LMFDB - Embedded newform 560.2.ci.c.353.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(17,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("560.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ci (of order $12$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.3
Root			$1.01089 - 0.750919i$ of defining polynomial
Character	$\chi$	$=$	560.353
Dual form			560.2.ci.c.257.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0749894 + 0.279864i) q^{3} +(2.20382 + 0.378409i) q^{5} +(-0.126334 + 2.64273i) q^{7} +(2.52538 - 1.45803i) q^{9} +O(q^{10})$	\(q+(0.0749894 + 0.279864i) q^{3} +(2.20382 + 0.378409i) q^{5} +(-0.126334 + 2.64273i) q^{7} +(2.52538 - 1.45803i) q^{9} +(2.81288 - 4.87205i) q^{11} +(-1.42962 + 1.42962i) q^{13} +(0.0593598 + 0.645146i) q^{15} +(-5.12784 + 1.37400i) q^{17} +(1.94590 + 3.37040i) q^{19} +(-0.749081 + 0.162821i) q^{21} +(0.290892 - 1.08562i) q^{23} +(4.71361 + 1.66789i) q^{25} +(1.21205 + 1.21205i) q^{27} +3.15502i q^{29} +(3.33287 + 1.92423i) q^{31} +(1.57445 + 0.421872i) q^{33} +(-1.27845 + 5.77629i) q^{35} +(4.86824 + 1.30444i) q^{37} +(-0.507306 - 0.292893i) q^{39} -7.21050i q^{41} +(-1.85669 - 1.85669i) q^{43} +(6.11719 - 2.25760i) q^{45} +(1.52590 - 5.69475i) q^{47} +(-6.96808 - 0.667734i) q^{49} +(-0.769067 - 1.33206i) q^{51} +(1.33599 - 0.357978i) q^{53} +(8.04270 - 9.67269i) q^{55} +(-0.797333 + 0.797333i) q^{57} +(-2.73923 + 4.74448i) q^{59} +(-3.99172 + 2.30462i) q^{61} +(3.53413 + 6.85809i) q^{63} +(-3.69160 + 2.60964i) q^{65} +(-0.218698 - 0.816193i) q^{67} +0.325641 q^{69} -4.77710 q^{71} +(1.45256 + 5.42104i) q^{73} +(-0.113311 + 1.44425i) q^{75} +(12.5202 + 8.04920i) q^{77} +(-5.41079 + 3.12392i) q^{79} +(4.12576 - 7.14603i) q^{81} +(-5.67281 + 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +(-0.882976 + 0.236593i) q^{87} +(-5.96090 - 10.3246i) q^{89} +(-3.59749 - 3.95871i) q^{91} +(-0.288594 + 1.07705i) q^{93} +(3.01302 + 8.16409i) q^{95} +(-6.63103 - 6.63103i) q^{97} -16.4050i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 - 8 * q^7	$ 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53} + 8 q^{57} - 12 q^{61} + 36 q^{63} - 8 q^{65} - 32 q^{67} - 16 q^{71} - 12 q^{73} + 48 q^{75} + 16 q^{77} + 24 q^{85} + 24 q^{87} + 16 q^{91} + 28 q^{93} - 20 q^{95}+O(q^{100}) $ 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0749894	+	0.279864i	0.0432952	+	0.161580i	0.984189	−	0.177122i	$-0.0566788\pi$
$3$	0.0749894	+	0.279864i	0.0432952	+	0.161580i	−0.940894	+	0.338702i	$0.890012\pi$
$4$		0			0
$5$	2.20382	+	0.378409i	0.985577	+	0.169230i
$5$	2.20382	+	0.378409i	0.985577	+	0.169230i
$6$		0			0
$7$	−0.126334	+	2.64273i	−0.0477497	+	0.998859i
$7$	−0.126334	+	2.64273i	−0.0477497	+	0.998859i
$8$		0			0
$9$	2.52538	−	1.45803i	0.841792	−	0.486009i
$10$		0			0
$11$	2.81288	−	4.87205i	0.848115	−	1.46898i	−0.0347729	−	0.999395i	$-0.511071\pi$
$11$	2.81288	−	4.87205i	0.848115	−	1.46898i	0.882888	−	0.469583i	$-0.155596\pi$
$12$		0			0
$13$	−1.42962	+	1.42962i	−0.396505	+	0.396505i	−0.876998	−	0.480493i	$-0.840458\pi$
$13$	−1.42962	+	1.42962i	−0.396505	+	0.396505i	0.480493	+	0.876998i	$0.340458\pi$
$14$		0			0
$15$	0.0593598	+	0.645146i	0.0153266	+	0.166576i
$16$		0			0
$17$	−5.12784	+	1.37400i	−1.24368	+	0.333244i	−0.819893	−	0.572516i	$-0.805967\pi$
$17$	−5.12784	+	1.37400i	−1.24368	+	0.333244i	−0.423790	+	0.905760i	$0.639301\pi$
$18$		0			0
$19$	1.94590	+	3.37040i	0.446420	+	0.773223i	0.998150	−	0.0608002i	$-0.0193652\pi$
$19$	1.94590	+	3.37040i	0.446420	+	0.773223i	−0.551729	+	0.834023i	$0.686032\pi$
$20$		0			0
$21$	−0.749081	+	0.162821i	−0.163463	+	0.0355304i
$22$		0			0
$23$	0.290892	−	1.08562i	0.0606552	−	0.226368i	−0.928944	−	0.370220i	$-0.879282\pi$
$23$	0.290892	−	1.08562i	0.0606552	−	0.226368i	0.989599	+	0.143852i	$0.0459489\pi$
$24$		0			0
$25$	4.71361	+	1.66789i	0.942723	+	0.333577i
$26$		0			0
$27$	1.21205	+	1.21205i	0.233259	+	0.233259i
$28$		0			0
$29$			3.15502i			0.585872i	0.956132	+	0.292936i	$0.0946322\pi$
$29$			3.15502i			0.585872i	−0.956132	+	0.292936i	$0.905368\pi$
$30$		0			0
$31$	3.33287	+	1.92423i	0.598601	+	0.345602i	0.768491	−	0.639861i	$-0.221008\pi$
$31$	3.33287	+	1.92423i	0.598601	+	0.345602i	−0.169890	+	0.985463i	$0.554341\pi$
$32$		0			0
$33$	1.57445	+	0.421872i	0.274076	+	0.0734386i
$34$		0			0
$35$	−1.27845	+	5.77629i	−0.216098	+	0.976372i
$36$		0			0
$37$	4.86824	+	1.30444i	0.800334	+	0.214449i	0.635731	−	0.771911i	$-0.280699\pi$
$37$	4.86824	+	1.30444i	0.800334	+	0.214449i	0.164603	+	0.986360i	$0.447366\pi$
$38$		0			0
$39$	−0.507306	−	0.292893i	−0.0812340	−	0.0469005i
$40$		0			0
$41$		−	7.21050i		−	1.12609i	−0.826426	−	0.563046i	$-0.809629\pi$
$41$		−	7.21050i		−	1.12609i	0.826426	−	0.563046i	$-0.190371\pi$
$42$		0			0
$43$	−1.85669	−	1.85669i	−0.283143	−	0.283143i	0.551218	−	0.834361i	$-0.314163\pi$
$43$	−1.85669	−	1.85669i	−0.283143	−	0.283143i	−0.834361	+	0.551218i	$0.814163\pi$
$44$		0			0
$45$	6.11719	−	2.25760i	0.911897	−	0.336543i
$46$		0			0
$47$	1.52590	−	5.69475i	0.222576	−	0.830665i	−0.760785	−	0.649004i	$-0.775186\pi$
$47$	1.52590	−	5.69475i	0.222576	−	0.830665i	0.983361	−	0.181661i	$-0.0581474\pi$
$48$		0			0
$49$	−6.96808	−	0.667734i	−0.995440	−	0.0953905i
$50$		0			0
$51$	−0.769067	−	1.33206i	−0.107691	−	0.186526i
$52$		0			0
$53$	1.33599	−	0.357978i	0.183512	−	0.0491720i	−0.165892	−	0.986144i	$-0.553050\pi$
$53$	1.33599	−	0.357978i	0.183512	−	0.0491720i	0.349405	+	0.936972i	$0.386384\pi$
$54$		0			0
$55$	8.04270	−	9.67269i	1.08448	−	1.30426i
$56$		0			0
$57$	−0.797333	+	0.797333i	−0.105609	+	0.105609i
$58$		0			0
$59$	−2.73923	+	4.74448i	−0.356617	+	0.617679i	−0.987393	−	0.158286i	$-0.949403\pi$
$59$	−2.73923	+	4.74448i	−0.356617	+	0.617679i	0.630776	+	0.775965i	$0.282737\pi$
$60$		0			0
$61$	−3.99172	+	2.30462i	−0.511088	+	0.295077i	−0.733281	−	0.679926i	$-0.762012\pi$
$61$	−3.99172	+	2.30462i	−0.511088	+	0.295077i	0.222193	+	0.975003i	$0.428678\pi$
$62$		0			0
$63$	3.53413	+	6.85809i	0.445259	+	0.864038i
$64$		0			0
$65$	−3.69160	+	2.60964i	−0.457887	+	0.323686i
$66$		0			0
$67$	−0.218698	−	0.816193i	−0.0267182	−	0.0997138i	0.951279	−	0.308331i	$-0.0997704\pi$
$67$	−0.218698	−	0.816193i	−0.0267182	−	0.0997138i	−0.977997	+	0.208617i	$0.933104\pi$
$68$		0			0
$69$	0.325641			0.0392026
$70$		0			0
$71$	−4.77710			−0.566937			−0.283469	−	0.958982i	$-0.591485\pi$
$71$	−4.77710			−0.566937			−0.283469	+	0.958982i	$0.591485\pi$
$72$		0			0
$73$	1.45256	+	5.42104i	0.170010	+	0.634485i	0.997348	+	0.0727807i	$0.0231873\pi$
$73$	1.45256	+	5.42104i	0.170010	+	0.634485i	−0.827338	+	0.561704i	$0.810146\pi$
$74$		0			0
$75$	−0.113311	+	1.44425i	−0.0130840	+	0.166767i
$76$		0			0
$77$	12.5202	+	8.04920i	1.42681	+	0.917291i
$78$		0			0
$79$	−5.41079	+	3.12392i	−0.608761	+	0.351469i	−0.772481	−	0.635038i	$-0.780984\pi$
$79$	−5.41079	+	3.12392i	−0.608761	+	0.351469i	0.163719	+	0.986507i	$0.447651\pi$
