LMFDB - Embedded newform 507.2.t.b.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	507.4
Dual form			507.2.t.b.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85726 - 0.0748449i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(1.45029 + 0.117079i) q^{4} +(-1.06783 - 0.404975i) q^{5} +(0.588611 - 1.76311i) q^{6} +(0.332955 + 0.781475i) q^{7} +(1.00563 + 0.122106i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})$	\(q+(-1.85726 - 0.0748449i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(1.45029 + 0.117079i) q^{4} +(-1.06783 - 0.404975i) q^{5} +(0.588611 - 1.76311i) q^{6} +(0.332955 + 0.781475i) q^{7} +(1.00563 + 0.122106i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(1.95292 + 0.832063i) q^{10} +(-2.33405 - 3.69100i) q^{11} +(-0.515951 + 1.36045i) q^{12} +(-0.346984 + 3.58882i) q^{13} +(-0.559894 - 1.47632i) q^{14} +(0.686075 - 0.912999i) q^{15} +(-4.73090 - 0.768847i) q^{16} +(-2.27717 + 0.970211i) q^{17} +(1.52973 + 1.05590i) q^{18} +(4.47551 - 2.58394i) q^{19} +(-1.50124 - 0.712350i) q^{20} +(-0.843255 + 0.102390i) q^{21} +(4.05868 + 7.02983i) q^{22} +(-0.0828629 + 0.143523i) q^{23} +(-0.397070 + 0.931957i) q^{24} +(-2.76630 - 2.45072i) q^{25} +(0.913043 - 6.63938i) q^{26} +(0.748511 - 0.663123i) q^{27} +(0.391386 + 1.17234i) q^{28} +(0.381267 - 9.46104i) q^{29} +(-1.34255 + 1.64433i) q^{30} +(4.15421 + 4.68913i) q^{31} +(6.74386 + 1.37677i) q^{32} +(4.19465 - 1.21499i) q^{33} +(4.30190 - 1.63150i) q^{34} +(-0.0390623 - 0.969321i) q^{35} +(-1.16319 - 0.874082i) q^{36} +(5.07334 - 1.03573i) q^{37} +(-8.50557 + 4.46407i) q^{38} +(-3.35059 - 1.33176i) q^{39} +(-1.02440 - 0.537645i) q^{40} +(-0.363440 - 0.105272i) q^{41} +(1.57380 - 0.127051i) q^{42} +(0.404977 - 1.98371i) q^{43} +(-2.95290 - 5.62628i) q^{44} +(0.686075 + 0.912999i) q^{45} +(0.164640 - 0.260357i) q^{46} +(10.1830 - 7.02879i) q^{47} +(2.05471 - 4.33021i) q^{48} +(4.34923 - 4.52802i) q^{49} +(4.95430 + 4.75867i) q^{50} +(-0.298357 - 2.45719i) q^{51} +(-0.923402 + 5.16418i) q^{52} +(0.281346 - 2.31710i) q^{53} +(-1.43981 + 1.17557i) q^{54} +(0.997606 + 4.88660i) q^{55} +(0.239408 + 0.826533i) q^{56} +(1.23675 + 5.01771i) q^{57} +(-1.41622 + 17.5431i) q^{58} +(-0.332007 - 2.04292i) q^{59} +(1.10190 - 1.24378i) q^{60} +(2.02809 - 1.52401i) q^{61} +(-7.36447 - 9.01984i) q^{62} +(0.136261 - 0.838448i) q^{63} +(-3.11465 - 0.767692i) q^{64} +(1.82390 - 3.69173i) q^{65} +(-7.88148 + 1.94261i) q^{66} +(-1.00553 - 12.4557i) q^{67} +(-3.41614 + 1.14047i) q^{68} +(-0.114802 - 0.119522i) q^{69} +1.80320i q^{70} +(-3.85525 + 3.70302i) q^{71} +(-0.784690 - 0.640679i) q^{72} +(6.99375 - 13.3255i) q^{73} +(-9.50001 + 1.54390i) q^{74} +(3.12360 - 1.97524i) q^{75} +(6.79330 - 3.22346i) q^{76} +(2.10729 - 3.05294i) q^{77} +(6.12322 + 2.72419i) q^{78} +(-2.73217 - 3.95822i) q^{79} +(4.74044 + 2.73689i) q^{80} +(0.428693 + 0.903450i) q^{81} +(0.667123 + 0.222718i) q^{82} +(-3.19781 + 12.9740i) q^{83} +(-1.23495 + 0.0497667i) q^{84} +(2.82454 - 0.113825i) q^{85} +(-0.900616 + 3.65394i) q^{86} +(8.98143 + 2.99844i) q^{87} +(-1.89650 - 3.99680i) q^{88} +(-8.81341 - 5.08842i) q^{89} +(-1.20588 - 1.74702i) q^{90} +(-2.92010 + 0.923756i) q^{91} +(-0.136978 + 0.198448i) q^{92} +(-5.65977 + 2.68559i) q^{93} +(-19.4384 + 12.2921i) q^{94} +(-5.82552 + 0.946739i) q^{95} +(-3.19867 + 6.09456i) q^{96} +(7.32515 + 5.98080i) q^{97} +(-8.41653 + 8.08419i) q^{98} +4.36707i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{78}\right)$

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 $

$2$	−1.85726	−	0.0748449i	−1.31328	−	0.0529233i	−0.626289	−	0.779591i	$-0.715427\pi$
$2$	−1.85726	−	0.0748449i	−1.31328	−	0.0529233i	−0.686989	+	0.726667i	$0.741068\pi$
$3$	−0.278217	+	0.960518i	−0.160629	+	0.554555i
$3$	−0.278217	+	0.960518i	−0.160629	+	0.554555i
$4$	1.45029	+	0.117079i	0.725143	+	0.0585396i
$5$	−1.06783	−	0.404975i	−0.477548	−	0.181110i	0.104073	−	0.994570i	$-0.466812\pi$
$5$	−1.06783	−	0.404975i	−0.477548	−	0.181110i	−0.581622	+	0.813459i	$0.697582\pi$
$6$	0.588611	−	1.76311i	0.240299	−	0.719785i
$7$	0.332955	+	0.781475i	0.125845	+	0.295370i	0.970971	−	0.239198i	$-0.0768846\pi$
$7$	0.332955	+	0.781475i	0.125845	+	0.295370i	−0.845125	+	0.534568i	$0.820474\pi$
$8$	1.00563	+	0.122106i	0.355545	+	0.0431710i
$9$	−0.845190	−	0.534466i	−0.281730	−	0.178155i
$10$	1.95292	+	0.832063i	0.617569	+	0.263122i
$11$	−2.33405	−	3.69100i	−0.703742	−	1.11288i	−0.988048	−	0.154146i	$-0.950737\pi$
$11$	−2.33405	−	3.69100i	−0.703742	−	1.11288i	0.284306	−	0.958734i	$-0.408237\pi$
$12$	−0.515951	+	1.36045i	−0.148942	+	0.392729i
$13$	−0.346984	+	3.58882i	−0.0962361	+	0.995359i
$13$	−0.346984	+	3.58882i	−0.0962361	+	0.995359i
$14$	−0.559894	−	1.47632i	−0.149638	−	0.394563i
$15$	0.686075	−	0.912999i	0.177144	−	0.235735i
$16$	−4.73090	−	0.768847i	−1.18273	−	0.192212i
$17$	−2.27717	+	0.970211i	−0.552295	+	0.235311i	−0.650039	−	0.759901i	$-0.725247\pi$
$17$	−2.27717	+	0.970211i	−0.552295	+	0.235311i	0.0977444	+	0.995212i	$0.468837\pi$
$18$	1.52973	+	1.05590i	0.360561	+	0.248878i
$19$	4.47551	−	2.58394i	1.02675	−	0.592796i	0.110700	−	0.993854i	$-0.464691\pi$
$19$	4.47551	−	2.58394i	1.02675	−	0.592796i	0.916053	+	0.401058i	$0.131357\pi$
$20$	−1.50124	−	0.712350i	−0.335689	−	0.159286i
$21$	−0.843255	+	0.102390i	−0.184013	+	0.0223433i
$22$	4.05868	+	7.02983i	0.865313	+	1.49877i
$23$	−0.0828629	+	0.143523i	−0.0172781	+	0.0299266i	−0.874535	−	0.484962i	$-0.838833\pi$
$23$	−0.0828629	+	0.143523i	−0.0172781	+	0.0299266i	0.857257	+	0.514889i	$0.172167\pi$
$24$	−0.397070	+	0.931957i	−0.0810515	+	0.190235i
$25$	−2.76630	−	2.45072i	−0.553259	−	0.490145i
$26$	0.913043	−	6.63938i	0.179062	−	1.30209i
$27$	0.748511	−	0.663123i	0.144051	−	0.127618i
$28$	0.391386	+	1.17234i	0.0739650	+	0.221552i
$29$	0.381267	−	9.46104i	0.0707995	−	1.75687i	−0.440761	−	0.897625i	$-0.645291\pi$
$29$	0.381267	−	9.46104i	0.0707995	−	1.75687i	0.511560	−	0.859247i	$-0.329068\pi$
$30$	−1.34255	+	1.64433i	−0.245115	+	0.300211i
$31$	4.15421	+	4.68913i	0.746117	+	0.842192i	0.991885	−	0.127136i	$-0.0405786\pi$
$31$	4.15421	+	4.68913i	0.746117	+	0.842192i	−0.245768	+	0.969329i	$0.579040\pi$
$32$	6.74386	+	1.37677i	1.19216	+	0.243381i
$33$	4.19465	−	1.21499i	0.730195	−	0.211503i
$34$	4.30190	−	1.63150i	0.737770	−	0.279799i
$35$	−0.0390623	−	0.969321i	−0.00660274	−	0.163845i
$36$	−1.16319	−	0.874082i	−0.193865	−	0.145680i
$37$	5.07334	−	1.03573i	0.834052	−	0.170273i	0.236023	−	0.971747i	$-0.424156\pi$
$37$	5.07334	−	1.03573i	0.834052	−	0.170273i	0.598029	+	0.801475i	$0.295951\pi$
$38$	−8.50557	+	4.46407i	−1.37979	+	0.724167i
$39$	−3.35059	−	1.33176i	−0.536523	−	0.213252i
$40$	−1.02440	−	0.537645i	−0.161971	−	0.0850091i
$41$	−0.363440	−	0.105272i	−0.0567599	−	0.0164407i	0.249716	−	0.968319i	$-0.419663\pi$
$41$	−0.363440	−	0.105272i	−0.0567599	−	0.0164407i	−0.306476	+	0.951878i	$0.599150\pi$
$42$	1.57380	−	0.127051i	0.242843	−	0.0196043i
$43$	0.404977	−	1.98371i	0.0617584	−	0.302513i	−0.937166	−	0.348884i	$-0.886561\pi$
$43$	0.404977	−	1.98371i	0.0617584	−	0.302513i	0.998924	+	0.0463715i	$0.0147658\pi$
$44$	−2.95290	−	5.62628i	−0.445166	−	0.848193i
$45$	0.686075	+	0.912999i	0.102274	+	0.136102i
$46$	0.164640	−	0.260357i	0.0242748	−	0.0383875i
$47$	10.1830	−	7.02879i	1.48534	−	1.02525i	0.497901	−	0.867234i	$-0.334104\pi$
$47$	10.1830	−	7.02879i	1.48534	−	1.02525i	0.987436	−	0.158020i	$-0.0505111\pi$
$48$	2.05471	−	4.33021i	0.296572	−	0.625012i
$49$	4.34923	−	4.52802i	0.621318	−	0.646861i
$50$	4.95430	+	4.75867i	0.700644	+	0.672977i
$51$	−0.298357	−	2.45719i	−0.0417784	−	0.344076i
$52$	−0.923402	+	5.16418i	−0.128053	+	0.716143i
$53$	0.281346	−	2.31710i	0.0386459	−	0.318277i	−0.960547	−	0.278117i	$-0.910290\pi$
$53$	0.281346	−	2.31710i	0.0386459	−	0.318277i	0.999193	−	0.0401610i	$-0.0127871\pi$
$54$	−1.43981	+	1.17557i	−0.195933	+	0.159974i
$55$	0.997606	+	4.88660i	0.134517	+	0.658909i
$56$	0.239408	+	0.826533i	0.0319923	+	0.110450i
$57$	1.23675	+	5.01771i	0.163812	+	0.664611i
$58$	−1.41622	+	17.5431i	−0.185959	+	2.30352i
$59$	−0.332007	−	2.04292i	−0.0432237	−	0.265966i	0.956439	−	0.291932i	$-0.0942980\pi$
$59$	−0.332007	−	2.04292i	−0.0432237	−	0.265966i	−0.999663	+	0.0259658i	$0.991734\pi$
$60$	1.10190	−	1.24378i	0.142254	−	0.160572i
$61$	2.02809	−	1.52401i	0.259670	−	0.195130i	−0.462932	−	0.886394i	$-0.653202\pi$
$61$	2.02809	−	1.52401i	0.259670	−	0.195130i	0.722602	+	0.691264i	$0.242946\pi$
$62$	−7.36447	−	9.01984i	−0.935288	−	1.14552i
$63$	0.136261	−	0.838448i	0.0171673	−	0.105635i
$64$	−3.11465	−	0.767692i	−0.389331	−	0.0959615i
$65$	1.82390	−	3.69173i	0.226227	−	0.457902i
$66$	−7.88148	+	1.94261i	−0.970143	+	0.239119i
$67$	−1.00553	−	12.4557i	−0.122845	−	1.52171i	−0.705337	−	0.708873i	$-0.749204\pi$
$67$	−1.00553	−	12.4557i	−0.122845	−	1.52171i	0.582491	−	0.812837i	$-0.302078\pi$
$68$	−3.41614	+	1.14047i	−0.414267	+	0.138303i
$69$	−0.114802	−	0.119522i	−0.0138206	−	0.0143887i
$70$			1.80320i			0.215524i
$71$	−3.85525	+	3.70302i	−0.457534	+	0.439468i	−0.885718	−	0.464224i	$-0.846333\pi$
$71$	−3.85525	+	3.70302i	−0.457534	+	0.439468i	0.428183	+	0.903692i	$0.359154\pi$
$72$	−0.784690	−	0.640679i	−0.0924766	−	0.0755048i
$73$	6.99375	−	13.3255i	0.818556	−	1.55963i	−0.0101525	−	0.999948i	$-0.503232\pi$
$73$	6.99375	−	13.3255i	0.818556	−	1.55963i	0.828709	−	0.559680i	$-0.189076\pi$
$74$	−9.50001	+	1.54390i	−1.10435	+	0.179475i
