LMFDB - Embedded newform 576.3.o.g.319.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,3,Mod(319,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("576.319");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	576.o (of order $6$, degree $2$, not 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:	$15.6948632272$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			319.2
Root			$1.63139 - 1.15696i$ of defining polynomial
Character	$\chi$	$=$	576.319
Dual form			576.3.o.g.511.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.67178 - 1.36441i) q^{3} +(-3.07403 + 5.32438i) q^{5} +(-0.511543 + 0.295340i) q^{7} +(5.27677 + 7.29079i) q^{9} +O(q^{10})$	\(q+(-2.67178 - 1.36441i) q^{3} +(-3.07403 + 5.32438i) q^{5} +(-0.511543 + 0.295340i) q^{7} +(5.27677 + 7.29079i) q^{9} +(15.1205 - 8.72982i) q^{11} +(0.892255 - 1.54543i) q^{13} +(15.4778 - 10.0313i) q^{15} -16.9171 q^{17} +19.5058i q^{19} +(1.76969 - 0.0911265i) q^{21} +(6.86778 + 3.96511i) q^{23} +(-6.39933 - 11.0840i) q^{25} +(-4.15071 - 26.6790i) q^{27} +(-3.17517 - 5.49956i) q^{29} +(-27.6558 - 15.9671i) q^{31} +(-52.3096 + 2.69357i) q^{33} -3.63153i q^{35} -58.2834 q^{37} +(-4.49251 + 2.91164i) q^{39} +(-2.66948 + 4.62368i) q^{41} +(-33.9324 + 19.5909i) q^{43} +(-55.0399 + 5.68339i) q^{45} +(9.64117 - 5.56633i) q^{47} +(-24.3255 + 42.1331i) q^{49} +(45.1987 + 23.0819i) q^{51} -35.8770 q^{53} +107.343i q^{55} +(26.6139 - 52.1151i) q^{57} +(-20.8974 - 12.0651i) q^{59} +(37.9460 + 65.7244i) q^{61} +(-4.85256 - 2.17112i) q^{63} +(5.48564 + 9.50141i) q^{65} +(-31.8200 - 18.3713i) q^{67} +(-12.9391 - 19.9644i) q^{69} -87.8370i q^{71} -60.0423 q^{73} +(1.97450 + 38.3452i) q^{75} +(-5.15652 + 8.93136i) q^{77} +(-32.1841 + 18.5815i) q^{79} +(-25.3114 + 76.9437i) q^{81} +(-66.0281 + 38.1214i) q^{83} +(52.0037 - 90.0730i) q^{85} +(0.979694 + 19.0258i) q^{87} -27.5873 q^{89} +1.05407i q^{91} +(52.1045 + 80.3944i) q^{93} +(-103.856 - 59.9614i) q^{95} +(13.0585 + 22.6180i) q^{97} +(143.435 + 64.1751i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{5} + 18 q^{9}+O(q^{10}) $ 16 * q - 6 * q^5 + 18 * q^9	$ 16 q - 6 q^{5} + 18 q^{9} + 46 q^{13} + 12 q^{17} + 66 q^{21} - 30 q^{25} - 42 q^{29} - 168 q^{33} - 56 q^{37} + 84 q^{41} - 174 q^{45} + 58 q^{49} + 72 q^{53} + 366 q^{57} + 34 q^{61} - 30 q^{65} + 54 q^{69} + 116 q^{73} + 330 q^{77} - 102 q^{81} + 140 q^{85} - 384 q^{89} + 486 q^{93} - 148 q^{97}+O(q^{100}) $ 16 * q - 6 * q^5 + 18 * q^9 + 46 * q^13 + 12 * q^17 + 66 * q^21 - 30 * q^25 - 42 * q^29 - 168 * q^33 - 56 * q^37 + 84 * q^41 - 174 * q^45 + 58 * q^49 + 72 * q^53 + 366 * q^57 + 34 * q^61 - 30 * q^65 + 54 * q^69 + 116 * q^73 + 330 * q^77 - 102 * q^81 + 140 * q^85 - 384 * q^89 + 486 * q^93 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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
$3$	−2.67178	−	1.36441i	−0.890592	−	0.454803i
$3$	−2.67178	−	1.36441i	−0.890592	−	0.454803i
$4$		0			0
$5$	−3.07403	+	5.32438i	−0.614806	+	1.06488i	0.375612	+	0.926777i	$0.377432\pi$
$5$	−3.07403	+	5.32438i	−0.614806	+	1.06488i	−0.990418	+	0.138099i	$0.955901\pi$
$6$		0			0
$7$	−0.511543	+	0.295340i	−0.0730776	+	0.0421914i	−0.536094	−	0.844159i	$-0.680101\pi$
$7$	−0.511543	+	0.295340i	−0.0730776	+	0.0421914i	0.463016	+	0.886350i	$0.346767\pi$
$8$		0			0
$9$	5.27677	+	7.29079i	0.586308	+	0.810088i
$10$		0			0
$11$	15.1205	−	8.72982i	1.37459	−	0.793620i	0.383088	−	0.923712i	$-0.374861\pi$
$11$	15.1205	−	8.72982i	1.37459	−	0.793620i	0.991502	+	0.130092i	$0.0415274\pi$
$12$		0			0
$13$	0.892255	−	1.54543i	0.0686350	−	0.118879i	−0.829666	−	0.558261i	$-0.811469\pi$
$13$	0.892255	−	1.54543i	0.0686350	−	0.118879i	0.898301	+	0.439381i	$0.144802\pi$
$14$		0			0
$15$	15.4778	−	10.0313i	1.03185	−	0.668754i
$16$		0			0
$17$	−16.9171			−0.995123			−0.497562	−	0.867429i	$-0.665771\pi$
$17$	−16.9171			−0.995123			−0.497562	+	0.867429i	$0.665771\pi$
$18$		0			0
$19$			19.5058i			1.02662i	0.858203	+	0.513310i	$0.171581\pi$
$19$			19.5058i			1.02662i	−0.858203	+	0.513310i	$0.828419\pi$
$20$		0			0
$21$	1.76969	−	0.0911265i	0.0842711	−	0.00433936i
$22$		0			0
$23$	6.86778	+	3.96511i	0.298599	+	0.172396i	0.641813	−	0.766861i	$-0.278182\pi$
$23$	6.86778	+	3.96511i	0.298599	+	0.172396i	−0.343214	+	0.939257i	$0.611516\pi$
$24$		0			0
$25$	−6.39933	−	11.0840i	−0.255973	−	0.443359i
$26$		0			0
$27$	−4.15071	−	26.6790i	−0.153730	−	0.988113i
$28$		0			0
$29$	−3.17517	−	5.49956i	−0.109489	−	0.189640i	0.806075	−	0.591814i	$-0.201588\pi$
$29$	−3.17517	−	5.49956i	−0.109489	−	0.189640i	−0.915563	+	0.402174i	$0.868255\pi$
$30$		0			0
$31$	−27.6558	−	15.9671i	−0.892124	−	0.515068i	−0.0174873	−	0.999847i	$-0.505567\pi$
$31$	−27.6558	−	15.9671i	−0.892124	−	0.515068i	−0.874637	+	0.484779i	$0.838900\pi$
$32$		0			0
$33$	−52.3096	+	2.69357i	−1.58514	+	0.0816233i
$34$		0			0
$35$		−	3.63153i		−	0.103758i
$36$		0			0
$37$	−58.2834			−1.57523			−0.787614	−	0.616169i	$-0.788684\pi$
$37$	−58.2834			−1.57523			−0.787614	+	0.616169i	$0.788684\pi$
$38$		0			0
$39$	−4.49251	+	2.91164i	−0.115192	+	0.0746575i
$40$		0			0
$41$	−2.66948	+	4.62368i	−0.0651093	+	0.112773i	−0.896742	−	0.442553i	$-0.854073\pi$
$41$	−2.66948	+	4.62368i	−0.0651093	+	0.112773i	0.831633	+	0.555325i	$0.187406\pi$
$42$		0			0
$43$	−33.9324	+	19.5909i	−0.789126	+	0.455602i	−0.839655	−	0.543121i	$-0.817243\pi$
$43$	−33.9324	+	19.5909i	−0.789126	+	0.455602i	0.0505290	+	0.998723i	$0.483909\pi$
$44$		0			0
$45$	−55.0399	+	5.68339i	−1.22311	+	0.126298i
$46$		0			0
$47$	9.64117	−	5.56633i	0.205131	−	0.118433i	−0.393915	−	0.919147i	$-0.628880\pi$
$47$	9.64117	−	5.56633i	0.205131	−	0.118433i	0.599047	+	0.800714i	$0.295546\pi$
$48$		0			0
$49$	−24.3255	+	42.1331i	−0.496440	+	0.859859i
$50$		0			0
$51$	45.1987	+	23.0819i	0.886249	+	0.452585i
$52$		0			0
$53$	−35.8770			−0.676925			−0.338462	−	0.940980i	$-0.609907\pi$
$53$	−35.8770			−0.676925			−0.338462	+	0.940980i	$0.609907\pi$
$54$		0			0
$55$			107.343i			1.95169i
$56$		0			0
$57$	26.6139	−	52.1151i	0.466910	−	0.914299i
$58$		0			0
$59$	−20.8974	−	12.0651i	−0.354194	−	0.204494i	0.312337	−	0.949971i	$-0.398888\pi$
$59$	−20.8974	−	12.0651i	−0.354194	−	0.204494i	−0.666531	+	0.745477i	$0.732222\pi$
$60$		0			0
$61$	37.9460	+	65.7244i	0.622066	+	1.07745i	0.989100	+	0.147243i	$0.0470398\pi$
$61$	37.9460	+	65.7244i	0.622066	+	1.07745i	−0.367034	+	0.930207i	$0.619627\pi$
$62$		0			0
$63$	−4.85256	−	2.17112i	−0.0770247	−	0.0344622i
$64$		0			0
$65$	5.48564	+	9.50141i	0.0843944	+	0.146175i
$66$		0			0
$67$	−31.8200	−	18.3713i	−0.474925	−	0.274198i	0.243374	−	0.969933i	$-0.421746\pi$
$67$	−31.8200	−	18.3713i	−0.474925	−	0.274198i	−0.718299	+	0.695734i	$0.755079\pi$
$68$		0			0
$69$	−12.9391	−	19.9644i	−0.187524	−	0.289339i
