LMFDB - Embedded newform 675.2.u.c.49.7

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			49.7
Character	$\chi$	$=$	675.49
Dual form			675.2.u.c.124.7

$q$-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} +(-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} - 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}+ \cdots - 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

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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	$-0.143270\pi$
$2$	0.446338	+	0.531925i	0.315608	+	0.376128i	−0.584797	+	0.811180i	$0.698826\pi$
$3$	−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	$-0.573105\pi$
$7$	−0.287167	+	0.0506352i	−0.108539	+	0.0191383i	0.119115	+	0.992880i	$0.461994\pi$
$8$	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	0.0760131	−	0.997107i	$-0.475781\pi$
$11$	−1.68049	−	0.611647i	−0.506685	−	0.184418i	−0.582698	+	0.812688i	$0.698003\pi$
$12$	1.02664	+	2.42023i	0.296365	+	0.698660i
$13$	−1.40837	+	1.67842i	−0.390610	+	0.465511i	−0.925133	−	0.379643i	$-0.876047\pi$
$13$	−1.40837	+	1.67842i	−0.390610	+	0.465511i	0.534523	+	0.845154i	$0.320491\pi$
$14$	−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	$-0.563969\pi$
$17$	−4.73339	−	2.73283i	−1.14802	−	0.662808i	−0.948403	+	0.317067i	$0.897302\pi$
$18$	2.00271	−	0.573226i	0.472044	−	0.135111i
$19$	−3.42243	−	5.92782i	−0.785159	−	1.35993i	−0.928904	−	0.370320i	$-0.879248\pi$
$19$	−3.42243	−	5.92782i	−0.785159	−	1.35993i	0.143745	−	0.989615i	$-0.454085\pi$
$20$		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	$-0.256396\pi$
$23$	5.26140	+	0.927728i	1.09708	+	0.193445i	0.404322	+	0.914616i	$0.367507\pi$
$24$	−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	−0.408144	−	0.912918i	$-0.633824\pi$
$29$	2.26194	−	1.89799i	0.420031	−	0.352448i	0.828175	+	0.560470i	$0.189379\pi$
$30$		0			0
$31$	1.08094	−	6.13030i	0.194142	−	1.10103i	−0.719493	−	0.694499i	$-0.755626\pi$
$31$	1.08094	−	6.13030i	0.194142	−	1.10103i	0.913635	−	0.406535i	$-0.133263\pi$
$32$	−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	$-0.581303\pi$
$37$	−7.40217	−	4.27364i	−1.21691	−	0.702583i	−0.964255	+	0.264974i	$0.914637\pi$
$38$	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	0.873226	−	0.487315i	$-0.162024\pi$
$41$	3.48938	+	2.92794i	0.544949	+	0.457267i	−0.328277	+	0.944581i	$0.606468\pi$
$42$	0.348078	+	0.0428237i	0.0537097	+	0.00660784i
$43$	3.20791	−	8.81367i	0.489202	−	1.34407i	−0.412202	−	0.911093i	$-0.635240\pi$
$43$	3.20791	−	8.81367i	0.489202	−	1.34407i	0.901404	−	0.432979i	$-0.142538\pi$
$44$	−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	$-0.425131\pi$
$47$	5.37922	−	0.948501i	0.784640	−	0.138353i	0.551594	+	0.834113i	$0.314020\pi$
$48$	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	0.387154	−	0.922015i	$-0.373458\pi$
$59$	9.80414	−	3.56842i	1.27639	−	0.464568i	0.889237	+	0.457447i	$0.151236\pi$
$60$		0			0
$61$	0.0515134	+	0.292147i	0.00659562	+	0.0374056i	0.987928	−	0.154914i	$-0.0495101\pi$
$61$	0.0515134	+	0.292147i	0.00659562	+	0.0374056i	−0.981332	+	0.192320i	$0.938399\pi$
$62$	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	$-0.865559\pi$
$67$	−2.86527	+	3.41470i	−0.350049	+	0.417172i	0.562075	+	0.827086i	$0.310003\pi$
$68$	−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	0.433912	+	0.900955i	$0.357133\pi$
$71$	−4.74640	+	8.22101i	−0.563294	+	0.975654i	−0.997206	+	0.0746990i	$0.976200\pi$
$72$	−0.762491	−	7.28836i	−0.0898604	−	0.858941i
