LMFDB - Embedded newform 198.3.j.b.73.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [198,3,Mod(19,198)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("198.19"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(198, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	198.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.39510923433$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.6879707136000000000000.7
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 $ x^16 - 4x^14 + 15x^12 - 56x^10 + 209x^8 - 56x^6 + 15x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			73.2
Root			$0.492303 - 0.159959i$ of defining polynomial
Character	$\chi$	$=$	198.73
Dual form			198.3.j.b.19.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.831254 + 1.14412i) q^{2} +(-0.618034 - 1.90211i) q^{4} +(-1.74791 + 1.26993i) q^{5} +(-1.27622 + 0.414669i) q^{7} +(2.68999 + 0.874032i) q^{8} -3.05545i q^{10} +(-10.9966 - 0.273421i) q^{11} +(-6.36050 + 8.75447i) q^{13} +(0.586431 - 1.80485i) q^{14} +(-3.23607 + 2.35114i) q^{16} +(-15.8880 - 21.8679i) q^{17} +(-9.95521 - 3.23464i) q^{19} +(3.49581 + 2.53986i) q^{20} +(9.45379 - 12.3542i) q^{22} -14.1912 q^{23} +(-6.28297 + 19.3370i) q^{25} +(-4.72900 - 14.5544i) q^{26} +(1.57749 + 2.17124i) q^{28} +(11.7472 - 3.81689i) q^{29} +(-20.7370 - 15.0663i) q^{31} -5.65685i q^{32} +38.2266 q^{34} +(1.70411 - 2.34551i) q^{35} +(-9.00782 - 27.7232i) q^{37} +(11.9761 - 8.70117i) q^{38} +(-5.81182 + 1.88837i) q^{40} +(10.1746 + 3.30593i) q^{41} -41.5007i q^{43} +(6.27620 + 21.0858i) q^{44} +(11.7965 - 16.2364i) q^{46} +(-21.6045 + 66.4919i) q^{47} +(-38.1850 + 27.7431i) q^{49} +(-16.9011 - 23.2624i) q^{50} +(20.5830 + 6.68782i) q^{52} +(48.5045 + 35.2406i) q^{53} +(19.5683 - 13.4870i) q^{55} -3.79546 q^{56} +(-5.39790 + 16.6130i) q^{58} +(16.2078 + 49.8825i) q^{59} +(64.7817 + 89.1643i) q^{61} +(34.4753 - 11.2017i) q^{62} +(6.47214 + 4.70228i) q^{64} -23.3794i q^{65} +60.0831 q^{67} +(-31.7760 + 43.7359i) q^{68} +(1.26700 + 3.89943i) q^{70} +(56.0995 - 40.7587i) q^{71} +(-69.7313 + 22.6571i) q^{73} +(39.2065 + 12.7390i) q^{74} +20.9350i q^{76} +(14.1475 - 4.21101i) q^{77} +(-58.9228 + 81.1003i) q^{79} +(2.67056 - 8.21915i) q^{80} +(-12.2401 + 8.89294i) q^{82} +(-59.8908 - 82.4326i) q^{83} +(55.5414 + 18.0465i) q^{85} +(47.4819 + 34.4976i) q^{86} +(-29.3418 - 10.3469i) q^{88} +55.9575 q^{89} +(4.48718 - 13.8101i) q^{91} +(8.77063 + 26.9932i) q^{92} +(-58.1161 - 79.9899i) q^{94} +(21.5085 - 6.98855i) q^{95} +(141.226 + 102.607i) q^{97} -66.7499i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 8 q^{5} + 60 q^{7} + 4 q^{11} - 60 q^{13} + 32 q^{14} - 16 q^{16} + 60 q^{17} + 16 q^{20} - 48 q^{22} + 8 q^{23} - 48 q^{25} - 48 q^{26} + 40 q^{28} + 160 q^{29} + 32 q^{31} - 64 q^{34}+ \cdots + 324 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 - 8 * q^5 + 60 * q^7 + 4 * q^11 - 60 * q^13 + 32 * q^14 - 16 * q^16 + 60 * q^17 + 16 * q^20 - 48 * q^22 + 8 * q^23 - 48 * q^25 - 48 * q^26 + 40 * q^28 + 160 * q^29 + 32 * q^31 - 64 * q^34 - 160 * q^35 - 84 * q^37 + 48 * q^38 - 80 * q^40 - 40 * q^41 - 168 * q^44 + 160 * q^46 - 372 * q^47 + 96 * q^49 - 160 * q^50 + 40 * q^52 + 124 * q^53 + 32 * q^55 + 96 * q^56 - 16 * q^58 + 172 * q^59 + 100 * q^61 + 40 * q^62 + 32 * q^64 + 248 * q^67 + 120 * q^68 + 8 * q^70 - 48 * q^71 + 160 * q^73 - 80 * q^74 + 172 * q^77 - 460 * q^79 + 48 * q^80 - 24 * q^82 + 420 * q^83 - 420 * q^85 + 456 * q^86 - 144 * q^88 + 360 * q^89 - 252 * q^91 + 64 * q^92 - 280 * q^94 - 180 * q^95 + 324 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	−0.831254	+	1.14412i	−0.415627	+	0.572061i
$2$	−0.831254	+	1.14412i	−0.415627	+	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.618034	−	1.90211i	−0.154508	−	0.475528i
$5$	−1.74791	+	1.26993i	−0.349581	+	0.253986i	−0.748693	−	0.662916i	$-0.769318\pi$
$5$	−1.74791	+	1.26993i	−0.349581	+	0.253986i	0.399112	+	0.916902i	$0.369318\pi$
$6$		0			0
$7$	−1.27622	+	0.414669i	−0.182317	+	0.0592384i	−0.398753	−	0.917058i	$-0.630557\pi$
$7$	−1.27622	+	0.414669i	−0.182317	+	0.0592384i	0.216436	+	0.976297i	$0.430557\pi$
$8$	2.68999	+	0.874032i	0.336249	+	0.109254i
$9$		0			0
$10$		−	3.05545i		−	0.305545i
$11$	−10.9966	−	0.273421i	−0.999691	−	0.0248564i
$11$	−10.9966	−	0.273421i	−0.999691	−	0.0248564i
$12$		0			0
$13$	−6.36050	+	8.75447i	−0.489269	+	0.673421i	−0.980253	−	0.197748i	$-0.936637\pi$
$13$	−6.36050	+	8.75447i	−0.489269	+	0.673421i	0.490984	+	0.871169i	$0.336637\pi$
$14$	0.586431	−	1.80485i	0.0418879	−	0.128918i
$15$		0			0
$16$	−3.23607	+	2.35114i	−0.202254	+	0.146946i
$17$	−15.8880	−	21.8679i	−0.934588	−	1.28635i	−0.958043	−	0.286625i	$-0.907467\pi$
$17$	−15.8880	−	21.8679i	−0.934588	−	1.28635i	0.0234551	−	0.999725i	$-0.492533\pi$
$18$		0			0
$19$	−9.95521	−	3.23464i	−0.523958	−	0.170244i	0.0350827	−	0.999384i	$-0.488831\pi$
$19$	−9.95521	−	3.23464i	−0.523958	−	0.170244i	−0.559041	+	0.829140i	$0.688831\pi$
$20$	3.49581	+	2.53986i	0.174791	+	0.126993i
$21$		0			0
$22$	9.45379	−	12.3542i	0.429718	−	0.561554i
$23$	−14.1912			−0.617007			−0.308504	−	0.951223i	$-0.599828\pi$
$23$	−14.1912			−0.617007			−0.308504	+	0.951223i	$0.599828\pi$
$24$		0			0
$25$	−6.28297	+	19.3370i	−0.251319	+	0.773479i
$26$	−4.72900	−	14.5544i	−0.181885	−	0.559784i
$27$		0			0
$28$	1.57749	+	2.17124i	0.0563391	+	0.0775441i
$29$	11.7472	−	3.81689i	0.405075	−	0.131617i	−0.0993909	−	0.995048i	$-0.531689\pi$
$29$	11.7472	−	3.81689i	0.405075	−	0.131617i	0.504466	+	0.863432i	$0.331689\pi$
$30$		0			0
$31$	−20.7370	−	15.0663i	−0.668934	−	0.486009i	0.200734	−	0.979646i	$-0.435667\pi$
$31$	−20.7370	−	15.0663i	−0.668934	−	0.486009i	−0.869668	+	0.493637i	$0.835667\pi$
$32$		−	5.65685i		−	0.176777i
$33$		0			0
$34$	38.2266			1.12431
$35$	1.70411	−	2.34551i	0.0486890	−	0.0670146i
$36$		0			0
$37$	−9.00782	−	27.7232i	−0.243455	−	0.749276i	−0.995887	−	0.0906063i	$-0.971120\pi$
$37$	−9.00782	−	27.7232i	−0.243455	−	0.749276i	0.752432	−	0.658670i	$-0.228880\pi$
$38$	11.9761	−	8.70117i	0.315161	−	0.228978i
$39$		0			0
$40$	−5.81182	+	1.88837i	−0.145295	+	0.0472093i
$41$	10.1746	+	3.30593i	0.248161	+	0.0806325i	0.430456	−	0.902611i	$-0.358353\pi$
$41$	10.1746	+	3.30593i	0.248161	+	0.0806325i	−0.182295	+	0.983244i	$0.558353\pi$
$42$		0			0
$43$		−	41.5007i		−	0.965132i	−0.875859	−	0.482566i	$-0.839705\pi$
$43$		−	41.5007i		−	0.965132i	0.875859	−	0.482566i	$-0.160295\pi$
$44$	6.27620	+	21.0858i	0.142641	+	0.479222i
$45$		0			0
$46$	11.7965	−	16.2364i	0.256445	−	0.352966i
$47$	−21.6045	+	66.4919i	−0.459671	+	1.41472i	0.405892	+	0.913921i	$0.366961\pi$
$47$	−21.6045	+	66.4919i	−0.459671	+	1.41472i	−0.865563	+	0.500800i	$0.833039\pi$
$48$		0			0
$49$	−38.1850	+	27.7431i	−0.779287	+	0.566185i
$50$	−16.9011	−	23.2624i	−0.338023	−	0.465249i
$51$		0			0
$52$	20.5830	+	6.68782i	0.395827	+	0.128612i
$53$	48.5045	+	35.2406i	0.915180	+	0.664917i	0.942320	−	0.334714i	$-0.108640\pi$
$53$	48.5045	+	35.2406i	0.915180	+	0.664917i	−0.0271395	+	0.999632i	$0.508640\pi$
$54$		0			0
$55$	19.5683	−	13.4870i	0.355786	−	0.245218i
$56$	−3.79546			−0.0677760
$57$		0			0
$58$	−5.39790	+	16.6130i	−0.0930672	+	0.286431i
$59$	16.2078	+	49.8825i	0.274708	+	0.845466i	0.989296	+	0.145920i	$0.0466142\pi$
$59$	16.2078	+	49.8825i	0.274708	+	0.845466i	−0.714588	+	0.699546i	$0.753386\pi$
$60$		0			0
$61$	64.7817	+	89.1643i	1.06199	+	1.46171i	0.877926	+	0.478797i	$0.158927\pi$
$61$	64.7817	+	89.1643i	1.06199	+	1.46171i	0.184069	+	0.982913i	$0.441073\pi$
$62$	34.4753	−	11.2017i	0.556054	−	0.180673i
$63$		0			0
$64$	6.47214	+	4.70228i	0.101127	+	0.0734732i
