LMFDB - Embedded newform 675.2.l.d.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.4
Character	$\chi$	$=$	675.151
Dual form			675.2.l.d.76.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.531925 + 0.446338i) q^{2} +(-0.942993 + 1.45285i) q^{3} +(-0.263570 - 1.49478i) q^{4} +(-1.15006 + 0.351912i) q^{6} +(0.0506352 - 0.287167i) q^{7} +(1.22136 - 2.11545i) q^{8} +(-1.22153 - 2.74005i) q^{9} +O(q^{10})$	\(q+(0.531925 + 0.446338i) q^{2} +(-0.942993 + 1.45285i) q^{3} +(-0.263570 - 1.49478i) q^{4} +(-1.15006 + 0.351912i) q^{6} +(0.0506352 - 0.287167i) q^{7} +(1.22136 - 2.11545i) q^{8} +(-1.22153 - 2.74005i) q^{9} +(-1.68049 + 0.611647i) q^{11} +(2.42023 + 1.02664i) q^{12} +(-1.67842 + 1.40837i) q^{13} +(0.155107 - 0.130151i) q^{14} +(-1.25873 + 0.458140i) q^{16} +(-2.73283 - 4.73339i) q^{17} +(0.573226 - 2.00271i) q^{18} +(3.42243 - 5.92782i) q^{19} +(0.369461 + 0.344361i) q^{21} +(-1.16689 - 0.424714i) q^{22} +(-0.927728 - 5.26140i) q^{23} +(1.92170 + 3.76930i) q^{24} -1.52140 q^{26} +(5.13276 + 0.809152i) q^{27} -0.442597 q^{28} +(-2.26194 - 1.89799i) q^{29} +(1.08094 + 6.13030i) q^{31} +(-5.46483 - 1.98904i) q^{32} +(0.696057 - 3.01827i) q^{33} +(0.659035 - 3.73757i) q^{34} +(-3.77381 + 2.54811i) q^{36} +(-4.27364 - 7.40217i) q^{37} +(4.46628 - 1.62559i) q^{38} +(-0.463397 - 3.76657i) q^{39} +(3.48938 - 2.92794i) q^{41} +(0.0428237 + 0.348078i) q^{42} +(8.81367 - 3.20791i) q^{43} +(1.35720 + 2.35074i) q^{44} +(1.85488 - 3.21275i) q^{46} +(-0.948501 + 5.37922i) q^{47} +(0.521366 - 2.26076i) q^{48} +(6.49795 + 2.36506i) q^{49} +(9.45393 + 0.493178i) q^{51} +(2.54758 + 2.13767i) q^{52} +2.24096 q^{53} +(2.36909 + 2.72135i) q^{54} +(-0.545643 - 0.457849i) q^{56} +(5.38489 + 10.5622i) q^{57} +(-0.356035 - 2.01918i) q^{58} +(-9.80414 - 3.56842i) q^{59} +(0.0515134 - 0.292147i) q^{61} +(-2.16121 + 3.74332i) q^{62} +(-0.848703 + 0.212039i) q^{63} +(-0.679583 - 1.17707i) q^{64} +(1.71742 - 1.29481i) q^{66} +(3.41470 - 2.86527i) q^{67} +(-6.35509 + 5.33255i) q^{68} +(8.51886 + 3.61362i) q^{69} +(-4.74640 - 8.22101i) q^{71} +(-7.28836 - 0.762491i) q^{72} +(-5.24212 + 9.07962i) q^{73} +(1.03061 - 5.84488i) q^{74} +(-9.76283 - 3.55338i) q^{76} +(0.0905528 + 0.513550i) q^{77} +(1.43467 - 2.21036i) q^{78} +(-5.45470 - 4.57704i) q^{79} +(-6.01573 + 6.69410i) q^{81} +3.16293 q^{82} +(4.75792 + 3.99237i) q^{83} +(0.417366 - 0.643025i) q^{84} +(6.12002 + 2.22750i) q^{86} +(4.89048 - 1.49646i) q^{87} +(-0.758562 + 4.30202i) q^{88} +(-6.18976 + 10.7210i) q^{89} +(0.319448 + 0.553300i) q^{91} +(-7.62012 + 2.77350i) q^{92} +(-9.92570 - 4.21039i) q^{93} +(-2.90548 + 2.43799i) q^{94} +(8.04306 - 6.06391i) q^{96} +(13.2307 - 4.81556i) q^{97} +(2.40080 + 4.15831i) q^{98} +(3.72870 + 3.85747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 9 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 9 * q^8 - 3 * q^9	$ 30 q - 3 q^{3} + 9 q^{8} - 3 q^{9} - 6 q^{11} - 3 q^{12} - 3 q^{13} - 9 q^{14} + 12 q^{16} + 12 q^{17} - 6 q^{18} + 24 q^{19} - 36 q^{21} + 51 q^{22} - 18 q^{23} + 45 q^{24} - 18 q^{26} + 9 q^{27} + 60 q^{28} + 18 q^{29} + 12 q^{31} - 36 q^{32} - 27 q^{33} - 69 q^{34} - 42 q^{36} - 24 q^{37} + 24 q^{38} + 6 q^{39} - 75 q^{41} + 18 q^{42} - 6 q^{43} + 12 q^{44} + 30 q^{46} - 45 q^{47} + 27 q^{48} - 36 q^{49} + 21 q^{51} - 30 q^{52} - 36 q^{53} + 18 q^{54} + 30 q^{56} - 30 q^{57} - 27 q^{58} - 27 q^{59} - 12 q^{61} - 36 q^{62} - 18 q^{63} + 27 q^{64} + 78 q^{66} + 30 q^{67} - 69 q^{68} - 117 q^{69} + 12 q^{71} - 9 q^{72} - 21 q^{73} - 30 q^{76} + 36 q^{77} - 66 q^{78} + 54 q^{79} - 27 q^{81} + 48 q^{82} + 87 q^{83} + 45 q^{84} + 18 q^{86} + 27 q^{87} + 18 q^{88} + 9 q^{89} + 51 q^{91} - 24 q^{92} - 36 q^{93} + 15 q^{94} - 15 q^{96} + 75 q^{97} + 15 q^{98} + 123 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 9 * q^8 - 3 * q^9 - 6 * q^11 - 3 * q^12 - 3 * q^13 - 9 * q^14 + 12 * q^16 + 12 * q^17 - 6 * q^18 + 24 * q^19 - 36 * q^21 + 51 * q^22 - 18 * q^23 + 45 * q^24 - 18 * q^26 + 9 * q^27 + 60 * q^28 + 18 * q^29 + 12 * q^31 - 36 * q^32 - 27 * q^33 - 69 * q^34 - 42 * q^36 - 24 * q^37 + 24 * q^38 + 6 * q^39 - 75 * q^41 + 18 * q^42 - 6 * q^43 + 12 * q^44 + 30 * q^46 - 45 * q^47 + 27 * q^48 - 36 * q^49 + 21 * q^51 - 30 * q^52 - 36 * q^53 + 18 * q^54 + 30 * q^56 - 30 * q^57 - 27 * q^58 - 27 * q^59 - 12 * q^61 - 36 * q^62 - 18 * q^63 + 27 * q^64 + 78 * q^66 + 30 * q^67 - 69 * q^68 - 117 * q^69 + 12 * q^71 - 9 * q^72 - 21 * q^73 - 30 * q^76 + 36 * q^77 - 66 * q^78 + 54 * q^79 - 27 * q^81 + 48 * q^82 + 87 * q^83 + 45 * q^84 + 18 * q^86 + 27 * q^87 + 18 * q^88 + 9 * q^89 + 51 * q^91 - 24 * q^92 - 36 * q^93 + 15 * q^94 - 15 * q^96 + 75 * q^97 + 15 * q^98 + 123 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.531925	+	0.446338i	0.376128	+	0.315608i	0.811180	−	0.584797i	$-0.198826\pi$
$2$	0.531925	+	0.446338i	0.376128	+	0.315608i	−0.435052	+	0.900405i	$0.643270\pi$
$3$	−0.942993	+	1.45285i	−0.544437	+	0.838802i
$3$	−0.942993	+	1.45285i	−0.544437	+	0.838802i
$4$	−0.263570	−	1.49478i	−0.131785	−	0.747390i
$5$		0			0
$5$		0			0
$6$	−1.15006	+	0.351912i	−0.469511	+	0.143667i
$7$	0.0506352	−	0.287167i	0.0191383	−	0.108539i	−0.973742	−	0.227654i	$-0.926895\pi$
$7$	0.0506352	−	0.287167i	0.0191383	−	0.108539i	0.992880	+	0.119115i	$0.0380057\pi$
$8$	1.22136	−	2.11545i	0.431814	−	0.747924i
$9$	−1.22153	−	2.74005i	−0.407176	−	0.913350i
$10$		0			0
$11$	−1.68049	+	0.611647i	−0.506685	+	0.184418i	−0.582698	−	0.812688i	$-0.698003\pi$
$11$	−1.68049	+	0.611647i	−0.506685	+	0.184418i	0.0760131	+	0.997107i	$0.475781\pi$
$12$	2.42023	+	1.02664i	0.698660	+	0.296365i
$13$	−1.67842	+	1.40837i	−0.465511	+	0.390610i	−0.845154	−	0.534523i	$-0.820491\pi$
$13$	−1.67842	+	1.40837i	−0.465511	+	0.390610i	0.379643	+	0.925133i	$0.376047\pi$
$14$	0.155107	−	0.130151i	0.0414542	−	0.0347842i
$15$		0			0
$16$	−1.25873	+	0.458140i	−0.314682	+	0.114535i
$17$	−2.73283	−	4.73339i	−0.662808	−	1.14802i	−0.979875	−	0.199613i	$-0.936031\pi$
$17$	−2.73283	−	4.73339i	−0.662808	−	1.14802i	0.317067	−	0.948403i	$-0.397302\pi$
$18$	0.573226	−	2.00271i	0.135111	−	0.472044i
$19$	3.42243	−	5.92782i	0.785159	−	1.35993i	−0.143745	−	0.989615i	$-0.545915\pi$
$19$	3.42243	−	5.92782i	0.785159	−	1.35993i	0.928904	−	0.370320i	$-0.120752\pi$
$20$		0			0
$21$	0.369461	+	0.344361i	0.0806229	+	0.0751458i
$22$	−1.16689	−	0.424714i	−0.248782	−	0.0905494i
$23$	−0.927728	−	5.26140i	−0.193445	−	1.09708i	−0.914616	−	0.404322i	$-0.867507\pi$
$23$	−0.927728	−	5.26140i	−0.193445	−	1.09708i	0.721172	−	0.692756i	$-0.243604\pi$
$24$	1.92170	+	3.76930i	0.392264	+	0.769404i
$25$		0			0
$26$	−1.52140			−0.298372
$27$	5.13276	+	0.809152i	0.987801	+	0.155721i
$28$	−0.442597			−0.0836429
$29$	−2.26194	−	1.89799i	−0.420031	−	0.352448i	0.408144	−	0.912918i	$-0.366176\pi$
$29$	−2.26194	−	1.89799i	−0.420031	−	0.352448i	−0.828175	+	0.560470i	$0.810621\pi$
$30$		0			0
$31$	1.08094	+	6.13030i	0.194142	+	1.10103i	0.913635	+	0.406535i	$0.133263\pi$
$31$	1.08094	+	6.13030i	0.194142	+	1.10103i	−0.719493	+	0.694499i	$0.755626\pi$
$32$	−5.46483	−	1.98904i	−0.966054	−	0.351615i
$33$	0.696057	−	3.01827i	0.121168	−	0.525413i
$34$	0.659035	−	3.73757i	0.113024	−	0.640988i
$35$		0			0
$36$	−3.77381	+	2.54811i	−0.628968	+	0.424685i
$37$	−4.27364	−	7.40217i	−0.702583	−	1.21691i	−0.967557	−	0.252653i	$-0.918697\pi$
$37$	−4.27364	−	7.40217i	−0.702583	−	1.21691i	0.264974	−	0.964255i	$-0.414637\pi$
$38$	4.46628	−	1.62559i	0.724527	−	0.263706i
$39$	−0.463397	−	3.76657i	−0.0742029	−	0.603134i
$40$		0			0
$41$	3.48938	−	2.92794i	0.544949	−	0.457267i	−0.328277	−	0.944581i	$-0.606468\pi$
$41$	3.48938	−	2.92794i	0.544949	−	0.457267i	0.873226	+	0.487315i	$0.162024\pi$
$42$	0.0428237	+	0.348078i	0.00660784	+	0.0537097i
$43$	8.81367	−	3.20791i	1.34407	−	0.489202i	0.432979	−	0.901404i	$-0.357462\pi$
$43$	8.81367	−	3.20791i	1.34407	−	0.489202i	0.911093	+	0.412202i	$0.135240\pi$
$44$	1.35720	+	2.35074i	0.204606	+	0.354388i
$45$		0			0
$46$	1.85488	−	3.21275i	0.273487	−	0.473694i
$47$	−0.948501	+	5.37922i	−0.138353	+	0.784640i	0.834113	+	0.551594i	$0.185980\pi$
$47$	−0.948501	+	5.37922i	−0.138353	+	0.784640i	−0.972466	+	0.233046i	$0.925131\pi$
$48$	0.521366	−	2.26076i	0.0752527	−	0.326313i
$49$	6.49795	+	2.36506i	0.928278	+	0.337866i
$50$		0			0
$51$	9.45393	+	0.493178i	1.32382	+	0.0690588i
$52$	2.54758	+	2.13767i	0.353286	+	0.296442i
$53$	2.24096			0.307820			0.153910	−	0.988085i	$-0.450813\pi$
$53$	2.24096			0.307820			0.153910	+	0.988085i	$0.450813\pi$
$54$	2.36909	+	2.72135i	0.322392	+	0.370329i
$55$		0			0
$56$	−0.545643	−	0.457849i	−0.0729146	−	0.0611826i
$57$	5.38489	+	10.5622i	0.713246	+	1.39899i
$58$	−0.356035	−	2.01918i	−0.0467497	−	0.265131i
$59$	−9.80414	−	3.56842i	−1.27639	−	0.464568i	−0.387154	−	0.922015i	$-0.626542\pi$
