LMFDB - Embedded newform 416.2.bg.a.389.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(77,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 4]))

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

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

chi := DirichletCharacter("416.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bg (of order $8$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			389.15
Character	$\chi$	$=$	416.389
Dual form			416.2.bg.a.77.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.988066 - 1.01179i) q^{2} +(0.708345 + 1.71010i) q^{3} +(-0.0474507 + 1.99944i) q^{4} +(0.188293 - 0.454578i) q^{5} +(1.03037 - 2.40639i) q^{6} +(0.461953 - 0.461953i) q^{7} +(2.06990 - 1.92757i) q^{8} +(-0.301353 + 0.301353i) q^{9} +O(q^{10})$	\(q+(-0.988066 - 1.01179i) q^{2} +(0.708345 + 1.71010i) q^{3} +(-0.0474507 + 1.99944i) q^{4} +(0.188293 - 0.454578i) q^{5} +(1.03037 - 2.40639i) q^{6} +(0.461953 - 0.461953i) q^{7} +(2.06990 - 1.92757i) q^{8} +(-0.301353 + 0.301353i) q^{9} +(-0.645985 + 0.258640i) q^{10} +(1.38159 + 0.572271i) q^{11} +(-3.45284 + 1.33515i) q^{12} +(2.41776 - 2.67478i) q^{13} +(-0.923842 - 0.0109608i) q^{14} +0.910748 q^{15} +(-3.99550 - 0.189749i) q^{16} +1.70465i q^{17} +(0.602664 + 0.00715020i) q^{18} +(1.71519 + 4.14085i) q^{19} +(0.899966 + 0.398049i) q^{20} +(1.11721 + 0.462762i) q^{21} +(-0.786077 - 1.96332i) q^{22} +(-0.296689 + 0.296689i) q^{23} +(4.76252 + 2.17435i) q^{24} +(3.36435 + 3.36435i) q^{25} +(-5.09523 + 0.196586i) q^{26} +(4.40148 + 1.82315i) q^{27} +(0.901727 + 0.945567i) q^{28} +(-0.673717 - 1.62650i) q^{29} +(-0.899880 - 0.921489i) q^{30} +5.90554i q^{31} +(3.75583 + 4.23010i) q^{32} +2.76801i q^{33} +(1.72476 - 1.68431i) q^{34} +(-0.123012 - 0.296976i) q^{35} +(-0.588237 - 0.616836i) q^{36} +(-1.12127 + 2.70698i) q^{37} +(2.49495 - 5.82685i) q^{38} +(6.28673 + 2.23993i) q^{39} +(-0.486483 - 1.30388i) q^{40} +(-6.52404 - 6.52404i) q^{41} +(-0.635654 - 1.58762i) q^{42} +(-0.359462 + 0.867818i) q^{43} +(-1.20978 + 2.73524i) q^{44} +(0.0802460 + 0.193731i) q^{45} +(0.593335 + 0.00703953i) q^{46} +2.98116 q^{47} +(-2.50570 - 6.96709i) q^{48} +6.57320i q^{49} +(0.0798258 - 6.72822i) q^{50} +(-2.91512 + 1.20748i) q^{51} +(5.23333 + 4.96108i) q^{52} +(4.36373 - 10.5350i) q^{53} +(-2.50430 - 6.25478i) q^{54} +(0.520284 - 0.520284i) q^{55} +(0.0657523 - 1.84664i) q^{56} +(-5.86629 + 5.86629i) q^{57} +(-0.980001 + 2.28875i) q^{58} +(3.83383 - 9.25569i) q^{59} +(-0.0432156 + 1.82098i) q^{60} +(-3.18927 - 7.69957i) q^{61} +(5.97518 - 5.83506i) q^{62} +0.278422i q^{63} +(0.568981 - 7.97974i) q^{64} +(-0.760651 - 1.60270i) q^{65} +(2.80065 - 2.73497i) q^{66} +(-3.91099 + 1.61998i) q^{67} +(-3.40835 - 0.0808869i) q^{68} +(-0.717523 - 0.297208i) q^{69} +(-0.178935 + 0.417895i) q^{70} +(3.34826 - 3.34826i) q^{71} +(-0.0428932 + 1.20465i) q^{72} +(-7.51457 - 7.51457i) q^{73} +(3.84679 - 1.54018i) q^{74} +(-3.37024 + 8.13647i) q^{75} +(-8.36075 + 3.23294i) q^{76} +(0.902591 - 0.373865i) q^{77} +(-3.94536 - 8.57407i) q^{78} -2.03132i q^{79} +(-0.838578 + 1.78054i) q^{80} +10.0969i q^{81} +(-0.154796 + 13.0472i) q^{82} +(0.942068 + 2.27435i) q^{83} +(-0.978276 + 2.21183i) q^{84} +(0.774899 + 0.320974i) q^{85} +(1.23322 - 0.493760i) q^{86} +(2.30424 - 2.30424i) q^{87} +(3.96284 - 1.47855i) q^{88} +(-8.61592 + 8.61592i) q^{89} +(0.116727 - 0.272612i) q^{90} +(-0.118731 - 2.35252i) q^{91} +(-0.579132 - 0.607288i) q^{92} +(-10.0990 + 4.18316i) q^{93} +(-2.94558 - 3.01632i) q^{94} +2.20530 q^{95} +(-4.57345 + 9.41919i) q^{96} +12.2702i q^{97} +(6.65072 - 6.49475i) q^{98} +(-0.588801 + 0.243889i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9}+O(q^{10}) $ 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9	$ 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38} - 28 q^{39} + 32 q^{40} + 32 q^{42} - 8 q^{43} - 112 q^{48} + 16 q^{51} - 12 q^{52} - 8 q^{53} - 40 q^{55} - 48 q^{56} - 8 q^{61} + 56 q^{62} - 8 q^{64} - 8 q^{65} - 56 q^{66} - 8 q^{69} - 8 q^{74} - 16 q^{75} - 8 q^{77} + 84 q^{78} - 88 q^{82} - 8 q^{87} + 72 q^{88} + 88 q^{90} + 44 q^{91} - 80 q^{92} + 24 q^{94} + 112 q^{95}+O(q^{100}) $ 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.988066	−	1.01179i	−0.698668	−	0.715446i
$2$	−0.988066	−	1.01179i	−0.698668	−	0.715446i
$3$	0.708345	+	1.71010i	0.408963	+	0.987324i	0.985411	+	0.170190i	$0.0544382\pi$
$3$	0.708345	+	1.71010i	0.408963	+	0.987324i	−0.576448	+	0.817134i	$0.695562\pi$
$4$	−0.0474507	+	1.99944i	−0.0237253	+	0.999719i
$5$	0.188293	−	0.454578i	0.0842070	−	0.203294i	−0.876167	−	0.482007i	$-0.839908\pi$
$5$	0.188293	−	0.454578i	0.0842070	−	0.203294i	0.960374	+	0.278713i	$0.0899080\pi$
$6$	1.03037	−	2.40639i	0.420647	−	0.982403i
$7$	0.461953	−	0.461953i	0.174602	−	0.174602i	−0.614396	−	0.788998i	$-0.710600\pi$
$7$	0.461953	−	0.461953i	0.174602	−	0.174602i	0.788998	+	0.614396i	$0.210600\pi$
$8$	2.06990	−	1.92757i	0.731821	−	0.681497i
$9$	−0.301353	+	0.301353i	−0.100451	+	0.100451i
$10$	−0.645985	+	0.258640i	−0.204278	+	0.0817893i
$11$	1.38159	+	0.572271i	0.416564	+	0.172546i	0.581114	−	0.813822i	$-0.302617\pi$
$11$	1.38159	+	0.572271i	0.416564	+	0.172546i	−0.164550	+	0.986369i	$0.552617\pi$
$12$	−3.45284	+	1.33515i	−0.996749	+	0.385423i
$13$	2.41776	−	2.67478i	0.670566	−	0.741850i
$13$	2.41776	−	2.67478i	0.670566	−	0.741850i
$14$	−0.923842	−	0.0109608i	−0.246907	−	0.00292939i
$15$	0.910748			0.235154
$16$	−3.99550	−	0.189749i	−0.998874	−	0.0474373i
$17$			1.70465i			0.413439i	0.978400	+	0.206720i	$0.0662788\pi$
$17$			1.70465i			0.413439i	−0.978400	+	0.206720i	$0.933721\pi$
$18$	0.602664	+	0.00715020i	0.142049	+	0.00168532i
$19$	1.71519	+	4.14085i	0.393493	+	0.949975i	0.989173	+	0.146754i	$0.0468824\pi$
$19$	1.71519	+	4.14085i	0.393493	+	0.949975i	−0.595681	+	0.803221i	$0.703118\pi$
$20$	0.899966	+	0.398049i	0.201239	+	0.0890065i
$21$	1.11721	+	0.462762i	0.243794	+	0.100983i
$22$	−0.786077	−	1.96332i	−0.167592	−	0.418581i
$23$	−0.296689	+	0.296689i	−0.0618638	+	0.0618638i	−0.737362	−	0.675498i	$-0.763929\pi$
$23$	−0.296689	+	0.296689i	−0.0618638	+	0.0618638i	0.675498	+	0.737362i	$0.263929\pi$
$24$	4.76252	+	2.17435i	0.972146	+	0.443837i
$25$	3.36435	+	3.36435i	0.672869	+	0.672869i
$26$	−5.09523	+	0.196586i	−0.999257	+	0.0385537i
$27$	4.40148	+	1.82315i	0.847065	+	0.350866i
$28$	0.901727	+	0.945567i	0.170410	+	0.178695i
$29$	−0.673717	−	1.62650i	−0.125106	−	0.302033i	0.848900	−	0.528553i	$-0.177265\pi$
$29$	−0.673717	−	1.62650i	−0.125106	−	0.302033i	−0.974007	+	0.226520i	$0.927265\pi$
$30$	−0.899880	−	0.921489i	−0.164295	−	0.168240i
$31$			5.90554i			1.06067i	0.847789	+	0.530333i	$0.177933\pi$
$31$			5.90554i			1.06067i	−0.847789	+	0.530333i	$0.822067\pi$
$32$	3.75583	+	4.23010i	0.663943	+	0.747783i
$33$			2.76801i			0.481848i
$34$	1.72476	−	1.68431i	0.295793	−	0.288857i
$35$	−0.123012	−	0.296976i	−0.0207928	−	0.0501982i
$36$	−0.588237	−	0.616836i	−0.0980395	−	0.102806i
$37$	−1.12127	+	2.70698i	−0.184335	+	0.445025i	−0.988851	−	0.148906i	$-0.952425\pi$
$37$	−1.12127	+	2.70698i	−0.184335	+	0.445025i	0.804516	+	0.593931i	$0.202425\pi$
$38$	2.49495	−	5.82685i	0.404735	−	0.945240i
$39$	6.28673	+	2.23993i	1.00668	+	0.358676i
$40$	−0.486483	−	1.30388i	−0.0769197	−	0.206161i
$41$	−6.52404	−	6.52404i	−1.01888	−	1.01888i	−0.999818	−	0.0190655i	$-0.993931\pi$
$41$	−6.52404	−	6.52404i	−1.01888	−	1.01888i	−0.0190655	−	0.999818i	$-0.506069\pi$
