LMFDB - Embedded newform 288.3.u.b.91.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(19,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

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

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

chi := DirichletCharacter("288.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.u (of order $8$, 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:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			91.3
Character	$\chi$	$=$	288.91
Dual form			288.3.u.b.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64362 + 1.13952i) q^{2} +(1.40297 - 3.74589i) q^{4} +(-0.838363 - 0.347262i) q^{5} +(8.29065 - 8.29065i) q^{7} +(1.96258 + 7.75553i) q^{8} +O(q^{10})$	\(q+(-1.64362 + 1.13952i) q^{2} +(1.40297 - 3.74589i) q^{4} +(-0.838363 - 0.347262i) q^{5} +(8.29065 - 8.29065i) q^{7} +(1.96258 + 7.75553i) q^{8} +(1.77366 - 0.384569i) q^{10} +(-6.14387 - 2.54487i) q^{11} +(-17.7917 + 7.36955i) q^{13} +(-4.17929 + 23.0741i) q^{14} +(-12.0633 - 10.5107i) q^{16} -24.0244i q^{17} +(5.48690 + 13.2466i) q^{19} +(-2.47700 + 2.65322i) q^{20} +(12.9981 - 2.81828i) q^{22} +(-10.1957 - 10.1957i) q^{23} +(-17.0954 - 17.0954i) q^{25} +(20.8450 - 32.3868i) q^{26} +(-19.4243 - 42.6874i) q^{28} +(-4.28415 - 10.3428i) q^{29} -17.7042i q^{31} +(31.8048 + 3.52921i) q^{32} +(27.3764 + 39.4871i) q^{34} +(-9.82961 + 4.07156i) q^{35} +(53.2287 + 22.0480i) q^{37} +(-24.1131 - 15.5198i) q^{38} +(1.04785 - 7.18348i) q^{40} +(23.6060 - 23.6060i) q^{41} +(-52.0091 - 21.5429i) q^{43} +(-18.1525 + 19.4439i) q^{44} +(28.3762 + 5.13963i) q^{46} -23.8851 q^{47} -88.4698i q^{49} +(47.5790 + 8.61773i) q^{50} +(2.64430 + 76.9849i) q^{52} +(24.9038 - 60.1231i) q^{53} +(4.26706 + 4.26706i) q^{55} +(80.5695 + 48.0274i) q^{56} +(18.8274 + 12.1178i) q^{58} +(19.1521 - 46.2372i) q^{59} +(-22.9673 - 55.4479i) q^{61} +(20.1744 + 29.0990i) q^{62} +(-56.2966 + 30.4416i) q^{64} +17.4750 q^{65} +(29.6299 - 12.2731i) q^{67} +(-89.9929 - 33.7056i) q^{68} +(11.5165 - 17.8932i) q^{70} +(-93.5151 + 93.5151i) q^{71} +(5.74210 - 5.74210i) q^{73} +(-112.612 + 24.4167i) q^{74} +(57.3181 - 1.96878i) q^{76} +(-72.0354 + 29.8380i) q^{77} +12.0352 q^{79} +(6.46349 + 13.0010i) q^{80} +(-11.8997 + 65.6989i) q^{82} +(33.2639 + 80.3062i) q^{83} +(-8.34277 + 20.1412i) q^{85} +(110.032 - 23.8573i) q^{86} +(7.67905 - 52.6435i) q^{88} +(37.0638 + 37.0638i) q^{89} +(-86.4062 + 208.603i) q^{91} +(-52.4964 + 23.8878i) q^{92} +(39.2580 - 27.2176i) q^{94} -13.0108i q^{95} +68.8610 q^{97} +(100.813 + 145.411i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 40 q^{10} - 32 q^{14} - 8 q^{16} + 160 q^{20} - 184 q^{22} - 128 q^{23} + 200 q^{26} - 120 q^{28} - 40 q^{32} + 120 q^{34} + 192 q^{35} - 280 q^{38} + 584 q^{40} - 192 q^{43} - 104 q^{44} + 32 q^{46} + 312 q^{50} - 424 q^{52} - 320 q^{53} - 256 q^{55} + 392 q^{56} - 352 q^{58} + 256 q^{59} + 64 q^{61} + 48 q^{62} + 408 q^{64} + 64 q^{67} - 856 q^{68} + 984 q^{70} - 512 q^{71} - 1056 q^{74} + 296 q^{76} + 448 q^{77} + 512 q^{79} - 328 q^{80} - 760 q^{82} + 448 q^{86} - 1072 q^{88} + 192 q^{91} + 784 q^{92} - 480 q^{94} - 272 q^{98}+O(q^{100}) $ 64 * q + 40 * q^10 - 32 * q^14 - 8 * q^16 + 160 * q^20 - 184 * q^22 - 128 * q^23 + 200 * q^26 - 120 * q^28 - 40 * q^32 + 120 * q^34 + 192 * q^35 - 280 * q^38 + 584 * q^40 - 192 * q^43 - 104 * q^44 + 32 * q^46 + 312 * q^50 - 424 * q^52 - 320 * q^53 - 256 * q^55 + 392 * q^56 - 352 * q^58 + 256 * q^59 + 64 * q^61 + 48 * q^62 + 408 * q^64 + 64 * q^67 - 856 * q^68 + 984 * q^70 - 512 * q^71 - 1056 * q^74 + 296 * q^76 + 448 * q^77 + 512 * q^79 - 328 * q^80 - 760 * q^82 + 448 * q^86 - 1072 * q^88 + 192 * q^91 + 784 * q^92 - 480 * q^94 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$-1$

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 $

$2$	−1.64362	+	1.13952i	−0.821810	+	0.569762i
$2$	−1.64362	+	1.13952i	−0.821810	+	0.569762i
$3$		0			0
$3$		0			0
$4$	1.40297	−	3.74589i	0.350743	−	0.936472i
$5$	−0.838363	−	0.347262i	−0.167673	−	0.0694523i	0.297268	−	0.954794i	$-0.403924\pi$
$5$	−0.838363	−	0.347262i	−0.167673	−	0.0694523i	−0.464941	+	0.885342i	$0.653924\pi$
$6$		0			0
$7$	8.29065	−	8.29065i	1.18438	−	1.18438i	0.205781	−	0.978598i	$-0.434027\pi$
$7$	8.29065	−	8.29065i	1.18438	−	1.18438i	0.978598	−	0.205781i	$-0.0659734\pi$
$8$	1.96258	+	7.75553i	0.245322	+	0.969442i
$9$		0			0
$10$	1.77366	−	0.384569i	0.177366	−	0.0384569i
$11$	−6.14387	−	2.54487i	−0.558534	−	0.231352i	0.0855148	−	0.996337i	$-0.472746\pi$
$11$	−6.14387	−	2.54487i	−0.558534	−	0.231352i	−0.644048	+	0.764985i	$0.722746\pi$
$12$		0			0
$13$	−17.7917	+	7.36955i	−1.36859	+	0.566889i	−0.941406	−	0.337276i	$-0.890494\pi$
$13$	−17.7917	+	7.36955i	−1.36859	+	0.566889i	−0.427184	+	0.904165i	$0.640494\pi$
$14$	−4.17929	+	23.0741i	−0.298520	+	1.64815i
$15$		0			0
$16$	−12.0633	−	10.5107i	−0.753959	−	0.656922i
$17$		−	24.0244i		−	1.41320i	−0.707612	−	0.706601i	$-0.750227\pi$
$17$		−	24.0244i		−	1.41320i	0.707612	−	0.706601i	$-0.249773\pi$
$18$		0			0
$19$	5.48690	+	13.2466i	0.288784	+	0.697187i	0.999983	−	0.00580389i	$-0.00184745\pi$
$19$	5.48690	+	13.2466i	0.288784	+	0.697187i	−0.711199	+	0.702991i	$0.751847\pi$
$20$	−2.47700	+	2.65322i	−0.123850	+	0.132661i
$21$		0			0
$22$	12.9981	−	2.81828i	0.590824	−	0.128104i
$23$	−10.1957	−	10.1957i	−0.443293	−	0.443293i	0.449824	−	0.893117i	$-0.351487\pi$
$23$	−10.1957	−	10.1957i	−0.443293	−	0.443293i	−0.893117	+	0.449824i	$0.851487\pi$
$24$		0			0
$25$	−17.0954	−	17.0954i	−0.683816	−	0.683816i
$26$	20.8450	−	32.3868i	0.801729	−	1.24564i
$27$		0			0
$28$	−19.4243	−	42.6874i	−0.693725	−	1.52455i
$29$	−4.28415	−	10.3428i	−0.147729	−	0.356650i	0.832642	−	0.553812i	$-0.186827\pi$
$29$	−4.28415	−	10.3428i	−0.147729	−	0.356650i	−0.980371	+	0.197162i	$0.936827\pi$
$30$		0			0
$31$		−	17.7042i		−	0.571104i	−0.958363	−	0.285552i	$-0.907823\pi$
$31$		−	17.7042i		−	0.571104i	0.958363	−	0.285552i	$-0.0921769\pi$
$32$	31.8048	+	3.52921i	0.993900	+	0.110288i
$33$		0			0
$34$	27.3764	+	39.4871i	0.805189	+	1.16138i
$35$	−9.82961	+	4.07156i	−0.280846	+	0.116330i
$36$		0			0
$37$	53.2287	+	22.0480i	1.43861	+	0.595893i	0.959462	−	0.281839i	$-0.0909445\pi$
$37$	53.2287	+	22.0480i	1.43861	+	0.595893i	0.479151	+	0.877732i	$0.340945\pi$
$38$	−24.1131	−	15.5198i	−0.634556	−	0.408417i
$39$		0			0
$40$	1.04785	−	7.18348i	0.0261962	−	0.179587i
$41$	23.6060	−	23.6060i	0.575756	−	0.575756i	−0.357975	−	0.933731i	$-0.616533\pi$
$41$	23.6060	−	23.6060i	0.575756	−	0.575756i	0.933731	+	0.357975i	$0.116533\pi$
$42$		0			0
$43$	−52.0091	−	21.5429i	−1.20951	−	0.500997i	−0.315452	−	0.948941i	$-0.602156\pi$
$43$	−52.0091	−	21.5429i	−1.20951	−	0.500997i	−0.894061	+	0.447944i	$0.852156\pi$
$44$	−18.1525	+	19.4439i	−0.412557	+	0.441906i
$45$		0			0
$46$	28.3762	+	5.13963i	0.616874	+	0.111731i
$47$	−23.8851			−0.508194			−0.254097	−	0.967179i	$-0.581778\pi$
$47$	−23.8851			−0.508194			−0.254097	+	0.967179i	$0.581778\pi$
$48$		0			0
$49$		−	88.4698i		−	1.80551i
$50$	47.5790	+	8.61773i	0.951579	+	0.172355i
$51$		0			0
$52$	2.64430	+	76.9849i	0.0508519	+	1.48048i
$53$	24.9038	−	60.1231i	0.469883	−	1.13440i	−0.494331	−	0.869274i	$-0.664587\pi$
$53$	24.9038	−	60.1231i	0.469883	−	1.13440i	0.964214	−	0.265125i	$-0.0854132\pi$
$54$		0			0
$55$	4.26706	+	4.26706i	0.0775829	+	0.0775829i
$56$	80.5695	+	48.0274i	1.43874	+	0.857632i
$57$		0			0
$58$	18.8274	+	12.1178i	0.324611	+	0.208928i
$59$	19.1521	−	46.2372i	0.324611	−	0.783681i	−0.674363	−	0.738400i	$-0.735582\pi$
$59$	19.1521	−	46.2372i	0.324611	−	0.783681i	0.998974	−	0.0452808i	$-0.0144182\pi$
$60$		0			0
$61$	−22.9673	−	55.4479i	−0.376512	−	0.908981i	−0.992614	−	0.121315i	$-0.961289\pi$
