LMFDB - Embedded newform 333.3.bb.c.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,3,Mod(82,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("333.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	333.bb (of order $12$, degree $4$, 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:	$9.07359280320$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 111)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			199.2
Character	$\chi$	$=$	333.199
Dual form			333.3.bb.c.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42776 + 0.382568i) q^{2} +(-1.57196 + 0.907569i) q^{4} +(-4.56711 - 1.22375i) q^{5} +(5.29119 + 9.16460i) q^{7} +(6.07795 - 6.07795i) q^{8} +O(q^{10})$	\(q+(-1.42776 + 0.382568i) q^{2} +(-1.57196 + 0.907569i) q^{4} +(-4.56711 - 1.22375i) q^{5} +(5.29119 + 9.16460i) q^{7} +(6.07795 - 6.07795i) q^{8} +6.98891 q^{10} +7.45500i q^{11} +(13.3598 + 3.57975i) q^{13} +(-11.0606 - 11.0606i) q^{14} +(-2.72236 + 4.71527i) q^{16} +(-2.29008 - 8.54668i) q^{17} +(-27.8934 - 7.47401i) q^{19} +(8.28993 - 2.22128i) q^{20} +(-2.85204 - 10.6440i) q^{22} +(-22.0996 + 22.0996i) q^{23} +(-2.28975 - 1.32199i) q^{25} -20.4441 q^{26} +(-16.6350 - 9.60424i) q^{28} +(-6.65051 - 6.65051i) q^{29} +(-38.0935 - 38.0935i) q^{31} +(-6.81576 + 25.4368i) q^{32} +(6.53937 + 11.3265i) q^{34} +(-12.9502 - 48.3308i) q^{35} +(32.7671 + 17.1848i) q^{37} +42.6844 q^{38} +(-35.1965 + 20.3207i) q^{40} +(-23.7443 + 13.7088i) q^{41} +(20.8153 - 20.8153i) q^{43} +(-6.76593 - 11.7189i) q^{44} +(23.0984 - 40.0076i) q^{46} -30.5216 q^{47} +(-31.4933 + 54.5480i) q^{49} +(3.77497 + 1.01150i) q^{50} +(-24.2499 + 6.49773i) q^{52} +(-22.2641 + 38.5626i) q^{53} +(9.12308 - 34.0478i) q^{55} +(87.8615 + 23.5424i) q^{56} +(12.0396 + 6.95107i) q^{58} +(-25.0887 - 93.6324i) q^{59} +(10.4385 - 38.9570i) q^{61} +(68.9617 + 39.8151i) q^{62} -60.7040i q^{64} +(-56.6349 - 32.6982i) q^{65} +(-75.0160 + 43.3105i) q^{67} +(11.3566 + 11.3566i) q^{68} +(36.9796 + 64.0506i) q^{70} +(8.44683 + 14.6303i) q^{71} -18.1941i q^{73} +(-53.3580 - 12.0001i) q^{74} +(50.6304 - 13.5664i) q^{76} +(-68.3222 + 39.4458i) q^{77} +(-52.6641 - 14.1113i) q^{79} +(18.2036 - 18.2036i) q^{80} +(28.6566 - 28.6566i) q^{82} +(59.7083 - 103.418i) q^{83} +41.8361i q^{85} +(-21.7560 + 37.6825i) q^{86} +(45.3111 + 45.3111i) q^{88} +(-124.150 + 33.2659i) q^{89} +(37.8822 + 141.378i) q^{91} +(14.6827 - 54.7966i) q^{92} +(43.5776 - 11.6766i) q^{94} +(118.246 + 68.2692i) q^{95} +(-33.1640 + 33.1640i) q^{97} +(24.0966 - 89.9299i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8}+O(q^{10}) $ 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8	$ 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8} + 36 q^{10} + 4 q^{13} + 6 q^{14} + 26 q^{16} - 46 q^{17} - 156 q^{19} - 68 q^{20} + 32 q^{22} - 10 q^{23} - 90 q^{25} + 164 q^{26} - 48 q^{28} + 28 q^{29} + 120 q^{31} - 90 q^{32} + 46 q^{34} + 186 q^{35} + 56 q^{37} - 4 q^{38} + 216 q^{40} + 30 q^{41} + 250 q^{43} - 284 q^{44} - 18 q^{46} - 232 q^{47} - 164 q^{49} - 226 q^{50} - 488 q^{52} - 122 q^{53} - 250 q^{55} + 632 q^{56} - 360 q^{58} + 258 q^{59} + 108 q^{61} + 186 q^{62} - 162 q^{65} + 60 q^{67} - 214 q^{68} + 246 q^{70} - 174 q^{71} + 8 q^{74} - 498 q^{76} - 666 q^{77} - 104 q^{79} + 24 q^{80} + 1114 q^{82} + 26 q^{83} + 72 q^{86} - 334 q^{88} - 16 q^{89} + 20 q^{91} + 918 q^{92} + 400 q^{94} + 372 q^{95} - 278 q^{97} - 950 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8 + 36 * q^10 + 4 * q^13 + 6 * q^14 + 26 * q^16 - 46 * q^17 - 156 * q^19 - 68 * q^20 + 32 * q^22 - 10 * q^23 - 90 * q^25 + 164 * q^26 - 48 * q^28 + 28 * q^29 + 120 * q^31 - 90 * q^32 + 46 * q^34 + 186 * q^35 + 56 * q^37 - 4 * q^38 + 216 * q^40 + 30 * q^41 + 250 * q^43 - 284 * q^44 - 18 * q^46 - 232 * q^47 - 164 * q^49 - 226 * q^50 - 488 * q^52 - 122 * q^53 - 250 * q^55 + 632 * q^56 - 360 * q^58 + 258 * q^59 + 108 * q^61 + 186 * q^62 - 162 * q^65 + 60 * q^67 - 214 * q^68 + 246 * q^70 - 174 * q^71 + 8 * q^74 - 498 * q^76 - 666 * q^77 - 104 * q^79 + 24 * q^80 + 1114 * q^82 + 26 * q^83 + 72 * q^86 - 334 * q^88 - 16 * q^89 + 20 * q^91 + 918 * q^92 + 400 * q^94 + 372 * q^95 - 278 * q^97 - 950 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	−1.42776	+	0.382568i	−0.713881	+	0.191284i	−0.597440	−	0.801914i	$-0.703815\pi$
$2$	−1.42776	+	0.382568i	−0.713881	+	0.191284i	−0.116441	+	0.993198i	$0.537149\pi$
$3$		0			0
$3$		0			0
$4$	−1.57196	+	0.907569i	−0.392989	+	0.226892i
$5$	−4.56711	−	1.22375i	−0.913421	−	0.244750i	−0.228650	−	0.973509i	$-0.573431\pi$
$5$	−4.56711	−	1.22375i	−0.913421	−	0.244750i	−0.684771	+	0.728758i	$0.740098\pi$
$6$		0			0
$7$	5.29119	+	9.16460i	0.755884	+	1.30923i	0.944934	+	0.327262i	$0.106126\pi$
$7$	5.29119	+	9.16460i	0.755884	+	1.30923i	−0.189050	+	0.981967i	$0.560541\pi$
$8$	6.07795	−	6.07795i	0.759744	−	0.759744i
$9$		0			0
$10$	6.98891			0.698891
$11$			7.45500i			0.677728i	0.940835	+	0.338864i	$0.110043\pi$
$11$			7.45500i			0.677728i	−0.940835	+	0.338864i	$0.889957\pi$
$12$		0			0
$13$	13.3598	+	3.57975i	1.02768	+	0.275365i	0.732998	−	0.680231i	$-0.238121\pi$
$13$	13.3598	+	3.57975i	1.02768	+	0.275365i	0.294679	+	0.955596i	$0.404787\pi$
$14$	−11.0606	−	11.0606i	−0.790045	−	0.790045i
$15$		0			0
$16$	−2.72236	+	4.71527i	−0.170147	+	0.294704i
$17$	−2.29008	−	8.54668i	−0.134710	−	0.502746i	−0.999999	−	0.00147179i	$-0.999532\pi$
$17$	−2.29008	−	8.54668i	−0.134710	−	0.502746i	0.865289	−	0.501274i	$-0.167135\pi$
$18$		0			0
$19$	−27.8934	−	7.47401i	−1.46807	−	0.393369i	−0.565803	−	0.824540i	$-0.691434\pi$
$19$	−27.8934	−	7.47401i	−1.46807	−	0.393369i	−0.902270	+	0.431171i	$0.858100\pi$
$20$	8.28993	−	2.22128i	0.414496	−	0.111064i
$21$		0			0
$22$	−2.85204	−	10.6440i	−0.129638	−	0.483817i
$23$	−22.0996	+	22.0996i	−0.960853	+	0.960853i	−0.999262	−	0.0384088i	$-0.987771\pi$
$23$	−22.0996	+	22.0996i	−0.960853	+	0.960853i	0.0384088	+	0.999262i	$0.487771\pi$
$24$		0			0
$25$	−2.28975	−	1.32199i	−0.0915901	−	0.0528795i
$26$	−20.4441			−0.786311
$27$		0			0
$28$	−16.6350	−	9.60424i	−0.594108	−	0.343008i
$29$	−6.65051	−	6.65051i	−0.229328	−	0.229328i	0.583084	−	0.812412i	$-0.301846\pi$
$29$	−6.65051	−	6.65051i	−0.229328	−	0.229328i	−0.812412	+	0.583084i	$0.801846\pi$
$30$		0			0
$31$	−38.0935	−	38.0935i	−1.22882	−	1.22882i	−0.964410	−	0.264411i	$-0.914822\pi$
$31$	−38.0935	−	38.0935i	−1.22882	−	1.22882i	−0.264411	−	0.964410i	$-0.585178\pi$
$32$	−6.81576	+	25.4368i	−0.212993	+	0.794899i
$33$		0			0
$34$	6.53937	+	11.3265i	0.192334	+	0.333133i
$35$	−12.9502	−	48.3308i	−0.370006	−	1.38088i
$36$		0			0
$37$	32.7671	+	17.1848i	0.885598	+	0.464453i
$37$	32.7671	+	17.1848i	0.885598	+	0.464453i
$38$	42.6844			1.12327
$39$		0			0
$40$	−35.1965	+	20.3207i	−0.879913	+	0.508018i
$41$	−23.7443	+	13.7088i	−0.579128	+	0.334360i	−0.760787	−	0.649002i	$-0.775187\pi$
$41$	−23.7443	+	13.7088i	−0.579128	+	0.334360i	0.181658	+	0.983362i	$0.441853\pi$
$42$		0			0
$43$	20.8153	−	20.8153i	0.484076	−	0.484076i	−0.422354	−	0.906431i	$-0.638796\pi$
$43$	20.8153	−	20.8153i	0.484076	−	0.484076i	0.906431	+	0.422354i	$0.138796\pi$
$44$	−6.76593	−	11.7189i	−0.153771	−	0.266339i
$45$		0			0
$46$	23.0984	−	40.0076i	0.502139	−	0.869730i
$47$	−30.5216			−0.649396			−0.324698	−	0.945818i	$-0.605263\pi$
$47$	−30.5216			−0.649396			−0.324698	+	0.945818i	$0.605263\pi$
$48$		0			0
$49$	−31.4933	+	54.5480i	−0.642721	+	1.11322i
$50$	3.77497	+	1.01150i	0.0754994	+	0.0202300i
$51$		0			0
$52$	−24.2499	+	6.49773i	−0.466344	+	0.124956i
$53$	−22.2641	+	38.5626i	−0.420078	+	0.727597i	−0.995947	−	0.0899457i	$-0.971331\pi$
$53$	−22.2641	+	38.5626i	−0.420078	+	0.727597i	0.575869	+	0.817542i	$0.304664\pi$
$54$		0			0
$55$	9.12308	−	34.0478i	0.165874	−	0.619051i