$75$	3.12360	−	1.97524i	0.360682	−	0.228081i
$76$	6.79330	−	3.22346i	0.779244	−	0.369756i
$77$	2.10729	−	3.05294i	0.240148	−	0.347915i
$78$	6.12322	+	2.72419i	0.693318	+	0.308453i
$79$	−2.73217	−	3.95822i	−0.307393	−	0.445335i	0.638593	−	0.769545i	$-0.279517\pi$
$79$	−2.73217	−	3.95822i	−0.307393	−	0.445335i	−0.945985	+	0.324210i	$0.894902\pi$
$80$	4.74044	+	2.73689i	0.529997	+	0.305994i
$81$	0.428693	+	0.903450i	0.0476325	+	0.100383i
$82$	0.667123	+	0.222718i	0.0736714	+	0.0245951i
$83$	−3.19781	+	12.9740i	−0.351006	+	1.42409i	0.484590	+	0.874741i	$0.338969\pi$
$83$	−3.19781	+	12.9740i	−0.351006	+	1.42409i	−0.835596	+	0.549345i	$0.814877\pi$
$84$	−1.23495	+	0.0497667i	−0.134744	+	0.00542999i
$85$	2.82454	−	0.113825i	0.306365	−	0.0123461i
$86$	−0.900616	+	3.65394i	−0.0971160	+	0.394015i
$87$	8.98143	+	2.99844i	0.962910	+	0.321467i
$88$	−1.89650	−	3.99680i	−0.202168	−	0.426060i
$89$	−8.81341	−	5.08842i	−0.934220	−	0.539372i	−0.0460760	−	0.998938i	$-0.514672\pi$
$89$	−8.81341	−	5.08842i	−0.934220	−	0.539372i	−0.888144	+	0.459566i	$0.848005\pi$
$90$	−1.20588	−	1.74702i	−0.127111	−	0.184152i
$91$	−2.92010	+	0.923756i	−0.306110	+	0.0968360i
$92$	−0.136978	+	0.198448i	−0.0142810	+	0.0206896i
$93$	−5.65977	+	2.68559i	−0.586890	+	0.278483i
$94$	−19.4384	+	12.2921i	−2.00492	+	1.26784i
$95$	−5.82552	+	0.946739i	−0.597685	+	0.0971333i
$96$	−3.19867	+	6.09456i	−0.326463	+	0.622024i
$97$	7.32515	+	5.98080i	0.743756	+	0.607258i	0.926672	−	0.375870i	$-0.122656\pi$
$97$	7.32515	+	5.98080i	0.743756	+	0.607258i	−0.182916	+	0.983129i	$0.558554\pi$
$98$	−8.41653	+	8.08419i	−0.850198	+	0.816626i
$99$			4.36707i			0.438907i
$100$	−3.72499	−	3.87813i	−0.372499	−	0.387813i
$101$	15.2669	−	5.09686i	1.51912	−	0.507156i	0.569883	−	0.821726i	$-0.306988\pi$
$101$	15.2669	−	5.09686i	1.51912	−	0.507156i	0.949234	+	0.314569i	$0.101860\pi$
$102$	0.370217	+	4.58597i	0.0366570	+	0.454078i
$103$	−9.31358	+	2.29559i	−0.917694	+	0.226191i	−0.669753	−	0.742584i	$-0.733600\pi$
$103$	−9.31358	+	2.29559i	−0.917694	+	0.226191i	−0.247941	+	0.968775i	$0.579754\pi$
$104$	−0.787155	+	3.56666i	−0.0771869	+	0.349740i
$105$	0.941918	+	0.232162i	0.0919218	+	0.0226567i
$106$	−0.695955	+	4.28238i	−0.0675971	+	0.415942i
$107$	−5.73476	−	7.02381i	−0.554400	−	0.679017i	0.419037	−	0.907969i	$-0.362368\pi$
$107$	−5.73476	−	7.02381i	−0.554400	−	0.679017i	−0.973438	+	0.228952i	$0.926470\pi$
$108$	1.16319	−	0.874082i	0.111928	−	0.0841086i
$109$	−7.34355	+	8.28915i	−0.703384	+	0.793957i	−0.986260	−	0.165200i	$-0.947173\pi$
$109$	−7.34355	+	8.28915i	−0.703384	+	0.793957i	0.282876	+	0.959157i	$0.408712\pi$
$110$	−1.48707	−	9.15033i	−0.141787	−	0.872450i
$111$	−0.416655	+	5.16119i	−0.0395471	+	0.489879i
$112$	−0.974345	−	3.95307i	−0.0920670	−	0.373530i
$113$	3.14855	+	10.8700i	0.296190	+	1.02257i	0.961227	+	0.275757i	$0.0889285\pi$
$113$	3.14855	+	10.8700i	0.296190	+	1.02257i	−0.665037	+	0.746810i	$0.731584\pi$
$114$	−1.92142	−	9.41173i	−0.179957	−	0.881490i
$115$	0.146607	−	0.119701i	0.0136711	−	0.0111621i
$116$	1.66064	−	13.6766i	0.154186	−	1.26984i
$117$	2.21137	−	2.84778i	0.204441	−	0.263277i
$118$	0.463720	+	3.81908i	0.0426889	+	0.351575i
$119$	−1.51639	−	1.45651i	−0.139007	−	0.133518i
$120$	0.801422	−	0.834369i	0.0731595	−	0.0761671i
$121$	−3.46010	+	7.29202i	−0.314555	+	0.662910i
$122$	−3.88075	+	2.67869i	−0.351346	+	0.242517i
$123$	0.202231	−	0.319803i	0.0182346	−	0.0288356i
$124$	5.47579	+	7.28695i	0.491740	+	0.654387i
$125$	4.61513	+	8.79339i	0.412790	+	0.786505i
$126$	−0.315825	+	1.54701i	−0.0281360	+	0.137819i
$127$	−21.8759	+	1.76601i	−1.94117	+	0.156708i	−0.988905	−	0.148551i	$-0.952539\pi$
$127$	−21.8759	+	1.76601i	−1.94117	+	0.156708i	−0.952270	+	0.305258i	$0.901257\pi$
$128$	−7.49518	−	2.17101i	−0.662487	−	0.191892i
$129$	1.79272	+	0.940890i	0.157840	+	0.0828407i
$130$	−3.66376	+	6.71998i	−0.321333	+	0.589381i
$131$	−13.0828	+	6.86637i	−1.14305	+	0.599918i	−0.926478	−	0.376349i	$-0.877179\pi$
$131$	−13.0828	+	6.86637i	−1.14305	+	0.599918i	−0.216570	+	0.976267i	$0.569487\pi$
$132$	6.22569	−	1.27098i	0.541877	−	0.110625i
$133$	3.50943	+	2.63716i	0.304306	+	0.228671i
$134$	0.935280	+	23.2087i	0.0807959	+	2.00493i
$135$	−1.06783	+	0.404975i	−0.0919042	+	0.0348547i
$136$	−2.40847	+	0.697621i	−0.206524	+	0.0598205i
$137$	15.1834	+	3.09972i	1.29721	+	0.264827i	0.798527	−	0.601959i	$-0.205613\pi$
$137$	15.1834	+	3.09972i	1.29721	+	0.264827i	0.498681	+	0.866786i	$0.333818\pi$
$138$	0.204272	+	0.230575i	0.0173888	+	0.0196279i
$139$	−1.86489	+	2.28407i	−0.158178	+	0.193733i	−0.847613	−	0.530614i	$-0.821961\pi$
$139$	−1.86489	+	2.28407i	−0.158178	+	0.193733i	0.689436	+	0.724347i	$0.257859\pi$
$140$	0.0568358	−	1.41037i	0.00480350	−	0.119198i
$141$	3.91820	+	11.7364i	0.329972	+	0.988387i
$142$	7.43735	−	6.58891i	0.624128	−	0.552929i
$143$	14.0562	−	7.09575i	1.17544	−	0.593377i
$144$	3.58759	+	3.17833i	0.298966	+	0.264861i
$145$	−4.23861	+	9.94839i	−0.351998	+	0.826169i
$146$	−13.9865	+	24.2254i	−1.15753	+	2.00491i
$147$	3.13922	+	5.43729i	0.258918	+	0.448460i
$148$	7.47905	−	0.908122i	0.614774	−	0.0746471i
$149$	11.4673	+	5.44130i	0.939438	+	0.445769i	0.835916	−	0.548858i	$-0.184937\pi$
$149$	11.4673	+	5.44130i	0.939438	+	0.445769i	0.103523	+	0.994627i	$0.466989\pi$
$150$	−5.94916	+	3.43475i	−0.485747	+	0.280446i
$151$	−7.91205	−	5.46129i	−0.643873	−	0.444434i	0.200861	−	0.979620i	$-0.435626\pi$
$151$	−7.91205	−	5.46129i	−0.643873	−	0.444434i	−0.844734	+	0.535186i	$0.820241\pi$
$152$	4.81624	−	2.05201i	0.390649	−	0.166440i
$153$	2.44319	+	0.397056i	0.197520	+	0.0321001i
$154$	−4.14228	+	5.51237i	−0.333794	+	0.444200i
$155$	−2.53701	−	6.68954i	−0.203777	−	0.537317i
$156$	−4.70339	−	2.32371i	−0.376572	−	0.186046i
$157$	2.13821	−	5.63799i	0.170647	−	0.449960i	−0.822222	−	0.569167i	$-0.807266\pi$
$157$	2.13821	−	5.63799i	0.170647	−	0.449960i	0.992869	+	0.119207i	$0.0380351\pi$
$158$	4.77808	+	7.55593i	0.380124	+	0.601117i
$159$	2.14734	+	0.914895i	0.170295	+	0.0725559i
$160$	−6.64375	−	4.20125i	−0.525234	−	0.332138i
$161$	−0.139749	−	0.0169686i	−0.0110138	−	0.00133731i
$162$	−0.728573	−	1.71002i	−0.0572421	−	0.134352i
$163$	1.69201	−	5.06818i	0.132528	−	0.396970i	−0.861273	−	0.508143i	$-0.830332\pi$
$163$	1.69201	−	5.06818i	0.132528	−	0.396970i	0.993801	+	0.111172i	$0.0354605\pi$
$164$	−0.514767	−	0.195225i	−0.0401966	−	0.0152445i
$165$	−4.97122	−	0.401318i	−0.387009	−	0.0312426i
$166$	6.91020	−	23.8568i	0.536336	−	1.85165i
$167$	0.799485	+	0.0322182i	0.0618660	+	0.00249312i	0.0711797	−	0.997464i	$-0.477324\pi$
$167$	0.799485	+	0.0322182i	0.0618660	+	0.00249312i	−0.00931363	+	0.999957i	$0.502965\pi$
$168$	−0.860508			−0.0663896
$169$	−12.7592	−	2.49052i	−0.981477	−	0.191579i
$170$	−5.25442			−0.402995
$171$	−5.16368	−	0.208089i	−0.394877	−	0.0159130i
$172$	0.819583	−	2.82953i	0.0624926	−	0.215750i
$173$	1.52027	+	0.122729i	0.115584	+	0.00933088i	0.138123	−	0.990415i	$-0.455893\pi$
$173$	1.52027	+	0.122729i	0.115584	+	0.00933088i	−0.0225394	+	0.999746i	$0.507175\pi$
$174$	−16.4564	−	6.24109i	−1.24756	−	0.473136i
$175$	0.994127	−	2.97777i	0.0751489	−	0.225099i
$176$	8.20435	+	19.2563i	0.618426	+	1.45150i
$177$	2.05463	+	0.249478i	0.154436	+	0.0187519i
$178$	15.9879	+	10.1101i	1.19835	+	0.757788i
$179$	−22.2272	−	9.47011i	−1.66134	−	0.707829i	−0.662197	−	0.749330i	$-0.730376\pi$
$179$	−22.2272	−	9.47011i	−1.66134	−	0.707829i	−0.999138	+	0.0415007i	$0.986786\pi$
$180$	0.888111	+	1.40443i	0.0661959	+	0.104680i
$181$	4.79937	−	12.6549i	0.356734	−	0.940630i	−0.629754	−	0.776795i	$-0.716844\pi$
$181$	4.79937	−	12.6549i	0.356734	−	0.940630i	0.986488	−	0.163835i	$-0.0523866\pi$
$182$	5.49251	−	1.49710i	0.407132	−	0.110972i
$183$	0.899590	+	2.37202i	0.0664996	+	0.175345i
$184$	−0.100855	+	0.134213i	−0.00743511	+	0.00989433i
$185$	−5.83691	−	0.948590i	−0.429138	−	0.0697417i
$186$	10.7126	−	4.56423i	0.785489	−	0.334666i
$187$	8.89608	+	6.14052i	0.650546	+	0.449039i
$188$	15.5911	−	9.00154i	1.13710	−	0.656505i
$189$	0.767434	+	0.364152i	0.0558226	+	0.0264882i
$190$	10.8903	−	1.32233i	0.790068	−	0.0959316i
$191$	−4.45047	−	7.70844i	−0.322025	−	0.557763i	0.658881	−	0.752247i	$-0.271030\pi$
$191$	−4.45047	−	7.70844i	−0.322025	−	0.557763i	−0.980906	+	0.194484i	$0.937697\pi$
$192$	1.60393	−	2.77809i	0.115754	−	0.200491i
$193$	8.21378	−	19.2784i	0.591241	−	1.38769i	−0.308482	−	0.951230i	$-0.599821\pi$
$193$	8.21378	−	19.2784i	0.591241	−	1.38769i	0.899722	−	0.436463i	$-0.143769\pi$
$194$	−13.1570	−	11.6561i	−0.944621	−	0.836861i
$195$	3.03853	+	2.77899i	0.217594	+	0.199008i
$196$	6.83776	−	6.05773i	0.488411	−	0.432695i
$197$	1.80800	+	5.41563i	0.128815	+	0.385848i	0.993117	−	0.117125i	$-0.0373678\pi$
$197$	1.80800	+	5.41563i	0.128815	+	0.385848i	−0.864302	+	0.502973i	$0.832240\pi$
$198$	0.326853	−	8.11077i	0.0232284	−	0.576407i
$199$	−2.93164	+	3.59060i	−0.207818	+	0.254531i	−0.867988	−	0.496585i	$-0.834587\pi$
$199$	−2.93164	+	3.59060i	−0.207818	+	0.254531i	0.660170	+	0.751117i	$0.270484\pi$
$200$	−2.48263	−	2.80231i	−0.175549	−	0.198153i
$201$	12.2437	+	2.49957i	0.863605	+	0.176306i
$202$	−28.7361	+	8.32352i	−2.02187	+	0.585641i
$203$	7.52051	−	2.85216i	0.527837	−	0.200182i
$204$	−0.145017	−	3.59856i	−0.0101532	−	0.251950i
$205$	0.345460	+	0.259597i	0.0241280	+	0.0181310i
$206$	17.4695	−	3.56643i	1.21716	−	0.248485i
$207$	0.146743	−	0.0770166i	0.0101993	−	0.00535303i
