LMFDB - Embedded newform 385.2.n.b.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(36,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("385.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.n (of order $5$, degree $4$, 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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	385.141
Dual form			385.2.n.b.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.690983 - 2.12663i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.11803 - 3.44095i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(-0.118034 + 0.363271i) q^{9} +O(q^{10})$	\(q+(0.690983 - 2.12663i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.11803 - 3.44095i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(-0.118034 + 0.363271i) q^{9} -2.23607 q^{10} +(-2.54508 - 2.12663i) q^{11} -4.85410 q^{12} +(0.736068 - 2.26538i) q^{13} +(1.80902 - 1.31433i) q^{14} +(-1.30902 - 0.951057i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.04508 + 3.21644i) q^{17} +(0.690983 + 0.502029i) q^{18} +(-1.00000 + 0.726543i) q^{19} +(-0.927051 + 2.85317i) q^{20} +1.61803 q^{21} +(-6.28115 + 3.94298i) q^{22} +4.47214 q^{23} +(-1.11803 + 3.44095i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-4.30902 - 3.13068i) q^{26} +(1.69098 + 5.20431i) q^{27} +(-0.927051 - 2.85317i) q^{28} +(4.73607 + 3.44095i) q^{29} +(-2.92705 + 2.12663i) q^{30} +(-0.381966 + 1.17557i) q^{31} -6.70820 q^{32} +(-5.35410 - 0.363271i) q^{33} +7.56231 q^{34} +(0.309017 - 0.951057i) q^{35} +(0.927051 - 0.673542i) q^{36} +(2.23607 + 1.62460i) q^{37} +(0.854102 + 2.62866i) q^{38} +(-1.19098 - 3.66547i) q^{39} +(1.80902 + 1.31433i) q^{40} +(5.23607 - 3.80423i) q^{41} +(1.11803 - 3.44095i) q^{42} -0.763932 q^{43} +(2.42705 + 9.64932i) q^{44} +0.381966 q^{45} +(3.09017 - 9.51057i) q^{46} +(6.35410 - 4.61653i) q^{47} +(-1.30902 - 0.951057i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.690983 + 2.12663i) q^{50} +(4.42705 + 3.21644i) q^{51} +(-5.78115 + 4.20025i) q^{52} +(-3.23607 + 9.95959i) q^{53} +12.2361 q^{54} +(-1.23607 + 3.07768i) q^{55} -2.23607 q^{56} +(-0.618034 + 1.90211i) q^{57} +(10.5902 - 7.69421i) q^{58} +(3.85410 + 2.80017i) q^{59} +(1.50000 + 4.61653i) q^{60} +(-2.85410 - 8.78402i) q^{61} +(2.23607 + 1.62460i) q^{62} +(-0.309017 + 0.224514i) q^{63} +(-4.01722 + 12.3637i) q^{64} -2.38197 q^{65} +(-4.47214 + 11.1352i) q^{66} -14.1803 q^{67} +(3.13525 - 9.64932i) q^{68} +(5.85410 - 4.25325i) q^{69} +(-1.80902 - 1.31433i) q^{70} +(0.208204 + 0.640786i) q^{71} +(-0.263932 - 0.812299i) q^{72} +(-6.97214 - 5.06555i) q^{73} +(5.00000 - 3.63271i) q^{74} +(-0.500000 + 1.53884i) q^{75} +3.70820 q^{76} +(-0.809017 - 3.21644i) q^{77} -8.61803 q^{78} +(-4.26393 + 13.1230i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(6.23607 + 4.53077i) q^{81} +(-4.47214 - 13.7638i) q^{82} +(-3.26393 - 10.0453i) q^{83} +(-3.92705 - 2.85317i) q^{84} +(2.73607 - 1.98787i) q^{85} +(-0.527864 + 1.62460i) q^{86} +9.47214 q^{87} +(7.39919 + 0.502029i) q^{88} +17.2361 q^{89} +(0.263932 - 0.812299i) q^{90} +(1.92705 - 1.40008i) q^{91} +(-10.8541 - 7.88597i) q^{92} +(0.618034 + 1.90211i) q^{93} +(-5.42705 - 16.7027i) q^{94} +(1.00000 + 0.726543i) q^{95} +(-8.78115 + 6.37988i) q^{96} +(0.100813 - 0.310271i) q^{97} +2.23607 q^{98} +(1.07295 - 0.673542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} + 3 q^{3} - 3 q^{4} + q^{5} + q^{7} - 5 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 5 * q^2 + 3 * q^3 - 3 * q^4 + q^5 + q^7 - 5 * q^8 + 4 * q^9	$ 4 q + 5 q^{2} + 3 q^{3} - 3 q^{4} + q^{5} + q^{7} - 5 q^{8} + 4 q^{9} + q^{11} - 6 q^{12} - 6 q^{13} + 5 q^{14} - 3 q^{15} + q^{16} - 7 q^{17} + 5 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 5 q^{22} - q^{25} - 15 q^{26} + 9 q^{27} + 3 q^{28} + 10 q^{29} - 5 q^{30} - 6 q^{31} - 8 q^{33} - 10 q^{34} - q^{35} - 3 q^{36} - 10 q^{38} - 7 q^{39} + 5 q^{40} + 12 q^{41} - 12 q^{43} + 3 q^{44} + 6 q^{45} - 10 q^{46} + 12 q^{47} - 3 q^{48} - q^{49} + 5 q^{50} + 11 q^{51} - 3 q^{52} - 4 q^{53} + 40 q^{54} + 4 q^{55} + 2 q^{57} + 20 q^{58} + 2 q^{59} + 6 q^{60} + 2 q^{61} + q^{63} + 13 q^{64} - 14 q^{65} - 12 q^{67} - 21 q^{68} + 10 q^{69} - 5 q^{70} - 26 q^{71} - 10 q^{72} - 10 q^{73} + 20 q^{74} - 2 q^{75} - 12 q^{76} - q^{77} - 30 q^{78} - 26 q^{79} - q^{80} + 16 q^{81} - 22 q^{83} - 9 q^{84} + 2 q^{85} - 20 q^{86} + 20 q^{87} + 5 q^{88} + 60 q^{89} + 10 q^{90} + q^{91} - 30 q^{92} - 2 q^{93} - 15 q^{94} + 4 q^{95} - 15 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) $ 4 * q + 5 * q^2 + 3 * q^3 - 3 * q^4 + q^5 + q^7 - 5 * q^8 + 4 * q^9 + q^11 - 6 * q^12 - 6 * q^13 + 5 * q^14 - 3 * q^15 + q^16 - 7 * q^17 + 5 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 5 * q^22 - q^25 - 15 * q^26 + 9 * q^27 + 3 * q^28 + 10 * q^29 - 5 * q^30 - 6 * q^31 - 8 * q^33 - 10 * q^34 - q^35 - 3 * q^36 - 10 * q^38 - 7 * q^39 + 5 * q^40 + 12 * q^41 - 12 * q^43 + 3 * q^44 + 6 * q^45 - 10 * q^46 + 12 * q^47 - 3 * q^48 - q^49 + 5 * q^50 + 11 * q^51 - 3 * q^52 - 4 * q^53 + 40 * q^54 + 4 * q^55 + 2 * q^57 + 20 * q^58 + 2 * q^59 + 6 * q^60 + 2 * q^61 + q^63 + 13 * q^64 - 14 * q^65 - 12 * q^67 - 21 * q^68 + 10 * q^69 - 5 * q^70 - 26 * q^71 - 10 * q^72 - 10 * q^73 + 20 * q^74 - 2 * q^75 - 12 * q^76 - q^77 - 30 * q^78 - 26 * q^79 - q^80 + 16 * q^81 - 22 * q^83 - 9 * q^84 + 2 * q^85 - 20 * q^86 + 20 * q^87 + 5 * q^88 + 60 * q^89 + 10 * q^90 + q^91 - 30 * q^92 - 2 * q^93 - 15 * q^94 + 4 * q^95 - 15 * q^96 + 25 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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 $

$2$	0.690983	−	2.12663i	0.488599	−	1.50375i	−0.338101	−	0.941110i	$-0.609785\pi$
$2$	0.690983	−	2.12663i	0.488599	−	1.50375i	0.826700	−	0.562643i	$-0.190215\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	−0.141846	−	0.989889i	$-0.545304\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	0.897607	+	0.440796i	$0.145304\pi$
$4$	−2.42705	−	1.76336i	−1.21353	−	0.881678i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	−1.11803	−	3.44095i	−0.456435	−	1.40476i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	−1.80902	+	1.31433i	−0.639584	+	0.464685i
$9$	−0.118034	+	0.363271i	−0.0393447	+	0.121090i
$10$	−2.23607			−0.707107
$11$	−2.54508	−	2.12663i	−0.767372	−	0.641202i
$11$	−2.54508	−	2.12663i	−0.767372	−	0.641202i
$12$	−4.85410			−1.40126
$13$	0.736068	−	2.26538i	0.204149	−	0.628305i	−0.795599	−	0.605824i	$-0.792844\pi$
$13$	0.736068	−	2.26538i	0.204149	−	0.628305i	0.999747	−	0.0224806i	$-0.00715641\pi$
$14$	1.80902	−	1.31433i	0.483480	−	0.351269i
$15$	−1.30902	−	0.951057i	−0.337987	−	0.245562i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	1.04508	+	3.21644i	0.253470	+	0.780101i	0.994127	+	0.108218i	$0.0345144\pi$
$17$	1.04508	+	3.21644i	0.253470	+	0.780101i	−0.740657	+	0.671883i	$0.765486\pi$
$18$	0.690983	+	0.502029i	0.162866	+	0.118329i
$19$	−1.00000	+	0.726543i	−0.229416	+	0.166680i	−0.696555	−	0.717504i	$-0.745285\pi$
$19$	−1.00000	+	0.726543i	−0.229416	+	0.166680i	0.467139	+	0.884184i	$0.345285\pi$
$20$	−0.927051	+	2.85317i	−0.207295	+	0.637988i
$21$	1.61803			0.353084
$22$	−6.28115	+	3.94298i	−1.33915	+	0.840647i
$23$	4.47214			0.932505			0.466252	−	0.884652i	$-0.345604\pi$
$23$	4.47214			0.932505			0.466252	+	0.884652i	$0.345604\pi$
$24$	−1.11803	+	3.44095i	−0.228218	+	0.702382i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−4.30902	−	3.13068i	−0.845068	−	0.613978i
$27$	1.69098	+	5.20431i	0.325430	+	1.00157i
$28$	−0.927051	−	2.85317i	−0.175196	−	0.539198i
$29$	4.73607	+	3.44095i	0.879466	+	0.638969i	0.933110	−	0.359591i	$-0.117084\pi$
$29$	4.73607	+	3.44095i	0.879466	+	0.638969i	−0.0536443	+	0.998560i	$0.517084\pi$
$30$	−2.92705	+	2.12663i	−0.534404	+	0.388267i
$31$	−0.381966	+	1.17557i	−0.0686031	+	0.211139i	−0.979481	−	0.201538i	$-0.935406\pi$
$31$	−0.381966	+	1.17557i	−0.0686031	+	0.211139i	0.910878	+	0.412677i	$0.135406\pi$
$32$	−6.70820			−1.18585
$33$	−5.35410	−	0.363271i	−0.932030	−	0.0632374i
$34$	7.56231			1.29692
$35$	0.309017	−	0.951057i	0.0522334	−	0.160758i
$36$	0.927051	−	0.673542i	0.154508	−	0.112257i
$37$	2.23607	+	1.62460i	0.367607	+	0.267082i	0.756218	−	0.654320i	$-0.227045\pi$
$37$	2.23607	+	1.62460i	0.367607	+	0.267082i	−0.388611	+	0.921402i	$0.627045\pi$
$38$	0.854102	+	2.62866i	0.138554	+	0.426424i
$39$	−1.19098	−	3.66547i	−0.190710	−	0.586945i
$40$	1.80902	+	1.31433i	0.286031	+	0.207813i
$41$	5.23607	−	3.80423i	0.817736	−	0.594120i	−0.0983268	−	0.995154i	$-0.531349\pi$
$41$	5.23607	−	3.80423i	0.817736	−	0.594120i	0.916063	+	0.401034i	$0.131349\pi$
$42$	1.11803	−	3.44095i	0.172516	−	0.530951i
$43$	−0.763932			−0.116499			−0.0582493	−	0.998302i	$-0.518552\pi$
$43$	−0.763932			−0.116499			−0.0582493	+	0.998302i	$0.518552\pi$
$44$	2.42705	+	9.64932i	0.365892	+	1.45469i
$45$	0.381966			0.0569401
$46$	3.09017	−	9.51057i	0.455621	−	1.40226i
$47$	6.35410	−	4.61653i	0.926841	−	0.673389i	−0.0183763	−	0.999831i	$-0.505850\pi$
$47$	6.35410	−	4.61653i	0.926841	−	0.673389i	0.945217	+	0.326442i	$0.105850\pi$
$48$	−1.30902	−	0.951057i	−0.188940	−	0.137273i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.690983	+	2.12663i	0.0977198	+	0.300750i
$51$	4.42705	+	3.21644i	0.619911	+	0.450392i
$52$	−5.78115	+	4.20025i	−0.801702	+	0.582470i
