LMFDB - Embedded newform 684.3.b.a.683.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(683,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("684.683");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.b (of order $2$, degree $1$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			683.3
Character	$\chi$	$=$	684.683
Dual form			684.3.b.a.683.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98202 + 0.267543i) q^{2} +(3.85684 - 1.06055i) q^{4} -4.56953i q^{5} -9.67098i q^{7} +(-7.36061 + 3.13391i) q^{8} +O(q^{10})$	\(q+(-1.98202 + 0.267543i) q^{2} +(3.85684 - 1.06055i) q^{4} -4.56953i q^{5} -9.67098i q^{7} +(-7.36061 + 3.13391i) q^{8} +(1.22255 + 9.05693i) q^{10} +2.25916 q^{11} -14.4261i q^{13} +(2.58740 + 19.1681i) q^{14} +(13.7505 - 8.18077i) q^{16} -2.47152i q^{17} +(8.92923 - 16.7711i) q^{19} +(-4.84623 - 17.6240i) q^{20} +(-4.47770 + 0.604422i) q^{22} -29.0241 q^{23} +4.11936 q^{25} +(3.85960 + 28.5928i) q^{26} +(-10.2566 - 37.2994i) q^{28} +10.3633 q^{29} -4.02586 q^{31} +(-25.0650 + 19.8933i) q^{32} +(0.661237 + 4.89861i) q^{34} -44.1919 q^{35} +33.0030i q^{37} +(-13.2110 + 35.6296i) q^{38} +(14.3205 + 33.6346i) q^{40} +1.46331 q^{41} +26.0088i q^{43} +(8.71321 - 2.39596i) q^{44} +(57.5265 - 7.76519i) q^{46} +6.14434 q^{47} -44.5278 q^{49} +(-8.16467 + 1.10211i) q^{50} +(-15.2996 - 55.6391i) q^{52} -16.4054 q^{53} -10.3233i q^{55} +(30.3080 + 71.1843i) q^{56} +(-20.5404 + 2.77264i) q^{58} +57.3091i q^{59} +94.3814 q^{61} +(7.97935 - 1.07709i) q^{62} +(44.3572 - 46.1350i) q^{64} -65.9205 q^{65} -120.267 q^{67} +(-2.62118 - 9.53225i) q^{68} +(87.5893 - 11.8232i) q^{70} -102.072i q^{71} +10.8998 q^{73} +(-8.82973 - 65.4128i) q^{74} +(16.6520 - 74.1533i) q^{76} -21.8483i q^{77} -54.0890 q^{79} +(-37.3823 - 62.8332i) q^{80} +(-2.90031 + 0.391498i) q^{82} -68.5339 q^{83} -11.2937 q^{85} +(-6.95846 - 51.5500i) q^{86} +(-16.6288 + 7.08000i) q^{88} +7.00476 q^{89} -139.514 q^{91} +(-111.941 + 30.7816i) q^{92} +(-12.1782 + 1.64387i) q^{94} +(-76.6360 - 40.8024i) q^{95} +29.0407i q^{97} +(88.2551 - 11.9131i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{4}+O(q^{10}) $ 80 * q - 8 * q^4	$ 80 q - 8 q^{4} - 56 q^{16} - 400 q^{25} - 464 q^{49} - 272 q^{58} - 352 q^{61} - 200 q^{64} + 480 q^{73} + 152 q^{76} + 32 q^{82} + 704 q^{85}+O(q^{100}) $ 80 * q - 8 * q^4 - 56 * q^16 - 400 * q^25 - 464 * q^49 - 272 * q^58 - 352 * q^61 - 200 * q^64 + 480 * q^73 + 152 * q^76 + 32 * q^82 + 704 * q^85

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.98202	+	0.267543i	−0.991012	+	0.133771i
$2$	−1.98202	+	0.267543i	−0.991012	+	0.133771i
$3$		0			0
$3$		0			0
$4$	3.85684	−	1.06055i	0.964210	−	0.265138i
$5$		−	4.56953i		−	0.913907i	−0.889491	−	0.456953i	$-0.848941\pi$
$5$		−	4.56953i		−	0.913907i	0.889491	−	0.456953i	$-0.151059\pi$
$6$		0			0
$7$		−	9.67098i		−	1.38157i	−0.723061	−	0.690784i	$-0.757266\pi$
$7$		−	9.67098i		−	1.38157i	0.723061	−	0.690784i	$-0.242734\pi$
$8$	−7.36061	+	3.13391i	−0.920076	+	0.391739i
$9$		0			0
$10$	1.22255	+	9.05693i	0.122255	+	0.905693i
$11$	2.25916			0.205378			0.102689	−	0.994714i	$-0.467255\pi$
$11$	2.25916			0.205378			0.102689	+	0.994714i	$0.467255\pi$
$12$		0			0
$13$		−	14.4261i		−	1.10970i	−0.831951	−	0.554849i	$-0.812776\pi$
$13$		−	14.4261i		−	1.10970i	0.831951	−	0.554849i	$-0.187224\pi$
$14$	2.58740	+	19.1681i	0.184814	+	1.36915i
$15$		0			0
$16$	13.7505	−	8.18077i	0.859403	−	0.511298i
$17$		−	2.47152i		−	0.145383i	−0.997354	−	0.0726917i	$-0.976841\pi$
$17$		−	2.47152i		−	0.145383i	0.997354	−	0.0726917i	$-0.0231589\pi$
$18$		0			0
$19$	8.92923	−	16.7711i	0.469959	−	0.882688i
$19$	8.92923	−	16.7711i	0.469959	−	0.882688i
$20$	−4.84623	−	17.6240i	−0.242312	−	0.881198i
$21$		0			0
$22$	−4.47770	+	0.604422i	−0.203532	+	0.0274737i
$23$	−29.0241			−1.26192			−0.630958	−	0.775817i	$-0.717338\pi$
$23$	−29.0241			−1.26192			−0.630958	+	0.775817i	$0.717338\pi$
$24$		0			0
$25$	4.11936			0.164774
$26$	3.85960	+	28.5928i	0.148446	+	1.09972i
$27$		0			0
$28$	−10.2566	−	37.2994i	−0.366307	−	1.33212i
$29$	10.3633			0.357356			0.178678	−	0.983908i	$-0.442818\pi$
$29$	10.3633			0.357356			0.178678	+	0.983908i	$0.442818\pi$
$30$		0			0
$31$	−4.02586			−0.129866			−0.0649332	−	0.997890i	$-0.520683\pi$
$31$	−4.02586			−0.129866			−0.0649332	+	0.997890i	$0.520683\pi$
$32$	−25.0650	+	19.8933i	−0.783282	+	0.621666i
$33$		0			0
$34$	0.661237	+	4.89861i	0.0194482	+	0.144077i
$35$	−44.1919			−1.26262
$36$		0			0
$37$			33.0030i			0.891974i	0.895040	+	0.445987i	$0.147147\pi$
$37$			33.0030i			0.891974i	−0.895040	+	0.445987i	$0.852853\pi$
$38$	−13.2110	+	35.6296i	−0.347657	+	0.937622i
$39$		0			0
$40$	14.3205	+	33.6346i	0.358013	+	0.840864i
$41$	1.46331			0.0356905			0.0178452	−	0.999841i	$-0.494319\pi$
$41$	1.46331			0.0356905			0.0178452	+	0.999841i	$0.494319\pi$
$42$		0			0
$43$			26.0088i			0.604855i	0.953172	+	0.302428i	$0.0977971\pi$
$43$			26.0088i			0.604855i	−0.953172	+	0.302428i	$0.902203\pi$
$44$	8.71321	−	2.39596i	0.198028	−	0.0544536i
$45$		0			0
