LMFDB - Embedded newform 29.2.e.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,2,Mod(4,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("29.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	29.e (of order $14$, degree $6$, 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:	$0.231566165862$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	12.0.7877952219361.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + 13x^{9} - 18x^{8} - 14x^{7} + 57x^{6} - 28x^{5} - 72x^{4} + 104x^{3} - 96x + 64 $ x^12 - 3x^11 + 13x^9 - 18x^8 - 14x^7 + 57x^6 - 28x^5 - 72x^4 + 104x^3 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			9.2
Root			$0.911180 + 1.08155i$ of defining polynomial
Character	$\chi$	$=$	29.9
Dual form			29.2.e.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0741982 + 0.154074i) q^{2} +(-0.879032 + 0.701005i) q^{3} +(1.22875 - 1.54080i) q^{4} +(-2.54740 + 1.22676i) q^{5} +(-0.173229 - 0.0834229i) q^{6} +(-1.82432 - 2.28763i) q^{7} +(0.662012 + 0.151100i) q^{8} +(-0.386273 + 1.69237i) q^{9} +O(q^{10})$	\(q+(0.0741982 + 0.154074i) q^{2} +(-0.879032 + 0.701005i) q^{3} +(1.22875 - 1.54080i) q^{4} +(-2.54740 + 1.22676i) q^{5} +(-0.173229 - 0.0834229i) q^{6} +(-1.82432 - 2.28763i) q^{7} +(0.662012 + 0.151100i) q^{8} +(-0.386273 + 1.69237i) q^{9} +(-0.378025 - 0.301465i) q^{10} +(3.89257 - 0.888454i) q^{11} +2.21577i q^{12} +(0.625512 + 2.74055i) q^{13} +(0.217103 - 0.450819i) q^{14} +(1.37928 - 2.86411i) q^{15} +(-0.851229 - 3.72948i) q^{16} -0.482650i q^{17} +(-0.289412 + 0.0660563i) q^{18} +(2.38432 + 1.90144i) q^{19} +(-1.23991 + 5.43242i) q^{20} +(3.20728 + 0.732040i) q^{21} +(0.425710 + 0.533823i) q^{22} +(-4.96829 - 2.39260i) q^{23} +(-0.687851 + 0.331252i) q^{24} +(1.86686 - 2.34097i) q^{25} +(-0.375836 + 0.299719i) q^{26} +(-2.31029 - 4.79737i) q^{27} -5.76640 q^{28} +(-4.99718 + 2.00704i) q^{29} +0.543625 q^{30} +(-1.67239 - 3.47275i) q^{31} +(1.57324 - 1.25462i) q^{32} +(-2.79888 + 3.50969i) q^{33} +(0.0743639 - 0.0358118i) q^{34} +(7.45366 + 3.58950i) q^{35} +(2.13297 + 2.67467i) q^{36} +(11.2541 + 2.56868i) q^{37} +(-0.116049 + 0.508446i) q^{38} +(-2.47098 - 1.97054i) q^{39} +(-1.87177 + 0.427220i) q^{40} -5.10756i q^{41} +(0.125186 + 0.548475i) q^{42} +(-3.56577 + 7.40439i) q^{43} +(3.41405 - 7.08936i) q^{44} +(-1.09215 - 4.78502i) q^{45} -0.943011i q^{46} +(2.32767 - 0.531276i) q^{47} +(3.36264 + 2.68162i) q^{48} +(-0.347443 + 1.52225i) q^{49} +(0.499200 + 0.113939i) q^{50} +(0.338340 + 0.424265i) q^{51} +(4.99123 + 2.40365i) q^{52} +(0.401975 - 0.193581i) q^{53} +(0.567732 - 0.711913i) q^{54} +(-8.82602 + 7.03852i) q^{55} +(-0.862063 - 1.79009i) q^{56} -3.42881 q^{57} +(-0.680015 - 0.621017i) q^{58} +1.24537 q^{59} +(-2.71823 - 5.64445i) q^{60} +(-6.71717 + 5.35677i) q^{61} +(0.410973 - 0.515344i) q^{62} +(4.57621 - 2.20378i) q^{63} +(-6.58308 - 3.17024i) q^{64} +(-4.95544 - 6.21392i) q^{65} +(-0.748425 - 0.170823i) q^{66} +(-0.210269 + 0.921249i) q^{67} +(-0.743667 - 0.593055i) q^{68} +(6.04451 - 1.37962i) q^{69} +1.41475i q^{70} +(1.33021 + 5.82802i) q^{71} +(-0.511435 + 1.06201i) q^{72} +(0.209705 - 0.435458i) q^{73} +(0.439268 + 1.92456i) q^{74} +3.36646i q^{75} +(5.85946 - 1.33738i) q^{76} +(-9.13376 - 7.28393i) q^{77} +(0.120267 - 0.526925i) q^{78} +(1.80484 + 0.411944i) q^{79} +(6.74361 + 8.45623i) q^{80} +(0.701839 + 0.337988i) q^{81} +(0.786943 - 0.378972i) q^{82} +(2.71744 - 3.40756i) q^{83} +(5.06885 - 4.04228i) q^{84} +(0.592098 + 1.22950i) q^{85} -1.40540 q^{86} +(2.98573 - 5.26730i) q^{87} +2.71117 q^{88} +(6.75011 + 14.0167i) q^{89} +(0.656213 - 0.523312i) q^{90} +(5.12822 - 6.43058i) q^{91} +(-9.79128 + 4.71523i) q^{92} +(3.90450 + 1.88031i) q^{93} +(0.254565 + 0.319215i) q^{94} +(-8.40645 - 1.91872i) q^{95} +(-0.503437 + 2.20570i) q^{96} +(1.88941 + 1.50675i) q^{97} +(-0.260319 + 0.0594161i) q^{98} +6.93087i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9} - 7 q^{10} + 7 q^{11} + 9 q^{13} - 7 q^{14} + 7 q^{15} + 9 q^{16} + 42 q^{18} - 7 q^{19} - 11 q^{20} - 7 q^{21} - 4 q^{22} - 5 q^{23} - 25 q^{24} + 13 q^{25} - 21 q^{26} - 7 q^{27} + 12 q^{28} - 15 q^{29} + 2 q^{30} - 21 q^{31} - 17 q^{33} - 13 q^{34} + 19 q^{35} - 40 q^{36} + 7 q^{37} + 28 q^{38} + 21 q^{39} + 35 q^{40} + 50 q^{42} + 7 q^{43} + 42 q^{44} + 16 q^{45} - 7 q^{47} - 14 q^{48} + 13 q^{49} - 28 q^{50} + 20 q^{51} - 6 q^{52} - 10 q^{53} - 38 q^{54} - 35 q^{55} - 21 q^{56} - 14 q^{57} - 57 q^{58} + 44 q^{59} - 28 q^{60} - 7 q^{61} + 37 q^{62} - 13 q^{63} - 26 q^{64} - 6 q^{65} + 21 q^{66} - 37 q^{67} + 14 q^{68} + 21 q^{69} - 21 q^{71} + 35 q^{72} + 14 q^{73} + 7 q^{76} - 7 q^{77} + 17 q^{78} + 49 q^{79} - 6 q^{80} + q^{81} + 22 q^{82} + 5 q^{83} + 21 q^{84} + 14 q^{85} - 44 q^{86} + 15 q^{87} - 66 q^{88} + 7 q^{89} + 28 q^{90} - 3 q^{91} - 6 q^{92} + 19 q^{93} + 66 q^{94} - 7 q^{95} + 30 q^{96} + 14 q^{97} - 42 q^{98}+O(q^{100}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9 - 7 * q^10 + 7 * q^11 + 9 * q^13 - 7 * q^14 + 7 * q^15 + 9 * q^16 + 42 * q^18 - 7 * q^19 - 11 * q^20 - 7 * q^21 - 4 * q^22 - 5 * q^23 - 25 * q^24 + 13 * q^25 - 21 * q^26 - 7 * q^27 + 12 * q^28 - 15 * q^29 + 2 * q^30 - 21 * q^31 - 17 * q^33 - 13 * q^34 + 19 * q^35 - 40 * q^36 + 7 * q^37 + 28 * q^38 + 21 * q^39 + 35 * q^40 + 50 * q^42 + 7 * q^43 + 42 * q^44 + 16 * q^45 - 7 * q^47 - 14 * q^48 + 13 * q^49 - 28 * q^50 + 20 * q^51 - 6 * q^52 - 10 * q^53 - 38 * q^54 - 35 * q^55 - 21 * q^56 - 14 * q^57 - 57 * q^58 + 44 * q^59 - 28 * q^60 - 7 * q^61 + 37 * q^62 - 13 * q^63 - 26 * q^64 - 6 * q^65 + 21 * q^66 - 37 * q^67 + 14 * q^68 + 21 * q^69 - 21 * q^71 + 35 * q^72 + 14 * q^73 + 7 * q^76 - 7 * q^77 + 17 * q^78 + 49 * q^79 - 6 * q^80 + q^81 + 22 * q^82 + 5 * q^83 + 21 * q^84 + 14 * q^85 - 44 * q^86 + 15 * q^87 - 66 * q^88 + 7 * q^89 + 28 * q^90 - 3 * q^91 - 6 * q^92 + 19 * q^93 + 66 * q^94 - 7 * q^95 + 30 * q^96 + 14 * q^97 - 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{14}\right)$

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 $

$2$	0.0741982	+	0.154074i	0.0524661	+	0.108947i	0.925554	−	0.378617i	$-0.123600\pi$
$2$	0.0741982	+	0.154074i	0.0524661	+	0.108947i	−0.873088	+	0.487563i	$0.837886\pi$
$3$	−0.879032	+	0.701005i	−0.507509	+	0.404725i	−0.843491	−	0.537143i	$-0.819503\pi$
$3$	−0.879032	+	0.701005i	−0.507509	+	0.404725i	0.335982	+	0.941869i	$0.390932\pi$
$4$	1.22875	−	1.54080i	0.614373	−	0.770399i
$5$	−2.54740	+	1.22676i	−1.13923	+	0.548626i	−0.905782	−	0.423743i	$-0.860716\pi$
$5$	−2.54740	+	1.22676i	−1.13923	+	0.548626i	−0.233450	+	0.972369i	$0.575002\pi$
$6$	−0.173229	−	0.0834229i	−0.0707206	−	0.0340572i
$7$	−1.82432	−	2.28763i	−0.689529	−	0.864642i	0.306664	−	0.951818i	$-0.400787\pi$
$7$	−1.82432	−	2.28763i	−0.689529	−	0.864642i	−0.996193	+	0.0871757i	$0.972216\pi$
$8$	0.662012	+	0.151100i	0.234057	+	0.0534219i
$9$	−0.386273	+	1.69237i	−0.128758	+	0.564124i
$10$	−0.378025	−	0.301465i	−0.119542	−	0.0953317i
$11$	3.89257	−	0.888454i	1.17365	−	0.267879i	0.409132	−	0.912475i	$-0.365832\pi$
$11$	3.89257	−	0.888454i	1.17365	−	0.267879i	0.764523	+	0.644596i	$0.222975\pi$
$12$			2.21577i			0.639637i
$13$	0.625512	+	2.74055i	0.173486	+	0.760091i	0.984546	+	0.175128i	$0.0560339\pi$
$13$	0.625512	+	2.74055i	0.173486	+	0.760091i	−0.811060	+	0.584963i	$0.801109\pi$
$14$	0.217103	−	0.450819i	0.0580232	−	0.120486i
$15$	1.37928	−	2.86411i	0.356129	−	0.739509i
$16$	−0.851229	−	3.72948i	−0.212807	−	0.932370i
$17$		−	0.482650i		−	0.117060i	−0.998286	−	0.0585299i	$-0.981359\pi$
$17$		−	0.482650i		−	0.117060i	0.998286	−	0.0585299i	$-0.0186413\pi$
$18$	−0.289412	+	0.0660563i	−0.0682150	+	0.0155696i
$19$	2.38432	+	1.90144i	0.547002	+	0.436219i	0.857596	−	0.514323i	$-0.171957\pi$
$19$	2.38432	+	1.90144i	0.547002	+	0.436219i	−0.310595	+	0.950542i	$0.600528\pi$
$20$	−1.23991	+	5.43242i	−0.277253	+	1.21473i
$21$	3.20728	+	0.732040i	0.699885	+	0.159744i
$22$	0.425710	+	0.533823i	0.0907616	+	0.113811i
$23$	−4.96829	−	2.39260i	−1.03596	−	0.498892i	−0.162970	−	0.986631i	$-0.552107\pi$
$23$	−4.96829	−	2.39260i	−1.03596	−	0.498892i	−0.872989	+	0.487739i	$0.837822\pi$
$24$	−0.687851	+	0.331252i	−0.140407	+	0.0676165i
$25$	1.86686	−	2.34097i	0.373372	−	0.468193i
$26$	−0.375836	+	0.299719i	−0.0737075	+	0.0587797i
$27$	−2.31029	−	4.79737i	−0.444616	−	0.923255i
$28$	−5.76640			−1.08975
$29$	−4.99718	+	2.00704i	−0.927953	+	0.372698i
$29$	−4.99718	+	2.00704i	−0.927953	+	0.372698i
$30$	0.543625			0.0992519
$31$	−1.67239	−	3.47275i	−0.300370	−	0.623724i	0.695088	−	0.718924i	$-0.255365\pi$
$31$	−1.67239	−	3.47275i	−0.300370	−	0.623724i	−0.995458	+	0.0952000i	$0.969651\pi$
$32$	1.57324	−	1.25462i	0.278112	−	0.221787i
$33$	−2.79888	+	3.50969i	−0.487223	+	0.610959i
$34$	0.0743639	−	0.0358118i	0.0127533	−	0.00614167i
$35$	7.45366	+	3.58950i	1.25990	+	0.606735i
$36$	2.13297	+	2.67467i	0.355496	+	0.445778i
$37$	11.2541	+	2.56868i	1.85016	+	0.422288i	0.995323	−	0.0966033i	$-0.0307978\pi$
$37$	11.2541	+	2.56868i	1.85016	+	0.422288i	0.854840	+	0.518891i	$0.173655\pi$
$38$	−0.116049	+	0.508446i	−0.0188257	+	0.0824808i
$39$	−2.47098	−	1.97054i	−0.395674	−	0.315539i
$40$	−1.87177	+	0.427220i	−0.295954	+	0.0675495i
$41$		−	5.10756i		−	0.797667i	−0.917023	−	0.398833i	$-0.869415\pi$
$41$		−	5.10756i		−	0.797667i	0.917023	−	0.398833i	$-0.130585\pi$
$42$	0.125186	+	0.548475i	0.0193166	+	0.0846315i
$43$	−3.56577	+	7.40439i	−0.543775	+	1.12916i	0.430248	+	0.902711i	$0.358426\pi$
$43$	−3.56577	+	7.40439i	−0.543775	+	1.12916i	−0.974023	+	0.226449i	$0.927288\pi$
$44$	3.41405	−	7.08936i	0.514688	−	1.06876i
$45$	−1.09215	−	4.78502i	−0.162808	−	0.713309i
$46$		−	0.943011i		−	0.139039i
$47$	2.32767	−	0.531276i	0.339526	−	0.0774946i	−0.0493584	−	0.998781i	$-0.515718\pi$
$47$	2.32767	−	0.531276i	0.339526	−	0.0774946i	0.388885	+	0.921287i	$0.372861\pi$
$48$	3.36264	+	2.68162i	0.485355	+	0.387058i
$49$	−0.347443	+	1.52225i	−0.0496347	+	0.217464i
$50$	0.499200	+	0.113939i	0.0705975	+	0.0161134i