$53$	−3.23607	+	9.95959i	−0.444508	+	1.36806i	0.438514	+	0.898724i	$0.355505\pi$
$53$	−3.23607	+	9.95959i	−0.444508	+	1.36806i	−0.883022	+	0.469331i	$0.844495\pi$
$54$	12.2361			1.66512
$55$	−1.23607	+	3.07768i	−0.166671	+	0.414995i
$56$	−2.23607			−0.298807
$57$	−0.618034	+	1.90211i	−0.0818606	+	0.251941i
$58$	10.5902	−	7.69421i	1.39056	−	1.01030i
$59$	3.85410	+	2.80017i	0.501761	+	0.364551i	0.809689	−	0.586859i	$-0.199636\pi$
$59$	3.85410	+	2.80017i	0.501761	+	0.364551i	−0.307928	+	0.951410i	$0.599636\pi$
$60$	1.50000	+	4.61653i	0.193649	+	0.595991i
$61$	−2.85410	−	8.78402i	−0.365430	−	1.12468i	−0.949711	−	0.313127i	$-0.898623\pi$
$61$	−2.85410	−	8.78402i	−0.365430	−	1.12468i	0.584281	−	0.811552i	$-0.301377\pi$
$62$	2.23607	+	1.62460i	0.283981	+	0.206324i
$63$	−0.309017	+	0.224514i	−0.0389325	+	0.0282861i
$64$	−4.01722	+	12.3637i	−0.502153	+	1.54547i
$65$	−2.38197			−0.295447
$66$	−4.47214	+	11.1352i	−0.550482	+	1.37064i
$67$	−14.1803			−1.73240			−0.866202	−	0.499694i	$-0.833446\pi$
$67$	−14.1803			−1.73240			−0.866202	+	0.499694i	$0.833446\pi$
$68$	3.13525	−	9.64932i	0.380206	−	1.17015i
$69$	5.85410	−	4.25325i	0.704751	−	0.512032i
$70$	−1.80902	−	1.31433i	−0.216219	−	0.157092i
$71$	0.208204	+	0.640786i	0.0247093	+	0.0760473i	0.962651	−	0.270746i	$-0.0872704\pi$
$71$	0.208204	+	0.640786i	0.0247093	+	0.0760473i	−0.937941	+	0.346794i	$0.887270\pi$
$72$	−0.263932	−	0.812299i	−0.0311047	−	0.0957304i
$73$	−6.97214	−	5.06555i	−0.816027	−	0.592878i	0.0995449	−	0.995033i	$-0.468261\pi$
$73$	−6.97214	−	5.06555i	−0.816027	−	0.592878i	−0.915572	+	0.402155i	$0.868261\pi$
$74$	5.00000	−	3.63271i	0.581238	−	0.422294i
$75$	−0.500000	+	1.53884i	−0.0577350	+	0.177690i
$76$	3.70820			0.425360
$77$	−0.809017	−	3.21644i	−0.0921960	−	0.366547i
$78$	−8.61803			−0.975800
$79$	−4.26393	+	13.1230i	−0.479730	+	1.47646i	0.359741	+	0.933052i	$0.382865\pi$
$79$	−4.26393	+	13.1230i	−0.479730	+	1.47646i	−0.839471	+	0.543404i	$0.817135\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	6.23607	+	4.53077i	0.692896	+	0.503419i
$82$	−4.47214	−	13.7638i	−0.493865	−	1.51996i
$83$	−3.26393	−	10.0453i	−0.358263	−	1.10262i	−0.954093	−	0.299510i	$-0.903177\pi$
$83$	−3.26393	−	10.0453i	−0.358263	−	1.10262i	0.595830	−	0.803111i	$-0.296823\pi$
$84$	−3.92705	−	2.85317i	−0.428476	−	0.311306i
$85$	2.73607	−	1.98787i	0.296768	−	0.215615i
$86$	−0.527864	+	1.62460i	−0.0569210	+	0.175185i
$87$	9.47214			1.01552
$88$	7.39919	+	0.502029i	0.788756	+	0.0535164i
$89$	17.2361			1.82702			0.913510	−	0.406817i	$-0.133361\pi$
$89$	17.2361			1.82702			0.913510	+	0.406817i	$0.133361\pi$
$90$	0.263932	−	0.812299i	0.0278209	−	0.0856239i
$91$	1.92705	−	1.40008i	0.202010	−	0.146769i
$92$	−10.8541	−	7.88597i	−1.13162	−	0.822169i
$93$	0.618034	+	1.90211i	0.0640871	+	0.197240i
$94$	−5.42705	−	16.7027i	−0.559758	−	1.72276i
$95$	1.00000	+	0.726543i	0.102598	+	0.0745417i
$96$	−8.78115	+	6.37988i	−0.896223	+	0.651144i
$97$	0.100813	−	0.310271i	0.0102360	−	0.0315032i	−0.945808	−	0.324726i	$-0.894728\pi$
$97$	0.100813	−	0.310271i	0.0102360	−	0.0315032i	0.956044	+	0.293223i	$0.0947278\pi$
$98$	2.23607			0.225877
$99$	1.07295	−	0.673542i	0.107835	−	0.0676935i
$100$	3.00000			0.300000
$101$	−0.0901699	+	0.277515i	−0.00897224	+	0.0276137i	−0.955442	−	0.295178i	$-0.904621\pi$
$101$	−0.0901699	+	0.277515i	−0.00897224	+	0.0276137i	0.946470	+	0.322791i	$0.104621\pi$
$102$	9.89919	−	7.19218i	0.980166	−	0.712132i
$103$	1.35410	+	0.983813i	0.133424	+	0.0969379i	0.652495	−	0.757793i	$-0.273722\pi$
$103$	1.35410	+	0.983813i	0.133424	+	0.0969379i	−0.519072	+	0.854731i	$0.673722\pi$
$104$	1.64590	+	5.06555i	0.161394	+	0.496718i
$105$	−0.500000	−	1.53884i	−0.0487950	−	0.150176i
$106$	18.9443	+	13.7638i	1.84003	+	1.33686i
$107$	2.23607	−	1.62460i	0.216169	−	0.157056i	−0.474432	−	0.880292i	$-0.657346\pi$
$107$	2.23607	−	1.62460i	0.216169	−	0.157056i	0.690600	+	0.723237i	$0.257346\pi$
$108$	5.07295	−	15.6129i	0.488145	−	1.50236i
$109$	−20.4721			−1.96087			−0.980437	−	0.196831i	$-0.936935\pi$
$109$	−20.4721			−1.96087			−0.980437	+	0.196831i	$0.936935\pi$
$110$	5.69098	+	4.75528i	0.542614	+	0.453398i
$111$	4.47214			0.424476
$112$	0.309017	−	0.951057i	0.0291994	−	0.0898664i
$113$	−1.23607	+	0.898056i	−0.116279	+	0.0844820i	−0.644405	−	0.764684i	$-0.722895\pi$
$113$	−1.23607	+	0.898056i	−0.116279	+	0.0844820i	0.528126	+	0.849166i	$0.322895\pi$
$114$	3.61803	+	2.62866i	0.338860	+	0.246196i
$115$	−1.38197	−	4.25325i	−0.128869	−	0.396618i
$116$	−5.42705	−	16.7027i	−0.503889	−	1.55081i
$117$	0.736068	+	0.534785i	0.0680495	+	0.0494409i
$118$	8.61803	−	6.26137i	0.793354	−	0.576406i
$119$	−1.04508	+	3.21644i	−0.0958028	+	0.294851i
$120$	3.61803			0.330280
$121$	1.95492	+	10.8249i	0.177720	+	0.984081i
$122$	−20.6525			−1.86979
$123$	3.23607	−	9.95959i	0.291786	−	0.898026i
$124$	3.00000	−	2.17963i	0.269408	−	0.195736i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	0.263932	+	0.812299i	0.0235129	+	0.0723654i
$127$	1.47214	+	4.53077i	0.130631	+	0.402041i	0.994885	−	0.101015i	$-0.0322090\pi$
$127$	1.47214	+	4.53077i	0.130631	+	0.402041i	−0.864254	+	0.503056i	$0.832209\pi$
$128$	12.6631	+	9.20029i	1.11927	+	0.813199i
$129$	−1.00000	+	0.726543i	−0.0880451	+	0.0639685i
$130$	−1.64590	+	5.06555i	−0.144355	+	0.444278i
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$	12.3541	+	10.3229i	1.07529	+	0.898490i
$133$	−1.23607			−0.107181
$134$	−9.79837	+	30.1563i	−0.846451	+	2.60511i
$135$	4.42705	−	3.21644i	0.381020	−	0.276827i
$136$	−6.11803	−	4.44501i	−0.524617	−	0.381157i
$137$	4.76393	+	14.6619i	0.407010	+	1.25265i	0.919205	+	0.393779i	$0.128833\pi$
$137$	4.76393	+	14.6619i	0.407010	+	1.25265i	−0.512195	+	0.858869i	$0.671167\pi$
$138$	−5.00000	−	15.3884i	−0.425628	−	1.30995i
$139$	−11.7082	−	8.50651i	−0.993077	−	0.721513i	−0.0324841	−	0.999472i	$-0.510342\pi$
$139$	−11.7082	−	8.50651i	−0.993077	−	0.721513i	−0.960593	+	0.277960i	$0.910342\pi$
$140$	−2.42705	+	1.76336i	−0.205123	+	0.149031i
$141$	3.92705	−	12.0862i	0.330717	−	1.01784i
$142$	1.50658			0.126429
$143$	−6.69098	+	4.20025i	−0.559528	+	0.351243i
$144$	0.381966			0.0318305
$145$	1.80902	−	5.56758i	0.150231	−	0.462363i
$146$	−15.5902	+	11.3269i	−1.29025	+	0.937423i
$147$	1.30902	+	0.951057i	0.107966	+	0.0784418i
$148$	−2.56231	−	7.88597i	−0.210620	−	0.648222i
$149$	−3.44427	−	10.6004i	−0.282166	−	0.868417i	−0.987234	−	0.159277i	$-0.949084\pi$
$149$	−3.44427	−	10.6004i	−0.282166	−	0.868417i	0.705068	−	0.709140i	$-0.250916\pi$
$150$	2.92705	+	2.12663i	0.238993	+	0.173638i
$151$	2.11803	−	1.53884i	0.172363	−	0.125229i	−0.498259	−	0.867028i	$-0.666027\pi$
$151$	2.11803	−	1.53884i	0.172363	−	0.125229i	0.670622	+	0.741799i	$0.266027\pi$
$152$	0.854102	−	2.62866i	0.0692768	−	0.213212i
$153$	−1.29180			−0.104436
$154$	−7.39919	−	0.502029i	−0.596243	−	0.0404546i
$155$	1.23607			0.0992834
$156$	−3.57295	+	10.9964i	−0.286065	+	0.880417i
$157$	3.97214	−	2.88593i	0.317011	−	0.230322i	−0.417888	−	0.908499i	$-0.637230\pi$
$157$	3.97214	−	2.88593i	0.317011	−	0.230322i	0.734899	+	0.678177i	$0.237230\pi$
$158$	24.9615	+	18.1356i	1.98583	+	1.44279i
$159$	5.23607	+	16.1150i	0.415247	+	1.27800i
$160$	2.07295	+	6.37988i	0.163881	+	0.504374i
$161$	3.61803	+	2.62866i	0.285141	+	0.207167i
$162$	13.9443	−	10.1311i	1.09557	−	0.795975i
$163$	0.0557281	−	0.171513i	0.00436496	−	0.0134340i	−0.948850	−	0.315726i	$-0.897752\pi$
$163$	0.0557281	−	0.171513i	0.00436496	−	0.0134340i	0.953215	+	0.302292i	$0.0977519\pi$
$164$	−19.4164			−1.51617
$165$	1.30902	+	5.20431i	0.101907	+	0.405155i
$166$	−23.6180			−1.83311
$167$	−3.70820	+	11.4127i	−0.286949	+	0.883140i	0.698858	+	0.715260i	$0.253692\pi$
$167$	−3.70820	+	11.4127i	−0.286949	+	0.883140i	−0.985808	+	0.167879i	$0.946308\pi$
$168$	−2.92705	+	2.12663i	−0.225827	+	0.164073i
$169$	5.92705	+	4.30625i	0.455927	+	0.331250i
$170$	−2.33688	−	7.19218i	−0.179231	−	0.551615i
$171$	−0.145898	−	0.449028i	−0.0111571	−	0.0343380i
$172$	1.85410	+	1.34708i	0.141374	+	0.102714i
$173$	−15.0172	+	10.9106i	−1.14174	+	0.829521i	−0.987360	−	0.158491i	$-0.949337\pi$
$173$	−15.0172	+	10.9106i	−1.14174	+	0.829521i	−0.154378	+	0.988012i	$0.549337\pi$
$174$	6.54508	−	20.1437i	0.496182	−	1.52709i
$175$	−1.00000			−0.0755929
$176$	−1.23607	+	3.07768i	−0.0931721	+	0.231989i
$177$	7.70820			0.579384
$178$	11.9098	−	36.6547i	0.892680	−	2.74739i
$179$	−14.0623	+	10.2169i	−1.05107	+	0.763644i	−0.972415	−	0.233258i	$-0.925061\pi$
$179$	−14.0623	+	10.2169i	−1.05107	+	0.763644i	−0.0786512	+	0.996902i	$0.525061\pi$
$180$	−0.927051	−	0.673542i	−0.0690983	−	0.0502029i
$181$	4.47214	+	13.7638i	0.332411	+	1.02306i	0.967983	+	0.251015i	$0.0807643\pi$
$181$	4.47214	+	13.7638i	0.332411	+	1.02306i	−0.635572	+	0.772042i	$0.719236\pi$
$182$	−1.64590	−	5.06555i	−0.122002	−	0.375484i
$183$	−12.0902	−	8.78402i	−0.893731	−	0.649334i
$184$	−8.09017	+	5.87785i	−0.596415	+	0.433321i
$185$	0.854102	−	2.62866i	0.0627948	−	0.193263i
$186$	4.47214			0.327913
$187$	4.18034	−	10.4086i	0.305697	−	0.761154i
$188$	−23.5623			−1.71846
$189$	−1.69098	+	5.20431i	−0.123001	+	0.378558i
$190$	2.23607	−	1.62460i	0.162221	−	0.117861i
$191$	−9.63525	−	7.00042i	−0.697183	−	0.506533i	0.181831	−	0.983330i	$-0.441798\pi$
$191$	−9.63525	−	7.00042i	−0.697183	−	0.506533i	−0.879013	+	0.476797i	$0.841798\pi$
