LMFDB - Embedded newform 360.2.bi.b.49.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(49,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))

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

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

chi := DirichletCharacter("360.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.11
Character	$\chi$	$=$	360.49
Dual form			360.2.bi.b.169.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11432 + 1.32601i) q^{3} +(-1.73442 + 1.41130i) q^{5} +(-2.19623 + 1.26799i) q^{7} +(-0.516592 + 2.95519i) q^{9} +O(q^{10})$	\(q+(1.11432 + 1.32601i) q^{3} +(-1.73442 + 1.41130i) q^{5} +(-2.19623 + 1.26799i) q^{7} +(-0.516592 + 2.95519i) q^{9} +(0.162174 + 0.280893i) q^{11} +(-4.05034 - 2.33846i) q^{13} +(-3.80410 - 0.727221i) q^{15} +5.64078i q^{17} +5.56655 q^{19} +(-4.12867 - 1.49927i) q^{21} +(-1.27535 - 0.736327i) q^{23} +(1.01646 - 4.89559i) q^{25} +(-4.49425 + 2.60801i) q^{27} +(4.86245 + 8.42201i) q^{29} +(3.52462 - 6.10482i) q^{31} +(-0.191753 + 0.528047i) q^{33} +(2.01967 - 5.29878i) q^{35} +4.20861i q^{37} +(-1.41254 - 7.97657i) q^{39} +(-0.881632 + 1.52703i) q^{41} +(1.77359 - 1.02398i) q^{43} +(-3.27467 - 5.85462i) q^{45} +(5.98066 - 3.45294i) q^{47} +(-0.284380 + 0.492561i) q^{49} +(-7.47971 + 6.28562i) q^{51} +4.99779i q^{53} +(-0.677703 - 0.258312i) q^{55} +(6.20291 + 7.38129i) q^{57} +(-3.40392 + 5.89576i) q^{59} +(5.14339 + 8.90861i) q^{61} +(-2.61261 - 7.14531i) q^{63} +(10.3253 - 1.66036i) q^{65} +(4.27739 + 2.46955i) q^{67} +(-0.444776 - 2.51163i) q^{69} +2.24803 q^{71} -12.7249i q^{73} +(7.62425 - 4.10742i) q^{75} +(-0.712341 - 0.411270i) q^{77} +(-8.27179 - 14.3272i) q^{79} +(-8.46627 - 3.05325i) q^{81} +(10.9169 - 6.30288i) q^{83} +(-7.96084 - 9.78350i) q^{85} +(-5.74933 + 15.8324i) q^{87} +3.66831 q^{89} +11.8606 q^{91} +(12.0226 - 2.12904i) q^{93} +(-9.65477 + 7.85608i) q^{95} +(1.69883 - 0.980821i) q^{97} +(-0.913869 + 0.334147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) $ 32 * q - 2 * q^5 + 4 * q^9	$ 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) $ 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.11432	+	1.32601i	0.643352	+	0.765571i
$3$	1.11432	+	1.32601i	0.643352	+	0.765571i
$4$		0			0
$5$	−1.73442	+	1.41130i	−0.775658	+	0.631153i
$5$	−1.73442	+	1.41130i	−0.775658	+	0.631153i
$6$		0			0
$7$	−2.19623	+	1.26799i	−0.830097	+	0.479257i	−0.853886	−	0.520460i	$-0.825760\pi$
$7$	−2.19623	+	1.26799i	−0.830097	+	0.479257i	0.0237887	+	0.999717i	$0.492427\pi$
$8$		0			0
$9$	−0.516592	+	2.95519i	−0.172197	+	0.985063i
$10$		0			0
$11$	0.162174	+	0.280893i	0.0488972	+	0.0846924i	0.889438	−	0.457056i	$-0.151096\pi$
$11$	0.162174	+	0.280893i	0.0488972	+	0.0846924i	−0.840541	+	0.541748i	$0.817763\pi$
$12$		0			0
$13$	−4.05034	−	2.33846i	−1.12336	−	0.648573i	−0.181105	−	0.983464i	$-0.557967\pi$
$13$	−4.05034	−	2.33846i	−1.12336	−	0.648573i	−0.942257	+	0.334890i	$0.891301\pi$
$14$		0			0
$15$	−3.80410	−	0.727221i	−0.982213	−	0.187768i
$16$		0			0
$17$			5.64078i			1.36809i	0.729440	+	0.684045i	$0.239781\pi$
$17$			5.64078i			1.36809i	−0.729440	+	0.684045i	$0.760219\pi$
$18$		0			0
$19$	5.56655			1.27705			0.638527	−	0.769599i	$-0.279544\pi$
$19$	5.56655			1.27705			0.638527	+	0.769599i	$0.279544\pi$
$20$		0			0
$21$	−4.12867	−	1.49927i	−0.900949	−	0.327167i
$22$		0			0
$23$	−1.27535	−	0.736327i	−0.265930	−	0.153535i	0.361107	−	0.932525i	$-0.382399\pi$
$23$	−1.27535	−	0.736327i	−0.265930	−	0.153535i	−0.627037	+	0.778990i	$0.715732\pi$
$24$		0			0
$25$	1.01646	−	4.89559i	0.203291	−	0.979118i
$26$		0			0
$27$	−4.49425	+	2.60801i	−0.864918	+	0.501913i
$28$		0			0
$29$	4.86245	+	8.42201i	0.902934	+	1.56393i	0.823667	+	0.567074i	$0.191925\pi$
$29$	4.86245	+	8.42201i	0.902934	+	1.56393i	0.0792671	+	0.996853i	$0.474742\pi$
$30$		0			0
$31$	3.52462	−	6.10482i	0.633041	−	1.09646i	−0.353886	−	0.935289i	$-0.615140\pi$
$31$	3.52462	−	6.10482i	0.633041	−	1.09646i	0.986927	−	0.161170i	$-0.0515268\pi$
$32$		0			0
$33$	−0.191753	+	0.528047i	−0.0333799	+	0.0919213i
$34$		0			0
$35$	2.01967	−	5.29878i	0.341387	−	0.895658i
$36$		0			0
$37$			4.20861i			0.691891i	0.938255	+	0.345946i	$0.112442\pi$
$37$			4.20861i			0.691891i	−0.938255	+	0.345946i	$0.887558\pi$
$38$		0			0
$39$	−1.41254	−	7.97657i	−0.226188	−	1.27727i
$40$		0			0
$41$	−0.881632	+	1.52703i	−0.137688	+	0.238482i	−0.926621	−	0.375997i	$-0.877300\pi$
$41$	−0.881632	+	1.52703i	−0.137688	+	0.238482i	0.788933	+	0.614479i	$0.210634\pi$
$42$		0			0
$43$	1.77359	−	1.02398i	0.270470	−	0.156156i	−0.358631	−	0.933479i	$-0.616756\pi$
$43$	1.77359	−	1.02398i	0.270470	−	0.156156i	0.629101	+	0.777323i	$0.283423\pi$
$44$		0			0
$45$	−3.27467	−	5.85462i	−0.488159	−	0.872755i
$46$		0			0
$47$	5.98066	−	3.45294i	0.872369	−	0.503662i	0.00423412	−	0.999991i	$-0.498652\pi$
$47$	5.98066	−	3.45294i	0.872369	−	0.503662i	0.868135	+	0.496329i	$0.165319\pi$
$48$		0			0
$49$	−0.284380	+	0.492561i	−0.0406257	+	0.0703658i
$50$		0			0
$51$	−7.47971	+	6.28562i	−1.04737	+	0.880163i
$52$		0			0
$53$			4.99779i			0.686500i	0.939244	+	0.343250i	$0.111528\pi$
$53$			4.99779i			0.686500i	−0.939244	+	0.343250i	$0.888472\pi$
$54$		0			0
$55$	−0.677703	−	0.258312i	−0.0913814	−	0.0348307i
$56$		0			0
$57$	6.20291	+	7.38129i	0.821595	+	0.977676i
$58$		0			0
$59$	−3.40392	+	5.89576i	−0.443152	+	0.767562i	−0.997921	−	0.0644422i	$-0.979473\pi$
$59$	−3.40392	+	5.89576i	−0.443152	+	0.767562i	0.554769	+	0.832004i	$0.312807\pi$
$60$		0			0
$61$	5.14339	+	8.90861i	0.658543	+	1.14063i	0.980993	+	0.194044i	$0.0621604\pi$
$61$	5.14339	+	8.90861i	0.658543	+	1.14063i	−0.322450	+	0.946587i	$0.604506\pi$
$62$		0			0
$63$	−2.61261	−	7.14531i	−0.329158	−	0.900224i
$64$		0			0
$65$	10.3253	−	1.66036i	1.28069	−	0.205942i
$66$		0			0
$67$	4.27739	+	2.46955i	0.522566	+	0.301704i	0.737984	−	0.674818i	$-0.235778\pi$
$67$	4.27739	+	2.46955i	0.522566	+	0.301704i	−0.215418	+	0.976522i	$0.569111\pi$
$68$		0			0
$69$	−0.444776	−	2.51163i	−0.0535448	−	0.302365i
$70$		0			0
$71$	2.24803			0.266792			0.133396	−	0.991063i	$-0.457412\pi$
$71$	2.24803			0.266792			0.133396	+	0.991063i	$0.457412\pi$
$72$		0			0
$73$		−	12.7249i		−	1.48934i	−0.667435	−	0.744668i	$-0.732608\pi$
$73$		−	12.7249i		−	1.48934i	0.667435	−	0.744668i	$-0.267392\pi$
$74$		0			0
$75$	7.62425	−	4.10742i	0.880372	−	0.474284i
$76$		0			0
$77$	−0.712341	−	0.411270i	−0.0811788	−	0.0468686i
$78$		0			0
$79$	−8.27179	−	14.3272i	−0.930649	−	1.61193i	−0.782215	−	0.623009i	$-0.785910\pi$
$79$	−8.27179	−	14.3272i	−0.930649	−	1.61193i	−0.148434	−	0.988922i	$-0.547423\pi$
$80$		0			0
$81$	−8.46627	−	3.05325i	−0.940696	−	0.339250i
