LMFDB - Embedded newform 414.2.p.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	414.5
Dual form			414.2.p.a.83.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.971812 + 0.235759i) q^{2} +(-0.304529 + 1.70507i) q^{3} +(0.888835 - 0.458227i) q^{4} +(0.311301 + 0.244810i) q^{5} +(-0.106041 - 1.72880i) q^{6} +(-0.315067 - 0.224358i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.81452 - 1.03849i) q^{9} +O(q^{10})$	\(q+(-0.971812 + 0.235759i) q^{2} +(-0.304529 + 1.70507i) q^{3} +(0.888835 - 0.458227i) q^{4} +(0.311301 + 0.244810i) q^{5} +(-0.106041 - 1.72880i) q^{6} +(-0.315067 - 0.224358i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.81452 - 1.03849i) q^{9} +(-0.360242 - 0.164517i) q^{10} +(1.33803 + 1.27581i) q^{11} +(0.510632 + 1.65507i) q^{12} +(3.89665 + 5.47208i) q^{13} +(0.359080 + 0.143754i) q^{14} +(-0.512218 + 0.456238i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-5.24869 + 3.37313i) q^{17} +(2.98002 + 0.345664i) q^{18} +(-1.13657 + 1.76854i) q^{19} +(0.388873 + 0.0749492i) q^{20} +(0.478493 - 0.468887i) q^{21} +(-1.60110 - 0.924396i) q^{22} +(-4.75405 - 0.631678i) q^{23} +(-0.886435 - 1.48803i) q^{24} +(-1.14182 - 4.70664i) q^{25} +(-5.07690 - 4.39916i) q^{26} +(2.62780 - 4.48271i) q^{27} +(-0.382849 - 0.0550454i) q^{28} +(-2.11319 + 4.09902i) q^{29} +(0.390217 - 0.564137i) q^{30} +(10.2541 - 1.97633i) q^{31} +(-0.371662 + 0.928368i) q^{32} +(-2.58282 + 1.89292i) q^{33} +(4.30549 - 4.51547i) q^{34} +(-0.0431555 - 0.146974i) q^{35} +(-2.97751 + 0.366646i) q^{36} +(-10.0155 + 1.44001i) q^{37} +(0.687584 - 1.98664i) q^{38} +(-10.5169 + 4.97765i) q^{39} +(-0.395582 + 0.0188439i) q^{40} +(-4.92745 + 6.26576i) q^{41} +(-0.354460 + 0.568479i) q^{42} +(-1.16543 + 6.04684i) q^{43} +(1.77390 + 0.520865i) q^{44} +(-0.621932 - 1.01230i) q^{45} +(4.76896 - 0.506938i) q^{46} +(-1.10891 + 0.640230i) q^{47} +(1.21226 + 1.23710i) q^{48} +(-2.24055 - 6.47363i) q^{49} +(2.21926 + 4.30477i) q^{50} +(-4.15304 - 9.97660i) q^{51} +(5.97093 + 3.07823i) q^{52} +(2.62276 + 5.74304i) q^{53} +(-1.49688 + 4.97588i) q^{54} +(0.104200 + 0.724725i) q^{55} +(0.385035 - 0.0367663i) q^{56} +(-2.66936 - 2.47650i) q^{57} +(1.08724 - 4.48168i) q^{58} +(5.04223 - 3.59055i) q^{59} +(-0.246217 + 0.640232i) q^{60} +(8.17086 + 2.82796i) q^{61} +(-9.49916 + 4.33812i) q^{62} +(0.653770 + 0.958653i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.126587 + 2.65740i) q^{65} +(2.06374 - 2.44848i) q^{66} +(7.76357 + 8.14220i) q^{67} +(-3.11956 + 5.40325i) q^{68} +(2.52480 - 7.91362i) q^{69} +(0.0765895 + 0.132657i) q^{70} +(1.88396 - 6.41617i) q^{71} +(2.80714 - 1.05829i) q^{72} +(-4.85043 - 3.11718i) q^{73} +(9.39367 - 3.76066i) q^{74} +(8.37286 - 0.513572i) q^{75} +(-0.199833 + 2.09275i) q^{76} +(-0.135331 - 0.702164i) q^{77} +(9.04693 - 7.31679i) q^{78} +(-0.395944 - 4.14651i) q^{79} +(0.379988 - 0.111575i) q^{80} +(6.84309 + 5.84569i) q^{81} +(3.31134 - 7.25083i) q^{82} +(13.7971 - 10.8501i) q^{83} +(0.210445 - 0.636021i) q^{84} +(-2.45970 - 0.234872i) q^{85} +(-0.293016 - 6.15115i) q^{86} +(-6.34559 - 4.85141i) q^{87} +(-1.84670 - 0.0879691i) q^{88} +(-1.54524 + 1.78330i) q^{89} +(0.843061 + 0.837143i) q^{90} -2.59831i q^{91} +(-4.51502 + 1.61697i) q^{92} +(0.247086 + 18.0859i) q^{93} +(0.926713 - 0.883619i) q^{94} +(-0.786771 + 0.272304i) q^{95} +(-1.46975 - 0.916425i) q^{96} +(4.15725 + 10.3843i) q^{97} +(3.70360 + 5.76292i) q^{98} +(-2.44101 - 4.98034i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{22}\right)$

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 $

$2$	−0.971812	+	0.235759i	−0.687175	+	0.166707i
$2$	−0.971812	+	0.235759i	−0.687175	+	0.166707i
$3$	−0.304529	+	1.70507i	−0.175820	+	0.984422i
$3$	−0.304529	+	1.70507i	−0.175820	+	0.984422i
$4$	0.888835	−	0.458227i	0.444418	−	0.229113i
$5$	0.311301	+	0.244810i	0.139218	+	0.109482i	0.685339	−	0.728224i	$-0.259654\pi$
$5$	0.311301	+	0.244810i	0.139218	+	0.109482i	−0.546121	+	0.837706i	$0.683896\pi$
$6$	−0.106041	−	1.72880i	−0.0432909	−	0.705780i
$7$	−0.315067	−	0.224358i	−0.119084	−	0.0847993i	0.518963	−	0.854797i	$-0.326318\pi$
$7$	−0.315067	−	0.224358i	−0.119084	−	0.0847993i	−0.638047	+	0.769997i	$0.720258\pi$
$8$	−0.755750	+	0.654861i	−0.267198	+	0.231528i
$9$	−2.81452	−	1.03849i	−0.938175	−	0.346162i
$10$	−0.360242	−	0.164517i	−0.113918	−	0.0520248i
$11$	1.33803	+	1.27581i	0.403432	+	0.384672i	0.864450	−	0.502719i	$-0.167667\pi$
$11$	1.33803	+	1.27581i	0.403432	+	0.384672i	−0.461017	+	0.887391i	$0.652515\pi$
$12$	0.510632	+	1.65507i	0.147407	+	0.477777i
$13$	3.89665	+	5.47208i	1.08074	+	1.51768i	0.836502	+	0.547964i	$0.184597\pi$
$13$	3.89665	+	5.47208i	1.08074	+	1.51768i	0.244234	+	0.969716i	$0.421464\pi$
$14$	0.359080	+	0.143754i	0.0959681	+	0.0384198i
$15$	−0.512218	+	0.456238i	−0.132254	+	0.117800i
$16$	0.580057	−	0.814576i	0.145014	−	0.203644i
$17$	−5.24869	+	3.37313i	−1.27299	+	0.818104i	−0.990007	−	0.141020i	$-0.954962\pi$
$17$	−5.24869	+	3.37313i	−1.27299	+	0.818104i	−0.282988	+	0.959124i	$0.591326\pi$
$18$	2.98002	+	0.345664i	0.702397	+	0.0814737i
$19$	−1.13657	+	1.76854i	−0.260747	+	0.405731i	−0.946801	−	0.321821i	$-0.895705\pi$
$19$	−1.13657	+	1.76854i	−0.260747	+	0.405731i	0.686053	+	0.727551i	$0.259342\pi$
$20$	0.388873	+	0.0749492i	0.0869547	+	0.0167592i
$21$	0.478493	−	0.468887i	0.104416	−	0.102319i
$22$	−1.60110	−	0.924396i	−0.341356	−	0.197082i
$23$	−4.75405	−	0.631678i	−0.991288	−	0.131714i
$23$	−4.75405	−	0.631678i	−0.991288	−	0.131714i
$24$	−0.886435	−	1.48803i	−0.180943	−	0.303743i
$25$	−1.14182	−	4.70664i	−0.228364	−	0.941328i
$26$	−5.07690	−	4.39916i	−0.995662	−	0.862746i
$27$	2.62780	−	4.48271i	0.505719	−	0.862698i
$28$	−0.382849	−	0.0550454i	−0.0723517	−	0.0104026i
$29$	−2.11319	+	4.09902i	−0.392410	+	0.761170i	−0.999438	−	0.0335107i	$-0.989331\pi$
$29$	−2.11319	+	4.09902i	−0.392410	+	0.761170i	0.607028	+	0.794680i	$0.292362\pi$
$30$	0.390217	−	0.564137i	0.0712435	−	0.102997i
$31$	10.2541	−	1.97633i	1.84170	−	0.354958i	0.855145	−	0.518389i	$-0.173468\pi$
$31$	10.2541	−	1.97633i	1.84170	−	0.354958i	0.986555	+	0.163431i	$0.0522561\pi$
$32$	−0.371662	+	0.928368i	−0.0657013	+	0.164114i
$33$	−2.58282	+	1.89292i	−0.449611	+	0.329515i
$34$	4.30549	−	4.51547i	0.738386	−	0.774397i
$35$	−0.0431555	−	0.146974i	−0.00729461	−	0.0248432i
$36$	−2.97751	+	0.366646i	−0.496252	+	0.0611077i
$37$	−10.0155	+	1.44001i	−1.64654	+	0.236736i	−0.902277	−	0.431156i	$-0.858106\pi$
$37$	−10.0155	+	1.44001i	−1.64654	+	0.236736i	−0.744258	+	0.667892i	$0.767197\pi$
$38$	0.687584	−	1.98664i	0.111541	−	0.322276i
$39$	−10.5169	+	4.97765i	−1.68405	+	0.797062i
$40$	−0.395582	+	0.0188439i	−0.0625469	+	0.00297948i
$41$	−4.92745	+	6.26576i	−0.769539	+	0.978548i	0.230446	+	0.973085i	$0.425981\pi$
$41$	−4.92745	+	6.26576i	−0.769539	+	0.978548i	−0.999985	+	0.00546305i	$0.998261\pi$
$42$	−0.354460	+	0.568479i	−0.0546944	+	0.0877181i
$43$	−1.16543	+	6.04684i	−0.177727	+	0.922135i	0.778086	+	0.628158i	$0.216191\pi$
$43$	−1.16543	+	6.04684i	−0.177727	+	0.922135i	−0.955813	+	0.293977i	$0.905021\pi$
$44$	1.77390	+	0.520865i	0.267426	+	0.0785233i
$45$	−0.621932	−	1.01230i	−0.0927122	−	0.150905i
$46$	4.76896	−	0.506938i	0.703145	−	0.0747439i
$47$	−1.10891	+	0.640230i	−0.161751	+	0.0933872i	−0.578691	−	0.815547i	$-0.696436\pi$
$47$	−1.10891	+	0.640230i	−0.161751	+	0.0933872i	0.416939	+	0.908934i	$0.363103\pi$
$48$	1.21226	+	1.23710i	0.174975	+	0.178560i
$49$	−2.24055	−	6.47363i	−0.320078	−	0.924804i
$50$	2.21926	+	4.30477i	0.313851	+	0.608787i
$51$	−4.15304	−	9.97660i	−0.581542	−	1.39700i
$52$	5.97093	+	3.07823i	0.828019	+	0.426873i
$53$	2.62276	+	5.74304i	0.360263	+	0.788867i	0.999798	+	0.0201044i	$0.00639986\pi$
$53$	2.62276	+	5.74304i	0.360263	+	0.788867i	−0.639534	+	0.768762i	$0.720873\pi$
$54$	−1.49688	+	4.97588i	−0.203700	+	0.677131i
$55$	0.104200	+	0.724725i	0.0140503	+	0.0977219i
$56$	0.385035	−	0.0367663i	0.0514524	−	0.00491311i
$57$	−2.66936	−	2.47650i	−0.353566	−	0.328021i
$58$	1.08724	−	4.48168i	0.142762	−	0.588474i
$59$	5.04223	−	3.59055i	0.656442	−	0.467450i	−0.202664	−	0.979248i	$-0.564960\pi$
$59$	5.04223	−	3.59055i	0.656442	−	0.467450i	0.859106	+	0.511798i	$0.171020\pi$
$60$	−0.246217	+	0.640232i	−0.0317865	+	0.0826536i
$61$	8.17086	+	2.82796i	1.04617	+	0.362084i	0.795478	−	0.605983i	$-0.207220\pi$
$61$	8.17086	+	2.82796i	1.04617	+	0.362084i	0.250694	+	0.968066i	$0.419341\pi$
$62$	−9.49916	+	4.33812i	−1.20640	+	0.550942i
$63$	0.653770	+	0.958653i	0.0823673	+	0.120779i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	−0.126587	+	2.65740i	−0.0157012	+	0.329610i
$66$	2.06374	−	2.44848i	0.254029	−	0.301387i
$67$	7.76357	+	8.14220i	0.948471	+	0.994727i	0.999992	−	0.00394443i	$-0.00125555\pi$
$67$	7.76357	+	8.14220i	0.948471	+	0.994727i	−0.0515215	+	0.998672i	$0.516407\pi$
$68$	−3.11956	+	5.40325i	−0.378303	+	0.655240i
$69$	2.52480	−	7.91362i	0.303950	−	0.952688i
$70$	0.0765895	+	0.132657i	0.00915419	+	0.0158555i
$71$	1.88396	−	6.41617i	0.223585	−	0.761460i	−0.768930	−	0.639333i	$-0.779210\pi$
$71$	1.88396	−	6.41617i	0.223585	−	0.761460i	0.992515	−	0.122126i	$-0.0389713\pi$
$72$	2.80714	−	1.05829i	0.330825	−	0.124720i
$73$	−4.85043	−	3.11718i	−0.567700	−	0.364839i	0.225086	−	0.974339i	$-0.427734\pi$
$73$	−4.85043	−	3.11718i	−0.567700	−	0.364839i	−0.792786	+	0.609500i	$0.791370\pi$
$74$	9.39367	−	3.76066i	1.09199	−	0.437168i
$75$	8.37286	−	0.513572i	0.966815	−	0.0593021i
