LMFDB - Embedded newform 288.3.u.b.19.9

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			19.9
Character	$\chi$	$=$	288.19
Dual form			288.3.u.b.91.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.712728 + 1.86869i) q^{2} +(-2.98404 + 2.66374i) q^{4} +(4.75081 - 1.96785i) q^{5} +(5.89664 + 5.89664i) q^{7} +(-7.10452 - 3.67773i) q^{8} +O(q^{10})$	\(q+(0.712728 + 1.86869i) q^{2} +(-2.98404 + 2.66374i) q^{4} +(4.75081 - 1.96785i) q^{5} +(5.89664 + 5.89664i) q^{7} +(-7.10452 - 3.67773i) q^{8} +(7.06335 + 7.47527i) q^{10} +(13.5471 - 5.61139i) q^{11} +(0.486020 + 0.201316i) q^{13} +(-6.81632 + 15.2217i) q^{14} +(1.80897 - 15.8974i) q^{16} +4.73160i q^{17} +(-14.0805 + 33.9933i) q^{19} +(-8.93476 + 18.5271i) q^{20} +(20.1413 + 21.3160i) q^{22} +(20.6308 - 20.6308i) q^{23} +(1.02010 - 1.02010i) q^{25} +(-0.0297983 + 1.05171i) q^{26} +(-33.3029 - 1.88868i) q^{28} +(-16.8801 + 40.7522i) q^{29} -18.3890i q^{31} +(30.9967 - 7.95011i) q^{32} +(-8.84191 + 3.37234i) q^{34} +(39.6175 + 16.4101i) q^{35} +(-28.2407 + 11.6977i) q^{37} +(-73.5587 - 2.08416i) q^{38} +(-40.9895 - 3.49158i) q^{40} +(-3.93731 - 3.93731i) q^{41} +(38.6661 - 16.0160i) q^{43} +(-25.4777 + 52.8305i) q^{44} +(53.2568 + 23.8485i) q^{46} -4.72399 q^{47} +20.5407i q^{49} +(2.63331 + 1.17920i) q^{50} +(-1.98656 + 0.693897i) q^{52} +(-10.9910 - 26.5346i) q^{53} +(53.3173 - 53.3173i) q^{55} +(-20.2066 - 63.5791i) q^{56} +(-88.1843 - 2.49855i) q^{58} +(-40.5941 - 98.0027i) q^{59} +(28.4740 - 68.7424i) q^{61} +(34.3634 - 13.1064i) q^{62} +(36.9485 + 52.2571i) q^{64} +2.70515 q^{65} +(-58.7449 - 24.3329i) q^{67} +(-12.6037 - 14.1193i) q^{68} +(-2.42899 + 85.7290i) q^{70} +(6.99598 + 6.99598i) q^{71} +(66.3081 + 66.3081i) q^{73} +(-41.9873 - 44.4360i) q^{74} +(-48.5327 - 138.944i) q^{76} +(112.971 + 46.7940i) q^{77} +119.008 q^{79} +(-22.6896 - 79.0854i) q^{80} +(4.55140 - 10.1639i) q^{82} +(16.7714 - 40.4898i) q^{83} +(9.31107 + 22.4789i) q^{85} +(57.4874 + 60.8401i) q^{86} +(-116.883 - 9.95634i) q^{88} +(35.3613 - 35.3613i) q^{89} +(1.67880 + 4.05298i) q^{91} +(-6.60800 + 116.518i) q^{92} +(-3.36692 - 8.82769i) q^{94} +189.204i q^{95} -113.437 q^{97} +(-38.3844 + 14.6400i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

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 $

$2$	0.712728	+	1.86869i	0.356364	+	0.934347i
$2$	0.712728	+	1.86869i	0.356364	+	0.934347i
$3$		0			0
$3$		0			0
$4$	−2.98404	+	2.66374i	−0.746010	+	0.665935i
$5$	4.75081	−	1.96785i	0.950162	−	0.393570i	0.146870	−	0.989156i	$-0.453080\pi$
$5$	4.75081	−	1.96785i	0.950162	−	0.393570i	0.803292	+	0.595586i	$0.203080\pi$
$6$		0			0
$7$	5.89664	+	5.89664i	0.842377	+	0.842377i	0.989168	−	0.146790i	$-0.0468943\pi$
$7$	5.89664	+	5.89664i	0.842377	+	0.842377i	−0.146790	+	0.989168i	$0.546894\pi$
$8$	−7.10452	−	3.67773i	−0.888066	−	0.459717i
$9$		0			0
$10$	7.06335	+	7.47527i	0.706335	+	0.747527i
$11$	13.5471	−	5.61139i	1.23155	−	0.510126i	0.330488	−	0.943810i	$-0.392787\pi$
$11$	13.5471	−	5.61139i	1.23155	−	0.510126i	0.901065	+	0.433684i	$0.142787\pi$
$12$		0			0
$13$	0.486020	+	0.201316i	0.0373862	+	0.0154859i	0.401298	−	0.915947i	$-0.368559\pi$
$13$	0.486020	+	0.201316i	0.0373862	+	0.0154859i	−0.363912	+	0.931433i	$0.618559\pi$
$14$	−6.81632	+	15.2217i	−0.486880	+	1.08727i
$15$		0			0
$16$	1.80897	−	15.8974i	0.113061	−	0.993588i
$17$			4.73160i			0.278329i	0.990269	+	0.139165i	$0.0444417\pi$
$17$			4.73160i			0.278329i	−0.990269	+	0.139165i	$0.955558\pi$
$18$		0			0
$19$	−14.0805	+	33.9933i	−0.741079	+	1.78912i	−0.139644	+	0.990202i	$0.544596\pi$
$19$	−14.0805	+	33.9933i	−0.741079	+	1.78912i	−0.601435	+	0.798922i	$0.705404\pi$
$20$	−8.93476	+	18.5271i	−0.446738	+	0.926353i
$21$		0			0
$22$	20.1413	+	21.3160i	0.915516	+	0.968908i
$23$	20.6308	−	20.6308i	0.896992	−	0.896992i	−0.0981769	−	0.995169i	$-0.531301\pi$
$23$	20.6308	−	20.6308i	0.896992	−	0.896992i	0.995169	+	0.0981769i	$0.0313011\pi$
$24$		0			0
$25$	1.02010	−	1.02010i	0.0408040	−	0.0408040i
$26$	−0.0297983	+	1.05171i	−0.00114609	+	0.0404503i
$27$		0			0
$28$	−33.3029	−	1.88868i	−1.18939	−	0.0674529i
$29$	−16.8801	+	40.7522i	−0.582073	+	1.40525i	0.308858	+	0.951108i	$0.400053\pi$
$29$	−16.8801	+	40.7522i	−0.582073	+	1.40525i	−0.890931	+	0.454140i	$0.849947\pi$
$30$		0			0
$31$		−	18.3890i		−	0.593194i	−0.955003	−	0.296597i	$-0.904148\pi$
$31$		−	18.3890i		−	0.593194i	0.955003	−	0.296597i	$-0.0958518\pi$
$32$	30.9967	−	7.95011i	0.968647	−	0.248441i
$33$		0			0
$34$	−8.84191	+	3.37234i	−0.260056	+	0.0991864i
$35$	39.6175	+	16.4101i	1.13193	+	0.468861i
$36$		0			0
$37$	−28.2407	+	11.6977i	−0.763262	+	0.316154i	−0.730140	−	0.683298i	$-0.760545\pi$
$37$	−28.2407	+	11.6977i	−0.763262	+	0.316154i	−0.0331223	+	0.999451i	$0.510545\pi$
$38$	−73.5587	−	2.08416i	−1.93576	−	0.0548464i
$39$		0			0
$40$	−40.9895	−	3.49158i	−1.02474	−	0.0872895i
$41$	−3.93731	−	3.93731i	−0.0960320	−	0.0960320i	0.657459	−	0.753491i	$-0.271631\pi$
$41$	−3.93731	−	3.93731i	−0.0960320	−	0.0960320i	−0.753491	+	0.657459i	$0.771631\pi$
$42$		0			0
$43$	38.6661	−	16.0160i	0.899211	−	0.372466i	0.115295	−	0.993331i	$-0.463219\pi$
$43$	38.6661	−	16.0160i	0.899211	−	0.372466i	0.783917	+	0.620866i	$0.213219\pi$
$44$	−25.4777	+	52.8305i	−0.579040	+	1.20069i
$45$		0			0
$46$	53.2568	+	23.8485i	1.15776	+	0.518447i
$47$	−4.72399			−0.100510			−0.0502552	−	0.998736i	$-0.516003\pi$
$47$	−4.72399			−0.100510			−0.0502552	+	0.998736i	$0.516003\pi$
$48$		0			0
$49$			20.5407i			0.419199i
$50$	2.63331	+	1.17920i	0.0526662	+	0.0235840i
$51$		0			0
$52$	−1.98656	+	0.693897i	−0.0382030	+	0.0133442i
$53$	−10.9910	−	26.5346i	−0.207377	−	0.500653i	0.785631	−	0.618695i	$-0.212338\pi$
$53$	−10.9910	−	26.5346i	−0.207377	−	0.500653i	−0.993009	+	0.118042i	$0.962338\pi$
$54$		0			0
$55$	53.3173	−	53.3173i	0.969405	−	0.969405i
$56$	−20.2066	−	63.5791i	−0.360831	−	1.13534i
$57$		0			0
$58$	−88.1843	−	2.49855i	−1.52042	−	0.0430785i
$59$	−40.5941	−	98.0027i	−0.688035	−	1.66106i	−0.748703	−	0.662905i	$-0.769323\pi$
$59$	−40.5941	−	98.0027i	−0.688035	−	1.66106i	0.0606687	−	0.998158i	$-0.480677\pi$
$60$		0			0
$61$	28.4740	−	68.7424i	0.466787	−	1.12692i	−0.498770	−	0.866734i	$-0.666215\pi$
$61$	28.4740	−	68.7424i	0.466787	−	1.12692i	0.965557	−	0.260190i	$-0.0837853\pi$
$62$	34.3634	−	13.1064i	0.554249	−	0.211393i
$63$		0			0
$64$	36.9485	+	52.2571i	0.577321	+	0.816517i
$65$	2.70515			0.0416177
$66$		0			0
$67$	−58.7449	−	24.3329i	−0.876789	−	0.363178i	−0.101539	−	0.994832i	$-0.532377\pi$
$67$	−58.7449	−	24.3329i	−0.876789	−	0.363178i	−0.775251	+	0.631654i	$0.782377\pi$
$68$	−12.6037	−	14.1193i	−0.185349	−	0.207636i
$69$		0			0
$70$	−2.42899	+	85.7290i	−0.0346998	+	1.22470i
$71$	6.99598	+	6.99598i	0.0985350	+	0.0985350i	0.754656	−	0.656121i	$-0.227804\pi$
$71$	6.99598	+	6.99598i	0.0985350	+	0.0985350i	−0.656121	+	0.754656i	$0.727804\pi$
$72$		0			0
$73$	66.3081	+	66.3081i	0.908330	+	0.908330i	0.996138	−	0.0878070i	$-0.0279859\pi$
$73$	66.3081	+	66.3081i	0.908330	+	0.908330i	−0.0878070	+	0.996138i	$0.527986\pi$
$74$	−41.9873	−	44.4360i	−0.567396	−	0.600486i
$75$		0			0
$76$	−48.5327	−	138.944i	−0.638588	−	1.82821i
$77$	112.971	+	46.7940i	1.46715	+	0.607714i
$78$		0			0
$79$	119.008			1.50643			0.753215	−	0.657774i	$-0.228502\pi$
$79$	119.008			1.50643			0.753215	+	0.657774i	$0.228502\pi$
$80$	−22.6896	−	79.0854i	−0.283621	−	0.988567i