$82$		0			0
$83$	10.9169	−	6.30288i	1.19829	−	0.691831i	0.238113	−	0.971237i	$-0.423471\pi$
$83$	10.9169	−	6.30288i	1.19829	−	0.691831i	0.960173	+	0.279406i	$0.0901377\pi$
$84$		0			0
$85$	−7.96084	−	9.78350i	−0.863474	−	1.06117i
$86$		0			0
$87$	−5.74933	+	15.8324i	−0.616393	+	1.69742i
$88$		0			0
$89$	3.66831			0.388840			0.194420	−	0.980918i	$-0.437718\pi$
$89$	3.66831			0.388840			0.194420	+	0.980918i	$0.437718\pi$
$90$		0			0
$91$	11.8606			1.24333
$92$		0			0
$93$	12.0226	−	2.12904i	1.24668	−	0.220771i
$94$		0			0
$95$	−9.65477	+	7.85608i	−0.990558	+	0.806017i
$96$		0			0
$97$	1.69883	−	0.980821i	0.172490	−	0.0995873i	−0.411269	−	0.911514i	$-0.634914\pi$
$97$	1.69883	−	0.980821i	0.172490	−	0.0995873i	0.583760	+	0.811927i	$0.301581\pi$
$98$		0			0
$99$	−0.913869	+	0.334147i	−0.0918473	+	0.0335830i
$100$		0			0
$101$	−8.41577	−	14.5765i	−0.837401	−	1.45042i	−0.892061	−	0.451916i	$-0.850741\pi$
$101$	−8.41577	−	14.5765i	−0.837401	−	1.45042i	0.0546600	−	0.998505i	$-0.482593\pi$
$102$		0			0
$103$	9.24649	+	5.33846i	0.911084	+	0.526015i	0.880780	−	0.473526i	$-0.157019\pi$
$103$	9.24649	+	5.33846i	0.911084	+	0.526015i	0.0303041	+	0.999541i	$0.490352\pi$
$104$		0			0
$105$	9.27679	−	3.22643i	0.905322	−	0.314867i
$106$		0			0
$107$			7.04573i			0.681136i	0.940220	+	0.340568i	$0.110619\pi$
$107$			7.04573i			0.681136i	−0.940220	+	0.340568i	$0.889381\pi$
$108$		0			0
$109$	−1.83913			−0.176157			−0.0880784	−	0.996114i	$-0.528073\pi$
$109$	−1.83913			−0.176157			−0.0880784	+	0.996114i	$0.528073\pi$
$110$		0			0
$111$	−5.58065	+	4.68973i	−0.529692	+	0.445129i
$112$		0			0
$113$	−5.70763	−	3.29530i	−0.536929	−	0.309996i	0.206905	−	0.978361i	$-0.433661\pi$
$113$	−5.70763	−	3.29530i	−0.536929	−	0.309996i	−0.743833	+	0.668365i	$0.766994\pi$
$114$		0			0
$115$	3.25119	−	0.522808i	0.303175	−	0.0487521i
$116$		0			0
$117$	9.00297	−	10.7615i	0.832325	−	0.994899i
$118$		0			0
$119$	−7.15247	−	12.3884i	−0.655666	−	1.13565i
$120$		0			0
$121$	5.44740	−	9.43517i	0.495218	−	0.857743i
$122$		0			0
$123$	−3.00727	+	0.532548i	−0.271157	+	0.0480182i
$124$		0			0
$125$	5.14619	+	9.92556i	0.460289	+	0.887769i
$126$		0			0
$127$			5.49270i			0.487398i	0.969851	+	0.243699i	$0.0783609\pi$
$127$			5.49270i			0.487398i	−0.969851	+	0.243699i	$0.921639\pi$
$128$		0			0
$129$	3.33415	+	1.21075i	0.293556	+	0.106601i
$130$		0			0
$131$	4.35241	−	7.53860i	0.380272	−	0.658651i	−0.610829	−	0.791763i	$-0.709164\pi$
$131$	4.35241	−	7.53860i	0.380272	−	0.658651i	0.991101	+	0.133112i	$0.0424970\pi$
$132$		0			0
$133$	−12.2254	+	7.05836i	−1.06008	+	0.612037i
$134$		0			0
$135$	4.11424	−	10.8661i	0.354097	−	0.935209i
$136$		0			0
$137$	−13.4131	+	7.74408i	−1.14596	+	0.661621i	−0.947900	−	0.318569i	$-0.896798\pi$
$137$	−13.4131	+	7.74408i	−1.14596	+	0.661621i	−0.198061	+	0.980190i	$0.563465\pi$
$138$		0			0
$139$	−3.27817	+	5.67796i	−0.278051	+	0.481598i	−0.970900	−	0.239484i	$-0.923022\pi$
$139$	−3.27817	+	5.67796i	−0.278051	+	0.481598i	0.692849	+	0.721082i	$0.256355\pi$
$140$		0			0
$141$	11.2430	+	4.08273i	0.946829	+	0.343828i
$142$		0			0
$143$		−	1.51695i		−	0.126854i
$144$		0			0
$145$	−20.3195	−	7.74495i	−1.68745	−	0.643184i
$146$		0			0
$147$	−0.970029	+	0.171779i	−0.0800067	+	0.0141681i
$148$		0			0
$149$	−3.52117	+	6.09885i	−0.288466	+	0.499638i	−0.973444	−	0.228926i	$-0.926479\pi$
$149$	−3.52117	+	6.09885i	−0.288466	+	0.499638i	0.684978	+	0.728564i	$0.259812\pi$
$150$		0			0
$151$	7.88584	+	13.6587i	0.641740	+	1.11153i	0.985044	+	0.172302i	$0.0551206\pi$
$151$	7.88584	+	13.6587i	0.641740	+	1.11153i	−0.343304	+	0.939224i	$0.611546\pi$
$152$		0			0
$153$	−16.6696	−	2.91398i	−1.34765	−	0.235581i
$154$		0			0
$155$	2.50256	+	15.5627i	0.201010	+	1.25002i
$156$		0			0
$157$	−3.33110	−	1.92321i	−0.265851	−	0.153489i	0.361150	−	0.932508i	$-0.382384\pi$
$157$	−3.33110	−	1.92321i	−0.265851	−	0.153489i	−0.627001	+	0.779019i	$0.715718\pi$
$158$		0			0
$159$	−6.62711	+	5.56913i	−0.525564	+	0.441661i
$160$		0			0
$161$	3.73463			0.294330
$162$		0			0
$163$			2.25624i			0.176722i	0.996089	+	0.0883612i	$0.0281630\pi$
$163$			2.25624i			0.176722i	−0.996089	+	0.0883612i	$0.971837\pi$
$164$		0			0
$165$	−0.412653	−	1.18648i	−0.0321250	−	0.0923673i
$166$		0			0
$167$	0.705248	+	0.407175i	0.0545737	+	0.0315081i	0.527039	−	0.849841i	$-0.323302\pi$
$167$	0.705248	+	0.407175i	0.0545737	+	0.0315081i	−0.472465	+	0.881349i	$0.656636\pi$
$168$		0			0
$169$	4.43683	+	7.68482i	0.341295	+	0.591140i
$170$		0			0
$171$	−2.87563	+	16.4502i	−0.219905	+	1.25798i
$172$		0			0
$173$	6.29917	−	3.63683i	0.478917	−	0.276503i	−0.241048	−	0.970513i	$-0.577491\pi$
$173$	6.29917	−	3.63683i	0.478917	−	0.276503i	0.719965	+	0.694010i	$0.244158\pi$
$174$		0			0
$175$	3.97521	+	12.0407i	0.300498	+	0.910192i
$176$		0			0
$177$	−11.6109	+	2.05613i	−0.872726	+	0.154548i
$178$		0			0
$179$	−0.167310			−0.0125053			−0.00625267	−	0.999980i	$-0.501990\pi$
$179$	−0.167310			−0.0125053			−0.00625267	+	0.999980i	$0.501990\pi$
$180$		0			0
$181$	0.0194975			0.00144924			0.000724619	−	1.00000i	$-0.499769\pi$
$181$	0.0194975			0.00144924			0.000724619		1.00000i	$0.499769\pi$
$182$		0			0
$183$	−6.08151	+	16.7472i	−0.449558	+	1.23799i
$184$		0			0
$185$	−5.93962	−	7.29952i	−0.436689	−	0.536671i
$186$		0			0
$187$	−1.58445	+	0.914785i	−0.115867	+	0.0668957i
$188$		0			0
$189$	6.56346	−	11.4265i	0.477421	−	0.831154i
$190$		0			0
$191$	−8.07558	−	13.9873i	−0.584328	−	1.01209i	−0.994959	−	0.100285i	$-0.968025\pi$
$191$	−8.07558	−	13.9873i	−0.584328	−	1.01209i	0.410630	−	0.911802i	$-0.365309\pi$
$192$		0			0
$193$	13.1494	+	7.59180i	0.946514	+	0.546470i	0.891996	−	0.452043i	$-0.149305\pi$
$193$	13.1494	+	7.59180i	0.946514	+	0.546470i	0.0545175	+	0.998513i	$0.482638\pi$
$194$		0			0
$195$	13.7073	+	11.8412i	0.981600	+	0.847969i
$196$		0			0
$197$			18.1743i			1.29487i	0.762121	+	0.647434i	$0.224158\pi$
$197$			18.1743i			1.29487i	−0.762121	+	0.647434i	$0.775842\pi$
$198$		0			0
$199$	−19.6978			−1.39634			−0.698171	−	0.715931i	$-0.746002\pi$
$199$	−19.6978			−1.39634			−0.698171	+	0.715931i	$0.746002\pi$
$200$		0			0
$201$	1.49173	+	8.42371i	0.105218	+	0.594163i
$202$		0			0
$203$	−21.3581	−	12.3311i	−1.49905	−	0.865475i
$204$		0			0
$205$	−0.625978	−	3.89277i	−0.0437202	−	0.271883i
$206$		0			0
$207$	2.83482	−	3.38853i	0.197034	−	0.235519i
$208$		0			0
$209$	0.902748	+	1.56361i	0.0624444	+	0.108157i
$210$		0			0
$211$	−14.0692	+	24.3687i	−0.968567	+	1.67761i	−0.268857	+	0.963180i	$0.586646\pi$
$211$	−14.0692	+	24.3687i	−0.968567	+	1.67761i	−0.699710	+	0.714427i	$0.746687\pi$
$212$		0			0
$213$	2.50502	+	2.98090i	0.171641	+	0.204248i
