LMFDB - Embedded newform 462.2.j.g.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.2
Root			$1.40126 + 1.01807i$ of defining polynomial
Character	$\chi$	$=$	462.379
Dual form			462.2.j.g.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.330792 - 1.01807i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.330792 - 1.01807i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.07047 q^{10} +(-3.25134 + 0.654803i) q^{11} +1.00000 q^{12} +(-2.12387 - 6.53660i) q^{13} +(0.809017 + 0.587785i) q^{14} +(-0.866025 + 0.629204i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.18850 + 6.73551i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-4.70378 - 3.41749i) q^{19} +(0.330792 + 1.01807i) q^{20} +1.00000 q^{21} +(1.62747 + 2.88987i) q^{22} -2.29850 q^{23} +(-0.309017 - 0.951057i) q^{24} +(3.11803 + 2.26538i) q^{25} +(-5.56036 + 4.03984i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-3.14275 + 2.28334i) q^{29} +(0.866025 + 0.629204i) q^{30} +(1.10570 + 3.40299i) q^{31} -1.00000 q^{32} +(3.01528 + 1.38135i) q^{33} +7.08214 q^{34} +(0.330792 + 1.01807i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-2.63799 + 1.91661i) q^{37} +(-1.79668 + 5.52962i) q^{38} +(-2.12387 + 6.53660i) q^{39} +(0.866025 - 0.629204i) q^{40} +(3.92055 + 2.84845i) q^{41} +(-0.309017 - 0.951057i) q^{42} -5.20419 q^{43} +(2.24551 - 2.44084i) q^{44} +1.07047 q^{45} +(0.710276 + 2.18600i) q^{46} +(-8.22489 - 5.97573i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(1.19098 - 3.66547i) q^{50} +(5.72957 - 4.16277i) q^{51} +(5.56036 + 4.03984i) q^{52} +(-3.18336 - 9.79737i) q^{53} -1.00000 q^{54} +(-0.408882 + 3.52671i) q^{55} -1.00000 q^{56} +(1.79668 + 5.52962i) q^{57} +(3.14275 + 2.28334i) q^{58} +(-0.410699 + 0.298390i) q^{59} +(0.330792 - 1.01807i) q^{60} +(2.47019 - 7.60246i) q^{61} +(2.89476 - 2.10317i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(0.309017 + 0.951057i) q^{64} -7.35730 q^{65} +(0.381966 - 3.29456i) q^{66} +3.79167 q^{67} +(-2.18850 - 6.73551i) q^{68} +(1.85953 + 1.35102i) q^{69} +(0.866025 - 0.629204i) q^{70} +(-4.39364 + 13.5222i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(10.4174 - 7.56869i) q^{73} +(2.63799 + 1.91661i) q^{74} +(-1.19098 - 3.66547i) q^{75} +5.81419 q^{76} +(2.24551 - 2.44084i) q^{77} +6.87298 q^{78} +(-2.77491 - 8.54029i) q^{79} +(-0.866025 - 0.629204i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.49752 - 4.60888i) q^{82} +(-0.553656 + 1.70398i) q^{83} +(-0.809017 + 0.587785i) q^{84} +(6.13331 + 4.45611i) q^{85} +(1.60818 + 4.94948i) q^{86} +3.88465 q^{87} +(-3.01528 - 1.38135i) q^{88} +6.23110 q^{89} +(-0.330792 - 1.01807i) q^{90} +(5.56036 + 4.03984i) q^{91} +(1.85953 - 1.35102i) q^{92} +(1.10570 - 3.40299i) q^{93} +(-3.14163 + 9.66893i) q^{94} +(-5.03523 + 3.65831i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-5.17839 - 15.9375i) q^{97} -1.00000 q^{98} +(-1.62747 - 2.88987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{11} + 8 q^{12} + 6 q^{13} + 2 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} + 8 q^{21} + 2 q^{22} + 2 q^{24} + 16 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} + 2 q^{29} - 4 q^{31} - 8 q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{36} - 24 q^{37} - 6 q^{38} + 6 q^{39} + 2 q^{42} + 8 q^{43} - 2 q^{44} - 10 q^{46} - 2 q^{47} - 2 q^{48} - 2 q^{49} + 14 q^{50} + 10 q^{51} + 6 q^{52} - 22 q^{53} - 8 q^{54} - 8 q^{56} + 6 q^{57} - 2 q^{58} + 10 q^{59} + 26 q^{61} - 6 q^{62} - 2 q^{63} - 2 q^{64} - 60 q^{65} + 12 q^{66} + 4 q^{67} - 10 q^{69} - 16 q^{71} + 2 q^{72} - 2 q^{73} + 24 q^{74} - 14 q^{75} - 4 q^{76} - 2 q^{77} + 24 q^{78} - 12 q^{79} - 2 q^{81} - 10 q^{82} - 38 q^{83} - 2 q^{84} + 24 q^{85} + 22 q^{86} - 28 q^{87} - 8 q^{88} - 12 q^{89} + 6 q^{91} - 10 q^{92} - 4 q^{93} - 8 q^{94} - 36 q^{95} + 2 q^{96} + 6 q^{97} - 8 q^{98} - 2 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^11 + 8 * q^12 + 6 * q^13 + 2 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 + 8 * q^21 + 2 * q^22 + 2 * q^24 + 16 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 + 2 * q^29 - 4 * q^31 - 8 * q^32 + 8 * q^33 + 20 * q^34 - 2 * q^36 - 24 * q^37 - 6 * q^38 + 6 * q^39 + 2 * q^42 + 8 * q^43 - 2 * q^44 - 10 * q^46 - 2 * q^47 - 2 * q^48 - 2 * q^49 + 14 * q^50 + 10 * q^51 + 6 * q^52 - 22 * q^53 - 8 * q^54 - 8 * q^56 + 6 * q^57 - 2 * q^58 + 10 * q^59 + 26 * q^61 - 6 * q^62 - 2 * q^63 - 2 * q^64 - 60 * q^65 + 12 * q^66 + 4 * q^67 - 10 * q^69 - 16 * q^71 + 2 * q^72 - 2 * q^73 + 24 * q^74 - 14 * q^75 - 4 * q^76 - 2 * q^77 + 24 * q^78 - 12 * q^79 - 2 * q^81 - 10 * q^82 - 38 * q^83 - 2 * q^84 + 24 * q^85 + 22 * q^86 - 28 * q^87 - 8 * q^88 - 12 * q^89 + 6 * q^91 - 10 * q^92 - 4 * q^93 - 8 * q^94 - 36 * q^95 + 2 * q^96 + 6 * q^97 - 8 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.330792	−	1.01807i	0.147935	−	0.455296i	−0.849442	−	0.527682i	$-0.823061\pi$
$5$	0.330792	−	1.01807i	0.147935	−	0.455296i	0.997377	+	0.0723856i	$0.0230612\pi$
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−1.07047			−0.338511
$11$	−3.25134	+	0.654803i	−0.980317	+	0.197430i
$11$	−3.25134	+	0.654803i	−0.980317	+	0.197430i
$12$	1.00000			0.288675
$13$	−2.12387	−	6.53660i	−0.589055	−	1.81293i	−0.582336	−	0.812948i	$-0.697861\pi$
$13$	−2.12387	−	6.53660i	−0.589055	−	1.81293i	−0.00671890	−	0.999977i	$-0.502139\pi$
$14$	0.809017	+	0.587785i	0.216219	+	0.157092i
$15$	−0.866025	+	0.629204i	−0.223607	+	0.162460i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.18850	+	6.73551i	−0.530789	+	1.63360i	0.221786	+	0.975095i	$0.428811\pi$
$17$	−2.18850	+	6.73551i	−0.530789	+	1.63360i	−0.752575	+	0.658506i	$0.771189\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	−4.70378	−	3.41749i	−1.07912	−	0.784027i	−0.101591	−	0.994826i	$-0.532393\pi$
$19$	−4.70378	−	3.41749i	−1.07912	−	0.784027i	−0.977529	+	0.210800i	$0.932393\pi$
$20$	0.330792	+	1.01807i	0.0739674	+	0.227648i
$21$	1.00000			0.218218
$22$	1.62747	+	2.88987i	0.346979	+	0.616122i
$23$	−2.29850			−0.479270			−0.239635	−	0.970863i	$-0.577028\pi$
$23$	−2.29850			−0.479270			−0.239635	+	0.970863i	$0.577028\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	3.11803	+	2.26538i	0.623607	+	0.453077i
$26$	−5.56036	+	4.03984i	−1.09048	+	0.792277i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	−3.14275	+	2.28334i	−0.583594	+	0.424006i	−0.840018	−	0.542559i	$-0.817456\pi$
$29$	−3.14275	+	2.28334i	−0.583594	+	0.424006i	0.256424	+	0.966564i	$0.417456\pi$
$30$	0.866025	+	0.629204i	0.158114	+	0.114876i
$31$	1.10570	+	3.40299i	0.198589	+	0.611196i	0.999916	+	0.0129682i	$0.00412803\pi$
$31$	1.10570	+	3.40299i	0.198589	+	0.611196i	−0.801326	+	0.598227i	$0.795872\pi$
$32$	−1.00000			−0.176777
$33$	3.01528	+	1.38135i	0.524892	+	0.240461i
$34$	7.08214			1.21458
$35$	0.330792	+	1.01807i	0.0559141	+	0.172086i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	−2.63799	+	1.91661i	−0.433683	+	0.315089i	−0.783120	−	0.621871i	$-0.786373\pi$
$37$	−2.63799	+	1.91661i	−0.433683	+	0.315089i	0.349437	+	0.936960i	$0.386373\pi$
$38$	−1.79668	+	5.52962i	−0.291460	+	0.897023i
$39$	−2.12387	+	6.53660i	−0.340091	+	1.04669i
$40$	0.866025	−	0.629204i	0.136931	−	0.0994859i
$41$	3.92055	+	2.84845i	0.612287	+	0.444853i	0.850219	−	0.526429i	$-0.176469\pi$
$41$	3.92055	+	2.84845i	0.612287	+	0.444853i	−0.237932	+	0.971282i	$0.576469\pi$
$42$	−0.309017	−	0.951057i	−0.0476824	−	0.146751i
$43$	−5.20419			−0.793631			−0.396816	−	0.917898i	$-0.629885\pi$
$43$	−5.20419			−0.793631			−0.396816	+	0.917898i	$0.629885\pi$
$44$	2.24551	−	2.44084i	0.338523	−	0.367970i
$45$	1.07047			0.159576
$46$	0.710276	+	2.18600i	0.104724	+	0.322309i
$47$	−8.22489	−	5.97573i	−1.19972	−	0.871650i	−0.205465	−	0.978664i	$-0.565871\pi$
$47$	−8.22489	−	5.97573i	−1.19972	−	0.871650i	−0.994257	+	0.107015i	$0.965871\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	1.19098	−	3.66547i	0.168430	−	0.518376i
$51$	5.72957	−	4.16277i	0.802300	−	0.582905i
$52$	5.56036	+	4.03984i	0.771083	+	0.560225i
$53$	−3.18336	−	9.79737i	−0.437268	−	1.34577i	−0.890744	−	0.454505i	$-0.849816\pi$
$53$	−3.18336	−	9.79737i	−0.437268	−	1.34577i	0.453476	−	0.891268i	$-0.350184\pi$
$54$	−1.00000			−0.136083
$55$	−0.408882	+	3.52671i	−0.0551336	+	0.475542i
$56$	−1.00000			−0.133631
$57$	1.79668	+	5.52962i	0.237976	+	0.732416i
$58$	3.14275	+	2.28334i	0.412663	+	0.299817i
$59$	−0.410699	+	0.298390i	−0.0534685	+	0.0388471i	−0.614198	−	0.789152i	$-0.710521\pi$
$59$	−0.410699	+	0.298390i	−0.0534685	+	0.0388471i	0.560730	+	0.827999i	$0.310521\pi$
$60$	0.330792	−	1.01807i	0.0427051	−	0.131433i
$61$	2.47019	−	7.60246i	0.316275	−	0.973396i	−0.658951	−	0.752186i	$-0.728999\pi$
$61$	2.47019	−	7.60246i	0.316275	−	0.973396i	0.975226	−	0.221210i	$-0.0710005\pi$
$62$	2.89476	−	2.10317i	0.367635	−	0.267102i
$63$	−0.809017	−	0.587785i	−0.101927	−	0.0740540i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−7.35730			−0.912560
$66$	0.381966	−	3.29456i	0.0470168	−	0.405532i
$67$	3.79167			0.463226			0.231613	−	0.972808i	$-0.425600\pi$
$67$	3.79167			0.463226			0.231613	+	0.972808i	$0.425600\pi$
