LMFDB - Embedded newform 546.2.bu.a.323.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			323.3
Character	$\chi$	$=$	546.323
Dual form			546.2.bu.a.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.847008 - 1.51082i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.36895 - 1.36895i) q^{5} +(0.427118 + 1.67856i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.56515 + 2.55935i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.847008 - 1.51082i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.36895 - 1.36895i) q^{5} +(0.427118 + 1.67856i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.56515 + 2.55935i) q^{9} +(-1.67662 + 0.967996i) q^{10} +(1.29660 - 4.83896i) q^{11} +(0.0218795 - 1.73191i) q^{12} +(3.60411 - 0.102093i) q^{13} -1.00000i q^{14} +(-3.22776 - 0.908727i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.540322 - 0.935866i) q^{17} +(2.17423 - 2.06705i) q^{18} +(2.27592 - 0.609830i) q^{19} +(1.87002 - 0.501072i) q^{20} +(1.24012 - 1.20918i) q^{21} +(-2.50483 + 4.33849i) q^{22} +(-1.57110 - 2.72123i) q^{23} +(-0.469386 + 1.66724i) q^{24} +1.25194i q^{25} +(-3.50772 - 0.834197i) q^{26} +(5.19242 + 0.196874i) q^{27} +(-0.258819 + 0.965926i) q^{28} +(-0.710895 + 0.410435i) q^{29} +(2.88258 + 1.71317i) q^{30} +(-4.20449 - 4.20449i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-8.40902 + 2.13972i) q^{33} +(-0.764131 + 0.764131i) q^{34} +(1.67662 + 0.967996i) q^{35} +(-2.63514 + 1.43389i) q^{36} +(0.524550 + 0.140553i) q^{37} -2.35620 q^{38} +(-3.20695 - 5.35868i) q^{39} -1.93599 q^{40} +(-5.18191 - 1.38849i) q^{41} +(-1.51082 + 0.847008i) q^{42} +(-4.92064 - 2.84093i) q^{43} +(3.54236 - 3.54236i) q^{44} +(1.36101 + 5.64626i) q^{45} +(0.813262 + 3.03513i) q^{46} +(0.118229 + 0.118229i) q^{47} +(0.884905 - 1.48894i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.324025 - 1.20928i) q^{50} +(-1.87158 - 0.0236440i) q^{51} +(3.17229 + 1.71364i) q^{52} -14.4313i q^{53} +(-4.96454 - 1.53406i) q^{54} +(-4.84933 - 8.39929i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-2.84906 - 2.92197i) q^{57} +(0.792900 - 0.212457i) q^{58} +(1.65760 - 0.444152i) q^{59} +(-2.34095 - 2.40086i) q^{60} +(-4.49739 + 7.78972i) q^{61} +(2.97302 + 5.14943i) q^{62} +(-2.87724 - 0.849414i) q^{63} +1.00000i q^{64} +(4.79409 - 5.07361i) q^{65} +(8.67629 + 0.109609i) q^{66} +(3.08685 - 11.5203i) q^{67} +(0.935866 - 0.540322i) q^{68} +(-2.78055 + 4.67855i) q^{69} +(-1.36895 - 1.36895i) q^{70} +(2.61215 + 9.74866i) q^{71} +(2.91647 - 0.703005i) q^{72} +(1.51217 - 1.51217i) q^{73} +(-0.470299 - 0.271527i) q^{74} +(1.89145 - 1.06040i) q^{75} +(2.27592 + 0.609830i) q^{76} +5.00966 q^{77} +(1.71075 + 6.00611i) q^{78} -1.54869 q^{79} +(1.87002 + 0.501072i) q^{80} +(-4.10058 - 8.01157i) q^{81} +(4.64597 + 2.68235i) q^{82} +(0.338916 - 0.338916i) q^{83} +(1.67856 - 0.427118i) q^{84} +(-0.541480 - 2.02083i) q^{85} +(4.01769 + 4.01769i) q^{86} +(1.22223 + 0.726392i) q^{87} +(-4.33849 + 2.50483i) q^{88} +(-4.35686 + 16.2600i) q^{89} +(0.146723 - 5.80612i) q^{90} +(1.03143 + 3.45488i) q^{91} -3.14220i q^{92} +(-2.79099 + 9.91347i) q^{93} +(-0.0836003 - 0.144800i) q^{94} +(2.28079 - 3.95045i) q^{95} +(-1.24012 + 1.20918i) q^{96} +(4.07964 - 1.09314i) q^{97} +(0.965926 - 0.258819i) q^{98} +(10.3552 + 10.8922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.847008	−	1.51082i	−0.489020	−	0.872272i
$3$	−0.847008	−	1.51082i	−0.489020	−	0.872272i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.36895	−	1.36895i	0.612214	−	0.612214i	−0.331308	−	0.943523i	$-0.607490\pi$
$5$	1.36895	−	1.36895i	0.612214	−	0.612214i	0.943523	+	0.331308i	$0.107490\pi$
$6$	0.427118	+	1.67856i	0.174370	+	0.685270i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.56515	+	2.55935i	−0.521718	+	0.853118i
$10$	−1.67662	+	0.967996i	−0.530193	+	0.306107i
$11$	1.29660	−	4.83896i	0.390938	−	1.45900i	−0.437651	−	0.899145i	$-0.644190\pi$
$11$	1.29660	−	4.83896i	0.390938	−	1.45900i	0.828590	−	0.559856i	$-0.189144\pi$
$12$	0.0218795	−	1.73191i	0.00631608	−	0.499960i
$13$	3.60411	−	0.102093i	0.999599	−	0.0283155i
$13$	3.60411	−	0.102093i	0.999599	−	0.0283155i
$14$		−	1.00000i		−	0.267261i
$15$	−3.22776	−	0.908727i	−0.833403	−	0.234632i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.540322	−	0.935866i	0.131047	−	0.226981i	−0.793033	−	0.609178i	$-0.791499\pi$
$17$	0.540322	−	0.935866i	0.131047	−	0.226981i	0.924081	+	0.382198i	$0.124833\pi$
$18$	2.17423	−	2.06705i	0.512472	−	0.487209i
$19$	2.27592	−	0.609830i	0.522131	−	0.139905i	0.0118790	−	0.999929i	$-0.496219\pi$
$19$	2.27592	−	0.609830i	0.522131	−	0.139905i	0.510252	+	0.860025i	$0.329552\pi$
$20$	1.87002	−	0.501072i	0.418150	−	0.112043i
$21$	1.24012	−	1.20918i	0.270616	−	0.263864i
$22$	−2.50483	+	4.33849i	−0.534032	+	0.924970i
$23$	−1.57110	−	2.72123i	−0.327597	−	0.567415i	0.654437	−	0.756116i	$-0.272906\pi$
$23$	−1.57110	−	2.72123i	−0.327597	−	0.567415i	−0.982035	+	0.188701i	$0.939572\pi$
$24$	−0.469386	+	1.66724i	−0.0958130	+	0.340323i
$25$			1.25194i			0.250387i
$26$	−3.50772	−	0.834197i	−0.687921	−	0.163599i
$27$	5.19242	+	0.196874i	0.999282	+	0.0378884i
$28$	−0.258819	+	0.965926i	−0.0489122	+	0.182543i
$29$	−0.710895	+	0.410435i	−0.132010	+	0.0762159i	−0.564551	−	0.825398i	$-0.690951\pi$
$29$	−0.710895	+	0.410435i	−0.132010	+	0.0762159i	0.432541	+	0.901614i	$0.357617\pi$
$30$	2.88258	+	1.71317i	0.526284	+	0.312780i
$31$	−4.20449	−	4.20449i	−0.755149	−	0.755149i	0.220286	−	0.975435i	$-0.429301\pi$
$31$	−4.20449	−	4.20449i	−0.755149	−	0.755149i	−0.975435	+	0.220286i	$0.929301\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−8.40902	+	2.13972i	−1.46382	+	0.372477i
$34$	−0.764131	+	0.764131i	−0.131047	+	0.131047i
$35$	1.67662	+	0.967996i	0.283400	+	0.163621i
$36$	−2.63514	+	1.43389i	−0.439190	+	0.238981i
$37$	0.524550	+	0.140553i	0.0862355	+	0.0231067i	0.301679	−	0.953410i	$-0.402453\pi$
$37$	0.524550	+	0.140553i	0.0862355	+	0.0231067i	−0.215443	+	0.976516i	$0.569120\pi$
$38$	−2.35620			−0.382227
$39$	−3.20695	−	5.35868i	−0.513523	−	0.858076i
$40$	−1.93599			−0.306107
$41$	−5.18191	−	1.38849i	−0.809278	−	0.216845i	−0.169625	−	0.985509i	$-0.554256\pi$
$41$	−5.18191	−	1.38849i	−0.809278	−	0.216845i	−0.639654	+	0.768663i	$0.720922\pi$
$42$	−1.51082	+	0.847008i	−0.233125	+	0.130696i
$43$	−4.92064	−	2.84093i	−0.750391	−	0.433239i	0.0754441	−	0.997150i	$-0.475963\pi$
$43$	−4.92064	−	2.84093i	−0.750391	−	0.433239i	−0.825835	+	0.563912i	$0.809296\pi$
$44$	3.54236	−	3.54236i	0.534032	−	0.534032i
$45$	1.36101	+	5.64626i	0.202888	+	0.841694i
$46$	0.813262	+	3.03513i	0.119909	+	0.447506i
$47$	0.118229	+	0.118229i	0.0172454	+	0.0172454i	0.715677	−	0.698431i	$-0.246118\pi$
$47$	0.118229	+	0.118229i	0.0172454	+	0.0172454i	−0.698431	+	0.715677i	$0.746118\pi$
$48$	0.884905	−	1.48894i	0.127725	−	0.214910i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	0.324025	−	1.20928i	0.0458240	−	0.171018i
$51$	−1.87158	−	0.0236440i	−0.262074	−	0.00331082i
$52$	3.17229	+	1.71364i	0.439918	+	0.237639i
$53$		−	14.4313i		−	1.98229i	−0.132795	−	0.991144i	$-0.542395\pi$
$53$		−	14.4313i		−	1.98229i	0.132795	−	0.991144i	$-0.457605\pi$
$54$	−4.96454	−	1.53406i	−0.675588	−	0.208760i
$55$	−4.84933	−	8.39929i	−0.653884	−	1.13256i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	−2.84906	−	2.92197i	−0.377368	−	0.387024i
$58$	0.792900	−	0.212457i	0.104113	−	0.0278970i
$59$	1.65760	−	0.444152i	0.215801	−	0.0578237i	−0.149299	−	0.988792i	$-0.547702\pi$
$59$	1.65760	−	0.444152i	0.215801	−	0.0578237i	0.365100	+	0.930968i	$0.381035\pi$
$60$	−2.34095	−	2.40086i	−0.302216	−	0.309950i
$61$	−4.49739	+	7.78972i	−0.575832	+	0.997371i	0.420118	+	0.907469i	$0.361989\pi$
$61$	−4.49739	+	7.78972i	−0.575832	+	0.997371i	−0.995951	+	0.0899015i	$0.971345\pi$
$62$	2.97302	+	5.14943i	0.377574	+	0.653978i
$63$	−2.87724	−	0.849414i	−0.362498	−	0.107016i
$64$			1.00000i			0.125000i
$65$	4.79409	−	5.07361i	0.594634	−	0.629304i
$66$	8.67629	+	0.109609i	1.06798	+	0.0134919i
$67$	3.08685	−	11.5203i	0.377118	−	1.40742i	−0.473107	−	0.881005i	$-0.656867\pi$
$67$	3.08685	−	11.5203i	0.377118	−	1.40742i	0.850225	−	0.526420i	$-0.176466\pi$
$68$	0.935866	−	0.540322i	0.113490	−	0.0655237i
$69$	−2.78055	+	4.67855i	−0.334739	+	0.563232i
$70$	−1.36895	−	1.36895i	−0.163621	−	0.163621i
$71$	2.61215	+	9.74866i	0.310005	+	1.15695i	0.928551	+	0.371205i	$0.121055\pi$
$71$	2.61215	+	9.74866i	0.310005	+	1.15695i	−0.618546	+	0.785748i	$0.712278\pi$
$72$	2.91647	−	0.703005i	0.343709	−	0.0828499i
$73$	1.51217	−	1.51217i	0.176986	−	0.176986i	−0.613055	−	0.790040i	$-0.710059\pi$
$73$	1.51217	−	1.51217i	0.176986	−	0.176986i	0.790040	+	0.613055i	$0.210059\pi$
$74$	−0.470299	−	0.271527i	−0.0546711	−	0.0315644i
$75$	1.89145	−	1.06040i	0.218406	−	0.122444i
$76$	2.27592	+	0.609830i	0.261066	+	0.0699523i
$77$	5.00966			0.570904
$78$	1.71075	+	6.00611i	0.193704	+	0.680058i
$79$	−1.54869			−0.174241			−0.0871205	−	0.996198i	$-0.527767\pi$
$79$	−1.54869			−0.174241			−0.0871205	+	0.996198i	$0.527767\pi$
$80$	1.87002	+	0.501072i	0.209075	+	0.0560215i