$81$		0			0
$82$	4.55140	−	10.1639i	0.0555049	−	0.123950i
$83$	16.7714	−	40.4898i	0.202065	−	0.487828i	−0.790067	−	0.613020i	$-0.789955\pi$
$83$	16.7714	−	40.4898i	0.202065	−	0.487828i	0.992133	+	0.125192i	$0.0399545\pi$
$84$		0			0
$85$	9.31107	+	22.4789i	0.109542	+	0.264458i
$86$	57.4874	+	60.8401i	0.668459	+	0.707442i
$87$		0			0
$88$	−116.883	−	9.95634i	−1.32821	−	0.113140i
$89$	35.3613	−	35.3613i	0.397318	−	0.397318i	−0.479968	−	0.877286i	$-0.659352\pi$
$89$	35.3613	−	35.3613i	0.397318	−	0.397318i	0.877286	+	0.479968i	$0.159352\pi$
$90$		0			0
$91$	1.67880	+	4.05298i	0.0184483	+	0.0445382i
$92$	−6.60800	+	116.518i	−0.0718261	+	1.26650i
$93$		0			0
$94$	−3.36692	−	8.82769i	−0.0358183	−	0.0939116i
$95$			189.204i			1.99162i
$96$		0			0
$97$	−113.437			−1.16945			−0.584725	−	0.811231i	$-0.698798\pi$
$97$	−113.437			−1.16945			−0.584725	+	0.811231i	$0.698798\pi$
$98$	−38.3844	+	14.6400i	−0.391677	+	0.149387i
$99$		0			0
$100$	−0.326736	+	5.76130i	−0.00326736	+	0.0576130i
$101$	−92.9990	+	38.5215i	−0.920783	+	0.381401i	−0.792174	−	0.610295i	$-0.791051\pi$
$101$	−92.9990	+	38.5215i	−0.920783	+	0.381401i	−0.128608	+	0.991695i	$0.541051\pi$
$102$		0			0
$103$	−17.4695	−	17.4695i	−0.169607	−	0.169607i	0.617199	−	0.786807i	$-0.288267\pi$
$103$	−17.4695	−	17.4695i	−0.169607	−	0.169607i	−0.786807	+	0.617199i	$0.788267\pi$
$104$	−2.71256	−	3.21771i	−0.0260823	−	0.0309395i
$105$		0			0
$106$	41.7515	−	39.4507i	0.393882	−	0.372177i
$107$	142.054	−	58.8407i	1.32761	−	0.549913i	0.397636	−	0.917543i	$-0.369831\pi$
$107$	142.054	−	58.8407i	1.32761	−	0.549913i	0.929972	+	0.367630i	$0.119831\pi$
$108$		0			0
$109$	−108.477	−	44.9328i	−0.995205	−	0.412227i	−0.175168	−	0.984539i	$-0.556047\pi$
$109$	−108.477	−	44.9328i	−0.995205	−	0.412227i	−0.820036	+	0.572311i	$0.806047\pi$
$110$	137.634	+	61.6330i	1.25122	+	0.560300i
$111$		0			0
$112$	104.408	−	83.0745i	0.932216	−	0.741736i
$113$		−	151.006i		−	1.33634i	−0.744010	−	0.668169i	$-0.767078\pi$
$113$		−	151.006i		−	1.33634i	0.744010	−	0.668169i	$-0.232922\pi$
$114$		0			0
$115$	57.4148	−	138.611i	0.499259	−	1.20532i
$116$	−58.1824	−	166.570i	−0.501572	−	1.43595i
$117$		0			0
$118$	154.205	−	145.707i	1.30682	−	1.23481i
$119$	−27.9005	+	27.9005i	−0.234458	+	0.234458i
$120$		0			0
$121$	66.4759	−	66.4759i	0.549387	−	0.549387i
$122$	148.753	+	4.21466i	1.21929	+	0.0345464i
$123$		0			0
$124$	48.9836	+	54.8735i	0.395029	+	0.442528i
$125$	−46.3574	+	111.917i	−0.370859	+	0.895333i
$126$		0			0
$127$		−	23.3676i		−	0.183997i	−0.995759	−	0.0919985i	$-0.970675\pi$
$127$		−	23.3676i		−	0.183997i	0.995759	−	0.0919985i	$-0.0293255\pi$
$128$	−71.3183	+	106.291i	−0.557174	+	0.830396i
$129$		0			0
$130$	1.92804	+	5.05510i	0.0148310	+	0.0388854i
$131$	−59.0143	−	24.4445i	−0.450491	−	0.186599i	0.145891	−	0.989301i	$-0.453395\pi$
$131$	−59.0143	−	24.4445i	−0.450491	−	0.186599i	−0.596381	+	0.802701i	$0.703395\pi$
$132$		0			0
$133$	−283.474	+	117.419i	−2.13138	+	0.882849i
$134$	3.60170	−	127.119i	0.0268784	−	0.948649i
$135$		0			0
$136$	17.4016	−	33.6157i	0.127953	−	0.247175i
$137$	−32.0534	−	32.0534i	−0.233966	−	0.233966i	0.580380	−	0.814346i	$-0.302904\pi$
$137$	−32.0534	−	32.0534i	−0.233966	−	0.233966i	−0.814346	+	0.580380i	$0.802904\pi$
$138$		0			0
$139$	219.159	−	90.7787i	1.57668	−	0.653084i	0.588800	−	0.808278i	$-0.299600\pi$
$139$	219.159	−	90.7787i	1.57668	−	0.653084i	0.987884	+	0.155194i	$0.0496004\pi$
$140$	−161.933	+	56.5624i	−1.15666	+	0.404017i
$141$		0			0
$142$	−8.08712	+	18.0596i	−0.0569516	+	0.127180i
$143$	7.71382			0.0539428
$144$		0			0
$145$			226.823i			1.56430i
$146$	−76.6500	+	171.169i	−0.525000	+	1.17239i
$147$		0			0
$148$	53.1117	−	110.132i	0.358863	−	0.744137i
$149$	−55.8473	−	134.827i	−0.374814	−	0.904881i	−0.992920	−	0.118786i	$-0.962100\pi$
$149$	−55.8473	−	134.827i	−0.374814	−	0.904881i	0.618106	−	0.786095i	$-0.287900\pi$
$150$		0			0
$151$	−121.176	+	121.176i	−0.802493	+	0.802493i	−0.983485	−	0.180992i	$-0.942069\pi$
$151$	−121.176	+	121.176i	−0.802493	+	0.802493i	0.180992	+	0.983485i	$0.442069\pi$
$152$	225.054	−	189.722i	1.48062	−	1.24817i
$153$		0			0
$154$	−6.92633	+	244.459i	−0.0449762	+	1.58740i
$155$	−36.1868	−	87.3627i	−0.233463	−	0.563630i
$156$		0			0
$157$	−65.4363	+	157.977i	−0.416792	+	1.00622i	0.566479	+	0.824076i	$0.308305\pi$
$157$	−65.4363	+	157.977i	−0.416792	+	1.00622i	−0.983271	+	0.182149i	$0.941695\pi$
$158$	84.8203	+	222.390i	0.536837	+	1.40753i
$159$		0			0
$160$	131.615	−	98.7664i	0.822593	−	0.617290i
$161$	243.305			1.51121
$162$		0			0
$163$	−214.324	−	88.7758i	−1.31487	−	0.544637i	−0.388568	−	0.921420i	$-0.627030\pi$
$163$	−214.324	−	88.7758i	−1.31487	−	0.544637i	−0.926302	+	0.376783i	$0.877030\pi$
$164$	22.2371	+	1.26111i	0.135592	+	0.00768971i
$165$		0			0
$166$	87.6164	+	2.48246i	0.527810	+	0.0149546i
$167$	−35.8263	−	35.8263i	−0.214529	−	0.214529i	0.591659	−	0.806188i	$-0.298473\pi$
$167$	−35.8263	−	35.8263i	−0.214529	−	0.214529i	−0.806188	+	0.591659i	$0.798473\pi$
$168$		0			0
$169$	−119.305	−	119.305i	−0.705949	−	0.705949i
$170$	−35.3700	+	33.4209i	−0.208059	+	0.196593i
$171$		0			0
$172$	−72.7186	+	150.789i	−0.422782	+	0.876679i
$173$	−285.445	−	118.235i	−1.64997	−	0.683440i	−0.652723	−	0.757597i	$-0.726373\pi$
$173$	−285.445	−	118.235i	−1.64997	−	0.683440i	−0.997247	+	0.0741574i	$0.976373\pi$
$174$		0			0
$175$	12.0303			0.0687447
$176$	−64.7002	−	225.514i	−0.367615	−	1.28133i
$177$		0			0
$178$	91.2824	+	40.8765i	0.512822	+	0.229643i
$179$	11.9854	−	28.9353i	0.0669576	−	0.161650i	−0.886858	−	0.462041i	$-0.847117\pi$
$179$	11.9854	−	28.9353i	0.0669576	−	0.161650i	0.953816	+	0.300391i	$0.0971172\pi$
$180$		0			0
$181$	86.2167	+	208.145i	0.476335	+	1.14997i	0.961315	+	0.275450i	$0.0888267\pi$
$181$	86.2167	+	208.145i	0.476335	+	1.14997i	−0.484980	+	0.874525i	$0.661173\pi$
$182$	−6.37725	+	6.02583i	−0.0350398	+	0.0331090i
$183$		0			0
$184$	−222.447	+	70.6975i	−1.20895	+	0.384225i
$185$	−111.147	+	111.147i	−0.600794	+	0.600794i
$186$		0			0
$187$	26.5508	+	64.0993i	0.141983	+	0.342777i
$188$	14.0966	−	12.5835i	0.0749817	−	0.0669334i
$189$		0			0
$190$	−353.565	+	134.851i	−1.86087	+	0.709743i
$191$			251.549i			1.31701i	0.752577	+	0.658505i	$0.228811\pi$
$191$			251.549i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$192$		0			0
$193$	130.718			0.677297			0.338648	−	0.940913i	$-0.390030\pi$
$193$	130.718			0.677297			0.338648	+	0.940913i	$0.390030\pi$
$194$	−80.8495	−	211.979i	−0.416750	−	1.09267i
$195$		0			0
$196$	−54.7152	−	61.2943i	−0.279159	−	0.312726i
$197$	−264.734	+	109.656i	−1.34383	+	0.556631i	−0.934567	−	0.355787i	$-0.884213\pi$
$197$	−264.734	+	109.656i	−1.34383	+	0.556631i	−0.409260	+	0.912418i	$0.634213\pi$
$198$		0			0
$199$	122.496	+	122.496i	0.615557	+	0.615557i	0.944389	−	0.328832i	$-0.106655\pi$
$199$	122.496	+	122.496i	0.615557	+	0.615557i	−0.328832	+	0.944389i	$0.606655\pi$
$200$	−10.9990	+	3.49567i	−0.0549949	+	0.0174784i
$201$		0			0
$202$	−138.268	−	146.331i	−0.684494	−	0.724413i
$203$	−339.837	+	140.765i	−1.67407	+	0.693424i
$204$		0			0
$205$	−26.4535	−	10.9574i	−0.129041	−	0.0534507i
$206$	20.1942	−	45.0963i	0.0980302	−	0.218914i
$207$		0			0
$208$	4.07960	−	7.36229i	0.0196135	−	0.0353956i
$209$			539.522i			2.58144i
$210$		0			0
$211$	45.2027	−	109.129i	0.214231	−	0.517199i	−0.779834	−	0.625986i	$-0.784697\pi$