$56$	87.8615	+	23.5424i	1.56896	+	0.420401i
$57$		0			0
$58$	12.0396	+	6.95107i	0.207579	+	0.119846i
$59$	−25.0887	−	93.6324i	−0.425233	−	1.58699i	−0.763414	−	0.645909i	$-0.776478\pi$
$59$	−25.0887	−	93.6324i	−0.425233	−	1.58699i	0.338181	−	0.941081i	$-0.390188\pi$
$60$		0			0
$61$	10.4385	−	38.9570i	0.171123	−	0.638639i	−0.826057	−	0.563587i	$-0.809421\pi$
$61$	10.4385	−	38.9570i	0.171123	−	0.638639i	0.997180	−	0.0750522i	$-0.0239123\pi$
$62$	68.9617	+	39.8151i	1.11229	+	0.642178i
$63$		0			0
$64$		−	60.7040i		−	0.948500i
$65$	−56.6349	−	32.6982i	−0.871306	−	0.503049i
$66$		0			0
$67$	−75.0160	+	43.3105i	−1.11964	+	0.646425i	−0.941309	−	0.337545i	$-0.890403\pi$
$67$	−75.0160	+	43.3105i	−1.11964	+	0.646425i	−0.178332	+	0.983970i	$0.557070\pi$
$68$	11.3566	+	11.3566i	0.167009	+	0.167009i
$69$		0			0
$70$	36.9796	+	64.0506i	0.528280	+	0.915008i
$71$	8.44683	+	14.6303i	0.118969	+	0.206061i	0.919360	−	0.393418i	$-0.128708\pi$
$71$	8.44683	+	14.6303i	0.118969	+	0.206061i	−0.800390	+	0.599480i	$0.795374\pi$
$72$		0			0
$73$		−	18.1941i		−	0.249234i	−0.992205	−	0.124617i	$-0.960230\pi$
$73$		−	18.1941i		−	0.249234i	0.992205	−	0.124617i	$-0.0397702\pi$
$74$	−53.3580	−	12.0001i	−0.721054	−	0.162164i
$75$		0			0
$76$	50.6304	−	13.5664i	0.666189	−	0.178505i
$77$	−68.3222	+	39.4458i	−0.887301	+	0.512283i
$78$		0			0
$79$	−52.6641	−	14.1113i	−0.666635	−	0.178624i	−0.0903962	−	0.995906i	$-0.528813\pi$
$79$	−52.6641	−	14.1113i	−0.666635	−	0.178624i	−0.576238	+	0.817282i	$0.695480\pi$
$80$	18.2036	−	18.2036i	0.227545	−	0.227545i
$81$		0			0
$82$	28.6566	−	28.6566i	0.349471	−	0.349471i
$83$	59.7083	−	103.418i	0.719378	−	1.24600i	−0.241869	−	0.970309i	$-0.577760\pi$
$83$	59.7083	−	103.418i	0.719378	−	1.24600i	0.961247	−	0.275690i	$-0.0889062\pi$
$84$		0			0
$85$			41.8361i			0.492189i
$86$	−21.7560	+	37.6825i	−0.252977	+	0.438169i
$87$		0			0
$88$	45.3111	+	45.3111i	0.514899	+	0.514899i
$89$	−124.150	+	33.2659i	−1.39494	+	0.373774i	−0.876527	−	0.481353i	$-0.840145\pi$
$89$	−124.150	+	33.2659i	−1.39494	+	0.373774i	−0.518418	+	0.855127i	$0.673479\pi$
$90$		0			0
$91$	37.8822	+	141.378i	0.416288	+	1.55361i
$92$	14.6827	−	54.7966i	0.159595	−	0.595615i
$93$		0			0
$94$	43.5776	−	11.6766i	0.463592	−	0.124219i
$95$	118.246	+	68.2692i	1.24469	+	0.718623i
$96$		0			0
$97$	−33.1640	+	33.1640i	−0.341897	+	0.341897i	−0.857080	−	0.515183i	$-0.827724\pi$
$97$	−33.1640	+	33.1640i	−0.341897	+	0.341897i	0.515183	+	0.857080i	$0.327724\pi$
$98$	24.0966	−	89.9299i	0.245884	−	0.917652i
$99$		0			0
$100$	4.79918			0.0479918
$101$			129.518i			1.28235i	0.767394	+	0.641176i	$0.221553\pi$
$101$			129.518i			1.28235i	−0.767394	+	0.641176i	$0.778447\pi$
$102$		0			0
$103$	−4.72144	−	4.72144i	−0.0458392	−	0.0458392i	0.683816	−	0.729655i	$-0.260319\pi$
$103$	−4.72144	−	4.72144i	−0.0458392	−	0.0458392i	−0.729655	+	0.683816i	$0.760319\pi$
$104$	102.958	−	59.4426i	0.989977	−	0.571564i
$105$		0			0
$106$	17.0351	−	63.5758i	0.160708	−	0.599771i
$107$	51.9594	+	89.9963i	0.485602	+	0.841087i	0.999863	−	0.0165465i	$-0.00526714\pi$
$107$	51.9594	+	89.9963i	0.485602	+	0.841087i	−0.514261	+	0.857634i	$0.671934\pi$
$108$		0			0
$109$	21.2890	+	79.4515i	0.195312	+	0.728913i	0.992186	+	0.124768i	$0.0398186\pi$
$109$	21.2890	+	79.4515i	0.195312	+	0.728913i	−0.796874	+	0.604145i	$0.793515\pi$
$110$			52.1023i			0.473658i
$111$		0			0
$112$	−57.6181			−0.514447
$113$	132.850	−	35.5972i	1.17567	−	0.315019i	0.382461	−	0.923972i	$-0.375077\pi$
$113$	132.850	−	35.5972i	1.17567	−	0.315019i	0.793207	+	0.608953i	$0.208410\pi$
$114$		0			0
$115$	127.976	−	73.8869i	1.11283	−	0.642494i
$116$	16.4901	+	4.41851i	0.142156	+	0.0380906i
$117$		0			0
$118$	71.6415	+	124.087i	0.607131	+	1.05158i
$119$	66.2097	−	66.2097i	0.556384	−	0.556384i
$120$		0			0
$121$	65.4229			0.540685
$122$			59.6147i			0.488645i
$123$		0			0
$124$	94.4537	+	25.3088i	0.761723	+	0.204103i
$125$	92.4236	+	92.4236i	0.739389	+	0.739389i
$126$		0			0
$127$	31.5577	−	54.6595i	0.248486	−	0.430390i	−0.714620	−	0.699513i	$-0.753400\pi$
$127$	31.5577	−	54.6595i	0.248486	−	0.430390i	0.963106	+	0.269123i	$0.0867338\pi$
$128$	−4.03966	−	15.0762i	−0.0315598	−	0.117783i
$129$		0			0
$130$	93.3703	+	25.0185i	0.718233	+	0.192450i
$131$	−157.824	+	42.2889i	−1.20477	+	0.322816i	−0.804706	−	0.593673i	$-0.797677\pi$
$131$	−157.824	+	42.2889i	−1.20477	+	0.322816i	−0.400059	+	0.916489i	$0.631010\pi$
$132$		0			0
$133$	−79.0928	−	295.178i	−0.594682	−	2.21939i
$134$	90.5357	−	90.5357i	0.675640	−	0.675640i
$135$		0			0
$136$	−65.8652	−	38.0273i	−0.484303	−	0.279613i
$137$	193.755			1.41427			0.707133	−	0.707080i	$-0.249988\pi$
$137$	193.755			1.41427			0.707133	+	0.707080i	$0.249988\pi$
$138$		0			0
$139$	−177.357	−	102.397i	−1.27595	−	0.736672i	−0.299851	−	0.953986i	$-0.596937\pi$
$139$	−177.357	−	102.397i	−1.27595	−	0.736672i	−0.976102	+	0.217314i	$0.930270\pi$
$140$	64.2207	+	64.2207i	0.458719	+	0.458719i
$141$		0			0
$142$	−17.6572	−	17.6572i	−0.124346	−	0.124346i
$143$	−26.6870	+	99.5973i	−0.186623	+	0.696485i
$144$		0			0
$145$	22.2350	+	38.5121i	0.153345	+	0.265601i
$146$	6.96046	+	25.9768i	0.0476744	+	0.177923i
$147$		0			0
$148$	−67.1048	+	2.72473i	−0.453411	+	0.0184103i
$149$	157.633			1.05794			0.528971	−	0.848640i	$-0.322578\pi$
$149$	157.633			1.05794			0.528971	+	0.848640i	$0.322578\pi$
$150$		0			0
$151$	−29.2554	+	16.8906i	−0.193745	+	0.111858i	−0.593734	−	0.804661i	$-0.702347\pi$
$151$	−29.2554	+	16.8906i	−0.193745	+	0.111858i	0.399990	+	0.916520i	$0.369014\pi$
$152$	−214.961	+	124.108i	−1.41422	+	0.816500i
$153$		0			0
$154$	82.4571	−	82.4571i	0.535436	−	0.535436i
$155$	127.360	+	220.594i	0.821677	+	1.42319i
$156$		0			0
$157$	−125.516	+	217.400i	−0.799464	+	1.38471i	0.120502	+	0.992713i	$0.461550\pi$
$157$	−125.516	+	217.400i	−0.799464	+	1.38471i	−0.919966	+	0.391999i	$0.871784\pi$
$158$	80.5904			0.510066
$159$		0			0
$160$	62.2566	−	107.832i	0.389104	−	0.673947i
$161$	−319.468	−	85.6011i	−1.98427	−	0.531684i
$162$		0			0
$163$	−241.010	+	64.5786i	−1.47859	+	0.396187i	−0.905868	−	0.423561i	$-0.860780\pi$
$163$	−241.010	+	64.5786i	−1.47859	+	0.396187i	−0.572724	+	0.819748i	$0.694113\pi$
$164$	24.8833	−	43.0991i	0.151727	−	0.262800i
$165$		0			0
$166$	−45.6850	+	170.499i	−0.275211	+	1.02710i
$167$	−141.509	−	37.9171i	−0.847357	−	0.227049i	−0.191085	−	0.981573i	$-0.561201\pi$
$167$	−141.509	−	37.9171i	−0.847357	−	0.227049i	−0.656271	+	0.754525i	$0.727867\pi$
$168$		0			0
$169$	19.3112	+	11.1493i	0.114267	+	0.0659723i
$170$	−16.0051	−	59.7319i	−0.0941478	−	0.351364i
$171$		0			0
$172$	−13.8294	+	51.6120i	−0.0804035	+	0.300070i
$173$	−165.191	−	95.3732i	−0.954862	−	0.551290i	−0.0602744	−	0.998182i	$-0.519198\pi$
$173$	−165.191	−	95.3732i	−0.954862	−	0.551290i	−0.894588	+	0.446892i	$0.852531\pi$
$174$		0			0
$175$		−	27.9796i		−	0.159883i
$176$	−35.1523	−	20.2952i	−0.199729	−	0.115314i
$177$		0			0
$178$	164.530	−	94.9916i	0.924327	−	0.533661i
$179$	−101.847	−	101.847i	−0.568977	−	0.568977i	0.362865	−	0.931842i	$-0.381799\pi$
$179$	−101.847	−	101.847i	−0.568977	−	0.568977i	−0.931842	+	0.362865i	$0.881799\pi$
$180$		0			0
$181$	62.1823	+	107.703i	0.343549	+	0.595043i	0.985089	−	0.172046i	$-0.0550377\pi$
$181$	62.1823	+	107.703i	0.343549	+	0.595043i	−0.641540	+	0.767089i	$0.721704\pi$
$182$	−108.174	−	187.362i	−0.594360	−	1.02946i
$183$		0			0
$184$			268.641i			1.46000i
$185$	−128.621	−	118.583i	−0.695249	−	0.640992i
$186$		0			0
$187$	63.7155	−	17.0725i	0.340725	−	0.0912969i
$188$	47.9786	−	27.7005i	0.255206	−	0.147343i
$189$		0			0
$190$	−194.944	−	52.2352i	−1.02602	−	0.274922i
$191$	11.1430	−	11.1430i	0.0583402	−	0.0583402i	−0.677335	−	0.735675i	$-0.736865\pi$
$191$	11.1430	−	11.1430i	0.0583402	−	0.0583402i	0.735675	+	0.677335i	$0.236865\pi$
