LMFDB - Embedded newform 560.2.q.l.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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.11337408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 12 $ x^6 + 18x^4 + 81x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$2.78499i$ of defining polynomial
Character	$\chi$	$=$	560.81
Dual form			560.2.q.l.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64497 + 2.84918i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.64497 + 0.0641892i) q^{7} +(-3.91187 - 6.77556i) q^{9} +O(q^{10})$	\(q+(-1.64497 + 2.84918i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.64497 + 0.0641892i) q^{7} +(-3.91187 - 6.77556i) q^{9} +(2.91187 - 5.04351i) q^{11} +2.75615 q^{13} +3.28995 q^{15} +(-1.00000 + 1.73205i) q^{17} +(-0.378076 - 0.654846i) q^{19} +(4.16802 - 7.64158i) q^{21} +(-0.266897 - 0.462279i) q^{23} +(-0.500000 + 0.866025i) q^{25} +15.8698 q^{27} -0.823739 q^{29} +(-1.28995 + 2.23425i) q^{31} +(9.57989 + 16.5929i) q^{33} +(1.37808 + 2.25852i) q^{35} +(-2.37808 - 4.11895i) q^{37} +(-4.53379 + 7.85276i) q^{39} +6.06759 q^{41} -0.710055 q^{43} +(-3.91187 + 6.77556i) q^{45} +(-6.44566 - 11.1642i) q^{47} +(6.99176 - 0.339557i) q^{49} +(-3.28995 - 5.69835i) q^{51} +(4.20181 - 7.27776i) q^{53} -5.82374 q^{55} +2.48770 q^{57} +(4.00000 - 6.92820i) q^{59} +(-4.70181 - 8.14378i) q^{61} +(10.7817 + 17.6701i) q^{63} +(-1.37808 - 2.38690i) q^{65} +(5.93492 - 10.2796i) q^{67} +1.75615 q^{69} +(-1.75615 + 3.04174i) q^{73} +(-1.64497 - 2.84918i) q^{75} +(-7.37808 + 13.5268i) q^{77} +(-4.75615 - 8.23790i) q^{79} +(-14.3698 + 24.8893i) q^{81} +6.71005 q^{83} +2.00000 q^{85} +(1.35503 - 2.34698i) q^{87} +(-0.878076 - 1.52087i) q^{89} +(-7.28995 + 0.176915i) q^{91} +(-4.24385 - 7.35056i) q^{93} +(-0.378076 + 0.654846i) q^{95} -2.00000 q^{97} -45.5634 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9}+O(q^{10}) $ 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9	$ 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9} + 3 q^{11} + 6 q^{13} - 6 q^{17} + 3 q^{19} + 3 q^{23} - 3 q^{25} + 36 q^{27} + 24 q^{29} + 12 q^{31} + 18 q^{33} + 3 q^{35} - 9 q^{37} - 18 q^{39} + 18 q^{41} - 24 q^{43} - 9 q^{45} - 15 q^{47} - 12 q^{49} - 9 q^{53} - 6 q^{55} + 36 q^{57} + 24 q^{59} + 6 q^{61} - 9 q^{63} - 3 q^{65} + 6 q^{67} - 39 q^{77} - 18 q^{79} - 27 q^{81} + 60 q^{83} + 12 q^{85} + 18 q^{87} - 24 q^{91} - 36 q^{93} + 3 q^{95} - 12 q^{97} - 126 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9 + 3 * q^11 + 6 * q^13 - 6 * q^17 + 3 * q^19 + 3 * q^23 - 3 * q^25 + 36 * q^27 + 24 * q^29 + 12 * q^31 + 18 * q^33 + 3 * q^35 - 9 * q^37 - 18 * q^39 + 18 * q^41 - 24 * q^43 - 9 * q^45 - 15 * q^47 - 12 * q^49 - 9 * q^53 - 6 * q^55 + 36 * q^57 + 24 * q^59 + 6 * q^61 - 9 * q^63 - 3 * q^65 + 6 * q^67 - 39 * q^77 - 18 * q^79 - 27 * q^81 + 60 * q^83 + 12 * q^85 + 18 * q^87 - 24 * q^91 - 36 * q^93 + 3 * q^95 - 12 * q^97 - 126 * 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
$3$	−1.64497	+	2.84918i	−0.949725	+	1.64497i	−0.203724	+	0.979028i	$0.565304\pi$
$3$	−1.64497	+	2.84918i	−0.949725	+	1.64497i	−0.746002	+	0.665944i	$0.768029\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.64497	+	0.0641892i	−0.999706	+	0.0242612i
$7$	−2.64497	+	0.0641892i	−0.999706	+	0.0242612i
$8$		0			0
$9$	−3.91187	−	6.77556i	−1.30396	−	2.25852i
$10$		0			0
$11$	2.91187	−	5.04351i	0.877962	−	1.52067i	0.0243876	−	0.999703i	$-0.492236\pi$
$11$	2.91187	−	5.04351i	0.877962	−	1.52067i	0.853574	−	0.520972i	$-0.174430\pi$
$12$		0			0
$13$	2.75615			0.764419			0.382209	−	0.924076i	$-0.375163\pi$
$13$	2.75615			0.764419			0.382209	+	0.924076i	$0.375163\pi$
$14$		0			0
$15$	3.28995			0.849460
$16$		0			0
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$		0			0
$19$	−0.378076	−	0.654846i	−0.0867365	−	0.150232i	0.819393	−	0.573232i	$-0.194310\pi$
$19$	−0.378076	−	0.654846i	−0.0867365	−	0.150232i	−0.906130	+	0.423000i	$0.860977\pi$
$20$		0			0
$21$	4.16802	−	7.64158i	0.909537	−	1.66753i
$22$		0			0
$23$	−0.266897	−	0.462279i	−0.0556518	−	0.0963918i	0.836857	−	0.547421i	$-0.184390\pi$
$23$	−0.266897	−	0.462279i	−0.0556518	−	0.0963918i	−0.892509	+	0.451029i	$0.851057\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	15.8698			3.05415
$28$		0			0
$29$	−0.823739			−0.152964			−0.0764822	−	0.997071i	$-0.524369\pi$
$29$	−0.823739			−0.152964			−0.0764822	+	0.997071i	$0.524369\pi$
$30$		0			0
$31$	−1.28995	+	2.23425i	−0.231681	+	0.401283i	−0.958303	−	0.285754i	$-0.907756\pi$
$31$	−1.28995	+	2.23425i	−0.231681	+	0.401283i	0.726622	+	0.687038i	$0.241089\pi$
$32$		0			0
$33$	9.57989	+	16.5929i	1.66764	+	2.88845i
$34$		0			0
$35$	1.37808	+	2.25852i	0.232937	+	0.381759i
$36$		0			0
$37$	−2.37808	−	4.11895i	−0.390953	−	0.677151i	0.601622	−	0.798781i	$-0.294521\pi$
$37$	−2.37808	−	4.11895i	−0.390953	−	0.677151i	−0.992576	+	0.121630i	$0.961188\pi$
$38$		0			0
$39$	−4.53379	+	7.85276i	−0.725988	+	1.25745i
$40$		0			0
$41$	6.06759			0.947598			0.473799	−	0.880633i	$-0.342882\pi$
$41$	6.06759			0.947598			0.473799	+	0.880633i	$0.342882\pi$
$42$		0			0
$43$	−0.710055			−0.108282			−0.0541412	−	0.998533i	$-0.517242\pi$
$43$	−0.710055			−0.108282			−0.0541412	+	0.998533i	$0.517242\pi$
$44$		0			0
$45$	−3.91187	+	6.77556i	−0.583147	+	1.01004i
$46$		0			0
$47$	−6.44566	−	11.1642i	−0.940197	−	1.62847i	−0.765095	−	0.643918i	$-0.777308\pi$
$47$	−6.44566	−	11.1642i	−0.940197	−	1.62847i	−0.175102	−	0.984550i	$-0.556026\pi$
$48$		0			0
$49$	6.99176	−	0.339557i	0.998823	−	0.0485082i
$50$		0			0
$51$	−3.28995	−	5.69835i	−0.460684	−	0.797929i
$52$		0			0
$53$	4.20181	−	7.27776i	0.577164	−	0.999677i	−0.418639	−	0.908153i	$-0.637493\pi$
$53$	4.20181	−	7.27776i	0.577164	−	0.999677i	0.995803	−	0.0915241i	$-0.0291738\pi$
$54$		0			0
$55$	−5.82374			−0.785273
$56$		0			0
$57$	2.48770			0.329504
$58$		0			0
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$		0			0
$61$	−4.70181	−	8.14378i	−0.602006	−	1.04270i	−0.992517	−	0.122106i	$-0.961035\pi$
$61$	−4.70181	−	8.14378i	−0.602006	−	1.04270i	0.390511	−	0.920598i	$-0.372298\pi$
$62$		0			0
$63$	10.7817	+	17.6701i	1.35837	+	2.22622i
$64$		0			0
$65$	−1.37808	−	2.38690i	−0.170929	−	0.296058i
$66$		0			0
$67$	5.93492	−	10.2796i	0.725066	−	1.25585i	−0.233881	−	0.972265i	$-0.575143\pi$
$67$	5.93492	−	10.2796i	0.725066	−	1.25585i	0.958947	−	0.283585i	$-0.0915239\pi$
$68$		0			0
$69$	1.75615			0.211416
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−1.75615	+	3.04174i	−0.205542	+	0.356009i	−0.950305	−	0.311320i	$-0.899229\pi$