$73$	−9.07962	+	5.24212i	−1.06269	+	0.613544i	−0.926175	−	0.377095i	$-0.876923\pi$
$73$	−9.07962	+	5.24212i	−1.06269	+	0.613544i	−0.136514	+	0.990638i	$0.543590\pi$
$74$	−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	−0.282115	−	0.959381i	$-0.591036\pi$
$79$	5.45470	−	4.57704i	0.613702	−	0.514957i	0.895817	+	0.444424i	$0.146592\pi$
$80$		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	$-0.332945\pi$
$83$	−3.99237	−	4.75792i	−0.438219	−	0.522249i	−0.939275	+	0.343166i	$0.888501\pi$
$84$	−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	0.981613	+	0.190880i	$0.0611340\pi$
$89$	6.18976	+	10.7210i	0.656113	+	1.13642i	−0.325500	+	0.945542i	$0.605533\pi$
$90$		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	0.412689	+	0.910872i	$0.364590\pi$
$97$	−4.81556	+	13.2307i	−0.488947	+	1.34337i	−0.901635	+	0.432497i	$0.857632\pi$
$98$	−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	−0.875821	−	0.482637i	$-0.839679\pi$
$101$	−2.18977	−	12.4188i	−0.217890	−	1.23572i	0.657931	−	0.753078i	$-0.271432\pi$
$102$	4.48198	+	4.80866i	0.443782	+	0.476128i
$103$	2.01626	+	5.53963i	0.198668	+	0.545836i	0.998521	−	0.0543593i	$-0.0173116\pi$
$103$	2.01626	+	5.53963i	0.198668	+	0.545836i	−0.799853	+	0.600196i	$0.795089\pi$
$104$	−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	$-0.144813\pi$
$113$	−0.768439	−	2.11127i	−0.0722887	−	0.198611i	−0.970575	+	0.240799i	$0.922590\pi$
$114$	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	$-0.723612\pi$
$127$	−3.47339	+	2.00536i	−0.308213	+	0.177947i	0.337913	+	0.941177i	$0.390279\pi$
$128$	−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	0.660610	+	0.750729i	$0.270298\pi$
$131$	−2.48282	+	14.0808i	−0.216925	+	1.23024i	−0.877535	+	0.479513i	$0.840813\pi$
$132$	−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	$-0.242552\pi$
$137$	−0.960393	−	1.14455i	−0.0820519	−	0.0977856i	−0.805508	+	0.592584i	$0.798108\pi$
$138$	−5.72446	−	2.91849i	−0.487298	−	0.248439i
$139$	0.755255	−	4.28326i	0.0640599	−	0.363302i	−0.935880	−	0.352319i	$-0.885393\pi$
$139$	0.755255	−	4.28326i	0.0640599	−	0.363302i	0.999940	−	0.0109822i	$-0.00349581\pi$
$140$		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	0.934387	−	0.356260i	$-0.115948\pi$
$149$	9.10358	+	7.63881i	0.745794	+	0.625796i	−0.188593	+	0.982055i	$0.560393\pi$
$150$		0			0
$151$	20.4667	+	7.44928i	1.66556	+	0.606214i	0.991222	−	0.132210i	$-0.0422072\pi$
$151$	20.4667	+	7.44928i	1.66556	+	0.606214i	0.674337	+	0.738423i	$0.264429\pi$
$152$	−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	−0.981982	−	0.188973i	$-0.939484\pi$
$157$	−4.40065	−	12.0907i	−0.351210	−	0.964941i	0.630772	−	0.775968i	$-0.282738\pi$
$158$	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	0.942133	+	0.335238i	$0.108817\pi$
$167$	5.63313	+	15.4769i	0.435904	+	1.19764i	−0.506229	+	0.862399i	$0.668961\pi$
$168$	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	0.731751	+	0.681572i	$0.238703\pi$
$173$	−3.51064	+	9.64540i	−0.266909	+	0.733326i	−0.998660	+	0.0517539i	$0.983519\pi$
$174$	−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	−0.710153	−	0.704048i	$-0.751374\pi$
$179$	3.40694	−	5.90100i	0.254647	−	0.441061i	0.964800	+	0.262986i	$0.0847074\pi$
$180$		0			0
$181$	12.9542	+	22.4373i	0.962876	+	1.66775i	0.715216	+	0.698904i	$0.246328\pi$
$181$	12.9542	+	22.4373i	0.962876	+	1.66775i	0.247661	+	0.968847i	$0.420338\pi$
$182$	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	0.0848945	−	0.996390i	$-0.472945\pi$