$81$	−4.10058	−	8.01157i	−0.455620	−	0.890174i
$82$	4.64597	+	2.68235i	0.513062	+	0.296216i
$83$	0.338916	−	0.338916i	0.0372008	−	0.0372008i	−0.688262	−	0.725463i	$-0.741626\pi$
$83$	0.338916	−	0.338916i	0.0372008	−	0.0372008i	0.725463	+	0.688262i	$0.241626\pi$
$84$	1.67856	−	0.427118i	0.183146	−	0.0466024i
$85$	−0.541480	−	2.02083i	−0.0587318	−	0.219190i
$86$	4.01769	+	4.01769i	0.433239	+	0.433239i
$87$	1.22223	+	0.726392i	0.131037	+	0.0778774i
$88$	−4.33849	+	2.50483i	−0.462485	+	0.267016i
$89$	−4.35686	+	16.2600i	−0.461826	+	1.72356i	0.205376	+	0.978683i	$0.434158\pi$
$89$	−4.35686	+	16.2600i	−0.461826	+	1.72356i	−0.667202	+	0.744877i	$0.732508\pi$
$90$	0.146723	−	5.80612i	0.0154659	−	0.612019i
$91$	1.03143	+	3.45488i	0.108123	+	0.362169i
$92$		−	3.14220i		−	0.327597i
$93$	−2.79099	+	9.91347i	−0.289412	+	1.02798i
$94$	−0.0836003	−	0.144800i	−0.00862272	−	0.0149350i
$95$	2.28079	−	3.95045i	0.234005	−	0.405308i
$96$	−1.24012	+	1.20918i	−0.126569	+	0.123411i
$97$	4.07964	−	1.09314i	0.414225	−	0.110991i	−0.0456868	−	0.998956i	$-0.514548\pi$
$97$	4.07964	−	1.09314i	0.414225	−	0.110991i	0.459912	+	0.887965i	$0.347881\pi$
$98$	0.965926	−	0.258819i	0.0975732	−	0.0261447i
$99$	10.3552	+	10.8922i	1.04074	+	1.09470i
$100$	−0.625968	+	1.08421i	−0.0625968	+	0.108421i
$101$	6.25605	+	10.8358i	0.622501	+	1.07820i	0.989018	+	0.147792i	$0.0472165\pi$
$101$	6.25605	+	10.8358i	0.622501	+	1.07820i	−0.366518	+	0.930411i	$0.619450\pi$
$102$	1.80169	+	0.507239i	0.178394	+	0.0502242i
$103$			1.28719i			0.126830i	0.997987	+	0.0634152i	$0.0201992\pi$
$103$			1.28719i			0.126830i	−0.997987	+	0.0634152i	$0.979801\pi$
$104$	−2.62068	−	2.47630i	−0.256979	−	0.242821i
$105$	0.0423586	−	3.35297i	0.00413378	−	0.327216i
$106$	−3.73509	+	13.9395i	−0.362784	+	1.35393i
$107$	4.87154	−	2.81258i	0.470949	−	0.271903i	−0.245688	−	0.969349i	$-0.579014\pi$
$107$	4.87154	−	2.81258i	0.470949	−	0.271903i	0.716637	+	0.697446i	$0.245680\pi$
$108$	4.39833	+	2.76671i	0.423230	+	0.266227i
$109$	13.5487	+	13.5487i	1.29773	+	1.29773i	0.929891	+	0.367834i	$0.119901\pi$
$109$	13.5487	+	13.5487i	1.29773	+	1.29773i	0.367834	+	0.929891i	$0.380099\pi$
$110$	2.51020	+	9.36819i	0.239338	+	0.893221i
$111$	−0.231948	−	0.911550i	−0.0220155	−	0.0865205i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$	−11.4378	−	6.60364i	−1.07598	−	0.621218i	−0.146172	−	0.989259i	$-0.546695\pi$
$113$	−11.4378	−	6.60364i	−1.07598	−	0.621218i	−0.929809	+	0.368041i	$0.880029\pi$
$114$	1.99572	+	3.55980i	0.186917	+	0.333406i
$115$	−5.87600	−	1.57447i	−0.547939	−	0.146820i
$116$	−0.820871			−0.0762159
$117$	−5.37969	+	9.38397i	−0.497353	+	0.867549i
$118$	−1.71607			−0.157977
$119$	1.04382	+	0.279691i	0.0956870	+	0.0256393i
$120$	1.63980	+	2.92494i	0.149693	+	0.267009i
$121$	−12.2081	−	7.04835i	−1.10983	−	0.640759i
$122$	6.36028	−	6.36028i	0.575832	−	0.575832i
$123$	2.29136	+	9.00499i	0.206605	+	0.811953i
$124$	−1.53895	−	5.74344i	−0.138202	−	0.515776i
$125$	8.55861	+	8.55861i	0.765505	+	0.765505i
$126$	2.55935	+	1.56515i	0.228005	+	0.139435i
$127$	12.1302	−	7.00340i	1.07638	−	0.621451i	0.146466	−	0.989216i	$-0.453210\pi$
$127$	12.1302	−	7.00340i	1.07638	−	0.621451i	0.929919	+	0.367765i	$0.119877\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−0.124317	+	9.84050i	−0.0109455	+	0.866408i
$130$	−5.94388	+	3.65993i	−0.521313	+	0.320997i
$131$		−	1.86345i		−	0.162810i	−0.996681	−	0.0814051i	$-0.974059\pi$
$131$		−	1.86345i		−	0.162810i	0.996681	−	0.0814051i	$-0.0259407\pi$
$132$	−8.35229	−	2.35146i	−0.726973	−	0.204669i
$133$	1.17810	+	2.04053i	0.102154	+	0.176937i
$134$	−5.96333	+	10.3288i	−0.515153	+	0.892272i
$135$	7.37769	−	6.83867i	0.634971	−	0.588579i
$136$	−1.04382	+	0.279691i	−0.0895070	+	0.0239833i
$137$	15.0687	−	4.03765i	1.28741	−	0.344959i	0.450731	−	0.892660i	$-0.351163\pi$
$137$	15.0687	−	4.03765i	1.28741	−	0.344959i	0.836675	+	0.547700i	$0.184497\pi$
$138$	3.89670	−	3.79948i	0.331709	−	0.323433i
$139$	4.68734	−	8.11872i	0.397575	−	0.688620i	−0.595851	−	0.803095i	$-0.703185\pi$
$139$	4.68734	−	8.11872i	0.397575	−	0.688620i	0.993426	+	0.114475i	$0.0365184\pi$
$140$	0.967996	+	1.67662i	0.0818106	+	0.141700i
$141$	0.0784817	−	0.278763i	0.00660935	−	0.0234761i
$142$		−	10.0926i		−	0.846949i
$143$	4.17904	−	17.5725i	0.349469	−	1.46949i
$144$	−2.99904	−	0.0757869i	−0.249920	−	0.00631558i
$145$	−0.411315	+	1.53505i	−0.0341578	+	0.127479i
$146$	−1.85202	+	1.06926i	−0.153274	+	0.0884929i
$147$	1.48894	+	0.884905i	0.122806	+	0.0729857i
$148$	0.383997	+	0.383997i	0.0315644	+	0.0315644i
$149$	2.84144	+	10.6044i	0.232780	+	0.868746i	0.979137	+	0.203201i	$0.0651344\pi$
$149$	2.84144	+	10.6044i	0.232780	+	0.868746i	−0.746357	+	0.665546i	$0.768199\pi$
$150$	−2.10145	+	0.534724i	−0.171583	+	0.0436601i
$151$	14.2677	−	14.2677i	1.16109	−	1.16109i	0.176854	−	0.984237i	$-0.443408\pi$
$151$	14.2677	−	14.2677i	1.16109	−	1.16109i	0.984237	−	0.176854i	$-0.0565919\pi$
$152$	−2.04053	−	1.17810i	−0.165509	−	0.0955566i
$153$	1.54952	+	2.84765i	0.125272	+	0.230219i
$154$	−4.83896	−	1.29660i	−0.389934	−	0.104483i
$155$	−11.5115			−0.924626
$156$	−0.0979600	−	6.24423i	−0.00784308	−	0.499938i
$157$	1.60781			0.128317			0.0641585	−	0.997940i	$-0.479564\pi$
$157$	1.60781			0.128317			0.0641585	+	0.997940i	$0.479564\pi$
$158$	1.49592	+	0.400830i	0.119009	+	0.0318883i
$159$	−21.8030	+	12.2234i	−1.72909	+	0.969379i
$160$	−1.67662	−	0.967996i	−0.132548	−	0.0765268i
$161$	2.22187	−	2.22187i	0.175108	−	0.175108i
$162$	1.88731	+	8.79989i	0.148281	+	0.691385i
$163$	1.98526	+	7.40908i	0.155497	+	0.580324i	0.999062	+	0.0432967i	$0.0137861\pi$
$163$	1.98526	+	7.40908i	0.155497	+	0.580324i	−0.843565	+	0.537027i	$0.819547\pi$
$164$	−3.79342	−	3.79342i	−0.296216	−	0.296216i
$165$	−8.58239	+	14.4407i	−0.668138	+	1.12421i
$166$	−0.415085	+	0.239650i	−0.0322169	+	0.0186004i
$167$	−5.14088	+	19.1860i	−0.397813	+	1.48466i	0.419123	+	0.907929i	$0.362338\pi$
$167$	−5.14088	+	19.1860i	−0.397813	+	1.48466i	−0.816936	+	0.576729i	$0.804329\pi$
$168$	−1.73191	−	0.0218795i	−0.133620	−	0.00168804i
$169$	12.9792	−	0.735908i	0.998396	−	0.0566083i
$170$			2.09212i			0.160458i
$171$	−2.00139	+	6.77935i	−0.153050	+	0.518430i
$172$	−2.84093	−	4.92064i	−0.216619	−	0.375196i
$173$	−0.377787	+	0.654347i	−0.0287226	+	0.0497490i	−0.880029	−	0.474919i	$-0.842477\pi$
$173$	−0.377787	+	0.654347i	−0.0287226	+	0.0497490i	0.851307	+	0.524668i	$0.175811\pi$
$174$	−0.992577	−	1.01798i	−0.0752471	−	0.0771726i
$175$	−1.20928	+	0.324025i	−0.0914128	+	0.0244940i
$176$	4.83896	−	1.29660i	0.364750	−	0.0977346i
$177$	−2.07503	−	2.12813i	−0.155969	−	0.159960i
$178$	8.41681	−	14.5783i	0.630867	−	1.09269i
$179$	5.46883	+	9.47230i	0.408760	+	0.707993i	0.994751	−	0.102325i	$-0.0326280\pi$
$179$	5.46883	+	9.47230i	0.408760	+	0.707993i	−0.585991	+	0.810317i	$0.699295\pi$
$180$	−1.64446	+	5.57031i	−0.122571	+	0.415186i
$181$			21.7176i			1.61425i	0.590378	+	0.807127i	$0.298979\pi$
$181$			21.7176i			1.61425i	−0.590378	+	0.807127i	$0.701021\pi$
$182$	−0.102093	−	3.60411i	−0.00756764	−	0.267154i
$183$	15.5782	+	0.196802i	1.15157	+	0.0145480i
$184$	−0.813262	+	3.03513i	−0.0599545	+	0.223753i
$185$	0.910494	−	0.525674i	0.0669409	−	0.0386483i
$186$	5.26169	−	8.85331i	0.385806	−	0.649156i
$187$	−3.82804	−	3.82804i	−0.279934	−	0.279934i
$188$	0.0432747	+	0.161503i	0.00315613	+	0.0117788i
$189$	1.15373	+	5.06645i	0.0839216	+	0.368530i
$190$	−3.22553	+	3.22553i	−0.234005	+	0.234005i
$191$	−17.2727	−	9.97242i	−1.24981	−	0.721579i	−0.278739	−	0.960367i	$-0.589917\pi$
$191$	−17.2727	−	9.97242i	−1.24981	−	0.721579i	−0.971072	+	0.238788i	$0.923250\pi$
$192$	1.51082	−	0.847008i	0.109034	−	0.0611275i
$193$	23.9757	+	6.42428i	1.72581	+	0.462429i	0.979211	−	0.202845i	$-0.0650186\pi$
$193$	23.9757	+	6.42428i	1.72581	+	0.462429i	0.746599	+	0.665274i	$0.231685\pi$
$194$	−4.22356			−0.303234
$195$	−11.7259	−	2.94562i	−0.839713	−	0.210940i
$196$	−1.00000			−0.0714286
$197$	−20.2111	−	5.41554i	−1.43998	−	0.385841i	−0.547453	−	0.836836i	$-0.684403\pi$
$197$	−20.2111	−	5.41554i	−1.43998	−	0.385841i	−0.892527	+	0.450995i	$0.851069\pi$
$198$	−7.18329	−	13.2012i	−0.510494	−	0.938165i
$199$	−9.02261	−	5.20920i	−0.639596	−	0.369271i	0.144863	−	0.989452i	$-0.453726\pi$
$199$	−9.02261	−	5.20920i	−0.639596	−	0.369271i	−0.784459	+	0.620181i	$0.787059\pi$
$200$	0.885252	−	0.885252i	0.0625968	−	0.0625968i
$201$	−20.0196	+	5.09409i	−1.41208	+	0.359309i
$202$	−3.23837	−	12.0858i	−0.227851	−	0.850352i
$203$	−0.580443	−	0.580443i	−0.0407391	−	0.0407391i
$204$	−1.60902	−	0.956267i	−0.112654	−	0.0669521i
$205$	−8.99456	+	5.19301i	−0.628208	+	0.362696i
$206$	0.333149	−	1.24333i	0.0232116	−	0.0866268i
$207$	9.42360	+	0.238138i	0.654985	+	0.0165517i
$208$	1.89047	+	3.07020i	0.131080	+	0.212880i
$209$		−	11.8038i		−	0.816484i
$210$	−0.908727	+	3.22776i	−0.0627081	+	0.222736i
$211$	1.54901	+	2.68296i	0.106638	+	0.184702i	0.914406	−	0.404798i	$-0.132658\pi$
$211$	1.54901	+	2.68296i	0.106638	+	0.184702i	−0.807768	+	0.589500i	$0.799325\pi$
$212$	7.21563	−	12.4978i	0.495572	−	0.858355i