$59$	−9.80414	−	3.56842i	−1.27639	−	0.464568i	−0.889237	+	0.457447i	$0.848764\pi$
$60$		0			0
$61$	0.0515134	−	0.292147i	0.00659562	−	0.0374056i	−0.981332	−	0.192320i	$-0.938399\pi$
$61$	0.0515134	−	0.292147i	0.00659562	−	0.0374056i	0.987928	+	0.154914i	$0.0495101\pi$
$62$	−2.16121	+	3.74332i	−0.274474	+	0.475402i
$63$	−0.848703	+	0.212039i	−0.106927	+	0.0267144i
$64$	−0.679583	−	1.17707i	−0.0849479	−	0.147134i
$65$		0			0
$66$	1.71742	−	1.29481i	0.211399	−	0.159381i
$67$	3.41470	−	2.86527i	0.417172	−	0.350049i	−0.409914	−	0.912124i	$-0.634441\pi$
$67$	3.41470	−	2.86527i	0.417172	−	0.350049i	0.827086	+	0.562075i	$0.189997\pi$
$68$	−6.35509	+	5.33255i	−0.770668	+	0.646667i
$69$	8.51886	+	3.61362i	1.02555	+	0.435029i
$70$		0			0
$71$	−4.74640	−	8.22101i	−0.563294	−	0.975654i	−0.997206	−	0.0746990i	$-0.976200\pi$
$71$	−4.74640	−	8.22101i	−0.563294	−	0.975654i	0.433912	−	0.900955i	$-0.357133\pi$
$72$	−7.28836	−	0.762491i	−0.858941	−	0.0898604i
$73$	−5.24212	+	9.07962i	−0.613544	+	1.06269i	0.377095	+	0.926175i	$0.376923\pi$
$73$	−5.24212	+	9.07962i	−0.613544	+	1.06269i	−0.990638	+	0.136514i	$0.956410\pi$
$74$	1.03061	−	5.84488i	0.119806	−	0.679454i
$75$		0			0
$76$	−9.76283	−	3.55338i	−1.11987	−	0.407601i
$77$	0.0905528	+	0.513550i	0.0103194	+	0.0585245i
$78$	1.43467	−	2.21036i	0.162445	−	0.250275i
$79$	−5.45470	−	4.57704i	−0.613702	−	0.514957i	0.282115	−	0.959381i	$-0.408964\pi$
$79$	−5.45470	−	4.57704i	−0.613702	−	0.514957i	−0.895817	+	0.444424i	$0.853408\pi$
$80$		0			0
$81$	−6.01573	+	6.69410i	−0.668415	+	0.743789i
$82$	3.16293			0.349288
$83$	4.75792	+	3.99237i	0.522249	+	0.438219i	0.865415	−	0.501056i	$-0.167055\pi$
$83$	4.75792	+	3.99237i	0.522249	+	0.438219i	−0.343166	+	0.939275i	$0.611499\pi$
$84$	0.417366	−	0.643025i	0.0455383	−	0.0701598i
$85$		0			0
$86$	6.12002	+	2.22750i	0.659939	+	0.240198i
$87$	4.89048	−	1.49646i	0.524315	−	0.160437i
$88$	−0.758562	+	4.30202i	−0.0808630	+	0.458597i
$89$	−6.18976	+	10.7210i	−0.656113	+	1.13642i	0.325500	+	0.945542i	$0.394467\pi$
$89$	−6.18976	+	10.7210i	−0.656113	+	1.13642i	−0.981613	+	0.190880i	$0.938866\pi$
$90$		0			0
$91$	0.319448	+	0.553300i	0.0334873	+	0.0580017i
$92$	−7.62012	+	2.77350i	−0.794452	+	0.289157i
$93$	−9.92570	−	4.21039i	−1.02925	−	0.436597i
$94$	−2.90548	+	2.43799i	−0.299677	+	0.251459i
$95$		0			0
$96$	8.04306	−	6.06391i	0.820891	−	0.618896i
$97$	13.2307	−	4.81556i	1.34337	−	0.488947i	0.432497	−	0.901635i	$-0.357632\pi$
$97$	13.2307	−	4.81556i	1.34337	−	0.488947i	0.910872	+	0.412689i	$0.135410\pi$
$98$	2.40080	+	4.15831i	0.242518	+	0.420053i
$99$	3.72870	+	3.85747i	0.374749	+	0.387690i
$100$		0			0
$101$	−2.18977	+	12.4188i	−0.217890	+	1.23572i	0.657931	+	0.753078i	$0.271432\pi$
$101$	−2.18977	+	12.4188i	−0.217890	+	1.23572i	−0.875821	+	0.482637i	$0.839679\pi$
$102$	4.80866	+	4.48198i	0.476128	+	0.443782i
$103$	−5.53963	−	2.01626i	−0.545836	−	0.198668i	0.0543593	−	0.998521i	$-0.482688\pi$
$103$	−5.53963	−	2.01626i	−0.545836	−	0.198668i	−0.600196	+	0.799853i	$0.704911\pi$
$104$	0.929373	+	5.27074i	0.0911326	+	0.516838i
$105$		0			0
$106$	1.19202	+	1.00023i	0.115780	+	0.0971507i
$107$	−6.13206			−0.592808			−0.296404	−	0.955063i	$-0.595788\pi$
$107$	−6.13206			−0.592808			−0.296404	+	0.955063i	$0.595788\pi$
$108$	−0.143339	−	7.88562i	−0.0137928	−	0.758794i
$109$	−5.00653			−0.479538			−0.239769	−	0.970830i	$-0.577072\pi$
$109$	−5.00653			−0.479538			−0.239769	+	0.970830i	$0.577072\pi$
$110$		0			0
$111$	14.7842	+	0.771241i	1.40326	+	0.0732030i
$112$	0.0678265	+	0.384663i	0.00640900	+	0.0363473i
$113$	2.11127	+	0.768439i	0.198611	+	0.0722887i	0.439411	−	0.898286i	$-0.355187\pi$
$113$	2.11127	+	0.768439i	0.198611	+	0.0722887i	−0.240799	+	0.970575i	$0.577410\pi$
$114$	−1.84993	+	8.02175i	−0.173262	+	0.751306i
$115$		0			0
$116$	−2.24090	+	3.88135i	−0.208062	+	0.360374i
$117$	5.90923	+	2.87861i	0.546309	+	0.266127i
$118$	−3.62235	−	6.27409i	−0.333464	−	0.577576i
$119$	−1.49765	+	0.545100i	−0.137289	+	0.0499692i
$120$		0			0
$121$	−5.97657	+	5.01494i	−0.543325	+	0.455903i
$122$	0.157798	−	0.132408i	0.0142863	−	0.0119877i
$123$	0.963384	+	7.83056i	0.0868654	+	0.706057i
$124$	8.87854	−	3.23152i	0.797317	−	0.290199i
$125$		0			0
$126$	−0.546087	−	0.266019i	−0.0486493	−	0.0236989i
$127$	2.00536	−	3.47339i	0.177947	−	0.308213i	−0.763230	−	0.646127i	$-0.776388\pi$
$127$	2.00536	−	3.47339i	0.177947	−	0.308213i	0.941177	+	0.337913i	$0.109721\pi$
$128$	−1.85583	+	10.5250i	−0.164034	+	0.930284i
$129$	−3.65062	+	15.8299i	−0.321419	+	1.39375i
$130$		0			0
$131$	−2.48282	−	14.0808i	−0.216925	−	1.23024i	−0.877535	−	0.479513i	$-0.840813\pi$
$131$	−2.48282	−	14.0808i	−0.216925	−	1.23024i	0.660610	−	0.750729i	$-0.270298\pi$
$132$	−4.69510	−	0.244927i	−0.408656	−	0.0213182i
$133$	−1.52898	−	1.28296i	−0.132579	−	0.111247i
$134$	3.09524			0.267388
$135$		0			0
$136$	−13.3510			−1.14484
$137$	−1.14455	−	0.960393i	−0.0977856	−	0.0820519i	0.592584	−	0.805508i	$-0.298108\pi$
$137$	−1.14455	−	0.960393i	−0.0977856	−	0.0820519i	−0.690370	+	0.723457i	$0.742552\pi$
$138$	2.91849	+	5.72446i	0.248439	+	0.487298i
$139$	−0.755255	−	4.28326i	−0.0640599	−	0.363302i	−0.999940	−	0.0109822i	$-0.996504\pi$
$139$	−0.755255	−	4.28326i	−0.0640599	−	0.363302i	0.935880	−	0.352319i	$-0.114607\pi$
$140$		0			0
$141$	−6.92075	−	6.45059i	−0.582832	−	0.543238i
$142$	1.14462	−	6.49146i	0.0960543	−	0.544751i
$143$	1.95915	−	3.39334i	0.163832	−	0.283765i
$144$	2.79290	+	2.88935i	0.232742	+	0.240779i
$145$		0			0
$146$	−6.84099	+	2.48992i	−0.566164	+	0.206067i
$147$	−9.56359	+	7.21029i	−0.788791	+	0.594695i
$148$	−9.93820	+	8.33914i	−0.816915	+	0.685473i
$149$	−9.10358	+	7.63881i	−0.745794	+	0.625796i	−0.934387	−	0.356260i	$-0.884052\pi$
$149$	−9.10358	+	7.63881i	−0.745794	+	0.625796i	0.188593	+	0.982055i	$0.439607\pi$
$150$		0			0
$151$	20.4667	−	7.44928i	1.66556	−	0.606214i	0.674337	−	0.738423i	$-0.264429\pi$
$151$	20.4667	−	7.44928i	1.66556	−	0.606214i	0.991222	+	0.132210i	$0.0422072\pi$
$152$	−8.36000	−	14.4799i	−0.678086	−	1.17448i
$153$	−9.63150	+	13.2701i	−0.778661	+	1.07282i
$154$	−0.181050	+	0.313587i	−0.0145894	+	0.0252696i
$155$		0			0
$156$	−5.50806	+	1.68543i	−0.440998	+	0.134943i
$157$	−12.0907	−	4.40065i	−0.964941	−	0.351210i	−0.188973	−	0.981982i	$-0.560516\pi$
$157$	−12.0907	−	4.40065i	−0.964941	−	0.351210i	−0.775968	+	0.630772i	$0.782738\pi$
$158$	−0.858585	−	4.86928i	−0.0683053	−	0.387379i
$159$	−2.11321	+	3.25578i	−0.167589	+	0.258200i
$160$		0			0
$161$	−1.55788			−0.122778
$162$	−6.18775	+	0.875706i	−0.486155	+	0.0688019i
$163$	16.1843			1.26765			0.633826	−	0.773476i	$-0.281484\pi$
$163$	16.1843			1.26765			0.633826	+	0.773476i	$0.281484\pi$
$164$	−5.29631	−	4.44414i	−0.413573	−	0.347029i
$165$		0			0
$166$	0.748909	+	4.24727i	0.0581266	+	0.329652i
$167$	15.4769	+	5.63313i	1.19764	+	0.435904i	0.862399	−	0.506229i	$-0.168961\pi$
$167$	15.4769	+	5.63313i	1.19764	+	0.435904i	0.335238	+	0.942133i	$0.391183\pi$
$168$	1.17972	−	0.360988i	0.0910175	−	0.0278508i
$169$	−1.42381	+	8.07483i	−0.109524	+	0.621141i
$170$		0			0
$171$	−20.4231	−	2.13662i	−1.56179	−	0.163391i
$172$	−7.11814	−	12.3290i	−0.542753	−	0.940076i
$173$	−9.64540	+	3.51064i	−0.733326	+	0.266909i	−0.681572	−	0.731751i	$-0.738703\pi$
$173$	−9.64540	+	3.51064i	−0.733326	+	0.266909i	−0.0517539	+	0.998660i	$0.516481\pi$
$174$	3.26929	+	1.38680i	0.247845	+	0.105133i
$175$		0			0
$176$	1.83506	−	1.53980i	0.138323	−	0.116066i
$177$	14.4296	−	10.8789i	1.08459	−	0.817710i
$178$	−8.07766	+	2.94003i	−0.605447	+	0.220365i
$179$	−3.40694	−	5.90100i	−0.254647	−	0.441061i	0.710153	−	0.704048i	$-0.248626\pi$
$179$	−3.40694	−	5.90100i	−0.254647	−	0.441061i	−0.964800	+	0.262986i	$0.915293\pi$
$180$		0			0
$181$	12.9542	−	22.4373i	0.962876	−	1.66775i	0.247661	−	0.968847i	$-0.420338\pi$
$181$	12.9542	−	22.4373i	0.962876	−	1.66775i	0.715216	−	0.698904i	$-0.246328\pi$
$182$	−0.0770365	+	0.436896i	−0.00571033	+	0.0323849i
$183$	0.375868	+	0.350334i	0.0277850	+	0.0258974i
$184$	−12.2633	−	4.46348i	−0.904064	−	0.329052i
$185$		0			0
$186$	−3.40047	−	6.66983i	−0.249334	−	0.489055i
$187$	7.48764	+	6.28287i	0.547550	+	0.459449i
$188$	8.29074			0.604665
$189$	0.492260	−	1.43299i	0.0358067	−	0.104234i
$190$		0			0
$191$	14.9382	+	12.5346i	1.08089	+	0.906973i	0.995994	−	0.0894165i	$-0.0285002\pi$
$191$	14.9382	+	12.5346i	1.08089	+	0.906973i	0.0848945	+	0.996390i	$0.472945\pi$
$192$	2.35095	+	0.122641i	0.169665	+	0.00885083i
$193$	2.97388	+	16.8657i	0.214064	+	1.21402i	0.882523	+	0.470270i	$0.155843\pi$
$193$	2.97388	+	16.8657i	0.214064	+	1.21402i	−0.668458	+	0.743750i	$0.733045\pi$
$194$	9.18708	+	3.34382i	0.659594	+	0.240073i
$195$		0			0
$196$	1.82258	−	10.3364i	0.130184	−	0.738311i
