LMFDB - Embedded newform 546.2.bn.e.101.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.14
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.e.173.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.57643 - 0.717543i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.41302 - 0.815806i) q^{5} +(-0.166804 + 1.72400i) q^{6} +(1.06124 + 2.42359i) q^{7} +1.00000 q^{8} +(1.97026 - 2.26231i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.57643 - 0.717543i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.41302 - 0.815806i) q^{5} +(-0.166804 + 1.72400i) q^{6} +(1.06124 + 2.42359i) q^{7} +1.00000 q^{8} +(1.97026 - 2.26231i) q^{9} +1.63161i q^{10} -2.07077 q^{11} +(-1.40963 - 1.00646i) q^{12} +(3.37445 - 1.27006i) q^{13} +(-2.62951 - 0.292738i) q^{14} +(1.64215 - 2.29996i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.52723 + 2.64525i) q^{17} +(0.974089 + 2.83745i) q^{18} +1.32484 q^{19} +(-1.41302 - 0.815806i) q^{20} +(3.41199 + 3.05914i) q^{21} +(1.03538 - 1.79334i) q^{22} +(-5.29037 - 3.05440i) q^{23} +(1.57643 - 0.717543i) q^{24} +(-1.16892 + 2.02463i) q^{25} +(-0.587322 + 3.55739i) q^{26} +(1.48267 - 4.98013i) q^{27} +(1.56827 - 2.13085i) q^{28} +(-2.79123 + 1.61152i) q^{29} +(1.17075 + 2.57212i) q^{30} +(3.28416 - 5.68833i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.26442 + 1.48586i) q^{33} -3.05447 q^{34} +(3.47672 + 2.55881i) q^{35} +(-2.94435 - 0.575141i) q^{36} +(6.87437 + 3.96892i) q^{37} +(-0.662420 + 1.14734i) q^{38} +(4.40827 - 4.42348i) q^{39} +(1.41302 - 0.815806i) q^{40} +(7.41619 - 4.28174i) q^{41} +(-4.35528 + 1.42530i) q^{42} +(2.69662 - 4.67069i) q^{43} +(1.03538 + 1.79334i) q^{44} +(0.938408 - 4.80404i) q^{45} +(5.29037 - 3.05440i) q^{46} +(0.714173 - 0.412328i) q^{47} +(-0.166804 + 1.72400i) q^{48} +(-4.74756 + 5.14399i) q^{49} +(-1.16892 - 2.02463i) q^{50} +(4.30566 + 3.07419i) q^{51} +(-2.78713 - 2.28733i) q^{52} +(-9.25742 - 5.34477i) q^{53} +(3.57158 + 3.77410i) q^{54} +(-2.92603 + 1.68934i) q^{55} +(1.06124 + 2.42359i) q^{56} +(2.08852 - 0.950630i) q^{57} -3.22304i q^{58} +(-11.7755 + 6.79857i) q^{59} +(-2.81290 - 0.272160i) q^{60} +15.5525i q^{61} +(3.28416 + 5.68833i) q^{62} +(7.57383 + 2.37426i) q^{63} +1.00000 q^{64} +(3.73204 - 4.54752i) q^{65} +(0.345413 - 3.57000i) q^{66} +3.27341i q^{67} +(1.52723 - 2.64525i) q^{68} +(-10.5316 - 1.01897i) q^{69} +(-3.95436 + 1.73152i) q^{70} +(-4.59225 + 7.95402i) q^{71} +(1.97026 - 2.26231i) q^{72} +(-1.43611 + 2.48741i) q^{73} +(-6.87437 + 3.96892i) q^{74} +(-0.389962 + 4.03044i) q^{75} +(-0.662420 - 1.14734i) q^{76} +(-2.19757 - 5.01869i) q^{77} +(1.62671 + 6.02941i) q^{78} +(-3.24657 - 5.62322i) q^{79} +1.63161i q^{80} +(-1.23612 - 8.91471i) q^{81} +8.56348i q^{82} -6.85946i q^{83} +(0.943293 - 4.48444i) q^{84} +(4.31602 + 2.49186i) q^{85} +(2.69662 + 4.67069i) q^{86} +(-3.24385 + 4.54327i) q^{87} -2.07077 q^{88} +(0.929234 + 0.536494i) q^{89} +(3.69122 + 3.21471i) q^{90} +(6.65920 + 6.83045i) q^{91} +6.10879i q^{92} +(1.09562 - 11.3238i) q^{93} +0.824656i q^{94} +(1.87202 - 1.08081i) q^{95} +(-1.40963 - 1.00646i) q^{96} +(4.58560 - 7.94250i) q^{97} +(-2.08105 - 6.68350i) q^{98} +(-4.07996 + 4.68472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.57643	−	0.717543i	0.910152	−	0.414274i
$3$	1.57643	−	0.717543i	0.910152	−	0.414274i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.41302	−	0.815806i	0.631921	−	0.364840i	−0.149575	−	0.988750i	$-0.547790\pi$
$5$	1.41302	−	0.815806i	0.631921	−	0.364840i	0.781496	+	0.623911i	$0.214457\pi$
$6$	−0.166804	+	1.72400i	−0.0680976	+	0.703820i
$7$	1.06124	+	2.42359i	0.401109	+	0.916030i
$7$	1.06124	+	2.42359i	0.401109	+	0.916030i
$8$	1.00000			0.353553
$9$	1.97026	−	2.26231i	0.656754	−	0.754104i
$10$			1.63161i			0.515961i
$11$	−2.07077			−0.624360			−0.312180	−	0.950023i	$-0.601059\pi$
$11$	−2.07077			−0.624360			−0.312180	+	0.950023i	$0.601059\pi$
$12$	−1.40963	−	1.00646i	−0.406924	−	0.290539i
$13$	3.37445	−	1.27006i	0.935905	−	0.352252i
$13$	3.37445	−	1.27006i	0.935905	−	0.352252i
$14$	−2.62951	−	0.292738i	−0.702765	−	0.0782374i
$15$	1.64215	−	2.29996i	0.424001	−	0.593848i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.52723	+	2.64525i	0.370409	+	0.641567i	0.989628	−	0.143651i	$-0.0458843\pi$
$17$	1.52723	+	2.64525i	0.370409	+	0.641567i	−0.619220	+	0.785218i	$0.712551\pi$
$18$	0.974089	+	2.83745i	0.229595	+	0.668795i
$19$	1.32484			0.303939			0.151970	−	0.988385i	$-0.451438\pi$
$19$	1.32484			0.303939			0.151970	+	0.988385i	$0.451438\pi$
$20$	−1.41302	−	0.815806i	−0.315960	−	0.182420i
$21$	3.41199	+	3.05914i	0.744558	+	0.667558i
$22$	1.03538	−	1.79334i	0.220744	−	0.382341i
$23$	−5.29037	−	3.05440i	−1.10312	−	0.636886i	−0.166080	−	0.986112i	$-0.553111\pi$
$23$	−5.29037	−	3.05440i	−1.10312	−	0.636886i	−0.937038	+	0.349226i	$0.886444\pi$
$24$	1.57643	−	0.717543i	0.321787	−	0.146468i
$25$	−1.16892	+	2.02463i	−0.233784	+	0.404926i
$26$	−0.587322	+	3.55739i	−0.115183	+	0.697662i
$27$	1.48267	−	4.98013i	0.285341	−	0.958426i
$28$	1.56827	−	2.13085i	0.296375	−	0.402693i
$29$	−2.79123	+	1.61152i	−0.518319	+	0.299251i	−0.736246	−	0.676714i	$-0.763404\pi$
$29$	−2.79123	+	1.61152i	−0.518319	+	0.299251i	0.217928	+	0.975965i	$0.430070\pi$
$30$	1.17075	+	2.57212i	0.213749	+	0.469603i
$31$	3.28416	−	5.68833i	0.589852	−	1.02165i	−0.404399	−	0.914583i	$-0.632519\pi$
$31$	3.28416	−	5.68833i	0.589852	−	1.02165i	0.994251	−	0.107071i	$-0.0341473\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−3.26442	+	1.48586i	−0.568262	+	0.258656i
$34$	−3.05447			−0.523837
$35$	3.47672	+	2.55881i	0.587673	+	0.432518i
$36$	−2.94435	−	0.575141i	−0.490725	−	0.0958569i
$37$	6.87437	+	3.96892i	1.13014	+	0.652486i	0.943970	−	0.330032i	$-0.107059\pi$
$37$	6.87437	+	3.96892i	1.13014	+	0.652486i	0.186169	+	0.982518i	$0.440393\pi$
$38$	−0.662420	+	1.14734i	−0.107459	+	0.186124i
$39$	4.40827	−	4.42348i	0.705888	−	0.708324i
$40$	1.41302	−	0.815806i	0.223418	−	0.128990i
$41$	7.41619	−	4.28174i	1.15821	−	0.668695i	0.207339	−	0.978269i	$-0.433520\pi$
$41$	7.41619	−	4.28174i	1.15821	−	0.668695i	0.950875	+	0.309574i	$0.100186\pi$
$42$	−4.35528	+	1.42530i	−0.672035	+	0.219929i
$43$	2.69662	−	4.67069i	0.411231	−	0.712273i	−0.583794	−	0.811902i	$-0.698432\pi$
$43$	2.69662	−	4.67069i	0.411231	−	0.712273i	0.995025	+	0.0996291i	$0.0317656\pi$
$44$	1.03538	+	1.79334i	0.156090	+	0.270356i
$45$	0.938408	−	4.80404i	0.139890	−	0.716145i
$46$	5.29037	−	3.05440i	0.780023	−	0.450346i
$47$	0.714173	−	0.412328i	0.104173	−	0.0601442i	−0.447008	−	0.894530i	$-0.647511\pi$
$47$	0.714173	−	0.412328i	0.104173	−	0.0601442i	0.551181	+	0.834386i	$0.314177\pi$
$48$	−0.166804	+	1.72400i	−0.0240761	+	0.248838i
$49$	−4.74756	+	5.14399i	−0.678223	+	0.734856i
$50$	−1.16892	−	2.02463i	−0.165310	−	0.286326i
$51$	4.30566	+	3.07419i	0.602913	+	0.430473i
$52$	−2.78713	−	2.28733i	−0.386506	−	0.317196i
$53$	−9.25742	−	5.34477i	−1.27160	−	0.734161i	−0.296314	−	0.955091i	$-0.595758\pi$
$53$	−9.25742	−	5.34477i	−1.27160	−	0.734161i	−0.975290	+	0.220930i	$0.929091\pi$
$54$	3.57158	+	3.77410i	0.486030	+	0.513590i
$55$	−2.92603	+	1.68934i	−0.394546	+	0.227791i
$56$	1.06124	+	2.42359i	0.141814	+	0.323866i
$57$	2.08852	−	0.950630i	0.276631	−	0.125914i
$58$		−	3.22304i		−	0.423205i
$59$	−11.7755	+	6.79857i	−1.53303	+	0.885098i	−0.533815	+	0.845601i	$0.679242\pi$
$59$	−11.7755	+	6.79857i	−1.53303	+	0.885098i	−0.999220	+	0.0394965i	$0.987425\pi$
$60$	−2.81290	−	0.272160i	−0.363144	−	0.0351357i
$61$			15.5525i			1.99129i	0.0932030	+	0.995647i	$0.470289\pi$
$61$			15.5525i			1.99129i	−0.0932030	+	0.995647i	$0.529711\pi$
$62$	3.28416	+	5.68833i	0.417088	+	0.722418i
$63$	7.57383	+	2.37426i	0.954213	+	0.299129i
$64$	1.00000			0.125000
$65$	3.73204	−	4.54752i	0.462903	−	0.564051i
$66$	0.345413	−	3.57000i	0.0425174	−	0.439437i
$67$			3.27341i			0.399910i	0.979805	+	0.199955i	$0.0640797\pi$
$67$			3.27341i			0.399910i	−0.979805	+	0.199955i	$0.935920\pi$
$68$	1.52723	−	2.64525i	0.185204	−	0.320783i
$69$	−10.5316	−	1.01897i	−1.26785	−	0.122670i
$70$	−3.95436	+	1.73152i	−0.472636	+	0.206957i
$71$	−4.59225	+	7.95402i	−0.545000	+	0.943968i	0.453607	+	0.891202i	$0.350137\pi$
$71$	−4.59225	+	7.95402i	−0.545000	+	0.943968i	−0.998607	+	0.0527663i	$0.983196\pi$
$72$	1.97026	−	2.26231i	0.232198	−	0.266616i
$73$	−1.43611	+	2.48741i	−0.168084	+	0.291129i	−0.937746	−	0.347322i	$-0.887091\pi$
$73$	−1.43611	+	2.48741i	−0.168084	+	0.291129i	0.769662	+	0.638451i	$0.220425\pi$
$74$	−6.87437	+	3.96892i	−0.799129	+	0.461377i
$75$	−0.389962	+	4.03044i	−0.0450289	+	0.465395i
$76$	−0.662420	−	1.14734i	−0.0759848	−	0.131609i
$77$	−2.19757	−	5.01869i	−0.250436	−	0.571932i
$78$	1.62671	+	6.02941i	0.184189	+	0.682696i
$79$	−3.24657	−	5.62322i	−0.365268	−	0.632662i	0.623551	−	0.781782i	$-0.285689\pi$