$192$		0			0
$193$	48.1548	−	48.1548i	0.249507	−	0.249507i	−0.571261	−	0.820768i	$-0.693546\pi$
$193$	48.1548	−	48.1548i	0.249507	−	0.249507i	0.820768	+	0.571261i	$0.193546\pi$
$194$	34.6628	−	60.0378i	0.178674	−	0.309473i
$195$		0			0
$196$		−	114.329i		−	0.583313i
$197$	−43.7645	+	75.8024i	−0.222155	+	0.384784i	−0.955462	−	0.295114i	$-0.904642\pi$
$197$	−43.7645	+	75.8024i	−0.222155	+	0.384784i	0.733307	+	0.679898i	$0.237976\pi$
$198$		0			0
$199$	151.368	+	151.368i	0.760646	+	0.760646i	0.976439	−	0.215794i	$-0.0692338\pi$
$199$	151.368	+	151.368i	0.760646	+	0.760646i	−0.215794	+	0.976439i	$0.569234\pi$
$200$	−21.9520	+	5.88201i	−0.109760	+	0.0294101i
$201$		0			0
$202$	−49.5492	−	184.920i	−0.245293	−	0.915447i
$203$	25.7602	−	96.1383i	0.126897	−	0.473588i
$204$		0			0
$205$	125.219	−	33.5522i	0.610823	−	0.163670i
$206$	8.54736	+	4.93482i	0.0414920	+	0.0239554i
$207$		0			0
$208$	−53.2496	+	53.2496i	−0.256008	+	0.256008i
$209$	55.7188	−	207.945i	0.266597	−	0.994954i
$210$		0			0
$211$	−409.973			−1.94300			−0.971500	−	0.237041i	$-0.923822\pi$
$211$	−409.973			−1.94300			−0.971500	+	0.237041i	$0.923822\pi$
$212$		−	80.8250i		−	0.381250i
$213$		0			0
$214$	−108.615	−	108.615i	−0.507548	−	0.507548i
$215$	−120.538	+	69.5928i	−0.560643	+	0.323688i
$216$		0			0
$217$	147.552	−	550.671i	0.679962	−	2.53765i
$218$	−60.7912	−	105.293i	−0.278859	−	0.482997i
$219$		0			0
$220$	16.5596	+	61.8014i	0.0752711	+	0.280916i
$221$		−	122.380i		−	0.553755i
$222$		0			0
$223$	256.325			1.14944			0.574719	−	0.818351i	$-0.305111\pi$
$223$	256.325			1.14944			0.574719	+	0.818351i	$0.305111\pi$
$224$	−269.181	+	72.1269i	−1.20170	+	0.321995i
$225$		0			0
$226$	−176.060	+	101.649i	−0.779028	+	0.449772i
$227$	101.011	+	27.0658i	0.444982	+	0.119233i	0.474351	−	0.880336i	$-0.342683\pi$
$227$	101.011	+	27.0658i	0.444982	+	0.119233i	−0.0293683	+	0.999569i	$0.509350\pi$
$228$		0			0
$229$	68.0484	+	117.863i	0.297155	+	0.514687i	0.975484	−	0.220071i	$-0.0706290\pi$
$229$	68.0484	+	117.863i	0.297155	+	0.514687i	−0.678329	+	0.734758i	$0.737296\pi$
$230$	−154.452	+	154.452i	−0.671531	+	0.671531i
$231$		0			0
$232$	−80.8429			−0.348461
$233$		−	15.4668i		−	0.0663812i	−0.999449	−	0.0331906i	$-0.989433\pi$
$233$		−	15.4668i		−	0.0663812i	0.999449	−	0.0331906i	$-0.0105668\pi$
$234$		0			0
$235$	139.395	+	37.3509i	0.593172	+	0.158940i
$236$	124.416	+	124.416i	0.527188	+	0.527188i
$237$		0			0
$238$	−69.2020	+	119.861i	−0.290765	+	0.503619i
$239$	−25.9797	−	96.9575i	−0.108702	−	0.405680i	0.890037	−	0.455888i	$-0.150678\pi$
$239$	−25.9797	−	96.9575i	−0.108702	−	0.405680i	−0.998739	+	0.0502080i	$0.984012\pi$
$240$		0			0
$241$	73.8227	+	19.7807i	0.306318	+	0.0820778i	0.408704	−	0.912667i	$-0.365981\pi$
$241$	73.8227	+	19.7807i	0.306318	+	0.0820778i	−0.102386	+	0.994745i	$0.532648\pi$
$242$	−93.4083	+	25.0287i	−0.385985	+	0.103424i
$243$		0			0
$244$	18.9473	+	70.7123i	0.0776529	+	0.289805i
$245$	210.587	−	210.587i	0.859537	−	0.859537i
$246$		0			0
$247$	−345.895	−	199.702i	−1.40038	−	0.808512i
$248$	−463.060			−1.86718
$249$		0			0
$250$	−167.317	−	96.6006i	−0.669269	−	0.386402i
$251$	276.253	+	276.253i	1.10061	+	1.10061i	0.994337	+	0.106271i	$0.0338912\pi$
$251$	276.253	+	276.253i	1.10061	+	1.10061i	0.106271	+	0.994337i	$0.466109\pi$
$252$		0			0
$253$	−164.753	−	164.753i	−0.651197	−	0.651197i
$254$	−24.1459	+	90.1137i	−0.0950625	+	0.354778i
$255$		0			0
$256$	132.943	+	230.265i	0.519310	+	0.899471i
$257$	−76.0050	−	283.654i	−0.295739	−	1.10371i	−0.940629	−	0.339438i	$-0.889763\pi$
$257$	−76.0050	−	283.654i	−0.295739	−	1.10371i	0.644889	−	0.764276i	$-0.276903\pi$
$258$		0			0
$259$	15.8853	+	391.225i	0.0613334	+	1.51052i
$260$	118.703			0.456551
$261$		0			0
$262$	209.157	−	120.757i	0.798310	−	0.460904i
$263$	−350.137	+	202.152i	−1.33132	+	0.768638i	−0.985502	−	0.169663i	$-0.945732\pi$
$263$	−350.137	+	202.152i	−1.33132	+	0.768638i	−0.345819	+	0.938301i	$0.612399\pi$
$264$		0			0
$265$	148.874	−	148.874i	0.561788	−	0.561788i
$266$	225.851	+	391.186i	0.849065	+	1.47062i
$267$		0			0
$268$	78.6145	−	136.164i	0.293338	−	0.508076i
$269$	−2.87158			−0.0106750			−0.00533752	−	0.999986i	$-0.501699\pi$
$269$	−2.87158			−0.0106750			−0.00533752	+	0.999986i	$0.501699\pi$
$270$		0			0
$271$	20.3264	−	35.2063i	0.0750050	−	0.129913i	−0.826083	−	0.563548i	$-0.809436\pi$
$271$	20.3264	−	35.2063i	0.0750050	−	0.129913i	0.901088	+	0.433635i	$0.142769\pi$
$272$	46.5343	+	12.4688i	0.171082	+	0.0458413i
$273$		0			0
$274$	−276.635	+	74.1242i	−1.00962	+	0.270526i
$275$	9.85543	−	17.0701i	0.0358379	−	0.0620731i
$276$		0			0
$277$	3.85189	−	14.3755i	0.0139057	−	0.0518969i	−0.958624	−	0.284674i	$-0.908115\pi$
$277$	3.85189	−	14.3755i	0.0139057	−	0.0518969i	0.972530	+	0.232777i	$0.0747813\pi$
$278$	292.398	+	78.3478i	1.05179	+	0.281827i
$279$		0			0
$280$	−372.463	−	215.042i	−1.33022	−	0.768005i
$281$	70.1739	+	261.892i	0.249729	+	0.932002i	0.970947	+	0.239294i	$0.0769159\pi$
$281$	70.1739	+	261.892i	0.249729	+	0.932002i	−0.721218	+	0.692708i	$0.756417\pi$
$282$		0			0
$283$	−83.2537	+	310.707i	−0.294183	+	1.09790i	0.647682	+	0.761911i	$0.275739\pi$
$283$	−83.2537	+	310.707i	−0.294183	+	1.09790i	−0.941864	+	0.335993i	$0.890928\pi$
$284$	−26.5561	−	15.3322i	−0.0935074	−	0.0539865i
$285$		0			0
$286$		−	152.411i		−	0.532905i
$287$	−251.271	−	145.071i	−0.875508	−	0.505475i
$288$		0			0
$289$	182.480	−	105.355i	0.631419	−	0.364550i
$290$	−46.4798	−	46.4798i	−0.160275	−	0.160275i
$291$		0			0
$292$	16.5124	+	28.6003i	0.0565492	+	0.0979461i
$293$	−15.7535	−	27.2859i	−0.0537663	−	0.0931260i	0.837890	−	0.545840i	$-0.183789\pi$
$293$	−15.7535	−	27.2859i	−0.0537663	−	0.0931260i	−0.891656	+	0.452714i	$0.850456\pi$
$294$		0			0
$295$			458.332i			1.55367i
$296$	303.605	−	94.7087i	1.02569	−	0.319962i
$297$		0			0
$298$	−225.063	+	60.3054i	−0.755244	+	0.202367i
$299$	−374.357	+	216.135i	−1.25203	+	0.722861i
$300$		0			0
$301$	300.901	+	80.6263i	0.999672	+	0.267861i
$302$	35.3080	−	35.3080i	0.116914	−	0.116914i
$303$		0			0
$304$	111.178	−	111.178i	0.365716	−	0.365716i
$305$	−95.3474	+	165.147i	−0.312614	+	0.541464i
$306$		0			0
$307$		−	245.140i		−	0.798500i	−0.916842	−	0.399250i	$-0.869270\pi$
$307$		−	245.140i		−	0.798500i	0.916842	−	0.399250i	$-0.130730\pi$
$308$	71.5996	−	124.014i	0.232466	−	0.402643i
$309$		0			0
$310$	−266.232	−	266.232i	−0.858812	−	0.858812i
$311$	274.154	−	73.4594i	0.881525	−	0.236204i	0.210460	−	0.977602i	$-0.432504\pi$
$311$	274.154	−	73.4594i	0.881525	−	0.236204i	0.671065	+	0.741399i	$0.265837\pi$
$312$		0			0
$313$	−31.0023	−	115.702i	−0.0990489	−	0.369655i	0.898553	−	0.438864i	$-0.144619\pi$
$313$	−31.0023	−	115.702i	−0.0990489	−	0.369655i	−0.997602	+	0.0692090i	$0.977952\pi$
$314$	96.0366	−	358.413i	0.305849	−	1.14144i
$315$		0			0
$316$	95.5927	−	25.6140i	0.302508	−	0.0810569i
$317$	236.287	+	136.420i	0.745385	+	0.430348i	0.824024	−	0.566555i	$-0.191724\pi$
$317$	236.287	+	136.420i	0.745385	+	0.430348i	−0.0786391	+	0.996903i	$0.525057\pi$
$318$		0			0
$319$	49.5796	−	49.5796i	0.155422	−	0.155422i
$320$	−74.2867	+	277.242i	−0.232146	+	0.866380i
$321$		0			0
$322$	488.872			1.51824
$323$			255.512i			0.791059i
$324$		0			0
$325$	−25.8582	−	25.8582i	−0.0795638	−	0.0795638i
$326$	319.400	−	184.406i	0.979754	−	0.565661i
$327$		0			0
$328$	−60.9953	+	227.638i	−0.185961	+	0.694017i
$329$	−161.496	−	279.719i	−0.490868	−	0.850208i
$330$		0			0
$331$	169.026	+	630.813i	0.510652	+	1.90578i	0.413485	+	0.910511i	$0.364311\pi$
$331$	169.026	+	630.813i	0.510652	+	1.90578i	0.0971665	+	0.995268i	$0.469022\pi$
$332$			216.758i			0.652885i
$333$		0			0
$334$	216.546			0.648343
$335$	395.607	−	106.003i	1.18092	−	0.316426i
$336$		0			0