$197$	−9.77759	+	16.9353i	−0.696624	+	1.20659i	0.273006	+	0.962012i	$0.411982\pi$
$197$	−9.77759	+	16.9353i	−0.696624	+	1.20659i	−0.969630	+	0.244576i	$0.921351\pi$
$198$	0.261655	+	3.71614i	0.0185950	+	0.264095i
$199$	10.6782	+	18.4951i	0.756956	+	1.31109i	0.944396	+	0.328810i	$0.106648\pi$
$199$	10.6782	+	18.4951i	0.756956	+	1.31109i	−0.187440	+	0.982276i	$0.560019\pi$
$200$		0			0
$201$	0.942767	+	7.66297i	0.0664976	+	0.540504i
$202$	−6.70776	+	5.62848i	−0.471957	+	0.396019i
$203$	−0.659574	+	0.553448i	−0.0462930	+	0.0388444i
$204$	−1.75458	−	14.2615i	−0.122845	−	0.998507i
$205$		0			0
$206$	−2.04673	−	3.54505i	−0.142603	−	0.246995i
$207$	−13.2833	+	8.96898i	−0.923250	+	0.623387i
$208$	1.46745	−	2.54171i	0.101750	−	0.176236i
$209$	−2.12561	+	12.0549i	−0.147031	+	0.833857i
$210$		0			0
$211$	−1.73810	−	0.632615i	−0.119655	−	0.0435510i	0.281499	−	0.959562i	$-0.409169\pi$
$211$	−1.73810	−	0.632615i	−0.119655	−	0.0435510i	−0.401154	+	0.916011i	$0.631391\pi$
$212$	−0.590651	−	3.34975i	−0.0405661	−	0.230062i
$213$	16.4197	+	0.856558i	1.12506	+	0.0586904i
$214$	−3.26179	−	2.73697i	−0.222972	−	0.187095i
$215$		0			0
$216$	7.98065	−	9.86984i	0.543014	−	0.671558i
$217$	1.81515			0.123220
$218$	−2.66310	−	2.23460i	−0.180368	−	0.151346i
$219$	−8.24801	−	16.1780i	−0.557349	−	1.09321i
$220$		0			0
$221$	11.2532	+	4.09583i	0.756972	+	0.275515i
$222$	7.51986	+	7.00900i	0.504700	+	0.470413i
$223$	0.462980	−	2.62569i	0.0310034	−	0.175829i	−0.965374	−	0.260869i	$-0.915991\pi$
$223$	0.462980	−	2.62569i	0.0310034	−	0.175829i	0.996378	+	0.0850403i	$0.0271019\pi$
$224$	−0.847897	+	1.46860i	−0.0566525	+	0.0981251i
$225$		0			0
$226$	0.780053	+	1.35109i	0.0518883	+	0.0898732i
$227$	−4.21086	+	1.53263i	−0.279485	+	0.101724i	−0.477959	−	0.878382i	$-0.658623\pi$
$227$	−4.21086	+	1.53263i	−0.279485	+	0.101724i	0.198475	+	0.980106i	$0.436401\pi$
$228$	14.3688	−	10.8331i	0.951597	−	0.717439i
$229$	18.6698	−	15.6659i	1.23374	−	1.03523i	0.235751	−	0.971814i	$-0.424245\pi$
$229$	18.6698	−	15.6659i	1.23374	−	1.03523i	0.997987	−	0.0634155i	$-0.0201993\pi$
$230$		0			0
$231$	−0.831500	−	0.352715i	−0.0547087	−	0.0232069i
$232$	−6.77774	+	2.46689i	−0.444980	+	0.161960i
$233$	−2.40236	−	4.16101i	−0.157384	−	0.272597i	0.776541	−	0.630067i	$-0.216973\pi$
$233$	−2.40236	−	4.16101i	−0.157384	−	0.272597i	−0.933924	+	0.357470i	$0.883639\pi$
$234$	1.85844	+	4.16872i	0.121490	+	0.272517i
$235$		0			0
$236$	−2.74992	+	15.5956i	−0.179004	+	1.01518i
$237$	11.7935	−	3.60873i	0.766069	−	0.234412i
$238$	−1.03994	−	0.378506i	−0.0674090	−	0.0245349i
$239$	−2.87553	−	16.3079i	−0.186003	−	1.05487i	−0.924661	−	0.380792i	$-0.875651\pi$
$239$	−2.87553	−	16.3079i	−0.186003	−	1.05487i	0.738658	−	0.674080i	$-0.235460\pi$
$240$		0			0
$241$	21.4121	+	17.9669i	1.37928	+	1.15735i	0.969479	+	0.245173i	$0.0788447\pi$
$241$	21.4121	+	17.9669i	1.37928	+	1.15735i	0.409796	+	0.912177i	$0.365600\pi$
$242$	−5.41744			−0.348246
$243$	−4.05270	−	15.0524i	−0.259981	−	0.965614i
$244$	−0.450273			−0.0288258
$245$		0			0
$246$	−2.98262	+	4.59526i	−0.190165	+	0.292983i
$247$	2.60425	+	14.7694i	0.165704	+	0.939756i
$248$	14.2885	+	5.20061i	0.907324	+	0.330239i
$249$	−10.2870	+	3.14775i	−0.651911	+	0.199481i
$250$		0			0
$251$	11.5611	−	20.0244i	0.729730	−	1.26393i	−0.227268	−	0.973832i	$-0.572979\pi$
$251$	11.5611	−	20.0244i	0.729730	−	1.26393i	0.956997	−	0.290097i	$-0.0936875\pi$
$252$	0.540645	+	1.21274i	0.0340574	+	0.0763952i
$253$	4.77715	+	8.27427i	0.300337	+	0.520199i
$254$	2.61701	−	0.952512i	0.164206	−	0.0597659i
$255$		0			0
$256$	−7.76722	+	6.51747i	−0.485451	+	0.407342i
$257$	21.3698	−	17.9314i	1.33301	−	1.11853i	0.349650	−	0.936880i	$-0.386300\pi$
$257$	21.3698	−	17.9314i	1.33301	−	1.11853i	0.983363	−	0.181651i	$-0.0581441\pi$
$258$	−9.00736	+	6.79093i	−0.560774	+	0.422785i
$259$	−2.34205	+	0.852437i	−0.145528	+	0.0529679i
$260$		0			0
$261$	−2.43757	+	8.51627i	−0.150882	+	0.527144i
$262$	4.96410	−	8.59808i	0.306683	−	0.531191i
$263$	2.67674	−	15.1806i	0.165055	−	0.936073i	−0.783953	−	0.620820i	$-0.786800\pi$
$263$	2.67674	−	15.1806i	0.165055	−	0.936073i	0.949008	−	0.315253i	$-0.102089\pi$
$264$	−5.53486	−	5.15885i	−0.340647	−	0.317505i
$265$		0			0
$266$	−0.240665	−	1.36488i	−0.0147561	−	0.0836861i
$267$	−9.73904	−	19.1026i	−0.596020	−	1.16906i
$268$	−5.18297	−	4.34903i	−0.316600	−	0.265659i
$269$	16.5120			1.00675			0.503377	−	0.864067i	$-0.332091\pi$
$269$	16.5120			1.00675			0.503377	+	0.864067i	$0.332091\pi$
$270$		0			0
$271$	−2.72926			−0.165791			−0.0828953	−	0.996558i	$-0.526417\pi$
$271$	−2.72926			−0.165791			−0.0828953	+	0.996558i	$0.526417\pi$
$272$	5.60845	+	4.70605i	0.340062	+	0.285346i
$273$	−1.10510	−	0.0576491i	−0.0668836	−	0.00348908i
$274$	−0.180156	−	1.02171i	−0.0108836	−	0.0617239i
$275$		0			0
$276$	3.15625	−	13.6863i	0.189984	−	0.823816i
$277$	−1.66485	+	9.44181i	−0.100031	+	0.567304i	0.893058	+	0.449941i	$0.148555\pi$
$277$	−1.66485	+	9.44181i	−0.100031	+	0.567304i	−0.993089	+	0.117362i	$0.962556\pi$
$278$	1.51004	−	2.61547i	0.0905664	−	0.156866i
$279$	15.4769	−	10.4502i	0.926579	−	0.625634i
$280$		0			0
$281$	−3.02203	+	1.09993i	−0.180279	+	0.0656162i	−0.430583	−	0.902551i	$-0.641692\pi$
$281$	−3.02203	+	1.09993i	−0.180279	+	0.0656162i	0.250303	+	0.968167i	$0.419470\pi$
$282$	−0.802175	−	6.52022i	−0.0477688	−	0.388274i
$283$	19.3889	−	16.2692i	1.15255	−	0.967103i	0.152772	−	0.988261i	$-0.451180\pi$
$283$	19.3889	−	16.2692i	1.15255	−	0.967103i	0.999776	+	0.0211585i	$0.00673546\pi$
$284$	−11.0376	+	9.26164i	−0.654960	+	0.549577i
$285$		0			0
$286$	2.55669	−	0.930560i	0.151180	−	0.0550252i
$287$	−0.664120	−	1.15029i	−0.0392018	−	0.0678995i
$288$	1.22539	+	17.4036i	0.0722070	+	1.02551i
$289$	−6.43668	+	11.1487i	−0.378628	+	0.655803i
$290$		0			0
$291$	−5.48013	+	23.7632i	−0.321251	+	1.39302i
$292$	14.9537	+	5.44270i	0.875098	+	0.318510i
$293$	−4.14918	−	23.5312i	−0.242398	−	1.37471i	−0.826459	−	0.562997i	$-0.809648\pi$
$293$	−4.14918	−	23.5312i	−0.242398	−	1.37471i	0.584061	−	0.811710i	$-0.301463\pi$
$294$	−8.30533	−	0.433260i	−0.484377	−	0.0252682i
$295$		0			0
$296$	−20.8785			−1.21354
$297$	−9.12045	+	1.77967i	−0.529222	+	0.103267i
$298$	−8.25191			−0.478020
$299$	8.96710	+	7.52429i	0.518581	+	0.435141i
$300$		0			0
$301$	−0.474923	−	2.69342i	−0.0273741	−	0.155246i
$302$	14.2117	+	5.17262i	0.817789	+	0.297651i
$303$	−15.9777	−	14.8922i	−0.917892	−	0.855536i
$304$	−1.59214	+	9.02947i	−0.0913155	+	0.517876i
$305$		0			0
$306$	−11.0462	+	2.75976i	−0.631467	+	0.157765i
$307$	−8.03880	−	13.9236i	−0.458799	−	0.794662i	0.540099	−	0.841601i	$-0.318387\pi$
$307$	−8.03880	−	13.9236i	−0.458799	−	0.794662i	−0.998898	+	0.0469390i	$0.985053\pi$
$308$	0.743777	−	0.270713i	0.0423806	−	0.0154253i
$309$	8.15315	−	6.14692i	0.463817	−	0.349686i
$310$		0			0
$311$	−13.2669	+	11.1322i	−0.752297	+	0.631252i	−0.936109	−	0.351710i	$-0.885600\pi$
$311$	−13.2669	+	11.1322i	−0.752297	+	0.631252i	0.183813	+	0.982961i	$0.441156\pi$
$312$	−8.53397	−	3.62003i	−0.483141	−	0.204944i
$313$	12.5953	−	4.58433i	0.711931	−	0.259122i	0.0394347	−	0.999222i	$-0.487444\pi$
$313$	12.5953	−	4.58433i	0.711931	−	0.259122i	0.672496	+	0.740100i	$0.265222\pi$
$314$	−4.46716	−	7.73734i	−0.252096	−	0.436643i
$315$		0			0
$316$	−5.40397	+	9.35994i	−0.303997	+	0.526538i
$317$	−3.71981	+	21.0961i	−0.208925	+	1.18487i	0.682217	+	0.731150i	$0.261016\pi$
$317$	−3.71981	+	21.0961i	−0.208925	+	1.18487i	−0.891142	+	0.453724i	$0.850095\pi$
$318$	−2.57725	+	0.788622i	−0.144525	+	0.0442237i
$319$	4.96205	+	1.80604i	0.277822	+	0.101119i
$320$		0			0
$321$	5.78249	−	8.90894i	0.322747	−	0.497249i
$322$	−0.828672	−	0.695339i	−0.0461801	−	0.0387497i
$323$	−37.4116			−2.08164
$324$	11.5918	+	7.22783i	0.643987	+	0.401546i
$325$		0			0
$326$	8.60882	+	7.22366i	0.476799	+	0.400082i
$327$	4.72112	−	7.27372i	0.261079	−	0.402238i
$328$	−1.93213	−	10.9577i	−0.106684	−	0.605035i
$329$	1.49670	+	0.544756i	0.0825160	+	0.0300334i
$330$		0			0
$331$	−1.39731	+	7.92456i	−0.0768033	+	0.435573i	0.922023	+	0.387135i	$0.126535\pi$
$331$	−1.39731	+	7.92456i	−0.0768033	+	0.435573i	−0.998826	+	0.0484378i	$0.984576\pi$
$332$	4.71366	−	8.16430i	0.258696	−	0.448074i
$333$	−15.0619	+	20.7520i	−0.825388	+	1.13720i
$334$	5.71826	+	9.90432i	0.312889	+	0.541940i
$335$		0			0
$336$	−0.622817	−	0.264193i	−0.0339774	−	0.0144129i
$337$	−15.8385	+	13.2901i	−0.862779	+	0.723957i	−0.962565	−	0.271052i	$-0.912629\pi$
$337$	−15.8385	+	13.2901i	−0.862779	+	0.723957i	0.0997862	+	0.995009i	$0.468184\pi$
$338$	−4.36146	+	3.65970i	−0.237232	+	0.199061i
$339$	−3.10734	+	2.34272i	−0.168767	+	0.127239i
$340$		0			0
$341$	−5.56608	−	9.64072i	−0.301420	−	0.522075i
$342$	−9.90990	−	10.2521i	−0.535866	−	0.554371i
