95} +(-10.4928 - 1.85016i) q^{97} +(-13.3841 - 4.87140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q+O(q^{10}) $ 180 * q	$ 180 q - 12 q^{15} + 12 q^{25} + 24 q^{35} - 18 q^{41} + 18 q^{45} + 90 q^{49} + 36 q^{51} - 36 q^{55} - 12 q^{59} + 48 q^{69} - 24 q^{71} - 156 q^{79} + 24 q^{81} + 12 q^{85} - 36 q^{89} + 36 q^{91} + 78 q^{95} + 42 q^{99}+O(q^{100}) $ 180 * q - 12 * q^15 + 12 * q^25 + 24 * q^35 - 18 * q^41 + 18 * q^45 + 90 * q^49 + 36 * q^51 - 36 * q^55 - 12 * q^59 + 48 * q^69 - 24 * q^71 - 156 * q^79 + 24 * q^81 + 12 * q^85 - 36 * q^89 + 36 * q^91 + 78 * q^95 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$-1$

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
$3$	0.248287	−	0.295897i	0.143349	−	0.170836i	−0.689593	−	0.724197i	$-0.742211\pi$
$3$	0.248287	−	0.295897i	0.143349	−	0.170836i	0.832942	+	0.553361i	$0.186655\pi$
$4$		0			0
$5$	1.42231	−	1.72541i	0.636076	−	0.771627i
$5$	1.42231	−	1.72541i	0.636076	−	0.771627i
$6$		0			0
$7$	1.75773	−	1.01483i	0.664360	−	0.383568i	−0.129576	−	0.991569i	$-0.541362\pi$
$7$	1.75773	−	1.01483i	0.664360	−	0.383568i	0.793936	+	0.608001i	$0.208028\pi$
$8$		0			0
$9$	0.495036	+	2.80749i	0.165012	+	0.935829i
$10$		0			0
$11$	−2.49808	+	4.32679i	−0.753198	+	1.30458i	0.193067	+	0.981186i	$0.438156\pi$
$11$	−2.49808	+	4.32679i	−0.753198	+	1.30458i	−0.946265	+	0.323392i	$0.895177\pi$
$12$		0			0
$13$	3.32037	+	3.95706i	0.920905	+	1.09749i	0.994963	+	0.100238i	$0.0319605\pi$
$13$	3.32037	+	3.95706i	0.920905	+	1.09749i	−0.0740581	+	0.997254i	$0.523595\pi$
$14$		0			0
$15$	−0.157403	−	0.849254i	−0.0406412	−	0.219276i
$16$		0			0
$17$	2.75531	+	0.485835i	0.668261	+	0.117832i	0.497478	−	0.867476i	$-0.334259\pi$
$17$	2.75531	+	0.485835i	0.668261	+	0.117832i	0.170782	+	0.985309i	$0.445370\pi$
$18$		0			0
$19$	2.11103	+	3.81360i	0.484304	+	0.874900i
$19$	2.11103	+	3.81360i	0.484304	+	0.874900i
$20$		0			0
$21$	0.136138	−	0.772075i	0.0297077	−	0.168481i
$22$		0			0
$23$	2.36723	−	6.50391i	0.493601	−	1.35616i	−0.403761	−	0.914864i	$-0.632297\pi$
$23$	2.36723	−	6.50391i	0.493601	−	1.35616i	0.897362	−	0.441294i	$-0.145480\pi$
$24$		0			0
$25$	−0.954078	−	4.90813i	−0.190816	−	0.981626i
$26$		0			0
$27$	1.95719	+	1.12998i	0.376661	+	0.217465i
$28$		0			0
$29$	−0.923331	−	5.23647i	−0.171458	−	0.972388i	−0.942153	−	0.335183i	$-0.891202\pi$
$29$	−0.923331	−	5.23647i	−0.171458	−	0.972388i	0.770695	−	0.637205i	$-0.219909\pi$
$30$		0			0
$31$	−3.07542	−	5.32678i	−0.552361	−	0.956717i	−0.998104	−	0.0615562i	$-0.980394\pi$
$31$	−3.07542	−	5.32678i	−0.552361	−	0.956717i	0.445743	−	0.895161i	$-0.352940\pi$
$32$		0			0
$33$	0.660045	+	1.81346i	0.114899	+	0.315683i
$34$		0			0
$35$	0.749044	−	4.47620i	0.126612	−	0.756616i
$36$		0			0
$37$			0.614404i			0.101007i	0.998724	+	0.0505037i	$0.0160827\pi$
$37$			0.614404i			0.101007i	−0.998724	+	0.0505037i	$0.983917\pi$
$38$		0			0
$39$	1.99529			0.319502
$40$		0			0
$41$	3.88992	+	3.26403i	0.607503	+	0.509756i	0.893847	−	0.448371i	$-0.147996\pi$
$41$	3.88992	+	3.26403i	0.607503	+	0.509756i	−0.286344	+	0.958127i	$0.592440\pi$
$42$		0			0
$43$	−1.00644	−	2.76516i	−0.153480	−	0.421683i	0.838994	−	0.544141i	$-0.183144\pi$
$43$	−1.00644	−	2.76516i	−0.153480	−	0.421683i	−0.992474	+	0.122458i	$0.960922\pi$
$44$		0			0
$45$	5.54816	+	3.13897i	0.827071	+	0.467931i
$46$		0			0
$47$	−10.7185	+	1.88996i	−1.56346	+	0.275679i	−0.887340	−	0.461116i	$-0.847449\pi$
$47$	−10.7185	+	1.88996i	−1.56346	+	0.275679i	−0.676115	+	0.736796i	$0.736338\pi$
$48$		0			0
$49$	−1.44026	+	2.49460i	−0.205751	+	0.356371i
$50$		0			0
$51$	0.827865	−	0.694661i	0.115924	−	0.0972720i
$52$		0			0
$53$	4.43998	−	12.1987i	0.609878	−	1.67562i	−0.120611	−	0.992700i	$-0.538485\pi$
$53$	4.43998	−	12.1987i	0.609878	−	1.67562i	0.730488	−	0.682925i	$-0.239292\pi$
$54$		0			0
$55$	3.91246	+	10.4642i	0.527556	+	1.41100i
$56$		0			0
$57$	1.65257	+	0.322219i	0.218889	+	0.0426790i
$58$		0			0
$59$	0.214362	−	1.21571i	0.0279076	−	0.158272i	−0.967669	−	0.252222i	$-0.918839\pi$
$59$	0.214362	−	1.21571i	0.0279076	−	0.158272i	0.995577	+	0.0939508i	$0.0299496\pi$
$60$		0			0
$61$	11.9813	+	4.36085i	1.53405	+	0.558350i	0.964610	−	0.263680i	$-0.0849364\pi$
$61$	11.9813	+	4.36085i	1.53405	+	0.558350i	0.569444	+	0.822030i	$0.307159\pi$
$62$		0			0
$63$	3.71925	+	4.43243i	0.468582	+	0.558434i
$64$		0			0
$65$	11.5502	−	0.100835i	1.43262	−	0.0125070i
$66$		0			0
$67$	−0.339144	+	0.0598002i	−0.0414330	+	0.00730575i	−0.194326	−	0.980937i	$-0.562252\pi$
$67$	−0.339144	+	0.0598002i	−0.0414330	+	0.00730575i	0.152893	+	0.988243i	$0.451141\pi$
$68$		0			0
$69$	−1.33673	−	2.31529i	−0.160924	−	0.278728i
$70$		0			0
$71$	−12.3969	+	4.51209i	−1.47124	+	0.535487i	−0.948436	−	0.316967i	$-0.897335\pi$
$71$	−12.3969	+	4.51209i	−1.47124	+	0.535487i	−0.522802	+	0.852454i	$0.675113\pi$
$72$		0			0
$73$	−2.77452	+	3.30654i	−0.324733	+	0.387001i	−0.903569	−	0.428442i	$-0.859063\pi$
$73$	−2.77452	+	3.30654i	−0.324733	+	0.387001i	0.578836	+	0.815444i	$0.303507\pi$
$74$		0			0
$75$	−1.68919	−	0.936316i	−0.195050	−	0.108116i
$76$		0			0
$77$			10.1404i			1.15561i
$78$		0			0
$79$	−1.12187	−	0.941358i	−0.126220	−	0.105911i	0.577493	−	0.816396i	$-0.304031\pi$
$79$	−1.12187	−	0.941358i	−0.126220	−	0.105911i	−0.703713	+	0.710485i	$0.748476\pi$
$80$		0			0
$81$	−7.21632	+	2.62653i	−0.801813	+	0.291836i
$82$		0			0
$83$	6.12427	−	3.53585i	0.672226	−	0.388110i	−0.124694	−	0.992195i	$-0.539795\pi$
$83$	6.12427	−	3.53585i	0.672226	−	0.388110i	0.796920	+	0.604086i	$0.206461\pi$
$84$		0			0
$85$	4.75717	−	4.06303i	0.515987	−	0.440697i
$86$		0			0
$87$	−1.77871	−	1.02694i	−0.190697	−	0.110099i
$88$		0			0
$89$	−2.07556	+	1.74160i	−0.220009	+	0.184609i	−0.746130	−	0.665800i	$-0.768090\pi$
$89$	−2.07556	+	1.74160i	−0.220009	+	0.184609i	0.526121	+	0.850410i	$0.323646\pi$
$90$		0			0
$91$	9.85205	+	3.58585i	1.03278	+	0.375900i
$92$		0			0
$93$	−2.33976	−	0.412563i	−0.242622	−	0.0427808i
$94$		0			0
$95$	9.58256	+	1.78172i	0.983150	+	0.182801i
$96$		0			0
$97$	−10.4928	−	1.85016i	−1.06538	−	0.187855i	−0.386638	−	0.922232i	$-0.626364\pi$
$97$	−10.4928	−	1.85016i	−1.06538	−	0.187855i	−0.678742	+	0.734377i	$0.737475\pi$
$98$		0			0
$99$	−13.3841	−	4.87140i	−1.34515	−	0.489594i
$100$		0			0
$101$	11.0280	−	9.25358i	1.09733	−	0.920765i	0.100083	−	0.994979i	$-0.468089\pi$
$101$	11.0280	−	9.25358i	1.09733	−	0.920765i	0.997242	+	0.0742138i	$0.0236447\pi$
$102$		0			0
$103$	−5.65583	−	3.26540i	−0.557286	−	0.321749i	0.194769	−	0.980849i	$-0.437604\pi$
$103$	−5.65583	−	3.26540i	−0.557286	−	0.321749i	−0.752055	+	0.659100i	$0.770937\pi$
$104$		0			0
