LMFDB - Embedded newform 360.2.bi.b.49.9

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			49.9
Character	$\chi$	$=$	360.49
Dual form			360.2.bi.b.169.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.284761 + 1.70848i) q^{3} +(1.07259 - 1.96203i) q^{5} +(-3.55262 + 2.05111i) q^{7} +(-2.83782 + 0.973019i) q^{9} +O(q^{10})$	\(q+(0.284761 + 1.70848i) q^{3} +(1.07259 - 1.96203i) q^{5} +(-3.55262 + 2.05111i) q^{7} +(-2.83782 + 0.973019i) q^{9} +(3.04732 + 5.27812i) q^{11} +(4.45043 + 2.56946i) q^{13} +(3.65752 + 1.27379i) q^{15} +2.73647i q^{17} -1.80595 q^{19} +(-4.51593 - 5.48551i) q^{21} +(-0.582439 - 0.336271i) q^{23} +(-2.69910 - 4.20890i) q^{25} +(-2.47049 - 4.57129i) q^{27} +(1.75334 + 3.03688i) q^{29} +(3.30067 - 5.71692i) q^{31} +(-8.14981 + 6.70930i) q^{33} +(0.213823 + 9.17033i) q^{35} -4.44214i q^{37} +(-3.12256 + 8.33516i) q^{39} +(-2.08923 + 3.61865i) q^{41} +(4.01162 - 2.31611i) q^{43} +(-1.13473 + 6.61153i) q^{45} +(1.38258 - 0.798234i) q^{47} +(4.91407 - 8.51143i) q^{49} +(-4.67521 + 0.779242i) q^{51} -8.02220i q^{53} +(13.6243 - 0.317676i) q^{55} +(-0.514264 - 3.08543i) q^{57} +(-2.65011 + 4.59012i) q^{59} +(-3.38942 - 5.87064i) q^{61} +(8.08594 - 9.27744i) q^{63} +(9.81483 - 5.97589i) q^{65} +(-9.82638 - 5.67327i) q^{67} +(0.408657 - 1.09084i) q^{69} +13.3686 q^{71} +6.50669i q^{73} +(6.42223 - 5.80990i) q^{75} +(-21.6520 - 12.5008i) q^{77} +(1.49502 + 2.58946i) q^{79} +(7.10647 - 5.52251i) q^{81} +(3.71043 - 2.14222i) q^{83} +(5.36903 + 2.93511i) q^{85} +(-4.68917 + 3.86034i) q^{87} +7.19878 q^{89} -21.0809 q^{91} +(10.7072 + 4.01117i) q^{93} +(-1.93704 + 3.54332i) q^{95} +(3.33696 - 1.92659i) q^{97} +(-13.7835 - 12.0133i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.284761	+	1.70848i	0.164407	+	0.986393i
$3$	0.284761	+	1.70848i	0.164407	+	0.986393i
$4$		0			0
$5$	1.07259	−	1.96203i	0.479677	−	0.877445i
$5$	1.07259	−	1.96203i	0.479677	−	0.877445i
$6$		0			0
$7$	−3.55262	+	2.05111i	−1.34276	+	0.775245i	−0.987212	−	0.159411i	$-0.949040\pi$
$7$	−3.55262	+	2.05111i	−1.34276	+	0.775245i	−0.355552	+	0.934657i	$0.615707\pi$
$8$		0			0
$9$	−2.83782	+	0.973019i	−0.945941	+	0.324340i
$10$		0			0
$11$	3.04732	+	5.27812i	0.918802	+	1.59141i	0.801237	+	0.598347i	$0.204175\pi$
$11$	3.04732	+	5.27812i	0.918802	+	1.59141i	0.117565	+	0.993065i	$0.462491\pi$
$12$		0			0
$13$	4.45043	+	2.56946i	1.23433	+	0.712639i	0.967929	−	0.251224i	$-0.0808330\pi$
$13$	4.45043	+	2.56946i	1.23433	+	0.712639i	0.266398	+	0.963863i	$0.414166\pi$
$14$		0			0
$15$	3.65752	+	1.27379i	0.944368	+	0.328891i
$16$		0			0
$17$			2.73647i			0.663692i	0.943334	+	0.331846i	$0.107671\pi$
$17$			2.73647i			0.663692i	−0.943334	+	0.331846i	$0.892329\pi$
$18$		0			0
$19$	−1.80595			−0.414313			−0.207156	−	0.978308i	$-0.566421\pi$
$19$	−1.80595			−0.414313			−0.207156	+	0.978308i	$0.566421\pi$
$20$		0			0
$21$	−4.51593	−	5.48551i	−0.985456	−	1.19704i
$22$		0			0
$23$	−0.582439	−	0.336271i	−0.121447	−	0.0701174i	0.438046	−	0.898953i	$-0.355671\pi$
$23$	−0.582439	−	0.336271i	−0.121447	−	0.0701174i	−0.559493	+	0.828835i	$0.689004\pi$
$24$		0			0
$25$	−2.69910	−	4.20890i	−0.539821	−	0.841780i
$26$		0			0
$27$	−2.47049	−	4.57129i	−0.475446	−	0.879745i
$28$		0			0
$29$	1.75334	+	3.03688i	0.325588	+	0.563935i	0.981631	−	0.190789i	$-0.0611045\pi$
$29$	1.75334	+	3.03688i	0.325588	+	0.563935i	−0.656043	+	0.754723i	$0.727771\pi$
$30$		0			0
$31$	3.30067	−	5.71692i	0.592817	−	1.02679i	−0.401034	−	0.916063i	$-0.631349\pi$
$31$	3.30067	−	5.71692i	0.592817	−	1.02679i	0.993851	−	0.110726i	$-0.0353176\pi$
$32$		0			0
$33$	−8.14981	+	6.70930i	−1.41870	+	1.16794i
$34$		0			0
$35$	0.213823	+	9.17033i	0.0361426	+	1.55007i
$36$		0			0
$37$		−	4.44214i		−	0.730283i	−0.930952	−	0.365141i	$-0.881021\pi$
$37$		−	4.44214i		−	0.730283i	0.930952	−	0.365141i	$-0.118979\pi$
$38$		0			0
$39$	−3.12256	+	8.33516i	−0.500010	+	1.33469i
$40$		0			0
$41$	−2.08923	+	3.61865i	−0.326283	+	0.565138i	−0.981771	−	0.190067i	$-0.939130\pi$
$41$	−2.08923	+	3.61865i	−0.326283	+	0.565138i	0.655488	+	0.755205i	$0.272463\pi$
$42$		0			0
$43$	4.01162	−	2.31611i	0.611767	−	0.353204i	−0.161890	−	0.986809i	$-0.551759\pi$
$43$	4.01162	−	2.31611i	0.611767	−	0.353204i	0.773657	+	0.633605i	$0.218426\pi$
$44$		0			0
$45$	−1.13473	+	6.61153i	−0.169155	+	0.985589i
$46$		0			0
$47$	1.38258	−	0.798234i	0.201670	−	0.116434i	−0.395764	−	0.918352i	$-0.629520\pi$
$47$	1.38258	−	0.798234i	0.201670	−	0.116434i	0.597434	+	0.801918i	$0.296187\pi$
$48$		0			0
$49$	4.91407	−	8.51143i	0.702011	−	1.21592i
$50$		0			0
$51$	−4.67521	+	0.779242i	−0.654661	+	0.109116i
$52$		0			0
$53$		−	8.02220i		−	1.10193i	−0.834527	−	0.550967i	$-0.814259\pi$
$53$		−	8.02220i		−	1.10193i	0.834527	−	0.550967i	$-0.185741\pi$
$54$		0			0
$55$	13.6243	−	0.317676i	1.83710	−	0.0428354i
$56$		0			0
$57$	−0.514264	−	3.08543i	−0.0681159	−	0.408675i
$58$		0			0
$59$	−2.65011	+	4.59012i	−0.345015	+	0.597583i	−0.985356	−	0.170507i	$-0.945459\pi$
$59$	−2.65011	+	4.59012i	−0.345015	+	0.597583i	0.640342	+	0.768090i	$0.278793\pi$
$60$		0			0
$61$	−3.38942	−	5.87064i	−0.433970	−	0.751659i	0.563241	−	0.826293i	$-0.309554\pi$
$61$	−3.38942	−	5.87064i	−0.433970	−	0.751659i	−0.997211	+	0.0746344i	$0.976221\pi$
$62$		0			0
$63$	8.08594	−	9.27744i	1.01873	−	1.16885i
$64$		0			0
$65$	9.81483	−	5.97589i	1.21738	−	0.741218i
$66$		0			0
$67$	−9.82638	−	5.67327i	−1.20048	−	0.693100i	−0.239821	−	0.970817i	$-0.577089\pi$
$67$	−9.82638	−	5.67327i	−1.20048	−	0.693100i	−0.960663	+	0.277717i	$0.910422\pi$
$68$		0			0
$69$	0.408657	−	1.09084i	0.0491966	−	0.131322i
$70$		0			0
$71$	13.3686			1.58656			0.793280	−	0.608857i	$-0.208372\pi$
$71$	13.3686			1.58656			0.793280	+	0.608857i	$0.208372\pi$
$72$		0			0
$73$			6.50669i			0.761550i	0.924668	+	0.380775i	$0.124343\pi$
$73$			6.50669i			0.761550i	−0.924668	+	0.380775i	$0.875657\pi$
$74$		0			0
$75$	6.42223	−	5.80990i	0.741575	−	0.670870i
$76$		0			0
$77$	−21.6520	−	12.5008i	−2.46747	−	1.42459i
$78$		0			0
$79$	1.49502	+	2.58946i	0.168203	+	0.291337i	0.937788	−	0.347208i	$-0.112870\pi$
$79$	1.49502	+	2.58946i	0.168203	+	0.291337i	−0.769585	+	0.638545i	$0.779537\pi$
$80$		0			0
$81$	7.10647	−	5.52251i	0.789607	−	0.613612i
$82$		0			0
$83$	3.71043	−	2.14222i	0.407273	−	0.235139i	−0.282344	−	0.959313i	$-0.591112\pi$
$83$	3.71043	−	2.14222i	0.407273	−	0.235139i	0.689617	+	0.724174i	$0.257779\pi$
$84$		0			0
$85$	5.36903	+	2.93511i	0.582354	+	0.318358i
$86$		0			0
$87$	−4.68917	+	3.86034i	−0.502732	+	0.413872i
$88$		0			0
$89$	7.19878			0.763070			0.381535	−	0.924354i	$-0.375396\pi$
