LMFDB - Embedded newform 560.2.ci.c.33.3

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			33.3
Root			$-1.01089 - 0.750919i$ of defining polynomial
Character	$\chi$	$=$	560.33
Dual form			560.2.ci.c.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.279864 + 0.0749894i) q^{3} +(0.774197 + 2.09777i) q^{5} +(-2.64273 + 0.126334i) q^{7} +(-2.52538 - 1.45803i) q^{9} +O(q^{10})$	\(q+(0.279864 + 0.0749894i) q^{3} +(0.774197 + 2.09777i) q^{5} +(-2.64273 + 0.126334i) q^{7} +(-2.52538 - 1.45803i) q^{9} +(2.81288 + 4.87205i) q^{11} +(1.42962 - 1.42962i) q^{13} +(0.0593598 + 0.645146i) q^{15} +(-1.37400 + 5.12784i) q^{17} +(-1.94590 + 3.37040i) q^{19} +(-0.749081 - 0.162821i) q^{21} +(-1.08562 + 0.290892i) q^{23} +(-3.80124 + 3.24817i) q^{25} +(-1.21205 - 1.21205i) q^{27} +3.15502i q^{29} +(3.33287 - 1.92423i) q^{31} +(0.421872 + 1.57445i) q^{33} +(-2.31101 - 5.44603i) q^{35} +(-1.30444 - 4.86824i) q^{37} +(0.507306 - 0.292893i) q^{39} +7.21050i q^{41} +(-1.85669 - 1.85669i) q^{43} +(1.10346 - 6.42644i) q^{45} +(5.69475 - 1.52590i) q^{47} +(6.96808 - 0.667734i) q^{49} +(-0.769067 + 1.33206i) q^{51} +(-0.357978 + 1.33599i) q^{53} +(-8.04270 + 9.67269i) q^{55} +(-0.797333 + 0.797333i) q^{57} +(2.73923 + 4.74448i) q^{59} +(-3.99172 - 2.30462i) q^{61} +(6.85809 + 3.53413i) q^{63} +(4.10581 + 1.89220i) q^{65} +(0.816193 + 0.218698i) q^{67} -0.325641 q^{69} -4.77710 q^{71} +(5.42104 + 1.45256i) q^{73} +(-1.30741 + 0.623993i) q^{75} +(-8.04920 - 12.5202i) q^{77} +(5.41079 + 3.12392i) q^{79} +(4.12576 + 7.14603i) q^{81} +(5.67281 - 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +(-0.236593 + 0.882976i) q^{87} +(5.96090 - 10.3246i) q^{89} +(-3.59749 + 3.95871i) q^{91} +(1.07705 - 0.288594i) q^{93} +(-8.57682 - 1.47269i) q^{95} +(6.63103 + 6.63103i) q^{97} -16.4050i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	0.279864	+	0.0749894i	0.161580	+	0.0432952i	0.338702	−	0.940894i	$-0.390012\pi$
$3$	0.279864	+	0.0749894i	0.161580	+	0.0432952i	−0.177122	+	0.984189i	$0.556679\pi$
$4$		0			0
$5$	0.774197	+	2.09777i	0.346231	+	0.938149i
$5$	0.774197	+	2.09777i	0.346231	+	0.938149i
$6$		0			0
$7$	−2.64273	+	0.126334i	−0.998859	+	0.0477497i
$7$	−2.64273	+	0.126334i	−0.998859	+	0.0477497i
$8$		0			0
$9$	−2.52538	−	1.45803i	−0.841792	−	0.486009i
$10$		0			0
$11$	2.81288	+	4.87205i	0.848115	+	1.46898i	0.882888	+	0.469583i	$0.155596\pi$
$11$	2.81288	+	4.87205i	0.848115	+	1.46898i	−0.0347729	+	0.999395i	$0.511071\pi$
$12$		0			0
$13$	1.42962	−	1.42962i	0.396505	−	0.396505i	−0.480493	−	0.876998i	$-0.659542\pi$
$13$	1.42962	−	1.42962i	0.396505	−	0.396505i	0.876998	+	0.480493i	$0.159542\pi$
$14$		0			0
$15$	0.0593598	+	0.645146i	0.0153266	+	0.166576i
$16$		0			0
$17$	−1.37400	+	5.12784i	−0.333244	+	1.24368i	0.572516	+	0.819893i	$0.305967\pi$
$17$	−1.37400	+	5.12784i	−0.333244	+	1.24368i	−0.905760	+	0.423790i	$0.860699\pi$
$18$		0			0
$19$	−1.94590	+	3.37040i	−0.446420	+	0.773223i	−0.998150	−	0.0608002i	$-0.980635\pi$
$19$	−1.94590	+	3.37040i	−0.446420	+	0.773223i	0.551729	+	0.834023i	$0.313968\pi$
$20$		0			0
$21$	−0.749081	−	0.162821i	−0.163463	−	0.0355304i
$22$		0			0
$23$	−1.08562	+	0.290892i	−0.226368	+	0.0606552i	−0.370220	−	0.928944i	$-0.620718\pi$
$23$	−1.08562	+	0.290892i	−0.226368	+	0.0606552i	0.143852	+	0.989599i	$0.454051\pi$
$24$		0			0
$25$	−3.80124	+	3.24817i	−0.760248	+	0.649633i
$26$		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	−0.169890	−	0.985463i	$-0.554341\pi$
$31$	3.33287	−	1.92423i	0.598601	−	0.345602i	0.768491	+	0.639861i	$0.221008\pi$
$32$		0			0
$33$	0.421872	+	1.57445i	0.0734386	+	0.274076i
$34$		0			0
$35$	−2.31101	−	5.44603i	−0.390633	−	0.920547i
$36$		0			0
$37$	−1.30444	−	4.86824i	−0.214449	−	0.800334i	−0.986360	−	0.164603i	$-0.947366\pi$
$37$	−1.30444	−	4.86824i	−0.214449	−	0.800334i	0.771911	−	0.635731i	$-0.219301\pi$
$38$		0			0
$39$	0.507306	−	0.292893i	0.0812340	−	0.0469005i
$40$		0			0
$41$			7.21050i			1.12609i	0.826426	+	0.563046i	$0.190371\pi$
$41$			7.21050i			1.12609i	−0.826426	+	0.563046i	$0.809629\pi$
$42$		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
$45$	1.10346	−	6.42644i	0.164494	−	0.957998i
$46$		0			0
$47$	5.69475	−	1.52590i	0.830665	−	0.222576i	0.181661	−	0.983361i	$-0.441853\pi$
$47$	5.69475	−	1.52590i	0.830665	−	0.222576i	0.649004	+	0.760785i	$0.275186\pi$
$48$		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
$53$	−0.357978	+	1.33599i	−0.0491720	+	0.183512i	−0.986144	−	0.165892i	$-0.946950\pi$
$53$	−0.357978	+	1.33599i	−0.0491720	+	0.183512i	0.936972	+	0.349405i	$0.113616\pi$
$54$		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	$-0.0505968\pi$
$59$	2.73923	+	4.74448i	0.356617	+	0.617679i	−0.630776	+	0.775965i	$0.717263\pi$
$60$		0			0
$61$	−3.99172	−	2.30462i	−0.511088	−	0.295077i	0.222193	−	0.975003i	$-0.428678\pi$
$61$	−3.99172	−	2.30462i	−0.511088	−	0.295077i	−0.733281	+	0.679926i	$0.762012\pi$
$62$		0			0
$63$	6.85809	+	3.53413i	0.864038	+	0.445259i
$64$		0			0
$65$	4.10581	+	1.89220i	0.509264	+	0.234699i
$66$		0			0
$67$	0.816193	+	0.218698i	0.0997138	+	0.0267182i	0.308331	−	0.951279i	$-0.400230\pi$
$67$	0.816193	+	0.218698i	0.0997138	+	0.0267182i	−0.208617	+	0.977997i	$0.566896\pi$
$68$		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
$73$	5.42104	+	1.45256i	0.634485	+	0.170010i	0.561704	−	0.827338i	$-0.310146\pi$
$73$	5.42104	+	1.45256i	0.634485	+	0.170010i	0.0727807	+	0.997348i	$0.476813\pi$
$74$		0			0
$75$	−1.30741	+	0.623993i	−0.150967	+	0.0720525i
$76$		0			0
$77$	−8.04920	−	12.5202i	−0.917291	−	1.42681i
$78$		0			0
$79$	5.41079	+	3.12392i	0.608761	+	0.351469i	0.772481	−	0.635038i	$-0.219016\pi$
