LMFDB - Embedded newform 675.2.u.c.124.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

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, 9]))

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

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

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not 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:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.4
Character	$\chi$	$=$	675.124
Dual form			675.2.u.c.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.446338 + 0.531925i) q^{2} +(1.45285 + 0.942993i) q^{3} +(0.263570 + 1.49478i) q^{4} +(-1.15006 + 0.351912i) q^{6} +(0.287167 + 0.0506352i) q^{7} +(-2.11545 - 1.22136i) q^{8} +(1.22153 + 2.74005i) q^{9} +O(q^{10})$	\(q+(-0.446338 + 0.531925i) q^{2} +(1.45285 + 0.942993i) q^{3} +(0.263570 + 1.49478i) q^{4} +(-1.15006 + 0.351912i) q^{6} +(0.287167 + 0.0506352i) q^{7} +(-2.11545 - 1.22136i) q^{8} +(1.22153 + 2.74005i) q^{9} +(-1.68049 + 0.611647i) q^{11} +(-1.02664 + 2.42023i) q^{12} +(1.40837 + 1.67842i) q^{13} +(-0.155107 + 0.130151i) q^{14} +(-1.25873 + 0.458140i) q^{16} +(4.73339 - 2.73283i) q^{17} +(-2.00271 - 0.573226i) q^{18} +(-3.42243 + 5.92782i) q^{19} +(0.369461 + 0.344361i) q^{21} +(0.424714 - 1.16689i) q^{22} +(-5.26140 + 0.927728i) q^{23} +(-1.92170 - 3.76930i) q^{24} -1.52140 q^{26} +(-0.809152 + 5.13276i) q^{27} +0.442597i q^{28} +(2.26194 + 1.89799i) q^{29} +(1.08094 + 6.13030i) q^{31} +(1.98904 - 5.46483i) q^{32} +(-3.01827 - 0.696057i) q^{33} +(-0.659035 + 3.73757i) q^{34} +(-3.77381 + 2.54811i) q^{36} +(7.40217 - 4.27364i) q^{37} +(-1.62559 - 4.46628i) q^{38} +(0.463397 + 3.76657i) q^{39} +(3.48938 - 2.92794i) q^{41} +(-0.348078 + 0.0428237i) q^{42} +(-3.20791 - 8.81367i) q^{43} +(-1.35720 - 2.35074i) q^{44} +(1.85488 - 3.21275i) q^{46} +(-5.37922 - 0.948501i) q^{47} +(-2.26076 - 0.521366i) q^{48} +(-6.49795 - 2.36506i) q^{49} +(9.45393 + 0.493178i) q^{51} +(-2.13767 + 2.54758i) q^{52} -2.24096i q^{53} +(-2.36909 - 2.72135i) q^{54} +(-0.545643 - 0.457849i) q^{56} +(-10.5622 + 5.38489i) q^{57} +(-2.01918 + 0.356035i) q^{58} +(9.80414 + 3.56842i) q^{59} +(0.0515134 - 0.292147i) q^{61} +(-3.74332 - 2.16121i) q^{62} +(0.212039 + 0.848703i) q^{63} +(0.679583 + 1.17707i) q^{64} +(1.71742 - 1.29481i) q^{66} +(2.86527 + 3.41470i) q^{67} +(5.33255 + 6.35509i) q^{68} +(-8.51886 - 3.61362i) q^{69} +(-4.74640 - 8.22101i) q^{71} +(0.762491 - 7.28836i) q^{72} +(9.07962 + 5.24212i) q^{73} +(-1.03061 + 5.84488i) q^{74} +(-9.76283 - 3.55338i) q^{76} +(-0.513550 + 0.0905528i) q^{77} +(-2.21036 - 1.43467i) q^{78} +(5.45470 + 4.57704i) q^{79} +(-6.01573 + 6.69410i) q^{81} +3.16293i q^{82} +(3.99237 - 4.75792i) q^{83} +(-0.417366 + 0.643025i) q^{84} +(6.12002 + 2.22750i) q^{86} +(1.49646 + 4.89048i) q^{87} +(4.30202 + 0.758562i) q^{88} +(6.18976 - 10.7210i) q^{89} +(0.319448 + 0.553300i) q^{91} +(-2.77350 - 7.62012i) q^{92} +(-4.21039 + 9.92570i) q^{93} +(2.90548 - 2.43799i) q^{94} +(8.04306 - 6.06391i) q^{96} +(4.81556 + 13.2307i) q^{97} +(4.15831 - 2.40080i) q^{98} +(-3.72870 - 3.85747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^9	$ 60 q + 6 q^{9} - 12 q^{11} + 18 q^{14} + 24 q^{16} - 48 q^{19} - 72 q^{21} - 90 q^{24} - 36 q^{26} - 36 q^{29} + 24 q^{31} + 138 q^{34} - 84 q^{36} - 12 q^{39} - 150 q^{41} - 24 q^{44} + 60 q^{46} + 72 q^{49} + 42 q^{51} - 36 q^{54} + 60 q^{56} + 54 q^{59} - 24 q^{61} - 54 q^{64} + 156 q^{66} + 234 q^{69} + 24 q^{71} - 60 q^{76} - 108 q^{79} - 54 q^{81} - 90 q^{84} + 36 q^{86} - 18 q^{89} + 102 q^{91} - 30 q^{94} - 30 q^{96} - 246 q^{99}+O(q^{100}) $ 60 * q + 6 * q^9 - 12 * q^11 + 18 * q^14 + 24 * q^16 - 48 * q^19 - 72 * q^21 - 90 * q^24 - 36 * q^26 - 36 * q^29 + 24 * q^31 + 138 * q^34 - 84 * q^36 - 12 * q^39 - 150 * q^41 - 24 * q^44 + 60 * q^46 + 72 * q^49 + 42 * q^51 - 36 * q^54 + 60 * q^56 + 54 * q^59 - 24 * q^61 - 54 * q^64 + 156 * q^66 + 234 * q^69 + 24 * q^71 - 60 * q^76 - 108 * q^79 - 54 * q^81 - 90 * q^84 + 36 * q^86 - 18 * q^89 + 102 * q^91 - 30 * q^94 - 30 * q^96 - 246 * 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 $

$2$	−0.446338	+	0.531925i	−0.315608	+	0.376128i	−0.900405	−	0.435052i	$-0.856730\pi$
$2$	−0.446338	+	0.531925i	−0.315608	+	0.376128i	0.584797	+	0.811180i	$0.301174\pi$
$3$	1.45285	+	0.942993i	0.838802	+	0.544437i
$3$	1.45285	+	0.942993i	0.838802	+	0.544437i
$4$	0.263570	+	1.49478i	0.131785	+	0.747390i
$5$		0			0
$5$		0			0
$6$	−1.15006	+	0.351912i	−0.469511	+	0.143667i
$7$	0.287167	+	0.0506352i	0.108539	+	0.0191383i	0.227654	−	0.973742i	$-0.426895\pi$
$7$	0.287167	+	0.0506352i	0.108539	+	0.0191383i	−0.119115	+	0.992880i	$0.538006\pi$
$8$	−2.11545	−	1.22136i	−0.747924	−	0.431814i
$9$	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	$0.475781\pi$
$12$	−1.02664	+	2.42023i	−0.296365	+	0.698660i
$13$	1.40837	+	1.67842i	0.390610	+	0.465511i	0.925133	−	0.379643i	$-0.123953\pi$
$13$	1.40837	+	1.67842i	0.390610	+	0.465511i	−0.534523	+	0.845154i	$0.679509\pi$
$14$	−0.155107	+	0.130151i	−0.0414542	+	0.0347842i
$15$		0			0
$16$	−1.25873	+	0.458140i	−0.314682	+	0.114535i
$17$	4.73339	−	2.73283i	1.14802	−	0.662808i	0.199613	−	0.979875i	$-0.436031\pi$
$17$	4.73339	−	2.73283i	1.14802	−	0.662808i	0.948403	+	0.317067i	$0.102698\pi$
$18$	−2.00271	−	0.573226i	−0.472044	−	0.135111i
$19$	−3.42243	+	5.92782i	−0.785159	+	1.35993i	0.143745	+	0.989615i	$0.454085\pi$
$19$	−3.42243	+	5.92782i	−0.785159	+	1.35993i	−0.928904	+	0.370320i	$0.879248\pi$
$20$		0			0
$21$	0.369461	+	0.344361i	0.0806229	+	0.0751458i
$22$	0.424714	−	1.16689i	0.0905494	−	0.248782i
$23$	−5.26140	+	0.927728i	−1.09708	+	0.193445i	−0.692756	−	0.721172i	$-0.743604\pi$
$23$	−5.26140	+	0.927728i	−1.09708	+	0.193445i	−0.404322	+	0.914616i	$0.632493\pi$
$24$	−1.92170	−	3.76930i	−0.392264	−	0.769404i
$25$		0			0
$26$	−1.52140			−0.298372
$27$	−0.809152	+	5.13276i	−0.155721	+	0.987801i
$28$			0.442597i			0.0836429i
$29$	2.26194	+	1.89799i	0.420031	+	0.352448i	0.828175	−	0.560470i	$-0.189379\pi$
$29$	2.26194	+	1.89799i	0.420031	+	0.352448i	−0.408144	+	0.912918i	$0.633824\pi$
$30$		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	$0.755626\pi$
$32$	1.98904	−	5.46483i	0.351615	−	0.966054i
$33$	−3.01827	−	0.696057i	−0.525413	−	0.121168i
$34$	−0.659035	+	3.73757i	−0.113024	+	0.640988i
$35$		0			0
$36$	−3.77381	+	2.54811i	−0.628968	+	0.424685i
$37$	7.40217	−	4.27364i	1.21691	−	0.702583i	0.252653	−	0.967557i	$-0.418697\pi$
$37$	7.40217	−	4.27364i	1.21691	−	0.702583i	0.964255	+	0.264974i	$0.0853635\pi$
$38$	−1.62559	−	4.46628i	−0.263706	−	0.724527i
$39$	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	$0.162024\pi$
$42$	−0.348078	+	0.0428237i	−0.0537097	+	0.00660784i
$43$	−3.20791	−	8.81367i	−0.489202	−	1.34407i	−0.901404	−	0.432979i	$-0.857462\pi$
$43$	−3.20791	−	8.81367i	−0.489202	−	1.34407i	0.412202	−	0.911093i	$-0.364760\pi$
$44$	−1.35720	−	2.35074i	−0.204606	−	0.354388i
$45$		0			0
$46$	1.85488	−	3.21275i	0.273487	−	0.473694i
$47$	−5.37922	−	0.948501i	−0.784640	−	0.138353i	−0.233046	−	0.972466i	$-0.574869\pi$
$47$	−5.37922	−	0.948501i	−0.784640	−	0.138353i	−0.551594	+	0.834113i	$0.685980\pi$
$48$	−2.26076	−	0.521366i	−0.326313	−	0.0752527i
$49$	−6.49795	−	2.36506i	−0.928278	−	0.337866i
$50$		0			0
$51$	9.45393	+	0.493178i	1.32382	+	0.0690588i
$52$	−2.13767	+	2.54758i	−0.296442	+	0.353286i
$53$		−	2.24096i		−	0.307820i	−0.988085	−	0.153910i	$-0.950813\pi$
$53$		−	2.24096i		−	0.307820i	0.988085	−	0.153910i	$-0.0491866\pi$
$54$	−2.36909	−	2.72135i	−0.322392	−	0.370329i
$55$		0			0
$56$	−0.545643	−	0.457849i	−0.0729146	−	0.0611826i
$57$	−10.5622	+	5.38489i	−1.39899	+	0.713246i
$58$	−2.01918	+	0.356035i	−0.265131	+	0.0467497i
$59$	9.80414	+	3.56842i	1.27639	+	0.464568i	0.889237	−	0.457447i	$-0.151236\pi$
$59$	9.80414	+	3.56842i	1.27639	+	0.464568i	0.387154	+	0.922015i	$0.373458\pi$
