LMFDB - Embedded newform 1040.2.da.a.881.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1040.881
Dual form			1040.2.da.a.641.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 0.633975i) q^{3} +1.00000i q^{5} +(-2.59808 - 1.50000i) q^{7} +(1.23205 - 2.13397i) q^{9} +O(q^{10})$	\(q+(0.366025 + 0.633975i) q^{3} +1.00000i q^{5} +(-2.59808 - 1.50000i) q^{7} +(1.23205 - 2.13397i) q^{9} +(-2.59808 + 1.50000i) q^{11} +(3.50000 + 0.866025i) q^{13} +(-0.633975 + 0.366025i) q^{15} +(-4.09808 + 7.09808i) q^{17} +(0.401924 + 0.232051i) q^{19} -2.19615i q^{21} +(4.73205 + 8.19615i) q^{23} -1.00000 q^{25} +4.00000 q^{27} +(1.26795 + 2.19615i) q^{29} +4.73205i q^{31} +(-1.90192 - 1.09808i) q^{33} +(1.50000 - 2.59808i) q^{35} +(-0.696152 + 0.401924i) q^{37} +(0.732051 + 2.53590i) q^{39} +(-9.00000 + 5.19615i) q^{41} +(1.00000 - 1.73205i) q^{43} +(2.13397 + 1.23205i) q^{45} +3.00000i q^{47} +(1.00000 + 1.73205i) q^{49} -6.00000 q^{51} +0.464102 q^{53} +(-1.50000 - 2.59808i) q^{55} +0.339746i q^{57} +(-9.00000 - 5.19615i) q^{59} +(-3.09808 + 5.36603i) q^{61} +(-6.40192 + 3.69615i) q^{63} +(-0.866025 + 3.50000i) q^{65} +(-3.46410 + 6.00000i) q^{69} +(5.19615 + 3.00000i) q^{71} -11.6603i q^{73} +(-0.366025 - 0.633975i) q^{75} +9.00000 q^{77} +4.19615 q^{79} +(-2.23205 - 3.86603i) q^{81} -8.19615i q^{83} +(-7.09808 - 4.09808i) q^{85} +(-0.928203 + 1.60770i) q^{87} +(5.89230 - 3.40192i) q^{89} +(-7.79423 - 7.50000i) q^{91} +(-3.00000 + 1.73205i) q^{93} +(-0.232051 + 0.401924i) q^{95} +(7.90192 + 4.56218i) q^{97} +7.39230i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{9} + 14 q^{13} - 6 q^{15} - 6 q^{17} + 12 q^{19} + 12 q^{23} - 4 q^{25} + 16 q^{27} + 12 q^{29} - 18 q^{33} + 6 q^{35} + 18 q^{37} - 4 q^{39} - 36 q^{41} + 4 q^{43} + 12 q^{45} + 4 q^{49} - 24 q^{51} - 12 q^{53} - 6 q^{55} - 36 q^{59} - 2 q^{61} - 36 q^{63} + 2 q^{75} + 36 q^{77} - 4 q^{79} - 2 q^{81} - 18 q^{85} + 24 q^{87} - 18 q^{89} - 12 q^{93} + 6 q^{95} + 42 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^9 + 14 * q^13 - 6 * q^15 - 6 * q^17 + 12 * q^19 + 12 * q^23 - 4 * q^25 + 16 * q^27 + 12 * q^29 - 18 * q^33 + 6 * q^35 + 18 * q^37 - 4 * q^39 - 36 * q^41 + 4 * q^43 + 12 * q^45 + 4 * q^49 - 24 * q^51 - 12 * q^53 - 6 * q^55 - 36 * q^59 - 2 * q^61 - 36 * q^63 + 2 * q^75 + 36 * q^77 - 4 * q^79 - 2 * q^81 - 18 * q^85 + 24 * q^87 - 18 * q^89 - 12 * q^93 + 6 * q^95 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	0.952129	−	0.305695i	$-0.0988889\pi$
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	−0.740805	+	0.671721i	$0.765556\pi$
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.0791130	−	0.996866i	$-0.525209\pi$
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.902867	+	0.429919i	$0.858542\pi$
$8$		0			0
$9$	1.23205	−	2.13397i	0.410684	−	0.711325i
$10$		0			0
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	−0.837616	−	0.546259i	$-0.816051\pi$
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$12$		0			0
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$		0			0
$15$	−0.633975	+	0.366025i	−0.163692	+	0.0945074i
$16$		0			0
$17$	−4.09808	+	7.09808i	−0.993929	+	1.72154i	−0.401685	+	0.915778i	$0.631575\pi$
$17$	−4.09808	+	7.09808i	−0.993929	+	1.72154i	−0.592244	+	0.805759i	$0.701758\pi$
$18$		0			0
$19$	0.401924	+	0.232051i	0.0922076	+	0.0532361i	0.545395	−	0.838179i	$-0.316380\pi$
$19$	0.401924	+	0.232051i	0.0922076	+	0.0532361i	−0.453187	+	0.891415i	$0.649713\pi$
$20$		0			0
$21$		−	2.19615i		−	0.479240i
$22$		0			0
$23$	4.73205	+	8.19615i	0.986701	+	1.70902i	0.634120	+	0.773234i	$0.281362\pi$
$23$	4.73205	+	8.19615i	0.986701	+	1.70902i	0.352581	+	0.935781i	$0.385304\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	1.26795	+	2.19615i	0.235452	+	0.407815i	0.959404	−	0.282035i	$-0.0910095\pi$
$29$	1.26795	+	2.19615i	0.235452	+	0.407815i	−0.723952	+	0.689851i	$0.757676\pi$
$30$		0			0
$31$			4.73205i			0.849901i	0.905216	+	0.424951i	$0.139709\pi$
$31$			4.73205i			0.849901i	−0.905216	+	0.424951i	$0.860291\pi$
$32$		0			0
$33$	−1.90192	−	1.09808i	−0.331082	−	0.191151i
$34$		0			0
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$		0			0
$37$	−0.696152	+	0.401924i	−0.114447	+	0.0660759i	−0.556131	−	0.831095i	$-0.687715\pi$
$37$	−0.696152	+	0.401924i	−0.114447	+	0.0660759i	0.441684	+	0.897171i	$0.354381\pi$
$38$		0			0
$39$	0.732051	+	2.53590i	0.117222	+	0.406069i
$40$		0			0
$41$	−9.00000	+	5.19615i	−1.40556	+	0.811503i	−0.994956	−	0.100309i	$-0.968017\pi$
$41$	−9.00000	+	5.19615i	−1.40556	+	0.811503i	−0.410608	+	0.911812i	$0.634683\pi$
$42$		0			0
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	−0.779647	−	0.626219i	$-0.784601\pi$
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	0.932145	+	0.362084i	$0.117935\pi$
$44$		0			0
$45$	2.13397	+	1.23205i	0.318114	+	0.183663i
$46$		0			0
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$		0			0
$49$	1.00000	+	1.73205i	0.142857	+	0.247436i
$50$		0			0
$51$	−6.00000			−0.840168
$52$		0			0
$53$	0.464102			0.0637493			0.0318746	−	0.999492i	$-0.489852\pi$
$53$	0.464102			0.0637493			0.0318746	+	0.999492i	$0.489852\pi$
$54$		0			0
$55$	−1.50000	−	2.59808i	−0.202260	−	0.350325i
$56$		0			0
$57$			0.339746i			0.0450005i
$58$		0			0
$59$	−9.00000	−	5.19615i	−1.17170	−	0.676481i	−0.217620	−	0.976034i	$-0.569829\pi$
$59$	−9.00000	−	5.19615i	−1.17170	−	0.676481i	−0.954080	+	0.299552i	$0.903163\pi$
$60$		0			0
$61$	−3.09808	+	5.36603i	−0.396668	+	0.687049i	−0.993313	−	0.115456i	$-0.963167\pi$
$61$	−3.09808	+	5.36603i	−0.396668	+	0.687049i	0.596645	+	0.802506i	$0.296500\pi$
$62$		0			0
$63$	−6.40192	+	3.69615i	−0.806567	+	0.465671i
$64$		0			0
$65$	−0.866025	+	3.50000i	−0.107417	+	0.434122i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$	−3.46410	+	6.00000i	−0.417029	+	0.722315i
$70$		0			0
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	0.775571	−	0.631260i	$-0.217462\pi$
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	−0.158901	+	0.987294i	$0.550795\pi$
$72$		0			0
$73$		−	11.6603i		−	1.36473i	−0.731012	−	0.682365i	$-0.760952\pi$
$73$		−	11.6603i		−	1.36473i	0.731012	−	0.682365i	$-0.239048\pi$
$74$		0			0
$75$	−0.366025	−	0.633975i	−0.0422650	−	0.0732051i
$76$		0			0
$77$	9.00000			1.02565
$78$		0			0
$79$	4.19615			0.472104			0.236052	−	0.971740i	$-0.424146\pi$
$79$	4.19615			0.472104			0.236052	+	0.971740i	$0.424146\pi$
$80$		0			0
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$		0			0
$83$		−	8.19615i		−	0.899645i	−0.893118	−	0.449822i	$-0.851487\pi$