$46$	57.5265	−	7.76519i	1.25058	−	0.168808i
$47$	6.14434			0.130731			0.0653653	−	0.997861i	$-0.479179\pi$
$47$	6.14434			0.130731			0.0653653	+	0.997861i	$0.479179\pi$
$48$		0			0
$49$	−44.5278			−0.908730
$50$	−8.16467	+	1.10211i	−0.163293	+	0.0220421i
$51$		0			0
$52$	−15.2996	−	55.6391i	−0.294224	−	1.06998i
$53$	−16.4054			−0.309536			−0.154768	−	0.987951i	$-0.549463\pi$
$53$	−16.4054			−0.309536			−0.154768	+	0.987951i	$0.549463\pi$
$54$		0			0
$55$		−	10.3233i		−	0.187696i
$56$	30.3080	+	71.1843i	0.541214	+	1.27115i
$57$		0			0
$58$	−20.5404	+	2.77264i	−0.354145	+	0.0478041i
$59$			57.3091i			0.971341i	0.874142	+	0.485670i	$0.161424\pi$
$59$			57.3091i			0.971341i	−0.874142	+	0.485670i	$0.838576\pi$
$60$		0			0
$61$	94.3814			1.54724			0.773618	−	0.633652i	$-0.218445\pi$
$61$	94.3814			1.54724			0.773618	+	0.633652i	$0.218445\pi$
$62$	7.97935	−	1.07709i	0.128699	−	0.0173724i
$63$		0			0
$64$	44.3572	−	46.1350i	0.693081	−	0.720860i
$65$	−65.9205			−1.01416
$66$		0			0
$67$	−120.267			−1.79503			−0.897515	−	0.440985i	$-0.854629\pi$
$67$	−120.267			−1.79503			−0.897515	+	0.440985i	$0.854629\pi$
$68$	−2.62118	−	9.53225i	−0.0385467	−	0.140180i
$69$		0			0
$70$	87.5893	−	11.8232i	1.25128	−	0.168903i
$71$		−	102.072i		−	1.43763i	−0.695202	−	0.718814i	$-0.744685\pi$
$71$		−	102.072i		−	1.43763i	0.695202	−	0.718814i	$-0.255315\pi$
$72$		0			0
$73$	10.8998			0.149313			0.0746563	−	0.997209i	$-0.476214\pi$
$73$	10.8998			0.149313			0.0746563	+	0.997209i	$0.476214\pi$
$74$	−8.82973	−	65.4128i	−0.119321	−	0.883957i
$75$		0			0
$76$	16.6520	−	74.1533i	0.219105	−	0.975701i
$77$		−	21.8483i		−	0.283744i
$78$		0			0
$79$	−54.0890			−0.684671			−0.342336	−	0.939578i	$-0.611218\pi$
$79$	−54.0890			−0.684671			−0.342336	+	0.939578i	$0.611218\pi$
$80$	−37.3823	−	62.8332i	−0.467279	−	0.785415i
$81$		0			0
$82$	−2.90031	+	0.391498i	−0.0353697	+	0.00477436i
$83$	−68.5339			−0.825710			−0.412855	−	0.910797i	$-0.635468\pi$
$83$	−68.5339			−0.825710			−0.412855	+	0.910797i	$0.635468\pi$
$84$		0			0
$85$	−11.2937			−0.132867
$86$	−6.95846	−	51.5500i	−0.0809124	−	0.599419i
$87$		0			0
$88$	−16.6288	+	7.08000i	−0.188963	+	0.0804546i
$89$	7.00476			0.0787051			0.0393526	−	0.999225i	$-0.487470\pi$
$89$	7.00476			0.0787051			0.0393526	+	0.999225i	$0.487470\pi$
$90$		0			0
$91$	−139.514			−1.53312
$92$	−111.941	+	30.7816i	−1.21675	+	0.334583i
$93$		0			0
$94$	−12.1782	+	1.64387i	−0.129556	+	0.0174880i
$95$	−76.6360	−	40.8024i	−0.806695	−	0.429499i
$96$		0			0
$97$			29.0407i			0.299389i	0.988732	+	0.149694i	$0.0478290\pi$
$97$			29.0407i			0.299389i	−0.988732	+	0.149694i	$0.952171\pi$
$98$	88.2551	−	11.9131i	0.900563	−	0.121562i
$99$		0			0
$100$	15.8877	−	4.36880i	0.158877	−	0.0436880i
$101$			33.9604i			0.336241i	0.985766	+	0.168121i	$0.0537698\pi$
$101$			33.9604i			0.336241i	−0.985766	+	0.168121i	$0.946230\pi$
$102$		0			0
$103$	−145.195			−1.40966			−0.704832	−	0.709374i	$-0.748978\pi$
$103$	−145.195			−1.40966			−0.704832	+	0.709374i	$0.748978\pi$
$104$	45.2101	+	106.185i	0.434712	+	1.02101i
$105$		0			0
$106$	32.5160	−	4.38916i	0.306754	−	0.0414072i
$107$		−	21.3857i		−	0.199866i	−0.994994	−	0.0999332i	$-0.968137\pi$
$107$		−	21.3857i		−	0.199866i	0.994994	−	0.0999332i	$-0.0318629\pi$
$108$		0			0
$109$		−	182.880i		−	1.67780i	−0.544285	−	0.838900i	$-0.683199\pi$
$109$		−	182.880i		−	1.67780i	0.544285	−	0.838900i	$-0.316801\pi$
$110$	2.76192	+	20.4610i	0.0251084	+	0.186009i
$111$		0			0
$112$	−79.1160	−	132.980i	−0.706393	−	1.18732i
$113$	186.968			1.65458			0.827292	−	0.561773i	$-0.189880\pi$
$113$	186.968			1.65458			0.827292	+	0.561773i	$0.189880\pi$
$114$		0			0
$115$			132.627i			1.15327i
$116$	39.9698	−	10.9909i	0.344567	−	0.0947489i
$117$		0			0
$118$	−15.3326	−	113.588i	−0.129938	−	0.962610i
$119$	−23.9020			−0.200857
$120$		0			0
$121$	−115.896			−0.957820
$122$	−187.066	+	25.2511i	−1.53333	+	0.206976i
$123$		0			0
$124$	−15.5271	+	4.26964i	−0.125219	+	0.0344326i
$125$		−	133.062i		−	1.06450i
$126$		0			0
$127$	−183.161			−1.44221			−0.721106	−	0.692825i	$-0.756366\pi$
$127$	−183.161			−1.44221			−0.721106	+	0.692825i	$0.756366\pi$
$128$	−75.5739	+	103.308i	−0.590421	+	0.807095i
$129$		0			0
$130$	130.656	−	17.6366i	1.00505	−	0.135666i
$131$	−117.754			−0.898885			−0.449443	−	0.893309i	$-0.648377\pi$
$131$	−117.754			−0.898885			−0.449443	+	0.893309i	$0.648377\pi$
$132$		0			0
$133$	−162.193	−	86.3544i	−1.21949	−	0.649281i
$134$	238.372	−	32.1766i	1.77890	−	0.240124i
$135$		0			0
$136$	7.74552	+	18.1919i	0.0569524	+	0.133764i
$137$			20.2096i			0.147516i	0.997276	+	0.0737578i	$0.0234992\pi$
$137$			20.2096i			0.147516i	−0.997276	+	0.0737578i	$0.976501\pi$
$138$		0			0
$139$			121.016i			0.870615i	0.900282	+	0.435308i	$0.143360\pi$
$139$			121.016i			0.870615i	−0.900282	+	0.435308i	$0.856640\pi$
$140$	−170.441	+	46.8678i	−1.21744	+	0.334770i
$141$		0			0
$142$	27.3085	+	202.308i	0.192314	+	1.42471i
$143$		−	32.5908i		−	0.227908i
$144$		0			0
$145$		−	47.3556i		−	0.326591i
