LMFDB - Embedded newform 1500.2.m.b.1201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(301,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("1500.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.m (of order $5$, degree $4$, 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:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1201.1
Root			$0.669131 + 0.743145i$ of defining polynomial
Character	$\chi$	$=$	1500.1201
Dual form			1500.2.m.b.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{3} -0.547318 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{3} -0.547318 q^{7} +(-0.809017 + 0.587785i) q^{9} +(1.08268 + 0.786610i) q^{11} +(0.244415 - 0.177578i) q^{13} +(-1.24898 + 3.84398i) q^{17} +(-1.74064 + 5.35713i) q^{19} +(0.169131 + 0.520530i) q^{21} +(0.198375 + 0.144128i) q^{23} +(0.809017 + 0.587785i) q^{27} +(-0.423273 - 1.30270i) q^{29} +(-1.09336 + 3.36501i) q^{31} +(0.413545 - 1.27276i) q^{33} +(-1.76988 + 1.28589i) q^{37} +(-0.244415 - 0.177578i) q^{39} +(7.93066 - 5.76196i) q^{41} +8.35963 q^{43} +(3.23656 + 9.96110i) q^{47} -6.70044 q^{49} +4.04179 q^{51} +(2.37819 + 7.31931i) q^{53} +5.63282 q^{57} +(-3.35916 + 2.44057i) q^{59} +(-1.67981 - 1.22046i) q^{61} +(0.442790 - 0.321706i) q^{63} +(-2.62230 + 8.07061i) q^{67} +(0.0757724 - 0.233204i) q^{69} +(-2.83777 - 8.73377i) q^{71} +(8.86356 + 6.43975i) q^{73} +(-0.592568 - 0.430526i) q^{77} +(4.69177 + 14.4398i) q^{79} +(0.309017 - 0.951057i) q^{81} +(2.05626 - 6.32850i) q^{83} +(-1.10814 + 0.805112i) q^{87} +(-4.02780 - 2.92637i) q^{89} +(-0.133773 + 0.0971915i) q^{91} +3.53818 q^{93} +(-1.25499 - 3.86248i) q^{97} -1.33826 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 8 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 8 * q^7 - 2 * q^9	$ 8 q + 2 q^{3} + 8 q^{7} - 2 q^{9} - 2 q^{11} - 7 q^{17} + 5 q^{19} - 3 q^{21} - 7 q^{23} + 2 q^{27} + 27 q^{29} - 3 q^{31} - 3 q^{33} + 9 q^{37} + 20 q^{41} + 68 q^{43} + 7 q^{47} - 8 q^{49} - 8 q^{51} + 11 q^{53} + 10 q^{57} + 2 q^{59} - 14 q^{61} - 7 q^{63} - 28 q^{67} + 2 q^{69} - 15 q^{71} - 6 q^{73} - 17 q^{77} + 24 q^{79} - 2 q^{81} - 2 q^{83} + 23 q^{87} + 5 q^{91} + 18 q^{93} - 34 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 8 * q^7 - 2 * q^9 - 2 * q^11 - 7 * q^17 + 5 * q^19 - 3 * q^21 - 7 * q^23 + 2 * q^27 + 27 * q^29 - 3 * q^31 - 3 * q^33 + 9 * q^37 + 20 * q^41 + 68 * q^43 + 7 * q^47 - 8 * q^49 - 8 * q^51 + 11 * q^53 + 10 * q^57 + 2 * q^59 - 14 * q^61 - 7 * q^63 - 28 * q^67 + 2 * q^69 - 15 * q^71 - 6 * q^73 - 17 * q^77 + 24 * q^79 - 2 * q^81 - 2 * q^83 + 23 * q^87 + 5 * q^91 + 18 * q^93 - 34 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.547318			−0.206867			−0.103433	−	0.994636i	$-0.532983\pi$
$7$	−0.547318			−0.206867			−0.103433	+	0.994636i	$0.532983\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	1.08268	+	0.786610i	0.326439	+	0.237172i	0.738918	−	0.673795i	$-0.235337\pi$
$11$	1.08268	+	0.786610i	0.326439	+	0.237172i	−0.412479	+	0.910967i	$0.635337\pi$
$12$		0			0
$13$	0.244415	−	0.177578i	0.0677885	−	0.0492512i	−0.553375	−	0.832932i	$-0.686660\pi$
$13$	0.244415	−	0.177578i	0.0677885	−	0.0492512i	0.621163	+	0.783681i	$0.286660\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.24898	+	3.84398i	−0.302923	+	0.932301i	0.677521	+	0.735503i	$0.263054\pi$
$17$	−1.24898	+	3.84398i	−0.302923	+	0.932301i	−0.980444	+	0.196798i	$0.936946\pi$
$18$		0			0
$19$	−1.74064	+	5.35713i	−0.399329	+	1.22901i	0.526209	+	0.850355i	$0.323613\pi$
$19$	−1.74064	+	5.35713i	−0.399329	+	1.22901i	−0.925538	+	0.378654i	$0.876387\pi$
$20$		0			0
$21$	0.169131	+	0.520530i	0.0369073	+	0.113589i
$22$		0			0
$23$	0.198375	+	0.144128i	0.0413640	+	0.0300527i	0.608275	−	0.793726i	$-0.291862\pi$
$23$	0.198375	+	0.144128i	0.0413640	+	0.0300527i	−0.566911	+	0.823779i	$0.691862\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	−0.423273	−	1.30270i	−0.0785997	−	0.241905i	0.904034	−	0.427460i	$-0.140592\pi$
$29$	−0.423273	−	1.30270i	−0.0785997	−	0.241905i	−0.982634	+	0.185555i	$0.940592\pi$
$30$		0			0
$31$	−1.09336	+	3.36501i	−0.196373	+	0.604374i	0.803585	+	0.595190i	$0.202923\pi$
$31$	−1.09336	+	3.36501i	−0.196373	+	0.604374i	−0.999958	+	0.00918358i	$0.997077\pi$
$32$		0			0
$33$	0.413545	−	1.27276i	0.0719890	−	0.221559i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.76988	+	1.28589i	−0.290967	+	0.211400i	−0.723687	−	0.690129i	$-0.757554\pi$
$37$	−1.76988	+	1.28589i	−0.290967	+	0.211400i	0.432720	+	0.901528i	$0.357554\pi$
$38$		0			0
$39$	−0.244415	−	0.177578i	−0.0391377	−	0.0284352i
$40$		0			0
$41$	7.93066	−	5.76196i	1.23856	−	0.899868i	0.241060	−	0.970510i	$-0.422505\pi$
$41$	7.93066	−	5.76196i	1.23856	−	0.899868i	0.997502	+	0.0706425i	$0.0225049\pi$
$42$		0			0
$43$	8.35963			1.27483			0.637415	−	0.770520i	$-0.280004\pi$
$43$	8.35963			1.27483			0.637415	+	0.770520i	$0.280004\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.23656	+	9.96110i	0.472100	+	1.45298i	0.849829	+	0.527059i	$0.176705\pi$
$47$	3.23656	+	9.96110i	0.472100	+	1.45298i	−0.377729	+	0.925916i	$0.623295\pi$
$48$		0			0
$49$	−6.70044			−0.957206
$50$		0			0
$51$	4.04179			0.565964
$52$		0			0
$53$	2.37819	+	7.31931i	0.326669	+	1.00538i	0.970682	+	0.240369i	$0.0772685\pi$
$53$	2.37819	+	7.31931i	0.326669	+	1.00538i	−0.644012	+	0.765015i	$0.722731\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.63282			0.746085
$58$		0			0
$59$	−3.35916	+	2.44057i	−0.437325	+	0.317735i	−0.784571	−	0.620039i	$-0.787117\pi$
$59$	−3.35916	+	2.44057i	−0.437325	+	0.317735i	0.347246	+	0.937774i	$0.387117\pi$
$60$		0			0
$61$	−1.67981	−	1.22046i	−0.215078	−	0.156263i	0.475030	−	0.879969i	$-0.342437\pi$
$61$	−1.67981	−	1.22046i	−0.215078	−	0.156263i	−0.690108	+	0.723706i	$0.742437\pi$
$62$		0			0
$63$	0.442790	−	0.321706i	0.0557863	−	0.0405311i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.62230	+	8.07061i	−0.320365	+	0.985982i	0.653125	+	0.757251i	$0.273458\pi$
$67$	−2.62230	+	8.07061i	−0.320365	+	0.985982i	−0.973490	+	0.228732i	$0.926542\pi$
$68$		0			0
$69$	0.0757724	−	0.233204i	0.00912193	−	0.0280744i
$70$		0			0
$71$	−2.83777	−	8.73377i	−0.336782	−	1.03651i	−0.965838	−	0.259148i	$-0.916558\pi$
$71$	−2.83777	−	8.73377i	−0.336782	−	1.03651i	0.629056	−	0.777360i	$-0.283442\pi$
$72$		0			0
$73$	8.86356	+	6.43975i	1.03740	+	0.753716i	0.969777	−	0.243995i	$-0.0784579\pi$