$51$	0.338340	+	0.424265i	0.0473771	+	0.0594090i
$52$	4.99123	+	2.40365i	0.692159	+	0.333326i
$53$	0.401975	−	0.193581i	0.0552156	−	0.0265904i	−0.406072	−	0.913841i	$-0.633102\pi$
$53$	0.401975	−	0.193581i	0.0552156	−	0.0265904i	0.461288	+	0.887251i	$0.347388\pi$
$54$	0.567732	−	0.711913i	0.0772585	−	0.0968791i
$55$	−8.82602	+	7.03852i	−1.19010	+	0.949074i
$56$	−0.862063	−	1.79009i	−0.115198	−	0.239211i
$57$	−3.42881			−0.454157
$58$	−0.680015	−	0.621017i	−0.0892904	−	0.0815436i
$59$	1.24537			0.162133			0.0810664	−	0.996709i	$-0.474167\pi$
$59$	1.24537			0.162133			0.0810664	+	0.996709i	$0.474167\pi$
$60$	−2.71823	−	5.64445i	−0.350921	−	0.728696i
$61$	−6.71717	+	5.35677i	−0.860046	+	0.685864i	−0.950731	−	0.310016i	$-0.899666\pi$
$61$	−6.71717	+	5.35677i	−0.860046	+	0.685864i	0.0906856	+	0.995880i	$0.471094\pi$
$62$	0.410973	−	0.515344i	0.0521936	−	0.0654487i
$63$	4.57621	−	2.20378i	0.576548	−	0.277651i
$64$	−6.58308	−	3.17024i	−0.822885	−	0.396280i
$65$	−4.95544	−	6.21392i	−0.614646	−	0.770742i
$66$	−0.748425	−	0.170823i	−0.0921248	−	0.0210269i
$67$	−0.210269	+	0.921249i	−0.0256885	+	0.112548i	−0.986147	−	0.165876i	$-0.946955\pi$
$67$	−0.210269	+	0.921249i	−0.0256885	+	0.112548i	0.960458	+	0.278424i	$0.0898121\pi$
$68$	−0.743667	−	0.593055i	−0.0901829	−	0.0719184i
$69$	6.04451	−	1.37962i	0.727673	−	0.166087i
$70$			1.41475i			0.169095i
$71$	1.33021	+	5.82802i	0.157867	+	0.691659i	0.990463	+	0.137779i	$0.0439962\pi$
$71$	1.33021	+	5.82802i	0.157867	+	0.691659i	−0.832597	+	0.553880i	$0.813147\pi$
$72$	−0.511435	+	1.06201i	−0.0602732	+	0.125158i
$73$	0.209705	−	0.435458i	0.0245442	−	0.0509665i	−0.888336	−	0.459193i	$-0.848138\pi$
$73$	0.209705	−	0.435458i	0.0245442	−	0.0509665i	0.912880	+	0.408227i	$0.133853\pi$
$74$	0.439268	+	1.92456i	0.0510639	+	0.223725i
$75$			3.36646i			0.388725i
$76$	5.85946	−	1.33738i	0.672126	−	0.153408i
$77$	−9.13376	−	7.28393i	−1.04089	−	0.830081i
$78$	0.120267	−	0.526925i	0.0136176	−	0.0596625i
$79$	1.80484	+	0.411944i	0.203061	+	0.0463473i	0.322841	−	0.946453i	$-0.395362\pi$
$79$	1.80484	+	0.411944i	0.203061	+	0.0463473i	−0.119781	+	0.992800i	$0.538219\pi$
$80$	6.74361	+	8.45623i	0.753959	+	0.945435i
$81$	0.701839	+	0.337988i	0.0779821	+	0.0375542i
$82$	0.786943	−	0.378972i	0.0869033	−	0.0418504i
$83$	2.71744	−	3.40756i	0.298277	−	0.374028i	−0.609996	−	0.792404i	$-0.708829\pi$
$83$	2.71744	−	3.40756i	0.298277	−	0.374028i	0.908274	+	0.418376i	$0.137401\pi$
$84$	5.06885	−	4.04228i	0.553057	−	0.441048i
$85$	0.592098	+	1.22950i	0.0642220	+	0.133358i
$86$	−1.40540			−0.151548
$87$	2.98573	−	5.26730i	0.320104	−	0.564714i
$88$	2.71117			0.289012
$89$	6.75011	+	14.0167i	0.715510	+	1.48577i	0.867525	+	0.497394i	$0.165710\pi$
$89$	6.75011	+	14.0167i	0.715510	+	1.48577i	−0.152015	+	0.988378i	$0.548576\pi$
$90$	0.656213	−	0.523312i	0.0691709	−	0.0551619i
$91$	5.12822	−	6.43058i	0.537583	−	0.674108i
$92$	−9.79128	+	4.71523i	−1.02081	+	0.491597i
$93$	3.90450	+	1.88031i	0.404878	+	0.194979i
$94$	0.254565	+	0.319215i	0.0262564	+	0.0329245i
$95$	−8.40645	−	1.91872i	−0.862483	−	0.196856i
$96$	−0.503437	+	2.20570i	−0.0513818	+	0.225118i
$97$	1.88941	+	1.50675i	0.191840	+	0.152988i	0.714700	−	0.699431i	$-0.246563\pi$
$97$	1.88941	+	1.50675i	0.191840	+	0.152988i	−0.522859	+	0.852419i	$0.675135\pi$
$98$	−0.260319	+	0.0594161i	−0.0262962	+	0.00600193i
$99$			6.93087i			0.696578i
$100$	−1.31306	−	5.75291i	−0.131306	−	0.575291i
$101$	5.85513	−	12.1583i	0.582607	−	1.20980i	−0.376411	−	0.926453i	$-0.622842\pi$
$101$	5.85513	−	12.1583i	0.582607	−	1.20980i	0.959018	−	0.283344i	$-0.0914437\pi$
$102$	−0.0402641	+	0.0836092i	−0.00398674	+	0.00827854i
$103$	−0.389459	−	1.70633i	−0.0383745	−	0.168130i	0.952110	−	0.305757i	$-0.0989095\pi$
$103$	−0.389459	−	1.70633i	−0.0383745	−	0.168130i	−0.990484	+	0.137627i	$0.956052\pi$
$104$			1.90879i			0.187172i
$105$	−9.06826	+	2.06977i	−0.884972	+	0.201989i
$106$	0.0596517	+	0.0475707i	0.00579389	+	0.00462047i
$107$	0.580401	−	2.54290i	0.0561095	−	0.245832i	−0.939094	−	0.343661i	$-0.888333\pi$
$107$	0.580401	−	2.54290i	0.0561095	−	0.245832i	0.995203	+	0.0978294i	$0.0311900\pi$
$108$	−10.2305	−	2.33506i	−0.984435	−	0.224691i
$109$	−5.70347	−	7.15192i	−0.546293	−	0.685030i	0.429665	−	0.902988i	$-0.358632\pi$
$109$	−5.70347	−	7.15192i	−0.546293	−	0.685030i	−0.975958	+	0.217959i	$0.930060\pi$
$110$	−1.73933	−	0.837617i	−0.165839	−	0.0798636i
$111$	−11.6934	+	5.63123i	−1.10989	+	0.534493i
$112$	−6.97874	+	8.75107i	−0.659429	+	0.826898i
$113$	9.93607	−	7.92375i	0.934706	−	0.745404i	−0.0324796	−	0.999472i	$-0.510340\pi$
$113$	9.93607	−	7.92375i	0.934706	−	0.745404i	0.967186	+	0.254069i	$0.0817690\pi$
$114$	−0.254412	−	0.528292i	−0.0238278	−	0.0494790i
$115$	15.5914			1.45390
$116$	−3.04782	+	10.1658i	−0.282983	+	0.943870i
$117$	−4.87965			−0.451123
$118$	0.0924039	+	0.191879i	0.00850647	+	0.0176639i
$119$	−1.10412	+	0.880510i	−0.101215	+	0.0807162i
$120$	1.34587	−	1.68766i	0.122860	−	0.154062i
$121$	4.45211	−	2.14402i	0.404737	−	0.194911i
$122$	−1.32374	−	0.637480i	−0.119846	−	0.0577148i
$123$	3.58042	+	4.48971i	0.322836	+	0.404823i
$124$	−7.40575	−	1.69031i	−0.665056	−	0.151795i
$125$	1.26196	−	5.52899i	0.112873	−	0.494528i
$126$	0.679093	+	0.541558i	0.0604984	+	0.0482459i
$127$	−1.11618	+	0.254762i	−0.0990453	+	0.0226064i	−0.271756	−	0.962366i	$-0.587604\pi$
$127$	−1.11618	+	0.254762i	−0.0990453	+	0.0226064i	0.172711	+	0.984973i	$0.444747\pi$
$128$		−	5.27401i		−	0.466161i
$129$	−2.05609	−	9.00832i	−0.181029	−	0.793138i
$130$	0.589720	−	1.22457i	0.0517219	−	0.107402i
$131$	−7.58804	+	15.7567i	−0.662970	+	1.37667i	0.249840	+	0.968287i	$0.419622\pi$
$131$	−7.58804	+	15.7567i	−0.662970	+	1.37667i	−0.912810	+	0.408385i	$0.866092\pi$
$132$	1.96861	+	8.62504i	0.171345	+	0.750713i
$133$		−	8.92328i		−	0.773746i
$134$	−0.157542	+	0.0359580i	−0.0136096	+	0.00310630i
$135$	11.7705	+	9.38665i	1.01304	+	0.807874i
$136$	0.0729284	−	0.319520i	0.00625356	−	0.0273986i
$137$	0.925317	+	0.211198i	0.0790552	+	0.0180438i	0.261866	−	0.965104i	$-0.415662\pi$
$137$	0.925317	+	0.211198i	0.0790552	+	0.0180438i	−0.182810	+	0.983148i	$0.558519\pi$
$138$	0.661055	+	0.828937i	0.0562728	+	0.0705638i
$139$	−6.53941	−	3.14921i	−0.554665	−	0.267113i	0.135484	−	0.990779i	$-0.456741\pi$
$139$	−6.53941	−	3.14921i	−0.554665	−	0.267113i	−0.690150	+	0.723667i	$0.742455\pi$
$140$	14.6893	−	7.07402i	1.24148	−	0.597864i
$141$	−1.67367	+	2.09872i	−0.140949	+	0.176744i
$142$	−0.799248	+	0.637379i	−0.0670714	+	0.0534877i
$143$	4.86970	+	10.1120i	0.407225	+	0.845611i
$144$	6.64048			0.553373
$145$	10.2677	−	11.2431i	0.852682	−	0.933689i
$146$	0.0826526			0.00684038
$147$	−0.761689	−	1.58166i	−0.0628231	−	0.130453i
$148$	17.7863	−	14.1841i	1.46202	−	1.16592i
$149$	−10.6334	+	13.3339i	−0.871126	+	1.09236i	0.123856	+	0.992300i	$0.460474\pi$
$149$	−10.6334	+	13.3339i	−0.871126	+	1.09236i	−0.994982	+	0.100057i	$0.968097\pi$
$150$	−0.518685	+	0.249785i	−0.0423504	+	0.0203949i
$151$	−8.86929	−	4.27122i	−0.721772	−	0.347587i	0.0366700	−	0.999327i	$-0.488325\pi$
$151$	−8.86929	−	4.27122i	−0.721772	−	0.347587i	−0.758442	+	0.651740i	$0.774039\pi$
$152$	1.29114	+	1.61904i	0.104726	+	0.131322i
$153$	0.816824	+	0.186435i	0.0660363	+	0.0150724i
$154$	0.444557	−	1.94773i	0.0358234	−	0.156953i
$155$	8.52049	+	6.79487i	0.684382	+	0.545777i
$156$	−6.07242	+	1.38599i	−0.486183	+	0.110968i
$157$			2.64062i			0.210744i	0.994433	+	0.105372i	$0.0336034\pi$
$157$			2.64062i			0.210744i	−0.994433	+	0.105372i	$0.966397\pi$
$158$	0.0704463	+	0.308645i	0.00560440	+	0.0245545i
$159$	−0.217648	+	0.451951i	−0.0172606	+	0.0358420i
$160$	−2.46856	+	5.12601i	−0.195157	+	0.405247i
$161$	3.59038	+	15.7305i	0.282961	+	1.23973i
$162$			0.133213i			0.0104662i
$163$	−9.53190	+	2.17559i	−0.746596	+	0.170406i	−0.578861	−	0.815426i	$-0.696502\pi$
$163$	−9.53190	+	2.17559i	−0.746596	+	0.170406i	−0.167735	+	0.985832i	$0.553645\pi$
$164$	−7.86972	−	6.27589i	−0.614522	−	0.490065i
$165$	2.82432	−	12.3742i	0.219873	−	0.963327i
$166$	0.726646	+	0.165852i	0.0563987	+	0.0128726i
$167$	−14.7231	−	18.4622i	−1.13931	−	1.42865i	−0.887462	−	0.460881i	$-0.847533\pi$
$167$	−14.7231	−	18.4622i	−1.13931	−	1.42865i	−0.251847	−	0.967767i	$-0.581038\pi$
$168$	2.01264	+	0.969238i	0.155279	+	0.0747784i
$169$	4.59326	−	2.21200i	0.353328	−	0.170154i
$170$	−0.145502	+	0.182454i	−0.0111595	+	0.0139936i
$171$	−4.13894	+	3.30069i	−0.316512	+	0.252410i
$172$	7.02726	+	14.5923i	0.535823	+	1.11265i
$173$	−5.22521			−0.397265			−0.198633	−	0.980074i	$-0.563650\pi$
$173$	−5.22521			−0.397265			−0.198633	+	0.980074i	$0.563650\pi$
$174$	1.03309	+	0.0692004i	0.0783184	+	0.00524607i
$175$	−8.76101			−0.662270
$176$	−6.62694	−	13.7610i	−0.499525	−	1.03727i
$177$	−1.09472	+	0.873007i	−0.0822839	+	0.0656192i
$178$	−1.65877	+	2.08004i	−0.124330	+	0.155905i
$179$	10.2128	−	4.91824i	0.763343	−	0.367607i	−0.0113570	−	0.999936i	$-0.503615\pi$
$179$	10.2128	−	4.91824i	0.763343	−	0.367607i	0.774700	+	0.632329i	$0.217901\pi$
$180$	−8.71473	−	4.19679i	−0.649557	−	0.312810i
$181$	6.44743	+	8.08482i	0.479233	+	0.600940i	0.961405	−	0.275137i	$-0.0887232\pi$
$181$	6.44743	+	8.08482i	0.479233	+	0.600940i	−0.482172	+	0.876077i	$0.660152\pi$
$182$	1.37129	+	0.312988i	0.101647	+	0.0232002i
$183$	2.14949	−	9.41754i	0.158895	−	0.696164i
$184$	−2.92754	−	2.33464i	−0.215821	−	0.172112i
$185$	−31.8199	+	7.26268i	−2.33944	+	0.533963i
$186$			0.741098i			0.0543399i
$187$	−0.428813	−	1.87875i	−0.0313579	−	0.137388i
$188$	2.04153	−	4.23928i	0.148894	−	0.309181i
$189$	−6.75988	+	14.0370i	−0.491709	+	1.02104i
$190$	−0.328119	−	1.43758i	−0.0238042	−	0.104293i
$191$		−	6.30617i		−	0.456299i	−0.973626	−	0.228149i	$-0.926733\pi$
$191$		−	6.30617i		−	0.456299i	0.973626	−	0.228149i	$-0.0732675\pi$
$192$	8.00909	−	1.82802i	0.578006	−	0.131926i
$193$	−3.20725	−	2.55769i	−0.230863	−	0.184107i	0.501226	−	0.865317i	$-0.332883\pi$
$193$	−3.20725	−	2.55769i	−0.230863	−	0.184107i	−0.732088	+	0.681210i	$0.761454\pi$