$146$	−21.6037	+	2.91617i	−0.147971	+	0.0199738i
$147$		0			0
$148$	35.0015	+	127.287i	0.236496	+	0.860050i
$149$		−	197.800i		−	1.32752i	−0.747946	−	0.663760i	$-0.768960\pi$
$149$		−	197.800i		−	1.32752i	0.747946	−	0.663760i	$-0.231040\pi$
$150$		0			0
$151$	174.253			1.15399			0.576997	−	0.816746i	$-0.304225\pi$
$151$	174.253			1.15399			0.576997	+	0.816746i	$0.304225\pi$
$152$	−13.1655	+	151.429i	−0.0866152	+	0.996242i
$153$		0			0
$154$	5.84535	+	43.3038i	0.0379568	+	0.281193i
$155$			18.3963i			0.118686i
$156$		0			0
$157$	240.144			1.52958			0.764790	−	0.644280i	$-0.222843\pi$
$157$	240.144			1.52958			0.764790	+	0.644280i	$0.222843\pi$
$158$	107.206	−	14.4711i	0.678517	−	0.0915895i
$159$		0			0
$160$	90.9032	+	114.535i	0.568145	+	0.715847i
$161$			280.691i			1.74342i
$162$		0			0
$163$			75.1019i			0.460748i	0.973102	+	0.230374i	$0.0739949\pi$
$163$			75.1019i			0.460748i	−0.973102	+	0.230374i	$0.926005\pi$
$164$	5.64375	−	1.55192i	0.0344131	−	0.00946291i
$165$		0			0
$166$	135.836	−	18.3358i	0.818288	−	0.110456i
$167$		−	237.513i		−	1.42223i	−0.703075	−	0.711116i	$-0.748190\pi$
$167$		−	237.513i		−	1.42223i	0.703075	−	0.711116i	$-0.251810\pi$
$168$		0			0
$169$	−39.1119			−0.231431
$170$	22.3844	−	3.02155i	0.131673	−	0.0177738i
$171$		0			0
$172$	27.5837	+	100.312i	0.160370	+	0.583208i
$173$	−155.335			−0.897890			−0.448945	−	0.893559i	$-0.648200\pi$
$173$	−155.335			−0.897890			−0.448945	+	0.893559i	$0.648200\pi$
$174$		0			0
$175$		−	39.8382i		−	0.227647i
$176$	31.0644	−	18.4816i	0.176502	−	0.105009i
$177$		0			0
$178$	−13.8836	+	1.87407i	−0.0779978	+	0.0105285i
$179$		−	344.237i		−	1.92311i	−0.274611	−	0.961555i	$-0.588549\pi$
$179$		−	344.237i		−	1.92311i	0.274611	−	0.961555i	$-0.411451\pi$
$180$		0			0
$181$			258.376i			1.42749i	0.700405	+	0.713746i	$0.253003\pi$
$181$			258.376i			1.42749i	−0.700405	+	0.713746i	$0.746997\pi$
$182$	276.521	−	37.3261i	1.51934	−	0.205088i
$183$		0			0
$184$	213.635	−	90.9590i	1.16106	−	0.494342i
$185$	150.808			0.815181
$186$		0			0
$187$		−	5.58355i		−	0.0298585i
$188$	23.6977	−	6.51640i	0.126052	−	0.0346617i
$189$		0			0
$190$	162.811	+	60.3680i	0.856899	+	0.317726i
$191$	337.360			1.76628			0.883142	−	0.469106i	$-0.155424\pi$
$191$	337.360			1.76628			0.883142	+	0.469106i	$0.155424\pi$
$192$		0			0
$193$		−	1.65785i		−	0.00858991i	−0.999991	−	0.00429495i	$-0.998633\pi$
$193$		−	1.65785i		−	0.00858991i	0.999991	−	0.00429495i	$-0.00136713\pi$
$194$	−7.76964	−	57.5594i	−0.0400497	−	0.296698i
$195$		0			0
$196$	−171.737	+	47.2241i	−0.876207	+	0.240939i
$197$		−	55.4402i		−	0.281422i	−0.990051	−	0.140711i	$-0.955061\pi$
$197$		−	55.4402i		−	0.281422i	0.990051	−	0.140711i	$-0.0449389\pi$
$198$		0			0
$199$			218.233i			1.09665i	0.836267	+	0.548323i	$0.184734\pi$
$199$			218.233i			1.09665i	−0.836267	+	0.548323i	$0.815266\pi$
$200$	−30.3210	+	12.9097i	−0.151605	+	0.0645486i
$201$		0			0
$202$	−9.08586	−	67.3103i	−0.0449795	−	0.333219i
$203$		−	100.224i		−	0.493712i
$204$		0			0
$205$		−	6.68664i		−	0.0326178i
$206$	287.781	−	38.8460i	1.39699	−	0.188573i
$207$		0			0
$208$	−118.016	−	198.365i	−0.567387	−	0.953679i
$209$	20.1725	−	37.8885i	0.0965193	−	0.181285i
$210$		0			0
$211$	166.163			0.787503			0.393751	−	0.919217i	$-0.371177\pi$
$211$	166.163			0.787503			0.393751	+	0.919217i	$0.371177\pi$
$212$	−63.2732	+	17.3988i	−0.298458	+	0.0820700i
$213$		0			0
$214$	5.72160	+	42.3870i	0.0267364	+	0.198070i
$215$	118.848			0.552781
$216$		0			0
$217$			38.9340i			0.179419i
$218$	48.9283	+	362.473i	0.224442	+	1.66272i
$219$		0			0
$220$	−10.9484	−	39.8153i	−0.0497655	−	0.180979i
$221$	−35.6543			−0.161332
$222$		0			0
$223$	65.0594			0.291746			0.145873	−	0.989303i	$-0.453401\pi$
$223$	65.0594			0.291746			0.145873	+	0.989303i	$0.453401\pi$
$224$	192.388	+	242.403i	0.858874	+	1.08216i
$225$		0			0
$226$	−370.575	+	50.0219i	−1.63971	+	0.221336i
$227$			224.720i			0.989954i	0.868906	+	0.494977i	$0.164824\pi$
$227$			224.720i			0.989954i	−0.868906	+	0.494977i	$0.835176\pi$
$228$		0			0
$229$	−54.6061			−0.238454			−0.119227	−	0.992867i	$-0.538042\pi$
$229$	−54.6061			−0.238454			−0.119227	+	0.992867i	$0.538042\pi$
$230$	−35.4833	−	262.869i	−0.154275	−	1.14291i
$231$		0			0
$232$	−76.2805	+	32.4778i	−0.328795	+	0.139991i
$233$			353.980i			1.51923i	0.650376	+	0.759613i	$0.274612\pi$
$233$			353.980i			1.51923i	−0.650376	+	0.759613i	$0.725388\pi$
$234$		0			0
$235$		−	28.0768i		−	0.119476i
$236$	60.7793	+	221.032i	0.257540	+	0.936577i
$237$		0			0
$238$	47.3743	−	6.39481i	0.199052	−	0.0268689i
$239$	352.007			1.47283			0.736416	−	0.676529i	$-0.236517\pi$
$239$	352.007			1.47283			0.736416	+	0.676529i	$0.236517\pi$
$240$		0			0
$241$			207.188i			0.859702i	0.902900	+	0.429851i	$0.141434\pi$
$241$			207.188i			0.859702i	−0.902900	+	0.429851i	$0.858566\pi$
$242$	229.709	−	31.0072i	0.949211	−	0.128129i
$243$		0			0
$244$	364.014	−	100.096i	1.49186	−	0.410231i
$245$			203.471i			0.830495i
$246$		0			0
$247$	−241.941	−	128.814i	−0.979518	−	0.521513i