$105$	−1.13852	−	1.33302i	−0.111108	−	0.130090i
$106$		0			0
$107$	−16.7052	+	9.64476i	−1.61495	+	0.932394i	−0.626756	+	0.779216i	$0.715618\pi$
$107$	−16.7052	+	9.64476i	−1.61495	+	0.932394i	−0.988199	+	0.153179i	$0.951049\pi$
$108$		0			0
$109$	−2.61682	+	0.952444i	−0.250646	+	0.0912276i	−0.464288	−	0.885684i	$-0.653690\pi$
$109$	−2.61682	+	0.952444i	−0.250646	+	0.0912276i	0.213642	+	0.976912i	$0.431467\pi$
$110$		0			0
$111$	0.181800	+	0.152548i	0.0172557	+	0.0144793i
$112$		0			0
$113$		−	4.77780i		−	0.449458i	−0.974421	−	0.224729i	$-0.927850\pi$
$113$		−	4.77780i		−	0.449458i	0.974421	−	0.224729i	$-0.0721497\pi$
$114$		0			0
$115$	−7.85498	−	13.3350i	−0.732480	−	1.24350i
$116$		0			0
$117$	−9.46571	+	11.2808i	−0.875105	+	1.04291i
$118$		0			0
$119$	5.33613	−	1.94219i	0.489162	−	0.178041i
$120$		0			0
$121$	−6.98076	−	12.0910i	−0.634615	−	1.09918i
$122$		0			0
$123$	1.93163	−	0.340599i	0.174169	−	0.0307108i
$124$		0			0
$125$	−9.82553	−	5.33470i	−0.878822	−	0.477150i
$126$		0			0
$127$	3.91649	+	4.66749i	0.347532	+	0.414173i	0.911289	−	0.411768i	$-0.135089\pi$
$127$	3.91649	+	4.66749i	0.347532	+	0.414173i	−0.563756	+	0.825941i	$0.690644\pi$
$128$		0			0
$129$	−1.06809	−	0.388752i	−0.0940399	−	0.0342277i
$130$		0			0
$131$	0.760180	−	4.31119i	0.0664172	−	0.376671i	−0.933423	−	0.358778i	$-0.883193\pi$
$131$	0.760180	−	4.31119i	0.0664172	−	0.376671i	0.999840	−	0.0178921i	$-0.00569555\pi$
$132$		0			0
$133$	7.58077	+	4.56095i	0.657336	+	0.395485i
$134$		0			0
$135$	4.73341	−	1.76977i	0.407387	−	0.152317i
$136$		0			0
$137$	0.0429522	−	0.118010i	0.00366966	−	0.0100823i	−0.937844	−	0.347056i	$-0.887181\pi$
$137$	0.0429522	−	0.118010i	0.00366966	−	0.0100823i	0.941514	+	0.336974i	$0.109403\pi$
$138$		0			0
$139$	1.18573	−	0.994942i	0.100572	−	0.0843899i	−0.591115	−	0.806587i	$-0.701312\pi$
$139$	1.18573	−	0.994942i	0.100572	−	0.0843899i	0.691687	+	0.722197i	$0.256868\pi$
$140$		0			0
$141$	−2.10203	+	3.64083i	−0.177023	+	0.306613i
$142$		0			0
$143$	−25.4159	+	4.48152i	−2.12539	+	0.374763i
$144$		0			0
$145$	−10.3483	−	5.85475i	−0.859381	−	0.486211i
$146$		0			0
$147$	0.380546	+	1.04554i	0.0313869	+	0.0862349i
$148$		0			0
$149$	17.0194	+	14.2810i	1.39428	+	1.16994i	0.963571	+	0.267454i	$0.0861825\pi$
$149$	17.0194	+	14.2810i	1.39428	+	1.16994i	0.430713	+	0.902489i	$0.358262\pi$
$150$		0			0
$151$	7.67004			0.624179			0.312089	−	0.950053i	$-0.398971\pi$
$151$	7.67004			0.624179			0.312089	+	0.950053i	$0.398971\pi$
$152$		0			0
$153$			7.97601i			0.644822i
$154$		0			0
$155$	−13.5651	−	2.26997i	−1.08957	−	0.182328i
$156$		0			0
$157$	5.95316	+	16.3562i	0.475114	+	1.30537i	0.913595	+	0.406625i	$0.133295\pi$
$157$	5.95316	+	16.3562i	0.475114	+	1.30537i	−0.438481	+	0.898741i	$0.644483\pi$
$158$		0			0
$159$	−2.50718	−	4.34256i	−0.198832	−	0.344388i
$160$		0			0
$161$	−2.43939	−	13.8344i	−0.192251	−	1.09031i
$162$		0			0
$163$	5.74508	+	3.31692i	0.449989	+	0.259801i	0.707826	−	0.706387i	$-0.249676\pi$
$163$	5.74508	+	3.31692i	0.449989	+	0.259801i	−0.257837	+	0.966189i	$0.583010\pi$
$164$		0			0
$165$	4.06775	+	1.44045i	0.316674	+	0.112139i
$166$		0			0
$167$	−2.44159	+	6.70822i	−0.188936	+	0.519098i	−0.997605	−	0.0691662i	$-0.977966\pi$
$167$	−2.44159	+	6.70822i	−0.188936	+	0.519098i	0.808669	+	0.588264i	$0.200188\pi$
$168$		0			0
$169$	−2.37607	+	13.4753i	−0.182774	+	1.03657i
$170$		0			0
$171$	−9.66160	+	7.81457i	−0.738841	+	0.597595i
$172$		0			0
$173$	−12.3799	−	2.18291i	−0.941228	−	0.165964i	−0.318077	−	0.948065i	$-0.603037\pi$
$173$	−12.3799	−	2.18291i	−0.941228	−	0.165964i	−0.623152	+	0.782101i	$0.714148\pi$
$174$		0			0
$175$	−6.65791	−	7.65895i	−0.503291	−	0.578962i
$176$		0			0
$177$	−0.306501	−	0.365274i	−0.0230380	−	0.0274557i
$178$		0			0
$179$	9.59664	−	16.6219i	0.717286	−	1.24238i	−0.244785	−	0.969577i	$-0.578717\pi$
$179$	9.59664	−	16.6219i	0.717286	−	1.24238i	0.962071	−	0.272799i	$-0.0879494\pi$
$180$		0			0
$181$	−2.30052	−	13.0469i	−0.170996	−	0.969769i	−0.942664	−	0.333743i	$-0.891688\pi$
$181$	−2.30052	−	13.0469i	−0.170996	−	0.969769i	0.771668	−	0.636026i	$-0.219423\pi$
$182$		0			0
$183$	4.26518	−	2.46250i	0.315291	−	0.182033i
$184$		0			0
$185$	1.06010	+	0.873871i	0.0779399	+	0.0642483i
$186$		0			0
$187$	−8.98508	+	10.7080i	−0.657054	+	0.783047i
$188$		0			0
$189$	4.58694			0.333651
$190$		0			0
$191$	−7.92695			−0.573574			−0.286787	−	0.957994i	$-0.592587\pi$
$191$	−7.92695			−0.573574			−0.286787	+	0.957994i	$0.592587\pi$
$192$		0			0
$193$	9.67275	−	11.5275i	0.696260	−	0.829770i	−0.295838	−	0.955238i	$-0.595599\pi$
$193$	9.67275	−	11.5275i	0.696260	−	0.829770i	0.992098	+	0.125468i	$0.0400432\pi$
$194$		0			0
$195$	2.83792	−	3.44269i	0.203227	−	0.246536i
$196$		0			0
$197$	−22.8011	+	13.1642i	−1.62451	+	0.937913i	−0.638822	+	0.769355i	$0.720578\pi$
$197$	−22.8011	+	13.1642i	−1.62451	+	0.937913i	−0.985692	+	0.168559i	$0.946089\pi$
$198$		0			0
$199$	−0.0152846	−	0.0866835i	−0.00108350	−	0.00614483i	0.984261	−	0.176720i	$-0.0565486\pi$
$199$	−0.0152846	−	0.0866835i	−0.00108350	−	0.00614483i	−0.985345	+	0.170575i	$0.945438\pi$
$200$		0			0
$201$	−0.0665103	+	0.115199i	−0.00469127	+	0.00812552i
$202$		0			0
$203$	−6.93707	−	8.26728i	−0.486887	−	0.580249i
$204$		0			0
$205$	11.1644	−	2.06925i	0.779759	−	0.144522i
$206$		0			0
$207$	19.4315	+	3.42630i	1.35058	+	0.238144i
$208$		0			0
$209$	−21.7742	−	0.392659i	−1.50615	−	0.0271608i
$210$		0			0
$211$	0.921667	−	5.22703i	0.0634502	−	0.359844i	−0.936508	−	0.350647i	$-0.885962\pi$
$211$	0.921667	−	5.22703i	0.0634502	−	0.359844i	0.999958	−	0.00919637i	$-0.00292734\pi$
$212$		0			0
$213$	−1.74287	+	4.78849i	−0.119419	+	0.328102i
$214$		0			0
$215$	−6.20250	−	2.19640i	−0.423007	−	0.149793i
$216$		0			0
$217$	−10.8115	−	6.24203i	−0.733933	−	0.423736i
$218$		0			0
$219$	0.289519	+	1.64194i	0.0195639	+	0.110952i
$220$		0			0
$221$	7.22617	+	12.5161i	0.486085	+	0.841923i
$222$		0			0
$223$	3.27745	+	9.00472i	0.219474	+	0.603000i	0.999748	−	0.0224374i	$-0.00714265\pi$
$223$	3.27745	+	9.00472i	0.219474	+	0.603000i	−0.780274	+	0.625438i	$0.784920\pi$
$224$		0			0
$225$	13.3072	−	5.10826i	0.887148	−	0.340551i
$226$		0			0
$227$		−	25.0428i		−	1.66215i	−0.556162	−	0.831074i	$-0.687727\pi$
$227$		−	25.0428i		−	1.66215i	0.556162	−	0.831074i	$-0.312273\pi$
$228$		0			0
$229$	−15.2215			−1.00587			−0.502933	−	0.864325i	$-0.667746\pi$
$229$	−15.2215			−1.00587			−0.502933	+	0.864325i	$0.667746\pi$
$230$		0			0
$231$	3.00053	+	2.51774i	0.197420	+	0.165655i
$232$		0			0
$233$	−7.01594	−	19.2761i	−0.459629	−	1.26282i	−0.925762	−	0.378106i	$-0.876575\pi$