$208$	4.40080	−	16.7116i	0.305140	−	1.15874i
$209$	−19.9834	−	10.4881i	−1.38228	−	0.725477i
$210$	−1.73201	−	0.501682i	−0.119520	−	0.0346194i
$211$	4.53006	−	0.365704i	0.311862	−	0.0251761i	0.0764553	−	0.997073i	$-0.475640\pi$
$211$	4.53006	−	0.365704i	0.311862	−	0.0251761i	0.235407	+	0.971897i	$0.424358\pi$
$212$	0.679316	−	3.32751i	0.0466556	−	0.228534i
$213$	−2.48422	−	4.73328i	−0.170216	−	0.324319i
$214$	10.1252	+	13.4742i	0.692146	+	0.921079i
$215$	−1.23580	+	1.95426i	−0.0842807	+	0.133279i
$216$	0.833699	−	0.575461i	0.0567260	−	0.0391551i
$217$	−2.28127	+	4.80768i	−0.154863	+	0.326366i
$218$	14.2593	−	14.8455i	0.965758	−	1.00546i
$219$	10.8536	+	10.4250i	0.733417	+	0.704456i
$220$	0.874695	+	7.20376i	0.0589719	+	0.485677i
$221$	−2.69177	−	8.50899i	−0.181068	−	0.572377i
$222$	1.16012	−	9.55447i	0.0778624	−	0.641254i
$223$	2.51570	−	2.05401i	0.168464	−	0.137546i	−0.544463	−	0.838785i	$-0.683267\pi$
$223$	2.51570	−	2.05401i	0.168464	−	0.137546i	0.712927	+	0.701238i	$0.247369\pi$
$224$	1.16949	+	5.72856i	0.0781402	+	0.382756i
$225$	1.02822	+	3.54982i	0.0685478	+	0.236655i
$226$	−5.03409	−	20.4241i	−0.334863	−	1.35859i
$227$	1.56017	−	19.3262i	0.103552	−	1.28273i	−0.711230	−	0.702959i	$-0.751862\pi$
$227$	1.56017	−	19.3262i	0.103552	−	1.28273i	0.814782	−	0.579767i	$-0.196856\pi$
$228$	1.20618	+	7.42191i	0.0798810	+	0.491528i
$229$	8.52379	−	9.62137i	0.563268	−	0.635798i	−0.396015	−	0.918244i	$-0.629607\pi$
$229$	8.52379	−	9.62137i	0.563268	−	0.635798i	0.959283	+	0.282446i	$0.0911457\pi$
$230$	−0.281245	+	0.211342i	−0.0185448	+	0.0139355i
$231$	2.34612	+	2.87347i	0.154363	+	0.189061i
$232$	1.53867	−	9.46779i	0.101018	−	0.621591i
$233$	−6.20066	−	1.52832i	−0.406218	−	0.100124i	0.0309117	−	0.999522i	$-0.490159\pi$
$233$	−6.20066	−	1.52832i	−0.406218	−	0.100124i	−0.437130	+	0.899398i	$0.644005\pi$
$234$	−4.32022	+	5.12355i	−0.282421	+	0.334937i
$235$	−13.7202	+	3.38171i	−0.895004	+	0.220599i
$236$	−0.242322	−	3.00169i	−0.0157738	−	0.195394i
$237$	4.56208	−	1.52305i	0.296339	−	0.0989325i
$238$	2.70732	+	2.81861i	0.175489	+	0.182704i
$239$			8.57361i			0.554580i	0.960786	+	0.277290i	$0.0894363\pi$
$239$			8.57361i			0.554580i	−0.960786	+	0.277290i	$0.910564\pi$
$240$	−3.94771	+	3.79183i	−0.254824	+	0.244761i
$241$	−23.5133	−	19.1980i	−1.51462	−	1.23665i	−0.890206	−	0.455559i	$-0.849439\pi$
$241$	−23.5133	−	19.1980i	−1.51462	−	1.23665i	−0.624416	−	0.781092i	$-0.714663\pi$
$242$	6.97207	−	13.2842i	0.448182	−	0.853939i
$243$	−0.987050	+	0.160411i	−0.0633193	+	0.0102904i
$244$	3.11974	−	1.97280i	0.199721	−	0.126296i
$245$	−6.47797	+	3.07384i	−0.413862	+	0.196380i
$246$	−0.399530	+	0.578820i	−0.0254731	+	0.0369042i
$247$	7.72035	+	16.9584i	0.491234	+	1.07904i
$248$	3.60504	+	5.22280i	0.228920	+	0.331648i
$249$	−11.5721	−	6.68116i	−0.733353	−	0.423402i
$250$	−7.91334	−	16.6770i	−0.500483	−	1.05475i
$251$	16.4150	+	5.48014i	1.03611	+	0.345903i	0.783320	−	0.621619i	$-0.213525\pi$
$251$	16.4150	+	5.48014i	1.03611	+	0.345903i	0.252787	+	0.967522i	$0.418653\pi$
$252$	0.295782	−	1.20004i	0.0186325	−	0.0755952i
$253$	0.723149	−	0.0291419i	0.0454640	−	0.00183214i
$254$	40.7614	−	1.64263i	2.55760	−	0.103068i
$255$	−0.676506	+	2.74469i	−0.0423644	+	0.171879i
$256$	19.8435	+	6.62475i	1.24022	+	0.414047i
$257$	9.70525	+	20.4534i	0.605397	+	1.27585i	0.942446	+	0.334360i	$0.108520\pi$
$257$	9.70525	+	20.4534i	0.605397	+	1.27585i	−0.337049	+	0.941487i	$0.609429\pi$
$258$	−3.25911	−	1.88165i	−0.202903	−	0.117146i
$259$	2.49859	+	3.61984i	0.155255	+	0.224926i
$260$	3.07740	−	5.14052i	0.190852	−	0.318801i
$261$	−5.37885	+	7.79261i	−0.332942	+	0.482350i
$262$	24.8120	−	11.7734i	1.53289	−	0.727365i
$263$	−5.37895	+	3.40144i	−0.331680	+	0.209742i	−0.689916	−	0.723889i	$-0.742353\pi$
$263$	−5.37895	+	3.40144i	−0.331680	+	0.209742i	0.358236	+	0.933631i	$0.383378\pi$
$264$	4.36664	−	0.709648i	0.268748	−	0.0436758i
$265$	−1.23879	+	2.36033i	−0.0760986	+	0.144994i
$266$	−6.32053	−	5.16055i	−0.387537	−	0.316414i
$267$	7.33957	−	7.04975i	0.449174	−	0.431438i
$268$		−	18.1821i		−	1.11065i
$269$	0.775098	+	0.806962i	0.0472585	+	0.0492013i	0.744412	−	0.667721i	$-0.232730\pi$
$269$	0.775098	+	0.806962i	0.0472585	+	0.0492013i	−0.697153	+	0.716922i	$0.745550\pi$
$270$	2.01355	−	0.672220i	0.122540	−	0.0409100i
$271$	0.298884	+	3.70234i	0.0181559	+	0.224901i	0.999472	+	0.0324978i	$0.0103462\pi$
$271$	0.298884	+	3.70234i	0.0181559	+	0.224901i	−0.981316	+	0.192403i	$0.938372\pi$
$272$	11.5190	−	2.83918i	0.698443	−	0.172151i
$273$	−0.0748617	−	3.06181i	−0.00453084	−	0.185309i
$274$	−27.9675	−	6.89338i	−1.68958	−	0.416444i
$275$	−2.58896	+	15.9305i	−0.156120	+	0.960647i
$276$	−0.152503	−	0.186782i	−0.00917958	−	0.0112429i
$277$	22.7543	−	17.0987i	1.36717	−	1.02736i	0.372101	−	0.928192i	$-0.378637\pi$
$277$	22.7543	−	17.0987i	1.36717	−	1.02736i	0.995070	−	0.0991710i	$-0.0316191\pi$
$278$	3.63453	−	4.10253i	0.217984	−	0.246054i
$279$	−1.00491	−	6.18349i	−0.0601626	−	0.370196i
$280$	0.0790776	−	0.979552i	0.00472579	−	0.0585394i
$281$	1.11812	+	4.53640i	0.0667015	+	0.270619i	0.994818	−	0.101671i	$-0.0324189\pi$
$281$	1.11812	+	4.53640i	0.0667015	+	0.270619i	−0.928117	+	0.372290i	$0.878573\pi$
$282$	−6.39869	−	22.0908i	−0.381037	−	1.31549i
$283$	2.06134	+	10.0971i	0.122534	+	0.600210i	0.993966	+	0.109693i	$0.0349868\pi$
$283$	2.06134	+	10.0971i	0.122534	+	0.600210i	−0.871432	+	0.490517i	$0.836808\pi$
$284$	−6.02476	+	4.91907i	−0.357504	+	0.291893i
$285$	0.711401	−	5.85891i	0.0421398	−	0.347052i
$286$	−26.6371	+	12.1266i	−1.57508	+	0.717061i
$287$	−0.0387422	−	0.319070i	−0.00228688	−	0.0188341i
$288$	−4.96401	−	4.76800i	−0.292507	−	0.280957i
$289$	−7.53212	+	7.84177i	−0.443066	+	0.461281i
$290$	8.61678	−	18.1595i	0.505994	−	1.06636i
$291$	−7.78265	+	5.37197i	−0.456227	+	0.314911i
$292$	11.7031	−	18.5069i	0.684870	−	1.08304i
$293$	4.27132	+	5.68410i	0.249533	+	0.332069i	0.906778	−	0.421609i	$-0.138534\pi$
$293$	4.27132	+	5.68410i	0.249533	+	0.332069i	−0.657244	+	0.753678i	$0.728278\pi$
$294$	−5.42338	−	10.3334i	−0.316298	−	0.602656i
$295$	−0.472805	+	2.31595i	−0.0275277	+	0.134840i
$296$	5.22839	−	0.422079i	0.303894	−	0.0245329i
$297$	−4.19465	−	1.21499i	−0.243398	−	0.0705012i
$298$	−20.8905	−	10.9642i	−1.21015	−	0.635137i
$299$	−0.486325	−	0.347180i	−0.0281249	−	0.0200779i
$300$	4.76137	−	2.49896i	0.274898	−	0.144277i
$301$	1.68506	−	0.344007i	0.0971251	−	0.0198282i
$302$	14.2859	+	10.7352i	0.822064	+	0.617741i
$303$	0.648091	+	16.0822i	0.0372319	+	0.923899i
$304$	−23.1599	+	8.78338i	−1.32831	+	0.503761i
$305$	−2.78284	+	0.806060i	−0.159345	+	0.0461549i
$306$	−4.50790	−	0.920295i	−0.257700	−	0.0526098i
$307$	19.2157	+	21.6900i	1.09670	+	1.23792i	0.969252	+	0.246070i	$0.0791392\pi$
$307$	19.2157	+	21.6900i	1.09670	+	1.23792i	0.127445	+	0.991846i	$0.459322\pi$
$308$	3.41361	−	4.18092i	0.194509	−	0.238230i
$309$	0.386244	−	9.58453i	0.0219726	−	0.545245i
$310$	4.21120	+	12.6141i	0.239180	+	0.716432i
$311$	−5.64637	+	5.00225i	−0.320176	+	0.283651i	−0.807867	−	0.589365i	$-0.799378\pi$
$311$	−5.64637	+	5.00225i	−0.320176	+	0.283651i	0.487691	+	0.873017i	$0.337839\pi$
$312$	−3.20685	−	1.74838i	−0.181552	−	0.0989828i
$313$	−22.5980	−	20.0201i	−1.27731	−	1.13160i	−0.984491	−	0.175436i	$-0.943867\pi$
$313$	−22.5980	−	20.0201i	−1.27731	−	1.13160i	−0.292824	−	0.956166i	$-0.594595\pi$
$314$	−4.39317	+	10.3112i	−0.247921	+	0.581892i
$315$	−0.485054	+	0.840138i	−0.0273297	+	0.0473364i
$316$	−3.49899	−	6.06044i	−0.196834	−	0.340926i
$317$	−1.88441	+	0.228808i	−0.105839	+	0.0128512i	−0.173285	−	0.984872i	$-0.555438\pi$
$317$	−1.88441	+	0.228808i	−0.105839	+	0.0128512i	0.0674459	+	0.997723i	$0.478515\pi$
$318$	−3.91968	−	1.85991i	−0.219805	−	0.104299i
$319$	−35.8106	+	20.6753i	−2.00501	+	1.15759i
$320$	3.01502	+	2.08112i	0.168545	+	0.116338i
$321$	8.34200	−	3.55420i	0.465605	−	0.198376i
$322$	0.258280	+	0.0419746i	0.0143934	+	0.00233915i
$323$	−7.68453	+	10.2263i	−0.427579	+	0.569004i
$324$	0.515951	+	1.36045i	0.0286640	+	0.0755807i
$325$	9.75506	−	9.07737i	0.541113	−	0.503522i
$326$	−3.52182	+	9.28627i	−0.195055	+	0.514319i
$327$	−5.91878	−	9.35980i	−0.327309	−	0.517598i
$328$	−0.352633	−	0.150243i	−0.0194709	−	0.00829579i
$329$	8.88329	+	5.61745i	0.489752	+	0.309700i
$330$	9.20279	+	1.11742i	0.506597	+	0.0615120i
$331$	−0.861687	−	2.02245i	−0.0473626	−	0.111164i	0.894618	−	0.446833i	$-0.147448\pi$
$331$	−0.861687	−	2.02245i	−0.0473626	−	0.111164i	−0.941980	+	0.335669i	$0.891038\pi$
$332$	−6.15673	+	18.4417i	−0.337895	+	1.01212i
$333$	−4.84150	−	1.83614i	−0.265312	−	0.100620i
$334$	−1.48244	−	0.119675i	−0.0811154	−	0.00654831i
$335$	−3.97052	+	13.7078i	−0.216933	+	0.748938i
$336$	4.06808	+	0.163938i	0.221932	+	0.00894355i
$337$	19.9311			1.08571			0.542857	−	0.839825i	$-0.317342\pi$
$337$	19.9311			1.08571			0.542857	+	0.839825i	$0.317342\pi$
$338$	23.5107	+	5.58050i	1.27881	+	0.303539i
$339$	−11.3169			−0.614647
$340$	4.10972	+	0.165616i	0.222881	+	0.00898179i
$341$	7.61147	−	26.2778i	0.412184	−	1.42303i
$342$	9.57471	+	0.772951i	0.517741	+	0.0417964i
$343$	10.5464	+	3.99971i	0.569451	+	0.215964i
$344$	0.649481	−	1.94543i	0.0350177	−	0.104891i
$345$	0.0741861	+	0.174121i	0.00399404	+	0.00937437i
$346$	−2.81434	−	0.341722i	−0.151300	−	0.0183711i
$347$	1.88169	+	1.18991i	0.101015	+	0.0638778i	0.584018	−	0.811741i	$-0.301480\pi$
$347$	1.88169	+	1.18991i	0.101015	+	0.0638778i	−0.483003	+	0.875619i	$0.660454\pi$