$214$		0			0
$215$	−1.63101	+	4.27909i	−0.111234	+	0.291832i
$216$		0			0
$217$			17.8768i			1.21356i
$218$		0			0
$219$	16.8733	−	14.1796i	1.14019	−	0.958167i
$220$		0			0
$221$	13.1908	−	22.8471i	0.887306	−	1.53686i
$222$		0			0
$223$	−11.9520	+	6.90048i	−0.800364	+	0.462091i	−0.843599	−	0.536974i	$-0.819567\pi$
$223$	−11.9520	+	6.90048i	−0.800364	+	0.462091i	0.0432342	+	0.999065i	$0.486234\pi$
$224$		0			0
$225$	13.9423	+	5.53284i	0.929487	+	0.368856i
$226$		0			0
$227$	21.6937	−	12.5249i	1.43986	−	0.831305i	0.442023	−	0.897004i	$-0.354261\pi$
$227$	21.6937	−	12.5249i	1.43986	−	0.831305i	0.997839	+	0.0656989i	$0.0209277\pi$
$228$		0			0
$229$	−4.58756	+	7.94589i	−0.303155	+	0.525079i	−0.976849	−	0.213931i	$-0.931373\pi$
$229$	−4.58756	+	7.94589i	−0.303155	+	0.525079i	0.673694	+	0.739010i	$0.264706\pi$
$230$		0			0
$231$	−0.248427	−	1.40286i	−0.0163453	−	0.0923012i
$232$		0			0
$233$		−	1.77211i		−	0.116095i	−0.998314	−	0.0580474i	$-0.981513\pi$
$233$		−	1.77211i		−	0.116095i	0.998314	−	0.0580474i	$-0.0184874\pi$
$234$		0			0
$235$	−5.49987	+	14.4294i	−0.358772	+	0.941268i
$236$		0			0
$237$	9.78052	−	26.9335i	0.635313	−	1.74952i
$238$		0			0
$239$	4.33313	−	7.50521i	0.280287	−	0.485471i	−0.691168	−	0.722694i	$-0.742904\pi$
$239$	4.33313	−	7.50521i	0.280287	−	0.485471i	0.971455	+	0.237222i	$0.0762370\pi$
$240$		0			0
$241$	4.58521	+	7.94181i	0.295359	+	0.511577i	0.975068	−	0.221905i	$-0.0712273\pi$
$241$	4.58521	+	7.94181i	0.295359	+	0.511577i	−0.679709	+	0.733482i	$0.737894\pi$
$242$		0			0
$243$	−5.38548	−	14.6286i	−0.345479	−	0.938427i
$244$		0			0
$245$	−0.201916	−	1.25566i	−0.0128999	−	0.0802209i
$246$		0			0
$247$	−22.5464	−	13.0172i	−1.43459	−	0.828264i
$248$		0			0
$249$	20.5226	+	7.45249i	1.30057	+	0.472282i
$250$		0			0
$251$	−20.8071			−1.31333			−0.656665	−	0.754183i	$-0.728033\pi$
$251$	−20.8071			−1.31333			−0.656665	+	0.754183i	$0.728033\pi$
$252$		0			0
$253$		−	0.477651i		−	0.0300297i
$254$		0			0
$255$	4.10209	−	21.4581i	0.256883	−	1.34376i
$256$		0			0
$257$	−25.4199	−	14.6762i	−1.58565	−	0.915476i	−0.994012	−	0.109274i	$-0.965147\pi$
$257$	−25.4199	−	14.6762i	−1.58565	−	0.915476i	−0.591640	−	0.806202i	$-0.701519\pi$
$258$		0			0
$259$	−5.33649	−	9.24308i	−0.331594	−	0.574337i
$260$		0			0
$261$	−27.4005	+	10.0187i	−1.69605	+	0.620142i
$262$		0			0
$263$	−11.1242	+	6.42258i	−0.685950	+	0.396033i	−0.802093	−	0.597199i	$-0.796280\pi$
$263$	−11.1242	+	6.42258i	−0.685950	+	0.396033i	0.116143	+	0.993233i	$0.462947\pi$
$264$		0			0
$265$	−7.05339	−	8.66829i	−0.433286	−	0.532489i
$266$		0			0
$267$	4.08766	+	4.86421i	0.250161	+	0.297685i
$268$		0			0
$269$	12.0183			0.732771			0.366385	−	0.930463i	$-0.380595\pi$
$269$	12.0183			0.732771			0.366385	+	0.930463i	$0.380595\pi$
$270$		0			0
$271$	29.7018			1.80426			0.902128	−	0.431469i	$-0.142004\pi$
$271$	29.7018			1.80426			0.902128	+	0.431469i	$0.142004\pi$
$272$		0			0
$273$	13.2165	+	15.7273i	0.799900	+	0.951859i
$274$		0			0
$275$	1.53998	−	0.508420i	0.0928643	−	0.0306589i
$276$		0			0
$277$	9.54900	−	5.51312i	0.573744	−	0.331251i	−0.184899	−	0.982757i	$-0.559196\pi$
$277$	9.54900	−	5.51312i	0.573744	−	0.331251i	0.758643	+	0.651506i	$0.225863\pi$
$278$		0			0
$279$	16.2201	+	13.5696i	0.971073	+	0.812392i
$280$		0			0
$281$	−13.2918	−	23.0221i	−0.792924	−	1.37338i	−0.924149	−	0.382031i	$-0.875225\pi$
$281$	−13.2918	−	23.0221i	−0.792924	−	1.37338i	0.131226	−	0.991353i	$-0.458109\pi$
$282$		0			0
$283$	17.6386	+	10.1837i	1.04851	+	0.605356i	0.922231	−	0.386639i	$-0.126364\pi$
$283$	17.6386	+	10.1837i	1.04851	+	0.605356i	0.126276	+	0.991995i	$0.459698\pi$
$284$		0			0
$285$	−21.1757	−	4.04812i	−1.25434	−	0.239790i
$286$		0			0
$287$		−	4.47162i		−	0.263951i
$288$		0			0
$289$	−14.8184			−0.871669
$290$		0			0
$291$	3.19361	+	1.15972i	0.187213	+	0.0679838i
$292$		0			0
$293$	23.3961	+	13.5077i	1.36681	+	0.789130i	0.990520	−	0.137370i	$-0.0438649\pi$
$293$	23.3961	+	13.5077i	1.36681	+	0.789130i	0.376294	+	0.926500i	$0.377198\pi$
$294$		0			0
$295$	−2.41685	−	15.0297i	−0.140715	−	0.875063i
$296$		0			0
$297$	−1.46142	−	0.839451i	−0.0848003	−	0.0487099i
$298$		0			0
$299$	3.44375	+	5.96474i	0.199157	+	0.344950i
$300$		0			0
$301$	−2.59681	+	4.49781i	−0.149678	+	0.259249i
$302$		0			0
$303$	9.95076	−	27.4023i	0.571656	−	1.57422i
$304$		0			0
$305$	−21.4935	−	8.19244i	−1.23072	−	0.469098i
$306$		0			0
$307$		−	30.3051i		−	1.72960i	−0.502113	−	0.864802i	$-0.667444\pi$
$307$		−	30.3051i		−	1.72960i	0.502113	−	0.864802i	$-0.332556\pi$
$308$		0			0
$309$	3.22469	+	18.2097i	0.183446	+	1.03591i
$310$		0			0
$311$	11.0014	−	19.0549i	0.623830	−	1.08051i	−0.364935	−	0.931033i	$-0.618909\pi$
$311$	11.0014	−	19.0549i	0.623830	−	1.08051i	0.988766	−	0.149473i	$-0.0477578\pi$
$312$		0			0
$313$	21.0849	−	12.1733i	1.19179	−	0.688078i	0.233075	−	0.972459i	$-0.425121\pi$
$313$	21.0849	−	12.1733i	1.19179	−	0.688078i	0.958712	+	0.284380i	$0.0917878\pi$
$314$		0			0
$315$	14.6156	+	8.70582i	0.823493	+	0.490518i
$316$		0			0
$317$	5.69605	−	3.28862i	0.319922	−	0.184707i	−0.331436	−	0.943478i	$-0.607533\pi$
$317$	5.69605	−	3.28862i	0.319922	−	0.184707i	0.651358	+	0.758771i	$0.274200\pi$
$318$		0			0
$319$	−1.57712	+	2.73165i	−0.0883019	+	0.152943i
$320$		0			0
$321$	−9.34269	+	7.85118i	−0.521458	+	0.438210i
$322$		0			0
$323$			31.3997i			1.74713i
$324$		0			0
$325$	−15.5652	+	17.4519i	−0.863400	+	0.968055i
$326$		0			0
$327$	−2.04938	−	2.43870i	−0.113331	−	0.134861i
$328$		0			0
$329$	−8.75661	+	15.1669i	−0.482767	+	0.836177i
$330$		0			0
$331$	−10.5238	−	18.2278i	−0.578441	−	1.00189i	−0.995658	−	0.0930830i	$-0.970328\pi$
$331$	−10.5238	−	18.2278i	−0.578441	−	1.00189i	0.417217	−	0.908807i	$-0.363006\pi$
$332$		0			0
$333$	−12.4372	−	2.17413i	−0.681556	−	0.119142i
$334$		0			0
$335$	−10.9041	+	1.75343i	−0.595754	+	0.0958003i
$336$		0			0
$337$	24.7840	+	14.3090i	1.35007	+	0.779463i	0.988259	−	0.152789i	$-0.0488254\pi$
$337$	24.7840	+	14.3090i	1.35007	+	0.779463i	0.361811	+	0.932252i	$0.382159\pi$
$338$		0			0
$339$	−1.99052	−	11.2404i	−0.108110	−	0.610493i
$340$		0			0
$341$	2.28640			0.123816
$342$		0			0
$343$		−	19.1943i		−	1.03639i
$344$		0			0
$345$	4.31610	+	3.72852i	0.232371	+	0.200737i
$346$		0			0
$347$	5.45837	+	3.15139i	0.293021	+	0.169176i	0.639303	−	0.768955i	$-0.279223\pi$
$347$	5.45837	+	3.15139i	0.293021	+	0.169176i	−0.346282	+	0.938130i	$0.612556\pi$
$348$		0			0
$349$	7.10465	+	12.3056i	0.380303	+	0.658705i	0.991106	−	0.133078i	$-0.0424862\pi$
$349$	7.10465	+	12.3056i	0.380303	+	0.658705i	−0.610802	+	0.791783i	$0.709153\pi$
$350$		0			0
$351$	24.3020	−	0.0537023i	1.29714	−	0.00286642i