$79$	−3.24657	−	5.62322i	−0.365268	−	0.632662i	−0.988819	+	0.149120i	$0.952356\pi$
$80$			1.63161i			0.182420i
$81$	−1.23612	−	8.91471i	−0.137347	−	0.990523i
$82$			8.56348i			0.945678i
$83$		−	6.85946i		−	0.752924i	−0.926432	−	0.376462i	$-0.877141\pi$
$83$		−	6.85946i		−	0.752924i	0.926432	−	0.376462i	$-0.122859\pi$
$84$	0.943293	−	4.48444i	0.102922	−	0.489292i
$85$	4.31602	+	2.49186i	0.468138	+	0.270280i
$86$	2.69662	+	4.67069i	0.290784	+	0.503653i
$87$	−3.24385	+	4.54327i	−0.347777	+	0.487090i
$88$	−2.07077			−0.220744
$89$	0.929234	+	0.536494i	0.0984986	+	0.0568682i	0.548440	−	0.836190i	$-0.315222\pi$
$89$	0.929234	+	0.536494i	0.0984986	+	0.0568682i	−0.449942	+	0.893058i	$0.648555\pi$
$90$	3.69122	+	3.21471i	0.389089	+	0.338860i
$91$	6.65920	+	6.83045i	0.698073	+	0.716026i
$92$			6.10879i			0.636886i
$93$	1.09562	−	11.3238i	0.113611	−	1.17422i
$94$			0.824656i			0.0850568i
$95$	1.87202	−	1.08081i	0.192065	−	0.110889i
$96$	−1.40963	−	1.00646i	−0.143869	−	0.102721i
$97$	4.58560	−	7.94250i	0.465598	−	0.806439i	−0.533631	−	0.845718i	$-0.679173\pi$
$97$	4.58560	−	7.94250i	0.465598	−	0.806439i	0.999228	+	0.0392790i	$0.0125061\pi$
$98$	−2.08105	−	6.68350i	−0.210218	−	0.675136i
$99$	−4.07996	+	4.68472i	−0.410051	+	0.470832i
$100$	2.33784			0.233784
$101$	0.762652			0.0758867			0.0379434	−	0.999280i	$-0.487919\pi$
$101$	0.762652			0.0758867			0.0379434	+	0.999280i	$0.487919\pi$
$102$	−4.81516	+	2.19171i	−0.476772	+	0.217012i
$103$	−11.8342	+	6.83246i	−1.16606	+	0.673222i	−0.952748	−	0.303763i	$-0.901757\pi$
$103$	−11.8342	+	6.83246i	−1.16606	+	0.673222i	−0.213307	+	0.976985i	$0.568424\pi$
$104$	3.37445	−	1.27006i	0.330893	−	0.124540i
$105$	7.31687	+	1.53909i	0.714053	+	0.150200i
$106$	9.25742	−	5.34477i	0.899160	−	0.519130i
$107$	−7.90733	−	4.56530i	−0.764431	−	0.441344i	0.0664535	−	0.997790i	$-0.478832\pi$
$107$	−7.90733	−	4.56530i	−0.764431	−	0.441344i	−0.830884	+	0.556445i	$0.812165\pi$
$108$	−5.05425	+	1.20603i	−0.486346	+	0.116050i
$109$	−14.4120	−	8.32078i	−1.38042	−	0.796986i	−0.388211	−	0.921570i	$-0.626907\pi$
$109$	−14.4120	−	8.32078i	−1.38042	−	0.796986i	−0.992209	+	0.124584i	$0.960240\pi$
$110$		−	3.37869i		−	0.322145i
$111$	13.6848	+	1.32407i	1.29891	+	0.125675i
$112$	−2.62951	−	0.292738i	−0.248465	−	0.0276611i
$113$	7.84130	+	4.52717i	0.737647	+	0.425881i	0.821213	−	0.570622i	$-0.193298\pi$
$113$	7.84130	+	4.52717i	0.737647	+	0.425881i	−0.0835662	+	0.996502i	$0.526631\pi$
$114$	−0.220989	+	2.28402i	−0.0206975	+	0.213918i
$115$	−9.96719			−0.929445
$116$	2.79123	+	1.61152i	0.259159	+	0.149626i
$117$	3.77529	−	10.1364i	0.349025	−	0.937113i
$118$		−	13.5971i		−	1.25172i
$119$	−4.79024	+	6.50862i	−0.439120	+	0.596644i
$120$	1.64215	−	2.29996i	0.149907	−	0.209957i
$121$	−6.71193			−0.610175
$122$	−13.4689	−	7.77625i	−1.21941	−	0.704029i
$123$	8.61877	−	12.0713i	0.777128	−	1.08843i
$124$	−6.56832			−0.589852
$125$			11.9725i			1.07085i
$126$	−5.84308	+	5.37200i	−0.520543	+	0.478576i
$127$	1.70273	+	2.94922i	0.151093	+	0.261701i	0.931630	−	0.363409i	$-0.118387\pi$
$127$	1.70273	+	2.94922i	0.151093	+	0.261701i	−0.780536	+	0.625110i	$0.785054\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	0.899616	−	9.29795i	0.0792068	−	0.818639i
$130$	2.07225	+	5.50580i	0.181748	+	0.482891i
$131$	−5.11851	−	8.86551i	−0.447206	−	0.774584i	0.550997	−	0.834507i	$-0.314248\pi$
$131$	−5.11851	−	8.86551i	−0.447206	−	0.774584i	−0.998203	+	0.0599237i	$0.980914\pi$
$132$	2.91901	+	2.08414i	0.254067	+	0.181401i
$133$	1.40597	+	3.21087i	0.121913	+	0.278417i
$134$	−2.83485	−	1.63670i	−0.244894	−	0.141390i
$135$	−1.96777	−	8.24659i	−0.169359	−	0.709753i
$136$	1.52723	+	2.64525i	0.130959	+	0.226828i
$137$	−1.84724	−	3.19951i	−0.157820	−	0.273353i	0.776262	−	0.630410i	$-0.217113\pi$
$137$	−1.84724	−	3.19951i	−0.157820	−	0.273353i	−0.934082	+	0.357058i	$0.883780\pi$
$138$	6.14824	−	8.61111i	0.523373	−	0.733027i
$139$	−11.8635	−	6.84939i	−1.00625	−	0.580958i	−0.0961575	−	0.995366i	$-0.530655\pi$
$139$	−11.8635	−	6.84939i	−1.00625	−	0.580958i	−0.910091	+	0.414408i	$0.863989\pi$
$140$	0.477634	−	4.29034i	0.0403675	−	0.362600i
$141$	0.829981	−	1.16246i	0.0698970	−	0.0978965i
$142$	−4.59225	−	7.95402i	−0.385373	−	0.667486i
$143$	−6.98771	+	2.63000i	−0.584341	+	0.219932i
$144$	0.974089	+	2.83745i	0.0811741	+	0.236455i
$145$	−2.62937	+	4.55421i	−0.218358	+	0.378206i
$146$	−1.43611	−	2.48741i	−0.118853	−	0.205860i
$147$	−3.79316	+	11.5157i	−0.312854	+	0.949801i
$148$		−	7.93783i		−	0.652486i
$149$	19.3433			1.58466			0.792332	−	0.610090i	$-0.208867\pi$
$149$	19.3433			1.58466			0.792332	+	0.610090i	$0.208867\pi$
$150$	−3.29548	−	2.35293i	−0.269075	−	0.192116i
$151$	−2.94889	−	1.70254i	−0.239977	−	0.138551i	0.375189	−	0.926948i	$-0.377578\pi$
$151$	−2.94889	−	1.70254i	−0.239977	−	0.138551i	−0.615166	+	0.788397i	$0.710911\pi$
$152$	1.32484			0.107459
$153$	8.99343	+	1.75675i	0.727076	+	0.142025i
$154$	5.44509	+	0.606191i	0.438778	+	0.0488483i
$155$		−	10.7169i		−	0.860806i
$156$	−6.03498	−	1.60593i	−0.483185	−	0.128577i
$157$	−16.4481	−	9.49631i	−1.31270	−	0.757888i	−0.330158	−	0.943926i	$-0.607102\pi$
$157$	−16.4481	−	9.49631i	−1.31270	−	0.757888i	−0.982543	+	0.186038i	$0.940435\pi$
$158$	6.49314			0.516567
$159$	−18.4288	−	1.78306i	−1.46150	−	0.141406i
$160$	−1.41302	−	0.815806i	−0.111709	−	0.0644952i
$161$	1.78827	−	16.0631i	0.140936	−	1.26595i
$162$	8.33842	+	3.38684i	0.655129	+	0.266095i
$163$		−	1.12220i		−	0.0878974i	−0.999034	−	0.0439487i	$-0.986006\pi$
$163$		−	1.12220i		−	0.0878974i	0.999034	−	0.0439487i	$-0.0139938\pi$
$164$	−7.41619	−	4.28174i	−0.579107	−	0.334348i
$165$	−3.40050	+	4.76269i	−0.264729	+	0.370775i
$166$	5.94047	+	3.42973i	0.461070	+	0.266199i
$167$	−1.05294	+	0.607914i	−0.0814787	+	0.0470418i	−0.540186	−	0.841546i	$-0.681646\pi$
$167$	−1.05294	+	0.607914i	−0.0814787	+	0.0470418i	0.458707	+	0.888588i	$0.348313\pi$
$168$	3.41199	+	3.05914i	0.263241	+	0.236017i
$169$	9.77389	−	8.57153i	0.751838	−	0.659348i
$170$	−4.31602	+	2.49186i	−0.331024	+	0.191117i
$171$	2.61028	−	2.99720i	0.199613	−	0.229202i
$172$	−5.39324			−0.411231
$173$	−19.2174			−1.46107			−0.730537	−	0.682873i	$-0.760730\pi$
$173$	−19.2174			−1.46107			−0.730537	+	0.682873i	$0.760730\pi$
$174$	−2.31267	−	5.08089i	−0.175323	−	0.385181i
$175$	−6.14736	−	0.684373i	−0.464697	−	0.0517338i
$176$	1.03538	−	1.79334i	0.0780450	−	0.135178i
$177$	−13.6849	+	19.1669i	−1.02862	+	1.44067i
$178$	−0.929234	+	0.536494i	−0.0696491	+	0.0402119i
$179$			16.5953i			1.24039i	0.784447	+	0.620196i	$0.212947\pi$
$179$			16.5953i			1.24039i	−0.784447	+	0.620196i	$0.787053\pi$
$180$	−4.62963	+	1.58934i	−0.345072	+	0.118462i
$181$			21.1467i			1.57182i	0.618341	+	0.785910i	$0.287805\pi$
$181$			21.1467i			1.57182i	−0.618341	+	0.785910i	$0.712195\pi$
$182$	−9.24495	+	2.35180i	−0.685281	+	0.174327i
$183$	11.1596	+	24.5174i	0.824941	+	1.81238i
$184$	−5.29037	−	3.05440i	−0.390011	−	0.225173i
$185$	12.9515			0.952211
$186$	9.25887	+	6.61073i	0.678893	+	0.484722i
$187$	−3.16255	−	5.47769i	−0.231268	−	0.400568i
$188$	−0.714173	−	0.412328i	−0.0520864	−	0.0300721i
$189$	13.6432	−	1.69169i	0.992400	−	0.123053i
$190$			2.16163i			0.156821i
$191$			6.55386i			0.474221i	0.971483	+	0.237110i	$0.0762003\pi$
$191$			6.55386i			0.474221i	−0.971483	+	0.237110i	$0.923800\pi$
$192$	1.57643	−	0.717543i	0.113769	−	0.0517842i
$193$			9.94353i			0.715751i	0.933769	+	0.357875i	$0.116499\pi$
$193$			9.94353i			0.715751i	−0.933769	+	0.357875i	$0.883501\pi$
$194$	4.58560	+	7.94250i	0.329227	+	0.570238i
$195$	2.62026	−	9.84675i	0.187641	−	0.705140i
$196$	6.82861	+	1.53951i	0.487758	+	0.109965i
$197$	0.185155	+	0.320698i	0.0131918	+	0.0228488i	0.872546	−	0.488532i	$-0.162467\pi$
$197$	0.185155	+	0.320698i	0.0131918	+	0.0228488i	−0.859354	+	0.511381i	$0.829134\pi$
$198$	−2.01711	−	5.87571i	−0.143350	−	0.417568i
$199$	14.6253	−	8.44390i	1.03676	−	0.598572i	0.117844	−	0.993032i	$-0.462402\pi$
$199$	14.6253	−	8.44390i	1.03676	−	0.598572i	0.918913	+	0.394460i	$0.129068\pi$
$200$	−1.16892	+	2.02463i	−0.0826551	+	0.143163i
$201$	2.34881	+	5.16030i	0.165672	+	0.363979i
$202$	−0.381326	+	0.660476i	−0.0268300	+	0.0464709i
$203$	−6.86781	−	5.05459i	−0.482026	−	0.354763i
$204$	0.509499	−	5.26590i	0.0356720	−	0.368687i
$205$	6.98614	−	12.1003i	0.487933	−	0.845125i
$206$		−	13.6649i		−	0.952080i
$207$	−17.3334	+	5.95051i	−1.20476	+	0.413589i
$208$	−0.587322	+	3.55739i	−0.0407235	+	0.246661i
$209$	−2.74343			−0.189767
$210$	−4.99132	+	5.56705i	−0.344434	+	0.384163i
$211$	−0.132711	−	0.229862i	−0.00913618	−	0.0158243i	0.861421	−	0.507891i	$-0.169575\pi$
$211$	−0.132711	−	0.229862i	−0.00913618	−	0.0158243i	−0.870557	+	0.492067i	$0.836242\pi$
$212$			10.6895i			0.734161i
$213$	−1.53202	+	15.8341i	−0.104972	+	1.08493i