$248$	29.6328	−	12.6167i	0.119487	−	0.0508738i
$249$		0			0
$250$	35.5998	+	263.732i	0.142399	+	1.05493i
$251$	−250.965			−0.999861			−0.499931	−	0.866065i	$-0.666641\pi$
$251$	−250.965			−0.999861			−0.499931	+	0.866065i	$0.666641\pi$
$252$		0			0
$253$	−65.5700			−0.259170
$254$	363.029	−	49.0034i	1.42925	−	0.192927i
$255$		0			0
$256$	122.150	−	224.979i	0.477148	−	0.878823i
$257$	56.2756			0.218971			0.109486	−	0.993988i	$-0.465080\pi$
$257$	56.2756			0.218971			0.109486	+	0.993988i	$0.465080\pi$
$258$		0			0
$259$	319.171			1.23232
$260$	−254.245	+	69.9122i	−0.977865	+	0.268893i
$261$		0			0
$262$	233.391	−	31.5042i	0.890806	−	0.120245i
$263$	116.802			0.444112			0.222056	−	0.975034i	$-0.428723\pi$
$263$	116.802			0.444112			0.222056	+	0.975034i	$0.428723\pi$
$264$		0			0
$265$			74.9652i			0.282888i
$266$	344.573	+	127.763i	1.29539	+	0.480312i
$267$		0			0
$268$	−463.851	+	127.549i	−1.73079	+	0.475931i
$269$	−436.834			−1.62392			−0.811959	−	0.583714i	$-0.801599\pi$
$269$	−436.834			−1.62392			−0.811959	+	0.583714i	$0.801599\pi$
$270$		0			0
$271$			198.846i			0.733747i	0.930271	+	0.366874i	$0.119572\pi$
$271$			198.846i			0.733747i	−0.930271	+	0.366874i	$0.880428\pi$
$272$	−20.2189	−	33.9845i	−0.0743343	−	0.124943i
$273$		0			0
$274$	−5.40695	−	40.0560i	−0.0197334	−	0.146190i
$275$	9.30628			0.0338410
$276$		0			0
$277$	−91.4350			−0.330090			−0.165045	−	0.986286i	$-0.552777\pi$
$277$	−91.4350			−0.330090			−0.165045	+	0.986286i	$0.552777\pi$
$278$	−32.3769	−	239.856i	−0.116464	−	0.862791i
$279$		0			0
$280$	325.279	−	138.493i	1.16171	−	0.494619i
$281$	−293.552			−1.04467			−0.522334	−	0.852741i	$-0.674939\pi$
$281$	−293.552			−1.04467			−0.522334	+	0.852741i	$0.674939\pi$
$282$		0			0
$283$		−	172.782i		−	0.610538i	−0.952266	−	0.305269i	$-0.901254\pi$
$283$		−	172.782i		−	0.610538i	0.952266	−	0.305269i	$-0.0987465\pi$
$284$	−108.252	−	393.674i	−0.381170	−	1.38618i
$285$		0			0
$286$	8.71944	+	64.5957i	0.0304875	+	0.225859i
$287$		−	14.1516i		−	0.0493088i
$288$		0			0
$289$	282.892			0.978864
$290$	12.6697	+	93.8600i	0.0436885	+	0.323655i
$291$		0			0
$292$	42.0389	−	11.5598i	0.143969	−	0.0395885i
$293$	455.722			1.55537			0.777683	−	0.628657i	$-0.216395\pi$
$293$	455.722			1.55537			0.777683	+	0.628657i	$0.216395\pi$
$294$		0			0
$295$	261.876			0.887715
$296$	−103.429	−	242.922i	−0.349421	−	0.820684i
$297$		0			0
$298$	52.9201	+	392.045i	0.177584	+	1.31559i
$299$			418.704i			1.40035i
$300$		0			0
$301$	251.530			0.835649
$302$	−345.374	+	46.6202i	−1.14362	+	0.154371i
$303$		0			0
$304$	−14.4193	−	303.658i	−0.0474321	−	0.998874i
$305$		−	431.279i		−	1.41403i
$306$		0			0
$307$	433.832			1.41313			0.706567	−	0.707646i	$-0.250243\pi$
$307$	433.832			1.41313			0.706567	+	0.707646i	$0.250243\pi$
$308$	−23.1712	−	84.2653i	−0.0752313	−	0.273588i
$309$		0			0
$310$	−4.92180	−	36.4619i	−0.0158768	−	0.117619i
$311$	62.7106			0.201642			0.100821	−	0.994905i	$-0.467853\pi$
$311$	62.7106			0.201642			0.100821	+	0.994905i	$0.467853\pi$
$312$		0			0
$313$	−222.649			−0.711339			−0.355669	−	0.934612i	$-0.615747\pi$
$313$	−222.649			−0.711339			−0.355669	+	0.934612i	$0.615747\pi$
$314$	−475.971	+	64.2488i	−1.51583	+	0.204614i
$315$		0			0
$316$	−208.613	+	57.3643i	−0.660167	+	0.181533i
$317$	277.405			0.875093			0.437547	−	0.899196i	$-0.355847\pi$
$317$	277.405			0.875093			0.437547	+	0.899196i	$0.355847\pi$
$318$		0			0
$319$	23.4124			0.0733931
$320$	−210.816	−	202.692i	−0.658799	−	0.633411i
$321$		0			0
$322$	−75.0970	−	556.337i	−0.233220	−	1.72775i
$323$	−41.4500	−	22.0688i	−0.128328	−	0.0683243i
$324$		0			0
$325$		−	59.4262i		−	0.182850i
$326$	−20.0930	−	148.854i	−0.0616349	−	0.456607i
$327$		0			0
$328$	−10.7708	+	4.58588i	−0.0328379	+	0.0139813i
$329$		−	59.4217i		−	0.180613i
$330$		0			0
$331$	−481.784			−1.45554			−0.727771	−	0.685820i	$-0.759444\pi$
$331$	−481.784			−1.45554			−0.727771	+	0.685820i	$0.759444\pi$
$332$	−264.324	+	72.6839i	−0.796158	+	0.218927i
$333$		0			0
$334$	63.5448	+	470.756i	0.190254	+	1.40945i
$335$			549.564i			1.64049i
$336$		0			0
$337$		−	197.246i		−	0.585300i	−0.956220	−	0.292650i	$-0.905463\pi$
$337$		−	197.246i		−	0.585300i	0.956220	−	0.292650i	$-0.0945371\pi$
$338$	77.5207	−	10.4641i	0.229351	−	0.0309589i
$339$		0			0
$340$	−43.5580	+	11.9776i	−0.128112	+	0.0352281i
$341$	−9.09505			−0.0266717
$342$		0			0
$343$		−	43.2508i		−	0.126096i
$344$	−81.5092	−	191.440i	−0.236945	−	0.556513i
$345$		0			0
$346$	307.878	−	41.5588i	0.889820	−	0.120112i
$347$	63.7435			0.183699			0.0918494	−	0.995773i	$-0.470722\pi$
$347$	63.7435			0.183699			0.0918494	+	0.995773i	$0.470722\pi$
$348$		0			0
$349$	124.985			0.358122			0.179061	−	0.983838i	$-0.442694\pi$
$349$	124.985			0.358122			0.179061	+	0.983838i	$0.442694\pi$
$350$	10.6584	+	78.9603i	0.0304527	+	0.225601i
$351$		0			0
$352$	−56.6258	+	44.9421i	−0.160869	+	0.127677i
$353$		−	367.068i		−	1.03985i	−0.854211	−	0.519926i	$-0.825959\pi$
$353$		−	367.068i		−	1.03985i	0.854211	−	0.519926i	$-0.174041\pi$
$354$		0			0