$192$	6.50000	+	20.0049i	0.469097	+	1.44373i
$193$	1.23607	+	3.80423i	0.0889741	+	0.273834i	0.985636	−	0.168881i	$-0.0540153\pi$
$193$	1.23607	+	3.80423i	0.0889741	+	0.273834i	−0.896662	+	0.442715i	$0.854015\pi$
$194$	−0.590170	−	0.428784i	−0.0423717	−	0.0307849i
$195$	−3.11803	+	2.26538i	−0.223287	+	0.162228i
$196$	0.927051	−	2.85317i	0.0662179	−	0.203798i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	−0.690983	−	2.74717i	−0.0491060	−	0.195233i
$199$	−18.0000			−1.27599			−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000			−1.27599			−0.637993	+	0.770042i	$0.720235\pi$
$200$	0.690983	−	2.12663i	0.0488599	−	0.150375i
$201$	−18.5623	+	13.4863i	−1.30928	+	0.951251i
$202$	0.527864	+	0.383516i	0.0371404	+	0.0269841i
$203$	1.80902	+	5.56758i	0.126968	+	0.390768i
$204$	−5.07295	−	15.6129i	−0.355177	−	1.09312i
$205$	−5.23607	−	3.80423i	−0.365703	−	0.265699i
$206$	3.02786	−	2.19987i	0.210961	−	0.153272i
$207$	−0.527864	+	1.62460i	−0.0366891	+	0.112917i
$208$	−2.38197			−0.165160
$209$	4.09017	+	0.277515i	0.282923	+	0.0191961i
$210$	−3.61803			−0.249668
$211$	7.20820	−	22.1846i	0.496233	−	1.52725i	−0.318793	−	0.947824i	$-0.603277\pi$
$211$	7.20820	−	22.1846i	0.496233	−	1.52725i	0.815026	−	0.579424i	$-0.196723\pi$
$212$	25.4164	−	18.4661i	1.74561	−	1.26826i
$213$	0.881966	+	0.640786i	0.0604313	+	0.0439059i
$214$	−1.90983	−	5.87785i	−0.130553	−	0.401802i
$215$	0.236068	+	0.726543i	0.0160997	+	0.0495498i
$216$	−9.89919	−	7.19218i	−0.673554	−	0.489366i
$217$	−1.00000	+	0.726543i	−0.0678844	+	0.0493209i
$218$	−14.1459	+	43.5366i	−0.958081	+	2.94867i
$219$	−13.9443			−0.942267
$220$	8.42705	−	5.29007i	0.568152	−	0.356656i
$221$	8.05573			0.541887
$222$	3.09017	−	9.51057i	0.207399	−	0.638307i
$223$	−8.47214	+	6.15537i	−0.567336	+	0.412194i	−0.834137	−	0.551558i	$-0.814034\pi$
$223$	−8.47214	+	6.15537i	−0.567336	+	0.412194i	0.266800	+	0.963752i	$0.414034\pi$
$224$	−5.42705	−	3.94298i	−0.362610	−	0.263452i
$225$	−0.118034	−	0.363271i	−0.00786893	−	0.0242181i
$226$	1.05573	+	3.24920i	0.0702260	+	0.216133i
$227$	−11.1631	−	8.11048i	−0.740922	−	0.538312i	0.152078	−	0.988369i	$-0.451404\pi$
$227$	−11.1631	−	8.11048i	−0.740922	−	0.538312i	−0.893000	+	0.450057i	$0.851404\pi$
$228$	4.85410	−	3.52671i	0.321471	−	0.233562i
$229$	−9.03444	+	27.8052i	−0.597013	+	1.83742i	−0.0525716	+	0.998617i	$0.516742\pi$
$229$	−9.03444	+	27.8052i	−0.597013	+	1.83742i	−0.544441	+	0.838799i	$0.683258\pi$
$230$	−10.0000			−0.659380
$231$	−4.11803	−	3.44095i	−0.270947	−	0.226398i
$232$	−13.0902			−0.859412
$233$	−7.61803	+	23.4459i	−0.499074	+	1.53599i	0.311436	+	0.950267i	$0.399190\pi$
$233$	−7.61803	+	23.4459i	−0.499074	+	1.53599i	−0.810510	+	0.585725i	$0.800810\pi$
$234$	1.64590	−	1.19581i	0.107596	−	0.0781729i
$235$	−6.35410	−	4.61653i	−0.414496	−	0.301149i
$236$	−4.41641	−	13.5923i	−0.287484	−	0.884784i
$237$	6.89919	+	21.2335i	0.448150	+	1.37926i
$238$	6.11803	+	4.44501i	0.396573	+	0.288127i
$239$	17.7812	−	12.9188i	1.15017	−	0.835645i	0.161664	−	0.986846i	$-0.448314\pi$
$239$	17.7812	−	12.9188i	1.15017	−	0.835645i	0.988503	+	0.151200i	$0.0483139\pi$
$240$	−0.500000	+	1.53884i	−0.0322749	+	0.0993318i
$241$	23.1246			1.48959			0.744794	−	0.667295i	$-0.232548\pi$
$241$	23.1246			1.48959			0.744794	+	0.667295i	$0.232548\pi$
$242$	24.3713	+	3.32244i	1.56665	+	0.213575i
$243$	−3.94427			−0.253025
$244$	−8.56231	+	26.3521i	−0.548145	+	1.68702i
$245$	0.809017	−	0.587785i	0.0516862	−	0.0375522i
$246$	−18.9443	−	13.7638i	−1.20784	−	0.877549i
$247$	0.909830	+	2.80017i	0.0578911	+	0.178170i
$248$	−0.854102	−	2.62866i	−0.0542355	−	0.166920i
$249$	−13.8262	−	10.0453i	−0.876202	−	0.636598i
$250$	1.80902	−	1.31433i	0.114412	−	0.0831254i
$251$	1.76393	−	5.42882i	0.111338	−	0.342664i	−0.879827	−	0.475293i	$-0.842342\pi$
$251$	1.76393	−	5.42882i	0.111338	−	0.342664i	0.991166	+	0.132629i	$0.0423419\pi$
$252$	1.14590			0.0721848
$253$	−11.3820	−	9.51057i	−0.715578	−	0.597924i
$254$	10.6525			0.668396
$255$	1.69098	−	5.20431i	0.105893	−	0.325907i
$256$	7.28115	−	5.29007i	0.455072	−	0.330629i
$257$	3.73607	+	2.71441i	0.233050	+	0.169320i	0.698181	−	0.715921i	$-0.253993\pi$
$257$	3.73607	+	2.71441i	0.233050	+	0.169320i	−0.465132	+	0.885242i	$0.653993\pi$
$258$	0.854102	+	2.62866i	0.0531741	+	0.163653i
$259$	0.854102	+	2.62866i	0.0530713	+	0.163337i
$260$	5.78115	+	4.20025i	0.358532	+	0.260489i
$261$	−1.80902	+	1.31433i	−0.111975	+	0.0813548i
$262$	5.52786	−	17.0130i	0.341513	−	1.05107i
$263$	−8.18034			−0.504421			−0.252211	−	0.967672i	$-0.581158\pi$
$263$	−8.18034			−0.504421			−0.252211	+	0.967672i	$0.581158\pi$
$264$	10.1631	−	6.37988i	0.625497	−	0.392655i
$265$	10.4721			0.643298
$266$	−0.854102	+	2.62866i	−0.0523684	+	0.161173i
$267$	22.5623	−	16.3925i	1.38079	−	1.00320i
$268$	34.4164	+	25.0050i	2.10232	+	1.52742i
$269$	3.90983	+	12.0332i	0.238387	+	0.733678i	0.996654	+	0.0817349i	$0.0260461\pi$
$269$	3.90983	+	12.0332i	0.238387	+	0.733678i	−0.758268	+	0.651943i	$0.773954\pi$
$270$	−3.78115	−	11.6372i	−0.230114	−	0.708217i
$271$	−15.1803	−	11.0292i	−0.922140	−	0.669974i	0.0219158	−	0.999760i	$-0.493023\pi$
$271$	−15.1803	−	11.0292i	−0.922140	−	0.669974i	−0.944056	+	0.329786i	$0.893023\pi$
$272$	2.73607	−	1.98787i	0.165898	−	0.120532i
$273$	1.19098	−	3.66547i	0.0720816	−	0.221844i
$274$	34.4721			2.08254
$275$	3.30902	+	0.224514i	0.199541	+	0.0135387i
$276$	−21.7082			−1.30668
$277$	5.38197	−	16.5640i	0.323371	−	0.995234i	−0.648800	−	0.760959i	$-0.724729\pi$
$277$	5.38197	−	16.5640i	0.323371	−	0.995234i	0.972171	−	0.234274i	$-0.0752714\pi$
$278$	−26.1803	+	19.0211i	−1.57019	+	1.14081i
$279$	−0.381966	−	0.277515i	−0.0228677	−	0.0166144i
$280$	0.690983	+	2.12663i	0.0412941	+	0.127090i
$281$	0.145898	+	0.449028i	0.00870355	+	0.0267868i	0.955314	−	0.295593i	$-0.0955172\pi$
$281$	0.145898	+	0.449028i	0.00870355	+	0.0267868i	−0.946610	+	0.322380i	$0.895517\pi$
$282$	−22.9894	−	16.7027i	−1.36900	−	0.994634i
$283$	22.2984	−	16.2007i	1.32550	−	0.963033i	0.325655	−	0.945489i	$-0.394415\pi$
$283$	22.2984	−	16.2007i	1.32550	−	0.963033i	0.999846	−	0.0175439i	$-0.00558467\pi$
$284$	0.624612	−	1.92236i	0.0370639	−	0.114071i
$285$	2.00000			0.118470
$286$	4.30902	+	17.1315i	0.254798	+	1.01301i
$287$	6.47214			0.382038
$288$	0.791796	−	2.43690i	0.0466570	−	0.143596i
$289$	4.50000	−	3.26944i	0.264706	−	0.192320i
$290$	−10.5902	−	7.69421i	−0.621876	−	0.451820i
$291$	−0.163119	−	0.502029i	−0.00956220	−	0.0294294i
$292$	7.98936	+	24.5887i	0.467542	+	1.43895i
$293$	−14.0902	−	10.2371i	−0.823157	−	0.598058i	0.0944584	−	0.995529i	$-0.469888\pi$
$293$	−14.0902	−	10.2371i	−0.823157	−	0.598058i	−0.917615	+	0.397471i	$0.869888\pi$
$294$	2.92705	−	2.12663i	0.170709	−	0.124027i
$295$	1.47214	−	4.53077i	0.0857111	−	0.263792i
$296$	−6.18034			−0.359225
$297$	6.76393	−	16.8415i	0.392483	−	0.977243i
$298$	−24.9230			−1.44375
$299$	3.29180	−	10.1311i	0.190369	−	0.585897i
$300$	3.92705	−	2.85317i	0.226728	−	0.164728i
$301$	−0.618034	−	0.449028i	−0.0356229	−	0.0258815i
$302$	−1.80902	−	5.56758i	−0.104097	−	0.320378i
$303$	0.145898	+	0.449028i	0.00838162	+	0.0257960i
$304$	1.00000	+	0.726543i	0.0573539	+	0.0416701i
$305$	−7.47214	+	5.42882i	−0.427853	+	0.310854i
$306$	−0.892609	+	2.74717i	−0.0510271	+	0.157045i
$307$	−0.437694			−0.0249805			−0.0124903	−	0.999922i	$-0.503976\pi$
$307$	−0.437694			−0.0249805			−0.0124903	+	0.999922i	$0.503976\pi$
$308$	−3.70820	+	9.23305i	−0.211295	+	0.526102i
$309$	2.70820			0.154064
$310$	0.854102	−	2.62866i	0.0485097	−	0.149298i
$311$	21.9443	−	15.9434i	1.24435	−	0.904070i	0.246466	−	0.969152i	$-0.420731\pi$
$311$	21.9443	−	15.9434i	1.24435	−	0.904070i	0.997880	+	0.0650816i	$0.0207308\pi$
$312$	6.97214	+	5.06555i	0.394719	+	0.286780i
$313$	−5.56231	−	17.1190i	−0.314400	−	0.967624i	−0.976001	−	0.217768i	$-0.930123\pi$
$313$	−5.56231	−	17.1190i	−0.314400	−	0.967624i	0.661601	−	0.749856i	$-0.269877\pi$
$314$	−3.39261	−	10.4414i	−0.191456	−	0.589241i
$315$	0.309017	+	0.224514i	0.0174111	+	0.0126499i
$316$	33.4894	−	24.3314i	1.88392	−	1.36875i
$317$	−9.41641	+	28.9807i	−0.528878	+	1.62772i	0.227639	+	0.973746i	$0.426899\pi$
$317$	−9.41641	+	28.9807i	−0.528878	+	1.62772i	−0.756517	+	0.653974i	$0.773101\pi$
$318$	37.8885			2.12468
$319$	−4.73607	−	18.8294i	−0.265169	−	1.05424i
$320$	13.0000			0.726722
$321$	1.38197	−	4.25325i	0.0771338	−	0.237393i
$322$	8.09017	−	5.87785i	0.450848	−	0.327560i
$323$	−3.38197	−	2.45714i	−0.188178	−	0.136719i
$324$	−7.14590	−	21.9928i	−0.396994	−	1.22182i
$325$	0.736068	+	2.26538i	0.0408297	+	0.125661i
$326$	−0.326238	−	0.237026i	−0.0180686	−	0.0131276i
$327$	−26.7984	+	19.4702i	−1.48195	+	1.07670i
$328$	−4.47214	+	13.7638i	−0.246932	+	0.759980i
$329$	7.85410			0.433011
$330$	11.9721	+	0.812299i	0.659044	+	0.0447156i
$331$	19.5066			1.07218			0.536089	−	0.844161i	$-0.319901\pi$
$331$	19.5066			1.07218			0.536089	+	0.844161i	$0.319901\pi$
$332$	−9.79180	+	30.1360i	−0.537395	+	1.65393i
$333$	−0.854102	+	0.620541i	−0.0468045	+	0.0340055i
$334$	21.7082	+	15.7719i	1.18782	+	0.863002i
$335$	4.38197	+	13.4863i	0.239412	+	0.736836i
$336$	−0.500000	−	1.53884i	−0.0272772	−	0.0839507i
$337$	3.70820	+	2.69417i	0.201999	+	0.146761i	0.684186	−	0.729307i	$-0.260158\pi$
$337$	3.70820	+	2.69417i	0.201999	+	0.146761i	−0.482187	+	0.876068i	$0.660158\pi$