$191$	14.9382	−	12.5346i	1.08089	−	0.906973i	0.995994	+	0.0894165i	$0.0285002\pi$
$192$	0.122641	+	2.35095i	0.00885083	+	0.169665i
$193$	−16.8657	−	2.97388i	−1.21402	−	0.214064i	−0.470270	−	0.882523i	$-0.655843\pi$
$193$	−16.8657	−	2.97388i	−1.21402	−	0.214064i	−0.743750	+	0.668458i	$0.766955\pi$
$194$	−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	$-0.421351\pi$
$197$	16.9353	−	9.77759i	1.20659	−	0.696624i	0.962012	+	0.273006i	$0.0880178\pi$
$198$	−3.71614	−	0.261655i	−0.264095	−	0.0185950i
$199$	−10.6782	+	18.4951i	−0.756956	+	1.31109i	0.187440	+	0.982276i	$0.439981\pi$
$199$	−10.6782	+	18.4951i	−0.756956	+	1.31109i	−0.944396	+	0.328810i	$0.893352\pi$
$200$		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	−0.401154	−	0.916011i	$-0.631391\pi$
$211$	−1.73810	+	0.632615i	−0.119655	+	0.0435510i	0.281499	+	0.959562i	$0.409169\pi$
$212$	−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	$-0.527102\pi$
$223$	2.62569	−	0.462980i	0.175829	−	0.0310034i	0.260869	+	0.965374i	$0.415991\pi$
$224$	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	$-0.841377\pi$
$227$	1.53263	−	4.21086i	0.101724	−	0.279485i	0.980106	+	0.198475i	$0.0635988\pi$
$228$	10.8331	−	14.3688i	0.717439	−	0.951597i
$229$	−18.6698	−	15.6659i	−1.23374	−	1.03523i	−0.997987	−	0.0634155i	$-0.979801\pi$
$229$	−18.6698	−	15.6659i	−1.23374	−	1.03523i	−0.235751	−	0.971814i	$-0.575755\pi$
$230$		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	$-0.283027\pi$
$233$	4.16101	+	2.40236i	0.272597	+	0.157384i	−0.357470	+	0.933924i	$0.616361\pi$
$234$	−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	−0.738658	−	0.674080i	$-0.764540\pi$
$239$	2.87553	−	16.3079i	0.186003	−	1.05487i	0.924661	−	0.380792i	$-0.124349\pi$
$240$		0			0
$241$	21.4121	−	17.9669i	1.37928	−	1.15735i	0.409796	−	0.912177i	$-0.365600\pi$
$241$	21.4121	−	17.9669i	1.37928	−	1.15735i	0.969479	−	0.245173i	$-0.0788447\pi$
$242$		−	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	0.956997	+	0.290097i	$0.0936875\pi$
$251$	11.5611	+	20.0244i	0.729730	+	1.26393i	−0.227268	+	0.973832i	$0.572979\pi$
$252$	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	−0.181651	+	0.983363i	$0.558144\pi$
$257$	−17.9314	+	21.3698i	−1.11853	+	1.33301i	−0.936880	+	0.349650i	$0.886300\pi$
$258$	−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	$-0.397911\pi$
$263$	15.1806	−	2.67674i	0.936073	−	0.165055i	0.620820	+	0.783953i	$0.286800\pi$
$264$	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	$-0.462556\pi$
$277$	9.44181	−	1.66485i	0.567304	−	0.100031i	0.449941	+	0.893058i	$0.351445\pi$
$278$	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	0.250303	−	0.968167i	$-0.419470\pi$
$281$	−3.02203	−	1.09993i	−0.180279	−	0.0656162i	−0.430583	+	0.902551i	$0.641692\pi$
$282$	−6.52022	−	0.802175i	−0.388274	−	0.0477688i
$283$	16.2692	−	19.3889i	0.967103	−	1.15255i	−0.0211585	−	0.999776i	$-0.506735\pi$
$283$	16.2692	−	19.3889i	0.967103	−	1.15255i	0.988261	−	0.152772i	$-0.0488201\pi$
$284$	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	$-0.198537\pi$
$293$	23.5312	+	4.14918i	1.37471	+	0.242398i	0.562997	+	0.826459i	$0.309648\pi$
$294$	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	$-0.485053\pi$
$307$	−13.9236	−	8.03880i	−0.794662	−	0.458799i	−0.841601	+	0.540099i	$0.818387\pi$
$308$	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	0.183813	−	0.982961i	$-0.441156\pi$