$355$	−466.420			−1.31386
$356$	27.0162	−	7.42892i	0.0758883	−	0.0208678i
$357$		0			0
$358$	92.0981	+	682.286i	0.257257	+	1.90583i
$359$	55.1266			0.153556			0.0767781	−	0.997048i	$-0.475537\pi$
$359$	55.1266			0.153556			0.0767781	+	0.997048i	$0.475537\pi$
$360$		0			0
$361$	−201.538	−	299.506i	−0.558276	−	0.829655i
$362$	−69.1266	−	512.107i	−0.190958	−	1.41466i
$363$		0			0
$364$	−538.085	+	147.962i	−1.47825	+	0.406490i
$365$		−	49.8071i		−	0.136458i
$366$		0			0
$367$		−	330.645i		−	0.900939i	−0.892792	−	0.450470i	$-0.851257\pi$
$367$		−	330.645i		−	0.900939i	0.892792	−	0.450470i	$-0.148743\pi$
$368$	−399.094	+	237.439i	−1.08450	+	0.645216i
$369$		0			0
$370$	−298.906	+	40.3477i	−0.807854	+	0.109048i
$371$			158.657i			0.427646i
$372$		0			0
$373$		−	575.367i		−	1.54254i	−0.636510	−	0.771269i	$-0.719622\pi$
$373$		−	575.367i		−	1.54254i	0.636510	−	0.771269i	$-0.280378\pi$
$374$	1.49384	+	11.0667i	0.00399422	+	0.0295902i
$375$		0			0
$376$	−45.2261	+	19.2558i	−0.120282	+	0.0512123i
$377$		−	149.502i		−	0.396558i
$378$		0			0
$379$	439.139			1.15868			0.579339	−	0.815087i	$-0.303311\pi$
$379$	439.139			1.15868			0.579339	+	0.815087i	$0.303311\pi$
$380$	−338.846	−	76.0919i	−0.891700	−	0.200242i
$381$		0			0
$382$	−668.656	+	90.2583i	−1.75041	+	0.236278i
$383$		−	145.105i		−	0.378865i	−0.981894	−	0.189433i	$-0.939335\pi$
$383$		−	145.105i		−	0.378865i	0.981894	−	0.189433i	$-0.0606649\pi$
$384$		0			0
$385$	−99.8363			−0.259315
$386$	0.443547	+	3.28590i	0.00114908	+	0.00851270i
$387$		0			0
$388$	30.7992	+	112.005i	0.0793794	+	0.288674i
$389$			573.996i			1.47557i	0.675037	+	0.737783i	$0.264127\pi$
$389$			573.996i			1.47557i	−0.675037	+	0.737783i	$0.735873\pi$
$390$		0			0
$391$			71.7336i			0.183462i
$392$	327.752	−	139.546i	0.836101	−	0.355985i
$393$		0			0
$394$	14.8326	+	109.884i	0.0376463	+	0.278893i
$395$			247.162i			0.625726i
$396$		0			0
$397$	−472.658			−1.19057			−0.595287	−	0.803513i	$-0.702962\pi$
$397$	−472.658			−1.19057			−0.595287	+	0.803513i	$0.702962\pi$
$398$	−58.3866	−	432.542i	−0.146700	−	1.08679i
$399$		0			0
$400$	56.6430	−	33.6995i	0.141608	−	0.0842488i
$401$	−479.989			−1.19698			−0.598490	−	0.801131i	$-0.704232\pi$
$401$	−479.989			−1.19698			−0.598490	+	0.801131i	$0.704232\pi$
$402$		0			0
$403$			58.0774i			0.144113i
$404$	36.0168	+	130.980i	0.0891505	+	0.324207i
$405$		0			0
$406$	26.8141	+	198.646i	0.0660446	+	0.489275i
$407$			74.5590i			0.183192i
$408$		0			0
$409$			361.938i			0.884933i	0.896785	+	0.442466i	$0.145896\pi$
$409$			361.938i			0.884933i	−0.896785	+	0.442466i	$0.854104\pi$
$410$	1.78896	+	13.2531i	0.00436332	+	0.0323246i
$411$		0			0
$412$	−559.996	+	153.987i	−1.35921	+	0.373756i
$413$	554.235			1.34197
$414$		0			0
$415$			313.168i			0.754622i
$416$	286.983	+	361.590i	0.689862	+	0.869207i
$417$		0			0
$418$	−29.8457	+	80.4929i	−0.0714011	+	0.192567i
$419$	−382.181			−0.912127			−0.456064	−	0.889947i	$-0.650741\pi$
$419$	−382.181			−0.912127			−0.456064	+	0.889947i	$0.650741\pi$
$420$		0			0
$421$			499.229i			1.18582i	0.805270	+	0.592908i	$0.202020\pi$
$421$			499.229i			1.18582i	−0.805270	+	0.592908i	$0.797980\pi$
$422$	−329.339	+	44.4558i	−0.780425	+	0.105345i
$423$		0			0
$424$	120.754	−	51.4132i	0.284797	−	0.121258i
$425$		−	10.1811i		−	0.0239555i
$426$		0			0
$427$		−	912.760i		−	2.13761i
$428$	−22.6807	−	82.4813i	−0.0529923	−	0.192713i
$429$		0			0
$430$	−235.560	+	31.7969i	−0.547813	+	0.0739464i
$431$		−	697.824i		−	1.61908i	−0.587064	−	0.809541i	$-0.699716\pi$
$431$		−	697.824i		−	1.61908i	0.587064	−	0.809541i	$-0.300284\pi$
$432$		0			0
$433$		−	487.071i		−	1.12488i	−0.826839	−	0.562438i	$-0.809863\pi$
$433$		−	487.071i		−	1.12488i	0.826839	−	0.562438i	$-0.190137\pi$
$434$	−10.4165	−	77.1681i	−0.0240012	−	0.177807i
$435$		0			0
$436$	−193.954	−	705.340i	−0.444849	−	1.61775i
$437$	−259.163	+	486.765i	−0.593050	+	1.11388i
$438$		0			0
$439$	710.575			1.61862			0.809311	−	0.587381i	$-0.199841\pi$
$439$	710.575			1.61862			0.809311	+	0.587381i	$0.199841\pi$
$440$	32.3523	+	75.9858i	0.0735280	+	0.172695i
$441$		0			0
$442$	70.6677	−	9.53906i	0.159882	−	0.0215816i
$443$	−229.818			−0.518776			−0.259388	−	0.965773i	$-0.583521\pi$
$443$	−229.818			−0.518776			−0.259388	+	0.965773i	$0.583521\pi$
$444$		0			0
$445$		−	32.0085i		−	0.0719292i
$446$	−128.949	+	17.4062i	−0.289124	+	0.0390273i
$447$		0			0
$448$	−446.171	−	428.977i	−0.995917	−	0.957538i
$449$	516.327			1.14995			0.574974	−	0.818172i	$-0.305012\pi$
$449$	516.327			1.14995			0.574974	+	0.818172i	$0.305012\pi$
$450$		0			0
$451$	3.30584			0.00733003
$452$	721.106	−	198.289i	1.59537	−	0.438693i
$453$		0			0
$454$	−60.1221	−	445.400i	−0.132428	−	0.981057i
$455$			637.515i			1.40113i
$456$		0			0
$457$	524.409			1.14750			0.573752	−	0.819029i	$-0.305487\pi$
$457$	524.409			1.14750			0.573752	+	0.819029i	$0.305487\pi$
$458$	108.231	−	14.6095i	0.236311	−	0.0318984i
$459$		0			0
$460$	140.658	+	511.520i	0.305777	+	1.11200i
$461$		−	367.478i		−	0.797133i	−0.917139	−	0.398567i	$-0.869508\pi$