$338$	13.2533	−	9.62908i	0.720884	−	0.523753i
$339$	−0.763932	+	2.35114i	−0.0414911	+	0.127696i
$340$	−10.1459			−0.550239
$341$	3.47214	−	2.17963i	0.188027	−	0.118033i
$342$	−1.05573			−0.0570872
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	1.38197	−	1.00406i	0.0745106	−	0.0541351i
$345$	−5.85410	−	4.25325i	−0.315174	−	0.228988i
$346$	12.8262	+	39.4751i	0.689543	+	2.12219i
$347$	−3.23607	−	9.95959i	−0.173721	−	0.534659i	0.825852	−	0.563888i	$-0.190695\pi$
$347$	−3.23607	−	9.95959i	−0.173721	−	0.534659i	−0.999573	+	0.0292287i	$0.990695\pi$
$348$	−22.9894	−	16.7027i	−1.23236	−	0.895361i
$349$	25.7984	−	18.7436i	1.38096	−	1.00332i	0.384165	−	0.923264i	$-0.374489\pi$
$349$	25.7984	−	18.7436i	1.38096	−	1.00332i	0.996790	−	0.0800583i	$-0.0255107\pi$
$350$	−0.690983	+	2.12663i	−0.0369346	+	0.113673i
$351$	13.0344			0.695727
$352$	17.0729	+	14.2658i	0.909991	+	0.760372i
$353$	6.56231			0.349276			0.174638	−	0.984633i	$-0.444124\pi$
$353$	6.56231			0.349276			0.174638	+	0.984633i	$0.444124\pi$
$354$	5.32624	−	16.3925i	0.283086	−	0.871250i
$355$	0.545085	−	0.396027i	0.0289301	−	0.0210190i
$356$	−41.8328	−	30.3933i	−2.21713	−	1.61084i
$357$	1.69098	+	5.20431i	0.0894963	+	0.275441i
$358$	12.0106	+	36.9650i	0.634782	+	1.95366i
$359$	−27.4894	−	19.9722i	−1.45083	−	1.05409i	−0.985636	−	0.168884i	$-0.945984\pi$
$359$	−27.4894	−	19.9722i	−1.45083	−	1.05409i	−0.465197	−	0.885207i	$-0.654016\pi$
$360$	−0.690983	+	0.502029i	−0.0364180	+	0.0264592i
$361$	−5.39919	+	16.6170i	−0.284168	+	0.874578i
$362$	32.3607			1.70084
$363$	12.8541	+	12.3107i	0.674665	+	0.646146i
$364$	−7.14590			−0.374547
$365$	−2.66312	+	8.19624i	−0.139394	+	0.429011i
$366$	−27.0344	+	19.6417i	−1.41311	+	1.02669i
$367$	−19.7812	−	14.3718i	−1.03257	−	0.750204i	−0.0637468	−	0.997966i	$-0.520305\pi$
$367$	−19.7812	−	14.3718i	−1.03257	−	0.750204i	−0.968821	+	0.247762i	$0.920305\pi$
$368$	−1.38197	−	4.25325i	−0.0720400	−	0.221716i
$369$	0.763932	+	2.35114i	0.0397687	+	0.122396i
$370$	−5.00000	−	3.63271i	−0.259938	−	0.188856i
$371$	−8.47214	+	6.15537i	−0.439851	+	0.319571i
$372$	1.85410	−	5.70634i	0.0961307	−	0.295860i
$373$	−29.1246			−1.50802			−0.754008	−	0.656866i	$-0.771882\pi$
$373$	−29.1246			−1.50802			−0.754008	+	0.656866i	$0.771882\pi$
$374$	−19.2467	−	16.0822i	−0.995224	−	0.831591i
$375$	1.61803			0.0835549
$376$	−5.42705	+	16.7027i	−0.279879	+	0.861378i
$377$	11.2812	−	8.19624i	0.581009	−	0.422128i
$378$	9.89919	+	7.19218i	0.509159	+	0.369926i
$379$	−5.48278	−	16.8743i	−0.281631	−	0.866772i	−0.987388	−	0.158318i	$-0.949393\pi$
$379$	−5.48278	−	16.8743i	−0.281631	−	0.866772i	0.705757	−	0.708454i	$-0.250607\pi$
$380$	−1.14590	−	3.52671i	−0.0587833	−	0.180916i
$381$	6.23607	+	4.53077i	0.319483	+	0.232118i
$382$	−21.5451	+	15.6534i	−1.10234	+	0.800899i
$383$	0.680340	−	2.09387i	0.0347637	−	0.106992i	−0.932169	−	0.362024i	$-0.882086\pi$
$383$	0.680340	−	2.09387i	0.0347637	−	0.106992i	0.966933	+	0.255032i	$0.0820860\pi$
$384$	25.3262			1.29242
$385$	−2.80902	+	1.76336i	−0.143161	+	0.0898689i
$386$	8.94427			0.455251
$387$	0.0901699	−	0.277515i	0.00458360	−	0.0141069i
$388$	−0.791796	+	0.575274i	−0.0401974	+	0.0292051i
$389$	10.8713	+	7.89848i	0.551198	+	0.400469i	0.828227	−	0.560393i	$-0.189350\pi$
$389$	10.8713	+	7.89848i	0.551198	+	0.400469i	−0.277029	+	0.960862i	$0.589350\pi$
$390$	2.66312	+	8.19624i	0.134852	+	0.415033i
$391$	4.67376	+	14.3844i	0.236362	+	0.727448i
$392$	−1.80902	−	1.31433i	−0.0913692	−	0.0663836i
$393$	10.4721	−	7.60845i	0.528249	−	0.383796i
$394$	−8.29180	+	25.5195i	−0.417735	+	1.28566i
$395$	13.7984			0.694272
$396$	−3.79180	−	0.257270i	−0.190545	−	0.0129283i
$397$	−34.1591			−1.71439			−0.857197	−	0.514989i	$-0.827796\pi$
$397$	−34.1591			−1.71439			−0.857197	+	0.514989i	$0.827796\pi$
$398$	−12.4377	+	38.2793i	−0.623445	+	1.91877i
$399$	−1.61803	+	1.17557i	−0.0810030	+	0.0588521i
$400$	0.809017	+	0.587785i	0.0404508	+	0.0293893i
$401$	−6.95492	−	21.4050i	−0.347312	−	1.06892i	−0.960334	−	0.278851i	$-0.910047\pi$
$401$	−6.95492	−	21.4050i	−0.347312	−	1.06892i	0.613023	−	0.790065i	$-0.289953\pi$
$402$	15.8541	+	48.7939i	0.790731	+	2.43362i
$403$	2.38197	+	1.73060i	0.118654	+	0.0862073i
$404$	0.708204	−	0.514540i	0.0352345	−	0.0255993i
$405$	2.38197	−	7.33094i	0.118361	−	0.364277i
$406$	13.0902			0.649654
$407$	−2.23607	−	8.89002i	−0.110838	−	0.440662i
$408$	−12.2361			−0.605776
$409$	0.381966	−	1.17557i	0.0188870	−	0.0581282i	−0.941169	−	0.337937i	$-0.890271\pi$
$409$	0.381966	−	1.17557i	0.0188870	−	0.0581282i	0.960056	+	0.279809i	$0.0902710\pi$
$410$	−11.7082	+	8.50651i	−0.578227	+	0.420106i
$411$	20.1803	+	14.6619i	0.995423	+	0.723217i
$412$	−1.55166	−	4.77553i	−0.0764449	−	0.235273i
$413$	1.47214	+	4.53077i	0.0724391	+	0.222945i
$414$	3.09017	+	2.24514i	0.151874	+	0.110343i
$415$	−8.54508	+	6.20837i	−0.419462	+	0.304757i
$416$	−4.93769	+	15.1967i	−0.242090	+	0.745078i
$417$	−23.4164			−1.14671
$418$	3.41641	−	8.50651i	0.167102	−	0.416067i
$419$	27.3050			1.33393			0.666967	−	0.745087i	$-0.267592\pi$
$419$	27.3050			1.33393			0.666967	+	0.745087i	$0.267592\pi$
$420$	−1.50000	+	4.61653i	−0.0731925	+	0.225263i
$421$	−2.83688	+	2.06111i	−0.138261	+	0.100453i	−0.654766	−	0.755832i	$-0.727233\pi$
$421$	−2.83688	+	2.06111i	−0.138261	+	0.100453i	0.516505	+	0.856284i	$0.327233\pi$
$422$	−42.1976	−	30.6583i	−2.05415	−	1.49242i
$423$	0.927051	+	2.85317i	0.0450748	+	0.138726i
$424$	−7.23607	−	22.2703i	−0.351415	−	1.08154i
$425$	−2.73607	−	1.98787i	−0.132719	−	0.0964258i
$426$	1.97214	−	1.43284i	0.0955503	−	0.0694214i
$427$	2.85410	−	8.78402i	0.138120	−	0.425089i
$428$	−8.29180			−0.400799
$429$	−4.76393	+	11.8617i	−0.230005	+	0.572689i
$430$	1.70820			0.0823769
$431$	3.19098	−	9.82084i	0.153704	−	0.473053i	−0.844323	−	0.535834i	$-0.819997\pi$
$431$	3.19098	−	9.82084i	0.153704	−	0.473053i	0.998027	+	0.0627814i	$0.0199971\pi$
$432$	4.42705	−	3.21644i	0.212997	−	0.154751i
$433$	13.7812	+	10.0126i	0.662280	+	0.481175i	0.867432	−	0.497556i	$-0.165769\pi$
$433$	13.7812	+	10.0126i	0.662280	+	0.481175i	−0.205152	+	0.978730i	$0.565769\pi$
$434$	0.854102	+	2.62866i	0.0409982	+	0.126180i
$435$	−2.92705	−	9.00854i	−0.140341	−	0.431926i
$436$	49.6869	+	36.0997i	2.37957	+	1.72886i
$437$	−4.47214	+	3.24920i	−0.213931	+	0.155430i
$438$	−9.63525	+	29.6543i	−0.460390	+	1.41694i
$439$	17.7082			0.845166			0.422583	−	0.906324i	$-0.361123\pi$
$439$	17.7082			0.845166			0.422583	+	0.906324i	$0.361123\pi$
$440$	−1.80902	−	7.19218i	−0.0862415	−	0.342874i
$441$	−0.381966			−0.0181889
$442$	5.56637	−	17.1315i	0.264765	−	0.814864i
$443$	28.0344	−	20.3682i	1.33196	−	0.967723i	0.332258	−	0.943189i	$-0.392190\pi$
$443$	28.0344	−	20.3682i	1.33196	−	0.967723i	0.999699	−	0.0245344i	$-0.00781031\pi$
$444$	−10.8541	−	7.88597i	−0.515113	−	0.374251i
$445$	−5.32624	−	16.3925i	−0.252488	−	0.777078i
$446$	7.23607	+	22.2703i	0.342638	+	1.05453i
$447$	−14.5902	−	10.6004i	−0.690091	−	0.501381i
$448$	−10.5172	+	7.64121i	−0.496892	+	0.361013i
$449$	7.50000	−	23.0826i	0.353947	−	1.08934i	−0.602671	−	0.797990i	$-0.705897\pi$
$449$	7.50000	−	23.0826i	0.353947	−	1.08934i	0.956618	−	0.291347i	$-0.0941033\pi$
$450$	−0.854102			−0.0402628
$451$	−21.4164	−	1.45309i	−1.00846	−	0.0684231i
$452$	4.58359			0.215594
$453$	1.30902	−	4.02874i	0.0615030	−	0.189287i
$454$	−24.9615	+	18.1356i	−1.17150	+	0.851145i
$455$	−1.92705	−	1.40008i	−0.0903415	−	0.0656370i
$456$	−1.38197	−	4.25325i	−0.0647165	−	0.199177i
$457$	10.4377	+	32.1239i	0.488255	+	1.50269i	0.827211	+	0.561891i	$0.189926\pi$
$457$	10.4377	+	32.1239i	0.488255	+	1.50269i	−0.338956	+	0.940802i	$0.610074\pi$
$458$	52.8885	+	38.4258i	2.47132	+	1.79552i
$459$	−14.9721	+	10.8779i	−0.698839	+	0.507737i
$460$	−4.14590	+	12.7598i	−0.193303	+	0.594927i
$461$	29.7082			1.38365			0.691825	−	0.722066i	$-0.256807\pi$
$461$	29.7082			1.38365			0.691825	+	0.722066i	$0.256807\pi$
$462$	−10.1631	+	6.37988i	−0.472831	+	0.296819i
$463$	23.1246			1.07469			0.537346	−	0.843362i	$-0.319427\pi$
$463$	23.1246			1.07469			0.537346	+	0.843362i	$0.319427\pi$
$464$	1.80902	−	5.56758i	0.0839815	−	0.258468i
$465$	1.61803	−	1.17557i	0.0750345	−	0.0545158i
$466$	44.5967	+	32.4014i	2.06590	+	1.50097i
$467$	−5.15248	−	15.8577i	−0.238428	−	0.733806i	−0.996648	−	0.0818076i	$-0.973931\pi$
$467$	−5.15248	−	15.8577i	−0.238428	−	0.733806i	0.758220	−	0.651999i	$-0.226069\pi$
$468$	−0.843459	−	2.59590i	−0.0389889	−	0.119995i
$469$	−11.4721	−	8.33499i	−0.529734	−	0.384874i
$470$	−14.2082	+	10.3229i	−0.655376	+	0.476158i
$471$	2.45492	−	7.55545i	0.113117	−	0.348137i
$472$	−10.6525			−0.490320
$473$	1.94427	+	1.62460i	0.0893977	+	0.0746991i
$474$	49.9230			2.29304
$475$	0.381966	−	1.17557i	0.0175258	−	0.0539389i
$476$	8.20820	−	5.96361i	0.376222	−	0.273342i
$477$	−3.23607	−	2.35114i	−0.148169	−	0.107651i
$478$	−15.1869	−	46.7405i	−0.694633	−	2.13786i
$479$	−2.67376	−	8.22899i	−0.122167	−	0.375992i	0.871207	−	0.490916i	$-0.163338\pi$
$479$	−2.67376	−	8.22899i	−0.122167	−	0.375992i	−0.993374	+	0.114923i	$0.963338\pi$
$480$	8.78115	+	6.37988i	0.400803	+	0.291200i
$481$	5.32624	−	3.86974i	0.242856	−	0.176445i
$482$	15.9787	−	49.1774i	0.727810	−	2.23997i
$483$	7.23607			0.329252
$484$	14.3435	−	29.7198i	0.651975	−	1.35090i
$485$	−0.326238			−0.0148137
