LMFDB - Embedded newform 546.2.bi.e.17.2

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			17.2
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.e.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.40963 - 1.00646i) q^{3} +1.00000 q^{4} +(-1.41302 + 0.815806i) q^{5} +(1.40963 + 1.00646i) q^{6} +(2.62951 + 0.292738i) q^{7} -1.00000 q^{8} +(0.974089 + 2.83745i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.40963 - 1.00646i) q^{3} +1.00000 q^{4} +(-1.41302 + 0.815806i) q^{5} +(1.40963 + 1.00646i) q^{6} +(2.62951 + 0.292738i) q^{7} -1.00000 q^{8} +(0.974089 + 2.83745i) q^{9} +(1.41302 - 0.815806i) q^{10} +(-1.03538 - 1.79334i) q^{11} +(-1.40963 - 1.00646i) q^{12} +(-3.37445 - 1.27006i) q^{13} +(-2.62951 - 0.292738i) q^{14} +(2.81290 + 0.272160i) q^{15} +1.00000 q^{16} -3.05447 q^{17} +(-0.974089 - 2.83745i) q^{18} +(0.662420 - 1.14734i) q^{19} +(-1.41302 + 0.815806i) q^{20} +(-3.41199 - 3.05914i) q^{21} +(1.03538 + 1.79334i) q^{22} +6.10879i q^{23} +(1.40963 + 1.00646i) 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} +(-2.81290 - 0.272160i) q^{30} +(-3.28416 + 5.68833i) q^{31} -1.00000 q^{32} +(-0.345413 + 3.57000i) q^{33} +3.05447 q^{34} +(-3.95436 + 1.73152i) q^{35} +(0.974089 + 2.83745i) q^{36} +7.93783i q^{37} +(-0.662420 + 1.14734i) q^{38} +(3.47846 + 5.18655i) q^{39} +(1.41302 - 0.815806i) q^{40} +(7.41619 + 4.28174i) q^{41} +(3.41199 + 3.05914i) 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} +(-1.40963 - 1.00646i) q^{48} +(6.82861 + 1.53951i) q^{49} +(1.16892 - 2.02463i) q^{50} +(4.30566 + 3.07419i) 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} +(2.81290 + 0.272160i) q^{60} +(-13.4689 - 7.77625i) q^{61} +(3.28416 - 5.68833i) q^{62} +(1.73074 + 7.74626i) q^{63} +1.00000 q^{64} +(5.80429 - 0.958282i) q^{65} +(0.345413 - 3.57000i) q^{66} +(-2.83485 + 1.63670i) q^{67} -3.05447 q^{68} +(6.14824 - 8.61111i) q^{69} +(3.95436 - 1.73152i) q^{70} +(4.59225 + 7.95402i) q^{71} +(-0.974089 - 2.83745i) 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} +(-3.47846 - 5.18655i) q^{78} +(-3.24657 - 5.62322i) q^{79} +(-1.41302 + 0.815806i) q^{80} +(-7.10230 + 5.52787i) q^{81} +(-7.41619 - 4.28174i) q^{82} +6.85946i q^{83} +(-3.41199 - 3.05914i) 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} +(1.40963 + 1.00646i) 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} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.40963	−	1.00646i	−0.813848	−	0.581078i
$3$	−1.40963	−	1.00646i	−0.813848	−	0.581078i
$4$	1.00000			0.500000
$5$	−1.41302	+	0.815806i	−0.631921	+	0.364840i	−0.781496	−	0.623911i	$-0.785543\pi$
$5$	−1.41302	+	0.815806i	−0.631921	+	0.364840i	0.149575	+	0.988750i	$0.452210\pi$
$6$	1.40963	+	1.00646i	0.575477	+	0.410884i
$7$	2.62951	+	0.292738i	0.993860	+	0.110644i
$7$	2.62951	+	0.292738i	0.993860	+	0.110644i
$8$	−1.00000			−0.353553
$9$	0.974089	+	2.83745i	0.324696	+	0.945818i
$10$	1.41302	−	0.815806i	0.446836	−	0.257981i
$11$	−1.03538	−	1.79334i	−0.312180	−	0.540711i	0.666654	−	0.745367i	$-0.267726\pi$
$11$	−1.03538	−	1.79334i	−0.312180	−	0.540711i	−0.978834	+	0.204656i	$0.934392\pi$
$12$	−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
$15$	2.81290	+	0.272160i	0.726288	+	0.0702714i
$16$	1.00000			0.250000
$17$	−3.05447			−0.740818			−0.370409	−	0.928869i	$-0.620782\pi$
$17$	−3.05447			−0.740818			−0.370409	+	0.928869i	$0.620782\pi$
$18$	−0.974089	−	2.83745i	−0.229595	−	0.668795i
$19$	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
$21$	−3.41199	−	3.05914i	−0.744558	−	0.667558i
$22$	1.03538	+	1.79334i	0.220744	+	0.382341i
$23$			6.10879i			1.27377i	0.770958	+	0.636886i	$0.219778\pi$
$23$			6.10879i			1.27377i	−0.770958	+	0.636886i	$0.780222\pi$
$24$	1.40963	+	1.00646i	0.287739	+	0.205442i
$25$	−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	0.736246	−	0.676714i	$-0.236596\pi$
$29$	2.79123	+	1.61152i	0.518319	+	0.299251i	−0.217928	+	0.975965i	$0.569930\pi$
$30$	−2.81290	−	0.272160i	−0.513563	−	0.0496894i
$31$	−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
$33$	−0.345413	+	3.57000i	−0.0601287	+	0.621458i
$34$	3.05447			0.523837
$35$	−3.95436	+	1.73152i	−0.668408	+	0.292681i
$36$	0.974089	+	2.83745i	0.162348	+	0.472909i
$37$			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
$39$	3.47846	+	5.18655i	0.556999	+	0.830513i
$40$	1.41302	−	0.815806i	0.223418	−	0.128990i
$41$	7.41619	+	4.28174i	1.15821	+	0.668695i	0.950875	−	0.309574i	$-0.100186\pi$
$41$	7.41619	+	4.28174i	1.15821	+	0.668695i	0.207339	+	0.978269i	$0.433520\pi$
$42$	3.41199	+	3.05914i	0.526482	+	0.472035i
$43$	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	−0.551181	−	0.834386i	$-0.685823\pi$
$47$	−0.714173	+	0.412328i	−0.104173	+	0.0601442i	0.447008	+	0.894530i	$0.352489\pi$
$48$	−1.40963	−	1.00646i	−0.203462	−	0.145270i
$49$	6.82861	+	1.53951i	0.975516	+	0.219930i
$50$	1.16892	−	2.02463i	0.165310	−	0.286326i
$51$	4.30566	+	3.07419i	0.602913	+	0.430473i
$52$	−3.37445	−	1.27006i	−0.467953	−	0.176126i
$53$	−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	$0.929091\pi$
$54$	−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	$0.345909\pi$
$59$			13.5971i			1.77020i	−0.465405	+	0.885098i	$0.654091\pi$
$60$	2.81290	+	0.272160i	0.363144	+	0.0351357i
$61$	−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
$63$	1.73074	+	7.74626i	0.218053	+	0.975937i
$64$	1.00000			0.125000
$65$	5.80429	−	0.958282i	0.719934	−	0.118860i
$66$	0.345413	−	3.57000i	0.0425174	−	0.439437i
$67$	−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
$69$	6.14824	−	8.61111i	0.740161	−	1.03666i
