LMFDB - Embedded newform 560.2.q.k.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	560.81
Dual form			560.2.q.k.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207107 + 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(-0.207107 + 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(1.41421 + 2.44949i) q^{9} +(-0.414214 + 0.717439i) q^{11} -4.82843 q^{13} +0.414214 q^{15} +(-2.41421 + 4.18154i) q^{17} +(1.41421 + 2.44949i) q^{19} +(0.671573 - 0.866025i) q^{21} +(0.207107 + 0.358719i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.41421 q^{27} -1.00000 q^{29} +(-3.00000 + 5.19615i) q^{31} +(-0.171573 - 0.297173i) q^{33} +(1.00000 + 2.44949i) q^{35} +(1.00000 - 1.73205i) q^{39} -7.82843 q^{41} -3.58579 q^{43} +(1.41421 - 2.44949i) q^{45} +(1.00000 + 1.73205i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(0.585786 - 1.01461i) q^{53} +0.828427 q^{55} -1.17157 q^{57} +(2.24264 - 3.88437i) q^{59} +(-2.74264 - 4.75039i) q^{61} +(-2.82843 - 6.92820i) q^{63} +(2.41421 + 4.18154i) q^{65} +(4.79289 - 8.30153i) q^{67} -0.171573 q^{69} -4.48528 q^{71} +(0.414214 - 0.717439i) q^{73} +(-0.207107 - 0.358719i) q^{75} +(1.34315 - 1.73205i) q^{77} +(7.41421 + 12.8418i) q^{79} +(-3.74264 + 6.48244i) q^{81} -13.7279 q^{83} +4.82843 q^{85} +(0.207107 - 0.358719i) q^{87} +(4.32843 + 7.49706i) q^{89} +(12.6569 + 1.73205i) q^{91} +(-1.24264 - 2.15232i) q^{93} +(1.41421 - 2.44949i) q^{95} +11.6569 q^{97} -2.34315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7	$ 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7} + 4 q^{11} - 8 q^{13} - 4 q^{15} - 4 q^{17} + 14 q^{21} - 2 q^{23} - 2 q^{25} - 4 q^{27} - 4 q^{29} - 12 q^{31} - 12 q^{33} + 4 q^{35} + 4 q^{39} - 20 q^{41} - 20 q^{43} + 4 q^{47} + 10 q^{49} - 4 q^{51} + 8 q^{53} - 8 q^{55} - 16 q^{57} - 8 q^{59} + 6 q^{61} + 4 q^{65} + 22 q^{67} - 12 q^{69} + 16 q^{71} - 4 q^{73} + 2 q^{75} + 28 q^{77} + 24 q^{79} + 2 q^{81} - 4 q^{83} + 8 q^{85} - 2 q^{87} + 6 q^{89} + 28 q^{91} + 12 q^{93} + 24 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7 + 4 * q^11 - 8 * q^13 - 4 * q^15 - 4 * q^17 + 14 * q^21 - 2 * q^23 - 2 * q^25 - 4 * q^27 - 4 * q^29 - 12 * q^31 - 12 * q^33 + 4 * q^35 + 4 * q^39 - 20 * q^41 - 20 * q^43 + 4 * q^47 + 10 * q^49 - 4 * q^51 + 8 * q^53 - 8 * q^55 - 16 * q^57 - 8 * q^59 + 6 * q^61 + 4 * q^65 + 22 * q^67 - 12 * q^69 + 16 * q^71 - 4 * q^73 + 2 * q^75 + 28 * q^77 + 24 * q^79 + 2 * q^81 - 4 * q^83 + 8 * q^85 - 2 * q^87 + 6 * q^89 + 28 * q^91 + 12 * q^93 + 24 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	−0.207107	+	0.358719i	−0.119573	+	0.207107i	−0.919599	−	0.392859i	$-0.871486\pi$
$3$	−0.207107	+	0.358719i	−0.119573	+	0.207107i	0.800025	+	0.599966i	$0.204819\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$8$		0			0
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$		0			0
$11$	−0.414214	+	0.717439i	−0.124890	+	0.216316i	−0.921690	−	0.387927i	$-0.873191\pi$
$11$	−0.414214	+	0.717439i	−0.124890	+	0.216316i	0.796800	+	0.604243i	$0.206524\pi$
$12$		0			0
$13$	−4.82843			−1.33916			−0.669582	−	0.742738i	$-0.733527\pi$
$13$	−4.82843			−1.33916			−0.669582	+	0.742738i	$0.733527\pi$
$14$		0			0
$15$	0.414214			0.106949
$16$		0			0
$17$	−2.41421	+	4.18154i	−0.585533	+	1.01417i	0.409276	+	0.912411i	$0.365781\pi$
$17$	−2.41421	+	4.18154i	−0.585533	+	1.01417i	−0.994809	+	0.101762i	$0.967552\pi$
$18$		0			0
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	0.981399	−	0.191977i	$-0.0614899\pi$
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	−0.656957	+	0.753928i	$0.728157\pi$
$20$		0			0
$21$	0.671573	−	0.866025i	0.146549	−	0.188982i
$22$		0			0
$23$	0.207107	+	0.358719i	0.0431847	+	0.0747982i	0.886810	−	0.462134i	$-0.152916\pi$
$23$	0.207107	+	0.358719i	0.0431847	+	0.0747982i	−0.843625	+	0.536933i	$0.819583\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−2.41421			−0.464616
$28$		0			0
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$		0			0
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$		0			0
$33$	−0.171573	−	0.297173i	−0.0298670	−	0.0517312i
$34$		0			0
$35$	1.00000	+	2.44949i	0.169031	+	0.414039i
$36$		0			0
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$		0			0
$39$	1.00000	−	1.73205i	0.160128	−	0.277350i
$40$		0			0
$41$	−7.82843			−1.22259			−0.611297	−	0.791401i	$-0.709352\pi$
$41$	−7.82843			−1.22259			−0.611297	+	0.791401i	$0.709352\pi$
$42$		0			0
$43$	−3.58579			−0.546827			−0.273414	−	0.961897i	$-0.588153\pi$
$43$	−3.58579			−0.546827			−0.273414	+	0.961897i	$0.588153\pi$
$44$		0			0
$45$	1.41421	−	2.44949i	0.210819	−	0.365148i
$46$		0			0
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$		0			0
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$		0			0
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$		0			0
$53$	0.585786	−	1.01461i	0.0804640	−	0.139368i	−0.822985	−	0.568063i	$-0.807693\pi$
$53$	0.585786	−	1.01461i	0.0804640	−	0.139368i	0.903449	+	0.428695i	$0.141026\pi$
$54$		0			0
$55$	0.828427			0.111705
$56$		0			0
$57$	−1.17157			−0.155179
$58$		0			0
$59$	2.24264	−	3.88437i	0.291967	−	0.505702i	−0.682308	−	0.731065i	$-0.739024\pi$
$59$	2.24264	−	3.88437i	0.291967	−	0.505702i	0.974275	+	0.225363i	$0.0723569\pi$
$60$		0			0
$61$	−2.74264	−	4.75039i	−0.351159	−	0.608226i	0.635294	−	0.772271i	$-0.280879\pi$
$61$	−2.74264	−	4.75039i	−0.351159	−	0.608226i	−0.986453	+	0.164045i	$0.947546\pi$
$62$		0			0
$63$	−2.82843	−	6.92820i	−0.356348	−	0.872872i
$64$		0			0
$65$	2.41421	+	4.18154i	0.299446	+	0.518656i
$66$		0			0
$67$	4.79289	−	8.30153i	0.585545	−	1.01419i	−0.409262	−	0.912417i	$-0.634214\pi$
$67$	4.79289	−	8.30153i	0.585545	−	1.01419i	0.994807	−	0.101777i	$-0.0324528\pi$
$68$		0			0
$69$	−0.171573			−0.0206549
$70$		0			0
$71$	−4.48528			−0.532305			−0.266152	−	0.963931i	$-0.585752\pi$
$71$	−4.48528			−0.532305			−0.266152	+	0.963931i	$0.585752\pi$
$72$		0			0
$73$	0.414214	−	0.717439i	0.0484800	−	0.0839699i	−0.840767	−	0.541397i	$-0.817896\pi$
$73$	0.414214	−	0.717439i	0.0484800	−	0.0839699i	0.889247	+	0.457427i	$0.151229\pi$
$74$		0			0
$75$	−0.207107	−	0.358719i	−0.0239146	−	0.0414214i
$76$		0			0
$77$	1.34315	−	1.73205i	0.153066	−	0.197386i
$78$		0			0
$79$	7.41421	+	12.8418i	0.834164	+	1.44481i	0.894709	+	0.446649i	$0.147383\pi$
$79$	7.41421	+	12.8418i	0.834164	+	1.44481i	−0.0605449	+	0.998165i	$0.519284\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$		0			0
$83$	−13.7279			−1.50684			−0.753418	−	0.657542i	$-0.771596\pi$