$486$	−2.72542	+	8.38800i	−0.123628	+	0.380487i
$487$	19.5623	−	14.2128i	0.886453	−	0.644046i	−0.0484980	−	0.998823i	$-0.515443\pi$
$487$	19.5623	−	14.2128i	0.886453	−	0.644046i	0.934951	+	0.354778i	$0.115443\pi$
$488$	16.7082	+	12.1392i	0.756345	+	0.549517i
$489$	−0.0901699	−	0.277515i	−0.00407763	−	0.0125496i
$490$	−0.690983	−	2.12663i	−0.0312154	−	0.0960712i
$491$	−30.6525	−	22.2703i	−1.38333	−	1.00505i	−0.996561	−	0.0828681i	$-0.973592\pi$
$491$	−30.6525	−	22.2703i	−1.38333	−	1.00505i	−0.386766	−	0.922178i	$-0.626408\pi$
$492$	−25.4164	+	18.4661i	−1.14586	+	0.832516i
$493$	−6.11803	+	18.8294i	−0.275542	+	0.848032i
$494$	6.58359			0.296210
$495$	−0.972136	−	0.812299i	−0.0436943	−	0.0365101i
$496$	1.23607			0.0555011
$497$	−0.208204	+	0.640786i	−0.00933922	+	0.0287432i
$498$	−30.9164	+	22.4621i	−1.38540	+	1.00655i
$499$	−4.88197	−	3.54696i	−0.218547	−	0.158784i	0.473125	−	0.880995i	$-0.343126\pi$
$499$	−4.88197	−	3.54696i	−0.218547	−	0.158784i	−0.691672	+	0.722212i	$0.743126\pi$
$500$	−0.927051	−	2.85317i	−0.0414590	−	0.127598i
$501$	6.00000	+	18.4661i	0.268060	+	0.825005i
$502$	−10.3262	−	7.50245i	−0.460883	−	0.334851i
$503$	6.54508	−	4.75528i	0.291831	−	0.212028i	−0.432230	−	0.901763i	$-0.642273\pi$
$503$	6.54508	−	4.75528i	0.291831	−	0.212028i	0.724061	+	0.689736i	$0.242273\pi$
$504$	0.263932	−	0.812299i	0.0117565	−	0.0361827i
$505$	0.291796			0.0129848
$506$	−28.0902	+	17.6336i	−1.24876	+	0.783907i
$507$	11.8541			0.526459
$508$	4.41641	−	13.5923i	0.195946	−	0.603061i
$509$	14.8541	−	10.7921i	0.658396	−	0.478353i	−0.207725	−	0.978187i	$-0.566606\pi$
$509$	14.8541	−	10.7921i	0.658396	−	0.478353i	0.866121	+	0.499834i	$0.166606\pi$
$510$	−9.89919	−	7.19218i	−0.438343	−	0.318475i
$511$	−2.66312	−	8.19624i	−0.117809	−	0.362580i
$512$	3.45492	+	10.6331i	0.152687	+	0.469923i
$513$	−5.47214	−	3.97574i	−0.241601	−	0.175533i
$514$	8.35410	−	6.06961i	0.368484	−	0.267719i
$515$	0.517221	−	1.59184i	0.0227915	−	0.0701450i
$516$	3.70820			0.163245
$517$	−25.9894	−	1.76336i	−1.14301	−	0.0775523i
$518$	6.18034			0.271549
$519$	−9.28115	+	28.5645i	−0.407397	+	1.25384i
$520$	4.30902	−	3.13068i	0.188963	−	0.137290i
$521$	−6.61803	−	4.80828i	−0.289941	−	0.210655i	0.433301	−	0.901249i	$-0.357349\pi$
$521$	−6.61803	−	4.80828i	−0.289941	−	0.210655i	−0.723242	+	0.690595i	$0.757349\pi$
$522$	1.54508	+	4.75528i	0.0676265	+	0.208133i
$523$	2.42705	+	7.46969i	0.106128	+	0.326627i	0.989993	−	0.141113i	$-0.0450682\pi$
$523$	2.42705	+	7.46969i	0.106128	+	0.326627i	−0.883866	+	0.467740i	$0.845068\pi$
$524$	−19.4164	−	14.1068i	−0.848210	−	0.616260i
$525$	−1.30902	+	0.951057i	−0.0571302	+	0.0415075i
$526$	−5.65248	+	17.3965i	−0.246460	+	0.758525i
$527$	−4.18034			−0.182098
$528$	1.30902	+	5.20431i	0.0569677	+	0.226489i
$529$	−3.00000			−0.130435
$530$	7.23607	−	22.2703i	0.314315	−	0.967361i
$531$	−1.47214	+	1.06957i	−0.0638853	+	0.0464154i
$532$	3.00000	+	2.17963i	0.130066	+	0.0944988i
$533$	−4.76393	−	14.6619i	−0.206349	−	0.635076i
$534$	−19.2705	−	59.3085i	−0.833917	−	2.56653i
$535$	−2.23607	−	1.62460i	−0.0966736	−	0.0702375i
$536$	25.6525	−	18.6376i	1.10802	−	0.805022i
$537$	−8.69098	+	26.7481i	−0.375044	+	1.15427i
$538$	28.2918			1.21975
$539$	1.23607	−	3.07768i	0.0532412	−	0.132565i
$540$	−16.4164			−0.706450
$541$	3.97214	−	12.2250i	0.170775	−	0.525593i	−0.828640	−	0.559782i	$-0.810885\pi$
$541$	3.97214	−	12.2250i	0.170775	−	0.525593i	0.999415	+	0.0341892i	$0.0108849\pi$
$542$	−33.9443	+	24.6620i	−1.45803	+	1.05932i
$543$	18.9443	+	13.7638i	0.812977	+	0.590662i
$544$	−7.01064	−	21.5765i	−0.300579	−	0.925087i
$545$	6.32624	+	19.4702i	0.270986	+	0.834010i
$546$	−6.97214	−	5.06555i	−0.298380	−	0.216786i
$547$	−32.4164	+	23.5519i	−1.38603	+	1.00701i	−0.389737	+	0.920926i	$0.627434\pi$
$547$	−32.4164	+	23.5519i	−1.38603	+	1.00701i	−0.996288	+	0.0860804i	$0.972566\pi$
$548$	14.2918	−	43.9856i	0.610515	−	1.87897i
$549$	3.52786			0.150566
$550$	2.76393	−	6.88191i	0.117854	−	0.293446i
$551$	−7.23607			−0.308267
$552$	−5.00000	+	15.3884i	−0.212814	+	0.654975i
$553$	−11.1631	+	8.11048i	−0.474704	+	0.344893i
$554$	−31.5066	−	22.8909i	−1.33859	−	0.972540i
$555$	−1.38197	−	4.25325i	−0.0586612	−	0.180541i
$556$	13.4164	+	41.2915i	0.568982	+	1.75115i
$557$	3.47214	+	2.52265i	0.147119	+	0.106888i	0.658910	−	0.752222i	$-0.271018\pi$
$557$	3.47214	+	2.52265i	0.147119	+	0.106888i	−0.511791	+	0.859110i	$0.671018\pi$
$558$	−0.854102	+	0.620541i	−0.0361570	+	0.0262696i
$559$	−0.562306	+	1.73060i	−0.0237830	+	0.0731966i
$560$	−1.00000			−0.0422577
$561$	−4.42705	−	17.6008i	−0.186910	−	0.743106i
$562$	1.05573			0.0445332
$563$	−6.60739	+	20.3355i	−0.278468	+	0.857037i	0.709812	+	0.704391i	$0.248780\pi$
$563$	−6.60739	+	20.3355i	−0.278468	+	0.857037i	−0.988281	+	0.152647i	$0.951220\pi$
$564$	−30.8435	+	22.4091i	−1.29874	+	0.943593i
$565$	1.23607	+	0.898056i	0.0520018	+	0.0377815i
$566$	−19.0451	−	58.6147i	−0.800525	−	2.46376i
$567$	2.38197	+	7.33094i	0.100033	+	0.307870i
$568$	−1.21885	−	0.885544i	−0.0511417	−	0.0371566i
$569$	10.6803	−	7.75972i	0.447743	−	0.325304i	−0.340961	−	0.940077i	$-0.610752\pi$
$569$	10.6803	−	7.75972i	0.447743	−	0.325304i	0.788704	+	0.614773i	$0.210752\pi$
$570$	1.38197	−	4.25325i	0.0578842	−	0.178149i
$571$	10.9787			0.459445			0.229722	−	0.973256i	$-0.426218\pi$
$571$	10.9787			0.459445			0.229722	+	0.973256i	$0.426218\pi$
$572$	23.6459	+	1.60435i	0.988685	+	0.0670814i
$573$	−19.2705			−0.805037
$574$	4.47214	−	13.7638i	0.186663	−	0.574491i
$575$	−3.61803	+	2.62866i	−0.150882	+	0.109623i
$576$	−4.01722	−	2.91868i	−0.167384	−	0.121612i
$577$	−5.62868	−	17.3233i	−0.234325	−	0.721178i	−0.997210	−	0.0746441i	$-0.976218\pi$
$577$	−5.62868	−	17.3233i	−0.234325	−	0.721178i	0.762885	−	0.646534i	$-0.223782\pi$
$578$	−3.84346	−	11.8290i	−0.159867	−	0.492019i
$579$	5.23607	+	3.80423i	0.217604	+	0.158098i
$580$	−14.2082	+	10.3229i	−0.589964	+	0.428634i
$581$	3.26393	−	10.0453i	0.135411	−	0.416751i
$582$	−1.18034			−0.0489267
$583$	29.4164	−	18.4661i	1.21830	−	0.764788i
$584$	19.2705			0.797419
$585$	0.281153	−	0.865300i	0.0116242	−	0.0357757i
$586$	−31.5066	+	22.8909i	−1.30152	+	0.945613i
$587$	−32.5795	−	23.6704i	−1.34470	−	0.976982i	−0.999257	−	0.0385431i	$-0.987728\pi$
$587$	−32.5795	−	23.6704i	−1.34470	−	0.976982i	−0.345444	−	0.938439i	$-0.612272\pi$
$588$	−1.50000	−	4.61653i	−0.0618590	−	0.190382i
$589$	−0.472136	−	1.45309i	−0.0194540	−	0.0598733i
$590$	−8.61803	−	6.26137i	−0.354799	−	0.257776i
$591$	−15.7082	+	11.4127i	−0.646149	+	0.469455i
$592$	0.854102	−	2.62866i	0.0351034	−	0.108037i
$593$	−14.7984			−0.607696			−0.303848	−	0.952720i	$-0.598272\pi$
$593$	−14.7984			−0.607696			−0.303848	+	0.952720i	$0.598272\pi$
$594$	−31.1418	−	26.0216i	−1.27776	−	1.06768i
$595$	3.38197			0.138647
$596$	−10.3328	+	31.8011i	−0.423249	+	1.30263i
$597$	−23.5623	+	17.1190i	−0.964341	+	0.700635i
$598$	−19.2705	−	14.0008i	−0.788030	−	0.572537i
$599$	−2.24671	−	6.91467i	−0.0917981	−	0.282526i	0.894608	−	0.446852i	$-0.147455\pi$
$599$	−2.24671	−	6.91467i	−0.0917981	−	0.282526i	−0.986406	+	0.164326i	$0.947455\pi$
$600$	−1.11803	−	3.44095i	−0.0456435	−	0.140476i
$601$	−9.23607	−	6.71040i	−0.376747	−	0.273723i	0.383256	−	0.923642i	$-0.374803\pi$
$601$	−9.23607	−	6.71040i	−0.376747	−	0.273723i	−0.760003	+	0.649919i	$0.774803\pi$
$602$	−1.38197	+	1.00406i	−0.0563247	+	0.0409223i
$603$	1.67376	−	5.15131i	0.0681609	−	0.209778i
$604$	−7.85410			−0.319579
$605$	9.69098	−	5.20431i	0.393994	−	0.211585i
$606$	1.05573			0.0428860
$607$	−4.04508	+	12.4495i	−0.164185	+	0.505309i	−0.998975	−	0.0452587i	$-0.985589\pi$
$607$	−4.04508	+	12.4495i	−0.164185	+	0.505309i	0.834790	+	0.550568i	$0.185589\pi$
$608$	6.70820	−	4.87380i	0.272054	−	0.197659i
$609$	7.66312	+	5.56758i	0.310525	+	0.225610i
$610$	6.38197	+	19.6417i	0.258398	+	0.795268i
$611$	−5.78115	−	17.7926i	−0.233880	−	0.719810i
$612$	3.13525	+	2.27790i	0.126735	+	0.0920785i
$613$	−10.3820	+	7.54294i	−0.419324	+	0.304656i	−0.777366	−	0.629049i	$-0.783444\pi$
$613$	−10.3820	+	7.54294i	−0.419324	+	0.304656i	0.358042	+	0.933705i	$0.383444\pi$
$614$	−0.302439	+	0.930812i	−0.0122055	+	0.0375645i
$615$	−10.4721			−0.422277
$616$	5.69098	+	4.75528i	0.229296	+	0.191596i
$617$	−7.23607			−0.291313			−0.145657	−	0.989335i	$-0.546529\pi$
$617$	−7.23607			−0.291313			−0.145657	+	0.989335i	$0.546529\pi$
$618$	1.87132	−	5.75934i	0.0752756	−	0.231675i
$619$	10.9443	−	7.95148i	0.439887	−	0.319597i	−0.345703	−	0.938344i	$-0.612359\pi$
$619$	10.9443	−	7.95148i	0.439887	−	0.319597i	0.785590	+	0.618747i	$0.212359\pi$
$620$	−3.00000	−	2.17963i	−0.120483	−	0.0875360i
$621$	7.56231	+	23.2744i	0.303465	+	0.933969i
$622$	−18.7426	−	57.6839i	−0.751512	−	2.31291i
$623$	13.9443	+	10.1311i	0.558665	+	0.405894i
$624$	−3.11803	+	2.26538i	−0.124821	+	0.0906880i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−40.2492			−1.60868
$627$	5.61803	−	3.52671i	0.224363	−	0.140843i
$628$	−14.7295			−0.587771
$629$	−2.88854	+	8.89002i	−0.115174	+	0.354468i
$630$	0.690983	−	0.502029i	0.0275294	−	0.0200013i
$631$	−23.0623	−	16.7557i	−0.918096	−	0.667036i	0.0249534	−	0.999689i	$-0.492056\pi$
$631$	−23.0623	−	16.7557i	−0.918096	−	0.667036i	−0.943049	+	0.332653i	$0.892056\pi$
$632$	−9.53444	−	29.3440i	−0.379260	−	1.16724i
$633$	−11.6631	−	35.8954i	−0.463567	−	1.42671i