$89$	7.19878			0.763070			0.381535	+	0.924354i	$0.375396\pi$
$90$		0			0
$91$	−21.0809			−2.20988
$92$		0			0
$93$	10.7072	+	4.01117i	1.11028	+	0.415939i
$94$		0			0
$95$	−1.93704	+	3.54332i	−0.198736	+	0.363537i
$96$		0			0
$97$	3.33696	−	1.92659i	0.338817	−	0.195616i	−0.320932	−	0.947102i	$-0.603996\pi$
$97$	3.33696	−	1.92659i	0.338817	−	0.195616i	0.659749	+	0.751486i	$0.270663\pi$
$98$		0			0
$99$	−13.7835	−	12.0133i	−1.38529	−	1.20738i
$100$		0			0
$101$	4.87483	+	8.44346i	0.485064	+	0.840155i	0.999853	−	0.0171617i	$-0.00546301\pi$
$101$	4.87483	+	8.44346i	0.485064	+	0.840155i	−0.514789	+	0.857317i	$0.672130\pi$
$102$		0			0
$103$	−9.64658	−	5.56946i	−0.950506	−	0.548775i	−0.0572679	−	0.998359i	$-0.518239\pi$
$103$	−9.64658	−	5.56946i	−0.950506	−	0.548775i	−0.893238	+	0.449584i	$0.851572\pi$
$104$		0			0
$105$	−15.6065	+	2.97667i	−1.52303	+	0.290493i
$106$		0			0
$107$			1.19494i			0.115519i	0.998331	+	0.0577595i	$0.0183956\pi$
$107$			1.19494i			0.115519i	−0.998331	+	0.0577595i	$0.981604\pi$
$108$		0			0
$109$	9.05323			0.867143			0.433571	−	0.901119i	$-0.357253\pi$
$109$	9.05323			0.867143			0.433571	+	0.901119i	$0.357253\pi$
$110$		0			0
$111$	7.58931	−	1.26495i	0.720346	−	0.120064i
$112$		0			0
$113$	6.85715	+	3.95898i	0.645066	+	0.372429i	0.786563	−	0.617510i	$-0.211858\pi$
$113$	6.85715	+	3.95898i	0.645066	+	0.372429i	−0.141497	+	0.989939i	$0.545192\pi$
$114$		0			0
$115$	−1.28449	+	0.782080i	−0.119779	+	0.0729293i
$116$		0			0
$117$	−15.1297	−	2.96131i	−1.39874	−	0.273773i
$118$		0			0
$119$	−5.61280	−	9.72165i	−0.514524	−	0.891182i
$120$		0			0
$121$	−13.0723	+	22.6420i	−1.18839	+	2.05836i
$122$		0			0
$123$	−6.77733	−	2.53896i	−0.611092	−	0.228930i
$124$		0			0
$125$	−11.1530	+	0.781290i	−0.997555	+	0.0698807i
$126$		0			0
$127$		−	9.00959i		−	0.799471i	−0.916630	−	0.399736i	$-0.869102\pi$
$127$		−	9.00959i		−	0.799471i	0.916630	−	0.399736i	$-0.130898\pi$
$128$		0			0
$129$	5.09939	+	6.19425i	0.448976	+	0.545373i
$130$		0			0
$131$	1.26972	−	2.19922i	0.110936	−	0.192147i	−0.805212	−	0.592987i	$-0.797948\pi$
$131$	1.26972	−	2.19922i	0.110936	−	0.192147i	0.916148	+	0.400840i	$0.131282\pi$
$132$		0			0
$133$	6.41585	−	3.70419i	0.556324	−	0.321194i
$134$		0			0
$135$	−11.6188	−	0.0559540i	−0.999988	−	0.00481575i
$136$		0			0
$137$	7.67867	−	4.43328i	0.656033	−	0.378761i	−0.134731	−	0.990882i	$-0.543017\pi$
$137$	7.67867	−	4.43328i	0.656033	−	0.378761i	0.790764	+	0.612121i	$0.209684\pi$
$138$		0			0
$139$	7.49731	−	12.9857i	0.635913	−	1.10143i	−0.350408	−	0.936597i	$-0.613957\pi$
$139$	7.49731	−	12.9857i	0.635913	−	1.10143i	0.986321	−	0.164837i	$-0.0527098\pi$
$140$		0			0
$141$	1.75747	+	2.13481i	0.148006	+	0.179783i
$142$		0			0
$143$			31.3198i			2.61910i
$144$		0			0
$145$	7.83906	−	0.182782i	0.650999	−	0.0151792i
$146$		0			0
$147$	15.9410	+	5.97188i	1.31479	+	0.492553i
$148$		0			0
$149$	6.89813	−	11.9479i	0.565117	−	0.978811i	−0.431922	−	0.901911i	$-0.642164\pi$
$149$	6.89813	−	11.9479i	0.565117	−	0.978811i	0.997039	−	0.0769000i	$-0.0245022\pi$
$150$		0			0
$151$	1.30312	+	2.25708i	0.106047	+	0.183678i	0.914165	−	0.405341i	$-0.132847\pi$
$151$	1.30312	+	2.25708i	0.106047	+	0.183678i	−0.808119	+	0.589020i	$0.799514\pi$
$152$		0			0
$153$	−2.66264	−	7.76562i	−0.215262	−	0.627813i
$154$		0			0
$155$	−7.67650	−	12.6079i	−0.616591	−	1.01269i
$156$		0			0
$157$	12.9478	+	7.47543i	1.03335	+	0.596604i	0.917942	−	0.396714i	$-0.129850\pi$
$157$	12.9478	+	7.47543i	1.03335	+	0.596604i	0.115407	+	0.993318i	$0.463183\pi$
$158$		0			0
$159$	13.7058	−	2.28441i	1.08694	−	0.181166i
$160$		0			0
$161$	2.75891			0.217433
$162$		0			0
$163$			9.49019i			0.743329i	0.928367	+	0.371664i	$0.121213\pi$
$163$			9.49019i			0.743329i	−0.928367	+	0.371664i	$0.878787\pi$
$164$		0			0
$165$	4.42243	+	23.1865i	0.344285	+	1.80506i
$166$		0			0
$167$	0.325986	+	0.188208i	0.0252256	+	0.0145640i	0.512560	−	0.858652i	$-0.328697\pi$
$167$	0.325986	+	0.188208i	0.0252256	+	0.0145640i	−0.487334	+	0.873216i	$0.662031\pi$
$168$		0			0
$169$	6.70422	+	11.6120i	0.515709	+	0.893234i
$170$		0			0
$171$	5.12496	−	1.75722i	0.391915	−	0.134378i
$172$		0			0
$173$	−0.253324	+	0.146257i	−0.0192598	+	0.0111197i	−0.509599	−	0.860412i	$-0.670206\pi$
$173$	−0.253324	+	0.146257i	−0.0192598	+	0.0111197i	0.490339	+	0.871532i	$0.336873\pi$
$174$		0			0
$175$	18.2218	+	9.41648i	1.37744	+	0.711819i
$176$		0			0
$177$	−8.59679	−	3.22057i	−0.646175	−	0.242073i
$178$		0			0
$179$	−23.4931			−1.75596			−0.877978	−	0.478702i	$-0.841108\pi$
$179$	−23.4931			−1.75596			−0.877978	+	0.478702i	$0.841108\pi$
$180$		0			0
$181$	−2.37931			−0.176853			−0.0884263	−	0.996083i	$-0.528184\pi$
$181$	−2.37931			−0.176853			−0.0884263	+	0.996083i	$0.528184\pi$
$182$		0			0
$183$	9.06471	−	7.46249i	0.670083	−	0.551643i
$184$		0			0
$185$	−8.71559	−	4.76459i	−0.640783	−	0.350300i
$186$		0			0
$187$	−14.4434	+	8.33891i	−1.05621	+	0.609802i
$188$		0			0
$189$	18.1529	+	11.1728i	1.32043	+	0.812703i
$190$		0			0
$191$	5.68671	+	9.84967i	0.411476	+	0.712697i	0.995051	−	0.0993618i	$-0.0316801\pi$
$191$	5.68671	+	9.84967i	0.411476	+	0.712697i	−0.583576	+	0.812059i	$0.698347\pi$
$192$		0			0
$193$	−18.7831	−	10.8444i	−1.35204	−	0.780600i	−0.363504	−	0.931593i	$-0.618420\pi$
$193$	−18.7831	−	10.8444i	−1.35204	−	0.780600i	−0.988535	+	0.150993i	$0.951753\pi$
$194$		0			0
$195$	13.0046	+	15.0668i	0.931278	+	1.07895i
$196$		0			0
$197$			14.2214i			1.01323i	0.862171	+	0.506617i	$0.169104\pi$
$197$			14.2214i			1.01323i	−0.862171	+	0.506617i	$0.830896\pi$
$198$		0			0
$199$	−18.3820			−1.30306			−0.651532	−	0.758621i	$-0.725873\pi$
$199$	−18.3820			−1.30306			−0.651532	+	0.758621i	$0.725873\pi$
$200$		0			0
$201$	6.89450	−	18.4037i	0.486300	−	1.29810i
$202$		0			0
$203$	−12.4579	−	7.19259i	−0.874376	−	0.504821i
$204$		0			0
$205$	4.85901	+	7.98045i	0.339368	+	0.557379i
$206$		0			0
$207$	1.98006	+	0.387554i	0.137623	+	0.0269368i
$208$		0			0
$209$	−5.50330	−	9.53200i	−0.380671	−	0.659342i
$210$		0			0
$211$	−7.11683	+	12.3267i	−0.489943	+	0.848606i	−0.999933	−	0.0115745i	$-0.996316\pi$
$211$	−7.11683	+	12.3267i	−0.489943	+	0.848606i	0.509990	+	0.860180i	$0.329649\pi$
$212$		0			0
$213$	3.80686	+	22.8400i	0.260842	+	1.56497i
$214$		0			0
$215$	−0.241449	−	10.3552i	−0.0164667	−	0.706216i
$216$		0			0
$217$			27.0801i			1.83831i
$218$		0			0
$219$	−11.1166	+	1.85285i	−0.751188	+	0.125204i
$220$		0			0
$221$	−7.03125	+	12.1785i	−0.472973	+	0.819213i
$222$		0			0
$223$	−3.04188	+	1.75623i	−0.203699	+	0.117606i	−0.598380	−	0.801213i	$-0.704189\pi$
