LMFDB - Embedded newform 418.2.f.g.229.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 7 x^{14} - 13 x^{13} + 51 x^{12} - 74 x^{11} + 332 x^{10} - 614 x^{9} + 1832 x^{8} + \cdots + 16 $ x^16 - x^15 + 7x^14 - 13x^13 + 51x^12 - 74x^11 + 332x^10 - 614x^9 + 1832x^8 - 2960x^7 + 5348x^6 - 6872x^5 + 8232x^4 - 6344x^3 + 3984x^2 - 400x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			229.3
Root			$0.956027 - 0.694595i$ of defining polynomial
Character	$\chi$	$=$	418.229
Dual form			418.2.f.g.115.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.956027 - 0.694595i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.0364140 - 0.112071i) q^{5} +(0.365170 + 1.12388i) q^{6} +(1.41067 + 1.02491i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.495524 + 1.52507i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.956027 - 0.694595i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.0364140 - 0.112071i) q^{5} +(0.365170 + 1.12388i) q^{6} +(1.41067 + 1.02491i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.495524 + 1.52507i) q^{9} +0.117838 q^{10} +(3.18641 - 0.920226i) q^{11} -1.18171 q^{12} +(0.656165 - 2.01947i) q^{13} +(-1.41067 + 1.02491i) q^{14} +(-0.112657 - 0.0818499i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.672362 + 2.06932i) q^{17} +(-1.29730 - 0.942543i) q^{18} +(-0.809017 + 0.587785i) q^{19} +(-0.0364140 + 0.112071i) q^{20} +2.06054 q^{21} +(-0.109466 + 3.31482i) q^{22} +6.90496 q^{23} +(0.365170 - 1.12388i) q^{24} +(4.03385 - 2.93076i) q^{25} +(1.71786 + 1.24810i) q^{26} +(1.68108 + 5.17383i) q^{27} +(-0.538830 - 1.65835i) q^{28} +(-2.35143 - 1.70841i) q^{29} +(0.112657 - 0.0818499i) q^{30} +(-0.633297 + 1.94909i) q^{31} -1.00000 q^{32} +(2.40711 - 3.09302i) q^{33} -2.17581 q^{34} +(0.0634948 - 0.195417i) q^{35} +(1.29730 - 0.942543i) q^{36} +(1.65368 + 1.20147i) q^{37} +(-0.309017 - 0.951057i) q^{38} +(-0.775400 - 2.38644i) q^{39} +(-0.0953332 - 0.0692636i) q^{40} +(-0.497734 + 0.361625i) q^{41} +(-0.636743 + 1.95969i) q^{42} -10.0414 q^{43} +(-3.11875 - 1.12844i) q^{44} +0.188960 q^{45} +(-2.13375 + 6.56701i) q^{46} +(4.93079 - 3.58243i) q^{47} +(0.956027 + 0.694595i) q^{48} +(-1.22357 - 3.76575i) q^{49} +(1.54079 + 4.74208i) q^{50} +(2.08013 + 1.51131i) q^{51} +(-1.71786 + 1.24810i) q^{52} +(-2.83556 + 8.72697i) q^{53} -5.44008 q^{54} +(-0.219161 - 0.323594i) q^{55} +1.74369 q^{56} +(-0.365170 + 1.12388i) q^{57} +(2.35143 - 1.70841i) q^{58} +(-4.54252 - 3.30034i) q^{59} +(0.0430310 + 0.132436i) q^{60} +(1.61691 + 4.97634i) q^{61} +(-1.65799 - 1.20460i) q^{62} +(-2.26209 + 1.64350i) q^{63} +(0.309017 - 0.951057i) q^{64} -0.250217 q^{65} +(2.19780 + 3.24509i) q^{66} -13.9348 q^{67} +(0.672362 - 2.06932i) q^{68} +(6.60133 - 4.79615i) q^{69} +(0.166231 + 0.120774i) q^{70} +(-2.83485 - 8.72478i) q^{71} +(0.495524 + 1.52507i) q^{72} +(-10.8850 - 7.90844i) q^{73} +(-1.65368 + 1.20147i) q^{74} +(1.82078 - 5.60378i) q^{75} +1.00000 q^{76} +(5.43813 + 1.96766i) q^{77} +2.50925 q^{78} +(-1.69197 + 5.20734i) q^{79} +(0.0953332 - 0.0692636i) q^{80} +(1.30897 + 0.951023i) q^{81} +(-0.190117 - 0.585121i) q^{82} +(2.92563 + 9.00415i) q^{83} +(-1.66701 - 1.21116i) q^{84} +(0.207427 - 0.150705i) q^{85} +(3.10295 - 9.54991i) q^{86} -3.43468 q^{87} +(2.03696 - 2.61740i) q^{88} +4.79411 q^{89} +(-0.0583917 + 0.179711i) q^{90} +(2.99542 - 2.17630i) q^{91} +(-5.58623 - 4.05863i) q^{92} +(0.748377 + 2.30327i) q^{93} +(1.88339 + 5.79649i) q^{94} +(0.0953332 + 0.0692636i) q^{95} +(-0.956027 + 0.694595i) q^{96} +(3.45324 - 10.6280i) q^{97} +3.95955 q^{98} +(-0.175535 + 5.31548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 - 10 * q^15 - 4 * q^16 + 6 * q^17 + q^18 - 4 * q^19 + q^20 + 14 * q^21 - 9 * q^22 - 26 * q^23 - q^24 + 33 * q^25 - 3 * q^26 + 13 * q^27 - 2 * q^28 + 10 * q^30 + 11 * q^31 - 16 * q^32 - 31 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 4 * q^38 + 12 * q^39 - q^40 - 7 * q^41 + 6 * q^42 + 66 * q^43 - 11 * q^44 - 42 * q^45 - 24 * q^46 + 47 * q^47 + q^48 + 24 * q^49 + 37 * q^50 - 41 * q^51 + 3 * q^52 + 15 * q^53 - 8 * q^54 - 9 * q^55 - 28 * q^56 + q^57 - 18 * q^59 + 5 * q^60 - 43 * q^61 + 9 * q^62 - 37 * q^63 - 4 * q^64 + 52 * q^65 - 39 * q^66 - 50 * q^67 + 6 * q^68 + 81 * q^69 - 11 * q^70 - 5 * q^71 + q^72 - 13 * q^73 + 39 * q^75 + 16 * q^76 - 10 * q^77 - 22 * q^78 + 5 * q^79 + q^80 + 2 * q^82 + 7 * q^83 - q^84 - 29 * q^85 + 29 * q^86 + 4 * q^87 - 4 * q^88 - 28 * q^89 - 18 * q^90 - 11 * q^92 - 5 * q^93 + 28 * q^94 + q^95 - q^96 - 11 * q^97 - 24 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	0.956027	−	0.694595i	0.551963	−	0.401024i	−0.276546	−	0.961001i	$-0.589190\pi$
$3$	0.956027	−	0.694595i	0.551963	−	0.401024i	0.828509	+	0.559976i	$0.189190\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.0364140	−	0.112071i	−0.0162849	−	0.0501196i	0.942584	−	0.333970i	$-0.108388\pi$
$5$	−0.0364140	−	0.112071i	−0.0162849	−	0.0501196i	−0.958869	+	0.283850i	$0.908388\pi$
$6$	0.365170	+	1.12388i	0.149080	+	0.458821i
$7$	1.41067	+	1.02491i	0.533185	+	0.387381i	0.821548	−	0.570140i	$-0.193111\pi$
$7$	1.41067	+	1.02491i	0.533185	+	0.387381i	−0.288363	+	0.957521i	$0.593111\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.495524	+	1.52507i	−0.165175	+	0.508356i
$10$	0.117838			0.0372638
$11$	3.18641	−	0.920226i	0.960738	−	0.277459i
$11$	3.18641	−	0.920226i	0.960738	−	0.277459i
$12$	−1.18171			−0.341132
$13$	0.656165	−	2.01947i	0.181987	−	0.560100i	−0.817896	−	0.575366i	$-0.804860\pi$
$13$	0.656165	−	2.01947i	0.181987	−	0.560100i	0.999883	+	0.0152662i	$0.00485958\pi$
$14$	−1.41067	+	1.02491i	−0.377018	+	0.273920i
$15$	−0.112657	−	0.0818499i	−0.0290878	−	0.0211335i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.672362	+	2.06932i	0.163072	+	0.501883i	0.998889	−	0.0471244i	$-0.0150057\pi$
$17$	0.672362	+	2.06932i	0.163072	+	0.501883i	−0.835817	+	0.549008i	$0.815006\pi$
$18$	−1.29730	−	0.942543i	−0.305776	−	0.222160i
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i
$20$	−0.0364140	+	0.112071i	−0.00814243	+	0.0250598i
$21$	2.06054			0.449647
$22$	−0.109466	+	3.31482i	−0.0233383	+	0.706722i
$23$	6.90496			1.43978			0.719892	−	0.694086i	$-0.244191\pi$
$23$	6.90496			1.43978			0.719892	+	0.694086i	$0.244191\pi$
$24$	0.365170	−	1.12388i	0.0745400	−	0.229411i
$25$	4.03385	−	2.93076i	0.806770	−	0.586153i
$26$	1.71786	+	1.24810i	0.336901	+	0.244773i
$27$	1.68108	+	5.17383i	0.323524	+	0.995703i
$28$	−0.538830	−	1.65835i	−0.101829	−	0.313398i
$29$	−2.35143	−	1.70841i	−0.436649	−	0.317244i	0.347653	−	0.937623i	$-0.386979\pi$
$29$	−2.35143	−	1.70841i	−0.436649	−	0.317244i	−0.784302	+	0.620379i	$0.786979\pi$
$30$	0.112657	−	0.0818499i	0.0205682	−	0.0149437i
$31$	−0.633297	+	1.94909i	−0.113744	+	0.350067i	−0.991683	−	0.128705i	$-0.958918\pi$
$31$	−0.633297	+	1.94909i	−0.113744	+	0.350067i	0.877939	+	0.478772i	$0.158918\pi$
$32$	−1.00000			−0.176777
$33$	2.40711	−	3.09302i	0.419024	−	0.538426i
$34$	−2.17581			−0.373148
$35$	0.0634948	−	0.195417i	0.0107326	−	0.0330315i
$36$	1.29730	−	0.942543i	0.216217	−	0.157091i
$37$	1.65368	+	1.20147i	0.271864	+	0.197521i	0.715361	−	0.698755i	$-0.246262\pi$
$37$	1.65368	+	1.20147i	0.271864	+	0.197521i	−0.443497	+	0.896276i	$0.646262\pi$
$38$	−0.309017	−	0.951057i	−0.0501292	−	0.154282i
$39$	−0.775400	−	2.38644i	−0.124163	−	0.382136i
$40$	−0.0953332	−	0.0692636i	−0.0150735	−	0.0109515i
$41$	−0.497734	+	0.361625i	−0.0777330	+	0.0564763i	−0.625973	−	0.779845i	$-0.715298\pi$
$41$	−0.497734	+	0.361625i	−0.0777330	+	0.0564763i	0.548240	+	0.836321i	$0.315298\pi$
$42$	−0.636743	+	1.95969i	−0.0982516	+	0.302387i
$43$	−10.0414			−1.53129			−0.765647	−	0.643261i	$-0.777581\pi$
$43$	−10.0414			−1.53129			−0.765647	+	0.643261i	$0.777581\pi$
$44$	−3.11875	−	1.12844i	−0.470170	−	0.170119i
$45$	0.188960			0.0281684
$46$	−2.13375	+	6.56701i	−0.314604	+	0.968253i
$47$	4.93079	−	3.58243i	0.719229	−	0.522551i	−0.166909	−	0.985972i	$-0.553379\pi$
$47$	4.93079	−	3.58243i	0.719229	−	0.522551i	0.886138	+	0.463422i	$0.153379\pi$
$48$	0.956027	+	0.694595i	0.137991	+	0.100256i
$49$	−1.22357	−	3.76575i	−0.174795	−	0.537965i
$50$	1.54079	+	4.74208i	0.217901	+	0.670631i
$51$	2.08013	+	1.51131i	0.291277	+	0.211625i
$52$	−1.71786	+	1.24810i	−0.238225	+	0.173080i
$53$	−2.83556	+	8.72697i	−0.389495	+	1.19874i	0.543672	+	0.839298i	$0.317034\pi$
$53$	−2.83556	+	8.72697i	−0.389495	+	1.19874i	−0.933167	+	0.359444i	$0.882966\pi$
$54$	−5.44008			−0.740302
$55$	−0.219161	−	0.323594i	−0.0295516	−	0.0436334i
$56$	1.74369			0.233010
$57$	−0.365170	+	1.12388i	−0.0483679	+	0.148861i
$58$	2.35143	−	1.70841i	0.308757	−	0.224325i
$59$	−4.54252	−	3.30034i	−0.591386	−	0.429667i	0.251425	−	0.967877i	$-0.419101\pi$
$59$	−4.54252	−	3.30034i	−0.591386	−	0.429667i	−0.842811	+	0.538210i	$0.819101\pi$
$60$	0.0430310	+	0.132436i	0.00555528	+	0.0170974i
$61$	1.61691	+	4.97634i	0.207024	+	0.637154i	0.999624	+	0.0274127i	$0.00872683\pi$
$61$	1.61691	+	4.97634i	0.207024	+	0.637154i	−0.792600	+	0.609742i	$0.791273\pi$
$62$	−1.65799	−	1.20460i	−0.210565	−	0.152985i
$63$	−2.26209	+	1.64350i	−0.284996	+	0.207062i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−0.250217			−0.0310356