$80$		0			0
$81$	4.12576	−	7.14603i	0.458418	−	0.794003i
$82$		0			0
$83$	−5.67281	+	5.67281i	−0.622672	+	0.622672i	−0.946214	−	0.323542i	$-0.895126\pi$
$83$	−5.67281	+	5.67281i	−0.622672	+	0.622672i	0.323542	+	0.946214i	$0.395126\pi$
$84$		0			0
$85$	−11.8207	+	1.08763i	−1.28214	+	0.117970i
$86$		0			0
$87$	−0.882976	+	0.236593i	−0.0946650	+	0.0253654i
$88$		0			0
$89$	−5.96090	−	10.3246i	−0.631855	−	1.09440i	−0.987172	−	0.159659i	$-0.948961\pi$
$89$	−5.96090	−	10.3246i	−0.631855	−	1.09440i	0.355318	−	0.934746i	$-0.384373\pi$
$90$		0			0
$91$	−3.59749	−	3.95871i	−0.377120	−	0.414986i
$92$		0			0
$93$	−0.288594	+	1.07705i	−0.0299258	+	0.111685i
$94$		0			0
$95$	3.01302	+	8.16409i	0.309129	+	0.837618i
$96$		0			0
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	0.285191	−	0.958471i	$-0.407943\pi$
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	−0.958471	+	0.285191i	$0.907943\pi$
$98$		0			0
$99$		−	16.4050i		−	1.64877i
$100$		0			0
$101$	13.9423	+	8.04960i	1.38731	+	0.800965i	0.993012	−	0.118016i	$-0.0376535\pi$
$101$	13.9423	+	8.04960i	1.38731	+	0.800965i	0.394301	+	0.918981i	$0.370987\pi$
$102$		0			0
$103$	−18.9993	−	5.09084i	−1.87206	−	0.501616i	−0.999924	−	0.0123445i	$-0.996071\pi$
$103$	−18.9993	−	5.09084i	−1.87206	−	0.501616i	−0.872132	−	0.489271i	$-0.837263\pi$
$104$		0			0
$105$	−1.71245	+	0.0753683i	−0.167118	+	0.00735519i
$106$		0			0
$107$	2.70557	+	0.724955i	0.261557	+	0.0700840i	0.387214	−	0.921990i	$-0.373437\pi$
$107$	2.70557	+	0.724955i	0.261557	+	0.0700840i	−0.125657	+	0.992074i	$0.540104\pi$
$108$		0			0
$109$	−5.11895	−	2.95543i	−0.490306	−	0.283078i	0.234395	−	0.972141i	$-0.424689\pi$
$109$	−5.11895	−	2.95543i	−0.490306	−	0.283078i	−0.724701	+	0.689063i	$0.758022\pi$
$110$		0			0
$111$			1.46027i			0.138602i
$112$		0			0
$113$	−13.5818	−	13.5818i	−1.27767	−	1.27767i	−0.941970	−	0.335697i	$-0.891028\pi$
$113$	−13.5818	−	13.5818i	−1.27767	−	1.27767i	−0.335697	−	0.941970i	$-0.608972\pi$
$114$		0			0
$115$	1.05188	−	2.28244i	0.0980886	−	0.212839i
$116$		0			0
$117$	−1.52590	+	5.69475i	−0.141070	+	0.526480i
$118$		0			0
$119$	−2.98330	−	13.7251i	−0.273478	−	1.25818i
$120$		0			0
$121$	−10.3246	−	17.8827i	−0.938599	−	1.62570i
$122$		0			0
$123$	2.01796	−	0.540712i	0.181954	−	0.0487543i
$124$		0			0
$125$	9.75680	+	5.45939i	0.872674	+	0.488303i
$126$		0			0
$127$	−4.63487	+	4.63487i	−0.411278	+	0.411278i	−0.882184	−	0.470906i	$-0.843927\pi$
$127$	−4.63487	+	4.63487i	−0.411278	+	0.411278i	0.470906	+	0.882184i	$0.343927\pi$
$128$		0			0
$129$	0.380390	−	0.658854i	0.0334915	−	0.0580089i
$130$		0			0
$131$	6.66437	−	3.84768i	0.582269	−	0.336173i	−0.179766	−	0.983709i	$-0.557534\pi$
$131$	6.66437	−	3.84768i	0.582269	−	0.336173i	0.762035	+	0.647536i	$0.224201\pi$
$132$		0			0
$133$	−9.15290	+	4.71670i	−0.793657	+	0.408990i
$134$		0			0
$135$	2.21249	+	3.12979i	0.190421	+	0.269369i
$136$		0			0
$137$	−2.28687	−	8.53471i	−0.195380	−	0.729170i	−0.992168	−	0.124910i	$-0.960136\pi$
$137$	−2.28687	−	8.53471i	−0.195380	−	0.729170i	0.796788	−	0.604259i	$-0.206531\pi$
$138$		0			0
$139$	−11.0631			−0.938361			−0.469180	−	0.883102i	$-0.655451\pi$
$139$	−11.0631			−0.938361			−0.469180	+	0.883102i	$0.655451\pi$
$140$		0			0
$141$	1.70818			0.143855
$142$		0			0
$143$	2.94383	+	10.9865i	0.246176	+	0.918740i
$144$		0			0
$145$	−1.19389	+	6.95307i	−0.0991468	+	0.577421i
$146$		0			0
$147$	−0.335657	−	2.00019i	−0.0276846	−	0.164973i
$148$		0			0
$149$	−4.37243	+	2.52443i	−0.358204	+	0.206809i	−0.668293	−	0.743899i	$-0.732975\pi$
$149$	−4.37243	+	2.52443i	−0.358204	+	0.206809i	0.310089	+	0.950708i	$0.399641\pi$
$150$		0			0
$151$	6.72142	−	11.6418i	0.546981	−	0.947399i	−0.451498	−	0.892272i	$-0.649110\pi$
$151$	6.72142	−	11.6418i	0.546981	−	0.947399i	0.998479	−	0.0551270i	$-0.0175564\pi$
$152$		0			0
$153$	−10.9464	+	10.9464i	−0.884963	+	0.884963i
$154$		0			0
$155$	6.61688	+	5.50184i	0.531481	+	0.441918i
$156$		0			0
$157$	−1.06529	+	0.285443i	−0.0850191	+	0.0227808i	−0.301078	−	0.953600i	$-0.597346\pi$
$157$	−1.06529	+	0.285443i	−0.0850191	+	0.0227808i	0.216059	+	0.976380i	$0.430680\pi$
$158$		0			0
$159$	0.200370	+	0.347052i	0.0158904	+	0.0275230i
$160$		0			0
$161$	2.83227	+	0.905902i	0.223214	+	0.0713951i
$162$		0			0
$163$	3.42705	−	12.7899i	0.268428	−	1.00179i	−0.691691	−	0.722193i	$-0.743134\pi$
$163$	3.42705	−	12.7899i	0.268428	−	1.00179i	0.960119	−	0.279592i	$-0.0901992\pi$
$164$		0			0
$165$	3.31016	+	1.52551i	0.257695	+	0.118761i
$166$		0			0
$167$	4.70680	+	4.70680i	0.364223	+	0.364223i	0.865365	−	0.501142i	$-0.167087\pi$
$167$	4.70680	+	4.70680i	0.364223	+	0.364223i	−0.501142	+	0.865365i	$0.667087\pi$
$168$		0			0
$169$			8.91237i			0.685567i
$170$		0			0
$171$	9.82827	+	5.67435i	0.751586	+	0.433929i
$172$		0			0
$173$	−6.81421	−	1.82586i	−0.518075	−	0.138818i	−0.00969875	−	0.999953i	$-0.503087\pi$
$173$	−6.81421	−	1.82586i	−0.518075	−	0.138818i	−0.508376	+	0.861135i	$0.669754\pi$
$174$		0			0
$175$	−5.00327	+	12.2461i	−0.378212	+	0.925719i
$176$		0			0
$177$	−1.53322	−	0.410826i	−0.115244	−	0.0308796i
$178$		0			0
$179$	−1.91075	−	1.10317i	−0.142816	−	0.0824550i	0.426889	−	0.904304i	$-0.359609\pi$
$179$	−1.91075	−	1.10317i	−0.142816	−	0.0824550i	−0.569706	+	0.821849i	$0.692943\pi$
$180$		0			0
$181$			4.11867i			0.306139i	0.988215	+	0.153069i	$0.0489158\pi$
$181$			4.11867i			0.306139i	−0.988215	+	0.153069i	$0.951084\pi$
$182$		0			0
$183$	−0.944318	−	0.944318i	−0.0698060	−	0.0698060i
$184$		0			0
$185$	10.2351	+	4.71693i	0.752499	+	0.346796i
$186$		0			0
$187$	−7.72980	+	28.8480i	−0.565259	+	2.10957i
$188$		0			0
$189$	−3.35625	+	3.05000i	−0.244131	+	0.221855i
$190$		0			0
$191$	−8.60117	−	14.8977i	−0.622359	−	1.07796i	−0.989045	−	0.147613i	$-0.952841\pi$
$191$	−8.60117	−	14.8977i	−0.622359	−	1.07796i	0.366686	−	0.930345i	$-0.380492\pi$
$192$		0			0
$193$	11.6562	−	3.12327i	0.839032	−	0.224818i	0.186382	−	0.982477i	$-0.440324\pi$
$193$	11.6562	−	3.12327i	0.839032	−	0.224818i	0.652650	+	0.757659i	$0.273657\pi$
$194$		0			0
$195$	−1.00718	−	0.837452i	−0.0721254	−	0.0599712i
$196$		0			0
$197$	14.3135	−	14.3135i	1.01979	−	1.01979i	0.0199932	−	0.999800i	$-0.493636\pi$
$197$	14.3135	−	14.3135i	1.01979	−	1.01979i	0.999800	−	0.0199932i	$-0.00636444\pi$
$198$		0			0
$199$	3.76653	−	6.52383i	0.267002	−	0.462462i	−0.701084	−	0.713079i	$-0.747300\pi$
$199$	3.76653	−	6.52383i	0.267002	−	0.462462i	0.968086	+	0.250617i	$0.0806335\pi$
$200$		0			0
$201$	0.212023	−	0.122412i	0.0149550	−	0.00863425i
$202$		0			0
$203$	−8.33786	−	0.398585i	−0.585203	−	0.0279752i
$204$		0			0
$205$	2.72852	−	15.8906i	0.190568	−	1.10985i
$206$		0			0
$207$	−0.848257	−	3.16574i	−0.0589579	−	0.220034i
$208$		0			0
$209$	21.8944			1.51446
$210$		0			0
$211$	−19.5766			−1.34771			−0.673854	−	0.738865i	$-0.735362\pi$
$211$	−19.5766			−1.34771			−0.673854	+	0.738865i	$0.735362\pi$
$212$		0			0
