LMFDB - Embedded newform 560.2.ci.c.17.3

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			17.3
Root			$-1.01089 + 0.750919i$ of defining polynomial
Character	$\chi$	$=$	560.17
Dual form			560.2.ci.c.33.3

$q$-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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

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

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	−0.177122	−	0.984189i	$-0.556679\pi$
$3$	0.279864	−	0.0749894i	0.161580	−	0.0432952i	0.338702	+	0.940894i	$0.390012\pi$
$4$		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	−0.0347729	−	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	$-0.159542\pi$
$13$	1.42962	+	1.42962i	0.396505	+	0.396505i	−0.480493	+	0.876998i	$0.659542\pi$
$14$		0			0
$15$	0.0593598	−	0.645146i	0.0153266	−	0.166576i
$16$		0			0
$17$	−1.37400	−	5.12784i	−0.333244	−	1.24368i	−0.905760	−	0.423790i	$-0.860699\pi$
$17$	−1.37400	−	5.12784i	−0.333244	−	1.24368i	0.572516	−	0.819893i	$-0.305967\pi$
$18$		0			0
$19$	−1.94590	−	3.37040i	−0.446420	−	0.773223i	0.551729	−	0.834023i	$-0.313968\pi$
$19$	−1.94590	−	3.37040i	−0.446420	−	0.773223i	−0.998150	+	0.0608002i	$0.980635\pi$
$20$		0			0
$21$	−0.749081	+	0.162821i	−0.163463	+	0.0355304i
$22$		0			0
$23$	−1.08562	−	0.290892i	−0.226368	−	0.0606552i	0.143852	−	0.989599i	$-0.454051\pi$
$23$	−1.08562	−	0.290892i	−0.226368	−	0.0606552i	−0.370220	+	0.928944i	$0.620718\pi$
$24$		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	$-0.905368\pi$
$29$		−	3.15502i		−	0.585872i	0.956132	−	0.292936i	$-0.0946322\pi$
$30$		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
$33$	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	0.771911	+	0.635731i	$0.219301\pi$
$37$	−1.30444	+	4.86824i	−0.214449	+	0.800334i	−0.986360	+	0.164603i	$0.947366\pi$
$38$		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	−0.834361	−	0.551218i	$-0.814163\pi$
$43$	−1.85669	+	1.85669i	−0.283143	+	0.283143i	0.551218	+	0.834361i	$0.314163\pi$
$44$		0			0
$45$	1.10346	+	6.42644i	0.164494	+	0.957998i
$46$		0			0
$47$	5.69475	+	1.52590i	0.830665	+	0.222576i	0.649004	−	0.760785i	$-0.275186\pi$
$47$	5.69475	+	1.52590i	0.830665	+	0.222576i	0.181661	+	0.983361i	$0.441853\pi$
$48$		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	0.936972	−	0.349405i	$-0.113616\pi$
$53$	−0.357978	−	1.33599i	−0.0491720	−	0.183512i	−0.986144	+	0.165892i	$0.946950\pi$
$54$		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	−0.630776	−	0.775965i	$-0.717263\pi$
$59$	2.73923	−	4.74448i	0.356617	−	0.617679i	0.987393	+	0.158286i	$0.0505968\pi$
$60$		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
$63$	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	−0.208617	−	0.977997i	$-0.566896\pi$
$67$	0.816193	−	0.218698i	0.0997138	−	0.0267182i	0.308331	+	0.951279i	$0.400230\pi$
$68$		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	0.0727807	−	0.997348i	$-0.476813\pi$
$73$	5.42104	−	1.45256i	0.634485	−	0.170010i	0.561704	+	0.827338i	$0.310146\pi$
$74$		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	−0.163719	−	0.986507i	$-0.552349\pi$
$79$	5.41079	−	3.12392i	0.608761	−	0.351469i	0.772481	+	0.635038i	$0.219016\pi$
$80$		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	$-0.104874\pi$
$83$	5.67281	+	5.67281i	0.622672	+	0.622672i	−0.323542	+	0.946214i	$0.604874\pi$
$84$		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	0.987172	+	0.159659i	$0.0510393\pi$
