LMFDB - Embedded newform 99.3.k.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(19,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, 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:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 21x^{14} + 227x^{12} - 1488x^{10} + 24225x^{8} - 62832x^{6} + 64372x^{4} + 7986x^{2} + 14641 $ x^16 - 21x^14 + 227x^12 - 1488x^10 + 24225x^8 - 62832x^6 + 64372x^4 + 7986*x^2 + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			73.1
Root			$3.67414 - 1.19380i$ of defining polynomial
Character	$\chi$	$=$	99.73
Dual form			99.3.k.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27075 + 3.12541i) q^{2} +(-3.37586 - 10.3898i) q^{4} +(3.35774 - 2.43954i) q^{5} +(7.08028 - 2.30052i) q^{7} +(25.4416 + 8.26648i) q^{8} +O(q^{10})$	\(q+(-2.27075 + 3.12541i) q^{2} +(-3.37586 - 10.3898i) q^{4} +(3.35774 - 2.43954i) q^{5} +(7.08028 - 2.30052i) q^{7} +(25.4416 + 8.26648i) q^{8} +16.0339i q^{10} +(-8.33649 - 7.17655i) q^{11} +(4.30510 - 5.92547i) q^{13} +(-8.88744 + 27.3527i) q^{14} +(-48.2552 + 35.0594i) q^{16} +(-2.10373 - 2.89553i) q^{17} +(28.5216 + 9.26724i) q^{19} +(-36.6816 - 26.6508i) q^{20} +(41.3598 - 9.75885i) q^{22} +20.6531 q^{23} +(-2.40236 + 7.39371i) q^{25} +(8.74374 + 26.9105i) q^{26} +(-47.8040 - 65.7966i) q^{28} +(16.3441 - 5.31051i) q^{29} +(-12.7620 - 9.27216i) q^{31} -123.425i q^{32} +13.8268 q^{34} +(18.1615 - 24.9972i) q^{35} +(-9.97336 - 30.6948i) q^{37} +(-93.7294 + 68.0984i) q^{38} +(105.593 - 34.3092i) q^{40} +(-15.4276 - 5.01273i) q^{41} +33.7299i q^{43} +(-46.4203 + 110.842i) q^{44} +(-46.8979 + 64.5494i) q^{46} +(12.0219 - 36.9995i) q^{47} +(5.19616 - 3.77523i) q^{49} +(-17.6532 - 24.2976i) q^{50} +(-76.0979 - 24.7257i) q^{52} +(-29.6211 - 21.5210i) q^{53} +(-45.4993 - 3.75979i) q^{55} +199.151 q^{56} +(-20.5157 + 63.1408i) q^{58} +(21.6165 + 66.5286i) q^{59} +(13.3727 + 18.4060i) q^{61} +(57.9586 - 18.8319i) q^{62} +(192.733 + 140.029i) q^{64} -30.3987i q^{65} -63.0682 q^{67} +(-22.9822 + 31.6323i) q^{68} +(36.8864 + 113.525i) q^{70} +(25.5595 - 18.5701i) q^{71} +(-98.3279 + 31.9487i) q^{73} +(118.581 + 38.5293i) q^{74} -327.620i q^{76} +(-75.5345 - 31.6337i) q^{77} +(10.7350 - 14.7755i) q^{79} +(-76.4994 + 235.441i) q^{80} +(50.6990 - 36.8350i) q^{82} +(69.9409 + 96.2654i) q^{83} +(-14.1276 - 4.59032i) q^{85} +(-105.420 - 76.5919i) q^{86} +(-152.769 - 251.496i) q^{88} -154.739 q^{89} +(16.8497 - 51.8580i) q^{91} +(-69.7218 - 214.581i) q^{92} +(88.3402 + 121.590i) q^{94} +(118.376 - 38.4627i) q^{95} +(55.9976 + 40.6846i) q^{97} +24.8128i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 30 q^{7}+O(q^{10}) $ 16 * q - 4 * q^4 + 30 * q^7	$ 16 q - 4 q^{4} + 30 q^{7} - 30 q^{13} - 176 q^{16} + 90 q^{22} - 74 q^{25} - 50 q^{28} + 130 q^{31} + 328 q^{34} + 90 q^{37} + 450 q^{40} - 370 q^{46} - 54 q^{49} - 790 q^{52} - 476 q^{55} - 630 q^{58} + 210 q^{61} + 1104 q^{64} + 300 q^{67} + 268 q^{70} - 170 q^{73} + 30 q^{79} + 90 q^{82} - 610 q^{85} - 600 q^{88} - 402 q^{91} + 1030 q^{94} + 870 q^{97}+O(q^{100}) $ 16 * q - 4 * q^4 + 30 * q^7 - 30 * q^13 - 176 * q^16 + 90 * q^22 - 74 * q^25 - 50 * q^28 + 130 * q^31 + 328 * q^34 + 90 * q^37 + 450 * q^40 - 370 * q^46 - 54 * q^49 - 790 * q^52 - 476 * q^55 - 630 * q^58 + 210 * q^61 + 1104 * q^64 + 300 * q^67 + 268 * q^70 - 170 * q^73 + 30 * q^79 + 90 * q^82 - 610 * q^85 - 600 * q^88 - 402 * q^91 + 1030 * q^94 + 870 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	−2.27075	+	3.12541i	−1.13537	+	1.56271i	−0.357936	+	0.933746i	$0.616519\pi$
$2$	−2.27075	+	3.12541i	−1.13537	+	1.56271i	−0.777437	+	0.628961i	$0.783481\pi$
$3$		0			0
$3$		0			0
$4$	−3.37586	−	10.3898i	−0.843964	−	2.59745i
$5$	3.35774	−	2.43954i	0.671548	−	0.487908i	−0.198995	−	0.980001i	$-0.563768\pi$
$5$	3.35774	−	2.43954i	0.671548	−	0.487908i	0.870543	+	0.492092i	$0.163768\pi$
$6$		0			0
$7$	7.08028	−	2.30052i	1.01147	−	0.328646i	0.244030	−	0.969768i	$-0.421531\pi$
$7$	7.08028	−	2.30052i	1.01147	−	0.328646i	0.767439	+	0.641122i	$0.221531\pi$
$8$	25.4416	+	8.26648i	3.18020	+	1.03331i
$9$		0			0
$10$			16.0339i			1.60339i
$11$	−8.33649	−	7.17655i	−0.757863	−	0.652414i
$11$	−8.33649	−	7.17655i	−0.757863	−	0.652414i
$12$		0			0
$13$	4.30510	−	5.92547i	0.331162	−	0.455805i	−0.610672	−	0.791884i	$-0.709101\pi$
$13$	4.30510	−	5.92547i	0.331162	−	0.455805i	0.941834	+	0.336078i	$0.109101\pi$
$14$	−8.88744	+	27.3527i	−0.634817	+	1.95377i
$15$		0			0
$16$	−48.2552	+	35.0594i	−3.01595	+	2.19121i
$17$	−2.10373	−	2.89553i	−0.123749	−	0.170326i	0.742648	−	0.669682i	$-0.233570\pi$
$17$	−2.10373	−	2.89553i	−0.123749	−	0.170326i	−0.866396	+	0.499357i	$0.833570\pi$
$18$		0			0
$19$	28.5216	+	9.26724i	1.50114	+	0.487750i	0.940350	−	0.340209i	$-0.110498\pi$
$19$	28.5216	+	9.26724i	1.50114	+	0.487750i	0.560789	+	0.827958i	$0.310498\pi$
$20$	−36.6816	−	26.6508i	−1.83408	−	1.33254i
$21$		0			0
$22$	41.3598	−	9.75885i	1.87999	−	0.443584i
$23$	20.6531			0.897959			0.448980	−	0.893542i	$-0.351788\pi$
$23$	20.6531			0.897959			0.448980	+	0.893542i	$0.351788\pi$
$24$		0			0
$25$	−2.40236	+	7.39371i	−0.0960944	+	0.295748i
$26$	8.74374	+	26.9105i	0.336298	+	1.03502i
$27$		0			0
$28$	−47.8040	−	65.7966i	−1.70729	−	2.34988i
$29$	16.3441	−	5.31051i	0.563589	−	0.183121i	−0.0133465	−	0.999911i	$-0.504248\pi$
$29$	16.3441	−	5.31051i	0.563589	−	0.183121i	0.576935	+	0.816790i	$0.304248\pi$
$30$		0			0
$31$	−12.7620	−	9.27216i	−0.411678	−	0.299102i	0.362603	−	0.931944i	$-0.381888\pi$
$31$	−12.7620	−	9.27216i	−0.411678	−	0.299102i	−0.774281	+	0.632842i	$0.781888\pi$
$32$		−	123.425i		−	3.85703i
$33$		0			0
$34$	13.8268			0.406670
$35$	18.1615	−	24.9972i	0.518901	−	0.714206i
$36$		0			0
$37$	−9.97336	−	30.6948i	−0.269550	−	0.829590i	−0.990610	−	0.136718i	$-0.956345\pi$
$37$	−9.97336	−	30.6948i	−0.269550	−	0.829590i	0.721060	−	0.692873i	$-0.243655\pi$
$38$	−93.7294	+	68.0984i	−2.46656	+	1.79206i
$39$		0			0
$40$	105.593	−	34.3092i	2.63982	−	0.857729i
$41$	−15.4276	−	5.01273i	−0.376283	−	0.122262i	0.114769	−	0.993392i	$-0.463387\pi$
$41$	−15.4276	−	5.01273i	−0.376283	−	0.122262i	−0.491052	+	0.871130i	$0.663387\pi$
$42$		0			0
$43$			33.7299i			0.784415i	0.919877	+	0.392208i	$0.128289\pi$
$43$			33.7299i			0.784415i	−0.919877	+	0.392208i	$0.871711\pi$
$44$	−46.4203	+	110.842i	−1.05501	+	2.51913i
$45$		0			0
$46$	−46.8979	+	64.5494i	−1.01952	+	1.40325i
$47$	12.0219	−	36.9995i	0.255785	−	0.787224i	−0.737889	−	0.674922i	$-0.764177\pi$
$47$	12.0219	−	36.9995i	0.255785	−	0.787224i	0.993674	−	0.112303i	$-0.0358226\pi$
$48$		0			0
$49$	5.19616	−	3.77523i	0.106044	−	0.0770456i
$50$	−17.6532	−	24.2976i	−0.353065	−	0.485952i
$51$		0			0
$52$	−76.0979	−	24.7257i	−1.46342	−	0.475495i
$53$	−29.6211	−	21.5210i	−0.558889	−	0.406056i	0.272163	−	0.962251i	$-0.412261\pi$
$53$	−29.6211	−	21.5210i	−0.558889	−	0.406056i	−0.831052	+	0.556195i	$0.812261\pi$
$54$		0			0
$55$	−45.4993	−	3.75979i	−0.827260	−	0.0683599i
$56$	199.151			3.55627
$57$		0			0
$58$	−20.5157	+	63.1408i	−0.353719	+	1.08863i
$59$	21.6165	+	66.5286i	0.366381	+	1.12760i	0.949112	+	0.314939i	$0.101984\pi$
$59$	21.6165	+	66.5286i	0.366381	+	1.12760i	−0.582731	+	0.812665i	$0.698016\pi$
$60$		0			0
$61$	13.3727	+	18.4060i	0.219225	+	0.301738i	0.904438	−	0.426605i	$-0.140291\pi$
$61$	13.3727	+	18.4060i	0.219225	+	0.301738i	−0.685213	+	0.728343i	$0.740291\pi$
$62$	57.9586	−	18.8319i	0.934817	−	0.303740i
$63$		0			0
$64$	192.733	+	140.029i	3.01145	+	2.18795i
$65$		−	30.3987i		−	0.467672i