$68$	−2.18850	−	6.73551i	−0.265395	−	0.816801i
$69$	1.85953	+	1.35102i	0.223861	+	0.162644i
$70$	0.866025	−	0.629204i	0.103510	−	0.0752043i
$71$	−4.39364	+	13.5222i	−0.521429	+	1.60479i	0.249843	+	0.968286i	$0.419621\pi$
$71$	−4.39364	+	13.5222i	−0.521429	+	1.60479i	−0.771272	+	0.636506i	$0.780379\pi$
$72$	−0.309017	+	0.951057i	−0.0364180	+	0.112083i
$73$	10.4174	−	7.56869i	1.21926	−	0.885848i	0.223226	−	0.974767i	$-0.428341\pi$
$73$	10.4174	−	7.56869i	1.21926	−	0.885848i	0.996039	+	0.0889190i	$0.0283412\pi$
$74$	2.63799	+	1.91661i	0.306660	+	0.222802i
$75$	−1.19098	−	3.66547i	−0.137523	−	0.423252i
$76$	5.81419			0.666933
$77$	2.24551	−	2.44084i	0.255899	−	0.278159i
$78$	6.87298			0.778212
$79$	−2.77491	−	8.54029i	−0.312201	−	0.960857i	−0.976891	−	0.213738i	$-0.931436\pi$
$79$	−2.77491	−	8.54029i	−0.312201	−	0.960857i	0.664690	−	0.747120i	$-0.268564\pi$
$80$	−0.866025	−	0.629204i	−0.0968246	−	0.0703472i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	1.49752	−	4.60888i	0.165373	−	0.508966i
$83$	−0.553656	+	1.70398i	−0.0607717	+	0.187036i	−0.976833	−	0.214001i	$-0.931350\pi$
$83$	−0.553656	+	1.70398i	−0.0607717	+	0.187036i	0.916062	+	0.401037i	$0.131350\pi$
$84$	−0.809017	+	0.587785i	−0.0882710	+	0.0641326i
$85$	6.13331	+	4.45611i	0.665251	+	0.483333i
$86$	1.60818	+	4.94948i	0.173415	+	0.533716i
$87$	3.88465			0.416478
$88$	−3.01528	−	1.38135i	−0.321429	−	0.147252i
$89$	6.23110			0.660496			0.330248	−	0.943894i	$-0.392868\pi$
$89$	6.23110			0.660496			0.330248	+	0.943894i	$0.392868\pi$
$90$	−0.330792	−	1.01807i	−0.0348686	−	0.107314i
$91$	5.56036	+	4.03984i	0.582884	+	0.423490i
$92$	1.85953	−	1.35102i	0.193869	−	0.140854i
$93$	1.10570	−	3.40299i	0.114656	−	0.352874i
$94$	−3.14163	+	9.66893i	−0.324034	+	0.997274i
$95$	−5.03523	+	3.65831i	−0.516604	+	0.375335i
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	−5.17839	−	15.9375i	−0.525786	−	1.61820i	−0.762756	−	0.646687i	$-0.776154\pi$
$97$	−5.17839	−	15.9375i	−0.525786	−	1.61820i	0.236969	−	0.971517i	$-0.423846\pi$
$98$	−1.00000			−0.101015
$99$	−1.62747	−	2.88987i	−0.163567	−	0.290442i
$100$	−3.85410			−0.385410
$101$	−4.42096	−	13.6063i	−0.439902	−	1.35388i	−0.887979	−	0.459885i	$-0.847891\pi$
$101$	−4.42096	−	13.6063i	−0.439902	−	1.35388i	0.448077	−	0.893995i	$-0.352109\pi$
$102$	−5.72957	−	4.16277i	−0.567312	−	0.412176i
$103$	5.22849	−	3.79872i	0.515179	−	0.374299i	−0.299606	−	0.954063i	$-0.596855\pi$
$103$	5.22849	−	3.79872i	0.515179	−	0.374299i	0.814785	+	0.579764i	$0.196855\pi$
$104$	2.12387	−	6.53660i	0.208262	−	0.640966i
$105$	0.330792	−	1.01807i	0.0322820	−	0.0993538i
$106$	−8.33414	+	6.05511i	−0.809484	+	0.588124i
$107$	−5.38424	−	3.91188i	−0.520514	−	0.378176i	0.296283	−	0.955100i	$-0.404253\pi$
$107$	−5.38424	−	3.91188i	−0.520514	−	0.378176i	−0.816798	+	0.576924i	$0.804253\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	−13.4250			−1.28588			−0.642941	−	0.765915i	$-0.722286\pi$
$109$	−13.4250			−1.28588			−0.642941	+	0.765915i	$0.722286\pi$
$110$	3.48045	−	0.700944i	0.331848	−	0.0668324i
$111$	3.26074			0.309495
$112$	0.309017	+	0.951057i	0.0291994	+	0.0898664i
$113$	10.5186	+	7.64223i	0.989509	+	0.718921i	0.959814	−	0.280638i	$-0.0905462\pi$
$113$	10.5186	+	7.64223i	0.989509	+	0.718921i	0.0296957	+	0.999559i	$0.490546\pi$
$114$	4.70378	−	3.41749i	0.440549	−	0.320078i
$115$	−0.760326	+	2.34004i	−0.0709008	+	0.218210i
$116$	1.20042	−	3.69452i	0.111457	−	0.343028i
$117$	5.56036	−	4.03984i	0.514055	−	0.373483i
$118$	0.410699	+	0.298390i	0.0378079	+	0.0274691i
$119$	−2.18850	−	6.73551i	−0.200619	−	0.617443i
$120$	−1.07047			−0.0977198
$121$	10.1425	−	4.25798i	0.922042	−	0.387089i
$122$	−7.99370			−0.723716
$123$	−1.49752	−	4.60888i	−0.135027	−	0.415569i
$124$	−2.89476	−	2.10317i	−0.259957	−	0.188870i
$125$	7.66788	−	5.57104i	0.685836	−	0.498289i
$126$	−0.309017	+	0.951057i	−0.0275294	+	0.0847268i
$127$	3.91968	−	12.0635i	0.347816	−	1.07047i	−0.612244	−	0.790669i	$-0.709733\pi$
$127$	3.91968	−	12.0635i	0.347816	−	1.07047i	0.960059	−	0.279797i	$-0.0902672\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	4.21028	+	3.05894i	0.370694	+	0.269325i
$130$	2.27353	+	6.99721i	0.199402	+	0.613695i
$131$	0.283254			0.0247480			0.0123740	−	0.999923i	$-0.496061\pi$
$131$	0.283254			0.0247480			0.0123740	+	0.999923i	$0.496061\pi$
$132$	−3.25134	+	0.654803i	−0.282993	+	0.0569933i
$133$	5.81419			0.504154
$134$	−1.17169	−	3.60609i	−0.101219	−	0.311519i
$135$	−0.866025	−	0.629204i	−0.0745356	−	0.0541533i
$136$	−5.72957	+	4.16277i	−0.491306	+	0.356955i
$137$	1.64564	−	5.06477i	0.140597	−	0.432713i	−0.855822	−	0.517271i	$-0.826948\pi$
$137$	1.64564	−	5.06477i	0.140597	−	0.432713i	0.996419	+	0.0845584i	$0.0269479\pi$
$138$	0.710276	−	2.18600i	0.0604627	−	0.186085i
$139$	−14.5449	+	10.5675i	−1.23368	+	0.896321i	−0.997161	−	0.0753053i	$-0.976007\pi$
$139$	−14.5449	+	10.5675i	−1.23368	+	0.896321i	−0.236520	+	0.971627i	$0.576007\pi$
$140$	−0.866025	−	0.629204i	−0.0731925	−	0.0531775i
$141$	3.14163	+	9.66893i	0.264573	+	0.814271i
$142$	14.2181			1.19316
$143$	11.1856	+	19.8620i	0.935387	+	1.66094i
$144$	1.00000			0.0833333
$145$	1.28501	+	3.95486i	0.106715	+	0.328434i
$146$	−10.4174	−	7.56869i	−0.862150	−	0.626389i
$147$	−0.809017	+	0.587785i	−0.0667266	+	0.0484797i
$148$	1.00762	−	3.10115i	0.0828261	−	0.254913i
$149$	−3.23607	+	9.95959i	−0.265109	+	0.815922i	0.726559	+	0.687104i	$0.241118\pi$
$149$	−3.23607	+	9.95959i	−0.265109	+	0.815922i	−0.991668	+	0.128818i	$0.958882\pi$
$150$	−3.11803	+	2.26538i	−0.254586	+	0.184968i
$151$	−4.14784	−	3.01358i	−0.337547	−	0.245242i	0.406079	−	0.913838i	$-0.366896\pi$
$151$	−4.14784	−	3.01358i	−0.337547	−	0.245242i	−0.743626	+	0.668596i	$0.766896\pi$
$152$	−1.79668	−	5.52962i	−0.145730	−	0.448511i
$153$	−7.08214			−0.572557
$154$	−3.01528	−	1.38135i	−0.242978	−	0.111312i
$155$	3.83026			0.307653
$156$	−2.12387	−	6.53660i	−0.170046	−	0.523346i
$157$	8.60503	+	6.25192i	0.686756	+	0.498958i	0.875592	−	0.483051i	$-0.160471\pi$
$157$	8.60503	+	6.25192i	0.686756	+	0.498958i	−0.188836	+	0.982009i	$0.560471\pi$
$158$	−7.26480	+	5.27819i	−0.577957	+	0.419910i
$159$	−3.18336	+	9.79737i	−0.252457	+	0.776982i
$160$	−0.330792	+	1.01807i	−0.0261514	+	0.0804858i
$161$	1.85953	−	1.35102i	0.146551	−	0.106476i
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	0.145898	+	0.449028i	0.0114276	+	0.0351706i	0.956608	−	0.291379i	$-0.0941140\pi$
$163$	0.145898	+	0.449028i	0.0114276	+	0.0351706i	−0.945180	+	0.326549i	$0.894114\pi$
$164$	−4.84607			−0.378414
$165$	2.40374	−	2.61283i	0.187131	−	0.203409i
$166$	1.79167			0.139061
$167$	−6.55854	−	20.1851i	−0.507515	−	1.56197i	−0.796501	−	0.604638i	$-0.793318\pi$
$167$	−6.55854	−	20.1851i	−0.507515	−	1.56197i	0.288985	−	0.957334i	$-0.406682\pi$
$168$	0.809017	+	0.587785i	0.0624170	+	0.0453486i
$169$	−27.6990	+	20.1245i	−2.13070	+	1.54804i
$170$	2.34272	−	7.21014i	0.179678	−	0.552992i
$171$	1.79668	−	5.52962i	0.137396	−	0.422861i
$172$	4.21028	−	3.05894i	0.321030	−	0.233242i
$173$	14.4774	+	10.5184i	1.10069	+	0.799700i	0.981173	−	0.193132i	$-0.0618645\pi$
$173$	14.4774	+	10.5184i	1.10069	+	0.799700i	0.119520	+	0.992832i	$0.461864\pi$
$174$	−1.20042	−	3.69452i	−0.0910039	−	0.280081i
$175$	−3.85410			−0.291343
$176$	−0.381966	+	3.29456i	−0.0287918	+	0.248337i
$177$	0.507652			0.0381575
$178$	−1.92552	−	5.92613i	−0.144324	−	0.444182i
$179$	10.3429	+	7.51457i	0.773066	+	0.561665i	0.902890	−	0.429872i	$-0.141441\pi$
$179$	10.3429	+	7.51457i	0.773066	+	0.561665i	−0.129824	+	0.991537i	$0.541441\pi$
$180$	−0.866025	+	0.629204i	−0.0645497	+	0.0468981i
$181$	0.785453	−	2.41738i	0.0583823	−	0.179682i	−0.917612	−	0.397476i	$-0.869886\pi$
$181$	0.785453	−	2.41738i	0.0583823	−	0.179682i	0.975995	+	0.217794i	$0.0698861\pi$
$182$	2.12387	−	6.53660i	0.157432	−	0.484525i
$183$	−6.46704	+	4.69858i	−0.478058	+	0.347329i
$184$	−1.85953	−	1.35102i	−0.137086	−	0.0995988i
$185$	1.07863	+	3.31967i	0.0793022	+	0.244067i
$186$	−3.57812			−0.262360
$187$	2.70514	−	23.3325i	0.197819	−	1.70624i
$188$	10.1665			0.741470
$189$	0.309017	+	0.951057i	0.0224777	+	0.0691792i
$190$	5.03523	+	3.65831i	0.365294	+	0.265402i
$191$	−6.16138	+	4.47650i	−0.445822	+	0.323908i	−0.787944	−	0.615747i	$-0.788854\pi$
$191$	−6.16138	+	4.47650i	−0.445822	+	0.323908i	0.342122	+	0.939655i	$0.388854\pi$
$192$	0.309017	−	0.951057i	0.0223014	−	0.0686366i
$193$	−4.15414	+	12.7851i	−0.299021	+	0.920293i	0.682820	+	0.730587i	$0.260753\pi$
$193$	−4.15414	+	12.7851i	−0.299021	+	0.920293i	−0.981841	+	0.189706i	$0.939247\pi$
$194$	−13.5572	+	9.84989i	−0.973351	+	0.707181i
$195$	5.95218	+	4.32451i	0.426244	+	0.309685i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	−6.97391			−0.496870			−0.248435	−	0.968649i	$-0.579916\pi$
$197$	−6.97391			−0.496870			−0.248435	+	0.968649i	$0.579916\pi$
$198$	−2.24551	+	2.44084i	−0.159581	+	0.173463i
$199$	24.6592			1.74804			0.874021	−	0.485887i	$-0.161503\pi$
$199$	24.6592			1.74804			0.874021	+	0.485887i	$0.161503\pi$
$200$	1.19098	+	3.66547i	0.0842152	+	0.259188i
$201$	−3.06753	−	2.22869i	−0.216367	−	0.157200i
$202$	−11.5742	+	8.40917i	−0.814360	+	0.591667i