$76$	−0.199833	+	2.09275i	−0.0229224	+	0.240055i
$77$	−0.135331	−	0.702164i	−0.0154224	−	0.0800190i
$78$	9.04693	−	7.31679i	1.02436	−	0.828464i
$79$	−0.395944	−	4.14651i	−0.0445472	−	0.466519i	−0.990031	−	0.140850i	$-0.955017\pi$
$79$	−0.395944	−	4.14651i	−0.0445472	−	0.466519i	0.945484	−	0.325669i	$-0.105590\pi$
$80$	0.379988	−	0.111575i	0.0424840	−	0.0124744i
$81$	6.84309	+	5.84569i	0.760344	+	0.649521i
$82$	3.31134	−	7.25083i	0.365677	−	0.800721i
$83$	13.7971	−	10.8501i	1.51443	−	1.19096i	0.591306	−	0.806447i	$-0.298613\pi$
$83$	13.7971	−	10.8501i	1.51443	−	1.19096i	0.923120	−	0.384511i	$-0.125630\pi$
$84$	0.210445	−	0.636021i	0.0229614	−	0.0693956i
$85$	−2.45970	−	0.234872i	−0.266791	−	0.0254755i
$86$	−0.293016	−	6.15115i	−0.0315967	−	0.663296i
$87$	−6.34559	−	4.85141i	−0.680319	−	0.520126i
$88$	−1.84670	−	0.0879691i	−0.196859	−	0.00937753i
$89$	−1.54524	+	1.78330i	−0.163795	+	0.189029i	−0.831714	−	0.555205i	$-0.812640\pi$
$89$	−1.54524	+	1.78330i	−0.163795	+	0.189029i	0.667919	+	0.744234i	$0.267185\pi$
$90$	0.843061	+	0.837143i	0.0888664	+	0.0882426i
$91$		−	2.59831i		−	0.272377i
$92$	−4.51502	+	1.61697i	−0.470723	+	0.168581i
$93$	0.247086	+	18.0859i	0.0256217	+	1.87542i
$94$	0.926713	−	0.883619i	0.0955832	−	0.0911384i
$95$	−0.786771	+	0.272304i	−0.0807210	+	0.0279378i
$96$	−1.46975	−	0.916425i	−0.150006	−	0.0935323i
$97$	4.15725	+	10.3843i	0.422105	+	1.05437i	0.975215	+	0.221258i	$0.0710164\pi$
$97$	4.15725	+	10.3843i	0.422105	+	1.05437i	−0.553111	+	0.833108i	$0.686559\pi$
$98$	3.70360	+	5.76292i	0.374121	+	0.582143i
$99$	−2.44101	−	4.98034i	−0.245331	−	0.500543i
$100$	−3.17160	−	3.66022i	−0.317160	−	0.366022i
$101$	−0.238532	−	0.303318i	−0.0237349	−	0.0301813i	0.774041	−	0.633136i	$-0.218233\pi$
$101$	−0.238532	−	0.303318i	−0.0237349	−	0.0301813i	−0.797776	+	0.602954i	$0.793990\pi$
$102$	6.38804	+	8.71626i	0.632511	+	0.863038i
$103$	4.47951	+	1.08672i	0.441379	+	0.107077i	0.450289	−	0.892883i	$-0.351321\pi$
$103$	4.47951	+	1.08672i	0.441379	+	0.107077i	−0.00890993	+	0.999960i	$0.502836\pi$
$104$	−6.52834	−	1.58376i	−0.640156	−	0.155300i
$105$	0.263743	−	0.0288252i	0.0257387	−	0.00281305i
$106$	−3.90280	−	4.96281i	−0.379073	−	0.482031i
$107$	4.44783	+	5.13306i	0.429988	+	0.496232i	0.928854	−	0.370447i	$-0.120795\pi$
$107$	4.44783	+	5.13306i	0.429988	+	0.496232i	−0.498866	+	0.866679i	$0.666250\pi$
$108$	0.281581	−	5.18852i	0.0270951	−	0.499265i
$109$	8.98237	+	13.9768i	0.860355	+	1.33874i	0.939738	+	0.341894i	$0.111068\pi$
$109$	8.98237	+	13.9768i	0.860355	+	1.33874i	−0.0793835	+	0.996844i	$0.525295\pi$
$110$	−0.272123	−	0.679730i	−0.0259459	−	0.0648097i
$111$	0.594689	−	17.5156i	0.0564454	−	1.66251i
$112$	−0.365513	+	0.126505i	−0.0345377	+	0.0119536i
$113$	10.8158	−	10.3128i	1.01746	−	0.970146i	0.0179011	−	0.999840i	$-0.494302\pi$
$113$	10.8158	−	10.3128i	1.01746	−	0.970146i	0.999559	+	0.0296934i	$0.00945310\pi$
$114$	3.17798	+	1.77737i	0.297645	+	0.166466i
$115$	−1.32530	−	1.36048i	−0.123585	−	0.126865i
$116$			4.61168i			0.428184i
$117$	−5.28453	−	19.4479i	−0.488555	−	1.79796i
$118$	−4.05359	+	4.67809i	−0.373163	+	0.430653i
$119$	2.41047	+	0.114825i	0.220968	+	0.0105260i
$120$	0.0883360	−	0.680233i	0.00806393	−	0.0620965i
$121$	−0.360765	−	7.57338i	−0.0327968	−	0.688489i
$122$	−8.60726	−	0.821894i	−0.779265	−	0.0744107i
$123$	−9.18301	−	10.3098i	−0.828004	−	0.929599i
$124$	8.20865	−	6.45535i	0.737158	−	0.579708i
$125$	1.61937	−	3.54592i	0.144841	−	0.317156i
$126$	−0.861352	−	0.777498i	−0.0767353	−	0.0692650i
$127$	6.35496	−	1.86599i	0.563912	−	0.165579i	0.0126622	−	0.999920i	$-0.495969\pi$
$127$	6.35496	−	1.86599i	0.563912	−	0.165579i	0.551250	+	0.834340i	$0.314151\pi$
$128$	0.0950560	+	0.995472i	0.00840185	+	0.0879881i
$129$	−9.95538	−	3.82858i	−0.876522	−	0.337088i
$130$	−0.503486	−	2.61233i	−0.0441587	−	0.229117i
$131$	0.252480	−	2.64409i	0.0220593	−	0.231015i	−0.977718	−	0.209922i	$-0.932679\pi$
$131$	0.252480	−	2.64409i	0.0220593	−	0.231015i	0.999778	−	0.0210936i	$-0.00671479\pi$
$132$	−1.42832	+	2.86601i	−0.124319	+	0.249454i
$133$	0.754881	−	0.302209i	0.0654565	−	0.0262048i
$134$	−9.46432	−	6.08235i	−0.817593	−	0.525435i
$135$	1.91545	−	0.752162i	0.164855	−	0.0647358i
$136$	1.75777	−	5.98640i	0.150727	−	0.513330i
$137$	8.63462	+	14.9556i	0.737705	+	1.27774i	0.953526	+	0.301310i	$0.0974239\pi$
$137$	8.63462	+	14.9556i	0.737705	+	1.27774i	−0.215821	+	0.976433i	$0.569243\pi$
$138$	−0.587924	+	8.28579i	−0.0500474	+	0.705333i
$139$	0.594716	−	1.03008i	0.0504431	−	0.0873701i	−0.839701	−	0.543048i	$-0.817270\pi$
$139$	0.594716	−	1.03008i	0.0504431	−	0.0873701i	0.890144	+	0.455678i	$0.150603\pi$
$140$	−0.105706	−	0.110861i	−0.00893375	−	0.00936945i
$141$	−0.753942	−	2.08574i	−0.0634933	−	0.175651i
$142$	−0.318182	+	6.67947i	−0.0267013	+	0.560529i
$143$	−1.76750	+	12.2932i	−0.147806	+	1.02801i
$144$	−2.47851	+	1.69026i	−0.206543	+	0.140855i
$145$	−1.66132	+	0.758699i	−0.137965	+	0.0630065i
$146$	5.44861	+	1.88578i	0.450930	+	0.156069i
$147$	11.7203	−	1.84888i	0.966674	−	0.152493i
$148$	−8.24227	+	5.86929i	−0.677510	+	0.482453i
$149$	1.70742	−	7.03809i	0.139877	−	0.576583i	−0.858127	−	0.513438i	$-0.828372\pi$
$149$	1.70742	−	7.03809i	0.139877	−	0.576583i	0.998004	−	0.0631450i	$-0.0201130\pi$
$150$	−8.01577	+	2.47307i	−0.654485	+	0.201925i
$151$	−9.62747	+	0.919312i	−0.783473	+	0.0748126i	−0.479123	−	0.877748i	$-0.659045\pi$
$151$	−9.62747	+	0.919312i	−0.783473	+	0.0748126i	−0.304350	+	0.952560i	$0.598439\pi$
$152$	−0.299184	−	2.08087i	−0.0242670	−	0.168781i
$153$	18.2755	−	4.04306i	1.47749	−	0.326862i
$154$	0.297058	+	0.650466i	0.0239376	+	0.0524160i
$155$	3.67595	+	1.89508i	0.295259	+	0.152217i
$156$	−7.06691	+	9.24344i	−0.565806	+	0.740067i
$157$	−7.55177	−	14.6484i	−0.602697	−	1.16907i	−0.970936	−	0.239338i	$-0.923070\pi$
$157$	−7.55177	−	14.6484i	−0.602697	−	1.16907i	0.368239	−	0.929731i	$-0.379961\pi$
$158$	1.36236	+	3.93628i	0.108384	+	0.313154i
$159$	−10.5910	+	2.72306i	−0.839920	+	0.215953i
$160$	−0.342972	+	0.198015i	−0.0271143	+	0.0156545i
$161$	1.35612	+	1.26563i	0.106877	+	0.0997455i
$162$	−8.02837	−	4.06759i	−0.630768	−	0.319580i
$163$	−11.6114	−	3.40941i	−0.909473	−	0.267045i	−0.206654	−	0.978414i	$-0.566257\pi$
$163$	−11.6114	−	3.40941i	−0.909473	−	0.267045i	−0.702819	+	0.711369i	$0.748076\pi$
$164$	−1.50855	+	7.82712i	−0.117798	+	0.611196i
$165$	−1.26744	−	0.0430320i	−0.0986699	−	0.00335004i
$166$	−10.8501	+	13.7971i	−0.842135	+	1.07086i
$167$	3.00003	−	0.142909i	0.232149	−	0.0110586i	0.0688152	−	0.997629i	$-0.478078\pi$
$167$	3.00003	−	0.142909i	0.232149	−	0.0110586i	0.163334	+	0.986571i	$0.447775\pi$
$168$	−0.0545650	+	0.667707i	−0.00420978	+	0.0515147i
$169$	−10.5079	+	30.3605i	−0.808298	+	2.33542i
$170$	2.44573	−	0.351643i	0.187579	−	0.0269698i
$171$	5.03551	−	3.79728i	0.385075	−	0.290385i
$172$	1.73495	+	5.90868i	0.132288	+	0.450533i
$173$	5.34740	−	5.60820i	0.406556	−	0.426383i	−0.488344	−	0.872651i	$-0.662399\pi$
$173$	5.34740	−	5.60820i	0.406556	−	0.426383i	0.894899	+	0.446268i	$0.147247\pi$
$174$	7.31048	+	3.21863i	0.554206	+	0.244004i
$175$	−0.696223	+	1.73908i	−0.0526295	+	0.131462i
$176$	1.81538	−	0.349886i	0.136840	−	0.0263737i
$177$	4.58664	+	9.69078i	0.344753	+	0.728403i
$178$	1.08125	−	2.09733i	0.0810431	−	0.157202i
$179$	−9.16302	−	1.31744i	−0.684876	−	0.0984703i	−0.208911	−	0.977935i	$-0.566992\pi$
$179$	−9.16302	−	1.31744i	−0.684876	−	0.0984703i	−0.475965	+	0.879464i	$0.657901\pi$
$180$	−1.01666	−	0.614786i	−0.0757774	−	0.0458234i
$181$	1.17306	+	1.01646i	0.0871927	+	0.0755529i	0.697367	−	0.716715i	$-0.254355\pi$
$181$	1.17306	+	1.01646i	0.0871927	+	0.0755529i	−0.610174	+	0.792268i	$0.708900\pi$
$182$	0.612575	+	2.52507i	0.0454071	+	0.187171i
$183$	−7.31014	+	13.0707i	−0.540381	+	0.966214i
$184$	4.00653	−	2.63585i	0.295365	−	0.194317i
$185$	−3.47036	−	2.00361i	−0.255146	−	0.147308i
$186$	−4.50403	−	17.5178i	−0.330252	−	1.28447i
$187$	−11.3264	−	2.18299i	−0.828269	−	0.159636i
$188$	−0.692269	+	1.07719i	−0.0504889	+	0.0785623i
$189$	−1.83366	+	0.822785i	−0.133379	+	0.0598488i
$190$	0.700395	−	0.450116i	0.0508120	−	0.0326549i
$191$	2.79819	−	3.92952i	0.202470	−	0.284330i	−0.700839	−	0.713319i	$-0.747191\pi$
$191$	2.79819	−	3.92952i	0.202470	−	0.284330i	0.903309	+	0.428990i	$0.141130\pi$
$192$	1.64438	+	0.544086i	0.118673	+	0.0392660i
$193$	18.4378	+	7.38139i	1.32718	+	0.531324i	0.923508	−	0.383578i	$-0.125308\pi$
$193$	18.4378	+	7.38139i	1.32718	+	0.531324i	0.403675	+	0.914902i	$0.367733\pi$
$194$	−6.48825	−	9.11148i	−0.465830	−	0.654166i
$195$	−4.49250	−	1.02510i	−0.321715	−	0.0734086i
$196$	−4.95787	−	4.72731i	−0.354133	−	0.337665i
$197$	−2.72061	−	1.24246i	−0.193835	−	0.0885216i	0.316133	−	0.948715i	$-0.397615\pi$
$197$	−2.72061	−	1.24246i	−0.193835	−	0.0885216i	−0.509968	+	0.860193i	$0.670343\pi$
$198$	3.54637	+	4.26446i	0.252029	+	0.303062i
$199$	−5.39094	+	4.67128i	−0.382154	+	0.331138i	−0.824661	−	0.565627i	$-0.808634\pi$
$199$	−5.39094	+	4.67128i	−0.382154	+	0.331138i	0.442508	+	0.896765i	$0.354089\pi$
$200$	3.94512	+	2.80931i	0.278962	+	0.198648i
$201$	−16.2472	+	10.7579i	−1.14599	+	0.758803i
$202$	0.303318	+	0.238532i	0.0213414	+	0.0167831i
$203$	1.58544	−	0.817354i	0.111276	−	0.0573670i
$204$	−8.26291	−	6.96452i	−0.578519	−	0.487614i
$205$	−3.06784	+	0.744250i	−0.214267	+	0.0519807i
$206$	−4.60944			−0.321155
$207$	12.7244	+	6.71489i	0.884407	+	0.466717i
$208$	6.71770			0.465789
$209$	−3.77709	+	0.916313i	−0.261267	+	0.0633827i