$73$	8.86356	+	6.43975i	1.03740	+	0.753716i	0.0676248	+	0.997711i	$0.478458\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.592568	−	0.430526i	−0.0675294	−	0.0490630i
$78$		0			0
$79$	4.69177	+	14.4398i	0.527866	+	1.62460i	0.758578	+	0.651582i	$0.225894\pi$
$79$	4.69177	+	14.4398i	0.527866	+	1.62460i	−0.230713	+	0.973022i	$0.574106\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	2.05626	−	6.32850i	0.225703	−	0.694643i	−0.772516	−	0.634995i	$-0.781002\pi$
$83$	2.05626	−	6.32850i	0.225703	−	0.694643i	0.998219	−	0.0596483i	$-0.0189979\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.10814	+	0.805112i	−0.118805	+	0.0863171i
$88$		0			0
$89$	−4.02780	−	2.92637i	−0.426946	−	0.310194i	0.353481	−	0.935442i	$-0.384998\pi$
$89$	−4.02780	−	2.92637i	−0.426946	−	0.310194i	−0.780427	+	0.625247i	$0.784998\pi$
$90$		0			0
$91$	−0.133773	+	0.0971915i	−0.0140232	+	0.0101884i
$92$		0			0
$93$	3.53818			0.366892
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.25499	−	3.86248i	−0.127425	−	0.392175i	0.866910	−	0.498465i	$-0.166103\pi$
$97$	−1.25499	−	3.86248i	−0.127425	−	0.392175i	−0.994335	+	0.106290i	$0.966103\pi$
$98$		0			0
$99$	−1.33826			−0.134500
$100$		0			0
$101$	18.4489			1.83573			0.917865	−	0.396892i	$-0.129911\pi$
$101$	18.4489			1.83573			0.917865	+	0.396892i	$0.129911\pi$
$102$		0			0
$103$	4.54762	+	13.9961i	0.448090	+	1.37908i	0.879059	+	0.476713i	$0.158172\pi$
$103$	4.54762	+	13.9961i	0.448090	+	1.37908i	−0.430969	+	0.902367i	$0.641828\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.10528			0.493546			0.246773	−	0.969073i	$-0.420630\pi$
$107$	5.10528			0.493546			0.246773	+	0.969073i	$0.420630\pi$
$108$		0			0
$109$	−3.82331	+	2.77780i	−0.366207	+	0.266065i	−0.755636	−	0.654991i	$-0.772672\pi$
$109$	−3.82331	+	2.77780i	−0.366207	+	0.266065i	0.389429	+	0.921056i	$0.372672\pi$
$110$		0			0
$111$	1.76988	+	1.28589i	0.167990	+	0.122052i
$112$		0			0
$113$	3.34799	−	2.43246i	0.314952	−	0.228826i	−0.419066	−	0.907956i	$-0.637643\pi$
$113$	3.34799	−	2.43246i	0.314952	−	0.228826i	0.734019	+	0.679129i	$0.237643\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.0933582	+	0.287327i	−0.00863097	+	0.0265634i
$118$		0			0
$119$	0.683591	−	2.10388i	0.0626647	−	0.192862i
$120$		0			0
$121$	−2.84576	−	8.75833i	−0.258705	−	0.796212i
$122$		0			0
$123$	−7.93066	−	5.76196i	−0.715084	−	0.519539i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−10.2568	−	7.45200i	−0.910144	−	0.661258i	0.0309074	−	0.999522i	$-0.490160\pi$
$127$	−10.2568	−	7.45200i	−0.910144	−	0.661258i	−0.941051	+	0.338264i	$0.890160\pi$
$128$		0			0
$129$	−2.58327	−	7.95048i	−0.227444	−	0.700000i
$130$		0			0
$131$	−3.81046	+	11.7274i	−0.332921	+	1.02463i	0.634815	+	0.772664i	$0.281076\pi$
$131$	−3.81046	+	11.7274i	−0.332921	+	1.02463i	−0.967737	+	0.251963i	$0.918924\pi$
$132$		0			0
$133$	0.952682	−	2.93205i	0.0826080	−	0.254241i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.67508	−	6.30281i	0.741162	−	0.538486i	−0.151913	−	0.988394i	$-0.548543\pi$
$137$	8.67508	−	6.30281i	0.741162	−	0.538486i	0.893075	+	0.449908i	$0.148543\pi$
$138$		0			0
$139$	11.0632	+	8.03786i	0.938365	+	0.681762i	0.948027	−	0.318191i	$-0.103075\pi$
$139$	11.0632	+	8.03786i	0.938365	+	0.681762i	−0.00966163	+	0.999953i	$0.503075\pi$
$140$		0			0
$141$	8.47341	−	6.15630i	0.713590	−	0.518454i
$142$		0			0
$143$	0.404307			0.0338098
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.07055	+	6.37250i	0.170776	+	0.525595i
$148$		0			0
$149$	8.88176			0.727622			0.363811	−	0.931473i	$-0.381475\pi$
$149$	8.88176			0.727622			0.363811	+	0.931473i	$0.381475\pi$
$150$		0			0
$151$	2.68310			0.218348			0.109174	−	0.994023i	$-0.465179\pi$
$151$	2.68310			0.218348			0.109174	+	0.994023i	$0.465179\pi$
$152$		0			0
$153$	−1.24898	−	3.84398i	−0.100974	−	0.310767i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−11.7576			−0.938355			−0.469178	−	0.883104i	$-0.655450\pi$
$157$	−11.7576			−0.938355			−0.469178	+	0.883104i	$0.655450\pi$
$158$		0			0
$159$	6.22618	−	4.52358i	0.493768	−	0.358743i
$160$		0			0
$161$	−0.108574	−	0.0788837i	−0.00855684	−	0.00621691i
$162$		0			0
$163$	−14.8153	+	10.7639i	−1.16042	+	0.843097i	−0.989831	−	0.142245i	$-0.954568\pi$
$163$	−14.8153	+	10.7639i	−1.16042	+	0.843097i	−0.170592	+	0.985342i	$0.554568\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.36097	+	4.18862i	−0.105315	+	0.324125i	−0.989804	−	0.142435i	$-0.954507\pi$
$167$	−1.36097	+	4.18862i	−0.105315	+	0.324125i	0.884489	+	0.466560i	$0.154507\pi$
$168$		0			0
$169$	−3.98902	+	12.2769i	−0.306847	+	0.944379i
$170$		0			0
$171$	−1.74064	−	5.35713i	−0.133110	−	0.409670i
$172$		0			0
$173$	−12.8882	−	9.36385i	−0.979875	−	0.711921i	−0.0221940	−	0.999754i	$-0.507065\pi$
$173$	−12.8882	−	9.36385i	−0.979875	−	0.711921i	−0.957681	+	0.287833i	$0.907065\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.35916	+	2.44057i	0.252490	+	0.183445i
$178$		0			0
$179$	1.16493	+	3.58528i	0.0870707	+	0.267976i	0.985106	−	0.171947i	$-0.0550057\pi$
$179$	1.16493	+	3.58528i	0.0870707	+	0.267976i	−0.898035	+	0.439923i	$0.855006\pi$
$180$		0			0
$181$	−8.24669	+	25.3807i	−0.612971	+	1.88653i	−0.185004	+	0.982738i	$0.559230\pi$
$181$	−8.24669	+	25.3807i	−0.612971	+	1.88653i	−0.427967	+	0.903794i	$0.640770\pi$
$182$		0			0
$183$	−0.641631	+	1.97474i	−0.0474308	+	0.145977i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−4.37595	+	3.17932i	−0.320001	+	0.232495i
$188$		0			0
$189$	−0.442790	−	0.321706i	−0.0322082	−	0.0234006i
$190$		0			0
$191$	−3.74803	+	2.72310i	−0.271198	+	0.197037i	−0.715069	−	0.699054i	$-0.753605\pi$
$191$	−3.74803	+	2.72310i	−0.271198	+	0.197037i	0.443871	+	0.896091i	$0.353605\pi$
$192$		0			0
$193$	20.7440			1.49319			0.746594	−	0.665280i	$-0.231688\pi$
$193$	20.7440			1.49319			0.746594	+	0.665280i	$0.231688\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.34529	−	19.5288i	−0.452083	−	1.39137i	−0.874526	−	0.484979i	$-0.838827\pi$
$197$	−6.34529	−	19.5288i	−0.452083	−	1.39137i	0.422443	−	0.906390i	$-0.361173\pi$
$198$		0			0
$199$	5.91437			0.419259			0.209629	−	0.977781i	$-0.432774\pi$
$199$	5.91437			0.419259			0.209629	+	0.977781i	$0.432774\pi$
$200$		0			0
$201$	8.48594			0.598552
$202$		0			0
$203$	0.231665	+	0.712991i	0.0162597	+	0.0500421i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.245205			−0.0170429
$208$		0			0
