LMFDB - Embedded newform 288.3.u.b.91.2

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			91.2
Character	$\chi$	$=$	288.91
Dual form			288.3.u.b.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92938 - 0.526758i) q^{2} +(3.44505 + 2.03264i) q^{4} +(-3.51382 - 1.45547i) q^{5} +(-1.77216 + 1.77216i) q^{7} +(-5.57613 - 5.73645i) q^{8} +O(q^{10})$	\(q+(-1.92938 - 0.526758i) q^{2} +(3.44505 + 2.03264i) q^{4} +(-3.51382 - 1.45547i) q^{5} +(-1.77216 + 1.77216i) q^{7} +(-5.57613 - 5.73645i) q^{8} +(6.01282 + 4.65909i) q^{10} +(3.84851 + 1.59411i) q^{11} +(5.91643 - 2.45067i) q^{13} +(4.35268 - 2.48568i) q^{14} +(7.73678 + 14.0051i) q^{16} +10.3089i q^{17} +(-2.86839 - 6.92491i) q^{19} +(-9.14684 - 12.1565i) q^{20} +(-6.58556 - 5.10288i) q^{22} +(29.6688 + 29.6688i) q^{23} +(-7.44916 - 7.44916i) q^{25} +(-12.7060 + 1.61175i) q^{26} +(-9.70735 + 2.50303i) q^{28} +(10.0526 + 24.2691i) q^{29} +7.83864i q^{31} +(-7.54994 - 31.0966i) q^{32} +(5.43029 - 19.8898i) q^{34} +(8.80638 - 3.64772i) q^{35} +(56.8298 + 23.5397i) q^{37} +(1.88648 + 14.8718i) q^{38} +(11.2443 + 28.2727i) q^{40} +(18.3495 - 18.3495i) q^{41} +(54.2671 + 22.4782i) q^{43} +(10.0181 + 13.3144i) q^{44} +(-41.6143 - 72.8708i) q^{46} +55.9090 q^{47} +42.7189i q^{49} +(10.4484 + 18.2962i) q^{50} +(25.3637 + 3.58328i) q^{52} +(-22.5283 + 54.3881i) q^{53} +(-11.2028 - 11.2028i) q^{55} +(20.0477 + 0.284113i) q^{56} +(-6.61138 - 52.1197i) q^{58} +(43.1567 - 104.190i) q^{59} +(-6.15421 - 14.8576i) q^{61} +(4.12906 - 15.1238i) q^{62} +(-1.81363 + 63.9743i) q^{64} -24.3561 q^{65} +(52.0912 - 21.5769i) q^{67} +(-20.9542 + 35.5147i) q^{68} +(-18.9124 + 2.39903i) q^{70} +(-56.0775 + 56.0775i) q^{71} +(-89.9701 + 89.9701i) q^{73} +(-97.2469 - 75.3527i) q^{74} +(4.19406 - 29.6871i) q^{76} +(-9.64521 + 3.99518i) q^{77} -17.3956 q^{79} +(-6.80164 - 60.4719i) q^{80} +(-45.0691 + 25.7376i) q^{82} +(-2.34511 - 5.66160i) q^{83} +(15.0043 - 36.2236i) q^{85} +(-92.8615 - 71.9546i) q^{86} +(-12.3153 - 30.9657i) q^{88} +(-82.3147 - 82.3147i) q^{89} +(-6.14190 + 14.8278i) q^{91} +(41.9047 + 162.516i) q^{92} +(-107.870 - 29.4505i) q^{94} +28.5077i q^{95} -96.8541 q^{97} +(22.5025 - 82.4212i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.92938	−	0.526758i	−0.964692	−	0.263379i
$2$	−1.92938	−	0.526758i	−0.964692	−	0.263379i
$3$		0			0
$3$		0			0
$4$	3.44505	+	2.03264i	0.861263	+	0.508159i
$5$	−3.51382	−	1.45547i	−0.702763	−	0.291094i	0.00254304	−	0.999997i	$-0.499191\pi$
$5$	−3.51382	−	1.45547i	−0.702763	−	0.291094i	−0.705306	+	0.708903i	$0.749191\pi$
$6$		0			0
$7$	−1.77216	+	1.77216i	−0.253166	+	0.253166i	−0.822267	−	0.569101i	$-0.807291\pi$
$7$	−1.77216	+	1.77216i	−0.253166	+	0.253166i	0.569101	+	0.822267i	$0.307291\pi$
$8$	−5.57613	−	5.73645i	−0.697016	−	0.717056i
$9$		0			0
$10$	6.01282	+	4.65909i	0.601282	+	0.465909i
$11$	3.84851	+	1.59411i	0.349865	+	0.144919i	0.550693	−	0.834708i	$-0.314363\pi$
$11$	3.84851	+	1.59411i	0.349865	+	0.144919i	−0.200828	+	0.979626i	$0.564363\pi$
$12$		0			0
$13$	5.91643	−	2.45067i	0.455110	−	0.188513i	−0.143339	−	0.989674i	$-0.545784\pi$
$13$	5.91643	−	2.45067i	0.455110	−	0.188513i	0.598449	+	0.801161i	$0.295784\pi$
$14$	4.35268	−	2.48568i	0.310906	−	0.177549i
$15$		0			0
$16$	7.73678	+	14.0051i	0.483549	+	0.875318i
$17$			10.3089i			0.606406i	0.952926	+	0.303203i	$0.0980560\pi$
$17$			10.3089i			0.606406i	−0.952926	+	0.303203i	$0.901944\pi$
$18$		0			0
$19$	−2.86839	−	6.92491i	−0.150968	−	0.364469i	0.830244	−	0.557399i	$-0.188201\pi$
$19$	−2.86839	−	6.92491i	−0.150968	−	0.364469i	−0.981212	+	0.192931i	$0.938201\pi$
$20$	−9.14684	−	12.1565i	−0.457342	−	0.607824i
$21$		0			0
$22$	−6.58556	−	5.10288i	−0.299344	−	0.231949i
$23$	29.6688	+	29.6688i	1.28995	+	1.28995i	0.934817	+	0.355131i	$0.115564\pi$
$23$	29.6688	+	29.6688i	1.28995	+	1.28995i	0.355131	+	0.934817i	$0.384436\pi$
$24$		0			0
$25$	−7.44916	−	7.44916i	−0.297966	−	0.297966i
$26$	−12.7060	+	1.61175i	−0.488692	+	0.0619905i
$27$		0			0
$28$	−9.70735	+	2.50303i	−0.346691	+	0.0893939i
$29$	10.0526	+	24.2691i	0.346641	+	0.836865i	0.997012	+	0.0772483i	$0.0246134\pi$
$29$	10.0526	+	24.2691i	0.346641	+	0.836865i	−0.650371	+	0.759617i	$0.725387\pi$
$30$		0			0
$31$			7.83864i			0.252859i	0.991976	+	0.126430i	$0.0403518\pi$
$31$			7.83864i			0.252859i	−0.991976	+	0.126430i	$0.959648\pi$
$32$	−7.54994	−	31.0966i	−0.235936	−	0.971769i
$33$		0			0
$34$	5.43029	−	19.8898i	0.159714	−	0.584995i
$35$	8.80638	−	3.64772i	0.251611	−	0.104221i
$36$		0			0
$37$	56.8298	+	23.5397i	1.53594	+	0.636208i	0.980707	−	0.195485i	$-0.0626282\pi$
$37$	56.8298	+	23.5397i	1.53594	+	0.636208i	0.555235	+	0.831693i	$0.312628\pi$
$38$	1.88648	+	14.8718i	0.0496443	+	0.391362i
$39$		0			0
$40$	11.2443	+	28.2727i	0.281106	+	0.706818i
$41$	18.3495	−	18.3495i	0.447550	−	0.447550i	−0.446989	−	0.894539i	$-0.647504\pi$
$41$	18.3495	−	18.3495i	0.447550	−	0.447550i	0.894539	+	0.446989i	$0.147504\pi$
$42$		0			0
$43$	54.2671	+	22.4782i	1.26202	+	0.522748i	0.910530	−	0.413442i	$-0.135674\pi$
$43$	54.2671	+	22.4782i	1.26202	+	0.522748i	0.351495	+	0.936190i	$0.385674\pi$
$44$	10.0181	+	13.3144i	0.227684	+	0.302600i
$45$		0			0
$46$	−41.6143	−	72.8708i	−0.904658	−	1.58415i
$47$	55.9090			1.18955			0.594777	−	0.803891i	$-0.297240\pi$
$47$	55.9090			1.18955			0.594777	+	0.803891i	$0.297240\pi$
$48$		0			0
$49$			42.7189i			0.871814i
$50$	10.4484	+	18.2962i	0.208968	+	0.365924i
$51$		0			0
$52$	25.3637	+	3.58328i	0.487764	+	0.0689092i
$53$	−22.5283	+	54.3881i	−0.425062	+	1.02619i	0.555771	+	0.831336i	$0.312423\pi$
$53$	−22.5283	+	54.3881i	−0.425062	+	1.02619i	−0.980832	+	0.194854i	$0.937577\pi$
$54$		0			0
$55$	−11.2028	−	11.2028i	−0.203687	−	0.203687i
$56$	20.0477	+	0.284113i	0.357995	+	0.00507345i
$57$		0			0
$58$	−6.61138	−	52.1197i	−0.113989	−	0.898615i
$59$	43.1567	−	104.190i	0.731470	−	1.76592i	0.0938327	−	0.995588i	$-0.470088\pi$
$59$	43.1567	−	104.190i	0.731470	−	1.76592i	0.637637	−	0.770337i	$-0.279912\pi$
$60$		0			0
$61$	−6.15421	−	14.8576i	−0.100889	−	0.243567i	0.865373	−	0.501128i	$-0.167081\pi$
$61$	−6.15421	−	14.8576i	−0.100889	−	0.243567i	−0.966262	+	0.257561i	$0.917081\pi$
$62$	4.12906	−	15.1238i	0.0665978	−	0.243932i
$63$		0			0
$64$	−1.81363	+	63.9743i	−0.0283380	+	0.999598i
$65$	−24.3561			−0.374710
$66$		0			0
$67$	52.0912	−	21.5769i	0.777480	−	0.322043i	0.0415819	−	0.999135i	$-0.486760\pi$
$67$	52.0912	−	21.5769i	0.777480	−	0.322043i	0.735898	+	0.677092i	$0.236760\pi$
$68$	−20.9542	+	35.5147i	−0.308151	+	0.522275i
$69$		0			0
$70$	−18.9124	+	2.39903i	−0.270177	+	0.0342719i
$71$	−56.0775	+	56.0775i	−0.789824	+	0.789824i	−0.981465	−	0.191641i	$-0.938619\pi$
$71$	−56.0775	+	56.0775i	−0.789824	+	0.789824i	0.191641	+	0.981465i	$0.438619\pi$
$72$		0			0
$73$	−89.9701	+	89.9701i	−1.23247	+	1.23247i	−0.269454	+	0.963013i	$0.586843\pi$
$73$	−89.9701	+	89.9701i	−1.23247	+	1.23247i	−0.963013	+	0.269454i	$0.913157\pi$
$74$	−97.2469	−	75.3527i	−1.31415	−	1.01828i
$75$		0			0
$76$	4.19406	−	29.6871i	0.0551850	−	0.390619i
$77$	−9.64521	+	3.99518i	−0.125262	+	0.0518854i
$78$		0			0
$79$	−17.3956			−0.220197			−0.110099	−	0.993921i	$-0.535117\pi$
$79$	−17.3956			−0.220197			−0.110099	+	0.993921i	$0.535117\pi$
$80$	−6.80164	−	60.4719i	−0.0850204	−	0.755899i
$81$		0			0
$82$	−45.0691	+	25.7376i	−0.549623	+	0.313873i