$66$	2.19780	+	3.24509i	0.270531	+	0.399443i
$67$	−13.9348			−1.70241			−0.851205	−	0.524833i	$-0.824128\pi$
$67$	−13.9348			−1.70241			−0.851205	+	0.524833i	$0.824128\pi$
$68$	0.672362	−	2.06932i	0.0815359	−	0.250942i
$69$	6.60133	−	4.79615i	0.794707	−	0.577388i
$70$	0.166231	+	0.120774i	0.0198685	+	0.0144353i
$71$	−2.83485	−	8.72478i	−0.336435	−	1.03544i	−0.966011	−	0.258501i	$-0.916771\pi$
$71$	−2.83485	−	8.72478i	−0.336435	−	1.03544i	0.629576	−	0.776939i	$-0.283229\pi$
$72$	0.495524	+	1.52507i	0.0583981	+	0.179731i
$73$	−10.8850	−	7.90844i	−1.27400	−	0.925613i	−0.274643	−	0.961546i	$-0.588560\pi$
$73$	−10.8850	−	7.90844i	−1.27400	−	0.925613i	−0.999354	+	0.0359327i	$0.988560\pi$
$74$	−1.65368	+	1.20147i	−0.192237	+	0.139668i
$75$	1.82078	−	5.60378i	0.210245	−	0.647069i
$76$	1.00000			0.114708
$77$	5.43813	+	1.96766i	0.619733	+	0.224235i
$78$	2.50925			0.284116
$79$	−1.69197	+	5.20734i	−0.190361	+	0.585871i	−0.999999	−	0.00105787i	$-0.999663\pi$
$79$	−1.69197	+	5.20734i	−0.190361	+	0.585871i	0.809638	+	0.586929i	$0.199663\pi$
$80$	0.0953332	−	0.0692636i	0.0106586	−	0.00774391i
$81$	1.30897	+	0.951023i	0.145441	+	0.105669i
$82$	−0.190117	−	0.585121i	−0.0209950	−	0.0646158i
$83$	2.92563	+	9.00415i	0.321129	+	0.988334i	0.973158	+	0.230140i	$0.0739183\pi$
$83$	2.92563	+	9.00415i	0.321129	+	0.988334i	−0.652028	+	0.758195i	$0.726082\pi$
$84$	−1.66701	−	1.21116i	−0.181886	−	0.132148i
$85$	0.207427	−	0.150705i	0.0224986	−	0.0163462i
$86$	3.10295	−	9.54991i	0.334600	−	1.02979i
$87$	−3.43468			−0.368236
$88$	2.03696	−	2.61740i	0.217141	−	0.279016i
$89$	4.79411			0.508174			0.254087	−	0.967181i	$-0.418225\pi$
$89$	4.79411			0.508174			0.254087	+	0.967181i	$0.418225\pi$
$90$	−0.0583917	+	0.179711i	−0.00615503	+	0.0189432i
$91$	2.99542	−	2.17630i	0.314005	−	0.228138i
$92$	−5.58623	−	4.05863i	−0.582405	−	0.423142i
$93$	0.748377	+	2.30327i	0.0776030	+	0.238838i
$94$	1.88339	+	5.79649i	0.194257	+	0.597862i
$95$	0.0953332	+	0.0692636i	0.00978098	+	0.00710630i
$96$	−0.956027	+	0.694595i	−0.0975741	+	0.0708918i
$97$	3.45324	−	10.6280i	0.350623	−	1.07911i	−0.607881	−	0.794028i	$-0.707980\pi$
$97$	3.45324	−	10.6280i	0.350623	−	1.07911i	0.958504	−	0.285079i	$-0.0920197\pi$
$98$	3.95955			0.399975
$99$	−0.175535	+	5.31548i	−0.0176419	+	0.534225i
$100$	−4.98611			−0.498611
$101$	1.04855	−	3.22711i	0.104335	−	0.321109i	−0.885239	−	0.465136i	$-0.846005\pi$
$101$	1.04855	−	3.22711i	0.104335	−	0.321109i	0.989574	+	0.144027i	$0.0460053\pi$
$102$	−2.08013	+	1.51131i	−0.205964	+	0.149642i
$103$	−14.3204	−	10.4044i	−1.41103	−	1.02517i	−0.993171	−	0.116664i	$-0.962780\pi$
$103$	−14.3204	−	10.4044i	−1.41103	−	1.02517i	−0.417861	−	0.908511i	$-0.637220\pi$
$104$	−0.656165	−	2.01947i	−0.0643423	−	0.198025i
$105$	−0.0750327	−	0.230927i	−0.00732244	−	0.0225362i
$106$	−7.42361	−	5.39356i	−0.721044	−	0.523869i
$107$	0.418265	−	0.303887i	0.0404352	−	0.0293779i	−0.567384	−	0.823453i	$-0.692045\pi$
$107$	0.418265	−	0.303887i	0.0404352	−	0.0293779i	0.607819	+	0.794075i	$0.292045\pi$
$108$	1.68108	−	5.17383i	0.161762	−	0.497852i
$109$	−7.94333			−0.760833			−0.380417	−	0.924815i	$-0.624219\pi$
$109$	−7.94333			−0.760833			−0.380417	+	0.924815i	$0.624219\pi$
$110$	0.375481	−	0.108438i	0.0358007	−	0.0103392i
$111$	2.41550			0.229270
$112$	−0.538830	+	1.65835i	−0.0509146	+	0.156699i
$113$	13.0739	−	9.49874i	1.22989	−	0.893566i	0.233007	−	0.972475i	$-0.425144\pi$
$113$	13.0739	−	9.49874i	1.22989	−	0.893566i	0.996882	+	0.0789087i	$0.0251436\pi$
$114$	−0.956027	−	0.694595i	−0.0895402	−	0.0650547i
$115$	−0.251438	−	0.773845i	−0.0234467	−	0.0721614i
$116$	0.898165	+	2.76427i	0.0833925	+	0.256656i
$117$	2.75468	+	2.00139i	0.254670	+	0.185029i
$118$	4.54252	−	3.30034i	0.418173	−	0.303821i
$119$	−1.17239	+	3.60825i	−0.107473	+	0.330768i
$120$	−0.139251			−0.0127118
$121$	9.30637	−	5.86443i	0.846033	−	0.533130i
$122$	−5.23243			−0.473722
$123$	−0.224665	+	0.691446i	−0.0202573	+	0.0623456i
$124$	1.65799	−	1.20460i	0.148892	−	0.108177i
$125$	−0.952008	−	0.691675i	−0.0851502	−	0.0618653i
$126$	−0.864040	−	2.65924i	−0.0769748	−	0.236904i
$127$	0.859002	+	2.64374i	0.0762241	+	0.234594i	0.981908	−	0.189361i	$-0.0606416\pi$
$127$	0.859002	+	2.64374i	0.0762241	+	0.234594i	−0.905683	+	0.423955i	$0.860642\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−9.59983	+	6.97468i	−0.845217	+	0.614086i
$130$	0.0773214	−	0.237971i	0.00678154	−	0.0208714i
$131$	−10.0755			−0.880298			−0.440149	−	0.897925i	$-0.645074\pi$
$131$	−10.0755			−0.880298			−0.440149	+	0.897925i	$0.645074\pi$
$132$	−3.76542	+	1.08745i	−0.327738	+	0.0946499i
$133$	−1.74369			−0.151197
$134$	4.30610	−	13.2528i	0.371990	−	1.14487i
$135$	0.518621	−	0.376800i	0.0446358	−	0.0324298i
$136$	1.76027	+	1.27891i	0.150942	+	0.109666i
$137$	−0.148894	−	0.458249i	−0.0127209	−	0.0391509i	0.944495	−	0.328527i	$-0.106552\pi$
$137$	−0.148894	−	0.458249i	−0.0127209	−	0.0391509i	−0.957215	+	0.289376i	$0.906552\pi$
$138$	2.52148	+	7.76033i	0.214643	+	0.660603i
$139$	−16.0011	−	11.6255i	−1.35720	−	0.986061i	−0.998618	−	0.0525610i	$-0.983262\pi$
$139$	−16.0011	−	11.6255i	−1.35720	−	0.986061i	−0.358578	−	0.933500i	$-0.616738\pi$
$140$	−0.166231	+	0.120774i	−0.0140491	+	0.0102073i
$141$	2.22563	−	6.84979i	0.187432	−	0.576857i
$142$	9.17377			0.769846
$143$	0.232441	−	7.03867i	0.0194377	−	0.588603i
$144$	−1.60355			−0.133629
$145$	−0.105838	+	0.325737i	−0.00878939	+	0.0270510i
$146$	10.8850	−	7.90844i	0.900852	−	0.654508i
$147$	−3.78544	−	2.75028i	−0.312218	−	0.226839i
$148$	−0.631651	−	1.94402i	−0.0519214	−	0.159798i
$149$	1.65901	+	5.10592i	0.135912	+	0.418293i	0.995731	−	0.0923058i	$-0.0294237\pi$
$149$	1.65901	+	5.10592i	0.135912	+	0.418293i	−0.859819	+	0.510599i	$0.829424\pi$
$150$	4.76686	+	3.46333i	0.389213	+	0.282780i
$151$	−16.8173	+	12.2185i	−1.36857	+	0.994324i	−0.370723	+	0.928744i	$0.620890\pi$
$151$	−16.8173	+	12.2185i	−1.36857	+	0.994324i	−0.997847	+	0.0655810i	$0.979110\pi$
$152$	−0.309017	+	0.951057i	−0.0250646	+	0.0771409i
$153$	−3.48902			−0.282071
$154$	−3.55183	+	4.56393i	−0.286214	+	0.367772i
$155$	0.241497			0.0193975
$156$	−0.775400	+	2.38644i	−0.0620817	+	0.191068i
$157$	−5.44933	+	3.95917i	−0.434904	+	0.315976i	−0.783607	−	0.621257i	$-0.786622\pi$
$157$	−5.44933	+	3.95917i	−0.434904	+	0.315976i	0.348703	+	0.937233i	$0.386622\pi$
$158$	−4.42963	−	3.21831i	−0.352402	−	0.256035i
$159$	3.35083	+	10.3128i	0.265738	+	0.817858i
$160$	0.0364140	+	0.112071i	0.00287878	+	0.00885998i
$161$	9.74065	+	7.07700i	0.767671	+	0.557745i
$162$	−1.30897	+	0.951023i	−0.102842	+	0.0747194i
$163$	1.39938	−	4.30684i	0.109608	−	0.337338i	−0.881177	−	0.472787i	$-0.843248\pi$
$163$	1.39938	−	4.30684i	0.109608	−	0.337338i	0.990784	+	0.135450i	$0.0432479\pi$
$164$	0.615233			0.0480416
$165$	−0.434290	−	0.157137i	−0.0338095	−	0.0122331i
$166$	−9.46753			−0.734823
$167$	−1.53398	+	4.72111i	−0.118703	+	0.365331i	−0.992701	−	0.120598i	$-0.961519\pi$
$167$	−1.53398	+	4.72111i	−0.118703	+	0.365331i	0.873998	+	0.485929i	$0.161519\pi$
$168$	1.66701	−	1.21116i	0.128613	−	0.0934428i
$169$	6.86952	+	4.99100i	0.528425	+	0.383923i
$170$	0.0792301	+	0.243845i	0.00607667	+	0.0187021i
$171$	−0.495524	−	1.52507i	−0.0378937	−	0.116625i
$172$	8.12364	+	5.90217i	0.619422	+	0.450036i
$173$	−0.717302	+	0.521150i	−0.0545355	+	0.0396223i	−0.614719	−	0.788746i	$-0.710731\pi$
$173$	−0.717302	+	0.521150i	−0.0545355	+	0.0396223i	0.560184	+	0.828369i	$0.310731\pi$
$174$	1.06137	−	3.26658i	0.0804626	−	0.247638i
$175$	8.69423			0.657222
$176$	1.85984	+	2.74609i	0.140191	+	0.206994i
$177$	−6.63517			−0.498730
$178$	−1.48146	+	4.55947i	−0.111040	+	0.341746i
$179$	2.18727	−	1.58914i	0.163484	−	0.118778i	−0.503035	−	0.864266i	$-0.667783\pi$
$179$	2.18727	−	1.58914i	0.163484	−	0.118778i	0.666519	+	0.745488i	$0.267783\pi$
$180$	−0.152872	−	0.111068i	−0.0113944	−	0.00827850i
$181$	4.95861	+	15.2610i	0.368571	+	1.13434i	0.947715	+	0.319118i	$0.103387\pi$
$181$	4.95861	+	15.2610i	0.368571	+	1.13434i	−0.579144	+	0.815225i	$0.696613\pi$
$182$	1.14415	+	3.52133i	0.0848099	+	0.261018i
$183$	5.00235	+	3.63442i	0.369784	+	0.268664i
$184$	5.58623	−	4.05863i	0.411822	−	0.299206i
$185$	0.0744328	−	0.229080i	0.00547240	−	0.0168423i
$186$	−2.42180			−0.177575
$187$	4.04666	+	5.97496i	0.295921	+	0.436933i
$188$	−6.09479			−0.444508
$189$	−2.93128	+	9.02154i	−0.213219	+	0.656221i
$190$	−0.0953332	+	0.0692636i	−0.00691620	+	0.00502491i
$191$	18.9608	+	13.7758i	1.37195	+	0.996783i	0.997582	+	0.0695052i	$0.0221420\pi$
$191$	18.9608	+	13.7758i	1.37195	+	0.996783i	0.374373	+	0.927278i	$0.377858\pi$
$192$	−0.365170	−	1.12388i	−0.0263539	−	0.0811089i
$193$	2.56418	+	7.89174i	0.184574	+	0.568060i	0.999941	−	0.0108849i	$-0.00346483\pi$
$193$	2.56418	+	7.89174i	0.184574	+	0.568060i	−0.815367	+	0.578944i	$0.803465\pi$
$194$	9.04069	+	6.56845i	0.649084	+	0.471587i
$195$	−0.239215	+	0.173800i	−0.0171305	+	0.0124460i
$196$	−1.22357	+	3.76575i	−0.0873977	+	0.268982i
$197$	25.7155			1.83215			0.916077	−	0.401003i	$-0.131338\pi$
$197$	25.7155			1.83215			0.916077	+	0.401003i	$0.131338\pi$
$198$	−5.00107	−	1.80952i	−0.355411	−	0.128597i