$70$	3.95436	−	1.73152i	0.472636	−	0.206957i
$71$	4.59225	+	7.95402i	0.545000	+	0.943968i	0.998607	+	0.0527663i	$0.0168038\pi$
$71$	4.59225	+	7.95402i	0.545000	+	0.943968i	−0.453607	+	0.891202i	$0.649863\pi$
$72$	−0.974089	−	2.83745i	−0.114798	−	0.334397i
$73$	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
$78$	−3.47846	−	5.18655i	−0.393858	−	0.587262i
$79$	−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
$81$	−7.10230	+	5.52787i	−0.789144	+	0.614208i
$82$	−7.41619	−	4.28174i	−0.818981	−	0.472839i
$83$			6.85946i			0.752924i	0.926432	+	0.376462i	$0.122859\pi$
$83$			6.85946i			0.752924i	−0.926432	+	0.376462i	$0.877141\pi$
$84$	−3.41199	−	3.05914i	−0.372279	−	0.333779i
$85$	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	$0.0181115\pi$
$89$			1.07299i			0.113736i	−0.998382	+	0.0568682i	$0.981889\pi$
$90$	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
$96$	1.40963	+	1.00646i	0.143869	+	0.102721i
$97$	−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	0.846430	−	0.532500i	$-0.178747\pi$
$101$	−0.381326	−	0.660476i	−0.0379434	−	0.0657198i	−0.884373	+	0.466780i	$0.845414\pi$
$102$	−4.30566	−	3.07419i	−0.426324	−	0.304390i
$103$	−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
$107$			9.13060i			0.882689i	0.897338	+	0.441344i	$0.145498\pi$
$107$			9.13060i			0.882689i	−0.897338	+	0.441344i	$0.854502\pi$
$108$	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
$111$	7.98909	−	11.1894i	0.758291	−	1.06205i
$112$	2.62951	+	0.292738i	0.248465	+	0.0276611i
$113$	−7.84130	+	4.52717i	−0.737647	+	0.425881i	−0.821213	−	0.570622i	$-0.806702\pi$
$113$	−7.84130	+	4.52717i	−0.737647	+	0.425881i	0.0835662	+	0.996502i	$0.473369\pi$
$114$	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
$117$	0.316722	−	10.8120i	0.0292809	−	0.999571i
$118$		−	13.5971i		−	1.25172i
$119$	−8.03175	−	0.894158i	−0.736269	−	0.0819673i
$120$	−2.81290	−	0.272160i	−0.256782	−	0.0248447i
$121$	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
$126$	−1.73074	−	7.74626i	−0.154187	−	0.690092i
$127$	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
$129$	0.899616	−	9.29795i	0.0792068	−	0.818639i
$130$	−5.80429	+	0.958282i	−0.509070	+	0.0840469i
$131$	−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	$0.980914\pi$
$132$	−0.345413	+	3.57000i	−0.0300643	+	0.310729i
$133$	2.07771	−	2.82304i	0.180160	−	0.244788i
$134$	2.83485	−	1.63670i	0.244894	−	0.141390i
$135$	1.96777	+	8.24659i	0.169359	+	0.709753i
$136$	3.05447			0.261919
$137$	−3.69448			−0.315641			−0.157820	−	0.987468i	$-0.550447\pi$
$137$	−3.69448			−0.315641			−0.157820	+	0.987468i	$0.550447\pi$
$138$	−6.14824	+	8.61111i	−0.523373	+	0.733027i
$139$	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
$141$	1.42171	+	0.137556i	0.119729	+	0.0115843i
$142$	−4.59225	−	7.95402i	−0.385373	−	0.667486i
$143$	1.21621	+	7.36653i	0.101704	+	0.616020i
$144$	0.974089	+	2.83745i	0.0811741	+	0.236455i
$145$	−5.25875			−0.436715
$146$	−1.43611	+	2.48741i	−0.118853	+	0.205860i
$147$	−8.07633	−	9.04283i	−0.666125	−	0.745840i
$148$			7.93783i			0.652486i
$149$	9.67165	−	16.7518i	0.792332	−	1.37236i	−0.132187	−	0.991225i	$-0.542200\pi$
$149$	9.67165	−	16.7518i	0.792332	−	1.37236i	0.924519	−	0.381135i	$-0.124467\pi$
$150$	−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
$153$	−2.97533	−	8.66692i	−0.240541	−	0.700679i
$154$	2.19757	+	5.01869i	0.177085	+	0.404417i
$155$		−	10.7169i		−	0.860806i
$156$	3.47846	+	5.18655i	0.278499	+	0.415257i
$157$	−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
$162$	7.10230	−	5.52787i	0.558009	−	0.434310i
$163$	−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	0.458707	−	0.888588i	$-0.348313\pi$
$167$	−1.05294	−	0.607914i	−0.0814787	−	0.0470418i	−0.540186	+	0.841546i	$0.681646\pi$
$168$	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
$171$	3.90080	+	0.761970i	0.298301	+	0.0582693i
$172$	2.69662	+	4.67069i	0.205615	+	0.356136i
$173$	9.60871	−	16.6428i	0.730537	−	1.26533i	−0.226117	−	0.974100i	$-0.572603\pi$
$173$	9.60871	−	16.6428i	0.730537	−	1.26533i	0.956654	−	0.291227i	$-0.0940635\pi$
$174$	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
$177$	13.6849	−	19.1669i	1.02862	−	1.44067i
$178$		−	1.07299i		−	0.0804238i
$179$	14.3720	−	8.29766i	1.07421	−	0.620196i	0.144882	−	0.989449i	$-0.453720\pi$
$179$	14.3720	−	8.29766i	1.07421	−	0.620196i	0.929329	+	0.369253i	$0.120386\pi$
$180$	−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
$189$	5.35657	−	12.6612i	0.389633	−	0.920970i
$190$		−	2.16163i		−	0.156821i
$191$	−5.67581	−	3.27693i	−0.410687	−	0.237110i	0.280398	−	0.959884i	$-0.409534\pi$
$191$	−5.67581	−	3.27693i	−0.410687	−	0.237110i	−0.691085	+	0.722774i	$0.742867\pi$
$192$	−1.40963	−	1.00646i	−0.101731	−	0.0726348i
$193$	−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
$195$	−9.14635	−	4.49095i	−0.654983	−	0.321603i
$196$	6.82861	+	1.53951i	0.487758	+	0.109965i
$197$	−0.185155	+	0.320698i	−0.0131918	+	0.0228488i	−0.872546	−	0.488532i	$-0.837533\pi$
$197$	−0.185155	+	0.320698i	−0.0131918	+	0.0228488i	0.859354	+	0.511381i	$0.170866\pi$
$198$	−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
$201$	5.64336	+	0.546019i	0.398052	+	0.0385132i
$202$	0.381326	+	0.660476i	0.0268300	+	0.0464709i
$203$	6.86781	+	5.05459i	0.482026	+	0.354763i
$204$	4.30566	+	3.07419i	0.301456	+	0.215236i
$205$	−13.9723			−0.975866
$206$	11.8342	−	6.83246i	0.824525	−	0.476040i
$207$	−17.3334	+	5.95051i	−1.20476	+	0.413589i
$208$	−3.37445	−	1.27006i	−0.233976	−	0.0880629i
$209$	−2.74343			−0.189767
$210$	−7.31687	−	1.53909i	−0.504912	−	0.106207i