$42$	−0.635654	−	1.58762i	−0.0980836	−	0.244975i
$43$	−0.359462	+	0.867818i	−0.0548174	+	0.132341i	−0.948916	−	0.315530i	$-0.897818\pi$
$43$	−0.359462	+	0.867818i	−0.0548174	+	0.132341i	0.894098	+	0.447871i	$0.147818\pi$
$44$	−1.20978	+	2.73524i	−0.182381	+	0.412353i
$45$	0.0802460	+	0.193731i	0.0119624	+	0.0288797i
$46$	0.593335	+	0.00703953i	0.0874825	+	0.00103792i
$47$	2.98116			0.434847			0.217423	−	0.976077i	$-0.430235\pi$
$47$	2.98116			0.434847			0.217423	+	0.976077i	$0.430235\pi$
$48$	−2.50570	−	6.96709i	−0.361667	−	1.00561i
$49$			6.57320i			0.939028i
$50$	0.0798258	−	6.72822i	0.0112891	−	0.951514i
$51$	−2.91512	+	1.20748i	−0.408198	+	0.169081i
$52$	5.23333	+	4.96108i	0.725732	+	0.687978i
$53$	4.36373	−	10.5350i	0.599405	−	1.44709i	−0.274784	−	0.961506i	$-0.588606\pi$
$53$	4.36373	−	10.5350i	0.599405	−	1.44709i	0.874189	−	0.485586i	$-0.161394\pi$
$54$	−2.50430	−	6.25478i	−0.340792	−	0.851168i
$55$	0.520284	−	0.520284i	0.0701551	−	0.0701551i
$56$	0.0657523	−	1.84664i	0.00878652	−	0.246768i
$57$	−5.86629	+	5.86629i	−0.777009	+	0.777009i
$58$	−0.980001	+	2.28875i	−0.128680	+	0.300527i
$59$	3.83383	−	9.25569i	0.499122	−	1.20499i	−0.450835	−	0.892607i	$-0.648874\pi$
$59$	3.83383	−	9.25569i	0.499122	−	1.20499i	0.949957	−	0.312380i	$-0.101126\pi$
$60$	−0.0432156	+	1.82098i	−0.00557911	+	0.235088i
$61$	−3.18927	−	7.69957i	−0.408344	−	0.985829i	−0.985574	−	0.169247i	$-0.945866\pi$
$61$	−3.18927	−	7.69957i	−0.408344	−	0.985829i	0.577230	−	0.816582i	$-0.304134\pi$
$62$	5.97518	−	5.83506i	0.758849	−	0.741054i
$63$			0.278422i			0.0350779i
$64$	0.568981	−	7.97974i	0.0711226	−	0.997468i
$65$	−0.760651	−	1.60270i	−0.0943471	−	0.198791i
$66$	2.80065	−	2.73497i	0.344736	−	0.336652i
$67$	−3.91099	+	1.61998i	−0.477803	+	0.197913i	−0.608569	−	0.793501i	$-0.708256\pi$
$67$	−3.91099	+	1.61998i	−0.477803	+	0.197913i	0.130766	+	0.991413i	$0.458256\pi$
$68$	−3.40835	−	0.0808869i	−0.413323	−	0.00980898i
$69$	−0.717523	−	0.297208i	−0.0863797	−	0.0357796i
$70$	−0.178935	+	0.417895i	−0.0213868	+	0.0499480i
$71$	3.34826	−	3.34826i	0.397365	−	0.397365i	−0.479938	−	0.877303i	$-0.659341\pi$
$71$	3.34826	−	3.34826i	0.397365	−	0.397365i	0.877303	+	0.479938i	$0.159341\pi$
$72$	−0.0428932	+	1.20465i	−0.00505501	+	0.141969i
$73$	−7.51457	−	7.51457i	−0.879514	−	0.879514i	0.113970	−	0.993484i	$-0.463643\pi$
$73$	−7.51457	−	7.51457i	−0.879514	−	0.879514i	−0.993484	+	0.113970i	$0.963643\pi$
$74$	3.84679	−	1.54018i	0.447180	−	0.179043i
$75$	−3.37024	+	8.13647i	−0.389161	+	0.939519i
$76$	−8.36075	+	3.23294i	−0.959043	+	0.370843i
$77$	0.902591	−	0.373865i	0.102860	−	0.0426059i
$78$	−3.94536	−	8.57407i	−0.446724	−	0.970823i
$79$		−	2.03132i		−	0.228541i	−0.993450	−	0.114271i	$-0.963547\pi$
$79$		−	2.03132i		−	0.228541i	0.993450	−	0.114271i	$-0.0364531\pi$
$80$	−0.838578	+	1.78054i	−0.0937559	+	0.199070i
$81$			10.0969i			1.12188i
$82$	−0.154796	+	13.0472i	−0.0170943	+	1.44082i
$83$	0.942068	+	2.27435i	0.103405	+	0.249643i	0.967111	−	0.254353i	$-0.0818626\pi$
$83$	0.942068	+	2.27435i	0.103405	+	0.249643i	−0.863706	+	0.503996i	$0.831863\pi$
$84$	−0.978276	+	2.21183i	−0.106739	+	0.241330i
$85$	0.774899	+	0.320974i	0.0840496	+	0.0348145i
$86$	1.23322	−	0.493760i	0.132982	−	0.0532436i
$87$	2.30424	−	2.30424i	0.247040	−	0.247040i
$88$	3.96284	−	1.47855i	0.422440	−	0.157614i
$89$	−8.61592	+	8.61592i	−0.913285	+	0.913285i	−0.996529	−	0.0832439i	$-0.973472\pi$
$89$	−8.61592	+	8.61592i	−0.913285	+	0.913285i	0.0832439	+	0.996529i	$0.473472\pi$
$90$	0.116727	−	0.272612i	0.0123041	−	0.0287358i
$91$	−0.118731	−	2.35252i	−0.0124464	−	0.246611i
$92$	−0.579132	−	0.607288i	−0.0603787	−	0.0633142i
$93$	−10.0990	+	4.18316i	−1.04722	+	0.433773i
$94$	−2.94558	−	3.01632i	−0.303814	−	0.311109i
$95$	2.20530			0.226259
$96$	−4.57345	+	9.41919i	−0.466776	+	0.961342i
$97$			12.2702i			1.24585i	0.782283	+	0.622923i	$0.214055\pi$
$97$			12.2702i			1.24585i	−0.782283	+	0.622923i	$0.785945\pi$
$98$	6.65072	−	6.49475i	0.671824	−	0.656069i
$99$	−0.588801	+	0.243889i	−0.0591767	+	0.0245118i
$100$	−6.88644	+	6.56716i	−0.688644	+	0.656716i
$101$	−11.2836	−	4.67382i	−1.12276	−	0.465063i	−0.257447	−	0.966292i	$-0.582881\pi$
$101$	−11.2836	−	4.67382i	−1.12276	−	0.465063i	−0.865314	+	0.501230i	$0.832881\pi$
$102$	4.10205	+	1.75643i	0.406164	+	0.173912i
$103$	2.38759	+	2.38759i	0.235257	+	0.235257i	0.814883	−	0.579626i	$-0.196801\pi$
$103$	2.38759	+	2.38759i	0.235257	+	0.235257i	−0.579626	+	0.814883i	$0.696801\pi$
$104$	−0.151290	−	10.1969i	−0.0148352	−	0.999890i
$105$	0.420723	−	0.420723i	0.0410584	−	0.0410584i
$106$	−14.9709	+	5.99407i	−1.45410	+	0.582195i
$107$	−1.74409	+	4.21061i	−0.168608	+	0.407055i	−0.985486	−	0.169754i	$-0.945703\pi$
$107$	−1.74409	+	4.21061i	−0.168608	+	0.407055i	0.816879	+	0.576810i	$0.195703\pi$
$108$	−3.85413	+	8.71398i	−0.370864	+	0.838503i
$109$	0.0424496	+	0.102482i	0.00406593	+	0.00981602i	0.925899	−	0.377770i	$-0.123309\pi$
$109$	0.0424496	+	0.102482i	0.00406593	+	0.00981602i	−0.921834	+	0.387586i	$0.873309\pi$
$110$	−1.04050	−	0.0123448i	−0.0992074	−	0.00117703i
$111$	−5.42343			−0.514770
$112$	−1.93339	+	1.75808i	−0.182688	+	0.166123i
$113$		−	0.620082i		−	0.0583324i	−0.999575	−	0.0291662i	$-0.990715\pi$
$113$		−	0.620082i		−	0.0583324i	0.999575	−	0.0291662i	$-0.00928521\pi$
$114$	11.7318	+	0.139189i	1.09878	+	0.0130363i
$115$	0.0790040	+	0.190732i	0.00736716	+	0.0177859i
$116$	3.28405	−	1.26988i	0.304916	−	0.117905i
$117$	0.0774536	+	1.53465i	0.00716059	+	0.141879i
$118$	−13.1529	+	5.26619i	−1.21082	+	0.484792i
$119$	0.787471	+	0.787471i	0.0721873	+	0.0721873i
$120$	1.88516	−	1.75553i	0.172091	−	0.160257i
$121$	−6.19689	−	6.19689i	−0.563354	−	0.563354i
$122$	−4.63916	+	10.8346i	−0.420010	+	0.980915i
$123$	6.53546	−	15.7780i	0.589283	−	1.42265i
$124$	−11.8078	−	0.280222i	−1.06037	−	0.0251647i
$125$	4.43573	−	1.83734i	0.396744	−	0.164337i
$126$	0.281706	−	0.275099i	0.0250963	−	0.0245078i
$127$	−0.973394			−0.0863748			−0.0431874	−	0.999067i	$-0.513751\pi$
$127$	−0.973394			−0.0863748			−0.0431874	+	0.999067i	$0.513751\pi$
$128$	−8.63604	+	7.30882i	−0.763325	+	0.646015i
$129$	−1.73867			−0.153082
$130$	−0.870030	+	2.35320i	−0.0763067	+	0.206389i
$131$	−5.01068	−	12.0968i	−0.437785	−	1.05691i	−0.976712	−	0.214554i	$-0.931170\pi$
$131$	−5.01068	−	12.0968i	−0.437785	−	1.05691i	0.538927	−	0.842352i	$-0.318830\pi$
$132$	−5.53446	−	0.131344i	−0.481713	−	0.0114320i
$133$	2.70522	+	1.12054i	0.234572	+	0.0971630i
$134$	5.50341	+	2.35646i	0.475422	+	0.203567i
$135$	1.65753	−	1.65753i	0.142658	−	0.142658i
$136$	3.28583	+	3.52846i	0.281758	+	0.302563i
$137$	0.364614	+	0.364614i	0.0311511	+	0.0311511i	0.722511	−	0.691360i	$-0.242988\pi$
$137$	0.364614	+	0.364614i	0.0311511	+	0.0311511i	−0.691360	+	0.722511i	$0.742988\pi$
$138$	0.408248	+	1.01965i	0.0347523	+	0.0867981i
$139$	3.43692	−	8.29746i	0.291516	−	0.703781i	−0.708482	−	0.705728i	$-0.750620\pi$
$139$	3.43692	−	8.29746i	0.291516	−	0.703781i	0.999998	+	0.00194742i	$0.000619883\pi$
$140$	0.599623	−	0.231862i	0.0506774	−	0.0195959i
$141$	2.11169	+	5.09807i	0.177836	+	0.429335i
$142$	−6.69604	−	0.0794441i	−0.561920	−	0.00666680i
$143$	4.87104	−	2.31182i	0.407337	−	0.193324i
$144$	1.26124	−	1.14687i	0.105103	−	0.0955728i
$145$	−0.866226			−0.0719362
$146$	−0.178298	+	15.0281i	−0.0147561	+	1.24373i
$147$	−11.2408	+	4.65609i	−0.927125	+	0.384028i
