LMFDB - Embedded newform 507.2.t.b.355.3

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			355.3
Character	$\chi$	$=$	507.355
Dual form			507.2.t.b.10.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83778 + 0.375186i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(1.39672 - 0.595086i) q^{4} +(-0.959864 - 3.89432i) q^{5} +(1.87417 - 0.0755263i) q^{6} +(1.09680 + 0.520440i) q^{7} +(0.743728 - 0.513358i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})$	\(q+(-1.83778 + 0.375186i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(1.39672 - 0.595086i) q^{4} +(-0.959864 - 3.89432i) q^{5} +(1.87417 - 0.0755263i) q^{6} +(1.09680 + 0.520440i) q^{7} +(0.743728 - 0.513358i) q^{8} +(0.948536 + 0.316668i) q^{9} +(3.22511 + 6.79678i) q^{10} +(0.488729 + 1.46392i) q^{11} +(-1.47409 + 0.363330i) q^{12} +(3.18414 - 1.69153i) q^{13} +(-2.21095 - 0.544950i) q^{14} +(0.322741 + 3.99786i) q^{15} +(-3.27760 + 3.41234i) q^{16} +(2.51381 - 5.29775i) q^{17} +(-1.86201 - 0.226089i) q^{18} +(0.135744 - 0.0783717i) q^{19} +(-3.65811 - 4.86806i) q^{20} +(-0.999117 - 0.689641i) q^{21} +(-1.44742 - 2.50700i) q^{22} +(-2.62322 + 4.54356i) q^{23} +(-0.816446 + 0.387408i) q^{24} +(-9.81711 + 5.15242i) q^{25} +(-5.21711 + 4.30330i) q^{26} +(-0.885456 - 0.464723i) q^{27} +(1.84163 + 0.0742153i) q^{28} +(-1.00384 - 4.91712i) q^{29} +(-2.09307 - 7.22611i) q^{30} +(2.75520 - 5.24959i) q^{31} +(3.77726 - 5.97326i) q^{32} +(-0.247570 - 1.52336i) q^{33} +(-2.63220 + 10.6792i) q^{34} +(0.973978 - 4.77086i) q^{35} +(1.51328 - 0.122165i) q^{36} +(3.10529 + 4.91063i) q^{37} +(-0.220063 + 0.194959i) q^{38} +(-3.41424 + 1.15885i) q^{39} +(-2.71306 - 2.40356i) q^{40} +(1.63757 - 10.0763i) q^{41} +(2.09490 + 0.892554i) q^{42} +(-3.48833 - 2.20589i) q^{43} +(1.55377 + 1.75385i) q^{44} +(0.322741 - 3.99786i) q^{45} +(3.11623 - 9.33426i) q^{46} +(3.35029 - 0.406799i) q^{47} +(3.78253 - 2.84239i) q^{48} +(-3.49500 - 4.28059i) q^{49} +(16.1086 - 13.1523i) q^{50} +(-3.33108 + 4.82590i) q^{51} +(3.44074 - 4.25742i) q^{52} +(-2.09308 - 3.03234i) q^{53} +(1.80163 + 0.521849i) q^{54} +(5.23186 - 3.30843i) q^{55} +(1.08290 - 0.175988i) q^{56} +(-0.146558 + 0.0555820i) q^{57} +(3.68967 + 8.65997i) q^{58} +(-10.7690 + 10.3437i) q^{59} +(2.82985 + 5.39183i) q^{60} +(-3.63272 - 0.293264i) q^{61} +(-3.09388 + 10.6813i) q^{62} +(0.875552 + 0.840979i) q^{63} +(-1.34510 + 3.54673i) q^{64} +(-9.64369 - 10.7764i) q^{65} +(1.02652 + 2.70672i) q^{66} +(-4.04330 + 9.48998i) q^{67} +(0.358472 - 8.89539i) q^{68} +(3.31809 - 4.06392i) q^{69} +9.13322i q^{70} +(-7.09252 - 5.79086i) q^{71} +(0.868017 - 0.251424i) q^{72} +(5.41543 - 6.11276i) q^{73} +(-7.54925 - 7.85960i) q^{74} +(10.5165 - 3.51092i) q^{75} +(0.142958 - 0.190242i) q^{76} +(-0.225844 + 1.85999i) q^{77} +(5.83985 - 3.41069i) q^{78} +(-1.60956 - 13.2559i) q^{79} +(16.4348 + 9.48864i) q^{80} +(0.799443 + 0.600742i) q^{81} +(0.771014 + 19.1325i) q^{82} +(-1.26698 - 0.480503i) q^{83} +(-1.80588 - 0.368673i) q^{84} +(-23.0440 - 4.70447i) q^{85} +(7.23841 + 2.74517i) q^{86} +(0.202076 + 5.01447i) q^{87} +(1.11500 + 0.837866i) q^{88} +(-4.98790 - 2.87976i) q^{89} +(0.906814 + 7.46829i) q^{90} +(4.37272 - 0.198122i) q^{91} +(-0.960097 + 7.90711i) q^{92} +(-3.56161 + 4.73965i) q^{93} +(-6.00447 + 2.00459i) q^{94} +(-0.435500 - 0.453404i) q^{95} +(-4.68652 + 5.28999i) q^{96} +(5.73060 - 1.65989i) q^{97} +(8.02905 + 6.55552i) q^{98} +1.54335i 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{73}{78}\right)$

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 $

$2$	−1.83778	+	0.375186i	−1.29951	+	0.265296i	−0.799469	−	0.600707i	$-0.794886\pi$
$2$	−1.83778	+	0.375186i	−1.29951	+	0.265296i	−0.500038	+	0.866003i	$0.666681\pi$
$3$	−0.987050	−	0.160411i	−0.569874	−	0.0926135i
$3$	−0.987050	−	0.160411i	−0.569874	−	0.0926135i
$4$	1.39672	−	0.595086i	0.698359	−	0.297543i
$5$	−0.959864	−	3.89432i	−0.429264	−	1.74159i	−0.644098	−	0.764943i	$-0.722767\pi$
$5$	−0.959864	−	3.89432i	−0.429264	−	1.74159i	0.214834	−	0.976651i	$-0.431079\pi$
$6$	1.87417	−	0.0755263i	0.765125	−	0.0308335i
$7$	1.09680	+	0.520440i	0.414553	+	0.196708i	0.624534	−	0.780998i	$-0.285289\pi$
$7$	1.09680	+	0.520440i	0.414553	+	0.196708i	−0.209981	+	0.977705i	$0.567340\pi$
$8$	0.743728	−	0.513358i	0.262948	−	0.181500i
$9$	0.948536	+	0.316668i	0.316179	+	0.105556i
$10$	3.22511	+	6.79678i	1.01987	+	2.14933i
$11$	0.488729	+	1.46392i	0.147357	+	0.441389i	0.996184	−	0.0872831i	$-0.0278185\pi$
$11$	0.488729	+	1.46392i	0.147357	+	0.441389i	−0.848826	+	0.528672i	$0.822690\pi$
$12$	−1.47409	+	0.363330i	−0.425533	+	0.104884i
$13$	3.18414	−	1.69153i	0.883121	−	0.469145i
$13$	3.18414	−	1.69153i	0.883121	−	0.469145i
$14$	−2.21095	−	0.544950i	−0.590901	−	0.145644i
$15$	0.322741	+	3.99786i	0.0833313	+	1.03224i
$16$	−3.27760	+	3.41234i	−0.819400	+	0.853086i
$17$	2.51381	−	5.29775i	0.609689	−	1.28489i	−0.330361	−	0.943855i	$-0.607170\pi$
$17$	2.51381	−	5.29775i	0.609689	−	1.28489i	0.940050	−	0.341037i	$-0.110778\pi$
$18$	−1.86201	−	0.226089i	−0.438880	−	0.0532897i
$19$	0.135744	−	0.0783717i	0.0311418	−	0.0179797i	−0.484348	−	0.874875i	$-0.660943\pi$
$19$	0.135744	−	0.0783717i	0.0311418	−	0.0179797i	0.515490	+	0.856896i	$0.327610\pi$
$20$	−3.65811	−	4.86806i	−0.817979	−	1.08853i
$21$	−0.999117	−	0.689641i	−0.218025	−	0.150492i
$22$	−1.44742	−	2.50700i	−0.308591	−	0.534495i
$23$	−2.62322	+	4.54356i	−0.546980	+	0.947397i	0.451499	+	0.892271i	$0.350889\pi$
$23$	−2.62322	+	4.54356i	−0.546980	+	0.947397i	−0.998479	+	0.0551258i	$0.982444\pi$
$24$	−0.816446	+	0.387408i	−0.166656	+	0.0790794i
$25$	−9.81711	+	5.15242i	−1.96342	+	1.03048i
$26$	−5.21711	+	4.30330i	−1.02316	+	0.843947i
$27$	−0.885456	−	0.464723i	−0.170406	−	0.0894360i
$28$	1.84163	+	0.0742153i	0.348036	+	0.0140254i
$29$	−1.00384	−	4.91712i	−0.186408	−	0.913087i	−0.960128	−	0.279560i	$-0.909812\pi$
$29$	−1.00384	−	4.91712i	−0.186408	−	0.913087i	0.773720	−	0.633527i	$-0.218394\pi$
$30$	−2.09307	−	7.22611i	−0.382140	−	1.31930i
$31$	2.75520	−	5.24959i	0.494848	−	0.942855i	−0.502101	−	0.864809i	$-0.667440\pi$
$31$	2.75520	−	5.24959i	0.494848	−	0.942855i	0.996950	−	0.0780460i	$-0.0248681\pi$
$32$	3.77726	−	5.97326i	0.667731	−	1.05593i
$33$	−0.247570	−	1.52336i	−0.0430964	−	0.265183i
$34$	−2.63220	+	10.6792i	−0.451418	+	1.83148i
$35$	0.973978	−	4.77086i	0.164632	−	0.806423i
$36$	1.51328	−	0.122165i	0.252214	−	0.0203608i
$37$	3.10529	+	4.91063i	0.510507	+	0.807302i	0.997825	−	0.0659224i	$-0.0209990\pi$
$37$	3.10529	+	4.91063i	0.510507	+	0.807302i	−0.487318	+	0.873225i	$0.662025\pi$
$38$	−0.220063	+	0.194959i	−0.0356990	+	0.0316266i
$39$	−3.41424	+	1.15885i	−0.546717	+	0.185565i
$40$	−2.71306	−	2.40356i	−0.428972	−	0.380036i
$41$	1.63757	−	10.0763i	0.255745	−	1.57366i	−0.468086	−	0.883683i	$-0.655056\pi$
$41$	1.63757	−	10.0763i	0.255745	−	1.57366i	0.723831	−	0.689978i	$-0.242380\pi$
$42$	2.09490	+	0.892554i	0.323250	+	0.137724i
$43$	−3.48833	−	2.20589i	−0.531966	−	0.336395i	0.241327	−	0.970444i	$-0.422417\pi$
$43$	−3.48833	−	2.20589i	−0.531966	−	0.336395i	−0.773293	+	0.634049i	$0.781392\pi$
$44$	1.55377	+	1.75385i	0.234240	+	0.264403i
$45$	0.322741	−	3.99786i	0.0481114	−	0.595966i
$46$	3.11623	−	9.33426i	0.459464	−	1.37626i
$47$	3.35029	−	0.406799i	0.488690	−	0.0593377i	0.127516	−	0.991836i	$-0.459299\pi$
$47$	3.35029	−	0.406799i	0.488690	−	0.0593377i	0.361173	+	0.932499i	$0.382376\pi$
$48$	3.78253	−	2.84239i	0.545962	−	0.410264i
$49$	−3.49500	−	4.28059i	−0.499285	−	0.611513i
$50$	16.1086	−	13.1523i	2.27810	−	1.86001i
$51$	−3.33108	+	4.82590i	−0.466444	+	0.675761i
$52$	3.44074	−	4.25742i	0.477144	−	0.590398i
$53$	−2.09308	−	3.03234i	−0.287506	−	0.416525i	0.652444	−	0.757837i	$-0.273744\pi$
$53$	−2.09308	−	3.03234i	−0.287506	−	0.416525i	−0.939950	+	0.341313i	$0.889129\pi$
$54$	1.80163	+	0.521849i	0.245171	+	0.0710147i
$55$	5.23186	−	3.30843i	0.705464	−	0.446109i
$56$	1.08290	−	0.175988i	0.144708	−	0.0235174i
$57$	−0.146558	+	0.0555820i	−0.0194120	+	0.00736201i
$58$	3.68967	+	8.65997i	0.484477	+	1.13711i
$59$	−10.7690	+	10.3437i	−1.40200	+	1.34664i	−0.538191	+	0.842823i	$0.680892\pi$
$59$	−10.7690	+	10.3437i	−1.40200	+	1.34664i	−0.863810	+	0.503817i	$0.831929\pi$
$60$	2.82985	+	5.39183i	0.365332	+	0.696082i
$61$	−3.63272	−	0.293264i	−0.465123	−	0.0375486i	−0.154316	−	0.988022i	$-0.549317\pi$
$61$	−3.63272	−	0.293264i	−0.465123	−	0.0375486i	−0.310807	+	0.950473i	$0.600599\pi$
$62$	−3.09388	+	10.6813i	−0.392923	+	1.35653i
$63$	0.875552	+	0.840979i	0.110309	+	0.105953i
$64$	−1.34510	+	3.54673i	−0.168137	+	0.443341i
$65$	−9.64369	−	10.7764i	−1.19615	−	1.33665i
$66$	1.02652	+	2.70672i	0.126356	+	0.333174i
$67$	−4.04330	+	9.48998i	−0.493968	+	1.15939i	0.467382	+	0.884056i	$0.345197\pi$
$67$	−4.04330	+	9.48998i	−0.493968	+	1.15939i	−0.961350	+	0.275330i	$0.911213\pi$
$68$	0.358472	−	8.89539i	0.0434711	−	1.07872i
$69$	3.31809	−	4.06392i	0.399451	−	0.489239i
$70$			9.13322i			1.09163i
$71$	−7.09252	−	5.79086i	−0.841727	−	0.687249i	0.110088	−	0.993922i	$-0.464887\pi$
$71$	−7.09252	−	5.79086i	−0.841727	−	0.687249i	−0.951815	+	0.306673i	$0.900784\pi$
$72$	0.868017	−	0.251424i	0.102297	−	0.0296306i
$73$	5.41543	−	6.11276i	0.633829	−	0.715445i	−0.340583	−	0.940214i	$-0.610625\pi$
$73$	5.41543	−	6.11276i	0.633829	−	0.715445i	0.974412	+	0.224770i	$0.0721630\pi$