$83$		−	8.19615i		−	0.899645i	0.893118	−	0.449822i	$-0.148513\pi$
$84$		0			0
$85$	−7.09808	−	4.09808i	−0.769894	−	0.444499i
$86$		0			0
$87$	−0.928203	+	1.60770i	−0.0995138	+	0.172363i
$88$		0			0
$89$	5.89230	−	3.40192i	0.624583	−	0.360603i	−0.154068	−	0.988060i	$-0.549238\pi$
$89$	5.89230	−	3.40192i	0.624583	−	0.360603i	0.778651	+	0.627457i	$0.215904\pi$
$90$		0			0
$91$	−7.79423	−	7.50000i	−0.817057	−	0.786214i
$92$		0			0
$93$	−3.00000	+	1.73205i	−0.311086	+	0.179605i
$94$		0			0
$95$	−0.232051	+	0.401924i	−0.0238079	+	0.0412365i
$96$		0			0
$97$	7.90192	+	4.56218i	0.802319	+	0.463219i	0.844281	−	0.535900i	$-0.180028\pi$
$97$	7.90192	+	4.56218i	0.802319	+	0.463219i	−0.0419625	+	0.999119i	$0.513361\pi$
$98$		0			0
$99$			7.39230i			0.742955i
$100$		0			0
$101$	−5.36603	−	9.29423i	−0.533939	−	0.924810i	−0.999214	−	0.0396438i	$-0.987378\pi$
$101$	−5.36603	−	9.29423i	−0.533939	−	0.924810i	0.465274	−	0.885167i	$-0.345956\pi$
$102$		0			0
$103$	9.19615			0.906124			0.453062	−	0.891479i	$-0.350332\pi$
$103$	9.19615			0.906124			0.453062	+	0.891479i	$0.350332\pi$
$104$		0			0
$105$	2.19615			0.214323
$106$		0			0
$107$	8.83013	+	15.2942i	0.853641	+	1.47855i	0.877900	+	0.478843i	$0.158944\pi$
$107$	8.83013	+	15.2942i	0.853641	+	1.47855i	−0.0242598	+	0.999706i	$0.507723\pi$
$108$		0			0
$109$			8.53590i			0.817591i	0.912626	+	0.408795i	$0.134051\pi$
$109$			8.53590i			0.817591i	−0.912626	+	0.408795i	$0.865949\pi$
$110$		0			0
$111$	−0.509619	−	0.294229i	−0.0483709	−	0.0279269i
$112$		0			0
$113$	−3.46410	+	6.00000i	−0.325875	+	0.564433i	−0.981689	−	0.190490i	$-0.938992\pi$
$113$	−3.46410	+	6.00000i	−0.325875	+	0.564433i	0.655814	+	0.754923i	$0.272326\pi$
$114$		0			0
$115$	−8.19615	+	4.73205i	−0.764295	+	0.441266i
$116$		0			0
$117$	6.16025	−	6.40192i	0.569516	−	0.591858i
$118$		0			0
$119$	21.2942	−	12.2942i	1.95204	−	1.12701i
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$		0			0
$123$	−6.58846	−	3.80385i	−0.594061	−	0.342981i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	5.40192	+	9.35641i	0.479343	+	0.830247i	0.999719	−	0.0236904i	$-0.00754158\pi$
$127$	5.40192	+	9.35641i	0.479343	+	0.830247i	−0.520376	+	0.853937i	$0.674208\pi$
$128$		0			0
$129$	1.46410			0.128907
$130$		0			0
$131$	−6.12436			−0.535087			−0.267544	−	0.963546i	$-0.586212\pi$
$131$	−6.12436			−0.535087			−0.267544	+	0.963546i	$0.586212\pi$
$132$		0			0
$133$	−0.696152	−	1.20577i	−0.0603641	−	0.104554i
$134$		0			0
$135$			4.00000i			0.344265i
$136$		0			0
$137$	1.90192	+	1.09808i	0.162492	+	0.0938150i	0.579041	−	0.815298i	$-0.303427\pi$
$137$	1.90192	+	1.09808i	0.162492	+	0.0938150i	−0.416549	+	0.909113i	$0.636760\pi$
$138$		0			0
$139$	0.598076	−	1.03590i	0.0507282	−	0.0878638i	−0.839546	−	0.543288i	$-0.817179\pi$
$139$	0.598076	−	1.03590i	0.0507282	−	0.0878638i	0.890274	+	0.455424i	$0.150512\pi$
$140$		0			0
$141$	−1.90192	+	1.09808i	−0.160171	+	0.0924747i
$142$		0			0
$143$	−10.3923	+	3.00000i	−0.869048	+	0.250873i
$144$		0			0
$145$	−2.19615	+	1.26795i	−0.182381	+	0.105297i
$146$		0			0
$147$	−0.732051	+	1.26795i	−0.0603785	+	0.104579i
$148$		0			0
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	0.697507	−	0.716578i	$-0.254293\pi$
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	−0.271821	+	0.962348i	$0.587626\pi$
$150$		0			0
$151$		−	23.6603i		−	1.92544i	−0.270492	−	0.962722i	$-0.587187\pi$
$151$		−	23.6603i		−	1.92544i	0.270492	−	0.962722i	$-0.412813\pi$
$152$		0			0
$153$	10.0981	+	17.4904i	0.816381	+	1.41401i
$154$		0			0
$155$	−4.73205			−0.380087
$156$		0			0
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$		0			0
$159$	0.169873	+	0.294229i	0.0134718	+	0.0233338i
$160$		0			0
$161$		−	28.3923i		−	2.23763i
$162$		0			0
$163$	9.29423	+	5.36603i	0.727980	+	0.420300i	0.817683	−	0.575669i	$-0.195258\pi$
$163$	9.29423	+	5.36603i	0.727980	+	0.420300i	−0.0897026	+	0.995969i	$0.528592\pi$
$164$		0			0
$165$	1.09808	−	1.90192i	0.0854851	−	0.148065i
$166$		0			0
$167$	−2.59808	+	1.50000i	−0.201045	+	0.116073i	−0.597143	−	0.802135i	$-0.703697\pi$
$167$	−2.59808	+	1.50000i	−0.201045	+	0.116073i	0.396098	+	0.918208i	$0.370364\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$		0			0
$171$	0.990381	−	0.571797i	0.0757363	−	0.0437264i
$172$		0			0
$173$	7.50000	−	12.9904i	0.570214	−	0.987640i	−0.426329	−	0.904568i	$-0.640193\pi$
$173$	7.50000	−	12.9904i	0.570214	−	0.987640i	0.996544	−	0.0830722i	$-0.0264732\pi$
$174$		0			0
$175$	2.59808	+	1.50000i	0.196396	+	0.113389i
$176$		0			0
$177$		−	7.60770i		−	0.571829i
$178$		0			0
$179$	−4.73205	−	8.19615i	−0.353690	−	0.612609i	0.633203	−	0.773986i	$-0.281740\pi$
$179$	−4.73205	−	8.19615i	−0.353690	−	0.612609i	−0.986893	+	0.161377i	$0.948407\pi$
$180$		0			0
$181$	14.5885			1.08435			0.542176	−	0.840265i	$-0.317601\pi$
$181$	14.5885			1.08435			0.542176	+	0.840265i	$0.317601\pi$
$182$		0			0
$183$	−4.53590			−0.335303
$184$		0			0
$185$	−0.401924	−	0.696152i	−0.0295500	−	0.0511821i
$186$		0			0
$187$		−	24.5885i		−	1.79809i
$188$		0			0
$189$	−10.3923	−	6.00000i	−0.755929	−	0.436436i
$190$		0			0
$191$	−11.3660	+	19.6865i	−0.822417	+	1.42447i	0.0814609	+	0.996677i	$0.474041\pi$
$191$	−11.3660	+	19.6865i	−0.822417	+	1.42447i	−0.903878	+	0.427791i	$0.859292\pi$
$192$		0			0
$193$	−14.1962	+	8.19615i	−1.02186	+	0.589972i	−0.914643	−	0.404263i	$-0.867528\pi$
$193$	−14.1962	+	8.19615i	−1.02186	+	0.589972i	−0.107219	+	0.994235i	$0.534195\pi$
$194$		0			0
$195$	−2.53590	+	0.732051i	−0.181599	+	0.0524232i
$196$		0			0
$197$	18.6962	−	10.7942i	1.33205	−	0.769057i	0.346433	−	0.938075i	$-0.387393\pi$
$197$	18.6962	−	10.7942i	1.33205	−	0.769057i	0.985613	+	0.169018i	$0.0540596\pi$
$198$		0			0
$199$	−3.19615	+	5.53590i	−0.226569	+	0.392429i	−0.956789	−	0.290783i	$-0.906084\pi$
$199$	−3.19615	+	5.53590i	−0.226569	+	0.392429i	0.730220	+	0.683212i	$0.239418\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	7.60770i		−	0.533956i
$204$		0			0
$205$	−5.19615	−	9.00000i	−0.362915	−	0.628587i
$206$		0			0
$207$	23.3205			1.62089
$208$		0			0
$209$	−1.39230			−0.0963077
$210$		0			0
$211$	−8.79423	−	15.2321i	−0.605420	−	1.04862i	−0.991985	−	0.126356i	$-0.959672\pi$
$211$	−8.79423	−	15.2321i	−0.605420	−	1.04862i	0.386565	−	0.922262i	$-0.373661\pi$
$212$		0			0
$213$			4.39230i			0.300956i
$214$		0			0
$215$	1.73205	+	1.00000i	0.118125	+	0.0681994i
$216$		0			0
$217$	7.09808	−	12.2942i	0.481849	−	0.834587i
$218$		0			0
$219$	7.39230	−	4.26795i	0.499526	−	0.288401i
$220$		0			0
$221$	−20.4904	+	21.2942i	−1.37833	+	1.43240i