$210$	−0.249513	+	0.0901925i	−0.0172180	+	0.00622387i
$211$	2.78151	−	1.43397i	0.191487	−	0.0987183i	−0.359817	−	0.933023i	$-0.617161\pi$
$211$	2.78151	−	1.43397i	0.191487	−	0.0987183i	0.551304	+	0.834305i	$0.314131\pi$
$212$	4.96281	+	3.90280i	0.340847	+	0.268045i
$213$	10.3663	+	5.16619i	0.710287	+	0.353981i
$214$	−5.53261	−	3.93976i	−0.378202	−	0.269316i
$215$	−1.84313	+	1.59708i	−0.125700	+	0.108920i
$216$	0.949596	+	5.10865i	0.0646118	+	0.347599i
$217$	−3.67414	−	1.67792i	−0.249417	−	0.113905i
$218$	−12.0243	−	11.4652i	−0.814391	−	0.776520i
$219$	6.79211	−	7.32105i	0.458969	−	0.494711i
$220$	0.424705	+	0.596414i	0.0286336	+	0.0402102i
$221$	−38.9103	−	15.5773i	−2.61739	−	1.04785i
$222$	3.55154	+	17.1621i	0.238364	+	1.15184i
$223$	−0.284032	+	0.398867i	−0.0190202	+	0.0267101i	−0.823977	−	0.566624i	$-0.808249\pi$
$223$	−0.284032	+	0.398867i	−0.0190202	+	0.0267101i	0.804956	+	0.593334i	$0.202189\pi$
$224$	0.325385	−	0.209112i	0.0217407	−	0.0139719i
$225$	−1.67410	+	14.4327i	−0.111607	+	0.962181i
$226$	−8.07954	+	12.5720i	−0.537443	+	0.836277i
$227$	17.6265	+	3.39724i	1.16991	+	0.225482i	0.736962	−	0.675935i	$-0.236260\pi$
$227$	17.6265	+	3.39724i	1.16991	+	0.225482i	0.432952	+	0.901417i	$0.357472\pi$
$228$	−3.50742	−	0.978031i	−0.232285	−	0.0647717i
$229$	−18.5844	−	10.7297i	−1.22809	−	0.709038i	−0.261460	−	0.965214i	$-0.584204\pi$
$229$	−18.5844	−	10.7297i	−1.22809	−	0.709038i	−0.966630	+	0.256177i	$0.917537\pi$
$230$	1.60869	+	1.00968i	0.106074	+	0.0665762i
$231$	1.23845	−	0.0169195i	0.0814841	−	0.00111322i
$232$	−1.08724	−	4.48168i	−0.0713811	−	0.294237i
$233$	13.3095	+	11.5327i	0.871932	+	0.755534i	0.970882	−	0.239559i	$-0.0770028\pi$
$233$	13.3095	+	11.5327i	0.871932	+	0.755534i	−0.0989496	+	0.995092i	$0.531548\pi$
$234$	9.72059	+	17.6538i	0.635455	+	1.15407i
$235$	−0.501940	−	0.0721680i	−0.0327429	−	0.00470772i
$236$	2.83642	−	5.50189i	0.184635	−	0.358143i
$237$	7.19067	+	0.587621i	0.467084	+	0.0381701i
$238$	−2.36960	+	0.456703i	−0.153598	+	0.0296036i
$239$	10.9034	−	27.2354i	0.705282	−	1.76171i	0.0594473	−	0.998231i	$-0.481066\pi$
$239$	10.9034	−	27.2354i	0.705282	−	1.76171i	0.645835	−	0.763477i	$-0.276510\pi$
$240$	0.0745250	+	0.681884i	0.00481057	+	0.0440154i
$241$	1.88022	−	1.97192i	0.121116	−	0.127022i	−0.660384	−	0.750928i	$-0.729607\pi$
$241$	1.88022	−	1.97192i	0.121116	−	0.127022i	0.781500	+	0.623906i	$0.214455\pi$
$242$	2.13609	+	7.27484i	0.137313	+	0.467645i
$243$	−12.0512	+	9.88777i	−0.773087	+	0.634301i
$244$	8.55840	−	1.23051i	0.547896	−	0.0787755i
$245$	0.887324	−	2.56375i	0.0566890	−	0.163792i
$246$	11.3548	+	7.85416i	0.723954	+	0.500763i
$247$	−14.1064	+	0.671970i	−0.897568	+	0.0427564i
$248$	−6.45535	+	8.20865i	−0.409915	+	0.521250i
$249$	14.2986	+	26.8292i	0.906140	+	1.70023i
$250$	−0.737737	+	3.82774i	−0.0466586	+	0.242088i
$251$	14.6728	+	4.30831i	0.926137	+	0.271938i	0.709819	−	0.704384i	$-0.248777\pi$
$251$	14.6728	+	4.30831i	0.926137	+	0.271938i	0.216318	+	0.976323i	$0.430595\pi$
$252$	1.02037	+	0.552510i	0.0642775	+	0.0348049i
$253$	−5.55518	−	6.91048i	−0.349251	−	0.434458i
$254$	−5.73590	+	3.31163i	−0.359903	+	0.207790i
$255$	1.14952	−	4.12243i	0.0719859	−	0.258156i
$256$	−0.327068	−	0.945001i	−0.0204417	−	0.0590626i
$257$	−4.23419	−	8.21318i	−0.264121	−	0.512324i	0.719062	−	0.694946i	$-0.244572\pi$
$257$	−4.23419	−	8.21318i	−0.264121	−	0.512324i	−0.983183	+	0.182622i	$0.941542\pi$
$258$	10.5774	+	1.37359i	0.658519	+	0.0855161i
$259$	3.47862	+	1.79335i	0.216151	+	0.111434i
$260$	1.10517	+	2.42000i	0.0685400	+	0.150082i
$261$	10.2044	−	9.34228i	0.631637	−	0.578273i
$262$	0.378005	+	2.62908i	0.0233532	+	0.162425i
$263$	−13.6115	+	1.29974i	−0.839321	+	0.0801455i	−0.505857	−	0.862617i	$-0.668824\pi$
$263$	−13.6115	+	1.29974i	−0.839321	+	0.0801455i	−0.333464	+	0.942763i	$0.608218\pi$
$264$	0.712366	−	3.12196i	0.0438431	−	0.192143i
$265$	−0.589484	+	2.42989i	−0.0362117	+	0.149267i
$266$	−0.662354	+	0.471660i	−0.0406115	+	0.0289193i
$267$	−2.57008	−	3.17780i	−0.157286	−	0.194478i
$268$	10.6315	+	3.67960i	0.649422	+	0.224767i
$269$	−7.51579	+	3.43234i	−0.458246	+	0.209274i	−0.631144	−	0.775666i	$-0.717414\pi$
$269$	−7.51579	+	3.43234i	−0.458246	+	0.209274i	0.172898	+	0.984940i	$0.444687\pi$
$270$	−1.68412	+	1.18254i	−0.102492	+	0.0719673i
$271$	−0.681857	+	4.74242i	−0.0414199	+	0.288082i	0.958575	+	0.284841i	$0.0919407\pi$
$271$	−0.681857	+	4.74242i	−0.0414199	+	0.288082i	−0.999995	+	0.00324086i	$0.998968\pi$
$272$	−0.296870	+	6.23206i	−0.0180004	+	0.377874i
$273$	4.43030	+	0.791261i	0.268134	+	0.0478893i
$274$	−11.9171	−	12.4983i	−0.719941	−	0.755052i
$275$	4.47700	−	7.75439i	0.269973	−	0.467607i
$276$	−1.38210	−	8.19084i	−0.0831926	−	0.493030i
$277$	−9.37210	−	16.2330i	−0.563115	−	0.975344i	−0.997222	−	0.0744828i	$-0.976269\pi$
$277$	−9.37210	−	16.2330i	−0.563115	−	0.975344i	0.434107	−	0.900861i	$-0.357064\pi$
$278$	−0.335102	+	1.14125i	−0.0200981	+	0.0684477i
$279$	−30.9129	−	5.08638i	−1.85071	−	0.304513i
$280$	0.128862	+	0.0828148i	0.00770100	+	0.00494913i
$281$	10.2721	−	4.11233i	0.612783	−	0.245321i	−0.0444468	−	0.999012i	$-0.514153\pi$
$281$	10.2721	−	4.11233i	0.612783	−	0.245321i	0.657229	+	0.753691i	$0.271728\pi$
$282$	1.22442	+	1.84920i	0.0729132	+	0.110118i
$283$	−1.38558	+	14.5105i	−0.0823644	+	0.862560i	0.856015	+	0.516952i	$0.172933\pi$
$283$	−1.38558	+	14.5105i	−0.0823644	+	0.862560i	−0.938379	+	0.345608i	$0.887673\pi$
$284$	−1.26553	−	6.56620i	−0.0750955	−	0.389632i
$285$	−0.224703	−	1.42442i	−0.0133102	−	0.0843755i
$286$	−1.18056	−	12.3634i	−0.0698080	−	0.731063i
$287$	2.95825	−	0.868620i	0.174620	−	0.0512730i
$288$	2.01015	−	2.22695i	0.118449	−	0.131224i
$289$	9.10870	−	19.9453i	0.535806	−	1.17325i
$290$	1.43562	−	1.12898i	0.0843025	−	0.0662962i
$291$	−18.9720	+	3.92608i	−1.11216	+	0.230151i
$292$	−5.73961	−	0.548067i	−0.335886	−	0.0320732i
$293$	1.40707	+	29.5381i	0.0822021	+	1.72563i	0.544373	+	0.838843i	$0.316768\pi$
$293$	1.40707	+	29.5381i	0.0822021	+	1.72563i	−0.462171	+	0.886791i	$0.652929\pi$
$294$	−10.9540	+	4.55993i	−0.638852	+	0.265940i
$295$	2.44865	+	0.116644i	0.142566	+	0.00679126i
$296$	6.62619	−	7.64703i	0.385140	−	0.444475i
$297$	9.23518	−	2.64544i	0.535879	−	0.153504i
$298$			7.24223i			0.419531i
$299$	−15.0683	−	28.4759i	−0.871420	−	1.64681i
$300$	7.20677	−	4.29315i	0.416083	−	0.247865i
$301$	1.72385	−	1.64368i	0.0993608	−	0.0947404i
$302$	9.13935	−	3.16316i	0.525911	−	0.182019i
$303$	0.589819	−	0.314345i	0.0338842	−	0.0180586i
$304$	0.781333	+	1.95168i	0.0448125	+	0.111936i
$305$	1.85128	+	2.88065i	0.106004	+	0.164946i
$306$	−16.8072	+	8.23771i	−0.960802	+	0.470918i
$307$	−3.20769	−	3.70187i	−0.183072	−	0.211277i	0.656794	−	0.754070i	$-0.271912\pi$
$307$	−3.20769	−	3.70187i	−0.183072	−	0.211277i	−0.839866	+	0.542793i	$0.817367\pi$
$308$	−0.442037	−	0.562096i	−0.0251874	−	0.0320284i
$309$	−3.21707	+	7.30693i	−0.183013	+	0.415677i
$310$	−4.01911	−	0.975026i	−0.228270	−	0.0553777i
$311$	16.1016	+	3.90619i	0.913035	+	0.221500i	0.664644	−	0.747160i	$-0.268583\pi$
$311$	16.1016	+	3.90619i	0.913035	+	0.221500i	0.248391	+	0.968660i	$0.420098\pi$
$312$	4.68848	−	10.6490i	0.265433	−	0.602879i
$313$	−1.72754	−	2.19674i	−0.0976461	−	0.124167i	0.734774	−	0.678311i	$-0.237288\pi$
$313$	−1.72754	−	2.19674i	−0.0976461	−	0.124167i	−0.832421	+	0.554144i	$0.813046\pi$
$314$	10.7924	+	12.4551i	0.609050	+	0.702881i
$315$	−0.0311684	+	0.458478i	−0.00175614	+	0.0258323i
$316$	−2.25197	−	3.50413i	−0.126683	−	0.197123i
$317$	−5.65220	−	14.1185i	−0.317459	−	0.792974i	−0.998173	−	0.0604248i	$-0.980754\pi$
$317$	−5.65220	−	14.1185i	−0.317459	−	0.792974i	0.680714	−	0.732550i	$-0.261670\pi$
$318$	9.65045	−	5.14322i	0.541171	−	0.288418i
$319$	−8.05711	+	2.78859i	−0.451112	+	0.156131i
$320$	0.286621	−	0.273292i	0.0160226	−	0.0152775i
$321$	−10.1067	+	6.02069i	−0.564102	+	0.336042i
$322$	−1.61628	−	0.910235i	−0.0900716	−	0.0507254i
$323$		−	13.1163i		−	0.729811i
$324$	8.76103	+	2.06017i	0.486724	+	0.114454i
$325$	21.3058	−	24.5882i	1.18183	−	1.36391i
$326$	12.0879	+	0.575816i	0.669485	+	0.0318915i
$327$	−26.5669	+	11.0592i	−1.46915	+	0.611576i
$328$	−0.379284	−	7.96214i	−0.0209424	−	0.439636i
$329$	0.493022	+	0.0470779i	0.0271812	+	0.00259549i
$330$	1.24186	−	0.256991i	0.0683619	−	0.0141469i
$331$	0.707809	−	0.556627i	0.0389047	−	0.0305950i	−0.598517	−	0.801110i	$-0.704243\pi$
$331$	0.707809	−	0.556627i	0.0389047	−	0.0305950i	0.637422	+	0.770515i	$0.280001\pi$
$332$	7.29151	−	15.9662i	0.400174	−	0.876258i
$333$	29.6843	+	6.34800i	1.62669	+	0.347868i
$334$	−2.88177	+	0.846165i	−0.157684	+	0.0463001i
$335$	0.423517	+	4.43527i	0.0231392	+	0.242325i
$336$	−0.104391	−	0.661750i	−0.00569500	−	0.0361014i
$337$	1.59385	+	8.26969i	0.0868227	+	0.450479i	0.999158	+	0.0410344i	$0.0130653\pi$
$337$	1.59385	+	8.26969i	0.0868227	+	0.450479i	−0.912335	+	0.409444i	$0.865723\pi$
$338$	3.05391	−	31.9820i	0.166111	−	1.73959i
$339$	14.2903	+	21.5822i	0.776144	+	1.17218i
$340$	−2.29389	+	0.918335i	−0.124404	+	0.0498037i
$341$	16.2418	+	10.4380i	0.879544	+	0.565248i
$342$	−3.99832	+	4.87741i	−0.216205	+	0.263740i
$343$	−1.50928	+	5.14014i	−0.0814935	+	0.277541i
$344$	−3.07906	−	5.33310i	−0.166012	−	0.287541i
$345$	2.72330	−	1.84542i	0.146618	−	0.0993541i
$346$	−3.87449	+	6.71081i	−0.208294	+	0.360775i
$347$	−19.1541	−	20.0882i	−1.02825	−	1.07839i	−0.996884	−	0.0788843i	$-0.974864\pi$
$347$	−19.1541	−	20.0882i	−1.02825	−	1.07839i	−0.0313613	−	0.999508i	$-0.509984\pi$