$148$	−5.35923	−	2.37035i	−0.440526	−	0.194842i
$149$	0.293634	+	0.121627i	0.0240554	+	0.00996408i	0.394679	−	0.918819i	$-0.370856\pi$
$149$	0.293634	+	0.121627i	0.0240554	+	0.00996408i	−0.370623	+	0.928783i	$0.620856\pi$
$150$	11.5624	−	4.62939i	0.944069	−	0.377988i
$151$	3.69084	+	3.69084i	0.300356	+	0.300356i	0.841153	−	0.540797i	$-0.181877\pi$
$151$	3.69084	+	3.69084i	0.300356	+	0.300356i	−0.540797	+	0.841153i	$0.681877\pi$
$152$	11.5320	+	5.26499i	0.935372	+	0.427047i
$153$	−0.513702	−	0.513702i	−0.0415304	−	0.0415304i
$154$	−1.27009	−	0.543832i	−0.102347	−	0.0438232i
$155$	2.68453	+	1.11197i	0.215627	+	0.0893155i
$156$	−4.77691	+	12.4636i	−0.382459	+	0.997890i
$157$	−7.38244	−	17.8228i	−0.589183	−	1.42241i	−0.884285	−	0.466947i	$-0.845354\pi$
$157$	−7.38244	−	17.8228i	−0.589183	−	1.42241i	0.295103	−	0.955466i	$-0.404646\pi$
$158$	−2.05527	+	2.00708i	−0.163509	+	0.159674i
$159$	21.1069			1.67388
$160$	2.63011	−	0.910822i	0.207928	−	0.0720068i
$161$			0.274113i			0.0216031i
$162$	10.2160	−	9.97641i	0.802643	−	0.783821i
$163$	−5.49408	+	2.27572i	−0.430330	+	0.178248i	−0.587325	−	0.809351i	$-0.699819\pi$
$163$	−5.49408	+	2.27572i	−0.430330	+	0.178248i	0.156996	+	0.987599i	$0.449819\pi$
$164$	13.3540	−	12.7348i	1.04277	−	0.994424i
$165$	1.25828	+	0.521195i	0.0979567	+	0.0405750i
$166$	1.37035	−	3.20039i	0.106360	−	0.248398i
$167$	10.1509	−	10.1509i	0.785502	−	0.785502i	−0.195251	−	0.980753i	$-0.562552\pi$
$167$	10.1509	−	10.1509i	0.785502	−	0.785502i	0.980753	+	0.195251i	$0.0625522\pi$
$168$	3.20451	−	1.19562i	0.247233	−	0.0922439i
$169$	−1.30888	−	12.9339i	−0.100683	−	0.994919i
$170$	−0.440892	−	1.10118i	−0.0338149	−	0.0844567i
$171$	−1.76473	−	0.730977i	−0.134953	−	0.0558992i
$172$	−1.71809	−	0.759900i	−0.131003	−	0.0579419i
$173$	−4.25029	+	1.76053i	−0.323143	+	0.133850i	−0.538358	−	0.842716i	$-0.680955\pi$
$173$	−4.25029	+	1.76053i	−0.323143	+	0.133850i	0.215214	+	0.976567i	$0.430955\pi$
$174$	−4.60816	−	0.0546727i	−0.349343	−	0.00414473i
$175$	3.10834			0.234969
$176$	−5.41153	−	2.54866i	−0.407910	−	0.192113i
$177$	18.5438			1.39384
$178$	17.2306	+	0.204430i	1.29149	+	0.0153227i
$179$	−13.8803	+	5.74941i	−1.03746	+	0.429731i	−0.835401	−	0.549641i	$-0.814764\pi$
$179$	−13.8803	+	5.74941i	−1.03746	+	0.429731i	−0.202063	+	0.979373i	$0.564764\pi$
$180$	−0.391161	+	0.151254i	−0.0291554	+	0.0112738i
$181$	1.30262	−	3.14481i	0.0968233	−	0.233752i	−0.868045	−	0.496485i	$-0.834624\pi$
$181$	1.30262	−	3.14481i	0.0968233	−	0.233752i	0.964869	+	0.262733i	$0.0846238\pi$
$182$	−2.26294	+	2.44457i	−0.167741	+	0.181204i
$183$	10.9079	−	10.9079i	0.806335	−	0.806335i
$184$	−0.0422293	+	1.18600i	−0.00311318	+	0.0874333i
$185$	1.01941	+	1.01941i	0.0749484	+	0.0749484i
$186$	14.2110	+	6.08490i	1.04200	+	0.446166i
$187$	−0.975524	+	2.35512i	−0.0713374	+	0.172224i
$188$	−0.141458	+	5.96064i	−0.0103169	+	0.434724i
$189$	2.87549	−	1.19107i	0.209161	−	0.0866374i
$190$	−2.17898	−	2.23130i	−0.158080	−	0.161876i
$191$	−12.1468			−0.878909			−0.439455	−	0.898265i	$-0.644828\pi$
$191$	−12.1468			−0.878909			−0.439455	+	0.898265i	$0.644828\pi$
$192$	14.0492	−	4.67940i	1.01391	−	0.337706i
$193$			1.62930i			0.117280i	0.998279	+	0.0586398i	$0.0186763\pi$
$193$			1.62930i			0.117280i	−0.998279	+	0.0586398i	$0.981324\pi$
$194$	12.4149	−	12.1237i	0.891335	−	0.870433i
$195$	2.20197	−	2.43605i	0.157686	−	0.174449i
$196$	−13.1427	−	0.311903i	−0.938764	−	0.0222788i
$197$	3.92644	−	9.47927i	0.279747	−	0.675370i	−0.720081	−	0.693890i	$-0.755895\pi$
$197$	3.92644	−	9.47927i	0.279747	−	0.675370i	0.999828	+	0.0185200i	$0.00589544\pi$
$198$	0.828539	+	0.354766i	0.0588817	+	0.0252121i
$199$	2.47641	+	2.47641i	0.175548	+	0.175548i	0.789412	−	0.613864i	$-0.210386\pi$
$199$	2.47641	+	2.47641i	0.175548	+	0.175548i	−0.613864	+	0.789412i	$0.710386\pi$
$200$	13.4489	+	0.478865i	0.950978	+	0.0338609i
$201$	−5.54066	−	5.54066i	−0.390808	−	0.390808i
$202$	6.42001	+	16.0347i	0.451710	+	1.12820i
$203$	−1.06259	−	0.440140i	−0.0745793	−	0.0308918i
$204$	−2.27596	−	5.88589i	−0.159349	−	0.412095i
$205$	−4.19412	+	1.73726i	−0.292930	+	0.121335i
$206$	0.0566505	−	4.77485i	0.00394702	−	0.332680i
$207$		−	0.178816i		−	0.0124286i
$208$	−10.1677	+	10.2283i	−0.705002	+	0.709205i
$209$			6.70249i			0.463621i
$210$	−0.841388	−	0.00998250i	−0.0580613	−	0.000688858i
$211$	−12.5227	+	5.18705i	−0.862095	+	0.357091i	−0.769527	−	0.638615i	$-0.779508\pi$
$211$	−12.5227	+	5.18705i	−0.862095	+	0.357091i	−0.0925685	+	0.995706i	$0.529508\pi$
$212$	20.8570	+	9.22490i	1.43246	+	0.633569i
$213$	8.09756	+	3.35412i	0.554836	+	0.229820i
$214$	5.98355	−	2.39570i	0.409027	−	0.163767i
$215$	0.326807	+	0.326807i	0.0222881	+	0.0222881i
$216$	12.6249	−	4.71040i	0.859014	−	0.320502i
$217$	2.72808	+	2.72808i	0.185194	+	0.185194i
$218$	0.0617479	−	0.144209i	0.00418210	−	0.00976710i
$219$	7.52773	−	18.1735i	0.508677	−	1.22805i
$220$	1.01559	+	1.06496i	0.0684709	+	0.0717998i
$221$	4.55957	+	4.12144i	0.306710	+	0.277238i
$222$	5.35871	+	5.48739i	0.359653	+	0.368290i
$223$			29.1843i			1.95433i	0.212486	+	0.977164i	$0.431844\pi$
$223$			29.1843i			1.95433i	−0.212486	+	0.977164i	$0.568156\pi$
$224$	3.68913	+	0.219092i	0.246490	+	0.0146387i
$225$	−2.02771			−0.135181
$226$	−0.627395	+	0.612682i	−0.0417337	+	0.0407550i
$227$	16.3200	−	6.75998i	1.08320	−	0.448676i	0.231569	−	0.972819i	$-0.425614\pi$
$227$	16.3200	−	6.75998i	1.08320	−	0.448676i	0.851630	+	0.524143i	$0.175614\pi$
$228$	−11.4509	−	12.0076i	−0.758356	−	0.795225i
$229$	8.92301	−	21.5421i	0.589649	−	1.42354i	−0.294190	−	0.955747i	$-0.595050\pi$
$229$	8.92301	−	21.5421i	0.589649	−	1.42354i	0.883839	−	0.467792i	$-0.154950\pi$
$230$	0.114921	−	0.268392i	0.00757764	−	0.0176972i
$231$	1.27869	+	1.27869i	0.0841317	+	0.0841317i
$232$	−4.52971	−	2.06805i	−0.297390	−	0.135774i
$233$	0.364868	−	0.364868i	0.0239033	−	0.0239033i	−0.695054	−	0.718957i	$-0.744620\pi$
$233$	0.364868	−	0.364868i	0.0239033	−	0.0239033i	0.718957	+	0.695054i	$0.244620\pi$
$234$	1.47622	−	1.59470i	0.0965035	−	0.104249i
$235$	0.561330	−	1.35517i	0.0366171	−	0.0884016i
$236$	18.3242	+	8.10469i	1.19281	+	0.527571i
$237$	3.47375	−	1.43887i	0.225644	−	0.0934648i
$238$	0.0186843	−	1.57483i	0.00121112	−	0.102081i
$239$	−20.7234			−1.34048			−0.670242	−	0.742142i	$-0.733810\pi$
$239$	−20.7234			−1.34048			−0.670242	+	0.742142i	$0.733810\pi$
$240$	−3.63889	−	0.172814i	−0.234889	−	0.0111551i
$241$	17.6098			1.13435			0.567174	−	0.823598i	$-0.308037\pi$
$241$	17.6098			1.13435			0.567174	+	0.823598i	$0.308037\pi$
$242$	−0.147034	+	12.3929i	−0.00945168	+	0.796646i
$243$	−4.06222	+	1.68263i	−0.260592	+	0.107941i
$244$	15.5461	−	6.01139i	0.995239	−	0.384840i
$245$	2.98803	+	1.23768i	0.190898	+	0.0790727i
$246$	−22.4215	+	8.97717i	−1.42954	+	0.572363i
$247$	15.2228	+	5.42380i	0.968602	+	0.345108i
$248$	11.3833	+	12.2239i	0.722841	+	0.776217i
$249$	−3.22205	+	3.22205i	−0.204189	+	0.204189i
$250$	−6.24181	−	2.67263i	−0.394766	−	0.169032i
$251$	−23.4125	−	9.69777i	−1.47778	−	0.612118i	−0.509164	−	0.860669i	$-0.670045\pi$
$251$	−23.4125	−	9.69777i	−1.47778	−	0.612118i	−0.968619	+	0.248552i	$0.920045\pi$
$252$	−0.556687	−	0.0132113i	−0.0350680	−	0.000832234i
$253$	−0.579687	+	0.240114i	−0.0364446	+	0.0150959i
$254$	0.961778	+	0.984874i	0.0603473	+	0.0617965i
$255$			1.55251i			0.0972220i
$256$	15.9280	+	1.51628i	0.995499	+	0.0947678i
$257$	−17.4302			−1.08727			−0.543634	−	0.839322i	$-0.682952\pi$