$83$	−13.7279			−1.50684			−0.753418	+	0.657542i	$0.771596\pi$
$84$		0			0
$85$	4.82843			0.523716
$86$		0			0
$87$	0.207107	−	0.358719i	0.0222042	−	0.0384588i
$88$		0			0
$89$	4.32843	+	7.49706i	0.458812	+	0.794686i	0.998898	−	0.0469234i	$-0.0149417\pi$
$89$	4.32843	+	7.49706i	0.458812	+	0.794686i	−0.540086	+	0.841610i	$0.681608\pi$
$90$		0			0
$91$	12.6569	+	1.73205i	1.32680	+	0.181568i
$92$		0			0
$93$	−1.24264	−	2.15232i	−0.128856	−	0.223185i
$94$		0			0
$95$	1.41421	−	2.44949i	0.145095	−	0.251312i
$96$		0			0
$97$	11.6569			1.18357			0.591787	−	0.806094i	$-0.298423\pi$
$97$	11.6569			1.18357			0.591787	+	0.806094i	$0.298423\pi$
$98$		0			0
$99$	−2.34315			−0.235495
$100$		0			0
$101$	5.15685	−	8.93193i	0.513126	−	0.888761i	−0.486758	−	0.873537i	$-0.661821\pi$
$101$	5.15685	−	8.93193i	0.513126	−	0.888761i	0.999884	−	0.0152237i	$-0.00484604\pi$
$102$		0			0
$103$	−1.20711	−	2.09077i	−0.118940	−	0.206010i	0.800408	−	0.599456i	$-0.204616\pi$
$103$	−1.20711	−	2.09077i	−0.118940	−	0.206010i	−0.919348	+	0.393446i	$0.871283\pi$
$104$		0			0
$105$	−1.08579	−	0.148586i	−0.105962	−	0.0145006i
$106$		0			0
$107$	5.62132	+	9.73641i	0.543434	+	0.941255i	0.998704	+	0.0509012i	$0.0162093\pi$
$107$	5.62132	+	9.73641i	0.543434	+	0.941255i	−0.455270	+	0.890353i	$0.650457\pi$
$108$		0			0
$109$	6.74264	−	11.6786i	0.645828	−	1.11861i	−0.338282	−	0.941045i	$-0.609846\pi$
$109$	6.74264	−	11.6786i	0.645828	−	1.11861i	0.984110	−	0.177562i	$-0.0568210\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.48528			−0.421940			−0.210970	−	0.977493i	$-0.567662\pi$
$113$	−4.48528			−0.421940			−0.210970	+	0.977493i	$0.567662\pi$
$114$		0			0
$115$	0.207107	−	0.358719i	0.0193128	−	0.0334508i
$116$		0			0
$117$	−6.82843	−	11.8272i	−0.631288	−	1.09342i
$118$		0			0
$119$	7.82843	−	10.0951i	0.717631	−	0.925419i
$120$		0			0
$121$	5.15685	+	8.93193i	0.468805	+	0.811994i
$122$		0			0
$123$	1.62132	−	2.80821i	0.146190	−	0.253208i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	9.31371			0.826458			0.413229	−	0.910627i	$-0.364401\pi$
$127$	9.31371			0.826458			0.413229	+	0.910627i	$0.364401\pi$
$128$		0			0
$129$	0.742641	−	1.28629i	0.0653859	−	0.113252i
$130$		0			0
$131$	−9.65685	−	16.7262i	−0.843723	−	1.46137i	−0.886725	−	0.462297i	$-0.847026\pi$
$131$	−9.65685	−	16.7262i	−0.843723	−	1.46137i	0.0430021	−	0.999075i	$-0.486308\pi$
$132$		0			0
$133$	−2.82843	−	6.92820i	−0.245256	−	0.600751i
$134$		0			0
$135$	1.20711	+	2.09077i	0.103891	+	0.179945i
$136$		0			0
$137$	4.82843	−	8.36308i	0.412520	−	0.714506i	−0.582644	−	0.812727i	$-0.697982\pi$
$137$	4.82843	−	8.36308i	0.412520	−	0.714506i	0.995165	+	0.0982211i	$0.0313152\pi$
$138$		0			0
$139$	16.1421			1.36916			0.684579	−	0.728939i	$-0.259986\pi$
$139$	16.1421			1.36916			0.684579	+	0.728939i	$0.259986\pi$
$140$		0			0
$141$	−0.828427			−0.0697661
$142$		0			0
$143$	2.00000	−	3.46410i	0.167248	−	0.289683i
$144$		0			0
$145$	0.500000	+	0.866025i	0.0415227	+	0.0719195i
$146$		0			0
$147$	−2.07107	+	2.02922i	−0.170819	+	0.167368i
$148$		0			0
$149$	1.08579	+	1.88064i	0.0889511	+	0.154068i	0.907068	−	0.420984i	$-0.138315\pi$
$149$	1.08579	+	1.88064i	0.0889511	+	0.154068i	−0.818117	+	0.575052i	$0.804982\pi$
$150$		0			0
$151$	5.82843	−	10.0951i	0.474311	−	0.821530i	−0.525257	−	0.850944i	$-0.676031\pi$
$151$	5.82843	−	10.0951i	0.474311	−	0.821530i	0.999567	+	0.0294137i	$0.00936401\pi$
$152$		0			0
$153$	−13.6569			−1.10409
$154$		0			0
$155$	6.00000			0.481932
$156$		0			0
$157$	−8.65685	+	14.9941i	−0.690892	+	1.19666i	0.280654	+	0.959809i	$0.409449\pi$
$157$	−8.65685	+	14.9941i	−0.690892	+	1.19666i	−0.971546	+	0.236851i	$0.923885\pi$
$158$		0			0
$159$	0.242641	+	0.420266i	0.0192427	+	0.0333293i
$160$		0			0
$161$	−0.414214	−	1.01461i	−0.0326446	−	0.0799626i
$162$		0			0
$163$	6.17157	+	10.6895i	0.483395	+	0.837265i	0.999818	−	0.0190689i	$-0.00607020\pi$
$163$	6.17157	+	10.6895i	0.483395	+	0.837265i	−0.516423	+	0.856333i	$0.672737\pi$
$164$		0			0
$165$	−0.171573	+	0.297173i	−0.0133569	+	0.0231349i
$166$		0			0
$167$	−22.4142			−1.73446			−0.867232	−	0.497904i	$-0.834103\pi$
$167$	−22.4142			−1.73446			−0.867232	+	0.497904i	$0.834103\pi$
$168$		0			0
$169$	10.3137			0.793362
$170$		0			0
$171$	−4.00000	+	6.92820i	−0.305888	+	0.529813i
$172$		0			0
$173$	−1.65685	−	2.86976i	−0.125968	−	0.218183i	0.796143	−	0.605109i	$-0.206870\pi$
$173$	−1.65685	−	2.86976i	−0.125968	−	0.218183i	−0.922111	+	0.386925i	$0.873537\pi$
$174$		0			0
$175$	1.62132	−	2.09077i	0.122560	−	0.158047i
$176$		0			0
$177$	0.928932	+	1.60896i	0.0698228	+	0.120937i
$178$		0			0
$179$	−5.00000	+	8.66025i	−0.373718	+	0.647298i	−0.990134	−	0.140122i	$-0.955250\pi$
$179$	−5.00000	+	8.66025i	−0.373718	+	0.647298i	0.616417	+	0.787420i	$0.288584\pi$
$180$		0			0
$181$	2.65685			0.197482			0.0987412	−	0.995113i	$-0.468518\pi$
$181$	2.65685			0.197482			0.0987412	+	0.995113i	$0.468518\pi$
$182$		0			0
$183$	2.27208			0.167957
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$		0			0
$189$	6.32843	+	0.866025i	0.460325	+	0.0629941i
$190$		0			0
$191$	−6.41421	−	11.1097i	−0.464116	−	0.803873i	0.535045	−	0.844824i	$-0.320295\pi$
$191$	−6.41421	−	11.1097i	−0.464116	−	0.803873i	−0.999161	+	0.0409507i	$0.986961\pi$
$192$		0			0
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$		0			0
$195$	−2.00000			−0.143223
$196$		0			0
$197$	−12.3431			−0.879413			−0.439706	−	0.898142i	$-0.644917\pi$
$197$	−12.3431			−0.879413			−0.439706	+	0.898142i	$0.644917\pi$
$198$		0			0
$199$	−4.82843	+	8.36308i	−0.342278	+	0.592843i	−0.984855	−	0.173378i	$-0.944532\pi$
$199$	−4.82843	+	8.36308i	−0.342278	+	0.592843i	0.642577	+	0.766221i	$0.277865\pi$
$200$		0			0
$201$	1.98528	+	3.43861i	0.140031	+	0.242541i
$202$		0			0
$203$	2.62132	+	0.358719i	0.183981	+	0.0251772i
$204$		0			0
$205$	3.91421	+	6.77962i	0.273381	+	0.473509i
$206$		0			0
$207$	−0.585786	+	1.01461i	−0.0407150	+	0.0705204i
$208$		0			0
$209$	−2.34315			−0.162079
$210$		0			0
$211$	−20.4853			−1.41026			−0.705132	−	0.709076i	$-0.749112\pi$
$211$	−20.4853			−1.41026			−0.705132	+	0.709076i	$0.749112\pi$
$212$		0			0
$213$	0.928932	−	1.60896i	0.0636494	−	0.110244i
$214$		0			0
$215$	1.79289	+	3.10538i	0.122274	+	0.211785i
$216$		0			0
$217$	9.72792	−	12.5446i	0.660374	−	0.851584i
$218$		0			0
$219$	0.171573	+	0.297173i	0.0115938	+	0.0200811i
$220$		0			0
$221$	11.6569	−	20.1903i	0.784125	−	1.35814i
$222$		0			0
$223$	−0.343146			−0.0229787			−0.0114894	−	0.999934i	$-0.503657\pi$