$70$		0			0
$71$		−	87.8370i		−	1.23714i	−0.785730	−	0.618570i	$-0.787712\pi$
$71$		−	87.8370i		−	1.23714i	0.785730	−	0.618570i	$-0.212288\pi$
$72$		0			0
$73$	−60.0423			−0.822498			−0.411249	−	0.911523i	$-0.634907\pi$
$73$	−60.0423			−0.822498			−0.411249	+	0.911523i	$0.634907\pi$
$74$		0			0
$75$	1.97450	+	38.3452i	0.0263267	+	0.511269i
$76$		0			0
$77$	−5.15652	+	8.93136i	−0.0669678	+	0.115992i
$78$		0			0
$79$	−32.1841	+	18.5815i	−0.407394	+	0.235209i	−0.689669	−	0.724124i	$-0.742244\pi$
$79$	−32.1841	+	18.5815i	−0.407394	+	0.235209i	0.282275	+	0.959333i	$0.408911\pi$
$80$		0			0
$81$	−25.3114	+	76.9437i	−0.312486	+	0.949922i
$82$		0			0
$83$	−66.0281	+	38.1214i	−0.795520	+	0.459294i	−0.841902	−	0.539630i	$-0.818564\pi$
$83$	−66.0281	+	38.1214i	−0.795520	+	0.459294i	0.0463824	+	0.998924i	$0.485231\pi$
$84$		0			0
$85$	52.0037	−	90.0730i	0.611808	−	1.05968i
$86$		0			0
$87$	0.979694	+	19.0258i	0.0112609	+	0.218688i
$88$		0			0
$89$	−27.5873			−0.309969			−0.154985	−	0.987917i	$-0.549533\pi$
$89$	−27.5873			−0.309969			−0.154985	+	0.987917i	$0.549533\pi$
$90$		0			0
$91$			1.05407i			0.0115832i
$92$		0			0
$93$	52.1045	+	80.3944i	0.560264	+	0.864456i
$94$		0			0
$95$	−103.856	−	59.9614i	−1.09322	−	0.631172i
$96$		0			0
$97$	13.0585	+	22.6180i	0.134624	+	0.233176i	0.925454	−	0.378861i	$-0.123684\pi$
$97$	13.0585	+	22.6180i	0.134624	+	0.233176i	−0.790830	+	0.612036i	$0.790351\pi$
$98$		0			0
$99$	143.435	+	64.1751i	1.44883	+	0.648234i
$100$		0			0
$101$	12.8831	+	22.3142i	0.127556	+	0.220933i	0.922729	−	0.385449i	$-0.125953\pi$
$101$	12.8831	+	22.3142i	0.127556	+	0.220933i	−0.795173	+	0.606382i	$0.792620\pi$
$102$		0			0
$103$	16.9947	+	9.81187i	0.164997	+	0.0952609i	0.580225	−	0.814457i	$-0.302965\pi$
$103$	16.9947	+	9.81187i	0.164997	+	0.0952609i	−0.415228	+	0.909717i	$0.636298\pi$
$104$		0			0
$105$	−4.95490	+	9.70264i	−0.0471895	+	0.0924061i
$106$		0			0
$107$		−	183.200i		−	1.71215i	−0.516850	−	0.856076i	$-0.672895\pi$
$107$		−	183.200i		−	1.71215i	0.516850	−	0.856076i	$-0.327105\pi$
$108$		0			0
$109$	−100.841			−0.925147			−0.462573	−	0.886581i	$-0.653074\pi$
$109$	−100.841			−0.925147			−0.462573	+	0.886581i	$0.653074\pi$
$110$		0			0
$111$	155.720	+	79.5225i	1.40288	+	0.716419i
$112$		0			0
$113$	−9.12484	+	15.8047i	−0.0807508	+	0.139865i	−0.903573	−	0.428435i	$-0.859065\pi$
$113$	−9.12484	+	15.8047i	−0.0807508	+	0.139865i	0.822822	+	0.568299i	$0.192398\pi$
$114$		0			0
$115$	−42.2235	+	24.3778i	−0.367161	+	0.211981i
$116$		0			0
$117$	15.9756	−	1.64964i	0.136544	−	0.0140995i
$118$		0			0
$119$	8.65383	−	4.99629i	0.0727212	−	0.0419856i
$120$		0			0
$121$	91.9194	−	159.209i	0.759664	−	1.31578i
$122$		0			0
$123$	13.4408	−	8.71116i	0.109275	−	0.0708224i
$124$		0			0
$125$	−75.0146			−0.600117
$126$		0			0
$127$		−	164.386i		−	1.29438i	−0.762331	−	0.647188i	$-0.775945\pi$
$127$		−	164.386i		−	1.29438i	0.762331	−	0.647188i	$-0.224055\pi$
$128$		0			0
$129$	117.390	−	6.04473i	0.909998	−	0.0468584i
$130$		0			0
$131$	−123.421	−	71.2570i	−0.942143	−	0.543947i	−0.0515116	−	0.998672i	$-0.516404\pi$
$131$	−123.421	−	71.2570i	−0.942143	−	0.543947i	−0.890631	+	0.454726i	$0.849737\pi$
$132$		0			0
$133$	−5.76083	−	9.97805i	−0.0433145	−	0.0750229i
$134$		0			0
$135$	154.809	+	59.9122i	1.14673	+	0.443794i
$136$		0			0
$137$	−3.08176	−	5.33777i	−0.0224946	−	0.0389618i	0.854559	−	0.519354i	$-0.173828\pi$
$137$	−3.08176	−	5.33777i	−0.0224946	−	0.0389618i	−0.877054	+	0.480393i	$0.840494\pi$
$138$		0			0
$139$	103.168	+	59.5642i	0.742218	+	0.428519i	0.822875	−	0.568222i	$-0.192369\pi$
$139$	103.168	+	59.5642i	0.742218	+	0.428519i	−0.0806575	+	0.996742i	$0.525702\pi$
$140$		0			0
$141$	−33.3538	+	1.71748i	−0.236552	+	0.0121807i
$142$		0			0
$143$		−	31.1569i		−	0.217880i
$144$		0			0
$145$	39.0423			0.269257
$146$		0			0
$147$	122.479	−	79.3801i	0.833192	−	0.540001i
$148$		0			0
$149$	103.365	−	179.034i	0.693726	−	1.20157i	−0.276882	−	0.960904i	$-0.589301\pi$
$149$	103.365	−	179.034i	0.693726	−	1.20157i	0.970608	−	0.240665i	$-0.0773657\pi$
$150$		0			0
$151$	−127.422	+	73.5670i	−0.843853	+	0.487199i	−0.858572	−	0.512693i	$-0.828648\pi$
$151$	−127.422	+	73.5670i	−0.843853	+	0.487199i	0.0147190	+	0.999892i	$0.495315\pi$
$152$		0			0
$153$	−89.2676	−	123.339i	−0.583449	−	0.806138i
$154$		0			0
$155$	170.030	−	98.1668i	1.09697	−	0.633334i
$156$		0			0
$157$	−31.4395	+	54.4548i	−0.200251	+	0.346846i	−0.948609	−	0.316449i	$-0.897509\pi$
$157$	−31.4395	+	54.4548i	−0.200251	+	0.346846i	0.748358	+	0.663295i	$0.230843\pi$
$158$		0			0
$159$	95.8554	+	48.9510i	0.602864	+	0.307868i
$160$		0			0
$161$	−4.68422			−0.0290946
$162$		0			0
$163$			143.325i			0.879292i	0.898171	+	0.439646i	$0.144896\pi$
$163$			143.325i			0.879292i	−0.898171	+	0.439646i	$0.855104\pi$
$164$		0			0
$165$	146.460	−	286.796i	0.887635	−	1.73816i
$166$		0			0
$167$	−150.531	−	86.9089i	−0.901381	−	0.520413i	−0.0237332	−	0.999718i	$-0.507555\pi$
$167$	−150.531	−	86.9089i	−0.901381	−	0.520413i	−0.877648	+	0.479306i	$0.840889\pi$
$168$		0			0
$169$	82.9078	+	143.600i	0.490578	+	0.849707i
$170$		0			0
$171$	−142.213	+	102.927i	−0.831653	+	0.601915i
$172$		0			0
$173$	125.806	+	217.902i	0.727201	+	1.25955i	0.958062	+	0.286562i	$0.0925125\pi$
$173$	125.806	+	217.902i	0.727201	+	1.25955i	−0.230861	+	0.972987i	$0.574154\pi$
$174$		0			0
$175$	6.54707	+	3.77995i	0.0374118	+	0.0215997i
$176$		0			0
$177$	39.3715	+	60.7480i	0.222438	+	0.343209i
$178$		0			0
$179$		−	96.0059i		−	0.536346i	−0.963371	−	0.268173i	$-0.913580\pi$
$179$		−	96.0059i		−	0.536346i	0.963371	−	0.268173i	$-0.0864199\pi$
$180$		0			0
$181$	328.757			1.81634			0.908170	−	0.418603i	$-0.137480\pi$
$181$	328.757			1.81634			0.908170	+	0.418603i	$0.137480\pi$
$182$		0			0
$183$	−11.7082	−	227.375i	−0.0639791	−	1.24249i
$184$		0			0
$185$	179.165	−	310.323i	0.968460	−	1.67742i
$186$		0			0
$187$	−255.795	+	147.683i	−1.36789	+	0.789749i
$188$		0			0
$189$	10.0027	+	12.4216i	0.0529241	+	0.0657229i
$190$		0			0
$191$	0.351914	−	0.203178i	0.00184248	−	0.00106376i	−0.499078	−	0.866557i	$-0.666328\pi$
$191$	0.351914	−	0.203178i	0.00184248	−	0.00106376i	0.500921	+	0.865493i	$0.332995\pi$
$192$		0			0
$193$	−31.2230	+	54.0798i	−0.161777	+	0.280206i	−0.935506	−	0.353311i	$-0.885056\pi$
$193$	−31.2230	+	54.0798i	−0.161777	+	0.280206i	0.773729	+	0.633517i	$0.218389\pi$
$194$		0			0
$195$	−1.69258	−	32.8703i	−0.00867992	−	0.168566i
$196$		0			0
$197$	207.861			1.05513			0.527566	−	0.849514i	$-0.323105\pi$
$197$	207.861			1.05513			0.527566	+	0.849514i	$0.323105\pi$
$198$		0			0
$199$			299.128i			1.50316i	0.659643	+	0.751579i	$0.270707\pi$
$199$			299.128i			1.50316i	−0.659643	+	0.751579i	$0.729293\pi$
$200$		0			0
