LMFDB - Embedded newform 912.2.ci.h.319.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			319.4
Character	$\chi$	$=$	912.319
Dual form			912.2.ci.h.223.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{3} +(1.30003 - 1.09086i) q^{5} +(1.57531 + 0.909508i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{3} +(1.30003 - 1.09086i) q^{5} +(1.57531 + 0.909508i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(5.51762 - 3.18560i) q^{11} +(-2.14934 - 0.378986i) q^{13} +(-1.30003 - 1.09086i) q^{15} +(-4.03001 - 1.46680i) q^{17} +(4.17968 + 1.23703i) q^{19} +(0.622140 - 1.70932i) q^{21} +(0.257666 - 0.307075i) q^{23} +(-0.368124 + 2.08774i) q^{25} +(0.500000 + 0.866025i) q^{27} +(1.76578 + 4.85144i) q^{29} +(2.11768 - 3.66793i) q^{31} +(-4.09533 - 4.88063i) q^{33} +(3.04010 - 0.536052i) q^{35} +0.939598i q^{37} +2.18249i q^{39} +(7.52894 - 1.32756i) q^{41} +(-3.71439 - 4.42664i) q^{43} +(-0.848536 + 1.46971i) q^{45} +(-3.21577 - 8.83526i) q^{47} +(-1.84559 - 3.19666i) q^{49} +(-0.744716 + 4.22350i) q^{51} +(0.589175 - 0.702151i) q^{53} +(3.69806 - 10.1603i) q^{55} +(0.492441 - 4.33099i) q^{57} +(10.8660 + 3.95489i) q^{59} +(-10.5766 - 8.87478i) q^{61} +(-1.79138 - 0.315869i) q^{63} +(-3.20763 + 1.85193i) q^{65} +(-6.48994 + 2.36215i) q^{67} +(-0.347153 - 0.200429i) q^{69} +(-0.701698 + 0.588794i) q^{71} +(-2.33910 - 13.2657i) q^{73} +2.11994 q^{75} +11.5893 q^{77} +(2.36208 + 13.3960i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-1.52259 - 0.879067i) q^{83} +(-6.83923 + 2.48927i) q^{85} +(4.47111 - 2.58139i) q^{87} +(-2.20458 - 0.388726i) q^{89} +(-3.04119 - 2.55186i) q^{91} +(-3.97993 - 1.44858i) q^{93} +(6.78315 - 2.95126i) q^{95} +(-1.26276 + 3.46941i) q^{97} +(-4.09533 + 4.88063i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 9 q^{7}+O(q^{10}) $ 24 * q + 9 * q^7	$ 24 q + 9 q^{7} - 9 q^{11} - 9 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 15 q^{23} + 6 q^{25} + 12 q^{27} - 6 q^{29} - 12 q^{31} - 3 q^{33} + 30 q^{41} + 9 q^{43} + 3 q^{45} + 15 q^{47} + 27 q^{49} - 3 q^{51} + 6 q^{53} - 21 q^{55} - 9 q^{57} + 36 q^{59} - 21 q^{61} + 3 q^{63} - 9 q^{65} - 45 q^{67} + 36 q^{71} - 42 q^{75} + 108 q^{77} - 36 q^{79} + 27 q^{83} - 9 q^{85} + 9 q^{87} - 27 q^{89} + 36 q^{91} - 18 q^{93} - 30 q^{95} - 51 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 9 * q^7 - 9 * q^11 - 9 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 15 * q^23 + 6 * q^25 + 12 * q^27 - 6 * q^29 - 12 * q^31 - 3 * q^33 + 30 * q^41 + 9 * q^43 + 3 * q^45 + 15 * q^47 + 27 * q^49 - 3 * q^51 + 6 * q^53 - 21 * q^55 - 9 * q^57 + 36 * q^59 - 21 * q^61 + 3 * q^63 - 9 * q^65 - 45 * q^67 + 36 * q^71 - 42 * q^75 + 108 * q^77 - 36 * q^79 + 27 * q^83 - 9 * q^85 + 9 * q^87 - 27 * q^89 + 36 * q^91 - 18 * q^93 - 30 * q^95 - 51 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$		0			0
$5$	1.30003	−	1.09086i	0.581393	−	0.487846i	−0.304012	−	0.952668i	$-0.598326\pi$
$5$	1.30003	−	1.09086i	0.581393	−	0.487846i	0.885404	+	0.464822i	$0.153882\pi$
$6$		0			0
$7$	1.57531	+	0.909508i	0.595413	+	0.343762i	0.767235	−	0.641366i	$-0.221632\pi$
$7$	1.57531	+	0.909508i	0.595413	+	0.343762i	−0.171822	+	0.985128i	$0.554965\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	5.51762	−	3.18560i	1.66363	−	0.960495i	0.692665	−	0.721260i	$-0.256437\pi$
$11$	5.51762	−	3.18560i	1.66363	−	0.960495i	0.970962	−	0.239236i	$-0.0768968\pi$
$12$		0			0
$13$	−2.14934	−	0.378986i	−0.596119	−	0.105112i	−0.132555	−	0.991176i	$-0.542318\pi$
$13$	−2.14934	−	0.378986i	−0.596119	−	0.105112i	−0.463563	+	0.886064i	$0.653429\pi$
$14$		0			0
$15$	−1.30003	−	1.09086i	−0.335667	−	0.281658i
$16$		0			0
$17$	−4.03001	−	1.46680i	−0.977422	−	0.355752i	−0.196584	−	0.980487i	$-0.562985\pi$
$17$	−4.03001	−	1.46680i	−0.977422	−	0.355752i	−0.780837	+	0.624735i	$0.785207\pi$
$18$		0			0
$19$	4.17968	+	1.23703i	0.958885	+	0.283794i
$19$	4.17968	+	1.23703i	0.958885	+	0.283794i
$20$		0			0
$21$	0.622140	−	1.70932i	0.135762	−	0.373003i
$22$		0			0
$23$	0.257666	−	0.307075i	0.0537271	−	0.0640295i	−0.738512	−	0.674241i	$-0.764471\pi$
$23$	0.257666	−	0.307075i	0.0537271	−	0.0640295i	0.792239	+	0.610211i	$0.208915\pi$
$24$		0			0
$25$	−0.368124	+	2.08774i	−0.0736249	+	0.417547i
$26$		0			0
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$		0			0
$29$	1.76578	+	4.85144i	0.327897	+	0.900889i	0.988643	+	0.150280i	$0.0480175\pi$
$29$	1.76578	+	4.85144i	0.327897	+	0.900889i	−0.660747	+	0.750609i	$0.729760\pi$
$30$		0			0
$31$	2.11768	−	3.66793i	0.380346	−	0.658779i	−0.610765	−	0.791812i	$-0.709138\pi$
$31$	2.11768	−	3.66793i	0.380346	−	0.658779i	0.991112	+	0.133033i	$0.0424715\pi$
$32$		0			0
$33$	−4.09533	−	4.88063i	−0.712906	−	0.849608i
$34$		0			0
$35$	3.04010	−	0.536052i	0.513871	−	0.0906094i
$36$		0			0
$37$			0.939598i			0.154469i	0.997013	+	0.0772345i	$0.0246090\pi$
$37$			0.939598i			0.154469i	−0.997013	+	0.0772345i	$0.975391\pi$
$38$		0			0
$39$			2.18249i			0.349479i
$40$		0			0
$41$	7.52894	−	1.32756i	1.17582	−	0.207329i	0.448601	−	0.893732i	$-0.351922\pi$
$41$	7.52894	−	1.32756i	1.17582	−	0.207329i	0.727222	+	0.686403i	$0.240811\pi$
$42$		0			0
$43$	−3.71439	−	4.42664i	−0.566439	−	0.675056i	0.404457	−	0.914557i	$-0.367460\pi$
$43$	−3.71439	−	4.42664i	−0.566439	−	0.675056i	−0.970896	+	0.239501i	$0.923016\pi$
$44$		0			0
$45$	−0.848536	+	1.46971i	−0.126492	+	0.219091i
$46$		0			0
$47$	−3.21577	−	8.83526i	−0.469069	−	1.28876i	−0.918493	−	0.395437i	$-0.870593\pi$
$47$	−3.21577	−	8.83526i	−0.469069	−	1.28876i	0.449424	−	0.893318i	$-0.351629\pi$
$48$		0			0
$49$	−1.84559	−	3.19666i	−0.263656	−	0.456665i
$50$		0			0
$51$	−0.744716	+	4.22350i	−0.104281	+	0.591408i
$52$		0			0
$53$	0.589175	−	0.702151i	0.0809294	−	0.0964479i	−0.724060	−	0.689737i	$-0.757726\pi$
$53$	0.589175	−	0.702151i	0.0809294	−	0.0964479i	0.804990	+	0.593289i	$0.202171\pi$
$54$		0			0
$55$	3.69806	−	10.1603i	0.498646	−	1.37002i
$56$		0			0
$57$	0.492441	−	4.33099i	0.0652254	−	0.573654i
$58$		0			0
$59$	10.8660	+	3.95489i	1.41463	+	0.514882i	0.932484	−	0.361210i	$-0.117636\pi$
$59$	10.8660	+	3.95489i	1.41463	+	0.514882i	0.482143	+	0.876093i	$0.339859\pi$
$60$		0			0
$61$	−10.5766	−	8.87478i	−1.35419	−	1.13630i	−0.977730	−	0.209866i	$-0.932697\pi$
$61$	−10.5766	−	8.87478i	−1.35419	−	1.13630i	−0.376459	−	0.926433i	$-0.622858\pi$
$62$		0			0
$63$	−1.79138	−	0.315869i	−0.225693	−	0.0397957i
$64$		0			0
$65$	−3.20763	+	1.85193i	−0.397857	+	0.229703i
$66$		0			0
$67$	−6.48994	+	2.36215i	−0.792872	+	0.288582i	−0.706530	−	0.707684i	$-0.749740\pi$
$67$	−6.48994	+	2.36215i	−0.792872	+	0.288582i	−0.0863428	+	0.996265i	$0.527518\pi$
$68$		0			0
$69$	−0.347153	−	0.200429i	−0.0417923	−	0.0241288i
$70$		0			0
$71$	−0.701698	+	0.588794i	−0.0832762	+	0.0698770i	−0.683475	−	0.729973i	$-0.739532\pi$
$71$	−0.701698	+	0.588794i	−0.0832762	+	0.0698770i	0.600199	+	0.799851i	$0.295088\pi$
