LMFDB - Embedded newform 1440.2.q.p.481.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(481,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1440.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.q (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:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8528759163648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 $ x^10 - 2x^9 + x^8 + 9x^6 - 36x^5 + 27x^4 + 27x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			481.5
Root			$0.756905 - 1.55791i$ of defining polynomial
Character	$\chi$	$=$	1440.481
Dual form			1440.2.q.p.961.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72765 - 0.123458i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.53662 - 2.66151i) q^{7} +(2.96952 - 0.426584i) q^{9} +O(q^{10})$	\(q+(1.72765 - 0.123458i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.53662 - 2.66151i) q^{7} +(2.96952 - 0.426584i) q^{9} +(-1.97074 - 3.41342i) q^{11} +(-0.396269 + 0.686358i) q^{13} +(-0.756905 + 1.55791i) q^{15} +4.70838 q^{17} +1.32879 q^{19} +(-2.98333 - 4.40844i) q^{21} +(0.536624 - 0.929459i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(5.07761 - 1.10360i) q^{27} +(-4.39940 - 7.61999i) q^{29} +(-0.855415 + 1.48162i) q^{31} +(-3.82616 - 5.65388i) q^{33} +3.07325 q^{35} +8.11804 q^{37} +(-0.599876 + 1.23471i) q^{39} +(-0.103731 + 0.179667i) q^{41} +(-5.35034 - 9.26705i) q^{43} +(-1.11533 + 2.78497i) q^{45} +(-4.62269 - 8.00673i) q^{47} +(-1.22242 + 2.11730i) q^{49} +(8.13441 - 0.581288i) q^{51} -12.7935 q^{53} +3.94148 q^{55} +(2.29567 - 0.164050i) q^{57} +(5.97265 - 10.3449i) q^{59} +(3.98069 + 6.89477i) q^{61} +(-5.69839 - 7.24790i) q^{63} +(-0.396269 - 0.686358i) q^{65} +(-0.00644531 + 0.0111636i) q^{67} +(0.812346 - 1.67203i) q^{69} +9.44240 q^{71} +7.14123 q^{73} +(-0.970741 - 1.43446i) q^{75} +(-6.05657 + 10.4903i) q^{77} +(3.60423 + 6.24272i) q^{79} +(8.63605 - 2.53349i) q^{81} +(5.70274 + 9.87744i) q^{83} +(-2.35419 + 4.07758i) q^{85} +(-8.54136 - 12.6215i) q^{87} -1.67993 q^{89} +2.43566 q^{91} +(-1.29494 + 2.66533i) q^{93} +(-0.664393 + 1.15076i) q^{95} +(7.12404 + 12.3392i) q^{97} +(-7.30826 - 9.29553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} - 5 q^{5} - q^{9}+O(q^{10}) $ 10 * q + q^3 - 5 * q^5 - q^9	$ 10 q + q^{3} - 5 q^{5} - q^{9} - 9 q^{11} - 4 q^{13} - 2 q^{15} + 6 q^{17} + 14 q^{19} + 12 q^{21} - 10 q^{23} - 5 q^{25} - 2 q^{27} - 2 q^{29} - 8 q^{31} - 27 q^{33} + 16 q^{37} + 26 q^{39} - q^{41} - q^{43} - q^{45} - 10 q^{47} - q^{49} - 3 q^{51} - 20 q^{53} + 18 q^{55} - 19 q^{57} - 13 q^{59} - 14 q^{61} - 30 q^{63} - 4 q^{65} - 15 q^{67} + 8 q^{69} + 32 q^{71} - 14 q^{73} + q^{75} + 12 q^{77} - 18 q^{79} + 35 q^{81} + 8 q^{83} - 3 q^{85} - 32 q^{87} + 28 q^{89} - 36 q^{91} + 16 q^{93} - 7 q^{95} + 17 q^{97}+O(q^{100}) $ 10 * q + q^3 - 5 * q^5 - q^9 - 9 * q^11 - 4 * q^13 - 2 * q^15 + 6 * q^17 + 14 * q^19 + 12 * q^21 - 10 * q^23 - 5 * q^25 - 2 * q^27 - 2 * q^29 - 8 * q^31 - 27 * q^33 + 16 * q^37 + 26 * q^39 - q^41 - q^43 - q^45 - 10 * q^47 - q^49 - 3 * q^51 - 20 * q^53 + 18 * q^55 - 19 * q^57 - 13 * q^59 - 14 * q^61 - 30 * q^63 - 4 * q^65 - 15 * q^67 + 8 * q^69 + 32 * q^71 - 14 * q^73 + q^75 + 12 * q^77 - 18 * q^79 + 35 * q^81 + 8 * q^83 - 3 * q^85 - 32 * q^87 + 28 * q^89 - 36 * q^91 + 16 * q^93 - 7 * q^95 + 17 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.72765	−	0.123458i	0.997456	−	0.0712786i
$3$	1.72765	−	0.123458i	0.997456	−	0.0712786i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−1.53662	−	2.66151i	−0.580789	−	1.00596i	−0.995386	−	0.0959511i	$-0.969411\pi$
$7$	−1.53662	−	2.66151i	−0.580789	−	1.00596i	0.414597	−	0.910005i	$-0.363923\pi$
$8$		0			0
$9$	2.96952	−	0.426584i	0.989839	−	0.142195i
$10$		0			0
$11$	−1.97074	−	3.41342i	−0.594201	−	1.02919i	−0.993659	−	0.112434i	$-0.964135\pi$
$11$	−1.97074	−	3.41342i	−0.594201	−	1.02919i	0.399459	−	0.916751i	$-0.369198\pi$
$12$		0			0
$13$	−0.396269	+	0.686358i	−0.109905	+	0.190361i	−0.915732	−	0.401790i	$-0.868388\pi$
$13$	−0.396269	+	0.686358i	−0.109905	+	0.190361i	0.805826	+	0.592152i	$0.201721\pi$
$14$		0			0
$15$	−0.756905	+	1.55791i	−0.195432	+	0.402252i
$16$		0			0
$17$	4.70838			1.14195			0.570975	−	0.820967i	$-0.306565\pi$
$17$	4.70838			1.14195			0.570975	+	0.820967i	$0.306565\pi$
$18$		0			0
$19$	1.32879			0.304845			0.152422	−	0.988315i	$-0.451293\pi$
$19$	1.32879			0.304845			0.152422	+	0.988315i	$0.451293\pi$
$20$		0			0
$21$	−2.98333	−	4.40844i	−0.651015	−	0.962000i
$22$		0			0
$23$	0.536624	−	0.929459i	0.111894	−	0.193806i	−0.804640	−	0.593763i	$-0.797642\pi$
$23$	0.536624	−	0.929459i	0.111894	−	0.193806i	0.916534	+	0.399957i	$0.130975\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	5.07761	−	1.10360i	0.977186	−	0.212387i
$28$		0			0
$29$	−4.39940	−	7.61999i	−0.816949	−	1.41500i	−0.907920	−	0.419143i	$-0.862331\pi$
$29$	−4.39940	−	7.61999i	−0.816949	−	1.41500i	0.0909717	−	0.995853i	$-0.471003\pi$
$30$		0			0
$31$	−0.855415	+	1.48162i	−0.153637	+	0.266107i	−0.932562	−	0.361010i	$-0.882432\pi$
$31$	−0.855415	+	1.48162i	−0.153637	+	0.266107i	0.778925	+	0.627117i	$0.215765\pi$
$32$		0			0
$33$	−3.82616	−	5.65388i	−0.666048	−	0.984214i
$34$		0			0
$35$	3.07325			0.519474
$36$		0			0
$37$	8.11804			1.33460			0.667299	−	0.744790i	$-0.267450\pi$
$37$	8.11804			1.33460			0.667299	+	0.744790i	$0.267450\pi$
$38$		0			0
$39$	−0.599876	+	1.23471i	−0.0960570	+	0.197711i
$40$		0			0
$41$	−0.103731	+	0.179667i	−0.0162001	+	0.0280593i	−0.874012	−	0.485905i	$-0.838490\pi$
$41$	−0.103731	+	0.179667i	−0.0162001	+	0.0280593i	0.857812	+	0.513964i	$0.171824\pi$
$42$		0			0
$43$	−5.35034	−	9.26705i	−0.815918	−	1.41321i	−0.908667	−	0.417523i	$-0.862898\pi$
$43$	−5.35034	−	9.26705i	−0.815918	−	1.41321i	0.0927481	−	0.995690i	$-0.470435\pi$
$44$		0			0
$45$	−1.11533	+	2.78497i	−0.166263	+	0.415159i
$46$		0			0
$47$	−4.62269	−	8.00673i	−0.674289	−	1.16790i	−0.976676	−	0.214717i	$-0.931117\pi$
$47$	−4.62269	−	8.00673i	−0.674289	−	1.16790i	0.302388	−	0.953185i	$-0.402216\pi$
$48$		0			0
$49$	−1.22242	+	2.11730i	−0.174632	+	0.302472i
$50$		0			0
$51$	8.13441	−	0.581288i	1.13905	−	0.0813966i
$52$		0			0
$53$	−12.7935			−1.75733			−0.878664	−	0.477440i	$-0.841565\pi$
$53$	−12.7935			−1.75733			−0.878664	+	0.477440i	$0.841565\pi$
$54$		0			0
$55$	3.94148			0.531469
$56$		0			0
$57$	2.29567	−	0.164050i	0.304069	−	0.0217289i
$58$		0			0
$59$	5.97265	−	10.3449i	0.777573	−	1.34680i	−0.155764	−	0.987794i	$-0.549784\pi$
$59$	5.97265	−	10.3449i	0.777573	−	1.34680i	0.933337	−	0.359001i	$-0.116883\pi$
$60$		0			0
$61$	3.98069	+	6.89477i	0.509676	+	0.882784i	0.999937	+	0.0112088i	$0.00356795\pi$
$61$	3.98069	+	6.89477i	0.509676	+	0.882784i	−0.490261	+	0.871575i	$0.663099\pi$
