LMFDB - Embedded newform 429.2.i.f.133.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.i (of order $3$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} + 4x^{7} + 32x^{6} + 3x^{5} + 30x^{4} - 7x^{3} + 26x^{2} - 5x + 1 $ x^10 - x^9 + 7x^8 + 4x^7 + 32x^6 + 3x^5 + 30x^4 - 7x^3 + 26x^2 - 5x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.2
Root			$0.440981 + 0.763802i$ of defining polynomial
Character	$\chi$	$=$	429.133
Dual form			429.2.i.f.100.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0590186 + 0.102223i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.993034 - 1.71998i) q^{4} -2.39753 q^{5} +(0.0590186 - 0.102223i) q^{6} +(1.48513 - 2.57233i) q^{7} +0.470505 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.0590186 + 0.102223i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.993034 - 1.71998i) q^{4} -2.39753 q^{5} +(0.0590186 - 0.102223i) q^{6} +(1.48513 - 2.57233i) q^{7} +0.470505 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.141499 - 0.245083i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.98607 q^{12} +(-3.31053 + 1.42842i) q^{13} +0.350603 q^{14} +(1.19876 + 2.07632i) q^{15} +(-1.95830 - 3.39187i) q^{16} +(-2.29228 + 3.97035i) q^{17} -0.118037 q^{18} +(2.42612 - 4.20216i) q^{19} +(-2.38082 + 4.12371i) q^{20} -2.97027 q^{21} +(0.0590186 - 0.102223i) q^{22} +(-0.876751 - 1.51858i) q^{23} +(-0.235252 - 0.407469i) q^{24} +0.748128 q^{25} +(-0.341401 - 0.254110i) q^{26} +1.00000 q^{27} +(-2.94958 - 5.10882i) q^{28} +(-2.71249 - 4.69817i) q^{29} +(-0.141499 + 0.245083i) q^{30} -1.91984 q^{31} +(0.701657 - 1.21531i) q^{32} +(-0.500000 + 0.866025i) q^{33} -0.541149 q^{34} +(-3.56065 + 6.16722i) q^{35} +(0.993034 + 1.71998i) q^{36} +(1.88372 + 3.26269i) q^{37} +0.572744 q^{38} +(2.89231 + 2.15279i) q^{39} -1.12805 q^{40} +(-2.70736 - 4.68928i) q^{41} +(-0.175301 - 0.303631i) q^{42} +(3.50746 - 6.07509i) q^{43} -1.98607 q^{44} +(1.19876 - 2.07632i) q^{45} +(0.103489 - 0.179249i) q^{46} +12.3378 q^{47} +(-1.95830 + 3.39187i) q^{48} +(-0.911251 - 1.57833i) q^{49} +(0.0441535 + 0.0764761i) q^{50} +4.58456 q^{51} +(-0.830608 + 7.11253i) q^{52} +4.41104 q^{53} +(0.0590186 + 0.102223i) q^{54} +(1.19876 + 2.07632i) q^{55} +(0.698763 - 1.21029i) q^{56} -4.85223 q^{57} +(0.320175 - 0.554559i) q^{58} +(-1.38465 + 2.39828i) q^{59} +4.76165 q^{60} +(-2.72039 + 4.71185i) q^{61} +(-0.113306 - 0.196252i) q^{62} +(1.48513 + 2.57233i) q^{63} -7.66755 q^{64} +(7.93708 - 3.42467i) q^{65} -0.118037 q^{66} +(-2.85016 - 4.93662i) q^{67} +(4.55262 + 7.88538i) q^{68} +(-0.876751 + 1.51858i) q^{69} -0.840579 q^{70} +(7.47527 - 12.9476i) q^{71} +(-0.235252 + 0.407469i) q^{72} +10.5499 q^{73} +(-0.222349 + 0.385120i) q^{74} +(-0.374064 - 0.647898i) q^{75} +(-4.81843 - 8.34577i) q^{76} -2.97027 q^{77} +(-0.0493653 + 0.422717i) q^{78} +2.55834 q^{79} +(4.69507 + 8.13210i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.319569 - 0.553510i) q^{82} -9.41168 q^{83} +(-2.94958 + 5.10882i) q^{84} +(5.49580 - 9.51901i) q^{85} +0.828021 q^{86} +(-2.71249 + 4.69817i) q^{87} +(-0.235252 - 0.407469i) q^{88} +(-0.0144232 - 0.0249817i) q^{89} +0.282997 q^{90} +(-1.24222 + 10.6372i) q^{91} -3.48257 q^{92} +(0.959919 + 1.66263i) q^{93} +(0.728161 + 1.26121i) q^{94} +(-5.81668 + 10.0748i) q^{95} -1.40331 q^{96} +(5.54057 - 9.59655i) q^{97} +(0.107562 - 0.186302i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} - 5 q^{11} + 12 q^{12} + 5 q^{13} + 14 q^{14} + 4 q^{15} - 12 q^{16} - 9 q^{17} - 8 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} + 4 q^{22} + 9 q^{23} + 9 q^{24} + 2 q^{25} - 12 q^{26} + 10 q^{27} - q^{28} - 8 q^{29} + 5 q^{30} - 12 q^{31} + 27 q^{32} - 5 q^{33} - 14 q^{34} + 2 q^{35} - 6 q^{36} + 17 q^{37} - 2 q^{38} + 2 q^{39} + 46 q^{40} + 6 q^{41} - 7 q^{42} - 13 q^{43} + 12 q^{44} + 4 q^{45} - 6 q^{46} - 32 q^{47} - 12 q^{48} + 18 q^{49} - 8 q^{50} + 18 q^{51} + 7 q^{52} - 26 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 18 q^{57} + 11 q^{58} + 8 q^{59} - 12 q^{60} - 4 q^{61} + 22 q^{62} + 3 q^{63} + 22 q^{64} + 26 q^{65} - 8 q^{66} + 5 q^{67} - 34 q^{68} + 9 q^{69} + 8 q^{70} + 19 q^{71} + 9 q^{72} - 4 q^{73} - 27 q^{74} - q^{75} - 6 q^{76} - 6 q^{77} - 3 q^{78} - 16 q^{79} + 32 q^{80} - 5 q^{81} - 16 q^{82} - 20 q^{83} - q^{84} + 21 q^{85} + 8 q^{86} - 8 q^{87} + 9 q^{88} + 32 q^{89} - 10 q^{90} - 17 q^{91} - 84 q^{92} + 6 q^{93} - 66 q^{94} - 11 q^{95} - 54 q^{96} - 5 q^{97} - 18 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 - 5 * q^11 + 12 * q^12 + 5 * q^13 + 14 * q^14 + 4 * q^15 - 12 * q^16 - 9 * q^17 - 8 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 + 4 * q^22 + 9 * q^23 + 9 * q^24 + 2 * q^25 - 12 * q^26 + 10 * q^27 - q^28 - 8 * q^29 + 5 * q^30 - 12 * q^31 + 27 * q^32 - 5 * q^33 - 14 * q^34 + 2 * q^35 - 6 * q^36 + 17 * q^37 - 2 * q^38 + 2 * q^39 + 46 * q^40 + 6 * q^41 - 7 * q^42 - 13 * q^43 + 12 * q^44 + 4 * q^45 - 6 * q^46 - 32 * q^47 - 12 * q^48 + 18 * q^49 - 8 * q^50 + 18 * q^51 + 7 * q^52 - 26 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 18 * q^57 + 11 * q^58 + 8 * q^59 - 12 * q^60 - 4 * q^61 + 22 * q^62 + 3 * q^63 + 22 * q^64 + 26 * q^65 - 8 * q^66 + 5 * q^67 - 34 * q^68 + 9 * q^69 + 8 * q^70 + 19 * q^71 + 9 * q^72 - 4 * q^73 - 27 * q^74 - q^75 - 6 * q^76 - 6 * q^77 - 3 * q^78 - 16 * q^79 + 32 * q^80 - 5 * q^81 - 16 * q^82 - 20 * q^83 - q^84 + 21 * q^85 + 8 * q^86 - 8 * q^87 + 9 * q^88 + 32 * q^89 - 10 * q^90 - 17 * q^91 - 84 * q^92 + 6 * q^93 - 66 * q^94 - 11 * q^95 - 54 * q^96 - 5 * q^97 - 18 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0590186	+	0.102223i	0.0417325	+	0.0722828i	0.886137	−	0.463423i	$-0.153379\pi$
$2$	0.0590186	+	0.102223i	0.0417325	+	0.0722828i	−0.844405	+	0.535706i	$0.820046\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.993034	−	1.71998i	0.496517	−	0.859992i
$5$	−2.39753			−1.07221			−0.536103	−	0.844153i	$-0.680104\pi$
$5$	−2.39753			−1.07221			−0.536103	+	0.844153i	$0.680104\pi$
$6$	0.0590186	−	0.102223i	0.0240943	−	0.0417325i
$7$	1.48513	−	2.57233i	0.561328	−	0.972249i	−0.436053	−	0.899921i	$-0.643624\pi$
$7$	1.48513	−	2.57233i	0.561328	−	0.972249i	0.997381	−	0.0723279i	$-0.0230428\pi$
$8$	0.470505			0.166348
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.141499	−	0.245083i	−0.0447458	−	0.0775020i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−1.98607			−0.573328
$13$	−3.31053	+	1.42842i	−0.918176	+	0.396172i
$13$	−3.31053	+	1.42842i	−0.918176	+	0.396172i
$14$	0.350603			0.0937025
$15$	1.19876	+	2.07632i	0.309519	+	0.536103i
$16$	−1.95830	−	3.39187i	−0.489575	−	0.847968i
$17$	−2.29228	+	3.97035i	−0.555960	+	0.962951i	0.441868	+	0.897080i	$0.354316\pi$
$17$	−2.29228	+	3.97035i	−0.555960	+	0.962951i	−0.997828	+	0.0658709i	$0.979017\pi$
$18$	−0.118037			−0.0278217
$19$	2.42612	−	4.20216i	0.556589	−	0.964041i	−0.441189	−	0.897414i	$-0.645443\pi$
$19$	2.42612	−	4.20216i	0.556589	−	0.964041i	0.997778	−	0.0666265i	$-0.0212236\pi$
$20$	−2.38082	+	4.12371i	−0.532368	+	0.922089i
$21$	−2.97027			−0.648166
$22$	0.0590186	−	0.102223i	0.0125828	−	0.0217941i
$23$	−0.876751	−	1.51858i	−0.182815	−	0.316645i	0.760023	−	0.649896i	$-0.225188\pi$
$23$	−0.876751	−	1.51858i	−0.182815	−	0.316645i	−0.942838	+	0.333251i	$0.891854\pi$
$24$	−0.235252	−	0.407469i	−0.0480207	−	0.0831742i
$25$	0.748128			0.149626
$26$	−0.341401	−	0.254110i	−0.0669542	−	0.0498351i
$27$	1.00000			0.192450
$28$	−2.94958	−	5.10882i	−0.557418	−	0.965476i
$29$	−2.71249	−	4.69817i	−0.503696	−	0.872428i	−0.999991	−	0.00427356i	$-0.998640\pi$
$29$	−2.71249	−	4.69817i	−0.503696	−	0.872428i	0.496294	−	0.868154i	$-0.334694\pi$
$30$	−0.141499	+	0.245083i	−0.0258340	+	0.0447458i
$31$	−1.91984			−0.344813			−0.172407	−	0.985026i	$-0.555154\pi$
$31$	−1.91984			−0.344813			−0.172407	+	0.985026i	$0.555154\pi$
$32$	0.701657	−	1.21531i	0.124037	−	0.214838i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	−0.541149			−0.0928063
$35$	−3.56065	+	6.16722i	−0.601859	+	1.04245i
$36$	0.993034	+	1.71998i	0.165506	+	0.286664i
$37$	1.88372	+	3.26269i	0.309681	+	0.536384i	0.978293	−	0.207228i	$-0.0664443\pi$
$37$	1.88372	+	3.26269i	0.309681	+	0.536384i	−0.668611	+	0.743612i	$0.733111\pi$
$38$	0.572744			0.0929114
$39$	2.89231	+	2.15279i	0.463141	+	0.344723i
$40$	−1.12805			−0.178360
$41$	−2.70736	−	4.68928i	−0.422818	−	0.732343i	0.573395	−	0.819279i	$-0.305626\pi$
$41$	−2.70736	−	4.68928i	−0.422818	−	0.732343i	−0.996214	+	0.0869357i	$0.972293\pi$
$42$	−0.175301	−	0.303631i	−0.0270496	−	0.0468512i
$43$	3.50746	−	6.07509i	0.534882	−	0.926443i	−0.464287	−	0.885685i	$-0.653689\pi$
$43$	3.50746	−	6.07509i	0.534882	−	0.926443i	0.999169	−	0.0407582i	$-0.0129773\pi$
$44$	−1.98607			−0.299411
$45$	1.19876	−	2.07632i	0.178701	−	0.309519i
$46$	0.103489	−	0.179249i	0.0152587	−	0.0264288i
$47$	12.3378			1.79966			0.899828	−	0.436246i	$-0.143692\pi$
$47$	12.3378			1.79966			0.899828	+	0.436246i	$0.143692\pi$
$48$	−1.95830	+	3.39187i	−0.282656	+	0.489575i
$49$	−0.911251	−	1.57833i	−0.130179	−	0.225476i