$72$		0			0
$73$	−2.33910	−	13.2657i	−0.273771	−	1.55263i	−0.742839	−	0.669470i	$-0.766521\pi$
$73$	−2.33910	−	13.2657i	−0.273771	−	1.55263i	0.469069	−	0.883162i	$-0.344590\pi$
$74$		0			0
$75$	2.11994			0.244790
$76$		0			0
$77$	11.5893			1.32073
$78$		0			0
$79$	2.36208	+	13.3960i	0.265754	+	1.50717i	0.766879	+	0.641792i	$0.221809\pi$
$79$	2.36208	+	13.3960i	0.265754	+	1.50717i	−0.501124	+	0.865375i	$0.667080\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	−1.52259	−	0.879067i	−0.167126	−	0.0964901i	0.414104	−	0.910230i	$-0.364095\pi$
$83$	−1.52259	−	0.879067i	−0.167126	−	0.0964901i	−0.581230	+	0.813739i	$0.697428\pi$
$84$		0			0
$85$	−6.83923	+	2.48927i	−0.741818	+	0.270000i
$86$		0			0
$87$	4.47111	−	2.58139i	0.479353	−	0.276755i
$88$		0			0
$89$	−2.20458	−	0.388726i	−0.233685	−	0.0412049i	0.0555794	−	0.998454i	$-0.482299\pi$
$89$	−2.20458	−	0.388726i	−0.233685	−	0.0412049i	−0.289264	+	0.957249i	$0.593411\pi$
$90$		0			0
$91$	−3.04119	−	2.55186i	−0.318803	−	0.267508i
$92$		0			0
$93$	−3.97993	−	1.44858i	−0.412700	−	0.150210i
$94$		0			0
$95$	6.78315	−	2.95126i	0.695937	−	0.302793i
$96$		0			0
$97$	−1.26276	+	3.46941i	−0.128214	+	0.352265i	−0.987145	−	0.159826i	$-0.948907\pi$
$97$	−1.26276	+	3.46941i	−0.128214	+	0.352265i	0.858931	+	0.512091i	$0.171129\pi$
$98$		0			0
$99$	−4.09533	+	4.88063i	−0.411596	+	0.490521i
$100$		0			0
$101$	−2.67373	+	15.1635i	−0.266046	+	1.50882i	0.499994	+	0.866029i	$0.333335\pi$
$101$	−2.67373	+	15.1635i	−0.266046	+	1.50882i	−0.766040	+	0.642792i	$0.777776\pi$
$102$		0			0
$103$	4.06923	+	7.04811i	0.400953	+	0.694471i	0.993841	−	0.110814i	$-0.0353457\pi$
$103$	4.06923	+	7.04811i	0.400953	+	0.694471i	−0.592888	+	0.805285i	$0.702012\pi$
$104$		0			0
$105$	−1.05582	−	2.90083i	−0.103037	−	0.283092i
$106$		0			0
$107$	4.86569	−	8.42762i	0.470384	−	0.814728i	−0.529043	−	0.848595i	$-0.677449\pi$
$107$	4.86569	−	8.42762i	0.470384	−	0.814728i	0.999426	+	0.0338668i	$0.0107822\pi$
$108$		0			0
$109$	3.75714	+	4.47759i	0.359869	+	0.428875i	0.915353	−	0.402652i	$-0.131912\pi$
$109$	3.75714	+	4.47759i	0.359869	+	0.428875i	−0.555484	+	0.831527i	$0.687467\pi$
$110$		0			0
$111$	0.925324	−	0.163160i	0.0878278	−	0.0154864i
$112$		0			0
$113$			0.691027i			0.0650063i	0.999472	+	0.0325032i	$0.0103479\pi$
$113$			0.691027i			0.0650063i	−0.999472	+	0.0325032i	$0.989652\pi$
$114$		0			0
$115$		−	0.680285i		−	0.0634369i
$116$		0			0
$117$	2.14934	−	0.378986i	0.198706	−	0.0350373i
$118$		0			0
$119$	−5.01446	−	5.97601i	−0.459675	−	0.547820i
$120$		0			0
$121$	14.7961	−	25.6276i	1.34510	−	2.32978i
$122$		0			0
$123$	−2.61477	−	7.18403i	−0.235766	−	0.647762i
$124$		0			0
$125$	6.04153	+	10.4642i	0.540371	+	0.935950i
$126$		0			0
$127$	−1.92145	+	10.8971i	−0.170501	+	0.966958i	0.772709	+	0.634760i	$0.218901\pi$
$127$	−1.92145	+	10.8971i	−0.170501	+	0.966958i	−0.943210	+	0.332197i	$0.892210\pi$
$128$		0			0
$129$	−3.71439	+	4.42664i	−0.327034	+	0.389744i
$130$		0			0
$131$	−0.989077	+	2.71747i	−0.0864161	+	0.237426i	−0.975372	−	0.220567i	$-0.929209\pi$
$131$	−0.989077	+	2.71747i	−0.0864161	+	0.237426i	0.888956	+	0.457993i	$0.151432\pi$
$132$		0			0
$133$	5.45923	+	5.75016i	0.473375	+	0.498603i
$134$		0			0
$135$	1.59473	+	0.580433i	0.137252	+	0.0499557i
$136$		0			0
$137$	12.5943	+	10.5679i	1.07600	+	0.902873i	0.995583	−	0.0938883i	$-0.0299296\pi$
$137$	12.5943	+	10.5679i	1.07600	+	0.902873i	0.0804192	+	0.996761i	$0.474374\pi$
$138$		0			0
$139$	8.59941	+	1.51631i	0.729392	+	0.128612i	0.525998	−	0.850486i	$-0.323692\pi$
$139$	8.59941	+	1.51631i	0.729392	+	0.128612i	0.203394	+	0.979097i	$0.434803\pi$
$140$		0			0
$141$	−8.14262	+	4.70114i	−0.685732	+	0.395908i
$142$		0			0
$143$	−13.0665	+	4.75583i	−1.09268	+	0.397702i
$144$		0			0
$145$	7.58780	+	4.38082i	0.630132	+	0.363807i
$146$		0			0
$147$	−2.82761	+	2.37265i	−0.233217	+	0.195692i
$148$		0			0
$149$	1.39036	+	7.88510i	0.113902	+	0.645973i	0.987288	+	0.158943i	$0.0508086\pi$
$149$	1.39036	+	7.88510i	0.113902	+	0.645973i	−0.873385	+	0.487030i	$0.838080\pi$
$150$		0			0
$151$	−23.0035			−1.87200			−0.936001	−	0.351997i	$-0.885503\pi$
$151$	−23.0035			−1.87200			−0.936001	+	0.351997i	$0.885503\pi$
$152$		0			0
$153$	4.28865			0.346717
$154$		0			0
$155$	−1.24813	−	7.07851i	−0.100252	−	0.568560i
$156$		0			0
$157$	−7.19585	+	6.03803i	−0.574291	+	0.481888i	−0.883067	−	0.469247i	$-0.844525\pi$
$157$	−7.19585	+	6.03803i	−0.574291	+	0.481888i	0.308776	+	0.951135i	$0.400081\pi$
$158$		0			0
$159$	−0.793793	−	0.458297i	−0.0629519	−	0.0363453i
$160$		0			0
$161$	0.685192	−	0.249390i	0.0540007	−	0.0196547i
$162$		0			0
$163$	−4.50130	+	2.59883i	−0.352569	+	0.203556i	−0.665816	−	0.746116i	$-0.731917\pi$
$163$	−4.50130	+	2.59883i	−0.352569	+	0.203556i	0.313247	+	0.949672i	$0.398583\pi$
$164$		0			0
$165$	−10.6481	−	1.87755i	−0.828956	−	0.146167i
$166$		0			0
$167$	9.83166	+	8.24974i	0.760796	+	0.638384i	0.938334	−	0.345730i	$-0.112369\pi$
$167$	9.83166	+	8.24974i	0.760796	+	0.638384i	−0.177538	+	0.984114i	$0.556813\pi$
$168$		0			0
$169$	−7.73999	−	2.81713i	−0.595384	−	0.216702i
$170$		0			0
$171$	−4.35071	+	0.267110i	−0.332707	+	0.0204264i
$172$		0			0
$173$	−3.01962	+	8.29633i	−0.229577	+	0.630758i	−0.999977	−	0.00680300i	$-0.997835\pi$
$173$	−3.01962	+	8.29633i	−0.229577	+	0.630758i	0.770400	+	0.637561i	$0.220057\pi$
$174$		0			0
$175$	−2.47872	+	2.95403i	−0.187374	+	0.223304i
$176$		0			0
$177$	2.00795	−	11.3876i	0.150927	−	0.855947i
$178$		0			0
$179$	−0.628936	−	1.08935i	−0.0470089	−	0.0814218i	0.841564	−	0.540158i	$-0.181636\pi$
$179$	−0.628936	−	1.08935i	−0.0470089	−	0.0814218i	−0.888572	+	0.458736i	$0.848302\pi$
$180$		0			0
$181$	8.94428	+	24.5742i	0.664823	+	1.82659i	0.553585	+	0.832792i	$0.313259\pi$
$181$	8.94428	+	24.5742i	0.664823	+	1.82659i	0.111238	+	0.993794i	$0.464519\pi$
$182$		0			0
$183$	−6.90335	+	11.9570i	−0.510311	+	0.883884i
$184$		0			0
$185$	1.02497	+	1.22151i	0.0753571	+	0.0898071i
$186$		0			0
$187$	−26.9088	+	4.74474i	−1.96776	+	0.346970i
$188$		0			0
$189$			1.81902i			0.132314i
$190$		0			0
$191$			0.466617i			0.0337632i	0.999857	+	0.0168816i	$0.00537384\pi$
$191$			0.466617i			0.0337632i	−0.999857	+	0.0168816i	$0.994626\pi$
$192$		0			0
$193$	−25.7369	+	4.53811i	−1.85258	+	0.326660i	−0.985257	−	0.171081i	$-0.945274\pi$
$193$	−25.7369	+	4.53811i	−1.85258	+	0.326660i	−0.867326	+	0.497741i	$0.834163\pi$
$194$		0			0
$195$	2.38079	+	2.83731i	0.170492	+	0.203184i
$196$		0			0
$197$	−2.78164	+	4.81795i	−0.198184	+	0.343264i	−0.947940	−	0.318450i	$-0.896838\pi$
$197$	−2.78164	+	4.81795i	−0.198184	+	0.343264i	0.749756	+	0.661715i	$0.230171\pi$
$198$		0			0
$199$	1.97168	+	5.41715i	0.139769	+	0.384011i	0.989752	−	0.142799i	$-0.0456101\pi$
$199$	1.97168	+	5.41715i	0.139769	+	0.384011i	−0.849983	+	0.526810i	$0.823388\pi$
$200$		0			0
$201$	3.45323	+	5.98116i	0.243572	+	0.421879i