$257$	−17.4302			−1.08727			−0.543634	+	0.839322i	$0.682952\pi$
$258$	1.71793	+	1.75918i	0.106953	+	0.109522i
$259$	0.732525	+	1.76847i	0.0455169	+	0.109887i
$260$	3.24060	−	1.44482i	0.200973	−	0.0896042i
$261$	0.693176	+	0.287123i	0.0429065	+	0.0177725i
$262$	−7.28862	+	17.0222i	−0.450293	+	1.05164i
$263$	14.0738	+	14.0738i	0.867829	+	0.867829i	0.992232	−	0.124403i	$-0.0397016\pi$
$263$	14.0738	+	14.0738i	0.867829	+	0.867829i	−0.124403	+	0.992232i	$0.539702\pi$
$264$	5.33552	+	5.72950i	0.328378	+	0.352626i
$265$	−3.96732	−	3.96732i	−0.243710	−	0.243710i
$266$	−1.53918	−	3.84429i	−0.0943733	−	0.235708i
$267$	−20.8371	−	8.63100i	−1.27521	−	0.528209i
$268$	−3.05348	−	7.89665i	−0.186521	−	0.482364i
$269$	−8.55228	+	3.54247i	−0.521442	+	0.215988i	−0.627850	−	0.778334i	$-0.716065\pi$
$269$	−8.55228	+	3.54247i	−0.521442	+	0.215988i	0.106408	+	0.994323i	$0.466065\pi$
$270$	−3.31483	−	0.0393283i	−0.201734	−	0.00239344i
$271$	−28.3589			−1.72268			−0.861341	−	0.508026i	$-0.830375\pi$
$271$	−28.3589			−1.72268			−0.861341	+	0.508026i	$0.830375\pi$
$272$	0.323457	−	6.81094i	0.0196124	−	0.412974i
$273$	3.93892	−	1.86943i	0.238394	−	0.113143i
$274$	0.00865119	−	0.729176i	0.000522638	−	0.0440511i
$275$	2.72281	+	6.57345i	0.164192	+	0.396394i
$276$	0.628296	−	1.42054i	0.0378189	−	0.0855065i
$277$	−5.29158	+	12.7750i	−0.317940	+	0.767575i	0.681423	+	0.731890i	$0.261361\pi$
$277$	−5.29158	+	12.7750i	−0.317940	+	0.767575i	−0.999363	+	0.0356855i	$0.988639\pi$
$278$	−11.7912	+	4.72098i	−0.707190	+	0.283146i
$279$	−1.77965	−	1.77965i	−0.106545	−	0.106545i
$280$	−0.827064	−	0.377599i	−0.0494265	−	0.0225658i
$281$	18.3723	−	18.3723i	1.09600	−	1.09600i	0.101128	−	0.994873i	$-0.467755\pi$
$281$	18.3723	−	18.3723i	1.09600	−	1.09600i	0.994873	−	0.101128i	$-0.0322450\pi$
$282$	3.07170	−	7.17382i	0.182917	−	0.427195i
$283$	−14.4932	−	6.00329i	−0.861532	−	0.356858i	−0.0922257	−	0.995738i	$-0.529398\pi$
$283$	−14.4932	−	6.00329i	−0.861532	−	0.356858i	−0.769307	+	0.638880i	$0.779398\pi$
$284$	6.53575	+	6.85351i	0.387826	+	0.406681i
$285$	1.56211	+	3.77127i	0.0925314	+	0.223391i
$286$	−7.15199	−	2.64425i	−0.422906	−	0.156358i
$287$	−6.02761			−0.355798
$288$	−2.40658	−	0.142924i	−0.141809	−	0.00842185i
$289$	14.0942			0.829068
$290$	0.855889	+	0.876442i	0.0502595	+	0.0514664i
$291$	−20.9831	+	8.69150i	−1.23005	+	0.509505i
$292$	15.3815	−	14.6683i	0.900133	−	0.858400i
$293$	2.89098	−	6.97945i	0.168893	−	0.407744i	−0.816658	−	0.577122i	$-0.804176\pi$
$293$	2.89098	−	6.97945i	0.168893	−	0.407744i	0.985551	+	0.169378i	$0.0541758\pi$
$294$	15.8176	+	6.77283i	0.922504	+	0.395000i
$295$	−3.48555	−	3.48555i	−0.202937	−	0.202937i
$296$	2.89697	+	7.76449i	0.168383	+	0.451302i
$297$	5.03768	+	5.03768i	0.292316	+	0.292316i
$298$	−0.167068	−	0.417272i	−0.00967800	−	0.0241719i
$299$	0.0762548	+	1.51090i	0.00440993	+	0.0873775i
$300$	−16.1084	−	7.12466i	−0.930021	−	0.411342i
$301$	0.234837	+	0.566946i	0.0135358	+	0.0326782i
$302$	0.0875725	−	7.38116i	0.00503923	−	0.424738i
$303$		−	22.6067i		−	1.29872i
$304$	−6.06733	−	16.8702i	−0.347985	−	0.967572i
$305$	−4.10057			−0.234798
$306$	−0.0121886	+	1.02733i	−0.000696777	+	0.0587287i
$307$	8.30084	+	20.0400i	0.473754	+	1.14374i	0.962491	+	0.271312i	$0.0874576\pi$
$307$	8.30084	+	20.0400i	0.473754	+	1.14374i	−0.488738	+	0.872431i	$0.662542\pi$
$308$	0.704692	+	1.82241i	0.0401535	+	0.103842i
$309$	−2.39177	+	5.77425i	−0.136063	+	0.328486i
$310$	−1.52741	−	3.81489i	−0.0867511	−	0.216671i
$311$	−14.7231	+	14.7231i	−0.834868	+	0.834868i	−0.988178	−	0.153310i	$-0.951007\pi$
$311$	−14.7231	+	14.7231i	−0.834868	+	0.834868i	0.153310	+	0.988178i	$0.451007\pi$
$312$	17.3305	−	7.48165i	0.981148	−	0.423565i
$313$	21.1911	+	21.1911i	1.19779	+	1.19779i	0.974827	+	0.222963i	$0.0715730\pi$
$313$	21.1911	+	21.1911i	1.19779	+	1.19779i	0.222963	+	0.974827i	$0.428427\pi$
$314$	−10.7386	+	25.0796i	−0.606016	+	1.41532i
$315$	0.126565	+	0.0524248i	0.00713111	+	0.00295380i
$316$	4.06149	+	0.0963873i	0.228477	+	0.00542221i
$317$	−12.3388	+	5.11092i	−0.693019	+	0.287058i	−0.701257	−	0.712908i	$-0.747378\pi$
$317$	−12.3388	+	5.11092i	−0.693019	+	0.287058i	0.00823863	+	0.999966i	$0.497378\pi$
$318$	−20.8550	−	21.3558i	−1.16949	−	1.19757i
$319$		−	2.63269i		−	0.147402i
$320$	−3.52028	−	1.76117i	−0.196790	−	0.0984525i
$321$	−8.43597			−0.470850
$322$	0.277345	−	0.270841i	0.0154558	−	0.0150934i
$323$	−7.05871	+	2.92381i	−0.392757	+	0.162685i
$324$	−20.1881	−	0.479105i	−1.12156	−	0.0266169i
$325$	17.1331	−	0.864703i	0.950371	−	0.0479651i
$326$	7.73108	+	3.31031i	0.428185	+	0.183341i
$327$	−0.145186	+	0.145186i	−0.00802878	+	0.00802878i
$328$	−26.0796	−	0.928601i	−1.44001	−	0.0512734i
$329$	1.37716	−	1.37716i	0.0759251	−	0.0759251i
$330$	−0.715919	−	1.78809i	−0.0394100	−	0.0984312i
$331$	−18.2407	−	7.55556i	−1.00260	−	0.415291i	−0.179851	−	0.983694i	$-0.557562\pi$
$331$	−18.2407	−	7.55556i	−1.00260	−	0.415291i	−0.822750	+	0.568403i	$0.807562\pi$
$332$	−4.59213	+	1.77569i	−0.252026	+	0.0974534i
$333$	−0.477859	−	1.15365i	−0.0261865	−	0.0632198i
$334$	−20.3004	−	0.240851i	−1.11079	−	0.0131788i
$335$			2.08288i			0.113800i
$336$	−4.37599	−	2.06095i	−0.238730	−	0.112434i
$337$			10.8947i			0.593471i	0.954960	+	0.296735i	$0.0958979\pi$
$337$			10.8947i			0.593471i	−0.954960	+	0.296735i	$0.904102\pi$
$338$	−11.7932	+	14.1039i	−0.641466	+	0.767151i
$339$	1.06040	−	0.439232i	0.0575930	−	0.0238558i
$340$	−0.678536	+	1.53413i	−0.0367988	+	0.0831999i
$341$	−3.37957	+	8.15901i	−0.183014	+	0.441835i
$342$	1.00408	+	2.50780i	0.0542943	+	0.135606i
$343$	6.27019	+	6.27019i	0.338558	+	0.338558i
$344$	0.928726	+	2.48918i	0.0500735	+	0.134208i
$345$	−0.270209	+	0.270209i	−0.0145475	+	0.0145475i
$346$	5.98085	+	2.56089i	0.321533	+	0.137675i
$347$	20.9941	+	8.69603i	1.12702	+	0.466827i	0.866767	−	0.498713i	$-0.166194\pi$
$347$	20.9941	+	8.69603i	1.12702	+	0.466827i	0.260254	+	0.965540i	$0.416194\pi$
$348$	4.49785	+	4.71652i	0.241110	+	0.252832i
$349$	−16.9769	+	7.03206i	−0.908752	+	0.376417i	−0.787579	−	0.616214i	$-0.788666\pi$
$349$	−16.9769	+	7.03206i	−0.908752	+	0.376417i	−0.121173	+	0.992631i	$0.538666\pi$
$350$	−3.07125	−	3.14500i	−0.164165	−	0.168107i
$351$	15.5183	−	7.36504i	0.828303	−	0.393117i
$352$	2.76823	+	7.99360i	0.147547	+	0.426060i
$353$		−	2.98134i		−	0.158681i	−0.996848	−	0.0793405i	$-0.974719\pi$
$353$		−	2.98134i		−	0.158681i	0.996848	−	0.0793405i	$-0.0252814\pi$
$354$	−18.3225	−	18.7625i	−0.973829	−	0.997214i
$355$	−0.891594	−	2.15250i	−0.0473209	−	0.114243i
$356$	−16.8182	−	17.6358i	−0.891360	−	0.934696i
$357$	−0.788849	+	1.90445i	−0.0417503	+	0.100794i
$358$	19.5319	+	8.36320i	1.03229	+	0.442009i
$359$	−15.3508	+	15.3508i	−0.810186	+	0.810186i	−0.984661	−	0.174476i	$-0.944177\pi$
$359$	−15.3508	+	15.3508i	−0.810186	+	0.810186i	0.174476	+	0.984661i	$0.444177\pi$
$360$	0.539531	+	0.246325i	0.0284358	+	0.0129824i
$361$	−0.769680	+	0.769680i	−0.0405095	+	0.0405095i
$362$	−4.46898	+	1.78930i	−0.234884	+	0.0940434i
$363$	6.20774	−	14.9868i	0.325822	−	0.786603i
$364$	4.70934	−	0.125767i	0.246837	−	0.00659198i
$365$	−4.83090	+	2.00102i	−0.252861	+	0.104738i
$366$	−21.8143	−	0.258812i	−1.14025	−	0.0135283i
$367$		−	16.4932i		−	0.860940i	−0.902605	−	0.430470i	$-0.858348\pi$
$367$		−	16.4932i		−	0.860940i	0.902605	−	0.430470i	$-0.141652\pi$
$368$	1.24171	−	1.12912i	0.0647289	−	0.0588595i
$369$	3.93208			0.204696