$61$	−22.9673	−	55.4479i	−0.376512	−	0.908981i	0.616102	−	0.787667i	$-0.288711\pi$
$62$	20.1744	+	29.0990i	0.325393	+	0.469339i
$63$		0			0
$64$	−56.2966	+	30.4416i	−0.879634	+	0.475651i
$65$	17.4750			0.268847
$66$		0			0
$67$	29.6299	−	12.2731i	0.442237	−	0.183181i	−0.150443	−	0.988619i	$-0.548070\pi$
$67$	29.6299	−	12.2731i	0.442237	−	0.183181i	0.592680	+	0.805438i	$0.298070\pi$
$68$	−89.9929	−	33.7056i	−1.32342	−	0.495671i
$69$		0			0
$70$	11.5165	−	17.8932i	0.164521	−	0.255617i
$71$	−93.5151	+	93.5151i	−1.31711	+	1.31711i	−0.401065	+	0.916049i	$0.631360\pi$
$71$	−93.5151	+	93.5151i	−1.31711	+	1.31711i	−0.916049	+	0.401065i	$0.868640\pi$
$72$		0			0
$73$	5.74210	−	5.74210i	0.0786589	−	0.0786589i	−0.666683	−	0.745342i	$-0.732286\pi$
$73$	5.74210	−	5.74210i	0.0786589	−	0.0786589i	0.745342	+	0.666683i	$0.232286\pi$
$74$	−112.612	+	24.4167i	−1.52178	+	0.329956i
$75$		0			0
$76$	57.3181	−	1.96878i	0.754185	−	0.0259050i
$77$	−72.0354	+	29.8380i	−0.935524	+	0.387507i
$78$		0			0
$79$	12.0352			0.152344			0.0761719	−	0.997095i	$-0.475730\pi$
$79$	12.0352			0.152344			0.0761719	+	0.997095i	$0.475730\pi$
$80$	6.46349	+	13.0010i	0.0807936	+	0.162512i
$81$		0			0
$82$	−11.8997	+	65.6989i	−0.145118	+	0.801206i
$83$	33.2639	+	80.3062i	0.400770	+	0.967545i	0.987480	+	0.157747i	$0.0504231\pi$
$83$	33.2639	+	80.3062i	0.400770	+	0.967545i	−0.586709	+	0.809798i	$0.699577\pi$
$84$		0			0
$85$	−8.34277	+	20.1412i	−0.0981502	+	0.236956i
$86$	110.032	−	23.8573i	1.27944	−	0.277411i
$87$		0			0
$88$	7.67905	−	52.6435i	0.0872619	−	0.598222i
$89$	37.0638	+	37.0638i	0.416447	+	0.416447i	0.883977	−	0.467530i	$-0.154856\pi$
$89$	37.0638	+	37.0638i	0.416447	+	0.416447i	−0.467530	+	0.883977i	$0.654856\pi$
$90$		0			0
$91$	−86.4062	+	208.603i	−0.949518	+	2.29234i
$92$	−52.4964	+	23.8878i	−0.570614	+	0.259650i
$93$		0			0
$94$	39.2580	−	27.2176i	0.417639	−	0.289549i
$95$		−	13.0108i		−	0.136956i
$96$		0			0
$97$	68.8610			0.709907			0.354954	−	0.934884i	$-0.384497\pi$
$97$	68.8610			0.709907			0.354954	+	0.934884i	$0.384497\pi$
$98$	100.813	+	145.411i	1.02871	+	1.48378i
$99$		0			0
$100$	−88.0218	+	40.0531i	−0.880218	+	0.400531i
$101$	−120.572	−	49.9426i	−1.19378	−	0.494481i	−0.304798	−	0.952417i	$-0.598589\pi$
$101$	−120.572	−	49.9426i	−1.19378	−	0.494481i	−0.888985	+	0.457936i	$0.848589\pi$
$102$		0			0
$103$	−102.029	+	102.029i	−0.990574	+	0.990574i	−0.999956	−	0.00938185i	$-0.997014\pi$
$103$	−102.029	+	102.029i	−0.990574	+	0.990574i	0.00938185	+	0.999956i	$0.497014\pi$
$104$	−92.0723	−	123.521i	−0.885310	−	1.18770i
$105$		0			0
$106$	27.5793	+	127.198i	0.260182	+	1.19998i
$107$	142.225	+	58.9117i	1.32921	+	0.550576i	0.930430	−	0.366470i	$-0.119434\pi$
$107$	142.225	+	58.9117i	1.32921	+	0.550576i	0.398779	+	0.917047i	$0.369434\pi$
$108$		0			0
$109$	−7.88125	+	3.26452i	−0.0723050	+	0.0299497i	−0.418543	−	0.908197i	$-0.637459\pi$
$109$	−7.88125	+	3.26452i	−0.0723050	+	0.0299497i	0.346238	+	0.938147i	$0.387459\pi$
$110$	−11.8758	−	2.15101i	−0.107962	−	0.0195546i
$111$		0			0
$112$	−187.154	+	12.8720i	−1.67102	+	0.114929i
$113$			76.6219i			0.678070i	0.940774	+	0.339035i	$0.110101\pi$
$113$			76.6219i			0.678070i	−0.940774	+	0.339035i	$0.889899\pi$
$114$		0			0
$115$	5.00715	+	12.0883i	0.0435404	+	0.105116i
$116$	−44.7537	+	1.53721i	−0.385808	+	0.0132518i
$117$		0			0
$118$	21.2096	+	97.8205i	0.179743	+	0.828988i
$119$	−199.178	−	199.178i	−1.67377	−	1.67377i
$120$		0			0
$121$	−54.2892	−	54.2892i	−0.448671	−	0.448671i
$122$	100.934	+	64.9635i	0.827324	+	0.532487i
$123$		0			0
$124$	−66.3180	−	24.8385i	−0.534823	−	0.200311i
$125$	17.0771	+	41.2278i	0.136617	+	0.329823i
$126$		0			0
$127$			33.7402i			0.265671i	0.991138	+	0.132836i	$0.0424082\pi$
$127$			33.7402i			0.265671i	−0.991138	+	0.132836i	$0.957592\pi$
$128$	57.8412	−	114.186i	0.451885	−	0.892076i
$129$		0			0
$130$	−28.7223	+	19.9132i	−0.220941	+	0.153179i
$131$	113.023	−	46.8157i	0.862771	−	0.357372i	0.0929806	−	0.995668i	$-0.470361\pi$
$131$	113.023	−	46.8157i	0.862771	−	0.357372i	0.769791	+	0.638296i	$0.220361\pi$
$132$		0			0
$133$	155.313	+	64.3326i	1.16776	+	0.483704i
$134$	−34.7148	+	53.9362i	−0.259065	+	0.402509i
$135$		0			0
$136$	186.322	−	47.1498i	1.37002	−	0.346690i
$137$	176.652	−	176.652i	1.28943	−	1.28943i	0.354300	−	0.935132i	$-0.384719\pi$
$137$	176.652	−	176.652i	1.28943	−	1.28943i	0.935132	−	0.354300i	$-0.115281\pi$
$138$		0			0
$139$	128.036	+	53.0343i	0.921122	+	0.381541i	0.792304	−	0.610127i	$-0.208882\pi$
$139$	128.036	+	53.0343i	0.921122	+	0.381541i	0.128819	+	0.991668i	$0.458882\pi$
$140$	1.46093	+	42.5329i	0.0104352	+	0.303806i
$141$		0			0
$142$	47.1406	−	260.266i	0.331976	−	1.83286i
$143$	128.064			0.895554
$144$		0			0
$145$			10.1588i			0.0700606i
$146$	−2.89457	+	15.9811i	−0.0198258	+	0.109459i
$147$		0			0
$148$	157.268	−	168.456i	1.06262	−	1.13822i
$149$	−48.0790	+	116.073i	−0.322678	+	0.779013i	0.676419	+	0.736517i	$0.263531\pi$
$149$	−48.0790	+	116.073i	−0.322678	+	0.779013i	−0.999097	+	0.0424957i	$0.986469\pi$
$150$		0			0
$151$	9.11537	+	9.11537i	0.0603667	+	0.0603667i	0.736646	−	0.676279i	$-0.236409\pi$
$151$	9.11537	+	9.11537i	0.0603667	+	0.0603667i	−0.676279	+	0.736646i	$0.736409\pi$
$152$	−91.9656	+	68.5512i	−0.605037	+	0.450995i
$153$		0			0
$154$	84.3976	−	131.128i	0.548036	−	0.851483i
$155$	−6.14800	+	14.8426i	−0.0396645	+	0.0957586i
$156$		0			0
$157$	−53.7611	−	129.791i	−0.342428	−	0.826693i	−0.997469	−	0.0711004i	$-0.977349\pi$
$157$	−53.7611	−	129.791i	−0.342428	−	0.826693i	0.655042	−	0.755593i	$-0.272651\pi$
$158$	−19.7812	+	13.7143i	−0.125198	+	0.0867996i
$159$		0			0
$160$	−25.4384	−	14.0033i	−0.158990	−	0.0875209i
$161$	−169.059			−1.05005
$162$		0			0
$163$	23.8951	−	9.89767i	0.146596	−	0.0607219i	−0.308179	−	0.951328i	$-0.599720\pi$
$163$	23.8951	−	9.89767i	0.146596	−	0.0607219i	0.454775	+	0.890606i	$0.349720\pi$
$164$	−55.3069	−	121.544i	−0.337237	−	0.741122i
$165$		0			0
$166$	−146.184	−	94.0879i	−0.880627	−	0.566794i
$167$	54.9882	−	54.9882i	0.329270	−	0.329270i	−0.523039	−	0.852309i	$-0.675202\pi$
$167$	54.9882	−	54.9882i	0.329270	−	0.329270i	0.852309	+	0.523039i	$0.175202\pi$
$168$		0			0
$169$	142.732	−	142.732i	0.844569	−	0.844569i
$170$	−9.23906	−	42.6113i	−0.0543474	−	0.250655i
$171$		0			0
$172$	−153.664	+	164.596i	−0.893398	+	0.956954i
$173$	8.82776	−	3.65658i	0.0510275	−	0.0211363i	−0.357024	−	0.934095i	$-0.616208\pi$
$173$	8.82776	−	3.65658i	0.0510275	−	0.0211363i	0.408051	+	0.912959i	$0.366208\pi$
$174$		0			0
$175$	−283.464			−1.61980
$176$	47.3671	+	95.2763i	0.269131	+	0.541343i
$177$		0			0
$178$	−103.154	−	18.6837i	−0.579516	−	0.104965i
$179$	66.9427	+	161.614i	0.373982	+	0.902871i	0.993067	+	0.117548i	$0.0375034\pi$
$179$	66.9427	+	161.614i	0.373982	+	0.902871i	−0.619086	+	0.785323i	$0.712497\pi$
$180$		0			0
$181$	−3.82502	+	9.23442i	−0.0211327	+	0.0510189i	−0.934094	−	0.357028i	$-0.883790\pi$
$181$	−3.82502	+	9.23442i	−0.0211327	+	0.0510189i	0.912961	+	0.408047i	$0.133790\pi$
$182$	−95.6891	−	441.326i	−0.525764	−	2.42487i
$183$		0			0
$184$	59.0635	−	99.0833i	0.320997	−	0.538496i
$185$	−36.9685	−	36.9685i	−0.199830	−	0.199830i
$186$		0			0
$187$	−61.1392	+	147.603i	−0.326948	+	0.789321i
$188$	−33.5101	+	89.4709i	−0.178245	+	0.475909i
$189$		0			0
$190$	14.8261	+	21.3848i	0.0780323	+	0.112552i
$191$			263.217i			1.37810i	0.724714	+	0.689050i	$0.241972\pi$
$191$			263.217i			1.37810i	−0.724714	+	0.689050i	$0.758028\pi$
$192$		0			0
$193$	300.436			1.55666			0.778332	−	0.627853i	$-0.216066\pi$
$193$	300.436			1.55666			0.778332	+	0.627853i	$0.216066\pi$
$194$	−113.181	+	78.4687i	−0.583409	+	0.404478i