$60$		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	$0.0495101\pi$
$62$	−3.74332	−	2.16121i	−0.475402	−	0.274474i
$63$	0.212039	+	0.848703i	0.0267144	+	0.106927i
$64$	0.679583	+	1.17707i	0.0849479	+	0.147134i
$65$		0			0
$66$	1.71742	−	1.29481i	0.211399	−	0.159381i
$67$	2.86527	+	3.41470i	0.350049	+	0.417172i	0.912124	−	0.409914i	$-0.134441\pi$
$67$	2.86527	+	3.41470i	0.350049	+	0.417172i	−0.562075	+	0.827086i	$0.689997\pi$
$68$	5.33255	+	6.35509i	0.646667	+	0.770668i
$69$	−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	$-0.357133\pi$
$72$	0.762491	−	7.28836i	0.0898604	−	0.858941i
$73$	9.07962	+	5.24212i	1.06269	+	0.613544i	0.926175	−	0.377095i	$-0.123077\pi$
$73$	9.07962	+	5.24212i	1.06269	+	0.613544i	0.136514	+	0.990638i	$0.456410\pi$
$74$	−1.03061	+	5.84488i	−0.119806	+	0.679454i
$75$		0			0
$76$	−9.76283	−	3.55338i	−1.11987	−	0.407601i
$77$	−0.513550	+	0.0905528i	−0.0585245	+	0.0103194i
$78$	−2.21036	−	1.43467i	−0.250275	−	0.162445i
$79$	5.45470	+	4.57704i	0.613702	+	0.514957i	0.895817	−	0.444424i	$-0.146592\pi$
$79$	5.45470	+	4.57704i	0.613702	+	0.514957i	−0.282115	+	0.959381i	$0.591036\pi$
$80$		0			0
$81$	−6.01573	+	6.69410i	−0.668415	+	0.743789i
$82$			3.16293i			0.349288i
$83$	3.99237	−	4.75792i	0.438219	−	0.522249i	−0.501056	−	0.865415i	$-0.667055\pi$
$83$	3.99237	−	4.75792i	0.438219	−	0.522249i	0.939275	+	0.343166i	$0.111499\pi$
$84$	−0.417366	+	0.643025i	−0.0455383	+	0.0701598i
$85$		0			0
$86$	6.12002	+	2.22750i	0.659939	+	0.240198i
$87$	1.49646	+	4.89048i	0.160437	+	0.524315i
$88$	4.30202	+	0.758562i	0.458597	+	0.0808630i
$89$	6.18976	−	10.7210i	0.656113	−	1.13642i	−0.325500	−	0.945542i	$-0.605533\pi$
$89$	6.18976	−	10.7210i	0.656113	−	1.13642i	0.981613	−	0.190880i	$-0.0611340\pi$
$90$		0			0
$91$	0.319448	+	0.553300i	0.0334873	+	0.0580017i
$92$	−2.77350	−	7.62012i	−0.289157	−	0.794452i
$93$	−4.21039	+	9.92570i	−0.436597	+	1.02925i
$94$	2.90548	−	2.43799i	0.299677	−	0.251459i
$95$		0			0
$96$	8.04306	−	6.06391i	0.820891	−	0.618896i
$97$	4.81556	+	13.2307i	0.488947	+	1.34337i	0.901635	+	0.432497i	$0.142368\pi$
$97$	4.81556	+	13.2307i	0.488947	+	1.34337i	−0.412689	+	0.910872i	$0.635410\pi$
$98$	4.15831	−	2.40080i	0.420053	−	0.242518i
$99$	−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	$0.839679\pi$
$102$	−4.48198	+	4.80866i	−0.443782	+	0.476128i
$103$	−2.01626	+	5.53963i	−0.198668	+	0.545836i	−0.998521	−	0.0543593i	$-0.982688\pi$
$103$	−2.01626	+	5.53963i	−0.198668	+	0.545836i	0.799853	+	0.600196i	$0.204911\pi$
$104$	−0.929373	−	5.27074i	−0.0911326	−	0.516838i
$105$		0			0
$106$	1.19202	+	1.00023i	0.115780	+	0.0971507i
$107$		−	6.13206i		−	0.592808i	−0.955063	−	0.296404i	$-0.904212\pi$
$107$		−	6.13206i		−	0.592808i	0.955063	−	0.296404i	$-0.0957875\pi$
$108$	−7.88562	+	0.143339i	−0.758794	+	0.0137928i
$109$	5.00653			0.479538			0.239769	−	0.970830i	$-0.422928\pi$
$109$	5.00653			0.479538			0.239769	+	0.970830i	$0.422928\pi$
$110$		0			0
$111$	14.7842	+	0.771241i	1.40326	+	0.0732030i
$112$	−0.384663	+	0.0678265i	−0.0363473	+	0.00640900i
$113$	0.768439	−	2.11127i	0.0722887	−	0.198611i	−0.898286	−	0.439411i	$-0.855187\pi$
$113$	0.768439	−	2.11127i	0.0722887	−	0.198611i	0.970575	+	0.240799i	$0.0774095\pi$
$114$	1.84993	−	8.02175i	0.173262	−	0.751306i
$115$		0			0
$116$	−2.24090	+	3.88135i	−0.208062	+	0.360374i
$117$	−2.87861	+	5.90923i	−0.266127	+	0.546309i
$118$	−6.27409	+	3.62235i	−0.577576	+	0.333464i
$119$	1.49765	−	0.545100i	0.137289	−	0.0499692i
$120$		0			0
$121$	−5.97657	+	5.01494i	−0.543325	+	0.455903i
$122$	0.132408	+	0.157798i	0.0119877	+	0.0142863i
$123$	7.83056	−	0.963384i	0.706057	−	0.0868654i
$124$	−8.87854	+	3.23152i	−0.797317	+	0.290199i
$125$		0			0
$126$	−0.546087	−	0.266019i	−0.0486493	−	0.0236989i
$127$	3.47339	+	2.00536i	0.308213	+	0.177947i	0.646127	−	0.763230i	$-0.276388\pi$
$127$	3.47339	+	2.00536i	0.308213	+	0.177947i	−0.337913	+	0.941177i	$0.609721\pi$
$128$	10.5250	+	1.85583i	0.930284	+	0.164034i
$129$	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	$-0.270298\pi$
$132$	0.244927	−	4.69510i	0.0213182	−	0.408656i
$133$	−1.28296	+	1.52898i	−0.111247	+	0.132579i
$134$	−3.09524			−0.267388
$135$		0			0
$136$	−13.3510			−1.14484
$137$	0.960393	−	1.14455i	0.0820519	−	0.0977856i	−0.723457	−	0.690370i	$-0.757448\pi$
$137$	0.960393	−	1.14455i	0.0820519	−	0.0977856i	0.805508	+	0.592584i	$0.201892\pi$
$138$	5.72446	−	2.91849i	0.487298	−	0.248439i
$139$	0.755255	+	4.28326i	0.0640599	+	0.363302i	0.999940	+	0.0109822i	$0.00349581\pi$
$139$	0.755255	+	4.28326i	0.0640599	+	0.363302i	−0.935880	+	0.352319i	$0.885393\pi$
$140$		0			0
$141$	−6.92075	−	6.45059i	−0.582832	−	0.543238i
$142$	6.49146	+	1.14462i	0.544751	+	0.0960543i
$143$	−3.39334	−	1.95915i	−0.283765	−	0.163832i
$144$	−2.79290	−	2.88935i	−0.232742	−	0.240779i
$145$		0			0
$146$	−6.84099	+	2.48992i	−0.566164	+	0.206067i
$147$	−7.21029	−	9.56359i	−0.594695	−	0.788791i
$148$	8.33914	+	9.93820i	0.685473	+	0.816915i
$149$	9.10358	−	7.63881i	0.745794	−	0.625796i	−0.188593	−	0.982055i	$-0.560393\pi$
$149$	9.10358	−	7.63881i	0.745794	−	0.625796i	0.934387	+	0.356260i	$0.115948\pi$
$150$		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	$0.0422072\pi$
$152$	14.4799	−	8.36000i	1.17448	−	0.678086i
$153$	13.2701	+	9.63150i	1.07282	+	0.778661i
$154$	0.181050	−	0.313587i	0.0145894	−	0.0252696i
$155$		0			0
$156$	−5.50806	+	1.68543i	−0.440998	+	0.134943i
$157$	4.40065	−	12.0907i	0.351210	−	0.964941i	−0.630772	−	0.775968i	$-0.717262\pi$
$157$	4.40065	−	12.0907i	0.351210	−	0.964941i	0.981982	−	0.188973i	$-0.0605160\pi$
$158$	−4.86928	+	0.858585i	−0.387379	+	0.0683053i
$159$	2.11321	−	3.25578i	0.167589	−	0.258200i
$160$		0			0
$161$	−1.55788			−0.122778
$162$	−0.875706	−	6.18775i	−0.0688019	−	0.486155i
$163$		−	16.1843i		−	1.26765i	−0.773476	−	0.633826i	$-0.781484\pi$
$163$		−	16.1843i		−	1.26765i	0.773476	−	0.633826i	$-0.218516\pi$
$164$	5.29631	+	4.44414i	0.413573	+	0.347029i
$165$		0			0
$166$	0.748909	+	4.24727i	0.0581266	+	0.329652i
$167$	−5.63313	+	15.4769i	−0.435904	+	1.19764i	0.506229	+	0.862399i	$0.331039\pi$
$167$	−5.63313	+	15.4769i	−0.435904	+	1.19764i	−0.942133	+	0.335238i	$0.891183\pi$
$168$	−0.360988	−	1.17972i	−0.0278508	−	0.0910175i
$169$	1.42381	−	8.07483i	0.109524	−	0.621141i
$170$		0			0
$171$	−20.4231	−	2.13662i	−1.56179	−	0.163391i
$172$	12.3290	−	7.11814i	0.940076	−	0.542753i
$173$	3.51064	+	9.64540i	0.266909	+	0.733326i	0.998660	+	0.0517539i	$0.0164811\pi$
$173$	3.51064	+	9.64540i	0.266909	+	0.733326i	−0.731751	+	0.681572i	$0.761297\pi$
$174$	−3.26929	−	1.38680i	−0.247845	−	0.105133i
$175$		0			0
$176$	1.83506	−	1.53980i	0.138323	−	0.116066i
$177$	10.8789	+	14.4296i	0.817710	+	1.08459i
$178$	2.94003	+	8.07766i	0.220365	+	0.605447i
$179$	3.40694	+	5.90100i	0.254647	+	0.441061i	0.964800	−	0.262986i	$-0.0847074\pi$
$179$	3.40694	+	5.90100i	0.254647	+	0.441061i	−0.710153	+	0.704048i	$0.751374\pi$
$180$		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	$-0.246328\pi$
$182$	−0.436896	−	0.0770365i	−0.0323849	−	0.00571033i
$183$	0.350334	−	0.375868i	0.0258974	−	0.0277850i
$184$	12.2633	+	4.46348i	0.904064	+	0.329052i
$185$		0			0
$186$	−3.40047	−	6.66983i	−0.249334	−	0.489055i
$187$	−6.28287	+	7.48764i	−0.459449	+	0.547550i
$188$		−	8.29074i		−	0.604665i
$189$	−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	$0.472945\pi$
$192$	−0.122641	+	2.35095i	−0.00885083	+	0.169665i
$193$	16.8657	−	2.97388i	1.21402	−	0.214064i	0.470270	−	0.882523i	$-0.344157\pi$
$193$	16.8657	−	2.97388i	1.21402	−	0.214064i	0.743750	+	0.668458i	$0.233045\pi$
$194$	−9.18708	−	3.34382i	−0.659594	−	0.240073i
$195$		0			0
$196$	1.82258	−	10.3364i	0.130184	−	0.738311i
$197$	−16.9353	−	9.77759i	−1.20659	−	0.696624i	−0.244576	−	0.969630i	$-0.578649\pi$
$197$	−16.9353	−	9.77759i	−1.20659	−	0.696624i	−0.962012	+	0.273006i	$0.911982\pi$
$198$	3.71614	−	0.261655i	0.264095	−	0.0185950i