$202$		0			0
$203$	−1.63076	+	9.24852i	−0.114457	+	0.649119i
$204$		0			0
$205$	8.33970	−	9.93887i	0.582470	−	0.694161i
$206$		0			0
$207$	−0.137101	+	0.376683i	−0.00952920	+	0.0261813i
$208$		0			0
$209$	27.0026	−	6.48935i	1.86781	−	0.448878i
$210$		0			0
$211$	0.822602	+	0.299403i	0.0566303	+	0.0206117i	0.370180	−	0.928960i	$-0.379296\pi$
$211$	0.822602	+	0.299403i	0.0566303	+	0.0206117i	−0.313550	+	0.949572i	$0.601518\pi$
$212$		0			0
$213$	0.701698	+	0.588794i	0.0480795	+	0.0403435i
$214$		0			0
$215$	−9.65766	−	1.70291i	−0.658647	−	0.116137i
$216$		0			0
$217$	6.67202	−	3.85209i	0.452926	−	0.261497i
$218$		0			0
$219$	−12.6580	+	4.60712i	−0.855346	+	0.311321i
$220$		0			0
$221$	8.10595	+	4.67997i	0.545265	+	0.314809i
$222$		0			0
$223$	17.4237	−	14.6202i	1.16678	−	0.979041i	0.166800	−	0.985991i	$-0.446657\pi$
$223$	17.4237	−	14.6202i	1.16678	−	0.979041i	0.999976	+	0.00694940i	$0.00221208\pi$
$224$		0			0
$225$	−0.368124	−	2.08774i	−0.0245416	−	0.139182i
$226$		0			0
$227$	23.3277			1.54831			0.774156	−	0.632995i	$-0.218175\pi$
$227$	23.3277			1.54831			0.774156	+	0.632995i	$0.218175\pi$
$228$		0			0
$229$	−6.96000			−0.459930			−0.229965	−	0.973199i	$-0.573861\pi$
$229$	−6.96000			−0.459930			−0.229965	+	0.973199i	$0.573861\pi$
$230$		0			0
$231$	−2.01246	−	11.4133i	−0.132410	−	0.750937i
$232$		0			0
$233$	9.68957	−	8.13051i	0.634785	−	0.532648i	−0.267627	−	0.963523i	$-0.586239\pi$
$233$	9.68957	−	8.13051i	0.634785	−	0.532648i	0.902412	+	0.430875i	$0.141795\pi$
$234$		0			0
$235$	−13.8186	−	7.97819i	−0.901428	−	0.520439i
$236$		0			0
$237$	12.7823	−	4.65238i	0.830300	−	0.302205i
$238$		0			0
$239$	−13.8282	+	7.98370i	−0.894470	+	0.516423i	−0.875402	−	0.483395i	$-0.839403\pi$
$239$	−13.8282	+	7.98370i	−0.894470	+	0.516423i	−0.0190683	+	0.999818i	$0.506070\pi$
$240$		0			0
$241$	−12.3512	−	2.17785i	−0.795610	−	0.140288i	−0.238954	−	0.971031i	$-0.576805\pi$
$241$	−12.3512	−	2.17785i	−0.795610	−	0.140288i	−0.556656	+	0.830743i	$0.687916\pi$
$242$		0			0
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$		0			0
$245$	−5.88643	−	2.14248i	−0.376070	−	0.136878i
$246$		0			0
$247$	−8.51473	−	4.24283i	−0.541779	−	0.269965i
$248$		0			0
$249$	−0.601317	+	1.65210i	−0.0381069	+	0.104698i
$250$		0			0
$251$	−2.31281	+	2.75630i	−0.145984	+	0.173976i	−0.834081	−	0.551642i	$-0.814002\pi$
$251$	−2.31281	+	2.75630i	−0.145984	+	0.173976i	0.688098	+	0.725618i	$0.258446\pi$
$252$		0			0
$253$	0.443488	−	2.51515i	0.0278818	−	0.158126i
$254$		0			0
$255$	3.63908	+	6.30306i	0.227888	+	0.394713i
$256$		0			0
$257$	−2.21224	−	6.07807i	−0.137996	−	0.379140i	0.851375	−	0.524558i	$-0.175769\pi$
$257$	−2.21224	−	6.07807i	−0.137996	−	0.379140i	−0.989370	+	0.145418i	$0.953547\pi$
$258$		0			0
$259$	−0.854572	+	1.48016i	−0.0531005	+	0.0919728i
$260$		0			0
$261$	−3.31858	−	3.95493i	−0.205415	−	0.244804i
$262$		0			0
$263$	−3.11265	+	0.548844i	−0.191934	+	0.0338432i	−0.268789	−	0.963199i	$-0.586623\pi$
$263$	−3.11265	+	0.548844i	−0.191934	+	0.0338432i	0.0768546	+	0.997042i	$0.475512\pi$
$264$		0			0
$265$		−	1.55553i		−	0.0955552i
$266$		0			0
$267$			2.23858i			0.136999i
$268$		0			0
$269$	22.9931	−	4.05431i	1.40192	−	0.247195i	0.578985	−	0.815338i	$-0.303449\pi$
$269$	22.9931	−	4.05431i	1.40192	−	0.247195i	0.822930	+	0.568143i	$0.192338\pi$
$270$		0			0
$271$	−3.34390	−	3.98510i	−0.203127	−	0.242078i	0.654858	−	0.755752i	$-0.272728\pi$
$271$	−3.34390	−	3.98510i	−0.203127	−	0.242078i	−0.857985	+	0.513674i	$0.828284\pi$
$272$		0			0
$273$	−1.98500	+	3.43811i	−0.120137	+	0.208084i
$274$		0			0
$275$	4.61953	+	12.6920i	0.278568	+	0.765359i
$276$		0			0
$277$	14.5353	+	25.1759i	0.873342	+	1.51267i	0.858518	+	0.512783i	$0.171386\pi$
$277$	14.5353	+	25.1759i	0.873342	+	1.51267i	0.0148243	+	0.999890i	$0.495281\pi$
$278$		0			0
$279$	−0.735462	+	4.17101i	−0.0440310	+	0.249712i
$280$		0			0
$281$	−0.486568	+	0.579870i	−0.0290262	+	0.0345921i	−0.780362	−	0.625328i	$-0.784965\pi$
$281$	−0.486568	+	0.579870i	−0.0290262	+	0.0345921i	0.751336	+	0.659920i	$0.229410\pi$
$282$		0			0
$283$	−5.27937	+	14.5050i	−0.313826	+	0.862230i	0.678049	+	0.735017i	$0.262826\pi$
$283$	−5.27937	+	14.5050i	−0.313826	+	0.862230i	−0.991875	+	0.127214i	$0.959397\pi$
$284$		0			0
$285$	−4.08431	−	6.16762i	−0.241933	−	0.365338i
$286$		0			0
$287$	13.0679	+	4.75632i	0.771372	+	0.280756i
$288$		0			0
$289$	1.06673	+	0.895092i	0.0627488	+	0.0526525i
$290$		0			0
$291$	3.63597	+	0.641120i	0.213145	+	0.0375831i
$292$		0			0
$293$	−28.1072	+	16.2277i	−1.64204	+	0.948034i	−0.661937	+	0.749560i	$0.730265\pi$
$293$	−28.1072	+	16.2277i	−1.64204	+	0.948034i	−0.980106	+	0.198474i	$0.936401\pi$
$294$		0			0
$295$	18.4403	−	6.71173i	1.07364	−	0.390772i
$296$		0			0
$297$	5.51762	+	3.18560i	0.320165	+	0.184847i
$298$		0			0
$299$	−0.670188	+	0.562355i	−0.0387580	+	0.0325218i
$300$		0			0
$301$	−1.82527	−	10.3516i	−0.105207	−	0.596657i
$302$		0			0
$303$	15.3974			0.884557
$304$		0			0
$305$	−23.4310			−1.34165
$306$		0			0
$307$	−0.709797	−	4.02546i	−0.0405103	−	0.229745i	0.957830	−	0.287335i	$-0.0927694\pi$
$307$	−0.709797	−	4.02546i	−0.0405103	−	0.229745i	−0.998340	+	0.0575902i	$0.981658\pi$
$308$		0			0
$309$	6.23442	−	5.23130i	0.354664	−	0.297598i
$310$		0			0
$311$	−22.7485	−	13.1338i	−1.28995	−	0.744752i	−0.311303	−	0.950311i	$-0.600766\pi$
$311$	−22.7485	−	13.1338i	−1.28995	−	0.744752i	−0.978645	+	0.205559i	$0.934099\pi$
$312$		0			0
$313$	−15.2948	+	5.56685i	−0.864513	+	0.314657i	−0.735943	−	0.677043i	$-0.763261\pi$
$313$	−15.2948	+	5.56685i	−0.864513	+	0.314657i	−0.128570	+	0.991700i	$0.541039\pi$
$314$		0			0
$315$	−2.67342	+	1.54350i	−0.150630	+	0.0869665i
$316$		0			0
$317$	−27.0407	−	4.76800i	−1.51876	−	0.267798i	−0.648812	−	0.760949i	$-0.724734\pi$
$317$	−27.0407	−	4.76800i	−1.51876	−	0.267798i	−0.869944	+	0.493151i	$0.835845\pi$
$318$		0			0
$319$	25.1976	+	21.1433i	1.41080	+	1.18380i
$320$		0			0
$321$	−9.14450	−	3.32833i	−0.510396	−	0.185769i
$322$		0			0
$323$	−15.0297	−	11.1160i	−0.836275	−	0.618512i
$324$		0			0
$325$	1.58245	−	4.34773i	0.0877783	−	0.241169i
$326$		0			0
$327$	3.75714	−	4.47759i	0.207770	−	0.247611i
$328$		0			0
$329$	2.96989	−	16.8431i	0.163735	−	0.928589i
$330$		0			0
$331$	9.68350	+	16.7723i	0.532253	+	0.921890i	0.999291	+	0.0376522i	$0.0119879\pi$
$331$	9.68350	+	16.7723i	0.532253	+	0.921890i	−0.467038	+	0.884237i	$0.654679\pi$
$332$		0			0
$333$	−0.321362	−	0.882934i	−0.0176105	−	0.0483845i
$334$		0			0
$335$	−5.86038	+	10.1505i	−0.320186	+	0.554579i
$336$		0			0
$337$	9.70507	+	11.5661i	0.528669	+	0.630043i	0.962608	−	0.270899i	$-0.0873210\pi$
$337$	9.70507	+	11.5661i	0.528669	+	0.630043i	−0.433939	+	0.900942i	$0.642877\pi$
$338$		0			0
$339$	0.680529	−	0.119996i	0.0369612	−	0.00651726i
$340$		0			0
$341$		−	26.9843i		−	1.46128i
$342$		0			0
$343$		−	19.4474i		−	1.05006i