$195$		0			0
$196$	−331.398	−	124.121i	−1.69081	−	0.633269i
$197$	235.055	+	97.3629i	1.19317	+	0.494228i	0.888787	−	0.458321i	$-0.151549\pi$
$197$	235.055	+	97.3629i	1.19317	+	0.494228i	0.304385	+	0.952549i	$0.401549\pi$
$198$		0			0
$199$	221.237	−	221.237i	1.11175	−	1.11175i	0.118831	−	0.992914i	$-0.462085\pi$
$199$	221.237	−	221.237i	1.11175	−	1.11175i	0.992914	−	0.118831i	$-0.0379147\pi$
$200$	99.0330	−	166.135i	0.495165	−	0.830675i
$201$		0			0
$202$	255.085	−	55.3081i	1.26280	−	0.273803i
$203$	−121.267	−	50.2306i	−0.597376	−	0.247441i
$204$		0			0
$205$	−27.9879	+	11.5930i	−0.136526	+	0.0565510i
$206$	51.4325	−	283.962i	0.249672	−	1.37845i
$207$		0			0
$208$	292.086	+	98.1023i	1.40426	+	0.471646i
$209$		−	95.3486i		−	0.456213i
$210$		0			0
$211$	−83.3217	−	201.156i	−0.394890	−	0.953348i	−0.988858	−	0.148860i	$-0.952440\pi$
$211$	−83.3217	−	201.156i	−0.394890	−	0.953348i	0.593969	−	0.804488i	$-0.297560\pi$
$212$	−190.275	−	177.638i	−0.897524	−	0.837915i
$213$		0			0
$214$	−300.896	+	65.2408i	−1.40605	+	0.304863i
$215$	36.1215	+	36.1215i	0.168007	+	0.168007i
$216$		0			0
$217$	−146.780	−	146.780i	−0.676404	−	0.676404i
$218$	9.23378	−	14.3465i	0.0423568	−	0.0658096i
$219$		0			0
$220$	21.9705	−	9.99736i	0.0998658	−	0.0454425i
$221$	177.049	+	427.435i	0.801128	+	1.93410i
$222$		0			0
$223$			203.035i			0.910472i	0.890371	+	0.455236i	$0.150445\pi$
$223$			203.035i			0.910472i	−0.890371	+	0.455236i	$0.849555\pi$
$224$	292.942	−	234.423i	1.30778	−	1.04653i
$225$		0			0
$226$	−87.3125	−	125.937i	−0.386338	−	0.557245i
$227$	−238.588	+	98.8263i	−1.05105	+	0.435358i	−0.840265	−	0.542175i	$-0.817601\pi$
$227$	−238.588	+	98.8263i	−1.05105	+	0.435358i	−0.210782	+	0.977533i	$0.567601\pi$
$228$		0			0
$229$	−254.337	−	105.350i	−1.11064	−	0.460043i	−0.249483	−	0.968379i	$-0.580261\pi$
$229$	−254.337	−	105.350i	−1.11064	−	0.460043i	−0.861159	+	0.508336i	$0.830261\pi$
$230$	−22.0048	−	14.1628i	−0.0956730	−	0.0615776i
$231$		0			0
$232$	71.8063	−	53.5245i	0.309510	−	0.230709i
$233$	282.833	−	282.833i	1.21388	−	1.21388i	0.244137	−	0.969741i	$-0.421495\pi$
$233$	282.833	−	282.833i	1.21388	−	1.21388i	0.969741	−	0.244137i	$-0.0785046\pi$
$234$		0			0
$235$	20.0244	+	8.29438i	0.0852102	+	0.0352952i
$236$	−146.329	−	136.611i	−0.620040	−	0.578860i
$237$		0			0
$238$	554.342	+	100.405i	2.32917	+	0.421870i
$239$	−102.987			−0.430908			−0.215454	−	0.976514i	$-0.569123\pi$
$239$	−102.987			−0.430908			−0.215454	+	0.976514i	$0.569123\pi$
$240$		0			0
$241$			407.448i			1.69065i	0.534249	+	0.845327i	$0.320595\pi$
$241$			407.448i			1.69065i	−0.534249	+	0.845327i	$0.679405\pi$
$242$	151.095	+	27.3670i	0.624358	+	0.113087i
$243$		0			0
$244$	−239.924	+	8.24097i	−0.983294	+	0.0337745i
$245$	−30.7222	+	74.1699i	−0.125397	+	0.302734i
$246$		0			0
$247$	−195.242	−	195.242i	−0.790455	−	0.790455i
$248$	137.306	−	34.7459i	0.553652	−	0.140104i
$249$		0			0
$250$	−75.0484	−	48.3031i	−0.300194	−	0.193212i
$251$	−126.908	+	306.384i	−0.505610	+	1.22065i	0.440777	+	0.897617i	$0.354703\pi$
$251$	−126.908	+	306.384i	−0.505610	+	1.22065i	−0.946387	+	0.323035i	$0.895297\pi$
$252$		0			0
$253$	36.6944	+	88.5882i	0.145037	+	0.350151i
$254$	−38.4478	−	55.4561i	−0.151369	−	0.218331i
$255$		0			0
$256$	35.0484	+	253.589i	0.136908	+	0.990584i
$257$	277.421			1.07946			0.539730	−	0.841838i	$-0.318527\pi$
$257$	277.421			1.07946			0.539730	+	0.841838i	$0.318527\pi$
$258$		0			0
$259$	624.093	−	258.508i	2.40963	−	0.998100i
$260$	24.5170	−	65.4596i	0.0942961	−	0.251768i
$261$		0			0
$262$	−132.419	+	205.740i	−0.505417	+	0.785266i
$263$	221.721	−	221.721i	0.843044	−	0.843044i	−0.146210	−	0.989254i	$-0.546707\pi$
$263$	221.721	−	221.721i	0.843044	−	0.843044i	0.989254	+	0.146210i	$0.0467074\pi$
$264$		0			0
$265$	−41.7569	+	41.7569i	−0.157573	+	0.157573i
$266$	−328.583	+	71.2441i	−1.23528	+	0.267835i
$267$		0			0
$268$	−4.40376	−	128.209i	−0.0164319	−	0.478392i
$269$	−367.681	+	152.298i	−1.36684	+	0.566165i	−0.940931	−	0.338599i	$-0.890047\pi$
$269$	−367.681	+	152.298i	−1.36684	+	0.566165i	−0.425913	+	0.904764i	$0.640047\pi$
$270$		0			0
$271$	203.695			0.751641			0.375820	−	0.926693i	$-0.377361\pi$
$271$	203.695			0.751641			0.375820	+	0.926693i	$0.377361\pi$
$272$	−252.515	+	289.815i	−0.928363	+	1.06550i
$273$		0			0
$274$	−89.0496	+	491.648i	−0.324999	+	1.79434i
$275$	61.5263	+	148.538i	0.223732	+	0.540137i
$276$		0			0
$277$	−71.2097	+	171.915i	−0.257075	+	0.620633i	−0.998742	−	0.0501341i	$-0.984035\pi$
$277$	−71.2097	+	171.915i	−0.257075	+	0.620633i	0.741668	+	0.670767i	$0.234035\pi$
$278$	−270.876	+	58.7319i	−0.974375	+	0.211266i
$279$		0			0
$280$	−50.8684	−	68.2431i	−0.181673	−	0.243725i
$281$	−345.145	−	345.145i	−1.22827	−	1.22827i	−0.964616	−	0.263658i	$-0.915071\pi$
$281$	−345.145	−	345.145i	−1.22827	−	1.22827i	−0.263658	−	0.964616i	$-0.584929\pi$
$282$		0			0
$283$	41.6129	−	100.462i	0.147042	−	0.354991i	−0.833148	−	0.553050i	$-0.813464\pi$
$283$	41.6129	−	100.462i	0.147042	−	0.354991i	0.980190	+	0.198059i	$0.0634638\pi$
$284$	219.098	+	481.496i	0.771472	+	1.69541i
$285$		0			0
$286$	−210.489	+	145.932i	−0.735975	+	0.510253i
$287$		−	391.418i		−	1.36383i
$288$		0			0
$289$	−288.174			−0.997142
$290$	−11.5762	−	16.6972i	−0.0399178	−	0.0575765i
$291$		0			0
$292$	−13.4533	−	29.5653i	−0.0460728	−	0.101251i
$293$	−89.1421	−	36.9239i	−0.304239	−	0.126020i	0.225341	−	0.974280i	$-0.427650\pi$
$293$	−89.1421	−	36.9239i	−0.304239	−	0.126020i	−0.529580	+	0.848260i	$0.677650\pi$
$294$		0			0
$295$	−32.1128	+	32.1128i	−0.108857	+	0.108857i
$296$	−66.5290	+	456.088i	−0.224760	+	1.54084i
$297$		0			0
$298$	−53.2443	−	245.567i	−0.178672	−	0.824050i
$299$	256.537	+	106.261i	0.857984	+	0.355389i
$300$		0			0
$301$	−609.794	+	252.585i	−2.02589	+	0.839152i
$302$	−25.3694	−	4.59502i	−0.0840046	−	0.0152153i
$303$		0			0
$304$	73.0408	−	217.469i	0.240266	−	0.715359i
$305$			54.4611i			0.178561i
$306$		0			0
$307$	−33.0409	−	79.7679i	−0.107625	−	0.259830i	0.860887	−	0.508796i	$-0.169909\pi$
$307$	−33.0409	−	79.7679i	−0.107625	−	0.259830i	−0.968512	+	0.248966i	$0.919909\pi$
$308$	10.7063	+	311.698i	0.0347607	+	1.01201i
$309$		0			0
$310$	−6.80850	−	31.4013i	−0.0219629	−	0.101295i
$311$	−239.396	−	239.396i	−0.769763	−	0.769763i	0.208302	−	0.978065i	$-0.433206\pi$
$311$	−239.396	−	239.396i	−0.769763	−	0.769763i	−0.978065	+	0.208302i	$0.933206\pi$
$312$		0			0
$313$	1.73481	+	1.73481i	0.00554252	+	0.00554252i	0.709873	−	0.704330i	$-0.248752\pi$
$313$	1.73481	+	1.73481i	0.00554252	+	0.00554252i	−0.704330	+	0.709873i	$0.748752\pi$
$314$	236.263	+	152.065i	0.752429	+	0.484282i
$315$		0			0
$316$	16.8850	−	45.0823i	0.0534335	−	0.142666i
$317$	−65.0038	−	156.933i	−0.205059	−	0.495057i	0.787573	−	0.616221i	$-0.211337\pi$
$317$	−65.0038	−	156.933i	−0.205059	−	0.495057i	−0.992632	+	0.121164i	$0.961337\pi$
$318$		0			0
$319$			74.4477i			0.233378i
$320$	57.7682	−	5.97151i	0.180526	−	0.0186610i
$321$		0			0
$322$	277.868	−	192.646i	0.862945	−	0.598281i
$323$	318.241	−	131.820i	0.985267	−	0.408111i
$324$		0			0
$325$	430.141	+	178.170i	1.32351	+	0.548217i
$326$	−27.9958	+	43.4970i	−0.0858767	+	0.133427i
$327$		0			0
$328$	229.406	+	136.749i	0.699408	+	0.416917i
$329$	−198.023	+	198.023i	−0.601894	+	0.601894i
$330$		0			0
$331$	121.585	+	50.3622i	0.367327	+	0.152152i	0.558709	−	0.829364i	$-0.311297\pi$
$331$	121.585	+	50.3622i	0.367327	+	0.152152i	−0.191382	+	0.981516i	$0.561297\pi$
$332$	347.486	−	11.9356i	1.04665	−	0.0359505i
$333$		0			0
$334$	−27.7193	+	153.040i	−0.0829920	+	0.458203i
$335$	−29.1026			−0.0868734
$336$		0			0
$337$			472.083i			1.40084i	0.713731	+	0.700420i	$0.247004\pi$
$337$			472.083i			1.40084i	−0.713731	+	0.700420i	$0.752996\pi$