$194$	−0.0919610	+	0.402908i	−0.00660242	+	0.0289271i
$195$	8.71198	+	1.98845i	0.623878	+	0.142396i
$196$	1.91856	+	2.40580i	0.137040	+	0.171843i
$197$	18.3245	+	8.82462i	1.30557	+	0.628728i	0.951833	−	0.306618i	$-0.0991974\pi$
$197$	18.3245	+	8.82462i	1.30557	+	0.628728i	0.353735	+	0.935346i	$0.384912\pi$
$198$	−1.06787	+	0.514258i	−0.0758901	+	0.0365467i
$199$	−1.22899	+	1.54111i	−0.0871211	+	0.109246i	−0.823482	−	0.567343i	$-0.807971\pi$
$199$	−1.22899	+	1.54111i	−0.0871211	+	0.109246i	0.736360	+	0.676589i	$0.236543\pi$
$200$	1.58960	−	1.26767i	0.112402	−	0.0896375i
$201$	−0.460967	−	0.957207i	−0.0325141	−	0.0675162i
$202$	2.30772			0.162371
$203$	13.7078	+	7.77019i	0.962101	+	0.545361i
$204$	1.06944			0.0748758
$205$	6.26577	+	13.0110i	0.437620	+	0.908728i
$206$	0.234004	−	0.186612i	0.0163038	−	0.0130019i
$207$	5.96829	−	7.48399i	0.414825	−	0.520173i
$208$	9.68836	−	4.66567i	0.671767	−	0.323506i
$209$	10.9705	+	5.28311i	0.758845	+	0.365440i
$210$	−0.991747	−	1.24361i	−0.0684371	−	0.0858174i
$211$	−17.3534	−	3.96080i	−1.19466	−	0.272673i	−0.421466	−	0.906844i	$-0.638484\pi$
$211$	−17.3534	−	3.96080i	−1.19466	−	0.272673i	−0.773192	+	0.634172i	$0.781341\pi$
$212$	0.195656	−	0.857226i	0.0134377	−	0.0588745i
$213$	−5.25476	−	4.19053i	−0.360050	−	0.287131i
$214$	0.434861	−	0.0992541i	0.0297265	−	0.00678487i
$215$		−	23.2363i		−	1.58470i
$216$	−0.804559	−	3.52500i	−0.0547433	−	0.239846i
$217$	−4.89339	+	10.1612i	−0.332185	+	0.689789i
$218$	0.678739	−	1.40942i	0.0459700	−	0.0954577i
$219$	0.120920	+	0.529786i	0.00817103	+	0.0357996i
$220$			22.2477i			1.49994i
$221$	1.32273	−	0.301904i	0.0889762	−	0.0203082i
$222$	−1.73526	−	1.38382i	−0.116463	−	0.0928759i
$223$	4.22512	−	18.5115i	0.282935	−	1.23962i	−0.611075	−	0.791572i	$-0.709263\pi$
$223$	4.22512	−	18.5115i	0.282935	−	1.23962i	0.894010	−	0.448047i	$-0.147880\pi$
$224$	−5.74020	−	1.31016i	−0.383533	−	0.0875390i
$225$	3.24067	+	4.06367i	0.216045	+	0.270911i
$226$	1.95808	+	0.942963i	0.130250	+	0.0627250i
$227$	−0.0933811	+	0.0449699i	−0.00619792	+	0.00298476i	−0.436980	−	0.899471i	$-0.643952\pi$
$227$	−0.0933811	+	0.0449699i	−0.00619792	+	0.00298476i	0.430782	+	0.902456i	$0.358238\pi$
$228$	−4.21314	+	5.28311i	−0.279022	+	0.349883i
$229$	10.3207	−	8.23049i	0.682012	−	0.543886i	−0.220053	−	0.975488i	$-0.570623\pi$
$229$	10.3207	−	8.23049i	0.682012	−	0.543886i	0.902064	+	0.431602i	$0.142051\pi$
$230$	1.15685	+	2.40223i	0.0762806	+	0.158398i
$231$	13.1349			0.864215
$232$	−3.61146	+	0.573612i	−0.237104	+	0.0376595i
$233$	−2.18750			−0.143308			−0.0716538	−	0.997430i	$-0.522828\pi$
$233$	−2.18750			−0.143308			−0.0716538	+	0.997430i	$0.522828\pi$
$234$	−0.362061	−	0.751828i	−0.0236687	−	0.0491485i
$235$	−5.27777	+	4.20888i	−0.344284	+	0.274557i
$236$	1.53024	−	1.91886i	0.0996100	−	0.124907i
$237$	−1.87529	+	0.903092i	−0.121813	+	0.0586621i
$238$	−0.217588	−	0.104785i	−0.0141041	−	0.00679219i
$239$	9.54386	+	11.9676i	0.617341	+	0.774121i	0.987968	−	0.154661i	$-0.0494285\pi$
$239$	9.54386	+	11.9676i	0.617341	+	0.774121i	−0.370627	+	0.928782i	$0.620857\pi$
$240$	−11.8557	−	2.70599i	−0.765283	−	0.174671i
$241$	−3.02515	+	13.2541i	−0.194867	+	0.853768i	0.779068	+	0.626940i	$0.215693\pi$
$241$	−3.02515	+	13.2541i	−0.194867	+	0.853768i	−0.973935	+	0.226829i	$0.927164\pi$
$242$	0.660677	+	0.526872i	0.0424699	+	0.0338686i
$243$	14.7197	−	3.35967i	0.944267	−	0.215523i
$244$			16.9319i			1.08395i
$245$	−0.982362	−	4.30401i	−0.0627608	−	0.274973i
$246$	−0.426087	+	0.884779i	−0.0271663	+	0.0564115i
$247$	−3.71955	+	7.72373i	−0.236669	+	0.491449i
$248$	−0.582409	−	2.55170i	−0.0369830	−	0.162033i
$249$			4.90029i			0.310543i
$250$	0.945510	−	0.215807i	0.0597993	−	0.0136488i
$251$	−16.0564	−	12.8046i	−1.01347	−	0.808216i	−0.0319344	−	0.999490i	$-0.510167\pi$
$251$	−16.0564	−	12.8046i	−1.01347	−	0.808216i	−0.981537	+	0.191274i	$0.938738\pi$
$252$	2.22741	−	9.75890i	0.140313	−	0.614753i
$253$	−21.4651	−	4.89927i	−1.34950	−	0.308015i
$254$	−0.122071	−	0.153072i	−0.00765942	−	0.00960461i
$255$	−1.38236	−	0.665710i	−0.0865668	−	0.0416884i
$256$	−12.3536	+	5.94916i	−0.772098	+	0.371823i
$257$	12.3518	−	15.4887i	0.770486	−	0.966159i	−0.229488	−	0.973311i	$-0.573705\pi$
$257$	12.3518	−	15.4887i	0.770486	−	0.966159i	0.999974	+	0.00715224i	$0.00227665\pi$
$258$	1.23539	−	0.985192i	0.0769121	−	0.0613354i
$259$	−14.6549	−	30.4313i	−0.910614	−	1.89091i
$260$	−15.6634			−0.971401
$261$	−1.46639	−	9.23235i	−0.0907671	−	0.571468i
$262$	−2.99072			−0.184768
$263$	6.45116	+	13.3960i	0.397796	+	0.826031i	0.999624	+	0.0274060i	$0.00872469\pi$
$263$	6.45116	+	13.3960i	0.397796	+	0.826031i	−0.601829	+	0.798625i	$0.705561\pi$
$264$	−2.38321	+	1.90055i	−0.146676	+	0.116971i
$265$	−0.786515	+	0.986258i	−0.0483152	+	0.0605854i
$266$	1.37485	−	0.662091i	0.0842973	−	0.0405954i
$267$	−15.7594	−	7.58931i	−0.964458	−	0.464458i
$268$	1.16109	+	1.45596i	0.0709250	+	0.0889371i
$269$	−1.51784	−	0.346436i	−0.0925441	−	0.0211226i	0.175998	−	0.984391i	$-0.443685\pi$
$269$	−1.51784	−	0.346436i	−0.0925441	−	0.0211226i	−0.268542	+	0.963268i	$0.586542\pi$
$270$	−0.572892	+	2.51000i	−0.0348651	+	0.152754i
$271$	9.50030	+	7.57624i	0.577102	+	0.460224i	0.868023	−	0.496523i	$-0.165390\pi$
$271$	9.50030	+	7.57624i	0.577102	+	0.460224i	−0.290921	+	0.956747i	$0.593962\pi$
$272$	−1.80003	+	0.410846i	−0.109143	+	0.0249112i
$273$			9.24759i			0.559690i
$274$	0.0361168	+	0.158238i	0.00218189	+	0.00955950i
$275$	5.18704	−	10.7710i	0.312790	−	0.649516i
$276$	5.30145	−	11.0086i	0.319110	−	0.662638i
$277$	2.67977	+	11.7409i	0.161012	+	0.705439i	0.989392	+	0.145272i	$0.0464059\pi$
$277$	2.67977	+	11.7409i	0.161012	+	0.705439i	−0.828380	+	0.560167i	$0.810737\pi$
$278$		−	1.24122i		−	0.0744434i
$279$	6.52319	−	1.48887i	0.390533	−	0.0891366i
$280$	4.39204	+	3.50254i	0.262475	+	0.209317i
$281$	−3.04306	+	13.3325i	−0.181534	+	0.795351i	0.799367	+	0.600843i	$0.205168\pi$
$281$	−3.04306	+	13.3325i	−0.181534	+	0.795351i	−0.980901	+	0.194508i	$0.937689\pi$
$282$	−0.447542	−	0.102149i	−0.0266507	−	0.00608286i
$283$	16.2063	+	20.3221i	0.963367	+	1.20802i	0.978101	+	0.208133i	$0.0667387\pi$
$283$	16.2063	+	20.3221i	0.963367	+	1.20802i	−0.0147331	+	0.999891i	$0.504690\pi$
$284$	10.6143	+	5.11157i	0.629842	+	0.303316i
$285$	8.73456	−	4.20634i	0.517391	−	0.249162i
$286$	−1.19668	+	1.50059i	−0.0707613	+	0.0887318i
$287$	−11.6842	+	9.31784i	−0.689696	+	0.550015i
$288$	1.51558	+	3.14714i	0.0893065	+	0.185447i
$289$	16.7670			0.986297
$290$	2.49411	+	0.747763i	0.146459	+	0.0439101i
$291$	−2.71709			−0.159279
$292$	−0.413278	−	0.858181i	−0.0241853	−	0.0502212i
$293$	−4.47701	+	3.57030i	−0.261550	+	0.208579i	−0.745481	−	0.666527i	$-0.767780\pi$
$293$	−4.47701	+	3.57030i	−0.261550	+	0.208579i	0.483931	+	0.875106i	$0.339209\pi$
$294$	0.187178	−	0.234713i	0.0109164	−	0.0136888i
$295$	−3.17245	+	1.52777i	−0.184707	+	0.0889502i
$296$	7.06223	+	3.40099i	0.410483	+	0.197678i
$297$	−13.2552	−	16.6215i	−0.769146	−	0.964479i
$298$	−2.84340	−	0.648987i	−0.164714	−	0.0375948i
$299$	3.44931	−	15.1124i	0.199479	−	0.873974i
$300$	5.18704	+	4.13653i	0.299474	+	0.238822i
$301$	23.4436	−	5.35085i	1.35127	−	0.308418i
$302$		−	1.68345i		−	0.0968714i
$303$	3.37618	+	14.7920i	0.193956	+	0.849779i
$304$	5.06176	−	10.5108i	0.290312	−	0.602838i
$305$	10.5398	−	21.8862i	0.603510	−	1.25320i
$306$	0.0318821	+	0.139685i	0.00182258	+	0.00798524i
$307$		−	12.7599i		−	0.728244i	−0.931351	−	0.364122i	$-0.881369\pi$
$307$		−	12.7599i		−	0.728244i	0.931351	−	0.364122i	$-0.118631\pi$
$308$	−22.4461	+	5.12319i	−1.27899	+	0.291921i
$309$	1.53849	+	1.22691i	0.0875217	+	0.0697963i
$310$	−0.414708	+	1.81695i	−0.0235538	+	0.103196i
$311$	12.2017	+	2.78495i	0.691893	+	0.157920i	0.553987	−	0.832525i	$-0.313106\pi$
$311$	12.2017	+	2.78495i	0.691893	+	0.157920i	0.137906	+	0.990445i	$0.455963\pi$
$312$	−1.33807	−	1.67789i	−0.0757533	−	0.0949917i
$313$	−23.2978	−	11.2196i	−1.31687	−	0.634171i	−0.362274	−	0.932072i	$-0.617999\pi$
$313$	−23.2978	−	11.2196i	−1.31687	−	0.634171i	−0.954597	+	0.297900i	$0.903714\pi$
$314$	−0.406851	+	0.195929i	−0.0229599	+	0.0110569i
$315$	−8.95391	+	11.2279i	−0.504496	+	0.632618i
$316$	2.85242	−	2.27473i	0.160461	−	0.127963i
$317$	11.7612	+	24.4225i	0.660577	+	1.37170i	0.914543	+	0.404489i	$0.132551\pi$
$317$	11.7612	+	24.4225i	0.660577	+	1.37170i	−0.253966	+	0.967213i	$0.581735\pi$
$318$	−0.0857831			−0.00481047
$319$	−17.6687	+	12.2523i	−0.989258	+	0.685998i
$320$	20.6589			1.15487
$321$	1.27240	+	2.64216i	0.0710182	+	0.147471i
$322$	−2.15726	+	1.72036i	−0.120219	+	0.0958717i
$323$	0.917728	−	1.15079i	0.0510638	−	0.0640319i
$324$	1.38315	−	0.666092i	0.0768419	−	0.0370051i
$325$	7.58327	+	3.65191i	0.420644	+	0.202572i
$326$	−1.04245	−	1.30719i	−0.0577361	−	0.0723988i
$327$	10.0271	+	2.28861i	0.554498	+	0.126560i
$328$	0.771752	−	3.38127i	0.0426129	−	0.186699i
$329$	−5.46179	−	4.35563i	−0.301118	−	0.240134i
$330$	2.11610	−	0.482986i	0.116487	−	0.0265875i
$331$		−	10.9792i		−	0.603470i	−0.953392	−	0.301735i	$-0.902434\pi$
$331$		−	10.9792i		−	0.603470i	0.953392	−	0.301735i	$-0.0975658\pi$
$332$	−1.91132	−	8.37405i	−0.104897	−	0.459586i
$333$	−8.69431	+	18.0539i	−0.476445	+	0.989349i
$334$	1.75212	−	3.63831i	0.0958717	−	0.199080i
$335$	−0.594515	−	2.60474i	−0.0324819	−	0.142312i
$336$		−	12.5846i		−	0.686546i
$337$	16.7612	−	3.82563i	0.913040	−	0.208395i	0.259902	−	0.965635i	$-0.416310\pi$
$337$	16.7612	−	3.82563i	0.913040	−	0.208395i	0.653137	+	0.757240i	$0.273452\pi$
$338$	0.681623	+	0.543576i	0.0370754	+	0.0295667i
$339$	−3.17954	+	13.9305i	−0.172689	+	0.756599i
$340$	2.62196	+	0.598444i	0.142196	+	0.0324552i
$341$	−9.59527	−	12.0321i	−0.519613	−	0.651574i
$342$	−0.815653	−	0.392798i	−0.0441055	−	0.0212401i
$343$	−14.3374	+	6.90451i	−0.774145	+	0.372809i
$344$	−3.47938	+	4.36301i	−0.187596	+	0.235238i
$345$	−13.7053	+	10.9296i	−0.737870	+	0.588431i
$346$	−0.387701	−	0.805070i	−0.0208429	−	0.0432808i