$89$	5.96090	+	10.3246i	0.631855	+	1.09440i	−0.355318	+	0.934746i	$0.615627\pi$
$90$		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	−0.285191	−	0.958471i	$-0.592057\pi$
$97$	6.63103	−	6.63103i	0.673279	−	0.673279i	0.958471	+	0.285191i	$0.0920572\pi$
$98$		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
$103$	−5.09084	+	18.9993i	−0.501616	+	1.87206i	−0.0123445	+	0.999924i	$0.503929\pi$
$103$	−5.09084	+	18.9993i	−0.501616	+	1.87206i	−0.489271	+	0.872132i	$0.662737\pi$
$104$		0			0
$105$	−0.238376	+	1.69745i	−0.0232631	+	0.165654i
$106$		0			0
$107$	−0.724955	+	2.70557i	−0.0700840	+	0.261557i	−0.992074	−	0.125657i	$-0.959896\pi$
$107$	−0.724955	+	2.70557i	−0.0700840	+	0.261557i	0.921990	+	0.387214i	$0.126563\pi$
$108$		0			0
$109$	5.11895	+	2.95543i	0.490306	+	0.283078i	0.724701	−	0.689063i	$-0.241978\pi$
$109$	5.11895	+	2.95543i	0.490306	+	0.283078i	−0.234395	+	0.972141i	$0.575311\pi$
$110$		0			0
$111$			1.46027i			0.138602i
$112$		0			0
$113$	−13.5818	+	13.5818i	−1.27767	+	1.27767i	−0.335697	+	0.941970i	$0.608972\pi$
$113$	−13.5818	+	13.5818i	−1.27767	+	1.27767i	−0.941970	+	0.335697i	$0.891028\pi$
$114$		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	0.470906	−	0.882184i	$-0.343927\pi$
$127$	−4.63487	−	4.63487i	−0.411278	−	0.411278i	−0.882184	+	0.470906i	$0.843927\pi$
$128$		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
$133$	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	0.124910	−	0.992168i	$-0.460136\pi$
$137$	8.53471	−	2.28687i	0.729170	−	0.195380i	0.604259	+	0.796788i	$0.293469\pi$
$138$		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	−0.310089	−	0.950708i	$-0.600359\pi$
$149$	4.37243	−	2.52443i	0.358204	−	0.206809i	0.668293	+	0.743899i	$0.267025\pi$
$150$		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
$157$	−0.285443	−	1.06529i	−0.0227808	−	0.0850191i	0.953600	−	0.301078i	$-0.0973464\pi$
$157$	−0.285443	−	1.06529i	−0.0227808	−	0.0850191i	−0.976380	+	0.216059i	$0.930680\pi$
$158$		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	−0.279592	−	0.960119i	$-0.590199\pi$
$163$	−12.7899	−	3.42705i	−1.00179	−	0.268428i	−0.722193	+	0.691691i	$0.756866\pi$
$164$		0			0
$165$	−2.97621	−	2.10392i	−0.231698	−	0.163790i
$166$		0			0
$167$	−4.70680	+	4.70680i	−0.364223	+	0.364223i	−0.865365	−	0.501142i	$-0.832913\pi$
$167$	−4.70680	+	4.70680i	−0.364223	+	0.364223i	0.501142	+	0.865365i	$0.332913\pi$
$168$		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	0.861135	+	0.508376i	$0.169754\pi$
$173$	−1.82586	+	6.81421i	−0.138818	+	0.518075i	−0.999953	+	0.00969875i	$0.996913\pi$
$174$		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	0.569706	−	0.821849i	$-0.307057\pi$
$179$	1.91075	+	1.10317i	0.142816	+	0.0824550i	−0.426889	+	0.904304i	$0.640391\pi$
$180$		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
$185$	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	−0.989045	−	0.147613i	$-0.952841\pi$
$191$	−8.60117	−	14.8977i	−0.622359	−	1.07796i	0.366686	−	0.930345i	$-0.380492\pi$
$192$		0			0
$193$	−3.12327	−	11.6562i	−0.224818	−	0.839032i	−0.982477	−	0.186382i	$-0.940324\pi$
$193$	−3.12327	−	11.6562i	−0.224818	−	0.839032i	0.757659	−	0.652650i	$-0.226343\pi$
$194$		0			0
$195$	1.00718	−	0.837452i	0.0721254	−	0.0599712i
$196$		0			0
$197$	14.3135	+	14.3135i	1.01979	+	1.01979i	0.999800	+	0.0199932i	$0.00636444\pi$
$197$	14.3135	+	14.3135i	1.01979	+	1.01979i	0.0199932	+	0.999800i	$0.493636\pi$
$198$		0			0