$370$	0.0241875	−	2.03867i	0.00125745	−	0.105986i
$371$	−2.85083	−	6.88252i	−0.148008	−	0.357322i
$372$	−7.88475	−	20.3909i	−0.408805	−	1.05722i
$373$	7.62771	−	18.4149i	0.394948	−	0.953489i	−0.593897	−	0.804541i	$-0.702411\pi$
$373$	7.62771	−	18.4149i	0.394948	−	0.953489i	0.988845	−	0.148948i	$-0.0475886\pi$
$374$	3.34678	−	1.33999i	0.173058	−	0.0692892i
$375$	6.28405	+	6.28405i	0.324507	+	0.324507i
$376$	6.17071	−	5.74638i	0.318230	−	0.296347i
$377$	−5.97940	−	2.13043i	−0.307955	−	0.109723i
$378$	−4.04629	−	1.73255i	−0.208119	−	0.0891127i
$379$	−7.99430	+	19.2999i	−0.410639	+	0.991371i	0.574327	+	0.818626i	$0.305264\pi$
$379$	−7.99430	+	19.2999i	−0.410639	+	0.991371i	−0.984967	+	0.172745i	$0.944736\pi$
$380$	−0.104643	+	4.40935i	−0.00536806	+	0.226195i
$381$	−0.689499	−	1.66460i	−0.0353241	−	0.0852799i
$382$	12.0018	+	12.2900i	0.614066	+	0.628812i
$383$		−	11.2990i		−	0.577350i	−0.957427	−	0.288675i	$-0.906785\pi$
$383$		−	11.2990i		−	0.577350i	0.957427	−	0.288675i	$-0.0932147\pi$
$384$	−18.6161	−	9.59128i	−0.949997	−	0.489453i
$385$		−	0.480694i		−	0.0244985i
$386$	1.64852	−	1.60986i	0.0839072	−	0.0819396i
$387$	−0.153195	−	0.369845i	−0.00778732	−	0.0188003i
$388$	−24.5334	−	0.582227i	−1.24549	−	0.0295581i
$389$	27.2079	+	11.2699i	1.37949	+	0.571405i	0.944346	−	0.328954i	$-0.106696\pi$
$389$	27.2079	+	11.2699i	1.37949	+	0.571405i	0.435148	+	0.900359i	$0.356696\pi$
$390$	−4.64047	+	0.179041i	−0.234979	+	0.00906608i
$391$	−0.505751	−	0.505751i	−0.0255769	−	0.0255769i
$392$	12.6703	+	13.6059i	0.639945	+	0.687200i
$393$	17.1375	−	17.1375i	0.864471	−	0.864471i
$394$	−13.4706	+	5.39340i	−0.678641	+	0.271715i
$395$	−0.923393	−	0.382482i	−0.0464609	−	0.0192448i
$396$	−0.459702	−	1.18884i	−0.0231009	−	0.0597416i
$397$	11.8644	+	28.6432i	0.595457	+	1.43756i	0.878166	+	0.478355i	$0.158767\pi$
$397$	11.8644	+	28.6432i	0.595457	+	1.43756i	−0.282709	+	0.959206i	$0.591233\pi$
$398$	0.0587578	−	4.95247i	0.00294526	−	0.248245i
$399$			5.41991i			0.271335i
$400$	−12.8039	−	14.0806i	−0.640193	−	0.704031i
$401$	−2.36965			−0.118335			−0.0591673	−	0.998248i	$-0.518845\pi$
$401$	−2.36965			−0.118335			−0.0591673	+	0.998248i	$0.518845\pi$
$402$	−0.131463	+	11.0805i	−0.00655679	+	0.552647i
$403$	15.7960	+	14.2782i	0.786855	+	0.711246i
$404$	9.88043	−	22.3391i	0.491570	−	1.11141i
$405$	4.58984	+	1.90117i	0.228071	+	0.0944700i
$406$	0.604580	+	1.51001i	0.0300048	+	0.0749405i
$407$	−3.09825	+	3.09825i	−0.153575	+	0.153575i
$408$	−3.70651	+	8.11845i	−0.183500	+	0.401923i
$409$	5.06984	−	5.06984i	0.250687	−	0.250687i	−0.570565	−	0.821252i	$-0.693276\pi$
$409$	5.06984	−	5.06984i	0.250687	−	0.250687i	0.821252	+	0.570565i	$0.193276\pi$
$410$	5.90181	+	2.52705i	0.291470	+	0.124802i
$411$	−0.365252	+	0.881796i	−0.0180166	+	0.0434958i
$412$	−4.88714	+	4.66055i	−0.240772	+	0.229609i
$413$	−2.50465	−	6.04675i	−0.123246	−	0.297541i
$414$	−0.180925	+	0.176682i	−0.00889197	+	0.00868345i
$415$	1.21126			0.0594582
$416$	20.3953	+	0.181356i	0.999960	+	0.00889170i
$417$	16.6240			0.814079
$418$	6.78153	−	6.62250i	0.331696	−	0.323917i
$419$	5.05066	+	12.1934i	0.246741	+	0.595685i	0.997924	−	0.0644091i	$-0.0205163\pi$
$419$	5.05066	+	12.1934i	0.246741	+	0.595685i	−0.751183	+	0.660094i	$0.770516\pi$
$420$	0.821246	+	0.861174i	0.0400727	+	0.0420210i
$421$	13.6692	−	33.0004i	0.666196	−	1.60834i	−0.121726	−	0.992564i	$-0.538843\pi$
$421$	13.6692	−	33.0004i	0.666196	−	1.60834i	0.787922	−	0.615775i	$-0.211157\pi$
$422$	17.6214	+	7.54518i	0.857798	+	0.367294i
$423$	−0.898381	+	0.898381i	−0.0436808	+	0.0436808i
$424$	−11.2744	−	30.2178i	−0.547532	−	1.46750i
$425$	−5.73505	+	5.73505i	−0.278191	+	0.278191i
$426$	−4.60725	−	11.5071i	−0.223222	−	0.557523i
$427$	−5.03013	−	2.08355i	−0.243425	−	0.100830i
$428$	−8.33610	−	3.68700i	−0.402941	−	0.178218i
$429$	7.40381	+	6.69238i	0.357459	+	0.323111i
$430$	0.00775416	−	0.653569i	0.000373939	−	0.0315179i
$431$	−22.0169			−1.06052			−0.530258	−	0.847836i	$-0.677905\pi$
$431$	−22.0169			−1.06052			−0.530258	+	0.847836i	$0.677905\pi$
$432$	−17.2402	−	8.11958i	−0.829468	−	0.390654i
$433$		−	22.2918i		−	1.07128i	−0.844448	−	0.535638i	$-0.820071\pi$
$433$		−	22.2918i		−	1.07128i	0.844448	−	0.535638i	$-0.179929\pi$
$434$	0.0647293	−	5.45578i	0.00310710	−	0.261886i
$435$	−0.613587	−	1.48133i	−0.0294192	−	0.0710243i
$436$	−0.206921	+	0.0800124i	−0.00990972	+	0.00383190i
$437$	−1.73742	−	0.719663i	−0.0831121	−	0.0344261i
$438$	−25.8258	+	10.3402i	−1.23400	+	0.494072i
$439$	−4.24373	+	4.24373i	−0.202542	+	0.202542i	−0.801088	−	0.598546i	$-0.795745\pi$
$439$	−4.24373	+	4.24373i	−0.202542	+	0.202542i	0.598546	+	0.801088i	$0.295745\pi$
$440$	0.0740548	−	2.07982i	0.00353043	−	0.0991515i
$441$	−1.98085	−	1.98085i	−0.0943263	−	0.0943263i
$442$	−0.335112	−	8.68560i	−0.0159396	−	0.413132i
$443$	14.7828	+	6.12325i	0.702354	+	0.290925i	0.705136	−	0.709072i	$-0.250886\pi$
$443$	14.7828	+	6.12325i	0.702354	+	0.290925i	−0.00278255	+	0.999996i	$0.500886\pi$
$444$	0.257346	−	10.8438i	0.0122131	−	0.514625i
$445$	2.29430	+	5.53892i	0.108760	+	0.262570i
$446$	29.5285	−	28.8361i	1.39822	−	1.36543i
$447$			0.588296i			0.0278254i
$448$	−3.42343	−	3.94911i	−0.161742	−	0.186578i
$449$			10.1764i			0.480254i	0.970742	+	0.240127i	$0.0771890\pi$
$449$			10.1764i			0.480254i	−0.970742	+	0.240127i	$0.922811\pi$
$450$	2.00351	+	2.05162i	0.0944465	+	0.0967145i
$451$	−5.28000	−	12.7470i	−0.248625	−	0.600235i
$452$	1.23981	+	0.0294233i	0.0583160	+	0.00138396i
$453$	−3.69730	+	8.92607i	−0.173714	+	0.419383i
$454$	−22.9650	−	9.83319i	−1.07780	−	0.461495i
$455$	−1.09176	−	0.388989i	−0.0511825	−	0.0182361i
$456$	−0.834980	+	23.4503i	−0.0391015	+	1.09816i
$457$	11.1580	+	11.1580i	0.521951	+	0.521951i	0.918160	−	0.396209i	$-0.129674\pi$
$457$	11.1580	+	11.1580i	0.521951	+	0.521951i	−0.396209	+	0.918160i	$0.629674\pi$
$458$	−30.6126	+	12.2567i	−1.43043	+	0.572719i
$459$	−3.10784	+	7.50300i	−0.145062	+	0.350210i
$460$	−0.385106	+	0.148913i	−0.0179557	+	0.00694311i
$461$	1.53461	+	3.70488i	0.0714740	+	0.172553i	0.955579	−	0.294734i	$-0.0952312\pi$
$461$	1.53461	+	3.70488i	0.0714740	+	0.172553i	−0.884105	+	0.467288i	$0.845231\pi$
$462$	0.0303395	−	2.55720i	0.00141152	−	0.118972i
$463$	−25.6755			−1.19324			−0.596620	−	0.802524i	$-0.703490\pi$
$463$	−25.6755			−1.19324			−0.596620	+	0.802524i	$0.703490\pi$
$464$	2.38321	+	6.62650i	0.110638	+	0.307627i
$465$			5.37846i			0.249420i
$466$	−0.729684	−	0.00865721i	−0.0338020	−	0.000401038i
$467$	36.7938	−	15.2405i	1.70261	−	0.705245i	0.702632	−	0.711553i	$-0.252008\pi$
$467$	36.7938	−	15.2405i	1.70261	−	0.705245i	0.999980	+	0.00630848i	$0.00200807\pi$
$468$	−3.07211	+	0.0820435i	−0.142009	+	0.00379246i
$469$	−1.05834	+	2.55505i	−0.0488695	+	0.117981i
$470$	−1.92578	+	0.771049i	−0.0888298	+	0.0355658i
$471$	25.2493	−	25.2493i	1.16343	−	1.16343i
$472$	−9.90529	−	26.5483i	−0.455928	−	1.22199i
$473$	−0.993255	+	0.993255i	−0.0456699	+	0.0456699i
$474$	−4.88813	−	2.09301i	−0.224519	−	0.0961352i
$475$	−8.16073	+	19.7017i	−0.374440	+	0.903978i
$476$	−1.61186	+	1.53713i	−0.0738797	+	0.0704543i
$477$	1.85972	+	4.48977i	0.0851510	+	0.205573i
$478$	20.4761	+	20.9678i	0.936554	+	0.959044i
$479$		−	31.1146i		−	1.42166i	−0.703362	−	0.710832i	$-0.748319\pi$
$479$		−	31.1146i		−	1.42166i	0.703362	−	0.710832i	$-0.251681\pi$
$480$	3.42061	+	3.85256i	0.156129	+	0.175844i
$481$	4.52961	+	9.54396i	0.206533	+	0.435167i
$482$	−17.3996	−	17.8175i	−0.792532	−	0.811564i