$233$	−7.01594	−	19.2761i	−0.459629	−	1.26282i	0.466133	−	0.884715i	$-0.345647\pi$
$234$		0			0
$235$	−11.9841	+	21.1819i	−0.781754	+	1.38176i
$236$		0			0
$237$	−0.557090	+	0.0982300i	−0.0361869	+	0.00638073i
$238$		0			0
$239$	3.71465	−	6.43396i	0.240281	−	0.416178i	−0.720513	−	0.693441i	$-0.756094\pi$
$239$	3.71465	−	6.43396i	0.240281	−	0.416178i	0.960794	+	0.277262i	$0.0894272\pi$
$240$		0			0
$241$	−18.0617	+	15.1556i	−1.16346	+	0.976257i	−0.999947	−	0.0102849i	$-0.996726\pi$
$241$	−18.0617	+	15.1556i	−1.16346	+	0.976257i	−0.163510	+	0.986542i	$0.552282\pi$
$242$		0			0
$243$	−3.33340	+	9.15844i	−0.213838	+	0.587514i
$244$		0			0
$245$	2.25571	+	6.03311i	0.144112	+	0.385442i
$246$		0			0
$247$	−8.08125	+	21.0161i	−0.514198	+	1.33722i
$248$		0			0
$249$	0.474330	−	2.69006i	0.0300594	−	0.170475i
$250$		0			0
$251$	19.2048	+	6.98998i	1.21220	+	0.441204i	0.867465	−	0.497498i	$-0.165748\pi$
$251$	19.2048	+	6.98998i	1.21220	+	0.441204i	0.344732	+	0.938701i	$0.387970\pi$
$252$		0			0
$253$	22.2276	+	26.4898i	1.39743	+	1.66540i
$254$		0			0
$255$	−0.0210959	−	2.41643i	−0.00132107	−	0.151323i
$256$		0			0
$257$	4.93687	−	0.870503i	0.307953	−	0.0543005i	−0.0175359	−	0.999846i	$-0.505582\pi$
$257$	4.93687	−	0.870503i	0.307953	−	0.0543005i	0.325489	+	0.945546i	$0.394471\pi$
$258$		0			0
$259$	0.623513	+	1.07996i	0.0387432	+	0.0671052i
$260$		0			0
$261$	14.2442	−	5.18448i	0.881697	−	0.320911i
$262$		0			0
$263$	9.96981	−	11.8816i	0.614765	−	0.732648i	−0.365396	−	0.930852i	$-0.619066\pi$
$263$	9.96981	−	11.8816i	0.614765	−	0.732648i	0.980161	+	0.198204i	$0.0635108\pi$
$264$		0			0
$265$	−14.7328	−	25.0111i	−0.905029	−	1.53642i
$266$		0			0
$267$			1.04657i			0.0640489i
$268$		0			0
$269$	−8.83952	−	7.41724i	−0.538955	−	0.452237i	0.332225	−	0.943200i	$-0.392201\pi$
$269$	−8.83952	−	7.41724i	−0.538955	−	0.452237i	−0.871180	+	0.490963i	$0.836645\pi$
$270$		0			0
$271$	−11.6772	+	4.25016i	−0.709341	+	0.258179i	−0.671394	−	0.741101i	$-0.734304\pi$
$271$	−11.6772	+	4.25016i	−0.709341	+	0.258179i	−0.0379471	+	0.999280i	$0.512082\pi$
$272$		0			0
$273$	3.50718	−	2.02487i	0.212264	−	0.122551i
$274$		0			0
$275$	23.6198	+	8.13278i	1.42433	+	0.490425i
$276$		0			0
$277$	−3.30673	−	1.90914i	−0.198682	−	0.114709i	0.397358	−	0.917663i	$-0.369927\pi$
$277$	−3.30673	−	1.90914i	−0.198682	−	0.114709i	−0.596041	+	0.802954i	$0.703260\pi$
$278$		0			0
$279$	13.4324	−	11.2711i	0.804178	−	0.674786i
$280$		0			0
$281$	−26.4742	−	9.63584i	−1.57932	−	0.574826i	−0.604265	−	0.796784i	$-0.706533\pi$
$281$	−26.4742	−	9.63584i	−1.57932	−	0.574826i	−0.975056	+	0.221958i	$0.928755\pi$
$282$		0			0
$283$	18.2545	+	3.21877i	1.08512	+	0.191336i	0.687478	−	0.726205i	$-0.258718\pi$
$283$	18.2545	+	3.21877i	1.08512	+	0.191336i	0.397641	+	0.917541i	$0.369829\pi$
$284$		0			0
$285$	2.90643	−	2.39307i	0.172162	−	0.141753i
$286$		0			0
$287$	10.1498	+	1.78969i	0.599127	+	0.105642i
$288$		0			0
$289$	−8.61908	−	3.13709i	−0.507005	−	0.184535i
$290$		0			0
$291$	−3.15268	+	2.64541i	−0.184813	+	0.155077i
$292$		0			0
$293$	−14.9665	−	8.64092i	−0.874353	−	0.504808i	−0.00556039	−	0.999985i	$-0.501770\pi$
$293$	−14.9665	−	8.64092i	−0.874353	−	0.504808i	−0.868792	+	0.495177i	$0.835103\pi$
$294$		0			0
$295$	−1.79271	−	2.09897i	−0.104375	−	0.122207i
$296$		0			0
$297$	−9.77840	+	5.64556i	−0.567400	+	0.327589i
$298$		0			0
$299$	33.5965	−	12.2281i	1.94293	−	0.707170i
$300$		0			0
$301$	−4.57520	−	3.83905i	−0.263710	−	0.221279i
$302$		0			0
$303$		−	5.56069i		−	0.319453i
$304$		0			0
$305$	24.5654	−	14.4702i	1.40661	−	0.828564i
$306$		0			0
$307$	−16.8445	+	20.0745i	−0.961369	+	1.14571i	0.0279006	+	0.999611i	$0.491118\pi$
$307$	−16.8445	+	20.0745i	−0.961369	+	1.14571i	−0.989269	+	0.146104i	$0.953327\pi$
$308$		0			0
$309$	−2.37049	+	0.862788i	−0.134853	+	0.0490823i
$310$		0			0
$311$	−2.13376	−	3.69578i	−0.120994	−	0.209568i	0.799166	−	0.601111i	$-0.205275\pi$
$311$	−2.13376	−	3.69578i	−0.120994	−	0.209568i	−0.920160	+	0.391542i	$0.871942\pi$
$312$		0			0
$313$	22.4255	−	3.95422i	1.26757	−	0.223506i	0.500873	−	0.865521i	$-0.333012\pi$
$313$	22.4255	−	3.95422i	1.26757	−	0.223506i	0.766692	+	0.642015i	$0.221901\pi$
$314$		0			0
$315$	12.9377	−	0.112948i	0.728956	−	0.00636392i
$316$		0			0
$317$	−13.0144	−	15.5100i	−0.730963	−	0.871127i	0.264684	−	0.964335i	$-0.414732\pi$
$317$	−13.0144	−	15.5100i	−0.730963	−	0.871127i	−0.995647	+	0.0932079i	$0.970288\pi$
$318$		0			0
$319$	24.9637	+	9.08603i	1.39770	+	0.508720i
$320$		0			0
$321$	−1.29383	+	7.33769i	−0.0722147	+	0.409550i
$322$		0			0
$323$	3.96377	+	11.5333i	0.220550	+	0.641728i
$324$		0			0
$325$	16.2539	−	20.0722i	0.901604	−	1.11340i
$326$		0			0
$327$	−0.367897	+	1.01079i	−0.0203447	+	0.0558967i
$328$		0			0
$329$	−16.9223	+	14.1995i	−0.932955	+	0.782842i
$330$		0			0
$331$	−8.22049	+	14.2383i	−0.451839	+	0.782608i	−0.998500	−	0.0547458i	$-0.982565\pi$
$331$	−8.22049	+	14.2383i	−0.451839	+	0.782608i	0.546661	+	0.837354i	$0.315898\pi$
$332$		0			0
$333$	−1.72493	+	0.304152i	−0.0945256	+	0.0166674i
$334$		0			0
$335$	−0.379187	+	0.670216i	−0.0207172	+	0.0366178i
$336$		0			0
$337$	−3.46485	−	9.51959i	−0.188742	−	0.518565i	0.808842	−	0.588025i	$-0.200094\pi$
$337$	−3.46485	−	9.51959i	−0.188742	−	0.518565i	−0.997585	+	0.0694603i	$0.977872\pi$
$338$		0			0
$339$	−1.41374	−	1.18627i	−0.0767837	−	0.0644291i
$340$		0			0
$341$	30.7305			1.66415
$342$		0			0
$343$			20.0540i			1.08281i
$344$		0			0
$345$	−5.89608	−	0.986645i	−0.317434	−	0.0531192i
$346$		0			0
$347$	0.284237	+	0.780935i	0.0152587	+	0.0419228i	0.947088	−	0.320974i	$-0.104010\pi$
$347$	0.284237	+	0.780935i	0.0152587	+	0.0419228i	−0.931829	+	0.362896i	$0.881788\pi$
$348$		0			0
$349$	−1.52695	−	2.64475i	−0.0817355	−	0.141570i	0.822260	−	0.569112i	$-0.192713\pi$
$349$	−1.52695	−	2.64475i	−0.0817355	−	0.141570i	−0.903995	+	0.427542i	$0.859380\pi$
$350$		0			0
$351$	2.02717	+	11.4967i	0.108203	+	0.613647i
$352$		0			0
$353$	−24.3150	−	14.0383i	−1.29416	−	0.747182i	−0.314769	−	0.949168i	$-0.601927\pi$
$353$	−24.3150	−	14.0383i	−1.29416	−	0.747182i	−0.979388	+	0.201986i	$0.935260\pi$
$354$		0			0
$355$	−9.84697	+	27.8073i	−0.522623	+	1.47586i
$356$		0			0
$357$	0.750203	−	2.06117i	0.0397050	−	0.109088i
$358$		0			0
$359$	2.57960	−	14.6296i	0.136146	−	0.772122i	−0.837909	−	0.545810i	$-0.816222\pi$
$359$	2.57960	−	14.6296i	0.136146	−	0.772122i	0.974055	−	0.226312i	$-0.0726668\pi$
$360$		0			0
$361$	−10.0871	+	16.1013i	−0.530899	+	0.847435i
$362$		0			0
$363$	−5.31093	−	0.936461i	−0.278752	−	0.0491514i
$364$		0			0
$365$	1.75892	+	9.49010i	0.0920660	+	0.496735i
$366$		0			0