$213$	−0.358232	−	1.33694i	−0.0245456	−	0.0916056i
$214$		0			0
$215$	−3.38922	−	4.79440i	−0.231143	−	0.326975i
$216$		0			0
$217$	−5.50629	+	8.56478i	−0.373791	+	0.581415i
$218$		0			0
$219$	−1.40823	+	0.813041i	−0.0951593	+	0.0549402i
$220$		0			0
$221$	5.36656	−	9.29516i	0.360994	−	0.625260i
$222$		0			0
$223$	−1.46027	+	1.46027i	−0.0977867	+	0.0977867i	−0.754308	−	0.656521i	$-0.772027\pi$
$223$	−1.46027	+	1.46027i	−0.0977867	+	0.0977867i	0.656521	+	0.754308i	$0.272027\pi$
$224$		0			0
$225$	14.3355	−	2.66053i	0.955698	−	0.177369i
$226$		0			0
$227$	18.0081	−	4.82525i	1.19524	−	0.320263i	0.394283	−	0.918989i	$-0.370993\pi$
$227$	18.0081	−	4.82525i	1.19524	−	0.320263i	0.800954	+	0.598726i	$0.204326\pi$
$228$		0			0
$229$	−2.00384	−	3.47074i	−0.132417	−	0.229353i	0.792191	−	0.610274i	$-0.208941\pi$
$229$	−2.00384	−	3.47074i	−0.132417	−	0.229353i	−0.924608	+	0.380920i	$0.875607\pi$
$230$		0			0
$231$	−1.31380	+	4.10755i	−0.0864419	+	0.270257i
$232$		0			0
$233$	−3.55400	+	13.2637i	−0.232830	+	0.868934i	0.746285	+	0.665627i	$0.231836\pi$
$233$	−3.55400	+	13.2637i	−0.232830	+	0.868934i	−0.979115	+	0.203307i	$0.934831\pi$
$234$		0			0
$235$	5.51775	−	11.9728i	0.359939	−	0.781017i
$236$		0			0
$237$	−1.28003	−	1.28003i	−0.0831466	−	0.0831466i
$238$		0			0
$239$			19.6621i			1.27183i	0.771758	+	0.635916i	$0.219378\pi$
$239$			19.6621i			1.27183i	−0.771758	+	0.635916i	$0.780622\pi$
$240$		0			0
$241$	−5.09667	−	2.94256i	−0.328305	−	0.189547i	0.326783	−	0.945099i	$-0.394035\pi$
$241$	−5.09667	−	2.94256i	−0.328305	−	0.189547i	−0.655088	+	0.755552i	$0.727369\pi$
$242$		0			0
$243$	7.27638	+	1.94970i	0.466780	+	0.125073i
$244$		0			0
$245$	−15.1037	−	4.10834i	−0.964939	−	0.262473i
$246$		0			0
$247$	−7.60029	−	2.03649i	−0.483595	−	0.129579i
$248$		0			0
$249$	−2.01302	−	1.16222i	−0.127570	−	0.0736525i
$250$		0			0
$251$		−	7.09950i		−	0.448116i	−0.974576	−	0.224058i	$-0.928069\pi$
$251$		−	7.09950i		−	0.448116i	0.974576	−	0.224058i	$-0.0719306\pi$
$252$		0			0
$253$	−4.47097	−	4.47097i	−0.281088	−	0.281088i
$254$		0			0
$255$	−1.19082	−	3.22665i	−0.0745720	−	0.202060i
$256$		0			0
$257$	−2.55891	+	9.54998i	−0.159620	+	0.595711i	0.839045	+	0.544062i	$0.183114\pi$
$257$	−2.55891	+	9.54998i	−0.159620	+	0.595711i	−0.998665	+	0.0516491i	$0.983552\pi$
$258$		0			0
$259$	−4.06231	+	12.7007i	−0.252420	+	0.789181i
$260$		0			0
$261$	4.60010	+	7.96760i	0.284739	+	0.493182i
$262$		0			0
$263$	13.2797	−	3.55829i	0.818861	−	0.219413i	0.175013	−	0.984566i	$-0.444003\pi$
$263$	13.2797	−	3.55829i	0.818861	−	0.219413i	0.643849	+	0.765153i	$0.277337\pi$
$264$		0			0
$265$	3.07974	−	0.283366i	0.189187	−	0.0174071i
$266$		0			0
$267$	2.44248	−	2.44248i	0.149477	−	0.149477i
$268$		0			0
$269$	−13.2510	+	22.9514i	−0.807928	+	1.39937i	0.106368	+	0.994327i	$0.466078\pi$
$269$	−13.2510	+	22.9514i	−0.807928	+	1.39937i	−0.914296	+	0.405046i	$0.867255\pi$
$270$		0			0
$271$	11.0824	−	6.39844i	0.673209	−	0.388678i	−0.124082	−	0.992272i	$-0.539599\pi$
$271$	11.0824	−	6.39844i	0.673209	−	0.388678i	0.797292	+	0.603594i	$0.206265\pi$
$272$		0			0
$273$	0.838129	−	1.30367i	0.0507259	−	0.0789018i
$274$		0			0
$275$	21.3849	−	18.2734i	1.28956	−	1.10193i
$276$		0			0
$277$	5.20313	+	19.4184i	0.312626	+	1.16674i	0.926180	+	0.377083i	$0.123073\pi$
$277$	5.20313	+	19.4184i	0.312626	+	1.16674i	−0.613554	+	0.789653i	$0.710261\pi$
$278$		0			0
$279$	11.2223			0.671863
$280$		0			0
$281$	−14.1498			−0.844107			−0.422054	−	0.906571i	$-0.638691\pi$
$281$	−14.1498			−0.844107			−0.422054	+	0.906571i	$0.638691\pi$
$282$		0			0
$283$	7.00563	+	26.1454i	0.416442	+	1.55418i	0.781930	+	0.623366i	$0.214235\pi$
$283$	7.00563	+	26.1454i	0.416442	+	1.55418i	−0.365489	+	0.930816i	$0.619098\pi$
$284$		0			0
$285$	−2.05889	+	1.45546i	−0.121958	+	0.0862139i
$286$		0			0
$287$	19.0554	+	0.910931i	1.12481	+	0.0537706i
$288$		0			0
$289$	9.68442	−	5.59130i	0.569672	−	0.328900i
$290$		0			0
$291$	1.35853	−	2.35305i	0.0796385	−	0.137938i
$292$		0			0
$293$	17.1191	−	17.1191i	1.00011	−	1.00011i	0.000106876	−	1.00000i	$-0.499966\pi$
$293$	17.1191	−	17.1191i	1.00011	−	1.00011i	1.00000		0.000106876i	$-3.40197e-5\pi$
$294$		0			0
$295$	−7.83211	+	9.41941i	−0.456003	+	0.548420i
$296$		0			0
$297$	9.31453	−	2.49582i	0.540484	−	0.144822i
$298$		0			0
$299$	1.13616	+	1.96790i	0.0657061	+	0.113806i
$300$		0			0
$301$	5.14131	−	4.67218i	0.296340	−	0.269300i
$302$		0			0
$303$	−1.20727	+	4.50559i	−0.0693558	+	0.258840i
$304$		0			0
$305$	−9.66911	+	3.56846i	−0.553652	+	0.204329i
$306$		0			0
$307$	−17.2974	−	17.2974i	−0.987217	−	0.987217i	0.0127019	−	0.999919i	$-0.495957\pi$
$307$	−17.2974	−	17.2974i	−0.987217	−	0.987217i	−0.999919	+	0.0127019i	$0.995957\pi$
$308$		0			0
$309$		−	5.69898i		−	0.324204i
$310$		0			0
$311$	9.51095	+	5.49115i	0.539316	+	0.311374i	0.744802	−	0.667286i	$-0.232544\pi$
$311$	9.51095	+	5.49115i	0.539316	+	0.311374i	−0.205486	+	0.978660i	$0.565877\pi$
$312$		0			0
$313$	28.4088	+	7.61212i	1.60576	+	0.430262i	0.946776	−	0.321893i	$-0.104319\pi$
$313$	28.4088	+	7.61212i	1.60576	+	0.430262i	0.658985	+	0.752156i	$0.270986\pi$
$314$		0			0
$315$	5.19342	+	16.4513i	0.292616	+	0.926927i
$316$		0			0
$317$	−4.14766	−	1.11136i	−0.232956	−	0.0624203i	0.140453	−	0.990087i	$-0.455144\pi$
$317$	−4.14766	−	1.11136i	−0.232956	−	0.0624203i	−0.373408	+	0.927667i	$0.621811\pi$
$318$		0			0
$319$	15.3714	+	8.87468i	0.860633	+	0.496887i
$320$		0			0
$321$			0.811556i			0.0452966i
$322$		0			0
$323$	−14.6092	−	14.6092i	−0.812878	−	0.812878i
$324$		0			0
$325$	−9.12312	+	4.35423i	−0.506060	+	0.241529i
$326$		0			0
$327$	0.443251	−	1.65424i	0.0245119	−	0.0914795i
$328$		0			0
$329$	14.8569	+	4.75200i	0.819089	+	0.261986i
$330$		0			0
$331$	17.7249	+	30.7005i	0.974250	+	1.68745i	0.682387	+	0.730991i	$0.260942\pi$
$331$	17.7249	+	30.7005i	0.974250	+	1.68745i	0.291863	+	0.956460i	$0.405725\pi$
$332$		0			0
$333$	14.1960	−	3.80382i	0.777939	−	0.208448i
$334$		0			0
$335$	−0.173116	−	1.88150i	−0.00945835	−	0.102797i
$336$		0			0
$337$	−12.1473	+	12.1473i	−0.661708	+	0.661708i	−0.955782	−	0.294075i	$-0.904989\pi$
$337$	−12.1473	+	12.1473i	−0.661708	+	0.661708i	0.294075	+	0.955782i	$0.404989\pi$
$338$		0			0
$339$	2.78257	−	4.81955i	0.151128	−	0.261762i
$340$		0			0
$341$	18.7499	−	10.8253i	1.01536	−	0.586221i
$342$		0			0
$343$	2.64495	−	18.3304i	0.142814	−	0.989750i
$344$		0			0
$345$	0.717654	+	0.123226i	0.0386372	+	0.00663424i
$346$		0			0
$347$	−2.32323	−	8.67040i	−0.124717	−	0.465452i	0.875112	−	0.483920i	$-0.160788\pi$
$347$	−2.32323	−	8.67040i	−0.124717	−	0.465452i	−0.999829	+	0.0184687i	$0.994121\pi$
$348$		0			0
$349$	−26.0251			−1.39309			−0.696546	−	0.717512i	$-0.745281\pi$
$349$	−26.0251			−1.39309			−0.696546	+	0.717512i	$0.745281\pi$
$350$		0			0
$351$	−3.46554			−0.184977
$352$		0			0
$353$	2.57944	+	9.62659i	0.137290	+	0.512372i	0.999978	+	0.00663577i	$0.00211225\pi$