$50$	0.0441535	+	0.0764761i	0.00624425	+	0.0108154i
$51$	4.58456			0.641967
$52$	−0.830608	+	7.11253i	−0.115185	+	0.986331i
$53$	4.41104			0.605903			0.302952	−	0.953006i	$-0.402028\pi$
$53$	4.41104			0.605903			0.302952	+	0.953006i	$0.402028\pi$
$54$	0.0590186	+	0.102223i	0.00803142	+	0.0139108i
$55$	1.19876	+	2.07632i	0.161641	+	0.279971i
$56$	0.698763	−	1.21029i	0.0933761	−	0.161732i
$57$	−4.85223			−0.642694
$58$	0.320175	−	0.554559i	0.0420410	−	0.0728172i
$59$	−1.38465	+	2.39828i	−0.180266	+	0.312230i	−0.941971	−	0.335694i	$-0.891029\pi$
$59$	−1.38465	+	2.39828i	−0.180266	+	0.312230i	0.761705	+	0.647924i	$0.224363\pi$
$60$	4.76165			0.614726
$61$	−2.72039	+	4.71185i	−0.348310	+	0.603290i	−0.985949	−	0.167045i	$-0.946578\pi$
$61$	−2.72039	+	4.71185i	−0.348310	+	0.603290i	0.637639	+	0.770335i	$0.279911\pi$
$62$	−0.113306	−	0.196252i	−0.0143899	−	0.0249240i
$63$	1.48513	+	2.57233i	0.187109	+	0.324083i
$64$	−7.66755			−0.958444
$65$	7.93708	−	3.42467i	0.984474	−	0.424778i
$66$	−0.118037			−0.0145294
$67$	−2.85016	−	4.93662i	−0.348203	−	0.603104i	0.637728	−	0.770262i	$-0.279875\pi$
$67$	−2.85016	−	4.93662i	−0.348203	−	0.603104i	−0.985930	+	0.167157i	$0.946541\pi$
$68$	4.55262	+	7.88538i	0.552087	+	0.956243i
$69$	−0.876751	+	1.51858i	−0.105548	+	0.182815i
$70$	−0.840579			−0.100468
$71$	7.47527	−	12.9476i	0.887152	−	1.53659i	0.0439246	−	0.999035i	$-0.486014\pi$
$71$	7.47527	−	12.9476i	0.887152	−	1.53659i	0.843227	−	0.537557i	$-0.180653\pi$
$72$	−0.235252	+	0.407469i	−0.0277247	+	0.0480207i
$73$	10.5499			1.23478			0.617389	−	0.786658i	$-0.288190\pi$
$73$	10.5499			1.23478			0.617389	+	0.786658i	$0.288190\pi$
$74$	−0.222349	+	0.385120i	−0.0258475	+	0.0447692i
$75$	−0.374064	−	0.647898i	−0.0431932	−	0.0748128i
$76$	−4.81843	−	8.34577i	−0.552712	−	0.957325i
$77$	−2.97027			−0.338494
$78$	−0.0493653	+	0.422717i	−0.00558951	+	0.0478632i
$79$	2.55834			0.287836			0.143918	−	0.989590i	$-0.454030\pi$
$79$	2.55834			0.287836			0.143918	+	0.989590i	$0.454030\pi$
$80$	4.69507	+	8.13210i	0.524925	+	0.909197i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.319569	−	0.553510i	0.0352905	−	0.0611250i
$83$	−9.41168			−1.03307			−0.516533	−	0.856267i	$-0.672778\pi$
$83$	−9.41168			−1.03307			−0.516533	+	0.856267i	$0.672778\pi$
$84$	−2.94958	+	5.10882i	−0.321825	+	0.557418i
$85$	5.49580	−	9.51901i	0.596104	−	1.03248i
$86$	0.828021			0.0892878
$87$	−2.71249	+	4.69817i	−0.290809	+	0.503696i
$88$	−0.235252	−	0.407469i	−0.0250780	−	0.0434363i
$89$	−0.0144232	−	0.0249817i	−0.00152886	−	0.00264806i	0.865260	−	0.501323i	$-0.167153\pi$
$89$	−0.0144232	−	0.0249817i	−0.00152886	−	0.00264806i	−0.866789	+	0.498675i	$0.833820\pi$
$90$	0.282997			0.0298305
$91$	−1.24222	+	10.6372i	−0.130220	+	1.11508i
$92$	−3.48257			−0.363083
$93$	0.959919	+	1.66263i	0.0995389	+	0.172407i
$94$	0.728161	+	1.26121i	0.0751041	+	0.130084i
$95$	−5.81668	+	10.0748i	−0.596778	+	1.03365i
$96$	−1.40331			−0.143225
$97$	5.54057	−	9.59655i	0.562560	−	0.974382i	−0.434712	−	0.900569i	$-0.643150\pi$
$97$	5.54057	−	9.59655i	0.562560	−	0.974382i	0.997272	−	0.0738128i	$-0.0235167\pi$
$98$	0.107562	−	0.186302i	0.0108654	−	0.0188194i
$99$	1.00000			0.100504
$100$	0.742916	−	1.28677i	0.0742916	−	0.128677i
$101$	6.42392	+	11.1266i	0.639204	+	1.10713i	0.985608	+	0.169048i	$0.0540693\pi$
$101$	6.42392	+	11.1266i	0.639204	+	1.10713i	−0.346404	+	0.938085i	$0.612597\pi$
$102$	0.270575	+	0.468649i	0.0267909	+	0.0464032i
$103$	16.2544			1.60159			0.800797	−	0.598935i	$-0.204409\pi$
$103$	16.2544			1.60159			0.800797	+	0.598935i	$0.204409\pi$
$104$	−1.55762	+	0.672078i	−0.152737	+	0.0659027i
$105$	7.12130			0.694967
$106$	0.260334	+	0.450911i	0.0252859	+	0.0437964i
$107$	0.424362	+	0.735016i	0.0410246	+	0.0710567i	0.885809	−	0.464051i	$-0.153604\pi$
$107$	0.424362	+	0.735016i	0.0410246	+	0.0710567i	−0.844784	+	0.535107i	$0.820271\pi$
$108$	0.993034	−	1.71998i	0.0955547	−	0.165506i
$109$	13.4908			1.29218			0.646092	−	0.763260i	$-0.276402\pi$
$109$	13.4908			1.29218			0.646092	+	0.763260i	$0.276402\pi$
$110$	−0.141499	+	0.245083i	−0.0134914	+	0.0233677i
$111$	1.88372	−	3.26269i	0.178795	−	0.309681i
$112$	−11.6334			−1.09925
$113$	−4.31598	+	7.47549i	−0.406013	+	0.703235i	−0.994439	−	0.105316i	$-0.966415\pi$
$113$	−4.31598	+	7.47549i	−0.406013	+	0.703235i	0.588426	+	0.808551i	$0.299748\pi$
$114$	−0.286372	−	0.496011i	−0.0268212	−	0.0464557i
$115$	2.10203	+	3.64083i	0.196016	+	0.339509i
$116$	−10.7744			−1.00037
$117$	0.418217	−	3.58121i	0.0386642	−	0.331083i
$118$	−0.326881			−0.0300918
$119$	6.80869	+	11.7930i	0.624152	+	1.08106i
$120$	0.564023	+	0.976917i	0.0514880	+	0.0891799i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−0.642214			−0.0581433
$123$	−2.70736	+	4.68928i	−0.244114	+	0.422818i
$124$	−1.90646	+	3.30209i	−0.171205	+	0.296537i
$125$	10.1940			0.911776
$126$	−0.175301	+	0.303631i	−0.0156171	+	0.0270496i
$127$	8.50225	+	14.7263i	0.754452	+	1.30675i	0.945646	+	0.325197i	$0.105431\pi$
$127$	8.50225	+	14.7263i	0.754452	+	1.30675i	−0.191194	+	0.981552i	$0.561236\pi$
$128$	−1.85584	−	3.21441i	−0.164035	−	0.284117i
$129$	−7.01491			−0.617629
$130$	0.818517	+	0.609235i	0.0717887	+	0.0534334i
$131$	−14.4417			−1.26178			−0.630889	−	0.775873i	$-0.717310\pi$
$131$	−14.4417			−1.26178			−0.630889	+	0.775873i	$0.717310\pi$
$132$	0.993034	+	1.71998i	0.0864325	+	0.149705i
$133$	−7.20622	−	12.4815i	−0.624858	−	1.08229i
$134$	0.336425	−	0.582706i	0.0290627	−	0.0503381i
$135$	−2.39753			−0.206346
$136$	−1.07853	+	1.86807i	−0.0924831	+	0.160185i
$137$	7.05345	−	12.2169i	0.602617	−	1.04376i	−0.389807	−	0.920897i	$-0.627458\pi$
$137$	7.05345	−	12.2169i	0.602617	−	1.04376i	0.992423	−	0.122866i	$-0.0392085\pi$
$138$	−0.206979			−0.0176192
$139$	−2.43569	+	4.21873i	−0.206592	+	0.357828i	−0.950639	−	0.310299i	$-0.899571\pi$
$139$	−2.43569	+	4.21873i	−0.206592	+	0.357828i	0.744047	+	0.668128i	$0.232904\pi$
$140$	7.07169	+	12.2485i	0.597667	+	1.03519i
$141$	−6.16891	−	10.6849i	−0.519516	−	0.899828i
$142$	1.76472			0.148092
$143$	2.89231	+	2.15279i	0.241867	+	0.180026i
$144$	3.91660			0.326383
$145$	6.50326	+	11.2640i	0.540066	+	0.935422i
$146$	0.622644	+	1.07845i	0.0515303	+	0.0892532i
$147$	−0.911251	+	1.57833i	−0.0751587	+	0.130179i
$148$	7.48238			0.615048
$149$	4.39462	−	7.61171i	0.360021	−	0.623575i	−0.627943	−	0.778260i	$-0.716103\pi$
$149$	4.39462	−	7.61171i	0.360021	−	0.623575i	0.987964	+	0.154684i	$0.0494361\pi$
$150$	0.0441535	−	0.0764761i	0.00360512	−	0.00624425i
$151$	−21.4502			−1.74559			−0.872797	−	0.488083i	$-0.837696\pi$
$151$	−21.4502			−1.74559			−0.872797	+	0.488083i	$0.837696\pi$
$152$	1.14150	−	1.97713i	0.0925878	−	0.160367i
$153$	−2.29228	−	3.97035i	−0.185320	−	0.320984i
$154$	−0.175301	−	0.303631i	−0.0141262	−	0.0244673i
$155$	4.60286			0.369711
$156$	6.57494	−	2.83694i	0.526416	−	0.227137i
$157$	−22.3349			−1.78252			−0.891259	−	0.453495i	$-0.850177\pi$
$157$	−22.3349			−1.78252			−0.891259	+	0.453495i	$0.850177\pi$
$158$	0.150990	+	0.261522i	0.0120121	+	0.0208056i
$159$	−2.20552	−	3.82008i	−0.174909	−	0.302952i
$160$	−1.68224	+	2.91373i	−0.132993	+	0.230350i
$161$	−5.20837			−0.410477
$162$	0.0590186	−	0.102223i	0.00463694	−	0.00803142i
$163$	9.38828	−	16.2610i	0.735347	−	1.27366i	−0.219224	−	0.975675i	$-0.570353\pi$
$163$	9.38828	−	16.2610i	0.735347	−	1.27366i	0.954571	−	0.297984i	$-0.0963141\pi$
$164$	−10.7540			−0.839746
$165$	1.19876	−	2.07632i	0.0933235	−	0.161641i
$166$	−0.555464	−	0.962093i	−0.0431124	−	0.0746729i
$167$	1.17759	+	2.03965i	0.0911247	+	0.157833i	0.907985	−	0.419003i	$-0.137620\pi$
$167$	1.17759	+	2.03965i	0.0911247	+	0.157833i	−0.816860	+	0.576836i	$0.804287\pi$
$168$	−1.39753			−0.107821
$169$	8.91923	−	9.45766i	0.686095	−	0.727512i
$170$	1.29742			0.0995075
$171$	2.42612	+	4.20216i	0.185530	+	0.321347i
$172$	−6.96604	−	12.0655i	−0.531156	−	0.919989i
$173$	0.734085	−	1.27147i	0.0558115	−	0.0966683i	−0.836770	−	0.547555i	$-0.815559\pi$
$173$	0.734085	−	1.27147i	0.0558115	−	0.0966683i	0.892581	+	0.450887i	$0.148892\pi$
$174$	−0.640350			−0.0485448
$175$	1.11107	−	1.92443i	0.0839891	−	0.145473i
$176$	−1.95830	+	3.39187i	−0.147612	+	0.255672i
$177$	2.76930			0.208153
$178$	0.00170248	−	0.00294877i	0.000127606	−	0.000221020i
$179$	−4.30609	−	7.45837i	−0.321852	−	0.557464i	0.659018	−	0.752127i	$-0.270972\pi$
$179$	−4.30609	−	7.45837i	−0.321852	−	0.557464i	−0.980870	+	0.194663i	$0.937639\pi$
$180$	−2.38082	−	4.12371i	−0.177456	−	0.307363i
$181$	−16.8486			−1.25235			−0.626173	−	0.779684i	$-0.715380\pi$
$181$	−16.8486			−1.25235			−0.626173	+	0.779684i	$0.715380\pi$
$182$	−1.16068	+	0.500808i	−0.0860354	+	0.0371223i
$183$	5.44077			0.402194
$184$	−0.412515	−	0.714497i	−0.0304110	−	0.0526735i
$185$	−4.51626	−	7.82239i	−0.332042	−	0.575114i
$186$	−0.113306	+	0.196252i	−0.00830801	+	0.0143899i
$187$	4.58456			0.335256
$188$	12.2519	−	21.2209i	0.893559	−	1.54769i
$189$	1.48513	−	2.57233i	0.108028	−	0.187109i
$190$	−1.37317			−0.0996202
