LMFDB - Embedded newform 684.2.j.a.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(49,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("684.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.j (of order $3$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	684.49
Dual form			684.2.j.a.349.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16446 + 1.28220i) q^{3} +(-0.145159 - 0.251423i) q^{5} +(-0.636745 - 1.10287i) q^{7} +(-0.288081 - 2.98614i) q^{9} +(1.06416 + 1.84317i) q^{11} +4.49268 q^{13} +(0.491407 + 0.106648i) q^{15} +(-2.20154 + 3.81318i) q^{17} +(1.25129 + 4.17544i) q^{19} +(2.15557 + 0.467814i) q^{21} +3.67595 q^{23} +(2.45786 - 4.25713i) q^{25} +(4.16429 + 3.10785i) q^{27} +(-0.420746 + 0.728753i) q^{29} +(-5.21805 + 9.03792i) q^{31} +(-3.60248 - 0.781831i) q^{33} +(-0.184859 + 0.320185i) q^{35} -5.64475 q^{37} +(-5.23153 + 5.76052i) q^{39} +(4.35898 + 7.54997i) q^{41} +3.30783 q^{43} +(-0.708967 + 0.505896i) q^{45} +(-6.24133 + 10.8103i) q^{47} +(2.68911 - 4.65768i) q^{49} +(-2.32566 - 7.26309i) q^{51} +(3.47517 + 6.01918i) q^{53} +(0.308944 - 0.535107i) q^{55} +(-6.81083 - 3.25770i) q^{57} +(-3.36518 - 5.82866i) q^{59} +(3.97416 - 6.88345i) q^{61} +(-3.10990 + 2.21912i) q^{63} +(-0.652154 - 1.12956i) q^{65} +16.2675 q^{67} +(-4.28049 + 4.71331i) q^{69} +(-1.77602 + 3.07616i) q^{71} +(1.63472 - 2.83142i) q^{73} +(2.59644 + 8.10872i) q^{75} +(1.35519 - 2.34726i) q^{77} -0.600638 q^{79} +(-8.83402 + 1.72050i) q^{81} +(7.47236 + 12.9425i) q^{83} +1.27830 q^{85} +(-0.444468 - 1.38808i) q^{87} +(1.55109 + 2.68657i) q^{89} +(-2.86069 - 4.95486i) q^{91} +(-5.51225 - 17.2149i) q^{93} +(0.868166 - 0.920708i) q^{95} -0.404463 q^{97} +(5.19740 - 3.70870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{3} - q^{7} - 2 q^{9} - q^{11} + 2 q^{13} + q^{15} + 5 q^{17} + q^{19} + 6 q^{21} + 8 q^{23} - 20 q^{25} + 7 q^{27} - 9 q^{29} + 2 q^{31} - q^{33} - 6 q^{35} + 2 q^{37} + 3 q^{39} - 25 q^{41}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q - 2 * q^3 - q^7 - 2 * q^9 - q^11 + 2 * q^13 + q^15 + 5 * q^17 + q^19 + 6 * q^21 + 8 * q^23 - 20 * q^25 + 7 * q^27 - 9 * q^29 + 2 * q^31 - q^33 - 6 * q^35 + 2 * q^37 + 3 * q^39 - 25 * q^41 - 16 * q^43 + 44 * q^45 - 10 * q^47 - 21 * q^49 + 19 * q^51 - 8 * q^53 - 22 * q^59 - 7 * q^61 + 10 * q^63 - 6 * q^65 + 20 * q^67 + 38 * q^69 - 5 * q^71 - 10 * q^73 - 10 * q^77 + 2 * q^79 + 22 * q^81 + q^83 - 52 * q^87 - 34 * q^89 + 16 * q^91 - 8 * q^93 + 36 * q^95 + 2 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.16446	+	1.28220i	−0.672299	+	0.740279i
$3$	−1.16446	+	1.28220i	−0.672299	+	0.740279i
$4$		0			0
$5$	−0.145159	−	0.251423i	−0.0649173	−	0.112440i	0.831740	−	0.555165i	$-0.187345\pi$
$5$	−0.145159	−	0.251423i	−0.0649173	−	0.112440i	−0.896657	+	0.442725i	$0.854012\pi$
$6$		0			0
$7$	−0.636745	−	1.10287i	−0.240667	−	0.416847i	0.720238	−	0.693727i	$-0.244033\pi$
$7$	−0.636745	−	1.10287i	−0.240667	−	0.416847i	−0.960904	+	0.276880i	$0.910699\pi$
$8$		0			0
$9$	−0.288081	−	2.98614i	−0.0960271	−	0.995379i
$10$		0			0
$11$	1.06416	+	1.84317i	0.320855	+	0.555737i	0.980665	−	0.195696i	$-0.0626964\pi$
$11$	1.06416	+	1.84317i	0.320855	+	0.555737i	−0.659810	+	0.751433i	$0.729363\pi$
$12$		0			0
$13$	4.49268			1.24604			0.623022	−	0.782204i	$-0.285905\pi$
$13$	4.49268			1.24604			0.623022	+	0.782204i	$0.285905\pi$
$14$		0			0
$15$	0.491407	+	0.106648i	0.126881	+	0.0275364i
$16$		0			0
$17$	−2.20154	+	3.81318i	−0.533951	+	0.924831i	0.465262	+	0.885173i	$0.345960\pi$
$17$	−2.20154	+	3.81318i	−0.533951	+	0.924831i	−0.999213	+	0.0396580i	$0.987373\pi$
$18$		0			0
$19$	1.25129	+	4.17544i	0.287066	+	0.957911i
$19$	1.25129	+	4.17544i	0.287066	+	0.957911i
$20$		0			0
$21$	2.15557	+	0.467814i	0.470384	+	0.102085i
$22$		0			0
$23$	3.67595			0.766489			0.383245	−	0.923647i	$-0.374807\pi$
$23$	3.67595			0.766489			0.383245	+	0.923647i	$0.374807\pi$
$24$		0			0
$25$	2.45786	−	4.25713i	0.491571	−	0.851427i
$26$		0			0
$27$	4.16429	+	3.10785i	0.801417	+	0.598106i
$28$		0			0
$29$	−0.420746	+	0.728753i	−0.0781305	+	0.135326i	−0.902443	−	0.430809i	$-0.858228\pi$
$29$	−0.420746	+	0.728753i	−0.0781305	+	0.135326i	0.824313	+	0.566135i	$0.191562\pi$
$30$		0			0
$31$	−5.21805	+	9.03792i	−0.937189	+	1.62326i	−0.166506	+	0.986041i	$0.553248\pi$
$31$	−5.21805	+	9.03792i	−0.937189	+	1.62326i	−0.770683	+	0.637218i	$0.780085\pi$
$32$		0			0
$33$	−3.60248	−	0.781831i	−0.627111	−	0.136099i
$34$		0			0
$35$	−0.184859	+	0.320185i	−0.0312469	+	0.0541212i
$36$		0			0
$37$	−5.64475			−0.927992			−0.463996	−	0.885837i	$-0.653585\pi$
$37$	−5.64475			−0.927992			−0.463996	+	0.885837i	$0.653585\pi$
$38$		0			0
$39$	−5.23153	+	5.76052i	−0.837715	+	0.922421i
$40$		0			0
$41$	4.35898	+	7.54997i	0.680758	+	1.17911i	0.974750	+	0.223300i	$0.0716829\pi$
$41$	4.35898	+	7.54997i	0.680758	+	1.17911i	−0.293992	+	0.955808i	$0.594984\pi$
$42$		0			0
$43$	3.30783			0.504439			0.252219	−	0.967670i	$-0.418840\pi$
$43$	3.30783			0.504439			0.252219	+	0.967670i	$0.418840\pi$
$44$		0			0
$45$	−0.708967	+	0.505896i	−0.105687	+	0.0754145i
$46$		0			0
$47$	−6.24133	+	10.8103i	−0.910392	+	1.57685i	−0.0968809	+	0.995296i	$0.530887\pi$
$47$	−6.24133	+	10.8103i	−0.910392	+	1.57685i	−0.813511	+	0.581549i	$0.802447\pi$
$48$		0			0
$49$	2.68911	−	4.65768i	0.384159	−	0.665383i
$50$		0			0
$51$	−2.32566	−	7.26309i	−0.325658	−	1.01704i
$52$		0			0
$53$	3.47517	+	6.01918i	0.477352	+	0.826798i	0.999663	−	0.0259572i	$-0.00826338\pi$
$53$	3.47517	+	6.01918i	0.477352	+	0.826798i	−0.522311	+	0.852755i	$0.674930\pi$
$54$		0			0
$55$	0.308944	−	0.535107i	0.0416581	−	0.0721539i
$56$		0			0
$57$	−6.81083	−	3.25770i	−0.902116	−	0.431493i
$58$		0			0
$59$	−3.36518	−	5.82866i	−0.438109	−	0.758827i	0.559435	−	0.828874i	$-0.311018\pi$
$59$	−3.36518	−	5.82866i	−0.438109	−	0.758827i	−0.997544	+	0.0700476i	$0.977685\pi$
$60$		0			0
$61$	3.97416	−	6.88345i	0.508839	−	0.881336i	−0.491108	−	0.871099i	$-0.663408\pi$
$61$	3.97416	−	6.88345i	0.508839	−	0.881336i	0.999948	−	0.0102370i	$-0.00325860\pi$
$62$		0			0
$63$	−3.10990	+	2.21912i	−0.391810	+	0.279583i
$64$		0			0
$65$	−0.652154	−	1.12956i	−0.0808898	−	0.140105i
$66$		0			0
$67$	16.2675			1.98739			0.993697	−	0.112099i	$-0.0357572\pi$
$67$	16.2675			1.98739			0.993697	+	0.112099i	$0.0357572\pi$
$68$		0			0
$69$	−4.28049	+	4.71331i	−0.515310	+	0.567416i
$70$		0			0
$71$	−1.77602	+	3.07616i	−0.210775	+	0.365073i	−0.951957	−	0.306231i	$-0.900932\pi$
$71$	−1.77602	+	3.07616i	−0.210775	+	0.365073i	0.741182	+	0.671304i	$0.234265\pi$
$72$		0			0