$344$		0			0
$345$	−0.669949	+	0.118130i	−0.0360689	+	0.00635991i
$346$		0			0
$347$	−11.1424	−	13.2790i	−0.598153	−	0.712852i	0.378998	−	0.925398i	$-0.376269\pi$
$347$	−11.1424	−	13.2790i	−0.598153	−	0.712852i	−0.977151	+	0.212546i	$0.931824\pi$
$348$		0			0
$349$	6.22990	−	10.7905i	0.333479	−	0.577602i	−0.649713	−	0.760180i	$-0.725111\pi$
$349$	6.22990	−	10.7905i	0.333479	−	0.577602i	0.983191	+	0.182578i	$0.0584441\pi$
$350$		0			0
$351$	−0.746457	−	2.05087i	−0.0398429	−	0.109467i
$352$		0			0
$353$	11.2871	+	19.5499i	0.600754	+	1.04054i	0.992707	+	0.120551i	$0.0384661\pi$
$353$	11.2871	+	19.5499i	0.600754	+	1.04054i	−0.391953	+	0.919985i	$0.628201\pi$
$354$		0			0
$355$	−0.269940	+	1.53090i	−0.0143269	+	0.0812520i
$356$		0			0
$357$	−5.01446	+	5.97601i	−0.265394	+	0.316284i
$358$		0			0
$359$	−3.28344	+	9.02118i	−0.173293	+	0.476120i	−0.995685	−	0.0928029i	$-0.970417\pi$
$359$	−3.28344	+	9.02118i	−0.173293	+	0.476120i	0.822391	+	0.568923i	$0.192640\pi$
$360$		0			0
$361$	15.9395	+	10.3408i	0.838922	+	0.544251i
$362$		0			0
$363$	−27.8076	−	10.1211i	−1.45952	−	0.531222i
$364$		0			0
$365$	−17.5119	−	14.6942i	−0.916614	−	0.769130i
$366$		0			0
$367$	10.4930	+	1.85020i	0.547732	+	0.0965798i	0.440664	−	0.897672i	$-0.354743\pi$
$367$	10.4930	+	1.85020i	0.547732	+	0.0965798i	0.107067	+	0.994252i	$0.465854\pi$
$368$		0			0
$369$	−6.62084	+	3.82254i	−0.344667	+	0.198994i
$370$		0			0
$371$	1.56675	−	0.570250i	0.0813415	−	0.0296059i
$372$		0			0
$373$	−0.584882	−	0.337682i	−0.0302841	−	0.0174845i	0.484782	−	0.874635i	$-0.338899\pi$
$373$	−0.584882	−	0.337682i	−0.0302841	−	0.0174845i	−0.515066	+	0.857151i	$0.672232\pi$
$374$		0			0
$375$	9.25616	−	7.76684i	0.477986	−	0.401078i
$376$		0			0
$377$	−1.95662	−	11.0966i	−0.100771	−	0.571502i
$378$		0			0
$379$	6.26208			0.321661			0.160831	−	0.986982i	$-0.448583\pi$
$379$	6.26208			0.321661			0.160831	+	0.986982i	$0.448583\pi$
$380$		0			0
$381$	11.0652			0.566885
$382$		0			0
$383$	−6.00085	−	34.0325i	−0.306629	−	1.73898i	−0.615736	−	0.787952i	$-0.711141\pi$
$383$	−6.00085	−	34.0325i	−0.306629	−	1.73898i	0.309107	−	0.951027i	$-0.399970\pi$
$384$		0			0
$385$	15.0665	−	12.6423i	0.767860	−	0.644311i
$386$		0			0
$387$	5.00438	+	2.88928i	0.254387	+	0.146870i
$388$		0			0
$389$	7.41893	−	2.70027i	0.376155	−	0.136909i	−0.147022	−	0.989133i	$-0.546969\pi$
$389$	7.41893	−	2.70027i	0.376155	−	0.136909i	0.523177	+	0.852224i	$0.324747\pi$
$390$		0			0
$391$	−1.48882	+	0.859569i	−0.0752927	+	0.0434703i
$392$		0			0
$393$	2.84793	+	0.502168i	0.143659	+	0.0253310i
$394$		0			0
$395$	17.6839	+	14.8386i	0.889774	+	0.746609i
$396$		0			0
$397$	19.7548	+	7.19015i	0.991464	+	0.360863i	0.786287	−	0.617861i	$-0.212001\pi$
$397$	19.7548	+	7.19015i	0.991464	+	0.360863i	0.205177	+	0.978725i	$0.434223\pi$
$398$		0			0
$399$	4.71482	−	6.37480i	0.236036	−	0.319139i
$400$		0			0
$401$	−4.96337	+	13.6367i	−0.247859	+	0.680986i	0.751905	+	0.659271i	$0.229135\pi$
$401$	−4.96337	+	13.6367i	−0.247859	+	0.680986i	−0.999764	+	0.0217154i	$0.993087\pi$
$402$		0			0
$403$	−5.94169	+	7.08104i	−0.295977	+	0.352732i
$404$		0			0
$405$	0.294694	−	1.67129i	0.0146434	−	0.0830471i
$406$		0			0
$407$	2.99319	+	5.18435i	0.148367	+	0.256979i
$408$		0			0
$409$	−9.06937	−	24.9179i	−0.448451	−	1.23211i	−0.933802	−	0.357791i	$-0.883530\pi$
$409$	−9.06937	−	24.9179i	−0.448451	−	1.23211i	0.485350	−	0.874320i	$-0.338692\pi$
$410$		0			0
$411$	8.22033	−	14.2380i	0.405479	−	0.702310i
$412$		0			0
$413$	13.5203	+	16.1129i	0.665290	+	0.792862i
$414$		0			0
$415$	−2.93835	+	0.518111i	−0.144238	+	0.0254331i
$416$		0			0
$417$		−	8.73207i		−	0.427611i
$418$		0			0
$419$		−	12.8872i		−	0.629583i	−0.949161	−	0.314791i	$-0.898065\pi$
$419$		−	12.8872i		−	0.629583i	0.949161	−	0.314791i	$-0.101935\pi$
$420$		0			0
$421$	−7.84436	+	1.38317i	−0.382311	+	0.0674117i	−0.361501	−	0.932372i	$-0.617736\pi$
$421$	−7.84436	+	1.38317i	−0.382311	+	0.0674117i	−0.0208099	+	0.999783i	$0.506624\pi$
$422$		0			0
$423$	6.04367	+	7.20257i	0.293854	+	0.350201i
$424$		0			0
$425$	4.54585	−	7.87364i	0.220506	−	0.381928i
$426$		0			0
$427$	−8.58971	−	23.6000i	−0.415685	−	1.14209i
$428$		0			0
$429$	6.95255	+	12.0422i	0.335673	+	0.581402i
$430$		0			0
$431$	3.10149	−	17.5895i	0.149394	−	0.847254i	−0.814340	−	0.580388i	$-0.802901\pi$
$431$	3.10149	−	17.5895i	0.149394	−	0.847254i	0.963734	−	0.266866i	$-0.0859881\pi$
$432$		0			0
$433$	−10.9635	+	13.0658i	−0.526873	+	0.627903i	−0.962192	−	0.272373i	$-0.912191\pi$
$433$	−10.9635	+	13.0658i	−0.526873	+	0.627903i	0.435318	+	0.900277i	$0.356636\pi$
$434$		0			0
$435$	2.99665	−	8.23324i	0.143679	−	0.394754i
$436$		0			0
$437$	1.45682	−	0.964735i	0.0696893	−	0.0461495i
$438$		0			0
$439$	−0.735068	−	0.267543i	−0.0350829	−	0.0127691i	0.324419	−	0.945913i	$-0.394831\pi$
$439$	−0.735068	−	0.267543i	−0.0350829	−	0.0127691i	−0.359502	+	0.933144i	$0.617053\pi$
$440$		0			0
$441$	2.82761	+	2.37265i	0.134648	+	0.112983i
$442$		0			0
$443$	37.8909	+	6.68118i	1.80025	+	0.317433i	0.970572	−	0.240810i	$-0.0774132\pi$
$443$	37.8909	+	6.68118i	1.80025	+	0.317433i	0.829677	+	0.558243i	$0.188524\pi$
$444$		0			0
$445$	−3.29007	+	1.89952i	−0.155964	+	0.0900459i
$446$		0			0
$447$	7.52388	−	2.73847i	0.355867	−	0.129525i
$448$		0			0
$449$	−26.2077	−	15.1310i	−1.23682	−	0.714078i	−0.268377	−	0.963314i	$-0.586487\pi$
$449$	−26.2077	−	15.1310i	−1.23682	−	0.714078i	−0.968443	+	0.249236i	$0.919821\pi$
$450$		0			0
$451$	37.3128	−	31.3092i	1.75699	−	1.47429i
$452$		0			0
$453$	3.99452	+	22.6541i	0.187679	+	1.06438i
$454$		0			0
$455$	−6.73736			−0.315852
$456$		0			0
$457$	7.19147			0.336403			0.168201	−	0.985753i	$-0.446204\pi$
$457$	7.19147			0.336403			0.168201	+	0.985753i	$0.446204\pi$
$458$		0			0
$459$	−0.744716	−	4.22350i	−0.0347604	−	0.197136i
$460$		0			0
$461$	4.43340	−	3.72006i	0.206484	−	0.173261i	−0.533681	−	0.845686i	$-0.679192\pi$
$461$	4.43340	−	3.72006i	0.206484	−	0.173261i	0.740165	+	0.672425i	$0.234747\pi$
$462$		0			0
$463$	2.74861	+	1.58691i	0.127739	+	0.0737501i	0.562508	−	0.826792i	$-0.309837\pi$
$463$	2.74861	+	1.58691i	0.127739	+	0.0737501i	−0.434769	+	0.900542i	$0.643170\pi$
$464$		0			0
$465$	−6.75424	+	2.45834i	−0.313220	+	0.114003i
$466$		0			0
$467$	13.9071	−	8.02927i	0.643544	−	0.371551i	−0.142434	−	0.989804i	$-0.545493\pi$
$467$	13.9071	−	8.02927i	0.643544	−	0.371551i	0.785979	+	0.618254i	$0.212160\pi$
$468$		0			0
$469$	−12.3721	−	2.18153i	−0.571290	−	0.100734i
$470$		0			0
$471$	7.19585	+	6.03803i	0.331567	+	0.278218i
$472$		0			0
$473$	−34.5961	−	12.5919i	−1.59073	−	0.578978i
$474$		0			0
$475$	−4.12123	+	8.27070i	−0.189095	+	0.379486i
$476$		0			0
$477$	−0.313493	+	0.861316i	−0.0143539	+	0.0394370i
$478$		0			0
$479$	−21.2206	+	25.2897i	−0.969593	+	1.15552i	0.0182143	+	0.999834i	$0.494202\pi$
$479$	−21.2206	+	25.2897i	−0.969593	+	1.15552i	−0.987807	+	0.155682i	$0.950243\pi$