$191$	1.83154	−	3.17232i	0.132526	−	0.229541i	−0.792124	−	0.610360i	$-0.791025\pi$
$191$	1.83154	−	3.17232i	0.132526	−	0.229541i	0.924650	+	0.380819i	$0.124358\pi$
$192$	3.83378	+	6.64029i	0.276679	+	0.479222i
$193$	1.96705	+	3.40703i	0.141591	+	0.245243i	0.928096	−	0.372341i	$-0.121445\pi$
$193$	1.96705	+	3.40703i	0.141591	+	0.245243i	−0.786505	+	0.617584i	$0.788111\pi$
$194$	1.30799			0.0939081
$195$	−6.93440	−	5.16138i	−0.496582	−	0.369614i
$196$	−3.61961			−0.258544
$197$	−8.59458	−	14.8863i	−0.612339	−	1.06060i	−0.990845	−	0.135003i	$-0.956896\pi$
$197$	−8.59458	−	14.8863i	−0.612339	−	1.06060i	0.378507	−	0.925599i	$-0.376438\pi$
$198$	0.0590186	+	0.102223i	0.00419427	+	0.00726469i
$199$	3.93525	−	6.81605i	0.278962	−	0.483177i	−0.692165	−	0.721739i	$-0.743343\pi$
$199$	3.93525	−	6.81605i	0.278962	−	0.483177i	0.971127	+	0.238563i	$0.0766762\pi$
$200$	0.351998			0.0248900
$201$	−2.85016	+	4.93662i	−0.201035	+	0.348203i
$202$	−0.758262	+	1.31335i	−0.0533511	+	0.0924069i
$203$	−16.1136			−1.13096
$204$	4.55262	−	7.88538i	0.318748	−	0.552087i
$205$	6.49096	+	11.2427i	0.453348	+	0.785223i
$206$	0.959313	+	1.66158i	0.0668385	+	0.115768i
$207$	1.75350			0.121877
$208$	11.3280	+	8.43163i	0.785457	+	0.584628i
$209$	−4.85223			−0.335636
$210$	0.420289	+	0.727962i	0.0290027	+	0.0502342i
$211$	−5.88058	−	10.1855i	−0.404836	−	0.701196i	0.589467	−	0.807793i	$-0.299338\pi$
$211$	−5.88058	−	10.1855i	−0.404836	−	0.701196i	−0.994302	+	0.106597i	$0.966005\pi$
$212$	4.38031	−	7.58693i	0.300841	−	0.521072i
$213$	−14.9505			−1.02439
$214$	−0.0500905	+	0.0867593i	−0.00342412	+	0.00593074i
$215$	−8.40922	+	14.5652i	−0.573504	+	0.993338i
$216$	0.470505			0.0320138
$217$	−2.85122	+	4.93845i	−0.193553	+	0.335244i
$218$	0.796208	+	1.37907i	0.0539260	+	0.0934026i
$219$	−5.27497	−	9.13652i	−0.356450	−	0.617389i
$220$	4.76165			0.321030
$221$	1.91734	−	16.4183i	0.128975	−	1.10441i
$222$	0.444698			0.0298462
$223$	12.6415	+	21.8957i	0.846536	+	1.46624i	0.884281	+	0.466956i	$0.154649\pi$
$223$	12.6415	+	21.8957i	0.846536	+	1.46624i	−0.0377447	+	0.999287i	$0.512017\pi$
$224$	−2.08411	−	3.60978i	−0.139250	−	0.241189i
$225$	−0.374064	+	0.647898i	−0.0249376	+	0.0431932i
$226$	−1.01889			−0.0677757
$227$	−5.87302	+	10.1724i	−0.389806	+	0.675163i	−0.992423	−	0.122867i	$-0.960791\pi$
$227$	−5.87302	+	10.1724i	−0.389806	+	0.675163i	0.602617	+	0.798030i	$0.294125\pi$
$228$	−4.81843	+	8.34577i	−0.319108	+	0.552712i
$229$	9.52159			0.629205			0.314602	−	0.949224i	$-0.398129\pi$
$229$	9.52159			0.629205			0.314602	+	0.949224i	$0.398129\pi$
$230$	−0.248118	+	0.429753i	−0.0163604	+	0.0283371i
$231$	1.48513	+	2.57233i	0.0977147	+	0.169247i
$232$	−1.27624	−	2.21051i	−0.0837891	−	0.145127i
$233$	3.30327			0.216404			0.108202	−	0.994129i	$-0.465491\pi$
$233$	3.30327			0.216404			0.108202	+	0.994129i	$0.465491\pi$
$234$	0.390766	−	0.168607i	0.0255452	−	0.0110222i
$235$	−29.5802			−1.92960
$236$	2.75001	+	4.76315i	0.179010	+	0.310055i
$237$	−1.27917	−	2.21559i	−0.0830911	−	0.143918i
$238$	−0.803680	+	1.39201i	−0.0520948	+	0.0902309i
$239$	−9.99602			−0.646589			−0.323294	−	0.946298i	$-0.604790\pi$
$239$	−9.99602			−0.646589			−0.323294	+	0.946298i	$0.604790\pi$
$240$	4.69507	−	8.13210i	0.303066	−	0.524925i
$241$	−0.632408	+	1.09536i	−0.0407370	+	0.0705586i	−0.885675	−	0.464306i	$-0.846304\pi$
$241$	−0.632408	+	1.09536i	−0.0407370	+	0.0705586i	0.844938	+	0.534864i	$0.179637\pi$
$242$	−0.118037			−0.00758772
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	5.40287	+	9.35805i	0.345883	+	0.599088i
$245$	2.18475	+	3.78409i	0.139578	+	0.241757i
$246$	−0.639139			−0.0407500
$247$	−2.02929	+	17.3769i	−0.129121	+	1.10566i
$248$	−0.903292			−0.0573591
$249$	4.70584	+	8.15075i	0.298220	+	0.516533i
$250$	0.601634	+	1.04206i	0.0380507	+	0.0659057i
$251$	6.23642	−	10.8018i	0.393639	−	0.681803i	−0.599287	−	0.800534i	$-0.704549\pi$
$251$	6.23642	−	10.8018i	0.393639	−	0.681803i	0.992926	+	0.118731i	$0.0378826\pi$
$252$	5.89916			0.371612
$253$	−0.876751	+	1.51858i	−0.0551209	+	0.0954721i
$254$	−1.00358	+	1.73825i	−0.0629703	+	0.109068i
$255$	−10.9916			−0.688321
$256$	−7.44849	+	12.9012i	−0.465531	+	0.806323i
$257$	−1.71111	−	2.96374i	−0.106736	−	0.184873i	0.807710	−	0.589580i	$-0.200707\pi$
$257$	−1.71111	−	2.96374i	−0.106736	−	0.184873i	−0.914446	+	0.404707i	$0.867373\pi$
$258$	−0.414011	−	0.717088i	−0.0257752	−	0.0446439i
$259$	11.1903			0.695331
$260$	1.99140	−	17.0525i	0.123502	−	1.05755i
$261$	5.42498			0.335798
$262$	−0.852329	−	1.47628i	−0.0526571	−	0.0912048i
$263$	10.1034	+	17.4997i	0.623004	+	1.07907i	0.988923	+	0.148428i	$0.0474213\pi$
$263$	10.1034	+	17.4997i	0.623004	+	1.07907i	−0.365919	+	0.930647i	$0.619245\pi$
$264$	−0.235252	+	0.407469i	−0.0144788	+	0.0250780i
$265$	−10.5756			−0.649653
$266$	0.850603	−	1.47329i	0.0521538	−	0.0903330i
$267$	−0.0144232	+	0.0249817i	−0.000882686	+	0.00152886i
$268$	−11.3212			−0.691554
$269$	12.3599	−	21.4080i	0.753598	−	1.30527i	−0.192470	−	0.981303i	$-0.561650\pi$
$269$	12.3599	−	21.4080i	0.753598	−	1.30527i	0.946068	−	0.323968i	$-0.105017\pi$
$270$	−0.141499	−	0.245083i	−0.00861134	−	0.0149153i
$271$	4.05382	+	7.02142i	0.246252	+	0.426521i	0.962483	−	0.271343i	$-0.0874676\pi$
$271$	4.05382	+	7.02142i	0.246252	+	0.426521i	−0.716231	+	0.697863i	$0.754134\pi$
$272$	17.9559			1.08874
$273$	9.83317	−	4.24279i	0.595131	−	0.256786i
$274$	1.66514			0.100595
$275$	−0.374064	−	0.647898i	−0.0225569	−	0.0390697i
$276$	1.74129	+	3.01600i	0.104813	+	0.181542i
$277$	−12.8819	+	22.3122i	−0.774001	+	1.34061i	0.161354	+	0.986897i	$0.448414\pi$
$277$	−12.8819	+	22.3122i	−0.774001	+	1.34061i	−0.935354	+	0.353712i	$0.884919\pi$
$278$	−0.575004			−0.0344864
$279$	0.959919	−	1.66263i	0.0574688	−	0.0995389i
$280$	−1.67530	+	2.90171i	−0.100118	+	0.173410i
$281$	−8.10067			−0.483245			−0.241623	−	0.970370i	$-0.577680\pi$
$281$	−8.10067			−0.483245			−0.241623	+	0.970370i	$0.577680\pi$
$282$	0.728161	−	1.26121i	0.0433614	−	0.0751041i
$283$	8.40583	+	14.5593i	0.499675	+	0.865462i	1.00000		0.000375400i	$-0.000119494\pi$
$283$	8.40583	+	14.5593i	0.499675	+	0.865462i	−0.500325	+	0.865838i	$0.666786\pi$
$284$	−14.8464	−	25.7147i	−0.880972	−	1.52589i
$285$	11.6334			0.689100
$286$	−0.0493653	+	0.422717i	−0.00291903	+	0.0249958i
$287$	−16.0832			−0.949360
$288$	0.701657	+	1.21531i	0.0413455	+	0.0716125i
$289$	−2.00911	−	3.47988i	−0.118183	−	0.204699i
$290$	−0.767627	+	1.32957i	−0.0450766	+	0.0780750i
$291$	−11.0811			−0.649588
$292$	10.4765	−	18.1457i	0.613088	−	1.06190i
$293$	8.10679	−	14.0414i	0.473604	−	0.820306i	−0.525940	−	0.850522i	$-0.676286\pi$
$293$	8.10679	−	14.0414i	0.473604	−	0.820306i	0.999543	+	0.0302161i	$0.00961954\pi$
$294$	−0.215123			−0.0125462
$295$	3.31973	−	5.74995i	0.193282	−	0.334775i
$296$	0.886298	+	1.53511i	0.0515150	+	0.0892266i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	1.03746			0.0600983
$299$	5.07168	+	3.77493i	0.293303	+	0.218310i
$300$	−1.48583			−0.0857846
$301$	−10.4181	−	18.0447i	−0.600489	−	1.04008i
$302$	−1.26596	−	2.19271i	−0.0728480	−	0.126176i
$303$	6.42392	−	11.1266i	0.369045	−	0.639204i
$304$	−19.0042			−1.08997
$305$	6.52220	−	11.2968i	0.373460	−	0.646852i
$306$	0.270575	−	0.468649i	0.0154677	−	0.0267909i
$307$	−3.19713			−0.182470			−0.0912349	−	0.995829i	$-0.529081\pi$
$307$	−3.19713			−0.182470			−0.0912349	+	0.995829i	$0.529081\pi$
$308$	−2.94958	+	5.10882i	−0.168068	+	0.291102i
$309$	−8.12721	−	14.0767i	−0.462341	−	0.800797i
$310$	0.271655	+	0.470519i	0.0154289	+	0.0267237i
$311$	−19.9402			−1.13071			−0.565353	−	0.824849i	$-0.691260\pi$
$311$	−19.9402			−1.13071			−0.565353	+	0.824849i	$0.691260\pi$
$312$	1.36085	+	1.01290i	0.0770428	+	0.0573441i
$313$	−21.3968			−1.20942			−0.604709	−	0.796447i	$-0.706711\pi$
$313$	−21.3968			−1.20942			−0.604709	+	0.796447i	$0.706711\pi$
$314$	−1.31817	−	2.28314i	−0.0743889	−	0.128845i
$315$	−3.56065	−	6.16722i	−0.200620	−	0.347484i
$316$	2.54052	−	4.40031i	0.142915	−	0.247537i
$317$	−13.6654			−0.767526			−0.383763	−	0.923432i	$-0.625372\pi$
$317$	−13.6654			−0.767526			−0.383763	+	0.923432i	$0.625372\pi$
$318$	0.260334	−	0.450911i	0.0145988	−	0.0252859i
$319$	−2.71249	+	4.69817i	−0.151870	+	0.263047i
$320$	18.3831			1.02765
$321$	0.424362	−	0.735016i	0.0236856	−	0.0410246i
$322$	−0.307391	−	0.532417i	−0.0171302	−	0.0296704i
$323$	11.1227	+	19.2651i	0.618883	+	1.07194i
$324$	−1.98607			−0.110337
$325$	−2.47670	+	1.06864i	−0.137383	+	0.0592775i
$326$	2.21633			0.122751
$327$	−6.74540	−	11.6834i	−0.373021	−	0.646092i
$328$	−1.27382	−	2.20633i	−0.0703352	−	0.121824i
$329$	18.3233	−	31.7369i	1.01020	−	1.74971i
$330$	0.282997			0.0155785
$331$	−4.78157	+	8.28192i	−0.262819	+	0.455216i	−0.966990	−	0.254815i	$-0.917986\pi$
$331$	−4.78157	+	8.28192i	−0.262819	+	0.455216i	0.704171	+	0.710030i	$0.251319\pi$
$332$	−9.34611	+	16.1879i	−0.512935	+	0.888429i
$333$	−3.76743			−0.206454
$334$	−0.139000	+	0.240754i	−0.00760572	+	0.0131735i
$335$	6.83333	+	11.8357i	0.373345	+	0.646652i
$336$	5.81668	+	10.0748i	0.317326	+	0.549624i