$214$	7.90733	−	4.56530i	0.540534	−	0.312078i
$215$		−	8.79969i		−	0.600134i
$216$	1.48267	−	4.98013i	0.100883	−	0.338855i
$217$	17.2714	+	1.92279i	1.17246	+	0.130528i
$218$	14.4120	−	8.32078i	0.976105	−	0.563554i
$219$	−0.479098	+	4.95170i	−0.0323744	+	0.334605i
$220$	2.92603	+	1.68934i	0.197273	+	0.113896i
$221$	8.51321	+	6.98659i	0.572660	+	0.469969i
$222$	−7.98909	+	11.1894i	−0.536192	+	0.750982i
$223$	−5.03909	−	8.72796i	−0.337442	−	0.584467i	0.646508	−	0.762907i	$-0.276229\pi$
$223$	−5.03909	−	8.72796i	−0.337442	−	0.584467i	−0.983951	+	0.178439i	$0.942895\pi$
$224$	1.56827	−	2.13085i	0.104785	−	0.142373i
$225$	2.27726	+	6.63351i	0.151818	+	0.442234i
$226$	−7.84130	+	4.52717i	−0.521595	+	0.301143i
$227$	−9.90698	+	5.71980i	−0.657550	+	0.379636i	−0.791343	−	0.611373i	$-0.790618\pi$
$227$	−9.90698	+	5.71980i	−0.657550	+	0.379636i	0.133793	+	0.991009i	$0.457284\pi$
$228$	−1.86753	−	1.33339i	−0.123680	−	0.0883062i
$229$	−4.74685	−	8.22179i	−0.313681	−	0.543311i	0.665475	−	0.746420i	$-0.268229\pi$
$229$	−4.74685	−	8.22179i	−0.313681	−	0.543311i	−0.979156	+	0.203109i	$0.934895\pi$
$230$	4.98359	−	8.63184i	0.328608	−	0.569166i
$231$	−7.06544	−	6.33475i	−0.464872	−	0.416796i
$232$	−2.79123	+	1.61152i	−0.183253	+	0.105801i
$233$	3.90224	−	2.25296i	0.255644	−	0.147596i	−0.366702	−	0.930339i	$-0.619513\pi$
$233$	3.90224	−	2.25296i	0.255644	−	0.147596i	0.622346	+	0.782742i	$0.286180\pi$
$234$	6.89076	+	8.33771i	0.450463	+	0.545053i
$235$	0.672760	−	1.16525i	0.0438860	−	0.0760128i
$236$	11.7755	+	6.79857i	0.766517	+	0.442549i
$237$	−9.15290	−	6.53507i	−0.594545	−	0.424498i
$238$	−3.24151	−	7.40277i	−0.210116	−	0.479851i
$239$	17.3876			1.12471			0.562354	−	0.826896i	$-0.309896\pi$
$239$	17.3876			1.12471			0.562354	+	0.826896i	$0.309896\pi$
$240$	1.17075	+	2.57212i	0.0755718	+	0.166030i
$241$	−0.714410	−	1.23739i	−0.0460192	−	0.0797076i	0.842098	−	0.539324i	$-0.181320\pi$
$241$	−0.714410	−	1.23739i	−0.0460192	−	0.0797076i	−0.888118	+	0.459616i	$0.847987\pi$
$242$	3.35596	−	5.81270i	0.215729	−	0.373654i
$243$	−8.34535	−	13.1664i	−0.535355	−	0.844627i
$244$	13.4689	−	7.77625i	0.862256	−	0.497824i
$245$	−2.51188	+	11.1416i	−0.160478	+	0.711814i
$246$	6.14466	+	13.4997i	0.391770	+	0.860711i
$247$	4.47061	−	1.68263i	0.284458	−	0.107063i
$248$	3.28416	−	5.68833i	0.208544	−	0.361209i
$249$	−4.92196	−	10.8135i	−0.311916	−	0.685275i
$250$	−10.3685	−	5.98626i	−0.655762	−	0.378604i
$251$	3.39863	−	5.88660i	0.214520	−	0.371559i	−0.738604	−	0.674139i	$-0.764515\pi$
$251$	3.39863	−	5.88660i	0.214520	−	0.371559i	0.953124	+	0.302580i	$0.0978480\pi$
$252$	−1.73074	−	7.74626i	−0.109027	−	0.487968i
$253$	10.9551	+	6.32494i	0.688743	+	0.397646i
$254$	−3.40547			−0.213678
$255$	8.59192	+	0.831305i	0.538047	+	0.0520583i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.07525	−	12.2547i	0.441342	−	0.764427i	−0.556447	−	0.830883i	$-0.687836\pi$
$257$	7.07525	−	12.2547i	0.441342	−	0.764427i	0.997789	+	0.0664559i	$0.0211692\pi$
$258$	7.60245	+	5.42807i	0.473308	+	0.337937i
$259$	−2.32370	+	20.8726i	−0.144388	+	1.29696i
$260$	−5.80429	−	0.958282i	−0.359967	−	0.0594301i
$261$	−1.85370	+	9.48975i	−0.114741	+	0.587401i
$262$	10.2370			0.632445
$263$			12.8664i			0.793376i	0.917953	+	0.396688i	$0.129841\pi$
$263$			12.8664i			0.793376i	−0.917953	+	0.396688i	$0.870159\pi$
$264$	−3.26442	+	1.48586i	−0.200911	+	0.0914486i
$265$	−17.4412			−1.07140
$266$	−3.48367	−	0.387830i	−0.213598	−	0.0237794i
$267$	1.84983	+	0.178979i	0.113208	+	0.0109533i
$268$	2.83485	−	1.63670i	0.173166	−	0.0999776i
$269$	13.6771	+	23.6895i	0.833909	+	1.44437i	0.894916	+	0.446236i	$0.147236\pi$
$269$	13.6771	+	23.6895i	0.833909	+	1.44437i	−0.0610064	+	0.998137i	$0.519431\pi$
$270$	8.12564	+	2.41915i	0.494511	+	0.147225i
$271$	−0.677785	+	1.17396i	−0.0411725	+	0.0713129i	−0.885877	−	0.463920i	$-0.846443\pi$
$271$	−0.677785	+	1.17396i	−0.0411725	+	0.0713129i	0.844705	+	0.535232i	$0.179776\pi$
$272$	−3.05447			−0.185204
$273$	15.3989	+	5.98947i	0.931984	+	0.362499i
$274$	3.69448			0.223192
$275$	2.42056	−	4.19253i	0.145965	−	0.252819i
$276$	4.38332	+	9.63009i	0.263845	+	0.579663i
$277$	10.4624	+	18.1215i	0.628627	+	1.08881i	0.987827	+	0.155554i	$0.0497161\pi$
$277$	10.4624	+	18.1215i	0.628627	+	1.08881i	−0.359200	+	0.933260i	$0.616951\pi$
$278$	11.8635	−	6.84939i	0.711525	−	0.410799i
$279$	−6.39813	−	18.6373i	−0.383046	−	1.11579i
$280$	3.47672	+	2.55881i	0.207774	+	0.152918i
$281$	4.08136			0.243474			0.121737	−	0.992562i	$-0.461154\pi$
$281$	4.08136			0.243474			0.121737	+	0.992562i	$0.461154\pi$
$282$	0.591726	+	1.30001i	0.0352368	+	0.0774146i
$283$		−	2.16327i		−	0.128593i	−0.997931	−	0.0642966i	$-0.979520\pi$
$283$		−	2.16327i		−	0.128593i	0.997931	−	0.0642966i	$-0.0204804\pi$
$284$	9.18451			0.545000
$285$	2.17558	−	3.04708i	0.128870	−	0.180494i
$286$	1.21621	−	7.36653i	0.0719158	−	0.435592i
$287$	18.2475	+	13.4299i	1.07712	+	0.792739i
$288$	−2.94435	−	0.575141i	−0.173498	−	0.0338905i
$289$	3.83511	−	6.64261i	0.225595	−	0.390741i
$290$	−2.62937	−	4.55421i	−0.154402	−	0.267432i
$291$	1.52980	−	15.8112i	0.0896783	−	0.926867i
$292$	2.87221			0.168084
$293$	5.29149	+	3.05504i	0.309132	+	0.178478i	0.646538	−	0.762882i	$-0.276216\pi$
$293$	5.29149	+	3.05504i	0.309132	+	0.178478i	−0.337406	+	0.941359i	$0.609549\pi$
$294$	−8.07633	−	9.04283i	−0.471021	−	0.527389i
$295$	−11.0926	+	19.2130i	−0.645838	+	1.11862i
$296$	6.87437	+	3.96892i	0.399564	+	0.230689i
$297$	−3.07027	+	10.3127i	−0.178155	+	0.598403i
$298$	−9.67165	+	16.7518i	−0.560263	+	0.970405i
$299$	−21.7314	−	3.58783i	−1.25676	−	0.207490i
$300$	3.68544	−	1.67750i	0.212779	−	0.0968506i
$301$	14.1816	+	1.57880i	0.817412	+	0.0910008i
$302$	2.94889	−	1.70254i	0.169689	−	0.0979703i
$303$	1.20227	−	0.547236i	0.0690685	−	0.0314379i
$304$	−0.662420	+	1.14734i	−0.0379924	+	0.0658047i
$305$	12.6878	+	21.9760i	0.726503	+	1.25834i
$306$	−6.01811	+	6.91017i	−0.344032	+	0.395028i
$307$	0.994225			0.0567434			0.0283717	−	0.999597i	$-0.490968\pi$
$307$	0.994225			0.0567434			0.0283717	+	0.999597i	$0.490968\pi$
$308$	−3.24752	+	4.41249i	−0.185045	+	0.251425i
$309$	−13.7532	+	19.2624i	−0.782389	+	1.09580i
$310$	9.28115	+	5.35847i	0.527134	+	0.304341i
$311$	0.596522	−	1.03321i	0.0338256	−	0.0585877i	−0.848617	−	0.529008i	$-0.822564\pi$
$311$	0.596522	−	1.03321i	0.0338256	−	0.0585877i	0.882443	+	0.470420i	$0.155898\pi$
$312$	4.40827	−	4.42348i	0.249569	−	0.250430i
$313$	22.7854	−	13.1551i	1.28791	−	0.743573i	0.309626	−	0.950859i	$-0.399796\pi$
$313$	22.7854	−	13.1551i	1.28791	−	0.743573i	0.978280	+	0.207285i	$0.0664629\pi$
$314$	16.4481	−	9.49631i	0.928219	−	0.535908i
$315$	12.6389	−	2.82390i	0.712121	−	0.159109i
$316$	−3.24657	+	5.62322i	−0.182634	+	0.316331i
$317$	11.3370	+	19.6363i	0.636751	+	1.10289i	0.986141	+	0.165908i	$0.0530555\pi$
$317$	11.3370	+	19.6363i	0.636751	+	1.10289i	−0.349390	+	0.936977i	$0.613611\pi$
$318$	10.7586	−	15.0683i	0.603310	−	0.844986i
$319$	5.77999	−	3.33708i	0.323617	−	0.186840i
$320$	1.41302	−	0.815806i	0.0789901	−	0.0456050i
$321$	−15.7412	−	1.52302i	−0.878586	−	0.0850069i
$322$	13.0169	+	9.58025i	0.725405	+	0.533886i
$323$	2.02334	+	3.50453i	0.112582	+	0.194997i
$324$	−7.10230	+	5.52787i	−0.394572	+	0.307104i
$325$	−1.37306	+	8.31662i	−0.0761639	+	0.461323i
$326$	0.971853	+	0.561100i	0.0538260	+	0.0310764i
$327$	−28.6900	−	2.77588i	−1.58656	−	0.153507i
$328$	7.41619	−	4.28174i	0.409490	−	0.236419i
$329$	1.75722	+	1.29328i	0.0968786	+	0.0713011i
$330$	−2.42436	−	5.32627i	−0.133456	−	0.293201i
$331$			5.13270i			0.282118i	0.990001	+	0.141059i	$0.0450508\pi$
$331$			5.13270i			0.282118i	−0.990001	+	0.141059i	$0.954949\pi$
$332$	−5.94047	+	3.42973i	−0.326025	+	0.188231i
$333$	22.5232	−	7.73216i	1.23427	−	0.423720i
$334$		−	1.21583i		−	0.0665271i
$335$	2.67047	+	4.62539i	0.145903	+	0.252712i
$336$	−4.35528	+	1.42530i	−0.237600	+	0.0777567i
$337$	8.20935			0.447192			0.223596	−	0.974682i	$-0.428220\pi$
$337$	8.20935			0.447192			0.223596	+	0.974682i	$0.428220\pi$
$338$	2.53622	+	12.7502i	0.137952	+	0.693519i
$339$	15.6097	+	1.51030i	0.847802	+	0.0820285i
$340$		−	4.98371i		−	0.270280i
$341$	−6.80072	+	11.7792i	−0.368280	+	0.637879i
$342$	1.29051	+	3.75917i	0.0697829	+	0.203273i
$343$	−17.5052	−	6.04714i	−0.945192	−	0.326515i
$344$	2.69662	−	4.67069i	0.145392	−	0.251827i
$345$	−15.7126	+	7.15189i	−0.845936	+	0.385045i
$346$	9.60871	−	16.6428i	0.516568	−	0.894721i
$347$	−9.27968	+	5.35762i	−0.498159	+	0.287612i	−0.727953	−	0.685627i	$-0.759528\pi$
$347$	−9.27968	+	5.35762i	−0.498159	+	0.287612i	0.229794	+	0.973239i	$0.426195\pi$
$348$	5.55651	+	0.537616i	0.297860	+	0.0288193i
$349$	−2.23834	−	3.87693i	−0.119816	−	0.207527i	0.799879	−	0.600162i	$-0.204897\pi$
$349$	−2.23834	−	3.87693i	−0.119816	−	0.207527i	−0.919695	+	0.392634i	$0.871564\pi$