$338$	−71.9507	+	397.244i	−0.212872	+	1.17528i
$339$		0			0
$340$	63.7421	+	59.5086i	0.187477	+	0.175025i
$341$	−45.0550	+	108.772i	−0.132126	+	0.318981i
$342$		0			0
$343$	−327.231	−	327.231i	−0.954025	−	0.954025i
$344$	65.0047	−	445.638i	0.188967	−	1.29546i
$345$		0			0
$346$	−10.3427	+	16.0695i	−0.0298923	+	0.0464435i
$347$	−46.0391	+	111.148i	−0.132677	+	0.320312i	−0.976231	−	0.216734i	$-0.930460\pi$
$347$	−46.0391	+	111.148i	−0.132677	+	0.320312i	0.843553	+	0.537045i	$0.180460\pi$
$348$		0			0
$349$	−11.7114	−	28.2738i	−0.0335570	−	0.0810138i	0.906213	−	0.422822i	$-0.138961\pi$
$349$	−11.7114	−	28.2738i	−0.0335570	−	0.0810138i	−0.939770	+	0.341809i	$0.888961\pi$
$350$	465.907	−	323.014i	1.33116	−	0.922897i
$351$		0			0
$352$	−186.423	−	102.622i	−0.529611	−	0.291540i
$353$	196.422			0.556437			0.278218	−	0.960518i	$-0.410256\pi$
$353$	196.422			0.556437			0.278218	+	0.960518i	$0.410256\pi$
$354$		0			0
$355$	110.874	−	45.9255i	0.312321	−	0.129368i
$356$	190.836	−	86.8374i	0.536057	−	0.243925i
$357$		0			0
$358$	−294.191	−	189.349i	−0.821763	−	0.528908i
$359$	−293.597	+	293.597i	−0.817820	+	0.817820i	−0.985792	−	0.167972i	$-0.946278\pi$
$359$	−293.597	+	293.597i	−0.817820	+	0.817820i	0.167972	+	0.985792i	$0.446278\pi$
$360$		0			0
$361$	109.900	−	109.900i	0.304433	−	0.304433i
$362$	−4.23596	−	19.5366i	−0.0117015	−	0.0539685i
$363$		0			0
$364$	660.178	+	616.332i	1.81367	+	1.69322i
$365$	−6.80798	+	2.81996i	−0.0186520	+	0.00772591i
$366$		0			0
$367$	287.361			0.783000			0.391500	−	0.920178i	$-0.371956\pi$
$367$	287.361			0.783000			0.391500	+	0.920178i	$0.371956\pi$
$368$	15.8299	+	230.160i	0.0430159	+	0.625434i
$369$		0			0
$370$	102.889	+	18.6357i	0.278078	+	0.0503667i
$371$	−291.991	−	704.929i	−0.787038	−	1.90008i
$372$		0			0
$373$	86.1683	−	208.029i	0.231014	−	0.557718i	−0.765283	−	0.643694i	$-0.777401\pi$
$373$	86.1683	−	208.029i	0.231014	−	0.557718i	0.996297	+	0.0859764i	$0.0274010\pi$
$374$	−67.7076	−	312.273i	−0.181036	−	0.834954i
$375$		0			0
$376$	−46.8763	−	185.242i	−0.124671	−	0.492664i
$377$	152.444	+	152.444i	0.404361	+	0.404361i
$378$		0			0
$379$	−63.5589	+	153.445i	−0.167701	+	0.404867i	−0.985280	−	0.170950i	$-0.945316\pi$
$379$	−63.5589	+	153.445i	−0.167701	+	0.404867i	0.817578	+	0.575818i	$0.195316\pi$
$380$	−48.7371	−	18.2538i	−0.128255	−	0.0480363i
$381$		0			0
$382$	−299.942	−	432.629i	−0.785189	−	1.13254i
$383$		−	46.0441i		−	0.120220i	−0.998192	−	0.0601098i	$-0.980855\pi$
$383$		−	46.0441i		−	0.120220i	0.998192	−	0.0601098i	$-0.0191451\pi$
$384$		0			0
$385$	70.7534			0.183775
$386$	−493.803	+	342.354i	−1.27928	+	0.886928i
$387$		0			0
$388$	96.6100	−	257.946i	0.248995	−	0.664808i
$389$	204.729	+	84.8014i	0.526295	+	0.217999i	0.629980	−	0.776612i	$-0.283063\pi$
$389$	204.729	+	84.8014i	0.526295	+	0.217999i	−0.103685	+	0.994610i	$0.533063\pi$
$390$		0			0
$391$	−244.947	+	244.947i	−0.626463	+	0.626463i
$392$	686.131	−	173.629i	1.75033	−	0.442930i
$393$		0			0
$394$	−497.288	+	107.823i	−1.26215	+	0.273662i
$395$	−10.0898	−	4.17935i	−0.0255439	−	0.0105806i
$396$		0			0
$397$	−201.362	+	83.4069i	−0.507209	+	0.210093i	−0.621588	−	0.783344i	$-0.713512\pi$
$397$	−201.362	+	83.4069i	−0.507209	+	0.210093i	0.114379	+	0.993437i	$0.463512\pi$
$398$	−111.525	+	615.735i	−0.280213	+	1.54707i
$399$		0			0
$400$	26.5422	+	385.913i	0.0663556	+	0.964783i
$401$		−	443.771i		−	1.10666i	−0.832962	−	0.553331i	$-0.813357\pi$
$401$		−	443.771i		−	1.10666i	0.832962	−	0.553331i	$-0.186643\pi$
$402$		0			0
$403$	130.472	+	314.988i	0.323752	+	0.781607i
$404$	−356.239	+	381.581i	−0.881779	+	0.944508i
$405$		0			0
$406$	256.556	−	55.6270i	0.631912	−	0.137012i
$407$	−270.921	−	270.921i	−0.665653	−	0.665653i
$408$		0			0
$409$	58.3505	+	58.3505i	0.142666	+	0.142666i	0.774833	−	0.632166i	$-0.217834\pi$
$409$	58.3505	+	58.3505i	0.142666	+	0.142666i	−0.632166	+	0.774833i	$0.717834\pi$
$410$	32.7910	−	50.9473i	0.0799780	−	0.124262i
$411$		0			0
$412$	239.046	+	525.334i	0.580208	+	1.27508i
$413$	−224.553	−	542.119i	−0.543712	−	1.31264i
$414$		0			0
$415$		−	78.8771i		−	0.190065i
$416$	−591.869	+	171.597i	−1.42276	+	0.412492i
$417$		0			0
$418$	108.652	+	156.717i	0.259933	+	0.374921i
$419$	676.851	−	280.361i	1.61540	−	0.669119i	0.621913	−	0.783087i	$-0.286356\pi$
$419$	676.851	−	280.361i	1.61540	−	0.669119i	0.993484	+	0.113967i	$0.0363559\pi$
$420$		0			0
$421$	327.388	+	135.608i	0.777643	+	0.322110i	0.735964	−	0.677021i	$-0.236729\pi$
$421$	327.388	+	135.608i	0.777643	+	0.322110i	0.0416793	+	0.999131i	$0.486729\pi$
$422$	366.172	+	235.678i	0.867705	+	0.558478i
$423$		0			0
$424$	515.163	+	75.1462i	1.21501	+	0.177232i
$425$	−410.708	+	410.708i	−0.966371	+	0.966371i
$426$		0			0
$427$	−650.112	−	269.285i	−1.52251	−	0.630645i
$428$	420.215	−	450.109i	0.981810	−	1.05166i
$429$		0			0
$430$	−100.531	−	18.2087i	−0.233794	−	0.0423458i
$431$	122.028			0.283128			0.141564	−	0.989929i	$-0.454787\pi$
$431$	122.028			0.283128			0.141564	+	0.989929i	$0.454787\pi$
$432$		0			0
$433$		−	103.627i		−	0.239322i	−0.992815	−	0.119661i	$-0.961819\pi$
$433$		−	103.627i		−	0.239322i	0.992815	−	0.119661i	$-0.0381808\pi$
$434$	408.509	+	73.9910i	0.941264	+	0.170486i
$435$		0			0
$436$	1.17136	+	34.1023i	0.00268660	+	0.0782163i
$437$	79.1154	−	191.002i	0.181042	−	0.437074i
$438$		0			0
$439$	−511.640	−	511.640i	−1.16547	−	1.16547i	−0.983260	−	0.182208i	$-0.941676\pi$
$439$	−511.640	−	511.640i	−1.16547	−	1.16547i	−0.182208	−	0.983260i	$-0.558324\pi$
$440$	−24.7189	+	41.4677i	−0.0561793	+	0.0942449i
$441$		0			0
$442$	−778.074	−	500.789i	−1.76035	−	1.13301i
$443$	169.759	−	409.835i	0.383204	−	0.925136i	−0.608138	−	0.793831i	$-0.708083\pi$
$443$	169.759	−	409.835i	0.383204	−	0.925136i	0.991342	−	0.131305i	$-0.0419167\pi$
$444$		0			0
$445$	−18.2021	−	43.9438i	−0.0409036	−	0.0987501i
$446$	−231.363	−	333.713i	−0.518752	−	0.748235i
$447$		0			0
$448$	−214.354	+	719.117i	−0.478470	+	1.60517i
$449$	−364.001			−0.810692			−0.405346	−	0.914163i	$-0.632849\pi$
$449$	−364.001			−0.810692			−0.405346	+	0.914163i	$0.632849\pi$
$450$		0			0
$451$	−205.107	+	84.9579i	−0.454782	+	0.188377i
$452$	287.017	+	107.498i	0.634994	+	0.237828i
$453$		0			0
$454$	279.533	−	434.309i	0.615710	−	0.956628i
$455$	144.880	−	144.880i	0.318417	−	0.318417i
$456$		0			0
$457$	421.367	−	421.367i	0.922027	−	0.922027i	−0.0751452	−	0.997173i	$-0.523942\pi$
$457$	421.367	−	421.367i	0.922027	−	0.922027i	0.997173	+	0.0751452i	$0.0239420\pi$
$458$	538.082	−	116.668i	1.17485	−	0.254734i
$459$		0			0
$460$	52.3064	−	1.79664i	0.113710	−	0.00390573i
$461$	−131.413	+	54.4331i	−0.285061	+	0.118076i	−0.520632	−	0.853781i	$-0.674304\pi$
$461$	−131.413	+	54.4331i	−0.285061	+	0.118076i	0.235572	+	0.971857i	$0.424304\pi$
$462$		0			0
$463$	740.121			1.59853			0.799267	−	0.600976i	$-0.205221\pi$
$463$	740.121			1.59853			0.799267	+	0.600976i	$0.205221\pi$
$464$	−57.0299	+	169.799i	−0.122909	+	0.365946i
$465$		0			0
$466$	−142.575	+	787.166i	−0.305955	+	1.68920i
$467$	55.4387	+	133.841i	0.118713	+	0.286597i	0.972055	−	0.234753i	$-0.0754283\pi$
$467$	55.4387	+	133.841i	0.118713	+	0.286597i	−0.853342	+	0.521351i	$0.825428\pi$
$468$		0			0
$469$	143.899	−	347.403i	0.306821	−	0.740731i
$470$	−42.3641	+	9.18547i	−0.0901365	+	0.0195436i
$471$		0			0
$472$	396.181	+	57.7905i	0.839367	+	0.122438i
$473$	264.713	+	264.713i	0.559647	+	0.559647i
$474$		0			0
$475$	132.654	−	320.256i	0.279272	−	0.674223i
$476$	−1025.54	+	466.658i	−2.15450	+	0.980374i
$477$		0			0
$478$	169.271	−	117.356i	0.354124	−	0.245515i
$479$		−	1.02682i		−	0.00214368i	−0.999999	−	0.00107184i	$-0.999659\pi$