$211$	45.2027	−	109.129i	0.214231	−	0.517199i	0.994065	+	0.108787i	$0.0346967\pi$
$212$	103.479	+	49.9031i	0.488108	+	0.235392i
$213$		0			0
$214$	211.201	+	223.518i	0.986921	+	1.04448i
$215$	152.178	−	152.178i	0.707805	−	0.707805i
$216$		0			0
$217$	108.433	−	108.433i	0.499693	−	0.499693i
$218$	6.65084	−	234.736i	0.0305084	−	1.07677i
$219$		0			0
$220$	−17.0774	+	301.124i	−0.0776245	+	1.36875i
$221$	−0.952547	+	2.29965i	−0.00431017	+	0.0104057i
$222$		0			0
$223$			268.911i			1.20588i	0.797787	+	0.602939i	$0.206004\pi$
$223$			268.911i			1.20588i	−0.797787	+	0.602939i	$0.793996\pi$
$224$	229.655	+	135.897i	1.02525	+	0.606685i
$225$		0			0
$226$	282.184	−	107.626i	1.24860	−	0.476222i
$227$	−137.850	−	57.0993i	−0.607268	−	0.251539i	0.0577918	−	0.998329i	$-0.481594\pi$
$227$	−137.850	−	57.0993i	−0.607268	−	0.251539i	−0.665060	+	0.746790i	$0.731594\pi$
$228$		0			0
$229$	75.4934	−	31.2704i	0.329665	−	0.136552i	−0.211711	−	0.977332i	$-0.567904\pi$
$229$	75.4934	−	31.2704i	0.329665	−	0.136552i	0.541376	+	0.840781i	$0.317904\pi$
$230$	299.944	+	8.49839i	1.30410	+	0.0369495i
$231$		0			0
$232$	269.801	−	227.444i	1.16293	−	0.980364i
$233$	−29.6368	−	29.6368i	−0.127196	−	0.127196i	0.640643	−	0.767839i	$-0.278668\pi$
$233$	−29.6368	−	29.6368i	−0.127196	−	0.127196i	−0.767839	+	0.640643i	$0.778668\pi$
$234$		0			0
$235$	−22.4428	+	9.29610i	−0.0955012	+	0.0395579i
$236$	382.188	+	184.312i	1.61944	+	0.780982i
$237$		0			0
$238$	−72.0230	−	32.2521i	−0.302618	−	0.135513i
$239$	94.0559			0.393539			0.196770	−	0.980450i	$-0.436955\pi$
$239$	94.0559			0.393539			0.196770	+	0.980450i	$0.436955\pi$
$240$		0			0
$241$		−	109.430i		−	0.454066i	−0.973887	−	0.227033i	$-0.927098\pi$
$241$		−	109.430i		−	0.454066i	0.973887	−	0.227033i	$-0.0729025\pi$
$242$	171.602	+	76.8439i	0.709100	+	0.317537i
$243$		0			0
$244$	98.1443	+	280.977i	0.402231	+	1.15155i
$245$	40.4211	+	97.5852i	0.164984	+	0.398307i
$246$		0			0
$247$	−13.6868	+	13.6868i	−0.0554122	+	0.0554122i
$248$	−67.6299	+	130.645i	−0.272701	+	0.526795i
$249$		0			0
$250$	−242.178	−	6.86170i	−0.968712	−	0.0274468i
$251$	−12.0040	−	28.9802i	−0.0478246	−	0.115459i	0.898162	−	0.439665i	$-0.144903\pi$
$251$	−12.0040	−	28.9802i	−0.0478246	−	0.115459i	−0.945986	+	0.324206i	$0.894903\pi$
$252$		0			0
$253$	163.720	−	395.255i	0.647114	−	1.56227i
$254$	43.6669	−	16.6547i	0.171917	−	0.0655699i
$255$		0			0
$256$	−249.455	−	57.5159i	−0.974435	−	0.224671i
$257$	434.950			1.69241			0.846206	−	0.532856i	$-0.178881\pi$
$257$	434.950			1.69241			0.846206	+	0.532856i	$0.178881\pi$
$258$		0			0
$259$	−235.502	−	97.5482i	−0.909275	−	0.376634i
$260$	−8.07228	+	7.20582i	−0.0310472	+	0.0277147i
$261$		0			0
$262$	3.61822	−	127.702i	0.0138100	−	0.487412i
$263$	80.8472	+	80.8472i	0.307404	+	0.307404i	0.843902	−	0.536498i	$-0.180253\pi$
$263$	80.8472	+	80.8472i	0.307404	+	0.307404i	−0.536498	+	0.843902i	$0.680253\pi$
$264$		0			0
$265$	−104.432	−	104.432i	−0.394084	−	0.394084i
$266$	−421.460	−	446.039i	−1.58444	−	1.67684i
$267$		0			0
$268$	240.114	−	83.8708i	0.895946	−	0.312951i
$269$	−127.935	−	52.9925i	−0.475596	−	0.196998i	0.131992	−	0.991251i	$-0.457863\pi$
$269$	−127.935	−	52.9925i	−0.475596	−	0.196998i	−0.607588	+	0.794253i	$0.707863\pi$
$270$		0			0
$271$	−181.643			−0.670269			−0.335135	−	0.942170i	$-0.608782\pi$
$271$	−181.643			−0.670269			−0.335135	+	0.942170i	$0.608782\pi$
$272$	75.2201	+	8.55931i	0.276545	+	0.0314681i
$273$		0			0
$274$	37.0526	−	82.7433i	0.135229	−	0.301983i
$275$	8.09521	−	19.5436i	0.0294371	−	0.0710675i
$276$		0			0
$277$	−64.2758	−	155.176i	−0.232043	−	0.560201i	0.764375	−	0.644772i	$-0.223048\pi$
$277$	−64.2758	−	155.176i	−0.232043	−	0.560201i	−0.996417	+	0.0845717i	$0.973048\pi$
$278$	325.838	+	344.841i	1.17208	+	1.24044i
$279$		0			0
$280$	−221.112	−	262.289i	−0.789685	−	0.936746i
$281$	193.622	−	193.622i	0.689048	−	0.689048i	−0.272974	−	0.962021i	$-0.588007\pi$
$281$	193.622	−	193.622i	0.689048	−	0.689048i	0.962021	+	0.272974i	$0.0880072\pi$
$282$		0			0
$283$	157.735	+	380.805i	0.557367	+	1.34560i	0.911844	+	0.410537i	$0.134659\pi$
$283$	157.735	+	380.805i	0.557367	+	1.34560i	−0.354477	+	0.935065i	$0.615341\pi$
$284$	−39.5118	−	2.24080i	−0.139126	−	0.00789013i
$285$		0			0
$286$	5.49785	+	14.4148i	0.0192233	+	0.0504013i
$287$		−	46.4338i		−	0.161790i
$288$		0			0
$289$	266.612			0.922533
$290$	−423.864	+	161.663i	−1.46160	+	0.557460i
$291$		0			0
$292$	−374.494	−	21.2383i	−1.28251	−	0.0727340i
$293$	−95.1653	+	39.4187i	−0.324796	+	0.134535i	−0.539123	−	0.842227i	$-0.681244\pi$
$293$	−95.1653	+	39.4187i	−0.324796	+	0.134535i	0.214327	+	0.976762i	$0.431244\pi$
$294$		0			0
$295$	−385.709	−	385.709i	−1.30749	−	1.30749i
$296$	243.658	+	20.7553i	0.823168	+	0.0701194i
$297$		0			0
$298$	212.147	−	200.457i	0.711903	−	0.672674i
$299$	14.1803	−	5.87368i	0.0474258	−	0.0196444i
$300$		0			0
$301$	322.441	+	133.559i	1.07123	+	0.443719i
$302$	−312.807	−	140.076i	−1.03579	−	0.463827i
$303$		0			0
$304$	514.935	+	285.336i	1.69386	+	0.938607i
$305$		−	382.615i		−	1.25447i
$306$		0			0
$307$	−90.1292	+	217.591i	−0.293581	+	0.708766i	0.706419	+	0.707794i	$0.250309\pi$
$307$	−90.1292	+	217.591i	−0.293581	+	0.708766i	−1.00000		0.000972180i	$0.999691\pi$
$308$	−461.756	+	161.289i	−1.49921	+	0.523667i
$309$		0			0
$310$	137.463	−	129.888i	0.443429	−	0.418993i
$311$	149.707	−	149.707i	0.481374	−	0.481374i	−0.424197	−	0.905570i	$-0.639443\pi$
$311$	149.707	−	149.707i	0.481374	−	0.481374i	0.905570	+	0.424197i	$0.139443\pi$
$312$		0			0
$313$	−25.2681	+	25.2681i	−0.0807289	+	0.0807289i	−0.746318	−	0.665589i	$-0.768180\pi$
$313$	−25.2681	+	25.2681i	−0.0807289	+	0.0807289i	0.665589	+	0.746318i	$0.268180\pi$
$314$	−341.850	−	9.68573i	−1.08869	−	0.0308463i
$315$		0			0
$316$	−355.124	+	317.006i	−1.12381	+	1.00319i
$317$	28.6835	−	69.2480i	0.0904841	−	0.218448i	−0.872158	−	0.489224i	$-0.837280\pi$
$317$	28.6835	−	69.2480i	0.0904841	−	0.218448i	0.962642	+	0.270776i	$0.0872802\pi$
$318$		0			0
$319$			646.794i			2.02757i
$320$	278.370	+	175.554i	0.869905	+	0.548608i
$321$		0			0
$322$	173.410	+	454.663i	0.538541	+	1.41200i
$323$	−160.843	−	66.6232i	−0.497965	−	0.206264i
$324$		0			0
$325$	0.701152	−	0.290427i	0.00215739	−	0.000893621i
$326$	13.1404	−	463.779i	0.0403079	−	1.42263i
$327$		0			0
$328$	13.4923	+	42.4531i	0.0411352	+	0.129430i
$329$	−27.8557	−	27.8557i	−0.0846677	−	0.0846677i
$330$		0			0
$331$	−30.1166	+	12.4747i	−0.0909867	+	0.0376879i	−0.427713	−	0.903915i	$-0.640680\pi$
$331$	−30.1166	+	12.4747i	−0.0909867	+	0.0376879i	0.336726	+	0.941603i	$0.390680\pi$
$332$	57.8077	+	165.498i	0.174120	+	0.498487i
$333$		0			0
$334$	41.4140	−	92.4828i	0.123994	−	0.276895i
$335$	−326.969			−0.976028
$336$		0			0
$337$		−	67.0180i		−	0.198867i	−0.995044	−	0.0994333i	$-0.968297\pi$
$337$		−	67.0180i		−	0.198867i	0.995044	−	0.0994333i	$-0.0317030\pi$
$338$	137.913	−	307.978i	0.408027	−	0.911176i
$339$		0			0
$340$	−87.6626	−	42.2757i	−0.257831	−	0.124340i
$341$	−103.188	−	249.117i	−0.302604	−	0.730550i
$342$		0			0
$343$	167.814	−	167.814i	0.489254	−	0.489254i
$344$	−333.607	−	28.4174i	−0.969787	−	0.0826087i
$345$		0			0
$346$	17.5009	−	617.678i	0.0505805	−	1.78520i
$347$	28.0052	+	67.6106i	0.0807067	+	0.194843i	0.959082	−	0.283128i	$-0.0913722\pi$
$347$	28.0052	+	67.6106i	0.0807067	+	0.194843i	−0.878375	+	0.477971i	$0.841372\pi$