$65$		−	23.3794i		−	0.359683i
$66$		0			0
$67$	60.0831			0.896762			0.448381	−	0.893843i	$-0.352001\pi$
$67$	60.0831			0.896762			0.448381	+	0.893843i	$0.352001\pi$
$68$	−31.7760	+	43.7359i	−0.467294	+	0.643175i
$69$		0			0
$70$	1.26700	+	3.89943i	0.0181000	+	0.0557061i
$71$	56.0995	−	40.7587i	0.790134	−	0.574066i	−0.117869	−	0.993029i	$-0.537606\pi$
$71$	56.0995	−	40.7587i	0.790134	−	0.574066i	0.908003	+	0.418963i	$0.137606\pi$
$72$		0			0
$73$	−69.7313	+	22.6571i	−0.955224	+	0.310371i	−0.744836	−	0.667247i	$-0.767473\pi$
$73$	−69.7313	+	22.6571i	−0.955224	+	0.310371i	−0.210387	+	0.977618i	$0.567473\pi$
$74$	39.2065	+	12.7390i	0.529818	+	0.172148i
$75$		0			0
$76$			20.9350i			0.275461i
$77$	14.1475	−	4.21101i	0.183733	−	0.0546884i
$78$		0			0
$79$	−58.9228	+	81.1003i	−0.745859	+	1.02659i	0.252401	+	0.967623i	$0.418780\pi$
$79$	−58.9228	+	81.1003i	−0.745859	+	1.02659i	−0.998260	+	0.0589638i	$0.981220\pi$
$80$	2.67056	−	8.21915i	0.0333820	−	0.102739i
$81$		0			0
$82$	−12.2401	+	8.89294i	−0.149269	+	0.108450i
$83$	−59.8908	−	82.4326i	−0.721575	−	0.993163i	−0.999470	−	0.0325518i	$-0.989637\pi$
$83$	−59.8908	−	82.4326i	−0.721575	−	0.993163i	0.277895	−	0.960612i	$-0.410363\pi$
$84$		0			0
$85$	55.5414	+	18.0465i	0.653429	+	0.212312i
$86$	47.4819	+	34.4976i	0.552115	+	0.401135i
$87$		0			0
$88$	−29.3418	−	10.3469i	−0.333430	−	0.117578i
$89$	55.9575			0.628736			0.314368	−	0.949301i	$-0.398207\pi$
$89$	55.9575			0.628736			0.314368	+	0.949301i	$0.398207\pi$
$90$		0			0
$91$	4.48718	−	13.8101i	0.0493097	−	0.151760i
$92$	8.77063	+	26.9932i	0.0953329	+	0.293404i
$93$		0			0
$94$	−58.1161	−	79.9899i	−0.618256	−	0.850956i
$95$	21.5085	−	6.98855i	0.226406	−	0.0735636i
$96$		0			0
$97$	141.226	+	102.607i	1.45594	+	1.05780i	0.984398	+	0.175956i	$0.0563017\pi$
$97$	141.226	+	102.607i	1.45594	+	1.05780i	0.471540	+	0.881845i	$0.343698\pi$
$98$		−	66.7499i		−	0.681121i
$99$		0			0
$100$	40.6642			0.406642
$101$	18.9336	−	26.0599i	0.187461	−	0.258019i	−0.704934	−	0.709273i	$-0.749023\pi$
$101$	18.9336	−	26.0599i	0.187461	−	0.258019i	0.892395	+	0.451254i	$0.149023\pi$
$102$		0			0
$103$	−54.8453	−	168.797i	−0.532479	−	1.63880i	−0.749034	−	0.662532i	$-0.769482\pi$
$103$	−54.8453	−	168.797i	−0.532479	−	1.63880i	0.216555	−	0.976270i	$-0.430518\pi$
$104$	−24.7614	+	17.9902i	−0.238090	+	0.172983i
$105$		0			0
$106$	−80.6392	+	26.2013i	−0.760747	+	0.247182i
$107$	−163.085	−	52.9896i	−1.52416	−	0.495230i	−0.577206	−	0.816599i	$-0.695857\pi$
$107$	−163.085	−	52.9896i	−1.52416	−	0.495230i	−0.946954	+	0.321369i	$0.895857\pi$
$108$		0			0
$109$		−	199.946i		−	1.83437i	−0.398466	−	0.917183i	$-0.630457\pi$
$109$		−	199.946i		−	1.83437i	0.398466	−	0.917183i	$-0.369543\pi$
$110$	−0.835424	+	33.5996i	−0.00759477	+	0.305451i
$111$		0			0
$112$	3.15499	−	4.34247i	0.0281696	−	0.0387721i
$113$	−57.2171	+	176.096i	−0.506346	+	1.55837i	0.292150	+	0.956373i	$0.405629\pi$
$113$	−57.2171	+	176.096i	−0.506346	+	1.55837i	−0.798496	+	0.602000i	$0.794371\pi$
$114$		0			0
$115$	24.8048	−	18.0218i	0.215694	−	0.156711i
$116$	−14.5203	−	19.9855i	−0.125175	−	0.172289i
$117$		0			0
$118$	−70.5445	−	22.9213i	−0.597835	−	0.194248i
$119$	29.3445	+	21.3201i	0.246593	+	0.179160i
$120$		0			0
$121$	120.850	+	6.01340i	0.998764	+	0.0496975i
$122$	−155.865			−1.27758
$123$		0			0
$124$	−15.8416	+	48.7555i	−0.127755	+	0.393190i
$125$	−30.2656	−	93.1478i	−0.242125	−	0.745183i
$126$		0			0
$127$	−90.8759	−	125.080i	−0.715558	−	0.984882i	−0.999660	−	0.0260874i	$-0.991695\pi$
$127$	−90.8759	−	125.080i	−0.715558	−	0.984882i	0.284101	−	0.958794i	$-0.408305\pi$
$128$	−10.7600	+	3.49613i	−0.0840623	+	0.0273135i
$129$		0			0
$130$	26.7489	+	19.4342i	0.205761	+	0.149494i
$131$		−	105.137i		−	0.802575i	−0.915952	−	0.401288i	$-0.868563\pi$
$131$		−	105.137i		−	0.802575i	0.915952	−	0.401288i	$-0.131437\pi$
$132$		0			0
$133$	14.0463			0.105612
$134$	−49.9443	+	68.7424i	−0.372718	+	0.513003i
$135$		0			0
$136$	−23.6253	−	72.7113i	−0.173716	−	0.534642i
$137$	−69.0877	+	50.1952i	−0.504290	+	0.366388i	−0.810653	−	0.585527i	$-0.800888\pi$
$137$	−69.0877	+	50.1952i	−0.504290	+	0.366388i	0.306363	+	0.951915i	$0.400888\pi$
$138$		0			0
$139$	−98.5146	+	32.0093i	−0.708738	+	0.230283i	−0.641134	−	0.767429i	$-0.721536\pi$
$139$	−98.5146	+	32.0093i	−0.708738	+	0.230283i	−0.0676046	+	0.997712i	$0.521536\pi$
$140$	−5.51463	−	1.79181i	−0.0393902	−	0.0127986i
$141$		0			0
$142$			98.0656i			0.690603i
$143$	72.3375	−	94.5303i	0.505857	−	0.661051i
$144$		0			0
$145$	−15.6858	+	21.5896i	−0.108178	+	0.148894i
$146$	32.0420	−	98.6150i	0.219465	−	0.675445i
$147$		0			0
$148$	−47.1655	+	34.2678i	−0.318686	+	0.231539i
$149$	53.4827	+	73.6126i	0.358944	+	0.494045i	0.949854	−	0.312693i	$-0.101231\pi$
$149$	53.4827	+	73.6126i	0.358944	+	0.494045i	−0.590910	+	0.806738i	$0.701231\pi$
$150$		0			0
$151$	−58.4781	−	19.0007i	−0.387272	−	0.125832i	0.108908	−	0.994052i	$-0.465264\pi$
$151$	−58.4781	−	19.0007i	−0.387272	−	0.125832i	−0.496180	+	0.868220i	$0.665264\pi$
$152$	−23.9523	−	17.4023i	−0.157581	−	0.114489i
$153$		0			0
$154$	−6.94223	+	19.6869i	−0.0450794	+	0.127837i
$155$	55.3793			0.357286
$156$		0			0
$157$	−40.7412	+	125.388i	−0.259498	+	0.798652i	0.733412	+	0.679784i	$0.237927\pi$
$157$	−40.7412	+	125.388i	−0.259498	+	0.798652i	−0.992910	+	0.118868i	$0.962073\pi$
$158$	−43.8089	−	134.830i	−0.277271	−	0.853354i
$159$		0			0
$160$	7.18380	+	9.88765i	0.0448987	+	0.0617978i
$161$	18.1111	−	5.88464i	0.112491	−	0.0365506i
$162$		0			0
$163$	12.4028	+	9.01116i	0.0760908	+	0.0552832i	0.625180	−	0.780480i	$-0.285025\pi$
$163$	12.4028	+	9.01116i	0.0760908	+	0.0552832i	−0.549090	+	0.835764i	$0.685025\pi$
$164$		−	21.3964i		−	0.130466i
$165$		0			0
$166$	144.097			0.868057
$167$	91.9802	−	126.600i	0.550780	−	0.758083i	−0.439338	−	0.898322i	$-0.644787\pi$
$167$	91.9802	−	126.600i	0.550780	−	0.758083i	0.990118	+	0.140239i	$0.0447870\pi$
$168$		0			0
$169$	16.0390	+	49.3630i	0.0949054	+	0.292089i
$170$	−66.8165	+	48.5450i	−0.393038	+	0.285559i
$171$		0			0
$172$	−78.9390	+	25.6488i	−0.458948	+	0.149121i
$173$	−157.889	−	51.3013i	−0.912654	−	0.296539i	−0.185204	−	0.982700i	$-0.559295\pi$
$173$	−157.889	−	51.3013i	−0.912654	−	0.296539i	−0.727450	+	0.686161i	$0.759295\pi$
$174$		0			0
$175$		−	27.2836i		−	0.155906i
$176$	36.2286	−	24.9698i	0.205844	−	0.141874i
$177$		0			0
$178$	−46.5149	+	64.0223i	−0.261320	+	0.359676i
$179$	−32.0420	+	98.6153i	−0.179006	+	0.550923i	−0.999794	−	0.0203097i	$-0.993535\pi$
$179$	−32.0420	+	98.6153i	−0.179006	+	0.550923i	0.820788	+	0.571233i	$0.193535\pi$
$180$		0			0
$181$	173.073	−	125.745i	0.956207	−	0.694725i	0.00394032	−	0.999992i	$-0.498746\pi$
$181$	173.073	−	125.745i	0.956207	−	0.694725i	0.952267	+	0.305267i	$0.0987458\pi$
$182$	12.0705	+	16.6136i	0.0663214	+	0.0912836i
$183$		0			0
$184$	−38.1742	−	12.4035i	−0.207468	−	0.0674105i
$185$	50.9513	+	37.0183i	0.275412	+	0.200099i
$186$		0			0
$187$	168.735	+	244.817i	0.902325	+	1.30918i
$188$	139.827			0.743763
$189$		0			0
$190$	−9.88330	+	30.4177i	−0.0520173	+	0.160093i
$191$	−16.5296	−	50.8728i	−0.0865422	−	0.266350i	0.898415	−	0.439147i	$-0.144719\pi$
$191$	−16.5296	−	50.8728i	−0.0865422	−	0.266350i	−0.984957	+	0.172798i	$0.944719\pi$
$192$		0			0
$193$	−52.5357	−	72.3091i	−0.272205	−	0.374659i	0.650927	−	0.759140i	$-0.274380\pi$
$193$	−52.5357	−	72.3091i	−0.272205	−	0.374659i	−0.923133	+	0.384481i	$0.874380\pi$
$194$	−234.789	+	76.2877i	−1.21025	+	0.393235i
$195$		0			0
$196$	76.3701	+	55.4861i	0.389643	+	0.283092i
$197$			146.368i			0.742986i	0.928436	+	0.371493i	$0.121154\pi$