$223$	−0.343146			−0.0229787			−0.0114894	+	0.999934i	$0.503657\pi$
$224$		0			0
$225$	−2.82843			−0.188562
$226$		0			0
$227$	−3.48528	+	6.03668i	−0.231326	+	0.400669i	−0.958199	−	0.286104i	$-0.907640\pi$
$227$	−3.48528	+	6.03668i	−0.231326	+	0.400669i	0.726872	+	0.686773i	$0.240973\pi$
$228$		0			0
$229$	5.82843	+	10.0951i	0.385153	+	0.667105i	0.991790	−	0.127874i	$-0.0408152\pi$
$229$	5.82843	+	10.0951i	0.385153	+	0.667105i	−0.606637	+	0.794979i	$0.707482\pi$
$230$		0			0
$231$	0.343146	+	0.840532i	0.0225773	+	0.0553029i
$232$		0			0
$233$	8.41421	+	14.5738i	0.551233	+	0.954764i	0.998186	+	0.0602067i	$0.0191760\pi$
$233$	8.41421	+	14.5738i	0.551233	+	0.954764i	−0.446952	+	0.894558i	$0.647491\pi$
$234$		0			0
$235$	1.00000	−	1.73205i	0.0652328	−	0.112987i
$236$		0			0
$237$	−6.14214			−0.398975
$238$		0			0
$239$	21.3137			1.37867			0.689335	−	0.724443i	$-0.257903\pi$
$239$	21.3137			1.37867			0.689335	+	0.724443i	$0.257903\pi$
$240$		0			0
$241$	−13.8284	+	23.9515i	−0.890767	+	1.54285i	−0.0518100	+	0.998657i	$0.516499\pi$
$241$	−13.8284	+	23.9515i	−0.890767	+	1.54285i	−0.838957	+	0.544197i	$0.816834\pi$
$242$		0			0
$243$	−5.17157	−	8.95743i	−0.331757	−	0.574619i
$244$		0			0
$245$	−1.74264	−	6.77962i	−0.111333	−	0.433134i
$246$		0			0
$247$	−6.82843	−	11.8272i	−0.434482	−	0.752546i
$248$		0			0
$249$	2.84315	−	4.92447i	0.180177	−	0.312076i
$250$		0			0
$251$	9.31371			0.587876			0.293938	−	0.955824i	$-0.405034\pi$
$251$	9.31371			0.587876			0.293938	+	0.955824i	$0.405034\pi$
$252$		0			0
$253$	−0.343146			−0.0215734
$254$		0			0
$255$	−1.00000	+	1.73205i	−0.0626224	+	0.108465i
$256$		0			0
$257$	−3.17157	−	5.49333i	−0.197837	−	0.342664i	0.749990	−	0.661450i	$-0.230058\pi$
$257$	−3.17157	−	5.49333i	−0.197837	−	0.342664i	−0.947827	+	0.318785i	$0.896725\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.41421	−	2.44949i	−0.0875376	−	0.151620i
$262$		0			0
$263$	−14.5208	+	25.1508i	−0.895392	+	1.55086i	−0.0620729	+	0.998072i	$0.519771\pi$
$263$	−14.5208	+	25.1508i	−0.895392	+	1.55086i	−0.833319	+	0.552793i	$0.813562\pi$
$264$		0			0
$265$	−1.17157			−0.0719691
$266$		0			0
$267$	−3.58579			−0.219447
$268$		0			0
$269$	−10.2279	+	17.7153i	−0.623607	+	1.08012i	0.365201	+	0.930929i	$0.381000\pi$
$269$	−10.2279	+	17.7153i	−0.623607	+	1.08012i	−0.988808	+	0.149191i	$0.952333\pi$
$270$		0			0
$271$	8.24264	+	14.2767i	0.500705	+	0.867246i	1.00000		0.000813982i	$0.000259099\pi$
$271$	8.24264	+	14.2767i	0.500705	+	0.867246i	−0.499295	+	0.866432i	$0.666408\pi$
$272$		0			0
$273$	−3.24264	+	4.18154i	−0.196254	+	0.253078i
$274$		0			0
$275$	−0.414214	−	0.717439i	−0.0249780	−	0.0432632i
$276$		0			0
$277$	−8.07107	+	13.9795i	−0.484943	+	0.839947i	−0.999850	−	0.0172994i	$-0.994493\pi$
$277$	−8.07107	+	13.9795i	−0.484943	+	0.839947i	0.514907	+	0.857246i	$0.327826\pi$
$278$		0			0
$279$	−16.9706			−1.01600
$280$		0			0
$281$	−30.2843			−1.80661			−0.903304	−	0.429001i	$-0.858866\pi$
$281$	−30.2843			−1.80661			−0.903304	+	0.429001i	$0.858866\pi$
$282$		0			0
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$		0			0
$285$	0.585786	+	1.01461i	0.0346990	+	0.0601004i
$286$		0			0
$287$	20.5208	+	2.80821i	1.21131	+	0.165763i
$288$		0			0
$289$	−3.15685	−	5.46783i	−0.185697	−	0.321637i
$290$		0			0
$291$	−2.41421	+	4.18154i	−0.141524	+	0.245126i
$292$		0			0
$293$	−16.0000			−0.934730			−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000			−0.934730			−0.467365	+	0.884064i	$0.654797\pi$
$294$		0			0
$295$	−4.48528			−0.261143
$296$		0			0
$297$	1.00000	−	1.73205i	0.0580259	−	0.100504i
$298$		0			0
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$		0			0
$301$	9.39949	+	1.28629i	0.541778	+	0.0741406i
$302$		0			0
$303$	2.13604	+	3.69973i	0.122712	+	0.212544i
$304$		0			0
$305$	−2.74264	+	4.75039i	−0.157043	+	0.272007i
$306$		0			0
$307$	4.75736			0.271517			0.135758	−	0.990742i	$-0.456653\pi$
$307$	4.75736			0.271517			0.135758	+	0.990742i	$0.456653\pi$
$308$		0			0
$309$	1.00000			0.0568880
$310$		0			0
$311$	−6.58579	+	11.4069i	−0.373446	+	0.646827i	−0.990093	−	0.140413i	$-0.955157\pi$
$311$	−6.58579	+	11.4069i	−0.373446	+	0.646827i	0.616647	+	0.787239i	$0.288490\pi$
$312$		0			0
$313$	3.17157	+	5.49333i	0.179268	+	0.310501i	0.941630	−	0.336650i	$-0.109294\pi$
$313$	3.17157	+	5.49333i	0.179268	+	0.310501i	−0.762362	+	0.647151i	$0.775960\pi$
$314$		0			0
$315$	−4.58579	+	5.91359i	−0.258380	+	0.333193i
$316$		0			0
$317$	6.89949	+	11.9503i	0.387514	+	0.671194i	0.992115	−	0.125335i	$-0.0400005\pi$
$317$	6.89949	+	11.9503i	0.387514	+	0.671194i	−0.604600	+	0.796529i	$0.706667\pi$
$318$		0			0
$319$	0.414214	−	0.717439i	0.0231915	−	0.0401689i
$320$		0			0
$321$	−4.65685			−0.259920
$322$		0			0
$323$	−13.6569			−0.759888
$324$		0			0
$325$	2.41421	−	4.18154i	0.133916	−	0.231950i
$326$		0			0
$327$	2.79289	+	4.83743i	0.154447	+	0.267511i
$328$		0			0
$329$	−2.00000	−	4.89898i	−0.110264	−	0.270089i
$330$		0			0
$331$	11.4853	+	19.8931i	0.631288	+	1.09342i	0.987289	+	0.158937i	$0.0508068\pi$
$331$	11.4853	+	19.8931i	0.631288	+	1.09342i	−0.356001	+	0.934486i	$0.615860\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.58579			−0.523727
$336$		0			0
$337$	9.17157			0.499607			0.249804	−	0.968296i	$-0.419634\pi$
$337$	9.17157			0.499607			0.249804	+	0.968296i	$0.419634\pi$
$338$		0			0
$339$	0.928932	−	1.60896i	0.0504527	−	0.0873866i
$340$		0			0
$341$	−2.48528	−	4.30463i	−0.134586	−	0.233109i
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$		0			0
$345$	0.0857864	+	0.148586i	0.00461859	+	0.00799963i
$346$		0			0
$347$	3.96447	−	6.86666i	0.212824	−	0.368621i	−0.739773	−	0.672856i	$-0.765067\pi$
$347$	3.96447	−	6.86666i	0.212824	−	0.368621i	0.952597	+	0.304235i	$0.0984007\pi$
$348$		0			0
$349$	−15.3431			−0.821300			−0.410650	−	0.911793i	$-0.634698\pi$
$349$	−15.3431			−0.821300			−0.410650	+	0.911793i	$0.634698\pi$
$350$		0			0
$351$	11.6569			0.622197
$352$		0			0
$353$	13.4142	−	23.2341i	0.713967	−	1.23663i	−0.249390	−	0.968403i	$-0.580230\pi$
$353$	13.4142	−	23.2341i	0.713967	−	1.23663i	0.963357	−	0.268223i	$-0.0864365\pi$
$354$		0			0
$355$	2.24264	+	3.88437i	0.119027	+	0.206161i
$356$		0			0
$357$	2.00000	+	4.89898i	0.105851	+	0.259281i
$358$		0			0
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	0.703382	−	0.710812i	$-0.251672\pi$
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	−0.967272	+	0.253741i	$0.918339\pi$
$360$		0			0