$83$	−2.34511	−	5.66160i	−0.0282544	−	0.0682121i	0.909123	−	0.416529i	$-0.136753\pi$
$83$	−2.34511	−	5.66160i	−0.0282544	−	0.0682121i	−0.937377	+	0.348317i	$0.886753\pi$
$84$		0			0
$85$	15.0043	−	36.2236i	0.176521	−	0.426160i
$86$	−92.8615	−	71.9546i	−1.07979	−	0.836682i
$87$		0			0
$88$	−12.3153	−	30.9657i	−0.139947	−	0.351883i
$89$	−82.3147	−	82.3147i	−0.924884	−	0.924884i	0.0724854	−	0.997369i	$-0.476907\pi$
$89$	−82.3147	−	82.3147i	−0.924884	−	0.924884i	−0.997369	+	0.0724854i	$0.976907\pi$
$90$		0			0
$91$	−6.14190	+	14.8278i	−0.0674934	+	0.162943i
$92$	41.9047	+	162.516i	0.455486	+	1.76648i
$93$		0			0
$94$	−107.870	−	29.4505i	−1.14755	−	0.313303i
$95$			28.5077i			0.300081i
$96$		0			0
$97$	−96.8541			−0.998496			−0.499248	−	0.866459i	$-0.666390\pi$
$97$	−96.8541			−0.998496			−0.499248	+	0.866459i	$0.666390\pi$
$98$	22.5025	−	82.4212i	0.229617	−	0.841032i
$99$		0			0
$100$	−10.5213	−	40.8042i	−0.105213	−	0.408042i
$101$	33.5632	+	13.9023i	0.332309	+	0.137647i	0.542598	−	0.839992i	$-0.317441\pi$
$101$	33.5632	+	13.9023i	0.332309	+	0.137647i	−0.210289	+	0.977639i	$0.567441\pi$
$102$		0			0
$103$	93.2695	−	93.2695i	0.905529	−	0.905529i	−0.0903781	−	0.995908i	$-0.528808\pi$
$103$	93.2695	−	93.2695i	0.905529	−	0.905529i	0.995908	+	0.0903781i	$0.0288075\pi$
$104$	−47.0489	−	20.2741i	−0.452393	−	0.194943i
$105$		0			0
$106$	72.1150	−	93.0686i	0.680330	−	0.878005i
$107$	−43.1008	−	17.8530i	−0.402812	−	0.166850i	0.172074	−	0.985084i	$-0.444953\pi$
$107$	−43.1008	−	17.8530i	−0.402812	−	0.166850i	−0.574885	+	0.818234i	$0.694953\pi$
$108$		0			0
$109$	−178.820	+	74.0698i	−1.64055	+	0.679539i	−0.996354	−	0.0853179i	$-0.972809\pi$
$109$	−178.820	+	74.0698i	−1.64055	+	0.679539i	−0.644200	+	0.764857i	$0.722809\pi$
$110$	15.7133	+	27.5157i	0.142849	+	0.250142i
$111$		0			0
$112$	−38.5301	−	11.1084i	−0.344019	−	0.0991826i
$113$			118.673i			1.05020i	0.851040	+	0.525100i	$0.175972\pi$
$113$			118.673i			1.05020i	−0.851040	+	0.525100i	$0.824028\pi$
$114$		0			0
$115$	−61.0686	−	147.433i	−0.531032	−	1.28202i
$116$	−14.6985	+	104.042i	−0.126712	+	0.896910i
$117$		0			0
$118$	−138.149	+	178.289i	−1.17075	+	1.51092i
$119$	−18.2690	−	18.2690i	−0.153521	−	0.153521i
$120$		0			0
$121$	−73.2900	−	73.2900i	−0.605703	−	0.605703i
$122$	4.04750	+	31.9078i	0.0331762	+	0.261539i
$123$		0			0
$124$	−15.9331	+	27.0045i	−0.128493	+	0.217779i
$125$	51.7197	+	124.862i	0.413758	+	0.998899i
$126$		0			0
$127$		−	62.6925i		−	0.493642i	−0.969061	−	0.246821i	$-0.920614\pi$
$127$		−	62.6925i		−	0.493642i	0.969061	−	0.246821i	$-0.0793859\pi$
$128$	37.1981	−	122.476i	0.290610	−	0.956841i
$129$		0			0
$130$	46.9923	+	12.8298i	0.361480	+	0.0986906i
$131$	17.7564	−	7.35493i	0.135545	−	0.0561445i	−0.313880	−	0.949463i	$-0.601629\pi$
$131$	17.7564	−	7.35493i	0.135545	−	0.0561445i	0.449425	+	0.893318i	$0.351629\pi$
$132$		0			0
$133$	17.3553	+	7.18881i	0.130491	+	0.0540512i
$134$	−111.870	+	14.1907i	−0.834848	+	0.105900i
$135$		0			0
$136$	59.1364	−	57.4837i	0.434827	−	0.422674i
$137$	92.0457	−	92.0457i	0.671866	−	0.671866i	−0.286280	−	0.958146i	$-0.592419\pi$
$137$	92.0457	−	92.0457i	0.671866	−	0.671866i	0.958146	+	0.286280i	$0.0924187\pi$
$138$		0			0
$139$	196.984	+	81.5935i	1.41715	+	0.587004i	0.954143	−	0.299350i	$-0.0967698\pi$
$139$	196.984	+	81.5935i	1.41715	+	0.587004i	0.463009	+	0.886354i	$0.346770\pi$
$140$	37.7529	+	5.33358i	0.269664	+	0.0380970i
$141$		0			0
$142$	137.734	−	78.6558i	0.969960	−	0.553914i
$143$	26.6761			0.186546
$144$		0			0
$145$		−	99.9083i		−	0.689023i
$146$	220.979	−	126.195i	1.51356	−	0.864346i
$147$		0			0
$148$	147.934	+	196.610i	0.999555	+	1.32845i
$149$	45.4882	−	109.818i	0.305290	−	0.737034i	−0.694556	−	0.719439i	$-0.744399\pi$
$149$	45.4882	−	109.818i	0.305290	−	0.737034i	0.999845	−	0.0175953i	$-0.00560106\pi$
$150$		0			0
$151$	34.9489	+	34.9489i	0.231449	+	0.231449i	0.813298	−	0.581848i	$-0.197670\pi$
$151$	34.9489	+	34.9489i	0.231449	+	0.231449i	−0.581848	+	0.813298i	$0.697670\pi$
$152$	−23.7299	+	55.0685i	−0.156117	+	0.362293i
$153$		0			0
$154$	20.7138	−	2.62754i	0.134505	−	0.0170620i
$155$	11.4089	−	27.5436i	0.0736059	−	0.177700i
$156$		0			0
$157$	9.76500	+	23.5748i	0.0621975	+	0.150158i	0.951923	−	0.306339i	$-0.0991040\pi$
$157$	9.76500	+	23.5748i	0.0621975	+	0.150158i	−0.889725	+	0.456497i	$0.849104\pi$
$158$	33.5627	+	9.16325i	0.212422	+	0.0579952i
$159$		0			0
$160$	−18.7311	+	120.256i	−0.117069	+	0.751603i
$161$	−105.156			−0.653142
$162$		0			0
$163$	106.511	−	44.1185i	0.653444	−	0.270666i	−0.0312326	−	0.999512i	$-0.509943\pi$
$163$	106.511	−	44.1185i	0.653444	−	0.270666i	0.684677	+	0.728847i	$0.259943\pi$
$164$	100.513	−	25.9172i	0.612885	−	0.158032i
$165$		0			0
$166$	1.54233	+	12.1587i	0.00929116	+	0.0732453i
$167$	−164.019	+	164.019i	−0.982148	+	0.982148i	−0.999843	−	0.0176954i	$-0.994367\pi$
$167$	−164.019	+	164.019i	−0.982148	+	0.982148i	0.0176954	+	0.999843i	$0.494367\pi$
$168$		0			0
$169$	−90.5027	+	90.5027i	−0.535519	+	0.535519i
$170$	−48.0301	+	61.9856i	−0.282530	+	0.364621i
$171$		0			0
$172$	141.263	+	187.744i	0.821297	+	1.09153i
$173$	108.211	−	44.8224i	0.625497	−	0.259089i	−0.0473416	−	0.998879i	$-0.515075\pi$
$173$	108.211	−	44.8224i	0.625497	−	0.259089i	0.672838	+	0.739790i	$0.265075\pi$
$174$		0			0
$175$	26.4022			0.150870
$176$	7.44950	+	66.2320i	0.0423267	+	0.376318i
$177$		0			0
$178$	115.457	+	202.177i	0.648634	+	1.13582i
$179$	−31.4630	−	75.9583i	−0.175771	−	0.424348i	0.811301	−	0.584629i	$-0.198760\pi$
$179$	−31.4630	−	75.9583i	−0.175771	−	0.424348i	−0.987071	+	0.160281i	$0.948760\pi$
$180$		0			0
$181$	−12.5046	+	30.1889i	−0.0690865	+	0.166789i	−0.954651	−	0.297726i	$-0.903772\pi$
$181$	−12.5046	+	30.1889i	−0.0690865	+	0.166789i	0.885565	+	0.464516i	$0.153772\pi$
$182$	19.6608	−	25.3733i	0.108026	−	0.139414i
$183$		0			0
$184$	4.75650	−	335.630i	0.0258505	−	1.82408i
$185$	−165.428	−	165.428i	−0.894207	−	0.894207i
$186$		0			0
$187$	−16.4335	+	39.6739i	−0.0878796	+	0.212160i
$188$	192.610	+	113.643i	1.02452	+	0.604483i
$189$		0			0
$190$	15.0167	−	55.0024i	0.0790350	−	0.289486i
$191$		−	39.4628i		−	0.206612i	−0.994650	−	0.103306i	$-0.967058\pi$
$191$		−	39.4628i		−	0.206612i	0.994650	−	0.103306i	$-0.0329420\pi$
$192$		0			0
$193$	240.789			1.24761			0.623806	−	0.781579i	$-0.285585\pi$
$193$	240.789			1.24761			0.623806	+	0.781579i	$0.285585\pi$
$194$	186.869	+	51.0186i	0.963242	+	0.262983i
$195$		0			0
$196$	−86.8320	+	147.169i	−0.443020	+	0.750861i
$197$	−45.4553	−	18.8282i	−0.230738	−	0.0955747i	0.264319	−	0.964435i	$-0.414853\pi$
$197$	−45.4553	−	18.8282i	−0.230738	−	0.0955747i	−0.495057	+	0.868861i	$0.664853\pi$
$198$		0			0
$199$	−142.223	+	142.223i	−0.714690	+	0.714690i	−0.967513	−	0.252823i	$-0.918641\pi$
$199$	−142.223	+	142.223i	−0.714690	+	0.714690i	0.252823	+	0.967513i	$0.418641\pi$
$200$	−1.19425	+	84.2691i	−0.00597124	+	0.421346i
$201$		0			0
$202$	−57.4332	−	44.5026i	−0.284323	−	0.220310i
$203$	−60.8236	−	25.1939i	−0.299623	−	0.124108i
$204$		0			0
$205$	−91.1841	+	37.7697i	−0.444801	+	0.184242i
$206$	−229.083	+	130.822i	−1.11205	+	0.635060i
$207$		0			0
$208$	80.0959	+	63.8998i	0.385076	+	0.307211i
$209$		−	31.2231i		−	0.149393i
$210$		0			0
$211$	−106.314	−	256.666i	−0.503860	−	1.21643i	−0.947366	−	0.320154i	$-0.896265\pi$
$211$	−106.314	−	256.666i	−0.503860	−	1.21643i	0.443506	−	0.896272i	$-0.353735\pi$