$461$		−	367.478i		−	0.797133i	0.917139	−	0.398567i	$-0.130492\pi$
$462$		0			0
$463$		−	209.731i		−	0.452983i	−0.974013	−	0.226492i	$-0.927274\pi$
$463$		−	209.731i		−	0.452983i	0.974013	−	0.226492i	$-0.0727256\pi$
$464$	142.501	−	84.7801i	0.307113	−	0.182716i
$465$		0			0
$466$	−94.7047	−	701.596i	−0.203229	−	1.50557i
$467$	−631.041			−1.35127			−0.675633	−	0.737238i	$-0.736129\pi$
$467$	−631.041			−1.35127			−0.675633	+	0.737238i	$0.736129\pi$
$468$		0			0
$469$			1163.10i			2.47995i
$470$	7.51174	+	55.6488i	0.0159824	+	0.118402i
$471$		0			0
$472$	−179.602	−	421.830i	−0.380512	−	0.893707i
$473$			58.7579i			0.124224i
$474$		0			0
$475$	36.7827	−	69.0861i	0.0774373	−	0.145444i
$476$	−92.1862	+	25.3493i	−0.193668	+	0.0532549i
$477$		0			0
$478$	−697.686	+	94.1769i	−1.45959	+	0.197023i
$479$	875.568			1.82791			0.913954	−	0.405818i	$-0.133013\pi$
$479$	875.568			1.82791			0.913954	+	0.405818i	$0.133013\pi$
$480$		0			0
$481$	476.104			0.989822
$482$	−55.4317	−	410.652i	−0.115004	−	0.851975i
$483$		0			0
$484$	−446.993	+	122.914i	−0.923540	+	0.253955i
$485$	132.703			0.273613
$486$		0			0
$487$	614.907			1.26264			0.631321	−	0.775521i	$-0.282513\pi$
$487$	614.907			1.26264			0.631321	+	0.775521i	$0.282513\pi$
$488$	−694.705	+	295.783i	−1.42357	+	0.606113i
$489$		0			0
$490$	−54.4373	−	403.285i	−0.111096	−	0.823030i
$491$	192.629			0.392320			0.196160	−	0.980572i	$-0.437153\pi$
$491$	192.629			0.392320			0.196160	+	0.980572i	$0.437153\pi$
$492$		0			0
$493$		−	25.6132i		−	0.0519537i
$494$	513.996	+	190.583i	1.04048	+	0.385795i
$495$		0			0
$496$	−55.3574	+	32.9346i	−0.111608	+	0.0664005i
$497$	−987.132			−1.98618
$498$		0			0
$499$		−	866.789i		−	1.73705i	−0.495643	−	0.868526i	$-0.665068\pi$
$499$		−	866.789i		−	1.73705i	0.495643	−	0.868526i	$-0.334932\pi$
$500$	−141.119	−	513.199i	−0.282238	−	1.02640i
$501$		0			0
$502$	497.419	−	67.1440i	0.990875	−	0.133753i
$503$	−801.068			−1.59258			−0.796291	−	0.604914i	$-0.793207\pi$
$503$	−801.068			−1.59258			−0.796291	+	0.604914i	$0.793207\pi$
$504$		0			0
$505$	155.183			0.307293
$506$	129.961	−	17.5428i	0.256841	−	0.0346695i
$507$		0			0
$508$	−706.422	+	194.252i	−1.39060	+	0.382385i
$509$	−577.610			−1.13479			−0.567397	−	0.823444i	$-0.692050\pi$
$509$	−577.610			−1.13479			−0.567397	+	0.823444i	$0.692050\pi$
$510$		0			0
$511$		−	105.412i		−	0.206285i
$512$	−181.913	+	478.594i	−0.355298	+	0.934753i
$513$		0			0
$514$	−111.540	+	15.0561i	−0.217003	+	0.0292921i
$515$			663.475i			1.28830i
$516$		0			0
$517$	13.8810			0.0268492
$518$	−632.606	+	85.3921i	−1.22125	+	0.164850i
$519$		0			0
$520$	485.215	−	206.589i	0.933106	−	0.397287i
$521$	408.835			0.784713			0.392356	−	0.919813i	$-0.371660\pi$
$521$	408.835			0.784713			0.392356	+	0.919813i	$0.371660\pi$
$522$		0			0
$523$	−102.291			−0.195586			−0.0977928	−	0.995207i	$-0.531178\pi$
$523$	−102.291			−0.195586			−0.0977928	+	0.995207i	$0.531178\pi$
$524$	−454.158	+	124.884i	−0.866715	+	0.238329i
$525$		0			0
$526$	−231.504	+	31.2494i	−0.440121	+	0.0594096i
$527$			9.94999i			0.0188804i
$528$		0			0
$529$	313.398			0.592434
$530$	−20.0564	−	148.583i	−0.0378423	−	0.280345i
$531$		0			0
$532$	−717.135	−	161.041i	−1.34800	−	0.302709i
$533$		−	21.1098i		−	0.0396057i
$534$		0			0
$535$	−97.7227			−0.182659
$536$	885.238	−	376.906i	1.65156	−	0.703183i
$537$		0			0
$538$	865.816	−	116.872i	1.60932	−	0.217234i
$539$	−100.595			−0.186633
$540$		0			0
$541$	−198.431			−0.366785			−0.183393	−	0.983040i	$-0.558708\pi$
$541$	−198.431			−0.366785			−0.183393	+	0.983040i	$0.558708\pi$
$542$	−53.1997	−	394.117i	−0.0981544	−	0.727152i
$543$		0			0
$544$	49.1667	+	61.9487i	0.0903800	+	0.113876i
$545$	−835.678			−1.53335
$546$		0			0
$547$	82.8915			0.151538			0.0757692	−	0.997125i	$-0.475859\pi$
$547$	82.8915			0.151538			0.0757692	+	0.997125i	$0.475859\pi$
$548$	21.4334	+	77.9454i	0.0391121	+	0.142236i
$549$		0			0
$550$	−18.4453	+	2.48983i	−0.0335369	+	0.00452696i
$551$	92.5366	−	173.804i	0.167943	−	0.315434i
$552$		0			0
$553$			523.094i			0.945920i
$554$	181.226	−	24.4628i	0.327123	−	0.0441567i
$555$		0			0
$556$	128.343	+	466.738i	0.230834	+	0.839456i
$557$		−	770.595i		−	1.38347i	−0.722149	−	0.691737i	$-0.756846\pi$
$557$		−	770.595i		−	1.38347i	0.722149	−	0.691737i	$-0.243154\pi$
$558$		0			0
$559$	375.205			0.671207
$560$	−607.658	+	361.523i	−1.08510	+	0.645578i
$561$		0			0
$562$	581.827	−	78.5377i	1.03528	−	0.139747i
$563$			608.743i			1.08125i	0.841264	+	0.540624i	$0.181812\pi$
$563$			608.743i			1.08125i	−0.841264	+	0.540624i	$0.818188\pi$
$564$		0			0
$565$		−	854.356i		−	1.51214i
$566$	46.2267	+	342.459i	0.0816726	+	0.605051i
$567$		0			0
$568$	319.884	+	751.309i	0.563175	+	1.32273i
$569$	668.134			1.17422			0.587112	−	0.809506i	$-0.300265\pi$
$569$	668.134			1.17422			0.587112	+	0.809506i	$0.300265\pi$
$570$		0			0
$571$		−	365.096i		−	0.639398i	−0.947519	−	0.319699i	$-0.896418\pi$
$571$		−	365.096i		−	0.639398i	0.947519	−	0.319699i	$-0.103582\pi$
