LMFDB - Embedded newform 546.2.bd.b.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(121,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("546.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bd (of order $6$, degree $2$, 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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$-1.05091i$ of defining polynomial
Character	$\chi$	$=$	546.361
Dual form			546.2.bd.b.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(0.910115 - 0.525455i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.61575 - 0.397291i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(0.910115 - 0.525455i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.61575 - 0.397291i) q^{7} -1.00000i q^{8} +1.00000 q^{9} -1.05091 q^{10} -6.56072i q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.07474 + 1.88307i) q^{13} +(-2.46395 - 0.963812i) q^{14} +(0.910115 - 0.525455i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.31143 + 4.00351i) q^{17} +(-0.866025 - 0.500000i) q^{18} -2.99423i q^{19} +(0.910115 + 0.525455i) q^{20} +(2.61575 - 0.397291i) q^{21} +(-3.28036 + 5.68175i) q^{22} +(1.59836 - 2.76844i) q^{23} -1.00000i q^{24} +(-1.94779 + 3.37368i) q^{25} +(3.60434 - 0.0934133i) q^{26} +1.00000 q^{27} +(1.65194 + 2.06666i) q^{28} +(-1.12381 - 1.94650i) q^{29} -1.05091 q^{30} +(7.58940 + 4.38174i) q^{31} +(0.866025 - 0.500000i) q^{32} -6.56072i q^{33} -4.62286i q^{34} +(2.17188 - 1.73604i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-4.02143 - 2.32178i) q^{37} +(-1.49712 + 2.59308i) q^{38} +(-3.07474 + 1.88307i) q^{39} +(-0.525455 - 0.910115i) q^{40} +(6.65179 - 3.84041i) q^{41} +(-2.46395 - 0.963812i) q^{42} +(0.696225 - 1.20590i) q^{43} +(5.68175 - 3.28036i) q^{44} +(0.910115 - 0.525455i) q^{45} +(-2.76844 + 1.59836i) q^{46} +(-9.01677 + 5.20584i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(6.68432 - 2.07843i) q^{49} +(3.37368 - 1.94779i) q^{50} +(2.31143 + 4.00351i) q^{51} +(-3.16816 - 1.72127i) q^{52} +(3.40268 - 5.89362i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-3.44736 - 5.97101i) q^{55} +(-0.397291 - 2.61575i) q^{56} -2.99423i q^{57} +2.24763i q^{58} +(-2.16500 + 1.24996i) q^{59} +(0.910115 + 0.525455i) q^{60} -9.90929 q^{61} +(-4.38174 - 7.58940i) q^{62} +(2.61575 - 0.397291i) q^{63} -1.00000 q^{64} +(-1.80890 + 3.32945i) q^{65} +(-3.28036 + 5.68175i) q^{66} +8.98392i q^{67} +(-2.31143 + 4.00351i) q^{68} +(1.59836 - 2.76844i) q^{69} +(-2.74892 + 0.417517i) q^{70} +(7.13127 + 4.11724i) q^{71} -1.00000i q^{72} +(8.18302 + 4.72447i) q^{73} +(2.32178 + 4.02143i) q^{74} +(-1.94779 + 3.37368i) q^{75} +(2.59308 - 1.49712i) q^{76} +(-2.60652 - 17.1612i) q^{77} +(3.60434 - 0.0934133i) q^{78} +(1.65111 + 2.85981i) q^{79} +1.05091i q^{80} +1.00000 q^{81} -7.68082 q^{82} -9.79351i q^{83} +(1.65194 + 2.06666i) q^{84} +(4.20733 + 2.42910i) q^{85} +(-1.20590 + 0.696225i) q^{86} +(-1.12381 - 1.94650i) q^{87} -6.56072 q^{88} +(-3.76799 - 2.17545i) q^{89} -1.05091 q^{90} +(-7.29464 + 6.14721i) q^{91} +3.19672 q^{92} +(7.58940 + 4.38174i) q^{93} +10.4117 q^{94} +(-1.57334 - 2.72510i) q^{95} +(0.866025 - 0.500000i) q^{96} +(5.83099 + 3.36652i) q^{97} +(-6.82801 - 1.54219i) q^{98} -6.56072i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.910115	−	0.525455i	0.407016	−	0.234991i	−0.282491	−	0.959270i	$-0.591161\pi$
$5$	0.910115	−	0.525455i	0.407016	−	0.234991i	0.689507	+	0.724279i	$0.257827\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	2.61575	−	0.397291i	0.988661	−	0.150162i
$7$	2.61575	−	0.397291i	0.988661	−	0.150162i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	−1.05091			−0.332327
$11$		−	6.56072i		−	1.97813i	−0.147475	−	0.989066i	$-0.547115\pi$
$11$		−	6.56072i		−	1.97813i	0.147475	−	0.989066i	$-0.452885\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−3.07474	+	1.88307i	−0.852781	+	0.522269i
$13$	−3.07474	+	1.88307i	−0.852781	+	0.522269i
$14$	−2.46395	−	0.963812i	−0.658519	−	0.257590i
$15$	0.910115	−	0.525455i	0.234991	−	0.135672i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.31143	+	4.00351i	0.560604	+	0.970994i	0.997444	+	0.0714547i	$0.0227641\pi$
$17$	2.31143	+	4.00351i	0.560604	+	0.970994i	−0.436840	+	0.899539i	$0.643903\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$		−	2.99423i		−	0.686925i	−0.939166	−	0.343462i	$-0.888400\pi$
$19$		−	2.99423i		−	0.686925i	0.939166	−	0.343462i	$-0.111600\pi$
$20$	0.910115	+	0.525455i	0.203508	+	0.117495i
$21$	2.61575	−	0.397291i	0.570804	−	0.0866961i
$22$	−3.28036	+	5.68175i	−0.699375	+	1.21135i
$23$	1.59836	−	2.76844i	0.333281	−	0.577259i	−0.649872	−	0.760043i	$-0.725178\pi$
$23$	1.59836	−	2.76844i	0.333281	−	0.577259i	0.983153	+	0.182784i	$0.0585110\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−1.94779	+	3.37368i	−0.389559	+	0.674736i
$26$	3.60434	−	0.0934133i	0.706869	−	0.0183199i
$27$	1.00000			0.192450
$28$	1.65194	+	2.06666i	0.312187	+	0.390562i
$29$	−1.12381	−	1.94650i	−0.208687	−	0.361456i	0.742614	−	0.669719i	$-0.233586\pi$
$29$	−1.12381	−	1.94650i	−0.208687	−	0.361456i	−0.951301	+	0.308263i	$0.900252\pi$
$30$	−1.05091			−0.191869
$31$	7.58940	+	4.38174i	1.36310	+	0.786984i	0.990035	−	0.140823i	$-0.0449747\pi$
$31$	7.58940	+	4.38174i	1.36310	+	0.786984i	0.373061	+	0.927807i	$0.378308\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		−	6.56072i		−	1.14207i
$34$		−	4.62286i		−	0.792813i
$35$	2.17188	−	1.73604i	0.367114	−	0.293445i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−4.02143	−	2.32178i	−0.661120	−	0.381698i	0.131584	−	0.991305i	$-0.457994\pi$
$37$	−4.02143	−	2.32178i	−0.661120	−	0.381698i	−0.792704	+	0.609607i	$0.791327\pi$
$38$	−1.49712	+	2.59308i	−0.242865	+	0.420654i
$39$	−3.07474	+	1.88307i	−0.492353	+	0.301532i
$40$	−0.525455	−	0.910115i	−0.0830818	−	0.143902i
$41$	6.65179	−	3.84041i	1.03883	−	0.599771i	0.119332	−	0.992854i	$-0.461925\pi$
$41$	6.65179	−	3.84041i	1.03883	−	0.599771i	0.919503	+	0.393083i	$0.128592\pi$
$42$	−2.46395	−	0.963812i	−0.380196	−	0.148719i
$43$	0.696225	−	1.20590i	0.106173	−	0.183898i	−0.808044	−	0.589123i	$-0.799474\pi$
$43$	0.696225	−	1.20590i	0.106173	−	0.183898i	0.914217	+	0.405225i	$0.132807\pi$
$44$	5.68175	−	3.28036i	0.856556	−	0.494533i
$45$	0.910115	−	0.525455i	0.135672	−	0.0783302i
$46$	−2.76844	+	1.59836i	−0.408184	+	0.235665i
$47$	−9.01677	+	5.20584i	−1.31523	+	0.759349i	−0.982957	−	0.183834i	$-0.941149\pi$
$47$	−9.01677	+	5.20584i	−1.31523	+	0.759349i	−0.332274	+	0.943183i	$0.607816\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	6.68432	−	2.07843i	0.954903	−	0.296919i
$50$	3.37368	−	1.94779i	0.477110	−	0.275460i
$51$	2.31143	+	4.00351i	0.323665	+	0.560604i
$52$	−3.16816	−	1.72127i	−0.439344	−	0.238698i
$53$	3.40268	−	5.89362i	0.467394	−	0.809551i	−0.531912	−	0.846800i	$-0.678526\pi$
$53$	3.40268	−	5.89362i	0.467394	−	0.809551i	0.999306	+	0.0372492i	$0.0118595\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−3.44736	−	5.97101i	−0.464842	−	0.805131i
$56$	−0.397291	−	2.61575i	−0.0530903	−	0.349545i
$57$		−	2.99423i		−	0.396596i
$58$			2.24763i			0.295128i
$59$	−2.16500	+	1.24996i	−0.281858	+	0.162731i	−0.634264	−	0.773116i	$-0.718697\pi$
$59$	−2.16500	+	1.24996i	−0.281858	+	0.162731i	0.352406	+	0.935847i	$0.385364\pi$
$60$	0.910115	+	0.525455i	0.117495	+	0.0678360i
$61$	−9.90929			−1.26875			−0.634377	−	0.773024i	$-0.718743\pi$
$61$	−9.90929			−1.26875			−0.634377	+	0.773024i	$0.718743\pi$
$62$	−4.38174	−	7.58940i	−0.556482	−	0.963855i
$63$	2.61575	−	0.397291i	0.329554	−	0.0500540i
$64$	−1.00000			−0.125000
$65$	−1.80890	+	3.32945i	−0.224367	+	0.412967i
$66$	−3.28036	+	5.68175i	−0.403784	+	0.699375i
$67$			8.98392i			1.09756i	0.835967	+	0.548780i	$0.184908\pi$
$67$			8.98392i			1.09756i	−0.835967	+	0.548780i	$0.815092\pi$
$68$	−2.31143	+	4.00351i	−0.280302	+	0.485497i
$69$	1.59836	−	2.76844i	0.192420	−	0.333281i
$70$	−2.74892	+	0.417517i	−0.328559	+	0.0499029i
$71$	7.13127	+	4.11724i	0.846326	+	0.488627i	0.859410	−	0.511288i	$-0.170831\pi$
$71$	7.13127	+	4.11724i	0.846326	+	0.488627i	−0.0130832	+	0.999914i	$0.504165\pi$
$72$		−	1.00000i		−	0.117851i
$73$	8.18302	+	4.72447i	0.957750	+	0.552957i	0.895480	−	0.445102i	$-0.146833\pi$
$73$	8.18302	+	4.72447i	0.957750	+	0.552957i	0.0622705	+	0.998059i	$0.480166\pi$
$74$	2.32178	+	4.02143i	0.269901	+	0.467482i
$75$	−1.94779	+	3.37368i	−0.224912	+	0.389559i
$76$	2.59308	−	1.49712i	0.297447	−	0.171731i
$77$	−2.60652	−	17.1612i	−0.297040	−	1.95570i
$78$	3.60434	−	0.0934133i	0.408111	−	0.0105770i