$199$	7.28088			0.516128			0.258064	−	0.966128i	$-0.416915\pi$
$199$	7.28088			0.516128			0.258064	+	0.966128i	$0.416915\pi$
$200$	1.54079	−	4.74208i	0.108951	−	0.335315i
$201$	−13.3221	+	9.67905i	−0.939667	+	0.682708i
$202$	2.74514	+	1.99446i	0.193148	+	0.140330i
$203$	−1.56612	−	4.82002i	−0.109920	−	0.338299i
$204$	−0.794541	−	2.44534i	−0.0556290	−	0.171208i
$205$	0.0586521	+	0.0426133i	0.00409644	+	0.00297624i
$206$	14.3204	−	10.4044i	0.997751	−	0.724908i
$207$	−3.42158	+	10.5305i	−0.237816	+	0.731922i
$208$	2.12340			0.147231
$209$	−2.03696	+	2.61740i	−0.140900	+	0.181049i
$210$	0.242811			0.0167555
$211$	3.03706	−	9.34710i	0.209080	−	0.643481i	−0.790442	−	0.612537i	$-0.790149\pi$
$211$	3.03706	−	9.34710i	0.209080	−	0.643481i	0.999521	−	0.0309432i	$-0.00985111\pi$
$212$	7.42361	−	5.39356i	0.509855	−	0.370432i
$213$	−8.77038	−	6.37205i	−0.600936	−	0.436606i
$214$	0.159763	+	0.491699i	0.0109212	+	0.0336119i
$215$	0.365647	+	1.12535i	0.0249369	+	0.0767479i
$216$	4.40112	+	3.19760i	0.299458	+	0.217569i
$217$	−2.89102	+	2.10045i	−0.196256	+	0.142588i
$218$	2.45462	−	7.55456i	0.166248	−	0.511659i
$219$	−15.8996			−1.07439
$220$	−0.0128993	+	0.390613i	−0.000869674	+	0.0263351i
$221$	4.62011			0.310782
$222$	−0.746432	+	2.29728i	−0.0500972	+	0.154183i
$223$	−1.21763	+	0.884658i	−0.0815383	+	0.0592411i	−0.627808	−	0.778369i	$-0.716048\pi$
$223$	−1.21763	+	0.884658i	−0.0815383	+	0.0592411i	0.546269	+	0.837610i	$0.316048\pi$
$224$	−1.41067	−	1.02491i	−0.0942546	−	0.0684800i
$225$	2.47074	+	7.60416i	0.164716	+	0.506944i
$226$	4.99378	+	15.3693i	0.332182	+	1.02235i
$227$	−0.204927	−	0.148888i	−0.0136015	−	0.00988206i	0.580964	−	0.813929i	$-0.302676\pi$
$227$	−0.204927	−	0.148888i	−0.0136015	−	0.00988206i	−0.594565	+	0.804047i	$0.702676\pi$
$228$	0.956027	−	0.694595i	0.0633145	−	0.0460006i
$229$	−2.70334	+	8.32002i	−0.178642	+	0.549803i	−0.999781	−	0.0209252i	$-0.993339\pi$
$229$	−2.70334	+	8.32002i	−0.178642	+	0.549803i	0.821139	+	0.570728i	$0.193339\pi$
$230$	0.813669			0.0536518
$231$	6.56573	−	1.89617i	0.431993	−	0.124759i
$232$	−2.90652			−0.190823
$233$	3.81895	−	11.7535i	0.250188	−	0.769998i	−0.744552	−	0.667564i	$-0.767337\pi$
$233$	3.81895	−	11.7535i	0.250188	−	0.769998i	0.994740	−	0.102434i	$-0.0326631\pi$
$234$	−2.75468	+	2.00139i	−0.180079	+	0.130835i
$235$	−0.581036	−	0.422147i	−0.0379026	−	0.0275378i
$236$	1.73509	+	5.34006i	0.112945	+	0.347608i
$237$	1.99942	+	6.15359i	0.129876	+	0.399718i
$238$	−3.06936	−	2.23002i	−0.198957	−	0.144551i
$239$	−15.5530	+	11.2999i	−1.00604	+	0.730929i	−0.963374	−	0.268160i	$-0.913584\pi$
$239$	−15.5530	+	11.2999i	−1.00604	+	0.730929i	−0.0426635	+	0.999089i	$0.513584\pi$
$240$	0.0430310	−	0.132436i	0.00277764	−	0.00854870i
$241$	19.1933			1.23635			0.618176	−	0.786040i	$-0.287872\pi$
$241$	19.1933			1.23635			0.618176	+	0.786040i	$0.287872\pi$
$242$	2.70158	+	10.6631i	0.173664	+	0.685449i
$243$	−14.4083			−0.924290
$244$	1.61691	−	4.97634i	0.103512	−	0.318577i
$245$	−0.377477	+	0.274253i	−0.0241161	+	0.0175214i
$246$	−0.588179	−	0.427337i	−0.0375010	−	0.0272460i
$247$	0.656165	+	2.01947i	0.0417508	+	0.128496i
$248$	0.633297	+	1.94909i	0.0402144	+	0.123767i
$249$	9.05122	+	6.57609i	0.573598	+	0.416743i
$250$	0.952008	−	0.691675i	0.0602103	−	0.0437453i
$251$	−2.70895	+	8.33729i	−0.170987	+	0.526245i	−0.999428	−	0.0338325i	$-0.989229\pi$
$251$	−2.70895	+	8.33729i	−0.170987	+	0.526245i	0.828440	+	0.560078i	$0.189229\pi$
$252$	2.79609			0.176137
$253$	22.0020	−	6.35413i	1.38325	−	0.399481i
$254$	−2.77979			−0.174419
$255$	0.0936273	−	0.288155i	0.00586317	−	0.0180450i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−20.4386	−	14.8495i	−1.27493	−	0.926288i	−0.275539	−	0.961290i	$-0.588856\pi$
$257$	−20.4386	−	14.8495i	−1.27493	−	0.926288i	−0.999387	+	0.0350021i	$0.988856\pi$
$258$	−3.66681	−	11.2853i	−0.228285	−	0.702590i
$259$	1.10140	+	3.38977i	0.0684379	+	0.210630i
$260$	0.202430	+	0.147074i	0.0125542	+	0.00912115i
$261$	3.77063	−	2.73952i	0.233396	−	0.169572i
$262$	3.11349	−	9.58235i	0.192352	−	0.591999i
$263$	−19.1737			−1.18230			−0.591149	−	0.806562i	$-0.701326\pi$
$263$	−19.1737			−1.18230			−0.591149	+	0.806562i	$0.701326\pi$
$264$	0.129358	−	3.91717i	0.00796144	−	0.241085i
$265$	1.08129			0.0664234
$266$	0.538830	−	1.65835i	0.0330378	−	0.101680i
$267$	4.58330	−	3.32996i	0.280493	−	0.203790i
$268$	11.2735	+	8.19069i	0.688639	+	0.500326i
$269$	2.55591	+	7.86628i	0.155836	+	0.479615i	0.998245	−	0.0592245i	$-0.0188628\pi$
$269$	2.55591	+	7.86628i	0.155836	+	0.479615i	−0.842408	+	0.538840i	$0.818863\pi$
$270$	0.198095	+	0.609675i	0.0120557	+	0.0371036i
$271$	7.35162	+	5.34126i	0.446579	+	0.324459i	0.788244	−	0.615363i	$-0.210991\pi$
$271$	7.35162	+	5.34126i	0.446579	+	0.324459i	−0.341665	+	0.939822i	$0.610991\pi$
$272$	−1.76027	+	1.27891i	−0.106732	+	0.0775453i
$273$	1.35206	−	4.16120i	0.0818302	−	0.251847i
$274$	0.481832			0.0291085
$275$	10.1565	−	13.0507i	0.612461	−	0.786984i
$276$	−8.15970			−0.491156
$277$	−1.41257	+	4.34743i	−0.0848729	+	0.261212i	−0.984482	−	0.175483i	$-0.943851\pi$
$277$	−1.41257	+	4.34743i	−0.0848729	+	0.261212i	0.899610	+	0.436695i	$0.143851\pi$
$278$	16.0011	−	11.6255i	0.959683	−	0.697250i
$279$	−2.65868	−	1.93164i	−0.159171	−	0.115644i
$280$	−0.0634948	−	0.195417i	−0.00379454	−	0.0116784i
$281$	−0.380386	−	1.17071i	−0.0226920	−	0.0698386i	0.939069	−	0.343728i	$-0.111690\pi$
$281$	−0.380386	−	1.17071i	−0.0226920	−	0.0698386i	−0.961761	+	0.273889i	$0.911690\pi$
$282$	5.82678	+	4.23341i	0.346980	+	0.252096i
$283$	−21.3806	+	15.5339i	−1.27095	+	0.923397i	−0.999240	−	0.0389825i	$-0.987588\pi$
$283$	−21.3806	+	15.5339i	−1.27095	+	0.923397i	−0.271708	+	0.962380i	$0.587588\pi$
$284$	−2.83485	+	8.72478i	−0.168218	+	0.517720i
$285$	0.139251			0.00824854
$286$	6.62234	+	2.39613i	0.391587	+	0.141686i
$287$	−1.07277			−0.0633239
$288$	0.495524	−	1.52507i	0.0291990	−	0.0898654i
$289$	9.92328	−	7.20969i	0.583722	−	0.424099i
$290$	−0.277088	−	0.201316i	−0.0162712	−	0.0118217i
$291$	−4.08074	−	12.5592i	−0.239217	−	0.736235i
$292$	4.15772	+	12.7961i	0.243312	+	0.748837i
$293$	−5.10406	−	3.70832i	−0.298183	−	0.216642i	0.428627	−	0.903482i	$-0.358998\pi$
$293$	−5.10406	−	3.70832i	−0.298183	−	0.216642i	−0.726809	+	0.686839i	$0.758998\pi$
$294$	3.78544	−	2.75028i	0.220771	−	0.160400i
$295$	−0.204460	+	0.629264i	−0.0119041	+	0.0366371i
$296$	2.04407			0.118809
$297$	10.1177	+	14.9389i	0.587088	+	0.866845i
$298$	−5.36868			−0.310999
$299$	4.53080	−	13.9444i	0.262023	−	0.806423i
$300$	−4.76686	+	3.46333i	−0.275215	+	0.199955i
$301$	−14.1651	−	10.2915i	−0.816463	−	0.593195i
$302$	−6.42363	−	19.7699i	−0.369638	−	1.13763i
$303$	−1.23909	−	3.81352i	−0.0711838	−	0.219081i
$304$	−0.809017	−	0.587785i	−0.0464003	−	0.0337118i
$305$	0.498824	−	0.362417i	0.0285626	−	0.0207519i
$306$	1.07817	−	3.31826i	0.0616347	−	0.189692i
$307$	−18.2913			−1.04394			−0.521971	−	0.852963i	$-0.674803\pi$
$307$	−18.2913			−1.04394			−0.521971	+	0.852963i	$0.674803\pi$
$308$	−3.24298	−	4.78832i	−0.184786	−	0.272840i
$309$	−20.9175			−1.18996
$310$	−0.0746267	+	0.229677i	−0.00423851	+	0.0130448i
$311$	23.3956	−	16.9979i	1.32665	−	0.963864i	0.326822	−	0.945086i	$-0.394022\pi$
$311$	23.3956	−	16.9979i	1.32665	−	0.963864i	0.999824	−	0.0187781i	$-0.00597761\pi$
$312$	−2.03002	−	1.47490i	−0.114927	−	0.0834997i
$313$	5.65605	+	17.4075i	0.319699	+	0.983932i	0.973777	+	0.227505i	$0.0730567\pi$
$313$	5.65605	+	17.4075i	0.319699	+	0.983932i	−0.654078	+	0.756427i	$0.726943\pi$
$314$	−2.08146	−	6.40607i	−0.117463	−	0.361515i
$315$	0.266560	+	0.193668i	0.0150190	+	0.0109119i
$316$	4.42963	−	3.21831i	0.249186	−	0.181044i
$317$	6.96560	−	21.4379i	0.391227	−	1.20407i	−0.540634	−	0.841258i	$-0.681816\pi$
$317$	6.96560	−	21.4379i	0.391227	−	1.20407i	0.931861	−	0.362816i	$-0.118184\pi$
$318$	−10.8435			−0.608074
$319$	−9.06472	−	3.27985i	−0.507527	−	0.183636i
$320$	−0.117838			−0.00658736
$321$	0.188794	−	0.581049i	0.0105375	−	0.0324310i
$322$	−9.74065	+	7.07700i	−0.542825	+	0.394386i
$323$	−1.76027	−	1.27891i	−0.0979439	−	0.0711604i
$324$	−0.499982	−	1.53879i	−0.0277768	−	0.0854882i
$325$	−3.27171	−	10.0693i	−0.181482	−	0.558544i
$326$	3.66362	+	2.66177i	0.202909	+	0.147422i
$327$	−7.59404	+	5.51739i	−0.419951	+	0.305113i
$328$	−0.190117	+	0.585121i	−0.0104975	+	0.0323079i
$329$	10.6274			0.585908
$330$	0.283650	−	0.364477i	0.0156144	−	0.0200638i
$331$	8.07958			0.444094			0.222047	−	0.975036i	$-0.428726\pi$
$331$	8.07958			0.444094			0.222047	+	0.975036i	$0.428726\pi$
$332$	2.92563	−	9.00415i	0.160565	−	0.494167i
$333$	−2.65177	+	1.92662i	−0.145316	+	0.105578i
$334$	−4.01602	−	2.91781i	−0.219747	−	0.159655i
$335$	0.507423	+	1.56169i	0.0277235	+	0.0853242i
$336$	0.636743	+	1.95969i	0.0347372	+	0.106910i
$337$	−25.5610	−	18.5711i	−1.39239	−	1.01163i	−0.995598	−	0.0937270i	$-0.970122\pi$
$337$	−25.5610	−	18.5711i	−1.39239	−	1.01163i	−0.396796	−	0.917907i	$-0.629878\pi$
$338$	−6.86952	+	4.99100i	−0.373653	+	0.271475i
$339$	5.90123	−	18.1621i	0.320511	−	0.986431i
$340$	−0.256394			−0.0139049
$341$	−0.224340	+	6.79336i	−0.0121487	+	0.367881i
$342$	1.60355			0.0867101