$480$		0			0
$481$	0.356095	−	2.01951i	0.0162365	−	0.0920819i
$482$		0			0
$483$	−0.364583	−	0.631477i	−0.0165891	−	0.0287332i
$484$		0			0
$485$	2.14300	+	5.88784i	0.0973085	+	0.267353i
$486$		0			0
$487$	2.76185	−	4.78367i	0.125151	−	0.216769i	−0.796641	−	0.604453i	$-0.793392\pi$
$487$	2.76185	−	4.78367i	0.125151	−	0.216769i	0.921792	+	0.387684i	$0.126725\pi$
$488$		0			0
$489$	3.34099	+	3.98163i	0.151085	+	0.180056i
$490$		0			0
$491$	22.0864	−	3.89442i	0.996744	−	0.175753i	0.348601	−	0.937271i	$-0.386657\pi$
$491$	22.0864	−	3.89442i	0.996744	−	0.175753i	0.648143	+	0.761518i	$0.275546\pi$
$492$		0			0
$493$		−	22.1414i		−	0.997198i
$494$		0			0
$495$			10.8124i			0.485981i
$496$		0			0
$497$	−1.64091	+	0.289336i	−0.0736047	+	0.0129785i
$498$		0			0
$499$	1.82781	+	2.17830i	0.0818241	+	0.0975141i	0.805403	−	0.592727i	$-0.201949\pi$
$499$	1.82781	+	2.17830i	0.0818241	+	0.0975141i	−0.723579	+	0.690241i	$0.757504\pi$
$500$		0			0
$501$	6.41716	−	11.1148i	0.286697	−	0.496575i
$502$		0			0
$503$	9.43970	+	25.9354i	0.420895	+	1.15640i	0.951195	+	0.308590i	$0.0998572\pi$
$503$	9.43970	+	25.9354i	0.420895	+	1.15640i	−0.530300	+	0.847810i	$0.677921\pi$
$504$		0			0
$505$	13.0652	+	22.6297i	0.581396	+	1.00701i
$506$		0			0
$507$	−1.43029	+	8.11159i	−0.0635215	+	0.360248i
$508$		0			0
$509$	10.8480	−	12.9281i	0.480827	−	0.573027i	−0.470033	−	0.882649i	$-0.655758\pi$
$509$	10.8480	−	12.9281i	0.480827	−	0.573027i	0.950860	+	0.309622i	$0.100202\pi$
$510$		0			0
$511$	8.38043	−	23.0251i	0.370729	−	1.01857i
$512$		0			0
$513$	1.01854	+	4.23823i	0.0449698	+	0.187122i
$514$		0			0
$515$	12.9786	+	4.72383i	0.571906	+	0.208157i
$516$		0			0
$517$	−45.8891	−	38.5055i	−2.01820	−	1.69347i
$518$		0			0
$519$	8.69464	+	1.53310i	0.381652	+	0.0672956i
$520$		0			0
$521$	−10.1975	+	5.88751i	−0.446759	+	0.257937i	−0.706461	−	0.707752i	$-0.749709\pi$
$521$	−10.1975	+	5.88751i	−0.446759	+	0.257937i	0.259701	+	0.965689i	$0.416376\pi$
$522$		0			0
$523$	23.2631	−	8.46708i	1.01723	−	0.370240i	0.221022	−	0.975269i	$-0.429061\pi$
$523$	23.2631	−	8.46708i	1.01723	−	0.370240i	0.796203	+	0.605029i	$0.206839\pi$
$524$		0			0
$525$	3.33958	+	1.92811i	0.145751	+	0.0841494i
$526$		0			0
$527$	−13.9144	+	11.6756i	−0.606121	+	0.508596i
$528$		0			0
$529$	3.96601	+	22.4923i	0.172435	+	0.977928i
$530$		0			0
$531$	−11.5633			−0.501805
$532$		0			0
$533$	−16.6853			−0.722723
$534$		0			0
$535$	−2.86777	−	16.2640i	−0.123985	−	0.703152i
$536$		0			0
$537$	−0.963586	+	0.808545i	−0.0415818	+	0.0348913i
$538$		0			0
$539$	−20.3665	−	11.7586i	−0.877249	−	0.506480i
$540$		0			0
$541$	−13.4252	+	4.88638i	−0.577195	+	0.210082i	−0.614088	−	0.789237i	$-0.710476\pi$
$541$	−13.4252	+	4.88638i	−0.577195	+	0.210082i	0.0368933	+	0.999319i	$0.488254\pi$
$542$		0			0
$543$	22.6477	−	13.0757i	0.971906	−	0.561130i
$544$		0			0
$545$	9.76882	+	1.72251i	0.418450	+	0.0737841i
$546$		0			0
$547$	−13.9797	−	11.7303i	−0.597727	−	0.501553i	0.292987	−	0.956116i	$-0.405351\pi$
$547$	−13.9797	−	11.7303i	−0.597727	−	0.501553i	−0.890714	+	0.454564i	$0.849795\pi$
$548$		0			0
$549$	12.9741	+	4.72217i	0.553719	+	0.201537i
$550$		0			0
$551$	1.37903	+	22.4618i	0.0587487	+	0.956904i
$552$		0			0
$553$	−8.46276	+	23.2512i	−0.359873	+	0.988743i
$554$		0			0
$555$	1.02497	−	1.22151i	0.0435075	−	0.0518502i
$556$		0			0
$557$	2.84249	−	16.1206i	0.120440	−	0.683050i	−0.863472	−	0.504397i	$-0.831715\pi$
$557$	2.84249	−	16.1206i	0.120440	−	0.683050i	0.983912	−	0.178653i	$-0.0571741\pi$
$558$		0			0
$559$	6.30584	+	10.9220i	0.266708	+	0.461953i
$560$		0			0
$561$	9.34531	+	25.6760i	0.394559	+	1.08404i
$562$		0			0
$563$	18.8443	−	32.6393i	0.794194	−	1.37558i	−0.129156	−	0.991624i	$-0.541227\pi$
$563$	18.8443	−	32.6393i	0.794194	−	1.37558i	0.923350	−	0.383960i	$-0.125440\pi$
$564$		0			0
$565$	0.753812	+	0.898358i	0.0317131	+	0.0377942i
$566$		0			0
$567$	1.79138	−	0.315869i	0.0752309	−	0.0132652i
$568$		0			0
$569$		−	32.7790i		−	1.37417i	−0.726579	−	0.687083i	$-0.758891\pi$
$569$		−	32.7790i		−	1.37417i	0.726579	−	0.687083i	$-0.241109\pi$
$570$		0			0
$571$			20.2350i			0.846810i	0.905940	+	0.423405i	$0.139165\pi$
$571$			20.2350i			0.846810i	−0.905940	+	0.423405i	$0.860835\pi$
$572$		0			0
$573$	0.459528	−	0.0810272i	0.0191971	−	0.00338496i
$574$		0			0
$575$	0.546238	+	0.650981i	0.0227797	+	0.0271478i
$576$		0			0
$577$	8.19636	−	14.1965i	0.341219	−	0.591008i	−0.643441	−	0.765496i	$-0.722494\pi$
$577$	8.19636	−	14.1965i	0.341219	−	0.591008i	0.984659	+	0.174488i	$0.0558269\pi$
$578$		0			0
$579$	8.93833	+	24.5579i	0.371464	+	1.02059i
$580$		0			0
$581$	−1.59904	−	2.76961i	−0.0663392	−	0.114903i
$582$		0			0
$583$	1.01407	−	5.75108i	0.0419985	−	0.238186i
$584$		0			0
$585$	2.38079	−	2.83731i	0.0984335	−	0.117308i
$586$		0			0
$587$	1.18017	−	3.24249i	0.0487108	−	0.133832i	−0.912952	−	0.408068i	$-0.866203\pi$
$587$	1.18017	−	3.24249i	0.0487108	−	0.133832i	0.961662	+	0.274236i	$0.0884249\pi$
$588$		0			0
$589$	13.3886	−	12.7111i	0.551666	−	0.523754i
$590$		0			0
$591$	5.22778	+	1.90276i	0.215042	+	0.0782689i
$592$		0			0
$593$	−11.7810	−	9.88542i	−0.483787	−	0.405946i	0.368006	−	0.929823i	$-0.380040\pi$
$593$	−11.7810	−	9.88542i	−0.483787	−	0.405946i	−0.851794	+	0.523878i	$0.824485\pi$
$594$		0			0
$595$	−13.0379	−	2.29894i	−0.534504	−	0.0942474i
$596$		0			0
$597$	4.99247	−	2.88240i	0.204328	−	0.117969i
$598$		0			0
$599$	11.5308	−	4.19686i	0.471135	−	0.171479i	−0.0955315	−	0.995426i	$-0.530455\pi$
$599$	11.5308	−	4.19686i	0.471135	−	0.171479i	0.566666	+	0.823947i	$0.308233\pi$
$600$		0			0
$601$	8.13877	+	4.69892i	0.331988	+	0.191673i	0.656723	−	0.754132i	$-0.271942\pi$
$601$	8.13877	+	4.69892i	0.331988	+	0.191673i	−0.324736	+	0.945805i	$0.605275\pi$
$602$		0			0
$603$	5.29065	−	4.43938i	0.215452	−	0.180786i
$604$		0			0
$605$	−8.72065	−	49.4572i	−0.354545	−	2.01072i
$606$		0			0
$607$	−35.2473			−1.43064			−0.715321	−	0.698796i	$-0.753720\pi$
$607$	−35.2473			−1.43064			−0.715321	+	0.698796i	$0.753720\pi$
$608$		0			0
$609$	9.39120			0.380551
$610$		0			0
$611$	3.56334	+	20.2087i	0.144157	+	0.817556i
$612$		0			0
$613$	20.6126	−	17.2960i	0.832535	−	0.698580i	−0.123336	−	0.992365i	$-0.539359\pi$
$613$	20.6126	−	17.2960i	0.832535	−	0.698580i	0.955872	+	0.293785i	$0.0949149\pi$
$614$		0			0
$615$	−11.2360	−	6.48713i	−0.453081	−	0.261587i
$616$		0			0
$617$	−36.6049	+	13.3231i	−1.47366	+	0.536368i	−0.949091	−	0.315001i	$-0.897995\pi$
$617$	−36.6049	+	13.3231i	−1.47366	+	0.536368i	−0.524567	+	0.851369i	$0.675773\pi$
$618$		0			0
$619$	33.6354	−	19.4194i	1.35192	−	0.780532i	0.363403	−	0.931632i	$-0.381615\pi$
$619$	33.6354	−	19.4194i	1.35192	−	0.780532i	0.988519	+	0.151099i	$0.0482814\pi$
$620$		0			0
$621$	0.394768	+	0.0696082i	0.0158415	+	0.00279328i
$622$		0			0
$623$	−3.11935	−	2.61745i	−0.124974	−	0.104866i
$624$		0			0