$367$	−3.60318	−	4.29410i	−0.188084	−	0.224150i	0.663759	−	0.747946i	$-0.268960\pi$
$367$	−3.60318	−	4.29410i	−0.188084	−	0.224150i	−0.851844	+	0.523796i	$0.824515\pi$
$368$		0			0
$369$	−7.23807	+	12.5367i	−0.376799	+	0.652635i
$370$		0			0
$371$	−4.57531	−	25.9479i	−0.237538	−	1.34715i
$372$		0			0
$373$	−4.33340	+	2.50189i	−0.224375	+	0.129543i	−0.607974	−	0.793957i	$-0.708018\pi$
$373$	−4.33340	+	2.50189i	−0.224375	+	0.129543i	0.383599	+	0.923500i	$0.374684\pi$
$374$		0			0
$375$	−4.01807	+	1.58281i	−0.207492	+	0.0817358i
$376$		0			0
$377$	17.6552	−	21.0407i	0.909291	−	1.08365i
$378$		0			0
$379$	27.2579			1.40014			0.700072	−	0.714072i	$-0.253151\pi$
$379$	27.2579			1.40014			0.700072	+	0.714072i	$0.253151\pi$
$380$		0			0
$381$	2.35351			0.120574
$382$		0			0
$383$	24.2773	−	28.9326i	1.24051	−	1.47839i	0.419213	−	0.907888i	$-0.362306\pi$
$383$	24.2773	−	28.9326i	1.24051	−	1.47839i	0.821300	−	0.570497i	$-0.193249\pi$
$384$		0			0
$385$	17.4964	+	14.4228i	0.891701	+	0.735056i
$386$		0			0
$387$	7.26494	−	4.19441i	0.369298	−	0.213214i
$388$		0			0
$389$	5.41583	+	30.7147i	0.274593	+	1.55730i	0.740251	+	0.672331i	$0.234707\pi$
$389$	5.41583	+	30.7147i	0.274593	+	1.55730i	−0.465657	+	0.884965i	$0.654182\pi$
$390$		0			0
$391$	9.68228	−	16.7702i	0.489654	−	0.848105i
$392$		0			0
$393$	−1.08693	−	1.29535i	−0.0548282	−	0.0653417i
$394$		0			0
$395$	−3.21987	+	0.596779i	−0.162009	+	0.0300272i
$396$		0			0
$397$	9.88334	+	1.74270i	0.496030	+	0.0874636i	0.416066	−	0.909334i	$-0.363408\pi$
$397$	9.88334	+	1.74270i	0.496030	+	0.0874636i	0.0799640	+	0.996798i	$0.474519\pi$
$398$		0			0
$399$	3.23178	−	1.11070i	0.161791	−	0.0556046i
$400$		0			0
$401$	−3.98188	+	22.5824i	−0.198846	+	1.12771i	0.707989	+	0.706223i	$0.249602\pi$
$401$	−3.98188	+	22.5824i	−0.198846	+	1.12771i	−0.906835	+	0.421486i	$0.861509\pi$
$402$		0			0
$403$	10.8669	−	29.8565i	0.541318	−	1.48726i
$404$		0			0
$405$	−5.73200	+	16.1868i	−0.284825	+	0.804331i
$406$		0			0
$407$	−2.65840	−	1.53483i	−0.131772	−	0.0760785i
$408$		0			0
$409$	1.91380	+	10.8537i	0.0946314	+	0.536681i	0.994860	+	0.101263i	$0.0322884\pi$
$409$	1.91380	+	10.8537i	0.0946314	+	0.536681i	−0.900228	+	0.435418i	$0.856601\pi$
$410$		0			0
$411$	−0.0242544	−	0.0420098i	−0.00119638	−	0.00207219i
$412$		0			0
$413$	−0.856942	−	2.35443i	−0.0421673	−	0.115854i
$414$		0			0
$415$	2.60981	−	15.5959i	0.128111	−	0.765575i
$416$		0			0
$417$		−	0.597884i		−	0.0292785i
$418$		0			0
$419$	−4.91341			−0.240036			−0.120018	−	0.992772i	$-0.538295\pi$
$419$	−4.91341			−0.240036			−0.120018	+	0.992772i	$0.538295\pi$
$420$		0			0
$421$	7.65017	+	6.41925i	0.372846	+	0.312855i	0.809886	−	0.586587i	$-0.199529\pi$
$421$	7.65017	+	6.41925i	0.372846	+	0.312855i	−0.437040	+	0.899442i	$0.643973\pi$
$422$		0			0
$423$	−10.6121	−	29.1565i	−0.515978	−	1.41764i
$424$		0			0
$425$	−0.244236	−	13.9869i	−0.0118472	−	0.678466i
$426$		0			0
$427$	25.4855	−	4.49378i	1.23333	−	0.217469i
$428$		0			0
$429$	−4.98438	+	8.63320i	−0.240648	+	0.416815i
$430$		0			0
$431$	13.7070	−	11.5015i	0.660241	−	0.554008i	−0.249918	−	0.968267i	$-0.580404\pi$
$431$	13.7070	−	11.5015i	0.660241	−	0.554008i	0.910159	+	0.414259i	$0.135959\pi$
$432$		0			0
$433$	4.08986	−	11.2368i	0.196546	−	0.540006i	−0.801794	−	0.597601i	$-0.796121\pi$
$433$	4.08986	−	11.2368i	0.196546	−	0.540006i	0.998340	+	0.0575945i	$0.0183431\pi$
$434$		0			0
$435$	−4.30176	+	1.60838i	−0.206253	+	0.0771158i
$436$		0			0
$437$	29.8006	−	4.70230i	1.42556	−	0.224941i
$438$		0			0
$439$	−5.93574	+	33.6632i	−0.283297	+	1.60666i	0.428008	+	0.903775i	$0.359215\pi$
$439$	−5.93574	+	33.6632i	−0.283297	+	1.60666i	−0.711305	+	0.702883i	$0.751896\pi$
$440$		0			0
$441$	−7.71653	−	2.80859i	−0.367454	−	0.133742i
$442$		0			0
$443$	17.3354	+	20.6595i	0.823631	+	0.981565i	0.999996	−	0.00276007i	$-0.000878560\pi$
$443$	17.3354	+	20.6595i	0.823631	+	0.981565i	−0.176366	+	0.984325i	$0.556434\pi$
$444$		0			0
$445$	0.0528899	+	6.05828i	0.00250722	+	0.287190i
$446$		0			0
$447$	8.45140	−	1.49021i	0.399737	−	0.0704845i
$448$		0			0
$449$	−6.24310	−	10.8134i	−0.294630	−	0.510315i	0.680269	−	0.732963i	$-0.261863\pi$
$449$	−6.24310	−	10.8134i	−0.294630	−	0.510315i	−0.974899	+	0.222648i	$0.928530\pi$
$450$		0			0
$451$	−23.8401	+	8.67708i	−1.12259	+	0.408588i
$452$		0			0
$453$	1.90437	−	2.26954i	0.0894752	−	0.106632i
$454$		0			0
$455$	20.1997	−	11.8986i	0.946978	−	0.557817i
$456$		0			0
$457$			37.2242i			1.74127i	0.491926	+	0.870637i	$0.336293\pi$
$457$			37.2242i			1.74127i	−0.491926	+	0.870637i	$0.663707\pi$
$458$		0			0
$459$	4.84367	+	4.06432i	0.226083	+	0.189706i
$460$		0			0
$461$	38.7689	−	14.1107i	1.80565	−	0.657203i	0.807962	−	0.589235i	$-0.200571\pi$
$461$	38.7689	−	14.1107i	1.80565	−	0.657203i	0.997688	−	0.0679675i	$-0.0216514\pi$
$462$		0			0
$463$	−36.7591	+	21.2229i	−1.70834	+	0.986311i	−0.771721	+	0.635961i	$0.780604\pi$
$463$	−36.7591	+	21.2229i	−1.70834	+	0.986311i	−0.936619	+	0.350349i	$0.886063\pi$
$464$		0			0
$465$	−4.03971	+	3.45026i	−0.187337	+	0.160002i
$466$		0			0
$467$	−7.73715	−	4.46704i	−0.358032	−	0.206710i	0.310185	−	0.950676i	$-0.399609\pi$
$467$	−7.73715	−	4.46704i	−0.358032	−	0.206710i	−0.668217	+	0.743966i	$0.732942\pi$
$468$		0			0
$469$	−0.535436	+	0.449284i	−0.0247242	+	0.0207460i
$470$		0			0
$471$	6.31784	+	2.29951i	0.291111	+	0.105956i
$472$		0			0
$473$	14.4784	+	2.55294i	0.665719	+	0.117384i
$474$		0			0
$475$	16.7036	−	13.9997i	0.766412	−	0.642350i
$476$		0			0
$477$	36.4458	+	6.42637i	1.66874	+	0.294243i
$478$		0			0
$479$	3.82965	+	1.39388i	0.174981	+	0.0636879i	0.428025	−	0.903767i	$-0.359210\pi$
$479$	3.82965	+	1.39388i	0.174981	+	0.0636879i	−0.253044	+	0.967455i	$0.581432\pi$
$480$		0			0
$481$	−2.43123	+	2.04005i	−0.110855	+	0.0930182i
$482$		0			0
$483$	−4.69924	−	2.71311i	−0.213823	−	0.123451i
$484$		0			0
$485$	−18.1162	+	15.4728i	−0.822616	+	0.702585i
$486$		0			0
$487$	5.29459	−	3.05683i	0.239921	−	0.138518i	−0.375220	−	0.926936i	$-0.622433\pi$
$487$	5.29459	−	3.05683i	0.239921	−	0.138518i	0.615140	+	0.788418i	$0.289099\pi$
$488$		0			0
$489$	2.40789	−	0.876402i	0.108889	−	0.0396323i
$490$		0			0
$491$	8.96177	+	7.51982i	0.404439	+	0.339365i	0.822206	−	0.569189i	$-0.192743\pi$
$491$	8.96177	+	7.51982i	0.404439	+	0.339365i	−0.417767	+	0.908554i	$0.637187\pi$
$492$		0			0
$493$		−	14.8767i		−	0.670012i
$494$		0			0
$495$	−27.4414	+	16.1644i	−1.23340	+	0.726534i
$496$		0			0
$497$	−17.2114	+	20.5117i	−0.772036	+	0.920076i
$498$		0			0
$499$	−7.99418	+	2.90964i	−0.357869	+	0.130254i	−0.514697	−	0.857372i	$-0.672095\pi$