$199$	−3.76653	+	6.52383i	−0.267002	+	0.462462i	−0.968086	−	0.250617i	$-0.919367\pi$
$199$	−3.76653	+	6.52383i	−0.267002	+	0.462462i	0.701084	+	0.713079i	$0.252700\pi$
$200$		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	0.754308	−	0.656521i	$-0.227973\pi$
$223$	1.46027	+	1.46027i	0.0977867	+	0.0977867i	−0.656521	+	0.754308i	$0.727973\pi$
$224$		0			0
$225$	14.3355	+	2.66053i	0.955698	+	0.177369i
$226$		0			0
$227$	4.82525	+	18.0081i	0.320263	+	1.19524i	0.918989	+	0.394283i	$0.129007\pi$
$227$	4.82525	+	18.0081i	0.320263	+	1.19524i	−0.598726	+	0.800954i	$0.704326\pi$
$228$		0			0
$229$	2.00384	+	3.47074i	0.132417	+	0.229353i	0.924608	−	0.380920i	$-0.124393\pi$
$229$	2.00384	+	3.47074i	0.132417	+	0.229353i	−0.792191	+	0.610274i	$0.791059\pi$
$230$		0			0
$231$	−1.31380	+	4.10755i	−0.0864419	+	0.270257i
$232$		0			0
$233$	13.2637	+	3.55400i	0.868934	+	0.232830i	0.665627	−	0.746285i	$-0.268164\pi$
$233$	13.2637	+	3.55400i	0.868934	+	0.232830i	0.203307	+	0.979115i	$0.434831\pi$
$234$		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	$-0.780622\pi$
$239$		−	19.6621i		−	1.27183i	0.771758	−	0.635916i	$-0.219378\pi$
$240$		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
$243$	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	$-0.928069\pi$
$251$		−	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
$255$	−3.38977	+	0.582044i	−0.212275	+	0.0364490i
$256$		0			0
$257$	−9.54998	−	2.55891i	−0.595711	−	0.159620i	−0.0516491	−	0.998665i	$-0.516448\pi$
$257$	−9.54998	−	2.55891i	−0.595711	−	0.159620i	−0.544062	+	0.839045i	$0.683114\pi$
$258$		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	−0.984566	−	0.175013i	$-0.944003\pi$
$263$	−3.55829	−	13.2797i	−0.219413	−	0.818861i	0.765153	−	0.643849i	$-0.222663\pi$
$264$		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	$-0.533922\pi$
$269$	13.2510	−	22.9514i	0.807928	−	1.39937i	0.914296	−	0.405046i	$-0.132745\pi$
$270$		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
$273$	−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	−0.789653	−	0.613554i	$-0.789739\pi$
$277$	−19.4184	+	5.20313i	−1.16674	+	0.312626i	−0.377083	+	0.926180i	$0.623073\pi$
$278$		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	0.623366	−	0.781930i	$-0.285765\pi$
$283$	26.1454	−	7.00563i	1.55418	−	0.416442i	0.930816	+	0.365489i	$0.119098\pi$
$284$		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	−1.00000		0.000106876i	$-0.999966\pi$
$293$	−17.1191	−	17.1191i	−1.00011	−	1.00011i	−0.000106876	−	1.00000i	$-0.500034\pi$
$294$		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	−0.0127019	−	0.999919i	$-0.504043\pi$
$307$	17.2974	−	17.2974i	0.987217	−	0.987217i	0.999919	+	0.0127019i	$0.00404326\pi$
$308$		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
$313$	7.61212	−	28.4088i	0.430262	−	1.60576i	−0.321893	−	0.946776i	$-0.604319\pi$
$313$	7.61212	−	28.4088i	0.430262	−	1.60576i	0.752156	−	0.658985i	$-0.229014\pi$
$314$		0			0
$315$	−2.10427	−	17.1228i	−0.118562	−	0.964760i
$316$		0			0
$317$	1.11136	−	4.14766i	0.0624203	−	0.232956i	−0.927667	−	0.373408i	$-0.878189\pi$
$317$	1.11136	−	4.14766i	0.0624203	−	0.232956i	0.990087	+	0.140453i	$0.0448558\pi$
$318$		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	0.682387	+	0.730991i	$0.260942\pi$
$331$	17.7249	+	30.7005i	0.974250	+	1.68745i	0.291863	+	0.956460i	$0.405725\pi$
$332$		0			0
$333$	−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	0.294075	−	0.955782i	$-0.404989\pi$