$66$		0			0
$67$	−63.0682			−0.941317			−0.470658	−	0.882315i	$-0.655984\pi$
$67$	−63.0682			−0.941317			−0.470658	+	0.882315i	$0.655984\pi$
$68$	−22.9822	+	31.6323i	−0.337973	+	0.465180i
$69$		0			0
$70$	36.8864	+	113.525i	0.526948	+	1.62178i
$71$	25.5595	−	18.5701i	0.359993	−	0.261550i	−0.393056	−	0.919514i	$-0.628582\pi$
$71$	25.5595	−	18.5701i	0.359993	−	0.261550i	0.753049	+	0.657964i	$0.228582\pi$
$72$		0			0
$73$	−98.3279	+	31.9487i	−1.34696	+	0.437653i	−0.891668	−	0.452690i	$-0.850464\pi$
$73$	−98.3279	+	31.9487i	−1.34696	+	0.437653i	−0.455290	+	0.890343i	$0.650464\pi$
$74$	118.581	+	38.5293i	1.60245	+	0.520666i
$75$		0			0
$76$		−	327.620i		−	4.31078i
$77$	−75.5345	−	31.6337i	−0.980968	−	0.410828i
$78$		0			0
$79$	10.7350	−	14.7755i	0.135886	−	0.187031i	−0.735651	−	0.677361i	$-0.763124\pi$
$79$	10.7350	−	14.7755i	0.135886	−	0.187031i	0.871537	+	0.490330i	$0.163124\pi$
$80$	−76.4994	+	235.441i	−0.956243	+	2.94301i
$81$		0			0
$82$	50.6990	−	36.8350i	0.618281	−	0.449207i
$83$	69.9409	+	96.2654i	0.842662	+	1.15982i	0.985432	+	0.170068i	$0.0543989\pi$
$83$	69.9409	+	96.2654i	0.842662	+	1.15982i	−0.142771	+	0.989756i	$0.545601\pi$
$84$		0			0
$85$	−14.1276	−	4.59032i	−0.166207	−	0.0540038i
$86$	−105.420	−	76.5919i	−1.22581	−	0.890604i
$87$		0			0
$88$	−152.769	−	251.496i	−1.73601	−	2.85791i
$89$	−154.739			−1.73864			−0.869320	−	0.494249i	$-0.835443\pi$
$89$	−154.739			−1.73864			−0.869320	+	0.494249i	$0.835443\pi$
$90$		0			0
$91$	16.8497	−	51.8580i	0.185161	−	0.569868i
$92$	−69.7218	−	214.581i	−0.757845	−	2.33241i
$93$		0			0
$94$	88.3402	+	121.590i	0.939790	+	1.29351i
$95$	118.376	−	38.4627i	1.24606	−	0.404871i
$96$		0			0
$97$	55.9976	+	40.6846i	0.577295	+	0.419429i	0.837748	−	0.546057i	$-0.183872\pi$
$97$	55.9976	+	40.6846i	0.577295	+	0.419429i	−0.260453	+	0.965486i	$0.583872\pi$
$98$			24.8128i			0.253191i
$99$		0			0
$100$	84.9293			0.849293
$101$	−80.6133	+	110.955i	−0.798151	+	1.09856i	0.194893	+	0.980824i	$0.437564\pi$
$101$	−80.6133	+	110.955i	−0.798151	+	1.09856i	−0.993045	+	0.117737i	$0.962436\pi$
$102$		0			0
$103$	6.34152	+	19.5172i	0.0615681	+	0.189487i	0.977110	−	0.212736i	$-0.0682375\pi$
$103$	6.34152	+	19.5172i	0.0615681	+	0.189487i	−0.915542	+	0.402223i	$0.868238\pi$
$104$	158.512	−	115.165i	1.52415	−	1.10736i
$105$		0			0
$106$	134.524	−	43.7095i	1.26909	−	0.412354i
$107$	56.4914	+	18.3552i	0.527957	+	0.171544i	0.560853	−	0.827915i	$-0.310473\pi$
$107$	56.4914	+	18.3552i	0.527957	+	0.171544i	−0.0328965	+	0.999459i	$0.510473\pi$
$108$		0			0
$109$		−	37.5085i		−	0.344115i	−0.985087	−	0.172058i	$-0.944958\pi$
$109$		−	37.5085i		−	0.344115i	0.985087	−	0.172058i	$-0.0550415\pi$
$110$	115.068	−	133.667i	1.04607	−	1.21515i
$111$		0			0
$112$	−261.005	+	359.243i	−2.33040	+	3.20752i
$113$	36.2025	−	111.420i	0.320376	−	0.986017i	−0.653108	−	0.757264i	$-0.726535\pi$
$113$	36.2025	−	111.420i	0.320376	−	0.986017i	0.973485	−	0.228752i	$-0.0734646\pi$
$114$		0			0
$115$	69.3477	−	50.3840i	0.603023	−	0.438122i
$116$	−110.350	−	151.884i	−0.951297	−	1.30935i
$117$		0			0
$118$	−257.015	−	83.5092i	−2.17809	−	0.707705i
$119$	−21.5562	−	15.6615i	−0.181145	−	0.131609i
$120$		0			0
$121$	17.9942	+	119.655i	0.148712	+	0.988881i
$122$	−87.8925			−0.720430
$123$		0			0
$124$	−53.2532	+	163.897i	−0.429461	+	1.32175i
$125$	42.0343	+	129.368i	0.336275	+	1.03495i
$126$		0			0
$127$	−17.9042	−	24.6430i	−0.140978	−	0.194039i	0.732690	−	0.680563i	$-0.238265\pi$
$127$	−17.9042	−	24.6430i	−0.140978	−	0.194039i	−0.873667	+	0.486524i	$0.838265\pi$
$128$	−405.760	+	131.839i	−3.17000	+	1.02999i
$129$		0			0
$130$	95.0085	+	69.0277i	0.730834	+	0.530982i
$131$			179.208i			1.36800i	0.729482	+	0.684000i	$0.239761\pi$
$131$			179.208i			1.36800i	−0.729482	+	0.684000i	$0.760239\pi$
$132$		0			0
$133$	223.261			1.67865
$134$	143.212	−	197.114i	1.06875	−	1.47100i
$135$		0			0
$136$	−29.5864	−	91.0575i	−0.217547	−	0.669540i
$137$	−155.409	+	112.911i	−1.13437	+	0.824169i	−0.986325	−	0.164811i	$-0.947299\pi$
$137$	−155.409	+	112.911i	−1.13437	+	0.824169i	−0.148046	+	0.988980i	$0.547299\pi$
$138$		0			0
$139$	23.3701	−	7.59342i	0.168130	−	0.0546289i	−0.223742	−	0.974648i	$-0.571827\pi$
$139$	23.3701	−	7.59342i	0.168130	−	0.0546289i	0.391873	+	0.920019i	$0.371827\pi$
$140$	−321.027	−	104.308i	−2.29305	−	0.745057i
$141$		0			0
$142$			122.052i			0.859520i
$143$	−78.4139	+	18.5018i	−0.548349	+	0.129383i
$144$		0			0
$145$	41.9240	−	57.7034i	0.289131	−	0.397954i
$146$	123.425	−	379.863i	0.845376	−	2.60180i
$147$		0			0
$148$	−285.245	+	207.243i	−1.92733	+	1.40029i
$149$	16.9485	+	23.3276i	0.113749	+	0.156561i	0.862095	−	0.506746i	$-0.169152\pi$
$149$	16.9485	+	23.3276i	0.113749	+	0.156561i	−0.748347	+	0.663308i	$0.769152\pi$
$150$		0			0
$151$	133.588	+	43.4054i	0.884690	+	0.287453i	0.715903	−	0.698200i	$-0.246015\pi$
$151$	133.588	+	43.4054i	0.884690	+	0.287453i	0.168786	+	0.985653i	$0.446015\pi$
$152$	649.029	+	471.547i	4.26993	+	3.10228i
$153$		0			0
$154$	270.388	−	164.245i	1.75577	−	1.06652i
$155$	−65.4714			−0.422396
$156$		0			0
$157$	81.8222	−	251.823i	0.521160	−	1.60397i	−0.250626	−	0.968084i	$-0.580636\pi$
$157$	81.8222	−	251.823i	0.521160	−	1.60397i	0.771786	−	0.635882i	$-0.219364\pi$
$158$	21.8030	+	67.1026i	0.137993	+	0.424700i
$159$		0			0
$160$	−301.100	−	414.429i	−1.88188	−	2.59018i
$161$	146.230	−	47.5129i	0.908258	−	0.295111i
$162$		0			0
$163$	−51.9749	−	37.7620i	−0.318864	−	0.231668i	0.416826	−	0.908986i	$-0.363142\pi$
$163$	−51.9749	−	37.7620i	−0.318864	−	0.231668i	−0.735691	+	0.677318i	$0.763142\pi$
$164$			177.212i			1.08056i
$165$		0			0
$166$	−459.687			−2.76920
$167$	67.5175	−	92.9299i	0.404297	−	0.556467i	−0.557519	−	0.830164i	$-0.688247\pi$
$167$	67.5175	−	92.9299i	0.404297	−	0.556467i	0.961816	+	0.273697i	$0.0882467\pi$
$168$		0			0
$169$	35.6466	+	109.709i	0.210927	+	0.649166i
$170$	46.4267	−	33.7310i	0.273098	−	0.198418i
$171$		0			0
$172$	350.447	−	113.867i	2.03748	−	0.662018i
$173$	−222.310	−	72.2328i	−1.28503	−	0.417530i	−0.414679	−	0.909968i	$-0.636106\pi$
$173$	−222.310	−	72.2328i	−1.28503	−	0.417530i	−0.870348	+	0.492437i	$0.836106\pi$
$174$		0			0
$175$			57.8762i			0.330721i
$176$	653.885	+	54.0332i	3.71525	+	0.307007i
$177$		0			0
$178$	351.373	−	483.623i	1.97401	−	2.71699i
$179$	68.7137	−	211.479i	0.383875	−	1.18145i	−0.553418	−	0.832904i	$-0.686677\pi$
$179$	68.7137	−	211.479i	0.383875	−	1.18145i	0.937293	−	0.348543i	$-0.113323\pi$
$180$		0			0
$181$	−217.959	+	158.357i	−1.20420	+	0.874899i	−0.994691	−	0.102909i	$-0.967185\pi$
$181$	−217.959	+	158.357i	−1.20420	+	0.874899i	−0.209504	+	0.977808i	$0.567185\pi$
$182$	123.816	+	170.419i	0.680309	+	0.936366i
$183$		0			0
$184$	525.447	+	170.728i	2.85569	+	0.927870i
$185$	−108.369	−	78.7349i	−0.585780	−	0.425594i
$186$		0			0
$187$	−3.24224	+	39.2361i	−0.0173382	+	0.209819i
$188$	−425.003			−2.26065
$189$		0			0
$190$	−148.590	+	457.314i	−0.782054	+	2.40691i
$191$	75.6944	+	232.963i	0.396306	+	1.21970i	0.927940	+	0.372730i	$0.121578\pi$
$191$	75.6944	+	232.963i	0.396306	+	1.21970i	−0.531634	+	0.846974i	$0.678422\pi$
$192$		0			0
$193$	−154.854	−	213.138i	−0.802350	−	1.10434i	−0.992459	−	0.122577i	$-0.960884\pi$
$193$	−154.854	−	213.138i	−0.802350	−	1.10434i	0.190109	−	0.981763i	$-0.439116\pi$
$194$	−254.313	+	82.6311i	−1.31089	+	0.425934i
$195$		0			0
$196$	−56.7655	−	41.2425i	−0.289620	−	0.210421i
$197$			256.209i			1.30055i	0.759697	+	0.650277i	$0.225347\pi$