$625$	9.30871	+	3.38809i	0.372348	+	0.135524i
$626$		0			0
$627$	−11.0797	−	25.4655i	−0.442481	−	1.01699i
$628$		0			0
$629$	1.37821	−	3.78659i	0.0549527	−	0.150981i
$630$		0			0
$631$	24.7327	−	29.4753i	0.984593	−	1.17339i	−0.000259682	−	1.00000i	$-0.500083\pi$
$631$	24.7327	−	29.4753i	0.984593	−	1.17339i	0.984853	−	0.173392i	$-0.0554729\pi$
$632$		0			0
$633$	0.152011	−	0.862096i	0.00604189	−	0.0342652i
$634$		0			0
$635$	9.38919	+	16.2626i	0.372599	+	0.645360i
$636$		0			0
$637$	2.75531	+	7.57014i	0.109169	+	0.299940i
$638$		0			0
$639$	0.458001	−	0.793280i	0.0181182	−	0.0313817i
$640$		0			0
$641$	8.77959	+	10.4631i	0.346773	+	0.413268i	0.911036	−	0.412327i	$-0.135284\pi$
$641$	8.77959	+	10.4631i	0.346773	+	0.413268i	−0.564263	+	0.825595i	$0.690840\pi$
$642$		0			0
$643$	−10.9475	+	1.93034i	−0.431727	+	0.0761251i	−0.385289	−	0.922796i	$-0.625898\pi$
$643$	−10.9475	+	1.93034i	−0.431727	+	0.0761251i	−0.0464380	+	0.998921i	$0.514787\pi$
$644$		0			0
$645$			9.80664i			0.386136i
$646$		0			0
$647$		−	4.44194i		−	0.174631i	−0.996181	−	0.0873153i	$-0.972171\pi$
$647$		−	4.44194i		−	0.174631i	0.996181	−	0.0873153i	$-0.0278288\pi$
$648$		0			0
$649$	72.5530	−	12.7930i	2.84795	−	0.502171i
$650$		0			0
$651$	−4.95215	−	5.90174i	−0.194090	−	0.231308i
$652$		0			0
$653$	9.29168	−	16.0937i	0.363612	−	0.629794i	−0.624941	−	0.780672i	$-0.714877\pi$
$653$	9.29168	−	16.0937i	0.363612	−	0.629794i	0.988552	+	0.150878i	$0.0482102\pi$
$654$		0			0
$655$	1.67854	+	4.61174i	0.0655858	+	0.180196i
$656$		0			0
$657$	6.73517	+	11.6656i	0.262764	+	0.455120i
$658$		0			0
$659$	−5.56868	+	31.5815i	−0.216925	+	1.23024i	0.660610	+	0.750729i	$0.270298\pi$
$659$	−5.56868	+	31.5815i	−0.216925	+	1.23024i	−0.877535	+	0.479513i	$0.840813\pi$
$660$		0			0
$661$	−27.6714	+	32.9775i	−1.07629	+	1.28267i	−0.119206	+	0.992870i	$0.538035\pi$
$661$	−27.6714	+	32.9775i	−1.07629	+	1.28267i	−0.957086	+	0.289805i	$0.906409\pi$
$662$		0			0
$663$	3.20129	−	8.79547i	0.124328	−	0.341588i
$664$		0			0
$665$	13.3698	+	1.52017i	0.518458	+	0.0589495i
$666$		0			0
$667$	1.94473	+	0.707825i	0.0753004	+	0.0274071i
$668$		0			0
$669$	−17.4237	−	14.6202i	−0.673638	−	0.565250i
$670$		0			0
$671$	−86.6290	−	15.2750i	−3.34427	−	0.589686i
$672$		0			0
$673$	−28.6140	+	16.5203i	−1.10299	+	0.636810i	−0.937004	−	0.349319i	$-0.886413\pi$
$673$	−28.6140	+	16.5203i	−1.10299	+	0.636810i	−0.165983	+	0.986129i	$0.553080\pi$
$674$		0			0
$675$	−1.99210	+	0.725063i	−0.0766758	+	0.0279077i
$676$		0			0
$677$	−37.8777	−	21.8687i	−1.45576	−	0.840482i	−0.456958	−	0.889488i	$-0.651061\pi$
$677$	−37.8777	−	21.8687i	−1.45576	−	0.840482i	−0.998798	+	0.0490066i	$0.984394\pi$
$678$		0			0
$679$	−5.14470	+	4.31691i	−0.197435	+	0.165668i
$680$		0			0
$681$	−4.05081	−	22.9733i	−0.155227	−	0.880337i
$682$		0			0
$683$	−31.0216			−1.18701			−0.593504	−	0.804831i	$-0.702256\pi$
$683$	−31.0216			−1.18701			−0.593504	+	0.804831i	$0.702256\pi$
$684$		0			0
$685$	27.9010			1.06604
$686$		0			0
$687$	1.20859	+	6.85427i	0.0461107	+	0.261507i
$688$		0			0
$689$	−1.53244	+	1.28587i	−0.0583813	+	0.0489878i
$690$		0			0
$691$	−15.4922	−	8.94445i	−0.589353	−	0.340263i	0.175489	−	0.984481i	$-0.443849\pi$
$691$	−15.4922	−	8.94445i	−0.589353	−	0.340263i	−0.764841	+	0.644219i	$0.777183\pi$
$692$		0			0
$693$	−10.8904	+	3.96378i	−0.413692	+	0.150572i
$694$		0			0
$695$	12.8336	−	7.40948i	0.486806	−	0.281057i
$696$		0			0
$697$	−32.2890	−	5.69342i	−1.22303	−	0.215654i
$698$		0			0
$699$	−9.68957	−	8.13051i	−0.366493	−	0.307524i
$700$		0			0
$701$	3.32764	+	1.21116i	0.125683	+	0.0457449i	0.404096	−	0.914717i	$-0.367586\pi$
$701$	3.32764	+	1.21116i	0.125683	+	0.0457449i	−0.278413	+	0.960461i	$0.589808\pi$
$702$		0			0
$703$	−1.16231	+	3.92722i	−0.0438374	+	0.148118i
$704$		0			0
$705$	−5.45740	+	14.9941i	−0.205538	+	0.564710i
$706$		0			0
$707$	−18.0033	+	21.4554i	−0.677082	+	0.806915i
$708$		0			0
$709$	6.18291	−	35.0650i	0.232204	−	1.31689i	−0.616219	−	0.787575i	$-0.711336\pi$
$709$	6.18291	−	35.0650i	0.232204	−	1.31689i	0.848423	−	0.529319i	$-0.177553\pi$
$710$		0			0
$711$	−6.80133	−	11.7802i	−0.255070	−	0.441794i
$712$		0			0
$713$	−0.580673	−	1.59539i	−0.0217464	−	0.0597477i
$714$		0			0
$715$	−11.7990	+	20.4365i	−0.441257	+	0.764280i
$716$		0			0
$717$	10.2636	+	12.2317i	0.383303	+	0.456803i
$718$		0			0
$719$	18.3716	−	3.23942i	0.685147	−	0.120810i	0.179770	−	0.983709i	$-0.442465\pi$
$719$	18.3716	−	3.23942i	0.685147	−	0.120810i	0.505377	+	0.862899i	$0.331354\pi$
$720$		0			0
$721$			14.8040i			0.551329i
$722$		0			0
$723$			12.5417i			0.466432i
$724$		0			0
$725$	−10.7785	+	1.90055i	−0.400305	+	0.0705846i
$726$		0			0
$727$	5.83018	+	6.94814i	0.216229	+	0.257692i	0.863246	−	0.504784i	$-0.168428\pi$
$727$	5.83018	+	6.94814i	0.216229	+	0.257692i	−0.647016	+	0.762476i	$0.723983\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	8.47602	+	23.2877i	0.313497	+	0.861326i
$732$		0			0
$733$	14.5357	+	25.1765i	0.536887	+	0.929916i	0.999069	+	0.0431313i	$0.0137334\pi$
$733$	14.5357	+	25.1765i	0.536887	+	0.929916i	−0.462182	+	0.886785i	$0.652933\pi$
$734$		0			0
$735$	−1.08777	+	6.16904i	−0.0401229	+	0.227548i
$736$		0			0
$737$	−28.2842	+	33.7078i	−1.04186	+	1.24164i
$738$		0			0
$739$	−17.9897	+	49.4264i	−0.661763	+	1.81818i	−0.0930184	+	0.995664i	$0.529652\pi$
$739$	−17.9897	+	49.4264i	−0.661763	+	1.81818i	−0.568744	+	0.822514i	$0.692571\pi$
$740$		0			0
$741$	−2.69981	+	9.12213i	−0.0991799	+	0.335110i
$742$		0			0
$743$	7.22686	+	2.63036i	0.265128	+	0.0964987i	0.471164	−	0.882046i	$-0.343834\pi$
$743$	7.22686	+	2.63036i	0.265128	+	0.0964987i	−0.206036	+	0.978544i	$0.566056\pi$
$744$		0			0
$745$	10.4090	+	8.73422i	0.381357	+	0.319997i
$746$		0			0
$747$	1.73142	+	0.305297i	0.0633495	+	0.0111702i
$748$		0			0
$749$	15.3300	−	8.85076i	0.560145	−	0.323400i
$750$		0			0
$751$	−36.7948	+	13.3922i	−1.34266	+	0.488688i	−0.910649	−	0.413180i	$-0.864418\pi$
$751$	−36.7948	+	13.3922i	−1.34266	+	0.488688i	−0.432011	+	0.901868i	$0.642196\pi$
$752$		0			0
$753$	3.11605	+	1.79905i	0.113555	+	0.0655610i
$754$		0			0
$755$	−29.9054	+	25.0936i	−1.08837	+	0.913249i
$756$		0			0
$757$	6.17313	+	35.0096i	0.224366	+	1.27244i	0.863893	+	0.503675i	$0.168019\pi$
$757$	6.17313	+	35.0096i	0.224366	+	1.27244i	−0.639527	+	0.768769i	$0.720870\pi$
$758$		0			0
$759$	−2.55395			−0.0927023
$760$		0			0
$761$	19.5119			0.707306			0.353653	−	0.935377i	$-0.384939\pi$
$761$	19.5119			0.707306			0.353653	+	0.935377i	$0.384939\pi$
$762$		0			0
$763$	1.84628	+	10.4708i	0.0668397	+	0.379067i
$764$		0			0
$765$	5.57539	−	4.67831i	0.201579	−	0.169144i
$766$		0			0
$767$	−21.8558	−	12.6184i	−0.789165	−	0.455625i
$768$		0			0
$769$	−26.0596	+	9.48491i	−0.939733	+	0.342035i	−0.766060	−	0.642769i	$-0.777786\pi$
$769$	−26.0596	+	9.48491i	−0.939733	+	0.342035i	−0.173672	+	0.984803i	$0.555563\pi$
$770$		0			0