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$		0			0
$363$	−4.27208			−0.224226
$364$		0			0
$365$	−0.828427			−0.0433619
$366$		0			0
$367$	−1.37868	+	2.38794i	−0.0719665	+	0.124650i	−0.899763	−	0.436379i	$-0.856261\pi$
$367$	−1.37868	+	2.38794i	−0.0719665	+	0.124650i	0.827797	+	0.561028i	$0.189594\pi$
$368$		0			0
$369$	−11.0711	−	19.1757i	−0.576337	−	0.998245i
$370$		0			0
$371$	−1.89949	+	2.44949i	−0.0986169	+	0.127171i
$372$		0			0
$373$	10.4853	+	18.1610i	0.542907	+	0.940343i	0.998735	+	0.0502752i	$0.0160098\pi$
$373$	10.4853	+	18.1610i	0.542907	+	0.940343i	−0.455828	+	0.890068i	$0.650657\pi$
$374$		0			0
$375$	−0.207107	+	0.358719i	−0.0106949	+	0.0185242i
$376$		0			0
$377$	4.82843			0.248677
$378$		0			0
$379$	−26.8284			−1.37808			−0.689042	−	0.724722i	$-0.741968\pi$
$379$	−26.8284			−1.37808			−0.689042	+	0.724722i	$0.741968\pi$
$380$		0			0
$381$	−1.92893	+	3.34101i	−0.0988222	+	0.171165i
$382$		0			0
$383$	−1.44975	−	2.51104i	−0.0740786	−	0.128308i	0.826607	−	0.562780i	$-0.190268\pi$
$383$	−1.44975	−	2.51104i	−0.0740786	−	0.128308i	−0.900685	+	0.434472i	$0.856935\pi$
$384$		0			0
$385$	−2.17157	−	0.297173i	−0.110674	−	0.0151453i
$386$		0			0
$387$	−5.07107	−	8.78335i	−0.257777	−	0.446483i
$388$		0			0
$389$	−11.8284	+	20.4874i	−0.599725	+	1.03875i	0.393136	+	0.919480i	$0.371390\pi$
$389$	−11.8284	+	20.4874i	−0.599725	+	1.03875i	−0.992861	+	0.119274i	$0.961943\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$		0			0
$393$	8.00000			0.403547
$394$		0			0
$395$	7.41421	−	12.8418i	0.373050	−	0.646141i
$396$		0			0
$397$	8.31371	+	14.3998i	0.417253	+	0.722704i	0.995662	−	0.0930434i	$-0.0296595\pi$
$397$	8.31371	+	14.3998i	0.417253	+	0.722704i	−0.578409	+	0.815747i	$0.696326\pi$
$398$		0			0
$399$	3.07107	+	0.420266i	0.153746	+	0.0210396i
$400$		0			0
$401$	−15.1569	−	26.2524i	−0.756897	−	1.31098i	−0.944426	−	0.328725i	$-0.893381\pi$
$401$	−15.1569	−	26.2524i	−0.756897	−	1.31098i	0.187528	−	0.982259i	$-0.439952\pi$
$402$		0			0
$403$	14.4853	−	25.0892i	0.721563	−	1.24978i
$404$		0			0
$405$	7.48528			0.371947
$406$		0			0
$407$		0			0
$408$		0			0
$409$	7.39949	−	12.8163i	0.365881	−	0.633725i	−0.623036	−	0.782193i	$-0.714101\pi$
$409$	7.39949	−	12.8163i	0.365881	−	0.633725i	0.988917	+	0.148468i	$0.0474342\pi$
$410$		0			0
$411$	2.00000	+	3.46410i	0.0986527	+	0.170872i
$412$		0			0
$413$	−7.27208	+	9.37769i	−0.357836	+	0.461446i
$414$		0			0
$415$	6.86396	+	11.8887i	0.336939	+	0.583595i
$416$		0			0
$417$	−3.34315	+	5.79050i	−0.163715	+	0.283562i
$418$		0			0
$419$	0.686292			0.0335275			0.0167638	−	0.999859i	$-0.494664\pi$
$419$	0.686292			0.0335275			0.0167638	+	0.999859i	$0.494664\pi$
$420$		0			0
$421$	13.4853			0.657232			0.328616	−	0.944464i	$-0.393418\pi$
$421$	13.4853			0.657232			0.328616	+	0.944464i	$0.393418\pi$
$422$		0			0
$423$	−2.82843	+	4.89898i	−0.137523	+	0.238197i
$424$		0			0
$425$	−2.41421	−	4.18154i	−0.117107	−	0.202835i
$426$		0			0
$427$	5.48528	+	13.4361i	0.265451	+	0.650220i
$428$		0			0
$429$	0.828427	+	1.43488i	0.0399968	+	0.0692766i
$430$		0			0
$431$	8.89949	−	15.4144i	0.428674	−	0.742484i	−0.568082	−	0.822972i	$-0.692314\pi$
$431$	8.89949	−	15.4144i	0.428674	−	0.742484i	0.996756	+	0.0804875i	$0.0256477\pi$
$432$		0			0
$433$	7.79899			0.374796			0.187398	−	0.982284i	$-0.439995\pi$
$433$	7.79899			0.374796			0.187398	+	0.982284i	$0.439995\pi$
$434$		0			0
$435$	−0.414214			−0.0198600
$436$		0			0
$437$	−0.585786	+	1.01461i	−0.0280220	+	0.0485355i
$438$		0			0
$439$	−16.9706	−	29.3939i	−0.809961	−	1.40289i	−0.912890	−	0.408205i	$-0.866155\pi$
$439$	−16.9706	−	29.3939i	−0.809961	−	1.40289i	0.102930	−	0.994689i	$-0.467178\pi$
$440$		0			0
$441$	4.92893	+	19.1757i	0.234711	+	0.913126i
$442$		0			0
$443$	15.1066	+	26.1654i	0.717736	+	1.24316i	0.961895	+	0.273420i	$0.0881550\pi$
$443$	15.1066	+	26.1654i	0.717736	+	1.24316i	−0.244158	+	0.969735i	$0.578512\pi$
$444$		0			0
$445$	4.32843	−	7.49706i	0.205187	−	0.355395i
$446$		0			0
$447$	−0.899495			−0.0425447
$448$		0			0
$449$	3.82843			0.180675			0.0903373	−	0.995911i	$-0.471205\pi$
$449$	3.82843			0.180675			0.0903373	+	0.995911i	$0.471205\pi$
$450$		0			0
$451$	3.24264	−	5.61642i	0.152690	−	0.264467i
$452$		0			0
$453$	2.41421	+	4.18154i	0.113430	+	0.196466i
$454$		0			0
$455$	−4.82843	−	11.8272i	−0.226360	−	0.554467i
$456$		0			0
$457$	−12.1421	−	21.0308i	−0.567985	−	0.983779i	−0.996765	−	0.0803702i	$-0.974390\pi$
$457$	−12.1421	−	21.0308i	−0.567985	−	0.983779i	0.428780	−	0.903409i	$-0.358944\pi$
$458$		0			0
$459$	5.82843	−	10.0951i	0.272048	−	0.471200i
$460$		0			0
$461$	41.3137			1.92417			0.962086	−	0.272748i	$-0.0879324\pi$
$461$	41.3137			1.92417			0.962086	+	0.272748i	$0.0879324\pi$
$462$		0			0
$463$	37.0416			1.72147			0.860735	−	0.509053i	$-0.170004\pi$
$463$	37.0416			1.72147			0.860735	+	0.509053i	$0.170004\pi$
$464$		0			0
$465$	−1.24264	+	2.15232i	−0.0576261	+	0.0998113i
$466$		0			0
$467$	−1.55025	−	2.68512i	−0.0717371	−	0.124252i	0.827926	−	0.560838i	$-0.189521\pi$
$467$	−1.55025	−	2.68512i	−0.0717371	−	0.124252i	−0.899663	+	0.436586i	$0.856188\pi$
$468$		0			0
$469$	−15.5416	+	20.0417i	−0.717646	+	0.925439i
$470$		0			0
$471$	−3.58579	−	6.21076i	−0.165224	−	0.286177i
$472$		0			0
$473$	1.48528	−	2.57258i	0.0682933	−	0.118287i
$474$		0			0
$475$	−2.82843			−0.129777
$476$		0			0
$477$	3.31371			0.151724
$478$		0			0
$479$	−17.8284	+	30.8797i	−0.814602	+	1.41093i	0.0950120	+	0.995476i	$0.469711\pi$
$479$	−17.8284	+	30.8797i	−0.814602	+	1.41093i	−0.909614	+	0.415455i	$0.863622\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	0.449747	+	0.0615465i	0.0204642	+	0.00280046i
$484$		0			0
$485$	−5.82843	−	10.0951i	−0.264655	−	0.458396i
$486$		0			0
$487$	2.17157	−	3.76127i	0.0984034	−	0.170440i	−0.812621	−	0.582793i	$-0.801960\pi$
$487$	2.17157	−	3.76127i	0.0984034	−	0.170440i	0.911024	+	0.412353i	$0.135293\pi$
$488$		0			0
$489$	−5.11270			−0.231204
$490$		0			0
$491$	−9.31371			−0.420322			−0.210161	−	0.977667i	$-0.567399\pi$
$491$	−9.31371			−0.420322			−0.210161	+	0.977667i	$0.567399\pi$
$492$		0			0
$493$	2.41421	−	4.18154i	0.108731	−	0.188327i
$494$		0			0
$495$	1.17157	+	2.02922i	0.0526583	+	0.0912068i
$496$		0			0
$497$	11.7574	+	1.60896i	0.527390	+	0.0721716i
$498$		0			0
$499$	−0.414214	−	0.717439i	−0.0185427	−	0.0321170i	0.856605	−	0.515973i	$-0.172569\pi$
$499$	−0.414214	−	0.717439i	−0.0185427	−	0.0321170i	−0.875148	+	0.483856i	$0.839236\pi$
$500$		0			0
$501$	4.64214	−	8.04041i	0.207395	−	0.359219i