$79$	5.41079	+	3.12392i	0.608761	+	0.351469i	−0.163719	+	0.986507i	$0.552349\pi$
$80$		0			0
$81$	4.12576	+	7.14603i	0.458418	+	0.794003i
$82$		0			0
$83$	5.67281	−	5.67281i	0.622672	−	0.622672i	−0.323542	−	0.946214i	$-0.604874\pi$
$83$	5.67281	−	5.67281i	0.622672	−	0.622672i	0.946214	+	0.323542i	$0.104874\pi$
$84$		0			0
$85$	−11.8207	+	1.08763i	−1.28214	+	0.117970i
$86$		0			0
$87$	−0.236593	+	0.882976i	−0.0253654	+	0.0946650i
$88$		0			0
$89$	5.96090	−	10.3246i	0.631855	−	1.09440i	−0.355318	−	0.934746i	$-0.615627\pi$
$89$	5.96090	−	10.3246i	0.631855	−	1.09440i	0.987172	−	0.159659i	$-0.0510393\pi$
$90$		0			0
$91$	−3.59749	+	3.95871i	−0.377120	+	0.414986i
$92$		0			0
$93$	1.07705	−	0.288594i	0.111685	−	0.0299258i
$94$		0			0
$95$	−8.57682	−	1.47269i	−0.879963	−	0.151095i
$96$		0			0
$97$	6.63103	+	6.63103i	0.673279	+	0.673279i	0.958471	−	0.285191i	$-0.0920572\pi$
$97$	6.63103	+	6.63103i	0.673279	+	0.673279i	−0.285191	+	0.958471i	$0.592057\pi$
$98$		0			0
$99$		−	16.4050i		−	1.64877i
$100$		0			0
$101$	13.9423	−	8.04960i	1.38731	−	0.800965i	0.394301	−	0.918981i	$-0.370987\pi$
$101$	13.9423	−	8.04960i	1.38731	−	0.800965i	0.993012	+	0.118016i	$0.0376535\pi$
$102$		0			0
$103$	−5.09084	−	18.9993i	−0.501616	−	1.87206i	−0.489271	−	0.872132i	$-0.662737\pi$
$103$	−5.09084	−	18.9993i	−0.501616	−	1.87206i	−0.0123445	−	0.999924i	$-0.503929\pi$
$104$		0			0
$105$	−0.238376	−	1.69745i	−0.0232631	−	0.165654i
$106$		0			0
$107$	−0.724955	−	2.70557i	−0.0700840	−	0.261557i	0.921990	−	0.387214i	$-0.126563\pi$
$107$	−0.724955	−	2.70557i	−0.0700840	−	0.261557i	−0.992074	+	0.125657i	$0.959896\pi$
$108$		0			0
$109$	5.11895	−	2.95543i	0.490306	−	0.283078i	−0.234395	−	0.972141i	$-0.575311\pi$
$109$	5.11895	−	2.95543i	0.490306	−	0.283078i	0.724701	+	0.689063i	$0.241978\pi$
$110$		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
$115$	−1.45071	−	2.05218i	−0.135279	−	0.191367i
$116$		0			0
$117$	−5.69475	+	1.52590i	−0.526480	+	0.141070i
$118$		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
$123$	−0.540712	+	2.01796i	−0.0487543	+	0.181954i
$124$		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	0.762035	−	0.647536i	$-0.224201\pi$
$131$	6.66437	+	3.84768i	0.582269	+	0.336173i	−0.179766	+	0.983709i	$0.557534\pi$
$132$		0			0
$133$	4.71670	−	9.15290i	0.408990	−	0.793657i
$134$		0			0
$135$	1.60423	−	3.48096i	0.138070	−	0.299594i
$136$		0			0
$137$	8.53471	+	2.28687i	0.729170	+	0.195380i	0.604259	−	0.796788i	$-0.293469\pi$
$137$	8.53471	+	2.28687i	0.729170	+	0.195380i	0.124910	+	0.992168i	$0.460136\pi$
$138$		0			0
$139$	11.0631			0.938361			0.469180	−	0.883102i	$-0.344549\pi$
$139$	11.0631			0.938361			0.469180	+	0.883102i	$0.344549\pi$
$140$		0			0
$141$	1.70818			0.143855
$142$		0			0
$143$	10.9865	+	2.94383i	0.918740	+	0.246176i
$144$		0			0
$145$	−6.61848	+	2.44260i	−0.549635	+	0.202847i
$146$		0			0
$147$	2.00019	+	0.335657i	0.164973	+	0.0276846i
$148$		0			0
$149$	4.37243	+	2.52443i	0.358204	+	0.206809i	0.668293	−	0.743899i	$-0.267025\pi$
$149$	4.37243	+	2.52443i	0.358204	+	0.206809i	−0.310089	+	0.950708i	$0.600359\pi$
$150$		0			0
$151$	6.72142	+	11.6418i	0.546981	+	0.947399i	0.998479	+	0.0551270i	$0.0175564\pi$
$151$	6.72142	+	11.6418i	0.546981	+	0.947399i	−0.451498	+	0.892272i	$0.649110\pi$
$152$		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
$157$	−0.285443	+	1.06529i	−0.0227808	+	0.0850191i	−0.976380	−	0.216059i	$-0.930680\pi$
$157$	−0.285443	+	1.06529i	−0.0227808	+	0.0850191i	0.953600	+	0.301078i	$0.0973464\pi$
$158$		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
$163$	−12.7899	+	3.42705i	−1.00179	+	0.268428i	−0.722193	−	0.691691i	$-0.756866\pi$
$163$	−12.7899	+	3.42705i	−1.00179	+	0.268428i	−0.279592	+	0.960119i	$0.590199\pi$
$164$		0			0
$165$	−2.97621	+	2.10392i	−0.231698	+	0.163790i
$166$		0			0
$167$	−4.70680	−	4.70680i	−0.364223	−	0.364223i	0.501142	−	0.865365i	$-0.332913\pi$
$167$	−4.70680	−	4.70680i	−0.364223	−	0.364223i	−0.865365	+	0.501142i	$0.832913\pi$
$168$		0			0
$169$			8.91237i			0.685567i
$170$		0			0
$171$	9.82827	−	5.67435i	0.751586	−	0.433929i
$172$		0			0
$173$	−1.82586	−	6.81421i	−0.138818	−	0.518075i	−0.999953	−	0.00969875i	$-0.996913\pi$
$173$	−1.82586	−	6.81421i	−0.138818	−	0.518075i	0.861135	−	0.508376i	$-0.169754\pi$
$174$		0			0
$175$	9.63531	−	9.06426i	0.728361	−	0.685194i
$176$		0			0
$177$	0.410826	+	1.53322i	0.0308796	+	0.115244i
$178$		0			0
$179$	1.91075	−	1.10317i	0.142816	−	0.0824550i	−0.426889	−	0.904304i	$-0.640391\pi$
$179$	1.91075	−	1.10317i	0.142816	−	0.0824550i	0.569706	+	0.821849i	$0.307057\pi$
$180$		0			0
$181$		−	4.11867i		−	0.306139i	−0.988215	−	0.153069i	$-0.951084\pi$
$181$		−	4.11867i		−	0.306139i	0.988215	−	0.153069i	$-0.0489158\pi$
$182$		0			0
$183$	−0.944318	−	0.944318i	−0.0698060	−	0.0698060i
$184$		0			0
$185$	9.20253	−	6.50539i	0.676584	−	0.478286i
$186$		0			0
$187$	−28.8480	+	7.72980i	−2.10957	+	0.565259i
$188$		0			0
$189$	3.35625	+	3.05000i	0.244131	+	0.221855i
$190$		0			0
$191$	−8.60117	+	14.8977i	−0.622359	+	1.07796i	0.366686	+	0.930345i	$0.380492\pi$
$191$	−8.60117	+	14.8977i	−0.622359	+	1.07796i	−0.989045	+	0.147613i	$0.952841\pi$
$192$		0			0
$193$	−3.12327	+	11.6562i	−0.224818	+	0.839032i	0.757659	+	0.652650i	$0.226343\pi$
$193$	−3.12327	+	11.6562i	−0.224818	+	0.839032i	−0.982477	+	0.186382i	$0.940324\pi$
$194$		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	$-0.252700\pi$
$199$	−3.76653	−	6.52383i	−0.267002	−	0.462462i	−0.968086	+	0.250617i	$0.919367\pi$
$200$		0			0
$201$	0.212023	+	0.122412i	0.0149550	+	0.00863425i
$202$		0			0