$311$	−13.2669	−	11.1322i	−0.752297	−	0.631252i	−0.936109	+	0.351710i	$0.885600\pi$
$312$	−3.62003	−	8.53397i	−0.204944	−	0.483141i
$313$	4.58433	−	12.5953i	0.259122	−	0.711931i	−0.740100	−	0.672496i	$-0.765222\pi$
$313$	4.58433	−	12.5953i	0.259122	−	0.711931i	0.999222	−	0.0394347i	$-0.0125557\pi$
$314$	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	$-0.350095\pi$
$317$	21.0961	−	3.71981i	1.18487	−	0.208925i	0.731150	+	0.682217i	$0.238984\pi$
$318$	−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	−0.998826	−	0.0484378i	$-0.984576\pi$
$331$	−1.39731	−	7.92456i	−0.0768033	−	0.435573i	0.922023	−	0.387135i	$-0.126535\pi$
$332$	−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	$-0.587371\pi$
$337$	13.2901	−	15.8385i	0.723957	−	0.862779i	0.995009	+	0.0997862i	$0.0318159\pi$
$338$	−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	$-0.365208\pi$
$347$	9.03912	+	1.59384i	0.485245	+	0.0855619i	0.0743269	+	0.997234i	$0.476319\pi$
$348$	6.91577	+	3.52586i	0.370724	+	0.189006i
$349$	15.5771	−	13.0707i	0.833823	−	0.699661i	−0.122342	−	0.992488i	$-0.539040\pi$
$349$	15.5771	−	13.0707i	0.833823	−	0.699661i	0.956165	+	0.292827i	$0.0945960\pi$
$350$		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	$-0.173566\pi$
$353$	3.67772	+	4.38294i	0.195745	+	0.233280i	−0.659240	+	0.751933i	$0.729122\pi$
$354$	−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	−0.875013	−	0.484100i	$-0.839147\pi$
$359$	−16.2331	−	28.1165i	−0.856749	−	1.48393i	0.0182634	−	0.999833i	$-0.494186\pi$
$360$		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	$-0.923740\pi$
$367$	−1.43192	+	3.93416i	−0.0747454	+	0.205361i	0.896693	+	0.442653i	$0.145963\pi$
$368$	−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	$-0.168351\pi$
$373$	−2.36288	−	6.49195i	−0.122345	−	0.336140i	−0.985713	+	0.168435i	$0.946129\pi$
$374$	−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	−0.866176	−	0.499739i	$-0.833429\pi$
$383$	−10.2524	−	28.1682i	−0.523873	−	1.43933i	0.342303	−	0.939590i	$-0.388793\pi$
$384$	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	0.0413802	−	0.999143i	$-0.486825\pi$
$389$	−11.2255	−	4.08576i	−0.569158	−	0.207157i	−0.610538	+	0.791987i	$0.709047\pi$
$390$		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	$-0.569926\pi$
$397$	10.3278	−	5.96277i	0.518338	−	0.299263i	0.736255	+	0.676705i	$0.236593\pi$
$398$	−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	0.331703	+	0.943384i	$0.392377\pi$
$401$	−6.06060	+	34.3714i	−0.302652	+	1.71643i	−0.634355	+	0.773042i	$0.718734\pi$
$402$	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	−0.895075	−	0.445916i	$-0.852878\pi$
$409$	1.99270	−	11.3012i	0.0985326	−	0.558806i	0.993607	−	0.112890i	$-0.0360109\pi$
$410$		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	−0.158187	−	0.987409i	$-0.550565\pi$
$419$	−23.7050	−	19.8908i	−1.15806	−	0.971731i	−0.999877	+	0.0156785i	$0.995009\pi$
$420$		0			0
$421$	−8.89101	−	3.23606i	−0.433322	−	0.157716i	0.116144	−	0.993232i	$-0.462947\pi$
$421$	−8.89101	−	3.23606i	−0.433322	−	0.157716i	−0.549466	+	0.835516i	$0.685169\pi$
$422$	−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	0.985146	+	0.171718i	$0.0549318\pi$
$439$	2.47536	+	14.0385i	0.118143	+	0.670020i	−0.867004	+	0.498302i	$0.833957\pi$
$440$		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	$-0.921030\pi$
$443$	−1.45129	+	3.98739i	−0.0689529	+	0.189447i	0.900430	+	0.435001i	$0.143252\pi$
$444$	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	−0.878703	−	0.477370i	$-0.841590\pi$