$337$	−12.1473	−	12.1473i	−0.661708	−	0.661708i	−0.955782	+	0.294075i	$0.904989\pi$
$338$		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	−0.0184687	−	0.999829i	$-0.505879\pi$
$347$	8.67040	−	2.32323i	0.465452	−	0.124717i	0.483920	+	0.875112i	$0.339212\pi$
$348$		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	0.00663577	−	0.999978i	$-0.497888\pi$
$353$	9.62659	−	2.57944i	0.512372	−	0.137290i	0.505736	+	0.862688i	$0.331221\pi$
$354$		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	−0.211598	−	0.977357i	$-0.567867\pi$
$359$	10.0235	−	5.78705i	0.529019	−	0.305429i	0.740617	+	0.671928i	$0.234533\pi$
$360$		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	−0.982185	−	0.187915i	$-0.939827\pi$
$367$	−4.32083	−	16.1256i	−0.225545	−	0.841747i	0.756640	−	0.653832i	$-0.226840\pi$
$368$		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	0.178446	−	0.983950i	$-0.442893\pi$
$373$	−3.07061	−	0.822767i	−0.158990	−	0.0426013i	−0.337436	+	0.941348i	$0.609560\pi$
$374$		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	$-0.941184\pi$
$379$		−	7.15349i		−	0.367450i	0.982978	−	0.183725i	$-0.0588156\pi$
$380$		0			0
$381$	−1.64470	−	0.949568i	−0.0842605	−	0.0486478i
$382$		0			0
$383$	3.77704	−	14.0961i	0.192998	−	0.720278i	−0.799778	−	0.600296i	$-0.795050\pi$
$383$	3.77704	−	14.0961i	0.192998	−	0.720278i	0.992776	−	0.119982i	$-0.0382837\pi$
$384$		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	0.357750	−	0.933817i	$-0.383544\pi$
$389$	−5.36634	−	3.09826i	−0.272084	−	0.157088i	−0.629834	+	0.776729i	$0.716877\pi$
$390$		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	0.328804	−	0.944398i	$-0.393354\pi$
$397$	2.81652	+	0.754685i	0.141357	+	0.0378766i	−0.187447	+	0.982275i	$0.560021\pi$
$398$		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
$403$	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	0.0322484	+	0.999480i	$0.489733\pi$
$409$	−17.1791	+	29.7550i	−0.849451	+	1.47129i	−0.881699	+	0.471812i	$0.843600\pi$
$410$		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	−0.987141	−	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	$-0.139837\pi$
$433$	9.98256	+	9.98256i	0.479731	+	0.479731i	−0.425315	+	0.905046i	$0.639837\pi$
$434$		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	0.803878	+	0.594794i	$0.202766\pi$
$439$	19.2142	+	33.2800i	0.917046	+	1.58837i	0.113167	+	0.993576i	$0.463900\pi$
$440$		0			0
$441$	−18.5706	+	8.47336i	−0.884314	+	0.403494i
$442$		0			0
$443$	5.54016	+	1.48448i	0.263221	+	0.0705299i	0.388016	−	0.921653i	$-0.373161\pi$
$443$	5.54016	+	1.48448i	0.263221	+	0.0705299i	−0.124795	+	0.992183i	$0.539827\pi$
$444$		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	$0.0551254\pi$
$449$			7.30267i			0.344635i	−0.985042	+	0.172317i	$0.944875\pi$
$450$		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	−0.927754	−	0.373192i	$-0.878263\pi$
$457$	1.33183	−	4.97047i	0.0623006	−	0.232509i	0.990055	+	0.140683i	$0.0449299\pi$
$458$		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	−0.606805	−	0.794851i	$-0.707549\pi$
$463$	4.04625	−	4.04625i	0.188045	−	0.188045i	0.794851	+	0.606805i	$0.207549\pi$
$464$		0			0
$465$	1.43925	−	2.03596i	0.0667436	−	0.0944156i
$466$		0			0
$467$	−16.0757	−	4.30747i	−0.743894	−	0.199326i	−0.133086	−	0.991105i	$-0.542489\pi$
$467$	−16.0757	−	4.30747i	−0.743894	−	0.199326i	−0.610808	+	0.791779i	$0.709155\pi$
$468$		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	−0.634950	−	0.772553i	$-0.718979\pi$