$74$	−7.54925	−	7.85960i	−0.877582	−	0.913660i
$75$	10.5165	−	3.51092i	1.21434	−	0.405406i
$76$	0.142958	−	0.190242i	0.0163984	−	0.0218223i
$77$	−0.225844	+	1.85999i	−0.0257373	+	0.211965i
$78$	5.83985	−	3.41069i	0.661233	−	0.386185i
$79$	−1.60956	−	13.2559i	−0.181090	−	1.49141i	−0.745829	−	0.666138i	$-0.767946\pi$
$79$	−1.60956	−	13.2559i	−0.181090	−	1.49141i	0.564739	−	0.825269i	$-0.308977\pi$
$80$	16.4348	+	9.48864i	1.83747	+	1.06086i
$81$	0.799443	+	0.600742i	0.0888270	+	0.0667491i
$82$	0.771014	+	19.1325i	0.0851442	+	2.11283i
$83$	−1.26698	−	0.480503i	−0.139069	−	0.0527420i	0.284088	−	0.958798i	$-0.408309\pi$
$83$	−1.26698	−	0.480503i	−0.139069	−	0.0527420i	−0.423158	+	0.906056i	$0.639078\pi$
$84$	−1.80588	−	0.368673i	−0.197038	−	0.0402255i
$85$	−23.0440	−	4.70447i	−2.49948	−	0.510272i
$86$	7.23841	+	2.74517i	0.780538	+	0.296019i
$87$	0.202076	+	5.01447i	0.0216649	+	0.537608i
$88$	1.11500	+	0.837866i	0.118859	+	0.0893168i
$89$	−4.98790	−	2.87976i	−0.528716	−	0.305254i	0.211777	−	0.977318i	$-0.432075\pi$
$89$	−4.98790	−	2.87976i	−0.528716	−	0.305254i	−0.740494	+	0.672064i	$0.765408\pi$
$90$	0.906814	+	7.46829i	0.0955866	+	0.787226i
$91$	4.37272	−	0.198122i	0.458385	−	0.0207689i
$92$	−0.960097	+	7.90711i	−0.100097	+	0.824373i
$93$	−3.56161	+	4.73965i	−0.369322	+	0.491479i
$94$	−6.00447	+	2.00459i	−0.619314	+	0.206757i
$95$	−0.435500	−	0.453404i	−0.0446814	−	0.0465182i
$96$	−4.68652	+	5.28999i	−0.478316	+	0.539907i
$97$	5.73060	−	1.65989i	0.581855	−	0.168536i	0.0257785	−	0.999668i	$-0.491794\pi$
$97$	5.73060	−	1.65989i	0.581855	−	0.168536i	0.556076	+	0.831131i	$0.312306\pi$
$98$	8.02905	+	6.55552i	0.811057	+	0.662208i
$99$			1.54335i			0.155112i
$100$	−10.6456	+	13.0385i	−1.06456	+	1.30385i
$101$	−0.567510	+	14.0826i	−0.0564694	+	1.40127i	0.684147	+	0.729344i	$0.260175\pi$
$101$	−0.567510	+	14.0826i	−0.0564694	+	1.40127i	−0.740616	+	0.671928i	$0.765466\pi$
$102$	4.31118	−	10.1187i	0.426871	−	1.00190i
$103$	0.761721	+	2.00849i	0.0750546	+	0.197903i	0.967293	−	0.253662i	$-0.0816352\pi$
$103$	0.761721	+	2.00849i	0.0750546	+	0.197903i	−0.892238	+	0.451565i	$0.850866\pi$
$104$	1.49977	−	2.89264i	0.147065	−	0.283647i
$105$	−1.72667	+	4.55284i	−0.168505	+	0.444312i
$106$	4.98431	+	4.78749i	0.484119	+	0.465003i
$107$	−3.08887	+	10.6640i	−0.298613	+	1.03093i	0.661182	+	0.750226i	$0.270055\pi$
$107$	−3.08887	+	10.6640i	−0.298613	+	1.03093i	−0.959794	+	0.280704i	$0.909432\pi$
$108$	−1.51328	−	0.122165i	−0.145616	−	0.0117553i
$109$	5.21251	+	9.93161i	0.499268	+	0.951276i	0.996495	+	0.0836549i	$0.0266594\pi$
$109$	5.21251	+	9.93161i	0.499268	+	0.951276i	−0.497227	+	0.867621i	$0.665648\pi$
$110$	−8.37375	+	8.04309i	−0.798405	+	0.766879i
$111$	−2.27736	−	5.34516i	−0.216157	−	0.507340i
$112$	−5.37081	+	2.03688i	−0.507494	+	0.192467i
$113$	−8.79942	+	1.43005i	−0.827780	+	0.134527i	−0.559518	−	0.828818i	$-0.689014\pi$
$113$	−8.79942	+	1.43005i	−0.827780	+	0.134527i	−0.268263	+	0.963346i	$0.586449\pi$
$114$	0.248487	−	0.157134i	0.0232730	−	0.0147169i
$115$	20.2120	+	5.85448i	1.88478	+	0.545933i
$116$	−4.32819	−	6.27046i	−0.401862	−	0.582198i
$117$	3.55592	−	0.596162i	0.328745	−	0.0551152i
$118$	15.9102	−	23.0499i	1.46465	−	2.12192i
$119$	5.51432	−	4.50230i	0.505497	−	0.412725i
$120$	2.29237	+	2.80764i	0.209264	+	0.256301i
$121$	6.88966	−	5.17725i	0.626333	−	0.470659i
$122$	6.78618	−	0.823991i	0.614392	−	0.0746007i
$123$	−3.23272	+	9.68317i	−0.291484	+	0.873102i
$124$	0.724277	−	8.97178i	0.0650420	−	0.805689i
$125$	16.1898	+	18.2745i	1.44806	+	1.63452i
$126$	−1.92460	−	1.21704i	−0.171457	−	0.108423i
$127$	−7.32427	−	3.12058i	−0.649924	−	0.276907i	0.0417376	−	0.999129i	$-0.486711\pi$
$127$	−7.32427	−	3.12058i	−0.649924	−	0.276907i	−0.691661	+	0.722222i	$0.743121\pi$
$128$	−1.12606	+	6.92890i	−0.0995302	+	0.612434i
$129$	3.08931	+	2.73689i	0.271999	+	0.240970i
$130$	21.7662	+	16.1865i	1.90902	+	1.41965i
$131$	2.32810	−	2.06252i	0.203407	−	0.180203i	−0.555269	−	0.831671i	$-0.687385\pi$
$131$	2.32810	−	2.06252i	0.203407	−	0.180203i	0.758676	+	0.651468i	$0.225846\pi$
$132$	−1.25232	−	1.98038i	−0.109000	−	0.172370i
$133$	0.189672	−	0.0153119i	0.0164467	−	0.00132771i
$134$	3.87020	−	18.9575i	0.334334	−	1.63768i
$135$	−0.959864	+	3.89432i	−0.0826119	+	0.335170i
$136$	−0.850050	−	5.23057i	−0.0728912	−	0.448518i
$137$	−8.66002	+	13.6947i	−0.739876	+	1.17002i	0.240070	+	0.970756i	$0.422830\pi$
$137$	−8.66002	+	13.6947i	−0.739876	+	1.17002i	−0.979946	+	0.199264i	$0.936145\pi$
$138$	−4.57320	+	8.71351i	−0.389297	+	0.741743i
$139$	−5.44986	−	18.8151i	−0.462251	−	1.59587i	−0.765813	−	0.643063i	$-0.777663\pi$
$139$	−5.44986	−	18.8151i	−0.462251	−	1.59587i	0.303563	−	0.952812i	$-0.401824\pi$
$140$	−1.47870	−	7.24314i	−0.124973	−	0.612157i
$141$	−3.37216	−	0.135893i	−0.283987	−	0.0114443i
$142$	15.2072	+	7.98133i	1.27616	+	0.669778i
$143$	4.03244	+	3.83463i	0.337210	+	0.320668i
$144$	−4.18950	+	2.19882i	−0.349125	+	0.183235i
$145$	−18.1853	+	8.62903i	−1.51021	+	0.716602i
$146$	−7.65896	+	13.2657i	−0.633860	+	1.09788i
$147$	2.76308	+	4.78580i	0.227895	+	0.394726i
$148$	7.25946	+	5.01084i	0.596724	+	0.411889i
$149$	1.45262	+	1.93309i	0.119003	+	0.158365i	0.855013	−	0.518606i	$-0.173549\pi$
$149$	1.45262	+	1.93309i	0.119003	+	0.158365i	−0.736010	+	0.676971i	$0.763292\pi$
$150$	−18.0098	+	10.3979i	−1.47049	+	0.848988i
$151$	−0.0734972	−	0.00892418i	−0.00598112	−	0.000726239i	0.117546	−	0.993067i	$-0.462497\pi$
$151$	−0.0734972	−	0.00892418i	−0.00598112	−	0.000726239i	−0.123527	+	0.992341i	$0.539420\pi$
$152$	0.0607237	−	0.127972i	0.00492534	−	0.0103799i
$153$	4.06207	−	4.22906i	0.328399	−	0.341899i
$154$	−0.282790	−	3.50299i	−0.0227879	−	0.282279i
$155$	−23.0882	−	5.69073i	−1.85449	−	0.457091i
$156$	−4.07912	+	3.65036i	−0.326591	+	0.292262i
$157$	7.31977	−	1.80416i	0.584182	−	0.143988i	0.0638609	−	0.997959i	$-0.479659\pi$
$157$	7.31977	−	1.80416i	0.584182	−	0.143988i	0.520321	+	0.853971i	$0.325812\pi$
$158$	7.93145	+	23.7576i	0.630992	+	1.89005i
$159$	1.57955	+	3.32883i	0.125266	+	0.263993i
$160$	−26.8874	−	8.97635i	−2.12564	−	0.709642i
$161$	−5.24181	+	3.61816i	−0.413113	+	0.285151i
$162$	−1.69459	−	0.804093i	−0.133140	−	0.0631755i
$163$	19.0246	−	0.766666i	1.49012	−	0.0600499i	0.718232	−	0.695804i	$-0.244952\pi$
$163$	19.0246	−	0.766666i	1.49012	−	0.0600499i	0.771892	+	0.635754i	$0.219311\pi$
$164$	−3.70907	−	15.0483i	−0.289630	−	1.17507i
$165$	−5.69482	+	2.42634i	−0.443341	+	0.188890i
$166$	2.50871	+	0.407705i	0.194714	+	0.0316441i
$167$	23.7151	−	4.84147i	1.83513	−	0.374644i	0.847416	−	0.530929i	$-0.178157\pi$
$167$	23.7151	−	4.84147i	1.83513	−	0.374644i	0.987712	+	0.156285i	$0.0499518\pi$
$168$	−1.09710			−0.0846434
$169$	7.27747	−	10.7721i	0.559805	−	0.828624i
$170$	44.1150			3.38346
$171$	0.153576	−	0.0313527i	0.0117442	−	0.00239760i
$172$	−6.18491	−	1.00515i	−0.471595	−	0.0766416i
$173$	−5.33124	+	2.27143i	−0.405327	+	0.172694i	−0.585001	−	0.811033i	$-0.698906\pi$
$173$	−5.33124	+	2.27143i	−0.405327	+	0.172694i	0.179674	+	0.983726i	$0.442496\pi$
$174$	−2.25273	−	9.13969i	−0.170779	−	0.692878i
$175$	−13.4490	+	0.541975i	−1.01665	+	0.0409695i
$176$	−6.59726	−	3.13044i	−0.497287	−	0.235966i
$177$	12.2888	−	8.48233i	0.923681	−	0.637571i
$178$	10.2471	+	3.42099i	0.768054	+	0.256414i
$179$	−8.66450	−	18.2600i	−0.647615	−	1.36482i	−0.915871	−	0.401472i	$-0.868499\pi$
$179$	−8.66450	−	18.2600i	−0.647615	−	1.36482i	0.268257	−	0.963347i	$-0.413552\pi$
$180$	−1.92829	−	5.77594i	−0.143726	−	0.430513i
$181$	−10.0398	+	2.47460i	−0.746254	+	0.183935i	−0.594066	−	0.804416i	$-0.702478\pi$
$181$	−10.0398	+	2.47460i	−0.746254	+	0.183935i	−0.152188	+	0.988351i	$0.548632\pi$
$182$	−7.96176	+	2.00469i	−0.590165	+	0.148597i
$183$	3.53864	+	0.872196i	0.261584	+	0.0644746i
$184$	0.381508	+	4.72583i	0.0281251	+	0.348392i
$185$	16.1429	−	16.8065i	1.18685	−	1.23564i
$186$	4.76722	−	10.0467i	0.349550	−	0.736660i
$187$	8.98405	+	1.09086i	0.656979	+	0.0797717i
$188$	4.43732	−	2.56189i	0.323625	−	0.186845i
$189$	−0.729312	−	0.970537i	−0.0530496	−	0.0705962i
$190$	0.970465	+	0.669863i	0.0704049	+	0.0485970i
$191$	0.826124	+	1.43089i	0.0597762	+	0.103536i	0.894365	−	0.447338i	$-0.147628\pi$
$191$	0.826124	+	1.43089i	0.0597762	+	0.103536i	−0.834589	+	0.550874i	$0.814295\pi$
$192$	1.89661	−	3.28503i	0.136876	−	0.237077i
$193$	4.25626	−	2.01962i	0.306372	−	0.145376i	−0.269299	−	0.963057i	$-0.586792\pi$
$193$	4.25626	−	2.01962i	0.306372	−	0.145376i	0.575671	+	0.817681i	$0.304741\pi$
$194$	−9.90883	+	5.20055i	−0.711412	+	0.373378i
$195$	7.79015	+	12.1838i	0.557864	+	0.872502i
$196$	−7.42884	−	3.89896i	−0.530631	−	0.278497i
$197$	−5.51207	−	0.222129i	−0.392719	−	0.0158260i	−0.156879	−	0.987618i	$-0.550143\pi$
$197$	−5.51207	−	0.222129i	−0.392719	−	0.0158260i	−0.235840	+	0.971792i	$0.575784\pi$
$198$	−0.579042	−	2.83633i	−0.0411507	−	0.201569i
$199$	−0.853196	−	2.94558i	−0.0604815	−	0.208806i	0.924586	−	0.380972i	$-0.124411\pi$
$199$	−0.853196	−	2.94558i	−0.0604815	−	0.208806i	−0.985068	+	0.172166i	$0.944923\pi$
$200$	−4.65623	+	8.87170i	−0.329245	+	0.627324i
$201$	5.51324	−	8.71850i	0.388874	−	0.614955i
$202$	−4.24064	−	26.0937i	−0.298370	−	1.83595i
$203$	1.45805	−	5.91556i	0.102335	−	0.415191i
$204$	−1.78075	+	8.72269i	−0.124677	+	0.610711i
$205$	−40.8123	+	3.29471i	−2.85046	+	0.230113i
$206$	−2.15343	−	3.40538i	−0.150037	−	0.237264i