$502$		0			0
$503$	15.8701			0.707611			0.353805	−	0.935319i	$-0.384887\pi$
$503$	15.8701			0.707611			0.353805	+	0.935319i	$0.384887\pi$
$504$		0			0
$505$	−10.3137			−0.458954
$506$		0			0
$507$	−2.13604	+	3.69973i	−0.0948648	+	0.164311i
$508$		0			0
$509$	−6.67157	−	11.5555i	−0.295712	−	0.512189i	0.679438	−	0.733733i	$-0.262224\pi$
$509$	−6.67157	−	11.5555i	−0.295712	−	0.512189i	−0.975150	+	0.221544i	$0.928890\pi$
$510$		0			0
$511$	−1.34315	+	1.73205i	−0.0594173	+	0.0766214i
$512$		0			0
$513$	−3.41421	−	5.91359i	−0.150741	−	0.261091i
$514$		0			0
$515$	−1.20711	+	2.09077i	−0.0531915	+	0.0921303i
$516$		0			0
$517$	−1.65685			−0.0728684
$518$		0			0
$519$	1.37258			0.0602497
$520$		0			0
$521$	−7.48528	+	12.9649i	−0.327936	+	0.568002i	−0.982102	−	0.188349i	$-0.939686\pi$
$521$	−7.48528	+	12.9649i	−0.327936	+	0.568002i	0.654166	+	0.756351i	$0.273020\pi$
$522$		0			0
$523$	17.8284	+	30.8797i	0.779583	+	1.35028i	0.932182	+	0.361989i	$0.117902\pi$
$523$	17.8284	+	30.8797i	0.779583	+	1.35028i	−0.152600	+	0.988288i	$0.548765\pi$
$524$		0			0
$525$	0.414214	+	1.01461i	0.0180778	+	0.0442813i
$526$		0			0
$527$	−14.4853	−	25.0892i	−0.630989	−	1.09290i
$528$		0			0
$529$	11.4142	−	19.7700i	0.496270	−	0.859565i
$530$		0			0
$531$	12.6863			0.550538
$532$		0			0
$533$	37.7990			1.63726
$534$		0			0
$535$	5.62132	−	9.73641i	0.243031	−	0.420942i
$536$		0			0
$537$	−2.07107	−	3.58719i	−0.0893732	−	0.154799i
$538$		0			0
$539$	−4.14214	+	4.05845i	−0.178414	+	0.174810i
$540$		0			0
$541$	−3.67157	−	6.35935i	−0.157853	−	0.273410i	0.776241	−	0.630436i	$-0.217124\pi$
$541$	−3.67157	−	6.35935i	−0.157853	−	0.273410i	−0.934094	+	0.357026i	$0.883791\pi$
$542$		0			0
$543$	−0.550253	+	0.953065i	−0.0236136	+	0.0408999i
$544$		0			0
$545$	−13.4853			−0.577646
$546$		0			0
$547$	−24.8995			−1.06463			−0.532313	−	0.846548i	$-0.678677\pi$
$547$	−24.8995			−1.06463			−0.532313	+	0.846548i	$0.678677\pi$
$548$		0			0
$549$	7.75736	−	13.4361i	0.331076	−	0.573441i
$550$		0			0
$551$	−1.41421	−	2.44949i	−0.0602475	−	0.104352i
$552$		0			0
$553$	−14.8284	−	36.3221i	−0.630569	−	1.54457i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.1421	+	19.2987i	−0.472107	+	0.817714i	−0.999491	−	0.0319135i	$-0.989840\pi$
$557$	−11.1421	+	19.2987i	−0.472107	+	0.817714i	0.527383	+	0.849628i	$0.323173\pi$
$558$		0			0
$559$	17.3137			0.732292
$560$		0			0
$561$	1.65685			0.0699524
$562$		0			0
$563$	20.8640	−	36.1374i	0.879311	−	1.52301i	0.0272129	−	0.999630i	$-0.491337\pi$
$563$	20.8640	−	36.1374i	0.879311	−	1.52301i	0.852098	−	0.523382i	$-0.175330\pi$
$564$		0			0
$565$	2.24264	+	3.88437i	0.0943486	+	0.163417i
$566$		0			0
$567$	12.1360	−	15.6500i	0.509666	−	0.657238i
$568$		0			0
$569$	−3.82843	−	6.63103i	−0.160496	−	0.277987i	0.774551	−	0.632512i	$-0.217976\pi$
$569$	−3.82843	−	6.63103i	−0.160496	−	0.277987i	−0.935047	+	0.354525i	$0.884643\pi$
$570$		0			0
$571$	4.58579	−	7.94282i	0.191909	−	0.332396i	−0.753974	−	0.656905i	$-0.771865\pi$
$571$	4.58579	−	7.94282i	0.191909	−	0.332396i	0.945883	+	0.324508i	$0.105199\pi$
$572$		0			0
$573$	5.31371			0.221983
$574$		0			0
$575$	−0.414214			−0.0172739
$576$		0			0
$577$	21.9706	−	38.0541i	0.914646	−	1.58421i	0.107228	−	0.994234i	$-0.465802\pi$
$577$	21.9706	−	38.0541i	0.914646	−	1.58421i	0.807418	−	0.589980i	$-0.200864\pi$
$578$		0			0
$579$	0.414214	+	0.717439i	0.0172141	+	0.0298157i
$580$		0			0
$581$	35.9853	+	4.92447i	1.49292	+	0.204302i
$582$		0			0
$583$	0.485281	+	0.840532i	0.0200983	+	0.0348113i
$584$		0			0
$585$	−6.82843	+	11.8272i	−0.282321	+	0.488994i
$586$		0			0
$587$	34.2843			1.41506			0.707532	−	0.706682i	$-0.249809\pi$
$587$	34.2843			1.41506			0.707532	+	0.706682i	$0.249809\pi$
$588$		0			0
$589$	−16.9706			−0.699260
$590$		0			0
$591$	2.55635	−	4.42773i	0.105154	−	0.182132i
$592$		0			0
$593$	−2.10051	−	3.63818i	−0.0862574	−	0.149402i	0.819669	−	0.572838i	$-0.194157\pi$
$593$	−2.10051	−	3.63818i	−0.0862574	−	0.149402i	−0.905926	+	0.423435i	$0.860824\pi$
$594$		0			0
$595$	−12.6569	−	1.73205i	−0.518880	−	0.0710072i
$596$		0			0
$597$	−2.00000	−	3.46410i	−0.0818546	−	0.141776i
$598$		0			0
$599$	3.17157	−	5.49333i	0.129587	−	0.224451i	−0.793930	−	0.608010i	$-0.791968\pi$
$599$	3.17157	−	5.49333i	0.129587	−	0.224451i	0.923517	+	0.383558i	$0.125302\pi$
$600$		0			0
$601$	19.6569			0.801820			0.400910	−	0.916117i	$-0.368694\pi$
$601$	19.6569			0.801820			0.400910	+	0.916117i	$0.368694\pi$
$602$		0			0
$603$	27.1127			1.10411
$604$		0			0
$605$	5.15685	−	8.93193i	0.209656	−	0.363135i
$606$		0			0
$607$	19.1066	+	33.0936i	0.775513	+	1.34323i	0.934506	+	0.355948i	$0.115842\pi$
$607$	19.1066	+	33.0936i	0.775513	+	1.34323i	−0.158993	+	0.987280i	$0.550825\pi$
$608$		0			0
$609$	−0.671573	+	0.866025i	−0.0272135	+	0.0350931i
$610$		0			0
$611$	−4.82843	−	8.36308i	−0.195337	−	0.338334i
$612$		0			0
$613$	−17.7279	+	30.7057i	−0.716024	+	1.24019i	0.246539	+	0.969133i	$0.420707\pi$
$613$	−17.7279	+	30.7057i	−0.716024	+	1.24019i	−0.962563	+	0.271057i	$0.912627\pi$
$614$		0			0
$615$	−3.24264			−0.130756
$616$		0			0
$617$	11.3137			0.455473			0.227736	−	0.973723i	$-0.426868\pi$
$617$	11.3137			0.455473			0.227736	+	0.973723i	$0.426868\pi$
$618$		0			0
$619$	12.7574	−	22.0964i	0.512762	−	0.888129i	−0.487129	−	0.873330i	$-0.661956\pi$
$619$	12.7574	−	22.0964i	0.512762	−	0.888129i	0.999890	−	0.0147990i	$-0.00471084\pi$
$620$		0			0
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$		0			0
$623$	−8.65685	−	21.2049i	−0.346830	−	0.849555i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	0.485281	−	0.840532i	0.0193803	−	0.0335676i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	20.1421			0.801846			0.400923	−	0.916112i	$-0.368690\pi$
$631$	20.1421			0.801846			0.400923	+	0.916112i	$0.368690\pi$
$632$		0			0
$633$	4.24264	−	7.34847i	0.168630	−	0.292075i
$634$		0			0
$635$	−4.65685	−	8.06591i	−0.184802	−	0.320086i
$636$		0			0
$637$	−32.5563	−	9.08052i	−1.28993	−	0.359783i
$638$		0			0
$639$	−6.34315	−	10.9867i	−0.250931	−	0.434625i
$640$		0			0
$641$	−15.7426	+	27.2671i	−0.621797	+	1.07698i	0.367354	+	0.930081i	$0.380264\pi$
$641$	−15.7426	+	27.2671i	−0.621797	+	1.07698i	−0.989151	+	0.146903i	$0.953070\pi$
$642$		0			0
$643$	−26.2843			−1.03655			−0.518275	−	0.855214i	$-0.673426\pi$
$643$	−26.2843			−1.03655			−0.518275	+	0.855214i	$0.673426\pi$
$644$		0			0
$645$	−1.48528			−0.0584829
$646$		0			0
$647$	−15.5208	+	26.8828i	−0.610186	+	1.05687i	0.381022	+	0.924566i	$0.375572\pi$