$572$	−34.5643	−	125.698i	−0.0604270	−	0.219751i
$573$		0			0
$574$	3.78617	+	28.0489i	0.00659611	+	0.0488656i
$575$	−119.561			−0.207932
$576$		0			0
$577$	562.686			0.975192			0.487596	−	0.873069i	$-0.337874\pi$
$577$	562.686			0.975192			0.487596	+	0.873069i	$0.337874\pi$
$578$	−560.698	+	75.6856i	−0.970066	+	0.130944i
$579$		0			0
$580$	−50.2232	−	182.643i	−0.0865917	−	0.314902i
$581$			662.790i			1.14077i
$582$		0			0
$583$	−37.0625			−0.0635720
$584$	−80.2293	+	34.1591i	−0.137379	+	0.0584916i
$585$		0			0
$586$	−903.252	+	121.925i	−1.54139	+	0.208063i
$587$	55.1680			0.0939830			0.0469915	−	0.998895i	$-0.485037\pi$
$587$	55.1680			0.0939830			0.0469915	+	0.998895i	$0.485037\pi$
$588$		0			0
$589$	−35.9478	+	67.5180i	−0.0610320	+	0.114632i
$590$	−519.044	+	70.0630i	−0.879736	+	0.118751i
$591$		0			0
$592$	269.990	+	453.807i	0.456065	+	0.766565i
$593$		−	1053.15i		−	1.77598i	−0.459865	−	0.887989i	$-0.652102\pi$
$593$		−	1053.15i		−	1.77598i	0.459865	−	0.887989i	$-0.347898\pi$
$594$		0			0
$595$			109.221i			0.183565i
$596$	−209.778	−	762.885i	−0.351976	−	1.28001i
$597$		0			0
$598$	−112.021	−	829.881i	−0.187327	−	1.38776i
$599$			121.364i			0.202611i	0.994855	+	0.101306i	$0.0323020\pi$
$599$			121.364i			0.202611i	−0.994855	+	0.101306i	$0.967698\pi$
$600$		0			0
$601$		−	457.914i		−	0.761921i	−0.924591	−	0.380960i	$-0.875593\pi$
$601$		−	457.914i		−	0.761921i	0.924591	−	0.380960i	$-0.124407\pi$
$602$	−498.539	+	67.2951i	−0.828138	+	0.111786i
$603$		0			0
$604$	672.066	−	184.805i	1.11269	−	0.305968i
$605$			529.592i			0.875358i
$606$		0			0
$607$	600.614			0.989479			0.494739	−	0.869041i	$-0.335264\pi$
$607$	600.614			0.989479			0.494739	+	0.869041i	$0.335264\pi$
$608$	109.821	+	597.999i	0.180627	+	0.983552i
$609$		0			0
$610$	115.386	+	854.805i	0.189157	+	1.40132i
$611$		−	88.6387i		−	0.145072i
$612$		0			0
$613$	−858.385			−1.40030			−0.700151	−	0.713995i	$-0.746884\pi$
$613$	−858.385			−1.40030			−0.700151	+	0.713995i	$0.746884\pi$
$614$	−859.866	+	116.069i	−1.40043	+	0.189037i
$615$		0			0
$616$	68.4705	+	160.816i	0.111153	+	0.261066i
$617$			176.653i			0.286310i	0.989700	+	0.143155i	$0.0457247\pi$
$617$			176.653i			0.286310i	−0.989700	+	0.143155i	$0.954275\pi$
$618$		0			0
$619$		−	837.153i		−	1.35243i	−0.736705	−	0.676214i	$-0.763619\pi$
$619$		−	837.153i		−	1.35243i	0.736705	−	0.676214i	$-0.236381\pi$
$620$	19.5103	+	70.9516i	0.0314682	+	0.114438i
$621$		0			0
$622$	−124.294	+	16.7778i	−0.199830	+	0.0269739i
$623$		−	67.7428i		−	0.108737i
$624$		0			0
$625$	−505.047			−0.808075
$626$	441.296	−	59.5682i	0.704946	−	0.0951569i
$627$		0			0
$628$	926.197	−	254.685i	1.47484	−	0.405550i
$629$	81.5676			0.129678
$630$		0			0
$631$			594.388i			0.941978i	0.882139	+	0.470989i	$0.156103\pi$
$631$			594.388i			0.941978i	−0.882139	+	0.470989i	$0.843897\pi$
$632$	398.128	−	169.510i	0.629950	−	0.268212i
$633$		0			0
$634$	−549.823	+	74.2176i	−0.867228	+	0.117063i
$635$			836.960i			1.31805i
$636$		0			0
$637$			642.361i			1.00842i
$638$	−46.4040	+	6.26382i	−0.0727335	+	0.00981791i
$639$		0			0
$640$	472.070	+	345.338i	0.737610	+	0.539590i
$641$	854.404			1.33292			0.666462	−	0.745539i	$-0.267808\pi$
$641$	854.404			1.33292			0.666462	+	0.745539i	$0.267808\pi$
$642$		0			0
$643$		−	619.587i		−	0.963587i	−0.876285	−	0.481794i	$-0.839986\pi$
$643$		−	619.587i		−	0.963587i	0.876285	−	0.481794i	$-0.160014\pi$
$644$	297.688	+	1082.58i	0.462249	+	1.68103i
$645$		0			0
$646$	88.0593	+	32.6512i	0.136315	+	0.0505436i
$647$	154.357			0.238573			0.119287	−	0.992860i	$-0.461939\pi$
$647$	154.357			0.238573			0.119287	+	0.992860i	$0.461939\pi$
$648$		0			0
$649$			129.470i			0.199492i
$650$	15.8991	+	117.784i	0.0244601	+	0.181206i
$651$		0			0
$652$	79.6495	+	289.656i	0.122162	+	0.444258i
$653$		−	707.136i		−	1.08290i	−0.840732	−	0.541452i	$-0.817875\pi$
$653$		−	707.136i		−	1.08290i	0.840732	−	0.541452i	$-0.182125\pi$
$654$		0			0
$655$			538.081i			0.821497i
$656$	20.1212	−	11.9710i	0.0306725	−	0.0182485i
$657$		0			0
$658$	15.8979	+	117.775i	0.0241609	+	0.178990i
$659$			260.219i			0.394870i	0.980316	+	0.197435i	$0.0632611\pi$
$659$			260.219i			0.394870i	−0.980316	+	0.197435i	$0.936739\pi$
$660$		0			0
$661$		−	386.207i		−	0.584277i	−0.956376	−	0.292139i	$-0.905633\pi$
$661$		−	386.207i		−	0.584277i	0.956376	−	0.292139i	$-0.0943669\pi$
$662$	954.908	−	128.898i	1.44246	−	0.194710i
$663$		0			0
$664$	504.451	−	214.779i	0.759716	−	0.323463i
$665$	−394.599	+	741.145i	−0.593382	+	1.11450i
$666$		0			0
$667$	−300.786			−0.450954
$668$	−251.895	−	916.049i	−0.377088	−	1.37133i
$669$		0			0
$670$	−147.032	−	1089.25i	−0.219451	−	1.62574i
$671$	213.222			0.317768
$672$		0			0
$673$		−	923.068i		−	1.37157i	−0.727804	−	0.685786i	$-0.759459\pi$
$673$		−	923.068i		−	1.37157i	0.727804	−	0.685786i	$-0.240541\pi$
$674$	52.7718	+	390.947i	0.0782965	+	0.580040i
$675$		0			0
$676$	−150.848	+	41.4802i	−0.223148	+	0.0613613i
$677$	223.855			0.330658			0.165329	−	0.986238i	$-0.447131\pi$
$677$	223.855			0.330658			0.165329	+	0.986238i	$0.447131\pi$