$203$	1.20042	−	3.69452i	0.0842532	−	0.259305i
$204$	−2.18850	+	6.73551i	−0.153226	+	0.471580i
$205$	4.19682	−	3.04917i	0.293118	−	0.212963i
$206$	−5.22849	−	3.79872i	−0.364286	−	0.264669i
$207$	−0.710276	−	2.18600i	−0.0493676	−	0.151938i
$208$	−6.87298			−0.476556
$209$	17.5314	+	8.03140i	1.21267	+	0.555543i
$210$	−1.07047			−0.0738692
$211$	6.73763	+	20.7363i	0.463838	+	1.42755i	0.860438	+	0.509554i	$0.170190\pi$
$211$	6.73763	+	20.7363i	0.463838	+	1.42755i	−0.396601	+	0.917991i	$0.629810\pi$
$212$	8.33414	+	6.05511i	0.572391	+	0.415867i
$213$	11.5027	−	8.35719i	0.788151	−	0.572625i
$214$	−2.05660	+	6.32956i	−0.140586	+	0.432680i
$215$	−1.72150	+	5.29825i	−0.117406	+	0.361337i
$216$	0.809017	−	0.587785i	0.0550466	−	0.0399937i
$217$	−2.89476	−	2.10317i	−0.196509	−	0.142772i
$218$	4.14856	+	12.7679i	0.280976	+	0.864754i
$219$	−12.8766			−0.870121
$220$	−1.74216	−	3.09350i	−0.117456	−	0.208564i
$221$	48.6754			3.27426
$222$	−1.00762	−	3.10115i	−0.0676272	−	0.208135i
$223$	6.81009	+	4.94782i	0.456038	+	0.331331i	0.791975	−	0.610554i	$-0.209053\pi$
$223$	6.81009	+	4.94782i	0.456038	+	0.331331i	−0.335937	+	0.941884i	$0.609053\pi$
$224$	0.809017	−	0.587785i	0.0540547	−	0.0392731i
$225$	−1.19098	+	3.66547i	−0.0793989	+	0.244365i
$226$	4.01776	−	12.3654i	0.267257	−	0.822533i
$227$	−17.0949	+	12.4202i	−1.13463	+	0.824357i	−0.986362	−	0.164590i	$-0.947370\pi$
$227$	−17.0949	+	12.4202i	−1.13463	+	0.824357i	−0.148268	+	0.988947i	$0.547370\pi$
$228$	−4.70378	−	3.41749i	−0.311515	−	0.226329i
$229$	−1.91899	−	5.90604i	−0.126810	−	0.390282i	0.867416	−	0.497583i	$-0.165779\pi$
$229$	−1.91899	−	5.90604i	−0.126810	−	0.390282i	−0.994227	+	0.107301i	$0.965779\pi$
$230$	2.46047			0.162238
$231$	−3.25134	+	0.654803i	−0.213923	+	0.0430829i
$232$	−3.88465			−0.255040
$233$	−6.05759	−	18.6434i	−0.396846	−	1.22137i	−0.927514	−	0.373787i	$-0.878059\pi$
$233$	−6.05759	−	18.6434i	−0.396846	−	1.22137i	0.530668	−	0.847580i	$-0.321941\pi$
$234$	−5.56036	−	4.03984i	−0.363492	−	0.264092i
$235$	−8.80446	+	6.39682i	−0.574340	+	0.417282i
$236$	0.156873	−	0.482806i	0.0102116	−	0.0314280i
$237$	−2.77491	+	8.54029i	−0.180250	+	0.554751i
$238$	−5.72957	+	4.16277i	−0.371393	+	0.269833i
$239$	−10.7383	−	7.80183i	−0.694603	−	0.504658i	0.183567	−	0.983007i	$-0.441235\pi$
$239$	−10.7383	−	7.80183i	−0.694603	−	0.504658i	−0.878170	+	0.478349i	$0.841235\pi$
$240$	0.330792	+	1.01807i	0.0213525	+	0.0657164i
$241$	−23.8051			−1.53342			−0.766710	−	0.641994i	$-0.778108\pi$
$241$	−23.8051			−1.53342			−0.766710	+	0.641994i	$0.778108\pi$
$242$	−7.18377	−	8.33027i	−0.461790	−	0.535490i
$243$	1.00000			0.0641500
$244$	2.47019	+	7.60246i	0.158138	+	0.486698i
$245$	−0.866025	−	0.629204i	−0.0553283	−	0.0401984i
$246$	−3.92055	+	2.84845i	−0.249965	+	0.181610i
$247$	−12.3486	+	38.0050i	−0.785721	+	2.41820i
$248$	−1.10570	+	3.40299i	−0.0702120	+	0.216090i
$249$	1.44949	−	1.05312i	0.0918578	−	0.0667386i
$250$	−7.66788	−	5.57104i	−0.484959	−	0.352343i
$251$	0.0931899	+	0.286809i	0.00588209	+	0.0181032i	0.953954	−	0.299951i	$-0.0969705\pi$
$251$	0.0931899	+	0.286809i	0.00588209	+	0.0181032i	−0.948072	+	0.318055i	$0.896970\pi$
$252$	1.00000			0.0629941
$253$	7.47321	−	1.50506i	0.469837	−	0.0946226i
$254$	−12.6844			−0.795887
$255$	−2.34272	−	7.21014i	−0.146707	−	0.451516i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	10.5015	−	7.62981i	0.655068	−	0.475935i	−0.209926	−	0.977717i	$-0.567322\pi$
$257$	10.5015	−	7.62981i	0.655068	−	0.475935i	0.864994	+	0.501783i	$0.167322\pi$
$258$	1.60818	−	4.94948i	0.100121	−	0.308141i
$259$	1.00762	−	3.10115i	0.0626107	−	0.192696i
$260$	5.95218	−	4.32451i	0.369138	−	0.268195i
$261$	−3.14275	−	2.28334i	−0.194531	−	0.141335i
$262$	−0.0875302	−	0.269390i	−0.00540763	−	0.0166430i
$263$	−2.73287			−0.168516			−0.0842581	−	0.996444i	$-0.526852\pi$
$263$	−2.73287			−0.168516			−0.0842581	+	0.996444i	$0.526852\pi$
$264$	1.62747	+	2.88987i	0.100164	+	0.177859i
$265$	−11.0275			−0.677413
$266$	−1.79668	−	5.52962i	−0.110162	−	0.339043i
$267$	−5.04107	−	3.66255i	−0.308508	−	0.224144i
$268$	−3.06753	+	2.22869i	−0.187379	+	0.136139i
$269$	−7.72212	+	23.7662i	−0.470826	+	1.44905i	0.380679	+	0.924707i	$0.375690\pi$
$269$	−7.72212	+	23.7662i	−0.470826	+	1.44905i	−0.851505	+	0.524346i	$0.824310\pi$
$270$	−0.330792	+	1.01807i	−0.0201314	+	0.0619580i
$271$	9.51279	−	6.91145i	0.577861	−	0.419841i	−0.260091	−	0.965584i	$-0.583753\pi$
$271$	9.51279	−	6.91145i	0.577861	−	0.419841i	0.837952	+	0.545743i	$0.183753\pi$
$272$	5.72957	+	4.16277i	0.347406	+	0.252405i
$273$	−2.12387	−	6.53660i	−0.128542	−	0.395613i
$274$	−5.32542			−0.321720
$275$	−11.6212	−	5.32385i	−0.700783	−	0.321040i
$276$	−2.29850			−0.138353
$277$	6.48406	+	19.9559i	0.389589	+	1.19903i	0.933096	+	0.359628i	$0.117096\pi$
$277$	6.48406	+	19.9559i	0.389589	+	1.19903i	−0.543506	+	0.839405i	$0.682904\pi$
$278$	14.5449	+	10.5675i	0.872344	+	0.633795i
$279$	−2.89476	+	2.10317i	−0.173305	+	0.125913i
$280$	−0.330792	+	1.01807i	−0.0197686	+	0.0608416i
$281$	−3.63083	+	11.1745i	−0.216597	+	0.666617i	0.782439	+	0.622727i	$0.213975\pi$
$281$	−3.63083	+	11.1745i	−0.216597	+	0.666617i	−0.999036	+	0.0438902i	$0.986025\pi$
$282$	8.22489	−	5.97573i	0.489785	−	0.355849i
$283$	−11.2499	−	8.17356i	−0.668739	−	0.485868i	0.200864	−	0.979619i	$-0.435625\pi$
$283$	−11.2499	−	8.17356i	−0.668739	−	0.485868i	−0.869603	+	0.493752i	$0.835625\pi$
$284$	−4.39364	−	13.5222i	−0.260714	−	0.802396i
$285$	6.22389			0.368671
$286$	15.4333	−	16.7758i	0.912593	−	0.991976i
$287$	−4.84607			−0.286054
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	−26.8243	−	19.4890i	−1.57790	−	1.14641i
$290$	3.36421	−	2.44424i	0.197553	−	0.143531i
$291$	−5.17839	+	15.9375i	−0.303563	+	0.934270i
$292$	−3.97909	+	12.2464i	−0.232859	+	0.716666i
$293$	−1.11642	+	0.811129i	−0.0652222	+	0.0473867i	−0.619919	−	0.784666i	$-0.712834\pi$
$293$	−1.11642	+	0.811129i	−0.0652222	+	0.0473867i	0.554696	+	0.832053i	$0.312834\pi$
$294$	0.809017	+	0.587785i	0.0471828	+	0.0342803i
$295$	0.167927	+	0.516827i	0.00977711	+	0.0300909i
$296$	−3.26074			−0.189526
$297$	−0.381966	+	3.29456i	−0.0221639	+	0.191170i
$298$	10.4721			0.606635
$299$	4.88171	+	15.0244i	0.282317	+	0.868881i
$300$	3.11803	+	2.26538i	0.180020	+	0.130792i
$301$	4.21028	−	3.05894i	0.242676	−	0.176315i
$302$	−1.58434	+	4.87608i	−0.0911683	+	0.280587i
$303$	−4.42096	+	13.6063i	−0.253978	+	0.781663i
$304$	−4.70378	+	3.41749i	−0.269780	+	0.196007i
$305$	−6.92275	−	5.02967i	−0.396396	−	0.287998i
$306$	2.18850	+	6.73551i	0.125108	+	0.385044i
$307$	−16.0206			−0.914345			−0.457173	−	0.889378i	$-0.651138\pi$
$307$	−16.0206			−0.914345			−0.457173	+	0.889378i	$0.651138\pi$
$308$	−0.381966	+	3.29456i	−0.0217645	+	0.187725i
$309$	−6.46277			−0.367654
$310$	−1.18361	−	3.64279i	−0.0672248	−	0.206897i
$311$	1.20621	+	0.876364i	0.0683980	+	0.0496940i	0.621459	−	0.783447i	$-0.286540\pi$
$311$	1.20621	+	0.876364i	0.0683980	+	0.0496940i	−0.553061	+	0.833141i	$0.686540\pi$
$312$	−5.56036	+	4.03984i	−0.314793	+	0.228711i
$313$	1.97226	−	6.07000i	0.111479	−	0.343097i	−0.879718	−	0.475497i	$-0.842268\pi$
$313$	1.97226	−	6.07000i	0.111479	−	0.343097i	0.991196	+	0.132400i	$0.0422684\pi$
$314$	3.28683	−	10.1158i	0.185487	−	0.570869i
$315$	−0.866025	+	0.629204i	−0.0487950	+	0.0354516i
$316$	7.26480	+	5.27819i	0.408677	+	0.296921i
$317$	1.40776	+	4.33264i	0.0790676	+	0.243345i	0.982775	−	0.184805i	$-0.0591654\pi$
$317$	1.40776	+	4.33264i	0.0790676	+	0.243345i	−0.903708	+	0.428150i	$0.859165\pi$
$318$	10.3016			0.577683
$319$	8.72302	−	9.48181i	0.488395	−	0.530879i
$320$	1.07047			0.0598409
$321$	2.05660	+	6.32956i	0.114788	+	0.353281i
$322$	−1.85953	−	1.35102i	−0.103627	−	0.0752896i
$323$	33.3128	−	24.2031i	1.85357	−	1.34670i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	8.18561	−	25.1927i	0.454056	−	1.39744i
$326$	0.381966	−	0.277515i	0.0211551	−	0.0153701i
$327$	10.8611	+	7.89102i	0.600618	+	0.436375i
$328$	1.49752	+	4.60888i	0.0826866	+	0.254483i
$329$	10.1665			0.560498
$330$	−3.22775	−	1.47868i	−0.177682	−	0.0813988i
$331$	9.56098			0.525519			0.262759	−	0.964861i	$-0.415367\pi$
$331$	9.56098			0.525519			0.262759	+	0.964861i	$0.415367\pi$
$332$	−0.553656	−	1.70398i	−0.0303858	−	0.0935180i
$333$	−2.63799	−	1.91661i	−0.144561	−	0.105030i
$334$	−17.1705	+	12.4751i	−0.939527	+	0.682607i
$335$	1.25426	−	3.86020i	0.0685273	−	0.210905i
$336$	0.309017	−	0.951057i	0.0168583	−	0.0518844i
$337$	−3.88867	+	2.82528i	−0.211829	+	0.153903i	−0.688641	−	0.725102i	$-0.741792\pi$
$337$	−3.88867	+	2.82528i	−0.211829	+	0.153903i	0.476812	+	0.879005i	$0.341792\pi$
$338$	27.6990	+	20.1245i	1.50663	+	1.09463i
$339$	−4.01776	−	12.3654i	−0.218215	−	0.671596i
$340$	−7.58119			−0.411148
$341$	−5.82330	−	10.3403i	−0.315349	−	0.559958i
$342$	−5.81419			−0.314395
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	−4.21028	−	3.05894i	−0.227003	−	0.164927i
$345$	1.99056	−	1.44623i	0.107168	−	0.0778622i
$346$	5.52986	−	17.0191i	0.297287	−	0.914955i
$347$	10.4322	−	32.1071i	0.560032	−	1.72360i	−0.122238	−	0.992501i	$-0.539007\pi$