$79$	1.65111	+	2.85981i	0.185765	+	0.321754i	0.943834	−	0.330420i	$-0.107190\pi$
$79$	1.65111	+	2.85981i	0.185765	+	0.321754i	−0.758069	+	0.652174i	$0.773857\pi$
$80$			1.05091i			0.117495i
$81$	1.00000			0.111111
$82$	−7.68082			−0.848205
$83$		−	9.79351i		−	1.07498i	−0.843271	−	0.537489i	$-0.819373\pi$
$83$		−	9.79351i		−	1.07498i	0.843271	−	0.537489i	$-0.180627\pi$
$84$	1.65194	+	2.06666i	0.180241	+	0.225491i
$85$	4.20733	+	2.42910i	0.456349	+	0.263473i
$86$	−1.20590	+	0.696225i	−0.130035	+	0.0750759i
$87$	−1.12381	−	1.94650i	−0.120485	−	0.208687i
$88$	−6.56072			−0.699375
$89$	−3.76799	−	2.17545i	−0.399407	−	0.230597i	0.286821	−	0.957984i	$-0.407401\pi$
$89$	−3.76799	−	2.17545i	−0.399407	−	0.230597i	−0.686228	+	0.727387i	$0.740735\pi$
$90$	−1.05091			−0.110776
$91$	−7.29464	+	6.14721i	−0.764686	+	0.644403i
$92$	3.19672			0.333281
$93$	7.58940	+	4.38174i	0.786984	+	0.454365i
$94$	10.4117			1.07388
$95$	−1.57334	−	2.72510i	−0.161421	−	0.279589i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	5.83099	+	3.36652i	0.592047	+	0.341819i	0.765907	−	0.642952i	$-0.222290\pi$
$97$	5.83099	+	3.36652i	0.592047	+	0.341819i	−0.173859	+	0.984770i	$0.555624\pi$
$98$	−6.82801	−	1.54219i	−0.689733	−	0.155784i
$99$		−	6.56072i		−	0.659377i
$100$	−3.89559			−0.389559
$101$	−7.15050			−0.711501			−0.355750	−	0.934581i	$-0.615775\pi$
$101$	−7.15050			−0.711501			−0.355750	+	0.934581i	$0.615775\pi$
$102$		−	4.62286i		−	0.457731i
$103$	0.342585	+	0.593375i	0.0337559	+	0.0584670i	0.882410	−	0.470482i	$-0.155920\pi$
$103$	0.342585	+	0.593375i	0.0337559	+	0.0584670i	−0.848654	+	0.528949i	$0.822586\pi$
$104$	1.88307	+	3.07474i	0.184650	+	0.301503i
$105$	2.17188	−	1.73604i	0.211953	−	0.169420i
$106$	−5.89362	+	3.40268i	−0.572439	+	0.330498i
$107$	−2.46873	+	4.27597i	−0.238662	+	0.413374i	−0.960330	−	0.278864i	$-0.910042\pi$
$107$	−2.46873	+	4.27597i	−0.238662	+	0.413374i	0.721669	+	0.692238i	$0.243375\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−6.18109	−	3.56865i	−0.592041	−	0.341815i	0.173863	−	0.984770i	$-0.444375\pi$
$109$	−6.18109	−	3.56865i	−0.592041	−	0.341815i	−0.765904	+	0.642955i	$0.777708\pi$
$110$			6.89473i			0.657387i
$111$	−4.02143	−	2.32178i	−0.381698	−	0.220373i
$112$	−0.963812	+	2.46395i	−0.0910717	+	0.232822i
$113$	−4.40041	+	7.62173i	−0.413955	+	0.716992i	−0.995318	−	0.0966527i	$-0.969186\pi$
$113$	−4.40041	+	7.62173i	−0.413955	+	0.716992i	0.581363	+	0.813644i	$0.302520\pi$
$114$	−1.49712	+	2.59308i	−0.140218	+	0.242865i
$115$		−	3.35946i		−	0.313271i
$116$	1.12381	−	1.94650i	0.104343	−	0.180728i
$117$	−3.07474	+	1.88307i	−0.284260	+	0.174090i
$118$	2.49992			0.230136
$119$	7.63668	+	9.55388i	0.700053	+	0.875803i
$120$	−0.525455	−	0.910115i	−0.0479673	−	0.0830818i
$121$	−32.0430			−2.91300
$122$	8.58169	+	4.95464i	0.776950	+	0.448572i
$123$	6.65179	−	3.84041i	0.599771	−	0.346278i
$124$			8.76348i			0.786984i
$125$			9.34846i			0.836152i
$126$	−2.46395	−	0.963812i	−0.219506	−	0.0858632i
$127$	10.2765	+	17.7995i	0.911895	+	1.57945i	0.811385	+	0.584513i	$0.198714\pi$
$127$	10.2765	+	17.7995i	0.911895	+	1.57945i	0.100511	+	0.994936i	$0.467952\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	0.696225	−	1.20590i	0.0612992	−	0.106173i
$130$	3.23128	−	1.97894i	0.283402	−	0.173564i
$131$	5.07036	+	8.78212i	0.442999	+	0.767297i	0.997910	−	0.0646123i	$-0.0205811\pi$
$131$	5.07036	+	8.78212i	0.442999	+	0.767297i	−0.554911	+	0.831910i	$0.687248\pi$
$132$	5.68175	−	3.28036i	0.494533	−	0.285519i
$133$	−1.18958	−	7.83218i	−0.103150	−	0.679136i
$134$	4.49196	−	7.78031i	0.388046	−	0.672116i
$135$	0.910115	−	0.525455i	0.0783302	−	0.0452240i
$136$	4.00351	−	2.31143i	0.343298	−	0.198203i
$137$	−11.3641	+	6.56106i	−0.970900	+	0.560549i	−0.899511	−	0.436899i	$-0.856077\pi$
$137$	−11.3641	+	6.56106i	−0.970900	+	0.560549i	−0.0713896	+	0.997449i	$0.522743\pi$
$138$	−2.76844	+	1.59836i	−0.235665	+	0.136061i
$139$	−4.82355	+	8.35464i	−0.409129	+	0.708631i	−0.994792	−	0.101923i	$-0.967501\pi$
$139$	−4.82355	+	8.35464i	−0.409129	+	0.708631i	0.585664	+	0.810554i	$0.300834\pi$
$140$	2.58939	+	1.01288i	0.218844	+	0.0856040i
$141$	−9.01677	+	5.20584i	−0.759349	+	0.438411i
$142$	−4.11724	−	7.13127i	−0.345511	−	0.598443i
$143$	12.3543	+	20.1725i	1.03312	+	1.68691i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.04560	−	1.18103i	−0.169878	−	0.0980789i
$146$	−4.72447	−	8.18302i	−0.391000	−	0.677232i
$147$	6.68432	−	2.07843i	0.551313	−	0.171426i
$148$		−	4.64355i		−	0.381698i
$149$			18.5203i			1.51724i	0.651532	+	0.758621i	$0.274126\pi$
$149$			18.5203i			1.51724i	−0.651532	+	0.758621i	$0.725874\pi$
$150$	3.37368	−	1.94779i	0.275460	−	0.159037i
$151$	−5.07128	−	2.92791i	−0.412695	−	0.238270i	0.279252	−	0.960218i	$-0.409914\pi$
$151$	−5.07128	−	2.92791i	−0.412695	−	0.238270i	−0.691947	+	0.721948i	$0.743247\pi$
$152$	−2.99423			−0.242865
$153$	2.31143	+	4.00351i	0.186868	+	0.323665i
$154$	−6.32330	+	16.1653i	−0.509546	+	1.30264i
$155$	9.20963			0.739736
$156$	−3.16816	−	1.72127i	−0.253656	−	0.137812i
$157$	−7.92320	+	13.7234i	−0.632341	+	1.09525i	0.354731	+	0.934968i	$0.384572\pi$
$157$	−7.92320	+	13.7234i	−0.632341	+	1.09525i	−0.987072	+	0.160278i	$0.948761\pi$
$158$		−	3.30223i		−	0.262711i
$159$	3.40268	−	5.89362i	0.269850	−	0.467394i
$160$	0.525455	−	0.910115i	0.0415409	−	0.0719509i
$161$	3.08103	−	7.87656i	0.242819	−	0.620760i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$			6.15647i			0.482212i	0.970499	+	0.241106i	$0.0775102\pi$
$163$			6.15647i			0.482212i	−0.970499	+	0.241106i	$0.922490\pi$
$164$	6.65179	+	3.84041i	0.519417	+	0.299886i
$165$	−3.44736	−	5.97101i	−0.268377	−	0.464842i
$166$	−4.89676	+	8.48143i	−0.380062	+	0.658287i
$167$	−6.82652	+	3.94129i	−0.528252	+	0.304986i	−0.740304	−	0.672272i	$-0.765319\pi$
$167$	−6.82652	+	3.94129i	−0.528252	+	0.304986i	0.212052	+	0.977258i	$0.431985\pi$
$168$	−0.397291	−	2.61575i	−0.0306517	−	0.201810i
$169$	5.90810	−	11.5799i	0.454470	−	0.890762i
$170$	−2.42910	−	4.20733i	−0.186304	−	0.322687i
$171$		−	2.99423i		−	0.228975i
$172$	1.39245			0.106173
$173$	−0.726363			−0.0552244			−0.0276122	−	0.999619i	$-0.508790\pi$
$173$	−0.726363			−0.0552244			−0.0276122	+	0.999619i	$0.508790\pi$
$174$			2.24763i			0.170392i
$175$	−3.75461	+	9.59855i	−0.283822	+	0.725582i
$176$	5.68175	+	3.28036i	0.428278	+	0.247266i
$177$	−2.16500	+	1.24996i	−0.162731	+	0.0939528i
$178$	2.17545	+	3.76799i	0.163057	+	0.282423i
$179$	−17.1109			−1.27893			−0.639464	−	0.768821i	$-0.720844\pi$
$179$	−17.1109			−1.27893			−0.639464	+	0.768821i	$0.720844\pi$
$180$	0.910115	+	0.525455i	0.0678360	+	0.0391651i
$181$	15.7454			1.17035			0.585173	−	0.810908i	$-0.301027\pi$
$181$	15.7454			1.17035			0.585173	+	0.810908i	$0.301027\pi$
$182$	9.39095	−	1.67632i	0.696104	−	0.124257i
$183$	−9.90929			−0.732516
$184$	−2.76844	−	1.59836i	−0.204092	−	0.117832i
$185$	−4.87996			−0.358782
$186$	−4.38174	−	7.58940i	−0.321285	−	0.556482i
$187$	26.2659	−	15.1646i	1.92075	−	1.10895i
$188$	−9.01677	−	5.20584i	−0.657616	−	0.379675i
$189$	2.61575	−	0.397291i	0.190268	−	0.0288987i
$190$			3.14667i			0.228284i
$191$	−19.2661			−1.39405			−0.697024	−	0.717047i	$-0.745493\pi$
$191$	−19.2661			−1.39405			−0.697024	+	0.717047i	$0.745493\pi$
$192$	−1.00000			−0.0721688
$193$		−	16.0550i		−	1.15567i	−0.816154	−	0.577834i	$-0.803898\pi$
$193$		−	16.0550i		−	1.15567i	0.816154	−	0.577834i	$-0.196102\pi$
$194$	−3.36652	−	5.83099i	−0.241702	−	0.418641i
$195$	−1.80890	+	3.32945i	−0.129538	+	0.238427i
$196$	5.14213	+	4.74957i	0.367295	+	0.339255i
$197$	−12.4157	+	7.16821i	−0.884582	+	0.510714i	−0.872166	−	0.489209i	$-0.837285\pi$
$197$	−12.4157	+	7.16821i	−0.884582	+	0.510714i	−0.0124154	+	0.999923i	$0.503952\pi$
$198$	−3.28036	+	5.68175i	−0.233125	+	0.403784i
$199$	−7.95650	−	13.7811i	−0.564022	−	0.976914i	−0.997140	−	0.0755770i	$-0.975920\pi$
$199$	−7.95650	−	13.7811i	−0.564022	−	0.976914i	0.433118	−	0.901337i	$-0.357413\pi$
$200$	3.37368	+	1.94779i	0.238555	+	0.137730i
$201$			8.98392i			0.633677i
$202$	6.19251	+	3.57525i	0.435704	+	0.251554i
$203$	−3.71294	−	4.64508i	−0.260598	−	0.326021i
$204$	−2.31143	+	4.00351i	−0.161832	+	0.280302i
$205$	4.03593	−	6.99043i	0.281881	−	0.488233i
$206$		−	0.685170i		−	0.0477381i
$207$	1.59836	−	2.76844i	0.111094	−	0.192420i
$208$	−0.0934133	−	3.60434i	−0.00647705	−	0.249916i
$209$	−19.6443			−1.35883
$210$	−2.74892	+	0.417517i	−0.189694	+	0.0288114i
$211$	−10.0909	−	17.4780i	−0.694688	−	1.20323i	−0.970286	−	0.241961i	$-0.922209\pi$
$211$	−10.0909	−	17.4780i	−0.694688	−	1.20323i	0.275598	−	0.961273i	$-0.411124\pi$