$73$	−1.75615	+	3.04174i	−0.205542	+	0.356009i	0.744763	+	0.667329i	$0.232562\pi$
$74$		0			0
$75$	−1.64497	−	2.84918i	−0.189945	−	0.328995i
$76$		0			0
$77$	−7.37808	+	13.5268i	−0.840810	+	1.54153i
$78$		0			0
$79$	−4.75615	−	8.23790i	−0.535109	−	0.926836i	−0.999158	−	0.0410263i	$-0.986937\pi$
$79$	−4.75615	−	8.23790i	−0.535109	−	0.926836i	0.464049	−	0.885809i	$-0.346396\pi$
$80$		0			0
$81$	−14.3698	+	24.8893i	−1.59665	+	2.76548i
$82$		0			0
$83$	6.71005			0.736524			0.368262	−	0.929722i	$-0.379953\pi$
$83$	6.71005			0.736524			0.368262	+	0.929722i	$0.379953\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$	1.35503	−	2.34698i	0.145274	−	0.251622i
$88$		0			0
$89$	−0.878076	−	1.52087i	−0.0930758	−	0.161212i	0.815728	−	0.578436i	$-0.196337\pi$
$89$	−0.878076	−	1.52087i	−0.0930758	−	0.161212i	−0.908804	+	0.417223i	$0.863003\pi$
$90$		0			0
$91$	−7.28995	+	0.176915i	−0.764194	+	0.0185458i
$92$		0			0
$93$	−4.24385	−	7.35056i	−0.440067	−	0.762218i
$94$		0			0
$95$	−0.378076	+	0.654846i	−0.0387898	+	0.0671858i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	−45.5634			−4.57929
$100$		0			0
$101$	−1.16802	+	2.02307i	−0.116222	+	0.201303i	−0.918268	−	0.395960i	$-0.870412\pi$
$101$	−1.16802	+	2.02307i	−0.116222	+	0.201303i	0.802045	+	0.597263i	$0.203745\pi$
$102$		0			0
$103$	−1.11118	−	1.92462i	−0.109488	−	0.189638i	0.806075	−	0.591813i	$-0.201588\pi$
$103$	−1.11118	−	1.92462i	−0.109488	−	0.189638i	−0.915563	+	0.402175i	$0.868254\pi$
$104$		0			0
$105$	−8.70181	+	0.211179i	−0.849210	+	0.0206090i
$106$		0			0
$107$	7.93492	+	13.7437i	0.767097	+	1.32865i	0.939131	+	0.343561i	$0.111633\pi$
$107$	7.93492	+	13.7437i	0.767097	+	1.32865i	−0.172033	+	0.985091i	$0.555034\pi$
$108$		0			0
$109$	1.63423	−	2.83056i	0.156531	−	0.271119i	−0.777085	−	0.629396i	$-0.783302\pi$
$109$	1.63423	−	2.83056i	0.156531	−	0.271119i	0.933615	+	0.358277i	$0.116636\pi$
$110$		0			0
$111$	15.6475			1.48519
$112$		0			0
$113$	−13.1598			−1.23797			−0.618984	−	0.785404i	$-0.712455\pi$
$113$	−13.1598			−1.23797			−0.618984	+	0.785404i	$0.712455\pi$
$114$		0			0
$115$	−0.266897	+	0.462279i	−0.0248883	+	0.0431077i
$116$		0			0
$117$	−10.7817	−	18.6745i	−0.996769	−	1.72645i
$118$		0			0
$119$	2.53379	−	4.64542i	0.232272	−	0.425845i
$120$		0			0
$121$	−11.4580	−	19.8458i	−1.04163	−	1.80416i
$122$		0			0
$123$	−9.98101	+	17.2876i	−0.899958	+	1.55877i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−11.9159			−1.05737			−0.528684	−	0.848819i	$-0.677314\pi$
$127$	−11.9159			−1.05737			−0.528684	+	0.848819i	$0.677314\pi$
$128$		0			0
$129$	1.16802	−	2.02307i	0.102839	−	0.178122i
$130$		0			0
$131$	10.7817	+	18.6745i	0.942002	+	1.63160i	0.761646	+	0.647994i	$0.224392\pi$
$131$	10.7817	+	18.6745i	0.942002	+	1.63160i	0.180356	+	0.983601i	$0.442275\pi$
$132$		0			0
$133$	1.04203	+	1.70778i	0.0903558	+	0.148084i
$134$		0			0
$135$	−7.93492	−	13.7437i	−0.682929	−	1.18287i
$136$		0			0
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	−0.938725	−	0.344668i	$-0.887992\pi$
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	0.767853	+	0.640626i	$0.221325\pi$
$138$		0			0
$139$	−6.57989			−0.558099			−0.279049	−	0.960277i	$-0.590019\pi$
$139$	−6.57989			−0.558099			−0.279049	+	0.960277i	$0.590019\pi$
$140$		0			0
$141$	42.4118			3.57171
$142$		0			0
$143$	8.02555	−	13.9007i	0.671130	−	1.16243i
$144$		0			0
$145$	0.411869	+	0.713379i	0.0342039	+	0.0592429i
$146$		0			0
$147$	−10.5338	+	20.4793i	−0.868813	+	1.68911i
$148$		0			0
$149$	−0.0543371	−	0.0941146i	−0.00445147	−	0.00771017i	0.863791	−	0.503850i	$-0.168084\pi$
$149$	−0.0543371	−	0.0941146i	−0.00445147	−	0.00771017i	−0.868243	+	0.496140i	$0.834750\pi$
$150$		0			0
$151$	−6.53379	+	11.3169i	−0.531713	+	0.920953i	0.467602	+	0.883939i	$0.345118\pi$
$151$	−6.53379	+	11.3169i	−0.531713	+	0.920953i	−0.999315	+	0.0370142i	$0.988215\pi$
$152$		0			0
$153$	15.6475			1.26502
$154$		0			0
$155$	2.57989			0.207222
$156$		0			0
$157$	−4.44566	+	7.70011i	−0.354803	+	0.614536i	−0.987084	−	0.160203i	$-0.948785\pi$
$157$	−4.44566	+	7.70011i	−0.354803	+	0.614536i	0.632282	+	0.774739i	$0.282119\pi$
$158$		0			0
$159$	13.8237	+	23.9434i	1.09629	+	1.89884i
$160$		0			0
$161$	0.735608	+	1.20558i	0.0579740	+	0.0950132i
$162$		0			0
$163$	−5.75615	−	9.96995i	−0.450857	−	0.780907i	0.547583	−	0.836751i	$-0.315548\pi$
$163$	−5.75615	−	9.96995i	−0.450857	−	0.780907i	−0.998439	+	0.0558449i	$0.982215\pi$
$164$		0			0
$165$	9.57989	−	16.5929i	0.745793	−	1.29175i
$166$		0			0
$167$	−1.46621			−0.113458			−0.0567292	−	0.998390i	$-0.518067\pi$
$167$	−1.46621			−0.113458			−0.0567292	+	0.998390i	$0.518067\pi$
$168$		0			0
$169$	−5.40363			−0.415664
$170$		0			0
$171$	−2.95797	+	5.12335i	−0.226201	+	0.391792i
$172$		0			0
$173$	5.62192	+	9.73746i	0.427427	+	0.740325i	0.996644	−	0.0818623i	$-0.0260868\pi$
$173$	5.62192	+	9.73746i	0.427427	+	0.740325i	−0.569217	+	0.822188i	$0.692753\pi$
$174$		0			0
$175$	1.26690	−	2.32271i	0.0957684	−	0.175580i
$176$		0			0
$177$	13.1598	+	22.7934i	0.989150	+	1.71326i
$178$		0			0
$179$	3.66802	−	6.35320i	0.274161	−	0.474860i	−0.695762	−	0.718272i	$-0.744933\pi$
$179$	3.66802	−	6.35320i	0.274161	−	0.474860i	0.969923	+	0.243412i	$0.0782666\pi$
$180$		0			0
$181$	−18.4712			−1.37295			−0.686477	−	0.727151i	$-0.740844\pi$
$181$	−18.4712			−1.37295			−0.686477	+	0.727151i	$0.740844\pi$
$182$		0			0
$183$	30.9374			2.28696
$184$		0			0
$185$	−2.37808	+	4.11895i	−0.174840	+	0.302831i
$186$		0			0
$187$	5.82374	+	10.0870i	0.425874	+	0.737635i
$188$		0			0
$189$	−41.9753	+	1.01867i	−3.05325	+	0.0740975i
$190$		0			0
$191$	7.28995	+	12.6266i	0.527482	+	0.913625i	0.999487	+	0.0320296i	$0.0101971\pi$
$191$	7.28995	+	12.6266i	0.527482	+	0.913625i	−0.472005	+	0.881596i	$0.656470\pi$
$192$		0			0
$193$	9.40363	−	16.2876i	0.676888	−	1.17240i	−0.299025	−	0.954245i	$-0.596661\pi$
$193$	9.40363	−	16.2876i	0.676888	−	1.17240i	0.975913	−	0.218159i	$-0.0700052\pi$
$194$		0			0
$195$	9.06759			0.649343
$196$		0			0
$197$	2.75615			0.196368			0.0981838	−	0.995168i	$-0.468697\pi$
$197$	2.75615			0.196368			0.0981838	+	0.995168i	$0.468697\pi$
$198$		0			0
$199$	7.51230	−	13.0117i	0.532533	−	0.922374i	−0.466745	−	0.884392i	$-0.654574\pi$
$199$	7.51230	−	13.0117i	0.532533	−	0.922374i	0.999278	−	0.0379825i	$-0.0120931\pi$
$200$		0			0
$201$	19.5256	+	33.8192i	1.37723	+	2.38543i
$202$		0			0
$203$	2.17877	−	0.0528751i	0.152919	−	0.00371111i
$204$		0			0
$205$	−3.03379	−	5.25468i	−0.211889	−	0.367003i
$206$		0			0
$207$	−2.08813	+	3.61675i	−0.145135	+	0.251381i
$208$		0			0
$209$	−4.40363			−0.304605
$210$		0			0