$479$	7.69460	−	13.3274i	0.351575	−	0.608946i	0.986526	+	0.163607i	$0.0523128\pi$
$480$		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	−0.937492	−	0.348007i	$-0.886858\pi$
$487$	−34.7656	+	9.31541i	−1.57538	+	0.422122i	−0.637888	+	0.770129i	$0.720192\pi$
$488$		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	−0.965875	−	0.259008i	$-0.916604\pi$
$499$	−27.3534	+	15.7925i	−1.22451	+	0.706969i	−0.258630	+	0.965976i	$0.583271\pi$
$500$		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	$-0.0702070\pi$
$503$	16.9777	+	16.9777i	0.756997	+	0.756997i	−0.218778	+	0.975775i	$0.570207\pi$
$504$		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	0.522848	−	0.852426i	$-0.324870\pi$
$509$	−10.7571	−	18.6318i	−0.476799	−	0.825840i	−0.999647	+	0.0265865i	$0.991536\pi$
$510$		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	0.729672	−	0.683798i	$-0.239673\pi$
$521$	11.4657	+	6.61973i	0.502322	+	0.290016i	−0.227350	+	0.973813i	$0.573006\pi$
$522$		0			0
$523$	6.97006	−	26.0126i	0.304779	−	1.13745i	−0.628356	−	0.777926i	$-0.716272\pi$
$523$	6.97006	−	26.0126i	0.304779	−	1.13745i	0.933135	−	0.359526i	$-0.117062\pi$
$524$		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	0.961724	−	0.274020i	$-0.0883536\pi$
$541$	5.66491	+	9.81190i	0.243553	+	0.421847i	−0.718171	+	0.695867i	$0.755020\pi$
$542$		0			0
$543$	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	0.912298	+	0.409527i	$0.134306\pi$
$547$	30.9149	+	30.9149i	1.32182	+	1.32182i	0.409527	+	0.912298i	$0.365694\pi$
$548$		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	0.325688	−	0.945477i	$-0.394404\pi$
$557$	25.5003	−	6.83277i	1.08048	−	0.289514i	0.754793	+	0.655963i	$0.227737\pi$
$558$		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	−0.645246	−	0.763975i	$-0.723245\pi$
$563$	−19.5055	+	5.22648i	−0.822058	+	0.220270i	−0.176812	+	0.984245i	$0.556578\pi$
$564$		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	−0.877481	−	0.479611i	$-0.840778\pi$
$569$	−21.4890	+	12.4067i	−0.900867	+	0.520116i	−0.0233856	+	0.999727i	$0.507445\pi$
$570$		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
$577$	−5.11957	−	19.1065i	−0.213131	−	0.795414i	−0.986816	−	0.161845i	$-0.948256\pi$
$577$	−5.11957	−	19.1065i	−0.213131	−	0.795414i	0.773686	−	0.633570i	$-0.218411\pi$
$578$		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	−0.183244	−	0.983068i	$-0.558660\pi$
$587$	19.3782	−	19.3782i	0.799824	−	0.799824i	0.983068	+	0.183244i	$0.0586597\pi$
$588$		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	−0.946583	−	0.322460i	$-0.895490\pi$
$593$	0.837988	−	3.12741i	0.0344121	−	0.128428i	0.980995	+	0.194033i	$0.0621568\pi$
$594$		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	0.631668	−	0.775239i	$-0.282371\pi$
$599$	6.75802	+	3.90174i	0.276125	+	0.159421i	−0.355543	+	0.934660i	$0.615704\pi$
$600$		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
$605$	−45.5070	+	7.81383i	−1.85012	+	0.317677i
$606$		0			0
$607$	−0.743495	−	0.199219i	−0.0301775	−	0.00808604i	0.243699	−	0.969851i	$-0.421639\pi$
$607$	−0.743495	−	0.199219i	−0.0301775	−	0.00808604i	−0.273876	+	0.961765i	$0.588306\pi$
$608$		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	0.866212	+	0.499676i	$0.166548\pi$
$613$	9.05898	+	33.8086i	0.365889	+	1.36552i	−0.500323	+	0.865839i	$0.666786\pi$
$614$		0			0
$615$	−4.65183	−	0.428014i	−0.187580	−	0.0172592i
$616$		0			0
$617$	21.5403	+	21.5403i	0.867179	+	0.867179i	0.992159	−	0.124980i	$-0.0398866\pi$