$213$	12.5160	−	12.2037i	0.857580	−	0.836182i
$214$	−5.43349	+	1.45590i	−0.371426	+	0.0995233i
$215$	−10.6252	+	2.84702i	−0.724635	+	0.194165i
$216$	−3.53239	−	3.81081i	−0.240348	−	0.259293i
$217$	2.97302	−	5.14943i	0.201822	−	0.349566i
$218$	−9.58034	−	16.5936i	−0.648863	−	1.12386i
$219$	−3.56543	−	1.00379i	−0.240929	−	0.0678302i
$220$		−	9.69866i		−	0.653884i
$221$	1.85183	−	3.42812i	0.124568	−	0.230600i
$222$	−0.0118818	+	0.940522i	−0.000797453	+	0.0631237i
$223$	−0.441102	+	1.64622i	−0.0295384	+	0.110239i	−0.979121	−	0.203278i	$-0.934841\pi$
$223$	−0.441102	+	1.64622i	−0.0295384	+	0.110239i	0.949583	+	0.313517i	$0.101507\pi$
$224$	0.866025	−	0.500000i	0.0578638	−	0.0334077i
$225$	−3.20415	−	1.95947i	−0.213610	−	0.130632i
$226$	9.33895	+	9.33895i	0.621218	+	0.621218i
$227$	−2.39763	−	8.94809i	−0.159136	−	0.593905i	−0.998716	−	0.0506680i	$-0.983865\pi$
$227$	−2.39763	−	8.94809i	−0.159136	−	0.593905i	0.839579	−	0.543238i	$-0.182802\pi$
$228$	−1.00638	−	3.95503i	−0.0666489	−	0.261928i
$229$	13.2081	−	13.2081i	0.872816	−	0.872816i	−0.119962	−	0.992778i	$-0.538277\pi$
$229$	13.2081	−	13.2081i	0.872816	−	0.872816i	0.992778	+	0.119962i	$0.0382774\pi$
$230$	5.26827	+	3.04164i	0.347380	+	0.200560i
$231$	−4.24322	−	7.56869i	−0.279184	−	0.497984i
$232$	0.792900	+	0.212457i	0.0520565	+	0.0139485i
$233$	19.6826			1.28945			0.644724	−	0.764415i	$-0.276972\pi$
$233$	19.6826			1.28945			0.644724	+	0.764415i	$0.276972\pi$
$234$	7.62513	−	7.67185i	0.498471	−	0.501525i
$235$	0.323699			0.0211158
$236$	1.65760	+	0.444152i	0.107900	+	0.0289119i
$237$	1.31175	+	2.33979i	0.0852074	+	0.151986i
$238$	−0.935866	−	0.540322i	−0.0606632	−	0.0350239i
$239$	−16.5276	+	16.5276i	−1.06908	+	1.06908i	−0.0716537	+	0.997430i	$0.522828\pi$
$239$	−16.5276	+	16.5276i	−1.06908	+	1.06908i	−0.997430	+	0.0716537i	$0.977172\pi$
$240$	−0.826897	−	3.24968i	−0.0533760	−	0.209766i
$241$	0.895014	+	3.34024i	0.0576529	+	0.215164i	0.988743	−	0.149627i	$-0.0478072\pi$
$241$	0.895014	+	3.34024i	0.0576529	+	0.215164i	−0.931090	+	0.364791i	$0.881141\pi$
$242$	9.96787	+	9.96787i	0.640759	+	0.640759i
$243$	−8.63081	+	12.9811i	−0.553667	+	0.832738i
$244$	−7.78972	+	4.49739i	−0.498685	+	0.287916i
$245$	−0.501072	+	1.87002i	−0.0320123	+	0.119471i
$246$	0.117377	−	9.29120i	0.00748371	−	0.592385i
$247$	8.14039	−	2.43025i	0.517960	−	0.154633i
$248$			5.94605i			0.377574i
$249$	−0.799105	−	0.224976i	−0.0506412	−	0.0142573i
$250$	−6.05185	−	10.4821i	−0.382752	−	0.662947i
$251$	9.03954	−	15.6569i	0.570571	−	0.988258i	−0.425936	−	0.904753i	$-0.640055\pi$
$251$	9.03954	−	15.6569i	0.570571	−	0.988258i	0.996507	−	0.0835047i	$-0.0266114\pi$
$252$	−2.06705	−	2.17423i	−0.130212	−	0.136964i
$253$	−15.2050	+	4.07417i	−0.955930	+	0.256141i
$254$	−13.5295	+	3.62522i	−0.848918	+	0.227467i
$255$	−2.59447	+	2.52974i	−0.162472	+	0.158418i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.6193	+	18.3931i	0.662411	+	1.14733i	0.979980	+	0.199095i	$0.0638002\pi$
$257$	10.6193	+	18.3931i	0.662411	+	1.14733i	−0.317569	+	0.948235i	$0.602866\pi$
$258$	2.66699	−	9.47302i	0.166040	−	0.589764i
$259$			0.543054i			0.0337437i
$260$	6.68861	−	1.99683i	0.414810	−	0.123838i
$261$	0.0622113	−	2.46183i	0.00385078	−	0.152383i
$262$	−0.482296	+	1.79995i	−0.0297963	+	0.111201i
$263$	−8.58055	+	4.95399i	−0.529100	+	0.305476i	−0.740650	−	0.671891i	$-0.765482\pi$
$263$	−8.58055	+	4.95399i	−0.529100	+	0.305476i	0.211550	+	0.977367i	$0.432149\pi$
$264$	7.45909	+	4.43307i	0.459075	+	0.272837i
$265$	−19.7557	−	19.7557i	−1.21358	−	1.21358i
$266$	−0.609830	−	2.27592i	−0.0373911	−	0.139545i
$267$	28.2563	−	7.18994i	1.72926	−	0.440017i
$268$	8.43342	−	8.43342i	0.515153	−	0.515153i
$269$	−21.2435	−	12.2650i	−1.29524	−	0.747808i	−0.315663	−	0.948871i	$-0.602227\pi$
$269$	−21.2435	−	12.2650i	−1.29524	−	0.747808i	−0.979578	+	0.201063i	$0.935560\pi$
$270$	−8.89628	+	4.69616i	−0.541410	+	0.285799i
$271$	15.4032	+	4.12726i	0.935675	+	0.250713i	0.694273	−	0.719712i	$-0.255726\pi$
$271$	15.4032	+	4.12726i	0.935675	+	0.250713i	0.241402	+	0.970425i	$0.422393\pi$
$272$	1.08064			0.0655237
$273$	4.34607	−	4.48461i	0.263036	−	0.271421i
$274$	−15.6003			−0.942446
$275$	6.05807	+	1.62325i	0.365315	+	0.0978859i
$276$	−4.74730	+	2.66147i	−0.285754	+	0.160202i
$277$	−12.4005	−	7.15946i	−0.745077	−	0.430170i	0.0788355	−	0.996888i	$-0.474880\pi$
$277$	−12.4005	−	7.15946i	−0.745077	−	0.430170i	−0.823912	+	0.566717i	$0.808213\pi$
$278$	−6.62890	+	6.62890i	−0.397575	+	0.397575i
$279$	17.3415	−	4.18010i	1.03821	−	0.250256i
$280$	−0.501072	−	1.87002i	−0.0299448	−	0.111755i
$281$	−2.01093	−	2.01093i	−0.119962	−	0.119962i	0.644577	−	0.764539i	$-0.277033\pi$
$281$	−2.01093	−	2.01093i	−0.119962	−	0.119962i	−0.764539	+	0.644577i	$0.777033\pi$
$282$	−0.147957	+	0.248952i	−0.00881069	+	0.0148249i
$283$	−18.6556	+	10.7708i	−1.10896	+	0.640260i	−0.938560	−	0.345115i	$-0.887840\pi$
$283$	−18.6556	+	10.7708i	−1.10896	+	0.640260i	−0.170402	+	0.985375i	$0.554507\pi$
$284$	−2.61215	+	9.74866i	−0.155002	+	0.578477i
$285$	−7.90027	−	0.0998055i	−0.467972	−	0.00591197i
$286$	−8.58474	+	15.8921i	−0.507626	+	0.939720i
$287$		−	5.36471i		−	0.316669i
$288$	2.87724	+	0.849414i	0.169543	+	0.0500522i
$289$	7.91610	+	13.7111i	0.465653	+	0.806535i
$290$	0.794600	−	1.37629i	0.0466605	−	0.0808183i
$291$	−5.10703	−	5.23771i	−0.299379	−	0.307040i
$292$	2.06566	−	0.553492i	0.120884	−	0.0323906i
$293$	12.9513	−	3.47030i	0.756626	−	0.202737i	0.140171	−	0.990127i	$-0.455235\pi$
$293$	12.9513	−	3.47030i	0.756626	−	0.202737i	0.616455	+	0.787390i	$0.288568\pi$
$294$	−1.20918	−	1.24012i	−0.0705206	−	0.0723252i
$295$	1.66115	−	2.87720i	0.0967160	−	0.167517i
$296$	−0.271527	−	0.470299i	−0.0157822	−	0.0273356i
$297$	7.68513	−	24.8707i	0.445937	−	1.44314i
$298$		−	10.9785i		−	0.635966i
$299$	−5.94023	−	9.64719i	−0.343533	−	0.557912i
$300$	2.16824	+	0.0273918i	0.125184	+	0.00158147i
$301$	1.47058	−	5.48826i	0.0847626	−	0.316338i
$302$	−17.4743	+	10.0888i	−1.00553	+	0.580545i
$303$	11.0720	−	18.6298i	0.636071	−	1.07025i
$304$	1.66609	+	1.66609i	0.0955566	+	0.0955566i
$305$	4.50703	+	16.8205i	0.258072	+	0.963138i
$306$	−0.759698	−	3.15166i	−0.0434291	−	0.180169i
$307$	−12.2012	+	12.2012i	−0.696358	+	0.696358i	−0.963623	−	0.267265i	$-0.913880\pi$
$307$	−12.2012	+	12.2012i	−0.696358	+	0.696358i	0.267265	+	0.963623i	$0.413880\pi$
$308$	4.33849	+	2.50483i	0.247209	+	0.142726i
$309$	1.94471	−	1.09026i	0.110631	−	0.0620227i
$310$	11.1193	+	2.97940i	0.631531	+	0.169218i
$311$	10.8848			0.617221			0.308610	−	0.951189i	$-0.400136\pi$
$311$	10.8848			0.617221			0.308610	+	0.951189i	$0.400136\pi$
$312$	−1.52150	+	6.05682i	−0.0861382	+	0.342900i
$313$	−26.3524			−1.48953			−0.744763	−	0.667329i	$-0.767438\pi$
$313$	−26.3524			−1.48953			−0.744763	+	0.667329i	$0.767438\pi$
$314$	−1.55302	−	0.416131i	−0.0876421	−	0.0234836i
$315$	−5.10161	+	2.77600i	−0.287443	+	0.156410i
$316$	−1.34120	−	0.774344i	−0.0754486	−	0.0435603i
$317$	16.1698	−	16.1698i	0.908185	−	0.908185i	−0.0879406	−	0.996126i	$-0.528029\pi$
$317$	16.1698	−	16.1698i	0.908185	−	0.908185i	0.996126	+	0.0879406i	$0.0280286\pi$
$318$	24.2238	−	6.16385i	1.35840	−	0.345652i
$319$	1.06434	+	3.97216i	0.0595914	+	0.222398i
$320$	1.36895	+	1.36895i	0.0765268	+	0.0765268i
$321$	−8.37554	−	4.97773i	−0.467477	−	0.277830i
$322$	−2.72123	+	1.57110i	−0.151648	+	0.0875541i
$323$	0.659010	−	2.45946i	0.0366683	−	0.136848i
$324$	0.454576	−	8.98851i	0.0252542	−	0.499362i
$325$	0.127814	+	4.51211i	0.00708984	+	0.250287i
$326$		−	7.67044i		−	0.424827i
$327$	8.99376	−	31.9454i	0.497356	−	1.76658i
$328$	2.68235	+	4.64597i	0.148108	+	0.256531i
$329$	−0.0836003	+	0.144800i	−0.00460904	+	0.00798308i
$330$	12.0275	−	11.7274i	0.662091	−	0.645571i
$331$	−14.3227	+	3.83777i	−0.787249	+	0.210943i	−0.629978	−	0.776613i	$-0.716936\pi$
$331$	−14.3227	+	3.83777i	−0.787249	+	0.210943i	−0.157271	+	0.987556i	$0.550270\pi$
$332$	0.462967	−	0.124052i	0.0254086	−	0.00680822i
$333$	−1.18073	+	1.12252i	−0.0647034	+	0.0615138i
$334$	9.93141	−	17.2017i	0.543423	−	0.941235i
$335$	−11.5450	−	19.9965i	−0.630768	−	1.09252i
$336$	1.66724	+	0.469386i	0.0909552	+	0.0256071i
$337$		−	18.7747i		−	1.02272i	−0.859366	−	0.511361i	$-0.829141\pi$
$337$		−	18.7747i		−	1.02272i	0.859366	−	0.511361i	$-0.170859\pi$
$338$	−12.7274	−	2.64842i	−0.692278	−	0.144055i
$339$	−0.288969	+	22.8738i	−0.0156947	+	1.24234i
$340$	0.541480	−	2.02083i	0.0293659	−	0.109595i
$341$	−25.7969	+	14.8938i	−1.39698	+	0.806547i
$342$	3.68782	−	6.03036i	0.199415	−	0.326084i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	1.47058	+	5.48826i	0.0792881	+	0.295907i
$345$	2.59828	+	10.2112i	0.139887	+	0.549750i
$346$	0.534272	−	0.534272i	0.0287226	−	0.0287226i
$347$	−8.16785	−	4.71571i	−0.438473	−	0.253152i	0.264477	−	0.964392i	$-0.414801\pi$
$347$	−8.16785	−	4.71571i	−0.438473	−	0.253152i	−0.702950	+	0.711240i	$0.748134\pi$
$348$	0.695284	+	1.24019i	0.0372711	+	0.0664811i
$349$	29.6009	+	7.93153i	1.58450	+	0.424565i	0.940315	−	0.340305i	$-0.110530\pi$
$349$	29.6009	+	7.93153i	1.58450	+	0.424565i	0.644184	+	0.764871i	$0.277197\pi$