$449$	−0.549598	+	0.951931i	−0.0259371	+	0.0449244i	0.852765	+	0.522294i	$0.174924\pi$
$450$		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	$-0.195902\pi$
$457$	2.26991	+	2.70517i	0.106182	+	0.126542i	−0.710336	+	0.703863i	$0.751457\pi$
$458$		−	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	−0.939727	−	0.341925i	$-0.888921\pi$
$461$	−16.4505	+	13.8036i	−0.766178	+	0.642900i	0.173549	+	0.984825i	$0.444477\pi$
$462$	−0.558748	−	0.284866i	−0.0259953	−	0.0132531i
$463$	23.0472	+	4.06385i	1.07110	+	0.188863i	0.681275	−	0.732027i	$-0.261426\pi$
$463$	23.0472	+	4.06385i	1.07110	+	0.188863i	0.389821	+	0.920891i	$0.372537\pi$
$464$	−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	$-0.907913\pi$
$467$	−25.7292	+	14.8548i	−1.19060	+	0.687396i	−0.232161	+	0.972677i	$0.574580\pi$
$468$	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	0.997219	+	0.0745327i	$0.0237465\pi$
$479$	1.87413	+	10.6287i	0.0856313	+	0.485639i	−0.911587	+	0.411107i	$0.865142\pi$
$480$		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	0.468826	−	0.883291i	$-0.344677\pi$
$491$	30.9274	−	11.2567i	1.39574	−	0.508006i	0.926910	+	0.375284i	$0.122455\pi$
$492$	−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	0.871064	−	0.491170i	$-0.163430\pi$
$499$	12.0317	+	10.0958i	0.538615	+	0.451952i	−0.332449	+	0.943121i	$0.607875\pi$
$500$		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	$-0.193438\pi$
$503$	16.5282	+	9.54257i	0.736957	+	0.425482i	−0.0840050	+	0.996465i	$0.526771\pi$
$504$	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	0.884861	+	0.465854i	$0.154253\pi$
$509$	−2.39075	+	13.5586i	−0.105968	+	0.600974i	−0.990829	+	0.135120i	$0.956858\pi$
$510$		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	0.642907	−	0.765945i	$-0.277728\pi$
$521$	−7.80342	−	13.5159i	−0.341874	−	0.592143i	−0.984781	+	0.173801i	$0.944395\pi$
$522$	3.44204	−	5.09774i	0.150654	−	0.223122i
$523$	−12.5985	−	7.27374i	−0.550893	−	0.318058i	0.198589	−	0.980083i	$-0.436364\pi$
$523$	−12.5985	−	7.27374i	−0.550893	−	0.318058i	−0.749482	+	0.662025i	$0.769697\pi$
$524$	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	$-0.357120\pi$
$547$	26.8931	−	4.74198i	1.14987	−	0.202753i	0.715918	+	0.698185i	$0.246009\pi$
$548$	−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	$-0.431568\pi$
$557$	−12.4162	−	7.16847i	−0.526090	−	0.303738i	−0.739423	+	0.673242i	$0.764901\pi$
$558$	−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	$-0.234812\pi$
$563$	28.6011	+	5.04314i	1.20539	+	0.212543i	0.465364	+	0.885119i	$0.345923\pi$
$564$	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	−0.581501	−	0.813545i	$-0.697535\pi$
$569$	2.83162	−	2.37601i	0.118708	−	0.0996077i	0.700209	+	0.713938i	$0.253090\pi$
$570$		0			0
$571$	0.927120	−	5.25796i	0.0387988	−	0.220039i	−0.959244	−	0.282581i	$-0.908810\pi$
$571$	0.927120	−	5.25796i	0.0387988	−	0.220039i	0.998042	+	0.0625417i	$0.0199207\pi$
$572$	−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	$-0.185923\pi$
$577$	18.5862	+	10.7308i	0.773754	+	0.446727i	−0.0604579	+	0.998171i	$0.519256\pi$
$578$	−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	$-0.595650\pi$
$587$	−5.99490	+	1.05706i	−0.247436	+	0.0436297i	0.0485544	+	0.998821i	$0.484539\pi$
$588$	−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	−0.500740	−	0.865598i	$-0.666939\pi$
$599$	−8.02599	+	2.92122i	−0.327933	+	0.119358i	0.172807	+	0.984956i	$0.444716\pi$
$600$		0			0
