LMFDB - Embedded newform 154.2.i.a.87.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(87,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("154.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.i (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:	$1.22969619113$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			87.3
Root			$-1.29724 + 0.347596i$ of defining polynomial
Character	$\chi$	$=$	154.87
Dual form			154.2.i.a.131.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.35034 + 0.779618i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.882559 - 0.509546i) q^{5} -1.55924 q^{6} +(2.25578 - 1.38256i) q^{7} +1.00000i q^{8} +(-0.284392 - 0.492581i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.35034 + 0.779618i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.882559 - 0.509546i) q^{5} -1.55924 q^{6} +(2.25578 - 1.38256i) q^{7} +1.00000i q^{8} +(-0.284392 - 0.492581i) q^{9} +(-0.509546 + 0.882559i) q^{10} +(-0.510616 + 3.27708i) q^{11} +(1.35034 - 0.779618i) q^{12} -0.167247 q^{13} +(-1.26228 + 2.32522i) q^{14} +1.58900 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.47616 + 2.55678i) q^{17} +(0.492581 + 0.284392i) q^{18} +(-0.155850 - 0.269940i) q^{19} -1.01909i q^{20} +(4.12393 - 0.108278i) q^{21} +(-1.19633 - 3.09335i) q^{22} +(0.237719 + 0.411742i) q^{23} +(-0.779618 + 1.35034i) q^{24} +(-1.98073 + 3.43072i) q^{25} +(0.144840 - 0.0836233i) q^{26} -5.56458i q^{27} +(-0.0694427 - 2.64484i) q^{28} -1.89701i q^{29} +(-1.37612 + 0.794502i) q^{30} +(-2.20834 - 1.27498i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.24438 + 4.02708i) q^{33} -2.95232i q^{34} +(1.28638 - 2.36961i) q^{35} -0.568783 q^{36} +(-3.04667 - 5.27699i) q^{37} +(0.269940 + 0.155850i) q^{38} +(-0.225839 - 0.130388i) q^{39} +(0.509546 + 0.882559i) q^{40} -10.2084 q^{41} +(-3.51729 + 2.15574i) q^{42} -10.1222i q^{43} +(2.58273 + 2.08075i) q^{44} +(-0.501985 - 0.289821i) q^{45} +(-0.411742 - 0.237719i) q^{46} +(-3.28968 + 1.89930i) q^{47} -1.55924i q^{48} +(3.17706 - 6.23749i) q^{49} -3.96145i q^{50} +(-3.98663 + 2.30168i) q^{51} +(-0.0836233 + 0.144840i) q^{52} +(-4.21079 + 7.29330i) q^{53} +(2.78229 + 4.81906i) q^{54} +(1.21917 + 3.15240i) q^{55} +(1.38256 + 2.25578i) q^{56} -0.486014i q^{57} +(0.948505 + 1.64286i) q^{58} +(5.40617 + 3.12126i) q^{59} +(0.794502 - 1.37612i) q^{60} +(5.93960 + 10.2877i) q^{61} +2.54997 q^{62} +(-1.32255 - 0.717964i) q^{63} -1.00000 q^{64} +(-0.147605 + 0.0852198i) q^{65} +(0.796171 - 5.10974i) q^{66} +(5.19151 - 8.99196i) q^{67} +(1.47616 + 2.55678i) q^{68} +0.741321i q^{69} +(0.0707684 + 2.69533i) q^{70} +14.5206 q^{71} +(0.492581 - 0.284392i) q^{72} +(-4.85385 + 8.40712i) q^{73} +(5.27699 + 3.04667i) q^{74} +(-5.34930 + 3.08842i) q^{75} -0.311700 q^{76} +(3.37892 + 8.09833i) q^{77} +0.260777 q^{78} +(6.06709 - 3.50284i) q^{79} +(-0.882559 - 0.509546i) q^{80} +(3.48507 - 6.03631i) q^{81} +(8.84069 - 5.10418i) q^{82} -14.6915 q^{83} +(1.96819 - 3.62557i) q^{84} +3.00868i q^{85} +(5.06112 + 8.76612i) q^{86} +(1.47894 - 2.56161i) q^{87} +(-3.27708 - 0.510616i) q^{88} +(5.97639 - 3.45047i) q^{89} +0.579642 q^{90} +(-0.377271 + 0.231228i) q^{91} +0.475438 q^{92} +(-1.98800 - 3.44332i) q^{93} +(1.89930 - 3.28968i) q^{94} +(-0.275094 - 0.158826i) q^{95} +(0.779618 + 1.35034i) q^{96} +11.0218i q^{97} +(0.367330 + 6.99036i) q^{98} +(1.75944 - 0.680455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 - 12 * q^5 + 16 * q^9	$ 16 q + 8 q^{4} - 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} - 36 q^{26} - 12 q^{31} - 24 q^{33} + 32 q^{36} - 16 q^{37} + 12 q^{38} + 12 q^{42} - 8 q^{44} - 108 q^{45} + 24 q^{47} + 8 q^{49} - 28 q^{53} - 4 q^{56} - 12 q^{58} + 60 q^{59} - 4 q^{60} - 16 q^{64} + 48 q^{66} + 12 q^{67} + 60 q^{70} + 8 q^{71} + 60 q^{75} + 44 q^{77} - 16 q^{78} + 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} + 96 q^{89} - 36 q^{91} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 12 * q^5 + 16 * q^9 + 8 * q^11 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^22 + 16 * q^23 - 36 * q^26 - 12 * q^31 - 24 * q^33 + 32 * q^36 - 16 * q^37 + 12 * q^38 + 12 * q^42 - 8 * q^44 - 108 * q^45 + 24 * q^47 + 8 * q^49 - 28 * q^53 - 4 * q^56 - 12 * q^58 + 60 * q^59 - 4 * q^60 - 16 * q^64 + 48 * q^66 + 12 * q^67 + 60 * q^70 + 8 * q^71 + 60 * q^75 + 44 * q^77 - 16 * q^78 + 12 * q^80 - 8 * q^81 + 20 * q^86 - 4 * q^88 + 96 * q^89 - 36 * q^91 + 32 * q^92 - 44 * q^93 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.35034	+	0.779618i	0.779618	+	0.450113i	0.836295	−	0.548280i	$-0.184717\pi$
$3$	1.35034	+	0.779618i	0.779618	+	0.450113i	−0.0566769	+	0.998393i	$0.518050\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.882559	−	0.509546i	0.394692	−	0.227876i	−0.289499	−	0.957178i	$-0.593489\pi$
$5$	0.882559	−	0.509546i	0.394692	−	0.227876i	0.684191	+	0.729303i	$0.260155\pi$
$6$	−1.55924			−0.636555
$7$	2.25578	−	1.38256i	0.852604	−	0.522558i
$7$	2.25578	−	1.38256i	0.852604	−	0.522558i
$8$			1.00000i			0.353553i
$9$	−0.284392	−	0.492581i	−0.0947972	−	0.164194i
$10$	−0.509546	+	0.882559i	−0.161132	+	0.279090i
$11$	−0.510616	+	3.27708i	−0.153957	+	0.988078i
$11$	−0.510616	+	3.27708i	−0.153957	+	0.988078i
$12$	1.35034	−	0.779618i	0.389809	−	0.225056i
$13$	−0.167247			−0.0463859			−0.0231929	−	0.999731i	$-0.507383\pi$
$13$	−0.167247			−0.0463859			−0.0231929	+	0.999731i	$0.507383\pi$
$14$	−1.26228	+	2.32522i	−0.337359	+	0.621441i
$15$	1.58900			0.410279
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.47616	+	2.55678i	−0.358021	+	0.620111i	−0.987630	−	0.156801i	$-0.949882\pi$
$17$	−1.47616	+	2.55678i	−0.358021	+	0.620111i	0.629609	+	0.776912i	$0.283215\pi$
$18$	0.492581	+	0.284392i	0.116102	+	0.0670318i
$19$	−0.155850	−	0.269940i	−0.0357545	−	0.0619286i	0.847594	−	0.530645i	$-0.178050\pi$
$19$	−0.155850	−	0.269940i	−0.0357545	−	0.0619286i	−0.883349	+	0.468716i	$0.844717\pi$
$20$		−	1.01909i		−	0.227876i
$21$	4.12393	−	0.108278i	0.899915	−	0.0236281i
$22$	−1.19633	−	3.09335i	−0.255059	−	0.659503i
$23$	0.237719	+	0.411742i	0.0495679	+	0.0858541i	0.889745	−	0.456458i	$-0.150882\pi$
$23$	0.237719	+	0.411742i	0.0495679	+	0.0858541i	−0.840177	+	0.542312i	$0.817549\pi$
$24$	−0.779618	+	1.35034i	−0.159139	+	0.275637i
$25$	−1.98073	+	3.43072i	−0.396145	+	0.686144i
$26$	0.144840	−	0.0836233i	0.0284054	−	0.0163999i
$27$		−	5.56458i		−	1.07090i
$28$	−0.0694427	−	2.64484i	−0.0131234	−	0.499828i
$29$		−	1.89701i		−	0.352266i	−0.984366	−	0.176133i	$-0.943641\pi$
$29$		−	1.89701i		−	0.352266i	0.984366	−	0.176133i	$-0.0563589\pi$
$30$	−1.37612	+	0.794502i	−0.251244	+	0.145056i
$31$	−2.20834	−	1.27498i	−0.396629	−	0.228994i	0.288400	−	0.957510i	$-0.406877\pi$
$31$	−2.20834	−	1.27498i	−0.396629	−	0.228994i	−0.685028	+	0.728516i	$0.740210\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−3.24438	+	4.02708i	−0.564774	+	0.701025i
$34$		−	2.95232i		−	0.506318i
$35$	1.28638	−	2.36961i	0.217438	−	0.400537i
$36$	−0.568783			−0.0947972
$37$	−3.04667	−	5.27699i	−0.500870	−	0.867532i	−0.999999	−	0.00100474i	$-0.999680\pi$
$37$	−3.04667	−	5.27699i	−0.500870	−	0.867532i	0.499130	−	0.866527i	$-0.333653\pi$
$38$	0.269940	+	0.155850i	0.0437901	+	0.0252822i
$39$	−0.225839	−	0.130388i	−0.0361633	−	0.0208789i
$40$	0.509546	+	0.882559i	0.0805662	+	0.139545i
$41$	−10.2084			−1.59428			−0.797138	−	0.603797i	$-0.793654\pi$
$41$	−10.2084			−1.59428			−0.797138	+	0.603797i	$0.793654\pi$
$42$	−3.51729	+	2.15574i	−0.542729	+	0.332637i
$43$		−	10.1222i		−	1.54363i	−0.635848	−	0.771814i	$-0.719350\pi$
$43$		−	10.1222i		−	1.54363i	0.635848	−	0.771814i	$-0.280650\pi$
$44$	2.58273	+	2.08075i	0.389361	+	0.313685i
$45$	−0.501985	−	0.289821i	−0.0748315	−	0.0432040i
$46$	−0.411742	−	0.237719i	−0.0607080	−	0.0350498i
$47$	−3.28968	+	1.89930i	−0.479849	+	0.277041i	−0.720354	−	0.693607i	$-0.756020\pi$
$47$	−3.28968	+	1.89930i	−0.479849	+	0.277041i	0.240505	+	0.970648i	$0.422687\pi$
$48$		−	1.55924i		−	0.225056i
$49$	3.17706	−	6.23749i	0.453866	−	0.891070i
$50$		−	3.96145i		−	0.560234i
$51$	−3.98663	+	2.30168i	−0.558239	+	0.322300i
$52$	−0.0836233	+	0.144840i	−0.0115965	+	0.0200857i
$53$	−4.21079	+	7.29330i	−0.578396	+	1.00181i	0.417268	+	0.908784i	$0.362988\pi$
$53$	−4.21079	+	7.29330i	−0.578396	+	1.00181i	−0.995664	+	0.0930275i	$0.970346\pi$
$54$	2.78229	+	4.81906i	0.378621	+	0.655791i
$55$	1.21917	+	3.15240i	0.164393	+	0.425070i
$56$	1.38256	+	2.25578i	0.184752	+	0.301441i
$57$		−	0.486014i		−	0.0643742i
$58$	0.948505	+	1.64286i	0.124545	+	0.215718i
$59$	5.40617	+	3.12126i	0.703824	+	0.406353i	0.808770	−	0.588125i	$-0.200134\pi$
$59$	5.40617	+	3.12126i	0.703824	+	0.406353i	−0.104946	+	0.994478i	$0.533467\pi$
$60$	0.794502	−	1.37612i	0.102570	−	0.177656i
$61$	5.93960	+	10.2877i	0.760488	+	1.31720i	0.942599	+	0.333926i	$0.108374\pi$
$61$	5.93960	+	10.2877i	0.760488	+	1.31720i	−0.182111	+	0.983278i	$0.558293\pi$
$62$	2.54997			0.323846
$63$	−1.32255	−	0.717964i	−0.166625	−	0.0904550i
$64$	−1.00000			−0.125000
$65$	−0.147605	+	0.0852198i	−0.0183081	+	0.0105702i