$222$		0			0
$223$	5.59808	−	3.23205i	0.374875	−	0.216434i	−0.300711	−	0.953715i	$-0.597224\pi$
$223$	5.59808	−	3.23205i	0.374875	−	0.216434i	0.675586	+	0.737281i	$0.263891\pi$
$224$		0			0
$225$	−1.23205	+	2.13397i	−0.0821367	+	0.142265i
$226$		0			0
$227$	−14.1962	−	8.19615i	−0.942232	−	0.543998i	−0.0515725	−	0.998669i	$-0.516423\pi$
$227$	−14.1962	−	8.19615i	−0.942232	−	0.543998i	−0.890659	+	0.454672i	$0.849757\pi$
$228$		0			0
$229$			1.26795i			0.0837884i	0.999122	+	0.0418942i	$0.0133392\pi$
$229$			1.26795i			0.0837884i	−0.999122	+	0.0418942i	$0.986661\pi$
$230$		0			0
$231$	3.29423	+	5.70577i	0.216744	+	0.375412i
$232$		0			0
$233$	4.73205			0.310007			0.155003	−	0.987914i	$-0.450461\pi$
$233$	4.73205			0.310007			0.155003	+	0.987914i	$0.450461\pi$
$234$		0			0
$235$	−3.00000			−0.195698
$236$		0			0
$237$	1.53590	+	2.66025i	0.0997673	+	0.172802i
$238$		0			0
$239$			2.19615i			0.142057i	0.997474	+	0.0710286i	$0.0226282\pi$
$239$			2.19615i			0.142057i	−0.997474	+	0.0710286i	$0.977372\pi$
$240$		0			0
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	0.238597	−	0.971119i	$-0.423312\pi$
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	−0.721715	+	0.692191i	$0.756646\pi$
$242$		0			0
$243$	7.63397	−	13.2224i	0.489720	−	0.848219i
$244$		0			0
$245$	−1.73205	+	1.00000i	−0.110657	+	0.0638877i
$246$		0			0
$247$	1.20577	+	1.16025i	0.0767214	+	0.0738252i
$248$		0			0
$249$	5.19615	−	3.00000i	0.329293	−	0.190117i
$250$		0			0
$251$	8.59808	−	14.8923i	0.542706	−	0.939994i	−0.456042	−	0.889958i	$-0.650733\pi$
$251$	8.59808	−	14.8923i	0.542706	−	0.939994i	0.998747	−	0.0500355i	$-0.0159335\pi$
$252$		0			0
$253$	−24.5885	−	14.1962i	−1.54586	−	0.892504i
$254$		0			0
$255$		−	6.00000i		−	0.375735i
$256$		0			0
$257$	6.92820	+	12.0000i	0.432169	+	0.748539i	0.997060	−	0.0766265i	$-0.0244149\pi$
$257$	6.92820	+	12.0000i	0.432169	+	0.748539i	−0.564890	+	0.825166i	$0.691082\pi$
$258$		0			0
$259$	2.41154			0.149846
$260$		0			0
$261$	6.24871			0.386786
$262$		0			0
$263$	1.79423	+	3.10770i	0.110637	+	0.191629i	0.916027	−	0.401116i	$-0.131378\pi$
$263$	1.79423	+	3.10770i	0.110637	+	0.191629i	−0.805390	+	0.592745i	$0.798044\pi$
$264$		0			0
$265$			0.464102i			0.0285095i
$266$		0			0
$267$	4.31347	+	2.49038i	0.263980	+	0.152409i
$268$		0			0
$269$	13.5622	−	23.4904i	0.826901	−	1.43223i	−0.0735575	−	0.997291i	$-0.523435\pi$
$269$	13.5622	−	23.4904i	0.826901	−	1.43223i	0.900458	−	0.434943i	$-0.143231\pi$
$270$		0			0
$271$	−8.19615	+	4.73205i	−0.497881	+	0.287452i	−0.727838	−	0.685749i	$-0.759475\pi$
$271$	−8.19615	+	4.73205i	−0.497881	+	0.287452i	0.229957	+	0.973201i	$0.426141\pi$
$272$		0			0
$273$	1.90192	−	7.68653i	0.115110	−	0.465210i
$274$		0			0
$275$	2.59808	−	1.50000i	0.156670	−	0.0904534i
$276$		0			0
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$		0			0
$279$	10.0981	+	5.83013i	0.604556	+	0.349041i
$280$		0			0
$281$			10.3923i			0.619953i	0.950744	+	0.309976i	$0.100321\pi$
$281$			10.3923i			0.619953i	−0.950744	+	0.309976i	$0.899679\pi$
$282$		0			0
$283$	−4.80385	−	8.32051i	−0.285559	−	0.494603i	0.687186	−	0.726482i	$-0.258846\pi$
$283$	−4.80385	−	8.32051i	−0.285559	−	0.494603i	−0.972745	+	0.231879i	$0.925513\pi$
$284$		0			0
$285$	−0.339746			−0.0201248
$286$		0			0
$287$	31.1769			1.84032
$288$		0			0
$289$	−25.0885	−	43.4545i	−1.47579	−	2.55615i
$290$		0			0
$291$			6.67949i			0.391559i
$292$		0			0
$293$	9.69615	+	5.59808i	0.566455	+	0.327043i	0.755732	−	0.654881i	$-0.227281\pi$
$293$	9.69615	+	5.59808i	0.566455	+	0.327043i	−0.189277	+	0.981924i	$0.560614\pi$
$294$		0			0
$295$	5.19615	−	9.00000i	0.302532	−	0.524000i
$296$		0			0
$297$	−10.3923	+	6.00000i	−0.603023	+	0.348155i
$298$		0			0
$299$	9.46410	+	32.7846i	0.547323	+	1.89598i
$300$		0			0
$301$	−5.19615	+	3.00000i	−0.299501	+	0.172917i
$302$		0			0
$303$	3.92820	−	6.80385i	0.225669	−	0.390871i
$304$		0			0
$305$	−5.36603	−	3.09808i	−0.307258	−	0.177395i
$306$		0			0
$307$		−	27.4641i		−	1.56746i	−0.621102	−	0.783730i	$-0.713315\pi$
$307$		−	27.4641i		−	1.56746i	0.621102	−	0.783730i	$-0.286685\pi$
$308$		0			0
$309$	3.36603	+	5.83013i	0.191486	+	0.331664i
$310$		0			0
$311$	9.12436			0.517395			0.258697	−	0.965958i	$-0.416707\pi$
$311$	9.12436			0.517395			0.258697	+	0.965958i	$0.416707\pi$
$312$		0			0
$313$	26.3923			1.49178			0.745891	−	0.666068i	$-0.232024\pi$
$313$	26.3923			1.49178			0.745891	+	0.666068i	$0.232024\pi$
$314$		0			0
$315$	−3.69615	−	6.40192i	−0.208255	−	0.360708i
$316$		0			0
$317$			23.1962i			1.30283i	0.758723	+	0.651413i	$0.225823\pi$
$317$			23.1962i			1.30283i	−0.758723	+	0.651413i	$0.774177\pi$
$318$		0			0
$319$	−6.58846	−	3.80385i	−0.368883	−	0.212975i
$320$		0			0
$321$	−6.46410	+	11.1962i	−0.360791	+	0.624908i
$322$		0			0
$323$	−3.29423	+	1.90192i	−0.183296	+	0.105826i
$324$		0			0
$325$	−3.50000	−	0.866025i	−0.194145	−	0.0480384i
$326$		0			0
$327$	−5.41154	+	3.12436i	−0.299259	+	0.172777i
$328$		0			0
$329$	4.50000	−	7.79423i	0.248093	−	0.429710i
$330$		0			0
$331$	−11.1962	−	6.46410i	−0.615396	−	0.355299i	0.159678	−	0.987169i	$-0.448954\pi$
$331$	−11.1962	−	6.46410i	−0.615396	−	0.355299i	−0.775074	+	0.631870i	$0.782288\pi$
$332$		0			0
$333$			1.98076i			0.108545i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	6.19615			0.337526			0.168763	−	0.985657i	$-0.446023\pi$
$337$	6.19615			0.337526			0.168763	+	0.985657i	$0.446023\pi$
$338$		0			0
$339$	−5.07180			−0.275462
$340$		0			0
$341$	−7.09808	−	12.2942i	−0.384382	−	0.665770i
$342$		0			0
$343$			15.0000i			0.809924i
$344$		0			0
$345$	−6.00000	−	3.46410i	−0.323029	−	0.186501i
$346$		0			0
$347$	−14.3660	+	24.8827i	−0.771209	+	1.33577i	0.165692	+	0.986178i	$0.447014\pi$
$347$	−14.3660	+	24.8827i	−0.771209	+	1.33577i	−0.936901	+	0.349595i	$0.886319\pi$
$348$		0			0
$349$	−3.50962	+	2.02628i	−0.187866	+	0.108464i	−0.590983	−	0.806684i	$-0.701260\pi$
$349$	−3.50962	+	2.02628i	−0.187866	+	0.108464i	0.403117	+	0.915148i	$0.367927\pi$
$350$		0			0
$351$	14.0000	+	3.46410i	0.747265	+	0.184900i
$352$		0			0
$353$	8.49038	−	4.90192i	0.451897	−	0.260903i	−0.256734	−	0.966482i	$-0.582646\pi$
$353$	8.49038	−	4.90192i	0.451897	−	0.260903i	0.708631	+	0.705579i	$0.249313\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$		0			0
$357$	15.5885	+	9.00000i	0.825029	+	0.476331i
$358$		0			0
$359$			1.60770i			0.0848509i	0.999100	+	0.0424255i	$0.0135085\pi$
$359$			1.60770i			0.0848509i	−0.999100	+	0.0424255i	$0.986492\pi$
$360$		0			0
$361$	−9.39230	−	16.2679i	−0.494332	−	0.856208i