$207$	−3.92702	+	3.47904i	−0.272947	+	0.241810i
$208$	−4.66426	+	16.4095i	−0.323408	+	1.13780i
$209$	0.181072	+	0.160416i	0.0125250	+	0.0110962i
$210$	1.46507	−	9.01495i	0.101100	−	0.622091i
$211$	16.2567	+	6.92633i	1.11916	+	0.476828i	0.870700	−	0.491815i	$-0.163666\pi$
$211$	16.2567	+	6.92633i	1.11916	+	0.476828i	0.248457	+	0.968643i	$0.420077\pi$
$212$	−4.72794	−	2.98977i	−0.324716	−	0.205338i
$213$	6.07175	+	6.85359i	0.416030	+	0.469600i
$214$	1.67568	−	20.7571i	0.114547	−	1.41892i
$215$	−5.24211	+	15.7020i	−0.357509	+	1.07087i
$216$	−0.897108	+	0.108929i	−0.0610405	+	0.00741166i
$217$	5.75401	−	4.32386i	0.390608	−	0.293523i
$218$	−13.3057	−	16.2965i	−0.901172	−	1.10374i
$219$	−6.32586	+	5.16491i	−0.427462	+	0.349012i
$220$	5.33864	−	7.73435i	0.359931	−	0.521450i
$221$	−0.956963	−	21.1209i	−0.0643723	−	1.42075i
$222$	6.19072	+	8.96880i	0.415494	+	0.601947i
$223$	2.17504	+	0.630008i	0.145652	+	0.0421885i	0.350242	−	0.936659i	$-0.386099\pi$
$223$	2.17504	+	0.630008i	0.145652	+	0.0421885i	−0.204591	+	0.978848i	$0.565586\pi$
$224$	7.25164	−	4.58566i	0.484521	−	0.306392i
$225$	−10.9435	+	1.77849i	−0.729566	+	0.118566i
$226$	15.6349	−	5.92953i	1.04002	−	0.394426i
$227$	3.44747	+	8.09151i	0.228817	+	0.537052i	0.994326	−	0.106372i	$-0.0339234\pi$
$227$	3.44747	+	8.09151i	0.228817	+	0.537052i	−0.765510	+	0.643424i	$0.777513\pi$
$228$	−0.171624	+	0.164847i	−0.0113660	+	0.0109172i
$229$	−10.2830	−	19.5927i	−0.679521	−	1.29472i	−0.943878	−	0.330295i	$-0.892852\pi$
$229$	−10.2830	−	19.5927i	−0.679521	−	1.29472i	0.264356	−	0.964425i	$-0.414840\pi$
$230$	−39.3418	−	3.17600i	−2.59412	−	0.209419i
$231$	0.521282	−	1.79967i	0.0342978	−	0.118410i
$232$	−3.27083	−	3.14167i	−0.214740	−	0.206261i
$233$	7.05418	−	18.6003i	0.462134	−	1.21855i	−0.478186	−	0.878258i	$-0.658706\pi$
$233$	7.05418	−	18.6003i	0.462134	−	1.21855i	0.940321	−	0.340290i	$-0.110525\pi$
$234$	−6.31134	+	2.42975i	−0.412585	+	0.158837i
$235$	−4.80002	−	12.6566i	−0.313119	−	0.825627i
$236$	−8.88580	+	20.8557i	−0.578416	+	1.35759i
$237$	−0.537682	+	13.3424i	−0.0349262	+	0.866685i
$238$	−8.44492	+	10.3431i	−0.547403	+	0.670446i
$239$			3.23767i			0.209428i	0.994502	+	0.104714i	$0.0333927\pi$
$239$			3.23767i			0.209428i	−0.994502	+	0.104714i	$0.966607\pi$
$240$	−14.6999	−	12.0021i	−0.948874	−	0.774732i
$241$	13.9956	−	4.05386i	0.901533	−	0.261132i	0.205089	−	0.978743i	$-0.434252\pi$
$241$	13.9956	−	4.05386i	0.901533	−	0.261132i	0.696444	+	0.717611i	$0.254764\pi$
$242$	−10.7193	+	12.0995i	−0.689060	+	0.777788i
$243$	−0.692724	−	0.721202i	−0.0444383	−	0.0462652i
$244$	−5.24840	+	1.75217i	−0.335995	+	0.112171i
$245$	−13.3153	+	17.7194i	−0.850682	+	1.13205i
$246$	2.30804	−	19.0084i	0.147155	−	1.21193i
$247$	0.299659	−	0.479161i	0.0190668	−	0.0304883i
$248$	−0.645804	−	5.31868i	−0.0410086	−	0.337736i
$249$	1.17350	+	0.677518i	0.0743673	+	0.0429360i
$250$	−36.6096	−	27.5103i	−2.31539	−	1.73991i
$251$	−0.598808	−	14.8593i	−0.0377964	−	0.937909i	−0.901202	−	0.433399i	$-0.857314\pi$
$251$	−0.598808	−	14.8593i	−0.0377964	−	0.937909i	0.863406	−	0.504510i	$-0.168327\pi$
$252$	1.72335	+	0.653582i	0.108561	+	0.0411718i
$253$	−7.93345	−	1.61963i	−0.498772	−	0.101825i
$254$	14.6312	+	2.98698i	0.918043	+	0.187420i
$255$	21.9910	+	8.34008i	1.37713	+	0.522276i
$256$	−0.835656	−	20.7366i	−0.0522285	−	1.29604i
$257$	7.84105	+	5.89217i	0.489112	+	0.367543i	0.816499	−	0.577347i	$-0.195912\pi$
$257$	7.84105	+	5.89217i	0.489112	+	0.367543i	−0.327388	+	0.944890i	$0.606168\pi$
$258$	−6.70432	−	3.87074i	−0.417393	−	0.240982i
$259$	0.850211	+	7.00212i	0.0528296	+	0.435091i
$260$	−19.8824	−	9.31279i	−1.23305	−	0.577554i
$261$	0.604919	−	4.98195i	0.0374435	−	0.308375i
$262$	−3.50471	+	4.66392i	−0.216522	+	0.288138i
$263$	23.8431	−	7.96000i	1.47023	−	0.490834i	0.534992	−	0.844857i	$-0.320315\pi$
$263$	23.8431	−	7.96000i	1.47023	−	0.490834i	0.935237	+	0.354023i	$0.115187\pi$
$264$	−0.966155	−	1.00587i	−0.0594627	−	0.0619073i
$265$	−9.79985	+	11.0617i	−0.602000	+	0.679518i
$266$	−0.342831	+	0.0993023i	−0.0210203	+	0.00608861i
$267$	4.46136	+	3.64259i	0.273031	+	0.222923i
$268$			15.6609i			0.956644i
$269$	−11.4570	+	14.0322i	−0.698543	+	0.855560i	−0.995040	−	0.0994735i	$-0.968284\pi$
$269$	−11.4570	+	14.0322i	−0.698543	+	0.855560i	0.296497	+	0.955034i	$0.404182\pi$
$270$	0.302926	−	7.51704i	0.0184355	−	0.457472i
$271$	−10.7185	+	25.1573i	−0.651103	+	1.52819i	0.186813	+	0.982395i	$0.440184\pi$
$271$	−10.7185	+	25.1573i	−0.651103	+	1.52819i	−0.837916	+	0.545799i	$0.816226\pi$
$272$	9.83846	+	25.9419i	0.596544	+	1.57296i
$273$	−4.34787	−	0.505876i	−0.263145	−	0.0306170i
$274$	10.7772	−	28.4170i	0.651072	−	1.71674i
$275$	−12.3406	−	11.8533i	−0.744168	−	0.714783i
$276$	2.21605	−	7.65070i	0.133391	−	0.460518i
$277$	2.59284	+	0.209316i	0.155789	+	0.0125766i	0.158115	−	0.987421i	$-0.449458\pi$
$277$	2.59284	+	0.209316i	0.155789	+	0.0125766i	−0.00232602	+	0.999997i	$0.500740\pi$
$278$	17.0748	+	32.5333i	1.02408	+	1.95122i
$279$	4.27579	−	4.10695i	0.255985	−	0.245877i
$280$	−1.72479	−	4.04822i	−0.103076	−	0.241928i
$281$	21.3546	−	8.09872i	1.27391	−	0.483129i	0.377356	−	0.926068i	$-0.376833\pi$
$281$	21.3546	−	8.09872i	1.27391	−	0.483129i	0.896552	+	0.442939i	$0.146064\pi$
$282$	6.24827	−	1.01544i	0.372079	−	0.0604688i
$283$	0.725279	−	0.458639i	0.0431134	−	0.0272632i	−0.512735	−	0.858547i	$-0.671368\pi$
$283$	0.725279	−	0.458639i	0.0431134	−	0.0272632i	0.555849	+	0.831284i	$0.312393\pi$
$284$	−13.3523	−	3.86754i	−0.792314	−	0.229496i
$285$	0.357129	+	0.517391i	0.0211545	+	0.0306476i
$286$	−8.84944	−	5.53429i	−0.523279	−	0.327250i
$287$	7.04022	−	10.1995i	0.415571	−	0.602059i
$288$	5.47441	−	4.46972i	0.322583	−	0.263381i
$289$	−10.9953	−	13.4668i	−0.646782	−	0.792164i
$290$	30.1831	−	22.6811i	1.77241	−	1.33188i
$291$	−5.92266	+	0.719141i	−0.347192	+	0.0421568i
$292$	3.92621	−	11.7604i	0.229764	−	0.688228i
$293$	2.17372	−	26.9264i	0.126990	−	1.57306i	−0.548793	−	0.835958i	$-0.684913\pi$
$293$	2.17372	−	26.9264i	0.126990	−	1.57306i	0.675784	−	0.737100i	$-0.263805\pi$
$294$	−6.87350	−	7.75858i	−0.400871	−	0.452490i
$295$	50.6186	+	32.0093i	2.94713	+	1.86365i
$296$	4.83041	+	2.05804i	0.280762	+	0.119621i
$297$	0.247570	−	1.52336i	0.0143655	−	0.0883944i
$298$	−3.39487	−	3.00759i	−0.196660	−	0.174225i
$299$	−0.667152	+	18.9046i	−0.0385824	+	1.09328i
$300$	12.5993	−	11.1620i	0.727419	−	0.644437i
$301$	−2.67799	−	4.23490i	−0.154357	−	0.244095i
$302$	0.138420	−	0.0111744i	0.00796518	−	0.000643016i
$303$	2.81917	−	13.8092i	0.161957	−	0.793319i
$304$	−0.177483	+	0.720076i	−0.0101793	+	0.0412992i
$305$	2.34486	+	14.4285i	0.134266	+	0.826172i
$306$	−5.87851	+	9.29612i	−0.336052	+	0.531424i
$307$	11.5458	−	21.9987i	0.658953	−	1.25553i	−0.294978	−	0.955504i	$-0.595312\pi$
$307$	11.5458	−	21.9987i	0.658953	−	1.25553i	0.953931	−	0.300027i	$-0.0969955\pi$
$308$	0.791413	+	2.73228i	0.0450950	+	0.155686i
$309$	−0.429672	−	2.10467i	−0.0244432	−	0.119731i
$310$	44.5662	+	1.79596i	2.53119	+	0.102003i
$311$	8.23324	+	4.32114i	0.466864	+	0.245029i	0.681715	−	0.731618i	$-0.261234\pi$
$311$	8.23324	+	4.32114i	0.466864	+	0.245029i	−0.214851	+	0.976647i	$0.568927\pi$
$312$	−1.94436	+	2.61460i	−0.110078	+	0.148023i
$313$	−23.0110	+	12.0771i	−1.30066	+	0.682638i	−0.965716	−	0.259600i	$-0.916409\pi$
$313$	−23.0110	+	12.0771i	−1.30066	+	0.682638i	−0.334943	+	0.942238i	$0.608717\pi$
$314$	−12.7752	+	6.06193i	−0.720949	+	0.342095i
$315$	2.43463	−	4.21691i	0.137176	−	0.237596i
$316$	−10.1365	−	17.5569i	−0.570223	−	0.987655i
$317$	23.4977	+	16.2193i	1.31976	+	0.910968i	0.999341	−	0.0363067i	$-0.0115593\pi$
$317$	23.4977	+	16.2193i	1.31976	+	0.910968i	0.320424	+	0.947274i	$0.396175\pi$
$318$	−4.15180	−	5.52504i	−0.232821	−	0.309829i
$319$	6.70767	−	3.87268i	0.375558	−	0.216828i
$320$	15.1032	+	1.83386i	0.844294	+	0.102516i
$321$	4.75950	−	10.0304i	0.265650	−	0.559845i
$322$	8.27583	−	8.61605i	0.461194	−	0.480154i
$323$	−0.0739591	−	0.916148i	−0.00411519	−	0.0509758i
$324$	1.47409	+	0.363330i	0.0818938	+	0.0201850i
$325$	−22.5436	+	33.0119i	−1.25049	+	1.83117i
$326$	−34.6755	+	8.54674i	−1.92050	+	0.473360i
$327$	−3.55187	−	10.6391i	−0.196419	−	0.588346i
$328$	−3.95487	−	8.33472i	−0.218371	−	0.460208i
$329$	3.88632	+	1.29745i	0.214260	+	0.0715305i
$330$	9.55551	−	6.59569i	0.526014	−	0.363081i
$331$	2.68756	+	1.27526i	0.147722	+	0.0700949i	0.501118	−	0.865379i	$-0.332922\pi$
$331$	2.68756	+	1.27526i	0.147722	+	0.0700949i	−0.353397	+	0.935474i	$0.614973\pi$
$332$	−2.05555	+	0.0828360i	−0.112813	+	0.00454622i
$333$	1.39044	+	5.64126i	0.0761959	+	0.309139i
$334$	−41.7667	+	17.7951i	−2.28537	+	0.973706i
$335$	40.8380	+	6.63683i	2.23122	+	0.362609i
$336$	5.62800	−	1.14896i	0.307032	−	0.0626811i
$337$	−12.6531			−0.689258			−0.344629	−	0.938739i	$-0.611995\pi$
$337$	−12.6531			−0.689258			−0.344629	+	0.938739i	$0.611995\pi$
$338$	−9.33285	+	22.5272i	−0.507640	+	1.22532i
$339$	8.91487			0.484189
$340$	−34.9856	+	7.14236i	−1.89736	+	0.387349i
$341$	9.03153	+	1.46777i	0.489085	+	0.0794840i
$342$	−0.270476	+	0.115239i	−0.0146256	+	0.00623140i
$343$	−3.63927	−	14.7651i	−0.196502	−	0.797240i
$344$	−3.72678	+	0.150184i	−0.200935	+	0.00809739i
$345$	−19.0111	−	9.02090i	−1.02353	−	0.485669i
$346$	8.94545	−	6.17460i	0.480910	−	0.331948i
$347$	18.0942	+	6.04074i	0.971349	+	0.324284i	0.757683	−	0.652623i	$-0.226331\pi$