$348$	12.6746	+	5.40014i	0.679429	+	0.289478i
$349$	2.70950	+	4.28474i	0.145036	+	0.229357i	0.909892	−	0.414845i	$-0.136164\pi$
$349$	2.70950	+	4.28474i	0.145036	+	0.229357i	−0.764856	+	0.644202i	$0.777190\pi$
$350$	−2.06922	+	5.45608i	−0.110604	+	0.291640i
$351$	2.12010	+	2.91636i	0.113163	+	0.155664i
$352$	−10.6588	−	28.1051i	−0.568119	−	1.49801i
$353$	−13.1662	+	17.5210i	−0.700764	+	0.932548i	−0.999764	−	0.0217052i	$-0.993090\pi$
$353$	−13.1662	+	17.5210i	−0.700764	+	0.932548i	0.299000	+	0.954253i	$0.403347\pi$
$354$	−3.79731	−	0.617123i	−0.201825	−	0.0327997i
$355$	5.61639	−	2.39292i	0.298087	−	0.127003i
$356$	−12.1862	−	8.41154i	−0.645868	−	0.445810i
$357$	1.82089	−	1.05129i	0.0963720	−	0.0556404i
$358$	40.5727	+	19.2520i	2.14434	+	1.01750i
$359$	−5.97077	+	0.724983i	−0.315125	+	0.0382631i	−0.276571	−	0.960993i	$-0.589198\pi$
$359$	−5.97077	+	0.724983i	−0.315125	+	0.0382631i	−0.0385538	+	0.999257i	$0.512275\pi$
$360$	0.578457	+	1.00192i	0.0304873	+	0.0528056i
$361$	3.85347	−	6.67441i	0.202814	−	0.351285i
$362$	−9.86081	+	23.1442i	−0.518273	+	1.21643i
$363$	−6.04145	−	5.35226i	−0.317094	−	0.280921i
$364$	−4.34313	+	0.997828i	−0.227642	+	0.0523004i
$365$	−12.8646	+	11.3971i	−0.673365	+	0.596549i
$366$	−1.49324	−	4.47279i	−0.0780527	−	0.233796i
$367$	−0.626418	+	15.5444i	−0.0326988	+	0.811412i	0.896767	+	0.442503i	$0.145909\pi$
$367$	−0.626418	+	15.5444i	−0.0326988	+	0.811412i	−0.929466	+	0.368908i	$0.879732\pi$
$368$	0.502364	−	0.615284i	0.0261875	−	0.0320739i
$369$	0.250912	+	0.283221i	0.0130620	+	0.0147439i
$370$	10.7696	+	2.19864i	0.559887	+	0.114302i
$371$	1.90443	−	0.551624i	0.0988730	−	0.0286389i
$372$	−8.52270	+	3.23224i	−0.441882	+	0.167584i
$373$	0.580678	+	14.4094i	0.0300663	+	0.746089i	0.941973	+	0.335690i	$0.108969\pi$
$373$	0.580678	+	14.4094i	0.0300663	+	0.746089i	−0.911906	+	0.410399i	$0.865390\pi$
$374$	−16.0627	−	12.0703i	−0.830583	−	0.624143i
$375$	−9.73022	+	1.98644i	−0.502466	+	0.102579i
$376$	11.0986	−	5.82498i	0.572365	−	0.300401i
$377$	33.8217	+	4.65113i	1.74190	+	0.239545i
$378$	−1.39807	−	0.733763i	−0.0719088	−	0.0377407i
$379$	14.4565	+	4.18738i	0.742582	+	0.215091i	0.627882	−	0.778309i	$-0.283922\pi$
$379$	14.4565	+	4.18738i	0.742582	+	0.215091i	0.114700	+	0.993400i	$0.463409\pi$
$380$	−8.55951	+	0.690995i	−0.439093	+	0.0354473i
$381$	4.38998	−	21.5036i	0.224906	−	1.10166i
$382$	7.68873	+	14.6497i	0.393390	+	0.749541i
$383$	−11.8794	−	15.8086i	−0.607008	−	0.807781i	0.386410	−	0.922327i	$-0.373715\pi$
$383$	−11.8794	−	15.8086i	−0.607008	−	0.807781i	−0.993418	+	0.114546i	$0.963459\pi$
$384$	4.17058	−	6.59524i	0.212829	−	0.336562i
$385$	−3.48660	+	2.40662i	−0.177693	+	0.122653i
$386$	−16.6980	+	35.1903i	−0.849905	+	1.79114i
$387$	−1.40251	+	1.46016i	−0.0712934	+	0.0742243i
$388$	9.92333	+	9.53149i	0.503781	+	0.483888i
$389$	−3.09556	−	25.4943i	−0.156951	−	1.29261i	−0.831974	−	0.554814i	$-0.812789\pi$
$389$	−3.09556	−	25.4943i	−0.156951	−	1.29261i	0.675023	−	0.737797i	$-0.264134\pi$
$390$	−5.43534	−	5.38872i	−0.275229	−	0.272868i
$391$	0.0494455	−	0.407220i	0.00250057	−	0.0205940i
$392$	4.92663	−	4.02247i	0.248832	−	0.203165i
$393$	−2.95542	−	14.4766i	−0.149081	−	0.730248i
$394$	−2.95259	−	10.1935i	−0.148750	−	0.513543i
$395$	1.31451	+	5.33317i	0.0661401	+	0.268341i
$396$	−0.511293	+	6.33350i	−0.0256934	+	0.318270i
$397$	−4.24085	−	26.0950i	−0.212842	−	1.30967i	−0.844973	−	0.534810i	$-0.820383\pi$
$397$	−4.24085	−	26.0950i	−0.212842	−	1.30967i	0.632130	−	0.774862i	$-0.282181\pi$
$398$	5.71354	−	6.44925i	0.286394	−	0.323272i
$399$	−3.50943	+	2.63716i	−0.175691	+	0.132023i
$400$	11.2029	+	13.7210i	0.560143	+	0.686050i
$401$	3.20338	−	19.7112i	0.159969	−	0.984329i	−0.775610	−	0.631212i	$-0.782558\pi$
$401$	3.20338	−	19.7112i	0.159969	−	0.984329i	0.935579	−	0.353117i	$-0.114878\pi$
$402$	−22.5526	−	5.55872i	−1.12482	−	0.277244i
$403$	−18.2699	+	13.2816i	−0.910087	+	0.661605i
$404$	22.7382	−	5.60446i	1.13127	−	0.278832i
$405$	−0.0918964	−	1.13834i	−0.00456637	−	0.0565646i
$406$	−14.1810	+	4.73431i	−0.703791	+	0.234960i
$407$	−15.6643	−	16.3083i	−0.776451	−	0.808371i
$408$		−	2.50747i		−	0.124138i
$409$	−19.5202	+	18.7494i	−0.965211	+	0.927098i	−0.997377	−	0.0723847i	$-0.976939\pi$
$409$	−19.5202	+	18.7494i	−0.965211	+	0.927098i	0.0321657	+	0.999483i	$0.489760\pi$
$410$	−0.622179	−	0.507993i	−0.0307272	−	0.0250880i
$411$	−7.20163	+	13.7216i	−0.355230	+	0.676835i
$412$	−13.7761	+	2.23884i	−0.678701	+	0.110300i
$413$	1.48595	−	0.939658i	0.0731188	−	0.0462375i
$414$	−0.278304	+	0.132057i	−0.0136779	+	0.00649023i
$415$	8.66888	−	12.5590i	0.425539	−	0.616499i
$416$	−7.28099	+	23.7248i	−0.356980	+	1.16320i
$417$	−1.67505	−	2.42673i	−0.0820275	−	0.118837i
$418$	36.3293	+	20.9747i	1.77692	+	1.02591i
$419$	3.35463	+	7.06974i	0.163884	+	0.345379i	0.968735	−	0.248099i	$-0.0798057\pi$
$419$	3.35463	+	7.06974i	0.163884	+	0.345379i	−0.804850	+	0.593478i	$0.797754\pi$
$420$	1.33887	+	0.446980i	0.0653301	+	0.0218104i
$421$	−1.70845	+	6.93145i	−0.0832647	+	0.337818i	−0.997769	−	0.0667574i	$-0.978735\pi$
$421$	−1.70845	+	6.93145i	−0.0832647	+	0.337818i	0.914505	+	0.404576i	$0.132581\pi$
$422$	−8.44086	+	0.340155i	−0.410895	+	0.0165585i
$423$	−12.3632	+	0.498219i	−0.601118	+	0.0242242i
$424$	0.565862	−	2.29579i	0.0274807	−	0.111494i
$425$	8.67705	+	2.89682i	0.420899	+	0.140517i
$426$	4.25957	+	8.97686i	0.206377	+	0.434930i
$427$	1.86624	+	1.07747i	0.0903137	+	0.0521426i
$428$	−7.49470	−	10.8579i	−0.362270	−	0.524839i
$429$	2.90492	+	15.4754i	0.140251	+	0.747160i
$430$	2.44146	−	3.53707i	0.117738	−	0.170572i
$431$	0.459606	−	0.218086i	0.0221384	−	0.0105048i	−0.417591	−	0.908635i	$-0.637126\pi$
$431$	0.459606	−	0.218086i	0.0221384	−	0.0105048i	0.439730	+	0.898130i	$0.355074\pi$
$432$	−4.05097	+	2.56168i	−0.194902	+	0.123249i
$433$	−24.1195	+	3.91980i	−1.15911	+	0.188374i	−0.709404	−	0.704803i	$-0.751036\pi$
$433$	−24.1195	+	3.91980i	−1.15911	+	0.188374i	−0.449707	+	0.893176i	$0.648472\pi$
$434$	4.59674	−	8.75835i	0.220650	−	0.420414i
$435$	−8.37635	−	6.83908i	−0.401615	−	0.327909i
$436$	−11.6207	+	11.1619i	−0.556532	+	0.534556i
$437$			0.856451i			0.0409696i
$438$	−19.3776	−	20.1742i	−0.925898	−	0.963962i
$439$	−8.06485	+	2.69244i	−0.384914	+	0.128503i	−0.502538	−	0.864555i	$-0.667600\pi$
$439$	−8.06485	+	2.69244i	−0.384914	+	0.128503i	0.117624	+	0.993058i	$0.462472\pi$
$440$	0.406543	+	5.03594i	0.0193812	+	0.240079i
$441$	−6.09600	+	1.50253i	−0.290286	+	0.0715490i
$442$	4.36245	+	16.0048i	0.207501	+	0.761273i
$443$	2.21851	+	0.546814i	0.105405	+	0.0259799i	0.291665	−	0.956520i	$-0.405791\pi$
$443$	2.21851	+	0.546814i	0.105405	+	0.0259799i	−0.186260	+	0.982500i	$0.559637\pi$
$444$	−1.20854	+	7.43642i	−0.0573546	+	0.352917i
$445$	7.35054	+	9.00278i	0.348449	+	0.426773i
$446$	−4.82603	+	3.62653i	−0.228519	+	0.171721i
$447$	−8.41688	+	9.50069i	−0.398105	+	0.449367i
$448$	−0.437107	−	2.68963i	−0.0206514	−	0.127073i
$449$	−2.25743	+	27.9632i	−0.106535	+	1.31967i	0.693824	+	0.720145i	$0.255925\pi$
$449$	−2.25743	+	27.9632i	−0.106535	+	1.31967i	−0.800358	+	0.599522i	$0.795357\pi$
$450$	−1.64398	−	6.66988i	−0.0774979	−	0.314421i
$451$	0.459729	+	1.58717i	0.0216478	+	0.0747369i
$452$	3.29364	+	16.1333i	0.154920	+	0.758846i
$453$	7.44694	−	6.08024i	0.349888	−	0.285674i
$454$	−4.34411	+	35.7770i	−0.203879	+	1.67910i
$455$	3.49227	+	0.196152i	0.163720	+	0.00919573i
$456$	0.631029	+	5.19699i	0.0295506	+	0.243371i
$457$	17.7679	+	17.0663i	0.831147	+	0.798327i	0.981732	−	0.190270i	$-0.0609362\pi$
$457$	17.7679	+	17.0663i	0.831147	+	0.798327i	−0.150585	+	0.988597i	$0.548116\pi$
$458$	−16.5510	+	17.2314i	−0.773377	+	0.805170i
$459$	−1.06112	+	2.23626i	−0.0495287	+	0.104379i
$460$	0.226636	−	0.156436i	0.0105670	−	0.00729384i
$461$	19.8675	−	31.4179i	0.925320	−	1.46328i	0.0395142	−	0.999219i	$-0.487419\pi$
$461$	19.8675	−	31.4179i	0.925320	−	1.46328i	0.885805	−	0.464057i	$-0.153607\pi$
$462$	−4.14228	−	5.51237i	−0.192716	−	0.256459i
$463$	−6.40329	−	12.2005i	−0.297586	−	0.567003i	0.690051	−	0.723761i	$-0.257588\pi$
$463$	−6.40329	−	12.2005i	−0.297586	−	0.567003i	−0.987637	+	0.156758i	$0.949896\pi$
$464$	−9.07783	+	44.4662i	−0.421428	+	2.06429i
$465$	7.13127	−	0.575695i	0.330705	−	0.0266972i
$466$	11.4018	+	3.30258i	0.528179	+	0.152989i
$467$	−21.5884	−	11.3305i	−0.998993	−	0.524312i	−0.115775	−	0.993275i	$-0.536935\pi$
$467$	−21.5884	−	11.3305i	−0.998993	−	0.524312i	−0.883218	+	0.468963i	$0.844628\pi$
$468$	3.54053	−	3.87119i	0.163661	−	0.178946i
$469$	9.39904	−	4.93300i	0.434007	−	0.227785i
$470$	25.7349	−	5.25383i	1.18706	−	0.242341i
$471$	4.82050	+	3.62237i	0.222117	+	0.166910i
$472$	−0.0844245	−	2.09497i	−0.00388595	−	0.0964289i
$473$	−8.26711	+	3.13530i	−0.380122	+	0.144161i
$474$	−8.58695	+	2.48724i	−0.394412	+	0.114243i
$475$	−18.7131	−	3.82031i	−0.858617	−	0.175288i
$476$	−2.02867	−	2.28990i	−0.0929841	−	0.104957i
$477$	−1.47620	+	1.80802i	−0.0675905	+	0.0827834i
$478$	0.641690	−	15.9234i	0.0293502	−	0.728319i
$479$	−4.47826	−	13.4140i	−0.204617	−	0.612903i	−0.999977	−	0.00676556i	$-0.997846\pi$
$479$	−4.47826	−	13.4140i	−0.204617	−	0.612903i	0.795360	−	0.606137i	$-0.207282\pi$
$480$	5.88378	−	5.21258i	0.268557	−	0.237921i
$481$	1.95668	+	18.5667i	0.0892167	+	0.846567i
$482$	42.2333	+	37.4154i	1.92367	+	1.70423i
$483$	0.0551793	−	0.129511i	0.00251075	−	0.00589294i