$209$	−6.09852	+	4.43083i	−0.421843	+	0.306487i
$210$		0			0
$211$	−18.5512	−	13.4782i	−1.27712	−	0.927880i	−0.277655	−	0.960681i	$-0.589557\pi$
$211$	−18.5512	−	13.4782i	−1.27712	−	0.927880i	−0.999462	+	0.0328013i	$0.989557\pi$
$212$		0			0
$213$	−7.42939	+	5.39777i	−0.509053	+	0.369849i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.598415	−	1.84173i	0.0406230	−	0.125025i
$218$		0			0
$219$	3.38558	−	10.4197i	0.228776	−	0.704101i
$220$		0			0
$221$	0.377335	+	1.16132i	0.0253823	+	0.0781186i
$222$		0			0
$223$	−10.3148	−	7.49414i	−0.690730	−	0.501845i	0.186170	−	0.982518i	$-0.440393\pi$
$223$	−10.3148	−	7.49414i	−0.690730	−	0.501845i	−0.876900	+	0.480673i	$0.840393\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.92301	+	6.48294i	0.592241	+	0.430288i	0.843116	−	0.537731i	$-0.180719\pi$
$227$	8.92301	+	6.48294i	0.592241	+	0.430288i	−0.250876	+	0.968019i	$0.580719\pi$
$228$		0			0
$229$	−7.13214	−	21.9505i	−0.471305	−	1.45053i	−0.850876	−	0.525366i	$-0.823928\pi$
$229$	−7.13214	−	21.9505i	−0.471305	−	1.45053i	0.379571	−	0.925163i	$-0.376072\pi$
$230$		0			0
$231$	−0.226341	+	0.696606i	−0.0148921	+	0.0458333i
$232$		0			0
$233$	9.05055	−	27.8547i	0.592921	−	1.82482i	0.0281067	−	0.999605i	$-0.491052\pi$
$233$	9.05055	−	27.8547i	0.592921	−	1.82482i	0.564814	−	0.825218i	$-0.308948\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	12.2832	−	8.92428i	0.797881	−	0.579694i
$238$		0			0
$239$	−8.57443	−	6.22969i	−0.554634	−	0.402965i	0.274857	−	0.961485i	$-0.411369\pi$
$239$	−8.57443	−	6.22969i	−0.554634	−	0.402965i	−0.829491	+	0.558520i	$0.811369\pi$
$240$		0			0
$241$	−15.3888	+	11.1806i	−0.991282	+	0.720208i	−0.960201	−	0.279309i	$-0.909895\pi$
$241$	−15.3888	+	11.1806i	−0.991282	+	0.720208i	−0.0310802	+	0.999517i	$0.509895\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.525870	+	1.61846i	0.0334603	+	0.102980i
$248$		0			0
$249$	−6.65418			−0.421692
$250$		0			0
$251$	0.0370816			0.00234057			0.00117028	−	0.999999i	$-0.499627\pi$
$251$	0.0370816			0.00234057			0.00117028	+	0.999999i	$0.499627\pi$
$252$		0			0
$253$	0.101403	+	0.312087i	0.00637517	+	0.0196208i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.0237			0.625262			0.312631	−	0.949875i	$-0.398790\pi$
$257$	10.0237			0.625262			0.312631	+	0.949875i	$0.398790\pi$
$258$		0			0
$259$	0.968688	−	0.703793i	0.0601913	−	0.0437316i
$260$		0			0
$261$	1.10814	+	0.805112i	0.0685923	+	0.0498352i
$262$		0			0
$263$	−10.3407	+	7.51296i	−0.637635	+	0.463269i	−0.859037	−	0.511914i	$-0.828937\pi$
$263$	−10.3407	+	7.51296i	−0.637635	+	0.463269i	0.221402	+	0.975183i	$0.428937\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.53848	+	4.73496i	−0.0941536	+	0.289775i
$268$		0			0
$269$	6.58562	−	20.2685i	0.401533	−	1.23579i	−0.522224	−	0.852809i	$-0.674897\pi$
$269$	6.58562	−	20.2685i	0.401533	−	1.23579i	0.923756	−	0.382981i	$-0.125103\pi$
$270$		0			0
$271$	−4.14194	−	12.7476i	−0.251605	−	0.774361i	−0.994480	−	0.104930i	$-0.966538\pi$
$271$	−4.14194	−	12.7476i	−0.251605	−	0.774361i	0.742875	−	0.669431i	$-0.233462\pi$
$272$		0			0
$273$	0.133773	+	0.0971915i	0.00809629	+	0.00588230i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−15.2678	−	11.0927i	−0.917354	−	0.666496i	0.0255104	−	0.999675i	$-0.491879\pi$
$277$	−15.2678	−	11.0927i	−0.917354	−	0.666496i	−0.942864	+	0.333178i	$0.891879\pi$
$278$		0			0
$279$	−1.09336	−	3.36501i	−0.0654576	−	0.201458i
$280$		0			0
$281$	−5.37674	+	16.5479i	−0.320750	+	0.987166i	0.652573	+	0.757726i	$0.273690\pi$
$281$	−5.37674	+	16.5479i	−0.320750	+	0.987166i	−0.973323	+	0.229440i	$0.926310\pi$
$282$		0			0
$283$	−7.31371	+	22.5093i	−0.434755	+	1.33804i	0.458583	+	0.888652i	$0.348357\pi$
$283$	−7.31371	+	22.5093i	−0.434755	+	1.33804i	−0.893338	+	0.449386i	$0.851643\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.34060	+	3.15363i	−0.256217	+	0.186153i
$288$		0			0
$289$	0.537103	+	0.390228i	0.0315943	+	0.0229546i
$290$		0			0
$291$	−3.28562	+	2.38714i	−0.192606	+	0.139937i
$292$		0			0
$293$	−19.0317			−1.11184			−0.555921	−	0.831235i	$-0.687634\pi$
$293$	−19.0317			−1.11184			−0.555921	+	0.831235i	$0.687634\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.413545	+	1.27276i	0.0239963	+	0.0738531i
$298$		0			0
$299$	0.0740796			0.00428414
$300$		0			0
$301$	−4.57537			−0.263720
$302$		0			0
$303$	−5.70101	−	17.5459i	−0.327515	−	1.00799i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	0.669899			0.0382332			0.0191166	−	0.999817i	$-0.493915\pi$
$307$	0.669899			0.0382332			0.0191166	+	0.999817i	$0.493915\pi$
$308$		0			0
$309$	11.9058	−	8.65009i	0.677299	−	0.492086i
$310$		0			0
$311$	−25.5534	−	18.5656i	−1.44900	−	1.05276i	−0.986064	−	0.166366i	$-0.946797\pi$
$311$	−25.5534	−	18.5656i	−1.44900	−	1.05276i	−0.462934	−	0.886393i	$-0.653203\pi$
$312$		0			0
$313$	−1.17726	+	0.855327i	−0.0665425	+	0.0483459i	−0.620559	−	0.784160i	$-0.713094\pi$
$313$	−1.17726	+	0.855327i	−0.0665425	+	0.0483459i	0.554017	+	0.832506i	$0.313094\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.95857	−	15.2609i	0.278501	−	0.857138i	−0.709771	−	0.704433i	$-0.751202\pi$
$317$	4.95857	−	15.2609i	0.278501	−	0.857138i	0.988272	−	0.152705i	$-0.0487984\pi$
$318$		0			0
$319$	0.566449	−	1.74335i	0.0317151	−	0.0976089i
$320$		0			0
$321$	−1.57762	−	4.85541i	−0.0880541	−	0.271003i
$322$		0			0
$323$	−18.4186	−	13.3819i	−1.02484	−	0.744590i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.82331	+	2.77780i	0.211430	+	0.153613i
$328$		0			0
$329$	−1.77143	−	5.45189i	−0.0976619	−	0.300572i
$330$		0			0
$331$	−8.31262	+	25.5836i	−0.456903	+	1.40620i	0.411984	+	0.911191i	$0.364836\pi$
$331$	−8.31262	+	25.5836i	−0.456903	+	1.40620i	−0.868887	+	0.495011i	$0.835164\pi$
$332$		0			0
$333$	0.676034	−	2.08062i	0.0370464	−	0.114017i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.10171	−	0.800436i	0.0600137	−	0.0436025i	−0.557374	−	0.830262i	$-0.688191\pi$
$337$	1.10171	−	0.800436i	0.0600137	−	0.0436025i	0.617388	+	0.786659i	$0.288191\pi$
$338$		0			0
$339$	−3.34799	−	2.43246i	−0.181838	−	0.132113i
$340$		0			0
$341$	−3.83070	+	2.78317i	−0.207444	+	0.150717i
$342$		0			0
$343$	7.49850			0.404881
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.712835	+	2.19388i	0.0382670	+	0.117774i	0.968365	−	0.249537i	$-0.0802785\pi$
$347$	0.712835	+	2.19388i	0.0382670	+	0.117774i	−0.930098	+	0.367311i	$0.880278\pi$