$362$		0			0
$363$	−1.46410			−0.0768454
$364$		0			0
$365$	11.6603			0.610326
$366$		0			0
$367$	−2.80385	−	4.85641i	−0.146360	−	0.253502i	0.783520	−	0.621367i	$-0.213422\pi$
$367$	−2.80385	−	4.85641i	−0.146360	−	0.253502i	−0.929879	+	0.367865i	$0.880089\pi$
$368$		0			0
$369$			25.6077i			1.33308i
$370$		0			0
$371$	−1.20577	−	0.696152i	−0.0626005	−	0.0361424i
$372$		0			0
$373$	0.196152	−	0.339746i	0.0101564	−	0.0175914i	−0.860903	−	0.508770i	$-0.830100\pi$
$373$	0.196152	−	0.339746i	0.0101564	−	0.0175914i	0.871059	+	0.491179i	$0.163434\pi$
$374$		0			0
$375$	0.633975	−	0.366025i	0.0327383	−	0.0189015i
$376$		0			0
$377$	2.53590	+	8.78461i	0.130605	+	0.452430i
$378$		0			0
$379$	−25.7942	+	14.8923i	−1.32496	+	0.764966i	−0.984515	−	0.175298i	$-0.943911\pi$
$379$	−25.7942	+	14.8923i	−1.32496	+	0.764966i	−0.340445	+	0.940264i	$0.610578\pi$
$380$		0			0
$381$	−3.95448	+	6.84936i	−0.202594	+	0.350904i
$382$		0			0
$383$	−19.3923	−	11.1962i	−0.990900	−	0.572097i	−0.0853571	−	0.996350i	$-0.527203\pi$
$383$	−19.3923	−	11.1962i	−0.990900	−	0.572097i	−0.905543	+	0.424254i	$0.860536\pi$
$384$		0			0
$385$			9.00000i			0.458682i
$386$		0			0
$387$	−2.46410	−	4.26795i	−0.125257	−	0.216952i
$388$		0			0
$389$	22.7321			1.15256			0.576280	−	0.817252i	$-0.304504\pi$
$389$	22.7321			1.15256			0.576280	+	0.817252i	$0.304504\pi$
$390$		0			0
$391$	−77.5692			−3.92284
$392$		0			0
$393$	−2.24167	−	3.88269i	−0.113077	−	0.195856i
$394$		0			0
$395$			4.19615i			0.211131i
$396$		0			0
$397$	−9.69615	−	5.59808i	−0.486636	−	0.280959i	0.236542	−	0.971621i	$-0.423986\pi$
$397$	−9.69615	−	5.59808i	−0.486636	−	0.280959i	−0.723178	+	0.690662i	$0.757319\pi$
$398$		0			0
$399$	0.509619	−	0.882686i	0.0255129	−	0.0441896i
$400$		0			0
$401$	−4.50000	+	2.59808i	−0.224719	+	0.129742i	−0.608134	−	0.793835i	$-0.708081\pi$
$401$	−4.50000	+	2.59808i	−0.224719	+	0.129742i	0.383414	+	0.923576i	$0.374748\pi$
$402$		0			0
$403$	−4.09808	+	16.5622i	−0.204140	+	0.825021i
$404$		0			0
$405$	3.86603	−	2.23205i	0.192104	−	0.110911i
$406$		0			0
$407$	1.20577	−	2.08846i	0.0597679	−	0.103521i
$408$		0			0
$409$	−14.0885	−	8.13397i	−0.696629	−	0.402199i	0.109461	−	0.993991i	$-0.465087\pi$
$409$	−14.0885	−	8.13397i	−0.696629	−	0.402199i	−0.806091	+	0.591792i	$0.798421\pi$
$410$		0			0
$411$			1.60770i			0.0793018i
$412$		0			0
$413$	15.5885	+	27.0000i	0.767058	+	1.32858i
$414$		0			0
$415$	8.19615			0.402333
$416$		0			0
$417$	0.875644			0.0428805
$418$		0			0
$419$	−8.66025	−	15.0000i	−0.423081	−	0.732798i	0.573158	−	0.819445i	$-0.305718\pi$
$419$	−8.66025	−	15.0000i	−0.423081	−	0.732798i	−0.996239	+	0.0866469i	$0.972385\pi$
$420$		0			0
$421$		−	2.87564i		−	0.140150i	−0.997542	−	0.0700752i	$-0.977676\pi$
$421$		−	2.87564i		−	0.140150i	0.997542	−	0.0700752i	$-0.0223239\pi$
$422$		0			0
$423$	6.40192	+	3.69615i	0.311272	+	0.179713i
$424$		0			0
$425$	4.09808	−	7.09808i	0.198786	−	0.344307i
$426$		0			0
$427$	16.0981	−	9.29423i	0.779041	−	0.449779i
$428$		0			0
$429$	−5.70577	−	5.49038i	−0.275477	−	0.265078i
$430$		0			0
$431$	7.09808	−	4.09808i	0.341902	−	0.197397i	−0.319211	−	0.947684i	$-0.603418\pi$
$431$	7.09808	−	4.09808i	0.341902	−	0.197397i	0.661113	+	0.750286i	$0.270084\pi$
$432$		0			0
$433$	−4.19615	+	7.26795i	−0.201654	+	0.349275i	−0.949062	−	0.315091i	$-0.897965\pi$
$433$	−4.19615	+	7.26795i	−0.201654	+	0.349275i	0.747407	+	0.664366i	$0.231298\pi$
$434$		0			0
$435$	−1.60770	−	0.928203i	−0.0770831	−	0.0445039i
$436$		0			0
$437$			4.39230i			0.210112i
$438$		0			0
$439$	−1.70577	−	2.95448i	−0.0814120	−	0.141010i	0.822445	−	0.568845i	$-0.192610\pi$
$439$	−1.70577	−	2.95448i	−0.0814120	−	0.141010i	−0.903857	+	0.427835i	$0.859276\pi$
$440$		0			0
$441$	4.92820			0.234676
$442$		0			0
$443$	22.3923			1.06389			0.531945	−	0.846779i	$-0.321461\pi$
$443$	22.3923			1.06389			0.531945	+	0.846779i	$0.321461\pi$
$444$		0			0
$445$	3.40192	+	5.89230i	0.161267	+	0.279322i
$446$		0			0
$447$			4.39230i			0.207749i
$448$		0			0
$449$	13.5000	+	7.79423i	0.637104	+	0.367832i	0.783498	−	0.621394i	$-0.213433\pi$
$449$	13.5000	+	7.79423i	0.637104	+	0.367832i	−0.146394	+	0.989226i	$0.546767\pi$
$450$		0			0
$451$	15.5885	−	27.0000i	0.734032	−	1.27138i
$452$		0			0
$453$	15.0000	−	8.66025i	0.704761	−	0.406894i
$454$		0			0
$455$	7.50000	−	7.79423i	0.351605	−	0.365399i
$456$		0			0
$457$	15.8827	−	9.16987i	0.742961	−	0.428949i	−0.0801841	−	0.996780i	$-0.525551\pi$
$457$	15.8827	−	9.16987i	0.742961	−	0.428949i	0.823145	+	0.567832i	$0.192217\pi$
$458$		0			0
$459$	−16.3923	+	28.3923i	−0.765127	+	1.32524i
$460$		0			0
$461$	−26.4904	−	15.2942i	−1.23378	−	0.712323i	−0.265964	−	0.963983i	$-0.585690\pi$
$461$	−26.4904	−	15.2942i	−1.23378	−	0.712323i	−0.967816	+	0.251660i	$0.919024\pi$
$462$		0			0
$463$			12.9282i			0.600825i	0.953809	+	0.300412i	$0.0971243\pi$
$463$			12.9282i			0.600825i	−0.953809	+	0.300412i	$0.902876\pi$
$464$		0			0
$465$	−1.73205	−	3.00000i	−0.0803219	−	0.139122i
$466$		0			0
$467$	37.8564			1.75179			0.875893	−	0.482506i	$-0.160273\pi$
$467$	37.8564			1.75179			0.875893	+	0.482506i	$0.160273\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−4.75833	−	8.24167i	−0.219252	−	0.379756i
$472$		0			0
$473$			6.00000i			0.275880i
$474$		0			0
$475$	−0.401924	−	0.232051i	−0.0184415	−	0.0106472i
$476$		0			0
$477$	0.571797	−	0.990381i	0.0261808	−	0.0453464i
$478$		0			0
$479$	35.4904	−	20.4904i	1.62160	−	0.936229i	0.635104	−	0.772427i	$-0.280957\pi$
$479$	35.4904	−	20.4904i	1.62160	−	0.936229i	0.986493	−	0.163803i	$-0.0523760\pi$
$480$		0			0
$481$	−2.78461	+	0.803848i	−0.126967	+	0.0366523i
$482$		0			0
$483$	18.0000	−	10.3923i	0.819028	−	0.472866i
$484$		0			0
$485$	−4.56218	+	7.90192i	−0.207158	+	0.358808i
$486$		0			0
$487$	13.2058	+	7.62436i	0.598411	+	0.345493i	0.768416	−	0.639951i	$-0.221045\pi$
$487$	13.2058	+	7.62436i	0.598411	+	0.345493i	−0.170005	+	0.985443i	$0.554379\pi$
$488$		0			0
$489$			7.85641i			0.355279i
$490$		0			0
$491$	10.3301	+	17.8923i	0.466192	+	0.807468i	0.999254	−	0.0386076i	$-0.0122922\pi$
$491$	10.3301	+	17.8923i	0.466192	+	0.807468i	−0.533062	+	0.846076i	$0.678959\pi$
$492$		0			0
$493$	−20.7846			−0.936092
$494$		0			0
$495$	−7.39230			−0.332259
$496$		0			0
$497$	−9.00000	−	15.5885i	−0.403705	−	0.699238i
$498$		0			0
$499$			25.8564i			1.15749i	0.815508	+	0.578746i	$0.196458\pi$
$499$			25.8564i			1.15749i	−0.815508	+	0.578746i	$0.803542\pi$
$500$		0			0
$501$	−1.90192	−	1.09808i	−0.0849717	−	0.0490584i
$502$		0			0