$201$	59.9499	+	92.4995i	0.298258	+	0.460196i
$202$		0			0
$203$	3.24848	+	1.87551i	0.0160024	+	0.00923896i
$204$		0			0
$205$	−16.4121	−	28.4266i	−0.0800592	−	0.138667i
$206$		0			0
$207$	7.33086	+	70.9946i	0.0354148	+	0.342969i
$208$		0			0
$209$	170.282	+	294.937i	0.814746	+	1.41118i
$210$		0			0
$211$	−141.744	−	81.8360i	−0.671773	−	0.387848i	0.124975	−	0.992160i	$-0.460115\pi$
$211$	−141.744	−	81.8360i	−0.671773	−	0.387848i	−0.796748	+	0.604311i	$0.793448\pi$
$212$		0			0
$213$	−119.846	+	234.681i	−0.562656	+	1.10179i
$214$		0			0
$215$		−	240.892i		−	1.12043i
$216$		0			0
$217$	18.8629			0.0869257
$218$		0			0
$219$	160.420	+	81.9223i	0.732510	+	0.374075i
$220$		0			0
$221$	−15.0944	+	26.1442i	−0.0683003	+	0.118300i
$222$		0			0
$223$	−330.681	+	190.919i	−1.48287	+	0.856138i	−0.999811	−	0.0194478i	$-0.993809\pi$
$223$	−330.681	+	190.919i	−1.48287	+	0.856138i	−0.483063	+	0.875586i	$0.660476\pi$
$224$		0			0
$225$	47.0431	−	105.144i	0.209081	−	0.467306i
$226$		0			0
$227$	−51.5472	+	29.7608i	−0.227080	+	0.131105i	−0.609224	−	0.792998i	$-0.708519\pi$
$227$	−51.5472	+	29.7608i	−0.227080	+	0.131105i	0.382144	+	0.924103i	$0.375186\pi$
$228$		0			0
$229$	−64.4366	+	111.608i	−0.281383	+	0.487369i	−0.971726	−	0.236113i	$-0.924126\pi$
$229$	−64.4366	+	111.608i	−0.281383	+	0.487369i	0.690343	+	0.723482i	$0.257460\pi$
$230$		0			0
$231$	25.9631	−	16.8270i	0.112394	−	0.0728441i
$232$		0			0
$233$	14.9939			0.0643513			0.0321757	−	0.999482i	$-0.489756\pi$
$233$	14.9939			0.0643513			0.0321757	+	0.999482i	$0.489756\pi$
$234$		0			0
$235$			68.4443i			0.291252i
$236$		0			0
$237$	111.342	−	5.73329i	0.469796	−	0.0241911i
$238$		0			0
$239$	315.244	+	182.006i	1.31901	+	0.761532i	0.983570	−	0.180529i	$-0.0577811\pi$
$239$	315.244	+	182.006i	1.31901	+	0.761532i	0.335442	+	0.942061i	$0.391114\pi$
$240$		0			0
$241$	−40.5235	−	70.1888i	−0.168147	−	0.291240i	0.769621	−	0.638501i	$-0.220445\pi$
$241$	−40.5235	−	70.1888i	−0.168147	−	0.291240i	−0.937769	+	0.347261i	$0.887112\pi$
$242$		0			0
$243$	172.609	−	171.041i	0.710326	−	0.703873i
$244$		0			0
$245$	−149.555	−	259.037i	−0.610428	−	1.05729i
$246$		0			0
$247$	30.1448	+	17.4041i	0.122044	+	0.0704620i
$248$		0			0
$249$	228.426	−	11.7623i	0.917372	−	0.0472381i
$250$		0			0
$251$			281.883i			1.12304i	0.827463	+	0.561520i	$0.189783\pi$
$251$			281.883i			1.12304i	−0.827463	+	0.561520i	$0.810217\pi$
$252$		0			0
$253$	138.459			0.547268
$254$		0			0
$255$	−261.839	+	169.701i	−1.02682	+	0.665492i
$256$		0			0
$257$	−37.6564	+	65.2227i	−0.146523	+	0.253785i	−0.929940	−	0.367711i	$-0.880142\pi$
$257$	−37.6564	+	65.2227i	−0.146523	+	0.253785i	0.783417	+	0.621496i	$0.213475\pi$
$258$		0			0
$259$	29.8145	−	17.2134i	0.115114	−	0.0664610i
$260$		0			0
$261$	23.3415	−	52.1695i	0.0894311	−	0.199883i
$262$		0			0
$263$	105.914	−	61.1497i	0.402716	−	0.232508i	−0.284939	−	0.958546i	$-0.591973\pi$
$263$	105.914	−	61.1497i	0.402716	−	0.232508i	0.687655	+	0.726037i	$0.258640\pi$
$264$		0			0
$265$	110.287	−	191.023i	0.416178	−	0.720841i
$266$		0			0
$267$	73.7070	+	37.6403i	0.276056	+	0.140975i
$268$		0			0
$269$	−280.452			−1.04257			−0.521287	−	0.853382i	$-0.674548\pi$
$269$	−280.452			−1.04257			−0.521287	+	0.853382i	$0.674548\pi$
$270$		0			0
$271$			81.4468i			0.300542i	0.988645	+	0.150271i	$0.0480146\pi$
$271$			81.4468i			0.300542i	−0.988645	+	0.150271i	$0.951985\pi$
$272$		0			0
$273$	1.43819	−	2.81625i	0.00526809	−	0.0103159i
$274$		0			0
$275$	−193.522	−	111.730i	−0.703716	−	0.406291i
$276$		0			0
$277$	−224.861	−	389.471i	−0.811774	−	1.40603i	−0.911622	−	0.411031i	$-0.865169\pi$
$277$	−224.861	−	389.471i	−0.811774	−	1.40603i	0.0998479	−	0.995003i	$-0.468164\pi$
$278$		0			0
$279$	−29.5206	−	285.888i	−0.105809	−	1.02469i
$280$		0			0
$281$	−37.8649	−	65.5838i	−0.134750	−	0.233394i	0.790752	−	0.612137i	$-0.209690\pi$
$281$	−37.8649	−	65.5838i	−0.134750	−	0.233394i	−0.925502	+	0.378743i	$0.876357\pi$
$282$		0			0
$283$	−322.061	−	185.942i	−1.13803	−	0.657039i	−0.192084	−	0.981378i	$-0.561525\pi$
$283$	−322.061	−	185.942i	−1.13803	−	0.657039i	−0.945941	+	0.324339i	$0.894858\pi$
$284$		0			0
$285$	195.668	+	301.906i	0.686556	+	1.05932i
$286$		0			0
$287$		−	3.15361i		−	0.0109882i
$288$		0			0
$289$	−2.81196			−0.00972996
$290$		0			0
$291$	−4.02919	−	78.2475i	−0.0138460	−	0.268892i
$292$		0			0
$293$	66.3946	−	114.999i	0.226603	−	0.392488i	−0.730196	−	0.683237i	$-0.760571\pi$
$293$	66.3946	−	114.999i	0.226603	−	0.392488i	0.956799	+	0.290750i	$0.0939047\pi$
$294$		0			0
$295$	128.479	−	74.1772i	0.435521	−	0.251448i
$296$		0			0
$297$	−295.664	−	367.165i	−0.995502	−	1.23625i
$298$		0			0
$299$	12.2556	−	7.07579i	0.0409887	−	0.0236648i
$300$		0			0
$301$	11.5719	−	20.0432i	0.0384450	−	0.0665886i
$302$		0			0
$303$	−3.97507	−	77.1965i	−0.0131190	−	0.254774i
$304$		0			0
$305$	−466.589			−1.52980
$306$		0			0
$307$			336.514i			1.09614i	0.836434	+	0.548068i	$0.184637\pi$
$307$			336.514i			1.09614i	−0.836434	+	0.548068i	$0.815363\pi$
$308$		0			0
$309$	−32.0185	−	49.4028i	−0.103620	−	0.159880i
$310$		0			0
$311$	−304.206	−	175.634i	−0.978156	−	0.564738i	−0.0764428	−	0.997074i	$-0.524356\pi$
$311$	−304.206	−	175.634i	−0.978156	−	0.564738i	−0.901713	+	0.432336i	$0.857690\pi$
$312$		0			0
$313$	−95.4299	−	165.289i	−0.304888	−	0.528081i	0.672349	−	0.740235i	$-0.265286\pi$
$313$	−95.4299	−	165.289i	−0.304888	−	0.528081i	−0.977236	+	0.212154i	$0.931952\pi$
$314$		0			0
$315$	26.4768	−	19.1628i	0.0840532	−	0.0608342i
$316$		0			0
$317$	202.797	+	351.255i	0.639738	+	1.10806i	0.985490	+	0.169733i	$0.0542906\pi$
$317$	202.797	+	351.255i	0.639738	+	1.10806i	−0.345752	+	0.938326i	$0.612376\pi$
$318$		0			0
$319$	−96.0203	−	55.4374i	−0.301004	−	0.173785i
$320$		0			0
$321$	−249.960	+	489.470i	−0.778693	+	1.52483i
$322$		0			0
$323$		−	329.981i		−	1.02161i
$324$		0			0
$325$	−22.8393			−0.0702749
$326$		0			0
$327$	269.424	+	137.588i	0.823928	+	0.420760i
$328$		0			0
$329$	−3.28792	+	5.69484i	−0.00999368	+	0.0173096i
$330$		0			0
$331$	384.104	−	221.763i	1.16044	−	0.669978i	0.209027	−	0.977910i	$-0.432970\pi$
$331$	384.104	−	221.763i	1.16044	−	0.669978i	0.951408	+	0.307932i	$0.0996370\pi$
$332$		0			0
$333$	−307.548	−	424.932i	−0.923568	−	1.27607i
$334$		0			0
$335$	195.631	−	112.948i	0.583974	−	0.337158i
$336$		0			0
$337$	−254.239	+	440.356i	−0.754420	+	1.30669i	0.191243	+	0.981543i	$0.438748\pi$
$337$	−254.239	+	440.356i	−0.754420	+	1.30669i	−0.945662	+	0.325150i	$0.894585\pi$
$338$		0			0
$339$	45.9436	−	29.7766i	0.135527	−	0.0878365i
$340$		0			0
$341$	−557.560			−1.63507
$342$		0			0
$343$		−	57.6805i		−	0.168165i
$344$		0			0
$345$	146.073	−	7.52172i	0.423400	−	0.0218021i
$346$		0			0
$347$	492.773	+	284.503i	1.42010	+	0.819893i	0.996307	−	0.0858678i	$-0.0273663\pi$