$66$	0.796171	−	5.10974i	0.0980019	−	0.628966i
$67$	5.19151	−	8.99196i	0.634244	−	1.09854i	−0.352431	−	0.935838i	$-0.614645\pi$
$67$	5.19151	−	8.99196i	0.634244	−	1.09854i	0.986675	−	0.162705i	$-0.0520219\pi$
$68$	1.47616	+	2.55678i	0.179011	+	0.310055i
$69$			0.741321i			0.0892445i
$70$	0.0707684	+	2.69533i	0.00845845	+	0.322154i
$71$	14.5206			1.72328			0.861639	−	0.507522i	$-0.169439\pi$
$71$	14.5206			1.72328			0.861639	+	0.507522i	$0.169439\pi$
$72$	0.492581	−	0.284392i	0.0580512	−	0.0335159i
$73$	−4.85385	+	8.40712i	−0.568101	+	0.983979i	0.428653	+	0.903469i	$0.358988\pi$
$73$	−4.85385	+	8.40712i	−0.568101	+	0.983979i	−0.996754	+	0.0805099i	$0.974345\pi$
$74$	5.27699	+	3.04667i	0.613438	+	0.354168i
$75$	−5.34930	+	3.08842i	−0.617684	+	0.356620i
$76$	−0.311700			−0.0357545
$77$	3.37892	+	8.09833i	0.385064	+	0.922890i
$78$	0.260777			0.0295272
$79$	6.06709	−	3.50284i	0.682601	−	0.394100i	−0.118233	−	0.992986i	$-0.537723\pi$
$79$	6.06709	−	3.50284i	0.682601	−	0.394100i	0.800834	+	0.598886i	$0.204390\pi$
$80$	−0.882559	−	0.509546i	−0.0986731	−	0.0569689i
$81$	3.48507	−	6.03631i	0.387230	−	0.670702i
$82$	8.84069	−	5.10418i	0.976291	−	0.563662i
$83$	−14.6915			−1.61261			−0.806303	−	0.591502i	$-0.798535\pi$
$83$	−14.6915			−1.61261			−0.806303	+	0.591502i	$0.798535\pi$
$84$	1.96819	−	3.62557i	0.214748	−	0.395582i
$85$			3.00868i			0.326337i
$86$	5.06112	+	8.76612i	0.545755	+	0.945275i
$87$	1.47894	−	2.56161i	0.158559	−	0.274633i
$88$	−3.27708	−	0.510616i	−0.349338	−	0.0544319i
$89$	5.97639	−	3.45047i	0.633496	−	0.365749i	−0.148609	−	0.988896i	$-0.547480\pi$
$89$	5.97639	−	3.45047i	0.633496	−	0.365749i	0.782105	+	0.623147i	$0.214146\pi$
$90$	0.579642			0.0610997
$91$	−0.377271	+	0.231228i	−0.0395488	+	0.0242393i
$92$	0.475438			0.0495679
$93$	−1.98800	−	3.44332i	−0.206146	−	0.357055i
$94$	1.89930	−	3.28968i	0.195898	−	0.339305i
$95$	−0.275094	−	0.158826i	−0.0282240	−	0.0162952i
$96$	0.779618	+	1.35034i	0.0795694	+	0.137818i
$97$			11.0218i			1.11909i	0.828799	+	0.559547i	$0.189025\pi$
$97$			11.0218i			1.11909i	−0.828799	+	0.559547i	$0.810975\pi$
$98$	0.367330	+	6.99036i	0.0371059	+	0.706133i
$99$	1.75944	−	0.680455i	0.176831	−	0.0683883i
$100$	1.98073	+	3.43072i	0.198073	+	0.343072i
$101$	−2.66752	+	4.62028i	−0.265428	+	0.459735i	−0.967676	−	0.252198i	$-0.918847\pi$
$101$	−2.66752	+	4.62028i	−0.265428	+	0.459735i	0.702248	+	0.711933i	$0.252180\pi$
$102$	2.30168	−	3.98663i	0.227900	−	0.394735i
$103$	−10.7849	+	6.22664i	−1.06266	+	0.613529i	−0.926168	−	0.377112i	$-0.876917\pi$
$103$	−10.7849	+	6.22664i	−1.06266	+	0.613529i	−0.136496	+	0.990641i	$0.543584\pi$
$104$		−	0.167247i		−	0.0163999i
$105$	3.58444	−	2.19689i	0.349805	−	0.214395i
$106$		−	8.42157i		−	0.817975i
$107$	6.28227	−	3.62707i	0.607330	−	0.350642i	−0.164590	−	0.986362i	$-0.552630\pi$
$107$	6.28227	−	3.62707i	0.607330	−	0.350642i	0.771920	+	0.635720i	$0.219297\pi$
$108$	−4.81906	−	2.78229i	−0.463715	−	0.267726i
$109$	1.01103	+	0.583716i	0.0968387	+	0.0559098i	0.547637	−	0.836716i	$-0.315527\pi$
$109$	1.01103	+	0.583716i	0.0968387	+	0.0559098i	−0.450799	+	0.892626i	$0.648861\pi$
$110$	−2.63204	−	2.12047i	−0.250955	−	0.202179i
$111$		−	9.50096i		−	0.901791i
$112$	−2.32522	−	1.26228i	−0.219713	−	0.119274i
$113$	−8.40135			−0.790333			−0.395166	−	0.918610i	$-0.629313\pi$
$113$	−8.40135			−0.790333			−0.395166	+	0.918610i	$0.629313\pi$
$114$	0.243007	+	0.420901i	0.0227597	+	0.0394210i
$115$	0.419602	+	0.242258i	0.0391281	+	0.0225906i
$116$	−1.64286	−	0.948505i	−0.152536	−	0.0880665i
$117$	0.0475636	+	0.0823825i	0.00439725	+	0.00761626i
$118$	−6.24251			−0.574670
$119$	0.205017	+	7.80841i	0.0187939	+	0.715796i
$120$			1.58900i			0.145056i
$121$	−10.4785	−	3.34666i	−0.952595	−	0.304242i
$122$	−10.2877	−	5.93960i	−0.931404	−	0.537746i
$123$	−13.7847	−	7.95862i	−1.24293	−	0.717604i
$124$	−2.20834	+	1.27498i	−0.198314	+	0.114497i
$125$			9.13254i			0.816839i
$126$	1.50434	−	0.0394979i	0.134017	−	0.00351875i
$127$			3.53324i			0.313525i	0.987636	+	0.156762i	$0.0501057\pi$
$127$			3.53324i			0.313525i	−0.987636	+	0.156762i	$0.949894\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	7.89149	−	13.6685i	0.694807	−	1.20344i
$130$	0.0852198	−	0.147605i	0.00747427	−	0.0129458i
$131$	−6.98984	−	12.1068i	−0.610705	−	1.05777i	−0.991122	−	0.132957i	$-0.957553\pi$
$131$	−6.98984	−	12.1068i	−0.610705	−	1.05777i	0.380417	−	0.924815i	$-0.375781\pi$
$132$	1.86537	+	4.82325i	0.162359	+	0.419810i
$133$	−0.724772	−	0.393453i	−0.0628457	−	0.0341167i
$134$			10.3830i			0.896957i
$135$	−2.83541	−	4.91107i	−0.244033	−	0.422677i
$136$	−2.55678	−	1.47616i	−0.219242	−	0.126580i
$137$	3.50529	−	6.07134i	0.299477	−	0.518709i	−0.676539	−	0.736406i	$-0.736521\pi$
$137$	3.50529	−	6.07134i	0.299477	−	0.518709i	0.976016	+	0.217697i	$0.0698545\pi$
$138$	−0.370660	−	0.642003i	−0.0315527	−	0.0546509i
$139$	11.4615			0.972148			0.486074	−	0.873918i	$-0.338429\pi$
$139$	11.4615			0.972148			0.486074	+	0.873918i	$0.338429\pi$
$140$	−1.40895	−	2.29884i	−0.119078	−	0.194288i
$141$	−5.92291			−0.498799
$142$	−12.5752	+	7.26030i	−1.05529	+	0.609270i
$143$	0.0853989	−	0.548081i	0.00714141	−	0.0458328i
$144$	−0.284392	+	0.492581i	−0.0236993	+	0.0410484i
$145$	−0.966613	−	1.67422i	−0.0802729	−	0.139037i
$146$		−	9.70771i		−	0.803416i
$147$	9.15297	−	5.94583i	0.754924	−	0.490403i
$148$	−6.09335			−0.500870
$149$	12.2602	−	7.07841i	1.00439	−	0.579886i	0.0948474	−	0.995492i	$-0.469764\pi$
$149$	12.2602	−	7.07841i	1.00439	−	0.579886i	0.909545	+	0.415606i	$0.136430\pi$
$150$	3.08842	−	5.34930i	0.252168	−	0.436768i
$151$	20.1819	+	11.6520i	1.64238	+	0.948228i	0.979985	+	0.199072i	$0.0637928\pi$
$151$	20.1819	+	11.6520i	1.64238	+	0.948228i	0.662394	+	0.749156i	$0.269541\pi$
$152$	0.269940	−	0.155850i	0.0218951	−	0.0126411i
$153$	1.67923			0.135758
$154$	−6.97540	−	5.32389i	−0.562093	−	0.429012i
$155$	−2.59865			−0.208728
$156$	−0.225839	+	0.130388i	−0.0180816	+	0.0104394i
$157$	3.49234	+	2.01630i	0.278719	+	0.160919i	0.632843	−	0.774280i	$-0.281888\pi$
$157$	3.49234	+	2.01630i	0.278719	+	0.160919i	−0.354124	+	0.935198i	$0.615221\pi$
$158$	−3.50284	+	6.06709i	−0.278671	+	0.482672i
$159$	−11.3720	+	6.56561i	−0.901856	+	0.520687i
$160$	1.01909			0.0805662
$161$	1.10550	+	0.600137i	0.0871255	+	0.0472974i
$162$			6.97014i			0.547626i
$163$	2.76994	+	4.79768i	0.216958	+	0.375783i	0.953877	−	0.300199i	$-0.0970530\pi$
$163$	2.76994	+	4.79768i	0.216958	+	0.375783i	−0.736918	+	0.675982i	$0.763720\pi$
$164$	−5.10418	+	8.84069i	−0.398569	+	0.690342i
$165$	−0.811371	+	5.20730i	−0.0631652	+	0.405388i
$166$	12.7233	−	7.34577i	0.987516	−	0.570143i
$167$	21.2252			1.64245			0.821226	−	0.570603i	$-0.193291\pi$
$167$	21.2252			1.64245			0.821226	+	0.570603i	$0.193291\pi$
$168$	0.108278	+	4.12393i	0.00835379	+	0.318168i
$169$	−12.9720			−0.997848
$170$	−1.50434	−	2.60560i	−0.115378	−	0.199840i
$171$	−0.0886450	+	0.153538i	−0.00677885	+	0.0117413i
$172$	−8.76612	−	5.06112i	−0.668411	−	0.385907i
$173$	−7.53277	−	13.0471i	−0.572706	−	0.991956i	−0.996287	−	0.0860973i	$-0.972560\pi$
$173$	−7.53277	−	13.0471i	−0.572706	−	0.991956i	0.423581	−	0.905858i	$-0.360773\pi$
$174$			2.95789i			0.224237i
$175$	0.275094	+	10.4774i	0.0207951	+	0.792018i
$176$	3.09335	−	1.19633i	0.233170	−	0.0901771i
$177$	4.86677	+	8.42950i	0.365809	+	0.633600i
$178$	−3.45047	+	5.97639i	−0.258623	+	0.447949i
$179$	1.08088	−	1.87214i	0.0807887	−	0.139930i	−0.822800	−	0.568331i	$-0.807589\pi$
$179$	1.08088	−	1.87214i	0.0807887	−	0.139930i	0.903589	+	0.428401i	$0.140923\pi$
$180$	−0.501985	+	0.289821i	−0.0374158	+	0.0216020i
$181$			5.39285i			0.400848i	0.979709	+	0.200424i	$0.0642319\pi$
$181$			5.39285i			0.400848i	−0.979709	+	0.200424i	$0.935768\pi$
$182$	0.211112	−	0.388885i	0.0156487	−	0.0288261i
$183$			18.5225i			1.36922i
$184$	−0.411742	+	0.237719i	−0.0303540	+	0.0175249i
$185$	−5.37774	−	3.10484i	−0.395379	−	0.228272i
$186$	3.44332	+	1.98800i	0.252476	+	0.145767i
$187$	−7.62504	−	6.14303i	−0.557598	−	0.449223i
$188$			3.79859i			0.277041i
$189$	−7.69335	−	12.5524i	−0.559609	−	0.913056i
$190$	0.317651			0.0230448
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$	−1.35034	−	0.779618i	−0.0974522	−	0.0562641i
$193$	8.31348	+	4.79979i	0.598417	+	0.345496i	0.768419	−	0.639947i	$-0.221044\pi$
$193$	8.31348	+	4.79979i	0.598417	+	0.345496i	−0.170001	+	0.985444i	$0.554377\pi$
$194$	−5.51090	−	9.54515i	−0.395659	−	0.685302i
$195$	−0.265756			−0.0190311
$196$	−3.81329	−	5.87016i	−0.272378	−	0.419297i
$197$		−	14.8180i		−	1.05574i	−0.849325	−	0.527870i	$-0.822991\pi$
$197$		−	14.8180i		−	1.05574i	0.849325	−	0.527870i	$-0.177009\pi$
$198$	−1.18350	+	1.46901i	−0.0841073	+	0.104398i
$199$	3.55962	+	2.05515i	0.252335	+	0.145686i	0.620833	−	0.783943i	$-0.286795\pi$
$199$	3.55962	+	2.05515i	0.252335	+	0.145686i	−0.368498	+	0.929629i	$0.620128\pi$
$200$	−3.43072	−	1.98073i	−0.242588	−	0.140059i
$201$	14.0206	−	8.09479i	0.988936	−	0.570963i
$202$		−	5.33504i		−	0.375372i
$203$	−2.62273	−	4.27923i	−0.184079	−	0.300343i