$337$	63.8910	−	36.8875i	0.189588	−	0.109458i	−0.402202	−	0.915551i	$-0.631755\pi$
$337$	63.8910	−	36.8875i	0.189588	−	0.109458i	0.591790	+	0.806093i	$0.298422\pi$
$338$	−31.8372	−	8.53074i	−0.0941928	−	0.0252389i
$339$		0			0
$340$	−37.9691	−	65.7645i	−0.111674	−	0.193425i
$341$	283.987	−	283.987i	0.832806	−	0.832806i
$342$		0			0
$343$	−148.012			−0.431521
$344$		−	253.028i		−	0.735548i
$345$		0			0
$346$	272.340	+	72.9734i	0.787111	+	0.210906i
$347$	234.444	+	234.444i	0.675631	+	0.675631i	0.959009	−	0.283377i	$-0.0914548\pi$
$347$	234.444	+	234.444i	0.675631	+	0.675631i	−0.283377	+	0.959009i	$0.591455\pi$
$348$		0			0
$349$	28.1990	−	48.8421i	0.0807994	−	0.139949i	−0.822794	−	0.568340i	$-0.807586\pi$
$349$	28.1990	−	48.8421i	0.0807994	−	0.139949i	0.903594	+	0.428391i	$0.140919\pi$
$350$	10.7041	+	39.9481i	0.0305831	+	0.114138i
$351$		0			0
$352$	−189.631	−	50.8115i	−0.538725	−	0.144351i
$353$	−192.253	+	51.5142i	−0.544627	+	0.145932i	−0.520634	−	0.853780i	$-0.674305\pi$
$353$	−192.253	+	51.5142i	−0.544627	+	0.145932i	−0.0239928	+	0.999712i	$0.507638\pi$
$354$		0			0
$355$	−20.6737	−	77.1551i	−0.0582357	−	0.217338i
$356$	164.967	−	164.967i	0.463391	−	0.463391i
$357$		0			0
$358$	184.376	+	106.450i	0.515018	+	0.297346i
$359$	−225.752			−0.628834			−0.314417	−	0.949285i	$-0.601809\pi$
$359$	−225.752			−0.628834			−0.314417	+	0.949285i	$0.601809\pi$
$360$		0			0
$361$	409.545	+	236.451i	1.13447	+	0.654989i
$362$	−129.985	−	129.985i	−0.359075	−	0.359075i
$363$		0			0
$364$	−187.860	−	187.860i	−0.516098	−	0.516098i
$365$	−22.2650	+	83.0942i	−0.0610000	+	0.227655i
$366$		0			0
$367$	−92.5322	−	160.270i	−0.252131	−	0.436704i	0.711981	−	0.702199i	$-0.247798\pi$
$367$	−92.5322	−	160.270i	−0.252131	−	0.436704i	−0.964112	+	0.265494i	$0.914465\pi$
$368$	−44.0425	−	164.369i	−0.119681	−	0.446654i
$369$		0			0
$370$	229.006	+	120.103i	0.618936	+	0.324602i
$371$	−471.215			−1.27012
$372$		0			0
$373$	−265.763	+	153.438i	−0.712501	+	0.411362i	−0.811986	−	0.583677i	$-0.801614\pi$
$373$	−265.763	+	153.438i	−0.712501	+	0.411362i	0.0994856	+	0.995039i	$0.468280\pi$
$374$	−84.4392	+	48.7510i	−0.225773	+	0.130350i
$375$		0			0
$376$	−185.509	+	185.509i	−0.493375	+	0.493375i
$377$	−65.0423	−	112.657i	−0.172526	−	0.298824i
$378$		0			0
$379$	142.520	−	246.853i	0.376043	−	0.651326i	−0.614439	−	0.788964i	$-0.710618\pi$
$379$	142.520	−	246.853i	0.376043	−	0.651326i	0.990483	+	0.137638i	$0.0439510\pi$
$380$	−247.836			−0.652200
$381$		0			0
$382$	−11.6466	+	20.1725i	−0.0304884	+	0.0528075i
$383$	61.1283	+	16.3793i	0.159604	+	0.0427658i	0.337736	−	0.941241i	$-0.390339\pi$
$383$	61.1283	+	16.3793i	0.159604	+	0.0427658i	−0.178132	+	0.984007i	$0.557005\pi$
$384$		0			0
$385$	360.306	−	96.5438i	0.935861	−	0.250763i
$386$	−50.3311	+	87.1760i	−0.130391	+	0.225845i
$387$		0			0
$388$	22.0337	−	82.2310i	0.0567880	−	0.211936i
$389$	185.532	+	49.7131i	0.476946	+	0.127797i	0.489280	−	0.872127i	$-0.337260\pi$
$389$	185.532	+	49.7131i	0.476946	+	0.127797i	−0.0123344	+	0.999924i	$0.503926\pi$
$390$		0			0
$391$	239.488	+	138.269i	0.612502	+	0.353628i
$392$	140.125	+	522.955i	0.357462	+	1.33407i
$393$		0			0
$394$	33.4858	−	124.971i	0.0849893	−	0.317184i
$395$	223.254	+	128.896i	0.565200	+	0.326318i
$396$		0			0
$397$			302.878i			0.762916i	0.924386	+	0.381458i	$0.124578\pi$
$397$			302.878i			0.762916i	−0.924386	+	0.381458i	$0.875422\pi$
$398$	−274.027	−	158.209i	−0.688509	−	0.397511i
$399$		0			0
$400$	12.4671	−	7.19786i	0.0311676	−	0.0179946i
$401$	438.304	+	438.304i	1.09303	+	1.09303i	0.995204	+	0.0978244i	$0.0311883\pi$
$401$	438.304	+	438.304i	1.09303	+	1.09303i	0.0978244	+	0.995204i	$0.468812\pi$
$402$		0			0
$403$	−372.556	−	645.286i	−0.924456	−	1.60120i
$404$	−117.546	−	203.596i	−0.290956	−	0.503950i
$405$		0			0
$406$			147.118i			0.362359i
$407$	−128.112	+	244.279i	−0.314773	+	0.600194i
$408$		0			0
$409$	−641.596	+	171.915i	−1.56869	+	0.420330i	−0.935403	−	0.353584i	$-0.884963\pi$
$409$	−641.596	+	171.915i	−1.56869	+	0.420330i	−0.633291	+	0.773914i	$0.718296\pi$
$410$	−165.946	+	95.8092i	−0.404747	+	0.233681i
$411$		0			0
$412$	11.7069	+	3.13686i	0.0284149	+	0.00761374i
$413$	725.355	−	725.355i	1.75631	−	1.75631i
$414$		0			0
$415$	−399.252	+	399.252i	−0.962053	+	0.962053i
$416$	−182.114	+	315.431i	−0.437775	+	0.758248i
$417$		0			0
$418$			318.213i			0.761274i
$419$	−282.446	+	489.211i	−0.674096	+	1.16757i	0.302636	+	0.953106i	$0.402133\pi$
$419$	−282.446	+	489.211i	−0.674096	+	1.16757i	−0.976732	+	0.214463i	$0.931200\pi$
$420$		0			0
$421$	67.8365	+	67.8365i	0.161132	+	0.161132i	0.783068	−	0.621936i	$-0.213654\pi$
$421$	67.8365	+	67.8365i	0.161132	+	0.161132i	−0.621936	+	0.783068i	$0.713654\pi$
$422$	585.343	−	156.842i	1.38707	−	0.371664i
$423$		0			0
$424$	99.0613	+	369.702i	0.233635	+	0.871938i
$425$	−6.05491	+	22.5972i	−0.0142468	+	0.0531699i
$426$		0			0
$427$	412.257	−	110.464i	0.965474	−	0.258698i
$428$	−163.356	−	94.3135i	−0.381672	−	0.220359i
$429$		0			0
$430$	145.476	−	145.476i	0.338316	−	0.338316i
$431$	181.289	−	676.580i	0.420624	−	1.56979i	−0.352673	−	0.935747i	$-0.614727\pi$
$431$	181.289	−	676.580i	0.420624	−	1.56979i	0.773297	−	0.634044i	$-0.218606\pi$
$432$		0			0
$433$	193.650			0.447230			0.223615	−	0.974678i	$-0.428214\pi$
$433$	193.650			0.447230			0.223615	+	0.974678i	$0.428214\pi$
$434$			842.676i			1.94165i
$435$		0			0
$436$	−105.573	−	105.573i	−0.242140	−	0.242140i
$437$	781.606	−	451.261i	1.78857	−	1.03263i
$438$		0			0
$439$	165.493	−	617.629i	0.376978	−	1.40690i	−0.473456	−	0.880817i	$-0.656994\pi$
$439$	165.493	−	617.629i	0.376978	−	1.40690i	0.850434	−	0.526082i	$-0.176340\pi$
$440$	−151.491	−	262.390i	−0.344298	−	0.596342i
$441$		0			0
$442$	46.8185	+	174.729i	0.105924	+	0.395315i
$443$		−	209.323i		−	0.472512i	−0.971691	−	0.236256i	$-0.924080\pi$
$443$		−	209.323i		−	0.472512i	0.971691	−	0.236256i	$-0.0759204\pi$
$444$		0			0
$445$	607.716			1.36565
$446$	−365.971	+	98.0616i	−0.820562	+	0.219869i
$447$		0			0
$448$	556.328	−	321.196i	1.24180	−	0.716956i
$449$	592.198	+	158.679i	1.31893	+	0.353405i	0.848576	−	0.529074i	$-0.177461\pi$
$449$	592.198	+	158.679i	1.31893	+	0.353405i	0.470351	+	0.882479i	$0.344127\pi$
$450$		0			0
$451$	−102.199	−	177.014i	−0.226605	−	0.392491i
$452$	−176.528	+	176.528i	−0.390549	+	0.390549i
$453$		0			0
$454$	−154.574			−0.340472
$455$		−	692.048i		−	1.52098i
$456$		0			0
$457$	−512.823	−	137.411i	−1.12215	−	0.300680i	−0.350398	−	0.936601i	$-0.613954\pi$
$457$	−512.823	−	137.411i	−1.12215	−	0.300680i	−0.771754	+	0.635922i	$0.780620\pi$
$458$	−142.248	−	142.248i	−0.310584	−	0.310584i
$459$		0			0
$460$	−134.115	+	232.294i	−0.291554	+	0.504986i
$461$	8.20363	+	30.6163i	0.0177953	+	0.0664129i	0.974253	−	0.225460i	$-0.0723884\pi$
$461$	8.20363	+	30.6163i	0.0177953	+	0.0664129i	−0.956457	+	0.291873i	$0.905722\pi$
$462$		0			0
$463$	−627.926	−	168.252i	−1.35621	−	0.363396i	−0.493788	−	0.869583i	$-0.664388\pi$
$463$	−627.926	−	168.252i	−1.35621	−	0.363396i	−0.862424	+	0.506187i	$0.831055\pi$
$464$	49.4640	−	13.2538i	0.106603	−	0.0285643i
$465$		0			0
$466$	5.91710	+	22.0829i	0.0126976	+	0.0473882i
$467$	−555.136	+	555.136i	−1.18873	+	1.18873i	−0.211308	+	0.977419i	$0.567772\pi$
$467$	−555.136	+	555.136i	−1.18873	+	1.18873i	−0.977419	+	0.211308i	$0.932228\pi$
$468$		0			0
$469$	−793.847	−	458.328i	−1.69264	−	0.977245i
$470$	−213.313			−0.453857
$471$		0			0
$472$	−721.581	−	416.605i	−1.52877	−	0.882638i
$473$	155.178	+	155.178i	0.328072	+	0.328072i
$474$		0			0
$475$	53.9884	+	53.9884i	0.113660	+	0.113660i
$476$	−43.9889	+	164.169i	−0.0924136	+	0.344892i
$477$		0			0
$478$	74.1856	+	128.493i	0.155200	+	0.268814i
$479$	−58.5513	−	218.516i	−0.122237	−	0.456193i	0.877490	−	0.479596i	$-0.159217\pi$