$347$	492.773	+	284.503i	1.42010	+	0.819893i	0.423790	+	0.905761i	$0.360700\pi$
$348$		0			0
$349$	206.901	+	358.363i	0.592840	+	1.02683i	0.993848	+	0.110754i	$0.0353266\pi$
$349$	206.901	+	358.363i	0.592840	+	1.02683i	−0.401008	+	0.916074i	$0.631340\pi$
$350$		0			0
$351$	−44.9341	−	17.3899i	−0.128017	−	0.0495438i
$352$		0			0
$353$	62.3070	+	107.919i	0.176507	+	0.305719i	0.940682	−	0.339290i	$-0.110187\pi$
$353$	62.3070	+	107.919i	0.176507	+	0.305719i	−0.764175	+	0.645009i	$0.776853\pi$
$354$		0			0
$355$	467.677	+	270.014i	1.31740	+	0.760602i
$356$		0			0
$357$	−29.9381	+	1.54160i	−0.0838601	+	0.00431820i
$358$		0			0
$359$			303.196i			0.844557i	0.906466	+	0.422278i	$0.138770\pi$
$359$			303.196i			0.844557i	−0.906466	+	0.422278i	$0.861230\pi$
$360$		0			0
$361$	−19.4752			−0.0539480
$362$		0			0
$363$	−462.814	+	299.955i	−1.27497	+	0.826323i
$364$		0			0
$365$	184.572	−	319.688i	0.505677	−	0.875858i
$366$		0			0
$367$	615.571	−	355.400i	1.67730	−	0.968392i	0.713936	−	0.700211i	$-0.246911\pi$
$367$	615.571	−	355.400i	1.67730	−	0.968392i	0.963369	−	0.268181i	$-0.0864224\pi$
$368$		0			0
$369$	−47.7965	+	4.93544i	−0.129530	+	0.0133752i
$370$		0			0
$371$	18.3527	−	10.5959i	0.0494681	−	0.0285604i
$372$		0			0
$373$	−166.740	+	288.803i	−0.447025	+	0.774271i	−0.998191	−	0.0601254i	$-0.980850\pi$
$373$	−166.740	+	288.803i	−0.447025	+	0.774271i	0.551166	+	0.834396i	$0.314183\pi$
$374$		0			0
$375$	200.422	+	102.351i	0.534459	+	0.272935i
$376$		0			0
$377$	−11.3323			−0.0300590
$378$		0			0
$379$		−	662.686i		−	1.74851i	−0.485465	−	0.874256i	$-0.661350\pi$
$379$		−	662.686i		−	1.74851i	0.485465	−	0.874256i	$-0.338650\pi$
$380$		0			0
$381$	−224.289	+	439.202i	−0.588686	+	1.15276i
$382$		0			0
$383$	69.9008	+	40.3572i	0.182509	+	0.105371i	0.588471	−	0.808518i	$-0.299730\pi$
$383$	69.9008	+	40.3572i	0.182509	+	0.105371i	−0.405962	+	0.913890i	$0.633064\pi$
$384$		0			0
$385$	−31.7026	−	54.9106i	−0.0823445	−	0.142625i
$386$		0			0
$387$	−321.887	−	144.018i	−0.831748	−	0.372139i
$388$		0			0
$389$	346.006	+	599.301i	0.889476	+	1.54062i	0.840495	+	0.541819i	$0.182264\pi$
$389$	346.006	+	599.301i	0.889476	+	1.54062i	0.0489809	+	0.998800i	$0.484403\pi$
$390$		0			0
$391$	−116.183	−	67.0782i	−0.297143	−	0.171556i
$392$		0			0
$393$	232.529	+	358.779i	0.591676	+	0.912924i
$394$		0			0
$395$		−	228.481i		−	0.578432i
$396$		0			0
$397$	−657.713			−1.65671			−0.828354	−	0.560206i	$-0.810722\pi$
$397$	−657.713			−1.65671			−0.828354	+	0.560206i	$0.810722\pi$
$398$		0			0
$399$	1.77749	+	34.5192i	0.00445487	+	0.0865144i
$400$		0			0
$401$	296.433	−	513.437i	0.739235	−	1.28039i	−0.213606	−	0.976920i	$-0.568521\pi$
$401$	296.433	−	513.437i	0.739235	−	1.28039i	0.952840	−	0.303472i	$-0.0981459\pi$
$402$		0			0
$403$	−49.3521	+	28.4935i	−0.122462	+	0.0707034i
$404$		0			0
$405$	−331.869	−	371.295i	−0.819431	−	0.916777i
$406$		0			0
$407$	−881.274	+	508.804i	−2.16529	+	1.25013i
$408$		0			0
$409$	−161.594	+	279.889i	−0.395095	+	0.684325i	−0.993113	−	0.117157i	$-0.962622\pi$
$409$	−161.594	+	279.889i	−0.395095	+	0.684325i	0.598018	+	0.801483i	$0.295955\pi$
$410$		0			0
$411$	0.950872	+	18.4661i	0.00231356	+	0.0449297i
$412$		0			0
$413$	14.2533			0.0345115
$414$		0			0
$415$		−	468.745i		−	1.12951i
$416$		0			0
$417$	−194.372	−	299.906i	−0.466121	−	0.719199i
$418$		0			0
$419$	−222.744	−	128.601i	−0.531608	−	0.306924i	0.210063	−	0.977688i	$-0.432633\pi$
$419$	−222.744	−	128.601i	−0.531608	−	0.306924i	−0.741671	+	0.670764i	$0.765967\pi$
$420$		0			0
$421$	−41.9905	−	72.7297i	−0.0997400	−	0.172755i	0.811837	−	0.583884i	$-0.198468\pi$
$421$	−41.9905	−	72.7297i	−0.0997400	−	0.172755i	−0.911577	+	0.411129i	$0.865134\pi$
$422$		0			0
$423$	91.4573	+	40.9196i	0.216211	+	0.0967365i
$424$		0			0
$425$	108.258	+	187.509i	0.254725	+	0.441197i
$426$		0			0
$427$	−38.8221	−	22.4139i	−0.0909182	−	0.0524917i
$428$		0			0
$429$	−42.5108	+	83.2442i	−0.0990927	+	0.194042i
$430$		0			0
$431$			144.348i			0.334914i	0.985879	+	0.167457i	$0.0535555\pi$
$431$			144.348i			0.334914i	−0.985879	+	0.167457i	$0.946445\pi$
$432$		0			0
$433$	395.353			0.913057			0.456528	−	0.889709i	$-0.349093\pi$
$433$	395.353			0.913057			0.456528	+	0.889709i	$0.349093\pi$
$434$		0			0
$435$	−104.312	−	53.2697i	−0.239798	−	0.122459i
$436$		0			0
$437$	−77.3426	+	133.961i	−0.176985	+	0.306548i
$438$		0			0
$439$	194.776	−	112.454i	0.443682	−	0.256160i	−0.261476	−	0.965210i	$-0.584209\pi$
$439$	194.776	−	112.454i	0.443682	−	0.256160i	0.705158	+	0.709050i	$0.250876\pi$
$440$		0			0
$441$	−435.544	+	44.9740i	−0.987628	+	0.101982i
$442$		0			0
$443$	−369.184	+	213.148i	−0.833373	+	0.481148i	−0.855006	−	0.518618i	$-0.826447\pi$
$443$	−369.184	+	213.148i	−0.833373	+	0.481148i	0.0216335	+	0.999766i	$0.493113\pi$
$444$		0			0
$445$	84.8041	−	146.885i	0.190571	−	0.330079i
$446$		0			0
$447$	−520.444	+	337.306i	−1.16430	+	0.754599i
$448$		0			0
$449$	−406.744			−0.905888			−0.452944	−	0.891539i	$-0.649626\pi$
$449$	−406.744			−0.905888			−0.452944	+	0.891539i	$0.649626\pi$
$450$		0			0
$451$			93.2163i			0.206688i
$452$		0			0
$453$	440.818	−	22.6990i	0.973108	−	0.0501081i
$454$		0			0
$455$	−5.61228	−	3.24025i	−0.0123347	−	0.00712144i
$456$		0			0
$457$	−159.600	−	276.435i	−0.349234	−	0.604891i	0.636879	−	0.770963i	$-0.280225\pi$
$457$	−159.600	−	276.435i	−0.349234	−	0.604891i	−0.986114	+	0.166072i	$0.946892\pi$
$458$		0			0
$459$	70.2180	+	451.332i	0.152980	+	0.983294i
$460$		0			0
$461$	−293.888	−	509.029i	−0.637501	−	1.10418i	−0.985979	−	0.166867i	$-0.946635\pi$
$461$	−293.888	−	509.029i	−0.637501	−	1.10418i	0.348478	−	0.937317i	$-0.386698\pi$
$462$		0			0
$463$	−230.088	−	132.841i	−0.496950	−	0.286914i	0.230503	−	0.973072i	$-0.425963\pi$
$463$	−230.088	−	132.841i	−0.496950	−	0.286914i	−0.727453	+	0.686157i	$0.759296\pi$
$464$		0			0
$465$	−588.221	+	30.2892i	−1.26499	+	0.0651380i
$466$		0			0
$467$			794.598i			1.70149i	0.525575	+	0.850747i	$0.323850\pi$
$467$			794.598i			1.70149i	−0.525575	+	0.850747i	$0.676150\pi$
$468$		0			0
$469$	21.7031			0.0462752
$470$		0			0
$471$	158.298	−	102.595i	0.336089	−	0.217823i
$472$		0			0
$473$	−342.050	+	592.447i	−0.723149	+	1.25253i
$474$		0			0
$475$	216.201	−	124.824i	0.455161	−	0.262787i
$476$		0			0
$477$	−189.315	−	261.572i	−0.396886	−	0.548369i
$478$		0			0
$479$	572.964	−	330.801i	1.19617	−	0.690607i	0.236468	−	0.971639i	$-0.424010\pi$
$479$	572.964	−	330.801i	1.19617	−	0.690607i	0.959698	+	0.281033i	$0.0906769\pi$
$480$		0			0
$481$	−52.0037	+	90.0730i	−0.108116	+	0.187262i
$482$		0			0
$483$	12.5152	+	6.39120i	0.0259114	+	0.0132323i
$484$		0			0
$485$	−160.569			−0.331071
$486$		0			0
$487$		−	57.1525i		−	0.117356i	−0.998277	−	0.0586781i	$-0.981311\pi$