$347$	18.0942	+	6.04074i	0.971349	+	0.324284i	0.213666	+	0.976907i	$0.431460\pi$
$348$	3.26629	+	6.88355i	0.175091	+	0.368997i
$349$	2.23496	+	6.69453i	0.119635	+	0.358350i	0.991277	−	0.131792i	$-0.0420731\pi$
$349$	2.23496	+	6.69453i	0.119635	+	0.358350i	−0.871643	+	0.490142i	$0.836945\pi$
$350$	24.5129	−	6.04190i	1.31027	−	0.322953i
$351$	−3.60551	+	0.0180312i	−0.192448	+	0.000962433i
$352$	10.5904	+	2.61031i	0.564472	+	0.139130i
$353$	−1.13190	−	14.0210i	−0.0602447	−	0.746265i	−0.954404	−	0.298517i	$-0.903508\pi$
$353$	−1.13190	−	14.0210i	−0.0602447	−	0.746265i	0.894160	−	0.447748i	$-0.147774\pi$
$354$	−19.4016	+	20.1992i	−1.03118	+	1.07358i
$355$	−15.7436	+	33.1790i	−0.835585	+	1.76096i
$356$	−8.68039	−	1.05399i	−0.460060	−	0.0558614i
$357$	−6.16513	+	3.55944i	−0.326293	+	0.188386i
$358$	22.7744	+	30.3072i	1.20366	+	1.60178i
$359$	7.75871	+	5.35545i	0.409489	+	0.282650i	0.754949	−	0.655784i	$-0.227662\pi$
$359$	7.75871	+	5.35545i	0.409489	+	0.282650i	−0.345460	+	0.938433i	$0.612277\pi$
$360$	−1.81231	−	3.13900i	−0.0955169	−	0.165440i
$361$	−9.48772	+	16.4332i	−0.499353	+	0.864906i
$362$	17.5226	−	8.31457i	0.920966	−	0.437004i
$363$	−7.63093	+	4.00502i	−0.400520	+	0.210209i
$364$	5.98955	−	2.87886i	0.313938	−	0.150893i
$365$	−29.0031	−	15.2220i	−1.51809	−	0.796757i
$366$	−6.83048	−	0.275259i	−0.357035	−	0.0143880i
$367$	−2.96920	−	14.5441i	−0.154991	−	0.759195i	−0.980765	−	0.195194i	$-0.937466\pi$
$367$	−2.96920	−	14.5441i	−0.154991	−	0.759195i	0.825774	−	0.564001i	$-0.190739\pi$
$368$	−6.90630	−	23.8433i	−0.360016	−	1.24292i
$369$	4.74415	−	9.03921i	0.246970	−	0.470563i
$370$	−23.3616	+	36.9433i	−1.21451	+	1.92059i
$371$	−0.717542	−	4.41521i	−0.0372529	−	0.229226i
$372$	−2.15407	+	8.73941i	−0.111683	+	0.453117i
$373$	−5.04048	+	24.6899i	−0.260986	+	1.27839i	0.612081	+	0.790795i	$0.290333\pi$
$373$	−5.04048	+	24.6899i	−0.260986	+	1.27839i	−0.873067	+	0.487600i	$0.837873\pi$
$374$	−16.9200	+	1.36592i	−0.874912	+	0.0706302i
$375$	−13.0487	−	20.6348i	−0.673831	−	1.06558i
$376$	2.28287	−	2.02245i	0.117730	−	0.104300i
$377$	−11.5138	−	13.9588i	−0.592991	−	0.718914i
$378$	1.70445	+	1.51001i	0.0876673	+	0.0776665i
$379$	−0.326059	+	2.00632i	−0.0167485	+	0.103058i	−0.994079	−	0.108664i	$-0.965343\pi$
$379$	−0.326059	+	2.00632i	−0.0167485	+	0.103058i	0.977330	+	0.211721i	$0.0679070\pi$
$380$	−0.878085	−	0.374117i	−0.0450448	−	0.0191918i
$381$	6.72885	+	4.25506i	0.344729	+	0.217994i
$382$	−2.05508	−	2.31971i	−0.105147	−	0.118687i
$383$	0.0990087	−	1.22644i	0.00505911	−	0.0626683i	−0.993735	−	0.111761i	$-0.964351\pi$
$383$	0.0990087	−	1.22644i	0.00505911	−	0.0626683i	0.998794	+	0.0490927i	$0.0156330\pi$
$384$	2.22295	−	6.65854i	0.113439	−	0.339792i
$385$	7.46017	−	0.905829i	0.380206	−	0.0461653i
$386$	−7.06435	+	5.30851i	−0.359566	+	0.270196i
$387$	−2.61028	−	3.19701i	−0.132688	−	0.162513i
$388$	7.01626	−	5.72860i	0.356196	−	0.290825i
$389$	−10.4605	+	15.1546i	−0.530367	+	0.768369i	−0.992992	−	0.118185i	$-0.962292\pi$
$389$	−10.4605	+	15.1546i	−0.530367	+	0.768369i	0.462625	+	0.886554i	$0.346908\pi$
$390$	−18.8878	−	19.4684i	−0.956420	−	0.985823i
$391$	17.4763	+	25.3188i	0.883816	+	1.28043i
$392$	−4.79680	−	1.38941i	−0.242275	−	0.0701759i
$393$	−2.62880	+	1.66235i	−0.132605	+	0.0838546i
$394$	10.2133	−	1.65983i	0.514539	−	0.0836208i
$395$	−50.0778	+	18.9920i	−2.51969	+	0.955592i
$396$	0.918424	+	2.15562i	0.0461525	+	0.108324i
$397$	15.2027	−	14.6024i	0.763000	−	0.732871i	−0.206371	−	0.978474i	$-0.566165\pi$
$397$	15.2027	−	14.6024i	0.763000	−	0.732871i	0.969371	+	0.245603i	$0.0789858\pi$
$398$	2.67313	+	5.09322i	0.133992	+	0.255300i
$399$	−0.189672	−	0.0153119i	−0.00949549	−	0.000766555i
$400$	14.5948	−	50.3869i	0.729738	−	2.51935i
$401$	−1.57674	−	1.51448i	−0.0787388	−	0.0756297i	0.652322	−	0.757942i	$-0.273795\pi$
$401$	−1.57674	−	1.51448i	−0.0787388	−	0.0756297i	−0.731061	+	0.682312i	$0.760974\pi$
$402$	−6.86108	+	18.0912i	−0.342200	+	0.902306i
$403$	−0.106901	−	21.3759i	−0.00532513	−	1.06481i
$404$	7.58771	+	20.0072i	0.377503	+	0.995393i
$405$	1.57213	−	3.68992i	0.0781196	−	0.183353i
$406$	−0.460152	+	11.4185i	−0.0228370	+	0.566693i
$407$	−5.67113	+	6.94587i	−0.281107	+	0.344294i
$408$			5.29919i			0.262349i
$409$	−21.3188	−	17.4063i	−1.05415	−	0.860686i	−0.0636173	−	0.997974i	$-0.520264\pi$
$409$	−21.3188	−	17.4063i	−1.05415	−	0.860686i	−0.990531	+	0.137289i	$0.956161\pi$
$410$	73.7680	−	21.3672i	3.64314	−	1.05525i
$411$	10.7447	−	12.1282i	0.529995	−	0.598241i
$412$	2.25913	+	2.35201i	0.111300	+	0.115875i
$413$	−17.1948	+	5.74045i	−0.846099	+	0.282469i
$414$	5.91172	−	7.86708i	0.290545	−	0.386646i
$415$	−0.655102	+	5.39525i	−0.0321577	+	0.264842i
$416$	1.92338	−	25.4090i	0.0943015	−	1.24578i
$417$	2.36113	+	19.4457i	0.115625	+	0.952258i
$418$	−0.392956	−	0.226873i	−0.0192201	−	0.0110967i
$419$	−8.72376	−	6.55548i	−0.426184	−	0.320256i	0.365916	−	0.930648i	$-0.380756\pi$
$419$	−8.72376	−	6.55548i	−0.426184	−	0.320256i	−0.792100	+	0.610392i	$0.791012\pi$
$420$	0.297668	+	7.38655i	0.0145247	+	0.360427i
$421$	32.2814	+	12.2427i	1.57330	+	0.596674i	0.978326	−	0.207072i	$-0.0663933\pi$
$421$	32.2814	+	12.2427i	1.57330	+	0.596674i	0.594974	+	0.803745i	$0.297163\pi$
$422$	−32.4749	−	6.62980i	−1.58085	−	0.322733i
$423$	3.30669	+	0.675065i	0.160777	+	0.0328228i
$424$	−3.11336	−	1.18074i	−0.151198	−	0.0573419i
$425$	2.61783	+	64.9608i	0.126983	+	3.15106i
$426$	−13.7299	−	10.3174i	−0.665217	−	0.499878i
$427$	−3.83176	−	2.21227i	−0.185432	−	0.107059i
$428$	2.03173	+	16.7328i	0.0982072	+	0.808809i
$429$	−3.36511	−	4.43182i	−0.162469	−	0.213970i
$430$	3.74267	−	30.8237i	0.180488	−	1.48645i
$431$	−10.1019	+	13.4432i	−0.486590	+	0.647534i	−0.974242	−	0.225504i	$-0.927597\pi$
$431$	−10.1019	+	13.4432i	−0.486590	+	0.647534i	0.487652	+	0.873038i	$0.337854\pi$
$432$	4.48797	−	1.49830i	0.215927	−	0.0720871i
$433$	24.2421	+	25.2387i	1.16500	+	1.21290i	0.972826	+	0.231536i	$0.0743750\pi$
$433$	24.2421	+	25.2387i	1.16500	+	1.21290i	0.192176	+	0.981360i	$0.438446\pi$
$434$	−8.95237	+	10.1051i	−0.429728	+	0.485062i
$435$	19.3340	−	5.60016i	0.926995	−	0.268507i
$436$	13.1906	+	10.7698i	0.631713	+	0.515778i
$437$			0.822346i			0.0393382i
$438$	9.68775	−	11.8653i	0.462899	−	0.566948i
$439$	−0.384933	+	9.55200i	−0.0183718	+	0.455892i	0.963655	+	0.267150i	$0.0860820\pi$
$439$	−0.384933	+	9.55200i	−0.0183718	+	0.455892i	−0.982027	+	0.188742i	$0.939559\pi$
$440$	2.19267	−	5.14639i	0.104532	−	0.245345i
$441$	−1.95960	−	5.16705i	−0.0933145	−	0.246050i
$442$	9.68296	+	38.4566i	0.460572	+	1.82920i
$443$	3.23758	−	8.53680i	0.153822	−	0.405595i	−0.835848	−	0.548961i	$-0.815023\pi$
$443$	3.23758	−	8.53680i	0.153822	−	0.405595i	0.989670	+	0.143366i	$0.0457926\pi$
$444$	−6.36166	−	6.11045i	−0.301911	−	0.289989i
$445$	−6.42702	+	22.1887i	−0.304670	+	1.05184i
$446$	−4.23362	−	0.341773i	−0.200468	−	0.0161834i
$447$	−1.12372	−	2.14107i	−0.0531502	−	0.101269i
$448$	−3.32117	+	3.19002i	−0.156910	+	0.150714i
$449$	0.281838	+	0.661499i	0.0133008	+	0.0312181i	0.926497	−	0.376301i	$-0.122804\pi$
$449$	0.281838	+	0.661499i	0.0133008	+	0.0312181i	−0.913197	+	0.407519i	$0.866394\pi$
$450$	19.4445	−	7.37432i	0.916622	−	0.347629i
$451$	15.5513	−	2.52733i	0.732282	−	0.119007i
$452$	−11.4393	+	7.23378i	−0.538060	+	0.340248i
$453$	0.0711139	+	0.0205984i	0.00334122	+	0.000967797i
$454$	−9.37152	−	13.5770i	−0.439827	−	0.637199i
$455$	−4.96876	−	16.8386i	−0.232939	−	0.789405i
$456$	−0.0804656	+	0.116574i	−0.00376815	+	0.00545910i
$457$	14.0117	−	11.4402i	0.655438	−	0.535149i	−0.245335	−	0.969438i	$-0.578898\pi$
$457$	14.0117	−	11.4402i	0.655438	−	0.535149i	0.900773	+	0.434290i	$0.143001\pi$
$458$	26.2488	+	32.1490i	1.22653	+	1.50222i
$459$	−4.68785	+	3.52269i	−0.218810	+	0.164425i
$460$	31.7144	−	3.85082i	1.47869	−	0.179546i
$461$	−8.15212	+	24.4186i	−0.379682	+	1.13729i	0.569347	+	0.822098i	$0.307196\pi$
$461$	−8.15212	+	24.4186i	−0.379682	+	1.13729i	−0.949029	+	0.315189i	$0.897932\pi$
$462$	−0.282790	+	3.50299i	−0.0131566	+	0.162974i
$463$	−2.44058	−	2.75485i	−0.113423	−	0.128029i	0.689057	−	0.724707i	$-0.258025\pi$
$463$	−2.44058	−	2.75485i	−0.113423	−	0.128029i	−0.802480	+	0.596679i	$0.796487\pi$
$464$	20.0691	+	12.6909i	0.931684	+	0.589161i
$465$	21.8764	+	9.32065i	1.01449	+	0.432235i
$466$	−5.98545	+	36.8300i	−0.277271	+	1.70612i
$467$	9.67246	+	8.56905i	0.447588	+	0.396528i	0.856584	−	0.516008i	$-0.172582\pi$
$467$	9.67246	+	8.56905i	0.447588	+	0.396528i	−0.408996	+	0.912536i	$0.634121\pi$
$468$	4.61185	−	2.94875i	0.213183	−	0.136306i
$469$	−9.37368	+	8.30436i	−0.432836	+	0.383460i
$470$	13.5700	+	21.4592i	0.625936	+	0.989839i
$471$	−7.51439	+	0.606625i	−0.346245	+	0.0279518i
$472$	−2.69914	+	13.2213i	−0.124238	+	0.608558i
$473$	1.52440	−	6.18472i	0.0700919	−	0.284374i
$474$	−4.01775	−	24.7222i	−0.184542	−	1.13553i
$475$	−0.928808	+	1.46879i	−0.0426166	+	0.0673928i
$476$	5.02269	−	9.56994i	0.230215	−	0.438637i
$477$	−1.02511	−	3.53910i	−0.0469367	−	0.162044i
$478$	−1.21473	−	5.95014i	−0.0555604	−	0.272153i
$479$	−25.5090	−	1.02798i	−1.16554	−	0.0469696i	−0.550061	−	0.835125i	$-0.685395\pi$
$479$	−25.5090	−	1.02798i	−1.16554	−	0.0469696i	−0.615477	+	0.788155i	$0.711037\pi$
$480$	25.0993	+	13.1732i	1.14562	+	0.601269i
$481$	18.1941	+	10.3834i	0.829582	+	0.473443i
$482$	−24.1998	+	12.7011i	−1.10227	+	0.578517i