$199$	−10.6782	−	18.4951i	−0.756956	−	1.31109i	−0.944396	−	0.328810i	$-0.893352\pi$
$199$	−10.6782	−	18.4951i	−0.756956	−	1.31109i	0.187440	−	0.982276i	$-0.439981\pi$
$200$		0			0
$201$	0.942767	+	7.66297i	0.0664976	+	0.540504i
$202$	−5.62848	−	6.70776i	−0.396019	−	0.471957i
$203$	0.553448	+	0.659574i	0.0388444	+	0.0462930i
$204$	1.75458	+	14.2615i	0.122845	+	0.998507i
$205$		0			0
$206$	−2.04673	−	3.54505i	−0.142603	−	0.246995i
$207$	−8.96898	−	13.2833i	−0.623387	−	0.923250i
$208$	−2.54171	−	1.46745i	−0.176236	−	0.101750i
$209$	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	$0.631391\pi$
$212$	3.34975	−	0.590651i	0.230062	−	0.0405661i
$213$	0.856558	−	16.4197i	0.0586904	−	1.12506i
$214$	3.26179	+	2.73697i	0.222972	+	0.187095i
$215$		0			0
$216$	7.98065	−	9.86984i	0.543014	−	0.671558i
$217$			1.81515i			0.123220i
$218$	−2.23460	+	2.66310i	−0.151346	+	0.180368i
$219$	8.24801	+	16.1780i	0.557349	+	1.09321i
$220$		0			0
$221$	11.2532	+	4.09583i	0.756972	+	0.275515i
$222$	−7.00900	+	7.51986i	−0.470413	+	0.504700i
$223$	−2.62569	−	0.462980i	−0.175829	−	0.0310034i	0.0850403	−	0.996378i	$-0.472898\pi$
$223$	−2.62569	−	0.462980i	−0.175829	−	0.0310034i	−0.260869	+	0.965374i	$0.584009\pi$
$224$	0.847897	−	1.46860i	0.0566525	−	0.0981251i
$225$		0			0
$226$	0.780053	+	1.35109i	0.0518883	+	0.0898732i
$227$	−1.53263	−	4.21086i	−0.101724	−	0.279485i	0.878382	−	0.477959i	$-0.158623\pi$
$227$	−1.53263	−	4.21086i	−0.101724	−	0.279485i	−0.980106	+	0.198475i	$0.936401\pi$
$228$	−10.8331	−	14.3688i	−0.717439	−	0.951597i
$229$	−18.6698	+	15.6659i	−1.23374	+	1.03523i	−0.235751	+	0.971814i	$0.575755\pi$
$229$	−18.6698	+	15.6659i	−1.23374	+	1.03523i	−0.997987	+	0.0634155i	$0.979801\pi$
$230$		0			0
$231$	−0.831500	−	0.352715i	−0.0547087	−	0.0232069i
$232$	−2.46689	−	6.77774i	−0.161960	−	0.444980i
$233$	−4.16101	+	2.40236i	−0.272597	+	0.157384i	−0.630067	−	0.776541i	$-0.716973\pi$
$233$	−4.16101	+	2.40236i	−0.272597	+	0.157384i	0.357470	+	0.933924i	$0.383639\pi$
$234$	−1.85844	−	4.16872i	−0.121490	−	0.272517i
$235$		0			0
$236$	−2.74992	+	15.5956i	−0.179004	+	1.01518i
$237$	3.60873	+	11.7935i	0.234412	+	0.766069i
$238$	−0.378506	+	1.03994i	−0.0245349	+	0.0674090i
$239$	2.87553	+	16.3079i	0.186003	+	1.05487i	0.924661	+	0.380792i	$0.124349\pi$
$239$	2.87553	+	16.3079i	0.186003	+	1.05487i	−0.738658	+	0.674080i	$0.764540\pi$
$240$		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	$0.365600\pi$
$242$		−	5.41744i		−	0.348246i
$243$	−15.0524	+	4.05270i	−0.965614	+	0.259981i
$244$	0.450273			0.0288258
$245$		0			0
$246$	−2.98262	+	4.59526i	−0.190165	+	0.292983i
$247$	−14.7694	+	2.60425i	−0.939756	+	0.165704i
$248$	5.20061	−	14.2885i	0.330239	−	0.907324i
$249$	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	$-0.0936875\pi$
$252$	−1.21274	+	0.540645i	−0.0763952	+	0.0340574i
$253$	8.27427	−	4.77715i	0.520199	−	0.300337i
$254$	−2.61701	+	0.952512i	−0.164206	+	0.0597659i
$255$		0			0
$256$	−7.76722	+	6.51747i	−0.485451	+	0.407342i
$257$	17.9314	+	21.3698i	1.11853	+	1.33301i	0.936880	+	0.349650i	$0.113700\pi$
$257$	17.9314	+	21.3698i	1.11853	+	1.33301i	0.181651	+	0.983363i	$0.441856\pi$
$258$	6.79093	+	9.00736i	0.422785	+	0.560774i
$259$	2.34205	−	0.852437i	0.145528	−	0.0529679i
$260$		0			0
$261$	−2.43757	+	8.51627i	−0.150882	+	0.527144i
$262$	8.59808	+	4.96410i	0.531191	+	0.306683i
$263$	−15.1806	−	2.67674i	−0.936073	−	0.165055i	−0.315253	−	0.949008i	$-0.602089\pi$
$263$	−15.1806	−	2.67674i	−0.936073	−	0.165055i	−0.620820	+	0.783953i	$0.713200\pi$
$264$	5.53486	+	5.15885i	0.340647	+	0.317505i
$265$		0			0
$266$	−0.240665	−	1.36488i	−0.0147561	−	0.0836861i
$267$	19.1026	−	9.73904i	1.16906	−	0.596020i
$268$	−4.34903	+	5.18297i	−0.265659	+	0.316600i
$269$	−16.5120			−1.00675			−0.503377	−	0.864067i	$-0.667909\pi$
$269$	−16.5120			−1.00675			−0.503377	+	0.864067i	$0.667909\pi$
$270$		0			0
$271$	−2.72926			−0.165791			−0.0828953	−	0.996558i	$-0.526417\pi$
$271$	−2.72926			−0.165791			−0.0828953	+	0.996558i	$0.526417\pi$
$272$	−4.70605	+	5.60845i	−0.285346	+	0.340062i
$273$	−0.0576491	+	1.10510i	−0.00348908	+	0.0668836i
$274$	0.180156	+	1.02171i	0.0108836	+	0.0617239i
$275$		0			0
$276$	3.15625	−	13.6863i	0.189984	−	0.823816i
$277$	−9.44181	−	1.66485i	−0.567304	−	0.100031i	−0.117362	−	0.993089i	$-0.537444\pi$
$277$	−9.44181	−	1.66485i	−0.567304	−	0.100031i	−0.449941	+	0.893058i	$0.648555\pi$
$278$	−2.61547	−	1.51004i	−0.156866	−	0.0905664i
$279$	−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	$0.419470\pi$
$282$	6.52022	−	0.802175i	0.388274	−	0.0477688i
$283$	−16.2692	−	19.3889i	−0.967103	−	1.15255i	−0.988261	−	0.152772i	$-0.951180\pi$
$283$	−16.2692	−	19.3889i	−0.967103	−	1.15255i	0.0211585	−	0.999776i	$-0.493265\pi$
$284$	11.0376	−	9.26164i	0.654960	−	0.549577i
$285$		0			0
$286$	2.55669	−	0.930560i	0.151180	−	0.0550252i
$287$	1.15029	−	0.664120i	0.0678995	−	0.0392018i
$288$	17.4036	−	1.22539i	1.02551	−	0.0722070i
$289$	6.43668	−	11.1487i	0.378628	−	0.655803i
$290$		0			0
$291$	−5.48013	+	23.7632i	−0.321251	+	1.39302i
$292$	−5.44270	+	14.9537i	−0.318510	+	0.875098i
$293$	−23.5312	+	4.14918i	−1.37471	+	0.242398i	−0.811710	−	0.584061i	$-0.801463\pi$
$293$	−23.5312	+	4.14918i	−1.37471	+	0.242398i	−0.562997	+	0.826459i	$0.690352\pi$
$294$	8.30533	+	0.433260i	0.484377	+	0.0252682i
$295$		0			0
$296$	−20.8785			−1.21354
$297$	−1.77967	−	9.12045i	−0.103267	−	0.529222i
$298$			8.25191i			0.478020i
$299$	−8.96710	−	7.52429i	−0.518581	−	0.435141i
$300$		0			0
$301$	−0.474923	−	2.69342i	−0.0273741	−	0.155246i
$302$	−5.17262	+	14.2117i	−0.297651	+	0.817789i
$303$	−14.8922	+	15.9777i	−0.855536	+	0.917892i
$304$	1.59214	−	9.02947i	0.0913155	−	0.517876i
$305$		0			0
$306$	−11.0462	+	2.75976i	−0.631467	+	0.157765i
$307$	13.9236	−	8.03880i	0.794662	−	0.458799i	−0.0469390	−	0.998898i	$-0.514947\pi$
$307$	13.9236	−	8.03880i	0.794662	−	0.458799i	0.841601	+	0.540099i	$0.181613\pi$
$308$	−0.270713	−	0.743777i	−0.0154253	−	0.0423806i
$309$	−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	$0.441156\pi$
$312$	3.62003	−	8.53397i	0.204944	−	0.483141i
$313$	−4.58433	−	12.5953i	−0.259122	−	0.711931i	−0.999222	−	0.0394347i	$-0.987444\pi$
$313$	−4.58433	−	12.5953i	−0.259122	−	0.711931i	0.740100	−	0.672496i	$-0.234778\pi$
$314$	4.46716	+	7.73734i	0.252096	+	0.436643i
$315$		0			0
$316$	−5.40397	+	9.35994i	−0.303997	+	0.526538i
$317$	−21.0961	−	3.71981i	−1.18487	−	0.208925i	−0.453724	−	0.891142i	$-0.649905\pi$
$317$	−21.0961	−	3.71981i	−1.18487	−	0.208925i	−0.731150	+	0.682217i	$0.761016\pi$
$318$	0.788622	+	2.57725i	0.0442237	+	0.144525i
$319$	−4.96205	−	1.80604i	−0.277822	−	0.101119i
$320$		0			0
$321$	5.78249	−	8.90894i	0.322747	−	0.497249i
$322$	0.695339	−	0.828672i	0.0387497	−	0.0461801i
$323$			37.4116i			2.08164i
$324$	−11.5918	−	7.22783i	−0.643987	−	0.401546i
$325$		0			0
$326$	8.60882	+	7.22366i	0.476799	+	0.400082i
$327$	7.27372	+	4.72112i	0.402238	+	0.261079i
$328$	−10.9577	+	1.93213i	−0.605035	+	0.106684i
$329$	−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	$0.984576\pi$
$332$	8.16430	+	4.71366i	0.448074	+	0.258696i
$333$	20.7520	+	15.0619i	1.13720	+	0.825388i
$334$	−5.71826	−	9.90432i	−0.312889	−	0.541940i
$335$		0			0
$336$	−0.622817	−	0.264193i	−0.0339774	−	0.0144129i
$337$	−13.2901	−	15.8385i	−0.723957	−	0.862779i	0.271052	−	0.962565i	$-0.412629\pi$
$337$	−13.2901	−	15.8385i	−0.723957	−	0.862779i	−0.995009	+	0.0997862i	$0.968184\pi$
$338$	3.65970	+	4.36146i	0.199061	+	0.237232i
$339$	3.10734	−	2.34272i	0.168767	−	0.127239i
$340$		0			0
$341$	−5.56608	−	9.64072i	−0.301420	−	0.522075i
$342$	10.2521	−	9.90990i	0.554371	−	0.535866i
$343$	−3.51395	−	2.02878i	−0.189735	−	0.109544i
$344$	−3.97844	+	22.5629i	−0.214503	+	1.21651i
$345$		0			0
$346$	−6.69755	−	2.43771i	−0.360063	−	0.131052i
$347$	−9.03912	+	1.59384i	−0.485245	+	0.0855619i	−0.410919	−	0.911672i	$-0.634792\pi$