$499$	−7.99418	+	2.90964i	−0.357869	+	0.130254i	0.156828	+	0.987626i	$0.449873\pi$
$500$		0			0
$501$	1.37873	+	2.38802i	0.0615969	+	0.106689i
$502$		0			0
$503$	−9.55700	+	1.68516i	−0.426125	+	0.0751374i	−0.382598	−	0.923915i	$-0.624971\pi$
$503$	−9.55700	+	1.68516i	−0.426125	+	0.0751374i	−0.0435272	+	0.999052i	$0.513860\pi$
$504$		0			0
$505$	−0.281018	−	32.1892i	−0.0125051	−	1.43240i
$506$		0			0
$507$	3.39737	+	4.04883i	0.150882	+	0.179815i
$508$		0			0
$509$	−29.4562	−	10.7212i	−1.30562	−	0.475208i	−0.406800	−	0.913517i	$-0.633355\pi$
$509$	−29.4562	−	10.7212i	−1.30562	−	0.475208i	−0.898824	+	0.438309i	$0.855578\pi$
$510$		0			0
$511$	−1.52129	+	8.62766i	−0.0672979	+	0.381665i
$512$		0			0
$513$	−0.177616	+	9.84936i	−0.00784192	+	0.434860i
$514$		0			0
$515$	−13.6785	+	5.11423i	−0.602746	+	0.225360i
$516$		0			0
$517$	18.5982	−	51.0980i	0.817946	−	2.24729i
$518$		0			0
$519$	−3.71969	+	3.12119i	−0.163276	+	0.137005i
$520$		0			0
$521$	3.69071	−	6.39250i	0.161693	−	0.280060i	−0.773783	−	0.633451i	$-0.781638\pi$
$521$	3.69071	−	6.39250i	0.161693	−	0.280060i	0.935476	+	0.353390i	$0.114971\pi$
$522$		0			0
$523$	10.6860	−	1.88424i	0.467268	−	0.0823919i	0.0649432	−	0.997889i	$-0.479313\pi$
$523$	10.6860	−	1.88424i	0.467268	−	0.0823919i	0.402325	+	0.915497i	$0.368202\pi$
$524$		0			0
$525$	−3.91933	+	0.0684382i	−0.171054	+	0.00298689i
$526$		0			0
$527$	−5.88579	−	16.1711i	−0.256389	−	0.704423i
$528$		0			0
$529$	−19.0780	−	16.0084i	−0.829480	−	0.696016i
$530$		0			0
$531$	3.51920			0.152720
$532$		0			0
$533$			26.2304i			1.13617i
$534$		0			0
$535$	−7.11881	+	42.5412i	−0.307773	+	1.83922i
$536$		0			0
$537$	−2.53564	−	6.96661i	−0.109421	−	0.300631i
$538$		0			0
$539$	−7.19573	−	12.4634i	−0.309942	−	0.536836i
$540$		0			0
$541$	−2.19629	−	12.4558i	−0.0944257	−	0.535515i	−0.994922	−	0.100651i	$-0.967908\pi$
$541$	−2.19629	−	12.4558i	−0.0944257	−	0.535515i	0.900496	−	0.434864i	$-0.143204\pi$
$542$		0			0
$543$	−4.43173	−	2.55866i	−0.190184	−	0.109803i
$544$		0			0
$545$	−2.07857	+	5.86975i	−0.0890360	+	0.251433i
$546$		0			0
$547$	5.41331	−	14.8730i	0.231457	−	0.635922i	−0.768536	−	0.639807i	$-0.779014\pi$
$547$	5.41331	−	14.8730i	0.231457	−	0.635922i	0.999992	+	0.00388494i	$0.00123662\pi$
$548$		0			0
$549$	−6.31185	+	35.7963i	−0.269383	+	1.52775i
$550$		0			0
$551$	18.0206	−	14.5756i	0.767704	−	0.620940i
$552$		0			0
$553$	−2.92726	−	0.516154i	−0.124480	−	0.0219491i
$554$		0			0
$555$	0.521784	−	0.0967088i	0.0221485	−	0.00410506i
$556$		0			0
$557$	−9.31207	−	11.0977i	−0.394565	−	0.470224i	0.531790	−	0.846876i	$-0.321520\pi$
$557$	−9.31207	−	11.0977i	−0.394565	−	0.470224i	−0.926355	+	0.376652i	$0.877075\pi$
$558$		0			0
$559$	7.60018	−	13.1639i	0.321453	−	0.556774i
$560$		0			0
$561$	0.937586	+	5.31732i	0.0395849	+	0.224497i
$562$		0			0
$563$	−35.3172	+	20.3904i	−1.48844	+	0.859354i	−0.999913	−	0.0131930i	$-0.995800\pi$
$563$	−35.3172	+	20.3904i	−1.48844	+	0.859354i	−0.488531	+	0.872547i	$0.662467\pi$
$564$		0			0
$565$	−8.24367	−	6.79551i	−0.346814	−	0.285889i
$566$		0			0
$567$	−10.0189	+	11.9400i	−0.420753	+	0.501434i
$568$		0			0
$569$	20.1384			0.844246			0.422123	−	0.906539i	$-0.361285\pi$
$569$	20.1384			0.844246			0.422123	+	0.906539i	$0.361285\pi$
$570$		0			0
$571$	−6.07939			−0.254415			−0.127207	−	0.991876i	$-0.540601\pi$
$571$	−6.07939			−0.254415			−0.127207	+	0.991876i	$0.540601\pi$
$572$		0			0
$573$	−1.96816	+	2.34556i	−0.0822211	+	0.0979872i
$574$		0			0
$575$	−34.1805	−	5.41343i	−1.42543	−	0.225756i
$576$		0			0
$577$	9.61953	−	5.55384i	0.400466	−	0.231209i	−0.286219	−	0.958164i	$-0.592398\pi$
$577$	9.61953	−	5.55384i	0.400466	−	0.231209i	0.686685	+	0.726955i	$0.259065\pi$
$578$		0			0
$579$	−1.00934	−	5.72428i	−0.0419469	−	0.237893i
$580$		0			0
$581$	7.17654	−	12.4301i	0.297733	−	0.515689i
$582$		0			0
$583$	41.6900	+	49.6842i	1.72662	+	2.05771i
$584$		0			0
$585$	6.00083	+	32.3770i	0.248104	+	1.33862i
$586$		0			0
$587$	12.3374	+	2.17542i	0.509220	+	0.0897893i	0.422355	−	0.906431i	$-0.361204\pi$
$587$	12.3374	+	2.17542i	0.509220	+	0.0897893i	0.0868659	+	0.996220i	$0.472315\pi$
$588$		0			0
$589$	13.8219	−	22.9734i	0.569521	−	0.946603i
$590$		0			0
$591$	−1.76597	+	10.0153i	−0.0726422	+	0.411974i
$592$		0			0
$593$	−4.12938	+	11.3454i	−0.169573	+	0.465899i	−0.995147	−	0.0983948i	$-0.968629\pi$
$593$	−4.12938	+	11.3454i	−0.169573	+	0.465899i	0.825574	+	0.564294i	$0.190851\pi$
$594$		0			0
$595$	4.23855	−	11.9694i	0.173763	−	0.490698i
$596$		0			0
$597$	−0.0294444	−	0.0169997i	−0.00120508	−	0.000695752i
$598$		0			0
$599$	−3.49998	−	19.8494i	−0.143005	−	0.811024i	−0.968947	−	0.247268i	$-0.920467\pi$
$599$	−3.49998	−	19.8494i	−0.143005	−	0.811024i	0.825942	−	0.563755i	$-0.190644\pi$
$600$		0			0
$601$	−8.65639	−	14.9933i	−0.353102	−	0.611590i	0.633689	−	0.773588i	$-0.281540\pi$
$601$	−8.65639	−	14.9933i	−0.353102	−	0.611590i	−0.986791	+	0.161997i	$0.948206\pi$
$602$		0			0
$603$	−0.335777	−	0.922539i	−0.0136739	−	0.0375687i
$604$		0			0
$605$	−30.7908	−	5.15250i	−1.25182	−	0.209479i
$606$		0			0
$607$		−	32.2776i		−	1.31011i	−0.755582	−	0.655054i	$-0.772646\pi$
$607$		−	32.2776i		−	1.31011i	0.755582	−	0.655054i	$-0.227354\pi$
$608$		0			0
$609$	−4.16865			−0.168922
$610$		0			0
$611$	−43.0681	−	36.1385i	−1.74235	−	1.46201i
$612$		0			0
$613$	−4.33958	−	11.9229i	−0.175274	−	0.481561i	0.820684	−	0.571382i	$-0.193593\pi$
$613$	−4.33958	−	11.9229i	−0.175274	−	0.481561i	−0.995958	+	0.0898212i	$0.971370\pi$
$614$		0			0
$615$	2.15970	−	3.81729i	0.0870877	−	0.153928i
$616$		0			0
$617$	22.8772	−	4.03388i	0.921003	−	0.162398i	0.307008	−	0.951707i	$-0.400672\pi$
$617$	22.8772	−	4.03388i	0.921003	−	0.162398i	0.613996	+	0.789309i	$0.289561\pi$
$618$		0			0
$619$	9.94737	−	17.2294i	0.399819	−	0.692506i	−0.593885	−	0.804550i	$-0.702406\pi$
$619$	9.94737	−	17.2294i	0.399819	−	0.692506i	0.993703	+	0.112044i	$0.0357398\pi$
$620$		0			0
$621$	11.9824	−	10.0544i	0.480838	−	0.403471i
$622$		0			0
$623$	−1.88085	+	5.16759i	−0.0753546	+	0.207035i
$624$		0			0
$625$	−23.1795	+	9.36547i	−0.927179	+	0.374619i
$626$		0			0
$627$	−5.52243	+	6.34542i	−0.220545	+	0.253412i
$628$		0			0
$629$	−0.298499	+	1.69287i	−0.0119019	+	0.0674992i
$630$		0			0
$631$	40.2762	+	14.6593i	1.60337	+	0.583579i	0.980114	−	0.198437i	$-0.0635865\pi$
$631$	40.2762	+	14.6593i	1.60337	+	0.583579i	0.623258	+	0.782016i	$0.285809\pi$
$632$		0			0
$633$	−1.31783	−	1.57052i	−0.0523789	−	0.0624227i
$634$		0			0
$635$	13.6238	−	0.118938i	0.540644	−	0.00471992i
$636$		0			0
$637$	−14.6535	+	2.58380i	−0.580591	+	0.102374i
$638$		0			0
$639$	−18.8045	−	32.5704i	−0.743896	−	1.28847i
