LMFDB - Embedded newform 546.2.bi.f.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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			17.7
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.f.257.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(0.166804 + 1.72400i) q^{3} +1.00000 q^{4} +(1.41302 - 0.815806i) q^{5} +(0.166804 + 1.72400i) q^{6} +(2.62951 + 0.292738i) q^{7} +1.00000 q^{8} +(-2.94435 + 0.575141i) q^{9} +(1.41302 - 0.815806i) q^{10} +(1.03538 + 1.79334i) q^{11} +(0.166804 + 1.72400i) q^{12} +(-3.37445 - 1.27006i) q^{13} +(2.62951 + 0.292738i) q^{14} +(1.64215 + 2.29996i) q^{15} +1.00000 q^{16} +3.05447 q^{17} +(-2.94435 + 0.575141i) q^{18} +(0.662420 - 1.14734i) q^{19} +(1.41302 - 0.815806i) q^{20} +(-0.0660664 + 4.58210i) q^{21} +(1.03538 + 1.79334i) q^{22} -6.10879i q^{23} +(0.166804 + 1.72400i) q^{24} +(-1.16892 + 2.02463i) q^{25} +(-3.37445 - 1.27006i) q^{26} +(-1.48267 - 4.98013i) q^{27} +(2.62951 + 0.292738i) q^{28} +(-2.79123 - 1.61152i) q^{29} +(1.64215 + 2.29996i) q^{30} +(-3.28416 + 5.68833i) q^{31} +1.00000 q^{32} +(-2.91901 + 2.08414i) q^{33} +3.05447 q^{34} +(3.95436 - 1.73152i) q^{35} +(-2.94435 + 0.575141i) q^{36} +7.93783i q^{37} +(0.662420 - 1.14734i) q^{38} +(1.62671 - 6.02941i) q^{39} +(1.41302 - 0.815806i) q^{40} +(-7.41619 - 4.28174i) q^{41} +(-0.0660664 + 4.58210i) q^{42} +(2.69662 + 4.67069i) q^{43} +(1.03538 + 1.79334i) q^{44} +(-3.69122 + 3.21471i) q^{45} -6.10879i q^{46} +(0.714173 - 0.412328i) q^{47} +(0.166804 + 1.72400i) q^{48} +(6.82861 + 1.53951i) q^{49} +(-1.16892 + 2.02463i) q^{50} +(0.509499 + 5.26590i) q^{51} +(-3.37445 - 1.27006i) q^{52} +(9.25742 + 5.34477i) q^{53} +(-1.48267 - 4.98013i) q^{54} +(2.92603 + 1.68934i) q^{55} +(2.62951 + 0.292738i) q^{56} +(2.08852 + 0.950630i) q^{57} +(-2.79123 - 1.61152i) q^{58} -13.5971i q^{59} +(1.64215 + 2.29996i) q^{60} +(-13.4689 - 7.77625i) q^{61} +(-3.28416 + 5.68833i) q^{62} +(-7.91056 + 0.650416i) q^{63} +1.00000 q^{64} +(-5.80429 + 0.958282i) q^{65} +(-2.91901 + 2.08414i) q^{66} +(-2.83485 + 1.63670i) q^{67} +3.05447 q^{68} +(10.5316 - 1.01897i) q^{69} +(3.95436 - 1.73152i) q^{70} +(-4.59225 - 7.95402i) q^{71} +(-2.94435 + 0.575141i) q^{72} +(1.43611 - 2.48741i) q^{73} +7.93783i q^{74} +(-3.68544 - 1.67750i) 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} +(1.41302 - 0.815806i) q^{80} +(8.33842 - 3.38684i) q^{81} +(-7.41619 - 4.28174i) q^{82} -6.85946i q^{83} +(-0.0660664 + 4.58210i) q^{84} +(4.31602 - 2.49186i) q^{85} +(2.69662 + 4.67069i) q^{86} +(2.31267 - 5.08089i) q^{87} +(1.03538 + 1.79334i) q^{88} -1.07299i q^{89} +(-3.69122 + 3.21471i) q^{90} +(-8.50136 - 4.32746i) q^{91} -6.10879i q^{92} +(-10.3545 - 4.71305i) q^{93} +(0.714173 - 0.412328i) q^{94} -2.16163i q^{95} +(0.166804 + 1.72400i) q^{96} +(-4.58560 - 7.94250i) q^{97} +(6.82861 + 1.53951i) q^{98} +(-4.07996 - 4.68472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20}+ \cdots - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.166804	+	1.72400i	0.0963045	+	0.995352i
$3$	0.166804	+	1.72400i	0.0963045	+	0.995352i
$4$	1.00000			0.500000
$5$	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
$7$	2.62951	+	0.292738i	0.993860	+	0.110644i
$7$	2.62951	+	0.292738i	0.993860	+	0.110644i
$8$	1.00000			0.353553
$9$	−2.94435	+	0.575141i	−0.981451	+	0.191714i
$10$	1.41302	−	0.815806i	0.446836	−	0.257981i
$11$	1.03538	+	1.79334i	0.312180	+	0.540711i	0.978834	−	0.204656i	$-0.0656075\pi$
$11$	1.03538	+	1.79334i	0.312180	+	0.540711i	−0.666654	+	0.745367i	$0.732274\pi$
$12$	0.166804	+	1.72400i	0.0481523	+	0.497676i
$13$	−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
$16$	1.00000			0.250000
$17$	3.05447			0.740818			0.370409	−	0.928869i	$-0.379218\pi$
$17$	3.05447			0.740818			0.370409	+	0.928869i	$0.379218\pi$
$18$	−2.94435	+	0.575141i	−0.693991	+	0.135562i
$19$	0.662420	−	1.14734i	0.151970	−	0.263219i	−0.779982	−	0.625802i	$-0.784772\pi$
$19$	0.662420	−	1.14734i	0.151970	−	0.263219i	0.931951	+	0.362583i	$0.118105\pi$
$20$	1.41302	−	0.815806i	0.315960	−	0.182420i
$21$	−0.0660664	+	4.58210i	−0.0144169	+	0.999896i
$22$	1.03538	+	1.79334i	0.220744	+	0.382341i
$23$		−	6.10879i		−	1.27377i	−0.770958	−	0.636886i	$-0.780222\pi$
$23$		−	6.10879i		−	1.27377i	0.770958	−	0.636886i	$-0.219778\pi$
$24$	0.166804	+	1.72400i	0.0340488	+	0.351910i
$25$	−1.16892	+	2.02463i	−0.233784	+	0.404926i
$26$	−3.37445	−	1.27006i	−0.661785	−	0.249080i
$27$	−1.48267	−	4.98013i	−0.285341	−	0.958426i
$28$	2.62951	+	0.292738i	0.496930	+	0.0553222i
$29$	−2.79123	−	1.61152i	−0.518319	−	0.299251i	0.217928	−	0.975965i	$-0.430070\pi$
$29$	−2.79123	−	1.61152i	−0.518319	−	0.299251i	−0.736246	+	0.676714i	$0.763404\pi$
$30$	1.64215	+	2.29996i	0.299814	+	0.419914i
$31$	−3.28416	+	5.68833i	−0.589852	+	1.02165i	0.404399	+	0.914583i	$0.367481\pi$
$31$	−3.28416	+	5.68833i	−0.589852	+	1.02165i	−0.994251	+	0.107071i	$0.965853\pi$
$32$	1.00000			0.176777
$33$	−2.91901	+	2.08414i	−0.508134	+	0.362802i
$34$	3.05447			0.523837
$35$	3.95436	−	1.73152i	0.668408	−	0.292681i
$36$	−2.94435	+	0.575141i	−0.490725	+	0.0958569i
$37$			7.93783i			1.30497i	0.757801	+	0.652486i	$0.226274\pi$
$37$			7.93783i			1.30497i	−0.757801	+	0.652486i	$0.773726\pi$
$38$	0.662420	−	1.14734i	0.107459	−	0.186124i
$39$	1.62671	−	6.02941i	0.260482	−	0.965479i
$40$	1.41302	−	0.815806i	0.223418	−	0.128990i
$41$	−7.41619	−	4.28174i	−1.15821	−	0.668695i	−0.207339	−	0.978269i	$-0.566480\pi$
$41$	−7.41619	−	4.28174i	−1.15821	−	0.668695i	−0.950875	+	0.309574i	$0.899814\pi$
$42$	−0.0660664	+	4.58210i	−0.0101943	+	0.707033i
$43$	2.69662	+	4.67069i	0.411231	+	0.712273i	0.995025	−	0.0996291i	$-0.0317656\pi$
$43$	2.69662	+	4.67069i	0.411231	+	0.712273i	−0.583794	+	0.811902i	$0.698432\pi$
$44$	1.03538	+	1.79334i	0.156090	+	0.270356i
$45$	−3.69122	+	3.21471i	−0.550255	+	0.479220i
$46$		−	6.10879i		−	0.900693i
$47$	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
$49$	6.82861	+	1.53951i	0.975516	+	0.219930i
$50$	−1.16892	+	2.02463i	−0.165310	+	0.286326i
$51$	0.509499	+	5.26590i	0.0713441	+	0.737374i
$52$	−3.37445	−	1.27006i	−0.467953	−	0.176126i
$53$	9.25742	+	5.34477i	1.27160	+	0.734161i	0.975290	−	0.220930i	$-0.0709092\pi$
$53$	9.25742	+	5.34477i	1.27160	+	0.734161i	0.296314	+	0.955091i	$0.404242\pi$
$54$	−1.48267	−	4.98013i	−0.201766	−	0.677710i
$55$	2.92603	+	1.68934i	0.394546	+	0.227791i
$56$	2.62951	+	0.292738i	0.351383	+	0.0391187i
$57$	2.08852	+	0.950630i	0.276631	+	0.125914i
$58$	−2.79123	−	1.61152i	−0.366507	−	0.211603i
$59$		−	13.5971i		−	1.77020i	−0.465405	−	0.885098i	$-0.654091\pi$
$59$		−	13.5971i		−	1.77020i	0.465405	−	0.885098i	$-0.345909\pi$
$60$	1.64215	+	2.29996i	0.212000	+	0.296924i
$61$	−13.4689	−	7.77625i	−1.72451	−	0.995647i	−0.908857	−	0.417107i	$-0.863044\pi$
$61$	−13.4689	−	7.77625i	−1.72451	−	0.995647i	−0.815654	−	0.578540i	$-0.803623\pi$
$62$	−3.28416	+	5.68833i	−0.417088	+	0.722418i
$63$	−7.91056	+	0.650416i	−0.996637	+	0.0819447i
$64$	1.00000			0.125000
$65$	−5.80429	+	0.958282i	−0.719934	+	0.118860i
$66$	−2.91901	+	2.08414i	−0.359305	+	0.256540i
$67$	−2.83485	+	1.63670i	−0.346333	+	0.199955i	−0.663069	−	0.748558i	$-0.730746\pi$
$67$	−2.83485	+	1.63670i	−0.346333	+	0.199955i	0.316736	+	0.948514i	$0.397413\pi$
$68$	3.05447			0.370409
$69$	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	−0.998607	−	0.0527663i	$-0.983196\pi$
$71$	−4.59225	−	7.95402i	−0.545000	−	0.943968i	0.453607	−	0.891202i	$-0.350137\pi$
$72$	−2.94435	+	0.575141i	−0.346995	+	0.0677811i
$73$	1.43611	−	2.48741i	0.168084	−	0.291129i	−0.769662	−	0.638451i	$-0.779575\pi$
$73$	1.43611	−	2.48741i	0.168084	−	0.291129i	0.937746	+	0.347322i	$0.112909\pi$
$74$			7.93783i			0.922755i
$75$	−3.68544	−	1.67750i	−0.425558	−	0.193701i
$76$	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	$0.952356\pi$
$80$	1.41302	−	0.815806i	0.157980	−	0.0912099i
$81$	8.33842	−	3.38684i	0.926492	−	0.376315i
$82$	−7.41619	−	4.28174i	−0.818981	−	0.472839i
$83$		−	6.85946i		−	0.752924i	−0.926432	−	0.376462i	$-0.877141\pi$
$83$		−	6.85946i		−	0.752924i	0.926432	−	0.376462i	$-0.122859\pi$
$84$	−0.0660664	+	4.58210i	−0.00720843	+	0.499948i