$197$			146.368i			0.742986i	−0.928436	+	0.371493i	$0.878846\pi$
$198$		0			0
$199$	−224.072			−1.12599			−0.562994	−	0.826461i	$-0.690351\pi$
$199$	−224.072			−1.12599			−0.562994	+	0.826461i	$0.690351\pi$
$200$	−33.8023	+	46.5249i	−0.169011	+	0.232624i
$201$		0			0
$202$	14.0771	+	43.3247i	0.0696884	+	0.214479i
$203$	−13.4092	+	9.74238i	−0.0660554	+	0.0479920i
$204$		0			0
$205$	−21.9826	+	7.14257i	−0.107232	+	0.0348418i
$206$	238.714	+	77.5630i	1.15881	+	0.376520i
$207$		0			0
$208$		−	43.2845i		−	0.208098i
$209$	108.589	+	38.2920i	0.519565	+	0.183215i
$210$		0			0
$211$	100.375	−	138.154i	0.475710	−	0.654758i	−0.501964	−	0.864889i	$-0.667389\pi$
$211$	100.375	−	138.154i	0.475710	−	0.654758i	0.977673	+	0.210130i	$0.0673889\pi$
$212$	37.0542	−	114.041i	0.174784	−	0.537929i
$213$		0			0
$214$	196.192	−	142.542i	0.916784	−	0.666082i
$215$	52.7029	+	72.5393i	0.245130	+	0.337392i
$216$		0			0
$217$	32.7124	+	10.6289i	0.150749	+	0.0489812i
$218$	228.763	+	166.206i	1.04937	+	0.762412i
$219$		0			0
$220$	−37.7476	−	28.8856i	−0.171580	−	0.131298i
$221$	292.498			1.32352
$222$		0			0
$223$	−99.6457	+	306.678i	−0.446842	+	1.37524i	0.433610	+	0.901101i	$0.357240\pi$
$223$	−99.6457	+	306.678i	−0.446842	+	1.37524i	−0.880451	+	0.474137i	$0.842760\pi$
$224$	2.34572	+	7.21939i	0.0104720	+	0.0322294i
$225$		0			0
$226$	−153.914	−	211.844i	−0.681034	−	0.937363i
$227$	−355.469	+	115.499i	−1.56594	+	0.508806i	−0.958387	−	0.285472i	$-0.907850\pi$
$227$	−355.469	+	115.499i	−1.56594	+	0.508806i	−0.607555	+	0.794277i	$0.707850\pi$
$228$		0			0
$229$	89.7934	+	65.2387i	0.392111	+	0.284885i	0.766320	−	0.642459i	$-0.222086\pi$
$229$	89.7934	+	65.2387i	0.392111	+	0.284885i	−0.374209	+	0.927344i	$0.622086\pi$
$230$			43.3604i			0.188524i
$231$		0			0
$232$	34.9359			0.150586
$233$	−137.117	+	188.725i	−0.588484	+	0.809979i	−0.994593	−	0.103845i	$-0.966885\pi$
$233$	−137.117	+	188.725i	−0.588484	+	0.809979i	0.406109	+	0.913825i	$0.366885\pi$
$234$		0			0
$235$	−46.6773	−	143.658i	−0.198627	−	0.611310i
$236$	84.8651	−	61.6581i	0.359598	−	0.261263i
$237$		0			0
$238$	−48.7855	+	15.8514i	−0.204981	+	0.0666024i
$239$	282.107	+	91.6620i	1.18036	+	0.383523i	0.832501	−	0.554023i	$-0.186908\pi$
$239$	282.107	+	91.6620i	1.18036	+	0.383523i	0.347861	+	0.937546i	$0.386908\pi$
$240$		0			0
$241$		−	30.0448i		−	0.124667i	−0.998055	−	0.0623336i	$-0.980146\pi$
$241$		−	30.0448i		−	0.124667i	0.998055	−	0.0623336i	$-0.0198543\pi$
$242$	−107.337	+	133.269i	−0.443543	+	0.550699i
$243$		0			0
$244$	129.563	−	178.329i	0.530997	−	0.730855i
$245$	31.5122	−	96.9845i	0.128621	−	0.395855i
$246$		0			0
$247$	91.6376	−	66.5786i	0.371003	−	0.269549i
$248$	−42.6139	−	58.6530i	−0.171830	−	0.236504i
$249$		0			0
$250$	131.731	+	42.8020i	0.526924	+	0.171208i
$251$	−142.859	−	103.793i	−0.569161	−	0.413520i	0.265639	−	0.964072i	$-0.414417\pi$
$251$	−142.859	−	103.793i	−0.569161	−	0.413520i	−0.834800	+	0.550553i	$0.814417\pi$
$252$		0			0
$253$	156.055	+	3.88016i	0.616817	+	0.0153366i
$254$	218.648			0.860818
$255$		0			0
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	−71.5241	−	220.129i	−0.278304	−	0.856531i	−0.988326	−	0.152352i	$-0.951315\pi$
$257$	−71.5241	−	220.129i	−0.278304	−	0.856531i	0.710022	−	0.704179i	$-0.248685\pi$
$258$		0			0
$259$	22.9919	+	31.6457i	0.0887719	+	0.122184i
$260$	−44.4702	+	14.4492i	−0.171039	+	0.0555740i
$261$		0			0
$262$	120.290	+	87.3958i	0.459122	+	0.333572i
$263$		−	55.9320i		−	0.212669i	−0.994330	−	0.106335i	$-0.966089\pi$
$263$		−	55.9320i		−	0.212669i	0.994330	−	0.106335i	$-0.0339115\pi$
$264$		0			0
$265$	−129.534			−0.488809
$266$	−11.6761	+	16.0707i	−0.0438950	+	0.0604163i
$267$		0			0
$268$	−37.1334	−	114.285i	−0.138557	−	0.426436i
$269$	1.67109	−	1.21412i	0.00621222	−	0.00451344i	−0.584675	−	0.811268i	$-0.698778\pi$
$269$	1.67109	−	1.21412i	0.00621222	−	0.00451344i	0.590887	+	0.806754i	$0.298778\pi$
$270$		0			0
$271$	−27.3691	+	8.89274i	−0.100993	+	0.0328146i	−0.359078	−	0.933308i	$-0.616909\pi$
$271$	−27.3691	+	8.89274i	−0.100993	+	0.0328146i	0.258085	+	0.966122i	$0.416909\pi$
$272$	102.829	+	33.4112i	0.378049	+	0.122835i
$273$		0			0
$274$		−	120.770i		−	0.440766i
$275$	74.3784	−	210.923i	0.270467	−	0.766993i
$276$		0			0
$277$	12.3226	−	16.9606i	0.0444859	−	0.0612296i	−0.786195	−	0.617979i	$-0.787952\pi$
$277$	12.3226	−	16.9606i	0.0444859	−	0.0612296i	0.830680	+	0.556749i	$0.187952\pi$
$278$	45.2680	−	139.321i	0.162835	−	0.501154i
$279$		0			0
$280$	6.63411	−	4.81996i	0.0236932	−	0.0172141i
$281$	166.769	+	229.538i	0.593484	+	0.816861i	0.995092	−	0.0989509i	$-0.0315487\pi$
$281$	166.769	+	229.538i	0.593484	+	0.816861i	−0.401608	+	0.915812i	$0.631549\pi$
$282$		0			0
$283$	−233.553	−	75.8861i	−0.825277	−	0.268149i	−0.134222	−	0.990951i	$-0.542854\pi$
$283$	−233.553	−	75.8861i	−0.825277	−	0.268149i	−0.691055	+	0.722803i	$0.742854\pi$
$284$	−112.199	−	81.5174i	−0.395067	−	0.287033i
$285$		0			0
$286$	48.0235	+	161.342i	0.167914	+	0.564132i
$287$	−14.3559			−0.0500206
$288$		0			0
$289$	−136.473	+	420.020i	−0.472224	+	1.45336i
$290$	−11.6623	−	35.8929i	−0.0402149	−	0.123769i
$291$		0			0
$292$	86.1927	+	118.634i	0.295180	+	0.406281i
$293$	106.632	−	34.6468i	0.363931	−	0.118249i	−0.121342	−	0.992611i	$-0.538720\pi$
$293$	106.632	−	34.6468i	0.363931	−	0.118249i	0.485274	+	0.874362i	$0.338720\pi$
$294$		0			0
$295$	−91.6769	−	66.6072i	−0.310769	−	0.225787i
$296$		−	82.4484i		−	0.278542i
$297$		0			0
$298$	−128.680			−0.431811
$299$	90.2629	−	124.236i	0.301883	−	0.415506i
$300$		0			0
$301$	17.2091	+	52.9640i	0.0571729	+	0.175960i
$302$	70.3492	−	51.1117i	0.232944	−	0.169244i
$303$		0			0
$304$	39.8208	−	12.9386i	0.130990	−	0.0425611i
$305$	−226.465	−	73.5828i	−0.742507	−	0.241255i
$306$		0			0
$307$			14.8337i			0.0483183i	0.999708	+	0.0241592i	$0.00769085\pi$
$307$			14.8337i			0.0483183i	−0.999708	+	0.0241592i	$0.992309\pi$
$308$	−16.7534	−	24.3075i	−0.0543942	−	0.0789206i
$309$		0			0
$310$	−46.0343	+	63.3608i	−0.148498	+	0.204390i
$311$	−85.4662	+	263.038i	−0.274811	+	0.845781i	0.714458	+	0.699678i	$0.246673\pi$
$311$	−85.4662	+	263.038i	−0.274811	+	0.845781i	−0.989269	+	0.146103i	$0.953327\pi$
$312$		0			0
$313$	−162.854	+	118.320i	−0.520299	+	0.378019i	−0.816717	−	0.577039i	$-0.804208\pi$
$313$	−162.854	+	118.320i	−0.520299	+	0.378019i	0.296417	+	0.955058i	$0.404208\pi$
$314$	−109.593	−	150.843i	−0.349024	−	0.480390i
$315$		0			0
$316$	190.678	+	61.9551i	0.603412	+	0.196061i
$317$	−388.142	−	282.001i	−1.22442	−	0.889594i	−0.227962	−	0.973670i	$-0.573206\pi$
$317$	−388.142	−	282.001i	−1.22442	−	0.889594i	−0.996459	+	0.0840757i	$0.973206\pi$
$318$		0			0
$319$	−130.223	+	38.7609i	−0.408221	+	0.121507i
$320$	−17.2842			−0.0540133
$321$		0			0
$322$	−8.32214	+	25.6129i	−0.0258451	+	0.0795432i
$323$	87.4333	+	269.092i	0.270691	+	0.833102i
$324$		0			0
$325$	−129.322	−	177.997i	−0.397915	−	0.547683i
$326$	−20.6198	+	6.69977i	−0.0632508	+	0.0205514i
$327$		0			0
$328$	24.4802	+	17.7859i	0.0746346	+	0.0542252i
$329$		−	93.8170i		−	0.285158i
$330$		0			0
$331$	406.762			1.22889			0.614444	−	0.788961i	$-0.289380\pi$
$331$	406.762			1.22889			0.614444	+	0.788961i	$0.289380\pi$
$332$	−119.782	+	164.865i	−0.360788	+	0.496582i
$333$		0			0
$334$	68.3869	+	210.473i	0.204751	+	0.630159i
$335$	−105.020	+	76.3012i	−0.313491	+	0.227765i
$336$		0			0
$337$	−338.761	+	110.070i	−1.00523	+	0.326618i	−0.764952	−	0.644087i	$-0.777237\pi$
$337$	−338.761	+	110.070i	−1.00523	+	0.326618i	−0.240274	+	0.970705i	$0.577237\pi$
$338$	−69.8098	−	22.6826i	−0.206538	−	0.0671083i