$479$	−58.5513	−	218.516i	−0.122237	−	0.456193i	−0.999726	+	0.0234027i	$0.992550\pi$
$480$		0			0
$481$	376.245	+	346.883i	0.782214	+	0.721170i
$482$	−112.969			−0.234375
$483$		0			0
$484$	−102.842	+	59.3758i	−0.212483	+	0.122677i
$485$	192.048	−	110.879i	0.395975	−	0.228617i
$486$		0			0
$487$	440.438	−	440.438i	0.904391	−	0.904391i	−0.0914212	−	0.995812i	$-0.529141\pi$
$487$	440.438	−	440.438i	0.904391	−	0.904391i	0.995812	+	0.0914212i	$0.0291410\pi$
$488$	−173.334	−	300.223i	−0.355192	−	0.615211i
$489$		0			0
$490$	−220.104	+	381.231i	−0.449191	+	0.778022i
$491$	518.481			1.05597			0.527985	−	0.849254i	$-0.322948\pi$
$491$	518.481			1.05597			0.527985	+	0.849254i	$0.322948\pi$
$492$		0			0
$493$	−41.6096	+	72.0699i	−0.0844008	+	0.146186i
$494$	570.255	+	152.799i	1.15436	+	0.309311i
$495$		0			0
$496$	283.325	−	75.9167i	0.571219	−	0.153058i
$497$	−89.3875	+	154.824i	−0.179854	+	0.311517i
$498$		0			0
$499$	−228.030	+	851.019i	−0.456974	+	1.70545i	0.225245	+	0.974302i	$0.427682\pi$
$499$	−228.030	+	851.019i	−0.456974	+	1.70545i	−0.682219	+	0.731148i	$0.738985\pi$
$500$	−229.167	−	61.4050i	−0.458333	−	0.122810i
$501$		0			0
$502$	−500.108	−	288.738i	−0.996232	−	0.575175i
$503$	211.738	+	790.217i	0.420950	+	1.57101i	0.772611	+	0.634880i	$0.218950\pi$
$503$	211.738	+	790.217i	0.420950	+	1.57101i	−0.351660	+	0.936128i	$0.614383\pi$
$504$		0			0
$505$	158.497	−	591.521i	0.313856	−	1.17133i
$506$	298.257	+	172.199i	0.589440	+	0.340314i
$507$		0			0
$508$			114.563i			0.225518i
$509$	129.276	+	74.6376i	0.253981	+	0.146636i	0.621586	−	0.783346i	$-0.286489\pi$
$509$	129.276	+	74.6376i	0.253981	+	0.146636i	−0.367605	+	0.929982i	$0.619822\pi$
$510$		0			0
$511$	166.741	−	96.2681i	0.326304	−	0.188392i
$512$	−233.757	−	233.757i	−0.456557	−	0.456557i
$513$		0			0
$514$	217.034	+	375.914i	0.422245	+	0.731350i
$515$	15.7854	+	27.3412i	0.0306513	+	0.0530897i
$516$		0			0
$517$		−	227.539i		−	0.440114i
$518$	−172.351	−	552.499i	−0.332723	−	1.06660i
$519$		0			0
$520$	−542.961	+	145.486i	−1.04416	+	0.279781i
$521$	−315.289	+	182.032i	−0.605162	+	0.349390i	−0.771069	−	0.636751i	$-0.780278\pi$
$521$	−315.289	+	182.032i	−0.605162	+	0.349390i	0.165908	+	0.986141i	$0.446945\pi$
$522$		0			0
$523$	367.684	+	98.5206i	0.703029	+	0.188376i	0.592587	−	0.805507i	$-0.298107\pi$
$523$	367.684	+	98.5206i	0.703029	+	0.188376i	0.110442	+	0.993883i	$0.464773\pi$
$524$	209.713	−	209.713i	0.400215	−	0.400215i
$525$		0			0
$526$	422.576	−	422.576i	0.803376	−	0.803376i
$527$	−238.336	+	412.809i	−0.452250	+	0.783320i
$528$		0			0
$529$		−	447.787i		−	0.846478i
$530$	−155.602	+	269.511i	−0.293589	+	0.508510i
$531$		0			0
$532$	392.225	+	392.225i	0.737265	+	0.737265i
$533$	−366.292	+	98.1477i	−0.687228	+	0.184142i
$534$		0			0
$535$	−127.171	−	474.608i	−0.237703	−	0.887118i
$536$	−192.704	+	719.182i	−0.359523	+	1.34176i
$537$		0			0
$538$	4.09994	−	1.09858i	0.00762070	−	0.00204196i
$539$	−406.656	−	234.783i	−0.754463	−	0.435589i
$540$		0			0
$541$	−399.009	+	399.009i	−0.737539	+	0.737539i	−0.972101	−	0.234562i	$-0.924634\pi$
$541$	−399.009	+	399.009i	−0.737539	+	0.737539i	0.234562	+	0.972101i	$0.424634\pi$
$542$	−15.5524	+	58.0424i	−0.0286945	+	0.107089i
$543$		0			0
$544$	233.009			0.428324
$545$		−	388.916i		−	0.713607i
$546$		0			0
$547$	572.703	+	572.703i	1.04699	+	1.04699i	0.998840	+	0.0481484i	$0.0153321\pi$
$547$	572.703	+	572.703i	1.04699	+	1.04699i	0.0481484	+	0.998840i	$0.484668\pi$
$548$	−304.574	+	175.846i	−0.555791	+	0.320886i
$549$		0			0
$550$	−7.54074	+	28.1424i	−0.0137104	+	0.0511680i
$551$	135.799	+	235.211i	0.246460	+	0.426881i
$552$		0			0
$553$	−149.331	−	557.311i	−0.270038	−	1.00780i
$554$			21.9983i			0.0397082i
$555$		0			0
$556$	371.731			0.668580
$557$	397.126	−	106.410i	0.712972	−	0.191040i	0.115939	−	0.993256i	$-0.463012\pi$
$557$	397.126	−	106.410i	0.712972	−	0.191040i	0.597034	+	0.802216i	$0.296346\pi$
$558$		0			0
$559$	352.601	−	203.574i	0.630771	−	0.364176i
$560$	263.148	+	70.5102i	0.469907	+	0.125911i
$561$		0			0
$562$	−200.383	−	347.074i	−0.356554	−	0.617569i
$563$	−655.561	+	655.561i	−1.16441	+	1.16441i	−0.180907	+	0.983500i	$0.557903\pi$
$563$	−655.561	+	655.561i	−1.16441	+	1.16441i	−0.983500	+	0.180907i	$0.942097\pi$
$564$		0			0
$565$	−650.304			−1.15098
$566$		−	475.466i		−	0.840045i
$567$		0			0
$568$	140.262	+	37.5831i	0.246940	+	0.0661673i
$569$	−249.652	−	249.652i	−0.438755	−	0.438755i	0.452838	−	0.891593i	$-0.350412\pi$
$569$	−249.652	−	249.652i	−0.438755	−	0.438755i	−0.891593	+	0.452838i	$0.850412\pi$
$570$		0			0
$571$	−459.237	+	795.423i	−0.804269	+	1.39303i	0.112515	+	0.993650i	$0.464109\pi$
$571$	−459.237	+	795.423i	−0.804269	+	1.39303i	−0.916784	+	0.399384i	$0.869224\pi$
$572$	−48.4406	−	180.783i	−0.0846864	−	0.316054i
$573$		0			0
$574$	414.254	+	110.999i	0.721697	+	0.193378i
$575$	79.8181	−	21.3872i	0.138814	−	0.0371951i
$576$		0			0
$577$	−19.0305	−	71.0228i	−0.0329818	−	0.123090i	0.947472	−	0.319838i	$-0.103629\pi$
$577$	−19.0305	−	71.0228i	−0.0329818	−	0.123090i	−0.980454	+	0.196748i	$0.936962\pi$
$578$	−220.233	+	220.233i	−0.381025	+	0.381025i
$579$		0			0
$580$	−69.9049	−	40.3596i	−0.120526	−	0.0695855i
$581$	1263.71			2.17506
$582$		0			0
$583$	−287.484	−	165.979i	−0.493112	−	0.284699i
$584$	−110.583	−	110.583i	−0.189354	−	0.189354i
$585$		0			0
$586$	32.9310	+	32.9310i	0.0561963	+	0.0561963i
$587$	197.235	−	736.090i	0.336005	−	1.25399i	−0.566771	−	0.823875i	$-0.691808\pi$
$587$	197.235	−	736.090i	0.336005	−	1.25399i	0.902776	−	0.430111i	$-0.141526\pi$
$588$		0			0
$589$	777.845	+	1347.27i	1.32062	+	2.28738i
$590$	−175.343	−	654.388i	−0.297191	−	1.10913i
$591$		0			0
$592$	−170.235	+	107.723i	−0.287558	+	0.181964i
$593$	212.001			0.357506			0.178753	−	0.983894i	$-0.442794\pi$
$593$	212.001			0.357506			0.178753	+	0.983894i	$0.442794\pi$
$594$		0			0
$595$	−383.411	+	221.362i	−0.644388	+	0.372038i
$596$	−247.793	+	143.063i	−0.415759	+	0.240039i
$597$		0			0
$598$	451.807	−	451.807i	0.755530	−	0.755530i
$599$	−539.557	−	934.540i	−0.900763	−	1.56017i	−0.826506	−	0.562929i	$-0.809675\pi$
$599$	−539.557	−	934.540i	−0.900763	−	1.56017i	−0.0742576	−	0.997239i	$-0.523659\pi$
$600$		0			0
$601$	−148.324	+	256.905i	−0.246796	+	0.427463i	−0.962635	−	0.270802i	$-0.912711\pi$
$601$	−148.324	+	256.905i	−0.246796	+	0.427463i	0.715839	+	0.698265i	$0.246044\pi$
$602$	−460.460			−0.764884
$603$		0			0
$604$	30.6588	−	53.1026i	0.0507596	−	0.0879183i
$605$	−298.793	−	80.0614i	−0.493873	−	0.132333i
$606$		0			0
$607$	519.458	−	139.188i	0.855779	−	0.229305i	0.195851	−	0.980634i	$-0.437253\pi$
$607$	519.458	−	139.188i	0.855779	−	0.229305i	0.659929	+	0.751328i	$0.270586\pi$
$608$	380.229	−	658.577i	0.625377	−	1.08319i
$609$		0			0
$610$	72.9537	−	272.267i	0.119596	−	0.446339i
$611$	−407.763	−	109.260i	−0.667369	−	0.178821i
$612$		0			0
$613$	−414.569	−	239.351i	−0.676295	−	0.390459i	0.122163	−	0.992510i	$-0.461017\pi$
$613$	−414.569	−	239.351i	−0.676295	−	0.390459i	−0.798458	+	0.602051i	$0.794350\pi$
$614$	93.7825	+	350.001i	0.152740	+	0.570034i
$615$		0			0
$616$	−175.509	+	655.008i	−0.284917	+	1.06332i
$617$	−792.489	−	457.544i	−1.28442	−	0.741562i	−0.306769	−	0.951784i	$-0.599248\pi$
$617$	−792.489	−	457.544i	−1.28442	−	0.741562i	−0.977654	+	0.210222i	$0.932581\pi$
$618$		0			0
$619$			677.450i			1.09443i	0.836993	+	0.547213i	$0.184311\pi$
$619$			677.450i			1.09443i	−0.836993	+	0.547213i	$0.815689\pi$
$620$	−400.408	−	231.176i	−0.645820	−	0.372864i
$621$		0			0
$622$	−363.324	+	209.765i	−0.584122	+	0.337243i
$623$	−961.770	−	961.770i	−1.54377	−	1.54377i
$624$		0			0
$625$	−275.955	−	477.968i	−0.441528	−	0.764749i
$626$	88.5278	+	153.335i	0.141418	+	0.244943i
$627$		0			0