$483$	−0.468759	+	0.194166i	−0.0213293	+	0.00883487i
$484$	12.6843	−	12.0962i	0.576561	−	0.549829i
$485$	5.57775	+	2.31038i	0.253272	+	0.104909i
$486$	5.71622	+	2.44758i	0.259293	+	0.111025i
$487$	16.0346	−	16.0346i	0.726597	−	0.726597i	−0.243343	−	0.969940i	$-0.578244\pi$
$487$	16.0346	−	16.0346i	0.726597	−	0.726597i	0.969940	+	0.243343i	$0.0782441\pi$
$488$	−21.4429	−	9.78983i	−0.970674	−	0.443165i
$489$	−7.78341	−	7.78341i	−0.351978	−	0.351978i
$490$	−1.70009	−	4.24619i	−0.0768025	−	0.191823i
$491$	7.98933	−	19.2879i	0.360553	−	0.870453i	−0.634666	−	0.772787i	$-0.718862\pi$
$491$	7.98933	−	19.2879i	0.360553	−	0.870453i	0.995219	−	0.0976660i	$-0.0311377\pi$
$492$	31.2370	+	13.8159i	1.40827	+	0.622870i
$493$	2.77261	−	1.14845i	0.124872	−	0.0517238i
$494$	−9.55334	−	20.7614i	−0.429825	−	0.934098i
$495$			0.313579i			0.0140943i
$496$	1.12057	−	23.5956i	0.0503151	−	1.05947i
$497$		−	3.09348i		−	0.138761i
$498$	6.44365	+	0.0764496i	0.288747	+	0.00342579i
$499$	−1.27410	−	3.07595i	−0.0570366	−	0.137698i	0.892792	−	0.450469i	$-0.148743\pi$
$499$	−1.27410	−	3.07595i	−0.0570366	−	0.137698i	−0.949829	+	0.312770i	$0.898743\pi$
$500$	3.46317	+	8.95615i	0.154878	+	0.400531i
$501$	24.5494	+	10.1687i	1.09679	+	0.454304i
$502$	13.3209	+	33.2706i	0.594543	+	1.48494i
$503$	−30.1649	+	30.1649i	−1.34499	+	1.34499i	−0.453970	+	0.891017i	$0.649993\pi$
$503$	−30.1649	+	30.1649i	−1.34499	+	1.34499i	−0.891017	+	0.453970i	$0.850007\pi$
$504$	0.536677	+	0.576306i	0.0239055	+	0.0256707i
$505$	−4.24924	+	4.24924i	−0.189089	+	0.189089i
$506$	0.815715	+	0.349275i	0.0362630	+	0.0155271i
$507$	21.1911	−	11.4000i	0.941131	−	0.506292i
$508$	0.0461882	−	1.94624i	0.00204927	−	0.0863505i
$509$	−35.6760	+	14.7775i	−1.58131	+	0.655000i	−0.988621	−	0.150431i	$-0.951934\pi$
$509$	−35.6760	+	14.7775i	−1.58131	+	0.655000i	−0.592690	+	0.805431i	$0.701934\pi$
$510$	1.57082	−	1.53398i	0.0695571	−	0.0679259i
$511$	−6.94277			−0.307130
$512$	−14.2037	−	17.6140i	−0.627723	−	0.778437i
$513$			21.3529i			0.942754i
$514$	17.2222	+	17.6358i	0.759640	+	0.777881i
$515$	1.53492	−	0.635783i	0.0676365	−	0.0280159i
$516$	0.0825013	−	3.47637i	0.00363192	−	0.153039i
$517$	4.11873	+	1.70603i	0.181141	+	0.0750312i
$518$	1.06554	−	2.48853i	0.0468173	−	0.109340i
$519$	−6.02134	−	6.02134i	−0.264307	−	0.264307i
$520$	−4.66379	−	1.85123i	−0.204521	−	0.0811818i
$521$	−21.8069	+	21.8069i	−0.955379	+	0.955379i	−0.999046	−	0.0436669i	$-0.986096\pi$
$521$	−21.8069	+	21.8069i	−0.955379	+	0.955379i	0.0436669	+	0.999046i	$0.486096\pi$
$522$	−0.394395	−	0.985047i	−0.0172622	−	0.0431143i
$523$	3.49352	−	8.43410i	0.152761	−	0.368798i	−0.828910	−	0.559382i	$-0.811038\pi$
$523$	3.49352	−	8.43410i	0.152761	−	0.368798i	0.981671	+	0.190585i	$0.0610384\pi$
$524$	24.4246	−	9.44453i	1.06700	−	0.412586i
$525$	2.20178	+	5.31556i	0.0960935	+	0.231990i
$526$	0.333929	−	28.1457i	0.0145600	−	1.22721i
$527$	−10.0669			−0.438521
$528$	0.525227	−	11.0596i	0.0228576	−	0.481306i
$529$			22.8240i			0.992346i
$530$	−0.0941326	+	7.93408i	−0.00408886	+	0.344634i
$531$	1.63389	+	3.94456i	0.0709049	+	0.171180i
$532$	−2.36881	+	5.35574i	−0.102701	+	0.232201i
$533$	−33.2239	+	1.67681i	−1.43909	+	0.0726306i
$534$	11.8556	+	29.6108i	0.513043	+	1.28138i
$535$	1.58565	+	1.58565i	0.0685538	+	0.0685538i
$536$	−4.97273	+	10.8919i	−0.214789	+	0.470458i
$537$	−19.6641	−	19.6641i	−0.848568	−	0.848568i
$538$	12.0345	+	5.15295i	0.518843	+	0.222159i
$539$	−3.76165	+	9.08143i	−0.162026	+	0.391165i
$540$	3.23548	+	3.39278i	0.139233	+	0.146002i
$541$	41.4646	−	17.1752i	1.78270	−	0.738420i	0.790701	−	0.612202i	$-0.209716\pi$
$541$	41.4646	−	17.1752i	1.78270	−	0.738420i	0.992002	−	0.126218i	$-0.0402840\pi$
$542$	28.0205	+	28.6934i	1.20358	+	1.23249i
$543$	6.30064			0.270386
$544$	−7.21086	+	6.40239i	−0.309163	+	0.274500i
$545$	0.0545792			0.00233791
$546$	−5.78340	−	2.13825i	−0.247506	−	0.0915087i
$547$	13.4907	+	32.5695i	0.576821	+	1.39257i	0.895651	+	0.444758i	$0.146710\pi$
$547$	13.4907	+	32.5695i	0.576821	+	1.39257i	−0.318830	+	0.947812i	$0.603290\pi$
$548$	−0.746323	+	0.711721i	−0.0318814	+	0.0304032i
$549$	3.28138	+	1.35919i	0.140046	+	0.0580089i
$550$	3.96065	−	9.24993i	0.168883	−	0.394418i
$551$	5.57952	−	5.57952i	0.237695	−	0.237695i
$552$	−2.05809	+	0.767883i	−0.0875981	+	0.0326833i
$553$	−0.938374	−	0.938374i	−0.0399037	−	0.0399037i
$554$	18.1541	−	7.26856i	0.771293	−	0.308812i
$555$	−1.02119	+	2.46538i	−0.0433472	+	0.104649i
$556$	16.4272	+	7.26562i	0.696667	+	0.308131i
$557$	12.0907	+	29.1896i	0.512300	+	1.23680i	0.942542	+	0.334088i	$0.108428\pi$
$557$	12.0907	+	29.1896i	0.512300	+	1.23680i	−0.430241	+	0.902714i	$0.641572\pi$
$558$	−0.0422258	+	3.55905i	−0.00178756	+	0.150667i
$559$	1.45213	+	3.05966i	0.0614185	+	0.129410i
$560$	0.435142	+	1.20991i	0.0183881	+	0.0511280i
$561$	−4.71849			−0.199215
$562$	−36.7421	−	0.435920i	−1.54987	−	0.0183882i
$563$	−14.3928	+	5.96171i	−0.606586	+	0.251256i	−0.664768	−	0.747050i	$-0.731470\pi$
$563$	−14.3928	+	5.96171i	−0.606586	+	0.251256i	0.0581820	+	0.998306i	$0.481470\pi$
$564$	−10.2935	+	3.98028i	−0.433433	+	0.167600i
$565$	−0.281876	−	0.116757i	−0.0118586	−	0.00491200i
$566$	8.24617	+	20.5958i	0.346612	+	0.865705i
$567$	4.66430	+	4.66430i	0.195882	+	0.195882i
$568$	0.476575	−	13.3846i	0.0199967	−	0.561603i
$569$	−7.36313	−	7.36313i	−0.308679	−	0.308679i	0.535718	−	0.844397i	$-0.320041\pi$
$569$	−7.36313	−	7.36313i	−0.308679	−	0.308679i	−0.844397	+	0.535718i	$0.820041\pi$
$570$	2.27227	−	5.30680i	0.0951751	−	0.222277i
$571$	26.2464	+	10.8716i	1.09838	+	0.454963i	0.856921	−	0.515448i	$-0.172375\pi$
$571$	26.2464	+	10.8716i	1.09838	+	0.454963i	0.241457	+	0.970411i	$0.422375\pi$
$572$	4.39121	+	9.84903i	0.183606	+	0.411809i
$573$	−8.60410	−	20.7721i	−0.359441	−	0.867768i
$574$	5.95567	+	6.09869i	0.248585	+	0.254554i
$575$	−1.99633			−0.0832526
$576$	2.23325	+	2.57618i	0.0930523	+	0.107341i
$577$		−	26.3446i		−	1.09674i	−0.836235	−	0.548371i	$-0.815248\pi$
$577$		−	26.3446i		−	1.09674i	0.836235	−	0.548371i	$-0.184752\pi$
$578$	−13.9260	−	14.2604i	−0.579243	−	0.593153i
$579$	−2.78626	+	1.15411i	−0.115793	+	0.0479630i
$580$	0.0411030	−	1.73196i	0.00170671	−	0.0719159i
$581$	1.48584	+	0.615454i	0.0616429	+	0.0255333i
$582$	29.5267	+	12.6428i	1.22392	+	0.524061i
$583$	12.0577	−	12.0577i	0.499381	−	0.499381i
$584$	−30.0393	−	1.06959i	−1.24303	−	0.0442599i
$585$	0.712203	+	0.253755i	0.0294460	+	0.0104915i
$586$	−9.91824	+	3.97108i	−0.409719	+	0.164044i
$587$	28.8897	+	11.9665i	1.19241	+	0.493911i	0.888538	−	0.458803i	$-0.151722\pi$
$587$	28.8897	+	11.9665i	1.19241	+	0.493911i	0.303869	+	0.952714i	$0.401722\pi$
$588$	−8.77617	−	22.6962i	−0.361923	−	0.935975i
$589$	−24.4539	+	10.1291i	−1.00761	+	0.417364i
$590$	−0.0827017	+	6.97062i	−0.00340478	+	0.286976i
$591$	18.9917			0.781215
$592$	4.99367	−	10.6030i	0.205238	−	0.435779i
$593$	2.98017			0.122381			0.0611904	−	0.998126i	$-0.480510\pi$
$593$	2.98017			0.122381			0.0611904	+	0.998126i	$0.480510\pi$
$594$	0.119529	−	10.0747i	0.00490434	−	0.413368i
$595$	0.506242	−	0.209692i	0.0207539	−	0.00859655i
$596$	−0.257119	+	0.581331i	−0.0105320	+	0.0238123i
$597$	−2.48075	+	5.98905i	−0.101530	+	0.245115i
$598$	1.45337	−	1.57002i	0.0594328	−	0.0642029i
$599$	−27.4165	+	27.4165i	−1.12021	+	1.12021i	−0.128499	+	0.991710i	$0.541016\pi$
$599$	−27.4165	+	27.4165i	−1.12021	+	1.12021i	−0.991710	+	0.128499i	$0.958984\pi$