$343$	2.02878	−	3.51395i	0.109544	−	0.189735i
$344$	3.97844	−	22.5629i	0.214503	−	1.21651i
$345$		0			0
$346$	−6.69755	−	2.43771i	−0.360063	−	0.131052i
$347$	1.59384	+	9.03912i	0.0855619	+	0.485245i	0.997234	+	0.0743269i	$0.0236808\pi$
$347$	1.59384	+	9.03912i	0.0855619	+	0.485245i	−0.911672	+	0.410919i	$0.865208\pi$
$348$	−3.52586	−	6.91577i	−0.189006	−	0.370724i
$349$	−15.5771	−	13.0707i	−0.833823	−	0.699661i	0.122342	−	0.992488i	$-0.460960\pi$
$349$	−15.5771	−	13.0707i	−0.833823	−	0.699661i	−0.956165	+	0.292827i	$0.905404\pi$
$350$		0			0
$351$	−9.75454	+	5.87071i	−0.520659	+	0.313355i
$352$	10.4002			0.554330
$353$	−4.38294	−	3.67772i	−0.233280	−	0.195745i	0.518653	−	0.854985i	$-0.326434\pi$
$353$	−4.38294	−	3.67772i	−0.233280	−	0.195745i	−0.751933	+	0.659240i	$0.770878\pi$
$354$	12.5311	+	0.653705i	0.666022	+	0.0347440i
$355$		0			0
$356$	17.6569	+	6.42660i	0.935816	+	0.340609i
$357$	0.620326	−	2.68988i	0.0328312	−	0.142364i
$358$	0.821602	−	4.65953i	0.0434230	−	0.246264i
$359$	16.2331	−	28.1165i	0.856749	−	1.48393i	−0.0182634	−	0.999833i	$-0.505814\pi$
$359$	16.2331	−	28.1165i	0.856749	−	1.48393i	0.875013	−	0.484100i	$-0.160853\pi$
$360$		0			0
$361$	−13.9260	−	24.1206i	−0.732949	−	1.26950i
$362$	16.9053	−	6.15301i	0.888520	−	0.323395i
$363$	−1.65007	−	13.4121i	−0.0866064	−	0.703952i
$364$	0.742865	−	0.623338i	0.0389367	−	0.0326718i
$365$		0			0
$366$	0.0435664	+	0.354116i	0.00227725	+	0.0185099i
$367$	3.93416	−	1.43192i	0.205361	−	0.0747454i	−0.237291	−	0.971439i	$-0.576260\pi$
$367$	3.93416	−	1.43192i	0.205361	−	0.0747454i	0.442653	+	0.896693i	$0.354037\pi$
$368$	3.57822	+	6.19766i	0.186528	+	0.323075i
$369$	−12.2851	−	5.98451i	−0.639535	−	0.311541i
$370$		0			0
$371$	0.113472	−	0.643530i	0.00589116	−	0.0334104i
$372$	−3.67749	+	15.9465i	−0.190669	+	0.826786i
$373$	6.49195	+	2.36288i	0.336140	+	0.122345i	0.504575	−	0.863368i	$-0.331649\pi$
$373$	6.49195	+	2.36288i	0.336140	+	0.122345i	−0.168435	+	0.985713i	$0.553871\pi$
$374$	1.17858	+	6.68403i	0.0609427	+	0.345623i
$375$		0			0
$376$	10.2210	+	8.57645i	0.527108	+	0.442296i
$377$	6.46956			0.333199
$378$	0.901442	−	0.542527i	0.0463652	−	0.0279046i
$379$	−9.83488			−0.505184			−0.252592	−	0.967573i	$-0.581283\pi$
$379$	−9.83488			−0.505184			−0.252592	+	0.967573i	$0.581283\pi$
$380$		0			0
$381$	3.15526	+	6.18886i	0.161649	+	0.317065i
$382$	2.35131	+	13.3349i	0.120304	+	0.682275i
$383$	28.1682	+	10.2524i	1.43933	+	0.523873i	0.939590	−	0.342303i	$-0.111207\pi$
$383$	28.1682	+	10.2524i	1.43933	+	0.523873i	0.499739	+	0.866176i	$0.333429\pi$
$384$	−13.5411	−	12.6212i	−0.691017	−	0.644073i
$385$		0			0
$386$	−5.94592	+	10.2986i	−0.302639	+	0.524187i
$387$	−19.5560	−	20.2313i	−0.994087	−	1.02842i
$388$	−10.6854	−	18.5077i	−0.542469	−	0.939585i
$389$	11.2255	−	4.08576i	0.569158	−	0.207157i	−0.0413802	−	0.999143i	$-0.513175\pi$
$389$	11.2255	−	4.08576i	0.569158	−	0.207157i	0.610538	+	0.791987i	$0.290953\pi$
$390$		0			0
$391$	−22.3690	+	18.7698i	−1.13125	+	0.949230i
$392$	12.9395	−	10.8575i	0.653542	−	0.548387i
$393$	22.7985	+	9.67090i	1.15003	+	0.487832i
$394$	−12.7598	+	4.64419i	−0.642829	+	0.233971i
$395$		0			0
$396$	4.78329	−	6.59030i	0.240369	−	0.331175i
$397$	−5.96277	+	10.3278i	−0.299263	+	0.518338i	−0.975967	−	0.217916i	$-0.930074\pi$
$397$	−5.96277	+	10.3278i	−0.299263	+	0.518338i	0.676705	+	0.736255i	$0.263407\pi$
$398$	−2.57510	+	14.6041i	−0.129078	+	0.732037i
$399$	3.30576	−	1.01154i	0.165495	−	0.0506405i
$400$		0			0
$401$	−6.06060	−	34.3714i	−0.302652	−	1.71643i	−0.634355	−	0.773042i	$-0.718734\pi$
$401$	−6.06060	−	34.3714i	−0.302652	−	1.71643i	0.331703	−	0.943384i	$-0.392377\pi$
$402$	−2.91879	+	4.49692i	−0.145576	+	0.224286i
$403$	−10.4480	−	8.76689i	−0.520451	−	0.436710i
$404$	19.1405			0.952275
$405$		0			0
$406$	−0.597868			−0.0296717
$407$	11.7093	+	9.82527i	0.580409	+	0.487021i
$408$	12.5899	−	19.3970i	0.623293	−	0.960293i
$409$	−1.99270	−	11.3012i	−0.0985326	−	0.558806i	−0.993607	−	0.112890i	$-0.963989\pi$
$409$	−1.99270	−	11.3012i	−0.0985326	−	0.558806i	0.895075	−	0.445916i	$-0.147122\pi$
$410$		0			0
$411$	2.47461	−	0.757215i	0.122063	−	0.0373506i
$412$	−1.55379	+	8.81196i	−0.0765495	+	0.434134i
$413$	−1.52116	+	2.63473i	−0.0748516	+	0.129647i
$414$	−11.0689	−	1.15800i	−0.544006	−	0.0569126i
$415$		0			0
$416$	11.9736	−	4.35803i	0.587054	−	0.213670i
$417$	6.93512	+	2.94182i	0.339615	+	0.144061i
$418$	−6.51123	+	5.46357i	−0.318475	+	0.267232i
$419$	23.7050	−	19.8908i	1.15806	−	0.971731i	0.158187	−	0.987409i	$-0.449435\pi$
$419$	23.7050	−	19.8908i	1.15806	−	0.971731i	0.999877	+	0.0156785i	$0.00499082\pi$
$420$		0			0
$421$	−8.89101	+	3.23606i	−0.433322	+	0.157716i	−0.549466	−	0.835516i	$-0.685169\pi$
$421$	−8.89101	+	3.23606i	−0.433322	+	0.157716i	0.116144	+	0.993232i	$0.462947\pi$
$422$	−0.642176	−	1.11228i	−0.0312606	−	0.0541450i
$423$	15.8979	−	3.97193i	0.772984	−	0.193122i
$424$	2.73701	−	4.74065i	0.132921	−	0.230226i
$425$		0			0
$426$	8.35172	+	7.78435i	0.404642	+	0.377153i
$427$	−0.0812866	−	0.0295859i	−0.00393373	−	0.00143176i
$428$	1.61623	+	9.16607i	0.0781232	+	0.443059i
$429$	3.08254	+	6.04624i	0.148827	+	0.291915i
$430$		0			0
$431$	−2.72680			−0.131345			−0.0656727	−	0.997841i	$-0.520919\pi$
$431$	−2.72680			−0.131345			−0.0656727	+	0.997841i	$0.520919\pi$
$432$	−6.83147	+	1.33302i	−0.328679	+	0.0641351i
$433$	18.8159			0.904237			0.452118	−	0.891958i	$-0.350668\pi$
$433$	18.8159			0.904237			0.452118	+	0.891958i	$0.350668\pi$
$434$	0.965523	+	0.810170i	0.0463466	+	0.0388894i
$435$		0			0
$436$	1.31957	+	7.48366i	0.0631960	+	0.358402i
$437$	−34.3637	−	12.5074i	−1.64384	−	0.598309i
$438$	2.83354	−	12.2869i	0.135392	−	0.587090i
$439$	−2.47536	+	14.0385i	−0.118143	+	0.670020i	0.867004	+	0.498302i	$0.166043\pi$
$439$	−2.47536	+	14.0385i	−0.118143	+	0.670020i	−0.985146	+	0.171718i	$0.945068\pi$
$440$		0			0
$441$	−1.45705	−	20.6937i	−0.0693834	−	0.985413i
$442$	4.15773	+	7.20140i	0.197763	+	0.342535i
$443$	−3.98739	+	1.45129i	−0.189447	+	0.0689529i	−0.435001	−	0.900430i	$-0.643252\pi$
$443$	−3.98739	+	1.45129i	−0.189447	+	0.0689529i	0.245555	+	0.969383i	$0.421030\pi$
$444$	−2.74384	−	22.3024i	−0.130217	−	1.05843i
$445$		0			0
$446$	1.41821	−	1.19002i	0.0671544	−	0.0563492i
$447$	−2.51341	−	20.4295i	−0.118880	−	0.966280i
$448$	−0.372427	+	0.135552i	−0.0175955	+	0.00640425i
$449$	0.549598	+	0.951931i	0.0259371	+	0.0449244i	0.878703	−	0.477370i	$-0.158410\pi$
$449$	0.549598	+	0.951931i	0.0259371	+	0.0449244i	−0.852765	+	0.522294i	$0.825076\pi$
$450$		0			0
$451$	−4.07299	+	7.05462i	−0.191789	+	0.332189i
$452$	0.592180	−	3.35842i	0.0278538	−	0.157967i
$453$	−8.47732	+	36.7596i	−0.398299	+	1.72712i
$454$	−2.92393	−	1.06422i	−0.137227	−	0.0499465i
$455$		0			0
$456$	28.9206	+	1.50868i	1.35433	+	0.0706506i
$457$	2.70517	+	2.26991i	0.126542	+	0.106182i	0.703863	−	0.710336i	$-0.251457\pi$
$457$	2.70517	+	2.26991i	0.126542	+	0.106182i	−0.577320	+	0.816518i	$0.695902\pi$
$458$	16.9232			0.790770
$459$	−10.1969	−	26.5067i	−0.475951	−	1.23723i
$460$		0			0
$461$	−16.4505	−	13.8036i	−0.766178	−	0.642900i	0.173549	−	0.984825i	$-0.444477\pi$
$461$	−16.4505	−	13.8036i	−0.766178	−	0.642900i	−0.939727	+	0.341925i	$0.888921\pi$
$462$	−0.284866	−	0.558748i	−0.0132531	−	0.0259953i
$463$	−4.06385	−	23.0472i	−0.188863	−	1.07110i	−0.920891	−	0.389821i	$-0.872537\pi$
$463$	−4.06385	−	23.0472i	−0.188863	−	1.07110i	0.732027	−	0.681275i	$-0.238574\pi$
$464$	3.71672	+	1.35277i	0.172544	+	0.0628009i
$465$		0			0
$466$	0.579341	−	3.28561i	0.0268374	−	0.152203i
$467$	14.8548	−	25.7292i	0.687396	−	1.19060i	−0.285281	−	0.958444i	$-0.592087\pi$
$467$	14.8548	−	25.7292i	0.687396	−	1.19060i	0.972677	−	0.232161i	$-0.0745796\pi$
$468$	2.74539	−	9.59172i	0.126905	−	0.443377i
$469$	−0.649907	−	1.12567i	−0.0300099	−	0.0519787i
$470$		0			0
$471$	17.7949	−	13.4161i	0.819945	−	0.618183i
$472$	−19.5231	+	16.3819i	−0.898625	+	0.754036i
$473$	−12.8491	+	10.7817i	−0.590804	+	0.495743i
$474$	7.88395	+	3.34430i	0.362122	+	0.153609i
$475$		0			0
$476$	1.20954	+	2.09498i	0.0554392	+	0.0960235i
$477$	−2.73740	−	6.14035i	−0.125337	−	0.281147i
$478$	5.74928	−	9.95805i	0.262966	−	0.455471i
$479$	−1.87413	+	10.6287i	−0.0856313	+	0.485639i	0.911587	+	0.411107i	$0.134858\pi$
$479$	−1.87413	+	10.6287i	−0.0856313	+	0.485639i	−0.997219	+	0.0745327i	$0.976253\pi$
$480$		0			0
$481$	17.5979	+	6.40513i	0.802397	+	0.292049i
$482$	3.37033	+	19.1141i	0.153514	+	0.870622i
$483$	1.46907	−	2.26335i	0.0668448	−	0.102986i
$484$	9.07147	+	7.61187i	0.412340	+	0.345994i
$485$		0			0
$486$	4.56273	−	9.81563i	0.206970	−	0.445246i
$487$	−27.9786			−1.26783			−0.633916	−	0.773402i	$-0.718554\pi$
$487$	−27.9786			−1.26783			−0.633916	+	0.773402i	$0.718554\pi$