$62$		0			0
$63$	−5.69839	−	7.24790i	−0.717929	−	0.913149i
$64$		0			0
$65$	−0.396269	−	0.686358i	−0.0491511	−	0.0851322i
$66$		0			0
$67$	−0.00644531	+	0.0111636i	−0.000787420	+	0.00136385i	−0.866419	−	0.499318i	$-0.833584\pi$
$67$	−0.00644531	+	0.0111636i	−0.000787420	+	0.00136385i	0.865631	+	0.500682i	$0.166917\pi$
$68$		0			0
$69$	0.812346	−	1.67203i	0.0977950	−	0.201288i
$70$		0			0
$71$	9.44240			1.12061			0.560303	−	0.828287i	$-0.310685\pi$
$71$	9.44240			1.12061			0.560303	+	0.828287i	$0.310685\pi$
$72$		0			0
$73$	7.14123			0.835818			0.417909	−	0.908489i	$-0.362763\pi$
$73$	7.14123			0.835818			0.417909	+	0.908489i	$0.362763\pi$
$74$		0			0
$75$	−0.970741	−	1.43446i	−0.112091	−	0.165637i
$76$		0			0
$77$	−6.05657	+	10.4903i	−0.690211	+	1.19548i
$78$		0			0
$79$	3.60423	+	6.24272i	0.405508	+	0.702360i	0.994380	−	0.105866i	$-0.0337613\pi$
$79$	3.60423	+	6.24272i	0.405508	+	0.702360i	−0.588872	+	0.808226i	$0.700428\pi$
$80$		0			0
$81$	8.63605	−	2.53349i	0.959561	−	0.281499i
$82$		0			0
$83$	5.70274	+	9.87744i	0.625957	+	1.08419i	0.988355	+	0.152166i	$0.0486250\pi$
$83$	5.70274	+	9.87744i	0.625957	+	1.08419i	−0.362397	+	0.932024i	$0.618042\pi$
$84$		0			0
$85$	−2.35419	+	4.07758i	−0.255348	+	0.442275i
$86$		0			0
$87$	−8.54136	−	12.6215i	−0.915730	−	1.35317i
$88$		0			0
$89$	−1.67993			−0.178072			−0.0890361	−	0.996028i	$-0.528379\pi$
$89$	−1.67993			−0.178072			−0.0890361	+	0.996028i	$0.528379\pi$
$90$		0			0
$91$	2.43566			0.255327
$92$		0			0
$93$	−1.29494	+	2.66533i	−0.134279	+	0.276381i
$94$		0			0
$95$	−0.664393	+	1.15076i	−0.0681653	+	0.118066i
$96$		0			0
$97$	7.12404	+	12.3392i	0.723337	+	1.25286i	0.959655	+	0.281180i	$0.0907259\pi$
$97$	7.12404	+	12.3392i	0.723337	+	1.25286i	−0.236318	+	0.971676i	$0.575941\pi$
$98$		0			0
$99$	−7.30826	−	9.29553i	−0.734507	−	0.934236i
$100$		0			0
$101$	1.07570	+	1.86316i	0.107036	+	0.185391i	0.914568	−	0.404432i	$-0.132531\pi$
$101$	1.07570	+	1.86316i	0.107036	+	0.185391i	−0.807532	+	0.589823i	$0.799197\pi$
$102$		0			0
$103$	7.51572	−	13.0176i	0.740546	−	1.28266i	−0.211701	−	0.977334i	$-0.567900\pi$
$103$	7.51572	−	13.0176i	0.740546	−	1.28266i	0.952247	−	0.305328i	$-0.0987663\pi$
$104$		0			0
$105$	5.30948	−	0.379417i	0.518152	−	0.0370273i
$106$		0			0
$107$	−1.91659			−0.185284			−0.0926420	−	0.995699i	$-0.529531\pi$
$107$	−1.91659			−0.185284			−0.0926420	+	0.995699i	$0.529531\pi$
$108$		0			0
$109$	−4.82726			−0.462367			−0.231184	−	0.972910i	$-0.574260\pi$
$109$	−4.82726			−0.462367			−0.231184	+	0.972910i	$0.574260\pi$
$110$		0			0
$111$	14.0251	−	1.00224i	1.33120	−	0.0951283i
$112$		0			0
$113$	−6.48291	+	11.2287i	−0.609861	+	1.05631i	0.381402	+	0.924409i	$0.375441\pi$
$113$	−6.48291	+	11.2287i	−0.609861	+	1.05631i	−0.991263	+	0.131901i	$0.957892\pi$
$114$		0			0
$115$	0.536624	+	0.929459i	0.0500404	+	0.0866725i
$116$		0			0
$117$	−0.883938	+	2.20719i	−0.0817201	+	0.204055i
$118$		0			0
$119$	−7.23501	−	12.5314i	−0.663232	−	1.14875i
$120$		0			0
$121$	−2.26764	+	3.92766i	−0.206149	+	0.357060i
$122$		0			0
$123$	−0.157029	+	0.323208i	−0.0141588	+	0.0291427i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	0.0801256			0.00711000			0.00355500	−	0.999994i	$-0.498868\pi$
$127$	0.0801256			0.00711000			0.00355500	+	0.999994i	$0.498868\pi$
$128$		0			0
$129$	−10.3876	−	15.3496i	−0.914575	−	1.35146i
$130$		0			0
$131$	−10.3126	+	17.8620i	−0.901017	+	1.56061i	−0.0748415	+	0.997195i	$0.523845\pi$
$131$	−10.3126	+	17.8620i	−0.901017	+	1.56061i	−0.826176	+	0.563412i	$0.809488\pi$
$132$		0			0
$133$	−2.04184	−	3.53658i	−0.177050	−	0.306660i
$134$		0			0
$135$	−1.58306	+	4.94913i	−0.136248	+	0.425954i
$136$		0			0
$137$	−0.907864	−	1.57247i	−0.0775640	−	0.134345i	0.824634	−	0.565666i	$-0.191381\pi$
$137$	−0.907864	−	1.57247i	−0.0775640	−	0.134345i	−0.902198	+	0.431321i	$0.858048\pi$
$138$		0			0
$139$	1.46129	−	2.53103i	0.123945	−	0.214679i	−0.797375	−	0.603484i	$-0.793779\pi$
$139$	1.46129	−	2.53103i	0.123945	−	0.214679i	0.921320	+	0.388805i	$0.127112\pi$
$140$		0			0
$141$	−8.97486	−	13.2621i	−0.755820	−	1.11687i
$142$		0			0
$143$	3.12377			0.261223
$144$		0			0
$145$	8.79881			0.730701
$146$		0			0
$147$	−1.85052	+	3.80886i	−0.152628	+	0.314150i
$148$		0			0
$149$	−6.05639	+	10.4900i	−0.496159	+	0.859372i	−0.999990	−	0.00442972i	$-0.998590\pi$
$149$	−6.05639	+	10.4900i	−0.496159	+	0.859372i	0.503831	+	0.863802i	$0.331923\pi$
$150$		0			0
$151$	6.71875	+	11.6372i	0.546764	+	0.947023i	0.998494	+	0.0548684i	$0.0174739\pi$
$151$	6.71875	+	11.6372i	0.546764	+	0.947023i	−0.451729	+	0.892155i	$0.649193\pi$
$152$		0			0
$153$	13.9816	−	2.00852i	1.13035	−	0.162379i
$154$		0			0
$155$	−0.855415	−	1.48162i	−0.0687086	−	0.119007i
$156$		0			0
$157$	−10.9538	+	18.9725i	−0.874205	+	1.51417i	−0.0165983	+	0.999862i	$0.505284\pi$
$157$	−10.9538	+	18.9725i	−0.874205	+	1.51417i	−0.857607	+	0.514306i	$0.828050\pi$
$158$		0			0
$159$	−22.1027	+	1.57947i	−1.75286	+	0.125260i
$160$		0			0
$161$	−3.29835			−0.259947
$162$		0			0
$163$	−7.91256			−0.619760			−0.309880	−	0.950776i	$-0.600289\pi$
$163$	−7.91256			−0.619760			−0.309880	+	0.950776i	$0.600289\pi$
$164$		0			0
$165$	6.80948	−	0.486608i	0.530117	−	0.0378824i
$166$		0			0
$167$	−0.972828	+	1.68499i	−0.0752797	+	0.130388i	−0.901208	−	0.433387i	$-0.857318\pi$
$167$	−0.972828	+	1.68499i	−0.0752797	+	0.130388i	0.825928	+	0.563775i	$0.190652\pi$
$168$		0			0
$169$	6.18594	+	10.7144i	0.475842	+	0.824182i
$170$		0			0
$171$	3.94585	−	0.566839i	0.301747	−	0.0433472i
$172$		0			0
$173$	−2.00429	−	3.47153i	−0.152383	−	0.263935i	0.779720	−	0.626128i	$-0.215361\pi$
$173$	−2.00429	−	3.47153i	−0.152383	−	0.263935i	−0.932103	+	0.362193i	$0.882028\pi$
$174$		0			0
$175$	−1.53662	+	2.66151i	−0.116158	+	0.201191i
$176$		0			0
$177$	9.04145	−	18.6097i	0.679597	−	1.39879i
$178$		0			0
$179$	−5.68505			−0.424920			−0.212460	−	0.977170i	$-0.568148\pi$
$179$	−5.68505			−0.424920			−0.212460	+	0.977170i	$0.568148\pi$
$180$		0			0
$181$	5.08812			0.378197			0.189098	−	0.981958i	$-0.439443\pi$
$181$	5.08812			0.378197			0.189098	+	0.981958i	$0.439443\pi$
$182$		0			0
$183$	7.72844	+	11.4203i	0.571303	+	0.844210i
$184$		0			0
$185$	−4.05902	+	7.03043i	−0.298425	+	0.516888i
$186$		0			0
$187$	−9.27900	−	16.0717i	−0.678547	−	1.17528i
$188$		0			0
$189$	−10.7396	−	11.8183i	−0.781191	−	0.859654i
$190$		0			0
$191$	5.14642	+	8.91387i	0.372382	+	0.644985i	0.989931	−	0.141547i	$-0.0452078\pi$
$191$	5.14642	+	8.91387i	0.372382	+	0.644985i	−0.617549	+	0.786532i	$0.711874\pi$
$192$		0			0
$193$	12.2648	−	21.2432i	0.882838	−	1.52912i	0.0346653	−	0.999399i	$-0.488963\pi$
$193$	12.2648	−	21.2432i	0.882838	−	1.52912i	0.848172	−	0.529721i	$-0.177703\pi$
$194$		0			0