$343$	5.90533	−	18.1747i	0.318858	−	0.981343i
$344$	−8.12364	+	5.90217i	−0.437997	+	0.318224i
$345$	−0.777890	−	0.565170i	−0.0418802	−	0.0304277i
$346$	−0.273985	−	0.843239i	−0.0147295	−	0.0453328i
$347$	−8.38797	−	25.8155i	−0.450290	−	1.38585i	−0.876577	−	0.481262i	$-0.840179\pi$
$347$	−8.38797	−	25.8155i	−0.450290	−	1.38585i	0.426287	−	0.904588i	$-0.359821\pi$
$348$	2.77872	+	2.01885i	0.148955	+	0.108222i
$349$	7.66322	−	5.56766i	0.410203	−	0.298030i	−0.363481	−	0.931602i	$-0.618412\pi$
$349$	7.66322	−	5.56766i	0.410203	−	0.298030i	0.773684	+	0.633572i	$0.218412\pi$
$350$	−2.68667	+	8.26871i	−0.143608	+	0.441981i
$351$	11.5514			0.616571
$352$	−3.18641	+	0.920226i	−0.169836	+	0.0490482i
$353$	12.0966			0.643837			0.321918	−	0.946767i	$-0.395672\pi$
$353$	12.0966			0.643837			0.321918	+	0.946767i	$0.395672\pi$
$354$	2.05038	−	6.31043i	0.108977	−	0.335395i
$355$	−0.874565	+	0.635409i	−0.0464171	+	0.0337240i
$356$	−3.87851	−	2.81790i	−0.205561	−	0.149349i
$357$	1.38543	+	4.26392i	0.0733248	+	0.225671i
$358$	0.835462	+	2.57129i	0.0441556	+	0.135897i
$359$	6.46948	+	4.70036i	0.341446	+	0.248075i	0.745272	−	0.666761i	$-0.232320\pi$
$359$	6.46948	+	4.70036i	0.341446	+	0.248075i	−0.403825	+	0.914836i	$0.632320\pi$
$360$	0.152872	−	0.111068i	0.00805704	−	0.00585378i
$361$	0.309017	−	0.951057i	0.0162641	−	0.0500556i
$362$	−16.0464			−0.843380
$363$	4.82374	−	12.0707i	0.253181	−	0.633548i
$364$	−3.70254			−0.194066
$365$	−0.489938	+	1.50787i	−0.0256445	+	0.0789258i
$366$	−5.00235	+	3.63442i	−0.261477	+	0.189974i
$367$	−1.05669	−	0.767732i	−0.0551589	−	0.0400753i	0.559864	−	0.828584i	$-0.310853\pi$
$367$	−1.05669	−	0.767732i	−0.0551589	−	0.0400753i	−0.615023	+	0.788509i	$0.710853\pi$
$368$	2.13375	+	6.56701i	0.111229	+	0.342329i
$369$	−0.304863	−	0.938271i	−0.0158705	−	0.0488444i
$370$	0.194867	+	0.141580i	0.0101307	+	0.00736037i
$371$	−12.9445	+	9.40470i	−0.672043	+	0.488268i
$372$	0.748377	−	2.30327i	0.0388015	−	0.119419i
$373$	11.9113			0.616744			0.308372	−	0.951266i	$-0.400216\pi$
$373$	11.9113			0.616744			0.308372	+	0.951266i	$0.400216\pi$
$374$	−6.93302	+	2.00224i	−0.358498	+	0.103533i
$375$	−1.39058			−0.0718092
$376$	1.88339	−	5.79649i	0.0971286	−	0.298931i
$377$	−4.99301	+	3.62763i	−0.257153	+	0.186833i
$378$	−7.67418	−	5.57562i	−0.394717	−	0.286779i
$379$	−4.83050	−	14.8668i	−0.248126	−	0.763654i	−0.995107	−	0.0988079i	$-0.968497\pi$
$379$	−4.83050	−	14.8668i	−0.248126	−	0.763654i	0.746980	−	0.664846i	$-0.231503\pi$
$380$	−0.0364140	−	0.112071i	−0.00186800	−	0.00574912i
$381$	2.65755	+	1.93083i	0.136151	+	0.0989192i
$382$	−18.9608	+	13.7758i	−0.970118	+	0.704832i
$383$	−3.81548	+	11.7428i	−0.194962	+	0.600031i	0.805015	+	0.593254i	$0.202157\pi$
$383$	−3.81548	+	11.7428i	−0.194962	+	0.600031i	−0.999977	+	0.00677661i	$0.997843\pi$
$384$	1.18171			0.0603041
$385$	0.0224924	−	0.681107i	0.00114632	−	0.0347124i
$386$	−8.29786			−0.422350
$387$	4.97574	−	15.3138i	0.252931	−	0.778442i
$388$	−9.04069	+	6.56845i	−0.458971	+	0.333462i
$389$	12.2598	+	8.90730i	0.621599	+	0.451618i	0.853480	−	0.521126i	$-0.174488\pi$
$389$	12.2598	+	8.90730i	0.621599	+	0.451618i	−0.231881	+	0.972744i	$0.574488\pi$
$390$	−0.0913719	−	0.281214i	−0.00462679	−	0.0142398i
$391$	4.64264	+	14.2886i	0.234788	+	0.722604i
$392$	−3.20334	−	2.32736i	−0.161793	−	0.117550i
$393$	−9.63243	+	6.99837i	−0.485892	+	0.353021i
$394$	−7.94653	+	24.4569i	−0.400340	+	1.23212i
$395$	0.645202			0.0324637
$396$	3.26637	−	4.19713i	0.164141	−	0.210914i
$397$	−1.08003			−0.0542050			−0.0271025	−	0.999633i	$-0.508628\pi$
$397$	−1.08003			−0.0542050			−0.0271025	+	0.999633i	$0.508628\pi$
$398$	−2.24992	+	6.92453i	−0.112778	+	0.347095i
$399$	−1.66701	+	1.21116i	−0.0834551	+	0.0606337i
$400$	4.03385	+	2.93076i	0.201693	+	0.146538i
$401$	7.06012	+	21.7288i	0.352566	+	1.08509i	0.957408	+	0.288740i	$0.0932363\pi$
$401$	7.06012	+	21.7288i	0.352566	+	1.08509i	−0.604842	+	0.796346i	$0.706764\pi$
$402$	−5.08858	−	15.6610i	−0.253795	−	0.781102i
$403$	3.52058	+	2.55785i	0.175372	+	0.127415i
$404$	−2.74514	+	1.99446i	−0.136576	+	0.0992282i
$405$	0.0589171	−	0.181328i	0.00292761	−	0.00901027i
$406$	5.06807			0.251524
$407$	6.37494	+	2.30661i	0.315994	+	0.114335i
$408$	2.57119			0.127293
$409$	5.09464	−	15.6797i	0.251914	−	0.775311i	−0.742508	−	0.669837i	$-0.766364\pi$
$409$	5.09464	−	15.6797i	0.251914	−	0.775311i	0.994422	−	0.105474i	$-0.0336359\pi$
$410$	−0.0586521	+	0.0426133i	−0.00289662	+	0.00210452i
$411$	−0.460644	−	0.334678i	−0.0227219	−	0.0165084i
$412$	5.46991	+	16.8347i	0.269483	+	0.829384i
$413$	−3.02546	−	9.31140i	−0.148873	−	0.458184i
$414$	−8.95780	−	6.50822i	−0.440252	−	0.319862i
$415$	0.902570	−	0.655755i	0.0443054	−	0.0321898i
$416$	−0.656165	+	2.01947i	−0.0321711	+	0.0990126i
$417$	−23.3725			−1.14456
$418$	−1.85984	−	2.74609i	−0.0909678	−	0.134315i
$419$	4.02294			0.196534			0.0982668	−	0.995160i	$-0.468670\pi$
$419$	4.02294			0.196534			0.0982668	+	0.995160i	$0.468670\pi$
$420$	−0.0750327	+	0.230927i	−0.00366122	+	0.0112681i
$421$	7.52733	−	5.46893i	0.366860	−	0.266539i	−0.389048	−	0.921218i	$-0.627196\pi$
$421$	7.52733	−	5.46893i	0.366860	−	0.266539i	0.755908	+	0.654678i	$0.227196\pi$
$422$	7.95111	+	5.77682i	0.387054	+	0.281211i
$423$	3.02011	+	9.29496i	0.146843	+	0.451936i
$424$	2.83556	+	8.72697i	0.137707	+	0.423819i
$425$	8.77689	+	6.37679i	0.425742	+	0.309320i
$426$	8.77038	−	6.37205i	0.424926	−	0.308727i
$427$	−2.81939	+	8.67718i	−0.136440	+	0.419918i
$428$	−0.517003			−0.0249903
$429$	−4.66680	−	6.89061i	−0.225315	−	0.332682i
$430$	−1.18326			−0.0570618
$431$	−0.789653	+	2.43030i	−0.0380362	+	0.117064i	−0.968272	−	0.249899i	$-0.919602\pi$
$431$	−0.789653	+	2.43030i	−0.0380362	+	0.117064i	0.930236	+	0.366963i	$0.119602\pi$
$432$	−4.40112	+	3.19760i	−0.211749	+	0.153845i
$433$	−31.1684	−	22.6452i	−1.49786	−	1.08826i	−0.971224	−	0.238168i	$-0.923453\pi$
$433$	−31.1684	−	22.6452i	−1.49786	−	1.08826i	−0.526636	−	0.850091i	$-0.676547\pi$
$434$	−1.10427	−	3.39860i	−0.0530068	−	0.163138i
$435$	0.125071	+	0.384928i	0.00599668	+	0.0184559i
$436$	6.42629	+	4.66897i	0.307763	+	0.223603i
$437$	−5.58623	+	4.05863i	−0.267226	+	0.194151i
$438$	4.91323	−	15.1214i	0.234763	−	0.722527i
$439$	34.2110			1.63280			0.816401	−	0.577485i	$-0.195966\pi$
$439$	34.2110			1.63280			0.816401	+	0.577485i	$0.195966\pi$
$440$	−0.367509	−	0.132974i	−0.0175203	−	0.00633928i
$441$	6.34933			0.302349
$442$	−1.42769	+	4.39398i	−0.0679083	+	0.209000i
$443$	−22.9403	+	16.6671i	−1.08992	+	0.791876i	−0.979386	−	0.201996i	$-0.935257\pi$
$443$	−22.9403	+	16.6671i	−1.08992	+	0.791876i	−0.110538	+	0.993872i	$0.535257\pi$
$444$	−1.95418	−	1.41980i	−0.0927415	−	0.0673806i
$445$	−0.174573	−	0.537280i	−0.00827554	−	0.0254695i
$446$	−0.465092	−	1.43141i	−0.0220228	−	0.0677791i
$447$	5.13260	+	3.72905i	0.242764	+	0.176378i
$448$	1.41067	−	1.02491i	0.0666481	−	0.0484227i
$449$	6.09749	−	18.7661i	0.287758	−	0.885629i	−0.697800	−	0.716293i	$-0.745838\pi$
$449$	6.09749	−	18.7661i	0.287758	−	0.885629i	0.985558	−	0.169336i	$-0.0541625\pi$
$450$	−7.99548			−0.376911
$451$	−1.25321	+	1.61031i	−0.0590111	+	0.0758266i
$452$	−16.1602			−0.760113
$453$	−7.59089	+	23.3624i	−0.356651	+	1.09766i
$454$	0.204927	−	0.148888i	0.00961771	−	0.00698767i
$455$	−0.352975	−	0.256451i	−0.0165477	−	0.0120226i
$456$	0.365170	+	1.12388i	0.0171007	+	0.0526304i
$457$	2.69412	+	8.29164i	0.126025	+	0.387866i	0.994087	−	0.108591i	$-0.0346339\pi$
$457$	2.69412	+	8.29164i	0.126025	+	0.387866i	−0.868061	+	0.496457i	$0.834634\pi$
$458$	−7.07743	−	5.14206i	−0.330707	−	0.240273i
$459$	−9.57600	+	6.95737i	−0.446969	+	0.324742i
$460$	−0.251438	+	0.773845i	−0.0117233	+	0.0360807i
$461$	10.8220			0.504033			0.252016	−	0.967723i	$-0.418906\pi$
$461$	10.8220			0.504033			0.252016	+	0.967723i	$0.418906\pi$
$462$	−0.225560	+	6.83032i	−0.0104940	+	0.317775i
$463$	38.6978			1.79844			0.899220	−	0.437496i	$-0.144135\pi$
$463$	38.6978			1.79844			0.899220	+	0.437496i	$0.144135\pi$
$464$	0.898165	−	2.76427i	0.0416963	−	0.128328i
$465$	0.230878	−	0.167743i	0.0107067	−	0.00777887i
$466$	9.99814	+	7.26407i	0.463155	+	0.336502i
$467$	2.02104	+	6.22011i	0.0935224	+	0.287832i	0.986866	−	0.161542i	$-0.0516469\pi$
$467$	2.02104	+	6.22011i	0.0935224	+	0.287832i	−0.893343	+	0.449375i	$0.851647\pi$
$468$	−1.05219	−	3.23832i	−0.0486377	−	0.149691i
$469$	−19.6575	−	14.2820i	−0.907699	−	0.659482i
$470$	0.581036	−	0.422147i	0.0268012	−	0.0194722i
$471$	−2.45969	+	7.57015i	−0.113337	+	0.348814i
$472$	−5.61487			−0.258445
$473$	−31.9959	+	9.24033i	−1.47117	+	0.424871i
$474$	−6.47027			−0.297189
$475$	−1.54079	+	4.74208i	−0.0706965	+	0.217581i
$476$	3.06936	−	2.23002i	0.140684	−	0.102213i
$477$	−11.9041	−	8.64885i	−0.545052	−	0.396004i
$478$	−5.94071	−	18.2836i	−0.271722	−	0.836273i
$479$	−10.2111	−	31.4264i	−0.466556	−	1.43591i	−0.857015	−	0.515291i	$-0.827684\pi$
$479$	−10.2111	−	31.4264i	−0.466556	−	1.43591i	0.390459	−	0.920620i	$-0.372316\pi$
$480$	0.112657	+	0.0818499i	0.00514205	+	0.00373592i
$481$	3.51143	−	2.55120i	0.160107	−	0.116325i
$482$	−5.93107	+	18.2539i	−0.270153	+	0.831444i
$483$	14.2280			0.647395