$640$		0			0
$641$	4.37943	−	1.59398i	0.172977	−	0.0629585i	−0.254080	−	0.967183i	$-0.581773\pi$
$641$	4.37943	−	1.59398i	0.172977	−	0.0629585i	0.427057	+	0.904225i	$0.359550\pi$
$642$		0			0
$643$	3.04048	−	3.62351i	0.119905	−	0.142897i	−0.702753	−	0.711434i	$-0.748046\pi$
$643$	3.04048	−	3.62351i	0.119905	−	0.142897i	0.822658	+	0.568537i	$0.192490\pi$
$644$		0			0
$645$	−2.18991	+	1.28996i	−0.0862275	+	0.0507923i
$646$		0			0
$647$			0.286876i			0.0112783i	0.999984	+	0.00563914i	$0.00179500\pi$
$647$			0.286876i			0.0112783i	−0.999984	+	0.00563914i	$0.998205\pi$
$648$		0			0
$649$	4.72463	+	3.96443i	0.185458	+	0.155618i
$650$		0			0
$651$	−4.53135	+	1.64928i	−0.177598	+	0.0646403i
$652$		0			0
$653$	−9.39185	+	5.42238i	−0.367531	+	0.212194i	−0.672379	−	0.740207i	$-0.734728\pi$
$653$	−9.39185	+	5.42238i	−0.367531	+	0.212194i	0.304848	+	0.952401i	$0.401394\pi$
$654$		0			0
$655$	−6.35736	−	7.44347i	−0.248403	−	0.290840i
$656$		0			0
$657$	−10.6566	−	6.15257i	−0.415752	−	0.240035i
$658$		0			0
$659$	−32.4787	+	27.2529i	−1.26519	+	1.06162i	−0.270082	+	0.962837i	$0.587051\pi$
$659$	−32.4787	+	27.2529i	−1.26519	+	1.06162i	−0.995109	+	0.0987834i	$0.968505\pi$
$660$		0			0
$661$	−22.7802	−	8.29133i	−0.886049	−	0.322495i	−0.141400	−	0.989952i	$-0.545161\pi$
$661$	−22.7802	−	8.29133i	−0.886049	−	0.322495i	−0.744648	+	0.667457i	$0.767383\pi$
$662$		0			0
$663$	5.49764	+	0.969382i	0.213511	+	0.0376477i
$664$		0			0
$665$	18.6517	−	6.59285i	0.723282	−	0.255660i
$666$		0			0
$667$	−36.2433	−	6.39066i	−1.40334	−	0.247447i
$668$		0			0
$669$	3.47822	+	1.26597i	0.134476	+	0.0489451i
$670$		0			0
$671$	−48.7988	+	40.9471i	−1.88386	+	1.58074i
$672$		0			0
$673$	−8.00813	−	4.62349i	−0.308691	−	0.178223i	0.337650	−	0.941272i	$-0.390368\pi$
$673$	−8.00813	−	4.62349i	−0.308691	−	0.178223i	−0.646340	+	0.763049i	$0.723701\pi$
$674$		0			0
$675$	3.67879	−	10.6842i	0.141597	−	0.411236i
$676$		0			0
$677$	−17.3070	+	9.99219i	−0.665161	+	0.384031i	−0.794241	−	0.607603i	$-0.792131\pi$
$677$	−17.3070	+	9.99219i	−0.665161	+	0.384031i	0.129079	+	0.991634i	$0.458798\pi$
$678$		0			0
$679$	−20.3211	+	7.39626i	−0.779851	+	0.283842i
$680$		0			0
$681$	−7.41008	−	6.21780i	−0.283955	−	0.238267i
$682$		0			0
$683$			7.54136i			0.288562i	0.989537	+	0.144281i	$0.0460869\pi$
$683$			7.54136i			0.288562i	−0.989537	+	0.144281i	$0.953913\pi$
$684$		0			0
$685$	−0.142525	−	0.241957i	−0.00544559	−	0.00924471i
$686$		0			0
$687$	−3.77930	+	4.50400i	−0.144189	+	0.171838i
$688$		0			0
$689$	63.0135	−	22.9351i	2.40062	−	0.873756i
$690$		0			0
$691$	13.4982	+	23.3795i	0.513495	+	0.889399i	0.999877	+	0.0156532i	$0.00498276\pi$
$691$	13.4982	+	23.3795i	0.513495	+	0.889399i	−0.486383	+	0.873746i	$0.661684\pi$
$692$		0			0
$693$	−28.4692	+	5.01989i	−1.08146	+	0.190690i
$694$		0			0
$695$	−0.0302150	−	3.46098i	−0.00114612	−	0.131282i
$696$		0			0
$697$	9.13215	+	10.8833i	0.345905	+	0.412233i
$698$		0			0
$699$	−7.44571	−	2.71002i	−0.281623	−	0.102502i
$700$		0			0
$701$	−7.13387	+	40.4582i	−0.269443	+	1.52809i	0.486636	+	0.873605i	$0.338224\pi$
$701$	−7.13387	+	40.4582i	−0.269443	+	1.52809i	−0.756079	+	0.654481i	$0.772887\pi$
$702$		0			0
$703$	−2.34309	+	1.29703i	−0.0883713	+	0.0489183i
$704$		0			0
$705$	3.29218	+	8.80525i	0.123991	+	0.331625i
$706$		0			0
$707$	9.99345	−	27.4568i	0.375842	−	1.03262i
$708$		0			0
$709$	8.86041	−	7.43476i	0.332760	−	0.279218i	−0.461064	−	0.887367i	$-0.652532\pi$
$709$	8.86041	−	7.43476i	0.332760	−	0.279218i	0.793823	+	0.608149i	$0.208088\pi$
$710$		0			0
$711$	2.08749	−	3.61564i	0.0782869	−	0.135597i
$712$		0			0
$713$	−41.9251	+	7.39252i	−1.57011	+	0.276852i
$714$		0			0
$715$	−28.4169	+	50.2270i	−1.06273	+	1.87838i
$716$		0			0
$717$	−0.981491	−	2.69662i	−0.0366544	−	0.100707i
$718$		0			0
$719$	−15.3867	−	12.9110i	−0.573829	−	0.481499i	0.309085	−	0.951034i	$-0.399977\pi$
$719$	−15.3867	−	12.9110i	−0.573829	−	0.481499i	−0.882914	+	0.469535i	$0.844422\pi$
$720$		0			0
$721$	−13.2552			−0.493651
$722$		0			0
$723$			9.10734i			0.338706i
$724$		0			0
$725$	−24.8203	+	9.52782i	−0.921804	+	0.353855i
$726$		0			0
$727$	−10.8824	−	29.8991i	−0.403605	−	1.10890i	−0.960492	−	0.278307i	$-0.910227\pi$
$727$	−10.8824	−	29.8991i	−0.403605	−	1.10890i	0.556887	−	0.830588i	$-0.311996\pi$
$728$		0			0
$729$	−9.63686	−	16.6915i	−0.356921	−	0.618205i
$730$		0			0
$731$	−1.42963	−	8.10784i	−0.0528768	−	0.299879i
$732$		0			0
$733$	−4.51550	−	2.60703i	−0.166784	−	0.0962927i	0.414285	−	0.910147i	$-0.364032\pi$
$733$	−4.51550	−	2.60703i	−0.166784	−	0.0962927i	−0.581068	+	0.813855i	$0.697365\pi$
$734$		0			0
$735$	2.34524	+	0.830486i	0.0865056	+	0.0306329i
$736$		0			0
$737$	0.588463	−	1.61679i	0.0216763	−	0.0595552i
$738$		0			0
$739$	4.28406	−	24.2961i	0.157592	−	0.893746i	−0.798786	−	0.601615i	$-0.794524\pi$
$739$	4.28406	−	24.2961i	0.157592	−	0.893746i	0.956378	−	0.292132i	$-0.0943646\pi$
$740$		0			0
$741$	4.21212	+	7.60923i	0.154736	+	0.279532i
$742$		0			0
$743$	2.06863	+	0.364755i	0.0758907	+	0.0133816i	0.211465	−	0.977386i	$-0.432177\pi$
$743$	2.06863	+	0.364755i	0.0758907	+	0.0133816i	−0.135574	+	0.990767i	$0.543288\pi$
$744$		0			0
$745$	48.8474	−	9.05349i	1.78963	−	0.331694i
$746$		0			0
$747$	12.9586	+	15.4434i	0.474130	+	0.565046i
$748$		0			0
$749$	−19.5755	+	33.9058i	−0.715274	+	1.23889i
$750$		0			0
$751$	3.55434	+	20.1577i	0.129700	+	0.735564i	0.978405	+	0.206697i	$0.0662716\pi$
$751$	3.55434	+	20.1577i	0.129700	+	0.735564i	−0.848705	+	0.528866i	$0.822617\pi$
$752$		0			0
$753$	6.83662	−	3.94712i	0.249140	−	0.143841i
$754$		0			0
$755$	10.9092	−	13.2340i	0.397025	−	0.481633i
$756$		0			0
$757$	−11.3376	+	13.5116i	−0.412072	+	0.491088i	−0.931661	−	0.363328i	$-0.881640\pi$
$757$	−11.3376	+	13.5116i	−0.412072	+	0.491088i	0.519590	+	0.854416i	$0.326085\pi$
$758$		0			0
$759$	13.3571			0.484830
$760$		0			0
$761$	13.3795			0.485006			0.242503	−	0.970151i	$-0.422032\pi$
$761$	13.3795			0.485006			0.242503	+	0.970151i	$0.422032\pi$
$762$		0			0
$763$	−3.63310	+	4.32976i	−0.131527	+	0.156748i
$764$		0			0
$765$	13.7619	+	11.3443i	0.497562	+	0.410155i
$766$		0			0
$767$	5.52240	−	3.18836i	0.199402	−	0.115125i
$768$		0			0
$769$	2.71812	+	15.4152i	0.0980179	+	0.555887i	0.993781	+	0.111355i	$0.0355190\pi$
$769$	2.71812	+	15.4152i	0.0980179	+	0.555887i	−0.895763	+	0.444532i	$0.853370\pi$
$770$		0			0
$771$	0.968181	−	1.67694i	0.0348682	−	0.0603935i
$772$		0			0
$773$	16.0681	+	19.1492i	0.577930	+	0.688750i	0.973238	−	0.229799i	$-0.0738068\pi$
$773$	16.0681	+	19.1492i	0.577930	+	0.688750i	−0.395309	+	0.918548i	$0.629362\pi$
$774$		0			0