$353$	2.57944	+	9.62659i	0.137290	+	0.512372i	−0.862688	+	0.505736i	$0.831221\pi$
$354$		0			0
$355$	−10.5278	−	1.80770i	−0.558760	−	0.0959425i
$356$		0			0
$357$	3.61745	−	1.86416i	0.191456	−	0.0986615i
$358$		0			0
$359$	−10.0235	+	5.78705i	−0.529019	+	0.305429i	−0.740617	−	0.671928i	$-0.765467\pi$
$359$	−10.0235	+	5.78705i	−0.529019	+	0.305429i	0.211598	+	0.977357i	$0.432133\pi$
$360$		0			0
$361$	1.92693	−	3.33754i	0.101417	−	0.175660i
$362$		0			0
$363$	4.23050	−	4.23050i	0.222044	−	0.222044i
$364$		0			0
$365$	1.14981	+	12.4966i	0.0601840	+	0.654104i
$366$		0			0
$367$	−16.1256	+	4.32083i	−0.841747	+	0.225545i	−0.653832	−	0.756640i	$-0.726840\pi$
$367$	−16.1256	+	4.32083i	−0.841747	+	0.225545i	−0.187915	+	0.982185i	$0.560173\pi$
$368$		0			0
$369$	−10.5131	−	18.2092i	−0.547290	−	0.947935i
$370$		0			0
$371$	0.777258	+	3.57589i	0.0403532	+	0.185651i
$372$		0			0
$373$	0.822767	−	3.07061i	0.0426013	−	0.158990i	−0.941348	−	0.337436i	$-0.890440\pi$
$373$	0.822767	−	3.07061i	0.0426013	−	0.158990i	0.983950	+	0.178446i	$0.0571070\pi$
$374$		0			0
$375$	−0.796232	+	3.13998i	−0.0411172	+	0.162148i
$376$		0			0
$377$	−4.51047	−	4.51047i	−0.232301	−	0.232301i
$378$		0			0
$379$			7.15349i			0.367450i	0.982978	+	0.183725i	$0.0588156\pi$
$379$			7.15349i			0.367450i	−0.982978	+	0.183725i	$0.941184\pi$
$380$		0			0
$381$	−1.64470	−	0.949568i	−0.0842605	−	0.0486478i
$382$		0			0
$383$	14.0961	+	3.77704i	0.720278	+	0.192998i	0.600296	−	0.799778i	$-0.295050\pi$
$383$	14.0961	+	3.77704i	0.720278	+	0.192998i	0.119982	+	0.992776i	$0.461716\pi$
$384$		0			0
$385$	24.5463	+	22.4767i	1.25099	+	1.14552i
$386$		0			0
$387$	−7.39595	−	1.98174i	−0.375957	−	0.100737i
$388$		0			0
$389$	5.36634	+	3.09826i	0.272084	+	0.157088i	0.629834	−	0.776729i	$-0.283123\pi$
$389$	5.36634	+	3.09826i	0.272084	+	0.157088i	−0.357750	+	0.933817i	$0.616456\pi$
$390$		0			0
$391$			5.96659i			0.301744i
$392$		0			0
$393$	1.57658	+	1.57658i	0.0795282	+	0.0795282i
$394$		0			0
$395$	−13.1065	+	4.83706i	−0.659460	+	0.243379i
$396$		0			0
$397$	0.754685	−	2.81652i	0.0378766	−	0.141357i	−0.944398	−	0.328804i	$-0.893354\pi$
$397$	0.754685	−	2.81652i	0.0378766	−	0.141357i	0.982275	+	0.187447i	$0.0600212\pi$
$398$		0			0
$399$	−2.00641	−	2.20787i	−0.100446	−	0.110532i
$400$		0			0
$401$	9.98528	+	17.2950i	0.498641	+	0.863672i	0.999999	−	0.00156835i	$-0.000499221\pi$
$401$	9.98528	+	17.2950i	0.498641	+	0.863672i	−0.501358	+	0.865240i	$0.667166\pi$
$402$		0			0
$403$	−7.51565	+	2.01381i	−0.374381	+	0.100315i
$404$		0			0
$405$	11.7965	−	14.1873i	0.586175	−	0.704973i
$406$		0			0
$407$	20.0491	−	20.0491i	0.993796	−	0.993796i
$408$		0			0
$409$	17.1791	−	29.7550i	0.849451	−	1.47129i	−0.0322484	−	0.999480i	$-0.510267\pi$
$409$	17.1791	−	29.7550i	0.849451	−	1.47129i	0.881699	−	0.471812i	$-0.156400\pi$
$410$		0			0
$411$	2.21707	−	1.28003i	0.109360	−	0.0631390i
$412$		0			0
$413$	−12.1923	−	7.83843i	−0.599946	−	0.385704i
$414$		0			0
$415$	−14.6485	+	10.3552i	−0.719065	+	0.508317i
$416$		0			0
$417$	−0.829616	−	3.09617i	−0.0406265	−	0.151620i
$418$		0			0
$419$	31.1360			1.52109			0.760547	−	0.649283i	$-0.224931\pi$
$419$	31.1360			1.52109			0.760547	+	0.649283i	$0.224931\pi$
$420$		0			0
$421$	−33.6728			−1.64111			−0.820555	−	0.571567i	$-0.806336\pi$
$421$	−33.6728			−1.64111			−0.820555	+	0.571567i	$0.806336\pi$
$422$		0			0
$423$	−4.44962	−	16.6062i	−0.216348	−	0.807421i
$424$		0			0
$425$	−26.4623	−	2.07615i	−1.28361	−	0.100708i
$426$		0			0
$427$	−5.58621	−	10.8402i	−0.270336	−	0.524594i
$428$		0			0
$429$	−2.85398	+	1.64775i	−0.137792	+	0.0795540i
$430$		0			0
$431$	−7.37284	+	12.7701i	−0.355137	+	0.615116i	−0.987141	−	0.159849i	$-0.948899\pi$
$431$	−7.37284	+	12.7701i	−0.355137	+	0.615116i	0.632004	+	0.774965i	$0.282233\pi$
$432$		0			0
$433$	−9.98256	+	9.98256i	−0.479731	+	0.479731i	−0.905046	−	0.425315i	$-0.860163\pi$
$433$	−9.98256	+	9.98256i	−0.479731	+	0.479731i	0.425315	+	0.905046i	$0.360163\pi$
$434$		0			0
$435$	−2.03545	+	0.187281i	−0.0975922	+	0.00897944i
$436$		0			0
$437$	4.22504	−	1.13210i	0.202111	−	0.0541555i
$438$		0			0
$439$	−19.2142	−	33.2800i	−0.917046	−	1.58837i	−0.803878	−	0.594794i	$-0.797234\pi$
$439$	−19.2142	−	33.2800i	−0.917046	−	1.58837i	−0.113167	−	0.993576i	$-0.536100\pi$
$440$		0			0
$441$	−18.5706	+	8.47336i	−0.884314	+	0.403494i
$442$		0			0
$443$	−1.48448	+	5.54016i	−0.0705299	+	0.263221i	−0.992183	−	0.124795i	$-0.960173\pi$
$443$	−1.48448	+	5.54016i	−0.0705299	+	0.263221i	0.921653	+	0.388016i	$0.126839\pi$
$444$		0			0
$445$	−9.22982	−	25.0092i	−0.437536	−	1.18555i
$446$		0			0
$447$	−1.03438	−	1.03438i	−0.0489247	−	0.0489247i
$448$		0			0
$449$		−	7.30267i		−	0.344635i	−0.985042	−	0.172317i	$-0.944875\pi$
$449$		−	7.30267i		−	0.344635i	0.985042	−	0.172317i	$-0.0551254\pi$
$450$		0			0
$451$	−35.1299	−	20.2823i	−1.65420	−	0.955055i
$452$		0			0
$453$	3.76217	+	1.00807i	0.176762	+	0.0473633i
$454$		0			0
$455$	−6.43021	−	10.0856i	−0.301453	−	0.472820i
$456$		0			0
$457$	−4.97047	−	1.33183i	−0.232509	−	0.0623006i	0.140683	−	0.990055i	$-0.455070\pi$
$457$	−4.97047	−	1.33183i	−0.232509	−	0.0623006i	−0.373192	+	0.927754i	$0.621737\pi$
$458$		0			0
$459$	−7.88056	−	4.54984i	−0.367833	−	0.212368i
$460$		0			0
$461$			29.4110i			1.36981i	0.728634	+	0.684903i	$0.240155\pi$
$461$			29.4110i			1.36981i	−0.728634	+	0.684903i	$0.759845\pi$
$462$		0			0
$463$	4.04625	+	4.04625i	0.188045	+	0.188045i	0.794851	−	0.606805i	$-0.207549\pi$
$463$	4.04625	+	4.04625i	0.188045	+	0.188045i	−0.606805	+	0.794851i	$0.707549\pi$
$464$		0			0
$465$	−1.04357	+	2.26441i	−0.0483945	+	0.105009i
$466$		0			0
$467$	−4.30747	+	16.0757i	−0.199326	+	0.743894i	0.791779	+	0.610808i	$0.209155\pi$
$467$	−4.30747	+	16.0757i	−0.199326	+	0.743894i	−0.991105	+	0.133086i	$0.957511\pi$
$468$		0			0
$469$	2.18461	−	0.474848i	0.100876	−	0.0219264i
$470$		0			0
$471$	−0.159770	−	0.276731i	−0.00736184	−	0.0127511i
$472$		0			0
$473$	−14.2686	+	3.82325i	−0.656069	+	0.175793i
$474$		0			0
$475$	3.55078	+	19.1323i	0.162921	+	0.877851i
$476$		0			0
$477$	2.85194	−	2.85194i	0.130581	−	0.130581i
$478$		0			0
$479$	−7.69460	+	13.3274i	−0.351575	+	0.608946i	−0.986526	−	0.163607i	$-0.947687\pi$
$479$	−7.69460	+	13.3274i	−0.351575	+	0.608946i	0.634950	+	0.772553i	$0.281021\pi$
$480$		0			0
$481$	−8.82459	+	5.09488i	−0.402367	+	0.232306i
$482$		0			0
$483$	−0.0411396	+	0.860583i	−0.00187191	+	0.0391579i
$484$		0			0
$485$	−12.1043	−	17.1228i	−0.549629	−	0.777507i
$486$		0			0
$487$	9.31541	+	34.7656i	0.422122	+	1.57538i	0.770129	+	0.637888i	$0.220192\pi$
$487$	9.31541	+	34.7656i	0.422122	+	1.57538i	−0.348007	+	0.937492i	$0.613142\pi$
$488$		0			0
$489$	3.83644			0.173490
$490$		0			0
$491$	15.2823			0.689680			0.344840	−	0.938661i	$-0.387933\pi$
$491$	15.2823			0.689680			0.344840	+	0.938661i	$0.387933\pi$
$492$		0			0