$85$	4.31602	−	2.49186i	0.468138	−	0.270280i
$86$	2.69662	+	4.67069i	0.290784	+	0.503653i
$87$	2.31267	−	5.08089i	0.247944	−	0.544729i
$88$	1.03538	+	1.79334i	0.110372	+	0.191170i
$89$		−	1.07299i		−	0.113736i	−0.998382	−	0.0568682i	$-0.981889\pi$
$89$		−	1.07299i		−	0.113736i	0.998382	−	0.0568682i	$-0.0181115\pi$
$90$	−3.69122	+	3.21471i	−0.389089	+	0.338860i
$91$	−8.50136	−	4.32746i	−0.891184	−	0.453641i
$92$		−	6.10879i		−	0.636886i
$93$	−10.3545	−	4.71305i	−1.07371	−	0.488721i
$94$	0.714173	−	0.412328i	0.0736613	−	0.0425284i
$95$		−	2.16163i		−	0.221778i
$96$	0.166804	+	1.72400i	0.0170244	+	0.175955i
$97$	−4.58560	−	7.94250i	−0.465598	−	0.806439i	0.533631	−	0.845718i	$-0.320827\pi$
$97$	−4.58560	−	7.94250i	−0.465598	−	0.806439i	−0.999228	+	0.0392790i	$0.987494\pi$
$98$	6.82861	+	1.53951i	0.689794	+	0.155514i
$99$	−4.07996	−	4.68472i	−0.410051	−	0.470832i
$100$	−1.16892	+	2.02463i	−0.116892	+	0.202463i
$101$	0.381326	+	0.660476i	0.0379434	+	0.0657198i	0.884373	−	0.466780i	$-0.154586\pi$
$101$	0.381326	+	0.660476i	0.0379434	+	0.0657198i	−0.846430	+	0.532500i	$0.821253\pi$
$102$	0.509499	+	5.26590i	0.0504479	+	0.521402i
$103$	−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
$105$	3.64475	+	6.52849i	0.355691	+	0.637115i
$106$	9.25742	+	5.34477i	0.899160	+	0.519130i
$107$		−	9.13060i		−	0.882689i	−0.897338	−	0.441344i	$-0.854502\pi$
$107$		−	9.13060i		−	0.882689i	0.897338	−	0.441344i	$-0.145498\pi$
$108$	−1.48267	−	4.98013i	−0.142670	−	0.479213i
$109$	14.4120	+	8.32078i	1.38042	+	0.796986i	0.992209	−	0.124584i	$-0.0397597\pi$
$109$	14.4120	+	8.32078i	1.38042	+	0.796986i	0.388211	+	0.921570i	$0.373093\pi$
$110$	2.92603	+	1.68934i	0.278986	+	0.161073i
$111$	−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	−0.0835662	−	0.996502i	$-0.526631\pi$
$113$	7.84130	−	4.52717i	0.737647	−	0.425881i	0.821213	+	0.570622i	$0.193298\pi$
$114$	2.08852	+	0.950630i	0.195608	+	0.0890346i
$115$	−4.98359	−	8.63184i	−0.464722	−	0.804923i
$116$	−2.79123	−	1.61152i	−0.259159	−	0.149626i
$117$	10.6660	+	1.79872i	0.986077	+	0.166292i
$118$		−	13.5971i		−	1.25172i
$119$	8.03175	+	0.894158i	0.736269	+	0.0819673i
$120$	1.64215	+	2.29996i	0.149907	+	0.209957i
$121$	3.35596	−	5.81270i	0.305088	−	0.528427i
$122$	−13.4689	−	7.77625i	−1.21941	−	0.704029i
$123$	6.14466	−	13.4997i	0.554046	−	1.21723i
$124$	−3.28416	+	5.68833i	−0.294926	+	0.510827i
$125$			11.9725i			1.07085i
$126$	−7.91056	+	0.650416i	−0.704729	+	0.0579436i
$127$	1.70273	−	2.94922i	0.151093	−	0.261701i	−0.780536	−	0.625110i	$-0.785054\pi$
$127$	1.70273	−	2.94922i	0.151093	−	0.261701i	0.931630	+	0.363409i	$0.118387\pi$
$128$	1.00000			0.0883883
$129$	−7.60245	+	5.42807i	−0.669359	+	0.477915i
$130$	−5.80429	+	0.958282i	−0.509070	+	0.0840469i
$131$	5.11851	+	8.86551i	0.447206	+	0.774584i	0.998203	−	0.0599237i	$-0.0190858\pi$
$131$	5.11851	+	8.86551i	0.447206	+	0.774584i	−0.550997	+	0.834507i	$0.685752\pi$
$132$	−2.91901	+	2.08414i	−0.254067	+	0.181401i
$133$	2.07771	−	2.82304i	0.180160	−	0.244788i
$134$	−2.83485	+	1.63670i	−0.244894	+	0.141390i
$135$	−6.15787	−	5.82744i	−0.529985	−	0.501546i
$136$	3.05447			0.261919
$137$	3.69448			0.315641			0.157820	−	0.987468i	$-0.449553\pi$
$137$	3.69448			0.315641			0.157820	+	0.987468i	$0.449553\pi$
$138$	10.5316	−	1.01897i	0.896506	−	0.0867408i
$139$	11.8635	−	6.84939i	1.00625	−	0.580958i	0.0961575	−	0.995366i	$-0.469345\pi$
$139$	11.8635	−	6.84939i	1.00625	−	0.580958i	0.910091	+	0.414408i	$0.136011\pi$
$140$	3.95436	−	1.73152i	0.334204	−	0.146341i
$141$	0.829981	+	1.16246i	0.0698970	+	0.0978965i
$142$	−4.59225	−	7.95402i	−0.385373	−	0.667486i
$143$	−1.21621	−	7.36653i	−0.101704	−	0.616020i
$144$	−2.94435	+	0.575141i	−0.245363	+	0.0479284i
$145$	−5.25875			−0.436715
$146$	1.43611	−	2.48741i	0.118853	−	0.205860i
$147$	−1.51507	+	12.0293i	−0.124961	+	0.992162i
$148$			7.93783i			0.652486i
$149$	−9.67165	+	16.7518i	−0.792332	+	1.37236i	0.132187	+	0.991225i	$0.457800\pi$
$149$	−9.67165	+	16.7518i	−0.792332	+	1.37236i	−0.924519	+	0.381135i	$0.875533\pi$
$150$	−3.68544	−	1.67750i	−0.300915	−	0.136967i
$151$	2.94889	+	1.70254i	0.239977	+	0.138551i	0.615166	−	0.788397i	$-0.289089\pi$
$151$	2.94889	+	1.70254i	0.239977	+	0.138551i	−0.375189	+	0.926948i	$0.622422\pi$
$152$	0.662420	−	1.14734i	0.0537293	−	0.0930619i
$153$	−8.99343	+	1.75675i	−0.727076	+	0.142025i
$154$	2.19757	+	5.01869i	0.177085	+	0.404417i
$155$			10.7169i			0.860806i
$156$	1.62671	−	6.02941i	0.130241	−	0.482739i
$157$	−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	$0.940435\pi$
$158$	−3.24657	−	5.62322i	−0.258283	−	0.447360i
$159$	−7.67021	+	16.8513i	−0.608287	+	1.33640i
$160$	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
$163$	−0.971853	−	0.561100i	−0.0761214	−	0.0439487i	0.461456	−	0.887163i	$-0.347327\pi$
$163$	−0.971853	−	0.561100i	−0.0761214	−	0.0439487i	−0.537578	+	0.843214i	$0.680660\pi$
$164$	−7.41619	−	4.28174i	−0.579107	−	0.334348i
$165$	−2.42436	+	5.32627i	−0.188736	+	0.414649i
$166$		−	6.85946i		−	0.532397i
$167$	1.05294	+	0.607914i	0.0814787	+	0.0470418i	0.540186	−	0.841546i	$-0.318354\pi$
$167$	1.05294	+	0.607914i	0.0814787	+	0.0470418i	−0.458707	+	0.888588i	$0.651687\pi$
$168$	−0.0660664	+	4.58210i	−0.00509713	+	0.353517i
$169$	9.77389	+	8.57153i	0.751838	+	0.659348i
$170$	4.31602	−	2.49186i	0.331024	−	0.191117i
$171$	−1.29051	+	3.75917i	−0.0986879	+	0.287471i
$172$	2.69662	+	4.67069i	0.205615	+	0.356136i
$173$	−9.60871	+	16.6428i	−0.730537	+	1.26533i	0.226117	+	0.974100i	$0.427397\pi$
$173$	−9.60871	+	16.6428i	−0.730537	+	1.26533i	−0.956654	+	0.291227i	$0.905937\pi$
$174$	2.31267	−	5.08089i	0.175323	−	0.385181i
$175$	−3.66637	+	4.98159i	−0.277151	+	0.376573i
$176$	1.03538	+	1.79334i	0.0780450	+	0.135178i
$177$	23.4415	−	2.26806i	1.76197	−	0.170478i
$178$		−	1.07299i		−	0.0804238i
$179$	−14.3720	+	8.29766i	−1.07421	+	0.620196i	−0.929329	−	0.369253i	$-0.879614\pi$
$179$	−14.3720	+	8.29766i	−1.07421	+	0.620196i	−0.144882	+	0.989449i	$0.546280\pi$
$180$	−3.69122	+	3.21471i	−0.275127	+	0.239610i
$181$			21.1467i			1.57182i	0.618341	+	0.785910i	$0.287805\pi$
$181$			21.1467i			1.57182i	−0.618341	+	0.785910i	$0.712195\pi$
$182$	−8.50136	−	4.32746i	−0.630162	−	0.320773i
$183$	11.1596	−	24.5174i	0.824941	−	1.81238i
$184$		−	6.10879i		−	0.450346i
$185$	6.47574	+	11.2163i	0.476106	+	0.824639i
$186$	−10.3545	−	4.71305i	−0.759228	−	0.345578i
$187$	3.16255	+	5.47769i	0.231268	+	0.400568i
$188$	0.714173	−	0.412328i	0.0520864	−	0.0300721i
$189$	−2.44083	−	13.5293i	−0.177544	−	0.984113i
$190$		−	2.16163i		−	0.156821i
$191$	5.67581	+	3.27693i	0.410687	+	0.237110i	0.691085	−	0.722774i	$-0.257133\pi$
$191$	5.67581	+	3.27693i	0.410687	+	0.237110i	−0.280398	+	0.959884i	$0.590466\pi$
$192$	0.166804	+	1.72400i	0.0120381	+	0.124419i
$193$	−8.61135	+	4.97176i	−0.619858	+	0.357875i	−0.776814	−	0.629730i	$-0.783165\pi$
$193$	−8.61135	+	4.97176i	−0.619858	+	0.357875i	0.156956	+	0.987606i	$0.449832\pi$
$194$	−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	−0.859354	−	0.511381i	$-0.829134\pi$
$197$	0.185155	−	0.320698i	0.0131918	−	0.0228488i	0.872546	+	0.488532i	$0.162467\pi$
$198$	−4.07996	−	4.68472i	−0.289950	−	0.332929i
$199$			16.8878i			1.19714i	0.801069	+	0.598572i	$0.204265\pi$
$199$			16.8878i			1.19714i	−0.801069	+	0.598572i	$0.795735\pi$
$200$	−1.16892	+	2.02463i	−0.0826551	+	0.143163i
$201$	−3.29454	−	4.61428i	−0.232379	−	0.325466i
$202$	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
$205$	−13.9723			−0.975866
$206$	−11.8342	+	6.83246i	−0.824525	+	0.476040i
$207$	3.51342	+	17.9864i	0.244200	+	1.25014i
$208$	−3.37445	−	1.27006i	−0.233976	−	0.0880629i
$209$	2.74343			0.189767
$210$	3.64475	+	6.52849i	0.251512	+	0.450508i
$211$	−0.132711	+	0.229862i	−0.00913618	+	0.0158243i	−0.870557	−	0.492067i	$-0.836242\pi$
$211$	−0.132711	+	0.229862i	−0.00913618	+	0.0158243i	0.861421	+	0.507891i	$0.169575\pi$
$212$	9.25742	+	5.34477i	0.635802	+	0.367080i
$213$	12.9467	−	9.24381i	0.887095	−	0.633376i
$214$		−	9.13060i		−	0.624155i
$215$	7.62075	+	4.39984i	0.519731	+	0.300067i
$216$	−1.48267	−	4.98013i	−0.100883	−	0.338855i
$217$	−10.3009	+	13.9961i	−0.699271	+	0.950117i