$775$	−23.2103	+	20.1767i	−0.833740	+	0.724768i
$776$		0			0
$777$	0.474366	+	0.0836435i	0.0170178	+	0.00300069i
$778$		0			0
$779$	−4.23596	+	21.7251i	−0.151769	+	0.778381i
$780$		0			0
$781$	11.4454	−	64.9103i	0.409550	−	2.32267i
$782$		0			0
$783$	4.10999	−	11.2921i	0.146879	−	0.403547i
$784$		0			0
$785$	36.6884	+	12.9919i	1.30946	+	0.463701i
$786$		0			0
$787$	21.3578	+	12.3309i	0.761323	+	0.439550i	0.829770	−	0.558105i	$-0.188471\pi$
$787$	21.3578	+	12.3309i	0.761323	+	0.439550i	−0.0684479	+	0.997655i	$0.521805\pi$
$788$		0			0
$789$	−1.04034	−	5.90007i	−0.0370372	−	0.210048i
$790$		0			0
$791$	−4.84864	−	8.39809i	−0.172398	−	0.298602i
$792$		0			0
$793$	22.5263	+	61.8906i	0.799934	+	2.19780i
$794$		0			0
$795$	−11.0587	−	1.85055i	−0.392211	−	0.0656323i
$796$		0			0
$797$		−	10.7215i		−	0.379776i	−0.981806	−	0.189888i	$-0.939188\pi$
$797$		−	10.7215i		−	0.379776i	0.981806	−	0.189888i	$-0.0608125\pi$
$798$		0			0
$799$	−30.4510			−1.07728
$800$		0			0
$801$	−5.91699	−	4.96495i	−0.209067	−	0.175428i
$802$		0			0
$803$	−7.37577	−	20.2648i	−0.260285	−	0.715128i
$804$		0			0
$805$	−27.3396	−	15.4679i	−0.963596	−	0.545172i
$806$		0			0
$807$	−4.38948	+	0.773983i	−0.154517	+	0.0272455i
$808$		0			0
$809$	−0.174831	+	0.302817i	−0.00614674	+	0.0106465i	−0.869082	−	0.494667i	$-0.835290\pi$
$809$	−0.174831	+	0.302817i	−0.00614674	+	0.0106465i	0.862936	+	0.505314i	$0.168623\pi$
$810$		0			0
$811$	0.144079	−	0.120897i	0.00505930	−	0.00424526i	−0.640254	−	0.768163i	$-0.721171\pi$
$811$	0.144079	−	0.120897i	0.00505930	−	0.00424526i	0.645314	+	0.763918i	$0.276727\pi$
$812$		0			0
$813$	−1.64169	+	4.51052i	−0.0575767	+	0.158191i
$814$		0			0
$815$	13.8943	−	5.19492i	0.486697	−	0.181970i
$816$		0			0
$817$	8.42060	−	9.67549i	0.294600	−	0.338503i
$818$		0			0
$819$	−5.19012	+	29.4346i	−0.181358	+	1.02853i
$820$		0			0
$821$	−10.1467	−	3.69308i	−0.354121	−	0.128889i	0.158833	−	0.987305i	$-0.449227\pi$
$821$	−10.1467	−	3.69308i	−0.354121	−	0.128889i	−0.512954	+	0.858416i	$0.671449\pi$
$822$		0			0
$823$	−20.7215	−	24.6950i	−0.722307	−	0.860812i	0.272546	−	0.962143i	$-0.412134\pi$
$823$	−20.7215	−	24.6950i	−0.722307	−	0.860812i	−0.994853	+	0.101331i	$0.967690\pi$
$824$		0			0
$825$	8.27096	−	4.96977i	0.287958	−	0.173025i
$826$		0			0
$827$	−0.955921	+	0.168555i	−0.0332406	+	0.00586122i	−0.190244	−	0.981737i	$-0.560928\pi$
$827$	−0.955921	+	0.168555i	−0.0332406	+	0.00586122i	0.157003	+	0.987598i	$0.449817\pi$
$828$		0			0
$829$	−7.94069	−	13.7537i	−0.275791	−	0.477685i	0.694543	−	0.719451i	$-0.255607\pi$
$829$	−7.94069	−	13.7537i	−0.275791	−	0.477685i	−0.970334	+	0.241766i	$0.922273\pi$
$830$		0			0
$831$	−1.38593	+	0.504436i	−0.0480773	+	0.0174987i
$832$		0			0
$833$	−5.18031	+	6.17366i	−0.179487	+	0.213904i
$834$		0			0
$835$	8.10173	+	13.7539i	0.280372	+	0.475974i
$836$		0			0
$837$		−	13.9007i		−	0.480477i
$838$		0			0
$839$	14.8550	+	12.4648i	0.512850	+	0.430333i	0.862131	−	0.506686i	$-0.169130\pi$
$839$	14.8550	+	12.4648i	0.512850	+	0.430333i	−0.349280	+	0.937018i	$0.613574\pi$
$840$		0			0
$841$	0.683015	−	0.248597i	0.0235522	−	0.00857232i
$842$		0			0
$843$	−9.42443	+	5.44119i	−0.324594	+	0.187405i
$844$		0			0
$845$	19.8710	+	23.2658i	0.683583	+	0.800368i
$846$		0			0
$847$	−24.5406	−	14.1685i	−0.843225	−	0.486836i
$848$		0			0
$849$	5.48479	−	4.60228i	0.188237	−	0.157950i
$850$		0			0
$851$	3.99602	+	1.45443i	0.136982	+	0.0498574i
$852$		0			0
$853$	46.5514	+	8.20827i	1.59389	+	0.281046i	0.898960	−	0.438031i	$-0.144324\pi$
$853$	46.5514	+	8.20827i	1.59389	+	0.281046i	0.694931	+	0.719077i	$0.255435\pi$
$854$		0			0
$855$	−0.258444	+	27.7849i	−0.00883859	+	0.950225i
$856$		0			0
$857$	14.4190	+	2.54245i	0.492543	+	0.0868486i	0.414402	−	0.910094i	$-0.363991\pi$
$857$	14.4190	+	2.54245i	0.492543	+	0.0868486i	0.0781404	+	0.996942i	$0.475102\pi$
$858$		0			0
$859$	27.7553	+	10.1021i	0.946997	+	0.344679i	0.768925	−	0.639339i	$-0.220792\pi$
$859$	27.7553	+	10.1021i	0.946997	+	0.344679i	0.178072	+	0.984017i	$0.443014\pi$
$860$		0			0
$861$	3.04964	−	2.55895i	0.103931	−	0.0872089i
$862$		0			0
$863$	6.58447	+	3.80155i	0.224138	+	0.129406i	0.607865	−	0.794040i	$-0.292026\pi$
$863$	6.58447	+	3.80155i	0.224138	+	0.129406i	−0.383727	+	0.923447i	$0.625360\pi$
$864$		0			0
$865$	−21.3745	+	18.2557i	−0.726755	+	0.620711i
$866$		0			0
$867$	−3.06826	+	1.77146i	−0.104204	+	0.0601620i
$868$		0			0
$869$	6.87557	−	2.50250i	0.233238	−	0.0848916i
$870$		0			0
$871$	−1.36272	−	1.14345i	−0.0461739	−	0.0387445i
$872$		0			0
$873$		−	30.3742i		−	1.02801i
$874$		0			0
$875$	−22.6844	+	0.594238i	−0.766873	+	0.0200889i
$876$		0			0
$877$	13.3391	−	15.8969i	0.450430	−	0.536801i	−0.492270	−	0.870442i	$-0.663833\pi$
$877$	13.3391	−	15.8969i	0.450430	−	0.536801i	0.942700	+	0.333641i	$0.108277\pi$
$878$		0			0
$879$	−6.27281	+	2.28312i	−0.211577	+	0.0770076i
$880$		0			0
$881$	6.17836	+	10.7012i	0.208154	+	0.360534i	0.951133	−	0.308781i	$-0.0999211\pi$
$881$	6.17836	+	10.7012i	0.208154	+	0.360534i	−0.742979	+	0.669315i	$0.766588\pi$
$882$		0			0
$883$	−36.5445	+	6.44379i	−1.22982	+	0.216851i	−0.750548	−	0.660815i	$-0.770211\pi$
$883$	−36.5445	+	6.44379i	−1.22982	+	0.216851i	−0.479273	+	0.877666i	$0.659100\pi$
$884$		0			0
$885$	−1.06619	+	0.00930800i	−0.0358394	+	0.000312885i
$886$		0			0
$887$	13.5613	+	16.1617i	0.455343	+	0.542656i	0.944055	−	0.329789i	$-0.106978\pi$
$887$	13.5613	+	16.1617i	0.455343	+	0.542656i	−0.488712	+	0.872445i	$0.662533\pi$
$888$		0			0
$889$	11.6208	+	4.22964i	0.389750	+	0.141857i
$890$		0			0
$891$	6.66248	−	37.7848i	0.223201	−	1.26584i
$892$		0			0
$893$	−29.8347	−	36.8863i	−0.998379	−	1.23435i
$894$		0			0
$895$	−15.0301	−	40.1995i	−0.502402	−	1.34372i
$896$		0			0
$897$	4.72331	−	12.9772i	0.157707	−	0.433295i
$898$		0			0
$899$	−25.0539	+	21.0227i	−0.835594	+	0.701146i
$900$		0			0
$901$	18.1601	−	31.4542i	0.605000	−	1.04789i
$902$		0			0
$903$	−2.27193	+	0.400602i	−0.0756050	+	0.0133312i
$904$		0			0
$905$	−25.7833	−	14.5874i	−0.857066	−	0.484901i
$906$		0			0
$907$	−10.7770	−	29.6094i	−0.357843	−	0.983165i	−0.979776	−	0.200095i	$-0.935875\pi$
$907$	−10.7770	−	29.6094i	−0.357843	−	0.983165i	0.621934	−	0.783070i	$-0.286347\pi$
$908$		0			0
$909$	31.4386	+	26.3801i	1.04275	+	0.874972i
$910$		0			0
$911$	−27.0162			−0.895085			−0.447543	−	0.894263i	$-0.647701\pi$
$911$	−27.0162			−0.895085			−0.447543	+	0.894263i	$0.647701\pi$
$912$		0			0
$913$			35.3313i			1.16929i
$914$		0			0
$915$	1.81757	−	10.8616i	0.0600871	−	0.359074i
$916$		0			0
$917$	−3.03892	−	8.34937i	−0.100354	−	0.275720i
$918$		0			0