$617$	21.5403	+	21.5403i	0.867179	+	0.867179i	−0.124980	+	0.992159i	$0.539887\pi$
$618$		0			0
$619$	−21.6707	+	37.5348i	−0.871021	+	1.50865i	−0.0100783	+	0.999949i	$0.503208\pi$
$619$	−21.6707	+	37.5348i	−0.871021	+	1.50865i	−0.860942	+	0.508703i	$0.830125\pi$
$620$		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	−0.999750	−	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	$-0.305465\pi$
$643$	−6.21713	−	6.21713i	−0.245180	−	0.245180i	−0.818989	+	0.573809i	$0.805465\pi$
$644$		0			0
$645$	1.08763	+	1.30805i	0.0428252	+	0.0515045i
$646$		0			0
$647$	−5.33869	−	19.9243i	−0.209886	−	0.783304i	−0.987905	−	0.155063i	$-0.950442\pi$
$647$	−5.33869	−	19.9243i	−0.209886	−	0.783304i	0.778019	−	0.628241i	$-0.216225\pi$
$648$		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	−0.271630	−	0.962402i	$-0.587563\pi$
$653$	−25.2490	−	6.76544i	−0.988069	−	0.264752i	−0.716439	+	0.697650i	$0.754229\pi$
$654$		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	$-0.843452\pi$
$659$		−	24.2448i		−	0.944443i	0.881480	−	0.472222i	$-0.156548\pi$
$660$		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
$663$	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	−0.794442	−	0.607340i	$-0.792237\pi$
$673$	−4.85386	+	4.85386i	−0.187103	+	0.187103i	0.607340	+	0.794442i	$0.292237\pi$
$674$		0			0
$675$	8.54424	−	0.670353i	0.328868	−	0.0258019i
$676$		0			0
$677$	−17.8506	−	4.78306i	−0.686055	−	0.183828i	−0.101079	−	0.994878i	$-0.532229\pi$
$677$	−17.8506	−	4.78306i	−0.686055	−	0.183828i	−0.584976	+	0.811051i	$0.698896\pi$
$678$		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	0.961992	+	0.273079i	$0.0880421\pi$
$683$	6.93661	+	25.8878i	0.265422	+	0.990569i	−0.696569	+	0.717489i	$0.745291\pi$
$684$		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
$693$	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	0.106958	−	0.994263i	$-0.465889\pi$
$709$	27.1994	−	15.7036i	1.02150	−	0.589760i	0.914537	+	0.404503i	$0.132555\pi$
$710$		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	0.747535	−	0.664222i	$-0.231237\pi$
$719$	−5.40214	−	9.35678i	−0.201466	−	0.348949i	−0.949001	+	0.315273i	$0.897904\pi$
$720$		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	0.289326	−	0.957231i	$-0.406569\pi$
$727$	33.6108	−	33.6108i	1.24656	−	1.24656i	0.957231	−	0.289326i	$-0.0934311\pi$
$728$		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	−0.726523	−	0.687143i	$-0.758865\pi$
$733$	6.66658	−	24.8800i	0.246236	−	0.918964i	0.972758	−	0.231822i	$-0.0744686\pi$
$734$		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	0.680451	−	0.732793i	$-0.261784\pi$
$739$	10.4948	+	6.05920i	0.386059	+	0.222891i	−0.294392	+	0.955685i	$0.595117\pi$
$740$		0			0
$741$		−	2.27977i		−	0.0837493i
$742$		0			0
$743$	−23.2618	+	23.2618i	−0.853393	+	0.853393i	−0.990549	−	0.137157i	$-0.956204\pi$
$743$	−23.2618	+	23.2618i	−0.853393	+	0.853393i	0.137157	+	0.990549i	$0.456204\pi$
$744$		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	0.964903	−	0.262607i	$-0.0845821\pi$
$751$	6.98887	+	12.1051i	0.255028	+	0.441721i	−0.709875	+	0.704327i	$0.751249\pi$
$752$		0			0
$753$	−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	0.950071	−	0.312035i	$-0.101010\pi$
$757$	17.5547	+	17.5547i	0.638036	+	0.638036i	−0.312035	+	0.950071i	$0.601010\pi$
$758$		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
$763$	−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	−0.362689	−	0.931910i	$-0.618141\pi$