$197$			256.209i			1.30055i	−0.759697	+	0.650277i	$0.774653\pi$
$198$		0			0
$199$	−7.63062			−0.0383448			−0.0191724	−	0.999816i	$-0.506103\pi$
$199$	−7.63062			−0.0383448			−0.0191724	+	0.999816i	$0.506103\pi$
$200$	−122.240	+	168.249i	−0.611199	+	0.841243i
$201$		0			0
$202$	−163.727	−	503.900i	−0.810530	−	2.49455i
$203$	103.504	−	75.1998i	0.509871	−	0.370443i
$204$		0			0
$205$	−64.0307	+	20.8048i	−0.312345	+	0.101487i
$206$	−75.3992	−	24.4987i	−0.366016	−	0.118926i
$207$		0			0
$208$			436.869i			2.10033i
$209$	−171.264	−	281.943i	−0.819443	−	1.34901i
$210$		0			0
$211$	−220.767	+	303.859i	−1.04629	+	1.44009i	−0.154304	+	0.988023i	$0.549313\pi$
$211$	−220.767	+	303.859i	−1.04629	+	1.44009i	−0.891984	+	0.452068i	$0.850687\pi$
$212$	−123.603	+	380.409i	−0.583031	+	1.79438i
$213$		0			0
$214$	−185.645	+	134.879i	−0.867500	+	0.630276i
$215$	82.2854	+	113.256i	0.382723	+	0.526773i
$216$		0			0
$217$	−111.690	−	36.2901i	−0.514699	−	0.167236i
$218$	117.230	+	85.1724i	0.537751	+	0.390699i
$219$		0			0
$220$	114.535	+	485.422i	0.520616	+	2.20646i
$221$	−26.2142			−0.118616
$222$		0			0
$223$	−8.70970	+	26.8057i	−0.0390569	+	0.120205i	−0.968684	−	0.248297i	$-0.920129\pi$
$223$	−8.70970	+	26.8057i	−0.0390569	+	0.120205i	0.929627	+	0.368502i	$0.120129\pi$
$224$	−283.942	−	873.883i	−1.26760	−	3.90126i
$225$		0			0
$226$	266.027	+	366.154i	1.17711	+	1.62015i
$227$	259.220	−	84.2257i	1.14194	−	0.371038i	0.323838	−	0.946113i	$-0.395027\pi$
$227$	259.220	−	84.2257i	1.14194	−	0.371038i	0.818101	+	0.575074i	$0.195027\pi$
$228$		0			0
$229$	−0.477513	−	0.346934i	−0.00208521	−	0.00151499i	0.586742	−	0.809774i	$-0.300410\pi$
$229$	−0.477513	−	0.346934i	−0.00208521	−	0.00151499i	−0.588827	+	0.808259i	$0.700410\pi$
$230$			331.149i			1.43978i
$231$		0			0
$232$	459.719			1.98155
$233$	109.069	−	150.121i	0.468107	−	0.644294i	−0.508058	−	0.861323i	$-0.669637\pi$
$233$	109.069	−	150.121i	0.468107	−	0.644294i	0.976165	+	0.217029i	$0.0696365\pi$
$234$		0			0
$235$	−49.8956	−	153.563i	−0.212322	−	0.653459i
$236$	618.246	−	449.182i	2.61969	−	1.90331i
$237$		0			0
$238$	97.8975	−	31.8088i	0.411334	−	0.133650i
$239$	256.033	+	83.1901i	1.07127	+	0.348076i	0.790981	−	0.611841i	$-0.209571\pi$
$239$	256.033	+	83.1901i	1.07127	+	0.348076i	0.280286	+	0.959917i	$0.409571\pi$
$240$		0			0
$241$			249.403i			1.03487i	0.855723	+	0.517434i	$0.173113\pi$
$241$			249.403i			1.03487i	−0.855723	+	0.517434i	$0.826887\pi$
$242$	−414.830	−	215.466i	−1.71417	−	0.890355i
$243$		0			0
$244$	146.091	−	201.076i	0.598732	−	0.824083i
$245$	8.23754	−	25.3525i	0.0336226	−	0.103480i
$246$		0			0
$247$	177.701	−	129.108i	0.719439	−	0.522703i
$248$	−248.038	−	341.396i	−1.00015	−	1.37659i
$249$		0			0
$250$	−499.779	−	162.388i	−1.99912	−	0.649552i
$251$	−259.715	−	188.694i	−1.03472	−	0.751769i	−0.0654735	−	0.997854i	$-0.520856\pi$
$251$	−259.715	−	188.694i	−1.03472	−	0.751769i	−0.969248	+	0.246085i	$0.920856\pi$
$252$		0			0
$253$	−172.174	−	148.218i	−0.680530	−	0.585841i
$254$	117.675			0.463289
$255$		0			0
$256$	214.855	−	661.255i	0.839277	−	2.58303i
$257$	−3.55693	−	10.9471i	−0.0138402	−	0.0425958i	0.943898	−	0.330237i	$-0.107129\pi$
$257$	−3.55693	−	10.9471i	−0.0138402	−	0.0425958i	−0.957738	+	0.287642i	$0.907129\pi$
$258$		0			0
$259$	−141.228	−	194.384i	−0.545283	−	0.750518i
$260$	−315.837	+	102.622i	−1.21476	+	0.394698i
$261$		0			0
$262$	−560.099	−	406.936i	−2.13778	−	1.55319i
$263$			184.999i			0.703417i	0.936110	+	0.351708i	$0.114399\pi$
$263$			184.999i			0.703417i	−0.936110	+	0.351708i	$0.885601\pi$
$264$		0			0
$265$	−151.961			−0.573439
$266$	−506.969	+	697.782i	−1.90590	+	2.62324i
$267$		0			0
$268$	212.909	+	655.267i	0.794437	+	2.44503i
$269$	−195.906	+	142.334i	−0.728275	+	0.529123i	−0.889017	−	0.457874i	$-0.848611\pi$
$269$	−195.906	+	142.334i	−0.728275	+	0.529123i	0.160742	+	0.986996i	$0.448611\pi$
$270$		0			0
$271$	−232.047	+	75.3968i	−0.856264	+	0.278217i	−0.704067	−	0.710133i	$-0.748635\pi$
$271$	−232.047	+	75.3968i	−0.856264	+	0.278217i	−0.152196	+	0.988350i	$0.548635\pi$
$272$	203.032	+	65.9689i	0.746439	+	0.242533i
$273$		0			0
$274$		−	742.110i		−	2.70843i
$275$	73.0886	−	44.3969i	0.265777	−	0.161443i
$276$		0			0
$277$	−84.7199	+	116.607i	−0.305848	+	0.420964i	−0.934081	−	0.357062i	$-0.883779\pi$
$277$	−84.7199	+	116.607i	−0.305848	+	0.420964i	0.628233	+	0.778025i	$0.283779\pi$
$278$	−29.3351	+	90.2841i	−0.105522	+	0.324763i
$279$		0			0
$280$	668.698	−	485.837i	2.38821	−	1.73513i
$281$	−211.176	−	290.658i	−0.751515	−	1.03437i	−0.997873	−	0.0651923i	$-0.979234\pi$
$281$	−211.176	−	290.658i	−0.751515	−	1.03437i	0.246358	−	0.969179i	$-0.420766\pi$
$282$		0			0
$283$	421.847	+	137.066i	1.49063	+	0.484334i	0.937268	−	0.348610i	$-0.113346\pi$
$283$	421.847	+	137.066i	1.49063	+	0.484334i	0.553358	+	0.832944i	$0.313346\pi$
$284$	−279.225	−	202.869i	−0.983186	−	0.714326i
$285$		0			0
$286$	120.232	−	287.089i	0.420393	−	1.00381i
$287$	−120.764			−0.420780
$288$		0			0
$289$	85.3475	−	262.672i	0.295320	−	0.908901i
$290$	85.1483	+	262.059i	0.293615	+	0.903653i
$291$		0			0
$292$	663.882	+	913.755i	2.27357	+	3.12930i
$293$	489.461	−	159.035i	1.67051	−	0.542783i	0.687480	−	0.726203i	$-0.258717\pi$
$293$	489.461	−	159.035i	1.67051	−	0.542783i	0.983035	+	0.183420i	$0.0587169\pi$
$294$		0			0
$295$	234.882	+	170.652i	0.796210	+	0.578480i
$296$		−	863.371i		−	2.91679i
$297$		0			0
$298$	−111.394			−0.373807
$299$	88.9136	−	122.379i	0.297370	−	0.409295i
$300$		0			0
$301$	77.5963	+	238.817i	0.257795	+	0.793412i
$302$	−439.005	+	318.955i	−1.45366	+	1.05614i
$303$		0			0
$304$	−1701.22	+	552.760i	−5.59612	+	1.81829i
$305$	89.8045	+	29.1792i	0.294441	+	0.0956696i
$306$		0			0
$307$		−	145.625i		−	0.474349i	−0.971467	−	0.237175i	$-0.923779\pi$
$307$		−	145.625i		−	0.474349i	0.971467	−	0.237175i	$-0.0762214\pi$
$308$	−73.6750	+	891.581i	−0.239204	+	2.89474i
$309$		0			0
$310$	148.669	−	204.625i	0.479577	−	0.660081i
$311$	122.477	−	376.945i	0.393816	−	1.21204i	−0.536063	−	0.844178i	$-0.680089\pi$
$311$	122.477	−	376.945i	0.393816	−	1.21204i	0.929879	−	0.367864i	$-0.119911\pi$
$312$		0			0
$313$	243.255	−	176.735i	0.777173	−	0.564649i	−0.126956	−	0.991908i	$-0.540521\pi$
$313$	243.255	−	176.735i	0.777173	−	0.564649i	0.904129	+	0.427259i	$0.140521\pi$
$314$	601.253	+	827.554i	1.91482	+	2.63552i
$315$		0			0
$316$	−189.754	−	61.6548i	−0.600488	−	0.195110i
$317$	218.488	+	158.741i	0.689236	+	0.500760i	0.876409	−	0.481567i	$-0.159932\pi$
$317$	218.488	+	158.741i	0.689236	+	0.500760i	−0.187173	+	0.982327i	$0.559932\pi$
$318$		0			0
$319$	−174.363	−	73.0231i	−0.546594	−	0.228913i
$320$	988.754			3.08986
$321$		0			0
$322$	−183.553	+	564.917i	−0.570040	+	1.75440i
$323$	−33.1682	−	102.081i	−0.102688	−	0.316041i
$324$		0			0
$325$	33.4688	+	46.0658i	0.102981	+	0.141741i
$326$	236.043	−	76.6952i	0.724060	−	0.235261i
$327$		0			0
$328$	−351.065	−	255.064i	−1.07032	−	0.777634i
$329$		−	289.624i		−	0.880316i
$330$		0			0
$331$	172.536			0.521257			0.260629	−	0.965439i	$-0.416070\pi$
$331$	172.536			0.521257			0.260629	+	0.965439i	$0.416070\pi$
$332$	764.069	−	1051.65i	2.30141	−	3.16762i
$333$		0			0
$334$	137.129	+	422.040i	0.410567	+	1.26359i
$335$	−211.767	+	153.858i	−0.632140	+	0.459276i
$336$		0			0
$337$	262.811	−	85.3923i	0.779853	−	0.253390i	0.108076	−	0.994143i	$-0.465531\pi$
$337$	262.811	−	85.3923i	0.779853	−	0.253390i	0.671777	+	0.740753i	$0.265531\pi$
$338$	−423.830	−	137.711i	−1.25394	−	0.407429i
$339$		0			0