$483$	5.75433	−	2.73046i	0.261831	−	0.124240i
$484$	6.54201	−	11.3311i	0.297364	−	0.515049i
$485$	−11.9647	−	20.7235i	−0.543291	−	0.941007i
$486$	1.54366	+	1.06551i	0.0700219	+	0.0483326i
$487$	−4.34495	−	5.78207i	−0.196888	−	0.262011i	0.690192	−	0.723627i	$-0.257526\pi$
$487$	−4.34495	−	5.78207i	−0.196888	−	0.262011i	−0.887080	+	0.461616i	$0.847270\pi$
$488$	−2.85231	+	1.64678i	−0.129118	+	0.0745463i
$489$	−18.9012	−	2.29503i	−0.854744	−	0.103785i
$490$	17.8225	−	37.5601i	0.805138	−	1.69679i
$491$	2.44349	−	2.54395i	0.110273	−	0.114807i	−0.663778	−	0.747930i	$-0.731048\pi$
$491$	2.44349	−	2.54395i	0.110273	−	0.114807i	0.774051	+	0.633123i	$0.218227\pi$
$492$	1.24712	+	15.4484i	0.0562247	+	0.696468i
$493$	−28.5731	−	7.04264i	−1.28687	−	0.317185i
$494$	−0.370933	+	0.993021i	−0.0166891	+	0.0446781i
$495$	6.01029	−	1.48140i	0.270142	−	0.0665841i
$496$	8.88297	+	26.6078i	0.398857	+	1.19472i
$497$	−4.76531	−	10.0427i	−0.213753	−	0.450476i
$498$	−2.41082	−	0.804851i	−0.108032	−	0.0360663i
$499$	22.1056	−	15.2584i	0.989584	−	0.683060i	0.0408595	−	0.999165i	$-0.486990\pi$
$499$	22.1056	−	15.2584i	0.989584	−	0.683060i	0.948724	+	0.316104i	$0.102375\pi$
$500$	33.4874	+	15.8900i	1.49760	+	0.710621i
$501$	−24.1846	+	0.974606i	−1.08049	+	0.0435422i
$502$	6.67547	+	27.0834i	0.297941	+	1.20879i
$503$	−32.4935	+	13.8442i	−1.44881	+	0.617281i	−0.966023	−	0.258456i	$-0.916786\pi$
$503$	−32.4935	+	13.8442i	−1.44881	+	0.617281i	−0.482788	+	0.875737i	$0.660376\pi$
$504$	1.08290	+	0.175988i	0.0482361	+	0.00783912i
$505$	55.3870	−	11.3073i	2.46469	−	0.503170i
$506$	15.1876			0.675172
$507$	−8.91119	+	9.46523i	−0.395760	+	0.420366i
$508$	−12.0869			−0.536272
$509$	31.6769	−	6.46688i	1.40405	−	0.286640i	0.562493	−	0.826802i	$-0.309842\pi$
$509$	31.6769	−	6.46688i	1.40405	−	0.286640i	0.841561	+	0.540163i	$0.181637\pi$
$510$	−43.5437	−	7.07654i	−1.92815	−	0.313354i
$511$	9.12100	−	3.88610i	0.403489	−	0.171911i
$512$	5.95592	+	24.1641i	0.263217	+	1.06791i
$513$	−0.156616	+	0.00631142i	−0.00691478	+	0.000278656i
$514$	−16.6208	−	7.88667i	−0.733112	−	0.347866i
$515$	7.09057	−	4.89427i	0.312448	−	0.215667i
$516$	5.94358	+	1.98426i	0.261651	+	0.0873521i
$517$	2.23290	+	4.70574i	0.0982029	+	0.206958i
$518$	−4.18960	−	12.5494i	−0.184080	−	0.551388i
$519$	5.62657	−	1.38682i	0.246979	−	0.0608748i
$520$	−12.7044	−	3.06405i	−0.557127	−	0.134368i
$521$	−4.30137	−	1.06019i	−0.188446	−	0.0464478i	0.143963	−	0.989583i	$-0.454015\pi$
$521$	−4.30137	−	1.06019i	−0.188446	−	0.0464478i	−0.332409	+	0.943135i	$0.607862\pi$
$522$	0.757450	+	9.38270i	0.0331527	+	0.410670i
$523$	−5.30792	+	5.52613i	−0.232099	+	0.241641i	−0.827060	−	0.562114i	$-0.809988\pi$
$523$	−5.30792	+	5.52613i	−0.232099	+	0.241641i	0.594960	+	0.803755i	$0.297168\pi$
$524$	2.02432	−	4.26617i	0.0884330	−	0.186368i
$525$	13.3618	+	1.62241i	0.583155	+	0.0708078i
$526$	−40.8319	+	23.5743i	−1.78036	+	1.02789i
$527$	−20.8850	−	27.7928i	−0.909763	−	1.21067i
$528$	6.00967	+	4.14817i	0.261537	+	0.180526i
$529$	−2.26261	−	3.91895i	−0.0983743	−	0.170389i
$530$	13.8598	−	24.0058i	0.602030	−	1.04275i
$531$	−13.4903	+	6.40122i	−0.585429	+	0.277789i
$532$	0.255807	−	0.134258i	0.0110906	−	0.00582081i
$533$	−11.8302	−	34.8545i	−0.512422	−	1.50971i
$534$	−9.56565	−	5.02044i	−0.413946	−	0.217256i
$535$	44.4940	+	1.79305i	1.92364	+	0.0775202i
$536$	1.86464	+	9.13363i	0.0805403	+	0.394513i
$537$	5.62318	+	19.4135i	0.242658	+	0.837753i
$538$	15.7907	−	30.0867i	0.680785	−	1.29713i
$539$	4.55834	−	7.20844i	0.196342	−	0.310490i
$540$	0.976796	+	6.01047i	0.0420346	+	0.258649i
$541$	−7.86380	+	31.9047i	−0.338091	+	1.37169i	0.518228	+	0.855243i	$0.326592\pi$
$541$	−7.86380	+	31.9047i	−0.338091	+	1.37169i	−0.856319	+	0.516447i	$0.827254\pi$
$542$	10.2596	−	50.2550i	0.440689	−	2.15864i
$543$	10.3068	−	0.832048i	0.442306	−	0.0357066i
$544$	−22.1495	−	35.0266i	−0.949651	−	1.50175i
$545$	33.6736	−	29.8322i	1.44242	−	1.27787i
$546$	8.18024	−	0.701570i	0.350082	−	0.0300244i
$547$	1.85206	+	1.64079i	0.0791886	+	0.0701549i	0.701789	−	0.712385i	$-0.252385\pi$
$547$	1.85206	+	1.64079i	0.0791886	+	0.0701549i	−0.622600	+	0.782540i	$0.713924\pi$
$548$	−3.94607	+	24.2811i	−0.168568	+	1.03724i
$549$	−3.35290	−	1.42854i	−0.143098	−	0.0609685i
$550$	27.1266	+	17.1538i	1.15668	+	0.731441i
$551$	−0.521628	−	0.588796i	−0.0222221	−	0.0250836i
$552$	0.381508	−	4.72583i	0.0162381	−	0.201144i
$553$	5.13354	−	15.3768i	0.218300	−	0.653889i
$554$	−4.84361	+	0.588121i	−0.205785	+	0.0249869i
$555$	−18.6298	+	13.9994i	−0.790792	+	0.594241i
$556$	−18.8085	−	23.0362i	−0.797658	−	0.976953i
$557$	2.19315	−	1.79065i	0.0929269	−	0.0758725i	−0.584843	−	0.811146i	$-0.698844\pi$
$557$	2.19315	−	1.79065i	0.0929269	−	0.0758725i	0.677770	+	0.735274i	$0.262947\pi$
$558$	−6.31709	+	9.15189i	−0.267424	+	0.387430i
$559$	−14.8387	−	1.12324i	−0.627608	−	0.0475079i
$560$	13.0875	+	18.9605i	0.553048	+	0.801228i
$561$	−8.69272	−	2.51788i	−0.367007	−	0.106305i
$562$	−36.2065	+	22.8956i	−1.52728	+	0.965793i
$563$	36.1897	−	5.88140i	1.52522	−	0.247872i	0.660766	−	0.750592i	$-0.270232\pi$
$563$	36.1897	−	5.88140i	1.52522	−	0.247872i	0.864449	+	0.502720i	$0.167667\pi$
$564$	−4.79082	+	1.81692i	−0.201730	+	0.0765060i
$565$	14.0153	+	32.8951i	0.589628	+	1.38391i
$566$	−1.16083	+	1.11499i	−0.0487933	+	0.0468666i
$567$	0.564182	+	1.07496i	0.0236934	+	0.0451440i
$568$	−8.24770	−	0.665823i	−0.346066	−	0.0279373i
$569$	1.33558	−	4.61095i	0.0559903	−	0.193301i	−0.927648	−	0.373456i	$-0.878173\pi$
$569$	1.33558	−	4.61095i	0.0559903	−	0.193301i	0.983638	+	0.180155i	$0.0576599\pi$
$570$	−0.850444	−	0.816862i	−0.0356212	−	0.0342146i
$571$	0.599449	−	1.58062i	0.0250862	−	0.0661468i	−0.921888	−	0.387456i	$-0.873354\pi$
$571$	0.599449	−	1.58062i	0.0250862	−	0.0661468i	0.946974	+	0.321310i	$0.104123\pi$
$572$	7.91411	+	2.95624i	0.330906	+	0.123607i
$573$	−0.585895	−	1.54488i	−0.0244761	−	0.0645383i
$574$	−9.11168	+	21.3859i	−0.380314	+	0.892630i
$575$	2.34218	−	58.1206i	0.0976756	−	2.42380i
$576$	−2.39901	+	2.93825i	−0.0999586	+	0.122427i
$577$		−	1.67511i		−	0.0697359i	−0.999392	−	0.0348679i	$-0.988899\pi$
$577$		−	1.67511i		−	0.0697359i	0.999392	−	0.0348679i	$-0.0111011\pi$
$578$	25.2595	+	20.6237i	1.05066	+	0.857834i
$579$	−4.52511	+	1.31072i	−0.188057	+	0.0544715i
$580$	−20.2647	+	22.8741i	−0.841447	+	0.949797i
$581$	−1.13956	−	1.18641i	−0.0472768	−	0.0492204i
$582$	10.6147	−	3.54372i	0.439995	−	0.146892i
$583$	3.41617	−	4.54609i	0.141483	−	0.188280i
$584$	0.889573	−	7.32629i	0.0368108	−	0.303164i
$585$	−5.73485	−	13.2757i	−0.237107	−	0.548881i
$586$	6.10758	+	50.3004i	0.252302	+	2.07789i
$587$	26.3659	+	15.2224i	1.08824	+	0.628295i	0.933107	−	0.359599i	$-0.117087\pi$
$587$	26.3659	+	15.2224i	1.08824	+	0.628295i	0.155132	+	0.987894i	$0.450420\pi$
$588$	6.70720	+	5.04014i	0.276600	+	0.207852i
$589$	−0.0374185	−	0.928529i	−0.00154180	−	0.0382594i
$590$	−105.035	−	39.8346i	−4.32424	−	1.63997i
$591$	5.40506	+	1.10345i	0.222334	+	0.0453899i
$592$	−26.9347	−	5.49875i	−1.10701	−	0.225997i
$593$	−42.9599	−	16.2925i	−1.76415	−	0.669055i	−0.999703	−	0.0243706i	$-0.992242\pi$
$593$	−42.9599	−	16.2925i	−1.76415	−	0.669055i	−0.764449	−	0.644684i	$-0.776989\pi$
$594$	0.116563	+	2.89249i	0.00478265	+	0.118680i
$595$	−22.8264	−	17.1529i	−0.935792	−	0.703202i
$596$	3.17926	+	1.83555i	0.130227	+	0.0751869i
$597$	0.369644	+	3.04429i	0.0151285	+	0.124595i
$598$	−5.86665	−	34.9928i	−0.239905	−	1.43096i
$599$	−2.84321	+	23.4159i	−0.116170	+	0.956748i	0.811759	+	0.583992i	$0.198510\pi$
$599$	−2.84321	+	23.4159i	−0.116170	+	0.956748i	−0.927929	+	0.372756i	$0.878413\pi$
$600$	6.01905	−	8.00990i	0.245727	−	0.327003i
$601$	14.8786	−	4.96720i	0.606910	−	0.202616i	0.00342938	−	0.999994i	$-0.498908\pi$
$601$	14.8786	−	4.96720i	0.606910	−	0.202616i	0.603480	+	0.797378i	$0.293780\pi$
$602$	6.51043	+	6.77807i	0.265345	+	0.276254i
$603$	−6.84039	+	7.72121i	−0.278562	+	0.314432i
$604$	−0.107966	+	0.0312726i	−0.00439305	+	0.00127246i
$605$	−26.7750	−	21.8611i	−1.08856	−	0.888780i
$606$			26.4360i			1.07389i
$607$	17.1329	−	20.9840i	0.695403	−	0.851714i	−0.299337	−	0.954147i	$-0.596766\pi$
$607$	17.1329	−	20.9840i	0.695403	−	0.851714i	0.994740	+	0.102434i	$0.0326630\pi$
$608$	0.0446051	−	1.10686i	0.00180897	−	0.0448892i
$609$	−2.38810	+	5.60507i	−0.0967705	+	0.227129i
$610$	−9.72269	−	25.6366i	−0.393660	−	1.03800i
$611$	9.97966	−	6.96241i	0.403734	−	0.281669i
$612$	3.15691	−	8.32408i	0.127610	−	0.336481i
$613$	−22.2342	−	21.3562i	−0.898029	−	0.862569i	0.0930746	−	0.995659i	$-0.470331\pi$
$613$	−22.2342	−	21.3562i	−0.898029	−	0.862569i	−0.991104	+	0.133090i	$0.957510\pi$
$614$	−12.9651	+	44.7606i	−0.523227	+	1.80639i
$615$	40.8123	+	3.29471i	1.64571	+	0.132856i
$616$	0.786875	+	1.49926i	0.0317041	+	0.0604071i
$617$	27.1651	−	26.0925i	1.09363	−	1.05044i	0.0951392	−	0.995464i	$-0.469670\pi$
$617$	27.1651	−	26.0925i	1.09363	−	1.05044i	0.998488	−	0.0549787i	$-0.0175091\pi$
$618$	1.57929	+	3.70672i	0.0635282	+	0.149106i
$619$	−27.4671	+	10.4169i	−1.10400	+	0.418691i	−0.838214	−	0.545341i	$-0.816400\pi$
$619$	−27.4671	+	10.4169i	−1.10400	+	0.418691i	−0.265784	+	0.964033i	$0.585631\pi$
$620$	−35.6342	+	5.79112i	−1.43110	+	0.232577i
$621$	4.43425	−	2.80405i	0.177940	−	0.112523i
$622$	−16.7521	−	4.85231i	−0.671699	−	0.194560i
$623$	−3.97200	−	5.75444i	−0.159135	−	0.230547i