$493$	−4.33499	−	16.1784i	−0.195238	−	0.728639i
$494$		0			0
$495$	6.20780	−	36.1536i	0.279020	−	1.62499i
$496$		0			0
$497$	0.603509	−	12.6246i	0.0270711	−	0.566290i
$498$		0			0
$499$	27.3534	−	15.7925i	1.22451	−	0.706969i	0.258630	−	0.965976i	$-0.416729\pi$
$499$	27.3534	−	15.7925i	1.22451	−	0.706969i	0.965875	+	0.259008i	$0.0833955\pi$
$500$		0			0
$501$	−0.964305	+	1.67023i	−0.0430820	+	0.0746202i
$502$		0			0
$503$	−16.9777	+	16.9777i	−0.756997	+	0.756997i	−0.975775	−	0.218778i	$-0.929793\pi$
$503$	−16.9777	+	16.9777i	−0.756997	+	0.756997i	0.218778	+	0.975775i	$0.429793\pi$
$504$		0			0
$505$	27.6803	+	23.0157i	1.23176	+	1.02419i
$506$		0			0
$507$	−2.49426	+	0.668334i	−0.110774	+	0.0296817i
$508$		0			0
$509$	10.7571	+	18.6318i	0.476799	+	0.825840i	0.999647	−	0.0265865i	$-0.00846373\pi$
$509$	10.7571	+	18.6318i	0.476799	+	0.825840i	−0.522848	+	0.852426i	$0.675130\pi$
$510$		0			0
$511$	−14.5099	+	3.15388i	−0.641879	+	0.139519i
$512$		0			0
$513$	−1.72657	+	6.44363i	−0.0762297	+	0.284493i
$514$		0			0
$515$	−39.9445	−	18.4088i	−1.76017	−	0.811188i
$516$		0			0
$517$	−23.4529	−	23.4529i	−1.03146	−	1.03146i
$518$		0			0
$519$		−	2.04397i		−	0.0897205i
$520$		0			0
$521$	11.4657	+	6.61973i	0.502322	+	0.290016i	0.729672	−	0.683798i	$-0.239673\pi$
$521$	11.4657	+	6.61973i	0.502322	+	0.290016i	−0.227350	+	0.973813i	$0.573006\pi$
$522$		0			0
$523$	26.0126	+	6.97006i	1.13745	+	0.304779i	0.777926	−	0.628356i	$-0.216272\pi$
$523$	26.0126	+	6.97006i	1.13745	+	0.304779i	0.359526	+	0.933135i	$0.382938\pi$
$524$		0			0
$525$	−3.80244	−	0.481908i	−0.165952	−	0.0210322i
$526$		0			0
$527$	−19.7343	−	5.28779i	−0.859640	−	0.230340i
$528$		0			0
$529$	18.8246	+	10.8684i	0.818462	+	0.472539i
$530$		0			0
$531$			15.9755i			0.693276i
$532$		0			0
$533$	10.3083	+	10.3083i	0.446501	+	0.446501i
$534$		0			0
$535$	5.68825	+	2.62148i	0.245924	+	0.113336i
$536$		0			0
$537$	0.165453	−	0.617477i	0.00713980	−	0.0266461i
$538$		0			0
$539$	−22.8536	+	32.0706i	−0.984374	+	1.38138i
$540$		0			0
$541$	5.66491	+	9.81190i	0.243553	+	0.421847i	0.961724	−	0.274020i	$-0.0883536\pi$
$541$	5.66491	+	9.81190i	0.243553	+	0.421847i	−0.718171	+	0.695867i	$0.755020\pi$
$542$		0			0
$543$	−1.15267	+	0.308857i	−0.0494658	+	0.0132543i
$544$		0			0
$545$	−10.1629	−	8.45027i	−0.435329	−	0.361970i
$546$		0			0
$547$	30.9149	−	30.9149i	1.32182	−	1.32182i	0.409527	−	0.912298i	$-0.365694\pi$
$547$	30.9149	−	30.9149i	1.32182	−	1.32182i	0.912298	−	0.409527i	$-0.134306\pi$
$548$		0			0
$549$	−6.72040	+	11.6401i	−0.286820	+	0.496786i
$550$		0			0
$551$	−10.6337	+	6.13935i	−0.453009	+	0.261545i
$552$		0			0
$553$	−7.57212	−	14.6939i	−0.321999	−	0.624850i
$554$		0			0
$555$	−0.552577	+	3.21816i	−0.0234556	+	0.136603i
$556$		0			0
$557$	−6.83277	−	25.5003i	−0.289514	−	1.08048i	−0.945477	−	0.325688i	$-0.894404\pi$
$557$	−6.83277	−	25.5003i	−0.289514	−	1.08048i	0.655963	−	0.754793i	$-0.272263\pi$
$558$		0			0
$559$	5.30873			0.224535
$560$		0			0
$561$	−8.65318			−0.365337
$562$		0			0
$563$	−5.22648	−	19.5055i	−0.220270	−	0.822058i	−0.984245	−	0.176812i	$-0.943422\pi$
$563$	−5.22648	−	19.5055i	−0.220270	−	0.822058i	0.763975	−	0.645246i	$-0.223245\pi$
$564$		0			0
$565$	−24.7923	−	35.0712i	−1.04302	−	1.47546i
$566$		0			0
$567$	18.3638	+	11.8061i	0.771208	+	0.495808i
$568$		0			0
$569$	21.4890	−	12.4067i	0.900867	−	0.520116i	0.0233856	−	0.999727i	$-0.492555\pi$
$569$	21.4890	−	12.4067i	0.900867	−	0.520116i	0.877481	+	0.479611i	$0.159222\pi$
$570$		0			0
$571$	2.29029	−	3.96690i	0.0958458	−	0.166010i	−0.814116	−	0.580703i	$-0.802778\pi$
$571$	2.29029	−	3.96690i	0.0958458	−	0.166010i	0.909961	+	0.414693i	$0.136111\pi$
$572$		0			0
$573$	3.52433	−	3.52433i	0.147231	−	0.147231i
$574$		0			0
$575$	3.18185	−	4.63204i	0.132692	−	0.193169i
$576$		0			0
$577$	−19.1065	+	5.11957i	−0.795414	+	0.213131i	−0.633570	−	0.773686i	$-0.718411\pi$
$577$	−19.1065	+	5.11957i	−0.795414	+	0.213131i	−0.161845	+	0.986816i	$0.551744\pi$
$578$		0			0
$579$	1.74818	+	3.02794i	0.0726520	+	0.125837i
$580$		0			0
$581$	−14.2751	−	15.7084i	−0.592229	−	0.651694i
$582$		0			0
$583$	2.01390	−	7.51596i	0.0834071	−	0.311279i
$584$		0			0
$585$	−5.51775	+	11.9728i	−0.228131	+	0.495013i
$586$		0			0
$587$	−19.3782	−	19.3782i	−0.799824	−	0.799824i	0.183244	−	0.983068i	$-0.441340\pi$
$587$	−19.3782	−	19.3782i	−0.799824	−	0.799824i	−0.983068	+	0.183244i	$0.941340\pi$
$588$		0			0
$589$			14.9775i			0.617136i
$590$		0			0
$591$	5.07919	+	2.93247i	0.208930	+	0.120626i
$592$		0			0
$593$	3.12741	+	0.837988i	0.128428	+	0.0344121i	0.322460	−	0.946583i	$-0.395490\pi$
$593$	3.12741	+	0.837988i	0.128428	+	0.0344121i	−0.194033	+	0.980995i	$0.562157\pi$
$594$		0			0
$595$	−1.38094	−	31.3765i	−0.0566131	−	1.28631i
$596$		0			0
$597$	2.10824	+	0.564900i	0.0862844	+	0.0231198i
$598$		0			0
$599$	−6.75802	−	3.90174i	−0.276125	−	0.159421i	0.355543	−	0.934660i	$-0.384296\pi$
$599$	−6.75802	−	3.90174i	−0.276125	−	0.159421i	−0.631668	+	0.775239i	$0.717629\pi$
$600$		0			0
$601$			31.7170i			1.29377i	0.762590	+	0.646883i	$0.223928\pi$
$601$			31.7170i			1.29377i	−0.762590	+	0.646883i	$0.776072\pi$
$602$		0			0
$603$	−1.74233	−	1.74233i	−0.0709530	−	0.0709530i
$604$		0			0
$605$	−15.9865	−	43.3171i	−0.649945	−	1.76109i
$606$		0			0
$607$	−0.199219	+	0.743495i	−0.00808604	+	0.0301775i	−0.969851	−	0.243699i	$-0.921639\pi$
$607$	−0.199219	+	0.743495i	−0.00808604	+	0.0301775i	0.961765	+	0.273876i	$0.0883059\pi$
$608$		0			0
$609$	−0.513702	−	2.36336i	−0.0208162	−	0.0957682i
$610$		0			0
$611$	5.95987	+	10.3228i	0.241110	+	0.417615i
$612$		0			0
$613$	−33.8086	+	9.05898i	−1.36552	+	0.365889i	−0.865839	−	0.500323i	$-0.833214\pi$
$613$	−33.8086	+	9.05898i	−1.36552	+	0.365889i	−0.499676	+	0.866212i	$0.666548\pi$
$614$		0			0
$615$	4.65183	−	0.428014i	0.187580	−	0.0172592i
$616$		0			0
$617$	21.5403	−	21.5403i	0.867179	−	0.867179i	−0.124980	−	0.992159i	$-0.539887\pi$
$617$	21.5403	−	21.5403i	0.867179	−	0.867179i	0.992159	+	0.124980i	$0.0398866\pi$
$618$		0			0
$619$	21.6707	−	37.5348i	0.871021	−	1.50865i	0.0100783	−	0.999949i	$-0.496792\pi$
$619$	21.6707	−	37.5348i	0.871021	−	1.50865i	0.860942	−	0.508703i	$-0.169875\pi$
$620$		0			0
$621$	1.66841	−	0.963256i	0.0669509	−	0.0386541i
$622$		0			0
$623$	28.0382	−	14.4487i	1.12333	−	0.578876i
$624$		0			0
$625$	19.4363	+	15.7235i	0.777452	+	0.628942i
$626$		0			0
$627$	1.64184	+	6.12745i	0.0655690	+	0.244707i
$628$		0			0
$629$	−26.7559			−1.06683
$630$		0			0
$631$	−7.53463			−0.299949			−0.149974	−	0.988690i	$-0.547919\pi$
$631$	−7.53463			−0.299949			−0.149974	+	0.988690i	$0.547919\pi$
$632$		0			0
$633$	−1.46804	−	5.47879i	−0.0583492	−	0.217762i
$634$		0			0
$635$	−11.9683	+	8.46052i	−0.474946	+	0.335746i
$636$		0			0
$637$	10.9163	−	9.00710i	0.432520	−	0.356874i
$638$		0			0
$639$	−12.0640	+	6.96513i	−0.477243	+	0.275536i
$640$		0			0