$350$	1.25194			0.0669188
$351$	18.7341	+	0.179445i	0.999954	+	0.00957805i
$352$	−5.00966			−0.267016
$353$	−20.9033	−	5.60102i	−1.11257	−	0.298112i	−0.344696	−	0.938714i	$-0.612018\pi$
$353$	−20.9033	−	5.60102i	−1.11257	−	0.298112i	−0.767873	+	0.640602i	$0.778685\pi$
$354$	1.45353	+	2.59268i	0.0772541	+	0.137799i
$355$	16.9214	+	9.76956i	0.898093	+	0.518514i
$356$	−11.9032	+	11.9032i	−0.630867	+	0.630867i
$357$	−0.461563	−	1.81393i	−0.0244285	−	0.0960033i
$358$	−2.83088	−	10.5650i	−0.149616	−	0.558376i
$359$	17.6778	+	17.6778i	0.932998	+	0.932998i	0.997892	−	0.0648939i	$-0.0206709\pi$
$359$	17.6778	+	17.6778i	0.932998	+	0.932998i	−0.0648939	+	0.997892i	$0.520671\pi$
$360$	3.03013	−	4.95489i	0.159702	−	0.261145i
$361$	−11.6466	+	6.72415i	−0.612978	+	0.353903i
$362$	5.62092	−	20.9776i	0.295429	−	1.10256i
$363$	−0.308429	+	24.4142i	−0.0161883	+	1.28142i
$364$	−0.834197	+	3.50772i	−0.0437238	+	0.183855i
$365$		−	4.14017i		−	0.216706i
$366$	−14.9964	−	4.22203i	−0.783876	−	0.220689i
$367$	9.29298	+	16.0959i	0.485090	+	0.840200i	0.999853	−	0.0171324i	$-0.00545369\pi$
$367$	9.29298	+	16.0959i	0.485090	+	0.840200i	−0.514764	+	0.857332i	$0.672120\pi$
$368$	1.57110	−	2.72123i	0.0818993	−	0.141854i
$369$	11.6641	−	11.0891i	0.607210	−	0.577277i
$370$	−1.01552	+	0.272109i	−0.0527946	+	0.0141463i
$371$	13.9395	−	3.73509i	0.723705	−	0.193916i
$372$	−7.37380	+	7.18982i	−0.382314	+	0.372775i
$373$	6.06668	−	10.5078i	0.314121	−	0.544073i	−0.665130	−	0.746728i	$-0.731624\pi$
$373$	6.06668	−	10.5078i	0.314121	−	0.544073i	0.979250	+	0.202655i	$0.0649571\pi$
$374$	2.70683	+	4.68837i	0.139967	+	0.242430i
$375$	5.68131	−	20.1797i	0.293381	−	1.04208i
$376$		−	0.167201i		−	0.00862272i
$377$	−2.52024	+	1.55183i	−0.129799	+	0.0799233i
$378$	0.196874	−	5.19242i	0.0101261	−	0.267069i
$379$	−0.775456	+	2.89404i	−0.0398325	+	0.148657i	−0.982978	−	0.183723i	$-0.941185\pi$
$379$	−0.775456	+	2.89404i	−0.0398325	+	0.148657i	0.943146	+	0.332380i	$0.107852\pi$
$380$	3.95045	−	2.28079i	0.202654	−	0.117002i
$381$	−20.8553	−	12.3947i	−1.06845	−	0.634998i
$382$	14.1031	+	14.1031i	0.721579	+	0.721579i
$383$	5.60300	+	20.9107i	0.286300	+	1.06848i	0.947884	+	0.318615i	$0.103218\pi$
$383$	5.60300	+	20.9107i	0.286300	+	1.06848i	−0.661585	+	0.749870i	$0.730116\pi$
$384$	−1.67856	+	0.427118i	−0.0856588	+	0.0217963i
$385$	6.85799	−	6.85799i	0.349515	−	0.349515i
$386$	−21.4960	−	12.4107i	−1.09412	−	0.631690i
$387$	14.9725	−	8.14716i	0.761096	−	0.414144i
$388$	4.07964	+	1.09314i	0.207113	+	0.0554956i
$389$	−35.3336			−1.79148			−0.895742	−	0.444575i	$-0.853355\pi$
$389$	−35.3336			−1.79148			−0.895742	+	0.444575i	$0.853355\pi$
$390$	10.5640	+	5.88015i	0.534930	+	0.297753i
$391$	−3.39560			−0.171723
$392$	0.965926	+	0.258819i	0.0487866	+	0.0130723i
$393$	−2.81533	+	1.57835i	−0.142015	+	0.0796175i
$394$	18.1208	+	10.4620i	0.912911	+	0.527069i
$395$	−2.12008	+	2.12008i	−0.106673	+	0.106673i
$396$	3.52181	+	14.6105i	0.176978	+	0.734206i
$397$	5.30676	+	19.8051i	0.266338	+	0.993988i	0.961426	+	0.275063i	$0.0886989\pi$
$397$	5.30676	+	19.8051i	0.266338	+	0.993988i	−0.695088	+	0.718925i	$0.744634\pi$
$398$	7.36693	+	7.36693i	0.369271	+	0.369271i
$399$	2.08501	−	3.50825i	0.104381	−	0.175632i
$400$	−1.08421	+	0.625968i	−0.0542104	+	0.0312984i
$401$	−8.51826	+	31.7906i	−0.425381	+	1.58755i	0.337707	+	0.941251i	$0.390349\pi$
$401$	−8.51826	+	31.7906i	−0.425381	+	1.58755i	−0.763088	+	0.646294i	$0.776318\pi$
$402$	20.6559	+	0.260950i	1.03022	+	0.0130150i
$403$	−15.5827	−	14.7242i	−0.776229	−	0.733464i
$404$			12.5121i			0.622501i
$405$	−16.5810	−	5.35396i	−0.823915	−	0.266040i
$406$	0.410435	+	0.710895i	0.0203696	+	0.0352811i
$407$	1.36026	−	2.35604i	0.0674255	−	0.116784i
$408$	1.30669	+	1.34013i	0.0646908	+	0.0663462i
$409$	−23.0665	+	6.18065i	−1.14057	+	0.305614i	−0.779178	−	0.626802i	$-0.784363\pi$
$409$	−23.0665	+	6.18065i	−1.14057	+	0.305614i	−0.361387	+	0.932416i	$0.617697\pi$
$410$	10.0321	−	2.68810i	0.495452	−	0.132756i
$411$	−18.8635	−	19.3462i	−0.930466	−	0.954276i
$412$	−0.643594	+	1.11474i	−0.0317076	+	0.0549192i
$413$	0.858036	+	1.48616i	0.0422212	+	0.0731293i
$414$	−9.04086	−	2.66903i	−0.444334	−	0.131176i
$415$		−	0.927919i		−	0.0455498i
$416$	−1.03143	−	3.45488i	−0.0505698	−	0.169389i
$417$	−16.2361	−	0.205114i	−0.795087	−	0.0100445i
$418$	−3.05504	+	11.4016i	−0.149427	+	0.557669i
$419$	−22.2097	+	12.8228i	−1.08501	+	0.626433i	−0.932244	−	0.361829i	$-0.882152\pi$
$419$	−22.2097	+	12.8228i	−1.08501	+	0.626433i	−0.152769	+	0.988262i	$0.548819\pi$
$420$	1.71317	−	2.88258i	0.0835940	−	0.140655i
$421$	−5.05403	−	5.05403i	−0.246318	−	0.246318i	0.573140	−	0.819458i	$-0.305725\pi$
$421$	−5.05403	−	5.05403i	−0.246318	−	0.246318i	−0.819458	+	0.573140i	$0.805725\pi$
$422$	−0.801825	−	2.99245i	−0.0390322	−	0.145670i
$423$	−0.487635	+	0.117543i	−0.0237096	+	0.00571513i
$424$	−10.2044	+	10.2044i	−0.495572	+	0.495572i
$425$	1.17164	+	0.676449i	0.0568331	+	0.0328126i
$426$	−15.2480	+	8.54848i	−0.738770	+	0.414175i
$427$	−8.68830	−	2.32802i	−0.420456	−	0.112661i
$428$	5.62516			0.271903
$429$	−30.0886	+	8.57026i	−1.45269	+	0.413776i
$430$	11.0001			0.530470
$431$	12.6301	+	3.38424i	0.608372	+	0.163013i	0.549836	−	0.835272i	$-0.314690\pi$
$431$	12.6301	+	3.38424i	0.608372	+	0.163013i	0.0585360	+	0.998285i	$0.481357\pi$
$432$	2.42571	+	4.59521i	0.116707	+	0.221087i
$433$	−4.68915	−	2.70728i	−0.225346	−	0.130104i	0.383077	−	0.923716i	$-0.374864\pi$
$433$	−4.68915	−	2.70728i	−0.225346	−	0.130104i	−0.608423	+	0.793613i	$0.708198\pi$
$434$	−4.20449	+	4.20449i	−0.201822	+	0.201822i
$435$	2.66757	−	0.678775i	0.127900	−	0.0325448i
$436$	4.95915	+	18.5078i	0.237500	+	0.886363i
$437$	−5.23518	−	5.23518i	−0.250433	−	0.250433i
$438$	3.18414	+	1.89239i	0.152144	+	0.0904220i
$439$	32.3470	−	18.6755i	1.54384	−	0.891335i	0.545245	−	0.838277i	$-0.316437\pi$
$439$	32.3470	−	18.6755i	1.54384	−	0.891335i	0.998591	−	0.0530580i	$-0.0168968\pi$
$440$	−2.51020	+	9.36819i	−0.119669	+	0.446611i
$441$	0.0757869	−	2.99904i	0.00360890	−	0.142812i
$442$	−2.67600	+	2.83202i	−0.127284	+	0.134706i
$443$			31.1461i			1.47980i	0.672720	+	0.739898i	$0.265126\pi$
$443$			31.1461i			1.47980i	−0.672720	+	0.739898i	$0.734874\pi$
$444$	0.254902	−	0.905400i	0.0120971	−	0.0429684i
$445$	16.2949	+	28.2236i	0.772451	+	1.33792i
$446$	0.852144	−	1.47596i	0.0403502	−	0.0698886i
$447$	13.6146	−	13.2749i	0.643949	−	0.627882i
$448$	−0.965926	+	0.258819i	−0.0456357	+	0.0122281i
$449$	14.2072	−	3.80679i	0.670477	−	0.179654i	0.0925073	−	0.995712i	$-0.470512\pi$
$449$	14.2072	−	3.80679i	0.670477	−	0.179654i	0.577970	+	0.816058i	$0.303845\pi$
$450$	2.58782	+	2.72200i	0.121991	+	0.128316i
$451$	−13.4377	+	23.2747i	−0.632756	+	1.09596i
$452$	−6.60364	−	11.4378i	−0.310609	−	0.537991i
$453$	−33.6408	−	9.47109i	−1.58058	−	0.444990i
$454$			9.26374i			0.434769i
$455$	6.14153	+	3.31759i	0.287920	+	0.155531i
$456$	−0.0515526	+	4.08074i	−0.00241417	+	0.191098i
$457$	2.20870	−	8.24299i	0.103319	−	0.385591i	−0.894830	−	0.446406i	$-0.852704\pi$
$457$	2.20870	−	8.24299i	0.103319	−	0.385591i	0.998149	+	0.0608158i	$0.0193702\pi$
$458$	−16.1766	+	9.33954i	−0.755881	+	0.436408i
$459$	2.98983	−	4.75303i	0.139553	−	0.221853i
$460$	−4.30153	−	4.30153i	−0.200560	−	0.200560i
$461$	1.14954	+	4.29016i	0.0535396	+	0.199812i	0.987515	−	0.157525i	$-0.0503514\pi$
$461$	1.14954	+	4.29016i	0.0535396	+	0.199812i	−0.933975	+	0.357337i	$0.883685\pi$
$462$	2.13972	+	8.40902i	0.0995486	+	0.391223i
$463$	−16.3629	+	16.3629i	−0.760446	+	0.760446i	−0.976403	−	0.215957i	$-0.930713\pi$
$463$	−16.3629	+	16.3629i	−0.760446	+	0.760446i	0.215957	+	0.976403i	$0.430713\pi$
$464$	−0.710895	−	0.410435i	−0.0330025	−	0.0190540i
$465$	9.75034	+	17.3918i	0.452161	+	0.806526i
$466$	−19.0119	−	5.09423i	−0.880710	−	0.235985i
$467$	35.6614			1.65021			0.825106	−	0.564978i	$-0.191116\pi$
$467$	35.6614			1.65021			0.825106	+	0.564978i	$0.191116\pi$
$468$	−9.35093	+	5.43691i	−0.432247	+	0.251321i
$469$	11.9267			0.550722
$470$	−0.312669	−	0.0837795i	−0.0144224	−	0.00386446i
$471$	−1.36183	−	2.42911i	−0.0627496	−	0.111927i
$472$	−1.48616	−	0.858036i	−0.0684062	−	0.0394943i
$473$	−20.1273	+	20.1273i	−0.925452	+	0.925452i
$474$	−0.661473	−	2.59957i	−0.0303825	−	0.119402i
$475$	0.763468	+	2.84930i	0.0350303	+	0.130735i
$476$	0.764131	+	0.764131i	0.0350239	+	0.0350239i
$477$	36.9347	+	22.5872i	1.69112	+	1.03420i
$478$	20.2421	−	11.6868i	0.925853	−	0.534542i
$479$	1.80118	−	6.72208i	0.0822978	−	0.307140i	−0.912491	−	0.409097i	$-0.865844\pi$
$479$	1.80118	−	6.72208i	0.0822978	−	0.307140i	0.994789	+	0.101957i	$0.0325105\pi$
$480$	−0.0423586	+	3.35297i	−0.00193340	+	0.153041i
$481$	1.90488	+	0.453014i	0.0868552	+	0.0206557i
$482$		−	3.45807i		−	0.157511i
$483$	−5.23879	−	1.47491i	−0.238373	−	0.0671105i
$484$	−7.04835	−	12.2081i	−0.320379	−	0.554913i
$485$	4.08839	−	7.08130i	0.185644	−	0.321545i
$486$	11.6965	−	10.3050i	0.530563	−	0.467443i
$487$	20.4001	−	5.46620i	0.924419	−	0.247697i	0.234946	−	0.972009i	$-0.424509\pi$
$487$	20.4001	−	5.46620i	0.924419	−	0.247697i	0.689473	+	0.724311i	$0.257842\pi$