$203$	−0.398585	−	8.33786i	−0.0279752	−	0.585203i
$204$		0			0
$205$	−15.1259	+	5.58235i	−1.05644	+	0.389888i
$206$		0			0
$207$	3.16574	+	0.848257i	0.220034	+	0.0589579i
$208$		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
$213$	−1.33694	−	0.358232i	−0.0916056	−	0.0245456i
$214$		0			0
$215$	2.45746	−	5.33235i	0.167597	−	0.363663i
$216$		0			0
$217$	−8.56478	+	5.50629i	−0.581415	+	0.373791i
$218$		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	−0.656521	−	0.754308i	$-0.727973\pi$
$223$	1.46027	−	1.46027i	0.0977867	−	0.0977867i	0.754308	+	0.656521i	$0.227973\pi$
$224$		0			0
$225$	14.3355	−	2.66053i	0.955698	−	0.177369i
$226$		0			0
$227$	4.82525	−	18.0081i	0.320263	−	1.19524i	−0.598726	−	0.800954i	$-0.704326\pi$
$227$	4.82525	−	18.0081i	0.320263	−	1.19524i	0.918989	−	0.394283i	$-0.129007\pi$
$228$		0			0
$229$	2.00384	−	3.47074i	0.132417	−	0.229353i	−0.792191	−	0.610274i	$-0.791059\pi$
$229$	2.00384	−	3.47074i	0.132417	−	0.229353i	0.924608	+	0.380920i	$0.124393\pi$
$230$		0			0
$231$	−1.31380	−	4.10755i	−0.0864419	−	0.270257i
$232$		0			0
$233$	13.2637	−	3.55400i	0.868934	−	0.232830i	0.203307	−	0.979115i	$-0.434831\pi$
$233$	13.2637	−	3.55400i	0.868934	−	0.232830i	0.665627	+	0.746285i	$0.268164\pi$
$234$		0			0
$235$	7.60984	+	10.7649i	0.496412	+	0.702225i
$236$		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	−0.655088	−	0.755552i	$-0.727369\pi$
$241$	−5.09667	+	2.94256i	−0.328305	+	0.189547i	0.326783	+	0.945099i	$0.394035\pi$
$242$		0			0
$243$	1.94970	+	7.27638i	0.125073	+	0.466780i
$244$		0			0
$245$	6.79541	+	14.1004i	0.434143	+	0.900844i
$246$		0			0
$247$	2.03649	+	7.60029i	0.129579	+	0.483595i
$248$		0			0
$249$	2.01302	−	1.16222i	0.127570	−	0.0736525i
$250$		0			0
$251$			7.09950i			0.448116i	0.974576	+	0.224058i	$0.0719306\pi$
$251$			7.09950i			0.448116i	−0.974576	+	0.224058i	$0.928069\pi$
$252$		0			0
$253$	−4.47097	−	4.47097i	−0.281088	−	0.281088i
$254$		0			0
$255$	−3.38977	−	0.582044i	−0.212275	−	0.0364490i
$256$		0			0
$257$	−9.54998	+	2.55891i	−0.595711	+	0.159620i	−0.544062	−	0.839045i	$-0.683114\pi$
$257$	−9.54998	+	2.55891i	−0.595711	+	0.159620i	−0.0516491	+	0.998665i	$0.516448\pi$
$258$		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
$263$	−3.55829	+	13.2797i	−0.219413	+	0.818861i	0.765153	+	0.643849i	$0.222663\pi$
$263$	−3.55829	+	13.2797i	−0.219413	+	0.818861i	−0.984566	+	0.175013i	$0.944003\pi$
$264$		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	0.914296	+	0.405046i	$0.132745\pi$
$269$	13.2510	+	22.9514i	0.807928	+	1.39937i	−0.106368	+	0.994327i	$0.533922\pi$
$270$		0			0
$271$	11.0824	+	6.39844i	0.673209	+	0.388678i	0.797292	−	0.603594i	$-0.206265\pi$
$271$	11.0824	+	6.39844i	0.673209	+	0.388678i	−0.124082	+	0.992272i	$0.539599\pi$
$272$		0			0
$273$	−1.30367	+	0.838129i	−0.0789018	+	0.0507259i
$274$		0			0
$275$	−26.5177	−	9.38313i	−1.59908	−	0.565824i
$276$		0			0
$277$	−19.4184	−	5.20313i	−1.16674	−	0.312626i	−0.377083	−	0.926180i	$-0.623073\pi$
$277$	−19.4184	−	5.20313i	−1.16674	−	0.312626i	−0.789653	+	0.613554i	$0.789739\pi$
$278$		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
$283$	26.1454	+	7.00563i	1.55418	+	0.416442i	0.930816	−	0.365489i	$-0.119098\pi$
$283$	26.1454	+	7.00563i	1.55418	+	0.416442i	0.623366	+	0.781930i	$0.285765\pi$
$284$		0			0
$285$	−2.28991	−	1.05532i	−0.135643	−	0.0625121i
$286$		0			0
$287$	−0.910931	−	19.0554i	−0.0537706	−	1.12481i
$288$		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	$0.500034\pi$
$293$	−17.1191	+	17.1191i	−1.00011	+	1.00011i	−1.00000		0.000106876i	$0.999966\pi$
$294$		0			0
$295$	−7.83211	+	9.41941i	−0.456003	+	0.548420i
$296$		0			0
$297$	2.49582	−	9.31453i	0.144822	−	0.540484i
$298$		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
$303$	4.50559	−	1.20727i	0.258840	−	0.0693558i
$304$		0			0
$305$	1.74418	−	10.1579i	0.0998713	−	0.581641i
$306$		0			0
$307$	17.2974	+	17.2974i	0.987217	+	0.987217i	0.999919	−	0.0127019i	$-0.00404326\pi$
$307$	17.2974	+	17.2974i	0.987217	+	0.987217i	−0.0127019	+	0.999919i	$0.504043\pi$
$308$		0			0
$309$		−	5.69898i		−	0.324204i
$310$		0			0
$311$	9.51095	−	5.49115i	0.539316	−	0.311374i	−0.205486	−	0.978660i	$-0.565877\pi$
$311$	9.51095	−	5.49115i	0.539316	−	0.311374i	0.744802	+	0.667286i	$0.232544\pi$
$312$		0			0
$313$	7.61212	+	28.4088i	0.430262	+	1.60576i	0.752156	+	0.658985i	$0.229014\pi$
$313$	7.61212	+	28.4088i	0.430262	+	1.60576i	−0.321893	+	0.946776i	$0.604319\pi$
$314$		0			0
$315$	−2.10427	+	17.1228i	−0.118562	+	0.964760i
$316$		0			0
$317$	1.11136	+	4.14766i	0.0624203	+	0.232956i	0.990087	−	0.140453i	$-0.0448558\pi$
$317$	1.11136	+	4.14766i	0.0624203	+	0.232956i	−0.927667	+	0.373408i	$0.878189\pi$
$318$		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
$325$	−0.790684	+	10.0780i	−0.0438593	+	0.559025i
$326$		0			0
$327$	1.65424	−	0.443251i	0.0914795	−	0.0245119i
$328$		0			0
$329$	−14.8569	+	4.75200i	−0.819089	+	0.261986i
$330$		0			0
$331$	17.7249	−	30.7005i	0.974250	−	1.68745i	0.291863	−	0.956460i	$-0.405725\pi$
$331$	17.7249	−	30.7005i	0.974250	−	1.68745i	0.682387	−	0.730991i	$-0.260942\pi$
$332$		0			0
$333$	−3.80382	+	14.1960i	−0.208448	+	0.777939i
$334$		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
$343$	−18.3304	+	2.64495i	−0.989750	+	0.142814i
$344$		0			0
$345$	−0.252110	−	0.683119i	−0.0135732	−	0.0367779i
$346$		0			0
$347$	8.67040	+	2.32323i	0.465452	+	0.124717i	0.483920	−	0.875112i	$-0.339212\pi$
$347$	8.67040	+	2.32323i	0.465452	+	0.124717i	−0.0184687	+	0.999829i	$0.505879\pi$
$348$		0			0
$349$	26.0251			1.39309			0.696546	−	0.717512i	$-0.254719\pi$