$347$	10.4322	−	32.1071i	0.560032	−	1.72360i	0.682270	−	0.731100i	$-0.260993\pi$
$348$	−3.14275	+	2.28334i	−0.168469	+	0.122400i
$349$	−26.0727	−	18.9429i	−1.39564	−	1.01399i	−0.995220	−	0.0976592i	$-0.968864\pi$
$349$	−26.0727	−	18.9429i	−1.39564	−	1.01399i	−0.400419	−	0.916332i	$-0.631136\pi$
$350$	1.19098	+	3.66547i	0.0636607	+	0.195928i
$351$	−6.87298			−0.366853
$352$	3.25134	−	0.654803i	0.173297	−	0.0349011i
$353$	−8.35904			−0.444907			−0.222453	−	0.974943i	$-0.571406\pi$
$353$	−8.35904			−0.444907			−0.222453	+	0.974943i	$0.571406\pi$
$354$	−0.156873	−	0.482806i	−0.00833771	−	0.0256608i
$355$	12.3132	+	8.94609i	0.653519	+	0.474809i
$356$	−5.04107	+	3.66255i	−0.267176	+	0.194115i
$357$	−2.18850	+	6.73551i	−0.115828	+	0.356481i
$358$	3.95064	−	12.1588i	0.208798	−	0.642614i
$359$	10.2223	−	7.42696i	0.539514	−	0.391980i	−0.284391	−	0.958708i	$-0.591791\pi$
$359$	10.2223	−	7.42696i	0.539514	−	0.391980i	0.823904	+	0.566729i	$0.191791\pi$
$360$	0.866025	+	0.629204i	0.0456435	+	0.0331620i
$361$	4.57492	+	14.0802i	0.240785	+	0.741061i
$362$	−2.54178			−0.133593
$363$	−10.7082	−	2.51682i	−0.562035	−	0.132099i
$364$	−6.87298			−0.360242
$365$	−4.25949	−	13.1093i	−0.222952	−	0.686175i
$366$	6.46704	+	4.69858i	0.338038	+	0.245599i
$367$	4.69728	−	3.41277i	0.245196	−	0.178145i	−0.458399	−	0.888746i	$-0.651577\pi$
$367$	4.69728	−	3.41277i	0.245196	−	0.178145i	0.703595	+	0.710601i	$0.251577\pi$
$368$	−0.710276	+	2.18600i	−0.0370257	+	0.113953i
$369$	−1.49752	+	4.60888i	−0.0779576	+	0.239929i
$370$	2.82388	−	2.05167i	0.146807	−	0.106661i
$371$	8.33414	+	6.05511i	0.432687	+	0.314366i
$372$	1.10570	+	3.40299i	0.0573278	+	0.176437i
$373$	31.9384			1.65371			0.826853	−	0.562417i	$-0.190129\pi$
$373$	31.9384			1.65371			0.826853	+	0.562417i	$0.190129\pi$
$374$	−23.0265	+	4.63740i	−1.19067	+	0.239794i
$375$	−9.47802			−0.489443
$376$	−3.14163	−	9.66893i	−0.162017	−	0.498637i
$377$	21.6001	+	15.6934i	1.11246	+	0.808250i
$378$	0.809017	−	0.587785i	0.0416113	−	0.0302324i
$379$	−0.906889	+	2.79112i	−0.0465838	+	0.143370i	−0.971643	−	0.236453i	$-0.924015\pi$
$379$	−0.906889	+	2.79112i	−0.0465838	+	0.143370i	0.925059	+	0.379823i	$0.124015\pi$
$380$	1.92329	−	5.91927i	0.0986626	−	0.303652i
$381$	−10.2619	+	7.45568i	−0.525731	+	0.381966i
$382$	6.16138	+	4.47650i	0.315243	+	0.229038i
$383$	−0.304288	−	0.936501i	−0.0155484	−	0.0478530i	0.942981	−	0.332846i	$-0.108009\pi$
$383$	−0.304288	−	0.936501i	−0.0155484	−	0.0478530i	−0.958530	+	0.284993i	$0.908009\pi$
$384$	−1.00000			−0.0510310
$385$	−1.74216	−	3.09350i	−0.0887885	−	0.157660i
$386$	13.4431			0.684234
$387$	−1.60818	−	4.94948i	−0.0817485	−	0.251596i
$388$	13.5572	+	9.84989i	0.688263	+	0.500052i
$389$	−2.73533	+	1.98733i	−0.138687	+	0.100762i	−0.654965	−	0.755659i	$-0.727317\pi$
$389$	−2.73533	+	1.98733i	−0.138687	+	0.100762i	0.516279	+	0.856421i	$0.327317\pi$
$390$	2.27353	−	6.99721i	0.115125	−	0.354317i
$391$	5.03027	−	15.4816i	0.254392	−	0.782937i
$392$	0.809017	−	0.587785i	0.0408615	−	0.0296876i
$393$	−0.229157	−	0.166492i	−0.0115594	−	0.00839842i
$394$	2.15506	+	6.63258i	0.108570	+	0.334145i
$395$	−9.61256			−0.483660
$396$	3.01528	+	1.38135i	0.151523	+	0.0694152i
$397$	−14.6427			−0.734896			−0.367448	−	0.930044i	$-0.619768\pi$
$397$	−14.6427			−0.734896			−0.367448	+	0.930044i	$0.619768\pi$
$398$	−7.62011	−	23.4523i	−0.381961	−	1.17556i
$399$	−4.70378	−	3.41749i	−0.235483	−	0.171089i
$400$	3.11803	−	2.26538i	0.155902	−	0.113269i
$401$	−6.85968	+	21.1119i	−0.342556	+	1.05428i	0.620323	+	0.784347i	$0.287002\pi$
$401$	−6.85968	+	21.1119i	−0.342556	+	1.05428i	−0.962879	+	0.269933i	$0.912998\pi$
$402$	−1.17169	+	3.60609i	−0.0584386	+	0.179856i
$403$	19.8956	−	14.4550i	0.991072	−	0.720056i
$404$	11.5742	+	8.40917i	0.575839	+	0.418372i
$405$	0.330792	+	1.01807i	0.0164372	+	0.0505885i
$406$	−3.88465			−0.192792
$407$	7.32201	−	7.95893i	0.362939	−	0.394510i
$408$	7.08214			0.350618
$409$	6.47659	+	19.9329i	0.320247	+	0.985619i	0.973541	+	0.228514i	$0.0733867\pi$
$409$	6.47659	+	19.9329i	0.320247	+	0.985619i	−0.653294	+	0.757105i	$0.726613\pi$
$410$	−4.19682	−	3.04917i	−0.207266	−	0.150588i
$411$	−4.30835	+	3.13020i	−0.212515	+	0.154401i
$412$	−1.99711	+	6.14646i	−0.0983904	+	0.302814i
$413$	0.156873	−	0.482806i	0.00771922	−	0.0237573i
$414$	−1.85953	+	1.35102i	−0.0913907	+	0.0663992i
$415$	1.55163	+	1.12733i	0.0761666	+	0.0553383i
$416$	2.12387	+	6.53660i	0.104131	+	0.320483i
$417$	17.9785			0.880409
$418$	2.22082	−	19.1552i	0.108624	−	0.936910i
$419$	−22.3088			−1.08986			−0.544929	−	0.838482i	$-0.683443\pi$
$419$	−22.3088			−1.08986			−0.544929	+	0.838482i	$0.683443\pi$
$420$	0.330792	+	1.01807i	0.0161410	+	0.0496769i
$421$	−11.9980	−	8.71706i	−0.584747	−	0.424844i	0.255685	−	0.966760i	$-0.417699\pi$
$421$	−11.9980	−	8.71706i	−0.584747	−	0.424844i	−0.840432	+	0.541917i	$0.817699\pi$
$422$	17.6393	−	12.8157i	0.858670	−	0.623860i
$423$	3.14163	−	9.66893i	0.152751	−	0.470120i
$424$	3.18336	−	9.79737i	0.154598	−	0.475803i
$425$	−22.0823	+	16.0438i	−1.07115	+	0.778237i
$426$	−11.5027	−	8.35719i	−0.557307	−	0.404907i
$427$	2.47019	+	7.60246i	0.119541	+	0.367909i
$428$	6.65529			0.321696
$429$	2.62525	−	22.6434i	0.126748	−	1.09324i
$430$	5.57091			0.268653
$431$	1.77035	+	5.44859i	0.0852749	+	0.262449i	0.984597	−	0.174837i	$-0.0559398\pi$
$431$	1.77035	+	5.44859i	0.0852749	+	0.262449i	−0.899323	+	0.437286i	$0.855940\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	3.76588	−	2.73607i	0.180977	−	0.131487i	−0.493609	−	0.869684i	$-0.664322\pi$
$433$	3.76588	−	2.73607i	0.180977	−	0.131487i	0.674585	+	0.738197i	$0.264322\pi$
$434$	−1.10570	+	3.40299i	−0.0530753	+	0.163349i
$435$	1.28501	−	3.95486i	0.0616117	−	0.189621i
$436$	10.8611	−	7.89102i	0.520150	−	0.377911i
$437$	10.8116	+	7.85511i	0.517190	+	0.375761i
$438$	3.97909	+	12.2464i	0.190128	+	0.585155i
$439$	−3.00895			−0.143609			−0.0718047	−	0.997419i	$-0.522876\pi$
$439$	−3.00895			−0.143609			−0.0718047	+	0.997419i	$0.522876\pi$
$440$	−2.40374	+	2.61283i	−0.114594	+	0.124562i
$441$	1.00000			0.0476190
$442$	−15.0415	−	46.2931i	−0.715452	−	2.20194i
$443$	−4.15033	−	3.01539i	−0.197188	−	0.143265i	0.484810	−	0.874619i	$-0.338889\pi$
$443$	−4.15033	−	3.01539i	−0.197188	−	0.143265i	−0.681998	+	0.731354i	$0.738889\pi$
$444$	−2.63799	+	1.91661i	−0.125194	+	0.0909584i
$445$	2.06120	−	6.34372i	0.0977103	−	0.300721i
$446$	2.60122	−	8.00574i	0.123172	−	0.379083i
$447$	8.47214	−	6.15537i	0.400718	−	0.291139i
$448$	−0.809017	−	0.587785i	−0.0382225	−	0.0277702i
$449$	1.15959	+	3.56886i	0.0547245	+	0.168425i	0.974683	−	0.223591i	$-0.0717779\pi$
$449$	1.15959	+	3.56886i	0.0547245	+	0.168425i	−0.919959	+	0.392016i	$0.871778\pi$
$450$	3.85410			0.181684
$451$	−14.6122	−	6.69409i	−0.688063	−	0.315212i
$452$	−13.0017			−0.611550
$453$	1.58434	+	4.87608i	0.0744386	+	0.229098i
$454$	17.0949	+	12.4202i	0.802305	+	0.582909i
$455$	5.95218	−	4.32451i	0.279042	−	0.202736i
$456$	−1.79668	+	5.52962i	−0.0841374	+	0.258948i
$457$	6.68850	−	20.5851i	0.312875	−	0.962930i	−0.663746	−	0.747958i	$-0.731034\pi$
$457$	6.68850	−	20.5851i	0.312875	−	0.962930i	0.976620	−	0.214971i	$-0.0689658\pi$
$458$	−5.02397	+	3.65013i	−0.234755	+	0.170559i
$459$	5.72957	+	4.16277i	0.267433	+	0.194302i
$460$	−0.760326	−	2.34004i	−0.0354504	−	0.109105i
$461$	4.96761			0.231365			0.115682	−	0.993286i	$-0.463095\pi$
$461$	4.96761			0.231365			0.115682	+	0.993286i	$0.463095\pi$
$462$	1.62747	+	2.88987i	0.0757170	+	0.134449i
$463$	−14.3253			−0.665754			−0.332877	−	0.942970i	$-0.608019\pi$
$463$	−14.3253			−0.665754			−0.332877	+	0.942970i	$0.608019\pi$
$464$	1.20042	+	3.69452i	0.0557283	+	0.171514i
$465$	−3.09874	−	2.25137i	−0.143701	−	0.104405i
$466$	−15.8590	+	11.5222i	−0.734653	+	0.533757i
$467$	1.86879	−	5.75155i	0.0864773	−	0.266150i	−0.898462	−	0.439052i	$-0.855314\pi$
$467$	1.86879	−	5.75155i	0.0864773	−	0.266150i	0.984939	+	0.172902i	$0.0553144\pi$
$468$	−2.12387	+	6.53660i	−0.0981759	+	0.302154i
$469$	−3.06753	+	2.22869i	−0.141645	+	0.102911i
$470$	8.80446	+	6.39682i	0.406120	+	0.295063i
$471$	−3.28683	−	10.1158i	−0.151449	−	0.466113i
$472$	−0.507652			−0.0233666
$473$	16.9206	−	3.40772i	0.778010	−	0.156687i
$474$	8.97979			0.412455
$475$	−6.92460	−	21.3117i	−0.317722	−	0.977849i
$476$	5.72957	+	4.16277i	0.262614	+	0.190800i
$477$	8.33414	−	6.05511i	0.381594	−	0.277244i
$478$	−4.10166	+	12.6236i	−0.187606	+	0.577391i
$479$	1.39446	−	4.29170i	0.0637144	−	0.196093i	−0.914132	−	0.405417i	$-0.867126\pi$
$479$	1.39446	−	4.29170i	0.0637144	−	0.196093i	0.977846	+	0.209324i	$0.0671264\pi$
$480$	0.866025	−	0.629204i	0.0395285	−	0.0287191i
$481$	18.1309	+	13.1729i	0.826697	+	0.600630i
$482$	7.35617	+	22.6400i	0.335065	+	1.03122i
$483$	−2.29850			−0.104585
$484$	−5.70265	+	9.40637i	−0.259211	+	0.427562i
$485$	−17.9385			−0.814545
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	0.573025	+	0.416327i	0.0259662	+	0.0188656i	0.600693	−	0.799480i	$-0.294892\pi$
$487$	0.573025	+	0.416327i	0.0259662	+	0.0188656i	−0.574726	+	0.818346i	$0.694892\pi$
$488$	6.46704	−	4.69858i	0.292749	−	0.212695i