$347$	−31.2968			−1.68010			−0.840049	−	0.542510i	$-0.817474\pi$
$347$	−31.2968			−1.68010			−0.840049	+	0.542510i	$0.817474\pi$
$348$	−4.44714	−	11.0726i	−0.238392	−	0.593553i
$349$	−16.8395			−0.901398			−0.450699	−	0.892676i	$-0.648825\pi$
$349$	−16.8395			−0.901398			−0.450699	+	0.892676i	$0.648825\pi$
$350$	−0.650051	−	1.34985i	−0.0347467	−	0.0721523i
$351$	11.7023	−	9.33228i	0.624623	−	0.498120i
$352$	5.00929	−	6.28145i	0.266996	−	0.334802i
$353$	−24.0306	+	11.5725i	−1.27902	+	0.615944i	−0.945138	−	0.326671i	$-0.894073\pi$
$353$	−24.0306	+	11.5725i	−1.27902	+	0.615944i	−0.333883	+	0.942615i	$0.608359\pi$
$354$	−0.215734	−	0.103892i	−0.0114661	−	0.00552179i
$355$	−10.5382	−	13.2145i	−0.559308	−	0.701350i
$356$	29.8912	+	6.82246i	1.58423	+	0.361590i
$357$	0.353319	−	1.54799i	0.0186996	−	0.0819284i
$358$	1.51555	+	1.20861i	0.0800992	+	0.0638770i
$359$	−11.7911	+	2.69123i	−0.622308	+	0.142038i	−0.522038	−	0.852923i	$-0.674828\pi$
$359$	−11.7911	+	2.69123i	−0.622308	+	0.142038i	−0.100270	+	0.994960i	$0.531971\pi$
$360$		−	3.33276i		−	0.175652i
$361$	−2.15835	−	9.45635i	−0.113597	−	0.497703i
$362$	−0.767274	+	1.59326i	−0.0403270	+	0.0837400i
$363$	−2.41058	+	5.00561i	−0.126522	+	0.262727i
$364$	−3.60696	−	15.8031i	−0.189056	−	0.828308i
$365$			1.36655i			0.0715282i
$366$	1.61049	−	0.367583i	0.0841816	−	0.0192139i
$367$	26.5559	+	21.1776i	1.38621	+	1.10546i	0.981595	+	0.190975i	$0.0611650\pi$
$367$	26.5559	+	21.1776i	1.38621	+	1.10546i	0.404612	+	0.914488i	$0.367406\pi$
$368$	−4.69400	+	20.5658i	−0.244692	+	1.07206i
$369$	8.64389	+	1.97291i	0.449983	+	0.102706i
$370$	−3.47997	−	4.36375i	−0.180915	−	0.226860i
$371$	−1.17617	−	0.566416i	−0.0610639	−	0.0294068i
$372$	7.69481	−	3.70563i	0.398957	−	0.192128i
$373$	3.86240	−	4.84329i	0.199987	−	0.250776i	−0.671718	−	0.740807i	$-0.734443\pi$
$373$	3.86240	−	4.84329i	0.199987	−	0.250776i	0.871705	+	0.490031i	$0.163015\pi$
$374$	0.257650	−	0.205469i	0.0133228	−	0.0106245i
$375$	2.76655	+	5.74480i	0.142864	+	0.296660i
$376$	1.62122			0.0836082
$377$	−8.62619	−	12.4396i	−0.444271	−	0.640671i
$378$	−2.66432			−0.137038
$379$	−11.3223	−	23.5109i	−0.581585	−	1.20767i	−0.959467	−	0.281820i	$-0.909062\pi$
$379$	−11.3223	−	23.5109i	−0.581585	−	1.20767i	0.377882	−	0.925854i	$-0.376652\pi$
$380$	−13.2857	+	10.5950i	−0.681544	+	0.543513i
$381$	0.802572	−	1.00639i	0.0411170	−	0.0515591i
$382$	0.971619	−	0.467907i	0.0497123	−	0.0239402i
$383$	18.8120	+	9.05940i	0.961250	+	0.462914i	0.847617	−	0.530609i	$-0.178037\pi$
$383$	18.8120	+	9.05940i	0.961250	+	0.462914i	0.113633	+	0.993523i	$0.463751\pi$
$384$	3.69711	+	4.63603i	0.188667	+	0.236581i
$385$	32.2030	+	7.35013i	1.64122	+	0.374597i
$386$	0.156103	−	0.683930i	0.00794541	−	0.0348111i
$387$	−11.1536	−	8.89473i	−0.566971	−	0.452144i
$388$	4.64321	−	1.05978i	0.235723	−	0.0538023i
$389$			15.7075i			0.796400i	0.917299	+	0.398200i	$0.130365\pi$
$389$			15.7075i			0.796400i	−0.917299	+	0.398200i	$0.869635\pi$
$390$	0.340044	+	1.48983i	0.0172188	+	0.0754405i
$391$	−1.15479	+	2.39794i	−0.0584002	+	0.121269i
$392$	−0.460023	+	0.955248i	−0.0232347	+	0.0482473i
$393$	−4.37541	−	19.1699i	−0.220710	−	0.966995i
$394$			3.47811i			0.175224i
$395$	−5.10302	+	1.16473i	−0.256761	+	0.0586040i
$396$	10.6791	+	8.51628i	0.536644	+	0.427959i
$397$	−2.57280	+	11.2722i	−0.129125	+	0.565734i	0.868428	+	0.495816i	$0.165131\pi$
$397$	−2.57280	+	11.2722i	−0.129125	+	0.565734i	−0.997553	+	0.0699182i	$0.977726\pi$
$398$	−0.328634	−	0.0750087i	−0.0164730	−	0.00375984i
$399$	6.25526	+	7.84385i	0.313155	+	0.392684i
$400$	−10.3197	−	4.96971i	−0.515985	−	0.248485i
$401$	4.33830	−	2.08921i	0.216644	−	0.104330i	−0.322414	−	0.946599i	$-0.604494\pi$
$401$	4.33830	−	2.08921i	0.216644	−	0.104330i	0.539059	+	0.842268i	$0.318780\pi$
$402$	0.113278	−	0.142046i	0.00564979	−	0.00708462i
$403$	8.47114	−	6.75551i	0.421978	−	0.336516i
$404$	−11.5390	−	23.9610i	−0.574088	−	1.19211i
$405$	−2.20250			−0.109443
$406$	−0.180090	+	2.68856i	−0.00893771	+	0.133431i
$407$	46.0896			2.28457
$408$	0.159879	+	0.331992i	0.00791518	+	0.0164360i
$409$	18.6701	−	14.8889i	0.923177	−	0.736209i	−0.0416399	−	0.999133i	$-0.513258\pi$
$409$	18.6701	−	14.8889i	0.923177	−	0.736209i	0.964817	+	0.262924i	$0.0846868\pi$
$410$	−1.53975	+	1.93079i	−0.0760429	+	0.0953548i
$411$	−0.961434	+	0.463002i	−0.0474240	+	0.0228382i
$412$	−3.10766	−	1.49657i	−0.153103	−	0.0737306i
$413$	−2.27195	−	2.84893i	−0.111795	−	0.140187i
$414$	1.59593	+	0.364260i	0.0784355	+	0.0179024i
$415$	−2.74213	+	12.0141i	−0.134606	+	0.589748i
$416$	4.42242	+	3.52676i	0.216827	+	0.172914i
$417$	7.95596	−	1.81590i	0.389605	−	0.0889248i
$418$			2.08227i			0.101847i
$419$	6.86486	+	30.0769i	0.335370	+	1.46935i	0.808571	+	0.588399i	$0.200242\pi$
$419$	6.86486	+	30.0769i	0.335370	+	1.46935i	−0.473200	+	0.880955i	$0.656901\pi$
$420$	−7.95349	+	16.5156i	−0.388091	+	0.805878i
$421$	4.52434	−	9.39489i	0.220503	−	0.457879i	−0.761145	−	0.648582i	$-0.775362\pi$
$421$	4.52434	−	9.39489i	0.220503	−	0.457879i	0.981648	+	0.190703i	$0.0610767\pi$
$422$	−0.677335	−	2.96760i	−0.0329721	−	0.144460i
$423$			4.14451i			0.201513i
$424$	0.295363	−	0.0674146i	0.0143441	−	0.00327394i
$425$	−1.12987	−	0.901039i	−0.0548066	−	0.0437068i
$426$	0.255759	−	1.12055i	0.0123916	−	0.0542910i
$427$	24.5086	+	5.59392i	1.18605	+	0.270709i
$428$	−3.20494	−	4.01886i	−0.154916	−	0.194259i
$429$	−11.3692	−	5.47512i	−0.548911	−	0.264341i
$430$	3.58012	−	1.72409i	0.172649	−	0.0831432i
$431$	6.65691	−	8.34750i	0.320652	−	0.402085i	−0.595215	−	0.803566i	$-0.702933\pi$
$431$	6.65691	−	8.34750i	0.320652	−	0.402085i	0.915867	+	0.401482i	$0.131505\pi$
$432$	−15.9251	+	12.6999i	−0.766197	+	0.611022i
$433$	−11.9500	−	24.8145i	−0.574282	−	1.19251i	−0.962586	−	0.270978i	$-0.912653\pi$
$433$	−11.9500	−	24.8145i	−0.574282	−	1.19251i	0.388303	−	0.921532i	$-0.373061\pi$
$434$	−1.92866			−0.0925788
$435$	−1.14413	+	17.0807i	−0.0548569	+	0.818958i
$436$	−18.0278			−0.863374
$437$	−7.29663	−	15.1516i	−0.349045	−	0.724800i
$438$	−0.0726543	+	0.0579398i	−0.00347155	+	0.00276847i
$439$	−16.1160	+	20.2088i	−0.769173	+	0.964512i	−0.999964	−	0.00849123i	$-0.997297\pi$
$439$	−16.1160	+	20.2088i	−0.769173	+	0.964512i	0.230791	+	0.973003i	$0.425869\pi$
$440$	−6.90645	+	3.32597i	−0.329252	+	0.158559i
$441$	−2.44200	−	1.17601i	−0.116286	−	0.0560003i
$442$	0.144659	+	0.181397i	0.00688075	+	0.00862819i
$443$	−13.7606	−	3.14077i	−0.653786	−	0.149222i	−0.117254	−	0.993102i	$-0.537409\pi$
$443$	−13.7606	−	3.14077i	−0.653786	−	0.149222i	−0.536533	+	0.843880i	$0.680266\pi$
$444$	−5.69159	+	24.9365i	−0.270111	+	1.18343i
$445$	−34.3905	−	27.4255i	−1.63027	−	1.30009i
$446$	3.16563	−	0.722535i	0.149897	−	0.0342130i
$447$		−	19.1750i		−	0.906948i
$448$	4.75732	+	20.8432i	0.224762	+	0.984748i
$449$	9.59709	−	19.9286i	0.452915	−	0.940487i	−0.542058	−	0.840341i	$-0.682355\pi$
$449$	9.59709	−	19.9286i	0.452915	−	0.940487i	0.994973	−	0.100146i	$-0.0319310\pi$
$450$	−0.385655	+	0.800821i	−0.0181800	+	0.0377511i
$451$	−4.53783	−	19.8815i	−0.213678	−	0.936185i
$452$		−	25.0458i		−	1.17805i
$453$	10.7905	−	2.46287i	0.506983	−	0.115716i
$454$	−0.0138574	−	0.0110509i	−0.000650361	−	0.000518645i
$455$	−5.17483	+	22.6724i	−0.242600	+	1.06290i
$456$	−2.26991	−	0.518093i	−0.106299	−	0.0242619i
$457$	6.08500	+	7.63035i	0.284644	+	0.356933i	0.903512	−	0.428562i	$-0.140980\pi$
$457$	6.08500	+	7.63035i	0.284644	+	0.356933i	−0.618868	+	0.785495i	$0.712408\pi$
$458$	2.03388	+	0.979467i	0.0950372	+	0.0457675i
$459$	−2.31545	+	1.11506i	−0.108076	+	0.0520467i
$460$	19.1578	−	24.0232i	0.893239	−	1.12009i
$461$	15.7515	−	12.5614i	0.733621	−	0.585043i	−0.183799	−	0.982964i	$-0.558840\pi$
$461$	15.7515	−	12.5614i	0.733621	−	0.585043i	0.917420	+	0.397921i	$0.130268\pi$
$462$	0.974589	+	2.02375i	0.0453420	+	0.0941536i
$463$	−15.7776			−0.733249			−0.366624	−	0.930369i	$-0.619487\pi$
$463$	−15.7776			−0.733249			−0.366624	+	0.930369i	$0.619487\pi$
$464$	11.7390	+	16.9284i	0.544968	+	0.785882i
$465$	−12.2530			−0.568220
$466$	−0.162308	−	0.337037i	−0.00751879	−	0.0156129i
$467$	−30.6532	+	24.4451i	−1.41846	+	1.13119i	−0.446849	+	0.894609i	$0.647454\pi$
$467$	−30.6532	+	24.4451i	−1.41846	+	1.13119i	−0.971613	+	0.236577i	$0.923975\pi$
$468$	−5.99585	+	7.51855i	−0.277158	+	0.347545i
$469$	2.49107	−	1.19964i	0.115027	−	0.0553941i
$470$	−1.04008	−	0.500877i	−0.0479754	−	0.0231037i
$471$	−1.85109	−	2.32119i	−0.0852935	−	0.106955i
$472$	0.824447	+	0.188175i	0.0379482	+	0.00866144i
$473$	−7.30155	+	31.9902i	−0.335725	+	1.47091i
$474$	−0.278286	−	0.221926i	−0.0127821	−	0.0101934i
$475$	8.90239	−	2.03191i	0.408470	−	0.0932305i
$476$			2.78316i			0.127566i
$477$	0.172339	+	0.755067i	0.00789087	+	0.0345722i
$478$	−1.13576	+	2.35844i	−0.0519487	+	0.107872i
$479$	18.3393	−	38.0820i	0.837945	−	1.74001i	0.184805	−	0.982775i	$-0.440835\pi$
$479$	18.3393	−	38.0820i	0.837945	−	1.74001i	0.653141	−	0.757236i	$-0.273451\pi$
$480$	−1.42342	−	6.23640i	−0.0649698	−	0.284651i
$481$			32.4492i			1.47955i
$482$	−2.26657	+	0.517329i	−0.103239	+	0.0235637i
$483$	−14.1832	−	11.3107i	−0.645357	−	0.514655i
$484$	2.16700	−	9.49426i	0.0985002	−	0.431557i
$485$	−6.66151	−	1.52045i	−0.302484	−	0.0690399i
$486$	1.60981	+	2.01864i	0.0730225	+	0.0915674i
$487$	12.2269	+	5.88815i	0.554052	+	0.266817i	0.689891	−	0.723914i	$-0.257659\pi$
$487$	12.2269	+	5.88815i	0.554052	+	0.266817i	−0.135839	+	0.990731i	$0.543373\pi$
$488$	−5.25625	+	2.53128i	−0.237939	+	0.114586i
$489$	6.85374	−	8.59432i	0.309937	−	0.388649i
$490$	0.590247	−	0.470706i	0.0266646	−	0.0212643i
$491$	−1.77332	−	3.68233i	−0.0800287	−	0.166181i	0.857115	−	0.515125i	$-0.172255\pi$
$491$	−1.77332	−	3.68233i	−0.0800287	−	0.166181i	−0.937144	+	0.348944i	$0.886540\pi$
$492$	11.3172			0.510217
$493$	0.968699	+	2.41189i	0.0436280	+	0.108626i
$494$	−1.46601			−0.0659590
$495$	−8.50254	−	17.6557i	−0.382161	−	0.793565i
$496$	−11.5280	+	9.19325i	−0.517621	+	0.412789i