$771$	−5.60158	+	3.23408i	−0.201736	+	0.116472i
$772$		0			0
$773$	−30.6646	−	5.40699i	−1.10293	−	0.194476i	−0.407594	−	0.913163i	$-0.633632\pi$
$773$	−30.6646	−	5.40699i	−1.10293	−	0.194476i	−0.695334	+	0.718687i	$0.744743\pi$
$774$		0			0
$775$	6.87809	+	5.77141i	0.247068	+	0.207315i
$776$		0			0
$777$	1.60607	+	0.584562i	0.0576175	+	0.0209710i
$778$		0			0
$779$	33.1108	+	3.76475i	1.18632	+	0.134886i
$780$		0			0
$781$	−1.99604	+	5.48407i	−0.0714239	+	0.196236i
$782$		0			0
$783$	−3.31858	+	3.95493i	−0.118596	+	0.141338i
$784$		0			0
$785$	−2.76821	+	15.6993i	−0.0988016	+	0.560332i
$786$		0			0
$787$	20.8980	+	36.1964i	0.744934	+	1.29026i	0.950225	+	0.311563i	$0.100853\pi$
$787$	20.8980	+	36.1964i	0.744934	+	1.29026i	−0.205291	+	0.978701i	$0.565814\pi$
$788$		0			0
$789$	1.08101	+	2.97006i	0.0384851	+	0.105737i
$790$		0			0
$791$	−0.628494	+	1.08858i	−0.0223467	+	0.0387056i
$792$		0			0
$793$	19.3692	+	23.0833i	0.687819	+	0.819710i
$794$		0			0
$795$	−1.53189	+	0.270114i	−0.0543307	+	0.00957997i
$796$		0			0
$797$		−	22.5327i		−	0.798148i	−0.916919	−	0.399074i	$-0.869332\pi$
$797$		−	22.5327i		−	0.798148i	0.916919	−	0.399074i	$-0.130668\pi$
$798$		0			0
$799$			40.3231i			1.42653i
$800$		0			0
$801$	2.20458	−	0.388726i	0.0778948	−	0.0137350i
$802$		0			0
$803$	−55.1655	−	65.7436i	−1.94675	−	2.32004i
$804$		0			0
$805$	0.618724	−	1.07166i	0.0218072	−	0.0377711i
$806$		0			0
$807$	−7.98543	−	21.9398i	−0.281100	−	0.772317i
$808$		0			0
$809$	4.89937	+	8.48596i	0.172253	+	0.298350i	0.939207	−	0.343351i	$-0.111562\pi$
$809$	4.89937	+	8.48596i	0.172253	+	0.298350i	−0.766954	+	0.641702i	$0.778229\pi$
$810$		0			0
$811$	2.85099	−	16.1688i	0.100112	−	0.567763i	−0.892949	−	0.450158i	$-0.851368\pi$
$811$	2.85099	−	16.1688i	0.100112	−	0.567763i	0.993061	−	0.117604i	$-0.0375214\pi$
$812$		0			0
$813$	−3.34390	+	3.98510i	−0.117276	+	0.139764i
$814$		0			0
$815$	−3.01689	+	8.28884i	−0.105677	+	0.290345i
$816$		0			0
$817$	−10.0491	−	23.0967i	−0.351573	−	0.808053i
$818$		0			0
$819$	3.73057	+	1.35782i	0.130357	+	0.0474460i
$820$		0			0
$821$	21.4357	+	17.9867i	0.748112	+	0.627741i	0.935003	−	0.354640i	$-0.115397\pi$
$821$	21.4357	+	17.9867i	0.748112	+	0.627741i	−0.186891	+	0.982381i	$0.559841\pi$
$822$		0			0
$823$	−27.7896	−	4.90005i	−0.968683	−	0.170805i	−0.333146	−	0.942875i	$-0.608110\pi$
$823$	−27.7896	−	4.90005i	−0.968683	−	0.170805i	−0.635537	+	0.772070i	$0.719221\pi$
$824$		0			0
$825$	11.6971	−	6.75330i	0.407239	−	0.235120i
$826$		0			0
$827$	9.07481	−	3.30296i	0.315562	−	0.114855i	−0.179383	−	0.983779i	$-0.557410\pi$
$827$	9.07481	−	3.30296i	0.315562	−	0.114855i	0.494946	+	0.868924i	$0.335188\pi$
$828$		0			0
$829$	35.5825	+	20.5436i	1.23583	+	0.713508i	0.968240	−	0.250024i	$-0.0804387\pi$
$829$	35.5825	+	20.5436i	1.23583	+	0.713508i	0.267592	+	0.963532i	$0.413772\pi$
$830$		0			0
$831$	22.2694	−	18.6862i	0.772517	−	0.648218i
$832$		0			0
$833$	2.74888	+	15.5897i	0.0952431	+	0.540151i
$834$		0			0
$835$	21.7808			0.753755
$836$		0			0
$837$	4.23536			0.146395
$838$		0			0
$839$	−0.662501	−	3.75723i	−0.0228721	−	0.129714i	0.971234	−	0.238128i	$-0.0765338\pi$
$839$	−0.662501	−	3.75723i	−0.0228721	−	0.129714i	−0.994106	+	0.108414i	$0.965423\pi$
$840$		0			0
$841$	1.79684	−	1.50772i	0.0619599	−	0.0519905i
$842$		0			0
$843$	0.655552	+	0.378483i	0.0225784	+	0.0130356i
$844$		0			0
$845$	−13.1353	+	4.78087i	−0.451869	+	0.164467i
$846$		0			0
$847$	46.6171	−	26.9144i	1.60178	−	0.924789i
$848$		0			0
$849$	15.2014	+	2.68041i	0.521709	+	0.0919914i
$850$		0			0
$851$	0.288527	+	0.242103i	0.00989057	+	0.00829918i
$852$		0			0
$853$	−45.6876	−	16.6289i	−1.56432	−	0.569364i	−0.592595	−	0.805500i	$-0.701897\pi$
$853$	−45.6876	−	16.6289i	−1.56432	−	0.569364i	−0.971720	+	0.236136i	$0.924119\pi$
$854$		0			0
$855$	−5.36469	+	5.09325i	−0.183468	+	0.174186i
$856$		0			0
$857$	1.18386	−	3.25264i	0.0404400	−	0.111108i	−0.917829	−	0.396976i	$-0.870060\pi$
$857$	1.18386	−	3.25264i	0.0404400	−	0.111108i	0.958269	+	0.285868i	$0.0922819\pi$
$858$		0			0
$859$	4.99673	−	5.95487i	0.170486	−	0.203177i	−0.674035	−	0.738699i	$-0.735441\pi$
$859$	4.99673	−	5.95487i	0.170486	−	0.203177i	0.844522	+	0.535522i	$0.179885\pi$
$860$		0			0
$861$	2.41484	−	13.6953i	0.0822977	−	0.466733i
$862$		0			0
$863$	−17.0151	−	29.4710i	−0.579201	−	1.00321i	−0.995571	−	0.0940103i	$-0.970031\pi$
$863$	−17.0151	−	29.4710i	−0.579201	−	1.00321i	0.416370	−	0.909195i	$-0.363302\pi$
$864$		0			0
$865$	5.12451	+	14.0795i	0.174239	+	0.478717i
$866$		0			0
$867$	0.696258	−	1.20595i	0.0236462	−	0.0409563i
$868$		0			0
$869$	55.7074	+	66.3895i	1.88974	+	2.25211i
$870$		0			0
$871$	14.8443	−	2.61745i	0.502979	−	0.0886888i
$872$		0			0
$873$		−	3.69206i		−	0.124957i
$874$		0			0
$875$			21.9793i			0.743035i
$876$		0			0
$877$	51.8382	−	9.14048i	1.75045	−	0.308652i	0.795620	−	0.605796i	$-0.207145\pi$
$877$	51.8382	−	9.14048i	1.75045	−	0.308652i	0.954833	+	0.297144i	$0.0960342\pi$
$878$		0			0
$879$	20.8620	+	24.8623i	0.703657	+	0.838585i
$880$		0			0
$881$	11.2103	−	19.4167i	0.377683	−	0.654167i	−0.613041	−	0.790051i	$-0.710054\pi$
$881$	11.2103	−	19.4167i	0.377683	−	0.654167i	0.990725	+	0.135884i	$0.0433875\pi$
$882$		0			0
$883$	−18.7946	−	51.6378i	−0.632489	−	1.73775i	−0.674126	−	0.738617i	$-0.735479\pi$
$883$	−18.7946	−	51.6378i	−0.632489	−	1.73775i	0.0416365	−	0.999133i	$-0.486743\pi$
$884$		0			0
$885$	−9.81189	−	16.9947i	−0.329823	−	0.571270i
$886$		0			0
$887$	−5.01805	+	28.4588i	−0.168490	+	0.955552i	0.776904	+	0.629620i	$0.216789\pi$
$887$	−5.01805	+	28.4588i	−0.168490	+	0.955552i	−0.945393	+	0.325932i	$0.894322\pi$
$888$		0			0
$889$	−12.9378	+	15.4187i	−0.433921	+	0.517127i
$890$		0			0
$891$	2.17908	−	5.98697i	0.0730019	−	0.200571i
$892$		0			0
$893$	−2.51144	−	40.9066i	−0.0840422	−	1.36889i
$894$		0			0
$895$	−2.00596	−	0.730111i	−0.0670520	−	0.0244049i
$896$		0			0
$897$	0.670188	+	0.562355i	0.0223769	+	0.0187765i
$898$		0			0
$899$	21.5341	+	3.79704i	0.718201	+	0.126638i
$900$		0			0
$901$	−3.40430	+	1.96547i	−0.113414	+	0.0654794i
$902$		0			0
$903$	−9.87739	+	3.59508i	−0.328699	+	0.119637i
$904$		0			0
$905$	38.4348	+	22.1904i	1.27762	+	0.737632i
$906$		0			0
$907$	−27.2637	+	22.8770i	−0.905278	+	0.759618i	−0.971215	−	0.238206i	$-0.923441\pi$
$907$	−27.2637	+	22.8770i	−0.905278	+	0.759618i	0.0659372	+	0.997824i	$0.478996\pi$
$908$		0			0
$909$	−2.67373	−	15.1635i	−0.0886820	−	0.502940i
$910$		0			0
$911$	−46.8829			−1.55330			−0.776650	−	0.629932i	$-0.783083\pi$
$911$	−46.8829			−1.55330			−0.776650	+	0.629932i	$0.783083\pi$
$912$		0			0
$913$	−11.2014			−0.370713
$914$		0			0
$915$	4.06875	+	23.0750i	0.134509	+	0.762837i
$916$		0			0
$917$	−4.02967	+	3.38129i	−0.133071	+	0.111660i
$918$		0			0
$919$	19.1921	+	11.0805i	0.633088	+	0.365514i	0.781947	−	0.623345i	$-0.214227\pi$