$350$	3.66637	−	4.98159i	0.195976	−	0.266277i
$351$	−1.32185	−	18.6883i	−0.0705551	−	0.997508i
$352$	1.03538	+	1.79334i	0.0551861	+	0.0955852i
$353$		−	17.9679i		−	0.956335i	−0.878269	−	0.478168i	$-0.841301\pi$
$353$		−	17.9679i		−	0.956335i	0.878269	−	0.478168i	$-0.158699\pi$
$354$	−9.75653	−	21.4349i	−0.518554	−	1.13925i
$355$			14.9856i			0.795351i
$356$		−	1.07299i		−	0.0568682i
$357$	−2.88126	+	13.6976i	−0.152492	+	0.724953i
$358$	−14.3720	−	8.29766i	−0.759582	−	0.438545i
$359$	−2.59460	−	4.49398i	−0.136938	−	0.237183i	0.789398	−	0.613881i	$-0.210393\pi$
$359$	−2.59460	−	4.49398i	−0.136938	−	0.237183i	−0.926336	+	0.376698i	$0.877059\pi$
$360$	0.938408	−	4.80404i	0.0494584	−	0.253195i
$361$	−17.2448			−0.907621
$362$	−18.3135	−	10.5733i	−0.962539	−	0.555722i
$363$	−10.5809	+	4.81610i	−0.555352	+	0.252780i
$364$	2.58575	−	9.18226i	0.135530	−	0.481281i
$365$			4.68634i			0.245294i
$366$	−26.8125	−	2.59423i	−1.40151	−	0.135602i
$367$			16.4813i			0.860319i	0.902753	+	0.430160i	$0.141543\pi$
$367$			16.4813i			0.860319i	−0.902753	+	0.430160i	$0.858457\pi$
$368$	5.29037	−	3.05440i	0.275780	−	0.159221i
$369$	4.92521	−	25.2139i	0.256396	−	1.31258i
$370$	−6.47574	+	11.2163i	−0.336657	+	0.583108i
$371$	3.12923	−	28.1082i	0.162462	−	1.45931i
$372$	−10.3545	+	4.71305i	−0.536855	+	0.244360i
$373$	35.5875			1.84265			0.921325	−	0.388794i	$-0.127108\pi$
$373$	35.5875			1.84265			0.921325	+	0.388794i	$0.127108\pi$
$374$	6.32509			0.327063
$375$	8.59080	+	18.8738i	0.443627	+	0.974640i
$376$	0.714173	−	0.412328i	0.0368307	−	0.0212642i
$377$	−7.37216	+	8.98303i	−0.379685	+	0.462649i
$378$	−5.35657	+	12.6612i	−0.275512	+	0.651224i
$379$	25.3582	−	14.6406i	1.30256	−	0.752035i	0.321720	−	0.946835i	$-0.395739\pi$
$379$	25.3582	−	14.6406i	1.30256	−	0.752035i	0.980843	+	0.194800i	$0.0624057\pi$
$380$	−1.87202	−	1.08081i	−0.0960327	−	0.0554445i
$381$	4.80044	+	3.42746i	0.245934	+	0.175594i
$382$	−5.67581	−	3.27693i	−0.290400	−	0.167662i
$383$			10.1419i			0.518228i	0.965847	+	0.259114i	$0.0834305\pi$
$383$			10.1419i			0.518228i	−0.965847	+	0.259114i	$0.916569\pi$
$384$	−0.166804	+	1.72400i	−0.00851220	+	0.0879775i
$385$	−7.19948	−	5.29870i	−0.366920	−	0.270047i
$386$	−8.61135	−	4.97176i	−0.438306	−	0.253056i
$387$	−5.25350	−	15.3031i	−0.267050	−	0.777900i
$388$	−9.17121			−0.465598
$389$	−23.9026	−	13.8002i	−1.21191	−	0.699696i	−0.248734	−	0.968572i	$-0.580015\pi$
$389$	−23.9026	−	13.8002i	−1.21191	−	0.699696i	−0.963175	+	0.268876i	$0.913348\pi$
$390$	7.21741	+	7.19259i	0.365468	+	0.364211i
$391$		−	18.6591i		−	0.943632i
$392$	−4.74756	+	5.14399i	−0.239788	+	0.259811i
$393$	−14.4304	−	10.3031i	−0.727915	−	0.519723i
$394$	−0.370310			−0.0186560
$395$	−9.17493	−	5.29715i	−0.461641	−	0.266528i
$396$	6.09707	+	1.19098i	0.306389	+	0.0598492i
$397$	0.219678			0.0110253			0.00551266	−	0.999985i	$-0.498245\pi$
$397$	0.219678			0.0110253			0.00551266	+	0.999985i	$0.498245\pi$
$398$			16.8878i			0.846509i
$399$	4.52034	+	4.05286i	0.226300	+	0.202897i
$400$	−1.16892	−	2.02463i	−0.0584460	−	0.101231i
$401$	11.9325	−	20.6677i	0.595882	−	1.03210i	−0.397540	−	0.917585i	$-0.630136\pi$
$401$	11.9325	−	20.6677i	0.595882	−	1.03210i	0.993422	−	0.114513i	$-0.0365307\pi$
$402$	−5.64336	−	0.546019i	−0.281465	−	0.0272329i
$403$	3.85772	−	23.3661i	0.192167	−	1.16395i
$404$	−0.381326	−	0.660476i	−0.0189717	−	0.0328599i
$405$	−9.01934	−	11.5882i	−0.448175	−	0.575822i
$406$	7.81131	−	3.42040i	0.387669	−	0.169752i
$407$	−14.2352	−	8.21870i	−0.705613	−	0.407386i
$408$	4.30566	+	3.07419i	0.213162	+	0.152195i
$409$	3.87344	+	6.70900i	0.191529	+	0.331739i	0.945757	−	0.324874i	$-0.105322\pi$
$409$	3.87344	+	6.70900i	0.191529	+	0.331739i	−0.754228	+	0.656613i	$0.771989\pi$
$410$	6.98614	+	12.1003i	0.345021	+	0.597594i
$411$	−5.20783	−	3.71833i	−0.256883	−	0.183412i
$412$	11.8342	+	6.83246i	0.583028	+	0.336611i
$413$	−28.9735	−	21.3240i	−1.42569	−	1.04929i
$414$	3.51342	−	17.9864i	0.172675	−	0.883985i
$415$	−5.59599	−	9.69254i	−0.274696	−	0.475788i
$416$	−2.78713	−	2.28733i	−0.136650	−	0.112146i
$417$	−23.6167	−	2.28502i	−1.15652	−	0.111898i
$418$	1.37172	−	2.37588i	0.0670929	−	0.116208i
$419$	−1.65804	−	2.87182i	−0.0810008	−	0.140297i	0.822679	−	0.568506i	$-0.192478\pi$
$419$	−1.65804	−	2.87182i	−0.0810008	−	0.140297i	−0.903680	+	0.428208i	$0.859145\pi$
$420$	−2.32554	−	7.10614i	−0.113475	−	0.346744i
$421$		−	25.2793i		−	1.23204i	−0.787731	−	0.616019i	$-0.788744\pi$
$421$		−	25.2793i		−	1.23204i	0.787731	−	0.616019i	$-0.211256\pi$
$422$	0.265421			0.0129205
$423$	0.474294	−	2.42808i	0.0230610	−	0.118057i
$424$	−9.25742	−	5.34477i	−0.449580	−	0.259565i
$425$	−7.14086			−0.346383
$426$	−12.9467	−	9.24381i	−0.627271	−	0.447864i
$427$	−37.6929	+	16.5049i	−1.82409	+	0.798726i
$428$			9.13060i			0.441344i
$429$	−9.12849	+	9.15999i	−0.440728	+	0.442249i
$430$	7.62075	+	4.39984i	0.367505	+	0.212179i
$431$	24.8809			1.19847			0.599235	−	0.800573i	$-0.295472\pi$
$431$	24.8809			1.19847			0.599235	+	0.800573i	$0.295472\pi$
$432$	3.57158	+	3.77410i	0.171838	+	0.181581i
$433$	17.2062	+	9.93398i	0.826875	+	0.477396i	0.852781	−	0.522268i	$-0.174914\pi$
$433$	17.2062	+	9.93398i	0.826875	+	0.477396i	−0.0259066	+	0.999664i	$0.508247\pi$
$434$	−10.3009	+	13.9961i	−0.494459	+	0.671834i
$435$	−0.877182	+	9.06608i	−0.0420576	+	0.434685i
$436$			16.6416i			0.796986i
$437$	−7.00889	−	4.04659i	−0.335281	−	0.193574i
$438$	−4.04875	−	2.89076i	−0.193457	−	0.138126i
$439$	1.13469	+	0.655115i	0.0541559	+	0.0312670i	0.526834	−	0.849969i	$-0.323379\pi$
$439$	1.13469	+	0.655115i	0.0541559	+	0.0312670i	−0.472678	+	0.881235i	$0.656712\pi$
$440$	−2.92603	+	1.68934i	−0.139493	+	0.0805363i
$441$	2.28338	+	20.8755i	0.108733	+	0.994071i
$442$	−10.3072	+	3.87936i	−0.490262	+	0.184522i
$443$	13.3621	−	7.71462i	0.634853	−	0.366533i	−0.147776	−	0.989021i	$-0.547211\pi$
$443$	13.3621	−	7.71462i	0.634853	−	0.366533i	0.782629	+	0.622488i	$0.213878\pi$
$444$	−5.69574	−	12.5134i	−0.270308	−	0.593862i
$445$	1.75070			0.0829911
$446$	10.0782			0.477216
$447$	30.4933	−	13.8796i	1.44229	−	0.656485i
$448$	1.06124	+	2.42359i	0.0501386	+	0.114504i
$449$	10.2266	−	17.7130i	0.482625	−	0.835930i	−0.517176	−	0.855879i	$-0.673017\pi$
$449$	10.2266	−	17.7130i	0.482625	−	0.835930i	0.999801	+	0.0199485i	$0.00635023\pi$
$450$	−6.88342	−	1.34459i	−0.324488	−	0.0633845i
$451$	−15.3572	+	8.86648i	−0.723142	+	0.417506i
$452$		−	9.05435i		−	0.425881i
$453$	−5.87036	−	0.567983i	−0.275814	−	0.0266862i
$454$		−	11.4396i		−	0.536887i
$455$	14.9819	+	4.21894i	0.702362	+	0.197787i
$456$	2.08852	−	0.950630i	0.0978038	−	0.0445173i
$457$	−28.1572	−	16.2566i	−1.31714	−	0.760450i	−0.333871	−	0.942619i	$-0.608355\pi$
$457$	−28.1572	−	16.2566i	−1.31714	−	0.760450i	−0.983267	+	0.182169i	$0.941688\pi$
$458$	9.49370			0.443612
$459$	15.4381	−	3.68378i	0.720587	−	0.171944i
$460$	4.98359	+	8.63184i	0.232361	+	0.402461i
$461$	20.3615	+	11.7557i	0.948329	+	0.547518i	0.892562	−	0.450926i	$-0.148906\pi$
$461$	20.3615	+	11.7557i	0.948329	+	0.547518i	0.0557678	+	0.998444i	$0.482239\pi$
$462$	9.01878	−	2.95147i	0.419592	−	0.137315i
$463$			33.0233i			1.53472i	0.641214	+	0.767362i	$0.278431\pi$
$463$			33.0233i			1.53472i	−0.641214	+	0.767362i	$0.721569\pi$
$464$		−	3.22304i		−	0.149626i
$465$	−7.68987	−	16.8945i	−0.356609	−	0.783465i
$466$			4.50592i			0.208733i
$467$	−14.2621	−	24.7027i	−0.659972	−	1.14310i	−0.980623	−	0.195907i	$-0.937235\pi$
$467$	−14.2621	−	24.7027i	−0.659972	−	1.14310i	0.320651	−	0.947197i	$-0.396098\pi$
$468$	−10.6660	+	1.79872i	−0.493038	+	0.0831458i
$469$	−7.93339	+	3.47386i	−0.366330	+	0.160408i
$470$	0.672760	+	1.16525i	0.0310321	+	0.0537491i
$471$	−32.7433	−	3.16805i	−1.50873	−	0.145976i
$472$	−11.7755	+	6.79857i	−0.542010	+	0.312929i
$473$	−5.58407	+	9.67190i	−0.256756	+	0.444714i
$474$	10.2360	−	4.65911i	0.470154	−	0.214000i
$475$	−1.54863	+	2.68231i	−0.0710561	+	0.123073i
$476$	8.03175	+	0.894158i	0.368134	+	0.0409836i
$477$	−30.3311	+	10.4126i	−1.38877	+	0.476759i
$478$	−8.69379	+	15.0581i	−0.397645	+	0.688741i
$479$			34.8785i			1.59364i	0.604216	+	0.796821i	$0.293487\pi$
$479$			34.8785i			1.59364i	−0.604216	+	0.796821i	$0.706513\pi$
$480$	−2.81290	−	0.272160i	−0.128391	−	0.0124224i
$481$	28.2380	+	4.66206i	1.28754	+	0.212572i
$482$	1.42882			0.0650810
$483$	−8.70689	−	26.6055i	−0.396177	−	1.21059i
$484$	3.35596	+	5.81270i	0.152544	+	0.264214i
$485$		−	14.9639i		−	0.679474i
$486$	15.5751	−	0.644067i	0.706503	−	0.0292155i
$487$	0.192670	−	0.111238i	0.00873073	−	0.00504069i	−0.495628	−	0.868535i	$-0.665062\pi$
$487$	0.192670	−	0.111238i	0.00873073	−	0.00504069i	0.504359	+	0.863494i	$0.331729\pi$
$488$			15.5525i			0.704029i
$489$	−0.805226	−	1.76907i	−0.0364136	−	0.0800000i
$490$	−8.39301	−	7.74618i	−0.379157	−	0.349937i