$489$	0.145898	−	0.449028i	0.00659774	−	0.0203057i
$490$	−0.330792	+	1.01807i	−0.0149437	+	0.0459919i
$491$	32.8358	−	23.8566i	1.48186	−	1.07663i	0.504904	−	0.863175i	$-0.331528\pi$
$491$	32.8358	−	23.8566i	1.48186	−	1.07663i	0.976953	−	0.213456i	$-0.0684722\pi$
$492$	3.92055	+	2.84845i	0.176752	+	0.128418i
$493$	−8.50156	−	26.1651i	−0.382891	−	1.17842i
$494$	39.9608			1.79792
$495$	−3.48045	+	0.700944i	−0.156435	+	0.0315051i
$496$	3.57812			0.160662
$497$	−4.39364	−	13.5222i	−0.197081	−	0.606554i
$498$	−1.44949	−	1.05312i	−0.0649533	−	0.0471913i
$499$	−4.72017	+	3.42941i	−0.211304	+	0.153521i	−0.688404	−	0.725328i	$-0.741688\pi$
$499$	−4.72017	+	3.42941i	−0.211304	+	0.153521i	0.477099	+	0.878849i	$0.341688\pi$
$500$	−2.92887	+	9.01413i	−0.130983	+	0.403124i
$501$	−6.55854	+	20.1851i	−0.293014	+	0.901805i
$502$	0.243974	−	0.177258i	0.0108891	−	0.00791140i
$503$	−17.4126	−	12.6510i	−0.776391	−	0.564081i	0.127502	−	0.991838i	$-0.459304\pi$
$503$	−17.4126	−	12.6510i	−0.776391	−	0.564081i	−0.903894	+	0.427757i	$0.859304\pi$
$504$	−0.309017	−	0.951057i	−0.0137647	−	0.0423634i
$505$	−15.3147			−0.681494
$506$	−3.74075	−	6.64236i	−0.166297	−	0.295289i
$507$	34.2379			1.52056
$508$	3.91968	+	12.0635i	0.173908	+	0.535233i
$509$	−13.7717	−	10.0057i	−0.610420	−	0.443496i	0.239142	−	0.970985i	$-0.423134\pi$
$509$	−13.7717	−	10.0057i	−0.610420	−	0.443496i	−0.849562	+	0.527488i	$0.823134\pi$
$510$	−6.13331	+	4.45611i	−0.271588	+	0.197320i
$511$	−3.97909	+	12.2464i	−0.176025	+	0.541748i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−4.70378	+	3.41749i	−0.207677	+	0.150886i
$514$	−10.5015	−	7.62981i	−0.463203	−	0.336537i
$515$	−2.13783	−	6.57958i	−0.0942043	−	0.289931i
$516$	−5.20419			−0.229102
$517$	30.6549	+	14.0435i	1.34820	+	0.617631i
$518$	−3.26074			−0.143269
$519$	−5.52986	−	17.0191i	−0.242734	−	0.747058i
$520$	−5.95218	−	4.32451i	−0.261020	−	0.189642i
$521$	−3.55614	+	2.58368i	−0.155797	+	0.113193i	−0.662953	−	0.748661i	$-0.730697\pi$
$521$	−3.55614	+	2.58368i	−0.155797	+	0.113193i	0.507156	+	0.861855i	$0.330697\pi$
$522$	−1.20042	+	3.69452i	−0.0525411	+	0.161705i
$523$	−8.16872	+	25.1407i	−0.357193	+	1.09933i	0.597534	+	0.801844i	$0.296147\pi$
$523$	−8.16872	+	25.1407i	−0.357193	+	1.09933i	−0.954727	+	0.297484i	$0.903853\pi$
$524$	−0.229157	+	0.166492i	−0.0100108	+	0.00727325i
$525$	3.11803	+	2.26538i	0.136082	+	0.0988695i
$526$	0.844504	+	2.59912i	0.0368221	+	0.113327i
$527$	−25.3407			−1.10386
$528$	2.24551	−	2.44084i	0.0977232	−	0.106224i
$529$	−17.7169			−0.770300
$530$	3.40768	+	10.4878i	0.148020	+	0.455559i
$531$	−0.410699	−	0.298390i	−0.0178228	−	0.0129490i
$532$	−4.70378	+	3.41749i	−0.203935	+	0.148167i
$533$	10.2924	−	31.6768i	0.445814	−	1.37207i
$534$	−1.92552	+	5.92613i	−0.0833253	+	0.256449i
$535$	−5.76365	+	4.18754i	−0.249184	+	0.181043i
$536$	3.06753	+	2.22869i	0.132497	+	0.0962646i
$537$	−3.95064	−	12.1588i	−0.170483	−	0.524692i
$538$	24.9893			1.07737
$539$	−0.381966	+	3.29456i	−0.0164524	+	0.141907i
$540$	1.07047			0.0460655
$541$	7.13141	+	21.9482i	0.306603	+	0.943628i	0.979074	+	0.203504i	$0.0652331\pi$
$541$	7.13141	+	21.9482i	0.306603	+	0.943628i	−0.672471	+	0.740124i	$0.734767\pi$
$542$	−9.51279	−	6.91145i	−0.408609	−	0.296872i
$543$	−2.05634	+	1.49402i	−0.0882461	+	0.0641146i
$544$	2.18850	−	6.73551i	0.0938312	−	0.288783i
$545$	−4.44089	+	13.6677i	−0.190227	+	0.585458i
$546$	−5.56036	+	4.03984i	−0.237961	+	0.172889i
$547$	3.13044	+	2.27440i	0.133848	+	0.0972464i	0.652695	−	0.757621i	$-0.273638\pi$
$547$	3.13044	+	2.27440i	0.133848	+	0.0972464i	−0.518847	+	0.854867i	$0.673638\pi$
$548$	1.64564	+	5.06477i	0.0702984	+	0.216356i
$549$	7.99370			0.341163
$550$	−1.47214	+	12.6976i	−0.0627721	+	0.541426i
$551$	22.5861			0.962200
$552$	0.710276	+	2.18600i	0.0302313	+	0.0930425i
$553$	7.26480	+	5.27819i	0.308931	+	0.224451i
$554$	16.9755	−	12.3334i	0.721219	−	0.523997i
$555$	1.07863	−	3.31967i	0.0457852	−	0.140912i
$556$	5.55565	−	17.0985i	0.235612	−	0.725139i
$557$	13.4192	−	9.74963i	0.568591	−	0.413105i	−0.266002	−	0.963972i	$-0.585703\pi$
$557$	13.4192	−	9.74963i	0.568591	−	0.413105i	0.834593	+	0.550867i	$0.185703\pi$
$558$	2.89476	+	2.10317i	0.122545	+	0.0890341i
$559$	11.0530	+	34.0177i	0.467492	+	1.43879i
$560$	1.07047			0.0452355
$561$	−15.9030	+	17.2863i	−0.671425	+	0.729830i
$562$	11.7496			0.495627
$563$	3.32053	+	10.2195i	0.139944	+	0.430702i	0.996326	−	0.0856397i	$-0.0272934\pi$
$563$	3.32053	+	10.2195i	0.139944	+	0.430702i	−0.856383	+	0.516342i	$0.827293\pi$
$564$	−8.22489	−	5.97573i	−0.346330	−	0.251624i
$565$	11.2598	−	8.18075i	0.473705	−	0.344167i
$566$	−4.29709	+	13.2251i	−0.180620	+	0.555892i
$567$	0.309017	−	0.951057i	0.0129775	−	0.0399406i
$568$	−11.5027	+	8.35719i	−0.482642	+	0.350660i
$569$	9.67653	+	7.03041i	0.405661	+	0.294730i	0.771843	−	0.635813i	$-0.219335\pi$
$569$	9.67653	+	7.03041i	0.405661	+	0.294730i	−0.366182	+	0.930543i	$0.619335\pi$
$570$	−1.92329	−	5.91927i	−0.0805577	−	0.247931i
$571$	8.27920			0.346474			0.173237	−	0.984880i	$-0.444577\pi$
$571$	8.27920			0.346474			0.173237	+	0.984880i	$0.444577\pi$
$572$	−20.7239	−	9.49396i	−0.866511	−	0.396963i
$573$	7.61588			0.318158
$574$	1.49752	+	4.60888i	0.0625052	+	0.192371i
$575$	−7.16680	−	5.20699i	−0.298876	−	0.217146i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−0.351208	+	1.08091i	−0.0146210	+	0.0449988i	−0.958101	−	0.286431i	$-0.907531\pi$
$577$	−0.351208	+	1.08091i	−0.0146210	+	0.0449988i	0.943480	+	0.331430i	$0.107531\pi$
$578$	−10.2460	+	31.5338i	−0.426176	+	1.31163i
$579$	10.8757	−	7.90164i	0.451977	−	0.328381i
$580$	−3.36421	−	2.44424i	−0.139691	−	0.101492i
$581$	−0.553656	−	1.70398i	−0.0229695	−	0.0706930i
$582$	16.7576			0.694626
$583$	16.7655	+	29.7702i	0.694358	+	1.23295i
$584$	12.8766			0.532838
$585$	−2.27353	−	6.99721i	−0.0939989	−	0.289299i
$586$	1.11642	+	0.811129i	0.0461190	+	0.0335074i
$587$	−9.04007	+	6.56799i	−0.373124	+	0.271090i	−0.758505	−	0.651667i	$-0.774070\pi$
$587$	−9.04007	+	6.56799i	−0.373124	+	0.271090i	0.385381	+	0.922757i	$0.374070\pi$
$588$	0.309017	−	0.951057i	0.0127436	−	0.0392209i
$589$	6.42874	−	19.7856i	0.264892	−	0.815253i
$590$	0.439640	−	0.319417i	0.0180997	−	0.0131502i
$591$	5.64201	+	4.09916i	0.232081	+	0.168617i
$592$	1.00762	+	3.10115i	0.0414131	+	0.127456i
$593$	−13.0875			−0.537440			−0.268720	−	0.963218i	$-0.586601\pi$
$593$	−13.0875			−0.537440			−0.268720	+	0.963218i	$0.586601\pi$
$594$	3.25134	−	0.654803i	0.133404	−	0.0268669i
$595$	−7.58119			−0.310798
$596$	−3.23607	−	9.95959i	−0.132555	−	0.407961i
$597$	−19.9497	−	14.4943i	−0.816487	−	0.593212i
$598$	12.7805	−	9.28557i	0.522633	−	0.379715i
$599$	−8.57349	+	26.3865i	−0.350303	+	1.07812i	0.608380	+	0.793646i	$0.291820\pi$
$599$	−8.57349	+	26.3865i	−0.350303	+	1.07812i	−0.958683	+	0.284476i	$0.908180\pi$
$600$	1.19098	−	3.66547i	0.0486217	−	0.149642i
$601$	−21.1077	+	15.3357i	−0.861002	+	0.625554i	−0.928157	−	0.372188i	$-0.878608\pi$
$601$	−21.1077	+	15.3357i	−0.861002	+	0.625554i	0.0671555	+	0.997743i	$0.478608\pi$
$602$	−4.21028	−	3.05894i	−0.171598	−	0.124673i
$603$	1.17169	+	3.60609i	0.0477149	+	0.146851i
$604$	5.12702			0.208615
$605$	−0.979885	−	11.7343i	−0.0398380	−	0.477067i
$606$	14.3065			0.581163
$607$	13.8113	+	42.5068i	0.560583	+	1.72530i	0.680724	+	0.732540i	$0.261665\pi$
$607$	13.8113	+	42.5068i	0.560583	+	1.72530i	−0.120141	+	0.992757i	$0.538335\pi$
$608$	4.70378	+	3.41749i	0.190763	+	0.138598i
$609$	−3.14275	+	2.28334i	−0.127351	+	0.0925257i
$610$	−2.64426	+	8.13818i	−0.107063	+	0.329505i
$611$	−21.5923	+	66.4544i	−0.873533	+	2.68846i
$612$	5.72957	−	4.16277i	0.231604	−	0.168270i
$613$	−30.6941	−	22.3006i	−1.23972	−	0.900712i	−0.242144	−	0.970240i	$-0.577851\pi$
$613$	−30.6941	−	22.3006i	−1.23972	−	0.900712i	−0.997580	+	0.0695281i	$0.977851\pi$
$614$	4.95064	+	15.2365i	0.199792	+	0.614896i
$615$	−5.18755			−0.209182
$616$	3.25134	−	0.654803i	0.131000	−	0.0263828i
$617$	−27.2763			−1.09810			−0.549052	−	0.835788i	$-0.685011\pi$
$617$	−27.2763			−1.09810			−0.549052	+	0.835788i	$0.685011\pi$
$618$	1.99711	+	6.14646i	0.0803354	+	0.247247i
$619$	32.4572	+	23.5815i	1.30456	+	0.947822i	0.999989	−	0.00466642i	$-0.00148537\pi$
$619$	32.4572	+	23.5815i	1.30456	+	0.947822i	0.304576	+	0.952488i	$0.401485\pi$
$620$	−3.09874	+	2.25137i	−0.124448	+	0.0904171i
$621$	−0.710276	+	2.18600i	−0.0285024	+	0.0877213i
$622$	0.460732	−	1.41799i	0.0184737	−	0.0568561i
$623$	−5.04107	+	3.66255i	−0.201966	+	0.146737i
$624$	5.56036	+	4.03984i	0.222593	+	0.161723i
$625$	2.81966	+	8.67802i	0.112786	+	0.347121i
$626$	−6.38237			−0.255091
$627$	−9.46244	−	16.8022i	−0.377893	−	0.671016i
$628$	−10.6364			−0.424439
$629$	−7.13612	−	21.9627i	−0.284536	−	0.875711i
$630$	0.866025	+	0.629204i	0.0345033	+	0.0250681i
$631$	27.5546	−	20.0196i	1.09693	−	0.796966i	0.116373	−	0.993206i	$-0.462873\pi$
$631$	27.5546	−	20.0196i	1.09693	−	0.796966i	0.980556	+	0.196240i	$0.0628731\pi$
$632$	2.77491	−	8.54029i	0.110380	−	0.339714i
$633$	6.73763	−	20.7363i	0.267797	−	0.824194i
$634$	3.68556	−	2.67772i	0.146372	−	0.106346i
$635$	−10.9850	−	7.98105i	−0.435925	−	0.316718i