$195$	−0.769349	−	1.13686i	−0.0550942	−	0.0814123i
$196$		0			0
$197$	−17.9124			−1.27621			−0.638103	−	0.769951i	$-0.720281\pi$
$197$	−17.9124			−1.27621			−0.638103	+	0.769951i	$0.720281\pi$
$198$		0			0
$199$	10.1152			0.717050			0.358525	−	0.933520i	$-0.383280\pi$
$199$	10.1152			0.717050			0.358525	+	0.933520i	$0.383280\pi$
$200$		0			0
$201$	−0.00975697	+	0.0200825i	−0.000688204	+	0.00141651i
$202$		0			0
$203$	−13.5205	+	23.4181i	−0.948950	+	1.64363i
$204$		0			0
$205$	−0.103731	−	0.179667i	−0.00724489	−	0.0125485i
$206$		0			0
$207$	1.19702	−	2.98896i	0.0831987	−	0.207747i
$208$		0			0
$209$	−2.61869	−	4.53571i	−0.181139	−	0.313742i
$210$		0			0
$211$	−2.90302	+	5.02819i	−0.199852	+	0.346155i	−0.948480	−	0.316836i	$-0.897380\pi$
$211$	−2.90302	+	5.02819i	−0.199852	+	0.346155i	0.748628	+	0.662990i	$0.230713\pi$
$212$		0			0
$213$	16.3131	−	1.16574i	1.11776	−	0.0798753i
$214$		0			0
$215$	10.7007			0.729780
$216$		0			0
$217$	5.25780			0.356923
$218$		0			0
$219$	12.3375	−	0.881643i	0.833692	−	0.0595759i
$220$		0			0
$221$	−1.86579	+	3.23163i	−0.125506	+	0.217383i
$222$		0			0
$223$	4.06325	+	7.03776i	0.272095	+	0.471283i	0.969398	−	0.245494i	$-0.0789500\pi$
$223$	4.06325	+	7.03776i	0.272095	+	0.471283i	−0.697303	+	0.716777i	$0.745617\pi$
$224$		0			0
$225$	−1.85419	−	2.35838i	−0.123613	−	0.157226i
$226$		0			0
$227$	−6.68438	−	11.5777i	−0.443658	−	0.768438i	0.554300	−	0.832317i	$-0.312986\pi$
$227$	−6.68438	−	11.5777i	−0.443658	−	0.768438i	−0.997958	+	0.0638789i	$0.979653\pi$
$228$		0			0
$229$	12.3128	−	21.3264i	0.813653	−	1.40929i	−0.0966389	−	0.995320i	$-0.530809\pi$
$229$	12.3128	−	21.3264i	0.813653	−	1.40929i	0.910291	−	0.413968i	$-0.135857\pi$
$230$		0			0
$231$	−9.16850	+	18.8712i	−0.603243	+	1.24164i
$232$		0			0
$233$	−21.3231			−1.39692			−0.698461	−	0.715648i	$-0.746131\pi$
$233$	−21.3231			−1.39692			−0.698461	+	0.715648i	$0.746131\pi$
$234$		0			0
$235$	9.24538			0.603102
$236$		0			0
$237$	6.99755	+	10.3402i	0.454540	+	0.671670i
$238$		0			0
$239$	−0.676476	+	1.17169i	−0.0437576	+	0.0757903i	−0.887075	−	0.461626i	$-0.847266\pi$
$239$	−0.676476	+	1.17169i	−0.0437576	+	0.0757903i	0.843317	+	0.537416i	$0.180600\pi$
$240$		0			0
$241$	6.94106	+	12.0223i	0.447113	+	0.774423i	0.998197	−	0.0600272i	$-0.0191187\pi$
$241$	6.94106	+	12.0223i	0.447113	+	0.774423i	−0.551083	+	0.834450i	$0.685785\pi$
$242$		0			0
$243$	14.6073	−	5.44317i	0.937056	−	0.349180i
$244$		0			0
$245$	−1.22242	−	2.11730i	−0.0780978	−	0.135269i
$246$		0			0
$247$	−0.526557	+	0.912023i	−0.0335040	+	0.0580306i
$248$		0			0
$249$	11.0718	+	16.3607i	0.701645	+	1.03682i
$250$		0			0
$251$	8.48547			0.535598			0.267799	−	0.963475i	$-0.413704\pi$
$251$	8.48547			0.535598			0.267799	+	0.963475i	$0.413704\pi$
$252$		0			0
$253$	−4.23018			−0.265949
$254$		0			0
$255$	−3.56380	+	7.33525i	−0.223174	+	0.459351i
$256$		0			0
$257$	10.2765	−	17.7995i	0.641033	−	1.11030i	−0.344169	−	0.938908i	$-0.611839\pi$
$257$	10.2765	−	17.7995i	0.641033	−	1.11030i	0.985202	−	0.171395i	$-0.0548274\pi$
$258$		0			0
$259$	−12.4744	−	21.6063i	−0.775120	−	1.34255i
$260$		0			0
$261$	−16.3147	−	20.7510i	−1.00985	−	1.28445i
$262$		0			0
$263$	−8.90021	−	15.4156i	−0.548811	−	0.950568i	−0.998356	−	0.0573104i	$-0.981748\pi$
$263$	−8.90021	−	15.4156i	−0.548811	−	0.950568i	0.449546	−	0.893257i	$-0.351586\pi$
$264$		0			0
$265$	6.39677	−	11.0795i	0.392951	−	0.680610i
$266$		0			0
$267$	−2.90232	+	0.207401i	−0.177619	+	0.0126927i
$268$		0			0
$269$	−3.05081			−0.186011			−0.0930055	−	0.995666i	$-0.529647\pi$
$269$	−3.05081			−0.186011			−0.0930055	+	0.995666i	$0.529647\pi$
$270$		0			0
$271$	6.75047			0.410062			0.205031	−	0.978755i	$-0.434270\pi$
$271$	6.75047			0.410062			0.205031	+	0.978755i	$0.434270\pi$
$272$		0			0
$273$	4.20796	−	0.300703i	0.254678	−	0.0181994i
$274$		0			0
$275$	−1.97074	+	3.41342i	−0.118840	+	0.205837i
$276$		0			0
$277$	−1.55047	−	2.68550i	−0.0931590	−	0.161356i	0.815680	−	0.578504i	$-0.196363\pi$
$277$	−1.55047	−	2.68550i	−0.0931590	−	0.161356i	−0.908839	+	0.417148i	$0.863030\pi$
$278$		0			0
$279$	−1.90813	+	4.76461i	−0.114237	+	0.285250i
$280$		0			0
$281$	−4.28629	−	7.42408i	−0.255699	−	0.442883i	0.709386	−	0.704820i	$-0.248972\pi$
$281$	−4.28629	−	7.42408i	−0.255699	−	0.442883i	−0.965085	+	0.261937i	$0.915639\pi$
$282$		0			0
$283$	−10.1865	+	17.6435i	−0.605524	+	1.04880i	0.386445	+	0.922313i	$0.373703\pi$
$283$	−10.1865	+	17.6435i	−0.605524	+	1.04880i	−0.991968	+	0.126485i	$0.959630\pi$
$284$		0			0
$285$	−1.00576	+	2.07013i	−0.0595764	+	0.122624i
$286$		0			0
$287$	0.637582			0.0376353
$288$		0			0
$289$	5.16885			0.304050
$290$		0			0
$291$	13.8312	+	20.4382i	0.810799	+	1.19811i
$292$		0			0
$293$	8.57795	−	14.8574i	0.501129	−	0.867981i	−0.498870	−	0.866677i	$-0.666251\pi$
$293$	8.57795	−	14.8574i	0.501129	−	0.867981i	0.999999	−	0.00130436i	$-0.000415189\pi$
$294$		0			0
$295$	5.97265	+	10.3449i	0.347741	+	0.602305i
$296$		0			0
$297$	−13.7737	−	15.1571i	−0.799230	−	0.879505i
$298$		0			0
$299$	0.425295	+	0.736632i	0.0245954	+	0.0426005i
$300$		0			0
$301$	−16.4429	+	28.4799i	−0.947753	+	1.64156i
$302$		0			0
$303$	2.08844	+	3.08608i	0.119978	+	0.177290i
$304$		0			0
$305$	−7.96139			−0.455868
$306$		0			0
$307$	−34.9119			−1.99253			−0.996263	−	0.0863739i	$-0.972472\pi$
$307$	−34.9119			−1.99253			−0.996263	+	0.0863739i	$0.972472\pi$
$308$		0			0
$309$	11.3774	−	23.4177i	0.647236	−	1.33219i
$310$		0			0
$311$	5.25737	−	9.10603i	0.298118	−	0.516355i	−0.677587	−	0.735442i	$-0.736974\pi$
$311$	5.25737	−	9.10603i	0.298118	−	0.516355i	0.975705	+	0.219087i	$0.0703078\pi$
$312$		0			0
$313$	13.7184	+	23.7610i	0.775412	+	1.34305i	0.934562	+	0.355799i	$0.115791\pi$
$313$	13.7184	+	23.7610i	0.775412	+	1.34305i	−0.159150	+	0.987254i	$0.550875\pi$
$314$		0			0
$315$	9.12606	−	1.31100i	0.514195	−	0.0738663i
$316$		0			0
$317$	13.0212	+	22.5535i	0.731346	+	1.26673i	0.956308	+	0.292361i	$0.0944408\pi$
$317$	13.0212	+	22.5535i	0.731346	+	1.26673i	−0.224962	+	0.974367i	$0.572226\pi$
$318$		0			0
$319$	−17.3402	+	30.0340i	−0.970863	+	1.68158i
$320$		0			0
$321$	−3.31119	+	0.236619i	−0.184813	+	0.0132068i
$322$		0			0
$323$	6.25643			0.348117
$324$		0			0
$325$	0.792538			0.0439621
$326$		0			0
$327$	−8.33979	+	0.595964i	−0.461191	+	0.0329569i
$328$		0			0
$329$	−14.2067	+	24.6067i	−0.783239	+	1.35661i
$330$		0			0
$331$	14.1007	+	24.4232i	0.775046	+	1.34242i	0.934769	+	0.355257i	$0.115607\pi$
$331$	14.1007	+	24.4232i	0.775046	+	1.34242i	−0.159723	+	0.987162i	$0.551060\pi$
$332$		0			0
$333$	24.1067	−	3.46303i	1.32104	−	0.189773i
$334$		0			0
$335$	−0.00644531	−	0.0111636i	−0.000352145	−	0.000609933i
$336$		0			0
$337$	−0.0283554	+	0.0491129i	−0.00154461	+	0.00267535i	−0.866797	−	0.498662i	$-0.833825\pi$