$349$	26.0251			1.39309			0.696546	+	0.717512i	$0.254719\pi$
$350$		0			0
$351$	−3.46554			−0.184977
$352$		0			0
$353$	9.62659	+	2.57944i	0.512372	+	0.137290i	0.505736	−	0.862688i	$-0.331221\pi$
$353$	9.62659	+	2.57944i	0.512372	+	0.137290i	0.00663577	+	0.999978i	$0.497888\pi$
$354$		0			0
$355$	−3.69841	−	10.0212i	−0.196291	−	0.531872i
$356$		0			0
$357$	1.86416	−	3.61745i	0.0986615	−	0.191456i
$358$		0			0
$359$	10.0235	+	5.78705i	0.529019	+	0.305429i	0.740617	−	0.671928i	$-0.234533\pi$
$359$	10.0235	+	5.78705i	0.529019	+	0.305429i	−0.211598	+	0.977357i	$0.567867\pi$
$360$		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
$367$	−4.32083	+	16.1256i	−0.225545	+	0.841747i	0.756640	+	0.653832i	$0.226840\pi$
$367$	−4.32083	+	16.1256i	−0.225545	+	0.841747i	−0.982185	+	0.187915i	$0.939827\pi$
$368$		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
$373$	−3.07061	+	0.822767i	−0.158990	+	0.0426013i	−0.337436	−	0.941348i	$-0.609560\pi$
$373$	−3.07061	+	0.822767i	−0.158990	+	0.0426013i	0.178446	+	0.983950i	$0.442893\pi$
$374$		0			0
$375$	−2.32118	−	2.25954i	−0.119865	−	0.116682i
$376$		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
$383$	3.77704	+	14.0961i	0.192998	+	0.720278i	0.992776	+	0.119982i	$0.0382837\pi$
$383$	3.77704	+	14.0961i	0.192998	+	0.720278i	−0.799778	+	0.600296i	$0.795050\pi$
$384$		0			0
$385$	20.0327	−	26.5784i	1.02096	−	1.35456i
$386$		0			0
$387$	1.98174	+	7.39595i	0.100737	+	0.375957i
$388$		0			0
$389$	−5.36634	+	3.09826i	−0.272084	+	0.157088i	−0.629834	−	0.776729i	$-0.716877\pi$
$389$	−5.36634	+	3.09826i	−0.272084	+	0.157088i	0.357750	+	0.933817i	$0.383544\pi$
$390$		0			0
$391$		−	5.96659i		−	0.301744i
$392$		0			0
$393$	1.57658	+	1.57658i	0.0795282	+	0.0795282i
$394$		0			0
$395$	−2.36424	+	13.7691i	−0.118958	+	0.692798i
$396$		0			0
$397$	2.81652	−	0.754685i	0.141357	−	0.0378766i	−0.187447	−	0.982275i	$-0.560021\pi$
$397$	2.81652	−	0.754685i	0.141357	−	0.0378766i	0.328804	+	0.944398i	$0.393354\pi$
$398$		0			0
$399$	2.00641	−	2.20787i	0.100446	−	0.110532i
$400$		0			0
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	−0.501358	−	0.865240i	$-0.667166\pi$
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	0.999999	+	0.00156835i	$0.000499221\pi$
$402$		0			0
$403$	2.01381	−	7.51565i	0.100315	−	0.374381i
$404$		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	−0.881699	−	0.471812i	$-0.843600\pi$
$409$	−17.1791	−	29.7550i	−0.849451	−	1.47129i	0.0322484	−	0.999480i	$-0.489733\pi$
$410$		0			0
$411$	2.21707	+	1.28003i	0.109360	+	0.0631390i
$412$		0			0
$413$	−7.83843	−	12.1923i	−0.385704	−	0.599946i
$414$		0			0
$415$	16.2921	+	7.50836i	0.799748	+	0.368571i
$416$		0			0
$417$	3.09617	+	0.829616i	0.151620	+	0.0406265i
$418$		0			0
$419$	−31.1360			−1.52109			−0.760547	−	0.649283i	$-0.775069\pi$
$419$	−31.1360			−1.52109			−0.760547	+	0.649283i	$0.775069\pi$
$420$		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
$423$	−16.6062	−	4.44962i	−0.807421	−	0.216348i
$424$		0			0
$425$	−11.4332	−	23.9551i	−0.554590	−	1.16199i
$426$		0			0
$427$	10.8402	+	5.58621i	0.524594	+	0.270336i
$428$		0			0
$429$	2.85398	+	1.64775i	0.137792	+	0.0795540i
$430$		0			0
$431$	−7.37284	−	12.7701i	−0.355137	−	0.615116i	0.632004	−	0.774965i	$-0.282233\pi$
$431$	−7.37284	−	12.7701i	−0.355137	−	0.615116i	−0.987141	+	0.159849i	$0.948899\pi$
$432$		0			0
$433$	9.98256	−	9.98256i	0.479731	−	0.479731i	−0.425315	−	0.905046i	$-0.639837\pi$
$433$	9.98256	−	9.98256i	0.479731	−	0.479731i	0.905046	+	0.425315i	$0.139837\pi$
$434$		0			0
$435$	−2.03545	+	0.187281i	−0.0975922	+	0.00897944i
$436$		0			0
$437$	1.13210	−	4.22504i	0.0541555	−	0.202111i
$438$		0			0
$439$	19.2142	−	33.2800i	0.917046	−	1.58837i	0.113167	−	0.993576i	$-0.463900\pi$
$439$	19.2142	−	33.2800i	0.917046	−	1.58837i	0.803878	−	0.594794i	$-0.202766\pi$
$440$		0			0
$441$	−18.5706	−	8.47336i	−0.884314	−	0.403494i
$442$		0			0
$443$	5.54016	−	1.48448i	0.263221	−	0.0705299i	−0.124795	−	0.992183i	$-0.539827\pi$
$443$	5.54016	−	1.48448i	0.263221	−	0.0705299i	0.388016	+	0.921653i	$0.373161\pi$
$444$		0			0
$445$	26.2735	+	4.51132i	1.24548	+	0.213857i
$446$		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
$453$	1.00807	+	3.76217i	0.0473633	+	0.176762i
$454$		0			0
$455$	−11.0896	−	4.48188i	−0.519889	−	0.210114i
$456$		0			0
$457$	1.33183	+	4.97047i	0.0623006	+	0.232509i	0.990055	−	0.140683i	$-0.0449299\pi$
$457$	1.33183	+	4.97047i	0.0623006	+	0.232509i	−0.927754	+	0.373192i	$0.878263\pi$
$458$		0			0
$459$	7.88056	−	4.54984i	0.367833	−	0.212368i
$460$		0			0
$461$		−	29.4110i		−	1.36981i	−0.728634	−	0.684903i	$-0.759845\pi$
$461$		−	29.4110i		−	1.36981i	0.728634	−	0.684903i	$-0.240155\pi$
$462$		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
$465$	1.43925	+	2.03596i	0.0667436	+	0.0944156i
$466$		0			0
$467$	−16.0757	+	4.30747i	−0.743894	+	0.199326i	−0.610808	−	0.791779i	$-0.709155\pi$
$467$	−16.0757	+	4.30747i	−0.743894	+	0.199326i	−0.133086	+	0.991105i	$0.542489\pi$
$468$		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
$473$	3.82325	−	14.2686i	0.175793	−	0.656069i
$474$		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	$-0.0523128\pi$
$479$	7.69460	+	13.3274i	0.351575	+	0.608946i	−0.634950	+	0.772553i	$0.718979\pi$
$480$		0			0
$481$	−8.82459	−	5.09488i	−0.402367	−	0.232306i
$482$		0			0
$483$	0.860583	−	0.0411396i	0.0391579	−	0.00187191i
$484$		0			0
$485$	−8.77662	+	19.0441i	−0.398526	+	0.864747i
$486$		0			0
$487$	−34.7656	−	9.31541i	−1.57538	−	0.422122i	−0.637888	−	0.770129i	$-0.720192\pi$
$487$	−34.7656	−	9.31541i	−1.57538	−	0.422122i	−0.937492	+	0.348007i	$0.886858\pi$