$348$		0			0
$349$	85.8637	−	207.293i	0.246028	−	0.593964i	−0.751832	−	0.659355i	$-0.770830\pi$
$349$	85.8637	−	207.293i	0.246028	−	0.593964i	0.997860	+	0.0653912i	$0.0208295\pi$
$350$	8.57435	+	22.4810i	0.0244981	+	0.0642315i
$351$		0			0
$352$	375.304	−	281.635i	1.06620	−	0.800100i
$353$	137.219			0.388723			0.194361	−	0.980930i	$-0.437737\pi$
$353$	137.219			0.388723			0.194361	+	0.980930i	$0.437737\pi$
$354$		0			0
$355$	47.0036	+	19.4695i	0.132405	+	0.0548438i
$356$	−11.3261	+	199.713i	−0.0318150	+	0.560991i
$357$		0			0
$358$	62.6136	+	1.77405i	0.174898	+	0.00495545i
$359$	318.940	+	318.940i	0.888413	+	0.888413i	0.994371	−	0.105958i	$-0.0337909\pi$
$359$	318.940	+	318.940i	0.888413	+	0.888413i	−0.105958	+	0.994371i	$0.533791\pi$
$360$		0			0
$361$	−702.021	−	702.021i	−1.94466	−	1.94466i
$362$	−327.511	+	309.464i	−0.904727	+	0.854872i
$363$		0			0
$364$	−15.8057	−	7.62236i	−0.0434222	−	0.0209405i
$365$	445.502	+	184.533i	1.22055	+	0.505570i
$366$		0			0
$367$	−394.250			−1.07425			−0.537126	−	0.843502i	$-0.680490\pi$
$367$	−394.250			−1.07425			−0.537126	+	0.843502i	$0.680490\pi$
$368$	−290.656	−	365.297i	−0.789826	−	0.992655i
$369$		0			0
$370$	−286.917	−	128.482i	−0.775452	−	0.347249i
$371$	91.6551	−	221.275i	0.247049	−	0.596428i
$372$		0			0
$373$	166.224	+	401.300i	0.445640	+	1.07587i	0.973939	+	0.226812i	$0.0728302\pi$
$373$	166.224	+	401.300i	0.445640	+	1.07587i	−0.528299	+	0.849059i	$0.677170\pi$
$374$	−100.859	+	95.3007i	−0.269675	+	0.254815i
$375$		0			0
$376$	33.5617	+	17.3736i	0.0892598	+	0.0462063i
$377$	−16.4082	+	16.4082i	−0.0435230	+	0.0435230i
$378$		0			0
$379$	−195.577	−	472.164i	−0.516034	−	1.24582i	−0.940321	−	0.340289i	$-0.889475\pi$
$379$	−195.577	−	472.164i	−0.516034	−	1.24582i	0.424287	−	0.905528i	$-0.360525\pi$
$380$	−503.991	−	564.593i	−1.32629	−	1.48577i
$381$		0			0
$382$	−470.068	+	179.286i	−1.23054	+	0.469335i
$383$		−	303.147i		−	0.791506i	−0.918357	−	0.395753i	$-0.870484\pi$
$383$		−	303.147i		−	0.791506i	0.918357	−	0.395753i	$-0.129516\pi$
$384$		0			0
$385$	628.785			1.63321
$386$	93.1665	+	244.273i	0.241364	+	0.632830i
$387$		0			0
$388$	338.500	−	302.166i	0.872421	−	0.778778i
$389$	312.370	−	129.388i	0.803009	−	0.332617i	0.0568480	−	0.998383i	$-0.481895\pi$
$389$	312.370	−	129.388i	0.803009	−	0.332617i	0.746161	+	0.665766i	$0.231895\pi$
$390$		0			0
$391$	97.6167	+	97.6167i	0.249659	+	0.249659i
$392$	75.5434	−	145.932i	0.192713	−	0.372276i
$393$		0			0
$394$	−393.597	−	416.552i	−0.998978	−	1.05724i
$395$	565.385	−	234.190i	1.43135	−	0.592886i
$396$		0			0
$397$	381.886	+	158.182i	0.961929	+	0.398444i	0.807702	−	0.589592i	$-0.200711\pi$
$397$	381.886	+	158.182i	0.961929	+	0.398444i	0.154227	+	0.988035i	$0.450711\pi$
$398$	−141.601	+	316.214i	−0.355782	+	0.794506i
$399$		0			0
$400$	−14.3716	−	18.0623i	−0.0359291	−	0.0451557i
$401$		−	67.8277i		−	0.169146i	−0.996417	−	0.0845732i	$-0.973047\pi$
$401$		−	67.8277i		−	0.169146i	0.996417	−	0.0845732i	$-0.0269527\pi$
$402$		0			0
$403$	3.70201	−	8.93743i	0.00918612	−	0.0221773i
$404$	174.902	−	362.675i	0.432925	−	0.897710i
$405$		0			0
$406$	−505.258	−	534.724i	−1.24448	−	1.31705i
$407$	−316.939	+	316.939i	−0.778720	+	0.778720i
$408$		0			0
$409$	185.053	−	185.053i	0.452452	−	0.452452i	−0.443715	−	0.896168i	$-0.646340\pi$
$409$	185.053	−	185.053i	0.452452	−	0.452452i	0.896168	+	0.443715i	$0.146340\pi$
$410$	1.62189	−	57.2431i	0.00395582	−	0.139617i
$411$		0			0
$412$	98.6641	+	5.59545i	0.239476	+	0.0135812i
$413$	338.518	−	817.255i	0.819657	−	1.97883i
$414$		0			0
$415$		−	225.363i		−	0.543043i
$416$	16.6655	+	2.37622i	0.0400613	+	0.00571208i
$417$		0			0
$418$	−1008.20	+	384.532i	−2.41197	+	0.919933i
$419$	−274.967	−	113.895i	−0.656247	−	0.271826i	0.0296116	−	0.999561i	$-0.490573\pi$
$419$	−274.967	−	113.895i	−0.656247	−	0.271826i	−0.685858	+	0.727735i	$0.740573\pi$
$420$		0			0
$421$	−502.521	+	208.151i	−1.19364	+	0.494421i	−0.888938	−	0.458028i	$-0.848556\pi$
$421$	−502.521	+	208.151i	−1.19364	+	0.494421i	−0.304700	+	0.952448i	$0.598556\pi$
$422$	236.146	+	6.69079i	0.559587	+	0.0158550i
$423$		0			0
$424$	−19.5014	+	228.938i	−0.0459940	+	0.539947i
$425$	4.82670	+	4.82670i	0.0113569	+	0.0113569i
$426$		0			0
$427$	573.250	−	237.448i	1.34251	−	0.556084i
$428$	−267.158	+	553.978i	−0.624202	+	1.29434i
$429$		0			0
$430$	392.836	+	175.913i	0.913572	+	0.409100i
$431$	90.9676			0.211062			0.105531	−	0.994416i	$-0.466346\pi$
$431$	90.9676			0.211062			0.105531	+	0.994416i	$0.466346\pi$
$432$		0			0
$433$			592.283i			1.36786i	0.729548	+	0.683930i	$0.239730\pi$
$433$			592.283i			1.36786i	−0.729548	+	0.683930i	$0.760270\pi$
$434$	279.912	+	125.345i	0.644959	+	0.288814i
$435$		0			0
$436$	443.390	−	154.874i	1.01695	−	0.355216i
$437$	410.818	+	991.803i	0.940087	+	2.26957i
$438$		0			0
$439$	455.329	−	455.329i	1.03720	−	1.03720i	0.0379161	−	0.999281i	$-0.487928\pi$
$439$	455.329	−	455.329i	1.03720	−	1.03720i	0.999281	−	0.0379161i	$-0.0120720\pi$
$440$	−574.881	+	182.707i	−1.30655	+	0.415243i
$441$		0			0
$442$	−4.97625	−	0.140994i	−0.0112585	−	0.000318990i
$443$	216.475	+	522.616i	0.488656	+	1.17972i	0.955397	+	0.295326i	$0.0954283\pi$
$443$	216.475	+	522.616i	0.488656	+	1.17972i	−0.466740	+	0.884394i	$0.654572\pi$
$444$		0			0
$445$	98.4090	−	237.580i	0.221144	−	0.533889i
$446$	−502.512	+	191.660i	−1.12671	+	0.429732i
$447$		0			0
$448$	−90.2691	+	526.014i	−0.201494	+	1.17414i
$449$	−609.904			−1.35836			−0.679180	−	0.733972i	$-0.737664\pi$
$449$	−609.904			−1.35836			−0.679180	+	0.733972i	$0.737664\pi$
$450$		0			0
$451$	−75.4329	−	31.2453i	−0.167257	−	0.0692801i
$452$	402.241	+	450.608i	0.889914	+	0.996920i
$453$		0			0
$454$	8.45170	−	298.296i	0.0186161	−	0.657039i
$455$	15.9513	+	15.9513i	0.0350578	+	0.0350578i
$456$		0			0
$457$	400.726	+	400.726i	0.876862	+	0.876862i	0.993209	−	0.116346i	$-0.0371183\pi$
$457$	400.726	+	400.726i	0.876862	+	0.876862i	−0.116346	+	0.993209i	$0.537118\pi$
$458$	112.241	+	118.787i	0.245068	+	0.259360i
$459$		0			0
$460$	197.897	+	566.560i	0.430211	+	1.23165i
$461$	−222.556	−	92.1857i	−0.482768	−	0.199969i	0.128007	−	0.991773i	$-0.459142\pi$
$461$	−222.556	−	92.1857i	−0.482768	−	0.199969i	−0.610775	+	0.791804i	$0.709142\pi$
$462$		0			0
$463$	88.7084			0.191595			0.0957974	−	0.995401i	$-0.469460\pi$
$463$	88.7084			0.191595			0.0957974	+	0.995401i	$0.469460\pi$
$464$	617.319	+	342.069i	1.33043	+	0.737219i
$465$		0			0
$466$	34.2591	−	76.5050i	0.0735174	−	0.164174i
$467$	−20.3015	+	49.0122i	−0.0434722	+	0.104951i	−0.944124	−	0.329590i	$-0.893089\pi$
$467$	−20.3015	+	49.0122i	−0.0434722	+	0.104951i	0.900652	+	0.434541i	$0.143089\pi$
$468$		0			0
$469$	−202.915	−	489.880i	−0.432654	−	1.04452i
$470$	−33.3672	−	35.3131i	−0.0709940	−	0.0751343i
$471$		0			0
$472$	−72.0265	+	845.557i	−0.152598	+	1.79143i
$473$	433.941	−	433.941i	0.917422	−	0.917422i
$474$		0			0
$475$	20.3131	+	49.0402i	0.0427644	+	0.103242i
$476$	8.93647	−	157.576i	0.0187741	−	0.331042i
$477$		0			0
$478$	67.0363	+	175.762i	0.140243	+	0.367703i
$479$			671.684i			1.40226i	0.713032	+	0.701132i	$0.247321\pi$
$479$			671.684i			1.40226i	−0.713032	+	0.701132i	$0.752679\pi$
$480$		0			0
$481$	−16.0805			−0.0334314
$482$	204.491	−	77.9937i	0.424255	−	0.161813i
$483$		0			0
$484$	−21.2921	+	375.441i	−0.0439919	+	0.775705i
$485$	−538.916	+	223.226i	−1.11117	+	0.460261i