$211$	21.9159			1.50875			0.754377	−	0.656441i	$-0.227939\pi$
$211$	21.9159			1.50875			0.754377	+	0.656441i	$0.227939\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.355027	+	0.614926i	0.0242127	+	0.0419376i
$216$		0			0
$217$	3.26845	−	5.99233i	0.221877	−	0.406786i
$218$		0			0
$219$	−5.77764	−	10.0072i	−0.390417	−	0.676222i
$220$		0			0
$221$	−2.75615	+	4.77379i	−0.185399	+	0.321120i
$222$		0			0
$223$	−18.8073			−1.25943			−0.629714	−	0.776827i	$-0.716828\pi$
$223$	−18.8073			−1.25943			−0.629714	+	0.776827i	$0.716828\pi$
$224$		0			0
$225$	7.82374			0.521583
$226$		0			0
$227$	8.33604	−	14.4384i	0.553283	−	0.958313i	−0.444752	−	0.895654i	$-0.646708\pi$
$227$	8.33604	−	14.4384i	0.553283	−	0.958313i	0.998035	−	0.0626599i	$-0.0199583\pi$
$228$		0			0
$229$	−9.75615	−	16.8982i	−0.644705	−	1.11666i	−0.984370	−	0.176115i	$-0.943647\pi$
$229$	−9.75615	−	16.8982i	−0.644705	−	1.11666i	0.339665	−	0.940546i	$-0.389686\pi$
$230$		0			0
$231$	−26.4036	−	43.2727i	−1.73723	−	2.84714i
$232$		0			0
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	−0.994283	−	0.106773i	$-0.965948\pi$
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	0.404674	−	0.914461i	$-0.367385\pi$
$234$		0			0
$235$	−6.44566	+	11.1642i	−0.420469	+	0.728273i
$236$		0			0
$237$	31.2950			2.03283
$238$		0			0
$239$	16.0922			1.04092			0.520459	−	0.853887i	$-0.325761\pi$
$239$	16.0922			1.04092			0.520459	+	0.853887i	$0.325761\pi$
$240$		0			0
$241$	−0.445663	+	0.771911i	−0.0287077	+	0.0497231i	−0.880022	−	0.474932i	$-0.842473\pi$
$241$	−0.445663	+	0.771911i	−0.0287077	+	0.0497231i	0.851315	+	0.524655i	$0.175806\pi$
$242$		0			0
$243$	−23.4712	−	40.6533i	−1.50568	−	2.60791i
$244$		0			0
$245$	−3.78995	−	5.88526i	−0.242131	−	0.375996i
$246$		0			0
$247$	−1.04203	−	1.80486i	−0.0663030	−	0.114840i
$248$		0			0
$249$	−11.0379	+	19.1181i	−0.699496	+	1.21156i
$250$		0			0
$251$	−17.4712			−1.10277			−0.551387	−	0.834250i	$-0.685901\pi$
$251$	−17.4712			−1.10277			−0.551387	+	0.834250i	$0.685901\pi$
$252$		0			0
$253$	−3.10867			−0.195441
$254$		0			0
$255$	−3.28995	+	5.69835i	−0.206024	+	0.356845i
$256$		0			0
$257$	3.51230	+	6.08349i	0.219091	+	0.379478i	0.954530	−	0.298113i	$-0.0963574\pi$
$257$	3.51230	+	6.08349i	0.219091	+	0.379478i	−0.735439	+	0.677591i	$0.763024\pi$
$258$		0			0
$259$	6.55434	+	10.7419i	0.407267	+	0.667467i
$260$		0			0
$261$	3.22236	+	5.58129i	0.199459	+	0.345473i
$262$		0			0
$263$	8.88882	−	15.3959i	0.548108	−	0.949351i	−0.450296	−	0.892879i	$-0.648682\pi$
$263$	8.88882	−	15.3959i	0.548108	−	0.949351i	0.998404	−	0.0564719i	$-0.0179851\pi$
$264$		0			0
$265$	−8.40363			−0.516231
$266$		0			0
$267$	5.77764			0.353586
$268$		0			0
$269$	4.70181	−	8.14378i	0.286675	−	0.496535i	−0.686339	−	0.727282i	$-0.740783\pi$
$269$	4.70181	−	8.14378i	0.286675	−	0.496535i	0.973014	+	0.230746i	$0.0741168\pi$
$270$		0			0
$271$	3.51230	+	6.08349i	0.213357	+	0.369546i	0.952763	−	0.303714i	$-0.0982269\pi$
$271$	3.51230	+	6.08349i	0.213357	+	0.369546i	−0.739406	+	0.673260i	$0.764894\pi$
$272$		0			0
$273$	11.4877	−	21.0614i	0.695267	−	1.27469i
$274$		0			0
$275$	2.91187	+	5.04351i	0.175592	+	0.304135i
$276$		0			0
$277$	−13.5799	+	23.5211i	−0.815937	+	1.41324i	0.0927170	+	0.995693i	$0.470445\pi$
$277$	−13.5799	+	23.5211i	−0.815937	+	1.41324i	−0.908653	+	0.417551i	$0.862889\pi$
$278$		0			0
$279$	20.1844			1.20841
$280$		0			0
$281$	−0.620977			−0.0370444			−0.0185222	−	0.999828i	$-0.505896\pi$
$281$	−0.620977			−0.0370444			−0.0185222	+	0.999828i	$0.505896\pi$
$282$		0			0
$283$	1.57989	−	2.73645i	0.0939147	−	0.162665i	−0.815240	−	0.579123i	$-0.803395\pi$
$283$	1.57989	−	2.73645i	0.0939147	−	0.162665i	0.909155	+	0.416458i	$0.136729\pi$
$284$		0			0
$285$	−1.24385	−	2.15441i	−0.0736792	−	0.127616i
$286$		0			0
$287$	−16.0486	+	0.389474i	−0.947319	+	0.0229899i
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	3.28995	−	5.69835i	0.192860	−	0.334043i
$292$		0			0
$293$	11.2438			0.656873			0.328436	−	0.944526i	$-0.393478\pi$
$293$	11.2438			0.656873			0.328436	+	0.944526i	$0.393478\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$		0			0
$297$	46.2109	−	80.0396i	2.68143	−	4.64437i
$298$		0			0
$299$	−0.735608	−	1.27411i	−0.0425413	−	0.0736837i
$300$		0			0
$301$	1.87808	−	0.0455779i	0.108250	−	0.00262706i
$302$		0			0
$303$	−3.84272	−	6.65579i	−0.220759	−	0.382365i
$304$		0			0
$305$	−4.70181	+	8.14378i	−0.269225	+	0.466312i
$306$		0			0
$307$	−23.5173			−1.34220			−0.671102	−	0.741365i	$-0.734179\pi$
$307$	−23.5173			−1.34220			−0.671102	+	0.741365i	$0.734179\pi$
$308$		0			0
$309$	7.31144			0.415933
$310$		0			0
$311$	−14.5799	+	25.2531i	−0.826750	+	1.43197i	0.0738250	+	0.997271i	$0.476479\pi$
$311$	−14.5799	+	25.2531i	−0.826750	+	1.43197i	−0.900575	+	0.434701i	$0.856854\pi$
$312$		0			0
$313$	12.0922	+	20.9443i	0.683491	+	1.18384i	0.973908	+	0.226941i	$0.0728726\pi$
$313$	12.0922	+	20.9443i	0.683491	+	1.18384i	−0.290417	+	0.956900i	$0.593794\pi$
$314$		0			0
$315$	9.91187	−	18.1723i	0.558471	−	1.02389i
$316$		0			0
$317$	−6.06759	−	10.5094i	−0.340790	−	0.590265i	0.643790	−	0.765202i	$-0.277361\pi$
$317$	−6.06759	−	10.5094i	−0.340790	−	0.590265i	−0.984580	+	0.174937i	$0.944028\pi$
$318$		0			0
$319$	−2.39862	+	4.15453i	−0.134297	+	0.232609i
$320$		0			0
$321$	−52.2109			−2.91413
$322$		0			0
$323$	1.51230			0.0841468
$324$		0			0
$325$	−1.37808	+	2.38690i	−0.0764419	+	0.132401i
$326$		0			0
$327$	5.37652	+	9.31240i	0.297322	+	0.514977i
$328$		0			0
$329$	17.7652	+	29.1153i	0.979428	+	1.60518i
$330$		0			0
$331$	−0.911869	−	1.57940i	−0.0501209	−	0.0868119i	0.839877	−	0.542778i	$-0.182627\pi$
$331$	−0.911869	−	1.57940i	−0.0501209	−	0.0868119i	−0.889997	+	0.455966i	$0.849294\pi$
$332$		0			0
$333$	−18.6054	+	32.2256i	−1.01957	+	1.76595i
$334$		0			0
$335$	−11.8698			−0.648518
$336$		0			0
$337$	−17.7827			−0.968683			−0.484341	−	0.874879i	$-0.660941\pi$
$337$	−17.7827			−0.968683			−0.484341	+	0.874879i	$0.660941\pi$
$338$		0			0
$339$	21.6475	−	37.4945i	1.17573	−	2.03642i
$340$		0			0
$341$	7.51230	+	13.0117i	0.406814	+	0.704623i
$342$		0			0
$343$	−18.4712	+	1.34692i	−0.997352	+	0.0727266i
$344$		0			0
$345$	−0.878076	−	1.52087i	−0.0472740	−	0.0818810i
$346$		0			0
$347$	−0.644973	+	1.11713i	−0.0346239	+	0.0599704i	−0.882818	−	0.469715i	$-0.844357\pi$
$347$	−0.644973	+	1.11713i	−0.0346239	+	0.0599704i	0.848194	+	0.529685i	$0.177690\pi$
$348$		0			0
$349$	1.31144			0.0701995			0.0350998	−	0.999384i	$-0.488825\pi$
$349$	1.31144			0.0701995			0.0350998	+	0.999384i	$0.488825\pi$
$350$		0			0