$218$	14.4120	+	8.32078i	0.976105	+	0.563554i
$219$	4.52785	+	2.06094i	0.305963	+	0.139265i
$220$	2.92603	+	1.68934i	0.197273	+	0.113896i
$221$	−10.3072	−	3.87936i	−0.693335	−	0.260954i
$222$	−13.6848	+	1.32407i	−0.918465	+	0.0888654i
$223$	5.03909	−	8.72796i	0.337442	−	0.584467i	−0.646508	−	0.762907i	$-0.723771\pi$
$223$	5.03909	−	8.72796i	0.337442	−	0.584467i	0.983951	+	0.178439i	$0.0571048\pi$
$224$	2.62951	+	0.292738i	0.175691	+	0.0195593i
$225$	2.27726	−	6.63351i	0.151818	−	0.442234i
$226$	7.84130	−	4.52717i	0.521595	−	0.301143i
$227$		−	11.4396i		−	0.759273i	−0.925136	−	0.379636i	$-0.876049\pi$
$227$		−	11.4396i		−	0.759273i	0.925136	−	0.379636i	$-0.123951\pi$
$228$	2.08852	+	0.950630i	0.138315	+	0.0629570i
$229$	4.74685	+	8.22179i	0.313681	+	0.543311i	0.979156	−	0.203109i	$-0.0651045\pi$
$229$	4.74685	+	8.22179i	0.313681	+	0.543311i	−0.665475	+	0.746420i	$0.731771\pi$
$230$	−4.98359	−	8.63184i	−0.328608	−	0.569166i
$231$	−8.28565	+	4.62575i	−0.545156	+	0.304352i
$232$	−2.79123	−	1.61152i	−0.183253	−	0.105801i
$233$	−3.90224	+	2.25296i	−0.255644	+	0.147596i	−0.622346	−	0.782742i	$-0.713820\pi$
$233$	−3.90224	+	2.25296i	−0.255644	+	0.147596i	0.366702	+	0.930339i	$0.380487\pi$
$234$	10.6660	+	1.79872i	0.697261	+	0.117586i
$235$	0.672760	−	1.16525i	0.0438860	−	0.0760128i
$236$		−	13.5971i		−	0.885098i
$237$	9.15290	−	6.53507i	0.594545	−	0.424498i
$238$	8.03175	+	0.894158i	0.520621	+	0.0579596i
$239$	17.3876			1.12471			0.562354	−	0.826896i	$-0.309896\pi$
$239$	17.3876			1.12471			0.562354	+	0.826896i	$0.309896\pi$
$240$	1.64215	+	2.29996i	0.106000	+	0.148462i
$241$	−1.42882			−0.0920384			−0.0460192	−	0.998941i	$-0.514654\pi$
$241$	−1.42882			−0.0920384			−0.0460192	+	0.998941i	$0.514654\pi$
$242$	3.35596	−	5.81270i	0.215729	−	0.373654i
$243$	7.22979	+	13.8105i	0.463792	+	0.885944i
$244$	−13.4689	−	7.77625i	−0.862256	−	0.497824i
$245$	10.9049	−	3.39547i	0.696688	−	0.216928i
$246$	6.14466	−	13.4997i	0.391770	−	0.860711i
$247$	−3.69250	+	3.03035i	−0.234948	+	0.192817i
$248$	−3.28416	+	5.68833i	−0.208544	+	0.361209i
$249$	11.8257	−	1.14419i	0.749424	−	0.0725099i
$250$			11.9725i			0.757208i
$251$	−3.39863	−	5.88660i	−0.214520	−	0.371559i	0.738604	−	0.674139i	$-0.235485\pi$
$251$	−3.39863	−	5.88660i	−0.214520	−	0.371559i	−0.953124	+	0.302580i	$0.902152\pi$
$252$	−7.91056	+	0.650416i	−0.498318	+	0.0409723i
$253$	10.9551	−	6.32494i	0.688743	−	0.397646i
$254$	1.70273	−	2.94922i	0.106839	−	0.185051i
$255$	5.01589	+	7.02517i	0.314107	+	0.439933i
$256$	1.00000			0.0625000
$257$	14.1505			0.882684			0.441342	−	0.897339i	$-0.354503\pi$
$257$	14.1505			0.882684			0.441342	+	0.897339i	$0.354503\pi$
$258$	−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
$261$	9.14522	+	3.13952i	0.566075	+	0.194332i
$262$	5.11851	+	8.86551i	0.316222	+	0.547713i
$263$	−11.1426	+	6.43320i	−0.687084	+	0.396688i	−0.802519	−	0.596627i	$-0.796507\pi$
$263$	−11.1426	+	6.43320i	−0.687084	+	0.396688i	0.115435	+	0.993315i	$0.463174\pi$
$264$	−2.91901	+	2.08414i	−0.179652	+	0.128270i
$265$	17.4412			1.07140
$266$	2.07771	−	2.82304i	0.127392	−	0.173091i
$267$	1.84983	−	0.178979i	0.113208	−	0.0109533i
$268$	−2.83485	+	1.63670i	−0.173166	+	0.0999776i
$269$	27.3543			1.66782			0.833909	−	0.551902i	$-0.186098\pi$
$269$	27.3543			1.66782			0.833909	+	0.551902i	$0.186098\pi$
$270$	−6.15787	−	5.82744i	−0.374756	−	0.354646i
$271$	−1.35557			−0.0823450			−0.0411725	−	0.999152i	$-0.513109\pi$
$271$	−1.35557			−0.0823450			−0.0411725	+	0.999152i	$0.513109\pi$
$272$	3.05447			0.185204
$273$	6.04249	−	15.3782i	0.365708	−	0.930730i
$274$	3.69448			0.223192
$275$	−4.84112			−0.291931
$276$	10.5316	−	1.01897i	0.633926	−	0.0613350i
$277$	−20.9249			−1.25725			−0.628627	−	0.777707i	$-0.716383\pi$
$277$	−20.9249			−1.25725			−0.628627	+	0.777707i	$0.716383\pi$
$278$	11.8635	−	6.84939i	0.711525	−	0.410799i
$279$	6.39813	−	18.6373i	0.383046	−	1.11579i
$280$	3.95436	−	1.73152i	0.236318	−	0.103478i
$281$	4.08136			0.243474			0.121737	−	0.992562i	$-0.461154\pi$
$281$	4.08136			0.243474			0.121737	+	0.992562i	$0.461154\pi$
$282$	0.829981	+	1.16246i	0.0494246	+	0.0692233i
$283$	−1.87345	+	1.08164i	−0.111365	+	0.0642966i	−0.554648	−	0.832085i	$-0.687147\pi$
$283$	−1.87345	+	1.08164i	−0.111365	+	0.0642966i	0.443283	+	0.896382i	$0.353814\pi$
$284$	−4.59225	−	7.95402i	−0.272500	−	0.471984i
$285$	3.72664	−	0.360568i	0.220747	−	0.0213582i
$286$	−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
$289$	−7.67022			−0.451189
$290$	−5.25875			−0.308804
$291$	12.9280	−	9.23043i	0.757851	−	0.541097i
$292$	1.43611	−	2.48741i	0.0840418	−	0.145565i
$293$	−5.29149	+	3.05504i	−0.309132	+	0.178478i	−0.646538	−	0.762882i	$-0.723784\pi$
$293$	−5.29149	+	3.05504i	−0.309132	+	0.178478i	0.337406	+	0.941359i	$0.390451\pi$
$294$	−1.51507	+	12.0293i	−0.0883609	+	0.701564i
$295$	−11.0926	−	19.2130i	−0.645838	−	1.11862i
$296$			7.93783i			0.461377i
$297$	7.39591	−	7.81528i	0.429154	−	0.453488i
$298$	−9.67165	+	16.7518i	−0.560263	+	0.970405i
$299$	−7.75854	+	20.6138i	−0.448688	+	1.19213i
$300$	−3.68544	−	1.67750i	−0.212779	−	0.0968506i
$301$	5.72350	+	13.0710i	0.329897	+	0.753400i
$302$	2.94889	+	1.70254i	0.169689	+	0.0979703i
$303$	−1.07505	+	0.767577i	−0.0617602	+	0.0440961i
$304$	0.662420	−	1.14734i	0.0379924	−	0.0658047i
$305$	−25.3757			−1.45301
$306$	−8.99343	+	1.75675i	−0.514120	+	0.100427i
$307$	−0.994225			−0.0567434			−0.0283717	−	0.999597i	$-0.509032\pi$
$307$	−0.994225			−0.0567434			−0.0283717	+	0.999597i	$0.509032\pi$
$308$	2.19757	+	5.01869i	0.125218	+	0.285966i
$309$	−13.7532	−	19.2624i	−0.782389	−	1.09580i
$310$			10.7169i			0.608682i
$311$	−0.596522	+	1.03321i	−0.0338256	+	0.0585877i	−0.882443	−	0.470420i	$-0.844102\pi$
$311$	−0.596522	+	1.03321i	−0.0338256	+	0.0585877i	0.848617	+	0.529008i	$0.177436\pi$
$312$	1.62671	−	6.02941i	0.0920944	−	0.341348i
$313$	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
$315$	−10.6472	+	7.37253i	−0.599899	+	0.415395i
$316$	−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	$0.613611\pi$
$318$	−7.67021	+	16.8513i	−0.430124	+	0.944975i
$319$		−	6.67415i		−	0.373681i
$320$	1.41302	−	0.815806i	0.0789901	−	0.0456050i
$321$	15.7412	−	1.52302i	0.878586	−	0.0850069i
$322$	1.78827	−	16.0631i	0.0996566	−	0.895162i
$323$	2.02334	−	3.50453i	0.112582	−	0.194997i
$324$	8.33842	−	3.38684i	0.463246	−	0.188158i
$325$	6.51587	−	5.34742i	0.361435	−	0.296621i
$326$	−0.971853	−	0.561100i	−0.0538260	−	0.0310764i
$327$	−11.9410	+	26.2343i	−0.660341	+	1.45076i
$328$	−7.41619	−	4.28174i	−0.409490	−	0.236419i
$329$	1.99863	−	0.875154i	0.110188	−	0.0482488i
$330$	−2.42436	+	5.32627i	−0.133456	+	0.293201i
$331$	4.44504	+	2.56635i	0.244322	+	0.141059i	0.617161	−	0.786837i	$-0.288283\pi$
$331$	4.44504	+	2.56635i	0.244322	+	0.141059i	−0.372840	+	0.927896i	$0.621616\pi$
$332$		−	6.85946i		−	0.376462i
$333$	−4.56538	−	23.3718i	−0.250181	−	1.28077i
$334$	1.05294	+	0.607914i	0.0576142	+	0.0332636i
$335$	−2.67047	+	4.62539i	−0.145903	+	0.252712i
$336$	−0.0660664	+	4.58210i	−0.00360422	+	0.249974i
$337$	8.20935			0.447192			0.223596	−	0.974682i	$-0.428220\pi$
$337$	8.20935			0.447192			0.223596	+	0.974682i	$0.428220\pi$
$338$	9.77389	+	8.57153i	0.531629	+	0.466230i
$339$	9.11281	+	12.7632i	0.494940	+	0.693204i
$340$	4.31602	−	2.49186i	0.234069	−	0.135140i
$341$	−13.6014			−0.736560
$342$	−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
$345$	14.0500	−	10.0315i	0.756427	−	0.540080i
$346$	−9.60871	+	16.6428i	−0.516568	+	0.894721i
$347$			10.7152i			0.575225i	0.957747	+	0.287612i	$0.0928615\pi$
$347$			10.7152i			0.575225i	−0.957747	+	0.287612i	$0.907139\pi$
$348$	2.31267	−	5.08089i	0.123972	−	0.272364i
$349$	2.23834	−	3.87693i	0.119816	−	0.207527i	−0.799879	−	0.600162i	$-0.795103\pi$
$349$	2.23834	−	3.87693i	0.119816	−	0.207527i	0.919695	+	0.392634i	$0.128436\pi$
$350$	−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
$353$	−15.5607	+	8.98395i	−0.828211	+	0.478168i	−0.853240	−	0.521519i	$-0.825366\pi$
$353$	−15.5607	+	8.98395i	−0.828211	+	0.478168i	0.0250291	+	0.999687i	$0.492032\pi$
$354$	23.4415	−	2.26806i	1.24590	−	0.120546i