$348$	−7.86323	−	1.40439i	−0.421514	−	0.0752832i
$349$	0.877439	−	18.4197i	0.0469682	−	0.985984i	−0.845247	−	0.534375i	$-0.820547\pi$
$349$	0.877439	−	18.4197i	0.0469682	−	0.985984i	0.892216	−	0.451609i	$-0.149150\pi$
$350$	0.266594	−	1.85420i	0.0142500	−	0.0991111i
$351$	34.7693	−	3.08805i	1.85585	−	0.164828i
$352$	−1.68172	+	0.768016i	−0.0896360	+	0.0409354i
$353$	−9.88409	−	3.42092i	−0.526077	−	0.182077i	0.0511039	−	0.998693i	$-0.483726\pi$
$353$	−9.88409	−	3.42092i	−0.526077	−	0.182077i	−0.577181	+	0.816616i	$0.695847\pi$
$354$	−6.74204	−	8.33627i	−0.358335	−	0.443068i
$355$	2.15722	−	1.53615i	0.114493	−	0.0815303i
$356$	−0.556306	+	2.29313i	−0.0294842	+	0.121535i
$357$	−0.929844	+	4.07506i	−0.0492126	+	0.215675i
$358$	9.21533	−	0.879957i	0.487045	−	0.0465072i
$359$	−2.29503	−	15.9623i	−0.121127	−	0.842456i	−0.956283	−	0.292443i	$-0.905532\pi$
$359$	−2.29503	−	15.9623i	−0.121127	−	0.842456i	0.835156	−	0.550013i	$-0.185377\pi$
$360$	1.13294	+	0.357770i	0.0597113	+	0.0188561i
$361$	6.05695	+	13.2629i	0.318787	+	0.698046i
$362$	−1.37963	−	0.711249i	−0.0725118	−	0.0373824i
$363$	13.0230	+	1.69118i	0.683530	+	0.0887642i
$364$	−1.19062	−	2.30947i	−0.0624052	−	0.121049i
$365$	−0.746827	−	2.15781i	−0.0390907	−	0.112945i
$366$	4.02255	−	14.4257i	0.210262	−	0.754043i
$367$	−24.1423	+	13.9386i	−1.26022	+	0.727587i	−0.973116	−	0.230314i	$-0.926025\pi$
$367$	−24.1423	+	13.9386i	−1.26022	+	0.727587i	−0.287101	+	0.957900i	$0.592691\pi$
$368$	−3.27217	+	3.50612i	−0.170574	+	0.182769i
$369$	20.3753	−	12.5181i	1.06070	−	0.651664i
$370$	3.84490	+	1.12896i	0.199887	+	0.0586921i
$371$	0.462152	−	2.39787i	0.0239938	−	0.124491i
$372$	8.50705	+	15.9622i	0.441070	+	0.827599i
$373$	−2.29829	+	2.92251i	−0.119001	+	0.151322i	−0.841904	−	0.539628i	$-0.818565\pi$
$373$	−2.29829	+	2.92251i	−0.119001	+	0.151322i	0.722903	+	0.690950i	$0.242807\pi$
$374$	11.5218	−	0.548850i	0.595778	−	0.0283804i
$375$	5.55289	+	3.84097i	0.286750	+	0.198347i
$376$	0.418798	−	1.21004i	0.0215978	−	0.0624029i
$377$	−30.6645	+	4.40890i	−1.57930	+	0.227070i
$378$	1.58799	−	1.23189i	0.0816776	−	0.0633618i
$379$	−8.77920	−	29.8992i	−0.450957	−	1.53582i	−0.800754	−	0.598994i	$-0.795567\pi$
$379$	−8.77920	−	29.8992i	−0.450957	−	1.53582i	0.349797	−	0.936826i	$-0.386251\pi$
$380$	−0.574533	+	0.602553i	−0.0294729	+	0.0309103i
$381$	1.24636	+	11.4039i	0.0638532	+	0.584240i
$382$	−1.79290	+	4.47845i	−0.0917327	+	0.229137i
$383$	20.6999	−	3.98958i	1.05772	−	0.203858i	0.369401	−	0.929270i	$-0.379563\pi$
$383$	20.6999	−	3.98958i	1.05772	−	0.203858i	0.688314	+	0.725412i	$0.258351\pi$
$384$	−1.72630	−	0.141073i	−0.0880947	−	0.00719910i
$385$	0.129768	−	0.251715i	0.00661358	−	0.0128286i
$386$	−19.6583	−	2.82644i	−1.00058	−	0.143862i
$387$	9.55970	−	15.8087i	0.485947	−	0.803601i
$388$	8.45347	+	7.32498i	0.429160	+	0.371869i
$389$	7.12110	+	29.3536i	0.361054	+	1.48829i	0.805562	+	0.592511i	$0.201863\pi$
$389$	7.12110	+	29.3536i	0.361054	+	1.48829i	−0.444508	+	0.895775i	$0.646621\pi$
$390$	4.60754	−	0.0629474i	0.233312	−	0.00318747i
$391$	27.0833	−	12.7205i	1.36966	−	0.643305i
$392$	5.93262	+	3.42520i	0.299642	+	0.172999i
$393$	4.43147	+	1.23570i	0.223538	+	0.0623327i
$394$	2.93684	+	0.566029i	0.147956	+	0.0285161i
$395$	0.891848	−	1.38774i	0.0448738	−	0.0698249i
$396$	−4.45178	−	3.30816i	−0.223710	−	0.166241i
$397$	−12.5026	+	8.03495i	−0.627489	+	0.403262i	−0.815379	−	0.578928i	$-0.803471\pi$
$397$	−12.5026	+	8.03495i	−0.627489	+	0.403262i	0.187890	+	0.982190i	$0.439835\pi$
$398$	4.13768	−	5.81056i	0.207403	−	0.291257i
$399$	0.285404	+	1.37916i	0.0142881	+	0.0690441i
$400$	−4.49623	−	1.80002i	−0.224812	−	0.0900010i
$401$	5.07549	+	7.12752i	0.253458	+	0.355931i	0.921626	−	0.388078i	$-0.126861\pi$
$401$	5.07549	+	7.12752i	0.253458	+	0.355931i	−0.668169	+	0.744010i	$0.732922\pi$
$402$	13.2530	−	14.2851i	0.660999	−	0.712475i
$403$	50.7714	+	48.4104i	2.52910	+	2.41150i
$404$	−0.351005	−	0.160298i	−0.0174631	−	0.00797514i
$405$	0.699179	+	3.49502i	0.0347425	+	0.173669i
$406$	−1.34806	+	1.16810i	−0.0669029	+	0.0579717i
$407$	−15.2382	−	10.8511i	−0.755332	−	0.537869i
$408$	9.67194	+	4.82015i	0.478832	+	0.238633i
$409$	7.96883	+	6.26675i	0.394033	+	0.309871i	0.795444	−	0.606027i	$-0.207238\pi$
$409$	7.96883	+	6.26675i	0.394033	+	0.309871i	−0.401411	+	0.915898i	$0.631480\pi$
$410$	2.80590	−	1.44654i	0.138573	−	0.0714396i
$411$	−28.1298	+	10.1682i	−1.38754	+	0.501561i
$412$	4.47951	−	1.08672i	0.220689	−	0.0535387i
$413$	−2.39421			−0.117811
$414$	−13.9488	−	3.52571i	−0.685547	−	0.173279i
$415$	6.95126			0.341224
$416$	−6.52834	+	1.58376i	−0.320078	+	0.0776501i
$417$	1.57525	+	1.32772i	0.0771401	+	0.0650187i
$418$	3.45459	−	1.78097i	0.168970	−	0.0871100i
$419$	9.57119	+	7.52687i	0.467583	+	0.367712i	0.823976	−	0.566625i	$-0.191751\pi$
$419$	9.57119	+	7.52687i	0.467583	+	0.367712i	−0.356393	+	0.934336i	$0.615993\pi$
$420$	0.221216	−	0.146475i	0.0107942	−	0.00714725i
$421$	−12.7647	−	9.08971i	−0.622114	−	0.443005i	0.225042	−	0.974349i	$-0.427748\pi$
$421$	−12.7647	−	9.08971i	−0.622114	−	0.443005i	−0.847156	+	0.531344i	$0.821687\pi$
$422$	−2.36503	+	2.04931i	−0.115128	+	0.0997589i
$423$	3.78593	−	0.650355i	0.184078	−	0.0316213i
$424$	−5.74304	−	2.62276i	−0.278907	−	0.127372i
$425$	21.8691	+	20.8522i	1.06081	+	1.01148i
$426$	−11.2921	−	2.57662i	−0.547102	−	0.124837i
$427$	−1.93989	−	2.72419i	−0.0938779	−	0.131833i
$428$	6.30549	+	2.52434i	0.304787	+	0.122018i
$429$	−20.4225	−	6.75735i	−0.986009	−	0.326248i
$430$	1.41465	−	1.98659i	0.0682203	−	0.0958020i
$431$	−21.8535	+	14.0444i	−1.05265	+	0.676495i	−0.948083	−	0.318023i	$-0.896981\pi$
$431$	−21.8535	+	14.0444i	−1.05265	+	0.676495i	−0.104564	+	0.994518i	$0.533345\pi$
$432$	−2.12724	−	4.74077i	−0.102347	−	0.228090i
$433$	6.69069	−	10.4109i	0.321534	−	0.500317i	−0.642432	−	0.766343i	$-0.722074\pi$
$433$	6.69069	−	10.4109i	0.321534	−	0.500317i	0.963966	+	0.266026i	$0.0857108\pi$
$434$	3.96616	+	0.764415i	0.190382	+	0.0366931i
$435$	−0.787715	−	3.06371i	−0.0377680	−	0.146894i
$436$	14.3884	+	8.30715i	0.689080	+	0.397840i
$437$	6.52046	−	7.68977i	0.311916	−	0.367852i
$438$	−4.87465	+	8.71599i	−0.232920	+	0.416466i
$439$	−7.05867	−	29.0962i	−0.336892	−	1.38869i	−0.848376	−	0.529394i	$-0.822419\pi$
$439$	−7.05867	−	29.0962i	−0.336892	−	1.38869i	0.511484	−	0.859293i	$-0.329096\pi$
$440$	−0.553343	−	0.479474i	−0.0263796	−	0.0228580i
$441$	−0.416707	+	20.5470i	−0.0198432	+	0.978427i
$442$	41.4860	+	5.96478i	1.97329	+	0.283716i
$443$	0.476673	−	0.924616i	0.0226474	−	0.0439298i	−0.877240	−	0.480051i	$-0.840618\pi$
$443$	0.476673	−	0.924616i	0.0226474	−	0.0439298i	0.899888	+	0.436122i	$0.143648\pi$
$444$	−7.49754	−	15.8410i	−0.355818	−	0.751781i
$445$	−0.917602	+	0.176853i	−0.0434985	+	0.00838365i
$446$	0.181989	−	0.454587i	0.00861744	−	0.0215253i
$447$	11.4805	+	5.05457i	0.543007	+	0.239073i
$448$	−0.266913	+	0.279930i	−0.0126104	+	0.0132255i
$449$	3.56972	+	12.1573i	0.168465	+	0.573740i	0.999838	+	0.0180242i	$0.00573759\pi$
$449$	3.56972	+	12.1573i	0.168465	+	0.573740i	−0.831372	+	0.555716i	$0.812444\pi$
$450$	−1.77573	−	14.4206i	−0.0837086	−	0.679792i
$451$	−14.5870	+	2.09730i	−0.686877	+	0.0987580i
$452$	4.88783	−	14.1224i	0.229904	−	0.664264i
$453$	1.36435	−	16.6955i	0.0641029	−	0.784421i
$454$	−17.9306	+	0.854139i	−0.841524	+	0.0400867i
$455$	0.636092	−	0.808856i	0.0298204	−	0.0379198i
$456$	3.63913	+	0.123556i	0.170418	+	0.00578602i
$457$	−3.10363	+	16.1032i	−0.145182	+	0.753274i	0.834232	+	0.551413i	$0.185911\pi$
$457$	−3.10363	+	16.1032i	−0.145182	+	0.753274i	−0.979414	+	0.201861i	$0.935301\pi$
$458$	20.5901	+	6.04581i	0.962113	+	0.282502i
$459$	1.32827	+	32.3922i	0.0619985	+	1.51194i
$460$	−1.80138	−	0.601955i	−0.0839898	−	0.0280663i
$461$	−10.9321	+	6.31166i	−0.509159	+	0.293963i	−0.732488	−	0.680780i	$-0.761641\pi$
$461$	−10.9321	+	6.31166i	−0.509159	+	0.293963i	0.223329	+	0.974743i	$0.428308\pi$
$462$	−1.19955	+	0.308418i	−0.0558082	+	0.0143489i
$463$	5.41042	+	15.6324i	0.251444	+	0.726499i	0.998119	+	0.0613097i	$0.0195277\pi$
$463$	5.41042	+	15.6324i	0.251444	+	0.726499i	−0.746675	+	0.665189i	$0.768351\pi$
$464$	2.11319	+	4.09902i	0.0981026	+	0.190292i
$465$	−4.35068	+	5.69064i	−0.201758	+	0.263897i
$466$	−15.6532	−	8.06980i	−0.725122	−	0.373826i
$467$	−3.71984	−	8.14530i	−0.172133	−	0.376920i	0.803828	−	0.594861i	$-0.202793\pi$
$467$	−3.71984	−	8.14530i	−0.172133	−	0.376920i	−0.975962	+	0.217942i	$0.930066\pi$
$468$	−13.6086	−	14.8645i	−0.629059	−	0.687111i
$469$	−0.619275	−	4.30715i	−0.0285955	−	0.198886i
$470$	0.504805	−	0.0482030i	0.0232849	−	0.00222344i
$471$	27.2763	−	8.41544i	1.25682	−	0.387763i
$472$	−1.45935	+	6.01552i	−0.0671720	+	0.276887i
$473$	−9.27403	+	6.60401i	−0.426420	+	0.303653i
$474$	−7.12651	+	1.12421i	−0.327331	+	0.0516365i
$475$	9.62163	+	3.33008i	0.441471	+	0.152794i
$476$	2.19513	−	1.00248i	0.100614	−	0.0459487i
$477$	−1.41775	−	18.8876i	−0.0649143	−	0.864804i
$478$	−4.17506	+	29.0382i	−0.190963	+	1.32818i
$479$	−0.699010	+	14.6740i	−0.0319386	+	0.670473i	0.924962	+	0.380059i	$0.124096\pi$
$479$	−0.699010	+	14.6740i	−0.0319386	+	0.670473i	−0.956901	+	0.290414i	$0.906207\pi$
$480$	−0.233185	−	0.645093i	−0.0106434	−	0.0294443i
$481$	−46.9067	−	49.1943i	−2.13876	−	2.24307i
$482$	−1.36232	+	2.35961i	−0.0620521	+	0.107477i
$483$	−2.57096	+	1.92686i	−0.116983	+	0.0876751i
$484$	−3.79098	−	6.56618i	−0.172317	−	0.298463i