$337$	−0.0283554	+	0.0491129i	−0.00154461	+	0.00267535i	0.865252	+	0.501337i	$0.167158\pi$
$338$		0			0
$339$	−9.81389	+	20.1996i	−0.533017	+	1.09709i
$340$		0			0
$341$	6.74320			0.365165
$342$		0			0
$343$	−13.9991			−0.755881
$344$		0			0
$345$	1.04184	+	1.53953i	0.0560910	+	0.0828853i
$346$		0			0
$347$	−11.4717	+	19.8695i	−0.615831	+	1.06665i	0.374407	+	0.927264i	$0.377846\pi$
$347$	−11.4717	+	19.8695i	−0.615831	+	1.06665i	−0.990238	+	0.139386i	$0.955487\pi$
$348$		0			0
$349$	13.8610	+	24.0079i	0.741960	+	1.28511i	0.951602	+	0.307334i	$0.0994370\pi$
$349$	13.8610	+	24.0079i	0.741960	+	1.28511i	−0.209641	+	0.977778i	$0.567230\pi$
$350$		0			0
$351$	−1.25464	+	3.92238i	−0.0669675	+	0.209361i
$352$		0			0
$353$	4.04406	+	7.00452i	0.215244	+	0.372813i	0.953348	−	0.301874i	$-0.0976121\pi$
$353$	4.04406	+	7.00452i	0.215244	+	0.372813i	−0.738104	+	0.674687i	$0.764279\pi$
$354$		0			0
$355$	−4.72120	+	8.17736i	−0.250575	+	0.434009i
$356$		0			0
$357$	−14.0466	−	20.7566i	−0.743427	−	1.09856i
$358$		0			0
$359$	9.65559			0.509603			0.254801	−	0.966993i	$-0.417990\pi$
$359$	9.65559			0.509603			0.254801	+	0.966993i	$0.417990\pi$
$360$		0			0
$361$	−17.2343			−0.907070
$362$		0			0
$363$	−3.43277	+	7.06556i	−0.180174	+	0.370846i
$364$		0			0
$365$	−3.57062	+	6.18449i	−0.186895	+	0.323711i
$366$		0			0
$367$	9.51291	+	16.4768i	0.496570	+	0.860084i	0.999992	−	0.00395655i	$-0.00125941\pi$
$367$	9.51291	+	16.4768i	0.496570	+	0.860084i	−0.503423	+	0.864040i	$0.667926\pi$
$368$		0			0
$369$	−0.231388	+	0.577775i	−0.0120456	+	0.0300778i
$370$		0			0
$371$	19.6589	+	34.0501i	1.02064	+	1.76780i
$372$		0			0
$373$	7.88569	−	13.6584i	0.408306	−	0.707206i	−0.586394	−	0.810026i	$-0.699453\pi$
$373$	7.88569	−	13.6584i	0.408306	−	0.707206i	0.994700	+	0.102820i	$0.0327864\pi$
$374$		0			0
$375$	1.72765	−	0.123458i	0.0892152	−	0.00637535i
$376$		0			0
$377$	6.97339			0.359148
$378$		0			0
$379$	−0.168851			−0.00867331			−0.00433665	−	0.999991i	$-0.501380\pi$
$379$	−0.168851			−0.00867331			−0.00433665	+	0.999991i	$0.501380\pi$
$380$		0			0
$381$	0.138429	−	0.00989216i	0.00709191	−	0.000506791i
$382$		0			0
$383$	5.83924	−	10.1139i	0.298371	−	0.516794i	−0.677392	−	0.735622i	$-0.736890\pi$
$383$	5.83924	−	10.1139i	0.298371	−	0.516794i	0.975764	+	0.218828i	$0.0702233\pi$
$384$		0			0
$385$	−6.05657	−	10.4903i	−0.308672	−	0.534635i
$386$		0			0
$387$	−19.8411	−	25.2363i	−1.00858	−	1.28283i
$388$		0			0
$389$	−1.32640	−	2.29740i	−0.0672513	−	0.116483i	0.830439	−	0.557109i	$-0.188090\pi$
$389$	−1.32640	−	2.29740i	−0.0672513	−	0.116483i	−0.897690	+	0.440627i	$0.854756\pi$
$390$		0			0
$391$	2.52663	−	4.37625i	0.127777	−	0.221316i
$392$		0			0
$393$	−15.6113	+	32.1323i	−0.787488	+	1.62086i
$394$		0			0
$395$	−7.20847			−0.362697
$396$		0			0
$397$	24.2138			1.21525			0.607627	−	0.794223i	$-0.292122\pi$
$397$	24.2138			1.21525			0.607627	+	0.794223i	$0.292122\pi$
$398$		0			0
$399$	−3.96420	−	5.85787i	−0.198458	−	0.293260i
$400$		0			0
$401$	15.1748	−	26.2836i	0.757796	−	1.31254i	−0.186177	−	0.982516i	$-0.559610\pi$
$401$	15.1748	−	26.2836i	0.757796	−	1.31254i	0.943972	−	0.330025i	$-0.107057\pi$
$402$		0			0
$403$	−0.677949	−	1.17424i	−0.0337710	−	0.0584931i
$404$		0			0
$405$	−2.12396	+	8.74579i	−0.105540	+	0.434582i
$406$		0			0
$407$	−15.9986	−	27.7103i	−0.793019	−	1.37355i
$408$		0			0
$409$	−10.9849	+	19.0265i	−0.543170	+	0.940798i	0.455550	+	0.890210i	$0.349443\pi$
$409$	−10.9849	+	19.0265i	−0.543170	+	0.940798i	−0.998720	+	0.0505874i	$0.983891\pi$
$410$		0			0
$411$	−1.76260	−	2.60458i	−0.0869426	−	0.128474i
$412$		0			0
$413$	−36.7109			−1.80642
$414$		0			0
$415$	−11.4055			−0.559873
$416$		0			0
$417$	2.21211	−	4.55312i	0.108328	−	0.222967i
$418$		0			0
$419$	−11.4500	+	19.8319i	−0.559367	+	0.968852i	0.438182	+	0.898886i	$0.355622\pi$
$419$	−11.4500	+	19.8319i	−0.559367	+	0.968852i	−0.997549	+	0.0699660i	$0.977711\pi$
$420$		0			0
$421$	5.53297	+	9.58338i	0.269660	+	0.467065i	0.968774	−	0.247945i	$-0.0797552\pi$
$421$	5.53297	+	9.58338i	0.269660	+	0.467065i	−0.699114	+	0.715010i	$0.746422\pi$
$422$		0			0
$423$	−17.1427	−	21.8042i	−0.833506	−	1.06015i
$424$		0			0
$425$	−2.35419	−	4.07758i	−0.114195	−	0.197792i
$426$		0			0
$427$	12.2337	−	21.1893i	0.592028	−	1.02542i
$428$		0			0
$429$	5.39677	−	0.385655i	0.260559	−	0.0186196i
$430$		0			0
$431$	23.0586			1.11069			0.555346	−	0.831619i	$-0.312586\pi$
$431$	23.0586			1.11069			0.555346	+	0.831619i	$0.312586\pi$
$432$		0			0
$433$	−12.3970			−0.595763			−0.297881	−	0.954603i	$-0.596280\pi$
$433$	−12.3970			−0.595763			−0.297881	+	0.954603i	$0.596280\pi$
$434$		0			0
$435$	15.2012	−	1.08628i	0.728842	−	0.0520833i
$436$		0			0
$437$	0.713058	−	1.23505i	0.0341102	−	0.0590806i
$438$		0			0
$439$	0.116062	+	0.201026i	0.00553934	+	0.00959443i	0.868782	−	0.495195i	$-0.164903\pi$
$439$	0.116062	+	0.201026i	0.00553934	+	0.00959443i	−0.863242	+	0.504790i	$0.831570\pi$
$440$		0			0
$441$	−2.72680	+	6.80883i	−0.129848	+	0.324230i
$442$		0			0
$443$	−18.7924	−	32.5493i	−0.892852	−	1.54646i	−0.836441	−	0.548057i	$-0.815368\pi$
$443$	−18.7924	−	32.5493i	−0.892852	−	1.54646i	−0.0564112	−	0.998408i	$-0.517966\pi$
$444$		0			0
$445$	0.839965	−	1.45486i	0.0398182	−	0.0689671i
$446$		0			0
$447$	−9.16822	+	18.8707i	−0.433642	+	0.892552i
$448$		0			0
$449$	15.5247			0.732658			0.366329	−	0.930485i	$-0.380614\pi$
$449$	15.5247			0.732658			0.366329	+	0.930485i	$0.380614\pi$
$450$		0			0
$451$	0.817708			0.0385044
$452$		0			0
$453$	13.0443	+	19.2755i	0.612876	+	0.905642i
$454$		0			0
$455$	−1.21783	+	2.10935i	−0.0570929	+	0.0988877i
$456$		0			0
$457$	−16.9907	−	29.4287i	−0.794791	−	1.37662i	−0.922972	−	0.384868i	$-0.874247\pi$
$457$	−16.9907	−	29.4287i	−0.794791	−	1.37662i	0.128181	−	0.991751i	$-0.459086\pi$
$458$		0			0
$459$	23.9073	−	5.19615i	1.11590	−	0.242536i
$460$		0			0
$461$	10.5502	+	18.2735i	0.491371	+	0.851080i	0.999951	−	0.00993538i	$-0.00316258\pi$
$461$	10.5502	+	18.2735i	0.491371	+	0.851080i	−0.508580	+	0.861015i	$0.669829\pi$
$462$		0			0
$463$	−4.62933	+	8.01824i	−0.215143	+	0.372639i	−0.953317	−	0.301972i	$-0.902355\pi$
$463$	−4.62933	+	8.01824i	−0.215143	+	0.372639i	0.738174	+	0.674611i	$0.235689\pi$
$464$		0			0
$465$	−1.66077	−	2.45411i	−0.0770164	−	0.113807i
$466$		0			0
$467$	32.8904			1.52199			0.760993	−	0.648761i	$-0.224712\pi$
$467$	32.8904			1.52199			0.760993	+	0.648761i	$0.224712\pi$
$468$		0			0
$469$	0.0396161			0.00182930
$470$		0			0
$471$	−16.5819	+	34.1300i	−0.764054	+	1.57263i
$472$		0			0
$473$	−21.0882	+	36.5259i	−0.969639	+	1.67946i
$474$		0			0
$475$	−0.664393	−	1.15076i	−0.0304845	−	0.0528006i
$476$		0			0
$477$	−37.9906	+	5.45752i	−1.73947	+	0.249883i
$478$		0			0