$355$	−12.9779	−	7.49278i	−0.688794	−	0.397676i
$356$		−	1.07299i		−	0.0568682i
$357$	−0.201798	+	13.9959i	−0.0106803	+	0.740741i
$358$	−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	$0.877059\pi$
$360$	−3.69122	+	3.21471i	−0.194544	+	0.169430i
$361$	8.62240	+	14.9344i	0.453811	+	0.786023i
$362$			21.1467i			1.11144i
$363$	10.5809	+	4.81610i	0.555352	+	0.252780i
$364$	−8.50136	−	4.32746i	−0.445592	−	0.226821i
$365$		−	4.68634i		−	0.245294i
$366$	11.1596	−	24.5174i	0.583321	−	1.28155i
$367$	14.2733	−	8.24067i	0.745058	−	0.430160i	−0.0788473	−	0.996887i	$-0.525124\pi$
$367$	14.2733	−	8.24067i	0.745058	−	0.430160i	0.823906	+	0.566727i	$0.191791\pi$
$368$		−	6.10879i		−	0.318443i
$369$	24.2985	+	8.34159i	1.26493	+	0.434246i
$370$	6.47574	+	11.2163i	0.336657	+	0.583108i
$371$	22.7778	+	16.7641i	1.18257	+	0.870349i
$372$	−10.3545	−	4.71305i	−0.536855	−	0.244360i
$373$	−17.7937	+	30.8197i	−0.921325	+	1.59578i	−0.123957	+	0.992288i	$0.539558\pi$
$373$	−17.7937	+	30.8197i	−0.921325	+	1.59578i	−0.797368	+	0.603494i	$0.793775\pi$
$374$	3.16255	+	5.47769i	0.163531	+	0.283245i
$375$	−20.6406	+	1.99707i	−1.06588	+	0.103128i
$376$	0.714173	−	0.412328i	0.0368307	−	0.0212642i
$377$	7.37216	+	8.98303i	0.379685	+	0.462649i
$378$	−2.44083	−	13.5293i	−0.125543	−	0.695873i
$379$	25.3582	+	14.6406i	1.30256	+	0.752035i	0.980843	−	0.194800i	$-0.0624057\pi$
$379$	25.3582	+	14.6406i	1.30256	+	0.752035i	0.321720	+	0.946835i	$0.395739\pi$
$380$		−	2.16163i		−	0.110889i
$381$	5.36848	+	2.44357i	0.275036	+	0.125188i
$382$	5.67581	+	3.27693i	0.290400	+	0.167662i
$383$	−8.78316	−	5.07096i	−0.448799	−	0.259114i	0.258524	−	0.966005i	$-0.416764\pi$
$383$	−8.78316	−	5.07096i	−0.448799	−	0.259114i	−0.707323	+	0.706891i	$0.750097\pi$
$384$	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
$387$	−10.6261	−	12.2012i	−0.540156	−	0.620222i
$388$	−4.58560	−	7.94250i	−0.232799	−	0.403219i
$389$	23.9026	+	13.8002i	1.21191	+	0.699696i	0.963175	−	0.268876i	$-0.0866521\pi$
$389$	23.9026	+	13.8002i	1.21191	+	0.699696i	0.248734	+	0.968572i	$0.419985\pi$
$390$	−2.62026	−	9.84675i	−0.132682	−	0.498610i
$391$		−	18.6591i		−	0.943632i
$392$	6.82861	+	1.53951i	0.344897	+	0.0777570i
$393$	−14.4304	+	10.3031i	−0.727915	+	0.519723i
$394$	0.185155	−	0.320698i	0.00932798	−	0.0161565i
$395$	−9.17493	−	5.29715i	−0.461641	−	0.266528i
$396$	−4.07996	−	4.68472i	−0.205025	−	0.235416i
$397$	0.109839	−	0.190247i	0.00551266	−	0.00954821i	−0.863256	−	0.504767i	$-0.831579\pi$
$397$	0.109839	−	0.190247i	0.00551266	−	0.00954821i	0.868769	+	0.495218i	$0.164912\pi$
$398$			16.8878i			0.846509i
$399$	5.21348	+	3.11107i	0.261001	+	0.155749i
$400$	−1.16892	+	2.02463i	−0.0584460	+	0.101231i
$401$	−23.8650			−1.19176			−0.595882	−	0.803072i	$-0.703197\pi$
$401$	−23.8650			−1.19176			−0.595882	+	0.803072i	$0.703197\pi$
$402$	−3.29454	−	4.61428i	−0.164317	−	0.230139i
$403$	18.3068	−	15.0239i	0.911925	−	0.748395i
$404$	0.381326	+	0.660476i	0.0189717	+	0.0328599i
$405$	9.01934	−	11.5882i	0.448175	−	0.575822i
$406$	−6.86781	−	5.05459i	−0.340844	−	0.250855i
$407$	−14.2352	+	8.21870i	−0.705613	+	0.407386i
$408$	0.509499	+	5.26590i	0.0252239	+	0.260701i
$409$	7.74689			0.383059			0.191529	−	0.981487i	$-0.438655\pi$
$409$	7.74689			0.383059			0.191529	+	0.981487i	$0.438655\pi$
$410$	−13.9723			−0.690042
$411$	0.616255	+	6.36928i	0.0303976	+	0.314174i
$412$	−11.8342	+	6.83246i	−0.583028	+	0.336611i
$413$	3.98039	−	35.7537i	0.195862	−	1.75933i
$414$	3.51342	+	17.9864i	0.172675	+	0.883985i
$415$	−5.59599	−	9.69254i	−0.274696	−	0.475788i
$416$	−3.37445	−	1.27006i	−0.165446	−	0.0622699i
$417$	13.7872	+	19.3102i	0.675164	+	0.945623i
$418$	2.74343			0.134186
$419$	1.65804	−	2.87182i	0.0810008	−	0.140297i	−0.822679	−	0.568506i	$-0.807522\pi$
$419$	1.65804	−	2.87182i	0.0810008	−	0.140297i	0.903680	+	0.428208i	$0.140855\pi$
$420$	3.64475	+	6.52849i	0.177846	+	0.318558i
$421$			25.2793i			1.23204i	0.787731	+	0.616019i	$0.211256\pi$
$421$			25.2793i			1.23204i	−0.787731	+	0.616019i	$0.788744\pi$
$422$	−0.132711	+	0.229862i	−0.00646026	+	0.0111895i
$423$	−1.86563	+	1.62479i	−0.0907100	+	0.0790000i
$424$	9.25742	+	5.34477i	0.449580	+	0.259565i
$425$	−3.57043	+	6.18417i	−0.173191	+	0.299976i
$426$	12.9467	−	9.24381i	0.627271	−	0.447864i
$427$	−33.1401	−	24.3905i	−1.60376	−	1.18034i
$428$		−	9.13060i		−	0.441344i
$429$	12.4970	−	3.32551i	0.603363	−	0.160557i
$430$	7.62075	+	4.39984i	0.367505	+	0.212179i
$431$	−12.4404	−	21.5475i	−0.599235	−	1.03790i	−0.992934	−	0.118666i	$-0.962138\pi$
$431$	−12.4404	−	21.5475i	−0.599235	−	1.03790i	0.393700	−	0.919239i	$-0.371195\pi$
$432$	−1.48267	−	4.98013i	−0.0713352	−	0.239607i
$433$	−17.2062	+	9.93398i	−0.826875	+	0.477396i	−0.852781	−	0.522268i	$-0.825086\pi$
$433$	−17.2062	+	9.93398i	−0.826875	+	0.477396i	0.0259066	+	0.999664i	$0.491753\pi$
$434$	−10.3009	+	13.9961i	−0.494459	+	0.671834i
$435$	−0.877182	−	9.06608i	−0.0420576	−	0.434685i
$436$	14.4120	+	8.32078i	0.690210	+	0.398493i
$437$	−7.00889	−	4.04659i	−0.335281	−	0.193574i
$438$	4.52785	+	2.06094i	0.216349	+	0.0984754i
$439$		−	1.31023i		−	0.0625339i	−0.999511	−	0.0312670i	$-0.990046\pi$
$439$		−	1.31023i		−	0.0625339i	0.999511	−	0.0312670i	$-0.00995420\pi$
$440$	2.92603	+	1.68934i	0.139493	+	0.0805363i
$441$	−20.9913	−	0.605446i	−0.999584	−	0.0288307i
$442$	−10.3072	−	3.87936i	−0.490262	−	0.184522i
$443$	−13.3621	+	7.71462i	−0.634853	+	0.366533i	−0.782629	−	0.622488i	$-0.786122\pi$
$443$	−13.3621	+	7.71462i	−0.634853	+	0.366533i	0.147776	+	0.989021i	$0.452789\pi$
$444$	−13.6848	+	1.32407i	−0.649453	+	0.0628374i
$445$	−0.875350	−	1.51615i	−0.0414956	−	0.0718724i
$446$	5.03909	−	8.72796i	0.238608	−	0.413281i
$447$	−30.4933	−	13.8796i	−1.44229	−	0.656485i
$448$	2.62951	+	0.292738i	0.124233	+	0.0138305i
$449$	10.2266	+	17.7130i	0.482625	+	0.835930i	0.999801	−	0.0199485i	$-0.00635023\pi$
$449$	10.2266	+	17.7130i	0.482625	+	0.835930i	−0.517176	+	0.855879i	$0.673017\pi$
$450$	2.27726	−	6.63351i	0.107351	−	0.312707i
$451$		−	17.7330i		−	0.835012i
$452$	7.84130	−	4.52717i	0.368823	−	0.212940i
$453$	−2.44329	+	5.36788i	−0.114796	+	0.252205i
$454$		−	11.4396i		−	0.536887i
$455$	−15.5429	+	0.820676i	−0.728664	+	0.0384739i
$456$	2.08852	+	0.950630i	0.0978038	+	0.0445173i
$457$		−	32.5131i		−	1.52090i	−0.649396	−	0.760450i	$-0.724978\pi$
$457$		−	32.5131i		−	1.52090i	0.649396	−	0.760450i	$-0.275022\pi$
$458$	4.74685	+	8.22179i	0.221806	+	0.384179i
$459$	−4.52878	−	15.2116i	−0.211386	−	0.710019i
$460$	−4.98359	−	8.63184i	−0.232361	−	0.402461i
$461$	−20.3615	+	11.7557i	−0.948329	+	0.547518i	−0.892562	−	0.450926i	$-0.851094\pi$
$461$	−20.3615	+	11.7557i	−0.948329	+	0.547518i	−0.0557678	+	0.998444i	$0.517761\pi$
$462$	−8.28565	+	4.62575i	−0.385483	+	0.215209i
$463$		−	33.0233i		−	1.53472i	−0.641214	−	0.767362i	$-0.721569\pi$
$463$		−	33.0233i		−	1.53472i	0.641214	−	0.767362i	$-0.278431\pi$
$464$	−2.79123	−	1.61152i	−0.129580	−	0.0748128i
$465$	−18.4760	+	1.78763i	−0.856805	+	0.0828995i
$466$	−3.90224	+	2.25296i	−0.180768	+	0.104366i
$467$	14.2621	+	24.7027i	0.659972	+	1.14310i	0.980623	+	0.195907i	$0.0627650\pi$
$467$	14.2621	+	24.7027i	0.659972	+	1.14310i	−0.320651	+	0.947197i	$0.603902\pi$
$468$	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
$471$	13.6280	−	29.9405i	0.627946	−	1.37959i
$472$		−	13.5971i		−	0.625859i
$473$	−5.58407	+	9.67190i	−0.256756	+	0.444714i
$474$	9.15290	−	6.53507i	0.420407	−	0.300166i
$475$	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
$478$	17.3876			0.795289
$479$	30.2057	−	17.4393i	1.38013	−	0.796821i	0.387959	−	0.921677i	$-0.373180\pi$
$479$	30.2057	−	17.4393i	1.38013	−	0.796821i	0.992175	+	0.124856i	$0.0398468\pi$
$480$	1.64215	+	2.29996i	0.0749535	+	0.104978i
$481$	10.0815	−	26.7859i	0.459678	−	1.22133i
$482$	−1.42882			−0.0650810
$483$	27.9911	+	0.403586i	1.27364	+	0.0183638i
$484$	3.35596	−	5.81270i	0.152544	−	0.264214i
$485$	−12.9591	−	7.48193i	−0.588442	−	0.339737i
$486$	7.22979	+	13.8105i	0.327950	+	0.626457i
$487$		−	0.222477i		−	0.0100814i	−0.999987	−	0.00504069i	$-0.998395\pi$
$487$		−	0.222477i		−	0.0100814i	0.999987	−	0.00504069i	$-0.00160451\pi$