$487$		−	57.1525i		−	0.117356i	0.998277	−	0.0586781i	$-0.0186886\pi$
$488$		0			0
$489$	195.553	−	382.931i	0.399905	−	0.783090i
$490$		0			0
$491$	48.6600	+	28.0939i	0.0991040	+	0.0572177i	0.548733	−	0.835998i	$-0.315110\pi$
$491$	48.6600	+	28.0939i	0.0991040	+	0.0572177i	−0.449629	+	0.893215i	$0.648444\pi$
$492$		0			0
$493$	53.7147	+	93.0366i	0.108955	+	0.188715i
$494$		0			0
$495$	−782.615	+	566.424i	−1.58104	+	1.14429i
$496$		0			0
$497$	25.9417	+	44.9324i	0.0521967	+	0.0904073i
$498$		0			0
$499$	522.225	+	301.507i	1.04654	+	0.604222i	0.921679	−	0.387952i	$-0.126817\pi$
$499$	522.225	+	301.507i	1.04654	+	0.604222i	0.124863	+	0.992174i	$0.460151\pi$
$500$		0			0
$501$	283.605	+	437.587i	0.566077	+	0.873427i
$502$		0			0
$503$			549.354i			1.09216i	0.837734	+	0.546078i	$0.183880\pi$
$503$			549.354i			1.09216i	−0.837734	+	0.546078i	$0.816120\pi$
$504$		0			0
$505$	−158.413			−0.313688
$506$		0			0
$507$	−25.5810	−	496.788i	−0.0504557	−	0.979859i
$508$		0			0
$509$	119.464	−	206.918i	0.234704	−	0.406519i	−0.724483	−	0.689293i	$-0.757921\pi$
$509$	119.464	−	206.918i	0.234704	−	0.406519i	0.959187	+	0.282774i	$0.0912547\pi$
$510$		0			0
$511$	30.7143	−	17.7329i	0.0601062	−	0.0347023i
$512$		0			0
$513$	520.395	−	80.9629i	1.01442	−	0.157822i
$514$		0			0
$515$	−104.484	+	60.3240i	−0.202882	+	0.117134i
$516$		0			0
$517$	97.1862	−	168.331i	0.187981	−	0.325593i
$518$		0			0
$519$	−38.8171	−	753.836i	−0.0747922	−	1.45248i
$520$		0			0
$521$	−567.711			−1.08966			−0.544828	−	0.838548i	$-0.683405\pi$
$521$	−567.711			−1.08966			−0.544828	+	0.838548i	$0.683405\pi$
$522$		0			0
$523$		−	941.999i		−	1.80114i	−0.434706	−	0.900572i	$-0.643148\pi$
$523$		−	941.999i		−	1.80114i	0.434706	−	0.900572i	$-0.356852\pi$
$524$		0			0
$525$	−12.3349	−	19.0321i	−0.0234950	−	0.0362516i
$526$		0			0
$527$	467.856	+	270.117i	0.887773	+	0.512556i
$528$		0			0
$529$	−233.056	−	403.664i	−0.440559	−	0.763071i
$530$		0			0
$531$	−22.3065	−	216.024i	−0.0420085	−	0.406825i
$532$		0			0
$533$	4.76372	+	8.25100i	0.00893755	+	0.0154803i
$534$		0			0
$535$	975.428	+	563.163i	1.82323	+	1.05264i
$536$		0			0
$537$	−130.991	+	256.506i	−0.243932	+	0.477665i
$538$		0			0
$539$			849.430i			1.57594i
$540$		0			0
$541$	242.245			0.447772			0.223886	−	0.974615i	$-0.428126\pi$
$541$	242.245			0.447772			0.223886	+	0.974615i	$0.428126\pi$
$542$		0			0
$543$	−878.366	−	448.560i	−1.61762	−	0.826077i
$544$		0			0
$545$	309.988	−	536.915i	0.568786	−	0.985166i
$546$		0			0
$547$	−170.503	+	98.4402i	−0.311706	+	0.179964i	−0.647690	−	0.761904i	$-0.724265\pi$
$547$	−170.503	+	98.4402i	−0.311706	+	0.179964i	0.335983	+	0.941868i	$0.390931\pi$
$548$		0			0
$549$	−278.951	+	623.470i	−0.508107	+	1.13565i
$550$		0			0
$551$	107.273	−	61.9342i	0.194688	−	0.112403i
$552$		0			0
$553$	10.9757	−	19.0105i	0.0198476	−	0.0343770i
$554$		0			0
$555$	−902.096	+	584.659i	−1.62540	+	1.05344i
$556$		0			0
$557$	−958.121			−1.72015			−0.860073	−	0.510171i	$-0.829582\pi$
$557$	−958.121			−1.72015			−0.860073	+	0.510171i	$0.829582\pi$
$558$		0			0
$559$			69.9202i			0.125081i
$560$		0			0
$561$	884.926	−	45.5674i	1.57741	−	0.0812253i
$562$		0			0
$563$	165.774	+	95.7097i	0.294448	+	0.169999i	0.639946	−	0.768420i	$-0.278957\pi$
$563$	165.774	+	95.7097i	0.294448	+	0.169999i	−0.345498	+	0.938419i	$0.612290\pi$
$564$		0			0
$565$	−56.1001	−	97.1682i	−0.0992922	−	0.171979i
$566$		0			0
$567$	−9.77666	−	46.8355i	−0.0172428	−	0.0826023i
$568$		0			0
$569$	228.215	+	395.280i	0.401081	+	0.694693i	0.993857	−	0.110675i	$-0.0353012\pi$
$569$	228.215	+	395.280i	0.401081	+	0.694693i	−0.592775	+	0.805368i	$0.701968\pi$
$570$		0			0
$571$	−842.764	−	486.570i	−1.47594	−	0.852136i	−0.476312	−	0.879276i	$-0.658027\pi$
$571$	−842.764	−	486.570i	−1.47594	−	0.852136i	−0.999632	+	0.0271399i	$0.991360\pi$
$572$		0			0
$573$	−1.21745	+	0.0626902i	−0.00212470	+	0.000109407i
$574$		0			0
$575$		−	101.496i		−	0.176515i
$576$		0			0
$577$	138.527			0.240081			0.120040	−	0.992769i	$-0.461698\pi$
$577$	138.527			0.240081			0.120040	+	0.992769i	$0.461698\pi$
$578$		0			0
$579$	157.208	−	101.888i	0.271516	−	0.175972i
$580$		0			0
$581$	22.5175	−	39.0015i	0.0387565	−	0.0671282i
$582$		0			0
$583$	−542.478	+	313.200i	−0.930494	+	0.537221i
$584$		0			0
$585$	−40.3263	+	90.1314i	−0.0689339	+	0.154071i
$586$		0			0
$587$	620.808	−	358.424i	1.05759	−	0.610602i	0.132829	−	0.991139i	$-0.457594\pi$
$587$	620.808	−	358.424i	1.05759	−	0.610602i	0.924766	+	0.380537i	$0.124261\pi$
$588$		0			0
$589$	311.451	−	539.449i	0.528779	−	0.915872i
$590$		0			0
$591$	−555.358	−	283.607i	−0.939691	−	0.479877i
$592$		0			0
$593$	542.129			0.914214			0.457107	−	0.889412i	$-0.348886\pi$
$593$	542.129			0.914214			0.457107	+	0.889412i	$0.348886\pi$
$594$		0			0
$595$			61.4350i			0.103252i
$596$		0			0
$597$	408.134	−	799.204i	0.683641	−	1.33870i
$598$		0			0
$599$	245.527	+	141.755i	0.409895	+	0.236653i	0.690744	−	0.723099i	$-0.257283\pi$
$599$	245.527	+	141.755i	0.409895	+	0.236653i	−0.280850	+	0.959752i	$0.590616\pi$
$600$		0			0
$601$	377.424	+	653.717i	0.627993	+	1.08772i	0.987954	+	0.154748i	$0.0494567\pi$
$601$	377.424	+	653.717i	0.627993	+	1.08772i	−0.359961	+	0.932967i	$0.617210\pi$
$602$		0			0
$603$	−33.9656	−	328.934i	−0.0563276	−	0.545496i
$604$		0			0
$605$	565.126	+	978.827i	0.934093	+	1.61790i
$606$		0			0
$607$	−77.2227	−	44.5845i	−0.127220	−	0.0734506i	0.435039	−	0.900411i	$-0.356734\pi$
$607$	−77.2227	−	44.5845i	−0.127220	−	0.0734506i	−0.562260	+	0.826961i	$0.690068\pi$
$608$		0			0
$609$	−6.12024	−	9.44320i	−0.0100497	−	0.0155061i
$610$		0			0
$611$		−	19.8664i		−	0.0325145i
$612$		0			0
$613$	316.779			0.516769			0.258385	−	0.966042i	$-0.416810\pi$
$613$	316.779			0.516769			0.258385	+	0.966042i	$0.416810\pi$
$614$		0			0
$615$	5.06393	+	98.3425i	0.00823404	+	0.159907i
$616$		0			0
$617$	534.934	−	926.533i	0.866992	−	1.50167i	0.00193565	−	0.999998i	$-0.499384\pi$
$617$	534.934	−	926.533i	0.866992	−	1.50167i	0.865056	−	0.501675i	$-0.167283\pi$
$618$		0			0
$619$	578.542	−	334.021i	0.934640	−	0.539615i	0.0463638	−	0.998925i	$-0.485237\pi$
$619$	578.542	−	334.021i	0.934640	−	0.539615i	0.888276	+	0.459310i	$0.151903\pi$
$620$		0			0
$621$	77.2793	−	199.684i	0.124443	−	0.321552i
$622$		0			0
$623$	14.1121	−	8.14762i	0.0226518	−	0.0130780i
$624$		0			0
$625$	390.580	−	676.505i	0.624929	−	1.08241i
$626$		0			0
$627$	−52.5402	−	1020.34i	−0.0837961	−	1.62734i
$628$		0			0
$629$	985.986			1.56755
$630$		0			0
$631$		−	150.631i		−	0.238718i	−0.992851	−	0.119359i	$-0.961916\pi$
$631$		−	150.631i		−	0.238718i	0.992851	−	0.119359i	$-0.0380839\pi$
$632$		0			0
$633$	267.051	+	412.045i	0.421881	+	0.650939i
$634$		0			0