$485$	−1.24802	+	4.25038i	−0.0566698	+	0.193000i
$486$	9.38039	−	12.4502i	0.425503	−	0.564754i
$487$	−3.38272	−	2.17394i	−0.153285	−	0.0985106i	0.461750	−	0.887010i	$-0.347222\pi$
$487$	−3.38272	−	2.17394i	−0.153285	−	0.0985106i	−0.615035	+	0.788500i	$0.710858\pi$
$488$	−8.02705	+	3.21355i	−0.363367	+	0.145470i
$489$	9.34928	−	18.7599i	0.422789	−	0.848354i
$490$	−0.257884	+	2.70068i	−0.0116500	+	0.122004i
$491$	4.39673	+	22.8124i	0.198422	+	1.02951i	0.935400	+	0.353592i	$0.115040\pi$
$491$	4.39673	+	22.8124i	0.198422	+	1.02951i	−0.736978	+	0.675917i	$0.763748\pi$
$492$	−12.8864	−	4.95578i	−0.580963	−	0.223424i
$493$	−2.73503	−	28.6426i	−0.123180	−	1.29000i
$494$	13.5503	−	3.97874i	0.609658	−	0.179012i
$495$	0.459344	−	2.14797i	0.0206460	−	0.0965439i
$496$	4.33812	−	9.49916i	0.194787	−	0.426525i
$497$	−2.03309	+	1.59884i	−0.0911966	+	0.0717178i
$498$	−20.2208	−	22.7019i	−0.906116	−	1.01729i
$499$	32.2000	+	3.07473i	1.44147	+	0.137644i	0.786303	−	0.617841i	$-0.211992\pi$
$499$	32.2000	+	3.07473i	1.44147	+	0.137644i	0.655167	+	0.755484i	$0.272598\pi$
$500$	−0.185483	−	3.89377i	−0.00829506	−	0.174135i
$501$	−0.669927	+	5.15878i	−0.0299301	+	0.230477i
$502$	−15.2749	−	0.727633i	−0.681752	−	0.0324758i
$503$	5.73759	−	6.62154i	0.255827	−	0.295240i	−0.613279	−	0.789866i	$-0.710150\pi$
$503$	5.73759	−	6.62154i	0.255827	−	0.295240i	0.869105	+	0.494627i	$0.164695\pi$
$504$	−1.12187	−	0.296373i	−0.0499721	−	0.0132015i
$505$		−	0.152818i		−	0.00680032i
$506$	7.02779	+	5.40600i	0.312423	+	0.240326i
$507$	−48.5668	−	27.1623i	−2.15693	−	1.20632i
$508$	4.79347	−	4.57057i	0.212676	−	0.202786i
$509$	−4.29339	+	1.48596i	−0.190301	+	0.0658639i	−0.420556	−	0.907266i	$-0.638165\pi$
$509$	−4.29339	+	1.48596i	−0.190301	+	0.0658639i	0.230255	+	0.973130i	$0.426044\pi$
$510$	−0.145220	+	4.27723i	−0.00643046	+	0.189399i
$511$	0.828844	+	2.07035i	0.0366659	+	0.0915870i
$512$	0.540641	+	0.841254i	0.0238932	+	0.0371785i
$513$	4.94117	+	9.74227i	0.218158	+	0.430132i
$514$	6.05116	+	6.98341i	0.266905	+	0.308025i
$515$	1.12844	+	1.43492i	0.0497248	+	0.0632302i
$516$	−10.6031	+	1.15884i	−0.466773	+	0.0510150i
$517$	−2.30058	−	0.558114i	−0.101179	−	0.0245458i
$518$	−3.80336	−	0.922686i	−0.167110	−	0.0405405i
$519$	7.93393	+	10.8256i	0.348261	+	0.475189i
$520$	−1.64456	−	2.09122i	−0.0721186	−	0.0917063i
$521$	−24.3398	−	28.0896i	−1.06634	−	1.23063i	−0.971974	−	0.235090i	$-0.924461\pi$
$521$	−24.3398	−	28.0896i	−1.06634	−	1.23063i	−0.0943710	−	0.995537i	$-0.530084\pi$
$522$	−7.71424	+	11.4847i	−0.337643	+	0.502672i
$523$	20.8494	+	32.4423i	0.911681	+	1.41860i	0.908166	+	0.418610i	$0.137483\pi$
$523$	20.8494	+	32.4423i	0.911681	+	1.41860i	0.00351505	+	0.999994i	$0.498881\pi$
$524$	−0.987178	−	2.46585i	−0.0431251	−	0.107721i
$525$	−2.75323	−	1.71671i	−0.120161	−	0.0749233i
$526$	12.9214	−	4.47214i	0.563400	−	0.194994i
$527$	−47.1545	+	44.9617i	−2.05408	+	1.95856i
$528$	0.0437439	+	3.20190i	0.00190371	+	0.139345i
$529$	22.2020	+	6.00606i	0.965303	+	0.261133i
$530$		−	2.50037i		−	0.108609i
$531$	−17.9202	+	4.86942i	−0.777671	+	0.211315i
$532$	0.532485	−	0.614520i	0.0230861	−	0.0266428i
$533$	−53.4873	−	2.54791i	−2.31679	−	0.110362i
$534$	3.24683	+	2.48230i	0.140504	+	0.107420i
$535$	0.127988	+	2.68680i	0.00553340	+	0.116160i
$536$	−11.1993	−	1.06941i	−0.483737	−	0.0461913i
$537$	5.03674	−	15.2224i	0.217351	−	0.656894i
$538$	6.49472	−	5.10751i	0.280007	−	0.220200i
$539$	5.26121	−	11.5205i	0.226617	−	0.496221i
$540$	1.35786	−	1.54626i	0.0584328	−	0.0665403i
$541$	−1.69529	+	0.497782i	−0.0728862	+	0.0214013i	−0.317972	−	0.948100i	$-0.603002\pi$
$541$	−1.69529	+	0.497782i	−0.0728862	+	0.0214013i	0.245086	+	0.969501i	$0.421184\pi$
$542$	−0.455431	−	4.76949i	−0.0195625	−	0.204867i
$543$	−2.09037	+	1.69060i	−0.0897062	+	0.0725508i
$544$	−1.18076	−	6.12638i	−0.0506248	−	0.262666i
$545$	−0.625446	+	6.54997i	−0.0267912	+	0.280570i
$546$	−4.49197	+	0.275526i	−0.192238	+	0.0117914i
$547$	2.84303	−	1.13818i	0.121559	−	0.0486650i	−0.310085	−	0.950709i	$-0.600358\pi$
$547$	2.84303	−	1.13818i	0.121559	−	0.0486650i	0.431645	+	0.902044i	$0.357933\pi$
$548$	14.5278	+	9.33645i	0.620597	+	0.398834i
$549$	−20.0603	−	16.4447i	−0.856153	−	0.701843i
$550$	−2.52263	+	8.59130i	−0.107565	+	0.366334i
$551$	−4.84749	−	8.39610i	−0.206510	−	0.357686i
$552$	3.27420	+	7.63411i	0.139359	+	0.324929i
$553$	−0.805554	+	1.39526i	−0.0342556	+	0.0593325i
$554$	12.9350	+	13.5658i	0.549555	+	0.576357i
$555$	4.47312	−	5.30704i	0.189873	−	0.225271i
$556$	0.0565954	−	1.18808i	0.00240018	−	0.0503860i
$557$	5.66833	−	39.4241i	0.240175	−	1.67045i	−0.411084	−	0.911597i	$-0.634850\pi$
$557$	5.66833	−	39.4241i	0.240175	−	1.67045i	0.651259	−	0.758856i	$-0.274241\pi$
$558$	31.2407	−	2.34500i	1.32252	−	0.0992718i
$559$	−37.6301	+	17.1851i	−1.59158	+	0.726851i
$560$	−0.144754	−	0.0500999i	−0.00611698	−	0.00211711i
$561$	7.17136	−	18.6475i	0.302775	−	0.787299i
$562$	−9.01303	+	6.41815i	−0.380192	+	0.270733i
$563$	−2.28015	+	9.39892i	−0.0960970	+	0.396117i	−0.999464	−	0.0327521i	$-0.989573\pi$
$563$	−2.28015	+	9.39892i	−0.0960970	+	0.396117i	0.903366	+	0.428869i	$0.141088\pi$
$564$	−1.62587	−	1.50840i	−0.0684615	−	0.0635153i
$565$	5.89162	−	0.562582i	0.247862	−	0.0236680i
$566$	−2.07445	−	14.4281i	−0.0871957	−	0.606460i
$567$	−0.844503	−	3.37708i	−0.0354658	−	0.141824i
$568$	2.77790	+	6.08275i	0.116558	+	0.255226i
$569$	20.1850	+	10.4061i	0.846197	+	0.436245i	0.826080	−	0.563553i	$-0.190566\pi$
$569$	20.1850	+	10.4061i	0.846197	+	0.436245i	0.0201170	+	0.999798i	$0.493596\pi$
$570$	0.554189	+	1.33130i	0.0232124	+	0.0557618i
$571$	18.2791	+	35.4565i	0.764956	+	1.48381i	0.871975	+	0.489550i	$0.162839\pi$
$571$	18.2791	+	35.4565i	0.764956	+	1.48381i	−0.107019	+	0.994257i	$0.534131\pi$
$572$	4.06206	+	11.7366i	0.169843	+	0.490730i
$573$	5.84796	+	5.96777i	0.244302	+	0.249307i
$574$	−2.67008	+	1.54157i	−0.111447	+	0.0643438i
$575$	2.45518	+	23.0969i	0.102388	+	0.963205i
$576$	−1.42846	+	2.63808i	−0.0595194	+	0.109920i
$577$	3.01037	+	0.883926i	0.125324	+	0.0367983i	0.343793	−	0.939046i	$-0.388288\pi$
$577$	3.01037	+	0.883926i	0.125324	+	0.0367983i	−0.218469	+	0.975844i	$0.570106\pi$
$578$	−4.14966	+	21.5305i	−0.172603	+	0.895551i
$579$	−18.2006	+	29.1899i	−0.756392	+	1.21309i
$580$	−1.12898	+	1.43562i	−0.0468785	+	0.0596108i
$581$	−6.78131	+	0.323034i	−0.281336	+	0.0134017i
$582$	17.5116	−	8.28822i	0.725878	−	0.343558i
$583$	−3.81770	+	11.0305i	−0.158113	+	0.456838i
$584$	5.70704	−	0.820548i	0.236159	−	0.0339545i
$585$	3.11595	−	7.34785i	0.128829	−	0.303796i
$586$	−8.33128	−	28.3737i	−0.344162	−	1.17211i
$587$	15.1802	−	15.9205i	0.626553	−	0.657110i	−0.331582	−	0.943426i	$-0.607582\pi$
$587$	15.1802	−	15.9205i	0.626553	−	0.657110i	0.958135	+	0.286317i	$0.0924309\pi$
$588$	9.57021	−	7.01390i	0.394669	−	0.289248i
$589$	−8.15936	+	20.3811i	−0.336201	+	0.839788i
$590$	−2.40713	+	0.463936i	−0.0990999	+	0.0190999i
$591$	2.94698	−	4.26046i	0.121223	−	0.175252i
$592$	−4.63655	+	8.99366i	−0.190561	+	0.369637i
$593$	−40.4885	−	5.82137i	−1.66267	−	0.239055i	−0.754088	−	0.656773i	$-0.771921\pi$
$593$	−40.4885	−	5.82137i	−1.66267	−	0.239055i	−0.908577	+	0.417718i	$0.862830\pi$
$594$	−8.35117	+	4.74815i	−0.342652	+	0.194819i
$595$	0.722272	+	0.625852i	0.0296103	+	0.0256574i
$596$	−1.70742	−	7.03809i	−0.0699387	−	0.288291i
$597$	−6.32315	−	10.6145i	−0.258789	−	0.434421i
$598$	21.3570	+	24.1208i	0.873352	+	0.986372i
$599$	35.5603	+	20.5307i	1.45295	+	0.838863i	0.998648	−	0.0519835i	$-0.0165543\pi$
$599$	35.5603	+	20.5307i	1.45295	+	0.838863i	0.454305	+	0.890846i	$0.349888\pi$
$600$	−5.99147	+	5.87119i	−0.244601	+	0.239690i
$601$	−19.5646	−	3.77077i	−0.798056	−	0.153813i	−0.226108	−	0.974102i	$-0.572600\pi$
$601$	−19.5646	−	3.77077i	−0.798056	−	0.153813i	−0.571948	+	0.820290i	$0.693812\pi$
$602$	−1.28774	+	2.00376i	−0.0524844	+	0.0816673i
$603$	−13.3952	−	30.9788i	−0.545494	−	1.26155i
$604$	−8.13599	+	5.22868i	−0.331049	+	0.212752i
$605$	1.74173	−	2.44592i	0.0708114	−	0.0994407i
$606$	−0.499083	+	0.444539i	−0.0202739	+	0.0180582i
$607$	1.62515	+	0.650612i	0.0659629	+	0.0264075i	0.404409	−	0.914578i	$-0.367477\pi$
$607$	1.62515	+	0.650612i	0.0659629	+	0.0264075i	−0.338446	+	0.940986i	$0.609901\pi$
$608$	−1.21943	−	1.71246i	−0.0494546	−	0.0694492i
$609$	0.910831	+	2.95220i	0.0369087	+	0.119629i
$610$	−2.47824	−	2.36300i	−0.100341	−	0.0956749i
$611$	−7.82443	−	3.57330i	−0.316542	−	0.144560i
$612$	14.3913	−	11.9679i	0.581733	−	0.483775i
$613$	21.7793	−	18.8719i	0.879659	−	0.762229i	−0.0927063	−	0.995693i	$-0.529552\pi$
$613$	21.7793	−	18.8719i	0.879659	−	0.762229i	0.972365	+	0.233465i	$0.0750063\pi$
$614$	3.99001	+	2.84128i	0.161024	+	0.114665i
$615$	−0.334752	−	5.45752i	−0.0134985	−	0.220069i
$616$	0.562096	+	0.442037i	0.0226475	+	0.0178102i
$617$	−20.0324	+	10.3274i	−0.806475	+	0.415767i	−0.811595	−	0.584220i	$-0.801400\pi$
$617$	−20.0324	+	10.3274i	−0.806475	+	0.415767i	0.00512044	+	0.999987i	$0.498370\pi$
$618$	1.40371	−	7.85942i	0.0564654	−	0.316152i
$619$	2.43475	−	0.590664i	0.0978609	−	0.0237408i	−0.186529	−	0.982449i	$-0.559724\pi$
$619$	2.43475	−	0.590664i	0.0978609	−	0.0237408i	0.284390	+	0.958709i	$0.408209\pi$
$620$	4.13569			0.166093
$621$	−15.3243	+	19.6511i	−0.614943	+	0.788572i
$622$	−16.5686			−0.664340
$623$	0.886949	−	0.215171i	0.0355349	−	0.00862066i
$624$	−2.04573	+	11.4541i	−0.0818949	+	0.458533i
$625$	−20.1517	+	10.3889i	−0.806067	+	0.415556i
$626$	2.19674	+	1.72754i	0.0877994	+	0.0690462i