$488$	−13.4689	−	7.77625i	−0.609707	−	0.352014i
$489$	0.805226	−	1.76907i	0.0364136	−	0.0800000i
$490$	10.9049	−	3.39547i	0.492633	−	0.153392i
$491$	25.2390	+	14.5717i	1.13902	+	0.657613i	0.946188	−	0.323619i	$-0.104899\pi$
$491$	25.2390	+	14.5717i	1.13902	+	0.657613i	0.192832	+	0.981232i	$0.438233\pi$
$492$	6.14466	−	13.4997i	0.277023	−	0.608614i
$493$	−8.52573	−	4.92233i	−0.383979	−	0.221691i
$494$	−3.69250	+	3.03035i	−0.166134	+	0.136342i
$495$	−9.58688	−	3.29114i	−0.430898	−	0.147926i
$496$	−3.28416	+	5.68833i	−0.147463	+	0.255413i
$497$	−9.74692	−	22.2595i	−0.437209	−	0.998474i
$498$	11.8257	−	1.14419i	0.529923	−	0.0512723i
$499$	34.1625	−	19.7237i	1.52932	−	0.882954i	0.529932	−	0.848040i	$-0.322218\pi$
$499$	34.1625	−	19.7237i	1.52932	−	0.882954i	0.999390	−	0.0349141i	$-0.0111158\pi$
$500$			11.9725i			0.535427i
$501$	−0.872409	+	1.91667i	−0.0389764	+	0.0856304i
$502$	−3.39863	−	5.88660i	−0.151688	−	0.262732i
$503$	−15.0219	−	26.0187i	−0.669793	−	1.16012i	−0.977962	−	0.208784i	$-0.933049\pi$
$503$	−15.0219	−	26.0187i	−0.669793	−	1.16012i	0.308169	−	0.951332i	$-0.400284\pi$
$504$	−7.91056	+	0.650416i	−0.352364	+	0.0289718i
$505$	1.07764	+	0.622177i	0.0479544	+	0.0276865i
$506$	10.9551	−	6.32494i	0.487015	−	0.281178i
$507$	−13.1470	+	18.2800i	−0.583878	+	0.811841i
$508$	1.70273	−	2.94922i	0.0755466	−	0.130851i
$509$		−	39.8865i		−	1.76794i	−0.467546	−	0.883969i	$-0.654862\pi$
$509$		−	39.8865i		−	1.76794i	0.467546	−	0.883969i	$-0.345138\pi$
$510$	5.01589	+	7.02517i	0.222107	+	0.311080i
$511$	4.50441	−	6.12026i	0.199263	−	0.270744i
$512$	1.00000			0.0441942
$513$	−6.69608	−	1.59780i	−0.295639	−	0.0705444i
$514$	14.1505			0.624152
$515$	−11.1479	+	19.3088i	−0.491236	+	0.850846i
$516$	−7.60245	+	5.42807i	−0.334679	+	0.238957i
$517$	1.47889	+	0.853835i	0.0650413	+	0.0375516i
$518$	−2.32370	+	20.8726i	−0.102098	+	0.917089i
$519$	−30.2949	−	13.7893i	−1.32980	−	0.605285i
$520$	−5.80429	+	0.958282i	−0.254535	+	0.0420234i
$521$	−11.5449	+	19.9963i	−0.505789	+	0.876052i	0.494188	+	0.869355i	$0.335465\pi$
$521$	−11.5449	+	19.9963i	−0.505789	+	0.876052i	−0.999978	+	0.00669760i	$0.997868\pi$
$522$	9.14522	+	3.13952i	0.400275	+	0.137413i
$523$			24.9466i			1.09084i	0.838163	+	0.545420i	$0.183630\pi$
$523$			24.9466i			1.09084i	−0.838163	+	0.545420i	$0.816370\pi$
$524$	5.11851	+	8.86551i	0.223603	+	0.387292i
$525$	−9.19982	−	5.48987i	−0.401513	−	0.239597i
$526$	−11.1426	+	6.43320i	−0.485842	+	0.280501i
$527$	−10.0314	+	17.3748i	−0.436973	+	0.756859i
$528$	−2.91901	+	2.08414i	−0.127033	+	0.0907004i
$529$	−14.3174			−0.622494
$530$	17.4412			0.757597
$531$	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
$534$	1.84983	−	0.178979i	0.0800500	−	0.00774518i
$535$	−7.44880	−	12.9017i	−0.322040	−	0.557789i
$536$	−2.83485	+	1.63670i	−0.122447	+	0.0706948i
$537$	−16.7025	−	23.3932i	−0.720765	−	1.00949i
$538$	27.3543			1.17933
$539$	4.30937	+	13.8400i	0.185618	+	0.596130i
$540$	−6.15787	−	5.82744i	−0.264992	−	0.250773i
$541$	−29.0831	+	16.7911i	−1.25038	+	0.721907i	−0.971185	−	0.238327i	$-0.923401\pi$
$541$	−29.0831	+	16.7911i	−1.25038	+	0.721907i	−0.279195	+	0.960234i	$0.590068\pi$
$542$	−1.35557			−0.0582267
$543$	−36.4569	+	3.52736i	−1.56451	+	0.151373i
$544$	3.05447			0.130959
$545$	27.1526			1.16309
$546$	6.04249	−	15.3782i	0.258594	−	0.658125i
$547$	−25.6327			−1.09597			−0.547987	−	0.836487i	$-0.684606\pi$
$547$	−25.6327			−1.09597			−0.547987	+	0.836487i	$0.684606\pi$
$548$	3.69448			0.157820
$549$	44.1295	+	15.1495i	1.88340	+	0.646566i
$550$	−4.84112			−0.206426
$551$	−3.69793	+	2.13500i	−0.157537	+	0.0909542i
$552$	10.5316	−	1.01897i	0.448253	−	0.0433704i
$553$	−6.89075	−	15.7367i	−0.293024	−	0.669193i
$554$	−20.9249			−0.889013
$555$	−18.2567	+	13.0351i	−0.774955	+	0.553309i
$556$	11.8635	−	6.84939i	0.503124	−	0.290479i
$557$	−15.0162	−	26.0087i	−0.636255	−	1.10203i	−0.986248	−	0.165273i	$-0.947149\pi$
$557$	−15.0162	−	26.0087i	−0.636255	−	1.10203i	0.349993	−	0.936752i	$-0.386184\pi$
$558$	6.39813	−	18.6373i	0.270854	−	0.788980i
$559$	−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
$562$	4.08136			0.172162
$563$	−26.1791			−1.10332			−0.551658	−	0.834070i	$-0.686005\pi$
$563$	−26.1791			−1.10332			−0.551658	+	0.834070i	$0.686005\pi$
$564$	0.829981	+	1.16246i	0.0349485	+	0.0489482i
$565$	7.38659	−	12.7940i	0.310756	−	0.538246i
$566$	−1.87345	+	1.08164i	−0.0787469	+	0.0454645i
$567$	22.9174	−	6.46474i	0.962440	−	0.271494i
$568$	−4.59225	−	7.95402i	−0.192687	−	0.333743i
$569$			5.85652i			0.245518i	0.992437	+	0.122759i	$0.0391742\pi$
$569$			5.85652i			0.245518i	−0.992437	+	0.122759i	$0.960826\pi$
$570$	3.72664	−	0.360568i	0.156092	−	0.0151026i
$571$	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	$-0.0589950\pi$
$572$	−1.21621	−	7.36653i	−0.0508522	−	0.308010i
$573$	−4.70268	+	10.3317i	−0.196457	+	0.431613i
$574$	−18.2475	−	13.4299i	−0.761635	−	0.560551i
$575$	12.3680	+	7.14069i	0.515783	+	0.297787i
$576$	−2.94435	+	0.575141i	−0.122681	+	0.0239642i
$577$	2.11078	−	3.65597i	0.0878727	−	0.152200i	−0.818739	−	0.574166i	$-0.805326\pi$
$577$	2.11078	−	3.65597i	0.0878727	−	0.152200i	0.906612	+	0.421966i	$0.138660\pi$
$578$	−7.67022			−0.319039
$579$	−10.0077	−	14.0167i	−0.415907	−	0.582512i
$580$	−5.25875			−0.218358
$581$	2.00802	−	18.0370i	0.0833068	−	0.748301i
$582$	12.9280	−	9.23043i	0.535882	−	0.382613i
$583$			22.1355i			0.916761i
$584$	1.43611	−	2.48741i	0.0594265	−	0.102930i
$585$	16.5387	−	6.15981i	0.683792	−	0.254677i
$586$	−5.29149	+	3.05504i	−0.218590	+	0.126203i
$587$	25.6971	+	14.8362i	1.06063	+	0.612358i	0.925608	−	0.378484i	$-0.123555\pi$
$587$	25.6971	+	14.8362i	1.06063	+	0.612358i	0.135027	+	0.990842i	$0.456888\pi$
$588$	−1.51507	+	12.0293i	−0.0624806	+	0.496081i
$589$	4.35098	+	7.53612i	0.179279	+	0.310521i
$590$	−11.0926	−	19.2130i	−0.456676	−	0.790986i
$591$	0.583768	+	0.265714i	0.0240130	+	0.0109300i
$592$			7.93783i			0.326243i
$593$	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
$595$	12.0785	−	5.28889i	0.495169	−	0.216823i
$596$	−9.67165	+	16.7518i	−0.396166	+	0.686180i
$597$	−29.1146	+	2.81696i	−1.19158	+	0.115290i
$598$	−7.75854	+	20.6138i	−0.317270	+	0.842963i
$599$	−31.7637	−	18.3388i	−1.29783	−	0.749302i	−0.317800	−	0.948158i	$-0.602944\pi$
$599$	−31.7637	−	18.3388i	−1.29783	−	0.749302i	−0.980029	+	0.198856i	$0.936277\pi$
$600$	−3.68544	−	1.67750i	−0.150457	−	0.0684837i
$601$	3.55065	+	2.04997i	0.144834	+	0.0836199i	0.570666	−	0.821182i	$-0.306685\pi$
$601$	3.55065	+	2.04997i	0.144834	+	0.0836199i	−0.425832	+	0.904802i	$0.640019\pi$
$602$	5.72350	+	13.0710i	0.233272	+	0.532734i
$603$	7.40548	−	6.44948i	0.301574	−	0.262643i
$604$	2.94889	+	1.70254i	0.119989	+	0.0692754i
$605$		−	10.9513i		−	0.445232i
$606$	−1.07505	+	0.767577i	−0.0436711	+	0.0311807i
$607$	3.85144	+	2.22363i	0.156325	+	0.0902543i	0.576122	−	0.817364i	$-0.304565\pi$
$607$	3.85144	+	2.22363i	0.156325	+	0.0902543i	−0.419797	+	0.907618i	$0.637899\pi$
$608$	0.662420	−	1.14734i	0.0268647	−	0.0465310i
$609$	7.56854	−	12.6832i	0.306693	−	0.513950i
$610$	−25.3757			−1.02743
$611$	−2.93363	+	0.484339i	−0.118682	+	0.0195942i
$612$	−8.99343	+	1.75675i	−0.363538	+	0.0710125i
$613$	−5.04378	+	2.91203i	−0.203716	+	0.117616i	−0.598388	−	0.801207i	$-0.704192\pi$
$613$	−5.04378	+	2.91203i	−0.203716	+	0.117616i	0.394671	+	0.918822i	$0.370858\pi$
$614$	−0.994225			−0.0401237
$615$	−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	−0.979946	−	0.199263i	$-0.936145\pi$
$617$	−16.4572	−	28.5046i	−0.662540	−	1.14755i	0.317406	−	0.948290i	$-0.397188\pi$
$618$	−13.7532	−	19.2624i	−0.553233	−	0.774848i
$619$	−13.6240	+	23.5975i	−0.547595	+	0.948463i	0.450843	+	0.892603i	$0.351123\pi$
$619$	−13.6240	+	23.5975i	−0.547595	+	0.948463i	−0.998439	+	0.0558598i	$0.982210\pi$
$620$			10.7169i			0.430403i
$621$	−30.4226	+	9.05735i	−1.22082	+	0.363459i
$622$	−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
$626$	22.7854	−	13.1551i	0.910687	−	0.525786i
$627$	0.457617	+	4.72968i	0.0182754	+	0.188885i
$628$	−16.4481	−	9.49631i	−0.656350	−	0.378944i
$629$			24.2459i			0.966746i
$630$	−10.6472	+	7.37253i	−0.424193	+	0.293729i