$73$	1.63472	−	2.83142i	0.191329	−	0.331392i	−0.754362	−	0.656459i	$-0.772053\pi$
$73$	1.63472	−	2.83142i	0.191329	−	0.331392i	0.945691	+	0.325067i	$0.105387\pi$
$74$		0			0
$75$	2.59644	+	8.10872i	0.299811	+	0.936314i
$76$		0			0
$77$	1.35519	−	2.34726i	0.154438	−	0.267495i
$78$		0			0
$79$	−0.600638			−0.0675770			−0.0337885	−	0.999429i	$-0.510757\pi$
$79$	−0.600638			−0.0675770			−0.0337885	+	0.999429i	$0.510757\pi$
$80$		0			0
$81$	−8.83402	+	1.72050i	−0.981558	+	0.191167i
$82$		0			0
$83$	7.47236	+	12.9425i	0.820198	+	1.42062i	0.905535	+	0.424272i	$0.139470\pi$
$83$	7.47236	+	12.9425i	0.820198	+	1.42062i	−0.0853371	+	0.996352i	$0.527197\pi$
$84$		0			0
$85$	1.27830			0.138651
$86$		0			0
$87$	−0.444468	−	1.38808i	−0.0476520	−	0.148818i
$88$		0			0
$89$	1.55109	+	2.68657i	0.164415	+	0.284776i	0.936448	−	0.350808i	$-0.114093\pi$
$89$	1.55109	+	2.68657i	0.164415	+	0.284776i	−0.772032	+	0.635584i	$0.780760\pi$
$90$		0			0
$91$	−2.86069	−	4.95486i	−0.299882	−	0.519410i
$92$		0			0
$93$	−5.51225	−	17.2149i	−0.571594	−	1.78510i
$94$		0			0
$95$	0.868166	−	0.920708i	0.0890719	−	0.0944627i
$96$		0			0
$97$	−0.404463			−0.0410670			−0.0205335	−	0.999789i	$-0.506536\pi$
$97$	−0.404463			−0.0410670			−0.0205335	+	0.999789i	$0.506536\pi$
$98$		0			0
$99$	5.19740	−	3.70870i	0.522358	−	0.372738i
$100$		0			0
$101$	0.920657	−	1.59462i	0.0916088	−	0.158671i	−0.816579	−	0.577233i	$-0.804132\pi$
$101$	0.920657	−	1.59462i	0.0916088	−	0.158671i	0.908188	+	0.418562i	$0.137466\pi$
$102$		0			0
$103$	4.15901	−	7.20361i	0.409799	−	0.709793i	−0.585068	−	0.810984i	$-0.698932\pi$
$103$	4.15901	−	7.20361i	0.409799	−	0.709793i	0.994867	+	0.101191i	$0.0322654\pi$
$104$		0			0
$105$	−0.195282	−	0.609868i	−0.0190575	−	0.0595170i
$106$		0			0
$107$	−9.64179			−0.932107			−0.466054	−	0.884757i	$-0.654325\pi$
$107$	−9.64179			−0.932107			−0.466054	+	0.884757i	$0.654325\pi$
$108$		0			0
$109$	2.61291	−	4.52569i	0.250271	−	0.433483i	−0.713329	−	0.700829i	$-0.752813\pi$
$109$	2.61291	−	4.52569i	0.250271	−	0.433483i	0.963600	+	0.267346i	$0.0861468\pi$
$110$		0			0
$111$	6.57307	−	7.23771i	0.623888	−	0.686973i
$112$		0			0
$113$	7.95431	−	13.7773i	0.748278	−	1.29606i	−0.200369	−	0.979721i	$-0.564214\pi$
$113$	7.95431	−	13.7773i	0.748278	−	1.29606i	0.948647	−	0.316336i	$-0.102453\pi$
$114$		0			0
$115$	−0.533599	−	0.924221i	−0.0497584	−	0.0861840i
$116$		0			0
$117$	−1.29426	−	13.4157i	−0.119654	−	1.24029i
$118$		0			0
$119$	5.60727			0.514018
$120$		0			0
$121$	3.23515	−	5.60344i	0.294104	−	0.509403i
$122$		0			0
$123$	−14.7564	−	3.20253i	−1.33054	−	0.288762i
$124$		0			0
$125$	−2.87872			−0.257480
$126$		0			0
$127$	6.00760	+	10.4055i	0.533088	+	0.923336i	0.999253	+	0.0386379i	$0.0123019\pi$
$127$	6.00760	+	10.4055i	0.533088	+	0.923336i	−0.466165	+	0.884698i	$0.654365\pi$
$128$		0			0
$129$	−3.85182	+	4.24130i	−0.339134	+	0.373426i
$130$		0			0
$131$	−11.1984	−	19.3962i	−0.978408	−	1.69465i	−0.668197	−	0.743984i	$-0.732934\pi$
$131$	−11.1984	−	19.3962i	−0.978408	−	1.69465i	−0.310210	−	0.950668i	$-0.600400\pi$
$132$		0			0
$133$	3.80823	−	4.03871i	0.330215	−	0.350200i
$134$		0			0
$135$	0.176900	−	1.49813i	0.0152252	−	0.128939i
$136$		0			0
$137$	−10.1018	+	17.4969i	−0.863057	+	1.49486i	0.00590605	+	0.999983i	$0.498120\pi$
$137$	−10.1018	+	17.4969i	−0.863057	+	1.49486i	−0.868963	+	0.494876i	$0.835213\pi$
$138$		0			0
$139$	−5.78269			−0.490481			−0.245241	−	0.969462i	$-0.578867\pi$
$139$	−5.78269			−0.490481			−0.245241	+	0.969462i	$0.578867\pi$
$140$		0			0
$141$	−6.59323	−	20.5908i	−0.555250	−	1.73406i
$142$		0			0
$143$	4.78091	+	8.28078i	0.399800	+	0.692473i
$144$		0			0
$145$	0.244301			0.0202881
$146$		0			0
$147$	2.84073	+	8.87165i	0.234299	+	0.731721i
$148$		0			0
$149$	−3.88343	−	6.72630i	−0.318143	−	0.551040i	0.661957	−	0.749541i	$-0.269726\pi$
$149$	−3.88343	−	6.72630i	−0.318143	−	0.551040i	−0.980101	+	0.198501i	$0.936393\pi$
$150$		0			0
$151$	−3.26026	−	5.64693i	−0.265316	−	0.459541i	0.702330	−	0.711851i	$-0.252143\pi$
$151$	−3.26026	−	5.64693i	−0.265316	−	0.459541i	−0.967646	+	0.252310i	$0.918810\pi$
$152$		0			0
$153$	12.0209	+	5.47559i	0.971831	+	0.442675i
$154$		0			0
$155$	3.02979			0.243359
$156$		0			0
$157$	−2.52958	−	4.38136i	−0.201882	−	0.349670i	0.747253	−	0.664540i	$-0.231373\pi$
$157$	−2.52958	−	4.38136i	−0.201882	−	0.349670i	−0.949135	+	0.314870i	$0.898039\pi$
$158$		0			0
$159$	−11.7645	−	2.55320i	−0.932985	−	0.202482i
$160$		0			0
$161$	−2.34064	−	4.05411i	−0.184469	−	0.319509i
$162$		0			0
$163$	−1.51786			−0.118888			−0.0594441	−	0.998232i	$-0.518933\pi$
$163$	−1.51786			−0.118888			−0.0594441	+	0.998232i	$0.518933\pi$
$164$		0			0
$165$	0.326363	+	1.01924i	0.0254073	+	0.0793476i
$166$		0			0
$167$	3.06451			0.237139			0.118570	−	0.992946i	$-0.462169\pi$
$167$	3.06451			0.237139			0.118570	+	0.992946i	$0.462169\pi$
$168$		0			0
$169$	7.18415			0.552627
$170$		0			0
$171$	12.1079	−	4.93940i	0.925918	−	0.377725i
$172$		0			0
$173$	5.98054			0.454692			0.227346	−	0.973814i	$-0.426995\pi$
$173$	5.98054			0.454692			0.227346	+	0.973814i	$0.426995\pi$
$174$		0			0
$175$	−6.26011			−0.473220
$176$		0			0
$177$	11.3921	+	2.47238i	0.856284	+	0.185836i
$178$		0			0
$179$	20.9986			1.56951			0.784756	−	0.619805i	$-0.212788\pi$
$179$	20.9986			1.56951			0.784756	+	0.619805i	$0.212788\pi$
$180$		0			0
$181$	−5.25317	−	9.09875i	−0.390465	−	0.676305i	0.602046	−	0.798461i	$-0.294352\pi$
$181$	−5.25317	−	9.09875i	−0.390465	−	0.676305i	−0.992511	+	0.122157i	$0.961019\pi$
$182$		0			0
$183$	4.19823	+	13.1112i	0.310342	+	0.969205i
$184$		0			0
$185$	0.819389	+	1.41922i	0.0602427	+	0.104343i
$186$		0			0
$187$	−9.37112			−0.685284
$188$		0			0
$189$	0.775977	−	6.57159i	0.0564440	−	0.478013i
$190$		0			0
$191$	−7.13902	−	12.3651i	−0.516561	−	0.894711i	−0.999815	−	0.0192303i	$-0.993878\pi$
$191$	−7.13902	−	12.3651i	−0.516561	−	0.894711i	0.483254	−	0.875480i	$-0.339455\pi$
$192$		0			0
$193$	2.58021	+	4.46905i	0.185727	+	0.321689i	0.943821	−	0.330456i	$-0.107203\pi$
$193$	2.58021	+	4.46905i	0.185727	+	0.321689i	−0.758094	+	0.652145i	$0.773869\pi$
$194$		0			0
$195$	2.20773	+	0.479136i	0.158099	+	0.0343116i
$196$		0			0
$197$	−23.2805			−1.65867			−0.829334	−	0.558753i	$-0.811280\pi$
$197$	−23.2805			−1.65867			−0.829334	+	0.558753i	$0.811280\pi$
$198$		0			0
$199$	−5.15739	−	8.93287i	−0.365598	−	0.633234i	0.623274	−	0.782004i	$-0.285802\pi$
$199$	−5.15739	−	8.93287i	−0.365598	−	0.633234i	−0.988872	+	0.148769i	$0.952469\pi$
$200$		0			0
$201$	−18.9428	+	20.8582i	−1.33612	+	1.47123i
$202$		0			0
$203$	1.07163			0.0752137
$204$		0			0