$351$	43.7397			2.33465
$352$		0			0
$353$	5.51230	−	9.54759i	0.293390	−	0.508167i	−0.681219	−	0.732080i	$-0.738550\pi$
$353$	5.51230	−	9.54759i	0.293390	−	0.508167i	0.974609	+	0.223913i	$0.0718831\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	9.06759	+	14.8608i	0.479908	+	0.786517i
$358$		0			0
$359$	5.11368	+	8.85716i	0.269890	+	0.467463i	0.968833	−	0.247714i	$-0.0796794\pi$
$359$	5.11368	+	8.85716i	0.269890	+	0.467463i	−0.698943	+	0.715177i	$0.746346\pi$
$360$		0			0
$361$	9.21412	−	15.9593i	0.484954	−	0.839964i
$362$		0			0
$363$	75.3922			3.95706
$364$		0			0
$365$	3.51230			0.183842
$366$		0			0
$367$	8.67053	−	15.0178i	0.452598	−	0.783922i	−0.545949	−	0.837819i	$-0.683831\pi$
$367$	8.67053	−	15.0178i	0.452598	−	0.783922i	0.998547	+	0.0538962i	$0.0171640\pi$
$368$		0			0
$369$	−23.7356	−	41.1113i	−1.23563	−	2.14017i
$370$		0			0
$371$	−10.6465	+	19.5192i	−0.552740	+	1.01339i
$372$		0			0
$373$	8.89133	+	15.4002i	0.460375	+	0.797394i	0.998980	−	0.0451654i	$-0.0143815\pi$
$373$	8.89133	+	15.4002i	0.460375	+	0.797394i	−0.538604	+	0.842559i	$0.681048\pi$
$374$		0			0
$375$	−1.64497	+	2.84918i	−0.0849460	+	0.147131i
$376$		0			0
$377$	−2.27035			−0.116929
$378$		0			0
$379$	33.2109			1.70593			0.852964	−	0.521969i	$-0.174802\pi$
$379$	33.2109			1.70593			0.852964	+	0.521969i	$0.174802\pi$
$380$		0			0
$381$	19.6014	−	33.9506i	1.00421	−	1.73934i
$382$		0			0
$383$	7.38058	+	12.7835i	0.377130	+	0.653208i	0.990643	−	0.136476i	$-0.0435776\pi$
$383$	7.38058	+	12.7835i	0.377130	+	0.653208i	−0.613513	+	0.789684i	$0.710244\pi$
$384$		0			0
$385$	15.4036	−	0.373821i	0.785042	−	0.0190517i
$386$		0			0
$387$	2.77764	+	4.81102i	0.141195	+	0.244558i
$388$		0			0
$389$	11.4036	−	19.7517i	0.578187	−	1.00145i	−0.417500	−	0.908677i	$-0.637094\pi$
$389$	11.4036	−	19.7517i	0.578187	−	1.00145i	0.995687	−	0.0927724i	$-0.0295729\pi$
$390$		0			0
$391$	1.06759			0.0539902
$392$		0			0
$393$	−70.9424			−3.57857
$394$		0			0
$395$	−4.75615	+	8.23790i	−0.239308	+	0.414494i
$396$		0			0
$397$	7.13517	+	12.3585i	0.358104	+	0.620255i	0.987644	−	0.156714i	$-0.0500899\pi$
$397$	7.13517	+	12.3585i	0.358104	+	0.620255i	−0.629540	+	0.776968i	$0.716757\pi$
$398$		0			0
$399$	−6.57989	+	0.159683i	−0.329407	+	0.00799416i
$400$		0			0
$401$	5.74385	+	9.94864i	0.286834	+	0.496811i	0.973052	−	0.230585i	$-0.0740638\pi$
$401$	5.74385	+	9.94864i	0.286834	+	0.496811i	−0.686218	+	0.727396i	$0.740730\pi$
$402$		0			0
$403$	−3.55528	+	6.15793i	−0.177101	+	0.306748i
$404$		0			0
$405$	28.7397			1.42809
$406$		0			0
$407$	−27.6986			−1.37297
$408$		0			0
$409$	−0.899566	+	1.55809i	−0.0444807	+	0.0770428i	−0.887409	−	0.460984i	$-0.847497\pi$
$409$	−0.899566	+	1.55809i	−0.0444807	+	0.0770428i	0.842928	+	0.538027i	$0.180830\pi$
$410$		0			0
$411$	−6.57989	−	11.3967i	−0.324562	−	0.562158i
$412$		0			0
$413$	−10.1352	+	18.5817i	−0.498719	+	0.914344i
$414$		0			0
$415$	−3.35503	−	5.81108i	−0.164692	−	0.285255i
$416$		0			0
$417$	10.8237	−	18.7473i	0.530041	−	0.918058i
$418$		0			0
$419$	−27.4282			−1.33996			−0.669978	−	0.742381i	$-0.733697\pi$
$419$	−27.4282			−1.33996			−0.669978	+	0.742381i	$0.733697\pi$
$420$		0			0
$421$	2.91593			0.142114			0.0710569	−	0.997472i	$-0.477363\pi$
$421$	2.91593			0.142114			0.0710569	+	0.997472i	$0.477363\pi$
$422$		0			0
$423$	−50.4292	+	87.3459i	−2.45195	+	4.24690i
$424$		0			0
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$		0			0
$427$	12.9589	+	21.2383i	0.627126	+	1.02779i
$428$		0			0
$429$	26.4036	+	45.7324i	1.27478	+	2.20798i
$430$		0			0
$431$	7.28995	−	12.6266i	0.351144	−	0.608200i	−0.635306	−	0.772261i	$-0.719126\pi$
$431$	7.28995	−	12.6266i	0.351144	−	0.608200i	0.986450	+	0.164061i	$0.0524593\pi$
$432$		0			0
$433$	21.1598			1.01687			0.508437	−	0.861099i	$-0.330223\pi$
$433$	21.1598			1.01687			0.508437	+	0.861099i	$0.330223\pi$
$434$		0			0
$435$	−2.71005			−0.129937
$436$		0			0
$437$	−0.201814	+	0.349553i	−0.00965409	+	0.0167214i
$438$		0			0
$439$	−15.4712	−	26.7969i	−0.738401	−	1.27895i	−0.953215	−	0.302293i	$-0.902248\pi$
$439$	−15.4712	−	26.7969i	−0.738401	−	1.27895i	0.214814	−	0.976655i	$-0.431085\pi$
$440$		0			0
$441$	−29.6515	−	46.0448i	−1.41198	−	2.19261i
$442$		0			0
$443$	18.7587	+	32.4909i	0.891251	+	1.54369i	0.838377	+	0.545090i	$0.183505\pi$
$443$	18.7587	+	32.4909i	0.891251	+	1.54369i	0.0528732	+	0.998601i	$0.483162\pi$
$444$		0			0
$445$	−0.878076	+	1.52087i	−0.0416248	+	0.0720962i
$446$		0			0
$447$	0.357532			0.0169107
$448$		0			0
$449$	31.0922			1.46733			0.733666	−	0.679511i	$-0.237808\pi$
$449$	31.0922			1.46733			0.733666	+	0.679511i	$0.237808\pi$
$450$		0			0
$451$	17.6680	−	30.6019i	0.831955	−	1.44099i
$452$		0			0
$453$	−21.4958	−	37.2319i	−1.00996	−	1.74931i
$454$		0			0
$455$	3.79819	+	6.22482i	0.178062	+	0.291824i
$456$		0			0
$457$	2.17626	+	3.76940i	0.101801	+	0.176325i	0.912427	−	0.409240i	$-0.134206\pi$
$457$	2.17626	+	3.76940i	0.101801	+	0.176325i	−0.810626	+	0.585565i	$0.800873\pi$
$458$		0			0
$459$	−15.8698	+	27.4874i	−0.740740	+	1.28300i
$460$		0			0
$461$	37.2950			1.73700			0.868500	−	0.495690i	$-0.165085\pi$
$461$	37.2950			1.73700			0.868500	+	0.495690i	$0.165085\pi$
$462$		0			0
$463$	9.81873			0.456315			0.228158	−	0.973624i	$-0.426730\pi$
$463$	9.81873			0.456315			0.228158	+	0.973624i	$0.426730\pi$
$464$		0			0
$465$	−4.24385	+	7.35056i	−0.196804	+	0.340874i
$466$		0			0
$467$	−11.4011	−	19.7473i	−0.527581	−	0.913797i	−0.999483	−	0.0321463i	$-0.989766\pi$
$467$	−11.4011	−	19.7473i	−0.527581	−	0.913797i	0.471902	−	0.881651i	$-0.343568\pi$
$468$		0			0
$469$	−15.0379	+	27.5702i	−0.694384	+	1.27307i
$470$		0			0
$471$	−14.6260	−	25.3330i	−0.673930	−	1.16728i
$472$		0			0
$473$	−2.06759	+	3.58117i	−0.0950678	+	0.164662i
$474$		0			0
$475$	0.756152			0.0346946
$476$		0			0
$477$	−65.7478			−3.01038
$478$		0			0
$479$	−10.2224	+	17.7056i	−0.467071	+	0.808991i	−0.999292	−	0.0376140i	$-0.988024\pi$
$479$	−10.2224	+	17.7056i	−0.467071	+	0.808991i	0.532221	+	0.846606i	$0.321358\pi$
$480$		0			0
$481$	−6.55434	−	11.3524i	−0.298852	−	0.517627i
$482$		0			0
$483$	−4.64497	+	0.112726i	−0.211354	+	0.00512921i
$484$		0			0
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$		0			0
$487$	−21.4036	+	37.0722i	−0.969891	+	1.67990i	−0.274034	+	0.961720i	$0.588358\pi$
$487$	−21.4036	+	37.0722i	−0.969891	+	1.67990i	−0.695857	+	0.718181i	$0.744975\pi$
$488$		0			0
$489$	37.8748			1.71276
$490$		0			0
$491$	18.8502			0.850699			0.425350	−	0.905029i	$-0.360151\pi$
$491$	18.8502			0.850699			0.425350	+	0.905029i	$0.360151\pi$
$492$		0			0