$204$			4.60336i			0.322300i
$205$	−9.00947	+	5.20162i	−0.629249	+	0.363297i
$206$	6.22664	−	10.7849i	0.433831	−	0.751417i
$207$	0.135211	−	0.234192i	0.00939780	−	0.0162775i
$208$	0.0836233	+	0.144840i	0.00579823	+	0.0100428i
$209$	0.964197	−	0.372898i	0.0666949	−	0.0257939i
$210$	−2.00577	+	3.69478i	−0.138411	+	0.254964i
$211$			7.52456i			0.518012i	0.965876	+	0.259006i	$0.0833950\pi$
$211$			7.52456i			0.518012i	−0.965876	+	0.259006i	$0.916605\pi$
$212$	4.21079	+	7.29330i	0.289198	+	0.500906i
$213$	19.6077	+	11.3205i	1.34350	+	0.775669i
$214$	−3.62707	+	6.28227i	−0.247941	+	0.429447i
$215$	−5.15775	−	8.93348i	−0.351755	−	0.609258i
$216$	5.56458			0.378621
$217$	−6.74425	+	0.177076i	−0.457830	+	0.0120207i
$218$	−1.16743			−0.0790685
$219$	−13.1087	+	7.56830i	−0.885803	+	0.511418i
$220$	3.33965	+	0.520365i	0.225159	+	0.0350830i
$221$	0.246883	−	0.427613i	0.0166071	−	0.0287644i
$222$	4.75048	+	8.22807i	0.318831	+	0.552232i
$223$			13.5885i			0.909951i	0.890504	+	0.454975i	$0.150352\pi$
$223$			13.5885i			0.909951i	−0.890504	+	0.454975i	$0.849648\pi$
$224$	2.64484	−	0.0694427i	0.176716	−	0.00463983i
$225$	2.25321			0.150214
$226$	7.27578	−	4.20068i	0.483978	−	0.279425i
$227$	−10.8318	+	18.7611i	−0.718929	+	1.24522i	0.242496	+	0.970152i	$0.422034\pi$
$227$	−10.8318	+	18.7611i	−0.718929	+	1.24522i	−0.961425	+	0.275069i	$0.911299\pi$
$228$	−0.420901	−	0.243007i	−0.0278748	−	0.0160935i
$229$	26.0355	−	15.0316i	1.72047	−	0.993317i	0.802527	−	0.596616i	$-0.203489\pi$
$229$	26.0355	−	15.0316i	1.72047	−	0.993317i	0.917948	−	0.396700i	$-0.129845\pi$
$230$	−0.484515			−0.0319480
$231$	−1.75091	+	13.5697i	−0.115201	+	0.892824i
$232$	1.89701			0.124545
$233$	14.0223	−	8.09580i	0.918633	−	0.530373i	0.0354345	−	0.999372i	$-0.488718\pi$
$233$	14.0223	−	8.09580i	0.918633	−	0.530373i	0.883199	+	0.468999i	$0.155385\pi$
$234$	−0.0823825	−	0.0475636i	−0.00538551	−	0.00310933i
$235$	−1.93556	+	3.35248i	−0.126262	+	0.218692i
$236$	5.40617	−	3.12126i	0.351912	−	0.203176i
$237$	10.9235			0.709558
$238$	−4.08175	−	6.65977i	−0.264581	−	0.431689i
$239$			26.0701i			1.68633i	0.537652	+	0.843167i	$0.319311\pi$
$239$			26.0701i			1.68633i	−0.537652	+	0.843167i	$0.680689\pi$
$240$	−0.794502	−	1.37612i	−0.0512849	−	0.0888280i
$241$	6.60221	−	11.4354i	0.425286	−	0.736617i	−0.571161	−	0.820838i	$-0.693507\pi$
$241$	6.60221	−	11.4354i	0.425286	−	0.736617i	0.996447	+	0.0842210i	$0.0268402\pi$
$242$	10.7480	−	2.34098i	0.690909	−	0.150484i
$243$	−5.04515	+	2.91282i	−0.323647	+	0.186858i
$244$	11.8792			0.760488
$245$	−0.374342	−	7.12381i	−0.0239159	−	0.455124i
$246$	15.9172			1.01485
$247$	0.0260654	+	0.0451466i	0.00165850	+	0.00287261i
$248$	1.27498	−	2.20834i	0.0809615	−	0.140229i
$249$	−19.8386	−	11.4538i	−1.25722	−	0.725855i
$250$	−4.56627	−	7.90901i	−0.288796	−	0.500210i
$251$		−	28.9829i		−	1.82939i	−0.404149	−	0.914693i	$-0.632432\pi$
$251$		−	28.9829i		−	1.82939i	0.404149	−	0.914693i	$-0.367568\pi$
$252$	−1.28305	+	0.786377i	−0.0808245	+	0.0495371i
$253$	−1.47070	+	0.568783i	−0.0924618	+	0.0357591i
$254$	−1.76662	−	3.05988i	−0.110848	−	0.191994i
$255$	−2.34562	+	4.06274i	−0.146889	+	0.254419i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.05007	−	3.49301i	0.377393	−	0.217888i	−0.299290	−	0.954162i	$-0.596750\pi$
$257$	6.05007	−	3.49301i	0.377393	−	0.217888i	0.676683	+	0.736274i	$0.263417\pi$
$258$			15.7830i			0.982605i
$259$	−14.1684	−	7.69151i	−0.880379	−	0.477927i
$260$			0.170440i			0.0105702i
$261$	−0.934431	+	0.539494i	−0.0578398	+	0.0333938i
$262$	12.1068	+	6.98984i	0.747958	+	0.431834i
$263$	−3.87174	−	2.23535i	−0.238741	−	0.137837i	0.375857	−	0.926678i	$-0.377348\pi$
$263$	−3.87174	−	2.23535i	−0.238741	−	0.137837i	−0.614598	+	0.788840i	$0.710682\pi$
$264$	−4.02708	−	3.24438i	−0.247850	−	0.199678i
$265$			8.58235i			0.527210i
$266$	0.824397	−	0.0216453i	0.0505470	−	0.00132716i
$267$	10.7602			0.658513
$268$	−5.19151	−	8.99196i	−0.317122	−	0.549272i
$269$	1.92024	+	1.10865i	0.117079	+	0.0675956i	0.557396	−	0.830247i	$-0.311801\pi$
$269$	1.92024	+	1.10865i	0.117079	+	0.0675956i	−0.440317	+	0.897842i	$0.645134\pi$
$270$	4.91107	+	2.83541i	0.298878	+	0.172557i
$271$	11.2561	+	19.4961i	0.683759	+	1.18431i	0.973825	+	0.227299i	$0.0729893\pi$
$271$	11.2561	+	19.4961i	0.683759	+	1.18431i	−0.290066	+	0.957007i	$0.593677\pi$
$272$	2.95232			0.179011
$273$	−0.689713	+	0.0181091i	−0.0417433	+	0.00109601i
$274$			7.01058i			0.423524i
$275$	−10.2314	−	8.24279i	−0.616974	−	0.497059i
$276$	0.642003	+	0.370660i	0.0386440	+	0.0223111i
$277$	−21.1880	−	12.2329i	−1.27306	−	0.735004i	−0.297500	−	0.954722i	$-0.596153\pi$
$277$	−21.1880	−	12.2329i	−1.27306	−	0.735004i	−0.975563	+	0.219718i	$0.929486\pi$
$278$	−9.92591	+	5.73073i	−0.595317	+	0.343706i
$279$			1.45038i			0.0868319i
$280$	2.36961	+	1.28638i	0.141611	+	0.0768759i
$281$			11.3532i			0.677273i	0.940917	+	0.338636i	$0.109966\pi$
$281$			11.3532i			0.677273i	−0.940917	+	0.338636i	$0.890034\pi$
$282$	5.12939	−	2.96145i	0.305451	−	0.176352i
$283$	10.8268	−	18.7526i	0.643589	−	1.11473i	−0.341037	−	0.940050i	$-0.610778\pi$
$283$	10.8268	−	18.7526i	0.643589	−	1.11473i	0.984626	−	0.174679i	$-0.0558886\pi$
$284$	7.26030	−	12.5752i	0.430819	−	0.746201i
$285$	−0.247646	−	0.428936i	−0.0146693	−	0.0254080i
$286$	0.200083	+	0.517352i	0.0118312	+	0.0305916i
$287$	−23.0278	+	14.1137i	−1.35929	+	0.833102i
$288$		−	0.568783i		−	0.0335159i
$289$	4.14191	+	7.17400i	0.243642	+	0.422000i
$290$	1.67422	+	0.966613i	0.0983138	+	0.0567615i
$291$	−8.59279	+	14.8831i	−0.503718	+	0.872465i
$292$	4.85385	+	8.40712i	0.284050	+	0.491990i
$293$	12.1233			0.708249			0.354124	−	0.935198i	$-0.384779\pi$
$293$	12.1233			0.708249			0.354124	+	0.935198i	$0.384779\pi$
$294$	−4.95379	+	9.72572i	−0.288911	+	0.567215i
$295$	6.36169			0.370392
$296$	5.27699	−	3.04667i	0.306719	−	0.177084i
$297$	18.2356	+	2.84136i	1.05814	+	0.164873i
$298$	−7.07841	+	12.2602i	−0.410041	+	0.710213i
$299$	−0.0397577	−	0.0688624i	−0.00229925	−	0.00398242i
$300$			6.17684i			0.356620i
$301$	−13.9946	−	22.8335i	−0.806636	−	1.31610i
$302$	−23.3040			−1.34100
$303$	−7.20410	+	4.15929i	−0.413865	+	0.238945i
$304$	−0.155850	+	0.269940i	−0.00893862	+	0.0154821i
$305$	10.4841	+	6.05300i	0.600318	+	0.346594i
$306$	−1.45426	+	0.839615i	−0.0831343	+	0.0479976i
$307$	9.65817			0.551221			0.275610	−	0.961269i	$-0.411120\pi$
$307$	9.65817			0.551221			0.275610	+	0.961269i	$0.411120\pi$
$308$	8.70282	+	1.12293i	0.495889	+	0.0639848i
$309$	−19.4176			−1.10463
$310$	2.25050	−	1.29932i	0.127820	−	0.0737967i
$311$	−15.3094	−	8.83890i	−0.868118	−	0.501208i	−0.00139530	−	0.999999i	$-0.500444\pi$
$311$	−15.3094	−	8.83890i	−0.868118	−	0.501208i	−0.866722	+	0.498791i	$0.833777\pi$
$312$	0.130388	−	0.225839i	0.00738179	−	0.0127856i
$313$	−24.9505	+	14.4052i	−1.41028	+	0.814228i	−0.995415	−	0.0956530i	$-0.969506\pi$
$313$	−24.9505	+	14.4052i	−1.41028	+	0.814228i	−0.414869	+	0.909881i	$0.636173\pi$
$314$	−4.03261			−0.227573
$315$	−1.53306	+	0.0402519i	−0.0863782	+	0.00226794i
$316$		−	7.00567i		−	0.394100i
$317$	−5.17280	−	8.95955i	−0.290533	−	0.503218i	0.683403	−	0.730042i	$-0.260499\pi$
$317$	−5.17280	−	8.95955i	−0.290533	−	0.503218i	−0.973936	+	0.226823i	$0.927166\pi$
$318$	6.56561	−	11.3720i	0.368181	−	0.637708i
$319$	6.21666	+	0.968644i	0.348066	+	0.0542337i
$320$	−0.882559	+	0.509546i	−0.0493366	+	0.0284845i
$321$	11.3109			0.631314
$322$	−1.25746	+	0.0330157i	−0.0700754	+	0.00183989i
$323$	0.920239			0.0512034
$324$	−3.48507	−	6.03631i	−0.193615	−	0.335351i
$325$	0.331270	−	0.573776i	0.0183755	−	0.0318274i
$326$	−4.79768	−	2.76994i	−0.265719	−	0.153413i
$327$	0.910151	+	1.57643i	0.0503315	+	0.0871766i
$328$		−	10.2084i		−	0.563662i
$329$	−4.79489	+	8.83257i	−0.264351	+	0.486955i
$330$	−1.90098	−	4.91534i	−0.104646	−	0.270580i
$331$	13.4224	+	23.2483i	0.737763	+	1.27784i	0.953500	+	0.301392i	$0.0974512\pi$
$331$	13.4224	+	23.2483i	0.737763	+	1.27784i	−0.215737	+	0.976451i	$0.569215\pi$
$332$	−7.34577	+	12.7233i	−0.403152	+	0.698279i
$333$	−1.73290	+	3.00147i	−0.0949622	+	0.164479i
$334$	−18.3815	+	10.6126i	−1.00579	+	0.580694i
$335$		−	10.5813i		−	0.578116i
$336$	−2.15574	−	3.51729i	−0.117605	−	0.191884i
$337$		−	14.5505i		−	0.792614i	−0.918118	−	0.396307i	$-0.870292\pi$
$337$		−	14.5505i		−	0.792614i	0.918118	−	0.396307i	$-0.129708\pi$
$338$	11.2341	−	6.48601i	0.611055	−	0.352793i
$339$	−11.3447	−	6.54984i	−0.616158	−	0.355739i
$340$	2.60560	+	1.50434i	0.141308	+	0.0815844i
$341$	5.30584	−	6.58587i	0.287327	−	0.356645i
$342$		−	0.177290i		−	0.00958674i
$343$	−1.45696	−	18.4629i	−0.0786683	−	0.996901i
$344$	10.1222			0.545755
$345$	0.377737	+	0.654259i	0.0203367	+	0.0352241i
$346$	13.0471	+	7.53277i	0.701418	+	0.404964i
$347$	−24.7179	−	14.2709i	−1.32693	−	0.766101i	−0.342102	−	0.939663i	$-0.611139\pi$
$347$	−24.7179	−	14.2709i	−1.32693	−	0.766101i	−0.984823	+	0.173562i	$0.944472\pi$
$348$	−1.47894	−	2.56161i	−0.0792797	−	0.137316i
$349$	−34.6026			−1.85224			−0.926118	−	0.377235i	$-0.876875\pi$