$636$	−3.18336	−	9.79737i	−0.126228	−	0.388491i
$637$	−6.87298			−0.272318
$638$	−11.7133	−	5.36605i	−0.463734	−	0.212444i
$639$	−14.2181			−0.562459
$640$	−0.330792	−	1.01807i	−0.0130757	−	0.0402429i
$641$	−40.1489	−	29.1699i	−1.58579	−	1.15214i	−0.909656	−	0.415362i	$-0.863655\pi$
$641$	−40.1489	−	29.1699i	−1.58579	−	1.15214i	−0.676132	−	0.736781i	$-0.736345\pi$
$642$	5.38424	−	3.91188i	0.212499	−	0.154390i
$643$	−3.73962	+	11.5094i	−0.147476	+	0.453886i	−0.997321	−	0.0731475i	$-0.976696\pi$
$643$	−3.73962	+	11.5094i	−0.147476	+	0.453886i	0.849845	+	0.527033i	$0.176696\pi$
$644$	−0.710276	+	2.18600i	−0.0279888	+	0.0861406i
$645$	4.50696	−	3.27450i	0.177461	−	0.128933i
$646$	−33.3128	−	24.2031i	−1.31067	−	0.952260i
$647$	−8.39964	−	25.8514i	−0.330224	−	1.01633i	−0.969027	−	0.246955i	$-0.920570\pi$
$647$	−8.39964	−	25.8514i	−0.330224	−	1.01633i	0.638803	−	0.769370i	$-0.279430\pi$
$648$	−1.00000			−0.0392837
$649$	1.13994	−	1.23910i	0.0447465	−	0.0486388i
$650$	−26.4892			−1.03899
$651$	1.10570	+	3.40299i	0.0433358	+	0.133374i
$652$	−0.381966	−	0.277515i	−0.0149589	−	0.0108683i
$653$	4.84934	−	3.52325i	0.189769	−	0.137876i	−0.488844	−	0.872371i	$-0.662581\pi$
$653$	4.84934	−	3.52325i	0.189769	−	0.137876i	0.678613	+	0.734496i	$0.262581\pi$
$654$	4.14856	−	12.7679i	0.162221	−	0.499266i
$655$	0.0936981	−	0.288373i	0.00366109	−	0.0112677i
$656$	3.92055	−	2.84845i	0.153072	−	0.111213i
$657$	10.4174	+	7.56869i	0.406422	+	0.295283i
$658$	−3.14163	−	9.66893i	−0.122473	−	0.376934i
$659$	−37.0565			−1.44352			−0.721758	−	0.692146i	$-0.756666\pi$
$659$	−37.0565			−1.44352			−0.721758	+	0.692146i	$0.756666\pi$
$660$	−0.408882	+	3.52671i	−0.0159157	+	0.137277i
$661$	−0.424601			−0.0165150			−0.00825752	−	0.999966i	$-0.502628\pi$
$661$	−0.424601			−0.0165150			−0.00825752	+	0.999966i	$0.502628\pi$
$662$	−2.95450	−	9.09303i	−0.114830	−	0.353411i
$663$	−39.3792	−	28.6107i	−1.52936	−	1.11115i
$664$	−1.44949	+	1.05312i	−0.0562512	+	0.0408689i
$665$	1.92329	−	5.91927i	0.0745819	−	0.229540i
$666$	−1.00762	+	3.10115i	−0.0390446	+	0.120167i
$667$	7.22361	−	5.24826i	0.279699	−	0.203213i
$668$	17.1705	+	12.4751i	0.664346	+	0.482676i
$669$	−2.60122	−	8.00574i	−0.100569	−	0.309520i
$670$	−4.05885			−0.156807
$671$	−3.05332	+	26.3357i	−0.117872	+	1.01668i
$672$	−1.00000			−0.0385758
$673$	0.423778	+	1.30426i	0.0163354	+	0.0502753i	0.958892	−	0.283771i	$-0.0915857\pi$
$673$	0.423778	+	1.30426i	0.0163354	+	0.0502753i	−0.942557	+	0.334047i	$0.891586\pi$
$674$	3.88867	+	2.82528i	0.149786	+	0.108826i
$675$	3.11803	−	2.26538i	0.120013	−	0.0871947i
$676$	10.5801	−	32.5622i	0.406927	−	1.25239i
$677$	−0.231575	+	0.712714i	−0.00890015	+	0.0273918i	−0.955408	−	0.295289i	$-0.904584\pi$
$677$	−0.231575	+	0.712714i	−0.00890015	+	0.0273918i	0.946508	+	0.322681i	$0.104584\pi$
$678$	−10.5186	+	7.64223i	−0.403965	+	0.293498i
$679$	13.5572	+	9.84989i	0.520278	+	0.378004i
$680$	2.34272	+	7.21014i	0.0898390	+	0.276496i
$681$	21.1305			0.809722
$682$	−8.03470	+	8.73361i	−0.307664	+	0.334427i
$683$	23.8913			0.914174			0.457087	−	0.889422i	$-0.348893\pi$
$683$	23.8913			0.914174			0.457087	+	0.889422i	$0.348893\pi$
$684$	1.79668	+	5.52962i	0.0686979	+	0.211430i
$685$	−4.61195	−	3.35077i	−0.176213	−	0.128027i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	−1.91899	+	5.90604i	−0.0732139	+	0.225329i
$688$	−1.60818	+	4.94948i	−0.0613114	+	0.188697i
$689$	−57.2804	+	41.6167i	−2.18221	+	1.58547i
$690$	−1.99056	−	1.44623i	−0.0757793	−	0.0550569i
$691$	−9.95200	−	30.6291i	−0.378592	−	1.16519i	−0.941023	−	0.338342i	$-0.890134\pi$
$691$	−9.95200	−	30.6291i	−0.378592	−	1.16519i	0.562431	−	0.826844i	$-0.309866\pi$
$692$	−17.8950			−0.680266
$693$	3.01528	+	1.38135i	0.114541	+	0.0524730i
$694$	−33.7594			−1.28149
$695$	5.94713	+	18.3034i	0.225588	+	0.694287i
$696$	3.14275	+	2.28334i	0.119126	+	0.0865498i
$697$	−27.7659	+	20.1731i	−1.05171	+	0.764110i
$698$	−9.95888	+	30.6503i	−0.376949	+	1.16013i
$699$	−6.05759	+	18.6434i	−0.229119	+	0.705157i
$700$	3.11803	−	2.26538i	0.117851	−	0.0856235i
$701$	−4.10892	−	2.98531i	−0.155192	−	0.112754i	0.507479	−	0.861664i	$-0.330577\pi$
$701$	−4.10892	−	2.98531i	−0.155192	−	0.112754i	−0.662671	+	0.748910i	$0.730577\pi$
$702$	2.12387	+	6.53660i	0.0801603	+	0.246708i
$703$	18.9585			0.715035
$704$	−1.62747	−	2.88987i	−0.0613378	−	0.108916i
$705$	10.8829			0.409874
$706$	2.58308	+	7.94991i	0.0972156	+	0.299199i
$707$	11.5742	+	8.40917i	0.435294	+	0.316259i
$708$	−0.410699	+	0.298390i	−0.0154350	+	0.0112142i
$709$	−3.78680	+	11.6546i	−0.142216	+	0.437697i	−0.996643	−	0.0818759i	$-0.973909\pi$
$709$	−3.78680	+	11.6546i	−0.142216	+	0.437697i	0.854426	+	0.519573i	$0.173909\pi$
$710$	4.70324	−	14.4751i	0.176509	−	0.543240i
$711$	7.26480	−	5.27819i	0.272451	−	0.197947i
$712$	5.04107	+	3.66255i	0.188922	+	0.137260i
$713$	−2.54145	−	7.82178i	−0.0951780	−	0.292928i
$714$	7.08214			0.265042
$715$	23.9211	−	4.81758i	0.894598	−	0.180167i
$716$	−12.7846			−0.477781
$717$	4.10166	+	12.6236i	0.153179	+	0.471438i
$718$	−10.2223	−	7.42696i	−0.381494	−	0.277172i
$719$	−17.1987	+	12.4956i	−0.641402	+	0.466006i	−0.860332	−	0.509735i	$-0.829744\pi$
$719$	−17.1987	+	12.4956i	−0.641402	+	0.466006i	0.218929	+	0.975741i	$0.429744\pi$
$720$	0.330792	−	1.01807i	0.0123279	−	0.0379414i
$721$	−1.99711	+	6.14646i	−0.0743761	+	0.228906i
$722$	11.9773	−	8.70202i	0.445749	−	0.323856i
$723$	19.2587	+	13.9923i	0.716239	+	0.520378i
$724$	0.785453	+	2.41738i	0.0291911	+	0.0898411i
$725$	−14.9718			−0.556040
$726$	0.915382	+	10.9618i	0.0339730	+	0.406832i
$727$	−27.9895			−1.03807			−0.519037	−	0.854752i	$-0.673709\pi$
$727$	−27.9895			−1.03807			−0.519037	+	0.854752i	$0.673709\pi$
$728$	2.12387	+	6.53660i	0.0787158	+	0.242262i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−11.1515	+	8.10202i	−0.412735	+	0.299869i
$731$	11.3894	−	35.0529i	0.421251	−	1.29648i
$732$	2.47019	−	7.60246i	0.0913009	−	0.280995i
$733$	−27.3088	+	19.8410i	−1.00867	+	0.732843i	−0.963930	−	0.266155i	$-0.914247\pi$
$733$	−27.3088	+	19.8410i	−1.00867	+	0.732843i	−0.0447419	+	0.998999i	$0.514247\pi$
$734$	−4.69728	−	3.41277i	−0.173380	−	0.125968i
$735$	0.330792	+	1.01807i	0.0122015	+	0.0375522i
$736$	2.29850			0.0847238
$737$	−12.3280	+	2.48280i	−0.454108	+	0.0914550i
$738$	4.84607			0.178386
$739$	5.83522	+	17.9590i	0.214652	+	0.660631i	0.999178	+	0.0405352i	$0.0129063\pi$
$739$	5.83522	+	17.9590i	0.214652	+	0.660631i	−0.784526	+	0.620096i	$0.787094\pi$
$740$	−2.82388	−	2.05167i	−0.103808	−	0.0754209i
$741$	32.3290	−	23.4884i	1.18763	−	0.862867i
$742$	3.18336	−	9.79737i	0.116865	−	0.359673i
$743$	15.2479	−	46.9281i	0.559390	−	1.72162i	−0.124669	−	0.992198i	$-0.539787\pi$
$743$	15.2479	−	46.9281i	0.559390	−	1.72162i	0.684059	−	0.729426i	$-0.260213\pi$
$744$	2.89476	−	2.10317i	0.106127	−	0.0771058i
$745$	9.06914	+	6.58911i	0.332267	+	0.241406i
$746$	−9.86950	−	30.3752i	−0.361348	−	1.11212i
$747$	−1.79167			−0.0655538
$748$	11.5260	+	20.4664i	0.421432	+	0.748327i
$749$	6.65529			0.243179
$750$	2.92887	+	9.01413i	0.106947	+	0.329150i
$751$	18.9891	+	13.7964i	0.692922	+	0.503437i	0.877619	−	0.479358i	$-0.159130\pi$
$751$	18.9891	+	13.7964i	0.692922	+	0.503437i	−0.184697	+	0.982795i	$0.559130\pi$
$752$	−8.22489	+	5.97573i	−0.299931	+	0.217912i
$753$	0.0931899	−	0.286809i	0.00339603	−	0.0104519i
$754$	8.25049	−	25.3924i	0.300465	−	0.924737i
$755$	−4.44013	+	3.22594i	−0.161593	+	0.117404i
$756$	−0.809017	−	0.587785i	−0.0294237	−	0.0213775i
$757$	11.4730	+	35.3101i	0.416992	+	1.28337i	0.910457	+	0.413603i	$0.135730\pi$
$757$	11.4730	+	35.3101i	0.416992	+	1.28337i	−0.493466	+	0.869765i	$0.664270\pi$
$758$	2.93476			0.106595
$759$	−6.93061	−	3.17502i	−0.251565	−	0.115246i
$760$	−6.22389			−0.225764
$761$	2.65437	+	8.16932i	0.0962209	+	0.296138i	0.987570	−	0.157180i	$-0.0502403\pi$
$761$	2.65437	+	8.16932i	0.0962209	+	0.296138i	−0.891349	+	0.453318i	$0.850240\pi$
$762$	10.2619	+	7.45568i	0.371748	+	0.270091i
$763$	10.8611	−	7.89102i	0.393197	−	0.285674i
$764$	2.35344	−	7.24313i	0.0851444	−	0.262047i
$765$	−2.34272	+	7.21014i	−0.0847011	+	0.260683i
$766$	−0.796636	+	0.578790i	−0.0287836	+	0.0209125i
$767$	2.82273	+	2.05083i	0.101923	+	0.0740513i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	−52.0121			−1.87561			−0.937803	−	0.347168i	$-0.887143\pi$
$769$	−52.0121			−1.87561			−0.937803	+	0.347168i	$0.887143\pi$
$770$	−2.40374	+	2.61283i	−0.0866248	+	0.0941600i
$771$	−12.9806			−0.467485
$772$	−4.15414	−	12.7851i	−0.149511	−	0.460146i
$773$	2.14672	+	1.55968i	0.0772122	+	0.0560979i	0.625722	−	0.780046i	$-0.284805\pi$
$773$	2.14672	+	1.55968i	0.0772122	+	0.0560979i	−0.548510	+	0.836144i	$0.684805\pi$
$774$	−4.21028	+	3.05894i	−0.151335	+	0.109951i
$775$	−4.26148	+	13.1155i	−0.153077	+	0.471122i
$776$	5.17839	−	15.9375i	0.185894	−	0.572121i
$777$	−2.63799	+	1.91661i	−0.0946374	+	0.0687581i
$778$	2.73533	+	1.98733i	0.0980662	+	0.0712493i
$779$	−8.70684	−	26.7969i	−0.311955	−	0.960099i
$780$	−7.35730			−0.263433
$781$	5.43083	−	46.8423i	0.194330	−	1.67615i
$782$	−16.2783			−0.582110