$503$	−13.3301	+	23.0885i	−0.594361	+	1.02946i	0.399276	+	0.916831i	$0.369262\pi$
$503$	−13.3301	+	23.0885i	−0.594361	+	1.02946i	−0.993637	+	0.112633i	$0.964072\pi$
$504$		0			0
$505$	9.29423	−	5.36603i	0.413588	−	0.238785i
$506$		0			0
$507$	0.366025	+	9.50962i	0.0162558	+	0.422337i
$508$		0			0
$509$	−19.3923	+	11.1962i	−0.859549	+	0.496261i	−0.863861	−	0.503730i	$-0.831961\pi$
$509$	−19.3923	+	11.1962i	−0.859549	+	0.496261i	0.00431237	+	0.999991i	$0.498627\pi$
$510$		0			0
$511$	−17.4904	+	30.2942i	−0.773729	+	1.34014i
$512$		0			0
$513$	1.60770	+	0.928203i	0.0709815	+	0.0409812i
$514$		0			0
$515$			9.19615i			0.405231i
$516$		0			0
$517$	−4.50000	−	7.79423i	−0.197910	−	0.342790i
$518$		0			0
$519$	10.9808			0.482002
$520$		0			0
$521$	6.46410			0.283197			0.141599	−	0.989924i	$-0.454776\pi$
$521$	6.46410			0.283197			0.141599	+	0.989924i	$0.454776\pi$
$522$		0			0
$523$	−1.19615	−	2.07180i	−0.0523041	−	0.0905933i	0.838688	−	0.544612i	$-0.183323\pi$
$523$	−1.19615	−	2.07180i	−0.0523041	−	0.0905933i	−0.890992	+	0.454019i	$0.849990\pi$
$524$		0			0
$525$			2.19615i			0.0958479i
$526$		0			0
$527$	−33.5885	−	19.3923i	−1.46314	−	0.844742i
$528$		0			0
$529$	−33.2846	+	57.6506i	−1.44716	+	2.50655i
$530$		0			0
$531$	−22.1769	+	12.8038i	−0.962396	+	0.555640i
$532$		0			0
$533$	−36.0000	+	10.3923i	−1.55933	+	0.450141i
$534$		0			0
$535$	−15.2942	+	8.83013i	−0.661227	+	0.381760i
$536$		0			0
$537$	3.46410	−	6.00000i	0.149487	−	0.258919i
$538$		0			0
$539$	−5.19615	−	3.00000i	−0.223814	−	0.129219i
$540$		0			0
$541$		−	22.0526i		−	0.948114i	−0.880494	−	0.474057i	$-0.842789\pi$
$541$		−	22.0526i		−	0.948114i	0.880494	−	0.474057i	$-0.157211\pi$
$542$		0			0
$543$	5.33975	+	9.24871i	0.229150	+	0.396900i
$544$		0			0
$545$	−8.53590			−0.365638
$546$		0			0
$547$	6.78461			0.290089			0.145044	−	0.989425i	$-0.453667\pi$
$547$	6.78461			0.290089			0.145044	+	0.989425i	$0.453667\pi$
$548$		0			0
$549$	7.63397	+	13.2224i	0.325810	+	0.564320i
$550$		0			0
$551$			1.17691i			0.0501382i
$552$		0			0
$553$	−10.9019	−	6.29423i	−0.463597	−	0.267658i
$554$		0			0
$555$	0.294229	−	0.509619i	0.0124893	−	0.0216321i
$556$		0			0
$557$	−5.89230	+	3.40192i	−0.249665	+	0.144144i	−0.619611	−	0.784909i	$-0.712710\pi$
$557$	−5.89230	+	3.40192i	−0.249665	+	0.144144i	0.369946	+	0.929053i	$0.379376\pi$
$558$		0			0
$559$	5.00000	−	5.19615i	0.211477	−	0.219774i
$560$		0			0
$561$	15.5885	−	9.00000i	0.658145	−	0.379980i
$562$		0			0
$563$	7.26795	−	12.5885i	0.306308	−	0.530540i	−0.671244	−	0.741236i	$-0.734240\pi$
$563$	7.26795	−	12.5885i	0.306308	−	0.530540i	0.977552	+	0.210696i	$0.0675731\pi$
$564$		0			0
$565$	−6.00000	−	3.46410i	−0.252422	−	0.145736i
$566$		0			0
$567$			13.3923i			0.562424i
$568$		0			0
$569$	13.6244	+	23.5981i	0.571163	+	0.989283i	0.996447	+	0.0842230i	$0.0268408\pi$
$569$	13.6244	+	23.5981i	0.571163	+	0.989283i	−0.425284	+	0.905060i	$0.639826\pi$
$570$		0			0
$571$	38.3731			1.60586			0.802931	−	0.596071i	$-0.203272\pi$
$571$	38.3731			1.60586			0.802931	+	0.596071i	$0.203272\pi$
$572$		0			0
$573$	−16.6410			−0.695188
$574$		0			0
$575$	−4.73205	−	8.19615i	−0.197340	−	0.341803i
$576$		0			0
$577$			26.4449i			1.10091i	0.834863	+	0.550457i	$0.185547\pi$
$577$			26.4449i			1.10091i	−0.834863	+	0.550457i	$0.814453\pi$
$578$		0			0
$579$	−10.3923	−	6.00000i	−0.431889	−	0.249351i
$580$		0			0
$581$	−12.2942	+	21.2942i	−0.510051	+	0.883433i
$582$		0			0
$583$	−1.20577	+	0.696152i	−0.0499379	+	0.0288317i
$584$		0			0
$585$	6.40192	+	6.16025i	0.264687	+	0.254695i
$586$		0			0
$587$	−25.9808	+	15.0000i	−1.07234	+	0.619116i	−0.928820	−	0.370531i	$-0.879176\pi$
$587$	−25.9808	+	15.0000i	−1.07234	+	0.619116i	−0.143521	+	0.989647i	$0.545842\pi$
$588$		0			0
$589$	−1.09808	+	1.90192i	−0.0452454	+	0.0783674i
$590$		0			0
$591$	13.6865	+	7.90192i	0.562989	+	0.325042i
$592$		0			0
$593$			20.7846i			0.853522i	0.904365	+	0.426761i	$0.140345\pi$
$593$			20.7846i			0.853522i	−0.904365	+	0.426761i	$0.859655\pi$
$594$		0			0
$595$	12.2942	+	21.2942i	0.504014	+	0.872978i
$596$		0			0
$597$	−4.67949			−0.191519
$598$		0			0
$599$	19.8564			0.811311			0.405655	−	0.914026i	$-0.367043\pi$
$599$	19.8564			0.811311			0.405655	+	0.914026i	$0.367043\pi$
$600$		0			0
$601$	18.8923	+	32.7224i	0.770633	+	1.33478i	0.937216	+	0.348748i	$0.113393\pi$
$601$	18.8923	+	32.7224i	0.770633	+	1.33478i	−0.166583	+	0.986027i	$0.553273\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.73205	−	1.00000i	−0.0704179	−	0.0406558i
$606$		0			0
$607$	−18.7942	+	32.5526i	−0.762834	+	1.32127i	0.178550	+	0.983931i	$0.442859\pi$
$607$	−18.7942	+	32.5526i	−0.762834	+	1.32127i	−0.941384	+	0.337337i	$0.890474\pi$
$608$		0			0
$609$	4.82309	−	2.78461i	0.195441	−	0.112838i
$610$		0			0
$611$	−2.59808	+	10.5000i	−0.105107	+	0.424785i
$612$		0			0
$613$	33.6962	−	19.4545i	1.36097	−	0.785759i	0.371221	−	0.928545i	$-0.378939\pi$
$613$	33.6962	−	19.4545i	1.36097	−	0.785759i	0.989754	+	0.142785i	$0.0456059\pi$
$614$		0			0
$615$	3.80385	−	6.58846i	0.153386	−	0.265672i
$616$		0			0
$617$	15.5885	+	9.00000i	0.627568	+	0.362326i	0.779809	−	0.626017i	$-0.215316\pi$
$617$	15.5885	+	9.00000i	0.627568	+	0.362326i	−0.152242	+	0.988343i	$0.548649\pi$
$618$		0			0
$619$		−	31.3923i		−	1.26176i	−0.775879	−	0.630882i	$-0.782693\pi$
$619$		−	31.3923i		−	1.26176i	0.775879	−	0.630882i	$-0.217307\pi$
$620$		0			0
$621$	18.9282	+	32.7846i	0.759563	+	1.31560i
$622$		0			0
$623$	−20.4115			−0.817771
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−0.509619	−	0.882686i	−0.0203522	−	0.0352511i
$628$		0			0
$629$		−	6.58846i		−	0.262699i
$630$		0			0
$631$	18.0000	+	10.3923i	0.716569	+	0.413711i	0.813488	−	0.581581i	$-0.197566\pi$
$631$	18.0000	+	10.3923i	0.716569	+	0.413711i	−0.0969198	+	0.995292i	$0.530899\pi$
$632$		0			0
$633$	6.43782	−	11.1506i	0.255880	−	0.443198i
$634$		0			0
$635$	−9.35641	+	5.40192i	−0.371298	+	0.214369i
$636$		0			0
$637$	2.00000	+	6.92820i	0.0792429	+	0.274505i
$638$		0			0
$639$	12.8038	−	7.39230i	0.506512	−	0.292435i
$640$		0			0
$641$	−16.0359	+	27.7750i	−0.633380	+	1.09705i	0.353476	+	0.935444i	$0.385000\pi$
$641$	−16.0359	+	27.7750i	−0.633380	+	1.09705i	−0.986856	+	0.161603i	$0.948334\pi$
$642$		0			0
$643$	9.29423	+	5.36603i	0.366529	+	0.211615i	0.671941	−	0.740605i	$-0.265461\pi$
$643$	9.29423	+	5.36603i	0.366529	+	0.211615i	−0.305412	+	0.952220i	$0.598794\pi$
$644$		0			0
$645$			1.46410i			0.0576489i
$646$		0			0
$647$	−0.401924	−	0.696152i	−0.0158013	−	0.0273686i	0.858017	−	0.513622i	$-0.171697\pi$