$349$	−34.6026			−1.85224			−0.926118	+	0.377235i	$0.876875\pi$
$350$	−5.47694	−	8.93615i	−0.292755	−	0.477658i
$351$			0.930656i			0.0496748i
$352$	−2.08075	+	2.58273i	−0.110904	+	0.137660i
$353$	−14.6534	−	8.46017i	−0.779924	−	0.450289i	0.0564792	−	0.998404i	$-0.482013\pi$
$353$	−14.6534	−	8.46017i	−0.779924	−	0.450289i	−0.836403	+	0.548114i	$0.815346\pi$
$354$	−8.42950	−	4.86677i	−0.448023	−	0.258666i
$355$	12.8153	−	7.39891i	0.680164	−	0.392693i
$356$		−	6.90094i		−	0.365749i
$357$	−5.81073	+	10.7038i	−0.307537	+	0.566507i
$358$			2.16176i			0.114252i
$359$	26.2848	−	15.1755i	1.38726	−	0.800934i	0.394254	−	0.919002i	$-0.371003\pi$
$359$	26.2848	−	15.1755i	1.38726	−	0.800934i	0.993006	+	0.118067i	$0.0376698\pi$
$360$	0.289821	−	0.501985i	0.0152749	−	0.0264569i
$361$	9.45142	−	16.3703i	0.497443	−	0.861597i
$362$	−2.69643	−	4.67035i	−0.141721	−	0.245468i
$363$	−11.5405	−	12.6884i	−0.605717	−	0.665968i
$364$	0.0116141	+	0.442341i	0.000608742	+	0.0231849i
$365$			9.89304i			0.517825i
$366$	−9.26124	−	16.0409i	−0.484093	−	0.838474i
$367$	−15.0875	−	8.71075i	−0.787559	−	0.454698i	0.0515432	−	0.998671i	$-0.483586\pi$
$367$	−15.0875	−	8.71075i	−0.787559	−	0.454698i	−0.839103	+	0.543973i	$0.816919\pi$
$368$	0.237719	−	0.411742i	0.0123920	−	0.0214635i
$369$	2.90317	+	5.02844i	0.151133	+	0.261770i
$370$	6.20968			0.322826
$371$	0.584817	+	22.2737i	0.0303622	+	1.15639i
$372$	−3.97600			−0.206146
$373$	7.92596	−	4.57606i	0.410391	−	0.236939i	−0.280567	−	0.959834i	$-0.590522\pi$
$373$	7.92596	−	4.57606i	0.410391	−	0.236939i	0.690958	+	0.722895i	$0.257189\pi$
$374$	9.67499	+	1.50750i	0.500282	+	0.0779511i
$375$	−7.11989	+	12.3320i	−0.367670	+	0.636822i
$376$	−1.89930	−	3.28968i	−0.0979488	−	0.169652i
$377$			0.317269i			0.0163402i
$378$	12.9389	+	7.02406i	0.665503	+	0.361278i
$379$	−6.15382			−0.316100			−0.158050	−	0.987431i	$-0.550521\pi$
$379$	−6.15382			−0.316100			−0.158050	+	0.987431i	$0.550521\pi$
$380$	−0.275094	+	0.158826i	−0.0141120	+	0.00814758i
$381$	−2.75458	+	4.77107i	−0.141121	+	0.244429i
$382$	5.19615	+	3.00000i	0.265858	+	0.153493i
$383$	11.2281	−	6.48253i	0.573728	−	0.331242i	−0.184909	−	0.982756i	$-0.559199\pi$
$383$	11.2281	−	6.48253i	0.573728	−	0.331242i	0.758637	+	0.651514i	$0.225866\pi$
$384$	1.55924			0.0795694
$385$	7.10857	+	5.42553i	0.362286	+	0.276511i
$386$	−9.59958			−0.488606
$387$	−4.98603	+	2.87868i	−0.253454	+	0.146332i
$388$	9.54515	+	5.51090i	0.484582	+	0.279773i
$389$	−2.58323	+	4.47429i	−0.130975	+	0.226856i	−0.924053	−	0.382265i	$-0.875144\pi$
$389$	−2.58323	+	4.47429i	−0.130975	+	0.226856i	0.793078	+	0.609121i	$0.208477\pi$
$390$	0.230151	−	0.132878i	0.0116542	−	0.00672853i
$391$	−1.40365			−0.0709854
$392$	6.23749	+	3.17706i	0.315041	+	0.160466i
$393$		−	21.7976i		−	1.09954i
$394$	7.40901	+	12.8328i	0.373261	+	0.646506i
$395$	3.56971	−	6.18292i	0.179612	−	0.311097i
$396$	0.290430	−	1.86395i	0.0145947	−	0.0936670i
$397$	8.01690	−	4.62856i	0.402357	−	0.232301i	−0.285144	−	0.958485i	$-0.592041\pi$
$397$	8.01690	−	4.62856i	0.402357	−	0.232301i	0.687500	+	0.726184i	$0.258708\pi$
$398$	−4.11030			−0.206030
$399$	−0.671943	−	1.09634i	−0.0336392	−	0.0548856i
$400$	3.96145			0.198073
$401$	15.4624	+	26.7816i	0.772155	+	1.33741i	0.936380	+	0.350988i	$0.114154\pi$
$401$	15.4624	+	26.7816i	0.772155	+	1.33741i	−0.164225	+	0.986423i	$0.552512\pi$
$402$	−8.09479	+	14.0206i	−0.403732	+	0.699284i
$403$	0.369337	+	0.213237i	0.0183980	+	0.0106221i
$404$	2.66752	+	4.62028i	0.132714	+	0.229867i
$405$		−	7.10320i		−	0.352961i
$406$	4.41097	+	2.39456i	0.218913	+	0.118840i
$407$	18.8488	−	7.28968i	0.934301	−	0.361336i
$408$	−2.30168	−	3.98663i	−0.113950	−	0.197367i
$409$	−11.9198	+	20.6458i	−0.589399	+	1.02087i	0.404913	+	0.914355i	$0.367302\pi$
$409$	−11.9198	+	20.6458i	−0.589399	+	1.02087i	−0.994311	+	0.106513i	$0.966031\pi$
$410$	5.20162	−	9.00947i	0.256890	−	0.444946i
$411$	9.46665	−	5.46557i	0.466955	−	0.269597i
$412$			12.4533i			0.613529i
$413$	16.5104	−	0.433497i	0.812426	−	0.0213310i
$414$			0.270422i			0.0132905i
$415$	−12.9662	+	7.48601i	−0.636484	+	0.367474i
$416$	−0.144840	−	0.0836233i	−0.00710136	−	0.00409997i
$417$	15.4768	+	8.93556i	0.757904	+	0.437576i
$418$	−0.648570	+	0.805037i	−0.0317226	+	0.0393757i
$419$		−	5.03426i		−	0.245940i	−0.992410	−	0.122970i	$-0.960758\pi$
$419$		−	5.03426i		−	0.245940i	0.992410	−	0.122970i	$-0.0392418\pi$
$420$	−0.110345	−	4.20266i	−0.00538427	−	0.205069i
$421$	−16.9250			−0.824872			−0.412436	−	0.910987i	$-0.635322\pi$
$421$	−16.9250			−0.824872			−0.412436	+	0.910987i	$0.635322\pi$
$422$	−3.76228	−	6.51646i	−0.183145	−	0.317216i
$423$	1.87112	+	1.08029i	0.0909767	+	0.0525254i
$424$	−7.29330	−	4.21079i	−0.354194	−	0.204494i
$425$	−5.84773	−	10.1286i	−0.283657	−	0.491308i
$426$	−22.6410			−1.09696
$427$	27.6218	+	14.9949i	1.33671	+	0.725654i
$428$		−	7.25414i		−	0.350642i
$429$	0.542611	−	0.673516i	0.0261975	−	0.0325177i
$430$	8.93348	+	5.15775i	0.430811	+	0.248729i
$431$	−5.19535	−	2.99953i	−0.250251	−	0.144482i	0.369628	−	0.929180i	$-0.379485\pi$
$431$	−5.19535	−	2.99953i	−0.250251	−	0.144482i	−0.619879	+	0.784697i	$0.712818\pi$
$432$	−4.81906	+	2.78229i	−0.231857	+	0.133863i
$433$			36.1175i			1.73570i	0.496829	+	0.867849i	$0.334498\pi$
$433$			36.1175i			1.73570i	−0.496829	+	0.867849i	$0.665502\pi$
$434$	5.75216	−	3.52548i	0.276112	−	0.169228i
$435$		−	3.01436i		−	0.144527i
$436$	1.01103	−	0.583716i	0.0484193	−	0.0279549i
$437$	0.0740971	−	0.128340i	0.00354455	−	0.00613934i
$438$	7.56830	−	13.1087i	0.361627	−	0.626357i
$439$	5.67481	+	9.82906i	0.270844	+	0.469116i	0.969078	−	0.246754i	$-0.0793639\pi$
$439$	5.67481	+	9.82906i	0.270844	+	0.469116i	−0.698234	+	0.715869i	$0.746031\pi$
$440$	−3.15240	+	1.21917i	−0.150285	+	0.0581219i
$441$	−3.97600	+	0.208931i	−0.189333	+	0.00994909i
$442$			0.493765i			0.0234860i
$443$	2.37538	+	4.11428i	0.112858	+	0.195475i	0.916921	−	0.399068i	$-0.130666\pi$
$443$	2.37538	+	4.11428i	0.112858	+	0.195475i	−0.804064	+	0.594543i	$0.797333\pi$
$444$	−8.22807	−	4.75048i	−0.390487	−	0.225448i
$445$	3.51634	−	6.09048i	0.166691	−	0.288717i
$446$	−6.79423	−	11.7680i	−0.321716	−	0.557229i
$447$	22.0738			1.04406
$448$	−2.25578	+	1.38256i	−0.106575	+	0.0653198i
$449$	7.33297			0.346064			0.173032	−	0.984916i	$-0.444644\pi$
$449$	7.33297			0.346064			0.173032	+	0.984916i	$0.444644\pi$
$450$	−1.95134	+	1.12660i	−0.0919869	+	0.0531086i
$451$	5.21255	−	33.4536i	0.245449	−	1.57527i
$452$	−4.20068	+	7.27578i	−0.197583	+	0.342224i
$453$	18.1682	+	31.4683i	0.853619	+	1.47851i
$454$		−	21.6635i		−	1.01672i
$455$	−0.215143	+	0.396310i	−0.0100860	+	0.0185793i
$456$	0.486014			0.0227597
$457$	−11.7066	+	6.75879i	−0.547610	+	0.316163i	−0.748158	−	0.663521i	$-0.769061\pi$
$457$	−11.7066	+	6.75879i	−0.547610	+	0.316163i	0.200547	+	0.979684i	$0.435728\pi$
$458$	−15.0316	+	26.0355i	−0.702381	+	1.21656i
$459$	14.2274	+	8.21420i	0.664079	+	0.383406i
$460$	0.419602	−	0.242258i	0.0195641	−	0.0112953i
$461$	−18.5730			−0.865033			−0.432516	−	0.901626i	$-0.642374\pi$
$461$	−18.5730			−0.865033			−0.432516	+	0.901626i	$0.642374\pi$
$462$	−5.26854	−	12.6272i	−0.245115	−	0.587470i
$463$	28.2849			1.31451			0.657256	−	0.753667i	$-0.271717\pi$
$463$	28.2849			1.31451			0.657256	+	0.753667i	$0.271717\pi$
$464$	−1.64286	+	0.948505i	−0.0762678	+	0.0440332i
$465$	−3.50905	−	2.02595i	−0.162728	−	0.0939513i
$466$	−8.09580	+	14.0223i	−0.375030	+	0.649572i
$467$	−18.6881	+	10.7896i	−0.864782	+	0.499282i	−0.865611	−	0.500717i	$-0.833070\pi$
$467$	−18.6881	+	10.7896i	−0.864782	+	0.499282i	0.000828665		1.00000i	$0.499736\pi$
$468$	0.0951271			0.00439725
$469$	−0.721025	−	27.4614i	−0.0332938	−	1.26805i
$470$		−	3.87112i		−	0.178561i
$471$	3.14389	+	5.44538i	0.144863	+	0.250910i
$472$	−3.12126	+	5.40617i	−0.143667	+	0.248839i
$473$	33.1714	+	5.16859i	1.52522	+	0.237652i
$474$	−9.46003	+	5.46175i	−0.434513	+	0.250866i
$475$	1.23479			0.0566559
$476$	6.86479	+	3.72665i	0.314647	+	0.170811i
$477$	4.79005			0.219321
$478$	−13.0350	−	22.5774i	−0.596209	−	1.03266i
$479$	−3.46780	+	6.00641i	−0.158448	+	0.274440i	−0.934309	−	0.356464i	$-0.883982\pi$
$479$	−3.46780	+	6.00641i	−0.158448	+	0.274440i	0.775861	+	0.630904i	$0.217316\pi$
$480$	1.37612	+	0.794502i	0.0628109	+	0.0362639i
$481$	0.509546	+	0.882559i	0.0232333	+	0.0402412i
$482$			13.2044i			0.601445i
$483$	1.02492	+	1.67225i	0.0466355	+	0.0760902i
$484$	−8.13757	+	7.40135i	−0.369889	+	0.336425i
$485$	5.61611	+	9.72738i	0.255014	+	0.441698i
$486$	2.91282	−	5.04515i	0.132128	−	0.228853i
$487$	6.08702	−	10.5430i	0.275829	−	0.477750i	−0.694515	−	0.719478i	$-0.744381\pi$
$487$	6.08702	−	10.5430i	0.275829	−	0.477750i	0.970344	+	0.241728i	$0.0777143\pi$
$488$	−10.2877	+	5.93960i	−0.465702	+	0.268873i
$489$			8.63798i			0.390623i
$490$	3.88610	+	5.98223i	0.175556	+	0.270250i
$491$			2.37152i			0.107025i	0.998567	+	0.0535125i	$0.0170417\pi$
$491$			2.37152i			0.107025i	−0.998567	+	0.0535125i	$0.982958\pi$
$492$	−13.7847	+	7.95862i	−0.621463	+	0.358802i
$493$	4.85024	+	2.80029i	0.218444	+	0.126119i