$352$		0			0
$353$	−2.77511	+	1.60221i	−0.147704	+	0.0852769i	−0.572031	−	0.820232i	$-0.693844\pi$
$353$	−2.77511	+	1.60221i	−0.147704	+	0.0852769i	0.424327	+	0.905509i	$0.360511\pi$
$354$		0			0
$355$	−3.89903	+	3.17264i	−0.206939	+	0.168387i
$356$		0			0
$357$	8.45705	−	23.2889i	0.447594	−	1.23258i
$358$		0			0
$359$	4.40277			0.232369			0.116185	−	0.993228i	$-0.462934\pi$
$359$	4.40277			0.232369			0.116185	+	0.993228i	$0.462934\pi$
$360$		0			0
$361$	11.9865			0.630869
$362$		0			0
$363$	18.5812	−	3.29049i	0.975262	−	0.172706i
$364$		0			0
$365$	17.9587	+	22.0704i	0.939999	+	1.15522i
$366$		0			0
$367$	22.1268	−	12.7749i	1.15501	−	0.666846i	0.204907	−	0.978781i	$-0.434311\pi$
$367$	22.1268	−	12.7749i	1.15501	−	0.666846i	0.950103	+	0.311936i	$0.100977\pi$
$368$		0			0
$369$	−4.05722	−	3.39424i	−0.211210	−	0.176697i
$370$		0			0
$371$	−6.33717	−	10.9763i	−0.329010	−	0.569861i
$372$		0			0
$373$	−16.8349	−	9.71963i	−0.871678	−	0.503264i	−0.00377260	−	0.999993i	$-0.501201\pi$
$373$	−16.8349	−	9.71963i	−0.871678	−	0.503264i	−0.867906	+	0.496729i	$0.834534\pi$
$374$		0			0
$375$	−7.42688	+	17.8841i	−0.383522	+	0.923532i
$376$		0			0
$377$		−	45.4826i		−	2.34248i
$378$		0			0
$379$	20.2946			1.04246			0.521232	−	0.853415i	$-0.325473\pi$
$379$	20.2946			1.04246			0.521232	+	0.853415i	$0.325473\pi$
$380$		0			0
$381$	−7.28336	+	6.12061i	−0.373138	+	0.313568i
$382$		0			0
$383$	4.64265	+	2.68044i	0.237228	+	0.136964i	0.613902	−	0.789382i	$-0.289599\pi$
$383$	4.64265	+	2.68044i	0.237228	+	0.136964i	−0.376674	+	0.926346i	$0.622932\pi$
$384$		0			0
$385$	1.81593	−	0.292011i	0.0925483	−	0.0148823i
$386$		0			0
$387$	2.10984	+	5.77028i	0.107249	+	0.293320i
$388$		0			0
$389$	−3.85542	−	6.67778i	−0.195477	−	0.338577i	0.751580	−	0.659643i	$-0.229292\pi$
$389$	−3.85542	−	6.67778i	−0.195477	−	0.338577i	−0.947057	+	0.321066i	$0.895959\pi$
$390$		0			0
$391$	4.15345	−	7.19399i	0.210049	−	0.363816i
$392$		0			0
$393$	14.8462	−	2.62907i	0.748893	−	0.132619i
$394$		0			0
$395$	34.5667	+	13.1754i	1.73924	+	0.662926i
$396$		0			0
$397$			6.59387i			0.330937i	0.986215	+	0.165469i	$0.0529136\pi$
$397$			6.59387i			0.330937i	−0.986215	+	0.165469i	$0.947086\pi$
$398$		0			0
$399$	−22.9825	−	8.34576i	−1.15056	−	0.417811i
$400$		0			0
$401$	−11.7871	+	20.4158i	−0.588618	+	1.01952i	0.405796	+	0.913964i	$0.366994\pi$
$401$	−11.7871	+	20.4158i	−0.588618	+	1.01952i	−0.994414	+	0.105552i	$0.966339\pi$
$402$		0			0
$403$	−28.5518	+	16.4844i	−1.42227	+	0.821147i
$404$		0			0
$405$	18.9932	−	6.65282i	0.943777	−	0.330581i
$406$		0			0
$407$	−1.18217	+	0.682525i	−0.0585979	+	0.0338315i
$408$		0			0
$409$	9.28164	−	16.0763i	0.458948	−	0.794921i	−0.539958	−	0.841692i	$-0.681560\pi$
$409$	9.28164	−	16.0763i	0.458948	−	0.794921i	0.998906	+	0.0467713i	$0.0148932\pi$
$410$		0			0
$411$	−25.2152	−	9.15655i	−1.24377	−	0.451659i
$412$		0			0
$413$		−	17.2646i		−	0.849535i
$414$		0			0
$415$	−10.0393	+	26.3389i	−0.492809	+	1.29293i
$416$		0			0
$417$	−11.1819	+	1.98017i	−0.547582	+	0.0969694i
$418$		0			0
$419$	−0.738584	+	1.27926i	−0.0360822	+	0.0624962i	−0.883503	−	0.468426i	$-0.844821\pi$
$419$	−0.738584	+	1.27926i	−0.0360822	+	0.0624962i	0.847420	+	0.530922i	$0.178154\pi$
$420$		0			0
$421$	3.08269	+	5.33937i	0.150241	+	0.260225i	0.931316	−	0.364212i	$-0.118662\pi$
$421$	3.08269	+	5.33937i	0.150241	+	0.260225i	−0.781075	+	0.624437i	$0.785328\pi$
$422$		0			0
$423$	7.11451	+	19.4577i	0.345919	+	0.946067i
$424$		0			0
$425$	27.6149	+	5.73360i	1.33952	+	0.278121i
$426$		0			0
$427$	−22.5921	−	13.0436i	−1.09331	−	0.631223i
$428$		0			0
$429$	2.01149	−	1.69036i	0.0971154	−	0.0816115i
$430$		0			0
$431$	10.3519			0.498631			0.249316	−	0.968422i	$-0.419794\pi$
$431$	10.3519			0.498631			0.249316	+	0.968422i	$0.419794\pi$
$432$		0			0
$433$			6.70177i			0.322066i	0.986949	+	0.161033i	$0.0514826\pi$
$433$			6.70177i			0.322066i	−0.986949	+	0.161033i	$0.948517\pi$
$434$		0			0
$435$	−12.3726	−	35.5742i	−0.593219	−	1.70565i
$436$		0			0
$437$	−7.09933	−	4.09880i	−0.339607	−	0.196072i
$438$		0			0
$439$	3.99445	+	6.91859i	0.190645	+	0.330206i	0.945464	−	0.325726i	$-0.105609\pi$
$439$	3.99445	+	6.91859i	0.190645	+	0.330206i	−0.754819	+	0.655933i	$0.772275\pi$
$440$		0			0
$441$	−1.30870	−	1.09485i	−0.0623191	−	0.0521357i
$442$		0			0
$443$	−12.9916	+	7.50073i	−0.617252	+	0.356371i	−0.775798	−	0.630981i	$-0.782653\pi$
$443$	−12.9916	+	7.50073i	−0.617252	+	0.356371i	0.158546	+	0.987352i	$0.449319\pi$
$444$		0			0
$445$	−6.36241	+	5.17709i	−0.301607	+	0.245418i
$446$		0			0
$447$	−12.0108	+	2.12696i	−0.568093	+	0.100602i
$448$		0			0
$449$	−21.6048			−1.01959			−0.509797	−	0.860294i	$-0.670280\pi$
$449$	−21.6048			−1.01959			−0.509797	+	0.860294i	$0.670280\pi$
$450$		0			0
$451$	−0.571910			−0.0269302
$452$		0			0
$453$	−9.32417	+	25.6768i	−0.438088	+	1.20640i
$454$		0			0
$455$	−20.5714	+	16.7389i	−0.964401	+	0.784733i
$456$		0			0
$457$	14.0216	−	8.09539i	0.655904	−	0.378686i	−0.134811	−	0.990871i	$-0.543043\pi$
$457$	14.0216	−	8.09539i	0.655904	−	0.378686i	0.790714	+	0.612185i	$0.209709\pi$
$458$		0			0
$459$	−14.7112	−	25.3511i	−0.686661	−	1.18329i
$460$		0			0
$461$	4.40602	+	7.63146i	0.205209	+	0.355432i	0.950199	−	0.311643i	$-0.100879\pi$
$461$	4.40602	+	7.63146i	0.205209	+	0.355432i	−0.744990	+	0.667075i	$0.767546\pi$
$462$		0			0
$463$	1.11553	+	0.644053i	0.0518432	+	0.0299317i	0.525698	−	0.850672i	$-0.323804\pi$
$463$	1.11553	+	0.644053i	0.0518432	+	0.0299317i	−0.473854	+	0.880603i	$0.657138\pi$
$464$		0			0
$465$	−17.8476	+	20.6602i	−0.827661	+	0.958092i
$466$		0			0
$467$		−	26.9289i		−	1.24612i	−0.782174	−	0.623060i	$-0.785889\pi$
$467$		−	26.9289i		−	1.24612i	0.782174	−	0.623060i	$-0.214111\pi$
$468$		0			0
$469$	−12.5255			−0.578374
$470$		0			0
$471$	−1.16171	−	6.56014i	−0.0535289	−	0.302275i
$472$		0			0
$473$	0.575260	+	0.332126i	0.0264505	+	0.0152712i
$474$		0			0
$475$	5.65816	−	27.2516i	0.259614	−	1.25039i
$476$		0			0
$477$	−14.7694	−	2.58182i	−0.676245	−	0.118213i
$478$		0			0
$479$	16.7302	+	28.9776i	0.764423	+	1.32402i	0.940551	+	0.339653i	$0.110310\pi$
$479$	16.7302	+	28.9776i	0.764423	+	1.32402i	−0.176128	+	0.984367i	$0.556357\pi$
$480$		0			0
$481$	9.84168	−	17.0463i	0.448742	−	0.777244i
$482$		0			0
$483$	4.16157	+	4.95215i	0.189358	+	0.225331i
$484$		0			0
$485$	−1.56226	+	4.09872i	−0.0709386	+	0.186113i
$486$		0			0
$487$		−	17.2245i		−	0.780517i	−0.920705	−	0.390259i	$-0.872386\pi$
$487$		−	17.2245i		−	0.780517i	0.920705	−	0.390259i	$-0.127614\pi$
$488$		0			0
$489$	−2.99179	+	2.51417i	−0.135293	+	0.113695i
$490$		0			0
$491$	4.83732	−	8.37849i	0.218305	−	0.378116i	−0.735985	−	0.676998i	$-0.763280\pi$