$627$	−0.412143	−	6.71925i	−0.0164594	−	0.268341i
$628$	−13.4246	−	9.55959i	−0.535698	−	0.381469i
$629$	47.7108	−	41.3417i	1.90236	−	1.64840i
$630$	−0.0778006	−	0.452903i	−0.00309965	−	0.0180441i
$631$	−23.9397	−	10.9329i	−0.953025	−	0.435232i	−0.122658	−	0.992449i	$-0.539142\pi$
$631$	−23.9397	−	10.9329i	−0.953025	−	0.435232i	−0.830367	+	0.557217i	$0.811869\pi$
$632$	3.01462	+	2.87444i	0.119915	+	0.114339i
$633$	1.59796	+	5.17935i	0.0635133	+	0.205861i
$634$	8.82143	+	12.3880i	0.350344	+	0.491989i
$635$	2.43512	+	0.974874i	0.0966346	+	0.0386867i
$636$	−8.16586	+	7.27342i	−0.323797	+	0.288410i
$637$	26.6936	−	37.4859i	1.05764	−	1.48525i
$638$	7.17256	−	4.60952i	0.283964	−	0.182493i
$639$	−11.9656	+	16.1020i	−0.473350	+	0.636986i
$640$	−0.214110	+	0.333162i	−0.00846344	+	0.0131694i
$641$	19.0033	+	3.66260i	0.750587	+	0.144664i	0.550177	−	0.835048i	$-0.314560\pi$
$641$	19.0033	+	3.66260i	0.750587	+	0.144664i	0.200410	+	0.979712i	$0.435772\pi$
$642$	8.40240	−	8.23372i	0.331616	−	0.324959i
$643$	10.0247	+	5.78779i	0.395337	+	0.228248i	0.684470	−	0.729041i	$-0.260034\pi$
$643$	10.0247	+	5.78779i	0.395337	+	0.228248i	−0.289133	+	0.957289i	$0.593367\pi$
$644$	1.78531	+	0.503526i	0.0703511	+	0.0198417i
$645$	−2.16184	−	3.62901i	−0.0851225	−	0.142892i
$646$	3.09229	+	12.7466i	0.121664	+	0.501508i
$647$	31.3732	+	27.1851i	1.23341	+	1.06875i	0.995232	+	0.0975330i	$0.0310951\pi$
$647$	31.3732	+	27.1851i	1.23341	+	1.06875i	0.238177	+	0.971222i	$0.423450\pi$
$648$	−8.99978	+	0.0633960i	−0.353545	+	0.00249043i
$649$	11.3275	+	1.62866i	0.444645	+	0.0639303i
$650$	−14.9083	+	28.9182i	−0.584754	+	1.13426i
$651$	3.97986	−	5.75369i	0.155983	−	0.225505i
$652$	−11.8829	+	2.29024i	−0.465370	+	0.0896926i
$653$	−4.48851	+	11.2118i	−0.175649	+	0.438750i	−0.989901	−	0.141762i	$-0.954723\pi$
$653$	−4.48851	+	11.2118i	−0.175649	+	0.438750i	0.814252	+	0.580512i	$0.197148\pi$
$654$	23.2107	−	17.0108i	0.907610	−	0.665177i
$655$	0.725895	−	0.761297i	0.0283631	−	0.0297463i
$656$	2.24574	+	7.64828i	0.0876814	+	0.298615i
$657$	10.4145	+	13.8105i	0.406309	+	0.538799i
$658$	−0.490223	+	0.0704834i	−0.0191109	+	0.00274773i
$659$	−12.1341	+	35.0592i	−0.472678	+	1.36571i	0.416910	+	0.908948i	$0.363113\pi$
$659$	−12.1341	+	35.0592i	−0.472678	+	1.36571i	−0.889588	+	0.456764i	$0.849008\pi$
$660$	−1.14626	+	0.542526i	−0.0446182	+	0.0211178i
$661$	14.6008	−	0.695520i	0.567904	−	0.0270526i	0.238333	−	0.971183i	$-0.423399\pi$
$661$	14.6008	−	0.695520i	0.567904	−	0.0270526i	0.329571	+	0.944131i	$0.393096\pi$
$662$	−0.556627	+	0.707809i	−0.0216339	+	0.0275098i
$663$	38.4098	−	61.6010i	1.49171	−	2.39239i
$664$	−3.32180	+	17.2352i	−0.128911	+	0.668854i
$665$	0.308979	+	0.0907243i	0.0119817	+	0.00351814i
$666$	−30.3441	+	0.829267i	−1.17581	+	0.0321334i
$667$	12.6355	−	18.1521i	0.489248	−	0.702852i
$668$	2.60105	−	1.50172i	0.100638	−	0.0581032i
$669$	−0.593600	−	0.605761i	−0.0229499	−	0.0234201i
$670$	−1.45723	−	4.21040i	−0.0562978	−	0.162662i
$671$	7.32494	+	14.2084i	0.282776	+	0.548509i
$672$	0.257462	+	0.618485i	0.00993180	+	0.0238586i
$673$	11.0533	+	5.69837i	0.426073	+	0.219656i	0.657907	−	0.753100i	$-0.271442\pi$
$673$	11.0533	+	5.69837i	0.426073	+	0.219656i	−0.231834	+	0.972755i	$0.574472\pi$
$674$	−3.49858	−	7.66082i	−0.134760	−	0.295084i
$675$	−24.0990	−	7.24964i	−0.927570	−	0.279039i
$676$	4.57222	+	31.8005i	0.175854	+	1.22309i
$677$	16.1668	−	1.54374i	0.621340	−	0.0593307i	0.220361	−	0.975418i	$-0.429276\pi$
$677$	16.1668	−	1.54374i	0.621340	−	0.0593307i	0.400978	+	0.916088i	$0.368670\pi$
$678$	−18.9757	−	17.6047i	−0.728757	−	0.676105i
$679$	1.01999	−	4.20446i	0.0391436	−	0.161352i
$680$	2.01272	−	1.43325i	0.0771844	−	0.0549628i
$681$	−11.1603	+	29.0199i	−0.427664	+	1.11205i
$682$	−18.2448	−	6.31460i	−0.698631	−	0.241798i
$683$	−5.11203	+	2.33458i	−0.195606	+	0.0893304i	−0.510810	−	0.859694i	$-0.670654\pi$
$683$	−5.11203	+	2.33458i	−0.195606	+	0.0893304i	0.315204	+	0.949024i	$0.397927\pi$
$684$	2.73572	−	5.68256i	0.104603	−	0.217278i
$685$	−0.973311	+	6.76953i	−0.0371883	+	0.258650i
$686$	0.254903	−	5.35107i	0.00973224	−	0.204305i
$687$	23.9543	−	28.4201i	0.913915	−	1.08430i
$688$	4.24960	+	4.45685i	0.162014	+	0.169916i
$689$	−21.2064	+	36.7305i	−0.807898	+	1.39932i
$690$	−2.21146	+	2.43544i	−0.0841889	+	0.0927158i
$691$	7.01893	+	12.1571i	0.267013	+	0.462480i	0.968089	−	0.250607i	$-0.0806301\pi$
$691$	7.01893	+	12.1571i	0.267013	+	0.462480i	−0.701076	+	0.713086i	$0.747297\pi$
$692$	2.18314	−	7.43509i	0.0829905	−	0.282640i
$693$	−0.348295	+	2.11680i	−0.0132306	+	0.0804105i
$694$	23.3501	+	15.0062i	0.886359	+	0.569628i
$695$	0.437308	−	0.175072i	0.0165881	−	0.00664085i
$696$	7.97268	−	0.489025i	0.302204	−	0.0185365i
$697$	4.72744	−	49.5080i	0.179065	−	1.87525i
$698$	3.48991	+	18.1074i	0.132095	+	0.685373i
$699$	−23.7172	+	19.1815i	−0.897067	+	0.725512i
$700$	0.178065	+	1.86478i	0.00673023	+	0.0704822i
$701$	−32.5674	+	9.56264i	−1.23005	+	0.361176i	−0.831270	−	0.555869i	$-0.812385\pi$
$701$	−32.5674	+	9.56264i	−1.23005	+	0.361176i	−0.398783	+	0.917045i	$0.630567\pi$
$702$	−33.0612	+	11.1982i	−1.24781	+	0.422648i
$703$	8.83660	−	19.3494i	0.333279	−	0.729778i
$704$	1.45325	−	1.14285i	0.0547714	−	0.0430727i
$705$	0.275907	−	0.833865i	0.0103912	−	0.0314052i
$706$	10.4120	+	0.994224i	0.391860	+	0.0374181i
$707$	0.00710166	+	0.149082i	0.000267085	+	0.00560681i
$708$	8.51734	+	6.51179i	0.320101	+	0.244728i
$709$	−16.8136	−	0.800930i	−0.631447	−	0.0300795i	−0.270581	−	0.962697i	$-0.587216\pi$
$709$	−16.8136	−	0.800930i	−0.631447	−	0.0300795i	−0.360866	+	0.932618i	$0.617519\pi$
$710$	−1.73425	+	2.00143i	−0.0650852	+	0.0751123i
$711$	−3.19170	+	12.0816i	−0.119698	+	0.453097i
$712$		−	2.35964i		−	0.0884313i
$713$	−49.9971	+	2.91823i	−1.87241	+	0.109288i
$714$	−0.0570984	−	4.17941i	−0.00213685	−	0.156410i
$715$	−3.55972	+	3.39419i	−0.133126	+	0.126935i
$716$	−8.74810	+	3.02775i	−0.326932	+	0.113152i
$717$	43.1178	+	26.8850i	1.61026	+	1.00404i
$718$	5.99358	+	14.9712i	0.223678	+	0.558722i
$719$	15.6799	+	24.3983i	0.584760	+	0.909904i	1.00000		0.000192440i	$6.12554e-5\pi$
$719$	15.6799	+	24.3983i	0.584760	+	0.909904i	−0.415240	+	0.909712i	$0.636302\pi$
$720$	−1.18535	−	0.0805831i	−0.0441756	−	0.00300315i
$721$	−1.16753	−	1.34740i	−0.0434811	−	0.0501798i
$722$	−9.01305	−	11.4610i	−0.335431	−	0.426535i
$723$	2.78968	+	3.80641i	0.103749	+	0.141562i
$724$	1.50842	+	0.365940i	0.0560602	+	0.0136001i
$725$	21.7055	+	5.26570i	0.806122	+	0.195563i
$726$	−13.0546	+	1.42678i	−0.484502	+	0.0529526i
$727$	−8.76932	−	11.1511i	−0.325236	−	0.413571i	0.595748	−	0.803171i	$-0.296856\pi$
$727$	−8.76932	−	11.1511i	−0.325236	−	0.413571i	−0.920984	+	0.389600i	$0.872613\pi$
$728$	1.70153	+	1.96367i	0.0630630	+	0.0727786i
$729$	−13.1894	−	23.5593i	−0.488496	−	0.872566i
$730$	1.23450	+	1.92092i	0.0456909	+	0.0710964i
$731$	−14.2798	−	35.6692i	−0.528157	−	1.31927i
$732$	−0.508172	+	14.9674i	−0.0187826	+	0.553211i
$733$	17.5597	−	6.07748i	0.648583	−	0.224477i	0.0170850	−	0.999854i	$-0.494561\pi$
$733$	17.5597	−	6.07748i	0.648583	−	0.224477i	0.631498	+	0.775377i	$0.282440\pi$
$734$	20.1756	−	19.2374i	0.744696	−	0.710066i
$735$	4.10116	+	2.29369i	0.151274	+	0.0846039i
$736$	2.35333	−	4.17874i	0.0867449	−	0.154030i
$737$			20.7994i			0.766155i
$738$	−16.8498	+	16.9689i	−0.620248	+	0.624632i
$739$	8.65878	−	9.99276i	0.318518	−	0.367590i	−0.573801	−	0.818995i	$-0.694532\pi$
$739$	8.65878	−	9.99276i	0.318518	−	0.367590i	0.892319	+	0.451405i	$0.149077\pi$
$740$	−4.00268	−	0.190671i	−0.147142	−	0.00700922i
$741$	3.15005	−	24.2570i	0.115720	−	0.891104i
$742$	0.116195	+	2.43924i	0.00426566	+	0.0895473i
$743$	−21.8653	−	2.08789i	−0.802162	−	0.0765972i	−0.314082	−	0.949396i	$-0.601697\pi$
$743$	−21.8653	−	2.08789i	−0.802162	−	0.0765972i	−0.488080	+	0.872799i	$0.662303\pi$
$744$	−12.0305	−	13.5066i	−0.441058	−	0.495176i
$745$	2.25451	−	1.77297i	0.0825990	−	0.0649565i
$746$	1.54449	−	3.38197i	0.0565479	−	0.123823i
$747$	−50.0999	+	16.2099i	−1.83306	+	0.593090i
$748$	−11.0676	+	3.24974i	−0.404672	+	0.118822i
$749$	−0.249718	−	2.61516i	−0.00912448	−	0.0955559i
$750$	−6.30191	−	2.42355i	−0.230113	−	0.0884956i
$751$	2.57763	+	13.3740i	0.0940590	+	0.488024i	0.998156	+	0.0606975i	$0.0193325\pi$
$751$	2.57763	+	13.3740i	0.0940590	+	0.488024i	−0.904097	+	0.427327i	$0.859455\pi$
$752$	−0.121716	+	1.27466i	−0.00443851	+	0.0464822i
$753$	−11.8143	+	23.7061i	−0.430536	+	0.863898i
$754$	28.7607	−	11.5141i	1.04740	−	0.419317i
$755$	−3.22210	−	2.07072i	−0.117264	−	0.0753610i
$756$	−1.25280	+	1.57155i	−0.0455639	+	0.0571568i
$757$	−3.23112	+	11.0042i	−0.117437	+	0.399954i	−0.997141	−	0.0755688i	$-0.975923\pi$
$757$	−3.23112	+	11.0042i	−0.117437	+	0.399954i	0.879704	+	0.475522i	$0.157741\pi$
$758$	15.5807	+	26.9866i	0.565918	+	0.980198i
$759$	13.4746	−	7.36752i	0.489096	−	0.267424i
$760$	0.416280	−	0.721019i	0.0151001	−	0.0261541i
$761$	1.05029	+	1.10151i	0.0380729	+	0.0399297i	0.742495	−	0.669852i	$-0.233642\pi$
$761$	1.05029	+	1.10151i	0.0380729	+	0.0399297i	−0.704422	+	0.709781i	$0.748794\pi$
$762$	−3.89980	−	10.7886i	−0.141275	−	0.390830i
$763$	0.305770	−	6.41890i	0.0110696	−	0.232380i
$764$	0.686527	−	4.77490i	0.0248377	−	0.172750i
$765$	6.67896	+	3.21541i	0.241478	+	0.116254i
$766$	−19.1758	+	8.75730i	−0.692850	+	0.316414i
$767$	39.2956	+	13.6003i	1.41888	+	0.491079i
$768$	1.71089	−	0.269893i	0.0617366	−	0.00973894i