$641$	−12.1657	+	21.0717i	−0.480518	+	0.832281i	−0.999750	−	0.0223521i	$-0.992885\pi$
$641$	−12.1657	+	21.0717i	−0.480518	+	0.832281i	0.519233	+	0.854633i	$0.326218\pi$
$642$		0			0
$643$	6.21713	−	6.21713i	0.245180	−	0.245180i	−0.573809	−	0.818989i	$-0.694535\pi$
$643$	6.21713	−	6.21713i	0.245180	−	0.245180i	0.818989	+	0.573809i	$0.194535\pi$
$644$		0			0
$645$	1.08763	−	1.30805i	0.0428252	−	0.0515045i
$646$		0			0
$647$	−19.9243	+	5.33869i	−0.783304	+	0.209886i	−0.628241	−	0.778019i	$-0.716225\pi$
$647$	−19.9243	+	5.33869i	−0.783304	+	0.209886i	−0.155063	+	0.987905i	$0.549558\pi$
$648$		0			0
$649$	15.4102	+	26.6913i	0.604905	+	1.04773i
$650$		0			0
$651$	−2.80989	−	0.898745i	−0.110128	−	0.0352246i
$652$		0			0
$653$	6.76544	−	25.2490i	0.264752	−	0.988069i	−0.697650	−	0.716439i	$-0.745771\pi$
$653$	6.76544	−	25.2490i	0.264752	−	0.988069i	0.962402	−	0.271630i	$-0.0875625\pi$
$654$		0			0
$655$	16.1430	−	5.95772i	0.630761	−	0.232787i
$656$		0			0
$657$	11.5723	+	11.5723i	0.451478	+	0.451478i
$658$		0			0
$659$			24.2448i			0.944443i	0.881480	+	0.472222i	$0.156548\pi$
$659$			24.2448i			0.944443i	−0.881480	+	0.472222i	$0.843452\pi$
$660$		0			0
$661$	15.5301	+	8.96630i	0.604050	+	0.348749i	0.770633	−	0.637279i	$-0.219940\pi$
$661$	15.5301	+	8.96630i	0.604050	+	0.348749i	−0.166583	+	0.986027i	$0.553273\pi$
$662$		0			0
$663$	3.00382	+	0.804871i	0.116659	+	0.0312586i
$664$		0			0
$665$	−21.9562	+	6.93121i	−0.851423	+	0.268781i
$666$		0			0
$667$	3.42516	+	0.917769i	0.132623	+	0.0355362i
$668$		0			0
$669$	−0.518181	−	0.299172i	−0.0200340	−	0.0115667i
$670$		0			0
$671$			25.9305i			1.00104i
$672$		0			0
$673$	−4.85386	−	4.85386i	−0.187103	−	0.187103i	0.607340	−	0.794442i	$-0.292237\pi$
$673$	−4.85386	−	4.85386i	−0.187103	−	0.187103i	−0.794442	+	0.607340i	$0.792237\pi$
$674$		0			0
$675$	3.69158	+	7.73470i	0.142089	+	0.297709i
$676$		0			0
$677$	−4.78306	+	17.8506i	−0.183828	+	0.686055i	0.811051	+	0.584976i	$0.198896\pi$
$677$	−4.78306	+	17.8506i	−0.183828	+	0.686055i	−0.994878	+	0.101079i	$0.967771\pi$
$678$		0			0
$679$	18.3618	−	16.6863i	0.704660	−	0.640362i
$680$		0			0
$681$	2.70083	+	4.67797i	0.103496	+	0.179260i
$682$		0			0
$683$	−25.8878	+	6.93661i	−0.990569	+	0.265422i	−0.717489	−	0.696569i	$-0.754709\pi$
$683$	−25.8878	+	6.93661i	−0.990569	+	0.265422i	−0.273079	+	0.961992i	$0.588042\pi$
$684$		0			0
$685$	−1.81023	−	19.6743i	−0.0691653	−	0.751717i
$686$		0			0
$687$	0.821071	−	0.821071i	0.0313258	−	0.0313258i
$688$		0			0
$689$	−1.39819	+	2.42173i	−0.0532667	+	0.0922606i
$690$		0			0
$691$	−25.1773	+	14.5361i	−0.957790	+	0.552980i	−0.895492	−	0.445077i	$-0.853176\pi$
$691$	−25.1773	+	14.5361i	−0.957790	+	0.552980i	−0.0622976	+	0.998058i	$0.519843\pi$
$692$		0			0
$693$	43.3541	+	2.07251i	1.64689	+	0.0787281i
$694$		0			0
$695$	−24.3811	−	4.18638i	−0.924827	−	0.158798i
$696$		0			0
$697$	9.90723	+	36.9743i	0.375263	+	1.40050i
$698$		0			0
$699$	−3.97855			−0.150483
$700$		0			0
$701$	25.4462			0.961089			0.480545	−	0.876970i	$-0.340439\pi$
$701$	25.4462			0.961089			0.480545	+	0.876970i	$0.340439\pi$
$702$		0			0
$703$	5.07663	+	18.9462i	0.191469	+	0.714571i
$704$		0			0
$705$	3.76452	+	0.646392i	0.141780	+	0.0243445i
$706$		0			0
$707$	−23.0343	+	35.8289i	−0.866295	+	1.34748i
$708$		0			0
$709$	−27.1994	+	15.7036i	−1.02150	+	0.589760i	−0.914537	−	0.404503i	$-0.867445\pi$
$709$	−27.1994	+	15.7036i	−1.02150	+	0.589760i	−0.106958	+	0.994263i	$0.534111\pi$
$710$		0			0
$711$	−9.10952	+	15.7781i	−0.341634	+	0.591727i
$712$		0			0
$713$	3.05850	−	3.05850i	0.114542	−	0.114542i
$714$		0			0
$715$	2.33027	+	25.3263i	0.0871470	+	0.947149i
$716$		0			0
$717$	−5.50271	+	1.47445i	−0.205502	+	0.0550642i
$718$		0			0
$719$	5.40214	+	9.35678i	0.201466	+	0.348949i	0.949001	−	0.315273i	$-0.102096\pi$
$719$	5.40214	+	9.35678i	0.201466	+	0.348949i	−0.747535	+	0.664222i	$0.768763\pi$
$720$		0			0
$721$	15.8540	−	49.5669i	0.590434	−	1.84597i
$722$		0			0
$723$	0.441322	−	1.64704i	0.0164129	−	0.0612539i
$724$		0			0
$725$	−5.26221	+	14.8715i	−0.195433	+	0.552315i
$726$		0			0
$727$	−33.6108	−	33.6108i	−1.24656	−	1.24656i	−0.957231	−	0.289326i	$-0.906569\pi$
$727$	−33.6108	−	33.6108i	−1.24656	−	1.24656i	−0.289326	−	0.957231i	$-0.593431\pi$
$728$		0			0
$729$		−	22.5720i		−	0.835998i
$730$		0			0
$731$	12.0719	+	6.96972i	0.446496	+	0.257785i
$732$		0			0
$733$	24.8800	+	6.66658i	0.918964	+	0.246236i	0.687143	−	0.726523i	$-0.258865\pi$
$733$	24.8800	+	6.66658i	0.918964	+	0.246236i	0.231822	+	0.972758i	$0.425531\pi$
$734$		0			0
$735$	0.0171620	−	4.53507i	0.000633031	−	0.167278i
$736$		0			0
$737$	−4.59170	−	1.23034i	−0.169138	−	0.0453203i
$738$		0			0
$739$	−10.4948	−	6.05920i	−0.386059	−	0.222891i	0.294392	−	0.955685i	$-0.404883\pi$
$739$	−10.4948	−	6.05920i	−0.386059	−	0.222891i	−0.680451	+	0.732793i	$0.738216\pi$
$740$		0			0
$741$		−	2.27977i		−	0.0837493i
$742$		0			0
$743$	−23.2618	−	23.2618i	−0.853393	−	0.853393i	0.137157	−	0.990549i	$-0.456204\pi$
$743$	−23.2618	−	23.2618i	−0.853393	−	0.853393i	−0.990549	+	0.137157i	$0.956204\pi$
$744$		0			0
$745$	−10.5913	+	3.90881i	−0.388036	+	0.143208i
$746$		0			0
$747$	−6.05487	+	22.5971i	−0.221536	+	0.826784i
$748$		0			0
$749$	−2.25767	+	7.05851i	−0.0824934	+	0.257912i
$750$		0			0
$751$	6.98887	+	12.1051i	0.255028	+	0.441721i	0.964903	−	0.262607i	$-0.0845821\pi$
$751$	6.98887	+	12.1051i	0.255028	+	0.441721i	−0.709875	+	0.704327i	$0.751249\pi$
$752$		0			0
$753$	1.98690	−	0.532387i	0.0724065	−	0.0194013i
$754$		0			0
$755$	19.2181	−	23.1130i	0.699420	−	0.841169i
$756$		0			0
$757$	17.5547	−	17.5547i	0.638036	−	0.638036i	−0.312035	−	0.950071i	$-0.601010\pi$
$757$	17.5547	−	17.5547i	0.638036	−	0.638036i	0.950071	+	0.312035i	$0.101010\pi$
$758$		0			0
$759$	0.915990	−	1.58654i	0.0332483	−	0.0575878i
$760$		0			0
$761$	18.9372	−	10.9334i	0.686471	−	0.396334i	−0.115817	−	0.993271i	$-0.536949\pi$
$761$	18.9372	−	10.9334i	0.686471	−	0.396334i	0.802289	+	0.596936i	$0.203615\pi$
$762$		0			0
$763$	8.45710	−	13.1546i	0.306168	−	0.476230i
$764$		0			0
$765$	−28.2660	+	19.9816i	−1.02196	+	0.722437i
$766$		0			0
$767$	−2.86675	−	10.6989i	−0.103512	−	0.386313i
$768$		0			0
$769$	31.0506			1.11971			0.559857	−	0.828589i	$-0.310856\pi$
$769$	31.0506			1.11971			0.559857	+	0.828589i	$0.310856\pi$
$770$		0			0
$771$	−2.86459			−0.103166
$772$		0			0
$773$	−1.57065	−	5.86173i	−0.0564922	−	0.210832i	0.931910	−	0.362689i	$-0.118141\pi$
$773$	−1.57065	−	5.86173i	−0.0564922	−	0.210832i	−0.988402	+	0.151857i	$0.951475\pi$
$774$		0			0
$775$	12.5004	+	14.6289i	0.449029	+	0.525487i
$776$		0			0
$777$	−3.85909	−	0.184481i	−0.138444	−	0.00661822i
$778$		0			0
$779$	24.3023	−	14.0309i	0.870720	−	0.502710i
$780$		0			0
$781$	−13.4374	+	23.2743i	−0.480828	+	0.832819i
$782$		0			0
$783$	−3.82404	+	3.82404i	−0.136660	+	0.136660i
$784$		0			0
$785$	−2.45571	+	0.225950i	−0.0876481	+	0.00806449i
$786$		0			0