$479$	−8.33678	−	14.4397i	−0.380917	−	0.659768i	0.610276	−	0.792189i	$-0.291058\pi$
$479$	−8.33678	−	14.4397i	−0.380917	−	0.659768i	−0.991194	+	0.132421i	$0.957725\pi$
$480$		0			0
$481$	−3.21693	+	5.57188i	−0.146679	+	0.254056i
$482$		0			0
$483$	−5.69839	+	0.407209i	−0.259286	+	0.0185286i
$484$		0			0
$485$	−14.2481			−0.646972
$486$		0			0
$487$	17.0258			0.771513			0.385757	−	0.922601i	$-0.373940\pi$
$487$	17.0258			0.771513			0.385757	+	0.922601i	$0.373940\pi$
$488$		0			0
$489$	−13.6701	+	0.976870i	−0.618183	+	0.0441756i
$490$		0			0
$491$	−19.1292	+	33.1328i	−0.863290	+	1.49526i	0.00544576	+	0.999985i	$0.498267\pi$
$491$	−19.1292	+	33.1328i	−0.863290	+	1.49526i	−0.868735	+	0.495276i	$0.835067\pi$
$492$		0			0
$493$	−20.7141	−	35.8778i	−0.932914	−	1.61586i
$494$		0			0
$495$	11.7043	−	1.68137i	0.526069	−	0.0755720i
$496$		0			0
$497$	−14.5094	−	25.1310i	−0.650836	−	1.12728i
$498$		0			0
$499$	4.77992	−	8.27906i	0.213978	−	0.370622i	−0.738978	−	0.673730i	$-0.764691\pi$
$499$	4.77992	−	8.27906i	0.213978	−	0.370622i	0.952956	+	0.303108i	$0.0980244\pi$
$500$		0			0
$501$	−1.47268	+	3.03116i	−0.0657943	+	0.135422i
$502$		0			0
$503$	−11.7155			−0.522370			−0.261185	−	0.965289i	$-0.584113\pi$
$503$	−11.7155			−0.522370			−0.261185	+	0.965289i	$0.584113\pi$
$504$		0			0
$505$	−2.15139			−0.0957357
$506$		0			0
$507$	12.0099	+	17.7469i	0.533378	+	0.788168i
$508$		0			0
$509$	17.0776	−	29.5793i	0.756953	−	1.31108i	−0.187445	−	0.982275i	$-0.560021\pi$
$509$	17.0776	−	29.5793i	0.756953	−	1.31108i	0.944398	−	0.328806i	$-0.106646\pi$
$510$		0			0
$511$	−10.9734	−	19.0065i	−0.485434	−	0.840796i
$512$		0			0
$513$	6.74705	−	1.46644i	0.297890	−	0.0647451i
$514$		0			0
$515$	7.51572	+	13.0176i	0.331182	+	0.573624i
$516$		0			0
$517$	−18.2202	+	31.5584i	−0.801325	+	1.38794i
$518$		0			0
$519$	−3.89128	−	5.75012i	−0.170808	−	0.252402i
$520$		0			0
$521$	14.5007			0.635288			0.317644	−	0.948210i	$-0.397108\pi$
$521$	14.5007			0.635288			0.317644	+	0.948210i	$0.397108\pi$
$522$		0			0
$523$	11.4900			0.502424			0.251212	−	0.967932i	$-0.419171\pi$
$523$	11.4900			0.502424			0.251212	+	0.967932i	$0.419171\pi$
$524$		0			0
$525$	−2.32616	+	4.78785i	−0.101522	+	0.208959i
$526$		0			0
$527$	−4.02762	+	6.97604i	−0.175446	+	0.303881i
$528$		0			0
$529$	10.9241	+	18.9210i	0.474960	+	0.822654i
$530$		0			0
$531$	13.3229	−	33.2673i	0.578165	−	1.44368i
$532$		0			0
$533$	−0.0822108	−	0.142393i	−0.00356094	−	0.00616774i
$534$		0			0
$535$	0.958297	−	1.65982i	0.0414308	−	0.0717602i
$536$		0			0
$537$	−9.82175	+	0.701866i	−0.423840	+	0.0302877i
$538$		0			0
$539$	9.63632			0.415066
$540$		0			0
$541$	38.1707			1.64109			0.820543	−	0.571585i	$-0.193671\pi$
$541$	38.1707			1.64109			0.820543	+	0.571585i	$0.193671\pi$
$542$		0			0
$543$	8.79046	−	0.628170i	0.377235	−	0.0269573i
$544$		0			0
$545$	2.41363	−	4.18053i	0.103388	−	0.179074i
$546$		0			0
$547$	−13.5359	−	23.4449i	−0.578754	−	1.00243i	−0.995623	−	0.0934646i	$-0.970206\pi$
$547$	−13.5359	−	23.4449i	−0.578754	−	1.00243i	0.416869	−	0.908967i	$-0.363128\pi$
$548$		0			0
$549$	14.7619	+	18.7760i	0.630024	+	0.801341i
$550$		0			0
$551$	−5.84587	−	10.1253i	−0.249042	−	0.431354i
$552$		0			0
$553$	11.0767	−	19.1854i	0.471029	−	0.815847i
$554$		0			0
$555$	−6.14459	+	12.6472i	−0.260823	+	0.536844i
$556$		0			0
$557$	20.3337			0.861568			0.430784	−	0.902455i	$-0.358237\pi$
$557$	20.3337			0.861568			0.430784	+	0.902455i	$0.358237\pi$
$558$		0			0
$559$	8.48069			0.358695
$560$		0			0
$561$	−18.0150	−	26.6206i	−0.760594	−	1.12392i
$562$		0			0
$563$	0.0968695	−	0.167783i	0.00408256	−	0.00707121i	−0.863977	−	0.503531i	$-0.832034\pi$
$563$	0.0968695	−	0.167783i	0.00408256	−	0.00707121i	0.868059	+	0.496460i	$0.165367\pi$
$564$		0			0
$565$	−6.48291	−	11.2287i	−0.272738	−	0.472396i
$566$		0			0
$567$	−20.0133	−	19.0919i	−0.840479	−	0.801785i
$568$		0			0
$569$	8.59136	+	14.8807i	0.360168	+	0.623830i	0.987988	−	0.154529i	$-0.0493859\pi$
$569$	8.59136	+	14.8807i	0.360168	+	0.623830i	−0.627820	+	0.778359i	$0.716053\pi$
$570$		0			0
$571$	12.8366	−	22.2336i	0.537195	−	0.930449i	−0.461859	−	0.886953i	$-0.652817\pi$
$571$	12.8366	−	22.2336i	0.537195	−	0.930449i	0.999054	−	0.0434953i	$-0.0138494\pi$
$572$		0			0
$573$	9.99168	+	14.7646i	0.417409	+	0.616801i
$574$		0			0
$575$	−1.07325			−0.0447575
$576$		0			0
$577$	−17.3942			−0.724132			−0.362066	−	0.932153i	$-0.617928\pi$
$577$	−17.3942			−0.724132			−0.362066	+	0.932153i	$0.617928\pi$
$578$		0			0
$579$	18.5665	−	38.2149i	0.771599	−	1.58816i
$580$		0			0
$581$	17.5259	−	30.3558i	0.727099	−	1.25937i
$582$		0			0
$583$	25.2128	+	43.6698i	1.04421	+	1.80862i
$584$		0			0
$585$	−1.46952	−	1.86911i	−0.0607570	−	0.0772781i
$586$		0			0
$587$	−6.75930	−	11.7074i	−0.278986	−	0.483218i	0.692147	−	0.721757i	$-0.256665\pi$
$587$	−6.75930	−	11.7074i	−0.278986	−	0.483218i	−0.971133	+	0.238539i	$0.923332\pi$
$588$		0			0
$589$	−1.13666	+	1.96876i	−0.0468354	+	0.0811213i
$590$		0			0
$591$	−30.9463	+	2.21143i	−1.27296	+	0.0909662i
$592$		0			0
$593$	−37.8636			−1.55487			−0.777437	−	0.628961i	$-0.783480\pi$
$593$	−37.8636			−1.55487			−0.777437	+	0.628961i	$0.783480\pi$
$594$		0			0
$595$	14.4700			0.593213
$596$		0			0
$597$	17.4755	−	1.24881i	0.715226	−	0.0511103i
$598$		0			0
$599$	−22.1071	+	38.2907i	−0.903273	+	1.56451i	−0.0800542	+	0.996791i	$0.525509\pi$
$599$	−22.1071	+	38.2907i	−0.903273	+	1.56451i	−0.823219	+	0.567724i	$0.807824\pi$
$600$		0			0
$601$	18.3066	+	31.7080i	0.746742	+	1.29340i	0.949376	+	0.314141i	$0.101717\pi$
$601$	18.3066	+	31.7080i	0.746742	+	1.29340i	−0.202634	+	0.979255i	$0.564950\pi$
$602$		0			0
$603$	−0.0143772	+	0.0359000i	−0.000585487	+	0.00146196i
$604$		0			0
$605$	−2.26764	−	3.92766i	−0.0921925	−	0.159682i
$606$		0			0
$607$	2.31634	−	4.01202i	0.0940174	−	0.162843i	−0.815181	−	0.579207i	$-0.803362\pi$
$607$	2.31634	−	4.01202i	0.0940174	−	0.162843i	0.909198	+	0.416364i	$0.136696\pi$
$608$		0			0
$609$	−20.4674	+	42.1274i	−0.829380	+	1.70709i
$610$		0			0
$611$	7.32731			0.296431
$612$		0			0
$613$	43.3957			1.75273			0.876367	−	0.481644i	$-0.159960\pi$
$613$	43.3957			1.75273			0.876367	+	0.481644i	$0.159960\pi$
$614$		0			0
$615$	−0.201392	−	0.297595i	−0.00812091	−	0.0120002i
$616$		0			0
$617$	10.5390	−	18.2540i	0.424283	−	0.734879i	−0.572070	−	0.820205i	$-0.693860\pi$
$617$	10.5390	−	18.2540i	0.424283	−	0.734879i	0.996353	+	0.0853252i	$0.0271929\pi$
$618$		0			0
$619$	−19.2694	−	33.3755i	−0.774502	−	1.34148i	−0.935074	−	0.354452i	$-0.884667\pi$
$619$	−19.2694	−	33.3755i	−0.774502	−	1.34148i	0.160572	−	0.987024i	$-0.448666\pi$
$620$		0			0
$621$	1.69901	−	5.31164i	0.0681791	−	0.213149i
$622$		0			0
$623$	2.58142	+	4.47115i	0.103422	+	0.179133i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−5.08414	−	7.51280i	−0.203041	−	0.300032i