$212$	6.80536			0.467394
$213$	7.13127	+	4.11724i	0.488627	+	0.282109i
$214$	4.27597	−	2.46873i	0.292299	−	0.168759i
$215$		−	1.46334i		−	0.0997989i
$216$		−	1.00000i		−	0.0680414i
$217$	21.5928	+	8.44635i	1.46582	+	0.573375i
$218$	3.56865	+	6.18109i	0.241700	+	0.418636i
$219$	8.18302	+	4.72447i	0.552957	+	0.319250i
$220$	3.44736	−	5.97101i	0.232421	−	0.402565i
$221$	−14.6459	−	7.95719i	−0.985192	−	0.535259i
$222$	2.32178	+	4.02143i	0.155827	+	0.269901i
$223$	17.2784	−	9.97570i	1.15705	−	0.668022i	0.206453	−	0.978456i	$-0.433808\pi$
$223$	17.2784	−	9.97570i	1.15705	−	0.668022i	0.950595	+	0.310434i	$0.100475\pi$
$224$	2.06666	−	1.65194i	0.138085	−	0.110375i
$225$	−1.94779	+	3.37368i	−0.129853	+	0.224912i
$226$	7.62173	−	4.40041i	0.506990	−	0.292711i
$227$	20.2480	−	11.6902i	1.34391	−	0.775906i	0.356529	−	0.934284i	$-0.383960\pi$
$227$	20.2480	−	11.6902i	1.34391	−	0.775906i	0.987378	+	0.158378i	$0.0506266\pi$
$228$	2.59308	−	1.49712i	0.171731	−	0.0991490i
$229$	4.68467	−	2.70470i	0.309572	−	0.178731i	−0.337163	−	0.941446i	$-0.609467\pi$
$229$	4.68467	−	2.70470i	0.309572	−	0.178731i	0.646735	+	0.762715i	$0.276134\pi$
$230$	−1.67973	+	2.90938i	−0.110758	+	0.191839i
$231$	−2.60652	−	17.1612i	−0.171496	−	1.12913i
$232$	−1.94650	+	1.12381i	−0.127794	+	0.0737819i
$233$	−10.7071	−	18.5453i	−0.701448	−	1.21494i	−0.967958	−	0.251111i	$-0.919204\pi$
$233$	−10.7071	−	18.5453i	−0.701448	−	1.21494i	0.266510	−	0.963832i	$-0.414129\pi$
$234$	3.60434	−	0.0934133i	0.235623	−	0.00610662i
$235$	−5.47087	+	9.47582i	−0.356880	+	0.618134i
$236$	−2.16500	−	1.24996i	−0.140929	−	0.0813655i
$237$	1.65111	+	2.85981i	0.107251	+	0.185765i
$238$	−1.83662	−	12.0922i	−0.119050	−	0.783824i
$239$			8.80379i			0.569470i	0.958606	+	0.284735i	$0.0919056\pi$
$239$			8.80379i			0.569470i	−0.958606	+	0.284735i	$0.908094\pi$
$240$			1.05091i			0.0678360i
$241$	11.6408	−	6.72082i	0.749850	−	0.432926i	−0.0757899	−	0.997124i	$-0.524148\pi$
$241$	11.6408	−	6.72082i	0.749850	−	0.432926i	0.825640	+	0.564198i	$0.190814\pi$
$242$	27.7501	+	16.0215i	1.78384	+	1.02990i
$243$	1.00000			0.0641500
$244$	−4.95464	−	8.58169i	−0.317189	−	0.549387i
$245$	4.99138	−	5.40392i	0.318887	−	0.345244i
$246$	−7.68082			−0.489711
$247$	5.63835	+	9.20651i	0.358760	+	0.585796i
$248$	4.38174	−	7.58940i	0.278241	−	0.481927i
$249$		−	9.79351i		−	0.620638i
$250$	4.67423	−	8.09601i	0.295624	−	0.512036i
$251$	−2.16506	+	3.75000i	−0.136658	+	0.236698i	−0.926229	−	0.376960i	$-0.876969\pi$
$251$	−2.16506	+	3.75000i	−0.136658	+	0.236698i	0.789572	+	0.613658i	$0.210303\pi$
$252$	1.65194	+	2.06666i	0.104062	+	0.130187i
$253$	−18.1629	−	10.4864i	−1.14189	−	0.659273i
$254$		−	20.5531i		−	1.28961i
$255$	4.20733	+	2.42910i	0.263473	+	0.152116i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.27315	+	2.20516i	−0.0794169	+	0.137554i	−0.902999	−	0.429644i	$-0.858639\pi$
$257$	−1.27315	+	2.20516i	−0.0794169	+	0.137554i	0.823582	+	0.567198i	$0.191973\pi$
$258$	−1.20590	+	0.696225i	−0.0750759	+	0.0433451i
$259$	−11.4415	−	4.47551i	−0.710940	−	0.278095i
$260$	−3.78784	+	0.0981690i	−0.234912	+	0.00608818i
$261$	−1.12381	−	1.94650i	−0.0695623	−	0.120485i
$262$		−	10.1407i		−	0.626496i
$263$	7.00731			0.432090			0.216045	−	0.976383i	$-0.430684\pi$
$263$	7.00731			0.432090			0.216045	+	0.976383i	$0.430684\pi$
$264$	−6.56072			−0.403784
$265$		−	7.15183i		−	0.439333i
$266$	−2.88588	+	7.37766i	−0.176945	+	0.452353i
$267$	−3.76799	−	2.17545i	−0.230597	−	0.133136i
$268$	−7.78031	+	4.49196i	−0.475258	+	0.274390i
$269$	0.701117	+	1.21437i	0.0427479	+	0.0740415i	0.886608	−	0.462522i	$-0.153055\pi$
$269$	0.701117	+	1.21437i	0.0427479	+	0.0740415i	−0.843860	+	0.536564i	$0.819722\pi$
$270$	−1.05091			−0.0639564
$271$	0.455960	+	0.263249i	0.0276976	+	0.0159912i	0.513785	−	0.857919i	$-0.328243\pi$
$271$	0.455960	+	0.263249i	0.0276976	+	0.0159912i	−0.486087	+	0.873910i	$0.661576\pi$
$272$	−4.62286			−0.280302
$273$	−7.29464	+	6.14721i	−0.441492	+	0.372046i
$274$	13.1221			0.792737
$275$	22.1338	+	12.7789i	1.33472	+	0.770598i
$276$	3.19672			0.192420
$277$	16.3572	+	28.3315i	0.982810	+	1.70228i	0.651292	+	0.758827i	$0.274227\pi$
$277$	16.3572	+	28.3315i	0.982810	+	1.70228i	0.331518	+	0.943449i	$0.392439\pi$
$278$	8.35464	−	4.82355i	0.501078	−	0.289298i
$279$	7.58940	+	4.38174i	0.454365	+	0.262328i
$280$	−1.73604	−	2.17188i	−0.103748	−	0.129794i
$281$		−	22.6836i		−	1.35319i	−0.736356	−	0.676594i	$-0.763455\pi$
$281$		−	22.6836i		−	1.35319i	0.736356	−	0.676594i	$-0.236545\pi$
$282$	10.4117			0.620006
$283$	5.48461			0.326026			0.163013	−	0.986624i	$-0.447879\pi$
$283$	5.48461			0.326026			0.163013	+	0.986624i	$0.447879\pi$
$284$			8.23449i			0.488627i
$285$	−1.57334	−	2.72510i	−0.0931964	−	0.161421i
$286$	−0.612859	−	23.6471i	−0.0362391	−	1.39828i
$287$	15.8737	−	12.6883i	0.936993	−	0.748964i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−2.18539	+	3.78521i	−0.128553	+	0.222660i
$290$	1.18103	+	2.04560i	0.0693523	+	0.120122i
$291$	5.83099	+	3.36652i	0.341819	+	0.197349i
$292$			9.44894i			0.552957i
$293$	−11.5606	−	6.67449i	−0.675375	−	0.389928i	0.122735	−	0.992439i	$-0.460833\pi$
$293$	−11.5606	−	6.67449i	−0.675375	−	0.389928i	−0.798110	+	0.602512i	$0.794167\pi$
$294$	−6.82801	−	1.54219i	−0.398217	−	0.0899421i
$295$	−1.31360	+	2.27522i	−0.0764805	+	0.132468i
$296$	−2.32178	+	4.02143i	−0.134951	+	0.233741i
$297$		−	6.56072i		−	0.380692i
$298$	9.26015	−	16.0390i	0.536426	−	0.929117i
$299$	0.298616	+	11.5221i	0.0172694	+	0.666337i
$300$	−3.89559			−0.224912
$301$	1.34206	−	3.43093i	0.0773550	−	0.197756i
$302$	2.92791	+	5.07128i	0.168482	+	0.291820i
$303$	−7.15050			−0.410785
$304$	2.59308	+	1.49712i	0.148724	+	0.0858656i
$305$	−9.01859	+	5.20689i	−0.516403	+	0.298145i
$306$		−	4.62286i		−	0.264271i
$307$		−	16.4170i		−	0.936969i	−0.883472	−	0.468485i	$-0.844800\pi$
$307$		−	16.4170i		−	0.936969i	0.883472	−	0.468485i	$-0.155200\pi$
$308$	13.5588	−	10.8379i	0.772584	−	0.617548i
$309$	0.342585	+	0.593375i	0.0194890	+	0.0337559i
$310$	−7.97578	−	4.60482i	−0.452994	−	0.261536i
$311$	−12.4093	+	21.4936i	−0.703669	+	1.21879i	0.263501	+	0.964659i	$0.415123\pi$
$311$	−12.4093	+	21.4936i	−0.703669	+	1.21879i	−0.967170	+	0.254131i	$0.918211\pi$
$312$	1.88307	+	3.07474i	0.106608	+	0.174073i
$313$	−11.2551	−	19.4943i	−0.636174	−	1.10189i	−0.986265	−	0.165170i	$-0.947183\pi$
$313$	−11.2551	−	19.4943i	−0.636174	−	1.10189i	0.350091	−	0.936716i	$-0.386151\pi$
$314$	13.7234	−	7.92320i	0.774456	−	0.447132i
$315$	2.17188	−	1.73604i	0.122371	−	0.0978148i
$316$	−1.65111	+	2.85981i	−0.0928824	+	0.160877i
$317$	−16.0776	+	9.28239i	−0.903006	+	0.521351i	−0.878174	−	0.478341i	$-0.841238\pi$
$317$	−16.0776	+	9.28239i	−0.903006	+	0.521351i	−0.0248317	+	0.999692i	$0.507905\pi$
$318$	−5.89362	+	3.40268i	−0.330498	+	0.190813i
$319$	−12.7704	+	7.37302i	−0.715008	+	0.412810i
$320$	−0.910115	+	0.525455i	−0.0508770	+	0.0293738i
$321$	−2.46873	+	4.27597i	−0.137791	+	0.238662i
$322$	−6.60653	+	5.28078i	−0.368168	+	0.294287i
$323$	11.9874	−	6.92096i	0.667000	−	0.385092i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−0.363900	−	14.0410i	−0.0201855	−	0.778856i
$326$	3.07824	−	5.33166i	0.170488	−	0.295293i
$327$	−6.18109	−	3.56865i	−0.341815	−	0.197347i
$328$	−3.84041	−	6.65179i	−0.212051	−	0.367283i
$329$	−21.5174	+	17.1995i	−1.18629	+	0.948237i
$330$			6.89473i			0.379542i
$331$			8.40902i			0.462202i	0.972930	+	0.231101i	$0.0742327\pi$
$331$			8.40902i			0.462202i	−0.972930	+	0.231101i	$0.925767\pi$
$332$	8.48143	−	4.89676i	0.465479	−	0.268744i
$333$	−4.02143	−	2.32178i	−0.220373	−	0.127233i
$334$	7.88258			0.431316
$335$	4.72065	+	8.17640i	0.257917	+	0.446725i
$336$	−0.963812	+	2.46395i	−0.0525802	+	0.134420i
$337$	4.80038			0.261493			0.130747	−	0.991416i	$-0.458263\pi$
$337$	4.80038			0.261493			0.130747	+	0.991416i	$0.458263\pi$
$338$	−10.9065	+	7.07444i	−0.593237	+	0.384799i
$339$	−4.40041	+	7.62173i	−0.238997	+	0.413955i
$340$			4.85821i			0.263473i
$341$	28.7474	−	49.7919i	1.55676	−	2.69638i
$342$	−1.49712	+	2.59308i	−0.0809548	+	0.140218i
$343$	16.6588	−	8.09228i	0.899490	−	0.436942i
$344$	−1.20590	−	0.696225i	−0.0650176	−	0.0375379i
$345$		−	3.35946i		−	0.180867i
$346$	0.629049	+	0.363182i	0.0338179	+	0.0195248i
$347$	−1.67396	−	2.89939i	−0.0898630	−	0.155647i	0.817590	−	0.575801i	$-0.195310\pi$
$347$	−1.67396	−	2.89939i	−0.0898630	−	0.155647i	−0.907453	+	0.420153i	$0.861976\pi$
$348$	1.12381	−	1.94650i	0.0602427	−	0.104343i
$349$	12.3261	−	7.11650i	0.659803	−	0.380938i	−0.132399	−	0.991197i	$-0.542268\pi$