$484$	−5.87188	+	10.1704i	−0.266904	+	0.462291i
$485$	−5.39994	−	9.35298i	−0.245199	−	0.424697i
$486$	1.84521	−	0.224049i	0.0837005	−	0.0101631i
$487$	13.5687	+	6.43845i	0.614858	+	0.291754i	0.710539	−	0.703658i	$-0.248451\pi$
$487$	13.5687	+	6.43845i	0.614858	+	0.291754i	−0.0956804	+	0.995412i	$0.530503\pi$
$488$	2.22561	−	1.28495i	0.100748	−	0.0581672i
$489$	4.39733	+	3.03526i	0.198854	+	0.137259i
$490$	12.2613	−	5.22406i	0.553910	−	0.235999i
$491$	4.03010	+	0.654955i	0.181876	+	0.0295577i	0.250667	−	0.968073i	$-0.419350\pi$
$491$	4.03010	+	0.654955i	0.181876	+	0.0295577i	−0.0687911	+	0.997631i	$0.521914\pi$
$492$	0.330735	−	0.440128i	0.0149107	−	0.0198425i
$493$	8.31100	+	21.9143i	0.374309	+	0.986971i
$494$	−13.0694	−	32.0739i	−0.588021	−	1.44307i
$495$	1.76855	−	4.66329i	0.0794905	−	0.209599i
$496$	−16.0479	−	25.3778i	−0.720573	−	1.13950i
$497$	−4.17745	−	1.77984i	−0.187384	−	0.0798369i
$498$	20.9923	+	13.2747i	0.940689	+	0.594856i
$499$	32.1518	+	3.90394i	1.43931	+	0.174764i	0.802683	−	0.596406i	$-0.203405\pi$
$499$	32.1518	+	3.90394i	1.43931	+	0.174764i	0.636629	+	0.771170i	$0.280328\pi$
$500$	5.66373	+	13.2933i	0.253290	+	0.594493i
$501$	−0.253377	+	0.758956i	−0.0113200	+	0.0339077i
$502$	−30.0767	−	11.4066i	−1.34239	−	0.509102i
$503$	−6.09180	−	0.491781i	−0.271620	−	0.0219274i	−0.0560939	−	0.998425i	$-0.517865\pi$
$503$	−6.09180	−	0.491781i	−0.271620	−	0.0219274i	−0.215526	+	0.976498i	$0.569147\pi$
$504$	0.239408	−	0.826533i	0.0106641	−	0.0368167i
$505$	−18.3666	−	0.740149i	−0.817303	−	0.0329362i
$506$	−1.34525			−0.0598039
$507$	5.94203	−	11.5625i	0.263895	−	0.513510i
$508$	−31.9331			−1.41680
$509$	−19.3049	−	0.777962i	−0.855676	−	0.0344826i	−0.391450	−	0.920199i	$-0.628026\pi$
$509$	−19.3049	−	0.777962i	−0.855676	−	0.0344826i	−0.464226	+	0.885717i	$0.653667\pi$
$510$	1.46187	−	5.04696i	0.0647327	−	0.223483i
$511$	12.7421	+	1.02865i	0.563679	+	0.0455048i
$512$	−21.7663	−	8.25488i	−0.961946	−	0.364818i
$513$	1.63650	−	4.90192i	0.0722533	−	0.216425i
$514$	−16.4943	−	38.7136i	−0.727533	−	1.70758i
$515$	10.8750	+	1.32046i	0.479209	+	0.0581865i
$516$	2.48979	+	1.57445i	0.109607	+	0.0693112i
$517$	−49.7108	−	21.1798i	−2.18628	−	0.931486i
$518$	−4.36960	−	6.90997i	−0.191989	−	0.303607i
$519$	−0.540847	+	1.42610i	−0.0237406	+	0.0625987i
$520$	2.28496	−	3.48982i	0.100202	−	0.153039i
$521$	−0.400511	−	1.05606i	−0.0175467	−	0.0462669i	0.925957	−	0.377630i	$-0.123261\pi$
$521$	−0.400511	−	1.05606i	−0.0175467	−	0.0462669i	−0.943503	+	0.331363i	$0.892492\pi$
$522$	10.5731	−	14.0703i	0.462774	−	0.615840i
$523$	−8.77810	−	1.42658i	−0.383839	−	0.0623800i	−0.0345699	−	0.999402i	$-0.511006\pi$
$523$	−8.77810	−	1.42658i	−0.383839	−	0.0623800i	−0.349270	+	0.937022i	$0.613570\pi$
$524$	−19.7777	+	8.42648i	−0.863992	+	0.368113i
$525$	2.58362	+	1.78335i	0.112759	+	0.0778316i
$526$	10.2447	−	5.91477i	0.446689	−	0.257896i
$527$	−14.0093	−	6.64748i	−0.610254	−	0.289569i
$528$	−20.7786	+	2.52298i	−0.904274	+	0.109799i
$529$	11.4863	+	19.8948i	0.499403	+	0.864991i
$530$	2.47742	−	4.29101i	0.107612	−	0.186390i
$531$	−0.811263	+	1.90410i	−0.0352058	+	0.0826311i
$532$	4.78092	+	4.23552i	0.207279	+	0.183633i
$533$	0.503909	−	1.26779i	0.0218267	−	0.0549142i
$534$	−14.1591	+	12.5439i	−0.612724	+	0.542826i
$535$	3.27929	+	9.82267i	0.141776	+	0.424671i
$536$	0.509724	−	12.6487i	0.0220167	−	0.546340i
$537$	15.2802	−	18.7148i	0.659389	−	0.807605i
$538$	−1.37916	−	1.55675i	−0.0594597	−	0.0671162i
$539$	−26.8643	−	5.48438i	−1.15713	−	0.236229i
$540$	−1.59607	+	0.462308i	−0.0686841	+	0.0198946i
$541$	4.20522	−	1.59483i	0.180797	−	0.0685672i	−0.262545	−	0.964920i	$-0.584562\pi$
$541$	4.20522	−	1.59483i	0.180797	−	0.0685672i	0.443342	+	0.896352i	$0.353793\pi$
$542$	−0.278003	−	6.89857i	−0.0119412	−	0.296319i
$543$	10.8200	+	8.13069i	0.464330	+	0.348921i
$544$	−16.6927	+	3.40783i	−0.715693	+	0.146110i
$545$	11.1986	−	5.87746i	0.479694	−	0.251763i
$546$	−0.0901237	+	5.69218i	−0.00385694	+	0.243603i
$547$	32.0008	+	16.7953i	1.36825	+	0.718115i	0.979161	−	0.203084i	$-0.0650965\pi$
$547$	32.0008	+	16.7953i	1.36825	+	0.718115i	0.389092	+	0.921199i	$0.372789\pi$
$548$	21.6574	+	6.27314i	0.925158	+	0.267975i
$549$	−2.52865	+	0.204134i	−0.107920	+	0.00871223i
$550$	6.00068	−	29.3933i	0.255870	−	1.25333i
$551$	−22.7404	−	43.3282i	−0.968773	−	1.84584i
$552$	−0.100855	−	0.134213i	−0.00429266	−	0.00571250i
$553$	2.18356	−	3.45303i	0.0928546	−	0.146838i
$554$	−43.5403	+	30.0537i	−1.84985	+	1.27686i
$555$	2.53507	−	5.34254i	0.107608	−	0.226778i
$556$	−2.97204	+	3.09422i	−0.126042	+	0.131224i
$557$	8.00692	+	7.69076i	0.339264	+	0.325868i	0.842922	−	0.538035i	$-0.180833\pi$
$557$	8.00692	+	7.69076i	0.339264	+	0.325868i	−0.503658	+	0.863903i	$0.668013\pi$
$558$	1.40358	+	11.5595i	0.0594183	+	0.489354i
$559$	6.97864	+	2.14170i	0.295165	+	0.0905844i
$560$	−0.560459	+	4.61580i	−0.0236837	+	0.195053i
$561$	−8.37312	+	6.83644i	−0.353514	+	0.288635i
$562$	−1.73711	−	8.50894i	−0.0732757	−	0.358928i
$563$	10.1319	+	34.9792i	0.427007	+	1.47420i	0.829361	+	0.558714i	$0.188705\pi$
$563$	10.1319	+	34.9792i	0.427007	+	1.47420i	−0.402354	+	0.915484i	$0.631808\pi$
$564$	4.30842	+	17.4799i	0.181417	+	0.736038i
$565$	1.03998	−	12.8824i	0.0437522	−	0.541968i
$566$	−3.07271	−	18.9072i	−0.129156	−	0.794728i
$567$	−0.563288	+	0.635821i	−0.0236559	+	0.0267020i
$568$	−4.32913	+	3.25313i	−0.181646	+	0.136498i
$569$	−9.56222	−	11.7116i	−0.400869	−	0.490976i	0.534241	−	0.845332i	$-0.320597\pi$
$569$	−9.56222	−	11.7116i	−0.400869	−	0.490976i	−0.935110	+	0.354356i	$0.884700\pi$
$570$	−1.75976	+	10.8283i	−0.0737084	+	0.453546i
$571$	20.4675	+	5.04478i	0.856538	+	0.211118i	0.643046	−	0.765827i	$-0.277670\pi$
$571$	20.4675	+	5.04478i	0.856538	+	0.211118i	0.213492	+	0.976945i	$0.431516\pi$
$572$	21.2163	−	8.64518i	0.887098	−	0.361473i
$573$	8.64230	−	2.13014i	0.361037	−	0.0889877i
$574$	0.0480733	+	0.595495i	0.00200654	+	0.0248555i
$575$	0.580958	−	0.193952i	0.0242276	−	0.00808837i
$576$	2.22217	+	2.31352i	0.0925902	+	0.0963966i
$577$			4.30643i			0.179279i	0.995974	+	0.0896396i	$0.0285715\pi$
$577$			4.30643i			0.179279i	−0.995974	+	0.0896396i	$0.971428\pi$
$578$	14.5760	−	14.0004i	0.606282	−	0.582342i
$579$	16.2321	+	13.2531i	0.674582	+	0.550779i
$580$	−7.31195	+	13.9318i	−0.303612	+	0.578484i
$581$	−11.2036	+	1.82077i	−0.464804	+	0.0755381i
$582$	14.8564	−	9.39464i	0.615819	−	0.389421i
$583$	−9.20908	+	4.36976i	−0.381401	+	0.180977i
$584$	8.66027	−	12.5466i	0.358364	−	0.519180i
$585$	−3.51464	+	2.14540i	−0.145313	+	0.0887013i
$586$	−7.50752	−	10.8765i	−0.310133	−	0.449305i
$587$	−20.9231	−	12.0799i	−0.863588	−	0.498593i	0.00162418	−	0.999999i	$-0.499483\pi$
$587$	−20.9231	−	12.0799i	−0.863588	−	0.498593i	−0.865212	+	0.501406i	$0.832816\pi$
$588$	3.91617	+	8.25316i	0.161500	+	0.340354i
$589$	30.7086	+	10.2520i	1.26533	+	0.422428i
$590$	1.05146	−	4.26593i	0.0432878	−	0.175625i
$591$	−5.70483	+	0.229897i	−0.234665	+	0.00945669i
$592$	−24.7978	+	0.999317i	−1.01918	+	0.0410717i
$593$	−4.08604	+	16.5777i	−0.167793	+	0.680765i	0.825426	+	0.564510i	$0.190935\pi$
$593$	−4.08604	+	16.5777i	−0.167793	+	0.680765i	−0.993219	+	0.116254i	$0.962911\pi$
$594$	7.69960	+	2.57051i	0.315919	+	0.105469i
$595$	1.02940	+	2.16941i	0.0422012	+	0.0889371i
$596$	15.9938	+	9.23403i	0.655132	+	0.378241i
$597$	−2.63321	−	3.81486i	−0.107770	−	0.156132i
$598$	0.877245	+	0.681201i	0.0358732	+	0.0278564i
$599$	16.3972	−	23.7554i	0.669971	−	0.970621i	−0.329677	−	0.944094i	$-0.606940\pi$
$599$	16.3972	−	23.7554i	0.669971	−	0.970621i	0.999648	−	0.0265269i	$-0.00844476\pi$
$600$	3.38238	−	1.60496i	0.138085	−	0.0655222i
$601$	22.2975	−	14.1001i	0.909536	−	0.575156i	0.00426529	−	0.999991i	$-0.498642\pi$
$601$	22.2975	−	14.1001i	0.909536	−	0.575156i	0.905271	+	0.424835i	$0.139668\pi$
$602$	−3.15533	+	0.512791i	−0.128602	+	0.0208998i
$603$	−5.80730	+	11.0649i	−0.236491	+	0.450597i
$604$	−10.8353	−	8.84677i	−0.440883	−	0.359970i
$605$	6.64789	−	6.38538i	0.270275	−	0.259603i
$606$		−	29.9173i		−	1.21531i
$607$	0.503796	+	0.524507i	0.0204484	+	0.0212891i	0.731348	−	0.682004i	$-0.238892\pi$
$607$	0.503796	+	0.524507i	0.0204484	+	0.0212891i	−0.710900	+	0.703293i	$0.751712\pi$
$608$	33.7397	−	11.2640i	1.36833	−	0.456815i
$609$	0.647208	+	8.01711i	0.0262262	+	0.324870i
$610$	5.22878	−	1.28878i	0.211707	−	0.0521811i
$611$	21.6917	+	38.9836i	0.877552	+	1.57711i
$612$	3.49683	+	0.861891i	0.141351	+	0.0348399i
$613$	6.65200	−	40.9314i	0.268672	−	1.65320i	−0.405106	−	0.914270i	$-0.632765\pi$
$613$	6.65200	−	40.9314i	0.268672	−	1.65320i	0.673778	−	0.738934i	$-0.264670\pi$
$614$	−34.0651	−	41.7221i	−1.37475	−	1.68377i
$615$	−0.345460	+	0.259597i	−0.0139303	+	0.0104679i
$616$	2.49195	−	2.81283i	0.100403	−	0.113332i
$617$	−5.70010	−	35.0741i	−0.229478	−	1.41203i	−0.804528	−	0.593914i	$-0.797582\pi$
$617$	−5.70010	−	35.0741i	−0.229478	−	1.41203i	0.575051	−	0.818118i	$-0.304982\pi$
$618$	−1.43471	+	17.7720i	−0.0577124	+	0.714896i
$619$	−6.27899	−	25.4749i	−0.252374	−	1.02392i	−0.951187	−	0.308617i	$-0.900134\pi$
$619$	−6.27899	−	25.4749i	−0.252374	−	1.02392i	0.698813	−	0.715305i	$-0.253712\pi$
$620$	−2.89618	−	9.99878i	−0.116313	−	0.401561i
$621$	0.0331494	+	0.162377i	0.00133024	+	0.00651595i
$622$	10.8611	−	8.86785i	0.435492	−	0.355568i
$623$	1.04200	−	8.58168i	0.0417470	−	0.343818i
$624$	14.8274	+	8.87650i	0.593570	+	0.355344i
$625$	0.860284	+	7.08508i	0.0344114	+	0.283403i