$635$	875.252	+	505.327i	1.37835	+	0.795790i
$636$		0			0
$637$	43.4092	+	75.1869i	0.0681463	+	0.118033i
$638$		0			0
$639$	640.401	−	463.496i	1.00219	−	0.725345i
$640$		0			0
$641$	351.521	+	608.852i	0.548395	+	0.949847i	0.998385	+	0.0568139i	$0.0180942\pi$
$641$	351.521	+	608.852i	0.548395	+	0.949847i	−0.449990	+	0.893034i	$0.648573\pi$
$642$		0			0
$643$	742.057	+	428.427i	1.15405	+	0.666293i	0.949872	−	0.312639i	$-0.101213\pi$
$643$	742.057	+	428.427i	1.15405	+	0.666293i	0.204182	+	0.978933i	$0.434546\pi$
$644$		0			0
$645$	−328.675	+	643.609i	−0.509574	+	0.997844i
$646$		0			0
$647$		−	156.257i		−	0.241510i	−0.992682	−	0.120755i	$-0.961468\pi$
$647$		−	156.257i		−	0.241510i	0.992682	−	0.120755i	$-0.0385316\pi$
$648$		0			0
$649$	−421.306			−0.649162
$650$		0			0
$651$	−50.3974	−	25.7367i	−0.0774154	−	0.0395341i
$652$		0			0
$653$	441.773	−	765.173i	0.676528	−	1.17178i	−0.299492	−	0.954099i	$-0.596817\pi$
$653$	441.773	−	765.173i	0.676528	−	1.17178i	0.976020	−	0.217682i	$-0.0698495\pi$
$654$		0			0
$655$	758.798	−	438.092i	1.15847	−	0.668843i
$656$		0			0
$657$	−316.830	−	437.756i	−0.482237	−	0.666296i
$658$		0			0
$659$	−379.533	+	219.123i	−0.575922	+	0.332509i	−0.759511	−	0.650494i	$-0.774562\pi$
$659$	−379.533	+	219.123i	−0.575922	+	0.332509i	0.183589	+	0.983003i	$0.441228\pi$
$660$		0			0
$661$	−233.924	+	405.168i	−0.353894	+	0.612963i	−0.986928	−	0.161161i	$-0.948476\pi$
$661$	−233.924	+	405.168i	−0.353894	+	0.612963i	0.633034	+	0.774124i	$0.281809\pi$
$662$		0			0
$663$	76.0002	−	49.2565i	0.114631	−	0.0742934i
$664$		0			0
$665$	70.8359			0.106520
$666$		0			0
$667$		−	50.3597i		−	0.0755018i
$668$		0			0
$669$	1144.00	−	58.9076i	1.71001	−	0.0880533i
$670$		0			0
$671$	1147.52	+	662.524i	1.71017	+	0.987368i
$672$		0			0
$673$	273.302	+	473.372i	0.406094	+	0.703376i	0.994448	−	0.105227i	$-0.0335571\pi$
$673$	273.302	+	473.372i	0.406094	+	0.703376i	−0.588354	+	0.808604i	$0.700224\pi$
$674$		0			0
$675$	−269.148	+	216.734i	−0.398738	+	0.321088i
$676$		0			0
$677$	−227.606	−	394.225i	−0.336198	−	0.582312i	0.647516	−	0.762052i	$-0.275808\pi$
$677$	−227.606	−	394.225i	−0.336198	−	0.582312i	−0.983714	+	0.179740i	$0.942475\pi$
$678$		0			0
$679$	−13.3600	−	7.71341i	−0.0196760	−	0.0113600i
$680$		0			0
$681$	178.329	−	9.18264i	0.261863	−	0.0134841i
$682$		0			0
$683$			123.214i			0.180400i	0.995924	+	0.0902002i	$0.0287507\pi$
$683$			123.214i			0.180400i	−0.995924	+	0.0902002i	$0.971249\pi$
$684$		0			0
$685$	37.8937			0.0553193
$686$		0			0
$687$	324.439	−	210.272i	0.472254	−	0.306073i
$688$		0			0
$689$	−32.0115	+	55.4455i	−0.0464607	+	0.0804724i
$690$		0			0
$691$	−163.326	+	94.2965i	−0.236362	+	0.136464i	−0.613504	−	0.789692i	$-0.710240\pi$
$691$	−163.326	+	94.2965i	−0.236362	+	0.136464i	0.377141	+	0.926156i	$0.376907\pi$
$692$		0			0
$693$	−92.3265	+	9.53359i	−0.133227	+	0.0137570i
$694$		0			0
$695$	−634.285	+	366.204i	−0.912640	+	0.526913i
$696$		0			0
$697$	45.1599	−	78.2192i	0.0647918	−	0.112223i
$698$		0			0
$699$	−40.0602	−	20.4578i	−0.0573107	−	0.0292672i
$700$		0			0
$701$	810.064			1.15558			0.577792	−	0.816184i	$-0.303915\pi$
$701$	810.064			1.15558			0.577792	+	0.816184i	$0.303915\pi$
$702$		0			0
$703$		−	1136.86i		−	1.61716i
$704$		0			0
$705$	93.3861	−	182.868i	0.132463	−	0.259387i
$706$		0			0
$707$	−13.1806	−	7.60980i	−0.0186429	−	0.0107635i
$708$		0			0
$709$	651.819	+	1128.98i	0.919349	+	1.59236i	0.800406	+	0.599459i	$0.204618\pi$
$709$	651.819	+	1128.98i	0.919349	+	1.59236i	0.118944	+	0.992901i	$0.462049\pi$
$710$		0			0
$711$	−305.302	−	136.597i	−0.429398	−	0.192120i
$712$		0			0
$713$	−126.623	−	219.317i	−0.177592	−	0.307598i
$714$		0			0
$715$	165.891	+	95.7772i	0.232015	+	0.133954i
$716$		0			0
$717$	−593.930	−	916.401i	−0.828354	−	1.27810i
$718$		0			0
$719$			788.981i			1.09733i	0.836042	+	0.548666i	$0.184864\pi$
$719$			788.981i			1.09733i	−0.836042	+	0.548666i	$0.815136\pi$
$720$		0			0
$721$	−11.5913			−0.0160768
$722$		0			0
$723$	12.5035	+	242.820i	0.0172939	+	0.335850i
$724$		0			0
$725$	−40.6380	+	70.3870i	−0.0560524	+	0.0970856i
$726$		0			0
$727$	232.676	−	134.335i	0.320049	−	0.184780i	−0.331365	−	0.943502i	$-0.607509\pi$
$727$	232.676	−	134.335i	0.320049	−	0.184780i	0.651414	+	0.758722i	$0.274176\pi$
$728$		0			0
$729$	−694.543	+	221.474i	−0.952734	+	0.303805i
$730$		0			0
$731$	574.038	−	331.421i	0.785277	−	0.453380i
$732$		0			0
$733$	36.8343	−	63.7989i	0.0502514	−	0.0870380i	−0.839806	−	0.542887i	$-0.817331\pi$
$733$	36.8343	−	63.7989i	0.0502514	−	0.0870380i	0.890057	+	0.455849i	$0.150664\pi$
$734$		0			0
$735$	46.1449	+	896.143i	0.0627822	+	1.21924i
$736$		0			0
$737$	−641.512			−0.870437
$738$		0			0
$739$			448.249i			0.606562i	0.952901	+	0.303281i	$0.0980820\pi$
$739$			448.249i			0.606562i	−0.952901	+	0.303281i	$0.901918\pi$
$740$		0			0
$741$	−56.7939	−	87.6298i	−0.0766449	−	0.118259i
$742$		0			0
$743$	−656.602	−	379.089i	−0.883718	−	0.510215i	−0.0118352	−	0.999930i	$-0.503767\pi$
$743$	−656.602	−	379.089i	−0.883718	−	0.510215i	−0.871882	+	0.489715i	$0.837101\pi$
$744$		0			0
$745$	635.496	+	1100.71i	0.853015	+	1.47746i
$746$		0			0
$747$	−626.350	−	280.240i	−0.838488	−	0.375154i
$748$		0			0
$749$	54.1063	+	93.7149i	0.0722381	+	0.125120i
$750$		0			0
$751$	−1141.58	−	659.091i	−1.52008	−	0.877618i	−0.999720	−	0.0236697i	$-0.992465\pi$
$751$	−1141.58	−	659.091i	−1.52008	−	0.877618i	−0.520358	−	0.853948i	$-0.674202\pi$
$752$		0			0
$753$	384.604	−	753.128i	0.510762	−	1.00017i
$754$		0			0
$755$		−	904.589i		−	1.19813i
$756$		0			0
$757$	−587.874			−0.776583			−0.388292	−	0.921537i	$-0.626935\pi$
$757$	−587.874			−0.776583			−0.388292	+	0.921537i	$0.626935\pi$
$758$		0			0
$759$	−369.931	−	188.915i	−0.487393	−	0.248899i
$760$		0			0
$761$	−188.496	+	326.485i	−0.247695	+	0.429021i	−0.962886	−	0.269908i	$-0.913007\pi$
$761$	−188.496	+	326.485i	−0.247695	+	0.429021i	0.715191	+	0.698929i	$0.246340\pi$
$762$		0			0
$763$	51.5845	−	29.7823i	0.0676075	−	0.0390332i
$764$		0			0
$765$	931.115	−	96.1465i	1.21714	−	0.125682i
$766$		0			0
$767$	−37.2917	+	21.5304i	−0.0486202	+	0.0280709i
$768$		0			0
$769$	643.939	−	1115.34i	0.837372	−	1.45037i	−0.0547122	−	0.998502i	$-0.517424\pi$
$769$	643.939	−	1115.34i	0.837372	−	1.45037i	0.892084	−	0.451869i	$-0.149243\pi$
$770$		0			0
$771$	189.600	−	122.882i	0.245914	−	0.159380i
$772$		0			0
$773$	−778.578			−1.00722			−0.503608	−	0.863932i	$-0.667994\pi$
$773$	−778.578			−1.00722			−0.503608	+	0.863932i	$0.667994\pi$
$774$		0			0
$775$			408.715i			0.527375i
$776$		0			0
$777$	−103.144	+	5.31117i	−0.132746	+	0.00683548i
$778$		0			0
$779$	−90.1884	−	52.0703i	−0.115775	−	0.0668425i
$780$		0			0
$781$	−766.801	−	1328.14i	−0.981819	−	1.70056i
$782$		0			0