$347$	−9.03912	+	1.59384i	−0.485245	+	0.0855619i	−0.0743269	+	0.997234i	$0.523681\pi$
$348$	−6.91577	+	3.52586i	−0.370724	+	0.189006i
$349$	15.5771	+	13.0707i	0.833823	+	0.699661i	0.956165	−	0.292827i	$-0.0945960\pi$
$349$	15.5771	+	13.0707i	0.833823	+	0.699661i	−0.122342	+	0.992488i	$0.539040\pi$
$350$		0			0
$351$	−9.75454	+	5.87071i	−0.520659	+	0.313355i
$352$			10.4002i			0.554330i
$353$	−3.67772	+	4.38294i	−0.195745	+	0.233280i	−0.854985	−	0.518653i	$-0.826434\pi$
$353$	−3.67772	+	4.38294i	−0.195745	+	0.233280i	0.659240	+	0.751933i	$0.270878\pi$
$354$	−12.5311	−	0.653705i	−0.666022	−	0.0347440i
$355$		0			0
$356$	17.6569	+	6.42660i	0.935816	+	0.340609i
$357$	2.68988	+	0.620326i	0.142364	+	0.0328312i
$358$	−4.65953	−	0.821602i	−0.246264	−	0.0434230i
$359$	−16.2331	+	28.1165i	−0.856749	+	1.48393i	0.0182634	+	0.999833i	$0.494186\pi$
$359$	−16.2331	+	28.1165i	−0.856749	+	1.48393i	−0.875013	+	0.484100i	$0.839147\pi$
$360$		0			0
$361$	−13.9260	−	24.1206i	−0.732949	−	1.26950i
$362$	6.15301	+	16.9053i	0.323395	+	0.888520i
$363$	−13.4121	+	1.65007i	−0.703952	+	0.0866064i
$364$	−0.742865	+	0.623338i	−0.0389367	+	0.0326718i
$365$		0			0
$366$	0.0435664	+	0.354116i	0.00227725	+	0.0185099i
$367$	1.43192	+	3.93416i	0.0747454	+	0.205361i	0.971439	−	0.237291i	$-0.0762596\pi$
$367$	1.43192	+	3.93416i	0.0747454	+	0.205361i	−0.896693	+	0.442653i	$0.854037\pi$
$368$	6.19766	−	3.57822i	0.323075	−	0.186528i
$369$	12.2851	+	5.98451i	0.639535	+	0.311541i
$370$		0			0
$371$	0.113472	−	0.643530i	0.00589116	−	0.0334104i
$372$	−15.9465	−	3.67749i	−0.826786	−	0.190669i
$373$	2.36288	−	6.49195i	0.122345	−	0.336140i	−0.863368	−	0.504575i	$-0.831649\pi$
$373$	2.36288	−	6.49195i	0.122345	−	0.336140i	0.985713	+	0.168435i	$0.0538713\pi$
$374$	−1.17858	−	6.68403i	−0.0609427	−	0.345623i
$375$		0			0
$376$	10.2210	+	8.57645i	0.527108	+	0.442296i
$377$			6.46956i			0.333199i
$378$	−0.542527	−	0.901442i	−0.0279046	−	0.0463652i
$379$	9.83488			0.505184			0.252592	−	0.967573i	$-0.418717\pi$
$379$	9.83488			0.505184			0.252592	+	0.967573i	$0.418717\pi$
$380$		0			0
$381$	3.15526	+	6.18886i	0.161649	+	0.317065i
$382$	−13.3349	+	2.35131i	−0.682275	+	0.120304i
$383$	10.2524	−	28.1682i	0.523873	−	1.43933i	−0.342303	−	0.939590i	$-0.611207\pi$
$383$	10.2524	−	28.1682i	0.523873	−	1.43933i	0.866176	−	0.499739i	$-0.166571\pi$
$384$	13.5411	+	12.6212i	0.691017	+	0.644073i
$385$		0			0
$386$	−5.94592	+	10.2986i	−0.302639	+	0.524187i
$387$	20.2313	−	19.5560i	1.02842	−	0.994087i
$388$	−18.5077	+	10.6854i	−0.939585	+	0.542469i
$389$	−11.2255	+	4.08576i	−0.569158	+	0.207157i	−0.610538	−	0.791987i	$-0.709047\pi$
$389$	−11.2255	+	4.08576i	−0.569158	+	0.207157i	0.0413802	+	0.999143i	$0.486825\pi$
$390$		0			0
$391$	−22.3690	+	18.7698i	−1.13125	+	0.949230i
$392$	10.8575	+	12.9395i	0.548387	+	0.653542i
$393$	9.67090	−	22.7985i	0.487832	−	1.15003i
$394$	12.7598	−	4.64419i	0.642829	−	0.233971i
$395$		0			0
$396$	4.78329	−	6.59030i	0.240369	−	0.331175i
$397$	−10.3278	−	5.96277i	−0.518338	−	0.299263i	0.217916	−	0.975967i	$-0.430074\pi$
$397$	−10.3278	−	5.96277i	−0.518338	−	0.299263i	−0.736255	+	0.676705i	$0.763407\pi$
$398$	14.6041	+	2.57510i	0.732037	+	0.129078i
$399$	−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	$-0.392377\pi$
$402$	−4.49692	−	2.91879i	−0.224286	−	0.145576i
$403$	−8.76689	+	10.4480i	−0.436710	+	0.520451i
$404$	−19.1405			−0.952275
$405$		0			0
$406$	−0.597868			−0.0296717
$407$	−9.82527	+	11.7093i	−0.487021	+	0.580409i
$408$	−19.3970	−	12.5899i	−0.960293	−	0.623293i
$409$	1.99270	+	11.3012i	0.0985326	+	0.558806i	0.993607	+	0.112890i	$0.0360109\pi$
$409$	1.99270	+	11.3012i	0.0985326	+	0.558806i	−0.895075	+	0.445916i	$0.852878\pi$
$410$		0			0
$411$	2.47461	−	0.757215i	0.122063	−	0.0373506i
$412$	−8.81196	−	1.55379i	−0.434134	−	0.0765495i
$413$	2.63473	+	1.52116i	0.129647	+	0.0748516i
$414$	11.0689	+	1.15800i	0.544006	+	0.0569126i
$415$		0			0
$416$	11.9736	−	4.35803i	0.587054	−	0.213670i
$417$	−2.94182	+	6.93512i	−0.144061	+	0.339615i
$418$	5.46357	+	6.51123i	0.267232	+	0.318475i
$419$	−23.7050	+	19.8908i	−1.15806	+	0.971731i	−0.999877	−	0.0156785i	$-0.995009\pi$
$419$	−23.7050	+	19.8908i	−1.15806	+	0.971731i	−0.158187	+	0.987409i	$0.550565\pi$
$420$		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	$0.462947\pi$
$422$	1.11228	−	0.642176i	0.0541450	−	0.0312606i
$423$	−3.97193	−	15.8979i	−0.193122	−	0.772984i
$424$	−2.73701	+	4.74065i	−0.132921	+	0.230226i
$425$		0			0
$426$	8.35172	+	7.78435i	0.404642	+	0.377153i
$427$	0.0295859	−	0.0812866i	0.00143176	−	0.00393373i
$428$	9.16607	−	1.61623i	0.443059	−	0.0781232i
$429$	−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	$0.520919\pi$
$432$	−1.33302	−	6.83147i	−0.0641351	−	0.328679i
$433$		−	18.8159i		−	0.904237i	−0.891958	−	0.452118i	$-0.850668\pi$
$433$		−	18.8159i		−	0.904237i	0.891958	−	0.452118i	$-0.149332\pi$
$434$	−0.965523	−	0.810170i	−0.0463466	−	0.0388894i
$435$		0			0
$436$	1.31957	+	7.48366i	0.0631960	+	0.358402i
$437$	12.5074	−	34.3637i	0.598309	−	1.64384i
$438$	−12.2869	−	2.83354i	−0.587090	−	0.135392i
$439$	2.47536	−	14.0385i	0.118143	−	0.670020i	−0.867004	−	0.498302i	$-0.833957\pi$
$439$	2.47536	−	14.0385i	0.118143	−	0.670020i	0.985146	−	0.171718i	$-0.0549318\pi$
$440$		0			0
$441$	−1.45705	−	20.6937i	−0.0693834	−	0.985413i
$442$	−7.20140	+	4.15773i	−0.342535	+	0.197763i
$443$	1.45129	+	3.98739i	0.0689529	+	0.189447i	0.969383	−	0.245555i	$-0.0789701\pi$
$443$	1.45129	+	3.98739i	0.0689529	+	0.189447i	−0.900430	+	0.435001i	$0.856748\pi$
$444$	2.74384	+	22.3024i	0.130217	+	1.05843i
$445$		0			0
$446$	1.41821	−	1.19002i	0.0671544	−	0.0563492i
$447$	20.4295	−	2.51341i	0.966280	−	0.118880i
$448$	0.135552	+	0.372427i	0.00640425	+	0.0175955i
$449$	−0.549598	−	0.951931i	−0.0259371	−	0.0449244i	0.852765	−	0.522294i	$-0.174924\pi$
$449$	−0.549598	−	0.951931i	−0.0259371	−	0.0449244i	−0.878703	+	0.477370i	$0.841590\pi$
$450$		0			0
$451$	−4.07299	+	7.05462i	−0.191789	+	0.332189i
$452$	3.35842	+	0.592180i	0.157967	+	0.0278538i
$453$	36.7596	+	8.47732i	1.72712	+	0.398299i
$454$	2.92393	+	1.06422i	0.137227	+	0.0499465i
$455$		0			0
$456$	28.9206	+	1.50868i	1.35433	+	0.0706506i
$457$	−2.26991	+	2.70517i	−0.106182	+	0.126542i	−0.816518	−	0.577320i	$-0.804098\pi$
$457$	−2.26991	+	2.70517i	−0.106182	+	0.126542i	0.710336	+	0.703863i	$0.248543\pi$
$458$		−	16.9232i		−	0.790770i
$459$	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	$0.888921\pi$
$462$	0.558748	−	0.284866i	0.0259953	−	0.0132531i
$463$	−23.0472	+	4.06385i	−1.07110	+	0.188863i	−0.681275	−	0.732027i	$-0.738574\pi$
$463$	−23.0472	+	4.06385i	−1.07110	+	0.188863i	−0.389821	+	0.920891i	$0.627463\pi$
$464$	−3.71672	−	1.35277i	−0.172544	−	0.0628009i
$465$		0			0
$466$	0.579341	−	3.28561i	0.0268374	−	0.152203i
$467$	25.7292	+	14.8548i	1.19060	+	0.687396i	0.958444	−	0.285281i	$-0.0920871\pi$
$467$	25.7292	+	14.8548i	1.19060	+	0.687396i	0.232161	+	0.972677i	$0.425420\pi$
$468$	−9.59172	−	2.74539i	−0.443377	−	0.126905i
$469$	0.649907	+	1.12567i	0.0300099	+	0.0519787i
$470$		0			0
$471$	17.7949	−	13.4161i	0.819945	−	0.618183i
$472$	−16.3819	−	19.5231i	−0.754036	−	0.898625i
$473$	10.7817	+	12.8491i	0.495743	+	0.590804i
$474$	−7.88395	−	3.34430i	−0.362122	−	0.153609i
$475$		0			0
$476$	1.20954	+	2.09498i	0.0554392	+	0.0960235i
$477$	6.14035	−	2.73740i	0.281147	−	0.125337i
$478$	−9.95805	−	5.74928i	−0.455471	−	0.262966i
$479$	1.87413	−	10.6287i	0.0856313	−	0.485639i	−0.911587	−	0.411107i	$-0.865142\pi$
$479$	1.87413	−	10.6287i	0.0856313	−	0.485639i	0.997219	−	0.0745327i	$-0.0237465\pi$
$480$		0			0
$481$	17.5979	+	6.40513i	0.802397	+	0.292049i
$482$	−19.1141	+	3.37033i	−0.870622	+	0.153514i
$483$	−2.26335	−	1.46907i	−0.102986	−	0.0668448i
$484$	−9.07147	−	7.61187i	−0.412340	−	0.345994i
$485$		0			0
$486$	4.56273	−	9.81563i	0.206970	−	0.445246i
$487$		−	27.9786i		−	1.26783i	−0.773402	−	0.633916i	$-0.781446\pi$