$631$	1.34761	−	0.778043i	0.0536475	−	0.0309734i	−0.472936	−	0.881097i	$-0.656806\pi$
$631$	1.34761	−	0.778043i	0.0536475	−	0.0309734i	0.526584	+	0.850123i	$0.323473\pi$
$632$	−3.24657	−	5.62322i	−0.129142	−	0.223680i
$633$	−0.418418	−	0.190451i	−0.0166306	−	0.00756976i
$634$	11.3370	+	19.6363i	0.450251	+	0.779858i
$635$		−	5.55641i		−	0.220499i
$636$	−7.67021	+	16.8513i	−0.304144	+	0.668198i
$637$	−21.0876	−	13.8678i	−0.835520	−	0.549461i
$638$		−	6.67415i		−	0.264232i
$639$	18.0959	+	20.7782i	0.715863	+	0.821974i
$640$	1.41302	−	0.815806i	0.0558544	−	0.0322476i
$641$			26.4241i			1.04369i	0.853041	+	0.521844i	$0.174756\pi$
$641$			26.4241i			1.04369i	−0.853041	+	0.521844i	$0.825244\pi$
$642$	15.7412	−	1.52302i	0.621254	−	0.0601090i
$643$	18.5300	+	32.0948i	0.730751	+	1.26570i	0.956563	+	0.291526i	$0.0941631\pi$
$643$	18.5300	+	32.0948i	0.730751	+	1.26570i	−0.225812	+	0.974171i	$0.572504\pi$
$644$	1.78827	−	16.0631i	0.0704678	−	0.632975i
$645$	−6.31415	+	13.8721i	−0.248620	+	0.546213i
$646$	2.02334	−	3.50453i	0.0796073	−	0.137884i
$647$	−18.7660	−	32.5037i	−0.737769	−	1.27785i	−0.953498	−	0.301401i	$-0.902546\pi$
$647$	−18.7660	−	32.5037i	−0.737769	−	1.27785i	0.215728	−	0.976453i	$-0.430788\pi$
$648$	8.33842	−	3.38684i	0.327564	−	0.133048i
$649$	24.3842	−	14.0782i	0.957165	−	0.552619i
$650$	6.51587	−	5.34742i	0.255573	−	0.209743i
$651$	−25.8475	−	15.4241i	−1.01304	−	0.604520i
$652$	−0.971853	−	0.561100i	−0.0380607	−	0.0219744i
$653$		−	42.7824i		−	1.67421i	−0.547045	−	0.837103i	$-0.684248\pi$
$653$		−	42.7824i		−	1.67421i	0.547045	−	0.837103i	$-0.315752\pi$
$654$	−11.9410	+	26.2343i	−0.466932	+	1.02584i
$655$	14.4651	+	8.35142i	0.565198	+	0.326317i
$656$	−7.41619	−	4.28174i	−0.289553	−	0.167174i
$657$	−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	0.162425	−	0.986721i	$-0.448068\pi$
$659$	28.1909	−	16.2760i	1.09816	−	0.634024i	0.935738	+	0.352696i	$0.114735\pi$
$660$	−2.42436	+	5.32627i	−0.0943679	+	0.207325i
$661$	−10.1442	−	17.5703i	−0.394565	−	0.683406i	0.598481	−	0.801137i	$-0.295771\pi$
$661$	−10.1442	−	17.5703i	−0.394565	−	0.683406i	−0.993046	+	0.117731i	$0.962438\pi$
$662$	4.44504	+	2.56635i	0.172762	+	0.0997439i
$663$	4.96874	−	18.4167i	0.192970	−	0.715243i
$664$		−	6.85946i		−	0.266199i
$665$	0.632789	−	5.68401i	0.0245385	−	0.220416i
$666$	−4.56538	−	23.3718i	−0.176905	−	0.905638i
$667$	−9.84443	+	17.0511i	−0.381178	+	0.660219i
$668$	1.05294	+	0.607914i	0.0407394	+	0.0235209i
$669$	15.8875	+	7.23153i	0.614248	+	0.279587i
$670$	−2.67047	+	4.62539i	−0.103169	+	0.178694i
$671$		−	32.2056i		−	1.24328i
$672$	−0.0660664	+	4.58210i	−0.00254857	+	0.176758i
$673$	−11.3708	+	19.6948i	−0.438312	+	0.759179i	−0.997559	−	0.0698219i	$-0.977757\pi$
$673$	−11.3708	+	19.6948i	−0.438312	+	0.759179i	0.559247	+	0.829001i	$0.311090\pi$
$674$	8.20935			0.316212
$675$	11.8160	+	2.81951i	0.454800	+	0.108523i
$676$	9.77389	+	8.57153i	0.375919	+	0.329674i
$677$	16.2207	+	28.0950i	0.623412	+	1.07978i	0.988846	+	0.148943i	$0.0475872\pi$
$677$	16.2207	+	28.0950i	0.623412	+	1.07978i	−0.365434	+	0.930837i	$0.619079\pi$
$678$	9.11281	+	12.7632i	0.349975	+	0.490169i
$679$	−9.73281	−	22.2272i	−0.373511	−	0.853003i
$680$	4.31602	−	2.49186i	0.165512	−	0.0955583i
$681$	19.7219	−	1.90817i	0.755744	−	0.0731214i
$682$	−13.6014			−0.520826
$683$	−7.19406			−0.275273			−0.137637	−	0.990483i	$-0.543951\pi$
$683$	−7.19406			−0.275273			−0.137637	+	0.990483i	$0.543951\pi$
$684$	−1.29051	+	3.75917i	−0.0493440	+	0.143736i
$685$	5.22037	−	3.01398i	0.199460	−	0.115158i
$686$	17.5052	+	6.04714i	0.668352	+	0.230881i
$687$	−13.3826	+	9.55500i	−0.510577	+	0.364546i
$688$	2.69662	+	4.67069i	0.102808	+	0.178068i
$689$	−24.4505	−	29.7932i	−0.931491	−	1.13503i
$690$	14.0500	−	10.0315i	0.534874	−	0.381894i
$691$	26.0372			0.990503			0.495252	−	0.868750i	$-0.335076\pi$
$691$	26.0372			0.990503			0.495252	+	0.868750i	$0.335076\pi$
$692$	−9.60871	+	16.6428i	−0.365268	+	0.632664i
$693$	−9.35688	−	13.5129i	−0.355438	−	0.513311i
$694$			10.7152i			0.406745i
$695$	11.1756	−	19.3566i	0.423913	−	0.734239i
$696$	2.31267	−	5.08089i	0.0876614	−	0.192591i
$697$	−22.6525	−	13.0784i	−0.858025	−	0.495381i
$698$	2.23834	−	3.87693i	0.0847226	−	0.146744i
$699$	−4.53501	−	6.35166i	−0.171530	−	0.240242i
$700$	−3.66637	+	4.98159i	−0.138576	+	0.188286i
$701$			26.3672i			0.995877i	0.867212	+	0.497938i	$0.165909\pi$
$701$			26.3672i			0.995877i	−0.867212	+	0.497938i	$0.834091\pi$
$702$	−1.32185	+	18.6883i	−0.0498900	+	0.705345i
$703$	9.10743	+	5.25818i	0.343493	+	0.198316i
$704$	1.03538	+	1.79334i	0.0390225	+	0.0675889i
$705$	2.12112	+	0.965468i	0.0798859	+	0.0363616i
$706$	−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
$709$	−24.4953	−	14.1424i	−0.919940	−	0.531127i	−0.0363238	−	0.999340i	$-0.511565\pi$
$709$	−24.4953	−	14.1424i	−0.919940	−	0.531127i	−0.883616	+	0.468213i	$0.844898\pi$
$710$	−12.9779	−	7.49278i	−0.487051	−	0.281199i
$711$	12.7932	+	14.6895i	0.479782	+	0.550900i
$712$		−	1.07299i		−	0.0402119i
$713$	34.7488	+	20.0622i	1.30135	+	0.751337i
$714$	−0.201798	+	13.9959i	−0.00755209	+	0.523783i
$715$	−7.72819	−	9.41685i	−0.289018	−	0.352170i
$716$	−14.3720	+	8.29766i	−0.537105	+	0.310098i
$717$	2.90032	+	29.9762i	0.108315	+	1.11948i
$718$	−2.59460	−	4.49398i	−0.0968295	−	0.167714i
$719$	9.30194	−	16.1114i	0.346904	−	0.600855i	−0.638794	−	0.769378i	$-0.720566\pi$
$719$	9.30194	−	16.1114i	0.346904	−	0.600855i	0.985698	+	0.168523i	$0.0538997\pi$
$720$	−3.69122	+	3.21471i	−0.137564	+	0.119805i
$721$	−33.1181	+	14.5017i	−1.23338	+	0.540071i
$722$	8.62240	+	14.9344i	0.320893	+	0.555802i
$723$	−0.238333	−	2.46329i	−0.00886372	−	0.0916106i
$724$			21.1467i			0.785910i
$725$	6.52545	−	3.76747i	0.242349	−	0.139920i
$726$	10.5809	+	4.81610i	0.392693	+	0.178742i
$727$			48.9063i			1.81383i	0.421309	+	0.906917i	$0.361571\pi$
$727$			48.9063i			1.81383i	−0.421309	+	0.906917i	$0.638429\pi$
$728$	−8.50136	−	4.32746i	−0.315081	−	0.160386i
$729$	−22.6034	+	14.7678i	−0.837161	+	0.546956i
$730$		−	4.68634i		−	0.173449i
$731$	8.23675	+	14.2665i	0.304647	+	0.527664i
$732$	11.1596	−	24.5174i	0.412471	−	0.906191i
$733$	0.276176	+	0.478352i	0.0102008	+	0.0176683i	0.871081	−	0.491140i	$-0.163420\pi$
$733$	0.276176	+	0.478352i	0.0102008	+	0.0176683i	−0.860880	+	0.508808i	$0.830086\pi$
$734$	14.2733	−	8.24067i	0.526836	−	0.304169i
$735$	7.67277	+	18.2337i	0.283014	+	0.672558i
$736$		−	6.10879i		−	0.225173i
$737$	−5.87032	−	3.38923i	−0.216236	−	0.124844i
$738$	24.2985	+	8.34159i	0.894439	+	0.307058i
$739$	27.9938	−	16.1622i	1.02977	−	0.594537i	0.112850	−	0.993612i	$-0.464002\pi$
$739$	27.9938	−	16.1622i	1.02977	−	0.594537i	0.916918	+	0.399075i	$0.130669\pi$
$740$	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	−0.263949	−	0.964537i	$-0.585025\pi$
$743$	19.1716	−	33.2062i	0.703339	−	1.21822i	0.967288	−	0.253682i	$-0.0816416\pi$
$744$	−10.3545	−	4.71305i	−0.379614	−	0.172789i
$745$			31.5608i			1.15630i
$746$	−17.7937	+	30.8197i	−0.651475	+	1.12839i
$747$	3.94516	+	20.1967i	0.144346	+	0.738957i
$748$	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
$751$	−14.1947			−0.517973			−0.258986	−	0.965881i	$-0.583388\pi$
$751$	−14.1947			−0.517973			−0.258986	+	0.965881i	$0.583388\pi$
$752$	0.714173	−	0.412328i	0.0260432	−	0.0150361i
$753$	9.58160	−	6.84115i	0.349173	−	0.249305i
$754$	7.37216	+	8.98303i	0.268478	+	0.327143i
$755$	5.55578			0.202195
$756$	−2.44083	−	13.5293i	−0.0887722	−	0.492056i
$757$	−16.0710	+	27.8358i	−0.584111	+	1.01171i	0.410875	+	0.911692i	$0.365223\pi$
$757$	−16.0710	+	27.8358i	−0.584111	+	1.01171i	−0.994986	+	0.100018i	$0.968110\pi$
$758$	25.3582	+	14.6406i	0.921051	+	0.531769i
$759$	12.7316	+	17.8316i	0.462127	+	0.647246i
$760$		−	2.16163i		−	0.0784104i
$761$	−4.03145	−	2.32756i	−0.146140	−	0.0843740i	0.425147	−	0.905124i	$-0.360222\pi$
$761$	−4.03145	−	2.32756i	−0.146140	−	0.0843740i	−0.571287	+	0.820750i	$0.693556\pi$
$762$	5.36848	+	2.44357i	0.194480	+	0.0885213i
$763$	35.4607	+	26.0985i	1.28376	+	0.944828i
$764$	5.67581	+	3.27693i	0.205344	+	0.118555i
$765$	−11.2747	+	9.81922i	−0.407638	+	0.355015i
$766$	−8.78316	−	5.07096i	−0.317348	−	0.183221i