$337$	30.5568			1.66453			0.832266	−	0.554376i	$-0.187043\pi$
$337$	30.5568			1.66453			0.832266	+	0.554376i	$0.187043\pi$
$338$	1.49319	+	0.353575i	0.0812190	+	0.0192319i
$339$	8.63196			0.468823
$340$	−10.9150	−	18.9054i	−0.591951	−	1.02529i
$341$	0.959919	+	1.66263i	0.0519825	+	0.0900364i
$342$	−0.286372	+	0.496011i	−0.0154852	+	0.0268212i
$343$	15.3786			0.830364
$344$	1.65027	−	2.85836i	0.0889768	−	0.154112i
$345$	2.10203	−	3.64083i	0.113170	−	0.196016i
$346$	0.173299			0.00931660
$347$	−3.80540	+	6.59115i	−0.204285	+	0.353831i	−0.949905	−	0.312540i	$-0.898820\pi$
$347$	−3.80540	+	6.59115i	−0.204285	+	0.353831i	0.745620	+	0.666371i	$0.232153\pi$
$348$	5.38718	+	9.33088i	0.288783	+	0.500187i
$349$	7.24205	+	12.5436i	0.387658	+	0.671444i	0.992134	−	0.125180i	$-0.0399508\pi$
$349$	7.24205	+	12.5436i	0.387658	+	0.671444i	−0.604476	+	0.796623i	$0.706617\pi$
$350$	0.262296			0.0140203
$351$	−3.31053	+	1.42842i	−0.176703	+	0.0762434i
$352$	−1.40331			−0.0747969
$353$	13.3236	+	23.0772i	0.709144	+	1.22827i	0.965175	+	0.261605i	$0.0842518\pi$
$353$	13.3236	+	23.0772i	0.709144	+	1.22827i	−0.256031	+	0.966669i	$0.582415\pi$
$354$	0.163440	+	0.283087i	0.00868675	+	0.0150459i
$355$	−17.9222	+	31.0421i	−0.951209	+	1.64754i
$356$	−0.0572909			−0.00303641
$357$	6.80869	−	11.7930i	0.360354	−	0.624152i
$358$	0.508279	−	0.880365i	0.0268634	−	0.0465287i
$359$	−26.4230			−1.39455			−0.697277	−	0.716802i	$-0.745605\pi$
$359$	−26.4230			−1.39455			−0.697277	+	0.716802i	$0.745605\pi$
$360$	0.564023	−	0.976917i	0.0297266	−	0.0514880i
$361$	−2.27208	−	3.93536i	−0.119583	−	0.207124i
$362$	−0.994381	−	1.72232i	−0.0522635	−	0.0905231i
$363$	1.00000			0.0524864
$364$	17.0622	+	12.6997i	0.894303	+	0.665643i
$365$	−25.2938			−1.32394
$366$	0.321107	+	0.556174i	0.0167845	+	0.0290717i
$367$	9.39339	+	16.2698i	0.490331	+	0.849278i	0.999938	−	0.0111290i	$-0.00354254\pi$
$367$	9.39339	+	16.2698i	0.490331	+	0.849278i	−0.509607	+	0.860407i	$0.670209\pi$
$368$	−3.43388	+	5.94766i	−0.179003	+	0.310043i
$369$	5.41472			0.281879
$370$	0.533087	−	0.923334i	0.0277139	−	0.0480018i
$371$	6.55100	−	11.3467i	0.340111	−	0.589089i
$372$	3.81293			0.197691
$373$	−11.3194	+	19.6059i	−0.586099	+	1.01515i	0.408639	+	0.912696i	$0.366004\pi$
$373$	−11.3194	+	19.6059i	−0.586099	+	1.01515i	−0.994737	+	0.102456i	$0.967330\pi$
$374$	0.270575	+	0.468649i	0.0139911	+	0.0242333i
$375$	−5.09699	−	8.82824i	−0.263207	−	0.455888i
$376$	5.80500			0.299370
$377$	15.6907	+	11.6789i	0.808114	+	0.601492i
$378$	0.350603			0.0180331
$379$	0.612870	+	1.06152i	0.0314810	+	0.0545268i	0.881337	−	0.472489i	$-0.156644\pi$
$379$	0.612870	+	1.06152i	0.0314810	+	0.0545268i	−0.849856	+	0.527016i	$0.823311\pi$
$380$	11.5523	+	20.0092i	0.592621	+	1.02645i
$381$	8.50225	−	14.7263i	0.435583	−	0.754452i
$382$	0.432380			0.0221225
$383$	−16.0998	+	27.8858i	−0.822664	+	1.42490i	0.0810281	+	0.996712i	$0.474180\pi$
$383$	−16.0998	+	27.8858i	−0.822664	+	1.42490i	−0.903692	+	0.428183i	$0.859154\pi$
$384$	−1.85584	+	3.21441i	−0.0947055	+	0.164035i
$385$	7.12130			0.362935
$386$	−0.232185	+	0.402156i	−0.0118179	+	0.0204692i
$387$	3.50746	+	6.07509i	0.178294	+	0.308814i
$388$	−11.0039	−	19.0594i	−0.558641	−	0.967594i
$389$	37.4190			1.89722			0.948609	−	0.316451i	$-0.102491\pi$
$389$	37.4190			1.89722			0.948609	+	0.316451i	$0.102491\pi$
$390$	0.118354	−	1.01347i	0.00599311	−	0.0513193i
$391$	8.03904			0.406552
$392$	−0.428748	−	0.742613i	−0.0216550	−	0.0375076i
$393$	7.22085	+	12.5069i	0.364244	+	0.630889i
$394$	1.01448	−	1.75713i	0.0511088	−	0.0885231i
$395$	−6.13369			−0.308619
$396$	0.993034	−	1.71998i	0.0499018	−	0.0864325i
$397$	5.57942	−	9.66384i	0.280023	−	0.485014i	−0.691367	−	0.722504i	$-0.742991\pi$
$397$	5.57942	−	9.66384i	0.280023	−	0.485014i	0.971390	+	0.237489i	$0.0763245\pi$
$398$	0.929012			0.0465672
$399$	−7.20622	+	12.4815i	−0.360762	+	0.624858i
$400$	−1.46506	−	2.53755i	−0.0732529	−	0.126878i
$401$	−4.96185	−	8.59417i	−0.247783	−	0.429172i	0.715128	−	0.698994i	$-0.246369\pi$
$401$	−4.96185	−	8.59417i	−0.247783	−	0.429172i	−0.962910	+	0.269822i	$0.913035\pi$
$402$	−0.672850			−0.0335587
$403$	6.35568	−	2.74233i	0.316599	−	0.136605i
$404$	25.5167			1.26950
$405$	1.19876	+	2.07632i	0.0595670	+	0.103173i
$406$	−0.951005	−	1.64719i	−0.0471976	−	0.0817486i
$407$	1.88372	−	3.26269i	0.0933724	−	0.161726i
$408$	2.15706			0.106790
$409$	−15.4465	+	26.7542i	−0.763782	+	1.32291i	0.177107	+	0.984192i	$0.443326\pi$
$409$	−15.4465	+	26.7542i	−0.763782	+	1.32291i	−0.940888	+	0.338717i	$0.890007\pi$
$410$	−0.766175	+	1.32705i	−0.0378387	+	0.0655386i
$411$	−14.1069			−0.695842
$412$	16.1412	−	27.9573i	0.795219	−	1.37736i
$413$	4.11278	+	7.12355i	0.202377	+	0.350527i
$414$	0.103489	+	0.179249i	0.00508622	+	0.00880959i
$415$	22.5647			1.10766
$416$	−0.586890	+	5.02557i	−0.0287747	+	0.246399i
$417$	4.87137			0.238552
$418$	−0.286372	−	0.496011i	−0.0140069	−	0.0242607i
$419$	−12.1305	−	21.0107i	−0.592616	−	1.02644i	−0.993879	−	0.110477i	$-0.964762\pi$
$419$	−12.1305	−	21.0107i	−0.592616	−	1.02644i	0.401263	−	0.915963i	$-0.368571\pi$
$420$	7.07169	−	12.2485i	0.345063	−	0.597667i
$421$	1.39751			0.0681103			0.0340551	−	0.999420i	$-0.489158\pi$
$421$	1.39751			0.0681103			0.0340551	+	0.999420i	$0.489158\pi$
$422$	0.694127	−	1.20226i	0.0337896	−	0.0585253i
$423$	−6.16891	+	10.6849i	−0.299943	+	0.519516i
$424$	2.07542			0.100791
$425$	−1.71492	+	2.97033i	−0.0831858	+	0.144082i
$426$	−0.882361	−	1.52829i	−0.0427505	−	0.0740461i
$427$	8.08028	+	13.9955i	0.391032	+	0.677288i
$428$	1.68562			0.0814776
$429$	0.418217	−	3.58121i	0.0201917	−	0.172903i
$430$	−1.98520			−0.0957349
$431$	12.6498	+	21.9101i	0.609320	+	1.05537i	0.991353	+	0.131224i	$0.0418907\pi$
$431$	12.6498	+	21.9101i	0.609320	+	1.05537i	−0.382033	+	0.924149i	$0.624776\pi$
$432$	−1.95830	−	3.39187i	−0.0942187	−	0.163192i
$433$	−16.9815	+	29.4129i	−0.816081	+	1.41349i	0.0924687	+	0.995716i	$0.470524\pi$
$433$	−16.9815	+	29.4129i	−0.816081	+	1.41349i	−0.908549	+	0.417778i	$0.862809\pi$
$434$	−0.673100			−0.0323098
$435$	6.50326	−	11.2640i	0.311807	−	0.540066i
$436$	13.3968	−	23.2040i	0.641591	−	1.11127i
$437$	−8.50840			−0.407012
$438$	0.622644	−	1.07845i	0.0297511	−	0.0515303i
$439$	5.77069	+	9.99514i	0.275420	+	0.477042i	0.970241	−	0.242141i	$-0.0778497\pi$
$439$	5.77069	+	9.99514i	0.275420	+	0.477042i	−0.694821	+	0.719183i	$0.744516\pi$
$440$	0.564023	+	0.976917i	0.0268888	+	0.0465727i
$441$	1.82250			0.0867858
$442$	1.79149	−	0.772989i	0.0852126	−	0.0367673i
$443$	41.2202			1.95843			0.979216	−	0.202823i	$-0.0650115\pi$
$443$	41.2202			1.95843			0.979216	+	0.202823i	$0.0650115\pi$
$444$	−3.74119	−	6.47993i	−0.177549	−	0.307524i
$445$	0.0345800	+	0.0598943i	0.00163925	+	0.00283926i
$446$	−1.49217	+	2.58451i	−0.0706561	+	0.122380i
$447$	−8.78924			−0.415717
$448$	−11.3873	+	19.7235i	−0.538002	+	0.931846i
$449$	−5.69652	+	9.86667i	−0.268836	+	0.465637i	−0.968561	−	0.248775i	$-0.919972\pi$
$449$	−5.69652	+	9.86667i	−0.268836	+	0.465637i	0.699726	+	0.714411i	$0.253305\pi$
$450$	−0.0883070			−0.00416283
$451$	−2.70736	+	4.68928i	−0.127485	+	0.220810i
$452$	8.57182	+	14.8468i	0.403185	+	0.698336i
$453$	10.7251	+	18.5764i	0.503910	+	0.872797i
$454$	−1.38647			−0.0650703
$455$	2.97825	−	25.5029i	0.139623	−	1.19559i
$456$	−2.28300			−0.106911
$457$	−4.84664	−	8.39463i	−0.226716	−	0.392684i	0.730117	−	0.683322i	$-0.239466\pi$
$457$	−4.84664	−	8.39463i	−0.226716	−	0.392684i	−0.956833	+	0.290638i	$0.906132\pi$
$458$	0.561951	+	0.973329i	0.0262583	+	0.0454807i
$459$	−2.29228	+	3.97035i	−0.106995	+	0.185320i
$460$	8.34956			0.389300
$461$	5.79030	−	10.0291i	0.269681	−	0.467102i	−0.699098	−	0.715026i	$-0.746415\pi$
$461$	5.79030	−	10.0291i	0.269681	−	0.467102i	0.968779	+	0.247924i	$0.0797483\pi$
$462$	−0.175301	+	0.303631i	−0.00815575	+	0.0141262i
$463$	34.5395			1.60519			0.802593	−	0.596527i	$-0.203453\pi$
$463$	34.5395			1.60519			0.802593	+	0.596527i	$0.203453\pi$
$464$	−10.6237	+	18.4008i	−0.493194	+	0.854237i
$465$	−2.30143	−	3.98619i	−0.106726	−	0.184855i
$466$	0.194954	+	0.337671i	0.00903108	+	0.0156423i
$467$	3.73036			0.172621			0.0863103	−	0.996268i	$-0.472492\pi$
$467$	3.73036			0.172621			0.0863103	+	0.996268i	$0.472492\pi$
$468$	−5.74433	−	4.27559i	−0.265532	−	0.197639i
$469$	−16.9315			−0.781824
$470$	−1.74578	−	3.02379i	−0.0805270	−	0.139477i
$471$	11.1674	+	19.3426i	0.514568	+	0.891259i
$472$	−0.651484	+	1.12840i	−0.0299870	+	0.0519390i
$473$	−7.01491			−0.322546
$474$	0.150990	−	0.261522i	0.00693519	−	0.0120121i
$475$	1.81505	−	3.14375i	0.0832800	−	0.144245i
$476$	27.0450			1.23961
$477$	−2.20552	+	3.82008i	−0.100984	+	0.174909i
$478$	−0.589952	−	1.02183i	−0.0269838	−	0.0467372i
$479$	7.09217	+	12.2840i	0.324050	+	0.561270i	0.981320	−	0.192385i	$-0.0616222\pi$
$479$	7.09217	+	12.2840i	0.324050	+	0.561270i	−0.657270	+	0.753655i	$0.728289\pi$
$480$	3.36448			0.153567
$481$	−10.8966	−	8.11051i	−0.496842	−	0.369807i
$482$	−0.149296			−0.00680022