$486$		0			0
$487$	128.644	+	128.644i	0.264157	+	0.264157i	0.826740	−	0.562584i	$-0.190193\pi$
$487$	128.644	+	128.644i	0.264157	+	0.264157i	−0.562584	+	0.826740i	$0.690193\pi$
$488$	−455.111	+	383.662i	−0.932604	+	0.786193i
$489$		0			0
$490$	−153.548	+	145.086i	−0.313362	+	0.296095i
$491$	324.052	−	134.227i	0.659983	−	0.273374i	−0.0274485	−	0.999623i	$-0.508738\pi$
$491$	324.052	−	134.227i	0.659983	−	0.273374i	0.687431	+	0.726249i	$0.258738\pi$
$492$		0			0
$493$	−192.823	−	79.8698i	−0.391121	−	0.162008i
$494$	−35.3315	−	15.8215i	−0.0715212	−	0.0320274i
$495$		0			0
$496$	−292.338	−	33.2652i	−0.589390	−	0.0670669i
$497$			82.5056i			0.166007i
$498$		0			0
$499$	−318.527	+	768.992i	−0.638330	+	1.54107i	0.190573	+	0.981673i	$0.438966\pi$
$499$	−318.527	+	768.992i	−0.638330	+	1.54107i	−0.828903	+	0.559392i	$0.811034\pi$
$500$	−159.785	−	457.447i	−0.319569	−	0.914895i
$501$		0			0
$502$	45.5995	−	43.0867i	0.0908357	−	0.0858301i
$503$	−243.693	+	243.693i	−0.484479	+	0.484479i	−0.906559	−	0.422080i	$-0.861300\pi$
$503$	−243.693	+	243.693i	−0.484479	+	0.484479i	0.422080	+	0.906559i	$0.361300\pi$
$504$		0			0
$505$	−366.016	+	366.016i	−0.724785	+	0.724785i
$506$	855.298	+	24.2334i	1.69031	+	0.0478921i
$507$		0			0
$508$	62.2453	+	69.7299i	0.122530	+	0.137264i
$509$	38.2136	−	92.2558i	0.0750758	−	0.181249i	−0.881886	−	0.471462i	$-0.843726\pi$
$509$	38.2136	−	92.2558i	0.0750758	−	0.181249i	0.956962	+	0.290213i	$0.0937263\pi$
$510$		0			0
$511$			781.990i			1.53031i
$512$	−70.3141	−	507.149i	−0.137332	−	0.990525i
$513$		0			0
$514$	310.001	+	812.789i	0.603115	+	1.58130i
$515$	−117.372	−	48.6170i	−0.227907	−	0.0944020i
$516$		0			0
$517$	−63.9963	+	26.5081i	−0.123784	+	0.0512730i
$518$	14.4389	−	509.607i	0.0278742	−	0.983798i
$519$		0			0
$520$	−19.2188	−	9.94883i	−0.0369593	−	0.0191324i
$521$	14.6773	+	14.6773i	0.0281714	+	0.0281714i	0.721052	−	0.692881i	$-0.243659\pi$
$521$	14.6773	+	14.6773i	0.0281714	+	0.0281714i	−0.692881	+	0.721052i	$0.743659\pi$
$522$		0			0
$523$	−640.514	+	265.309i	−1.22469	+	0.507284i	−0.898898	−	0.438157i	$-0.855631\pi$
$523$	−640.514	+	265.309i	−1.22469	+	0.507284i	−0.325793	+	0.945441i	$0.605631\pi$
$524$	241.215	−	84.2553i	0.460333	−	0.160793i
$525$		0			0
$526$	−93.4566	+	208.701i	−0.177674	+	0.396769i
$527$	87.0093			0.165103
$528$		0			0
$529$		−	322.261i		−	0.609189i
$530$	120.720	−	269.584i	0.227774	−	0.508649i
$531$		0			0
$532$	533.124	−	1105.48i	1.00211	−	2.07798i
$533$	−1.12097	−	2.70626i	−0.00210313	−	0.00507741i
$534$		0			0
$535$	559.082	−	559.082i	1.04501	−	1.04501i
$536$	327.864	+	388.922i	0.611687	+	0.725601i
$537$		0			0
$538$	7.84382	−	276.841i	0.0145796	−	0.514574i
$539$	115.262	+	278.267i	0.213844	+	0.516265i
$540$		0			0
$541$	37.2775	−	89.9959i	0.0689049	−	0.166351i	−0.885675	−	0.464305i	$-0.846304\pi$
$541$	37.2775	−	89.9959i	0.0689049	−	0.166351i	0.954580	+	0.297954i	$0.0963042\pi$
$542$	−129.462	−	339.435i	−0.238860	−	0.626264i
$543$		0			0
$544$	37.6167	+	146.664i	0.0691484	+	0.269603i
$545$	−603.776			−1.10785
$546$		0			0
$547$	−407.706	−	168.877i	−0.745350	−	0.308734i	−0.0225072	−	0.999747i	$-0.507165\pi$
$547$	−407.706	−	168.877i	−0.745350	−	0.308734i	−0.722843	+	0.691013i	$0.757165\pi$
$548$	181.030	+	10.2666i	0.330347	+	0.0187347i
$549$		0			0
$550$	42.2906	+	1.19823i	0.0768920	+	0.00217861i
$551$	−1147.62	−	1147.62i	−2.08280	−	2.08280i
$552$		0			0
$553$	701.747	+	701.747i	1.26898	+	1.26898i
$554$	244.165	−	230.710i	0.440730	−	0.416444i
$555$		0			0
$556$	−412.168	+	854.670i	−0.741310	+	1.53718i
$557$	645.440	+	267.350i	1.15878	+	0.479982i	0.877468	−	0.479635i	$-0.159231\pi$
$557$	645.440	+	267.350i	1.15878	+	0.479982i	0.281311	+	0.959617i	$0.409231\pi$
$558$		0			0
$559$	22.0168			0.0393860
$560$	332.545	−	600.131i	0.593831	−	1.07166i
$561$		0			0
$562$	499.821	+	223.821i	0.889362	+	0.398258i
$563$	−325.476	+	785.768i	−0.578109	+	1.39568i	0.316398	+	0.948626i	$0.397526\pi$
$563$	−325.476	+	785.768i	−0.578109	+	1.39568i	−0.894507	+	0.447053i	$0.852474\pi$
$564$		0			0
$565$	−297.157	−	717.402i	−0.525942	−	1.26974i
$566$	−599.187	+	566.169i	−1.05863	+	1.00030i
$567$		0			0
$568$	−23.9738	−	75.4325i	−0.0422073	−	0.132804i
$569$	454.558	−	454.558i	0.798872	−	0.798872i	−0.184046	−	0.982918i	$-0.558920\pi$
$569$	454.558	−	454.558i	0.798872	−	0.798872i	0.982918	+	0.184046i	$0.0589195\pi$
$570$		0			0
$571$	−53.5551	−	129.294i	−0.0937918	−	0.226433i	0.870020	−	0.493016i	$-0.164106\pi$
$571$	−53.5551	−	129.294i	−0.0937918	−	0.226433i	−0.963812	+	0.266582i	$0.914106\pi$
$572$	−23.0183	+	20.5476i	−0.0402419	+	0.0359224i
$573$		0			0
$574$	86.7707	−	33.0947i	0.151168	−	0.0576563i
$575$		−	42.0910i		−	0.0732018i
$576$		0			0
$577$	684.354			1.18605			0.593027	−	0.805182i	$-0.297933\pi$
$577$	684.354			1.18605			0.593027	+	0.805182i	$0.297933\pi$
$578$	190.022	+	498.216i	0.328757	+	0.861966i
$579$		0			0
$580$	−604.199	−	676.850i	−1.04172	−	1.16698i
$581$	337.648	−	139.859i	0.581151	−	0.240720i
$582$		0			0
$583$	−297.792	−	297.792i	−0.510792	−	0.510792i
$584$	−227.224	−	714.951i	−0.389082	−	1.22423i
$585$		0			0
$586$	−141.488	−	149.740i	−0.241448	−	0.255529i
$587$	−287.871	+	119.240i	−0.490410	+	0.203135i	−0.614164	−	0.789178i	$-0.710507\pi$
$587$	−287.871	+	119.240i	−0.490410	+	0.203135i	0.123754	+	0.992313i	$0.460507\pi$
$588$		0			0
$589$	625.104	+	258.927i	1.06130	+	0.439604i
$590$	445.867	−	995.679i	0.755707	−	1.68759i
$591$		0			0
$592$	134.876	+	470.115i	0.227831	+	0.794113i
$593$			567.119i			0.956356i	0.878263	+	0.478178i	$0.158703\pi$
$593$			567.119i			0.956356i	−0.878263	+	0.478178i	$0.841297\pi$
$594$		0			0
$595$	−77.6460	+	187.454i	−0.130498	+	0.315049i
$596$	525.796	+	253.567i	0.882207	+	0.425448i
$597$		0			0
$598$	21.0828	+	22.3123i	0.0352555	+	0.0373116i
$599$	−372.981	+	372.981i	−0.622673	+	0.622673i	−0.946214	−	0.323541i	$-0.895127\pi$
$599$	−372.981	+	372.981i	−0.622673	+	0.622673i	0.323541	+	0.946214i	$0.395127\pi$
$600$		0			0
$601$	−210.468	+	210.468i	−0.350196	+	0.350196i	−0.860182	−	0.509987i	$-0.829650\pi$
$601$	−210.468	+	210.468i	−0.350196	+	0.350196i	0.509987	+	0.860182i	$0.329650\pi$
$602$	−19.7691	+	697.735i	−0.0328391	+	1.15903i
$603$		0			0
$604$	38.8125	−	684.378i	0.0642591	−	1.13308i
$605$	185.000	−	446.629i	0.305785	−	0.738230i
$606$		0			0
$607$			495.918i			0.816998i	0.912759	+	0.408499i	$0.133948\pi$
$607$			495.918i			0.816998i	−0.912759	+	0.408499i	$0.866052\pi$
$608$	−166.198	+	1165.62i	−0.273353	+	1.91714i
$609$		0			0
$610$	714.990	−	272.700i	1.17212	−	0.447049i
$611$	−2.29595	−	0.951016i	−0.00375770	−	0.00155649i
$612$		0			0
$613$	−646.592	+	267.827i	−1.05480	+	0.436912i	−0.841603	−	0.540097i	$-0.818387\pi$
$613$	−646.592	+	267.827i	−1.05480	+	0.436912i	−0.213196	+	0.977009i	$0.568387\pi$
$614$	−470.849	−	13.3407i	−0.766855	−	0.0217275i
$615$		0			0
$616$	−630.507	−	747.925i	−1.02355	−	1.21416i
$617$	−104.419	−	104.419i	−0.169236	−	0.169236i	0.617407	−	0.786644i	$-0.288183\pi$
$617$	−104.419	−	104.419i	−0.169236	−	0.169236i	−0.786644	+	0.617407i	$0.788183\pi$
$618$		0			0
$619$	164.163	−	67.9986i	0.265207	−	0.109852i	−0.246118	−	0.969240i	$-0.579155\pi$
$619$	164.163	−	67.9986i	0.265207	−	0.109852i	0.511325	+	0.859388i	$0.329155\pi$
$620$	340.694	+	164.301i	0.549507	+	0.265002i
$621$		0			0
$622$	386.458	+	173.057i	0.621314	+	0.278226i