$497$	10.9056	−	13.6752i	0.489184	−	0.613417i
$498$	−0.755008	+	0.363593i	−0.0338327	+	0.0162930i
$499$	11.2754	+	5.42993i	0.504755	+	0.243077i	0.668891	−	0.743361i	$-0.266769\pi$
$499$	11.2754	+	5.42993i	0.504755	+	0.243077i	−0.164136	+	0.986438i	$0.552484\pi$
$500$	−6.96844	−	8.73815i	−0.311638	−	0.390782i
$501$	25.8842	+	5.90790i	1.15642	+	0.263945i
$502$	0.781495	−	3.42395i	0.0348798	−	0.152818i
$503$	20.1194	+	16.0447i	0.897080	+	0.715398i	0.959217	−	0.282670i	$-0.0912201\pi$
$503$	20.1194	+	16.0447i	0.897080	+	0.715398i	−0.0621370	+	0.998068i	$0.519792\pi$
$504$	3.36249	−	0.767467i	0.149777	−	0.0341857i
$505$			38.1549i			1.69787i
$506$	−0.837822	−	3.67074i	−0.0372457	−	0.163184i
$507$	−2.48700	+	5.16431i	−0.110452	+	0.229355i
$508$	−0.978970	+	2.03285i	−0.0434348	+	0.0901932i
$509$	−3.53552	−	15.4901i	−0.156709	−	0.686588i	−0.990842	−	0.135024i	$-0.956889\pi$
$509$	−3.53552	−	15.4901i	−0.156709	−	0.686588i	0.834133	−	0.551563i	$-0.185968\pi$
$510$		−	0.262381i		−	0.0116184i
$511$	−1.37874	+	0.314687i	−0.0609917	+	0.0139210i
$512$	−10.0800	−	8.03853i	−0.445477	−	0.355256i
$513$	3.61341	−	15.8314i	0.159536	−	0.698972i
$514$	3.30290	+	0.753864i	0.145684	+	0.0332515i
$515$	3.08537	+	3.86893i	0.135958	+	0.170486i
$516$	−16.4064	−	7.90092i	−0.722253	−	0.347818i
$517$	8.58862	−	4.13606i	0.377727	−	0.181904i
$518$	3.60131	−	4.51590i	0.158232	−	0.198417i
$519$	4.59313	−	3.66289i	0.201616	−	0.160783i
$520$	−2.34164	−	4.86246i	−0.102688	−	0.213233i
$521$	−22.1399			−0.969965			−0.484982	−	0.874524i	$-0.661174\pi$
$521$	−22.1399			−0.969965			−0.484982	+	0.874524i	$0.661174\pi$
$522$	1.31366	−	0.910957i	0.0574975	−	0.0398715i
$523$	31.1728			1.36309			0.681546	−	0.731775i	$-0.261308\pi$
$523$	31.1728			1.36309			0.681546	+	0.731775i	$0.261308\pi$
$524$	14.9542	+	31.0527i	0.653276	+	1.35654i
$525$	7.70121	−	6.14151i	0.336108	−	0.268037i
$526$	−1.58531	+	1.98792i	−0.0691228	+	0.0866772i
$527$	−1.67612	+	0.807179i	−0.0730131	+	0.0351613i
$528$	15.4718	+	7.45083i	0.673324	+	0.324256i
$529$	4.61906	+	5.79212i	0.200829	+	0.251831i
$530$	−0.210315	−	0.0480030i	−0.00913550	−	0.00208512i
$531$	−0.481051	+	2.10762i	−0.0208758	+	0.0914630i
$532$	−13.7490	−	10.9644i	−0.596094	−	0.475369i
$533$	13.9975	−	3.19484i	0.606300	−	0.138384i
$534$		−	2.99123i		−	0.129443i
$535$	1.64103	+	7.18981i	0.0709478	+	0.310843i
$536$	−0.278401	+	0.578106i	−0.0120251	+	0.0249704i
$537$	−5.52970	+	11.4825i	−0.238624	+	0.495508i
$538$	−0.0592439	−	0.259564i	−0.00255419	−	0.0111906i
$539$			6.23415i			0.268524i
$540$	28.9259	−	6.60214i	1.24477	−	0.284111i
$541$	−0.559338	−	0.446058i	−0.0240478	−	0.0191775i	0.611392	−	0.791328i	$-0.290610\pi$
$541$	−0.559338	−	0.446058i	−0.0240478	−	0.0191775i	−0.635440	+	0.772150i	$0.719181\pi$
$542$	−0.462397	+	2.02589i	−0.0198617	+	0.0870196i
$543$	−11.3350	−	2.58714i	−0.486431	−	0.111025i
$544$	−0.605542	−	0.759325i	−0.0259624	−	0.0325558i
$545$	23.3027	+	11.2220i	0.998180	+	0.480698i
$546$	−1.42482	+	0.686155i	−0.0609765	+	0.0293647i
$547$	−25.7613	+	32.3036i	−1.10147	+	1.38120i	−0.184225	+	0.982884i	$0.558977\pi$
$547$	−25.7613	+	32.3036i	−1.10147	+	1.38120i	−0.917247	+	0.398318i	$0.869594\pi$
$548$	1.46239	−	1.16622i	0.0624703	−	0.0498184i
$549$	−6.47098	−	13.4371i	−0.276175	−	0.573483i
$550$	2.04440			0.0871736
$551$	−15.7312	−	4.71637i	−0.670170	−	0.200924i
$552$	4.21000			0.179189
$553$	−2.35024	−	4.88033i	−0.0999425	−	0.207533i
$554$	−1.61013	+	1.28403i	−0.0684078	+	0.0545534i
$555$	22.8795	−	28.6900i	0.971182	−	1.21782i
$556$	−12.8876	+	6.20633i	−0.546555	+	0.263207i
$557$	−19.1398	−	9.21726i	−0.810981	−	0.390548i	−0.0180332	−	0.999837i	$-0.505740\pi$
$557$	−19.1398	−	9.21726i	−0.810981	−	0.390548i	−0.792948	+	0.609290i	$0.791455\pi$
$558$	0.713406	+	0.894583i	0.0302009	+	0.0378707i
$559$	−22.5225	−	5.14062i	−0.952601	−	0.217425i
$560$	7.04217	−	30.8538i	0.297586	−	1.30381i
$561$	1.69395	+	1.35088i	0.0715187	+	0.0570343i
$562$	−2.27998	+	0.520392i	−0.0961753	+	0.0219514i
$563$		−	14.3265i		−	0.603790i	−0.953341	−	0.301895i	$-0.902381\pi$
$563$		−	14.3265i		−	0.603790i	0.953341	−	0.301895i	$-0.0976193\pi$
$564$	1.17719	+	5.15759i	0.0495684	+	0.217174i
$565$	−15.5906	+	32.3742i	−0.655901	+	1.36199i
$566$	−1.92863	+	4.00485i	−0.0810664	+	0.168336i
$567$	−0.507190	−	2.22215i	−0.0213000	−	0.0933214i
$568$			4.05921i			0.170321i
$569$	−16.7463	+	3.82222i	−0.702039	+	0.160236i	−0.558617	−	0.829426i	$-0.688668\pi$
$569$	−16.7463	+	3.82222i	−0.702039	+	0.160236i	−0.143422	+	0.989662i	$0.545811\pi$
$570$	1.29618	+	1.03367i	0.0542909	+	0.0432956i
$571$	−0.918962	+	4.02624i	−0.0384574	+	0.168493i	−0.990510	−	0.137442i	$-0.956112\pi$
$571$	−0.918962	+	4.02624i	−0.0384574	+	0.168493i	0.952052	+	0.305935i	$0.0989690\pi$
$572$	21.5642	+	4.92190i	0.901647	+	0.205795i
$573$	4.42066	+	5.54333i	0.184676	+	0.231576i
$574$	−2.30259	−	1.10887i	−0.0961080	−	0.0462832i
$575$	−14.8761	+	7.16394i	−0.620375	+	0.298757i
$576$	7.90810	−	9.91644i	0.329504	−	0.413185i
$577$	−35.6466	+	28.4272i	−1.48399	+	1.18344i	−0.545510	+	0.838104i	$0.683664\pi$
$577$	−35.6466	+	28.4272i	−1.48399	+	1.18344i	−0.938479	+	0.345338i	$0.887764\pi$
$578$	1.24409	+	2.58337i	0.0517471	+	0.107454i
$579$	4.61223			0.191678
$580$	−4.70702	−	29.6353i	−0.195448	−	1.23054i
$581$	−12.7527			−0.529071
$582$	−0.201603	−	0.418634i	−0.00835673	−	0.0173529i
$583$	1.39273	−	1.11067i	0.0576810	−	0.0459991i
$584$	0.204625	−	0.256592i	0.00846745	−	0.0106178i
$585$	12.4304	−	5.98618i	0.513935	−	0.247498i
$586$	−0.882277	−	0.424882i	−0.0364465	−	0.0175517i
$587$	−12.0226	−	15.0759i	−0.496227	−	0.622249i	0.469147	−	0.883120i	$-0.344562\pi$
$587$	−12.0226	−	15.0759i	−0.496227	−	0.622249i	−0.965374	+	0.260871i	$0.915990\pi$
$588$	−3.37295	−	0.769853i	−0.139098	−	0.0317482i
$589$	2.61569	−	11.4601i	0.107778	−	0.472205i
$590$	−0.470780	−	0.375434i	−0.0193817	−	0.0154564i
$591$	−22.2939	+	5.08844i	−0.917050	+	0.209311i
$592$		−	44.1585i		−	1.81490i
$593$	−7.52102	−	32.9517i	−0.308851	−	1.35317i	−0.856366	−	0.516370i	$-0.827283\pi$
$593$	−7.52102	−	32.9517i	−0.308851	−	1.35317i	0.547514	−	0.836796i	$-0.315574\pi$
$594$	1.57743	−	3.27558i	0.0647229	−	0.134399i
$595$	1.73247	−	3.59751i	0.0710244	−	0.147484i
$596$	7.47909	+	32.7680i	0.306355	+	1.34223i
$597$		−	2.21622i		−	0.0907036i
$598$	2.58437	−	0.589865i	0.105683	−	0.0241214i
$599$	15.1458	+	12.0784i	0.618841	+	0.493509i	0.882004	−	0.471242i	$-0.156194\pi$
$599$	15.1458	+	12.0784i	0.618841	+	0.493509i	−0.263163	+	0.964751i	$0.584766\pi$
$600$	−0.508672	+	2.22864i	−0.0207664	+	0.0909837i
$601$	−16.6470	−	3.79958i	−0.679047	−	0.154988i	−0.130932	−	0.991391i	$-0.541797\pi$
$601$	−16.6470	−	3.79958i	−0.679047	−	0.154988i	−0.548114	+	0.836403i	$0.684654\pi$
$602$	2.56390	+	3.21503i	0.104497	+	0.131035i
$603$	−1.47788	−	0.711707i	−0.0601837	−	0.0289830i
$604$	−17.4792	+	8.41754i	−0.711218	+	0.342505i
$605$	−8.71110	+	10.9234i	−0.354157	+	0.444098i
$606$	−2.02856	+	1.61772i	−0.0824046	+	0.0657155i
$607$	17.9395	+	37.2517i	0.728140	+	1.51200i	0.854182	+	0.519973i	$0.174058\pi$
$607$	17.9395	+	37.2517i	0.728140	+	1.51200i	−0.126042	+	0.992025i	$0.540228\pi$
$608$	6.13669			0.248876
$609$	−17.4966	+	2.77900i	−0.708996	+	0.112611i
$610$	4.15414			0.168196
$611$	2.91198	+	6.04678i	0.117806	+	0.244627i
$612$	1.29093	−	1.02948i	0.0521827	−	0.0416143i
$613$	6.00843	−	7.53434i	0.242678	−	0.304309i	−0.645544	−	0.763723i	$-0.723369\pi$
$613$	6.00843	−	7.53434i	0.242678	−	0.304309i	0.888222	+	0.459414i	$0.151941\pi$
$614$	1.96597	−	0.946759i	0.0793399	−	0.0382081i
$615$	−14.6286	−	7.04476i	−0.589882	−	0.284072i
$616$	−4.94606	−	6.20216i	−0.199282	−	0.249892i
$617$	12.1657	+	2.77673i	0.489771	+	0.111787i	0.460272	−	0.887778i	$-0.347752\pi$
$617$	12.1657	+	2.77673i	0.489771	+	0.111787i	0.0294988	+	0.999565i	$0.490609\pi$
$618$	−0.0748812	+	0.328076i	−0.00301217	+	0.0131972i
$619$	24.5785	+	19.6007i	0.987892	+	0.787818i	0.977242	−	0.212125i	$-0.0680385\pi$
$619$	24.5785	+	19.6007i	0.987892	+	0.787818i	0.0106499	+	0.999943i	$0.496610\pi$
$620$	20.9390	−	4.77920i	0.840932	−	0.191937i
$621$			29.3623i			1.17827i
$622$	0.476253	+	2.08660i	0.0190960	+	0.0836651i
$623$	19.7507	−	41.0128i	0.791296	−	1.64314i
$624$	−5.24572	+	10.8929i	−0.209997	+	0.436063i
$625$	6.89943	+	30.2284i	0.275977	+	1.20914i
$626$		−	4.42207i		−	0.176741i
$627$	−13.3469	+	3.04634i	−0.533024	+	0.121659i
$628$	4.06866	+	3.24465i	0.162357	+	0.129476i
$629$	1.23977	−	5.43180i	0.0494329	−	0.216580i
$630$	−2.39429	−	0.546480i	−0.0953907	−	0.0217723i
$631$	2.93725	+	3.68320i	0.116930	+	0.146626i	0.836852	−	0.547430i	$-0.184394\pi$
$631$	2.93725	+	3.68320i	0.116930	+	0.146626i	−0.719922	+	0.694055i	$0.755822\pi$
$632$	1.13258	+	0.545423i	0.0450517	+	0.0216958i
$633$	18.0307	−	8.68315i	0.716658	−	0.345124i
$634$	−2.89021	+	3.62421i	−0.114785	+	0.143936i
$635$	2.53084	−	2.01827i	0.100433	−	0.0800928i
$636$	0.428931	+	0.890685i	0.0170082	+	0.0353179i
$637$	−4.38912			−0.173903
$638$	−3.19875	−	1.81319i	−0.126640	−	0.0717850i
$639$	−10.3770			−0.410508
$640$	6.46997	+	13.4350i	0.255748	+	0.531066i
$641$	22.8183	−	18.1970i	0.901268	−	0.718738i	−0.0588691	−	0.998266i	$-0.518749\pi$
$641$	22.8183	−	18.1970i	0.901268	−	0.718738i	0.960137	+	0.279528i	$0.0901780\pi$
$642$	−0.312679	+	0.392087i	−0.0123404	+	0.0154744i
$643$	11.9567	−	5.75803i	0.471526	−	0.227075i	−0.183003	−	0.983112i	$-0.558582\pi$
$643$	11.9567	−	5.75803i	0.471526	−	0.227075i	0.654528	+	0.756038i	$0.272867\pi$
$644$	28.6491	+	13.7967i	1.12893	+	0.543666i
$645$	16.2888	+	20.4255i	0.641370	+	0.804252i
$646$	0.245402	+	0.0560113i	0.00965519	+	0.00220374i
$647$	7.64780	−	33.5072i	0.300666	−	1.31730i	−0.568459	−	0.822712i	$-0.692460\pi$
$647$	7.64780	−	33.5072i	0.300666	−	1.31730i	0.869125	−	0.494592i	$-0.164683\pi$
$648$	0.413556	+	0.329800i	0.0162460	+	0.0129558i
$649$	4.84767	−	1.10645i	0.190288	−	0.0434320i
$650$			1.43935i			0.0564560i
$651$	−2.82162	−	12.3623i	−0.110588	−	0.484518i