$628$		0			0
$629$	38.2228			1.52404
$630$		0			0
$631$	17.6062			0.700891			0.350446	−	0.936583i	$-0.386030\pi$
$631$	17.6062			0.700891			0.350446	+	0.936583i	$0.386030\pi$
$632$		0			0
$633$	−4.39463	+	9.04532i	−0.174671	+	0.359519i
$634$		0			0
$635$	−0.0400628	+	0.0693908i	−0.00158984	+	0.00275369i
$636$		0			0
$637$	−0.968818	−	1.67804i	−0.0383859	−	0.0664864i
$638$		0			0
$639$	28.0394	−	4.02797i	1.10922	−	0.159344i
$640$		0			0
$641$	24.6556	+	42.7047i	0.973836	+	1.68673i	0.683722	+	0.729742i	$0.260360\pi$
$641$	24.6556	+	42.7047i	0.973836	+	1.68673i	0.290114	+	0.956992i	$0.406307\pi$
$642$		0			0
$643$	19.7262	−	34.1668i	0.777926	−	1.34741i	−0.155209	−	0.987882i	$-0.549605\pi$
$643$	19.7262	−	34.1668i	0.777926	−	1.34741i	0.933135	−	0.359526i	$-0.117061\pi$
$644$		0			0
$645$	18.4870	−	1.32108i	0.727923	−	0.0520177i
$646$		0			0
$647$	−27.4491			−1.07914			−0.539568	−	0.841942i	$-0.681412\pi$
$647$	−27.4491			−1.07914			−0.539568	+	0.841942i	$0.681412\pi$
$648$		0			0
$649$	−47.0822			−1.84814
$650$		0			0
$651$	9.08362	−	0.649119i	0.356015	−	0.0254410i
$652$		0			0
$653$	−9.35165	+	16.1975i	−0.365958	+	0.633858i	−0.988929	−	0.148387i	$-0.952592\pi$
$653$	−9.35165	+	16.1975i	−0.365958	+	0.633858i	0.622971	+	0.782245i	$0.285925\pi$
$654$		0			0
$655$	−10.3126	−	17.8620i	−0.402947	−	0.697925i
$656$		0			0
$657$	21.2060	−	3.04633i	0.827325	−	0.118849i
$658$		0			0
$659$	2.00345	+	3.47008i	0.0780435	+	0.135175i	0.902406	−	0.430887i	$-0.141799\pi$
$659$	2.00345	+	3.47008i	0.0780435	+	0.135175i	−0.824362	+	0.566063i	$0.808466\pi$
$660$		0			0
$661$	8.56654	−	14.8377i	0.333200	−	0.577119i	−0.649938	−	0.759988i	$-0.725205\pi$
$661$	8.56654	−	14.8377i	0.333200	−	0.577119i	0.983137	+	0.182869i	$0.0585383\pi$
$662$		0			0
$663$	−2.82444	+	5.81346i	−0.109692	+	0.225776i
$664$		0			0
$665$	4.08369			0.158359
$666$		0			0
$667$	−9.44329			−0.365646
$668$		0			0
$669$	7.88873	+	11.6571i	0.304996	+	0.450690i
$670$		0			0
$671$	15.6898	−	27.1756i	0.605699	−	1.04910i
$672$		0			0
$673$	−24.1171	−	41.7720i	−0.929646	−	1.61019i	−0.783914	−	0.620870i	$-0.786779\pi$
$673$	−24.1171	−	41.7720i	−0.929646	−	1.61019i	−0.145732	−	0.989324i	$-0.546554\pi$
$674$		0			0
$675$	−3.49455	−	3.84554i	−0.134505	−	0.148015i
$676$		0			0
$677$	−13.2099	−	22.8803i	−0.507699	−	0.879361i	−0.999960	−	0.00891350i	$-0.997163\pi$
$677$	−13.2099	−	22.8803i	−0.507699	−	0.879361i	0.492261	−	0.870448i	$-0.336171\pi$
$678$		0			0
$679$	21.8939	−	37.9214i	0.840212	−	1.45529i
$680$		0			0
$681$	−12.9776	−	19.1769i	−0.497303	−	0.734861i
$682$		0			0
$683$	22.7063			0.868832			0.434416	−	0.900712i	$-0.356955\pi$
$683$	22.7063			0.868832			0.434416	+	0.900712i	$0.356955\pi$
$684$		0			0
$685$	1.81573			0.0693754
$686$		0			0
$687$	18.6392	−	38.3646i	0.711131	−	1.46370i
$688$		0			0
$689$	5.06968	−	8.78095i	0.193140	−	0.334528i
$690$		0			0
$691$	24.4050	+	42.2707i	0.928411	+	1.60805i	0.785982	+	0.618249i	$0.212158\pi$
$691$	24.4050	+	42.2707i	0.928411	+	1.60805i	0.142429	+	0.989805i	$0.454509\pi$
$692$		0			0
$693$	−13.5101	+	33.7347i	−0.513206	+	1.28148i
$694$		0			0
$695$	1.46129	+	2.53103i	0.0554299	+	0.0960073i
$696$		0			0
$697$	−0.488405	+	0.845943i	−0.0184997	+	0.0320424i
$698$		0			0
$699$	−36.8387	+	2.63251i	−1.39337	+	0.0995706i
$700$		0			0
$701$	52.3028			1.97545			0.987724	−	0.156208i	$-0.0499271\pi$
$701$	52.3028			1.97545			0.987724	+	0.156208i	$0.0499271\pi$
$702$		0			0
$703$	10.7871			0.406845
$704$		0			0
$705$	15.9727	−	1.14142i	0.601568	−	0.0429883i
$706$		0			0
$707$	3.30588	−	5.72595i	0.124330	−	0.215347i
$708$		0			0
$709$	−23.0672	−	39.9535i	−0.866307	−	1.50049i	−0.865744	−	0.500487i	$-0.833154\pi$
$709$	−23.0672	−	39.9535i	−0.866307	−	1.50049i	−0.000562604	−	1.00000i	$-0.500179\pi$
$710$		0			0
$711$	13.3659	+	17.0003i	0.501259	+	0.637562i
$712$		0			0
$713$	0.918072	+	1.59015i	0.0343821	+	0.0595515i
$714$		0			0
$715$	−1.56189	+	2.70527i	−0.0584112	+	0.101171i
$716$		0			0
$717$	−1.02406	+	2.10778i	−0.0382440	+	0.0787165i
$718$		0			0
$719$	21.8099			0.813371			0.406685	−	0.913568i	$-0.366685\pi$
$719$	21.8099			0.813371			0.406685	+	0.913568i	$0.366685\pi$
$720$		0			0
$721$	−46.1953			−1.72040
$722$		0			0
$723$	13.4759	+	19.9133i	0.501176	+	0.740584i
$724$		0			0
$725$	−4.39940	+	7.61999i	−0.163390	+	0.282999i
$726$		0			0
$727$	−0.596047	−	1.03238i	−0.0221061	−	0.0382890i	0.854761	−	0.519022i	$-0.173704\pi$
$727$	−0.596047	−	1.03238i	−0.0221061	−	0.0382890i	−0.876867	+	0.480733i	$0.840371\pi$
$728$		0			0
$729$	24.5641	−	11.2073i	0.909783	−	0.415083i
$730$		0			0
$731$	−25.1914	−	43.6328i	−0.931738	−	1.61382i
$732$		0			0
$733$	12.8883	−	22.3231i	0.476039	−	0.824523i	−0.523585	−	0.851974i	$-0.675406\pi$
$733$	12.8883	−	22.3231i	0.476039	−	0.824523i	0.999623	+	0.0274508i	$0.00873895\pi$
$734$		0			0
$735$	−2.37331	−	3.50703i	−0.0875410	−	0.129359i
$736$		0			0
$737$	0.0508081			0.00187154
$738$		0			0
$739$	−45.7839			−1.68419			−0.842094	−	0.539331i	$-0.818677\pi$
$739$	−45.7839			−1.68419			−0.842094	+	0.539331i	$0.818677\pi$
$740$		0			0
$741$	−0.797107	+	1.64066i	−0.0292824	+	0.0602712i
$742$		0			0
$743$	11.0670	−	19.1686i	0.406009	−	0.703228i	−0.588430	−	0.808549i	$-0.700254\pi$
$743$	11.0670	−	19.1686i	0.406009	−	0.703228i	0.994438	+	0.105321i	$0.0335869\pi$
$744$		0			0
$745$	−6.05639	−	10.4900i	−0.221889	−	0.384323i
$746$		0			0
$747$	21.1479	+	26.8985i	0.773763	+	0.984166i
$748$		0			0
$749$	2.94508	+	5.10103i	0.107611	+	0.186388i
$750$		0			0
$751$	−7.62749	+	13.2112i	−0.278331	+	0.482084i	−0.970970	−	0.239201i	$-0.923115\pi$
$751$	−7.62749	+	13.2112i	−0.278331	+	0.482084i	0.692639	+	0.721284i	$0.256448\pi$
$752$		0			0
$753$	14.6599	−	1.04760i	0.534236	−	0.0381767i
$754$		0			0
$755$	−13.4375			−0.489041
$756$		0			0
$757$	−28.3178			−1.02923			−0.514614	−	0.857422i	$-0.672065\pi$
$757$	−28.3178			−1.02923			−0.514614	+	0.857422i	$0.672065\pi$
$758$		0			0
$759$	−7.30826	+	0.522251i	−0.265273	+	0.0189565i
$760$		0			0
$761$	9.79106	−	16.9586i	0.354925	−	0.614749i	−0.632180	−	0.774822i	$-0.717840\pi$
$761$	9.79106	−	16.9586i	0.354925	−	0.614749i	0.987105	+	0.160073i	$0.0511729\pi$
$762$		0			0
$763$	7.41768	+	12.8478i	0.268538	+	0.465121i
$764$		0			0
$765$	−5.25138	+	13.1127i	−0.189864	+	0.474090i
$766$		0			0
$767$	4.73355	+	8.19875i	0.170919	+	0.296040i
$768$		0			0
$769$	12.0853	−	20.9324i	0.435809	−	0.754843i	−0.561553	−	0.827441i	$-0.689796\pi$
$769$	12.0853	−	20.9324i	0.435809	−	0.754843i	0.997361	+	0.0725983i	$0.0231291\pi$
$770$		0			0
$771$	15.5567	−	32.0200i	0.560262	−	1.15317i
$772$		0			0
$773$	33.7841			1.21513			0.607565	−	0.794270i	$-0.292147\pi$