$494$	−0.0451466	−	0.0260654i	−0.00203124	−	0.00117274i
$495$	1.20609	−	1.49706i	0.0542097	−	0.0672878i
$496$			2.54997i			0.114497i
$497$	32.7552	−	20.0756i	1.46927	−	0.900513i
$498$	22.9076			1.02651
$499$	1.96446	+	3.40255i	0.0879413	+	0.152319i	0.906641	−	0.421903i	$-0.138638\pi$
$499$	1.96446	+	3.40255i	0.0879413	+	0.152319i	−0.818699	+	0.574222i	$0.805305\pi$
$500$	7.90901	+	4.56627i	0.353702	+	0.204210i
$501$	28.6611	+	16.5475i	1.28048	+	0.739288i
$502$	14.4915	+	25.1000i	0.646786	+	1.12027i
$503$	−19.8703			−0.885971			−0.442986	−	0.896529i	$-0.646081\pi$
$503$	−19.8703			−0.885971			−0.442986	+	0.896529i	$0.646081\pi$
$504$	0.717964	−	1.32255i	0.0319807	−	0.0589109i
$505$			5.43689i			0.241938i
$506$	0.989268	−	1.22793i	0.0439783	−	0.0545881i
$507$	−17.5166	−	10.1132i	−0.777940	−	0.449144i
$508$	3.05988	+	1.76662i	0.135760	+	0.0783812i
$509$	13.2438	−	7.64634i	0.587023	−	0.338918i	−0.176896	−	0.984229i	$-0.556606\pi$
$509$	13.2438	−	7.64634i	0.587023	−	0.338918i	0.763920	+	0.645312i	$0.223272\pi$
$510$		−	4.69125i		−	0.207732i
$511$	0.674129	+	25.6753i	0.0298217	+	1.13581i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.50210	+	0.867240i	−0.0663195	+	0.0382896i
$514$	−3.49301	+	6.05007i	−0.154070	+	0.266857i
$515$	−6.34552	+	10.9908i	−0.279617	+	0.484311i
$516$	−7.89149	−	13.6685i	−0.347403	−	0.601720i
$517$	−4.54439	−	11.7504i	−0.199862	−	0.516780i
$518$	16.1159	−	0.423138i	0.708093	−	0.0185916i
$519$		−	23.4907i		−	1.03113i
$520$	−0.0852198	−	0.147605i	−0.00373714	−	0.00647291i
$521$	−0.121861	−	0.0703565i	−0.00533883	−	0.00308237i	0.497328	−	0.867562i	$-0.334314\pi$
$521$	−0.121861	−	0.0703565i	−0.00533883	−	0.00308237i	−0.502667	+	0.864480i	$0.667648\pi$
$522$	0.539494	−	0.934431i	0.0236130	−	0.0408989i
$523$	−4.56153	−	7.90081i	−0.199462	−	0.345478i	0.748892	−	0.662692i	$-0.230586\pi$
$523$	−4.56153	−	7.90081i	−0.199462	−	0.345478i	−0.948354	+	0.317214i	$0.897253\pi$
$524$	−13.9797			−0.610705
$525$	−7.79691	+	14.3625i	−0.340285	+	0.626831i
$526$	4.47070			0.194932
$527$	6.51971	−	3.76416i	0.284003	−	0.163969i
$528$	5.10974	+	0.796171i	0.222373	+	0.0346489i
$529$	11.3870	−	19.7228i	0.495086	−	0.857514i
$530$	−4.29118	−	7.43253i	−0.186397	−	0.322849i
$531$		−	3.55064i		−	0.154085i
$532$	−0.703126	+	0.430944i	−0.0304844	+	0.0186838i
$533$	1.70731			0.0739519
$534$	−9.31859	+	5.38009i	−0.403255	+	0.232819i
$535$	3.69632	−	6.40221i	0.159806	−	0.276792i
$536$	8.99196	+	5.19151i	0.388394	+	0.224239i
$537$	2.91910	−	1.68534i	0.125969	−	0.0727280i
$538$	−2.21730			−0.0955946
$539$	18.8185	+	13.5965i	0.810571	+	0.585641i
$540$	−5.67081			−0.244033
$541$	−21.6730	+	12.5129i	−0.931797	+	0.537973i	−0.887379	−	0.461040i	$-0.847476\pi$
$541$	−21.6730	+	12.5129i	−0.931797	+	0.537973i	−0.0444172	+	0.999013i	$0.514143\pi$
$542$	−19.4961	−	11.2561i	−0.837430	−	0.483491i
$543$	−4.20437	+	7.28217i	−0.180427	+	0.312508i
$544$	−2.55678	+	1.47616i	−0.109621	+	0.0632898i
$545$	1.18972			0.0509620
$546$	0.588255	−	0.360540i	0.0251750	−	0.0154297i
$547$		−	36.7246i		−	1.57023i	−0.619348	−	0.785116i	$-0.712603\pi$
$547$		−	36.7246i		−	1.57023i	0.619348	−	0.785116i	$-0.287397\pi$
$548$	−3.50529	−	6.07134i	−0.149738	−	0.259355i
$549$	3.37835	−	5.85147i	0.144184	−	0.249735i
$550$	12.9820	+	2.02278i	0.553555	+	0.0862517i
$551$	−0.512080	+	0.295649i	−0.0218153	+	0.0125951i
$552$	−0.741321			−0.0315527
$553$	8.84313	−	16.2897i	0.376048	−	0.692710i
$554$	24.4658			1.03945
$555$	−4.84117	−	8.38516i	−0.205496	−	0.355930i
$556$	5.73073	−	9.92591i	0.243037	−	0.420952i
$557$	−33.5815	−	19.3883i	−1.42290	−	0.821509i	−0.426350	−	0.904558i	$-0.640201\pi$
$557$	−33.5815	−	19.3883i	−1.42290	−	0.821509i	−0.996545	+	0.0830490i	$0.973534\pi$
$558$	−0.725189	−	1.25606i	−0.0306997	−	0.0531735i
$559$			1.69291i			0.0716025i
$560$	−2.69533	+	0.0707684i	−0.113899	+	0.00299051i
$561$	−5.50716	−	14.2398i	−0.232512	−	0.601204i
$562$	−5.67658	−	9.83212i	−0.239452	−	0.414743i
$563$	−21.6247	+	37.4550i	−0.911371	+	1.57854i	−0.0992415	+	0.995063i	$0.531642\pi$
$563$	−21.6247	+	37.4550i	−0.911371	+	1.57854i	−0.812129	+	0.583477i	$0.801692\pi$
$564$	−2.96145	+	5.12939i	−0.124700	+	0.215986i
$565$	−7.41469	+	4.28087i	−0.311938	+	0.180098i
$566$			21.6537i			0.910172i
$567$	−0.484025	−	18.4349i	−0.0203271	−	0.774193i
$568$			14.5206i			0.609270i
$569$	−18.4783	+	10.6685i	−0.774651	+	0.447245i	−0.834531	−	0.550961i	$-0.814261\pi$
$569$	−18.4783	+	10.6685i	−0.774651	+	0.447245i	0.0598803	+	0.998206i	$0.480928\pi$
$570$	0.428936	+	0.247646i	0.0179662	+	0.0103728i
$571$	19.5677	+	11.2974i	0.818883	+	0.472782i	0.850031	−	0.526733i	$-0.176583\pi$
$571$	19.5677	+	11.2974i	0.818883	+	0.472782i	−0.0311482	+	0.999515i	$0.509916\pi$
$572$	−0.431953	−	0.347998i	−0.0180608	−	0.0145505i
$573$		−	9.35542i		−	0.390828i
$574$	12.8858	−	23.7367i	0.537843	−	0.990749i
$575$	−1.88343			−0.0785443
$576$	0.284392	+	0.492581i	0.0118497	+	0.0205242i
$577$	−29.3358	−	16.9370i	−1.22126	−	0.705097i	−0.256077	−	0.966656i	$-0.582430\pi$
$577$	−29.3358	−	16.9370i	−1.22126	−	0.705097i	−0.965187	+	0.261559i	$0.915763\pi$
$578$	−7.17400	−	4.14191i	−0.298399	−	0.172281i
$579$	7.48400	+	12.9627i	0.311025	+	0.538710i
$580$	−1.93323			−0.0802729
$581$	−33.1409	+	20.3119i	−1.37491	+	0.842681i
$582$		−	17.1856i		−	0.712365i
$583$	−21.7506	−	17.5232i	−0.900819	−	0.725736i
$584$	−8.40712	−	4.85385i	−0.347889	−	0.200854i
$585$	0.0839553	+	0.0484716i	0.00347112	+	0.00200405i
$586$	−10.4991	+	6.06163i	−0.433712	+	0.250404i
$587$		−	6.07819i		−	0.250874i	−0.992102	−	0.125437i	$-0.959967\pi$
$587$		−	6.07819i		−	0.250874i	0.992102	−	0.125437i	$-0.0400332\pi$
$588$	−0.572753	−	10.8996i	−0.0236200	−	0.449492i
$589$			0.794825i			0.0327502i
$590$	−5.50939	+	3.18085i	−0.226818	+	0.130953i
$591$	11.5524	−	20.0093i	0.475202	−	0.823074i
$592$	−3.04667	+	5.27699i	−0.125217	+	0.216883i
$593$	−0.809196	−	1.40157i	−0.0332297	−	0.0575555i	0.848932	−	0.528502i	$-0.177246\pi$
$593$	−0.809196	−	1.40157i	−0.0332297	−	0.0575555i	−0.882162	+	0.470946i	$0.843913\pi$
$594$	−17.2132	+	6.65709i	−0.706264	+	0.273144i
$595$	4.15968	+	6.78692i	0.170530	+	0.278236i
$596$		−	14.1568i		−	0.579886i
$597$	3.20446	+	5.55029i	0.131150	+	0.227158i
$598$	0.0688624	+	0.0397577i	0.00281599	+	0.00162581i
$599$	−2.63955	+	4.57184i	−0.107849	+	0.186800i	−0.914899	−	0.403684i	$-0.867730\pi$
$599$	−2.63955	+	4.57184i	−0.107849	+	0.186800i	0.807050	+	0.590484i	$0.201063\pi$
$600$	−3.08842	−	5.34930i	−0.126084	−	0.218384i
$601$	−32.7945			−1.33771			−0.668857	−	0.743391i	$-0.733216\pi$
$601$	−32.7945			−1.33771			−0.668857	+	0.743391i	$0.733216\pi$
$602$	23.5365	+	12.7771i	0.959274	+	0.520756i
$603$	−5.90569			−0.240498
$604$	20.1819	−	11.6520i	0.821189	−	0.474114i
$605$	−10.9532	+	2.38567i	−0.445311	+	0.0969912i
$606$	4.15929	−	7.20410i	0.168960	−	0.292647i
$607$	0.332910	+	0.576616i	0.0135124	+	0.0234041i	0.872703	−	0.488252i	$-0.162365\pi$
$607$	0.332910	+	0.576616i	0.0135124	+	0.0234041i	−0.859190	+	0.511656i	$0.829032\pi$
$608$		−	0.311700i		−	0.0126411i
$609$	−0.205404	−	7.82314i	−0.00832337	−	0.317009i
$610$	−12.1060			−0.490158
$611$	0.550188	−	0.317651i	0.0222582	−	0.0128508i
$612$	0.839615	−	1.45426i	0.0339394	−	0.0587848i
$613$	3.71908	+	2.14721i	0.150212	+	0.0867251i	0.573222	−	0.819400i	$-0.305693\pi$
$613$	3.71908	+	2.14721i	0.150212	+	0.0867251i	−0.423010	+	0.906125i	$0.639027\pi$
$614$	−8.36422	+	4.82908i	−0.337552	+	0.194886i
$615$	−16.2211			−0.654098
$616$	−8.09833	+	3.37892i	−0.326291	+	0.136141i
$617$	−30.9913			−1.24766			−0.623831	−	0.781559i	$-0.714425\pi$
$617$	−30.9913			−1.24766			−0.623831	+	0.781559i	$0.714425\pi$
$618$	16.8161	−	9.70880i	0.676444	−	0.390545i
$619$	−0.685357	−	0.395691i	−0.0275468	−	0.0159042i	0.486163	−	0.873868i	$-0.338396\pi$
$619$	−0.685357	−	0.395691i	−0.0275468	−	0.0159042i	−0.513710	+	0.857964i	$0.671729\pi$
$620$	−1.29932	+	2.25050i	−0.0521821	+	0.0903821i
$621$	2.29117	−	1.32281i	0.0919414	−	0.0530824i
$622$	17.6778			0.708815
$623$	8.71092	−	16.0462i	0.348996	−	0.642877i
$624$			0.260777i			0.0104394i
$625$	−5.25019	−	9.09359i	−0.210007	−	0.363744i
$626$	14.4052	−	24.9505i	0.575746	−	0.997222i
$627$	1.59271	+	0.248167i	0.0636067	+	0.00991083i
$628$	3.49234	−	2.01630i	0.139360	−	0.0804593i
$629$	17.9895			0.717288
$630$	1.30754	−	0.801390i	0.0520938	−	0.0319281i
$631$	−34.3677			−1.36816			−0.684078	−	0.729409i	$-0.739795\pi$
$631$	−34.3677			−1.36816			−0.684078	+	0.729409i	$0.739795\pi$
$632$	3.50284	+	6.06709i	0.139335	+	0.241336i
$633$	−5.86628	+	10.1607i	−0.233164	+	0.403852i
$634$	8.95955	+	5.17280i	0.355829	+	0.205438i
$635$	1.80035	+	3.11830i	0.0714447	+	0.123746i
$636$			13.1312i			0.520687i
$637$	−0.531353	+	1.04320i	−0.0210530	+	0.0413331i
$638$	−5.86811	+	2.26946i	−0.232321	+	0.0898488i
$639$	−4.12954	−	7.15257i	−0.163362	−	0.282951i
$640$	0.509546	−	0.882559i	0.0201416	−	0.0348862i
$641$	−2.47939	+	4.29443i	−0.0979301	+	0.169620i	−0.910828	−	0.412787i	$-0.864556\pi$
$641$	−2.47939	+	4.29443i	−0.0979301	+	0.169620i	0.812898	+	0.582407i	$0.197889\pi$