$652$	−8.36013	+	17.3600i	−0.327408	+	0.679870i
$653$	12.5243	−	26.0069i	0.490112	−	1.01773i	−0.498451	−	0.866918i	$-0.666098\pi$
$653$	12.5243	−	26.0069i	0.490112	−	1.01773i	0.988563	−	0.150810i	$-0.0481882\pi$
$654$	0.391374	+	1.71472i	0.0153039	+	0.0670509i
$655$		−	49.4475i		−	1.93207i
$656$	−19.0485	+	4.34770i	−0.743721	+	0.169749i
$657$	0.655953	+	0.523105i	0.0255912	+	0.0204083i
$658$	0.265835	−	1.16470i	0.0103633	−	0.0454048i
$659$	−32.7737	−	7.48039i	−1.27668	−	0.291395i	−0.470152	−	0.882585i	$-0.655801\pi$
$659$	−32.7737	−	7.48039i	−1.27668	−	0.291395i	−0.806532	+	0.591191i	$0.798658\pi$
$660$	−15.5957	−	19.5564i	−0.607063	−	0.761233i
$661$	16.8358	+	8.10769i	0.654836	+	0.315353i	0.731638	−	0.681694i	$-0.238756\pi$
$661$	16.8358	+	8.10769i	0.654836	+	0.315353i	−0.0768012	+	0.997046i	$0.524471\pi$
$662$	1.69161	−	0.814636i	0.0657462	−	0.0316617i
$663$	−0.951083	+	1.19262i	−0.0369370	+	0.0463175i
$664$	2.31386	−	1.84524i	0.0897951	−	0.0716092i
$665$	10.9468	+	22.7312i	0.424497	+	0.881477i
$666$	−3.42675			−0.132784
$667$	29.6295	+	1.98469i	1.14726	+	0.0768476i
$668$	−46.5375			−1.80059
$669$	9.26260	+	19.2340i	0.358113	+	0.743629i
$670$	0.357212	−	0.284867i	0.0138003	−	0.0110054i
$671$	−21.3878	+	26.8195i	−0.825668	+	1.03536i
$672$	5.96425	−	2.87223i	0.230076	−	0.110799i
$673$	−28.7262	−	13.8338i	−1.10731	−	0.533254i	−0.211363	−	0.977408i	$-0.567790\pi$
$673$	−28.7262	−	13.8338i	−1.10731	−	0.533254i	−0.895951	+	0.444153i	$0.853505\pi$
$674$	1.83308	+	2.29861i	0.0706076	+	0.0885392i
$675$	−15.5435	−	3.54770i	−0.598269	−	0.136551i
$676$	2.23571	−	9.79527i	0.0859887	−	0.376741i
$677$	29.5275	+	23.5474i	1.13483	+	0.905000i	0.996350	−	0.0853646i	$-0.0272055\pi$
$677$	29.5275	+	23.5474i	1.13483	+	0.905000i	0.138484	+	0.990365i	$0.455777\pi$
$678$	−2.38224	+	0.543731i	−0.0914894	+	0.0208819i
$679$		−	7.07107i		−	0.271363i
$680$	0.206198	+	0.903412i	0.00790733	+	0.0346443i
$681$	0.0505608	−	0.104991i	0.00193749	−	0.00402325i
$682$	1.14188	−	2.37114i	0.0437249	−	0.0907958i
$683$	3.52930	+	15.4629i	0.135045	+	0.591671i	0.996482	+	0.0838066i	$0.0267078\pi$
$683$	3.52930	+	15.4629i	0.135045	+	0.591671i	−0.861437	+	0.507864i	$0.830435\pi$
$684$			10.4330i			0.398915i
$685$	−2.61624	+	0.597141i	−0.0999615	+	0.0228156i
$686$	−2.12762	−	1.69672i	−0.0812327	−	0.0647809i
$687$	−3.30262	+	14.4697i	−0.126003	+	0.552055i
$688$	30.6498	+	6.99562i	1.16851	+	0.266706i
$689$	0.781959	+	0.980546i	0.0297903	+	0.0373558i
$690$	−2.70088	−	1.30068i	−0.102821	−	0.0495159i
$691$	26.4855	−	12.7548i	1.00756	−	0.485214i	0.144061	−	0.989569i	$-0.453984\pi$
$691$	26.4855	−	12.7548i	1.00756	−	0.485214i	0.863496	+	0.504355i	$0.168270\pi$
$692$	−6.42045	+	8.05099i	−0.244069	+	0.306053i
$693$	15.8552	−	12.6441i	0.602291	−	0.480311i
$694$	−2.32216	−	4.82202i	−0.0881482	−	0.183042i
$695$	20.5218			0.778438
$696$	2.77248	−	3.03587i	0.105091	−	0.115074i
$697$	−2.46516			−0.0933748
$698$	−1.24946	−	2.59453i	−0.0472928	−	0.0982045i
$699$	1.92288	−	1.53344i	0.0727299	−	0.0580002i
$700$	−10.7651	+	13.4990i	−0.406881	+	0.510213i
$701$	−9.93285	+	4.78341i	−0.375159	+	0.180667i	−0.611955	−	0.790892i	$-0.709617\pi$
$701$	−9.93285	+	4.78341i	−0.375159	+	0.180667i	0.236797	+	0.971559i	$0.423902\pi$
$702$	2.30615	+	1.11059i	0.0870402	+	0.0419164i
$703$	21.9493	+	27.5235i	0.827832	+	1.03807i
$704$	−28.4417	−	6.49164i	−1.07194	−	0.244663i
$705$	1.68888	−	7.39948i	0.0636070	−	0.278681i
$706$	−3.56606	−	2.84384i	−0.134210	−	0.107029i
$707$	−38.4953	+	8.78630i	−1.44777	+	0.330443i
$708$			2.75944i			0.103706i
$709$	−7.44065	−	32.5996i	−0.279439	−	1.22430i	−0.898505	−	0.438964i	$-0.855346\pi$
$709$	−7.44065	−	32.5996i	−0.279439	−	1.22430i	0.619065	−	0.785340i	$-0.287512\pi$
$710$	1.25409	−	2.60415i	0.0470653	−	0.0977320i
$711$	−1.39432	+	2.89534i	−0.0522912	+	0.108584i
$712$	2.35072	+	10.2992i	0.0880971	+	0.385979i
$713$			21.2550i			0.796005i
$714$	0.264721	−	0.0604209i	0.00990695	−	0.00226120i
$715$	−24.8102	−	19.7855i	−0.927848	−	0.739934i
$716$	4.97096	−	21.7792i	0.185773	−	0.813927i
$717$	−16.7787	−	3.82963i	−0.626613	−	0.143020i
$718$	−1.28952	−	1.61701i	−0.0481246	−	0.0603464i
$719$	−44.2582	−	21.3136i	−1.65055	−	0.794864i	−0.999353	−	0.0359569i	$-0.988552\pi$
$719$	−44.2582	−	21.3136i	−1.65055	−	0.794864i	−0.651199	−	0.758907i	$-0.725734\pi$
$720$	−16.9160	+	8.14630i	−0.630421	+	0.303595i
$721$	−3.19295	+	4.00383i	−0.118912	+	0.149111i
$722$	1.29683	−	1.03419i	0.0482632	−	0.0384886i
$723$	−6.63195	−	13.7714i	−0.246645	−	0.512163i
$724$	20.3793			0.757392
$725$	−4.63061	+	15.4451i	−0.171976	+	0.573616i
$726$	−0.950096			−0.0352614
$727$	−15.3329	−	31.8392i	−0.568667	−	1.18085i	−0.964880	−	0.262691i	$-0.915390\pi$
$727$	−15.3329	−	31.8392i	−0.568667	−	1.18085i	0.396213	−	0.918159i	$-0.370324\pi$
$728$	4.36660	−	3.48225i	0.161837	−	0.129061i
$729$	−12.0410	+	15.0989i	−0.445962	+	0.559219i
$730$	−0.210549	+	0.101395i	−0.00779278	+	0.00375281i
$731$	3.57373	+	1.72102i	0.132179	+	0.0636542i
$732$	−11.8694	−	14.8837i	−0.438704	−	0.550117i
$733$	−16.5129	−	3.76896i	−0.609918	−	0.139210i	−0.0936046	−	0.995609i	$-0.529839\pi$
$733$	−16.5129	−	3.76896i	−0.609918	−	0.139210i	−0.516314	+	0.856400i	$0.672696\pi$
$734$	−1.29253	+	5.66292i	−0.0477080	+	0.209022i
$735$	3.88066	+	3.09472i	0.143140	+	0.114150i
$736$	−10.8181	+	2.46916i	−0.398761	+	0.0910146i
$737$			3.77284i			0.138974i
$738$	0.337387	+	1.47819i	0.0124194	+	0.0544128i
$739$	14.8159	−	30.7656i	0.545012	−	1.13173i	−0.428594	−	0.903497i	$-0.640991\pi$
$739$	14.8159	−	30.7656i	0.545012	−	1.13173i	0.973607	−	0.228233i	$-0.0732947\pi$
$740$	−27.9082	+	57.9520i	−1.02593	+	2.13036i
$741$	−2.14476	−	9.39682i	−0.0787899	−	0.345201i
$742$		−	0.223245i		−	0.00819559i
$743$	26.8583	−	6.13024i	0.985337	−	0.224897i	0.300650	−	0.953734i	$-0.402796\pi$
$743$	26.8583	−	6.13024i	0.985337	−	0.224897i	0.684686	+	0.728838i	$0.259939\pi$
$744$	2.30071	+	1.83475i	0.0843481	+	0.0672654i
$745$	10.7301	−	47.0116i	0.393120	−	1.72237i
$746$	1.03281	+	0.235732i	0.0378138	+	0.00863076i
$747$	4.71719	+	5.91516i	0.172593	+	0.216424i
$748$	−3.42168	−	1.64779i	−0.125109	−	0.0602493i
$749$	−6.87606	+	3.31133i	−0.251246	+	0.120994i
$750$	−0.679853	+	0.852508i	−0.0248247	+	0.0311292i
$751$	4.50823	−	3.59519i	0.164508	−	0.131190i	−0.537776	−	0.843088i	$-0.680735\pi$
$751$	4.50823	−	3.59519i	0.164508	−	0.131190i	0.702284	+	0.711897i	$0.252164\pi$
$752$	−3.96277	−	8.22877i	−0.144507	−	0.300072i
$753$	23.0901			0.841452
$754$	1.27657	−	2.25207i	0.0464899	−	0.0820155i
$755$	27.8334			1.01296
$756$	13.3221	+	27.6636i	0.484519	+	1.00611i
$757$	3.55347	−	2.83380i	0.129153	−	0.102996i	−0.556783	−	0.830658i	$-0.687964\pi$
$757$	3.55347	−	2.83380i	0.129153	−	0.102996i	0.685936	+	0.727662i	$0.259393\pi$
$758$	2.78233	−	3.48893i	0.101059	−	0.126724i
$759$	22.3029	−	10.7405i	0.809546	−	0.389857i
$760$	−5.27525	−	2.54043i	−0.191353	−	0.0921509i
$761$	22.6200	+	28.3646i	0.819974	+	1.02822i	0.999015	+	0.0443736i	$0.0141292\pi$
$761$	22.6200	+	28.3646i	0.819974	+	1.02822i	−0.179041	+	0.983842i	$0.557299\pi$
$762$	0.214609	+	0.0489830i	0.00777445	+	0.00177447i
$763$	−5.95597	+	26.0948i	−0.215621	+	0.944696i
$764$	−9.71655	−	7.74869i	−0.351532	−	0.280338i
$765$	−2.30949	+	0.527126i	−0.0834998	+	0.0190583i
$766$			3.57064i			0.129012i
$767$	0.778991	+	3.41298i	0.0281277	+	0.123236i
$768$	6.68879	−	13.8894i	0.241361	−	0.501191i
$769$	−14.7542	+	30.6375i	−0.532052	+	1.10482i	0.445725	+	0.895170i	$0.352946\pi$
$769$	−14.7542	+	30.6375i	−0.532052	+	1.10482i	−0.977777	+	0.209647i	$0.932768\pi$
$770$	1.25694	+	5.50702i	0.0452970	+	0.198459i
$771$			22.2738i			0.802170i
$772$	−7.88178	+	1.79897i	−0.283672	+	0.0647462i
$773$	5.50787	+	4.39238i	0.198104	+	0.157983i	0.717518	−	0.696540i	$-0.245278\pi$
$773$	5.50787	+	4.39238i	0.198104	+	0.157983i	−0.519414	+	0.854523i	$0.673850\pi$
$774$	0.542868	−	2.37846i	0.0195130	−	0.0854920i
$775$	−11.2517	−	2.56813i	−0.404173	−	0.0922499i
$776$	1.02314	+	1.28298i	0.0367286	+	0.0460562i
$777$	34.2146	+	16.4769i	1.22744	+	0.591106i
$778$	−2.42011	+	1.16547i	−0.0867653	+	0.0417840i
$779$	9.71169	−	12.1781i	0.347958	−	0.436325i
$780$	13.7686	−	10.9801i	0.492995	−	0.393151i
$781$	10.3559	+	21.5042i	0.370562	+	0.769479i
$782$	−0.455145			−0.0162759
$783$	21.1735	+	19.3365i	0.756678	+	0.691029i
$784$	5.97294			0.213319
$785$	−3.23942	−	6.72672i	−0.115620	−	0.240087i
$786$	2.62894	−	2.09651i	0.0937713	−	0.0747801i
$787$	30.6610	−	38.4477i	1.09295	−	1.37051i	0.170062	−	0.985433i	$-0.445603\pi$
$787$	30.6610	−	38.4477i	1.09295	−	1.37051i	0.922884	−	0.385077i	$-0.125825\pi$
$788$	36.1131	−	17.3912i	1.28648	−	0.619535i
$789$	−15.0614	−	7.25320i	−0.536201	−	0.258221i
$790$	−0.558090	−	0.699823i	−0.0198559	−	0.0248986i
$791$	−36.2532	−	8.27455i	−1.28901	−	0.294209i
$792$	−1.04725	+	4.58832i	−0.0372125	+	0.163039i
$793$	−18.8821	−	15.0580i	−0.670525	−	0.534726i
$794$	−1.92765	+	0.439973i	−0.0684097	+	0.0156141i
$795$		−	1.41830i		−	0.0503020i
$796$	0.864418	+	3.78726i	0.0306385	+	0.134236i
$797$	−15.0982	+	31.3518i	−0.534806	+	1.11054i	0.442119	+	0.896956i	$0.354227\pi$
$797$	−15.0982	+	31.3518i	−0.534806	+	1.11054i	−0.976925	+	0.213581i	$0.931487\pi$
$798$	−0.744405	+	1.54577i	−0.0263517	+	0.0547198i
$799$	−0.256421	−	1.12345i	−0.00907151	−	0.0397449i
$800$		−	6.02510i		−	0.213019i
$801$	−26.3289	+	6.00941i	−0.930287	+	0.212332i
$802$	0.643788	+	0.513404i	0.0227329	+	0.0181289i
$803$	0.429409	−	1.88136i	0.0151535	−	0.0663919i
$804$	−2.04127	−	0.465908i	−0.0719902	−	0.0164313i
$805$	−28.4437	−	35.6673i	−1.00251	−	1.25711i
$806$	1.66939	+	0.803937i	0.0588019	+	0.0283175i
$807$	1.57708	−	0.759482i	0.0555159	−	0.0267350i
$808$	5.71328	−	7.16423i	0.200993	−	0.252037i
$809$	39.3593	−	31.3880i	1.38380	−	1.10354i	0.401576	−	0.915826i	$-0.368463\pi$
$809$	39.3593	−	31.3880i	1.38380	−	1.10354i	0.982223	−	0.187717i	$-0.0601088\pi$
$810$	−0.163421	−	0.339348i	−0.00574205	−	0.0119235i