$626$	40.4719	+	38.8738i	1.61758	+	1.55371i
$627$	15.6337	−	16.2764i	0.624351	−	0.650018i
$628$	3.76110	−	7.92635i	0.150084	−	0.316296i
$629$	−10.5480	+	7.28074i	−0.420575	+	0.290302i
$630$	0.963750	−	1.52405i	0.0383967	−	0.0607195i
$631$	1.43619	+	1.91122i	0.0571739	+	0.0760846i	0.827124	−	0.562019i	$-0.189975\pi$
$631$	1.43619	+	1.91122i	0.0571739	+	0.0760846i	−0.769950	+	0.638104i	$0.779719\pi$
$632$	−2.26423	−	4.31414i	−0.0900664	−	0.171607i
$633$	−0.909077	+	4.45295i	−0.0361326	+	0.176989i
$634$	3.51695	−	0.283918i	0.139676	−	0.0112758i
$635$	24.0750	+	6.97340i	0.955386	+	0.276731i
$636$	3.00714	+	1.57827i	0.119241	+	0.0625823i
$637$	14.7411	+	17.1797i	0.584065	+	0.680686i
$638$	68.0570	−	35.7191i	2.69440	−	1.41413i
$639$	5.23756	−	1.06926i	0.207195	−	0.0422991i
$640$	7.12438	+	5.35362i	0.281616	+	0.211621i
$641$	0.384581	+	9.54328i	0.0151900	+	0.376937i	0.988848	+	0.148925i	$0.0475814\pi$
$641$	0.384581	+	9.54328i	0.0151900	+	0.376937i	−0.973658	+	0.228012i	$0.926778\pi$
$642$	−15.7593	+	5.97670i	−0.621968	+	0.235881i
$643$	−28.8178	+	8.34717i	−1.13646	+	0.329180i	−0.792541	−	0.609818i	$-0.791242\pi$
$643$	−28.8178	+	8.34717i	−1.13646	+	0.329180i	−0.343921	+	0.938999i	$0.611755\pi$
$644$	−0.200689	−	0.0409711i	−0.00790827	−	0.00161449i
$645$	−1.53328	−	1.73072i	−0.0603728	−	0.0681468i
$646$	15.0375	−	18.4176i	0.591644	−	0.724632i
$647$	−1.62378	+	40.2936i	−0.0638372	+	1.58410i	0.577205	+	0.816599i	$0.304143\pi$
$647$	−1.62378	+	40.2936i	−0.0638372	+	1.58410i	−0.641042	+	0.767506i	$0.721498\pi$
$648$	0.320791	+	0.960886i	0.0126019	+	0.0377472i
$649$	−6.76552	+	5.99372i	−0.265570	+	0.235274i
$650$	−18.7970	+	16.1289i	−0.737281	+	0.632627i
$651$	−3.98317	−	3.52878i	−0.156113	−	0.138304i
$652$	3.04727	−	7.15221i	0.119340	−	0.280102i
$653$	1.69484	−	2.93554i	0.0663241	−	0.114877i	−0.830956	−	0.556337i	$-0.812206\pi$
$653$	1.69484	−	2.93554i	0.0663241	−	0.114877i	0.897281	+	0.441461i	$0.145540\pi$
$654$	10.2922	+	17.8265i	0.402455	+	0.697073i
$655$	16.7509	−	2.03393i	0.654512	−	0.0794721i
$656$	1.63846	+	0.777461i	0.0639713	+	0.0303547i
$657$	−13.0331	+	7.52464i	−0.508468	+	0.293564i
$658$	−16.0781	−	11.0979i	−0.626790	−	0.432642i
$659$	−5.65040	+	2.40741i	−0.220108	+	0.0937794i	−0.499206	−	0.866483i	$-0.666375\pi$
$659$	−5.65040	+	2.40741i	−0.220108	+	0.0937794i	0.279098	+	0.960263i	$0.409965\pi$
$660$	−7.16270	−	1.16405i	−0.278808	−	0.0453106i
$661$	21.5261	−	28.6460i	0.837268	−	1.11420i	−0.154731	−	0.987957i	$-0.549451\pi$
$661$	21.5261	−	28.6460i	0.837268	−	1.11420i	0.991999	−	0.126245i	$-0.0402926\pi$
$662$	1.44900	+	3.82071i	0.0563171	+	0.148496i
$663$	8.92194	−	0.218142i	0.346499	−	0.00847195i
$664$	−4.80004	+	12.6567i	−0.186278	+	0.491174i
$665$	−2.67949	−	4.23727i	−0.103906	−	0.164314i
$666$	8.85448	+	3.77254i	0.343104	+	0.146183i
$667$	1.32628	+	0.838690i	0.0513539	+	0.0324742i
$668$	1.15571	+	0.140329i	0.0447158	+	0.00542948i
$669$	1.27300	+	2.98784i	0.0492169	+	0.115516i
$670$	8.40023	−	25.1618i	0.324529	−	0.972084i
$671$	−10.3588	−	3.92857i	−0.399897	−	0.151661i
$672$	−5.82776	−	0.470466i	−0.224811	−	0.0181486i
$673$	−13.8870	+	47.9435i	−0.535305	+	1.84809i	−0.00547074	+	0.999985i	$0.501741\pi$
$673$	−13.8870	+	47.9435i	−0.535305	+	1.84809i	−0.529834	+	0.848101i	$0.677746\pi$
$674$	−37.0171	−	1.49174i	−1.42585	−	0.0574596i
$675$	−3.69573			−0.142249
$676$	−18.2129	−	5.10581i	−0.700496	−	0.196377i
$677$	16.8874			0.649035			0.324517	−	0.945880i	$-0.394798\pi$
$677$	16.8874			0.649035			0.324517	+	0.945880i	$0.394798\pi$
$678$	21.0183	+	0.847008i	0.807203	+	0.0325292i
$679$	−2.23490	+	7.71576i	−0.0857675	+	0.296104i
$680$	2.85435	+	0.230427i	0.109459	+	0.00883648i
$681$	18.1291	+	6.87547i	0.694709	+	0.263468i
$682$	−16.1032	+	48.2350i	−0.616624	+	1.84701i
$683$	−18.4147	−	43.2209i	−0.704620	−	1.65380i	−0.755542	−	0.655101i	$-0.772626\pi$
$683$	−18.4147	−	43.2209i	−0.704620	−	1.65380i	0.0509220	−	0.998703i	$-0.483784\pi$
$684$	−7.46445	−	0.906349i	−0.285411	−	0.0346551i
$685$	−14.9580	−	9.45888i	−0.571516	−	0.361405i
$686$	−19.2880	−	8.21783i	−0.736418	−	0.313758i
$687$	6.87004	+	10.8641i	0.262108	+	0.414491i
$688$	−3.44107	+	9.07337i	−0.131190	+	0.345919i
$689$	8.21801	+	1.81370i	0.313081	+	0.0690963i
$690$	−0.124751	−	0.328940i	−0.00474917	−	0.0125225i
$691$	−16.3732	+	21.7887i	−0.622864	+	0.828882i	−0.995060	−	0.0992724i	$-0.968348\pi$
$691$	−16.3732	+	21.7887i	−0.622864	+	0.828882i	0.372196	+	0.928154i	$0.378605\pi$
$692$	2.19045	+	0.355983i	0.0832684	+	0.0135324i
$693$	−3.41276	+	1.45404i	−0.129640	+	0.0552344i
$694$	−3.40573	−	2.35081i	−0.129280	−	0.0892354i
$695$	2.91638	−	1.68377i	0.110624	−	0.0638691i
$696$	8.66590	+	4.11202i	0.328480	+	0.155866i
$697$	0.929751	−	0.112892i	0.0352168	−	0.00427610i
$698$	−4.71155	−	8.16065i	−0.178335	−	0.308885i
$699$	3.19311	−	5.53064i	0.120775	−	0.209188i
$700$	1.79040	−	4.20223i	0.0676709	−	0.158829i
$701$	32.6795	+	28.9515i	1.23429	+	1.09348i	0.992384	+	0.123183i	$0.0393102\pi$
$701$	32.6795	+	28.9515i	1.23429	+	1.09348i	0.241904	+	0.970300i	$0.422228\pi$
$702$	−3.71930	−	5.57511i	−0.140376	−	0.210419i
$703$	20.0295	−	17.7446i	0.755428	−	0.669251i
$704$	4.43619	+	13.2880i	0.167195	+	0.500811i
$705$	0.568989	−	14.1193i	0.0214293	−	0.531764i
$706$	25.7643	−	31.5555i	0.969652	−	1.18761i
$707$	9.06628	+	10.2337i	0.340972	+	0.384878i
$708$	2.95060	+	0.602369i	0.110890	+	0.0226384i
$709$	−13.3675	+	3.87195i	−0.502028	+	0.145414i	−0.519563	−	0.854432i	$-0.673905\pi$
$709$	−13.3675	+	3.87195i	−0.502028	+	0.145414i	0.0175354	+	0.999846i	$0.494418\pi$
$710$	−10.6102	+	4.02391i	−0.398192	+	0.151014i
$711$	0.193663	+	4.80570i	0.00726294	+	0.180228i
$712$	−8.24173	−	6.19326i	−0.308872	−	0.232102i
$713$	−1.01723	+	0.207668i	−0.0380954	+	0.00777724i
$714$	−3.46055	+	1.81624i	−0.129508	+	0.0679710i
$715$	−17.8833	+	1.88465i	−0.668796	+	0.0704820i
$716$	−31.1270	−	16.3367i	−1.16327	−	0.610531i
$717$	−8.23510	−	2.38533i	−0.307546	−	0.0890817i
$718$	11.1435	−	0.899597i	0.415872	−	0.0335727i
$719$	9.38772	−	45.9841i	0.350103	−	1.71492i	−0.299031	−	0.954243i	$-0.596664\pi$
$719$	9.38772	−	45.9841i	0.350103	−	1.71492i	0.649134	−	0.760674i	$-0.275131\pi$
$720$	−2.54380	−	4.84680i	−0.0948017	−	0.180630i
$721$	−4.89495	−	6.51400i	−0.182298	−	0.242594i
$722$	−7.65643	+	12.1077i	−0.284943	+	0.450601i
$723$	24.9818	−	17.2437i	0.929083	−	0.641300i
$724$	8.44207	−	17.7913i	0.313747	−	0.661208i
$725$	−24.2411	+	25.2377i	−0.900292	+	0.937304i
$726$	10.8199	+	10.3927i	0.401565	+	0.385709i
$727$	1.36972	+	11.2807i	0.0508001	+	0.418377i	0.995818	+	0.0913584i	$0.0291209\pi$
$727$	1.36972	+	11.2807i	0.0508001	+	0.418377i	−0.945018	+	0.327019i	$0.893956\pi$
$728$	−3.04935	+	0.572398i	−0.113016	+	0.0212145i
$729$	0.120537	−	0.992709i	0.00446432	−	0.0367670i
$730$	24.7459	−	20.2044i	0.915887	−	0.747799i
$731$	1.00241	+	4.91015i	0.0370756	+	0.181609i
$732$	1.02695	+	3.54544i	0.0379571	+	0.131043i
$733$	−1.28478	−	5.21255i	−0.0474544	−	0.192530i	0.942431	−	0.334402i	$-0.108534\pi$
$733$	−1.28478	−	5.21255i	−0.0474544	−	0.192530i	−0.989885	+	0.141871i	$0.954688\pi$
$734$	2.32684	−	28.8231i	0.0858852	−	1.06388i
$735$	−1.15019	−	7.07740i	−0.0424254	−	0.261054i
$736$	−0.756414	+	0.853815i	−0.0278818	+	0.0314720i
$737$	−43.6272	+	32.7837i	−1.60703	+	1.20760i
$738$	−0.444810	−	0.544794i	−0.0163737	−	0.0200541i
$739$	3.79718	−	23.3650i	0.139681	−	0.859494i	−0.818746	−	0.574156i	$-0.805330\pi$
$739$	3.79718	−	23.3650i	0.139681	−	0.859494i	0.958427	−	0.285338i	$-0.0921058\pi$
$740$	−8.35413	−	2.05911i	−0.307104	−	0.0756943i
$741$	−18.4368	+	2.69742i	−0.677291	+	0.0990921i
$742$	−3.57830	+	0.881971i	−0.131363	+	0.0323782i
$743$	−0.790138	−	9.78761i	−0.0289873	−	0.359073i	−0.994949	−	0.100386i	$-0.967992\pi$
$743$	−0.790138	−	9.78761i	−0.0289873	−	0.359073i	0.965961	−	0.258687i	$-0.0832898\pi$
$744$	−6.01958	+	2.00963i	−0.220688	+	0.0736766i
$745$	−10.0415	−	10.4544i	−0.367894	−	0.383018i
$746$		−	26.8053i		−	0.981414i
$747$	9.63694	−	9.25641i	0.352597	−	0.338674i
$748$	12.1829	+	9.94705i	0.445452	+	0.363700i
$749$	3.57951	−	6.82019i	0.130792	−	0.249204i
$750$	18.2202	−	2.96107i	0.665307	−	0.108123i
$751$	19.0191	−	12.0269i	0.694016	−	0.438869i	−0.140334	−	0.990104i	$-0.544818\pi$
$751$	19.0191	−	12.0269i	0.694016	−	0.438869i	0.834350	+	0.551235i	$0.185843\pi$
$752$	−53.5786	+	25.4234i	−1.95381	+	0.927095i
$753$	−9.83072	+	14.2423i	−0.358251	+	0.519017i
$754$	−62.4674	−	11.1697i	−2.27493	−	0.406777i
$755$	6.23704	+	9.03591i	0.226989	+	0.328850i
$756$	1.07036	+	0.617975i	0.0389288	+	0.0224755i
$757$	−8.63287	−	18.1934i	−0.313767	−	0.661250i	0.683896	−	0.729580i	$-0.260284\pi$
$757$	−8.63287	−	18.1934i	−0.313767	−	0.661250i	−0.997663	+	0.0683296i	$0.978233\pi$
$758$	−26.5361	−	8.85904i	−0.963833	−	0.321775i
$759$	−0.173201	+	0.702706i	−0.00628681	+	0.0255066i
$760$	−5.97394	+	0.240741i	−0.216697	+	0.00873261i
$761$	45.5758	−	1.83664i	1.65212	−	0.0665782i	0.803407	−	0.595430i	$-0.203018\pi$
$761$	45.5758	−	1.83664i	1.65212	−	0.0665782i	0.848714	+	0.528852i	$0.177377\pi$
$762$	−9.76275	+	39.6091i	−0.353667	+	1.43488i
$763$	−8.92284	−	2.97888i	−0.323028	−	0.107843i
$764$	−5.55196	−	11.7005i	−0.200863	−	0.423309i
$765$	−2.44811	−	1.41342i	−0.0885116	−	0.0511022i
$766$	20.8799	+	30.2497i	0.754420	+	1.09297i
$767$	7.44688	−	0.482652i	0.268891	−	0.0174275i
$768$	−11.8840	+	17.2170i	−0.428827	+	0.621263i