$600$	8.70752	+	23.3380i	0.355483	+	0.952771i
$601$	15.2667	+	15.2667i	0.622740	+	0.622740i	0.946231	−	0.323491i	$-0.104857\pi$
$601$	15.2667	+	15.2667i	0.622740	+	0.622740i	−0.323491	+	0.946231i	$0.604857\pi$
$602$	0.341598	−	0.797787i	0.0139225	−	0.0325154i
$603$	0.690401	−	1.66678i	0.0281153	−	0.0678763i
$604$	−7.55473	+	7.20446i	−0.307398	+	0.293146i
$605$	−3.98380	+	1.65014i	−0.161965	+	0.0670879i
$606$	−22.8733	+	22.3369i	−0.929166	+	0.907376i
$607$	−40.3989			−1.63974			−0.819870	−	0.572550i	$-0.805954\pi$
$607$	−40.3989			−1.63974			−0.819870	+	0.572550i	$0.805954\pi$
$608$	−11.0742	+	22.8077i	−0.449119	+	0.924976i
$609$		−	2.12890i		−	0.0862675i
$610$	4.05164	+	4.14893i	0.164046	+	0.167985i
$611$	7.20773	−	7.97394i	0.291593	−	0.322591i
$612$	1.05149	−	1.00274i	0.0425040	−	0.0405334i
$613$	8.65286	−	20.8899i	0.349486	−	0.843733i	−0.647195	−	0.762324i	$-0.724058\pi$
$613$	8.65286	−	20.8899i	0.349486	−	0.843733i	0.996681	−	0.0814088i	$-0.0259419\pi$
$614$	12.0746	−	28.1996i	0.487289	−	1.13804i
$615$	−5.94176	−	5.94176i	−0.239595	−	0.239595i
$616$	1.14762	−	2.51367i	0.0462391	−	0.101279i
$617$	−8.57525	−	8.57525i	−0.345227	−	0.345227i	0.513101	−	0.858328i	$-0.328496\pi$
$617$	−8.57525	−	8.57525i	−0.345227	−	0.345227i	−0.858328	+	0.513101i	$0.828496\pi$
$618$	8.20558	−	3.28536i	0.330077	−	0.132157i
$619$	−41.8914	−	17.3520i	−1.68376	−	0.697435i	−0.684263	−	0.729235i	$-0.739876\pi$
$619$	−41.8914	−	17.3520i	−1.68376	−	0.697435i	−0.999494	+	0.0318003i	$0.989876\pi$
$620$	−2.35069	+	5.31479i	−0.0944062	+	0.213447i
$621$	−1.84678	+	0.764961i	−0.0741087	+	0.0306968i
$622$	29.4441	+	0.349334i	1.18060	+	0.0140070i
$623$			7.96030i			0.318923i
$624$	−24.6936	−	10.1425i	−0.988535	−	0.406027i
$625$			21.4272i			0.857087i
$626$	0.502801	−	42.3792i	0.0200960	−	1.69381i
$627$	−11.4619	+	4.74767i	−0.457744	+	0.189604i
$628$	35.9858	−	13.9150i	1.43599	−	0.555270i
$629$	−4.61446	−	1.91137i	−0.183991	−	0.0762114i
$630$	−0.0720112	−	0.179856i	−0.00286900	−	0.00716565i
$631$	−6.56786	−	6.56786i	−0.261463	−	0.261463i	0.564186	−	0.825648i	$-0.309190\pi$
$631$	−6.56786	−	6.56786i	−0.261463	−	0.261463i	−0.825648	+	0.564186i	$0.809190\pi$
$632$	−3.91550	−	4.20463i	−0.155750	−	0.167251i
$633$	−17.7407	−	17.7407i	−0.705130	−	0.705130i
$634$	17.3628	+	7.43443i	0.689564	+	0.295259i
$635$	−0.183283	+	0.442484i	−0.00727336	+	0.0175594i
$636$	−1.00153	+	42.2018i	−0.0397134	+	1.67341i
$637$	17.5819	+	15.8924i	0.696618	+	0.629680i
$638$	−2.66374	+	2.60127i	−0.105458	+	0.102985i
$639$			2.01801i			0.0798314i
$640$	1.69633	+	5.30195i	0.0670534	+	0.209578i
$641$	−38.7471			−1.53042			−0.765209	−	0.643781i	$-0.777365\pi$
$641$	−38.7471			−1.53042			−0.765209	+	0.643781i	$0.777365\pi$
$642$	8.33530	+	8.53546i	0.328968	+	0.336868i
$643$	43.8206	−	18.1511i	1.72812	−	0.715809i	0.728593	−	0.684947i	$-0.240175\pi$
$643$	43.8206	−	18.1511i	1.72812	−	0.715809i	0.999524	−	0.0308625i	$-0.00982540\pi$
$644$	−0.548071	−	0.0130068i	−0.0215970	−	0.000512541i
$645$	−0.327379	+	0.790364i	−0.0128906	+	0.0311206i
$646$	9.93276	+	4.25303i	0.390799	+	0.167333i
$647$	−21.2512	−	21.2512i	−0.835470	−	0.835470i	0.152789	−	0.988259i	$-0.451174\pi$
$647$	−21.2512	−	21.2512i	−0.835470	−	0.835470i	−0.988259	+	0.152789i	$0.951174\pi$
$648$	19.4624	+	20.8996i	0.764557	+	0.821014i
$649$	10.5935	−	10.5935i	0.415832	−	0.415832i
$650$	−17.8035	−	16.4807i	−0.698311	−	0.646427i
$651$	−2.73286	+	6.59771i	−0.107109	+	0.258585i
$652$	−4.28947	−	11.0931i	−0.167989	−	0.434438i
$653$	13.2308	−	5.48038i	0.517761	−	0.214464i	−0.108472	−	0.994100i	$-0.534596\pi$
$653$	13.2308	−	5.48038i	0.517761	−	0.214464i	0.626233	+	0.779636i	$0.284596\pi$
$654$	0.290351	+	0.00344482i	0.0113536	+	0.000134703i
$655$	−6.44244			−0.251727
$656$	24.8288	+	27.3047i	0.969404	+	1.06607i
$657$	4.52908			0.176696
$658$	−2.75412	−	0.0326758i	−0.107367	−	0.00127384i
$659$	41.4075	−	17.1515i	1.61301	−	0.668129i	0.619828	−	0.784738i	$-0.287202\pi$
$659$	41.4075	−	17.1515i	1.61301	−	0.668129i	0.993178	+	0.116609i	$0.0372023\pi$
$660$	−1.10180	+	2.49111i	−0.0428876	+	0.0969665i
$661$	−14.5349	−	6.02056i	−0.565342	−	0.234172i	0.0816603	−	0.996660i	$-0.473978\pi$
$661$	−14.5349	−	6.02056i	−0.565342	−	0.234172i	−0.647003	+	0.762488i	$0.723978\pi$
$662$	10.3784	+	25.9212i	0.403367	+	1.00746i
$663$	−3.81831	+	10.7167i	−0.148291	+	0.416202i
$664$	6.33395	+	2.89179i	0.245805	+	0.112223i
$665$	1.01874	−	1.01874i	0.0395052	−	0.0395052i
$666$	−0.695102	+	1.62338i	−0.0269347	+	0.0629047i
$667$	0.682447	+	0.282679i	0.0264245	+	0.0109454i
$668$	19.8145	+	20.7778i	0.766645	+	0.803917i
$669$	−49.9080	+	20.6726i	−1.92956	+	0.799248i
$670$	2.10745	−	2.05803i	0.0814178	−	0.0795085i
$671$		−	12.4627i		−	0.481119i
$672$	2.23851	+	6.46395i	0.0863522	+	0.249352i
$673$	15.4736			0.596462			0.298231	−	0.954494i	$-0.403603\pi$
$673$	15.4736			0.596462			0.298231	+	0.954494i	$0.403603\pi$
$674$	11.0232	−	10.7647i	0.424596	−	0.414639i
$675$	8.67439	+	20.9418i	0.333877	+	0.806051i
$676$	25.9227	−	2.00330i	0.997027	−	0.0770502i
$677$	−23.6793	−	9.80828i	−0.910069	−	0.376963i	−0.121986	−	0.992532i	$-0.538926\pi$
$677$	−23.6793	−	9.80828i	−0.910069	−	0.376963i	−0.788083	+	0.615569i	$0.788926\pi$
$678$	−1.49216	−	0.638915i	−0.0573059	−	0.0245374i
$679$	5.66824	+	5.66824i	0.217527	+	0.217527i
$680$	2.22266	−	0.829285i	0.0852352	−	0.0318016i
$681$	23.1204	+	23.1204i	0.885976	+	0.885976i
$682$	11.5945	−	4.64221i	0.443975	−	0.177759i
$683$	8.90393	+	3.68813i	0.340700	+	0.141122i	0.546472	−	0.837478i	$-0.315971\pi$
$683$	8.90393	+	3.68813i	0.340700	+	0.141122i	−0.205772	+	0.978600i	$0.565971\pi$
$684$	1.54528	−	3.49379i	0.0590853	−	0.133588i
$685$	0.234400	−	0.0970915i	0.00895595	−	0.00370968i
$686$	0.148773	−	12.5395i	0.00568017	−	0.478760i
$687$	43.1595			1.64664
$688$	1.60090	−	3.39916i	0.0610336	−	0.129592i
$689$	−17.6283	−	37.1431i	−0.671585	−	1.41504i
$690$	0.540379	+	0.00641124i	0.0205719	+	0.000244072i
$691$	−6.64580	−	16.0444i	−0.252818	−	0.610357i	0.745611	−	0.666381i	$-0.232158\pi$
$691$	−6.64580	−	16.0444i	−0.252818	−	0.610357i	−0.998429	+	0.0560242i	$0.982158\pi$
$692$	−3.31838	−	8.58172i	−0.126146	−	0.326228i
$693$	−0.159333	+	0.384664i	−0.00605256	+	0.0146122i
$694$	−11.9449	−	29.8339i	−0.453424	−	1.13248i
$695$	−3.12470	−	3.12470i	−0.118527	−	0.118527i
$696$	0.327975	−	9.21112i	0.0124318	−	0.349147i
$697$	11.1212	−	11.1212i	0.421247	−	0.421247i
$698$	23.8893	+	10.2290i	0.904223	+	0.387172i
$699$	0.882410	+	0.365506i	0.0333758	+	0.0138247i
$700$	−0.147493	+	6.21494i	−0.00557471	+	0.234903i
$701$	5.86249	+	14.1533i	0.221423	+	0.534563i	0.995084	−	0.0990377i	$-0.0315764\pi$
$701$	5.86249	+	14.1533i	0.221423	+	0.534563i	−0.773661	+	0.633600i	$0.781576\pi$
$702$	−22.7850	−	8.42411i	−0.859963	−	0.317948i
$703$	−13.1324			−0.495297
$704$	5.35267	−	10.6991i	0.201736	−	0.403237i
$705$	2.71509			0.102256
$706$	−3.01650	+	2.94577i	−0.113528	+	0.110865i
$707$	−7.37159	+	3.05341i	−0.277237	+	0.114835i
$708$	−0.879915	+	37.0771i	−0.0330692	+	1.39344i
$709$	7.86177	−	18.9800i	0.295255	−	0.712809i	−0.704739	−	0.709466i	$-0.748936\pi$
$709$	7.86177	−	18.9800i	0.295255	−	0.712809i	0.999994	−	0.00334251i	$-0.00106396\pi$
$710$	−1.29693	+	3.02892i	−0.0486729	+	0.113673i
$711$	0.612143	+	0.612143i	0.0229572	+	0.0229572i
$712$	−1.22635	+	34.4418i	−0.0459594	+	1.29076i
$713$	−1.75211	−	1.75211i	−0.0656169	−	0.0656169i