$349$	12.3261	−	7.11650i	0.659803	−	0.380938i	0.792202	+	0.610259i	$0.208935\pi$
$350$	8.05086	−	6.43528i	0.430337	−	0.343980i
$351$	−3.07474	+	1.88307i	−0.164118	+	0.100511i
$352$	−3.28036	−	5.68175i	−0.174844	−	0.302838i
$353$			29.2083i			1.55460i	0.629130	+	0.777300i	$0.283411\pi$
$353$			29.2083i			1.55460i	−0.629130	+	0.777300i	$0.716589\pi$
$354$	2.49992			0.132869
$355$	8.65371			0.459291
$356$		−	4.35090i		−	0.230597i
$357$	7.63668	+	9.55388i	0.404176	+	0.505645i
$358$	14.8185	+	8.55545i	0.783180	+	0.452169i
$359$	22.2918	−	12.8702i	1.17652	−	0.679262i	0.221310	−	0.975204i	$-0.428967\pi$
$359$	22.2918	−	12.8702i	1.17652	−	0.679262i	0.955206	+	0.295942i	$0.0956334\pi$
$360$	−0.525455	−	0.910115i	−0.0276939	−	0.0479673i
$361$	10.0346			0.528135
$362$	−13.6359	−	7.87270i	−0.716688	−	0.413780i
$363$	−32.0430			−1.68182
$364$	−8.97096	−	3.24374i	−0.470206	−	0.170018i
$365$	9.92999			0.519759
$366$	8.58169	+	4.95464i	0.448572	+	0.258983i
$367$	19.5416			1.02006			0.510030	−	0.860156i	$-0.329634\pi$
$367$	19.5416			1.02006			0.510030	+	0.860156i	$0.329634\pi$
$368$	1.59836	+	2.76844i	0.0833202	+	0.144315i
$369$	6.65179	−	3.84041i	0.346278	−	0.199924i
$370$	4.22617	+	2.43998i	0.219708	+	0.126848i
$371$	6.55909	−	16.7681i	0.340531	−	0.870556i
$372$			8.76348i			0.454365i
$373$	−19.0435			−0.986034			−0.493017	−	0.870020i	$-0.664106\pi$
$373$	−19.0435			−0.986034			−0.493017	+	0.870020i	$0.664106\pi$
$374$	−30.3293			−1.56829
$375$			9.34846i			0.482753i
$376$	5.20584	+	9.01677i	0.268471	+	0.465005i
$377$	7.12083	+	3.86878i	0.366742	+	0.199252i
$378$	−2.46395	−	0.963812i	−0.126732	−	0.0495731i
$379$	−23.8073	+	13.7451i	−1.22290	+	0.706040i	−0.965535	−	0.260274i	$-0.916187\pi$
$379$	−23.8073	+	13.7451i	−1.22290	+	0.706040i	−0.257363	+	0.966315i	$0.582854\pi$
$380$	1.57334	−	2.72510i	0.0807104	−	0.139795i
$381$	10.2765	+	17.7995i	0.526483	+	0.911895i
$382$	16.6850	+	9.63307i	0.853677	+	0.492871i
$383$			10.1657i			0.519444i	0.965683	+	0.259722i	$0.0836309\pi$
$383$			10.1657i			0.519444i	−0.965683	+	0.259722i	$0.916369\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$	−11.3897	−	14.2491i	−0.580472	−	0.726200i
$386$	−8.02752	+	13.9041i	−0.408590	+	0.707699i
$387$	0.696225	−	1.20590i	0.0353911	−	0.0612992i
$388$			6.73305i			0.341819i
$389$	11.6154	−	20.1184i	0.588922	−	1.02004i	−0.405452	−	0.914116i	$-0.632886\pi$
$389$	11.6154	−	20.1184i	0.588922	−	1.02004i	0.994374	−	0.105926i	$-0.0337808\pi$
$390$	3.23128	−	1.97894i	0.163622	−	0.100207i
$391$	14.7780			0.747353
$392$	−2.07843	−	6.68432i	−0.104977	−	0.337609i
$393$	5.07036	+	8.78212i	0.255766	+	0.442999i
$394$	14.3364			0.722258
$395$	3.00541	+	1.73517i	0.151218	+	0.0873060i
$396$	5.68175	−	3.28036i	0.285519	−	0.164844i
$397$			34.1545i			1.71417i	0.515178	+	0.857083i	$0.327726\pi$
$397$			34.1545i			1.71417i	−0.515178	+	0.857083i	$0.672274\pi$
$398$			15.9130i			0.797647i
$399$	−1.18958	−	7.83218i	−0.0595537	−	0.392099i
$400$	−1.94779	−	3.37368i	−0.0973897	−	0.168684i
$401$	−27.2130	−	15.7114i	−1.35895	−	0.784590i	−0.369468	−	0.929244i	$-0.620460\pi$
$401$	−27.2130	−	15.7114i	−1.35895	−	0.784590i	−0.989482	+	0.144653i	$0.953793\pi$
$402$	4.49196	−	7.78031i	0.224039	−	0.388046i
$403$	−31.5866	+	0.818626i	−1.57344	+	0.0407787i
$404$	−3.57525	−	6.19251i	−0.177875	−	0.308089i
$405$	0.910115	−	0.525455i	0.0452240	−	0.0261101i
$406$	0.892962	+	5.87923i	0.0443170	+	0.291781i
$407$	−15.2325	+	26.3835i	−0.755048	+	1.30778i
$408$	4.00351	−	2.31143i	0.198203	−	0.114433i
$409$	−1.59937	+	0.923399i	−0.0790839	+	0.0456591i	−0.539021	−	0.842293i	$-0.681205\pi$
$409$	−1.59937	+	0.923399i	−0.0790839	+	0.0456591i	0.459937	+	0.887952i	$0.347872\pi$
$410$	−6.99043	+	4.03593i	−0.345233	+	0.199320i
$411$	−11.3641	+	6.56106i	−0.560549	+	0.323633i
$412$	−0.342585	+	0.593375i	−0.0168780	+	0.0292335i
$413$	−5.16649	+	4.12972i	−0.254226	+	0.203210i
$414$	−2.76844	+	1.59836i	−0.136061	+	0.0785550i
$415$	−5.14605	−	8.91322i	−0.252610	−	0.437533i
$416$	−1.72127	+	3.16816i	−0.0843923	+	0.155332i
$417$	−4.82355	+	8.35464i	−0.236210	+	0.409129i
$418$	17.0125	+	9.82217i	0.832108	+	0.480418i
$419$	14.5391	+	25.1824i	0.710281	+	1.23024i	0.964752	+	0.263162i	$0.0847655\pi$
$419$	14.5391	+	25.1824i	0.710281	+	1.23024i	−0.254470	+	0.967081i	$0.581901\pi$
$420$	2.58939	+	1.01288i	0.126349	+	0.0494235i
$421$		−	10.0596i		−	0.490275i	−0.969488	−	0.245138i	$-0.921167\pi$
$421$		−	10.0596i		−	0.490275i	0.969488	−	0.245138i	$-0.0788331\pi$
$422$			20.1818i			0.982437i
$423$	−9.01677	+	5.20584i	−0.438411	+	0.253116i
$424$	−5.89362	−	3.40268i	−0.286219	−	0.165249i
$425$	−18.0087			−0.873552
$426$	−4.11724	−	7.13127i	−0.199481	−	0.345511i
$427$	−25.9202	+	3.93687i	−1.25437	+	0.190519i
$428$	−4.93747			−0.238662
$429$	12.3543	+	20.1725i	0.596471	+	0.973939i
$430$	−0.731670	+	1.26729i	−0.0352843	+	0.0611141i
$431$		−	15.6490i		−	0.753784i	−0.926257	−	0.376892i	$-0.876993\pi$
$431$		−	15.6490i		−	0.753784i	0.926257	−	0.376892i	$-0.123007\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	14.9276	−	25.8553i	0.717373	−	1.24253i	−0.244664	−	0.969608i	$-0.578678\pi$
$433$	14.9276	−	25.8553i	0.717373	−	1.24253i	0.962037	−	0.272919i	$-0.0879892\pi$
$434$	−14.4768	−	18.1112i	−0.694906	−	0.869363i
$435$	−2.04560	−	1.18103i	−0.0980789	−	0.0566259i
$436$		−	7.13731i		−	0.341815i
$437$	−8.28935	−	4.78586i	−0.396533	−	0.228939i
$438$	−4.72447	−	8.18302i	−0.225744	−	0.391000i
$439$	−6.18523	+	10.7131i	−0.295205	+	0.511310i	−0.975033	−	0.222062i	$-0.928721\pi$
$439$	−6.18523	+	10.7131i	−0.295205	+	0.511310i	0.679827	+	0.733372i	$0.262055\pi$
$440$	−5.97101	+	3.44736i	−0.284657	+	0.164347i
$441$	6.68432	−	2.07843i	0.318301	−	0.0989729i
$442$	8.70515	+	14.2141i	0.414062	+	0.676096i
$443$	16.2819	+	28.2010i	0.773574	+	1.33987i	0.935592	+	0.353082i	$0.114866\pi$
$443$	16.2819	+	28.2010i	0.773574	+	1.33987i	−0.162018	+	0.986788i	$0.551800\pi$
$444$		−	4.64355i		−	0.220373i
$445$	−4.57241			−0.216753
$446$	−19.9514			−0.944726
$447$			18.5203i			0.875980i
$448$	−2.61575	+	0.397291i	−0.123583	+	0.0187702i
$449$	−8.92105	−	5.15057i	−0.421010	−	0.243070i	0.274499	−	0.961587i	$-0.411488\pi$
$449$	−8.92105	−	5.15057i	−0.421010	−	0.243070i	−0.695509	+	0.718517i	$0.744821\pi$
$450$	3.37368	−	1.94779i	0.159037	−	0.0918199i
$451$	−25.1959	−	43.6405i	−1.18643	−	2.05495i
$452$	−8.80081			−0.413955
$453$	−5.07128	−	2.92791i	−0.238270	−	0.137565i
$454$	−23.3804			−1.09730
$455$	−3.40888	+	9.42768i	−0.159811	+	0.441976i
$456$	−2.99423			−0.140218
$457$	−15.6594	−	9.04098i	−0.732517	−	0.422919i	0.0868250	−	0.996224i	$-0.472328\pi$
$457$	−15.6594	−	9.04098i	−0.732517	−	0.422919i	−0.819342	+	0.573304i	$0.805661\pi$
$458$	−5.40940			−0.252764
$459$	2.31143	+	4.00351i	0.107888	+	0.186868i
$460$	2.90938	−	1.67973i	0.135650	−	0.0783178i
$461$	−3.44357	−	1.98814i	−0.160383	−	0.0925971i	0.417660	−	0.908603i	$-0.362850\pi$
$461$	−3.44357	−	1.98814i	−0.160383	−	0.0925971i	−0.578043	+	0.816006i	$0.696184\pi$
$462$	−6.32330	+	16.1653i	−0.294187	+	0.752078i
$463$			9.46729i			0.439982i	0.975502	+	0.219991i	$0.0706029\pi$
$463$			9.46729i			0.439982i	−0.975502	+	0.219991i	$0.929397\pi$
$464$	2.24763			0.104343
$465$	9.20963			0.427087
$466$			21.4143i			0.991997i
$467$	5.16932	+	8.95352i	0.239208	+	0.414320i	0.960487	−	0.278324i	$-0.0897790\pi$
$467$	5.16932	+	8.95352i	0.239208	+	0.414320i	−0.721280	+	0.692644i	$0.756446\pi$
$468$	−3.16816	−	1.72127i	−0.146448	−	0.0795658i
$469$	3.56923	+	23.4997i	0.164812	+	1.08512i
$470$	9.47582	−	5.47087i	0.437087	−	0.252352i
$471$	−7.92320	+	13.7234i	−0.365082	+	0.632341i
$472$	1.24996	+	2.16500i	0.0575341	+	0.0996520i
$473$	−7.91155	−	4.56774i	−0.363774	−	0.210025i
$474$		−	3.30223i		−	0.151676i
$475$	10.1016	+	5.83215i	0.463492	+	0.267597i
$476$	−4.45556	+	11.3905i	−0.204220	+	0.522083i
$477$	3.40268	−	5.89362i	0.155798	−	0.269850i
$478$	4.40190	−	7.62431i	0.201338	−	0.348728i
$479$		−	27.8712i		−	1.27347i	−0.771083	−	0.636735i	$-0.780285\pi$
$479$		−	27.8712i		−	1.27347i	0.771083	−	0.636735i	$-0.219715\pi$
$480$	0.525455	−	0.910115i	0.0239836	−	0.0415409i
$481$	16.7369	−	0.433770i	0.763139	−	0.0197782i
$482$	−13.4416			−0.612250
$483$	3.08103	−	7.87656i	0.140192	−	0.358396i
$484$	−16.0215	−	27.7501i	−0.728251	−	1.26137i
$485$	7.07583			0.321297
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	12.4031	−	7.16092i	0.562037	−	0.324492i	−0.191926	−	0.981409i	$-0.561473\pi$
$487$	12.4031	−	7.16092i	0.562037	−	0.324492i	0.753963	+	0.656917i	$0.228140\pi$