$340$			162.279i			0.477291i
$341$	39.8484	+	168.885i	0.116857	+	0.495263i
$342$		0			0
$343$	−186.312	+	256.436i	−0.543183	+	0.747627i
$344$	−278.827	+	858.142i	−0.810544	+	2.49460i
$345$		0			0
$346$	730.566	−	530.787i	2.11146	−	1.53407i
$347$	84.9201	+	116.883i	0.244727	+	0.336837i	0.913656	−	0.406489i	$-0.133247\pi$
$347$	84.9201	+	116.883i	0.244727	+	0.336837i	−0.668929	+	0.743326i	$0.733247\pi$
$348$		0			0
$349$	140.652	+	45.7007i	0.403015	+	0.130948i	0.503509	−	0.863990i	$-0.332042\pi$
$349$	140.652	+	45.7007i	0.403015	+	0.130948i	−0.100494	+	0.994938i	$0.532042\pi$
$350$	−180.887	−	131.422i	−0.516820	−	0.375492i
$351$		0			0
$352$	−885.765	+	1028.93i	−2.51638	+	2.92310i
$353$	−24.8683			−0.0704485			−0.0352243	−	0.999379i	$-0.511215\pi$
$353$	−24.8683			−0.0704485			−0.0352243	+	0.999379i	$0.511215\pi$
$354$		0			0
$355$	40.5197	−	124.707i	0.114140	−	0.351287i
$356$	522.377	+	1607.71i	1.46735	+	4.51604i
$357$		0			0
$358$	504.928	+	694.973i	1.41041	+	1.94127i
$359$	−222.237	+	72.2091i	−0.619044	+	0.201140i	−0.601716	−	0.798710i	$-0.705516\pi$
$359$	−222.237	+	72.2091i	−0.619044	+	0.201140i	−0.0173283	+	0.999850i	$0.505516\pi$
$360$		0			0
$361$	435.547	+	316.444i	1.20650	+	0.876575i
$362$		−	1040.80i		−	2.87514i
$363$		0			0
$364$	−595.677			−1.63648
$365$	−252.220	+	347.150i	−0.691013	+	0.951097i
$366$		0			0
$367$	−169.389	−	521.325i	−0.461550	−	1.42050i	−0.863271	−	0.504741i	$-0.831588\pi$
$367$	−169.389	−	521.325i	−0.461550	−	1.42050i	0.401721	−	0.915762i	$-0.368412\pi$
$368$	−996.617	+	724.085i	−2.70820	+	1.96762i
$369$		0			0
$370$	492.158	−	159.912i	1.33016	−	0.432195i
$371$	−259.235	−	84.2306i	−0.698747	−	0.227037i
$372$		0			0
$373$		−	84.3957i		−	0.226262i	−0.993580	−	0.113131i	$-0.963912\pi$
$373$		−	84.3957i		−	0.226262i	0.993580	−	0.113131i	$-0.0360879\pi$
$374$	−115.267	−	99.2286i	−0.308200	−	0.265317i
$375$		0			0
$376$	611.712	−	841.949i	1.62689	−	2.23923i
$377$	38.8957	−	119.709i	0.103172	−	0.317529i
$378$		0			0
$379$	−108.721	+	78.9901i	−0.286862	+	0.208417i	−0.721905	−	0.691993i	$-0.756733\pi$
$379$	−108.721	+	78.9901i	−0.286862	+	0.208417i	0.435043	+	0.900410i	$0.356733\pi$
$380$	−799.242	−	1100.06i	−2.10327	−	2.89490i
$381$		0			0
$382$	−899.990	−	292.424i	−2.35599	−	0.765509i
$383$	−334.786	−	243.236i	−0.874114	−	0.635081i	0.0575737	−	0.998341i	$-0.481664\pi$
$383$	−334.786	−	243.236i	−0.874114	−	0.635081i	−0.931688	+	0.363260i	$0.881664\pi$
$384$		0			0
$385$	−330.797	+	78.0518i	−0.859214	+	0.202732i
$386$	1017.78			2.63673
$387$		0			0
$388$	233.666	−	719.150i	0.602232	−	1.85348i
$389$	66.3903	+	204.328i	0.170669	+	0.525266i	0.999409	−	0.0343680i	$-0.0109418\pi$
$389$	66.3903	+	204.328i	0.170669	+	0.525266i	−0.828740	+	0.559634i	$0.810942\pi$
$390$		0			0
$391$	−43.4484	−	59.8016i	−0.111121	−	0.152945i
$392$	163.407	−	53.0940i	0.416854	−	0.135444i
$393$		0			0
$394$	−800.759	−	581.786i	−2.03238	−	1.47661i
$395$		−	75.8007i		−	0.191900i
$396$		0			0
$397$	633.921			1.59678			0.798389	−	0.602142i	$-0.205686\pi$
$397$	633.921			1.59678			0.798389	+	0.602142i	$0.205686\pi$
$398$	17.3272	−	23.8488i	0.0435357	−	0.0599217i
$399$		0			0
$400$	−143.293	−	441.010i	−0.358232	−	1.10252i
$401$	256.209	−	186.147i	0.638926	−	0.464207i	−0.220555	−	0.975375i	$-0.570787\pi$
$401$	256.209	−	186.147i	0.638926	−	0.464207i	0.859481	+	0.511167i	$0.170787\pi$
$402$		0			0
$403$	−109.884	+	35.7034i	−0.272664	+	0.0885940i
$404$	1424.94	+	462.990i	3.52707	+	1.14602i
$405$		0			0
$406$			494.252i			1.21737i
$407$	−137.140	+	327.462i	−0.336954	+	0.804574i
$408$		0			0
$409$	222.429	−	306.148i	0.543837	−	0.748527i	−0.445323	−	0.895370i	$-0.646911\pi$
$409$	222.429	−	306.148i	0.543837	−	0.748527i	0.989160	+	0.146843i	$0.0469111\pi$
$410$	80.3737	−	247.365i	0.196033	−	0.603329i
$411$		0			0
$412$	181.372	−	131.774i	0.440223	−	0.319841i
$413$	306.101	+	421.312i	0.741166	+	1.02013i
$414$		0			0
$415$	469.687	+	152.611i	1.13178	+	0.367736i
$416$	−731.350	−	531.357i	−1.75805	−	1.27730i
$417$		0			0
$418$	1270.09	+	104.952i	3.03848	+	0.251082i
$419$	−187.826			−0.448273			−0.224137	−	0.974558i	$-0.571956\pi$
$419$	−187.826			−0.448273			−0.224137	+	0.974558i	$0.571956\pi$
$420$		0			0
$421$	−47.4276	+	145.967i	−0.112655	+	0.346715i	−0.991451	−	0.130482i	$-0.958347\pi$
$421$	−47.4276	+	145.967i	−0.112655	+	0.346715i	0.878796	+	0.477198i	$0.158347\pi$
$422$	−448.381	−	1379.97i	−1.06251	−	3.27008i
$423$		0			0
$424$	−575.705	−	792.391i	−1.35780	−	1.86885i
$425$	26.4626	−	8.59823i	0.0622650	−	0.0202311i
$426$		0			0
$427$	137.026	+	99.5554i	0.320905	+	0.233151i
$428$		−	648.899i		−	1.51612i
$429$		0			0
$430$	−540.822			−1.25772
$431$	−116.691	+	160.612i	−0.270745	+	0.372649i	−0.922641	−	0.385660i	$-0.873974\pi$
$431$	−116.691	+	160.612i	−0.270745	+	0.372649i	0.651896	+	0.758308i	$0.273974\pi$
$432$		0			0
$433$	25.5258	+	78.5605i	0.0589511	+	0.181433i	0.976196	−	0.216892i	$-0.0695918\pi$
$433$	25.5258	+	78.5605i	0.0589511	+	0.181433i	−0.917245	+	0.398324i	$0.869592\pi$
$434$	367.040	−	266.670i	0.845715	−	0.614448i
$435$		0			0
$436$	−389.707	+	126.623i	−0.893823	+	0.290421i
$437$	589.059	+	191.397i	1.34796	+	0.437979i
$438$		0			0
$439$		−	231.295i		−	0.526868i	−0.964677	−	0.263434i	$-0.915145\pi$
$439$		−	231.295i		−	0.526868i	0.964677	−	0.263434i	$-0.0848550\pi$
$440$	−1126.49	−	471.774i	−2.56022	−	1.07221i
$441$		0			0
$442$	59.5257	−	81.9301i	0.134674	−	0.185362i
$443$	−186.202	+	573.072i	−0.420321	+	1.29362i	0.487083	+	0.873356i	$0.338061\pi$
$443$	−186.202	+	573.072i	−0.420321	+	1.29362i	−0.907404	+	0.420259i	$0.861939\pi$
$444$		0			0
$445$	−519.574	+	377.492i	−1.16758	+	0.848297i
$446$	−64.0014	−	88.0903i	−0.143501	−	0.197512i
$447$		0			0
$448$	1686.74	+	548.056i	3.76505	+	1.22334i
$449$	215.793	+	156.783i	0.480608	+	0.349182i	0.801561	−	0.597913i	$-0.204003\pi$
$449$	215.793	+	156.783i	0.480608	+	0.349182i	−0.320953	+	0.947095i	$0.604003\pi$
$450$		0			0
$451$	92.6380	+	152.506i	0.205406	+	0.338150i
$452$	−1279.85			−2.83152
$453$		0			0
$454$	−325.383	+	1001.43i	−0.716702	+	2.20578i
$455$	−69.9329	−	215.231i	−0.153699	−	0.473036i
$456$		0			0
$457$	−480.092	−	660.790i	−1.05053	−	1.44593i	−0.888348	−	0.459170i	$-0.848147\pi$
$457$	−480.092	−	660.790i	−1.05053	−	1.44593i	−0.162182	−	0.986761i	$-0.551853\pi$
$458$	2.16862	−	0.704628i	0.00473499	−	0.00153849i
$459$		0			0
$460$	−757.588	−	550.420i	−1.64693	−	1.19657i
$461$			193.244i			0.419185i	0.977789	+	0.209592i	$0.0672137\pi$
$461$			193.244i			0.419185i	−0.977789	+	0.209592i	$0.932786\pi$
$462$		0			0
$463$	−530.341			−1.14545			−0.572723	−	0.819749i	$-0.694113\pi$
$463$	−530.341			−1.14545			−0.572723	+	0.819749i	$0.694113\pi$
$464$	−602.502	+	829.273i	−1.29850	+	1.78723i
$465$		0			0
$466$	221.521	+	681.771i	0.475367	+	1.46303i
$467$	−82.1324	+	59.6726i	−0.175872	+	0.127779i	−0.672239	−	0.740334i	$-0.734667\pi$
$467$	−82.1324	+	59.6726i	−0.175872	+	0.127779i	0.496367	+	0.868113i	$0.334667\pi$
$468$		0			0
$469$	−446.541	+	145.090i	−0.952113	+	0.309360i
$470$	593.247	+	192.758i	1.26223	+	0.410123i
$471$		0			0
$472$			1871.29i			3.96459i
$473$	242.064	−	281.189i	0.511763	−	0.594479i
$474$		0			0
$475$	−137.039	+	188.617i	−0.288502	+	0.397089i
$476$	−89.9496	+	276.836i	−0.188970	+	0.581589i
$477$		0			0
$478$	−841.389	+	611.305i	−1.76023	+	1.27888i
$479$	−276.910	−	381.134i	−0.578100	−	0.795686i	0.415386	−	0.909645i	$-0.363647\pi$
$479$	−276.910	−	381.134i	−0.578100	−	0.795686i	−0.993485	+	0.113959i	$0.963647\pi$