$783$	−133.544	+	107.538i	−0.170554	+	0.137341i
$784$		0			0
$785$	−193.292	−	334.791i	−0.246232	−	0.426486i
$786$		0			0
$787$	−390.283	−	225.330i	−0.495913	−	0.286315i	0.231111	−	0.972927i	$-0.425764\pi$
$787$	−390.283	−	225.330i	−0.495913	−	0.286315i	−0.727024	+	0.686612i	$0.759097\pi$
$788$		0			0
$789$	−366.413	+	18.8676i	−0.464402	+	0.0239134i
$790$		0			0
$791$		−	10.7797i		−	0.0136280i
$792$		0			0
$793$	135.430			0.170782
$794$		0			0
$795$	−555.296	+	359.893i	−0.698485	+	0.452696i
$796$		0			0
$797$	182.891	−	316.776i	0.229474	−	0.397461i	−0.728178	−	0.685388i	$-0.759633\pi$
$797$	182.891	−	316.776i	0.229474	−	0.397461i	0.957652	+	0.287927i	$0.0929661\pi$
$798$		0			0
$799$	−163.101	+	94.1662i	−0.204131	+	0.117855i
$800$		0			0
$801$	−145.572	−	201.133i	−0.181737	−	0.251103i
$802$		0			0
$803$	−907.869	+	524.158i	−1.13060	+	0.652750i
$804$		0			0
$805$	14.3994	−	24.9406i	0.0178875	−	0.0309821i
$806$		0			0
$807$	749.305	+	382.652i	0.928507	+	0.474166i
$808$		0			0
$809$	1167.70			1.44339			0.721695	−	0.692212i	$-0.243364\pi$
$809$	1167.70			1.44339			0.721695	+	0.692212i	$0.243364\pi$
$810$		0			0
$811$			810.121i			0.998916i	0.866338	+	0.499458i	$0.166467\pi$
$811$			810.121i			0.998916i	−0.866338	+	0.499458i	$0.833533\pi$
$812$		0			0
$813$	111.127	−	217.608i	0.136687	−	0.267660i
$814$		0			0
$815$	−763.114	−	440.584i	−0.936336	−	0.540594i
$816$		0			0
$817$	−382.135	−	661.878i	−0.467730	−	0.810132i
$818$		0			0
$819$	−7.68503	+	5.56210i	−0.00938343	+	0.00679134i
$820$		0			0
$821$	280.513	+	485.862i	0.341672	+	0.591793i	0.984743	−	0.174013i	$-0.0556734\pi$
$821$	280.513	+	485.862i	0.341672	+	0.591793i	−0.643071	+	0.765806i	$0.722340\pi$
$822$		0			0
$823$	1016.04	+	586.612i	1.23456	+	0.712773i	0.967977	−	0.251039i	$-0.0807722\pi$
$823$	1016.04	+	586.612i	1.23456	+	0.712773i	0.266583	+	0.963812i	$0.414105\pi$
$824$		0			0
$825$	364.602	+	562.561i	0.441942	+	0.681892i
$826$		0			0
$827$			267.739i			0.323747i	0.986811	+	0.161874i	$0.0517537\pi$
$827$			267.739i			0.323747i	−0.986811	+	0.161874i	$0.948246\pi$
$828$		0			0
$829$	432.474			0.521682			0.260841	−	0.965382i	$-0.416000\pi$
$829$	432.474			0.521682			0.260841	+	0.965382i	$0.416000\pi$
$830$		0			0
$831$	69.3806	+	1347.38i	0.0834904	+	1.62140i
$832$		0			0
$833$	411.518	−	712.769i	0.494019	−	0.855665i
$834$		0			0
$835$	925.472	−	534.321i	1.10835	−	0.639906i
$836$		0			0
$837$	−311.196	+	804.106i	−0.371799	+	0.960701i
$838$		0			0
$839$	459.103	−	265.063i	0.547202	−	0.315927i	−0.200790	−	0.979634i	$-0.564351\pi$
$839$	459.103	−	265.063i	0.547202	−	0.315927i	0.747993	+	0.663707i	$0.231018\pi$
$840$		0			0
$841$	400.337	−	693.403i	0.476024	−	0.824499i
$842$		0			0
$843$	11.6831	+	226.889i	0.0138590	+	0.269144i
$844$		0			0
$845$	−1019.44			−1.20644
$846$		0			0
$847$			108.590i			0.128205i
$848$		0			0
$849$	606.774	+	936.219i	0.714692	+	1.10273i
$850$		0			0
$851$	−400.278	−	231.100i	−0.470361	−	0.271563i
$852$		0			0
$853$	−88.3868	−	153.090i	−0.103619	−	0.179473i	0.809554	−	0.587045i	$-0.199709\pi$
$853$	−88.3868	−	153.090i	−0.103619	−	0.179473i	−0.913173	+	0.407572i	$0.866376\pi$
$854$		0			0
$855$	−110.859	−	1073.60i	−0.129660	−	1.25567i
$856$		0			0
$857$	−194.859	−	337.505i	−0.227373	−	0.393821i	0.729656	−	0.683815i	$-0.239680\pi$
$857$	−194.859	−	337.505i	−0.227373	−	0.393821i	−0.957029	+	0.289993i	$0.906347\pi$
$858$		0			0
$859$	−503.279	−	290.568i	−0.585889	−	0.338263i	0.177581	−	0.984106i	$-0.443173\pi$
$859$	−503.279	−	290.568i	−0.585889	−	0.338263i	−0.763470	+	0.645843i	$0.776506\pi$
$860$		0			0
$861$	−4.30282	+	8.42575i	−0.00499747	+	0.00978601i
$862$		0			0
$863$			827.326i			0.958663i	0.877634	+	0.479331i	$0.159121\pi$
$863$			827.326i			0.958663i	−0.877634	+	0.479331i	$0.840879\pi$
$864$		0			0
$865$	−1546.92			−1.78835
$866$		0			0
$867$	7.51293	+	3.83667i	0.00866543	+	0.00442522i
$868$		0			0
$869$	−324.426	+	561.923i	−0.373333	+	0.646632i
$870$		0			0
$871$	−56.7831	+	32.7837i	−0.0651930	+	0.0376392i
$872$		0			0
$873$	−95.9966	+	214.557i	−0.109962	+	0.245770i
$874$		0			0
$875$	38.3732	−	22.1548i	0.0438551	−	0.0253198i
$876$		0			0
$877$	279.815	−	484.653i	0.319059	−	0.552626i	−0.661233	−	0.750181i	$-0.729967\pi$
$877$	279.815	−	484.653i	0.319059	−	0.552626i	0.980292	+	0.197554i	$0.0632999\pi$
$878$		0			0
$879$	−334.297	+	216.662i	−0.380315	+	0.246487i
$880$		0			0
$881$	−957.127			−1.08641			−0.543205	−	0.839600i	$-0.682789\pi$
$881$	−957.127			−1.08641			−0.543205	+	0.839600i	$0.682789\pi$
$882$		0			0
$883$		−	625.252i		−	0.708100i	−0.935227	−	0.354050i	$-0.884804\pi$
$883$		−	625.252i		−	0.708100i	0.935227	−	0.354050i	$-0.115196\pi$
$884$		0			0
$885$	−444.475	+	22.8873i	−0.502231	+	0.0258613i
$886$		0			0
$887$	−921.187	−	531.847i	−1.03854	−	0.599602i	−0.119122	−	0.992880i	$-0.538008\pi$
$887$	−921.187	−	531.847i	−1.03854	−	0.599602i	−0.919420	+	0.393277i	$0.871341\pi$
$888$		0			0
$889$	48.5496	+	84.0904i	0.0546115	+	0.0945899i
$890$		0			0
$891$	288.984	+	1384.39i	0.324337	+	1.55375i
$892$		0			0
$893$	108.576	+	188.059i	0.121585	+	0.210592i
$894$		0			0
$895$	511.172	+	295.125i	0.571142	+	0.329749i
$896$		0			0
$897$	−42.3985	+	2.18322i	−0.0472670	+	0.00243391i
$898$		0			0
$899$			202.793i			0.225577i
$900$		0			0
$901$	606.935			0.673624
$902$		0			0
$903$	−58.2647	+	37.7620i	−0.0645235	+	0.0418184i
$904$		0			0
$905$	−1010.61	+	1750.43i	−1.11670	+	1.93418i
$906$		0			0
$907$	207.207	−	119.631i	0.228453	−	0.131898i	−0.381405	−	0.924408i	$-0.624560\pi$
$907$	207.207	−	119.631i	0.228453	−	0.131898i	0.609858	+	0.792510i	$0.291226\pi$
$908$		0			0
$909$	−94.7072	+	211.675i	−0.104188	+	0.232866i
$910$		0			0
$911$	−175.804	+	101.501i	−0.192980	+	0.111417i	−0.593377	−	0.804925i	$-0.702206\pi$
$911$	−175.804	+	101.501i	−0.192980	+	0.111417i	0.400397	+	0.916342i	$0.368872\pi$
$912$		0			0
$913$	−665.585	+	1152.83i	−0.729009	+	1.26268i
$914$		0			0
$915$	1246.62	+	636.619i	1.36243	+	0.695758i
$916$		0			0
$917$	84.1801			0.0917994
$918$		0			0
$919$			878.708i			0.956156i	0.878317	+	0.478078i	$0.158666\pi$
$919$			878.708i			0.956156i	−0.878317	+	0.478078i	$0.841334\pi$
$920$		0			0
$921$	459.143	−	899.090i	0.498527	−	0.976210i
$922$		0			0
$923$	−135.746	−	78.3730i	−0.147070	−	0.0849111i
$924$		0			0
$925$	372.975	+	646.011i	0.403216	+	0.698391i
$926$		0			0
$927$	18.1406	+	175.680i	0.0195691	+	0.189514i
$928$		0			0
$929$	300.259	+	520.064i	0.323207	+	0.559810i	0.981148	−	0.193259i	$-0.0619058\pi$
$929$	300.259	+	520.064i	0.323207	+	0.559810i	−0.657941	+	0.753069i	$0.728572\pi$
$930$		0			0
$931$	−821.838	−	474.489i	−0.882748	−	0.509655i
$932$		0			0
$933$	573.135	+	884.316i	0.614293	+	0.947820i
$934$		0			0
$935$		−	1815.93i		−	1.94217i