$623$	417.025			0.669383
$624$		0			0
$625$			658.985i			1.05438i
$626$	−65.2277	−	29.2091i	−0.104198	−	0.0466599i
$627$		0			0
$628$	−225.546	−	645.716i	−0.359150	−	1.02821i
$629$	−55.3487	−	133.624i	−0.0879947	−	0.212438i
$630$		0			0
$631$	56.9727	−	56.9727i	0.0902895	−	0.0902895i	−0.660519	−	0.750809i	$-0.729664\pi$
$631$	56.9727	−	56.9727i	0.0902895	−	0.0902895i	0.750809	+	0.660519i	$0.229664\pi$
$632$	−845.495	−	437.680i	−1.33781	−	0.692531i
$633$		0			0
$634$	149.847	+	4.24566i	0.236352	+	0.00669662i
$635$	−45.9840	−	111.015i	−0.0724157	−	0.174827i
$636$		0			0
$637$	−4.13518	+	9.98322i	−0.00649165	+	0.0156722i
$638$	−1208.66	+	460.988i	−1.89445	+	0.722552i
$639$		0			0
$640$	−129.656	+	645.310i	−0.202587	+	1.00830i
$641$	−41.8316			−0.0652599			−0.0326300	−	0.999468i	$-0.510388\pi$
$641$	−41.8316			−0.0652599			−0.0326300	+	0.999468i	$0.510388\pi$
$642$		0			0
$643$	−2.76710	−	1.14617i	−0.00430343	−	0.00178254i	0.380531	−	0.924768i	$-0.375741\pi$
$643$	−2.76710	−	1.14617i	−0.00430343	−	0.00178254i	−0.384834	+	0.922986i	$0.625741\pi$
$644$	−726.032	+	648.101i	−1.12738	+	1.00637i
$645$		0			0
$646$	9.86141	−	348.050i	0.0152653	−	0.538777i
$647$	385.669	+	385.669i	0.596088	+	0.596088i	0.939269	−	0.343181i	$-0.111504\pi$
$647$	385.669	+	385.669i	0.596088	+	0.596088i	−0.343181	+	0.939269i	$0.611504\pi$
$648$		0			0
$649$	−1099.86	−	1099.86i	−1.69470	−	1.69470i
$650$	1.04245	+	1.10324i	0.00160377	+	0.00169730i
$651$		0			0
$652$	876.026	−	305.993i	1.34360	−	0.469314i
$653$	−660.676	−	273.661i	−1.01175	−	0.419082i	−0.185660	−	0.982614i	$-0.559442\pi$
$653$	−660.676	−	273.661i	−1.01175	−	0.419082i	−0.826095	+	0.563532i	$0.809442\pi$
$654$		0			0
$655$	−328.469			−0.501479
$656$	−69.7156	+	55.4706i	−0.106274	+	0.0845589i
$657$		0			0
$658$	32.2002	−	71.9072i	0.0489365	−	0.109281i
$659$	248.478	−	599.878i	0.377052	−	0.910285i	−0.615463	−	0.788166i	$-0.711031\pi$
$659$	248.478	−	599.878i	0.377052	−	0.910285i	0.992515	−	0.122119i	$-0.0389690\pi$
$660$		0			0
$661$	−193.393	−	466.891i	−0.292576	−	0.706341i	0.707424	−	0.706789i	$-0.249857\pi$
$661$	−193.393	−	466.891i	−0.292576	−	0.706341i	−1.00000		0.000448817i	$0.999857\pi$
$662$	−44.7764	−	47.3877i	−0.0676380	−	0.0715826i
$663$		0			0
$664$	−268.063	+	225.980i	−0.403710	+	0.340331i
$665$	−1115.67	+	1115.67i	−1.67770	+	1.67770i
$666$		0			0
$667$	492.500	+	1189.00i	0.738381	+	1.78261i
$668$	202.339	+	11.4751i	0.302903	+	0.0171783i
$669$		0			0
$670$	−233.040	−	611.006i	−0.347821	−	0.911949i
$671$		−	1091.04i		−	1.62599i
$672$		0			0
$673$	−933.266			−1.38673			−0.693363	−	0.720589i	$-0.743872\pi$
$673$	−933.266			−1.38673			−0.693363	+	0.720589i	$0.743872\pi$
$674$	125.236	−	47.7656i	0.185810	−	0.0708689i
$675$		0			0
$676$	673.810	+	38.2132i	0.996761	+	0.0565284i
$677$	−313.722	+	129.948i	−0.463400	+	0.191947i	−0.602154	−	0.798380i	$-0.705691\pi$
$677$	−313.722	+	129.948i	−0.463400	+	0.191947i	0.138753	+	0.990327i	$0.455691\pi$
$678$		0			0
$679$	−668.896	−	668.896i	−0.985119	−	0.985119i
$680$	16.5207	−	193.946i	0.0242952	−	0.285214i
$681$		0			0
$682$	391.980	−	370.379i	0.574750	−	0.543078i
$683$	899.397	−	372.543i	1.31683	−	0.545450i	0.389963	−	0.920831i	$-0.372488\pi$
$683$	899.397	−	372.543i	1.31683	−	0.545450i	0.926871	+	0.375380i	$0.122488\pi$
$684$		0			0
$685$	−215.356	−	89.2033i	−0.314388	−	0.130224i
$686$	433.199	+	193.987i	0.631485	+	0.282781i
$687$		0			0
$688$	−184.667	−	643.663i	−0.268412	−	0.935557i
$689$		−	15.1090i		−	0.0219289i
$690$		0			0
$691$	272.535	−	657.958i	0.394407	−	0.952182i	−0.594561	−	0.804051i	$-0.702674\pi$
$691$	272.535	−	657.958i	0.394407	−	0.952182i	0.988968	−	0.148131i	$-0.0473259\pi$
$692$	1166.73	−	407.533i	1.68602	−	0.588920i
$693$		0			0
$694$	−106.383	+	100.521i	−0.153290	+	0.144843i
$695$	862.545	−	862.545i	1.24107	−	1.24107i
$696$		0			0
$697$	18.6298	−	18.6298i	0.0267285	−	0.0267285i
$698$	448.565	+	12.7093i	0.642644	+	0.0182082i
$699$		0			0
$700$	−35.8990	+	32.0457i	−0.0512842	+	0.0457795i
$701$	−502.382	+	1212.86i	−0.716664	+	1.73018i	−0.0340293	+	0.999421i	$0.510834\pi$
$701$	−502.382	+	1212.86i	−0.716664	+	1.73018i	−0.682635	+	0.730760i	$0.739166\pi$
$702$		0			0
$703$		−	1124.71i		−	1.59987i
$704$	793.780	+	500.599i	1.12753	+	0.711078i
$705$		0			0
$706$	97.7998	+	256.421i	0.138527	+	0.363202i
$707$	−775.529	−	321.235i	−1.09693	−	0.454363i
$708$		0			0
$709$	454.191	−	188.132i	0.640608	−	0.265349i	−0.0386445	−	0.999253i	$-0.512304\pi$
$709$	454.191	−	188.132i	0.640608	−	0.265349i	0.679253	+	0.733904i	$0.262304\pi$
$710$	−2.88183	+	101.712i	−0.00405892	+	0.143256i
$711$		0			0
$712$	−381.274	+	121.176i	−0.535498	+	0.170191i
$713$	−379.380	−	379.380i	−0.532090	−	0.532090i
$714$		0			0
$715$	36.6469	−	15.1796i	0.0512544	−	0.0212303i
$716$	41.3113	+	118.270i	0.0576974	+	0.165182i
$717$		0			0
$718$	−368.684	+	823.319i	−0.513488	+	1.14668i
$719$	167.727			0.233278			0.116639	−	0.993174i	$-0.462788\pi$
$719$	167.727			0.233278			0.116639	+	0.993174i	$0.462788\pi$
$720$		0			0
$721$		−	206.023i		−	0.285746i
$722$	811.513	−	1812.21i	1.12398	−	2.50999i
$723$		0			0
$724$	−811.719	−	391.455i	−1.12116	−	0.540684i
$725$	24.3519	+	58.7907i	0.0335888	+	0.0810907i
$726$		0			0
$727$	−655.837	+	655.837i	−0.902114	+	0.902114i	−0.995619	−	0.0935047i	$-0.970193\pi$
$727$	−655.837	+	655.837i	−0.902114	+	0.902114i	0.0935047	+	0.995619i	$0.470193\pi$
$728$	2.97871	−	34.9686i	0.00409164	−	0.0480339i
$729$		0			0
$730$	−27.3141	+	964.029i	−0.0374166	+	1.32059i
$731$	75.7813	+	182.952i	0.103668	+	0.250277i
$732$		0			0
$733$	−319.390	+	771.076i	−0.435730	+	1.05195i	0.541678	+	0.840586i	$0.317789\pi$
$733$	−319.390	+	771.076i	−0.435730	+	1.05195i	−0.977408	+	0.211360i	$0.932211\pi$
$734$	−280.993	−	736.733i	−0.382824	−	1.00372i
$735$		0			0
$736$	475.470	−	803.505i	0.646019	−	1.09172i
$737$	−932.363			−1.26508
$738$		0			0
$739$	1029.37	+	426.379i	1.39292	+	0.576968i	0.947905	−	0.318553i	$-0.103197\pi$
$739$	1029.37	+	426.379i	1.39292	+	0.576968i	0.445019	+	0.895521i	$0.353197\pi$
$740$	35.6001	−	627.733i	0.0481082	−	0.848288i
$741$		0			0
$742$	478.820	+	13.5666i	0.645310	+	0.0182838i
$743$	−733.991	−	733.991i	−0.987875	−	0.987875i	0.0120522	−	0.999927i	$-0.496164\pi$
$743$	−733.991	−	733.991i	−0.987875	−	0.987875i	−0.999927	+	0.0120522i	$0.996164\pi$
$744$		0			0
$745$	−530.640	−	530.640i	−0.712268	−	0.712268i
$746$	−631.434	+	596.639i	−0.846426	+	0.799784i
$747$		0			0
$748$	−249.973	−	120.550i	−0.334188	−	0.161164i
$749$	1184.60	+	490.679i	1.58158	+	0.655112i
$750$		0			0
$751$	446.102			0.594010			0.297005	−	0.954876i	$-0.404012\pi$
$751$	446.102			0.594010			0.297005	+	0.954876i	$0.404012\pi$
$752$	−8.54555	+	75.0992i	−0.0113638	+	0.0998659i
$753$		0			0
$754$	−42.3564	−	18.9673i	−0.0561756	−	0.0251555i
$755$	−337.229	+	814.143i	−0.446661	+	1.07834i
$756$		0			0
$757$	410.910	+	992.026i	0.542814	+	1.31047i	0.922729	+	0.385448i	$0.125953\pi$
$757$	410.910	+	992.026i	0.542814	+	1.31047i	−0.379915	+	0.925021i	$0.624047\pi$
$758$	742.938	−	701.998i	0.980129	−	0.926119i
$759$		0			0
$760$	695.843	−	1344.21i	0.915583	−	1.76869i
$761$	−253.936	+	253.936i	−0.333687	+	0.333687i	−0.853985	−	0.520298i	$-0.825821\pi$
$761$	−253.936	+	253.936i	−0.333687	+	0.333687i	0.520298	+	0.853985i	$0.325821\pi$
$762$		0			0
$763$	−374.699	−	904.604i	−0.491087	−	1.18559i