$488$	−0.555107	−	0.465790i	−0.0251285	−	0.0210853i
$489$	−15.2617	+	23.5133i	−0.690157	+	1.06331i
$490$		0			0
$491$	30.9274	+	11.2567i	1.39574	+	0.508006i	0.926910	−	0.375284i	$-0.122455\pi$
$491$	30.9274	+	11.2567i	1.39574	+	0.508006i	0.468826	+	0.883291i	$0.344677\pi$
$492$	11.4510	−	3.50395i	0.516253	−	0.157970i
$493$	−2.80246	+	15.8935i	−0.126216	+	0.715808i
$494$	−5.20689	+	9.01860i	−0.234269	+	0.405766i
$495$		0			0
$496$	−4.16914	−	7.22117i	−0.187200	−	0.324240i
$497$	−2.60113	+	0.946736i	−0.116677	+	0.0424669i
$498$	−6.87686	−	2.91710i	−0.308159	−	0.130718i
$499$	−12.0317	+	10.0958i	−0.538615	+	0.451952i	−0.871064	−	0.491170i	$-0.836570\pi$
$499$	−12.0317	+	10.0958i	−0.538615	+	0.451952i	0.332449	+	0.943121i	$0.392125\pi$
$500$		0			0
$501$	−22.7787	+	17.1736i	−1.01768	+	0.767258i
$502$	15.0873	−	5.49132i	0.673378	−	0.245090i
$503$	−9.54257	−	16.5282i	−0.425482	−	0.736957i	0.570983	−	0.820962i	$-0.306562\pi$
$503$	−9.54257	−	16.5282i	−0.425482	−	0.736957i	−0.996465	+	0.0840050i	$0.973229\pi$
$504$	−0.588009	+	2.05436i	−0.0261920	+	0.0915086i
$505$		0			0
$506$	−1.15203	+	6.53351i	−0.0512142	+	0.290450i
$507$	−10.3888	−	9.68309i	−0.461385	−	0.430041i
$508$	−5.72050	−	2.08209i	−0.253806	−	0.0923779i
$509$	2.39075	+	13.5586i	0.105968	+	0.600974i	0.990829	+	0.135120i	$0.0431418\pi$
$509$	2.39075	+	13.5586i	0.105968	+	0.600974i	−0.884861	+	0.465854i	$0.845747\pi$
$510$		0			0
$511$	2.34193	+	1.96511i	0.103601	+	0.0869313i
$512$	14.3341			0.633483
$513$	22.3630	−	27.6568i	0.987352	−	1.22108i
$514$	19.3706			0.854401
$515$		0			0
$516$	24.6245	+	1.28457i	1.08403	+	0.0565501i
$517$	−1.69624	−	9.61985i	−0.0746005	−	0.423080i
$518$	−1.62627	−	0.591914i	−0.0714542	−	0.0260072i
$519$	3.99512	−	17.3238i	0.175366	−	0.760430i
$520$		0			0
$521$	−7.80342	+	13.5159i	−0.341874	+	0.592143i	−0.984781	−	0.173801i	$-0.944395\pi$
$521$	−7.80342	+	13.5159i	−0.341874	+	0.592143i	0.642907	+	0.765945i	$0.277728\pi$
$522$	−5.09774	+	3.44204i	−0.223122	+	0.150654i
$523$	7.27374	+	12.5985i	0.318058	+	0.550893i	0.980083	−	0.198589i	$-0.0636359\pi$
$523$	7.27374	+	12.5985i	0.318058	+	0.550893i	−0.662025	+	0.749482i	$0.730303\pi$
$524$	−20.3932	+	7.42253i	−0.890883	+	0.324255i
$525$		0			0
$526$	8.19948	−	6.88018i	0.357514	−	0.299990i
$527$	26.0631	−	21.8695i	1.13533	−	0.952652i
$528$	0.506642	+	4.11807i	0.0220488	+	0.179216i
$529$	−5.20877	+	1.89584i	−0.226468	+	0.0824276i
$530$		0			0
$531$	2.19841	+	31.2227i	0.0954028	+	1.35495i
$532$	−1.51476	+	2.62363i	−0.0656730	+	0.113749i
$533$	−1.73305	+	9.82864i	−0.0750669	+	0.425726i
$534$	3.34577	−	14.5080i	0.144786	−	0.627824i
$535$		0			0
$536$	−1.89078	−	10.7231i	−0.0816693	−	0.463169i
$537$	11.7860	+	0.614833i	0.508602	+	0.0265320i
$538$	8.78314	+	7.36993i	0.378668	+	0.317740i
$539$	−12.3663			−0.532654
$540$		0			0
$541$	−1.02903			−0.0442416			−0.0221208	−	0.999755i	$-0.507042\pi$
$541$	−1.02903			−0.0442416			−0.0221208	+	0.999755i	$0.507042\pi$
$542$	−1.45176	−	1.21817i	−0.0623584	−	0.0523249i
$543$	20.3823	+	39.9786i	0.874686	+	1.71565i
$544$	5.51954	+	31.3029i	0.236648	+	1.34210i
$545$		0			0
$546$	−0.562098	−	0.523912i	−0.0240556	−	0.0224214i
$547$	−4.74198	+	26.8931i	−0.202753	+	1.14987i	0.698185	+	0.715918i	$0.253991\pi$
$547$	−4.74198	+	26.8931i	−0.202753	+	1.14987i	−0.900937	+	0.433949i	$0.857120\pi$
$548$	−1.13391	+	1.96398i	−0.0484381	+	0.0838972i
$549$	−0.863423	+	0.215717i	−0.0368500	+	0.00920658i
$550$		0			0
$551$	−18.9923	+	6.91262i	−0.809098	+	0.294488i
$552$	18.0490	−	13.6077i	0.768216	−	0.579182i
$553$	−1.59057	+	1.33465i	−0.0676380	+	0.0567550i
$554$	−5.09981	+	4.27925i	−0.216670	+	0.181808i
$555$		0			0
$556$	−6.20347	+	2.25788i	−0.263086	+	0.0957554i
$557$	−7.16847	−	12.4162i	−0.303738	−	0.526090i	0.673242	−	0.739423i	$-0.264901\pi$
$557$	−7.16847	−	12.4162i	−0.303738	−	0.526090i	−0.976980	+	0.213333i	$0.931568\pi$
$558$	12.8969	+	1.34924i	0.545967	+	0.0571178i
$559$	−10.2752	+	17.7971i	−0.434593	+	0.752737i
$560$		0			0
$561$	−16.1888	+	4.95369i	−0.683494	+	0.209145i
$562$	−2.09843	−	0.763766i	−0.0885170	−	0.0322175i
$563$	−5.04314	−	28.6011i	−0.212543	−	1.20539i	−0.885119	−	0.465364i	$-0.845923\pi$
$563$	−5.04314	−	28.6011i	−0.212543	−	1.20539i	0.672576	−	0.740028i	$-0.265188\pi$
$564$	−7.81811	+	12.0452i	−0.329202	+	0.507194i
$565$		0			0
$566$	17.5750			0.738731
$567$	1.61771	+	2.06648i	0.0679376	+	0.0867838i
$568$	−23.1882			−0.972954
$569$	−2.83162	−	2.37601i	−0.118708	−	0.0996077i	0.581501	−	0.813545i	$-0.302465\pi$
$569$	−2.83162	−	2.37601i	−0.118708	−	0.0996077i	−0.700209	+	0.713938i	$0.746910\pi$
$570$		0			0
$571$	0.927120	+	5.25796i	0.0387988	+	0.220039i	0.998042	−	0.0625417i	$-0.0199207\pi$
$571$	0.927120	+	5.25796i	0.0387988	+	0.220039i	−0.959244	+	0.282581i	$0.908810\pi$
$572$	−5.58867	−	2.03411i	−0.233674	−	0.0850504i
$573$	−32.2975	+	9.88283i	−1.34925	+	0.412861i
$574$	0.160156	−	0.908289i	0.00668478	−	0.0379113i
$575$		0			0
$576$	−2.39511	+	3.29992i	−0.0997961	+	0.137497i
$577$	10.7308	+	18.5862i	0.446727	+	0.773754i	0.998171	−	0.0604579i	$-0.0192561\pi$
$577$	10.7308	+	18.5862i	0.446727	+	0.773754i	−0.551443	+	0.834212i	$0.685923\pi$
$578$	−8.39989	+	3.05731i	−0.349389	+	0.127167i
$579$	−27.3076	−	11.5836i	−1.13487	−	0.481400i
$580$		0			0
$581$	1.38739	−	1.16416i	0.0575587	−	0.0482975i
$582$	−13.5214	+	10.1942i	−0.560481	+	0.422564i
$583$	−3.76591	+	1.37068i	−0.155968	+	0.0567677i
$584$	12.8050	+	22.1789i	0.529874	+	0.917768i
$585$		0			0
$586$	8.29581	−	14.3688i	0.342697	−	0.593568i
$587$	1.05706	−	5.99490i	0.0436297	−	0.247436i	−0.955191	−	0.295991i	$-0.904350\pi$
$587$	1.05706	−	5.99490i	0.0436297	−	0.247436i	0.998821	+	0.0485544i	$0.0154614\pi$
$588$	13.2985	+	12.3950i	0.548420	+	0.511163i
$589$	40.0387	+	14.5729i	1.64977	+	0.600466i
$590$		0			0
$591$	−15.3842	−	30.1752i	−0.632820	−	1.24124i
$592$	8.77059	+	7.35940i	0.360469	+	0.302470i
$593$	−0.198543			−0.00815319			−0.00407660	−	0.999992i	$-0.501298\pi$
$593$	−0.198543			−0.00815319			−0.00407660	+	0.999992i	$0.501298\pi$
$594$	−5.64573	−	3.12415i	−0.231647	−	0.128185i
$595$		0			0
$596$	13.8178	+	11.5945i	0.565998	+	0.474929i
$597$	−36.9401	−	1.92703i	−1.51186	−	0.0788682i
$598$	1.41145	+	8.00471i	0.0577183	+	0.327337i
$599$	8.02599	+	2.92122i	0.327933	+	0.119358i	0.500740	−	0.865598i	$-0.333061\pi$
$599$	8.02599	+	2.92122i	0.327933	+	0.119358i	−0.172807	+	0.984956i	$0.555284\pi$
$600$		0			0
$601$	2.31320	−	13.1188i	0.0943574	−	0.535128i	−0.900585	−	0.434680i	$-0.856861\pi$
$601$	2.31320	−	13.1188i	0.0943574	−	0.535128i	0.994942	−	0.100448i	$-0.0320275\pi$
$602$	0.949554	−	1.64468i	0.0387009	−	0.0670319i
$603$	−12.0221	−	5.85643i	−0.489580	−	0.238492i
$604$	−16.5294	−	28.6298i	−0.672574	−	1.16493i
$605$		0			0
$606$	−1.85195	−	15.0530i	−0.0752303	−	0.611485i
$607$	0.960494	−	0.805951i	0.0389853	−	0.0327125i	−0.623087	−	0.782153i	$-0.714122\pi$
$607$	0.960494	−	0.805951i	0.0389853	−	0.0327125i	0.662072	+	0.749440i	$0.269677\pi$
$608$	−30.4936	+	25.5872i	−1.23668	+	1.03770i
$609$	−0.182102	−	1.48016i	−0.00737915	−	0.0599790i
$610$		0			0
$611$	−5.98392	−	10.3645i	−0.242083	−	0.419301i
$612$	22.3744	+	10.8994i	0.904431	+	0.440582i
$613$	−7.38826	+	12.7968i	−0.298409	+	0.516860i	−0.975772	−	0.218789i	$-0.929789\pi$
$613$	−7.38826	+	12.7968i	−0.298409	+	0.516860i	0.677363	+	0.735649i	$0.263123\pi$
$614$	1.93860	−	10.9943i	0.0782354	−	0.443695i
$615$		0			0
$616$	1.19699	+	0.435667i	0.0482280	+	0.0175535i
$617$	−0.369516	−	2.09563i	−0.0148762	−	0.0843669i	0.976466	−	0.215672i	$-0.0691943\pi$
$617$	−0.369516	−	2.09563i	−0.0148762	−	0.0843669i	−0.991342	+	0.131305i	$0.958083\pi$
$618$	7.08047	+	0.369363i	0.284818	+	0.0148580i
$619$	−13.5591	−	11.3775i	−0.544987	−	0.457298i	0.328252	−	0.944590i	$-0.393540\pi$
$619$	−13.5591	−	11.3775i	−0.544987	−	0.457298i	−0.873239	+	0.487292i	$0.837985\pi$
$620$		0			0
$621$	−0.504531	−	27.7562i	−0.0202461	−	1.11382i
$622$	−12.0257			−0.482188
$623$	2.76529	+	2.32035i	0.110789	+	0.0929629i
$624$	2.30891	+	4.52880i	0.0924304	+	0.181297i
$625$		0			0
$626$	8.74593	+	3.18326i	0.349558	+	0.127229i
$627$	−15.5095	−	14.4559i	−0.619391	−	0.577313i
$628$	−3.39126	+	19.2328i	−0.135326	+	0.767471i
$629$	−23.3582	+	40.4577i	−0.931354	+	1.61315i
$630$		0			0
$631$	−6.04045	−	10.4624i	−0.240466	−	0.416500i	0.720381	−	0.693579i	$-0.243967\pi$
$631$	−6.04045	−	10.4624i	−0.240466	−	0.416500i	−0.960847	+	0.277079i	$0.910634\pi$
$632$	−16.3446	+	5.94895i	−0.650154	+	0.236637i
$633$	2.55810	−	1.92864i	0.101676	−	0.0766564i
$634$	−11.3946	+	9.56124i	−0.452539	+	0.379725i
$635$		0			0
$636$	5.42365	+	2.30066i	0.215062	+	0.0912272i
$637$	−14.2372	+	5.18191i	−0.564098	+	0.205315i
$638$	1.83333	+	3.17543i	0.0725824	+	0.125716i
$639$	−16.7281	+	23.0476i	−0.661753	+	0.911748i