$634$	55.1246	+	40.0504i	2.18928	+	1.59060i
$635$	3.85410	−	2.80017i	0.152945	−	0.111121i
$636$	15.7082	−	48.3449i	0.622871	−	1.91700i
$637$	2.38197			0.0943769
$638$	−43.3156	−	2.93893i	−1.71488	−	0.116353i
$639$	−0.257354			−0.0101808
$640$	4.83688	−	14.8864i	0.191195	−	0.588436i
$641$	21.0172	−	15.2699i	0.830130	−	0.603125i	−0.0894659	−	0.995990i	$-0.528516\pi$
$641$	21.0172	−	15.2699i	0.830130	−	0.603125i	0.919596	+	0.392865i	$0.128516\pi$
$642$	−8.09017	−	5.87785i	−0.319294	−	0.231980i
$643$	−4.26393	−	13.1230i	−0.168153	−	0.517522i	0.831102	−	0.556120i	$-0.187711\pi$
$643$	−4.26393	−	13.1230i	−0.168153	−	0.517522i	−0.999255	+	0.0385985i	$0.987711\pi$
$644$	−4.14590	−	12.7598i	−0.163371	−	0.502805i
$645$	1.00000	+	0.726543i	0.0393750	+	0.0286076i
$646$	−7.56231	+	5.49434i	−0.297535	+	0.216172i
$647$	−12.4058	+	38.1810i	−0.487721	+	1.50105i	0.340280	+	0.940324i	$0.389478\pi$
$647$	−12.4058	+	38.1810i	−0.487721	+	1.50105i	−0.828001	+	0.560727i	$0.810522\pi$
$648$	−17.2361			−0.677097
$649$	−3.85410	−	15.3229i	−0.151287	−	0.601477i
$650$	5.32624			0.208912
$651$	−0.618034	+	1.90211i	−0.0242227	+	0.0745497i
$652$	−0.437694	+	0.318003i	−0.0171414	+	0.0124540i
$653$	12.7984	+	9.29856i	0.500839	+	0.363881i	0.809337	−	0.587344i	$-0.199826\pi$
$653$	12.7984	+	9.29856i	0.500839	+	0.363881i	−0.308498	+	0.951225i	$0.599826\pi$
$654$	22.8885	+	70.4437i	0.895013	+	2.75457i
$655$	−2.47214	−	7.60845i	−0.0965943	−	0.297287i
$656$	−5.23607	−	3.80423i	−0.204434	−	0.148530i
$657$	2.66312	−	1.93487i	0.103898	−	0.0754864i
$658$	5.42705	−	16.7027i	0.211568	−	0.651141i
$659$	25.0344			0.975203			0.487602	−	0.873066i	$-0.337872\pi$
$659$	25.0344			0.975203			0.487602	+	0.873066i	$0.337872\pi$
$660$	6.00000	−	14.9394i	0.233550	−	0.581515i
$661$	−33.4164			−1.29975			−0.649874	−	0.760042i	$-0.725178\pi$
$661$	−33.4164			−1.29975			−0.649874	+	0.760042i	$0.725178\pi$
$662$	13.4787	−	41.4832i	0.523865	−	1.61229i
$663$	10.5451	−	7.66145i	0.409537	−	0.297546i
$664$	19.1074	+	13.8823i	0.741511	+	0.538739i
$665$	0.381966	+	1.17557i	0.0148120	+	0.0455867i
$666$	0.729490	+	2.24514i	0.0282672	+	0.0869974i
$667$	21.1803	+	15.3884i	0.820106	+	0.595842i
$668$	29.1246	−	21.1603i	1.12687	−	0.818715i
$669$	−5.23607	+	16.1150i	−0.202438	+	0.623040i
$670$	31.7082			1.22499
$671$	−11.4164	+	28.4257i	−0.440726	+	1.09736i
$672$	−10.8541			−0.418706
$673$	−4.29180	+	13.2088i	−0.165437	+	0.509161i	−0.999068	−	0.0431594i	$-0.986258\pi$
$673$	−4.29180	+	13.2088i	−0.165437	+	0.509161i	0.833632	+	0.552321i	$0.186258\pi$
$674$	8.29180	−	6.02434i	0.319388	−	0.232049i
$675$	−4.42705	−	3.21644i	−0.170397	−	0.123801i
$676$	−6.79180	−	20.9030i	−0.261223	−	0.803961i
$677$	13.0238	+	40.0831i	0.500545	+	1.54052i	0.808133	+	0.589000i	$0.200478\pi$
$677$	13.0238	+	40.0831i	0.500545	+	1.54052i	−0.307588	+	0.951520i	$0.599522\pi$
$678$	4.47214	+	3.24920i	0.171751	+	0.124785i
$679$	0.263932	−	0.191758i	0.0101288	−	0.00735899i
$680$	−2.33688	+	7.19218i	−0.0896153	+	0.275808i
$681$	−22.3262			−0.855543
$682$	−2.23607	−	8.89002i	−0.0856235	−	0.340417i
$683$	39.2361			1.50133			0.750663	−	0.660685i	$-0.229734\pi$
$683$	39.2361			1.50133			0.750663	+	0.660685i	$0.229734\pi$
$684$	−0.437694	+	1.34708i	−0.0167357	+	0.0515070i
$685$	12.4721	−	9.06154i	0.476536	−	0.346224i
$686$	1.80902	+	1.31433i	0.0690686	+	0.0501813i
$687$	14.6180	+	44.9897i	0.557713	+	1.71646i
$688$	0.236068	+	0.726543i	0.00900001	+	0.0276992i
$689$	20.1803	+	14.6619i	0.768810	+	0.558573i
$690$	−13.0902	+	9.51057i	−0.498334	+	0.362061i
$691$	8.29180	−	25.5195i	0.315435	−	0.970808i	−0.660140	−	0.751142i	$-0.729503\pi$
$691$	8.29180	−	25.5195i	0.315435	−	0.970808i	0.975575	−	0.219666i	$-0.0704968\pi$
$692$	55.6869			2.11690
$693$	1.26393	+	0.0857567i	0.0480128	+	0.00325763i
$694$	−23.4164			−0.888875
$695$	−4.47214	+	13.7638i	−0.169638	+	0.522091i
$696$	−17.1353	+	12.4495i	−0.649510	+	0.471897i
$697$	17.7082	+	12.8658i	0.670746	+	0.487326i
$698$	−22.0344	−	67.8150i	−0.834016	−	2.56684i
$699$	12.3262	+	37.9363i	0.466221	+	1.43488i
$700$	2.42705	+	1.76336i	0.0917339	+	0.0666486i
$701$	−9.14590	+	6.64488i	−0.345436	+	0.250974i	−0.746952	−	0.664878i	$-0.768483\pi$
$701$	−9.14590	+	6.64488i	−0.345436	+	0.250974i	0.401516	+	0.915852i	$0.368483\pi$
$702$	9.00658	−	27.7194i	0.339931	−	1.04620i
$703$	−3.41641			−0.128852
$704$	36.5172	−	22.9236i	1.37629	−	0.863967i
$705$	−12.7082			−0.478619
$706$	4.53444	−	13.9556i	0.170656	−	0.525225i
$707$	−0.236068	+	0.171513i	−0.00887825	+	0.00645043i
$708$	−18.7082	−	13.5923i	−0.703097	−	0.510830i
$709$	13.2082	+	40.6507i	0.496045	+	1.52667i	0.815323	+	0.579007i	$0.196560\pi$
$709$	13.2082	+	40.6507i	0.496045	+	1.52667i	−0.319278	+	0.947661i	$0.603440\pi$
$710$	−0.465558	−	1.43284i	−0.0174721	−	0.0537736i
$711$	−4.26393	−	3.09793i	−0.159910	−	0.116181i
$712$	−31.1803	+	22.6538i	−1.16853	+	0.848989i
$713$	−1.70820	+	5.25731i	−0.0639727	+	0.196888i
$714$	12.2361			0.457923
$715$	6.06231	+	5.06555i	0.226717	+	0.189441i
$716$	52.1459			1.94878
$717$	10.9894	−	33.8218i	0.410405	−	1.26310i
$718$	−61.4681	+	44.6592i	−2.29397	+	1.66667i
$719$	11.2361	+	8.16348i	0.419035	+	0.304446i	0.777249	−	0.629193i	$-0.216614\pi$
$719$	11.2361	+	8.16348i	0.419035	+	0.304446i	−0.358215	+	0.933639i	$0.616614\pi$
$720$	−0.118034	−	0.363271i	−0.00439887	−	0.0135383i
$721$	0.517221	+	1.59184i	0.0192623	+	0.0592833i
$722$	31.6074	+	22.9641i	1.17631	+	0.854636i
$723$	30.2705	−	21.9928i	1.12577	−	0.817922i
$724$	13.4164	−	41.2915i	0.498617	−	1.53458i
$725$	−5.85410			−0.217416
$726$	35.0623	−	18.8294i	1.30128	−	0.698824i
$727$	−21.4377			−0.795080			−0.397540	−	0.917585i	$-0.630136\pi$
$727$	−21.4377			−0.795080			−0.397540	+	0.917585i	$0.630136\pi$
$728$	−1.64590	+	5.06555i	−0.0610010	+	0.187742i
$729$	−23.8713	+	17.3435i	−0.884123	+	0.642353i
$730$	15.5902	+	11.3269i	0.577018	+	0.419228i
$731$	−0.798374	−	2.45714i	−0.0295289	−	0.0908807i
$732$	13.8541	+	42.6385i	0.512062	+	1.57597i
$733$	38.7254	+	28.1357i	1.43036	+	1.03921i	0.989950	+	0.141416i	$0.0451655\pi$
$733$	38.7254	+	28.1357i	1.43036	+	1.03921i	0.440406	+	0.897799i	$0.354835\pi$
$734$	−44.2320	+	32.1364i	−1.63263	+	1.18618i
$735$	0.500000	−	1.53884i	0.0184428	−	0.0567610i
$736$	−30.0000			−1.10581
$737$	36.0902	+	30.1563i	1.32940	+	1.11082i
$738$	5.52786			0.203483
$739$	3.70820	−	11.4127i	0.136408	−	0.419822i	−0.859398	−	0.511307i	$-0.829161\pi$
$739$	3.70820	−	11.4127i	0.136408	−	0.419822i	0.995806	+	0.0914851i	$0.0291614\pi$
$740$	−6.70820	+	4.87380i	−0.246598	+	0.179164i
$741$	3.85410	+	2.80017i	0.141584	+	0.102867i
$742$	7.23607	+	22.2703i	0.265644	+	0.817569i
$743$	11.3262	+	34.8586i	0.415519	+	1.27884i	0.911786	+	0.410667i	$0.134704\pi$
$743$	11.3262	+	34.8586i	0.415519	+	1.27884i	−0.496266	+	0.868170i	$0.665296\pi$
$744$	−3.61803	−	2.62866i	−0.132644	−	0.0963712i
$745$	−9.01722	+	6.55139i	−0.330365	+	0.240025i
$746$	−20.1246	+	61.9372i	−0.736814	+	2.26768i
$747$	4.03444			0.147613
$748$	−28.5000	+	17.8908i	−1.04206	+	0.654153i
$749$	2.76393			0.100992
$750$	1.11803	−	3.44095i	0.0408248	−	0.125646i
$751$	−17.5344	+	12.7395i	−0.639841	+	0.464872i	−0.859796	−	0.510638i	$-0.829409\pi$
$751$	−17.5344	+	12.7395i	−0.639841	+	0.464872i	0.219955	+	0.975510i	$0.429409\pi$
$752$	−6.35410	−	4.61653i	−0.231710	−	0.168347i
$753$	−2.85410	−	8.78402i	−0.104009	−	0.320108i
$754$	−9.63525	−	29.6543i	−0.350895	−	1.07994i
$755$	−2.11803	−	1.53884i	−0.0770831	−	0.0560042i
$756$	13.2812	−	9.64932i	0.483031	−	0.350942i
$757$	−5.61803	+	17.2905i	−0.204191	+	0.628435i	0.795555	+	0.605882i	$0.207180\pi$
$757$	−5.61803	+	17.2905i	−0.204191	+	0.628435i	−0.999746	+	0.0225533i	$0.992820\pi$
$758$	−39.6738			−1.44102
$759$	−23.9443	−	1.62460i	−0.869122	−	0.0589692i
$760$	−2.76393			−0.100258
$761$	−1.49342	+	4.59628i	−0.0541365	+	0.166615i	−0.974469	−	0.224522i	$-0.927918\pi$
$761$	−1.49342	+	4.59628i	−0.0541365	+	0.166615i	0.920333	+	0.391137i	$0.127918\pi$
$762$	13.9443	−	10.1311i	0.505148	−	0.367011i
$763$	−16.5623	−	12.0332i	−0.599596	−	0.435632i
$764$	11.0410	+	33.9808i	0.399450	+	1.22938i
$765$	0.399187	+	1.22857i	0.0144326	+	0.0444191i
$766$	−3.98278	−	2.89366i	−0.143904	−	0.104552i
$767$	9.18034	−	6.66991i	0.331483	−	0.240836i
$768$	4.50000	−	13.8496i	0.162380	−	0.499754i
$769$	−1.70820			−0.0615994			−0.0307997	−	0.999526i	$-0.509805\pi$
$769$	−1.70820			−0.0615994			−0.0307997	+	0.999526i	$0.509805\pi$
$770$	1.80902	+	7.19218i	0.0651924	+	0.259188i
$771$	7.47214			0.269102
$772$	3.70820	−	11.4127i	0.133461	−	0.410751i
$773$	23.9615	−	17.4090i	0.861835	−	0.626160i	−0.0665486	−	0.997783i	$-0.521199\pi$
$773$	23.9615	−	17.4090i	0.861835	−	0.626160i	0.928384	+	0.371623i	$0.121199\pi$
$774$	−0.527864	−	0.383516i	−0.0189737	−	0.0137852i
$775$	−0.381966	−	1.17557i	−0.0137206	−	0.0422277i
$776$	0.225425	+	0.693786i	0.00809228	+	0.0249055i
$777$	3.61803	+	2.62866i	0.129796	+	0.0943025i
$778$	24.3090	−	17.6615i	0.871520	−	0.633197i
$779$	−2.47214	+	7.60845i	−0.0885735	+	0.272601i
$780$	11.5623			0.413997
$781$	0.832816	−	2.07363i	0.0298005	−	0.0742002i
$782$	33.8197			1.20939
$783$	−9.89919	+	30.4666i	−0.353768	+	1.08879i
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	−3.97214	−	2.88593i	−0.141772	−	0.103003i