$223$	−3.04188	+	1.75623i	−0.203699	+	0.117606i	0.394680	+	0.918818i	$0.370855\pi$
$224$		0			0
$225$	11.7549	+	9.31783i	0.783661	+	0.621189i
$226$		0			0
$227$	6.99580	−	4.03903i	0.464328	−	0.268080i	−0.249535	−	0.968366i	$-0.580278\pi$
$227$	6.99580	−	4.03903i	0.464328	−	0.268080i	0.713862	+	0.700286i	$0.246944\pi$
$228$		0			0
$229$	−6.97185	+	12.0756i	−0.460713	+	0.797978i	−0.998997	−	0.0447858i	$-0.985739\pi$
$229$	−6.97185	+	12.0756i	−0.460713	+	0.797978i	0.538284	+	0.842764i	$0.319073\pi$
$230$		0			0
$231$	15.1917	−	40.5517i	0.999540	−	2.66811i
$232$		0			0
$233$			5.09746i			0.333946i	0.985961	+	0.166973i	$0.0533992\pi$
$233$			5.09746i			0.333946i	−0.985961	+	0.166973i	$0.946601\pi$
$234$		0			0
$235$	−0.0832139	−	3.56884i	−0.00542828	−	0.232805i
$236$		0			0
$237$	−3.99832	+	3.29160i	−0.259719	+	0.213812i
$238$		0			0
$239$	4.80932	−	8.32999i	0.311089	−	0.538822i	−0.667509	−	0.744601i	$-0.732640\pi$
$239$	4.80932	−	8.32999i	0.311089	−	0.538822i	0.978598	+	0.205779i	$0.0659729\pi$
$240$		0			0
$241$	−12.3198	−	21.3385i	−0.793586	−	1.37453i	−0.923733	−	0.383036i	$-0.874878\pi$
$241$	−12.3198	−	21.3385i	−0.793586	−	1.37453i	0.130147	−	0.991495i	$-0.458455\pi$
$242$		0			0
$243$	11.4588	+	10.5687i	0.735080	+	0.677981i
$244$		0			0
$245$	−11.4289	−	18.7708i	−0.730163	−	1.19922i
$246$		0			0
$247$	−8.03724	−	4.64030i	−0.511398	−	0.295256i
$248$		0			0
$249$	4.71653	+	5.72919i	0.298898	+	0.363072i
$250$		0			0
$251$	−16.2882			−1.02810			−0.514052	−	0.857759i	$-0.671856\pi$
$251$	−16.2882			−1.02810			−0.514052	+	0.857759i	$0.671856\pi$
$252$		0			0
$253$		−	4.09891i		−	0.257696i
$254$		0			0
$255$	−3.48569	+	10.0087i	−0.218283	+	0.626769i
$256$		0			0
$257$	14.7891	+	8.53851i	0.922521	+	0.532618i	0.884439	−	0.466657i	$-0.154542\pi$
$257$	14.7891	+	8.53851i	0.922521	+	0.532618i	0.0380828	+	0.999275i	$0.487875\pi$
$258$		0			0
$259$	9.11129	+	15.7812i	0.566148	+	0.980598i
$260$		0			0
$261$	−7.93062	−	6.91209i	−0.490893	−	0.427848i
$262$		0			0
$263$	15.2639	−	8.81262i	0.941213	−	0.543409i	0.0508724	−	0.998705i	$-0.483800\pi$
$263$	15.2639	−	8.81262i	0.941213	−	0.543409i	0.890340	+	0.455296i	$0.150467\pi$
$264$		0			0
$265$	−15.7398	−	8.60453i	−0.966887	−	0.528572i
$266$		0			0
$267$	2.04994	+	12.2990i	0.125454	+	0.752686i
$268$		0			0
$269$	−11.9751			−0.730132			−0.365066	−	0.930982i	$-0.618954\pi$
$269$	−11.9751			−0.730132			−0.365066	+	0.930982i	$0.618954\pi$
$270$		0			0
$271$	−1.08606			−0.0659734			−0.0329867	−	0.999456i	$-0.510502\pi$
$271$	−1.08606			−0.0659734			−0.0329867	+	0.999456i	$0.510502\pi$
$272$		0			0
$273$	−6.00303	−	36.0164i	−0.363320	−	2.17981i
$274$		0			0
$275$	13.9900	−	27.0721i	0.843631	−	1.63251i
$276$		0			0
$277$	13.6902	−	7.90405i	0.822565	−	0.474908i	−0.0287349	−	0.999587i	$-0.509148\pi$
$277$	13.6902	−	7.90405i	0.822565	−	0.474908i	0.851300	+	0.524679i	$0.175815\pi$
$278$		0			0
$279$	−3.80403	+	19.4352i	−0.227741	+	1.16356i
$280$		0			0
$281$	−0.731476	−	1.26695i	−0.0436362	−	0.0755801i	0.843382	−	0.537314i	$-0.180561\pi$
$281$	−0.731476	−	1.26695i	−0.0436362	−	0.0755801i	−0.887019	+	0.461734i	$0.847228\pi$
$282$		0			0
$283$	12.1349	+	7.00608i	0.721344	+	0.416468i	0.815247	−	0.579113i	$-0.196601\pi$
$283$	12.1349	+	7.00608i	0.721344	+	0.416468i	−0.0939029	+	0.995581i	$0.529934\pi$
$284$		0			0
$285$	−6.60529	−	2.30040i	−0.391264	−	0.136264i
$286$		0			0
$287$		−	17.1409i		−	1.01180i
$288$		0			0
$289$	9.51172			0.559513
$290$		0			0
$291$	4.24179	+	5.15251i	0.248658	+	0.302046i
$292$		0			0
$293$	−17.0624	−	9.85101i	−0.996799	−	0.575502i	−0.0894991	−	0.995987i	$-0.528527\pi$
$293$	−17.0624	−	9.85101i	−0.996799	−	0.575502i	−0.907300	+	0.420485i	$0.861860\pi$
$294$		0			0
$295$	6.16347	+	10.1229i	0.358851	+	0.589378i
$296$		0			0
$297$	16.5994	−	26.9697i	0.963196	−	1.56494i
$298$		0			0
$299$	−1.72807	−	2.99310i	−0.0999368	−	0.173096i
$300$		0			0
$301$	−9.50119	+	16.4565i	−0.547639	+	0.948539i
$302$		0			0
$303$	−13.0373	+	10.7329i	−0.748975	+	0.616591i
$304$		0			0
$305$	−15.1538	+	0.353338i	−0.867705	+	0.0202321i
$306$		0			0
$307$		−	21.0537i		−	1.20160i	−0.799400	−	0.600799i	$-0.794849\pi$
$307$		−	21.0537i		−	1.20160i	0.799400	−	0.600799i	$-0.205151\pi$
$308$		0			0
$309$	6.76834	−	18.0670i	0.385038	−	1.02779i
$310$		0			0
$311$	0.261873	−	0.453578i	0.0148495	−	0.0257200i	−0.858505	−	0.512805i	$-0.828606\pi$
$311$	0.261873	−	0.453578i	0.0148495	−	0.0257200i	0.873355	+	0.487085i	$0.161940\pi$
$312$		0			0
$313$	7.90085	−	4.56156i	0.446582	−	0.257834i	−0.259803	−	0.965662i	$-0.583658\pi$
$313$	7.90085	−	4.56156i	0.446582	−	0.257834i	0.706386	+	0.707827i	$0.250324\pi$
$314$		0			0
$315$	−9.52970	−	25.8157i	−0.536938	−	1.45455i
$316$		0			0
$317$	−13.5322	+	7.81279i	−0.760041	+	0.438810i	−0.829311	−	0.558788i	$-0.811267\pi$
$317$	−13.5322	+	7.81279i	−0.760041	+	0.438810i	0.0692693	+	0.997598i	$0.477933\pi$
$318$		0			0
$319$	−10.6860	+	18.5087i	−0.598302	+	1.03629i
$320$		0			0
$321$	−2.04153	+	0.340272i	−0.113947	+	0.0189921i
$322$		0			0
$323$		−	4.94193i		−	0.274976i
$324$		0			0
$325$	−1.19758	−	25.6666i	−0.0664297	−	1.42373i
$326$		0			0
$327$	2.57801	+	15.4673i	0.142564	+	0.855343i
$328$		0			0
$329$	−3.27452	+	5.67164i	−0.180530	+	0.312688i
$330$		0			0
$331$	13.1692	+	22.8097i	0.723845	+	1.25374i	0.959448	+	0.281887i	$0.0909604\pi$
$331$	13.1692	+	22.8097i	0.723845	+	1.25374i	−0.235602	+	0.971850i	$0.575706\pi$
$332$		0			0
$333$	4.32228	+	12.6060i	0.236860	+	0.690804i
$334$		0			0
$335$	−21.6708	+	13.1945i	−1.18400	+	0.720895i
$336$		0			0
$337$	23.5926	+	13.6212i	1.28517	+	0.741994i	0.977789	−	0.209592i	$-0.0672135\pi$
$337$	23.5926	+	13.6212i	1.28517	+	0.741994i	0.307383	+	0.951586i	$0.400547\pi$
$338$		0			0
$339$	−4.81119	+	12.8427i	−0.261308	+	0.697518i
$340$		0			0
$341$	40.2328			2.17873
$342$		0			0
$343$			11.6017i			0.626431i
$344$		0			0
$345$	−1.70194	−	1.97182i	−0.0916295	−	0.106159i
$346$		0			0
$347$	14.1764	+	8.18475i	0.761029	+	0.439380i	0.829665	−	0.558261i	$-0.188531\pi$
$347$	14.1764	+	8.18475i	0.761029	+	0.439380i	−0.0686360	+	0.997642i	$0.521865\pi$
$348$		0			0
$349$	−9.14725	−	15.8435i	−0.489641	−	0.848083i	0.510288	−	0.860004i	$-0.329539\pi$
$349$	−9.14725	−	15.8435i	−0.489641	−	0.848083i	−0.999929	+	0.0119207i	$0.996205\pi$
$350$		0			0
$351$	0.751000	−	26.6920i	0.0400854	−	1.42471i
$352$		0			0
$353$	17.6650	−	10.1989i	0.940215	−	0.542833i	0.0501873	−	0.998740i	$-0.484018\pi$
$353$	17.6650	−	10.1989i	0.940215	−	0.542833i	0.890028	+	0.455906i	$0.150685\pi$
$354$		0			0