$491$	4.83732	−	8.37849i	0.218305	−	0.378116i	0.954290	+	0.298882i	$0.0966138\pi$
$492$		0			0
$493$	−47.5067	+	27.4280i	−2.13959	+	1.23529i
$494$		0			0
$495$	1.11345	−	1.86930i	0.0500461	−	0.0840186i
$496$		0			0
$497$	−4.93719	+	2.85049i	−0.221463	+	0.127862i
$498$		0			0
$499$	3.52127	−	6.09901i	0.157634	−	0.273029i	−0.776381	−	0.630263i	$-0.782947\pi$
$499$	3.52127	−	6.09901i	0.157634	−	0.273029i	0.934015	+	0.357234i	$0.116280\pi$
$500$		0			0
$501$	0.245953	+	1.38889i	0.0109884	+	0.0620508i
$502$		0			0
$503$		−	3.33237i		−	0.148583i	−0.997237	−	0.0742914i	$-0.976330\pi$
$503$		−	3.33237i		−	0.148583i	0.997237	−	0.0742914i	$-0.0236695\pi$
$504$		0			0
$505$	35.1684	+	13.4047i	1.56497	+	0.596502i
$506$		0			0
$507$	−5.24608	+	14.4466i	−0.232987	+	0.641596i
$508$		0			0
$509$	14.4508	−	25.0296i	0.640521	−	1.10942i	−0.344795	−	0.938678i	$-0.612052\pi$
$509$	14.4508	−	25.0296i	0.640521	−	1.10942i	0.985317	−	0.170738i	$-0.0546151\pi$
$510$		0			0
$511$	16.1351	+	27.9468i	0.713775	+	1.23629i
$512$		0			0
$513$	−25.0175	+	14.5176i	−1.10455	+	0.640970i
$514$		0			0
$515$	−23.5715	+	3.79042i	−1.03869	+	0.167026i
$516$		0			0
$517$	1.93981	+	1.11995i	0.0853128	+	0.0492553i
$518$		0			0
$519$	11.8417	+	4.30016i	0.519794	+	0.188756i
$520$		0			0
$521$	13.5133			0.592027			0.296014	−	0.955184i	$-0.404343\pi$
$521$	13.5133			0.592027			0.296014	+	0.955184i	$0.404343\pi$
$522$		0			0
$523$		−	43.7368i		−	1.91248i	−0.292588	−	0.956239i	$-0.594517\pi$
$523$		−	43.7368i		−	1.91248i	0.292588	−	0.956239i	$-0.405483\pi$
$524$		0			0
$525$	−11.5364	+	18.6883i	−0.503491	+	0.815626i
$526$		0			0
$527$	34.4359	+	19.8816i	1.50005	+	0.866056i
$528$		0			0
$529$	−10.4156	−	18.0404i	−0.452854	−	0.784366i
$530$		0			0
$531$	−15.6646	−	13.1049i	−0.679787	−	0.568705i
$532$		0			0
$533$	7.14182	−	4.12333i	0.309346	−	0.178601i
$534$		0			0
$535$	−9.94365	−	12.2203i	−0.429901	−	0.528329i
$536$		0			0
$537$	−0.186437	−	0.221854i	−0.00804533	−	0.00957372i
$538$		0			0
$539$	−0.184476			−0.00794594
$540$		0			0
$541$	17.1176			0.735943			0.367971	−	0.929837i	$-0.380052\pi$
$541$	17.1176			0.735943			0.367971	+	0.929837i	$0.380052\pi$
$542$		0			0
$543$	0.0217264	+	0.0258538i	0.000932370	+	0.00110949i
$544$		0			0
$545$	3.18984	−	2.59557i	0.136638	−	0.111182i
$546$		0			0
$547$	−38.1966	+	22.0528i	−1.63317	+	0.942910i	−0.650061	+	0.759882i	$0.725257\pi$
$547$	−38.1966	+	22.0528i	−1.63317	+	0.942910i	−0.983108	+	0.183028i	$0.941410\pi$
$548$		0			0
$549$	−28.9836	+	10.5976i	−1.23699	+	0.452293i
$550$		0			0
$551$	27.0671	+	46.8816i	1.15310	+	1.99722i
$552$		0			0
$553$	36.3335	+	20.9772i	1.54506	+	0.892040i
$554$		0			0
$555$	3.06059	−	16.0100i	0.129915	−	0.679585i
$556$		0			0
$557$			18.5675i			0.786730i	0.919382	+	0.393365i	$0.128689\pi$
$557$			18.5675i			0.786730i	−0.919382	+	0.393365i	$0.871311\pi$
$558$		0			0
$559$	−9.57820			−0.405115
$560$		0			0
$561$	−2.97860	−	1.08164i	−0.125757	−	0.0456667i
$562$		0			0
$563$	14.1962	+	8.19620i	0.598300	+	0.345429i	0.768373	−	0.640003i	$-0.221067\pi$
$563$	14.1962	+	8.19620i	0.598300	+	0.345429i	−0.170072	+	0.985432i	$0.554400\pi$
$564$		0			0
$565$	14.5501	−	2.33973i	0.612128	−	0.0984334i
$566$		0			0
$567$	22.4654	−	4.02954i	0.943457	−	0.169225i
$568$		0			0
$569$	14.9696	+	25.9280i	0.627556	+	1.08696i	0.988041	+	0.154194i	$0.0492781\pi$
$569$	14.9696	+	25.9280i	0.627556	+	1.08696i	−0.360484	+	0.932765i	$0.617389\pi$
$570$		0			0
$571$	−0.897238	+	1.55406i	−0.0375483	+	0.0650355i	−0.884189	−	0.467130i	$-0.845288\pi$
$571$	−0.897238	+	1.55406i	−0.0375483	+	0.0650355i	0.846641	+	0.532165i	$0.178621\pi$
$572$		0			0
$573$	9.54852	−	26.2946i	0.398895	−	1.09847i
$574$		0			0
$575$	−4.90110	+	5.49517i	−0.204390	+	0.229165i
$576$		0			0
$577$			9.43023i			0.392586i	0.980545	+	0.196293i	$0.0628903\pi$
$577$			9.43023i			0.392586i	−0.980545	+	0.196293i	$0.937110\pi$
$578$		0			0
$579$	4.58581	+	25.8959i	0.190580	+	1.07620i
$580$		0			0
$581$	−15.9840	+	27.6852i	−0.663129	+	1.14857i
$582$		0			0
$583$	−1.40384	+	0.810510i	−0.0581413	+	0.0335679i
$584$		0			0
$585$	−0.427281	+	31.3709i	−0.0176659	+	1.29703i
$586$		0			0
$587$	−24.1783	+	13.9593i	−0.997944	+	0.576163i	−0.907639	−	0.419751i	$-0.862117\pi$
$587$	−24.1783	+	13.9593i	−0.997944	+	0.576163i	−0.0903048	+	0.995914i	$0.528784\pi$
$588$		0			0
$589$	19.6200	−	33.9828i	0.808428	−	1.40024i
$590$		0			0
$591$	−24.0993	+	20.2520i	−0.991314	+	0.833056i
$592$		0			0
$593$		−	1.85554i		−	0.0761979i	−0.999274	−	0.0380990i	$-0.987870\pi$
$593$		−	1.85554i		−	0.0761979i	0.999274	−	0.0380990i	$-0.0121302\pi$
$594$		0			0
$595$	29.8893	+	11.3925i	1.22534	+	0.467048i
$596$		0			0
$597$	−21.9496	−	26.1195i	−0.898339	−	1.06900i
$598$		0			0
$599$	−15.2369	+	26.3911i	−0.622563	+	1.07831i	0.366444	+	0.930440i	$0.380575\pi$
$599$	−15.2369	+	26.3911i	−0.622563	+	1.07831i	−0.989007	+	0.147870i	$0.952758\pi$
$600$		0			0
$601$	1.06482	+	1.84432i	0.0434349	+	0.0752315i	0.886926	−	0.461912i	$-0.152837\pi$
$601$	1.06482	+	1.84432i	0.0434349	+	0.0752315i	−0.843491	+	0.537144i	$0.819503\pi$
$602$		0			0
$603$	−9.50765	+	11.3647i	−0.387181	+	0.462808i
$604$		0			0
$605$	3.86777	+	24.0525i	0.157247	+	0.977874i
$606$		0			0
$607$	−24.8858	−	14.3679i	−1.01009	−	0.583173i	−0.0988688	−	0.995100i	$-0.531522\pi$
$607$	−24.8858	−	14.3679i	−1.01009	−	0.583173i	−0.911217	+	0.411927i	$0.864856\pi$
$608$		0			0
$609$	−7.44858	−	42.0618i	−0.301832	−	1.70443i
$610$		0			0
$611$	−32.2983			−1.30665
$612$		0			0
$613$		−	21.8854i		−	0.883942i	−0.897029	−	0.441971i	$-0.854279\pi$
$613$		−	21.8854i		−	0.883942i	0.897029	−	0.441971i	$-0.145721\pi$
$614$		0			0
$615$	4.46430	−	5.16783i	0.180018	−	0.208387i
$616$		0			0
$617$	0.0554525	+	0.0320155i	0.00223243	+	0.00128890i	0.501116	−	0.865380i	$-0.332923\pi$
$617$	0.0554525	+	0.0320155i	0.00223243	+	0.00128890i	−0.498883	+	0.866669i	$0.666256\pi$
$618$		0			0
$619$	0.602331	+	1.04327i	0.0242097	+	0.0419325i	0.877876	−	0.478887i	$-0.158960\pi$
$619$	0.602331	+	1.04327i	0.0242097	+	0.0419325i	−0.853667	+	0.520820i	$0.825626\pi$
$620$		0			0
$621$	7.65211	−	0.0169096i	0.307069	−	0.000678557i
$622$		0			0
$623$	−8.05645	+	4.65140i	−0.322775	+	0.186354i
$624$		0			0
$625$	−22.9336	−	9.95231i	−0.917345	−	0.398092i
$626$		0			0
$627$	−1.06740	+	2.93940i	−0.0426280	+	0.117388i
$628$		0			0
$629$	−23.7398			−0.946569
$630$		0			0
$631$	−6.76752			−0.269411			−0.134705	−	0.990886i	$-0.543009\pi$
$631$	−6.76752			−0.269411			−0.134705	+	0.990886i	$0.543009\pi$
$632$		0			0
$633$	−47.9906	+	8.49850i	−1.90746	+	0.337785i
$634$		0			0