$640$		0			0
$641$	2.45761	−	13.9378i	0.0970699	−	0.550511i	−0.897023	−	0.441983i	$-0.854275\pi$
$641$	2.45761	−	13.9378i	0.0970699	−	0.550511i	0.994093	−	0.108528i	$-0.0346137\pi$
$642$	7.05224	−	2.15794i	0.278330	−	0.0851672i
$643$	22.1681	+	8.06852i	0.874223	+	0.318191i	0.739876	−	0.672743i	$-0.234884\pi$
$643$	22.1681	+	8.06852i	0.874223	+	0.318191i	0.134347	+	0.990934i	$0.457106\pi$
$644$	0.410609	+	2.32868i	0.0161803	+	0.0917629i
$645$		0			0
$646$	−19.9001	−	16.6982i	−0.782961	−	0.656982i
$647$	−0.0994615			−0.00391023			−0.00195512	−	0.999998i	$-0.500622\pi$
$647$	−0.0994615			−0.00391023			−0.00195512	+	0.999998i	$0.500622\pi$
$648$	6.81368	+	20.9019i	0.267666	+	0.821102i
$649$	18.6583			0.732403
$650$		0			0
$651$	−1.71167	+	2.63714i	−0.0670858	+	0.103358i
$652$	−4.26569	−	24.1920i	−0.167057	−	0.947430i
$653$	15.4322	+	5.61686i	0.603909	+	0.219805i	0.625836	−	0.779955i	$-0.284758\pi$
$653$	15.4322	+	5.61686i	0.603909	+	0.219805i	−0.0219271	+	0.999760i	$0.506980\pi$
$654$	5.75782	−	1.76186i	0.225148	−	0.0688940i
$655$		0			0
$656$	−3.05078	+	5.28411i	−0.119113	+	0.206310i
$657$	31.2820	+	3.27265i	1.22043	+	0.127678i
$658$	0.552989	+	0.957805i	0.0215578	+	0.0373391i
$659$	35.6457	−	12.9740i	1.38856	−	0.505394i	0.463797	−	0.885942i	$-0.346487\pi$
$659$	35.6457	−	12.9740i	1.38856	−	0.505394i	0.924761	+	0.380548i	$0.124264\pi$
$660$		0			0
$661$	−10.0083	+	8.39796i	−0.389278	+	0.326643i	−0.816332	−	0.577583i	$-0.803996\pi$
$661$	−10.0083	+	8.39796i	−0.389278	+	0.326643i	0.427054	+	0.904226i	$0.359551\pi$
$662$	−4.28030	+	3.59159i	−0.166358	+	0.139591i
$663$	−16.5623	+	12.4868i	−0.643226	+	0.484948i
$664$	14.2568	−	5.18903i	0.553269	−	0.201374i
$665$		0			0
$666$	−17.2742	+	4.31577i	−0.669361	+	0.167233i
$667$	−7.88764	+	13.6618i	−0.305411	+	0.528987i
$668$	4.34104	−	24.6193i	0.167960	−	0.952548i
$669$	3.37814	+	3.14864i	0.130606	+	0.121734i
$670$		0			0
$671$	0.0921233	+	0.522457i	0.00355638	+	0.0201692i
$672$	−1.33409	−	2.61675i	−0.0514637	−	0.100943i
$673$	−3.10076	−	2.60185i	−0.119526	−	0.100294i	0.581066	−	0.813857i	$-0.302636\pi$
$673$	−3.10076	−	2.60185i	−0.119526	−	0.100294i	−0.700591	+	0.713563i	$0.747080\pi$
$674$	−14.3568			−0.553002
$675$		0			0
$676$	12.4454			0.478668
$677$	11.4316	+	9.59228i	0.439353	+	0.368661i	0.835467	−	0.549540i	$-0.185197\pi$
$677$	11.4316	+	9.59228i	0.439353	+	0.368661i	−0.396114	+	0.918201i	$0.629641\pi$
$678$	−2.69851	−	0.140772i	−0.103636	−	0.00540631i
$679$	−0.712932	−	4.04324i	−0.0273598	−	0.155165i
$680$		0			0
$681$	1.74414	−	7.56299i	0.0668355	−	0.289815i
$682$	1.34229	−	7.61249i	0.0513988	−	0.291497i
$683$	−11.6849	+	20.2388i	−0.447110	+	0.774417i	−0.998197	−	0.0600307i	$-0.980880\pi$
$683$	−11.6849	+	20.2388i	−0.447110	+	0.774417i	0.551086	+	0.834448i	$0.314213\pi$
$684$	2.18915	+	31.0912i	0.0837041	+	1.18880i
$685$		0			0
$686$	2.64757	−	0.963635i	0.101085	−	0.0367918i
$687$	5.15457	+	41.8972i	0.196659	+	1.59848i
$688$	−9.62435	+	8.07579i	−0.366925	+	0.307887i
$689$	−3.76129	+	3.15610i	−0.143294	+	0.120238i
$690$		0			0
$691$	−11.8093	+	4.29822i	−0.449245	+	0.163512i	−0.556728	−	0.830695i	$-0.687943\pi$
$691$	−11.8093	+	4.29822i	−0.449245	+	0.163512i	0.107482	+	0.994207i	$0.465721\pi$
$692$	7.78986	+	13.4924i	0.296126	+	0.512906i
$693$	1.29654	−	0.875435i	0.0492515	−	0.0332550i
$694$	−3.18670	+	5.51952i	−0.120965	+	0.209518i
$695$		0			0
$696$	2.80734	−	12.1733i	0.106412	−	0.461427i
$697$	−23.3949	−	8.51506i	−0.886146	−	0.322531i
$698$	−2.45188	−	13.9053i	−0.0928050	−	0.526323i
$699$	8.31071	+	0.433541i	0.314340	+	0.0163980i
$700$		0			0
$701$	−38.3903			−1.44998			−0.724991	−	0.688758i	$-0.758156\pi$
$701$	−38.3903			−1.44998			−0.724991	+	0.688758i	$0.758156\pi$
$702$	−7.80900	−	1.23105i	−0.294732	−	0.0464628i
$703$	−58.5049			−2.20656
$704$	1.86198	+	1.56239i	0.0701761	+	0.0588847i
$705$		0			0
$706$	−0.689887	−	3.91254i	−0.0259642	−	0.147251i
$707$	3.45538	+	1.25766i	0.129953	+	0.0472990i
$708$	−20.0648	−	18.7017i	−0.754081	−	0.702853i
$709$	−1.35456	+	7.68211i	−0.0508717	+	0.288508i	−0.999621	−	0.0275213i	$-0.991239\pi$
$709$	−1.35456	+	7.68211i	−0.0508717	+	0.288508i	0.948750	+	0.316029i	$0.102350\pi$
$710$		0			0
$711$	−5.87823	+	20.5371i	−0.220451	+	0.770202i
$712$	15.1198	+	26.1883i	0.566638	+	0.981446i
$713$	31.2512	−	11.3745i	1.17037	−	0.425978i
$714$	1.53056	−	1.15394i	0.0572799	−	0.0431851i
$715$		0			0
$716$	−7.92272	+	6.64795i	−0.296086	+	0.248446i
$717$	26.4045	+	11.2006i	0.986096	+	0.418293i
$718$	21.1842	−	7.71043i	0.790589	−	0.287751i
$719$	14.8476	+	25.7168i	0.553722	+	0.959074i	0.998002	+	0.0631860i	$0.0201261\pi$
$719$	14.8476	+	25.7168i	0.553722	+	0.959074i	−0.444280	+	0.895888i	$0.646541\pi$
$720$		0			0
$721$	−0.859504	+	1.48870i	−0.0320096	+	0.0554422i
$722$	3.35833	−	19.0460i	0.124984	−	0.708820i
$723$	−46.2946	+	14.1659i	−1.72172	+	0.526834i
$724$	−36.9531	−	13.4498i	−1.37335	−	0.499859i
$725$		0			0
$726$	5.10861	−	7.87071i	0.189598	−	0.292110i
$727$	−0.590717	−	0.495670i	−0.0219085	−	0.0183834i	0.631768	−	0.775158i	$-0.282330\pi$
$727$	−0.590717	−	0.495670i	−0.0219085	−	0.0183834i	−0.653676	+	0.756774i	$0.726774\pi$
$728$	1.56064			0.0578411
$729$	25.6905	+	8.30637i	0.951502	+	0.307643i
$730$		0			0
$731$	−39.2705	−	32.9519i	−1.45247	−	1.21877i
$732$	0.424604	−	0.654178i	0.0156938	−	0.0241791i
$733$	0.355120	+	2.01399i	0.0131167	+	0.0743882i	0.990663	−	0.136330i	$-0.0435308\pi$
$733$	0.355120	+	2.01399i	0.0131167	+	0.0743882i	−0.977547	+	0.210718i	$0.932420\pi$
$734$	2.73179	+	0.994292i	0.100832	+	0.0367000i
$735$		0			0
$736$	−5.39525	+	30.5980i	−0.198871	+	1.12786i
$737$	−3.98582	+	6.90364i	−0.146820	+	0.254299i
$738$	−3.86362	−	8.66660i	−0.142222	−	0.319022i
$739$	4.28264	+	7.41775i	0.157539	+	0.272866i	0.933981	−	0.357323i	$-0.116311\pi$
$739$	4.28264	+	7.41775i	0.157539	+	0.272866i	−0.776441	+	0.630189i	$0.782977\pi$
$740$		0			0
$741$	−23.9135	−	10.1439i	−0.878485	−	0.372645i
$742$	0.347590	−	0.291663i	0.0127604	−	0.0107073i
$743$	−25.7194	+	21.5811i	−0.943552	+	0.791734i	−0.978200	−	0.207666i	$-0.933413\pi$
$743$	−25.7194	+	21.5811i	−0.943552	+	0.791734i	0.0346482	+	0.999400i	$0.488969\pi$
$744$	−21.0297	+	15.8549i	−0.770986	+	0.581270i
$745$		0			0
$746$	2.39859	+	4.15447i	0.0878185	+	0.152106i
$747$	5.12734	−	17.9137i	0.187600	−	0.655428i
$748$	7.41800	−	12.8483i	0.271229	−	0.469782i
$749$	−0.310498	+	1.76092i	−0.0113454	+	0.0643427i
$750$		0			0
$751$	22.0296	+	8.01813i	0.803872	+	0.292586i	0.711090	−	0.703101i	$-0.248202\pi$
$751$	22.0296	+	8.01813i	0.803872	+	0.292586i	0.0927821	+	0.995686i	$0.470424\pi$
$752$	−1.27053	−	7.20553i	−0.0463314	−	0.262759i
$753$	18.1904	+	35.6794i	0.662894	+	1.30023i
$754$	3.44132	+	2.88761i	0.125325	+	0.105160i
$755$		0			0
$756$	−2.27174	−	0.358128i	−0.0826226	−	0.0130250i
$757$	−2.94896			−0.107182			−0.0535909	−	0.998563i	$-0.517067\pi$
$757$	−2.94896			−0.107182			−0.0535909	+	0.998563i	$0.517067\pi$
$758$	−5.23142	−	4.38968i	−0.190014	−	0.159440i
$759$	−16.5261	−	0.862107i	−0.599858	−	0.0312925i
$760$		0			0
$761$	27.9592	+	10.1763i	1.01352	+	0.368892i	0.794784	−	0.606892i	$-0.207584\pi$
$761$	27.9592	+	10.1763i	1.01352	+	0.368892i	0.218737	+	0.975784i	$0.429806\pi$
$762$	−1.08396	+	4.70032i	−0.0392678	+	0.170275i
$763$	−0.253507	+	1.43771i	−0.00917756	+	0.0520485i
$764$	14.7992	−	25.6330i	0.535418	−	0.927371i
$765$		0			0
$766$	10.4073	+	18.0260i	0.376033	+	0.651307i
$767$	21.4811	−	7.81850i	0.775639	−	0.282310i
$768$	−2.14445	−	17.4305i	−0.0773813	−	0.628969i
$769$	−6.11306	+	5.12946i	−0.220442	+	0.184973i	−0.746320	−	0.665587i	$-0.768181\pi$
$769$	−6.11306	+	5.12946i	−0.220442	+	0.184973i	0.525878	+	0.850560i	$0.323737\pi$
$770$		0			0
$771$	5.90001	+	47.9563i	0.212484	+	1.72710i
$772$	24.4267	−	8.89058i	0.879135	−	0.319979i
$773$	0.187968	+	0.325571i	0.00676076	+	0.0117100i	0.869386	−	0.494134i	$-0.164515\pi$
$773$	0.187968	+	0.325571i	0.00676076	+	0.0117100i	−0.862625	+	0.505844i	$0.831181\pi$
$774$	−1.37231	−	19.4901i	−0.0493266	−	0.700558i
$775$		0			0
$776$	5.97225	−	33.8703i	0.214391	−	1.21587i
$777$	0.970078	−	4.20649i	0.0348013	−	0.150907i
$778$	7.79478	+	2.83707i	0.279456	+	0.101714i
$779$	−5.41413	−	30.7051i	−0.193981	−	1.10012i
$780$		0			0
$781$	13.0046	+	10.9122i	0.465342	+	0.390468i
$782$	−20.2763			−0.725078
$783$	−10.0742	−	11.5722i	−0.360024	−	0.413557i
$784$	−9.26269			−0.330810
$785$		0			0
$786$	7.81058	+	15.3200i	0.278594	+	0.546447i
$787$	1.02591	+	5.81822i	0.0365697	+	0.207397i	0.997618	−	0.0689843i	$-0.0219758\pi$
$787$	1.02591	+	5.81822i	0.0365697	+	0.207397i	−0.961048	+	0.276381i	$0.910865\pi$
$788$	27.8916	+	10.1517i	0.993597	+	0.361640i
$789$	19.5309	+	18.2041i	0.695318	+	0.648081i
$790$		0			0