$624$	7.23613	−	15.4488i	0.289677	−	0.618448i
$625$	24.1358	−	34.9668i	0.965432	−	1.39867i
$626$	37.7580	−	30.8285i	1.50911	−	1.23215i
$627$	−0.152995	−	0.187384i	−0.00611001	−	0.00748341i
$628$	9.15002	−	6.87580i	0.365126	−	0.274374i
$629$	33.8214	−	4.10666i	1.34855	−	0.163743i
$630$	−2.89220	+	8.66319i	−0.115228	+	0.345150i
$631$	−0.763509	+	9.45775i	−0.0303948	+	0.376507i	0.963621	+	0.267272i	$0.0861222\pi$
$631$	−0.763509	+	9.45775i	−0.0303948	+	0.376507i	−0.994016	+	0.109235i	$0.965160\pi$
$632$	−8.00211	−	9.03252i	−0.318307	−	0.359294i
$633$	−14.9351	−	9.44439i	−0.593617	−	0.375381i
$634$	−49.2690	−	20.9915i	−1.95672	−	0.833681i
$635$	−5.12224	+	31.5184i	−0.203270	+	1.25077i
$636$	4.18712	+	3.70947i	0.166030	+	0.147090i
$637$	−18.3693	−	7.71811i	−0.727818	−	0.305803i
$638$	−10.8743	+	9.63376i	−0.430516	+	0.381404i
$639$	−4.89373	−	7.73882i	−0.193593	−	0.306143i
$640$	28.0642	−	2.26558i	1.10934	−	0.0895548i
$641$	−3.82071	+	18.7151i	−0.150909	+	0.739202i	0.831951	+	0.554849i	$0.187224\pi$
$641$	−3.82071	+	18.7151i	−0.150909	+	0.739202i	−0.982860	+	0.184353i	$0.940981\pi$
$642$	−4.98365	+	20.2195i	−0.196689	+	0.797998i
$643$	3.12220	+	19.2116i	0.123127	+	0.757633i	0.973027	+	0.230689i	$0.0740981\pi$
$643$	3.12220	+	19.2116i	0.123127	+	0.757633i	−0.849900	+	0.526944i	$0.823338\pi$
$644$	−5.16822	+	8.17288i	−0.203656	+	0.322057i
$645$	7.69301	−	14.6578i	0.302912	−	0.577151i
$646$	0.479646	+	1.65593i	0.0188714	+	0.0651517i
$647$	−1.84924	−	9.05816i	−0.0727010	−	0.356113i	0.927125	−	0.374751i	$-0.122272\pi$
$647$	−1.84924	−	9.05816i	−0.0727010	−	0.356113i	−0.999826	+	0.0186385i	$0.994067\pi$
$648$	0.902964	+	0.0363882i	0.0354718	+	0.00142946i
$649$	−20.4055	−	10.7096i	−0.800987	−	0.420390i
$650$	29.0446	−	69.1267i	1.13922	−	2.71137i
$651$	−6.37310	+	3.34486i	−0.249781	+	0.131095i
$652$	26.1158	−	12.3921i	1.02277	−	0.485312i
$653$	−23.2547	+	40.2783i	−0.910026	+	1.57621i	−0.0960021	+	0.995381i	$0.530606\pi$
$653$	−23.2547	+	40.2783i	−0.910026	+	1.57621i	−0.814024	+	0.580831i	$0.802728\pi$
$654$	10.5192	+	18.2198i	0.411334	+	0.712451i
$655$	−10.2668	−	7.08663i	−0.401155	−	0.276898i
$656$	29.0167	+	38.6142i	1.13291	+	1.50763i
$657$	7.07245	−	4.08328i	0.275923	−	0.159304i
$658$	−7.62900	−	0.926328i	−0.297409	−	0.0361120i
$659$	15.8322	−	33.3657i	0.616735	−	1.29974i	−0.319239	−	0.947674i	$-0.603427\pi$
$659$	15.8322	−	33.3657i	0.616735	−	1.29974i	0.935974	−	0.352068i	$-0.114521\pi$
$660$	−6.51018	+	6.77781i	−0.253408	+	0.263826i
$661$	−3.04712	−	37.7454i	−0.118519	−	1.46812i	−0.733558	−	0.679627i	$-0.762142\pi$
$661$	−3.04712	−	37.7454i	−0.118519	−	1.46812i	0.615039	−	0.788497i	$-0.289140\pi$
$662$	−5.41761	−	1.33532i	−0.210562	−	0.0518988i
$663$	−2.44347	+	21.0009i	−0.0948963	+	0.815609i
$664$	−1.18896	+	0.293052i	−0.0461406	+	0.0113726i
$665$	−0.241689	−	0.723947i	−0.00937230	−	0.0280735i
$666$	−4.67185	−	9.84572i	−0.181031	−	0.381514i
$667$	24.9745	+	8.33772i	0.967017	+	0.322838i
$668$	30.2422	−	20.8747i	1.17011	−	0.807665i
$669$	−2.04581	−	0.970751i	−0.0790958	−	0.0375314i
$670$	−77.5414	+	3.12481i	−2.99569	+	0.120722i
$671$	−1.34610	−	5.46134i	−0.0519656	−	0.210833i
$672$	−7.89332	+	3.36303i	−0.304492	+	0.129732i
$673$	22.5180	+	3.65953i	0.868004	+	0.141064i	0.578075	−	0.815984i	$-0.303804\pi$
$673$	22.5180	+	3.65953i	0.868004	+	0.141064i	0.289929	+	0.957048i	$0.406368\pi$
$674$	23.2536	−	4.74726i	0.895696	−	0.182858i
$675$	11.0871			0.426742
$676$	3.75423	−	19.3763i	0.144393	−	0.745243i
$677$	20.2626			0.778756			0.389378	−	0.921078i	$-0.372690\pi$
$677$	20.2626			0.778756			0.389378	+	0.921078i	$0.372690\pi$
$678$	−16.3836	+	3.34473i	−0.629208	+	0.128454i
$679$	7.14922	+	1.16186i	0.274362	+	0.0445882i
$680$	−19.5536	+	8.33100i	−0.749846	+	0.319479i
$681$	−2.10486	−	8.53974i	−0.0806583	−	0.327244i
$682$	−17.1487	+	0.691068i	−0.656656	+	0.0264624i
$683$	−11.4118	−	5.41494i	−0.436659	−	0.207197i	0.197657	−	0.980271i	$-0.436667\pi$
$683$	−11.4118	−	5.41494i	−0.436659	−	0.207197i	−0.634316	+	0.773074i	$0.718718\pi$
$684$	0.195844	−	0.135182i	0.00748830	−	0.00516880i
$685$	61.6441	+	20.5798i	2.35530	+	0.786315i
$686$	12.2278	+	25.7696i	0.466861	+	0.983888i
$687$	7.00698	+	20.9885i	0.267333	+	0.800760i
$688$	18.9606	−	4.67337i	0.722866	−	0.178171i
$689$	−11.7939	−	6.11491i	−0.449313	−	0.232959i
$690$	38.3228	+	9.44573i	1.45893	+	0.359593i
$691$	−3.37200	−	41.7697i	−0.128277	−	1.58899i	−0.666053	−	0.745905i	$-0.732017\pi$
$691$	−3.37200	−	41.7697i	−0.128277	−	1.58899i	0.537776	−	0.843088i	$-0.319265\pi$
$692$	−6.09454	+	6.34509i	−0.231680	+	0.241204i
$693$	−0.803220	+	1.69275i	−0.0305118	+	0.0643023i
$694$	−35.5196	−	4.31286i	−1.34831	−	0.163714i
$695$	−68.0408	+	39.2834i	−2.58094	+	1.49010i
$696$	2.72451	+	3.62567i	0.103272	+	0.137431i
$697$	−49.2654	−	34.0054i	−1.86606	−	1.28805i
$698$	−6.61907	−	11.4646i	−0.250535	−	0.433940i
$699$	−9.94653	+	17.2279i	−0.376212	+	0.651619i
$700$	−18.4619	+	8.76028i	−0.697794	+	0.331108i
$701$	−32.8740	+	17.2536i	−1.24163	+	0.651660i	−0.952182	−	0.305532i	$-0.901166\pi$
$701$	−32.8740	+	17.2536i	−1.24163	+	0.651660i	−0.289453	+	0.957192i	$0.593473\pi$
$702$	6.61937	−	1.38587i	0.249832	−	0.0523064i
$703$	0.806379	+	0.423220i	0.0304131	+	0.0159621i
$704$	−5.84951	−	0.235727i	−0.220462	−	0.00888431i
$705$	2.70760	+	13.2627i	0.101974	+	0.499502i
$706$	7.34067	+	25.3429i	0.276270	+	0.953794i
$707$	−7.95161	+	15.1505i	−0.299051	+	0.569794i
$708$	12.1162	−	19.1603i	0.455356	−	0.720088i
$709$	−6.03662	−	37.1448i	−0.226710	−	1.39500i	−0.811753	−	0.584001i	$-0.801486\pi$
$709$	−6.03662	−	37.1448i	−0.226710	−	1.39500i	0.585043	−	0.811003i	$-0.301078\pi$
$710$	16.4851	−	66.8825i	0.618673	−	2.51006i
$711$	2.67100	−	13.0834i	0.100170	−	0.490666i
$712$	−5.18799	+	0.418818i	−0.194428	+	0.0156959i
$713$	16.6243	+	26.2893i	0.622586	+	0.984541i
$714$	9.99471	−	8.85454i	0.374043	−	0.331373i
$715$	11.0627	−	19.3843i	0.413720	−	0.724933i
$716$	−22.9681	−	20.3480i	−0.858360	−	0.760440i
$717$	0.519360	−	3.19575i	0.0193958	−	0.119347i
$718$	−16.2681	−	6.93119i	−0.607120	−	0.258670i
$719$	−32.4975	−	20.5502i	−1.21195	−	0.766391i	−0.233397	−	0.972382i	$-0.574984\pi$
$719$	−32.4975	−	20.5502i	−1.21195	−	0.766391i	−0.978554	+	0.205990i	$0.933959\pi$
$720$	12.5843	+	14.2047i	0.468988	+	0.529378i
$721$	−0.209842	+	2.59936i	−0.00781491	+	0.0968050i
$722$	11.2708	−	33.7603i	0.419457	−	1.25643i
$723$	−14.4646	+	1.75632i	−0.537945	+	0.0653183i
$724$	−12.5502	+	9.43087i	−0.466425	+	0.350495i
$725$	35.1899	+	43.0998i	1.30692	+	1.60068i
$726$	12.5214	−	10.2234i	0.464711	−	0.379425i
$727$	−28.9540	+	41.9471i	−1.07385	+	1.55573i	−0.268174	+	0.963371i	$0.586420\pi$
$727$	−28.9540	+	41.9471i	−1.07385	+	1.55573i	−0.805671	+	0.592363i	$0.798195\pi$
$728$	3.15040	−	2.39212i	0.116762	−	0.0886579i
$729$	0.568065	+	0.822984i	0.0210394	+	0.0304809i
$730$	59.0125	+	17.0932i	2.18415	+	0.632647i
$731$	−20.4552	+	12.9351i	−0.756565	+	0.478422i
$732$	5.46151	−	0.887581i	0.201863	−	0.0328060i
$733$	−31.8510	+	12.0795i	−1.17644	+	0.446167i	−0.863864	−	0.503725i	$-0.831963\pi$
$733$	−31.8510	+	12.0795i	−1.17644	+	0.446167i	−0.312580	+	0.949891i	$0.601193\pi$
$734$	10.9135	+	25.6149i	0.402824	+	0.945462i
$735$	15.9852	−	15.3540i	0.589625	−	0.566342i
$736$	17.2312	+	32.8314i	0.635152	+	1.21018i
$737$	−15.8687	−	1.28105i	−0.584529	−	0.0471881i
$738$	−5.32732	+	18.3920i	−0.196101	+	0.677020i
$739$	−20.0390	−	19.2477i	−0.737146	−	0.708039i	0.226857	−	0.973928i	$-0.427155\pi$
$739$	−20.0390	−	19.2477i	−0.737146	−	0.708039i	−0.964004	+	0.265889i	$0.914334\pi$
$740$	12.5457	−	33.0804i	0.461191	−	1.21606i
$741$	−0.372641	+	0.424887i	−0.0136893	+	0.0156086i
$742$	2.97521	+	7.84498i	0.109223	+	0.287998i
$743$	0.577366	−	1.35513i	0.0211815	−	0.0497148i	−0.909053	−	0.416681i	$-0.863193\pi$
$743$	0.577366	−	1.35513i	0.0211815	−	0.0497148i	0.930234	+	0.366966i	$0.119604\pi$
$744$	−0.215734	+	5.35339i	−0.00790921	+	0.196265i
$745$	6.13375	−	7.51248i	0.224723	−	0.275236i
$746$		−	47.2658i		−	1.73052i
$747$	−1.04962	−	0.856986i	−0.0384035	−	0.0313555i
$748$	13.1973	−	3.82266i	0.482542	−	0.139770i
$749$	−8.93788	+	10.0888i	−0.326583	+	0.368636i
$750$	31.7225	+	33.0267i	1.15834	+	1.20596i
$751$	14.2305	−	4.75085i	0.519279	−	0.173361i	−0.0449341	−	0.998990i	$-0.514308\pi$
$751$	14.2305	−	4.75085i	0.519279	−	0.173361i	0.564213	+	0.825629i	$0.309180\pi$
$752$	−9.59277	+	12.7657i	−0.349812	+	0.465515i
$753$	−1.79254	+	14.7629i	−0.0653238	+	0.537990i
$754$	26.3970	+	21.3334i	0.961322	+	0.776915i
$755$	0.0357937	+	0.294788i	0.00130267	+	0.0107284i
$756$	−1.59620	−	0.921564i	−0.0580531	−	0.0335169i
$757$	19.2358	+	14.4548i	0.699138	+	0.525368i	0.889836	−	0.456281i	$-0.150819\pi$
$757$	19.2358	+	14.4548i	0.699138	+	0.525368i	−0.190698	+	0.981649i	$0.561075\pi$
$758$	−0.153518	−	3.80951i	−0.00557603	−	0.138368i
$759$	7.57091	+	2.87127i	0.274807	+	0.104220i
$760$	−0.556652	−	0.113641i	−0.0201919	−	0.00412221i
$761$	50.3753	+	10.2842i	1.82610	+	0.372802i	0.985612	−	0.169022i	$-0.0540609\pi$
$761$	50.3753	+	10.2842i	1.82610	+	0.372802i	0.840492	+	0.541824i	$0.182266\pi$
$762$	−13.9626	−	5.29531i	−0.505811	−	0.191829i
$763$	0.548296	+	13.6058i	0.0198497	+	0.492564i
$764$	2.00536	+	1.50693i	0.0725515	+	0.0545189i
$765$	−20.3684	−	11.7597i	−0.736419	−	0.425172i
$766$	0.278187	+	2.29108i	0.0100513	+	0.0827801i