$212$	−188.162	+	141.578i	−0.887558	+	0.667820i
$213$		0			0
$214$	73.7539	+	57.1489i	0.344645	+	0.267051i
$215$	−157.968	−	157.968i	−0.734736	−	0.734736i
$216$		0			0
$217$	−13.8913	−	13.8913i	−0.0640154	−	0.0640154i
$218$	384.030	−	48.7142i	1.76161	−	0.223460i
$219$		0			0
$220$	−15.8230	−	61.3654i	−0.0719228	−	0.278934i
$221$	25.2637	+	60.9919i	0.114315	+	0.275981i
$222$		0			0
$223$			271.082i			1.21561i	0.794085	+	0.607807i	$0.207951\pi$
$223$			271.082i			1.21561i	−0.794085	+	0.607807i	$0.792049\pi$
$224$	68.4879	+	41.7285i	0.305750	+	0.186288i
$225$		0			0
$226$	62.5117	−	228.965i	0.276601	−	1.01312i
$227$	347.113	−	143.779i	1.52913	−	0.633387i	0.549736	−	0.835338i	$-0.314728\pi$
$227$	347.113	−	143.779i	1.52913	−	0.633387i	0.979396	+	0.201951i	$0.0647283\pi$
$228$		0			0
$229$	280.382	+	116.138i	1.22438	+	0.507153i	0.898798	−	0.438362i	$-0.144441\pi$
$229$	280.382	+	116.138i	1.22438	+	0.507153i	0.325578	+	0.945515i	$0.394441\pi$
$230$	40.1636	+	316.623i	0.174624	+	1.37662i
$231$		0			0
$232$	83.1638	−	192.994i	0.358465	−	0.831869i
$233$	−225.247	+	225.247i	−0.966727	+	0.966727i	−0.999464	−	0.0327367i	$-0.989578\pi$
$233$	−225.247	+	225.247i	−0.966727	+	0.966727i	0.0327367	+	0.999464i	$0.489578\pi$
$234$		0			0
$235$	−196.454	−	81.3740i	−0.835975	−	0.346272i
$236$	360.457	−	271.217i	1.52736	−	1.14922i
$237$		0			0
$238$	25.6246	+	44.8713i	0.107667	+	0.188535i
$239$	117.750			0.492680			0.246340	−	0.969183i	$-0.420772\pi$
$239$	117.750			0.492680			0.246340	+	0.969183i	$0.420772\pi$
$240$		0			0
$241$		−	147.107i		−	0.610402i	−0.952288	−	0.305201i	$-0.901276\pi$
$241$		−	147.107i		−	0.610402i	0.952288	−	0.305201i	$-0.0987236\pi$
$242$	102.799	+	180.011i	0.424788	+	0.743846i
$243$		0			0
$244$	8.99848	−	63.6944i	0.0368790	−	0.261043i
$245$	62.1761	−	150.106i	0.253780	−	0.612679i
$246$		0			0
$247$	−33.9413	−	33.9413i	−0.137414	−	0.137414i
$248$	44.9660	−	43.7093i	0.181314	−	0.176247i
$249$		0			0
$250$	−34.0150	−	268.151i	−0.136060	−	1.07261i
$251$	45.2497	−	109.242i	0.180278	−	0.435228i	−0.807746	−	0.589530i	$-0.799313\pi$
$251$	45.2497	−	109.242i	0.180278	−	0.435228i	0.988024	+	0.154302i	$0.0493128\pi$
$252$		0			0
$253$	66.8856	+	161.476i	0.264370	+	0.638245i
$254$	−33.0237	+	120.958i	−0.130015	+	0.476212i
$255$		0			0
$256$	−136.285	+	216.708i	−0.532362	+	0.846517i
$257$	−352.412			−1.37125			−0.685627	−	0.727953i	$-0.740472\pi$
$257$	−352.412			−1.37125			−0.685627	+	0.727953i	$0.740472\pi$
$258$		0			0
$259$	−142.428	+	58.9955i	−0.549914	+	0.227782i
$260$	−83.9081	−	49.5071i	−0.322724	−	0.190412i
$261$		0			0
$262$	−38.1331	+	4.83719i	−0.145546	+	0.0184625i
$263$	−141.253	+	141.253i	−0.537083	+	0.537083i	−0.922671	−	0.385588i	$-0.873999\pi$
$263$	−141.253	+	141.253i	−0.537083	+	0.537083i	0.385588	+	0.922671i	$0.373999\pi$
$264$		0			0
$265$	158.320	−	158.320i	0.597435	−	0.597435i
$266$	−29.6983	−	23.0120i	−0.111648	−	0.0865113i
$267$		0			0
$268$	223.315	+	31.5490i	0.833264	+	0.117720i
$269$	−3.70368	+	1.53411i	−0.0137683	+	0.00570302i	−0.389557	−	0.921002i	$-0.627372\pi$
$269$	−3.70368	+	1.53411i	−0.0137683	+	0.00570302i	0.375789	+	0.926705i	$0.377372\pi$
$270$		0			0
$271$	257.032			0.948457			0.474229	−	0.880402i	$-0.342727\pi$
$271$	257.032			0.948457			0.474229	+	0.880402i	$0.342727\pi$
$272$	−144.377	+	79.7576i	−0.530797	+	0.293227i
$273$		0			0
$274$	−226.077	+	129.106i	−0.825100	+	0.471189i
$275$	−16.7934	−	40.5429i	−0.0610670	−	0.147429i
$276$		0			0
$277$	113.407	−	273.788i	0.409410	−	0.988404i	−0.575883	−	0.817532i	$-0.695342\pi$
$277$	113.407	−	273.788i	0.409410	−	0.988404i	0.985293	−	0.170872i	$-0.0546584\pi$
$278$	−337.078	−	261.188i	−1.21251	−	0.939526i
$279$		0			0
$280$	−70.0305	−	30.1772i	−0.250109	−	0.107776i
$281$	−158.872	−	158.872i	−0.565379	−	0.565379i	0.365451	−	0.930830i	$-0.380915\pi$
$281$	−158.872	−	158.872i	−0.565379	−	0.565379i	−0.930830	+	0.365451i	$0.880915\pi$
$282$		0			0
$283$	−60.7983	+	146.780i	−0.214835	+	0.518657i	−0.994154	−	0.107970i	$-0.965565\pi$
$283$	−60.7983	+	146.780i	−0.214835	+	0.518657i	0.779319	+	0.626627i	$0.215565\pi$
$284$	−307.175	+	79.2047i	−1.08160	+	0.278890i
$285$		0			0
$286$	−51.4684	−	14.0518i	−0.179960	−	0.0491323i
$287$			65.0367i			0.226609i
$288$		0			0
$289$	182.727			0.632272
$290$	−52.6275	+	192.762i	−0.181474	+	0.664695i
$291$		0			0
$292$	−492.828	+	127.075i	−1.68777	+	0.435189i
$293$	226.956	+	94.0083i	0.774595	+	0.320848i	0.734732	−	0.678358i	$-0.237308\pi$
$293$	226.956	+	94.0083i	0.774595	+	0.320848i	0.0398627	+	0.999205i	$0.487308\pi$
$294$		0			0
$295$	−303.290	+	303.290i	−1.02810	+	1.02810i
$296$	−181.856	−	457.262i	−0.614379	−	1.54480i
$297$		0			0
$298$	−145.612	+	187.920i	−0.488630	+	0.630605i
$299$	248.242	+	102.825i	0.830240	+	0.343897i
$300$		0			0
$301$	−136.005	+	56.3351i	−0.451844	+	0.187160i
$302$	−49.0202	−	85.8394i	−0.162319	−	0.284236i
$303$		0			0
$304$	74.7918	−	93.7485i	0.246026	−	0.308383i
$305$			61.1641i			0.200538i
$306$		0			0
$307$	−148.584	−	358.713i	−0.483987	−	1.16845i	−0.957700	−	0.287768i	$-0.907087\pi$
$307$	−148.584	−	358.713i	−0.483987	−	1.16845i	0.473714	−	0.880679i	$-0.342913\pi$
$308$	−41.3490	−	5.84161i	−0.134250	−	0.0189663i
$309$		0			0
$310$	−36.5210	+	47.1324i	−0.117810	+	0.152040i
$311$	−29.7614	−	29.7614i	−0.0956957	−	0.0956957i	0.657638	−	0.753334i	$-0.271556\pi$
$311$	−29.7614	−	29.7614i	−0.0956957	−	0.0956957i	−0.753334	+	0.657638i	$0.771556\pi$
$312$		0			0
$313$	−337.512	−	337.512i	−1.07831	−	1.07831i	−0.996661	−	0.0816511i	$-0.973981\pi$
$313$	−337.512	−	337.512i	−1.07831	−	1.07831i	−0.0816511	−	0.996661i	$-0.526019\pi$
$314$	−6.42224	−	50.6287i	−0.0204530	−	0.161238i
$315$		0			0
$316$	−59.9286	−	35.3589i	−0.189648	−	0.111895i
$317$	60.4601	+	145.964i	0.190726	+	0.460453i	0.990097	−	0.140385i	$-0.0448339\pi$
$317$	60.4601	+	145.964i	0.190726	+	0.460453i	−0.799371	+	0.600837i	$0.794834\pi$
$318$		0			0
$319$			109.425i			0.343024i
$320$	99.4855	−	222.154i	0.310892	−	0.694232i
$321$		0			0
$322$	202.886	+	55.3916i	0.630081	+	0.172024i
$323$	71.3882	−	29.5699i	0.221016	−	0.0915478i
$324$		0			0
$325$	−62.3278	−	25.8170i	−0.191778	−	0.0794370i
$326$	−228.741	+	29.0158i	−0.701661	+	0.0890056i
$327$		0			0
$328$	−207.581	−	2.94180i	−0.632867	−	0.00896890i
$329$	−99.0799	+	99.0799i	−0.301155	+	0.301155i
$330$		0			0
$331$	−129.204	−	53.5180i	−0.390344	−	0.161686i	0.178875	−	0.983872i	$-0.442754\pi$
$331$	−129.204	−	53.5180i	−0.390344	−	0.161686i	−0.569219	+	0.822186i	$0.692754\pi$
$332$	3.42895	−	24.2713i	0.0103281	−	0.0731063i
$333$		0			0
$334$	402.853	−	230.057i	1.20615	−	0.688794i
$335$	−214.443			−0.640129
$336$		0			0
$337$			445.030i			1.32056i	0.751018	+	0.660282i	$0.229563\pi$
$337$			445.030i			1.32056i	−0.751018	+	0.660282i	$0.770437\pi$
$338$	222.287	−	126.942i	0.657655	−	0.375567i
$339$		0			0
$340$	125.320	−	94.2938i	0.368588	−	0.277335i
$341$	−12.4956	+	30.1671i	−0.0366441	+	0.0884667i
$342$		0			0
$343$	−162.541	−	162.541i	−0.473880	−	0.473880i
$344$	−173.655	−	436.641i	−0.504812	−	1.26931i
$345$		0			0
$346$	−232.391	+	29.4788i	−0.671651	+	0.0851988i
$347$	−146.847	+	354.520i	−0.423190	+	1.02167i	0.558211	+	0.829699i	$0.311488\pi$
$347$	−146.847	+	354.520i	−0.423190	+	1.02167i	−0.981401	+	0.191971i	$0.938512\pi$
$348$		0			0