$488$	8.68830	−	2.32802i	0.393301	−	0.105385i
$489$	9.51226	−	9.27491i	0.430159	−	0.419426i
$490$	0.967996	−	1.67662i	0.0437296	−	0.0757419i
$491$	−4.70139	−	8.14304i	−0.212171	−	0.367490i	0.740223	−	0.672361i	$-0.234720\pi$
$491$	−4.70139	−	8.14304i	−0.212171	−	0.367490i	−0.952394	+	0.304871i	$0.901387\pi$
$492$	−2.51812	+	8.94423i	−0.113526	+	0.403237i
$493$			0.887069i			0.0399516i
$494$	−8.49200	+	0.240552i	−0.382073	+	0.0108229i
$495$	29.0867	+	0.735032i	1.30735	+	0.0330372i
$496$	1.53895	−	5.74344i	0.0691009	−	0.257888i
$497$	−8.74041	+	5.04628i	−0.392061	+	0.226357i
$498$	0.713648	+	0.424134i	0.0319793	+	0.0190059i
$499$	−29.6535	−	29.6535i	−1.32747	−	1.32747i	−0.907568	−	0.419905i	$-0.862063\pi$
$499$	−29.6535	−	29.6535i	−1.32747	−	1.32747i	−0.419905	−	0.907568i	$-0.637937\pi$
$500$	3.13267	+	11.6913i	0.140097	+	0.522850i
$501$	33.3410	−	8.48377i	1.48956	−	0.379027i
$502$	−12.7838	+	12.7838i	−0.570571	+	0.570571i
$503$	17.6305	+	10.1790i	0.786105	+	0.453858i	0.838590	−	0.544764i	$-0.183381\pi$
$503$	17.6305	+	10.1790i	0.786105	+	0.453858i	−0.0524842	+	0.998622i	$0.516714\pi$
$504$	1.43389	+	2.63514i	0.0638704	+	0.117378i
$505$	23.3979	+	6.26946i	1.04120	+	0.278987i
$506$	15.7414			0.699789
$507$	−12.1053	−	18.9858i	−0.537614	−	0.843191i
$508$	14.0068			0.621451
$509$	40.7355	+	10.9151i	1.80557	+	0.483801i	0.994826	−	0.101598i	$-0.0323955\pi$
$509$	40.7355	+	10.9151i	1.80557	+	0.483801i	0.810745	+	0.585399i	$0.199062\pi$
$510$	3.16082	−	1.77204i	0.139963	−	0.0784673i
$511$	1.85202	+	1.06926i	0.0819285	+	0.0473014i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	11.9376	−	2.71843i	0.527057	−	0.120021i
$514$	−5.49693	−	20.5148i	−0.242459	−	0.904871i
$515$	1.76210	+	1.76210i	0.0776474	+	0.0776474i
$516$	−5.02791	+	8.45997i	−0.221341	+	0.372429i
$517$	0.725399	−	0.418809i	0.0319030	−	0.0184192i
$518$	0.140553	−	0.524550i	0.00617553	−	0.0230474i
$519$	1.30859	+	0.0165316i	0.0574407	+	0.000725658i
$520$	−6.97752	+	0.197651i	−0.305984	+	0.00866758i
$521$			44.6047i			1.95417i	0.212854	+	0.977084i	$0.431724\pi$
$521$			44.6047i			1.95417i	−0.212854	+	0.977084i	$0.568276\pi$
$522$	−0.697259	+	2.36184i	−0.0305182	+	0.103375i
$523$	8.20723	+	14.2153i	0.358877	+	0.621593i	0.987774	−	0.155896i	$-0.0498264\pi$
$523$	8.20723	+	14.2153i	0.358877	+	0.621593i	−0.628896	+	0.777489i	$0.716493\pi$
$524$	0.931723	−	1.61379i	0.0407025	−	0.0704988i
$525$	1.51381	+	1.55255i	0.0660681	+	0.0677588i
$526$	9.57036	−	2.56437i	0.417288	−	0.111812i
$527$	−6.20662	+	1.66306i	−0.270365	+	0.0724440i
$528$	−6.05756	−	6.21257i	−0.263621	−	0.270367i
$529$	6.56328	−	11.3679i	0.285360	−	0.494258i
$530$	13.9694	+	24.1957i	0.606792	+	1.05100i
$531$	−1.45766	+	4.93755i	−0.0632569	+	0.214271i
$532$			2.35620i			0.102154i
$533$	−18.8179	−	4.47522i	−0.815094	−	0.193843i
$534$	−29.1544	−	0.368312i	−1.26163	−	0.0159384i
$535$	2.81861	−	10.5192i	0.121859	−	0.454784i
$536$	−10.3288	+	5.96333i	−0.446136	+	0.257577i
$537$	9.67879	−	16.2855i	0.417671	−	0.702773i
$538$	17.3453	+	17.3453i	0.747808	+	0.747808i
$539$	1.29660	+	4.83896i	0.0558483	+	0.208429i
$540$	9.80860	−	2.23362i	0.422095	−	0.0961195i
$541$	26.3985	−	26.3985i	1.13496	−	1.13496i	0.145619	−	0.989341i	$-0.453483\pi$
$541$	26.3985	−	26.3985i	1.13496	−	1.13496i	0.989341	−	0.145619i	$-0.0465173\pi$
$542$	−13.8101	−	7.97326i	−0.593194	−	0.342481i
$543$	32.8113	−	18.3950i	1.40807	−	0.789403i
$544$	−1.04382	−	0.279691i	−0.0447535	−	0.0119917i
$545$	37.0949			1.58897
$546$	−5.35868	+	3.20695i	−0.229330	+	0.137245i
$547$	13.5658			0.580032			0.290016	−	0.957022i	$-0.406339\pi$
$547$	13.5658			0.580032			0.290016	+	0.957022i	$0.406339\pi$
$548$	15.0687	+	4.03765i	0.643703	+	0.172480i
$549$	−12.8975	−	23.7025i	−0.550453	−	1.01160i
$550$	−5.43151	−	3.13589i	−0.231601	−	0.133715i
$551$	−1.36764	+	1.36764i	−0.0582635	+	0.0582635i
$552$	5.27438	−	1.34209i	0.224493	−	0.0571232i
$553$	−0.400830	−	1.49592i	−0.0170450	−	0.0636129i
$554$	10.1250	+	10.1250i	0.430170	+	0.430170i
$555$	−1.56540	−	0.930343i	−0.0664473	−	0.0394909i
$556$	8.11872	−	4.68734i	0.344310	−	0.198788i
$557$	4.55992	−	17.0179i	0.193210	−	0.721070i	−0.799513	−	0.600649i	$-0.794909\pi$
$557$	4.55992	−	17.0179i	0.193210	−	0.721070i	0.992723	−	0.120421i	$-0.0384244\pi$
$558$	−17.8325	−	0.450633i	−0.754908	−	0.0190768i
$559$	−18.0246	−	9.73667i	−0.762358	−	0.411817i
$560$			1.93599i			0.0818106i
$561$	−2.54110	+	9.02585i	−0.107285	+	0.381072i
$562$	1.42194	+	2.46287i	0.0599809	+	0.103890i
$563$	−13.1207	+	22.7258i	−0.552972	+	0.957776i	0.445086	+	0.895488i	$0.353173\pi$
$563$	−13.1207	+	22.7258i	−0.552972	+	0.957776i	−0.998058	+	0.0622884i	$0.980160\pi$
$564$	0.207349	−	0.202175i	0.00873095	−	0.00851310i
$565$	−24.6979	+	6.61779i	−1.03905	+	0.278413i
$566$	20.8077	−	5.57539i	0.874611	−	0.234351i
$567$	6.67727	−	6.03440i	0.280419	−	0.253421i
$568$	5.04628	−	8.74041i	0.211737	−	0.366740i
$569$	−7.41148	−	12.8371i	−0.310705	−	0.538157i	0.667810	−	0.744332i	$-0.267232\pi$
$569$	−7.41148	−	12.8371i	−0.310705	−	0.538157i	−0.978515	+	0.206174i	$0.933899\pi$
$570$	7.60525	+	2.14115i	0.318549	+	0.0896827i
$571$			7.26369i			0.303976i	0.988382	+	0.151988i	$0.0485675\pi$
$571$			7.26369i			0.303976i	−0.988382	+	0.151988i	$0.951432\pi$
$572$	12.4054	−	13.1287i	0.518696	−	0.548939i
$573$	−0.436384	+	34.5427i	−0.0182302	+	1.44304i
$574$	−1.38849	+	5.18191i	−0.0579544	+	0.216289i
$575$	3.40680	−	1.96692i	0.142073	−	0.0820262i
$576$	−2.55935	−	1.56515i	−0.106640	−	0.0652148i
$577$	15.1240	+	15.1240i	0.629619	+	0.629619i	0.947972	−	0.318353i	$-0.103130\pi$
$577$	15.1240	+	15.1240i	0.629619	+	0.629619i	−0.318353	+	0.947972i	$0.603130\pi$
$578$	−4.09768	−	15.2927i	−0.170441	−	0.636094i
$579$	−10.6017	−	41.6644i	−0.440592	−	1.73151i
$580$	−1.12373	+	1.12373i	−0.0466605	+	0.0466605i
$581$	0.415085	+	0.239650i	0.0172206	+	0.00994234i
$582$	3.57739	+	6.38104i	0.148288	+	0.264503i
$583$	−69.8323	−	18.7115i	−2.89216	−	0.774952i
$584$	−2.13853			−0.0884929
$585$	5.48167	+	20.2108i	0.226639	+	0.835612i
$586$	−13.4082			−0.553888
$587$	14.4371	+	3.86840i	0.595881	+	0.159666i	0.544140	−	0.838995i	$-0.316856\pi$
$587$	14.4371	+	3.86840i	0.595881	+	0.159666i	0.0517414	+	0.998661i	$0.483523\pi$
$588$	0.847008	+	1.51082i	0.0349300	+	0.0623052i
$589$	−12.1331	−	7.00505i	−0.499936	−	0.288638i
$590$	−2.34922	+	2.34922i	−0.0967160	+	0.0967160i
$591$	8.93704	+	35.1223i	0.367621	+	1.44474i
$592$	0.140553	+	0.524550i	0.00577668	+	0.0215589i
$593$	−11.2075	−	11.2075i	−0.460239	−	0.460239i	0.438495	−	0.898734i	$-0.355512\pi$
$593$	−11.2075	−	11.2075i	−0.460239	−	0.460239i	−0.898734	+	0.438495i	$0.855512\pi$
$594$	−13.8603	+	22.0341i	−0.568694	+	0.904072i
$595$	1.81183	−	1.04606i	0.0742777	−	0.0428843i
$596$	−2.84144	+	10.6044i	−0.116390	+	0.434373i
$597$	−0.227950	+	18.0438i	−0.00932937	+	0.738483i
$598$	3.24095	+	10.8559i	0.132532	+	0.443931i
$599$		−	19.7299i		−	0.806143i	−0.915168	−	0.403072i	$-0.867943\pi$
$599$		−	19.7299i		−	0.806143i	0.915168	−	0.403072i	$-0.132057\pi$
$600$	−2.08727	−	0.587641i	−0.0852126	−	0.0239904i
$601$	−21.8523	−	37.8493i	−0.891374	−	1.54390i	−0.838229	−	0.545318i	$-0.816409\pi$
$601$	−21.8523	−	37.8493i	−0.891374	−	1.54390i	−0.0531444	−	0.998587i	$-0.516924\pi$
$602$	−2.84093	+	4.92064i	−0.115788	+	0.200550i
$603$	24.6530	+	25.9313i	1.00395	+	1.05601i
$604$	19.4901	−	5.22235i	0.793040	−	0.212494i
$605$	−26.3612	+	7.06345i	−1.07173	+	0.287170i
$606$	−15.5165	+	15.1293i	−0.630315	+	0.614587i
$607$	−0.403192	+	0.698348i	−0.0163650	+	0.0283451i	−0.874092	−	0.485760i	$-0.838543\pi$
$607$	−0.403192	+	0.698348i	−0.0163650	+	0.0283451i	0.857727	+	0.514106i	$0.171876\pi$
$608$	−1.17810	−	2.04053i	−0.0477783	−	0.0827545i
$609$	−0.385305	+	1.36859i	−0.0156134	+	0.0554579i
$610$		−	17.4138i		−	0.705066i
$611$	0.438179	+	0.414038i	0.0177268	+	0.0167502i
$612$	−0.0818987	+	3.24090i	−0.00331056	+	0.131006i
$613$	−1.19793	+	4.47072i	−0.0483838	+	0.180571i	−0.985889	−	0.167401i	$-0.946463\pi$
$613$	−1.19793	+	4.47072i	−0.0483838	+	0.180571i	0.937505	+	0.347971i	$0.113129\pi$
$614$	14.9433	−	8.62754i	0.603064	−	0.348179i
$615$	15.4642	+	9.19064i	0.623576	+	0.370602i
$616$	−3.54236	−	3.54236i	−0.142726	−	0.142726i
$617$	−5.55124	−	20.7175i	−0.223484	−	0.834055i	−0.983006	−	0.183573i	$-0.941234\pi$
$617$	−5.55124	−	20.7175i	−0.223484	−	0.834055i	0.759522	−	0.650482i	$-0.225433\pi$
$618$	−2.16062	+	0.549781i	−0.0869131	+	0.0221154i
$619$	−33.9860	+	33.9860i	−1.36601	+	1.36601i	−0.499969	+	0.866043i	$0.666655\pi$
$619$	−33.9860	+	33.9860i	−1.36601	+	1.36601i	−0.866043	+	0.499969i	$0.833345\pi$
$620$	−9.96925	−	5.75575i	−0.400375	−	0.231157i
$621$	−7.62208	−	14.4391i	−0.305864	−	0.579420i
$622$	−10.5139	−	2.81720i	−0.421570	−	0.112959i
$623$	−16.8336			−0.674425
$624$	3.03728	−	5.45664i	0.121588	−	0.218440i
$625$	17.1730			0.686919
$626$	25.4545	+	6.82051i	1.01737	+	0.272602i
$627$	−17.8334	+	9.99789i	−0.712197	+	0.399277i
$628$	1.39240	+	0.803903i	0.0555629	+	0.0320792i
$629$	0.414964	−	0.414964i	0.0165457	−	0.0165457i