$355$	14.3390	−	26.2295i	0.761036	−	1.39212i
$356$		0			0
$357$	15.0110	−	12.3577i	0.794464	−	0.654039i
$358$		0			0
$359$	9.33006			0.492422			0.246211	−	0.969216i	$-0.420814\pi$
$359$	9.33006			0.492422			0.246211	+	0.969216i	$0.420814\pi$
$360$		0			0
$361$	−15.7386			−0.828345
$362$		0			0
$363$	−42.4059	−	15.8863i	−2.22573	−	0.833815i
$364$		0			0
$365$	12.7663	+	6.97901i	0.668219	+	0.365298i
$366$		0			0
$367$	7.93529	−	4.58144i	0.414219	−	0.239149i	−0.278382	−	0.960470i	$-0.589798\pi$
$367$	7.93529	−	4.58144i	0.414219	−	0.239149i	0.692601	+	0.721321i	$0.256465\pi$
$368$		0			0
$369$	2.40784	−	12.3020i	0.125347	−	0.640414i
$370$		0			0
$371$	16.4544	+	28.4998i	0.854269	+	1.47964i
$372$		0			0
$373$	−21.0965	−	12.1801i	−1.09233	−	0.630659i	−0.158137	−	0.987417i	$-0.550549\pi$
$373$	−21.0965	−	12.1801i	−1.09233	−	0.630659i	−0.934197	+	0.356758i	$0.883882\pi$
$374$		0			0
$375$	−4.51076	−	18.8322i	−0.232935	−	0.972492i
$376$		0			0
$377$			18.0206i			0.928107i
$378$		0			0
$379$	7.84198			0.402815			0.201408	−	0.979508i	$-0.435448\pi$
$379$	7.84198			0.402815			0.201408	+	0.979508i	$0.435448\pi$
$380$		0			0
$381$	15.3927	−	2.56558i	0.788593	−	0.131439i
$382$		0			0
$383$	−26.6868	−	15.4076i	−1.36363	−	0.787292i	−0.373525	−	0.927620i	$-0.621851\pi$
$383$	−26.6868	−	15.4076i	−1.36363	−	0.787292i	−0.990105	+	0.140328i	$0.955184\pi$
$384$		0			0
$385$	−47.7505	+	29.0735i	−2.43359	+	1.48172i
$386$		0			0
$387$	−9.13065	+	10.4761i	−0.464137	+	0.532530i
$388$		0			0
$389$	−2.37020	−	4.10531i	−0.120174	−	0.208147i	0.799662	−	0.600450i	$-0.205012\pi$
$389$	−2.37020	−	4.10531i	−0.120174	−	0.208147i	−0.919836	+	0.392303i	$0.871679\pi$
$390$		0			0
$391$	0.920197	−	1.59383i	0.0465364	−	0.0806033i
$392$		0			0
$393$	4.11890	+	1.54304i	0.207771	+	0.0778363i
$394$		0			0
$395$	6.68413	−	0.155853i	0.336315	−	0.00784179i
$396$		0			0
$397$		−	36.8417i		−	1.84903i	−0.381146	−	0.924515i	$-0.624471\pi$
$397$		−	36.8417i		−	1.84903i	0.381146	−	0.924515i	$-0.375529\pi$
$398$		0			0
$399$	8.15553	+	9.90655i	0.408287	+	0.495948i
$400$		0			0
$401$	3.70249	−	6.41289i	0.184893	−	0.320245i	−0.758647	−	0.651502i	$-0.774139\pi$
$401$	3.70249	−	6.41289i	0.184893	−	0.320245i	0.943541	+	0.331257i	$0.107473\pi$
$402$		0			0
$403$	29.3788	−	16.9618i	1.46346	−	0.844929i
$404$		0			0
$405$	−3.21299	−	19.8665i	−0.159655	−	0.987173i
$406$		0			0
$407$	23.4461	−	13.5366i	1.16218	−	0.670985i
$408$		0			0
$409$	−0.304008	+	0.526557i	−0.0150322	+	0.0260366i	−0.873444	−	0.486925i	$-0.838118\pi$
$409$	−0.304008	+	0.526557i	−0.0150322	+	0.0260366i	0.858411	+	0.512962i	$0.171452\pi$
$410$		0			0
$411$	9.76077	+	11.8564i	0.481463	+	0.584835i
$412$		0			0
$413$		−	21.7426i		−	1.06988i
$414$		0			0
$415$	−0.223321	−	9.57769i	−0.0109624	−	0.470150i
$416$		0			0
$417$	24.3208	+	9.11119i	1.19100	+	0.446177i
$418$		0			0
$419$	−6.18339	+	10.7099i	−0.302078	+	0.523215i	−0.976607	−	0.215034i	$-0.931014\pi$
$419$	−6.18339	+	10.7099i	−0.302078	+	0.523215i	0.674528	+	0.738249i	$0.264347\pi$
$420$		0			0
$421$	−6.49789	−	11.2547i	−0.316688	−	0.548519i	0.663107	−	0.748524i	$-0.269237\pi$
$421$	−6.49789	−	11.2547i	−0.316688	−	0.548519i	−0.979795	+	0.200005i	$0.935904\pi$
$422$		0			0
$423$	−3.14682	+	3.61052i	−0.153004	+	0.175550i
$424$		0			0
$425$	11.5175	−	7.38602i	0.558683	−	0.358275i
$426$		0			0
$427$	24.0826	+	13.9041i	1.16544	+	0.672867i
$428$		0			0
$429$	−53.5094	+	8.91868i	−2.58346	+	0.430598i
$430$		0			0
$431$	−4.47990			−0.215789			−0.107895	−	0.994162i	$-0.534411\pi$
$431$	−4.47990			−0.215789			−0.107895	+	0.994162i	$0.534411\pi$
$432$		0			0
$433$			16.5313i			0.794443i	0.917723	+	0.397222i	$0.130026\pi$
$433$			16.5313i			0.794443i	−0.917723	+	0.397222i	$0.869974\pi$
$434$		0			0
$435$	2.54454	+	13.3409i	0.122001	+	0.639645i
$436$		0			0
$437$	1.05185	+	0.607288i	0.0503170	+	0.0290505i
$438$		0			0
$439$	−11.6927	−	20.2523i	−0.558060	−	0.966588i	−0.997658	−	0.0683936i	$-0.978213\pi$
$439$	−11.6927	−	20.2523i	−0.558060	−	0.966588i	0.439599	−	0.898194i	$-0.355121\pi$
$440$		0			0
$441$	−5.66349	+	28.9354i	−0.269690	+	1.37788i
$442$		0			0
$443$	−17.8422	+	10.3012i	−0.847709	+	0.489425i	−0.859877	−	0.510501i	$-0.829460\pi$
$443$	−17.8422	+	10.3012i	−0.847709	+	0.489425i	0.0121681	+	0.999926i	$0.496127\pi$
$444$		0			0
$445$	7.72134	−	14.1242i	0.366027	−	0.669552i
$446$		0			0
$447$	22.3771	+	8.38303i	1.05840	+	0.396504i
$448$		0			0
$449$	−13.1837			−0.622177			−0.311088	−	0.950381i	$-0.600694\pi$
$449$	−13.1837			−0.622177			−0.311088	+	0.950381i	$0.600694\pi$
$450$		0			0
$451$	−25.4662			−1.19916
$452$		0			0
$453$	−3.48510	+	2.86909i	−0.163744	+	0.134802i
$454$		0			0
$455$	−22.6112	+	41.3613i	−1.06003	+	1.93905i
$456$		0			0
$457$	−31.7886	+	18.3532i	−1.48701	+	0.858525i	−0.999890	−	0.0148107i	$-0.995285\pi$
$457$	−31.7886	+	18.3532i	−1.48701	+	0.858525i	−0.487119	+	0.873336i	$0.661952\pi$
$458$		0			0
$459$	12.5092	−	6.76042i	0.583880	−	0.315549i
$460$		0			0
$461$	−7.68518	−	13.3111i	−0.357934	−	0.619961i	0.629681	−	0.776854i	$-0.283186\pi$
$461$	−7.68518	−	13.3111i	−0.357934	−	0.619961i	−0.987616	+	0.156893i	$0.949852\pi$
$462$		0			0
$463$	0.704658	+	0.406834i	0.0327482	+	0.0189072i	0.516285	−	0.856417i	$-0.327315\pi$
$463$	0.704658	+	0.406834i	0.0327482	+	0.0189072i	−0.483537	+	0.875324i	$0.660648\pi$
$464$		0			0
$465$	19.3544	−	16.7054i	0.897540	−	0.774694i
$466$		0			0
$467$		−	15.2103i		−	0.703850i	−0.936028	−	0.351925i	$-0.885527\pi$
$467$		−	15.2103i		−	0.703850i	0.936028	−	0.351925i	$-0.114473\pi$
$468$		0			0
$469$	46.5459			2.14929
$470$		0			0
$471$	−9.08460	+	24.2498i	−0.418596	+	1.11737i
$472$		0			0
$473$	24.4494	+	14.1159i	1.12419	+	0.649049i
$474$		0			0
$475$	4.87444	+	7.60105i	0.223655	+	0.348760i
$476$		0			0
$477$	7.80575	+	22.7656i	0.357401	+	1.04236i
$478$		0			0
$479$	−3.70488	−	6.41703i	−0.169280	−	0.293202i	0.768887	−	0.639385i	$-0.220811\pi$
$479$	−3.70488	−	6.41703i	−0.169280	−	0.293202i	−0.938167	+	0.346183i	$0.887478\pi$
$480$		0			0
$481$	11.4139	−	19.7694i	0.520428	−	0.901408i
$482$		0			0
$483$	0.785631	+	4.71355i	0.0357475	+	0.214474i
$484$		0			0
$485$	−0.200843	−	8.61365i	−0.00911979	−	0.391126i
$486$		0			0
$487$			42.0092i			1.90362i	0.306692	+	0.951809i	$0.400778\pi$
$487$			42.0092i			1.90362i	−0.306692	+	0.951809i	$0.599222\pi$
$488$		0			0
$489$	−16.2138	+	2.70244i	−0.733214	+	0.122208i
$490$		0			0
$491$	−3.84004	+	6.65115i	−0.173299	+	0.300162i	−0.939571	−	0.342354i	$-0.888776\pi$
$491$	−3.84004	+	6.65115i	−0.173299	+	0.300162i	0.766272	+	0.642516i	$0.222109\pi$
$492$		0			0