$211$	−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
$213$	1.53202	−	15.8341i	0.104972	−	1.08493i
$214$		−	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
$222$	−7.98909	+	11.1894i	−0.536192	+	0.750982i
$223$	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
$225$	−6.88342	−	1.34459i	−0.458895	−	0.0896392i
$226$	7.84130	−	4.52717i	0.521595	−	0.301143i
$227$			11.4396i			0.759273i	0.925136	+	0.379636i	$0.123951\pi$
$227$			11.4396i			0.759273i	−0.925136	+	0.379636i	$0.876049\pi$
$228$	−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
$231$	−1.95334	+	9.28623i	−0.128520	+	0.610989i
$232$	−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	$0.286180\pi$
$234$	−0.316722	+	10.8120i	−0.0207047	+	0.706804i
$235$	0.672760	−	1.16525i	0.0438860	−	0.0760128i
$236$			13.5971i			0.885098i
$237$	−1.08308	+	11.1942i	−0.0703539	+	0.727140i
$238$	8.03175	+	0.894158i	0.520621	+	0.0579596i
$239$	−17.3876			−1.12471			−0.562354	−	0.826896i	$-0.690104\pi$
$239$	−17.3876			−1.12471			−0.562354	+	0.826896i	$0.690104\pi$
$240$	2.81290	+	0.272160i	0.181572	+	0.0175679i
$241$	−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
$243$	15.5751	−	0.644067i	0.999146	−	0.0413169i
$244$	−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
$249$	6.90375	−	9.66927i	0.437507	−	0.612765i
$250$			11.9725i			0.757208i
$251$	3.39863	+	5.88660i	0.214520	+	0.371559i	0.953124	−	0.302580i	$-0.0978480\pi$
$251$	3.39863	+	5.88660i	0.214520	+	0.371559i	−0.738604	+	0.674139i	$0.764515\pi$
$252$	1.73074	+	7.74626i	0.109027	+	0.487968i
$253$	10.9551	−	6.32494i	0.688743	−	0.397646i
$254$	−1.70273	+	2.94922i	−0.106839	+	0.185051i
$255$	−8.59192	−	0.831305i	−0.538047	−	0.0520583i
$256$	1.00000			0.0625000
$257$	−14.1505			−0.882684			−0.441342	−	0.897339i	$-0.645497\pi$
$257$	−14.1505			−0.882684			−0.441342	+	0.897339i	$0.645497\pi$
$258$	−0.899616	+	9.29795i	−0.0560077	+	0.578865i
$259$	−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
$262$	5.11851	+	8.86551i	0.316222	+	0.547713i
$263$	11.1426	−	6.43320i	0.687084	−	0.396688i	−0.115435	−	0.993315i	$-0.536826\pi$
$263$	11.1426	−	6.43320i	0.687084	−	0.396688i	0.802519	+	0.596627i	$0.203493\pi$
$264$	0.345413	−	3.57000i	0.0212587	−	0.219718i
$265$	17.4412			1.07140
$266$	−2.07771	+	2.82304i	−0.127392	+	0.173091i
$267$	1.07992	−	1.51251i	0.0660898	−	0.0925641i
$268$	−2.83485	+	1.63670i	−0.173166	+	0.0999776i
$269$	−27.3543			−1.66782			−0.833909	−	0.551902i	$-0.813902\pi$
$269$	−27.3543			−1.66782			−0.833909	+	0.551902i	$0.813902\pi$
$270$	−1.96777	−	8.24659i	−0.119755	−	0.501871i
$271$	−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
$273$	7.62832	+	14.6564i	0.461687	+	0.887043i
$274$	3.69448			0.223192
$275$	4.84112			0.291931
$276$	6.14824	−	8.61111i	0.370080	−	0.518328i
$277$	−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
$279$	−19.3394	−	3.77771i	−1.15782	−	0.226166i
$280$	3.95436	−	1.73152i	0.236318	−	0.103478i
$281$	−4.08136			−0.243474			−0.121737	−	0.992562i	$-0.538846\pi$
$281$	−4.08136			−0.243474			−0.121737	+	0.992562i	$0.538846\pi$
$282$	−1.42171	−	0.137556i	−0.0846614	−	0.00819135i
$283$	−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
$285$	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
$288$	−0.974089	−	2.83745i	−0.0573988	−	0.167199i
$289$	−7.67022			−0.451189
$290$	5.25875			0.308804
$291$	−1.52980	+	15.8112i	−0.0896783	+	0.926867i
$292$	1.43611	−	2.48741i	0.0840418	−	0.145565i
$293$	5.29149	−	3.05504i	0.309132	−	0.178478i	−0.337406	−	0.941359i	$-0.609549\pi$
$293$	5.29149	−	3.05504i	0.309132	−	0.178478i	0.646538	+	0.762882i	$0.276216\pi$
$294$	8.07633	+	9.04283i	0.471021	+	0.527389i
$295$	−11.0926	−	19.2130i	−0.645838	−	1.11862i
$296$		−	7.93783i		−	0.461377i
$297$	−10.4662	+	2.49741i	−0.607309	+	0.144914i
$298$	−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
$303$	−0.127214	+	1.31481i	−0.00730824	+	0.0755340i
$304$	0.662420	−	1.14734i	0.0379924	−	0.0658047i
$305$	25.3757			1.45301
$306$	2.97533	+	8.66692i	0.170088	+	0.495455i
$307$	−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
$309$	23.5583	+	2.27937i	1.34019	+	0.129669i
$310$			10.7169i			0.608682i
$311$	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	$0.155898\pi$
$312$	−3.47846	−	5.18655i	−0.196929	−	0.293631i
$313$	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
$315$	−8.76502	−	9.53365i	−0.493853	−	0.537160i
$316$	−3.24657	−	5.62322i	−0.182634	−	0.316331i
$317$	−11.3370	−	19.6363i	−0.636751	−	1.10289i	−0.986141	−	0.165908i	$-0.946945\pi$
$317$	−11.3370	−	19.6363i	−0.636751	−	1.10289i	0.349390	−	0.936977i	$-0.386389\pi$
$318$	−7.67021	−	16.8513i	−0.430124	−	0.944975i
$319$		−	6.67415i		−	0.373681i
$320$	−1.41302	+	0.815806i	−0.0789901	+	0.0456050i
$321$	9.18956	−	12.8707i	0.512911	−	0.718374i
$322$	1.78827	−	16.0631i	0.0996566	−	0.895162i
$323$	−2.02334	+	3.50453i	−0.112582	+	0.194997i
$324$	−7.10230	+	5.52787i	−0.394572	+	0.307104i
$325$	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
$333$	−22.5232	+	7.73216i	−1.23427	+	0.423720i
$334$	1.05294	+	0.607914i	0.0576142	+	0.0332636i
$335$	2.67047	−	4.62539i	0.145903	−	0.252712i
$336$	−3.41199	−	3.05914i	−0.186139	−	0.166890i
$337$	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
$339$	15.6097	+	1.51030i	0.847802	+	0.0820285i
$340$	4.31602	−	2.49186i	0.234069	−	0.135140i
$341$	13.6014			0.736560
$342$	−3.90080	−	0.761970i	−0.210931	−	0.0412026i
$343$	17.5052	+	6.04714i	0.945192	+	0.326515i
$344$	−2.69662	−	4.67069i	−0.145392	−	0.251827i
$345$	−1.66257	+	17.1834i	−0.0895098	+	0.925125i
$346$	−9.60871	+	16.6428i	−0.516568	+	0.894721i