$642$	−9.79554	+	5.65546i	−0.386599	+	0.223203i
$643$		−	48.1404i		−	1.89847i	−0.314562	−	0.949237i	$-0.601858\pi$
$643$		−	48.1404i		−	1.89847i	0.314562	−	0.949237i	$-0.398142\pi$
$644$	1.07248	−	0.657322i	0.0422618	−	0.0259021i
$645$		−	16.0843i		−	0.633318i
$646$	−0.796950	+	0.460119i	−0.0313556	+	0.0181031i
$647$	−2.74160	−	1.58286i	−0.107783	−	0.0622287i	0.445139	−	0.895461i	$-0.353154\pi$
$647$	−2.74160	−	1.58286i	−0.107783	−	0.0622287i	−0.552923	+	0.833233i	$0.686487\pi$
$648$	6.03631	+	3.48507i	0.237129	+	0.136906i
$649$	−12.9891	+	16.1227i	−0.509867	+	0.632872i
$650$			0.662540i			0.0259869i
$651$	−9.24507	−	5.01883i	−0.362343	−	0.196703i
$652$	5.53988			0.216958
$653$	11.0606	+	19.1575i	0.432833	+	0.749689i	0.997116	−	0.0758922i	$-0.0241805\pi$
$653$	11.0606	+	19.1575i	0.432833	+	0.749689i	−0.564283	+	0.825582i	$0.690847\pi$
$654$	−1.57643	−	0.910151i	−0.0616432	−	0.0355897i
$655$	−12.3379	−	7.12329i	−0.482081	−	0.278330i
$656$	5.10418	+	8.84069i	0.199285	+	0.345171i
$657$	5.52158			0.215417
$658$	−0.263785	−	10.0467i	−0.0102834	−	0.391660i
$659$			24.6258i			0.959286i	0.877464	+	0.479643i	$0.159234\pi$
$659$			24.6258i			0.959286i	−0.877464	+	0.479643i	$0.840766\pi$
$660$	4.10397	+	3.30632i	0.159747	+	0.128698i
$661$	24.0205	+	13.8682i	0.934289	+	0.539412i	0.888166	−	0.459524i	$-0.151980\pi$
$661$	24.0205	+	13.8682i	0.934289	+	0.539412i	0.0461236	+	0.998936i	$0.485313\pi$
$662$	−23.2483	−	13.4224i	−0.903572	−	0.521677i
$663$	0.666750	−	0.384948i	0.0258944	−	0.0149502i
$664$		−	14.6915i		−	0.570143i
$665$	−0.840136	+	0.0220585i	−0.0325791	+	0.000855394i
$666$		−	3.46579i		−	0.134297i
$667$	0.781078	−	0.450956i	0.0302435	−	0.0174611i
$668$	10.6126	−	18.3815i	0.410613	−	0.711202i
$669$	−10.5938	+	18.3490i	−0.409580	+	0.709414i
$670$	5.29063	+	9.16363i	0.204395	+	0.354022i
$671$	−36.7465	+	14.2115i	−1.41858	+	0.548629i
$672$	3.62557	+	1.96819i	0.139859	+	0.0759247i
$673$			15.9518i			0.614897i	0.951565	+	0.307449i	$0.0994752\pi$
$673$			15.9518i			0.614897i	−0.951565	+	0.307449i	$0.900525\pi$
$674$	7.27523	+	12.6011i	0.280231	+	0.485375i
$675$	19.0905	+	11.0219i	0.734793	+	0.424233i
$676$	−6.48601	+	11.2341i	−0.249462	+	0.432081i
$677$	7.52574	+	13.0350i	0.289238	+	0.500974i	0.973628	−	0.228141i	$-0.0732649\pi$
$677$	7.52574	+	13.0350i	0.289238	+	0.500974i	−0.684390	+	0.729116i	$0.739932\pi$
$678$	13.0997			0.503091
$679$	15.2383	+	24.8627i	0.584792	+	0.954143i
$680$	−3.00868			−0.115378
$681$	−29.2531	+	16.8893i	−1.12098	+	0.647198i
$682$	−1.30205	+	8.35645i	−0.0498582	+	0.319985i
$683$	2.64673	−	4.58427i	0.101274	−	0.175412i	−0.810936	−	0.585135i	$-0.801041\pi$
$683$	2.64673	−	4.58427i	0.101274	−	0.175412i	0.912210	+	0.409723i	$0.134375\pi$
$684$	0.0886450	+	0.153538i	0.00338943	+	0.00587066i
$685$		−	7.14442i		−	0.272974i
$686$	10.4932	+	15.2608i	0.400632	+	0.582661i
$687$	46.8756			1.78842
$688$	−8.76612	+	5.06112i	−0.334205	+	0.192954i
$689$	0.704240	−	1.21978i	0.0268294	−	0.0464699i
$690$	−0.654259	−	0.377737i	−0.0249072	−	0.0143802i
$691$	−23.4089	+	13.5151i	−0.890517	+	0.514140i	−0.874112	−	0.485725i	$-0.838556\pi$
$691$	−23.4089	+	13.5151i	−0.890517	+	0.514140i	−0.0164055	+	0.999865i	$0.505222\pi$
$692$	−15.0655			−0.572706
$693$	3.02814	−	3.96749i	0.115030	−	0.150712i
$694$	28.5417			1.08343
$695$	10.1154	−	5.84014i	0.383699	−	0.221529i
$696$	2.56161	+	1.47894i	0.0970974	+	0.0560592i
$697$	15.0692	−	26.1005i	0.570785	−	0.988629i
$698$	29.9667	−	17.3013i	1.13426	−	0.654864i
$699$	25.2465			0.954911
$700$	9.21125	+	5.00047i	0.348152	+	0.189000i
$701$		−	19.9250i		−	0.752555i	−0.926507	−	0.376278i	$-0.877204\pi$
$701$		−	19.9250i		−	0.752555i	0.926507	−	0.376278i	$-0.122796\pi$
$702$	−0.465328	−	0.805972i	−0.0175627	−	0.0304195i
$703$	−0.949649	+	1.64484i	−0.0358167	+	0.0620363i
$704$	0.510616	−	3.27708i	0.0192446	−	0.123510i
$705$	−5.22731	+	3.01799i	−0.196872	+	0.113664i
$706$	16.9203			0.636805
$707$	0.370479	+	14.1103i	0.0139333	+	0.530673i
$708$	9.73355			0.365809
$709$	−4.98412	−	8.63276i	−0.187183	−	0.324210i	0.757127	−	0.653268i	$-0.226602\pi$
$709$	−4.98412	−	8.63276i	−0.187183	−	0.324210i	−0.944310	+	0.329058i	$0.893269\pi$
$710$	−7.39891	+	12.8153i	−0.277676	+	0.480949i
$711$	−3.45086	−	1.99236i	−0.129417	−	0.0747192i
$712$	3.45047	+	5.97639i	0.129312	+	0.223975i
$713$		−	1.21235i		−	0.0454029i
$714$	−0.319670	−	12.1752i	−0.0119633	−	0.455644i
$715$	−0.203903	−	0.527228i	−0.00762553	−	0.0197172i
$716$	−1.08088	−	1.87214i	−0.0403943	−	0.0699650i
$717$	−20.3247	+	35.2034i	−0.759040	+	1.31470i
$718$	−15.1755	+	26.2848i	−0.566346	+	0.980940i
$719$	35.6817	−	20.6008i	1.33070	−	0.768282i	0.345295	−	0.938494i	$-0.387779\pi$
$719$	35.6817	−	20.6008i	1.33070	−	0.768282i	0.985407	+	0.170212i	$0.0544454\pi$
$720$			0.579642i			0.0216020i
$721$	−15.7195	+	28.9566i	−0.585426	+	1.07840i
$722$			18.9028i			0.703491i
$723$	17.8304	−	10.2944i	0.663121	−	0.382853i
$724$	4.67035	+	2.69643i	0.173572	+	0.100212i
$725$	6.50811	+	3.75746i	0.241705	+	0.139549i
$726$	16.3385	+	5.21824i	0.606379	+	0.193667i
$727$			0.0415718i			0.00154181i	1.00000		0.000770906i	$0.000245387\pi$
$727$			0.0415718i			0.00154181i	−1.00000		0.000770906i	$0.999755\pi$
$728$	−0.231228	−	0.377271i	−0.00856989	−	0.0139826i
$729$	−29.9940			−1.11089
$730$	−4.94652	−	8.56762i	−0.183079	−	0.317102i
$731$	25.8804	+	14.9420i	0.957221	+	0.552652i
$732$	16.0409	+	9.26124i	0.592890	+	0.342305i
$733$	4.40404	+	7.62803i	0.162667	+	0.281748i	0.935824	−	0.352467i	$-0.114657\pi$
$733$	4.40404	+	7.62803i	0.162667	+	0.281748i	−0.773157	+	0.634214i	$0.781324\pi$
$734$	17.4215			0.643040
$735$	5.04836	−	9.91140i	0.186212	−	0.365587i
$736$			0.475438i			0.0175249i
$737$	26.8165	+	21.6045i	0.987800	+	0.795810i
$738$	−5.02844	−	2.90317i	−0.185099	−	0.106867i
$739$	−28.4003	−	16.3969i	−1.04472	−	0.603170i	−0.123555	−	0.992338i	$-0.539429\pi$
$739$	−28.4003	−	16.3969i	−1.04472	−	0.603170i	−0.921167	+	0.389167i	$0.872763\pi$
$740$	−5.37774	+	3.10484i	−0.197690	+	0.114136i
$741$			0.0812842i			0.00298605i
$742$	−11.6433	−	18.9972i	−0.427440	−	0.697409i
$743$		−	25.7575i		−	0.944952i	−0.881344	−	0.472476i	$-0.843360\pi$
$743$		−	25.7575i		−	0.944952i	0.881344	−	0.472476i	$-0.156640\pi$
$744$	3.44332	−	1.98800i	0.126238	−	0.0728836i
$745$	7.21355	−	12.4942i	0.264284	−	0.457753i
$746$	−4.57606	+	7.92596i	−0.167541	+	0.290190i
$747$	4.17815	+	7.23678i	0.152871	+	0.264780i
$748$	−9.13254	+	3.53196i	−0.333919	+	0.129141i
$749$	9.15676	−	16.8675i	0.334581	−	0.616324i
$750$		−	14.2398i		−	0.519963i
$751$	−5.73290	−	9.92967i	−0.209196	−	0.362339i	0.742265	−	0.670106i	$-0.233751\pi$
$751$	−5.73290	−	9.92967i	−0.209196	−	0.362339i	−0.951462	+	0.307767i	$0.900418\pi$
$752$	3.28968	+	1.89930i	0.119962	+	0.0692603i
$753$	22.5956	−	39.1367i	0.823430	−	1.42622i
$754$	−0.158634	−	0.274763i	−0.00577712	−	0.0100063i
$755$	23.7489			0.864313
$756$	−14.7174	+	0.386419i	−0.535267	+	0.0140539i
$757$	21.9741			0.798661			0.399331	−	0.916807i	$-0.369243\pi$
$757$	21.9741			0.798661			0.399331	+	0.916807i	$0.369243\pi$
$758$	5.32936	−	3.07691i	0.193571	−	0.111758i
$759$	−2.42937	−	0.378530i	−0.0881805	−	0.0137398i
$760$	0.158826	−	0.275094i	0.00576121	−	0.00997871i
$761$	13.0047	+	22.5249i	0.471421	+	0.816526i	0.999466	−	0.0326910i	$-0.0104077\pi$
$761$	13.0047	+	22.5249i	0.471421	+	0.816526i	−0.528044	+	0.849217i	$0.677074\pi$
$762$		−	5.50916i		−	0.199576i
$763$	3.08767	−	0.0810696i	0.111781	−	0.00293492i
$764$	−6.00000			−0.217072
$765$	1.48202	−	0.855644i	0.0535825	−	0.0309359i
$766$	−6.48253	+	11.2281i	−0.234223	+	0.405687i
$767$	−0.904164	−	0.522020i	−0.0326475	−	0.0188490i
$768$	−1.35034	+	0.779618i	−0.0487261	+	0.0281320i
$769$	−40.8753			−1.47400			−0.737001	−	0.675891i	$-0.763759\pi$
$769$	−40.8753			−1.47400			−0.737001	+	0.675891i	$0.763759\pi$
$770$	−8.86897	−	1.14437i	−0.319615	−	0.0412401i
$771$	10.8929			0.392296
$772$	8.31348	−	4.79979i	0.299209	−	0.172748i
$773$	40.8229	+	23.5691i	1.46830	+	0.847722i	0.999369	−	0.0355144i	$-0.0113070\pi$
$773$	40.8229	+	23.5691i	1.46830	+	0.847722i	0.468928	+	0.883236i	$0.344640\pi$
$774$	2.87868	−	4.98603i	0.103472	−	0.179219i
$775$	8.74822	−	5.05078i	0.314245	−	0.181430i
$776$	−11.0218			−0.395659
$777$	−13.1356	−	21.4321i	−0.471239	−	0.768871i
$778$		−	5.16647i		−	0.185227i
$779$	1.59097	+	2.75565i	0.0570025	+	0.0987313i
$780$	−0.132878	+	0.230151i	−0.00475779	+	0.00824073i
$781$	−7.41445	+	47.5852i	−0.265310	+	1.70273i
$782$	1.21559	−	0.701823i	0.0434695	−	0.0250971i
$783$	−10.5561			−0.377243
$784$	−6.99036	+	0.367330i	−0.249656	+	0.0131189i
$785$	4.10960			0.146678
$786$	10.8988	+	18.8773i	0.388748	+	0.673331i
$787$	12.0746	−	20.9137i	0.430411	−	0.745494i	−0.566497	−	0.824064i	$-0.691702\pi$
$787$	12.0746	−	20.9137i	0.430411	−	0.745494i	0.996909	+	0.0785692i	$0.0250352\pi$
$788$	−12.8328	−	7.40901i	−0.457149	−	0.263935i
$789$	−3.48543	−	6.03695i	−0.124085	−	0.214921i
$790$			7.13942i			0.254009i
$791$	−18.9516	+	11.6154i	−0.673840	+	0.412995i