$488$		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
$493$	−16.1784	−	4.33499i	−0.728639	−	0.195238i
$494$		0			0
$495$	34.4139	−	12.7007i	1.54679	−	0.570854i
$496$		0			0
$497$	12.6246	−	0.603509i	0.566290	−	0.0270711i
$498$		0			0
$499$	−27.3534	−	15.7925i	−1.22451	−	0.706969i	−0.258630	−	0.965976i	$-0.583271\pi$
$499$	−27.3534	−	15.7925i	−1.22451	−	0.706969i	−0.965875	+	0.259008i	$0.916604\pi$
$500$		0			0
$501$	−0.964305	−	1.67023i	−0.0430820	−	0.0746202i
$502$		0			0
$503$	16.9777	−	16.9777i	0.756997	−	0.756997i	−0.218778	−	0.975775i	$-0.570207\pi$
$503$	16.9777	−	16.9777i	0.756997	−	0.756997i	0.975775	+	0.218778i	$0.0702070\pi$
$504$		0			0
$505$	27.6803	+	23.0157i	1.23176	+	1.02419i
$506$		0			0
$507$	−0.668334	+	2.49426i	−0.0296817	+	0.110774i
$508$		0			0
$509$	−10.7571	+	18.6318i	−0.476799	+	0.825840i	−0.999647	−	0.0265865i	$-0.991536\pi$
$509$	−10.7571	+	18.6318i	−0.476799	+	0.825840i	0.522848	+	0.852426i	$0.324870\pi$
$510$		0			0
$511$	−14.5099	−	3.15388i	−0.641879	−	0.139519i
$512$		0			0
$513$	6.44363	−	1.72657i	0.284493	−	0.0762297i
$514$		0			0
$515$	35.9147	−	25.3886i	1.58259	−	1.11875i
$516$		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	−0.227350	−	0.973813i	$-0.573006\pi$
$521$	11.4657	−	6.61973i	0.502322	−	0.290016i	0.729672	+	0.683798i	$0.239673\pi$
$522$		0			0
$523$	6.97006	+	26.0126i	0.304779	+	1.13745i	0.933135	+	0.359526i	$0.117062\pi$
$523$	6.97006	+	26.0126i	0.304779	+	1.13745i	−0.628356	+	0.777926i	$0.716272\pi$
$524$		0			0
$525$	3.37630	−	1.81422i	0.147354	−	0.0791789i
$526$		0			0
$527$	5.28779	+	19.7343i	0.230340	+	0.859640i
$528$		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
$535$	5.11439	−	3.61543i	0.221114	−	0.156309i
$536$		0			0
$537$	0.617477	−	0.165453i	0.0266461	−	0.00713980i
$538$		0			0
$539$	22.8536	+	32.0706i	0.984374	+	1.38138i
$540$		0			0
$541$	5.66491	−	9.81190i	0.243553	−	0.421847i	−0.718171	−	0.695867i	$-0.755020\pi$
$541$	5.66491	−	9.81190i	0.243553	−	0.421847i	0.961724	+	0.274020i	$0.0883536\pi$
$542$		0			0
$543$	0.308857	−	1.15267i	0.0132543	−	0.0494658i
$544$		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
$553$	−14.6939	−	7.57212i	−0.624850	−	0.321999i
$554$		0			0
$555$	3.06330	−	1.13053i	0.130030	−	0.0479885i
$556$		0			0
$557$	25.5003	+	6.83277i	1.08048	+	0.289514i	0.754793	−	0.655963i	$-0.227737\pi$
$557$	25.5003	+	6.83277i	1.08048	+	0.289514i	0.325688	+	0.945477i	$0.394404\pi$
$558$		0			0
$559$	−5.30873			−0.224535
$560$		0			0
$561$	−8.65318			−0.365337
$562$		0			0
$563$	−19.5055	−	5.22648i	−0.822058	−	0.220270i	−0.176812	−	0.984245i	$-0.556578\pi$
$563$	−19.5055	−	5.22648i	−0.822058	−	0.220270i	−0.645246	+	0.763975i	$0.723245\pi$
$564$		0			0
$565$	17.9764	−	39.0064i	0.756274	−	1.64101i
$566$		0			0
$567$	−11.8061	−	18.3638i	−0.495808	−	0.771208i
$568$		0			0
$569$	−21.4890	−	12.4067i	−0.900867	−	0.520116i	−0.0233856	−	0.999727i	$-0.507445\pi$
$569$	−21.4890	−	12.4067i	−0.900867	−	0.520116i	−0.877481	+	0.479611i	$0.840778\pi$
$570$		0			0
$571$	2.29029	+	3.96690i	0.0958458	+	0.166010i	0.909961	−	0.414693i	$-0.136111\pi$
$571$	2.29029	+	3.96690i	0.0958458	+	0.166010i	−0.814116	+	0.580703i	$0.802778\pi$
$572$		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
$577$	−5.11957	+	19.1065i	−0.213131	+	0.795414i	0.773686	+	0.633570i	$0.218411\pi$
$577$	−5.11957	+	19.1065i	−0.213131	+	0.795414i	−0.986816	+	0.161845i	$0.948256\pi$
$578$		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
$583$	−7.51596	+	2.01390i	−0.311279	+	0.0834071i
$584$		0			0
$585$	−7.60984	−	10.7649i	−0.314628	−	0.445074i
$586$		0			0
$587$	19.3782	+	19.3782i	0.799824	+	0.799824i	0.983068	−	0.183244i	$-0.0586597\pi$
$587$	19.3782	+	19.3782i	0.799824	+	0.799824i	−0.183244	+	0.983068i	$0.558660\pi$
$588$		0			0
$589$			14.9775i			0.617136i
$590$		0			0
$591$	5.07919	−	2.93247i	0.208930	−	0.120626i
$592$		0			0
$593$	0.837988	+	3.12741i	0.0344121	+	0.128428i	0.980995	−	0.194033i	$-0.0621568\pi$
$593$	0.837988	+	3.12741i	0.0344121	+	0.128428i	−0.946583	+	0.322460i	$0.895490\pi$
$594$		0			0
$595$	31.1017	−	4.36767i	1.27504	−	0.179057i
$596$		0			0
$597$	−0.564900	−	2.10824i	−0.0231198	−	0.0862844i
$598$		0			0
$599$	6.75802	−	3.90174i	0.276125	−	0.159421i	−0.355543	−	0.934660i	$-0.615704\pi$
$599$	6.75802	−	3.90174i	0.276125	−	0.159421i	0.631668	+	0.775239i	$0.282371\pi$
$600$		0			0
$601$		−	31.7170i		−	1.29377i	−0.762590	−	0.646883i	$-0.776072\pi$
$601$		−	31.7170i		−	1.29377i	0.762590	−	0.646883i	$-0.223928\pi$
$602$		0			0
$603$	−1.74233	−	1.74233i	−0.0709530	−	0.0709530i
$604$		0			0
$605$	−45.5070	−	7.81383i	−1.85012	−	0.317677i
$606$		0			0
$607$	−0.743495	+	0.199219i	−0.0301775	+	0.00808604i	−0.273876	−	0.961765i	$-0.588306\pi$
$607$	−0.743495	+	0.199219i	−0.0301775	+	0.00808604i	0.243699	+	0.969851i	$0.421639\pi$
$608$		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
$613$	9.05898	−	33.8086i	0.365889	−	1.36552i	−0.500323	−	0.865839i	$-0.666786\pi$
$613$	9.05898	−	33.8086i	0.365889	−	1.36552i	0.866212	−	0.499676i	$-0.166548\pi$
$614$		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	−0.860942	−	0.508703i	$-0.830125\pi$
$619$	−21.6707	−	37.5348i	−0.871021	−	1.50865i	−0.0100783	−	0.999949i	$-0.503208\pi$
$620$		0			0
$621$	1.66841	+	0.963256i	0.0669509	+	0.0386541i
$622$		0			0
$623$	−14.4487	+	28.0382i	−0.578876	+	1.12333i
$624$		0			0
$625$	3.89884	−	24.6941i	0.155953	−	0.987764i
$626$		0			0
$627$	−6.12745	−	1.64184i	−0.244707	−	0.0655690i
$628$		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
$633$	−5.47879	−	1.46804i	−0.217762	−	0.0583492i
$634$		0			0