$628$		−	455.657i		−	0.725569i
$629$	71.8335	−	319.404i	0.114203	−	0.507797i
$630$		0			0
$631$	489.396	−	131.133i	0.775587	−	0.207818i	0.150749	−	0.988572i	$-0.451831\pi$
$631$	489.396	−	131.133i	0.775587	−	0.207818i	0.624838	+	0.780754i	$0.285165\pi$
$632$	−405.858	+	234.322i	−0.642180	+	0.370763i
$633$		0			0
$634$	−389.552	−	104.380i	−0.614435	−	0.164637i
$635$	−211.017	+	211.017i	−0.332310	+	0.332310i
$636$		0			0
$637$	−616.012	+	616.012i	−0.967052	+	0.967052i
$638$	−51.8203	+	89.7553i	−0.0812230	+	0.140682i
$639$		0			0
$640$			73.7981i			0.115310i
$641$	−426.808	+	739.253i	−0.665847	+	1.15328i	0.313208	+	0.949685i	$0.398596\pi$
$641$	−426.808	+	739.253i	−0.665847	+	1.15328i	−0.979055	+	0.203597i	$0.934737\pi$
$642$		0			0
$643$	−500.049	−	500.049i	−0.777682	−	0.777682i	0.201754	−	0.979436i	$-0.435336\pi$
$643$	−500.049	−	500.049i	−0.777682	−	0.777682i	−0.979436	+	0.201754i	$0.935336\pi$
$644$	579.878	−	155.378i	0.900431	−	0.241270i
$645$		0			0
$646$	−97.7506	−	364.810i	−0.151317	−	0.564722i
$647$	152.768	−	570.139i	0.236118	−	0.881205i	−0.741524	−	0.670927i	$-0.765896\pi$
$647$	152.768	−	570.139i	0.236118	−	0.881205i	0.977642	−	0.210278i	$-0.0674368\pi$
$648$		0			0
$649$	698.030	−	187.037i	1.07555	−	0.288192i
$650$	46.8119	+	27.0269i	0.0720183	+	0.0415798i
$651$		0			0
$652$	320.248	−	320.248i	0.491178	−	0.491178i
$653$	−82.0809	+	306.330i	−0.125698	+	0.469112i	−0.999864	−	0.0165162i	$-0.994742\pi$
$653$	−82.0809	+	306.330i	−0.125698	+	0.469112i	0.874165	+	0.485628i	$0.161409\pi$
$654$		0			0
$655$	772.551			1.17947
$656$		−	149.281i		−	0.227562i
$657$		0			0
$658$	337.589	+	337.589i	0.513052	+	0.513052i
$659$	291.323	−	168.195i	0.442068	−	0.255228i	−0.262406	−	0.964957i	$-0.584516\pi$
$659$	291.323	−	168.195i	0.442068	−	0.255228i	0.704475	+	0.709729i	$0.251183\pi$
$660$		0			0
$661$	43.2808	−	161.526i	0.0654777	−	0.244366i	−0.925428	−	0.378923i	$-0.876294\pi$
$661$	43.2808	−	161.526i	0.0654777	−	0.244366i	0.990906	+	0.134557i	$0.0429611\pi$
$662$	−482.657	−	835.987i	−0.729089	−	1.26282i
$663$		0			0
$664$	−265.664	−	991.473i	−0.400097	−	1.49318i
$665$			1444.90i			2.17278i
$666$		0			0
$667$	293.947			0.440701
$668$	256.858	−	68.8248i	0.384517	−	0.103031i
$669$		0			0
$670$	−524.280	+	302.693i	−0.782507	+	0.451781i
$671$	290.424	+	77.8190i	0.432823	+	0.115975i
$672$		0			0
$673$	440.255	+	762.545i	0.654168	+	1.13305i	0.982102	+	0.188352i	$0.0603146\pi$
$673$	440.255	+	762.545i	0.654168	+	1.13305i	−0.327933	+	0.944701i	$0.606352\pi$
$674$	−77.1092	+	77.1092i	−0.114405	+	0.114405i
$675$		0			0
$676$	−40.4751			−0.0598745
$677$		−	589.252i		−	0.870387i	−0.900337	−	0.435194i	$-0.856680\pi$
$677$		−	589.252i		−	0.870387i	0.900337	−	0.435194i	$-0.143320\pi$
$678$		0			0
$679$	−479.412	−	128.458i	−0.706056	−	0.189187i
$680$	254.278	+	254.278i	0.373938	+	0.373938i
$681$		0			0
$682$	−296.821	+	514.110i	−0.435222	+	0.753827i
$683$	132.731	+	495.358i	0.194335	+	0.725269i	0.992438	+	0.122747i	$0.0391705\pi$
$683$	132.731	+	495.358i	0.194335	+	0.725269i	−0.798103	+	0.602521i	$0.794163\pi$
$684$		0			0
$685$	−884.897	−	237.108i	−1.29182	−	0.346142i
$686$	211.325	−	56.6244i	0.308054	−	0.0825429i
$687$		0			0
$688$	41.4829	+	154.816i	0.0602949	+	0.225024i
$689$	−435.489	+	435.489i	−0.632059	+	0.632059i
$690$		0			0
$691$	129.121	+	74.5479i	0.186861	+	0.107884i	0.590512	−	0.807029i	$-0.298926\pi$
$691$	129.121	+	74.5479i	0.186861	+	0.107884i	−0.403651	+	0.914913i	$0.632259\pi$
$692$	346.231			0.500334
$693$		0			0
$694$	−424.421	−	245.040i	−0.611558	−	0.353083i
$695$	684.701	+	684.701i	0.985181	+	0.985181i
$696$		0			0
$697$	171.541	+	171.541i	0.246113	+	0.246113i
$698$	−21.5760	+	80.5229i	−0.0309112	+	0.115362i
$699$		0			0
$700$	25.3934	+	43.9826i	0.0362763	+	0.0628323i
$701$	−6.65363	−	24.8317i	−0.00949162	−	0.0354232i	0.961018	−	0.276487i	$-0.0891703\pi$
$701$	−6.65363	−	24.8317i	−0.00949162	−	0.0354232i	−0.970509	+	0.241064i	$0.922504\pi$
$702$		0			0
$703$	−785.547	−	724.243i	−1.11742	−	1.03022i
$704$	452.549			0.642825
$705$		0			0
$706$	254.784	−	147.100i	0.360885	−	0.208357i
$707$	−1186.98	+	685.302i	−1.67889	+	0.969310i
$708$		0			0
$709$	−78.1673	+	78.1673i	−0.110250	+	0.110250i	−0.760080	−	0.649830i	$-0.774840\pi$
$709$	−78.1673	+	78.1673i	−0.110250	+	0.110250i	0.649830	+	0.760080i	$0.274840\pi$
$710$	59.0341	+	102.250i	0.0831466	+	0.144014i
$711$		0			0
$712$	−552.389	+	956.766i	−0.775828	+	1.34377i
$713$	1683.70			2.36143
$714$		0			0
$715$	243.765	−	422.213i	0.340930	−	0.590508i
$716$	252.532	+	67.6657i	0.352698	+	0.0945052i
$717$		0			0
$718$	322.319	−	86.3652i	0.448913	−	0.120286i
$719$	−611.146	+	1058.54i	−0.849995	+	1.47223i	0.0312174	+	0.999513i	$0.490062\pi$
$719$	−611.146	+	1058.54i	−0.849995	+	1.47223i	−0.881212	+	0.472721i	$0.843272\pi$
$720$		0			0
$721$	18.2881	−	68.2521i	0.0253649	−	0.0946632i
$722$	−675.191	−	180.917i	−0.935168	−	0.250578i
$723$		0			0
$724$	−195.496	−	112.869i	−0.270022	−	0.155897i
$725$	6.43611	+	24.0199i	0.00887740	+	0.0331309i
$726$		0			0
$727$	−271.272	+	1012.40i	−0.373139	+	1.39258i	0.482905	+	0.875673i	$0.339582\pi$
$727$	−271.272	+	1012.40i	−0.373139	+	1.39258i	−0.856044	+	0.516903i	$0.827085\pi$
$728$	1089.54	+	629.044i	1.49662	+	0.864071i
$729$		0			0
$730$		−	127.157i		−	0.174187i
$731$	−225.570	−	130.233i	−0.308577	−	0.178157i
$732$		0			0
$733$	711.608	−	410.847i	0.970816	−	0.560501i	0.0713308	−	0.997453i	$-0.477275\pi$
$733$	711.608	−	410.847i	0.970816	−	0.560501i	0.899485	+	0.436952i	$0.143942\pi$
$734$	193.428	+	193.428i	0.263526	+	0.263526i
$735$		0			0
$736$	−411.517	−	712.769i	−0.559127	−	0.968436i
$737$	−322.880	−	559.244i	−0.438100	−	0.758812i
$738$		0			0
$739$		−	977.228i		−	1.32237i	−0.750225	−	0.661183i	$-0.770055\pi$
$739$		−	977.228i		−	1.32237i	0.750225	−	0.661183i	$-0.229945\pi$
$740$	309.809	+	69.6756i	0.418661	+	0.0941562i
$741$		0			0
$742$	672.783	−	180.272i	0.906715	−	0.242954i
$743$	−302.107	+	174.422i	−0.406605	+	0.234753i	−0.689330	−	0.724448i	$-0.742095\pi$
$743$	−302.107	+	174.422i	−0.406605	+	0.234753i	0.282725	+	0.959201i	$0.408762\pi$
$744$		0			0
$745$	−719.928	−	192.904i	−0.966346	−	0.258932i
$746$	320.745	−	320.745i	0.429954	−	0.429954i
$747$		0			0
$748$	−84.6635	+	84.6635i	−0.113187	+	0.113187i
$749$	−549.854	+	952.375i	−0.734117	+	1.27153i
$750$		0			0
$751$		−	357.504i		−	0.476038i	−0.971261	−	0.238019i	$-0.923502\pi$
$751$		−	357.504i		−	0.476038i	0.971261	−	0.238019i	$-0.0764980\pi$
$752$	83.0908	−	143.918i	0.110493	−	0.191380i
$753$		0			0
$754$	135.964	+	135.964i	0.180323	+	0.180323i
$755$	154.283	−	41.3399i	0.204348	−	0.0547548i
$756$		0			0
$757$	−110.753	−	413.337i	−0.146306	−	0.546020i	−0.999694	−	0.0247442i	$-0.992123\pi$
$757$	−110.753	−	413.337i	−0.146306	−	0.546020i	0.853388	−	0.521276i	$-0.174544\pi$
$758$	−109.047	+	406.970i	−0.143862	+	0.536900i
$759$		0			0
$760$	1133.63	−	303.755i	1.49162	−	0.399677i
$761$	−573.605	−	331.171i	−0.753751	−	0.435178i	0.0732965	−	0.997310i	$-0.476648\pi$
$761$	−573.605	−	331.171i	−0.753751	−	0.435178i	−0.827048	+	0.562132i	$0.809981\pi$
$762$		0			0
$763$	−615.498	+	615.498i	−0.806681	+	0.806681i
$764$	−7.40325	+	27.6293i	−0.00969012	+	0.0361640i
$765$		0			0
$766$	−93.5429			−0.122119
$767$		−	1340.72i		−	1.74801i
$768$		0			0
$769$	−341.720	−	341.720i	−0.444369	−	0.444369i	0.449109	−	0.893477i	$-0.351742\pi$
$769$	−341.720	−	341.720i	−0.444369	−	0.444369i	−0.893477	+	0.449109i	$0.851742\pi$
$770$	−477.497	+	275.683i	−0.620126	+	0.358030i
$771$		0			0
$772$	−31.9934	+	119.401i	−0.0414422	+	0.154665i
$773$	−678.332	−	1174.91i	−0.877532	−	1.51993i	−0.854041	−	0.520206i	$-0.825855\pi$
$773$	−678.332	−	1174.91i	−0.877532	−	1.51993i	−0.0234915	−	0.999724i	$-0.507478\pi$