$493$	0.823739	−	1.42676i	0.0370993	−	0.0642579i
$494$		0			0
$495$	22.7817	+	39.4591i	1.02396	+	1.77355i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	13.8698	+	24.0233i	0.620899	+	1.07543i	0.989319	+	0.145769i	$0.0465657\pi$
$499$	13.8698	+	24.0233i	0.620899	+	1.07543i	−0.368420	+	0.929660i	$0.620101\pi$
$500$		0			0
$501$	2.41187	−	4.17748i	0.107754	−	0.186636i
$502$		0			0
$503$	−14.7101			−0.655889			−0.327944	−	0.944697i	$-0.606356\pi$
$503$	−14.7101			−0.655889			−0.327944	+	0.944697i	$0.606356\pi$
$504$		0			0
$505$	2.33604			0.103952
$506$		0			0
$507$	8.88882	−	15.3959i	0.394766	−	0.683755i
$508$		0			0
$509$	6.99176	+	12.1101i	0.309904	+	0.536770i	0.978341	−	0.206999i	$-0.0663697\pi$
$509$	6.99176	+	12.1101i	0.309904	+	0.536770i	−0.668437	+	0.743769i	$0.733036\pi$
$510$		0			0
$511$	4.44973	−	8.15805i	0.196844	−	0.360891i
$512$		0			0
$513$	−6.00000	−	10.3923i	−0.264906	−	0.458831i
$514$		0			0
$515$	−1.11118	+	1.92462i	−0.0489644	+	0.0848088i
$516$		0			0
$517$	−75.0757			−3.30183
$518$		0			0
$519$	−36.9916			−1.62375
$520$		0			0
$521$	−10.3616	+	17.9468i	−0.453950	+	0.786264i	−0.998627	−	0.0523817i	$-0.983319\pi$
$521$	−10.3616	+	17.9468i	−0.453950	+	0.786264i	0.544677	+	0.838646i	$0.316652\pi$
$522$		0			0
$523$	−11.1763	−	19.3579i	−0.488704	−	0.846460i	0.511212	−	0.859455i	$-0.329197\pi$
$523$	−11.1763	−	19.3579i	−0.488704	−	0.846460i	−0.999916	+	0.0129950i	$0.995863\pi$
$524$		0			0
$525$	4.53379	+	7.43040i	0.197871	+	0.324289i
$526$		0			0
$527$	−2.57989	−	4.46850i	−0.112382	−	0.194651i
$528$		0			0
$529$	11.3575	−	19.6718i	0.493806	−	0.855297i
$530$		0			0
$531$	−62.5899			−2.71617
$532$		0			0
$533$	16.7232			0.724362
$534$		0			0
$535$	7.93492	−	13.7437i	0.343056	−	0.594191i
$536$		0			0
$537$	12.0676	+	20.9017i	0.520755	+	0.901974i
$538$		0			0
$539$	18.6465	−	36.2517i	0.803163	−	1.56147i
$540$		0			0
$541$	−16.3278	−	28.2806i	−0.701987	−	1.21588i	−0.967768	−	0.251844i	$-0.918963\pi$
$541$	−16.3278	−	28.2806i	−0.701987	−	1.21588i	0.265781	−	0.964033i	$-0.414370\pi$
$542$		0			0
$543$	30.3846	−	52.6277i	1.30393	−	2.25847i
$544$		0			0
$545$	−3.26845			−0.140005
$546$		0			0
$547$	−31.1648			−1.33251			−0.666255	−	0.745724i	$-0.732104\pi$
$547$	−31.1648			−1.33251			−0.666255	+	0.745724i	$0.732104\pi$
$548$		0			0
$549$	−36.7858	+	63.7148i	−1.56998	+	2.71928i
$550$		0			0
$551$	0.311436	+	0.539422i	0.0132676	+	0.0229802i
$552$		0			0
$553$	13.1087	+	21.4837i	0.557438	+	0.913581i
$554$		0			0
$555$	−7.82374	−	13.5511i	−0.332099	−	0.575213i
$556$		0			0
$557$	22.3616	−	38.7314i	0.947491	−	1.64110i	0.196806	−	0.980442i	$-0.436943\pi$
$557$	22.3616	−	38.7314i	0.947491	−	1.64110i	0.750685	−	0.660660i	$-0.229724\pi$
$558$		0			0
$559$	−1.95702			−0.0827731
$560$		0			0
$561$	−38.3196			−1.61785
$562$		0			0
$563$	−16.2464	+	28.1395i	−0.684702	+	1.18594i	0.288828	+	0.957381i	$0.406734\pi$
$563$	−16.2464	+	28.1395i	−0.684702	+	1.18594i	−0.973530	+	0.228558i	$0.926599\pi$
$564$		0			0
$565$	6.57989	+	11.3967i	0.276818	+	0.479463i
$566$		0			0
$567$	36.4102	−	66.7539i	1.52908	−	2.80340i
$568$		0			0
$569$	−17.3370	−	30.0285i	−0.726804	−	1.25886i	−0.958227	−	0.286009i	$-0.907671\pi$
$569$	−17.3370	−	30.0285i	−0.726804	−	1.25886i	0.231423	−	0.972853i	$-0.425662\pi$
$570$		0			0
$571$	1.55528	−	2.69383i	0.0650866	−	0.112733i	−0.831646	−	0.555306i	$-0.812601\pi$
$571$	1.55528	−	2.69383i	0.0650866	−	0.112733i	0.896732	+	0.442573i	$0.145934\pi$
$572$		0			0
$573$	−47.9670			−2.00385
$574$		0			0
$575$	0.533794			0.0222607
$576$		0			0
$577$	−0.336042	+	0.582041i	−0.0139896	+	0.0242307i	−0.872935	−	0.487836i	$-0.837787\pi$
$577$	−0.336042	+	0.582041i	−0.0139896	+	0.0242307i	0.858946	+	0.512066i	$0.171120\pi$
$578$		0			0
$579$	30.9374	+	53.5852i	1.28572	+	2.22692i
$580$		0			0
$581$	−17.7479	+	0.430713i	−0.736307	+	0.0178690i
$582$		0			0
$583$	−24.4703	−	42.3837i	−1.01345	−	1.75536i
$584$		0			0
$585$	−10.7817	+	18.6745i	−0.445769	+	0.772094i
$586$		0			0
$587$	4.67208			0.192838			0.0964188	−	0.995341i	$-0.469261\pi$
$587$	4.67208			0.192838			0.0964188	+	0.995341i	$0.469261\pi$
$588$		0			0
$589$	1.95079			0.0803808
$590$		0			0
$591$	−4.53379	+	7.85276i	−0.186495	+	0.323019i
$592$		0			0
$593$	−10.0922	−	17.4802i	−0.414437	−	0.717825i	0.580932	−	0.813952i	$-0.302688\pi$
$593$	−10.0922	−	17.4802i	−0.414437	−	0.717825i	−0.995369	+	0.0961264i	$0.969355\pi$
$594$		0			0
$595$	−5.28995	+	0.128378i	−0.216867	+	0.00526300i
$596$		0			0
$597$	24.7151	+	42.8077i	1.01152	+	1.75200i
$598$		0			0
$599$	10.7562	−	18.6302i	0.439484	−	0.761209i	−0.558165	−	0.829730i	$-0.688494\pi$
$599$	10.7562	−	18.6302i	0.439484	−	0.761209i	0.997650	+	0.0685204i	$0.0218278\pi$
$600$		0			0
$601$	5.29495			0.215986			0.107993	−	0.994152i	$-0.465558\pi$
$601$	5.29495			0.215986			0.107993	+	0.994152i	$0.465558\pi$
$602$		0			0
$603$	−92.8665			−3.78182
$604$		0			0
$605$	−11.4580	+	19.8458i	−0.465833	+	0.806846i
$606$		0			0
$607$	18.3591	+	31.7989i	0.745172	+	1.29068i	0.950114	+	0.311902i	$0.100966\pi$
$607$	18.3591	+	31.7989i	0.745172	+	1.29068i	−0.204942	+	0.978774i	$0.565700\pi$
$608$		0			0
$609$	−3.43336	+	6.29467i	−0.139127	+	0.255073i
$610$		0			0
$611$	−17.7652	−	30.7703i	−0.718704	−	1.24483i
$612$		0			0
$613$	−20.3616	+	35.2673i	−0.822397	+	1.42443i	0.0814954	+	0.996674i	$0.474030\pi$
$613$	−20.3616	+	35.2673i	−0.822397	+	1.42443i	−0.903892	+	0.427760i	$0.859303\pi$
$614$		0			0
$615$	19.9620			0.804947
$616$		0			0
$617$	16.8073			0.676635			0.338317	−	0.941032i	$-0.390142\pi$
$617$	16.8073			0.676635			0.338317	+	0.941032i	$0.390142\pi$
$618$		0			0
$619$	−17.8954	+	30.9957i	−0.719276	+	1.24582i	0.242010	+	0.970274i	$0.422193\pi$
$619$	−17.8954	+	30.9957i	−0.719276	+	1.24582i	−0.961287	+	0.275550i	$0.911140\pi$
$620$		0			0
$621$	−4.23561	−	7.33629i	−0.169969	−	0.294395i
$622$		0			0
$623$	2.42011	+	3.96630i	0.0969597	+	0.158907i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	7.24385	−	12.5467i	0.289291	−	0.501067i
$628$		0			0
$629$	9.51230			0.379280
$630$		0			0
$631$	32.4447			1.29160			0.645802	−	0.763505i	$-0.276523\pi$
$631$	32.4447			1.29160			0.645802	+	0.763505i	$0.276523\pi$
$632$		0			0
$633$	−36.0511	+	62.4423i	−1.43290	+	2.48186i
$634$		0			0
$635$	5.95797	+	10.3195i	0.236435	+	0.409517i
$636$		0			0
$637$	19.2703	−	0.935872i	0.763519	−	0.0370806i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−8.45390	+	14.6426i	−0.333909	+	0.578348i	−0.983275	−	0.182129i	$-0.941701\pi$
$641$	−8.45390	+	14.6426i	−0.333909	+	0.578348i	0.649366	+	0.760476i	$0.275035\pi$