$647$	−0.401924	−	0.696152i	−0.0158013	−	0.0273686i	−0.873818	+	0.486253i	$0.838363\pi$
$648$		0			0
$649$	31.1769			1.22380
$650$		0			0
$651$	10.3923			0.407307
$652$		0			0
$653$	−0.696152	−	1.20577i	−0.0272425	−	0.0471855i	0.852083	−	0.523407i	$-0.175339\pi$
$653$	−0.696152	−	1.20577i	−0.0272425	−	0.0471855i	−0.879325	+	0.476222i	$0.842006\pi$
$654$		0			0
$655$		−	6.12436i		−	0.239298i
$656$		0			0
$657$	−24.8827	−	14.3660i	−0.970766	−	0.560472i
$658$		0			0
$659$	−2.66025	+	4.60770i	−0.103629	+	0.179490i	−0.913177	−	0.407563i	$-0.866379\pi$
$659$	−2.66025	+	4.60770i	−0.103629	+	0.179490i	0.809548	+	0.587053i	$0.199712\pi$
$660$		0			0
$661$	31.0981	−	17.9545i	1.20957	−	0.698348i	0.246909	−	0.969039i	$-0.420585\pi$
$661$	31.0981	−	17.9545i	1.20957	−	0.698348i	0.962666	+	0.270690i	$0.0872520\pi$
$662$		0			0
$663$	−21.0000	−	5.19615i	−0.815572	−	0.201802i
$664$		0			0
$665$	1.20577	−	0.696152i	0.0467578	−	0.0269956i
$666$		0			0
$667$	−12.0000	+	20.7846i	−0.464642	+	0.804783i
$668$		0			0
$669$	4.09808	+	2.36603i	0.158441	+	0.0914758i
$670$		0			0
$671$		−	18.5885i		−	0.717599i
$672$		0			0
$673$	−12.1962	−	21.1244i	−0.470127	−	0.814284i	0.529289	−	0.848441i	$-0.322459\pi$
$673$	−12.1962	−	21.1244i	−0.470127	−	0.814284i	−0.999416	+	0.0341573i	$0.989125\pi$
$674$		0			0
$675$	−4.00000			−0.153960
$676$		0			0
$677$	−25.8564			−0.993742			−0.496871	−	0.867824i	$-0.665518\pi$
$677$	−25.8564			−0.993742			−0.496871	+	0.867824i	$0.665518\pi$
$678$		0			0
$679$	−13.6865	−	23.7058i	−0.525241	−	0.909744i
$680$		0			0
$681$		−	12.0000i		−	0.459841i
$682$		0			0
$683$	−27.0000	−	15.5885i	−1.03313	−	0.596476i	−0.115248	−	0.993337i	$-0.536766\pi$
$683$	−27.0000	−	15.5885i	−1.03313	−	0.596476i	−0.917879	+	0.396861i	$0.870099\pi$
$684$		0			0
$685$	−1.09808	+	1.90192i	−0.0419553	+	0.0726688i
$686$		0			0
$687$	−0.803848	+	0.464102i	−0.0306687	+	0.0177066i
$688$		0			0
$689$	1.62436	+	0.401924i	0.0618830	+	0.0153121i
$690$		0			0
$691$	31.7942	−	18.3564i	1.20951	−	0.698311i	0.246857	−	0.969052i	$-0.420602\pi$
$691$	31.7942	−	18.3564i	1.20951	−	0.698311i	0.962652	+	0.270741i	$0.0872688\pi$
$692$		0			0
$693$	11.0885	−	19.2058i	0.421216	−	0.729567i
$694$		0			0
$695$	1.03590	+	0.598076i	0.0392939	+	0.0226863i
$696$		0			0
$697$		−	85.1769i		−	3.22631i
$698$		0			0
$699$	1.73205	+	3.00000i	0.0655122	+	0.113470i
$700$		0			0
$701$	35.9090			1.35626			0.678131	−	0.734941i	$-0.262790\pi$
$701$	35.9090			1.35626			0.678131	+	0.734941i	$0.262790\pi$
$702$		0			0
$703$	−0.373067			−0.0140705
$704$		0			0
$705$	−1.09808	−	1.90192i	−0.0413559	−	0.0716306i
$706$		0			0
$707$			32.1962i			1.21086i
$708$		0			0
$709$	9.50962	+	5.49038i	0.357141	+	0.206196i	0.667826	−	0.744317i	$-0.267225\pi$
$709$	9.50962	+	5.49038i	0.357141	+	0.206196i	−0.310685	+	0.950513i	$0.600558\pi$
$710$		0			0
$711$	5.16987	−	8.95448i	0.193885	−	0.335819i
$712$		0			0
$713$	−38.7846	+	22.3923i	−1.45250	+	0.838598i
$714$		0			0
$715$	−3.00000	−	10.3923i	−0.112194	−	0.388650i
$716$		0			0
$717$	−1.39230	+	0.803848i	−0.0519966	+	0.0300202i
$718$		0			0
$719$	12.9282	−	22.3923i	0.482141	−	0.835092i	−0.517649	−	0.855593i	$-0.673193\pi$
$719$	12.9282	−	22.3923i	0.482141	−	0.835092i	0.999790	+	0.0205009i	$0.00652609\pi$
$720$		0			0
$721$	−23.8923	−	13.7942i	−0.889796	−	0.513724i
$722$		0			0
$723$		−	6.33975i		−	0.235778i
$724$		0			0
$725$	−1.26795	−	2.19615i	−0.0470905	−	0.0815631i
$726$		0			0
$727$	−34.3731			−1.27483			−0.637413	−	0.770522i	$-0.719996\pi$
$727$	−34.3731			−1.27483			−0.637413	+	0.770522i	$0.719996\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$		0			0
$731$	8.19615	+	14.1962i	0.303146	+	0.525064i
$732$		0			0
$733$		−	14.9090i		−	0.550675i	−0.961348	−	0.275338i	$-0.911210\pi$
$733$		−	14.9090i		−	0.550675i	0.961348	−	0.275338i	$-0.0887896\pi$
$734$		0			0
$735$	−1.26795	−	0.732051i	−0.0467690	−	0.0270021i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−28.2058	+	16.2846i	−1.03757	+	0.599039i	−0.919143	−	0.393924i	$-0.871117\pi$
$739$	−28.2058	+	16.2846i	−1.03757	+	0.599039i	−0.118423	+	0.992963i	$0.537784\pi$
$740$		0			0
$741$	−0.294229	+	1.18911i	−0.0108088	+	0.0436831i
$742$		0			0
$743$	11.7846	−	6.80385i	0.432335	−	0.249609i	−0.268006	−	0.963417i	$-0.586365\pi$
$743$	11.7846	−	6.80385i	0.432335	−	0.249609i	0.700341	+	0.713808i	$0.253031\pi$
$744$		0			0
$745$	−3.00000	+	5.19615i	−0.109911	+	0.190372i
$746$		0			0
$747$	−17.4904	−	10.0981i	−0.639940	−	0.369469i
$748$		0			0
$749$		−	52.9808i		−	1.93587i
$750$		0			0
$751$	−10.1962	−	17.6603i	−0.372063	−	0.644432i	0.617820	−	0.786320i	$-0.288016\pi$
$751$	−10.1962	−	17.6603i	−0.372063	−	0.644432i	−0.989883	+	0.141888i	$0.954683\pi$
$752$		0			0
$753$	12.5885			0.458749
$754$		0			0
$755$	23.6603			0.861085
$756$		0			0
$757$	18.8923	+	32.7224i	0.686652	+	1.18932i	0.972914	+	0.231166i	$0.0742539\pi$
$757$	18.8923	+	32.7224i	0.686652	+	1.18932i	−0.286262	+	0.958151i	$0.592413\pi$
$758$		0			0
$759$		−	20.7846i		−	0.754434i
$760$		0			0
$761$	16.2846	+	9.40192i	0.590317	+	0.340819i	0.765223	−	0.643766i	$-0.222629\pi$
$761$	16.2846	+	9.40192i	0.590317	+	0.340819i	−0.174906	+	0.984585i	$0.555962\pi$
$762$		0			0
$763$	12.8038	−	22.1769i	0.463530	−	0.802858i
$764$		0			0
$765$	−17.4904	+	10.0981i	−0.632366	+	0.365097i
$766$		0			0
$767$	−27.0000	−	25.9808i	−0.974913	−	0.938111i
$768$		0			0
$769$	−33.0000	+	19.0526i	−1.19001	+	0.687053i	−0.958309	−	0.285734i	$-0.907763\pi$
$769$	−33.0000	+	19.0526i	−1.19001	+	0.687053i	−0.231701	+	0.972787i	$0.574429\pi$
$770$		0			0
$771$	−5.07180	+	8.78461i	−0.182656	+	0.316370i
$772$		0			0
$773$	2.08846	+	1.20577i	0.0751166	+	0.0433686i	0.537088	−	0.843526i	$-0.319524\pi$
$773$	2.08846	+	1.20577i	0.0751166	+	0.0433686i	−0.461971	+	0.886895i	$0.652858\pi$
$774$		0			0
$775$		−	4.73205i		−	0.169980i
$776$		0			0
$777$	0.882686	+	1.52886i	0.0316662	+	0.0548474i
$778$		0			0
$779$	−4.82309			−0.172805
$780$		0			0
$781$	−18.0000			−0.644091
$782$		0			0
$783$	5.07180	+	8.78461i	0.181251	+	0.313936i
$784$		0			0
$785$		−	13.0000i		−	0.463990i
$786$		0			0
$787$	37.0981	+	21.4186i	1.32240	+	0.763490i	0.984112	−	0.177551i	$-0.0568175\pi$
$787$	37.0981	+	21.4186i	1.32240	+	0.763490i	0.338292	+	0.941041i	$0.390151\pi$
$788$		0			0
$789$	−1.31347	+	2.27499i	−0.0467606	+	0.0809918i
$790$		0			0
$791$	18.0000	−	10.3923i	0.640006	−	0.369508i
$792$		0			0
$793$	−15.4904	+	16.0981i	−0.550080	+	0.571659i
$794$		0			0
$795$	−0.294229	+	0.169873i	−0.0104352	+	0.00602477i