$484$	−10.9760	−	0.725723i	−0.498911	−	0.0329874i
$485$	−1.31683			−0.0597943
$486$	4.45240	−	13.7031i	0.201965	−	0.621584i
$487$	−5.17764	+	3.76178i	−0.234621	+	0.170462i	−0.698884	−	0.715235i	$-0.746320\pi$
$487$	−5.17764	+	3.76178i	−0.234621	+	0.170462i	0.464262	+	0.885698i	$0.346320\pi$
$488$	4.23312	+	3.07554i	0.191625	+	0.139223i
$489$	−1.65366	−	5.08946i	−0.0747813	−	0.230153i
$490$	−0.144183	−	0.443750i	−0.00651353	−	0.0200466i
$491$	23.9935	+	17.4323i	1.08281	+	0.786708i	0.978171	−	0.207803i	$-0.0666312\pi$
$491$	23.9935	+	17.4323i	1.08281	+	0.786708i	0.104639	+	0.994510i	$0.466631\pi$
$492$	0.588179	−	0.427337i	0.0265172	−	0.0192659i
$493$	1.95424	−	6.01452i	0.0880144	−	0.270880i
$494$	−2.12340			−0.0955361
$495$	0.602102	−	0.173886i	0.0270625	−	0.00781558i
$496$	−2.04939			−0.0920204
$497$	4.94310	−	15.2133i	0.221728	−	0.682410i
$498$	−9.05122	+	6.57609i	−0.405595	+	0.294682i
$499$	8.39708	+	6.10083i	0.375905	+	0.273111i	0.759655	−	0.650326i	$-0.225368\pi$
$499$	8.39708	+	6.10083i	0.375905	+	0.273111i	−0.383750	+	0.923437i	$0.625368\pi$
$500$	0.363635	+	1.11915i	0.0162622	+	0.0500500i
$501$	1.81273	+	5.57901i	0.0809868	+	0.249252i
$502$	−7.09212	−	5.15273i	−0.316537	−	0.229978i
$503$	−4.30292	+	3.12625i	−0.191858	+	0.139393i	−0.679567	−	0.733613i	$-0.737832\pi$
$503$	−4.30292	+	3.12625i	−0.191858	+	0.139393i	0.487710	+	0.873006i	$0.337832\pi$
$504$	−0.864040	+	2.65924i	−0.0384874	+	0.118452i
$505$	−0.399847			−0.0177930
$506$	−0.755862	+	22.8887i	−0.0336021	+	1.01753i
$507$	10.0342			0.445633
$508$	0.859002	−	2.64374i	0.0381120	−	0.117297i
$509$	−17.5568	+	12.7558i	−0.778193	+	0.565391i	−0.904436	−	0.426609i	$-0.859708\pi$
$509$	−17.5568	+	12.7558i	−0.778193	+	0.565391i	0.126243	+	0.991999i	$0.459708\pi$
$510$	0.245120	+	0.178090i	0.0108541	+	0.00788595i
$511$	−7.24976	−	22.3125i	−0.320711	−	0.987046i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−4.40112	−	3.19760i	−0.194314	−	0.141178i
$514$	20.4386	−	14.8495i	0.901509	−	0.654984i
$515$	−0.644565	+	1.98377i	−0.0284029	+	0.0874153i
$516$	11.8660			0.522373
$517$	12.4148	−	15.9525i	0.546004	−	0.701590i
$518$	−3.56422			−0.156603
$519$	−0.323772	+	0.996468i	−0.0142120	+	0.0437401i
$520$	−0.202430	+	0.147074i	−0.00887715	+	0.00644962i
$521$	−12.6096	−	9.16142i	−0.552437	−	0.401369i	0.276246	−	0.961087i	$-0.410910\pi$
$521$	−12.6096	−	9.16142i	−0.552437	−	0.401369i	−0.828683	+	0.559718i	$0.810910\pi$
$522$	1.44025	+	4.43264i	0.0630381	+	0.194011i
$523$	−1.07576	−	3.31086i	−0.0470399	−	0.144774i	0.924778	−	0.380508i	$-0.124251\pi$
$523$	−1.07576	−	3.31086i	−0.0470399	−	0.144774i	−0.971818	+	0.235734i	$0.924251\pi$
$524$	8.15123	+	5.92222i	0.356088	+	0.258713i
$525$	8.31192	−	6.03897i	0.362762	−	0.263562i
$526$	5.92499	−	18.2352i	0.258342	−	0.795094i
$527$	−4.45909			−0.194241
$528$	3.68548	+	1.33350i	0.160390	+	0.0580331i
$529$	24.6785			1.07298
$530$	−0.334138	+	1.02837i	−0.0145140	+	0.0446696i
$531$	7.28417	−	5.29226i	0.316106	−	0.229664i
$532$	1.41067	+	1.02491i	0.0611605	+	0.0444357i
$533$	0.403694	+	1.24244i	0.0174859	+	0.0538162i
$534$	1.75066	+	5.38799i	0.0757586	+	0.233161i
$535$	−0.0492876	−	0.0358095i	−0.00213089	−	0.00154818i
$536$	−11.2735	+	8.19069i	−0.486942	+	0.353784i
$537$	0.987278	−	3.03853i	0.0426042	−	0.131122i
$538$	−8.27109			−0.356592
$539$	−7.36413	−	10.8733i	−0.317196	−	0.468345i
$540$	−0.641050			−0.0275864
$541$	−0.649898	+	2.00018i	−0.0279413	+	0.0859945i	−0.964055	−	0.265704i	$-0.914396\pi$
$541$	−0.649898	+	2.00018i	−0.0279413	+	0.0859945i	0.936113	+	0.351698i	$0.114396\pi$
$542$	−7.35162	+	5.34126i	−0.315779	+	0.229427i
$543$	15.3408	+	11.1457i	0.658337	+	0.478309i
$544$	−0.672362	−	2.06932i	−0.0288273	−	0.0887213i
$545$	0.289249	+	0.890216i	0.0123901	+	0.0381327i
$546$	3.53973	+	2.57176i	0.151486	+	0.110061i
$547$	−8.19322	+	5.95272i	−0.350317	+	0.254520i	−0.749002	−	0.662568i	$-0.769467\pi$
$547$	−8.19322	+	5.95272i	−0.350317	+	0.254520i	0.398685	+	0.917088i	$0.369467\pi$
$548$	−0.148894	+	0.458249i	−0.00636045	+	0.0195754i
$549$	−8.39046			−0.358096
$550$	9.27338	+	13.6923i	0.395418	+	0.583842i
$551$	2.90652			0.123822
$552$	2.52148	−	7.76033i	0.107322	−	0.330302i
$553$	−7.72389	+	5.61173i	−0.328453	+	0.238635i
$554$	−3.69815	−	2.68686i	−0.157119	−	0.114154i
$555$	−0.0879583	−	0.270708i	−0.00373362	−	0.0114909i
$556$	6.11188	+	18.8104i	0.259201	+	0.797740i
$557$	−0.494297	−	0.359127i	−0.0209440	−	0.0152167i	0.577264	−	0.816558i	$-0.304120\pi$
$557$	−0.494297	−	0.359127i	−0.0209440	−	0.0152167i	−0.598208	+	0.801341i	$0.704120\pi$
$558$	2.65868	−	1.93164i	0.112551	−	0.0817729i
$559$	−6.58880	+	20.2782i	−0.278676	+	0.857678i
$560$	0.205473			0.00868284
$561$	8.01890	+	2.90144i	0.338558	+	0.122499i
$562$	1.23096			0.0519248
$563$	−8.51870	+	26.2179i	−0.359020	+	1.10495i	0.594621	+	0.804006i	$0.297302\pi$
$563$	−8.51870	+	26.2179i	−0.359020	+	1.10495i	−0.953642	+	0.300945i	$0.902698\pi$
$564$	−5.82678	+	4.23341i	−0.245352	+	0.178259i
$565$	−1.54061	−	1.11932i	−0.0648138	−	0.0470900i
$566$	−8.16668	−	25.1345i	−0.343271	−	1.05648i
$567$	0.871814	+	2.68317i	0.0366127	+	0.112682i
$568$	−7.42174	−	5.39221i	−0.311409	−	0.226252i
$569$	−17.3837	+	12.6300i	−0.728765	+	0.529478i	−0.889172	−	0.457572i	$-0.848719\pi$
$569$	−17.3837	+	12.6300i	−0.728765	+	0.529478i	0.160408	+	0.987051i	$0.448719\pi$
$570$	−0.0430310	+	0.132436i	−0.00180237	+	0.00554713i
$571$	29.1419			1.21955			0.609775	−	0.792575i	$-0.291260\pi$
$571$	29.1419			1.21955			0.609775	+	0.792575i	$0.291260\pi$
$572$	−4.32527	+	5.55778i	−0.180849	+	0.232382i
$573$	27.6956			1.15700
$574$	0.331506	−	1.02027i	0.0138368	−	0.0425852i
$575$	27.8536	−	20.2368i	1.16157	−	0.843933i
$576$	1.29730	+	0.942543i	0.0540541	+	0.0392726i
$577$	−11.1128	−	34.2016i	−0.462631	−	1.42383i	−0.861938	−	0.507014i	$-0.830749\pi$
$577$	−11.1128	−	34.2016i	−0.462631	−	1.42383i	0.399306	−	0.916818i	$-0.369251\pi$
$578$	3.79036	+	11.6655i	0.157658	+	0.485222i
$579$	7.93298	+	5.76365i	0.329684	+	0.239529i
$580$	0.277088	−	0.201316i	0.0115055	−	0.00835920i
$581$	−5.10138	+	15.7004i	−0.211641	+	0.651364i
$582$	13.2056			0.547388
$583$	−1.00447	+	30.4170i	−0.0416010	+	1.25974i
$584$	−13.4547			−0.556757
$585$	0.123989	−	0.381598i	0.00512630	−	0.0157771i
$586$	5.10406	−	3.70832i	0.210847	−	0.153189i
$587$	−32.1187	−	23.3356i	−1.32568	−	0.963162i	−0.999843	−	0.0177358i	$-0.994354\pi$
$587$	−32.1187	−	23.3356i	−1.32568	−	0.963162i	−0.325836	−	0.945426i	$-0.605646\pi$
$588$	1.44591	+	4.45005i	0.0596283	+	0.183517i
$589$	−0.633297	−	1.94909i	−0.0260946	−	0.0803108i
$590$	−0.535284	−	0.388906i	−0.0220373	−	0.0160110i
$591$	24.5847	−	17.8618i	1.01128	−	0.734738i
$592$	−0.631651	+	1.94402i	−0.0259607	+	0.0798989i
$593$	−16.7269			−0.686892			−0.343446	−	0.939172i	$-0.611594\pi$
$593$	−16.7269			−0.686892			−0.343446	+	0.939172i	$0.611594\pi$
$594$	−17.3343	+	5.00611i	−0.711236	+	0.205403i
$595$	0.447071			0.0183281
$596$	1.65901	−	5.10592i	0.0679558	−	0.209146i
$597$	6.96072	−	5.05726i	0.284883	−	0.206980i
$598$	11.8618	+	8.61808i	0.485064	+	0.352420i
$599$	13.4287	+	41.3293i	0.548682	+	1.68867i	0.712070	+	0.702108i	$0.247758\pi$
$599$	13.4287	+	41.3293i	0.548682	+	1.68867i	−0.163388	+	0.986562i	$0.552242\pi$
$600$	−1.82078	−	5.60378i	−0.0743330	−	0.228773i
$601$	4.87881	+	3.54467i	0.199011	+	0.144590i	0.682828	−	0.730579i	$-0.260750\pi$
$601$	4.87881	+	3.54467i	0.199011	+	0.144590i	−0.483817	+	0.875169i	$0.660750\pi$
$602$	14.1651	−	10.2915i	0.577326	−	0.419452i
$603$	6.90504	−	21.2515i	0.281195	−	0.865430i
$604$	20.7873			0.845823
$605$	−0.996114	−	0.829426i	−0.0404978	−	0.0337209i
$606$	4.00977			0.162886
$607$	13.4942	−	41.5307i	0.547711	−	1.68568i	−0.166745	−	0.986000i	$-0.553326\pi$
$607$	13.4942	−	41.5307i	0.547711	−	1.68568i	0.714456	−	0.699680i	$-0.246674\pi$
$608$	0.809017	−	0.587785i	0.0328100	−	0.0238378i
$609$	−4.84521	−	3.52025i	−0.196338	−	0.142648i
$610$	0.190534	+	0.586403i	0.00771449	+	0.0237428i
$611$	−3.99919	−	12.3082i	−0.161790	−	0.497938i
$612$	2.82268	+	2.05079i	0.114100	+	0.0828985i
$613$	17.8057	−	12.9366i	0.719166	−	0.522505i	−0.166952	−	0.985965i	$-0.553392\pi$
$613$	17.8057	−	12.9366i	0.719166	−	0.522505i	0.886118	+	0.463461i	$0.153392\pi$
$614$	5.65233	−	17.3961i	0.228110	−	0.702049i
$615$	0.0856720			0.00345463
$616$	5.55610	−	1.60459i	0.223862	−	0.0646507i
$617$	2.73799			0.110227			0.0551137	−	0.998480i	$-0.482448\pi$
$617$	2.73799			0.110227			0.0551137	+	0.998480i	$0.482448\pi$
$618$	6.46388	−	19.8938i	0.260015	−	0.800245i
$619$	−17.2900	+	12.5619i	−0.694942	+	0.504905i	−0.878281	−	0.478145i	$-0.841309\pi$
$619$	−17.2900	+	12.5619i	−0.694942	+	0.504905i	0.183339	+	0.983050i	$0.441309\pi$
$620$	−0.195375	−	0.141948i	−0.00784646	−	0.00570078i
$621$	11.6078	+	35.7251i	0.465804	+	1.43360i
$622$	8.93634	+	27.5032i	0.358315	+	1.10278i
$623$	6.76292	+	4.91355i	0.270951	+	0.196857i
$624$	2.03002	−	1.47490i	0.0812660	−	0.0590432i
$625$	7.66112	−	23.5785i	0.306445	−	0.943140i
$626$	−18.3034			−0.731549
$627$	−0.129358	+	3.91717i	−0.00516607	+	0.156437i
$628$	6.73574			0.268785
$629$	−1.37435	+	4.22983i	−0.0547991	+	0.168654i