$769$	19.7650	−	14.0746i	0.712745	−	0.507543i	−0.165227	−	0.986256i	$-0.552836\pi$
$769$	19.7650	−	14.0746i	0.712745	−	0.507543i	0.877972	+	0.478712i	$0.158896\pi$
$770$	−0.0667660	+	0.275213i	−0.00240608	+	0.00991799i
$771$	15.2935	−	4.71843i	0.550781	−	0.169930i
$772$	19.7705	−	1.88786i	0.711557	−	0.0679455i
$773$	−5.14690	−	35.7975i	−0.185121	−	1.28755i	−0.844426	−	0.535671i	$-0.820059\pi$
$773$	−5.14690	−	35.7975i	−0.185121	−	1.28755i	0.659305	−	0.751875i	$-0.270851\pi$
$774$	−5.56319	+	17.6169i	−0.199965	+	0.633225i
$775$	−21.0102	−	46.0060i	−0.754710	−	1.65258i
$776$	−9.94211	−	5.12551i	−0.356901	−	0.183995i
$777$	−4.11713	+	5.38516i	−0.147701	+	0.193192i
$778$	−13.8407	−	26.8473i	−0.496215	−	0.962522i
$779$	−5.48085	−	15.8359i	−0.196372	−	0.567379i
$780$	−4.46282	+	1.14744i	−0.159795	+	0.0410850i
$781$	10.7066	−	6.18148i	0.383113	−	0.221191i
$782$	−23.3208	+	18.7471i	−0.833952	+	0.670394i
$783$	12.8217	+	20.2442i	0.458210	+	0.723470i
$784$	−6.57291	−	1.92998i	−0.234747	−	0.0689278i
$785$	1.23520	−	6.40880i	0.0440860	−	0.228740i
$786$	−4.59788	−	0.156107i	−0.164001	−	0.00556815i
$787$	−6.78032	+	8.62187i	−0.241692	+	0.307337i	−0.891732	−	0.452563i	$-0.850510\pi$
$787$	−6.78032	+	8.62187i	−0.241692	+	0.307337i	0.650040	+	0.759900i	$0.274752\pi$
$788$	−2.98750	+	0.142312i	−0.106425	+	0.00506966i
$789$	1.92895	−	23.6044i	0.0686724	−	0.840338i
$790$	−0.539536	+	1.55889i	−0.0191958	+	0.0554627i
$791$	−5.72144	+	0.822619i	−0.203431	+	0.0292489i
$792$	5.10622	+	2.16536i	0.181442	+	0.0769428i
$793$	16.3641	+	55.7312i	0.581108	+	1.97907i
$794$	10.2559	−	10.7561i	0.363968	−	0.381718i
$795$	−3.96361	−	1.74508i	−0.140575	−	0.0618917i
$796$	−2.65116	+	6.62227i	−0.0939677	+	0.234720i
$797$	−25.0752	+	4.83285i	−0.888209	+	0.171188i	−0.612894	−	0.790166i	$-0.709995\pi$
$797$	−25.0752	+	4.83285i	−0.888209	+	0.171188i	−0.275316	+	0.961354i	$0.588782\pi$
$798$	−0.602507	−	1.27299i	−0.0213285	−	0.0450635i
$799$	3.66075	−	7.10087i	0.129508	−	0.251211i
$800$	4.79386	+	0.689254i	0.169489	+	0.0243688i
$801$	6.20103	−	3.41443i	0.219103	−	0.120643i
$802$	−6.61279	−	5.73002i	−0.233506	−	0.202334i
$803$	−2.51310	−	10.3591i	−0.0886854	−	0.365566i
$804$	−9.51157	+	17.0069i	−0.335447	+	0.599787i
$805$	0.112323	+	0.725982i	0.00395887	+	0.0255875i
$806$	−60.7534	−	35.0760i	−2.13995	−	1.23550i
$807$	−3.56361	−	13.8602i	−0.125445	−	0.487902i
$808$	0.378902	+	0.0730274i	0.0133297	+	0.00256909i
$809$	27.9791	−	43.5363i	0.983693	−	1.53066i	0.142589	−	0.989782i	$-0.454457\pi$
$809$	27.9791	−	43.5363i	0.983693	−	1.53066i	0.841104	−	0.540873i	$-0.181906\pi$
$810$	−1.50345	−	3.23167i	−0.0528260	−	0.113549i
$811$	−8.04304	+	5.16895i	−0.282429	+	0.181506i	−0.674184	−	0.738563i	$-0.735505\pi$
$811$	−8.04304	+	5.16895i	−0.282429	+	0.181506i	0.391755	+	0.920070i	$0.371868\pi$
$812$	1.03467	−	1.45299i	0.0363097	−	0.0509898i
$813$	−7.87851	−	2.60682i	−0.276311	−	0.0914251i
$814$	17.3669	+	6.95268i	0.608711	+	0.243691i
$815$	−2.77997	−	3.90393i	−0.0973783	−	0.136749i
$816$	−10.5357	−	2.40403i	−0.368823	−	0.0841578i
$817$	−9.36948	−	8.93378i	−0.327797	−	0.312553i
$818$	−9.22164	−	4.21138i	−0.322427	−	0.147248i
$819$	−2.69831	+	7.31301i	−0.0942866	+	0.255537i
$820$	−2.38577	+	2.06728i	−0.0833147	+	0.0721926i
$821$	10.0123	+	7.12971i	0.349431	+	0.248829i	0.741273	−	0.671204i	$-0.234223\pi$
$821$	10.0123	+	7.12971i	0.349431	+	0.248829i	−0.391842	+	0.920033i	$0.628162\pi$
$822$	24.9396	−	16.5134i	0.869870	−	0.575972i
$823$	15.7653	+	12.3980i	0.549543	+	0.432166i	0.853934	−	0.520382i	$-0.174210\pi$
$823$	15.7653	+	12.3980i	0.549543	+	0.432166i	−0.304391	+	0.952547i	$0.598453\pi$
$824$	−4.09703	+	2.11217i	−0.142727	+	0.0735808i
$825$	11.8584	+	9.99503i	0.412856	+	0.347982i
$826$	2.32672	−	0.564455i	0.0809568	−	0.0196399i
$827$	−33.2893			−1.15758			−0.578791	−	0.815476i	$-0.696475\pi$
$827$	−33.2893			−1.15758			−0.578791	+	0.815476i	$0.696475\pi$
$828$	14.3868	+	0.137773i	0.499977	+	0.00478795i
$829$	21.6572			0.752185			0.376092	−	0.926582i	$-0.377268\pi$
$829$	21.6572			0.752185			0.376092	+	0.926582i	$0.377268\pi$
$830$	−6.75532	+	1.63882i	−0.234480	+	0.0568843i
$831$	30.5324	−	11.0367i	1.05916	−	0.382858i
$832$	5.97093	−	3.07823i	0.207005	−	0.106718i
$833$	33.5963	+	26.4204i	1.16404	+	0.915414i
$834$	−1.84386	−	0.918915i	−0.0638478	−	0.0318194i
$835$	0.968898	+	0.689949i	0.0335301	+	0.0238767i
$836$	−2.93734	+	2.54522i	−0.101590	+	0.0880281i
$837$	18.0865	−	51.1598i	0.625161	−	1.76834i
$838$	−11.0759	−	5.05820i	−0.382611	−	0.174733i
$839$	−30.2770	−	28.8691i	−1.04528	−	0.996671i	−0.0452810	−	0.998974i	$-0.514418\pi$
$839$	−30.2770	−	28.8691i	−1.04528	−	0.996671i	−0.999997	+	0.00230336i	$0.999267\pi$
$840$	−0.180447	+	0.194500i	−0.00622602	+	0.00671088i
$841$	4.48524	+	6.29864i	0.154663	+	0.217194i
$842$	14.5479	+	5.82409i	0.501353	+	0.200711i
$843$	3.88366	+	18.7670i	0.133760	+	0.646369i
$844$	1.81522	−	2.54912i	0.0624825	−	0.0877444i
$845$	−10.7036	+	6.87882i	−0.368217	+	0.236638i
$846$	−3.52588	+	1.52459i	−0.121222	+	0.0524164i
$847$	−1.58548	+	2.46706i	−0.0544778	+	0.0847691i
$848$	6.19949	+	1.19485i	0.212891	+	0.0410314i
$849$	−24.3195	−	6.78138i	−0.834642	−	0.232737i
$850$	−26.1688	−	15.1086i	−0.897582	−	0.518219i
$851$	48.5237	−	0.519315i	1.66337	−	0.0178019i
$852$	11.5812	−	0.158221i	0.396766	−	0.00542055i
$853$	2.25162	+	9.28131i	0.0770941	+	0.317786i	0.997281	−	0.0736933i	$-0.0234786\pi$
$853$	2.25162	+	9.28131i	0.0770941	+	0.317786i	−0.920187	+	0.391479i	$0.871963\pi$
$854$	2.52746	+	2.19006i	0.0864879	+	0.0749422i
$855$	2.49717	+	0.0506443i	0.0854014	+	0.00173200i
$856$	−6.72288	−	0.966605i	−0.229783	−	0.0330379i
$857$	0.760059	−	1.47431i	0.0259631	−	0.0503614i	−0.875497	−	0.483223i	$-0.839466\pi$
$857$	0.760059	−	1.47431i	0.0259631	−	0.0503614i	0.901460	+	0.432862i	$0.142496\pi$
$858$	21.4400	+	1.75207i	0.731948	+	0.0598148i
$859$	−10.3160	+	1.98824i	−0.351976	+	0.0678379i	−0.362175	−	0.932110i	$-0.617966\pi$
$859$	−10.3160	+	1.98824i	−0.351976	+	0.0678379i	0.0101986	+	0.999948i	$0.496754\pi$
$860$	−0.906412	+	2.26411i	−0.0309084	+	0.0772055i
$861$	0.580185	+	5.30854i	0.0197727	+	0.180915i
$862$	17.9264	−	18.8007i	0.610576	−	0.640354i
$863$	−13.4998	−	45.9759i	−0.459537	−	1.56504i	−0.785007	−	0.619487i	$-0.787341\pi$
$863$	−13.4998	−	45.9759i	−0.459537	−	1.56504i	0.325470	−	0.945552i	$-0.394477\pi$
$864$	3.18495	+	4.10562i	0.108354	+	0.139676i
$865$	3.03759	−	0.436740i	0.103281	−	0.0148496i
$866$	−4.04762	+	11.6948i	−0.137544	+	0.397407i
$867$	31.2342	+	21.6049i	1.06077	+	0.733740i
$868$	−4.03458	+	0.192191i	−0.136943	+	0.00652338i
$869$	4.76039	−	6.05332i	0.161485	−	0.205345i
$870$	1.48781	+	2.79164i	0.0504414	+	0.0946454i
$871$	−14.3028	+	74.2101i	−0.484633	+	2.51451i
$872$	−15.9413	−	4.68079i	−0.539841	−	0.158512i
$873$	−0.916720	−	33.5441i	−0.0310263	−	1.13530i
$874$	−4.52373	+	9.01027i	−0.153017	+	0.304777i
$875$	−1.30576	+	0.753882i	−0.0441428	+	0.0254859i
$876$	2.68237	−	9.61954i	0.0906289	−	0.325014i
$877$	−10.9600	−	31.6668i	−0.370093	−	1.06931i	−0.964257	−	0.264969i	$-0.914638\pi$
$877$	−10.9600	−	31.6668i	−0.370093	−	1.06931i	0.594164	−	0.804344i	$-0.297483\pi$
$878$	13.7194	+	26.6119i	0.463007	+	0.898108i
$879$	−50.7930	−	6.59605i	−1.71321	−	0.222479i
$880$	0.650785	+	0.335503i	0.0219380	+	0.0113098i
$881$	10.6590	+	23.3400i	0.359111	+	0.786344i	0.999828	+	0.0185666i	$0.00591027\pi$
$881$	10.6590	+	23.3400i	0.359111	+	0.786344i	−0.640716	+	0.767778i	$0.721362\pi$
$882$	−4.43917	−	20.0660i	−0.149475	−	0.675658i
$883$	3.29215	+	22.8974i	0.110790	+	0.770559i	0.967155	+	0.254188i	$0.0818083\pi$
$883$	3.29215	+	22.8974i	0.110790	+	0.770559i	−0.856365	+	0.516371i	$0.827283\pi$
$884$	−41.7228	+	3.98405i	−1.40329	+	0.133998i
$885$	−0.944571	+	4.13960i	−0.0317514	+	0.139151i
$886$	−0.245249	+	1.01093i	−0.00823932	+	0.0339629i
$887$	16.9479	−	12.0685i	0.569054	−	0.405222i	−0.258994	−	0.965879i	$-0.583391\pi$
$887$	16.9479	−	12.0685i	0.569054	−	0.405222i	0.828048	+	0.560657i	$0.189452\pi$
$888$	11.0209	+	13.6269i	0.369836	+	0.457288i
$889$	−2.42088	−	0.837876i	−0.0811939	−	0.0281015i
$890$	0.850041	−	0.388201i	0.0284934	−	0.0130125i
$891$	1.69829	+	16.5522i	0.0568947	+	0.554521i
$892$	−0.0696862	+	0.484678i	−0.00233327	+	0.0162282i
$893$	0.128084	−	2.68882i	0.00428618	−	0.0899779i
$894$	−12.3485	−	2.20547i	−0.412996	−	0.0737620i
$895$	−2.52993	−	2.65332i	−0.0845663	−	0.0886906i
$896$	0.193393	−	0.334966i	0.00646081	−	0.0111904i
$897$	53.1422	−	17.0207i	1.77437	−	0.568304i
$898$	−6.33529	−	10.9730i	−0.211411	−	0.366175i
$899$	−13.5680	+	46.2084i	−0.452518	+	1.54114i
$900$	5.12545	+	13.5954i	0.170848	+	0.453181i
$901$	−33.1380	−	21.2965i	−1.10399	−	0.709490i
$902$	13.6814	−	5.47721i	0.455541	−	0.182371i
$903$	2.27763	+	3.43983i	0.0757949	+	0.114470i
$904$	−1.42055	+	14.8767i	−0.0472469	+	0.494792i
$905$	0.116335	+	0.603601i	0.00386709	+	0.0200644i
$906$	2.61021	+	16.5465i	0.0867185	+	0.549721i
$907$	−1.64814	−	17.2601i	−0.0547256	−	0.573112i	−0.980699	−	0.195524i	$-0.937359\pi$
$907$	−1.64814	−	17.2601i	−0.0547256	−	0.573112i	0.925973	−	0.377589i	$-0.123247\pi$
$908$	17.2238	−	5.05736i	0.571591	−	0.167834i
$909$	0.356363	+	1.10141i	0.0118198	+	0.0365315i
$910$	−0.427466	+	0.936020i	−0.0141704	+	0.0310288i
$911$	−18.2207	+	14.3289i	−0.603680	+	0.474739i	−0.872608	−	0.488421i	$-0.837573\pi$
$911$	−18.2207	+	14.3289i	−0.603680	+	0.474739i	0.268928	+	0.963160i	$0.413331\pi$
$912$	−3.56568	+	0.737886i	−0.118072	+	0.0244338i