$714$	2.70634	−	1.08357i	0.101282	−	0.0405516i
$715$	−0.133723	−	2.64957i	−0.00500097	−	0.0990882i
$716$	−10.8370	−	28.0256i	−0.404996	−	1.04737i
$717$	−14.6793	−	35.4390i	−0.548208	−	1.32349i
$718$	30.6995	+	0.364229i	1.14570	+	0.0135929i
$719$			32.0956i			1.19696i	0.801137	+	0.598481i	$0.204229\pi$
$719$			32.0956i			1.19696i	−0.801137	+	0.598481i	$0.795771\pi$
$720$	−0.283862	−	0.789279i	−0.0105789	−	0.0294147i
$721$	2.20592			0.0821526
$722$	1.53925	+	0.0182622i	0.0572850	+	0.000679649i
$723$	12.4738	+	30.1144i	0.463906	+	1.11997i
$724$	6.22605	+	2.75374i	0.231389	+	0.102342i
$725$	3.20548	−	7.73871i	0.119049	−	0.287409i
$726$	−21.2972	+	8.52701i	−0.790413	+	0.316467i
$727$	−11.6971	+	11.6971i	−0.433822	+	0.433822i	−0.889926	−	0.456104i	$-0.849244\pi$
$727$	−11.6971	+	11.6971i	−0.433822	+	0.433822i	0.456104	+	0.889926i	$0.349244\pi$
$728$	−4.78039	−	4.64061i	−0.177173	−	0.171993i
$729$	15.6639	+	15.6639i	0.580143	+	0.580143i
$730$	6.79787	+	2.91073i	0.251601	+	0.107731i
$731$	−1.47933	−	0.612758i	−0.0547150	−	0.0226637i
$732$	21.2921	+	22.3272i	0.786977	+	0.825238i
$733$	7.03835	−	2.91538i	0.259967	−	0.107682i	−0.248893	−	0.968531i	$-0.580067\pi$
$733$	7.03835	−	2.91538i	0.259967	−	0.107682i	0.508861	+	0.860849i	$0.330067\pi$
$734$	−16.6878	+	16.2964i	−0.615956	+	0.601512i
$735$			5.98653i			0.220816i
$736$	−2.36933	−	0.140711i	−0.0873348	−	0.00518669i
$737$	−6.33044			−0.233185
$738$	−3.88515	−	3.97845i	−0.143014	−	0.146449i
$739$	0.212356	−	0.0879608i	0.00781165	−	0.00323569i	−0.378774	−	0.925489i	$-0.623654\pi$
$739$	0.212356	−	0.0879608i	0.00781165	−	0.00323569i	0.386586	+	0.922253i	$0.373654\pi$
$740$	−2.08661	+	1.98987i	−0.0767054	+	0.0731491i
$741$	1.50775	+	29.8743i	0.0553887	+	1.09746i
$742$	−4.14687	+	9.68483i	−0.152236	+	0.355541i
$743$	35.8526	−	35.8526i	1.31530	−	1.31530i	0.397857	−	0.917447i	$-0.369754\pi$
$743$	35.8526	−	35.8526i	1.31530	−	1.31530i	0.917447	−	0.397857i	$-0.130246\pi$
$744$	−12.8407	+	28.1253i	−0.470763	+	1.03112i
$745$	0.110578	−	0.110578i	0.00405127	−	0.00405127i
$746$	−26.1688	+	10.4775i	−0.958107	+	0.383608i
$747$	−0.969278	−	0.401488i	−0.0354640	−	0.0146897i
$748$	−4.66263	−	2.06225i	−0.170483	−	0.0754034i
$749$	1.13942	+	2.75080i	0.0416334	+	0.100512i
$750$	0.149102	−	12.5672i	0.00544443	−	0.458890i
$751$		−	38.2722i		−	1.39657i	−0.715819	−	0.698286i	$-0.753946\pi$
$751$		−	38.2722i		−	1.39657i	0.715819	−	0.698286i	$-0.246054\pi$
$752$	−11.9112	−	0.565673i	−0.434357	−	0.0206280i
$753$		−	46.9069i		−	1.70938i
$754$	3.75249	+	8.15493i	0.136658	+	0.296985i
$755$	2.37273	−	0.982818i	0.0863526	−	0.0357684i
$756$	2.24502	+	5.80588i	0.0816506	+	0.211158i
$757$	13.2943	−	32.0953i	0.483191	−	1.16653i	−0.474895	−	0.880043i	$-0.657514\pi$
$757$	13.2943	−	32.0953i	0.483191	−	1.16653i	0.958085	−	0.286483i	$-0.0924861\pi$
$758$	27.4264	−	10.9810i	0.996173	−	0.398849i
$759$	−0.821236	−	0.821236i	−0.0298090	−	0.0298090i
$760$	4.56475	−	4.25086i	0.165581	−	0.154195i
$761$	27.8021	−	27.8021i	1.00782	−	1.00782i	0.00785529	−	0.999969i	$-0.497500\pi$
$761$	27.8021	−	27.8021i	1.00782	−	1.00782i	0.999969	−	0.00785529i	$-0.00250044\pi$
$762$	−1.00296	+	2.34236i	−0.0363333	+	0.0848548i
$763$	0.0669518	+	0.0277323i	0.00242382	+	0.00100398i
$764$	0.576372	−	24.2867i	0.0208524	−	0.878662i
$765$	−0.330244	+	0.136792i	−0.0119400	+	0.00494571i
$766$	−11.4322	+	11.1641i	−0.413062	+	0.403376i
$767$	−15.4876	−	32.6327i	−0.559226	−	1.17830i
$768$	8.68951	+	28.3124i	0.313556	+	1.02164i
$769$		−	25.1124i		−	0.905576i	−0.891618	−

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bg (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.988066 - 1.01179i) q^{2} +(0.708345 + 1.71010i) q^{3} +(-0.0474507 + 1.99944i) q^{4} +(0.188293 - 0.454578i) q^{5} +(1.03037 - 2.40639i) q^{6} +(0.461953 - 0.461953i) q^{7} +(2.06990 - 1.92757i) q^{8} +(-0.301353 + 0.301353i) q^{9} +O(q^{10})\)	\(q+(-0.988066 - 1.01179i) q^{2} +(0.708345 + 1.71010i) q^{3} +(-0.0474507 + 1.99944i) q^{4} +(0.188293 - 0.454578i) q^{5} +(1.03037 - 2.40639i) q^{6} +(0.461953 - 0.461953i) q^{7} +(2.06990 - 1.92757i) q^{8} +(-0.301353 + 0.301353i) q^{9} +(-0.645985 + 0.258640i) q^{10} +(1.38159 + 0.572271i) q^{11} +(-3.45284 + 1.33515i) q^{12} +(2.41776 - 2.67478i) q^{13} +(-0.923842 - 0.0109608i) q^{14} +0.910748 q^{15} +(-3.99550 - 0.189749i) q^{16} +1.70465i q^{17} +(0.602664 + 0.00715020i) q^{18} +(1.71519 + 4.14085i) q^{19} +(0.899966 + 0.398049i) q^{20} +(1.11721 + 0.462762i) q^{21} +(-0.786077 - 1.96332i) q^{22} +(-0.296689 + 0.296689i) q^{23} +(4.76252 + 2.17435i) q^{24} +(3.36435 + 3.36435i) q^{25} +(-5.09523 + 0.196586i) q^{26} +(4.40148 + 1.82315i) q^{27} +(0.901727 + 0.945567i) q^{28} +(-0.673717 - 1.62650i) q^{29} +(-0.899880 - 0.921489i) q^{30} +5.90554i q^{31} +(3.75583 + 4.23010i) q^{32} +2.76801i q^{33} +(1.72476 - 1.68431i) q^{34} +(-0.123012 - 0.296976i) q^{35} +(-0.588237 - 0.616836i) q^{36} +(-1.12127 + 2.70698i) q^{37} +(2.49495 - 5.82685i) q^{38} +(6.28673 + 2.23993i) q^{39} +(-0.486483 - 1.30388i) q^{40} +(-6.52404 - 6.52404i) q^{41} +(-0.635654 - 1.58762i) q^{42} +(-0.359462 + 0.867818i) q^{43} +(-1.20978 + 2.73524i) q^{44} +(0.0802460 + 0.193731i) q^{45} +(0.593335 + 0.00703953i) q^{46} +2.98116 q^{47} +(-2.50570 - 6.96709i) q^{48} +6.57320i q^{49} +(0.0798258 - 6.72822i) q^{50} +(-2.91512 + 1.20748i) q^{51} +(5.23333 + 4.96108i) q^{52} +(4.36373 - 10.5350i) q^{53} +(-2.50430 - 6.25478i) q^{54} +(0.520284 - 0.520284i) q^{55} +(0.0657523 - 1.84664i) q^{56} +(-5.86629 + 5.86629i) q^{57} +(-0.980001 + 2.28875i) q^{58} +(3.83383 - 9.25569i) q^{59} +(-0.0432156 + 1.82098i) q^{60} +(-3.18927 - 7.69957i) q^{61} +(5.97518 - 5.83506i) q^{62} +0.278422i q^{63} +(0.568981 - 7.97974i) q^{64} +(-0.760651 - 1.60270i) q^{65} +(2.80065 - 2.73497i) q^{66} +(-3.91099 + 1.61998i) q^{67} +(-3.40835 - 0.0808869i) q^{68} +(-0.717523 - 0.297208i) q^{69} +(-0.178935 + 0.417895i) q^{70} +(3.34826 - 3.34826i) q^{71} +(-0.0428932 + 1.20465i) q^{72} +(-7.51457 - 7.51457i) q^{73} +(3.84679 - 1.54018i) q^{74} +(-3.37024 + 8.13647i) q^{75} +(-8.36075 + 3.23294i) q^{76} +(0.902591 - 0.373865i) q^{77} +(-3.94536 - 8.57407i) q^{78} -2.03132i q^{79} +(-0.838578 + 1.78054i) q^{80} +10.0969i q^{81} +(-0.154796 + 13.0472i) q^{82} +(0.942068 + 2.27435i) q^{83} +(-0.978276 + 2.21183i) q^{84} +(0.774899 + 0.320974i) q^{85} +(1.23322 - 0.493760i) q^{86} +(2.30424 - 2.30424i) q^{87} +(3.96284 - 1.47855i) q^{88} +(-8.61592 + 8.61592i) q^{89} +(0.116727 - 0.272612i) q^{90} +(-0.118731 - 2.35252i) q^{91} +(-0.579132 - 0.607288i) q^{92} +(-10.0990 + 4.18316i) q^{93} +(-2.94558 - 3.01632i) q^{94} +2.20530 q^{95} +(-4.57345 + 9.41919i) q^{96} +12.2702i q^{97} +(6.65072 - 6.49475i) q^{98} +(-0.588801 + 0.243889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9}+O(q^{10}) \) 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9	\( 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38} - 28 q^{39} + 32 q^{40} + 32 q^{42} - 8 q^{43} - 112 q^{48} + 16 q^{51} - 12 q^{52} - 8 q^{53} - 40 q^{55} - 48 q^{56} - 8 q^{61} + 56 q^{62} - 8 q^{64} - 8 q^{65} - 56 q^{66} - 8 q^{69} - 8 q^{74} - 16 q^{75} - 8 q^{77} + 84 q^{78} - 88 q^{82} - 8 q^{87} + 72 q^{88} + 88 q^{90} + 44 q^{91} - 80 q^{92} + 24 q^{94} + 112 q^{95}+O(q^{100}) \) 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Introduction

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