$487$		−	27.9786i		−	1.26783i	0.773402	−	0.633916i	$-0.218554\pi$
$488$	−0.465790	+	0.555107i	−0.0210853	+	0.0251285i
$489$	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	$0.344677\pi$
$492$	3.50395	+	11.4510i	0.157970	+	0.516253i
$493$	15.8935	+	2.80246i	0.715808	+	0.126216i
$494$	5.20689	−	9.01860i	0.234269	−	0.405766i
$495$		0			0
$496$	−4.16914	−	7.22117i	−0.187200	−	0.324240i
$497$	−0.946736	−	2.60113i	−0.0424669	−	0.116677i
$498$	−2.91710	+	6.87686i	−0.130718	+	0.308159i
$499$	12.0317	−	10.0958i	0.538615	−	0.451952i	−0.332449	−	0.943121i	$-0.607875\pi$
$499$	12.0317	−	10.0958i	0.538615	−	0.451952i	0.871064	+	0.491170i	$0.163430\pi$
$500$		0			0
$501$	−22.7787	+	17.1736i	−1.01768	+	0.767258i
$502$	5.49132	+	15.0873i	0.245090	+	0.673378i
$503$	−16.5282	+	9.54257i	−0.736957	+	0.425482i	−0.820962	−	0.570983i	$-0.806562\pi$
$503$	−16.5282	+	9.54257i	−0.736957	+	0.425482i	0.0840050	+	0.996465i	$0.473229\pi$
$504$	0.588009	−	2.05436i	0.0261920	−	0.0915086i
$505$		0			0
$506$	−1.15203	+	6.53351i	−0.0512142	+	0.290450i
$507$	9.68309	−	10.3888i	0.430041	−	0.461385i
$508$	−2.08209	+	5.72050i	−0.0923779	+	0.253806i
$509$	−2.39075	−	13.5586i	−0.105968	−	0.600974i	−0.990829	−	0.135120i	$-0.956858\pi$
$509$	−2.39075	−	13.5586i	−0.105968	−	0.600974i	0.884861	−	0.465854i	$-0.154253\pi$
$510$		0			0
$511$	2.34193	+	1.96511i	0.103601	+	0.0869313i
$512$			14.3341i			0.633483i
$513$	−27.6568	−	22.3630i	−1.22108	−	0.987352i
$514$	−19.3706			−0.854401
$515$		0			0
$516$	24.6245	+	1.28457i	1.08403	+	0.0565501i
$517$	9.61985	−	1.69624i	0.423080	−	0.0746005i
$518$	−0.591914	+	1.62627i	−0.0260072	+	0.0714542i
$519$	−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	$0.277728\pi$
$522$	−3.44204	−	5.09774i	−0.150654	−	0.223122i
$523$	12.5985	−	7.27374i	0.550893	−	0.318058i	−0.198589	−	0.980083i	$-0.563636\pi$
$523$	12.5985	−	7.27374i	0.550893	−	0.318058i	0.749482	+	0.662025i	$0.230303\pi$
$524$	20.3932	−	7.42253i	0.890883	−	0.324255i
$525$		0			0
$526$	8.19948	−	6.88018i	0.357514	−	0.299990i
$527$	21.8695	+	26.0631i	0.952652	+	1.13533i
$528$	4.11807	−	0.506642i	0.179216	−	0.0220488i
$529$	5.20877	−	1.89584i	0.226468	−	0.0824276i
$530$		0			0
$531$	2.19841	+	31.2227i	0.0954028	+	1.35495i
$532$	−2.62363	−	1.51476i	−0.113749	−	0.0656730i
$533$	9.82864	+	1.73305i	0.425726	+	0.0750669i
$534$	−3.34577	+	14.5080i	−0.144786	+	0.627824i
$535$		0			0
$536$	−1.89078	−	10.7231i	−0.0816693	−	0.463169i
$537$	−0.614833	+	11.7860i	−0.0265320	+	0.508602i
$538$	7.36993	−	8.78314i	0.317740	−	0.378668i
$539$	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	$0.507042\pi$
$542$	1.21817	−	1.45176i	0.0523249	−	0.0623584i
$543$	39.9786	−	20.3823i	1.71565	−	0.874686i
$544$	−5.51954	−	31.3029i	−0.236648	−	1.34210i
$545$		0			0
$546$	−0.562098	−	0.523912i	−0.0240556	−	0.0224214i
$547$	−26.8931	−	4.74198i	−1.14987	−	0.202753i	−0.433949	−	0.900937i	$-0.642880\pi$
$547$	−26.8931	−	4.74198i	−1.14987	−	0.202753i	−0.715918	+	0.698185i	$0.753991\pi$
$548$	1.96398	+	1.13391i	0.0838972	+	0.0484381i
$549$	0.863423	−	0.215717i	0.0368500	−	0.00920658i
$550$		0			0
$551$	−18.9923	+	6.91262i	−0.809098	+	0.294488i
$552$	13.6077	+	18.0490i	0.579182	+	0.768216i
$553$	1.33465	+	1.59057i	0.0567550	+	0.0676380i
$554$	5.09981	−	4.27925i	0.216670	−	0.181808i
$555$		0			0
$556$	−6.20347	+	2.25788i	−0.263086	+	0.0957554i
$557$	12.4162	−	7.16847i	0.526090	−	0.303738i	−0.213333	−	0.976980i	$-0.568432\pi$
$557$	12.4162	−	7.16847i	0.526090	−	0.303738i	0.739423	+	0.673242i	$0.235099\pi$
$558$	1.34924	−	12.8969i	0.0571178	−	0.545967i
$559$	10.2752	−	17.7971i	0.434593	−	0.752737i
$560$		0			0
$561$	−16.1888	+	4.95369i	−0.683494	+	0.209145i
$562$	0.763766	−	2.09843i	0.0322175	−	0.0885170i
$563$	−28.6011	+	5.04314i	−1.20539	+	0.212543i	−0.740028	−	0.672576i	$-0.765188\pi$
$563$	−28.6011	+	5.04314i	−1.20539	+	0.212543i	−0.465364	+	0.885119i	$0.654077\pi$
$564$	7.81811	−	12.0452i	0.329202	−	0.507194i
$565$		0			0
$566$	17.5750			0.738731
$567$	−2.06648	+	1.61771i	−0.0867838	+	0.0679376i
$568$			23.1882i			0.972954i
$569$	2.83162	+	2.37601i	0.118708	+	0.0996077i	0.700209	−	0.713938i	$-0.253090\pi$
$569$	2.83162	+	2.37601i	0.118708	+	0.0996077i	−0.581501	+	0.813545i	$0.697535\pi$
$570$		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	$0.908810\pi$
$572$	2.03411	−	5.58867i	0.0850504	−	0.233674i
$573$	9.88283	+	32.2975i	0.412861	+	1.34925i
$574$	−0.160156	+	0.908289i	−0.00668478	+	0.0379113i
$575$		0			0
$576$	−2.39511	+	3.29992i	−0.0997961	+	0.137497i
$577$	−18.5862	+	10.7308i	−0.773754	+	0.446727i	−0.834212	−	0.551443i	$-0.814077\pi$
$577$	−18.5862	+	10.7308i	−0.773754	+	0.446727i	0.0604579	+	0.998171i	$0.480744\pi$
$578$	3.05731	+	8.39989i	0.127167	+	0.349389i
$579$	27.3076	+	11.5836i	1.13487	+	0.481400i
$580$		0			0
$581$	1.38739	−	1.16416i	0.0575587	−	0.0482975i
$582$	−10.1942	−	13.5214i	−0.422564	−	0.560481i
$583$	1.37068	+	3.76591i	0.0567677	+	0.155968i
$584$	−12.8050	−	22.1789i	−0.529874	−	0.917768i
$585$		0			0
$586$	8.29581	−	14.3688i	0.342697	−	0.593568i
$587$	5.99490	+	1.05706i	0.247436	+	0.0436297i	0.295991	−	0.955191i	$-0.404350\pi$
$587$	5.99490	+	1.05706i	0.247436	+	0.0436297i	−0.0485544	+	0.998821i	$0.515461\pi$
$588$	12.3950	−	13.2985i	0.511163	−	0.548420i
$589$	−40.0387	−	14.5729i	−1.64977	−	0.600466i
$590$		0			0
$591$	−15.3842	−	30.1752i	−0.632820	−	1.24124i
$592$	−7.35940	+	8.77059i	−0.302470	+	0.360469i
$593$			0.198543i			0.00815319i	0.999992	+	0.00407660i	$0.00129762\pi$
$593$			0.198543i			0.00815319i	−0.999992	+	0.00407660i	$0.998702\pi$
$594$	5.64573	+	3.12415i	0.231647	+	0.128185i
$595$		0			0
$596$	13.8178	+	11.5945i	0.565998	+	0.474929i
$597$	1.92703	−	36.9401i	0.0788682	−	1.51186i
$598$	8.00471	−	1.41145i	0.327337	−	0.0577183i
$599$	−8.02599	−	2.92122i	−0.327933	−	0.119358i	0.172807	−	0.984956i	$-0.444716\pi$
$599$	−8.02599	−	2.92122i	−0.327933	−	0.119358i	−0.500740	+	0.865598i	$0.666939\pi$
$600$		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	$-0.0320275\pi$
$602$	1.64468	+	0.949554i	0.0670319	+	0.0387009i
$603$	−5.85643	+	12.0221i	−0.238492	+	0.489580i
$604$	16.5294	+	28.6298i	0.672574	+	1.16493i
$605$		0			0
$606$	−1.85195	−	15.0530i	−0.0752303	−	0.611485i
$607$	0.805951	+	0.960494i	0.0327125	+	0.0389853i	0.782153	−	0.623087i	$-0.214122\pi$
$607$	0.805951	+	0.960494i	0.0327125	+	0.0389853i	−0.749440	+	0.662072i	$0.769677\pi$
$608$	25.5872	+	30.4936i	1.03770	+	1.23668i
$609$	0.182102	+	1.48016i	0.00737915	+	0.0599790i
$610$		0			0
$611$	−5.98392	−	10.3645i	−0.242083	−	0.419301i
$612$	−10.8994	+	22.3744i	−0.440582	+	0.904431i
$613$	12.7968	+	7.38826i	0.516860	+	0.298409i	0.735649	−	0.677363i	$-0.236877\pi$
$613$	12.7968	+	7.38826i	0.516860	+	0.298409i	−0.218789	+	0.975772i	$0.570211\pi$
$614$	−1.93860	+	10.9943i	−0.0782354	+	0.443695i
$615$		0			0
$616$	1.19699	+	0.435667i	0.0482280	+	0.0175535i
$617$	2.09563	−	0.369516i	0.0843669	−	0.0148762i	−0.131305	−	0.991342i	$-0.541917\pi$
$617$	2.09563	−	0.369516i	0.0843669	−	0.0148762i	0.215672	+	0.976466i	$0.430806\pi$
$618$	0.369363	−	7.08047i	0.0148580	−	0.284818i
$619$	13.5591	+	11.3775i	0.544987	+	0.457298i	0.873239	−	0.487292i	$-0.162015\pi$
$619$	13.5591	+	11.3775i	0.544987	+	0.457298i	−0.328252	+	0.944590i	$0.606460\pi$
$620$		0			0
$621$	−0.504531	−	27.7562i	−0.0202461	−	1.11382i
$622$		−	12.0257i		−	0.482188i
$623$	2.32035	−	2.76529i	0.0929629	−	0.110789i
$624$	−2.30891	−	4.52880i	−0.0924304	−	0.181297i
$625$		0			0
$626$	8.74593	+	3.18326i	0.349558	+	0.127229i
$627$	14.4559	−	15.5095i	0.577313	−	0.619391i
$628$	19.2328	+	3.39126i	0.767471	+	0.135326i
$629$	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	$0.910634\pi$
$632$	−5.94895	−	16.3446i	−0.236637	−	0.650154i
$633$	−1.92864	−	2.55810i	−0.0766564	−	0.101676i
$634$	11.3946	−	9.56124i	0.452539	−	0.379725i
$635$		0			0
$636$	5.42365	+	2.30066i	0.215062	+	0.0912272i