$339$		0			0
$340$		−	116.799i		−	0.343528i
$341$	223.917	+	171.348i	0.656647	+	0.502486i
$342$		0			0
$343$	75.8770	−	104.436i	0.221216	−	0.304477i
$344$	36.2729	−	111.637i	0.105445	−	0.324525i
$345$		0			0
$346$	189.941	−	138.000i	0.548962	−	0.398844i
$347$	185.698	+	255.591i	0.535152	+	0.736574i	0.987905	−	0.155062i	$-0.0495578\pi$
$347$	185.698	+	255.591i	0.535152	+	0.736574i	−0.452752	+	0.891636i	$0.649558\pi$
$348$		0			0
$349$	−61.5955	−	20.0136i	−0.176491	−	0.0573455i	0.219438	−	0.975626i	$-0.429578\pi$
$349$	−61.5955	−	20.0136i	−0.176491	−	0.0573455i	−0.395930	+	0.918281i	$0.629578\pi$
$350$	31.2158	+	22.6796i	0.0891880	+	0.0647988i
$351$		0			0
$352$	−1.54670	+	62.2062i	−0.00439404	+	0.176722i
$353$	−518.482			−1.46879			−0.734394	−	0.678723i	$-0.762533\pi$
$353$	−518.482			−1.46879			−0.734394	+	0.678723i	$0.762533\pi$
$354$		0			0
$355$	−46.2961	+	142.485i	−0.130412	+	0.401366i
$356$	−34.5836	−	106.437i	−0.0971450	−	0.298982i
$357$		0			0
$358$	−86.1929	−	118.634i	−0.240762	−	0.331381i
$359$	−413.135	+	134.236i	−1.15079	+	0.373915i	−0.821442	−	0.570292i	$-0.806830\pi$
$359$	−413.135	+	134.236i	−1.15079	+	0.373915i	−0.329351	+	0.944207i	$0.606830\pi$
$360$		0			0
$361$	−203.412	−	147.787i	−0.563468	−	0.409383i
$362$			302.544i			0.835756i
$363$		0			0
$364$	−29.0417			−0.0797848
$365$	93.1110	−	128.156i	0.255099	−	0.351113i
$366$		0			0
$367$	−190.780	−	587.161i	−0.519837	−	1.59989i	−0.774305	−	0.632812i	$-0.781901\pi$
$367$	−190.780	−	587.161i	−0.519837	−	1.59989i	0.254468	−	0.967081i	$-0.418099\pi$
$368$	45.9236	−	33.3654i	0.124792	−	0.0906670i
$369$		0			0
$370$	−84.7069	+	27.5230i	−0.228938	+	0.0743864i
$371$	−76.5157	−	24.8614i	−0.206242	−	0.0670120i
$372$		0			0
$373$		−	307.758i		−	0.825087i	−0.910938	−	0.412544i	$-0.864640\pi$
$373$		−	307.758i		−	0.825087i	0.910938	−	0.412544i	$-0.135360\pi$
$374$	−420.362	−	10.4519i	−1.12396	−	0.0279464i
$375$		0			0
$376$	−116.232	+	159.980i	−0.309128	+	0.425478i
$377$	−41.3030	+	127.118i	−0.109557	+	0.337182i
$378$		0			0
$379$	131.079	−	95.2347i	0.345856	−	0.251279i	−0.401273	−	0.915959i	$-0.631432\pi$
$379$	131.079	−	95.2347i	0.345856	−	0.251279i	0.747128	+	0.664680i	$0.231432\pi$
$380$	−26.5860	−	36.5925i	−0.0699632	−	0.0962961i
$381$		0			0
$382$	71.9450	+	23.3763i	0.188338	+	0.0611946i
$383$	−154.593	−	112.319i	−0.403638	−	0.293260i	0.367383	−	0.930070i	$-0.380254\pi$
$383$	−154.593	−	112.319i	−0.403638	−	0.293260i	−0.771021	+	0.636810i	$0.780254\pi$
$384$		0			0
$385$	−19.3808	+	25.3267i	−0.0503397	+	0.0657837i
$386$	126.401			0.327464
$387$		0			0
$388$	107.887	−	332.042i	0.278059	−	0.855779i
$389$	−100.541	−	309.435i	−0.258461	−	0.795462i	−0.993128	−	0.117034i	$-0.962661\pi$
$389$	−100.541	−	309.435i	−0.258461	−	0.795462i	0.734666	−	0.678428i	$-0.237339\pi$
$390$		0			0
$391$	225.469	+	310.332i	0.576648	+	0.793687i
$392$	−126.966	+	41.2537i	−0.323893	+	0.105239i
$393$		0			0
$394$	−167.463	−	121.669i	−0.425034	−	0.308805i
$395$		−	216.584i		−	0.548313i
$396$		0			0
$397$	37.1303			0.0935272			0.0467636	−	0.998906i	$-0.485109\pi$
$397$	37.1303			0.0935272			0.0467636	+	0.998906i	$0.485109\pi$
$398$	186.260	−	256.365i	0.467991	−	0.644134i
$399$		0			0
$400$	−25.1319	−	77.3479i	−0.0628297	−	0.193370i
$401$	448.881	−	326.131i	1.11940	−	0.813294i	0.135285	−	0.990807i	$-0.456805\pi$
$401$	448.881	−	326.131i	1.11940	−	0.813294i	0.984119	+	0.177512i	$0.0568050\pi$
$402$		0			0
$403$	263.795	−	85.7121i	0.654577	−	0.212685i
$404$	−61.2704	−	19.9080i	−0.151660	−	0.0492772i
$405$		0			0
$406$		−	23.4402i		−	0.0577345i
$407$	91.4753	+	307.324i	0.224755	+	0.755096i
$408$		0			0
$409$	−9.54089	+	13.1319i	−0.0233274	+	0.0321074i	−0.820521	−	0.571616i	$-0.806317\pi$
$409$	−9.54089	+	13.1319i	−0.0233274	+	0.0321074i	0.797194	+	0.603723i	$0.206317\pi$
$410$	10.1011	−	31.0880i	0.0246369	−	0.0758245i
$411$		0			0
$412$	−287.174	+	208.644i	−0.697024	+	0.506418i
$413$	−41.3694	−	56.9402i	−0.100168	−	0.137870i
$414$		0			0
$415$	209.367	+	68.0274i	0.504498	+	0.163921i
$416$	49.5228	+	35.9804i	0.119045	+	0.0864913i
$417$		0			0
$418$	−134.076	+	92.4088i	−0.320756	+	0.221074i
$419$	−287.971			−0.687281			−0.343640	−	0.939101i	$-0.611660\pi$
$419$	−287.971			−0.687281			−0.343640	+	0.939101i	$0.611660\pi$
$420$		0			0
$421$	207.751	−	639.393i	0.493471	−	1.51875i	−0.325855	−	0.945420i	$-0.605652\pi$
$421$	207.751	−	639.393i	0.493471	−	1.51875i	0.819326	−	0.573328i	$-0.194348\pi$
$422$	74.6282	+	229.682i	0.176844	+	0.544270i
$423$		0			0
$424$	99.6755	+	137.192i	0.235084	+	0.323565i
$425$	522.684	−	169.830i	1.22984	−	0.399601i
$426$		0			0
$427$	−119.649	−	86.9304i	−0.280209	−	0.203584i
$428$			342.956i			0.801298i
$429$		0			0
$430$	−126.803			−0.294892
$431$	352.378	−	485.006i	0.817581	−	1.12530i	−0.172528	−	0.985005i	$-0.555193\pi$
$431$	352.378	−	485.006i	0.817581	−	1.12530i	0.990109	−	0.140300i	$-0.0448066\pi$
$432$		0			0
$433$	225.782	+	694.886i	0.521437	+	1.60482i	0.771256	+	0.636525i	$0.219629\pi$
$433$	225.782	+	694.886i	0.521437	+	1.60482i	−0.249819	+	0.968293i	$0.580371\pi$
$434$	−39.3531	+	28.5917i	−0.0906754	+	0.0658795i
$435$		0			0
$436$	−380.320	+	123.573i	−0.872293	+	0.283425i
$437$	141.276	+	45.9034i	0.323286	+	0.105042i
$438$		0			0
$439$			633.002i			1.44192i	0.692978	+	0.720959i	$0.256298\pi$
$439$			633.002i			1.44192i	−0.692978	+	0.720959i	$0.743702\pi$
$440$	64.4265	−	19.1766i	0.146424	−	0.0435832i
$441$		0			0
$442$	−243.140	+	334.653i	−0.550090	+	0.757134i
$443$	−54.1925	+	166.787i	−0.122331	+	0.376495i	−0.993405	−	0.114656i	$-0.963424\pi$
$443$	−54.1925	+	166.787i	−0.122331	+	0.376495i	0.871075	+	0.491151i	$0.163424\pi$
$444$		0			0
$445$	−97.8085	+	71.0620i	−0.219794	+	0.159690i
$446$	−268.046	−	368.934i	−0.601001	−	0.827207i
$447$		0			0
$448$	−10.2098	−	3.31735i	−0.0227896	−	0.00740480i
$449$	−43.3782	−	31.5161i	−0.0966108	−	0.0701919i	0.538431	−	0.842670i	$-0.319017\pi$
$449$	−43.3782	−	31.5161i	−0.0966108	−	0.0701919i	−0.635042	+	0.772478i	$0.719017\pi$
$450$		0			0
$451$	−110.982	−	39.1360i	−0.246080	−	0.0867760i
$452$	370.317			0.819285
$453$		0			0
$454$	163.340	−	502.709i	0.359780	−	1.10729i
$455$	9.69470	+	29.8372i	0.0213070	+	0.0655763i
$456$		0			0
$457$	−91.5322	−	125.983i	−0.200289	−	0.275675i	0.697044	−	0.717029i	$-0.254498\pi$
$457$	−91.5322	−	125.983i	−0.200289	−	0.275675i	−0.897333	+	0.441354i	$0.854498\pi$
$458$	−149.282	+	48.5048i	−0.325944	+	0.105906i
$459$		0			0
$460$	−49.6097	−	36.0435i	−0.107847	−	0.0783555i
$461$		−	550.272i		−	1.19365i	−0.802372	−	0.596824i	$-0.796429\pi$
$461$		−	550.272i		−	1.19365i	0.802372	−	0.596824i	$-0.203571\pi$
$462$		0			0
$463$	857.277			1.85157			0.925785	−	0.378050i	$-0.123405\pi$
$463$	857.277			1.85157			0.925785	+	0.378050i	$0.123405\pi$
$464$	−29.0406	+	39.9710i	−0.0625875	+	0.0861443i
$465$		0			0
$466$	−101.946	−	313.757i	−0.218768	−	0.673298i
$467$	10.1109	−	7.34601i	0.0216508	−	0.0157302i	−0.576907	−	0.816810i	$-0.695741\pi$
$467$	10.1109	−	7.34601i	0.0216508	−	0.0157302i	0.598558	+	0.801079i	$0.295741\pi$
$468$		0			0
$469$	−76.6792	+	24.9146i	−0.163495	+	0.0531228i
$470$	203.163	+	66.0116i	0.432261	+	0.140450i
$471$		0			0
$472$			148.350i			0.314300i
$473$	−11.3472	+	456.367i	−0.0239898	+	0.964834i
$474$		0			0
$475$	125.096	−	172.180i	0.263361	−	0.362485i
$476$	22.4172	−	68.9931i	0.0470950	−	0.144944i
$477$		0			0
$478$	−339.375	+	246.570i	−0.709989	+	0.515837i
$479$	77.0500	+	106.050i	0.160856	+	0.221399i	0.881836	−	0.471557i	$-0.156308\pi$
$479$	77.0500	+	106.050i	0.160856	+	0.221399i	−0.720980	+	0.692956i	$0.756308\pi$