$480$		0			0
$481$	−224.818	−	73.0477i	−0.467396	−	0.151866i
$482$	−779.489	−	566.332i	−1.61720	−	1.17496i
$483$		0			0
$484$	1182.44	−	590.892i	2.44306	−	1.22085i
$485$	287.277			0.592324
$486$		0			0
$487$	221.332	−	681.191i	0.454481	−	1.39875i	−0.417262	−	0.908786i	$-0.637010\pi$
$487$	221.332	−	681.191i	0.454481	−	1.39875i	0.871743	−	0.489963i	$-0.162990\pi$
$488$	188.071	+	578.824i	0.385392	+	1.18611i
$489$		0			0
$490$	60.5318	+	83.3149i	0.123534	+	0.170030i
$491$	−763.104	+	247.948i	−1.55418	+	0.504985i	−0.955246	−	0.295811i	$-0.904410\pi$
$491$	−763.104	+	247.948i	−1.55418	+	0.504985i	−0.598937	+	0.800796i	$0.704410\pi$
$492$		0			0
$493$	−49.7603	−	36.1529i	−0.100934	−	0.0733326i
$494$			848.561i			1.71774i
$495$		0			0
$496$	940.910			1.89700
$497$	138.248	−	190.282i	0.278164	−	0.382860i
$498$		0			0
$499$	55.1167	+	169.632i	0.110454	+	0.339943i	0.990972	−	0.134070i	$-0.0428048\pi$
$499$	55.1167	+	169.632i	0.110454	+	0.339943i	−0.880518	+	0.474013i	$0.842805\pi$
$500$	1202.21	−	873.458i	2.40442	−	1.74692i
$501$		0			0
$502$	1179.49	−	383.241i	2.34959	−	0.763428i
$503$	−430.463	−	139.866i	−0.855792	−	0.278064i	−0.151922	−	0.988392i	$-0.548546\pi$
$503$	−430.463	−	139.866i	−0.855792	−	0.278064i	−0.703870	+	0.710329i	$0.748546\pi$
$504$		0			0
$505$			569.217i			1.12716i
$506$	854.206	−	201.550i	1.68815	−	0.398321i
$507$		0			0
$508$	−195.594	+	269.212i	−0.385028	+	0.529946i
$509$	−280.675	+	863.828i	−0.551424	+	1.69711i	0.153782	+	0.988105i	$0.450854\pi$
$509$	−280.675	+	863.828i	−0.551424	+	1.69711i	−0.705206	+	0.709002i	$0.749146\pi$
$510$		0			0
$511$	−622.691	+	452.411i	−1.21857	+	0.885345i
$512$	575.722	+	792.413i	1.12446	+	1.54768i
$513$		0			0
$514$	42.2911	+	13.7412i	0.0822785	+	0.0267339i
$515$	68.9061	+	50.0632i	0.133798	+	0.0972102i
$516$		0			0
$517$	−365.749	+	222.171i	−0.707446	+	0.429731i
$518$	928.225			1.79194
$519$		0			0
$520$	251.290	−	773.391i	0.483250	−	1.48729i
$521$	−79.4973	−	244.668i	−0.152586	−	0.469612i	0.845322	−	0.534257i	$-0.179408\pi$
$521$	−79.4973	−	244.668i	−0.152586	−	0.469612i	−0.997908	+	0.0646452i	$0.979408\pi$
$522$		0			0
$523$	125.048	+	172.114i	0.239097	+	0.329089i	0.911656	−	0.410955i	$-0.134805\pi$
$523$	125.048	+	172.114i	0.239097	+	0.329089i	−0.672559	+	0.740044i	$0.734805\pi$
$524$	1861.94	−	604.980i	3.55332	−	1.15454i
$525$		0			0
$526$	−578.197	−	420.085i	−1.09923	−	0.798641i
$527$			56.4590i			0.107133i
$528$		0			0
$529$	−102.451			−0.193669
$530$	345.066	−	474.942i	0.651067	−	0.896117i
$531$		0			0
$532$	−753.696	−	2319.64i	−1.41672	−	4.36022i
$533$	−96.1203	+	69.8355i	−0.180338	+	0.131023i
$534$		0			0
$535$	234.462	−	76.1812i	0.438246	−	0.142395i
$536$	−1604.56	−	521.352i	−2.99358	−	0.972672i
$537$		0			0
$538$		−	935.492i		−	1.73883i
$539$	−70.4110	−	5.81834i	−0.130633	−	0.0107947i
$540$		0			0
$541$	35.0313	−	48.2164i	0.0647528	−	0.0891246i	−0.775412	−	0.631455i	$-0.782458\pi$
$541$	35.0313	−	48.2164i	0.0647528	−	0.0891246i	0.840165	+	0.542331i	$0.182458\pi$
$542$	291.275	−	896.451i	0.537407	−	1.65397i
$543$		0			0
$544$	−357.381	+	259.652i	−0.656950	+	0.477302i
$545$	−91.5037	−	125.944i	−0.167897	−	0.231090i
$546$		0			0
$547$	−509.553	−	165.564i	−0.931541	−	0.302676i	−0.196349	−	0.980534i	$-0.562908\pi$
$547$	−509.553	−	165.564i	−0.931541	−	0.302676i	−0.735193	+	0.677858i	$0.762908\pi$
$548$	1697.76	+	1233.50i	3.09811	+	2.25091i
$549$		0			0
$550$	−27.2070	+	329.246i	−0.0494672	+	0.598629i
$551$	515.374			0.935343
$552$		0			0
$553$	42.0155	−	129.311i	0.0759775	−	0.233835i
$554$	−172.067	−	529.569i	−0.310591	−	0.955901i
$555$		0			0
$556$	−157.788	−	217.177i	−0.283792	−	0.390606i
$557$	−410.696	+	133.443i	−0.737336	+	0.239575i	−0.653523	−	0.756907i	$-0.726710\pi$
$557$	−410.696	+	133.443i	−0.737336	+	0.239575i	−0.0838128	+	0.996482i	$0.526710\pi$
$558$		0			0
$559$	199.865	+	145.211i	0.357541	+	0.259768i
$560$			1842.98i			3.29103i
$561$		0			0
$562$	1387.95			2.46967
$563$	91.5835	−	126.054i	0.162670	−	0.223897i	−0.719899	−	0.694079i	$-0.755812\pi$
$563$	91.5835	−	126.054i	0.162670	−	0.223897i	0.882569	+	0.470182i	$0.155812\pi$
$564$		0			0
$565$	−150.255	−	462.437i	−0.265938	−	0.818472i
$566$	−1386.30	+	1007.20i	−2.44929	+	1.77951i
$567$		0			0
$568$	803.784	−	261.165i	1.41511	−	0.459798i
$569$	−592.120	−	192.391i	−1.04063	−	0.338122i	−0.261647	−	0.965164i	$-0.584265\pi$
$569$	−592.120	−	192.391i	−1.04063	−	0.338122i	−0.778986	+	0.627042i	$0.784265\pi$
$570$		0			0
$571$			327.913i			0.574279i	0.957889	+	0.287139i	$0.0927043\pi$
$571$			327.913i			0.574279i	−0.957889	+	0.287139i	$0.907296\pi$
$572$	456.944	+	752.247i	0.798854	+	1.31512i
$573$		0			0
$574$	274.224	−	377.437i	0.477742	−	0.657555i
$575$	−49.6161	+	152.703i	−0.0862889	+	0.265570i
$576$		0			0
$577$	592.123	−	430.202i	1.02621	−	0.745585i	0.0586629	−	0.998278i	$-0.481316\pi$
$577$	592.123	−	430.202i	1.02621	−	0.745585i	0.967546	+	0.252693i	$0.0813163\pi$
$578$	627.158	+	863.209i	1.08505	+	1.49344i
$579$		0			0
$580$	−741.057	−	240.784i	−1.27768	−	0.415145i
$581$	716.662	+	520.686i	1.23350	+	0.896189i
$582$		0			0
$583$	92.4895	+	391.987i	0.158644	+	0.672362i
$584$	−2765.72			−4.73583
$585$		0			0
$586$	−614.390	+	1890.90i	−1.04845	+	3.22679i
$587$	33.7805	+	103.966i	0.0575477	+	0.177114i	0.975698	−	0.219118i	$-0.0703178\pi$
$587$	33.7805	+	103.966i	0.0575477	+	0.177114i	−0.918151	+	0.396231i	$0.870318\pi$
$588$		0			0
$589$	−278.067	−	382.726i	−0.472100	−	0.649789i
$590$	−1066.71	+	346.597i	−1.80799	+	0.587452i
$591$		0			0
$592$	1557.41	+	1131.52i	2.63076	+	1.91136i
$593$		−	903.281i		−	1.52324i	−0.648024	−	0.761620i	$-0.724404\pi$
$593$		−	903.281i		−	1.52324i	0.648024	−	0.761620i	$-0.275596\pi$
$594$		0			0
$595$	−110.587			−0.185861
$596$	185.154	−	254.843i	0.310661	−	0.427589i
$597$		0			0
$598$	180.585	+	555.784i	0.301982	+	0.929404i
$599$	630.442	−	458.043i	1.05249	−	0.764679i	0.0798057	−	0.996810i	$-0.474570\pi$
$599$	630.442	−	458.043i	1.05249	−	0.764679i	0.972684	+	0.232132i	$0.0745700\pi$
$600$		0			0
$601$	−536.922	+	174.456i	−0.893381	+	0.290277i	−0.719502	−	0.694490i	$-0.755630\pi$
$601$	−536.922	+	174.456i	−0.893381	+	0.290277i	−0.173878	+	0.984767i	$0.555630\pi$
$602$	−922.603	−	299.772i	−1.53256	−	0.497960i
$603$		0			0
$604$		−	1534.49i		−	2.54054i
$605$	352.322	+	357.872i	0.582351	+	0.591523i
$606$		0			0
$607$	79.0628	−	108.821i	0.130252	−	0.179276i	−0.738910	−	0.673804i	$-0.764659\pi$
$607$	79.0628	−	108.821i	0.130252	−	0.179276i	0.869162	+	0.494528i	$0.164659\pi$
$608$	1143.81	−	3520.28i	1.88126	−	5.78993i
$609$		0			0
$610$	−295.120	+	214.417i	−0.483804	+	0.351504i
$611$	−167.484	−	230.522i	−0.274115	−	0.377287i
$612$		0			0
$613$	513.793	+	166.941i	0.838162	+	0.272335i	0.696479	−	0.717577i	$-0.254749\pi$
$613$	513.793	+	166.941i	0.838162	+	0.272335i	0.141682	+	0.989912i	$0.454749\pi$
$614$	455.139	+	330.678i	0.741269	+	0.538564i
$615$		0			0
$616$	−1660.22	−	1429.22i	−2.69516	−	2.32016i
$617$	684.941			1.11011			0.555057	−	0.831812i	$-0.312696\pi$
$617$	684.941			1.11011			0.555057	+	0.831812i	$0.312696\pi$
$618$		0			0
$619$	336.723	−	1036.33i	0.543979	−	1.67420i	−0.179426	−	0.983772i	$-0.557424\pi$
$619$	336.723	−	1036.33i	0.543979	−	1.67420i	0.723405	−	0.690424i	$-0.242576\pi$
$620$	221.022	+	680.236i	0.356487	+	1.09715i
$621$		0			0
$622$	899.996	+	1238.74i	1.44694	+	1.99154i
$623$	−1095.60	+	355.981i	−1.75858	+	0.571398i
$624$		0			0
$625$	299.504	+	217.602i	0.479206	+	0.348163i