$488$			9.90929i			0.448572i
$489$			6.15647i			0.278405i
$490$	−7.02462	+	2.18424i	−0.317340	+	0.0986741i
$491$	3.52525	+	6.10592i	0.159093	+	0.275556i	0.934542	−	0.355854i	$-0.115810\pi$
$491$	3.52525	+	6.10592i	0.159093	+	0.275556i	−0.775449	+	0.631410i	$0.782477\pi$
$492$	6.65179	+	3.84041i	0.299886	+	0.173139i
$493$	5.19522	−	8.99839i	0.233981	−	0.405267i
$494$	−0.279701	−	10.7922i	−0.0125844	−	0.485566i
$495$	−3.44736	−	5.97101i	−0.154947	−	0.268377i
$496$	−7.58940	+	4.38174i	−0.340774	+	0.196746i
$497$	20.2894	+	7.93649i	0.910103	+	0.356000i
$498$	−4.89676	+	8.48143i	−0.219429	+	0.380062i
$499$	32.3050	−	18.6513i	1.44617	−	0.834947i	0.447920	−	0.894074i	$-0.352165\pi$
$499$	32.3050	−	18.6513i	1.44617	−	0.834947i	0.998250	+	0.0591270i	$0.0188317\pi$
$500$	−8.09601	+	4.67423i	−0.362064	+	0.209038i
$501$	−6.82652	+	3.94129i	−0.304986	+	0.176084i
$502$	3.75000	−	2.16506i	0.167371	−	0.0966316i
$503$	−1.61562	+	2.79834i	−0.0720370	+	0.124772i	−0.899794	−	0.436315i	$-0.856283\pi$
$503$	−1.61562	+	2.79834i	−0.0720370	+	0.124772i	0.827757	+	0.561087i	$0.189617\pi$
$504$	−0.397291	−	2.61575i	−0.0176968	−	0.116515i
$505$	−6.50777	+	3.75726i	−0.289592	+	0.167196i
$506$	10.4864	+	18.1629i	0.466176	+	0.807441i
$507$	5.90810	−	11.5799i	0.262388	−	0.514282i
$508$	−10.2765	+	17.7995i	−0.455948	+	0.789724i
$509$	33.6874	+	19.4494i	1.49317	+	0.862080i	0.999969	−	0.00783837i	$-0.00249505\pi$
$509$	33.6874	+	19.4494i	1.49317	+	0.862080i	0.493196	+	0.869918i	$0.335828\pi$
$510$	−2.42910	−	4.20733i	−0.107562	−	0.186304i
$511$	23.2818	+	9.10700i	1.02992	+	0.402870i
$512$			1.00000i			0.0441942i
$513$		−	2.99423i		−	0.132199i
$514$	2.20516	−	1.27315i	0.0972655	−	0.0561562i
$515$	0.623584	+	0.360026i	0.0274784	+	0.0158647i
$516$	1.39245			0.0612992
$517$	34.1540	+	59.1565i	1.50209	+	2.60170i
$518$	7.67087	+	9.59666i	0.337039	+	0.421653i
$519$	−0.726363			−0.0318838
$520$	3.32945	+	1.80890i	0.146006	+	0.0793256i
$521$	−1.54776	+	2.68079i	−0.0678085	+	0.117448i	−0.897936	−	0.440125i	$-0.854934\pi$
$521$	−1.54776	+	2.68079i	−0.0678085	+	0.117448i	0.830128	+	0.557573i	$0.188267\pi$
$522$			2.24763i			0.0983759i
$523$	12.0472	−	20.8664i	0.526789	−	0.912425i	−0.472724	−	0.881211i	$-0.656729\pi$
$523$	12.0472	−	20.8664i	0.526789	−	0.912425i	0.999513	−	0.0312143i	$-0.00993744\pi$
$524$	−5.07036	+	8.78212i	−0.221500	+	0.383649i
$525$	−3.75461	+	9.59855i	−0.163865	+	0.418915i
$526$	−6.06851	−	3.50366i	−0.264600	−	0.152767i
$527$			40.5123i			1.76474i
$528$	5.68175	+	3.28036i	0.247266	+	0.142759i
$529$	6.39051	+	11.0687i	0.277848	+	0.481247i
$530$	−3.57591	+	6.19366i	−0.155328	+	0.269036i
$531$	−2.16500	+	1.24996i	−0.0939528	+	0.0542437i
$532$	6.18807	−	4.94630i	0.268287	−	0.214449i
$533$	−13.2208	+	24.3341i	−0.572656	+	1.05402i
$534$	2.17545	+	3.76799i	0.0941410	+	0.163057i
$535$			5.18884i			0.224333i
$536$	8.98392			0.388046
$537$	−17.1109			−0.738389
$538$		−	1.40223i		−	0.0604546i
$539$	−13.6360	−	43.8539i	−0.587344	−	1.88892i
$540$	0.910115	+	0.525455i	0.0391651	+	0.0226120i
$541$	−15.0491	+	8.68860i	−0.647011	+	0.373552i	−0.787310	−	0.616557i	$-0.788527\pi$
$541$	−15.0491	+	8.68860i	−0.647011	+	0.373552i	0.140299	+	0.990109i	$0.455194\pi$
$542$	−0.263249	−	0.455960i	−0.0113075	−	0.0195851i
$543$	15.7454			0.675700
$544$	4.00351	+	2.31143i	0.171649	+	0.0991016i
$545$	−7.50067			−0.321293
$546$	9.39095	−	1.67632i	0.401896	−	0.0717398i
$547$	35.1878			1.50452			0.752262	−	0.658865i	$-0.228963\pi$
$547$	35.1878			1.50452			0.752262	+	0.658865i	$0.228963\pi$
$548$	−11.3641	−	6.56106i	−0.485450	−	0.280275i
$549$	−9.90929			−0.422918
$550$	−12.7789	−	22.1338i	−0.544895	−	0.943787i
$551$	−5.82828	+	3.36496i	−0.248293	+	0.143352i
$552$	−2.76844	−	1.59836i	−0.117832	−	0.0680306i
$553$	5.45508	+	6.82459i	0.231974	+	0.290211i
$554$		−	32.7144i		−	1.38990i
$555$	−4.87996			−0.207143
$556$	−9.64711			−0.409129
$557$		−	28.2088i		−	1.19524i	−0.801778	−	0.597622i	$-0.796112\pi$
$557$		−	28.2088i		−	1.19524i	0.801778	−	0.597622i	$-0.203888\pi$
$558$	−4.38174	−	7.58940i	−0.185494	−	0.321285i
$559$	0.130073	+	5.01886i	0.00550152	+	0.212275i
$560$	0.417517	+	2.74892i	0.0176433	+	0.116163i
$561$	26.2659	−	15.1646i	1.10895	−	0.640251i
$562$	−11.3418	+	19.6445i	−0.478424	+	0.828655i
$563$	−18.8177	−	32.5932i	−0.793072	−	1.37364i	−0.924056	−	0.382257i	$-0.875147\pi$
$563$	−18.8177	−	32.5932i	−0.793072	−	1.37364i	0.130984	−	0.991384i	$-0.458186\pi$
$564$	−9.01677	−	5.20584i	−0.379675	−	0.219205i
$565$			9.24886i			0.389103i
$566$	−4.74981	−	2.74231i	−0.199649	−	0.115268i
$567$	2.61575	−	0.397291i	0.109851	−	0.0166847i
$568$	4.11724	−	7.13127i	0.172756	−	0.299222i
$569$	14.5293	−	25.1655i	0.609100	−	1.05499i	−0.382289	−	0.924043i	$-0.624864\pi$
$569$	14.5293	−	25.1655i	0.609100	−	1.05499i	0.991389	−	0.130950i	$-0.0418026\pi$
$570$			3.14667i			0.131800i
$571$	−2.09456	+	3.62788i	−0.0876546	+	0.151822i	−0.906519	−	0.422164i	$-0.861271\pi$
$571$	−2.09456	+	3.62788i	−0.0876546	+	0.151822i	0.818865	+	0.573987i	$0.194604\pi$
$572$	−11.2928	+	20.7854i	−0.472175	+	0.869081i
$573$	−19.2661			−0.804854
$574$	−20.0911	+	3.05152i	−0.838587	+	0.127368i
$575$	6.22654	+	10.7847i	0.259665	+	0.449753i
$576$	−1.00000			−0.0416667
$577$	−32.9451	−	19.0209i	−1.37152	−	0.791848i	−0.380402	−	0.924821i	$-0.624214\pi$
$577$	−32.9451	−	19.0209i	−1.37152	−	0.791848i	−0.991120	+	0.132973i	$0.957548\pi$
$578$	3.78521	−	2.18539i	0.157444	−	0.0909004i
$579$		−	16.0550i		−	0.667225i
$580$		−	2.36205i		−	0.0980789i
$581$	−3.89088	−	25.6174i	−0.161421	−	1.06279i
$582$	−3.36652	−	5.83099i	−0.139547	−	0.241702i
$583$	−38.6664	−	22.3240i	−1.60140	−	0.924567i
$584$	4.72447	−	8.18302i	0.195500	−	0.338616i
$585$	−1.80890	+	3.32945i	−0.0747889	+	0.137656i
$586$	6.67449	+	11.5606i	0.275721	+	0.477562i
$587$	16.5253	−	9.54089i	0.682073	−	0.393795i	−0.118563	−	0.992947i	$-0.537829\pi$
$587$	16.5253	−	9.54089i	0.682073	−	0.393795i	0.800635	+	0.599152i	$0.204495\pi$
$588$	5.14213	+	4.74957i	0.212058	+	0.195869i
$589$	13.1200	−	22.7244i	0.540599	−	0.936344i
$590$	2.27522	−	1.31360i	0.0936691	−	0.0540799i
$591$	−12.4157	+	7.16821i	−0.510714	+	0.294861i
$592$	4.02143	−	2.32178i	0.165280	−	0.0954244i
$593$	41.9869	−	24.2412i	1.72420	−	0.995466i	0.814538	−	0.580110i	$-0.196990\pi$
$593$	41.9869	−	24.2412i	1.72420	−	0.995466i	0.909659	−	0.415356i	$-0.136343\pi$
$594$	−3.28036	+	5.68175i	−0.134595	+	0.233125i
$595$	11.9704	+	4.68240i	0.490738	+	0.191960i
$596$	−16.0390	+	9.26015i	−0.656985	+	0.379310i
$597$	−7.95650	−	13.7811i	−0.325638	−	0.564022i
$598$	5.50242	−	10.1277i	0.225011	−	0.414152i
$599$	−4.69140	+	8.12575i	−0.191686	+	0.332009i	−0.945809	−	0.324724i	$-0.894729\pi$
$599$	−4.69140	+	8.12575i	−0.191686	+	0.332009i	0.754123	+	0.656733i	$0.228062\pi$
$600$	3.37368	+	1.94779i	0.137730	+	0.0795183i
$601$	1.92984	+	3.34259i	0.0787200	+	0.136347i	0.902698	−	0.430275i	$-0.141583\pi$
$601$	1.92984	+	3.34259i	0.0787200	+	0.136347i	−0.823978	+	0.566622i	$0.808250\pi$
$602$	−2.87772	+	2.30024i	−0.117287	+	0.0937509i
$603$			8.98392i			0.365854i
$604$		−	5.85581i		−	0.238270i
$605$	−29.1629	+	16.8372i	−1.18564	+	0.684529i
$606$	6.19251	+	3.57525i	0.251554	+	0.145235i
$607$	−2.14815			−0.0871907			−0.0435953	−	0.999049i	$-0.513881\pi$
$607$	−2.14815			−0.0871907			−0.0435953	+	0.999049i	$0.513881\pi$
$608$	−1.49712	−	2.59308i	−0.0607161	−	0.105163i
$609$	−3.71294	−	4.64508i	−0.150456	−	0.188228i
$610$	10.4138			0.421641
$611$	17.9213	−	32.9858i	0.725019	−	1.33446i
$612$	−2.31143	+	4.00351i	−0.0934339	+	0.161832i
$613$			41.6192i			1.68099i	0.541823	+	0.840493i	$0.317734\pi$
$613$			41.6192i			1.68099i	−0.541823	+	0.840493i	$0.682266\pi$
$614$	−8.20851	+	14.2176i	−0.331269	+	0.573774i
$615$	4.03593	−	6.99043i	0.162744	−	0.281881i
$616$	−17.1612	+	2.60652i	−0.691445	+	0.105020i
$617$	6.91756	+	3.99385i	0.278490	+	0.160786i	0.632740	−	0.774364i	$-0.281930\pi$
$617$	6.91756	+	3.99385i	0.278490	+	0.160786i	−0.354249	+	0.935151i	$0.615264\pi$
$618$		−	0.685170i		−	0.0275616i
$619$	−20.7319	−	11.9696i	−0.833285	−	0.481098i	0.0216909	−	0.999765i	$-0.493095\pi$
$619$	−20.7319	−	11.9696i	−0.833285	−	0.481098i	−0.854976	+	0.518667i	$0.826428\pi$
$620$	4.60482	+	7.97578i	0.184934	+	0.320315i
$621$	1.59836	−	2.76844i	0.0641399	−	0.111094i
$622$	21.4936	−	12.4093i	0.861815	−	0.497569i
$623$	−10.7204	−	4.19345i	−0.429505	−	0.168007i
$624$	−0.0934133	−	3.60434i	−0.00373952	−	0.144289i
$625$	−4.82677	−	8.36021i	−0.193071	−	0.334408i
$626$			22.5101i			0.899686i
$627$	−19.6443			−0.784519