$349$	69.5654	+	167.946i	0.199328	+	0.481220i	0.991662	−	0.128868i	$-0.0411343\pi$
$349$	69.5654	+	167.946i	0.199328	+	0.481220i	−0.792334	+	0.610088i	$0.791134\pi$
$350$	−50.9401	−	13.9076i	−0.145543	−	0.0397359i
$351$		0			0
$352$	20.5153	−	131.711i	0.0582820	−	0.374179i
$353$	564.907			1.60030			0.800151	−	0.599799i	$-0.204753\pi$
$353$	564.907			1.60030			0.800151	+	0.599799i	$0.204753\pi$
$354$		0			0
$355$	278.665	−	115.427i	0.784972	−	0.325146i
$356$	−116.263	−	450.894i	−0.326580	−	1.26656i
$357$		0			0
$358$	20.6925	+	163.126i	0.0578004	+	0.455660i
$359$	32.3280	−	32.3280i	0.0900501	−	0.0900501i	−0.660647	−	0.750697i	$-0.729718\pi$
$359$	32.3280	−	32.3280i	0.0900501	−	0.0900501i	0.750697	+	0.660647i	$0.229718\pi$
$360$		0			0
$361$	215.539	−	215.539i	0.597061	−	0.597061i
$362$	40.0285	−	51.6591i	0.110576	−	0.142705i
$363$		0			0
$364$	−51.2988	+	38.5985i	−0.140931	+	0.106040i
$365$	447.087	−	185.190i	1.22490	−	0.507369i
$366$		0			0
$367$	104.874			0.285762			0.142881	−	0.989740i	$-0.454363\pi$
$367$	104.874			0.285762			0.142881	+	0.989740i	$0.454363\pi$
$368$	−185.973	+	645.055i	−0.505361	+	1.75287i
$369$		0			0
$370$	232.034	+	406.316i	0.627120	+	1.09815i
$371$	−56.4607	−	136.308i	−0.152185	−	0.367407i
$372$		0			0
$373$	222.064	−	536.109i	0.595345	−	1.43729i	−0.282934	−	0.959139i	$-0.591308\pi$
$373$	222.064	−	536.109i	0.595345	−	1.43729i	0.878278	−	0.478150i	$-0.158692\pi$
$374$	52.6051	−	67.8898i	0.140655	−	0.181524i
$375$		0			0
$376$	−311.756	−	320.719i	−0.829138	−	0.852977i
$377$	118.951	+	118.951i	0.315519	+	0.315519i
$378$		0			0
$379$	−208.624	+	503.662i	−0.550458	+	1.32892i	0.366677	+	0.930348i	$0.380495\pi$
$379$	−208.624	+	503.662i	−0.550458	+	1.32892i	−0.917135	+	0.398576i	$0.869505\pi$
$380$	−57.9458	+	98.2106i	−0.152489	+	0.258449i
$381$		0			0
$382$	−20.7873	+	76.1389i	−0.0544171	+	0.199317i
$383$			639.737i			1.67033i	0.549997	+	0.835166i	$0.314629\pi$
$383$			639.737i			1.67033i	−0.549997	+	0.835166i	$0.685371\pi$
$384$		0			0
$385$	39.7063			0.103133
$386$	−464.575	−	126.838i	−1.20356	−	0.328595i
$387$		0			0
$388$	−333.668	−	196.869i	−0.859968	−	0.507395i
$389$	202.334	+	83.8094i	0.520138	+	0.215448i	0.627278	−	0.778796i	$-0.284169\pi$
$389$	202.334	+	83.8094i	0.520138	+	0.215448i	−0.107140	+	0.994244i	$0.534169\pi$
$390$		0			0
$391$	−305.852	+	305.852i	−0.782231	+	0.782231i
$392$	245.055	−	238.206i	0.625139	−	0.607668i
$393$		0			0
$394$	77.7829	+	60.2708i	0.197419	+	0.152972i
$395$	61.1248	+	25.3187i	0.154746	+	0.0640980i
$396$		0			0
$397$	385.027	−	159.483i	0.969841	−	0.401721i	0.159188	−	0.987248i	$-0.449112\pi$
$397$	385.027	−	159.483i	0.969841	−	0.401721i	0.810653	+	0.585527i	$0.199112\pi$
$398$	349.321	−	199.486i	0.877690	−	0.501222i
$399$		0			0
$400$	46.6936	−	161.959i	0.116734	−	0.404896i
$401$		−	380.200i		−	0.948131i	−0.880490	−	0.474065i	$-0.842786\pi$
$401$		−	380.200i		−	0.948131i	0.880490	−	0.474065i	$-0.157214\pi$
$402$		0			0
$403$	19.2099	+	46.3768i	0.0476672	+	0.115079i
$404$	87.3686	+	116.116i	0.216259	+	0.287416i
$405$		0			0
$406$	104.081	+	80.6481i	0.256357	+	0.198641i
$407$	181.186	+	181.186i	0.445174	+	0.445174i
$408$		0			0
$409$	−211.885	−	211.885i	−0.518056	−	0.518056i	0.398927	−	0.916983i	$-0.369383\pi$
$409$	−211.885	−	211.885i	−0.518056	−	0.518056i	−0.916983	+	0.398927i	$0.869383\pi$
$410$	195.825	−	24.8404i	0.477621	−	0.0605862i
$411$		0			0
$412$	510.902	−	131.735i	1.24005	−	0.319746i
$413$	108.160	+	261.121i	0.261889	+	0.632255i
$414$		0			0
$415$			23.3071i			0.0561616i
$416$	−120.876	−	165.478i	−0.290567	−	0.397785i
$417$		0			0
$418$	−16.4470	+	60.2414i	−0.0393469	+	0.144118i
$419$	−299.129	+	123.903i	−0.713913	+	0.295712i	−0.709923	−	0.704280i	$-0.751270\pi$
$419$	−299.129	+	123.903i	−0.713913	+	0.295712i	−0.00399003	+	0.999992i	$0.501270\pi$
$420$		0			0
$421$	−61.3330	−	25.4050i	−0.145684	−	0.0603444i	0.308650	−	0.951176i	$-0.400123\pi$
$421$	−61.3330	−	25.4050i	−0.145684	−	0.0603444i	−0.454334	+	0.890831i	$0.650123\pi$
$422$	69.9208	+	551.209i	0.165689	+	1.30618i
$423$		0			0
$424$	437.615	−	174.042i	1.03211	−	0.410477i
$425$	76.7926	−	76.7926i	0.180688	−	0.180688i
$426$		0			0
$427$	37.2363	+	15.4238i	0.0872044	+	0.0361213i
$428$	−112.196	−	149.113i	−0.262140	−	0.348394i
$429$		0			0
$430$	221.571	+	387.993i	0.515280	+	0.902308i
$431$	141.289			0.327818			0.163909	−	0.986475i	$-0.447590\pi$
$431$	141.289			0.327818			0.163909	+	0.986475i	$0.447590\pi$
$432$		0			0
$433$			37.0779i			0.0856302i	0.999083	+	0.0428151i	$0.0136326\pi$
$433$			37.0779i			0.0856302i	−0.999083	+	0.0428151i	$0.986367\pi$
$434$	19.4844	+	34.1191i	0.0448949	+	0.0786155i
$435$		0			0
$436$	−766.602	−	108.302i	−1.75826	−	0.248400i
$437$	120.352	−	290.555i	0.275405	−	0.664886i
$438$		0			0
$439$	−388.870	−	388.870i	−0.885809	−	0.885809i	0.108308	−	0.994117i	$-0.465457\pi$
$439$	−388.870	−	388.870i	−0.885809	−	0.885809i	−0.994117	+	0.108308i	$0.965457\pi$
$440$	−1.79603	+	126.732i	−0.00408189	+	0.288028i
$441$		0			0
$442$	−16.6154	−	130.985i	−0.0375914	−	0.296345i
$443$	−148.114	+	357.578i	−0.334342	+	0.807174i	0.663895	+	0.747826i	$0.268902\pi$
$443$	−148.114	+	357.578i	−0.334342	+	0.807174i	−0.998237	+	0.0593479i	$0.981098\pi$
$444$		0			0
$445$	169.432	+	409.045i	0.380746	+	0.919203i
$446$	142.794	−	523.021i	0.320167	−	1.17269i
$447$		0			0
$448$	−110.159	−	116.587i	−0.245890	−	0.260239i
$449$	448.262			0.998357			0.499178	−	0.866499i	$-0.333635\pi$
$449$	448.262			0.998357			0.499178	+	0.866499i	$0.333635\pi$
$450$		0			0
$451$	99.8696	−	41.3673i	0.221440	−	0.0917236i
$452$	−241.218	+	408.834i	−0.533669	+	0.904499i
$453$		0			0
$454$	−745.451	+	94.5604i	−1.64196	+	0.208283i
$455$	43.1630	−	43.1630i	0.0948637	−	0.0948637i
$456$		0			0
$457$	−124.862	+	124.862i	−0.273220	+	0.273220i	−0.830395	−	0.557175i	$-0.811885\pi$
$457$	−124.862	+	124.862i	−0.273220	+	0.273220i	0.557175	+	0.830395i	$0.311885\pi$
$458$	−479.788	−	371.768i	−1.04757	−	0.811722i
$459$		0			0
$460$	89.2925	−	632.044i	0.194114	−	1.37401i
$461$	−719.707	+	298.112i	−1.56119	+	0.646664i	−0.985295	−	0.170862i	$-0.945345\pi$
$461$	−719.707	+	298.112i	−1.56119	+	0.646664i	−0.575891	+	0.817526i	$0.695345\pi$
$462$		0			0
$463$	638.467			1.37898			0.689490	−	0.724296i	$-0.257835\pi$
$463$	638.467			1.37898			0.689490	+	0.724296i	$0.257835\pi$
$464$	−262.116	+	328.552i	−0.564905	+	0.708086i
$465$		0			0
$466$	553.240	−	315.938i	1.18721	−	0.677979i
$467$	−198.699	−	479.701i	−0.425479	−	1.02720i	−0.980704	−	0.195498i	$-0.937368\pi$
$467$	−198.699	−	479.701i	−0.425479	−	1.02720i	0.555225	−	0.831700i	$-0.312632\pi$
$468$		0			0
$469$	−54.0763	+	130.552i	−0.115301	+	0.278362i
$470$	336.171	+	260.485i	0.715258	+	0.554224i
$471$		0			0
$472$	−838.325	+	333.408i	−1.77611	+	0.706373i
$473$	173.015	+	173.015i	0.365782	+	0.365782i
$474$		0			0
$475$	−30.2176	+	72.9518i	−0.0636161	+	0.153583i
$476$	−25.8035	−	100.072i	−0.0542090	−	0.210235i
$477$		0			0
$478$	−227.186	−	62.0260i	−0.475285	−	0.129761i
$479$		−	187.389i		−	0.391210i	−0.980683	−	0.195605i	$-0.937333\pi$
$479$		−	187.389i		−	0.391210i	0.980683	−	0.195605i	$-0.0626670\pi$
$480$		0			0
$481$	393.918			0.818956
$482$	−77.4896	+	283.826i	−0.160767	+	0.588850i
$483$		0			0
$484$	−103.516	−	401.460i	−0.213876	−	0.829463i
$485$	340.328	+	140.968i	0.701706	+	0.290656i