$637$	−5.18191	−	14.2372i	−0.205315	−	0.564098i
$638$	3.17543	−	1.83333i	0.125716	−	0.0725824i
$639$	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	$-0.0346137\pi$
$642$	2.15794	+	7.05224i	0.0851672	+	0.278330i
$643$	8.06852	−	22.1681i	0.318191	−	0.874223i	−0.672743	−	0.739876i	$-0.734884\pi$
$643$	8.06852	−	22.1681i	0.318191	−	0.874223i	0.990934	−	0.134347i	$-0.0428937\pi$
$644$	−0.410609	−	2.32868i	−0.0161803	−	0.0917629i
$645$		0			0
$646$	−19.9001	−	16.6982i	−0.782961	−	0.656982i
$647$		−	0.0994615i		−	0.00391023i	−0.999998	−	0.00195512i	$-0.999378\pi$
$647$		−	0.0994615i		−	0.00391023i	0.999998	−	0.00195512i	$-0.000622333\pi$
$648$	20.9019	−	6.81368i	0.821102	−	0.267666i
$649$	−18.6583			−0.732403
$650$		0			0
$651$	−1.71167	+	2.63714i	−0.0670858	+	0.103358i
$652$	24.1920	−	4.26569i	0.947430	−	0.167057i
$653$	5.61686	−	15.4322i	0.219805	−	0.603909i	−0.779955	−	0.625836i	$-0.784758\pi$
$653$	5.61686	−	15.4322i	0.219805	−	0.603909i	0.999760	+	0.0219271i	$0.00698017\pi$
$654$	−5.75782	+	1.76186i	−0.225148	+	0.0688940i
$655$		0			0
$656$	−3.05078	+	5.28411i	−0.119113	+	0.206310i
$657$	−3.27265	+	31.2820i	−0.127678	+	1.22043i
$658$	0.957805	−	0.552989i	0.0373391	−	0.0215578i
$659$	−35.6457	+	12.9740i	−1.38856	+	0.505394i	−0.924761	−	0.380548i	$-0.875736\pi$
$659$	−35.6457	+	12.9740i	−1.38856	+	0.505394i	−0.463797	+	0.885942i	$0.653513\pi$
$660$		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	$0.359551\pi$
$662$	−3.59159	−	4.28030i	−0.139591	−	0.166358i
$663$	12.4868	+	16.5623i	0.484948	+	0.643226i
$664$	−14.2568	+	5.18903i	−0.553269	+	0.201374i
$665$		0			0
$666$	−17.2742	+	4.31577i	−0.669361	+	0.167233i
$667$	−13.6618	−	7.88764i	−0.528987	−	0.305411i
$668$	−24.6193	−	4.34104i	−0.952548	−	0.167960i
$669$	−3.37814	−	3.14864i	−0.130606	−	0.121734i
$670$		0			0
$671$	0.0921233	+	0.522457i	0.00355638	+	0.0201692i
$672$	2.61675	−	1.33409i	0.100943	−	0.0514637i
$673$	−2.60185	+	3.10076i	−0.100294	+	0.119526i	−0.813857	−	0.581066i	$-0.802636\pi$
$673$	−2.60185	+	3.10076i	−0.100294	+	0.119526i	0.713563	+	0.700591i	$0.247080\pi$
$674$	14.3568			0.553002
$675$		0			0
$676$	12.4454			0.478668
$677$	−9.59228	+	11.4316i	−0.368661	+	0.439353i	−0.918201	−	0.396114i	$-0.870359\pi$
$677$	−9.59228	+	11.4316i	−0.368661	+	0.439353i	0.549540	+	0.835467i	$0.314803\pi$
$678$	−0.140772	+	2.69851i	−0.00540631	+	0.103636i
$679$	0.712932	+	4.04324i	0.0273598	+	0.155165i
$680$		0			0
$681$	1.74414	−	7.56299i	0.0668355	−	0.289815i
$682$	7.61249	+	1.34229i	0.291497	+	0.0513988i
$683$	20.2388	+	11.6849i	0.774417	+	0.447110i	0.834448	−	0.551086i	$-0.185787\pi$
$683$	20.2388	+	11.6849i	0.774417	+	0.447110i	−0.0600307	+	0.998197i	$0.519120\pi$
$684$	−2.18915	−	31.0912i	−0.0837041	−	1.18880i
$685$		0			0
$686$	2.64757	−	0.963635i	0.101085	−	0.0367918i
$687$	−41.8972	+	5.15457i	−1.59848	+	0.196659i
$688$	8.07579	+	9.62435i	0.307887	+	0.366925i
$689$	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	$0.465721\pi$
$692$	−13.4924	+	7.78986i	−0.512906	+	0.296126i
$693$	−0.875435	−	1.29654i	−0.0332550	−	0.0492515i
$694$	3.18670	−	5.51952i	0.120965	−	0.209518i
$695$		0			0
$696$	2.80734	−	12.1733i	0.106412	−	0.461427i
$697$	8.51506	−	23.3949i	0.322531	−	0.886146i
$698$	−13.9053	+	2.45188i	−0.526323	+	0.0928050i
$699$	−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	$0.758156\pi$
$702$	1.23105	−	7.80900i	0.0464628	−	0.294732i
$703$			58.5049i			2.20656i
$704$	−1.86198	−	1.56239i	−0.0701761	−	0.0588847i
$705$		0			0
$706$	−0.689887	−	3.91254i	−0.0259642	−	0.147251i
$707$	−1.25766	+	3.45538i	−0.0472990	+	0.129953i
$708$	−18.7017	+	20.0648i	−0.702853	+	0.754081i
$709$	1.35456	−	7.68211i	0.0508717	−	0.288508i	−0.948750	−	0.316029i	$-0.897650\pi$
$709$	1.35456	−	7.68211i	0.0508717	−	0.288508i	0.999621	+	0.0275213i	$0.00876139\pi$
$710$		0			0
$711$	−5.87823	+	20.5371i	−0.220451	+	0.770202i
$712$	−26.1883	+	15.1198i	−0.981446	+	0.566638i
$713$	−11.3745	−	31.2512i	−0.425978	−	1.17037i
$714$	−1.53056	+	1.15394i	−0.0572799	+	0.0431851i
$715$		0			0
$716$	−7.92272	+	6.64795i	−0.296086	+	0.248446i
$717$	−11.2006	+	26.4045i	−0.418293	+	0.986096i
$718$	−7.71043	−	21.1842i	−0.287751	−	0.790589i
$719$	−14.8476	−	25.7168i	−0.553722	−	0.959074i	−0.998002	−	0.0631860i	$-0.979874\pi$
$719$	−14.8476	−	25.7168i	−0.553722	−	0.959074i	0.444280	−	0.895888i	$-0.353459\pi$
$720$		0			0
$721$	−0.859504	+	1.48870i	−0.0320096	+	0.0554422i
$722$	19.0460	+	3.35833i	0.708820	+	0.124984i
$723$	14.1659	+	46.2946i	0.526834	+	1.72172i
$724$	36.9531	+	13.4498i	1.37335	+	0.499859i
$725$		0			0
$726$	5.10861	−	7.87071i	0.189598	−	0.292110i
$727$	0.495670	−	0.590717i	0.0183834	−	0.0219085i	−0.756774	−	0.653676i	$-0.773226\pi$
$727$	0.495670	−	0.590717i	0.0183834	−	0.0219085i	0.775158	+	0.631768i	$0.217670\pi$
$728$		−	1.56064i		−	0.0578411i
$729$	−25.6905	−	8.30637i	−0.951502	−	0.307643i
$730$		0			0
$731$	−39.2705	−	32.9519i	−1.45247	−	1.21877i
$732$	0.654178	+	0.424604i	0.0241791	+	0.0156938i
$733$	2.01399	−	0.355120i	0.0743882	−	0.0131167i	−0.136330	−	0.990663i	$-0.543531\pi$
$733$	2.01399	−	0.355120i	0.0743882	−	0.0131167i	0.210718	+	0.977547i	$0.432420\pi$
$734$	−2.73179	−	0.994292i	−0.100832	−	0.0367000i
$735$		0			0
$736$	−5.39525	+	30.5980i	−0.198871	+	1.12786i
$737$	−6.90364	−	3.98582i	−0.254299	−	0.146820i
$738$	−8.66660	+	3.86362i	−0.319022	+	0.142222i
$739$	−4.28264	−	7.41775i	−0.157539	−	0.272866i	0.776441	−	0.630189i	$-0.217023\pi$
$739$	−4.28264	−	7.41775i	−0.157539	−	0.272866i	−0.933981	+	0.357323i	$0.883689\pi$
$740$		0			0
$741$	−23.9135	−	10.1439i	−0.878485	−	0.372645i
$742$	0.291663	+	0.347590i	0.0107073	+	0.0127604i
$743$	21.5811	+	25.7194i	0.791734	+	0.943552i	0.999400	−	0.0346482i	$-0.0110311\pi$
$743$	21.5811	+	25.7194i	0.791734	+	0.943552i	−0.207666	+	0.978200i	$0.566587\pi$
$744$	21.0297	−	15.8549i	0.770986	−	0.581270i
$745$		0			0
$746$	2.39859	+	4.15447i	0.0878185	+	0.152106i
$747$	17.9137	+	5.12734i	0.655428	+	0.187600i
$748$	−12.8483	−	7.41800i	−0.469782	−	0.271229i
$749$	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	$0.470424\pi$
$752$	7.20553	−	1.27053i	0.262759	−	0.0463314i
$753$	35.6794	−	18.1904i	1.30023	−	0.662894i
$754$	−3.44132	−	2.88761i	−0.125325	−	0.105160i
$755$		0			0
$756$	−2.27174	−	0.358128i	−0.0826226	−	0.0130250i
$757$		−	2.94896i		−	0.107182i	−0.998563	−	0.0535909i	$-0.982933\pi$
$757$		−	2.94896i		−	0.107182i	0.998563	−	0.0535909i	$-0.0170667\pi$
$758$	−4.38968	+	5.23142i	−0.159440	+	0.190014i
$759$	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	$0.429806\pi$
$762$	−4.70032	−	1.08396i	−0.170275	−	0.0392678i
$763$	1.43771	+	0.253507i	0.0520485	+	0.00917756i
$764$	−14.7992	+	25.6330i	−0.535418	+	0.927371i
$765$		0			0
$766$	10.4073	+	18.0260i	0.376033	+	0.651307i
$767$	7.81850	+	21.4811i	0.282310	+	0.775639i
$768$	−17.4305	+	2.14445i	−0.628969	+	0.0773813i
$769$	6.11306	−	5.12946i	0.220442	−	0.184973i	−0.525878	−	0.850560i	$-0.676263\pi$
$769$	6.11306	−	5.12946i	0.220442	−	0.184973i	0.746320	+	0.665587i	$0.231819\pi$
$770$		0			0
$771$	5.90001	+	47.9563i	0.212484	+	1.72710i
$772$	8.89058	+	24.4267i	0.319979	+	0.879135i
$773$	0.325571	−	0.187968i	0.0117100	−	0.00676076i	−0.494134	−	0.869386i	$-0.664515\pi$
$773$	0.325571	−	0.187968i	0.0117100	−	0.00676076i	0.505844	+	0.862625i	$0.331181\pi$
$774$	1.37231	+	19.4901i	0.0493266	+	0.700558i
$775$		0			0
$776$	5.97225	−	33.8703i	0.214391	−	1.21587i
$777$	4.20649	+	0.970078i	0.150907	+	0.0348013i
$778$	2.83707	−	7.79478i	0.101714	−	0.279456i
$779$	5.41413	+	30.7051i	0.193981	+	1.10012i
$780$		0			0
$781$	13.0046	+	10.9122i	0.465342	+	0.390468i
$782$		−	20.2763i		−	0.725078i
$783$	−11.5722	+	10.0742i	−0.413557	+	0.360024i
$784$	9.26269			0.330810
$785$		0			0
$786$	7.81058	+	15.3200i	0.278594	+	0.546447i
$787$	−5.81822	+	1.02591i	−0.207397	+	0.0365697i	−0.276381	−	0.961048i	$-0.589135\pi$