$601$	2.31320	+	13.1188i	0.0943574	+	0.535128i	0.994942	+	0.100448i	$0.0320275\pi$
$601$	2.31320	+	13.1188i	0.0943574	+	0.535128i	−0.900585	+	0.434680i	$0.856861\pi$
$602$	−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	$-0.785878\pi$
$607$	−0.805951	+	0.960494i	−0.0327125	+	0.0389853i	0.749440	+	0.662072i	$0.230323\pi$
$608$	−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	$-0.763123\pi$
$613$	−12.7968	+	7.38826i	−0.516860	+	0.298409i	0.218789	+	0.975772i	$0.429789\pi$
$614$	−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	$-0.458083\pi$
$617$	−2.09563	−	0.369516i	−0.0843669	−	0.0148762i	−0.215672	+	0.976466i	$0.569194\pi$
$618$	−0.369363	−	7.08047i	−0.0148580	−	0.284818i
$619$	13.5591	−	11.3775i	0.544987	−	0.457298i	−0.328252	−	0.944590i	$-0.606460\pi$
$619$	13.5591	−	11.3775i	0.544987	−	0.457298i	0.873239	+	0.487292i	$0.162015\pi$
$620$		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	−0.960847	−	0.277079i	$-0.910634\pi$
$631$	−6.04045	+	10.4624i	−0.240466	+	0.416500i	0.720381	+	0.693579i	$0.243967\pi$
$632$	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	0.994093	+	0.108528i	$0.0346137\pi$
$641$	2.45761	+	13.9378i	0.0970699	+	0.550511i	−0.897023	+	0.441983i	$0.854275\pi$
$642$	−2.15794	+	7.05224i	−0.0851672	+	0.278330i
$643$	−8.06852	−	22.1681i	−0.318191	−	0.874223i	−0.990934	−	0.134347i	$-0.957106\pi$
$643$	−8.06852	−	22.1681i	−0.318191	−	0.874223i	0.672743	−	0.739876i	$-0.265116\pi$
$644$	−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	$-0.215242\pi$
$653$	−5.61686	−	15.4322i	−0.219805	−	0.603909i	−0.999760	+	0.0219271i	$0.993020\pi$
$654$	−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	−0.463797	−	0.885942i	$-0.653513\pi$
$659$	−35.6457	−	12.9740i	−1.38856	−	0.505394i	−0.924761	+	0.380548i	$0.875736\pi$
$660$		0			0
$661$	−10.0083	−	8.39796i	−0.389278	−	0.326643i	0.427054	−	0.904226i	$-0.359551\pi$
$661$	−10.0083	−	8.39796i	−0.389278	−	0.326643i	−0.816332	+	0.577583i	$0.803996\pi$
$662$	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	$-0.197364\pi$
$673$	2.60185	+	3.10076i	0.100294	+	0.119526i	−0.713563	+	0.700591i	$0.752920\pi$
$674$	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	$-0.129641\pi$
$677$	9.59228	+	11.4316i	0.368661	+	0.439353i	−0.549540	+	0.835467i	$0.685197\pi$
$678$	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	$-0.814213\pi$
$683$	−20.2388	+	11.6849i	−0.774417	+	0.447110i	0.0600307	+	0.998197i	$0.480880\pi$
$684$	−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	0.107482	−	0.994207i	$-0.465721\pi$
$691$	−11.8093	−	4.29822i	−0.449245	−	0.163512i	−0.556728	+	0.830695i	$0.687943\pi$
$692$	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	0.999621	−	0.0275213i	$-0.00876139\pi$
$709$	1.35456	+	7.68211i	0.0508717	+	0.288508i	−0.948750	+	0.316029i	$0.897650\pi$
$710$		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	0.444280	+	0.895888i	$0.353459\pi$
$719$	−14.8476	+	25.7168i	−0.553722	+	0.959074i	−0.998002	+	0.0631860i	$0.979874\pi$
$720$		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	$-0.226774\pi$
$727$	−0.495670	−	0.590717i	−0.0183834	−	0.0219085i	−0.775158	+	0.631768i	$0.782330\pi$
$728$		−	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	$-0.456469\pi$
$733$	−2.01399	−	0.355120i	−0.0743882	−	0.0131167i	−0.210718	+	0.977547i	$0.567580\pi$
$734$	−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	−0.933981	−	0.357323i	$-0.883689\pi$
$739$	−4.28264	+	7.41775i	−0.157539	+	0.272866i	0.776441	+	0.630189i	$0.217023\pi$