$493$	−8.31034	+	4.79798i	−0.374279	+	0.216090i
$494$		0			0
$495$	−38.3543	+	14.1582i	−1.72390	+	0.636366i
$496$		0			0
$497$	−47.4935	+	27.4204i	−2.13038	+	1.22997i
$498$		0			0
$499$	19.8363	−	34.3574i	0.887993	−	1.53805i	0.0457495	−	0.998953i	$-0.485432\pi$
$499$	19.8363	−	34.3574i	0.887993	−	1.53805i	0.842244	−	0.539097i	$-0.181234\pi$
$500$		0			0
$501$	−0.228722	+	0.610536i	−0.0102186	+	0.0272767i
$502$		0			0
$503$		−	26.0215i		−	1.16024i	−0.814530	−	0.580121i	$-0.803005\pi$
$503$		−	26.0215i		−	1.16024i	0.814530	−	0.580121i	$-0.196995\pi$
$504$		0			0
$505$	21.7950	−	0.508189i	0.969864	−	0.0226141i
$506$		0			0
$507$	−17.9299	+	14.7607i	−0.796294	+	0.655546i
$508$		0			0
$509$	−7.06530	+	12.2375i	−0.313164	+	0.542416i	−0.979046	−	0.203641i	$-0.934722\pi$
$509$	−7.06530	+	12.2375i	−0.313164	+	0.542416i	0.665881	+	0.746058i	$0.268056\pi$
$510$		0			0
$511$	−13.3459	−	23.1158i	−0.590388	−	1.02258i
$512$		0			0
$513$	4.46157	+	8.25551i	0.196983	+	0.364490i
$514$		0			0
$515$	−21.2743	+	12.9531i	−0.937456	+	0.570783i
$516$		0			0
$517$	8.42634	+	4.86495i	0.370590	+	0.213960i
$518$		0			0
$519$	−0.322013	−	0.391151i	−0.0141348	−	0.0171696i
$520$		0			0
$521$	13.0285			0.570788			0.285394	−	0.958410i	$-0.407876\pi$
$521$	13.0285			0.570788			0.285394	+	0.958410i	$0.407876\pi$
$522$		0			0
$523$			21.9922i			0.961651i	0.876816	+	0.480826i	$0.159663\pi$
$523$			21.9922i			0.961651i	−0.876816	+	0.480826i	$0.840337\pi$
$524$		0			0
$525$	−10.8990	+	33.8130i	−0.475672	+	1.47572i
$526$		0			0
$527$	15.6442	+	9.03218i	0.681472	+	0.393448i
$528$		0			0
$529$	−11.2738	−	19.5269i	−0.490167	−	0.848994i
$530$		0			0
$531$	3.05426	−	15.6046i	0.132544	−	0.677180i
$532$		0			0
$533$	−18.5959	+	10.7364i	−0.805480	+	0.465044i
$534$		0			0
$535$	2.34450	+	1.28168i	0.101362	+	0.0554117i
$536$		0			0
$537$	−6.68992	−	40.1375i	−0.288691	−	1.73206i
$538$		0			0
$539$	59.8991			2.58003
$540$		0			0
$541$	−24.7006			−1.06196			−0.530981	−	0.847384i	$-0.678177\pi$
$541$	−24.7006			−1.06196			−0.530981	+	0.847384i	$0.678177\pi$
$542$		0			0
$543$	−0.677535	−	4.06501i	−0.0290758	−	0.174446i
$544$		0			0
$545$	9.71041	−	17.7627i	0.415948	−	0.760870i
$546$		0			0
$547$	−9.78713	+	5.65060i	−0.418467	+	0.241602i	−0.694421	−	0.719569i	$-0.744340\pi$
$547$	−9.78713	+	5.65060i	−0.418467	+	0.241602i	0.275954	+	0.961171i	$0.411006\pi$
$548$		0			0
$549$	15.3308	+	13.3619i	0.654303	+	0.570271i
$550$		0			0
$551$	−3.16645	−	5.48445i	−0.134895	−	0.233645i
$552$		0			0
$553$	−10.6225	−	6.13291i	−0.451715	−	0.260798i
$554$		0			0
$555$	5.65835	−	16.2472i	0.240184	−	0.689656i
$556$		0			0
$557$			25.0264i			1.06040i	0.847872	+	0.530201i	$0.177884\pi$
$557$			25.0264i			1.06040i	−0.847872	+	0.530201i	$0.822116\pi$
$558$		0			0
$559$	23.8046			1.00683
$560$		0			0
$561$	−18.3598	−	22.3017i	−0.775152	−	0.941580i
$562$		0			0
$563$	23.7163	+	13.6926i	0.999522	+	0.577074i	0.908107	−	0.418739i	$-0.137528\pi$
$563$	23.7163	+	13.6926i	0.999522	+	0.577074i	0.0914149	+	0.995813i	$0.470861\pi$
$564$		0			0
$565$	15.1225	−	9.20755i	0.636209	−	0.387365i
$566$		0			0
$567$	−13.9193	+	34.1955i	−0.584557	+	1.43608i
$568$		0			0
$569$	18.1180	+	31.3813i	0.759545	+	1.31557i	0.943083	+	0.332558i	$0.107912\pi$
$569$	18.1180	+	31.3813i	0.759545	+	1.31557i	−0.183538	+	0.983013i	$0.558755\pi$
$570$		0			0
$571$	5.89985	−	10.2188i	0.246901	−	0.427645i	−0.715763	−	0.698343i	$-0.753921\pi$
$571$	5.89985	−	10.2188i	0.246901	−	0.427645i	0.962664	+	0.270698i	$0.0872543\pi$
$572$		0			0
$573$	−15.2086	+	12.5204i	−0.635350	+	0.523049i
$574$		0			0
$575$	0.156730	+	3.35906i	0.00653610	+	0.140082i
$576$		0			0
$577$		−	8.24270i		−	0.343148i	−0.985171	−	0.171574i	$-0.945115\pi$
$577$		−	8.24270i		−	0.343148i	0.985171	−	0.171574i	$-0.0548853\pi$
$578$		0			0
$579$	13.1788	−	35.1787i	0.547693	−	1.46198i
$580$		0			0
$581$	−8.78784	+	15.2210i	−0.364581	+	0.631473i
$582$		0			0
$583$	42.3421	−	24.4462i	1.75363	−	1.01246i
$584$		0			0
$585$	−22.0381	+	26.5085i	−0.911163	+	1.09599i
$586$		0			0
$587$	37.3803	−	21.5815i	1.54285	−	0.890764i	0.544191	−	0.838961i	$-0.316837\pi$
$587$	37.3803	−	21.5815i	1.54285	−	0.890764i	0.998657	−	0.0518030i	$-0.0164968\pi$
$588$		0			0
$589$	−5.96083	+	10.3245i	−0.245612	+	0.425412i
$590$		0			0
$591$	−24.2971	+	4.04971i	−0.999447	+	0.166583i
$592$		0			0
$593$			41.9976i			1.72464i	0.506367	+	0.862318i	$0.330988\pi$
$593$			41.9976i			1.72464i	−0.506367	+	0.862318i	$0.669012\pi$
$594$		0			0
$595$	−25.0944	+	0.585120i	−1.02877	+	0.0239876i
$596$		0			0
$597$	−5.23447	−	31.4053i	−0.214233	−	1.28533i
$598$		0			0
$599$	−0.845089	+	1.46374i	−0.0345294	+	0.0598067i	−0.882774	−	0.469799i	$-0.844327\pi$
$599$	−0.845089	+	1.46374i	−0.0345294	+	0.0598067i	0.848244	+	0.529605i	$0.177660\pi$
$600$		0			0
$601$	14.1126	+	24.4438i	0.575666	+	0.997083i	0.995969	+	0.0896992i	$0.0285906\pi$
$601$	14.1126	+	24.4438i	0.575666	+	0.997083i	−0.420303	+	0.907384i	$0.638076\pi$
$602$		0			0
$603$	33.4057	+	6.53846i	1.36039	+	0.266267i
$604$		0			0
$605$	30.4029	+	49.9338i	1.23605	+	2.03010i
$606$		0			0
$607$	−13.0986	−	7.56250i	−0.531657	−	0.306952i	0.210034	−	0.977694i	$-0.432643\pi$
$607$	−13.0986	−	7.56250i	−0.531657	−	0.306952i	−0.741691	+	0.670742i	$0.765976\pi$
$608$		0			0
$609$	8.74088	−	23.3323i	0.354198	−	0.945474i
$610$		0			0
$611$	8.20411			0.331903
$612$		0			0
$613$			33.1010i			1.33694i	0.743741	+	0.668468i	$0.233050\pi$
$613$			33.1010i			1.33694i	−0.743741	+	0.668468i	$0.766950\pi$
$614$		0			0
$615$	−12.2508	+	10.5741i	−0.494000	+	0.426387i
$616$		0			0
$617$	39.4974	+	22.8039i	1.59011	+	0.918048i	0.993287	+	0.115673i	$0.0369024\pi$
$617$	39.4974	+	22.8039i	1.59011	+	0.918048i	0.596819	+	0.802376i	$0.296431\pi$
$618$		0			0
$619$	0.819595	+	1.41958i	0.0329423	+	0.0570578i	0.882027	−	0.471200i	$-0.156179\pi$
$619$	0.819595	+	1.41958i	0.0329423	+	0.0570578i	−0.849084	+	0.528258i	$0.822846\pi$
$620$		0			0
$621$	−0.0982852	+	3.49325i	−0.00394405	+	0.140179i
$622$		0			0
$623$	−25.5745	+	14.7655i	−1.02462	+	0.591566i
$624$		0			0
$625$	−10.4297	+	22.7205i	−0.417188	+	0.908820i
$626$		0			0
$627$	14.7181	−	12.1166i	0.587785	−	0.483892i
$628$		0			0
$629$	12.1558			0.484683
$630$		0			0
$631$	28.4741			1.13354			0.566769	−	0.823877i	$-0.308193\pi$
$631$	28.4741			1.13354			0.566769	+	0.823877i	$0.308193\pi$
$632$		0			0
$633$	−23.0866	−	8.64880i	−0.917608	−	0.343759i
$634$		0			0
$635$	−17.6771	−	9.66359i	−0.701492	−	0.383488i
$636$		0			0
$637$	43.7395	−	25.2530i	1.73302	−	1.00056i
$638$		0			0
$639$	−37.9377	+	13.0079i	−1.50079	+	0.514584i