$348$		0			0
$349$	2.35292			0.125949			0.0629744	−	0.998015i	$-0.479941\pi$
$349$	2.35292			0.125949			0.0629744	+	0.998015i	$0.479941\pi$
$350$		0			0
$351$	0.302113			0.0161256
$352$		0			0
$353$	9.55559	+	29.4091i	0.508593	+	1.56529i	0.794646	+	0.607073i	$0.207657\pi$
$353$	9.55559	+	29.4091i	0.508593	+	1.56529i	−0.286053	+	0.958214i	$0.592343\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−2.21215			−0.117079
$358$		0			0
$359$	15.8812	−	11.5383i	0.838176	−	0.608971i	−0.0836845	−	0.996492i	$-0.526669\pi$
$359$	15.8812	−	11.5383i	0.838176	−	0.608971i	0.921861	+	0.387522i	$0.126669\pi$
$360$		0			0
$361$	−10.2977	−	7.48170i	−0.541983	−	0.393774i
$362$		0			0
$363$	−7.45028	+	5.41295i	−0.391038	+	0.284106i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	9.94076	−	30.5945i	0.518903	−	1.59702i	−0.257163	−	0.966368i	$-0.582788\pi$
$367$	9.94076	−	30.5945i	0.518903	−	1.59702i	0.776066	−	0.630652i	$-0.217212\pi$
$368$		0			0
$369$	−3.02924	+	9.32306i	−0.157696	+	0.485339i
$370$		0			0
$371$	−1.30163	−	4.00599i	−0.0675770	−	0.207981i
$372$		0			0
$373$	−11.0291	−	8.01309i	−0.571064	−	0.414902i	0.264428	−	0.964406i	$-0.414817\pi$
$373$	−11.0291	−	8.01309i	−0.571064	−	0.414902i	−0.835492	+	0.549503i	$0.814817\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.334784	−	0.243235i	−0.0172423	−	0.0125272i
$378$		0			0
$379$	7.62106	+	23.4552i	0.391467	+	1.20481i	0.931679	+	0.363283i	$0.118344\pi$
$379$	7.62106	+	23.4552i	0.391467	+	1.20481i	−0.540211	+	0.841529i	$0.681656\pi$
$380$		0			0
$381$	−3.91775	+	12.0576i	−0.200712	+	0.617729i
$382$		0			0
$383$	3.79232	−	11.6716i	0.193779	−	0.596389i	−0.806210	−	0.591629i	$-0.798485\pi$
$383$	3.79232	−	11.6716i	0.193779	−	0.596389i	0.999989	−	0.00475994i	$-0.00151514\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.76308	+	4.91366i	−0.343787	+	0.249776i
$388$		0			0
$389$	−9.39823	−	6.82822i	−0.476509	−	0.346204i	0.323463	−	0.946241i	$-0.395153\pi$
$389$	−9.39823	−	6.82822i	−0.476509	−	0.346204i	−0.799973	+	0.600036i	$0.795153\pi$
$390$		0			0
$391$	−0.801790	+	0.582535i	−0.0405483	+	0.0294600i
$392$		0			0
$393$	12.3309			0.622012
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−5.26383	−	16.2004i	−0.264184	−	0.813075i	−0.991880	−	0.127175i	$-0.959409\pi$
$397$	−5.26383	−	16.2004i	−0.264184	−	0.813075i	0.727696	−	0.685900i	$-0.240591\pi$
$398$		0			0
$399$	−3.08294			−0.154340
$400$		0			0
$401$	32.2134			1.60866			0.804330	−	0.594183i	$-0.202524\pi$
$401$	32.2134			1.60866			0.804330	+	0.594183i	$0.202524\pi$
$402$		0			0
$403$	0.330318	+	1.01661i	0.0164543	+	0.0506412i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.92770			−0.145121
$408$		0			0
$409$	5.64632	−	4.10229i	0.279193	−	0.202845i	−0.439373	−	0.898305i	$-0.644799\pi$
$409$	5.64632	−	4.10229i	0.279193	−	0.202845i	0.718565	+	0.695460i	$0.244799\pi$
$410$		0			0
$411$	−8.67508	−	6.30281i	−0.427910	−	0.310895i
$412$		0			0
$413$	1.83853	−	1.33577i	0.0904681	−	0.0657289i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	4.22575	−	13.0055i	0.206936	−	0.636883i
$418$		0			0
$419$	8.60796	−	26.4926i	0.420526	−	1.29425i	−0.486687	−	0.873576i	$-0.661795\pi$
$419$	8.60796	−	26.4926i	0.420526	−	1.29425i	0.907214	−	0.420670i	$-0.138205\pi$
$420$		0			0
$421$	2.65766	+	8.17943i	0.129526	+	0.398641i	0.994699	−	0.102834i	$-0.0327910\pi$
$421$	2.65766	+	8.17943i	0.129526	+	0.398641i	−0.865172	+	0.501475i	$0.832791\pi$
$422$		0			0
$423$	−8.47341	−	6.15630i	−0.411991	−	0.299329i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.919392	+	0.667977i	0.0444925	+	0.0323257i
$428$		0			0
$429$	−0.124938	−	0.384518i	−0.00603204	−	0.0185647i
$430$		0			0
$431$	0.0559037	−	0.172054i	0.00269278	−	0.00828754i	−0.949701	−	0.313158i	$-0.898613\pi$
$431$	0.0559037	−	0.172054i	0.00269278	−	0.00828754i	0.952394	+	0.304870i	$0.0986131\pi$
$432$		0			0
$433$	9.71549	−	29.9012i	0.466897	−	1.43696i	−0.389684	−	0.920948i	$-0.627416\pi$
$433$	9.71549	−	29.9012i	0.466897	−	1.43696i	0.856581	−	0.516012i	$-0.172584\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.11741	+	0.811845i	−0.0534529	+	0.0388358i
$438$		0			0
$439$	13.6019	+	9.88233i	0.649181	+	0.471658i	0.862992	−	0.505217i	$-0.168588\pi$
$439$	13.6019	+	9.88233i	0.649181	+	0.471658i	−0.213811	+	0.976875i	$0.568588\pi$
$440$		0			0
$441$	5.42077	−	3.93842i	0.258132	−	0.187544i
$442$		0			0
$443$	−36.1952			−1.71969			−0.859843	−	0.510559i	$-0.829439\pi$
$443$	−36.1952			−1.71969			−0.859843	+	0.510559i	$0.829439\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−2.74461	−	8.44705i	−0.129816	−	0.399532i
$448$		0			0
$449$	28.3299			1.33697			0.668486	−	0.743725i	$-0.266943\pi$
$449$	28.3299			1.33697			0.668486	+	0.743725i	$0.266943\pi$
$450$		0			0
$451$	13.1188			0.617738
$452$		0			0
$453$	−0.829124	−	2.55178i	−0.0389557	−	0.119893i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−16.5396			−0.773691			−0.386846	−	0.922144i	$-0.626435\pi$
$457$	−16.5396			−0.773691			−0.386846	+	0.922144i	$0.626435\pi$
$458$		0			0
$459$	−3.26988	+	2.37571i	−0.152625	+	0.110889i
$460$		0			0
$461$	−0.351142	−	0.255120i	−0.0163543	−	0.0118821i	0.579578	−	0.814917i	$-0.303217\pi$
$461$	−0.351142	−	0.255120i	−0.0163543	−	0.0118821i	−0.595932	+	0.803035i	$0.703217\pi$
$462$		0			0
$463$	−16.1500	+	11.7337i	−0.750556	+	0.545311i	−0.895999	−	0.444056i	$-0.853539\pi$
$463$	−16.1500	+	11.7337i	−0.750556	+	0.545311i	0.145443	+	0.989367i	$0.453539\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.91815	−	5.90347i	0.0887615	−	0.273180i	−0.896816	−	0.442403i	$-0.854126\pi$
$467$	1.91815	−	5.90347i	0.0887615	−	0.273180i	0.985578	+	0.169223i	$0.0541260\pi$
$468$		0			0
$469$	1.43523	−	4.41719i	0.0662729	−	0.203967i
$470$		0			0
$471$	3.63328	+	11.1821i	0.167413	+	0.515244i
$472$		0			0
$473$	9.05077	+	6.57577i	0.416155	+	0.302354i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−6.22618	−	4.52358i	−0.285077	−	0.207121i
$478$		0			0
$479$	7.25191	+	22.3191i	0.331348	+	1.01978i	0.968493	+	0.249041i	$0.0801153\pi$
$479$	7.25191	+	22.3191i	0.331348	+	1.01978i	−0.637145	+	0.770744i	$0.719885\pi$
$480$		0			0
$481$	−0.204239	+	0.628583i	−0.00931250	+	0.0286609i
$482$		0			0
$483$	−0.0414716	+	0.127637i	−0.00188702	+	0.00580766i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−2.70709	+	1.96682i	−0.122670	+	0.0891250i	−0.647429	−	0.762126i	$-0.724156\pi$