$774$		0			0
$775$	36.8654	+	137.584i	0.0475683	+	0.177527i
$776$			403.138i			0.519508i
$777$		0			0
$778$	−283.914			−0.364928
$779$	764.768	−	204.919i	0.981730	−	0.263054i
$780$		0			0
$781$	−109.069	+	62.9712i	−0.139653	+	0.0806289i
$782$	−394.829	−	105.794i	−0.504897	−	0.135287i
$783$		0			0
$784$	−171.472	−	296.999i	−0.218715	−	0.378825i
$785$	839.287	−	839.287i	1.06916	−	1.06916i
$786$		0			0
$787$	1099.37			1.39691			0.698455	−	0.715654i	$-0.253871\pi$
$787$	1099.37			1.39691			0.698455	+	0.715654i	$0.253871\pi$
$788$		−	158.877i		−	0.201621i
$789$		0			0
$790$	−368.065	−	98.6226i	−0.465905	−	0.124839i
$791$	1029.17	+	1029.17i	1.30110	+	1.30110i
$792$		0			0
$793$	278.912	−	483.090i	0.351718	−	0.609193i
$794$	−115.871	−	432.437i	−0.145934	−	0.544631i
$795$		0			0
$796$	−375.322	−	100.567i	−0.471510	−	0.126341i
$797$	1205.32	−	322.966i	1.51233	−	0.405227i	0.595119	−	0.803638i	$-0.297105\pi$
$797$	1205.32	−	322.966i	1.51233	−	0.405227i	0.917207	+	0.398411i	$0.130438\pi$
$798$		0			0
$799$	69.8968	+	260.859i	0.0874804	+	0.326481i
$800$	49.2335	−	49.2335i	0.0615419	−	0.0615419i
$801$		0			0
$802$	−793.475	−	458.113i	−0.989370	−	0.571213i
$803$	135.637			0.168913
$804$		0			0
$805$	1354.29	+	781.898i	1.68234	+	0.971302i
$806$	778.786	+	778.786i	0.966236	+	0.966236i
$807$		0			0
$808$	787.201	+	787.201i	0.974259	+	0.974259i
$809$	163.181	−	609.002i	0.201708	−	0.752783i	−0.788720	−	0.614752i	$-0.789256\pi$
$809$	163.181	−	609.002i	0.201708	−	0.752783i	0.990428	−	0.138031i	$-0.0440773\pi$
$810$		0			0
$811$	117.951	+	204.296i	0.145438	+	0.251907i	0.929536	−	0.368730i	$-0.120207\pi$
$811$	117.951	+	204.296i	0.145438	+	0.251907i	−0.784098	+	0.620637i	$0.786874\pi$
$812$	46.7583	+	174.504i	0.0575841	+	0.214907i
$813$		0			0
$814$	89.4609	−	397.784i	0.109903	−	0.488678i
$815$	1179.75			1.44754
$816$		0			0
$817$	−736.182	+	425.035i	−0.901080	+	0.520239i
$818$	850.277	−	490.907i	1.03946	−	0.600131i
$819$		0			0
$820$	−166.387	+	166.387i	−0.202911	+	0.202911i
$821$	513.502	+	889.411i	0.625459	+	1.08333i	0.988452	+	0.151534i	$0.0484215\pi$
$821$	513.502	+	889.411i	0.625459	+	1.08333i	−0.362993	+	0.931792i	$0.618245\pi$
$822$		0			0
$823$	627.831	−	1087.44i	0.762857	−	1.32131i	−0.178515	−	0.983937i	$-0.557129\pi$
$823$	627.831	−	1087.44i	0.762857	−	1.32131i	0.941372	−	0.337370i	$-0.109537\pi$
$824$	−57.3933			−0.0696521
$825$		0			0
$826$	−758.137	+	1313.13i	−0.917841	+	1.58975i
$827$	−680.638	−	182.377i	−0.823021	−	0.220528i	−0.177354	−	0.984147i	$-0.556754\pi$
$827$	−680.638	−	182.377i	−0.823021	−	0.220528i	−0.645667	+	0.763619i	$0.723421\pi$
$828$		0			0
$829$	−59.2592	+	15.8784i	−0.0714827	+	0.0191537i	−0.294383	−	0.955687i	$-0.595114\pi$
$829$	−59.2592	+	15.8784i	−0.0714827	+	0.0191537i	0.222900	+	0.974841i	$0.428448\pi$
$830$	417.296	−	722.778i	0.502766	−	0.870817i
$831$		0			0
$832$	217.305	−	810.993i	0.261184	−	0.974751i
$833$	538.326	+	144.244i	0.646250	+	0.173162i
$834$		0			0
$835$	599.884	+	346.343i	0.718423	+	0.414782i
$836$	101.137	+	377.450i	0.120978	+	0.451495i
$837$		0			0
$838$	216.110	−	806.532i	0.257887	−	0.962449i
$839$	−1272.33	−	734.583i	−1.51649	−	0.875545i	−0.999812	−	0.0193647i	$-0.993836\pi$
$839$	−1272.33	−	734.583i	−1.51649	−	0.875545i	−0.516677	−	0.856181i	$-0.672831\pi$
$840$		0			0
$841$		−	752.541i		−	0.894817i
$842$	−122.806	−	70.9023i	−0.145851	−	0.0842070i
$843$		0			0
$844$	644.459	−	372.079i	0.763577	−	0.440852i
$845$	−74.5523	−	74.5523i	−0.0882275	−	0.0882275i
$846$		0			0
$847$	346.165	+	599.575i	0.408695	+	0.707881i
$848$	−121.222	−	209.963i	−0.142950	−	0.247597i
$849$		0			0
$850$		−	34.5799i		−	0.0406822i
$851$	−1103.92	+	344.364i	−1.29720	+	0.404658i
$852$		0			0
$853$	−274.803	+	73.6331i	−0.322160	+	0.0863225i	−0.416275	−	0.909239i	$-0.636665\pi$
$853$	−274.803	+	73.6331i	−0.322160	+	0.0863225i	0.0941148	+	0.995561i	$0.469998\pi$
$854$	−546.345	+	315.433i	−0.639749	+	0.369359i
$855$		0			0
$856$	862.800	+	231.186i	1.00794	+	0.270078i
$857$	−1.74318	+	1.74318i	−0.00203405	+	0.00203405i	−0.708123	−	0.706089i	$-0.750458\pi$
$857$	−1.74318	+	1.74318i	−0.00203405	+	0.00203405i	0.706089	+	0.708123i	$0.250458\pi$
$858$		0			0
$859$	190.721	−	190.721i	0.222027	−	0.222027i	−0.587325	−	0.809352i	$-0.699819\pi$
$859$	190.721	−	190.721i	0.222027	−	0.222027i	0.809352	+	0.587325i	$0.199819\pi$
$860$	126.321	−	218.794i	0.146884	−	0.254411i
$861$		0			0
$862$			1035.35i			1.20110i
$863$	−379.114	+	656.644i	−0.439298	+	0.760886i	−0.997635	−	0.0687280i	$-0.978106\pi$
$863$	−379.114	+	656.644i	−0.439298	+	0.760886i	0.558338	+	0.829614i	$0.311439\pi$
$864$		0			0
$865$	637.733	+	637.733i	0.737263	+	0.737263i
$866$	−276.487	+	74.0844i	−0.319269	+	0.0855478i
$867$		0			0
$868$	267.827	+	999.544i	0.308556	+	1.15155i
$869$	105.200	−	392.611i	0.121059	−	0.451797i
$870$		0			0
$871$	−1157.24	+	310.081i	−1.32863	+	0.356006i
$872$	612.295	+	353.509i	0.702174	+	0.405400i
$873$		0			0
$874$	−943.310	+	943.310i	−1.07930	+	1.07930i
$875$	−357.995	+	1336.06i	−0.409137	+	1.52692i
$876$		0			0
$877$	−670.270			−0.764276			−0.382138	−	0.924105i	$-0.624812\pi$
$877$	−670.270			−0.764276			−0.382138	+	0.924105i	$0.624812\pi$
$878$			945.139i			1.07647i
$879$		0			0
$880$	135.708	+	135.708i	0.154214	+	0.154214i
$881$	−871.329	+	503.062i	−0.989023	+	0.571013i	−0.904982	−	0.425449i	$-0.860116\pi$
$881$	−871.329	+	503.062i	−0.989023	+	0.571013i	−0.0840410	+	0.996462i	$0.526783\pi$
$882$		0			0
$883$	−276.226	+	1030.89i	−0.312827	+	1.16749i	0.613169	+	0.789952i	$0.289895\pi$
$883$	−276.226	+	1030.89i	−0.312827	+	1.16749i	−0.925996	+	0.377534i	$0.876772\pi$
$884$	111.068	+	192.376i	0.125643	+	0.217619i
$885$		0			0
$886$	80.0801	+	298.863i	0.0903839	+	0.337317i
$887$		−	712.078i		−	0.802794i	−0.915904	−	0.401397i	$-0.868525\pi$
$887$		−	712.078i		−	0.802794i	0.915904	−	0.401397i	$-0.131475\pi$
$888$		0			0
$889$	667.910			0.751305
$890$	−867.673	+	232.492i	−0.974914	+	0.261227i
$891$		0			0
$892$	−402.931	+	232.633i	−0.451717	+	0.260799i
$893$	851.352	+	228.119i	0.953361	+	0.255452i
$894$		0			0
$895$	340.510	+	589.781i	0.380458	+	0.658973i
$896$	116.793	−	116.793i	0.130349	−	0.130349i
$897$		0			0
$898$	−906.223			−1.00916
$899$			506.682i			0.563606i
$900$		0			0
$901$	380.569	+	101.973i	0.422385	+	0.113178i
$902$	213.635	+	213.635i	0.236846	+	0.236846i
$903$		0			0
$904$	591.100	−	1023.82i	0.653872	−	1.13254i
$905$	−152.191	−	567.986i	−0.168167	−	0.627609i
$906$		0			0
$907$	467.692	+	125.318i	0.515648	+	0.138167i	0.507253	−	0.861797i	$-0.330661\pi$
$907$	467.692	+	125.318i	0.515648	+	0.138167i	0.00839496	+	0.999965i	$0.497328\pi$
$908$	−183.349	+	49.1282i	−0.201926	+	0.0541059i
$909$		0			0
$910$	264.755	+	988.080i	0.290940	+	1.08580i
$911$	−253.840	+	253.840i	−0.278639	+	0.278639i	−0.832566	−	0.553926i	$-0.813129\pi$
$911$	−253.840	+	253.840i	−0.278639	+	0.278639i	0.553926	+	0.832566i	$0.313129\pi$
$912$		0			0
$913$	770.981	+	445.126i	0.844448	+	0.487542i
$914$	784.758			0.858598
$915$		0			0
$916$	−213.938	−	123.517i	−0.233557	−	0.134844i
$917$	−1222.64	−	1222.64i	−1.33330	−	1.33330i
$918$		0			0
$919$	139.040	+	139.040i	0.151295	+	0.151295i	0.778696	−	0.627401i	$-0.215881\pi$
$919$	139.040	+	139.040i	0.151295	+	0.151295i	−0.627401	+	0.778696i	$0.715881\pi$
$920$	328.750	−	1226.91i	0.357337	−	1.33360i
$921$		0			0
$922$	−23.4256	−	40.5744i	−0.0254074	−	0.0440070i
$923$	60.4750	+	225.696i	0.0655201	+	0.244524i
$924$		0			0
$925$	−52.3105	−	82.6666i	−0.0565519	−	0.0893693i
$926$	960.896			1.03769
$927$		0			0
$928$	214.496	−	123.839i	0.231138	−	0.133447i
$929$	787.773	−	454.821i	0.847980	−	0.489581i	−0.0119891	−	0.999928i	$-0.503816\pi$
$929$	787.773	−	454.821i	0.847980	−	0.489581i	0.859969	+	0.510347i	$0.170483\pi$