$486$		0			0
$487$	−102.810	+	102.810i	−0.211109	+	0.211109i	−0.804738	−	0.593630i	$-0.797694\pi$
$487$	−102.810	+	102.810i	−0.211109	+	0.211109i	0.593630	+	0.804738i	$0.297694\pi$
$488$	−50.9130	+	118.151i	−0.104330	+	0.242113i
$489$		0			0
$490$	−199.031	+	256.861i	−0.406186	+	0.524206i
$491$	−27.1673	−	11.2530i	−0.0553305	−	0.0229186i	0.354847	−	0.934925i	$-0.384533\pi$
$491$	−27.1673	−	11.2530i	−0.0553305	−	0.0229186i	−0.410177	+	0.912006i	$0.634533\pi$
$492$		0			0
$493$	−250.187	+	103.631i	−0.507480	+	0.210205i
$494$	47.6070	+	83.3646i	0.0963704	+	0.168754i
$495$		0			0
$496$	−109.781	+	60.6458i	−0.221332	+	0.122270i
$497$		−	198.757i		−	0.399913i
$498$		0			0
$499$	337.667	+	815.199i	0.676687	+	1.63367i	0.770011	+	0.638031i	$0.220251\pi$
$499$	337.667	+	815.199i	0.676687	+	1.63367i	−0.0933244	+	0.995636i	$0.529749\pi$
$500$	−75.6228	+	535.285i	−0.151246	+	1.07057i
$501$		0			0
$502$	−144.848	+	186.935i	−0.288542	+	0.372380i
$503$	−227.122	−	227.122i	−0.451535	−	0.451535i	0.444329	−	0.895864i	$-0.353442\pi$
$503$	−227.122	−	227.122i	−0.451535	−	0.451535i	−0.895864	+	0.444329i	$0.853442\pi$
$504$		0			0
$505$	−97.7005	−	97.7005i	−0.193466	−	0.193466i
$506$	−43.9893	−	346.782i	−0.0869353	−	0.685340i
$507$		0			0
$508$	127.431	−	215.979i	0.250848	−	0.425155i
$509$	−368.723	−	890.175i	−0.724406	−	1.74887i	−0.660392	−	0.750921i	$-0.729610\pi$
$509$	−368.723	−	890.175i	−0.724406	−	1.74887i	−0.0640139	−	0.997949i	$-0.520390\pi$
$510$		0			0
$511$		−	318.883i		−	0.624038i
$512$	377.098	−	346.325i	0.736520	−	0.676416i
$513$		0			0
$514$	679.939	+	185.636i	1.32284	+	0.361159i
$515$	−463.483	+	191.981i	−0.899967	+	0.372779i
$516$		0			0
$517$	215.167	+	89.1250i	0.416183	+	0.172389i
$518$	305.874	−	38.8002i	0.590491	−	0.0749038i
$519$		0			0
$520$	135.813	+	139.718i	0.261178	+	0.268688i
$521$	−32.7289	+	32.7289i	−0.0628193	+	0.0628193i	−0.737818	−	0.674999i	$-0.764144\pi$
$521$	−32.7289	+	32.7289i	−0.0628193	+	0.0628193i	0.674999	+	0.737818i	$0.264144\pi$
$522$		0			0
$523$	935.815	+	387.627i	1.78932	+	0.741161i	0.990142	+	0.140069i	$0.0447324\pi$
$523$	935.815	+	387.627i	1.78932	+	0.741161i	0.799180	+	0.601092i	$0.205268\pi$
$524$	76.1215	+	10.7541i	0.145270	+	0.0205231i
$525$		0			0
$526$	346.937	−	198.125i	0.659576	−	0.376664i
$527$	−80.8077			−0.153335
$528$		0			0
$529$			1231.47i			2.32793i
$530$	−388.857	+	222.065i	−0.733693	+	0.418990i
$531$		0			0
$532$	45.1777	+	60.0429i	0.0849206	+	0.112863i
$533$	63.5952	−	153.532i	0.119316	−	0.288053i
$534$		0			0
$535$	125.464	+	125.464i	0.234512	+	0.234512i
$536$	−414.241	−	178.503i	−0.772838	−	0.333028i
$537$		0			0
$538$	7.95392	−	1.00895i	0.0147842	−	0.00187538i
$539$	−68.0985	+	164.404i	−0.126342	+	0.305017i
$540$		0			0
$541$	−163.969	−	395.857i	−0.303086	−	0.731713i	−0.999895	−	0.0144574i	$-0.995398\pi$
$541$	−163.969	−	395.857i	−0.303086	−	0.731713i	0.696810	−	0.717256i	$-0.254602\pi$
$542$	−495.913	−	135.393i	−0.914969	−	0.249803i
$543$		0			0
$544$	320.572	−	77.8315i	0.589286	−	0.143073i
$545$	736.148			1.35073
$546$		0			0
$547$	−343.207	+	142.161i	−0.627436	+	0.259892i	−0.673663	−	0.739039i	$-0.735280\pi$
$547$	−343.207	+	142.161i	−0.627436	+	0.259892i	0.0462275	+	0.998931i	$0.485280\pi$
$548$	504.198	−	130.007i	0.920069	−	0.237239i
$549$		0			0
$550$	11.0447	+	87.0690i	0.0200813	+	0.158307i
$551$	139.226	−	139.226i	0.252680	−	0.252680i
$552$		0			0
$553$	30.8278	−	30.8278i	0.0557464	−	0.0557464i
$554$	−363.025	+	468.504i	−0.655280	+	0.845676i
$555$		0			0
$556$	512.771	+	681.491i	0.922250	+	1.22570i
$557$	−899.481	+	372.577i	−1.61487	+	0.668900i	−0.993417	−	0.114554i	$-0.963456\pi$
$557$	−899.481	+	372.577i	−1.61487	+	0.668900i	−0.621450	+	0.783454i	$0.713456\pi$
$558$		0			0
$559$	376.154			0.672905
$560$	119.220	+	95.1125i	0.212892	+	0.169844i
$561$		0			0
$562$	222.838	+	390.211i	0.396508	+	0.694326i
$563$	−151.645	−	366.103i	−0.269351	−	0.650271i	0.730102	−	0.683338i	$-0.239473\pi$
$563$	−151.645	−	366.103i	−0.269351	−	0.650271i	−0.999453	+	0.0330670i	$0.989473\pi$
$564$		0			0
$565$	172.725	−	416.994i	0.305707	−	0.738042i
$566$	194.621	−	251.169i	0.343853	−	0.443762i
$567$		0			0
$568$	634.381	+	8.99034i	1.11687	+	0.0158281i
$569$	39.9530	+	39.9530i	0.0702161	+	0.0702161i	0.741343	−	0.671127i	$-0.234189\pi$
$569$	39.9530	+	39.9530i	0.0702161	+	0.0702161i	−0.671127	+	0.741343i	$0.734189\pi$
$570$		0			0
$571$	219.435	−	529.764i	0.384300	−	0.927783i	−0.606823	−	0.794837i	$-0.707556\pi$
$571$	219.435	−	529.764i	0.384300	−	0.927783i	0.991123	−	0.132946i	$-0.0424437\pi$
$572$	91.9005	+	54.2228i	0.160665	+	0.0947951i
$573$		0			0
$574$	34.2586	−	125.481i	0.0596839	−	0.218608i
$575$		−	442.015i		−	0.768722i
$576$		0			0
$577$	379.788			0.658211			0.329106	−	0.944293i	$-0.393253\pi$
$577$	379.788			0.658211			0.329106	+	0.944293i	$0.393253\pi$
$578$	−352.550	−	96.2527i	−0.609948	−	0.166527i
$579$		0			0
$580$	203.077	−	344.190i	0.350133	−	0.593430i
$581$	14.1892	+	5.87736i	0.0244220	+	0.0101159i
$582$		0			0
$583$	−173.401	+	173.401i	−0.297428	+	0.297428i
$584$	1017.79	+	14.4240i	1.74280	+	0.0246986i
$585$		0			0
$586$	−388.366	−	300.929i	−0.662741	−	0.513531i
$587$	356.813	+	147.797i	0.607859	+	0.251783i	0.665313	−	0.746565i	$-0.268298\pi$
$587$	356.813	+	147.797i	0.607859	+	0.251783i	−0.0574538	+	0.998348i	$0.518298\pi$
$588$		0			0
$589$	54.2819	−	22.4843i	0.0921594	−	0.0381737i
$590$	744.923	−	425.402i	1.26258	−	0.721021i
$591$		0			0
$592$	110.005	+	978.028i	0.185819	+	1.65207i
$593$			458.301i			0.772852i	0.922320	+	0.386426i	$0.126290\pi$
$593$			458.301i			0.772852i	−0.922320	+	0.386426i	$0.873710\pi$
$594$		0			0
$595$	37.6040	+	90.7841i	0.0632000	+	0.152578i
$596$	379.929	−	285.868i	0.637466	−	0.479645i
$597$		0			0
$598$	−424.790	−	329.152i	−0.710351	−	0.550422i
$599$	591.730	+	591.730i	0.987864	+	0.987864i	0.999927	−	0.0120636i	$-0.00384006\pi$
$599$	591.730	+	591.730i	0.987864	+	0.987864i	−0.0120636	+	0.999927i	$0.503840\pi$
$600$		0			0
$601$	−173.189	−	173.189i	−0.288168	−	0.288168i	0.548188	−	0.836355i	$-0.315318\pi$
$601$	−173.189	−	173.189i	−0.288168	−	0.288168i	−0.836355	+	0.548188i	$0.815318\pi$
$602$	292.081	−	37.0504i	0.485184	−	0.0615456i
$603$		0			0
$604$	49.3623	+	191.439i	0.0817257	+	0.316952i
$605$	150.856	+	364.199i	0.249349	+	0.601982i
$606$		0			0
$607$		−	945.400i		−	1.55750i	−0.627337	−	0.778748i	$-0.715855\pi$
$607$		−	945.400i		−	1.55750i	0.627337	−	0.778748i	$-0.284145\pi$
$608$	−193.685	+	141.480i	−0.318561	+	0.232697i
$609$		0			0
$610$	32.2186	−	118.009i	0.0528174	−	0.193457i
$611$	330.782	−	137.014i	0.541378	−	0.224246i
$612$		0			0
$613$	−1004.10	−	415.913i	−1.63801	−	0.678487i	−0.641918	−	0.766773i	$-0.721861\pi$
$613$	−1004.10	−	415.913i	−1.63801	−	0.678487i	−0.996095	+	0.0882859i	$0.971861\pi$
$614$	97.7206	+	770.363i	0.159154	+	1.25466i
$615$		0			0
$616$	76.7010	+	33.0516i	0.124515	+	0.0536552i
$617$	534.837	−	534.837i	0.866834	−	0.866834i	−0.125287	−	0.992121i	$-0.539985\pi$
$617$	534.837	−	534.837i	0.866834	−	0.866834i	0.992121	+	0.125287i	$0.0399850\pi$
$618$		0			0
$619$	−690.590	−	286.052i	−1.11565	−	0.462119i	−0.252773	−	0.967526i	$-0.581343\pi$
$619$	−690.590	−	286.052i	−1.11565	−	0.462119i	−0.862881	+	0.505406i	$0.831343\pi$
$620$	95.2903	−	71.6988i	0.153694	−	0.115643i
$621$		0			0
$622$	41.7441	+	73.0982i	0.0671127	+	0.117521i