$787$	−5.81822	+	1.02591i	−0.207397	+	0.0365697i	0.0689843	+	0.997618i	$0.478024\pi$
$788$	10.1517	−	27.8916i	0.361640	−	0.993597i
$789$	−19.5309	−	18.2041i	−0.695318	−	0.648081i
$790$		0			0
$791$	0.327575	−	0.567376i	0.0116472	−	0.0201736i
$792$	3.17654	+	12.7143i	0.112874	+	0.451785i
$793$	0.562897	−	0.324989i	0.0199891	−	0.0115407i
$794$	7.78144	−	2.83221i	0.276153	−	0.100511i
$795$		0			0
$796$	24.8317	−	20.8363i	0.880137	−	0.738522i
$797$	−33.1370	−	39.4911i	−1.17377	−	1.39885i	−0.899345	−	0.437239i	$-0.855956\pi$
$797$	−33.1370	−	39.4911i	−1.17377	−	1.39885i	−0.274427	−	0.961608i	$-0.588488\pi$
$798$	0.937422	−	2.20991i	0.0331844	−	0.0782299i
$799$	−28.0540	+	10.2108i	−0.992481	+	0.361234i
$800$		0			0
$801$	36.9370	+	3.86426i	1.30510	+	0.136537i
$802$	20.9881	+	12.1175i	0.741114	+	0.427883i
$803$	−18.4645	−	3.25579i	−0.651598	−	0.114894i
$804$	−11.2060	+	3.42896i	−0.395204	+	0.120930i
$805$		0			0
$806$	−1.64454	−	9.32665i	−0.0579264	−	0.328517i
$807$	−23.9894	−	15.5707i	−0.844468	−	0.548115i
$808$	19.8001	−	23.5968i	0.696565	−	0.830134i
$809$	37.4718			1.31744			0.658719	−	0.752389i	$-0.271099\pi$
$809$	37.4718			1.31744			0.658719	+	0.752389i	$0.271099\pi$
$810$		0			0
$811$	27.5789			0.968426			0.484213	−	0.874950i	$-0.339106\pi$
$811$	27.5789			0.968426			0.484213	+	0.874950i	$0.339106\pi$
$812$	−0.840045	+	1.00113i	−0.0294798	+	0.0351326i
$813$	−3.96520	−	2.57367i	−0.139065	−	0.0902626i
$814$	−1.84308	−	10.4526i	−0.0645998	−	0.366364i
$815$		0			0
$816$	−12.1259	+	3.71045i	−0.424491	+	0.129892i
$817$	63.2247	+	11.1482i	2.21195	+	0.390027i
$818$	−6.90078	−	3.98417i	−0.241280	−	0.139303i
$819$	−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	$0.105626\pi$
$822$	−0.701730	+	1.65428i	−0.0244756	+	0.0576996i
$823$	−16.2597	−	19.3775i	−0.566776	−	0.675458i	0.404190	−	0.914675i	$-0.367554\pi$
$823$	−16.2597	−	19.3775i	−0.566776	−	0.675458i	−0.970966	+	0.239217i	$0.923109\pi$
$824$	11.0312	−	9.25624i	0.384289	−	0.322456i
$825$		0			0
$826$	−1.98513	+	0.722527i	−0.0690714	+	0.0251399i
$827$	−16.4007	+	9.46894i	−0.570307	+	0.329267i	−0.757272	−	0.653099i	$-0.773468\pi$
$827$	−16.4007	+	9.46894i	−0.570307	+	0.329267i	0.186965	+	0.982367i	$0.440135\pi$
$828$	17.4916	−	16.9077i	0.607875	−	0.587583i
$829$	1.72605	−	2.98961i	0.0599482	−	0.103833i	−0.834494	−	0.551017i	$-0.814240\pi$
$829$	1.72605	−	2.98961i	0.0599482	−	0.103833i	0.894442	+	0.447184i	$0.147573\pi$
$830$		0			0
$831$	−12.1476	−	11.3223i	−0.421395	−	0.392767i
$832$	−1.01853	+	2.79838i	−0.0353111	+	0.0970163i
$833$	−37.2206	+	6.56300i	−1.28962	+	0.227395i
$834$	−2.37592	−	4.66023i	−0.0822714	−	0.161371i
$835$		0			0
$836$	18.5797			0.642593
$837$	−32.3400	+	0.587852i	−1.11783	+	0.0203191i
$838$		−	21.4873i		−	0.742266i
$839$	14.6910	+	12.3272i	0.507189	+	0.425582i	0.860139	−	0.510060i	$-0.170377\pi$
$839$	14.6910	+	12.3272i	0.507189	+	0.425582i	−0.352950	+	0.935642i	$0.614821\pi$
$840$		0			0
$841$	−3.52180	−	19.9731i	−0.121442	−	0.688729i
$842$	2.24705	−	6.17373i	0.0774386	−	0.212761i
$843$	−5.42777	−	1.25172i	−0.186942	−	0.0431117i
$844$	0.487510	−	2.76481i	0.0167808	−	0.0951686i
$845$		0			0
$846$	10.2293	+	4.98308i	0.351692	+	0.171322i
$847$	−1.97020	+	1.13750i	−0.0676970	+	0.0390849i
$848$	1.02668	+	2.82077i	0.0352562	+	0.0968656i
$849$	−5.35308	−	43.5108i	−0.183717	−	1.49329i
$850$		0			0
$851$	−34.9810	+	29.3526i	−1.19913	+	1.00619i
$852$	24.7696	−	3.04737i	0.848592	−	0.104401i
$853$	2.00055	+	5.49647i	0.0684975	+	0.188195i	0.969218	−	0.246203i	$-0.0791831\pi$
$853$	2.00055	+	5.49647i	0.0684975	+	0.188195i	−0.900721	+	0.434399i	$0.856961\pi$
$854$	0.0300330	+	0.0520187i	0.00102771	+	0.00178004i
$855$		0			0
$856$	−7.48942	+	12.9721i	−0.255983	+	0.443376i
$857$	−48.6607	−	8.58019i	−1.66222	−	0.293094i	−0.737954	−	0.674851i	$-0.764208\pi$
$857$	−48.6607	−	8.58019i	−1.66222	−	0.293094i	−0.924263	+	0.381757i	$0.875319\pi$
$858$	4.59200	+	1.05898i	0.156768	+	0.0361531i
$859$	7.31048	+	2.66080i	0.249430	+	0.0907852i	0.463710	−	0.885987i	$-0.346518\pi$
$859$	7.31048	+	2.66080i	0.249430	+	0.0907852i	−0.214279	+	0.976772i	$0.568740\pi$
$860$		0			0
$861$	2.29746	+	0.119850i	0.0782971	+	0.00408448i
$862$	1.21707	−	1.45045i	0.0414537	−	0.0494026i
$863$		−	11.8283i		−	0.402639i	−0.979526	−	0.201320i	$-0.935477\pi$
$863$		−	11.8283i		−	0.402639i	0.979526	−	0.201320i	$-0.0645230\pi$
$864$	26.4403	+	14.6311i	0.899516	+	0.497761i
$865$		0			0
$866$	10.0087	+	8.39827i	0.340108	+	0.285385i
$867$	19.8646	−	10.1275i	0.674637	−	0.343949i
$868$	−2.71325	+	0.478419i	−0.0920937	+	0.0162386i
$869$	−11.9661	−	4.35529i	−0.405921	−	0.147743i
$870$		0			0
$871$	−1.69597	+	9.61830i	−0.0574656	+	0.325904i
$872$	−10.5911	−	6.11475i	−0.358659	−	0.207072i
$873$	−30.3703	+	29.3565i	−1.02788	+	0.993567i
$874$	12.6964	+	21.9908i	0.429462	+	0.743850i
$875$		0			0
$876$	−22.0086	+	16.5930i	−0.743603	+	0.560625i
$877$	30.5859	+	36.4509i	1.03281	+	1.23086i	0.972554	+	0.232676i	$0.0747480\pi$
$877$	30.5859	+	36.4509i	1.03281	+	1.23086i	0.0602584	+	0.998183i	$0.480808\pi$
$878$	6.36256	+	7.58261i	0.214726	+	0.255901i
$879$	−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	$0.690694\pi$
$882$	11.6578	+	8.46133i	0.392539	+	0.284908i
$883$	−38.9336	−	22.4783i	−1.31022	−	0.756456i	−0.328088	−	0.944647i	$-0.606404\pi$
$883$	−38.9336	−	22.4783i	−1.31022	−	0.756456i	−0.982133	+	0.188191i	$0.939738\pi$
$884$	−3.15635	+	17.9006i	−0.106160	+	0.602062i
$885$		0			0
$886$	−2.76876	−	1.00774i	−0.0930182	−	0.0338558i
$887$	−14.3878	+	2.53696i	−0.483095	+	0.0851827i	−0.409891	−	0.912134i	$-0.634433\pi$
$887$	−14.3878	+	2.53696i	−0.483095	+	0.0851827i	−0.0732037	+	0.997317i	$0.523322\pi$
$888$	−30.3333	−	19.6883i	−1.01792	−	0.660697i
$889$	0.895899	+	0.751749i	0.0300475	+	0.0252128i
$890$		0			0
$891$	6.01493	−	14.9288i	0.201508	−	0.500135i
$892$		−	4.04685i		−	0.135499i
$893$	24.0325	−	28.6409i	0.804218	−	0.958430i
$894$	−7.78149	+	11.9888i	−0.260252	+	0.400964i
$895$		0			0
$896$	2.92845	+	1.06587i	0.0978325	+	0.0356081i
$897$	−5.93247	−	19.3876i	−0.198080	−	0.647332i
$898$	0.751662	+	0.132538i	0.0250833	+	0.00442286i
$899$	−9.19024	+	15.9180i	−0.306512	+	0.530894i
$900$		0			0
$901$	−6.12417	−	10.6074i	−0.204026	−	0.353383i
$902$	−1.93460	−	5.31527i	−0.0644151	−	0.176979i
$903$	1.84989	−	4.36098i	0.0615605	−	0.145124i
$904$	−4.20420	+	3.52775i	−0.139830	+	0.117331i
$905$		0			0
$906$	−20.9165	+	15.7696i	−0.694905	+	0.523910i
$907$	−11.0519	−	30.3649i	−0.366973	−	1.00825i	−0.976506	−	0.215489i	$-0.930865\pi$
$907$	−11.0519	−	30.3649i	−0.366973	−	1.00825i	0.609533	−	0.792761i	$-0.291357\pi$
$908$	5.89035	−	3.40080i	0.195478	−	0.112859i
$909$	−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	$0.998102\pi$
$912$	10.8279	−	11.6171i	0.358546	−	0.384680i
$913$	−3.79895	+	10.4375i	−0.125727	+	0.345432i
$914$	−0.425801	−	2.41484i	−0.0140842	−	0.0798757i
$915$		0			0
$916$	−28.3378	−	23.7782i	−0.936308	−	0.785655i
$917$		−	4.16924i		−	0.137681i
$918$	−18.6508	−	6.40693i	−0.615569	−	0.211460i
$919$	7.87445			0.259754			0.129877	−	0.991530i	$-0.458542\pi$
$919$	7.87445			0.259754			0.129877	+	0.991530i	$0.458542\pi$
$920$		0			0
$921$	27.8094	+	1.45072i	0.916351	+	0.0478028i
$922$	14.6850	−	2.58936i	0.483625	−	0.0852761i
$923$	7.11368	−	19.5447i	0.234150	−	0.643321i
$924$	0.308072	−	1.33587i	0.0101348	−	0.0439471i
$925$		0			0
$926$	8.12519	−	14.0732i	0.267010	−	0.462476i
$927$	−17.6418	+	1.24217i	−0.579432	+	0.0407981i
$928$	14.8713	−	8.58593i	0.488173	−	0.281847i
$929$	30.4449	−	11.0810i	0.998865	−	0.363557i	0.209718	−	0.977762i	$-0.432745\pi$
$929$	30.4449	−	11.0810i	0.998865	−	0.363557i	0.789147	+	0.614205i	$0.210523\pi$
$930$		0			0
$931$	36.2584	−	30.4244i	1.18832	−	0.997120i
$932$	−4.68771	−	5.58660i	−0.153551	−	0.182995i
$933$	−29.7724	+	3.66286i	−0.974705	+	0.119917i
$934$	−19.3855	+	7.05575i	−0.634313	+	0.230871i
$935$		0			0