$640$		0			0
$641$	21.4614	+	37.1722i	0.847674	+	1.46821i	0.883278	+	0.468849i	$0.155331\pi$
$641$	21.4614	+	37.1722i	0.847674	+	1.46821i	−0.0356042	+	0.999366i	$0.511336\pi$
$642$		0			0
$643$	−43.7060	−	25.2337i	−1.72360	−	0.995118i	−0.911142	−	0.412093i	$-0.864798\pi$
$643$	−43.7060	−	25.2337i	−1.72360	−	0.995118i	−0.812454	−	0.583025i	$-0.801869\pi$
$644$		0			0
$645$	17.6228	−	3.36126i	0.693899	−	0.132349i
$646$		0			0
$647$		−	13.8898i		−	0.546064i	−0.962005	−	0.273032i	$-0.911974\pi$
$647$		−	13.8898i		−	0.546064i	0.962005	−	0.273032i	$-0.0880265\pi$
$648$		0			0
$649$	−32.3029			−1.26800
$650$		0			0
$651$	−46.2658	+	7.71135i	−1.81330	+	0.302232i
$652$		0			0
$653$	9.60198	+	5.54371i	0.375755	+	0.216942i	0.675970	−	0.736930i	$-0.263725\pi$
$653$	9.60198	+	5.54371i	0.375755	+	0.216942i	−0.300215	+	0.953872i	$0.597058\pi$
$654$		0			0
$655$	−2.95305	−	4.85010i	−0.115385	−	0.189509i
$656$		0			0
$657$	−6.33113	−	18.4648i	−0.247001	−	0.720381i
$658$		0			0
$659$	2.32773	+	4.03175i	0.0906755	+	0.157055i	0.907796	−	0.419413i	$-0.137764\pi$
$659$	2.32773	+	4.03175i	0.0906755	+	0.157055i	−0.817120	+	0.576468i	$0.804431\pi$
$660$		0			0
$661$	21.0556	−	36.4693i	0.818966	−	1.41849i	−0.0874783	−	0.996166i	$-0.527881\pi$
$661$	21.0556	−	36.4693i	0.818966	−	1.41849i	0.906445	−	0.422325i	$-0.138786\pi$
$662$		0			0
$663$	−22.8089	−	8.54480i	−0.885826	−	0.331853i
$664$		0			0
$665$	−0.386153	−	16.5611i	−0.0149744	−	0.642214i
$666$		0			0
$667$		−	2.35840i		−	0.0913175i
$668$		0			0
$669$	−3.86670	−	4.69689i	−0.149495	−	0.181592i
$670$		0			0
$671$	20.6573	−	35.7795i	0.797465	−	1.38125i
$672$		0			0
$673$	7.89063	−	4.55566i	0.304161	−	0.175608i	−0.340149	−	0.940371i	$-0.610478\pi$
$673$	7.89063	−	4.55566i	0.304161	−	0.175608i	0.644311	+	0.764764i	$0.277144\pi$
$674$		0			0
$675$	−12.5720	+	22.7364i	−0.483897	+	0.875125i
$676$		0			0
$677$	−14.1996	+	8.19813i	−0.545734	+	0.315080i	−0.747400	−	0.664375i	$-0.768698\pi$
$677$	−14.1996	+	8.19813i	−0.545734	+	0.315080i	0.201665	+	0.979454i	$0.435365\pi$
$678$		0			0
$679$	−7.90330	+	13.6889i	−0.303301	+	0.525332i
$680$		0			0
$681$	8.89274	+	10.8020i	0.340771	+	0.413935i
$682$		0			0
$683$		−	31.3665i		−	1.20021i	−0.799923	−	0.600103i	$-0.795126\pi$
$683$		−	31.3665i		−	1.20021i	0.799923	−	0.600103i	$-0.204874\pi$
$684$		0			0
$685$	−0.462159	−	19.8209i	−0.0176582	−	0.757316i
$686$		0			0
$687$	−22.6163	−	8.47262i	−0.862864	−	0.323250i
$688$		0			0
$689$	20.6127	−	35.7022i	0.785281	−	1.36015i
$690$		0			0
$691$	1.56088	+	2.70353i	0.0593788	+	0.102847i	0.894187	−	0.447694i	$-0.147755\pi$
$691$	1.56088	+	2.70353i	0.0593788	+	0.102847i	−0.834808	+	0.550541i	$0.814421\pi$
$692$		0			0
$693$	73.6079	+	14.4072i	2.79613	+	0.547283i
$694$		0			0
$695$	−17.4368	−	28.6383i	−0.661415	−	1.08631i
$696$		0			0
$697$	−9.90234	−	5.71712i	−0.375078	−	0.216551i
$698$		0			0
$699$	−8.70892	+	1.45156i	−0.329402	+	0.0549030i
$700$		0			0
$701$	−36.9206			−1.39447			−0.697236	−	0.716841i	$-0.745587\pi$
$701$	−36.9206			−1.39447			−0.697236	+	0.716841i	$0.745587\pi$
$702$		0			0
$703$			8.02227i			0.302566i
$704$		0			0
$705$	6.07360	−	1.15844i	0.228745	−	0.0436293i
$706$		0			0
$707$	−34.6369	−	19.9976i	−1.30265	−	0.752087i
$708$		0			0
$709$	−16.6544	−	28.8463i	−0.625471	−	1.08335i	−0.988450	−	0.151550i	$-0.951574\pi$
$709$	−16.6544	−	28.8463i	−0.625471	−	1.08335i	0.362979	−	0.931797i	$-0.381760\pi$
$710$		0			0
$711$	−6.76220	−	5.89373i	−0.253602	−	0.221032i
$712$		0			0
$713$	−3.84487	+	2.21984i	−0.143992	+	0.0831336i
$714$		0			0
$715$	61.4504	+	33.5933i	2.29811	+	1.25632i
$716$		0			0
$717$	15.6011	+	5.84458i	0.582635	+	0.218270i
$718$		0			0
$719$	−40.6734			−1.51686			−0.758431	−	0.651753i	$-0.774034\pi$
$719$	−40.6734			−1.51686			−0.758431	+	0.651753i	$0.774034\pi$
$720$		0			0
$721$	45.6942			1.70174
$722$		0			0
$723$	32.9482	−	27.1245i	1.22536	−	1.00877i
$724$		0			0
$725$	8.04948	−	15.5765i	0.298950	−	0.578497i
$726$		0			0
$727$	−28.9235	+	16.6990i	−1.07271	+	0.619332i	−0.928922	−	0.370276i	$-0.879263\pi$
$727$	−28.9235	+	16.6990i	−1.07271	+	0.619332i	−0.143793	+	0.989608i	$0.545930\pi$
$728$		0			0
$729$	−14.7934	+	22.5866i	−0.547903	+	0.836542i
$730$		0			0
$731$	6.33798	+	10.9777i	0.234419	+	0.406025i
$732$		0			0
$733$	−45.9504	−	26.5295i	−1.69722	−	0.979889i	−0.948380	−	0.317136i	$-0.897279\pi$
$733$	−45.9504	−	26.5295i	−1.69722	−	0.979889i	−0.748838	−	0.662753i	$-0.769388\pi$
$734$		0			0
$735$	28.8151	−	24.8712i	1.06286	−	0.917388i
$736$		0			0
$737$		−	69.1531i		−	2.54729i
$738$		0			0
$739$	9.18128			0.337739			0.168869	−	0.985638i	$-0.445988\pi$
$739$	9.18128			0.337739			0.168869	+	0.985638i	$0.445988\pi$
$740$		0			0
$741$	5.63918	−	15.0529i	0.207161	−	0.552981i
$742$		0			0
$743$	31.4494	+	18.1573i	1.15377	+	0.666128i	0.949802	−	0.312850i	$-0.101284\pi$
$743$	31.4494	+	18.1573i	1.15377	+	0.666128i	0.203965	+	0.978978i	$0.434617\pi$
$744$		0			0
$745$	−16.0433	−	26.3495i	−0.587780	−	0.965372i
$746$		0			0
$747$	−8.44513	+	9.68956i	−0.308991	+	0.354522i
$748$		0			0
$749$	−2.45094	−	4.24516i	−0.0895555	−	0.155115i
$750$		0			0
$751$	7.29856	−	12.6415i	0.266328	−	0.461294i	−0.701582	−	0.712588i	$-0.747523\pi$
$751$	7.29856	−	12.6415i	0.266328	−	0.461294i	0.967911	+	0.251294i	$0.0808561\pi$
$752$		0			0
$753$	−4.63826	−	27.8281i	−0.169027	−	1.01411i
$754$		0			0
$755$	5.82616	−	0.135847i	0.212036	−	0.00494399i
$756$		0			0
$757$			44.8778i			1.63111i	0.578677	+	0.815556i	$0.303569\pi$
$757$			44.8778i			1.63111i	−0.578677	+	0.815556i	$0.696431\pi$
$758$		0			0
$759$	7.00291	−	1.16721i	0.254189	−	0.0423670i
$760$		0			0
$761$	−22.4488	+	38.8825i	−0.813769	+	1.40949i	0.0964392	+	0.995339i	$0.469255\pi$
$761$	−22.4488	+	38.8825i	−0.813769	+	1.40949i	−0.910208	+	0.414151i	$0.864079\pi$
$762$		0			0
$763$	−32.1627	+	18.5691i	−1.16437	+	0.672248i
$764$		0			0
$765$	−18.0923	−	3.10515i	−0.654128	−	0.112267i
$766$		0			0
$767$	−23.5883	+	13.6187i	−0.851722	+	0.491742i
$768$		0			0
$769$	−8.43182	+	14.6043i	−0.304059	+	0.526646i	−0.977051	−	0.213004i	$-0.931675\pi$
$769$	−8.43182	+	14.6043i	−0.304059	+	0.526646i	0.672992	+	0.739649i	$0.265009\pi$
$770$		0			0
$771$	−10.3765	+	27.6984i	−0.373701	+	0.997534i
$772$		0			0
$773$		−	41.8399i		−	1.50488i	−0.658663	−	0.752438i	$-0.728878\pi$
$773$		−	41.8399i		−	1.50488i	0.658663	−	0.752438i	$-0.271122\pi$
$774$		0			0
$775$	−32.9708	+	1.53838i	−1.18435	+	0.0552603i
$776$		0			0
$777$	−24.3674	+	20.0604i	−0.874175	+	0.719662i
$778$		0			0
$779$	3.77304	−	6.53510i	0.135183	−	0.234144i