$740$		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	$-0.988969\pi$
$743$	−21.5811	+	25.7194i	−0.791734	+	0.943552i	0.207666	+	0.978200i	$0.433413\pi$
$744$	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	0.0927821	−	0.995686i	$-0.470424\pi$
$751$	22.0296	−	8.01813i	0.803872	−	0.292586i	0.711090	+	0.703101i	$0.248202\pi$
$752$	−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	0.218737	−	0.975784i	$-0.429806\pi$
$761$	27.9592	−	10.1763i	1.01352	−	0.368892i	0.794784	+	0.606892i	$0.207584\pi$
$762$	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	0.746320	−	0.665587i	$-0.231819\pi$
$769$	6.11306	+	5.12946i	0.220442	+	0.184973i	−0.525878	+	0.850560i	$0.676263\pi$
$770$		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	$-0.335485\pi$
$773$	−0.325571	−	0.187968i	−0.0117100	−	0.00676076i	−0.505844	+	0.862625i	$0.668819\pi$
$774$	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	$-0.410865\pi$
$787$	5.81822	+	1.02591i	0.207397	+	0.0365697i	−0.0689843	+	0.997618i	$0.521976\pi$
$788$	−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	0.274427	−	0.961608i	$-0.411512\pi$
$797$	33.1370	−	39.4911i	1.17377	−	1.39885i	0.899345	−	0.437239i	$-0.144044\pi$
$798$	−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	0.945447	−	0.325776i	$-0.105626\pi$
$821$	41.8420	+	15.2293i	1.46030	+	0.531505i	0.514850	+	0.857280i	$0.327848\pi$
$822$	0.701730	+	1.65428i	0.0244756	+	0.0576996i
$823$	16.2597	−	19.3775i	0.566776	−	0.675458i	−0.404190	−	0.914675i	$-0.632446\pi$
$823$	16.2597	−	19.3775i	0.566776	−	0.675458i	0.970966	+	0.239217i	$0.0768908\pi$
$824$	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	$-0.226532\pi$
$827$	16.4007	+	9.46894i	0.570307	+	0.329267i	−0.186965	+	0.982367i	$0.559865\pi$
$828$	−17.4916	−	16.9077i	−0.607875	−	0.587583i
$829$	1.72605	+	2.98961i	0.0599482	+	0.103833i	0.894442	−	0.447184i	$-0.147573\pi$
$829$	1.72605	+	2.98961i	0.0599482	+	0.103833i	−0.834494	+	0.551017i	$0.814240\pi$
$830$		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	−0.352950	−	0.935642i	$-0.614821\pi$
$839$	14.6910	−	12.3272i	0.507189	−	0.425582i	0.860139	+	0.510060i	$0.170377\pi$
$840$		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	$-0.920817\pi$
$853$	−2.00055	+	5.49647i	−0.0684975	+	0.188195i	0.900721	+	0.434399i	$0.143039\pi$
$854$	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	$-0.235792\pi$
$857$	48.6607	−	8.58019i	1.66222	−	0.293094i	0.924263	+	0.381757i	$0.124681\pi$
$858$	−4.59200	+	1.05898i	−0.156768	+	0.0361531i
$859$	7.31048	−	2.66080i	0.249430	−	0.0907852i	−0.214279	−	0.976772i	$-0.568740\pi$
$859$	7.31048	−	2.66080i	0.249430	−	0.0907852i	0.463710	+	0.885987i	$0.346518\pi$
$860$		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	−0.0602584	+	0.998183i	$0.519192\pi$
$877$	−30.5859	+	36.4509i	−1.03281	+	1.23086i	−0.972554	+	0.232676i	$0.925252\pi$
$878$	−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	−0.563885	−	0.825853i	$-0.690694\pi$
$881$	12.8601	−	22.2743i	0.433268	−	0.750441i	0.997152	+	0.0754120i	$0.0240272\pi$
$882$	−11.6578	+	8.46133i	−0.392539	+	0.284908i
$883$	38.9336	−	22.4783i	1.31022	−	0.756456i	0.328088	−	0.944647i	$-0.393596\pi$
$883$	38.9336	−	22.4783i	1.31022	−	0.756456i	0.982133	+	0.188191i	$0.0602623\pi$
$884$	−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	$-0.365567\pi$
$887$	14.3878	+	2.53696i	0.483095	+	0.0851827i	0.0732037	+	0.997317i	$0.476678\pi$