$647$	−15.5208	+	26.8828i	−0.610186	+	1.05687i	−0.991209	+	0.132308i	$0.957761\pi$
$648$		0			0
$649$	1.85786	+	3.21792i	0.0729276	+	0.126314i
$650$		0			0
$651$	2.48528	+	6.08767i	0.0974059	+	0.238595i
$652$		0			0
$653$	9.58579	+	16.6031i	0.375121	+	0.649728i	0.990345	−	0.138624i	$-0.0442679\pi$
$653$	9.58579	+	16.6031i	0.375121	+	0.649728i	−0.615224	+	0.788352i	$0.710935\pi$
$654$		0			0
$655$	−9.65685	+	16.7262i	−0.377325	+	0.653545i
$656$		0			0
$657$	2.34315			0.0914148
$658$		0			0
$659$	−21.1716			−0.824727			−0.412364	−	0.911019i	$-0.635297\pi$
$659$	−21.1716			−0.824727			−0.412364	+	0.911019i	$0.635297\pi$
$660$		0			0
$661$	−15.9142	+	27.5642i	−0.618991	+	1.07212i	0.370679	+	0.928761i	$0.379125\pi$
$661$	−15.9142	+	27.5642i	−0.618991	+	1.07212i	−0.989670	+	0.143363i	$0.954208\pi$
$662$		0			0
$663$	4.82843	+	8.36308i	0.187521	+	0.324795i
$664$		0			0
$665$	−4.58579	+	5.91359i	−0.177829	+	0.229319i
$666$		0			0
$667$	−0.207107	−	0.358719i	−0.00801921	−	0.0138897i
$668$		0			0
$669$	0.0710678	−	0.123093i	0.00274764	−	0.00475905i
$670$		0			0
$671$	4.54416			0.175425
$672$		0			0
$673$	29.6569			1.14319			0.571594	−	0.820537i	$-0.306325\pi$
$673$	29.6569			1.14319			0.571594	+	0.820537i	$0.306325\pi$
$674$		0			0
$675$	1.20711	−	2.09077i	0.0464616	−	0.0804738i
$676$		0			0
$677$	14.0711	+	24.3718i	0.540795	+	0.936685i	0.998859	+	0.0477651i	$0.0152099\pi$
$677$	14.0711	+	24.3718i	0.540795	+	0.936685i	−0.458064	+	0.888919i	$0.651457\pi$
$678$		0			0
$679$	−30.5563	−	4.18154i	−1.17265	−	0.160473i
$680$		0			0
$681$	−1.44365	−	2.50048i	−0.0553208	−	0.0958185i
$682$		0			0
$683$	−17.3787	+	30.1008i	−0.664977	+	1.15177i	0.314315	+	0.949319i	$0.398225\pi$
$683$	−17.3787	+	30.1008i	−0.664977	+	1.15177i	−0.979292	+	0.202455i	$0.935108\pi$
$684$		0			0
$685$	−9.65685			−0.368969
$686$		0			0
$687$	−4.82843			−0.184216
$688$		0			0
$689$	−2.82843	+	4.89898i	−0.107754	+	0.186636i
$690$		0			0
$691$	0.414214	+	0.717439i	0.0157574	+	0.0272927i	0.873797	−	0.486292i	$-0.161651\pi$
$691$	0.414214	+	0.717439i	0.0157574	+	0.0272927i	−0.858039	+	0.513584i	$0.828317\pi$
$692$		0			0
$693$	6.14214	+	0.840532i	0.233320	+	0.0319292i
$694$		0			0
$695$	−8.07107	−	13.9795i	−0.306153	−	0.530273i
$696$		0			0
$697$	18.8995	−	32.7349i	0.715869	−	1.23992i
$698$		0			0
$699$	−6.97056			−0.263651
$700$		0			0
$701$	−3.20101			−0.120900			−0.0604502	−	0.998171i	$-0.519254\pi$
$701$	−3.20101			−0.120900			−0.0604502	+	0.998171i	$0.519254\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.414214	+	0.717439i	0.0156002	+	0.0270203i
$706$		0			0
$707$	−16.7218	+	21.5636i	−0.628889	+	0.810982i
$708$		0			0
$709$	−7.84315	−	13.5847i	−0.294556	−	0.510185i	0.680326	−	0.732910i	$-0.261838\pi$
$709$	−7.84315	−	13.5847i	−0.294556	−	0.510185i	−0.974881	+	0.222725i	$0.928505\pi$
$710$		0			0
$711$	−20.9706	+	36.3221i	−0.786458	+	1.36218i
$712$		0			0
$713$	−2.48528			−0.0930745
$714$		0			0
$715$	−4.00000			−0.149592
$716$		0			0
$717$	−4.41421	+	7.64564i	−0.164852	+	0.285532i
$718$		0			0
$719$	10.5563	+	18.2841i	0.393685	+	0.681883i	0.992932	−	0.118681i	$-0.0378666\pi$
$719$	10.5563	+	18.2841i	0.393685	+	0.681883i	−0.599247	+	0.800564i	$0.704533\pi$
$720$		0			0
$721$	2.41421	+	5.91359i	0.0899100	+	0.220234i
$722$		0			0
$723$	−5.72792	−	9.92105i	−0.213024	−	0.368968i
$724$		0			0
$725$	0.500000	−	0.866025i	0.0185695	−	0.0321634i
$726$		0			0
$727$	37.5858			1.39398			0.696990	−	0.717081i	$-0.254522\pi$
$727$	37.5858			1.39398			0.696990	+	0.717081i	$0.254522\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$		0			0
$731$	8.65685	−	14.9941i	0.320185	−	0.554577i
$732$		0			0
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$		0			0
$735$	2.79289	+	0.778985i	0.103017	+	0.0287333i
$736$		0			0
$737$	3.97056	+	6.87722i	0.146258	+	0.253326i
$738$		0			0
$739$	−10.5563	+	18.2841i	−0.388322	+	0.672593i	−0.992224	−	0.124466i	$-0.960278\pi$
$739$	−10.5563	+	18.2841i	−0.388322	+	0.672593i	0.603902	+	0.797058i	$0.293612\pi$
$740$		0			0
$741$	5.65685			0.207810
$742$		0			0
$743$	16.0711			0.589590			0.294795	−	0.955560i	$-0.404749\pi$
$743$	16.0711			0.589590			0.294795	+	0.955560i	$0.404749\pi$
$744$		0			0
$745$	1.08579	−	1.88064i	0.0397801	−	0.0689012i
$746$		0			0
$747$	−19.4142	−	33.6264i	−0.710329	−	1.23033i
$748$		0			0
$749$	−11.2426	−	27.5387i	−0.410797	−	1.00624i
$750$		0			0
$751$	−15.1716	−	26.2779i	−0.553619	−	0.958895i	−0.998010	−	0.0630625i	$-0.979913\pi$
$751$	−15.1716	−	26.2779i	−0.553619	−	0.958895i	0.444391	−	0.895833i	$-0.353420\pi$
$752$		0			0
$753$	−1.92893	+	3.34101i	−0.0702942	+	0.121753i
$754$		0			0
$755$	−11.6569			−0.424236
$756$		0			0
$757$	−31.4558			−1.14328			−0.571641	−	0.820504i	$-0.693693\pi$
$757$	−31.4558			−1.14328			−0.571641	+	0.820504i	$0.693693\pi$
$758$		0			0
$759$	0.0710678	−	0.123093i	0.00257960	−	0.00446800i
$760$		0			0
$761$	−4.65685	−	8.06591i	−0.168811	−	0.292389i	0.769191	−	0.639019i	$-0.220659\pi$
$761$	−4.65685	−	8.06591i	−0.168811	−	0.292389i	−0.938002	+	0.346630i	$0.887326\pi$
$762$		0			0
$763$	−21.8640	+	28.1946i	−0.791529	+	1.02071i
$764$		0			0
$765$	6.82843	+	11.8272i	0.246882	+	0.427613i
$766$		0			0
$767$	−10.8284	+	18.7554i	−0.390992	+	0.677218i
$768$		0			0
$769$	−0.627417			−0.0226252			−0.0113126	−	0.999936i	$-0.503601\pi$
$769$	−0.627417			−0.0226252			−0.0113126	+	0.999936i	$0.503601\pi$
$770$		0			0
$771$	2.62742			0.0946241
$772$		0			0
$773$	18.5563	−	32.1405i	0.667425	−	1.15601i	−0.311196	−	0.950346i	$-0.600730\pi$
$773$	18.5563	−	32.1405i	0.667425	−	1.15601i	0.978622	−	0.205669i	$-0.0659371\pi$
$774$		0			0
$775$	−3.00000	−	5.19615i	−0.107763	−	0.186651i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−11.0711	−	19.1757i	−0.396662	−	0.687039i
$780$		0			0
$781$	1.85786	−	3.21792i	0.0664796	−	0.115146i
$782$		0			0
$783$	2.41421			0.0862770
$784$		0			0
$785$	17.3137			0.617953
$786$		0			0
$787$	1.27817	−	2.21386i	0.0455620	−	0.0789157i	−0.842345	−	0.538939i	$-0.818825\pi$
$787$	1.27817	−	2.21386i	0.0455620	−	0.0789157i	0.887907	+	0.460023i	$0.152159\pi$
$788$		0			0
$789$	−6.01472	−	10.4178i	−0.214130	−	0.370883i
$790$		0			0
$791$	11.7574	+	1.60896i	0.418044	+	0.0572080i
$792$		0			0
$793$	13.2426	+	22.9369i	0.470260	+	0.814514i
$794$		0			0
$795$	0.242641	−	0.420266i	0.00860558	−	0.0149053i
$796$		0			0
$797$	−8.00000			−0.283375			−0.141687	−	0.989911i	$-0.545253\pi$
$797$	−8.00000			−0.283375			−0.141687	+	0.989911i	$0.545253\pi$