$767$	−16.7932	+	51.1519i	−0.606366	+	1.84699i
$768$	−2.50155	+	20.6021i	−0.0902668	+	0.743414i
$769$	−10.1346	+	13.4867i	−0.365463	+	0.486343i	−0.944293	−	0.329105i	$-0.893253\pi$
$769$	−10.1346	+	13.4867i	−0.365463	+	0.486343i	0.578830	+	0.815448i	$0.303509\pi$
$770$	−13.3703	+	4.46367i	−0.481833	+	0.160859i
$771$	−6.79434	−	7.07366i	−0.244692	−	0.254752i
$772$	4.74295	−	5.35368i	0.170702	−	0.192683i
$773$	10.3485	−	2.99748i	0.372210	−	0.107812i	−0.0868401	−	0.996222i	$-0.527677\pi$
$773$	10.3485	−	2.99748i	0.372210	−	0.107812i	0.459050	+	0.888410i	$0.348190\pi$
$774$	5.99659	+	4.89606i	0.215543	+	0.175985i
$775$			65.7318i			2.36116i
$776$	3.40989	−	4.17636i	0.122408	−	0.149923i
$777$	0.284018	−	7.04783i	0.0101891	−	0.252839i
$778$	13.5383	−	31.7755i	0.485370	−	1.13921i
$779$	−0.567411	−	1.49614i	−0.0203296	−	0.0536048i
$780$	18.1311	+	12.3815i	0.649196	+	0.443331i
$781$	5.01105	−	13.2130i	0.179309	−	0.472800i
$782$	−41.6169	−	39.9736i	−1.48822	−	1.42945i
$783$	−1.39625	+	4.82040i	−0.0498978	+	0.172267i
$784$	26.0620	+	2.10395i	0.930787	+	0.0751409i
$785$	−14.0520	−	26.7738i	−0.501536	−	0.955598i
$786$	4.20747	−	4.04133i	0.150076	−	0.144150i
$787$	20.0372	+	47.0290i	0.714248	+	1.67640i	0.736309	+	0.676645i	$0.236567\pi$
$787$	20.0372	+	47.0290i	0.714248	+	1.67640i	−0.0220610	+	0.999757i	$0.507023\pi$
$788$	−7.83099	+	2.96990i	−0.278967	+	0.105798i
$789$	−24.8112	+	4.03221i	−0.883302	+	0.143551i
$790$	84.9066	−	53.6917i	3.02084	−	1.91026i
$791$	−10.3955	−	3.01109i	−0.369622	−	0.107062i
$792$	0.792290	+	1.14783i	0.0281528	+	0.0407864i
$793$	−12.0632	+	5.21106i	−0.428375	+	0.185050i
$794$	−22.4606	+	32.5398i	−0.797096	+	1.15479i
$795$	11.4474	−	9.34649i	0.405997	−	0.331486i
$796$	−2.94454	−	3.60641i	−0.104367	−	0.127826i
$797$	17.0307	−	12.7978i	0.603260	−	0.453320i	−0.254712	−	0.967017i	$-0.581981\pi$
$797$	17.0307	−	12.7978i	0.603260	−	0.453320i	0.857972	+	0.513697i	$0.171724\pi$
$798$	0.354321	−	0.0430223i	0.0125428	−	0.00152297i
$799$	6.26688	−	18.7716i	0.221706	−	0.664091i
$800$	−6.30506	+	78.1022i	−0.222918	+	2.76133i
$801$	−3.81927	−	4.31107i	−0.134947	−	0.152324i
$802$	3.46592	+	2.19172i	0.122386	+	0.0773922i
$803$	11.5953	+	4.94029i	0.409188	+	0.174339i
$804$	2.51219	−	15.4581i	0.0885981	−	0.545166i
$805$	19.1217	+	16.9404i	0.673952	+	0.597069i
$806$	8.21640	+	39.2442i	0.289410	+	1.38232i
$807$	13.5595	−	12.0127i	0.477318	−	0.422867i
$808$	6.80736	+	10.7650i	0.239482	+	0.378710i
$809$	−1.42606	+	0.115124i	−0.0501376	+	0.00404753i	−0.105510	−	0.994418i	$-0.533647\pi$
$809$	−1.42606	+	0.115124i	−0.0501376	+	0.00404753i	0.0553723	+	0.998466i	$0.482365\pi$
$810$	−1.50482	+	7.37110i	−0.0528740	+	0.258994i
$811$	−6.88607	+	27.9379i	−0.241803	+	0.981032i	0.717026	+	0.697046i	$0.245503\pi$
$811$	−6.88607	+	27.9379i	−0.241803	+	0.981032i	−0.958829	+	0.283985i	$0.908343\pi$
$812$	−1.48377	−	9.13003i	−0.0520703	−	0.320401i
$813$	14.6152	−	23.1121i	0.512578	−	0.810577i
$814$	7.81630	−	14.8927i	0.273961	−	0.521989i
$815$	−21.2467	−	73.3521i	−0.744239	−	2.56941i
$816$	−5.54968	−	27.1841i	−0.194278	−	0.951635i
$817$	−0.646399	−	0.0260490i	−0.0226146	−	0.000911338i
$818$	45.7099	+	23.9904i	1.59821	+	0.838806i
$819$	4.21042	+	1.19677i	0.147124	+	0.0418186i
$820$	−55.0427	+	28.8886i	−1.92217	+	1.00883i
$821$	32.0078	−	15.1879i	1.11708	−	0.530061i	0.221588	−	0.975140i	$-0.428876\pi$
$821$	32.0078	−	15.1879i	1.11708	−	0.530061i	0.895491	+	0.445080i	$0.146825\pi$
$822$	−15.1960	+	26.3203i	−0.530022	+	0.918025i
$823$	−0.00247171	−	0.00428112i	−8.61583e−5	−	0.000149230i	0.865982	−	0.500075i	$-0.166694\pi$
$823$	−0.00247171	−	0.00428112i	−8.61583e−5	−	0.000149230i	−0.866068	+	0.499925i	$0.833361\pi$
$824$	1.59759	+	1.10274i	0.0556547	+	0.0384157i
$825$	10.2794	+	13.6794i	0.357883	+	0.476256i
$826$	29.4465	−	17.0009i	1.02457	−	0.591538i
$827$	38.3586	+	4.65758i	1.33386	+	0.161960i	0.756213	−	0.654326i	$-0.227048\pi$
$827$	38.3586	+	4.65758i	1.33386	+	0.161960i	0.577648	+	0.816286i	$0.303971\pi$
$828$	−3.41461	+	7.19615i	−0.118666	+	0.250083i
$829$	6.71672	−	6.99285i	0.233281	−	0.242872i	−0.594265	−	0.804270i	$-0.702557\pi$
$829$	6.71672	−	6.99285i	0.233281	−	0.242872i	0.827546	+	0.561398i	$0.189736\pi$
$830$	−0.820286	−	10.1611i	−0.0284726	−	0.352696i
$831$	−2.52569	−	0.622527i	−0.0876153	−	0.0215952i
$832$	1.71642	+	13.5685i	0.0595060	+	0.470404i
$833$	−31.4632	+	7.75499i	−1.09014	+	0.268695i
$834$	−11.6350	−	34.8510i	−0.402886	−	1.20679i
$835$	−41.6175	−	87.7070i	−1.44023	−	3.03523i
$836$	0.348367	+	0.116302i	0.0120485	+	0.00402239i
$837$	−4.87922	+	3.36788i	−0.168650	+	0.116411i
$838$	18.4919	+	8.77451i	0.638792	+	0.303110i
$839$	50.5457	−	2.03692i	1.74503	−	0.0703223i	0.852893	−	0.522086i	$-0.174846\pi$
$839$	50.5457	−	2.03692i	1.74503	−	0.0703223i	0.892138	+	0.451763i	$0.149205\pi$
$840$	1.05307	+	4.27247i	0.0363344	+	0.147414i
$841$	3.50900	−	1.49504i	0.121000	−	0.0515532i
$842$	−63.9195	−	10.3879i	−2.20281	−	0.357991i
$843$	−22.3772	+	4.56833i	−0.770711	+	0.157342i
$844$	26.8277			0.923449
$845$	−48.9355	−	18.0010i	−1.68343	−	0.619254i
$846$	−6.33025			−0.217638
$847$	10.2511	−	2.09277i	0.352231	−	0.0719084i
$848$	17.2077	+	2.79652i	0.590914	+	0.0960328i
$849$	−0.789458	+	0.336356i	−0.0270941	+	0.0115437i
$850$	−29.1834	−	118.402i	−1.00098	−	4.06114i
$851$	−30.4576	+	1.22740i	−1.04407	+	0.0420747i
$852$	12.5590	+	5.95932i	0.430264	+	0.204163i
$853$	−0.656311	+	0.453019i	−0.0224717	+	0.0155111i	−0.579248	−	0.815152i	$-0.696654\pi$
$853$	−0.656311	+	0.453019i	−0.0224717	+	0.0155111i	0.556776	+	0.830663i	$0.312038\pi$
$854$	7.87195	+	2.62804i	0.269373	+	0.0899298i
$855$	−0.269509	−	0.567979i	−0.00921702	−	0.0194245i
$856$	3.17719	+	9.51684i	0.108594	+	0.325279i
$857$	20.0579	−	4.94383i	0.685165	−	0.168878i	0.118658	−	0.992935i	$-0.462141\pi$
$857$	20.0579	−	4.94383i	0.685165	−	0.168878i	0.566507	+	0.824057i	$0.308295\pi$
$858$	7.84708	+	6.88217i	0.267895	+	0.234954i
$859$	−1.55976	−	0.384446i	−0.0532183	−	0.0131171i	0.212617	−	0.977136i	$-0.431801\pi$
$859$	−1.55976	−	0.384446i	−0.0532183	−	0.0131171i	−0.265835	+	0.964019i	$0.585648\pi$
$860$	2.02231	+	25.0508i	0.0689602	+	0.854226i
$861$	−8.58517	+	8.93811i	−0.292582	+	0.304610i
$862$	13.5214	−	28.4957i	0.460539	−	0.970566i
$863$	16.1523	+	1.96125i	0.549831	+	0.0667616i	0.390738	−	0.920502i	$-0.372220\pi$
$863$	16.1523	+	1.96125i	0.549831	+	0.0667616i	0.159093	+	0.987264i	$0.449143\pi$
$864$	−6.12051	+	3.53368i	−0.208224	+	0.120218i
$865$	13.9629	+	18.5813i	0.474754	+	0.631783i
$866$	−54.0210	−	37.2880i	−1.83571	−	1.26710i
$867$	8.69268	+	15.0562i	0.295219	+	0.511334i
$868$	5.46366	−	9.46334i	0.185449	−	0.321207i
$869$	18.6190	−	8.83481i	0.631605	−	0.299701i
$870$	−33.4306	+	17.5457i	−1.13340	+	0.594856i
$871$	3.17814	+	37.0568i	0.107687	+	1.25562i
$872$	8.97517	+	4.71053i	0.303937	+	0.159519i
$873$	5.96132	+	0.240233i	0.201760	+	0.00813065i
$874$	−0.308533	−	1.51129i	−0.0104363	−	0.0511202i
$875$	8.24624	+	28.4693i	0.278774	+	0.962439i
$876$	−5.76188	+	10.9783i	−0.194676	+	0.370924i
$877$	5.23080	−	8.27185i	0.176632	−	0.279321i	−0.745256	−	0.666779i	$-0.767673\pi$
$877$	5.23080	−	8.27185i	0.176632	−	0.279321i	0.921887	+	0.387458i	$0.126647\pi$
$878$	−2.87635	−	17.6989i	−0.0970722	−	0.597309i
$879$	−6.46488	+	26.2290i	−0.218055	+	0.884683i
$880$	−5.85846	+	28.6966i	−0.197489	+	0.967363i
$881$	17.3786	−	1.40294i	0.585498	−	0.0472663i	0.215831	−	0.976431i	$-0.430754\pi$
$881$	17.3786	−	1.40294i	0.585498	−	0.0472663i	0.369667	+	0.929164i	$0.379472\pi$
$882$	5.53993	+	8.76069i	0.186539	+	0.294988i
$883$	−39.9171	+	35.3635i	−1.34332	+	1.19008i	−0.378981	+	0.925405i	$0.623725\pi$
$883$	−39.9171	+	35.3635i	−1.34332	+	1.19008i	−0.964338	+	0.264672i	$0.914736\pi$
$884$	−13.9054	−	28.9305i	−0.467688	−	0.973038i
$885$	−44.8284	−	39.7145i	−1.50689	−	1.33499i
$886$	−2.74708	+	16.9035i	−0.0922900	+	0.567883i
$887$	−39.9094	−	17.0038i	−1.34003	−	0.570932i	−0.401411	−	0.915898i	$-0.631480\pi$
$887$	−39.9094	−	17.0038i	−1.34003	−	0.570932i	−0.938615	+	0.344966i	$0.887890\pi$
$888$	−4.43772	−	2.80624i	−0.148920	−	0.0941714i
$889$	−6.40922	−	7.23451i	−0.214958	−	0.242638i
$890$	3.48659	−	43.1892i	0.116871	−	1.44771i
$891$	−0.488729	+	1.46392i	−0.0163730	+	0.0490432i
$892$	3.41283	−	0.414392i	0.114270	−	0.0138749i
$893$	0.422899	−	0.317788i	0.0141518	−	0.0106344i
$894$	2.86846	+	3.51322i	0.0959355	+	0.117500i
$895$	−62.7937	+	51.2695i	−2.09896	+	1.71375i
$896$	−4.84114	+	7.01360i	−0.161731	+	0.234308i
$897$	3.69102	−	18.5527i	0.123240	−	0.619458i
$898$	−0.766143	−	1.10995i	−0.0255665	−	0.0370395i
$899$	−28.5787	−	8.27791i	−0.953152	−	0.276084i
$900$	−14.2266	+	8.99637i	−0.474221	+	0.299879i
$901$	−21.3262	+	3.46584i	−0.710478	+	0.115464i
$902$	−27.6317	+	10.4793i	−0.920034	+	0.348923i
$903$	1.96398	+	4.60964i	0.0653572	+	0.153399i
$904$	−5.81025	+	5.58082i	−0.193246	+	0.185615i
$905$	19.2737	+	36.7230i	0.640681	+	1.22071i
$906$	−0.138420	−	0.0111744i	−0.00459870	−	0.000371245i
$907$	−5.78029	+	19.9559i	−0.191932	+	0.662624i	0.805604	+	0.592455i	$0.201841\pi$
$907$	−5.78029	+	19.9559i	−0.191932	+	0.662624i	−0.997535	+	0.0701695i	$0.977646\pi$
$908$	9.63028	+	9.25001i	0.319592	+	0.306972i
$909$	−4.99782	+	13.1782i	−0.165767	+	0.437092i
$910$	15.4491	+	29.0814i	0.512133	+	0.964040i
$911$	7.84285	+	20.6799i	0.259845	+	0.685156i	0.999920	+	0.0126314i	$0.00402080\pi$