$630$	5.64626	−	1.36101i	0.224952	−	0.0542240i
$631$	−2.19913	−	8.20725i	−0.0875458	−	0.326725i	0.908238	−	0.418453i	$-0.137428\pi$
$631$	−2.19913	−	8.20725i	−0.0875458	−	0.326725i	−0.995784	+	0.0917279i	$0.970761\pi$
$632$	1.09509	+	1.09509i	0.0435603	+	0.0435603i
$633$	2.74145	−	4.61276i	0.108963	−	0.183341i
$634$	−19.8039	+	11.4338i	−0.786511	+	0.454093i
$635$	7.01841	−	26.1930i	0.278517	−	1.03944i
$636$	−24.9937	−	0.315750i	−0.991064	−	0.0125203i
$637$	−3.07020	+	1.89047i	−0.121646	+	0.0749031i
$638$		−	4.11228i		−	0.162807i
$639$	−29.0387	−	8.57276i	−1.14875	−	0.339133i
$640$	−0.967996	−	1.67662i	−0.0382634	−	0.0662741i
$641$	9.14555	−	15.8406i	0.361228	−	0.625664i	−0.626936	−	0.779071i	$-0.715691\pi$
$641$	9.14555	−	15.8406i	0.361228	−	0.625664i	0.988163	+	0.153407i	$0.0490244\pi$
$642$	6.80181	+	6.97587i	0.268446	+	0.275316i
$643$	−23.2648	+	6.23377i	−0.917472	+	0.245836i	−0.686505	−	0.727125i	$-0.740856\pi$
$643$	−23.2648	+	6.23377i	−0.917472	+	0.245836i	−0.230968	+	0.972961i	$0.574189\pi$
$644$	3.03513	−	0.813262i	0.119601	−	0.0320470i
$645$	13.3010	+	13.6414i	0.523726	+	0.537128i
$646$	−1.27311	+	2.20509i	−0.0500898	+	0.0867581i
$647$	4.83585	+	8.37595i	0.190117	+	0.329292i	0.945289	−	0.326235i	$-0.105780\pi$
$647$	4.83585	+	8.37595i	0.190117	+	0.329292i	−0.755172	+	0.655527i	$0.772447\pi$
$648$	−2.76549	+	8.56458i	−0.108639	+	0.336449i
$649$		−	8.59694i		−	0.337459i
$650$	1.04436	−	4.39144i	0.0409632	−	0.172247i
$651$	−10.2980	−	0.130097i	−0.403612	−	0.00509890i
$652$	−1.98526	+	7.40908i	−0.0777486	+	0.290162i
$653$	22.6224	−	13.0610i	0.885282	−	0.511118i	0.0128859	−	0.999917i	$-0.495898\pi$
$653$	22.6224	−	13.0610i	0.885282	−	0.511118i	0.872396	+	0.488799i	$0.162565\pi$
$654$	−16.9554	+	28.5291i	−0.663008	+	1.11558i
$655$	−2.55097	−	2.55097i	−0.0996747	−	0.0996747i
$656$	−1.38849	−	5.18191i	−0.0542114	−	0.202320i
$657$	1.50339	+	6.23695i	0.0586530	+	0.243326i
$658$	0.118229	−	0.118229i	0.00460904	−	0.00460904i
$659$	−19.6160	−	11.3253i	−0.764132	−	0.441172i	0.0666453	−	0.997777i	$-0.478770\pi$
$659$	−19.6160	−	11.3253i	−0.764132	−	0.441172i	−0.830777	+	0.556605i	$0.812104\pi$
$660$	−14.6529	+	8.21484i	−0.570365	+	0.319762i
$661$	29.3854	+	7.87378i	1.14296	+	0.306255i	0.780140	−	0.625605i	$-0.215148\pi$
$661$	29.3854	+	7.87378i	1.14296	+	0.306255i	0.362818	+	0.931860i	$0.381815\pi$
$662$	14.8280			0.576306
$663$	−6.74779	+	0.105860i	−0.262063	+	0.00411126i
$664$	−0.479299			−0.0186004
$665$	4.40616	+	1.18063i	0.170863	+	0.0457827i
$666$	1.43102	−	0.778679i	0.0554511	−	0.0301732i
$667$	2.23378	+	1.28967i	0.0864921	+	0.0499363i
$668$	−14.0451	+	14.0451i	−0.543423	+	0.543423i
$669$	2.86075	−	0.727932i	0.110603	−	0.0281435i
$670$	5.97611	+	22.3031i	0.230877	+	0.861646i
$671$	31.8628	+	31.8628i	1.23005	+	1.23005i
$672$	−1.48894	−	0.884905i	−0.0574371	−	0.0341359i
$673$	16.9366	−	9.77835i	0.652858	−	0.376928i	−0.136692	−	0.990614i	$-0.543647\pi$
$673$	16.9366	−	9.77835i	0.652858	−	0.376928i	0.789550	+	0.613686i	$0.210314\pi$
$674$	−4.85925	+	18.1350i	−0.187171	+	0.698533i
$675$	−0.246474	+	6.50058i	−0.00948677	+	0.250207i
$676$	11.6082	+	5.85226i	0.446470	+	0.225087i
$677$		−	47.5793i		−	1.82862i	−0.405015	−	0.914310i	$-0.632734\pi$
$677$		−	47.5793i		−	1.82862i	0.405015	−	0.914310i	$-0.367266\pi$
$678$	6.19931	−	22.0196i	0.238083	−	0.845660i
$679$	2.11178	+	3.65771i	0.0810427	+	0.140370i
$680$	−1.04606	+	1.81183i	−0.0401145	+	0.0694804i
$681$	−11.4881	+	11.2015i	−0.440226	+	0.429242i
$682$	28.7727	−	7.70962i	1.10176	−	0.295217i
$683$	−29.7216	+	7.96389i	−1.13727	+	0.304730i	−0.777852	−	0.628448i	$-0.783691\pi$
$683$	−29.7216	+	7.96389i	−1.13727	+	0.304730i	−0.359415	+	0.933178i	$0.617024\pi$
$684$	−5.12293	+	4.87040i	−0.195880	+	0.186224i
$685$	15.1010	−	26.1557i	0.576979	−	0.999357i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	−31.1424	−	8.76770i	−1.18816	−	0.334509i
$688$		−	5.68187i		−	0.216619i
$689$	−1.47333	−	52.0118i	−0.0561295	−	1.98149i
$690$	0.133099	−	10.5357i	0.00506701	−	0.401087i
$691$	−3.74279	+	13.9683i	−0.142383	+	0.531379i	0.857475	+	0.514525i	$0.172032\pi$
$691$	−3.74279	+	13.9683i	−0.142383	+	0.531379i	−0.999858	+	0.0168540i	$0.994635\pi$
$692$	−0.654347	+	0.377787i	−0.0248745	+	0.0143613i
$693$	−7.84089	+	12.8215i	−0.297851	+	0.487048i
$694$	6.66902	+	6.66902i	0.253152	+	0.253152i
$695$	−4.69739	−	17.5309i	−0.178182	−	0.664985i
$696$	−0.350609	−	1.37788i	−0.0132898	−	0.0522285i
$697$	−4.09934	+	4.09934i	−0.155274	+	0.155274i
$698$	−26.5394	−	15.3225i	−1.00453	−	0.579967i
$699$	−16.6713	−	29.7368i	−0.630567	−	1.12475i
$700$	−1.20928	−	0.324025i	−0.0457064	−	0.0122470i
$701$	0.0793469			0.00299689			0.00149845	−	0.999999i	$-0.499523\pi$
$701$	0.0793469			0.00299689			0.00149845	+	0.999999i	$0.499523\pi$
$702$	−18.0493	−	5.02208i	−0.681228	−	0.189546i
$703$	1.27955			0.0482590
$704$	4.83896	+	1.29660i	0.182375	+	0.0488673i
$705$	−0.274176	−	0.489051i	−0.0103261	−	0.0184187i
$706$	18.7414	+	10.8203i	0.705341	+	0.407229i
$707$	−8.84740	+	8.84740i	−0.332741	+	0.332741i
$708$	−0.732965	−	2.88053i	−0.0275465	−	0.108257i
$709$	0.737752	+	2.75333i	0.0277068	+	0.103403i	0.978395	−	0.206746i	$-0.0662875\pi$
$709$	0.737752	+	2.75333i	0.0277068	+	0.103403i	−0.950688	+	0.310150i	$0.899621\pi$
$710$	−13.8162	−	13.8162i	−0.518514	−	0.518514i
$711$	2.42394	−	3.96364i	0.0909048	−	0.148648i
$712$	14.5783	−	8.41681i	0.546347	−	0.315433i
$713$	−4.83570	+	18.0471i	−0.181098	+	0.675868i
$714$	−0.0236440	+	1.87158i	−0.000884855	+	0.0700422i
$715$	−18.3350	−	29.7768i	−0.685690	−	1.11359i
$716$			10.9377i			0.408760i
$717$	38.9693	+	10.9712i	1.45534	+	0.409728i
$718$	−12.5001	−	21.6508i	−0.466499	−	0.808000i
$719$	0.842006	−	1.45840i	0.0314015	−	0.0543890i	−0.849898	−	0.526948i	$-0.823336\pi$
$719$	0.842006	−	1.45840i	0.0314015	−	0.0543890i	0.881299	+	0.472559i	$0.156670\pi$
$720$	−4.20930	+	4.00180i	−0.156871	+	0.149138i
$721$	−1.24333	+	0.333149i	−0.0463040	+	0.0124071i
$722$	12.9901	−	3.48068i	0.483440	−	0.129537i
$723$	4.28842	−	4.18141i	0.159488	−	0.155508i
$724$	−10.8588	+	18.8080i	−0.403564	+	0.698993i
$725$	−0.513839	−	0.889995i	−0.0190835	−	0.0330536i
$726$	6.61679	−	23.5025i	0.245572	−	0.872260i
$727$			34.6532i			1.28521i	0.766196	+	0.642607i	$0.222147\pi$
$727$			34.6532i			1.28521i	−0.766196	+	0.642607i	$0.777853\pi$
$728$	1.71364	−	3.17229i	0.0635116	−	0.117573i
$729$	26.9225	+	2.04451i	0.997129	+	0.0757224i
$730$	−1.07156	+	3.99910i	−0.0396600	+	0.148013i
$731$	−5.31747	+	3.07004i	−0.196674	+	0.113550i
$732$	13.3927	+	7.95953i	0.495009	+	0.294193i
$733$	−27.6020	−	27.6020i	−1.01950	−	1.01950i	−0.999806	−	0.0196968i	$-0.993730\pi$
$733$	−27.6020	−	27.6020i	−1.01950	−	1.01950i	−0.0196968	−	0.999806i	$-0.506270\pi$
$734$	−4.81040	−	17.9527i	−0.177555	−	0.662645i
$735$	3.24968	−	0.826897i	0.119866	−	0.0305005i
$736$	−2.22187	+	2.22187i	−0.0818993	+	0.0818993i
$737$	−51.7437	−	29.8743i	−1.90600	−	1.10043i
$738$	−14.1368	+	7.69239i	−0.520381	+	0.283161i
$739$	−27.2046	−	7.28945i	−1.00074	−	0.268147i	−0.278983	−	0.960296i	$-0.589997\pi$
$739$	−27.2046	−	7.28945i	−1.00074	−	0.268147i	−0.721754	+	0.692149i	$0.756664\pi$
$740$	1.05135			0.0386483
$741$	−10.5666	−	10.2402i	−0.388175	−	0.376184i
$742$	−14.4313			−0.529789
$743$	−11.2794	−	3.02232i	−0.413803	−	0.110878i	0.0459104	−	0.998946i	$-0.485381\pi$
$743$	−11.2794	−	3.02232i	−0.413803	−	0.110878i	−0.459713	+	0.888067i	$0.652048\pi$
$744$	8.98341	−	5.03635i	0.329348	−	0.184642i
$745$	18.4067	+	10.6271i	0.674370	+	0.389348i
$746$	−8.57957	+	8.57957i	−0.314121	+	0.314121i
$747$	0.336950	+	1.39786i	0.0123283	+	0.0511450i
$748$	−1.40116	−	5.22919i	−0.0512314	−	0.191198i
$749$	3.97759	+	3.97759i	0.145338	+	0.145338i
$750$	−10.7106	+	18.0217i	−0.391096	+	0.658059i
$751$	−12.5124	+	7.22401i	−0.456582	+	0.263608i	−0.710606	−	0.703590i	$-0.751579\pi$
$751$	−12.5124	+	7.22401i	−0.456582	+	0.263608i	0.254024	+	0.967198i	$0.418246\pi$
$752$	−0.0432747	+	0.161503i	−0.00157807	+	0.00588942i
$753$	−31.3114	−	0.395562i	−1.14105	−	0.0144151i
$754$	2.83601	−	0.846667i	0.103281	−	0.0308338i
$755$		−	39.0637i		−	1.42167i
$756$	−1.53406	+	4.96454i	−0.0557933	+	0.180559i
$757$	13.1472	+	22.7715i	0.477842	+	0.827646i	0.999677	−	0.0254000i	$-0.00808594\pi$
$757$	13.1472	+	22.7715i	0.477842	+	0.827646i	−0.521836	+	0.853046i	$0.674753\pi$
$758$	1.49807	−	2.59473i	0.0544122	−	0.0942448i
$759$	19.0341	+	19.5212i	0.690893	+	0.708573i
$760$	−4.40616	+	1.18063i	−0.159828	+	0.0428258i
$761$	34.8239	−	9.33104i	1.26237	−	0.338250i	0.435264	−	0.900303i	$-0.356655\pi$
$761$	34.8239	−	9.33104i	1.26237	−	0.338250i	0.827101	+	0.562053i	$0.189988\pi$
$762$	16.9367	+	17.3701i	0.613551	+	0.629252i
$763$	−9.58034	+	16.5936i	−0.346832	+	0.600730i
$764$	−9.97242	−	17.2727i	−0.360789	−	0.624905i
$765$	6.01952	+	1.77707i	0.217636	+	0.0642503i
$766$		−	21.6483i		−	0.782185i
$767$	5.92882	−	1.77000i	0.214077	−	0.0639110i
$768$	1.73191	+	0.0218795i	0.0624950	+	0.000789510i
$769$	8.80289	−	32.8528i	0.317440	−	1.18470i	−0.604256	−	0.796791i	$-0.706529\pi$