$919$	19.1921	+	11.0805i	0.633088	+	0.365514i	−0.148859	+	0.988858i	$0.547560\pi$
$920$		0			0
$921$	−3.84105	+	1.39803i	−0.126567	+	0.0460666i
$922$		0			0
$923$	1.73133	−	0.999583i	0.0569874	−	0.0329017i
$924$		0			0
$925$	−1.96163	−	0.345889i	−0.0644981	−	0.0113728i
$926$		0			0
$927$	−6.23442	−	5.23130i	−0.204765	−	0.171818i
$928$		0			0
$929$	17.8591	+	6.50017i	0.585937	+	0.213264i	0.617941	−	0.786224i	$-0.287967\pi$
$929$	17.8591	+	6.50017i	0.585937	+	0.213264i	−0.0320046	+	0.999488i	$0.510189\pi$
$930$		0			0
$931$	−3.75963	−	15.6441i	−0.123217	−	0.512713i
$932$		0			0
$933$	−8.98408	+	24.6835i	−0.294125	+	0.808103i
$934$		0			0
$935$	−29.8064	+	35.5219i	−0.974775	+	1.16169i
$936$		0			0
$937$	2.01287	−	11.4156i	0.0657576	−	0.372930i	−0.934115	−	0.356972i	$-0.883809\pi$
$937$	2.01287	−	11.4156i	0.0657576	−	0.372930i	0.999873	−	0.0159578i	$-0.00507975\pi$
$938$		0			0
$939$	8.13819	+	14.0958i	0.265580	+	0.459998i
$940$		0			0
$941$	−15.5214	−	42.6447i	−0.505983	−	1.39018i	−0.885347	−	0.464930i	$-0.846080\pi$
$941$	−15.5214	−	42.6447i	−0.505983	−	1.39018i	0.379364	−	0.925247i	$-0.376143\pi$
$942$		0			0
$943$	1.53230	−	2.65401i	0.0498984	−	0.0864266i
$944$		0			0
$945$	1.98429	+	2.36478i	0.0645489	+	0.0769263i
$946$		0			0
$947$	−9.04987	+	1.59574i	−0.294081	+	0.0518544i	−0.318742	−	0.947841i	$-0.603260\pi$
$947$	−9.04987	+	1.59574i	−0.294081	+	0.0518544i	0.0246611	+	0.999696i	$0.492149\pi$
$948$		0			0
$949$			29.3989i			0.954329i
$950$		0			0
$951$			27.4578i			0.890381i
$952$		0			0
$953$	20.0821	−	3.54102i	0.650523	−	0.114705i	0.161358	−	0.986896i	$-0.448413\pi$
$953$	20.0821	−	3.54102i	0.650523	−	0.114705i	0.489165	+	0.872191i	$0.337301\pi$
$954$		0			0
$955$	0.509012	+	0.606617i	0.0164713	+	0.0196297i
$956$		0			0
$957$	16.4466	−	28.4863i	0.531643	−	0.920832i
$958$		0			0
$959$	10.2284	+	28.1023i	0.330292	+	0.907470i
$960$		0			0
$961$	6.53088	+	11.3118i	0.210674	+	0.364897i
$962$		0			0
$963$	−1.68984	+	9.58353i	−0.0544542	+	0.308825i
$964$		0			0
$965$	−28.5084	+	33.9750i	−0.917718	+	1.09369i
$966$		0			0
$967$	−1.67871	+	4.61221i	−0.0539836	+	0.148319i	−0.963754	−	0.266794i	$-0.914036\pi$
$967$	−1.67871	+	4.61221i	−0.0539836	+	0.148319i	0.909770	+	0.415113i	$0.136258\pi$
$968$		0			0
$969$	−8.33726	+	16.7316i	−0.267831	+	0.537498i
$970$		0			0
$971$	37.5957	+	13.6837i	1.20650	+	0.439131i	0.865490	−	0.500927i	$-0.167008\pi$
$971$	37.5957	+	13.6837i	1.20650	+	0.439131i	0.341014	+	0.940058i	$0.389230\pi$
$972$		0			0
$973$	12.1677	+	10.2099i	0.390078	+	0.327314i
$974$		0			0
$975$	−4.55647	−	0.803429i	−0.145924	−	0.0257303i
$976$		0			0
$977$	−38.5728	+	22.2700i	−1.23405	+	0.712481i	−0.967872	−	0.251442i	$-0.919095\pi$
$977$	−38.5728	+	22.2700i	−1.23405	+	0.712481i	−0.266181	+	0.963923i	$0.585762\pi$
$978$		0			0
$979$	−13.4023	+	4.87806i	−0.428341	+	0.155903i
$980$		0			0
$981$	−5.06198	−	2.92254i	−0.161617	−	0.0933094i
$982$		0			0
$983$	2.74787	−	2.30574i	0.0876435	−	0.0735417i	−0.597913	−	0.801561i	$-0.704003\pi$
$983$	2.74787	−	2.30574i	0.0876435	−	0.0735417i	0.685557	+	0.728019i	$0.259559\pi$
$984$		0			0
$985$	1.63946	+	9.29786i	0.0522377	+	0.296255i
$986$		0			0
$987$	−17.1029			−0.544392
$988$		0			0
$989$	−2.31638			−0.0736566
$990$		0			0
$991$	−5.36714	−	30.4386i	−0.170493	−	0.966914i	−0.943218	−	0.332173i	$-0.892218\pi$
$991$	−5.36714	−	30.4386i	−0.170493	−	0.966914i	0.772725	−	0.634740i	$-0.218893\pi$
$992$		0			0
$993$	14.8360	−	12.4489i	0.470806	−	0.395053i
$994$		0			0
$995$	8.47259	+	4.89165i	0.268599	+	0.155076i
$996$		0			0
$997$	28.4588	−	10.3582i	0.901299	−	0.328046i	0.150526	−	0.988606i	$-0.451903\pi$
$997$	28.4588	−	10.3582i	0.901299	−	0.328046i	0.750773	+	0.660560i	$0.229681\pi$
$998$		0			0
$999$	−0.813716	+	0.469799i	−0.0257448	+	0.0148638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.h.319.4	yes	24
4.3	odd	2		912.2.ci.g.319.4	yes	24
19.14	odd	18		912.2.ci.g.223.4	✓	24
76.71	even	18	inner	912.2.ci.h.223.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.g.223.4	✓	24	19.14	odd	18
912.2.ci.g.319.4	yes	24	4.3	odd	2
912.2.ci.h.223.4	yes	24	76.71	even	18	inner
912.2.ci.h.319.4	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{3} +(1.30003 - 1.09086i) q^{5} +(1.57531 + 0.909508i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{3} +(1.30003 - 1.09086i) q^{5} +(1.57531 + 0.909508i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(5.51762 - 3.18560i) q^{11} +(-2.14934 - 0.378986i) q^{13} +(-1.30003 - 1.09086i) q^{15} +(-4.03001 - 1.46680i) q^{17} +(4.17968 + 1.23703i) q^{19} +(0.622140 - 1.70932i) q^{21} +(0.257666 - 0.307075i) q^{23} +(-0.368124 + 2.08774i) q^{25} +(0.500000 + 0.866025i) q^{27} +(1.76578 + 4.85144i) q^{29} +(2.11768 - 3.66793i) q^{31} +(-4.09533 - 4.88063i) q^{33} +(3.04010 - 0.536052i) q^{35} +0.939598i q^{37} +2.18249i q^{39} +(7.52894 - 1.32756i) q^{41} +(-3.71439 - 4.42664i) q^{43} +(-0.848536 + 1.46971i) q^{45} +(-3.21577 - 8.83526i) q^{47} +(-1.84559 - 3.19666i) q^{49} +(-0.744716 + 4.22350i) q^{51} +(0.589175 - 0.702151i) q^{53} +(3.69806 - 10.1603i) q^{55} +(0.492441 - 4.33099i) q^{57} +(10.8660 + 3.95489i) q^{59} +(-10.5766 - 8.87478i) q^{61} +(-1.79138 - 0.315869i) q^{63} +(-3.20763 + 1.85193i) q^{65} +(-6.48994 + 2.36215i) q^{67} +(-0.347153 - 0.200429i) q^{69} +(-0.701698 + 0.588794i) q^{71} +(-2.33910 - 13.2657i) q^{73} +2.11994 q^{75} +11.5893 q^{77} +(2.36208 + 13.3960i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-1.52259 - 0.879067i) q^{83} +(-6.83923 + 2.48927i) q^{85} +(4.47111 - 2.58139i) q^{87} +(-2.20458 - 0.388726i) q^{89} +(-3.04119 - 2.55186i) q^{91} +(-3.97993 - 1.44858i) q^{93} +(6.78315 - 2.95126i) q^{95} +(-1.26276 + 3.46941i) q^{97} +(-4.09533 + 4.88063i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 9 q^{7}+O(q^{10}) \) 24 * q + 9 * q^7	\( 24 q + 9 q^{7} - 9 q^{11} - 9 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 15 q^{23} + 6 q^{25} + 12 q^{27} - 6 q^{29} - 12 q^{31} - 3 q^{33} + 30 q^{41} + 9 q^{43} + 3 q^{45} + 15 q^{47} + 27 q^{49} - 3 q^{51} + 6 q^{53} - 21 q^{55} - 9 q^{57} + 36 q^{59} - 21 q^{61} + 3 q^{63} - 9 q^{65} - 45 q^{67} + 36 q^{71} - 42 q^{75} + 108 q^{77} - 36 q^{79} + 27 q^{83} - 9 q^{85} + 9 q^{87} - 27 q^{89} + 36 q^{91} - 18 q^{93} - 30 q^{95} - 51 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 9 * q^7 - 9 * q^11 - 9 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 15 * q^23 + 6 * q^25 + 12 * q^27 - 6 * q^29 - 12 * q^31 - 3 * q^33 + 30 * q^41 + 9 * q^43 + 3 * q^45 + 15 * q^47 + 27 * q^49 - 3 * q^51 + 6 * q^53 - 21 * q^55 - 9 * q^57 + 36 * q^59 - 21 * q^61 + 3 * q^63 - 9 * q^65 - 45 * q^67 + 36 * q^71 - 42 * q^75 + 108 * q^77 - 36 * q^79 + 27 * q^83 - 9 * q^85 + 9 * q^87 - 27 * q^89 + 36 * q^91 - 18 * q^93 - 30 * q^95 - 51 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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