$483$	2.60419	+	4.51058i	0.118495	+	0.205239i
$484$	0.993034	+	1.71998i	0.0451379	+	0.0781811i
$485$	−13.2837	+	23.0080i	−0.603180	+	1.04474i
$486$	−0.118037			−0.00535428
$487$	13.4371	−	23.2737i	0.608892	−	1.05463i	−0.382531	−	0.923943i	$-0.624948\pi$
$487$	13.4371	−	23.2737i	0.608892	−	1.05463i	0.991423	−	0.130690i	$-0.0417191\pi$
$488$	−1.27995	+	2.21695i	−0.0579408	+	0.100356i
$489$	−18.7766			−0.849105
$490$	−0.257882	+	0.446664i	−0.0116499	+	0.0201782i
$491$	−17.0307	−	29.4981i	−0.768585	−	1.33123i	−0.938330	−	0.345741i	$-0.887628\pi$
$491$	−17.0307	−	29.4981i	−0.768585	−	1.33123i	0.169745	−	0.985488i	$-0.445706\pi$
$492$	5.37700	+	9.31323i	0.242414	+	0.419873i
$493$	24.8711			1.12014
$494$	−1.89609	+	0.818119i	−0.0853090	+	0.0368089i
$495$	−2.39753			−0.107761
$496$	3.75962	+	6.51184i	0.168812	+	0.292390i
$497$	−22.2036	−	38.4577i	−0.995967	−	1.72506i
$498$	−0.555464	+	0.962093i	−0.0248910	+	0.0431124i
$499$	−0.146884			−0.00657542			−0.00328771	−	0.999995i	$-0.501047\pi$
$499$	−0.146884			−0.00657542			−0.00328771	+	0.999995i	$0.501047\pi$
$500$	10.1230	−	17.5335i	0.452712	−	0.784121i
$501$	1.17759	−	2.03965i	0.0526109	−	0.0911247i
$502$	1.47226			0.0657102
$503$	−3.65379	+	6.32854i	−0.162914	+	0.282176i	−0.935913	−	0.352232i	$-0.885423\pi$
$503$	−3.65379	+	6.32854i	−0.162914	+	0.282176i	0.772998	+	0.634408i	$0.218756\pi$
$504$	0.698763	+	1.21029i	0.0311254	+	0.0539107i
$505$	−15.4015	−	26.6762i	−0.685358	−	1.18708i
$506$	−0.206979			−0.00920132
$507$	−12.6502	−	2.99545i	−0.561815	−	0.133033i
$508$	33.7721			1.49839
$509$	−11.0567	−	19.1508i	−0.490081	−	0.848846i	0.509854	−	0.860261i	$-0.329700\pi$
$509$	−11.0567	−	19.1508i	−0.490081	−	0.848846i	−0.999935	+	0.0114156i	$0.996366\pi$
$510$	−0.648710	−	1.12360i	−0.0287253	−	0.0497538i
$511$	15.6681	−	27.1379i	0.693116	−	1.20051i
$512$	−9.18177			−0.405781
$513$	2.42612	−	4.20216i	0.107116	−	0.185530i
$514$	0.201975	−	0.349831i	0.00890875	−	0.0154304i
$515$	−38.9704			−1.71724
$516$	−6.96604	+	12.0655i	−0.306663	+	0.531156i
$517$	−6.16891	−	10.6849i	−0.271308	−	0.469920i
$518$	0.660436	+	1.14391i	0.0290179	+	0.0502605i
$519$	−1.46817			−0.0644455
$520$	3.73443	−	1.61132i	0.163766	−	0.0706612i
$521$	−3.57882			−0.156791			−0.0783954	−	0.996922i	$-0.524980\pi$
$521$	−3.57882			−0.156791			−0.0783954	+	0.996922i	$0.524980\pi$
$522$	0.320175	+	0.554559i	0.0140137	+	0.0242724i
$523$	−9.61599	−	16.6554i	−0.420478	−	0.728289i	0.575508	−	0.817796i	$-0.304804\pi$
$523$	−9.61599	−	16.6554i	−0.420478	−	0.728289i	−0.995986	+	0.0895070i	$0.971471\pi$
$524$	−14.3411	+	24.8395i	−0.626494	+	1.08512i
$525$	−2.22214			−0.0969822
$526$	−1.19258	+	2.06561i	−0.0519990	+	0.0900649i
$527$	4.40081	−	7.62242i	0.191702	−	0.332038i
$528$	3.91660			0.170448
$529$	9.96262	−	17.2558i	0.433157	−	0.750250i
$530$	−0.624157	−	1.08107i	−0.0271116	−	0.0469587i
$531$	−1.38465	−	2.39828i	−0.0600887	−	0.104077i
$532$	−28.6241			−1.24101
$533$	15.6611	+	11.6568i	0.678356	+	0.504911i
$534$	−0.00340495			−0.000147347
$535$	−1.01742	−	1.76222i	−0.0439868	−	0.0761874i
$536$	−1.34101	−	2.32270i	−0.0579230	−	0.100326i
$537$	−4.30609	+	7.45837i	−0.185821	+	0.321852i
$538$	2.91787			0.125798
$539$	−0.911251	+	1.57833i	−0.0392504	+	0.0679836i
$540$	−2.38082	+	4.12371i	−0.102454	+	0.177456i
$541$	−13.5069			−0.580705			−0.290353	−	0.956920i	$-0.593773\pi$
$541$	−13.5069			−0.580705			−0.290353	+	0.956920i	$0.593773\pi$
$542$	−0.478501	+	0.828789i	−0.0205534	+	0.0355995i
$543$	8.42430	+	14.5913i	0.361521	+	0.626173i
$544$	3.21679	+	5.57164i	0.137919	+	0.238882i
$545$	−32.3445			−1.38549
$546$	1.01405	+	0.754775i	0.0433974	+	0.0323014i
$547$	−44.5839			−1.90627			−0.953134	−	0.302548i	$-0.902163\pi$
$547$	−44.5839			−1.90627			−0.953134	+	0.302548i	$0.902163\pi$
$548$	−14.0086	−	24.2636i	−0.598419	−	1.03649i
$549$	−2.72039	−	4.71185i	−0.116103	−	0.201097i
$550$	0.0441535	−	0.0764761i	0.00188271	−	0.00326095i
$551$	−26.3232			−1.12141
$552$	−0.412515	+	0.714497i	−0.0175578	+	0.0304110i
$553$	3.79948	−	6.58090i	0.161570	−	0.279848i
$554$	−3.04110			−0.129204
$555$	−4.51626	+	7.82239i	−0.191705	+	0.332042i
$556$	4.83744	+	8.37869i	0.205153	+	0.355336i
$557$	9.00831	+	15.6028i	0.381694	+	0.661114i	0.991305	−	0.131587i	$-0.0420074\pi$
$557$	9.00831	+	15.6028i	0.381694	+	0.661114i	−0.609610	+	0.792701i	$0.708674\pi$
$558$	0.226612			0.00959327
$559$	−2.93376	+	25.1219i	−0.124085	+	1.06254i
$560$	27.8913			1.17862
$561$	−2.29228	−	3.97035i	−0.0967802	−	0.167628i
$562$	−0.478091	−	0.828077i	−0.0201670	−	0.0349303i
$563$	11.6372	−	20.1563i	0.490450	−	0.849485i	−0.509489	−	0.860477i	$-0.670166\pi$
$563$	11.6372	−	20.1563i	0.490450	−	0.849485i	0.999940	+	0.0109921i	$0.00349898\pi$
$564$	−24.5037			−1.03179
$565$	10.3477	−	17.9227i	0.435330	−	0.754013i
$566$	−0.992202	+	1.71854i	−0.0417053	+	0.0722358i
$567$	−2.97027			−0.124740
$568$	3.51715	−	6.09188i	0.147576	−	0.255610i
$569$	16.4062	+	28.4164i	0.687785	+	1.19128i	0.972553	+	0.232682i	$0.0747502\pi$
$569$	16.4062	+	28.4164i	0.687785	+	1.19128i	−0.284768	+	0.958597i	$0.591917\pi$
$570$	0.686585	+	1.18920i	0.0287579	+	0.0498101i
$571$	−22.2440			−0.930883			−0.465441	−	0.885079i	$-0.654104\pi$
$571$	−22.2440			−0.930883			−0.465441	+	0.885079i	$0.654104\pi$
$572$	6.57494	−	2.83694i	0.274912	−	0.118618i
$573$	−3.66308			−0.153027
$574$	−0.949207	−	1.64407i	−0.0396191	−	0.0686224i
$575$	−0.655922	−	1.13609i	−0.0273538	−	0.0473782i
$576$	3.83378	−	6.64029i	0.159741	−	0.276679i
$577$	15.5700			0.648188			0.324094	−	0.946025i	$-0.394941\pi$
$577$	15.5700			0.648188			0.324094	+	0.946025i	$0.394941\pi$
$578$	0.237150	−	0.410755i	0.00986413	−	0.0170852i
$579$	1.96705	−	3.40703i	0.0817477	−	0.141591i
$580$	25.8318			1.07261
$581$	−13.9776	+	24.2099i	−0.579889	+	1.00440i
$582$	−0.653994	−	1.13275i	−0.0271089	−	0.0469540i
$583$	−2.20552	−	3.82008i	−0.0913434	−	0.158211i
$584$	4.96380			0.205403
$585$	−1.00269	+	8.58605i	−0.0414560	+	0.354990i
$586$	1.91381			0.0790586
$587$	−4.08175	−	7.06980i	−0.168472	−	0.291802i	0.769411	−	0.638754i	$-0.220550\pi$
$587$	−4.08175	−	7.06980i	−0.168472	−	0.291802i	−0.937883	+	0.346952i	$0.887217\pi$
$588$	1.80981	+	3.13468i	0.0746351	+	0.129272i
$589$	−4.65775	+	8.06746i	−0.191919	+	0.332414i
$590$	0.783704			0.0322646
$591$	−8.59458	+	14.8863i	−0.353534	+	0.612339i
$592$	7.37776	−	12.7787i	0.303224	−	0.525200i
$593$	19.9116			0.817673			0.408837	−	0.912608i	$-0.365935\pi$
$593$	19.9116			0.817673			0.408837	+	0.912608i	$0.365935\pi$
$594$	0.0590186	−	0.102223i	0.00242156	−	0.00419427i
$595$	−16.3240	−	28.2740i	−0.669219	−	1.15912i
$596$	−8.72801	−	15.1174i	−0.357513	−	0.619231i
$597$	−7.87050			−0.322118
$598$	−0.0865621	+	0.741235i	−0.00353979	+	0.0303113i
$599$	29.4044			1.20143			0.600716	−	0.799463i	$-0.294882\pi$
$599$	29.4044			1.20143			0.600716	+	0.799463i	$0.294882\pi$
$600$	−0.175999	−	0.304839i	−0.00718512	−	0.0124450i
$601$	−9.45805	−	16.3818i	−0.385802	−	0.668228i	0.606078	−	0.795405i	$-0.292742\pi$
$601$	−9.45805	−	16.3818i	−0.385802	−	0.668228i	−0.991880	+	0.127177i	$0.959409\pi$
$602$	1.22972	−	2.12994i	0.0501198	−	0.0868100i
$603$	5.70032			0.232135
$604$	−21.3008	+	36.8941i	−0.866717	+	1.50120i
$605$	1.19876	−	2.07632i	0.0487366	−	0.0844143i
$606$	1.51652			0.0616046
$607$	23.4726	−	40.6557i	0.952722	−	1.65016i	0.213223	−	0.977003i	$-0.431604\pi$
$607$	23.4726	−	40.6557i	0.952722	−	1.65016i	0.739498	−	0.673159i	$-0.235063\pi$
$608$	−3.40460	−	5.89694i	−0.138075	−	0.239153i
$609$	8.05682	+	13.9548i	0.326479	+	0.565478i
$610$	1.53972			0.0623416
$611$	−40.8447	+	17.6236i	−1.65240	+	0.712974i
$612$	−9.10525			−0.368058
$613$	−18.2431	−	31.5979i	−0.736830	−	1.27623i	−0.953916	−	0.300075i	$-0.902988\pi$
$613$	−18.2431	−	31.5979i	−0.736830	−	1.27623i	0.217085	−	0.976153i	$-0.430345\pi$
$614$	−0.188690	−	0.326821i	−0.00761492	−	0.0131894i
$615$	6.49096	−	11.2427i	0.261741	−	0.453348i
$616$	−1.39753			−0.0563079
$617$	1.71798	−	2.97562i	0.0691632	−	0.119794i	−0.829370	−	0.558700i	$-0.811300\pi$
$617$	1.71798	−	2.97562i	0.0691632	−	0.119794i	0.898533	+	0.438906i	$0.144634\pi$
$618$	0.959313	−	1.66158i	0.0385892	−	0.0668385i
$619$	39.5437			1.58939			0.794697	−	0.607006i	$-0.207630\pi$
$619$	39.5437			1.58939			0.794697	+	0.607006i	$0.207630\pi$
$620$	4.57079	−	7.91685i	0.183568	−	0.317948i
$621$	−0.876751	−	1.51858i	−0.0351828	−	0.0609384i
$622$	−1.17684	−	2.03835i	−0.0471871	−	0.0817305i
$623$	−0.0856816			−0.00343276
$624$	1.63799	−	14.0262i	0.0655721	−	0.561496i
$625$	−28.1809			−1.12724
$626$	−1.26281	−	2.18725i	−0.0504720	−	0.0874201i
$627$	2.42612	+	4.20216i	0.0968897	+	0.167818i
$628$	−22.1793	+	38.4157i	−0.885050	+	1.53295i
$629$	−17.2720			−0.688681
$630$	0.420289	−	0.727962i	0.0167447	−	0.0290027i
$631$	−5.20714	+	9.01903i	−0.207293	+	0.359042i	−0.950861	−	0.309618i	$-0.899799\pi$
$631$	−5.20714	+	9.01903i	−0.207293	+	0.359042i	0.743568	+	0.668660i	$0.233132\pi$
$632$	1.20371			0.0478811
$633$	−5.88058	+	10.1855i	−0.233732	+	0.404836i