$888$	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	−0.609533	−	0.792761i	$-0.708643\pi$
$907$	11.0519	−	30.3649i	0.366973	−	1.00825i	0.976506	−	0.215489i	$-0.0691347\pi$
$908$	−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	−0.999982	−	0.00596215i	$-0.998102\pi$
$911$	−1.88176	−	10.6720i	−0.0623455	−	0.353579i	0.937637	−	0.347617i	$-0.113009\pi$
$912$	−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	0.789147	−	0.614205i	$-0.210523\pi$
$929$	30.4449	+	11.0810i	0.998865	+	0.363557i	0.209718	+	0.977762i	$0.432745\pi$
$930$		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	−0.819835	+	0.572600i	$0.805935\pi$
$937$	−52.8226	+	30.4971i	−1.72564	+	0.996298i	−0.905804	+	0.423698i	$0.860732\pi$
$938$	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	−0.910255	−	0.414048i	$-0.864115\pi$
$941$	2.66012	−	15.0863i	0.0867176	−	0.491800i	0.996973	−	0.0777521i	$-0.0247743\pi$
$942$	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	−0.911441	−	0.411431i	$-0.865029\pi$
$947$	−35.6464	−	42.4817i	−1.15835	−	1.38047i	−0.246910	−	0.969038i	$-0.579415\pi$
$948$	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	$-0.651887\pi$
$953$	2.48180	−	1.43287i	0.0803935	−	0.0464152i	0.539658	+	0.841884i	$0.318554\pi$
$954$	−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	0.882903	+	0.469555i	$0.155586\pi$
$967$	15.8090	+	43.4350i	0.508384	+	1.39677i	−0.374519	+	0.927219i	$0.622192\pi$
$968$	−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	−0.997063	−	0.0765840i	$-0.975599\pi$
$977$	−8.82997	−	24.2601i	−0.282496	−	0.776151i	0.714567	−	0.699567i	$-0.246624\pi$
$978$	−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	$-0.834476\pi$
$983$	3.64829	−	10.0236i	0.116362	−	0.319703i	0.984178	+	0.177184i	$0.0566986\pi$
$984$	−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	−0.759831	−	0.650121i	$-0.774718\pi$
$991$	−29.6838	−	51.4138i	−0.942937	−	1.63321i	−0.183106	−	0.983093i	$-0.558615\pi$
$992$	−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	$-0.367459\pi$
$997$	−17.8854	−	21.3149i	−0.566435	−	0.675051i	−0.970895	+	0.239505i	$0.923015\pi$
$998$			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.49.7		60
5.2	odd	4		135.2.k.a.76.2	yes	30
5.3	odd	4		675.2.l.d.76.4		30
5.4	even	2	inner	675.2.u.c.49.4		60
15.2	even	4		405.2.k.a.361.4		30
27.16	even	9	inner	675.2.u.c.124.4		60
135.43	odd	36		675.2.l.d.151.4		30
135.77	even	36		3645.2.a.g.1.10		15
135.92	even	36		405.2.k.a.46.4		30
135.97	odd	36		135.2.k.a.16.2	✓	30
135.112	odd	36		3645.2.a.h.1.6		15
135.124	even	18	inner	675.2.u.c.124.7		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.16.2	✓	30	135.97	odd	36
135.2.k.a.76.2	yes	30	5.2	odd	4
405.2.k.a.46.4		30	135.92	even	36
405.2.k.a.361.4		30	15.2	even	4
675.2.l.d.76.4		30	5.3	odd	4
675.2.l.d.151.4		30	135.43	odd	36
675.2.u.c.49.4		60	5.4	even	2	inner
675.2.u.c.49.7		60	1.1	even	1	trivial
675.2.u.c.124.4		60	27.16	even	9	inner
675.2.u.c.124.7		60	135.124	even	18	inner
3645.2.a.g.1.10		15	135.77	even	36
3645.2.a.h.1.6		15	135.112	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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{9} - 12 q^{11} + 18 q^{14} + 24 q^{16} - 48 q^{19} - 72 q^{21} - 90 q^{24} - 36 q^{26} - 36 q^{29} + 24 q^{31} + 138 q^{34} - 84 q^{36} - 12 q^{39} - 150 q^{41} - 24 q^{44} + 60 q^{46} + 72 q^{49}+ \cdots - 246 q^{99}+O(q^{100}) \) 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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