$798$		0			0
$799$	−9.65685			−0.341635
$800$		0			0
$801$	−12.2426	+	21.2049i	−0.432572	+	0.749237i
$802$		0			0
$803$	0.343146	+	0.594346i	0.0121094	+	0.0209740i
$804$		0			0
$805$	−0.671573	+	0.866025i	−0.0236698	+	0.0305234i
$806$		0			0
$807$	−4.23654	−	7.33791i	−0.149133	−	0.258307i
$808$		0			0
$809$	−17.8137	+	30.8542i	−0.626297	+	1.08478i	0.361992	+	0.932181i	$0.382097\pi$
$809$	−17.8137	+	30.8542i	−0.626297	+	1.08478i	−0.988289	+	0.152596i	$0.951237\pi$
$810$		0			0
$811$	20.6274			0.724327			0.362163	−	0.932115i	$-0.382038\pi$
$811$	20.6274			0.724327			0.362163	+	0.932115i	$0.382038\pi$
$812$		0			0
$813$	−6.82843			−0.239483
$814$		0			0
$815$	6.17157	−	10.6895i	0.216181	−	0.374436i
$816$		0			0
$817$	−5.07107	−	8.78335i	−0.177414	−	0.307290i
$818$		0			0
$819$	13.6569	+	33.4523i	0.477209	+	1.16892i
$820$		0			0
$821$	−23.9706	−	41.5182i	−0.836578	−	1.44900i	−0.892739	−	0.450575i	$-0.851219\pi$
$821$	−23.9706	−	41.5182i	−0.836578	−	1.44900i	0.0561604	−	0.998422i	$-0.482114\pi$
$822$		0			0
$823$	1.03553	−	1.79360i	0.0360964	−	0.0625209i	−0.847413	−	0.530935i	$-0.821841\pi$
$823$	1.03553	−	1.79360i	0.0360964	−	0.0625209i	0.883509	+	0.468414i	$0.155174\pi$
$824$		0			0
$825$	0.343146			0.0119468
$826$		0			0
$827$	26.2132			0.911522			0.455761	−	0.890102i	$-0.349367\pi$
$827$	26.2132			0.911522			0.455761	+	0.890102i	$0.349367\pi$
$828$		0			0
$829$	−14.6569	+	25.3864i	−0.509054	+	0.881707i	0.490891	+	0.871221i	$0.336671\pi$
$829$	−14.6569	+	25.3864i	−0.509054	+	0.881707i	−0.999945	+	0.0104859i	$0.996662\pi$
$830$		0			0
$831$	−3.34315	−	5.79050i	−0.115972	−	0.200870i
$832$		0			0
$833$	−24.1421	+	23.6544i	−0.836475	+	0.819575i
$834$		0			0
$835$	11.2071	+	19.4113i	0.387838	+	0.671755i
$836$		0			0
$837$	7.24264	−	12.5446i	0.250342	−	0.433606i
$838$		0			0
$839$	−15.1716			−0.523781			−0.261890	−	0.965098i	$-0.584346\pi$
$839$	−15.1716			−0.523781			−0.261890	+	0.965098i	$0.584346\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$		0			0
$843$	6.27208	−	10.8636i	0.216022	−	0.374161i
$844$		0			0
$845$	−5.15685	−	8.93193i	−0.177401	−	0.307268i
$846$		0			0
$847$	−10.3137	−	25.2633i	−0.354383	−	0.868058i
$848$		0			0
$849$	2.89949	+	5.02207i	0.0995104	+	0.172357i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	2.54416			0.0871102			0.0435551	−	0.999051i	$-0.486132\pi$
$853$	2.54416			0.0871102			0.0435551	+	0.999051i	$0.486132\pi$
$854$		0			0
$855$	8.00000			0.273594
$856$		0			0
$857$	−17.1421	+	29.6910i	−0.585564	+	1.01423i	0.409241	+	0.912426i	$0.365794\pi$
$857$	−17.1421	+	29.6910i	−0.585564	+	1.01423i	−0.994805	+	0.101800i	$0.967540\pi$
$858$		0			0
$859$	0.686292	+	1.18869i	0.0234160	+	0.0405576i	0.877496	−	0.479584i	$-0.159212\pi$
$859$	0.686292	+	1.18869i	0.0234160	+	0.0405576i	−0.854080	+	0.520142i	$0.825879\pi$
$860$		0			0
$861$	−5.25736	+	6.77962i	−0.179170	+	0.231049i
$862$		0			0
$863$	7.27817	+	12.6062i	0.247752	+	0.429119i	0.962902	−	0.269852i	$-0.0869749\pi$
$863$	7.27817	+	12.6062i	0.247752	+	0.429119i	−0.715150	+	0.698971i	$0.753642\pi$
$864$		0			0
$865$	−1.65685	+	2.86976i	−0.0563347	+	0.0975746i
$866$		0			0
$867$	2.61522			0.0888177
$868$		0			0
$869$	−12.2843			−0.416715
$870$		0			0
$871$	−23.1421	+	40.0834i	−0.784141	+	1.35817i
$872$		0			0
$873$	16.4853	+	28.5533i	0.557942	+	0.966384i
$874$		0			0
$875$	−2.62132	−	0.358719i	−0.0886168	−	0.0121269i
$876$		0			0
$877$	−12.5858	−	21.7992i	−0.424992	−	0.736107i	0.571428	−	0.820652i	$-0.306390\pi$
$877$	−12.5858	−	21.7992i	−0.424992	−	0.736107i	−0.996420	+	0.0845449i	$0.973056\pi$
$878$		0			0
$879$	3.31371	−	5.73951i	0.111769	−	0.193589i
$880$		0			0
$881$	1.82843			0.0616013			0.0308006	−	0.999526i	$-0.490194\pi$
$881$	1.82843			0.0616013			0.0308006	+	0.999526i	$0.490194\pi$
$882$		0			0
$883$	−18.2843			−0.615315			−0.307657	−	0.951497i	$-0.599545\pi$
$883$	−18.2843			−0.615315			−0.307657	+	0.951497i	$0.599545\pi$
$884$		0			0
$885$	0.928932	−	1.60896i	0.0312257	−	0.0540845i
$886$		0			0
$887$	14.9645	+	25.9192i	0.502458	+	0.870282i	0.999996	+	0.00284012i	$0.000904038\pi$
$887$	14.9645	+	25.9192i	0.502458	+	0.870282i	−0.497538	+	0.867442i	$0.665763\pi$
$888$		0			0
$889$	−24.4142	−	3.34101i	−0.818826	−	0.112054i
$890$		0			0
$891$	−3.10051	−	5.37023i	−0.103871	−	0.179910i
$892$		0			0
$893$	−2.82843	+	4.89898i	−0.0946497	+	0.163938i
$894$		0			0
$895$	10.0000			0.334263
$896$		0			0
$897$	0.828427			0.0276604
$898$		0			0
$899$	3.00000	−	5.19615i	0.100056	−	0.173301i
$900$		0			0
$901$	2.82843	+	4.89898i	0.0942286	+	0.163209i
$902$		0			0
$903$	−2.40812	+	3.10538i	−0.0801371	+	0.103341i
$904$		0			0
$905$	−1.32843	−	2.30090i	−0.0441584	−	0.0764846i
$906$		0			0
$907$	−7.10660	+	12.3090i	−0.235971	+	0.408713i	−0.959554	−	0.281523i	$-0.909160\pi$
$907$	−7.10660	+	12.3090i	−0.235971	+	0.408713i	0.723584	+	0.690237i	$0.242494\pi$
$908$		0			0
$909$	29.1716			0.967560
$910$		0			0
$911$	10.2010			0.337975			0.168987	−	0.985618i	$-0.445950\pi$
$911$	10.2010			0.337975			0.168987	+	0.985618i	$0.445950\pi$
$912$		0			0
$913$	5.68629	−	9.84895i	0.188189	−	0.325953i
$914$		0			0
$915$	−1.13604	−	1.96768i	−0.0375563	−	0.0650494i
$916$		0			0
$917$	19.3137	+	47.3087i	0.637795	+	1.56227i
$918$		0			0
$919$	−21.5563	−	37.3367i	−0.711078	−	1.23162i	−0.964453	−	0.264256i	$-0.914874\pi$
$919$	−21.5563	−	37.3367i	−0.711078	−	1.23162i	0.253374	−	0.967368i	$-0.418460\pi$
$920$		0			0
$921$	−0.985281	+	1.70656i	−0.0324661	+	0.0562330i
$922$		0			0
$923$	21.6569			0.712844
$924$		0			0
$925$		0			0
$926$		0			0
$927$	3.41421	−	5.91359i	0.112137	−	0.194228i
$928$		0			0
$929$	−2.74264	−	4.75039i	−0.0899831	−	0.155855i	0.817521	−	0.575899i	$-0.195348\pi$
$929$	−2.74264	−	4.75039i	−0.0899831	−	0.155855i	−0.907504	+	0.420044i	$0.862015\pi$
$930$		0			0
$931$	4.92893	+	19.1757i	0.161539	+	0.628457i
$932$		0			0
$933$	−2.72792	−	4.72490i	−0.0893082	−	0.154686i
$934$		0			0
$935$	−2.00000	+	3.46410i	−0.0654070	+	0.113288i
$936$		0			0
$937$	34.6274			1.13123			0.565614	−	0.824670i	$-0.308639\pi$
$937$	34.6274			1.13123			0.565614	+	0.824670i	$0.308639\pi$
$938$		0			0
$939$	−2.62742			−0.0857425
$940$		0			0
$941$	23.1421	−	40.0834i	0.754412	−	1.30668i	−0.191254	−	0.981541i	$-0.561255\pi$
$941$	23.1421	−	40.0834i	0.754412	−	1.30668i	0.945666	−	0.325139i	$-0.105411\pi$
$942$		0			0
$943$	−1.62132	−	2.80821i	−0.0527975	−	0.0914479i
$944$		0			0
$945$	−2.41421	−	5.91359i	−0.0785344	−	0.192369i
$946$		0			0