$479$		−	1.02682i		−	0.00214368i	0.999999	−	0.00107184i	$-0.000341178\pi$
$480$		0			0
$481$	−1109.51			−2.30668
$482$	−464.296	−	669.689i	−0.963271	−	1.38940i
$483$		0			0
$484$	−279.527	+	127.195i	−0.577536	+	0.262799i
$485$	−57.7306	−	23.9128i	−0.119032	−	0.0493047i
$486$		0			0
$487$	246.035	−	246.035i	0.505205	−	0.505205i	−0.407846	−	0.913051i	$-0.633720\pi$
$487$	246.035	−	246.035i	0.505205	−	0.505205i	0.913051	+	0.407846i	$0.133720\pi$
$488$	384.953	−	286.944i	0.788838	−	0.588000i
$489$		0			0
$490$	−34.0228	−	156.916i	−0.0694342	−	0.320236i
$491$	−726.245	−	300.821i	−1.47911	−	0.612669i	−0.510198	−	0.860057i	$-0.670428\pi$
$491$	−726.245	−	300.821i	−1.47911	−	0.612669i	−0.968916	+	0.247388i	$0.920428\pi$
$492$		0			0
$493$	−248.481	+	102.924i	−0.504019	+	0.208771i
$494$	543.387	+	98.4209i	1.09997	+	0.199233i
$495$		0			0
$496$	−186.085	+	213.572i	−0.375171	+	0.430589i
$497$			1550.60i			3.11993i
$498$		0			0
$499$	−95.2554	−	229.967i	−0.190893	−	0.460856i	0.799236	−	0.601017i	$-0.205238\pi$
$499$	−95.2554	−	229.967i	−0.190893	−	0.460856i	−0.990129	+	0.140162i	$0.955238\pi$
$500$	178.394	−	6.12751i	0.356787	−	0.0122550i
$501$		0			0
$502$	−140.542	−	648.193i	−0.279965	−	1.29122i
$503$	622.020	+	622.020i	1.23662	+	1.23662i	0.961373	+	0.275248i	$0.0887599\pi$
$503$	622.020	+	622.020i	1.23662	+	1.23662i	0.275248	+	0.961373i	$0.411240\pi$
$504$		0			0
$505$	83.7401	+	83.7401i	0.165822	+	0.165822i
$506$	−161.260	−	103.791i	−0.318696	−	0.205121i
$507$		0			0
$508$	126.387	+	47.3366i	0.248794	+	0.0931823i
$509$	−242.724	−	585.988i	−0.476865	−	1.15125i	−0.961071	−	0.276300i	$-0.910892\pi$
$509$	−242.724	−	585.988i	−0.476865	−	1.15125i	0.484207	−	0.874954i	$-0.339108\pi$
$510$		0			0
$511$		−	95.2115i		−	0.186324i
$512$	−346.577	−	376.866i	−0.676909	−	0.736067i
$513$		0			0
$514$	−455.975	+	316.128i	−0.887110	+	0.615035i
$515$	120.968	−	50.1067i	0.234890	−	0.0972946i
$516$		0			0
$517$	146.747	+	60.7846i	0.283843	+	0.117572i
$518$	−731.196	+	1136.06i	−1.41158	+	2.19316i
$519$		0			0
$520$	34.2961	+	135.528i	0.0659540	+	0.260631i
$521$	50.5476	−	50.5476i	0.0970204	−	0.0970204i	−0.656931	−	0.753951i	$-0.728146\pi$
$521$	50.5476	−	50.5476i	0.0970204	−	0.0970204i	0.753951	+	0.656931i	$0.228146\pi$
$522$		0			0
$523$	−575.164	−	238.241i	−1.09974	−	0.455527i	−0.242347	−	0.970190i	$-0.577917\pi$
$523$	−575.164	−	238.241i	−1.09974	−	0.455527i	−0.857393	+	0.514662i	$0.827917\pi$
$524$	−16.7981	−	489.053i	−0.0320575	−	0.933307i
$525$		0			0
$526$	−111.768	+	617.080i	−0.212488	+	1.17316i
$527$	−425.334			−0.807086
$528$		0			0
$529$		−	321.094i		−	0.606982i
$530$	21.0495	−	116.215i	0.0397160	−	0.219274i
$531$		0			0
$532$	458.882	−	491.527i	0.862560	−	0.923922i
$533$	−246.025	+	593.956i	−0.461585	+	1.11436i
$534$		0			0
$535$	−98.7788	−	98.7788i	−0.184633	−	0.184633i
$536$	153.335	+	205.709i	0.286073	+	0.383785i
$537$		0			0
$538$	430.780	−	669.302i	0.800706	−	1.24406i
$539$	−225.145	+	543.547i	−0.417708	+	1.00844i
$540$		0			0
$541$	−22.3416	−	53.9373i	−0.0412968	−	0.0996993i	0.901885	−	0.431976i	$-0.142183\pi$
$541$	−22.3416	−	53.9373i	−0.0412968	−	0.0996993i	−0.943182	+	0.332276i	$0.892183\pi$
$542$	−334.796	+	232.115i	−0.617706	+	0.428256i
$543$		0			0
$544$	84.7873	−	764.092i	0.155859	−	1.40458i
$545$	7.74099			0.0142037
$546$		0			0
$547$	286.069	−	118.494i	0.522978	−	0.216624i	−0.105547	−	0.994414i	$-0.533659\pi$
$547$	286.069	−	118.494i	0.522978	−	0.216624i	0.628524	+	0.777790i	$0.283659\pi$
$548$	−413.881	−	909.557i	−0.755257	−	1.65978i
$549$		0			0
$550$	−270.388	−	174.029i	−0.491614	−	0.316416i
$551$	113.500	−	113.500i	0.205990	−	0.205990i
$552$		0			0
$553$	99.7793	−	99.7793i	0.180433	−	0.180433i
$554$	−78.8600	−	363.709i	−0.142347	−	0.656514i
$555$		0			0
$556$	378.291	−	405.203i	0.680380	−	0.728782i
$557$	−305.243	+	126.436i	−0.548013	+	0.226994i	−0.639472	−	0.768814i	$-0.720847\pi$
$557$	−305.243	+	126.436i	−0.548013	+	0.226994i	0.0914589	+	0.995809i	$0.470847\pi$
$558$		0			0
$559$	1084.09			1.93934
$560$	161.373	+	54.1999i	0.288166	+	0.0967856i
$561$		0			0
$562$	960.588	+	173.986i	1.70923	+	0.309584i
$563$	−73.2914	−	176.941i	−0.130180	−	0.314283i	0.845327	−	0.534249i	$-0.179405\pi$
$563$	−73.2914	−	176.941i	−0.130180	−	0.314283i	−0.975508	+	0.219966i	$0.929405\pi$
$564$		0			0
$565$	26.6078	−	64.2370i	0.0470935	−	0.113694i
$566$	46.0835	+	212.541i	0.0814196	+	0.375514i
$567$		0			0
$568$	−908.790	−	541.729i	−1.59998	−	0.953749i
$569$	−492.425	−	492.425i	−0.865421	−	0.865421i	0.126540	−	0.991962i	$-0.459613\pi$
$569$	−492.425	−	492.425i	−0.865421	−	0.865421i	−0.991962	+	0.126540i	$0.959613\pi$
$570$		0			0
$571$	−162.364	+	391.981i	−0.284350	+	0.686481i	−0.999927	−	0.0120523i	$-0.996164\pi$
$571$	−162.364	+	391.981i	−0.284350	+	0.686481i	0.715578	+	0.698533i	$0.246164\pi$
$572$	179.671	−	479.714i	0.314109	−	0.838661i
$573$		0			0
$574$	446.031	+	643.343i	0.777057	+	1.12081i
$575$			348.601i			0.606262i
$576$		0			0
$577$	513.338			0.889668			0.444834	−	0.895613i	$-0.353263\pi$
$577$	513.338			0.889668			0.444834	+	0.895613i	$0.353263\pi$
$578$	473.648	−	328.381i	0.819461	−	0.568133i
$579$		0			0
$580$	38.0537	+	14.2525i	0.0656098	+	0.0245733i
$581$	941.571	+	390.011i	1.62060	+	0.671276i
$582$		0			0
$583$	−306.012	+	306.012i	−0.524891	+	0.524891i
$584$	55.8023	+	33.2637i	0.0955520	+	0.0569585i
$585$		0			0
$586$	188.591	−	40.8907i	0.321828	−	0.0697794i
$587$	239.651	+	99.2668i	0.408265	+	0.169109i	0.577358	−	0.816491i	$-0.304084\pi$
$587$	239.651	+	99.2668i	0.408265	+	0.169109i	−0.169093	+	0.985600i	$0.554084\pi$
$588$		0			0
$589$	234.520	−	97.1413i	0.398166	−	0.164926i
$590$	16.1879	−	89.3744i	0.0274372	−	0.151482i
$591$		0			0
$592$	−410.374	−	825.446i	−0.693200	−	1.39433i
$593$		−	1088.92i		−	1.83629i	−0.396242	−	0.918146i	$-0.629686\pi$
$593$		−	1088.92i		−	1.83629i	0.396242	−	0.918146i	$-0.370314\pi$
$594$		0			0
$595$	97.8169	+	236.151i	0.164398	+	0.396892i
$596$	367.343	+	342.945i	0.616346	+	0.575412i
$597$		0			0
$598$	−542.737	+	117.677i	−0.907587	+	0.196785i
$599$	195.870	+	195.870i	0.326995	+	0.326995i	0.851443	−	0.524448i	$-0.175728\pi$
$599$	195.870	+	195.870i	0.326995	+	0.326995i	−0.524448	+	0.851443i	$0.675728\pi$
$600$		0			0
$601$	−539.884	−	539.884i	−0.898309	−	0.898309i	0.0969773	−	0.995287i	$-0.469083\pi$
$601$	−539.884	−	539.884i	−0.898309	−	0.898309i	−0.995287	+	0.0969773i	$0.969083\pi$
$602$	714.443	−	1110.03i	1.18678	−	1.84390i
$603$		0			0
$604$	46.9338	−	21.3565i	0.0777049	−	0.0353585i
$605$	26.6615	+	64.3666i	0.0440686	+	0.106391i
$606$		0			0
$607$			488.167i			0.804229i	0.915589	+	0.402114i	$0.131725\pi$
$607$			488.167i			0.804229i	−0.915589	+	0.402114i	$0.868275\pi$
$608$	127.760	+	440.668i	0.210131	+	0.724783i
$609$		0			0
$610$	−62.0597	−	89.5133i	−0.101737	−	0.146743i
$611$	424.956	−	176.022i	0.695509	−	0.288089i
$612$		0			0
$613$	−137.883	−	57.1129i	−0.224931	−	0.0931695i	0.267372	−	0.963593i	$-0.413845\pi$
$613$	−137.883	−	57.1129i	−0.224931	−	0.0931695i	−0.492303	+	0.870424i	$0.663845\pi$
$614$	145.204	+	93.4571i	0.236489	+	0.152210i
$615$		0			0
$616$	−372.785	−	500.113i	−0.605170	−	0.811872i
$617$	128.731	−	128.731i	0.208640	−	0.208640i	−0.595049	−	0.803689i	$-0.702867\pi$
$617$	128.731	−	128.731i	0.208640	−	0.208640i	0.803689	+	0.595049i	$0.202867\pi$
$618$		0			0
$619$	502.886	+	208.302i	0.812417	+	0.336514i	0.749918	−	0.661531i	$-0.230093\pi$
$619$	502.886	+	208.302i	0.812417	+	0.336514i	0.0624991	+	0.998045i	$0.480093\pi$
$620$	46.9731	+	43.8534i	0.0757631	+	0.0707313i
$621$		0			0
$622$	666.274	+	120.679i	1.07118	+	0.194017i
$623$	614.566			0.986463
$624$		0			0
$625$			563.920i			0.902272i