$635$	−13.3112	−	6.13457i	−0.528237	−	0.243443i
$636$		0			0
$637$	9.00710	−	10.9163i	0.356874	−	0.432520i
$638$		0			0
$639$	12.0640	+	6.96513i	0.477243	+	0.275536i
$640$		0			0
$641$	−12.1657	−	21.0717i	−0.480518	−	0.832281i	0.519233	−	0.854633i	$-0.326218\pi$
$641$	−12.1657	−	21.0717i	−0.480518	−	0.832281i	−0.999750	+	0.0223521i	$0.992885\pi$
$642$		0			0
$643$	−6.21713	+	6.21713i	−0.245180	+	0.245180i	−0.818989	−	0.573809i	$-0.805465\pi$
$643$	−6.21713	+	6.21713i	−0.245180	+	0.245180i	0.573809	+	0.818989i	$0.305465\pi$
$644$		0			0
$645$	1.08763	−	1.30805i	0.0428252	−	0.0515045i
$646$		0			0
$647$	−5.33869	+	19.9243i	−0.209886	+	0.783304i	0.778019	+	0.628241i	$0.216225\pi$
$647$	−5.33869	+	19.9243i	−0.209886	+	0.783304i	−0.987905	+	0.155063i	$0.950442\pi$
$648$		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
$653$	−25.2490	+	6.76544i	−0.988069	+	0.264752i	−0.716439	−	0.697650i	$-0.754229\pi$
$653$	−25.2490	+	6.76544i	−0.988069	+	0.264752i	−0.271630	+	0.962402i	$0.587563\pi$
$654$		0			0
$655$	−2.91199	+	16.9591i	−0.113781	+	0.662649i
$656$		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	−0.166583	−	0.986027i	$-0.553273\pi$
$661$	15.5301	−	8.96630i	0.604050	−	0.348749i	0.770633	+	0.637279i	$0.219940\pi$
$662$		0			0
$663$	0.804871	+	3.00382i	0.0312586	+	0.116659i
$664$		0			0
$665$	22.8523	+	2.80839i	0.886174	+	0.108905i
$666$		0			0
$667$	−0.917769	−	3.42516i	−0.0355362	−	0.132623i
$668$		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
$675$	8.54424	+	0.670353i	0.328868	+	0.0258019i
$676$		0			0
$677$	−17.8506	+	4.78306i	−0.686055	+	0.183828i	−0.584976	−	0.811051i	$-0.698896\pi$
$677$	−17.8506	+	4.78306i	−0.686055	+	0.183828i	−0.101079	+	0.994878i	$0.532229\pi$
$678$		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
$683$	6.93661	−	25.8878i	0.265422	−	0.990569i	−0.696569	−	0.717489i	$-0.745291\pi$
$683$	6.93661	−	25.8878i	0.265422	−	0.990569i	0.961992	−	0.273079i	$-0.0880421\pi$
$684$		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	−0.0622976	−	0.998058i	$-0.519843\pi$
$691$	−25.1773	−	14.5361i	−0.957790	−	0.552980i	−0.895492	+	0.445077i	$0.853176\pi$
$692$		0			0
$693$	2.07251	+	43.3541i	0.0787281	+	1.64689i
$694$		0			0
$695$	8.56502	+	23.2078i	0.324890	+	0.880323i
$696$		0			0
$697$	−36.9743	−	9.90723i	−1.40050	−	0.375263i
$698$		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
$703$	18.9462	+	5.07663i	0.714571	+	0.191469i
$704$		0			0
$705$	1.32247	+	3.58337i	0.0498071	+	0.134957i
$706$		0			0
$707$	−35.8289	+	23.0343i	−1.34748	+	0.866295i
$708$		0			0
$709$	27.1994	+	15.7036i	1.02150	+	0.589760i	0.914537	−	0.404503i	$-0.132555\pi$
$709$	27.1994	+	15.7036i	1.02150	+	0.589760i	0.106958	+	0.994263i	$0.465889\pi$
$710$		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
$717$	−1.47445	+	5.50271i	−0.0550642	+	0.205502i
$718$		0			0
$719$	−5.40214	+	9.35678i	−0.201466	+	0.348949i	−0.949001	−	0.315273i	$-0.897904\pi$
$719$	−5.40214	+	9.35678i	−0.201466	+	0.348949i	0.747535	+	0.664222i	$0.231237\pi$
$720$		0			0
$721$	15.8540	+	49.5669i	0.590434	+	1.84597i
$722$		0			0
$723$	−1.64704	+	0.441322i	−0.0612539	+	0.0164129i
$724$		0			0
$725$	−10.2480	−	11.9930i	−0.380602	−	0.445408i
$726$		0			0
$727$	33.6108	+	33.6108i	1.24656	+	1.24656i	0.957231	+	0.289326i	$0.0934311\pi$
$727$	33.6108	+	33.6108i	1.24656	+	1.24656i	0.289326	+	0.957231i	$0.406569\pi$
$728$		0			0
$729$		−	22.5720i		−	0.835998i
$730$		0			0
$731$	12.0719	−	6.96972i	0.446496	−	0.257785i
$732$		0			0
$733$	6.66658	+	24.8800i	0.246236	+	0.918964i	0.972758	+	0.231822i	$0.0744686\pi$
$733$	6.66658	+	24.8800i	0.246236	+	0.918964i	−0.726523	+	0.687143i	$0.758865\pi$
$734$		0			0
$735$	0.844410	+	4.45579i	0.0311465	+	0.164354i
$736$		0			0
$737$	1.23034	+	4.59170i	0.0453203	+	0.169138i
$738$		0			0
$739$	10.4948	−	6.05920i	0.386059	−	0.222891i	−0.294392	−	0.955685i	$-0.595117\pi$
$739$	10.4948	−	6.05920i	0.386059	−	0.222891i	0.680451	+	0.732793i	$0.261784\pi$
$740$		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
$745$	−1.91053	+	11.1267i	−0.0699964	+	0.407652i
$746$		0			0
$747$	−22.5971	+	6.05487i	−0.826784	+	0.221536i
$748$		0			0
$749$	2.25767	+	7.05851i	0.0824934	+	0.257912i
$750$		0			0
$751$	6.98887	−	12.1051i	0.255028	−	0.441721i	−0.709875	−	0.704327i	$-0.751249\pi$
$751$	6.98887	−	12.1051i	0.255028	−	0.441721i	0.964903	+	0.262607i	$0.0845821\pi$
$752$		0			0
$753$	−0.532387	+	1.98690i	−0.0194013	+	0.0724065i
$754$		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	0.802289	−	0.596936i	$-0.203615\pi$
$761$	18.9372	+	10.9334i	0.686471	+	0.396334i	−0.115817	+	0.993271i	$0.536949\pi$
$762$		0			0
$763$	−13.1546	+	8.45710i	−0.476230	+	0.306168i
$764$		0			0
$765$	31.4376	+	14.4883i	1.13663	+	0.523826i
$766$		0			0
$767$	10.6989	+	2.86675i	0.386313	+	0.103512i
$768$		0			0
$769$	−31.0506			−1.11971			−0.559857	−	0.828589i	$-0.689144\pi$
$769$	−31.0506			−1.11971			−0.559857	+	0.828589i	$0.689144\pi$
$770$		0			0
$771$	−2.86459			−0.103166
$772$		0			0
$773$	−5.86173	−	1.57065i	−0.210832	−	0.0564922i	0.151857	−	0.988402i	$-0.451475\pi$
$773$	−5.86173	−	1.57065i	−0.210832	−	0.0564922i	−0.362689	+	0.931910i	$0.618141\pi$
$774$		0			0
$775$	−6.41880	+	18.1402i	−0.230570	+	0.651614i
$776$		0			0
$777$	0.184481	+	3.85909i	0.00661822	+	0.138444i
$778$		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
$787$	5.78752	−	21.5993i	0.206303	−	0.769932i	−0.782746	−	0.622342i	$-0.786182\pi$
$787$	5.78752	−	21.5993i	0.206303	−	0.769932i	0.989049	−	0.147591i	$-0.0471518\pi$
$788$		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
$793$	−9.00138	+	2.41191i	−0.319648	+	0.0856495i