$491$	25.2390	−	14.5717i	1.13902	−	0.657613i	0.192832	−	0.981232i	$-0.438233\pi$
$491$	25.2390	−	14.5717i	1.13902	−	0.657613i	0.946188	+	0.323619i	$0.104899\pi$
$492$	−14.7634	−	1.42843i	−0.665587	−	0.0643984i
$493$	−8.52573	−	4.92233i	−0.383979	−	0.221691i
$494$	−0.778107	+	4.71298i	−0.0350087	+	0.212047i
$495$	−1.94322	+	9.94805i	−0.0873414	+	0.447132i
$496$	3.28416	+	5.68833i	0.147463	+	0.255413i
$497$	−24.1507	−	2.68865i	−1.08331	−	0.120602i
$498$	11.8257	+	1.14419i	0.529923	+	0.0512723i
$499$	−34.1625	+	19.7237i	−1.52932	+	0.882954i	−0.529932	+	0.848040i	$0.677782\pi$
$499$	−34.1625	+	19.7237i	−1.52932	+	0.882954i	−0.999390	+	0.0349141i	$0.988884\pi$
$500$	10.3685	−	5.98626i	0.463693	−	0.267714i
$501$	−1.22368	+	1.71386i	−0.0546699	+	0.0765697i
$502$	3.39863	+	5.88660i	0.151688	+	0.262732i
$503$	15.0219	−	26.0187i	0.669793	−	1.16012i	−0.308169	−	0.951332i	$-0.599716\pi$
$503$	15.0219	−	26.0187i	0.669793	−	1.16012i	0.977962	−	0.208784i	$-0.0669505\pi$
$504$	7.57383	+	2.37426i	0.337365	+	0.105758i
$505$	1.07764	−	0.622177i	0.0479544	−	0.0276865i
$506$	−10.9551	+	6.32494i	−0.487015	+	0.281178i
$507$	9.25741	−	20.5256i	0.411136	−	0.911574i
$508$	1.70273	−	2.94922i	0.0755466	−	0.130851i
$509$	34.5427	+	19.9432i	1.53108	+	0.883969i	0.999312	+	0.0370772i	$0.0118048\pi$
$509$	34.5427	+	19.9432i	1.53108	+	0.883969i	0.531766	+	0.846891i	$0.321529\pi$
$510$	−5.01589	+	7.02517i	−0.222107	+	0.311080i
$511$	−7.55251	−	0.840805i	−0.334103	−	0.0371950i
$512$	1.00000			0.0441942
$513$	1.96431	−	6.59787i	0.0867262	−	0.291303i
$514$	7.07525	+	12.2547i	0.312076	+	0.540532i
$515$	−11.1479	+	19.3088i	−0.491236	+	0.850846i
$516$	−8.50207	+	3.86989i	−0.374283	+	0.170362i
$517$	−1.47889	+	0.853835i	−0.0650413	+	0.0375516i
$518$	−16.9143	−	12.4487i	−0.743173	−	0.546964i
$519$	−30.2949	+	13.7893i	−1.32980	+	0.605285i
$520$	3.73204	−	4.54752i	0.163661	−	0.199422i
$521$	11.5449	−	19.9963i	0.505789	−	0.876052i	−0.494188	−	0.869355i	$-0.664535\pi$
$521$	11.5449	−	19.9963i	0.505789	−	0.876052i	0.999978	−	0.00669760i	$-0.00213193\pi$
$522$	−7.29152	−	6.35023i	−0.319141	−	0.277942i
$523$	−21.6044	−	12.4733i	−0.944696	−	0.545420i	−0.0532666	−	0.998580i	$-0.516963\pi$
$523$	−21.6044	−	12.4733i	−0.944696	−	0.545420i	−0.891429	+	0.453160i	$0.850297\pi$
$524$	−5.11851	+	8.86551i	−0.223603	+	0.387292i
$525$	−10.1820	+	3.33213i	−0.444377	+	0.145426i
$526$	−11.1426	−	6.43320i	−0.485842	−	0.280501i
$527$	20.0627			0.873946
$528$	0.345413	−	3.57000i	0.0150322	−	0.155364i
$529$	7.15868	+	12.3992i	0.311247	+	0.539096i
$530$	8.72060	−	15.1045i	0.378799	−	0.656098i
$531$	−7.82027	+	40.0348i	−0.339371	+	1.73736i
$532$	2.07771	−	2.82304i	0.0900801	−	0.122394i
$533$	19.5875	−	23.8675i	0.848430	−	1.03382i
$534$	−1.07992	+	1.51251i	−0.0467325	+	0.0654527i
$535$	−14.8976			−0.644080
$536$			3.27341i			0.141390i
$537$	11.9079	+	26.1613i	0.513862	+	1.12895i
$538$	−27.3543			−1.17933
$539$	9.83109	−	10.6520i	0.423455	−	0.458815i
$540$	−6.15787	+	5.82744i	−0.264992	+	0.250773i
$541$	29.0831	−	16.7911i	1.25038	−	0.721907i	0.279195	−	0.960234i	$-0.409932\pi$
$541$	29.0831	−	16.7911i	1.25038	−	0.721907i	0.971185	+	0.238327i	$0.0765990\pi$
$542$	−0.677785	−	1.17396i	−0.0291134	−	0.0504258i
$543$	15.1736	+	33.3362i	0.651164	+	1.43059i
$544$	1.52723	−	2.64525i	0.0654796	−	0.113414i
$545$	−27.1526			−1.16309
$546$	−12.8865	+	10.3411i	−0.551491	+	0.442558i
$547$	−25.6327			−1.09597			−0.547987	−	0.836487i	$-0.684606\pi$
$547$	−25.6327			−1.09597			−0.547987	+	0.836487i	$0.684606\pi$
$548$	−1.84724	+	3.19951i	−0.0789102	+	0.136676i
$549$	35.1846	+	30.6425i	1.50164	+	1.30779i
$550$	2.42056	+	4.19253i	0.103213	+	0.178770i
$551$	−3.69793	+	2.13500i	−0.157537	+	0.0909542i
$552$	−10.5316	−	1.01897i	−0.448253	−	0.0433704i
$553$	10.1830	−	13.8359i	0.433025	−	0.588363i
$554$	−20.9249			−0.889013
$555$	20.4171	−	9.29324i	0.866657	−	0.394476i
$556$			13.6988i			0.580958i
$557$	30.0323			1.27251			0.636255	−	0.771479i	$-0.280483\pi$
$557$	30.0323			1.27251			0.636255	+	0.771479i	$0.280483\pi$
$558$	19.3394	+	3.77771i	0.818704	+	0.159923i
$559$	3.16757	−	19.1859i	0.133974	−	0.811477i
$560$	−3.95436	+	1.73152i	−0.167102	+	0.0731703i
$561$	−8.91601	−	6.36593i	−0.376434	−	0.268770i
$562$	−2.04068	+	3.53456i	−0.0860810	+	0.149097i
$563$	−13.0895	−	22.6717i	−0.551658	−	0.955500i	−0.998155	−	0.0607150i	$-0.980662\pi$
$563$	−13.0895	−	22.6717i	−0.551658	−	0.955500i	0.446497	−	0.894785i	$-0.352671\pi$
$564$	−1.42171	−	0.137556i	−0.0598647	−	0.00579216i
$565$	14.7732			0.621513
$566$	1.87345	+	1.08164i	0.0787469	+	0.0454645i
$567$	20.2938	−	12.4565i	0.852258	−	0.523122i
$568$	−4.59225	+	7.95402i	−0.192687	+	0.333743i
$569$	5.07189	+	2.92826i	0.212625	+	0.122759i	0.602531	−	0.798096i	$-0.294159\pi$
$569$	5.07189	+	2.92826i	0.212625	+	0.122759i	−0.389906	+	0.920855i	$0.627492\pi$
$570$	1.55106	+	3.40765i	0.0649667	+	0.142731i
$571$	15.5567	−	26.9450i	0.651027	−	1.12761i	−0.331847	−	0.943333i	$-0.607672\pi$
$571$	15.5567	−	26.9450i	0.651027	−	1.12761i	0.982874	−	0.184279i	$-0.0589950\pi$
$572$	5.77150	+	4.73653i	0.241319	+	0.198044i
$573$	4.70268	+	10.3317i	0.196457	+	0.431613i
$574$	−20.7543	+	9.08786i	−0.866269	+	0.379320i
$575$	12.3680	−	7.14069i	0.515783	−	0.297787i
$576$	1.97026	−	2.26231i	0.0820943	−	0.0942631i
$577$	−2.11078	+	3.65597i	−0.0878727	+	0.152200i	−0.906612	−	0.421966i	$-0.861340\pi$
$577$	−2.11078	+	3.65597i	−0.0878727	+	0.152200i	0.818739	+	0.574166i	$0.194674\pi$
$578$	3.83511	+	6.64261i	0.159520	+	0.276296i
$579$	7.13491	+	15.6753i	0.296517	+	0.651442i
$580$	5.25875			0.218358
$581$	16.6245	−	7.27950i	0.689701	−	0.302005i
$582$	12.9280	+	9.23043i	0.535882	+	0.382613i
$583$	19.1699	+	11.0678i	0.793938	+	0.458380i
$584$	−1.43611	+	2.48741i	−0.0594265	+	0.102930i
$585$	−2.93481	−	17.4029i	−0.121340	−	0.719520i
$586$	−5.29149	+	3.05504i	−0.218590	+	0.126203i
$587$	−25.6971	+	14.8362i	−1.06063	+	0.612358i	−0.925608	−	0.378484i	$-0.876445\pi$
$587$	−25.6971	+	14.8362i	−1.06063	+	0.612358i	−0.135027	+	0.990842i	$0.543112\pi$
$588$	11.8695	−	2.47289i	0.489490	−	0.101980i
$589$	4.35098	−	7.53612i	0.179279	−	0.310521i
$590$	−11.0926	−	19.2130i	−0.456676	−	0.790986i
$591$	0.521999	+	0.372701i	0.0214722	+	0.0153309i
$592$	−6.87437	+	3.96892i	−0.282535	+	0.163121i
$593$	32.5826	−	18.8116i	1.33801	−	0.772500i	0.351497	−	0.936189i	$-0.385673\pi$
$593$	32.5826	−	18.8116i	1.33801	−	0.772500i	0.986512	+	0.163690i	$0.0523396\pi$
$594$	−7.39591	−	7.81528i	−0.303458	−	0.320665i
$595$	−1.45892	+	13.1047i	−0.0598098	+	0.537240i
$596$	−9.67165	−	16.7518i	−0.396166	−	0.686180i
$597$	16.9968	−	23.8055i	0.695635	−	0.974294i
$598$	13.9728	−	17.0260i	0.571392	−	0.696246i
$599$	31.7637	+	18.3388i	1.29783	+	0.749302i	0.980029	−	0.198856i	$-0.0637226\pi$
$599$	31.7637	+	18.3388i	1.29783	+	0.749302i	0.317800	+	0.948158i	$0.397056\pi$
$600$	−0.389962	+	4.03044i	−0.0159201	+	0.164542i
$601$	−3.55065	+	2.04997i	−0.144834	+	0.0836199i	−0.570666	−	0.821182i	$-0.693315\pi$
$601$	−3.55065	+	2.04997i	−0.144834	+	0.0836199i	0.425832	+	0.904802i	$0.359981\pi$
$602$	−8.45807	+	11.4922i	−0.344725	+	0.468387i
$603$	7.40548	+	6.44948i	0.301574	+	0.262643i
$604$			3.40508i			0.138551i
$605$	−9.48407	+	5.47563i	−0.385582	+	0.222616i
$606$	−0.127214	+	1.31481i	−0.00516770	+	0.0534106i
$607$		−	4.44726i		−	0.180509i	−0.995919	−	0.0902543i	$-0.971232\pi$
$607$		−	4.44726i		−	0.180509i	0.995919	−	0.0902543i	$-0.0287680\pi$
$608$	−0.662420	−	1.14734i	−0.0268647	−	0.0465310i
$609$	−14.4535	−	3.04027i	−0.585686	−	0.123198i
$610$	−25.3757			−1.02743
$611$	1.88626	−	2.29843i	0.0763100	−	0.0929843i
$612$	−2.97533	−	8.66692i	−0.120270	−	0.350339i
$613$			5.82405i			0.235231i	0.993059	+	0.117616i	$0.0375251\pi$
$613$			5.82405i			0.235231i	−0.993059	+	0.117616i	$0.962475\pi$
$614$	−0.497113	+	0.861024i	−0.0200618	+	0.0347481i
$615$	2.33064	−	24.0882i	0.0939803	−	0.971330i
$616$	−2.19757	−	5.01869i	−0.0885426	−	0.202209i
$617$	−16.4572	+	28.5046i	−0.662540	+	1.14755i	0.317406	+	0.948290i	$0.397188\pi$
$617$	−16.4572	+	28.5046i	−0.662540	+	1.14755i	−0.979946	+	0.199263i	$0.936145\pi$
$618$	−9.80517	−	21.5418i	−0.394422	−	0.866538i
$619$	13.6240	−	23.5975i	0.547595	−	0.948463i	−0.450843	−	0.892603i	$-0.648877\pi$
$619$	13.6240	−	23.5975i	0.547595	−	0.948463i	0.998439	−	0.0558598i	$-0.0177900\pi$
$620$	−9.28115	+	5.35847i	−0.372740	+	0.215202i
$621$	−23.0552	+	21.8180i	−0.925173	+	0.875528i
$622$	0.596522	+	1.03321i	0.0239183	+	0.0414278i
$623$	−0.314104	+	2.82143i	−0.0125843	+	0.113038i
$624$	1.62671	+	6.02941i	0.0651206	+	0.241370i
$625$	3.92265	+	6.79423i	0.156906	+	0.271769i
$626$			26.3103i			1.05157i
$627$	−4.32483	+	1.96853i	−0.172717	+	0.0786156i
$628$			18.9926i			0.757888i
$629$			24.2459i			0.966746i
$630$	−3.87387	+	12.3576i	−0.154339	+	0.492337i