$773$	−5.86173	+	1.57065i	−0.210832	+	0.0564922i	0.151857	+	0.988402i	$0.451475\pi$
$774$		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	0.989049	+	0.147591i	$0.0471518\pi$
$787$	5.78752	+	21.5993i	0.206303	+	0.769932i	−0.782746	+	0.622342i	$0.786182\pi$
$788$		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	−0.936636	−	0.350305i	$-0.886078\pi$
$797$	−16.5528	+	16.5528i	−0.586330	+	0.586330i	0.350305	+	0.936636i	$0.386078\pi$
$798$		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	0.449219	−	0.893422i	$-0.351702\pi$
$809$	−2.84139	−	1.64048i	−0.0998980	−	0.0576762i	−0.549117	+	0.835746i	$0.685036\pi$
$810$		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
$815$	−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	0.950516	−	0.310677i	$-0.100556\pi$
$821$	5.90837	+	10.2336i	0.206204	+	0.357155i	−0.744312	+	0.667832i	$0.767222\pi$
$822$		0			0
$823$	−9.13692	−	34.0995i	−0.318493	−	1.18863i	−0.920693	−	0.390287i	$-0.872376\pi$
$823$	−9.13692	−	34.0995i	−0.318493	−	1.18863i	0.602200	−	0.798345i	$-0.294291\pi$
$824$		0			0
$825$	−6.71771	+	4.61455i	−0.233881	+	0.160658i
$826$		0			0
$827$	17.2835	+	17.2835i	0.601005	+	0.601005i	0.940579	−	0.339574i	$-0.110283\pi$
$827$	17.2835	+	17.2835i	0.601005	+	0.601005i	−0.339574	+	0.940579i	$0.610283\pi$
$828$		0			0
$829$	−17.2877	+	29.9431i	−0.600426	+	1.03997i	0.392330	+	0.919824i	$0.371669\pi$
$829$	−17.2877	+	29.9431i	−0.600426	+	1.03997i	−0.992756	+	0.120144i	$0.961664\pi$
$830$		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	0.746596	−	0.665278i	$-0.231687\pi$
$853$	2.37500	+	2.37500i	0.0813183	+	0.0813183i	−0.665278	+	0.746596i	$0.731687\pi$
$854$		0			0
$855$	19.5125	−	16.2243i	0.667312	−	0.554860i
$856$		0			0
$857$	−10.8545	−	40.5097i	−0.370784	−	1.38378i	−0.859408	−	0.511290i	$-0.829168\pi$
$857$	−10.8545	−	40.5097i	−0.370784	−	1.38378i	0.488624	−	0.872494i	$-0.337499\pi$
$858$		0			0
$859$	−1.17847	−	2.04117i	−0.0402090	−	0.0696440i	0.845221	−	0.534418i	$-0.179469\pi$
$859$	−1.17847	−	2.04117i	−0.0402090	−	0.0696440i	−0.885430	+	0.464774i	$0.846136\pi$
$860$		0			0
$861$	1.17402	+	5.40125i	0.0400105	+	0.184074i
$862$		0			0
$863$	46.7022	+	12.5138i	1.58976	+	0.425975i	0.941930	−	0.335808i	$-0.109009\pi$
$863$	46.7022	+	12.5138i	1.58976	+	0.425975i	0.647831	+	0.761784i	$0.275676\pi$
$864$		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	−0.999636	−	0.0269665i	$-0.991415\pi$
$877$	−3.56681	+	13.3115i	−0.120443	+	0.449498i	0.879194	+	0.476465i	$0.158082\pi$
$878$		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	0.282191	−	0.959358i	$-0.408939\pi$
$883$	36.8930	−	36.8930i	1.24155	−	1.24155i	0.959358	−	0.282191i	$-0.0910610\pi$
$884$		0			0
$885$	−2.89828	−	2.04883i	−0.0974247	−	0.0688708i
$886$		0			0
$887$	34.6001	+	9.27107i	1.16176	+	0.311292i	0.787668	−	0.616101i	$-0.211289\pi$
$887$	34.6001	+	9.27107i	1.16176	+	0.311292i	0.374090	+	0.927392i	$0.377955\pi$
$888$		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	−0.524721	−	0.851274i	$-0.675830\pi$
$907$	−16.6696	+	4.46661i	−0.553506	+	0.148312i	−0.0287849	+	0.999586i	$0.509164\pi$
$908$		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	−0.408640	−	0.912696i	$-0.633997\pi$
$919$	5.37964	−	3.10593i	0.177458	−	0.102455i	0.586098	+	0.810240i	$0.300663\pi$
$920$		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	0.864467	−	0.502689i	$-0.167656\pi$
$929$	−0.0947297	−	0.164077i	−0.00310798	−	0.00538318i	−0.867575	+	0.497306i	$0.834323\pi$