$783$	1.20042	+	3.69452i	0.0428996	+	0.132032i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	9.21140	−	6.69247i	0.328769	−	0.238865i
$786$	−0.0875302	+	0.269390i	−0.00312210	+	0.00960883i
$787$	10.3016	−	31.7049i	0.367211	−	1.13016i	−0.581375	−	0.813636i	$-0.697485\pi$
$787$	10.3016	−	31.7049i	0.367211	−	1.13016i	0.948585	−	0.316522i	$-0.102515\pi$
$788$	5.64201	−	4.09916i	0.200988	−	0.146027i
$789$	2.21094	+	1.60634i	0.0787116	+	0.0571873i
$790$	2.97044	+	9.14209i	0.105684	+	0.325261i
$791$	−13.0017			−0.462289
$792$	0.381966	−	3.29456i	0.0135726	−	0.117067i
$793$	−54.9406			−1.95100
$794$	4.52484	+	13.9260i	0.160581	+	0.494217i
$795$	8.92142	+	6.48179i	0.316410	+	0.229885i
$796$	−19.9497	+	14.4943i	−0.707098	+	0.513737i
$797$	8.76659	−	26.9808i	0.310529	−	0.955709i	−0.667028	−	0.745033i	$-0.732434\pi$
$797$	8.76659	−	26.9808i	0.310529	−	0.955709i	0.977556	−	0.210675i	$-0.0675663\pi$
$798$	−1.79668	+	5.52962i	−0.0636019	+	0.195746i
$799$	58.2498	−	42.3209i	2.06073	−	1.49721i
$800$	−3.11803	−	2.26538i	−0.110239	−	0.0800934i
$801$	1.92552	+	5.92613i	0.0680348	+	0.209390i
$802$	22.1984			0.783853
$803$	−28.9146	+	31.4297i	−1.02037	+	1.10913i
$804$	3.79167			0.133722
$805$	−0.760326	−	2.34004i	−0.0267980	−	0.0824757i
$806$	−19.8956	−	14.4550i	−0.700794	−	0.509156i
$807$	20.2168	−	14.6883i	0.711664	−	0.517054i
$808$	4.42096	−	13.6063i	0.155529	−	0.478669i
$809$	−9.33527	+	28.7310i	−0.328211	+	1.01013i	0.641760	+	0.766906i	$0.278205\pi$
$809$	−9.33527	+	28.7310i	−0.328211	+	1.01013i	−0.969971	+	0.243223i	$0.921795\pi$
$810$	0.866025	−	0.629204i	0.0304290	−	0.0221080i
$811$	31.4385	+	22.8414i	1.10396	+	0.802071i	0.981701	−	0.190428i	$-0.0609877\pi$
$811$	31.4385	+	22.8414i	1.10396	+	0.802071i	0.122254	+	0.992499i	$0.460988\pi$
$812$	1.20042	+	3.69452i	0.0421266	+	0.129652i
$813$	−11.7585			−0.412387
$814$	−9.83202	−	4.50420i	−0.344612	−	0.157872i
$815$	0.505406			0.0177036
$816$	−2.18850	−	6.73551i	−0.0766128	−	0.235790i
$817$	24.4793	+	17.7853i	0.856423	+	0.622228i
$818$	16.9559	−	12.3192i	0.592851	−	0.430731i
$819$	−2.12387	+	6.53660i	−0.0742140	+	0.228407i
$820$	−1.60304	+	4.93366i	−0.0559806	+	0.172291i
$821$	19.4618	−	14.1398i	0.679221	−	0.493483i	−0.193878	−	0.981026i	$-0.562107\pi$
$821$	19.4618	−	14.1398i	0.679221	−	0.493483i	0.873099	+	0.487543i	$0.162107\pi$
$822$	4.30835	+	3.13020i	0.150271	+	0.109178i
$823$	0.925820	+	2.84938i	0.0322720	+	0.0993231i	0.965895	−	0.258934i	$-0.0833712\pi$
$823$	0.925820	+	2.84938i	0.0322720	+	0.0993231i	−0.933623	+	0.358257i	$0.883371\pi$
$824$	6.46277			0.225141
$825$	6.27245	+	11.1378i	0.218379	+	0.387770i
$826$	−0.507652			−0.0176635
$827$	−0.0102920	−	0.0316754i	−0.000357886	−	0.00110146i	0.950877	−	0.309568i	$-0.100184\pi$
$827$	−0.0102920	−	0.0316754i	−0.000357886	−	0.00110146i	−0.951235	+	0.308466i	$0.900184\pi$
$828$	1.85953	+	1.35102i	0.0646230	+	0.0469513i
$829$	7.49283	−	5.44386i	0.260237	−	0.189073i	−0.450015	−	0.893021i	$-0.648581\pi$
$829$	7.49283	−	5.44386i	0.260237	−	0.189073i	0.710251	+	0.703948i	$0.248581\pi$
$830$	0.592671	−	1.82405i	0.0205719	−	0.0633138i
$831$	6.48406	−	19.9559i	0.224930	−	0.692262i
$832$	5.56036	−	4.03984i	0.192771	−	0.140056i
$833$	5.72957	+	4.16277i	0.198518	+	0.144232i
$834$	−5.55565	−	17.0985i	−0.192376	−	0.592074i
$835$	−22.7195			−0.786239
$836$	−18.9039	+	3.80714i	−0.653806	+	0.131673i
$837$	3.57812			0.123678
$838$	6.89381	+	21.2170i	0.238143	+	0.732928i
$839$	2.43698	+	1.77057i	0.0841338	+	0.0611268i	0.629057	−	0.777359i	$-0.283441\pi$
$839$	2.43698	+	1.77057i	0.0841338	+	0.0611268i	−0.544923	+	0.838486i	$0.683441\pi$
$840$	0.866025	−	0.629204i	0.0298807	−	0.0217096i
$841$	−4.29826	+	13.2287i	−0.148216	+	0.456162i
$842$	−4.58283	+	14.1045i	−0.157935	+	0.486073i
$843$	9.50563	−	6.90624i	0.327391	−	0.237864i
$844$	−17.6393	−	12.8157i	−0.607171	−	0.441136i
$845$	11.3256	+	34.8567i	0.389614	+	1.19911i
$846$	−10.1665			−0.349532
$847$	−5.70265	+	9.40637i	−0.195945	+	0.323207i
$848$	−10.3016			−0.353757
$849$	4.29709	+	13.2251i	0.147476	+	0.453884i
$850$	22.0823	+	16.0438i	0.757418	+	0.550296i
$851$	6.06342	−	4.40534i	0.207851	−	0.151013i
$852$	−4.39364	+	13.5222i	−0.150523	+	0.463264i
$853$	−12.0965	+	37.2293i	−0.414177	+	1.27471i	0.498808	+	0.866713i	$0.333771\pi$
$853$	−12.0965	+	37.2293i	−0.414177	+	1.27471i	−0.912985	+	0.407993i	$0.866229\pi$
$854$	6.46704	−	4.69858i	0.221298	−	0.160782i
$855$	−5.03523	−	3.65831i	−0.172201	−	0.125112i
$856$	−2.05660	−	6.32956i	−0.0702930	−	0.216340i
$857$	−5.97666			−0.204159			−0.102079	−	0.994776i	$-0.532550\pi$
$857$	−5.97666			−0.204159			−0.102079	+	0.994776i	$0.532550\pi$
$858$	−22.3464	+	4.50045i	−0.762894	+	0.153643i
$859$	−4.14359			−0.141378			−0.0706888	−	0.997498i	$-0.522520\pi$
$859$	−4.14359			−0.141378			−0.0706888	+	0.997498i	$0.522520\pi$
$860$	−1.72150	−	5.29825i	−0.0587028	−	0.180669i
$861$	3.92055	+	2.84845i	0.133612	+	0.0970748i
$862$	4.63484	−	3.36741i	0.157863	−	0.114694i
$863$	0.746156	−	2.29643i	0.0253994	−	0.0781715i	−0.937553	−	0.347842i	$-0.886915\pi$
$863$	0.746156	−	2.29643i	0.0253994	−	0.0781715i	0.962953	+	0.269670i	$0.0869147\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	15.4975	−	11.2596i	0.526931	−	0.382838i
$866$	−3.76588	−	2.73607i	−0.127970	−	0.0929755i
$867$	10.2460	+	31.5338i	0.347971	+	1.07095i
$868$	3.57812			0.121449
$869$	14.6144	+	25.9504i	0.495759	+	0.880307i
$870$	−4.15839			−0.140983
$871$	−8.05301	−	24.7846i	−0.272866	−	0.839795i
$872$	−10.8611	−	7.89102i	−0.367802	−	0.267224i
$873$	13.5572	−	9.84989i	0.458842	−	0.333368i
$874$	4.12967	−	12.7098i	0.139688	−	0.429916i
$875$	−2.92887	+	9.01413i	−0.0990138	+	0.304733i
$876$	10.4174	−	7.56869i	0.351971	−	0.255722i
$877$	16.4440	+	11.9473i	0.555274	+	0.403430i	0.829726	−	0.558171i	$-0.188497\pi$
$877$	16.4440	+	11.9473i	0.555274	+	0.403430i	−0.274452	+	0.961601i	$0.588497\pi$
$878$	0.929817	+	2.86168i	0.0313798	+	0.0965771i
$879$	1.37998			0.0465454
$880$	3.22775	+	1.47868i	0.108807	+	0.0498464i
$881$	33.4251			1.12612			0.563060	−	0.826416i	$-0.309624\pi$
$881$	33.4251			1.12612			0.563060	+	0.826416i	$0.309624\pi$
$882$	−0.309017	−	0.951057i	−0.0104051	−	0.0320237i
$883$	26.2444	+	19.0677i	0.883194	+	0.641678i	0.934094	−	0.357026i	$-0.116209\pi$
$883$	26.2444	+	19.0677i	0.883194	+	0.641678i	−0.0509007	+	0.998704i	$0.516209\pi$
$884$	−39.3792	+	28.6107i	−1.32447	+	0.962281i
$885$	0.167927	−	0.516827i	0.00564482	−	0.0173730i
$886$	−1.58528	+	4.87900i	−0.0532586	+	0.163913i
$887$	7.37964	−	5.36162i	0.247784	−	0.180026i	−0.456960	−	0.889487i	$-0.651062\pi$
$887$	7.37964	−	5.36162i	0.247784	−	0.180026i	0.704744	+	0.709462i	$0.251062\pi$
$888$	2.63799	+	1.91661i	0.0885252	+	0.0643173i
$889$	3.91968	+	12.0635i	0.131462	+	0.404598i
$890$	−6.67019			−0.223585
$891$	2.24551	−	2.44084i	0.0752274	−	0.0817712i
$892$	−8.41774			−0.281847
$893$	18.2660	+	56.2170i	0.611249	+	1.88123i
$894$	−8.47214	−	6.15537i	−0.283351	−	0.205866i
$895$	11.0717	−	8.04409i	0.370088	−	0.268884i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	4.88171	−	15.0244i	0.162996	−	0.501649i
$898$	3.03585	−	2.20568i	0.101308	−	0.0736043i
$899$	−11.2451	−	8.17007i	−0.375046	−	0.272487i
$900$	−1.19098	−	3.66547i	−0.0396994	−	0.122182i
$901$	72.9571			2.43055
$902$	−1.85103	+	15.9656i	−0.0616327	+	0.531598i
$903$	−5.20419			−0.173184
$904$	4.01776	+	12.3654i	0.133629	+	0.411267i
$905$	−2.20125	−	1.59930i	−0.0731719	−	0.0531625i
$906$	4.14784	−	3.01358i	0.137803	−	0.100120i
$907$	0.253053	−	0.778816i	0.00840248	−	0.0258602i	−0.946767	−	0.321919i	$-0.895672\pi$
$907$	0.253053	−	0.778816i	0.00840248	−	0.0258602i	0.955170	+	0.296058i	$0.0956723\pi$
$908$	6.52968	−	20.0963i	0.216695	−	0.666919i
$909$	11.5742	−	8.40917i	0.383893	−	0.278915i
$910$	−5.95218	−	4.32451i	−0.197313	−	0.143356i
$911$	−7.04494	−	21.6821i	−0.233409	−	0.718360i	−0.997328	−	0.0730479i	$-0.976727\pi$
$911$	−7.04494	−	21.6821i	−0.233409	−	0.718360i	0.763919	−	0.645312i	$-0.223273\pi$
$912$	5.81419			0.192527
$913$	0.684357	−	5.90276i	0.0226489	−	0.195353i
$914$	−21.6444			−0.715934
$915$	2.64426	+	8.13818i	0.0874164	+	0.269040i
$916$	5.02397	+	3.65013i	0.165997	+	0.120604i
$917$	−0.229157	+	0.166492i	−0.00756743	+	0.00549806i
$918$	2.18850	−	6.73551i	0.0722313	−	0.222305i
$919$	17.2494	−	53.0883i	0.569006	−	1.75122i	−0.0867314	−	0.996232i	$-0.527642\pi$
$919$	17.2494	−	53.0883i	0.569006	−	1.75122i	0.655738	−	0.754989i	$-0.272358\pi$
$920$	−1.99056	+	1.44623i	−0.0656268	+	0.0476807i
$921$	12.9610	+	9.41668i	0.427078	+	0.310290i
$922$	−1.53508	−	4.72448i	−0.0505550	−	0.155592i
$923$	97.7208			3.21652
$924$	2.24551	−	2.44084i	0.0738718	−	0.0802977i
$925$	−12.5672			−0.413207
$926$	4.42677	+	13.6242i	0.145473	+	0.447719i
$927$	5.22849	+	3.79872i	0.171726	+	0.124766i
$928$	3.14275	−	2.28334i	0.103166	−	0.0749544i
$929$	9.99045	−	30.7474i	0.327776	−	1.00879i	−0.642396	−	0.766373i	$-0.722059\pi$
$929$	9.99045	−	30.7474i	0.327776	−	1.00879i	0.970172	−	0.242418i	$-0.0779405\pi$
$930$	−1.18361	+	3.64279i	−0.0388122	+	0.119452i
$931$	−4.70378	+	3.41749i	−0.154160	+	0.112004i
$932$	15.8590	+	11.5222i	0.519478	+	0.377423i