$780$		0			0
$781$	40.7384	+	70.5610i	1.45773	+	2.52487i
$782$		0			0
$783$	9.55085	−	15.5176i	0.341320	−	0.554555i
$784$		0			0
$785$	28.5547	−	17.3859i	1.01916	−	0.620530i
$786$		0			0
$787$	−28.1768	−	16.2679i	−1.00440	−	0.579888i	−0.0948495	−	0.995492i	$-0.530237\pi$
$787$	−28.1768	−	16.2679i	−1.00440	−	0.579888i	−0.909546	+	0.415604i	$0.863570\pi$
$788$		0			0
$789$	19.4028	+	23.5686i	0.690757	+	0.839065i
$790$		0			0
$791$	−32.4811			−1.15490
$792$		0			0
$793$		−	34.8358i		−	1.23706i
$794$		0			0
$795$	10.2186	−	29.3414i	0.362417	−	1.04063i
$796$		0			0
$797$	−33.8845	−	19.5632i	−1.20025	−	0.692965i	−0.239639	−	0.970862i	$-0.577029\pi$
$797$	−33.8845	−	19.5632i	−1.20025	−	0.692965i	−0.960611	+	0.277897i	$0.910363\pi$
$798$		0			0
$799$	2.18434	+	3.78340i	0.0772766	+	0.133847i
$800$		0			0
$801$	−20.4289	+	7.00456i	−0.721819	+	0.247494i
$802$		0			0
$803$	−34.3431	+	19.8280i	−1.21194	+	0.699714i
$804$		0			0
$805$	2.95918	−	5.41306i	0.104297	−	0.190785i
$806$		0			0
$807$	−3.41003	−	20.4592i	−0.120039	−	0.720197i
$808$		0			0
$809$	−31.5260			−1.10840			−0.554198	−	0.832385i	$-0.686975\pi$
$809$	−31.5260			−1.10840			−0.554198	+	0.832385i	$0.686975\pi$
$810$		0			0
$811$	−6.54430			−0.229801			−0.114901	−	0.993377i	$-0.536655\pi$
$811$	−6.54430			−0.229801			−0.114901	+	0.993377i	$0.536655\pi$
$812$		0			0
$813$	−0.309268	−	1.85551i	−0.0108465	−	0.0650757i
$814$		0			0
$815$	18.6200	+	10.1791i	0.652230	+	0.356557i
$816$		0			0
$817$	−7.24478	+	4.18278i	−0.253463	+	0.146337i
$818$		0			0
$819$	59.8239	−	20.5121i	2.09042	−	0.716752i
$820$		0			0
$821$	−26.6905	−	46.2293i	−0.931505	−	1.61341i	−0.780750	−	0.624843i	$-0.785163\pi$
$821$	−26.6905	−	46.2293i	−0.931505	−	1.61341i	−0.150755	−	0.988571i	$-0.548170\pi$
$822$		0			0
$823$	32.7001	+	18.8794i	1.13985	+	0.658095i	0.946395	−	0.323013i	$-0.104696\pi$
$823$	32.7001	+	18.8794i	1.13985	+	0.658095i	0.193460	+	0.981108i	$0.438029\pi$
$824$		0			0
$825$	50.2359	+	16.1926i	1.74899	+	0.563756i
$826$		0			0
$827$		−	6.15055i		−	0.213875i	−0.994266	−	0.106938i	$-0.965895\pi$
$827$		−	6.15055i		−	0.213875i	0.994266	−	0.106938i	$-0.0341045\pi$
$828$		0			0
$829$	−43.1456			−1.49851			−0.749255	−	0.662282i	$-0.769588\pi$
$829$	−43.1456			−1.49851			−0.749255	+	0.662282i	$0.769588\pi$
$830$		0			0
$831$	17.4024	+	21.1387i	0.603682	+	0.733294i
$832$		0			0
$833$	23.2913	+	13.4472i	0.806995	+	0.465919i
$834$		0			0
$835$	0.718919	−	0.437724i	0.0248792	−	0.0151481i
$836$		0			0
$837$	−34.2880	−	0.964718i	−1.18517	−	0.0333455i
$838$		0			0
$839$	17.8927	+	30.9911i	0.617726	+	1.06993i	0.989900	+	0.141769i	$0.0452792\pi$
$839$	17.8927	+	30.9911i	0.617726	+	1.06993i	−0.372174	+	0.928163i	$0.621388\pi$
$840$		0			0
$841$	8.35157	−	14.4653i	0.287985	−	0.498805i
$842$		0			0
$843$	1.95627	−	1.61049i	0.0673776	−	0.0554683i
$844$		0			0
$845$	29.9740	−	0.698898i	1.03114	−	0.0240428i
$846$		0			0
$847$		−	107.251i		−	3.68519i
$848$		0			0
$849$	−8.51422	+	22.7273i	−0.292207	+	0.779999i
$850$		0			0
$851$	−1.49376	+	2.58727i	−0.0512055	+	0.0886906i
$852$		0			0
$853$	13.1522	−	7.59341i	0.450322	−	0.259993i	−0.257644	−	0.966240i	$-0.582946\pi$
$853$	13.1522	−	7.59341i	0.450322	−	0.259993i	0.707966	+	0.706246i	$0.249613\pi$
$854$		0			0
$855$	2.04926	−	11.9401i	0.0700832	−	0.408342i
$856$		0			0
$857$	0.919391	−	0.530811i	0.0314058	−	0.0181321i	−0.484215	−	0.874949i	$-0.660895\pi$
$857$	0.919391	−	0.530811i	0.0314058	−	0.0181321i	0.515621	+	0.856817i	$0.327561\pi$
$858$		0			0
$859$	0.604035	−	1.04622i	0.0206094	−	0.0356965i	−0.855537	−	0.517742i	$-0.826773\pi$
$859$	0.604035	−	1.04622i	0.0206094	−	0.0356965i	0.876146	+	0.482046i	$0.160106\pi$
$860$		0			0
$861$	29.2850	−	4.88107i	0.998029	−	0.166347i
$862$		0			0
$863$		−	13.2305i		−	0.450373i	−0.974316	−	0.225186i	$-0.927701\pi$
$863$		−	13.2305i		−	0.450373i	0.974316	−	0.225186i	$-0.0722991\pi$
$864$		0			0
$865$	0.0152469	+	0.653901i	0.000518409	+	0.0222333i
$866$		0			0
$867$	2.70857	+	16.2506i	0.0919878	+	0.551899i
$868$		0			0
$869$	−9.11164	+	15.7818i	−0.309091	+	0.535361i
$870$		0			0
$871$	−29.1544	−	50.4969i	−0.987860	−	1.71102i
$872$		0			0
$873$	−7.59508	+	8.71425i	−0.257055	+	0.294933i
$874$		0			0
$875$	38.0199	−	25.6516i	1.28531	−	0.867183i
$876$		0			0
$877$	35.4105	+	20.4443i	1.19573	+	0.690355i	0.959600	−	0.281367i	$-0.0907879\pi$
$877$	35.4105	+	20.4443i	1.19573	+	0.690355i	0.236129	+	0.971722i	$0.424121\pi$
$878$		0			0
$879$	11.9715	−	31.9561i	0.403790	−	1.07785i
$880$		0			0
$881$	23.2103			0.781975			0.390988	−	0.920396i	$-0.372133\pi$
$881$	23.2103			0.781975			0.390988	+	0.920396i	$0.372133\pi$
$882$		0			0
$883$		−	20.1285i		−	0.677377i	−0.940899	−	0.338689i	$-0.890017\pi$
$883$		−	20.1285i		−	0.677377i	0.940899	−	0.338689i	$-0.109983\pi$
$884$		0			0
$885$	−15.5397	+	13.4128i	−0.522361	+	0.450866i
$886$		0			0
$887$	0.946216	+	0.546298i	0.0317708	+	0.0183429i	0.515801	−	0.856708i	$-0.327494\pi$
$887$	0.946216	+	0.546298i	0.0317708	+	0.0183429i	−0.484030	+	0.875051i	$0.660828\pi$
$888$		0			0
$889$	18.4796	+	32.0076i	0.619786	+	1.07350i
$890$		0			0
$891$	50.8041	+	20.6799i	1.70200	+	0.692803i
$892$		0			0
$893$	−2.49687	+	1.44157i	−0.0835546	+	0.0482402i
$894$		0			0
$895$	−25.1984	+	46.0941i	−0.842291	+	1.54075i
$896$		0			0
$897$	4.62158	−	3.80469i	0.154310	−	0.127035i
$898$		0			0
$899$	23.1488			0.772056
$900$		0			0
$901$	21.9525			0.731345
$902$		0			0
$903$	−30.8213	−	11.5464i	−1.02567	−	0.384241i
$904$		0			0
$905$	−2.55202	+	4.66827i	−0.0848321	+	0.155179i
$906$		0			0
$907$	3.59622	−	2.07628i	0.119410	−	0.0689416i	−0.439105	−	0.898436i	$-0.644704\pi$
$907$	3.59622	−	2.07628i	0.119410	−	0.0689416i	0.558516	+	0.829494i	$0.311371\pi$
$908$		0			0
$909$	−22.0495	−	19.2177i	−0.731337	−	0.637412i
$910$		0			0
$911$	−14.0374	−	24.3135i	−0.465080	−	0.805542i	0.534125	−	0.845405i	$-0.320641\pi$
$911$	−14.0374	−	24.3135i	−0.465080	−	0.805542i	−0.999205	+	0.0398635i	$0.987308\pi$
$912$		0			0
$913$	22.6138	+	13.0561i	0.748406	+	0.432093i
$914$		0			0
$915$	−4.91889	−	25.7894i	−0.162614	−	0.852571i
$916$		0			0
$917$			10.4173i			0.344011i
$918$		0			0
$919$	18.0993			0.597041			0.298520	−	0.954403i	$-0.403507\pi$
$919$	18.0993			0.597041			0.298520	+	0.954403i	$0.403507\pi$
$920$		0			0
$921$	35.9698	−	5.99528i	1.18525	−	0.197551i
$922$		0			0
$923$	59.4960	+	34.3500i	1.95833	+	1.13064i
$924$		0			0
$925$	−18.6965	+	11.9898i	−0.614738	+	0.394222i
$926$		0			0
$927$	32.7945	+	6.41882i	1.07711	+	0.210822i
$928$		0			0