$347$		−	10.7152i		−	0.575225i	−0.957747	−	0.287612i	$-0.907139\pi$
$347$		−	10.7152i		−	0.575225i	0.957747	−	0.287612i	$-0.0928615\pi$
$348$	−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
$351$	−11.3283	+	14.9221i	−0.604659	+	0.796484i
$352$	1.03538	+	1.79334i	0.0551861	+	0.0955852i
$353$	15.5607	−	8.98395i	0.828211	−	0.478168i	−0.0250291	−	0.999687i	$-0.507968\pi$
$353$	15.5607	−	8.98395i	0.828211	−	0.478168i	0.853240	+	0.521519i	$0.174634\pi$
$354$	−13.6849	+	19.1669i	−0.727346	+	1.01871i
$355$	−12.9779	−	7.49278i	−0.688794	−	0.397676i
$356$			1.07299i			0.0568682i
$357$	10.4218	+	9.34403i	0.551581	+	0.494539i
$358$	−14.3720	+	8.29766i	−0.759582	+	0.438545i
$359$	2.59460	+	4.49398i	0.136938	+	0.237183i	0.926336	−	0.376698i	$-0.122941\pi$
$359$	2.59460	+	4.49398i	0.136938	+	0.237183i	−0.789398	+	0.613881i	$0.789607\pi$
$360$	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
$369$	−4.92521	+	25.2139i	−0.256396	+	1.31258i
$370$	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
$375$	−12.0498	+	16.8768i	−0.622250	+	0.871512i
$376$	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	0.980843	−	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	0.707323	−	0.706891i	$-0.249903\pi$
$383$	8.78316	+	5.07096i	0.448799	+	0.259114i	−0.258524	+	0.966005i	$0.583236\pi$
$384$	1.40963	+	1.00646i	0.0719347	+	0.0513605i
$385$	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	−0.248734	−	0.968572i	$-0.580015\pi$
$389$	−23.9026	−	13.8002i	−1.21191	−	0.699696i	−0.963175	+	0.268876i	$0.913348\pi$
$390$	9.14635	+	4.49095i	0.463143	+	0.227408i
$391$		−	18.6591i		−	0.943632i
$392$	−6.82861	−	1.53951i	−0.344897	−	0.0777570i
$393$	−1.70758	+	17.6486i	−0.0861359	+	0.890255i
$394$	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
$399$	−5.77005	+	1.88830i	−0.288864	+	0.0945332i
$400$	−1.16892	+	2.02463i	−0.0584460	+	0.101231i
$401$	23.8650			1.19176			0.595882	−	0.803072i	$-0.296803\pi$
$401$	23.8650			1.19176			0.595882	+	0.803072i	$0.296803\pi$
$402$	−5.64336	−	0.546019i	−0.281465	−	0.0272329i
$403$	18.3068	−	15.0239i	0.911925	−	0.748395i
$404$	−0.381326	−	0.660476i	−0.0189717	−	0.0328599i
$405$	5.52601	−	13.6051i	0.274590	−	0.676042i
$406$	−6.86781	−	5.05459i	−0.340844	−	0.250855i
$407$	14.2352	−	8.21870i	0.705613	−	0.407386i
$408$	−4.30566	−	3.07419i	−0.213162	−	0.152195i
$409$	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
$411$	5.20783	+	3.71833i	0.256883	+	0.183412i
$412$	−11.8342	+	6.83246i	−0.583028	+	0.336611i
$413$	−3.98039	+	35.7537i	−0.195862	+	1.75933i
$414$	17.3334	−	5.95051i	0.851891	−	0.292452i
$415$	−5.59599	−	9.69254i	−0.274696	−	0.475788i
$416$	3.37445	+	1.27006i	0.165446	+	0.0622699i
$417$	−23.6167	−	2.28502i	−1.15652	−	0.111898i
$418$	2.74343			0.134186
$419$	−1.65804	+	2.87182i	−0.0810008	+	0.140297i	−0.903680	−	0.428208i	$-0.859145\pi$
$419$	−1.65804	+	2.87182i	−0.0810008	+	0.140297i	0.822679	+	0.568506i	$0.192478\pi$
$420$	7.31687	+	1.53909i	0.357027	+	0.0750998i
$421$			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
$426$	−1.53202	+	15.8341i	−0.0742264	+	0.767164i
$427$	−33.1401	−	24.3905i	−1.60376	−	1.18034i
$428$			9.13060i			0.441344i
$429$	5.69970	−	11.6081i	0.275184	−	0.560445i
$430$	7.62075	+	4.39984i	0.367505	+	0.212179i
$431$	12.4404	+	21.5475i	0.599235	+	1.03790i	0.992934	+	0.118666i	$0.0378617\pi$
$431$	12.4404	+	21.5475i	0.599235	+	1.03790i	−0.393700	+	0.919239i	$0.628805\pi$
$432$	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
$435$	7.41286	+	5.29270i	0.355420	+	0.253766i
$436$	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
$441$	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	$0.213878\pi$
$444$	7.98909	−	11.1894i	0.379145	−	0.531024i
$445$	−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	0.517176	−	0.855879i	$-0.326983\pi$
$449$	−10.2266	−	17.7130i	−0.482625	−	0.835930i	−0.999801	+	0.0199485i	$0.993650\pi$
$450$	6.88342	+	1.34459i	0.324488	+	0.0633845i
$451$		−	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	0.0557678	−	0.998444i	$-0.482239\pi$
$461$	20.3615	−	11.7557i	0.948329	−	0.547518i	0.892562	+	0.450926i	$0.148906\pi$
$462$	1.95334	−	9.28623i	0.0908775	−	0.432034i
$463$		−	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
$465$	−10.7861	+	15.1069i	−0.500196	+	0.700565i
$466$	−3.90224	+	2.25296i	−0.180768	+	0.104366i
$467$	−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	$-0.396098\pi$
$468$	0.316722	−	10.8120i	0.0146405	−	0.499786i
$469$	−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
$474$	1.08308	−	11.1942i	0.0497477	−	0.514165i
$475$	1.54863	+	2.68231i	0.0710561	+	0.123073i
$476$	−8.03175	−	0.894158i	−0.368134	−	0.0409836i
$477$	6.14800	−	31.4738i	0.281498	−	1.44109i
$478$	17.3876			0.795289
$479$	−30.2057	+	17.4393i	−1.38013	+	0.796821i	−0.992175	−	0.124856i	$-0.960153\pi$
$479$	−30.2057	+	17.4393i	−1.38013	+	0.796821i	−0.387959	+	0.921677i	$0.626820\pi$
$480$	−2.81290	−	0.272160i	−0.128391	−	0.0124224i
$481$	10.0815	−	26.7859i	0.459678	−	1.22133i
$482$	1.42882			0.0650810
$483$	18.6876	−	20.8432i	0.850316	−	0.948397i
$484$	3.35596	−	5.81270i	0.152544	−	0.264214i
$485$	12.9591	+	7.48193i	0.588442	+	0.339737i
$486$	−15.5751	+	0.644067i	−0.706503	+	0.0292155i
$487$		−	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	−0.192832	−	0.981232i	$-0.561767\pi$
$491$	−25.2390	−	14.5717i	−1.13902	−	0.657613i	−0.946188	+	0.323619i	$0.895101\pi$
$492$	−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
$495$	−1.94322	+	9.94805i	−0.0873414	+	0.447132i
$496$	−3.28416	+	5.68833i	−0.147463	+	0.255413i