$769$	8.80289	−	32.8528i	0.317440	−	1.18470i	0.921696	−	0.387913i	$-0.126804\pi$
$770$	−8.39929	+	4.84933i	−0.302689	+	0.174758i
$771$	18.7941	−	31.6229i	0.676852	−	1.13887i
$772$	17.5514	+	17.5514i	0.631690	+	0.631690i
$773$	3.54196	+	13.2188i	0.127396	+	0.475447i	0.999914	−	0.0131349i	$-0.00418109\pi$
$773$	3.54196	+	13.2188i	0.127396	+	0.475447i	−0.872518	+	0.488582i	$0.837514\pi$
$774$	−16.5710	+	3.99438i	−0.595632	+	0.143575i
$775$	5.26375	−	5.26375i	0.189080	−	0.189080i
$776$	−3.65771	−	2.11178i	−0.131304	−	0.0758085i
$777$	0.820457	−	0.459971i	0.0294337	−	0.0165014i
$778$	34.1296	+	9.14500i	1.22361	+	0.327864i
$779$	−12.6403			−0.452887
$780$	−8.68216	−	8.41395i	−0.310871	−	0.301268i
$781$	50.5603			1.80919
$782$	3.27990	+	0.878847i	0.117289	+	0.0314275i
$783$	−3.77207	+	1.99120i	−0.134803	+	0.0711596i
$784$	−0.866025	−	0.500000i	−0.0309295	−	0.0178571i
$785$	2.20101	−	2.20101i	0.0785575	−	0.0785575i
$786$	3.12791	−	0.795912i	0.111569	−	0.0283892i
$787$	3.23906	+	12.0883i	0.115460	+	0.430903i	0.999321	−	0.0368470i	$-0.0117314\pi$
$787$	3.23906	+	12.0883i	0.115460	+	0.430903i	−0.883861	+	0.467750i	$0.845065\pi$
$788$	−14.7955	−	14.7955i	−0.527069	−	0.527069i
$789$	14.7524	+	8.76761i	0.525199	+	0.312135i
$790$	2.59656	−	1.49912i	0.0923814	−	0.0533365i
$791$	3.41829	−	12.7572i	0.121541	−	0.453596i
$792$	0.379667	−	15.0242i	0.0134909	−	0.533861i
$793$	−15.4138	+	28.5341i	−0.547360	+	1.01328i
$794$		−	20.5037i		−	0.727650i
$795$	−13.1141	+	46.5806i	−0.465109	+	1.65204i
$796$	−5.20920	−	9.02261i	−0.184635	−	0.319798i
$797$	−3.71160	+	6.42868i	−0.131472	+	0.227716i	−0.924244	−	0.381802i	$-0.875304\pi$
$797$	−3.71160	+	6.42868i	−0.131472	+	0.227716i	0.792772	+	0.609518i	$0.208637\pi$
$798$	−2.92197	+	2.84906i	−0.103437	+	0.100856i
$799$	0.174528	−	0.0467646i	0.00617435	−	0.00165441i
$800$	1.20928	−	0.324025i	0.0427544	−	0.0114560i
$801$	−34.7960	−	36.6002i	−1.22946	−	1.29320i
$802$	16.4560	−	28.5026i	0.581082	−	1.00646i
$803$	−5.35665	−	9.27798i	−0.189032	−	0.327413i
$804$	−19.8846	−	5.59821i	−0.701274	−	0.197434i
$805$		−	6.08328i		−	0.214407i
$806$	11.2408	+	18.2556i	0.395941	+	0.643025i
$807$	−0.536704	+	42.4837i	−0.0188929	+	1.49550i
$808$	3.23837	−	12.0858i	0.113926	−	0.425176i
$809$	−37.3624	+	21.5712i	−1.31359	+	0.758403i	−0.982689	−	0.185262i	$-0.940687\pi$
$809$	−37.3624	+	21.5712i	−1.31359	+	0.758403i	−0.330903	+	0.943665i	$0.607353\pi$
$810$	14.6303	+	9.46299i	0.514055	+	0.332496i
$811$	−12.4189	−	12.4189i	−0.436088	−	0.436088i	0.454605	−	0.890693i	$-0.349780\pi$
$811$	−12.4189	−	12.4189i	−0.436088	−	0.436088i	−0.890693	+	0.454605i	$0.849780\pi$
$812$	−0.212457	−	0.792900i	−0.00745578	−	0.0278253i
$813$	−6.81104	−	26.7672i	−0.238874	−	0.938767i
$814$	−1.92370	+	1.92370i	−0.0674255	+	0.0674255i
$815$	12.8604	+	7.42496i	0.450480	+	0.260085i
$816$	−0.915315	−	1.63266i	−0.0320424	−	0.0571545i
$817$	−12.9315	−	3.46498i	−0.452415	−	0.121224i
$818$	23.8802			0.834952
$819$	−10.4566	−	2.76763i	−0.365383	−	0.0967089i
$820$	−10.3860			−0.362696
$821$	−17.7860	−	4.76575i	−0.620736	−	0.166326i	−0.0652737	−	0.997867i	$-0.520792\pi$
$821$	−17.7860	−	4.76575i	−0.620736	−	0.166326i	−0.555462	+	0.831542i	$0.687459\pi$
$822$	13.2135	+	23.5692i	0.460875	+	0.822070i
$823$	−21.7279	−	12.5446i	−0.757387	−	0.437277i	0.0709700	−	0.997478i	$-0.477391\pi$
$823$	−21.7279	−	12.5446i	−0.757387	−	0.437277i	−0.828357	+	0.560201i	$0.810724\pi$
$824$	0.910179	−	0.910179i	0.0317076	−	0.0317076i
$825$	−2.67879	−	10.5276i	−0.0932634	−	0.366523i
$826$	−0.444152	−	1.65760i	−0.0154540	−	0.0576752i
$827$	26.1867	+	26.1867i	0.910600	+	0.910600i	0.996319	−	0.0857194i	$-0.0273188\pi$
$827$	26.1867	+	26.1867i	0.910600	+	0.910600i	−0.0857194	+	0.996319i	$0.527319\pi$
$828$	8.04201	+	4.91803i	0.279479	+	0.170913i
$829$	44.5004	−	25.6923i	1.54556	−	0.892331i	0.547090	−	0.837074i	$-0.315736\pi$
$829$	44.5004	−	25.6923i	1.54556	−	0.892331i	0.998472	−	0.0552565i	$-0.0175977\pi$
$830$	−0.240163	+	0.896301i	−0.00833619	+	0.0311111i
$831$	−0.313291	+	24.7991i	−0.0108680	+	0.860272i
$832$	0.102093	+	3.60411i	0.00353944	+	0.124950i
$833$			1.08064i			0.0374421i
$834$	15.6298	+	4.40035i	0.541216	+	0.152372i
$835$	19.2271	+	33.3024i	0.665382	+	1.15248i
$836$	5.90189	−	10.2224i	0.204121	−	0.353548i
$837$	−21.0037	−	22.6592i	−0.725995	−	0.783218i
$838$	24.7717	−	6.63755i	0.855723	−	0.229290i
$839$	−5.72503	+	1.53402i	−0.197650	+	0.0529601i	−0.356286	−	0.934377i	$-0.615957\pi$
$839$	−5.72503	+	1.53402i	−0.197650	+	0.0529601i	0.158636	+	0.987337i	$0.449290\pi$
$840$	−2.40086	+	2.34095i	−0.0828375	+	0.0807706i
$841$	−14.1631	+	24.5312i	−0.488382	+	0.845903i
$842$	3.57374	+	6.18989i	0.123159	+	0.213318i
$843$	−1.33488	+	4.74142i	−0.0459756	+	0.163303i
$844$			3.09801i			0.106638i
$845$	16.7604	−	18.7753i	0.576576	−	0.645889i
$846$	0.501442	+	0.0126716i	0.0172399	+	0.000435659i
$847$	3.64849	−	13.6164i	0.125364	−	0.467864i
$848$	12.4978	−	7.21563i	0.429178	−	0.247786i
$849$	32.0743	+	19.0623i	1.10079	+	0.654217i
$850$	−0.956643	−	0.956643i	−0.0328126	−	0.0328126i
$851$	−0.441645	−	1.64824i	−0.0151394	−	0.0565010i
$852$	16.9410	−	4.31071i	0.580389	−	0.147683i
$853$	4.35862	−	4.35862i	0.149236	−	0.149236i	−0.628540	−	0.777777i	$-0.716347\pi$
$853$	4.35862	−	4.35862i	0.149236	−	0.149236i	0.777777	+	0.628540i	$0.216347\pi$
$854$	7.78972	+	4.49739i	0.266559	+	0.153898i
$855$	6.54081	+	12.0204i	0.223691	+	0.411090i
$856$	−5.43349	−	1.45590i	−0.185713	−	0.0497616i
$857$	21.7425			0.742711			0.371356	−	0.928491i	$-0.378893\pi$
$857$	21.7425			0.742711			0.371356	+	0.928491i	$0.378893\pi$
$858$	31.2815	−	0.490746i	1.06793	−	0.0167538i
$859$	−3.52824			−0.120382			−0.0601910	−	0.998187i	$-0.519171\pi$
$859$	−3.52824			−0.120382			−0.0601910	+	0.998187i	$0.519171\pi$
$860$	−10.6252	−	2.84702i	−0.362318	−	0.0970827i
$861$	−8.10511	+	4.54395i	−0.276221	+	0.154857i
$862$	−11.3239	−	6.53784i	−0.385693	−	0.222680i
$863$	13.3323	−	13.3323i	0.453836	−	0.453836i	−0.442790	−	0.896625i	$-0.646011\pi$
$863$	13.3323	−	13.3323i	0.453836	−	0.453836i	0.896625	+	0.442790i	$0.146011\pi$
$864$	−1.15373	−	5.06645i	−0.0392508	−	0.172364i
$865$	0.378597	+	1.41294i	0.0128727	+	0.0480415i
$866$	3.82867	+	3.82867i	0.130104	+	0.130104i
$867$	14.0100	−	23.5732i	0.475804	−	0.800588i
$868$	5.14943	−	2.97302i	0.174783	−	0.100911i
$869$	−2.00802	+	7.49404i	−0.0681175	+	0.254218i
$870$	−2.75235	−	0.0347709i	−0.0933135	−	0.00117885i
$871$	9.94918	−	41.8354i	0.337115	−	1.41754i
$872$		−	19.1607i		−	0.648863i
$873$	−3.58755	+	12.1522i	−0.121420	+	0.411289i
$874$	3.70183	+	6.41176i	0.125216	+	0.216881i
$875$	−6.05185	+	10.4821i	−0.204590	+	0.354360i
$876$	−2.58586	−	2.65203i	−0.0873680	−	0.0896037i
$877$	−8.74624	+	2.34355i	−0.295340	+	0.0791360i	−0.403446	−	0.915003i	$-0.632188\pi$
$877$	−8.74624	+	2.34355i	−0.295340	+	0.0791360i	0.108107	+	0.994139i	$0.465521\pi$
$878$	−36.0784	+	9.66717i	−1.21759	+	0.326251i
$879$	−16.2129	−	16.6278i	−0.546847	−	0.560841i
$880$	4.84933	−	8.39929i	0.163471	−	0.283140i
$881$	−4.54322	−	7.86909i	−0.153065	−	0.265116i	0.779288	−	0.626666i	$-0.215581\pi$
$881$	−4.54322	−	7.86909i	−0.153065	−	0.265116i	−0.932353	+	0.361550i	$0.882248\pi$
$882$	−0.849414	+	2.87724i	−0.0286013	+	0.0968816i
$883$			11.8352i			0.398285i	0.979971	+	0.199142i	$0.0638157\pi$
$883$			11.8352i			0.398285i	−0.979971	+	0.199142i	$0.936184\pi$
$884$	3.31780	−	2.04292i	0.111590	−	0.0687110i
$885$	−5.75394	−	0.0726905i	−0.193416	−	0.00244346i
$886$	8.06120	−	30.0848i	0.270821	−	1.01072i
$887$	49.8352	−	28.7724i	1.67330	−	0.966082i	0.707535	−	0.706678i	$-0.249807\pi$
$887$	49.8352	−	28.7724i	1.67330	−	0.966082i	0.965769	−	0.259404i	$-0.0835262\pi$
$888$	−0.480551	+	0.808575i	−0.0161262	+	0.0271340i
$889$	9.90430	+	9.90430i	0.332180	+	0.332180i
$890$	−8.43485	−	31.4793i	−0.282737	−	1.05519i
$891$	−44.0845	+	9.45479i	−1.47688	+	0.316747i
$892$	−1.20511	+	1.20511i	−0.0403502	+	0.0403502i
$893$	0.341178	+	0.196979i	0.0114171	+	0.00659166i
$894$	−16.5865	+	9.29886i	−0.554736	+	0.311001i
$895$	20.4537	+	5.48055i	0.683692	+	0.183195i
$896$	1.00000			0.0334077
$897$	−9.54375	+	17.1459i	−0.318656	+	0.572484i
$898$	−14.7083			−0.490823
$899$	4.71462	+	1.26328i	0.157242	+	0.0421327i
$900$	−1.79514	−	3.29903i	−0.0598379	−	0.109968i
$901$	−13.5057	−	7.79753i	−0.449941	−	0.259774i
$902$	19.0037	−	19.0037i	0.632756	−	0.632756i
$903$	−9.53737	+	2.42683i	−0.317384	+	0.0807598i
$904$	3.41829	+	12.7572i	0.113691	+	0.424300i
$905$	29.7303	+	29.7303i	0.988270	+	0.988270i
$906$	30.0433	+	17.8553i	0.998120	+	0.593201i
$907$	−31.4200	+	18.1404i	−1.04328	+	0.602341i	−0.920762	−	0.390125i	$-0.872432\pi$
$907$	−31.4200	+	18.1404i	−1.04328	+	0.602341i	−0.122523	+	0.992466i	$0.539098\pi$
$908$	2.39763	−	8.94809i	0.0795682	−	0.296953i
$909$	−37.5243	−	0.948254i	−1.24460	−	0.0314516i
$910$	−5.07361	−	4.79409i	−0.168189	−	0.158923i
$911$		−	52.0683i		−	1.72510i	−0.505973	−	0.862549i	$-0.668867\pi$
$911$		−	52.0683i		−	1.72510i	0.505973	−	0.862549i	$-0.331133\pi$
$912$	1.10597	−	3.92835i	0.0366223	−	0.130081i
$913$	−1.20056	−	2.07944i	−0.0397328	−	0.0688193i