$929$	−14.5132	−	25.1377i	−0.476164	−	0.824740i	0.523463	−	0.852048i	$-0.324640\pi$
$929$	−14.5132	−	25.1377i	−0.476164	−	0.824740i	−0.999627	+	0.0273082i	$0.991306\pi$
$930$		0			0
$931$	−8.87456	+	15.3712i	−0.290852	+	0.503770i
$932$		0			0
$933$	0.849501	+	0.318245i	0.0278114	+	0.0104189i
$934$		0			0
$935$	0.869311	+	37.2826i	0.0284295	+	1.21927i
$936$		0			0
$937$		−	26.8353i		−	0.876672i	−0.898811	−	0.438336i	$-0.855568\pi$
$937$		−	26.8353i		−	0.876672i	0.898811	−	0.438336i	$-0.144432\pi$
$938$		0			0
$939$	10.0432	+	12.1995i	0.327747	+	0.398116i
$940$		0			0
$941$	20.7696	−	35.9741i	0.677071	−	1.17272i	−0.298789	−	0.954319i	$-0.596583\pi$
$941$	20.7696	−	35.9741i	0.677071	−	1.17272i	0.975859	−	0.218401i	$-0.0700841\pi$
$942$		0			0
$943$	2.43370	−	1.40510i	0.0792521	−	0.0457562i
$944$		0			0
$945$	41.3920	−	23.6326i	1.34648	−	0.768770i
$946$		0			0
$947$	−38.0805	+	21.9858i	−1.23745	+	0.714443i	−0.968573	−	0.248731i	$-0.919986\pi$
$947$	−38.0805	+	21.9858i	−1.23745	+	0.714443i	−0.268879	+	0.963174i	$0.586653\pi$
$948$		0			0
$949$	−16.7187	+	28.9576i	−0.542711	+	0.940002i
$950$		0			0
$951$	−17.2014	−	20.8947i	−0.557795	−	0.677556i
$952$		0			0
$953$			19.3790i			0.627749i	0.949465	+	0.313874i	$0.101627\pi$
$953$			19.3790i			0.627749i	−0.949465	+	0.313874i	$0.898373\pi$
$954$		0			0
$955$	25.4248	−	0.592825i	0.822728	−	0.0191834i
$956$		0			0
$957$	−34.6648	−	12.9863i	−1.12055	−	0.419787i
$958$		0			0
$959$	−18.1863	+	31.4995i	−0.587265	+	1.01717i
$960$		0			0
$961$	−6.28879	−	10.8925i	−0.202864	−	0.351371i
$962$		0			0
$963$	−1.16270	−	3.39102i	−0.0374674	−	0.109274i
$964$		0			0
$965$	−41.4237	+	25.2214i	−1.33347	+	0.811904i
$966$		0			0
$967$	1.64129	+	0.947601i	0.0527804	+	0.0304728i	0.526158	−	0.850387i	$-0.323632\pi$
$967$	1.64129	+	0.947601i	0.0527804	+	0.0304728i	−0.473378	+	0.880860i	$0.656965\pi$
$968$		0			0
$969$	8.44319	−	1.40727i	0.271234	−	0.0452080i
$970$		0			0
$971$	−36.8043			−1.18111			−0.590553	−	0.806999i	$-0.701090\pi$
$971$	−36.8043			−1.18111			−0.590553	+	0.806999i	$0.701090\pi$
$972$		0			0
$973$			61.5111i			1.97196i
$974$		0			0
$975$	43.5100	−	9.35491i	1.39343	−	0.299597i
$976$		0			0
$977$	−34.2472	−	19.7726i	−1.09566	−	0.632582i	−0.160585	−	0.987022i	$-0.551338\pi$
$977$	−34.2472	−	19.7726i	−1.09566	−	0.632582i	−0.935079	+	0.354440i	$0.884672\pi$
$978$		0			0
$979$	21.9370	+	37.9960i	0.701110	+	1.21436i
$980$		0			0
$981$	−25.6915	+	8.80897i	−0.820265	+	0.281249i
$982$		0			0
$983$	13.4295	−	7.75350i	0.428333	−	0.247298i	−0.270303	−	0.962775i	$-0.587124\pi$
$983$	13.4295	−	7.75350i	0.428333	−	0.247298i	0.698636	+	0.715477i	$0.253791\pi$
$984$		0			0
$985$	27.9028	+	15.2538i	0.889058	+	0.486025i
$986$		0			0
$987$	−10.6224	−	3.97940i	−0.338113	−	0.126666i
$988$		0			0
$989$	−3.11537			−0.0990629
$990$		0			0
$991$	23.4814			0.745910			0.372955	−	0.927849i	$-0.378345\pi$
$991$	23.4814			0.745910			0.372955	+	0.927849i	$0.378345\pi$
$992$		0			0
$993$	−35.2200	+	28.9947i	−1.11767	+	0.920119i
$994$		0			0
$995$	−19.7163	+	36.0659i	−0.625049	+	1.14337i
$996$		0			0
$997$	−23.5213	+	13.5800i	−0.744928	+	0.430084i	−0.823858	−	0.566796i	$-0.808183\pi$
$997$	−23.5213	+	13.5800i	−0.744928	+	0.430084i	0.0789305	+	0.996880i	$0.474849\pi$
$998$		0			0
$999$	−20.3063	+	10.9742i	−0.642463	+	0.347210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bi.b.49.9	yes	32
3.2	odd	2		1080.2.bi.b.1009.6		32
4.3	odd	2		720.2.by.f.49.8		32
5.4	even	2	inner	360.2.bi.b.49.8	✓	32
9.2	odd	6		1080.2.bi.b.289.5		32
9.4	even	3		3240.2.f.k.649.2		16
9.5	odd	6		3240.2.f.i.649.15		16
9.7	even	3	inner	360.2.bi.b.169.8	yes	32
12.11	even	2		2160.2.by.f.1009.6		32
15.14	odd	2		1080.2.bi.b.1009.5		32
20.19	odd	2		720.2.by.f.49.9		32
36.7	odd	6		720.2.by.f.529.9		32
36.11	even	6		2160.2.by.f.289.5		32
45.4	even	6		3240.2.f.k.649.1		16
45.14	odd	6		3240.2.f.i.649.16		16
45.29	odd	6		1080.2.bi.b.289.6		32
45.34	even	6	inner	360.2.bi.b.169.9	yes	32
60.59	even	2		2160.2.by.f.1009.5		32
180.79	odd	6		720.2.by.f.529.8		32
180.119	even	6		2160.2.by.f.289.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bi.b.49.8	✓	32	5.4	even	2	inner
360.2.bi.b.49.9	yes	32	1.1	even	1	trivial
360.2.bi.b.169.8	yes	32	9.7	even	3	inner
360.2.bi.b.169.9	yes	32	45.34	even	6	inner
720.2.by.f.49.8		32	4.3	odd	2
720.2.by.f.49.9		32	20.19	odd	2
720.2.by.f.529.8		32	180.79	odd	6
720.2.by.f.529.9		32	36.7	odd	6
1080.2.bi.b.289.5		32	9.2	odd	6
1080.2.bi.b.289.6		32	45.29	odd	6
1080.2.bi.b.1009.5		32	15.14	odd	2
1080.2.bi.b.1009.6		32	3.2	odd	2
2160.2.by.f.289.5		32	36.11	even	6
2160.2.by.f.289.6		32	180.119	even	6
2160.2.by.f.1009.5		32	60.59	even	2
2160.2.by.f.1009.6		32	12.11	even	2
3240.2.f.i.649.15		16	9.5	odd	6
3240.2.f.i.649.16		16	45.14	odd	6
3240.2.f.k.649.1		16	45.4	even	6
3240.2.f.k.649.2		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)

\(f(q)\)	\(=\)	\(q+(0.284761 + 1.70848i) q^{3} +(1.07259 - 1.96203i) q^{5} +(-3.55262 + 2.05111i) q^{7} +(-2.83782 + 0.973019i) q^{9} +O(q^{10})\)	\(q+(0.284761 + 1.70848i) q^{3} +(1.07259 - 1.96203i) q^{5} +(-3.55262 + 2.05111i) q^{7} +(-2.83782 + 0.973019i) q^{9} +(3.04732 + 5.27812i) q^{11} +(4.45043 + 2.56946i) q^{13} +(3.65752 + 1.27379i) q^{15} +2.73647i q^{17} -1.80595 q^{19} +(-4.51593 - 5.48551i) q^{21} +(-0.582439 - 0.336271i) q^{23} +(-2.69910 - 4.20890i) q^{25} +(-2.47049 - 4.57129i) q^{27} +(1.75334 + 3.03688i) q^{29} +(3.30067 - 5.71692i) q^{31} +(-8.14981 + 6.70930i) q^{33} +(0.213823 + 9.17033i) q^{35} -4.44214i q^{37} +(-3.12256 + 8.33516i) q^{39} +(-2.08923 + 3.61865i) q^{41} +(4.01162 - 2.31611i) q^{43} +(-1.13473 + 6.61153i) q^{45} +(1.38258 - 0.798234i) q^{47} +(4.91407 - 8.51143i) q^{49} +(-4.67521 + 0.779242i) q^{51} -8.02220i q^{53} +(13.6243 - 0.317676i) q^{55} +(-0.514264 - 3.08543i) q^{57} +(-2.65011 + 4.59012i) q^{59} +(-3.38942 - 5.87064i) q^{61} +(8.08594 - 9.27744i) q^{63} +(9.81483 - 5.97589i) q^{65} +(-9.82638 - 5.67327i) q^{67} +(0.408657 - 1.09084i) q^{69} +13.3686 q^{71} +6.50669i q^{73} +(6.42223 - 5.80990i) q^{75} +(-21.6520 - 12.5008i) q^{77} +(1.49502 + 2.58946i) q^{79} +(7.10647 - 5.52251i) q^{81} +(3.71043 - 2.14222i) q^{83} +(5.36903 + 2.93511i) q^{85} +(-4.68917 + 3.86034i) q^{87} +7.19878 q^{89} -21.0809 q^{91} +(10.7072 + 4.01117i) q^{93} +(-1.93704 + 3.54332i) q^{95} +(3.33696 - 1.92659i) q^{97} +(-13.7835 - 12.0133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) \) 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

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Database

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