$487$	−2.70709	+	1.96682i	−0.122670	+	0.0891250i	0.524759	+	0.851251i	$0.324156\pi$
$488$		0			0
$489$	14.8153	+	10.7639i	0.669971	+	0.486762i
$490$		0			0
$491$	0.442522	−	0.321511i	0.0199708	−	0.0145096i	−0.577755	−	0.816210i	$-0.696071\pi$
$491$	0.442522	−	0.321511i	0.0199708	−	0.0145096i	0.597726	+	0.801701i	$0.296071\pi$
$492$		0			0
$493$	5.53620			0.249338
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.55316	+	4.78015i	0.0696690	+	0.214419i
$498$		0			0
$499$	−8.08164			−0.361784			−0.180892	−	0.983503i	$-0.557898\pi$
$499$	−8.08164			−0.361784			−0.180892	+	0.983503i	$0.557898\pi$
$500$		0			0
$501$	4.40418			0.196764
$502$		0			0
$503$	8.74922	+	26.9273i	0.390109	+	1.20063i	0.932706	+	0.360638i	$0.117441\pi$
$503$	8.74922	+	26.9273i	0.390109	+	1.20063i	−0.542597	+	0.839993i	$0.682559\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	12.9087			0.573297
$508$		0			0
$509$	−4.61968	+	3.35639i	−0.204764	+	0.148770i	−0.685441	−	0.728128i	$-0.740391\pi$
$509$	−4.61968	+	3.35639i	−0.204764	+	0.148770i	0.480678	+	0.876897i	$0.340391\pi$
$510$		0			0
$511$	−4.85119	−	3.52459i	−0.214604	−	0.155919i
$512$		0			0
$513$	−4.55705	+	3.31089i	−0.201198	+	0.146179i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−4.33136	+	13.3305i	−0.190493	+	0.586277i
$518$		0			0
$519$	−4.92287	+	15.1510i	−0.216090	+	0.665056i
$520$		0			0
$521$	−7.87683	−	24.2424i	−0.345090	−	1.06208i	−0.961536	−	0.274681i	$-0.911428\pi$
$521$	−7.87683	−	24.2424i	−0.345090	−	1.06208i	0.616445	−	0.787398i	$-0.288572\pi$
$522$		0			0
$523$	2.29098	+	1.66449i	0.100177	+	0.0727832i	0.636746	−	0.771073i	$-0.280280\pi$
$523$	2.29098	+	1.66449i	0.100177	+	0.0727832i	−0.536569	+	0.843857i	$0.680280\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−11.5694	−	8.40568i	−0.503972	−	0.366157i
$528$		0			0
$529$	−7.08881	−	21.8171i	−0.308209	−	0.948570i
$530$		0			0
$531$	1.28308	−	3.94893i	0.0556811	−	0.171369i
$532$		0			0
$533$	0.915175	−	2.81662i	0.0396406	−	0.122001i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	3.04982	−	2.21582i	0.131609	−	0.0956198i
$538$		0			0
$539$	−7.25441	−	5.27064i	−0.312470	−	0.227022i
$540$		0			0
$541$	−3.64130	+	2.64556i	−0.156552	+	0.113742i	−0.663303	−	0.748351i	$-0.730846\pi$
$541$	−3.64130	+	2.64556i	−0.156552	+	0.113742i	0.506752	+	0.862092i	$0.330846\pi$
$542$		0			0
$543$	26.6868			1.14524
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−2.94045	−	9.04979i	−0.125725	−	0.386941i	0.868308	−	0.496026i	$-0.165208\pi$
$547$	−2.94045	−	9.04979i	−0.125725	−	0.386941i	−0.994032	+	0.109085i	$0.965208\pi$
$548$		0			0
$549$	2.07636			0.0886170
$550$		0			0
$551$	7.71549			0.328691
$552$		0			0
$553$	−2.56789	−	7.90316i	−0.109198	−	0.336077i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−25.5173			−1.08120			−0.540601	−	0.841279i	$-0.681803\pi$
$557$	−25.5173			−1.08120			−0.540601	+	0.841279i	$0.681803\pi$
$558$		0			0
$559$	2.04322	−	1.48448i	0.0864189	−	0.0627870i
$560$		0			0
$561$	4.37595	+	3.17932i	0.184753	+	0.134231i
$562$		0			0
$563$	11.1180	−	8.07772i	0.468569	−	0.340435i	−0.328314	−	0.944569i	$-0.606480\pi$
$563$	11.1180	−	8.07772i	0.468569	−	0.340435i	0.796883	+	0.604133i	$0.206480\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.169131	+	0.520530i	−0.00710282	+	0.0218602i
$568$		0			0
$569$	−8.75873	+	26.9566i	−0.367185	+	1.13008i	0.581416	+	0.813606i	$0.302499\pi$
$569$	−8.75873	+	26.9566i	−0.367185	+	1.13008i	−0.948601	+	0.316473i	$0.897501\pi$
$570$		0			0
$571$	−0.603552	−	1.85754i	−0.0252579	−	0.0777357i	0.937633	−	0.347627i	$-0.113012\pi$
$571$	−0.603552	−	1.85754i	−0.0252579	−	0.0777357i	−0.962891	+	0.269891i	$0.913012\pi$
$572$		0			0
$573$	3.74803	+	2.72310i	0.156576	+	0.113759i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	34.6572	+	25.1799i	1.44280	+	1.04825i	0.987448	+	0.157942i	$0.0504858\pi$
$577$	34.6572	+	25.1799i	1.44280	+	1.04825i	0.455350	+	0.890313i	$0.349514\pi$
$578$		0			0
$579$	−6.41026	−	19.7287i	−0.266401	−	0.819898i
$580$		0			0
$581$	−1.12543	+	3.46370i	−0.0466905	+	0.143699i
$582$		0			0
$583$	−3.18264	+	9.79515i	−0.131811	+	0.405674i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.59845	+	1.16134i	−0.0659751	+	0.0479337i	−0.620284	−	0.784377i	$-0.712983\pi$
$587$	−1.59845	+	1.16134i	−0.0659751	+	0.0479337i	0.554309	+	0.832311i	$0.312983\pi$
$588$		0			0
$589$	−16.1237	−	11.7145i	−0.664364	−	0.482688i
$590$		0			0
$591$	−16.6122	+	12.0695i	−0.683334	+	0.496471i
$592$		0			0
$593$	17.3986			0.714475			0.357237	−	0.934014i	$-0.383719\pi$
$593$	17.3986			0.714475			0.357237	+	0.934014i	$0.383719\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.82764	−	5.62490i	−0.0748004	−	0.230212i
$598$		0			0
$599$	−3.17298			−0.129644			−0.0648222	−	0.997897i	$-0.520648\pi$
$599$	−3.17298			−0.129644			−0.0648222	+	0.997897i	$0.520648\pi$
$600$		0			0
$601$	32.1659			1.31207			0.656037	−	0.754729i	$-0.272232\pi$
$601$	32.1659			1.31207			0.656037	+	0.754729i	$0.272232\pi$
$602$		0			0
$603$	−2.62230	−	8.07061i	−0.106788	−	0.328661i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	28.4215			1.15359			0.576797	−	0.816888i	$-0.304302\pi$
$607$	28.4215			1.15359			0.576797	+	0.816888i	$0.304302\pi$
$608$		0			0
$609$	0.606506	−	0.440652i	0.0245769	−	0.0178561i
$610$		0			0
$611$	2.55993	+	1.85990i	0.103564	+	0.0752435i
$612$		0			0
$613$	−2.00920	+	1.45977i	−0.0811510	+	0.0589597i	−0.627621	−	0.778519i	$-0.715971\pi$
$613$	−2.00920	+	1.45977i	−0.0811510	+	0.0589597i	0.546470	+	0.837479i	$0.315971\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.03970	+	9.35524i	−0.122374	+	0.376628i	−0.993413	−	0.114585i	$-0.963446\pi$
$617$	−3.03970	+	9.35524i	−0.122374	+	0.376628i	0.871040	+	0.491213i	$0.163446\pi$
$618$		0			0
$619$	−4.22997	+	13.0185i	−0.170017	+	0.523258i	−0.999371	−	0.0354655i	$-0.988709\pi$
$619$	−4.22997	+	13.0185i	−0.170017	+	0.523258i	0.829354	+	0.558723i	$0.188709\pi$
$620$		0			0
$621$	0.0757724	+	0.233204i	0.00304064	+	0.00935814i
$622$		0			0
$623$	2.20449	+	1.60165i	0.0883210	+	0.0641689i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.09852	+	4.43083i	0.243551	+	0.176950i
$628$		0			0
$629$	−2.73239	−	8.40944i	−0.108948	−	0.335306i
$630$		0			0
$631$	6.15441	−	18.9413i	0.245003	−	0.754042i	−0.750633	−	0.660720i	$-0.770251\pi$