$914$	−4.26688	+	7.39046i	−0.141136	+	0.244455i
$915$	21.5952	−	21.0564i	0.713916	−	0.696103i
$916$	18.0426	−	4.83450i	0.596144	−	0.159736i
$917$	1.79995	−	0.482296i	0.0594396	−	0.0159268i
$918$	−4.11813	+	3.81725i	−0.135918	+	0.125988i
$919$	−7.22692	+	12.5174i	−0.238394	+	0.412911i	−0.960254	−	0.279129i	$-0.909954\pi$
$919$	−7.22692	+	12.5174i	−0.238394	+	0.412911i	0.721860	+	0.692040i	$0.243288\pi$
$920$	3.04164	+	5.26827i	0.100280	+	0.173690i
$921$	28.7683	+	8.09929i	0.947948	+	0.266881i
$922$		−	4.44150i		−	0.146273i
$923$	10.4097	+	34.8685i	0.342640	+	1.14771i
$924$	0.109609	−	8.67629i	0.00360587	−	0.285429i
$925$	−0.175963	+	0.656703i	−0.00578563	+	0.0215923i
$926$	20.0403	−	11.5703i	0.658566	−	0.380223i
$927$	−3.29437	−	2.01465i	−0.108201	−	0.0661697i
$928$	0.580443	+	0.580443i	0.0190540	+	0.0190540i
$929$	−4.12844	−	15.4075i	−0.135450	−	0.505505i	−0.999996	−	0.00295146i	$-0.999061\pi$
$929$	−4.12844	−	15.4075i	−0.135450	−	0.505505i	0.864546	−	0.502554i	$-0.167606\pi$
$930$	−4.91677	−	19.3228i	−0.161227	−	0.633619i
$931$	−1.66609	+	1.66609i	−0.0546038	+	0.0546038i
$932$	17.0456	+	9.84129i	0.558348	+	0.322362i
$933$	−9.21952	−	16.4450i	−0.301834	−	0.538385i
$934$	−34.4462	−	9.22984i	−1.12712	−	0.302010i
$935$	−10.4808			−0.342759
$936$	10.4395	−	2.83145i	0.341225	−	0.0925490i
$937$	−46.0175			−1.50333			−0.751663	−	0.659548i	$-0.770748\pi$
$937$	−46.0175			−1.50333			−0.751663	+	0.659548i	$0.770748\pi$
$938$	−11.5203	−	3.08685i	−0.376150	−	0.100789i
$939$	22.3207	+	39.8138i	0.728409	+	1.29927i
$940$	0.280332	+	0.161850i	0.00914341	+	0.00527895i
$941$	1.86084	−	1.86084i	0.0606616	−	0.0606616i	−0.676125	−	0.736787i	$-0.736342\pi$
$941$	1.86084	−	1.86084i	0.0606616	−	0.0606616i	0.736787	+	0.676125i	$0.236342\pi$
$942$	0.686723	+	2.69880i	0.0223747	+	0.0879318i
$943$	4.36291	+	16.2826i	0.142076	+	0.530235i
$944$	1.21345	+	1.21345i	0.0394943	+	0.0394943i
$945$	8.51513	+	5.35633i	0.276997	+	0.174241i
$946$	24.6507	−	14.2321i	0.801465	−	0.462726i
$947$	3.16917	−	11.8275i	0.102984	−	0.384342i	−0.895125	−	0.445816i	$-0.852913\pi$
$947$	3.16917	−	11.8275i	0.102984	−	0.384342i	0.998109	+	0.0614741i	$0.0195802\pi$
$948$	−0.0338846	+	2.68219i	−0.00110052	+	0.0871136i
$949$	5.29563	−	5.60439i	0.171903	−	0.181926i
$950$		−	2.94981i		−	0.0957046i
$951$	−38.1256	−	10.7337i	−1.23631	−	0.348064i
$952$	−0.540322	−	0.935866i	−0.0175119	−	0.0303316i
$953$	10.7134	−	18.5561i	0.347040	−	0.601091i	−0.638682	−	0.769471i	$-0.720520\pi$
$953$	10.7134	−	18.5561i	0.347040	−	0.601091i	0.985722	+	0.168379i	$0.0538534\pi$
$954$	−29.8302	−	31.3769i	−0.965789	−	1.01587i
$955$	−37.2973	+	9.99379i	−1.20691	+	0.323391i
$956$	−22.5772	+	6.04953i	−0.730197	+	0.195656i
$957$	5.09972	−	4.97247i	0.164850	−	0.160737i
$958$	−3.47960	+	6.02685i	−0.112421	+	0.194719i
$959$	7.80013	+	13.5102i	0.251879	+	0.436268i
$960$	0.908727	−	3.22776i	0.0293291	−	0.104175i
$961$			4.35550i			0.140500i
$962$	−1.72273	−	0.930598i	−0.0555429	−	0.0300037i
$963$	−0.426314	+	16.8701i	−0.0137378	+	0.543632i
$964$	−0.895014	+	3.34024i	−0.0288265	+	0.107582i
$965$	41.6162	−	24.0271i	1.33967	−	0.773460i
$966$	4.67855	+	2.78055i	0.150530	+	0.0894627i
$967$	14.4200	+	14.4200i	0.463717	+	0.463717i	0.899872	−	0.436155i	$-0.143660\pi$
$967$	14.4200	+	14.4200i	0.463717	+	0.463717i	−0.436155	+	0.899872i	$0.643660\pi$
$968$	3.64849	+	13.6164i	0.117267	+	0.437646i
$969$	−4.27398	+	1.08754i	−0.137300	+	0.0349367i
$970$	−5.78185	+	5.78185i	−0.185644	+	0.185644i
$971$	34.4575	+	19.8940i	1.10579	+	0.638430i	0.937737	−	0.347347i	$-0.112917\pi$
$971$	34.4575	+	19.8940i	1.10579	+	0.638430i	0.168057	+	0.985777i	$0.446251\pi$
$972$	−13.9651	+	6.92656i	−0.447929	+	0.222170i
$973$	9.05525	+	2.42635i	0.290298	+	0.0777851i
$974$	−21.1198			−0.676721
$975$	6.70873	−	4.01490i	0.214851	−	0.128580i
$976$	−8.99479			−0.287916
$977$	23.8452	+	6.38931i	0.762877	+	0.204412i	0.619222	−	0.785216i	$-0.287448\pi$
$977$	23.8452	+	6.38931i	0.762877	+	0.204412i	0.143654	+	0.989628i	$0.454115\pi$
$978$	−11.5887	+	6.49693i	−0.370564	+	0.207749i
$979$	73.0325	+	42.1654i	2.33413	+	1.34761i
$980$	−1.36895	+	1.36895i	−0.0437296	+	0.0437296i
$981$	−55.8815	+	13.4701i	−1.78416	+	0.430066i
$982$	2.43362	+	9.08238i	0.0776598	+	0.289830i
$983$	−40.2203	−	40.2203i	−1.28283	−	1.28283i	−0.939051	−	0.343778i	$-0.888293\pi$
$983$	−40.2203	−	40.2203i	−1.28283	−	1.28283i	−0.343778	−	0.939051i	$-0.611707\pi$
$984$	4.74725	−	7.98773i	0.151337	−	0.254640i
$985$	−35.0816	+	20.2544i	−1.11779	+	0.645359i
$986$	0.229590	−	0.856843i	0.00731165	−	0.0272874i
$987$	0.289577	+	0.00365827i	0.00921734	+	0.000116444i
$988$	8.26490	+	1.96554i	0.262942	+	0.0625321i
$989$			17.8536i			0.567711i
$990$	−27.9053	−	8.23818i	−0.886890	−	0.261826i
$991$	8.91385	+	15.4392i	0.283158	+	0.490443i	0.972161	−	0.234315i	$-0.0752847\pi$
$991$	8.91385	+	15.4392i	0.283158	+	0.490443i	−0.689003	+	0.724758i	$0.741951\pi$
$992$	−2.97302	+	5.14943i	−0.0943936	+	0.163495i
$993$	17.9297	+	18.3885i	0.568980	+	0.583540i
$994$	9.74866	−	2.61215i	0.309209	−	0.0828523i
$995$	−19.4827	+	5.22037i	−0.617642	+	0.165497i
$996$	−0.579557	−	0.594388i	−0.0183640	−	0.0188339i
$997$	12.3556	−	21.4006i	0.391306	−	0.677762i	−0.601316	−	0.799011i	$-0.705357\pi$
$997$	12.3556	−	21.4006i	0.391306	−	0.677762i	0.992622	+	0.121249i	$0.0386900\pi$
$998$	20.9682	+	36.3180i	0.663737	+	1.14963i
$999$	2.69601	+	0.833079i	0.0852981	+	0.0263575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.323.3	yes	56
3.2	odd	2		546.2.bu.b.323.9	yes	56
13.6	odd	12		546.2.bu.b.71.9	yes	56
39.32	even	12	inner	546.2.bu.a.71.3	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.3	✓	56	39.32	even	12	inner
546.2.bu.a.323.3	yes	56	1.1	even	1	trivial
546.2.bu.b.71.9	yes	56	13.6	odd	12
546.2.bu.b.323.9	yes	56	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.847008 - 1.51082i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.36895 - 1.36895i) q^{5} +(0.427118 + 1.67856i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.56515 + 2.55935i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.847008 - 1.51082i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.36895 - 1.36895i) q^{5} +(0.427118 + 1.67856i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.56515 + 2.55935i) q^{9} +(-1.67662 + 0.967996i) q^{10} +(1.29660 - 4.83896i) q^{11} +(0.0218795 - 1.73191i) q^{12} +(3.60411 - 0.102093i) q^{13} -1.00000i q^{14} +(-3.22776 - 0.908727i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.540322 - 0.935866i) q^{17} +(2.17423 - 2.06705i) q^{18} +(2.27592 - 0.609830i) q^{19} +(1.87002 - 0.501072i) q^{20} +(1.24012 - 1.20918i) q^{21} +(-2.50483 + 4.33849i) q^{22} +(-1.57110 - 2.72123i) q^{23} +(-0.469386 + 1.66724i) q^{24} +1.25194i q^{25} +(-3.50772 - 0.834197i) q^{26} +(5.19242 + 0.196874i) q^{27} +(-0.258819 + 0.965926i) q^{28} +(-0.710895 + 0.410435i) q^{29} +(2.88258 + 1.71317i) q^{30} +(-4.20449 - 4.20449i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-8.40902 + 2.13972i) q^{33} +(-0.764131 + 0.764131i) q^{34} +(1.67662 + 0.967996i) q^{35} +(-2.63514 + 1.43389i) q^{36} +(0.524550 + 0.140553i) q^{37} -2.35620 q^{38} +(-3.20695 - 5.35868i) q^{39} -1.93599 q^{40} +(-5.18191 - 1.38849i) q^{41} +(-1.51082 + 0.847008i) q^{42} +(-4.92064 - 2.84093i) q^{43} +(3.54236 - 3.54236i) q^{44} +(1.36101 + 5.64626i) q^{45} +(0.813262 + 3.03513i) q^{46} +(0.118229 + 0.118229i) q^{47} +(0.884905 - 1.48894i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.324025 - 1.20928i) q^{50} +(-1.87158 - 0.0236440i) q^{51} +(3.17229 + 1.71364i) q^{52} -14.4313i q^{53} +(-4.96454 - 1.53406i) q^{54} +(-4.84933 - 8.39929i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-2.84906 - 2.92197i) q^{57} +(0.792900 - 0.212457i) q^{58} +(1.65760 - 0.444152i) q^{59} +(-2.34095 - 2.40086i) q^{60} +(-4.49739 + 7.78972i) q^{61} +(2.97302 + 5.14943i) q^{62} +(-2.87724 - 0.849414i) q^{63} +1.00000i q^{64} +(4.79409 - 5.07361i) q^{65} +(8.67629 + 0.109609i) q^{66} +(3.08685 - 11.5203i) q^{67} +(0.935866 - 0.540322i) q^{68} +(-2.78055 + 4.67855i) q^{69} +(-1.36895 - 1.36895i) q^{70} +(2.61215 + 9.74866i) q^{71} +(2.91647 - 0.703005i) q^{72} +(1.51217 - 1.51217i) q^{73} +(-0.470299 - 0.271527i) q^{74} +(1.89145 - 1.06040i) q^{75} +(2.27592 + 0.609830i) q^{76} +5.00966 q^{77} +(1.71075 + 6.00611i) q^{78} -1.54869 q^{79} +(1.87002 + 0.501072i) q^{80} +(-4.10058 - 8.01157i) q^{81} +(4.64597 + 2.68235i) q^{82} +(0.338916 - 0.338916i) q^{83} +(1.67856 - 0.427118i) q^{84} +(-0.541480 - 2.02083i) q^{85} +(4.01769 + 4.01769i) q^{86} +(1.22223 + 0.726392i) q^{87} +(-4.33849 + 2.50483i) q^{88} +(-4.35686 + 16.2600i) q^{89} +(0.146723 - 5.80612i) q^{90} +(1.03143 + 3.45488i) q^{91} -3.14220i q^{92} +(-2.79099 + 9.91347i) q^{93} +(-0.0836003 - 0.144800i) q^{94} +(2.28079 - 3.95045i) q^{95} +(-1.24012 + 1.20918i) q^{96} +(4.07964 - 1.09314i) q^{97} +(0.965926 - 0.258819i) q^{98} +(10.3552 + 10.8922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Introduction

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