$205$	1.26549	−	2.19190i	0.0883859	−	0.153089i
$206$		0			0
$207$	−1.05897	−	10.9769i	−0.0736038	−	0.762947i
$208$		0			0
$209$	−6.36447	+	6.74966i	−0.440240	+	0.466884i
$210$		0			0
$211$	−4.92848	−	8.53638i	−0.339291	−	0.587669i	0.645009	−	0.764175i	$-0.276854\pi$
$211$	−4.92848	−	8.53638i	−0.339291	−	0.587669i	−0.984300	+	0.176506i	$0.943520\pi$
$212$		0			0
$213$	−1.87616	−	5.85928i	−0.128552	−	0.401471i
$214$		0			0
$215$	−0.480162	−	0.831665i	−0.0327468	−	0.0567191i
$216$		0			0
$217$	13.2903			0.902201
$218$		0			0
$219$	1.72689	+	5.39310i	0.116692	+	0.364432i
$220$		0			0
$221$	−9.89080	+	17.1314i	−0.665327	+	1.15238i
$222$		0			0
$223$	7.16349			0.479703			0.239851	−	0.970810i	$-0.422901\pi$
$223$	7.16349			0.479703			0.239851	+	0.970810i	$0.422901\pi$
$224$		0			0
$225$	−13.4204	−	6.11310i	−0.894696	−	0.407540i
$226$		0			0
$227$	8.20819	+	14.2170i	0.544796	+	0.943615i	0.998620	+	0.0525234i	$0.0167264\pi$
$227$	8.20819	+	14.2170i	0.544796	+	0.943615i	−0.453823	+	0.891092i	$0.649940\pi$
$228$		0			0
$229$	−2.24189	+	3.88306i	−0.148148	+	0.256600i	−0.930543	−	0.366183i	$-0.880665\pi$
$229$	−2.24189	+	3.88306i	−0.148148	+	0.256600i	0.782395	+	0.622783i	$0.213998\pi$
$230$		0			0
$231$	1.43160	+	4.47091i	0.0941923	+	0.294164i
$232$		0			0
$233$	0.611208	−	1.05864i	0.0400416	−	0.0693540i	−0.845310	−	0.534276i	$-0.820584\pi$
$233$	0.611208	−	1.05864i	0.0400416	−	0.0693540i	0.885352	+	0.464922i	$0.153918\pi$
$234$		0			0
$235$	3.62395			0.236401
$236$		0			0
$237$	0.699417	−	0.770139i	0.0454320	−	0.0500259i
$238$		0			0
$239$	−7.57388	+	13.1183i	−0.489913	+	0.848555i	−0.999933	−	0.0116081i	$-0.996305\pi$
$239$	−7.57388	+	13.1183i	−0.489913	+	0.848555i	0.510019	+	0.860163i	$0.329638\pi$
$240$		0			0
$241$	−8.09984	+	14.0293i	−0.521756	+	0.903709i	0.477923	+	0.878402i	$0.341390\pi$
$241$	−8.09984	+	14.0293i	−0.521756	+	0.903709i	−0.999680	+	0.0253070i	$0.991944\pi$
$242$		0			0
$243$	8.08080	−	13.3304i	0.518384	−	0.855148i
$244$		0			0
$245$	−1.56140			−0.0997542
$246$		0			0
$247$	5.62166	+	18.7589i	0.357698	+	1.19360i
$248$		0			0
$249$	−25.2961	−	5.48991i	−1.60308	−	0.347909i
$250$		0			0
$251$	−12.9736	−	22.4709i	−0.818883	−	1.41835i	−0.906506	−	0.422194i	$-0.861260\pi$
$251$	−12.9736	−	22.4709i	−0.818883	−	1.41835i	0.0876223	−	0.996154i	$-0.472073\pi$
$252$		0			0
$253$	3.91179	+	6.77541i	0.245932	+	0.425967i
$254$		0			0
$255$	−1.48852	+	1.63903i	−0.0932147	+	0.102640i
$256$		0			0
$257$	28.8641			1.80049			0.900247	−	0.435380i	$-0.143386\pi$
$257$	28.8641			1.80049			0.900247	+	0.435380i	$0.143386\pi$
$258$		0			0
$259$	3.59427	+	6.22545i	0.223337	+	0.386831i
$260$		0			0
$261$	2.29737	+	1.04646i	0.142203	+	0.0647745i
$262$		0			0
$263$	0.941621			0.0580628			0.0290314	−	0.999578i	$-0.490758\pi$
$263$	0.941621			0.0580628			0.0290314	+	0.999578i	$0.490758\pi$
$264$		0			0
$265$	1.00891	−	1.74748i	0.0619768	−	0.107347i
$266$		0			0
$267$	−5.25090	−	1.13958i	−0.321350	−	0.0697413i
$268$		0			0
$269$	−5.87750	+	10.1801i	−0.358358	+	0.620694i	−0.987687	−	0.156445i	$-0.949997\pi$
$269$	−5.87750	+	10.1801i	−0.358358	+	0.620694i	0.629329	+	0.777139i	$0.283330\pi$
$270$		0			0
$271$	−13.4557	+	23.3060i	−0.817375	+	1.41574i	0.0902341	+	0.995921i	$0.471238\pi$
$271$	−13.4557	+	23.3060i	−0.817375	+	1.41574i	−0.907610	+	0.419815i	$0.862095\pi$
$272$		0			0
$273$	9.68427	+	2.10174i	0.586119	+	0.127203i
$274$		0			0
$275$	10.4622			0.630893
$276$		0			0
$277$	−3.40921	−	5.90492i	−0.204839	−	0.354792i	0.745242	−	0.666794i	$-0.232334\pi$
$277$	−3.40921	−	5.90492i	−0.204839	−	0.354792i	−0.950082	+	0.312002i	$0.899001\pi$
$278$		0			0
$279$	28.4917	+	12.9781i	1.70575	+	0.776981i
$280$		0			0
$281$	−4.44909	+	7.70605i	−0.265410	+	0.459704i	−0.967671	−	0.252216i	$-0.918841\pi$
$281$	−4.44909	+	7.70605i	−0.265410	+	0.459704i	0.702261	+	0.711920i	$0.252174\pi$
$282$		0			0
$283$	−4.22174	−	7.31226i	−0.250956	−	0.434669i	0.712833	−	0.701334i	$-0.247412\pi$
$283$	−4.22174	−	7.31226i	−0.250956	−	0.434669i	−0.963789	+	0.266665i	$0.914078\pi$
$284$		0			0
$285$	0.169592	+	2.18529i	0.0100458	+	0.129445i
$286$		0			0
$287$	5.55111	−	9.61481i	0.327672	−	0.567544i
$288$		0			0
$289$	−1.19354	−	2.06727i	−0.0702083	−	0.121604i
$290$		0			0
$291$	0.470980	−	0.518603i	0.0276093	−	0.0304011i
$292$		0			0
$293$	8.47638	−	14.6815i	0.495195	−	0.857704i	−0.504789	−	0.863243i	$-0.668430\pi$
$293$	8.47638	−	14.6815i	0.495195	−	0.857704i	0.999985	+	0.00553903i	$0.00176314\pi$
$294$		0			0
$295$	−0.976974	+	1.69217i	−0.0568816	+	0.0985219i
$296$		0			0
$297$	−1.29685	+	10.9827i	−0.0752507	+	0.637283i
$298$		0			0
$299$	16.5149			0.955080
$300$		0			0
$301$	−2.10624	−	3.64812i	−0.121402	−	0.210274i
$302$		0			0
$303$	0.972565	+	3.03734i	0.0558724	+	0.174491i
$304$		0			0
$305$	−2.30755			−0.132130
$306$		0			0
$307$	−2.47411	+	4.28529i	−0.141205	+	0.244574i	−0.927951	−	0.372703i	$-0.878431\pi$
$307$	−2.47411	+	4.28529i	−0.141205	+	0.244574i	0.786746	+	0.617277i	$0.211764\pi$
$308$		0			0
$309$	4.39350	+	13.7210i	0.249937	+	0.780559i
$310$		0			0
$311$	9.46035	−	16.3858i	0.536447	−	0.929154i	−0.462644	−	0.886544i	$-0.653099\pi$
$311$	9.46035	−	16.3858i	0.536447	−	0.929154i	0.999092	−	0.0426102i	$-0.0135673\pi$
$312$		0			0
$313$	1.24126	−	2.14992i	0.0701601	−	0.121521i	−0.828811	−	0.559528i	$-0.810982\pi$
$313$	1.24126	−	2.14992i	0.0701601	−	0.121521i	0.898971	+	0.438007i	$0.144316\pi$
$314$		0			0
$315$	1.00937	+	0.459775i	0.0568716	+	0.0259054i
$316$		0			0
$317$	10.8303	−	18.7586i	0.608290	−	1.05359i	−0.383232	−	0.923652i	$-0.625189\pi$
$317$	10.8303	−	18.7586i	0.608290	−	1.05359i	0.991522	−	0.129937i	$-0.0414776\pi$
$318$		0			0
$319$	−1.79096			−0.100274
$320$		0			0
$321$	11.2274	−	12.3627i	0.626655	−	0.690020i
$322$		0			0
$323$	−18.6764	−	4.42098i	−1.03919	−	0.245990i
$324$		0			0
$325$	11.0424	−	19.1259i	0.612520	−	1.06092i
$326$		0			0
$327$	2.76023	+	8.62025i	0.152641	+	0.476701i
$328$		0			0
$329$	15.8965			0.876405
$330$		0			0
$331$	−8.25161	−	14.2922i	−0.453549	−	0.785570i	0.545054	−	0.838401i	$-0.316509\pi$
$331$	−8.25161	−	14.2922i	−0.453549	−	0.785570i	−0.998603	+	0.0528304i	$0.983176\pi$
$332$		0			0
$333$	1.62615	+	16.8560i	0.0891124	+	0.923703i
$334$		0			0
$335$	−2.36138	−	4.09004i	−0.129016	−	0.223463i
$336$		0			0
$337$	1.69767	+	2.94045i	0.0924778	+	0.160176i	0.908553	−	0.417769i	$-0.137188\pi$
$337$	1.69767	+	2.94045i	0.0924778	+	0.160176i	−0.816075	+	0.577946i	$0.803855\pi$
$338$		0			0
$339$	8.40278	+	26.2421i	0.456377	+	1.42527i
$340$		0			0
$341$	−22.2113			−1.20281
$342$		0			0
$343$	−15.7635			−0.851151