$480$		0			0
$481$	299.996	+	97.4747i	0.623693	+	0.202650i
$482$	34.3749	+	24.9749i	0.0713173	+	0.0518151i
$483$		0			0
$484$	−63.2515	−	233.588i	−0.130685	−	0.482619i
$485$	−377.153			−0.777635
$486$		0			0
$487$	−5.81646	+	17.9012i	−0.0119435	+	0.0367582i	−0.956851	−	0.290580i	$-0.906152\pi$
$487$	−5.81646	+	17.9012i	−0.0119435	+	0.0367582i	0.944907	+	0.327338i	$0.106152\pi$
$488$	96.3298	+	296.473i	0.197397	+	0.607526i
$489$		0			0
$490$	84.7676	+	116.673i	0.172995	+	0.238107i
$491$	674.188	−	219.057i	1.37309	−	0.446145i	0.472700	−	0.881223i	$-0.343279\pi$
$491$	674.188	−	219.057i	1.37309	−	0.446145i	0.900392	+	0.435079i	$0.143279\pi$
$492$		0			0
$493$	−270.107	−	196.244i	−0.547883	−	0.398061i
$494$			160.188i			0.324268i
$495$		0			0
$496$	102.529			0.206712
$497$	−54.6940	+	75.2798i	−0.110048	+	0.151468i
$498$		0			0
$499$	133.801	+	411.799i	0.268139	+	0.825248i	0.990954	+	0.134205i	$0.0428482\pi$
$499$	133.801	+	411.799i	0.268139	+	0.825248i	−0.722814	+	0.691042i	$0.757152\pi$
$500$	−158.473	+	115.137i	−0.316945	+	0.230274i
$501$		0			0
$502$	237.505	−	77.1700i	0.473117	−	0.153725i
$503$	82.4069	+	26.7756i	0.163831	+	0.0532318i	0.389784	−	0.920906i	$-0.372550\pi$
$503$	82.4069	+	26.7756i	0.163831	+	0.0532318i	−0.225953	+	0.974138i	$0.572550\pi$
$504$		0			0
$505$			69.5945i			0.137811i
$506$	−134.160	+	175.320i	−0.265139	+	0.346483i
$507$		0			0
$508$	−181.752	+	250.160i	−0.357779	+	0.492441i
$509$	−127.798	+	393.322i	−0.251077	+	0.772735i	0.743501	+	0.668735i	$0.233164\pi$
$509$	−127.798	+	393.322i	−0.251077	+	0.772735i	−0.994577	+	0.104000i	$0.966836\pi$
$510$		0			0
$511$	79.5973	−	57.8309i	0.155768	−	0.113172i
$512$	13.3001	+	18.3060i	0.0259767	+	0.0357538i
$513$		0			0
$514$	311.309	+	101.150i	0.605659	+	0.196791i
$515$	310.224	+	225.391i	0.602377	+	0.437652i
$516$		0			0
$517$	255.757	−	725.278i	0.494694	−	1.40286i
$518$	−55.3186			−0.106793
$519$		0			0
$520$	20.4343	−	62.8904i	0.0392968	−	0.120943i
$521$	131.733	+	405.433i	0.252847	+	0.778182i	0.994246	+	0.107118i	$0.0341623\pi$
$521$	131.733	+	405.433i	0.252847	+	0.778182i	−0.741400	+	0.671064i	$0.765838\pi$
$522$		0			0
$523$	493.752	+	679.592i	0.944077	+	1.29941i	0.954109	+	0.299461i	$0.0968067\pi$
$523$	493.752	+	679.592i	0.944077	+	1.29941i	−0.0100317	+	0.999950i	$0.503193\pi$
$524$	−199.983	+	64.9785i	−0.381647	+	0.124005i
$525$		0			0
$526$	63.9931	+	46.4937i	0.121660	+	0.0883910i
$527$			692.848i			1.31470i
$528$		0			0
$529$	−327.611			−0.619302
$530$	107.676	−	148.203i	0.203162	−	0.279629i
$531$		0			0
$532$	−8.68112	−	26.7177i	−0.0163179	−	0.0502213i
$533$	−93.6573	+	68.0460i	−0.175717	+	0.127666i
$534$		0			0
$535$	352.350	−	114.486i	0.658599	−	0.213992i
$536$	161.623	+	52.5145i	0.301536	+	0.0979748i
$537$		0			0
$538$			2.92117i			0.00542968i
$539$	427.491	−	294.639i	0.793119	−	0.546640i
$540$		0			0
$541$	398.981	−	549.150i	0.737488	−	1.01507i	−0.261271	−	0.965266i	$-0.584142\pi$
$541$	398.981	−	549.150i	0.737488	−	1.01507i	0.998759	−	0.0498001i	$-0.0158584\pi$
$542$	12.5762	−	38.7057i	0.0232034	−	0.0714127i
$543$		0			0
$544$	−123.704	+	89.8761i	−0.227397	+	0.165213i
$545$	253.917	+	349.487i	0.465903	+	0.641260i
$546$		0			0
$547$	−1000.68	−	325.141i	−1.82940	−	0.594407i	−0.999324	−	0.0367506i	$-0.988299\pi$
$547$	−1000.68	−	325.141i	−1.82940	−	0.594407i	−0.830072	−	0.557656i	$-0.811701\pi$
$548$	138.175	+	100.390i	0.252145	+	0.183194i
$549$		0			0
$550$	179.495	+	260.429i	0.326354	+	0.473507i
$551$	−129.292			−0.234649
$552$		0			0
$553$	41.5687	−	127.935i	0.0751695	−	0.231348i
$554$	9.16180	+	28.1971i	0.0165375	+	0.0508973i
$555$		0			0
$556$	121.771	+	167.603i	0.219012	+	0.301444i
$557$	888.124	−	288.569i	1.59448	−	0.518077i	0.628744	−	0.777613i	$-0.283569\pi$
$557$	888.124	−	288.569i	1.59448	−	0.518077i	0.965734	+	0.259535i	$0.0835694\pi$
$558$		0			0
$559$	363.317	+	263.965i	0.649940	+	0.472209i
$560$			11.5968i			0.0207086i
$561$		0			0
$562$	−401.247			−0.713962
$563$	−27.4743	+	37.8151i	−0.0487998	+	0.0671672i	−0.832720	−	0.553695i	$-0.813217\pi$
$563$	−27.4743	+	37.8151i	−0.0487998	+	0.0671672i	0.783920	+	0.620862i	$0.213217\pi$
$564$		0			0
$565$	−123.619	−	380.461i	−0.218795	−	0.673383i
$566$	280.965	−	204.133i	0.496405	−	0.360659i
$567$		0			0
$568$	186.532	−	60.6079i	0.328401	−	0.106704i
$569$	−929.644	−	302.060i	−1.63382	−	0.530861i	−0.658676	−	0.752427i	$-0.728883\pi$
$569$	−929.644	−	302.060i	−1.63382	−	0.530861i	−0.975145	+	0.221566i	$0.928883\pi$
$570$		0			0
$571$			477.709i			0.836618i	0.908305	+	0.418309i	$0.137377\pi$
$571$			477.709i			0.836618i	−0.908305	+	0.418309i	$0.862623\pi$
$572$	−224.514	−	79.1711i	−0.392508	−	0.138411i
$573$		0			0
$574$	11.9334	−	16.4249i	0.0207899	−	0.0286149i
$575$	89.1626	−	274.414i	0.155065	−	0.477242i
$576$		0			0
$577$	−623.214	+	452.791i	−1.08009	+	0.784734i	−0.977699	−	0.210010i	$-0.932650\pi$
$577$	−623.214	+	452.791i	−1.08009	+	0.784734i	−0.102394	+	0.994744i	$0.532650\pi$
$578$	−367.111	−	505.285i	−0.635140	−	0.874196i
$579$		0			0
$580$	50.7603	+	16.4930i	0.0875177	+	0.0284362i
$581$	110.616	+	80.3672i	0.190389	+	0.138326i
$582$		0			0
$583$	−523.750	−	400.789i	−0.898370	−	0.687460i
$584$	−207.380			−0.355103
$585$		0			0
$586$	−48.9980	+	150.800i	−0.0836143	+	0.257338i
$587$	337.777	+	1039.57i	0.575430	+	1.77099i	0.634710	+	0.772750i	$0.281119\pi$
$587$	337.777	+	1039.57i	0.575430	+	1.77099i	−0.0592805	+	0.998241i	$0.518881\pi$
$588$		0			0
$589$	157.707	+	217.065i	0.267753	+	0.368531i
$590$	152.414	−	49.5222i	0.258328	−	0.0839359i
$591$		0			0
$592$	94.3311	+	68.5355i	0.159343	+	0.115769i
$593$		−	141.847i		−	0.239203i	−0.992822	−	0.119601i	$-0.961838\pi$
$593$		−	141.847i		−	0.239203i	0.992822	−	0.119601i	$-0.0381617\pi$
$594$		0			0
$595$	−78.3664			−0.131708
$596$	106.965	−	147.225i	0.179472	−	0.247022i
$597$		0			0
$598$	67.1101	+	206.544i	0.112224	+	0.345391i
$599$	171.663	−	124.720i	0.286582	−	0.208214i	−0.435201	−	0.900333i	$-0.643323\pi$
$599$	171.663	−	124.720i	0.286582	−	0.208214i	0.721783	+	0.692119i	$0.243323\pi$
$600$		0			0
$601$	266.370	−	86.5488i	0.443211	−	0.144008i	−0.0789057	−	0.996882i	$-0.525143\pi$
$601$	266.370	−	86.5488i	0.443211	−	0.144008i	0.522117	+	0.852874i	$0.325143\pi$
$602$	−74.9024	−	24.3373i	−0.124423	−	0.0404274i
$603$		0			0
$604$			122.975i			0.203601i
$605$	−218.872	+	142.961i	−0.361772	+	0.236298i
$606$		0			0
$607$	−218.388	+	300.585i	−0.359783	+	0.495198i	−0.950088	−	0.311982i	$-0.899007\pi$
$607$	−218.388	+	300.585i	−0.359783	+	0.495198i	0.590305	+	0.807180i	$0.299007\pi$
$608$	−18.2979	+	56.3152i	−0.0300952	+	0.0926236i
$609$		0			0
$610$	272.437	−	197.937i	0.446619	−	0.324487i
$611$	−444.686	−	612.058i	−0.727800	−	1.00173i
$612$		0			0
$613$	82.7051	+	26.8725i	0.134919	+	0.0438377i	0.375698	−	0.926742i	$-0.377403\pi$
$613$	82.7051	+	26.8725i	0.134919	+	0.0438377i	−0.240779	+	0.970580i	$0.577403\pi$
$614$	−16.9716	−	12.3306i	−0.0276410	−	0.0200824i
$615$		0			0
$616$	41.7371	+	1.03776i	0.0677551	+	0.00168467i
$617$	−853.166			−1.38277			−0.691383	−	0.722489i	$-0.742998\pi$
$617$	−853.166			−1.38277			−0.691383	+	0.722489i	$0.742998\pi$
$618$		0			0
$619$	56.1260	−	172.738i	0.0906720	−	0.279060i	−0.895430	−	0.445203i	$-0.853131\pi$
$619$	56.1260	−	172.738i	0.0906720	−	0.279060i	0.986102	+	0.166143i	$0.0531315\pi$
$620$	−34.2263	−	105.338i	−0.0552037	−	0.169900i
$621$		0			0
$622$	−229.904	−	316.435i	−0.369620	−	0.508738i
$623$	−71.4141	+	23.2038i	−0.114629	+	0.0372453i
$624$		0			0
$625$	−240.033	−	174.394i	−0.384053	−	0.279031i