$628$	−15.8464			−0.632341
$629$		−	21.4665i		−	0.855924i
$630$	−2.74892	+	0.417517i	−0.109520	+	0.0166343i
$631$	−30.4945	−	17.6060i	−1.21397	−	0.700885i	−0.250347	−	0.968156i	$-0.580545\pi$
$631$	−30.4945	−	17.6060i	−1.21397	−	0.700885i	−0.963621	+	0.267271i	$0.913878\pi$
$632$	2.85981	−	1.65111i	0.113757	−	0.0656778i
$633$	−10.0909	−	17.4780i	−0.401078	−	0.694688i
$634$	18.5648			0.737301
$635$	18.7057	+	10.7997i	0.742311	+	0.428574i
$636$	6.80536			0.269850
$637$	−16.6387	+	18.9777i	−0.659251	+	0.751923i
$638$	14.7460			0.583801
$639$	7.13127	+	4.11724i	0.282109	+	0.162876i
$640$	1.05091			0.0415409
$641$	10.4211	+	18.0498i	0.411608	+	0.712926i	0.995066	−	0.0992178i	$-0.0316340\pi$
$641$	10.4211	+	18.0498i	0.411608	+	0.712926i	−0.583458	+	0.812143i	$0.698301\pi$
$642$	4.27597	−	2.46873i	0.168759	−	0.0974332i
$643$	−7.74134	−	4.46946i	−0.305289	−	0.176258i	0.339528	−	0.940596i	$-0.389733\pi$
$643$	−7.74134	−	4.46946i	−0.305289	−	0.176258i	−0.644816	+	0.764338i	$0.723066\pi$
$644$	8.36182	−	1.27003i	0.329502	−	0.0500461i
$645$		−	1.46334i		−	0.0576189i
$646$	−13.8419			−0.544603
$647$	23.9738			0.942508			0.471254	−	0.881997i	$-0.343801\pi$
$647$	23.9738			0.942508			0.471254	+	0.881997i	$0.343801\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	8.20064	+	14.2039i	0.321903	+	0.557553i
$650$	−6.70537	+	12.3418i	−0.263006	+	0.484087i
$651$	21.5928	+	8.44635i	0.846289	+	0.331038i
$652$	−5.33166	+	3.07824i	−0.208804	+	0.120553i
$653$	4.14381	−	7.17729i	0.162160	−	0.280869i	−0.773483	−	0.633817i	$-0.781487\pi$
$653$	4.14381	−	7.17729i	0.162160	−	0.280869i	0.935643	+	0.352948i	$0.114821\pi$
$654$	3.56865	+	6.18109i	0.139545	+	0.241700i
$655$	9.22922	+	5.32849i	0.360615	+	0.208201i
$656$			7.68082i			0.299886i
$657$	8.18302	+	4.72447i	0.319250	+	0.184319i
$658$	27.2344	−	4.13647i	1.06171	−	0.161256i
$659$	22.9958	−	39.8298i	0.895788	−	1.55155i	0.0629613	−	0.998016i	$-0.479946\pi$
$659$	22.9958	−	39.8298i	0.895788	−	1.55155i	0.832827	−	0.553534i	$-0.186721\pi$
$660$	3.44736	−	5.97101i	0.134188	−	0.232421i
$661$		−	0.691835i		−	0.0269093i	−0.999909	−	0.0134546i	$-0.995717\pi$
$661$		−	0.691835i		−	0.0269093i	0.999909	−	0.0134546i	$-0.00428287\pi$
$662$	4.20451	−	7.28243i	0.163413	−	0.283040i
$663$	−14.6459	−	7.95719i	−0.568801	−	0.309032i
$664$	−9.79351			−0.380062
$665$	−5.19812	−	6.50311i	−0.201574	−	0.252180i
$666$	2.32178	+	4.02143i	0.0899670	+	0.155827i
$667$	−7.18502			−0.278205
$668$	−6.82652	−	3.94129i	−0.264126	−	0.152493i
$669$	17.2784	−	9.97570i	0.668022	−	0.385683i
$670$		−	9.44130i		−	0.364749i
$671$			65.0121i			2.50976i
$672$	2.06666	−	1.65194i	0.0797232	−	0.0637250i
$673$	8.59837	+	14.8928i	0.331443	+	0.574076i	0.982795	−	0.184700i	$-0.0591313\pi$
$673$	8.59837	+	14.8928i	0.331443	+	0.574076i	−0.651352	+	0.758776i	$0.725798\pi$
$674$	−4.15725	−	2.40019i	−0.160131	−	0.0924518i
$675$	−1.94779	+	3.37368i	−0.0749706	+	0.129853i
$676$	12.9825	−	0.673387i	0.499329	−	0.0258995i
$677$	−5.97634	−	10.3513i	−0.229689	−	0.397834i	0.728027	−	0.685549i	$-0.240438\pi$
$677$	−5.97634	−	10.3513i	−0.229689	−	0.397834i	−0.957716	+	0.287715i	$0.907104\pi$
$678$	7.62173	−	4.40041i	0.292711	−	0.168997i
$679$	16.5899	+	6.48939i	0.636662	+	0.249040i
$680$	2.42910	−	4.20733i	0.0931518	−	0.161344i
$681$	20.2480	−	11.6902i	0.775906	−	0.447969i
$682$	−49.7919	+	28.7474i	−1.90663	+	1.10079i
$683$	−17.0585	+	9.84872i	−0.652725	+	0.376851i	−0.789499	−	0.613751i	$-0.789660\pi$
$683$	−17.0585	+	9.84872i	−0.652725	+	0.376851i	0.136775	+	0.990602i	$0.456326\pi$
$684$	2.59308	−	1.49712i	0.0991490	−	0.0572437i
$685$	−6.89509	+	11.9426i	−0.263448	+	0.456305i
$686$	−18.4731	−	1.32127i	−0.705305	−	0.0504462i
$687$	4.68467	−	2.70470i	0.178731	−	0.103191i
$688$	0.696225	+	1.20590i	0.0265433	+	0.0459744i
$689$	0.635711	+	24.5289i	0.0242187	+	0.934475i
$690$	−1.67973	+	2.90938i	−0.0639462	+	0.110758i
$691$	−19.1933	−	11.0812i	−0.730147	−	0.421551i	0.0883289	−	0.996091i	$-0.471847\pi$
$691$	−19.1933	−	11.0812i	−0.730147	−	0.421551i	−0.818476	+	0.574541i	$0.805181\pi$
$692$	−0.363182	−	0.629049i	−0.0138061	−	0.0239129i
$693$	−2.60652	−	17.1612i	−0.0990134	−	0.651901i
$694$			3.34793i			0.127086i
$695$			10.1382i			0.384566i
$696$	−1.94650	+	1.12381i	−0.0737819	+	0.0425980i
$697$	30.7502	+	17.7537i	1.16475	+	0.672468i
$698$	−14.2330			−0.538727
$699$	−10.7071	−	18.5453i	−0.404981	−	0.701448i
$700$	−10.1899	+	1.54768i	−0.385142	+	0.0584969i
$701$	−45.6839			−1.72546			−0.862728	−	0.505668i	$-0.831246\pi$
$701$	−45.6839			−1.72546			−0.862728	+	0.505668i	$0.831246\pi$
$702$	3.60434	−	0.0934133i	0.136037	−	0.00352566i
$703$	−6.95194	+	12.0411i	−0.262198	+	0.454139i
$704$			6.56072i			0.247266i
$705$	−5.47087	+	9.47582i	−0.206045	+	0.356880i
$706$	14.6041	−	25.2951i	0.549634	−	0.951994i
$707$	−18.7039	+	2.84083i	−0.703433	+	0.106840i
$708$	−2.16500	−	1.24996i	−0.0813655	−	0.0469764i
$709$		−	22.1597i		−	0.832224i	−0.909313	−	0.416112i	$-0.863392\pi$
$709$		−	22.1597i		−	0.832224i	0.909313	−	0.416112i	$-0.136608\pi$
$710$	−7.49433	−	4.32685i	−0.281257	−	0.162384i
$711$	1.65111	+	2.85981i	0.0619216	+	0.107251i
$712$	−2.17545	+	3.76799i	−0.0815285	+	0.141212i
$713$	24.2611	−	14.0072i	0.908587	−	0.524573i
$714$	−1.83662	−	12.0922i	−0.0687338	−	0.452541i
$715$	21.8436	+	11.8677i	0.816904	+	0.443827i
$716$	−8.55545	−	14.8185i	−0.319732	−	0.553792i
$717$			8.80379i			0.328784i
$718$	−25.7403			−0.960621
$719$	−6.75191			−0.251804			−0.125902	−	0.992043i	$-0.540182\pi$
$719$	−6.75191			−0.251804			−0.125902	+	0.992043i	$0.540182\pi$
$720$			1.05091i			0.0391651i
$721$	1.13186	+	1.41602i	0.0421527	+	0.0527352i
$722$	−8.69018	−	5.01728i	−0.323415	−	0.186724i
$723$	11.6408	−	6.72082i	0.432926	−	0.249950i
$724$	7.87270	+	13.6359i	0.292587	+	0.506775i
$725$	8.75582			0.325183
$726$	27.7501	+	16.0215i	1.02990	+	0.594615i
$727$	1.00891			0.0374184			0.0187092	−	0.999825i	$-0.494044\pi$
$727$	1.00891			0.0374184			0.0187092	+	0.999825i	$0.494044\pi$
$728$	6.14721	+	7.29464i	0.227831	+	0.270357i
$729$	1.00000			0.0370370
$730$	−8.59962	−	4.96499i	−0.318286	−	0.183763i
$731$	6.43709			0.238084
$732$	−4.95464	−	8.58169i	−0.183129	−	0.317189i
$733$	−26.2879	+	15.1773i	−0.970965	+	0.560587i	−0.899530	−	0.436858i	$-0.856091\pi$
$733$	−26.2879	+	15.1773i	−0.970965	+	0.560587i	−0.0714349	+	0.997445i	$0.522758\pi$
$734$	−16.9235	−	9.77078i	−0.624657	−	0.360646i
$735$	4.99138	−	5.40392i	0.184110	−	0.199327i
$736$		−	3.19672i		−	0.117832i
$737$	58.9410			2.17112
$738$	−7.68082			−0.282735
$739$			14.1058i			0.518890i	0.965758	+	0.259445i	$0.0835397\pi$
$739$			14.1058i			0.518890i	−0.965758	+	0.259445i	$0.916460\pi$
$740$	−2.43998	−	4.22617i	−0.0896954	−	0.155357i
$741$	5.63835	+	9.20651i	0.207130	+	0.338209i
$742$	−14.0644	+	11.2421i	−0.516320	+	0.412709i
$743$	10.5028	−	6.06381i	0.385311	−	0.222459i	−0.294815	−	0.955554i	$-0.595258\pi$
$743$	10.5028	−	6.06381i	0.385311	−	0.222459i	0.680127	+	0.733095i	$0.261925\pi$
$744$	4.38174	−	7.58940i	0.160642	−	0.278241i
$745$	9.73158	+	16.8556i	0.356538	+	0.617541i
$746$	16.4921	+	9.52174i	0.603820	+	0.348616i
$747$		−	9.79351i		−	0.358326i
$748$	26.2659	+	15.1646i	0.960377	+	0.554474i
$749$	−4.75879	+	12.1657i	−0.173882	+	0.444525i
$750$	4.67423	−	8.09601i	0.170679	−	0.295624i
$751$	−12.4488	+	21.5619i	−0.454263	+	0.786807i	−0.998645	−	0.0520306i	$-0.983431\pi$
$751$	−12.4488	+	21.5619i	−0.454263	+	0.786807i	0.544383	+	0.838837i	$0.316764\pi$
$752$		−	10.4117i		−	0.379675i
$753$	−2.16506	+	3.75000i	−0.0788993	+	0.136658i
$754$	−4.23243	−	6.91087i	−0.154136	−	0.251679i
$755$	−6.15394			−0.223965
$756$	1.65194	+	2.06666i	0.0600805	+	0.0751638i
$757$	17.0830	+	29.5886i	0.620892	+	1.07542i	0.989320	+	0.145760i	$0.0465627\pi$
$757$	17.0830	+	29.5886i	0.620892	+	1.07542i	−0.368428	+	0.929656i	$0.620104\pi$
$758$	27.4903			0.998492
$759$	−18.1629	−	10.4864i	−0.659273	−	0.380631i
$760$	−2.72510	+	1.57334i	−0.0988497	+	0.0570709i
$761$		−	10.7480i		−	0.389614i	−0.980842	−	0.194807i	$-0.937592\pi$
$761$		−	10.7480i		−	0.389614i	0.980842	−	0.194807i	$-0.0624080\pi$
$762$		−	20.5531i		−	0.744559i
$763$	−17.5860	−	6.87902i	−0.636656	−	0.249037i
$764$	−9.63307	−	16.6850i	−0.348512	−	0.603641i
$765$	4.20733	+	2.42910i	0.152116	+	0.0878244i
$766$	5.08286	−	8.80377i	0.183651	−	0.318093i
$767$	4.30304	−	7.92014i	0.155374	−	0.285980i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−42.3478	+	24.4495i	−1.52710	+	0.881673i	−0.527620	+	0.849481i	$0.676915\pi$
$769$	−42.3478	+	24.4495i	−1.52710	+	0.881673i	−0.999482	+	0.0321920i	$0.989751\pi$