$913$	32.3037	+	3.08463i	1.06910	+	0.102086i
$914$	−0.780321	−	16.3810i	−0.0258107	−	0.541834i
$915$	−5.47548	+	2.27932i	−0.181014	+	0.0753522i
$916$	−21.4351	−	1.02108i	−0.708235	−	0.0337374i
$917$	−0.672770	+	0.776418i	−0.0222168	+	0.0256396i
$918$	−8.92759	−	31.1660i	−0.294655	−	1.02863i
$919$		−	49.7083i		−	1.63973i	−0.572559	−	0.819863i	$-0.694049\pi$
$919$		−	49.7083i		−	1.63973i	0.572559	−	0.819863i	$-0.305951\pi$
$920$	1.89252	+	0.160295i	0.0623945	+	0.00528478i
$921$	7.28877	−	4.34200i	0.240173	−	0.143074i
$922$	9.13592	−	8.71109i	0.300876	−	0.286884i
$923$	42.4509	−	14.6924i	1.39729	−	0.483606i
$924$	1.09303	−	0.582530i	0.0359579	−	0.0191638i
$925$	18.2135	+	45.4950i	0.598855	+	1.49587i
$926$	−8.94338	−	13.9162i	−0.293898	−	0.457314i
$927$	−11.4791	−	7.71050i	−0.377024	−	0.253246i
$928$	−3.02001	−	3.48527i	−0.0991366	−	0.114410i
$929$	−22.9996	−	29.2463i	−0.754591	−	0.959541i	0.245360	−	0.969432i	$-0.421094\pi$
$929$	−22.9996	−	29.2463i	−0.754591	−	0.959541i	−0.999951	+	0.00989113i	$0.996852\pi$
$930$	2.88642	−	6.55594i	0.0946495	−	0.214978i
$931$	13.9954	+	3.39525i	0.458681	+	0.111275i
$932$	17.1145	+	4.15194i	0.560605	+	0.136001i
$933$	−11.5637	+	26.2647i	−0.378579	+	0.859868i
$934$	5.53531	+	7.03872i	0.181121	+	0.230314i
$935$	−2.99150	−	3.45238i	−0.0978326	−	0.112905i
$936$	16.7295	+	11.2371i	0.546819	+	0.367296i
$937$	−4.34331	−	6.75833i	−0.141890	−	0.220785i	0.763034	−	0.646358i	$-0.223709\pi$
$937$	−4.34331	−	6.75833i	−0.141890	−	0.220785i	−0.904924	+	0.425573i	$0.860072\pi$
$938$	1.61727	+	4.03974i	0.0528057	+	0.131902i
$939$	4.27168	−	2.27660i	0.139401	−	0.0742939i
$940$	−0.479211	+	0.165857i	−0.0156301	+	0.00540964i
$941$	18.0065	−	17.1692i	0.586995	−	0.559699i	−0.337290	−	0.941401i	$-0.609510\pi$
$941$	18.0065	−	17.1692i	0.586995	−	0.559699i	0.924285	+	0.381702i	$0.124662\pi$
$942$	−24.5234	+	14.6088i	−0.799015	+	0.475982i
$943$	27.3833	−	26.6752i	0.891723	−	0.868664i
$944$		−	6.19000i		−	0.201467i
$945$	−0.772246	−	0.192764i	−0.0251212	−	0.00627062i
$946$	7.45566	−	8.60429i	0.242404	−	0.279749i
$947$	21.5666	+	1.02734i	0.700820	+	0.0333842i	0.394968	−	0.918695i	$-0.370756\pi$
$947$	21.5666	+	1.02734i	0.700820	+	0.0333842i	0.305852	+	0.952079i	$0.401059\pi$
$948$	6.66058	−	2.77266i	0.216326	−	0.0900517i
$949$	−1.84296	−	38.6885i	−0.0598250	−	1.25588i
$950$	−10.1355	−	0.967824i	−0.328839	−	0.0314003i
$951$	25.7943	−	5.33789i	0.836437	−	0.173093i
$952$	−1.89691	+	1.49175i	−0.0614792	+	0.0483478i
$953$	1.08026	−	2.36543i	0.0349930	−	0.0766239i	−0.891328	−	0.453358i	$-0.850226\pi$
$953$	1.08026	−	2.36543i	0.0349930	−	0.0766239i	0.926321	+	0.376734i	$0.122953\pi$
$954$	5.83071	+	18.0210i	0.188776	+	0.583450i
$955$	1.83306	−	0.538236i	0.0593165	−	0.0174169i
$956$	−2.78864	−	29.2040i	−0.0901911	−	0.944524i
$957$	−2.30112	−	14.5871i	−0.0743847	−	0.471535i
$958$	−2.78023	−	14.4252i	−0.0898250	−	0.466056i
$959$	0.634927	−	6.64925i	0.0205028	−	0.214716i
$960$	0.378698	+	0.571933i	0.0122224	+	0.0184591i
$961$	72.4623	−	29.0095i	2.33749	−	0.935791i
$962$	57.1824	+	36.7489i	1.84364	+	1.18483i
$963$	−7.18790	−	19.0661i	−0.231627	−	0.614398i
$964$	0.767621	−	2.61428i	0.0247234	−	0.0842002i
$965$	3.93267	+	6.81159i	0.126597	+	0.219273i
$966$	2.04422	−	2.47867i	0.0657716	−	0.0797499i
$967$	11.1019	−	19.2291i	0.357013	−	0.618365i	−0.630447	−	0.776232i	$-0.717128\pi$
$967$	11.1019	−	19.2291i	0.357013	−	0.618365i	0.987460	+	0.157867i	$0.0504617\pi$
$968$	5.23216	+	5.48733i	0.168168	+	0.176369i
$969$	22.3642	+	3.99430i	0.718442	+	0.128315i
$970$	0.210779	−	4.42480i	0.00676771	−	0.142072i
$971$	3.07362	−	21.3775i	0.0986371	−	0.686036i	−0.879167	−	0.476514i	$-0.841900\pi$
$971$	3.07362	−	21.3775i	0.0986371	−	0.686036i	0.977804	−	0.209522i	$-0.0671908\pi$
$972$	−6.18072	+	14.3108i	−0.198247	+	0.459019i
$973$	−0.418481	+	0.191114i	−0.0134159	+	0.00612683i
$974$	3.79989	+	1.31515i	0.121756	+	0.0421402i
$975$	35.4364	+	43.8157i	1.13487	+	1.40323i
$976$	7.04316	−	5.01541i	0.225446	−	0.160539i
$977$	6.34591	−	26.1582i	0.203023	−	0.836874i	−0.775602	−	0.631223i	$-0.782553\pi$
$977$	6.34591	−	26.1582i	0.203023	−	0.836874i	0.978625	−	0.205652i	$-0.0659314\pi$
$978$	−4.66291	+	20.4353i	−0.149104	+	0.653449i
$979$	−4.34273	+	0.414681i	−0.138794	+	0.0132532i
$980$	−0.386095	−	2.68535i	−0.0123334	−	0.0857804i
$981$	−10.7663	−	48.6662i	−0.343743	−	1.55379i
$982$	−9.65102	−	21.1328i	−0.307976	−	0.674374i
$983$	−33.0454	−	17.0361i	−1.05399	−	0.543367i	−0.157994	−	0.987440i	$-0.550503\pi$
$983$	−33.0454	−	17.0361i	−1.05399	−	0.543367i	−0.895991	+	0.444073i	$0.853533\pi$
$984$	13.6915	+	1.77800i	0.436469	+	0.0566805i
$985$	−0.542761	−	1.05281i	−0.0172938	−	0.0335453i
$986$	9.41068	+	27.1904i	0.299697	+	0.865918i
$987$	−0.230410	+	0.826300i	−0.00733404	+	0.0263014i
$988$	−12.2303	+	7.06119i	−0.389099	+	0.224647i
$989$	9.36019	−	28.0108i	0.297637	−	0.890692i
$990$	0.0600061	+	2.19571i	0.00190712	+	0.0697843i
$991$	32.9766	+	9.68281i	1.04754	+	0.307584i	0.759822	−	0.650132i	$-0.225286\pi$
$991$	32.9766	+	9.68281i	1.04754	+	0.307584i	0.287715	+	0.957716i	$0.407104\pi$
$992$	−1.97633	+	10.2541i	−0.0627484	+	0.325570i
$993$	0.733539	+	1.37637i	0.0232782	+	0.0436779i
$994$	1.59884	−	2.03309i	0.0507121	−	0.0644857i
$995$	−2.82178	+	0.134418i	−0.0894563	+	0.00426133i
$996$	25.0030	+	17.2947i	0.792250	+	0.548004i
$997$	0.439336	−	1.26938i	0.0139139	−	0.0402016i	−0.937830	−	0.347095i	$-0.887168\pi$
$997$	0.439336	−	1.26938i	0.0139139	−	0.0402016i	0.951744	+	0.306893i	$0.0992894\pi$
$998$	−32.0172	+	4.60338i	−1.01349	+	0.145718i
$999$	−19.8635	+	48.6806i	−0.628453	+	1.54019i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.5.6	✓	480
9.2	odd	6	inner	414.2.p.a.281.1	yes	480
23.14	odd	22	inner	414.2.p.a.221.1	yes	480
207.83	even	66	inner	414.2.p.a.83.6	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.5.6	✓	480	1.1	even	1	trivial
414.2.p.a.83.6	yes	480	207.83	even	66	inner
414.2.p.a.221.1	yes	480	23.14	odd	22	inner
414.2.p.a.281.1	yes	480	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.971812 + 0.235759i) q^{2} +(-0.304529 + 1.70507i) q^{3} +(0.888835 - 0.458227i) q^{4} +(0.311301 + 0.244810i) q^{5} +(-0.106041 - 1.72880i) q^{6} +(-0.315067 - 0.224358i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.81452 - 1.03849i) q^{9} +O(q^{10})\)	\(q+(-0.971812 + 0.235759i) q^{2} +(-0.304529 + 1.70507i) q^{3} +(0.888835 - 0.458227i) q^{4} +(0.311301 + 0.244810i) q^{5} +(-0.106041 - 1.72880i) q^{6} +(-0.315067 - 0.224358i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.81452 - 1.03849i) q^{9} +(-0.360242 - 0.164517i) q^{10} +(1.33803 + 1.27581i) q^{11} +(0.510632 + 1.65507i) q^{12} +(3.89665 + 5.47208i) q^{13} +(0.359080 + 0.143754i) q^{14} +(-0.512218 + 0.456238i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-5.24869 + 3.37313i) q^{17} +(2.98002 + 0.345664i) q^{18} +(-1.13657 + 1.76854i) q^{19} +(0.388873 + 0.0749492i) q^{20} +(0.478493 - 0.468887i) q^{21} +(-1.60110 - 0.924396i) q^{22} +(-4.75405 - 0.631678i) q^{23} +(-0.886435 - 1.48803i) q^{24} +(-1.14182 - 4.70664i) q^{25} +(-5.07690 - 4.39916i) q^{26} +(2.62780 - 4.48271i) q^{27} +(-0.382849 - 0.0550454i) q^{28} +(-2.11319 + 4.09902i) q^{29} +(0.390217 - 0.564137i) q^{30} +(10.2541 - 1.97633i) q^{31} +(-0.371662 + 0.928368i) q^{32} +(-2.58282 + 1.89292i) q^{33} +(4.30549 - 4.51547i) q^{34} +(-0.0431555 - 0.146974i) q^{35} +(-2.97751 + 0.366646i) q^{36} +(-10.0155 + 1.44001i) q^{37} +(0.687584 - 1.98664i) q^{38} +(-10.5169 + 4.97765i) q^{39} +(-0.395582 + 0.0188439i) q^{40} +(-4.92745 + 6.26576i) q^{41} +(-0.354460 + 0.568479i) q^{42} +(-1.16543 + 6.04684i) q^{43} +(1.77390 + 0.520865i) q^{44} +(-0.621932 - 1.01230i) q^{45} +(4.76896 - 0.506938i) q^{46} +(-1.10891 + 0.640230i) q^{47} +(1.21226 + 1.23710i) q^{48} +(-2.24055 - 6.47363i) q^{49} +(2.21926 + 4.30477i) q^{50} +(-4.15304 - 9.97660i) q^{51} +(5.97093 + 3.07823i) q^{52} +(2.62276 + 5.74304i) q^{53} +(-1.49688 + 4.97588i) q^{54} +(0.104200 + 0.724725i) q^{55} +(0.385035 - 0.0367663i) q^{56} +(-2.66936 - 2.47650i) q^{57} +(1.08724 - 4.48168i) q^{58} +(5.04223 - 3.59055i) q^{59} +(-0.246217 + 0.640232i) q^{60} +(8.17086 + 2.82796i) q^{61} +(-9.49916 + 4.33812i) q^{62} +(0.653770 + 0.958653i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.126587 + 2.65740i) q^{65} +(2.06374 - 2.44848i) q^{66} +(7.76357 + 8.14220i) q^{67} +(-3.11956 + 5.40325i) q^{68} +(2.52480 - 7.91362i) q^{69} +(0.0765895 + 0.132657i) q^{70} +(1.88396 - 6.41617i) q^{71} +(2.80714 - 1.05829i) q^{72} +(-4.85043 - 3.11718i) q^{73} +(9.39367 - 3.76066i) q^{74} +(8.37286 - 0.513572i) q^{75} +(-0.199833 + 2.09275i) q^{76} +(-0.135331 - 0.702164i) q^{77} +(9.04693 - 7.31679i) q^{78} +(-0.395944 - 4.14651i) q^{79} +(0.379988 - 0.111575i) q^{80} +(6.84309 + 5.84569i) q^{81} +(3.31134 - 7.25083i) q^{82} +(13.7971 - 10.8501i) q^{83} +(0.210445 - 0.636021i) q^{84} +(-2.45970 - 0.234872i) q^{85} +(-0.293016 - 6.15115i) q^{86} +(-6.34559 - 4.85141i) q^{87} +(-1.84670 - 0.0879691i) q^{88} +(-1.54524 + 1.78330i) q^{89} +(0.843061 + 0.837143i) q^{90} -2.59831i q^{91} +(-4.51502 + 1.61697i) q^{92} +(0.247086 + 18.0859i) q^{93} +(0.926713 - 0.883619i) q^{94} +(-0.786771 + 0.272304i) q^{95} +(-1.46975 - 0.916425i) q^{96} +(4.15725 + 10.3843i) q^{97} +(3.70360 + 5.76292i) q^{98} +(-2.44101 - 4.98034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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