$626$		−	284.679i		−	0.454758i
$627$		0			0
$628$	263.682			0.419876
$629$	−463.134	+	637.449i	−0.736301	+	1.01343i
$630$		0			0
$631$	301.955	+	929.322i	0.478534	+	1.47278i	0.841131	+	0.540831i	$0.181890\pi$
$631$	301.955	+	929.322i	0.478534	+	1.47278i	−0.362597	+	0.931946i	$0.618110\pi$
$632$	−229.386	+	166.659i	−0.362953	+	0.263701i
$633$		0			0
$634$	645.288	−	209.667i	1.01781	−	0.330705i
$635$	317.685	+	103.222i	0.500292	+	0.162555i
$636$		0			0
$637$		−	510.749i		−	0.801805i
$638$	63.9009	−	181.211i	0.100158	−	0.284029i
$639$		0			0
$640$	14.3676	−	19.7753i	0.0224494	−	0.0308989i
$641$	313.133	−	963.726i	0.488508	−	1.50347i	−0.338328	−	0.941028i	$-0.609861\pi$
$641$	313.133	−	963.726i	0.488508	−	1.50347i	0.826835	−	0.562444i	$-0.190139\pi$
$642$		0			0
$643$	−368.704	+	267.879i	−0.573411	+	0.416608i	−0.836343	−	0.548207i	$-0.815311\pi$
$643$	−368.704	+	267.879i	−0.573411	+	0.416608i	0.262931	+	0.964815i	$0.415311\pi$
$644$	−22.3865	−	30.8124i	−0.0347616	−	0.0478453i
$645$		0			0
$646$	−380.553	−	123.649i	−0.589092	−	0.191408i
$647$	−516.200	−	375.041i	−0.797836	−	0.579661i	0.112443	−	0.993658i	$-0.464132\pi$
$647$	−516.200	−	375.041i	−0.797836	−	0.579661i	−0.910278	+	0.413997i	$0.864132\pi$
$648$		0			0
$649$	−164.592	−	552.969i	−0.253608	−	0.852033i
$650$	311.150			0.478692
$651$		0			0
$652$	9.47490	−	29.1607i	0.0145321	−	0.0447251i
$653$	−336.398	−	1035.33i	−0.515157	−	1.58549i	−0.782995	−	0.622027i	$-0.786309\pi$
$653$	−336.398	−	1035.33i	−0.515157	−	1.58549i	0.267838	−	0.963464i	$-0.413691\pi$
$654$		0			0
$655$	133.517	+	183.770i	0.203843	+	0.280565i
$656$	−40.6985	+	13.2237i	−0.0620403	+	0.0201581i
$657$		0			0
$658$	107.338	+	77.9858i	0.163128	+	0.118519i
$659$		−	13.0543i		−	0.0198092i	−0.999951	−	0.00990462i	$-0.996847\pi$
$659$		−	13.0543i		−	0.0198092i	0.999951	−	0.00990462i	$-0.00315279\pi$
$660$		0			0
$661$	−1062.94			−1.60808			−0.804040	−	0.594575i	$-0.797320\pi$
$661$	−1062.94			−1.60808			−0.804040	+	0.594575i	$0.797320\pi$
$662$	−338.122	+	465.386i	−0.510759	+	0.702999i
$663$		0			0
$664$	−89.0571	−	274.090i	−0.134122	−	0.412785i
$665$	−24.5517	+	17.8378i	−0.0369198	+	0.0268238i
$666$		0			0
$667$	−166.706	+	54.1661i	−0.249934	+	0.0812086i
$668$	−297.654	−	96.7137i	−0.445590	−	0.144781i
$669$		0			0
$670$		−	183.581i		−	0.274001i
$671$	−687.999	−	998.217i	−1.02533	−	1.48766i
$672$		0			0
$673$	−32.6746	+	44.9727i	−0.0485507	+	0.0668243i	−0.832602	−	0.553872i	$-0.813150\pi$
$673$	−32.6746	+	44.9727i	−0.0485507	+	0.0668243i	0.784051	+	0.620696i	$0.213150\pi$
$674$	155.663	−	479.081i	0.230954	−	0.710802i
$675$		0			0
$676$	83.9814	−	61.0160i	0.124233	−	0.0902604i
$677$	134.729	+	185.439i	0.199009	+	0.273912i	0.896845	−	0.442345i	$-0.145853\pi$
$677$	134.729	+	185.439i	0.199009	+	0.273912i	−0.697836	+	0.716258i	$0.745853\pi$
$678$		0			0
$679$	−222.783	−	72.3867i	−0.328105	−	0.106608i
$680$	133.633	+	97.0900i	0.196519	+	0.142779i
$681$		0			0
$682$	−382.174	+	113.755i	−0.560373	+	0.166796i
$683$	518.623			0.759331			0.379666	−	0.925124i	$-0.376039\pi$
$683$	518.623			0.759331			0.379666	+	0.925124i	$0.376039\pi$
$684$		0			0
$685$	57.0146	−	175.473i	0.0832330	−	0.256165i
$686$	56.4142	+	173.625i	0.0822365	+	0.253098i
$687$		0			0
$688$	97.5740	+	134.299i	0.141823	+	0.195202i
$689$	−617.026	+	200.484i	−0.895538	+	0.290978i
$690$		0			0
$691$	−741.292	−	538.580i	−1.07278	−	0.779421i	−0.0963710	−	0.995345i	$-0.530724\pi$
$691$	−741.292	−	538.580i	−1.07278	−	0.779421i	−0.976410	+	0.215924i	$0.930724\pi$
$692$			332.029i			0.479810i
$693$		0			0
$694$	−446.790			−0.643789
$695$	131.545	−	181.056i	0.189273	−	0.260512i
$696$		0			0
$697$	−89.3602	−	275.023i	−0.128207	−	0.394580i
$698$	74.0995	−	53.8364i	0.106160	−	0.0771296i
$699$		0			0
$700$	−51.8965	+	16.8622i	−0.0741378	+	0.0240888i
$701$	−69.1203	−	22.4586i	−0.0986024	−	0.0320379i	0.259300	−	0.965797i	$-0.416508\pi$
$701$	−69.1203	−	22.4586i	−0.0986024	−	0.0320379i	−0.357903	+	0.933759i	$0.616508\pi$
$702$		0			0
$703$			305.127i			0.434036i
$704$	−69.8858	−	53.4787i	−0.0992696	−	0.0759641i
$705$		0			0
$706$	430.990	−	593.207i	0.610468	−	0.840237i
$707$	−13.3572	+	41.1093i	−0.0188928	+	0.0581461i
$708$		0			0
$709$	405.483	−	294.601i	0.571908	−	0.415516i	−0.263890	−	0.964553i	$-0.585006\pi$
$709$	405.483	−	294.601i	0.571908	−	0.415516i	0.835798	+	0.549037i	$0.185006\pi$
$710$	−124.536	−	171.409i	−0.175403	−	0.241422i
$711$		0			0
$712$	150.525	+	48.9086i	0.211412	+	0.0686919i
$713$	294.282	+	213.808i	0.412737	+	0.299871i
$714$		0			0
$715$	−6.39241	+	257.094i	−0.00894043	+	0.359571i
$716$	207.380			0.289638
$717$		0			0
$718$	189.838	−	584.261i	0.264398	−	0.813734i
$719$	75.9387	+	233.715i	0.105617	+	0.325056i	0.989875	−	0.141943i	$-0.0453350\pi$
$719$	75.9387	+	233.715i	0.105617	+	0.325056i	−0.884258	+	0.466999i	$0.845335\pi$
$720$		0			0
$721$	139.989	+	192.679i	0.194160	+	0.267239i
$722$	338.174	−	109.879i	0.468385	−	0.152187i
$723$		0			0
$724$	−346.147	−	251.490i	−0.478104	−	0.347363i
$725$			251.136i			0.346395i
$726$		0			0
$727$	14.3190			0.0196960			0.00984799	−	0.999952i	$-0.496865\pi$
$727$	14.3190			0.0196960			0.00984799	+	0.999952i	$0.496865\pi$
$728$	24.1410	−	33.2272i	0.0331607	−	0.0456418i
$729$		0			0
$730$	69.2276	+	213.061i	0.0948324	+	0.291864i
$731$	−907.535	+	659.363i	−1.24150	+	0.902001i
$732$		0			0
$733$	809.261	−	262.945i	1.10404	−	0.358724i	0.300384	−	0.953818i	$-0.402885\pi$
$733$	809.261	−	262.945i	1.10404	−	0.358724i	0.803656	+	0.595094i	$0.202885\pi$
$734$	830.371	+	269.804i	1.13130	+	0.367580i
$735$		0			0
$736$			80.2774i			0.109073i
$737$	−660.709	−	16.4280i	−0.896485	−	0.0222903i
$738$		0			0
$739$	−281.680	+	387.699i	−0.381163	+	0.524626i	−0.955892	−	0.293718i	$-0.905107\pi$
$739$	−281.680	+	387.699i	−0.381163	+	0.524626i	0.574729	+	0.818344i	$0.305107\pi$
$740$	38.9233	−	119.794i	0.0525991	−	0.161883i
$741$		0			0
$742$	92.0485	−	66.8772i	0.124055	−	0.0901309i
$743$	−132.746	−	182.709i	−0.178662	−	0.245907i	0.710288	−	0.703911i	$-0.248565\pi$
$743$	−132.746	−	182.709i	−0.178662	−	0.245907i	−0.888950	+	0.458004i	$0.848565\pi$
$744$		0			0
$745$	−186.966	−	60.7488i	−0.250960	−	0.0815420i
$746$	352.112	+	255.825i	0.472001	+	0.342928i
$747$		0			0
$748$	361.386	−	472.258i	0.483137	−	0.631361i
$749$	230.106			0.307217
$750$		0			0
$751$	86.2162	−	265.346i	0.114802	−	0.353324i	−0.877104	−	0.480301i	$-0.840527\pi$
$751$	86.2162	−	265.346i	0.114802	−	0.353324i	0.991906	+	0.126977i	$0.0405275\pi$
$752$	−86.4181	−	265.968i	−0.114918	−	0.353680i
$753$		0			0
$754$	−111.105	−	152.923i	−0.147354	−	0.202815i
$755$	126.344	−	41.0515i	0.167343	−	0.0543729i
$756$		0			0
$757$	404.416	+	293.826i	0.534236	+	0.388145i	0.821940	−	0.569574i	$-0.192892\pi$
$757$	404.416	+	293.826i	0.534236	+	0.388145i	−0.287704	+	0.957719i	$0.592892\pi$
$758$			229.135i			0.302289i
$759$		0			0
$760$	63.9660			0.0841658
$761$	−780.973	+	1074.92i	−1.02625	+	1.41251i	−0.118515	+	0.992952i	$0.537814\pi$
$761$	−780.973	+	1074.92i	−1.02625	+	1.41251i	−0.907730	+	0.419554i	$0.862186\pi$
$762$		0			0
$763$	82.9114	+	255.175i	0.108665	+	0.334436i
$764$	−86.5499	+	62.8822i	−0.113285	+	0.0823066i
$765$		0			0
$766$	257.013	−	83.5084i	0.335525	−	0.109019i
$767$	−539.784	−	175.387i	−0.703761	−	0.228666i
$768$		0			0
$769$			1064.10i			1.38375i	0.722019	+	0.691873i	$0.243214\pi$
$769$			1064.10i			1.38375i	−0.722019	+	0.691873i	$0.756786\pi$
$770$	−12.8665	−	43.2269i	−0.0167098	−	0.0561388i
$771$		0			0
$772$	−105.071	+	144.618i	−0.136103	+	0.187329i
$773$	3.55834	−	10.9514i	0.00460328	−	0.0141674i	−0.948728	−	0.316092i	$-0.897629\pi$