$344$		0			0
$345$	1.80639	+	0.392034i	0.0972528	+	0.0211064i
$346$		0			0
$347$	−1.82834	−	3.16677i	−0.0981502	−	0.170001i	0.812769	−	0.582586i	$-0.197959\pi$
$347$	−1.82834	−	3.16677i	−0.0981502	−	0.170001i	−0.910919	+	0.412585i	$0.864626\pi$
$348$		0			0
$349$	6.35856	+	11.0133i	0.340366	+	0.589531i	0.984501	−	0.175381i	$-0.0561158\pi$
$349$	6.35856	+	11.0133i	0.340366	+	0.589531i	−0.644135	+	0.764912i	$0.722782\pi$
$350$		0			0
$351$	18.7088	+	13.9626i	0.998602	+	0.745266i
$352$		0			0
$353$	10.4938	+	18.1758i	0.558530	+	0.967402i	0.997620	+	0.0689587i	$0.0219677\pi$
$353$	10.4938	+	18.1758i	0.558530	+	0.967402i	−0.439090	+	0.898443i	$0.644699\pi$
$354$		0			0
$355$	1.03123			0.0547318
$356$		0			0
$357$	−6.52942	+	7.18965i	−0.345574	+	0.380517i
$358$		0			0
$359$	−4.64643	+	8.04785i	−0.245229	+	0.424749i	−0.962196	−	0.272358i	$-0.912197\pi$
$359$	−4.64643	+	8.04785i	−0.245229	+	0.424749i	0.716967	+	0.697107i	$0.245530\pi$
$360$		0			0
$361$	−15.8685	+	10.4494i	−0.835186	+	0.549968i
$362$		0			0
$363$	3.41755	+	10.6731i	0.179375	+	0.560191i
$364$		0			0
$365$	−0.949179			−0.0496823
$366$		0			0
$367$	−6.99598	+	12.1174i	−0.365187	+	0.632523i	−0.988806	−	0.149205i	$-0.952328\pi$
$367$	−6.99598	+	12.1174i	−0.365187	+	0.632523i	0.623619	+	0.781729i	$0.285662\pi$
$368$		0			0
$369$	21.2895	−	15.1915i	1.10829	−	0.790839i
$370$		0			0
$371$	4.42560	−	7.66536i	0.229766	−	0.397966i
$372$		0			0
$373$	−16.1239	+	27.9273i	−0.834862	+	1.44602i	0.0592816	+	0.998241i	$0.481119\pi$
$373$	−16.1239	+	27.9273i	−0.834862	+	1.44602i	−0.894143	+	0.447781i	$0.852214\pi$
$374$		0			0
$375$	3.35214	−	3.69110i	0.173104	−	0.190607i
$376$		0			0
$377$	−1.89028	+	3.27405i	−0.0973541	+	0.168622i
$378$		0			0
$379$	17.9462			0.921832			0.460916	−	0.887444i	$-0.347521\pi$
$379$	17.9462			0.921832			0.460916	+	0.887444i	$0.347521\pi$
$380$		0			0
$381$	−20.3375	−	4.41376i	−1.04192	−	0.226124i
$382$		0			0
$383$	−18.2810	−	31.6637i	−0.934118	−	1.61794i	−0.776200	−	0.630487i	$-0.782855\pi$
$383$	−18.2810	−	31.6637i	−0.934118	−	1.61794i	−0.157918	−	0.987452i	$-0.550478\pi$
$384$		0			0
$385$	−0.786875			−0.0401028
$386$		0			0
$387$	−0.952924	−	9.87762i	−0.0484398	−	0.502108i
$388$		0			0
$389$	5.19563	−	8.99910i	0.263429	−	0.456273i	−0.703722	−	0.710476i	$-0.748480\pi$
$389$	5.19563	−	8.99910i	0.263429	−	0.456273i	0.967151	+	0.254203i	$0.0818132\pi$
$390$		0			0
$391$	−8.09275	+	14.0171i	−0.409268	+	0.708873i
$392$		0			0
$393$	37.9098	+	8.22742i	1.91230	+	0.415018i
$394$		0			0
$395$	0.0871882	+	0.151014i	0.00438692	+	0.00759836i
$396$		0			0
$397$	10.5523	−	18.2771i	0.529604	−	0.917301i	−0.469800	−	0.882773i	$-0.655674\pi$
$397$	10.5523	−	18.2771i	0.529604	−	0.917301i	0.999404	−	0.0345277i	$-0.0109927\pi$
$398$		0			0
$399$	0.743921	+	9.58581i	0.0372426	+	0.479891i
$400$		0			0
$401$	−0.431270	−	0.746982i	−0.0215366	−	0.0373025i	0.855056	−	0.518535i	$-0.173523\pi$
$401$	−0.431270	−	0.746982i	−0.0215366	−	0.0373025i	−0.876593	+	0.481233i	$0.840189\pi$
$402$		0			0
$403$	−23.4430	+	40.6045i	−1.16778	+	2.02265i
$404$		0			0
$405$	1.71492	+	1.97133i	0.0852148	+	0.0979563i
$406$		0			0
$407$	−6.00690	−	10.4042i	−0.297751	−	0.515719i
$408$		0			0
$409$	22.4810			1.11162			0.555808	−	0.831311i	$-0.312409\pi$
$409$	22.4810			1.11162			0.555808	+	0.831311i	$0.312409\pi$
$410$		0			0
$411$	−10.6714	−	33.3269i	−0.526380	−	1.64390i
$412$		0			0
$413$	−4.28552	+	7.42273i	−0.210877	+	0.365249i
$414$		0			0
$415$	2.16937	−	3.75745i	0.106490	−	0.184446i
$416$		0			0
$417$	6.73369	−	7.41457i	0.329750	−	0.363093i
$418$		0			0
$419$	−12.1706	+	21.0801i	−0.594572	+	1.02983i	0.399035	+	0.916936i	$0.369345\pi$
$419$	−12.1706	+	21.0801i	−0.594572	+	1.02983i	−0.993607	+	0.112894i	$0.963988\pi$
$420$		0			0
$421$	19.9752			0.973531			0.486765	−	0.873533i	$-0.338177\pi$
$421$	19.9752			0.973531			0.486765	+	0.873533i	$0.338177\pi$
$422$		0			0
$423$	34.0791	+	15.5232i	1.65698	+	0.754765i
$424$		0			0
$425$	10.8221	+	18.7445i	0.524951	+	0.909241i
$426$		0			0
$427$	−10.1221			−0.489843
$428$		0			0
$429$	−16.1848	−	3.51252i	−0.781409	−	0.169586i
$430$		0			0
$431$	−13.6581	−	23.6566i	−0.657889	−	1.13950i	−0.981161	−	0.193191i	$-0.938116\pi$
$431$	−13.6581	−	23.6566i	−0.657889	−	1.13950i	0.323272	−	0.946306i	$-0.395217\pi$
$432$		0			0
$433$	9.69487	+	16.7920i	0.465906	+	0.806972i	0.999242	−	0.0389311i	$-0.0123953\pi$
$433$	9.69487	+	16.7920i	0.465906	+	0.806972i	−0.533336	+	0.845903i	$0.679062\pi$
$434$		0			0
$435$	−0.284478	+	0.313243i	−0.0136397	+	0.0150188i
$436$		0			0
$437$	4.59970	+	15.3487i	0.220033	+	0.734228i
$438$		0			0
$439$	−38.2832			−1.82716			−0.913578	−	0.406664i	$-0.866692\pi$
$439$	−38.2832			−1.82716			−0.913578	+	0.406664i	$0.866692\pi$
$440$		0			0
$441$	−14.6831	−	6.68827i	−0.699198	−	0.318489i
$442$		0			0
$443$	2.68749	−	4.65487i	0.127687	−	0.221160i	−0.795093	−	0.606487i	$-0.792578\pi$
$443$	2.68749	−	4.65487i	0.127687	−	0.221160i	0.922780	+	0.385327i	$0.125911\pi$
$444$		0			0
$445$	0.450311	−	0.779962i	0.0213468	−	0.0369737i
$446$		0			0
$447$	13.1466	+	2.85315i	0.621811	+	0.134949i
$448$		0			0
$449$	−27.9420			−1.31867			−0.659333	−	0.751851i	$-0.729161\pi$
$449$	−27.9420			−1.31867			−0.659333	+	0.751851i	$0.729161\pi$
$450$		0			0
$451$	−9.27726	+	16.0687i	−0.436849	+	0.756645i
$452$		0			0
$453$	11.0369	+	2.39530i	0.518560	+	0.112541i
$454$		0			0
$455$	−0.830512	+	1.43849i	−0.0389350	+	0.0674374i
$456$		0			0
$457$	10.8732	+	18.8330i	0.508628	+	0.880970i	0.999950	+	0.00999197i	$0.00318060\pi$
$457$	10.8732	+	18.8330i	0.508628	+	0.880970i	−0.491322	+	0.870978i	$0.663486\pi$
$458$		0			0
$459$	−21.0186	+	9.03711i	−0.981065	+	0.421816i
$460$		0			0
$461$	26.2273			1.22153			0.610764	−	0.791813i	$-0.290862\pi$
$461$	26.2273			1.22153			0.610764	+	0.791813i	$0.290862\pi$
$462$		0			0
$463$	6.54052	−	11.3285i	0.303964	−	0.526480i	−0.673066	−	0.739582i	$-0.735023\pi$
$463$	6.54052	−	11.3285i	0.303964	−	0.526480i	0.977030	+	0.213102i	$0.0683565\pi$
$464$		0			0
$465$	−3.52806	+	3.88481i	−0.163610	+	0.180154i
$466$		0			0
$467$	8.33824			0.385848			0.192924	−	0.981214i	$-0.438203\pi$
$467$	8.33824			0.385848			0.192924	+	0.981214i	$0.438203\pi$
$468$		0			0
$469$	−10.3583	−	17.9410i	−0.478300	−	0.828440i
$470$		0			0
$471$	8.56337	+	1.85847i	0.394579	+	0.0856339i
$472$		0			0
$473$	3.52004	+	6.09689i	0.161852	+	0.280335i
$474$		0			0
$475$	20.8509	+	4.93570i	0.956705	+	0.226466i
$476$		0			0
$477$	16.9730	−	12.1114i	0.777138	−	0.554541i
$478$		0			0
$479$	16.9374	−	29.3364i	0.773887	−	1.34041i	−0.161530	−	0.986868i	$-0.551643\pi$