$792$	0.680455	+	1.75944i	0.0241789	+	0.0625191i
$793$	−0.993379	−	1.72058i	−0.0352759	−	0.0610997i
$794$	−4.62856	+	8.01690i	−0.164261	+	0.284509i
$795$	−6.69096	+	11.5891i	−0.237304	+	0.411022i
$796$	3.55962	−	2.05515i	0.126167	−	0.0728428i
$797$		−	20.3073i		−	0.719321i	−0.933083	−	0.359660i	$-0.882893\pi$
$797$		−	20.3073i		−	0.719321i	0.933083	−	0.359660i	$-0.117107\pi$
$798$	1.13009	+	0.613486i	0.0400048	+	0.0217172i
$799$		−	11.2147i		−	0.396746i
$800$	−3.43072	+	1.98073i	−0.121294	+	0.0700293i
$801$	−3.39927	−	1.96257i	−0.120107	−	0.0693440i
$802$	−26.7816	−	15.4624i	−0.945692	−	0.545996i
$803$	−25.0724	−	20.1993i	−0.884785	−	0.712818i
$804$		−	16.1896i		−	0.570963i
$805$	1.28147	−	0.0336460i	0.0451657	−	0.00118587i
$806$	−0.426473			−0.0150219
$807$	1.72865	+	2.99410i	0.0608513	+	0.105397i
$808$	−4.62028	−	2.66752i	−0.162541	−	0.0938430i
$809$	−23.4501	−	13.5389i	−0.824461	−	0.476003i	0.0274911	−	0.999622i	$-0.491248\pi$
$809$	−23.4501	−	13.5389i	−0.824461	−	0.476003i	−0.851953	+	0.523619i	$0.824582\pi$
$810$	3.55160	+	6.15156i	0.124791	+	0.216144i
$811$	23.5808			0.828033			0.414016	−	0.910269i	$-0.364126\pi$
$811$	23.5808			0.828033			0.414016	+	0.910269i	$0.364126\pi$
$812$	−5.01729	+	0.131733i	−0.176072	+	0.00462294i
$813$			35.1018i			1.23107i
$814$	−12.6787	+	15.7375i	−0.444389	+	0.551598i
$815$	4.88927	+	2.82282i	0.171264	+	0.0988792i
$816$	3.98663	+	2.30168i	0.139560	+	0.0805749i
$817$	−2.73240	+	1.57755i	−0.0955947	+	0.0551916i
$818$		−	23.8397i		−	0.833535i
$819$	0.221191	+	0.120077i	0.00772905	+	0.00419583i
$820$			10.4032i			0.363297i
$821$	29.4247	−	16.9884i	1.02693	−	0.592898i	0.110826	−	0.993840i	$-0.464650\pi$
$821$	29.4247	−	16.9884i	1.02693	−	0.592898i	0.916104	+	0.400942i	$0.131317\pi$
$822$	−5.46557	+	9.46665i	−0.190634	+	0.330187i
$823$	5.90033	−	10.2197i	0.205673	−	0.356235i	−0.744674	−	0.667428i	$-0.767395\pi$
$823$	5.90033	−	10.2197i	0.205673	−	0.356235i	0.950347	+	0.311193i	$0.100728\pi$
$824$	−6.22664	−	10.7849i	−0.216915	−	0.375708i
$825$	−7.38957	−	19.1071i	−0.257272	−	0.665224i
$826$	−14.0817	+	8.63064i	−0.489966	+	0.300298i
$827$			17.0595i			0.593217i	0.954999	+	0.296609i	$0.0958557\pi$
$827$			17.0595i			0.593217i	−0.954999	+	0.296609i	$0.904144\pi$
$828$	−0.135211	−	0.234192i	−0.00469890	−	0.00813873i
$829$	−21.7387	−	12.5508i	−0.755015	−	0.435908i	0.0724880	−	0.997369i	$-0.476906\pi$
$829$	−21.7387	−	12.5508i	−0.755015	−	0.435908i	−0.827503	+	0.561461i	$0.810239\pi$
$830$	7.48601	−	12.9662i	0.259843	−	0.450062i
$831$	−19.0740	−	33.0371i	−0.661669	−	1.14604i
$832$	0.167247			0.00579823
$833$	11.2581	+	17.3306i	0.390069	+	0.600469i
$834$	−17.8711			−0.618826
$835$	18.7324	−	10.8152i	0.648263	−	0.374275i
$836$	0.159159	−	1.02147i	0.00550464	−	0.0353282i
$837$	−7.09474	+	12.2884i	−0.245230	+	0.424751i
$838$	2.51713	+	4.35980i	0.0869528	+	0.150607i
$839$			41.1030i			1.41903i	0.704688	+	0.709517i	$0.251087\pi$
$839$			41.1030i			1.41903i	−0.704688	+	0.709517i	$0.748913\pi$
$840$	2.19689	+	3.58444i	0.0758000	+	0.123675i
$841$	25.4014			0.875909
$842$	14.6574	−	8.46248i	0.505129	−	0.291636i
$843$	−8.85113	+	15.3306i	−0.304849	+	0.528014i
$844$	6.51646	+	3.76228i	0.224306	+	0.129503i
$845$	−11.4486	+	6.60984i	−0.393843	+	0.227385i
$846$	−2.16058			−0.0742822
$847$	−28.2642	+	6.93787i	−0.971170	+	0.238388i
$848$	8.42157			0.289198
$849$	29.2398	−	16.8816i	1.00351	−	0.579375i
$850$	10.1286	+	5.84773i	0.347407	+	0.200576i
$851$	1.44851	−	2.50888i	0.0496541	−	0.0860035i
$852$	19.6077	−	11.3205i	0.671749	−	0.387834i
$853$	52.7195			1.80508			0.902541	−	0.430605i	$-0.141700\pi$
$853$	52.7195			1.80508			0.902541	+	0.430605i	$0.141700\pi$
$854$	−31.4186	+	0.824924i	−1.07512	+	0.0282283i
$855$			0.180675i			0.00617894i
$856$	3.62707	+	6.28227i	0.123971	+	0.214724i
$857$	−10.9387	+	18.9464i	−0.373659	+	0.647197i	−0.990125	−	0.140184i	$-0.955230\pi$
$857$	−10.9387	+	18.9464i	−0.373659	+	0.647197i	0.616466	+	0.787382i	$0.288564\pi$
$858$	−0.133157	+	0.854588i	−0.00454590	+	0.0291751i
$859$	11.8529	−	6.84326i	0.404415	−	0.233489i	−0.283972	−	0.958832i	$-0.591652\pi$
$859$	11.8529	−	6.84326i	0.404415	−	0.233489i	0.688387	+	0.725344i	$0.258319\pi$
$860$	−10.3155			−0.351755
$861$	−42.0985	+	1.10534i	−1.43471	+	0.0376697i
$862$	5.99907			0.204329
$863$	−15.0240	−	26.0223i	−0.511423	−	0.885810i	−0.999912	−	0.0132402i	$-0.995785\pi$
$863$	−15.0240	−	26.0223i	−0.511423	−	0.885810i	0.488490	−	0.872570i	$-0.337548\pi$
$864$	2.78229	−	4.81906i	0.0946553	−	0.163948i
$865$	−13.2962	−	7.67658i	−0.452085	−	0.261012i
$866$	−18.0588	−	31.2787i	−0.613662	−	1.06289i
$867$			12.9164i			0.438665i
$868$	−3.21877	+	5.92923i	−0.109252	+	0.201251i
$869$	8.38113	+	21.6710i	0.284310	+	0.735137i
$870$	1.50718	+	2.61051i	0.0510981	+	0.0885046i
$871$	−0.868263	+	1.50388i	−0.0294200	+	0.0509569i
$872$	−0.583716	+	1.01103i	−0.0197671	+	0.0342377i
$873$	5.42913	−	3.13451i	0.183748	−	0.106087i
$874$			0.148194i			0.00501275i
$875$	12.6263	+	20.6010i	0.426846	+	0.696440i
$876$			15.1366i			0.511418i
$877$	−12.2786	+	7.08908i	−0.414620	+	0.239381i	−0.692773	−	0.721156i	$-0.743611\pi$
$877$	−12.2786	+	7.08908i	−0.414620	+	0.239381i	0.278153	+	0.960537i	$0.410278\pi$
$878$	−9.82906	−	5.67481i	−0.331715	−	0.191516i
$879$	16.3705	+	9.45151i	0.552163	+	0.318792i
$880$	2.12047	−	2.63204i	0.0714811	−	0.0887259i
$881$			22.3264i			0.752196i	0.926580	+	0.376098i	$0.122734\pi$
$881$			22.3264i			0.752196i	−0.926580	+	0.376098i	$0.877266\pi$
$882$	3.33885	−	2.16894i	0.112425	−	0.0730320i
$883$	−4.45618			−0.149962			−0.0749812	−	0.997185i	$-0.523890\pi$
$883$	−4.45618			−0.149962			−0.0749812	+	0.997185i	$0.523890\pi$
$884$	−0.246883	−	0.427613i	−0.00830356	−	0.0143822i
$885$	8.59043	+	4.95969i	0.288764	+	0.166718i
$886$	−4.11428	−	2.37538i	−0.138222	−	0.0798025i
$887$	−4.50070	−	7.79545i	−0.151119	−	0.261746i	0.780520	−	0.625131i	$-0.214954\pi$
$887$	−4.50070	−	7.79545i	−0.151119	−	0.261746i	−0.931639	+	0.363385i	$0.881621\pi$
$888$	9.50096			0.318831
$889$	4.88492	+	7.97021i	0.163835	+	0.267312i
$890$			7.03268i			0.235736i
$891$	18.0020	+	14.5031i	0.603089	+	0.485872i
$892$	11.7680	+	6.79423i	0.394020	+	0.227488i
$893$	1.02539	+	0.592012i	0.0343135	+	0.0198109i
$894$	−19.1165	+	11.0369i	−0.639351	+	0.369130i
$895$		−	2.20303i		−	0.0736391i
$896$	1.26228	−	2.32522i	0.0421698	−	0.0776801i
$897$		−	0.123983i		−	0.00413968i
$898$	−6.35054	+	3.66649i	−0.211920	+	0.122352i
$899$	−2.41866	+	4.18924i	−0.0806667	+	0.139719i
$900$	1.12660	−	1.95134i	0.0375535	−	0.0650445i
$901$	−12.4316	−	21.5321i	−0.414156	−	0.717339i
$902$	12.2126	+	31.5780i	0.406635	+	1.05143i
$903$	−1.09601	−	41.7434i	−0.0364730	−	1.38913i
$904$		−	8.40135i		−	0.279425i
$905$	2.74791	+	4.75951i	0.0913435	+	0.158212i
$906$	−31.4683	−	18.1682i	−1.04547	−	0.603600i
$907$	−10.6872	+	18.5107i	−0.354862	+	0.614638i	−0.987094	−	0.160140i	$-0.948805\pi$
$907$	−10.6872	+	18.5107i	−0.354862	+	0.614638i	0.632233	+	0.774779i	$0.282139\pi$
$908$	10.8318	+	18.7611i	0.359464	+	0.622611i
$909$	3.03448			0.100647
$910$	−0.0118358	−	0.450785i	−0.000392352	−	0.0149434i
$911$	−28.4299			−0.941924			−0.470962	−	0.882153i	$-0.656093\pi$
$911$	−28.4299			−0.941924			−0.470962	+	0.882153i	$0.656093\pi$
$912$	−0.420901	+	0.243007i	−0.0139374	+	0.00804677i
$913$	7.50174	−	48.1454i	0.248271	−	1.59338i
$914$	6.75879	−	11.7066i	0.223561	−	0.387219i
$915$	9.43805	+	16.3472i	0.312012	+	0.540421i
$916$		−	30.0632i		−	0.993317i
$917$	−32.5058	−	17.6463i	−1.07344	−	0.582732i
$918$	−16.4284			−0.542218
$919$	18.2320	−	10.5263i	0.601419	−	0.347229i	−0.168181	−	0.985756i	$-0.553789\pi$
$919$	18.2320	−	10.5263i	0.601419	−	0.347229i	0.769600	+	0.638527i	$0.220456\pi$
$920$	−0.242258	+	0.419602i	−0.00798700	+	0.0138339i
$921$	13.0418	+	7.52968i	0.429741	+	0.248111i
$922$	16.0847	−	9.28652i	0.529722	−	0.305835i
$923$	−2.42852			−0.0799357
$924$	10.8763	+	8.30121i	0.357804	+	0.273090i
$925$	24.1385			0.793669
$926$	−24.4955	+	14.1425i	−0.804971	+	0.464750i
$927$	6.13425	+	3.54161i	0.201475	+	0.116322i
$928$	0.948505	−	1.64286i	0.0311362	−	0.0539295i
$929$	10.8055	−	6.23858i	0.354518	−	0.204681i	−0.312155	−	0.950031i	$-0.601051\pi$
$929$	10.8055	−	6.23858i	0.354518	−	0.204681i	0.666674	+	0.745350i	$0.267718\pi$
$930$	4.05191			0.132867
$931$	−2.17890	+	0.114497i	−0.0714104	+	0.00375248i
$932$		−	16.1916i		−	0.530373i
$933$	−13.7819	−	23.8710i	−0.451200	−	0.781501i
$934$	10.7896	−	18.6881i	0.353046	−	0.611493i
$935$	−9.85970	−	1.53628i	−0.322447	−	0.0502418i
$936$	−0.0823825	+	0.0475636i	−0.00269276	+	0.00155466i
$937$	43.2128			1.41170			0.705850	−	0.708362i	$-0.250565\pi$
$937$	43.2128			1.41170			0.705850	+	0.708362i	$0.250565\pi$
$938$	14.3551	+	23.4218i	0.468712	+	0.764749i
$939$	−44.9221			−1.46598
$940$	1.93556	+	3.35248i	0.0631309	+	0.109346i
$941$	7.73754	−	13.4018i	0.252236	−	0.436886i	−0.711905	−	0.702276i	$-0.752167\pi$
$941$	7.73754	−	13.4018i	0.252236	−	0.436886i	0.964141	+	0.265390i	$0.0855006\pi$
$942$	−5.44538	−	3.14389i	−0.177420	−	0.102434i