$773$	3.55834	−	10.9514i	0.00460328	−	0.0141674i	0.953332	+	0.301925i	$0.0976291\pi$
$774$		0			0
$775$	421.626	−	306.329i	0.544034	−	0.395263i
$776$	290.216	+	399.447i	0.373989	+	0.514752i
$777$		0			0
$778$	437.607	+	142.187i	0.562477	+	0.182760i
$779$	−90.5969	−	65.8225i	−0.116299	−	0.0844961i
$780$		0			0
$781$	−628.049	+	432.868i	−0.804159	+	0.554249i
$782$	−542.480			−0.693708
$783$		0			0
$784$	58.3416	−	179.557i	0.0744153	−	0.229027i
$785$	−88.0226	−	270.906i	−0.112131	−	0.345103i
$786$		0			0
$787$	−660.564	−	909.188i	−0.839344	−	1.15526i	−0.986111	−	0.166087i	$-0.946887\pi$
$787$	−660.564	−	909.188i	−0.839344	−	1.15526i	0.146767	−	0.989171i	$-0.453113\pi$
$788$	278.409	−	90.4605i	0.353311	−	0.114798i
$789$		0			0
$790$	247.798	+	180.036i	0.313669	+	0.227894i
$791$		−	248.464i		−	0.314113i
$792$		0			0
$793$	−1192.63			−1.50395
$794$	−30.8647	+	42.4816i	−0.0388724	+	0.0535033i
$795$		0			0
$796$	138.484	+	426.210i	0.173975	+	0.535439i
$797$	98.7861	−	71.7723i	0.123947	−	0.0900531i	−0.524084	−	0.851666i	$-0.675592\pi$
$797$	98.7861	−	71.7723i	0.123947	−	0.0900531i	0.648032	+	0.761613i	$0.275592\pi$
$798$		0			0
$799$	1797.29	−	583.976i	2.24943	−	0.730884i
$800$	109.386	+	35.5418i	0.136733	+	0.0444273i
$801$		0			0
$802$			784.673i			0.978395i
$803$	773.003	−	230.085i	0.962643	−	0.286532i
$804$		0			0
$805$	−24.1834	+	33.2855i	−0.0300414	+	0.0413485i
$806$	−121.215	+	373.062i	−0.150391	+	0.462856i
$807$		0			0
$808$	73.7085	−	53.5523i	0.0912233	−	0.0662776i
$809$	827.897	+	1139.50i	1.02336	+	1.40853i	0.909822	+	0.414998i	$0.136218\pi$
$809$	827.897	+	1139.50i	1.02336	+	1.40853i	0.113536	+	0.993534i	$0.463782\pi$
$810$		0			0
$811$	−11.2136	−	3.64351i	−0.0138269	−	0.00449262i	0.302095	−	0.953278i	$-0.402314\pi$
$811$	−11.2136	−	3.64351i	−0.0138269	−	0.00449262i	−0.315922	+	0.948785i	$0.602314\pi$
$812$	26.8185	+	19.4848i	0.0330277	+	0.0239960i
$813$		0			0
$814$	−427.656	−	150.805i	−0.525375	−	0.185265i
$815$	−33.1225			−0.0406411
$816$		0			0
$817$	−134.240	+	413.148i	−0.164308	+	0.505689i
$818$	−7.09361	−	21.8319i	−0.00867190	−	0.0266894i
$819$		0			0
$820$	27.1719	+	37.3990i	0.0331365	+	0.0456085i
$821$	801.903	−	260.554i	0.976740	−	0.317362i	0.223206	−	0.974771i	$-0.428348\pi$
$821$	801.903	−	260.554i	0.976740	−	0.317362i	0.753534	+	0.657409i	$0.228348\pi$
$822$		0			0
$823$	78.5581	+	57.0758i	0.0954534	+	0.0693509i	0.634488	−	0.772933i	$-0.281211\pi$
$823$	78.5581	+	57.0758i	0.0954534	+	0.0693509i	−0.539035	+	0.842283i	$0.681211\pi$
$824$		−	501.998i		−	0.609221i
$825$		0			0
$826$	99.5350			0.120502
$827$	466.210	−	641.683i	0.563736	−	0.775916i	−0.428060	−	0.903751i	$-0.640803\pi$
$827$	466.210	−	641.683i	0.563736	−	0.775916i	0.991796	+	0.127835i	$0.0408026\pi$
$828$		0			0
$829$	480.733	+	1479.54i	0.579895	+	1.78473i	0.618869	+	0.785494i	$0.287591\pi$
$829$	480.733	+	1479.54i	0.579895	+	1.78473i	−0.0389734	+	0.999240i	$0.512409\pi$
$830$	−251.869	+	182.993i	−0.303456	+	0.220474i
$831$		0			0
$832$	−82.3320	+	26.7513i	−0.0989567	+	0.0321530i
$833$	1213.37	+	394.247i	1.45662	+	0.473286i
$834$		0			0
$835$			338.093i			0.404902i
$836$	5.72408	−	230.214i	0.00684698	−	0.275376i
$837$		0			0
$838$	239.377	−	329.474i	0.285652	−	0.393167i
$839$	−248.504	+	764.818i	−0.296191	+	0.911582i	0.686628	+	0.727009i	$0.259090\pi$
$839$	−248.504	+	764.818i	−0.296191	+	0.911582i	−0.982819	+	0.184573i	$0.940910\pi$
$840$		0			0
$841$	−556.956	+	404.652i	−0.662254	+	0.481156i
$842$	558.850	+	769.191i	0.663717	+	0.913528i
$843$		0			0
$844$	−324.820	−	105.540i	−0.384857	−	0.125048i
$845$	−90.7222	−	65.9135i	−0.107364	−	0.0780042i
$846$		0			0
$847$	−156.725	+	42.4385i	−0.185036	+	0.0501045i
$848$	−239.820			−0.282806
$849$		0			0
$850$	−240.176	+	739.187i	−0.282560	+	0.869631i
$851$	127.831	+	393.425i	0.150213	+	0.462309i
$852$		0			0
$853$	91.4258	+	125.837i	0.107181	+	0.147523i	0.859238	−	0.511576i	$-0.170938\pi$
$853$	91.4258	+	125.837i	0.107181	+	0.147523i	−0.752057	+	0.659098i	$0.770938\pi$
$854$	198.918	−	64.6324i	0.232925	−	0.0756819i
$855$		0			0
$856$	−392.383	−	285.083i	−0.458392	−	0.333041i
$857$		−	286.106i		−	0.333846i	−0.985970	−	0.166923i	$-0.946617\pi$
$857$		−	286.106i		−	0.333846i	0.985970	−	0.166923i	$-0.0533832\pi$
$858$		0			0
$859$	−777.069			−0.904621			−0.452310	−	0.891861i	$-0.649400\pi$
$859$	−777.069			−0.904621			−0.452310	+	0.891861i	$0.649400\pi$
$860$	105.406	−	145.079i	0.122565	−	0.168696i
$861$		0			0
$862$	261.991	+	806.327i	0.303934	+	0.935414i
$863$	−484.736	+	352.181i	−0.561687	+	0.408089i	−0.832076	−	0.554662i	$-0.812848\pi$
$863$	−484.736	+	352.181i	−0.561687	+	0.408089i	0.270389	+	0.962751i	$0.412848\pi$
$864$		0			0
$865$	341.124	−	110.838i	0.394363	−	0.128136i
$866$	−982.717	−	319.304i	−1.13478	−	0.368712i
$867$		0			0
$868$		−	68.7918i		−	0.0792532i
$869$	670.125	−	875.717i	0.771145	−	1.00773i
$870$		0			0
$871$	−382.158	+	525.995i	−0.438758	+	0.603898i
$872$	174.759	−	537.853i	0.200412	−	0.616804i
$873$		0			0
$874$	−169.955	+	123.480i	−0.194457	+	0.141281i
$875$	77.2510	+	106.327i	0.0882869	+	0.121517i
$876$		0			0
$877$	780.633	+	253.643i	0.890118	+	0.289217i	0.718152	−	0.695886i	$-0.244988\pi$
$877$	780.633	+	253.643i	0.890118	+	0.289217i	0.171966	+	0.985103i	$0.444988\pi$
$878$	−724.232	−	526.185i	−0.824865	−	0.599300i
$879$		0			0
$880$	−31.6144	+	89.6525i	−0.0359255	+	0.101878i
$881$	1182.04			1.34170			0.670849	−	0.741594i	$-0.265930\pi$
$881$	1182.04			1.34170			0.670849	+	0.741594i	$0.265930\pi$
$882$		0			0
$883$	155.341	−	478.089i	0.175924	−	0.541437i	−0.823751	−	0.566952i	$-0.808122\pi$
$883$	155.341	−	478.089i	0.175924	−	0.541437i	0.999674	+	0.0255147i	$0.00812248\pi$
$884$	−180.774	−	556.364i	−0.204495	−	0.629371i
$885$		0			0
$886$	−145.778	−	200.646i	−0.164534	−	0.226462i
$887$	63.0596	−	20.4893i	0.0710931	−	0.0230996i	−0.273255	−	0.961942i	$-0.588100\pi$
$887$	63.0596	−	20.4893i	0.0710931	−	0.0230996i	0.344348	+	0.938842i	$0.388100\pi$
$888$		0			0
$889$	167.844	+	121.946i	0.188801	+	0.137172i
$890$		−	170.975i		−	0.192107i
$891$		0			0
$892$	644.921			0.723005
$893$	430.155	−	592.058i	0.481697	−	0.662998i
$894$		0			0
$895$	−69.2278	−	213.061i	−0.0773495	−	0.238057i
$896$	12.2824	−	8.92366i	0.0137080	−	0.00995944i
$897$		0			0
$898$	72.1167	−	23.4321i	0.0803081	−	0.0260937i
$899$	−301.107	−	97.8356i	−0.334935	−	0.108827i
$900$		0			0
$901$		−	1620.60i		−	1.79867i
$902$	137.031	−	94.4454i	0.151919	−	0.104707i
$903$		0			0
$904$	−307.827	+	423.688i	−0.340517	+	0.468681i
$905$	−142.829	+	439.582i	−0.157822	+	0.485726i
$906$		0			0
$907$	899.683	−	653.658i	0.991933	−	0.720682i	0.0315896	−	0.999501i	$-0.489943\pi$
$907$	899.683	−	653.658i	0.991933	−	0.720682i	0.960344	+	0.278819i	$0.0899431\pi$
$908$	439.384	+	604.760i	0.483903	+	0.666035i
$909$		0			0
$910$	−42.1962	−	13.7104i	−0.0463695	−	0.0150663i
$911$	883.114	+	641.620i	0.969389	+	0.704303i	0.955312	−	0.295598i	$-0.0955190\pi$
$911$	883.114	+	641.620i	0.969389	+	0.704303i	0.0140771	+	0.999901i	$0.495519\pi$
$912$		0			0
$913$	636.056	+	922.853i	0.696666	+	1.01079i
$914$	220.227			0.240948
$915$		0			0
$916$	68.5961	−	211.117i	0.0748865	−	0.230477i
$917$	43.5972	+	134.178i	0.0475433	+	0.146323i
$918$		0			0
$919$	−708.836	−	975.629i	−0.771312	−	1.06162i	−0.996188	−	0.0872324i	$-0.972198\pi$
$919$	−708.836	−	975.629i	−0.771312	−	1.06162i	0.224876	−	0.974387i	$-0.427802\pi$
$920$	82.4765	−	26.7982i	0.0896483	−	0.0291285i
$921$		0			0
$922$	629.579	+	457.416i	0.682840	+	0.496113i
$923$			750.367i			0.812966i