$631$	6.15441	−	18.9413i	0.245003	−	0.754042i	0.995636	−	0.0933224i	$-0.0297487\pi$
$632$		0			0
$633$	−7.08592	+	21.8082i	−0.281640	+	0.866799i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.63769	+	1.18985i	−0.0648876	+	0.0471436i
$638$		0			0
$639$	7.42939	+	5.39777i	0.293902	+	0.213532i
$640$		0			0
$641$	10.6407	−	7.73090i	0.420281	−	0.305352i	−0.357470	−	0.933925i	$-0.616360\pi$
$641$	10.6407	−	7.73090i	0.420281	−	0.305352i	0.777751	+	0.628572i	$0.216360\pi$
$642$		0			0
$643$	34.4841			1.35992			0.679960	−	0.733249i	$-0.261997\pi$
$643$	34.4841			1.35992			0.679960	+	0.733249i	$0.261997\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.7895	+	36.2842i	0.463492	+	1.42648i	0.860870	+	0.508825i	$0.169920\pi$
$647$	11.7895	+	36.2842i	0.463492	+	1.42648i	−0.397378	+	0.917655i	$0.630080\pi$
$648$		0			0
$649$	−5.55666			−0.218118
$650$		0			0
$651$	−1.93651			−0.0758978
$652$		0			0
$653$	10.7056	+	32.9484i	0.418942	+	1.28937i	0.908677	+	0.417499i	$0.137093\pi$
$653$	10.7056	+	32.9484i	0.418942	+	1.28937i	−0.489736	+	0.871871i	$0.662907\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−10.9560			−0.427433
$658$		0			0
$659$	−40.6525	+	29.5358i	−1.58360	+	1.15055i	−0.671178	+	0.741297i	$0.734211\pi$
$659$	−40.6525	+	29.5358i	−1.58360	+	1.15055i	−0.912420	+	0.409254i	$0.865789\pi$
$660$		0			0
$661$	−8.72436	−	6.33862i	−0.339338	−	0.246544i	0.405044	−	0.914297i	$-0.367256\pi$
$661$	−8.72436	−	6.33862i	−0.339338	−	0.246544i	−0.744383	+	0.667753i	$0.767256\pi$
$662$		0			0
$663$	0.987875	−	0.717733i	0.0383659	−	0.0278744i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.103788	−	0.319428i	0.00401870	−	0.0123683i
$668$		0			0
$669$	−3.93990	+	12.1258i	−0.152325	+	0.468810i
$670$		0			0
$671$	−0.858670	−	2.64272i	−0.0331486	−	0.102021i
$672$		0			0
$673$	−13.6011	−	9.88179i	−0.524285	−	0.380915i	0.293931	−	0.955827i	$-0.405036\pi$
$673$	−13.6011	−	9.88179i	−0.524285	−	0.380915i	−0.818216	+	0.574912i	$0.805036\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	30.1258	+	21.8877i	1.15783	+	0.841211i	0.989502	−	0.144521i	$-0.0461640\pi$
$677$	30.1258	+	21.8877i	1.15783	+	0.841211i	0.168325	+	0.985731i	$0.446164\pi$
$678$		0			0
$679$	0.686881	+	2.11400i	0.0263601	+	0.0811280i
$680$		0			0
$681$	3.40828	−	10.4896i	0.130606	−	0.401963i
$682$		0			0
$683$	9.83629	−	30.2730i	0.376375	−	1.15836i	−0.566171	−	0.824288i	$-0.691576\pi$
$683$	9.83629	−	30.2730i	0.376375	−	1.15836i	0.942546	−	0.334076i	$-0.108424\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−18.6722	+	13.5661i	−0.712389	+	0.517581i
$688$		0			0
$689$	1.88101	+	1.36663i	0.0716608	+	0.0520646i
$690$		0			0
$691$	15.3436	−	11.1478i	0.583699	−	0.424082i	−0.256357	−	0.966582i	$-0.582522\pi$
$691$	15.3436	−	11.1478i	0.583699	−	0.424082i	0.840056	+	0.542500i	$0.182522\pi$
$692$		0			0
$693$	0.732455			0.0278237
$694$		0			0
$695$		0			0
$696$		0			0
$697$	12.2436	+	37.6819i	0.463759	+	1.42730i
$698$		0			0
$699$	−29.2882			−1.10778
$700$		0			0
$701$	−19.2027			−0.725275			−0.362638	−	0.931930i	$-0.618124\pi$
$701$	−19.2027			−0.725275			−0.362638	+	0.931930i	$0.618124\pi$
$702$		0			0
$703$	−3.80798	−	11.7197i	−0.143621	−	0.442019i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−10.0974			−0.379752
$708$		0			0
$709$	8.91896	−	6.48000i	0.334959	−	0.243362i	−0.407573	−	0.913173i	$-0.633625\pi$
$709$	8.91896	−	6.48000i	0.334959	−	0.243362i	0.742532	+	0.669811i	$0.233625\pi$
$710$		0			0
$711$	−12.2832	−	8.92428i	−0.460657	−	0.334687i
$712$		0			0
$713$	−0.701886	+	0.509950i	−0.0262858	+	0.0190978i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−3.27514	+	10.0798i	−0.122312	+	0.376439i
$718$		0			0
$719$	8.20996	−	25.2676i	0.306180	−	0.942324i	−0.673055	−	0.739593i	$-0.735018\pi$
$719$	8.20996	−	25.2676i	0.306180	−	0.942324i	0.979234	−	0.202732i	$-0.0649819\pi$
$720$		0			0
$721$	−2.48899	−	7.66034i	−0.0926950	−	0.285286i
$722$		0			0
$723$	15.3888	+	11.1806i	0.572317	+	0.415812i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	22.1224	+	16.0729i	0.820474	+	0.596109i	0.916848	−	0.399236i	$-0.130725\pi$
$727$	22.1224	+	16.0729i	0.820474	+	0.596109i	−0.0963741	+	0.995345i	$0.530725\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−10.4410	+	32.1342i	−0.386176	+	1.18853i
$732$		0			0
$733$	−2.56626	+	7.89814i	−0.0947871	+	0.291725i	−0.987198	−	0.159499i	$-0.949012\pi$
$733$	−2.56626	+	7.89814i	−0.0947871	+	0.291725i	0.892411	+	0.451223i	$0.149012\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.18753	+	6.67513i	−0.338427	+	0.245882i
$738$		0			0
$739$	−1.30623	−	0.949030i	−0.0480504	−	0.0349106i	0.563501	−	0.826116i	$-0.309454\pi$
$739$	−1.30623	−	0.949030i	−0.0480504	−	0.0349106i	−0.611551	+	0.791205i	$0.709454\pi$
$740$		0			0
$741$	1.37674	−	1.00026i	0.0505760	−	0.0367456i
$742$		0			0
$743$	3.77367			0.138443			0.0692213	−	0.997601i	$-0.477949\pi$
$743$	3.77367			0.138443			0.0692213	+	0.997601i	$0.477949\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.05626	+	6.32850i	0.0752344	+	0.231548i
$748$		0			0
$749$	−2.79421			−0.102098
$750$		0			0
$751$	53.4032			1.94871			0.974355	−	0.225016i	$-0.0722435\pi$
$751$	53.4032			1.94871			0.974355	+	0.225016i	$0.0722435\pi$
$752$		0			0
$753$	−0.0114588	−	0.0352667i	−0.000417583	−	0.00128519i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−11.6322			−0.422781			−0.211390	−	0.977402i	$-0.567799\pi$
$757$	−11.6322			−0.422781			−0.211390	+	0.977402i	$0.567799\pi$
$758$		0			0
$759$	0.265477	−	0.192881i	0.00963622	−	0.00700112i
$760$		0			0
$761$	−3.77626	−	2.74361i	−0.136889	−	0.0994560i	0.517233	−	0.855844i	$-0.326962\pi$
$761$	−3.77626	−	2.74361i	−0.136889	−	0.0994560i	−0.654123	+	0.756389i	$0.726962\pi$
$762$		0			0
$763$	2.09257	−	1.52034i	0.0757561	−	0.0550400i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.387637	+	1.19302i	−0.0139968	+	0.0430776i
$768$		0			0
$769$	−6.98515	+	21.4981i	−0.251891	+	0.775241i	0.742535	+	0.669807i	$0.233623\pi$
$769$	−6.98515	+	21.4981i	−0.251891	+	0.775241i	−0.994426	+	0.105434i	$0.966377\pi$
$770$		0			0
$771$	−3.09750	−	9.53312i	−0.111554	−	0.343327i
$772$		0			0
$773$	32.1006	+	23.3225i	1.15458	+	0.838851i	0.989083	−	0.147359i	$-0.0470772\pi$
$773$	32.1006	+	23.3225i	1.15458	+	0.838851i	0.165497	+	0.986210i	$0.447077\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.968688	−	0.703793i	−0.0347515	−	0.0252484i