$786$	−8.94427	−	27.5276i	−0.319032	−	0.981878i
$787$	3.38854	+	10.4289i	0.120789	+	0.371749i	0.993110	−	0.117183i	$-0.0373865\pi$
$787$	3.38854	+	10.4289i	0.120789	+	0.371749i	−0.872322	+	0.488932i	$0.837387\pi$
$788$	29.1246	+	21.1603i	1.03752	+	0.753803i
$789$	−10.7082	+	7.77997i	−0.381222	+	0.276974i
$790$	9.53444	−	29.3440i	0.339220	−	1.04401i
$791$	−1.52786			−0.0543246
$792$	−1.05573	+	2.62866i	−0.0375137	+	0.0934052i
$793$	−22.0000			−0.781243
$794$	−23.6033	+	72.6436i	−0.837651	+	2.57802i
$795$	13.7082	−	9.95959i	0.486180	−	0.353230i
$796$	43.6869	+	31.7404i	1.54844	+	1.12501i
$797$	−13.3197	−	40.9937i	−0.471807	−	1.45207i	−0.850217	−	0.526433i	$-0.823529\pi$
$797$	−13.3197	−	40.9937i	−0.471807	−	1.45207i	0.378410	−	0.925638i	$-0.376471\pi$
$798$	1.38197	+	4.25325i	0.0489211	+	0.150564i
$799$	21.4894	+	15.6129i	0.760239	+	0.552346i
$800$	5.42705	−	3.94298i	0.191875	−	0.139406i
$801$	−2.03444	+	6.26137i	−0.0718835	+	0.221235i
$802$	−50.3262			−1.77708
$803$	6.97214	+	27.7194i	0.246041	+	0.978196i
$804$	68.8328			2.42755
$805$	1.38197	−	4.25325i	0.0487079	−	0.149908i
$806$	5.32624	−	3.86974i	0.187609	−	0.136306i
$807$	16.5623	+	12.0332i	0.583021	+	0.423589i
$808$	−0.201626	−	0.620541i	−0.00709318	−	0.0218306i
$809$	2.50000	+	7.69421i	0.0878953	+	0.270514i	0.985337	−	0.170619i	$-0.0545767\pi$
$809$	2.50000	+	7.69421i	0.0878953	+	0.270514i	−0.897442	+	0.441133i	$0.854577\pi$
$810$	−13.9443	−	10.1311i	−0.489952	−	0.355971i
$811$	−3.70820	+	2.69417i	−0.130213	+	0.0946050i	−0.650985	−	0.759090i	$-0.725644\pi$
$811$	−3.70820	+	2.69417i	−0.130213	+	0.0946050i	0.520772	+	0.853696i	$0.325644\pi$
$812$	5.42705	−	16.7027i	0.190452	−	0.586151i
$813$	−30.3607			−1.06480
$814$	−20.4508	−	1.38757i	−0.716802	−	0.0486344i
$815$	−0.180340			−0.00631703
$816$	1.69098	−	5.20431i	0.0591962	−	0.182187i
$817$	0.763932	−	0.555029i	0.0267266	−	0.0194180i
$818$	−2.23607	−	1.62460i	−0.0781823	−	0.0568028i
$819$	0.281153	+	0.865300i	0.00982428	+	0.0302360i
$820$	6.00000	+	18.4661i	0.209529	+	0.644864i
$821$	−22.9164	−	16.6497i	−0.799788	−	0.581080i	0.111064	−	0.993813i	$-0.464574\pi$
$821$	−22.9164	−	16.6497i	−0.799788	−	0.581080i	−0.910852	+	0.412733i	$0.864574\pi$
$822$	45.1246	−	32.7849i	1.57390	−	1.14351i
$823$	−6.18034	+	19.0211i	−0.215433	+	0.663035i	0.783689	+	0.621153i	$0.213335\pi$
$823$	−6.18034	+	19.0211i	−0.215433	+	0.663035i	−0.999123	+	0.0418821i	$0.986665\pi$
$824$	−3.74265			−0.130381
$825$	4.54508	−	2.85317i	0.158240	−	0.0993346i
$826$	10.6525			0.370647
$827$	−0.652476	+	2.00811i	−0.0226888	+	0.0698290i	−0.961760	−	0.273894i	$-0.911688\pi$
$827$	−0.652476	+	2.00811i	−0.0226888	+	0.0698290i	0.939071	+	0.343723i	$0.111688\pi$
$828$	4.14590	−	3.01217i	0.144080	−	0.104680i
$829$	1.52786	+	1.11006i	0.0530649	+	0.0385539i	0.614002	−	0.789305i	$-0.289559\pi$
$829$	1.52786	+	1.11006i	0.0530649	+	0.0385539i	−0.560937	+	0.827859i	$0.689559\pi$
$830$	7.29837	+	22.4621i	0.253330	+	0.779670i
$831$	−8.70820	−	26.8011i	−0.302084	−	0.929720i
$832$	25.0517	+	18.2011i	0.868510	+	0.631010i
$833$	−2.73607	+	1.98787i	−0.0947991	+	0.0688756i
$834$	−16.1803	+	49.7980i	−0.560279	+	1.72436i
$835$	12.0000			0.415277
$836$	−9.43769	−	7.88597i	−0.326409	−	0.272742i
$837$	−6.76393			−0.233796
$838$	18.8673	−	58.0674i	0.651759	−	2.00591i
$839$	−42.3607	+	30.7768i	−1.46245	+	1.06253i	−0.479738	+	0.877412i	$0.659268\pi$
$839$	−42.3607	+	30.7768i	−1.46245	+	1.06253i	−0.982715	+	0.185122i	$0.940732\pi$
$840$	2.92705	+	2.12663i	0.100993	+	0.0733756i
$841$	1.62868	+	5.01255i	0.0561613	+	0.172847i
$842$	2.42299	+	7.45718i	0.0835016	+	0.256992i
$843$	0.618034	+	0.449028i	0.0212862	+	0.0154653i
$844$	−56.6140	+	41.1325i	−1.94873	+	1.41584i
$845$	2.26393	−	6.96767i	0.0778816	−	0.239695i
$846$	6.70820			0.230633
$847$	−4.78115	+	9.90659i	−0.164282	+	0.340395i
$848$	10.4721			0.359615
$849$	13.7812	−	42.4140i	0.472968	−	1.45565i
$850$	−6.11803	+	4.44501i	−0.209847	+	0.152463i
$851$	10.0000	+	7.26543i	0.342796	+	0.249056i
$852$	−1.01064	−	3.11044i	−0.0346241	−	0.106562i
$853$	11.9164	+	36.6749i	0.408010	+	1.25573i	0.918356	+	0.395756i	$0.129518\pi$
$853$	11.9164	+	36.6749i	0.408010	+	1.25573i	−0.510346	+	0.859969i	$0.670482\pi$
$854$	−16.7082	−	12.1392i	−0.571743	−	0.415396i
$855$	−0.381966	+	0.277515i	−0.0130630	+	0.00949080i
$856$	−1.90983	+	5.87785i	−0.0652766	+	0.200901i
$857$	41.1935			1.40714			0.703572	−	0.710624i	$-0.251587\pi$
$857$	41.1935			1.40714			0.703572	+	0.710624i	$0.251587\pi$
$858$	21.9336	+	18.3273i	0.748802	+	0.625685i
$859$	−28.9443			−0.987566			−0.493783	−	0.869585i	$-0.664386\pi$
$859$	−28.9443			−0.987566			−0.493783	+	0.869585i	$0.664386\pi$
$860$	0.708204	−	2.17963i	0.0241496	−	0.0743247i
$861$	8.47214	−	6.15537i	0.288730	−	0.209774i
$862$	−18.6803	−	13.5721i	−0.636255	−	0.462266i
$863$	6.47214	+	19.9192i	0.220314	+	0.678057i	0.998734	+	0.0503125i	$0.0160217\pi$
$863$	6.47214	+	19.9192i	0.220314	+	0.678057i	−0.778419	+	0.627744i	$0.783978\pi$
$864$	−11.3435	−	34.9116i	−0.385912	−	1.18772i
$865$	15.0172	+	10.9106i	0.510601	+	0.370973i
$866$	30.8156	−	22.3888i	1.04716	−	0.760804i
$867$	2.78115	−	8.55951i	0.0944529	−	0.290696i
$868$	3.70820			0.125865
$869$	38.7599	−	24.3314i	1.31484	−	0.825388i
$870$	−21.1803			−0.718081
$871$	−10.4377	+	32.1239i	−0.353668	+	1.08848i
$872$	37.0344	−	26.9071i	1.25414	−	0.911189i
$873$	0.100813	+	0.0732450i	0.00341201	+	0.00247897i
$874$	3.81966	+	11.7557i	0.129202	+	0.397643i
$875$	0.309017	+	0.951057i	0.0104467	+	0.0321516i
$876$	33.8435	+	24.5887i	1.14346	+	0.830776i
$877$	17.0000	−	12.3512i	0.574049	−	0.417071i	−0.262525	−	0.964925i	$-0.584555\pi$
$877$	17.0000	−	12.3512i	0.574049	−	0.417071i	0.836574	+	0.547854i	$0.184555\pi$
$878$	12.2361	−	37.6587i	0.412947	−	1.27092i
$879$	−28.1803			−0.950499
$880$	3.30902	+	0.224514i	0.111547	+	0.00756837i
$881$	−0.763932			−0.0257375			−0.0128688	−	0.999917i	$-0.504096\pi$
$881$	−0.763932			−0.0257375			−0.0128688	+	0.999917i	$0.504096\pi$
$882$	−0.263932	+	0.812299i	−0.00888705	+	0.0273515i
$883$	−9.85410	+	7.15942i	−0.331617	+	0.240934i	−0.741116	−	0.671377i	$-0.765703\pi$
$883$	−9.85410	+	7.15942i	−0.331617	+	0.240934i	0.409499	+	0.912310i	$0.365703\pi$
$884$	−19.5517	−	14.2051i	−0.657594	−	0.477770i
$885$	−2.38197	−	7.33094i	−0.0800689	−	0.246427i
$886$	−23.9443	−	73.6929i	−0.804424	−	2.47576i
$887$	22.5344	+	16.3722i	0.756633	+	0.549726i	0.897876	−	0.440249i	$-0.145110\pi$
$887$	22.5344	+	16.3722i	0.756633	+	0.549726i	−0.141243	+	0.989975i	$0.545110\pi$
$888$	−8.09017	+	5.87785i	−0.271488	+	0.197248i
$889$	−1.47214	+	4.53077i	−0.0493739	+	0.151957i
$890$	−38.5410			−1.29190
$891$	−6.23607	−	24.7930i	−0.208916	−	0.830596i
$892$	31.4164			1.05190
$893$	−3.00000	+	9.23305i	−0.100391	+	0.308972i
$894$	−32.6246	+	23.7032i	−1.09113	+	0.792753i
$895$	14.0623	+	10.2169i	0.470051	+	0.341512i
$896$	4.83688	+	14.8864i	0.161589	+	0.497319i
$897$	−5.32624	−	16.3925i	−0.177838	−	0.547329i
$898$	−43.9058	−	31.8994i	−1.46515	−	1.06450i
$899$	−5.85410	+	4.25325i	−0.195245	+	0.141854i
$900$	−0.354102	+	1.08981i	−0.0118034	+	0.0363271i
$901$	−35.4164			−1.17989
$902$	−17.8885	+	44.5407i	−0.595623	+	1.48304i
$903$	−1.23607			−0.0411338
$904$	1.05573	−	3.24920i	0.0351130	−	0.108067i
$905$	11.7082	−	8.50651i	0.389194	−	0.282766i
$906$	−7.66312	−	5.56758i	−0.254590	−	0.184971i
$907$	−2.43769	−	7.50245i	−0.0809423	−	0.249115i	0.902394	−	0.430913i	$-0.141808\pi$
$907$	−2.43769	−	7.50245i	−0.0809423	−	0.249115i	−0.983336	+	0.181798i	$0.941808\pi$
$908$	12.7918	+	39.3691i	0.424511	+	1.30651i
$909$	−0.0901699	−	0.0655123i	−0.00299075	−	0.00217291i
$910$	−4.30902	+	3.13068i	−0.142843	+	0.103781i
$911$	11.2812	−	34.7198i	0.373761	−	1.15032i	−0.570549	−	0.821263i	$-0.693270\pi$
$911$	11.2812	−	34.7198i	0.373761	−	1.15032i	0.944311	−	0.329056i	$-0.106730\pi$
$912$	2.00000			0.0662266
$913$	−13.0557	+	32.5074i	−0.432082	+	1.07584i
$914$	75.5279			2.49824
$915$	−4.61803	+	14.2128i	−0.152667	+	0.469862i
$916$	70.9574	−	51.5536i	2.34450	−	1.70338i
$917$	6.47214	+	4.70228i	0.213729	+	0.155283i
$918$	12.7877	+	39.3566i	0.422058	+	1.29896i
$919$	−9.66312	−	29.7400i	−0.318757	−	0.981033i	−0.974180	−	0.225771i	$-0.927510\pi$
$919$	−9.66312	−	29.7400i	−0.318757	−	0.981033i	0.655423	−	0.755262i	$-0.272490\pi$
$920$	8.09017	+	5.87785i	0.266725	+	0.193787i
$921$	−0.572949	+	0.416272i	−0.0188793	+	0.0137166i
$922$	20.5279	−	63.1783i	0.676049	−	2.08067i
$923$	1.60488			0.0528252
$924$	3.92705	+	15.6129i	0.129190	+	0.513628i
$925$	−2.76393			−0.0908775
$926$	15.9787	−	49.1774i	0.525093	−	1.61607i
$927$	−0.517221	+	0.375783i	−0.0169878	+	0.0123423i
$928$	−31.7705	−	23.0826i	−1.04292	−	0.757724i
$929$	5.52786	+	17.0130i	0.181363	+	0.558179i	0.999867	−	0.0163227i	$-0.00519590\pi$
$929$	5.52786	+	17.0130i	0.181363	+	0.558179i	−0.818503	+	0.574502i	$0.805196\pi$
$930$	−1.38197	−	4.25325i	−0.0453165	−	0.139470i
$931$	−1.00000	−	0.726543i	−0.0327737	−	0.0238115i
$932$	59.8328	−	43.4711i	1.95989	−	1.42394i
$933$	13.5623	−	41.7405i	0.444010	−	1.36652i
$934$	−37.2837			−1.21996
$935$	−11.1910	−	0.759299i	−0.365984	−	0.0248317i
$936$	−2.03444			−0.0664978
$937$	17.4443	−	53.6879i	0.569880	−	1.75391i	−0.0831084	−	0.996541i	$-0.526485\pi$
$937$	17.4443	−	53.6879i	0.569880	−	1.75391i	0.652988	−	0.757368i	$-0.273515\pi$