$623$	291.750			0.468298
$624$		0			0
$625$		−	250.653i		−	0.401044i
$626$	473.403	+	828.977i	0.756235	+	1.32424i
$627$		0			0
$628$	−14.2781	+	101.065i	−0.0227358	+	0.160932i
$629$	−242.668	+	585.853i	−0.385800	+	0.931404i
$630$		0			0
$631$	−842.968	−	842.968i	−1.33592	−	1.33592i	−0.899969	−	0.435955i	$-0.856411\pi$
$631$	−842.968	−	842.968i	−1.33592	−	1.33592i	−0.435955	−	0.899969i	$-0.643589\pi$
$632$	96.9999	+	99.7887i	0.153481	+	0.157894i
$633$		0			0
$634$	−39.7634	−	313.468i	−0.0627182	−	0.494429i
$635$	−91.2470	+	220.290i	−0.143696	+	0.346913i
$636$		0			0
$637$	104.690	+	252.743i	0.164348	+	0.396771i
$638$	57.6404	−	211.123i	0.0903454	−	0.330913i
$639$		0			0
$640$	−308.967	+	376.216i	−0.482761	+	0.587838i
$641$	−777.384			−1.21277			−0.606384	−	0.795172i	$-0.707380\pi$
$641$	−777.384			−1.21277			−0.606384	+	0.795172i	$0.707380\pi$
$642$		0			0
$643$	−227.049	+	94.0468i	−0.353109	+	0.146262i	−0.552185	−	0.833722i	$-0.686206\pi$
$643$	−227.049	+	94.0468i	−0.353109	+	0.146262i	0.199076	+	0.979984i	$0.436206\pi$
$644$	−362.267	−	213.744i	−0.562527	−	0.331900i
$645$		0			0
$646$	−153.311	+	19.4475i	−0.237324	+	0.0301046i
$647$	565.813	−	565.813i	0.874518	−	0.874518i	−0.118443	−	0.992961i	$-0.537790\pi$
$647$	565.813	−	565.813i	0.874518	−	0.874518i	0.992961	+	0.118443i	$0.0377902\pi$
$648$		0			0
$649$	332.179	−	332.179i	0.511831	−	0.511831i
$650$	106.655	+	82.6427i	0.164085	+	0.127143i
$651$		0			0
$652$	456.614	+	64.5085i	0.700329	+	0.0989395i
$653$	−898.790	+	372.291i	−1.37640	+	0.570124i	−0.943517	−	0.331325i	$-0.892504\pi$
$653$	−898.790	+	372.291i	−1.37640	+	0.570124i	−0.432885	+	0.901449i	$0.642504\pi$
$654$		0			0
$655$	−73.0975			−0.111599
$656$	398.953	+	115.020i	0.608160	+	0.175336i
$657$		0			0
$658$	243.354	−	138.972i	0.369839	−	0.211204i
$659$	−41.7411	−	100.772i	−0.0633401	−	0.152916i	0.889040	−	0.457829i	$-0.151373\pi$
$659$	−41.7411	−	100.772i	−0.0633401	−	0.152916i	−0.952380	+	0.304913i	$0.901373\pi$
$660$		0			0
$661$	146.403	−	353.448i	0.221487	−	0.534717i	−0.773605	−	0.633668i	$-0.781549\pi$
$661$	146.403	−	353.448i	0.221487	−	0.534717i	0.995092	+	0.0989510i	$0.0315487\pi$
$662$	221.093	+	171.316i	0.333977	+	0.258785i
$663$		0			0
$664$	−19.4008	+	45.0224i	−0.0292181	+	0.0678049i
$665$	−50.5203	−	50.5203i	−0.0759704	−	0.0759704i
$666$		0			0
$667$	−421.786	+	1018.28i	−0.632363	+	1.52666i
$668$	−898.444	+	231.663i	−1.34498	+	0.346800i
$669$		0			0
$670$	413.744	+	112.960i	0.617528	+	0.168596i
$671$		−	66.9901i		−	0.0998362i
$672$		0			0
$673$	−963.294			−1.43134			−0.715672	−	0.698437i	$-0.753879\pi$
$673$	−963.294			−1.43134			−0.715672	+	0.698437i	$0.753879\pi$
$674$	234.423	−	858.634i	0.347809	−	1.27394i
$675$		0			0
$676$	−495.745	+	127.827i	−0.733351	+	0.189094i
$677$	−831.075	−	344.243i	−1.22759	−	0.508482i	−0.327772	−	0.944757i	$-0.606298\pi$
$677$	−831.075	−	344.243i	−1.22759	−	0.508482i	−0.899814	+	0.436274i	$0.856298\pi$
$678$		0			0
$679$	171.641	−	171.641i	0.252785	−	0.252785i
$680$	−291.460	+	115.916i	−0.428618	+	0.170464i
$681$		0			0
$682$	39.9997	−	51.6218i	0.0586505	−	0.0756918i
$683$	18.6885	+	7.74102i	0.0273623	+	0.0113338i	0.396323	−	0.918111i	$-0.370286\pi$
$683$	18.6885	+	7.74102i	0.0273623	+	0.0113338i	−0.368960	+	0.929445i	$0.620286\pi$
$684$		0			0
$685$	−457.401	+	189.462i	−0.667739	+	0.276587i
$686$	227.984	+	399.223i	0.332338	+	0.581958i
$687$		0			0
$688$	105.044	+	933.923i	0.152680	+	1.35745i
$689$			376.992i			0.547159i
$690$		0			0
$691$	−446.223	−	1077.28i	−0.645764	−	1.55901i	−0.818789	−	0.574095i	$-0.805354\pi$
$691$	−446.223	−	1077.28i	−0.645764	−	1.55901i	0.173025	−	0.984918i	$-0.444646\pi$
$692$	463.900	+	65.5378i	0.670376	+	0.0947079i
$693$		0			0
$694$	470.070	−	606.652i	0.677335	−	0.874139i
$695$	−573.409	−	573.409i	−0.825049	−	0.825049i
$696$		0			0
$697$	189.163	+	189.163i	0.271397	+	0.271397i
$698$	−45.7517	−	360.676i	−0.0655469	−	0.516728i
$699$		0			0
$700$	90.9571	+	53.6661i	0.129939	+	0.0766659i
$701$	−306.247	−	739.346i	−0.436872	−	1.05470i	−0.977023	−	0.213133i	$-0.931633\pi$
$701$	−306.247	−	739.346i	−0.436872	−	1.05470i	0.540152	−	0.841568i	$-0.318367\pi$
$702$		0			0
$703$		−	461.063i		−	0.655850i
$704$	−108.962	+	243.315i	−0.154775	+	0.345618i
$705$		0			0
$706$	−1089.92	−	297.569i	−1.54380	−	0.421486i
$707$	−84.1166	+	34.8423i	−0.118977	+	0.0492818i
$708$		0			0
$709$	154.774	+	64.1095i	0.218299	+	0.0904225i	0.489153	−	0.872198i	$-0.337306\pi$
$709$	154.774	+	64.1095i	0.218299	+	0.0904225i	−0.270854	+	0.962620i	$0.587306\pi$
$710$	−598.454	+	75.9139i	−0.842893	+	0.106921i
$711$		0			0
$712$	−13.1967	+	931.191i	−0.0185347	+	1.30785i
$713$	−232.563	+	232.563i	−0.326175	+	0.326175i
$714$		0			0
$715$	−93.7349	−	38.8263i	−0.131098	−	0.0543025i
$716$	46.0041	−	325.633i	0.0642515	−	0.454795i
$717$		0			0
$718$	−79.4022	+	45.3441i	−0.110588	+	0.0631534i
$719$	385.344			0.535945			0.267972	−	0.963427i	$-0.413646\pi$
$719$	385.344			0.535945			0.267972	+	0.963427i	$0.413646\pi$
$720$		0			0
$721$			330.577i			0.458499i
$722$	−529.394	+	302.321i	−0.733233	+	0.418727i
$723$		0			0
$724$	−104.442	+	78.5849i	−0.144257	+	0.108543i
$725$	105.901	−	255.668i	0.146070	−	0.352645i
$726$		0			0
$727$	536.444	+	536.444i	0.737887	+	0.737887i	0.972169	−	0.234282i	$-0.0752738\pi$
$727$	536.444	+	536.444i	0.737887	+	0.737887i	−0.234282	+	0.972169i	$0.575274\pi$
$728$	119.307	−	47.4493i	0.163883	−	0.0651776i
$729$		0			0
$730$	−960.154	+	121.795i	−1.31528	+	0.166843i
$731$	−231.725	+	559.434i	−0.316997	+	0.765299i
$732$		0			0
$733$	−242.875	−	586.351i	−0.331343	−	0.799933i	−0.998486	−	0.0550036i	$-0.982483\pi$
$733$	−242.875	−	586.351i	−0.331343	−	0.799933i	0.667143	−	0.744930i	$-0.267517\pi$
$734$	−202.343	−	55.2434i	−0.275672	−	0.0752635i
$735$		0			0
$736$	698.601	−	1146.60i	0.949186	−	1.55788i
$737$	234.869			0.318683
$738$		0			0
$739$	54.0032	−	22.3689i	0.0730761	−	0.0302691i	−0.345846	−	0.938291i	$-0.612408\pi$
$739$	54.0032	−	22.3689i	0.0730761	−	0.0302691i	0.418922	+	0.908022i	$0.362408\pi$
$740$	−233.654	−	906.165i	−0.315748	−	1.22455i
$741$		0			0
$742$	37.1330	+	292.732i	0.0500445	+	0.394518i
$743$	133.806	−	133.806i	0.180089	−	0.180089i	−0.611306	−	0.791395i	$-0.709355\pi$
$743$	133.806	−	133.806i	0.180089	−	0.180089i	0.791395	+	0.611306i	$0.209355\pi$
$744$		0			0
$745$	−319.674	+	319.674i	−0.429093	+	0.429093i
$746$	−710.845	+	917.387i	−0.952876	+	1.22974i
$747$		0			0
$748$	−137.257	+	103.275i	−0.183499	+	0.138069i
$749$	108.020	−	44.7433i	0.144219	−	0.0597374i
$750$		0			0
$751$	−130.879			−0.174274			−0.0871368	−	0.996196i	$-0.527772\pi$
$751$	−130.879			−0.174274			−0.0871368	+	0.996196i	$0.527772\pi$
$752$	432.556	+	783.011i	0.575207	+	1.04124i
$753$		0			0
$754$	−166.844	−	292.160i	−0.221278	−	0.387480i
$755$	−71.9369	−	173.671i	−0.0952806	−	0.230028i
$756$		0			0
$757$	−227.679	+	549.666i	−0.300765	+	0.726111i	0.699173	+	0.714953i	$0.253552\pi$
$757$	−227.679	+	549.666i	−0.300765	+	0.726111i	−0.999938	+	0.0111581i	$0.996448\pi$
$758$	667.823	−	861.864i	0.881033	−	1.13702i
$759$		0			0
$760$	163.533	−	158.963i	0.215175	−	0.209161i
$761$	−492.512	−	492.512i	−0.647190	−	0.647190i	0.305123	−	0.952313i	$-0.401302\pi$
$761$	−492.512	−	492.512i	−0.647190	−	0.647190i	−0.952313	+	0.305123i	$0.901302\pi$
$762$		0			0