$626$	−4.82822	−	0.874511i	−0.00771282	−	0.00139698i
$627$		0			0
$628$	−561.607	+	19.2902i	−0.894279	+	0.0307170i
$629$	529.692	−	1278.79i	0.842118	−	2.03305i
$630$		0			0
$631$	179.020	+	179.020i	0.283709	+	0.283709i	0.834586	−	0.550877i	$-0.185707\pi$
$631$	179.020	+	179.020i	0.283709	+	0.283709i	−0.550877	+	0.834586i	$0.685707\pi$
$632$	23.6199	+	93.3390i	0.0373732	+	0.147688i
$633$		0			0
$634$	285.670	+	183.865i	0.450584	+	0.290008i
$635$	11.7167	−	28.2866i	0.0184515	−	0.0445458i
$636$		0			0
$637$	651.983	+	1574.03i	1.02352	+	2.47100i
$638$	−84.8349	−	122.364i	−0.132970	−	0.191793i
$639$		0			0
$640$	−88.1443	+	75.6432i	−0.137725	+	0.118192i
$641$	1162.88			1.81416			0.907080	−	0.420957i	$-0.138306\pi$
$641$	1162.88			1.81416			0.907080	+	0.420957i	$0.138306\pi$
$642$		0			0
$643$	−940.645	+	389.628i	−1.46290	+	0.605953i	−0.965227	−	0.261412i	$-0.915812\pi$
$643$	−940.645	+	389.628i	−1.46290	+	0.605953i	−0.497673	+	0.867365i	$0.665812\pi$
$644$	−237.185	+	633.275i	−0.368299	+	0.983346i
$645$		0			0
$646$	−372.856	+	579.305i	−0.577176	+	0.896757i
$647$	−156.882	+	156.882i	−0.242476	+	0.242476i	−0.817874	−	0.575398i	$-0.804847\pi$
$647$	−156.882	+	156.882i	−0.242476	+	0.242476i	0.575398	+	0.817874i	$0.304847\pi$
$648$		0			0
$649$	−235.336	+	235.336i	−0.362612	+	0.362612i
$650$	−910.018	+	197.312i	−1.40003	+	0.303557i
$651$		0			0
$652$	−3.55142	−	103.394i	−0.00544697	−	0.158581i
$653$	144.809	−	59.9817i	0.221759	−	0.0918556i	−0.269038	−	0.963130i	$-0.586706\pi$
$653$	144.809	−	59.9817i	0.221759	−	0.0918556i	0.490797	+	0.871274i	$0.336706\pi$
$654$		0			0
$655$	−111.012			−0.169483
$656$	−532.884	+	36.6506i	−0.812323	+	0.0558698i
$657$		0			0
$658$	99.8227	−	551.127i	0.151706	−	0.837578i
$659$	−144.038	−	347.738i	−0.218571	−	0.527676i	0.776120	−	0.630585i	$-0.217185\pi$
$659$	−144.038	−	347.738i	−0.218571	−	0.527676i	−0.994691	+	0.102909i	$0.967185\pi$
$660$		0			0
$661$	107.864	−	260.406i	0.163182	−	0.393957i	−0.821045	−	0.570863i	$-0.806609\pi$
$661$	107.864	−	260.406i	0.163182	−	0.393957i	0.984228	+	0.176906i	$0.0566087\pi$
$662$	−257.229	+	55.7728i	−0.388563	+	0.0842490i
$663$		0			0
$664$	−557.535	+	415.587i	−0.839661	+	0.625883i
$665$	−107.868	−	107.868i	−0.162208	−	0.162208i
$666$		0			0
$667$	−61.7729	+	149.133i	−0.0926131	+	0.223588i
$668$	−128.833	−	283.126i	−0.192863	−	0.423842i
$669$		0			0
$670$	47.8336	−	33.1631i	0.0713934	−	0.0494971i
$671$			399.113i			0.594804i
$672$		0			0
$673$	46.2868			0.0687769			0.0343884	−	0.999409i	$-0.489052\pi$
$673$	46.2868			0.0687769			0.0343884	+	0.999409i	$0.489052\pi$
$674$	−537.950	−	775.925i	−0.798145	−	1.15122i
$675$		0			0
$676$	−334.409	−	734.908i	−0.494689	−	1.08714i
$677$	−79.6078	−	32.9746i	−0.117589	−	0.0487070i	0.323113	−	0.946360i	$-0.395271\pi$
$677$	−79.6078	−	32.9746i	−0.117589	−	0.0487070i	−0.440702	+	0.897653i	$0.645271\pi$
$678$		0			0
$679$	570.903	−	570.903i	0.840799	−	0.840799i
$680$	−172.579	−	25.1739i	−0.253793	−	0.0370205i
$681$		0			0
$682$	−49.8955	−	230.122i	−0.0731605	−	0.337422i
$683$	−537.472	−	222.628i	−0.786928	−	0.325956i	−0.0472202	−	0.998885i	$-0.515036\pi$
$683$	−537.472	−	222.628i	−0.786928	−	0.325956i	−0.739708	+	0.672928i	$0.765036\pi$
$684$		0			0
$685$	−209.443	+	86.7542i	−0.305756	+	0.126648i
$686$	910.730	+	164.956i	1.32759	+	0.240460i
$687$		0			0
$688$	400.972	+	806.533i	0.582808	+	1.17229i
$689$			1253.22i			1.81890i
$690$		0			0
$691$	−42.8826	−	103.528i	−0.0620588	−	0.149823i	0.889808	−	0.456335i	$-0.150838\pi$
$691$	−42.8826	−	103.528i	−0.0620588	−	0.149823i	−0.951867	+	0.306512i	$0.900838\pi$
$692$	−1.31203	−	38.1979i	−0.00189600	−	0.0551992i
$693$		0			0
$694$	−50.9852	−	235.148i	−0.0734657	−	0.338830i
$695$	−88.9240	−	88.9240i	−0.127948	−	0.127948i
$696$		0			0
$697$	−567.121	−	567.121i	−0.813661	−	0.813661i
$698$	51.4677	+	33.1260i	0.0737360	+	0.0474584i
$699$		0			0
$700$	−397.692	+	1061.82i	−0.568132	+	1.51689i
$701$	−197.792	−	477.513i	−0.282157	−	0.681188i	0.717728	−	0.696323i	$-0.245182\pi$
$701$	−197.792	−	477.513i	−0.282157	−	0.681188i	−0.999885	+	0.0151356i	$0.995182\pi$
$702$		0			0
$703$			826.072i			1.17507i
$704$	423.349	−	43.7617i	0.601348	−	0.0621615i
$705$		0			0
$706$	−322.843	+	223.828i	−0.457285	+	0.317036i
$707$	−1413.68	+	585.565i	−1.99954	+	0.828238i
$708$		0			0
$709$	256.234	+	106.136i	0.361402	+	0.149698i	0.555993	−	0.831187i	$-0.312338\pi$
$709$	256.234	+	106.136i	0.361402	+	0.149698i	−0.194591	+	0.980884i	$0.562338\pi$
$710$	−129.901	+	201.827i	−0.182960	+	0.284264i
$711$		0			0
$712$	−214.709	+	360.190i	−0.301558	+	0.505885i
$713$	−180.508	+	180.508i	−0.253167	+	0.253167i
$714$		0			0
$715$	−107.364	−	44.4718i	−0.150160	−	0.0621983i
$716$	699.306	−	24.0200i	0.976685	−	0.0335475i
$717$		0			0
$718$	148.001	−	817.123i	0.206130	−	1.13805i
$719$	35.7527			0.0497256			0.0248628	−	0.999691i	$-0.492085\pi$
$719$	35.7527			0.0497256			0.0248628	+	0.999691i	$0.492085\pi$
$720$		0			0
$721$			1691.78i			2.34643i
$722$	−55.4004	+	305.869i	−0.0767318	+	0.423641i
$723$		0			0
$724$	29.2247	+	27.2837i	0.0403656	+	0.0376847i
$725$	−103.576	+	250.054i	−0.142863	+	0.344903i
$726$		0			0
$727$	648.949	+	648.949i	0.892639	+	0.892639i	0.994771	−	0.102132i	$-0.0325663\pi$
$727$	648.949	+	648.949i	0.892639	+	0.892639i	−0.102132	+	0.994771i	$0.532566\pi$
$728$	−1787.41	−	260.727i	−2.45523	−	0.358141i
$729$		0			0
$730$	7.97632	−	12.3928i	0.0109265	−	0.0169764i
$731$	−517.556	+	1249.49i	−0.708010	+	1.70929i
$732$		0			0
$733$	−422.521	−	1020.06i	−0.576427	−	1.39162i	−0.895999	−	0.444056i	$-0.853539\pi$
$733$	−422.521	−	1020.06i	−0.576427	−	1.39162i	0.319572	−	0.947562i	$-0.396461\pi$
$734$	−472.312	+	327.455i	−0.643477	+	0.446124i
$735$		0			0
$736$	−288.291	−	360.256i	−0.391699	−	0.489479i
$737$	−213.276			−0.289383
$738$		0			0
$739$	263.965	−	109.338i	0.357193	−	0.147954i	−0.196869	−	0.980430i	$-0.563077\pi$
$739$	263.965	−	109.338i	0.357193	−	0.147954i	0.554061	+	0.832476i	$0.313077\pi$
$740$	−190.346	+	86.6142i	−0.257224	+	0.117046i
$741$		0			0
$742$	1283.21	+	825.904i	1.72939	+	1.11308i
$743$	−77.4110	+	77.4110i	−0.104187	+	0.104187i	−0.757279	−	0.653092i	$-0.773472\pi$
$743$	−77.4110	+	77.4110i	−0.104187	+	0.104187i	0.653092	+	0.757279i	$0.273472\pi$
$744$		0			0
$745$	80.6153	−	80.6153i	0.108208	−	0.108208i
$746$	95.4257	+	440.111i	0.127916	+	0.589961i
$747$		0			0
$748$	467.128	+	436.103i	0.624503	+	0.583026i
$749$	1667.56	−	690.725i	2.22638	−	0.922196i
$750$		0			0
$751$	−930.609			−1.23916			−0.619580	−	0.784934i	$-0.712697\pi$
$751$	−930.609			−1.23916			−0.619580	+	0.784934i	$0.712697\pi$
$752$	288.134	+	251.050i	0.383157	+	0.333843i
$753$		0			0
$754$	−424.274	−	76.8466i	−0.562698	−	0.101919i
$755$	−4.47658	−	10.8074i	−0.00592924	−	0.0143145i
$756$		0			0
$757$	302.700	−	730.783i	0.399868	−	0.965367i	−0.587829	−	0.808985i	$-0.700017\pi$
$757$	302.700	−	730.783i	0.399868	−	0.965367i	0.987697	−	0.156381i	$-0.0499829\pi$
$758$	−70.3872	−	324.631i	−0.0928591	−	0.428274i
$759$		0			0
$760$	100.906	−	25.5347i	0.132771	−	0.0335983i
$761$	673.118	+	673.118i	0.884518	+	0.884518i	0.993990	−	0.109472i	$-0.0349160\pi$
$761$	673.118	+	673.118i	0.884518	+	0.884518i	−0.109472	+	0.993990i	$0.534916\pi$
$762$		0			0
$763$	−38.2757	+	92.4057i	−0.0501647	+	0.121108i
$764$	985.982	+	369.286i	1.29055	+	0.483359i
$765$		0			0
$766$	52.4683	+	75.6790i	0.0684965	+	0.0987976i
$767$			963.778i			1.25656i
$768$		0			0
$769$	0.669073			0.000870056			0.000435028	−	1.00000i	$-0.499862\pi$
$769$	0.669073			0.000870056			0.000435028		1.00000i	$0.499862\pi$
$770$	−116.292	+	80.6252i	−0.151028	+	0.104708i
$771$		0			0
$772$	421.504	−	1125.40i	0.545989	−	1.45777i