$479$	16.9374	−	29.3364i	0.773887	−	1.34041i	0.935418	−	0.353545i	$-0.115024\pi$
$480$		0			0
$481$	−25.3601			−1.15632
$482$		0			0
$483$	7.92377	+	1.71966i	0.360544	+	0.0782474i
$484$		0			0
$485$	0.0587116	+	0.101692i	0.00266596	+	0.00461758i
$486$		0			0
$487$	−27.9572			−1.26686			−0.633431	−	0.773799i	$-0.718354\pi$
$487$	−27.9572			−1.26686			−0.633431	+	0.773799i	$0.718354\pi$
$488$		0			0
$489$	1.76749	−	1.94621i	0.0799285	−	0.0880106i
$490$		0			0
$491$	−2.95338	−	5.11541i	−0.133284	−	0.230855i	0.791656	−	0.610967i	$-0.209219\pi$
$491$	−2.95338	−	5.11541i	−0.133284	−	0.230855i	−0.924941	+	0.380111i	$0.875886\pi$
$492$		0			0
$493$	−1.85258	−	3.20876i	−0.0834358	−	0.144515i
$494$		0			0
$495$	−1.68690	−	0.768396i	−0.0758207	−	0.0345368i
$496$		0			0
$497$	4.52349			0.202906
$498$		0			0
$499$	−12.6112	−	21.8432i	−0.564553	−	0.977834i	−0.997091	−	0.0762186i	$-0.975715\pi$
$499$	−12.6112	−	21.8432i	−0.564553	−	0.977834i	0.432538	−	0.901616i	$-0.357618\pi$
$500$		0			0
$501$	−3.56849	+	3.92932i	−0.159429	+	0.175549i
$502$		0			0
$503$	0.835140	+	1.44650i	0.0372370	+	0.0644965i	0.884043	−	0.467405i	$-0.154811\pi$
$503$	0.835140	+	1.44650i	0.0372370	+	0.0644965i	−0.846806	+	0.531901i	$0.821478\pi$
$504$		0			0
$505$	−0.534568			−0.0237880
$506$		0			0
$507$	−8.36563	+	9.21153i	−0.371531	+	0.409098i
$508$		0			0
$509$	9.08472			0.402673			0.201337	−	0.979522i	$-0.435472\pi$
$509$	9.08472			0.402673			0.201337	+	0.979522i	$0.435472\pi$
$510$		0			0
$511$	−4.16359			−0.184186
$512$		0			0
$513$	−7.76587	+	21.2765i	−0.342872	+	0.939382i
$514$		0			0
$515$	−2.41488			−0.106412
$516$		0			0
$517$	−26.5670			−1.16842
$518$		0			0
$519$	−6.96408	+	7.66826i	−0.305689	+	0.336599i
$520$		0			0
$521$	−9.04505			−0.396271			−0.198135	−	0.980175i	$-0.563489\pi$
$521$	−9.04505			−0.396271			−0.198135	+	0.980175i	$0.563489\pi$
$522$		0			0
$523$	15.4496	+	26.7595i	0.675565	+	1.17011i	0.976303	+	0.216406i	$0.0694335\pi$
$523$	15.4496	+	26.7595i	0.675565	+	1.17011i	−0.300739	+	0.953707i	$0.597233\pi$
$524$		0			0
$525$	7.28963	−	8.02672i	0.318145	−	0.350315i
$526$		0			0
$527$	−22.9755	−	39.7947i	−1.00083	−	1.73348i
$528$		0			0
$529$	−9.48737			−0.412494
$530$		0			0
$531$	−16.4357	+	11.7280i	−0.713250	+	0.508952i
$532$		0			0
$533$	19.5835	+	33.9196i	0.848255	+	1.46922i
$534$		0			0
$535$	1.39960	+	2.42417i	0.0605098	+	0.104806i
$536$		0			0
$537$	−24.4520	+	26.9245i	−1.05518	+	1.16188i
$538$		0			0
$539$	11.4465			0.493037
$540$		0			0
$541$	5.91573	+	10.2463i	0.254337	+	0.440525i	0.964715	−	0.263295i	$-0.0848094\pi$
$541$	5.91573	+	10.2463i	0.254337	+	0.440525i	−0.710378	+	0.703820i	$0.751476\pi$
$542$		0			0
$543$	17.7835	+	3.85948i	0.763164	+	0.165626i
$544$		0			0
$545$	−1.51715			−0.0649877
$546$		0			0
$547$	15.3623	−	26.6083i	0.656844	−	1.13769i	−0.324584	−	0.945857i	$-0.605224\pi$
$547$	15.3623	−	26.6083i	0.656844	−	1.13769i	0.981428	−	0.191831i	$-0.0614425\pi$
$548$		0			0
$549$	−21.6998	−	9.88439i	−0.926125	−	0.421856i
$550$		0			0
$551$	−3.56934	−	0.844913i	−0.152059	−	0.0359945i
$552$		0			0
$553$	0.382453	+	0.662428i	0.0162636	+	0.0281693i
$554$		0			0
$555$	−2.77387	−	0.602002i	−0.117744	−	0.0255536i
$556$		0			0
$557$	−18.0718	−	31.3013i	−0.765727	−	1.32628i	−0.939861	−	0.341557i	$-0.889046\pi$
$557$	−18.0718	−	31.3013i	−0.765727	−	1.32628i	0.174134	−	0.984722i	$-0.444287\pi$
$558$		0			0
$559$	14.8610			0.628553
$560$		0			0
$561$	10.9123	−	12.0157i	0.460716	−	0.507302i
$562$		0			0
$563$	−4.46878	+	7.74016i	−0.188337	+	0.326209i	−0.944696	−	0.327948i	$-0.893643\pi$
$563$	−4.46878	+	7.74016i	−0.188337	+	0.326209i	0.756359	+	0.654157i	$0.226976\pi$
$564$		0			0
$565$	−4.61857			−0.194305
$566$		0			0
$567$	7.52251	+	8.64729i	0.315916	+	0.363152i
$568$		0			0
$569$	−7.21977	−	12.5050i	−0.302668	−	0.524237i	0.674071	−	0.738666i	$-0.264544\pi$
$569$	−7.21977	−	12.5050i	−0.302668	−	0.524237i	−0.976739	+	0.214430i	$0.931211\pi$
$570$		0			0
$571$	12.2425	−	21.2047i	0.512334	−	0.887389i	−0.487563	−	0.873088i	$-0.662114\pi$
$571$	12.2425	−	21.2047i	0.512334	−	0.887389i	0.999898	−	0.0143016i	$-0.00455251\pi$
$572$		0			0
$573$	24.1677	+	5.24501i	1.00962	+	0.219114i
$574$		0			0
$575$	9.03497	−	15.6490i	0.376784	−	0.652610i
$576$		0			0
$577$	6.89561			0.287068			0.143534	−	0.989645i	$-0.454153\pi$
$577$	6.89561			0.287068			0.143534	+	0.989645i	$0.454153\pi$
$578$		0			0
$579$	−8.73476	−	1.89567i	−0.363004	−	0.0787813i
$580$		0			0
$581$	9.51597	−	16.4821i	0.394789	−	0.683794i
$582$		0			0
$583$	−7.39625	+	12.8107i	−0.306321	+	0.530564i
$584$		0			0
$585$	−3.18516	+	2.27283i	−0.131690	+	0.0939699i
$586$		0			0
$587$	−28.6419			−1.18218			−0.591090	−	0.806606i	$-0.701302\pi$
$587$	−28.6419			−1.18218			−0.591090	+	0.806606i	$0.701302\pi$
$588$		0			0
$589$	−44.2666	−	10.4785i	−1.82397	−	0.431760i
$590$		0			0
$591$	27.1092	−	29.8503i	1.11512	−	1.22788i
$592$		0			0
$593$	−17.9752	−	31.1339i	−0.738151	−	1.27852i	−0.953327	−	0.301940i	$-0.902366\pi$
$593$	−17.9752	−	31.1339i	−0.738151	−	1.27852i	0.215176	−	0.976575i	$-0.430967\pi$
$594$		0			0
$595$	−0.813948	−	1.40980i	−0.0333686	−	0.0577961i
$596$		0			0
$597$	17.4593	+	3.78912i	0.714562	+	0.155078i
$598$		0			0
$599$	1.43325			0.0585612			0.0292806	−	0.999571i	$-0.490678\pi$
$599$	1.43325			0.0585612			0.0292806	+	0.999571i	$0.490678\pi$
$600$		0			0
$601$	15.4452	+	26.7520i	0.630025	+	1.09123i	0.987546	+	0.157330i	$0.0502886\pi$
$601$	15.4452	+	26.7520i	0.630025	+	1.09123i	−0.357521	+	0.933905i	$0.616378\pi$
$602$		0			0
$603$	−4.68637	−	48.5770i	−0.190844	−	1.97821i
$604$		0			0
$605$	−1.87845			−0.0763697
$606$		0			0
$607$	−6.05564	+	10.4887i	−0.245791	+	0.425722i	−0.962354	−	0.271800i	$-0.912381\pi$
$607$	−6.05564	+	10.4887i	−0.245791	+	0.425722i	0.716563	+	0.697522i	$0.245714\pi$
$608$		0			0
$609$	−1.24787	+	1.37405i	−0.0505661	+	0.0556792i
$610$		0			0
$611$	−28.0403	+	48.5672i	−1.13439	+	1.96482i
$612$		0			0
$613$	4.25365	−	7.36754i	0.171803	−	0.297572i	−0.767247	−	0.641352i	$-0.778374\pi$
$613$	4.25365	−	7.36754i	0.171803	−	0.297572i	0.939050	+	0.343780i	$0.111707\pi$
$614$		0			0
$615$	1.33684	+	4.17499i	0.0539068	+	0.168352i
$616$		0			0
$617$	0.522849			0.0210491			0.0105246	−	0.999945i	$-0.496650\pi$
$617$	0.522849			0.0210491			0.0105246	+	0.999945i	$0.496650\pi$
$618$		0			0
$619$	−7.14110	−	12.3688i	−0.287025	−	0.497142i	0.686073	−	0.727533i	$-0.259333\pi$
$619$	−7.14110	−	12.3688i	−0.287025	−	0.497142i	−0.973098	+	0.230391i	$0.926000\pi$
$620$		0			0
$621$	15.3077	+	11.4243i	0.614278	+	0.458441i
$622$		0			0