$631$	1.34761	+	0.778043i	0.0536475	+	0.0309734i	0.526584	−	0.850123i	$-0.323473\pi$
$631$	1.34761	+	0.778043i	0.0536475	+	0.0309734i	−0.472936	+	0.881097i	$0.656806\pi$
$632$	−3.24657	−	5.62322i	−0.129142	−	0.223680i
$633$	−0.374145	−	0.267135i	−0.0148709	−	0.0106177i
$634$	−22.6741			−0.900502
$635$	4.81199	+	2.77820i	0.190958	+	0.110250i
$636$	7.67021	+	16.8513i	0.304144	+	0.668198i
$637$	−9.48724	+	23.3879i	−0.375898	+	0.926661i
$638$			6.67415i			0.264232i
$639$	8.94653	+	26.0606i	0.353919	+	1.03094i
$640$			1.63161i			0.0644952i
$641$	−22.8839	+	13.2120i	−0.903861	+	0.521844i	−0.878451	−	0.477833i	$-0.841423\pi$
$641$	−22.8839	+	13.2120i	−0.903861	+	0.521844i	−0.0254102	+	0.999677i	$0.508089\pi$
$642$	9.18956	−	12.8707i	0.362683	−	0.507967i
$643$	−18.5300	+	32.0948i	−0.730751	+	1.26570i	0.225812	+	0.974171i	$0.427496\pi$
$643$	−18.5300	+	32.0948i	−0.730751	+	1.26570i	−0.956563	+	0.291526i	$0.905837\pi$
$644$	−14.8052	+	6.48287i	−0.583407	+	0.255461i
$645$	−6.31415	−	13.8721i	−0.248620	−	0.546213i
$646$	−4.04668			−0.159215
$647$	−37.5321			−1.47554			−0.737769	−	0.675053i	$-0.764121\pi$
$647$	−37.5321			−1.47554			−0.737769	+	0.675053i	$0.764121\pi$
$648$	−1.23612	−	8.91471i	−0.0485596	−	0.350203i
$649$	24.3842	−	14.0782i	0.957165	−	0.552619i
$650$	−6.51587	−	5.34742i	−0.255573	−	0.209743i
$651$	28.6069	−	9.36185i	1.12119	−	0.366920i
$652$	−0.971853	+	0.561100i	−0.0380607	+	0.0219744i
$653$	−37.0507	−	21.3912i	−1.44990	−	0.837103i	−0.451430	−	0.892307i	$-0.649086\pi$
$653$	−37.0507	−	21.3912i	−1.44990	−	0.837103i	−0.998475	+	0.0552038i	$0.982419\pi$
$654$	16.7490	−	23.4584i	0.654938	−	0.917295i
$655$	−14.4651	−	8.35142i	−0.565198	−	0.326317i
$656$			8.56348i			0.334348i
$657$	2.79779	+	8.14978i	0.109152	+	0.317953i
$658$	−1.99863	+	0.875154i	−0.0779146	+	0.0341170i
$659$	28.1909	+	16.2760i	1.09816	+	0.634024i	0.935738	−	0.352696i	$-0.114735\pi$
$659$	28.1909	+	16.2760i	1.09816	+	0.634024i	0.162425	+	0.986721i	$0.448068\pi$
$660$	5.82486	+	0.563580i	0.226732	+	0.0219373i
$661$	−20.2885			−0.789130			−0.394565	−	0.918868i	$-0.629105\pi$
$661$	−20.2885			−0.789130			−0.394565	+	0.918868i	$0.629105\pi$
$662$	−4.44504	−	2.56635i	−0.172762	−	0.0997439i
$663$	18.4337	+	4.90527i	0.715904	+	0.190505i
$664$		−	6.85946i		−	0.266199i
$665$	4.60610	+	3.39002i	0.178617	+	0.131459i
$666$	−4.56538	+	23.3718i	−0.176905	+	0.905638i
$667$	19.6889			0.762356
$668$	1.05294	+	0.607914i	0.0407394	+	0.0235209i
$669$	−14.2065	−	10.1433i	−0.549254	−	0.392161i
$670$	−5.34093			−0.206338
$671$		−	32.2056i		−	1.24328i
$672$	0.943293	−	4.48444i	0.0363883	−	0.172991i
$673$	−11.3708	−	19.6948i	−0.438312	−	0.759179i	0.559247	−	0.829001i	$-0.311090\pi$
$673$	−11.3708	−	19.6948i	−0.438312	−	0.759179i	−0.997559	+	0.0698219i	$0.977757\pi$
$674$	−4.10467	+	7.10950i	−0.158106	+	0.273848i
$675$	8.34978	+	8.82324i	0.321383	+	0.339607i
$676$	−12.3101	−	4.17867i	−0.473466	−	0.160718i
$677$	−16.2207	−	28.0950i	−0.623412	−	1.07978i	−0.988846	−	0.148943i	$-0.952413\pi$
$677$	−16.2207	−	28.0950i	−0.623412	−	1.07978i	0.365434	−	0.930837i	$-0.380921\pi$
$678$	−9.11281	+	12.7632i	−0.349975	+	0.490169i
$679$	24.1158	+	2.68476i	0.925478	+	0.103032i
$680$	4.31602	+	2.49186i	0.165512	+	0.0955583i
$681$	−11.5135	+	16.1256i	−0.441197	+	0.617933i
$682$	−6.80072	−	11.7792i	−0.260413	−	0.451049i
$683$	3.59703	+	6.23024i	0.137637	+	0.238393i	0.926602	−	0.376045i	$-0.122716\pi$
$683$	3.59703	+	6.23024i	0.137637	+	0.238393i	−0.788965	+	0.614438i	$0.789383\pi$
$684$	−3.90080	−	0.761970i	−0.149151	−	0.0291347i
$685$	−5.22037	−	3.01398i	−0.199460	−	0.115158i
$686$	13.9896	−	12.1364i	0.534125	−	0.463369i
$687$	−13.3826	−	9.55500i	−0.510577	−	0.364546i
$688$	2.69662	+	4.67069i	0.102808	+	0.178068i
$689$	−38.0269	−	6.27820i	−1.44871	−	0.239181i
$690$	1.66257	−	17.1834i	0.0632930	−	0.654162i
$691$	13.0186	−	22.5489i	0.495252	−	0.857801i	−0.504733	−	0.863275i	$-0.668409\pi$
$691$	13.0186	−	22.5489i	0.495252	−	0.857801i	0.999985	+	0.00547440i	$0.00174257\pi$
$692$	9.60871	+	16.6428i	0.365268	+	0.632664i
$693$	−15.6836	−	4.91654i	−0.595772	−	0.186764i
$694$		−	10.7152i		−	0.406745i
$695$	−22.3511			−0.847826
$696$	−3.24385	+	4.54327i	−0.122958	+	0.172212i
$697$	22.6525	+	13.0784i	0.858025	+	0.495381i
$698$	4.47669			0.169445
$699$	4.53501	−	6.35166i	0.171530	−	0.240242i
$700$	2.48100	+	5.66596i	0.0937729	+	0.214153i
$701$		−	26.3672i		−	0.995877i	−0.867212	−	0.497938i	$-0.834091\pi$
$701$		−	26.3672i		−	0.995877i	0.867212	−	0.497938i	$-0.165909\pi$
$702$	16.8455	+	8.19940i	0.635791	+	0.309466i
$703$	9.10743	+	5.25818i	0.343493	+	0.198316i
$704$	−2.07077			−0.0780450
$705$	0.224438	−	2.31968i	0.00845284	−	0.0873640i
$706$	15.5607	+	8.98395i	0.585633	+	0.338116i
$707$	0.809353	+	1.84835i	0.0304389	+	0.0695145i
$708$	23.4415	+	2.26806i	0.880984	+	0.0852389i
$709$		−	28.2847i		−	1.06225i	−0.847292	−	0.531127i	$-0.821769\pi$
$709$		−	28.2847i		−	1.06225i	0.847292	−	0.531127i	$-0.178231\pi$
$710$	−12.9779	−	7.49278i	−0.487051	−	0.281199i
$711$	−19.1181	−	3.73447i	−0.716985	−	0.140054i
$712$	0.929234	+	0.536494i	0.0348245	+	0.0201060i
$713$	−34.7488	+	20.0622i	−1.30135	+	0.751337i
$714$	−10.4218	−	9.34403i	−0.390027	−	0.349692i
$715$	−7.72819	+	9.41685i	−0.289018	+	0.352170i
$716$	14.3720	−	8.29766i	0.537105	−	0.310098i
$717$	27.4103	−	12.4763i	1.02366	−	0.465937i
$718$	5.18920			0.193659
$719$	18.6039			0.693807			0.346904	−	0.937901i	$-0.387233\pi$
$719$	18.6039			0.693807			0.346904	+	0.937901i	$0.387233\pi$
$720$	3.69122	+	3.21471i	0.137564	+	0.119805i
$721$	−29.1179	−	21.4303i	−1.08441	−	0.798106i
$722$	8.62240	−	14.9344i	0.320893	−	0.555802i
$723$	−2.01410	−	1.43805i	−0.0749053	−	0.0534815i
$724$	18.3135	−	10.5733i	0.680618	−	0.392955i
$725$		−	7.53494i		−	0.279841i
$726$	1.11958	−	11.5714i	0.0415515	−	0.429453i
$727$			48.9063i			1.81383i	0.421309	+	0.906917i	$0.361571\pi$
$727$			48.9063i			1.81383i	−0.421309	+	0.906917i	$0.638429\pi$
$728$	6.65920	+	6.83045i	0.246806	+	0.253154i
$729$	−22.6034	−	14.7678i	−0.837161	−	0.546956i
$730$	−4.05849	−	2.34317i	−0.150211	−	0.0867246i
$731$	16.4735			0.609294
$732$	15.6529	−	21.9232i	0.578549	−	0.810305i
$733$	−0.276176	−	0.478352i	−0.0102008	−	0.0176683i	0.860880	−	0.508808i	$-0.169914\pi$
$733$	−0.276176	−	0.478352i	−0.0102008	−	0.0176683i	−0.871081	+	0.491140i	$0.836580\pi$
$734$	−14.2733	−	8.24067i	−0.526836	−	0.304169i
$735$	4.03480	+	19.3664i	0.148826	+	0.714341i
$736$			6.10879i			0.225173i
$737$		−	6.77846i		−	0.249688i
$738$	19.3733	+	16.8723i	0.713140	+	0.621078i
$739$		−	32.3244i		−	1.18907i	−0.804068	−	0.594537i	$-0.797335\pi$
$739$		−	32.3244i		−	1.18907i	0.804068	−	0.594537i	$-0.202665\pi$
$740$	−6.47574	−	11.2163i	−0.238053	−	0.412320i
$741$	5.84025	−	5.86040i	0.214547	−	0.215287i
$742$	22.7778	+	16.7641i	0.836200	+	0.615430i
$743$	19.1716	+	33.2062i	0.703339	+	1.21822i	0.967288	+	0.253682i	$0.0816416\pi$
$743$	19.1716	+	33.2062i	0.703339	+	1.21822i	−0.263949	+	0.964537i	$0.585025\pi$
$744$	1.09562	−	11.3238i	0.0401675	−	0.415150i
$745$	27.3324	−	15.7804i	1.00138	−	0.578148i
$746$	−17.7937	+	30.8197i	−0.651475	+	1.12839i
$747$	−15.5182	−	13.5149i	−0.567783	−	0.494486i
$748$	−3.16255	+	5.47769i	−0.115634	+	0.200284i
$749$	2.67287	−	24.0090i	0.0976645	−	0.877269i
$750$	−20.6406	−	1.99707i	−0.753689	−	0.0729226i
$751$	7.09736	−	12.2930i	0.258986	−	0.448577i	−0.706984	−	0.707229i	$-0.749945\pi$
$751$	7.09736	−	12.2930i	0.258986	−	0.448577i	0.965971	+	0.258652i	$0.0832782\pi$
$752$			0.824656i			0.0300721i
$753$	1.13381	−	11.7185i	0.0413184	−	0.427045i
$754$	−4.09345	−	10.8760i	−0.149075	−	0.396080i
$755$	−5.55578			−0.202195
$756$	−8.28667	−	10.9696i	−0.301383	−	0.398959i
$757$	−16.0710	−	27.8358i	−0.584111	−	1.01171i	−0.994986	−	0.100018i	$-0.968110\pi$
$757$	−16.0710	−	27.8358i	−0.584111	−	1.01171i	0.410875	−	0.911692i	$-0.365223\pi$
$758$			29.2811i			1.06354i
$759$	21.8084	+	2.11006i	0.791595	+	0.0765902i
$760$	1.87202	−	1.08081i	0.0679054	−	0.0392052i
$761$			4.65512i			0.168748i	0.996434	+	0.0843740i	$0.0268890\pi$
$761$			4.65512i			0.168748i	−0.996434	+	0.0843740i	$0.973111\pi$
$762$	−5.36848	+	2.44357i	−0.194480	+	0.0885213i
$763$	4.87161	−	43.7591i	0.176364	−	1.58419i
$764$	5.67581	−	3.27693i	0.205344	−	0.118555i
$765$	14.1411	−	4.85458i	0.511271	−	0.175518i
$766$	−8.78316	−	5.07096i	−0.317348	−	0.183221i
$767$	−31.1012	+	37.8970i	−1.12300	+	1.36838i
$768$	−1.40963	−	1.00646i	−0.0508655	−	0.0363174i
$769$	20.9476	+	36.2823i	0.755389	+	1.30837i	0.945181	+	0.326548i	$0.105885\pi$
$769$	20.9476	+	36.2823i	0.755389	+	1.30837i	−0.189792	+	0.981824i	$0.560781\pi$
$770$	8.18855	−	3.58558i	0.295095	−	0.129215i
$771$	2.36037	−	24.3955i	0.0850065	−	0.878582i
$772$	8.61135	−	4.97176i	0.309929	−	0.178938i