$773$	−139.387	−	57.7360i	−0.180320	−	0.0746908i	0.290697	−	0.956815i	$-0.406113\pi$
$773$	−139.387	−	57.7360i	−0.180320	−	0.0746908i	−0.471017	+	0.882124i	$0.656113\pi$
$774$		0			0
$775$	−302.661	+	302.661i	−0.390530	+	0.390530i
$776$	135.145	+	534.054i	0.174156	+	0.688214i
$777$		0			0
$778$	−433.129	+	93.9120i	−0.556722	+	0.120709i
$779$	442.222	+	183.174i	0.567679	+	0.235140i
$780$		0			0
$781$	812.529	−	336.561i	1.04037	−	0.430935i
$782$	123.477	−	681.723i	0.157899	−	0.871768i
$783$		0			0
$784$	−929.884	+	1067.24i	−1.18608	+	1.36128i
$785$			127.481i			0.162396i
$786$		0			0
$787$	−78.0050	−	188.321i	−0.0991169	−	0.239289i	0.866541	−	0.499106i	$-0.166338\pi$
$787$	−78.0050	−	188.321i	−0.0991169	−	0.239289i	−0.965658	+	0.259816i	$0.916338\pi$
$788$	694.486	−	743.891i	0.881327	−	0.944025i
$789$		0			0
$790$	21.3463	−	4.62835i	0.0270206	−	0.00585867i
$791$	635.246	+	635.246i	0.803092	+	0.803092i
$792$		0			0
$793$	817.252	+	817.252i	1.03058	+	1.03058i
$794$	235.919	−	366.546i	0.297127	−	0.461645i
$795$		0			0
$796$	−518.340	−	1139.12i	−0.651182	−	1.43106i
$797$	315.999	+	762.889i	0.396485	+	0.957200i	0.988493	+	0.151268i	$0.0483356\pi$
$797$	315.999	+	762.889i	0.396485	+	0.957200i	−0.592007	+	0.805933i	$0.701664\pi$
$798$		0			0
$799$			573.826i			0.718181i
$800$	−483.383	−	604.049i	−0.604228	−	0.755061i
$801$		0			0
$802$	505.688	+	729.391i	0.630534	+	0.909466i
$803$	−49.8916	+	20.6658i	−0.0621315	+	0.0257357i
$804$		0			0
$805$	141.733	+	58.7076i	0.176065	+	0.0729287i
$806$	−573.383	−	369.044i	−0.711393	−	0.457871i
$807$		0			0
$808$	150.700	−	1033.12i	0.186509	−	1.27861i
$809$	−419.458	+	419.458i	−0.518490	+	0.518490i	−0.917114	−	0.398624i	$-0.869488\pi$
$809$	−419.458	+	419.458i	−0.518490	+	0.518490i	0.398624	+	0.917114i	$0.369488\pi$
$810$		0			0
$811$	433.066	+	179.382i	0.533990	+	0.221186i	0.633350	−	0.773866i	$-0.281680\pi$
$811$	433.066	+	179.382i	0.533990	+	0.221186i	−0.0993599	+	0.995052i	$0.531680\pi$
$812$	−358.293	+	383.782i	−0.441247	+	0.472638i
$813$		0			0
$814$	754.011	+	136.570i	0.926303	+	0.167776i
$815$	−23.4699			−0.0287974
$816$		0			0
$817$		−	807.145i		−	0.987937i
$818$	−162.398	−	29.4143i	−0.198530	−	0.0359587i
$819$		0			0
$820$	4.15972	+	121.104i	0.00507283	+	0.147688i
$821$	28.5629	−	68.9569i	0.0347903	−	0.0839913i	−0.905529	−	0.424284i	$-0.860526\pi$
$821$	28.5629	−	68.9569i	0.0347903	−	0.0839913i	0.940320	+	0.340292i	$0.110526\pi$
$822$		0			0
$823$	−243.818	−	243.818i	−0.296255	−	0.296255i	0.543290	−	0.839545i	$-0.317178\pi$
$823$	−243.818	−	243.818i	−0.296255	−	0.296255i	−0.839545	+	0.543290i	$0.817178\pi$
$824$	−991.530	−	591.051i	−1.20331	−	0.717294i
$825$		0			0
$826$	986.838	+	635.154i	1.19472	+	0.768952i
$827$	−22.1014	+	53.3576i	−0.0267248	+	0.0645195i	−0.936679	−	0.350190i	$-0.886117\pi$
$827$	−22.1014	+	53.3576i	−0.0267248	+	0.0645195i	0.909954	+	0.414710i	$0.136117\pi$
$828$		0			0
$829$	−553.388	−	1336.00i	−0.667537	−	1.61158i	−0.785719	−	0.618584i	$-0.787707\pi$
$829$	−553.388	−	1336.00i	−0.667537	−	1.61158i	0.118182	−	0.992992i	$-0.462293\pi$
$830$	89.8823	+	129.644i	0.108292	+	0.156198i
$831$		0			0
$832$	777.269	−	956.488i	0.934218	−	1.14963i
$833$	−2125.44			−2.55155
$834$		0			0
$835$	−65.1953	+	27.0048i	−0.0780783	+	0.0323411i
$836$	−357.165	−	133.771i	−0.427231	−	0.160014i
$837$		0			0
$838$	−793.008	+	1232.10i	−0.946311	+	1.47028i
$839$	109.789	−	109.789i	0.130857	−	0.130857i	−0.638645	−	0.769502i	$-0.720505\pi$
$839$	109.789	−	109.789i	0.130857	−	0.130857i	0.769502	+	0.638645i	$0.220505\pi$
$840$		0			0
$841$	506.056	−	506.056i	0.601732	−	0.601732i
$842$	−692.630	+	150.177i	−0.822601	+	0.178358i
$843$		0			0
$844$	−870.407	+	29.8970i	−1.03129	+	0.0354230i
$845$	−169.227	+	70.0961i	−0.200268	+	0.0829539i
$846$		0			0
$847$	−900.185			−1.06279
$848$	−932.362	+	463.528i	−1.09948	+	0.546613i
$849$		0			0
$850$	207.036	−	1143.06i	0.243572	−	1.34477i
$851$	−317.910	−	767.502i	−0.373572	−	0.901883i
$852$		0			0
$853$	−182.460	+	440.498i	−0.213904	+	0.516410i	−0.994017	−	0.109229i	$-0.965162\pi$
$853$	−182.460	+	440.498i	−0.213904	+	0.516410i	0.780112	+	0.625639i	$0.215162\pi$
$854$	1375.39	−	298.216i	1.61053	−	0.349199i
$855$		0			0
$856$	−177.763	+	1218.65i	−0.207668	+	1.42366i
$857$	4.48184	+	4.48184i	0.00522968	+	0.00522968i	0.709717	−	0.704487i	$-0.248823\pi$
$857$	4.48184	+	4.48184i	0.00522968	+	0.00522968i	−0.704487	+	0.709717i	$0.748823\pi$
$858$		0			0
$859$	−354.405	+	855.609i	−0.412579	+	0.996053i	0.571864	+	0.820348i	$0.306220\pi$
$859$	−354.405	+	855.609i	−0.412579	+	0.996053i	−0.984443	+	0.175705i	$0.943780\pi$
$860$	185.985	−	84.6297i	0.216261	−	0.0984066i
$861$		0			0
$862$	−200.568	+	139.054i	−0.232677	+	0.161315i
$863$			1058.54i			1.22658i	0.789859	+	0.613289i	$0.210154\pi$
$863$			1058.54i			1.22658i	−0.789859	+	0.613289i	$0.789846\pi$
$864$		0			0
$865$	−8.67066			−0.0100239
$866$	118.085	+	170.323i	0.136357	+	0.196678i
$867$		0			0
$868$	−755.747	+	343.892i	−0.870677	+	0.396189i
$869$	−73.9424	−	30.6279i	−0.0850891	−	0.0352451i
$870$		0			0
$871$	−436.718	+	436.718i	−0.501398	+	0.501398i
$872$	−40.7856	−	54.7164i	−0.0467725	−	0.0627482i
$873$		0			0
$874$	87.6151	+	404.088i	0.100246	+	0.462343i
$875$	483.386	+	200.225i	0.552441	+	0.228829i
$876$		0			0
$877$	171.983	−	71.2376i	0.196104	−	0.0812288i	−0.282470	−	0.959276i	$-0.591154\pi$
$877$	171.983	−	71.2376i	0.196104	−	0.0812288i	0.478574	+	0.878047i	$0.341154\pi$
$878$	1423.97	+	257.916i	1.62183	+	0.293754i
$879$		0			0
$880$	−6.62501	−	96.3250i	−0.00752842	−	0.109460i
$881$		−	300.374i		−	0.340947i	−0.985362	−	0.170473i	$-0.945470\pi$
$881$		−	300.374i		−	0.340947i	0.985362	−	0.170473i	$-0.0545297\pi$
$882$		0			0
$883$	−459.602	−	1109.58i	−0.520500	−	1.25660i	−0.937593	−	0.347735i	$-0.886951\pi$
$883$	−459.602	−	1109.58i	−0.520500	−	1.25660i	0.417092	−	0.908864i	$-0.363049\pi$
$884$	1849.52	−	63.5278i	2.09222	−	0.0718640i
$885$		0			0
$886$	187.997	+	867.058i	0.212186	+	0.978621i
$887$	−162.763	−	162.763i	−0.183498	−	0.183498i	0.609380	−	0.792878i	$-0.291418\pi$
$887$	−162.763	−	162.763i	−0.183498	−	0.183498i	−0.792878	+	0.609380i	$0.791418\pi$
$888$		0			0
$889$	279.729	+	279.729i	0.314655	+	0.314655i
$890$	79.9923	+	51.4851i	0.0898790	+	0.0578485i
$891$		0			0
$892$	760.547	+	284.853i	0.852631	+	0.319342i
$893$	−131.055	−	316.395i	−0.146758	−	0.354306i
$894$		0			0
$895$		−	158.738i		−	0.177361i
$896$	−467.133	−	1426.22i	−0.521354	−	1.59176i
$897$		0			0
$898$	598.279	−	414.787i	0.666235	−	0.461901i
$899$	−183.112	+	75.8475i	−0.203684	+	0.0843688i
$900$		0			0
$901$	−1444.43	−	598.300i	−1.60314	−	0.664040i
$902$	240.306	−	373.362i	0.266414	−	0.413927i
$903$		0			0
$904$	−594.244	+	150.376i	−0.657349	+	0.166345i
$905$	6.41352	−	6.41352i	0.00708676	−	0.00708676i
$906$		0			0
$907$	879.455	+	364.282i	0.969630	+	0.401634i	0.810574	−	0.585636i	$-0.199155\pi$
$907$	879.455	+	364.282i	0.969630	+	0.401634i	0.159056	+	0.987270i	$0.449155\pi$
$908$	35.4602	+	1032.37i	0.0390531	+	1.13697i
$909$		0			0
$910$	−73.0332	+	403.221i	−0.0802563	+	0.443100i
$911$	634.430			0.696410			0.348205	−	0.937418i	$-0.386791\pi$
$911$	634.430			0.696410			0.348205	+	0.937418i	$0.386791\pi$
$912$		0			0
$913$		−	578.044i		−	0.633125i
$914$	−212.409	+	1172.72i	−0.232395	+	1.28307i
$915$		0			0
$916$	−751.456	+	804.915i	−0.820367	+	0.878728i
$917$	548.902	−	1325.17i	0.598585	−	1.44511i
$918$		0			0
$919$	68.4805	+	68.4805i	0.0745163	+	0.0745163i	0.743383	−	0.668866i	$-0.233220\pi$
$919$	68.4805	+	68.4805i	0.0745163	+	0.0745163i	−0.668866	+	0.743383i	$0.733220\pi$
$920$	−83.9245	+	62.5574i	−0.0912223	+	0.0679971i
$921$		0			0