$930$		0			0
$931$	1286.15	−	1286.15i	1.38147	−	1.38147i
$932$	14.0372	+	24.3131i	0.0150614	+	0.0260871i
$933$		0			0
$934$	580.225	−	1004.98i	0.621226	−	1.07599i
$935$	−311.888			−0.333570
$936$		0			0
$937$	−288.355	+	499.445i	−0.307742	+	0.533025i	−0.977868	−	0.209222i	$-0.932907\pi$
$937$	−288.355	+	499.445i	−0.307742	+	0.533025i	0.670126	+	0.742248i	$0.266240\pi$
$938$	1308.77	+	350.683i	1.39527	+	0.373862i
$939$		0			0
$940$	−253.022	+	67.7971i	−0.269172	+	0.0721245i
$941$	168.639	−	292.092i	0.179213	−	0.310406i	−0.762398	−	0.647108i	$-0.775978\pi$
$941$	168.639	−	292.092i	0.179213	−	0.310406i	0.941611	+	0.336702i	$0.109312\pi$
$942$		0			0
$943$	221.781	−	827.698i	0.235187	−	0.877728i
$944$	509.802	+	136.601i	0.540045	+	0.144705i
$945$		0			0
$946$	−280.923	−	162.191i	−0.296959	−	0.171449i
$947$	63.7196	+	237.805i	0.0672858	+	0.251114i	0.991374	−	0.131066i	$-0.0418400\pi$
$947$	63.7196	+	237.805i	0.0672858	+	0.251114i	−0.924088	+	0.382180i	$0.875173\pi$
$948$		0			0
$949$	65.1301	−	243.069i	0.0686302	−	0.256132i
$950$	−97.7367	−	56.4283i	−0.102881	−	0.0593982i
$951$		0			0
$952$		−	804.838i		−	0.845419i
$953$	−139.338	−	80.4471i	−0.146210	−	0.0844146i	0.425110	−	0.905142i	$-0.360235\pi$
$953$	−139.338	−	80.4471i	−0.146210	−	0.0844146i	−0.571321	+	0.820727i	$0.693569\pi$
$954$		0			0
$955$	−64.5275	+	37.2549i	−0.0675680	+	0.0390104i
$956$	128.835	+	128.835i	0.134764	+	0.134764i
$957$		0			0
$958$	167.195	+	289.590i	0.174525	+	0.302286i
$959$	1025.19	+	1775.68i	1.06902	+	1.85160i
$960$		0			0
$961$			1941.22i			2.02000i
$962$	−669.894	−	351.327i	−0.696356	−	0.365205i
$963$		0			0
$964$	−133.998	+	35.9048i	−0.139003	+	0.0372456i
$965$	−278.858	+	160.999i	−0.288972	+	0.166838i
$966$		0			0
$967$	169.499	+	45.4170i	0.175283	+	0.0469669i	0.345393	−	0.938458i	$-0.387746\pi$
$967$	169.499	+	45.4170i	0.175283	+	0.0469669i	−0.170110	+	0.985425i	$0.554412\pi$
$968$	397.637	−	397.637i	0.410782	−	0.410782i
$969$		0			0
$970$	−231.780	+	231.780i	−0.238949	+	0.238949i
$971$	−97.7021	+	169.225i	−0.100620	+	0.174279i	−0.911940	−	0.410323i	$-0.865416\pi$
$971$	−97.7021	+	169.225i	−0.100620	+	0.174279i	0.811320	+	0.584602i	$0.198749\pi$
$972$		0			0
$973$		−	2167.21i		−	2.22735i
$974$	−460.344	+	797.339i	−0.472632	+	0.818623i
$975$		0			0
$976$	155.275	+	155.275i	0.159093	+	0.159093i
$977$	469.773	−	125.875i	0.480832	−	0.128839i	−0.0102579	−	0.999947i	$-0.503265\pi$
$977$	469.773	−	125.875i	0.480832	−	0.128839i	0.491090	+	0.871109i	$0.336599\pi$
$978$		0			0
$979$	−247.997	−	925.539i	−0.253317	−	0.945392i
$980$	−139.911	+	522.155i	−0.142766	+	0.532811i
$981$		0			0
$982$	−740.268	+	198.354i	−0.753837	+	0.201990i
$983$	−500.998	−	289.252i	−0.509663	−	0.294254i	0.223032	−	0.974811i	$-0.428404\pi$
$983$	−500.998	−	289.252i	−0.509663	−	0.294254i	−0.732695	+	0.680557i	$0.761738\pi$
$984$		0			0
$985$	292.641	−	292.641i	0.297097	−	0.297097i
$986$	31.8370	−	118.817i	0.0322890	−	0.120504i
$987$		0			0
$988$	724.975			0.733781
$989$			920.020i			0.930253i
$990$		0			0
$991$	573.392	+	573.392i	0.578600	+	0.578600i	0.934517	−	0.355918i	$-0.115832\pi$
$991$	573.392	+	573.392i	0.578600	+	0.578600i	−0.355918	+	0.934517i	$0.615832\pi$
$992$	1228.61	−	709.338i	1.23852	−	0.715059i
$993$		0			0
$994$	68.3935	−	255.248i	0.0688064	−	0.256789i
$995$	−506.078	−	876.553i	−0.508621	−	0.880958i
$996$		0			0
$997$	403.328	+	1505.24i	0.404542	+	1.50977i	0.804899	+	0.593412i	$0.202219\pi$
$997$	403.328	+	1505.24i	0.404542	+	1.50977i	−0.400357	+	0.916359i	$0.631114\pi$
$998$		−	1302.29i		−	1.30490i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.bb.c.199.2		24
3.2	odd	2		111.3.l.a.88.5	yes	24
37.8	odd	12	inner	333.3.bb.c.82.2		24
111.8	even	12		111.3.l.a.82.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.3.l.a.82.5	✓	24	111.8	even	12
111.3.l.a.88.5	yes	24	3.2	odd	2
333.3.bb.c.82.2		24	37.8	odd	12	inner
333.3.bb.c.199.2		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:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42776 + 0.382568i) q^{2} +(-1.57196 + 0.907569i) q^{4} +(-4.56711 - 1.22375i) q^{5} +(5.29119 + 9.16460i) q^{7} +(6.07795 - 6.07795i) q^{8} +O(q^{10})\)	\(q+(-1.42776 + 0.382568i) q^{2} +(-1.57196 + 0.907569i) q^{4} +(-4.56711 - 1.22375i) q^{5} +(5.29119 + 9.16460i) q^{7} +(6.07795 - 6.07795i) q^{8} +6.98891 q^{10} +7.45500i q^{11} +(13.3598 + 3.57975i) q^{13} +(-11.0606 - 11.0606i) q^{14} +(-2.72236 + 4.71527i) q^{16} +(-2.29008 - 8.54668i) q^{17} +(-27.8934 - 7.47401i) q^{19} +(8.28993 - 2.22128i) q^{20} +(-2.85204 - 10.6440i) q^{22} +(-22.0996 + 22.0996i) q^{23} +(-2.28975 - 1.32199i) q^{25} -20.4441 q^{26} +(-16.6350 - 9.60424i) q^{28} +(-6.65051 - 6.65051i) q^{29} +(-38.0935 - 38.0935i) q^{31} +(-6.81576 + 25.4368i) q^{32} +(6.53937 + 11.3265i) q^{34} +(-12.9502 - 48.3308i) q^{35} +(32.7671 + 17.1848i) q^{37} +42.6844 q^{38} +(-35.1965 + 20.3207i) q^{40} +(-23.7443 + 13.7088i) q^{41} +(20.8153 - 20.8153i) q^{43} +(-6.76593 - 11.7189i) q^{44} +(23.0984 - 40.0076i) q^{46} -30.5216 q^{47} +(-31.4933 + 54.5480i) q^{49} +(3.77497 + 1.01150i) q^{50} +(-24.2499 + 6.49773i) q^{52} +(-22.2641 + 38.5626i) q^{53} +(9.12308 - 34.0478i) q^{55} +(87.8615 + 23.5424i) q^{56} +(12.0396 + 6.95107i) q^{58} +(-25.0887 - 93.6324i) q^{59} +(10.4385 - 38.9570i) q^{61} +(68.9617 + 39.8151i) q^{62} -60.7040i q^{64} +(-56.6349 - 32.6982i) q^{65} +(-75.0160 + 43.3105i) q^{67} +(11.3566 + 11.3566i) q^{68} +(36.9796 + 64.0506i) q^{70} +(8.44683 + 14.6303i) q^{71} -18.1941i q^{73} +(-53.3580 - 12.0001i) q^{74} +(50.6304 - 13.5664i) q^{76} +(-68.3222 + 39.4458i) q^{77} +(-52.6641 - 14.1113i) q^{79} +(18.2036 - 18.2036i) q^{80} +(28.6566 - 28.6566i) q^{82} +(59.7083 - 103.418i) q^{83} +41.8361i q^{85} +(-21.7560 + 37.6825i) q^{86} +(45.3111 + 45.3111i) q^{88} +(-124.150 + 33.2659i) q^{89} +(37.8822 + 141.378i) q^{91} +(14.6827 - 54.7966i) q^{92} +(43.5776 - 11.6766i) q^{94} +(118.246 + 68.2692i) q^{95} +(-33.1640 + 33.1640i) q^{97} +(24.0966 - 89.9299i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8}+O(q^{10}) \) 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8	\( 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8} + 36 q^{10} + 4 q^{13} + 6 q^{14} + 26 q^{16} - 46 q^{17} - 156 q^{19} - 68 q^{20} + 32 q^{22} - 10 q^{23} - 90 q^{25} + 164 q^{26} - 48 q^{28} + 28 q^{29} + 120 q^{31} - 90 q^{32} + 46 q^{34} + 186 q^{35} + 56 q^{37} - 4 q^{38} + 216 q^{40} + 30 q^{41} + 250 q^{43} - 284 q^{44} - 18 q^{46} - 232 q^{47} - 164 q^{49} - 226 q^{50} - 488 q^{52} - 122 q^{53} - 250 q^{55} + 632 q^{56} - 360 q^{58} + 258 q^{59} + 108 q^{61} + 186 q^{62} - 162 q^{65} + 60 q^{67} - 214 q^{68} + 246 q^{70} - 174 q^{71} + 8 q^{74} - 498 q^{76} - 666 q^{77} - 104 q^{79} + 24 q^{80} + 1114 q^{82} + 26 q^{83} + 72 q^{86} - 334 q^{88} - 16 q^{89} + 20 q^{91} + 918 q^{92} + 400 q^{94} + 372 q^{95} - 278 q^{97} - 950 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8 + 36 * q^10 + 4 * q^13 + 6 * q^14 + 26 * q^16 - 46 * q^17 - 156 * q^19 - 68 * q^20 + 32 * q^22 - 10 * q^23 - 90 * q^25 + 164 * q^26 - 48 * q^28 + 28 * q^29 + 120 * q^31 - 90 * q^32 + 46 * q^34 + 186 * q^35 + 56 * q^37 - 4 * q^38 + 216 * q^40 + 30 * q^41 + 250 * q^43 - 284 * q^44 - 18 * q^46 - 232 * q^47 - 164 * q^49 - 226 * q^50 - 488 * q^52 - 122 * q^53 - 250 * q^55 + 632 * q^56 - 360 * q^58 + 258 * q^59 + 108 * q^61 + 186 * q^62 - 162 * q^65 + 60 * q^67 - 214 * q^68 + 246 * q^70 - 174 * q^71 + 8 * q^74 - 498 * q^76 - 666 * q^77 - 104 * q^79 + 24 * q^80 + 1114 * q^82 + 26 * q^83 + 72 * q^86 - 334 * q^88 - 16 * q^89 + 20 * q^91 + 918 * q^92 + 400 * q^94 + 372 * q^95 - 278 * q^97 - 950 * q^98

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