$811$	8.56424			0.300731			0.150366	−	0.988630i	$-0.451955\pi$
$811$	8.56424			0.300731			0.150366	+	0.988630i	$0.451955\pi$
$812$	28.8157	−	11.5734i	1.01123	−	0.406147i
$813$	−13.6620			−0.479149
$814$	3.41976	+	7.10121i	0.119863	+	0.248897i
$815$	21.6126	−	17.2355i	0.757058	−	0.603733i
$816$	1.29428	−	1.62298i	0.0453089	−	0.0568156i
$817$	−22.5809	+	10.8744i	−0.790007	+	0.380447i
$818$	3.67928	+	1.77185i	0.128643	+	0.0619513i
$819$	8.90205	+	11.1628i	0.311063	+	0.390060i
$820$	27.7464	+	6.33293i	0.968946	+	0.221156i
$821$	−7.23124	+	31.6821i	−0.252372	+	1.10571i	0.676829	+	0.736140i	$0.263354\pi$
$821$	−7.23124	+	31.6821i	−0.252372	+	1.10571i	−0.929201	+	0.369574i	$0.879504\pi$
$822$	−0.142673	−	0.113778i	−0.00497630	−	0.00396847i
$823$	−34.0344	+	7.76814i	−1.18637	+	0.270780i	−0.769776	−	0.638314i	$-0.779632\pi$
$823$	−34.0344	+	7.76814i	−1.18637	+	0.270780i	−0.416590	+	0.909094i	$0.636775\pi$
$824$		−	1.18846i		−	0.0414019i
$825$	2.99095	+	13.1042i	0.104131	+	0.456229i
$826$	0.270372	−	0.561434i	0.00940746	−	0.0195348i
$827$	−18.3769	+	38.1600i	−0.639027	+	1.32695i	0.290030	+	0.957018i	$0.406335\pi$
$827$	−18.3769	+	38.1600i	−0.639027	+	1.32695i	−0.929057	+	0.369936i	$0.879380\pi$
$828$	−4.19782	−	18.3919i	−0.145884	−	0.639161i
$829$			23.0078i			0.799094i	0.916713	+	0.399547i	$0.130833\pi$
$829$			23.0078i			0.799094i	−0.916713	+	0.399547i	$0.869167\pi$
$830$	−2.05452	+	0.468931i	−0.0713134	+	0.0162768i
$831$	−10.5860	−	8.44205i	−0.367224	−	0.292852i
$832$	4.57041	−	20.0243i	0.158450	−	0.694217i
$833$	0.734713	+	0.167693i	0.0254563	+	0.00581023i
$834$	0.870101	+	1.09107i	0.0301291	+	0.0377807i
$835$	60.1545	+	28.9689i	2.08173	+	1.00251i
$836$	21.6202	−	10.4117i	0.747749	−	0.360097i
$837$	−12.7964	+	16.0461i	−0.442307	+	0.554636i
$838$	−4.12472	+	3.28935i	−0.142486	+	0.113629i
$839$	1.67573	+	3.47970i	0.0578528	+	0.120132i	0.927891	−	0.372852i	$-0.121620\pi$
$839$	1.67573	+	3.47970i	0.0578528	+	0.120132i	−0.870038	+	0.492985i	$0.835906\pi$
$840$	−6.31604			−0.217924
$841$	20.9436	−	20.0591i	0.722192	−	0.691693i
$842$	1.78321			0.0614534
$843$	−6.67120	−	13.8529i	−0.229768	−	0.477119i
$844$	−27.4257	+	21.8713i	−0.944033	+	0.752841i
$845$	−8.98728	+	11.2697i	−0.309172	+	0.387689i
$846$	−0.638562	+	0.307515i	−0.0219542	+	0.0105726i
$847$	−13.0268	−	6.27338i	−0.447606	−	0.215556i
$848$	−1.06413	−	1.33438i	−0.0365424	−	0.0458227i
$849$	−28.4918	−	6.50307i	−0.977836	−	0.223185i
$850$	0.0549927	−	0.240939i	0.00188624	−	0.00826414i
$851$	−49.7678	−	39.6885i	−1.70602	−	1.36050i
$852$	−12.9135	+	2.94743i	−0.442411	+	0.100977i
$853$			3.55963i			0.121879i	0.998141	+	0.0609397i	$0.0194097\pi$
$853$			3.55963i			0.121879i	−0.998141	+	0.0609397i	$0.980590\pi$
$854$	0.956614	+	4.19120i	0.0327346	+	0.143420i
$855$	6.49437	−	13.4857i	0.222103	−	0.461201i
$856$	0.768465	−	1.59573i	0.0262656	−	0.0545411i
$857$	4.27323	+	18.7222i	0.145971	+	0.639540i	0.993980	+	0.109559i	$0.0349438\pi$
$857$	4.27323	+	18.7222i	0.145971	+	0.639540i	−0.848010	+	0.529981i	$0.822199\pi$
$858$		−	2.15795i		−	0.0736711i
$859$	13.6690	−	3.11986i	0.466380	−	0.106448i	0.0171282	−	0.999853i	$-0.494548\pi$
$859$	13.6690	−	3.11986i	0.466380	−	0.106448i	0.449252	+	0.893405i	$0.351691\pi$
$860$	−35.8025	−	28.5515i	−1.22086	−	0.973600i
$861$	3.73894	−	16.3814i	0.127423	−	0.558275i
$862$	1.78006	+	0.406288i	0.0606292	+	0.0138382i
$863$	0.523014	+	0.655839i	0.0178036	+	0.0223250i	0.790654	−	0.612264i	$-0.209741\pi$
$863$	0.523014	+	0.655839i	0.0178036	+	0.0223250i	−0.772850	+	0.634589i	$0.781169\pi$
$864$	−9.65352	−	4.64889i	−0.328419	−	0.158158i
$865$	13.3107	−	6.41010i	0.452578	−	0.217950i
$866$	2.93661	−	3.68239i	0.0997899	−	0.125133i
$867$	−14.7388	+	11.7538i	−0.500555	+	0.399179i
$868$	9.64367	+	20.0253i	0.327327	+	0.679702i
$869$	7.39147			0.250739
$870$	−2.71659	+	1.09108i	−0.0921011	+	0.0369910i
$871$	−2.65625			−0.0900037
$872$	−2.69511	−	5.59645i	−0.0912679	−	0.189520i
$873$	−3.27982	+	2.61557i	−0.111005	+	0.0885235i
$874$	1.79307	−	2.24844i	0.0606517	−	0.0760548i
$875$	−14.9505	+	7.19978i	−0.505419	+	0.243397i
$876$	0.964873	+	0.464659i	0.0326001	+	0.0156994i
$877$	−32.4944	−	40.7467i	−1.09726	−	1.37592i	−0.920076	−	0.391739i	$-0.871873\pi$
$877$	−32.4944	−	40.7467i	−1.09726	−	1.37592i	−0.177182	−	0.984178i	$-0.556698\pi$
$878$	−4.30943	−	0.983598i	−0.145436	−	0.0331948i
$879$	1.43264	−	6.27681i	0.0483218	−	0.211712i
$880$	33.7630	+	26.9251i	1.13815	+	0.907644i
$881$	−6.55060	+	1.49513i	−0.220695	+	0.0503722i	−0.331439	−	0.943477i	$-0.607534\pi$
$881$	−6.55060	+	1.49513i	−0.220695	+	0.0503722i	0.110743	+	0.993849i	$0.464677\pi$
$882$		−	0.463507i		−	0.0156071i
$883$	−3.79146	−	16.6115i	−0.127593	−	0.559020i	−0.997798	−	0.0663303i	$-0.978871\pi$
$883$	−3.79146	−	16.6115i	−0.127593	−	0.559020i	0.870205	−	0.492690i	$-0.163986\pi$
$884$	1.16012	−	2.40902i	0.0390191	−	0.0810240i
$885$	1.71771	−	3.56686i	0.0577401	−	0.119899i
$886$	−0.537101	−	2.35320i	−0.0180443	−	0.0790571i
$887$			15.9991i			0.537197i	0.963252	+	0.268598i	$0.0865604\pi$
$887$			15.9991i			0.537197i	−0.963252	+	0.268598i	$0.913440\pi$
$888$	−8.59203	+	1.96107i	−0.288330	+	0.0658094i
$889$	2.61908	+	2.08865i	0.0878411	+	0.0700509i
$890$	1.67385	−	7.33361i	0.0561075	−	0.245823i
$891$	3.03225	+	0.692091i	0.101584	+	0.0231859i
$892$	−23.3308	−	29.2559i	−0.781174	−	0.979561i
$893$	6.56012	+	3.15919i	0.219526	+	0.105718i
$894$	2.95438	−	1.42275i	0.0988092	−	0.0475840i
$895$	−19.9827	+	25.0575i	−0.667947	+	0.837579i
$896$	−12.0650	+	9.62150i	−0.403063	+	0.321432i
$897$	7.56182	+	15.7023i	0.252482	+	0.524284i
$898$	3.78256			0.126226
$899$	15.3272	+	13.9974i	0.511190	+	0.466839i
$900$	10.2433			0.341442
$901$	−0.0934320	−	0.194014i	−0.00311267	−	0.00646353i
$902$	2.72653	−	2.17434i	0.0907837	−	0.0723975i
$903$	−16.8567	+	21.1377i	−0.560956	+	0.703417i
$904$	7.77507	−	3.74428i	0.258595	−	0.124533i
$905$	−26.3424	−	12.6858i	−0.875649	−	0.421691i
$906$	1.18010	+	1.47980i	0.0392063	+	0.0491631i
$907$	−1.50979	−	0.344600i	−0.0501318	−	0.0114422i	0.197381	−	0.980327i	$-0.436756\pi$
$907$	−1.50979	−	0.344600i	−0.0501318	−	0.0114422i	−0.247513	+	0.968885i	$0.579613\pi$
$908$	−0.0454520	+	0.199138i	−0.00150838	+	0.00660863i
$909$	18.3147	+	14.6055i	0.607460	+	0.484433i
$910$	−3.87719	+	0.884944i	−0.128528	+	0.0293356i
$911$		−	19.4756i		−	0.645256i	−0.946526	−	0.322628i	$-0.895434\pi$
$911$		−	19.4756i		−	0.645256i	0.946526	−	0.322628i	$-0.104566\pi$
$912$	2.91871	+	12.7877i	0.0966480	+	0.423443i
$913$	7.55036	−	15.6785i	0.249880	−	0.518882i
$914$	−0.724144	+	1.50370i	−0.0239525	+	0.0497380i
$915$	6.07748	+	26.6272i	0.200915	+	0.880267i
$916$		−	26.0153i		−	0.859570i
$917$	49.8886	−	11.3867i	1.64747	−	0.376023i
$918$	−0.343605	−	0.274016i	−0.0113407	−	0.00904387i
$919$	−9.23637	+	40.4672i	−0.304680	+	1.33489i	0.558295	+	0.829642i	$0.311456\pi$
$919$	−9.23637	+	40.4672i	−0.304680	+	1.33489i	−0.862975	+	0.505247i	$0.831401\pi$
$920$	10.3217	+	2.35586i	0.340296	+	0.0776703i
$921$	8.94473	+	11.2163i	0.294739	+	0.369591i
$922$	3.10412	+	1.49487i	0.102229	+	0.0492308i
$923$	−15.1399	+	7.29099i	−0.498336	+	0.239986i
$924$	16.1395	−	20.2383i	0.530951	−	0.665791i
$925$	27.0230	−	21.5501i	0.888511	−	0.708564i
$926$	−1.17067	−	2.43093i	−0.0384707	−	0.0798852i
$927$	3.03818			0.0997870
$928$	−5.34370	+	9.42711i	−0.175415	+	0.309460i
$929$	−12.1373			−0.398211			−0.199105	−	0.979978i	$-0.563804\pi$
$929$	−12.1373			−0.398211			−0.199105	+	0.979978i	$0.563804\pi$
$930$	−0.909152	−	1.88787i	−0.0298123	−	0.0619058i
$931$	−3.72287	+	2.96889i	−0.122012	+	0.0973015i
$932$	−2.68788	+	3.37049i	−0.0880443	+	0.110404i
$933$	−12.6779	+	6.10536i	−0.415056	+	0.199881i
$934$	−6.04078	−	2.90909i	−0.197660	−	0.0951882i
$935$	3.39714	+	4.25988i	0.111098	+	0.139313i
$936$	−3.23038	−	0.737314i	−0.105588	−	0.0240999i
$937$	11.9126	−	52.1927i	0.389169	−	1.70506i	−0.278361	−	0.960477i	$-0.589791\pi$
$937$	11.9126	−	52.1927i	0.389169	−	1.70506i	0.667530	−	0.744583i	$-0.267352\pi$
$938$	0.369667	+	0.294799i	0.0120700	+	0.00962554i
$939$	28.3445	−	6.46946i	0.924989	−	0.211123i
$940$			13.3036i			0.433917i
$941$	3.25236	+	14.2495i	0.106024	+	0.464521i	0.999870	+	0.0161466i	$0.00513986\pi$
$941$	3.25236	+	14.2495i	0.106024	+	0.464521i	−0.893846	+	0.448375i	$0.852003\pi$
$942$	0.220288	−	0.457433i	0.00717737	−	0.0149040i
$943$	−12.2203	+	25.3758i	−0.397949	+	0.826350i
$944$	−1.06009	−	4.64456i	−0.0345030	−	0.151168i
$945$		−	44.0508i		−	1.43297i
$946$	−5.47062	+	1.24863i	−0.177865	+	0.0405966i
$947$	11.2593	+	8.97899i	0.365878	+	0.291778i	0.789120	−	0.614239i	$-0.210537\pi$
$947$	11.2593	+	8.97899i	0.365878	+	0.291778i	−0.423242	+	0.906016i	$0.639108\pi$
$948$	−0.912772	+	3.99911i	−0.0296454	+	0.129885i
$949$	1.32457	+	0.302324i	0.0429972	+	0.00981384i
$950$	0.973607	+	1.22086i	0.0315880	+	0.0396101i
$951$	−27.4588	−	13.2234i	−0.890411	−	0.428799i
$952$	−0.863988	+	0.416075i	−0.0280020	+	0.0134851i
$953$	4.15499	−	5.21020i	0.134593	−	0.168775i	−0.709967	−	0.704235i	$-0.751290\pi$
$953$	4.15499	−	5.21020i	0.134593	−	0.168775i	0.844561	+	0.535460i	$0.179862\pi$
$954$	−0.103549	+	0.0825777i	−0.00335253	+	0.00267355i
$955$	7.73619	+	16.0644i	0.250337	+	0.519831i
$956$	30.1667			0.975660
$957$	6.94243	−	23.1560i	0.224417	−	0.748528i
$958$	7.22820			0.233533
$959$	−1.20494	−	2.50207i	−0.0389094	−	0.0807962i
$960$	−18.1598	+	14.4820i	−0.586106	+	0.467404i
$961$	10.0651	−	12.6212i	0.324680	−	0.407135i
$962$	−4.99958	+	2.40767i	−0.161193	+	0.0776264i
$963$	4.07935	+	1.96451i	0.131455	+	0.0633055i
$964$	16.7047	+	20.9470i	0.538022	+	0.674658i
$965$	11.3078	+	2.58094i	0.364012	+	0.0830834i
$966$	0.690322	−	3.02450i	0.0222107	−	0.0973116i
$967$	13.9834	+	11.1514i	0.449677	+	0.358605i	0.821990	−	0.569502i	$-0.192864\pi$
$967$	13.9834	+	11.1514i	0.449677	+	0.358605i	−0.372313	+	0.928107i	$0.621435\pi$
$968$	3.27131	−	0.746655i	0.105144	−	0.0239984i
$969$			1.65492i			0.0531636i
$970$	−0.260011	−	1.13918i	−0.00834845	−	0.0365769i