$623$	1.97530	−	3.42132i	0.0791387	−	0.137072i
$624$		0			0
$625$	−11.8714	−	20.5619i	−0.474857	−	0.822476i
$626$		0			0
$627$	−1.24327	−	16.0202i	−0.0496515	−	0.639786i
$628$		0			0
$629$	12.4271	−	21.5244i	0.495503	−	0.858236i
$630$		0			0
$631$	−18.9476	−	32.8182i	−0.754292	−	1.30647i	−0.945725	−	0.324967i	$-0.894647\pi$
$631$	−18.9476	−	32.8182i	−0.754292	−	1.30647i	0.191433	−	0.981506i	$-0.438686\pi$
$632$		0			0
$633$	16.6844	+	3.62094i	0.663144	+	0.143919i
$634$		0			0
$635$	1.74412	−	3.02090i	0.0692132	−	0.119881i
$636$		0			0
$637$	12.0813	−	20.9255i	0.478679	−	0.829097i
$638$		0			0
$639$	9.69748	+	4.41726i	0.383626	+	0.174744i
$640$		0			0
$641$	−28.8687			−1.14025			−0.570123	−	0.821559i	$-0.693105\pi$
$641$	−28.8687			−1.14025			−0.570123	+	0.821559i	$0.693105\pi$
$642$		0			0
$643$	13.6186	+	23.5881i	0.537065	+	0.930224i	0.999060	+	0.0433415i	$0.0138004\pi$
$643$	13.6186	+	23.5881i	0.537065	+	0.930224i	−0.461995	+	0.886882i	$0.652866\pi$
$644$		0			0
$645$	1.62549	+	0.352774i	0.0640036	+	0.0138904i
$646$		0			0
$647$	27.5980			1.08499			0.542495	−	0.840059i	$-0.317480\pi$
$647$	27.5980			1.08499			0.542495	+	0.840059i	$0.317480\pi$
$648$		0			0
$649$	7.16215	−	12.4052i	0.281139	−	0.486947i
$650$		0			0
$651$	−15.4759	+	17.0408i	−0.606549	+	0.667881i
$652$		0			0
$653$	16.0989	−	27.8842i	0.629999	−	1.09119i	−0.357552	−	0.933893i	$-0.616388\pi$
$653$	16.0989	−	27.8842i	0.629999	−	1.09119i	0.987551	−	0.157298i	$-0.0502782\pi$
$654$		0			0
$655$	−3.25110	+	5.63108i	−0.127031	+	0.220024i
$656$		0			0
$657$	−8.92592	−	4.06581i	−0.348233	−	0.158623i
$658$		0			0
$659$	16.2854	−	28.2072i	0.634390	−	1.09880i	−0.352253	−	0.935905i	$-0.614584\pi$
$659$	16.2854	−	28.2072i	0.634390	−	1.09880i	0.986644	−	0.162892i	$-0.0520822\pi$
$660$		0			0
$661$	44.5122			1.73132			0.865661	−	0.500630i	$-0.166898\pi$
$661$	44.5122			1.73132			0.865661	+	0.500630i	$0.166898\pi$
$662$		0			0
$663$	−10.4485	−	32.6307i	−0.405785	−	1.26727i
$664$		0			0
$665$	−1.56822	−	0.371221i	−0.0608132	−	0.0143953i
$666$		0			0
$667$	−1.54664	+	2.67886i	−0.0598862	+	0.103726i
$668$		0			0
$669$	−8.34157	+	9.18504i	−0.322504	+	0.355114i
$670$		0			0
$671$	16.9165			0.653055
$672$		0			0
$673$	6.40866	+	11.1001i	0.247036	+	0.427879i	0.962702	−	0.270564i	$-0.0872101\pi$
$673$	6.40866	+	11.1001i	0.247036	+	0.427879i	−0.715666	+	0.698442i	$0.753877\pi$
$674$		0			0
$675$	23.4657	−	10.0893i	0.903197	−	0.388337i
$676$		0			0
$677$	−15.8594	−	27.4693i	−0.609527	−	1.05573i	−0.991318	−	0.131483i	$-0.958026\pi$
$677$	−15.8594	−	27.4693i	−0.609527	−	1.05573i	0.381792	−	0.924248i	$-0.375307\pi$
$678$		0			0
$679$	0.257540	+	0.446072i	0.00988347	+	0.0171187i
$680$		0			0
$681$	−27.7871	−	6.03053i	−1.06481	−	0.231090i
$682$		0			0
$683$	45.5013			1.74106			0.870529	−	0.492117i	$-0.163777\pi$
$683$	45.5013			1.74106			0.870529	+	0.492117i	$0.163777\pi$
$684$		0			0
$685$	5.86550			0.224109
$686$		0			0
$687$	−2.36829	−	7.39621i	−0.0903558	−	0.282183i
$688$		0			0
$689$	15.6128	+	27.0422i	0.594802	+	1.03023i
$690$		0			0
$691$	−12.1160	−	20.9856i	−0.460915	−	0.798329i	0.538092	−	0.842886i	$-0.319145\pi$
$691$	−12.1160	−	20.9856i	−0.460915	−	0.798329i	−0.999007	+	0.0445578i	$0.985812\pi$
$692$		0			0
$693$	−7.39964	−	3.37058i	−0.281089	−	0.128038i
$694$		0			0
$695$	0.839412	+	1.45390i	0.0318407	+	0.0551497i
$696$		0			0
$697$	−38.3858			−1.45397
$698$		0			0
$699$	0.645669	+	2.01644i	0.0244214	+	0.0762686i
$700$		0			0
$701$	16.3608	−	28.3378i	0.617941	−	1.07030i	−0.371920	−	0.928265i	$-0.621301\pi$
$701$	16.3608	−	28.3378i	0.617941	−	1.07030i	0.989861	−	0.142040i	$-0.0453662\pi$
$702$		0			0
$703$	−7.06324	−	23.5693i	−0.266395	−	0.888933i
$704$		0			0
$705$	−4.21994	+	4.64664i	−0.158932	+	0.175003i
$706$		0			0
$707$	−2.34489			−0.0881888
$708$		0			0
$709$	−8.15120	+	14.1183i	−0.306125	+	0.530224i	−0.977511	−	0.210884i	$-0.932366\pi$
$709$	−8.15120	+	14.1183i	−0.306125	+	0.530224i	0.671386	+	0.741108i	$0.265699\pi$
$710$		0			0
$711$	0.173033	+	1.79359i	0.00648923	+	0.0672648i
$712$		0			0
$713$	−19.1813	+	33.2230i	−0.718345	+	1.24421i
$714$		0			0
$715$	1.38799	−	2.40407i	0.0519078	−	0.0899069i
$716$		0			0
$717$	−8.00090	−	24.9870i	−0.298799	−	0.933156i
$718$		0			0
$719$	3.33657	−	5.77911i	0.124433	−	0.215524i	−0.797078	−	0.603876i	$-0.793622\pi$
$719$	3.33657	−	5.77911i	0.124433	−	0.215524i	0.921511	+	0.388352i	$0.126955\pi$
$720$		0			0
$721$	−10.5929			−0.394500
$722$		0			0
$723$	−8.55652	−	26.7222i	−0.318220	−	0.993808i
$724$		0			0
$725$	2.06827	+	3.58234i	0.0768135	+	0.133045i
$726$		0			0
$727$	−25.0392			−0.928652			−0.464326	−	0.885664i	$-0.653703\pi$
$727$	−25.0392			−0.928652			−0.464326	+	0.885664i	$0.653703\pi$
$728$		0			0
$729$	7.68257	+	25.8839i	0.284539	+	0.958664i
$730$		0			0
$731$	−7.28231	+	12.6133i	−0.269346	+	0.466521i
$732$		0			0
$733$	19.0459	−	32.9884i	0.703476	−	1.21846i	−0.263763	−	0.964588i	$-0.584964\pi$
$733$	19.0459	−	32.9884i	0.703476	−	1.21846i	0.967239	−	0.253869i	$-0.0817031\pi$
$734$		0			0
$735$	1.81818	−	2.00203i	0.0670647	−	0.0738460i
$736$		0			0
$737$	17.3112	+	29.9838i	0.637665	+	1.10447i
$738$		0			0
$739$	16.3836	−	28.3772i	0.602680	−	1.04387i	−0.389734	−	0.920928i	$-0.627433\pi$
$739$	16.3836	−	28.3772i	0.602680	−	1.04387i	0.992414	−	0.122945i	$-0.0392337\pi$
$740$		0			0
$741$	−30.5989	−	14.6358i	−1.12408	−	0.537660i
$742$		0			0
$743$	−20.4120	−	35.3546i	−0.748842	−	1.29703i	−0.948378	−	0.317142i	$-0.897277\pi$
$743$	−20.4120	−	35.3546i	−0.748842	−	1.29703i	0.199536	−	0.979891i	$-0.436057\pi$
$744$		0			0
$745$	−1.12743	+	1.95277i	−0.0413060	+	0.0715440i
$746$		0			0
$747$	36.4954	−	26.0420i	1.33530	−	0.952826i
$748$		0			0
$749$	6.13936	+	10.6337i	0.224327	+	0.388546i
$750$		0			0
$751$	−14.3875			−0.525007			−0.262503	−	0.964931i	$-0.584548\pi$
$751$	−14.3875			−0.525007			−0.262503	+	0.964931i	$0.584548\pi$
$752$		0			0
$753$	43.9193	+	9.53162i	1.60051	+	0.347352i
$754$		0			0
$755$	−0.946514	+	1.63941i	−0.0344472	+	0.0596643i
$756$		0			0
$757$	−17.4397	+	30.2064i	−0.633855	+	1.09787i	0.352901	+	0.935661i	$0.385195\pi$
$757$	−17.4397	+	30.2064i	−0.633855	+	1.09787i	−0.986756	+	0.162209i	$0.948138\pi$
$758$		0			0
$759$	−13.2426	−	2.87398i	−0.480674	−	0.104319i
$760$		0			0
$761$	−19.1522	+	33.1726i	−0.694268	+	1.20251i	0.276159	+	0.961112i	$0.410938\pi$
$761$	−19.1522	+	33.1726i	−0.694268	+	1.20251i	−0.970427	+	0.241395i	$0.922395\pi$
$762$		0			0
$763$	−6.65503			−0.240928
$764$		0			0
$765$	−0.368253	−	3.81717i	−0.0133142	−	0.138010i
$766$		0			0