$763$	185.635	−	448.162i	0.243296	−	0.587369i
$764$	80.2135	−	135.951i	0.104992	−	0.177947i
$765$		0			0
$766$	336.987	−	1234.30i	0.439930	−	1.61136i
$767$		−	722.193i		−	0.941582i
$768$		0			0
$769$	580.628			0.755043			0.377521	−	0.926001i	$-0.376776\pi$
$769$	580.628			0.755043			0.377521	+	0.926001i	$0.376776\pi$
$770$	−76.6088	−	20.9156i	−0.0994920	−	0.0271631i
$771$		0			0
$772$	829.532	+	489.437i	1.07452	+	0.633986i
$773$	−223.125	−	92.4212i	−0.288648	−	0.119562i	0.233661	−	0.972318i	$-0.424929\pi$
$773$	−223.125	−	92.4212i	−0.288648	−	0.119562i	−0.522309	+	0.852756i	$0.674929\pi$
$774$		0			0
$775$	58.3913	−	58.3913i	0.0753436	−	0.0753436i
$776$	540.071	+	555.598i	0.695968	+	0.715977i
$777$		0			0
$778$	−346.232	−	268.281i	−0.445029	−	0.344835i
$779$	−179.703	−	74.4352i	−0.230684	−	0.0955523i
$780$		0			0
$781$	−305.208	+	126.421i	−0.390792	+	0.161871i
$782$	751.217	−	428.997i	0.960636	−	0.548590i
$783$		0			0
$784$	−598.281	+	330.506i	−0.763114	+	0.421564i
$785$		−	97.0502i		−	0.123631i
$786$		0			0
$787$	13.5600	+	32.7368i	0.0172300	+	0.0415970i	0.932260	−	0.361788i	$-0.117834\pi$
$787$	13.5600	+	32.7368i	0.0172300	+	0.0415970i	−0.915030	+	0.403385i	$0.867834\pi$
$788$	−118.325	−	157.258i	−0.150159	−	0.199566i
$789$		0			0
$790$	−104.596	−	81.0475i	−0.132401	−	0.102592i
$791$	−210.307	−	210.307i	−0.265875	−	0.265875i
$792$		0			0
$793$	−72.8219	−	72.8219i	−0.0918309	−	0.0918309i
$794$	−826.874	+	104.889i	−1.04140	+	0.132102i
$795$		0			0
$796$	−779.055	+	200.878i	−0.978712	+	0.252360i
$797$	−172.698	−	416.930i	−0.216685	−	0.523124i	0.777738	−	0.628589i	$-0.216367\pi$
$797$	−172.698	−	416.930i	−0.216685	−	0.523124i	−0.994423	+	0.105464i	$0.966367\pi$
$798$		0			0
$799$			576.360i			0.721352i
$800$	−175.403	+	287.884i	−0.219253	+	0.359855i
$801$		0			0
$802$	−200.273	+	733.553i	−0.249718	+	0.914655i
$803$	−489.673	+	202.829i	−0.609805	+	0.252589i
$804$		0			0
$805$	369.498	+	153.051i	0.459004	+	0.190126i
$806$	−12.6340	−	99.5976i	−0.0156749	−	0.123570i
$807$		0			0
$808$	−107.403	−	270.055i	−0.132924	−	0.334226i
$809$	−563.586	+	563.586i	−0.696645	+	0.696645i	−0.963685	−	0.267040i	$-0.913954\pi$
$809$	−563.586	+	563.586i	−0.696645	+	0.696645i	0.267040	+	0.963685i	$0.413954\pi$
$810$		0			0
$811$	−152.099	−	63.0013i	−0.187544	−	0.0776835i	0.286935	−	0.957950i	$-0.407364\pi$
$811$	−152.099	−	63.0013i	−0.187544	−	0.0776835i	−0.474479	+	0.880267i	$0.657364\pi$
$812$	−158.330	−	210.427i	−0.194988	−	0.259146i
$813$		0			0
$814$	−254.136	−	445.018i	−0.312206	−	0.546705i
$815$	−438.475			−0.538006
$816$		0			0
$817$		−	440.271i		−	0.538887i
$818$	297.196	+	520.419i	0.363320	+	0.636210i
$819$		0			0
$820$	−390.906	−	55.2256i	−0.476715	−	0.0673483i
$821$	211.711	−	511.115i	0.257869	−	0.622552i	−0.740928	−	0.671585i	$-0.765614\pi$
$821$	211.711	−	511.115i	0.257869	−	0.622552i	0.998797	+	0.0490328i	$0.0156139\pi$
$822$		0			0
$823$	620.858	+	620.858i	0.754384	+	0.754384i	0.975294	−	0.220910i	$-0.0709028\pi$
$823$	620.858	+	620.858i	0.754384	+	0.754384i	−0.220910	+	0.975294i	$0.570903\pi$
$824$	−1055.12	−	14.9530i	−1.28048	−	0.0181468i
$825$		0			0
$826$	−71.1347	−	560.778i	−0.0861194	−	0.678908i
$827$	466.847	−	1127.07i	0.564507	−	1.36284i	−0.341622	−	0.939837i	$-0.610976\pi$
$827$	466.847	−	1127.07i	0.564507	−	1.36284i	0.906129	−	0.423002i	$-0.139024\pi$
$828$		0			0
$829$	314.009	+	758.085i	0.378780	+	0.914457i	0.992195	+	0.124696i	$0.0397955\pi$
$829$	314.009	+	758.085i	0.378780	+	0.914457i	−0.613415	+	0.789761i	$0.710204\pi$
$830$	12.2772	−	44.9683i	0.0147918	−	0.0541787i
$831$		0			0
$832$	146.049	+	382.944i	0.175540	+	0.460269i
$833$	−440.385			−0.528673
$834$		0			0
$835$	815.056	−	337.607i	0.976115	−	0.404320i
$836$	63.4653	−	107.565i	0.0759154	−	0.128667i
$837$		0			0
$838$	642.403	−	81.4888i	0.766590	−	0.0972420i
$839$	−400.852	+	400.852i	−0.477773	+	0.477773i	−0.904419	−	0.426646i	$-0.859695\pi$
$839$	−400.852	+	400.852i	−0.477773	+	0.477773i	0.426646	+	0.904419i	$0.359695\pi$
$840$		0			0
$841$	106.743	−	106.743i	0.126924	−	0.126924i
$842$	104.953	+	81.3236i	0.124647	+	0.0965839i
$843$		0			0
$844$	155.449	−	1100.33i	0.184182	−	1.30370i
$845$	449.734	−	186.286i	0.532229	−	0.220457i
$846$		0			0
$847$	259.764			0.306687
$848$	−936.005	+	105.278i	−1.10378	+	0.124149i
$849$		0			0
$850$	−188.614	+	107.711i	−0.221898	+	0.126719i
$851$	987.679	+	2384.47i	1.16061	+	2.80196i
$852$		0			0
$853$	−104.229	+	251.630i	−0.122191	+	0.294995i	−0.973125	−	0.230278i	$-0.926037\pi$
$853$	−104.229	+	251.630i	−0.122191	+	0.294995i	0.850934	+	0.525272i	$0.176037\pi$
$854$	−63.7186	−	49.3729i	−0.0746119	−	0.0578137i
$855$		0			0
$856$	137.923	+	346.796i	0.161125	+	0.405135i
$857$	324.238	+	324.238i	0.378341	+	0.378341i	0.870503	−	0.492163i	$-0.163793\pi$
$857$	324.238	+	324.238i	0.378341	+	0.378341i	−0.492163	+	0.870503i	$0.663793\pi$
$858$		0			0
$859$	97.4053	−	235.157i	0.113394	−	0.273757i	−0.856987	−	0.515339i	$-0.827666\pi$
$859$	97.4053	−	235.157i	0.113394	−	0.273757i	0.970381	+	0.241582i	$0.0776662\pi$
$860$	−223.117	−	865.301i	−0.259438	−	1.00616i
$861$		0			0
$862$	−272.602	−	74.4253i	−0.316243	−	0.0863402i
$863$		−	1430.88i		−	1.65803i	−0.559223	−	0.829017i	$-0.688900\pi$
$863$		−	1430.88i		−	1.65803i	0.559223	−	0.829017i	$-0.311100\pi$
$864$		0			0
$865$	−445.471			−0.514995
$866$	19.5311	−	71.5375i	0.0225532	−	0.0826068i
$867$		0			0
$868$	−19.6204	−	76.0925i	−0.0226041	−	0.0876641i
$869$	−66.9471	−	27.7304i	−0.0770392	−	0.0319107i
$870$		0			0
$871$	255.316	−	255.316i	0.293130	−	0.293130i
$872$	1422.02	+	612.771i	1.63076	+	0.702719i
$873$		0			0
$874$	−385.258	+	497.197i	−0.440798	+	0.568875i
$875$	−312.932	−	129.621i	−0.357637	−	0.148138i
$876$		0			0
$877$	−1336.54	+	553.615i	−1.52400	+	0.631260i	−0.978387	−	0.206780i	$-0.933702\pi$
$877$	−1336.54	+	553.615i	−1.52400	+	0.631260i	−0.545609	+	0.838040i	$0.683702\pi$
$878$	545.440	+	955.121i	0.621230	+	1.08784i
$879$		0			0
$880$	70.2225	−	243.570i	0.0797983	−	0.276784i
$881$			1351.61i			1.53417i	0.641545	+	0.767086i	$0.278294\pi$
$881$			1351.61i			1.53417i	−0.641545	+	0.767086i	$0.721706\pi$
$882$		0			0
$883$	81.5101	+	196.783i	0.0923104	+	0.222857i	0.963290	−	0.268461i	$-0.0865152\pi$
$883$	81.5101	+	196.783i	0.0923104	+	0.222857i	−0.870980	+	0.491318i	$0.836515\pi$
$884$	−36.9397	+	261.472i	−0.0417869	+	0.295783i
$885$		0			0
$886$	474.125	−	611.885i	0.535130	−	0.690616i
$887$	−445.286	−	445.286i	−0.502014	−	0.502014i	0.410049	−	0.912063i	$-0.365511\pi$
$887$	−445.286	−	445.286i	−0.502014	−	0.502014i	−0.912063	+	0.410049i	$0.865511\pi$
$888$		0			0
$889$	111.101	+	111.101i	0.124973	+	0.124973i
$890$	−111.432	−	878.455i	−0.125205	−	0.987029i
$891$		0			0
$892$	−551.011	+	933.892i	−0.617725	+	1.04696i
$893$	−160.369	−	387.165i	−0.179585	−	0.433555i
$894$		0			0
$895$			312.697i			0.349382i
$896$	151.126	+	282.968i	0.168667	+	0.315812i
$897$		0			0
$898$	−864.870	−	236.125i	−0.963107	−	0.262946i
$899$	−190.237	+	78.7986i	−0.211609	+	0.0876514i
$900$		0			0
$901$	−560.681	−	232.242i	−0.622287	−	0.257760i
$902$	−214.477	+	27.2065i	−0.237780	+	0.0301624i
$903$		0			0
$904$	680.759	−	661.734i	0.753052	−	0.732006i
$905$	87.8781	−	87.8781i	0.0971028	−	0.0971028i
$906$		0			0
$907$	100.115	+	41.4691i	0.110381	+	0.0457212i	0.437190	−	0.899369i	$-0.355974\pi$