$794$		0			0
$795$	−0.883159	−	0.151644i	−0.0313224	−	0.00537825i
$796$		0			0
$797$	−16.5528	−	16.5528i	−0.586330	−	0.586330i	0.350305	−	0.936636i	$-0.386078\pi$
$797$	−16.5528	−	16.5528i	−0.586330	−	0.586330i	−0.936636	+	0.350305i	$0.886078\pi$
$798$		0			0
$799$			31.2984i			1.10726i
$800$		0			0
$801$	−30.1070	+	17.3823i	−1.06378	+	0.614174i
$802$		0			0
$803$	8.17177	+	30.4975i	0.288376	+	1.07623i
$804$		0			0
$805$	4.09310	+	5.24008i	0.144263	+	0.184689i
$806$		0			0
$807$	1.98737	+	7.41697i	0.0699588	+	0.261090i
$808$		0			0
$809$	−2.84139	+	1.64048i	−0.0998980	+	0.0576762i	−0.549117	−	0.835746i	$-0.685036\pi$
$809$	−2.84139	+	1.64048i	−0.0998980	+	0.0576762i	0.449219	+	0.893422i	$0.351702\pi$
$810$		0			0
$811$		−	17.8693i		−	0.627476i	−0.949510	−	0.313738i	$-0.898419\pi$
$811$		−	17.8693i		−	0.627476i	0.949510	−	0.313738i	$-0.101581\pi$
$812$		0			0
$813$	2.62176	+	2.62176i	0.0919491	+	0.0919491i
$814$		0			0
$815$	−17.0911	−	24.1771i	−0.598674	−	0.846886i
$816$		0			0
$817$	9.87074	−	2.64486i	0.345333	−	0.0925318i
$818$		0			0
$819$	14.8569	−	4.75200i	0.519143	−	0.166048i
$820$		0			0
$821$	5.90837	−	10.2336i	0.206204	−	0.357155i	−0.744312	−	0.667832i	$-0.767222\pi$
$821$	5.90837	−	10.2336i	0.206204	−	0.357155i	0.950516	+	0.310677i	$0.100556\pi$
$822$		0			0
$823$	−9.13692	+	34.0995i	−0.318493	+	1.18863i	0.602200	+	0.798345i	$0.294291\pi$
$823$	−9.13692	+	34.0995i	−0.318493	+	1.18863i	−0.920693	+	0.390287i	$0.872376\pi$
$824$		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	−0.992756	−	0.120144i	$-0.961664\pi$
$829$	−17.2877	−	29.9431i	−0.600426	−	1.03997i	0.392330	−	0.919824i	$-0.371669\pi$
$830$		0			0
$831$	−5.04433	−	2.91234i	−0.174986	−	0.101028i
$832$		0			0
$833$	−6.15011	+	36.6487i	−0.213089	+	1.26980i
$834$		0			0
$835$	6.22977	−	13.5177i	0.215590	−	0.467801i
$836$		0			0
$837$	−6.37187	−	1.70734i	−0.220244	−	0.0590142i
$838$		0			0
$839$	−50.1328			−1.73078			−0.865388	−	0.501102i	$-0.832928\pi$
$839$	−50.1328			−1.73078			−0.865388	+	0.501102i	$0.832928\pi$
$840$		0			0
$841$	19.0459			0.656754
$842$		0			0
$843$	−3.96003	−	1.06109i	−0.136391	−	0.0365458i
$844$		0			0
$845$	−18.6961	+	6.89993i	−0.643164	+	0.237365i
$846$		0			0
$847$	25.0259	−	48.5636i	0.859901	−	1.66866i
$848$		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	−0.665278	−	0.746596i	$-0.731687\pi$
$853$	2.37500	−	2.37500i	0.0813183	−	0.0813183i	0.746596	+	0.665278i	$0.231687\pi$
$854$		0			0
$855$	19.5125	+	16.2243i	0.667312	+	0.554860i
$856$		0			0
$857$	−10.8545	+	40.5097i	−0.370784	+	1.38378i	0.488624	+	0.872494i	$0.337499\pi$
$857$	−10.8545	+	40.5097i	−0.370784	+	1.38378i	−0.859408	+	0.511290i	$0.829168\pi$
$858$		0			0
$859$	−1.17847	+	2.04117i	−0.0402090	+	0.0696440i	−0.885430	−	0.464774i	$-0.846136\pi$
$859$	−1.17847	+	2.04117i	−0.0402090	+	0.0696440i	0.845221	+	0.534418i	$0.179469\pi$
$860$		0			0
$861$	1.17402	−	5.40125i	0.0400105	−	0.184074i
$862$		0			0
$863$	46.7022	−	12.5138i	1.58976	−	0.425975i	0.647831	−	0.761784i	$-0.275676\pi$
$863$	46.7022	−	12.5138i	1.58976	−	0.425975i	0.941930	+	0.335808i	$0.109009\pi$
$864$		0			0
$865$	12.8810	−	9.10577i	0.437968	−	0.309605i
$866$		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
$873$	−7.07763	−	26.4141i	−0.239541	−	0.893980i
$874$		0			0
$875$	26.4743	+	13.1951i	0.894995	+	0.446076i
$876$		0			0
$877$	−3.56681	−	13.3115i	−0.120443	−	0.449498i	0.879194	−	0.476465i	$-0.158082\pi$
$877$	−3.56681	−	13.3115i	−0.120443	−	0.449498i	−0.999636	+	0.0269665i	$0.991415\pi$
$878$		0			0
$879$	−6.07477	+	3.50727i	−0.204897	+	0.118297i
$880$		0			0
$881$			3.32542i			0.112036i	0.998430	+	0.0560181i	$0.0178405\pi$
$881$			3.32542i			0.112036i	−0.998430	+	0.0560181i	$0.982160\pi$
$882$		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
$885$	−2.89828	+	2.04883i	−0.0974247	+	0.0688708i
$886$		0			0
$887$	34.6001	−	9.27107i	1.16176	−	0.311292i	0.374090	−	0.927392i	$-0.377955\pi$
$887$	34.6001	−	9.27107i	1.16176	−	0.311292i	0.787668	+	0.616101i	$0.211289\pi$
$888$		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
$893$	−5.93852	+	22.1628i	−0.198725	+	0.741651i
$894$		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
$903$	1.08850	+	1.69312i	0.0362232	+	0.0563435i
$904$		0			0
$905$	8.64001	−	3.18866i	0.287204	−	0.105995i
$906$		0			0
$907$	−16.6696	−	4.46661i	−0.553506	−	0.148312i	−0.0287849	−	0.999586i	$-0.509164\pi$
$907$	−16.6696	−	4.46661i	−0.553506	−	0.148312i	−0.524721	+	0.851274i	$0.675830\pi$
$908$		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
$913$	43.5952	+	11.6813i	1.44279	+	0.386594i
$914$		0			0
$915$	1.24987	−	2.71205i	0.0413194	−	0.0896575i
$916$		0			0
$917$	−18.0982	−	9.32645i	−0.597657	−	0.307986i
$918$		0			0
$919$	5.37964	+	3.10593i	0.177458	+	0.102455i	0.586098	−	0.810240i	$-0.300663\pi$
$919$	5.37964	+	3.10593i	0.177458	+	0.102455i	−0.408640	+	0.912696i	$0.633997\pi$
$920$		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
$927$	−14.8452	+	55.4029i	−0.487579	+	1.81967i
$928$		0			0
$929$	−0.0947297	+	0.164077i	−0.00310798	+	0.00538318i	−0.867575	−	0.497306i	$-0.834323\pi$
$929$	−0.0947297	+	0.164077i	−0.00310798	+	0.00538318i	0.864467	+	0.502689i	$0.167656\pi$
$930$		0			0
$931$	−11.3087	+	24.7846i	−0.370627	+	0.812281i
$932$		0			0
$933$	3.07355	−	0.823556i	0.100624	−	0.0269620i
$934$		0			0
$935$	−38.5493	−	54.5319i	−1.26070	−	1.78338i
$936$		0			0
$937$	34.2022	+	34.2022i	1.11734	+	1.11734i	0.992131	+	0.125208i	$0.0399598\pi$
$937$	34.2022	+	34.2022i	1.11734	+	1.11734i	0.125208	+	0.992131i	$0.460040\pi$
$938$		0			0
$939$			8.52144i			0.278087i