$767$	−15.1187	−	26.1863i	−0.545903	−	0.945532i
$768$		0			0
$769$	34.5329			1.24529			0.622643	−	0.782506i	$-0.286059\pi$
$769$	34.5329			1.24529			0.622643	+	0.782506i	$0.286059\pi$
$770$		0			0
$771$	−33.6110	+	37.0096i	−1.21047	+	1.33287i
$772$		0			0
$773$	3.97749	+	6.88921i	0.143060	+	0.247788i	0.928648	−	0.370963i	$-0.120972\pi$
$773$	3.97749	+	6.88921i	0.143060	+	0.247788i	−0.785587	+	0.618751i	$0.787639\pi$
$774$		0			0
$775$	25.6504	+	44.4279i	0.921391	+	1.59590i
$776$		0			0
$777$	−12.1677	−	2.64069i	−0.436512	−	0.0947344i
$778$		0			0
$779$	−26.0701	+	27.6479i	−0.934057	+	0.990588i
$780$		0			0
$781$	−7.55986			−0.270513
$782$		0			0
$783$	−4.01696	+	1.72712i	−0.143554	+	0.0617223i
$784$		0			0
$785$	−0.734384	+	1.27199i	−0.0262113	+	0.0453993i
$786$		0			0
$787$	7.74601	−	13.4165i	0.276116	−	0.478246i	−0.694300	−	0.719685i	$-0.744286\pi$
$787$	7.74601	−	13.4165i	0.276116	−	0.478246i	0.970416	+	0.241439i	$0.0776194\pi$
$788$		0			0
$789$	−1.09648	+	1.20735i	−0.0390356	+	0.0429827i
$790$		0			0
$791$	−20.2595			−0.720343
$792$		0			0
$793$	17.8546	−	30.9251i	0.634036	−	1.09818i
$794$		0			0
$795$	1.06579	+	3.32849i	0.0377998	+	0.118049i
$796$		0			0
$797$	−20.7284	+	35.9026i	−0.734237	+	1.27174i	0.220820	+	0.975315i	$0.429127\pi$
$797$	−20.7284	+	35.9026i	−0.734237	+	1.27174i	−0.955057	+	0.296422i	$0.904207\pi$
$798$		0			0
$799$	−27.4811	−	47.5986i	−0.972210	−	1.68392i
$800$		0			0
$801$	7.57562	−	5.40572i	0.267672	−	0.191002i
$802$		0			0
$803$	6.95838			0.245556
$804$		0			0
$805$	−0.679533	+	1.17699i	−0.0239504	+	0.0414833i
$806$		0			0
$807$	−6.20889	−	19.3905i	−0.218563	−	0.682577i
$808$		0			0
$809$	21.2966			0.748747			0.374374	−	0.927278i	$-0.377858\pi$
$809$	21.2966			0.748747			0.374374	+	0.927278i	$0.377858\pi$
$810$		0			0
$811$	−2.91941	−	5.05656i	−0.102514	−	0.177560i	0.810206	−	0.586146i	$-0.199355\pi$
$811$	−2.91941	−	5.05656i	−0.102514	−	0.177560i	−0.912720	+	0.408586i	$0.866022\pi$
$812$		0			0
$813$	−14.2144	−	44.3917i	−0.498519	−	1.55688i
$814$		0			0
$815$	0.220332	+	0.381627i	0.00771790	+	0.0133678i
$816$		0			0
$817$	4.13906	+	13.8116i	0.144807	+	0.483207i
$818$		0			0
$819$	−13.9718	+	9.96981i	−0.488213	+	0.348373i
$820$		0			0
$821$	−15.8447	+	27.4439i	−0.552985	+	0.957798i	0.445073	+	0.895494i	$0.353178\pi$
$821$	−15.8447	+	27.4439i	−0.552985	+	0.957798i	−0.998057	+	0.0623031i	$0.980155\pi$
$822$		0			0
$823$	8.68183			0.302629			0.151315	−	0.988486i	$-0.451649\pi$
$823$	8.68183			0.302629			0.151315	+	0.988486i	$0.451649\pi$
$824$		0			0
$825$	−12.1827	+	13.4146i	−0.424149	+	0.467037i
$826$		0			0
$827$	9.32786	+	16.1563i	0.324361	+	0.561811i	0.981383	−	0.192061i	$-0.0615173\pi$
$827$	9.32786	+	16.1563i	0.324361	+	0.561811i	−0.657021	+	0.753872i	$0.728184\pi$
$828$		0			0
$829$	11.3604			0.394564			0.197282	−	0.980347i	$-0.436789\pi$
$829$	11.3604			0.394564			0.197282	+	0.980347i	$0.436789\pi$
$830$		0			0
$831$	11.5412	+	2.50473i	0.400359	+	0.0868882i
$832$		0			0
$833$	11.8404	+	20.5081i	0.410244	+	0.710564i
$834$		0			0
$835$	−0.444843	−	0.770491i	−0.0153944	−	0.0266639i
$836$		0			0
$837$	−49.8179	+	21.4196i	−1.72196	+	0.740370i
$838$		0			0
$839$	31.7973			1.09776			0.548882	−	0.835900i	$-0.315054\pi$
$839$	31.7973			1.09776			0.548882	+	0.835900i	$0.315054\pi$
$840$		0			0
$841$	14.1459	+	24.5015i	0.487791	+	0.844879i
$842$		0			0
$843$	−4.69994	−	14.6780i	−0.161874	−	0.505537i
$844$		0			0
$845$	−1.04285	−	1.80626i	−0.0358750	−	0.0621374i
$846$		0			0
$847$	−8.23985			−0.283124
$848$		0			0
$849$	14.2918	+	3.10170i	0.490494	+	0.106450i
$850$		0			0
$851$	−20.7499			−0.711296
$852$		0			0
$853$	45.5465			1.55948			0.779742	−	0.626102i	$-0.215350\pi$
$853$	45.5465			1.55948			0.779742	+	0.626102i	$0.215350\pi$
$854$		0			0
$855$	−2.99946	−	2.32722i	−0.102579	−	0.0795893i
$856$		0			0
$857$	12.1517			0.415096			0.207548	−	0.978225i	$-0.433452\pi$
$857$	12.1517			0.415096			0.207548	+	0.978225i	$0.433452\pi$
$858$		0			0
$859$	−9.38809			−0.320317			−0.160159	−	0.987091i	$-0.551201\pi$
$859$	−9.38809			−0.320317			−0.160159	+	0.987091i	$0.551201\pi$
$860$		0			0
$861$	5.86409	+	18.3137i	0.199848	+	0.624128i
$862$		0			0
$863$	0.676256			0.0230200			0.0115100	−	0.999934i	$-0.496336\pi$
$863$	0.676256			0.0230200			0.0115100	+	0.999934i	$0.496336\pi$
$864$		0			0
$865$	−0.868132	−	1.50365i	−0.0295174	−	0.0511256i
$866$		0			0
$867$	4.04049	+	0.876891i	0.137222	+	0.0297808i
$868$		0			0
$869$	−0.639172	−	1.10708i	−0.0216824	−	0.0375551i
$870$		0			0
$871$	73.0847			2.47638
$872$		0			0
$873$	0.116518	+	1.20778i	0.00394355	+	0.0408772i
$874$		0			0
$875$	1.83301	+	3.17486i	0.0619670	+	0.107330i
$876$		0			0
$877$	21.7012	+	37.5876i	0.732797	+	1.26924i	0.955683	+	0.294397i	$0.0951188\pi$
$877$	21.7012	+	37.5876i	0.732797	+	1.26924i	−0.222886	+	0.974844i	$0.571548\pi$
$878$		0			0
$879$	8.95429	+	27.9644i	0.302021	+	0.943216i
$880$		0			0
$881$	45.7419			1.54108			0.770541	−	0.637390i	$-0.219986\pi$
$881$	45.7419			1.54108			0.770541	+	0.637390i	$0.219986\pi$
$882$		0			0
$883$	9.03829	+	15.6548i	0.304163	+	0.526825i	0.977075	−	0.212898i	$-0.0682900\pi$
$883$	9.03829	+	15.6548i	0.304163	+	0.526825i	−0.672912	+	0.739723i	$0.734957\pi$
$884$		0			0
$885$	−1.03206	−	3.22314i	−0.0346922	−	0.108345i
$886$		0			0
$887$	1.15706			0.0388502			0.0194251	−	0.999811i	$-0.493816\pi$
$887$	1.15706			0.0388502			0.0194251	+	0.999811i	$0.493816\pi$
$888$		0			0
$889$	7.65061	−	13.2512i	0.256593	−	0.444432i
$890$		0			0
$891$	−12.5719	−	14.4517i	−0.421176	−	0.484151i
$892$		0			0
$893$	−52.9475	−	12.5334i	−1.77182	−	0.419415i
$894$		0			0
$895$	−3.04815	−	5.27955i	−0.101888	−	0.176476i
$896$		0			0
$897$	−19.2309	+	21.1754i	−0.642100	+	0.707026i
$898$		0			0
$899$	−4.39094	−	7.60534i	−0.146446	−	0.253652i
$900$		0			0
$901$	−30.6029			−1.01953
$902$		0			0
$903$	7.13025	+	1.54745i	0.237280	+	0.0514959i
$904$		0			0
$905$	−1.52509	+	2.64154i	−0.0506958	+	0.0878077i
$906$		0			0
$907$	2.60402			0.0864651			0.0432325	−	0.999065i	$-0.486234\pi$
$907$	2.60402			0.0864651			0.0432325	+	0.999065i	$0.486234\pi$
$908$		0			0
$909$	−5.02699	−	2.28982i	−0.166735	−	0.0759487i
$910$		0			0
$911$	−10.8197	−	18.7403i	−0.358474	−	0.620895i	0.629232	−	0.777217i	$-0.283369\pi$
$911$	−10.8197	−	18.7403i	−0.358474	−	0.620895i	−0.987706	+	0.156323i	$0.950036\pi$
$912$		0			0
$913$	−15.9035	+	27.5457i	−0.526329	+	0.911629i
$914$		0			0
$915$	2.68704	−	2.95874i	0.0888308	−	0.0978130i
$916$		0			0
$917$	−14.2610	+	24.7008i	−0.470941	+	0.815693i
$918$		0			0
$919$	−23.9210			−0.789080			−0.394540	−	0.918879i	$-0.629096\pi$