$634$	−0.806514	−	1.39692i	−0.0320308	−	0.0554789i
$635$	−20.3843	−	35.3067i	−0.808928	−	1.40110i
$636$	−8.76063			−0.347382
$637$	5.27125	+	3.92347i	0.208854	+	0.155454i
$638$	−0.640350			−0.0253517
$639$	7.47527	+	12.9476i	0.295717	+	0.512197i
$640$	4.44943	+	7.70664i	0.175879	+	0.304632i
$641$	24.5850	−	42.5824i	0.971049	−	1.68191i	0.278646	−	0.960394i	$-0.410114\pi$
$641$	24.5850	−	42.5824i	0.971049	−	1.68191i	0.692402	−	0.721512i	$-0.256552\pi$
$642$	0.100181			0.00395383
$643$	1.50115	−	2.60007i	0.0591995	−	0.102537i	−0.834907	−	0.550391i	$-0.814479\pi$
$643$	1.50115	−	2.60007i	0.0591995	−	0.102537i	0.894106	+	0.447855i	$0.147812\pi$
$644$	−5.17209	+	8.95832i	−0.203809	+	0.353007i
$645$	16.8184			0.662225
$646$	−1.31289	+	2.27399i	−0.0516550	+	0.0894691i
$647$	−0.153491	−	0.265855i	−0.00603437	−	0.0104518i	0.862992	−	0.505217i	$-0.168587\pi$
$647$	−0.153491	−	0.265855i	−0.00603437	−	0.0104518i	−0.869027	+	0.494765i	$0.835254\pi$
$648$	−0.235252	−	0.407469i	−0.00924158	−	0.0160069i
$649$	2.76930			0.108705
$650$	−0.255412	−	0.190107i	−0.0100181	−	0.00745660i
$651$	5.70244			0.223496
$652$	−18.6458	−	32.2954i	−0.730224	−	1.26479i
$653$	25.2279	+	43.6959i	0.987243	+	1.70995i	0.631513	+	0.775365i	$0.282434\pi$
$653$	25.2279	+	43.6959i	0.987243	+	1.70995i	0.355730	+	0.934589i	$0.384232\pi$
$654$	0.796208	−	1.37907i	0.0311342	−	0.0539260i
$655$	34.6243			1.35288
$656$	−10.6036	+	18.3660i	−0.414002	+	0.717073i
$657$	−5.27497	+	9.13652i	−0.205796	+	0.356450i
$658$	4.32567			0.168632
$659$	−18.8802	+	32.7014i	−0.735468	+	1.27387i	0.219050	+	0.975714i	$0.429704\pi$
$659$	−18.8802	+	32.7014i	−0.735468	+	1.27387i	−0.954518	+	0.298154i	$0.903629\pi$
$660$	−2.38082	−	4.12371i	−0.0926734	−	0.160515i
$661$	1.69990	+	2.94432i	0.0661186	+	0.114521i	0.897190	−	0.441646i	$-0.145605\pi$
$661$	1.69990	+	2.94432i	0.0661186	+	0.114521i	−0.831071	+	0.556166i	$0.812272\pi$
$662$	−1.12881			−0.0438723
$663$	−15.1773	+	6.54868i	−0.589439	+	0.254330i
$664$	−4.42824			−0.171849
$665$	17.2771	+	29.9248i	0.669977	+	1.16043i
$666$	−0.222349	−	0.385120i	−0.00861584	−	0.0149231i
$667$	−4.75635	+	8.23825i	−0.184167	+	0.318986i
$668$	4.67755			0.180980
$669$	12.6415	−	21.8957i	0.488748	−	0.846536i
$670$	−0.806588	+	1.39705i	−0.0311612	+	0.0539728i
$671$	5.44077			0.210039
$672$	−2.08411	+	3.60978i	−0.0803963	+	0.139250i
$673$	−11.8925	−	20.5985i	−0.458423	−	0.794012i	0.540455	−	0.841373i	$-0.318252\pi$
$673$	−11.8925	−	20.5985i	−0.458423	−	0.794012i	−0.998878	+	0.0473609i	$0.984919\pi$
$674$	1.80342	+	3.12361i	0.0694651	+	0.120317i
$675$	0.748128			0.0287955
$676$	−7.40993	−	24.7327i	−0.284997	−	0.951258i
$677$	−50.2857			−1.93264			−0.966319	−	0.257349i	$-0.917151\pi$
$677$	−50.2857			−1.93264			−0.966319	+	0.257349i	$0.917151\pi$
$678$	0.509446	+	0.882387i	0.0195652	+	0.0338879i
$679$	−16.4570	−	28.5043i	−0.631561	−	1.09390i
$680$	2.58580	−	4.47874i	0.0991609	−	0.171752i
$681$	11.7460			0.450109
$682$	−0.113306	+	0.196252i	−0.00433872	+	0.00751488i
$683$	4.84133	−	8.38543i	0.185248	−	0.320859i	−0.758412	−	0.651776i	$-0.774024\pi$
$683$	4.84133	−	8.38543i	0.185248	−	0.320859i	0.943660	+	0.330916i	$0.107358\pi$
$684$	9.63686			0.368475
$685$	−16.9108	+	29.2904i	−0.646129	+	1.11913i
$686$	0.907622	+	1.57205i	0.0346532	+	0.0600211i
$687$	−4.76080	−	8.24594i	−0.181636	−	0.314602i
$688$	−27.4746			−1.04746
$689$	−14.6029	+	6.30082i	−0.556326	+	0.240042i
$690$	0.496236			0.0188914
$691$	−3.72449	−	6.45101i	−0.141686	−	0.245408i	0.786445	−	0.617660i	$-0.211919\pi$
$691$	−3.72449	−	6.45101i	−0.141686	−	0.245408i	−0.928132	+	0.372252i	$0.878586\pi$
$692$	−1.45794	−	2.52523i	−0.0554227	−	0.0959948i
$693$	1.48513	−	2.57233i	0.0564156	−	0.0977147i
$694$	−0.898359			−0.0341012
$695$	5.83962	−	10.1145i	0.221509	−	0.383666i
$696$	−1.27624	+	2.21051i	−0.0483757	+	0.0837891i
$697$	24.8241			0.940280
$698$	−0.854832	+	1.48061i	−0.0323559	+	0.0560420i
$699$	−1.65163	−	2.86071i	−0.0624705	−	0.108202i
$700$	−2.20666	−	3.82205i	−0.0834040	−	0.144460i
$701$	33.0152			1.24697			0.623483	−	0.781837i	$-0.285717\pi$
$701$	33.0152			1.24697			0.623483	+	0.781837i	$0.285717\pi$
$702$	−0.341401	−	0.254110i	−0.0128853	−	0.00959076i
$703$	18.2805			0.689461
$704$	3.83378	+	6.64029i	0.144491	+	0.250266i
$705$	14.7901	+	25.6172i	0.557028	+	0.964801i
$706$	−1.57268	+	2.72397i	−0.0591887	+	0.102518i
$707$	38.1615			1.43521
$708$	2.75001	−	4.76315i	0.103352	−	0.179010i
$709$	−15.0689	+	26.1000i	−0.565923	+	0.980208i	0.431040	+	0.902333i	$0.358147\pi$
$709$	−15.0689	+	26.1000i	−0.565923	+	0.980208i	−0.996963	+	0.0778750i	$0.975186\pi$
$710$	−4.23097			−0.158785
$711$	−1.27917	+	2.21559i	−0.0479727	+	0.0830911i
$712$	−0.00678618	−	0.0117540i	−0.000254323	−	0.000440500i
$713$	1.68322	+	2.91542i	0.0630371	+	0.109183i
$714$	1.60736			0.0601539
$715$	−6.93440	−	5.16138i	−0.259332	−	0.193025i
$716$	−17.1044			−0.639220
$717$	4.99801	+	8.65681i	0.186654	+	0.323294i
$718$	−1.55945	−	2.70105i	−0.0581982	−	0.100802i
$719$	7.77971	−	13.4748i	0.290134	−	0.502527i	−0.683707	−	0.729756i	$-0.739633\pi$
$719$	7.77971	−	13.4748i	0.290134	−	0.502527i	0.973841	+	0.227230i	$0.0729668\pi$
$720$	−9.39014			−0.349950
$721$	24.1400	−	41.8117i	0.899020	−	1.55715i
$722$	0.268190	−	0.464519i	0.00998100	−	0.0172876i
$723$	1.26482			0.0470390
$724$	−16.7312	+	28.9793i	−0.621811	+	1.07701i
$725$	−2.02929	−	3.51483i	−0.0753659	−	0.130538i
$726$	0.0590186	+	0.102223i	0.00219039	+	0.00379386i
$727$	−41.0629			−1.52294			−0.761469	−	0.648201i	$-0.775522\pi$
$727$	−41.0629			−1.52294			−0.761469	+	0.648201i	$0.775522\pi$
$728$	−0.584470	+	5.00484i	−0.0216619	+	0.185492i
$729$	1.00000			0.0370370
$730$	−1.49280	−	2.58561i	−0.0552511	−	0.0956978i
$731$	16.0802	+	27.8516i	0.594746	+	1.03013i
$732$	5.40287	−	9.35805i	0.199696	−	0.345883i
$733$	−2.28843			−0.0845251			−0.0422625	−	0.999107i	$-0.513457\pi$
$733$	−2.28843			−0.0845251			−0.0422625	+	0.999107i	$0.513457\pi$
$734$	−1.10877	+	1.92045i	−0.0409255	+	0.0708850i
$735$	2.18475	−	3.78409i	0.0805856	−	0.139578i
$736$	−2.46071			−0.0907031
$737$	−2.85016	+	4.93662i	−0.104987	+	0.181843i
$738$	0.319569	+	0.553510i	0.0117635	+	0.0203750i
$739$	−22.3475	−	38.7070i	−0.822066	−	1.42386i	−0.904141	−	0.427233i	$-0.859488\pi$
$739$	−22.3475	−	38.7070i	−0.822066	−	1.42386i	0.0820757	−	0.996626i	$-0.473845\pi$
$740$	−17.9392			−0.659458
$741$	16.0635	−	6.93103i	0.590106	−	0.254618i
$742$	1.54652			0.0567747
$743$	−10.4657	−	18.1272i	−0.383951	−	0.665022i	0.607672	−	0.794188i	$-0.292103\pi$
$743$	−10.4657	−	18.1272i	−0.383951	−	0.665022i	−0.991623	+	0.129166i	$0.958770\pi$
$744$	0.451646	+	0.782274i	0.0165582	+	0.0286796i
$745$	−10.5362	+	18.2493i	−0.386017	+	0.668601i
$746$	−2.67223			−0.0978374
$747$	4.70584	−	8.15075i	0.172178	−	0.298220i
$748$	4.55262	−	7.88538i	0.166460	−	0.288318i
$749$	2.52094			0.0921130
$750$	0.601634	−	1.04206i	0.0219686	−	0.0380507i
$751$	0.685542	+	1.18739i	0.0250158	+	0.0433286i	0.878262	−	0.478179i	$-0.158703\pi$
$751$	0.685542	+	1.18739i	0.0250158	+	0.0433286i	−0.853246	+	0.521508i	$0.825370\pi$
$752$	−24.1611	−	41.8483i	−0.881066	−	1.52605i
$753$	−12.4728			−0.454536
$754$	−0.267805	+	2.29323i	−0.00975290	+	0.0835145i
$755$	51.4275			1.87164
$756$	−2.94958	−	5.10882i	−0.107275	−	0.185806i
$757$	4.58471	+	7.94095i	0.166634	+	0.288619i	0.937234	−	0.348700i	$-0.113377\pi$
$757$	4.58471	+	7.94095i	0.166634	+	0.288619i	−0.770600	+	0.637319i	$0.780043\pi$
$758$	−0.0723416	+	0.125299i	−0.00262756	+	0.00455107i
$759$	1.75350			0.0636481
$760$	−2.73677	+	4.74023i	−0.0992732	+	0.171946i
$761$	14.7679	−	25.5788i	0.535337	−	0.927231i	−0.463810	−	0.885935i	$-0.653518\pi$
$761$	14.7679	−	25.5788i	0.535337	−	0.927231i	0.999147	−	0.0412965i	$-0.0131488\pi$
$762$	2.00716			0.0727119
$763$	20.0356	−	34.7028i	0.725339	−	1.25632i
$764$	−3.63756	−	6.30044i	−0.131602	−	0.227942i
$765$	5.49580	+	9.51901i	0.198701	+	0.344161i
$766$	−3.80076			−0.137327
$767$	1.15817	−	9.91745i	0.0418191	−	0.358099i
$768$	14.8970			0.537549
$769$	−10.5859	−	18.3353i	−0.381737	−	0.661189i	0.609573	−	0.792730i	$-0.291341\pi$
$769$	−10.5859	−	18.3353i	−0.381737	−	0.661189i	−0.991311	+	0.131541i	$0.958007\pi$
$770$	0.420289	+	0.727962i	0.0151462	+	0.0262339i
$771$	−1.71111	+	2.96374i	−0.0616243	+	0.106736i
$772$	7.81338			0.281210
$773$	−23.1530	+	40.1022i	−0.832755	+	1.44237i	0.0630898	+	0.998008i	$0.479905\pi$
$773$	−23.1530	+	40.1022i	−0.832755	+	1.44237i	−0.895845	+	0.444367i	$0.853429\pi$
$774$	−0.414011	+	0.717088i	−0.0148813	+	0.0257752i
$775$	−1.43628			−0.0515929
$776$	2.60686	−	4.51522i	0.0935810	−	0.162087i
$777$	−5.59515	−	9.69108i	−0.200725	−	0.347666i
$778$	2.20842	+	3.82509i	0.0791756	+	0.137136i
$779$	−26.2735			−0.941345
$780$	−15.7636	+	6.80163i	−0.564427	+	0.243537i
$781$	−14.9505			−0.534973
$782$	0.474453	+	0.821777i	0.0169664	+	0.0293867i
$783$	−2.71249	−	4.69817i	−0.0969364	−	0.167899i
$784$	−3.56900	+	6.18170i	−0.127464	+	0.220775i
$785$	53.5484			1.91123
$786$	−0.852329	+	1.47628i	−0.0304016	+	0.0526571i