$907$	100.115	+	41.4691i	0.110381	+	0.0457212i	−0.326810	+	0.945090i	$0.605974\pi$
$908$	1488.07	+	210.229i	1.63885	+	0.231529i
$909$		0			0
$910$	−106.014	+	60.5416i	−0.116499	+	0.0665292i
$911$	631.401			0.693086			0.346543	−	0.938034i	$-0.387355\pi$
$911$	631.401			0.693086			0.346543	+	0.938034i	$0.387355\pi$
$912$		0			0
$913$		−	25.5271i		−	0.0279596i
$914$	306.678	−	175.134i	0.335534	−	0.191613i
$915$		0			0
$916$	729.865	+	970.017i	0.796795	+	1.05897i
$917$	−18.4330	+	44.5013i	−0.0201015	+	0.0485292i
$918$		0			0
$919$	72.8137	+	72.8137i	0.0792315	+	0.0792315i	0.745612	−	0.666380i	$-0.232157\pi$
$919$	72.8137	+	72.8137i	0.0792315	+	0.0792315i	−0.666380	+	0.745612i	$0.732157\pi$
$920$	−505.214	+	1172.42i	−0.549145	+	1.27437i
$921$		0			0
$922$	1545.62	−	196.062i	1.67638	−	0.212649i
$923$	−194.351	+	469.206i	−0.210565	+	0.508349i
$924$		0			0
$925$	−247.984	−	598.685i	−0.268090	−	0.647228i
$926$	−1231.85	−	336.318i	−1.33029	−	0.363194i
$927$		0			0
$928$	678.790	−	495.831i	0.731454	−	0.534301i
$929$	1010.36			1.08757			0.543786	−	0.839224i	$-0.316990\pi$
$929$	1010.36			1.08757			0.543786	+	0.839224i	$0.316990\pi$
$930$		0			0
$931$	295.824	−	122.534i	0.317749	−	0.131616i
$932$	−1233.84	+	318.143i	−1.32386	+	0.341355i
$933$		0			0
$934$	130.680	+	1030.19i	0.139915	+	1.10299i
$935$	115.488	−	115.488i	0.123517	−	0.123517i
$936$		0			0
$937$	−545.021	+	545.021i	−0.581666	+	0.581666i	−0.935361	−	0.353695i	$-0.884925\pi$
$937$	−545.021	+	545.021i	−0.581666	+	0.581666i	0.353695	+	0.935361i	$0.384925\pi$
$938$	173.103	−	223.399i	0.184545	−	0.238166i
$939$		0			0
$940$	−511.391	−	679.657i	−0.544033	−	0.723040i
$941$	1689.17	−	699.676i	1.79508	−	0.743545i	0.806810	−	0.590810i	$-0.201192\pi$
$941$	1689.17	−	699.676i	1.79508	−	0.743545i	0.988267	−	0.152735i	$-0.0488081\pi$
$942$		0			0
$943$	1088.82			1.15463
$944$	1793.08	−	201.678i	1.89945	−	0.213642i
$945$		0			0
$946$	−242.676	−	424.950i	−0.256528	−	0.449207i
$947$	13.6607	+	32.9800i	0.0144253	+	0.0348257i	0.930928	−	0.365203i	$-0.119000\pi$
$947$	13.6607	+	32.9800i	0.0144253	+	0.0348257i	−0.916503	+	0.400028i	$0.869000\pi$
$948$		0			0
$949$	−311.815	+	752.789i	−0.328572	+	0.793244i
$950$	96.7294	−	124.835i	0.101820	−	0.131405i
$951$		0			0
$952$	−2.92889	+	206.670i	−0.00307657	+	0.217090i
$953$	1013.75	+	1013.75i	1.06374	+	1.06374i	0.997825	+	0.0659179i	$0.0209975\pi$
$953$	1013.75	+	1013.75i	1.06374	+	1.06374i	0.0659179	+	0.997825i	$0.479002\pi$
$954$		0			0
$955$	−57.4369	+	138.665i	−0.0601434	+	0.145199i
$956$	405.657	+	239.344i	0.424327	+	0.250360i
$957$		0			0
$958$	−98.7088	+	361.546i	−0.103036	+	0.377397i
$959$			326.240i			0.340187i
$960$		0			0
$961$	899.556			0.936062
$962$	−760.019	−	207.499i	−0.790041	−	0.215696i
$963$		0			0
$964$	299.015	−	506.791i	0.310181	−	0.525716i
$965$	−846.089	−	350.462i	−0.876776	−	0.363173i
$966$		0			0
$967$	1260.66	−	1260.66i	1.30368	−	1.30368i	0.377792	−	0.925890i	$-0.376683\pi$
$967$	1260.66	−	1260.66i	1.30368	−	1.30368i	0.925890	−	0.377792i	$-0.123317\pi$
$968$	−11.7499	+	829.099i	−0.0121383	+	0.856507i
$969$		0			0
$970$	−582.367	−	451.252i	−0.600378	−	0.465209i
$971$	679.896	+	281.622i	0.700202	+	0.290033i	0.704243	−	0.709959i	$-0.251286\pi$
$971$	679.896	+	281.622i	0.700202	+	0.290033i	−0.00404133	+	0.999992i	$0.501286\pi$
$972$		0			0
$973$	−493.685	+	204.491i	−0.507384	+	0.210165i
$974$	252.516	−	144.204i	0.259257	−	0.148053i
$975$		0			0
$976$	160.468	−	201.140i	0.164414	−	0.206086i
$977$		−	1197.26i		−	1.22545i	−0.790297	−	0.612724i	$-0.790074\pi$
$977$		−	1197.26i		−	1.22545i	0.790297	−	0.612724i	$-0.209926\pi$
$978$		0			0
$979$	−185.571	−	448.008i	−0.189551	−	0.457618i
$980$	519.311	−	390.743i	0.529910	−	0.398717i
$981$		0			0
$982$	46.4885	+	36.0220i	0.0473406	+	0.0366823i
$983$	500.134	+	500.134i	0.508784	+	0.508784i	0.914153	−	0.405369i	$-0.132857\pi$
$983$	500.134	+	500.134i	0.508784	+	0.508784i	−0.405369	+	0.914153i	$0.632857\pi$
$984$		0			0
$985$	132.318	+	132.318i	0.134333	+	0.134333i
$986$	537.296	−	68.1560i	0.544925	−	0.0691237i
$987$		0			0
$988$	−47.9392	−	185.920i	−0.0485215	−	0.188178i
$989$	943.139	+	2276.94i	0.953629	+	2.30226i
$990$		0			0
$991$			417.702i			0.421495i	0.977540	+	0.210748i	$0.0675898\pi$
$991$			417.702i			0.421495i	−0.977540	+	0.210748i	$0.932410\pi$
$992$	243.755	−	59.1813i	0.245721	−	0.0596585i
$993$		0			0
$994$	−104.697	+	383.478i	−0.105329	+	0.385793i
$995$	706.748	−	292.745i	0.710300	−	0.294216i
$996$		0			0
$997$	1031.85	+	427.407i	1.03496	+	0.428694i	0.834500	−	0.551009i	$-0.185757\pi$
$997$	1031.85	+	427.407i	1.03496	+	0.428694i	0.200458	+	0.979702i	$0.435757\pi$
$998$	−222.076	−	1750.70i	−0.222522	−	1.75421i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.b.91.2		64
3.2	odd	2		96.3.m.a.91.15	yes	64
12.11	even	2		384.3.m.a.271.14		64
32.19	odd	8	inner	288.3.u.b.19.2		64
96.77	odd	8		384.3.m.a.367.14		64
96.83	even	8		96.3.m.a.19.15	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.3.m.a.19.15	✓	64	96.83	even	8
96.3.m.a.91.15	yes	64	3.2	odd	2
288.3.u.b.19.2		64	32.19	odd	8	inner
288.3.u.b.91.2		64	1.1	even	1	trivial
384.3.m.a.271.14		64	12.11	even	2
384.3.m.a.367.14		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)

\(f(q)\)	\(=\)	\(q+(-1.92938 - 0.526758i) q^{2} +(3.44505 + 2.03264i) q^{4} +(-3.51382 - 1.45547i) q^{5} +(-1.77216 + 1.77216i) q^{7} +(-5.57613 - 5.73645i) q^{8} +O(q^{10})\)	\(q+(-1.92938 - 0.526758i) q^{2} +(3.44505 + 2.03264i) q^{4} +(-3.51382 - 1.45547i) q^{5} +(-1.77216 + 1.77216i) q^{7} +(-5.57613 - 5.73645i) q^{8} +(6.01282 + 4.65909i) q^{10} +(3.84851 + 1.59411i) q^{11} +(5.91643 - 2.45067i) q^{13} +(4.35268 - 2.48568i) q^{14} +(7.73678 + 14.0051i) q^{16} +10.3089i q^{17} +(-2.86839 - 6.92491i) q^{19} +(-9.14684 - 12.1565i) q^{20} +(-6.58556 - 5.10288i) q^{22} +(29.6688 + 29.6688i) q^{23} +(-7.44916 - 7.44916i) q^{25} +(-12.7060 + 1.61175i) q^{26} +(-9.70735 + 2.50303i) q^{28} +(10.0526 + 24.2691i) q^{29} +7.83864i q^{31} +(-7.54994 - 31.0966i) q^{32} +(5.43029 - 19.8898i) q^{34} +(8.80638 - 3.64772i) q^{35} +(56.8298 + 23.5397i) q^{37} +(1.88648 + 14.8718i) q^{38} +(11.2443 + 28.2727i) q^{40} +(18.3495 - 18.3495i) q^{41} +(54.2671 + 22.4782i) q^{43} +(10.0181 + 13.3144i) q^{44} +(-41.6143 - 72.8708i) q^{46} +55.9090 q^{47} +42.7189i q^{49} +(10.4484 + 18.2962i) q^{50} +(25.3637 + 3.58328i) q^{52} +(-22.5283 + 54.3881i) q^{53} +(-11.2028 - 11.2028i) q^{55} +(20.0477 + 0.284113i) q^{56} +(-6.61138 - 52.1197i) q^{58} +(43.1567 - 104.190i) q^{59} +(-6.15421 - 14.8576i) q^{61} +(4.12906 - 15.1238i) q^{62} +(-1.81363 + 63.9743i) q^{64} -24.3561 q^{65} +(52.0912 - 21.5769i) q^{67} +(-20.9542 + 35.5147i) q^{68} +(-18.9124 + 2.39903i) q^{70} +(-56.0775 + 56.0775i) q^{71} +(-89.9701 + 89.9701i) q^{73} +(-97.2469 - 75.3527i) q^{74} +(4.19406 - 29.6871i) q^{76} +(-9.64521 + 3.99518i) q^{77} -17.3956 q^{79} +(-6.80164 - 60.4719i) q^{80} +(-45.0691 + 25.7376i) q^{82} +(-2.34511 - 5.66160i) q^{83} +(15.0043 - 36.2236i) q^{85} +(-92.8615 - 71.9546i) q^{86} +(-12.3153 - 30.9657i) q^{88} +(-82.3147 - 82.3147i) q^{89} +(-6.14190 + 14.8278i) q^{91} +(41.9047 + 162.516i) q^{92} +(-107.870 - 29.4505i) q^{94} +28.5077i q^{95} -96.8541 q^{97} +(22.5025 - 82.4212i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 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