$630$	−0.266560	+	0.193668i	−0.0106200	+	0.00771590i
$631$	26.0784	+	18.9470i	1.03816	+	0.754270i	0.969926	−	0.243399i	$-0.0782626\pi$
$631$	26.0784	+	18.9470i	1.03816	+	0.754270i	0.0682371	+	0.997669i	$0.478263\pi$
$632$	1.69197	+	5.20734i	0.0673028	+	0.207137i
$633$	−3.58893	−	11.0456i	−0.142647	−	0.439023i
$634$	18.2362	+	13.2494i	0.724251	+	0.526199i
$635$	0.265006	−	0.192538i	0.0105164	−	0.00764065i
$636$	3.35083	−	10.3128i	0.132869	−	0.408929i
$637$	−8.40769			−0.333125
$638$	5.92047	−	7.60754i	0.234394	−	0.301185i
$639$	14.7106			0.581943
$640$	0.0364140	−	0.112071i	0.00143939	−	0.00442999i
$641$	−20.7925	+	15.1067i	−0.821255	+	0.596677i	−0.917072	−	0.398722i	$-0.869454\pi$
$641$	−20.7925	+	15.1067i	−0.821255	+	0.596677i	0.0958166	+	0.995399i	$0.469454\pi$
$642$	0.494269	+	0.359108i	0.0195073	+	0.0141729i
$643$	−2.05507	−	6.32486i	−0.0810442	−	0.249428i	0.902322	−	0.431063i	$-0.141861\pi$
$643$	−2.05507	−	6.32486i	−0.0810442	−	0.249428i	−0.983366	+	0.181634i	$0.941861\pi$
$644$	−3.72060	−	11.4508i	−0.146612	−	0.451226i
$645$	1.13123	+	0.821885i	0.0445420	+	0.0323617i
$646$	1.76027	−	1.27891i	0.0692568	−	0.0503180i
$647$	−9.34865	+	28.7722i	−0.367533	+	1.13115i	0.580846	+	0.814013i	$0.302722\pi$
$647$	−9.34865	+	28.7722i	−0.367533	+	1.13115i	−0.948380	+	0.317138i	$0.897278\pi$
$648$	1.61798			0.0635602
$649$	−17.5114	−	6.33606i	−0.687382	−	0.248712i
$650$	10.5875			0.415276
$651$	−1.30494	+	4.01618i	−0.0511445	+	0.157407i
$652$	−3.66362	+	2.66177i	−0.143478	+	0.104243i
$653$	−12.9982	−	9.44375i	−0.508659	−	0.369562i	0.303656	−	0.952782i	$-0.401793\pi$
$653$	−12.9982	−	9.44375i	−0.508659	−	0.369562i	−0.812315	+	0.583219i	$0.801793\pi$
$654$	−2.90067	−	8.92733i	−0.113425	−	0.349086i
$655$	0.366889	+	1.12917i	0.0143355	+	0.0441202i
$656$	−0.497734	−	0.361625i	−0.0194332	−	0.0141191i
$657$	17.4547	−	12.6816i	0.680973	−	0.494756i
$658$	−3.28405	+	10.1073i	−0.128026	+	0.394022i
$659$	−8.59809			−0.334934			−0.167467	−	0.985878i	$-0.553559\pi$
$659$	−8.59809			−0.334934			−0.167467	+	0.985878i	$0.553559\pi$
$660$	0.258985	+	0.382396i	0.0100810	+	0.0148848i
$661$	−24.7734			−0.963573			−0.481787	−	0.876289i	$-0.660012\pi$
$661$	−24.7734			−0.963573			−0.481787	+	0.876289i	$0.660012\pi$
$662$	−2.49673	+	7.68414i	−0.0970381	+	0.298652i
$663$	4.41695	−	3.20910i	0.171540	−	0.124631i
$664$	7.65939	+	5.56487i	0.297242	+	0.215959i
$665$	0.0634948	+	0.195417i	0.00246222	+	0.00757794i
$666$	−1.01288	−	3.11734i	−0.0392485	−	0.120794i
$667$	−16.2365	−	11.7965i	−0.628680	−	0.456763i
$668$	4.01602	−	2.91781i	0.155384	−	0.112893i
$669$	−0.549606	+	1.69151i	−0.0212490	+	0.0653977i
$670$	−1.64206			−0.0634382
$671$	9.73148	+	14.3687i	0.375680	+	0.554698i
$672$	−2.06054			−0.0794872
$673$	−12.1070	+	37.2614i	−0.466689	+	1.43632i	0.390157	+	0.920748i	$0.372421\pi$
$673$	−12.1070	+	37.2614i	−0.466689	+	1.43632i	−0.856846	+	0.515572i	$0.827579\pi$
$674$	25.5610	−	18.5711i	0.984571	−	0.715333i
$675$	21.9445	+	15.9436i	0.844644	+	0.613670i
$676$	−2.62392	−	8.07560i	−0.100920	−	0.310600i
$677$	5.29532	+	16.2973i	0.203516	+	0.626356i	0.999771	+	0.0213960i	$0.00681109\pi$
$677$	5.29532	+	16.2973i	0.203516	+	0.626356i	−0.796256	+	0.604960i	$0.793189\pi$
$678$	15.4496	+	11.2248i	0.593339	+	0.431086i
$679$	15.7641	−	11.4533i	0.604973	−	0.439538i
$680$	0.0792301	−	0.243845i	0.00303833	−	0.00935103i
$681$	−0.299333			−0.0114705
$682$	−6.39155	−	2.31262i	−0.244745	−	0.0885550i
$683$	45.1219			1.72654			0.863271	−	0.504740i	$-0.168412\pi$
$683$	45.1219			1.72654			0.863271	+	0.504740i	$0.168412\pi$
$684$	−0.495524	+	1.52507i	−0.0189468	+	0.0583124i
$685$	−0.0459346	+	0.0333734i	−0.00175507	+	0.00127513i
$686$	15.4604	+	11.2326i	0.590279	+	0.428863i
$687$	3.19458	+	9.83189i	0.121881	+	0.375110i
$688$	−3.10295	−	9.54991i	−0.118299	−	0.364087i
$689$	15.7632	+	11.4527i	0.600532	+	0.436312i
$690$	0.777890	−	0.565170i	0.0296138	−	0.0215157i
$691$	−2.25598	+	6.94318i	−0.0858214	+	0.264131i	−0.984753	−	0.173958i	$-0.944344\pi$
$691$	−2.25598	+	6.94318i	−0.0858214	+	0.264131i	0.898932	+	0.438089i	$0.144344\pi$
$692$	0.886634			0.0337048
$693$	−5.69553	+	7.31850i	−0.216355	+	0.278007i
$694$	27.1440			1.03037
$695$	−0.720214	+	2.21659i	−0.0273193	+	0.0840800i
$696$	−2.77872	+	2.01885i	−0.105327	+	0.0765245i
$697$	−1.08297	−	0.786827i	−0.0410206	−	0.0298032i
$698$	2.92709	+	9.00866i	0.110792	+	0.340983i
$699$	−4.51291	−	13.8893i	−0.170694	−	0.525342i
$700$	−7.03378	−	5.11034i	−0.265852	−	0.193153i
$701$	23.4387	−	17.0292i	0.885268	−	0.643185i	−0.0493722	−	0.998780i	$-0.515722\pi$
$701$	23.4387	−	17.0292i	0.885268	−	0.643185i	0.934640	+	0.355596i	$0.115722\pi$
$702$	−3.56959	+	10.9861i	−0.134726	+	0.414643i
$703$	−2.04407			−0.0770934
$704$	0.109466	−	3.31482i	0.00412567	−	0.124932i
$705$	−0.848707			−0.0319642
$706$	−3.73805	+	11.5045i	−0.140683	+	0.432979i
$707$	4.78667	−	3.47772i	0.180021	−	0.130793i
$708$	5.36797	+	3.90006i	0.201741	+	0.146573i
$709$	10.3751	+	31.9313i	0.389645	+	1.19920i	0.933054	+	0.359736i	$0.117133\pi$
$709$	10.3751	+	31.9313i	0.389645	+	1.19920i	−0.543409	+	0.839468i	$0.682867\pi$
$710$	−0.334054	−	1.02811i	−0.0125368	−	0.0385844i
$711$	−7.10313	−	5.16072i	−0.266388	−	0.193542i
$712$	3.87851	−	2.81790i	0.145353	−	0.105605i
$713$	−4.37289	+	13.4584i	−0.163766	+	0.504020i
$714$	−4.48335			−0.167785
$715$	−0.797294	+	0.230257i	−0.0298171	+	0.00861111i
$716$	−2.70361			−0.101039
$717$	−7.02022	+	21.6060i	−0.262175	+	0.806891i
$718$	−6.46948	+	4.70036i	−0.241439	+	0.175416i
$719$	−8.70969	−	6.32796i	−0.324817	−	0.235993i	0.413411	−	0.910544i	$-0.364337\pi$
$719$	−8.70969	−	6.32796i	−0.324817	−	0.235993i	−0.738228	+	0.674551i	$0.764337\pi$
$720$	0.0583917	+	0.179711i	0.00217613	+	0.00669745i
$721$	−9.53782	−	29.3544i	−0.355207	−	1.09322i
$722$	0.809017	+	0.587785i	0.0301085	+	0.0218751i
$723$	18.3494	−	13.3316i	0.682420	−	0.495807i
$724$	4.95861	−	15.2610i	0.184285	−	0.567172i
$725$	−14.4923			−0.538229
$726$	9.98931	+	8.31770i	0.370738	+	0.308699i
$727$	−6.94503			−0.257577			−0.128788	−	0.991672i	$-0.541109\pi$
$727$	−6.94503			−0.257577			−0.128788	+	0.991672i	$0.541109\pi$
$728$	1.14415	−	3.52133i	0.0424049	−	0.130509i
$729$	−17.7016	+	12.8610i	−0.655615	+	0.476332i
$730$	−1.28268	−	0.931918i	−0.0474739	−	0.0344918i
$731$	−6.75144	−	20.7788i	−0.249711	−	0.768531i
$732$	−1.91073	−	5.88061i	−0.0706225	−	0.217354i
$733$	−23.8218	−	17.3075i	−0.879878	−	0.639268i	0.0533415	−	0.998576i	$-0.483013\pi$
$733$	−23.8218	−	17.3075i	−0.879878	−	0.639268i	−0.933219	+	0.359308i	$0.883013\pi$
$734$	1.05669	−	0.767732i	0.0390032	−	0.0283375i
$735$	−0.170383	+	0.524386i	−0.00628469	+	0.0193423i
$736$	−6.90496			−0.254520
$737$	−44.4020	+	12.8232i	−1.63557	+	0.472348i
$738$	0.986557			0.0363157
$739$	−13.0387	+	40.1289i	−0.479635	+	1.47617i	0.359967	+	0.932965i	$0.382788\pi$
$739$	−13.0387	+	40.1289i	−0.479635	+	1.47617i	−0.839603	+	0.543201i	$0.817212\pi$
$740$	−0.194867	+	0.141580i	−0.00716347	+	0.00520457i
$741$	2.03002	+	1.47490i	0.0745748	+	0.0541818i
$742$	−4.94434	−	15.2171i	−0.181513	−	0.558638i
$743$	9.82253	+	30.2306i	0.360354	+	1.10905i	0.952840	+	0.303474i	$0.0981465\pi$
$743$	9.82253	+	30.2306i	0.360354	+	1.10905i	−0.592486	+	0.805581i	$0.701853\pi$
$744$	1.95928	+	1.42350i	0.0718305	+	0.0521879i
$745$	0.511813	−	0.371854i	0.0187514	−	0.0136237i
$746$	−3.68080	+	11.3283i	−0.134764	+	0.414759i
$747$	−15.1817			−0.555468
$748$	0.238178	−	7.21241i	0.00870866	−	0.263712i
$749$	0.901493			0.0329398
$750$	0.429713	−	1.32252i	0.0156909	−	0.0482916i
$751$	−10.2131	+	7.42024i	−0.372681	+	0.270768i	−0.758322	−	0.651881i	$-0.773980\pi$
$751$	−10.2131	+	7.42024i	−0.372681	+	0.270768i	0.385641	+	0.922649i	$0.373980\pi$
$752$	4.93079	+	3.58243i	0.179807	+	0.130638i
$753$	3.20121	+	9.85230i	0.116658	+	0.359038i
$754$	−1.90716	−	5.86963i	−0.0694546	−	0.213759i
$755$	1.98172	+	1.43980i	0.0721222	+	0.0523998i
$756$	7.67418	−	5.57562i	0.279107	−	0.202783i
$757$	−4.62211	+	14.2254i	−0.167994	+	0.517031i	−0.999244	−	0.0388664i	$-0.987625\pi$
$757$	−4.62211	+	14.2254i	−0.167994	+	0.517031i	0.831251	+	0.555898i	$0.187625\pi$
$758$	15.6318			0.567774
$759$	16.6210	−	21.3572i	0.603303	−	0.775217i
$760$	0.117838			0.00427445
$761$	−15.6462	+	48.1539i	−0.567173	+	1.74558i	0.0942319	+	0.995550i	$0.469961\pi$
$761$	−15.6462	+	48.1539i	−0.567173	+	1.74558i	−0.661405	+	0.750029i	$0.730039\pi$
$762$	−2.65755	+	1.93083i	−0.0962730	+	0.0699464i
$763$	−11.2054	−	8.14124i	−0.405665	−	0.294733i
$764$	−7.24238	−	22.2897i	−0.262020	−	0.806415i
$765$	0.127049	+	0.391018i	0.00459348	+	0.0141373i
$766$	−9.98905	−	7.25747i	−0.360919	−	0.262223i
$767$	−9.64557	+	7.00792i	−0.348282	+	0.253041i
$768$	−0.365170	+	1.12388i	−0.0131769	+	0.0405544i
$769$	29.6272			1.06839			0.534193	−	0.845363i	$-0.320616\pi$
$769$	29.6272			1.06839			0.534193	+	0.845363i	$0.320616\pi$
$770$	0.640821	+	0.231865i	0.0230936	+	0.00835584i
$771$	−29.8543			−1.07518
$772$	2.56418	−	7.89174i	0.0922869	−	0.284030i
$773$	−2.56970	+	1.86699i	−0.0924255	+	0.0671511i	−0.633038	−	0.774120i	$-0.718192\pi$
$773$	−2.56970	+	1.86699i	−0.0924255	+	0.0671511i	0.540613	+	0.841272i	$0.318192\pi$