$911$	7.84285	+	20.6799i	0.259845	+	0.685156i	−0.740075	+	0.672524i	$0.765210\pi$
$912$	0.290693	−	0.682281i	0.00962579	−	0.0225926i
$913$	0.0842078	−	2.08960i	0.00278687	−	0.0691555i
$914$	−21.4582	+	26.2815i	−0.709774	+	0.869315i
$915$		−	14.6178i		−	0.483249i
$916$	−26.0218	−	21.2461i	−0.859784	−	0.701992i
$917$	3.62689	−	1.05054i	0.119770	−	0.0346919i
$918$	7.29359	−	8.23276i	0.240724	−	0.271722i
$919$	30.9915	+	32.2656i	1.02232	+	1.06434i	0.997909	+	0.0646416i	$0.0205904\pi$
$919$	30.9915	+	32.2656i	1.02232	+	1.06434i	0.0244075	+	0.999702i	$0.492230\pi$
$920$	18.0377	−	6.02186i	0.594685	−	0.198535i
$921$	−14.9251	+	19.8617i	−0.491799	+	0.654466i
$922$	5.82031	−	47.9346i	0.191682	−	1.57864i
$923$	−32.3790	−	6.44171i	−1.06577	−	0.212031i
$924$	−0.342877	−	2.82384i	−0.0112798	−	0.0928977i
$925$	−55.7866	−	32.2084i	−1.83425	−	1.05901i
$926$	5.51883	+	4.14713i	0.181360	+	0.136283i
$927$	0.0864946	+	2.14634i	0.00284086	+	0.0704951i
$928$	−33.1630	−	12.5771i	−1.08863	−	0.412862i
$929$	44.0128	+	8.98527i	1.44401	+	0.294797i	0.857224	−	0.514944i	$-0.172187\pi$
$929$	44.0128	+	8.98527i	1.44401	+	0.294797i	0.586788	+	0.809741i	$0.300392\pi$
$930$	−43.7010	−	8.92162i	−1.43301	−	0.292551i
$931$	−0.809901	−	0.307155i	−0.0265434	−	0.0100666i
$932$	−1.21610	−	30.1772i	−0.0398347	−	0.988489i
$933$	−7.43346	−	5.58589i	−0.243361	−	0.182874i
$934$	−20.9909	−	12.1191i	−0.686842	−	0.396548i
$935$	−4.37530	−	36.0339i	−0.143088	−	1.17843i
$936$	2.33860	−	2.26885i	0.0764394	−	0.0741595i
$937$	6.40713	−	52.7674i	0.209312	−	1.72384i	−0.387855	−	0.921720i	$-0.626784\pi$
$937$	6.40713	−	52.7674i	0.209312	−	1.72384i	0.597167	−	0.802117i	$-0.296293\pi$
$938$	14.1111	−	18.7785i	0.460744	−	0.613139i
$939$	24.6503	−	8.22949i	0.804433	−	0.268559i
$940$	−14.2360	−	14.8213i	−0.464329	−	0.483417i
$941$	25.3799	−	28.6479i	0.827360	−	0.933896i	−0.171323	−	0.985215i	$-0.554804\pi$
$941$	25.3799	−	28.6479i	0.827360	−	0.933896i	0.998682	+	0.0513190i	$0.0163425\pi$
$942$	13.5822	−	3.93414i	0.442532	−	0.128181i
$943$	41.4867	+	33.8729i	1.35099	+	1.10305i
$944$		−	70.6501i		−	2.29946i
$945$	−3.07954	+	3.77176i	−0.100178	+	0.122695i
$946$	−0.481089	+	11.9381i	−0.0156416	+	0.388141i
$947$	−7.91966	+	18.5881i	−0.257354	+	0.604033i	−0.997670	−	0.0682266i	$-0.978266\pi$
$947$	−7.91966	+	18.5881i	−0.257354	+	0.604033i	0.740315	+	0.672260i	$0.234676\pi$
$948$	7.18891	+	18.9556i	0.233485	+	0.615649i
$949$	6.90358	−	28.6242i	0.224100	−	0.929182i
$950$	1.15588	−	3.04780i	0.0375016	−	0.0988836i
$951$	−20.5917	−	19.7786i	−0.667731	−	0.641365i
$952$	1.78986	−	6.17931i	0.0580097	−	0.200273i
$953$	28.2202	+	2.27817i	0.914140	+	0.0737970i	0.528578	−	0.848885i	$-0.322725\pi$
$953$	28.2202	+	2.27817i	0.914140	+	0.0737970i	0.385562	+	0.922682i	$0.374007\pi$
$954$	3.21175	+	6.11948i	0.103984	+	0.198126i
$955$	4.77937	−	4.59065i	0.154657	−	0.148550i
$956$	1.92669	+	4.52212i	0.0623137	+	0.146256i
$957$	−7.24203	+	2.74654i	−0.234102	+	0.0887830i
$958$	47.2657	−	7.68143i	1.52709	−	0.248176i
$959$	−16.6256	+	10.5134i	−0.536870	+	0.339496i
$960$	−14.6134	−	4.23284i	−0.471647	−	0.136614i
$961$	−2.35710	−	3.41485i	−0.0760355	−	0.110156i
$962$	−37.3326	−	12.2563i	−1.20365	−	0.395158i
$963$	−6.30686	+	9.13707i	−0.203236	+	0.294438i
$964$	17.1354	−	13.9907i	0.551896	−	0.450609i
$965$	−11.9505	−	14.6367i	−0.384700	−	0.471172i
$966$	−9.55077	+	7.17694i	−0.307291	+	0.230914i
$967$	5.01590	−	0.609040i	0.161300	−	0.0195854i	−0.0394880	−	0.999220i	$-0.512573\pi$
$967$	5.01590	−	0.609040i	0.161300	−	0.0195854i	0.200788	+	0.979635i	$0.435650\pi$
$968$	2.46625	−	7.38733i	0.0792684	−	0.237438i
$969$	−0.0739591	+	0.916148i	−0.00237591	+	0.0294309i
$970$	29.7638	+	33.5963i	0.955656	+	1.07871i
$971$	5.72724	+	3.62169i	0.183796	+	0.116225i	0.623195	−	0.782066i	$-0.285834\pi$
$971$	5.72724	+	3.62169i	0.183796	+	0.116225i	−0.439399	+	0.898292i	$0.644809\pi$
$972$	−1.39672	−	0.595086i	−0.0447997	−	0.0190874i
$973$	3.81470	−	23.4728i	0.122294	−	0.752503i
$974$	10.1544	+	8.99603i	0.325368	+	0.288251i
$975$	27.5471	−	28.9682i	0.882214	−	0.927725i
$976$	12.9073	−	11.4349i	0.413154	−	0.366022i
$977$	20.8340	+	32.9463i	0.666538	+	1.05405i	0.994021	+	0.109189i	$0.0348253\pi$
$977$	20.8340	+	32.9463i	0.666538	+	1.05405i	−0.327483	+	0.944857i	$0.606200\pi$
$978$	35.5974	−	2.87372i	1.13828	−	0.0918915i
$979$	1.77802	−	8.70931i	0.0568257	−	0.278351i
$980$	−8.05311	+	32.6727i	−0.257247	+	1.04369i
$981$	1.79923	+	11.0711i	0.0574451	+	0.353474i
$982$	−3.53615	+	5.59198i	−0.112843	+	0.178447i
$983$	12.7027	−	24.2030i	0.405154	−	0.771956i	−0.594325	−	0.804225i	$-0.702581\pi$
$983$	12.7027	−	24.2030i	0.405154	−	0.771956i	0.999479	+	0.0322686i	$0.0102732\pi$
$984$	2.56668	+	8.86119i	0.0818226	+	0.282484i
$985$	4.42579	+	21.6790i	0.141018	+	0.690749i
$986$	55.1535	+	2.22261i	1.75644	+	0.0707823i
$987$	−3.62787	−	1.90405i	−0.115476	−	0.0606067i
$988$	0.133397	−	0.847575i	0.00424393	−	0.0269650i
$989$	19.1733	−	10.0629i	0.609674	−	0.319982i
$990$	−10.4898	+	4.97747i	−0.333388	+	0.158194i
$991$	−0.317752	+	0.550363i	−0.0100937	+	0.0174829i	−0.871028	−	0.491233i	$-0.836546\pi$
$991$	−0.317752	+	0.550363i	−0.0100937	+	0.0174829i	0.860934	+	0.508716i	$0.169880\pi$
$992$	−20.9501	−	36.2866i	−0.665166	−	1.15210i
$993$	−2.44819	−	1.68987i	−0.0776911	−	0.0536263i
$994$	12.5255	+	16.6684i	0.397284	+	0.528689i
$995$	−10.6521	+	6.14997i	−0.337693	+	0.194967i
$996$	2.04222	+	0.247971i	0.0647103	+	0.00785726i
$997$	10.6901	−	22.5290i	0.338560	−	0.713499i	−0.660752	−	0.750605i	$-0.729762\pi$
$997$	10.6901	−	22.5290i	0.338560	−	0.713499i	0.999311	+	0.0371052i	$0.0118137\pi$
$998$	−34.9006	+	36.3353i	−1.10476	+	1.15018i
$999$	−0.467518	−	5.79125i	−0.0147916	−	0.183227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.355.3	yes	360
169.10	even	78	inner	507.2.t.b.10.3	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.10.3	✓	360	169.10	even	78	inner
507.2.t.b.355.3	yes	360	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.83778 + 0.375186i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(1.39672 - 0.595086i) q^{4} +(-0.959864 - 3.89432i) q^{5} +(1.87417 - 0.0755263i) q^{6} +(1.09680 + 0.520440i) q^{7} +(0.743728 - 0.513358i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})\)	\(q+(-1.83778 + 0.375186i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(1.39672 - 0.595086i) q^{4} +(-0.959864 - 3.89432i) q^{5} +(1.87417 - 0.0755263i) q^{6} +(1.09680 + 0.520440i) q^{7} +(0.743728 - 0.513358i) q^{8} +(0.948536 + 0.316668i) q^{9} +(3.22511 + 6.79678i) q^{10} +(0.488729 + 1.46392i) q^{11} +(-1.47409 + 0.363330i) q^{12} +(3.18414 - 1.69153i) q^{13} +(-2.21095 - 0.544950i) q^{14} +(0.322741 + 3.99786i) q^{15} +(-3.27760 + 3.41234i) q^{16} +(2.51381 - 5.29775i) q^{17} +(-1.86201 - 0.226089i) q^{18} +(0.135744 - 0.0783717i) q^{19} +(-3.65811 - 4.86806i) q^{20} +(-0.999117 - 0.689641i) q^{21} +(-1.44742 - 2.50700i) q^{22} +(-2.62322 + 4.54356i) q^{23} +(-0.816446 + 0.387408i) q^{24} +(-9.81711 + 5.15242i) q^{25} +(-5.21711 + 4.30330i) q^{26} +(-0.885456 - 0.464723i) q^{27} +(1.84163 + 0.0742153i) q^{28} +(-1.00384 - 4.91712i) q^{29} +(-2.09307 - 7.22611i) q^{30} +(2.75520 - 5.24959i) q^{31} +(3.77726 - 5.97326i) q^{32} +(-0.247570 - 1.52336i) q^{33} +(-2.63220 + 10.6792i) q^{34} +(0.973978 - 4.77086i) q^{35} +(1.51328 - 0.122165i) q^{36} +(3.10529 + 4.91063i) q^{37} +(-0.220063 + 0.194959i) q^{38} +(-3.41424 + 1.15885i) q^{39} +(-2.71306 - 2.40356i) q^{40} +(1.63757 - 10.0763i) q^{41} +(2.09490 + 0.892554i) q^{42} +(-3.48833 - 2.20589i) q^{43} +(1.55377 + 1.75385i) q^{44} +(0.322741 - 3.99786i) q^{45} +(3.11623 - 9.33426i) q^{46} +(3.35029 - 0.406799i) q^{47} +(3.78253 - 2.84239i) q^{48} +(-3.49500 - 4.28059i) q^{49} +(16.1086 - 13.1523i) q^{50} +(-3.33108 + 4.82590i) q^{51} +(3.44074 - 4.25742i) q^{52} +(-2.09308 - 3.03234i) q^{53} +(1.80163 + 0.521849i) q^{54} +(5.23186 - 3.30843i) q^{55} +(1.08290 - 0.175988i) q^{56} +(-0.146558 + 0.0555820i) q^{57} +(3.68967 + 8.65997i) q^{58} +(-10.7690 + 10.3437i) q^{59} +(2.82985 + 5.39183i) q^{60} +(-3.63272 - 0.293264i) q^{61} +(-3.09388 + 10.6813i) q^{62} +(0.875552 + 0.840979i) q^{63} +(-1.34510 + 3.54673i) q^{64} +(-9.64369 - 10.7764i) q^{65} +(1.02652 + 2.70672i) q^{66} +(-4.04330 + 9.48998i) q^{67} +(0.358472 - 8.89539i) q^{68} +(3.31809 - 4.06392i) q^{69} +9.13322i q^{70} +(-7.09252 - 5.79086i) q^{71} +(0.868017 - 0.251424i) q^{72} +(5.41543 - 6.11276i) q^{73} +(-7.54925 - 7.85960i) q^{74} +(10.5165 - 3.51092i) q^{75} +(0.142958 - 0.190242i) q^{76} +(-0.225844 + 1.85999i) q^{77} +(5.83985 - 3.41069i) q^{78} +(-1.60956 - 13.2559i) q^{79} +(16.4348 + 9.48864i) q^{80} +(0.799443 + 0.600742i) q^{81} +(0.771014 + 19.1325i) q^{82} +(-1.26698 - 0.480503i) q^{83} +(-1.80588 - 0.368673i) q^{84} +(-23.0440 - 4.70447i) q^{85} +(7.23841 + 2.74517i) q^{86} +(0.202076 + 5.01447i) q^{87} +(1.11500 + 0.837866i) q^{88} +(-4.98790 - 2.87976i) q^{89} +(0.906814 + 7.46829i) q^{90} +(4.37272 - 0.198122i) q^{91} +(-0.960097 + 7.90711i) q^{92} +(-3.56161 + 4.73965i) q^{93} +(-6.00447 + 2.00459i) q^{94} +(-0.435500 - 0.453404i) q^{95} +(-4.68652 + 5.28999i) q^{96} +(5.73060 - 1.65989i) q^{97} +(8.02905 + 6.55552i) q^{98} +1.54335i 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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