$764$	−670.061	−	750.631i	−0.877043	−	0.982502i
$765$		0			0
$766$	566.489	−	216.061i	0.739542	−	0.282064i
$767$		−	55.8036i		−	0.0727556i
$768$		0			0
$769$	−7.50291			−0.00975671			−0.00487836	−	0.999988i	$-0.501553\pi$
$769$	−7.50291			−0.00975671			−0.00487836	+	0.999988i	$0.501553\pi$
$770$	448.153	+	1175.01i	0.582017	+	1.52598i
$771$		0			0
$772$	−390.068	+	348.200i	−0.505270	+	0.451036i
$773$	49.4764	−	20.4938i	0.0640057	−	0.0265120i	−0.350451	−	0.936581i	$-0.613972\pi$
$773$	49.4764	−	20.4938i	0.0640057	−	0.0265120i	0.414457	+	0.910069i	$0.363972\pi$
$774$		0			0
$775$	−18.7586	−	18.7586i	−0.0242047	−	0.0242047i
$776$	805.914	+	417.190i	1.03855	+	0.537616i
$777$		0			0
$778$	464.422	+	491.506i	0.596943	+	0.631756i
$779$	189.282	−	78.4031i	0.242981	−	0.100646i
$780$		0			0
$781$	134.032	+	55.5180i	0.171616	+	0.0710858i
$782$	−112.842	+	251.990i	−0.144299	+	0.322238i
$783$		0			0
$784$	326.544	+	37.1576i	0.416511	+	0.0473949i
$785$			879.289i			1.12011i
$786$		0			0
$787$	−87.7539	+	211.857i	−0.111504	+	0.269195i	−0.969775	−	0.244003i	$-0.921539\pi$
$787$	−87.7539	+	211.857i	−0.111504	+	0.269195i	0.858270	+	0.513198i	$0.171539\pi$
$788$	497.880	−	1032.40i	0.631827	−	1.31015i
$789$		0			0
$790$	840.595	+	889.617i	1.06404	+	1.12610i
$791$	890.429	−	890.429i	1.12570	−	1.12570i
$792$		0			0
$793$	27.6779	−	27.6779i	0.0349028	−	0.0349028i
$794$	−23.4137	+	826.368i	−0.0294883	+	1.04077i
$795$		0			0
$796$	−691.829	−	39.2351i	−0.869133	−	0.0492904i
$797$	−58.8409	+	142.054i	−0.0738279	+	0.178236i	−0.956485	−	0.291781i	$-0.905752\pi$
$797$	−58.8409	+	142.054i	−0.0738279	+	0.178236i	0.882657	+	0.470017i	$0.155752\pi$
$798$		0			0
$799$		−	22.3520i		−	0.0279750i
$800$	23.5098	−	39.7297i	0.0293873	−	0.0496621i
$801$		0			0
$802$	126.749	−	48.3427i	0.158041	−	0.0602776i
$803$	1270.36	+	526.201i	1.58202	+	0.655294i
$804$		0			0
$805$	1155.90	−	478.788i	1.43590	−	0.594768i
$806$	19.3399	+	0.547962i	0.0239949	+	0.000679854i
$807$		0			0
$808$	802.386	+	68.3491i	0.993052	+	0.0845904i
$809$	−743.075	−	743.075i	−0.918510	−	0.918510i	0.0784111	−	0.996921i	$-0.475015\pi$
$809$	−743.075	−	743.075i	−0.918510	−	0.918510i	−0.996921	+	0.0784111i	$0.975015\pi$
$810$		0			0
$811$	517.790	−	214.475i	0.638458	−	0.264458i	−0.0398838	−	0.999204i	$-0.512699\pi$
$811$	517.790	−	214.475i	0.638458	−	0.264458i	0.678342	+	0.734746i	$0.262699\pi$
$812$	639.125	−	1325.29i	0.787099	−	1.63213i
$813$		0			0
$814$	−818.153	−	366.371i	−1.00510	−	0.450087i
$815$	−1192.91			−1.46369
$816$		0			0
$817$			1539.90i			1.88483i
$818$	477.700	+	213.915i	0.583985	+	0.261510i
$819$		0			0
$820$	108.126	−	37.7679i	0.131861	−	0.0460585i
$821$	−249.469	−	602.273i	−0.303860	−	0.733584i	−0.999879	−	0.0155602i	$-0.995047\pi$
$821$	−249.469	−	602.273i	−0.303860	−	0.733584i	0.696018	−	0.718024i	$-0.254953\pi$
$822$		0			0
$823$	1017.71	−	1017.71i	1.23659	−	1.23659i	0.275205	−	0.961386i	$-0.411254\pi$
$823$	1017.71	−	1017.71i	1.23659	−	1.23659i	0.961386	−	0.275205i	$-0.0887457\pi$
$824$	59.8645	+	188.361i	0.0726510	+	0.228594i
$825$		0			0
$826$	1768.47	+	50.1067i	2.14101	+	0.0606618i
$827$	109.427	+	264.181i	0.132318	+	0.319445i	0.976127	−	0.217199i	$-0.0696920\pi$
$827$	109.427	+	264.181i	0.132318	+	0.319445i	−0.843809	+	0.536644i	$0.819692\pi$
$828$		0			0
$829$	4.55662	−	11.0007i	0.00549653	−	0.0132698i	−0.921107	−	0.389308i	$-0.872714\pi$
$829$	4.55662	−	11.0007i	0.00549653	−	0.0132698i	0.926604	+	0.376039i	$0.122714\pi$
$830$	421.134	−	160.622i	0.507391	−	0.193521i
$831$		0			0
$832$	7.43754	+	32.8364i	0.00893935	+	0.0394668i
$833$	−97.1905			−0.116675
$834$		0			0
$835$	−240.705	−	99.7032i	−0.288269	−	0.119405i
$836$	−1437.15	−	1609.95i	−1.71907	−	1.92578i
$837$		0			0
$838$	16.8585	−	595.006i	0.0201175	−	0.710031i
$839$	207.243	+	207.243i	0.247012	+	0.247012i	0.819743	−	0.572731i	$-0.194116\pi$
$839$	207.243	+	207.243i	0.247012	+	0.247012i	−0.572731	+	0.819743i	$0.694116\pi$
$840$		0			0
$841$	−781.126	−	781.126i	−0.928806	−	0.928806i
$842$	−747.132	−	790.704i	−0.887330	−	0.939078i
$843$		0			0
$844$	155.805	+	446.053i	0.184603	+	0.528499i
$845$	−801.572	−	332.022i	−0.948606	−	0.392926i
$846$		0			0
$847$	783.969			0.925583
$848$	−441.714	+	126.728i	−0.520889	+	0.149443i
$849$		0			0
$850$	−5.57951	+	12.4598i	−0.00656413	+	0.0146585i
$851$	−341.296	+	823.961i	−0.401053	+	0.968227i
$852$		0			0
$853$	360.308	+	869.862i	0.422401	+	1.01977i	0.981637	+	0.190759i	$0.0610947\pi$
$853$	360.308	+	869.862i	0.422401	+	1.01977i	−0.559236	+	0.829009i	$0.688905\pi$
$854$	852.289	+	901.994i	0.997997	+	1.05620i
$855$		0			0
$856$	−1225.63	−	104.402i	−1.43181	−	0.121965i
$857$	−377.742	+	377.742i	−0.440772	+	0.440772i	−0.892271	−	0.451499i	$-0.850889\pi$
$857$	−377.742	+	377.742i	−0.440772	+	0.440772i	0.451499	+	0.892271i	$0.350889\pi$
$858$		0			0
$859$	101.948	+	246.125i	0.118682	+	0.286525i	0.972046	−	0.234792i	$-0.0754409\pi$
$859$	101.948	+	246.125i	0.118682	+	0.286525i	−0.853363	+	0.521317i	$0.825441\pi$
$860$	−48.7423	+	859.469i	−0.0566771	+	0.999382i
$861$		0			0
$862$	64.8351	+	169.991i	0.0752148	+	0.197205i
$863$			138.935i			0.160990i	0.996755	+	0.0804952i	$0.0256502\pi$
$863$			138.935i			0.160990i	−0.996755	+	0.0804952i	$0.974350\pi$
$864$		0			0
$865$	−1588.76			−1.83672
$866$	−1106.80	+	422.137i	−1.27806	+	0.487456i
$867$		0			0
$868$	−34.7310	+	612.408i	−0.0400126	+	0.705539i
$869$	1612.21	−	667.800i	1.85525	−	0.768469i
$870$		0			0
$871$	−23.6526	−	23.6526i	−0.0271557	−	0.0271557i
$872$	605.429	+	718.177i	0.694299	+	0.823597i
$873$		0			0
$874$	−1560.57	+	1474.58i	−1.78555	+	1.68716i
$875$	−933.284	+	386.579i	−1.06661	+	0.441805i
$876$		0			0
$877$	−1048.28	−	434.212i	−1.19530	−	0.495111i	−0.305825	−	0.952088i	$-0.598932\pi$
$877$	−1048.28	−	434.212i	−1.19530	−	0.495111i	−0.889479	+	0.456977i	$0.848932\pi$
$878$	1175.40	+	526.346i	1.33872	+	0.599483i
$879$		0			0
$880$	−751.157	−	944.056i	−0.853587	−	1.07279i
$881$		−	375.449i		−	0.426162i	−0.977035	−	0.213081i	$-0.931650\pi$
$881$		−	375.449i		−	0.426162i	0.977035	−	0.213081i	$-0.0683499\pi$
$882$		0			0
$883$	187.585	−	452.871i	0.212441	−	0.512877i	−0.781356	−	0.624085i	$-0.785472\pi$
$883$	187.585	−	452.871i	0.212441	−	0.512877i	0.993797	+	0.111208i	$0.0354719\pi$
$884$	−3.28324	−	9.39959i	−0.00371407	−	0.0106330i
$885$		0			0
$886$	−822.322	+	777.008i	−0.928129	+	0.876984i
$887$	−761.091	+	761.091i	−0.858051	+	0.858051i	−0.991108	−	0.133057i	$-0.957521\pi$
$887$	−761.091	+	761.091i	−0.858051	+	0.858051i	0.133057	+	0.991108i	$0.457521\pi$
$888$		0			0
$889$	137.790	−	137.790i	0.154995	−	0.154995i
$890$	514.104	+	14.5663i	0.577645	+	0.0163666i
$891$		0			0
$892$	−716.309	−	802.441i	−0.803037	−	0.899597i
$893$	66.5161	−	160.584i	0.0744862	−	0.179825i
$894$		0			0
$895$		−	161.052i		−	0.179946i
$896$	−1047.30	+	206.219i	−1.16886	+	0.230155i
$897$		0			0
$898$	−434.695	−	1139.72i	−0.484070	−	1.26918i
$899$	749.392	+	310.408i	0.833584	+	0.345282i
$900$		0			0
$901$	125.551	−	52.0049i	0.139346	−	0.0577191i
$902$	4.62486	−	163.230i	0.00512734	−	0.180965i
$903$		0			0
$904$	−555.360	+	1072.83i	−0.614337	+	1.18676i
$905$	819.198	+	819.198i	0.905191	+	0.905191i
$906$		0			0
$907$	911.623	−	377.607i	1.00510	−	0.416325i	0.181433	−	0.983403i	$-0.441926\pi$
$907$	911.623	−	377.607i	1.00510	−	0.416325i	0.823664	+	0.567079i	$0.191926\pi$