$773$	33.7841			1.21513			0.607565	+	0.794270i	$0.292147\pi$
$774$		0			0
$775$	1.71083			0.0614548
$776$		0			0
$777$	−24.2188	−	35.7879i	−0.868843	−	1.28388i
$778$		0			0
$779$	−0.137836	+	0.238740i	−0.00493850	+	0.00855374i
$780$		0			0
$781$	−18.6085	−	32.2309i	−0.665865	−	1.15331i
$782$		0			0
$783$	−30.7478	−	33.8361i	−1.09884	−	1.20920i
$784$		0			0
$785$	−10.9538	−	18.9725i	−0.390956	−	0.677156i
$786$		0			0
$787$	1.92949	−	3.34198i	0.0687791	−	0.119129i	−0.829585	−	0.558380i	$-0.811423\pi$
$787$	1.92949	−	3.34198i	0.0687791	−	0.119129i	0.898364	+	0.439252i	$0.144756\pi$
$788$		0			0
$789$	−17.2796	−	25.5339i	−0.615170	−	0.909031i
$790$		0			0
$791$	39.8472			1.41680
$792$		0			0
$793$	−6.30970			−0.224064
$794$		0			0
$795$	9.68349	−	19.9312i	0.343438	−	0.706888i
$796$		0			0
$797$	−0.0297864	+	0.0515916i	−0.00105509	+	0.00182747i	−0.866552	−	0.499086i	$-0.833669\pi$
$797$	−0.0297864	+	0.0515916i	−0.00105509	+	0.00182747i	0.865497	+	0.500913i	$0.167003\pi$
$798$		0			0
$799$	−21.7654	−	37.6988i	−0.770004	−	1.33369i
$800$		0			0
$801$	−4.98858	+	0.716631i	−0.176263	+	0.0253209i
$802$		0			0
$803$	−14.0735	−	24.3760i	−0.496644	−	0.860212i
$804$		0			0
$805$	1.64918	−	2.85646i	0.0581259	−	0.100677i
$806$		0			0
$807$	−5.27071	+	0.376647i	−0.185538	+	0.0132586i
$808$		0			0
$809$	−20.1327			−0.707828			−0.353914	−	0.935278i	$-0.615150\pi$
$809$	−20.1327			−0.707828			−0.353914	+	0.935278i	$0.615150\pi$
$810$		0			0
$811$	−7.24301			−0.254337			−0.127168	−	0.991881i	$-0.540589\pi$
$811$	−7.24301			−0.254337			−0.127168	+	0.991881i	$0.540589\pi$
$812$		0			0
$813$	11.6624	−	0.833401i	0.409019	−	0.0292286i
$814$		0			0
$815$	3.95628	−	6.85248i	0.138582	−	0.240032i
$816$		0			0
$817$	−7.10945	−	12.3139i	−0.248728	−	0.430810i
$818$		0			0
$819$	7.23275	−	1.03902i	0.252733	−	0.0363061i
$820$		0			0
$821$	−20.1910	−	34.9718i	−0.704670	−	1.22052i	−0.966811	−	0.255494i	$-0.917762\pi$
$821$	−20.1910	−	34.9718i	−0.704670	−	1.22052i	0.262141	−	0.965030i	$-0.415571\pi$
$822$		0			0
$823$	6.32199	−	10.9500i	0.220371	−	0.381693i	−0.734550	−	0.678555i	$-0.762607\pi$
$823$	6.32199	−	10.9500i	0.220371	−	0.381693i	0.954921	+	0.296861i	$0.0959400\pi$
$824$		0			0
$825$	−2.98333	+	6.14049i	−0.103866	+	0.213784i
$826$		0			0
$827$	11.7305			0.407910			0.203955	−	0.978980i	$-0.434620\pi$
$827$	11.7305			0.407910			0.203955	+	0.978980i	$0.434620\pi$
$828$		0			0
$829$	23.9910			0.833242			0.416621	−	0.909080i	$-0.363214\pi$
$829$	23.9910			0.833242			0.416621	+	0.909080i	$0.363214\pi$
$830$		0			0
$831$	−3.01022	−	4.44817i	−0.104423	−	0.154305i
$832$		0			0
$833$	−5.75564	+	9.96906i	−0.199421	+	0.345407i
$834$		0			0
$835$	−0.972828	−	1.68499i	−0.0336661	−	0.0583114i
$836$		0			0
$837$	−2.70835	+	8.46712i	−0.0936141	+	0.292667i
$838$		0			0
$839$	−21.7069	−	37.5974i	−0.749404	−	1.29801i	−0.948109	−	0.317947i	$-0.897007\pi$
$839$	−21.7069	−	37.5974i	−0.749404	−	1.29801i	0.198704	−	0.980059i	$-0.436327\pi$
$840$		0			0
$841$	−24.2095	+	41.9321i	−0.834810	+	1.44593i
$842$		0			0
$843$	−8.32175	−	12.2970i	−0.286616	−	0.423531i
$844$		0			0
$845$	−12.3719			−0.425606
$846$		0			0
$847$	13.9380			0.478916
$848$		0			0
$849$	−15.4204	+	31.7393i	−0.529227	+	1.08929i
$850$		0			0
$851$	4.35633	−	7.54539i	0.149333	−	0.258653i
$852$		0			0
$853$	−12.6124	−	21.8453i	−0.431839	−	0.747967i	0.565193	−	0.824959i	$-0.308802\pi$
$853$	−12.6124	−	21.8453i	−0.431839	−	0.747967i	−0.997032	+	0.0769917i	$0.975469\pi$
$854$		0			0
$855$	−1.48203	+	3.70063i	−0.0506843	+	0.126559i
$856$		0			0
$857$	11.8982	+	20.6083i	0.406435	+	0.703965i	0.994487	−	0.104857i	$-0.0334386\pi$
$857$	11.8982	+	20.6083i	0.406435	+	0.703965i	−0.588053	+	0.808823i	$0.700105\pi$
$858$		0			0
$859$	−24.8368	+	43.0186i	−0.847420	+	1.46777i	0.0360829	+	0.999349i	$0.488512\pi$
$859$	−24.8368	+	43.0186i	−0.847420	+	1.46777i	−0.883503	+	0.468426i	$0.844821\pi$
$860$		0			0
$861$	1.10152	−	0.0787147i	0.0375396	−	0.00268259i
$862$		0			0
$863$	38.0981			1.29688			0.648438	−	0.761268i	$-0.275423\pi$
$863$	38.0981			1.29688			0.648438	+	0.761268i	$0.275423\pi$
$864$		0			0
$865$	4.00857			0.136296
$866$		0			0
$867$	8.92994	−	0.638137i	0.303277	−	0.0216723i
$868$		0			0
$869$	14.2060	−	24.6055i	0.481906	−	0.834686i
$870$		0			0
$871$	−0.00510815	−	0.00884758i	−0.000173083	−	0.000299789i
$872$		0			0
$873$	26.4187	+	33.6025i	0.894136	+	1.13727i
$874$		0			0
$875$	−1.53662	−	2.66151i	−0.0519474	−	0.0899755i
$876$		0			0
$877$	−8.34546	+	14.4548i	−0.281806	+	0.488103i	−0.971830	−	0.235684i	$-0.924267\pi$
$877$	−8.34546	+	14.4548i	−0.281806	+	0.488103i	0.690023	+	0.723787i	$0.257600\pi$
$878$		0			0
$879$	12.9854	−	26.7274i	0.437986	−	0.901493i
$880$		0			0
$881$	37.2975			1.25658			0.628292	−	0.777978i	$-0.283754\pi$
$881$	37.2975			1.25658			0.628292	+	0.777978i	$0.283754\pi$
$882$		0			0
$883$	−50.9964			−1.71617			−0.858083	−	0.513511i	$-0.828345\pi$
$883$	−50.9964			−1.71617			−0.858083	+	0.513511i	$0.828345\pi$
$884$		0			0
$885$	11.5958	+	17.1350i	0.389788	+	0.575987i
$886$		0			0
$887$	14.1983	−	24.5922i	0.476733	−	0.825726i	−0.522912	−	0.852387i	$-0.675154\pi$
$887$	14.1983	−	24.5922i	0.476733	−	0.825726i	0.999645	+	0.0266613i	$0.00848757\pi$
$888$		0			0
$889$	−0.123123	−	0.213255i	−0.00412941	−	0.00715235i
$890$		0			0
$891$	−25.6673	−	24.4856i	−0.859887	−	0.820300i
$892$		0			0
$893$	−6.14257	−	10.6392i	−0.205553	−	0.356029i
$894$		0			0
$895$	2.84252	−	4.92340i	0.0950151	−	0.164571i
$896$		0			0
$897$	0.825701	+	1.22013i	0.0275694	+	0.0407390i
$898$		0			0
$899$	15.0533			0.502054
$900$		0			0
$901$	−60.2369			−2.00678
$902$		0			0
$903$	−24.8914	+	51.2332i	−0.828335	+	1.70494i
$904$		0			0
$905$	−2.54406	+	4.40644i	−0.0845674	+	0.146475i
$906$		0			0
$907$	6.06162	+	10.4990i	0.201273	+	0.348615i	0.948939	−	0.315460i	$-0.102159\pi$
$907$	6.06162	+	10.4990i	0.201273	+	0.348615i	−0.747666	+	0.664075i	$0.768826\pi$
$908$		0			0
$909$	3.98909	+	5.07381i	0.132310	+	0.168288i
$910$		0			0
$911$	−6.66557	−	11.5451i	−0.220840	−	0.382506i	0.734223	−	0.678908i	$-0.237547\pi$
$911$	−6.66557	−	11.5451i	−0.220840	−	0.382506i	−0.955063	+	0.296402i	$0.904213\pi$
$912$		0			0
$913$	22.4773	−	38.9318i	0.743889	−	1.28845i
$914$		0			0
$915$	−13.7545	+	0.982898i	−0.454708	+	0.0324936i
$916$		0			0
$917$	63.3864			2.09320
$918$		0			0
$919$	41.0122			1.35287			0.676434	−	0.736503i	$-0.263524\pi$
$919$	41.0122			1.35287			0.676434	+	0.736503i	$0.263524\pi$
$920$		0			0
$921$	−60.3153	+	4.31015i	−1.98746	+	0.142024i
$922$		0			0
$923$	−3.74173	+	6.48087i	−0.123161	+	0.213320i
$924$		0			0
$925$	−4.05902	−	7.03043i	−0.133460	−	0.231159i
$926$		0			0
$927$	16.7649	−	41.8621i	0.550633	−	1.37493i
$928$		0			0