$971$	−13.2900	+	27.5969i	−0.426495	+	0.885627i	0.571393	+	0.820676i	$0.306403\pi$
$971$	−13.2900	+	27.5969i	−0.426495	+	0.885627i	−0.997889	+	0.0649502i	$0.979311\pi$
$972$	12.9102	−	26.8082i	0.414094	−	0.859874i
$973$	4.72576	+	20.7049i	0.151501	+	0.663769i
$974$			2.32073i			0.0743611i
$975$	−9.22595	+	2.10576i	−0.295467	+	0.0674384i
$976$	25.6958	+	20.4917i	0.822503	+	0.655924i
$977$	6.02069	−	26.3784i	0.192619	−	0.843919i	−0.782573	−	0.622559i	$-0.786093\pi$
$977$	6.02069	−	26.3784i	0.192619	−	0.843919i	0.975192	−	0.221360i	$-0.0710497\pi$
$978$	1.83270	+	0.418302i	0.0586032	+	0.0133758i
$979$	38.7285	+	48.5640i	1.23777	+	1.55211i
$980$	−7.83868	−	3.77491i	−0.250398	−	0.120585i
$981$	14.3068	−	6.88979i	0.456781	−	0.219974i
$982$	0.435775	−	0.546445i	0.0139062	−	0.0174378i
$983$	−24.8942	+	19.8524i	−0.794001	+	0.633195i	−0.934128	−	0.356939i	$-0.883820\pi$
$983$	−24.8942	+	19.8524i	−0.794001	+	0.633195i	0.140127	+	0.990134i	$0.455249\pi$
$984$	1.69189	+	3.51324i	0.0539354	+	0.111998i
$985$	−57.5056			−1.83228
$986$	−0.299734	+	0.328209i	−0.00954548	+	0.0104523i
$987$	7.85441			0.250009
$988$	7.33033	+	15.2216i	0.233209	+	0.484263i
$989$	35.4315	−	28.2557i	1.12666	−	0.898479i
$990$	2.08942	−	2.62004i	0.0664060	−	0.0832705i
$991$	21.9543	−	10.5726i	0.697401	−	0.335851i	−0.0513697	−	0.998680i	$-0.516359\pi$
$991$	21.9543	−	10.5726i	0.697401	−	0.335851i	0.748771	+	0.662829i	$0.230644\pi$
$992$	−6.98805	−	3.36527i	−0.221871	−	0.106847i
$993$	7.69646	+	9.65105i	0.244240	+	0.306267i
$994$	2.91617	+	0.665598i	0.0924954	+	0.0211115i
$995$	1.24016	−	5.43351i	0.0393158	−	0.172254i
$996$	7.55036	+	6.02121i	0.239242	+	0.190789i
$997$	−24.5985	+	5.61446i	−0.779044	+	0.177812i	−0.593510	−	0.804826i	$-0.702258\pi$
$997$	−24.5985	+	5.61446i	−0.779044	+	0.177812i	−0.185533	+	0.982638i	$0.559401\pi$
$998$			2.14013i			0.0677448i
$999$	−13.6774	−	59.9245i	−0.432733	−	1.89593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.2.e.a.9.2	✓	12
3.2	odd	2		261.2.o.a.154.1		12
4.3	odd	2		464.2.y.d.241.2		12
5.2	odd	4		725.2.p.a.299.2		24
5.3	odd	4		725.2.p.a.299.3		24
5.4	even	2		725.2.q.a.676.1		12
29.2	odd	28		841.2.d.k.645.3		24
29.3	odd	28		841.2.d.l.574.2		24
29.4	even	14		841.2.b.e.840.7		12
29.5	even	14		841.2.e.e.196.2		12
29.6	even	14		841.2.e.h.63.1		12
29.7	even	7		841.2.e.h.267.1		12
29.8	odd	28		841.2.d.k.605.2		24
29.9	even	14		841.2.e.f.236.1		12
29.10	odd	28		841.2.a.k.1.7		12
29.11	odd	28		841.2.d.m.190.3		24
29.12	odd	4		841.2.d.m.571.2		24
29.13	even	14	inner	29.2.e.a.13.2	yes	12
29.14	odd	28		841.2.d.l.778.2		24
29.15	odd	28		841.2.d.l.778.3		24
29.16	even	7		841.2.e.i.651.1		12
29.17	odd	4		841.2.d.m.571.3		24
29.18	odd	28		841.2.d.m.190.2		24
29.19	odd	28		841.2.a.k.1.6		12
29.20	even	7		841.2.e.e.236.2		12
29.21	odd	28		841.2.d.k.605.3		24
29.22	even	14		841.2.e.a.267.2		12
29.23	even	7		841.2.e.a.63.2		12
29.24	even	7		841.2.e.f.196.1		12
29.25	even	7		841.2.b.e.840.6		12
29.26	odd	28		841.2.d.l.574.3		24
29.27	odd	28		841.2.d.k.645.2		24
29.28	even	2		841.2.e.i.270.1		12
87.68	even	28		7569.2.a.bp.1.6		12
87.71	odd	14		261.2.o.a.100.1		12
87.77	even	28		7569.2.a.bp.1.7		12
116.71	odd	14		464.2.y.d.129.2		12
145.13	odd	28		725.2.p.a.274.2		24
145.42	odd	28		725.2.p.a.274.3		24
145.129	even	14		725.2.q.a.651.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.9.2	✓	12	1.1	even	1	trivial
29.2.e.a.13.2	yes	12	29.13	even	14	inner
261.2.o.a.100.1		12	87.71	odd	14
261.2.o.a.154.1		12	3.2	odd	2
464.2.y.d.129.2		12	116.71	odd	14
464.2.y.d.241.2		12	4.3	odd	2
725.2.p.a.274.2		24	145.13	odd	28
725.2.p.a.274.3		24	145.42	odd	28
725.2.p.a.299.2		24	5.2	odd	4
725.2.p.a.299.3		24	5.3	odd	4
725.2.q.a.651.1		12	145.129	even	14
725.2.q.a.676.1		12	5.4	even	2
841.2.a.k.1.6		12	29.19	odd	28
841.2.a.k.1.7		12	29.10	odd	28
841.2.b.e.840.6		12	29.25	even	7
841.2.b.e.840.7		12	29.4	even	14
841.2.d.k.605.2		24	29.8	odd	28
841.2.d.k.605.3		24	29.21	odd	28
841.2.d.k.645.2		24	29.27	odd	28
841.2.d.k.645.3		24	29.2	odd	28
841.2.d.l.574.2		24	29.3	odd	28
841.2.d.l.574.3		24	29.26	odd	28
841.2.d.l.778.2		24	29.14	odd	28
841.2.d.l.778.3		24	29.15	odd	28
841.2.d.m.190.2		24	29.18	odd	28
841.2.d.m.190.3		24	29.11	odd	28
841.2.d.m.571.2		24	29.12	odd	4
841.2.d.m.571.3		24	29.17	odd	4
841.2.e.a.63.2		12	29.23	even	7
841.2.e.a.267.2		12	29.22	even	14
841.2.e.e.196.2		12	29.5	even	14
841.2.e.e.236.2		12	29.20	even	7
841.2.e.f.196.1		12	29.24	even	7
841.2.e.f.236.1		12	29.9	even	14
841.2.e.h.63.1		12	29.6	even	14
841.2.e.h.267.1		12	29.7	even	7
841.2.e.i.270.1		12	29.28	even	2
841.2.e.i.651.1		12	29.16	even	7
7569.2.a.bp.1.6		12	87.68	even	28
7569.2.a.bp.1.7		12	87.77	even	28

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	29.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0741982 + 0.154074i) q^{2} +(-0.879032 + 0.701005i) q^{3} +(1.22875 - 1.54080i) q^{4} +(-2.54740 + 1.22676i) q^{5} +(-0.173229 - 0.0834229i) q^{6} +(-1.82432 - 2.28763i) q^{7} +(0.662012 + 0.151100i) q^{8} +(-0.386273 + 1.69237i) q^{9} +O(q^{10})\)	\(q+(0.0741982 + 0.154074i) q^{2} +(-0.879032 + 0.701005i) q^{3} +(1.22875 - 1.54080i) q^{4} +(-2.54740 + 1.22676i) q^{5} +(-0.173229 - 0.0834229i) q^{6} +(-1.82432 - 2.28763i) q^{7} +(0.662012 + 0.151100i) q^{8} +(-0.386273 + 1.69237i) q^{9} +(-0.378025 - 0.301465i) q^{10} +(3.89257 - 0.888454i) q^{11} +2.21577i q^{12} +(0.625512 + 2.74055i) q^{13} +(0.217103 - 0.450819i) q^{14} +(1.37928 - 2.86411i) q^{15} +(-0.851229 - 3.72948i) q^{16} -0.482650i q^{17} +(-0.289412 + 0.0660563i) q^{18} +(2.38432 + 1.90144i) q^{19} +(-1.23991 + 5.43242i) q^{20} +(3.20728 + 0.732040i) q^{21} +(0.425710 + 0.533823i) q^{22} +(-4.96829 - 2.39260i) q^{23} +(-0.687851 + 0.331252i) q^{24} +(1.86686 - 2.34097i) q^{25} +(-0.375836 + 0.299719i) q^{26} +(-2.31029 - 4.79737i) q^{27} -5.76640 q^{28} +(-4.99718 + 2.00704i) q^{29} +0.543625 q^{30} +(-1.67239 - 3.47275i) q^{31} +(1.57324 - 1.25462i) q^{32} +(-2.79888 + 3.50969i) q^{33} +(0.0743639 - 0.0358118i) q^{34} +(7.45366 + 3.58950i) q^{35} +(2.13297 + 2.67467i) q^{36} +(11.2541 + 2.56868i) q^{37} +(-0.116049 + 0.508446i) q^{38} +(-2.47098 - 1.97054i) q^{39} +(-1.87177 + 0.427220i) q^{40} -5.10756i q^{41} +(0.125186 + 0.548475i) q^{42} +(-3.56577 + 7.40439i) q^{43} +(3.41405 - 7.08936i) q^{44} +(-1.09215 - 4.78502i) q^{45} -0.943011i q^{46} +(2.32767 - 0.531276i) q^{47} +(3.36264 + 2.68162i) q^{48} +(-0.347443 + 1.52225i) q^{49} +(0.499200 + 0.113939i) q^{50} +(0.338340 + 0.424265i) q^{51} +(4.99123 + 2.40365i) q^{52} +(0.401975 - 0.193581i) q^{53} +(0.567732 - 0.711913i) q^{54} +(-8.82602 + 7.03852i) q^{55} +(-0.862063 - 1.79009i) q^{56} -3.42881 q^{57} +(-0.680015 - 0.621017i) q^{58} +1.24537 q^{59} +(-2.71823 - 5.64445i) q^{60} +(-6.71717 + 5.35677i) q^{61} +(0.410973 - 0.515344i) q^{62} +(4.57621 - 2.20378i) q^{63} +(-6.58308 - 3.17024i) q^{64} +(-4.95544 - 6.21392i) q^{65} +(-0.748425 - 0.170823i) q^{66} +(-0.210269 + 0.921249i) q^{67} +(-0.743667 - 0.593055i) q^{68} +(6.04451 - 1.37962i) q^{69} +1.41475i q^{70} +(1.33021 + 5.82802i) q^{71} +(-0.511435 + 1.06201i) q^{72} +(0.209705 - 0.435458i) q^{73} +(0.439268 + 1.92456i) q^{74} +3.36646i q^{75} +(5.85946 - 1.33738i) q^{76} +(-9.13376 - 7.28393i) q^{77} +(0.120267 - 0.526925i) q^{78} +(1.80484 + 0.411944i) q^{79} +(6.74361 + 8.45623i) q^{80} +(0.701839 + 0.337988i) q^{81} +(0.786943 - 0.378972i) q^{82} +(2.71744 - 3.40756i) q^{83} +(5.06885 - 4.04228i) q^{84} +(0.592098 + 1.22950i) q^{85} -1.40540 q^{86} +(2.98573 - 5.26730i) q^{87} +2.71117 q^{88} +(6.75011 + 14.0167i) q^{89} +(0.656213 - 0.523312i) q^{90} +(5.12822 - 6.43058i) q^{91} +(-9.79128 + 4.71523i) q^{92} +(3.90450 + 1.88031i) q^{93} +(0.254565 + 0.319215i) q^{94} +(-8.40645 - 1.91872i) q^{95} +(-0.503437 + 2.20570i) q^{96} +(1.88941 + 1.50675i) q^{97} +(-0.260319 + 0.0594161i) q^{98} +6.93087i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9} - 7 q^{10} + 7 q^{11} + 9 q^{13} - 7 q^{14} + 7 q^{15} + 9 q^{16} + 42 q^{18} - 7 q^{19} - 11 q^{20} - 7 q^{21} - 4 q^{22} - 5 q^{23} - 25 q^{24} + 13 q^{25} - 21 q^{26} - 7 q^{27} + 12 q^{28} - 15 q^{29} + 2 q^{30} - 21 q^{31} - 17 q^{33} - 13 q^{34} + 19 q^{35} - 40 q^{36} + 7 q^{37} + 28 q^{38} + 21 q^{39} + 35 q^{40} + 50 q^{42} + 7 q^{43} + 42 q^{44} + 16 q^{45} - 7 q^{47} - 14 q^{48} + 13 q^{49} - 28 q^{50} + 20 q^{51} - 6 q^{52} - 10 q^{53} - 38 q^{54} - 35 q^{55} - 21 q^{56} - 14 q^{57} - 57 q^{58} + 44 q^{59} - 28 q^{60} - 7 q^{61} + 37 q^{62} - 13 q^{63} - 26 q^{64} - 6 q^{65} + 21 q^{66} - 37 q^{67} + 14 q^{68} + 21 q^{69} - 21 q^{71} + 35 q^{72} + 14 q^{73} + 7 q^{76} - 7 q^{77} + 17 q^{78} + 49 q^{79} - 6 q^{80} + q^{81} + 22 q^{82} + 5 q^{83} + 21 q^{84} + 14 q^{85} - 44 q^{86} + 15 q^{87} - 66 q^{88} + 7 q^{89} + 28 q^{90} - 3 q^{91} - 6 q^{92} + 19 q^{93} + 66 q^{94} - 7 q^{95} + 30 q^{96} + 14 q^{97} - 42 q^{98}+O(q^{100}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9 - 7 * q^10 + 7 * q^11 + 9 * q^13 - 7 * q^14 + 7 * q^15 + 9 * q^16 + 42 * q^18 - 7 * q^19 - 11 * q^20 - 7 * q^21 - 4 * q^22 - 5 * q^23 - 25 * q^24 + 13 * q^25 - 21 * q^26 - 7 * q^27 + 12 * q^28 - 15 * q^29 + 2 * q^30 - 21 * q^31 - 17 * q^33 - 13 * q^34 + 19 * q^35 - 40 * q^36 + 7 * q^37 + 28 * q^38 + 21 * q^39 + 35 * q^40 + 50 * q^42 + 7 * q^43 + 42 * q^44 + 16 * q^45 - 7 * q^47 - 14 * q^48 + 13 * q^49 - 28 * q^50 + 20 * q^51 - 6 * q^52 - 10 * q^53 - 38 * q^54 - 35 * q^55 - 21 * q^56 - 14 * q^57 - 57 * q^58 + 44 * q^59 - 28 * q^60 - 7 * q^61 + 37 * q^62 - 13 * q^63 - 26 * q^64 - 6 * q^65 + 21 * q^66 - 37 * q^67 + 14 * q^68 + 21 * q^69 - 21 * q^71 + 35 * q^72 + 14 * q^73 + 7 * q^76 - 7 * q^77 + 17 * q^78 + 49 * q^79 - 6 * q^80 + q^81 + 22 * q^82 + 5 * q^83 + 21 * q^84 + 14 * q^85 - 44 * q^86 + 15 * q^87 - 66 * q^88 + 7 * q^89 + 28 * q^90 - 3 * q^91 - 6 * q^92 + 19 * q^93 + 66 * q^94 - 7 * q^95 + 30 * q^96 + 14 * q^97 - 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more