$773$	−42.2523	+	24.3944i	−1.51971	+	0.877406i	−0.519981	+	0.854178i	$0.674061\pi$
$773$	−42.2523	+	24.3944i	−1.51971	+	0.877406i	−0.999730	+	0.0232279i	$0.992606\pi$
$774$	15.8796	+	3.10188i	0.570781	+	0.111495i
$775$	7.67784	+	13.2984i	0.275796	+	0.477693i
$776$	4.58560	−	7.94250i	0.164614	−	0.285119i
$777$	11.3138	+	34.5715i	0.405881	+	1.24025i
$778$	23.9026	−	13.8002i	0.856949	−	0.494760i
$779$	9.82526	−	5.67262i	0.352026	−	0.203243i
$780$	−9.83767	+	2.65416i	−0.352245	+	0.0950343i
$781$	9.50949	−	16.4709i	0.340276	−	0.589376i
$782$	16.1593	+	9.32956i	0.577854	+	0.333624i
$783$	3.88708	+	16.2900i	0.138913	+	0.582159i
$784$	−2.08105	−	6.68350i	−0.0743232	−	0.238697i
$785$	−30.9886			−1.10603
$786$	16.1379	−	7.34550i	0.575621	−	0.262005i
$787$	9.63012	+	16.6799i	0.343277	+	0.594573i	0.985039	−	0.172331i	$-0.0551298\pi$
$787$	9.63012	+	16.6799i	0.343277	+	0.594573i	−0.641763	+	0.766903i	$0.721797\pi$
$788$	0.185155	−	0.320698i	0.00659588	−	0.0114244i
$789$	9.23220	+	20.2830i	0.328675	+	0.722093i
$790$	9.17493	−	5.29715i	0.326429	−	0.188464i
$791$	−2.65055	+	23.8085i	−0.0942426	+	0.846532i
$792$	−4.07996	+	4.68472i	−0.144975	+	0.166464i
$793$	19.7526	+	52.4812i	0.701437	+	1.86366i
$794$	−0.109839	+	0.190247i	−0.00389804	+	0.00675161i
$795$	−27.4948	+	12.5148i	−0.975141	+	0.443855i
$796$	−14.6253	−	8.44390i	−0.518379	−	0.299286i
$797$	−0.0214000	+	0.0370659i	−0.000758027	+	0.00131294i	−0.866404	−	0.499343i	$-0.833575\pi$
$797$	−0.0214000	+	0.0370659i	−0.000758027	+	0.00131294i	0.865646	+	0.500656i	$0.166908\pi$
$798$	−5.77005	+	1.88830i	−0.204258	+	0.0668451i
$799$	2.18142	+	1.25944i	0.0771731	+	0.0445559i
$800$	2.33784			0.0826551
$801$	3.04455	−	1.04519i	0.107574	−	0.0369298i
$802$	11.9325	+	20.6677i	0.421352	+	0.729803i
$803$	2.97384	−	5.15085i	0.104945	−	0.181769i
$804$	3.29454	−	4.61428i	0.116190	−	0.162733i
$805$	−10.5775	−	24.1564i	−0.372809	−	0.851400i
$806$	18.3068	+	15.0239i	0.644828	+	0.529195i
$807$	38.5593	+	27.5309i	1.35735	+	0.969133i
$808$	0.762652			0.0268300
$809$		−	20.7962i		−	0.731156i	−0.930781	−	0.365578i	$-0.880871\pi$
$809$		−	20.7962i		−	0.731156i	0.930781	−	0.365578i	$-0.119129\pi$
$810$	14.5453	−	2.01688i	0.511071	−	0.0708658i
$811$	40.3139			1.41561			0.707807	−	0.706406i	$-0.249685\pi$
$811$	40.3139			1.41561			0.707807	+	0.706406i	$0.249685\pi$
$812$	−0.943503	+	8.47499i	−0.0331105	+	0.297414i
$813$	−0.226115	+	2.33700i	−0.00793020	+	0.0819622i
$814$	14.2352	−	8.21870i	0.498944	−	0.288065i
$815$	−0.915497	−	1.58569i	−0.0320685	−	0.0555442i
$816$	−4.81516	+	2.19171i	−0.168564	+	0.0767253i
$817$	3.57259	−	6.18791i	0.124989	−	0.216488i
$818$	−7.74689			−0.270864
$819$	28.5730	−	1.60739i	0.998421	−	0.0561668i
$820$	−13.9723			−0.487933
$821$	−8.74944	+	15.1545i	−0.305357	+	0.528895i	−0.977341	−	0.211672i	$-0.932109\pi$
$821$	−8.74944	+	15.1545i	−0.305357	+	0.528895i	0.671983	+	0.740566i	$0.265443\pi$
$822$	5.82409	−	2.65095i	0.203138	−	0.0924625i
$823$	−14.2667	−	24.7106i	−0.497306	−	0.861359i	0.502690	−	0.864467i	$-0.332344\pi$
$823$	−14.2667	−	24.7106i	−0.497306	−	0.861359i	−0.999995	+	0.00310845i	$0.999011\pi$
$824$	−11.8342	+	6.83246i	−0.412263	+	0.238020i
$825$	0.807520	−	8.34609i	0.0281142	−	0.290574i
$826$	32.9538	−	14.4298i	1.14661	−	0.502075i
$827$	17.6018			0.612075			0.306037	−	0.952020i	$-0.400997\pi$
$827$	17.6018			0.612075			0.306037	+	0.952020i	$0.400997\pi$
$828$	13.8200	+	12.0359i	0.480278	+	0.418278i
$829$		−	2.29195i		−	0.0796028i	−0.999208	−	0.0398014i	$-0.987327\pi$
$829$		−	2.29195i		−	0.0796028i	0.999208	−	0.0398014i	$-0.0126725\pi$
$830$	11.1920			0.388479
$831$	29.4963	+	21.0600i	1.02321	+	0.730563i
$832$	3.37445	−	1.27006i	0.116988	−	0.0440315i
$833$	−20.8578	−	4.70239i	−0.722679	−	0.162928i
$834$	13.7872	−	19.3102i	0.477413	−	0.668656i
$835$	−0.991880	+	1.71799i	−0.0343254	+	0.0594534i
$836$	1.37172	+	2.37588i	0.0474418	+	0.0821716i
$837$	−23.4593	−	24.7895i	−0.810871	−	0.856849i
$838$	3.31609			0.114552
$839$	10.6696	+	6.16009i	0.368355	+	0.212670i	0.672740	−	0.739879i	$-0.265117\pi$
$839$	10.6696	+	6.16009i	0.368355	+	0.212670i	−0.304384	+	0.952549i	$0.598451\pi$
$840$	7.31687	+	1.53909i	0.252456	+	0.0531036i
$841$	−9.30602	+	16.1185i	−0.320897	+	0.555810i
$842$	21.8925	+	12.6397i	0.754467	+	0.435592i
$843$	6.43398	−	2.92856i	0.221598	−	0.100865i
$844$	−0.132711	+	0.229862i	−0.00456809	+	0.00791217i
$845$	6.81797	−	20.0853i	0.234545	−	0.690956i
$846$	1.86563	+	1.62479i	0.0641417	+	0.0558614i
$847$	−7.12293	−	16.2669i	−0.244747	−	0.558939i
$848$	9.25742	−	5.34477i	0.317901	−	0.183540i
$849$	−1.55224	−	3.41025i	−0.0532728	−	0.117039i
$850$	3.57043	−	6.18417i	0.122465	−	0.212115i
$851$	−24.2453	−	41.9941i	−0.831118	−	1.43954i
$852$	14.4787	−	6.59028i	0.496033	−	0.225779i
$853$	−36.0741			−1.23515			−0.617577	−	0.786510i	$-0.711886\pi$
$853$	−36.0741			−1.23515			−0.617577	+	0.786510i	$0.711886\pi$
$854$	4.55280	−	40.8954i	0.155794	−	1.39941i
$855$	1.24324	−	6.36459i	0.0425179	−	0.217664i
$856$	−7.90733	−	4.56530i	−0.270267	−	0.156039i
$857$	−7.21848	+	12.5028i	−0.246579	+	0.427087i	−0.962574	−	0.271018i	$-0.912640\pi$
$857$	−7.21848	+	12.5028i	−0.246579	+	0.427087i	0.715996	+	0.698105i	$0.245973\pi$
$858$	−3.36854	−	12.4855i	−0.115000	−	0.426248i
$859$	40.0257	−	23.1088i	1.36566	−	0.788463i	0.375288	−	0.926908i	$-0.377544\pi$
$859$	40.0257	−	23.1088i	1.36566	−	0.788463i	0.990370	+	0.138446i	$0.0442106\pi$
$860$	−7.62075	+	4.39984i	−0.259865	+	0.150033i
$861$	38.4024	+	8.07786i	1.30875	+	0.275293i
$862$	−12.4404	+	21.5475i	−0.423723	+	0.733909i
$863$	14.6218	+	25.3257i	0.497731	+	0.862095i	0.999997	−	0.00261814i	$-0.000833382\pi$
$863$	14.6218	+	25.3257i	0.497731	+	0.862095i	−0.502266	+	0.864713i	$0.667500\pi$
$864$	−5.05425	+	1.20603i	−0.171949	+	0.0410300i
$865$	−27.1546	+	15.6777i	−0.923283	+	0.533058i
$866$	−17.2062	+	9.93398i	−0.584689	+	0.337570i
$867$	1.27943	−	13.2235i	0.0434516	−	0.449092i
$868$	−6.97053	−	15.9189i	−0.236595	−	0.540322i
$869$	6.72289	+	11.6444i	0.228058	+	0.395009i
$870$	−7.41286	−	5.29270i	−0.251320	−	0.179439i
$871$	4.15743	+	11.0460i	0.140869	+	0.374278i
$872$	−14.4120	−	8.32078i	−0.488052	−	0.281777i
$873$	−8.93358	−	26.0229i	−0.302356	−	0.880741i
$874$	7.00889	−	4.04659i	0.237079	−	0.136878i
$875$	−29.0164	+	12.7057i	−0.980935	+	0.429529i
$876$	4.52785	−	2.06094i	0.152982	−	0.0696326i
$877$		−	24.8567i		−	0.839352i	−0.907674	−	0.419676i	$-0.862144\pi$
$877$		−	24.8567i		−	0.839352i	0.907674	−	0.419676i	$-0.137856\pi$
$878$	−1.13469	+	0.655115i	−0.0382940	+	0.0221091i
$879$	10.5338	+	1.01919i	0.355296	+	0.0343764i
$880$		−	3.37869i		−	0.113896i
$881$	11.1486	+	19.3099i	0.375606	+	0.650568i	0.990418	−	0.138106i	$-0.0441014\pi$
$881$	11.1486	+	19.3099i	0.375606	+	0.650568i	−0.614812	+	0.788674i	$0.710768\pi$
$882$	−19.2204	−	8.46028i	−0.647184	−	0.284872i
$883$	28.3409			0.953749			0.476874	−	0.878971i	$-0.341770\pi$
$883$	28.3409			0.953749			0.476874	+	0.878971i	$0.341770\pi$
$884$	1.79396	−	10.8659i	0.0603373	−	0.365461i
$885$	−3.70060	+	38.2474i	−0.124394	+	1.28567i
$886$			15.4292i			0.518356i
$887$	−11.9202	+	20.6464i	−0.400241	+	0.693237i	−0.993755	−	0.111587i	$-0.964407\pi$
$887$	−11.9202	+	20.6464i	−0.400241	+	0.693237i	0.593514	+	0.804824i	$0.297740\pi$
$888$	13.6848	+	1.32407i	0.459233	+	0.0444327i
$889$	−5.34070	+	7.25655i	−0.179121	+	0.243377i
$890$	−0.875350	+	1.51615i	−0.0293418	+	0.0508215i
$891$	2.55973	+	18.4603i	0.0857540	+	0.618443i
$892$	−5.03909	+	8.72796i	−0.168721	+	0.292234i
$893$	0.946165	−	0.546268i	0.0316622	−	0.0182802i
$894$	−3.22655	+	33.3478i	−0.107912	+	1.11532i
$895$	13.5386	+	23.4495i	0.452544	+	0.783829i
$896$	−2.62951	−	0.292738i	−0.0878456	−	0.00977967i
$897$	−36.8324	+	9.93725i	−1.22980	+	0.331795i
$898$	10.2266	+	17.7130i	0.341267	+	0.591092i
$899$			21.1699i			0.706056i
$900$	4.60616	−	5.28893i	0.153539	−	0.176298i
$901$		−	32.6509i		−	1.08776i
$902$		−	17.7330i		−	0.590443i
$903$	23.4891	−	7.68701i	0.781669	−	0.255808i
$904$	7.84130	+	4.52717i	0.260798	+	0.150572i
$905$	17.2516	+	29.8806i	0.573462	+	0.993265i
$906$	3.42707	−	4.79989i	0.113857	−	0.159466i
$907$	18.1124			0.601414			0.300707	−	0.953717i	$-0.402777\pi$
$907$	18.1124			0.601414			0.300707	+	0.953717i	$0.402777\pi$
$908$	9.90698	+	5.71980i	0.328775	+	0.189818i
$909$	1.50263	−	1.72536i	0.0498389	−	0.0572265i
$910$	−11.1447	+	10.8652i	−0.369442	+	0.360179i
$911$		−	54.3855i		−	1.80187i	−0.433952	−	0.900936i	$-0.642881\pi$
$911$		−	54.3855i		−	1.80187i	0.433952	−	0.900936i	$-0.357119\pi$
$912$	−0.220989	+	2.28402i	−0.00731768	+	0.0756316i
$913$			14.2043i			0.470095i
$914$	28.1572	−	16.2566i	0.931357	−	0.537719i
$915$	35.7702	+	25.5395i	1.18253	+	0.844310i
$916$	−4.74685	+	8.22179i	−0.156840	+	0.271655i
$917$	16.0544	−	21.8135i	0.530163	−	0.720347i