$936$	13.3068	−	8.98489i	0.434947	−	0.293680i
$937$	52.8226	+	30.4971i	1.72564	+	0.996298i	0.905804	+	0.423698i	$0.139268\pi$
$937$	52.8226	+	30.4971i	1.72564	+	0.996298i	0.819835	+	0.572600i	$0.194065\pi$
$938$	−0.888851	−	0.156728i	−0.0290220	−	0.00511736i
$939$	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	$0.864115\pi$
$942$	−0.806163	+	15.4537i	−0.0262662	+	0.503508i
$943$	−15.6427	+	18.6422i	−0.509396	+	0.607075i
$944$	−13.9756			−0.454867
$945$		0			0
$946$	−11.6470			−0.378678
$947$	35.6464	−	42.4817i	1.15835	−	1.38047i	0.246910	−	0.969038i	$-0.420585\pi$
$947$	35.6464	−	42.4817i	1.15835	−	1.38047i	0.911441	−	0.411431i	$-0.134971\pi$
$948$	−16.6775	+	8.50266i	−0.541660	+	0.276154i
$949$	3.98892	+	22.6223i	0.129486	+	0.734350i
$950$		0			0
$951$	−27.1416	−	25.2978i	−0.880128	−	0.820336i
$952$	−3.83396	−	0.676031i	−0.124259	−	0.0219103i
$953$	−2.48180	−	1.43287i	−0.0803935	−	0.0464152i	0.459264	−	0.888300i	$-0.348113\pi$
$953$	−2.48180	−	1.43287i	−0.0803935	−	0.0464152i	−0.539658	+	0.841884i	$0.681446\pi$
$954$	−1.28458	+	4.48801i	−0.0415898	+	0.145305i
$955$		0			0
$956$	−23.6189	+	8.59657i	−0.763889	+	0.278033i
$957$	−5.50602	−	7.30308i	−0.177984	−	0.236075i
$958$	4.81719	+	5.74090i	0.155636	+	0.185480i
$959$	0.333747	−	0.280047i	0.0107773	−	0.00904320i
$960$		0			0
$961$	−7.28166	+	2.65031i	−0.234892	+	0.0854938i
$962$	−11.2617	+	6.50193i	−0.363091	+	0.209631i
$963$	16.8021	−	7.49048i	0.541441	−	0.241377i
$964$	−21.2130	+	36.7419i	−0.683223	+	1.18338i
$965$		0			0
$966$	1.79165	−	0.548235i	0.0576455	−	0.0176392i
$967$	−15.8090	+	43.4350i	−0.508384	+	1.39677i	0.374519	+	0.927219i	$0.377808\pi$
$967$	−15.8090	+	43.4350i	−0.508384	+	1.39677i	−0.882903	+	0.469555i	$0.844414\pi$
$968$	18.7682	−	3.30933i	0.603231	−	0.106366i
$969$	−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	$0.309043\pi$
$972$	−10.0253	−	21.4319i	−0.321561	−	0.687428i
$973$			1.26825i			0.0406583i
$974$	14.8825	+	12.4879i	0.476867	+	0.400139i
$975$		0			0
$976$	0.0690029	+	0.391335i	0.00220873	+	0.0125263i
$977$	8.82997	−	24.2601i	0.282496	−	0.776151i	−0.714567	−	0.699567i	$-0.753376\pi$
$977$	8.82997	−	24.2601i	0.282496	−	0.776151i	0.997063	−	0.0765840i	$-0.0244014\pi$
$978$	5.69544	+	18.6129i	0.182120	+	0.595176i
$979$	−3.84435	+	21.8024i	−0.122866	+	0.696808i
$980$		0			0
$981$	6.11562	+	13.7181i	0.195257	+	0.437986i
$982$	−19.7918	+	11.4268i	−0.631581	+	0.364643i
$983$	−3.64829	−	10.0236i	−0.116362	−	0.319703i	0.867815	−	0.496887i	$-0.165524\pi$
$983$	−3.64829	−	10.0236i	−0.116362	−	0.319703i	−0.984178	+	0.177184i	$0.943301\pi$
$984$	−17.7418	−	7.52590i	−0.565587	−	0.239917i
$985$		0			0
$986$	−8.58458	+	7.20331i	−0.273389	+	0.229400i
$987$	−1.66078	−	2.20283i	−0.0528633	−	0.0701168i
$988$	−7.78555	−	21.3906i	−0.247691	−	0.680527i
$989$	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	$0.774718\pi$
$992$	35.6511	+	6.28624i	1.13192	+	0.199588i
$993$	−9.50289	+	10.1955i	−0.301565	+	0.323545i
$994$	1.80617	+	0.657393i	0.0572883	+	0.0208512i
$995$		0			0
$996$	7.41653	+	14.5471i	0.235002	+	0.460943i
$997$	17.8854	−	21.3149i	0.566435	−	0.675051i	−0.404460	−	0.914556i	$-0.632541\pi$
$997$	17.8854	−	21.3149i	0.566435	−	0.675051i	0.970895	+	0.239505i	$0.0769850\pi$
$998$			10.9061i			0.345228i
$999$	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.u.c.124.4		60
5.2	odd	4		135.2.k.a.16.2	✓	30
5.3	odd	4		675.2.l.d.151.4		30
5.4	even	2	inner	675.2.u.c.124.7		60
15.2	even	4		405.2.k.a.46.4		30
27.22	even	9	inner	675.2.u.c.49.7		60
135.7	odd	36		3645.2.a.h.1.6		15
135.22	odd	36		135.2.k.a.76.2	yes	30
135.32	even	36		405.2.k.a.361.4		30
135.47	even	36		3645.2.a.g.1.10		15
135.49	even	18	inner	675.2.u.c.49.4		60
135.103	odd	36		675.2.l.d.76.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.16.2	✓	30	5.2	odd	4
135.2.k.a.76.2	yes	30	135.22	odd	36
405.2.k.a.46.4		30	15.2	even	4
405.2.k.a.361.4		30	135.32	even	36
675.2.l.d.76.4		30	135.103	odd	36
675.2.l.d.151.4		30	5.3	odd	4
675.2.u.c.49.4		60	135.49	even	18	inner
675.2.u.c.49.7		60	27.22	even	9	inner
675.2.u.c.124.4		60	1.1	even	1	trivial
675.2.u.c.124.7		60	5.4	even	2	inner
3645.2.a.g.1.10		15	135.47	even	36
3645.2.a.h.1.6		15	135.7	odd	36

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.446338 + 0.531925i) q^{2} +(1.45285 + 0.942993i) q^{3} +(0.263570 + 1.49478i) q^{4} +(-1.15006 + 0.351912i) q^{6} +(0.287167 + 0.0506352i) q^{7} +(-2.11545 - 1.22136i) q^{8} +(1.22153 + 2.74005i) q^{9} +O(q^{10})\)	\(q+(-0.446338 + 0.531925i) q^{2} +(1.45285 + 0.942993i) q^{3} +(0.263570 + 1.49478i) q^{4} +(-1.15006 + 0.351912i) q^{6} +(0.287167 + 0.0506352i) q^{7} +(-2.11545 - 1.22136i) q^{8} +(1.22153 + 2.74005i) q^{9} +(-1.68049 + 0.611647i) q^{11} +(-1.02664 + 2.42023i) q^{12} +(1.40837 + 1.67842i) q^{13} +(-0.155107 + 0.130151i) q^{14} +(-1.25873 + 0.458140i) q^{16} +(4.73339 - 2.73283i) q^{17} +(-2.00271 - 0.573226i) q^{18} +(-3.42243 + 5.92782i) q^{19} +(0.369461 + 0.344361i) q^{21} +(0.424714 - 1.16689i) q^{22} +(-5.26140 + 0.927728i) q^{23} +(-1.92170 - 3.76930i) q^{24} -1.52140 q^{26} +(-0.809152 + 5.13276i) q^{27} +0.442597i q^{28} +(2.26194 + 1.89799i) q^{29} +(1.08094 + 6.13030i) q^{31} +(1.98904 - 5.46483i) q^{32} +(-3.01827 - 0.696057i) q^{33} +(-0.659035 + 3.73757i) q^{34} +(-3.77381 + 2.54811i) q^{36} +(7.40217 - 4.27364i) q^{37} +(-1.62559 - 4.46628i) q^{38} +(0.463397 + 3.76657i) q^{39} +(3.48938 - 2.92794i) q^{41} +(-0.348078 + 0.0428237i) q^{42} +(-3.20791 - 8.81367i) q^{43} +(-1.35720 - 2.35074i) q^{44} +(1.85488 - 3.21275i) q^{46} +(-5.37922 - 0.948501i) q^{47} +(-2.26076 - 0.521366i) q^{48} +(-6.49795 - 2.36506i) q^{49} +(9.45393 + 0.493178i) q^{51} +(-2.13767 + 2.54758i) q^{52} -2.24096i q^{53} +(-2.36909 - 2.72135i) q^{54} +(-0.545643 - 0.457849i) q^{56} +(-10.5622 + 5.38489i) q^{57} +(-2.01918 + 0.356035i) q^{58} +(9.80414 + 3.56842i) q^{59} +(0.0515134 - 0.292147i) q^{61} +(-3.74332 - 2.16121i) q^{62} +(0.212039 + 0.848703i) q^{63} +(0.679583 + 1.17707i) q^{64} +(1.71742 - 1.29481i) q^{66} +(2.86527 + 3.41470i) q^{67} +(5.33255 + 6.35509i) q^{68} +(-8.51886 - 3.61362i) q^{69} +(-4.74640 - 8.22101i) q^{71} +(0.762491 - 7.28836i) q^{72} +(9.07962 + 5.24212i) q^{73} +(-1.03061 + 5.84488i) q^{74} +(-9.76283 - 3.55338i) q^{76} +(-0.513550 + 0.0905528i) q^{77} +(-2.21036 - 1.43467i) q^{78} +(5.45470 + 4.57704i) q^{79} +(-6.01573 + 6.69410i) q^{81} +3.16293i q^{82} +(3.99237 - 4.75792i) q^{83} +(-0.417366 + 0.643025i) q^{84} +(6.12002 + 2.22750i) q^{86} +(1.49646 + 4.89048i) q^{87} +(4.30202 + 0.758562i) q^{88} +(6.18976 - 10.7210i) q^{89} +(0.319448 + 0.553300i) q^{91} +(-2.77350 - 7.62012i) q^{92} +(-4.21039 + 9.92570i) q^{93} +(2.90548 - 2.43799i) q^{94} +(8.04306 - 6.06391i) q^{96} +(4.81556 + 13.2307i) q^{97} +(4.15831 - 2.40080i) q^{98} +(-3.72870 - 3.85747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^9	\( 60 q + 6 q^{9} - 12 q^{11} + 18 q^{14} + 24 q^{16} - 48 q^{19} - 72 q^{21} - 90 q^{24} - 36 q^{26} - 36 q^{29} + 24 q^{31} + 138 q^{34} - 84 q^{36} - 12 q^{39} - 150 q^{41} - 24 q^{44} + 60 q^{46} + 72 q^{49} + 42 q^{51} - 36 q^{54} + 60 q^{56} + 54 q^{59} - 24 q^{61} - 54 q^{64} + 156 q^{66} + 234 q^{69} + 24 q^{71} - 60 q^{76} - 108 q^{79} - 54 q^{81} - 90 q^{84} + 36 q^{86} - 18 q^{89} + 102 q^{91} - 30 q^{94} - 30 q^{96} - 246 q^{99}+O(q^{100}) \) 60 * q + 6 * q^9 - 12 * q^11 + 18 * q^14 + 24 * q^16 - 48 * q^19 - 72 * q^21 - 90 * q^24 - 36 * q^26 - 36 * q^29 + 24 * q^31 + 138 * q^34 - 84 * q^36 - 12 * q^39 - 150 * q^41 - 24 * q^44 + 60 * q^46 + 72 * q^49 + 42 * q^51 - 36 * q^54 + 60 * q^56 + 54 * q^59 - 24 * q^61 - 54 * q^64 + 156 * q^66 + 234 * q^69 + 24 * q^71 - 60 * q^76 - 108 * q^79 - 54 * q^81 - 90 * q^84 + 36 * q^86 - 18 * q^89 + 102 * q^91 - 30 * q^94 - 30 * q^96 - 246 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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