$908$	563.447	−	196.810i	0.620536	−	0.216751i
$909$		0			0
$910$	−18.4392	+	41.1771i	−0.0202628	+	0.0452495i
$911$	314.118			0.344806			0.172403	−	0.985026i	$-0.444847\pi$
$911$	314.118			0.344806			0.172403	+	0.985026i	$0.444847\pi$
$912$		0			0
$913$		−	642.629i		−	0.703865i
$914$	−463.226	+	1034.44i	−0.506812	+	1.13178i
$915$		0			0
$916$	−141.979	+	294.407i	−0.154999	+	0.321405i
$917$	−203.845	−	492.126i	−0.222296	−	0.536670i
$918$		0			0
$919$	−161.147	+	161.147i	−0.175351	+	0.175351i	−0.789326	−	0.613975i	$-0.789570\pi$
$919$	−161.147	+	161.147i	−0.175351	+	0.175351i	0.613975	+	0.789326i	$0.289570\pi$
$920$	−917.681	+	773.612i	−0.997479	+	0.840883i
$921$		0			0
$922$	13.6451	−	481.593i	0.0147995	−	0.522335i
$923$	1.99179	+	4.80859i	0.00215795	+	0.00520974i
$924$		0			0
$925$	−16.8755	+	40.7412i	−0.0182438	+	0.0440445i
$926$	63.2249	+	165.769i	0.0682775	+	0.179016i
$927$		0			0
$928$	−199.243	+	1397.38i	−0.214702	+	1.50580i
$929$	773.364			0.832469			0.416235	−	0.909257i	$-0.363349\pi$
$929$	773.364			0.832469			0.416235	+	0.909257i	$0.363349\pi$
$930$		0			0
$931$	−698.248	−	289.224i	−0.749998	−	0.310659i
$932$	167.382	+	9.49258i	0.179594	+	0.0101852i
$933$		0			0
$934$	−106.058	−	3.00498i	−0.113553	−	0.00321732i
$935$	252.276	+	252.276i	0.269814	+	0.269814i
$936$		0			0
$937$	458.830	+	458.830i	0.489680	+	0.489680i	0.908205	−	0.418525i	$-0.137453\pi$
$937$	458.830	+	458.830i	0.489680	+	0.489680i	−0.418525	+	0.908205i	$0.637453\pi$
$938$	770.813	−	728.337i	0.821762	−	0.776479i
$939$		0			0
$940$	42.2077	−	87.5217i	0.0449018	−	0.0931082i
$941$	531.693	+	220.235i	0.565030	+	0.234043i	0.646867	−	0.762603i	$-0.276079\pi$
$941$	531.693	+	220.235i	0.565030	+	0.234043i	−0.0818371	+	0.996646i	$0.526079\pi$
$942$		0			0
$943$	−162.460			−0.172280
$944$	−1631.42	+	468.056i	−1.72820	+	0.495822i
$945$		0			0
$946$	1120.18	+	501.621i	1.18413	+	0.530255i
$947$	164.850	−	397.982i	0.174076	−	0.420256i	−0.812629	−	0.582782i	$-0.801964\pi$
$947$	164.850	−	397.982i	0.174076	−	0.420256i	0.986704	+	0.162526i	$0.0519642\pi$
$948$		0			0
$949$	18.8782	+	45.5760i	0.0198927	+	0.0480253i
$950$	−77.1634	+	72.9112i	−0.0812246	+	0.0767487i
$951$		0			0
$952$	300.831	−	95.6092i	0.315999	−	0.100430i
$953$	−195.550	+	195.550i	−0.205194	+	0.205194i	−0.802221	−	0.597027i	$-0.796349\pi$
$953$	−195.550	+	195.550i	−0.205194	+	0.205194i	0.597027	+	0.802221i	$0.296349\pi$
$954$		0			0
$955$	495.010	+	1195.06i	0.518336	+	1.25137i
$956$	−280.667	+	250.541i	−0.293584	+	0.262072i
$957$		0			0
$958$	−1255.17	+	478.728i	−1.31020	+	0.499716i
$959$		−	378.014i		−	0.394176i
$960$		0			0
$961$	622.844			0.648121
$962$	−11.4610	−	30.0495i	−0.0119137	−	0.0312365i
$963$		0			0
$964$	291.493	+	326.543i	0.302378	+	0.338737i
$965$	621.018	−	257.234i	0.643542	−	0.266564i
$966$		0			0
$967$	447.573	+	447.573i	0.462847	+	0.462847i	0.899588	−	0.436740i	$-0.143867\pi$
$967$	447.573	+	447.573i	0.462847	+	0.462847i	−0.436740	+	0.899588i	$0.643867\pi$
$968$	−716.760	+	227.799i	−0.740455	+	0.235329i
$969$		0			0
$970$	−801.243	−	847.970i	−0.826023	−	0.874196i
$971$	−1520.65	+	629.874i	−1.56607	+	0.648685i	−0.986130	−	0.165977i	$-0.946922\pi$
$971$	−1520.65	+	629.874i	−1.56607	+	0.648685i	−0.579936	+	0.814662i	$0.696922\pi$
$972$		0			0
$973$	1827.59	+	757.013i	1.87831	+	0.778020i
$974$	−148.709	+	332.085i	−0.152678	+	0.340950i
$975$		0			0
$976$	−1041.32	−	577.016i	−1.06692	−	0.591205i
$977$			384.575i			0.393628i	0.980441	+	0.196814i	$0.0630596\pi$
$977$			384.575i			0.393628i	−0.980441	+	0.196814i	$0.936940\pi$
$978$		0			0
$979$	280.616	−	677.468i	0.286636	−	0.692000i
$980$	−380.560	−	183.527i	−0.388326	−	0.187272i
$981$		0			0
$982$	481.789	+	509.886i	0.490620	+	0.519233i
$983$	1030.98	−	1030.98i	1.04881	−	1.04881i	0.0500652	−	0.998746i	$-0.484057\pi$
$983$	1030.98	−	1030.98i	1.04881	−	1.04881i	0.998746	−	0.0500652i	$-0.0159429\pi$
$984$		0			0
$985$	−1041.91	+	1041.91i	−1.05778	+	1.05778i
$986$	11.8221	−	417.252i	0.0119900	−	0.423177i
$987$		0			0
$988$	4.38386	−	77.3002i	0.00443710	−	0.0782390i
$989$	467.289	−	1128.14i	0.472487	−	1.14068i
$990$		0			0
$991$		−	300.634i		−	0.303364i	−0.988429	−	0.151682i	$-0.951531\pi$
$991$		−	300.634i		−	0.303364i	0.988429	−	0.151682i	$-0.0484690\pi$
$992$	−146.195	−	569.999i	−0.147374	−	0.574595i
$993$		0			0
$994$	−154.178	+	58.8040i	−0.155108	+	0.0591590i
$995$	823.008	+	340.901i	0.827144	+	0.342614i
$996$		0			0
$997$	−1059.12	+	438.701i	−1.06231	+	0.440021i	−0.844269	−	0.535919i	$-0.819965\pi$
$997$	−1059.12	+	438.701i	−1.06231	+	0.440021i	−0.218036	+	0.975941i	$0.569965\pi$
$998$	−1664.03	−	47.1476i	−1.66737	−	0.0472420i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.b.19.9		64
3.2	odd	2		96.3.m.a.19.8	✓	64
12.11	even	2		384.3.m.a.367.10		64
32.27	odd	8	inner	288.3.u.b.91.9		64
96.5	odd	8		384.3.m.a.271.10		64
96.59	even	8		96.3.m.a.91.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.3.m.a.19.8	✓	64	3.2	odd	2
96.3.m.a.91.8	yes	64	96.59	even	8
288.3.u.b.19.9		64	1.1	even	1	trivial
288.3.u.b.91.9		64	32.27	odd	8	inner
384.3.m.a.271.10		64	96.5	odd	8
384.3.m.a.367.10		64	12.11	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.712728 + 1.86869i) q^{2} +(-2.98404 + 2.66374i) q^{4} +(4.75081 - 1.96785i) q^{5} +(5.89664 + 5.89664i) q^{7} +(-7.10452 - 3.67773i) q^{8} +O(q^{10})\)	\(q+(0.712728 + 1.86869i) q^{2} +(-2.98404 + 2.66374i) q^{4} +(4.75081 - 1.96785i) q^{5} +(5.89664 + 5.89664i) q^{7} +(-7.10452 - 3.67773i) q^{8} +(7.06335 + 7.47527i) q^{10} +(13.5471 - 5.61139i) q^{11} +(0.486020 + 0.201316i) q^{13} +(-6.81632 + 15.2217i) q^{14} +(1.80897 - 15.8974i) q^{16} +4.73160i q^{17} +(-14.0805 + 33.9933i) q^{19} +(-8.93476 + 18.5271i) q^{20} +(20.1413 + 21.3160i) q^{22} +(20.6308 - 20.6308i) q^{23} +(1.02010 - 1.02010i) q^{25} +(-0.0297983 + 1.05171i) q^{26} +(-33.3029 - 1.88868i) q^{28} +(-16.8801 + 40.7522i) q^{29} -18.3890i q^{31} +(30.9967 - 7.95011i) q^{32} +(-8.84191 + 3.37234i) q^{34} +(39.6175 + 16.4101i) q^{35} +(-28.2407 + 11.6977i) q^{37} +(-73.5587 - 2.08416i) q^{38} +(-40.9895 - 3.49158i) q^{40} +(-3.93731 - 3.93731i) q^{41} +(38.6661 - 16.0160i) q^{43} +(-25.4777 + 52.8305i) q^{44} +(53.2568 + 23.8485i) q^{46} -4.72399 q^{47} +20.5407i q^{49} +(2.63331 + 1.17920i) q^{50} +(-1.98656 + 0.693897i) q^{52} +(-10.9910 - 26.5346i) q^{53} +(53.3173 - 53.3173i) q^{55} +(-20.2066 - 63.5791i) q^{56} +(-88.1843 - 2.49855i) q^{58} +(-40.5941 - 98.0027i) q^{59} +(28.4740 - 68.7424i) q^{61} +(34.3634 - 13.1064i) q^{62} +(36.9485 + 52.2571i) q^{64} +2.70515 q^{65} +(-58.7449 - 24.3329i) q^{67} +(-12.6037 - 14.1193i) q^{68} +(-2.42899 + 85.7290i) q^{70} +(6.99598 + 6.99598i) q^{71} +(66.3081 + 66.3081i) q^{73} +(-41.9873 - 44.4360i) q^{74} +(-48.5327 - 138.944i) q^{76} +(112.971 + 46.7940i) q^{77} +119.008 q^{79} +(-22.6896 - 79.0854i) q^{80} +(4.55140 - 10.1639i) q^{82} +(16.7714 - 40.4898i) q^{83} +(9.31107 + 22.4789i) q^{85} +(57.4874 + 60.8401i) q^{86} +(-116.883 - 9.95634i) q^{88} +(35.3613 - 35.3613i) q^{89} +(1.67880 + 4.05298i) q^{91} +(-6.60800 + 116.518i) q^{92} +(-3.36692 - 8.82769i) q^{94} +189.204i q^{95} -113.437 q^{97} +(-38.3844 + 14.6400i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 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

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