$770$	2.73922	+	18.0349i	0.0987145	+	0.649933i
$771$	−1.27315	+	2.20516i	−0.0458514	+	0.0794169i
$772$	13.9041	−	8.02752i	0.500419	−	0.288917i
$773$	9.59631	−	5.54043i	0.345155	−	0.199275i	−0.317394	−	0.948294i	$-0.602808\pi$
$773$	9.59631	−	5.54043i	0.345155	−	0.199275i	0.662549	+	0.749018i	$0.269474\pi$
$774$	−1.20590	+	0.696225i	−0.0433451	+	0.0250253i
$775$	−29.5652	+	17.0695i	−1.06201	+	0.613153i
$776$	3.36652	−	5.83099i	0.120851	−	0.209320i
$777$	−11.4415	−	4.47551i	−0.410461	−	0.160558i
$778$	−20.1184	+	11.6154i	−0.721279	+	0.416431i
$779$	−11.4991	−	19.9170i	−0.411998	−	0.713601i
$780$	−3.78784	+	0.0981690i	−0.135626	+	0.00351501i
$781$	27.0121	−	46.7863i	0.966568	−	1.67415i
$782$	−12.7981	−	7.38898i	−0.457658	−	0.264229i
$783$	−1.12381	−	1.94650i	−0.0401618	−	0.0695623i
$784$	−1.54219	+	6.82801i	−0.0550781	+	0.243857i
$785$			16.6532i			0.594377i
$786$		−	10.1407i		−	0.361707i
$787$	43.6547	−	25.2041i	1.55612	−	0.898428i	0.558502	−	0.829504i	$-0.311376\pi$
$787$	43.6547	−	25.2041i	1.55612	−	0.898428i	0.997622	−	0.0689247i	$-0.0219568\pi$
$788$	−12.4157	−	7.16821i	−0.442291	−	0.255357i
$789$	7.00731			0.249467
$790$	−1.73517	−	3.00541i	−0.0617347	−	0.106928i
$791$	−8.48233	+	21.6848i	−0.301597	+	0.771022i
$792$	−6.56072			−0.233125
$793$	30.4685	−	18.6599i	1.08197	−	0.662631i
$794$	17.0773	−	29.5787i	0.606049	−	1.04971i
$795$		−	7.15183i		−	0.253649i
$796$	7.95650	−	13.7811i	0.282011	−	0.488457i
$797$	3.24783	−	5.62541i	0.115044	−	0.199262i	−0.802753	−	0.596311i	$-0.796632\pi$
$797$	3.24783	−	5.62541i	0.115044	−	0.199262i	0.917797	+	0.397049i	$0.129966\pi$
$798$	−2.88588	+	7.37766i	−0.102159	+	0.261166i
$799$	−41.6832	−	24.0658i	−1.47465	−	0.851388i
$800$			3.89559i			0.137730i
$801$	−3.76799	−	2.17545i	−0.133136	−	0.0768658i
$802$	15.7114	+	27.2130i	0.554789	+	0.960923i
$803$	30.9959	−	53.6865i	1.09382	−	1.89456i
$804$	−7.78031	+	4.49196i	−0.274390	+	0.158419i
$805$	−1.33468	−	8.78752i	−0.0470415	−	0.309719i
$806$	27.7641	+	15.0843i	0.977948	+	0.531323i
$807$	0.701117	+	1.21437i	0.0246805	+	0.0427479i
$808$			7.15050i			0.251554i
$809$	−18.0493			−0.634579			−0.317289	−	0.948329i	$-0.602773\pi$
$809$	−18.0493			−0.634579			−0.317289	+	0.948329i	$0.602773\pi$
$810$	−1.05091			−0.0369252
$811$		−	47.3832i		−	1.66385i	−0.554889	−	0.831924i	$-0.687239\pi$
$811$		−	47.3832i		−	1.66385i	0.554889	−	0.831924i	$-0.312761\pi$
$812$	2.16629	−	5.53805i	0.0760218	−	0.194347i
$813$	0.455960	+	0.263249i	0.0159912	+	0.00923253i
$814$	26.3835	−	15.2325i	0.924742	−	0.533900i
$815$	3.23495	+	5.60310i	0.113315	+	0.196268i
$816$	−4.62286			−0.161832
$817$	−3.61074	−	2.08466i	−0.126324	−	0.0729330i
$818$	1.84680			0.0645718
$819$	−7.29464	+	6.14721i	−0.254895	+	0.214801i
$820$	8.07185			0.281881
$821$	−5.86148	−	3.38413i	−0.204567	−	0.118107i	0.394217	−	0.919017i	$-0.371016\pi$
$821$	−5.86148	−	3.38413i	−0.204567	−	0.118107i	−0.598784	+	0.800911i	$0.704349\pi$
$822$	13.1221			0.457687
$823$	14.1503	+	24.5090i	0.493247	+	0.854329i	0.999970	−	0.00778027i	$-0.00247656\pi$
$823$	14.1503	+	24.5090i	0.493247	+	0.854329i	−0.506723	+	0.862109i	$0.669143\pi$
$824$	0.593375	−	0.342585i	0.0206712	−	0.0119345i
$825$	22.1338	+	12.7789i	0.770598	+	0.444905i
$826$	6.53917	−	0.993197i	0.227527	−	0.0345577i
$827$		−	18.4833i		−	0.642726i	−0.946956	−	0.321363i	$-0.895859\pi$
$827$		−	18.4833i		−	0.642726i	0.946956	−	0.321363i	$-0.104141\pi$
$828$	3.19672			0.111094
$829$	2.76426			0.0960068			0.0480034	−	0.998847i	$-0.484714\pi$
$829$	2.76426			0.0960068			0.0480034	+	0.998847i	$0.484714\pi$
$830$			10.2921i			0.357244i
$831$	16.3572	+	28.3315i	0.567425	+	0.982810i
$832$	3.07474	−	1.88307i	0.106598	−	0.0652837i
$833$	23.7713	+	21.9566i	0.823628	+	0.760751i
$834$	8.35464	−	4.82355i	0.289298	−	0.167026i
$835$	−4.14194	+	7.17406i	−0.143338	+	0.248269i
$836$	−9.82217	−	17.0125i	−0.339707	−	0.588389i
$837$	7.58940	+	4.38174i	0.262328	+	0.151455i
$838$		−	29.0782i		−	1.00449i
$839$	28.1152	+	16.2323i	0.970646	+	0.560403i	0.899433	−	0.437058i	$-0.143980\pi$
$839$	28.1152	+	16.2323i	0.970646	+	0.560403i	0.0712130	+	0.997461i	$0.477313\pi$
$840$	−1.73604	−	2.17188i	−0.0598991	−	0.0749369i
$841$	11.9741	−	20.7397i	0.412900	−	0.715163i
$842$	−5.02980	+	8.71187i	−0.173338	+	0.300231i
$843$		−	22.6836i		−	0.781263i
$844$	10.0909	−	17.4780i	0.347344	−	0.601617i
$845$	−0.707669	−	13.6435i	−0.0243446	−	0.469350i
$846$	10.4117			0.357961
$847$	−83.8167	+	12.7304i	−2.87998	+	0.437423i
$848$	3.40268	+	5.89362i	0.116849	+	0.202388i
$849$	5.48461			0.188231
$850$	15.5960	+	9.00437i	0.534939	+	0.308847i
$851$	−12.8554	+	7.42206i	−0.440677	+	0.254425i
$852$			8.23449i			0.282109i
$853$			10.6429i			0.364404i	0.983261	+	0.182202i	$0.0583225\pi$
$853$			10.6429i			0.364404i	−0.983261	+	0.182202i	$0.941677\pi$
$854$	24.4160	+	9.55069i	0.835499	+	0.326818i
$855$	−1.57334	−	2.72510i	−0.0538070	−	0.0931964i
$856$	4.27597	+	2.46873i	0.146150	+	0.0843796i
$857$	−18.2812	+	31.6639i	−0.624473	+	1.08162i	0.364169	+	0.931333i	$0.381353\pi$
$857$	−18.2812	+	31.6639i	−0.624473	+	1.08162i	−0.988642	+	0.150287i	$0.951980\pi$
$858$	−0.612859	−	23.6471i	−0.0209226	−	0.807298i
$859$	1.98873	+	3.44459i	0.0678547	+	0.117528i	0.897957	−	0.440084i	$-0.145051\pi$
$859$	1.98873	+	3.44459i	0.0678547	+	0.117528i	−0.830102	+	0.557612i	$0.811718\pi$
$860$	1.26729	−	0.731670i	0.0432142	−	0.0249497i
$861$	15.8737	−	12.6883i	0.540973	−	0.432415i
$862$	−7.82448	+	13.5524i	−0.266503	+	0.461596i
$863$	31.8449	−	18.3857i	1.08401	−	0.625855i	0.152037	−	0.988375i	$-0.451417\pi$
$863$	31.8449	−	18.3857i	1.08401	−	0.625855i	0.931976	+	0.362520i	$0.118083\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−0.661074	+	0.381671i	−0.0224772	+	0.0129772i
$866$	−25.8553	+	14.9276i	−0.878599	+	0.507260i
$867$	−2.18539	+	3.78521i	−0.0742199	+	0.128553i
$868$	3.48166	+	22.9231i	0.118175	+	0.778061i
$869$	18.7624	−	10.8325i	0.636472	−	0.367467i
$870$	1.18103	+	2.04560i	0.0400405	+	0.0693523i
$871$	−16.9173	−	27.6233i	−0.573222	−	0.935979i
$872$	−3.56865	+	6.18109i	−0.120850	+	0.209318i
$873$	5.83099	+	3.36652i	0.197349	+	0.113940i
$874$	4.78586	+	8.28935i	0.161884	+	0.280391i
$875$	3.71406	+	24.4533i	0.125558	+	0.826671i
$876$			9.44894i			0.319250i
$877$		−	56.7616i		−	1.91670i	−0.285590	−	0.958352i	$-0.592190\pi$
$877$		−	56.7616i		−	1.91670i	0.285590	−	0.958352i	$-0.407810\pi$
$878$	10.7131	−	6.18523i	0.361551	−	0.208742i
$879$	−11.5606	−	6.67449i	−0.389928	−	0.225125i
$880$	6.89473			0.232421
$881$	−12.8086	−	22.1851i	−0.431532	−	0.747435i	0.565474	−	0.824766i	$-0.308693\pi$
$881$	−12.8086	−	22.1851i	−0.431532	−	0.747435i	−0.997005	+	0.0773317i	$0.975360\pi$
$882$	−6.82801	−	1.54219i	−0.229911	−	0.0519281i
$883$	15.7725			0.530785			0.265393	−	0.964140i	$-0.414498\pi$
$883$	15.7725			0.530785			0.265393	+	0.964140i	$0.414498\pi$
$884$	−0.431836	−	16.6623i	−0.0145242	−	0.560415i
$885$	−1.31360	+	2.27522i	−0.0441561	+	0.0764805i
$886$		−	32.5637i		−	1.09400i
$887$	2.85218	−	4.94012i	0.0957667	−	0.165873i	−0.814162	−	0.580638i	$-0.802803\pi$
$887$	2.85218	−	4.94012i	0.0957667	−	0.165873i	0.909928	+	0.414765i	$0.136136\pi$
$888$	−2.32178	+	4.02143i	−0.0779137	+	0.134951i
$889$	33.9525	+	42.4763i	1.13873	+	1.42461i
$890$	3.95982	+	2.28620i	0.132734	+	0.0766338i
$891$		−	6.56072i		−	0.219792i
$892$	17.2784	+	9.97570i	0.578524	+	0.334011i
$893$	15.5875	+	26.9983i	0.521616	+	0.903465i
$894$	9.26015	−	16.0390i	0.309706	−	0.536426i
$895$	−15.5729	+	8.99101i	−0.520544	+	0.300536i
$896$	2.46395	+	0.963812i	0.0823149	+	0.0321987i
$897$	0.298616	+	11.5221i	0.00997049	+	0.384710i
$898$	5.15057	+	8.92105i	0.171877	+	0.297699i
$899$		−	19.6970i		−	0.656933i
$900$	−3.89559			−0.129853
$901$	31.4602			1.04809
$902$			50.3917i			1.67786i
$903$	1.34206	−	3.43093i	0.0446609	−	0.114174i
$904$	7.62173	+	4.40041i	0.253495	+	0.146355i
$905$	14.3301	−	8.27350i	0.476349	−	0.275020i
$906$	2.92791	+	5.07128i	0.0972732	+	0.168482i
$907$	−12.9554			−0.430178			−0.215089	−	0.976594i	$-0.569004\pi$
$907$	−12.9554			−0.430178			−0.215089	+	0.976594i	$0.569004\pi$
$908$	20.2480	+	11.6902i	0.671954	+	0.387953i
$909$	−7.15050			−0.237167
$910$	7.66601	−	6.46017i	0.254126	−	0.214152i
$911$	−23.0999			−0.765334			−0.382667	−	0.923886i	$-0.624994\pi$
$911$	−23.0999			−0.765334			−0.382667	+	0.923886i	$0.624994\pi$
$912$	2.59308	+	1.49712i	0.0858656	+	0.0495745i
$913$	−64.2525			−2.12645
$914$	9.04098	+	15.6594i	0.299049	+	0.517968i
$915$	−9.01859	+	5.20689i	−0.298145	+	0.172134i