$936$		0			0
$937$	−184.325			−0.196718			−0.0983589	−	0.995151i	$-0.531359\pi$
$937$	−184.325			−0.196718			−0.0983589	+	0.995151i	$0.531359\pi$
$938$		0			0
$939$	29.4447	+	571.822i	0.0313575	+	0.608969i
$940$		0			0
$941$	377.587	−	653.999i	0.401261	−	0.695005i	−0.592617	−	0.805484i	$-0.701905\pi$
$941$	377.587	−	653.999i	0.401261	−	0.695005i	0.993878	+	0.110479i	$0.0352386\pi$
$942$		0			0
$943$	−36.6668	+	21.1696i	−0.0388831	+	0.0224492i
$944$		0			0
$945$	−96.8859	+	15.0735i	−0.102525	+	0.0159507i
$946$		0			0
$947$	−769.965	+	444.539i	−0.813057	+	0.469419i	−0.848016	−	0.529970i	$-0.822203\pi$
$947$	−769.965	+	444.539i	−0.813057	+	0.469419i	0.0349595	+	0.999389i	$0.488870\pi$
$948$		0			0
$949$	−53.5731	+	92.7913i	−0.0564521	+	0.0977779i
$950$		0			0
$951$	−62.5727	−	1215.17i	−0.0657967	−	1.27778i
$952$		0			0
$953$	15.5920			0.0163610			0.00818050	−	0.999967i	$-0.497396\pi$
$953$	15.5920			0.0163610			0.00818050	+	0.999967i	$0.497396\pi$
$954$		0			0
$955$			2.49830i			0.00261602i
$956$		0			0
$957$	180.905	+	279.127i	0.189034	+	0.291669i
$958$		0			0
$959$	3.15291	+	1.82033i	0.00328770	+	0.00189816i
$960$		0			0
$961$	29.3970	+	50.9172i	0.0305900	+	0.0529835i
$962$		0			0
$963$	1335.68	−	966.706i	1.38699	−	1.00385i
$964$		0			0
$965$	−191.961	−	332.486i	−0.198923	−	0.344545i
$966$		0			0
$967$	−847.921	−	489.548i	−0.876858	−	0.506254i	−0.00723669	−	0.999974i	$-0.502304\pi$
$967$	−847.921	−	489.548i	−0.876858	−	0.506254i	−0.869621	+	0.493720i	$0.835637\pi$
$968$		0			0
$969$	−450.229	+	881.635i	−0.464633	+	0.909840i
$970$		0			0
$971$		−	67.3838i		−	0.0693963i	−0.999398	−	0.0346982i	$-0.988953\pi$
$971$		−	67.3838i		−	0.0693963i	0.999398	−	0.0346982i	$-0.0110470\pi$
$972$		0			0
$973$	−70.3667			−0.0723193
$974$		0			0
$975$	61.0216	+	31.1622i	0.0625863	+	0.0319613i
$976$		0			0
$977$	353.710	−	612.644i	0.362037	−	0.627067i	−0.626259	−	0.779615i	$-0.715415\pi$
$977$	353.710	−	612.644i	0.362037	−	0.627067i	0.988296	+	0.152549i	$0.0487480\pi$
$978$		0			0
$979$	−417.133	+	240.832i	−0.426081	+	0.245998i
$980$		0			0
$981$	−532.115	−	735.211i	−0.542421	−	0.749451i
$982$		0			0
$983$	338.829	−	195.623i	0.344689	−	0.199006i	−0.317655	−	0.948206i	$-0.602895\pi$
$983$	338.829	−	195.623i	0.344689	−	0.199006i	0.662343	+	0.749200i	$0.269562\pi$
$984$		0			0
$985$	−638.971	+	1106.73i	−0.648701	+	1.12358i
$986$		0			0
$987$	16.5547	−	10.7293i	0.0167727	−	0.0108706i
$988$		0			0
$989$	−310.720			−0.314176
$990$		0			0
$991$			104.988i			0.105941i	0.998596	+	0.0529706i	$0.0168690\pi$
$991$			104.988i			0.105941i	−0.998596	+	0.0529706i	$0.983131\pi$
$992$		0			0
$993$	−1328.81	+	68.4244i	−1.33818	+	0.0689068i
$994$		0			0
$995$	−1592.67	−	919.530i	−1.60068	−	0.924151i
$996$		0			0
$997$	39.0028	+	67.5547i	0.0391201	+	0.0677580i	0.884923	−	0.465738i	$-0.154211\pi$
$997$	39.0028	+	67.5547i	0.0391201	+	0.0677580i	−0.845802	+	0.533496i	$0.820878\pi$
$998$		0			0
$999$	241.918	+	1554.95i	0.242160	+	1.55650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.o.g.319.2		16
3.2	odd	2		1728.3.o.g.1279.7		16
4.3	odd	2	inner	576.3.o.g.319.7		16
8.3	odd	2		36.3.f.c.31.4	yes	16
8.5	even	2		36.3.f.c.31.3	yes	16
9.2	odd	6		1728.3.o.g.127.8		16
9.7	even	3	inner	576.3.o.g.511.7		16
12.11	even	2		1728.3.o.g.1279.8		16
24.5	odd	2		108.3.f.c.91.6		16
24.11	even	2		108.3.f.c.91.5		16
36.7	odd	6	inner	576.3.o.g.511.2		16
36.11	even	6		1728.3.o.g.127.7		16
72.5	odd	6		324.3.d.g.163.2		8
72.11	even	6		108.3.f.c.19.6		16
72.13	even	6		324.3.d.i.163.7		8
72.29	odd	6		108.3.f.c.19.5		16
72.43	odd	6		36.3.f.c.7.3	✓	16
72.59	even	6		324.3.d.g.163.1		8
72.61	even	6		36.3.f.c.7.4	yes	16
72.67	odd	6		324.3.d.i.163.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.3	✓	16	72.43	odd	6
36.3.f.c.7.4	yes	16	72.61	even	6
36.3.f.c.31.3	yes	16	8.5	even	2
36.3.f.c.31.4	yes	16	8.3	odd	2
108.3.f.c.19.5		16	72.29	odd	6
108.3.f.c.19.6		16	72.11	even	6
108.3.f.c.91.5		16	24.11	even	2
108.3.f.c.91.6		16	24.5	odd	2
324.3.d.g.163.1		8	72.59	even	6
324.3.d.g.163.2		8	72.5	odd	6
324.3.d.i.163.7		8	72.13	even	6
324.3.d.i.163.8		8	72.67	odd	6
576.3.o.g.319.2		16	1.1	even	1	trivial
576.3.o.g.319.7		16	4.3	odd	2	inner
576.3.o.g.511.2		16	36.7	odd	6	inner
576.3.o.g.511.7		16	9.7	even	3	inner
1728.3.o.g.127.7		16	36.11	even	6
1728.3.o.g.127.8		16	9.2	odd	6
1728.3.o.g.1279.7		16	3.2	odd	2
1728.3.o.g.1279.8		16	12.11	even	2

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.67178 - 1.36441i) q^{3} +(-3.07403 + 5.32438i) q^{5} +(-0.511543 + 0.295340i) q^{7} +(5.27677 + 7.29079i) q^{9} +O(q^{10})\)	\(q+(-2.67178 - 1.36441i) q^{3} +(-3.07403 + 5.32438i) q^{5} +(-0.511543 + 0.295340i) q^{7} +(5.27677 + 7.29079i) q^{9} +(15.1205 - 8.72982i) q^{11} +(0.892255 - 1.54543i) q^{13} +(15.4778 - 10.0313i) q^{15} -16.9171 q^{17} +19.5058i q^{19} +(1.76969 - 0.0911265i) q^{21} +(6.86778 + 3.96511i) q^{23} +(-6.39933 - 11.0840i) q^{25} +(-4.15071 - 26.6790i) q^{27} +(-3.17517 - 5.49956i) q^{29} +(-27.6558 - 15.9671i) q^{31} +(-52.3096 + 2.69357i) q^{33} -3.63153i q^{35} -58.2834 q^{37} +(-4.49251 + 2.91164i) q^{39} +(-2.66948 + 4.62368i) q^{41} +(-33.9324 + 19.5909i) q^{43} +(-55.0399 + 5.68339i) q^{45} +(9.64117 - 5.56633i) q^{47} +(-24.3255 + 42.1331i) q^{49} +(45.1987 + 23.0819i) q^{51} -35.8770 q^{53} +107.343i q^{55} +(26.6139 - 52.1151i) q^{57} +(-20.8974 - 12.0651i) q^{59} +(37.9460 + 65.7244i) q^{61} +(-4.85256 - 2.17112i) q^{63} +(5.48564 + 9.50141i) q^{65} +(-31.8200 - 18.3713i) q^{67} +(-12.9391 - 19.9644i) q^{69} -87.8370i q^{71} -60.0423 q^{73} +(1.97450 + 38.3452i) q^{75} +(-5.15652 + 8.93136i) q^{77} +(-32.1841 + 18.5815i) q^{79} +(-25.3114 + 76.9437i) q^{81} +(-66.0281 + 38.1214i) q^{83} +(52.0037 - 90.0730i) q^{85} +(0.979694 + 19.0258i) q^{87} -27.5873 q^{89} +1.05407i q^{91} +(52.1045 + 80.3944i) q^{93} +(-103.856 - 59.9614i) q^{95} +(13.0585 + 22.6180i) q^{97} +(143.435 + 64.1751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{5} + 18 q^{9}+O(q^{10}) \) 16 * q - 6 * q^5 + 18 * q^9	\( 16 q - 6 q^{5} + 18 q^{9} + 46 q^{13} + 12 q^{17} + 66 q^{21} - 30 q^{25} - 42 q^{29} - 168 q^{33} - 56 q^{37} + 84 q^{41} - 174 q^{45} + 58 q^{49} + 72 q^{53} + 366 q^{57} + 34 q^{61} - 30 q^{65} + 54 q^{69} + 116 q^{73} + 330 q^{77} - 102 q^{81} + 140 q^{85} - 384 q^{89} + 486 q^{93} - 148 q^{97}+O(q^{100}) \) 16 * q - 6 * q^5 + 18 * q^9 + 46 * q^13 + 12 * q^17 + 66 * q^21 - 30 * q^25 - 42 * q^29 - 168 * q^33 - 56 * q^37 + 84 * q^41 - 174 * q^45 + 58 * q^49 + 72 * q^53 + 366 * q^57 + 34 * q^61 - 30 * q^65 + 54 * q^69 + 116 * q^73 + 330 * q^77 - 102 * q^81 + 140 * q^85 - 384 * q^89 + 486 * q^93 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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