$642$		0			0
$643$	−0.135174			−0.00533075			−0.00266538	−	0.999996i	$-0.500848\pi$
$643$	−0.135174			−0.00533075			−0.00266538	+	0.999996i	$0.500848\pi$
$644$		0			0
$645$	−2.33604			−0.0919816
$646$		0			0
$647$	−2.04454	+	3.54125i	−0.0803791	+	0.139221i	−0.903413	−	0.428772i	$-0.858946\pi$
$647$	−2.04454	+	3.54125i	−0.0803791	+	0.139221i	0.823034	+	0.567993i	$0.192280\pi$
$648$		0			0
$649$	−23.2950	−	40.3480i	−0.914407	−	1.58380i
$650$		0			0
$651$	11.6967	+	19.1696i	0.458429	+	0.751317i
$652$		0			0
$653$	−15.9580	−	27.6400i	−0.624483	−	1.08164i	−0.988641	−	0.150300i	$-0.951976\pi$
$653$	−15.9580	−	27.6400i	−0.624483	−	1.08164i	0.364157	−	0.931338i	$-0.381357\pi$
$654$		0			0
$655$	10.7817	−	18.6745i	0.421276	−	0.729672i
$656$		0			0
$657$	27.4793			1.07207
$658$		0			0
$659$	−4.70505			−0.183283			−0.0916413	−	0.995792i	$-0.529211\pi$
$659$	−4.70505			−0.183283			−0.0916413	+	0.995792i	$0.529211\pi$
$660$		0			0
$661$	−2.25710	+	3.90941i	−0.0877910	+	0.152058i	−0.906577	−	0.422040i	$-0.861314\pi$
$661$	−2.25710	+	3.90941i	−0.0877910	+	0.152058i	0.818786	+	0.574099i	$0.194647\pi$
$662$		0			0
$663$	−9.06759	−	15.7055i	−0.352156	−	0.609952i
$664$		0			0
$665$	0.957966	−	1.75632i	0.0371483	−	0.0681071i
$666$		0			0
$667$	0.219853	+	0.380797i	0.00851275	+	0.0147445i
$668$		0			0
$669$	30.9374	−	53.5852i	1.19611	−	2.07172i
$670$		0			0
$671$	−54.7643			−2.11415
$672$		0			0
$673$	46.9424			1.80950			0.904749	−	0.425945i	$-0.140058\pi$
$673$	46.9424			1.80950			0.904749	+	0.425945i	$0.140058\pi$
$674$		0			0
$675$	−7.93492	+	13.7437i	−0.305415	+	0.528995i
$676$		0			0
$677$	5.20181	+	9.00981i	0.199922	+	0.346275i	0.948503	−	0.316768i	$-0.102598\pi$
$677$	5.20181	+	9.00981i	0.199922	+	0.346275i	−0.748581	+	0.663043i	$0.769264\pi$
$678$		0			0
$679$	5.28995	−	0.128378i	0.203009	−	0.00492671i
$680$		0			0
$681$	27.4251	+	47.5017i	1.05093	+	1.82027i
$682$		0			0
$683$	2.53129	−	4.38432i	0.0968571	−	0.167761i	−0.813525	−	0.581530i	$-0.802454\pi$
$683$	2.53129	−	4.38432i	0.0968571	−	0.167761i	0.910382	+	0.413768i	$0.135788\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$		0			0
$687$	64.1944			2.44917
$688$		0			0
$689$	11.5808	−	20.0586i	0.441195	−	0.764172i
$690$		0			0
$691$	−2.22236	−	3.84924i	−0.0845425	−	0.146432i	0.820654	−	0.571426i	$-0.193610\pi$
$691$	−2.22236	−	3.84924i	−0.0845425	−	0.146432i	−0.905196	+	0.424994i	$0.860276\pi$
$692$		0			0
$693$	120.514	−	2.92468i	4.57795	−	0.111099i
$694$		0			0
$695$	3.28995	+	5.69835i	0.124795	+	0.216151i
$696$		0			0
$697$	−6.06759	+	10.5094i	−0.229826	+	0.398071i
$698$		0			0
$699$	59.2190			2.23987
$700$		0			0
$701$	21.7562			0.821719			0.410859	−	0.911699i	$-0.365229\pi$
$701$	21.7562			0.821719			0.410859	+	0.911699i	$0.365229\pi$
$702$		0			0
$703$	−1.79819	+	3.11455i	−0.0678199	+	0.117467i
$704$		0			0
$705$	−21.2059	−	36.7297i	−0.798660	−	1.38332i
$706$		0			0
$707$	2.95952	−	5.42594i	0.111304	−	0.204064i
$708$		0			0
$709$	20.5041	+	35.5141i	0.770046	+	1.33376i	0.937537	+	0.347886i	$0.113100\pi$
$709$	20.5041	+	35.5141i	0.770046	+	1.33376i	−0.167491	+	0.985874i	$0.553566\pi$
$710$		0			0
$711$	−37.2109	+	64.4511i	−1.39552	+	2.41711i
$712$		0			0
$713$	1.37713			0.0515739
$714$		0			0
$715$	−16.0511			−0.600277
$716$		0			0
$717$	−26.4712	+	45.8495i	−0.988586	+	1.71228i
$718$		0			0
$719$	11.8698	+	20.5592i	0.442670	+	0.766727i	0.997887	−	0.0649787i	$-0.0206979\pi$
$719$	11.8698	+	20.5592i	0.442670	+	0.766727i	−0.555216	+	0.831706i	$0.687365\pi$
$720$		0			0
$721$	3.06258	+	5.01924i	0.114056	+	0.186926i
$722$		0			0
$723$	−1.46621	−	2.53954i	−0.0545288	−	0.0944467i
$724$		0			0
$725$	0.411869	−	0.713379i	0.0152964	−	0.0264942i
$726$		0			0
$727$	28.8534			1.07011			0.535056	−	0.844817i	$-0.320291\pi$
$727$	28.8534			1.07011			0.535056	+	0.844817i	$0.320291\pi$
$728$		0			0
$729$	68.2190			2.52663
$730$		0			0
$731$	0.710055	−	1.22985i	0.0262623	−	0.0454877i
$732$		0			0
$733$	−23.4292	−	40.5805i	−0.865377	−	1.49888i	−0.866673	−	0.498877i	$-0.833746\pi$
$733$	−23.4292	−	40.5805i	−0.865377	−	1.49888i	0.00129620	−	0.999999i	$-0.499587\pi$
$734$		0			0
$735$	23.0025	−	1.11713i	0.848460	−	0.0412058i
$736$		0			0
$737$	−34.5634	−	59.8656i	−1.27316	−	2.20518i
$738$		0			0
$739$	8.07165	−	13.9805i	0.296920	−	0.514281i	−0.678509	−	0.734592i	$-0.737374\pi$
$739$	8.07165	−	13.9805i	0.296920	−	0.514281i	0.975430	+	0.220310i	$0.0707071\pi$
$740$		0			0
$741$	6.85647			0.251879
$742$		0			0
$743$	16.2243			0.595210			0.297605	−	0.954689i	$-0.403812\pi$
$743$	16.2243			0.595210			0.297605	+	0.954689i	$0.403812\pi$
$744$		0			0
$745$	−0.0543371	+	0.0941146i	−0.00199076	+	0.00344809i
$746$		0			0
$747$	−26.2489	−	45.4644i	−0.960395	−	1.66345i
$748$		0			0
$749$	−21.8698	−	35.8423i	−0.799106	−	1.30965i
$750$		0			0
$751$	10.7562	+	18.6302i	0.392498	+	0.679826i	0.992778	−	0.119964i	$-0.0382778\pi$
$751$	10.7562	+	18.6302i	0.392498	+	0.679826i	−0.600281	+	0.799789i	$0.704944\pi$
$752$		0			0
$753$	28.7397	−	49.7786i	1.04733	−	1.81403i
$754$		0			0
$755$	13.0676			0.475578
$756$		0			0
$757$	0.840220			0.0305383			0.0152692	−	0.999883i	$-0.495139\pi$
$757$	0.840220			0.0305383			0.0152692	+	0.999883i	$0.495139\pi$
$758$		0			0
$759$	5.11368	−	8.85716i	0.185615	−	0.321495i
$760$		0			0
$761$	14.4457	+	25.0206i	0.523655	+	0.906997i	0.999621	+	0.0275332i	$0.00876519\pi$
$761$	14.4457	+	25.0206i	0.523655	+	0.906997i	−0.475966	+	0.879464i	$0.657901\pi$
$762$		0			0
$763$	−4.14079	+	7.59167i	−0.149907	+	0.274837i
$764$		0			0
$765$	−7.82374	−	13.5511i	−0.282868	−	0.489942i
$766$		0			0
$767$	11.0246	−	19.0952i	0.398075	−	0.689487i
$768$		0			0
$769$	−27.3790			−0.987313			−0.493656	−	0.869657i	$-0.664340\pi$
$769$	−27.3790			−0.987313			−0.493656	+	0.869657i	$0.664340\pi$
$770$		0			0
$771$	−23.1106			−0.832307
$772$		0			0
$773$	19.1177	−	33.1129i	0.687618	−	1.19099i	−0.284989	−	0.958531i	$-0.591990\pi$
$773$	19.1177	−	33.1129i	0.687618	−	1.19099i	0.972607	−	0.232458i	$-0.0746767\pi$
$774$		0			0
$775$	−1.28995	−	2.23425i	−0.0463362	−	0.0802566i
$776$		0			0
$777$	−41.3871	+	1.00440i	−1.48476	+	0.0360326i
$778$		0			0
$779$	−2.29401	−	3.97334i	−0.0821914	−	0.142360i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−13.0726			−0.467176
$784$		0			0
$785$	8.89133			0.317345
$786$		0			0
$787$	3.66646	−	6.35050i	0.130695	−	0.226371i	−0.793249	−	0.608897i	$-0.791612\pi$
$787$	3.66646	−	6.35050i	0.130695	−	0.226371i	0.923945	+	0.382526i	$0.124946\pi$
$788$		0			0
$789$	29.2437	+	50.6516i	1.04110	+	1.80325i
$790$		0			0