$787$	21.5993	−	5.78752i	0.769932	−	0.206303i	0.147591	−	0.989049i	$-0.452848\pi$
$787$	21.5993	−	5.78752i	0.769932	−	0.206303i	0.622342	+	0.782746i	$0.286182\pi$
$788$		0			0
$789$	1.99167	+	3.44968i	0.0709055	+	0.122812i
$790$		0			0
$791$	37.6089	−	34.1772i	1.33722	−	1.21520i
$792$		0			0
$793$	2.41191	−	9.00138i	0.0856495	−	0.319648i
$794$		0			0
$795$	0.310252	+	0.840660i	0.0110035	+	0.0298151i
$796$		0			0
$797$	16.5528	+	16.5528i	0.586330	+	0.586330i	0.936636	−	0.350305i	$-0.113922\pi$
$797$	16.5528	+	16.5528i	0.586330	+	0.586330i	−0.350305	+	0.936636i	$0.613922\pi$
$798$		0			0
$799$			31.2984i			1.10726i
$800$		0			0
$801$	−30.1070	−	17.3823i	−1.06378	−	0.614174i
$802$		0			0
$803$	30.4975	+	8.17177i	1.07623	+	0.288376i
$804$		0			0
$805$	5.89899	+	3.06820i	0.207912	+	0.108140i
$806$		0			0
$807$	−7.41697	−	1.98737i	−0.261090	−	0.0699588i
$808$		0			0
$809$	2.84139	+	1.64048i	0.0998980	+	0.0576762i	0.549117	−	0.835746i	$-0.314964\pi$
$809$	2.84139	+	1.64048i	0.0998980	+	0.0576762i	−0.449219	+	0.893422i	$0.648298\pi$
$810$		0			0
$811$			17.8693i			0.627476i	0.949510	+	0.313738i	$0.101581\pi$
$811$			17.8693i			0.627476i	−0.949510	+	0.313738i	$0.898419\pi$
$812$		0			0
$813$	2.62176	+	2.62176i	0.0919491	+	0.0919491i
$814$		0			0
$815$	12.3924	−	26.8898i	0.434088	−	0.941910i
$816$		0			0
$817$	2.64486	−	9.87074i	0.0925318	−	0.345333i
$818$		0			0
$819$	−14.8569	−	4.75200i	−0.519143	−	0.166048i
$820$		0			0
$821$	5.90837	+	10.2336i	0.206204	+	0.357155i	0.950516	−	0.310677i	$-0.100556\pi$
$821$	5.90837	+	10.2336i	0.206204	+	0.357155i	−0.744312	+	0.667832i	$0.767222\pi$
$822$		0			0
$823$	34.0995	−	9.13692i	1.18863	−	0.318493i	0.390287	−	0.920693i	$-0.372376\pi$
$823$	34.0995	−	9.13692i	1.18863	−	0.318493i	0.798345	+	0.602200i	$0.205709\pi$
$824$		0			0
$825$	6.71771	+	4.61455i	0.233881	+	0.160658i
$826$		0			0
$827$	17.2835	−	17.2835i	0.601005	−	0.601005i	−0.339574	−	0.940579i	$-0.610283\pi$
$827$	17.2835	−	17.2835i	0.601005	−	0.601005i	0.940579	+	0.339574i	$0.110283\pi$
$828$		0			0
$829$	17.2877	−	29.9431i	0.600426	−	1.03997i	−0.392330	−	0.919824i	$-0.628331\pi$
$829$	17.2877	−	29.9431i	0.600426	−	1.03997i	0.992756	−	0.120144i	$-0.0383357\pi$
$830$		0			0
$831$	−5.04433	+	2.91234i	−0.174986	+	0.101028i
$832$		0			0
$833$	36.6487	−	6.15011i	1.26980	−	0.213089i
$834$		0			0
$835$	8.59183	+	12.1540i	0.297332	+	0.420607i
$836$		0			0
$837$	1.70734	+	6.37187i	0.0590142	+	0.220244i
$838$		0			0
$839$	50.1328			1.73078			0.865388	−	0.501102i	$-0.167072\pi$
$839$	50.1328			1.73078			0.865388	+	0.501102i	$0.167072\pi$
$840$		0			0
$841$	19.0459			0.656754
$842$		0			0
$843$	−1.06109	−	3.96003i	−0.0365458	−	0.136391i
$844$		0			0
$845$	−3.37252	+	19.6412i	−0.116018	+	0.675679i
$846$		0			0
$847$	48.5636	−	25.0259i	1.66866	−	0.859901i
$848$		0			0
$849$	−6.79181	+	3.92125i	−0.233094	+	0.134577i
$850$		0			0
$851$	2.83227	−	4.90563i	0.0970888	−	0.168163i
$852$		0			0
$853$	−2.37500	+	2.37500i	−0.0813183	+	0.0813183i	−0.746596	−	0.665278i	$-0.768313\pi$
$853$	−2.37500	+	2.37500i	−0.0813183	+	0.0813183i	0.665278	+	0.746596i	$0.268313\pi$
$854$		0			0
$855$	19.5125	+	16.2243i	0.667312	+	0.554860i
$856$		0			0
$857$	−40.5097	+	10.8545i	−1.38378	+	0.370784i	−0.872494	−	0.488624i	$-0.837499\pi$
$857$	−40.5097	+	10.8545i	−1.38378	+	0.370784i	−0.511290	+	0.859408i	$0.670832\pi$
$858$		0			0
$859$	1.17847	+	2.04117i	0.0402090	+	0.0696440i	0.885430	−	0.464774i	$-0.153864\pi$
$859$	1.17847	+	2.04117i	0.0402090	+	0.0696440i	−0.845221	+	0.534418i	$0.820531\pi$
$860$		0			0
$861$	1.17402	+	5.40125i	0.0400105	+	0.184074i
$862$		0			0
$863$	−12.5138	+	46.7022i	−0.425975	+	1.58976i	0.335808	+	0.941930i	$0.390991\pi$
$863$	−12.5138	+	46.7022i	−0.425975	+	1.58976i	−0.761784	+	0.647831i	$0.775676\pi$
$864$		0			0
$865$	−14.3263	−	6.60242i	−0.487110	−	0.224489i
$866$		0			0
$867$	2.29104	+	2.29104i	0.0778076	+	0.0778076i
$868$		0			0
$869$			35.1489i			1.19234i
$870$		0			0
$871$	1.47950	+	0.854190i	0.0501310	+	0.0289431i
$872$		0			0
$873$	−26.4141	−	7.07763i	−0.893980	−	0.239541i
$874$		0			0
$875$	−15.6603	+	25.0949i	−0.529416	+	0.848363i
$876$		0			0
$877$	13.3115	+	3.56681i	0.449498	+	0.120443i	0.476465	−	0.879194i	$-0.341918\pi$
$877$	13.3115	+	3.56681i	0.449498	+	0.120443i	−0.0269665	+	0.999636i	$0.508585\pi$
$878$		0			0
$879$	6.07477	+	3.50727i	0.204897	+	0.118297i
$880$		0			0
$881$		−	3.32542i		−	0.112036i	−0.998430	−	0.0560181i	$-0.982160\pi$
$881$		−	3.32542i		−	0.112036i	0.998430	−	0.0560181i	$-0.0178405\pi$
$882$		0			0
$883$	36.8930	+	36.8930i	1.24155	+	1.24155i	0.959358	+	0.282191i	$0.0910610\pi$
$883$	36.8930	+	36.8930i	1.24155	+	1.24155i	0.282191	+	0.959358i	$0.408939\pi$
$884$		0			0
$885$	−3.22348	−	1.48557i	−0.108356	−	0.0499369i
$886$		0			0
$887$	9.27107	−	34.6001i	0.311292	−	1.16176i	−0.616101	−	0.787668i	$-0.711289\pi$
$887$	9.27107	−	34.6001i	0.311292	−	1.16176i	0.927392	−	0.374090i	$-0.122045\pi$
$888$		0			0
$889$	−11.6632	−	12.8343i	−0.391170	−	0.430447i
$890$		0			0
$891$	−23.2105	−	40.2018i	−0.777582	−	1.34681i
$892$		0			0
$893$	22.1628	−	5.93852i	0.741651	−	0.198725i
$894$		0			0
$895$	−3.79349	−	3.15423i	−0.126803	−	0.105434i
$896$		0			0
$897$	−0.465543	+	0.465543i	−0.0155440	+	0.0155440i
$898$		0			0
$899$	−6.07098	+	10.5152i	−0.202479	+	0.350703i
$900$		0			0
$901$	−6.35888	+	3.67130i	−0.211845	+	0.122309i
$902$		0			0
$903$	1.69312	+	1.08850i	0.0563435	+	0.0362232i
$904$		0			0
$905$	−1.55854	+	9.07680i	−0.0518077	+	0.301723i
$906$		0			0
$907$	4.46661	+	16.6696i	0.148312	+	0.553506i	0.999586	+	0.0287849i	$0.00916377\pi$
$907$	4.46661	+	16.6696i	0.148312	+	0.553506i	−0.851274	+	0.524721i	$0.824170\pi$
$908$		0			0
$909$	46.9461			1.55710
$910$		0			0
$911$	−5.56820			−0.184483			−0.0922414	−	0.995737i	$-0.529403\pi$
$911$	−5.56820			−0.184483			−0.0922414	+	0.995737i	$0.529403\pi$
$912$		0			0
$913$	11.6813	+	43.5952i	0.386594	+	1.44279i
$914$		0			0
$915$	−1.72377	−	2.43844i	−0.0569859	−	0.0806124i
$916$		0			0
$917$	9.32645	+	18.0982i	0.307986	+	0.597657i
$918$		0			0
$919$	−5.37964	+	3.10593i	−0.177458	+	0.102455i	−0.586098	−	0.810240i	$-0.699337\pi$
$919$	−5.37964	+	3.10593i	−0.177458	+	0.102455i	0.408640	+	0.912696i	$0.366003\pi$
$920$		0			0
$921$	3.54381	−	6.13806i	0.116773	−	0.202256i
$922$		0			0
$923$	6.82943	−	6.82943i	0.224794	−	0.224794i
$924$		0			0
$925$	20.7713	+	14.2683i	0.682958	+	0.469139i
$926$		0			0
$927$	−55.4029	+	14.8452i	−1.81967	+	0.487579i
$928$		0			0
$929$	0.0947297	+	0.164077i	0.00310798	+	0.00538318i	0.867575	−	0.497306i	$-0.165677\pi$
$929$	0.0947297	+	0.164077i	0.00310798	+	0.00538318i	−0.864467	+	0.502689i	$0.832344\pi$
$930$		0			0
$931$	−11.3087	−	24.7846i	−0.370627	−	0.812281i
$932$		0			0
$933$	−0.823556	+	3.07355i	−0.0269620	+	0.100624i
$934$		0			0
$935$	−27.9514	+	60.6507i	−0.914108	+	1.98349i
$936$		0			0