$778$		0			0
$779$	17.0632	+	52.5151i	0.611352	+	1.88155i
$780$		0			0
$781$	3.79768	−	11.6881i	0.135892	−	0.418232i
$782$		0			0
$783$	0.423273	−	1.30270i	0.0151265	−	0.0465547i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	3.83261	−	2.78456i	0.136618	−	0.0992587i	−0.517377	−	0.855757i	$-0.673092\pi$
$787$	3.83261	−	2.78456i	0.136618	−	0.0992587i	0.653995	+	0.756499i	$0.273092\pi$
$788$		0			0
$789$	10.3407	+	7.51296i	0.368139	+	0.267468i
$790$		0			0
$791$	−1.83241	+	1.33133i	−0.0651532	+	0.0473365i
$792$		0			0
$793$	−0.627297			−0.0222760
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.93088	−	27.4864i	−0.316348	−	0.973619i	−0.975196	−	0.221343i	$-0.928956\pi$
$797$	−8.93088	−	27.4864i	−0.316348	−	0.973619i	0.658848	−	0.752276i	$-0.271044\pi$
$798$		0			0
$799$	−42.3326			−1.49762
$800$		0			0
$801$	4.97864			0.175911
$802$		0			0
$803$	4.53079	+	13.9443i	0.159888	+	0.492085i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−21.3115			−0.750201
$808$		0			0
$809$	−36.1225	+	26.2445i	−1.27000	+	0.922709i	−0.999203	−	0.0399280i	$-0.987287\pi$
$809$	−36.1225	+	26.2445i	−1.27000	+	0.922709i	−0.270797	+	0.962637i	$0.587287\pi$
$810$		0			0
$811$	36.5354	+	26.5445i	1.28293	+	0.932105i	0.999637	−	0.0269280i	$-0.00857248\pi$
$811$	36.5354	+	26.5445i	1.28293	+	0.932105i	0.283295	+	0.959033i	$0.408572\pi$
$812$		0			0
$813$	−10.8437	+	7.87844i	−0.380307	+	0.276309i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−14.5511	+	44.7836i	−0.509077	+	1.56678i
$818$		0			0
$819$	0.0510966	−	0.157259i	0.00178546	−	0.00549508i
$820$		0			0
$821$	14.7519	+	45.4016i	0.514844	+	1.58453i	0.783566	+	0.621308i	$0.213399\pi$
$821$	14.7519	+	45.4016i	0.514844	+	1.58453i	−0.268722	+	0.963218i	$0.586601\pi$
$822$		0			0
$823$	−5.22903	−	3.79912i	−0.182273	−	0.132429i	0.492907	−	0.870082i	$-0.335934\pi$
$823$	−5.22903	−	3.79912i	−0.182273	−	0.132429i	−0.675180	+	0.737653i	$0.735934\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−40.6005	−	29.4980i	−1.41182	−	1.02575i	−0.993055	−	0.117650i	$-0.962464\pi$
$827$	−40.6005	−	29.4980i	−1.41182	−	1.02575i	−0.418763	−	0.908095i	$-0.637536\pi$
$828$		0			0
$829$	−11.5098	−	35.4234i	−0.399751	−	1.23031i	−0.925200	−	0.379481i	$-0.876103\pi$
$829$	−11.5098	−	35.4234i	−0.399751	−	1.23031i	0.525449	−	0.850825i	$-0.323897\pi$
$830$		0			0
$831$	−5.83178	+	17.9484i	−0.202302	+	0.622622i
$832$		0			0
$833$	8.36874	−	25.7563i	0.289960	−	0.892404i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.86245	+	2.07969i	−0.0989407	+	0.0718846i
$838$		0			0
$839$	−10.7171	−	7.78643i	−0.369995	−	0.268817i	0.387214	−	0.921990i	$-0.373438\pi$
$839$	−10.7171	−	7.78643i	−0.369995	−	0.268817i	−0.757209	+	0.653173i	$0.773438\pi$
$840$		0			0
$841$	21.9436	−	15.9430i	0.756677	−	0.549758i
$842$		0			0
$843$	17.3995			0.599271
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.55753	+	4.79359i	0.0535175	+	0.164710i
$848$		0			0
$849$	23.6677			0.812272
$850$		0			0
$851$	−0.536433			−0.0183887
$852$		0			0
$853$	−13.8064	−	42.4917i	−0.472722	−	1.45489i	−0.849006	−	0.528384i	$-0.822798\pi$
$853$	−13.8064	−	42.4917i	−0.472722	−	1.45489i	0.376284	−	0.926504i	$-0.377202\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	41.6798			1.42375			0.711877	−	0.702304i	$-0.247845\pi$
$857$	41.6798			1.42375			0.711877	+	0.702304i	$0.247845\pi$
$858$		0			0
$859$	30.4001	−	22.0870i	1.03724	−	0.753597i	0.0674930	−	0.997720i	$-0.478500\pi$
$859$	30.4001	−	22.0870i	1.03724	−	0.753597i	0.969744	+	0.244123i	$0.0785000\pi$
$860$		0			0
$861$	4.34060	+	3.15363i	0.147927	+	0.107475i
$862$		0			0
$863$	45.4724	−	33.0376i	1.54790	−	1.12461i	0.602768	−	0.797916i	$-0.294064\pi$
$863$	45.4724	−	33.0376i	1.54790	−	1.12461i	0.945129	−	0.326697i	$-0.105936\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	0.205155	−	0.631402i	0.00696743	−	0.0214435i
$868$		0			0
$869$	−6.27882	+	19.3242i	−0.212994	+	0.655529i
$870$		0			0
$871$	0.792232	+	2.43824i	0.0268438	+	0.0826166i
$872$		0			0
$873$	3.28562	+	2.38714i	0.111201	+	0.0807925i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.91115	+	1.38853i	0.0645349	+	0.0468873i	0.619585	−	0.784930i	$-0.287301\pi$
$877$	1.91115	+	1.38853i	0.0645349	+	0.0468873i	−0.555050	+	0.831817i	$0.687301\pi$
$878$		0			0
$879$	5.88111	+	18.1002i	0.198365	+	0.610505i
$880$		0			0
$881$	14.7309	−	45.3372i	0.496298	−	1.52745i	−0.318626	−	0.947881i	$-0.603221\pi$
$881$	14.7309	−	45.3372i	0.496298	−	1.52745i	0.814924	−	0.579568i	$-0.196779\pi$
$882$		0			0
$883$	−3.07555	+	9.46556i	−0.103500	+	0.318541i	−0.989376	−	0.145382i	$-0.953559\pi$
$883$	−3.07555	+	9.46556i	−0.103500	+	0.318541i	0.885875	+	0.463924i	$0.153559\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.8114	+	7.85495i	−0.363012	+	0.263743i	−0.754307	−	0.656522i	$-0.772027\pi$
$887$	−10.8114	+	7.85495i	−0.363012	+	0.263743i	0.391296	+	0.920265i	$0.372027\pi$
$888$		0			0
$889$	5.61373	+	4.07862i	0.188279	+	0.136792i
$890$		0			0
$891$	1.08268	−	0.786610i	0.0362710	−	0.0263524i
$892$		0			0
$893$	−58.9965			−1.97424
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.0228919	−	0.0704539i	−0.000764337	−	0.00235239i
$898$		0			0
$899$	4.84638			0.161636
$900$		0			0
$901$	−31.1056			−1.03628
$902$		0			0
$903$	1.41387	+	4.35144i	0.0470506	+	0.144807i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	32.4136			1.07627			0.538137	−	0.842857i	$-0.319128\pi$
$907$	32.4136			1.07627			0.538137	+	0.842857i	$0.319128\pi$
$908$		0			0
$909$	−14.9254	+	10.8440i	−0.495046	+	0.359672i
$910$		0			0
$911$	32.4946	+	23.6087i	1.07659	+	0.782191i	0.977086	−	0.212846i	$-0.0682733\pi$
$911$	32.4946	+	23.6087i	1.07659	+	0.782191i	0.0995074	+	0.995037i	$0.468273\pi$
$912$		0			0
$913$	7.20432	−	5.23425i	0.238428	−	0.173228i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.08553	−	6.41861i	0.0688704	−	0.211961i
$918$		0			0
$919$	9.99204	−	30.7523i	0.329607	−	1.01443i	−0.639711	−	0.768616i	$-0.720946\pi$
$919$	9.99204	−	30.7523i	0.329607	−	1.01443i	0.969318	−	0.245810i	$-0.0790540\pi$
$920$		0			0
$921$	−0.207010	−	0.637112i	−0.00682122	−	0.0209936i
$922$		0			0
$923$	−2.24452	−	1.63074i	−0.0738792	−	0.0536764i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−11.9058	−	8.65009i	−0.391039	−	0.284106i
$928$		0			0
$929$	16.4945	+	50.7648i	0.541167	+	1.66554i	0.729934	+	0.683518i	$0.239551\pi$