$791$	34.8073	−	0.844716i	1.23760	−	0.0300346i
$792$		0			0
$793$	−12.9589	−	22.4455i	−0.460184	−	0.797063i
$794$		0			0
$795$	13.8237	−	23.9434i	0.490277	−	0.849186i
$796$		0			0
$797$	14.4877			0.513181			0.256590	−	0.966520i	$-0.417401\pi$
$797$	14.4877			0.513181			0.256590	+	0.966520i	$0.417401\pi$
$798$		0			0
$799$	25.7827			0.912125
$800$		0			0
$801$	−6.86984	+	11.8989i	−0.242734	+	0.420427i
$802$		0			0
$803$	10.2274	+	17.7143i	0.360916	+	0.625125i
$804$		0			0
$805$	0.676261	−	1.23985i	0.0238351	−	0.0436989i
$806$		0			0
$807$	15.4687	+	26.7926i	0.544524	+	0.943144i
$808$		0			0
$809$	5.67626	−	9.83157i	0.199567	−	0.345660i	−0.748821	−	0.662772i	$-0.769380\pi$
$809$	5.67626	−	9.83157i	0.199567	−	0.345660i	0.948388	+	0.317112i	$0.102713\pi$
$810$		0			0
$811$	28.7662			1.01012			0.505058	−	0.863085i	$-0.331471\pi$
$811$	28.7662			1.01012			0.505058	+	0.863085i	$0.331471\pi$
$812$		0			0
$813$	−23.1106			−0.810523
$814$		0			0
$815$	−5.75615	+	9.96995i	−0.201629	+	0.349232i
$816$		0			0
$817$	0.268455	+	0.464977i	0.00939204	+	0.0162675i
$818$		0			0
$819$	29.7160	+	48.7014i	1.03836	+	1.70176i
$820$		0			0
$821$	8.02461	+	13.8990i	0.280061	+	0.485079i	0.971399	−	0.237451i	$-0.0763121\pi$
$821$	8.02461	+	13.8990i	0.280061	+	0.485079i	−0.691339	+	0.722531i	$0.742979\pi$
$822$		0			0
$823$	7.00250	−	12.1287i	0.244092	−	0.422780i	−0.717784	−	0.696266i	$-0.754843\pi$
$823$	7.00250	−	12.1287i	0.244092	−	0.422780i	0.961876	+	0.273486i	$0.0881768\pi$
$824$		0			0
$825$	−19.1598			−0.667058
$826$		0			0
$827$	−15.2899			−0.531683			−0.265842	−	0.964017i	$-0.585650\pi$
$827$	−15.2899			−0.531683			−0.265842	+	0.964017i	$0.585650\pi$
$828$		0			0
$829$	10.6475	−	18.4420i	0.369802	−	0.640516i	−0.619732	−	0.784813i	$-0.712759\pi$
$829$	10.6475	−	18.4420i	0.369802	−	0.640516i	0.989534	+	0.144297i	$0.0460921\pi$
$830$		0			0
$831$	−44.6771	−	77.3830i	−1.54983	−	2.68439i
$832$		0			0
$833$	−6.40363	+	12.4496i	−0.221873	+	0.431354i
$834$		0			0
$835$	0.733103	+	1.26977i	0.0253701	+	0.0439423i
$836$		0			0
$837$	−20.4712	+	35.4572i	−0.707589	+	1.22558i
$838$		0			0
$839$	−42.2274			−1.45785			−0.728925	−	0.684593i	$-0.759980\pi$
$839$	−42.2274			−1.45785			−0.728925	+	0.684593i	$0.759980\pi$
$840$		0			0
$841$	−28.3215			−0.976602
$842$		0			0
$843$	1.02149	−	1.76927i	0.0351820	−	0.0609370i
$844$		0			0
$845$	2.70181	+	4.67968i	0.0929452	+	0.160986i
$846$		0			0
$847$	31.5799	+	51.7561i	1.08510	+	1.77836i
$848$		0			0
$849$	5.19775	+	9.00277i	0.178386	+	0.308974i
$850$		0			0
$851$	−1.26940	+	2.19867i	−0.0435145	+	0.0753694i
$852$		0			0
$853$	−13.2931			−0.455146			−0.227573	−	0.973761i	$-0.573079\pi$
$853$	−13.2931			−0.455146			−0.227573	+	0.973761i	$0.573079\pi$
$854$		0			0
$855$	5.91593			0.202321
$856$		0			0
$857$	−19.2274	+	33.3028i	−0.656794	+	1.13760i	0.324646	+	0.945835i	$0.394755\pi$
$857$	−19.2274	+	33.3028i	−0.656794	+	1.13760i	−0.981441	+	0.191766i	$0.938579\pi$
$858$		0			0
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$		0			0
$861$	25.2898	−	46.3660i	0.861875	−	1.58015i
$862$		0			0
$863$	−23.5404	−	40.7731i	−0.801323	−	1.38793i	−0.918745	−	0.394850i	$-0.870796\pi$
$863$	−23.5404	−	40.7731i	−0.801323	−	1.38793i	0.117422	−	0.993082i	$-0.462537\pi$
$864$		0			0
$865$	5.62192	−	9.73746i	0.191151	−	0.331084i
$866$		0			0
$867$	−42.7693			−1.45252
$868$		0			0
$869$	−55.3972			−1.87922
$870$		0			0
$871$	16.3575	−	28.3321i	0.554254	−	0.959996i
$872$		0			0
$873$	7.82374	+	13.5511i	0.264793	+	0.458636i
$874$		0			0
$875$	−2.64497	+	0.0641892i	−0.0894164	+	0.00216999i
$876$		0			0
$877$	2.28588	+	3.95926i	0.0771888	+	0.133695i	0.902036	−	0.431661i	$-0.142072\pi$
$877$	2.28588	+	3.95926i	0.0771888	+	0.133695i	−0.824847	+	0.565356i	$0.808739\pi$
$878$		0			0
$879$	−18.4958	+	32.0357i	−0.623849	+	1.08054i
$880$		0			0
$881$	−14.2849			−0.481272			−0.240636	−	0.970615i	$-0.577356\pi$
$881$	−14.2849			−0.481272			−0.240636	+	0.970615i	$0.577356\pi$
$882$		0			0
$883$	15.9670			0.537334			0.268667	−	0.963233i	$-0.413417\pi$
$883$	15.9670			0.537334			0.268667	+	0.963233i	$0.413417\pi$
$884$		0			0
$885$	13.1598	−	22.7934i	0.442361	−	0.766192i
$886$		0			0
$887$	−3.58239	−	6.20489i	−0.120285	−	0.208340i	0.799595	−	0.600540i	$-0.205048\pi$
$887$	−3.58239	−	6.20489i	−0.120285	−	0.208340i	−0.919880	+	0.392200i	$0.871714\pi$
$888$		0			0
$889$	31.5173	−	0.764874i	1.05706	−	0.0256531i
$890$		0			0
$891$	83.6862	+	144.949i	2.80359	+	4.85596i
$892$		0			0
$893$	−4.87390	+	8.44184i	−0.163099	+	0.282495i
$894$		0			0
$895$	−7.33604			−0.245217
$896$		0			0
$897$	4.84022			0.161610
$898$		0			0
$899$	1.06258	−	1.84044i	0.0354389	−	0.0613821i
$900$		0			0
$901$	8.40363	+	14.5555i	0.279965	+	0.484914i
$902$		0			0
$903$	−2.95952	+	5.42594i	−0.0984868	+	0.180564i
$904$		0			0
$905$	9.23561	+	15.9965i	0.307002	+	0.531743i
$906$		0			0
$907$	4.13267	−	7.15799i	0.137223	−	0.237677i	−0.789221	−	0.614109i	$-0.789516\pi$
$907$	4.13267	−	7.15799i	0.137223	−	0.237677i	0.926444	+	0.376431i	$0.122849\pi$
$908$		0			0
$909$	18.2766			0.606196
$910$		0			0
$911$	−26.2274			−0.868951			−0.434476	−	0.900684i	$-0.643066\pi$
$911$	−26.2274			−0.868951			−0.434476	+	0.900684i	$0.643066\pi$
$912$		0			0
$913$	19.5388	−	33.8422i	0.646640	−	1.12001i
$914$		0			0
$915$	−15.4687	−	26.7926i	−0.511380	−	0.885736i
$916$		0			0
$917$	−29.7160	−	48.7014i	−0.981309	−	1.60826i
$918$		0			0
$919$	−9.37902	−	16.2449i	−0.309385	−	0.535871i	0.668843	−	0.743404i	$-0.266790\pi$
$919$	−9.37902	−	16.2449i	−0.309385	−	0.535871i	−0.978228	+	0.207533i	$0.933457\pi$
$920$		0			0
$921$	38.6853	−	67.0050i	1.27473	−	2.20789i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	4.75615			0.156381
$926$		0			0
$927$	−8.69357	+	15.0577i	−0.285534	+	0.494560i
$928$		0			0
$929$	6.45390	+	11.1785i	0.211746	+	0.366754i	0.952261	−	0.305285i	$-0.0987518\pi$
$929$	6.45390	+	11.1785i	0.211746	+	0.366754i	−0.740515	+	0.672040i	$0.765418\pi$
$930$		0			0
$931$	−2.86577	−	4.45015i	−0.0939219	−	0.145848i
$932$		0			0
$933$	−47.9670	−	83.0813i	−1.57037	−	2.71996i
$934$		0			0
$935$	5.82374	−	10.0870i	0.190457	−	0.329881i
$936$		0			0
$937$	1.78265			0.0582367			0.0291183	−	0.999576i	$-0.490730\pi$
$937$	1.78265			0.0582367			0.0291183	+	0.999576i	$0.490730\pi$
$938$		0			0
$939$	−79.5653			−2.59652
$940$		0			0
$941$	22.5634	−	39.0810i	0.735546	−	1.27400i	−0.218937	−	0.975739i	$-0.570259\pi$
$941$	22.5634	−	39.0810i	0.735546	−	1.27400i	0.954483	−	0.298264i	$-0.0964077\pi$
$942$		0			0
$943$	−1.61942	−	2.80492i	−0.0527356	−	0.0913407i
$944$		0			0