$943$	−2.42672	−	4.20321i	−0.0790249	−	0.136875i
$944$		−	6.24251i		−	0.203176i
$945$	−13.1859	−	7.15816i	−0.428937	−	0.232855i
$946$	−31.3116	+	12.1096i	−1.01803	+	0.393717i
$947$	−16.7488	−	29.0098i	−0.544264	−	0.942693i	−0.998653	−	0.0518895i	$-0.983476\pi$
$947$	−16.7488	−	29.0098i	−0.544264	−	0.942693i	0.454389	−	0.890803i	$-0.349858\pi$
$948$	5.46175	−	9.46003i	0.177389	−	0.307247i
$949$	0.811791	−	1.40606i	0.0263518	−	0.0456427i
$950$	−1.06936	+	0.617393i	−0.0346945	+	0.0200309i
$951$		−	16.1312i		−	0.523091i
$952$	−7.80841	+	0.205017i	−0.253072	+	0.00664464i
$953$			25.4820i			0.825444i	0.910857	+	0.412722i	$0.135422\pi$
$953$			25.4820i			0.825444i	−0.910857	+	0.412722i	$0.864578\pi$
$954$	−4.14831	+	2.39503i	−0.134306	+	0.0775418i
$955$	−5.29535	−	3.05727i	−0.171354	−	0.0989311i
$956$	22.5774	+	13.0350i	0.730204	+	0.421583i
$957$	7.63942	+	6.15462i	0.246947	+	0.198951i
$958$		−	6.93560i		−	0.224079i
$959$	−0.486833	−	18.5419i	−0.0157207	−	0.598748i
$960$	−1.58900			−0.0512849
$961$	−12.2488	−	21.2156i	−0.395124	−	0.684374i
$962$	−0.882559	−	0.509546i	−0.0284548	−	0.0164284i
$963$	−3.57325	−	2.06302i	−0.115146	−	0.0664798i
$964$	−6.60221	−	11.4354i	−0.212643	−	0.368309i
$965$	9.78285			0.314921
$966$	−1.72373	−	0.935755i	−0.0554602	−	0.0301074i
$967$			39.6417i			1.27479i	0.770537	+	0.637395i	$0.219988\pi$
$967$			39.6417i			1.27479i	−0.770537	+	0.637395i	$0.780012\pi$
$968$	3.34666	−	10.4785i	0.107566	−	0.336793i
$969$	1.24263	+	0.717434i	0.0399191	+	0.0230473i
$970$	−9.72738	−	5.61611i	−0.312327	−	0.180322i
$971$	−16.5082	+	9.53101i	−0.529773	+	0.305865i	−0.740924	−	0.671589i	$-0.765612\pi$
$971$	−16.5082	+	9.53101i	−0.529773	+	0.305865i	0.211151	+	0.977454i	$0.432279\pi$
$972$			5.82564i			0.186858i
$973$	25.8545	−	15.8461i	0.828857	−	0.508004i
$974$			12.1740i			0.390081i
$975$	0.894652	−	0.516528i	0.0286518	−	0.0165421i
$976$	5.93960	−	10.2877i	0.190122	−	0.329301i
$977$	−23.8348	+	41.2832i	−0.762544	+	1.32077i	0.178991	+	0.983851i	$0.442717\pi$
$977$	−23.8348	+	41.2832i	−0.762544	+	1.32077i	−0.941535	+	0.336915i	$0.890617\pi$
$978$	−4.31899	−	7.48071i	−0.138106	−	0.239207i
$979$	8.25583	+	21.3470i	0.263857	+	0.682252i
$980$	−6.35657	−	3.23772i	−0.203053	−	0.103425i
$981$		−	0.664016i		−	0.0212004i
$982$	−1.18576	−	2.05379i	−0.0378391	−	0.0655392i
$983$	40.2377	+	23.2312i	1.28338	+	0.740961i	0.977465	−	0.211097i	$-0.0677035\pi$
$983$	40.2377	+	23.2312i	1.28338	+	0.740961i	0.305917	+	0.952058i	$0.401037\pi$
$984$	7.95862	−	13.7847i	0.253711	−	0.439441i
$985$	−7.55046	−	13.0778i	−0.240578	−	0.416693i
$986$	−5.60058			−0.178359
$987$	−13.3608	+	8.18877i	−0.425278	+	0.260651i
$988$	0.0521308			0.00165850
$989$	4.16775	−	2.40625i	0.132527	−	0.0765144i
$990$	−0.295975	+	1.89954i	−0.00940670	+	0.0603712i
$991$	7.28588	−	12.6195i	0.231444	−	0.400872i	−0.726790	−	0.686860i	$-0.758988\pi$
$991$	7.28588	−	12.6195i	0.231444	−	0.400872i	0.958233	+	0.285988i	$0.0923218\pi$
$992$	−1.27498	−	2.20834i	−0.0404808	−	0.0701147i
$993$			41.8575i			1.32831i
$994$	−18.3291	+	33.7636i	−0.581363	+	1.07092i
$995$	4.18877			0.132793
$996$	−19.8386	+	11.4538i	−0.628609	+	0.362927i
$997$	−2.05848	+	3.56539i	−0.0651927	+	0.112917i	−0.896779	−	0.442478i	$-0.854100\pi$
$997$	−2.05848	+	3.56539i	−0.0651927	+	0.112917i	0.831587	+	0.555395i	$0.187433\pi$
$998$	−3.40255	−	1.96446i	−0.107706	−	0.0621839i
$999$	−29.3642	+	16.9534i	−0.929043	+	0.536383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.i.a.87.3	✓	16
3.2	odd	2		1386.2.bk.c.703.6		16
4.3	odd	2		1232.2.bn.b.241.3		16
7.2	even	3		1078.2.i.c.901.6		16
7.3	odd	6		1078.2.c.b.1077.6		16
7.4	even	3		1078.2.c.b.1077.3		16
7.5	odd	6	inner	154.2.i.a.131.7	yes	16
7.6	odd	2		1078.2.i.c.1011.2		16
11.10	odd	2	inner	154.2.i.a.87.7	yes	16
21.5	even	6		1386.2.bk.c.901.2		16
28.19	even	6		1232.2.bn.b.593.4		16
33.32	even	2		1386.2.bk.c.703.2		16
44.43	even	2		1232.2.bn.b.241.4		16
77.10	even	6		1078.2.c.b.1077.14		16
77.32	odd	6		1078.2.c.b.1077.11		16
77.54	even	6	inner	154.2.i.a.131.3	yes	16
77.65	odd	6		1078.2.i.c.901.2		16
77.76	even	2		1078.2.i.c.1011.6		16
231.131	odd	6		1386.2.bk.c.901.6		16
308.131	odd	6		1232.2.bn.b.593.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.3	✓	16	1.1	even	1	trivial
154.2.i.a.87.7	yes	16	11.10	odd	2	inner
154.2.i.a.131.3	yes	16	77.54	even	6	inner
154.2.i.a.131.7	yes	16	7.5	odd	6	inner
1078.2.c.b.1077.3		16	7.4	even	3
1078.2.c.b.1077.6		16	7.3	odd	6
1078.2.c.b.1077.11		16	77.32	odd	6
1078.2.c.b.1077.14		16	77.10	even	6
1078.2.i.c.901.2		16	77.65	odd	6
1078.2.i.c.901.6		16	7.2	even	3
1078.2.i.c.1011.2		16	7.6	odd	2
1078.2.i.c.1011.6		16	77.76	even	2
1232.2.bn.b.241.3		16	4.3	odd	2
1232.2.bn.b.241.4		16	44.43	even	2
1232.2.bn.b.593.3		16	308.131	odd	6
1232.2.bn.b.593.4		16	28.19	even	6
1386.2.bk.c.703.2		16	33.32	even	2
1386.2.bk.c.703.6		16	3.2	odd	2
1386.2.bk.c.901.2		16	21.5	even	6
1386.2.bk.c.901.6		16	231.131	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:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.35034 + 0.779618i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.882559 - 0.509546i) q^{5} -1.55924 q^{6} +(2.25578 - 1.38256i) q^{7} +1.00000i q^{8} +(-0.284392 - 0.492581i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.35034 + 0.779618i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.882559 - 0.509546i) q^{5} -1.55924 q^{6} +(2.25578 - 1.38256i) q^{7} +1.00000i q^{8} +(-0.284392 - 0.492581i) q^{9} +(-0.509546 + 0.882559i) q^{10} +(-0.510616 + 3.27708i) q^{11} +(1.35034 - 0.779618i) q^{12} -0.167247 q^{13} +(-1.26228 + 2.32522i) q^{14} +1.58900 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.47616 + 2.55678i) q^{17} +(0.492581 + 0.284392i) q^{18} +(-0.155850 - 0.269940i) q^{19} -1.01909i q^{20} +(4.12393 - 0.108278i) q^{21} +(-1.19633 - 3.09335i) q^{22} +(0.237719 + 0.411742i) q^{23} +(-0.779618 + 1.35034i) q^{24} +(-1.98073 + 3.43072i) q^{25} +(0.144840 - 0.0836233i) q^{26} -5.56458i q^{27} +(-0.0694427 - 2.64484i) q^{28} -1.89701i q^{29} +(-1.37612 + 0.794502i) q^{30} +(-2.20834 - 1.27498i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.24438 + 4.02708i) q^{33} -2.95232i q^{34} +(1.28638 - 2.36961i) q^{35} -0.568783 q^{36} +(-3.04667 - 5.27699i) q^{37} +(0.269940 + 0.155850i) q^{38} +(-0.225839 - 0.130388i) q^{39} +(0.509546 + 0.882559i) q^{40} -10.2084 q^{41} +(-3.51729 + 2.15574i) q^{42} -10.1222i q^{43} +(2.58273 + 2.08075i) q^{44} +(-0.501985 - 0.289821i) q^{45} +(-0.411742 - 0.237719i) q^{46} +(-3.28968 + 1.89930i) q^{47} -1.55924i q^{48} +(3.17706 - 6.23749i) q^{49} -3.96145i q^{50} +(-3.98663 + 2.30168i) q^{51} +(-0.0836233 + 0.144840i) q^{52} +(-4.21079 + 7.29330i) q^{53} +(2.78229 + 4.81906i) q^{54} +(1.21917 + 3.15240i) q^{55} +(1.38256 + 2.25578i) q^{56} -0.486014i q^{57} +(0.948505 + 1.64286i) q^{58} +(5.40617 + 3.12126i) q^{59} +(0.794502 - 1.37612i) q^{60} +(5.93960 + 10.2877i) q^{61} +2.54997 q^{62} +(-1.32255 - 0.717964i) q^{63} -1.00000 q^{64} +(-0.147605 + 0.0852198i) q^{65} +(0.796171 - 5.10974i) q^{66} +(5.19151 - 8.99196i) q^{67} +(1.47616 + 2.55678i) q^{68} +0.741321i q^{69} +(0.0707684 + 2.69533i) q^{70} +14.5206 q^{71} +(0.492581 - 0.284392i) q^{72} +(-4.85385 + 8.40712i) q^{73} +(5.27699 + 3.04667i) q^{74} +(-5.34930 + 3.08842i) q^{75} -0.311700 q^{76} +(3.37892 + 8.09833i) q^{77} +0.260777 q^{78} +(6.06709 - 3.50284i) q^{79} +(-0.882559 - 0.509546i) q^{80} +(3.48507 - 6.03631i) q^{81} +(8.84069 - 5.10418i) q^{82} -14.6915 q^{83} +(1.96819 - 3.62557i) q^{84} +3.00868i q^{85} +(5.06112 + 8.76612i) q^{86} +(1.47894 - 2.56161i) q^{87} +(-3.27708 - 0.510616i) q^{88} +(5.97639 - 3.45047i) q^{89} +0.579642 q^{90} +(-0.377271 + 0.231228i) q^{91} +0.475438 q^{92} +(-1.98800 - 3.44332i) q^{93} +(1.89930 - 3.28968i) q^{94} +(-0.275094 - 0.158826i) q^{95} +(0.779618 + 1.35034i) q^{96} +11.0218i q^{97} +(0.367330 + 6.99036i) q^{98} +(1.75944 - 0.680455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 - 12 * q^5 + 16 * q^9	\( 16 q + 8 q^{4} - 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} - 36 q^{26} - 12 q^{31} - 24 q^{33} + 32 q^{36} - 16 q^{37} + 12 q^{38} + 12 q^{42} - 8 q^{44} - 108 q^{45} + 24 q^{47} + 8 q^{49} - 28 q^{53} - 4 q^{56} - 12 q^{58} + 60 q^{59} - 4 q^{60} - 16 q^{64} + 48 q^{66} + 12 q^{67} + 60 q^{70} + 8 q^{71} + 60 q^{75} + 44 q^{77} - 16 q^{78} + 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} + 96 q^{89} - 36 q^{91} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 12 * q^5 + 16 * q^9 + 8 * q^11 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^22 + 16 * q^23 - 36 * q^26 - 12 * q^31 - 24 * q^33 + 32 * q^36 - 16 * q^37 + 12 * q^38 + 12 * q^42 - 8 * q^44 - 108 * q^45 + 24 * q^47 + 8 * q^49 - 28 * q^53 - 4 * q^56 - 12 * q^58 + 60 * q^59 - 4 * q^60 - 16 * q^64 + 48 * q^66 + 12 * q^67 + 60 * q^70 + 8 * q^71 + 60 * q^75 + 44 * q^77 - 16 * q^78 + 12 * q^80 - 8 * q^81 + 20 * q^86 - 4 * q^88 + 96 * q^89 - 36 * q^91 + 32 * q^92 - 44 * q^93 + 56 * q^99

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