$919$	−1.94333	−	3.36595i	−0.0641045	−	0.111032i	0.832192	−	0.554488i	$-0.187086\pi$
$919$	−1.94333	−	3.36595i	−0.0641045	−	0.111032i	−0.896296	+	0.443455i	$0.853752\pi$
$920$		0			0
$921$	1.75771	+	9.96850i	0.0579187	+	0.328473i
$922$		0			0
$923$	−59.0169	−	34.0734i	−1.94256	−	1.12154i
$924$		0			0
$925$	3.01557	−	0.586189i	0.0991514	−	0.0192738i
$926$		0			0
$927$	6.36772	−	17.4952i	0.209144	−	0.574617i
$928$		0			0
$929$	5.87379	−	33.3119i	0.192713	−	1.09293i	−0.722926	−	0.690926i	$-0.757203\pi$
$929$	5.87379	−	33.3119i	0.192713	−	1.09293i	0.915638	−	0.402003i	$-0.131686\pi$
$930$		0			0
$931$	−12.5538	−	0.226386i	−0.411435	−	0.00741949i
$932$		0			0
$933$	−1.62335	−	0.286241i	−0.0531462	−	0.00937111i
$934$		0			0
$935$	5.69613	+	30.7330i	0.186284	+	1.00508i
$936$		0			0
$937$	4.26094	+	5.07798i	0.139199	+	0.165891i	0.831140	−	0.556063i	$-0.187689\pi$
$937$	4.26094	+	5.07798i	0.139199	+	0.165891i	−0.691941	+	0.721954i	$0.743244\pi$
$938$		0			0
$939$	4.39792	−	7.61743i	0.143521	−	0.248585i
$940$		0			0
$941$	3.66372	+	20.7780i	0.119434	+	0.677344i	0.984459	+	0.175615i	$0.0561913\pi$
$941$	3.66372	+	20.7780i	0.119434	+	0.677344i	−0.865025	+	0.501729i	$0.832698\pi$
$942$		0			0
$943$	30.4373	−	17.5730i	0.991174	−	0.572254i
$944$		0			0
$945$	6.52405	−	7.91436i	0.212227	−	0.257454i
$946$		0			0
$947$	17.0313	−	20.2971i	0.553442	−	0.659567i	−0.414703	−	0.909957i	$-0.636114\pi$
$947$	17.0313	−	20.2971i	0.553442	−	0.659567i	0.968145	+	0.250390i	$0.0805589\pi$
$948$		0			0
$949$	−22.2966			−0.723779
$950$		0			0
$951$	−7.82067			−0.253603
$952$		0			0
$953$	−24.6105	+	29.3297i	−0.797214	+	0.950083i	−0.999573	−	0.0292289i	$-0.990695\pi$
$953$	−24.6105	+	29.3297i	−0.797214	+	0.950083i	0.202359	+	0.979311i	$0.435139\pi$
$954$		0			0
$955$	−11.2746	+	13.6772i	−0.364837	+	0.442585i
$956$		0			0
$957$	8.88669	−	5.13073i	0.287266	−	0.165853i
$958$		0			0
$959$	−0.0442615	−	0.251019i	−0.00142928	−	0.00810583i
$960$		0			0
$961$	−3.41637	+	5.91733i	−0.110206	+	0.190882i
$962$		0			0
$963$	−35.3472	−	42.1252i	−1.13905	−	1.35747i
$964$		0			0
$965$	−6.13209	−	33.0852i	−0.197399	−	1.06505i
$966$		0			0
$967$	48.8965	+	8.62177i	1.57241	+	0.277257i	0.890777	−	0.454441i	$-0.150161\pi$
$967$	48.8965	+	8.62177i	1.57241	+	0.277257i	0.681628	+	0.731699i	$0.261272\pi$
$968$		0			0
$969$	4.39681	+	1.69069i	0.141246	+	0.0543129i
$970$		0			0
$971$	−7.62257	+	43.2298i	−0.244620	+	1.38731i	0.576754	+	0.816918i	$0.304319\pi$
$971$	−7.62257	+	43.2298i	−0.244620	+	1.38731i	−0.821374	+	0.570391i	$0.806792\pi$
$972$		0			0
$973$	1.07449	−	2.95215i	0.0344467	−	0.0946415i
$974$		0			0
$975$	−1.90366	−	9.79314i	−0.0609659	−	0.313631i
$976$		0			0
$977$	−25.7948	−	14.8927i	−0.825250	−	0.476458i	0.0269734	−	0.999636i	$-0.491413\pi$
$977$	−25.7948	−	14.8927i	−0.825250	−	0.476458i	−0.852224	+	0.523178i	$0.824746\pi$
$978$		0			0
$979$	−2.35064	−	13.3311i	−0.0751268	−	0.426065i
$980$		0			0
$981$	−3.96939	−	6.87519i	−0.126733	−	0.219508i
$982$		0			0
$983$	14.8621	+	40.8333i	0.474028	+	1.30238i	0.914490	+	0.404610i	$0.132593\pi$
$983$	14.8621	+	40.8333i	0.474028	+	1.30238i	−0.440462	+	0.897771i	$0.645185\pi$
$984$		0			0
$985$	−9.71654	+	58.0649i	−0.309595	+	1.85010i
$986$		0			0
$987$			8.53279i			0.271602i
$988$		0			0
$989$	−20.3668			−0.647627
$990$		0			0
$991$	−45.0781	−	37.8250i	−1.43195	−	1.20155i	−0.944547	−	0.328377i	$-0.893498\pi$
$991$	−45.0781	−	37.8250i	−1.43195	−	1.20155i	−0.487407	−	0.873175i	$-0.662057\pi$
$992$		0			0
$993$	2.17203	+	5.96760i	0.0689273	+	0.189376i
$994$		0			0
$995$	−0.171304	−	0.0969184i	−0.00543070	−	0.00307252i
$996$		0			0
$997$	29.2085	−	5.15024i	0.925042	−	0.163110i	0.309216	−	0.950992i	$-0.399933\pi$
$997$	29.2085	−	5.15024i	0.925042	−	0.163110i	0.615826	+	0.787882i	$0.288822\pi$
$998$		0			0
$999$	−0.694265	+	1.20250i	−0.0219656	+	0.0380455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.cg.a.169.18	yes	180
5.4	even	2	inner	760.2.cg.a.169.13	yes	180
19.9	even	9	inner	760.2.cg.a.9.13	✓	180
95.9	even	18	inner	760.2.cg.a.9.18	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.cg.a.9.13	✓	180	19.9	even	9	inner
760.2.cg.a.9.18	yes	180	95.9	even	18	inner
760.2.cg.a.169.13	yes	180	5.4	even	2	inner
760.2.cg.a.169.18	yes	180	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:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.cg (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.248287 - 0.295897i) q^{3} +(1.42231 - 1.72541i) q^{5} +(1.75773 - 1.01483i) q^{7} +(0.495036 + 2.80749i) q^{9} +O(q^{10})\)	\(q+(0.248287 - 0.295897i) q^{3} +(1.42231 - 1.72541i) q^{5} +(1.75773 - 1.01483i) q^{7} +(0.495036 + 2.80749i) q^{9} +(-2.49808 + 4.32679i) q^{11} +(3.32037 + 3.95706i) q^{13} +(-0.157403 - 0.849254i) q^{15} +(2.75531 + 0.485835i) q^{17} +(2.11103 + 3.81360i) q^{19} +(0.136138 - 0.772075i) q^{21} +(2.36723 - 6.50391i) q^{23} +(-0.954078 - 4.90813i) q^{25} +(1.95719 + 1.12998i) q^{27} +(-0.923331 - 5.23647i) q^{29} +(-3.07542 - 5.32678i) q^{31} +(0.660045 + 1.81346i) q^{33} +(0.749044 - 4.47620i) q^{35} +0.614404i q^{37} +1.99529 q^{39} +(3.88992 + 3.26403i) q^{41} +(-1.00644 - 2.76516i) q^{43} +(5.54816 + 3.13897i) q^{45} +(-10.7185 + 1.88996i) q^{47} +(-1.44026 + 2.49460i) q^{49} +(0.827865 - 0.694661i) q^{51} +(4.43998 - 12.1987i) q^{53} +(3.91246 + 10.4642i) q^{55} +(1.65257 + 0.322219i) q^{57} +(0.214362 - 1.21571i) q^{59} +(11.9813 + 4.36085i) q^{61} +(3.71925 + 4.43243i) q^{63} +(11.5502 - 0.100835i) q^{65} +(-0.339144 + 0.0598002i) q^{67} +(-1.33673 - 2.31529i) q^{69} +(-12.3969 + 4.51209i) q^{71} +(-2.77452 + 3.30654i) q^{73} +(-1.68919 - 0.936316i) q^{75} +10.1404i q^{77} +(-1.12187 - 0.941358i) q^{79} +(-7.21632 + 2.62653i) q^{81} +(6.12427 - 3.53585i) q^{83} +(4.75717 - 4.06303i) q^{85} +(-1.77871 - 1.02694i) q^{87} +(-2.07556 + 1.74160i) q^{89} +(9.85205 + 3.58585i) q^{91} +(-2.33976 - 0.412563i) q^{93} +(9.58256 + 1.78172i) q^{95} +(-10.4928 - 1.85016i) q^{97} +(-13.3841 - 4.87140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q+O(q^{10}) \) 180 * q	\( 180 q - 12 q^{15} + 12 q^{25} + 24 q^{35} - 18 q^{41} + 18 q^{45} + 90 q^{49} + 36 q^{51} - 36 q^{55} - 12 q^{59} + 48 q^{69} - 24 q^{71} - 156 q^{79} + 24 q^{81} + 12 q^{85} - 36 q^{89} + 36 q^{91} + 78 q^{95} + 42 q^{99}+O(q^{100}) \) 180 * q - 12 * q^15 + 12 * q^25 + 24 * q^35 - 18 * q^41 + 18 * q^45 + 90 * q^49 + 36 * q^51 - 36 * q^55 - 12 * q^59 + 48 * q^69 - 24 * q^71 - 156 * q^79 + 24 * q^81 + 12 * q^85 - 36 * q^89 + 36 * q^91 + 78 * q^95 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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