$626$			1161.59i			1.85558i
$627$		0			0
$628$	−2892.61			−4.60607
$629$	−67.8967	+	93.4518i	−0.107944	+	0.148572i
$630$		0			0
$631$	265.180	+	816.141i	0.420254	+	1.29341i	0.907466	+	0.420126i	$0.138014\pi$
$631$	265.180	+	816.141i	0.420254	+	1.29341i	−0.487212	+	0.873284i	$0.661986\pi$
$632$	395.257	−	287.171i	0.625406	−	0.454384i
$633$		0			0
$634$	−992.261	+	322.405i	−1.56508	+	0.508526i
$635$	−120.235	−	39.0668i	−0.189347	−	0.0615226i
$636$		0			0
$637$		−	47.0425i		−	0.0738501i
$638$	624.162	−	379.141i	0.978311	−	0.594265i
$639$		0			0
$640$	−1040.81	+	1432.55i	−1.62626	+	2.23836i
$641$	217.501	−	669.400i	0.339315	−	1.04431i	−0.625242	−	0.780431i	$-0.715000\pi$
$641$	217.501	−	669.400i	0.339315	−	1.04431i	0.964557	−	0.263874i	$-0.0850003\pi$
$642$		0			0
$643$	392.142	−	284.908i	0.609863	−	0.443092i	−0.239503	−	0.970896i	$-0.576984\pi$
$643$	392.142	−	284.908i	0.609863	−	0.443092i	0.849366	+	0.527804i	$0.176984\pi$
$644$	−987.299	−	1358.90i	−1.53307	−	2.11009i
$645$		0			0
$646$	394.362	+	128.136i	0.610468	+	0.198353i
$647$	616.902	+	448.205i	0.953480	+	0.692744i	0.951627	−	0.307254i	$-0.0994102\pi$
$647$	616.902	+	448.205i	0.953480	+	0.692744i	0.00185290	+	0.999998i	$0.499410\pi$
$648$		0			0
$649$	297.241	−	709.747i	0.457998	−	1.09360i
$650$	−219.974			−0.338421
$651$		0			0
$652$	−216.880	+	667.488i	−0.332638	+	1.02375i
$653$	−92.0616	−	283.336i	−0.140982	−	0.433899i	0.855490	−	0.517819i	$-0.173256\pi$
$653$	−92.0616	−	283.336i	−0.140982	−	0.433899i	−0.996473	+	0.0839198i	$0.973256\pi$
$654$		0			0
$655$	437.186	+	601.734i	0.667459	+	0.918678i
$656$	920.205	−	298.993i	1.40275	−	0.455782i
$657$		0			0
$658$	905.194	+	657.662i	1.37568	+	0.999487i
$659$		−	622.572i		−	0.944722i	−0.881405	−	0.472361i	$-0.843402\pi$
$659$		−	622.572i		−	0.944722i	0.881405	−	0.472361i	$-0.156598\pi$
$660$		0			0
$661$	1201.96			1.81840			0.909199	−	0.416361i	$-0.136695\pi$
$661$	1201.96			1.81840			0.909199	+	0.416361i	$0.136695\pi$
$662$	−391.786	+	539.247i	−0.591821	+	0.814572i
$663$		0			0
$664$	983.633	+	3027.31i	1.48138	+	4.55920i
$665$	749.652	−	544.654i	1.12730	−	0.819029i
$666$		0			0
$667$	337.555	−	109.678i	0.506080	−	0.164435i
$668$	−1193.45	−	387.777i	−1.78661	−	0.580504i
$669$		0			0
$670$		−	1011.23i		−	1.50930i
$671$	20.6099	−	249.412i	0.0307152	−	0.371702i
$672$		0			0
$673$	−172.534	+	237.473i	−0.256366	+	0.352858i	−0.917728	−	0.397209i	$-0.869979\pi$
$673$	−172.534	+	237.473i	−0.256366	+	0.352858i	0.661362	+	0.750067i	$0.269979\pi$
$674$	−329.890	+	1015.30i	−0.489451	+	1.50637i
$675$		0			0
$676$	1019.52	−	740.724i	1.50816	−	1.09574i
$677$	100.962	+	138.963i	0.149132	+	0.205263i	0.877047	−	0.480405i	$-0.159510\pi$
$677$	100.962	+	138.963i	0.149132	+	0.205263i	−0.727915	+	0.685668i	$0.759510\pi$
$678$		0			0
$679$	490.075	+	159.235i	0.721759	+	0.234514i
$680$	−321.482	−	233.570i	−0.472767	−	0.343486i
$681$		0			0
$682$	−618.320	−	258.951i	−0.906627	−	0.379694i
$683$	−371.395			−0.543770			−0.271885	−	0.962330i	$-0.587647\pi$
$683$	−371.395			−0.543770			−0.271885	+	0.962330i	$0.587647\pi$
$684$		0			0
$685$	−246.371	+	758.253i	−0.359666	+	1.10694i
$686$	−378.402	−	1164.60i	−0.551606	−	1.69767i
$687$		0			0
$688$	−1182.55	−	1627.64i	−1.71882	−	2.36576i
$689$	−255.044	+	82.8688i	−0.370165	+	0.120274i
$690$		0			0
$691$	−383.375	−	278.538i	−0.554812	−	0.403094i	0.274745	−	0.961517i	$-0.411407\pi$
$691$	−383.375	−	278.538i	−0.554812	−	0.403094i	−0.829556	+	0.558423i	$0.811407\pi$
$692$			2553.60i			3.69018i
$693$		0			0
$694$	−558.138			−0.804234
$695$	59.9464	−	82.5092i	0.0862538	−	0.118718i
$696$		0			0
$697$	17.9410	+	55.2166i	0.0257403	+	0.0792204i
$698$	−462.219	+	335.822i	−0.662205	+	0.481120i
$699$		0			0
$700$	601.323	−	195.382i	0.859033	−	0.279117i
$701$	502.781	+	163.364i	0.717235	+	0.233044i	0.644824	−	0.764331i	$-0.276931\pi$
$701$	502.781	+	163.364i	0.717235	+	0.233044i	0.0724108	+	0.997375i	$0.476931\pi$
$702$		0			0
$703$		−	967.893i		−	1.37680i
$704$	−601.794	−	2550.51i	−0.854820	−	3.62288i
$705$		0			0
$706$	56.4697	−	77.7238i	0.0799854	−	0.110090i
$707$	−315.511	+	971.043i	−0.446267	+	1.37347i
$708$		0			0
$709$	871.733	−	633.351i	1.22953	−	0.893302i	0.232671	−	0.972556i	$-0.425254\pi$
$709$	871.733	−	633.351i	1.22953	−	0.893302i	0.996855	+	0.0792533i	$0.0252536\pi$
$710$	297.751	+	409.819i	0.419367	+	0.577210i
$711$		0			0
$712$	−3936.81	−	1279.15i	−5.52923	−	1.79655i
$713$	−263.575	−	191.498i	−0.369670	−	0.268581i
$714$		0			0
$715$	−218.158	+	253.418i	−0.305116	+	0.354431i
$716$	−2429.19			−3.39273
$717$		0			0
$718$	278.960	−	858.551i	0.388524	−	1.19575i
$719$	−380.165	−	1170.03i	−0.528742	−	1.62730i	−0.756796	−	0.653652i	$-0.773236\pi$
$719$	−380.165	−	1170.03i	−0.528742	−	1.62730i	0.228054	−	0.973649i	$-0.426764\pi$
$720$		0			0
$721$	89.7994	+	123.598i	0.124548	+	0.171426i
$722$	−1978.03	+	642.702i	−2.73966	+	0.890170i
$723$		0			0
$724$	2381.10	+	1729.97i	3.28881	+	2.38946i
$725$			133.601i			0.184277i
$726$		0			0
$727$	−389.945			−0.536376			−0.268188	−	0.963367i	$-0.586425\pi$
$727$	−389.945			−0.536376			−0.268188	+	0.963367i	$0.586425\pi$
$728$	857.366	−	1180.06i	1.17770	−	1.62097i
$729$		0			0
$730$	−512.262	−	1576.58i	−0.701729	−	2.15970i
$731$	97.6659	−	70.9585i	0.133606	−	0.0970704i
$732$		0			0
$733$	−178.666	+	58.0522i	−0.243747	+	0.0791981i	−0.428343	−	0.903616i	$-0.640902\pi$
$733$	−178.666	+	58.0522i	−0.243747	+	0.0791981i	0.184596	+	0.982814i	$0.440902\pi$
$734$	2013.99	+	654.386i	2.74386	+	0.891535i
$735$		0			0
$736$		−	2549.10i		−	3.46345i
$737$	525.768	+	452.613i	0.713389	+	0.614128i
$738$		0			0
$739$	−432.278	+	594.979i	−0.584949	+	0.805114i	−0.994227	−	0.107296i	$-0.965781\pi$
$739$	−432.278	+	594.979i	−0.584949	+	0.805114i	0.409278	+	0.912410i	$0.365781\pi$
$740$	−452.202	+	1391.74i	−0.611084	+	1.88072i
$741$		0			0
$742$	851.913	−	618.951i	1.14813	−	0.834166i
$743$	−197.349	−	271.627i	−0.265610	−	0.365581i	0.655291	−	0.755376i	$-0.272546\pi$
$743$	−197.349	−	271.627i	−0.265610	−	0.365581i	−0.920902	+	0.389795i	$0.872546\pi$
$744$		0			0
$745$	113.818	+	36.9816i	0.152775	+	0.0496397i
$746$	263.771	+	191.641i	0.353581	+	0.256892i
$747$		0			0
$748$	418.601	−	98.7692i	0.559627	−	0.132044i
$749$	442.201			0.590389
$750$		0			0
$751$	115.417	−	355.216i	0.153684	−	0.472991i	−0.844341	−	0.535806i	$-0.820008\pi$
$751$	115.417	−	355.216i	0.153684	−	0.472991i	0.998025	+	0.0628149i	$0.0200078\pi$
$752$	717.065	+	2206.90i	0.953544	+	2.93471i
$753$		0			0
$754$	285.817	+	393.393i	0.379067	+	0.521741i
$755$	554.444	−	180.150i	0.734363	−	0.238609i
$756$		0			0
$757$	−1010.21	−	733.961i	−1.33449	−	0.969566i	−0.999627	−	0.0272996i	$-0.991309\pi$
$757$	−1010.21	−	733.961i	−1.33449	−	0.969566i	−0.334865	−	0.942266i	$-0.608691\pi$
$758$		−	519.163i		−	0.684912i
$759$		0			0
$760$	3329.63			4.38109
$761$	−161.102	+	221.738i	−0.211698	+	0.291377i	−0.901640	−	0.432487i	$-0.857636\pi$
$761$	−161.102	+	221.738i	−0.211698	+	0.291377i	0.689942	+	0.723865i	$0.257636\pi$
$762$		0			0
$763$	−86.2893	−	265.571i	−0.113092	−	0.348062i
$764$	2164.91	−	1572.90i	2.83366	−	2.05877i
$765$		0			0
$766$	1520.43	−	494.017i	1.98489	−	0.644930i
$767$	487.275	+	158.325i	0.635299	+	0.206421i
$768$		0			0
$769$			1313.03i			1.70745i	0.520722	+	0.853726i	$0.325663\pi$
$769$			1313.03i			1.70745i	−0.520722	+	0.853726i	$0.674337\pi$
$770$	507.213	−	1211.11i	0.658718	−	1.57288i
$771$		0			0
$772$	−1691.70	+	2328.42i	−2.19132	+	3.01609i