$930$		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	0.125208	−	0.992131i	$-0.460040\pi$
$937$	34.2022	−	34.2022i	1.11734	−	1.11734i	0.992131	−	0.125208i	$-0.0399598\pi$
$938$		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
$943$	−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	0.422560	+	0.906335i	$0.361131\pi$
$947$	−12.2033	+	45.5435i	−0.396555	+	1.47996i	−0.819115	+	0.573629i	$0.805535\pi$
$948$		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	−0.332658	−	0.943047i	$-0.607946\pi$
$953$	18.8431	−	18.8431i	0.610389	−	0.610389i	0.943047	+	0.332658i	$0.107946\pi$
$954$		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	0.113383	−	0.993551i	$-0.463831\pi$
$967$	−27.3703	−	27.3703i	−0.880169	−	0.880169i	−0.993551	+	0.113383i	$0.963831\pi$
$968$		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
$973$	−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	0.119470	−	0.992838i	$-0.461881\pi$
$977$	22.4848	−	6.02479i	0.719353	−	0.192750i	0.599883	+	0.800088i	$0.295214\pi$
$978$		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	−0.986160	−	0.165793i	$-0.946981\pi$
$983$	−55.0964	+	14.7630i	−1.75730	+	0.470868i	−0.771143	+	0.636662i	$0.780315\pi$
$984$		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	−0.105440	+	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
$997$	6.27762	+	23.4284i	0.198814	+	0.741985i	0.991246	+	0.132025i	$0.0421479\pi$
$997$	6.27762	+	23.4284i	0.198814	+	0.741985i	−0.792432	+	0.609960i	$0.791185\pi$
$998$		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.17.3		16
4.3	odd	2		70.2.k.a.17.3	yes	16
5.3	odd	4	inner	560.2.ci.c.353.3		16
7.5	odd	6	inner	560.2.ci.c.257.3		16
12.11	even	2		630.2.bv.c.577.1		16
20.3	even	4		70.2.k.a.3.1	✓	16
20.7	even	4		350.2.o.c.143.4		16
20.19	odd	2		350.2.o.c.157.2		16
28.3	even	6		490.2.g.c.97.6		16
28.11	odd	6		490.2.g.c.97.7		16
28.19	even	6		70.2.k.a.47.1	yes	16
28.23	odd	6		490.2.l.c.117.2		16
28.27	even	2		490.2.l.c.227.4		16
35.33	even	12	inner	560.2.ci.c.33.3		16
60.23	odd	4		630.2.bv.c.73.3		16
84.47	odd	6		630.2.bv.c.397.3		16
140.3	odd	12		490.2.g.c.293.7		16
140.19	even	6		350.2.o.c.257.4		16
140.23	even	12		490.2.l.c.313.4		16
140.47	odd	12		350.2.o.c.243.2		16
140.83	odd	4		490.2.l.c.423.2		16
140.103	odd	12		70.2.k.a.33.3	yes	16
140.123	even	12		490.2.g.c.293.6		16
420.383	even	12		630.2.bv.c.523.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.1	✓	16	20.3	even	4
70.2.k.a.17.3	yes	16	4.3	odd	2
70.2.k.a.33.3	yes	16	140.103	odd	12
70.2.k.a.47.1	yes	16	28.19	even	6
350.2.o.c.143.4		16	20.7	even	4
350.2.o.c.157.2		16	20.19	odd	2
350.2.o.c.243.2		16	140.47	odd	12
350.2.o.c.257.4		16	140.19	even	6
490.2.g.c.97.6		16	28.3	even	6
490.2.g.c.97.7		16	28.11	odd	6
490.2.g.c.293.6		16	140.123	even	12
490.2.g.c.293.7		16	140.3	odd	12
490.2.l.c.117.2		16	28.23	odd	6
490.2.l.c.227.4		16	28.27	even	2
490.2.l.c.313.4		16	140.23	even	12
490.2.l.c.423.2		16	140.83	odd	4
560.2.ci.c.17.3		16	1.1	even	1	trivial
560.2.ci.c.33.3		16	35.33	even	12	inner
560.2.ci.c.257.3		16	7.5	odd	6	inner
560.2.ci.c.353.3		16	5.3	odd	4	inner
630.2.bv.c.73.3		16	60.23	odd	4
630.2.bv.c.397.3		16	84.47	odd	6
630.2.bv.c.523.1		16	420.383	even	12
630.2.bv.c.577.1		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
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

Varieties

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Database

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