$933$	−0.460732	−	1.41799i	−0.0150837	−	0.0464228i
$934$	−6.04754			−0.197881
$935$	−22.8594	−	10.4722i	−0.747581	−	0.342479i
$936$	6.87298			0.224650
$937$	3.69697	+	11.3781i	0.120775	+	0.371707i	0.993108	−	0.117206i	$-0.0373937\pi$
$937$	3.69697	+	11.3781i	0.120775	+	0.371707i	−0.872333	+	0.488913i	$0.837394\pi$
$938$	3.06753	+	2.22869i	0.100158	+	0.0727692i
$939$	−5.16345	+	3.75147i	−0.168503	+	0.122424i
$940$	3.36301	−	10.3503i	0.109689	−	0.337588i
$941$	−3.75840	+	11.5672i	−0.122520	+	0.377079i	−0.993441	−	0.114345i	$-0.963523\pi$
$941$	−3.75840	+	11.5672i	−0.122520	+	0.377079i	0.870921	+	0.491423i	$0.163523\pi$
$942$	−8.60503	+	6.25192i	−0.280367	+	0.203699i
$943$	−9.01139	−	6.54716i	−0.293451	−	0.213205i
$944$	0.156873	+	0.482806i	0.00510579	+	0.0157140i
$945$	1.07047			0.0348223
$946$	−8.46968	−	15.0394i	−0.275373	−	0.488973i
$947$	0.662536			0.0215295			0.0107648	−	0.999942i	$-0.496573\pi$
$947$	0.662536			0.0215295			0.0107648	+	0.999942i	$0.496573\pi$
$948$	−2.77491	−	8.54029i	−0.0901248	−	0.277376i
$949$	−71.5986	−	52.0195i	−2.32419	−	1.68862i
$950$	−18.1288	+	13.1714i	−0.588177	+	0.427336i
$951$	1.40776	−	4.33264i	0.0456497	−	0.140495i
$952$	2.18850	−	6.73551i	0.0709297	−	0.218299i
$953$	−43.6292	+	31.6985i	−1.41329	+	1.02681i	−0.420455	+	0.907314i	$0.638129\pi$
$953$	−43.6292	+	31.6985i	−1.41329	+	1.02681i	−0.992834	+	0.119501i	$0.961871\pi$
$954$	−8.33414	−	6.05511i	−0.269828	−	0.196041i
$955$	2.51927	+	7.75353i	0.0815218	+	0.250898i
$956$	13.2733			0.429288
$957$	−12.6303	+	2.54368i	−0.408281	+	0.0822255i
$958$	−4.51256			−0.145794
$959$	1.64564	+	5.06477i	0.0531406	+	0.163550i
$960$	−0.866025	−	0.629204i	−0.0279508	−	0.0203075i
$961$	14.7217	−	10.6960i	0.474895	−	0.345031i
$962$	6.92538	−	21.3141i	0.223283	−	0.687195i
$963$	2.05660	−	6.32956i	0.0662729	−	0.203967i
$964$	19.2587	−	13.9923i	0.620281	−	0.450661i
$965$	11.6420	+	8.45844i	0.374770	+	0.272287i
$966$	0.710276	+	2.18600i	0.0228527	+	0.0703335i
$967$	55.7169			1.79173			0.895867	−	0.444322i	$-0.146555\pi$
$967$	55.7169			1.79173			0.895867	+	0.444322i	$0.146555\pi$
$968$	10.7082	+	2.51682i	0.344175	+	0.0808936i
$969$	−41.1769			−1.32279
$970$	5.54330	+	17.0605i	0.177985	+	0.547780i
$971$	−22.1000	−	16.0566i	−0.709223	−	0.515281i	0.173700	−	0.984799i	$-0.444428\pi$
$971$	−22.1000	−	16.0566i	−0.709223	−	0.515281i	−0.882923	+	0.469518i	$0.844428\pi$
$972$	−0.809017	+	0.587785i	−0.0259492	+	0.0188532i
$973$	5.55565	−	17.0985i	0.178106	−	0.548154i
$974$	0.218876	−	0.673631i	0.00701324	−	0.0215845i
$975$	−21.4302	+	15.5699i	−0.686316	+	0.498637i
$976$	−6.46704	−	4.69858i	−0.207005	−	0.150398i
$977$	−4.78177	−	14.7168i	−0.152982	−	0.470831i	0.844969	−	0.534816i	$-0.179619\pi$
$977$	−4.78177	−	14.7168i	−0.152982	−	0.470831i	−0.997951	+	0.0639848i	$0.979619\pi$
$978$	−0.472136			−0.0150972
$979$	−20.2595	+	4.08014i	−0.647495	+	0.130402i
$980$	1.07047			0.0341948
$981$	−4.14856	−	12.7679i	−0.132453	−	0.407649i
$982$	−32.8358	−	23.8566i	−1.04783	−	0.761294i
$983$	19.7819	−	14.3724i	0.630944	−	0.458408i	−0.225783	−	0.974178i	$-0.572494\pi$
$983$	19.7819	−	14.3724i	0.630944	−	0.458408i	0.856727	+	0.515770i	$0.172494\pi$
$984$	1.49752	−	4.60888i	0.0477391	−	0.146926i
$985$	−2.30691	+	7.09995i	−0.0735044	+	0.226223i
$986$	−22.2574	+	16.1709i	−0.708819	+	0.514987i
$987$	−8.22489	−	5.97573i	−0.261801	−	0.190210i
$988$	−12.3486	−	38.0050i	−0.392860	−	1.20910i
$989$	11.9618			0.380364
$990$	1.74216	+	3.09350i	0.0553694	+	0.0983180i
$991$	59.1364			1.87853			0.939264	−	0.343194i	$-0.111509\pi$
$991$	59.1364			1.87853			0.939264	+	0.343194i	$0.111509\pi$
$992$	−1.10570	−	3.40299i	−0.0351060	−	0.108045i
$993$	−7.73499	−	5.61980i	−0.245463	−	0.178339i
$994$	−11.5027	+	8.35719i	−0.364843	+	0.265074i
$995$	8.15707	−	25.1049i	0.258596	−	0.795878i
$996$	−0.553656	+	1.70398i	−0.0175433	+	0.0539927i
$997$	13.5068	−	9.81323i	0.427763	−	0.310788i	−0.352991	−	0.935627i	$-0.614835\pi$
$997$	13.5068	−	9.81323i	0.427763	−	0.310788i	0.780754	+	0.624839i	$0.214835\pi$
$998$	4.72017	+	3.42941i	0.149415	+	0.108556i
$999$	1.00762	+	3.10115i	0.0318798	+	0.0981159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.g.379.2	yes	8
11.3	even	5		5082.2.a.bz.1.3		4
11.8	odd	10		5082.2.a.ce.1.3		4
11.9	even	5	inner	462.2.j.g.295.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.g.295.2	✓	8	11.9	even	5	inner
462.2.j.g.379.2	yes	8	1.1	even	1	trivial
5082.2.a.bz.1.3		4	11.3	even	5
5082.2.a.ce.1.3		4	11.8	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.330792 - 1.01807i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.330792 - 1.01807i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.07047 q^{10} +(-3.25134 + 0.654803i) q^{11} +1.00000 q^{12} +(-2.12387 - 6.53660i) q^{13} +(0.809017 + 0.587785i) q^{14} +(-0.866025 + 0.629204i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.18850 + 6.73551i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-4.70378 - 3.41749i) q^{19} +(0.330792 + 1.01807i) q^{20} +1.00000 q^{21} +(1.62747 + 2.88987i) q^{22} -2.29850 q^{23} +(-0.309017 - 0.951057i) q^{24} +(3.11803 + 2.26538i) q^{25} +(-5.56036 + 4.03984i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-3.14275 + 2.28334i) q^{29} +(0.866025 + 0.629204i) q^{30} +(1.10570 + 3.40299i) q^{31} -1.00000 q^{32} +(3.01528 + 1.38135i) q^{33} +7.08214 q^{34} +(0.330792 + 1.01807i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-2.63799 + 1.91661i) q^{37} +(-1.79668 + 5.52962i) q^{38} +(-2.12387 + 6.53660i) q^{39} +(0.866025 - 0.629204i) q^{40} +(3.92055 + 2.84845i) q^{41} +(-0.309017 - 0.951057i) q^{42} -5.20419 q^{43} +(2.24551 - 2.44084i) q^{44} +1.07047 q^{45} +(0.710276 + 2.18600i) q^{46} +(-8.22489 - 5.97573i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(1.19098 - 3.66547i) q^{50} +(5.72957 - 4.16277i) q^{51} +(5.56036 + 4.03984i) q^{52} +(-3.18336 - 9.79737i) q^{53} -1.00000 q^{54} +(-0.408882 + 3.52671i) q^{55} -1.00000 q^{56} +(1.79668 + 5.52962i) q^{57} +(3.14275 + 2.28334i) q^{58} +(-0.410699 + 0.298390i) q^{59} +(0.330792 - 1.01807i) q^{60} +(2.47019 - 7.60246i) q^{61} +(2.89476 - 2.10317i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(0.309017 + 0.951057i) q^{64} -7.35730 q^{65} +(0.381966 - 3.29456i) q^{66} +3.79167 q^{67} +(-2.18850 - 6.73551i) q^{68} +(1.85953 + 1.35102i) q^{69} +(0.866025 - 0.629204i) q^{70} +(-4.39364 + 13.5222i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(10.4174 - 7.56869i) q^{73} +(2.63799 + 1.91661i) q^{74} +(-1.19098 - 3.66547i) q^{75} +5.81419 q^{76} +(2.24551 - 2.44084i) q^{77} +6.87298 q^{78} +(-2.77491 - 8.54029i) q^{79} +(-0.866025 - 0.629204i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.49752 - 4.60888i) q^{82} +(-0.553656 + 1.70398i) q^{83} +(-0.809017 + 0.587785i) q^{84} +(6.13331 + 4.45611i) q^{85} +(1.60818 + 4.94948i) q^{86} +3.88465 q^{87} +(-3.01528 - 1.38135i) q^{88} +6.23110 q^{89} +(-0.330792 - 1.01807i) q^{90} +(5.56036 + 4.03984i) q^{91} +(1.85953 - 1.35102i) q^{92} +(1.10570 - 3.40299i) q^{93} +(-3.14163 + 9.66893i) q^{94} +(-5.03523 + 3.65831i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-5.17839 - 15.9375i) q^{97} -1.00000 q^{98} +(-1.62747 - 2.88987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{11} + 8 q^{12} + 6 q^{13} + 2 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} + 8 q^{21} + 2 q^{22} + 2 q^{24} + 16 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} + 2 q^{29} - 4 q^{31} - 8 q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{36} - 24 q^{37} - 6 q^{38} + 6 q^{39} + 2 q^{42} + 8 q^{43} - 2 q^{44} - 10 q^{46} - 2 q^{47} - 2 q^{48} - 2 q^{49} + 14 q^{50} + 10 q^{51} + 6 q^{52} - 22 q^{53} - 8 q^{54} - 8 q^{56} + 6 q^{57} - 2 q^{58} + 10 q^{59} + 26 q^{61} - 6 q^{62} - 2 q^{63} - 2 q^{64} - 60 q^{65} + 12 q^{66} + 4 q^{67} - 10 q^{69} - 16 q^{71} + 2 q^{72} - 2 q^{73} + 24 q^{74} - 14 q^{75} - 4 q^{76} - 2 q^{77} + 24 q^{78} - 12 q^{79} - 2 q^{81} - 10 q^{82} - 38 q^{83} - 2 q^{84} + 24 q^{85} + 22 q^{86} - 28 q^{87} - 8 q^{88} - 12 q^{89} + 6 q^{91} - 10 q^{92} - 4 q^{93} - 8 q^{94} - 36 q^{95} + 2 q^{96} + 6 q^{97} - 8 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^11 + 8 * q^12 + 6 * q^13 + 2 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 + 8 * q^21 + 2 * q^22 + 2 * q^24 + 16 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 + 2 * q^29 - 4 * q^31 - 8 * q^32 + 8 * q^33 + 20 * q^34 - 2 * q^36 - 24 * q^37 - 6 * q^38 + 6 * q^39 + 2 * q^42 + 8 * q^43 - 2 * q^44 - 10 * q^46 - 2 * q^47 - 2 * q^48 - 2 * q^49 + 14 * q^50 + 10 * q^51 + 6 * q^52 - 22 * q^53 - 8 * q^54 - 8 * q^56 + 6 * q^57 - 2 * q^58 + 10 * q^59 + 26 * q^61 - 6 * q^62 - 2 * q^63 - 2 * q^64 - 60 * q^65 + 12 * q^66 + 4 * q^67 - 10 * q^69 - 16 * q^71 + 2 * q^72 - 2 * q^73 + 24 * q^74 - 14 * q^75 - 4 * q^76 - 2 * q^77 + 24 * q^78 - 12 * q^79 - 2 * q^81 - 10 * q^82 - 38 * q^83 - 2 * q^84 + 24 * q^85 + 22 * q^86 - 28 * q^87 - 8 * q^88 - 12 * q^89 + 6 * q^91 - 10 * q^92 - 4 * q^93 - 8 * q^94 - 36 * q^95 + 2 * q^96 + 6 * q^97 - 8 * q^98 - 2 * q^99

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