$767$	−17.2692	+	45.8829i	−0.623554	+	1.65674i
$768$	0.166804	+	1.72400i	0.00601903	+	0.0622095i
$769$	−20.9476	+	36.2823i	−0.755389	+	1.30837i	0.189792	+	0.981824i	$0.439219\pi$
$769$	−20.9476	+	36.2823i	−0.755389	+	1.30837i	−0.945181	+	0.326548i	$0.894115\pi$
$770$	7.19948	+	5.29870i	0.259451	+	0.190952i
$771$	2.36037	+	24.3955i	0.0850065	+	0.878582i
$772$	−8.61135	+	4.97176i	−0.309929	+	0.178938i
$773$		−	48.7888i		−	1.75481i	−0.479749	−	0.877406i	$-0.659272\pi$
$773$		−	48.7888i		−	1.75481i	0.479749	−	0.877406i	$-0.340728\pi$
$774$	−10.6261	−	12.2012i	−0.381948	−	0.438563i
$775$	−7.67784	−	13.2984i	−0.275796	−	0.477693i
$776$	−4.58560	−	7.94250i	−0.164614	−	0.285119i
$777$	−36.3719	−	0.524424i	−1.30484	−	0.0188136i
$778$	23.9026	+	13.8002i	0.856949	+	0.494760i
$779$	−9.82526	+	5.67262i	−0.352026	+	0.203243i
$780$	−2.62026	−	9.84675i	−0.0938203	−	0.352570i
$781$	9.50949	−	16.4709i	0.340276	−	0.589376i
$782$		−	18.6591i		−	0.667249i
$783$	−3.88708	+	16.2900i	−0.138913	+	0.582159i
$784$	6.82861	+	1.53951i	0.243879	+	0.0549825i
$785$	−30.9886			−1.10603
$786$	−14.4304	+	10.3031i	−0.514714	+	0.367500i
$787$	19.2602			0.686553			0.343277	−	0.939234i	$-0.388463\pi$
$787$	19.2602			0.686553			0.343277	+	0.939234i	$0.388463\pi$
$788$	0.185155	−	0.320698i	0.00659588	−	0.0114244i
$789$	−12.9495	−	18.1368i	−0.461014	−	0.645688i
$790$	−9.17493	−	5.29715i	−0.326429	−	0.188464i
$791$	21.9440	−	9.60879i	0.780239	−	0.341649i
$792$	−4.07996	−	4.68472i	−0.144975	−	0.166464i
$793$	35.5738	+	43.3469i	1.26326	+	1.53929i
$794$	0.109839	−	0.190247i	0.00389804	−	0.00675161i
$795$	2.90927	+	30.0686i	0.103181	+	1.06642i
$796$			16.8878i			0.598572i
$797$	0.0214000	+	0.0370659i	0.000758027	+	0.00131294i	0.866404	−	0.499343i	$-0.166425\pi$
$797$	0.0214000	+	0.0370659i	0.000758027	+	0.00131294i	−0.865646	+	0.500656i	$0.833092\pi$
$798$	5.21348	+	3.11107i	0.184555	+	0.110131i
$799$	2.18142	−	1.25944i	0.0771731	−	0.0445559i
$800$	−1.16892	+	2.02463i	−0.0413276	+	0.0715814i
$801$	0.617119	+	3.15925i	0.0218048	+	0.111627i
$802$	−23.8650			−0.842704
$803$	5.94769			0.209889
$804$	−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
$807$	4.56281	+	47.1587i	0.160618	+	1.66007i
$808$	0.381326	+	0.660476i	0.0134150	+	0.0232355i
$809$	18.0101	−	10.3981i	0.633200	−	0.365578i	−0.148790	−	0.988869i	$-0.547538\pi$
$809$	18.0101	−	10.3981i	0.633200	−	0.365578i	0.781990	+	0.623291i	$0.214205\pi$
$810$	9.01934	−	11.5882i	0.316907	−	0.407168i
$811$	−40.3139			−1.41561			−0.707807	−	0.706406i	$-0.750315\pi$
$811$	−40.3139			−1.41561			−0.707807	+	0.706406i	$0.750315\pi$
$812$	−6.86781	−	5.05459i	−0.241013	−	0.177381i
$813$	−0.226115	−	2.33700i	−0.00793020	−	0.0819622i
$814$	−14.2352	+	8.21870i	−0.498944	+	0.288065i
$815$	−1.83099			−0.0641369
$816$	0.509499	+	5.26590i	0.0178360	+	0.184344i
$817$	7.14518			0.249978
$818$	7.74689			0.270864
$819$	27.5199	+	7.85210i	0.961623	+	0.274375i
$820$	−13.9723			−0.487933
$821$	17.4989			0.610715			0.305357	−	0.952238i	$-0.401224\pi$
$821$	17.4989			0.610715			0.305357	+	0.952238i	$0.401224\pi$
$822$	0.616255	+	6.36928i	0.0214944	+	0.222154i
$823$	28.5334			0.994611			0.497306	−	0.867575i	$-0.334323\pi$
$823$	28.5334			0.994611			0.497306	+	0.867575i	$0.334323\pi$
$824$	−11.8342	+	6.83246i	−0.412263	+	0.238020i
$825$	−0.807520	−	8.34609i	−0.0281142	−	0.290574i
$826$	3.98039	−	35.7537i	0.138496	−	1.24403i
$827$	17.6018			0.612075			0.306037	−	0.952020i	$-0.400997\pi$
$827$	17.6018			0.612075			0.306037	+	0.952020i	$0.400997\pi$
$828$	3.51342	+	17.9864i	0.122100	+	0.625072i
$829$	−1.98489	+	1.14598i	−0.0689380	+	0.0398014i	−0.534073	−	0.845438i	$-0.679339\pi$
$829$	−1.98489	+	1.14598i	−0.0689380	+	0.0398014i	0.465135	+	0.885240i	$0.346006\pi$
$830$	−5.59599	−	9.69254i	−0.194240	−	0.336433i
$831$	−3.49036	−	36.0745i	−0.121079	−	1.25141i
$832$	−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
$835$	1.98376			0.0686508
$836$	2.74343			0.0948836
$837$	33.1979	+	7.92159i	1.14749	+	0.273810i
$838$	1.65804	−	2.87182i	0.0572762	−	0.0992053i
$839$	−10.6696	+	6.16009i	−0.368355	+	0.212670i	−0.672740	−	0.739879i	$-0.734883\pi$
$839$	−10.6696	+	6.16009i	−0.368355	+	0.212670i	0.304384	+	0.952549i	$0.401549\pi$
$840$	3.64475	+	6.52849i	0.125756	+	0.225254i
$841$	−9.30602	−	16.1185i	−0.320897	−	0.555810i
$842$			25.2793i			0.871183i
$843$	0.680789	+	7.03627i	0.0234476	+	0.242342i
$844$	−0.132711	+	0.229862i	−0.00456809	+	0.00791217i
$845$	20.8034	+	4.13812i	0.715658	+	0.142356i
$846$	−1.86563	+	1.62479i	−0.0641417	+	0.0558614i
$847$	10.5261	−	14.3021i	0.361682	−	0.491426i
$848$	9.25742	+	5.34477i	0.317901	+	0.183540i
$849$	−2.17724	−	3.04940i	−0.0747226	−	0.104655i
$850$	−3.57043	+	6.18417i	−0.122465	+	0.212115i
$851$	48.4906			1.66224
$852$	12.9467	−	9.24381i	0.443547	−	0.316688i
$853$	36.0741			1.23515			0.617577	−	0.786510i	$-0.288114\pi$
$853$	36.0741			1.23515			0.617577	+	0.786510i	$0.288114\pi$
$854$	−33.1401	−	24.3905i	−1.13403	−	0.834627i
$855$	1.24324	+	6.36459i	0.0425179	+	0.217664i
$856$		−	9.13060i		−	0.312078i
$857$	7.21848	−	12.5028i	0.246579	−	0.427087i	−0.715996	−	0.698105i	$-0.754027\pi$
$857$	7.21848	−	12.5028i	0.246579	−	0.427087i	0.962574	+	0.271018i	$0.0873603\pi$
$858$	12.4970	−	3.32551i	0.426642	−	0.113531i
$859$	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
$861$	20.1093	−	33.6988i	0.685323	−	1.14845i
$862$	−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	$0.667500\pi$
$864$	−1.48267	−	4.98013i	−0.0504416	−	0.169427i
$865$			31.3554i			1.06612i
$866$	−17.2062	+	9.93398i	−0.584689	+	0.337570i
$867$	−1.27943	−	13.2235i	−0.0434516	−	0.449092i
$868$	−10.3009	+	13.9961i	−0.349635	+	0.475059i
$869$	6.72289	−	11.6444i	0.228058	−	0.395009i
$870$	−0.877182	−	9.06608i	−0.0297392	−	0.307369i
$871$	11.6448	−	1.92254i	0.394569	−	0.0651429i
$872$	14.4120	+	8.32078i	0.488052	+	0.281777i
$873$	18.0697	+	20.7481i	0.611567	+	0.702218i
$874$	−7.00889	−	4.04659i	−0.237079	−	0.136878i
$875$	−3.50480	+	31.4818i	−0.118484	+	1.06428i
$876$	4.52785	+	2.06094i	0.152982	+	0.0696326i
$877$	−21.5265	−	12.4284i	−0.726900	−	0.419676i	0.0903872	−	0.995907i	$-0.471190\pi$
$877$	−21.5265	−	12.4284i	−0.726900	−	0.419676i	−0.817287	+	0.576231i	$0.804523\pi$
$878$		−	1.31023i		−	0.0442181i
$879$	−6.14954	−	8.61294i	−0.207419	−	0.290507i
$880$	2.92603	+	1.68934i	0.0986365	+	0.0569478i
$881$	−11.1486	+	19.3099i	−0.375606	+	0.650568i	−0.990418	−	0.138106i	$-0.955899\pi$
$881$	−11.1486	+	19.3099i	−0.375606	+	0.650568i	0.614812	+	0.788674i	$0.289232\pi$
$882$	−20.9913	−	0.605446i	−0.706813	−	0.0203864i
$883$	28.3409			0.953749			0.476874	−	0.878971i	$-0.341770\pi$
$883$	28.3409			0.953749			0.476874	+	0.878971i	$0.341770\pi$
$884$	−10.3072	−	3.87936i	−0.346668	−	0.130477i
$885$	31.2729	−	22.3285i	1.05123	−	0.750564i
$886$	−13.3621	+	7.71462i	−0.448909	+	0.259178i
$887$	−23.8404			−0.800481			−0.400241	−	0.916410i	$-0.631073\pi$
$887$	−23.8404			−0.800481			−0.400241	+	0.916410i	$0.631073\pi$
$888$	−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
$891$	14.7072	+	11.4469i	0.492710	+	0.383486i
$892$	5.03909	−	8.72796i	0.168721	−	0.292234i
$893$		−	1.09254i		−	0.0365604i
$894$	−30.4933	−	13.8796i	−1.01985	−	0.464205i
$895$	−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
$899$	18.3337	−	10.5850i	0.611463	−	0.353028i
$900$	2.27726	−	6.63351i	0.0759088	−	0.221117i
$901$	28.2765	+	16.3254i	0.942026	+	0.543879i
$902$		−	17.7330i		−	0.590443i
$903$	−21.5797	+	12.0476i	−0.718128	+	0.400919i
$904$	7.84130	−	4.52717i	0.260798	−	0.150572i
$905$	17.2516	+	29.8806i	0.573462	+	0.993265i
$906$	−2.44329	+	5.36788i	−0.0811730	+	0.178336i
$907$	−9.05622	−	15.6858i	−0.300707	−	0.520840i	0.675589	−	0.737278i	$-0.263889\pi$
$907$	−9.05622	−	15.6858i	−0.300707	−	0.520840i	−0.976296	+	0.216438i	$0.930556\pi$
$908$		−	11.4396i		−	0.379636i
$909$	−1.50263	−	1.72536i	−0.0498389	−	0.0572265i
$910$	−15.5429	+	0.820676i	−0.515244	+	0.0272051i
$911$			54.3855i			1.80187i	0.433952	+	0.900936i	$0.357119\pi$
$911$			54.3855i			1.80187i	−0.433952	+	0.900936i	$0.642881\pi$
$912$	2.08852	+	0.950630i	0.0691577	+	0.0314785i