$796$		0			0
$797$	6.46410	−	11.1962i	0.228970	−	0.396588i	−0.728533	−	0.685011i	$-0.759797\pi$
$797$	6.46410	−	11.1962i	0.228970	−	0.396588i	0.957503	+	0.288423i	$0.0931308\pi$
$798$		0			0
$799$	−21.2942	−	12.2942i	−0.753336	−	0.434939i
$800$		0			0
$801$		−	16.7654i		−	0.592375i
$802$		0			0
$803$	17.4904	+	30.2942i	0.617222	+	1.06906i
$804$		0			0
$805$	28.3923			1.00070
$806$		0			0
$807$	19.8564			0.698979
$808$		0			0
$809$	−12.0000	−	20.7846i	−0.421898	−	0.730748i	0.574228	−	0.818696i	$-0.305302\pi$
$809$	−12.0000	−	20.7846i	−0.421898	−	0.730748i	−0.996125	+	0.0879478i	$0.971969\pi$
$810$		0			0
$811$			43.3923i			1.52371i	0.647748	+	0.761855i	$0.275711\pi$
$811$			43.3923i			1.52371i	−0.647748	+	0.761855i	$0.724289\pi$
$812$		0			0
$813$	−6.00000	−	3.46410i	−0.210429	−	0.121491i
$814$		0			0
$815$	−5.36603	+	9.29423i	−0.187964	+	0.325563i
$816$		0			0
$817$	0.803848	−	0.464102i	0.0281231	−	0.0162369i
$818$		0			0
$819$	−25.6077	+	7.39230i	−0.894805	+	0.258308i
$820$		0			0
$821$	17.4904	−	10.0981i	0.610419	−	0.352425i	−0.162711	−	0.986674i	$-0.552024\pi$
$821$	17.4904	−	10.0981i	0.610419	−	0.352425i	0.773129	+	0.634249i	$0.218690\pi$
$822$		0			0
$823$	−13.5981	+	23.5526i	−0.473999	+	0.820991i	−0.999557	−	0.0297674i	$-0.990523\pi$
$823$	−13.5981	+	23.5526i	−0.473999	+	0.820991i	0.525558	+	0.850758i	$0.323857\pi$
$824$		0			0
$825$	1.90192	+	1.09808i	0.0662165	+	0.0382301i
$826$		0			0
$827$		−	42.5885i		−	1.48095i	−0.672086	−	0.740473i	$-0.734602\pi$
$827$		−	42.5885i		−	1.48095i	0.672086	−	0.740473i	$-0.265398\pi$
$828$		0			0
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	0.985771	−	0.168091i	$-0.0537604\pi$
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	−0.638457	+	0.769657i	$0.720427\pi$
$830$		0			0
$831$	0.732051			0.0253946
$832$		0			0
$833$	−16.3923			−0.567960
$834$		0			0
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$		0			0
$837$			18.9282i			0.654254i
$838$		0			0
$839$	−18.8827	−	10.9019i	−0.651903	−	0.376376i	0.137282	−	0.990532i	$-0.456163\pi$
$839$	−18.8827	−	10.9019i	−0.651903	−	0.376376i	−0.789185	+	0.614156i	$0.789497\pi$
$840$		0			0
$841$	11.2846	−	19.5455i	0.389124	−	0.673983i
$842$		0			0
$843$	−6.58846	+	3.80385i	−0.226919	+	0.131011i
$844$		0			0
$845$	−6.06218	+	11.5000i	−0.208545	+	0.395612i
$846$		0			0
$847$	5.19615	−	3.00000i	0.178542	−	0.103081i
$848$		0			0
$849$	3.51666	−	6.09103i	0.120691	−	0.209044i
$850$		0			0
$851$	−6.58846	−	3.80385i	−0.225849	−	0.130394i
$852$		0			0
$853$		−	13.8564i		−	0.474434i	−0.971457	−	0.237217i	$-0.923765\pi$
$853$		−	13.8564i		−	0.474434i	0.971457	−	0.237217i	$-0.0762353\pi$
$854$		0			0
$855$	0.571797	+	0.990381i	0.0195550	+	0.0338703i
$856$		0			0
$857$	−16.7321			−0.571556			−0.285778	−	0.958296i	$-0.592252\pi$
$857$	−16.7321			−0.571556			−0.285778	+	0.958296i	$0.592252\pi$
$858$		0			0
$859$	20.3731			0.695120			0.347560	−	0.937658i	$-0.387010\pi$
$859$	20.3731			0.695120			0.347560	+	0.937658i	$0.387010\pi$
$860$		0			0
$861$	11.4115	+	19.7654i	0.388904	+	0.673602i
$862$		0			0
$863$			43.1769i			1.46976i	0.678198	+	0.734880i	$0.262761\pi$
$863$			43.1769i			1.46976i	−0.678198	+	0.734880i	$0.737239\pi$
$864$		0			0
$865$	12.9904	+	7.50000i	0.441686	+	0.255008i
$866$		0			0
$867$	18.3660	−	31.8109i	0.623743	−	1.08035i
$868$		0			0
$869$	−10.9019	+	6.29423i	−0.369822	+	0.213517i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	19.4711	−	11.2417i	0.658998	−	0.380473i
$874$		0			0
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$		0			0
$877$	−23.7846	−	13.7321i	−0.803149	−	0.463698i	0.0414220	−	0.999142i	$-0.486811\pi$
$877$	−23.7846	−	13.7321i	−0.803149	−	0.463698i	−0.844571	+	0.535443i	$0.820145\pi$
$878$		0			0
$879$			8.19615i			0.276449i
$880$		0			0
$881$	−13.1603	−	22.7942i	−0.443380	−	0.767957i	0.554558	−	0.832145i	$-0.312888\pi$
$881$	−13.1603	−	22.7942i	−0.443380	−	0.767957i	−0.997938	+	0.0641883i	$0.979554\pi$
$882$		0			0
$883$	−4.58846			−0.154414			−0.0772069	−	0.997015i	$-0.524600\pi$
$883$	−4.58846			−0.154414			−0.0772069	+	0.997015i	$0.524600\pi$
$884$		0			0
$885$	7.60770			0.255730
$886$		0			0
$887$	−20.3827	−	35.3038i	−0.684384	−	1.18539i	−0.973630	−	0.228133i	$-0.926738\pi$
$887$	−20.3827	−	35.3038i	−0.684384	−	1.18539i	0.289246	−	0.957255i	$-0.406595\pi$
$888$		0			0
$889$		−	32.4115i		−	1.08705i
$890$		0			0
$891$	11.5981	+	6.69615i	0.388550	+	0.224330i
$892$		0			0
$893$	−0.696152	+	1.20577i	−0.0232959	+	0.0403496i
$894$		0			0
$895$	8.19615	−	4.73205i	0.273967	−	0.158175i
$896$		0			0
$897$	−17.3205	+	18.0000i	−0.578315	+	0.601003i
$898$		0			0
$899$	−10.3923	+	6.00000i	−0.346603	+	0.200111i
$900$		0			0
$901$	−1.90192	+	3.29423i	−0.0633623	+	0.109747i
$902$		0			0
$903$	−3.80385	−	2.19615i	−0.126584	−	0.0730834i
$904$		0			0
$905$			14.5885i			0.484937i
$906$		0			0
$907$	2.29423	+	3.97372i	0.0761786	+	0.131945i	0.901598	−	0.432574i	$-0.142395\pi$
$907$	2.29423	+	3.97372i	0.0761786	+	0.131945i	−0.825420	+	0.564520i	$0.809061\pi$
$908$		0			0
$909$	−26.4449			−0.877121
$910$		0			0
$911$	21.4641			0.711137			0.355569	−	0.934650i	$-0.384287\pi$
$911$	21.4641			0.711137			0.355569	+	0.934650i	$0.384287\pi$
$912$		0			0
$913$	12.2942	+	21.2942i	0.406880	+	0.704736i
$914$		0			0
$915$		−	4.53590i		−	0.149952i
$916$		0			0
$917$	15.9115	+	9.18653i	0.525445	+	0.303366i
$918$		0			0
$919$	15.3923	−	26.6603i	0.507745	−	0.879441i	−0.492215	−	0.870474i	$-0.663812\pi$
$919$	15.3923	−	26.6603i	0.507745	−	0.879441i	0.999960	−	0.00896670i	$-0.00285423\pi$
$920$		0			0
$921$	17.4115	−	10.0526i	0.573730	−	0.331243i
$922$		0			0
$923$	15.5885	+	15.0000i	0.513100	+	0.493731i
$924$		0			0
$925$	0.696152	−	0.401924i	0.0228894	−	0.0132152i
$926$		0			0
$927$	11.3301	−	19.6244i	0.372130	−	0.644548i
$928$		0			0
$929$	−2.78461	−	1.60770i	−0.0913601	−	0.0527468i	0.453624	−	0.891193i	$-0.350131\pi$
$929$	−2.78461	−	1.60770i	−0.0913601	−	0.0527468i	−0.544984	+	0.838446i	$0.683464\pi$
$930$		0			0
$931$			0.928203i			0.0304206i
$932$		0			0
$933$	3.33975	+	5.78461i	0.109338	+	0.189380i
$934$		0			0
$935$	24.5885			0.804129
$936$		0			0
$937$	−9.60770			−0.313870			−0.156935	−	0.987609i	$-0.550161\pi$
$937$	−9.60770			−0.313870			−0.156935	+	0.987609i	$0.550161\pi$
$938$		0			0
$939$	9.66025	+	16.7321i	0.315250	+	0.546030i
$940$		0			0
$941$		−	3.21539i		−	0.104819i	−0.998626	−	0.0524094i	$-0.983310\pi$
$941$		−	3.21539i		−	0.104819i	0.998626	−	0.0524094i	$-0.0166901\pi$
$942$		0			0
$943$	−85.1769	−	49.1769i	−2.77374	−	1.60142i