$497$	9.74692	+	22.2595i	0.437209	+	0.998474i
$498$	−6.90375	+	9.66927i	−0.309364	+	0.433290i
$499$	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	$0.0669505\pi$
$503$	15.0219	+	26.0187i	0.669793	+	1.16012i	−0.308169	+	0.951332i	$0.599716\pi$
$504$	−1.73074	−	7.74626i	−0.0770935	−	0.345046i
$505$	1.07764	+	0.622177i	0.0479544	+	0.0276865i
$506$	−10.9551	+	6.32494i	−0.487015	+	0.281178i
$507$	−5.15065	−	21.9196i	−0.228748	−	0.973486i
$508$	1.70273	−	2.94922i	0.0755466	−	0.130851i
$509$			39.8865i			1.76794i	0.467546	+	0.883969i	$0.345138\pi$
$509$			39.8865i			1.76794i	−0.467546	+	0.883969i	$0.654862\pi$
$510$	8.59192	+	0.831305i	0.380456	+	0.0368108i
$511$	4.50441	−	6.12026i	0.199263	−	0.270744i
$512$	−1.00000			−0.0441942
$513$	−4.73177	−	5.00007i	−0.208913	−	0.220759i
$514$	14.1505			0.624152
$515$	11.1479	−	19.3088i	0.491236	−	0.850846i
$516$	0.899616	−	9.29795i	0.0396034	−	0.409320i
$517$	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	$-0.664535\pi$
$521$	11.5449	−	19.9963i	0.505789	−	0.876052i	0.999978	−	0.00669760i	$-0.00213193\pi$
$522$	1.85370	−	9.48975i	0.0811343	−	0.415355i
$523$			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
$525$	10.1820	−	3.33213i	0.444377	−	0.145426i
$526$	−11.1426	+	6.43320i	−0.485842	+	0.280501i
$527$	10.0314	−	17.3748i	0.436973	−	0.756859i
$528$	−0.345413	+	3.57000i	−0.0150322	+	0.155364i
$529$	−14.3174			−0.622494
$530$	−17.4412			−0.757597
$531$	−38.5812	+	13.2448i	−1.67428	+	0.574776i
$532$	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
$535$	−7.44880	−	12.9017i	−0.322040	−	0.557789i
$536$	2.83485	−	1.63670i	0.122447	−	0.0706948i
$537$	−28.6103	−	2.76817i	−1.23463	−	0.119455i
$538$	27.3543			1.17933
$539$	−4.30937	−	13.8400i	−0.185618	−	0.596130i
$540$	1.96777	+	8.24659i	0.0846795	+	0.354877i
$541$	−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
$543$	21.2832	−	29.8089i	0.913350	−	1.27922i
$544$	3.05447			0.130959
$545$	−27.1526			−1.16309
$546$	−7.62832	−	14.6564i	−0.326462	−	0.627234i
$547$	−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
$549$	8.94489	−	45.7921i	0.381759	−	1.95436i
$550$	−4.84112			−0.206426
$551$	3.69793	−	2.13500i	0.157537	−	0.0909542i
$552$	−6.14824	+	8.61111i	−0.261686	+	0.366513i
$553$	−6.89075	−	15.7367i	−0.293024	−	0.669193i
$554$	20.9249			0.889013
$555$	−2.16036	+	22.3283i	−0.0917022	+	0.947785i
$556$	11.8635	−	6.84939i	0.503124	−	0.290479i
$557$	15.0162	+	26.0087i	0.636255	+	1.10203i	0.986248	+	0.165273i	$0.0528506\pi$
$557$	15.0162	+	26.0087i	0.636255	+	1.10203i	−0.349993	+	0.936752i	$0.613816\pi$
$558$	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
$561$	1.05505	−	10.9045i	0.0445444	−	0.460387i
$562$	4.08136			0.172162
$563$	26.1791			1.10332			0.551658	−	0.834070i	$-0.313995\pi$
$563$	26.1791			1.10332			0.551658	+	0.834070i	$0.313995\pi$
$564$	1.42171	+	0.137556i	0.0598647	+	0.00579216i
$565$	7.38659	−	12.7940i	0.310756	−	0.538246i
$566$	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
$569$		−	5.85652i		−	0.245518i	−0.992437	−	0.122759i	$-0.960826\pi$
$569$		−	5.85652i		−	0.245518i	0.992437	−	0.122759i	$-0.0391742\pi$
$570$	−2.17558	+	3.04708i	−0.0911251	+	0.127628i
$571$	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
$576$	0.974089	+	2.83745i	0.0405871	+	0.118227i
$577$	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
$579$	17.1426	+	1.65862i	0.712424	+	0.0689300i
$580$	−5.25875			−0.218358
$581$	−2.00802	+	18.0370i	−0.0833068	+	0.748301i
$582$	1.52980	−	15.8112i	0.0634121	−	0.655394i
$583$			22.1355i			0.916761i
$584$	−1.43611	+	2.48741i	−0.0594265	+	0.102930i
$585$	8.37298	+	15.5360i	0.346180	+	0.642333i
$586$	−5.29149	+	3.05504i	−0.218590	+	0.126203i
$587$	−25.6971	−	14.8362i	−1.06063	−	0.612358i	−0.135027	−	0.990842i	$-0.543112\pi$
$587$	−25.6971	−	14.8362i	−1.06063	−	0.612358i	−0.925608	+	0.378484i	$0.876445\pi$
$588$	−8.07633	−	9.04283i	−0.333062	−	0.372920i
$589$	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	−0.986512	−	0.163690i	$-0.947660\pi$
$593$	−32.5826	+	18.8116i	−1.33801	+	0.772500i	−0.351497	+	0.936189i	$0.614327\pi$
$594$	10.4662	−	2.49741i	0.429433	−	0.102470i
$595$	12.0785	−	5.28889i	0.495169	−	0.216823i
$596$	9.67165	−	16.7518i	0.396166	−	0.686180i
$597$	16.9968	−	23.8055i	0.695635	−	0.974294i
$598$	−7.75854	+	20.6138i	−0.317270	+	0.842963i
$599$	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	$0.397056\pi$
$600$	−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
$606$	0.127214	−	1.31481i	0.00516770	−	0.0534106i
$607$	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
$609$	−4.59381	−	14.0372i	−0.186150	−	0.568818i
$610$	−25.3757			−1.02743
$611$	2.93363	−	0.484339i	0.118682	−	0.0195942i
$612$	−2.97533	−	8.66692i	−0.120270	−	0.350339i
$613$	−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
$615$	19.6957	+	14.0625i	0.794207	+	0.567054i
$616$	2.19757	+	5.01869i	0.0885426	+	0.202209i
$617$	16.4572	+	28.5046i	0.662540	+	1.14755i	0.979946	+	0.199263i	$0.0638549\pi$
$617$	16.4572	+	28.5046i	0.662540	+	1.14755i	−0.317406	+	0.948290i	$0.602812\pi$
$618$	−23.5583	−	2.27937i	−0.947655	−	0.0916896i
$619$	−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
$624$	3.47846	+	5.18655i	0.139250	+	0.207628i
$625$	3.92265	+	6.79423i	0.156906	+	0.271769i
$626$	−22.7854	+	13.1551i	−0.910687	+	0.525786i
$627$	3.86721	+	2.76115i	0.154442	+	0.110270i
$628$	−16.4481	−	9.49631i	−0.656350	−	0.378944i
$629$		−	24.2459i		−	0.966746i
$630$	8.76502	+	9.53365i	0.349207	+	0.379830i
$631$	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	$-0.825244\pi$
$641$		−	26.4241i		−	1.04369i	0.853041	−	0.521844i	$-0.174756\pi$