$791$	0.327575	−	0.567376i	0.0116472	−	0.0201736i
$792$	12.7143	−	3.17654i	0.451785	−	0.112874i
$793$	0.324989	+	0.562897i	0.0115407	+	0.0199891i
$794$	−7.78144	+	2.83221i	−0.276153	+	0.100511i
$795$		0			0
$796$	24.8317	−	20.8363i	0.880137	−	0.738522i
$797$	−39.4911	+	33.1370i	−1.39885	+	1.17377i	−0.437239	+	0.899345i	$0.644044\pi$
$797$	−39.4911	+	33.1370i	−1.39885	+	1.17377i	−0.961608	+	0.274427i	$0.911512\pi$
$798$	2.20991	+	0.937422i	0.0782299	+	0.0331844i
$799$	28.0540	−	10.2108i	0.992481	−	0.361234i
$800$		0			0
$801$	36.9370	+	3.86426i	1.30510	+	0.136537i
$802$	12.1175	−	20.9881i	0.427883	−	0.741114i
$803$	3.25579	−	18.4645i	0.114894	−	0.651598i
$804$	11.2060	−	3.42896i	0.395204	−	0.120930i
$805$		0			0
$806$	−1.64454	−	9.32665i	−0.0579264	−	0.328517i
$807$	−15.5707	+	23.9894i	−0.548115	+	0.844468i
$808$	23.5968	+	19.8001i	0.830134	+	0.696565i
$809$	−37.4718			−1.31744			−0.658719	−	0.752389i	$-0.728901\pi$
$809$	−37.4718			−1.31744			−0.658719	+	0.752389i	$0.728901\pi$
$810$		0			0
$811$	27.5789			0.968426			0.484213	−	0.874950i	$-0.339106\pi$
$811$	27.5789			0.968426			0.484213	+	0.874950i	$0.339106\pi$
$812$	1.00113	+	0.840045i	0.0351326	+	0.0294798i
$813$	2.57367	−	3.96520i	0.0902626	−	0.139065i
$814$	1.84308	+	10.4526i	0.0645998	+	0.366364i
$815$		0			0
$816$	−12.1259	+	3.71045i	−0.424491	+	0.129892i
$817$	11.1482	−	63.2247i	0.390027	−	2.21195i
$818$	3.98417	−	6.90078i	0.139303	−	0.241280i
$819$	1.12586	−	1.55118i	0.0393406	−	0.0542025i
$820$		0			0
$821$	41.8420	−	15.2293i	1.46030	−	0.531505i	0.514850	−	0.857280i	$-0.327848\pi$
$821$	41.8420	−	15.2293i	1.46030	−	0.531505i	0.945447	+	0.325776i	$0.105626\pi$
$822$	1.65428	+	0.701730i	0.0576996	+	0.0244756i
$823$	19.3775	−	16.2597i	0.675458	−	0.566776i	−0.239217	−	0.970966i	$-0.576891\pi$
$823$	19.3775	−	16.2597i	0.675458	−	0.566776i	0.914675	+	0.404190i	$0.132446\pi$
$824$	−11.0312	+	9.25624i	−0.384289	+	0.322456i
$825$		0			0
$826$	−1.98513	+	0.722527i	−0.0690714	+	0.0251399i
$827$	9.46894	+	16.4007i	0.329267	+	0.570307i	0.982367	−	0.186965i	$-0.0598650\pi$
$827$	9.46894	+	16.4007i	0.329267	+	0.570307i	−0.653099	+	0.757272i	$0.726532\pi$
$828$	16.9077	+	17.4916i	0.587583	+	0.607875i
$829$	−1.72605	+	2.98961i	−0.0599482	+	0.103833i	−0.894442	−	0.447184i	$-0.852427\pi$
$829$	−1.72605	+	2.98961i	−0.0599482	+	0.103833i	0.834494	+	0.551017i	$0.185760\pi$
$830$		0			0
$831$	−12.1476	−	11.3223i	−0.421395	−	0.392767i
$832$	2.79838	+	1.01853i	0.0970163	+	0.0353111i
$833$	−6.56300	−	37.2206i	−0.227395	−	1.28962i
$834$	2.37592	+	4.66023i	0.0822714	+	0.161371i
$835$		0			0
$836$	18.5797			0.642593
$837$	0.587852	+	32.3400i	0.0203191	+	1.11783i
$838$	21.4873			0.742266
$839$	−14.6910	−	12.3272i	−0.507189	−	0.425582i	0.352950	−	0.935642i	$-0.385179\pi$
$839$	−14.6910	−	12.3272i	−0.507189	−	0.425582i	−0.860139	+	0.510060i	$0.829623\pi$
$840$		0			0
$841$	−3.52180	−	19.9731i	−0.121442	−	0.688729i
$842$	−6.17373	−	2.24705i	−0.212761	−	0.0774386i
$843$	1.25172	−	5.42777i	0.0431117	−	0.186942i
$844$	−0.487510	+	2.76481i	−0.0167808	+	0.0951686i
$845$		0			0
$846$	10.2293	+	4.98308i	0.351692	+	0.171322i
$847$	1.13750	+	1.97020i	0.0390849	+	0.0676970i
$848$	−2.82077	+	1.02668i	−0.0968656	+	0.0352562i
$849$	5.35308	+	43.5108i	0.183717	+	1.49329i
$850$		0			0
$851$	−34.9810	+	29.3526i	−1.19913	+	1.00619i
$852$	−3.04737	−	24.7696i	−0.104401	−	0.848592i
$853$	−5.49647	+	2.00055i	−0.188195	+	0.0684975i	−0.434399	−	0.900721i	$-0.643039\pi$
$853$	−5.49647	+	2.00055i	−0.188195	+	0.0684975i	0.246203	+	0.969218i	$0.420817\pi$
$854$	−0.0300330	−	0.0520187i	−0.00102771	−	0.00178004i
$855$		0			0
$856$	−7.48942	+	12.9721i	−0.255983	+	0.443376i
$857$	−8.58019	+	48.6607i	−0.293094	+	1.66222i	0.381757	+	0.924263i	$0.375319\pi$
$857$	−8.58019	+	48.6607i	−0.293094	+	1.66222i	−0.674851	+	0.737954i	$0.735792\pi$
$858$	−1.05898	+	4.59200i	−0.0361531	+	0.156768i
$859$	−7.31048	−	2.66080i	−0.249430	−	0.0907852i	0.214279	−	0.976772i	$-0.431260\pi$
$859$	−7.31048	−	2.66080i	−0.249430	−	0.0907852i	−0.463710	+	0.885987i	$0.653482\pi$
$860$		0			0
$861$	2.29746	+	0.119850i	0.0782971	+	0.00408448i
$862$	−1.45045	−	1.21707i	−0.0494026	−	0.0414537i
$863$	11.8283			0.402639			0.201320	−	0.979526i	$-0.435477\pi$
$863$	11.8283			0.402639			0.201320	+	0.979526i	$0.435477\pi$
$864$	−26.4403	−	14.6311i	−0.899516	−	0.497761i
$865$		0			0
$866$	10.0087	+	8.39827i	0.340108	+	0.285385i
$867$	−10.1275	−	19.8646i	−0.343949	−	0.674637i
$868$	−0.478419	−	2.71325i	−0.0162386	−	0.0920937i
$869$	11.9661	+	4.35529i	0.405921	+	0.147743i
$870$		0			0
$871$	−1.69597	+	9.61830i	−0.0574656	+	0.325904i
$872$	−6.11475	+	10.5911i	−0.207072	+	0.358659i
$873$	−29.3565	−	30.3703i	−0.993567	−	1.02788i
$874$	−12.6964	−	21.9908i	−0.429462	−	0.743850i
$875$		0			0
$876$	−22.0086	+	16.5930i	−0.743603	+	0.560625i
$877$	36.4509	−	30.5859i	1.23086	−	1.03281i	0.232676	−	0.972554i	$-0.425252\pi$
$877$	36.4509	−	30.5859i	1.23086	−	1.03281i	0.998183	−	0.0602584i	$-0.0191925\pi$
$878$	−7.58261	+	6.36256i	−0.255901	+	0.214726i
$879$	38.0999	+	16.1616i	1.28508	+	0.545118i
$880$		0			0
$881$	12.8601	+	22.2743i	0.433268	+	0.750441i	0.997152	−	0.0754120i	$-0.0240272\pi$
$881$	12.8601	+	22.2743i	0.433268	+	0.750441i	−0.563885	+	0.825853i	$0.690694\pi$
$882$	8.46133	−	11.6578i	0.284908	−	0.392539i
$883$	22.4783	−	38.9336i	0.756456	−	1.31022i	−0.188191	−	0.982133i	$-0.560262\pi$
$883$	22.4783	−	38.9336i	0.756456	−	1.31022i	0.944647	−	0.328088i	$-0.106404\pi$
$884$	3.15635	−	17.9006i	0.106160	−	0.602062i
$885$		0			0
$886$	−2.76876	−	1.00774i	−0.0930182	−	0.0338558i
$887$	2.53696	+	14.3878i	0.0851827	+	0.483095i	0.997317	+	0.0732037i	$0.0233223\pi$
$887$	2.53696	+	14.3878i	0.0851827	+	0.483095i	−0.912134	+	0.409891i	$0.865567\pi$
$888$	19.6883	−	30.3333i	0.660697	−	1.01792i
$889$	−0.895899	−	0.751749i	−0.0300475	−	0.0252128i
$890$		0			0
$891$	6.01493	−	14.9288i	0.201508	−	0.500135i
$892$	−4.04685			−0.135499
$893$	28.6409	+	24.0325i	0.958430	+	0.804218i
$894$	7.78149	−	11.9888i	0.260252	−	0.400964i
$895$		0			0
$896$	2.92845	+	1.06587i	0.0978325	+	0.0356081i
$897$	−19.3876	+	5.93247i	−0.647332	+	0.198080i
$898$	−0.132538	+	0.751662i	−0.00442286	+	0.0250833i
$899$	9.19024	−	15.9180i	0.306512	−	0.530894i
$900$		0			0
$901$	−6.12417	−	10.6074i	−0.204026	−	0.353383i
$902$	−5.31527	+	1.93460i	−0.176979	+	0.0644151i
$903$	4.36098	+	1.84989i	0.145124	+	0.0615605i
$904$	4.20420	−	3.52775i	0.139830	−	0.117331i
$905$		0			0
$906$	−20.9165	+	15.7696i	−0.694905	+	0.523910i
$907$	−30.3649	+	11.0519i	−1.00825	+	0.366973i	−0.792761	−	0.609533i	$-0.791357\pi$
$907$	−30.3649	+	11.0519i	−1.00825	+	0.366973i	−0.215489	+	0.976506i	$0.569135\pi$
$908$	3.40080	+	5.89035i	0.112859	+	0.195478i
$909$	36.7029	−	9.16983i	1.21736	−	0.304144i
$910$		0			0
$911$	−1.88176	+	10.6720i	−0.0623455	+	0.353579i	0.937637	+	0.347617i	$0.113009\pi$
$911$	−1.88176	+	10.6720i	−0.0623455	+	0.353579i	−0.999982	+	0.00596215i	$0.998102\pi$
$912$	−11.6171	−	10.8279i	−0.384680	−	0.358546i
$913$	−10.4375	−	3.79895i	−0.345432	−	0.125727i
$914$	0.425801	+	2.41484i	0.0140842	+	0.0798757i
$915$		0			0
$916$	−28.3378	−	23.7782i	−0.936308	−	0.785655i
$917$	−4.16924			−0.137681
$918$	6.40693	−	18.6508i	0.211460	−	0.615569i
$919$	−7.87445			−0.259754			−0.129877	−	0.991530i	$-0.541458\pi$
$919$	−7.87445			−0.259754			−0.129877	+	0.991530i	$0.541458\pi$
$920$		0			0
$921$	27.8094	+	1.45072i	0.916351	+	0.0478028i
$922$	−2.58936	−	14.6850i	−0.0852761	−	0.483625i
$923$	19.5447	+	7.11368i	0.643321	+	0.234150i
$924$	−0.308072	+	1.33587i	−0.0101348	+	0.0439471i
$925$		0			0
$926$	8.12519	−	14.0732i	0.267010	−	0.462476i
$927$	1.24217	+	17.6418i	0.0407981	+	0.579432i
$928$	8.58593	+	14.8713i	0.281847	+	0.488173i
$929$	−30.4449	+	11.0810i	−0.998865	+	0.363557i	−0.789147	−	0.614205i	$-0.789477\pi$
$929$	−30.4449	+	11.0810i	−0.998865	+	0.363557i	−0.209718	+	0.977762i	$0.567255\pi$
$930$		0			0
$931$	36.2584	−	30.4244i	1.18832	−	0.997120i
$932$	−5.58660	+	4.68771i	−0.182995	+	0.153551i
$933$	−3.66286	−	29.7724i	−0.119917	−	0.974705i
$934$	19.3855	−	7.05575i	0.634313	−	0.230871i
$935$		0			0
$936$	13.3068	−	8.98489i	0.434947	−	0.293680i
$937$	30.4971	−	52.8226i	0.996298	−	1.72564i	0.423698	−	0.905804i	$-0.360732\pi$
$937$	30.4971	−	52.8226i	0.996298	−	1.72564i	0.572600	−	0.819835i	$-0.305935\pi$
$938$	0.156728	−	0.888851i	0.00511736	−	0.0290220i
$939$	−5.21699	+	22.6221i	−0.170250	+	0.738244i
$940$		0			0
$941$	2.66012	+	15.0863i	0.0867176	+	0.491800i	0.996973	+	0.0777521i	$0.0247743\pi$
$941$	2.66012	+	15.0863i	0.0867176	+	0.491800i	−0.910255	+	0.414048i	$0.864115\pi$
$942$	15.4537	+	0.806163i	0.503508	+	0.0262662i
$943$	−18.6422	−	15.6427i	−0.607075	−	0.509396i
$944$	13.9756			0.454867