$929$	16.4945	+	50.7648i	0.541167	+	1.66554i	−0.188767	+	0.982022i	$0.560449\pi$
$930$		0			0
$931$	11.6630	−	35.8951i	0.382241	−	1.17642i
$932$		0			0
$933$	−9.76052	+	30.0398i	−0.319545	+	0.983458i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−6.92518	+	5.03143i	−0.226236	+	0.164370i	−0.695129	−	0.718885i	$-0.744653\pi$
$937$	−6.92518	+	5.03143i	−0.226236	+	0.164370i	0.468893	+	0.883255i	$0.344653\pi$
$938$		0			0
$939$	1.17726	+	0.855327i	0.0384183	+	0.0279125i
$940$		0			0
$941$	−27.3583	+	19.8770i	−0.891856	+	0.647971i	−0.936361	−	0.351038i	$-0.885829\pi$
$941$	−27.3583	+	19.8770i	−0.891856	+	0.647971i	0.0445052	+	0.999009i	$0.485829\pi$
$942$		0			0
$943$	2.40370			0.0782753
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.26850	+	16.2148i	0.171203	+	0.526909i	0.999440	−	0.0334693i	$-0.0106556\pi$
$947$	5.26850	+	16.2148i	0.171203	+	0.526909i	−0.828236	+	0.560379i	$0.810656\pi$
$948$		0			0
$949$	3.30994			0.107445
$950$		0			0
$951$	−16.0463			−0.520336
$952$		0			0
$953$	11.6221	+	35.7692i	0.376478	+	1.15868i	0.942476	+	0.334273i	$0.108491\pi$
$953$	11.6221	+	35.7692i	0.376478	+	1.15868i	−0.565999	+	0.824406i	$0.691509\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.83307			−0.0592547
$958$		0			0
$959$	−4.74803	+	3.44964i	−0.153322	+	0.111395i
$960$		0			0
$961$	14.9517	+	10.8630i	0.482312	+	0.350420i
$962$		0			0
$963$	−4.13026	+	3.00081i	−0.133096	+	0.0966998i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	5.17395	−	15.9238i	0.166383	−	0.512074i	−0.832753	−	0.553645i	$-0.813236\pi$
$967$	5.17395	−	15.9238i	0.166383	−	0.512074i	0.999136	+	0.0415712i	$0.0132363\pi$
$968$		0			0
$969$	−7.03529	+	21.6524i	−0.226006	+	0.695576i
$970$		0			0
$971$	−1.90916	−	5.87580i	−0.0612680	−	0.188563i	0.915738	−	0.401777i	$-0.131607\pi$
$971$	−1.90916	−	5.87580i	−0.0612680	−	0.188563i	−0.977006	+	0.213213i	$0.931607\pi$
$972$		0			0
$973$	−6.05507	−	4.39926i	−0.194117	−	0.141034i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.6508	+	7.73829i	0.340750	+	0.247570i	0.744978	−	0.667089i	$-0.232460\pi$
$977$	10.6508	+	7.73829i	0.340750	+	0.247570i	−0.404228	+	0.914658i	$0.632460\pi$
$978$		0			0
$979$	−2.05889	−	6.33662i	−0.0658025	−	0.202519i
$980$		0			0
$981$	1.46038	−	4.49457i	0.0466262	−	0.143501i
$982$		0			0
$983$	−4.24039	+	13.0506i	−0.135248	+	0.416249i	−0.995628	−	0.0934024i	$-0.970226\pi$
$983$	−4.24039	+	13.0506i	−0.135248	+	0.416249i	0.860381	+	0.509652i	$0.170226\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.63765	+	3.36945i	−0.147618	+	0.107251i
$988$		0			0
$989$	1.65834	+	1.20485i	0.0527321	+	0.0383121i
$990$		0			0
$991$	38.5515	−	28.0093i	1.22463	−	0.889744i	0.228152	−	0.973626i	$-0.426732\pi$
$991$	38.5515	−	28.0093i	1.22463	−	0.889744i	0.996476	+	0.0838819i	$0.0267318\pi$
$992$		0			0
$993$	26.9002			0.853652
$994$		0			0
$995$		0			0
$996$		0			0
$997$	6.13379	+	18.8779i	0.194259	+	0.597868i	0.999984	+	0.00557886i	$0.00177582\pi$
$997$	6.13379	+	18.8779i	0.194259	+	0.597868i	−0.805725	+	0.592289i	$0.798224\pi$
$998$		0			0
$999$	−2.18769			−0.0692155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.m.b.1201.1		8
5.2	odd	4		1500.2.o.a.49.1		16
5.3	odd	4		1500.2.o.a.49.4		16
5.4	even	2		300.2.m.a.241.2	yes	8
15.14	odd	2		900.2.n.a.541.1		8
25.2	odd	20		1500.2.o.a.949.3		16
25.6	even	5		7500.2.a.d.1.2		4
25.8	odd	20		7500.2.d.d.1249.3		8
25.11	even	5	inner	1500.2.m.b.301.1		8
25.14	even	10		300.2.m.a.61.2	✓	8
25.17	odd	20		7500.2.d.d.1249.6		8
25.19	even	10		7500.2.a.g.1.3		4
25.23	odd	20		1500.2.o.a.949.2		16
75.14	odd	10		900.2.n.a.361.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.a.61.2	✓	8	25.14	even	10
300.2.m.a.241.2	yes	8	5.4	even	2
900.2.n.a.361.1		8	75.14	odd	10
900.2.n.a.541.1		8	15.14	odd	2
1500.2.m.b.301.1		8	25.11	even	5	inner
1500.2.m.b.1201.1		8	1.1	even	1	trivial
1500.2.o.a.49.1		16	5.2	odd	4
1500.2.o.a.49.4		16	5.3	odd	4
1500.2.o.a.949.2		16	25.23	odd	20
1500.2.o.a.949.3		16	25.2	odd	20
7500.2.a.d.1.2		4	25.6	even	5
7500.2.a.g.1.3		4	25.19	even	10
7500.2.d.d.1249.3		8	25.8	odd	20
7500.2.d.d.1249.6		8	25.17	odd	20

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} -0.547318 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{3} -0.547318 q^{7} +(-0.809017 + 0.587785i) q^{9} +(1.08268 + 0.786610i) q^{11} +(0.244415 - 0.177578i) q^{13} +(-1.24898 + 3.84398i) q^{17} +(-1.74064 + 5.35713i) q^{19} +(0.169131 + 0.520530i) q^{21} +(0.198375 + 0.144128i) q^{23} +(0.809017 + 0.587785i) q^{27} +(-0.423273 - 1.30270i) q^{29} +(-1.09336 + 3.36501i) q^{31} +(0.413545 - 1.27276i) q^{33} +(-1.76988 + 1.28589i) q^{37} +(-0.244415 - 0.177578i) q^{39} +(7.93066 - 5.76196i) q^{41} +8.35963 q^{43} +(3.23656 + 9.96110i) q^{47} -6.70044 q^{49} +4.04179 q^{51} +(2.37819 + 7.31931i) q^{53} +5.63282 q^{57} +(-3.35916 + 2.44057i) q^{59} +(-1.67981 - 1.22046i) q^{61} +(0.442790 - 0.321706i) q^{63} +(-2.62230 + 8.07061i) q^{67} +(0.0757724 - 0.233204i) q^{69} +(-2.83777 - 8.73377i) q^{71} +(8.86356 + 6.43975i) q^{73} +(-0.592568 - 0.430526i) q^{77} +(4.69177 + 14.4398i) q^{79} +(0.309017 - 0.951057i) q^{81} +(2.05626 - 6.32850i) q^{83} +(-1.10814 + 0.805112i) q^{87} +(-4.02780 - 2.92637i) q^{89} +(-0.133773 + 0.0971915i) q^{91} +3.53818 q^{93} +(-1.25499 - 3.86248i) q^{97} -1.33826 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 8 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 8 * q^7 - 2 * q^9	\( 8 q + 2 q^{3} + 8 q^{7} - 2 q^{9} - 2 q^{11} - 7 q^{17} + 5 q^{19} - 3 q^{21} - 7 q^{23} + 2 q^{27} + 27 q^{29} - 3 q^{31} - 3 q^{33} + 9 q^{37} + 20 q^{41} + 68 q^{43} + 7 q^{47} - 8 q^{49} - 8 q^{51} + 11 q^{53} + 10 q^{57} + 2 q^{59} - 14 q^{61} - 7 q^{63} - 28 q^{67} + 2 q^{69} - 15 q^{71} - 6 q^{73} - 17 q^{77} + 24 q^{79} - 2 q^{81} - 2 q^{83} + 23 q^{87} + 5 q^{91} + 18 q^{93} - 34 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 8 * q^7 - 2 * q^9 - 2 * q^11 - 7 * q^17 + 5 * q^19 - 3 * q^21 - 7 * q^23 + 2 * q^27 + 27 * q^29 - 3 * q^31 - 3 * q^33 + 9 * q^37 + 20 * q^41 + 68 * q^43 + 7 * q^47 - 8 * q^49 - 8 * q^51 + 11 * q^53 + 10 * q^57 + 2 * q^59 - 14 * q^61 - 7 * q^63 - 28 * q^67 + 2 * q^69 - 15 * q^71 - 6 * q^73 - 17 * q^77 + 24 * q^79 - 2 * q^81 - 2 * q^83 + 23 * q^87 + 5 * q^91 + 18 * q^93 - 34 * q^97 - 2 * q^99

Introduction

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