$922$	153.965	−	239.216i	0.166991	−	0.259453i
$923$	974.626	−	2352.96i	1.05593	−	2.54925i
$924$		0			0
$925$	−533.046	−	1286.89i	−0.576266	−	1.39123i
$926$	−1216.48	+	843.385i	−1.31369	+	0.910783i
$927$		0			0
$928$	−99.7544	−	344.072i	−0.107494	−	0.370767i
$929$	312.186			0.336045			0.168022	−	0.985783i	$-0.446262\pi$
$929$	312.186			0.336045			0.168022	+	0.985783i	$0.446262\pi$
$930$		0			0
$931$	1171.92	−	485.425i	1.25878	−	0.521402i
$932$	−662.655	−	1456.27i	−0.711003	−	1.56252i
$933$		0			0
$934$	−243.635	−	156.810i	−0.260851	−	0.167891i
$935$	102.514	−	102.514i	0.109640	−	0.109640i
$936$		0			0
$937$	−193.132	+	193.132i	−0.206117	+	0.206117i	−0.802615	−	0.596498i	$-0.796559\pi$
$937$	−193.132	+	193.132i	−0.206117	+	0.206117i	0.596498	+	0.802615i	$0.296559\pi$
$938$	159.359	+	734.975i	0.169892	+	0.783555i
$939$		0			0
$940$	59.1635	−	63.3724i	0.0629399	−	0.0674174i
$941$	389.257	−	161.235i	0.413663	−	0.171345i	−0.166139	−	0.986102i	$-0.553130\pi$
$941$	389.257	−	161.235i	0.413663	−	0.171345i	0.579802	+	0.814758i	$0.303130\pi$
$942$		0			0
$943$	−481.362			−0.510458
$944$	−717.025	+	356.472i	−0.759560	+	0.377619i
$945$		0			0
$946$	−736.735	−	133.441i	−0.778789	−	0.141058i
$947$	206.698	+	499.012i	0.218266	+	0.526940i	0.994648	−	0.103322i	$-0.0329473\pi$
$947$	206.698	+	499.012i	0.218266	+	0.526940i	−0.776382	+	0.630262i	$0.782947\pi$
$948$		0			0
$949$	−59.8448	+	144.478i	−0.0630609	+	0.152243i
$950$	146.906	+	677.542i	0.154638	+	0.713202i
$951$		0			0
$952$	1153.83	−	1935.64i	1.21201	−	2.03323i
$953$	−1112.21	−	1112.21i	−1.16706	−	1.16706i	−0.982896	−	0.184163i	$-0.941043\pi$
$953$	−1112.21	−	1112.21i	−1.16706	−	1.16706i	−0.184163	−	0.982896i	$-0.558957\pi$
$954$		0			0
$955$	91.4052	−	220.672i	0.0957122	−	0.231070i
$956$	−144.488	+	385.778i	−0.151138	+	0.403533i
$957$		0			0
$958$	1.17009	+	1.68771i	0.00122139	+	0.00176170i
$959$		−	2929.12i		−	3.05435i
$960$		0			0
$961$	647.560			0.673840
$962$	1823.61	−	1264.31i	1.89565	−	1.31426i
$963$		0			0
$964$	1526.25	+	571.638i	1.58325	+	0.592985i
$965$	−251.875	−	104.330i	−0.261010	−	0.108114i
$966$		0			0
$967$	392.270	−	392.270i	0.405657	−	0.405657i	−0.474564	−	0.880221i	$-0.657394\pi$
$967$	392.270	−	392.270i	0.405657	−	0.405657i	0.880221	+	0.474564i	$0.157394\pi$
$968$	314.495	−	527.588i	0.324891	−	0.545029i
$969$		0			0
$970$	122.136	−	26.4818i	0.125914	−	0.0273008i
$971$	−1618.70	−	670.485i	−1.66704	−	0.690510i	−0.668458	−	0.743750i	$-0.733045\pi$
$971$	−1618.70	−	670.485i	−1.66704	−	0.690510i	−0.998582	+	0.0532400i	$0.983045\pi$
$972$		0			0
$973$	1501.19	−	621.814i	1.54285	−	0.639068i
$974$	−124.025	+	684.750i	−0.127336	+	0.703029i
$975$		0			0
$976$	−305.737	+	910.289i	−0.313255	+	0.932674i
$977$		−	129.654i		−	0.132706i	−0.997796	−	0.0663532i	$-0.978864\pi$
$977$		−	129.654i		−	0.132706i	0.997796	−	0.0663532i	$-0.0211364\pi$
$978$		0			0
$979$	−133.393	−	322.038i	−0.136254	−	0.328946i
$980$	234.730	+	219.140i	0.239520	+	0.223612i
$981$		0			0
$982$	1536.46	−	333.139i	1.56463	−	0.339245i
$983$	54.8426	+	54.8426i	0.0557910	+	0.0557910i	0.734452	−	0.678661i	$-0.237439\pi$
$983$	54.8426	+	54.8426i	0.0557910	+	0.0557910i	−0.678661	+	0.734452i	$0.737439\pi$
$984$		0			0
$985$	−163.251	−	163.251i	−0.165737	−	0.165737i
$986$	291.124	−	452.319i	0.295258	−	0.458741i
$987$		0			0
$988$	−1005.28	+	457.436i	−1.01748	+	0.462992i
$989$	310.626	+	749.917i	0.314081	+	0.758258i
$990$		0			0
$991$			320.337i			0.323246i	0.986853	+	0.161623i	$0.0516729\pi$
$991$			320.337i			0.323246i	−0.986853	+	0.161623i	$0.948327\pi$
$992$	62.4819	−	563.079i	0.0629858	−	0.567620i
$993$		0			0
$994$	−1766.95	−	2548.60i	−1.77761	−	2.56399i
$995$	−262.305	+	108.650i	−0.263623	+	0.109196i
$996$		0			0
$997$	213.663	+	88.5020i	0.214306	+	0.0887683i	0.487254	−	0.873260i	$-0.337999\pi$
$997$	213.663	+	88.5020i	0.214306	+	0.0887683i	−0.272948	+	0.962029i	$0.587999\pi$
$998$	418.617	+	269.432i	0.419455	+	0.269972i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.b.91.3		64
3.2	odd	2		96.3.m.a.91.14	yes	64
12.11	even	2		384.3.m.a.271.13		64
32.19	odd	8	inner	288.3.u.b.19.3		64
96.77	odd	8		384.3.m.a.367.13		64
96.83	even	8		96.3.m.a.19.14	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.3.m.a.19.14	✓	64	96.83	even	8
96.3.m.a.91.14	yes	64	3.2	odd	2
288.3.u.b.19.3		64	32.19	odd	8	inner
288.3.u.b.91.3		64	1.1	even	1	trivial
384.3.m.a.271.13		64	12.11	even	2
384.3.m.a.367.13		64	96.77	odd	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64362 + 1.13952i) q^{2} +(1.40297 - 3.74589i) q^{4} +(-0.838363 - 0.347262i) q^{5} +(8.29065 - 8.29065i) q^{7} +(1.96258 + 7.75553i) q^{8} +O(q^{10})\)	\(q+(-1.64362 + 1.13952i) q^{2} +(1.40297 - 3.74589i) q^{4} +(-0.838363 - 0.347262i) q^{5} +(8.29065 - 8.29065i) q^{7} +(1.96258 + 7.75553i) q^{8} +(1.77366 - 0.384569i) q^{10} +(-6.14387 - 2.54487i) q^{11} +(-17.7917 + 7.36955i) q^{13} +(-4.17929 + 23.0741i) q^{14} +(-12.0633 - 10.5107i) q^{16} -24.0244i q^{17} +(5.48690 + 13.2466i) q^{19} +(-2.47700 + 2.65322i) q^{20} +(12.9981 - 2.81828i) q^{22} +(-10.1957 - 10.1957i) q^{23} +(-17.0954 - 17.0954i) q^{25} +(20.8450 - 32.3868i) q^{26} +(-19.4243 - 42.6874i) q^{28} +(-4.28415 - 10.3428i) q^{29} -17.7042i q^{31} +(31.8048 + 3.52921i) q^{32} +(27.3764 + 39.4871i) q^{34} +(-9.82961 + 4.07156i) q^{35} +(53.2287 + 22.0480i) q^{37} +(-24.1131 - 15.5198i) q^{38} +(1.04785 - 7.18348i) q^{40} +(23.6060 - 23.6060i) q^{41} +(-52.0091 - 21.5429i) q^{43} +(-18.1525 + 19.4439i) q^{44} +(28.3762 + 5.13963i) q^{46} -23.8851 q^{47} -88.4698i q^{49} +(47.5790 + 8.61773i) q^{50} +(2.64430 + 76.9849i) q^{52} +(24.9038 - 60.1231i) q^{53} +(4.26706 + 4.26706i) q^{55} +(80.5695 + 48.0274i) q^{56} +(18.8274 + 12.1178i) q^{58} +(19.1521 - 46.2372i) q^{59} +(-22.9673 - 55.4479i) q^{61} +(20.1744 + 29.0990i) q^{62} +(-56.2966 + 30.4416i) q^{64} +17.4750 q^{65} +(29.6299 - 12.2731i) q^{67} +(-89.9929 - 33.7056i) q^{68} +(11.5165 - 17.8932i) q^{70} +(-93.5151 + 93.5151i) q^{71} +(5.74210 - 5.74210i) q^{73} +(-112.612 + 24.4167i) q^{74} +(57.3181 - 1.96878i) q^{76} +(-72.0354 + 29.8380i) q^{77} +12.0352 q^{79} +(6.46349 + 13.0010i) q^{80} +(-11.8997 + 65.6989i) q^{82} +(33.2639 + 80.3062i) q^{83} +(-8.34277 + 20.1412i) q^{85} +(110.032 - 23.8573i) q^{86} +(7.67905 - 52.6435i) q^{88} +(37.0638 + 37.0638i) q^{89} +(-86.4062 + 208.603i) q^{91} +(-52.4964 + 23.8878i) q^{92} +(39.2580 - 27.2176i) q^{94} -13.0108i q^{95} +68.8610 q^{97} +(100.813 + 145.411i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 40 q^{10} - 32 q^{14} - 8 q^{16} + 160 q^{20} - 184 q^{22} - 128 q^{23} + 200 q^{26} - 120 q^{28} - 40 q^{32} + 120 q^{34} + 192 q^{35} - 280 q^{38} + 584 q^{40} - 192 q^{43} - 104 q^{44} + 32 q^{46} + 312 q^{50} - 424 q^{52} - 320 q^{53} - 256 q^{55} + 392 q^{56} - 352 q^{58} + 256 q^{59} + 64 q^{61} + 48 q^{62} + 408 q^{64} + 64 q^{67} - 856 q^{68} + 984 q^{70} - 512 q^{71} - 1056 q^{74} + 296 q^{76} + 448 q^{77} + 512 q^{79} - 328 q^{80} - 760 q^{82} + 448 q^{86} - 1072 q^{88} + 192 q^{91} + 784 q^{92} - 480 q^{94} - 272 q^{98}+O(q^{100}) \) 64 * q + 40 * q^10 - 32 * q^14 - 8 * q^16 + 160 * q^20 - 184 * q^22 - 128 * q^23 + 200 * q^26 - 120 * q^28 - 40 * q^32 + 120 * q^34 + 192 * q^35 - 280 * q^38 + 584 * q^40 - 192 * q^43 - 104 * q^44 + 32 * q^46 + 312 * q^50 - 424 * q^52 - 320 * q^53 - 256 * q^55 + 392 * q^56 - 352 * q^58 + 256 * q^59 + 64 * q^61 + 48 * q^62 + 408 * q^64 + 64 * q^67 - 856 * q^68 + 984 * q^70 - 512 * q^71 - 1056 * q^74 + 296 * q^76 + 448 * q^77 + 512 * q^79 - 328 * q^80 - 760 * q^82 + 448 * q^86 - 1072 * q^88 + 192 * q^91 + 784 * q^92 - 480 * q^94 - 272 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more