$918$	−4.52878	+	15.2116i	−0.149472	+	0.502059i
$919$	0.999449			0.0329688			0.0164844	−	0.999864i	$-0.494753\pi$
$919$	0.999449			0.0329688			0.0164844	+	0.999864i	$0.494753\pi$
$920$	−9.96719			−0.328608
$921$	1.56733	−	0.713400i	0.0516452	−	0.0235073i
$922$	−20.3615	+	11.7557i	−0.670570	+	0.387154i
$923$	−5.39426	+	32.6729i	−0.177554	+	1.07544i
$924$	−1.95334	+	9.28623i	−0.0642601	+	0.305494i
$925$	−16.0712	+	9.27869i	−0.528417	+	0.305082i
$926$	−28.5990	−	16.5117i	−0.939823	−	0.542607i
$927$	−7.85926	+	40.2343i	−0.258132	+	1.32147i
$928$	2.79123	+	1.61152i	0.0916266	+	0.0529007i
$929$			19.9879i			0.655781i	0.944716	+	0.327890i	$0.106338\pi$
$929$			19.9879i			0.655781i	−0.944716	+	0.327890i	$0.893662\pi$
$930$	18.4760	+	1.78763i	0.605853	+	0.0586188i
$931$	−6.28976	+	6.81497i	−0.206138	+	0.223352i
$932$	−3.90224	−	2.25296i	−0.127822	−	0.0737981i
$933$	0.199005	−	2.05681i	0.00651512	−	0.0673368i
$934$	28.5242			0.933341
$935$	−8.93747	−	5.16005i	−0.292287	−	0.168752i
$936$	3.77529	−	10.1364i	0.123399	−	0.331320i
$937$		−	19.6207i		−	0.640980i	−0.947252	−	0.320490i	$-0.896152\pi$
$937$		−	19.6207i		−	0.640980i	0.947252	−	0.320490i	$-0.103848\pi$
$938$	0.958249	−	8.60745i	0.0312880	−	0.281043i
$939$	26.4802	−	37.0877i	0.864148	−	1.21031i
$940$	−1.34552			−0.0438860
$941$	−14.7948	−	8.54179i	−0.482297	−	0.278454i	0.239076	−	0.971001i	$-0.423155\pi$
$941$	−14.7948	−	8.54179i	−0.482297	−	0.278454i	−0.721373	+	0.692546i	$0.756489\pi$
$942$	19.1152	−	26.7725i	0.622808	−	0.872294i
$943$	−52.3125			−1.70353
$944$		−	13.5971i		−	0.442549i
$945$	17.8981	−	13.5206i	0.582224	−	0.439827i
$946$	−5.58407	−	9.67190i	−0.181554	−	0.314461i
$947$	3.24886	−	5.62718i	0.105574	−	0.182859i	−0.808399	−	0.588635i	$-0.799665\pi$
$947$	3.24886	−	5.62718i	0.105574	−	0.182859i	0.913972	+	0.405776i	$0.132999\pi$
$948$	−1.08308	+	11.1942i	−0.0351769	+	0.363570i
$949$	−1.68691	+	10.2176i	−0.0547596	+	0.331677i
$950$	−1.54863	−	2.68231i	−0.0502442	−	0.0870256i
$951$	31.9619	+	22.8205i	1.03644	+	0.740004i
$952$	−4.79024	+	6.50862i	−0.155252	+	0.210945i
$953$	−46.4669	−	26.8277i	−1.50521	−	0.869034i	−0.999982	−	0.00604840i	$-0.998075\pi$
$953$	−46.4669	−	26.8277i	−1.50521	−	0.869034i	−0.505229	−	0.862985i	$-0.668592\pi$
$954$	6.14800	−	31.4738i	0.199049	−	1.01900i
$955$	5.34668	+	9.26072i	0.173015	+	0.299670i
$956$	−8.69379	−	15.0581i	−0.281177	−	0.487013i
$957$	6.71725	−	9.40806i	0.217138	−	0.304119i
$958$	−30.2057	−	17.4393i	−0.975902	−	0.563437i
$959$	5.79395	−	7.87238i	0.187096	−	0.254213i
$960$	1.64215	−	2.29996i	0.0530001	−	0.0742310i
$961$	−6.07139	−	10.5160i	−0.195851	−	0.339224i
$962$	−18.1565	+	22.1238i	−0.585388	+	0.713300i
$963$	−25.9077	+	8.89402i	−0.834863	+	0.286606i
$964$	−0.714410	+	1.23739i	−0.0230096	+	0.0398538i
$965$	8.11199	+	14.0504i	0.261134	+	0.452298i
$966$	27.3945	+	5.76238i	0.881404	+	0.185402i
$967$			30.5255i			0.981633i	0.871263	+	0.490817i	$0.163301\pi$
$967$			30.5255i			0.981633i	−0.871263	+	0.490817i	$0.836699\pi$
$968$	−6.71193			−0.215729
$969$	5.70431	+	4.07281i	0.183249	+	0.130838i
$970$	12.9591	+	7.48193i	0.416091	+	0.240230i
$971$	−7.06480			−0.226720			−0.113360	−	0.993554i	$-0.536161\pi$
$971$	−7.06480			−0.226720			−0.113360	+	0.993554i	$0.536161\pi$
$972$	−7.22979	+	13.8105i	−0.231896	+	0.442972i
$973$	4.01015	−	36.0210i	0.128559	−	1.15478i
$974$			0.222477i			0.00712861i
$975$	3.80299	+	14.0958i	0.121793	+	0.451427i
$976$	−13.4689	−	7.77625i	−0.431128	−	0.248912i
$977$	51.1279			1.63573			0.817863	−	0.575412i	$-0.195158\pi$
$977$	51.1279			1.63573			0.817863	+	0.575412i	$0.195158\pi$
$978$	1.93467	+	0.187188i	0.0618640	+	0.00598560i
$979$	−1.92423	−	1.11095i	−0.0614986	−	0.0355062i
$980$	10.9049	−	3.39547i	0.348344	−	0.108464i
$981$	−47.2197	+	16.2104i	−1.50761	+	0.517557i
$982$			29.1435i			0.930006i
$983$	−18.5961	−	10.7365i	−0.593123	−	0.342440i	0.173208	−	0.984885i	$-0.444587\pi$
$983$	−18.5961	−	10.7365i	−0.593123	−	0.342440i	−0.766331	+	0.642445i	$0.777920\pi$
$984$	8.61877	−	12.0713i	0.274756	−	0.384819i
$985$	0.523255	+	0.302101i	0.0166723	+	0.00962575i
$986$	8.52573	−	4.92233i	0.271514	−	0.156759i
$987$	3.69812	+	0.777892i	0.117712	+	0.0247606i
$988$	−3.69250	−	3.03035i	−0.117474	−	0.0964083i
$989$	−28.5323	+	16.4731i	−0.907273	+	0.523814i
$990$	−7.64365	−	6.65691i	−0.242931	−	0.211570i
$991$	12.7737			0.405770			0.202885	−	0.979203i	$-0.434968\pi$
$991$	12.7737			0.405770			0.202885	+	0.979203i	$0.434968\pi$
$992$	−6.56832			−0.208544
$993$	3.68293	+	8.09133i	0.116874	+	0.256771i
$994$	14.4038	−	19.5708i	0.456861	−	0.620749i
$995$	13.7772	−	23.8628i	0.436766	−	0.756501i
$996$	−6.90375	+	9.66927i	−0.218754	+	0.306383i
$997$	28.2116	−	16.2880i	0.893469	−	0.515845i	0.0183936	−	0.999831i	$-0.494145\pi$
$997$	28.2116	−	16.2880i	0.893469	−	0.515845i	0.875076	+	0.483986i	$0.160811\pi$
$998$		−	39.4474i		−	1.24869i
$999$	29.9582	−	28.3506i	0.947834	−	0.896974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.e.101.14	yes	34
3.2	odd	2		546.2.bn.f.101.4	yes	34
7.5	odd	6		546.2.bi.f.257.7	yes	34
13.4	even	6		546.2.bi.e.17.2	✓	34
21.5	even	6		546.2.bi.e.257.2	yes	34
39.17	odd	6		546.2.bi.f.17.7	yes	34
91.82	odd	6		546.2.bn.f.173.4	yes	34
273.173	even	6	inner	546.2.bn.e.173.14	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.2	✓	34	13.4	even	6
546.2.bi.e.257.2	yes	34	21.5	even	6
546.2.bi.f.17.7	yes	34	39.17	odd	6
546.2.bi.f.257.7	yes	34	7.5	odd	6
546.2.bn.e.101.14	yes	34	1.1	even	1	trivial
546.2.bn.e.173.14	yes	34	273.173	even	6	inner
546.2.bn.f.101.4	yes	34	3.2	odd	2
546.2.bn.f.173.4	yes	34	91.82	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.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.57643 - 0.717543i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.41302 - 0.815806i) q^{5} +(-0.166804 + 1.72400i) q^{6} +(1.06124 + 2.42359i) q^{7} +1.00000 q^{8} +(1.97026 - 2.26231i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.57643 - 0.717543i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.41302 - 0.815806i) q^{5} +(-0.166804 + 1.72400i) q^{6} +(1.06124 + 2.42359i) q^{7} +1.00000 q^{8} +(1.97026 - 2.26231i) q^{9} +1.63161i q^{10} -2.07077 q^{11} +(-1.40963 - 1.00646i) q^{12} +(3.37445 - 1.27006i) q^{13} +(-2.62951 - 0.292738i) q^{14} +(1.64215 - 2.29996i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.52723 + 2.64525i) q^{17} +(0.974089 + 2.83745i) q^{18} +1.32484 q^{19} +(-1.41302 - 0.815806i) q^{20} +(3.41199 + 3.05914i) q^{21} +(1.03538 - 1.79334i) q^{22} +(-5.29037 - 3.05440i) q^{23} +(1.57643 - 0.717543i) q^{24} +(-1.16892 + 2.02463i) q^{25} +(-0.587322 + 3.55739i) q^{26} +(1.48267 - 4.98013i) q^{27} +(1.56827 - 2.13085i) q^{28} +(-2.79123 + 1.61152i) q^{29} +(1.17075 + 2.57212i) q^{30} +(3.28416 - 5.68833i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.26442 + 1.48586i) q^{33} -3.05447 q^{34} +(3.47672 + 2.55881i) q^{35} +(-2.94435 - 0.575141i) q^{36} +(6.87437 + 3.96892i) q^{37} +(-0.662420 + 1.14734i) q^{38} +(4.40827 - 4.42348i) q^{39} +(1.41302 - 0.815806i) q^{40} +(7.41619 - 4.28174i) q^{41} +(-4.35528 + 1.42530i) q^{42} +(2.69662 - 4.67069i) q^{43} +(1.03538 + 1.79334i) q^{44} +(0.938408 - 4.80404i) q^{45} +(5.29037 - 3.05440i) q^{46} +(0.714173 - 0.412328i) q^{47} +(-0.166804 + 1.72400i) q^{48} +(-4.74756 + 5.14399i) q^{49} +(-1.16892 - 2.02463i) q^{50} +(4.30566 + 3.07419i) q^{51} +(-2.78713 - 2.28733i) q^{52} +(-9.25742 - 5.34477i) q^{53} +(3.57158 + 3.77410i) q^{54} +(-2.92603 + 1.68934i) q^{55} +(1.06124 + 2.42359i) q^{56} +(2.08852 - 0.950630i) q^{57} -3.22304i q^{58} +(-11.7755 + 6.79857i) q^{59} +(-2.81290 - 0.272160i) q^{60} +15.5525i q^{61} +(3.28416 + 5.68833i) q^{62} +(7.57383 + 2.37426i) q^{63} +1.00000 q^{64} +(3.73204 - 4.54752i) q^{65} +(0.345413 - 3.57000i) q^{66} +3.27341i q^{67} +(1.52723 - 2.64525i) q^{68} +(-10.5316 - 1.01897i) q^{69} +(-3.95436 + 1.73152i) q^{70} +(-4.59225 + 7.95402i) q^{71} +(1.97026 - 2.26231i) q^{72} +(-1.43611 + 2.48741i) q^{73} +(-6.87437 + 3.96892i) q^{74} +(-0.389962 + 4.03044i) q^{75} +(-0.662420 - 1.14734i) q^{76} +(-2.19757 - 5.01869i) q^{77} +(1.62671 + 6.02941i) q^{78} +(-3.24657 - 5.62322i) q^{79} +1.63161i q^{80} +(-1.23612 - 8.91471i) q^{81} +8.56348i q^{82} -6.85946i q^{83} +(0.943293 - 4.48444i) q^{84} +(4.31602 + 2.49186i) q^{85} +(2.69662 + 4.67069i) q^{86} +(-3.24385 + 4.54327i) q^{87} -2.07077 q^{88} +(0.929234 + 0.536494i) q^{89} +(3.69122 + 3.21471i) q^{90} +(6.65920 + 6.83045i) q^{91} +6.10879i q^{92} +(1.09562 - 11.3238i) q^{93} +0.824656i q^{94} +(1.87202 - 1.08081i) q^{95} +(-1.40963 - 1.00646i) q^{96} +(4.58560 - 7.94250i) q^{97} +(-2.08105 - 6.68350i) q^{98} +(-4.07996 + 4.68472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Introduction

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