$945$	21.8698	+	35.8423i	0.711426	+	1.16595i
$946$		0			0
$947$	11.0436	+	19.1281i	0.358869	+	0.621579i	0.987772	−	0.155905i	$-0.0498293\pi$
$947$	11.0436	+	19.1281i	0.358869	+	0.621579i	−0.628904	+	0.777483i	$0.716496\pi$
$948$		0			0
$949$	−4.84022	+	8.38351i	−0.157120	+	0.272140i
$950$		0			0
$951$	39.9241			1.29463
$952$		0			0
$953$	−45.3442			−1.46884			−0.734421	−	0.678694i	$-0.762546\pi$
$953$	−45.3442			−1.46884			−0.734421	+	0.678694i	$0.762546\pi$
$954$		0			0
$955$	7.28995	−	12.6266i	0.235897	−	0.408586i
$956$		0			0
$957$	−7.89133	−	13.6682i	−0.255090	−	0.441829i
$958$		0			0
$959$	5.06759	−	9.29083i	0.163641	−	0.300017i
$960$		0			0
$961$	12.1721	+	21.0827i	0.392648	+	0.680086i
$962$		0			0
$963$	62.0807	−	107.527i	2.00052	−	3.46501i
$964$		0			0
$965$	−18.8073			−0.605427
$966$		0			0
$967$	17.0296			0.547636			0.273818	−	0.961782i	$-0.411713\pi$
$967$	17.0296			0.547636			0.273818	+	0.961782i	$0.411713\pi$
$968$		0			0
$969$	−2.48770	+	4.30882i	−0.0799163	+	0.138419i
$970$		0			0
$971$	−14.6054	−	25.2974i	−0.468711	−	0.811831i	0.530649	−	0.847591i	$-0.321948\pi$
$971$	−14.6054	−	25.2974i	−0.468711	−	0.811831i	−0.999360	+	0.0357602i	$0.988615\pi$
$972$		0			0
$973$	17.4036	−	0.422358i	0.557935	−	0.0135402i
$974$		0			0
$975$	−4.53379	−	7.85276i	−0.145198	−	0.251490i
$976$		0			0
$977$	−0.420110	+	0.727652i	−0.0134405	+	0.0232796i	−0.872667	−	0.488315i	$-0.837612\pi$
$977$	−0.420110	+	0.727652i	−0.0134405	+	0.0232796i	0.859227	+	0.511595i	$0.170945\pi$
$978$		0			0
$979$	−10.2274			−0.326868
$980$		0			0
$981$	−25.5715			−0.816436
$982$		0			0
$983$	4.15822	−	7.20225i	0.132627	−	0.229716i	−0.792062	−	0.610441i	$-0.790992\pi$
$983$	4.15822	−	7.20225i	0.132627	−	0.229716i	0.924688	+	0.380725i	$0.124326\pi$
$984$		0			0
$985$	−1.37808	−	2.38690i	−0.0439091	−	0.0760529i
$986$		0			0
$987$	−112.178	+	2.72238i	−3.57066	+	0.0866542i
$988$		0			0
$989$	0.189511	+	0.328243i	0.00602611	+	0.0104375i
$990$		0			0
$991$	−10.1302	+	17.5460i	−0.321795	+	0.557366i	−0.980859	−	0.194722i	$-0.937620\pi$
$991$	−10.1302	+	17.5460i	−0.321795	+	0.557366i	0.659063	+	0.752088i	$0.270953\pi$
$992$		0			0
$993$	6.00000			0.190404
$994$		0			0
$995$	−15.0246			−0.476312
$996$		0			0
$997$	26.5388	−	45.9666i	0.840492	−	1.45578i	−0.0489867	−	0.998799i	$-0.515599\pi$
$997$	26.5388	−	45.9666i	0.840492	−	1.45578i	0.889479	−	0.456976i	$-0.151067\pi$
$998$		0			0
$999$	−37.7397	−	65.3670i	−1.19403	−	2.06812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.q.l.81.1		6
4.3	odd	2		280.2.q.e.81.3	✓	6
7.2	even	3	inner	560.2.q.l.401.1		6
7.3	odd	6		3920.2.a.cb.1.1		3
7.4	even	3		3920.2.a.cc.1.3		3
12.11	even	2		2520.2.bi.q.361.3		6
20.3	even	4		1400.2.bh.i.249.6		12
20.7	even	4		1400.2.bh.i.249.1		12
20.19	odd	2		1400.2.q.j.1201.1		6
28.3	even	6		1960.2.a.v.1.3		3
28.11	odd	6		1960.2.a.w.1.1		3
28.19	even	6		1960.2.q.w.961.1		6
28.23	odd	6		280.2.q.e.121.3	yes	6
28.27	even	2		1960.2.q.w.361.1		6
84.23	even	6		2520.2.bi.q.1801.3		6
140.23	even	12		1400.2.bh.i.849.1		12
140.39	odd	6		9800.2.a.ce.1.3		3
140.59	even	6		9800.2.a.cf.1.1		3
140.79	odd	6		1400.2.q.j.401.1		6
140.107	even	12		1400.2.bh.i.849.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.3	✓	6	4.3	odd	2
280.2.q.e.121.3	yes	6	28.23	odd	6
560.2.q.l.81.1		6	1.1	even	1	trivial
560.2.q.l.401.1		6	7.2	even	3	inner
1400.2.q.j.401.1		6	140.79	odd	6
1400.2.q.j.1201.1		6	20.19	odd	2
1400.2.bh.i.249.1		12	20.7	even	4
1400.2.bh.i.249.6		12	20.3	even	4
1400.2.bh.i.849.1		12	140.23	even	12
1400.2.bh.i.849.6		12	140.107	even	12
1960.2.a.v.1.3		3	28.3	even	6
1960.2.a.w.1.1		3	28.11	odd	6
1960.2.q.w.361.1		6	28.27	even	2
1960.2.q.w.961.1		6	28.19	even	6
2520.2.bi.q.361.3		6	12.11	even	2
2520.2.bi.q.1801.3		6	84.23	even	6
3920.2.a.cb.1.1		3	7.3	odd	6
3920.2.a.cc.1.3		3	7.4	even	3
9800.2.a.ce.1.3		3	140.39	odd	6
9800.2.a.cf.1.1		3	140.59	even	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)

\(f(q)\)	\(=\)	\(q+(-1.64497 + 2.84918i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.64497 + 0.0641892i) q^{7} +(-3.91187 - 6.77556i) q^{9} +O(q^{10})\)	\(q+(-1.64497 + 2.84918i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.64497 + 0.0641892i) q^{7} +(-3.91187 - 6.77556i) q^{9} +(2.91187 - 5.04351i) q^{11} +2.75615 q^{13} +3.28995 q^{15} +(-1.00000 + 1.73205i) q^{17} +(-0.378076 - 0.654846i) q^{19} +(4.16802 - 7.64158i) q^{21} +(-0.266897 - 0.462279i) q^{23} +(-0.500000 + 0.866025i) q^{25} +15.8698 q^{27} -0.823739 q^{29} +(-1.28995 + 2.23425i) q^{31} +(9.57989 + 16.5929i) q^{33} +(1.37808 + 2.25852i) q^{35} +(-2.37808 - 4.11895i) q^{37} +(-4.53379 + 7.85276i) q^{39} +6.06759 q^{41} -0.710055 q^{43} +(-3.91187 + 6.77556i) q^{45} +(-6.44566 - 11.1642i) q^{47} +(6.99176 - 0.339557i) q^{49} +(-3.28995 - 5.69835i) q^{51} +(4.20181 - 7.27776i) q^{53} -5.82374 q^{55} +2.48770 q^{57} +(4.00000 - 6.92820i) q^{59} +(-4.70181 - 8.14378i) q^{61} +(10.7817 + 17.6701i) q^{63} +(-1.37808 - 2.38690i) q^{65} +(5.93492 - 10.2796i) q^{67} +1.75615 q^{69} +(-1.75615 + 3.04174i) q^{73} +(-1.64497 - 2.84918i) q^{75} +(-7.37808 + 13.5268i) q^{77} +(-4.75615 - 8.23790i) q^{79} +(-14.3698 + 24.8893i) q^{81} +6.71005 q^{83} +2.00000 q^{85} +(1.35503 - 2.34698i) q^{87} +(-0.878076 - 1.52087i) q^{89} +(-7.28995 + 0.176915i) q^{91} +(-4.24385 - 7.35056i) q^{93} +(-0.378076 + 0.654846i) q^{95} -2.00000 q^{97} -45.5634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9}+O(q^{10}) \) 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9	\( 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9} + 3 q^{11} + 6 q^{13} - 6 q^{17} + 3 q^{19} + 3 q^{23} - 3 q^{25} + 36 q^{27} + 24 q^{29} + 12 q^{31} + 18 q^{33} + 3 q^{35} - 9 q^{37} - 18 q^{39} + 18 q^{41} - 24 q^{43} - 9 q^{45} - 15 q^{47} - 12 q^{49} - 9 q^{53} - 6 q^{55} + 36 q^{57} + 24 q^{59} + 6 q^{61} - 9 q^{63} - 3 q^{65} + 6 q^{67} - 39 q^{77} - 18 q^{79} - 27 q^{81} + 60 q^{83} + 12 q^{85} + 18 q^{87} - 24 q^{91} - 36 q^{93} + 3 q^{95} - 12 q^{97} - 126 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9 + 3 * q^11 + 6 * q^13 - 6 * q^17 + 3 * q^19 + 3 * q^23 - 3 * q^25 + 36 * q^27 + 24 * q^29 + 12 * q^31 + 18 * q^33 + 3 * q^35 - 9 * q^37 - 18 * q^39 + 18 * q^41 - 24 * q^43 - 9 * q^45 - 15 * q^47 - 12 * q^49 - 9 * q^53 - 6 * q^55 + 36 * q^57 + 24 * q^59 + 6 * q^61 - 9 * q^63 - 3 * q^65 + 6 * q^67 - 39 * q^77 - 18 * q^79 - 27 * q^81 + 60 * q^83 + 12 * q^85 + 18 * q^87 - 24 * q^91 - 36 * q^93 + 3 * q^95 - 12 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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