$924$		0			0
$925$	592.679			0.640734
$926$	−712.615	+	980.830i	−0.769562	+	1.05921i
$927$		0			0
$928$	−21.5916	−	66.4521i	−0.0232668	−	0.0716078i
$929$	−264.766	+	192.364i	−0.285001	+	0.207066i	−0.721096	−	0.692835i	$-0.756361\pi$
$929$	−264.766	+	192.364i	−0.285001	+	0.207066i	0.436094	+	0.899901i	$0.356361\pi$
$930$		0			0
$931$	469.879	−	152.673i	0.504703	−	0.163988i
$932$	443.719	+	144.173i	0.476094	+	0.154692i
$933$		0			0
$934$			17.6745i			0.0189235i
$935$	−605.833	−	213.636i	−0.647950	−	0.228488i
$936$		0			0
$937$	−18.9967	+	26.1467i	−0.0202739	+	0.0279047i	−0.819034	−	0.573745i	$-0.805490\pi$
$937$	−18.9967	+	26.1467i	−0.0202739	+	0.0279047i	0.798760	+	0.601650i	$0.205490\pi$
$938$	35.2345	−	108.441i	0.0375635	−	0.115608i
$939$		0			0
$940$	−244.405	+	177.571i	−0.260006	+	0.188905i
$941$	−271.712	−	373.980i	−0.288748	−	0.397428i	0.639859	−	0.768493i	$-0.278993\pi$
$941$	−271.712	−	373.980i	−0.288748	−	0.397428i	−0.928607	+	0.371065i	$0.878993\pi$
$942$		0			0
$943$	−144.390	−	46.9151i	−0.153117	−	0.0497508i
$944$	−169.730	−	123.316i	−0.179799	−	0.130632i
$945$		0			0
$946$	−512.707	−	392.339i	−0.541974	−	0.414735i
$947$	763.125			0.805834			0.402917	−	0.915236i	$-0.367996\pi$
$947$	763.125			0.805834			0.402917	+	0.915236i	$0.367996\pi$
$948$		0			0
$949$	245.175	−	754.571i	0.258351	−	0.795122i
$950$	93.0087	+	286.251i	0.0979039	+	0.301317i
$951$		0			0
$952$	60.3022	+	82.9989i	0.0633427	+	0.0871837i
$953$	−91.1784	+	29.6256i	−0.0956751	+	0.0310867i	−0.356463	−	0.934309i	$-0.616018\pi$
$953$	−91.1784	+	29.6256i	−0.0956751	+	0.0310867i	0.260788	+	0.965396i	$0.416018\pi$
$954$		0			0
$955$	93.4969	+	67.9295i	0.0979025	+	0.0711303i
$956$		−	593.249i		−	0.620553i
$957$		0			0
$958$	−185.383			−0.193510
$959$	67.3567	−	92.7086i	0.0702364	−	0.0966722i
$960$		0			0
$961$	−93.9368	−	289.108i	−0.0977490	−	0.300841i
$962$	−360.896	+	262.206i	−0.375152	+	0.272564i
$963$		0			0
$964$	−57.1486	+	18.5687i	−0.0592828	+	0.0192621i
$965$	183.655	+	59.6731i	0.190316	+	0.0618374i
$966$		0			0
$967$		−	1051.57i		−	1.08745i	−0.839263	−	0.543726i	$-0.817013\pi$
$967$		−	1051.57i		−	1.08745i	0.839263	−	0.543726i	$-0.182987\pi$
$968$	319.831	+	121.803i	0.330404	+	0.125830i
$969$		0			0
$970$	313.510	−	431.509i	0.323206	−	0.444855i
$971$	−104.760	+	322.418i	−0.107889	+	0.332048i	−0.990398	−	0.138248i	$-0.955853\pi$
$971$	−104.760	+	322.418i	−0.107889	+	0.332048i	0.882509	+	0.470296i	$0.155853\pi$
$972$		0			0
$973$	112.453	−	81.7019i	0.115574	−	0.0839691i
$974$	−15.6462	−	21.5352i	−0.0160639	−	0.0221101i
$975$		0			0
$976$	−419.276	−	136.231i	−0.429586	−	0.139581i
$977$	−757.533	−	550.380i	−0.775367	−	0.563337i	0.128218	−	0.991746i	$-0.459074\pi$
$977$	−757.533	−	550.380i	−0.775367	−	0.563337i	−0.903585	+	0.428409i	$0.859074\pi$
$978$		0			0
$979$	−615.342	−	15.2999i	−0.628542	−	0.0156281i
$980$	−203.951			−0.208113
$981$		0			0
$982$	−309.793	+	953.446i	−0.315472	+	0.970923i
$983$	188.645	+	580.591i	0.191908	+	0.590631i	0.999999	+	0.00157368i	$0.000500918\pi$
$983$	188.645	+	580.591i	0.191908	+	0.590631i	−0.808091	+	0.589058i	$0.799499\pi$
$984$		0			0
$985$	−185.877	−	255.838i	−0.188708	−	0.259734i
$986$	449.054	−	145.907i	0.455430	−	0.147978i
$987$		0			0
$988$	−183.275	−	133.157i	−0.185501	−	0.134775i
$989$			588.943i			0.595494i
$990$		0			0
$991$	187.306			0.189008			0.0945038	−	0.995525i	$-0.469874\pi$
$991$	187.306			0.189008			0.0945038	+	0.995525i	$0.469874\pi$
$992$	−85.2277	+	117.306i	−0.0859151	+	0.118252i
$993$		0			0
$994$	−40.6648	−	125.153i	−0.0409102	−	0.125909i
$995$	391.656	−	284.555i	0.393624	−	0.285985i
$996$		0			0
$997$	−231.035	+	75.0680i	−0.231731	+	0.0752939i	−0.422581	−	0.906325i	$-0.638876\pi$
$997$	−231.035	+	75.0680i	−0.231731	+	0.0752939i	0.190850	+	0.981619i	$0.438876\pi$
$998$	−582.371	−	189.224i	−0.583538	−	0.189603i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.3.j.b.73.2		16
3.2	odd	2		66.3.f.a.7.4	✓	16
11.5	even	5		2178.3.d.m.1693.5		16
11.6	odd	10		2178.3.d.m.1693.13		16
11.8	odd	10	inner	198.3.j.b.19.2		16
12.11	even	2		528.3.bf.c.337.1		16
33.5	odd	10		726.3.d.e.241.15		16
33.8	even	10		66.3.f.a.19.4	yes	16
33.17	even	10		726.3.d.e.241.7		16
132.107	odd	10		528.3.bf.c.481.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.f.a.7.4	✓	16	3.2	odd	2
66.3.f.a.19.4	yes	16	33.8	even	10
198.3.j.b.19.2		16	11.8	odd	10	inner
198.3.j.b.73.2		16	1.1	even	1	trivial
528.3.bf.c.337.1		16	12.11	even	2
528.3.bf.c.481.1		16	132.107	odd	10
726.3.d.e.241.7		16	33.17	even	10
726.3.d.e.241.15		16	33.5	odd	10
2178.3.d.m.1693.5		16	11.5	even	5
2178.3.d.m.1693.13		16	11.6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	198.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.831254 + 1.14412i) q^{2} +(-0.618034 - 1.90211i) q^{4} +(-1.74791 + 1.26993i) q^{5} +(-1.27622 + 0.414669i) q^{7} +(2.68999 + 0.874032i) q^{8} -3.05545i q^{10} +(-10.9966 - 0.273421i) q^{11} +(-6.36050 + 8.75447i) q^{13} +(0.586431 - 1.80485i) q^{14} +(-3.23607 + 2.35114i) q^{16} +(-15.8880 - 21.8679i) q^{17} +(-9.95521 - 3.23464i) q^{19} +(3.49581 + 2.53986i) q^{20} +(9.45379 - 12.3542i) q^{22} -14.1912 q^{23} +(-6.28297 + 19.3370i) q^{25} +(-4.72900 - 14.5544i) q^{26} +(1.57749 + 2.17124i) q^{28} +(11.7472 - 3.81689i) q^{29} +(-20.7370 - 15.0663i) q^{31} -5.65685i q^{32} +38.2266 q^{34} +(1.70411 - 2.34551i) q^{35} +(-9.00782 - 27.7232i) q^{37} +(11.9761 - 8.70117i) q^{38} +(-5.81182 + 1.88837i) q^{40} +(10.1746 + 3.30593i) q^{41} -41.5007i q^{43} +(6.27620 + 21.0858i) q^{44} +(11.7965 - 16.2364i) q^{46} +(-21.6045 + 66.4919i) q^{47} +(-38.1850 + 27.7431i) q^{49} +(-16.9011 - 23.2624i) q^{50} +(20.5830 + 6.68782i) q^{52} +(48.5045 + 35.2406i) q^{53} +(19.5683 - 13.4870i) q^{55} -3.79546 q^{56} +(-5.39790 + 16.6130i) q^{58} +(16.2078 + 49.8825i) q^{59} +(64.7817 + 89.1643i) q^{61} +(34.4753 - 11.2017i) q^{62} +(6.47214 + 4.70228i) q^{64} -23.3794i q^{65} +60.0831 q^{67} +(-31.7760 + 43.7359i) q^{68} +(1.26700 + 3.89943i) q^{70} +(56.0995 - 40.7587i) q^{71} +(-69.7313 + 22.6571i) q^{73} +(39.2065 + 12.7390i) q^{74} +20.9350i q^{76} +(14.1475 - 4.21101i) q^{77} +(-58.9228 + 81.1003i) q^{79} +(2.67056 - 8.21915i) q^{80} +(-12.2401 + 8.89294i) q^{82} +(-59.8908 - 82.4326i) q^{83} +(55.5414 + 18.0465i) q^{85} +(47.4819 + 34.4976i) q^{86} +(-29.3418 - 10.3469i) q^{88} +55.9575 q^{89} +(4.48718 - 13.8101i) q^{91} +(8.77063 + 26.9932i) q^{92} +(-58.1161 - 79.9899i) q^{94} +(21.5085 - 6.98855i) q^{95} +(141.226 + 102.607i) q^{97} -66.7499i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 8 q^{5} + 60 q^{7} + 4 q^{11} - 60 q^{13} + 32 q^{14} - 16 q^{16} + 60 q^{17} + 16 q^{20} - 48 q^{22} + 8 q^{23} - 48 q^{25} - 48 q^{26} + 40 q^{28} + 160 q^{29} + 32 q^{31} - 64 q^{34}+ \cdots + 324 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 - 8 * q^5 + 60 * q^7 + 4 * q^11 - 60 * q^13 + 32 * q^14 - 16 * q^16 + 60 * q^17 + 16 * q^20 - 48 * q^22 + 8 * q^23 - 48 * q^25 - 48 * q^26 + 40 * q^28 + 160 * q^29 + 32 * q^31 - 64 * q^34 - 160 * q^35 - 84 * q^37 + 48 * q^38 - 80 * q^40 - 40 * q^41 - 168 * q^44 + 160 * q^46 - 372 * q^47 + 96 * q^49 - 160 * q^50 + 40 * q^52 + 124 * q^53 + 32 * q^55 + 96 * q^56 - 16 * q^58 + 172 * q^59 + 100 * q^61 + 40 * q^62 + 32 * q^64 + 248 * q^67 + 120 * q^68 + 8 * q^70 - 48 * q^71 + 160 * q^73 - 80 * q^74 + 172 * q^77 - 460 * q^79 + 48 * q^80 - 24 * q^82 + 420 * q^83 - 420 * q^85 + 456 * q^86 - 144 * q^88 + 360 * q^89 - 252 * q^91 + 64 * q^92 - 280 * q^94 - 180 * q^95 + 324 * q^97

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