$773$	−177.292	+	545.649i	−0.229356	+	0.705885i	0.768464	+	0.639893i	$0.221021\pi$
$773$	−177.292	+	545.649i	−0.229356	+	0.705885i	−0.997820	+	0.0659920i	$0.978979\pi$
$774$		0			0
$775$	99.2146	−	72.0836i	0.128019	−	0.0930111i
$776$	1088.35	+	1497.98i	1.40251	+	1.93039i
$777$		0			0
$778$	−789.366	−	256.481i	−1.01461	−	0.329667i
$779$	−393.567	−	285.943i	−0.505220	−	0.367064i
$780$		0			0
$781$	−346.346	−	28.6200i	−0.443464	−	0.0366453i
$782$	285.565			0.365173
$783$		0			0
$784$	−118.384	+	364.349i	−0.151000	+	0.464731i
$785$	−339.594	−	1045.16i	−0.432604	−	1.33142i
$786$		0			0
$787$	−161.144	−	221.796i	−0.204758	−	0.281825i	0.694272	−	0.719713i	$-0.255727\pi$
$787$	−161.144	−	221.796i	−0.204758	−	0.281825i	−0.899029	+	0.437888i	$0.855727\pi$
$788$	2661.96	−	864.925i	3.37813	−	1.09762i
$789$		0			0
$790$	236.908	+	172.124i	0.299884	+	0.217879i
$791$		−	872.169i		−	1.10262i
$792$		0			0
$793$	166.635			0.210133
$794$	−1439.47	+	1981.27i	−1.81294	+	2.49530i
$795$		0			0
$796$	25.7599	+	79.2807i	0.0323616	+	0.0995989i
$797$	277.721	−	201.776i	0.348458	−	0.253170i	−0.399764	−	0.916618i	$-0.630908\pi$
$797$	277.721	−	201.776i	0.348458	−	0.253170i	0.748222	+	0.663448i	$0.230908\pi$
$798$		0			0
$799$	−132.424	+	43.0272i	−0.165737	+	0.0538514i
$800$	912.567	+	296.511i	1.14071	+	0.370639i
$801$		0			0
$802$			1223.45i			1.52550i
$803$	1048.99	+	439.316i	1.30634	+	0.547093i
$804$		0			0
$805$	375.091	−	516.269i	0.465952	−	0.641328i
$806$	137.930	−	424.505i	0.171129	−	0.526682i
$807$		0			0
$808$	−2968.14	+	2156.48i	−3.67344	+	2.66891i
$809$	−332.686	−	457.903i	−0.411231	−	0.566011i	0.552287	−	0.833654i	$-0.313755\pi$
$809$	−332.686	−	457.903i	−0.411231	−	0.566011i	−0.963518	+	0.267643i	$0.913755\pi$
$810$		0			0
$811$	14.9054	+	4.84305i	0.0183790	+	0.00597170i	0.318192	−	0.948026i	$-0.396924\pi$
$811$	14.9054	+	4.84305i	0.0183790	+	0.00597170i	−0.299813	+	0.953998i	$0.596924\pi$
$812$	−1130.73	−	821.521i	−1.39252	−	1.01172i
$813$		0			0
$814$	−712.042	−	1172.20i	−0.874745	−	1.44005i
$815$	−266.640			−0.327166
$816$		0			0
$817$	−312.583	+	962.031i	−0.382598	+	1.17752i
$818$	451.758	+	1390.37i	0.552271	+	1.69972i
$819$		0			0
$820$	432.317	+	595.033i	0.527216	+	0.725650i
$821$	−1331.93	+	432.769i	−1.62232	+	0.527124i	−0.972488	−	0.232953i	$-0.925161\pi$
$821$	−1331.93	+	432.769i	−1.62232	+	0.527124i	−0.649833	+	0.760077i	$0.725161\pi$
$822$		0			0
$823$	−480.348	−	348.993i	−0.583655	−	0.424050i	0.256385	−	0.966575i	$-0.417469\pi$
$823$	−480.348	−	348.993i	−0.583655	−	0.424050i	−0.840040	+	0.542524i	$0.817469\pi$
$824$			548.970i			0.666226i
$825$		0			0
$826$	−2011.85			−2.43566
$827$	−319.771	+	440.128i	−0.386664	+	0.532198i	−0.957335	−	0.288981i	$-0.906683\pi$
$827$	−319.771	+	440.128i	−0.386664	+	0.532198i	0.570670	+	0.821179i	$0.306683\pi$
$828$		0			0
$829$	181.299	+	557.980i	0.218696	+	0.673076i	0.998871	+	0.0475143i	$0.0151300\pi$
$829$	181.299	+	557.980i	0.218696	+	0.673076i	−0.780175	+	0.625561i	$0.784870\pi$
$830$	−1543.51	+	1121.43i	−1.85965	+	1.35112i
$831$		0			0
$832$	1659.47	−	539.195i	1.99456	−	0.648071i
$833$	−21.8626	−	7.10360i	−0.0262457	−	0.00852773i
$834$		0			0
$835$		−	476.747i		−	0.570954i
$836$	−2351.18	+	2731.20i	−2.81241	+	3.26698i
$837$		0			0
$838$	426.506	−	587.035i	0.508957	−	0.700519i
$839$	204.272	−	628.685i	0.243471	−	0.749326i	−0.752413	−	0.658691i	$-0.771110\pi$
$839$	204.272	−	628.685i	0.243471	−	0.749326i	0.995884	−	0.0906351i	$-0.0288897\pi$
$840$		0			0
$841$	−441.456	+	320.737i	−0.524918	+	0.381375i
$842$	−348.511	−	479.685i	−0.413909	−	0.569697i
$843$		0			0
$844$	3902.32	+	1267.94i	4.62360	+	1.50230i
$845$	387.332	+	281.413i	0.458381	+	0.333033i
$846$		0			0
$847$	402.672	+	805.792i	0.475409	+	0.951348i
$848$	2183.88			2.57534
$849$		0			0
$850$	−33.2169	+	102.231i	−0.0390787	+	0.120272i
$851$	−205.980	−	633.943i	−0.242045	−	0.744938i
$852$		0			0
$853$	−278.247	−	382.975i	−0.326198	−	0.448974i	0.614149	−	0.789190i	$-0.289500\pi$
$853$	−278.247	−	382.975i	−0.326198	−	0.448974i	−0.940347	+	0.340217i	$0.889500\pi$
$854$	−622.304	+	202.199i	−0.728693	+	0.236767i
$855$		0			0
$856$	1285.50	+	933.969i	1.50175	+	1.09109i
$857$		−	461.983i		−	0.539070i	−0.962991	−	0.269535i	$-0.913130\pi$
$857$		−	461.983i		−	0.539070i	0.962991	−	0.269535i	$-0.0868701\pi$
$858$		0			0
$859$	−787.819			−0.917135			−0.458567	−	0.888660i	$-0.651637\pi$
$859$	−787.819			−0.917135			−0.458567	+	0.888660i	$0.651637\pi$
$860$	898.927	−	1237.27i	1.04526	−	1.43868i
$861$		0			0
$862$	−237.002	−	729.417i	−0.274944	−	0.846191i
$863$	−699.098	+	507.925i	−0.810079	+	0.588557i	−0.913854	−	0.406044i	$-0.866908\pi$
$863$	−699.098	+	507.925i	−0.810079	+	0.588557i	0.103774	+	0.994601i	$0.466908\pi$
$864$		0			0
$865$	−922.673	+	299.795i	−1.06667	+	0.346583i
$866$	−303.497	−	98.6120i	−0.350458	−	0.113871i
$867$		0			0
$868$			1282.94i			1.47805i
$869$	−195.529	+	46.1352i	−0.225005	+	0.0530900i
$870$		0			0
$871$	−271.515	+	373.709i	−0.311728	+	0.429057i
$872$	310.064	−	954.277i	0.355577	−	1.09435i
$873$		0			0
$874$	−1935.80	+	1406.44i	−2.21487	+	1.60920i
$875$	595.230	+	819.264i	0.680263	+	0.936301i
$876$		0			0
$877$	71.5453	+	23.2465i	0.0815796	+	0.0265068i	0.349522	−	0.936928i	$-0.386344\pi$
$877$	71.5453	+	23.2465i	0.0815796	+	0.0265068i	−0.267943	+	0.963435i	$0.586344\pi$
$878$	722.892	+	525.212i	0.823339	+	0.598191i
$879$		0			0
$880$	2327.39	−	1413.75i	2.64476	−	1.60653i
$881$	−405.703			−0.460503			−0.230252	−	0.973131i	$-0.573955\pi$
$881$	−405.703			−0.460503			−0.230252	+	0.973131i	$0.573955\pi$
$882$		0			0
$883$	−42.1015	+	129.575i	−0.0476801	+	0.146744i	−0.972062	−	0.234724i	$-0.924581\pi$
$883$	−42.1015	+	129.575i	−0.0476801	+	0.146744i	0.924382	+	0.381468i	$0.124581\pi$
$884$	88.4952	+	272.360i	0.100108	+	0.308100i
$885$		0			0
$886$	−1368.27	−	1883.26i	−1.54432	−	2.12557i
$887$	67.7935	−	22.0275i	0.0764301	−	0.0248337i	−0.270552	−	0.962705i	$-0.587206\pi$
$887$	67.7935	−	22.0275i	0.0764301	−	0.0248337i	0.346982	+	0.937872i	$0.387206\pi$
$888$		0			0
$889$	−183.459	−	133.290i	−0.206365	−	0.149933i
$890$		−	2481.07i		−	2.78772i
$891$		0			0
$892$	307.909			0.345189
$893$	685.768	−	943.878i	0.767937	−	1.05697i
$894$		0			0
$895$	−285.189	−	877.721i	−0.318647	−	0.980694i
$896$	−2569.59	+	1866.92i	−2.86785	+	2.08362i
$897$		0			0
$898$	−980.023	+	318.429i	−1.09134	+	0.354598i
$899$	−257.823	−	83.7719i	−0.286789	−	0.0931834i
$900$		0			0
$901$			131.043i			0.145442i
$902$	−687.001	−	56.7697i	−0.761641	−	0.0629375i
$903$		0			0
$904$	1842.10	−	2535.43i	2.03772	−	2.80468i
$905$	−345.533	+	1063.44i	−0.381805	+	1.17507i
$906$		0			0
$907$	−483.722	+	351.445i	−0.533321	+	0.387481i	−0.821599	−	0.570066i	$-0.806917\pi$
$907$	−483.722	+	351.445i	−0.533321	+	0.387481i	0.288277	+	0.957547i	$0.406917\pi$
$908$	−1750.18	−	2408.91i	−1.92751	−	2.65299i
$909$		0			0
$910$	831.486	+	270.166i	0.913721	+	0.296886i
$911$	1418.22	+	1030.39i	1.55677	+	1.13106i	0.938597	+	0.345014i	$0.112126\pi$
$911$	1418.22	+	1030.39i	1.55677	+	1.13106i	0.618171	+	0.786044i	$0.287874\pi$
$912$		0			0
$913$	107.792	−	1304.45i	0.118064	−	1.42875i
$914$	3155.41			3.45231
$915$		0			0
$916$	−1.99256	+	6.13247i	−0.00217529	+	0.00669484i
$917$	412.272	+	1268.84i	0.449588	+	1.38369i
$918$		0			0
$919$	−327.127	−	450.251i	−0.355960	−	0.489936i	0.593058	−	0.805160i	$-0.297921\pi$
$919$	−327.127	−	450.251i	−0.355960	−	0.489936i	−0.949017	+	0.315224i	$0.897921\pi$