$635$	−7.75185	−	9.52667i	−0.307623	−	0.378054i
$636$		0			0
$637$	2.30367	−	1.33003i	0.0912748	−	0.0526975i
$638$		0			0
$639$	−1.16131	+	6.64334i	−0.0459408	+	0.262807i
$640$		0			0
$641$	−4.15956	−	7.20456i	−0.164293	−	0.284563i	0.772111	−	0.635487i	$-0.219201\pi$
$641$	−4.15956	−	7.20456i	−0.164293	−	0.284563i	−0.936404	+	0.350924i	$0.885867\pi$
$642$		0			0
$643$	26.5090	+	15.3050i	1.04541	+	0.603570i	0.921362	−	0.388706i	$-0.127078\pi$
$643$	26.5090	+	15.3050i	1.04541	+	0.603570i	0.124052	+	0.992276i	$0.460411\pi$
$644$		0			0
$645$	−7.49158	+	2.60554i	−0.294981	+	0.102593i
$646$		0			0
$647$			0.0235583i			0.000926173i	1.00000		0.000463087i	$0.000147405\pi$
$647$			0.0235583i			0.000926173i	−1.00000		0.000463087i	$0.999853\pi$
$648$		0			0
$649$	−2.20810			−0.0866756
$650$		0			0
$651$	−23.7048	+	19.9204i	−0.929063	+	0.780744i
$652$		0			0
$653$	−2.40979	−	1.39129i	−0.0943024	−	0.0544455i	0.452107	−	0.891964i	$-0.350672\pi$
$653$	−2.40979	−	1.39129i	−0.0943024	−	0.0544455i	−0.546410	+	0.837518i	$0.684006\pi$
$654$		0			0
$655$	3.09031	+	19.2177i	0.120748	+	0.750898i
$656$		0			0
$657$	37.6045	+	6.57357i	1.46709	+	0.256460i
$658$		0			0
$659$	−4.73335	−	8.19840i	−0.184385	−	0.319364i	0.758984	−	0.651109i	$-0.225696\pi$
$659$	−4.73335	−	8.19840i	−0.184385	−	0.319364i	−0.943369	+	0.331745i	$0.892363\pi$
$660$		0			0
$661$	16.6423	−	28.8253i	0.647311	−	1.12118i	−0.336452	−	0.941701i	$-0.609227\pi$
$661$	16.6423	−	28.8253i	0.647311	−	1.12118i	0.983763	−	0.179475i	$-0.0574398\pi$
$662$		0			0
$663$	44.9941	−	7.96785i	1.74742	−	0.309445i
$664$		0			0
$665$	11.2426	−	29.4960i	0.435970	−	1.14380i
$666$		0			0
$667$		−	14.3214i		−	0.554527i
$668$		0			0
$669$	−22.4684	−	8.15909i	−0.868679	−	0.315449i
$670$		0			0
$671$	−1.66824	+	2.88948i	−0.0644018	+	0.111547i
$672$		0			0
$673$	16.5053	−	9.52936i	0.636234	−	0.367330i	−0.146928	−	0.989147i	$-0.546939\pi$
$673$	16.5053	−	9.52936i	0.636234	−	0.367330i	0.783162	+	0.621817i	$0.213605\pi$
$674$		0			0
$675$	8.19956	+	24.6529i	0.315601	+	0.948892i
$676$		0			0
$677$	−9.80147	+	5.65888i	−0.376701	+	0.217488i	−0.676382	−	0.736551i	$-0.736453\pi$
$677$	−9.80147	+	5.65888i	−0.376701	+	0.217488i	0.299681	+	0.954039i	$0.403120\pi$
$678$		0			0
$679$	−2.48735	+	4.30822i	−0.0954558	+	0.165334i
$680$		0			0
$681$	40.7818	+	14.8093i	1.56276	+	0.567495i
$682$		0			0
$683$		−	21.7166i		−	0.830961i	−0.909602	−	0.415480i	$-0.863613\pi$
$683$		−	21.7166i		−	0.830961i	0.909602	−	0.415480i	$-0.136387\pi$
$684$		0			0
$685$	12.3348	−	32.3615i	0.471290	−	1.23647i
$686$		0			0
$687$	−15.6483	+	2.77110i	−0.597020	+	0.105724i
$688$		0			0
$689$	11.6872	−	20.2428i	0.445245	−	0.771188i
$690$		0			0
$691$	−15.9498	−	27.6258i	−0.606757	−	1.05093i	−0.991771	−	0.128023i	$-0.959137\pi$
$691$	−15.9498	−	27.6258i	−0.606757	−	1.05093i	0.385014	−	0.922911i	$-0.374197\pi$
$692$		0			0
$693$	1.58337	−	1.89264i	0.0601473	−	0.0718956i
$694$		0			0
$695$	−2.32757	−	14.4745i	−0.0882898	−	0.549048i
$696$		0			0
$697$	−8.61364	−	4.97309i	−0.326265	−	0.188369i
$698$		0			0
$699$	2.34983	−	1.97469i	0.0888787	−	0.0746897i
$700$		0			0
$701$	11.7711			0.444587			0.222294	−	0.974980i	$-0.428646\pi$
$701$	11.7711			0.444587			0.222294	+	0.974980i	$0.428646\pi$
$702$		0			0
$703$			23.4275i			0.883583i
$704$		0			0
$705$	−25.2621	+	8.78604i	−0.951424	+	0.330901i
$706$		0			0
$707$	36.9660	+	21.3423i	1.39025	+	0.802660i
$708$		0			0
$709$	3.48864	+	6.04250i	0.131019	+	0.226931i	0.924070	−	0.382224i	$-0.124842\pi$
$709$	3.48864	+	6.04250i	0.131019	+	0.226931i	−0.793051	+	0.609155i	$0.791509\pi$
$710$		0			0
$711$	46.6126	−	17.0434i	1.74811	−	0.639177i
$712$		0			0
$713$	−8.99029	+	5.19054i	−0.336689	+	0.194387i
$714$		0			0
$715$	2.14087	+	2.63103i	0.0800641	+	0.0983951i
$716$		0			0
$717$	14.7804	−	2.61742i	0.551986	−	0.0977493i
$718$		0			0
$719$	2.45112			0.0914115			0.0457057	−	0.998955i	$-0.485446\pi$
$719$	2.45112			0.0914115			0.0457057	+	0.998955i	$0.485446\pi$
$720$		0			0
$721$	−27.0766			−1.00838
$722$		0			0
$723$	−5.42152	+	14.9297i	−0.201629	+	0.555242i
$724$		0			0
$725$	46.1732	−	15.2440i	1.71483	−	0.566146i
$726$		0			0
$727$	13.7095	−	7.91516i	0.508456	−	0.293557i	−0.223743	−	0.974648i	$-0.571828\pi$
$727$	13.7095	−	7.91516i	0.508456	−	0.293557i	0.732199	+	0.681091i	$0.238494\pi$
$728$		0			0
$729$	13.3965	−	23.4421i	0.496168	−	0.868227i
$730$		0			0
$731$	5.77606	+	10.0044i	0.213635	+	0.370027i
$732$		0			0
$733$	−8.76380	−	5.05978i	−0.323698	−	0.186887i	0.329341	−	0.944211i	$-0.393173\pi$
$733$	−8.76380	−	5.05978i	−0.323698	−	0.186887i	−0.653040	+	0.757323i	$0.726507\pi$
$734$		0			0
$735$	1.44001	−	1.66694i	0.0531156	−	0.0614861i
$736$		0			0
$737$			1.60198i			0.0590098i
$738$		0			0
$739$	19.7596			0.726868			0.363434	−	0.931620i	$-0.381604\pi$
$739$	19.7596			0.726868			0.363434	+	0.931620i	$0.381604\pi$
$740$		0			0
$741$	−7.86300	−	44.4020i	−0.288855	−	1.63115i
$742$		0			0
$743$	21.9270	+	12.6596i	0.804424	+	0.464434i	0.845016	−	0.534742i	$-0.179591\pi$
$743$	21.9270	+	12.6596i	0.804424	+	0.464434i	−0.0405919	+	0.999176i	$0.512924\pi$
$744$		0			0
$745$	−2.50011	−	15.5474i	−0.0915969	−	0.569614i
$746$		0			0
$747$	12.9866	+	35.5175i	0.475155	+	1.29952i
$748$		0			0
$749$	−8.93395	−	15.4740i	−0.326439	−	0.565409i
$750$		0			0
$751$	11.1684	−	19.3443i	0.407542	−	0.705883i	−0.587072	−	0.809535i	$-0.699719\pi$
$751$	11.1684	−	19.3443i	0.407542	−	0.705883i	0.994614	+	0.103652i	$0.0330528\pi$
$752$		0			0
$753$	−23.1857	−	27.5903i	−0.844933	−	1.00545i
$754$		0			0
$755$	−32.9539	−	12.5606i	−1.19931	−	0.457128i
$756$		0			0
$757$			53.7616i			1.95400i	0.213244	+	0.976999i	$0.431597\pi$
$757$			53.7616i			1.95400i	−0.213244	+	0.976999i	$0.568403\pi$
$758$		0			0
$759$	0.633369	−	0.532255i	0.0229898	−	0.0193196i
$760$		0			0
$761$	9.95943	−	17.2502i	0.361029	−	0.625320i	−0.627102	−	0.778938i	$-0.715759\pi$
$761$	9.95943	−	17.2502i	0.361029	−	0.625320i	0.988130	+	0.153617i	$0.0490922\pi$
$762$		0			0
$763$	4.03916	−	2.33201i	0.146227	−	0.0844244i
$764$		0			0
$765$	33.0246	−	18.4717i	1.19401	−	0.667845i
$766$		0			0
$767$	27.5740	−	15.9199i	0.995640	−	0.574833i
$768$		0			0
$769$	4.85706	−	8.41267i	0.175150	−	0.303369i	−0.765063	−	0.643955i	$-0.777292\pi$
$769$	4.85706	−	8.41267i	0.175150	−	0.303369i	0.940213	+	0.340587i	$0.110626\pi$
$770$		0			0
$771$	−8.86513	−	50.0610i	−0.319270	−	1.80290i
$772$		0			0
$773$		−	39.7847i		−	1.43096i	−0.698635	−	0.715478i	$-0.746209\pi$
$773$		−	39.7847i		−	1.43096i	0.698635	−	0.715478i	$-0.253791\pi$
$774$		0			0
$775$	−26.3041	−	23.4604i	−0.944871	−	0.842722i
$776$		0			0
$777$	6.30984	−	17.3760i	0.226364	−	0.623359i