$769$	13.9060	−	6.59849i	0.501464	−	0.237948i	−0.161121	−	0.986935i	$-0.551511\pi$
$769$	13.9060	−	6.59849i	0.501464	−	0.237948i	0.662585	+	0.748987i	$0.269460\pi$
$770$	6.65562	−	4.20876i	0.239852	−	0.151673i
$771$	−22.3460	+	3.63158i	−0.804772	+	0.130788i
$772$	14.1694	−	26.9976i	0.509969	−	0.971665i
$773$	32.5603	+	26.5847i	1.17111	+	0.956184i	0.999580	−	0.0289946i	$-0.00923057\pi$
$773$	32.5603	+	26.5847i	1.17111	+	0.956184i	0.171533	+	0.985178i	$0.445128\pi$
$774$	2.71410	−	2.60693i	0.0975563	−	0.0937041i
$775$		−	23.1523i		−	0.831656i
$776$	6.63612	+	6.90893i	0.238223	+	0.248016i
$777$	−4.17207	+	1.39284i	−0.149672	+	0.0499679i
$778$	3.84114	+	47.5811i	0.137712	+	1.70586i
$779$	−1.89860	+	0.467962i	−0.0680243	+	0.0167665i
$780$	4.08137	+	4.38608i	0.146137	+	0.157047i
$781$	22.6662	+	5.58672i	0.811061	+	0.199909i
$782$	−0.122311	+	0.752612i	−0.00437384	+	0.0269133i
$783$	−5.98845	−	7.33452i	−0.214010	−	0.262114i
$784$	−24.0571	+	18.0778i	−0.859183	+	0.645634i
$785$	−4.56648	+	5.15449i	−0.162985	+	0.183972i
$786$	4.40547	+	27.1079i	0.157138	+	0.966908i
$787$	−3.77746	+	46.7923i	−0.134652	+	1.66796i	0.478567	+	0.878051i	$0.341156\pi$
$787$	−3.77746	+	46.7923i	−0.134652	+	1.66796i	−0.613219	+	0.789913i	$0.710126\pi$
$788$	1.98806	+	8.06589i	0.0708218	+	0.287336i
$789$	−1.77063	−	6.11292i	−0.0630361	−	0.217626i
$790$	−2.04222	−	10.0035i	−0.0726589	−	0.355907i
$791$	−7.44634	+	6.07975i	−0.264761	+	0.216171i
$792$	−0.533245	+	4.39167i	−0.0189480	+	0.156051i
$793$	4.76568	+	7.80725i	0.169234	+	0.277244i
$794$	5.92328	+	48.7826i	0.210209	+	1.73123i
$795$	−1.92248	−	1.84657i	−0.0681834	−	0.0654911i
$796$	−4.67209	+	4.86416i	−0.165598	+	0.172406i
$797$	19.5288	−	41.1560i	0.691745	−	1.45782i	−0.187899	−	0.982188i	$-0.560168\pi$
$797$	19.5288	−	41.1560i	0.691745	−	1.45782i	0.879644	−	0.475633i	$-0.157781\pi$
$798$	6.71529	−	4.63523i	0.237719	−	0.164085i
$799$	−16.3689	+	25.8854i	−0.579090	+	0.915758i
$800$	−15.2814	−	20.3359i	−0.540281	−	0.718983i
$801$	4.72942	+	9.01115i	0.167106	+	0.318393i
$802$	−7.42477	+	36.3689i	−0.262178	+	1.28423i
$803$	−65.5081	+	5.28836i	−2.31173	+	0.186622i
$804$	17.4642	+	5.05857i	0.615916	+	0.178402i
$805$	0.142357	+	0.0747145i	0.00501741	+	0.00263334i
$806$	34.9259	−	23.3000i	1.23021	−	0.820707i
$807$	−0.990747	+	0.519984i	−0.0348760	+	0.0183043i
$808$	15.9753	−	3.26138i	0.562009	−	0.114735i
$809$	−0.0700679	−	0.0526526i	−0.00246346	−	0.00185117i	0.599510	−	0.800367i	$-0.295362\pi$
$809$	−0.0700679	−	0.0526526i	−0.00246346	−	0.00185117i	−0.601973	+	0.798516i	$0.705619\pi$
$810$	0.0854762	+	2.12107i	0.00300333	+	0.0745268i
$811$	−4.46797	+	1.69448i	−0.156892	+	0.0595011i	−0.431800	−	0.901969i	$-0.642122\pi$
$811$	−4.46797	+	1.69448i	−0.156892	+	0.0595011i	0.274909	+	0.961470i	$0.411352\pi$
$812$	11.2408	−	3.25594i	0.394476	−	0.114261i
$813$	−3.63932	−	0.742973i	−0.127637	−	0.0260572i
$814$	27.8720	+	31.4610i	0.976915	+	1.10271i
$815$	−3.85926	+	4.72674i	−0.135184	+	0.165570i
$816$	−0.477705	+	11.8541i	−0.0167230	+	0.414978i
$817$	−3.31330	−	9.92454i	−0.115918	−	0.347216i
$818$	37.6573	−	33.3614i	1.31666	−	1.16646i
$819$	2.96176	+	0.779944i	0.103492	+	0.0272535i
$820$	0.470623	+	0.416935i	0.0164349	+	0.0145600i
$821$	−3.11378	+	7.30831i	−0.108672	+	0.255062i	−0.965433	−	0.260651i	$-0.916063\pi$
$821$	−3.11378	+	7.30831i	−0.108672	+	0.255062i	0.856761	+	0.515713i	$0.172473\pi$
$822$	14.4023	−	24.9455i	0.502337	−	0.870073i
$823$	−21.3361	−	36.9553i	−0.743731	−	1.28818i	−0.950785	−	0.309851i	$-0.899721\pi$
$823$	−21.3361	−	36.9553i	−0.743731	−	1.28818i	0.207054	−	0.978329i	$-0.433612\pi$
$824$	−9.64635	+	1.17128i	−0.336047	+	0.0408034i
$825$	−14.5813	−	6.91889i	−0.507654	−	0.240885i
$826$	−2.83012	+	1.63397i	−0.0984724	+	0.0568531i
$827$	25.1825	+	17.3822i	0.875681	+	0.604439i	0.918840	−	0.394630i	$-0.129127\pi$
$827$	25.1825	+	17.3822i	0.875681	+	0.604439i	−0.0431597	+	0.999068i	$0.513742\pi$
$828$	0.221836	−	0.0945156i	0.00770934	−	0.00328464i
$829$	−32.5371	−	5.28780i	−1.13006	−	0.183653i	−0.433503	−	0.901152i	$-0.642722\pi$
$829$	−32.5371	−	5.28780i	−1.13006	−	0.183653i	−0.696559	+	0.717499i	$0.745287\pi$
$830$	−17.0403	+	22.6765i	−0.591478	+	0.787114i
$831$	10.0930	+	26.6131i	0.350122	+	0.923197i
$832$	3.83584	−	10.9115i	0.132984	−	0.378289i
$833$	−5.51079	+	14.5307i	−0.190937	+	0.503461i
$834$	2.92937	+	4.63243i	0.101436	+	0.160408i
$835$	−0.840667	−	0.358175i	−0.0290925	−	0.0123951i
$836$	−27.7537	−	17.5504i	−0.959881	−	0.606992i
$837$	6.21894	+	0.755115i	0.214958	+	0.0261006i
$838$	−5.70128	−	13.3814i	−0.196947	−	0.462252i
$839$	17.0708	−	51.1334i	0.589351	−	1.76532i	−0.0526444	−	0.998613i	$-0.516765\pi$
$839$	17.0708	−	51.1334i	0.589351	−	1.76532i	0.641995	−	0.766708i	$-0.278107\pi$
$840$	0.918876	+	0.348484i	0.0317042	+	0.0120238i
$841$	−60.4600	−	4.88084i	−2.08483	−	0.168305i
$842$	3.69181	−	12.7456i	0.127228	−	0.439243i
$843$	−4.66837	−	0.188129i	−0.160787	−	0.00647951i
$844$	6.61270			0.227619
$845$	12.6161	+	7.82661i	0.434006	+	0.269244i
$846$	22.9989			0.790718
$847$	−6.85059	−	0.276069i	−0.235389	−	0.00948585i
$848$	−3.11251	+	10.7456i	−0.106884	+	0.369007i
$849$	−10.2719	−	0.829237i	−0.352532	−	0.0284593i
$850$	−15.8987	−	6.02958i	−0.545320	−	0.206813i
$851$	−0.271741	+	0.813963i	−0.00931516	+	0.0279023i
$852$	−3.04866	−	7.15547i	−0.104445	−	0.245142i
$853$	32.4827	+	3.94411i	1.11219	+	0.135044i	0.655942	−	0.754811i	$-0.272272\pi$
$853$	32.4827	+	3.94411i	1.11219	+	0.135044i	0.456243	+	0.889855i	$0.349195\pi$
$854$	−3.38544	−	2.14082i	−0.115847	−	0.0732575i
$855$	5.42967	+	2.31337i	0.185691	+	0.0791154i
$856$	−4.90942	−	7.76362i	−0.167800	−	0.265355i
$857$	−6.70981	+	17.6923i	−0.229203	+	0.604358i	−0.999442	−	0.0333970i	$-0.989367\pi$
$857$	−6.70981	+	17.6923i	−0.229203	+	0.604358i	0.770239	+	0.637755i	$0.220137\pi$
$858$	−4.23692	−	28.9592i	−0.144646	−	0.988652i
$859$	0.0692497	+	0.182596i	0.00236277	+	0.00623011i	0.936192	−	0.351488i	$-0.114324\pi$
$859$	0.0692497	+	0.182596i	0.00236277	+	0.00623011i	−0.933830	+	0.357718i	$0.883555\pi$
$860$	−2.02106	+	2.68955i	−0.0689177	+	0.0917128i
$861$	0.317252	+	0.0515584i	0.0108119	+	0.00175711i
$862$	−0.869929	+	0.370642i	−0.0296299	+	0.0126241i
$863$	−12.6463	−	8.72910i	−0.430484	−	0.297142i	0.333050	−	0.942909i	$-0.391922\pi$
$863$	−12.6463	−	8.72910i	−0.430484	−	0.297142i	−0.763534	+	0.645767i	$0.776538\pi$
$864$	5.96082	−	3.44148i	0.202791	−	0.117082i
$865$	−1.57368	−	0.746722i	−0.0535069	−	0.0253893i
$866$	45.0895	−	5.47486i	1.53220	−	0.186043i
$867$	−5.43660	−	9.41646i	−0.184636	−	0.319800i
$868$	−3.87137	+	6.70542i	−0.131403	+	0.227597i
$869$	−8.23281	+	19.3231i	−0.279279	+	0.655492i
$870$	15.0452	+	13.3289i	0.510079	+	0.451890i
$871$	45.0502	+	0.713276i	1.52647	+	0.0241684i
$872$	−8.39707	+	7.43916i	−0.284361	+	0.251922i
$873$	−2.99461	−	8.96995i	−0.101352	−	0.303587i
$874$	0.0641009	−	1.59065i	0.00216825	−	0.0538045i
$875$	−5.33518	+	6.53441i	−0.180362	+	0.220903i
$876$	14.5202	+	16.3900i	0.490593	+	0.553765i
$877$	−14.7422	−	3.00965i	−0.497809	−	0.101629i	−0.0554411	−	0.998462i	$-0.517656\pi$
$877$	−14.7422	−	3.00965i	−0.497809	−	0.101629i	−0.442368	+	0.896833i	$0.645862\pi$
$878$	15.1800	−	4.39694i	0.512301	−	0.148390i
$879$	−6.64804	+	2.52127i	−0.224233	+	0.0850402i
$880$	−0.962534	−	23.8850i	−0.0324470	−	0.805164i
$881$	35.5029	+	26.6787i	1.19612	+	0.898829i	0.996707	−	0.0810860i	$-0.0258388\pi$
$881$	35.5029	+	26.6787i	1.19612	+	0.898829i	0.199417	+	0.979915i	$0.436095\pi$
$882$	11.4343	−	2.33433i	0.385013	−	0.0786009i
$883$	−2.31193	+	1.21339i	−0.0778026	+	0.0408339i	−0.503176	−	0.864184i	$-0.667835\pi$
$883$	−2.31193	+	1.21339i	−0.0778026	+	0.0408339i	0.425373	+	0.905018i	$0.360143\pi$
$884$	−2.90761	−	12.6556i	−0.0977934	−	0.425654i
$885$	−2.09297	−	1.09848i	−0.0703544	−	0.0369248i
$886$	−4.07942	−	1.18162i	−0.137051	−	0.0396973i
$887$	−11.9326	+	0.963300i	−0.400658	+	0.0323445i	−0.279154	−	0.960246i	$-0.590054\pi$
$887$	−11.9326	+	0.963300i	−0.400658	+	0.0323445i	−0.121504	+	0.992591i	$0.538772\pi$
$888$	−1.04921	+	5.13939i	−0.0352093	+	0.172467i
$889$	−8.66380	−	16.5075i	−0.290574	−	0.553643i
$890$	−12.9780	−	17.2706i	−0.435025	−	0.578913i
$891$	2.33405	−	3.69100i	0.0781936	−	0.123653i
$892$	3.88896	−	2.68436i	0.130212	−	0.0898790i
$893$	27.4120	−	57.7695i	0.917307	−	1.93318i
$894$	16.3434	−	17.0153i	0.546604	−	0.569075i
$895$	19.8997	+	19.1139i	0.665173	+	0.638907i
$896$	−0.798974	−	6.58014i	−0.0266919	−	0.219827i
$897$	0.468777	−	0.370532i	0.0156520	−	0.0123717i
$898$	6.28553	−	51.7660i	0.209751	−	1.72745i
$899$	45.9479	−	37.5153i	1.53245	−	1.25121i
$900$	1.07560	+	5.26863i	0.0358533	+	0.175621i
$901$	1.60740	+	5.54938i	0.0535502	+	0.184877i
$902$	−0.735044	−	2.98219i	−0.0244743	−	0.0992960i
$903$	−0.138388	+	1.71424i	−0.00460525	+	0.0570462i
$904$	1.83899	+	11.3157i	0.0611637	+	0.376356i
$905$	−10.2498	+	11.5697i	−0.340715	+	0.384588i
$906$	−14.2859	+	10.7352i	−0.474619	+	0.356653i
$907$	14.8938	+	18.2416i	0.494542	+	0.605704i	0.960218	−	0.279251i	$-0.0900863\pi$
$907$	14.8938	+	18.2416i	0.494542	+	0.605704i	−0.465676	+	0.884955i	$0.654189\pi$
$908$	4.52540	−	27.8459i	0.150181	−	0.924098i
$909$	−15.6276	−	3.85185i	−0.518334	−	0.127758i
$910$	−6.47136	−	0.625682i	−0.214524	−	0.0207412i
$911$	−25.1373	+	6.19578i	−0.832835	+	0.205275i	−0.632606	−	0.774474i	$-0.718015\pi$