$642$	−9.18956	+	12.8707i	−0.362683	+	0.507967i
$643$	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	$0.0974542\pi$
$647$	18.7660	+	32.5037i	0.737769	+	1.27785i	−0.215728	+	0.976453i	$0.569212\pi$
$648$	7.10230	−	5.52787i	0.279005	−	0.217155i
$649$	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
$653$			42.7824i			1.67421i	0.547045	+	0.837103i	$0.315752\pi$
$653$			42.7824i			1.67421i	−0.547045	+	0.837103i	$0.684248\pi$
$654$	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
$657$	8.45681	+	1.65193i	0.329932	+	0.0644479i
$658$	1.99863	−	0.875154i	0.0779146	−	0.0341170i
$659$	−28.1909	+	16.2760i	−1.09816	+	0.634024i	−0.935738	−	0.352696i	$-0.885265\pi$
$659$	−28.1909	+	16.2760i	−1.09816	+	0.634024i	−0.162425	+	0.986721i	$0.551932\pi$
$660$	−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
$663$	−10.6248	−	15.8422i	−0.412634	−	0.615259i
$664$		−	6.85946i		−	0.266199i
$665$	−0.632789	+	5.68401i	−0.0245385	+	0.220416i
$666$	22.5232	−	7.73216i	0.872758	−	0.299615i
$667$	−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
$672$	3.41199	+	3.05914i	0.131620	+	0.118009i
$673$	−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
$675$	8.34978	+	8.82324i	0.321383	+	0.339607i
$676$	9.77389	+	8.57153i	0.375919	+	0.329674i
$677$	−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	$-0.380921\pi$
$678$	−15.6097	−	1.51030i	−0.599487	−	0.0580029i
$679$	−9.73281	−	22.2272i	−0.373511	−	0.853003i
$680$	−4.31602	+	2.49186i	−0.165512	+	0.0955583i
$681$	11.5135	−	16.1256i	0.441197	−	0.617933i
$682$	−13.6014			−0.520826
$683$	7.19406			0.275273			0.137637	−	0.990483i	$-0.456049\pi$
$683$	7.19406			0.275273			0.137637	+	0.990483i	$0.456049\pi$
$684$	3.90080	+	0.761970i	0.149151	+	0.0291347i
$685$	5.22037	−	3.01398i	0.199460	−	0.115158i
$686$	−17.5052	−	6.04714i	−0.668352	−	0.230881i
$687$	1.58359	−	16.3671i	0.0604177	−	0.624445i
$688$	2.69662	+	4.67069i	0.102808	+	0.178068i
$689$	24.4505	+	29.7932i	0.931491	+	1.13503i
$690$	1.66257	−	17.1834i	0.0632930	−	0.654162i
$691$	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
$693$	12.0997	−	11.1242i	0.459628	−	0.422572i
$694$			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
$699$	−7.76820	−	0.751607i	−0.293820	−	0.0284284i
$700$	−3.66637	+	4.98159i	−0.138576	+	0.188286i
$701$		−	26.3672i		−	0.995877i	−0.867212	−	0.497938i	$-0.834091\pi$
$701$		−	26.3672i		−	0.995877i	0.867212	−	0.497938i	$-0.165909\pi$
$702$	11.3283	−	14.9221i	0.427559	−	0.563199i
$703$	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
$708$	13.6849	−	19.1669i	0.514311	−	0.720335i
$709$	−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
$714$	−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
$717$	24.5100	+	17.4998i	0.915342	+	0.653544i
$718$	−2.59460	−	4.49398i	−0.0968295	−	0.167714i
$719$	−9.30194	+	16.1114i	−0.346904	+	0.600855i	−0.985698	−	0.168523i	$-0.946100\pi$
$719$	−9.30194	+	16.1114i	−0.346904	+	0.600855i	0.638794	+	0.769378i	$0.279434\pi$
$720$	−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
$723$	2.01410	+	1.43805i	0.0749053	+	0.0534815i
$724$			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
$735$	18.7892	+	6.18896i	0.693050	+	0.228283i
$736$		−	6.10879i		−	0.225173i
$737$	5.87032	+	3.38923i	0.216236	+	0.124844i
$738$	4.92521	−	25.2139i	0.181299	−	0.928136i
$739$	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
$741$	8.25496	−	0.555312i	0.303254	−	0.0203999i
$742$	22.7778	+	16.7641i	0.836200	+	0.615430i
$743$	−19.1716	+	33.2062i	−0.703339	+	1.21822i	0.263949	+	0.964537i	$0.414975\pi$
$743$	−19.1716	+	33.2062i	−0.703339	+	1.21822i	−0.967288	+	0.253682i	$0.918358\pi$
$744$	−10.3545	+	4.71305i	−0.379614	+	0.172789i
$745$			31.5608i			1.15630i
$746$	17.7937	−	30.8197i	0.651475	−	1.12839i
$747$	−19.4634	+	6.68173i	−0.712129	+	0.244472i
$748$	3.16255	+	5.47769i	0.115634	+	0.200284i
$749$	−2.67287	+	24.0090i	−0.0976645	+	0.877269i
$750$	12.0498	−	16.8768i	0.439997	−	0.616252i
$751$	−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
$753$	1.13381	−	11.7185i	0.0413184	−	0.427045i
$754$	7.37216	+	8.98303i	0.268478	+	0.327143i
$755$	−5.55578			−0.202195
$756$	5.35657	−	12.6612i	0.194817	−	0.460485i
$757$	−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
$759$	−21.8084	−	2.11006i	−0.791595	−	0.0765902i
$760$		−	2.16163i		−	0.0784104i
$761$	4.03145	+	2.32756i	0.146140	+	0.0843740i	0.571287	−	0.820750i	$-0.306444\pi$
$761$	4.03145	+	2.32756i	0.146140	+	0.0843740i	−0.425147	+	0.905124i	$0.639778\pi$
$762$	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
$768$	−1.40963	−	1.00646i	−0.0508655	−	0.0363174i
$769$	−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
$771$	19.9469	+	14.2419i	0.718371	+	0.512909i
$772$	−8.61135	+	4.97176i	−0.309929	+	0.178938i
$773$			48.7888i			1.75481i	0.479749	+	0.877406i	$0.340728\pi$
$773$			48.7888i			1.75481i	−0.479749	+	0.877406i	$0.659272\pi$
$774$	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
$777$	24.2829	−	27.0838i	0.871144	−	0.971627i
$778$	23.9026	+	13.8002i	0.856949	+	0.494760i
$779$	9.82526	−	5.67262i	0.352026	−	0.203243i
$780$	−9.14635	−	4.49095i	−0.327492	−	0.160802i
$781$	9.50949	−	16.4709i	0.340276	−	0.589376i
$782$			18.6591i			0.667249i
$783$	12.1641	−	11.5113i	0.434708	−	0.411381i
$784$	6.82861	+	1.53951i	0.243879	+	0.0549825i
$785$	30.9886			1.10603
$786$	1.70758	−	17.6486i	0.0609073	−	0.629505i
$787$	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
$789$	−22.1817	−	2.14617i	−0.789689	−	0.0764057i
$790$	−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