$778$		0			0
$779$	−4.90765	+	8.50030i	−0.175835	+	0.304555i
$780$		0			0
$781$	0.364571	+	0.631455i	0.0130454	+	0.0225952i
$782$		0			0
$783$	−43.8178	−	25.1693i	−1.56592	−	0.899476i
$784$		0			0
$785$	8.49178	−	1.36552i	0.303085	−	0.0487376i
$786$		0			0
$787$	−1.89005	−	1.09122i	−0.0673730	−	0.0388978i	0.465935	−	0.884819i	$-0.345718\pi$
$787$	−1.89005	−	1.09122i	−0.0673730	−	0.0388978i	−0.533308	+	0.845921i	$0.679051\pi$
$788$		0			0
$789$	−20.9123	−	7.59403i	−0.744499	−	0.270355i
$790$		0			0
$791$	16.7137			0.594271
$792$		0			0
$793$		−	48.1105i		−	1.70845i
$794$		0			0
$795$	3.63450	−	19.0121i	0.128903	−	0.674289i
$796$		0			0
$797$	−2.45201	−	1.41567i	−0.0868548	−	0.0501457i	0.455944	−	0.890009i	$-0.349302\pi$
$797$	−2.45201	−	1.41567i	−0.0868548	−	0.0501457i	−0.542798	+	0.839863i	$0.682635\pi$
$798$		0			0
$799$	19.4772	+	33.7356i	0.689055	+	1.19348i
$800$		0			0
$801$	−1.89502	+	10.8405i	−0.0669572	+	0.383032i
$802$		0			0
$803$	3.57433	−	2.06364i	0.126135	−	0.0728244i
$804$		0			0
$805$	−6.47744	+	5.27069i	−0.228300	+	0.185767i
$806$		0			0
$807$	13.3922	+	15.9364i	0.471429	+	0.560988i
$808$		0			0
$809$	−6.35037			−0.223267			−0.111634	−	0.993749i	$-0.535608\pi$
$809$	−6.35037			−0.223267			−0.111634	+	0.993749i	$0.535608\pi$
$810$		0			0
$811$	−42.8516			−1.50472			−0.752361	−	0.658751i	$-0.771085\pi$
$811$	−42.8516			−1.50472			−0.752361	+	0.658751i	$0.771085\pi$
$812$		0			0
$813$	33.0972	+	39.3848i	1.16077	+	1.38129i
$814$		0			0
$815$	−3.18423	−	3.91328i	−0.111539	−	0.137076i
$816$		0			0
$817$	9.87279	−	5.70006i	0.345405	−	0.199420i
$818$		0			0
$819$	−6.12711	+	35.0504i	−0.214098	+	1.22476i
$820$		0			0
$821$	8.99370	+	15.5775i	0.313882	+	0.543660i	0.979199	−	0.202901i	$-0.0650369\pi$
$821$	8.99370	+	15.5775i	0.313882	+	0.543660i	−0.665317	+	0.746561i	$0.731704\pi$
$822$		0			0
$823$	34.4335	+	19.8802i	1.20028	+	0.692980i	0.960617	−	0.277877i	$-0.0896306\pi$
$823$	34.4335	+	19.8802i	1.20028	+	0.692980i	0.239660	+	0.970857i	$0.422964\pi$
$824$		0			0
$825$	2.39020	+	1.47548i	0.0832159	+	0.0513697i
$826$		0			0
$827$		−	0.771494i		−	0.0268275i	−0.999910	−	0.0134137i	$-0.995730\pi$
$827$		−	0.771494i		−	0.0268275i	0.999910	−	0.0134137i	$-0.00426985\pi$
$828$		0			0
$829$	22.5744			0.784040			0.392020	−	0.919957i	$-0.371776\pi$
$829$	22.5744			0.784040			0.392020	+	0.919957i	$0.371776\pi$
$830$		0			0
$831$	17.9511	+	6.51868i	0.622715	+	0.226130i
$832$		0			0
$833$	−2.77843	−	1.60413i	−0.0962668	−	0.0555796i
$834$		0			0
$835$	−1.79785	+	0.289103i	−0.0622170	+	0.0100048i
$836$		0			0
$837$	0.0809421	+	36.6289i	0.00279777	+	1.26608i
$838$		0			0
$839$	−7.41266	−	12.8391i	−0.255913	−	0.443255i	0.709230	−	0.704977i	$-0.249043\pi$
$839$	−7.41266	−	12.8391i	−0.255913	−	0.443255i	−0.965143	+	0.261722i	$0.915709\pi$
$840$		0			0
$841$	−32.7868	+	56.7884i	−1.13058	+	1.95822i
$842$		0			0
$843$	15.7162	−	43.2790i	0.541294	−	1.49061i
$844$		0			0
$845$	−18.5409	−	7.06703i	−0.637828	−	0.243113i
$846$		0			0
$847$			27.6291i			0.949347i
$848$		0			0
$849$	6.15142	+	34.7368i	0.211116	+	1.19216i
$850$		0			0
$851$	3.09891	−	5.36747i	0.106229	−	0.183995i
$852$		0			0
$853$	−30.5738	+	17.6518i	−1.04683	+	0.604385i	−0.921759	−	0.387763i	$-0.873248\pi$
$853$	−30.5738	+	17.6518i	−1.04683	+	0.604385i	−0.125067	+	0.992148i	$0.539914\pi$
$854$		0			0
$855$	−18.2286	−	32.5900i	−0.623406	−	1.11456i
$856$		0			0
$857$	−33.3517	+	19.2556i	−1.13927	+	0.657758i	−0.946250	−	0.323436i	$-0.895162\pi$
$857$	−33.3517	+	19.2556i	−1.13927	+	0.657758i	−0.193021	+	0.981195i	$0.561829\pi$
$858$		0			0
$859$	−22.6019	+	39.1476i	−0.771167	+	1.33570i	0.165757	+	0.986167i	$0.446993\pi$
$859$	−22.6019	+	39.1476i	−0.771167	+	1.33570i	−0.936924	+	0.349533i	$0.886340\pi$
$860$		0			0
$861$	5.92940	−	4.98280i	0.202073	−	0.169814i
$862$		0			0
$863$		−	40.6971i		−	1.38534i	−0.721252	−	0.692672i	$-0.756433\pi$
$863$		−	40.6971i		−	1.38534i	0.721252	−	0.692672i	$-0.243567\pi$
$864$		0			0
$865$	−5.79277	+	15.1978i	−0.196960	+	0.516741i
$866$		0			0
$867$	−16.5124	−	19.6493i	−0.560789	−	0.667324i
$868$		0			0
$869$	2.68293	−	4.64697i	0.0910122	−	0.157638i
$870$		0			0
$871$	−11.5499	−	20.0050i	−0.391354	−	0.677845i
$872$		0			0
$873$	2.02091	+	5.52705i	0.0683973	+	0.187062i
$874$		0			0
$875$	−23.8878	−	15.2735i	−0.807554	−	0.516338i
$876$		0			0
$877$	35.1374	+	20.2866i	1.18650	+	0.685029i	0.957510	−	0.288399i	$-0.0931230\pi$
$877$	35.1374	+	20.2866i	1.18650	+	0.685029i	0.228994	+	0.973428i	$0.426456\pi$
$878$		0			0
$879$	8.15932	+	46.0753i	0.275207	+	1.55408i
$880$		0			0
$881$	−19.3588			−0.652215			−0.326108	−	0.945333i	$-0.605737\pi$
$881$	−19.3588			−0.652215			−0.326108	+	0.945333i	$0.605737\pi$
$882$		0			0
$883$			24.3681i			0.820052i	0.912074	+	0.410026i	$0.134480\pi$
$883$			24.3681i			0.820052i	−0.912074	+	0.410026i	$0.865520\pi$
$884$		0			0
$885$	17.2363	−	19.9526i	0.579393	−	0.670700i
$886$		0			0
$887$	−39.1545	−	22.6059i	−1.31468	−	0.759031i	−0.331812	−	0.943345i	$-0.607660\pi$
$887$	−39.1545	−	22.6059i	−1.31468	−	0.759031i	−0.982867	+	0.184315i	$0.940993\pi$
$888$		0			0
$889$	−6.96471	−	12.0632i	−0.233589	−	0.404588i
$890$		0			0
$891$	−0.515369	−	2.87327i	−0.0172655	−	0.0962582i
$892$		0			0
$893$	33.2917	−	19.2209i	1.11406	−	0.643205i
$894$		0			0
$895$	0.290187	−	0.236125i	0.00969987	−	0.00789278i
$896$		0			0
$897$	−4.07187	+	11.2131i	−0.135956	+	0.374393i
$898$		0			0
$899$	68.5532			2.28638
$900$		0			0
$901$	−28.1914			−0.939193
$902$		0			0
$903$	−8.85780	+	1.56860i	−0.294769	+	0.0521997i
$904$		0			0
$905$	−0.0338169	+	0.0275169i	−0.00112411	+	0.000914691i
$906$		0			0
$907$	48.6855	−	28.1086i	1.61658	−	0.933330i	0.628779	−	0.777584i	$-0.283555\pi$
$907$	48.6855	−	28.1086i	1.61658	−	0.933330i	0.987797	−	0.155746i	$-0.0497782\pi$
$908$		0			0
$909$	47.4239	−	17.3401i	1.57295	−	0.575134i
$910$		0			0
$911$	8.49492	+	14.7136i	0.281449	+	0.487484i	0.971742	−	0.236046i	$-0.0758516\pi$
$911$	8.49492	+	14.7136i	0.281449	+	0.487484i	−0.690293	+	0.723530i	$0.742518\pi$
$912$		0			0
$913$	3.54087	+	2.04432i	0.117186	+	0.0676572i
$914$		0			0
$915$	−13.0874	−	37.6296i	−0.432656	−	1.24400i
$916$		0			0
$917$			22.0753i			0.728992i
$918$		0			0
$919$	−1.45989			−0.0481575			−0.0240787	−	0.999710i	$-0.507665\pi$
$919$	−1.45989			−0.0481575			−0.0240787	+	0.999710i	$0.507665\pi$
$920$		0			0
$921$	40.1848	−	33.7695i	1.32413	−	1.11274i
$922$		0			0
$923$	−9.10527	−	5.25693i	−0.299704	−	0.173034i
$924$		0			0
$925$	20.6036	+	4.27787i	0.677443	+	0.140655i
$926$		0			0
$927$	−20.5528	+	24.5673i	−0.675043	+	0.806896i
$928$		0			0