$911$	−25.1373	+	6.19578i	−0.832835	+	0.205275i	−0.200229	+	0.979749i	$0.564169\pi$
$912$	−1.99312	−	24.6892i	−0.0659986	−	0.817540i
$913$	55.3511	−	18.4789i	1.83185	−	0.611563i
$914$	−31.7222	−	33.0263i	−1.04928	−	1.09241i
$915$		−	2.89723i		−	0.0957795i
$916$	13.4884	−	12.9558i	0.445669	−	0.428071i
$917$	−9.72188	−	7.93767i	−0.321045	−	0.262125i
$918$	2.13814	−	4.07388i	0.0705691	−	0.134458i
$919$	5.07440	−	0.824670i	0.167389	−	0.0272034i	−0.0761391	−	0.997097i	$-0.524259\pi$
$919$	5.07440	−	0.824670i	0.167389	−	0.0272034i	0.243528	+	0.969894i	$0.421695\pi$
$920$	0.162049	−	0.102473i	0.00534259	−	0.00337845i
$921$	−26.1798	+	12.4225i	−0.862654	+	0.409334i
$922$	−39.2504	+	56.8641i	−1.29264	+	1.87272i
$923$	−11.9517	−	15.1207i	−0.393397	−	0.497703i
$924$	3.06612	+	4.44204i	0.100868	+	0.146132i
$925$	−16.5727	−	9.56822i	−0.544905	−	0.314601i
$926$	10.9794	+	23.1386i	0.360806	+	0.760382i
$927$	9.09866	+	3.03758i	0.298839	+	0.0997672i
$928$	15.5969	−	63.2791i	0.511993	−	2.07724i
$929$	9.94652	−	0.400831i	0.326335	−	0.0131508i	0.123442	−	0.992352i	$-0.460607\pi$
$929$	9.94652	−	0.400831i	0.326335	−	0.0131508i	0.202893	+	0.979201i	$0.434966\pi$
$930$	−13.2877	+	0.535475i	−0.435720	+	0.0175589i
$931$	7.76488	−	31.5034i	0.254484	−	1.03248i
$932$	−8.81379	−	2.94247i	−0.288705	−	0.0963839i
$933$	−3.23383	−	6.81515i	−0.105871	−	0.223118i
$934$	39.2472	+	22.6594i	1.28421	+	0.741438i
$935$	−7.01275	−	10.1597i	−0.229341	−	0.332258i
$936$	2.57156	−	2.59380i	0.0840539	−	0.0847811i
$937$	11.7557	−	17.0311i	0.384042	−	0.556381i	−0.582519	−	0.812817i	$-0.697933\pi$
$937$	11.7557	−	17.0311i	0.384042	−	0.556381i	0.966561	+	0.256436i	$0.0825483\pi$
$938$	−17.8256	+	8.45837i	−0.582028	+	0.276176i
$939$	25.5168	−	16.1359i	0.832710	−	0.526574i
$940$	−20.2941	+	3.29811i	−0.661919	+	0.107572i
$941$	6.40676	−	12.2071i	0.208855	−	0.397939i	−0.758384	−	0.651808i	$-0.774011\pi$
$941$	6.40676	−	12.2071i	0.208855	−	0.397939i	0.967239	+	0.253869i	$0.0817032\pi$
$942$	−8.68179	−	7.08846i	−0.282868	−	0.230955i
$943$	0.0452246	−	0.0434389i	0.00147272	−	0.00141456i
$944$			9.92014i			0.322873i
$945$	−0.672017	−	0.699644i	−0.0218607	−	0.0227594i
$946$	15.5888	−	5.20431i	0.506836	−	0.169207i
$947$	−2.45215	−	30.3753i	−0.0796841	−	0.987065i	−0.905839	−	0.423622i	$-0.860759\pi$
$947$	−2.45215	−	30.3753i	−0.0796841	−	0.987065i	0.826155	−	0.563443i	$-0.190523\pi$
$948$	6.79464	−	1.67473i	0.220680	−	0.0543926i
$949$	45.3960	+	29.7230i	1.47362	+	0.964849i
$950$	34.4691	+	8.49588i	1.11833	+	0.275643i
$951$	0.304500	−	1.87366i	0.00987410	−	0.0607577i
$952$	−1.34708	−	1.64988i	−0.0436593	−	0.0534729i
$953$	−10.5957	+	7.96215i	−0.343228	+	0.257919i	−0.758352	−	0.651846i	$-0.773995\pi$
$953$	−10.5957	+	7.96215i	−0.343228	+	0.257919i	0.415123	+	0.909765i	$0.363739\pi$
$954$	2.87700	−	3.24746i	0.0931464	−	0.105141i
$955$	1.63062	+	10.0336i	0.0527658	+	0.324681i
$956$	−1.00379	+	12.4342i	−0.0324649	+	0.402150i
$957$	−9.89584	−	40.1490i	−0.319887	−	1.29783i
$958$	7.31331	+	25.2485i	0.236282	+	0.815741i
$959$	2.63305	+	12.8975i	0.0850257	+	0.416483i
$960$	−2.83778	+	2.31698i	−0.0915891	+	0.0747802i
$961$	−0.993868	+	8.18524i	−0.0320603	+	0.264040i
$962$	−2.24443	−	34.6295i	−0.0723633	−	1.11650i
$963$	1.09298	+	9.00149i	0.0352207	+	0.290069i
$964$	−31.8533	−	30.5955i	−1.02592	−	0.985414i
$965$	−16.5782	+	17.2597i	−0.533671	+	0.555611i
$966$	−0.112175	+	0.236405i	−0.00360918	+	0.00760619i
$967$	8.68057	−	5.99176i	0.279148	−	0.192682i	−0.420262	−	0.907403i	$-0.638062\pi$
$967$	8.68057	−	5.99176i	0.279148	−	0.192682i	0.699410	+	0.714721i	$0.253446\pi$
$968$	−4.37000	+	6.91059i	−0.140457	+	0.222115i
$969$	−7.68453	−	10.2263i	−0.246863	−	0.328515i
$970$	9.32906	+	17.7750i	0.299538	+	0.570722i
$971$	−2.35924	+	11.5563i	−0.0757115	+	0.370860i	−0.999940	−	0.0109810i	$-0.996505\pi$
$971$	−2.35924	+	11.5563i	−0.0757115	+	0.370860i	0.924228	+	0.381841i	$0.124710\pi$
$972$	−1.45029	+	0.117079i	−0.0465179	+	0.00375532i
$973$	−2.40587	−	0.696869i	−0.0771287	−	0.0223406i
$974$	−24.7187	−	12.9734i	−0.792040	−	0.415694i
$975$	6.00495	+	11.8954i	0.192312	+	0.380958i
$976$	−10.7664	+	5.65066i	−0.344625	+	0.180873i
$977$	−28.7437	+	5.86806i	−0.919591	+	0.187736i	−0.636428	−	0.771336i	$-0.719589\pi$
$977$	−28.7437	+	5.86806i	−0.919591	+	0.187736i	−0.283163	+	0.959072i	$0.591384\pi$
$978$	−7.93980	−	5.96637i	−0.253887	−	0.190784i
$979$	1.78954	+	44.4070i	0.0571939	+	1.41925i
$980$	−9.75479	+	3.69950i	−0.311605	+	0.118176i
$981$	10.6370	−	3.08103i	0.339612	−	0.0983698i
$982$	−7.43591	−	1.51805i	−0.237289	−	0.0484430i
$983$	37.5092	+	42.3392i	1.19636	+	1.35041i	0.921237	+	0.389001i	$0.127180\pi$
$983$	37.5092	+	42.3392i	1.19636	+	1.35041i	0.275121	+	0.961409i	$0.411282\pi$
$984$	0.242420	−	0.296911i	0.00772807	−	0.00946516i
$985$	0.262552	−	6.51517i	0.00836562	−	0.207591i
$986$	−13.7955	−	41.3225i	−0.439338	−	1.31598i
$987$	−7.86715	+	6.96969i	−0.250414	+	0.221848i
$988$	9.21124	+	25.4984i	0.293048	+	0.811211i
$989$	0.251150	+	0.222499i	0.00798610	+	0.00707506i
$990$	−3.63368	+	8.52856i	−0.115486	+	0.271055i
$991$	6.48423	−	11.2310i	0.205978	−	0.356765i	−0.744466	−	0.667661i	$-0.767296\pi$
$991$	6.48423	−	11.2310i	0.205978	−	0.356765i	0.950444	+	0.310896i	$0.100629\pi$
$992$	21.5595	+	37.3422i	0.684516	+	1.18562i
$993$	2.18234	−	0.264984i	0.0692545	−	0.00840901i
$994$	7.62538	+	3.61829i	0.241862	+	0.114765i
$995$	4.58459	−	2.64692i	0.145341	−	0.0839129i
$996$	−16.0006	−	11.0444i	−0.507000	−	0.349957i
$997$	−4.39598	+	1.87295i	−0.139222	+	0.0593170i	−0.460454	−	0.887684i	$-0.652313\pi$
$997$	−4.39598	+	1.87295i	−0.139222	+	0.0593170i	0.321232	+	0.947001i	$0.395903\pi$
$998$	−59.4220	−	9.65701i	−1.88097	−	0.305687i
$999$	3.11063	−	4.13950i	0.0984161	−	0.130968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.4.3	✓	360
169.127	even	78	inner	507.2.t.b.127.3	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.4.3	✓	360	1.1	even	1	trivial
507.2.t.b.127.3	yes	360	169.127	even	78	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85726 - 0.0748449i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(1.45029 + 0.117079i) q^{4} +(-1.06783 - 0.404975i) q^{5} +(0.588611 - 1.76311i) q^{6} +(0.332955 + 0.781475i) q^{7} +(1.00563 + 0.122106i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})\)	\(q+(-1.85726 - 0.0748449i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(1.45029 + 0.117079i) q^{4} +(-1.06783 - 0.404975i) q^{5} +(0.588611 - 1.76311i) q^{6} +(0.332955 + 0.781475i) q^{7} +(1.00563 + 0.122106i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(1.95292 + 0.832063i) q^{10} +(-2.33405 - 3.69100i) q^{11} +(-0.515951 + 1.36045i) q^{12} +(-0.346984 + 3.58882i) q^{13} +(-0.559894 - 1.47632i) q^{14} +(0.686075 - 0.912999i) q^{15} +(-4.73090 - 0.768847i) q^{16} +(-2.27717 + 0.970211i) q^{17} +(1.52973 + 1.05590i) q^{18} +(4.47551 - 2.58394i) q^{19} +(-1.50124 - 0.712350i) q^{20} +(-0.843255 + 0.102390i) q^{21} +(4.05868 + 7.02983i) q^{22} +(-0.0828629 + 0.143523i) q^{23} +(-0.397070 + 0.931957i) q^{24} +(-2.76630 - 2.45072i) q^{25} +(0.913043 - 6.63938i) q^{26} +(0.748511 - 0.663123i) q^{27} +(0.391386 + 1.17234i) q^{28} +(0.381267 - 9.46104i) q^{29} +(-1.34255 + 1.64433i) q^{30} +(4.15421 + 4.68913i) q^{31} +(6.74386 + 1.37677i) q^{32} +(4.19465 - 1.21499i) q^{33} +(4.30190 - 1.63150i) q^{34} +(-0.0390623 - 0.969321i) q^{35} +(-1.16319 - 0.874082i) q^{36} +(5.07334 - 1.03573i) q^{37} +(-8.50557 + 4.46407i) q^{38} +(-3.35059 - 1.33176i) q^{39} +(-1.02440 - 0.537645i) q^{40} +(-0.363440 - 0.105272i) q^{41} +(1.57380 - 0.127051i) q^{42} +(0.404977 - 1.98371i) q^{43} +(-2.95290 - 5.62628i) q^{44} +(0.686075 + 0.912999i) q^{45} +(0.164640 - 0.260357i) q^{46} +(10.1830 - 7.02879i) q^{47} +(2.05471 - 4.33021i) q^{48} +(4.34923 - 4.52802i) q^{49} +(4.95430 + 4.75867i) q^{50} +(-0.298357 - 2.45719i) q^{51} +(-0.923402 + 5.16418i) q^{52} +(0.281346 - 2.31710i) q^{53} +(-1.43981 + 1.17557i) q^{54} +(0.997606 + 4.88660i) q^{55} +(0.239408 + 0.826533i) q^{56} +(1.23675 + 5.01771i) q^{57} +(-1.41622 + 17.5431i) q^{58} +(-0.332007 - 2.04292i) q^{59} +(1.10190 - 1.24378i) q^{60} +(2.02809 - 1.52401i) q^{61} +(-7.36447 - 9.01984i) q^{62} +(0.136261 - 0.838448i) q^{63} +(-3.11465 - 0.767692i) q^{64} +(1.82390 - 3.69173i) q^{65} +(-7.88148 + 1.94261i) q^{66} +(-1.00553 - 12.4557i) q^{67} +(-3.41614 + 1.14047i) q^{68} +(-0.114802 - 0.119522i) q^{69} +1.80320i q^{70} +(-3.85525 + 3.70302i) q^{71} +(-0.784690 - 0.640679i) q^{72} +(6.99375 - 13.3255i) q^{73} +(-9.50001 + 1.54390i) q^{74} +(3.12360 - 1.97524i) q^{75} +(6.79330 - 3.22346i) q^{76} +(2.10729 - 3.05294i) q^{77} +(6.12322 + 2.72419i) q^{78} +(-2.73217 - 3.95822i) q^{79} +(4.74044 + 2.73689i) q^{80} +(0.428693 + 0.903450i) q^{81} +(0.667123 + 0.222718i) q^{82} +(-3.19781 + 12.9740i) q^{83} +(-1.23495 + 0.0497667i) q^{84} +(2.82454 - 0.113825i) q^{85} +(-0.900616 + 3.65394i) q^{86} +(8.98143 + 2.99844i) q^{87} +(-1.89650 - 3.99680i) q^{88} +(-8.81341 - 5.08842i) q^{89} +(-1.20588 - 1.74702i) q^{90} +(-2.92010 + 0.923756i) q^{91} +(-0.136978 + 0.198448i) q^{92} +(-5.65977 + 2.68559i) q^{93} +(-19.4384 + 12.2921i) q^{94} +(-5.82552 + 0.946739i) q^{95} +(-3.19867 + 6.09456i) q^{96} +(7.32515 + 5.98080i) q^{97} +(-8.41653 + 8.08419i) q^{98} +4.36707i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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