$913$	12.3013	−	7.10217i	0.407114	−	0.235048i
$914$		−	32.5131i		−	1.07544i
$915$	−4.23277	−	43.7477i	−0.139931	−	1.44625i
$916$	4.74685	+	8.22179i	0.156840	+	0.271655i
$917$	10.8639	+	24.8103i	0.358757	+	0.819308i
$918$	−4.52878	−	15.2116i	−0.149472	−	0.502059i
$919$	−0.499725	+	0.865548i	−0.0164844	+	0.0285518i	−0.874150	−	0.485656i	$-0.838581\pi$
$919$	−0.499725	+	0.865548i	−0.0164844	+	0.0285518i	0.857666	+	0.514208i	$0.171914\pi$
$920$	−4.98359	−	8.63184i	−0.164304	−	0.284583i
$921$	−0.165841	−	1.71404i	−0.00546465	−	0.0564797i
$922$	−20.3615	+	11.7557i	−0.670570	+	0.387154i
$923$	5.39426	+	32.6729i	0.177554	+	1.07544i
$924$	−8.28565	+	4.62575i	−0.272578	+	0.152176i
$925$	−16.0712	−	9.27869i	−0.528417	−	0.305082i
$926$		−	33.0233i		−	1.08521i
$927$	30.9143	−	26.9235i	1.01536	−	0.884283i
$928$	−2.79123	−	1.61152i	−0.0916266	−	0.0529007i
$929$	−17.3100	−	9.99393i	−0.567923	−	0.327890i	0.188397	−	0.982093i	$-0.439671\pi$
$929$	−17.3100	−	9.99393i	−0.567923	−	0.327890i	−0.756319	+	0.654203i	$0.773004\pi$
$930$	−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
$933$	−1.88075	−	0.856060i	−0.0615730	−	0.0280262i
$934$	14.2621	+	24.7027i	0.466670	+	0.808297i
$935$	8.93747	+	5.16005i	0.292287	+	0.168752i
$936$	10.6660	+	1.79872i	0.348631	+	0.0587930i
$937$		−	19.6207i		−	0.640980i	−0.947252	−	0.320490i	$-0.896152\pi$
$937$		−	19.6207i		−	0.640980i	0.947252	−	0.320490i	$-0.103848\pi$
$938$	−7.93339	+	3.47386i	−0.259034	+	0.113425i
$939$	26.4802	+	37.0877i	0.864148	+	1.21031i
$940$	0.672760	−	1.16525i	0.0219430	−	0.0380064i
$941$	−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	$0.756489\pi$
$942$	13.6280	−	29.9405i	0.444025	−	0.975515i
$943$	−26.1563	+	45.3040i	−0.851765	+	1.47530i
$944$		−	13.5971i		−	0.442549i
$945$	−14.4862	−	17.1259i	−0.471237	−	0.557106i
$946$	−5.58407	+	9.67190i	−0.181554	+	0.314461i
$947$	−6.49771			−0.211147			−0.105574	−	0.994411i	$-0.533668\pi$
$947$	−6.49771			−0.211147			−0.105574	+	0.994411i	$0.533668\pi$
$948$	9.15290	−	6.53507i	0.297272	−	0.212249i
$949$	−8.00524	+	6.56971i	−0.259861	+	0.213262i
$950$	1.54863	+	2.68231i	0.0502442	+	0.0870256i
$951$	−31.9619	+	22.8205i	−1.03644	+	0.740004i
$952$	8.03175	+	0.894158i	0.260310	+	0.0289798i
$953$	−46.4669	+	26.8277i	−1.50521	+	0.869034i	−0.505229	+	0.862985i	$0.668592\pi$
$953$	−46.4669	+	26.8277i	−1.50521	+	0.869034i	−0.999982	+	0.00604840i	$0.998075\pi$
$954$	−30.3311	−	10.4126i	−0.982005	−	0.337119i
$955$	10.6934			0.346029
$956$	17.3876			0.562354
$957$	11.5062	−	1.11328i	0.371944	−	0.0359872i
$958$	30.2057	−	17.4393i	0.975902	−	0.563437i
$959$	9.71466	+	1.08151i	0.313703	+	0.0349239i
$960$	1.64215	+	2.29996i	0.0530001	+	0.0742310i
$961$	−6.07139	−	10.5160i	−0.195851	−	0.339224i
$962$	10.0815	−	26.7859i	0.325042	−	0.863611i
$963$	5.25139	+	26.8837i	0.169224	+	0.866316i
$964$	−1.42882			−0.0460192
$965$	−8.11199	+	14.0504i	−0.261134	+	0.452298i
$966$	27.9911	+	0.403586i	0.900599	+	0.0129852i
$967$		−	30.5255i		−	0.981633i	−0.871263	−	0.490817i	$-0.836699\pi$
$967$		−	30.5255i		−	0.981633i	0.871263	−	0.490817i	$-0.163301\pi$
$968$	3.35596	−	5.81270i	0.107865	−	0.186827i
$969$	6.37931	+	2.90367i	0.204933	+	0.0932793i
$970$	−12.9591	−	7.48193i	−0.416091	−	0.240230i
$971$	−3.53240	+	6.11830i	−0.113360	+	0.196346i	−0.917123	−	0.398604i	$-0.869495\pi$
$971$	−3.53240	+	6.11830i	−0.113360	+	0.196346i	0.803763	+	0.594950i	$0.202828\pi$
$972$	7.22979	+	13.8105i	0.231896	+	0.442972i
$973$	33.2002	−	14.5376i	1.06435	−	0.466055i
$974$		−	0.222477i		−	0.00712861i
$975$	10.3058	+	10.3414i	0.330051	+	0.331189i
$976$	−13.4689	−	7.77625i	−0.431128	−	0.248912i
$977$	−25.5640	−	44.2781i	−0.817863	−	1.41658i	−0.907253	−	0.420584i	$-0.861825\pi$
$977$	−25.5640	−	44.2781i	−0.817863	−	1.41658i	0.0893900	−	0.995997i	$-0.471508\pi$
$978$	0.805226	−	1.76907i	0.0257483	−	0.0565686i
$979$	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
$982$	25.2390	+	14.5717i	0.805408	+	0.465003i
$983$	−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	$0.777920\pi$
$984$	6.14466	−	13.4997i	0.195885	−	0.430355i
$985$		−	0.604203i		−	0.0192515i
$986$	−8.52573	−	4.92233i	−0.271514	−	0.156759i
$987$	1.84214	+	3.29965i	0.0586361	+	0.105029i
$988$	−3.69250	+	3.03035i	−0.117474	+	0.0964083i
$989$	28.5323	−	16.4731i	0.907273	−	0.523814i
$990$	−9.58688	−	3.29114i	−0.304691	−	0.104599i
$991$	−6.38685	−	11.0623i	−0.202885	−	0.351407i	0.746572	−	0.665305i	$-0.231698\pi$
$991$	−6.38685	−	11.0623i	−0.202885	−	0.351407i	−0.949457	+	0.313898i	$0.898365\pi$
$992$	−3.28416	+	5.68833i	−0.104272	+	0.180605i
$993$	−3.68293	+	8.09133i	−0.116874	+	0.256771i
$994$	−9.74692	−	22.2595i	−0.309154	−	0.706028i
$995$	13.7772	+	23.8628i	0.436766	+	0.756501i
$996$	11.8257	−	1.14419i	0.374712	−	0.0362550i
$997$			32.5759i			1.03169i	0.856682	+	0.515845i	$0.172522\pi$
$997$			32.5759i			1.03169i	−0.856682	+	0.515845i	$0.827478\pi$
$998$	34.1625	−	19.7237i	1.08139	−	0.624343i
$999$	39.5314	−	11.7692i	1.25072	−	0.372362i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.2	✓	34	3.2	odd	2
546.2.bi.e.257.2	yes	34	91.75	odd	6
546.2.bi.f.17.7	yes	34	1.1	even	1	trivial
546.2.bi.f.257.7	yes	34	273.257	even	6	inner
546.2.bn.e.101.14	yes	34	39.23	odd	6
546.2.bn.e.173.14	yes	34	7.5	odd	6
546.2.bn.f.101.4	yes	34	13.10	even	6
546.2.bn.f.173.4	yes	34	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.166804 + 1.72400i) q^{3} +1.00000 q^{4} +(1.41302 - 0.815806i) q^{5} +(0.166804 + 1.72400i) q^{6} +(2.62951 + 0.292738i) q^{7} +1.00000 q^{8} +(-2.94435 + 0.575141i) q^{9} +(1.41302 - 0.815806i) q^{10} +(1.03538 + 1.79334i) q^{11} +(0.166804 + 1.72400i) q^{12} +(-3.37445 - 1.27006i) q^{13} +(2.62951 + 0.292738i) q^{14} +(1.64215 + 2.29996i) q^{15} +1.00000 q^{16} +3.05447 q^{17} +(-2.94435 + 0.575141i) q^{18} +(0.662420 - 1.14734i) q^{19} +(1.41302 - 0.815806i) q^{20} +(-0.0660664 + 4.58210i) q^{21} +(1.03538 + 1.79334i) q^{22} -6.10879i q^{23} +(0.166804 + 1.72400i) q^{24} +(-1.16892 + 2.02463i) q^{25} +(-3.37445 - 1.27006i) q^{26} +(-1.48267 - 4.98013i) q^{27} +(2.62951 + 0.292738i) q^{28} +(-2.79123 - 1.61152i) q^{29} +(1.64215 + 2.29996i) q^{30} +(-3.28416 + 5.68833i) q^{31} +1.00000 q^{32} +(-2.91901 + 2.08414i) q^{33} +3.05447 q^{34} +(3.95436 - 1.73152i) q^{35} +(-2.94435 + 0.575141i) q^{36} +7.93783i q^{37} +(0.662420 - 1.14734i) q^{38} +(1.62671 - 6.02941i) q^{39} +(1.41302 - 0.815806i) q^{40} +(-7.41619 - 4.28174i) q^{41} +(-0.0660664 + 4.58210i) q^{42} +(2.69662 + 4.67069i) q^{43} +(1.03538 + 1.79334i) q^{44} +(-3.69122 + 3.21471i) q^{45} -6.10879i q^{46} +(0.714173 - 0.412328i) q^{47} +(0.166804 + 1.72400i) q^{48} +(6.82861 + 1.53951i) q^{49} +(-1.16892 + 2.02463i) q^{50} +(0.509499 + 5.26590i) q^{51} +(-3.37445 - 1.27006i) q^{52} +(9.25742 + 5.34477i) q^{53} +(-1.48267 - 4.98013i) q^{54} +(2.92603 + 1.68934i) q^{55} +(2.62951 + 0.292738i) q^{56} +(2.08852 + 0.950630i) q^{57} +(-2.79123 - 1.61152i) q^{58} -13.5971i q^{59} +(1.64215 + 2.29996i) q^{60} +(-13.4689 - 7.77625i) q^{61} +(-3.28416 + 5.68833i) q^{62} +(-7.91056 + 0.650416i) q^{63} +1.00000 q^{64} +(-5.80429 + 0.958282i) q^{65} +(-2.91901 + 2.08414i) q^{66} +(-2.83485 + 1.63670i) q^{67} +3.05447 q^{68} +(10.5316 - 1.01897i) q^{69} +(3.95436 - 1.73152i) q^{70} +(-4.59225 - 7.95402i) q^{71} +(-2.94435 + 0.575141i) q^{72} +(1.43611 - 2.48741i) q^{73} +7.93783i q^{74} +(-3.68544 - 1.67750i) 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} +(1.41302 - 0.815806i) q^{80} +(8.33842 - 3.38684i) q^{81} +(-7.41619 - 4.28174i) q^{82} -6.85946i q^{83} +(-0.0660664 + 4.58210i) q^{84} +(4.31602 - 2.49186i) q^{85} +(2.69662 + 4.67069i) q^{86} +(2.31267 - 5.08089i) q^{87} +(1.03538 + 1.79334i) q^{88} -1.07299i q^{89} +(-3.69122 + 3.21471i) q^{90} +(-8.50136 - 4.32746i) q^{91} -6.10879i q^{92} +(-10.3545 - 4.71305i) q^{93} +(0.714173 - 0.412328i) q^{94} -2.16163i q^{95} +(0.166804 + 1.72400i) q^{96} +(-4.58560 - 7.94250i) q^{97} +(6.82861 + 1.53951i) q^{98} +(-4.07996 - 4.68472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20}+ \cdots - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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