$929$	−12.7328	−	22.0538i	−0.417749	−	0.723562i	0.577964	−	0.816062i	$-0.303847\pi$
$929$	−12.7328	−	22.0538i	−0.417749	−	0.723562i	−0.995713	+	0.0925001i	$0.970514\pi$
$930$		0			0
$931$	−1.58302	+	2.74187i	−0.0518813	+	0.0898610i
$932$		0			0
$933$	37.5260	−	6.64535i	1.22855	−	0.217559i
$934$		0			0
$935$	1.45708	−	3.82277i	0.0476516	−	0.125018i
$936$		0			0
$937$		−	2.21996i		−	0.0725228i	−0.999342	−	0.0362614i	$-0.988455\pi$
$937$		−	2.21996i		−	0.0725228i	0.999342	−	0.0362614i	$-0.0115449\pi$
$938$		0			0
$939$	39.6372	+	14.3937i	1.29351	+	0.469721i
$940$		0			0
$941$	−18.6131	+	32.2388i	−0.606769	+	1.05095i	0.385000	+	0.922917i	$0.374201\pi$
$941$	−18.6131	+	32.2388i	−0.606769	+	1.05095i	−0.991769	+	0.128038i	$0.959132\pi$
$942$		0			0
$943$	2.24879	−	1.29834i	0.0732306	−	0.0422797i
$944$		0			0
$945$	4.74239	+	29.0814i	0.154270	+	0.946018i
$946$		0			0
$947$	−8.33276	+	4.81092i	−0.270778	+	0.156334i	−0.629241	−	0.777210i	$-0.716634\pi$
$947$	−8.33276	+	4.81092i	−0.270778	+	0.156334i	0.358463	+	0.933544i	$0.383301\pi$
$948$		0			0
$949$	−29.7567	+	51.5401i	−0.965944	+	1.67306i
$950$		0			0
$951$	10.7079	+	3.88844i	0.347229	+	0.126091i
$952$		0			0
$953$			57.4175i			1.85993i	0.367642	+	0.929967i	$0.380165\pi$
$953$			57.4175i			1.85993i	−0.367642	+	0.929967i	$0.619835\pi$
$954$		0			0
$955$	33.7468	+	12.8629i	1.09202	+	0.416233i
$956$		0			0
$957$	−5.37961	+	0.952657i	−0.173898	+	0.0307950i
$958$		0			0
$959$	19.6389	−	34.0156i	0.634173	−	1.09842i
$960$		0			0
$961$	−9.34591	−	16.1876i	−0.301481	−	0.522181i
$962$		0			0
$963$	−20.8215	−	3.63976i	−0.670962	−	0.117290i
$964$		0			0
$965$	−33.5209	+	5.39034i	−1.07908	+	0.173521i
$966$		0			0
$967$	8.93386	+	5.15796i	0.287293	+	0.165869i	0.636721	−	0.771095i	$-0.280290\pi$
$967$	8.93386	+	5.15796i	0.287293	+	0.165869i	−0.349427	+	0.936964i	$0.613624\pi$
$968$		0			0
$969$	−41.6362	+	34.9892i	−1.33755	+	1.12402i
$970$		0			0
$971$	−40.1209			−1.28754			−0.643771	−	0.765218i	$-0.722631\pi$
$971$	−40.1209			−1.28754			−0.643771	+	0.765218i	$0.722631\pi$
$972$		0			0
$973$		−	16.6268i		−	0.533031i
$974$		0			0
$975$	−40.4858	−	1.19260i	−1.29658	−	0.0381938i
$976$		0			0
$977$	33.7320	+	19.4752i	1.07918	+	0.623065i	0.930675	−	0.365846i	$-0.119220\pi$
$977$	33.7320	+	19.4752i	1.07918	+	0.623065i	0.148505	+	0.988912i	$0.452554\pi$
$978$		0			0
$979$	0.594903	+	1.03040i	0.0190132	+	0.0329318i
$980$		0			0
$981$	0.950080	−	5.43498i	0.0303337	−	0.173526i
$982$		0			0
$983$	−33.4112	+	19.2899i	−1.06565	+	0.615254i	−0.926990	−	0.375086i	$-0.877613\pi$
$983$	−33.4112	+	19.2899i	−1.06565	+	0.615254i	−0.138661	+	0.990340i	$0.544280\pi$
$984$		0			0
$985$	−25.6495	−	31.5220i	−0.817260	−	1.00438i
$986$		0			0
$987$	−29.8690	+	5.28941i	−0.950742	+	0.168364i
$988$		0			0
$989$	−3.01595			−0.0959015
$990$		0			0
$991$	−17.3171			−0.550096			−0.275048	−	0.961430i	$-0.588694\pi$
$991$	−17.3171			−0.550096			−0.275048	+	0.961430i	$0.588694\pi$
$992$		0			0
$993$	12.4433	−	34.2662i	0.394876	−	1.08741i
$994$		0			0
$995$	34.1644	−	27.7996i	1.08308	−	0.881305i
$996$		0			0
$997$	−21.1637	+	12.2189i	−0.670261	+	0.386975i	−0.796175	−	0.605066i	$-0.793147\pi$
$997$	−21.1637	+	12.2189i	−0.670261	+	0.386975i	0.125915	+	0.992041i	$0.459813\pi$
$998$		0			0
$999$	−10.9761	−	18.9145i	−0.347269	−	0.598429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bi.b.49.11	yes	32
3.2	odd	2		1080.2.bi.b.1009.12		32
4.3	odd	2		720.2.by.f.49.6		32
5.4	even	2	inner	360.2.bi.b.49.6	✓	32
9.2	odd	6		1080.2.bi.b.289.10		32
9.4	even	3		3240.2.f.k.649.16		16
9.5	odd	6		3240.2.f.i.649.1		16
9.7	even	3	inner	360.2.bi.b.169.6	yes	32
12.11	even	2		2160.2.by.f.1009.12		32
15.14	odd	2		1080.2.bi.b.1009.10		32
20.19	odd	2		720.2.by.f.49.11		32
36.7	odd	6		720.2.by.f.529.11		32
36.11	even	6		2160.2.by.f.289.10		32
45.4	even	6		3240.2.f.k.649.15		16
45.14	odd	6		3240.2.f.i.649.2		16
45.29	odd	6		1080.2.bi.b.289.12		32
45.34	even	6	inner	360.2.bi.b.169.11	yes	32
60.59	even	2		2160.2.by.f.1009.10		32
180.79	odd	6		720.2.by.f.529.6		32
180.119	even	6		2160.2.by.f.289.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bi.b.49.6	✓	32	5.4	even	2	inner
360.2.bi.b.49.11	yes	32	1.1	even	1	trivial
360.2.bi.b.169.6	yes	32	9.7	even	3	inner
360.2.bi.b.169.11	yes	32	45.34	even	6	inner
720.2.by.f.49.6		32	4.3	odd	2
720.2.by.f.49.11		32	20.19	odd	2
720.2.by.f.529.6		32	180.79	odd	6
720.2.by.f.529.11		32	36.7	odd	6
1080.2.bi.b.289.10		32	9.2	odd	6
1080.2.bi.b.289.12		32	45.29	odd	6
1080.2.bi.b.1009.10		32	15.14	odd	2
1080.2.bi.b.1009.12		32	3.2	odd	2
2160.2.by.f.289.10		32	36.11	even	6
2160.2.by.f.289.12		32	180.119	even	6
2160.2.by.f.1009.10		32	60.59	even	2
2160.2.by.f.1009.12		32	12.11	even	2
3240.2.f.i.649.1		16	9.5	odd	6
3240.2.f.i.649.2		16	45.14	odd	6
3240.2.f.k.649.15		16	45.4	even	6
3240.2.f.k.649.16		16	9.4	even	3

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11432 + 1.32601i) q^{3} +(-1.73442 + 1.41130i) q^{5} +(-2.19623 + 1.26799i) q^{7} +(-0.516592 + 2.95519i) q^{9} +O(q^{10})\)	\(q+(1.11432 + 1.32601i) q^{3} +(-1.73442 + 1.41130i) q^{5} +(-2.19623 + 1.26799i) q^{7} +(-0.516592 + 2.95519i) q^{9} +(0.162174 + 0.280893i) q^{11} +(-4.05034 - 2.33846i) q^{13} +(-3.80410 - 0.727221i) q^{15} +5.64078i q^{17} +5.56655 q^{19} +(-4.12867 - 1.49927i) q^{21} +(-1.27535 - 0.736327i) q^{23} +(1.01646 - 4.89559i) q^{25} +(-4.49425 + 2.60801i) q^{27} +(4.86245 + 8.42201i) q^{29} +(3.52462 - 6.10482i) q^{31} +(-0.191753 + 0.528047i) q^{33} +(2.01967 - 5.29878i) q^{35} +4.20861i q^{37} +(-1.41254 - 7.97657i) q^{39} +(-0.881632 + 1.52703i) q^{41} +(1.77359 - 1.02398i) q^{43} +(-3.27467 - 5.85462i) q^{45} +(5.98066 - 3.45294i) q^{47} +(-0.284380 + 0.492561i) q^{49} +(-7.47971 + 6.28562i) q^{51} +4.99779i q^{53} +(-0.677703 - 0.258312i) q^{55} +(6.20291 + 7.38129i) q^{57} +(-3.40392 + 5.89576i) q^{59} +(5.14339 + 8.90861i) q^{61} +(-2.61261 - 7.14531i) q^{63} +(10.3253 - 1.66036i) q^{65} +(4.27739 + 2.46955i) q^{67} +(-0.444776 - 2.51163i) q^{69} +2.24803 q^{71} -12.7249i q^{73} +(7.62425 - 4.10742i) q^{75} +(-0.712341 - 0.411270i) q^{77} +(-8.27179 - 14.3272i) q^{79} +(-8.46627 - 3.05325i) q^{81} +(10.9169 - 6.30288i) q^{83} +(-7.96084 - 9.78350i) q^{85} +(-5.74933 + 15.8324i) q^{87} +3.66831 q^{89} +11.8606 q^{91} +(12.0226 - 2.12904i) q^{93} +(-9.65477 + 7.85608i) q^{95} +(1.69883 - 0.980821i) q^{97} +(-0.913869 + 0.334147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) \) 32 * q - 2 * q^5 + 4 * q^9	\( 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) \) 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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