$944$		0			0
$945$	6.00000	−	10.3923i	0.195180	−	0.338062i
$946$		0			0
$947$	−13.3135	+	7.68653i	−0.432630	+	0.249779i	−0.700466	−	0.713686i	$-0.747025\pi$
$947$	−13.3135	+	7.68653i	−0.432630	+	0.249779i	0.267837	+	0.963464i	$0.413691\pi$
$948$		0			0
$949$	10.0981	−	40.8109i	0.327797	−	1.32478i
$950$		0			0
$951$	−14.7058	+	8.49038i	−0.476867	+	0.275319i
$952$		0			0
$953$	3.29423	−	5.70577i	0.106711	−	0.184828i	−0.807725	−	0.589559i	$-0.799302\pi$
$953$	3.29423	−	5.70577i	0.106711	−	0.184828i	0.914436	+	0.404731i	$0.132635\pi$
$954$		0			0
$955$	−19.6865	−	11.3660i	−0.637041	−	0.367796i
$956$		0			0
$957$		−	5.56922i		−	0.180027i
$958$		0			0
$959$	−3.29423	−	5.70577i	−0.106376	−	0.184249i
$960$		0			0
$961$	8.60770			0.277668
$962$		0			0
$963$	43.5167			1.40230
$964$		0			0
$965$	−8.19615	−	14.1962i	−0.263843	−	0.456990i
$966$		0			0
$967$		−	44.5692i		−	1.43325i	−0.697459	−	0.716625i	$-0.745686\pi$
$967$		−	44.5692i		−	1.43325i	0.697459	−	0.716625i	$-0.254314\pi$
$968$		0			0
$969$	−2.41154	−	1.39230i	−0.0774699	−	0.0447273i
$970$		0			0
$971$	23.3827	−	40.5000i	0.750386	−	1.29971i	−0.197250	−	0.980353i	$-0.563201\pi$
$971$	23.3827	−	40.5000i	0.750386	−	1.29971i	0.947636	−	0.319354i	$-0.103466\pi$
$972$		0			0
$973$	−3.10770	+	1.79423i	−0.0996281	+	0.0575203i
$974$		0			0
$975$	−0.732051	−	2.53590i	−0.0234444	−	0.0812137i
$976$		0			0
$977$	14.1962	−	8.19615i	0.454175	−	0.262218i	−0.255417	−	0.966831i	$-0.582213\pi$
$977$	14.1962	−	8.19615i	0.454175	−	0.262218i	0.709592	+	0.704613i	$0.248879\pi$
$978$		0			0
$979$	−10.2058	+	17.6769i	−0.326178	+	0.564957i
$980$		0			0
$981$	18.2154	+	10.5167i	0.581573	+	0.335771i
$982$		0			0
$983$			44.5692i			1.42154i	0.703426	+	0.710769i	$0.251653\pi$
$983$			44.5692i			1.42154i	−0.703426	+	0.710769i	$0.748347\pi$
$984$		0			0
$985$	10.7942	+	18.6962i	0.343933	+	0.595709i
$986$		0			0
$987$	6.58846			0.209713
$988$		0			0
$989$	18.9282			0.601882
$990$		0			0
$991$	−5.58846	−	9.67949i	−0.177523	−	0.307479i	0.763508	−	0.645798i	$-0.223475\pi$
$991$	−5.58846	−	9.67949i	−0.177523	−	0.307479i	−0.941032	+	0.338319i	$0.890142\pi$
$992$		0			0
$993$		−	9.46410i		−	0.300334i
$994$		0			0
$995$	−5.53590	−	3.19615i	−0.175500	−	0.101325i
$996$		0			0
$997$	−20.2846	+	35.1340i	−0.642420	+	1.11270i	0.342471	+	0.939528i	$0.388736\pi$
$997$	−20.2846	+	35.1340i	−0.642420	+	1.11270i	−0.984891	+	0.173176i	$0.944597\pi$
$998$		0			0
$999$	−2.78461	+	1.60770i	−0.0881012	+	0.0508652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.a.881.2		4
4.3	odd	2		130.2.l.a.101.1	✓	4
12.11	even	2		1170.2.bs.c.361.2		4
13.4	even	6	inner	1040.2.da.a.641.2		4
20.3	even	4		650.2.n.b.49.1		4
20.7	even	4		650.2.n.a.49.2		4
20.19	odd	2		650.2.m.a.101.2		4
52.3	odd	6		1690.2.d.f.1351.2		4
52.7	even	12		1690.2.e.l.191.1		4
52.11	even	12		1690.2.a.m.1.2		2
52.15	even	12		1690.2.a.j.1.2		2
52.19	even	12		1690.2.e.n.191.1		4
52.23	odd	6		1690.2.d.f.1351.4		4
52.31	even	4		1690.2.e.n.991.1		4
52.35	odd	6		1690.2.l.g.1161.2		4
52.43	odd	6		130.2.l.a.121.1	yes	4
52.47	even	4		1690.2.e.l.991.1		4
52.51	odd	2		1690.2.l.g.361.2		4
156.95	even	6		1170.2.bs.c.901.2		4
260.43	even	12		650.2.n.a.199.2		4
260.119	even	12		8450.2.a.bm.1.1		2
260.147	even	12		650.2.n.b.199.1		4
260.199	odd	6		650.2.m.a.251.2		4
260.219	even	12		8450.2.a.bf.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.1	✓	4	4.3	odd	2
130.2.l.a.121.1	yes	4	52.43	odd	6
650.2.m.a.101.2		4	20.19	odd	2
650.2.m.a.251.2		4	260.199	odd	6
650.2.n.a.49.2		4	20.7	even	4
650.2.n.a.199.2		4	260.43	even	12
650.2.n.b.49.1		4	20.3	even	4
650.2.n.b.199.1		4	260.147	even	12
1040.2.da.a.641.2		4	13.4	even	6	inner
1040.2.da.a.881.2		4	1.1	even	1	trivial
1170.2.bs.c.361.2		4	12.11	even	2
1170.2.bs.c.901.2		4	156.95	even	6
1690.2.a.j.1.2		2	52.15	even	12
1690.2.a.m.1.2		2	52.11	even	12
1690.2.d.f.1351.2		4	52.3	odd	6
1690.2.d.f.1351.4		4	52.23	odd	6
1690.2.e.l.191.1		4	52.7	even	12
1690.2.e.l.991.1		4	52.47	even	4
1690.2.e.n.191.1		4	52.19	even	12
1690.2.e.n.991.1		4	52.31	even	4
1690.2.l.g.361.2		4	52.51	odd	2
1690.2.l.g.1161.2		4	52.35	odd	6
8450.2.a.bf.1.1		2	260.219	even	12
8450.2.a.bm.1.1		2	260.119	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 0.633975i) q^{3} +1.00000i q^{5} +(-2.59808 - 1.50000i) q^{7} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 0.633975i) q^{3} +1.00000i q^{5} +(-2.59808 - 1.50000i) q^{7} +(1.23205 - 2.13397i) q^{9} +(-2.59808 + 1.50000i) q^{11} +(3.50000 + 0.866025i) q^{13} +(-0.633975 + 0.366025i) q^{15} +(-4.09808 + 7.09808i) q^{17} +(0.401924 + 0.232051i) q^{19} -2.19615i q^{21} +(4.73205 + 8.19615i) q^{23} -1.00000 q^{25} +4.00000 q^{27} +(1.26795 + 2.19615i) q^{29} +4.73205i q^{31} +(-1.90192 - 1.09808i) q^{33} +(1.50000 - 2.59808i) q^{35} +(-0.696152 + 0.401924i) q^{37} +(0.732051 + 2.53590i) q^{39} +(-9.00000 + 5.19615i) q^{41} +(1.00000 - 1.73205i) q^{43} +(2.13397 + 1.23205i) q^{45} +3.00000i q^{47} +(1.00000 + 1.73205i) q^{49} -6.00000 q^{51} +0.464102 q^{53} +(-1.50000 - 2.59808i) q^{55} +0.339746i q^{57} +(-9.00000 - 5.19615i) q^{59} +(-3.09808 + 5.36603i) q^{61} +(-6.40192 + 3.69615i) q^{63} +(-0.866025 + 3.50000i) q^{65} +(-3.46410 + 6.00000i) q^{69} +(5.19615 + 3.00000i) q^{71} -11.6603i q^{73} +(-0.366025 - 0.633975i) q^{75} +9.00000 q^{77} +4.19615 q^{79} +(-2.23205 - 3.86603i) q^{81} -8.19615i q^{83} +(-7.09808 - 4.09808i) q^{85} +(-0.928203 + 1.60770i) q^{87} +(5.89230 - 3.40192i) q^{89} +(-7.79423 - 7.50000i) q^{91} +(-3.00000 + 1.73205i) q^{93} +(-0.232051 + 0.401924i) q^{95} +(7.90192 + 4.56218i) q^{97} +7.39230i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{9} + 14 q^{13} - 6 q^{15} - 6 q^{17} + 12 q^{19} + 12 q^{23} - 4 q^{25} + 16 q^{27} + 12 q^{29} - 18 q^{33} + 6 q^{35} + 18 q^{37} - 4 q^{39} - 36 q^{41} + 4 q^{43} + 12 q^{45} + 4 q^{49} - 24 q^{51} - 12 q^{53} - 6 q^{55} - 36 q^{59} - 2 q^{61} - 36 q^{63} + 2 q^{75} + 36 q^{77} - 4 q^{79} - 2 q^{81} - 18 q^{85} + 24 q^{87} - 18 q^{89} - 12 q^{93} + 6 q^{95} + 42 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^9 + 14 * q^13 - 6 * q^15 - 6 * q^17 + 12 * q^19 + 12 * q^23 - 4 * q^25 + 16 * q^27 + 12 * q^29 - 18 * q^33 + 6 * q^35 + 18 * q^37 - 4 * q^39 - 36 * q^41 + 4 * q^43 + 12 * q^45 + 4 * q^49 - 24 * q^51 - 12 * q^53 - 6 * q^55 - 36 * q^59 - 2 * q^61 - 36 * q^63 + 2 * q^75 + 36 * q^77 - 4 * q^79 - 2 * q^81 - 18 * q^85 + 24 * q^87 - 18 * q^89 - 12 * q^93 + 6 * q^95 + 42 * q^97

Introduction

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