$919$	−23.9210			−0.789080			−0.394540	+	0.918879i	$0.629096\pi$
$920$		0			0
$921$	−2.61361	−	8.16234i	−0.0861213	−	0.268958i
$922$		0			0
$923$	−7.97910	+	13.8202i	−0.262635	+	0.454897i
$924$		0			0
$925$	−13.8740	+	24.0305i	−0.456174	+	0.790117i
$926$		0			0
$927$	−22.7091	−	10.3441i	−0.745865	−	0.339746i
$928$		0			0
$929$	−23.0274			−0.755505			−0.377752	−	0.925907i	$-0.623303\pi$
$929$	−23.0274			−0.755505			−0.377752	+	0.925907i	$0.623303\pi$
$930$		0			0
$931$	22.8127	+	5.40009i	0.747656	+	0.176981i
$932$		0			0
$933$	9.99374	+	31.2106i	0.327180	+	1.02179i
$934$		0			0
$935$	1.36031	+	2.35612i	0.0444868	+	0.0770533i
$936$		0			0
$937$	13.1743	+	22.8186i	0.430387	+	0.745452i	0.996907	−	0.0785962i	$-0.0250438\pi$
$937$	13.1743	+	22.8186i	0.430387	+	0.745452i	−0.566520	+	0.824048i	$0.691710\pi$
$938$		0			0
$939$	1.31124	+	4.09503i	0.0427908	+	0.133636i
$940$		0			0
$941$	36.6588			1.19504			0.597521	−	0.801854i	$-0.296153\pi$
$941$	36.6588			1.19504			0.597521	+	0.801854i	$0.296153\pi$
$942$		0			0
$943$	16.0234	+	27.7533i	0.521794	+	0.903773i
$944$		0			0
$945$	−1.76489	+	0.758829i	−0.0574119	+	0.0246847i
$946$		0			0
$947$	27.0490			0.878974			0.439487	−	0.898249i	$-0.355160\pi$
$947$	27.0490			0.878974			0.439487	+	0.898249i	$0.355160\pi$
$948$		0			0
$949$	7.34426	−	12.7206i	0.238405	−	0.412929i
$950$		0			0
$951$	11.4409	+	35.7302i	0.370997	+	1.15863i
$952$		0			0
$953$	−7.43257	+	12.8736i	−0.240765	+	0.417016i	−0.960932	−	0.276784i	$-0.910731\pi$
$953$	−7.43257	+	12.8736i	−0.240765	+	0.417016i	0.720168	+	0.693800i	$0.244065\pi$
$954$		0			0
$955$	−2.07259	+	3.58984i	−0.0670675	+	0.116164i
$956$		0			0
$957$	2.08549	−	2.29637i	0.0674143	−	0.0742310i
$958$		0			0
$959$	25.7291			0.830837
$960$		0			0
$961$	−38.9560	−	67.4738i	−1.25665	−	2.17658i
$962$		0			0
$963$	2.77762	+	28.7917i	0.0895076	+	0.927800i
$964$		0			0
$965$	0.749082	−	1.29745i	0.0241138	−	0.0417664i
$966$		0			0
$967$	23.7327	+	41.1062i	0.763191	+	1.32189i	0.941198	+	0.337857i	$0.109702\pi$
$967$	23.7327	+	41.1062i	0.763191	+	1.32189i	−0.178006	+	0.984029i	$0.556965\pi$
$968$		0			0
$969$	27.4165	−	18.7989i	0.880745	−	0.603908i
$970$		0			0
$971$	−18.0232	+	31.2170i	−0.578391	+	1.00180i	0.417273	+	0.908781i	$0.362986\pi$
$971$	−18.0232	+	31.2170i	−0.578391	+	1.00180i	−0.995664	+	0.0930215i	$0.970347\pi$
$972$		0			0
$973$	3.68210	+	6.37758i	0.118043	+	0.204456i
$974$		0			0
$975$	11.6649	+	36.4299i	0.373577	+	1.16669i
$976$		0			0
$977$	9.29364	−	16.0971i	0.297330	−	0.514990i	−0.678194	−	0.734883i	$-0.737237\pi$
$977$	9.29364	−	16.0971i	0.297330	−	0.514990i	0.975524	+	0.219892i	$0.0705706\pi$
$978$		0			0
$979$	−3.30121	+	5.71786i	−0.105507	+	0.182744i
$980$		0			0
$981$	−14.2671	−	6.49874i	−0.455512	−	0.207489i
$982$		0			0
$983$	−22.7514			−0.725658			−0.362829	−	0.931856i	$-0.618189\pi$
$983$	−22.7514			−0.725658			−0.362829	+	0.931856i	$0.618189\pi$
$984$		0			0
$985$	3.37939	+	5.85327i	0.107676	+	0.186501i
$986$		0			0
$987$	−18.5108	+	20.3826i	−0.589206	+	0.648784i
$988$		0			0
$989$	12.1594			0.386647
$990$		0			0
$991$	−1.75547	+	3.04057i	−0.0557644	+	0.0965868i	−0.892560	−	0.450929i	$-0.851093\pi$
$991$	−1.75547	+	3.04057i	−0.0557644	+	0.0965868i	0.836796	+	0.547515i	$0.184426\pi$
$992$		0			0
$993$	27.9341	+	6.06243i	0.886462	+	0.192385i
$994$		0			0
$995$	−1.49729	+	2.59338i	−0.0474672	+	0.0822157i
$996$		0			0
$997$	14.5615	−	25.2212i	0.461167	−	0.798764i	−0.537853	−	0.843039i	$-0.680764\pi$
$997$	14.5615	−	25.2212i	0.461167	−	0.798764i	0.999019	+	0.0442748i	$0.0140977\pi$
$998$		0			0
$999$	−23.5064	−	17.5430i	−0.743709	−	0.555037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.j.a.49.5	✓	40
3.2	odd	2		2052.2.j.a.1873.10		40
9.2	odd	6		2052.2.l.a.505.11		40
9.7	even	3		684.2.l.a.277.9	yes	40
19.7	even	3		684.2.l.a.121.9	yes	40
57.26	odd	6		2052.2.l.a.577.11		40
171.7	even	3	inner	684.2.j.a.349.5	yes	40
171.83	odd	6		2052.2.j.a.1261.10		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.j.a.49.5	✓	40	1.1	even	1	trivial
684.2.j.a.349.5	yes	40	171.7	even	3	inner
684.2.l.a.121.9	yes	40	19.7	even	3
684.2.l.a.277.9	yes	40	9.7	even	3
2052.2.j.a.1261.10		40	171.83	odd	6
2052.2.j.a.1873.10		40	3.2	odd	2
2052.2.l.a.505.11		40	9.2	odd	6
2052.2.l.a.577.11		40	57.26	odd	6

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16446 + 1.28220i) q^{3} +(-0.145159 - 0.251423i) q^{5} +(-0.636745 - 1.10287i) q^{7} +(-0.288081 - 2.98614i) q^{9} +(1.06416 + 1.84317i) q^{11} +4.49268 q^{13} +(0.491407 + 0.106648i) q^{15} +(-2.20154 + 3.81318i) q^{17} +(1.25129 + 4.17544i) q^{19} +(2.15557 + 0.467814i) q^{21} +3.67595 q^{23} +(2.45786 - 4.25713i) q^{25} +(4.16429 + 3.10785i) q^{27} +(-0.420746 + 0.728753i) q^{29} +(-5.21805 + 9.03792i) q^{31} +(-3.60248 - 0.781831i) q^{33} +(-0.184859 + 0.320185i) q^{35} -5.64475 q^{37} +(-5.23153 + 5.76052i) q^{39} +(4.35898 + 7.54997i) q^{41} +3.30783 q^{43} +(-0.708967 + 0.505896i) q^{45} +(-6.24133 + 10.8103i) q^{47} +(2.68911 - 4.65768i) q^{49} +(-2.32566 - 7.26309i) q^{51} +(3.47517 + 6.01918i) q^{53} +(0.308944 - 0.535107i) q^{55} +(-6.81083 - 3.25770i) q^{57} +(-3.36518 - 5.82866i) q^{59} +(3.97416 - 6.88345i) q^{61} +(-3.10990 + 2.21912i) q^{63} +(-0.652154 - 1.12956i) q^{65} +16.2675 q^{67} +(-4.28049 + 4.71331i) q^{69} +(-1.77602 + 3.07616i) q^{71} +(1.63472 - 2.83142i) q^{73} +(2.59644 + 8.10872i) q^{75} +(1.35519 - 2.34726i) q^{77} -0.600638 q^{79} +(-8.83402 + 1.72050i) q^{81} +(7.47236 + 12.9425i) q^{83} +1.27830 q^{85} +(-0.444468 - 1.38808i) q^{87} +(1.55109 + 2.68657i) q^{89} +(-2.86069 - 4.95486i) q^{91} +(-5.51225 - 17.2149i) q^{93} +(0.868166 - 0.920708i) q^{95} -0.404463 q^{97} +(5.19740 - 3.70870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{3} - q^{7} - 2 q^{9} - q^{11} + 2 q^{13} + q^{15} + 5 q^{17} + q^{19} + 6 q^{21} + 8 q^{23} - 20 q^{25} + 7 q^{27} - 9 q^{29} + 2 q^{31} - q^{33} - 6 q^{35} + 2 q^{37} + 3 q^{39} - 25 q^{41}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q - 2 * q^3 - q^7 - 2 * q^9 - q^11 + 2 * q^13 + q^15 + 5 * q^17 + q^19 + 6 * q^21 + 8 * q^23 - 20 * q^25 + 7 * q^27 - 9 * q^29 + 2 * q^31 - q^33 - 6 * q^35 + 2 * q^37 + 3 * q^39 - 25 * q^41 - 16 * q^43 + 44 * q^45 - 10 * q^47 - 21 * q^49 + 19 * q^51 - 8 * q^53 - 22 * q^59 - 7 * q^61 + 10 * q^63 - 6 * q^65 + 20 * q^67 + 38 * q^69 - 5 * q^71 - 10 * q^73 - 10 * q^77 + 2 * q^79 + 22 * q^81 + q^83 - 52 * q^87 - 34 * q^89 + 16 * q^91 - 8 * q^93 + 36 * q^95 + 2 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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