$929$	9.91815	+	17.1787i	0.325404	+	0.563616i	0.981594	−	0.190980i	$-0.0611664\pi$
$929$	9.91815	+	17.1787i	0.325404	+	0.563616i	−0.656190	+	0.754596i	$0.727833\pi$
$930$		0			0
$931$	−1.62434	+	2.81344i	−0.0532356	+	0.0922068i
$932$		0			0
$933$	7.95865	−	16.3810i	0.260555	−	0.536291i
$934$		0			0
$935$	18.5580			0.606911
$936$		0			0
$937$	26.4809			0.865094			0.432547	−	0.901611i	$-0.357615\pi$
$937$	26.4809			0.865094			0.432547	+	0.901611i	$0.357615\pi$
$938$		0			0
$939$	26.6341	+	39.3570i	0.869171	+	1.28437i
$940$		0			0
$941$	−14.1482	+	24.5055i	−0.461219	+	0.798855i	−0.999022	−	0.0442156i	$-0.985921\pi$
$941$	−14.1482	+	24.5055i	−0.461219	+	0.798855i	0.537803	+	0.843071i	$0.319254\pi$
$942$		0			0
$943$	0.111329	+	0.192828i	0.00362537	+	0.00627933i
$944$		0			0
$945$	15.6047	−	3.39162i	0.507622	−	0.110330i
$946$		0			0
$947$	11.7550	+	20.3603i	0.381988	+	0.661622i	0.991346	−	0.131273i	$-0.0419063\pi$
$947$	11.7550	+	20.3603i	0.381988	+	0.661622i	−0.609359	+	0.792895i	$0.708573\pi$
$948$		0			0
$949$	−2.82985	+	4.90144i	−0.0918608	+	0.159108i
$950$		0			0
$951$	25.2805	+	37.3568i	0.819776	+	1.21138i
$952$		0			0
$953$	34.8684			1.12950			0.564749	−	0.825263i	$-0.308973\pi$
$953$	34.8684			1.12950			0.564749	+	0.825263i	$0.308973\pi$
$954$		0			0
$955$	−10.2928			−0.333069
$956$		0			0
$957$	−26.2497	+	54.0290i	−0.848532	+	1.74651i
$958$		0			0
$959$	−2.79009	+	4.83258i	−0.0900967	+	0.156052i
$960$		0			0
$961$	14.0365	+	24.3120i	0.452791	+	0.784258i
$962$		0			0
$963$	−5.69135	+	0.817588i	−0.183401	+	0.0263464i
$964$		0			0
$965$	12.2648	+	21.2432i	0.394817	+	0.683843i
$966$		0			0
$967$	−17.6356	+	30.5458i	−0.567123	+	0.982286i	0.429725	+	0.902960i	$0.358610\pi$
$967$	−17.6356	+	30.5458i	−0.567123	+	0.982286i	−0.996849	+	0.0793268i	$0.974723\pi$
$968$		0			0
$969$	10.8089	−	0.772408i	0.347232	−	0.0248133i
$970$		0			0
$971$	−59.4015			−1.90629			−0.953143	−	0.302520i	$-0.902172\pi$
$971$	−59.4015			−1.90629			−0.953143	+	0.302520i	$0.902172\pi$
$972$		0			0
$973$	−8.98181			−0.287943
$974$		0			0
$975$	1.36922	−	0.0978453i	0.0438503	−	0.00313356i
$976$		0			0
$977$	6.79748	−	11.7736i	0.217471	−	0.376670i	−0.736563	−	0.676369i	$-0.763553\pi$
$977$	6.79748	−	11.7736i	0.217471	−	0.376670i	0.954034	+	0.299698i	$0.0968860\pi$
$978$		0			0
$979$	3.31071	+	5.73431i	0.105811	+	0.183269i
$980$		0			0
$981$	−14.3346	+	2.05923i	−0.457669	+	0.0657461i
$982$		0			0
$983$	3.39921	+	5.88760i	0.108418	+	0.187785i	0.915130	−	0.403160i	$-0.132088\pi$
$983$	3.39921	+	5.88760i	0.108418	+	0.187785i	−0.806712	+	0.590945i	$0.798755\pi$
$984$		0			0
$985$	8.95621	−	15.5126i	0.285369	−	0.494273i
$986$		0			0
$987$	−21.5062	+	44.2655i	−0.684550	+	1.40899i
$988$		0			0
$989$	−11.4845			−0.365185
$990$		0			0
$991$	−39.1401			−1.24333			−0.621663	−	0.783285i	$-0.713543\pi$
$991$	−39.1401			−1.24333			−0.621663	+	0.783285i	$0.713543\pi$
$992$		0			0
$993$	27.3763	+	40.4537i	0.868760	+	1.28376i
$994$		0			0
$995$	−5.05761	+	8.76005i	−0.160337	+	0.277712i
$996$		0			0
$997$	16.4055	+	28.4151i	0.519567	+	0.899916i	0.999741	+	0.0227434i	$0.00724006\pi$
$997$	16.4055	+	28.4151i	0.519567	+	0.899916i	−0.480174	+	0.877173i	$0.659427\pi$
$998$		0			0
$999$	41.2202	−	8.95904i	1.30415	−	0.283452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.q.p.481.5	yes	10
3.2	odd	2		4320.2.q.p.1441.1		10
4.3	odd	2		1440.2.q.o.481.1	✓	10
9.2	odd	6		4320.2.q.p.2881.1		10
9.7	even	3	inner	1440.2.q.p.961.5	yes	10
12.11	even	2		4320.2.q.o.1441.5		10
36.7	odd	6		1440.2.q.o.961.1	yes	10
36.11	even	6		4320.2.q.o.2881.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1440.2.q.o.481.1	✓	10	4.3	odd	2
1440.2.q.o.961.1	yes	10	36.7	odd	6
1440.2.q.p.481.5	yes	10	1.1	even	1	trivial
1440.2.q.p.961.5	yes	10	9.7	even	3	inner
4320.2.q.o.1441.5		10	12.11	even	2
4320.2.q.o.2881.5		10	36.11	even	6
4320.2.q.p.1441.1		10	3.2	odd	2
4320.2.q.p.2881.1		10	9.2	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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72765 - 0.123458i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.53662 - 2.66151i) q^{7} +(2.96952 - 0.426584i) q^{9} +O(q^{10})\)	\(q+(1.72765 - 0.123458i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.53662 - 2.66151i) q^{7} +(2.96952 - 0.426584i) q^{9} +(-1.97074 - 3.41342i) q^{11} +(-0.396269 + 0.686358i) q^{13} +(-0.756905 + 1.55791i) q^{15} +4.70838 q^{17} +1.32879 q^{19} +(-2.98333 - 4.40844i) q^{21} +(0.536624 - 0.929459i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(5.07761 - 1.10360i) q^{27} +(-4.39940 - 7.61999i) q^{29} +(-0.855415 + 1.48162i) q^{31} +(-3.82616 - 5.65388i) q^{33} +3.07325 q^{35} +8.11804 q^{37} +(-0.599876 + 1.23471i) q^{39} +(-0.103731 + 0.179667i) q^{41} +(-5.35034 - 9.26705i) q^{43} +(-1.11533 + 2.78497i) q^{45} +(-4.62269 - 8.00673i) q^{47} +(-1.22242 + 2.11730i) q^{49} +(8.13441 - 0.581288i) q^{51} -12.7935 q^{53} +3.94148 q^{55} +(2.29567 - 0.164050i) q^{57} +(5.97265 - 10.3449i) q^{59} +(3.98069 + 6.89477i) q^{61} +(-5.69839 - 7.24790i) q^{63} +(-0.396269 - 0.686358i) q^{65} +(-0.00644531 + 0.0111636i) q^{67} +(0.812346 - 1.67203i) q^{69} +9.44240 q^{71} +7.14123 q^{73} +(-0.970741 - 1.43446i) q^{75} +(-6.05657 + 10.4903i) q^{77} +(3.60423 + 6.24272i) q^{79} +(8.63605 - 2.53349i) q^{81} +(5.70274 + 9.87744i) q^{83} +(-2.35419 + 4.07758i) q^{85} +(-8.54136 - 12.6215i) q^{87} -1.67993 q^{89} +2.43566 q^{91} +(-1.29494 + 2.66533i) q^{93} +(-0.664393 + 1.15076i) q^{95} +(7.12404 + 12.3392i) q^{97} +(-7.30826 - 9.29553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} - 5 q^{5} - q^{9}+O(q^{10}) \) 10 * q + q^3 - 5 * q^5 - q^9	\( 10 q + q^{3} - 5 q^{5} - q^{9} - 9 q^{11} - 4 q^{13} - 2 q^{15} + 6 q^{17} + 14 q^{19} + 12 q^{21} - 10 q^{23} - 5 q^{25} - 2 q^{27} - 2 q^{29} - 8 q^{31} - 27 q^{33} + 16 q^{37} + 26 q^{39} - q^{41} - q^{43} - q^{45} - 10 q^{47} - q^{49} - 3 q^{51} - 20 q^{53} + 18 q^{55} - 19 q^{57} - 13 q^{59} - 14 q^{61} - 30 q^{63} - 4 q^{65} - 15 q^{67} + 8 q^{69} + 32 q^{71} - 14 q^{73} + q^{75} + 12 q^{77} - 18 q^{79} + 35 q^{81} + 8 q^{83} - 3 q^{85} - 32 q^{87} + 28 q^{89} - 36 q^{91} + 16 q^{93} - 7 q^{95} + 17 q^{97}+O(q^{100}) \) 10 * q + q^3 - 5 * q^5 - q^9 - 9 * q^11 - 4 * q^13 - 2 * q^15 + 6 * q^17 + 14 * q^19 + 12 * q^21 - 10 * q^23 - 5 * q^25 - 2 * q^27 - 2 * q^29 - 8 * q^31 - 27 * q^33 + 16 * q^37 + 26 * q^39 - q^41 - q^43 - q^45 - 10 * q^47 - q^49 - 3 * q^51 - 20 * q^53 + 18 * q^55 - 19 * q^57 - 13 * q^59 - 14 * q^61 - 30 * q^63 - 4 * q^65 - 15 * q^67 + 8 * q^69 + 32 * q^71 - 14 * q^73 + q^75 + 12 * q^77 - 18 * q^79 + 35 * q^81 + 8 * q^83 - 3 * q^85 - 32 * q^87 + 28 * q^89 - 36 * q^91 + 16 * q^93 - 7 * q^95 + 17 * q^97

Introduction

L-functions

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