$774$	13.0267	+	9.46442i	0.468234	+	0.340192i
$775$	3.15769	+	9.71838i	0.113428	+	0.349094i
$776$	−3.45324	−	10.6280i	−0.123964	−	0.381522i
$777$	3.40749	+	2.47569i	0.122243	+	0.0888147i
$778$	−12.2598	+	8.90730i	−0.439537	+	0.319342i
$779$	0.190117	−	0.585121i	0.00681166	−	0.0209641i
$780$	0.295686			0.0105872
$781$	−17.0618	−	25.1920i	−0.610518	−	0.901440i
$782$	−15.0239			−0.537253
$783$	4.88609	−	15.0378i	0.174615	−	0.537409i
$784$	3.20334	−	2.32736i	0.114405	−	0.0831202i
$785$	0.642140	+	0.466542i	0.0229190	+	0.0166516i
$786$	−3.67926	−	11.3236i	−0.131235	−	0.403899i
$787$	−7.93976	−	24.4361i	−0.283022	−	0.871052i	−0.986985	−	0.160815i	$-0.948588\pi$
$787$	−7.93976	−	24.4361i	−0.283022	−	0.871052i	0.703963	−	0.710237i	$-0.251412\pi$
$788$	−20.8043	−	15.1152i	−0.741122	−	0.538456i
$789$	−18.3305	+	13.3179i	−0.652585	+	0.474130i
$790$	−0.199379	+	0.613624i	−0.00709357	+	0.0218318i
$791$	28.1784			1.00191
$792$	2.98235	+	4.40349i	0.105973	+	0.156471i
$793$	11.1105			0.394546
$794$	0.333746	−	1.02717i	0.0118442	−	0.0364528i
$795$	1.03375	−	0.751061i	0.0366632	−	0.0266374i
$796$	−5.89035	−	4.27959i	−0.208778	−	0.151686i
$797$	−10.3187	−	31.7577i	−0.365508	−	1.12492i	−0.949663	−	0.313274i	$-0.898574\pi$
$797$	−10.3187	−	31.7577i	−0.365508	−	1.12492i	0.584155	−	0.811642i	$-0.301426\pi$
$798$	−0.636743	−	1.95969i	−0.0225405	−	0.0693724i
$799$	10.7285	+	7.79468i	0.379545	+	0.275756i
$800$	−4.03385	+	2.93076i	−0.142618	+	0.103618i
$801$	−2.37560	+	7.31133i	−0.0839375	+	0.258333i
$802$	−22.8470			−0.806757
$803$	−41.9617	−	15.1828i	−1.48080	−	0.535790i
$804$	16.4670			0.580746
$805$	0.438429	−	1.34935i	0.0154526	−	0.0475582i
$806$	−3.52058	+	2.55785i	−0.124007	+	0.0900963i
$807$	7.90739	+	5.74506i	0.278353	+	0.202236i
$808$	−1.04855	−	3.22711i	−0.0368879	−	0.113529i
$809$	5.98968	+	18.4343i	0.210586	+	0.648116i	0.999438	+	0.0335329i	$0.0106759\pi$
$809$	5.98968	+	18.4343i	0.210586	+	0.648116i	−0.788852	+	0.614583i	$0.789324\pi$
$810$	0.154247	+	0.112067i	0.00541969	+	0.00393763i
$811$	38.9301	−	28.2844i	1.36702	−	0.993200i	0.369059	−	0.929406i	$-0.379680\pi$
$811$	38.9301	−	28.2844i	1.36702	−	0.993200i	0.997963	−	0.0637935i	$-0.0203199\pi$
$812$	−1.56612	+	4.82002i	−0.0549600	+	0.169150i
$813$	10.7384			0.376611
$814$	−4.16369	+	5.35014i	−0.145937	+	0.187522i
$815$	−0.533629			−0.0186922
$816$	−0.794541	+	2.44534i	−0.0278145	+	0.0856042i
$817$	8.12364	−	5.90217i	0.284210	−	0.206491i
$818$	13.3379	+	9.69058i	0.466350	+	0.338823i
$819$	1.83470	+	5.64662i	0.0641096	+	0.197309i
$820$	−0.0224031	−	0.0689497i	−0.000782351	−	0.00240783i
$821$	−20.8040	−	15.1150i	−0.726063	−	0.527516i	0.162252	−	0.986749i	$-0.448124\pi$
$821$	−20.8040	−	15.1150i	−0.726063	−	0.527516i	−0.888316	+	0.459233i	$0.848124\pi$
$822$	0.460644	−	0.334678i	0.0160668	−	0.0116732i
$823$	−11.5079	+	35.4176i	−0.401139	+	1.23458i	0.522937	+	0.852371i	$0.324836\pi$
$823$	−11.5079	+	35.4176i	−0.401139	+	1.23458i	−0.924076	+	0.382208i	$0.875164\pi$
$824$	−17.7010			−0.616644
$825$	0.644994	−	19.5315i	0.0224558	−	0.679998i
$826$	9.79059			0.340658
$827$	6.97834	−	21.4771i	0.242661	−	0.746833i	−0.753352	−	0.657618i	$-0.771564\pi$
$827$	6.97834	−	21.4771i	0.242661	−	0.746833i	0.996012	−	0.0892150i	$-0.0284358\pi$
$828$	8.95780	−	6.50822i	0.311305	−	0.226176i
$829$	−27.7912	−	20.1915i	−0.965229	−	0.701280i	−0.0108696	−	0.999941i	$-0.503460\pi$
$829$	−27.7912	−	20.1915i	−0.965229	−	0.701280i	−0.954359	+	0.298661i	$0.903460\pi$
$830$	0.344751	+	1.06103i	0.0119665	+	0.0368290i
$831$	1.66925	+	5.13743i	0.0579057	+	0.178215i
$832$	−1.71786	−	1.24810i	−0.0595562	−	0.0432701i
$833$	6.96987	−	5.06390i	0.241492	−	0.175454i
$834$	7.22250	−	22.2286i	0.250095	−	0.769712i
$835$	0.584958			0.0202433
$836$	3.18641	−	0.920226i	0.110204	−	0.0318267i
$837$	−11.1489			−0.385361
$838$	−1.24316	+	3.82604i	−0.0429441	+	0.132169i
$839$	−2.47258	+	1.79643i	−0.0853630	+	0.0620198i	−0.629648	−	0.776880i	$-0.716801\pi$
$839$	−2.47258	+	1.79643i	−0.0853630	+	0.0620198i	0.544285	+	0.838900i	$0.316801\pi$
$840$	−0.196438	−	0.142721i	−0.00677776	−	0.00492433i
$841$	−6.35096	−	19.5462i	−0.218999	−	0.674008i
$842$	2.87519	+	8.84891i	0.0990854	+	0.304954i
$843$	−1.17683	−	0.855016i	−0.0405321	−	0.0294483i
$844$	−7.95111	+	5.77682i	−0.273689	+	0.198846i
$845$	0.309199	−	0.951616i	0.0106368	−	0.0327366i
$846$	−9.77330			−0.336013
$847$	19.1388	+	1.26543i	0.657617	+	0.0434809i
$848$	−9.17608			−0.315108
$849$	−9.65069	+	29.7018i	−0.331211	+	1.01936i
$850$	−8.77689	+	6.37679i	−0.301045	+	0.218722i
$851$	11.4186	+	8.29612i	0.391426	+	0.284387i
$852$	3.34999	+	10.3102i	0.114769	+	0.353222i
$853$	−1.01187	−	3.11423i	−0.0346459	−	0.106629i	0.932238	−	0.361846i	$-0.117853\pi$
$853$	−1.01187	−	3.11423i	−0.0346459	−	0.106629i	−0.966884	+	0.255217i	$0.917853\pi$
$854$	−7.38125	−	5.36279i	−0.252581	−	0.183511i
$855$	−0.152872	+	0.111068i	−0.00522810	+	0.00379844i
$856$	0.159763	−	0.491699i	0.00546058	−	0.0168059i
$857$	−6.04478			−0.206486			−0.103243	−	0.994656i	$-0.532922\pi$
$857$	−6.04478			−0.206486			−0.103243	+	0.994656i	$0.532922\pi$
$858$	7.99548	−	2.30908i	0.272961	−	0.0788305i
$859$	1.52525			0.0520409			0.0260204	−	0.999661i	$-0.491717\pi$
$859$	1.52525			0.0520409			0.0260204	+	0.999661i	$0.491717\pi$
$860$	0.365647	−	1.12535i	0.0124685	−	0.0383740i
$861$	−1.02560	+	0.745143i	−0.0349524	+	0.0253944i
$862$	−2.06734	−	1.50201i	−0.0704138	−	0.0511586i
$863$	−11.2931	−	34.7567i	−0.384423	−	1.18313i	−0.936898	−	0.349602i	$-0.886317\pi$
$863$	−11.2931	−	34.7567i	−0.384423	−	1.18313i	0.552475	−	0.833529i	$-0.313683\pi$
$864$	−1.68108	−	5.17383i	−0.0571914	−	0.176017i
$865$	0.0845257	+	0.0614115i	0.00287396	+	0.00208805i
$866$	31.1684	−	22.6452i	1.05915	−	0.769515i
$867$	4.47912	−	13.7853i	0.152119	−	0.468174i
$868$	3.57350			0.121293
$869$	−0.599364	+	18.1497i	−0.0203320	+	0.615686i
$870$	−0.404737			−0.0137219
$871$	−9.14355	+	28.1409i	−0.309817	+	0.953520i
$872$	−6.42629	+	4.66897i	−0.217622	+	0.158111i
$873$	14.4972	+	10.5328i	0.490656	+	0.356482i
$874$	−2.13375	−	6.56701i	−0.0721752	−	0.222132i
$875$	−0.634066	−	1.95145i	−0.0214353	−	0.0659712i
$876$	12.8630	+	9.34553i	0.434601	+	0.315756i
$877$	6.61954	−	4.80938i	0.223526	−	0.162401i	−0.470386	−	0.882461i	$-0.655885\pi$
$877$	6.61954	−	4.80938i	0.223526	−	0.162401i	0.693912	+	0.720059i	$0.255885\pi$
$878$	−10.5718	+	32.5366i	−0.356780	+	1.09806i
$879$	−7.45540			−0.251465
$880$	0.240032	−	0.308430i	0.00809148	−	0.0103972i
$881$	−23.0229			−0.775662			−0.387831	−	0.921731i	$-0.626776\pi$
$881$	−23.0229			−0.775662			−0.387831	+	0.921731i	$0.626776\pi$
$882$	−1.96205	+	6.03858i	−0.0660657	+	0.203329i
$883$	−43.6925	+	31.7445i	−1.47037	+	1.06829i	−0.489865	+	0.871798i	$0.662954\pi$
$883$	−43.6925	+	31.7445i	−1.47037	+	1.06829i	−0.980506	+	0.196489i	$0.937046\pi$
$884$	−3.73774	−	2.71563i	−0.125714	−	0.0913365i
$885$	0.241614	+	0.743610i	0.00812175	+	0.0249962i
$886$	−8.76240	−	26.9679i	−0.294378	−	0.906004i
$887$	−25.5025	−	18.5286i	−0.856289	−	0.622130i	0.0705838	−	0.997506i	$-0.477514\pi$
$887$	−25.5025	−	18.5286i	−0.856289	−	0.622130i	−0.926873	+	0.375375i	$0.877514\pi$
$888$	1.95418	−	1.41980i	0.0655781	−	0.0476453i
$889$	−1.49783	+	4.60985i	−0.0502357	+	0.154609i
$890$	0.564929			0.0189365
$891$	5.04607	+	1.82580i	0.169050	+	0.0611665i
$892$	1.50507			0.0503935
$893$	−1.88339	+	5.79649i	−0.0630253	+	0.193972i
$894$	−5.13260	+	3.72905i	−0.171660	+	0.124718i
$895$	−0.257744	−	0.187262i	−0.00861544	−	0.00625948i
$896$	0.538830	+	1.65835i	0.0180010	+	0.0554015i
$897$	−5.35411	−	16.4782i	−0.178768	−	0.550193i
$898$	15.9634	+	11.5981i	0.532707	+	0.387034i
$899$	4.81899	−	3.50120i	0.160722	−	0.116772i
$900$	2.47074	−	7.60416i	0.0823580	−	0.253472i
$901$	−19.9654			−0.665144
$902$	−1.14424	−	1.68948i	−0.0380989	−	0.0562536i
$903$	−20.6907			−0.688543
$904$	4.99378	−	15.3693i	0.166091	−	0.511175i
$905$	1.52975	−	1.11143i	0.0508508	−	0.0369452i
$906$	−19.8732	−	14.4387i	−0.660244	−	0.479695i
$907$	0.596394	+	1.83551i	0.0198029	+	0.0609472i	0.960470	−	0.278385i	$-0.0897990\pi$
$907$	0.596394	+	1.83551i	0.0198029	+	0.0609472i	−0.940667	+	0.339332i	$0.889799\pi$
$908$	0.0782752	+	0.240906i	0.00259765	+	0.00799476i
$909$	4.40197	+	3.19822i	0.146004	+	0.106078i
$910$	0.352975	−	0.256451i	0.0117010	−	0.00850128i
$911$	0.124252	−	0.382407i	0.00411664	−	0.0126697i	−0.948977	−	0.315345i	$-0.897880\pi$
$911$	0.124252	−	0.382407i	0.00411664	−	0.0126697i	0.953094	+	0.302675i	$0.0978798\pi$
$912$	−1.18171			−0.0391305
$913$	17.6081	+	25.9987i	0.582743	+	0.860430i
$914$	−8.71834			−0.288377
$915$	0.225157	−	0.692961i	0.00744345	−	0.0229086i
$916$	7.07743	−	5.14206i	0.233845	−	0.169898i
$917$	−14.2132	−	10.3265i	−0.469362	−	0.341011i
$918$	−3.65771	−	11.2573i	−0.120722	−	0.371545i
$919$	−11.9961	−	36.9202i	−0.395714	−	1.21788i	−0.928404	−	0.371573i	$-0.878819\pi$
$919$	−11.9961	−	36.9202i	−0.395714	−	1.21788i	0.532689	−	0.846311i	$-0.321181\pi$
$920$	−0.658272	−	0.478263i	−0.0217026	−	0.0157679i
$921$	−17.4870	+	12.7051i	−0.576217	+	0.418646i
$922$	−3.34419	+	10.2924i	−0.110135	+	0.338961i