$787$	4.56379	−	7.90471i	0.162681	−	0.281773i	−0.773148	−	0.634226i	$-0.781319\pi$
$787$	4.56379	−	7.90471i	0.162681	−	0.281773i	0.935830	+	0.352453i	$0.114652\pi$
$788$	−34.1388			−1.21615
$789$	10.1034	−	17.4997i	0.359692	−	0.623004i
$790$	−0.362002	−	0.627006i	−0.0128795	−	0.0223079i
$791$	12.8196	+	22.2042i	0.455813	+	0.789492i
$792$	0.470505			0.0167187
$793$	2.27543	−	19.4846i	0.0808028	−	0.691918i
$794$	1.31716			0.0467442
$795$	5.28779	+	9.15873i	0.187539	+	0.324827i
$796$	−7.81567	−	13.5371i	−0.277019	−	0.479811i
$797$	13.4526	−	23.3005i	0.476514	−	0.825346i	−0.523124	−	0.852257i	$-0.675234\pi$
$797$	13.4526	−	23.3005i	0.476514	−	0.825346i	0.999638	+	0.0269105i	$0.00856690\pi$
$798$	−1.70121			−0.0602220
$799$	−28.2817	+	48.9854i	−1.00054	+	1.73298i
$800$	0.524929	−	0.909204i	0.0185590	−	0.0321452i
$801$	0.0288464			0.00101924
$802$	0.585683	−	1.01443i	0.0206812	−	0.0358209i
$803$	−5.27497	−	9.13652i	−0.186150	−	0.322421i
$804$	5.66061	+	9.80447i	0.199634	+	0.345777i
$805$	12.4872			0.440116
$806$	0.655434	+	0.487850i	0.0230867	+	0.0171838i
$807$	−24.7199			−0.870181
$808$	3.02248	+	5.23509i	0.106331	+	0.184170i
$809$	7.83885	+	13.5773i	0.275599	+	0.477352i	0.970286	−	0.241960i	$-0.0777904\pi$
$809$	7.83885	+	13.5773i	0.275599	+	0.477352i	−0.694687	+	0.719312i	$0.744457\pi$
$810$	−0.141499	+	0.245083i	−0.00497176	+	0.00861134i
$811$	21.5800			0.757775			0.378888	−	0.925443i	$-0.376307\pi$
$811$	21.5800			0.757775			0.378888	+	0.925443i	$0.376307\pi$
$812$	−16.0014	+	27.7152i	−0.561539	+	0.972614i
$813$	4.05382	−	7.02142i	0.142174	−	0.246252i
$814$	0.444698			0.0155866
$815$	−22.5086	+	38.9861i	−0.788443	+	1.36562i
$816$	−8.97794	−	15.5503i	−0.314291	−	0.544368i
$817$	−17.0190	−	29.4778i	−0.595419	−	1.03130i
$818$	−3.64653			−0.127498
$819$	−8.59095	−	6.39438i	−0.300192	−	0.223438i
$820$	25.7830			0.900380
$821$	25.5703	+	44.2890i	0.892408	+	1.54570i	0.836980	+	0.547234i	$0.184319\pi$
$821$	25.5703	+	44.2890i	0.892408	+	1.54570i	0.0554286	+	0.998463i	$0.482347\pi$
$822$	−0.832570	−	1.44205i	−0.0290392	−	0.0502974i
$823$	23.2631	−	40.2928i	0.810900	−	1.40452i	−0.101335	−	0.994852i	$-0.532311\pi$
$823$	23.2631	−	40.2928i	0.810900	−	1.40452i	0.912235	−	0.409667i	$-0.134355\pi$
$824$	7.64777			0.266423
$825$	−0.374064	+	0.647898i	−0.0130232	+	0.0225569i
$826$	−0.485462	+	0.840844i	−0.0168914	+	0.0292567i
$827$	−47.1916			−1.64101			−0.820506	−	0.571637i	$-0.806308\pi$
$827$	−47.1916			−1.64101			−0.820506	+	0.571637i	$0.806308\pi$
$828$	1.74129	−	3.01600i	0.0605139	−	0.104813i
$829$	25.7938	+	44.6761i	0.895855	+	1.55167i	0.832743	+	0.553660i	$0.186769\pi$
$829$	25.7938	+	44.6761i	0.895855	+	1.55167i	0.0631117	+	0.998006i	$0.479898\pi$
$830$	1.33174	+	2.30664i	0.0462254	+	0.0800647i
$831$	25.7639			0.893739
$832$	25.3837	−	10.9525i	0.880020	−	0.379709i
$833$	8.35538			0.289497
$834$	0.287502	+	0.497968i	0.00995538	+	0.0172432i
$835$	−2.82330	−	4.89011i	−0.0977045	−	0.169229i
$836$	−4.81843	+	8.34577i	−0.166649	+	0.288644i
$837$	−1.91984			−0.0663593
$838$	1.43186	−	2.48005i	0.0494626	−	0.0856718i
$839$	19.1907	−	33.2393i	0.662536	−	1.14755i	−0.317411	−	0.948288i	$-0.602813\pi$
$839$	19.1907	−	33.2393i	0.662536	−	1.14755i	0.979947	−	0.199259i	$-0.0638534\pi$
$840$	3.35060			0.115607
$841$	−0.215186	+	0.372714i	−0.00742022	+	0.0128522i
$842$	0.0824789	+	0.142858i	0.00284241	+	0.00492320i
$843$	4.05034	+	7.01539i	0.139501	+	0.241623i
$844$	−23.3584			−0.804031
$845$	−21.3841	+	22.6750i	−0.735635	+	0.780043i
$846$	−1.45632			−0.0500694
$847$	1.48513	+	2.57233i	0.0510298	+	0.0883863i
$848$	−8.63814	−	14.9617i	−0.296635	−	0.513787i
$849$	8.40583	−	14.5593i	0.288487	−	0.499675i
$850$	−0.404849			−0.0138862
$851$	3.30310	−	5.72114i	0.113229	−	0.196118i
$852$	−14.8464	+	25.7147i	−0.508629	+	0.880972i
$853$	17.7010			0.606070			0.303035	−	0.952979i	$-0.402000\pi$
$853$	17.7010			0.606070			0.303035	+	0.952979i	$0.402000\pi$
$854$	−0.953775	+	1.65199i	−0.0326375	+	0.0565298i
$855$	−5.81668	−	10.0748i	−0.198926	−	0.344550i
$856$	0.199664	+	0.345828i	0.00682438	+	0.0118202i
$857$	−4.15263			−0.141851			−0.0709256	−	0.997482i	$-0.522595\pi$
$857$	−4.15263			−0.141851			−0.0709256	+	0.997482i	$0.522595\pi$
$858$	0.390766	−	0.168607i	0.0133405	−	0.00575614i
$859$	18.5684			0.633547			0.316773	−	0.948501i	$-0.397401\pi$
$859$	18.5684			0.633547			0.316773	+	0.948501i	$0.397401\pi$
$860$	16.7013	+	28.9274i	0.569509	+	0.986418i
$861$	8.04159	+	13.9284i	0.274057	+	0.474680i
$862$	−1.49315	+	2.58621i	−0.0508568	+	0.0880866i
$863$	−2.09641			−0.0713626			−0.0356813	−	0.999363i	$-0.511360\pi$
$863$	−2.09641			−0.0713626			−0.0356813	+	0.999363i	$0.511360\pi$
$864$	0.701657	−	1.21531i	0.0238708	−	0.0413455i
$865$	−1.75999	+	3.04839i	−0.0598414	+	0.103648i
$866$	−4.00891			−0.136228
$867$	−2.00911	+	3.47988i	−0.0682329	+	0.118183i
$868$	5.66271	+	9.80810i	0.192205	+	0.332909i
$869$	−1.27917	−	2.21559i	−0.0433929	−	0.0751587i
$870$	1.53525			0.0520500
$871$	16.4871	+	12.2716i	0.558645	+	0.415808i
$872$	6.34748			0.214953
$873$	5.54057	+	9.59655i	0.187520	+	0.324794i
$874$	−0.502154	−	0.869756i	−0.0169856	−	0.0294200i
$875$	15.1394	−	26.2222i	0.511806	−	0.886474i
$876$	−20.9529			−0.707933
$877$	3.89195	−	6.74105i	0.131422	−	0.227629i	−0.792803	−	0.609478i	$-0.791379\pi$
$877$	3.89195	−	6.74105i	0.131422	−	0.227629i	0.924225	+	0.381849i	$0.124712\pi$
$878$	−0.681157	+	1.17980i	−0.0229879	+	0.0398163i
$879$	−16.2136			−0.546871
$880$	4.69507	−	8.13210i	0.158271	−	0.274133i
$881$	−27.4561	−	47.5553i	−0.925019	−	1.60218i	−0.791531	−	0.611129i	$-0.790716\pi$
$881$	−27.4561	−	47.5553i	−0.925019	−	1.60218i	−0.133488	−	0.991050i	$-0.542618\pi$
$882$	0.107562	+	0.186302i	0.00362179	+	0.00627312i
$883$	12.5693			0.422990			0.211495	−	0.977379i	$-0.432167\pi$
$883$	12.5693			0.422990			0.211495	+	0.977379i	$0.432167\pi$
$884$	−26.3352	−	19.6017i	−0.885750	−	0.659277i
$885$	−6.63947			−0.223183
$886$	2.43276	+	4.21366i	0.0817302	+	0.141561i
$887$	15.9718	+	27.6641i	0.536282	+	0.928868i	0.999100	+	0.0424146i	$0.0135051\pi$
$887$	15.9718	+	27.6641i	0.536282	+	0.928868i	−0.462818	+	0.886453i	$0.653162\pi$
$888$	0.886298	−	1.53511i	0.0297422	−	0.0515150i
$889$	50.5079			1.69398
$890$	−0.00408173	+	0.00706976i	−0.000136820	+	0.000236979i
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	50.2136			1.68128
$893$	29.9330	−	51.8454i	1.00167	−	1.73494i
$894$	−0.518729	−	0.898465i	−0.0173489	−	0.0300492i
$895$	10.3240	+	17.8816i	0.345092	+	0.597717i
$896$	−11.0247			−0.368309
$897$	0.733345	−	6.27967i	0.0244857	−	0.209672i
$898$	−1.34480			−0.0448767
$899$	5.20754	+	9.01972i	0.173681	+	0.300824i
$900$	0.742916	+	1.28677i	0.0247639	+	0.0428923i
$901$	−10.1114	+	17.5134i	−0.336858	+	0.583455i
$902$	−0.639139			−0.0212810
$903$	−10.4181	+	18.0447i	−0.346692	+	0.600489i
$904$	−2.03069	+	3.51725i	−0.0675396	+	0.116982i
$905$	40.3949			1.34277
$906$	−1.26596	+	2.19271i	−0.0420588	+	0.0728480i
$907$	7.58635	+	13.1400i	0.251901	+	0.436305i	0.964049	−	0.265724i	$-0.0856110\pi$
$907$	7.58635	+	13.1400i	0.251901	+	0.436305i	−0.712148	+	0.702029i	$0.752278\pi$
$908$	11.6642	+	20.2030i	0.387090	+	0.670460i
$909$	−12.8478			−0.426136
$910$	2.78276	−	1.20070i	0.0922476	−	0.0398028i
$911$	39.7790			1.31794			0.658969	−	0.752170i	$-0.270993\pi$
$911$	39.7790			1.31794			0.658969	+	0.752170i	$0.270993\pi$
$912$	9.50212	+	16.4582i	0.314647	+	0.544984i
$913$	4.70584	+	8.15075i	0.155741	+	0.269751i
$914$	0.572084	−	0.990879i	0.0189229	−	0.0327754i
$915$	−13.0444			−0.431234
$916$	9.45526	−	16.3770i	0.312411	−	0.541111i
$917$	−21.4479	+	37.1488i	−0.708271	+	1.22676i
$918$	−0.541149			−0.0178606
$919$	14.9113	−	25.8271i	0.491878	−	0.851958i	−0.508078	−	0.861311i	$-0.669644\pi$
$919$	14.9113	−	25.8271i	0.491878	−	0.851958i	0.999956	+	0.00935278i	$0.00297713\pi$
$920$	0.989016	+	1.71303i	0.0326069	+	0.0564768i
$921$	1.59856	+	2.76880i	0.0526745	+	0.0912349i
$922$	1.36694			0.0450179
$923$	−6.25258	+	53.5411i	−0.205806	+	1.76233i
$924$	5.89916			0.194068
$925$	1.40926	+	2.44091i	0.0463362	+	0.0802567i
$926$	2.03847	+	3.53074i	0.0669884	+	0.116027i
$927$	−8.12721	+	14.0767i	−0.266932	+	0.462341i
$928$	−7.61294			−0.249907
$929$	−12.6087	+	21.8388i	−0.413676	+	0.716509i	−0.995289	−	0.0969577i	$-0.969089\pi$
$929$	−12.6087	+	21.8388i	−0.413676	+	0.716509i	0.581612	+	0.813466i	$0.302422\pi$
$930$	0.271655	−	0.470519i	0.00890790	−	0.0154289i
$931$	−8.84320			−0.289824
$932$	3.28025	−	5.68157i	0.107448	−	0.186106i
$933$	9.97010	+	17.2687i	0.326407	+	0.565353i
$934$	0.220161	+	0.381330i	0.00720388	+	0.0124775i
$935$	−10.9916			−0.359464
$936$	0.196773	−	1.68498i	0.00643173	−	0.0550752i
$937$	−5.42706			−0.177294			−0.0886471	−	0.996063i	$-0.528254\pi$
$937$	−5.42706			−0.177294			−0.0886471	+	0.996063i	$0.528254\pi$
$938$	−0.999274	−	1.73079i	−0.0326274	−	0.0565124i
$939$	10.6984	+	18.5302i	0.349129	+	0.604709i
$940$	−29.3742	+	50.8775i	−0.958079	+	1.65944i
$941$	−25.3338			−0.825859			−0.412929	−	0.910763i	$-0.635494\pi$