$920$	2180.81	−	708.589i	2.37045	−	0.770206i
$921$		0			0
$922$	−603.968	−	438.808i	−0.655063	−	0.475931i
$923$		−	231.398i		−	0.250702i
$924$		0			0
$925$	250.908			0.271252
$926$	1204.27	−	1657.54i	1.30051	−	1.79000i
$927$		0			0
$928$	−655.449	−	2017.27i	−0.706303	−	2.17378i
$929$	−569.380	+	413.678i	−0.612895	+	0.445294i	−0.850433	−	0.526084i	$-0.823660\pi$
$929$	−569.380	+	413.678i	−0.612895	+	0.445294i	0.237537	+	0.971378i	$0.423660\pi$
$930$		0			0
$931$	183.189	−	59.5218i	0.196766	−	0.0639332i
$932$	−1927.93	−	626.421i	−2.06859	−	0.672125i
$933$		0			0
$934$		−	392.199i		−	0.419913i
$935$	84.8316	+	139.654i	0.0907289	+	0.149363i
$936$		0			0
$937$	239.494	−	329.635i	0.255596	−	0.351798i	−0.661865	−	0.749623i	$-0.730235\pi$
$937$	239.494	−	329.635i	0.255596	−	0.351798i	0.917461	+	0.397825i	$0.130235\pi$
$938$	560.515	−	1725.09i	0.597564	−	1.83911i
$939$		0			0
$940$	−1427.05	+	1036.81i	−1.51814	+	1.10299i
$941$	−274.780	−	378.203i	−0.292009	−	0.401916i	0.637656	−	0.770321i	$-0.279904\pi$
$941$	−274.780	−	378.203i	−0.292009	−	0.401916i	−0.929665	+	0.368405i	$0.879904\pi$
$942$		0			0
$943$	−318.627	−	103.528i	−0.337887	−	0.109786i
$944$	−3375.56	−	2452.49i	−3.57581	−	2.59798i
$945$		0			0
$946$	329.165	+	1395.06i	0.347954	+	1.47469i
$947$	1795.45			1.89594			0.947969	−	0.318363i	$-0.103133\pi$
$947$	1795.45			1.89594			0.947969	+	0.318363i	$0.103133\pi$
$948$		0			0
$949$	−234.001	+	720.181i	−0.246576	+	0.758884i
$950$	−278.328	−	856.604i	−0.292976	−	0.901689i
$951$		0			0
$952$	−418.960	−	576.648i	−0.440084	−	0.605723i
$953$	−434.275	+	141.105i	−0.455693	+	0.148064i	−0.527865	−	0.849329i	$-0.677007\pi$
$953$	−434.275	+	141.105i	−0.455693	+	0.148064i	0.0721715	+	0.997392i	$0.477007\pi$
$954$		0			0
$955$	822.486	+	597.571i	0.861242	+	0.625729i
$956$		−	2940.97i		−	3.07633i
$957$		0			0
$958$	1819.99			1.89978
$959$	−840.584	+	1156.96i	−0.876522	+	1.20643i
$960$		0			0
$961$	−220.069	−	677.302i	−0.229000	−	0.704789i
$962$	738.808	−	536.776i	0.767992	−	0.557979i
$963$		0			0
$964$	2591.26	−	841.950i	2.68802	−	0.873392i
$965$	−1039.92	−	337.889i	−1.07763	−	0.350145i
$966$		0			0
$967$			42.6322i			0.0440871i	0.999757	+	0.0220436i	$0.00701725\pi$
$967$			42.6322i			0.0440871i	−0.999757	+	0.0220436i	$0.992983\pi$
$968$	−531.321	+	3192.95i	−0.548886	+	3.29850i
$969$		0			0
$970$	−652.334	+	897.860i	−0.672509	+	0.925629i
$971$	−176.322	+	542.665i	−0.181589	+	0.558872i	−0.999873	−	0.0159415i	$-0.994925\pi$
$971$	−176.322	+	542.665i	−0.181589	+	0.558872i	0.818284	+	0.574814i	$0.194925\pi$
$972$		0			0
$973$	147.998	−	107.527i	0.152105	−	0.110511i
$974$	1626.41	+	2238.57i	1.66983	+	2.29832i
$975$		0			0
$976$	−1290.61	−	419.344i	−1.32234	−	0.429656i
$977$	−1297.78	−	942.894i	−1.32833	−	0.965091i	−0.999788	−	0.0206035i	$-0.993441\pi$
$977$	−1297.78	−	942.894i	−1.32833	−	0.965091i	−0.328547	−	0.944488i	$-0.606559\pi$
$978$		0			0
$979$	1289.98	+	1110.49i	1.31765	+	1.13431i
$980$	−291.217			−0.297160
$981$		0			0
$982$	957.877	−	2948.04i	0.975435	−	3.00208i
$983$	393.921	+	1212.37i	0.400734	+	1.23333i	0.924405	+	0.381412i	$0.124562\pi$
$983$	393.921	+	1212.37i	0.400734	+	1.23333i	−0.523671	+	0.851920i	$0.675438\pi$
$984$		0			0
$985$	625.033	+	860.284i	0.634551	+	0.873384i
$986$	225.986	−	73.4272i	0.229195	−	0.0744698i
$987$		0			0
$988$	−1941.30	−	1410.44i	−1.96488	−	1.42757i
$989$			696.625i			0.704373i
$990$		0			0
$991$	−1336.90			−1.34904			−0.674519	−	0.738258i	$-0.735649\pi$
$991$	−1336.90			−1.34904			−0.674519	+	0.738258i	$0.735649\pi$
$992$	−1144.41	+	1575.15i	−1.15364	+	1.58785i
$993$		0			0
$994$	280.783	+	864.162i	0.282478	+	0.869378i
$995$	−25.6217	+	18.6152i	−0.0257504	+	0.0187088i
$996$		0			0
$997$	1712.69	−	556.486i	1.71784	−	0.558161i	0.726234	−	0.687447i	$-0.241269\pi$
$997$	1712.69	−	556.486i	1.71784	−	0.558161i	0.991607	+	0.129287i	$0.0412688\pi$
$998$	−655.325	−	212.928i	−0.656638	−	0.213355i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.k.b.73.1	yes	16
3.2	odd	2	inner	99.3.k.b.73.4	yes	16
11.5	even	5		1089.3.c.l.604.1		16
11.6	odd	10		1089.3.c.l.604.15		16
11.8	odd	10	inner	99.3.k.b.19.1	✓	16
33.5	odd	10		1089.3.c.l.604.16		16
33.8	even	10	inner	99.3.k.b.19.4	yes	16
33.17	even	10		1089.3.c.l.604.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.k.b.19.1	✓	16	11.8	odd	10	inner
99.3.k.b.19.4	yes	16	33.8	even	10	inner
99.3.k.b.73.1	yes	16	1.1	even	1	trivial
99.3.k.b.73.4	yes	16	3.2	odd	2	inner
1089.3.c.l.604.1		16	11.5	even	5
1089.3.c.l.604.2		16	33.17	even	10
1089.3.c.l.604.15		16	11.6	odd	10
1089.3.c.l.604.16		16	33.5	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27075 + 3.12541i) q^{2} +(-3.37586 - 10.3898i) q^{4} +(3.35774 - 2.43954i) q^{5} +(7.08028 - 2.30052i) q^{7} +(25.4416 + 8.26648i) q^{8} +O(q^{10})\)	\(q+(-2.27075 + 3.12541i) q^{2} +(-3.37586 - 10.3898i) q^{4} +(3.35774 - 2.43954i) q^{5} +(7.08028 - 2.30052i) q^{7} +(25.4416 + 8.26648i) q^{8} +16.0339i q^{10} +(-8.33649 - 7.17655i) q^{11} +(4.30510 - 5.92547i) q^{13} +(-8.88744 + 27.3527i) q^{14} +(-48.2552 + 35.0594i) q^{16} +(-2.10373 - 2.89553i) q^{17} +(28.5216 + 9.26724i) q^{19} +(-36.6816 - 26.6508i) q^{20} +(41.3598 - 9.75885i) q^{22} +20.6531 q^{23} +(-2.40236 + 7.39371i) q^{25} +(8.74374 + 26.9105i) q^{26} +(-47.8040 - 65.7966i) q^{28} +(16.3441 - 5.31051i) q^{29} +(-12.7620 - 9.27216i) q^{31} -123.425i q^{32} +13.8268 q^{34} +(18.1615 - 24.9972i) q^{35} +(-9.97336 - 30.6948i) q^{37} +(-93.7294 + 68.0984i) q^{38} +(105.593 - 34.3092i) q^{40} +(-15.4276 - 5.01273i) q^{41} +33.7299i q^{43} +(-46.4203 + 110.842i) q^{44} +(-46.8979 + 64.5494i) q^{46} +(12.0219 - 36.9995i) q^{47} +(5.19616 - 3.77523i) q^{49} +(-17.6532 - 24.2976i) q^{50} +(-76.0979 - 24.7257i) q^{52} +(-29.6211 - 21.5210i) q^{53} +(-45.4993 - 3.75979i) q^{55} +199.151 q^{56} +(-20.5157 + 63.1408i) q^{58} +(21.6165 + 66.5286i) q^{59} +(13.3727 + 18.4060i) q^{61} +(57.9586 - 18.8319i) q^{62} +(192.733 + 140.029i) q^{64} -30.3987i q^{65} -63.0682 q^{67} +(-22.9822 + 31.6323i) q^{68} +(36.8864 + 113.525i) q^{70} +(25.5595 - 18.5701i) q^{71} +(-98.3279 + 31.9487i) q^{73} +(118.581 + 38.5293i) q^{74} -327.620i q^{76} +(-75.5345 - 31.6337i) q^{77} +(10.7350 - 14.7755i) q^{79} +(-76.4994 + 235.441i) q^{80} +(50.6990 - 36.8350i) q^{82} +(69.9409 + 96.2654i) q^{83} +(-14.1276 - 4.59032i) q^{85} +(-105.420 - 76.5919i) q^{86} +(-152.769 - 251.496i) q^{88} -154.739 q^{89} +(16.8497 - 51.8580i) q^{91} +(-69.7218 - 214.581i) q^{92} +(88.3402 + 121.590i) q^{94} +(118.376 - 38.4627i) q^{95} +(55.9976 + 40.6846i) q^{97} +24.8128i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 30 q^{7}+O(q^{10}) \) 16 * q - 4 * q^4 + 30 * q^7	\( 16 q - 4 q^{4} + 30 q^{7} - 30 q^{13} - 176 q^{16} + 90 q^{22} - 74 q^{25} - 50 q^{28} + 130 q^{31} + 328 q^{34} + 90 q^{37} + 450 q^{40} - 370 q^{46} - 54 q^{49} - 790 q^{52} - 476 q^{55} - 630 q^{58} + 210 q^{61} + 1104 q^{64} + 300 q^{67} + 268 q^{70} - 170 q^{73} + 30 q^{79} + 90 q^{82} - 610 q^{85} - 600 q^{88} - 402 q^{91} + 1030 q^{94} + 870 q^{97}+O(q^{100}) \) 16 * q - 4 * q^4 + 30 * q^7 - 30 * q^13 - 176 * q^16 + 90 * q^22 - 74 * q^25 - 50 * q^28 + 130 * q^31 + 328 * q^34 + 90 * q^37 + 450 * q^40 - 370 * q^46 - 54 * q^49 - 790 * q^52 - 476 * q^55 - 630 * q^58 + 210 * q^61 + 1104 * q^64 + 300 * q^67 + 268 * q^70 - 170 * q^73 + 30 * q^79 + 90 * q^82 - 610 * q^85 - 600 * q^88 - 402 * q^91 + 1030 * q^94 + 870 * q^97

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