$795$	−24.5856	−	17.5538i	−0.871960	−	0.622569i
$796$			16.8878i			0.598572i
$797$	−0.0214000	−	0.0370659i	−0.000758027	−	0.00131294i	0.865646	−	0.500656i	$-0.166908\pi$
$797$	−0.0214000	−	0.0370659i	−0.000758027	−	0.00131294i	−0.866404	+	0.499343i	$0.833575\pi$
$798$	5.77005	−	1.88830i	0.204258	−	0.0668451i
$799$	2.18142	−	1.25944i	0.0771731	−	0.0445559i
$800$	1.16892	−	2.02463i	0.0413276	−	0.0715814i
$801$	−3.04455	+	1.04519i	−0.107574	+	0.0369298i
$802$	−23.8650			−0.842704
$803$	−5.94769			−0.209889
$804$	5.64336	+	0.546019i	0.199026	+	0.0192566i
$805$	−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
$808$	0.381326	+	0.660476i	0.0134150	+	0.0232355i
$809$	−18.0101	+	10.3981i	−0.633200	+	0.365578i	−0.781990	−	0.623291i	$-0.785795\pi$
$809$	−18.0101	+	10.3981i	−0.633200	+	0.365578i	0.148790	+	0.988869i	$0.452462\pi$
$810$	−5.52601	+	13.6051i	−0.194164	+	0.478034i
$811$	−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
$813$	1.91085	+	1.36432i	0.0670163	+	0.0478489i
$814$	−14.2352	+	8.21870i	−0.498944	+	0.288065i
$815$	1.83099			0.0641369
$816$	4.30566	+	3.07419i	0.150728	+	0.107618i
$817$	7.14518			0.249978
$818$	−7.74689			−0.270864
$819$	3.99790	−	28.3376i	0.139698	−	0.990194i
$820$	−13.9723			−0.487933
$821$	−17.4989			−0.610715			−0.305357	−	0.952238i	$-0.598776\pi$
$821$	−17.4989			−0.610715			−0.305357	+	0.952238i	$0.598776\pi$
$822$	−5.20783	−	3.71833i	−0.181644	−	0.129692i
$823$	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
$825$	−6.82417	−	4.87238i	−0.237587	−	0.169634i
$826$	3.98039	−	35.7537i	0.138496	−	1.24403i
$827$	−17.6018			−0.612075			−0.306037	−	0.952020i	$-0.599003\pi$
$827$	−17.6018			−0.612075			−0.306037	+	0.952020i	$0.599003\pi$
$828$	−17.3334	+	5.95051i	−0.602378	+	0.206795i
$829$	−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
$831$	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
$834$	23.6167	+	2.28502i	0.817780	+	0.0791237i
$835$	1.98376			0.0686508
$836$	−2.74343			−0.0948836
$837$	23.4593	+	24.7895i	0.810871	+	0.856849i
$838$	1.65804	−	2.87182i	0.0572762	−	0.0992053i
$839$	10.6696	−	6.16009i	0.368355	−	0.212670i	−0.304384	−	0.952549i	$-0.598451\pi$
$839$	10.6696	−	6.16009i	0.368355	−	0.212670i	0.672740	+	0.739879i	$0.265117\pi$
$840$	−7.31687	−	1.53909i	−0.252456	−	0.0531036i
$841$	−9.30602	−	16.1185i	−0.320897	−	0.555810i
$842$		−	25.2793i		−	0.871183i
$843$	5.75320	+	4.10772i	0.198151	+	0.141477i
$844$	−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
$849$	3.72948	+	0.360843i	0.127995	+	0.0123841i
$850$	−3.57043	+	6.18417i	−0.122465	+	0.212115i
$851$	−48.4906			−1.66224
$852$	1.53202	−	15.8341i	0.0524860	−	0.542467i
$853$	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
$855$	−6.13351	+	2.10562i	−0.209762	+	0.0720105i
$856$		−	9.13060i		−	0.312078i
$857$	−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	$0.245973\pi$
$858$	−5.69970	+	11.6081i	−0.194585	+	0.396294i
$859$	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
$861$	−12.2056	−	37.2964i	−0.415964	−	1.27106i
$862$	−12.4404	−	21.5475i	−0.423723	−	0.733909i
$863$	−14.6218	−	25.3257i	−0.497731	−	0.862095i	0.502266	−	0.864713i	$-0.332500\pi$
$863$	−14.6218	−	25.3257i	−0.497731	−	0.862095i	−0.999997	+	0.00261814i	$0.999167\pi$
$864$	−1.48267	+	4.98013i	−0.0504416	+	0.169427i
$865$			31.3554i			1.06612i
$866$	17.2062	−	9.93398i	0.584689	−	0.337570i
$867$	10.8121	+	7.71975i	0.367199	+	0.262176i
$868$	−10.3009	+	13.9961i	−0.349635	+	0.475059i
$869$	−6.72289	+	11.6444i	−0.228058	+	0.395009i
$870$	−7.41286	−	5.29270i	−0.251320	−	0.179439i
$871$	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
$879$	−10.5338	−	1.01919i	−0.355296	−	0.0343764i
$880$	2.92603	+	1.68934i	0.0986365	+	0.0569478i
$881$	11.1486	−	19.3099i	0.375606	−	0.650568i	−0.614812	−	0.788674i	$-0.710768\pi$
$881$	11.1486	−	19.3099i	0.375606	−	0.650568i	0.990418	+	0.138106i	$0.0441014\pi$
$882$	−2.28338	−	20.8755i	−0.0768855	−	0.702914i
$883$	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
$885$	−3.70060	+	38.2474i	−0.124394	+	1.28567i
$886$	−13.3621	+	7.71462i	−0.448909	+	0.259178i
$887$	23.8404			0.800481			0.400241	−	0.916410i	$-0.368927\pi$
$887$	23.8404			0.800481			0.400241	+	0.916410i	$0.368927\pi$
$888$	−7.98909	+	11.1894i	−0.268096	+	0.375491i
$889$	5.34070	−	7.25655i	0.179121	−	0.243377i
$890$	0.875350	+	1.51615i	0.0293418	+	0.0508215i
$891$	17.2669	+	7.01335i	0.578464	+	0.234956i
$892$	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
$897$	−31.6836	+	21.2492i	−1.05788	+	0.709489i
$898$	10.2266	+	17.7130i	0.341267	+	0.591092i
$899$	−18.3337	+	10.5850i	−0.611463	+	0.353028i
$900$	−6.88342	−	1.34459i	−0.229447	−	0.0448196i
$901$	28.2765	+	16.3254i	0.942026	+	0.543879i
$902$			17.7330i			0.590443i
$903$	5.08741	−	24.1857i	0.169298	−	0.804849i
$904$	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	$-0.642881\pi$
$911$		−	54.3855i		−	1.80187i	0.433952	−	0.900936i	$-0.357119\pi$
$912$	−2.08852	+	0.950630i	−0.0691577	+	0.0314785i
$913$	12.3013	−	7.10217i	0.407114	−	0.235048i
$914$			32.5131i			1.07544i
$915$	−35.7702	−	25.5395i	−1.18253	−	0.844310i
$916$	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
$921$	1.40149	+	1.00064i	0.0461805	+	0.0329724i
$922$	−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
$926$			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	0.756319	−	0.654203i	$-0.226996\pi$
$929$	17.3100	+	9.99393i	0.567923	+	0.327890i	−0.188397	+	0.982093i	$0.560329\pi$
$930$	10.7861	−	15.1069i	0.353692	−	0.495374i
$931$	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
$936$	−0.316722	+	10.8120i	−0.0103524	+	0.353402i