$923$	−19.4795			−0.641177
$924$	−6.42632	−	2.32521i	−0.211411	−	0.0764937i
$925$	10.1920			0.335109
$926$	−11.9583	+	36.8038i	−0.392974	+	1.20945i
$927$	22.9635	−	16.6840i	0.754220	−	0.547973i
$928$	2.35143	+	1.70841i	0.0771893	+	0.0560813i
$929$	−1.80186	−	5.54554i	−0.0591170	−	0.181943i	0.917137	−	0.398572i	$-0.130494\pi$
$929$	−1.80186	−	5.54554i	−0.0591170	−	0.181943i	−0.976254	+	0.216628i	$0.930494\pi$
$930$	0.0881875	+	0.271413i	0.00289178	+	0.00889999i
$931$	3.20334	+	2.32736i	0.104985	+	0.0762763i
$932$	−9.99814	+	7.26407i	−0.327500	+	0.237943i
$933$	10.5602	−	32.5010i	0.345726	−	1.06403i
$934$	−6.54021			−0.214002
$935$	0.522264	−	0.671086i	0.0170799	−	0.0219468i
$936$	3.40497			0.111295
$937$	4.24996	−	13.0800i	0.138840	−	0.427306i	−0.857327	−	0.514771i	$-0.827877\pi$
$937$	4.24996	−	13.0800i	0.138840	−	0.427306i	0.996168	+	0.0874656i	$0.0278768\pi$
$938$	19.6575	−	14.2820i	0.641840	−	0.466324i
$939$	17.4985	+	12.7134i	0.571042	+	0.414887i
$940$	0.221936	+	0.683048i	0.00723875	+	0.0222786i
$941$	−12.8489	−	39.5449i	−0.418863	−	1.28913i	−0.908750	−	0.417341i	$-0.862962\pi$
$941$	−12.8489	−	39.5449i	−0.418863	−	1.28913i	0.489887	−	0.871786i	$-0.337038\pi$
$942$	−6.43955	−	4.67861i	−0.209812	−	0.152437i
$943$	−3.43683	+	2.49701i	−0.111919	+	0.0813137i
$944$	1.73509	−	5.34006i	0.0564724	−	0.173804i
$945$	1.11779			0.0363618
$946$	1.09919	−	33.2853i	0.0357379	−	1.08220i
$947$	14.7404			0.478999			0.239500	−	0.970896i	$-0.423017\pi$
$947$	14.7404			0.478999			0.239500	+	0.970896i	$0.423017\pi$
$948$	1.99942	−	6.15359i	0.0649382	−	0.199859i
$949$	−23.1132	+	16.7928i	−0.750288	+	0.545116i
$950$	−4.03385	−	2.93076i	−0.130875	−	0.0950866i
$951$	−8.23136	−	25.3335i	−0.266920	−	0.821495i
$952$	1.17239	+	3.60825i	0.0379974	+	0.116944i
$953$	24.6250	+	17.8911i	0.797683	+	0.579551i	0.910233	−	0.414095i	$-0.135902\pi$
$953$	24.6250	+	17.8911i	0.797683	+	0.579551i	−0.112550	+	0.993646i	$0.535902\pi$
$954$	11.9041	−	8.64885i	0.385410	−	0.280017i
$955$	0.853430	−	2.62659i	0.0276163	−	0.0849943i
$956$	19.2245			0.621766
$957$	−10.9443	+	3.16068i	−0.353779	+	0.102170i
$958$	33.0437			1.06759
$959$	0.259625	−	0.799044i	0.00838374	−	0.0258025i
$960$	−0.112657	+	0.0818499i	−0.00363598	+	0.00264169i
$961$	21.6816	+	15.7526i	0.699408	+	0.508150i
$962$	1.34125	+	4.12793i	0.0432435	+	0.133090i
$963$	0.256188	+	0.788465i	0.00825553	+	0.0254079i
$964$	−15.5277	−	11.2816i	−0.500115	−	0.363355i
$965$	0.791062	−	0.574740i	0.0254652	−	0.0185015i
$966$	−4.39668	+	13.5316i	−0.141461	+	0.435372i
$967$	9.20321			0.295955			0.147978	−	0.988991i	$-0.452724\pi$
$967$	9.20321			0.295955			0.147978	+	0.988991i	$0.452724\pi$
$968$	4.08198	−	10.2146i	0.131200	−	0.328309i
$969$	−2.57119			−0.0825984
$970$	0.406924	−	1.25238i	0.0130655	−	0.0402116i
$971$	−9.93200	+	7.21602i	−0.318733	+	0.231573i	−0.735635	−	0.677378i	$-0.763116\pi$
$971$	−9.93200	+	7.21602i	−0.318733	+	0.231573i	0.416902	+	0.908952i	$0.363116\pi$
$972$	11.6565	+	8.46896i	0.373883	+	0.271642i
$973$	−10.6572	−	32.7995i	−0.341655	−	1.05150i
$974$	−1.97768	−	6.08668i	−0.0633691	−	0.195030i
$975$	−10.1219	−	7.35401i	−0.324161	−	0.235517i
$976$	−4.23312	+	3.07554i	−0.135499	+	0.0984458i
$977$	−7.56956	+	23.2967i	−0.242172	+	0.745328i	0.753917	+	0.656970i	$0.228162\pi$
$977$	−7.56956	+	23.2967i	−0.242172	+	0.745328i	−0.996089	+	0.0883583i	$0.971838\pi$
$978$	5.35137			0.171118
$979$	15.2760	−	4.41166i	0.488222	−	0.140997i
$980$	0.466587			0.0149046
$981$	3.93611	−	12.1141i	0.125670	−	0.386774i
$982$	−23.9935	+	17.4323i	−0.765662	+	0.556286i
$983$	27.0287	+	19.6375i	0.862082	+	0.626339i	0.928451	−	0.371456i	$-0.121141\pi$
$983$	27.0287	+	19.6375i	0.862082	+	0.626339i	−0.0663685	+	0.997795i	$0.521141\pi$
$984$	0.224665	+	0.691446i	0.00716204	+	0.0220425i
$985$	−0.936406	−	2.88196i	−0.0298364	−	0.0918269i
$986$	5.11626	+	3.71718i	0.162935	+	0.118379i
$987$	10.1601	−	7.38174i	0.323399	−	0.234963i
$988$	0.656165	−	2.01947i	0.0208754	−	0.0642479i
$989$	−69.3353			−2.20473
$990$	−0.0206847	+	0.626367i	−0.000657404	+	0.0199072i
$991$	−18.4683			−0.586664			−0.293332	−	0.956011i	$-0.594764\pi$
$991$	−18.4683			−0.586664			−0.293332	+	0.956011i	$0.594764\pi$
$992$	0.633297	−	1.94909i	0.0201072	−	0.0618836i
$993$	7.72430	−	5.61203i	0.245123	−	0.178092i
$994$	12.9412	+	9.40233i	0.410470	+	0.298224i
$995$	−0.265126	−	0.815975i	−0.00840507	−	0.0258681i
$996$	−3.45726	−	10.6403i	−0.109547	−	0.337152i
$997$	−30.1618	−	21.9138i	−0.955234	−	0.694018i	−0.00319484	−	0.999995i	$-0.501017\pi$
$997$	−30.1618	−	21.9138i	−0.955234	−	0.694018i	−0.952039	+	0.305977i	$0.901017\pi$
$998$	−8.39708	+	6.10083i	−0.265805	+	0.193118i
$999$	−3.43624	+	10.5756i	−0.108718	+	0.334599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.g.229.3	yes	16
11.4	even	5		4598.2.a.bw.1.4		8
11.5	even	5	inner	418.2.f.g.115.3	✓	16
11.7	odd	10		4598.2.a.bz.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.g.115.3	✓	16	11.5	even	5	inner
418.2.f.g.229.3	yes	16	1.1	even	1	trivial
4598.2.a.bw.1.4		8	11.4	even	5
4598.2.a.bz.1.4		8	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.956027 - 0.694595i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.0364140 - 0.112071i) q^{5} +(0.365170 + 1.12388i) q^{6} +(1.41067 + 1.02491i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.495524 + 1.52507i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.956027 - 0.694595i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.0364140 - 0.112071i) q^{5} +(0.365170 + 1.12388i) q^{6} +(1.41067 + 1.02491i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.495524 + 1.52507i) q^{9} +0.117838 q^{10} +(3.18641 - 0.920226i) q^{11} -1.18171 q^{12} +(0.656165 - 2.01947i) q^{13} +(-1.41067 + 1.02491i) q^{14} +(-0.112657 - 0.0818499i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.672362 + 2.06932i) q^{17} +(-1.29730 - 0.942543i) q^{18} +(-0.809017 + 0.587785i) q^{19} +(-0.0364140 + 0.112071i) q^{20} +2.06054 q^{21} +(-0.109466 + 3.31482i) q^{22} +6.90496 q^{23} +(0.365170 - 1.12388i) q^{24} +(4.03385 - 2.93076i) q^{25} +(1.71786 + 1.24810i) q^{26} +(1.68108 + 5.17383i) q^{27} +(-0.538830 - 1.65835i) q^{28} +(-2.35143 - 1.70841i) q^{29} +(0.112657 - 0.0818499i) q^{30} +(-0.633297 + 1.94909i) q^{31} -1.00000 q^{32} +(2.40711 - 3.09302i) q^{33} -2.17581 q^{34} +(0.0634948 - 0.195417i) q^{35} +(1.29730 - 0.942543i) q^{36} +(1.65368 + 1.20147i) q^{37} +(-0.309017 - 0.951057i) q^{38} +(-0.775400 - 2.38644i) q^{39} +(-0.0953332 - 0.0692636i) q^{40} +(-0.497734 + 0.361625i) q^{41} +(-0.636743 + 1.95969i) q^{42} -10.0414 q^{43} +(-3.11875 - 1.12844i) q^{44} +0.188960 q^{45} +(-2.13375 + 6.56701i) q^{46} +(4.93079 - 3.58243i) q^{47} +(0.956027 + 0.694595i) q^{48} +(-1.22357 - 3.76575i) q^{49} +(1.54079 + 4.74208i) q^{50} +(2.08013 + 1.51131i) q^{51} +(-1.71786 + 1.24810i) q^{52} +(-2.83556 + 8.72697i) q^{53} -5.44008 q^{54} +(-0.219161 - 0.323594i) q^{55} +1.74369 q^{56} +(-0.365170 + 1.12388i) q^{57} +(2.35143 - 1.70841i) q^{58} +(-4.54252 - 3.30034i) q^{59} +(0.0430310 + 0.132436i) q^{60} +(1.61691 + 4.97634i) q^{61} +(-1.65799 - 1.20460i) q^{62} +(-2.26209 + 1.64350i) q^{63} +(0.309017 - 0.951057i) q^{64} -0.250217 q^{65} +(2.19780 + 3.24509i) q^{66} -13.9348 q^{67} +(0.672362 - 2.06932i) q^{68} +(6.60133 - 4.79615i) q^{69} +(0.166231 + 0.120774i) q^{70} +(-2.83485 - 8.72478i) q^{71} +(0.495524 + 1.52507i) q^{72} +(-10.8850 - 7.90844i) q^{73} +(-1.65368 + 1.20147i) q^{74} +(1.82078 - 5.60378i) q^{75} +1.00000 q^{76} +(5.43813 + 1.96766i) q^{77} +2.50925 q^{78} +(-1.69197 + 5.20734i) q^{79} +(0.0953332 - 0.0692636i) q^{80} +(1.30897 + 0.951023i) q^{81} +(-0.190117 - 0.585121i) q^{82} +(2.92563 + 9.00415i) q^{83} +(-1.66701 - 1.21116i) q^{84} +(0.207427 - 0.150705i) q^{85} +(3.10295 - 9.54991i) q^{86} -3.43468 q^{87} +(2.03696 - 2.61740i) q^{88} +4.79411 q^{89} +(-0.0583917 + 0.179711i) q^{90} +(2.99542 - 2.17630i) q^{91} +(-5.58623 - 4.05863i) q^{92} +(0.748377 + 2.30327i) q^{93} +(1.88339 + 5.79649i) q^{94} +(0.0953332 + 0.0692636i) q^{95} +(-0.956027 + 0.694595i) q^{96} +(3.45324 - 10.6280i) q^{97} +3.95955 q^{98} +(-0.175535 + 5.31548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 - 10 * q^15 - 4 * q^16 + 6 * q^17 + q^18 - 4 * q^19 + q^20 + 14 * q^21 - 9 * q^22 - 26 * q^23 - q^24 + 33 * q^25 - 3 * q^26 + 13 * q^27 - 2 * q^28 + 10 * q^30 + 11 * q^31 - 16 * q^32 - 31 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 4 * q^38 + 12 * q^39 - q^40 - 7 * q^41 + 6 * q^42 + 66 * q^43 - 11 * q^44 - 42 * q^45 - 24 * q^46 + 47 * q^47 + q^48 + 24 * q^49 + 37 * q^50 - 41 * q^51 + 3 * q^52 + 15 * q^53 - 8 * q^54 - 9 * q^55 - 28 * q^56 + q^57 - 18 * q^59 + 5 * q^60 - 43 * q^61 + 9 * q^62 - 37 * q^63 - 4 * q^64 + 52 * q^65 - 39 * q^66 - 50 * q^67 + 6 * q^68 + 81 * q^69 - 11 * q^70 - 5 * q^71 + q^72 - 13 * q^73 + 39 * q^75 + 16 * q^76 - 10 * q^77 - 22 * q^78 + 5 * q^79 + q^80 + 2 * q^82 + 7 * q^83 - q^84 - 29 * q^85 + 29 * q^86 + 4 * q^87 - 4 * q^88 - 28 * q^89 - 18 * q^90 - 11 * q^92 - 5 * q^93 + 28 * q^94 + q^95 - q^96 - 11 * q^97 - 24 * q^98 + 43 * q^99

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