$945$		0			0
$946$	−11.6470			−0.378678
$947$	−42.4817	−	35.6464i	−1.38047	−	1.15835i	−0.969038	−	0.246910i	$-0.920585\pi$
$947$	−42.4817	−	35.6464i	−1.38047	−	1.15835i	−0.411431	−	0.911441i	$-0.634971\pi$
$948$	−8.50266	−	16.6775i	−0.276154	−	0.541660i
$949$	−3.98892	−	22.6223i	−0.129486	−	0.734350i
$950$		0			0
$951$	−27.1416	−	25.2978i	−0.880128	−	0.820336i
$952$	−0.676031	+	3.83396i	−0.0219103	+	0.124259i
$953$	1.43287	−	2.48180i	0.0464152	−	0.0803935i	−0.841884	−	0.539658i	$-0.818554\pi$
$953$	1.43287	−	2.48180i	0.0464152	−	0.0803935i	0.888300	+	0.459264i	$0.151887\pi$
$954$	1.28458	−	4.48801i	0.0415898	−	0.145305i
$955$		0			0
$956$	−23.6189	+	8.59657i	−0.763889	+	0.278033i
$957$	−7.30308	+	5.50602i	−0.236075	+	0.177984i
$958$	−5.74090	+	4.81719i	−0.185480	+	0.155636i
$959$	−0.333747	+	0.280047i	−0.0107773	+	0.00904320i
$960$		0			0
$961$	−7.28166	+	2.65031i	−0.234892	+	0.0854938i
$962$	6.50193	+	11.2617i	0.209631	+	0.363091i
$963$	7.49048	+	16.8021i	0.241377	+	0.541441i
$964$	21.2130	−	36.7419i	0.683223	−	1.18338i
$965$		0			0
$966$	1.79165	−	0.548235i	0.0576455	−	0.0176392i
$967$	43.4350	+	15.8090i	1.39677	+	0.508384i	0.927219	−	0.374519i	$-0.122192\pi$
$967$	43.4350	+	15.8090i	1.39677	+	0.508384i	0.469555	+	0.882903i	$0.344414\pi$
$968$	3.30933	+	18.7682i	0.106366	+	0.603231i
$969$	35.2789	−	54.3533i	1.13332	−	1.74608i
$970$		0			0
$971$	35.1848			1.12914			0.564568	−	0.825387i	$-0.309043\pi$
$971$	35.1848			1.12914			0.564568	+	0.825387i	$0.309043\pi$
$972$	−21.4319	+	10.0253i	−0.687428	+	0.321561i
$973$	−1.26825			−0.0406583
$974$	−14.8825	−	12.4879i	−0.476867	−	0.400139i
$975$		0			0
$976$	0.0690029	+	0.391335i	0.00220873	+	0.0125263i
$977$	−24.2601	−	8.82997i	−0.776151	−	0.282496i	−0.0765840	−	0.997063i	$-0.524401\pi$
$977$	−24.2601	−	8.82997i	−0.776151	−	0.282496i	−0.699567	+	0.714567i	$0.746624\pi$
$978$	−18.6129	+	5.69544i	−0.595176	+	0.182120i
$979$	3.84435	−	21.8024i	0.122866	−	0.696808i
$980$		0			0
$981$	6.11562	+	13.7181i	0.195257	+	0.437986i
$982$	11.4268	+	19.7918i	0.364643	+	0.631581i
$983$	10.0236	−	3.64829i	0.319703	−	0.116362i	−0.177184	−	0.984178i	$-0.556699\pi$
$983$	10.0236	−	3.64829i	0.319703	−	0.116362i	0.496887	+	0.867815i	$0.334476\pi$
$984$	17.7418	+	7.52590i	0.565587	+	0.239917i
$985$		0			0
$986$	−8.58458	+	7.20331i	−0.273389	+	0.229400i
$987$	−2.20283	+	1.66078i	−0.0701168	+	0.0528633i
$988$	21.3906	−	7.78555i	0.680527	−	0.247691i
$989$	−25.0548	−	43.3962i	−0.796696	−	1.37992i
$990$		0			0
$991$	−29.6838	+	51.4138i	−0.942937	+	1.63321i	−0.183106	+	0.983093i	$0.558615\pi$
$991$	−29.6838	+	51.4138i	−0.942937	+	1.63321i	−0.759831	+	0.650121i	$0.774718\pi$
$992$	6.28624	−	35.6511i	0.199588	−	1.13192i
$993$	−10.1955	−	9.50289i	−0.323545	−	0.301565i
$994$	−1.80617	−	0.657393i	−0.0572883	−	0.0208512i
$995$		0			0
$996$	7.41653	+	14.5471i	0.235002	+	0.460943i
$997$	−21.3149	−	17.8854i	−0.675051	−	0.566435i	0.239505	−	0.970895i	$-0.423015\pi$
$997$	−21.3149	−	17.8854i	−0.675051	−	0.566435i	−0.914556	+	0.404460i	$0.867459\pi$
$998$	−10.9061			−0.345228
$999$	−15.9461	−	41.4516i	−0.504513	−	1.31147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.d.151.4		30
5.2	odd	4		675.2.u.c.124.4		60
5.3	odd	4		675.2.u.c.124.7		60
5.4	even	2		135.2.k.a.16.2	✓	30
15.14	odd	2		405.2.k.a.46.4		30
27.22	even	9	inner	675.2.l.d.76.4		30
135.22	odd	36		675.2.u.c.49.7		60
135.34	even	18		3645.2.a.h.1.6		15
135.49	even	18		135.2.k.a.76.2	yes	30
135.59	odd	18		405.2.k.a.361.4		30
135.74	odd	18		3645.2.a.g.1.10		15
135.103	odd	36		675.2.u.c.49.4		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.16.2	✓	30	5.4	even	2
135.2.k.a.76.2	yes	30	135.49	even	18
405.2.k.a.46.4		30	15.14	odd	2
405.2.k.a.361.4		30	135.59	odd	18
675.2.l.d.76.4		30	27.22	even	9	inner
675.2.l.d.151.4		30	1.1	even	1	trivial
675.2.u.c.49.4		60	135.103	odd	36
675.2.u.c.49.7		60	135.22	odd	36
675.2.u.c.124.4		60	5.2	odd	4
675.2.u.c.124.7		60	5.3	odd	4
3645.2.a.g.1.10		15	135.74	odd	18
3645.2.a.h.1.6		15	135.34	even	18

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.531925 + 0.446338i) q^{2} +(-0.942993 + 1.45285i) q^{3} +(-0.263570 - 1.49478i) q^{4} +(-1.15006 + 0.351912i) q^{6} +(0.0506352 - 0.287167i) q^{7} +(1.22136 - 2.11545i) q^{8} +(-1.22153 - 2.74005i) q^{9} +O(q^{10})\)	\(q+(0.531925 + 0.446338i) q^{2} +(-0.942993 + 1.45285i) q^{3} +(-0.263570 - 1.49478i) q^{4} +(-1.15006 + 0.351912i) q^{6} +(0.0506352 - 0.287167i) q^{7} +(1.22136 - 2.11545i) q^{8} +(-1.22153 - 2.74005i) q^{9} +(-1.68049 + 0.611647i) q^{11} +(2.42023 + 1.02664i) q^{12} +(-1.67842 + 1.40837i) q^{13} +(0.155107 - 0.130151i) q^{14} +(-1.25873 + 0.458140i) q^{16} +(-2.73283 - 4.73339i) q^{17} +(0.573226 - 2.00271i) q^{18} +(3.42243 - 5.92782i) q^{19} +(0.369461 + 0.344361i) q^{21} +(-1.16689 - 0.424714i) q^{22} +(-0.927728 - 5.26140i) q^{23} +(1.92170 + 3.76930i) q^{24} -1.52140 q^{26} +(5.13276 + 0.809152i) q^{27} -0.442597 q^{28} +(-2.26194 - 1.89799i) q^{29} +(1.08094 + 6.13030i) q^{31} +(-5.46483 - 1.98904i) q^{32} +(0.696057 - 3.01827i) q^{33} +(0.659035 - 3.73757i) q^{34} +(-3.77381 + 2.54811i) q^{36} +(-4.27364 - 7.40217i) q^{37} +(4.46628 - 1.62559i) q^{38} +(-0.463397 - 3.76657i) q^{39} +(3.48938 - 2.92794i) q^{41} +(0.0428237 + 0.348078i) q^{42} +(8.81367 - 3.20791i) q^{43} +(1.35720 + 2.35074i) q^{44} +(1.85488 - 3.21275i) q^{46} +(-0.948501 + 5.37922i) q^{47} +(0.521366 - 2.26076i) q^{48} +(6.49795 + 2.36506i) q^{49} +(9.45393 + 0.493178i) q^{51} +(2.54758 + 2.13767i) q^{52} +2.24096 q^{53} +(2.36909 + 2.72135i) q^{54} +(-0.545643 - 0.457849i) q^{56} +(5.38489 + 10.5622i) q^{57} +(-0.356035 - 2.01918i) q^{58} +(-9.80414 - 3.56842i) q^{59} +(0.0515134 - 0.292147i) q^{61} +(-2.16121 + 3.74332i) q^{62} +(-0.848703 + 0.212039i) q^{63} +(-0.679583 - 1.17707i) q^{64} +(1.71742 - 1.29481i) q^{66} +(3.41470 - 2.86527i) q^{67} +(-6.35509 + 5.33255i) q^{68} +(8.51886 + 3.61362i) q^{69} +(-4.74640 - 8.22101i) q^{71} +(-7.28836 - 0.762491i) q^{72} +(-5.24212 + 9.07962i) q^{73} +(1.03061 - 5.84488i) q^{74} +(-9.76283 - 3.55338i) q^{76} +(0.0905528 + 0.513550i) q^{77} +(1.43467 - 2.21036i) q^{78} +(-5.45470 - 4.57704i) q^{79} +(-6.01573 + 6.69410i) q^{81} +3.16293 q^{82} +(4.75792 + 3.99237i) q^{83} +(0.417366 - 0.643025i) q^{84} +(6.12002 + 2.22750i) q^{86} +(4.89048 - 1.49646i) q^{87} +(-0.758562 + 4.30202i) q^{88} +(-6.18976 + 10.7210i) q^{89} +(0.319448 + 0.553300i) q^{91} +(-7.62012 + 2.77350i) q^{92} +(-9.92570 - 4.21039i) q^{93} +(-2.90548 + 2.43799i) q^{94} +(8.04306 - 6.06391i) q^{96} +(13.2307 - 4.81556i) q^{97} +(2.40080 + 4.15831i) q^{98} +(3.72870 + 3.85747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 9 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 9 * q^8 - 3 * q^9	\( 30 q - 3 q^{3} + 9 q^{8} - 3 q^{9} - 6 q^{11} - 3 q^{12} - 3 q^{13} - 9 q^{14} + 12 q^{16} + 12 q^{17} - 6 q^{18} + 24 q^{19} - 36 q^{21} + 51 q^{22} - 18 q^{23} + 45 q^{24} - 18 q^{26} + 9 q^{27} + 60 q^{28} + 18 q^{29} + 12 q^{31} - 36 q^{32} - 27 q^{33} - 69 q^{34} - 42 q^{36} - 24 q^{37} + 24 q^{38} + 6 q^{39} - 75 q^{41} + 18 q^{42} - 6 q^{43} + 12 q^{44} + 30 q^{46} - 45 q^{47} + 27 q^{48} - 36 q^{49} + 21 q^{51} - 30 q^{52} - 36 q^{53} + 18 q^{54} + 30 q^{56} - 30 q^{57} - 27 q^{58} - 27 q^{59} - 12 q^{61} - 36 q^{62} - 18 q^{63} + 27 q^{64} + 78 q^{66} + 30 q^{67} - 69 q^{68} - 117 q^{69} + 12 q^{71} - 9 q^{72} - 21 q^{73} - 30 q^{76} + 36 q^{77} - 66 q^{78} + 54 q^{79} - 27 q^{81} + 48 q^{82} + 87 q^{83} + 45 q^{84} + 18 q^{86} + 27 q^{87} + 18 q^{88} + 9 q^{89} + 51 q^{91} - 24 q^{92} - 36 q^{93} + 15 q^{94} - 15 q^{96} + 75 q^{97} + 15 q^{98} + 123 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 9 * q^8 - 3 * q^9 - 6 * q^11 - 3 * q^12 - 3 * q^13 - 9 * q^14 + 12 * q^16 + 12 * q^17 - 6 * q^18 + 24 * q^19 - 36 * q^21 + 51 * q^22 - 18 * q^23 + 45 * q^24 - 18 * q^26 + 9 * q^27 + 60 * q^28 + 18 * q^29 + 12 * q^31 - 36 * q^32 - 27 * q^33 - 69 * q^34 - 42 * q^36 - 24 * q^37 + 24 * q^38 + 6 * q^39 - 75 * q^41 + 18 * q^42 - 6 * q^43 + 12 * q^44 + 30 * q^46 - 45 * q^47 + 27 * q^48 - 36 * q^49 + 21 * q^51 - 30 * q^52 - 36 * q^53 + 18 * q^54 + 30 * q^56 - 30 * q^57 - 27 * q^58 - 27 * q^59 - 12 * q^61 - 36 * q^62 - 18 * q^63 + 27 * q^64 + 78 * q^66 + 30 * q^67 - 69 * q^68 - 117 * q^69 + 12 * q^71 - 9 * q^72 - 21 * q^73 - 30 * q^76 + 36 * q^77 - 66 * q^78 + 54 * q^79 - 27 * q^81 + 48 * q^82 + 87 * q^83 + 45 * q^84 + 18 * q^86 + 27 * q^87 + 18 * q^88 + 9 * q^89 + 51 * q^91 - 24 * q^92 - 36 * q^93 + 15 * q^94 - 15 * q^96 + 75 * q^97 + 15 * q^98 + 123 * q^99

Introduction

L-functions

Modular forms

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Database

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