$938$	−25.6525	+	18.6376i	−0.837583	+	0.608540i
$939$	−23.5623	−	17.1190i	−0.768927	−	0.558658i
$940$	7.28115	+	22.4091i	0.237485	+	0.730904i
$941$	11.2918	+	34.7526i	0.368102	+	1.13290i	0.948016	+	0.318224i	$0.103086\pi$
$941$	11.2918	+	34.7526i	0.368102	+	1.13290i	−0.579914	+	0.814678i	$0.696914\pi$
$942$	−14.3713	−	10.4414i	−0.468243	−	0.340198i
$943$	23.4164	−	17.0130i	0.762543	−	0.554020i
$944$	1.47214	−	4.53077i	0.0479139	−	0.147464i
$945$	5.47214			0.178009
$946$	4.79837	−	3.01217i	0.156009	−	0.0979341i
$947$	−24.0689			−0.782134			−0.391067	−	0.920362i	$-0.627894\pi$
$947$	−24.0689			−0.782134			−0.391067	+	0.920362i	$0.627894\pi$
$948$	20.6976	−	63.7005i	0.672226	−	2.06890i
$949$	−16.6074	+	12.0660i	−0.539099	+	0.391678i
$950$	−2.23607	−	1.62460i	−0.0725476	−	0.0527089i
$951$	15.2361	+	46.8918i	0.494063	+	1.52057i
$952$	−2.33688	−	7.19218i	−0.0757387	−	0.233100i
$953$	−20.2705	−	14.7274i	−0.656626	−	0.477067i	0.208896	−	0.977938i	$-0.433013\pi$
$953$	−20.2705	−	14.7274i	−0.656626	−	0.477067i	−0.865522	+	0.500871i	$0.833013\pi$
$954$	−7.23607	+	5.25731i	−0.234276	+	0.170212i
$955$	−3.68034	+	11.3269i	−0.119093	+	0.366531i
$956$	−65.9361			−2.13253
$957$	−24.1074	−	20.1437i	−0.779281	−	0.651153i
$958$	−19.3475			−0.625090
$959$	−4.76393	+	14.6619i	−0.153835	+	0.473457i
$960$	17.0172	−	12.3637i	0.549228	−	0.399038i
$961$	23.8435	+	17.3233i	0.769144	+	0.558816i
$962$	−4.54915	−	14.0008i	−0.146670	−	0.451405i
$963$	0.326238	+	1.00406i	0.0105129	+	0.0323553i
$964$	−56.1246	−	40.7769i	−1.80765	−	1.31334i
$965$	3.23607	−	2.35114i	0.104173	−	0.0756859i
$966$	5.00000	−	15.3884i	0.160872	−	0.495114i
$967$	−21.2361			−0.682906			−0.341453	−	0.939899i	$-0.610919\pi$
$967$	−21.2361			−0.682906			−0.341453	+	0.939899i	$0.610919\pi$
$968$	−17.7639	−	17.0130i	−0.570954	−	0.546819i
$969$	−6.76393			−0.217289
$970$	−0.225425	+	0.693786i	−0.00723796	+	0.0222761i
$971$	23.7984	−	17.2905i	0.763726	−	0.554880i	−0.136325	−	0.990664i	$-0.543529\pi$
$971$	23.7984	−	17.2905i	0.763726	−	0.554880i	0.900051	+	0.435785i	$0.143529\pi$
$972$	9.57295	+	6.95515i	0.307052	+	0.223087i
$973$	−4.47214	−	13.7638i	−0.143370	−	0.441248i
$974$	−16.7082	−	51.4226i	−0.535365	−	1.64769i
$975$	3.11803	+	2.26538i	0.0998570	+	0.0725504i
$976$	−7.47214	+	5.42882i	−0.239177	+	0.173772i
$977$	11.3607	−	34.9646i	0.363460	−	1.11862i	−0.587479	−	0.809239i	$-0.699880\pi$
$977$	11.3607	−	34.9646i	0.363460	−	1.11862i	0.950940	−	0.309377i	$-0.100120\pi$
$978$	−0.652476			−0.0208639
$979$	−43.8673	−	36.6547i	−1.40200	−	1.17149i
$980$	−3.00000			−0.0958315
$981$	2.41641	−	7.43694i	0.0771500	−	0.237443i
$982$	−68.5410	+	49.7980i	−2.18723	+	1.58912i
$983$	−15.3541	−	11.1554i	−0.489720	−	0.355802i	0.315357	−	0.948973i	$-0.397876\pi$
$983$	−15.3541	−	11.1554i	−0.489720	−	0.355802i	−0.805077	+	0.593171i	$0.797876\pi$
$984$	7.23607	+	22.2703i	0.230677	+	0.709952i
$985$	3.70820	+	11.4127i	0.118153	+	0.363638i
$986$	35.8156	+	26.0216i	1.14060	+	0.828695i
$987$	10.2812	−	7.46969i	0.327253	−	0.237763i
$988$	2.72949	−	8.40051i	0.0868367	−	0.267256i
$989$	−3.41641			−0.108635
$990$	−2.39919	+	1.50609i	−0.0762512	+	0.0478665i
$991$	7.14590			0.226997			0.113498	−	0.993538i	$-0.463794\pi$
$991$	7.14590			0.226997			0.113498	+	0.993538i	$0.463794\pi$
$992$	2.56231	−	7.88597i	0.0813533	−	0.250380i
$993$	25.5344	−	18.5519i	0.810311	−	0.588725i
$994$	1.21885	+	0.885544i	0.0386595	+	0.0280878i
$995$	5.56231	+	17.1190i	0.176337	+	0.542709i
$996$	15.8435	+	48.7612i	0.502019	+	1.54506i
$997$	−21.2082	−	15.4087i	−0.671671	−	0.487997i	0.198913	−	0.980017i	$-0.436259\pi$
$997$	−21.2082	−	15.4087i	−0.671671	−	0.487997i	−0.870584	+	0.492020i	$0.836259\pi$
$998$	−10.9164	+	7.93123i	−0.345553	+	0.251059i
$999$	−4.67376	+	14.3844i	−0.147871	+	0.455101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.n.b.141.1	yes	4
11.4	even	5		4235.2.a.j.1.2		2
11.5	even	5	inner	385.2.n.b.71.1	✓	4
11.7	odd	10		4235.2.a.k.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.b.71.1	✓	4	11.5	even	5	inner
385.2.n.b.141.1	yes	4	1.1	even	1	trivial
4235.2.a.j.1.2		2	11.4	even	5
4235.2.a.k.1.1		2	11.7	odd	10

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.690983 - 2.12663i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.11803 - 3.44095i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(-0.118034 + 0.363271i) q^{9} +O(q^{10})\)	\(q+(0.690983 - 2.12663i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.11803 - 3.44095i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(-0.118034 + 0.363271i) q^{9} -2.23607 q^{10} +(-2.54508 - 2.12663i) q^{11} -4.85410 q^{12} +(0.736068 - 2.26538i) q^{13} +(1.80902 - 1.31433i) q^{14} +(-1.30902 - 0.951057i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.04508 + 3.21644i) q^{17} +(0.690983 + 0.502029i) q^{18} +(-1.00000 + 0.726543i) q^{19} +(-0.927051 + 2.85317i) q^{20} +1.61803 q^{21} +(-6.28115 + 3.94298i) q^{22} +4.47214 q^{23} +(-1.11803 + 3.44095i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-4.30902 - 3.13068i) q^{26} +(1.69098 + 5.20431i) q^{27} +(-0.927051 - 2.85317i) q^{28} +(4.73607 + 3.44095i) q^{29} +(-2.92705 + 2.12663i) q^{30} +(-0.381966 + 1.17557i) q^{31} -6.70820 q^{32} +(-5.35410 - 0.363271i) q^{33} +7.56231 q^{34} +(0.309017 - 0.951057i) q^{35} +(0.927051 - 0.673542i) q^{36} +(2.23607 + 1.62460i) q^{37} +(0.854102 + 2.62866i) q^{38} +(-1.19098 - 3.66547i) q^{39} +(1.80902 + 1.31433i) q^{40} +(5.23607 - 3.80423i) q^{41} +(1.11803 - 3.44095i) q^{42} -0.763932 q^{43} +(2.42705 + 9.64932i) q^{44} +0.381966 q^{45} +(3.09017 - 9.51057i) q^{46} +(6.35410 - 4.61653i) q^{47} +(-1.30902 - 0.951057i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.690983 + 2.12663i) q^{50} +(4.42705 + 3.21644i) q^{51} +(-5.78115 + 4.20025i) q^{52} +(-3.23607 + 9.95959i) q^{53} +12.2361 q^{54} +(-1.23607 + 3.07768i) q^{55} -2.23607 q^{56} +(-0.618034 + 1.90211i) q^{57} +(10.5902 - 7.69421i) q^{58} +(3.85410 + 2.80017i) q^{59} +(1.50000 + 4.61653i) q^{60} +(-2.85410 - 8.78402i) q^{61} +(2.23607 + 1.62460i) q^{62} +(-0.309017 + 0.224514i) q^{63} +(-4.01722 + 12.3637i) q^{64} -2.38197 q^{65} +(-4.47214 + 11.1352i) q^{66} -14.1803 q^{67} +(3.13525 - 9.64932i) q^{68} +(5.85410 - 4.25325i) q^{69} +(-1.80902 - 1.31433i) q^{70} +(0.208204 + 0.640786i) q^{71} +(-0.263932 - 0.812299i) q^{72} +(-6.97214 - 5.06555i) q^{73} +(5.00000 - 3.63271i) q^{74} +(-0.500000 + 1.53884i) q^{75} +3.70820 q^{76} +(-0.809017 - 3.21644i) q^{77} -8.61803 q^{78} +(-4.26393 + 13.1230i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(6.23607 + 4.53077i) q^{81} +(-4.47214 - 13.7638i) q^{82} +(-3.26393 - 10.0453i) q^{83} +(-3.92705 - 2.85317i) q^{84} +(2.73607 - 1.98787i) q^{85} +(-0.527864 + 1.62460i) q^{86} +9.47214 q^{87} +(7.39919 + 0.502029i) q^{88} +17.2361 q^{89} +(0.263932 - 0.812299i) q^{90} +(1.92705 - 1.40008i) q^{91} +(-10.8541 - 7.88597i) q^{92} +(0.618034 + 1.90211i) q^{93} +(-5.42705 - 16.7027i) q^{94} +(1.00000 + 0.726543i) q^{95} +(-8.78115 + 6.37988i) q^{96} +(0.100813 - 0.310271i) q^{97} +2.23607 q^{98} +(1.07295 - 0.673542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} + 3 q^{3} - 3 q^{4} + q^{5} + q^{7} - 5 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 5 * q^2 + 3 * q^3 - 3 * q^4 + q^5 + q^7 - 5 * q^8 + 4 * q^9	\( 4 q + 5 q^{2} + 3 q^{3} - 3 q^{4} + q^{5} + q^{7} - 5 q^{8} + 4 q^{9} + q^{11} - 6 q^{12} - 6 q^{13} + 5 q^{14} - 3 q^{15} + q^{16} - 7 q^{17} + 5 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 5 q^{22} - q^{25} - 15 q^{26} + 9 q^{27} + 3 q^{28} + 10 q^{29} - 5 q^{30} - 6 q^{31} - 8 q^{33} - 10 q^{34} - q^{35} - 3 q^{36} - 10 q^{38} - 7 q^{39} + 5 q^{40} + 12 q^{41} - 12 q^{43} + 3 q^{44} + 6 q^{45} - 10 q^{46} + 12 q^{47} - 3 q^{48} - q^{49} + 5 q^{50} + 11 q^{51} - 3 q^{52} - 4 q^{53} + 40 q^{54} + 4 q^{55} + 2 q^{57} + 20 q^{58} + 2 q^{59} + 6 q^{60} + 2 q^{61} + q^{63} + 13 q^{64} - 14 q^{65} - 12 q^{67} - 21 q^{68} + 10 q^{69} - 5 q^{70} - 26 q^{71} - 10 q^{72} - 10 q^{73} + 20 q^{74} - 2 q^{75} - 12 q^{76} - q^{77} - 30 q^{78} - 26 q^{79} - q^{80} + 16 q^{81} - 22 q^{83} - 9 q^{84} + 2 q^{85} - 20 q^{86} + 20 q^{87} + 5 q^{88} + 60 q^{89} + 10 q^{90} + q^{91} - 30 q^{92} - 2 q^{93} - 15 q^{94} + 4 q^{95} - 15 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 + 3 * q^3 - 3 * q^4 + q^5 + q^7 - 5 * q^8 + 4 * q^9 + q^11 - 6 * q^12 - 6 * q^13 + 5 * q^14 - 3 * q^15 + q^16 - 7 * q^17 + 5 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 5 * q^22 - q^25 - 15 * q^26 + 9 * q^27 + 3 * q^28 + 10 * q^29 - 5 * q^30 - 6 * q^31 - 8 * q^33 - 10 * q^34 - q^35 - 3 * q^36 - 10 * q^38 - 7 * q^39 + 5 * q^40 + 12 * q^41 - 12 * q^43 + 3 * q^44 + 6 * q^45 - 10 * q^46 + 12 * q^47 - 3 * q^48 - q^49 + 5 * q^50 + 11 * q^51 - 3 * q^52 - 4 * q^53 + 40 * q^54 + 4 * q^55 + 2 * q^57 + 20 * q^58 + 2 * q^59 + 6 * q^60 + 2 * q^61 + q^63 + 13 * q^64 - 14 * q^65 - 12 * q^67 - 21 * q^68 + 10 * q^69 - 5 * q^70 - 26 * q^71 - 10 * q^72 - 10 * q^73 + 20 * q^74 - 2 * q^75 - 12 * q^76 - q^77 - 30 * q^78 - 26 * q^79 - q^80 + 16 * q^81 - 22 * q^83 - 9 * q^84 + 2 * q^85 - 20 * q^86 + 20 * q^87 + 5 * q^88 + 60 * q^89 + 10 * q^90 + q^91 - 30 * q^92 - 2 * q^93 - 15 * q^94 + 4 * q^95 - 15 * q^96 + 25 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more