$937$		−	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
$939$	−45.3590	−	4.38867i	−1.48023	−	0.143219i
$940$	0.672760	−	1.16525i	0.0219430	−	0.0380064i
$941$	14.7948	+	8.54179i	0.482297	+	0.278454i	0.721373	−	0.692546i	$-0.243511\pi$
$941$	14.7948	+	8.54179i	0.482297	+	0.278454i	−0.239076	+	0.971001i	$0.576845\pi$
$942$	−13.6280	−	29.9405i	−0.444025	−	0.975515i
$943$	−26.1563	+	45.3040i	−0.851765	+	1.47530i
$944$			13.5971i			0.442549i
$945$	2.76019	+	22.2605i	0.0897890	+	0.724134i
$946$	−5.58407	+	9.67190i	−0.181554	+	0.314461i
$947$	6.49771			0.211147			0.105574	−	0.994411i	$-0.466332\pi$
$947$	6.49771			0.211147			0.105574	+	0.994411i	$0.466332\pi$
$948$	−1.08308	+	11.1942i	−0.0351769	+	0.363570i
$949$	−8.00524	+	6.56971i	−0.259861	+	0.213262i
$950$	−1.54863	−	2.68231i	−0.0502442	−	0.0870256i
$951$	−3.78213	+	39.0901i	−0.122644	+	1.26758i
$952$	8.03175	+	0.894158i	0.260310	+	0.0289798i
$953$	46.4669	−	26.8277i	1.50521	−	0.869034i	0.505229	−	0.862985i	$-0.331408\pi$
$953$	46.4669	−	26.8277i	1.50521	−	0.869034i	0.999982	−	0.00604840i	$-0.00192528\pi$
$954$	−6.14800	+	31.4738i	−0.199049	+	1.01900i
$955$	10.6934			0.346029
$956$	−17.3876			−0.562354
$957$	−6.71725	+	9.40806i	−0.217138	+	0.304119i
$958$	30.2057	−	17.4393i	0.975902	−	0.563437i
$959$	−9.71466	−	1.08151i	−0.313703	−	0.0349239i
$960$	2.81290	+	0.272160i	0.0907860	+	0.00878393i
$961$	−6.07139	−	10.5160i	−0.195851	−	0.339224i
$962$	−10.0815	+	26.7859i	−0.325042	+	0.863611i
$963$	−25.9077	+	8.89402i	−0.834863	+	0.286606i
$964$	−1.42882			−0.0460192
$965$	8.11199	−	14.0504i	0.261134	−	0.452298i
$966$	−18.6876	+	20.8432i	−0.601265	+	0.670618i
$967$		−	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	−0.803763	−	0.594950i	$-0.797172\pi$
$971$	3.53240	−	6.11830i	0.113360	−	0.196346i	0.917123	+	0.398604i	$0.130505\pi$
$972$	15.5751	−	0.644067i	0.499573	−	0.0206585i
$973$	33.2002	−	14.5376i	1.06435	−	0.466055i
$974$			0.222477i			0.00712861i
$975$	−14.5669	+	0.979916i	−0.466514	+	0.0313824i
$976$	−13.4689	−	7.77625i	−0.431128	−	0.248912i
$977$	25.5640	+	44.2781i	0.817863	+	1.41658i	0.907253	+	0.420584i	$0.138175\pi$
$977$	25.5640	+	44.2781i	0.817863	+	1.41658i	−0.0893900	+	0.995997i	$0.528492\pi$
$978$	−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
$981$	−9.57125	+	48.9986i	−0.305586	+	1.56441i
$982$	25.2390	+	14.5717i	0.805408	+	0.465003i
$983$	18.5961	+	10.7365i	0.593123	+	0.342440i	0.766331	−	0.642445i	$-0.222080\pi$
$983$	18.5961	+	10.7365i	0.593123	+	0.342440i	−0.173208	+	0.984885i	$0.555413\pi$
$984$	6.14466	+	13.4997i	0.195885	+	0.430355i
$985$		−	0.604203i		−	0.0192515i
$986$	8.52573	+	4.92233i	0.271514	+	0.156759i
$987$	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
$990$	1.94322	−	9.94805i	0.0617597	−	0.316170i
$991$	−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
$996$	6.90375	−	9.66927i	0.218754	−	0.306383i
$997$			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.e.17.2	✓	34
3.2	odd	2		546.2.bi.f.17.7	yes	34
7.5	odd	6		546.2.bn.f.173.4	yes	34
13.10	even	6		546.2.bn.e.101.14	yes	34
21.5	even	6		546.2.bn.e.173.14	yes	34
39.23	odd	6		546.2.bn.f.101.4	yes	34
91.75	odd	6		546.2.bi.f.257.7	yes	34
273.257	even	6	inner	546.2.bi.e.257.2	yes	34

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.40963 - 1.00646i) q^{3} +1.00000 q^{4} +(-1.41302 + 0.815806i) q^{5} +(1.40963 + 1.00646i) q^{6} +(2.62951 + 0.292738i) q^{7} -1.00000 q^{8} +(0.974089 + 2.83745i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.40963 - 1.00646i) q^{3} +1.00000 q^{4} +(-1.41302 + 0.815806i) q^{5} +(1.40963 + 1.00646i) q^{6} +(2.62951 + 0.292738i) q^{7} -1.00000 q^{8} +(0.974089 + 2.83745i) q^{9} +(1.41302 - 0.815806i) q^{10} +(-1.03538 - 1.79334i) q^{11} +(-1.40963 - 1.00646i) q^{12} +(-3.37445 - 1.27006i) q^{13} +(-2.62951 - 0.292738i) q^{14} +(2.81290 + 0.272160i) q^{15} +1.00000 q^{16} -3.05447 q^{17} +(-0.974089 - 2.83745i) q^{18} +(0.662420 - 1.14734i) q^{19} +(-1.41302 + 0.815806i) q^{20} +(-3.41199 - 3.05914i) q^{21} +(1.03538 + 1.79334i) q^{22} +6.10879i q^{23} +(1.40963 + 1.00646i) 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} +(-2.81290 - 0.272160i) q^{30} +(-3.28416 + 5.68833i) q^{31} -1.00000 q^{32} +(-0.345413 + 3.57000i) q^{33} +3.05447 q^{34} +(-3.95436 + 1.73152i) q^{35} +(0.974089 + 2.83745i) q^{36} +7.93783i q^{37} +(-0.662420 + 1.14734i) q^{38} +(3.47846 + 5.18655i) q^{39} +(1.41302 - 0.815806i) q^{40} +(7.41619 + 4.28174i) q^{41} +(3.41199 + 3.05914i) 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} +(-1.40963 - 1.00646i) q^{48} +(6.82861 + 1.53951i) q^{49} +(1.16892 - 2.02463i) q^{50} +(4.30566 + 3.07419i) 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} +(2.81290 + 0.272160i) q^{60} +(-13.4689 - 7.77625i) q^{61} +(3.28416 - 5.68833i) q^{62} +(1.73074 + 7.74626i) q^{63} +1.00000 q^{64} +(5.80429 - 0.958282i) q^{65} +(0.345413 - 3.57000i) q^{66} +(-2.83485 + 1.63670i) q^{67} -3.05447 q^{68} +(6.14824 - 8.61111i) q^{69} +(3.95436 - 1.73152i) q^{70} +(4.59225 + 7.95402i) q^{71} +(-0.974089 - 2.83745i) 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} +(-3.47846 - 5.18655i) q^{78} +(-3.24657 - 5.62322i) q^{79} +(-1.41302 + 0.815806i) q^{80} +(-7.10230 + 5.52787i) q^{81} +(-7.41619 - 4.28174i) q^{82} +6.85946i q^{83} +(-3.41199 - 3.05914i) 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} +(1.40963 + 1.00646i) q^{96} +(-4.58560 - 7.94250i) q^{97} +(-6.82861 - 1.53951i) q^{98} +(4.07996 - 4.68472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

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