$916$	4.68467	+	2.70470i	0.154786	+	0.0893657i
$917$	16.7519	+	20.9574i	0.553195	+	0.692076i
$918$		−	4.62286i		−	0.152577i
$919$	−34.1883			−1.12777			−0.563883	−	0.825854i	$-0.690693\pi$
$919$	−34.1883			−1.12777			−0.563883	+	0.825854i	$0.690693\pi$
$920$	−3.35946			−0.110758
$921$		−	16.4170i		−	0.540959i
$922$	1.98814	+	3.44357i	0.0654760	+	0.113408i
$923$	−29.6799	+	0.769210i	−0.976926	+	0.0253189i
$924$	13.5588	−	10.8379i	0.446052	−	0.356541i
$925$	15.6659	−	9.04468i	0.515090	−	0.297387i
$926$	4.73365	−	8.19892i	0.155557	−	0.269433i
$927$	0.342585	+	0.593375i	0.0112520	+	0.0194890i
$928$	−1.94650	−	1.12381i	−0.0638970	−	0.0368910i
$929$			33.4666i			1.09800i	0.835822	+	0.549001i	$0.184992\pi$
$929$			33.4666i			1.09800i	−0.835822	+	0.549001i	$0.815008\pi$
$930$	−7.97578	−	4.60482i	−0.261536	−	0.150998i
$931$	−6.22331	−	20.0144i	−0.203961	−	0.655946i
$932$	10.7071	−	18.5453i	0.350724	−	0.607472i
$933$	−12.4093	+	21.4936i	−0.406263	+	0.703669i
$934$		−	10.3386i		−	0.338291i
$935$	15.9367	−	27.6031i	0.521185	−	0.902718i
$936$	1.88307	+	3.07474i	0.0615500	+	0.100501i
$937$	4.42393			0.144523			0.0722617	−	0.997386i	$-0.476978\pi$
$937$	4.42393			0.144523			0.0722617	+	0.997386i	$0.476978\pi$
$938$	8.65881	−	22.1360i	0.282720	−	0.722765i
$939$	−11.2551	−	19.4943i	−0.367295	−	0.636174i
$940$	−10.9417			−0.356880
$941$	9.59182	+	5.53784i	0.312684	+	0.180528i	0.648127	−	0.761532i	$-0.275553\pi$
$941$	9.59182	+	5.53784i	0.312684	+	0.180528i	−0.335443	+	0.942061i	$0.608886\pi$
$942$	13.7234	−	7.92320i	0.447132	−	0.258152i
$943$		−	24.5534i		−	0.799569i
$944$		−	2.49992i		−	0.0813655i
$945$	2.17188	−	1.73604i	0.0706512	−	0.0564734i
$946$	4.56774	+	7.91155i	0.148510	+	0.257227i
$947$	25.8388	+	14.9180i	0.839648	+	0.484771i	0.857145	−	0.515076i	$-0.172236\pi$
$947$	25.8388	+	14.9180i	0.839648	+	0.484771i	−0.0174964	+	0.999847i	$0.505570\pi$
$948$	−1.65111	+	2.85981i	−0.0536257	+	0.0928824i
$949$	−34.0572	+	0.882657i	−1.10554	+	0.0286523i
$950$	−5.83215	−	10.1016i	−0.189220	−	0.327739i
$951$	−16.0776	+	9.28239i	−0.521351	+	0.301002i
$952$	9.55388	−	7.63668i	0.309643	−	0.247506i
$953$	9.34420	−	16.1846i	0.302688	−	0.524272i	−0.674056	−	0.738681i	$-0.735449\pi$
$953$	9.34420	−	16.1846i	0.302688	−	0.524272i	0.976744	+	0.214409i	$0.0687825\pi$
$954$	−5.89362	+	3.40268i	−0.190813	+	0.110166i
$955$	−17.5344	+	10.1235i	−0.567400	+	0.327588i
$956$	−7.62431	+	4.40190i	−0.246588	+	0.142368i
$957$	−12.7704	+	7.37302i	−0.412810	+	0.238336i
$958$	−13.9356	+	24.1372i	−0.450239	+	0.779837i
$959$	−27.1190	+	21.6770i	−0.875718	+	0.699986i
$960$	−0.910115	+	0.525455i	−0.0293738	+	0.0169590i
$961$	22.8993	+	39.6628i	0.738688	+	1.27944i
$962$	−14.7115	−	7.99282i	−0.474318	−	0.257699i
$963$	−2.46873	+	4.27597i	−0.0795538	+	0.137791i
$964$	11.6408	+	6.72082i	0.374925	+	0.216463i
$965$	−8.43621	−	14.6119i	−0.271571	−	0.470375i
$966$	−6.60653	+	5.28078i	−0.212562	+	0.169906i
$967$			0.591853i			0.0190327i	0.999955	+	0.00951636i	$0.00302920\pi$
$967$			0.591853i			0.0190327i	−0.999955	+	0.00951636i	$0.996971\pi$
$968$			32.0430i			1.02990i
$969$	11.9874	−	6.92096i	0.385092	−	0.222333i
$970$	−6.12785	−	3.53791i	−0.196753	−	0.113596i
$971$	−19.8952			−0.638468			−0.319234	−	0.947676i	$-0.603426\pi$
$971$	−19.8952			−0.638468			−0.319234	+	0.947676i	$0.603426\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−9.29800	+	23.7700i	−0.298080	+	0.762032i
$974$	−14.3218			−0.458901
$975$	−0.363900	−	14.0410i	−0.0116541	−	0.449673i
$976$	4.95464	−	8.58169i	0.158594	−	0.274693i
$977$		−	35.1242i		−	1.12372i	−0.827231	−	0.561862i	$-0.810085\pi$
$977$		−	35.1242i		−	1.12372i	0.827231	−	0.561862i	$-0.189915\pi$
$978$	3.07824	−	5.33166i	0.0984311	−	0.170488i
$979$	−14.2725	+	24.7208i	−0.456152	+	0.790079i
$980$	7.17562	+	1.62070i	0.229217	+	0.0517713i
$981$	−6.18109	−	3.56865i	−0.197347	−	0.113938i
$982$		−	7.05051i		−	0.224991i
$983$	−25.2058	−	14.5526i	−0.803941	−	0.464156i	0.0409061	−	0.999163i	$-0.486976\pi$
$983$	−25.2058	−	14.5526i	−0.803941	−	0.464156i	−0.844847	+	0.535007i	$0.820309\pi$
$984$	−3.84041	−	6.65179i	−0.122428	−	0.212051i
$985$	−7.53314	+	13.0478i	−0.240026	+	0.415737i
$986$	−8.99839	+	5.19522i	−0.286567	+	0.165450i
$987$	−21.5174	+	17.1995i	−0.684907	+	0.547465i
$988$	−5.15389	+	9.48621i	−0.163967	+	0.301796i
$989$	−2.22563	−	3.85491i	−0.0707710	−	0.122579i
$990$			6.89473i			0.219129i
$991$	−8.36093			−0.265594			−0.132797	−	0.991143i	$-0.542396\pi$
$991$	−8.36093			−0.265594			−0.132797	+	0.991143i	$0.542396\pi$
$992$	8.76348			0.278241
$993$			8.40902i			0.266852i
$994$	−13.6029	−	17.0179i	−0.431457	−	0.539775i
$995$	−14.4827	−	8.36157i	−0.459131	−	0.265080i
$996$	8.48143	−	4.89676i	0.268744	−	0.155160i
$997$	17.6607	+	30.5892i	0.559320	+	0.968770i	0.997553	+	0.0699089i	$0.0222709\pi$
$997$	17.6607	+	30.5892i	0.559320	+	0.968770i	−0.438234	+	0.898861i	$0.644396\pi$
$998$	−37.3026			−1.18079
$999$	−4.02143	−	2.32178i	−0.127233	−	0.0734578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bd.b.361.3	yes	20
3.2	odd	2		1638.2.cr.b.361.8		20
7.2	even	3		546.2.bm.b.205.8	yes	20
13.4	even	6		546.2.bm.b.277.3	yes	20
21.2	odd	6		1638.2.dt.b.1297.3		20
39.17	odd	6		1638.2.dt.b.1369.8		20
91.30	even	6	inner	546.2.bd.b.121.3	✓	20
273.212	odd	6		1638.2.cr.b.667.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.3	✓	20	91.30	even	6	inner
546.2.bd.b.361.3	yes	20	1.1	even	1	trivial
546.2.bm.b.205.8	yes	20	7.2	even	3
546.2.bm.b.277.3	yes	20	13.4	even	6
1638.2.cr.b.361.8		20	3.2	odd	2
1638.2.cr.b.667.8		20	273.212	odd	6
1638.2.dt.b.1297.3		20	21.2	odd	6
1638.2.dt.b.1369.8		20	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(0.910115 - 0.525455i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.61575 - 0.397291i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(0.910115 - 0.525455i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.61575 - 0.397291i) q^{7} -1.00000i q^{8} +1.00000 q^{9} -1.05091 q^{10} -6.56072i q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.07474 + 1.88307i) q^{13} +(-2.46395 - 0.963812i) q^{14} +(0.910115 - 0.525455i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.31143 + 4.00351i) q^{17} +(-0.866025 - 0.500000i) q^{18} -2.99423i q^{19} +(0.910115 + 0.525455i) q^{20} +(2.61575 - 0.397291i) q^{21} +(-3.28036 + 5.68175i) q^{22} +(1.59836 - 2.76844i) q^{23} -1.00000i q^{24} +(-1.94779 + 3.37368i) q^{25} +(3.60434 - 0.0934133i) q^{26} +1.00000 q^{27} +(1.65194 + 2.06666i) q^{28} +(-1.12381 - 1.94650i) q^{29} -1.05091 q^{30} +(7.58940 + 4.38174i) q^{31} +(0.866025 - 0.500000i) q^{32} -6.56072i q^{33} -4.62286i q^{34} +(2.17188 - 1.73604i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-4.02143 - 2.32178i) q^{37} +(-1.49712 + 2.59308i) q^{38} +(-3.07474 + 1.88307i) q^{39} +(-0.525455 - 0.910115i) q^{40} +(6.65179 - 3.84041i) q^{41} +(-2.46395 - 0.963812i) q^{42} +(0.696225 - 1.20590i) q^{43} +(5.68175 - 3.28036i) q^{44} +(0.910115 - 0.525455i) q^{45} +(-2.76844 + 1.59836i) q^{46} +(-9.01677 + 5.20584i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(6.68432 - 2.07843i) q^{49} +(3.37368 - 1.94779i) q^{50} +(2.31143 + 4.00351i) q^{51} +(-3.16816 - 1.72127i) q^{52} +(3.40268 - 5.89362i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-3.44736 - 5.97101i) q^{55} +(-0.397291 - 2.61575i) q^{56} -2.99423i q^{57} +2.24763i q^{58} +(-2.16500 + 1.24996i) q^{59} +(0.910115 + 0.525455i) q^{60} -9.90929 q^{61} +(-4.38174 - 7.58940i) q^{62} +(2.61575 - 0.397291i) q^{63} -1.00000 q^{64} +(-1.80890 + 3.32945i) q^{65} +(-3.28036 + 5.68175i) q^{66} +8.98392i q^{67} +(-2.31143 + 4.00351i) q^{68} +(1.59836 - 2.76844i) q^{69} +(-2.74892 + 0.417517i) q^{70} +(7.13127 + 4.11724i) q^{71} -1.00000i q^{72} +(8.18302 + 4.72447i) q^{73} +(2.32178 + 4.02143i) q^{74} +(-1.94779 + 3.37368i) q^{75} +(2.59308 - 1.49712i) q^{76} +(-2.60652 - 17.1612i) q^{77} +(3.60434 - 0.0934133i) q^{78} +(1.65111 + 2.85981i) q^{79} +1.05091i q^{80} +1.00000 q^{81} -7.68082 q^{82} -9.79351i q^{83} +(1.65194 + 2.06666i) q^{84} +(4.20733 + 2.42910i) q^{85} +(-1.20590 + 0.696225i) q^{86} +(-1.12381 - 1.94650i) q^{87} -6.56072 q^{88} +(-3.76799 - 2.17545i) q^{89} -1.05091 q^{90} +(-7.29464 + 6.14721i) q^{91} +3.19672 q^{92} +(7.58940 + 4.38174i) q^{93} +10.4117 q^{94} +(-1.57334 - 2.72510i) q^{95} +(0.866025 - 0.500000i) q^{96} +(5.83099 + 3.36652i) q^{97} +(-6.82801 - 1.54219i) q^{98} -6.56072i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

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