$947$	16.5919	+	28.7380i	0.539164	+	0.933859i	0.998949	+	0.0458290i	$0.0145929\pi$
$947$	16.5919	+	28.7380i	0.539164	+	0.933859i	−0.459786	+	0.888030i	$0.652074\pi$
$948$		0			0
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$		0			0
$951$	−5.71573			−0.185345
$952$		0			0
$953$	−13.6569			−0.442389			−0.221194	−	0.975230i	$-0.570996\pi$
$953$	−13.6569			−0.442389			−0.221194	+	0.975230i	$0.570996\pi$
$954$		0			0
$955$	−6.41421	+	11.1097i	−0.207559	+	0.359503i
$956$		0			0
$957$	0.171573	+	0.297173i	0.00554616	+	0.00960624i
$958$		0			0
$959$	−15.6569	+	20.1903i	−0.505586	+	0.651978i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$	−15.8995	+	27.5387i	−0.512354	+	0.887423i
$964$		0			0
$965$	−2.00000			−0.0643823
$966$		0			0
$967$	−37.5269			−1.20678			−0.603392	−	0.797445i	$-0.706185\pi$
$967$	−37.5269			−1.20678			−0.603392	+	0.797445i	$0.706185\pi$
$968$		0			0
$969$	2.82843	−	4.89898i	0.0908622	−	0.157378i
$970$		0			0
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$		0			0
$973$	−42.3137	−	5.79050i	−1.35652	−	0.185635i
$974$		0			0
$975$	1.00000	+	1.73205i	0.0320256	+	0.0554700i
$976$		0			0
$977$	0.656854	−	1.13770i	0.0210146	−	0.0363984i	−0.855327	−	0.518089i	$-0.826644\pi$
$977$	0.656854	−	1.13770i	0.0210146	−	0.0363984i	0.876341	+	0.481690i	$0.159977\pi$
$978$		0			0
$979$	−7.17157			−0.229204
$980$		0			0
$981$	38.1421			1.21778
$982$		0			0
$983$	14.1066	−	24.4334i	0.449931	−	0.779303i	−0.548450	−	0.836183i	$-0.684782\pi$
$983$	14.1066	−	24.4334i	0.449931	−	0.779303i	0.998381	+	0.0568803i	$0.0181153\pi$
$984$		0			0
$985$	6.17157	+	10.6895i	0.196643	+	0.340595i
$986$		0			0
$987$	2.17157	+	0.297173i	0.0691219	+	0.00945912i
$988$		0			0
$989$	−0.742641	−	1.28629i	−0.0236146	−	0.0409017i
$990$		0			0
$991$	−2.17157	+	3.76127i	−0.0689823	+	0.119481i	−0.898454	−	0.439069i	$-0.855309\pi$
$991$	−2.17157	+	3.76127i	−0.0689823	+	0.119481i	0.829471	+	0.558549i	$0.188642\pi$
$992$		0			0
$993$	−9.51472			−0.301940
$994$		0			0
$995$	9.65685			0.306143
$996$		0			0
$997$	−16.7279	+	28.9736i	−0.529779	+	0.917603i	0.469618	+	0.882870i	$0.344392\pi$
$997$	−16.7279	+	28.9736i	−0.529779	+	0.917603i	−0.999397	+	0.0347337i	$0.988942\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.q.k.81.1		4
4.3	odd	2		35.2.e.a.11.1	✓	4
7.2	even	3	inner	560.2.q.k.401.1		4
7.3	odd	6		3920.2.a.bv.1.1		2
7.4	even	3		3920.2.a.bq.1.2		2
12.11	even	2		315.2.j.e.46.2		4
20.3	even	4		175.2.k.a.74.1		8
20.7	even	4		175.2.k.a.74.4		8
20.19	odd	2		175.2.e.c.151.2		4
28.3	even	6		245.2.a.g.1.2		2
28.11	odd	6		245.2.a.h.1.2		2
28.19	even	6		245.2.e.e.226.1		4
28.23	odd	6		35.2.e.a.16.1	yes	4
28.27	even	2		245.2.e.e.116.1		4
84.11	even	6		2205.2.a.n.1.1		2
84.23	even	6		315.2.j.e.226.2		4
84.59	odd	6		2205.2.a.q.1.1		2
140.3	odd	12		1225.2.b.h.99.1		4
140.23	even	12		175.2.k.a.149.4		8
140.39	odd	6		1225.2.a.k.1.1		2
140.59	even	6		1225.2.a.m.1.1		2
140.67	even	12		1225.2.b.g.99.4		4
140.79	odd	6		175.2.e.c.51.2		4
140.87	odd	12		1225.2.b.h.99.4		4
140.107	even	12		175.2.k.a.149.1		8
140.123	even	12		1225.2.b.g.99.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.e.a.11.1	✓	4	4.3	odd	2
35.2.e.a.16.1	yes	4	28.23	odd	6
175.2.e.c.51.2		4	140.79	odd	6
175.2.e.c.151.2		4	20.19	odd	2
175.2.k.a.74.1		8	20.3	even	4
175.2.k.a.74.4		8	20.7	even	4
175.2.k.a.149.1		8	140.107	even	12
175.2.k.a.149.4		8	140.23	even	12
245.2.a.g.1.2		2	28.3	even	6
245.2.a.h.1.2		2	28.11	odd	6
245.2.e.e.116.1		4	28.27	even	2
245.2.e.e.226.1		4	28.19	even	6
315.2.j.e.46.2		4	12.11	even	2
315.2.j.e.226.2		4	84.23	even	6
560.2.q.k.81.1		4	1.1	even	1	trivial
560.2.q.k.401.1		4	7.2	even	3	inner
1225.2.a.k.1.1		2	140.39	odd	6
1225.2.a.m.1.1		2	140.59	even	6
1225.2.b.g.99.1		4	140.123	even	12
1225.2.b.g.99.4		4	140.67	even	12
1225.2.b.h.99.1		4	140.3	odd	12
1225.2.b.h.99.4		4	140.87	odd	12
2205.2.a.n.1.1		2	84.11	even	6
2205.2.a.q.1.1		2	84.59	odd	6
3920.2.a.bq.1.2		2	7.4	even	3
3920.2.a.bv.1.1		2	7.3	odd	6

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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 + 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(-0.207107 + 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(1.41421 + 2.44949i) q^{9} +(-0.414214 + 0.717439i) q^{11} -4.82843 q^{13} +0.414214 q^{15} +(-2.41421 + 4.18154i) q^{17} +(1.41421 + 2.44949i) q^{19} +(0.671573 - 0.866025i) q^{21} +(0.207107 + 0.358719i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.41421 q^{27} -1.00000 q^{29} +(-3.00000 + 5.19615i) q^{31} +(-0.171573 - 0.297173i) q^{33} +(1.00000 + 2.44949i) q^{35} +(1.00000 - 1.73205i) q^{39} -7.82843 q^{41} -3.58579 q^{43} +(1.41421 - 2.44949i) q^{45} +(1.00000 + 1.73205i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(0.585786 - 1.01461i) q^{53} +0.828427 q^{55} -1.17157 q^{57} +(2.24264 - 3.88437i) q^{59} +(-2.74264 - 4.75039i) q^{61} +(-2.82843 - 6.92820i) q^{63} +(2.41421 + 4.18154i) q^{65} +(4.79289 - 8.30153i) q^{67} -0.171573 q^{69} -4.48528 q^{71} +(0.414214 - 0.717439i) q^{73} +(-0.207107 - 0.358719i) q^{75} +(1.34315 - 1.73205i) q^{77} +(7.41421 + 12.8418i) q^{79} +(-3.74264 + 6.48244i) q^{81} -13.7279 q^{83} +4.82843 q^{85} +(0.207107 - 0.358719i) q^{87} +(4.32843 + 7.49706i) q^{89} +(12.6569 + 1.73205i) q^{91} +(-1.24264 - 2.15232i) q^{93} +(1.41421 - 2.44949i) q^{95} +11.6569 q^{97} -2.34315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7	\( 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7} + 4 q^{11} - 8 q^{13} - 4 q^{15} - 4 q^{17} + 14 q^{21} - 2 q^{23} - 2 q^{25} - 4 q^{27} - 4 q^{29} - 12 q^{31} - 12 q^{33} + 4 q^{35} + 4 q^{39} - 20 q^{41} - 20 q^{43} + 4 q^{47} + 10 q^{49} - 4 q^{51} + 8 q^{53} - 8 q^{55} - 16 q^{57} - 8 q^{59} + 6 q^{61} + 4 q^{65} + 22 q^{67} - 12 q^{69} + 16 q^{71} - 4 q^{73} + 2 q^{75} + 28 q^{77} + 24 q^{79} + 2 q^{81} - 4 q^{83} + 8 q^{85} - 2 q^{87} + 6 q^{89} + 28 q^{91} + 12 q^{93} + 24 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7 + 4 * q^11 - 8 * q^13 - 4 * q^15 - 4 * q^17 + 14 * q^21 - 2 * q^23 - 2 * q^25 - 4 * q^27 - 4 * q^29 - 12 * q^31 - 12 * q^33 + 4 * q^35 + 4 * q^39 - 20 * q^41 - 20 * q^43 + 4 * q^47 + 10 * q^49 - 4 * q^51 + 8 * q^53 - 8 * q^55 - 16 * q^57 - 8 * q^59 + 6 * q^61 + 4 * q^65 + 22 * q^67 - 12 * q^69 + 16 * q^71 - 4 * q^73 + 2 * q^75 + 28 * q^77 + 24 * q^79 + 2 * q^81 - 4 * q^83 + 8 * q^85 - 2 * q^87 + 6 * q^89 + 28 * q^91 + 12 * q^93 + 24 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more