$937$	−34.2022	−	34.2022i	−1.11734	−	1.11734i	−0.992131	−	0.125208i	$-0.960040\pi$
$937$	−34.2022	−	34.2022i	−1.11734	−	1.11734i	−0.125208	−	0.992131i	$-0.539960\pi$
$938$		0			0
$939$			8.52144i			0.278087i
$940$		0			0
$941$	−16.3826	−	9.45851i	−0.534058	−	0.308339i	0.208609	−	0.977999i	$-0.433106\pi$
$941$	−16.3826	−	9.45851i	−0.534058	−	0.308339i	−0.742667	+	0.669660i	$0.766440\pi$
$942$		0			0
$943$	−7.82790	−	2.09748i	−0.254911	−	0.0683033i
$944$		0			0
$945$	−8.55071	+	5.45161i	−0.278155	+	0.177341i
$946$		0			0
$947$	45.5435	+	12.2033i	1.47996	+	0.396555i	0.906335	−	0.422560i	$-0.138869\pi$
$947$	45.5435	+	12.2033i	1.47996	+	0.396555i	0.573629	+	0.819115i	$0.305535\pi$
$948$		0			0
$949$	−9.82664	−	5.67341i	−0.318986	−	0.184167i
$950$		0			0
$951$		−	1.24412i		−	0.0403434i
$952$		0			0
$953$	18.8431	+	18.8431i	0.610389	+	0.610389i	0.943047	−	0.332658i	$-0.107946\pi$
$953$	18.8431	+	18.8431i	0.610389	+	0.610389i	−0.332658	+	0.943047i	$0.607946\pi$
$954$		0			0
$955$	−13.3180	−	36.0865i	−0.430960	−	1.16773i
$956$		0			0
$957$	−1.33101	+	4.96741i	−0.0430256	+	0.160574i
$958$		0			0
$959$	22.8439	−	4.96536i	0.737667	−	0.160340i
$960$		0			0
$961$	−8.09467	−	14.0204i	−0.261118	−	0.452270i
$962$		0			0
$963$	7.88958	−	2.11401i	0.254238	−	0.0681229i
$964$		0			0
$965$	26.8700	−	2.47231i	0.864976	−	0.0795863i
$966$		0			0
$967$	−27.3703	+	27.3703i	−0.880169	+	0.880169i	−0.993551	−	0.113383i	$-0.963831\pi$
$967$	−27.3703	+	27.3703i	−0.880169	+	0.880169i	0.113383	+	0.993551i	$0.463831\pi$
$968$		0			0
$969$	2.99306	−	5.18413i	0.0961509	−	0.166538i
$970$		0			0
$971$	27.8750	−	16.0936i	0.894550	−	0.516469i	0.0191221	−	0.999817i	$-0.493913\pi$
$971$	27.8750	−	16.0936i	0.894550	−	0.516469i	0.875428	+	0.483348i	$0.160580\pi$
$972$		0			0
$973$	1.39765	−	29.2369i	0.0448065	−	0.937291i
$974$		0			0
$975$	−1.90273	−	2.22671i	−0.0609362	−	0.0713119i
$976$		0			0
$977$	−6.02479	−	22.4848i	−0.192750	−	0.719353i	−0.992838	−	0.119470i	$-0.961881\pi$
$977$	−6.02479	−	22.4848i	−0.192750	−	0.719353i	0.800088	−	0.599883i	$-0.204786\pi$
$978$		0			0
$979$	−67.0692			−2.14354
$980$		0			0
$981$	−17.2364			−0.550314
$982$		0			0
$983$	−14.7630	−	55.0964i	−0.470868	−	1.75730i	−0.636662	−	0.771143i	$-0.719685\pi$
$983$	−14.7630	−	55.0964i	−0.470868	−	1.75730i	0.165793	−	0.986160i	$-0.446981\pi$
$984$		0			0
$985$	36.9606	−	26.1279i	1.17766	−	0.832505i
$986$		0			0
$987$	−0.215802	+	4.51427i	−0.00686904	+	0.143691i
$988$		0			0
$989$	−2.55577	+	1.47557i	−0.0812687	+	0.0469205i
$990$		0			0
$991$	−28.7703	+	49.8316i	−0.913918	+	1.58295i	−0.105440	+	0.994426i	$0.533625\pi$
$991$	−28.7703	+	49.8316i	−0.913918	+	1.58295i	−0.808478	+	0.588526i	$0.799708\pi$
$992$		0			0
$993$	−7.26279	+	7.26279i	−0.230478	+	0.230478i
$994$		0			0
$995$	10.7694	−	12.9520i	0.341414	−	0.410607i
$996$		0			0
$997$	23.4284	−	6.27762i	0.741985	−	0.198814i	0.132025	−	0.991246i	$-0.457852\pi$
$997$	23.4284	−	6.27762i	0.741985	−	0.198814i	0.609960	+	0.792432i	$0.291185\pi$
$998$		0			0
$999$	4.31951	+	7.48160i	0.136663	+	0.236707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.c.353.3		16
4.3	odd	2		70.2.k.a.3.1	✓	16
5.2	odd	4	inner	560.2.ci.c.17.3		16
7.5	odd	6	inner	560.2.ci.c.33.3		16
12.11	even	2		630.2.bv.c.73.3		16
20.3	even	4		350.2.o.c.157.2		16
20.7	even	4		70.2.k.a.17.3	yes	16
20.19	odd	2		350.2.o.c.143.4		16
28.3	even	6		490.2.g.c.293.7		16
28.11	odd	6		490.2.g.c.293.6		16
28.19	even	6		70.2.k.a.33.3	yes	16
28.23	odd	6		490.2.l.c.313.4		16
28.27	even	2		490.2.l.c.423.2		16
35.12	even	12	inner	560.2.ci.c.257.3		16
60.47	odd	4		630.2.bv.c.577.1		16
84.47	odd	6		630.2.bv.c.523.1		16
140.19	even	6		350.2.o.c.243.2		16
140.27	odd	4		490.2.l.c.227.4		16
140.47	odd	12		70.2.k.a.47.1	yes	16
140.67	even	12		490.2.g.c.97.7		16
140.87	odd	12		490.2.g.c.97.6		16
140.103	odd	12		350.2.o.c.257.4		16
140.107	even	12		490.2.l.c.117.2		16
420.47	even	12		630.2.bv.c.397.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.1	✓	16	4.3	odd	2
70.2.k.a.17.3	yes	16	20.7	even	4
70.2.k.a.33.3	yes	16	28.19	even	6
70.2.k.a.47.1	yes	16	140.47	odd	12
350.2.o.c.143.4		16	20.19	odd	2
350.2.o.c.157.2		16	20.3	even	4
350.2.o.c.243.2		16	140.19	even	6
350.2.o.c.257.4		16	140.103	odd	12
490.2.g.c.97.6		16	140.87	odd	12
490.2.g.c.97.7		16	140.67	even	12
490.2.g.c.293.6		16	28.11	odd	6
490.2.g.c.293.7		16	28.3	even	6
490.2.l.c.117.2		16	140.107	even	12
490.2.l.c.227.4		16	140.27	odd	4
490.2.l.c.313.4		16	28.23	odd	6
490.2.l.c.423.2		16	28.27	even	2
560.2.ci.c.17.3		16	5.2	odd	4	inner
560.2.ci.c.33.3		16	7.5	odd	6	inner
560.2.ci.c.257.3		16	35.12	even	12	inner
560.2.ci.c.353.3		16	1.1	even	1	trivial
630.2.bv.c.73.3		16	12.11	even	2
630.2.bv.c.397.3		16	420.47	even	12
630.2.bv.c.523.1		16	84.47	odd	6
630.2.bv.c.577.1		16	60.47	odd	4

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0749894 + 0.279864i) q^{3} +(2.20382 + 0.378409i) q^{5} +(-0.126334 + 2.64273i) q^{7} +(2.52538 - 1.45803i) q^{9} +O(q^{10})\)	\(q+(0.0749894 + 0.279864i) q^{3} +(2.20382 + 0.378409i) q^{5} +(-0.126334 + 2.64273i) q^{7} +(2.52538 - 1.45803i) q^{9} +(2.81288 - 4.87205i) q^{11} +(-1.42962 + 1.42962i) q^{13} +(0.0593598 + 0.645146i) q^{15} +(-5.12784 + 1.37400i) q^{17} +(1.94590 + 3.37040i) q^{19} +(-0.749081 + 0.162821i) q^{21} +(0.290892 - 1.08562i) q^{23} +(4.71361 + 1.66789i) q^{25} +(1.21205 + 1.21205i) q^{27} +3.15502i q^{29} +(3.33287 + 1.92423i) q^{31} +(1.57445 + 0.421872i) q^{33} +(-1.27845 + 5.77629i) q^{35} +(4.86824 + 1.30444i) q^{37} +(-0.507306 - 0.292893i) q^{39} -7.21050i q^{41} +(-1.85669 - 1.85669i) q^{43} +(6.11719 - 2.25760i) q^{45} +(1.52590 - 5.69475i) q^{47} +(-6.96808 - 0.667734i) q^{49} +(-0.769067 - 1.33206i) q^{51} +(1.33599 - 0.357978i) q^{53} +(8.04270 - 9.67269i) q^{55} +(-0.797333 + 0.797333i) q^{57} +(-2.73923 + 4.74448i) q^{59} +(-3.99172 + 2.30462i) q^{61} +(3.53413 + 6.85809i) q^{63} +(-3.69160 + 2.60964i) q^{65} +(-0.218698 - 0.816193i) q^{67} +0.325641 q^{69} -4.77710 q^{71} +(1.45256 + 5.42104i) q^{73} +(-0.113311 + 1.44425i) q^{75} +(12.5202 + 8.04920i) q^{77} +(-5.41079 + 3.12392i) q^{79} +(4.12576 - 7.14603i) q^{81} +(-5.67281 + 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +(-0.882976 + 0.236593i) q^{87} +(-5.96090 - 10.3246i) q^{89} +(-3.59749 - 3.95871i) q^{91} +(-0.288594 + 1.07705i) q^{93} +(3.01302 + 8.16409i) q^{95} +(-6.63103 - 6.63103i) q^{97} -16.4050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 - 8 * q^7	\( 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53} + 8 q^{57} - 12 q^{61} + 36 q^{63} - 8 q^{65} - 32 q^{67} - 16 q^{71} - 12 q^{73} + 48 q^{75} + 16 q^{77} + 24 q^{85} + 24 q^{87} + 16 q^{91} + 28 q^{93} - 20 q^{95}+O(q^{100}) \) 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Introduction

L-functions

Modular forms

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Database

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