$941$	−25.3338			−0.825859			−0.412929	+	0.910763i	$0.635494\pi$
$942$	−1.31817	+	2.28314i	−0.0429484	+	0.0743889i
$943$	−4.74736	+	8.22267i	−0.154595	+	0.267767i
$944$	10.8462			0.353015
$945$	−3.56065	+	6.16722i	−0.115828	+	0.200620i
$946$	−0.414011	−	0.717088i	−0.0134606	−	0.0233145i
$947$	28.7519	+	49.7998i	0.934312	+	1.61828i	0.775857	+	0.630909i	$0.217318\pi$
$947$	28.7519	+	49.7998i	0.934312	+	1.61828i	0.158455	+	0.987366i	$0.449349\pi$
$948$	−5.08104			−0.165024
$949$	−34.9259	+	15.0698i	−1.13374	+	0.489185i
$950$	0.428486			0.0139019
$951$	6.83271	+	11.8346i	0.221566	+	0.383763i
$952$	3.20352	+	5.54866i	0.103827	+	0.179833i
$953$	−6.27492	+	10.8685i	−0.203265	+	0.352064i	−0.949578	−	0.313530i	$-0.898488\pi$
$953$	−6.27492	+	10.8685i	−0.203265	+	0.352064i	0.746314	+	0.665594i	$0.231822\pi$
$954$	−0.520668			−0.0168572
$955$	−4.39116	+	7.60572i	−0.142095	+	0.246115i
$956$	−9.92638	+	17.1930i	−0.321042	+	0.556061i
$957$	5.42498			0.175365
$958$	−0.837141	+	1.44997i	−0.0270468	+	0.0468464i
$959$	−20.9506	−	36.2876i	−0.676531	−	1.17179i
$960$	−9.19157	−	15.9203i	−0.296657	−	0.513825i
$961$	−27.3142			−0.881104
$962$	0.185980	−	1.59256i	0.00599625	−	0.0513461i
$963$	−0.848723			−0.0273497
$964$	1.25601	+	2.17547i	0.0404532	+	0.0700670i
$965$	−4.71605	−	8.16843i	−0.151815	−	0.262951i
$966$	−0.307391	+	0.532417i	−0.00989015	+	0.0171302i
$967$	−1.49036			−0.0479266			−0.0239633	−	0.999713i	$-0.507628\pi$
$967$	−1.49036			−0.0479266			−0.0239633	+	0.999713i	$0.507628\pi$
$968$	−0.235252	+	0.407469i	−0.00756129	+	0.0130965i
$969$	11.1227	−	19.2651i	0.357312	−	0.618883i
$970$	−3.13593			−0.100689
$971$	19.7394	−	34.1896i	0.633466	−	1.09720i	−0.353372	−	0.935483i	$-0.614965\pi$
$971$	19.7394	−	34.1896i	0.633466	−	1.09720i	0.986838	−	0.161712i	$-0.0517016\pi$
$972$	0.993034	+	1.71998i	0.0318516	+	0.0551685i
$973$	7.23465	+	12.5308i	0.231932	+	0.401718i
$974$	3.17215			0.101642
$975$	2.16382	+	1.61057i	0.0692977	+	0.0515794i
$976$	21.3093			0.682095
$977$	9.37539	+	16.2387i	0.299945	+	0.519521i	0.976123	−	0.217218i	$-0.0696982\pi$
$977$	9.37539	+	16.2387i	0.299945	+	0.519521i	−0.676178	+	0.736738i	$0.736365\pi$
$978$	−1.10817	−	1.91940i	−0.0354353	−	0.0613757i
$979$	−0.0144232	+	0.0249817i	−0.000460968	+	0.000798419i
$980$	8.67811			0.277212
$981$	−6.74540	+	11.6834i	−0.215364	+	0.373021i
$982$	2.01026	−	3.48187i	0.0641499	−	0.111111i
$983$	−23.9822			−0.764914			−0.382457	−	0.923973i	$-0.624922\pi$
$983$	−23.9822			−0.764914			−0.382457	+	0.923973i	$0.624922\pi$
$984$	−1.27382	+	2.20633i	−0.0406080	+	0.0703352i
$985$	20.6057	+	35.6902i	0.656553	+	1.13718i
$986$	1.46786	+	2.54241i	0.0467462	+	0.0809668i
$987$	−36.6466			−1.16648
$988$	27.8728	+	20.7462i	0.886753	+	0.660024i
$989$	−12.3007			−0.391138
$990$	−0.141499	−	0.245083i	−0.00449712	−	0.00778925i
$991$	10.8821	+	18.8484i	0.345683	+	0.598740i	0.985478	−	0.169806i	$-0.0543140\pi$
$991$	10.8821	+	18.8484i	0.345683	+	0.598740i	−0.639795	+	0.768546i	$0.720981\pi$
$992$	−1.34707	+	2.33319i	−0.0427694	+	0.0740788i
$993$	9.56314			0.303477
$994$	2.62085	−	4.53945i	0.0831283	−	0.143982i
$995$	−9.43486	+	16.3417i	−0.299105	+	0.518065i
$996$	18.6922			0.592286
$997$	17.2698	−	29.9122i	0.546941	−	0.947330i	−0.451541	−	0.892250i	$-0.649126\pi$
$997$	17.2698	−	29.9122i	0.546941	−	0.947330i	0.998482	−	0.0550793i	$-0.0175412\pi$
$998$	−0.00866888	−	0.0150149i	−0.000274408	−	0.000475289i
$999$	1.88372	+	3.26269i	0.0595982	+	0.103227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.f.133.2	yes	10
13.3	even	3		5577.2.a.n.1.4		5
13.9	even	3	inner	429.2.i.f.100.2	✓	10
13.10	even	6		5577.2.a.w.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.f.100.2	✓	10	13.9	even	3	inner
429.2.i.f.133.2	yes	10	1.1	even	1	trivial
5577.2.a.n.1.4		5	13.3	even	3
5577.2.a.w.1.2		5	13.10	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0590186 + 0.102223i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.993034 - 1.71998i) q^{4} -2.39753 q^{5} +(0.0590186 - 0.102223i) q^{6} +(1.48513 - 2.57233i) q^{7} +0.470505 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.0590186 + 0.102223i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.993034 - 1.71998i) q^{4} -2.39753 q^{5} +(0.0590186 - 0.102223i) q^{6} +(1.48513 - 2.57233i) q^{7} +0.470505 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.141499 - 0.245083i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.98607 q^{12} +(-3.31053 + 1.42842i) q^{13} +0.350603 q^{14} +(1.19876 + 2.07632i) q^{15} +(-1.95830 - 3.39187i) q^{16} +(-2.29228 + 3.97035i) q^{17} -0.118037 q^{18} +(2.42612 - 4.20216i) q^{19} +(-2.38082 + 4.12371i) q^{20} -2.97027 q^{21} +(0.0590186 - 0.102223i) q^{22} +(-0.876751 - 1.51858i) q^{23} +(-0.235252 - 0.407469i) q^{24} +0.748128 q^{25} +(-0.341401 - 0.254110i) q^{26} +1.00000 q^{27} +(-2.94958 - 5.10882i) q^{28} +(-2.71249 - 4.69817i) q^{29} +(-0.141499 + 0.245083i) q^{30} -1.91984 q^{31} +(0.701657 - 1.21531i) q^{32} +(-0.500000 + 0.866025i) q^{33} -0.541149 q^{34} +(-3.56065 + 6.16722i) q^{35} +(0.993034 + 1.71998i) q^{36} +(1.88372 + 3.26269i) q^{37} +0.572744 q^{38} +(2.89231 + 2.15279i) q^{39} -1.12805 q^{40} +(-2.70736 - 4.68928i) q^{41} +(-0.175301 - 0.303631i) q^{42} +(3.50746 - 6.07509i) q^{43} -1.98607 q^{44} +(1.19876 - 2.07632i) q^{45} +(0.103489 - 0.179249i) q^{46} +12.3378 q^{47} +(-1.95830 + 3.39187i) q^{48} +(-0.911251 - 1.57833i) q^{49} +(0.0441535 + 0.0764761i) q^{50} +4.58456 q^{51} +(-0.830608 + 7.11253i) q^{52} +4.41104 q^{53} +(0.0590186 + 0.102223i) q^{54} +(1.19876 + 2.07632i) q^{55} +(0.698763 - 1.21029i) q^{56} -4.85223 q^{57} +(0.320175 - 0.554559i) q^{58} +(-1.38465 + 2.39828i) q^{59} +4.76165 q^{60} +(-2.72039 + 4.71185i) q^{61} +(-0.113306 - 0.196252i) q^{62} +(1.48513 + 2.57233i) q^{63} -7.66755 q^{64} +(7.93708 - 3.42467i) q^{65} -0.118037 q^{66} +(-2.85016 - 4.93662i) q^{67} +(4.55262 + 7.88538i) q^{68} +(-0.876751 + 1.51858i) q^{69} -0.840579 q^{70} +(7.47527 - 12.9476i) q^{71} +(-0.235252 + 0.407469i) q^{72} +10.5499 q^{73} +(-0.222349 + 0.385120i) q^{74} +(-0.374064 - 0.647898i) q^{75} +(-4.81843 - 8.34577i) q^{76} -2.97027 q^{77} +(-0.0493653 + 0.422717i) q^{78} +2.55834 q^{79} +(4.69507 + 8.13210i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.319569 - 0.553510i) q^{82} -9.41168 q^{83} +(-2.94958 + 5.10882i) q^{84} +(5.49580 - 9.51901i) q^{85} +0.828021 q^{86} +(-2.71249 + 4.69817i) q^{87} +(-0.235252 - 0.407469i) q^{88} +(-0.0144232 - 0.0249817i) q^{89} +0.282997 q^{90} +(-1.24222 + 10.6372i) q^{91} -3.48257 q^{92} +(0.959919 + 1.66263i) q^{93} +(0.728161 + 1.26121i) q^{94} +(-5.81668 + 10.0748i) q^{95} -1.40331 q^{96} +(5.54057 - 9.59655i) q^{97} +(0.107562 - 0.186302i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} - 5 q^{11} + 12 q^{12} + 5 q^{13} + 14 q^{14} + 4 q^{15} - 12 q^{16} - 9 q^{17} - 8 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} + 4 q^{22} + 9 q^{23} + 9 q^{24} + 2 q^{25} - 12 q^{26} + 10 q^{27} - q^{28} - 8 q^{29} + 5 q^{30} - 12 q^{31} + 27 q^{32} - 5 q^{33} - 14 q^{34} + 2 q^{35} - 6 q^{36} + 17 q^{37} - 2 q^{38} + 2 q^{39} + 46 q^{40} + 6 q^{41} - 7 q^{42} - 13 q^{43} + 12 q^{44} + 4 q^{45} - 6 q^{46} - 32 q^{47} - 12 q^{48} + 18 q^{49} - 8 q^{50} + 18 q^{51} + 7 q^{52} - 26 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 18 q^{57} + 11 q^{58} + 8 q^{59} - 12 q^{60} - 4 q^{61} + 22 q^{62} + 3 q^{63} + 22 q^{64} + 26 q^{65} - 8 q^{66} + 5 q^{67} - 34 q^{68} + 9 q^{69} + 8 q^{70} + 19 q^{71} + 9 q^{72} - 4 q^{73} - 27 q^{74} - q^{75} - 6 q^{76} - 6 q^{77} - 3 q^{78} - 16 q^{79} + 32 q^{80} - 5 q^{81} - 16 q^{82} - 20 q^{83} - q^{84} + 21 q^{85} + 8 q^{86} - 8 q^{87} + 9 q^{88} + 32 q^{89} - 10 q^{90} - 17 q^{91} - 84 q^{92} + 6 q^{93} - 66 q^{94} - 11 q^{95} - 54 q^{96} - 5 q^{97} - 18 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 - 5 * q^11 + 12 * q^12 + 5 * q^13 + 14 * q^14 + 4 * q^15 - 12 * q^16 - 9 * q^17 - 8 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 + 4 * q^22 + 9 * q^23 + 9 * q^24 + 2 * q^25 - 12 * q^26 + 10 * q^27 - q^28 - 8 * q^29 + 5 * q^30 - 12 * q^31 + 27 * q^32 - 5 * q^33 - 14 * q^34 + 2 * q^35 - 6 * q^36 + 17 * q^37 - 2 * q^38 + 2 * q^39 + 46 * q^40 + 6 * q^41 - 7 * q^42 - 13 * q^43 + 12 * q^44 + 4 * q^45 - 6 * q^46 - 32 * q^47 - 12 * q^48 + 18 * q^49 - 8 * q^50 + 18 * q^51 + 7 * q^52 - 26 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 18 * q^57 + 11 * q^58 + 8 * q^59 - 12 * q^60 - 4 * q^61 + 22 * q^62 + 3 * q^63 + 22 * q^64 + 26 * q^65 - 8 * q^66 + 5 * q^67 - 34 * q^68 + 9 * q^69 + 8 * q^70 + 19 * q^71 + 9 * q^72 - 4 * q^73 - 27 * q^74 - q^75 - 6 * q^76 - 6 * q^77 - 3 * q^78 - 16 * q^79 + 32 * q^80 - 5 * q^81 - 16 * q^82 - 20 * q^83 - q^84 + 21 * q^85 + 8 * q^86 - 8 * q^87 + 9 * q^88 + 32 * q^89 - 10 * q^90 - 17 * q^91 - 84 * q^92 + 6 * q^93 - 66 * q^94 - 11 * q^95 - 54 * q^96 - 5 * q^97 - 18 * q^98 + 10 * q^99

Introduction

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