$940$		0			0
$941$	−16.3826	+	9.45851i	−0.534058	+	0.308339i	−0.742667	−	0.669660i	$-0.766440\pi$
$941$	−16.3826	+	9.45851i	−0.534058	+	0.308339i	0.208609	+	0.977999i	$0.433106\pi$
$942$		0			0
$943$	−2.09748	−	7.82790i	−0.0683033	−	0.254911i
$944$		0			0
$945$	−3.79979	+	9.40193i	−0.123607	+	0.305845i
$946$		0			0
$947$	−12.2033	−	45.5435i	−0.396555	−	1.47996i	−0.819115	−	0.573629i	$-0.805535\pi$
$947$	−12.2033	−	45.5435i	−0.396555	−	1.47996i	0.422560	−	0.906335i	$-0.361131\pi$
$948$		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
$955$	−37.9108	−	6.50952i	−1.22677	−	0.210643i
$956$		0			0
$957$	−4.96741	+	1.33101i	−0.160574	+	0.0430256i
$958$		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
$963$	−2.11401	+	7.88958i	−0.0681229	+	0.254238i
$964$		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	0.875428	−	0.483348i	$-0.160580\pi$
$971$	27.8750	+	16.0936i	0.894550	+	0.516469i	0.0191221	+	0.999817i	$0.493913\pi$
$972$		0			0
$973$	−29.2369	+	1.39765i	−0.937291	+	0.0448065i
$974$		0			0
$975$	−0.977025	+	2.76117i	−0.0312899	+	0.0884282i
$976$		0			0
$977$	22.4848	+	6.02479i	0.719353	+	0.192750i	0.599883	−	0.800088i	$-0.295214\pi$
$977$	22.4848	+	6.02479i	0.719353	+	0.192750i	0.119470	+	0.992838i	$0.461881\pi$
$978$		0			0
$979$	67.0692			2.14354
$980$		0			0
$981$	−17.2364			−0.550314
$982$		0			0
$983$	−55.0964	−	14.7630i	−1.75730	−	0.470868i	−0.771143	−	0.636662i	$-0.780315\pi$
$983$	−55.0964	−	14.7630i	−1.75730	−	0.470868i	−0.986160	+	0.165793i	$0.946981\pi$
$984$		0			0
$985$	41.1078	+	18.9449i	1.30980	+	0.603634i
$986$		0			0
$987$	−4.51427	+	0.215802i	−0.143691	+	0.00686904i
$988$		0			0
$989$	2.55577	+	1.47557i	0.0812687	+	0.0469205i
$990$		0			0
$991$	−28.7703	−	49.8316i	−0.913918	−	1.58295i	−0.808478	−	0.588526i	$-0.799708\pi$
$991$	−28.7703	−	49.8316i	−0.913918	−	1.58295i	−0.105440	−	0.994426i	$-0.533625\pi$
$992$		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
$997$	6.27762	−	23.4284i	0.198814	−	0.741985i	−0.792432	−	0.609960i	$-0.791185\pi$
$997$	6.27762	−	23.4284i	0.198814	−	0.741985i	0.991246	−	0.132025i	$-0.0421479\pi$
$998$		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.33.3		16
4.3	odd	2		70.2.k.a.33.3	yes	16
5.2	odd	4	inner	560.2.ci.c.257.3		16
7.3	odd	6	inner	560.2.ci.c.353.3		16
12.11	even	2		630.2.bv.c.523.1		16
20.3	even	4		350.2.o.c.257.4		16
20.7	even	4		70.2.k.a.47.1	yes	16
20.19	odd	2		350.2.o.c.243.2		16
28.3	even	6		70.2.k.a.3.1	✓	16
28.11	odd	6		490.2.l.c.423.2		16
28.19	even	6		490.2.g.c.293.6		16
28.23	odd	6		490.2.g.c.293.7		16
28.27	even	2		490.2.l.c.313.4		16
35.17	even	12	inner	560.2.ci.c.17.3		16
60.47	odd	4		630.2.bv.c.397.3		16
84.59	odd	6		630.2.bv.c.73.3		16
140.3	odd	12		350.2.o.c.157.2		16
140.27	odd	4		490.2.l.c.117.2		16
140.47	odd	12		490.2.g.c.97.7		16
140.59	even	6		350.2.o.c.143.4		16
140.67	even	12		490.2.l.c.227.4		16
140.87	odd	12		70.2.k.a.17.3	yes	16
140.107	even	12		490.2.g.c.97.6		16
420.227	even	12		630.2.bv.c.577.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.1	✓	16	28.3	even	6
70.2.k.a.17.3	yes	16	140.87	odd	12
70.2.k.a.33.3	yes	16	4.3	odd	2
70.2.k.a.47.1	yes	16	20.7	even	4
350.2.o.c.143.4		16	140.59	even	6
350.2.o.c.157.2		16	140.3	odd	12
350.2.o.c.243.2		16	20.19	odd	2
350.2.o.c.257.4		16	20.3	even	4
490.2.g.c.97.6		16	140.107	even	12
490.2.g.c.97.7		16	140.47	odd	12
490.2.g.c.293.6		16	28.19	even	6
490.2.g.c.293.7		16	28.23	odd	6
490.2.l.c.117.2		16	140.27	odd	4
490.2.l.c.227.4		16	140.67	even	12
490.2.l.c.313.4		16	28.27	even	2
490.2.l.c.423.2		16	28.11	odd	6
560.2.ci.c.17.3		16	35.17	even	12	inner
560.2.ci.c.33.3		16	1.1	even	1	trivial
560.2.ci.c.257.3		16	5.2	odd	4	inner
560.2.ci.c.353.3		16	7.3	odd	6	inner
630.2.bv.c.73.3		16	84.59	odd	6
630.2.bv.c.397.3		16	60.47	odd	4
630.2.bv.c.523.1		16	12.11	even	2
630.2.bv.c.577.1		16	420.227	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.279864 + 0.0749894i) q^{3} +(0.774197 + 2.09777i) q^{5} +(-2.64273 + 0.126334i) q^{7} +(-2.52538 - 1.45803i) q^{9} +O(q^{10})\)	\(q+(0.279864 + 0.0749894i) q^{3} +(0.774197 + 2.09777i) q^{5} +(-2.64273 + 0.126334i) q^{7} +(-2.52538 - 1.45803i) q^{9} +(2.81288 + 4.87205i) q^{11} +(1.42962 - 1.42962i) q^{13} +(0.0593598 + 0.645146i) q^{15} +(-1.37400 + 5.12784i) q^{17} +(-1.94590 + 3.37040i) q^{19} +(-0.749081 - 0.162821i) q^{21} +(-1.08562 + 0.290892i) q^{23} +(-3.80124 + 3.24817i) q^{25} +(-1.21205 - 1.21205i) q^{27} +3.15502i q^{29} +(3.33287 - 1.92423i) q^{31} +(0.421872 + 1.57445i) q^{33} +(-2.31101 - 5.44603i) q^{35} +(-1.30444 - 4.86824i) q^{37} +(0.507306 - 0.292893i) q^{39} +7.21050i q^{41} +(-1.85669 - 1.85669i) q^{43} +(1.10346 - 6.42644i) q^{45} +(5.69475 - 1.52590i) q^{47} +(6.96808 - 0.667734i) q^{49} +(-0.769067 + 1.33206i) q^{51} +(-0.357978 + 1.33599i) q^{53} +(-8.04270 + 9.67269i) q^{55} +(-0.797333 + 0.797333i) q^{57} +(2.73923 + 4.74448i) q^{59} +(-3.99172 - 2.30462i) q^{61} +(6.85809 + 3.53413i) q^{63} +(4.10581 + 1.89220i) q^{65} +(0.816193 + 0.218698i) q^{67} -0.325641 q^{69} -4.77710 q^{71} +(5.42104 + 1.45256i) q^{73} +(-1.30741 + 0.623993i) q^{75} +(-8.04920 - 12.5202i) q^{77} +(5.41079 + 3.12392i) q^{79} +(4.12576 + 7.14603i) q^{81} +(5.67281 - 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +(-0.236593 + 0.882976i) q^{87} +(5.96090 - 10.3246i) q^{89} +(-3.59749 + 3.95871i) q^{91} +(1.07705 - 0.288594i) q^{93} +(-8.57682 - 1.47269i) q^{95} +(6.63103 + 6.63103i) q^{97} -16.4050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) \) 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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