$678$		0			0
$679$	280.852			0.413626
$680$	83.1284	−	35.3934i	0.122248	−	0.0520492i
$681$		0			0
$682$	18.0266	−	2.43332i	0.0264320	−	0.00356791i
$683$		−	47.7204i		−	0.0698688i	−0.999390	−	0.0349344i	$-0.988878\pi$
$683$		−	47.7204i		−	0.0698688i	0.999390	−	0.0349344i	$-0.0111222\pi$
$684$		0			0
$685$	92.3487			0.134816
$686$	11.5714	+	85.7241i	0.0168680	+	0.124962i
$687$		0			0
$688$	212.772	+	357.632i	0.309261	+	0.519815i
$689$			236.666i			0.343492i
$690$		0			0
$691$			725.953i			1.05058i	0.850922	+	0.525292i	$0.176044\pi$
$691$			725.953i			1.05058i	−0.850922	+	0.525292i	$0.823956\pi$
$692$	−599.102	+	164.741i	−0.865755	+	0.238065i
$693$		0			0
$694$	−126.341	+	17.0541i	−0.182048	+	0.0245737i
$695$	552.985			0.795661
$696$		0			0
$697$		−	3.61659i		−	0.00518880i
$698$	−247.722	+	33.4387i	−0.354903	+	0.0479065i
$699$		0			0
$700$	−42.2505	−	153.650i	−0.0603579	−	0.219500i
$701$			834.855i			1.19095i	0.803374	+	0.595474i	$0.203036\pi$
$701$			834.855i			1.19095i	−0.803374	+	0.595474i	$0.796964\pi$
$702$		0			0
$703$	553.496	+	294.692i	0.787335	+	0.419192i
$704$	100.210	−	104.226i	0.142344	−	0.148049i
$705$		0			0
$706$	98.2064	+	727.538i	0.139103	+	1.03051i
$707$	328.430			0.464540
$708$		0			0
$709$	301.789			0.425654			0.212827	−	0.977090i	$-0.431733\pi$
$709$	301.789			0.425654			0.212827	+	0.977090i	$0.431733\pi$
$710$	924.455	−	124.787i	1.30205	−	0.175757i
$711$		0			0
$712$	−51.5593	+	21.9523i	−0.0724147	+	0.0308319i
$713$	116.847			0.163881
$714$		0			0
$715$	−148.925			−0.208286
$716$	−365.081	−	1327.67i	−0.509890	−	1.85428i
$717$		0			0
$718$	−109.262	+	14.7487i	−0.152176	+	0.0205414i
$719$	607.670			0.845159			0.422580	−	0.906326i	$-0.361125\pi$
$719$	607.670			0.845159			0.422580	+	0.906326i	$0.361125\pi$
$720$		0			0
$721$			1404.18i			1.94755i
$722$	479.583	+	539.707i	0.664243	+	0.747517i
$723$		0			0
$724$	274.021	+	996.515i	0.378483	+	1.37640i
$725$	42.6903			0.0588832
$726$		0			0
$727$			1210.47i			1.66502i	0.554011	+	0.832510i	$0.313097\pi$
$727$			1210.47i			1.66502i	−0.554011	+	0.832510i	$0.686903\pi$
$728$	1026.91	−	437.226i	1.41059	−	0.600585i
$729$		0			0
$730$	13.3255	+	98.7189i	0.0182542	+	0.135231i
$731$	64.2812			0.0879359
$732$		0			0
$733$	611.968			0.834881			0.417441	−	0.908704i	$-0.362927\pi$
$733$	611.968			0.834881			0.417441	+	0.908704i	$0.362927\pi$
$734$	88.4617	+	655.346i	0.120520	+	0.892842i
$735$		0			0
$736$	727.490	−	577.386i	0.988437	−	0.784491i
$737$	−271.702			−0.368659
$738$		0			0
$739$			563.737i			0.762837i	0.924402	+	0.381419i	$0.124564\pi$
$739$			563.737i			0.762837i	−0.924402	+	0.381419i	$0.875436\pi$
$740$	581.644	−	159.940i	0.786006	−	0.216136i
$741$		0			0
$742$	−42.4474	−	314.461i	−0.0572068	−	0.423802i
$743$		−	475.145i		−	0.639496i	−0.947503	−	0.319748i	$-0.896402\pi$
$743$		−	475.145i		−	0.639496i	0.947503	−	0.319748i	$-0.103598\pi$
$744$		0			0
$745$	−903.856			−1.21323
$746$	153.935	+	1140.39i	0.206348	+	1.52867i
$747$		0			0
$748$	−5.92165	−	21.5349i	−0.00791664	−	0.0287899i
$749$	−206.821			−0.276129
$750$		0			0
$751$	−690.118			−0.918932			−0.459466	−	0.888195i	$-0.651959\pi$
$751$	−690.118			−0.918932			−0.459466	+	0.888195i	$0.651959\pi$
$752$	84.4874	−	50.2654i	0.112350	−	0.0668423i
$753$		0			0
$754$	39.9983	+	296.317i	0.0530481	+	0.392994i
$755$		−	796.255i		−	1.05464i
$756$		0			0
$757$	−565.079			−0.746471			−0.373236	−	0.927737i	$-0.621752\pi$
$757$	−565.079			−0.746471			−0.373236	+	0.927737i	$0.621752\pi$
$758$	−870.384	+	117.489i	−1.14826	+	0.154998i
$759$		0			0
$760$	691.959	+	60.1602i	0.910472	+	0.0791582i
$761$		−	96.6715i		−	0.127032i	−0.997981	−	0.0635161i	$-0.979769\pi$
$761$		−	96.6715i		−	0.127032i	0.997981	−	0.0635161i	$-0.0202314\pi$
$762$		0			0
$763$	−1768.63			−2.31800
$764$	1301.14	−	357.788i	1.70307	−	0.468309i
$765$		0			0
$766$	38.8219	+	287.603i	0.0506814	+	0.375460i
$767$	826.746			1.07790
$768$		0			0
$769$	−711.471			−0.925189			−0.462595	−	0.886570i	$-0.653081\pi$
$769$	−711.471			−0.925189			−0.462595	+	0.886570i	$0.653081\pi$
$770$	197.878	−	26.7105i	0.256984	−	0.0346890i
$771$		0			0
$772$	−1.75824	−	6.39407i	−0.00227751	−	0.00828248i
$773$	325.033			0.420482			0.210241	−	0.977650i	$-0.432575\pi$
$773$	325.033			0.420482			0.210241	+	0.977650i	$0.432575\pi$
$774$		0			0
$775$	−16.5840			−0.0213987
$776$	−91.0111	−	213.757i	−0.117282	−	0.275461i
$777$		0			0
$778$	−153.568	−	1137.67i	−0.197389	−	1.46230i
$779$	13.0662	−	24.5413i	0.0167731	−	0.0315035i
$780$		0			0
$781$		−	230.596i		−	0.295257i
$782$	−19.1918	−	142.178i	−0.0245420	−	0.181813i
$783$		0			0
$784$	−612.277	+	364.272i	−0.780966	+	0.464632i
$785$		−	1097.35i		−	1.39789i
$786$		0			0
$787$	556.671			0.707333			0.353666	−	0.935372i	$-0.384935\pi$
$787$	556.671			0.707333			0.353666	+	0.935372i	$0.384935\pi$
$788$	−58.7973	−	213.824i	−0.0746158	−	0.271350i
$789$		0			0
$790$	−66.1263	−	489.880i	−0.0837042	−	0.620102i
$791$		−	1808.16i		−	2.28592i
$792$		0			0
$793$		−	1361.55i		−	1.71697i
$794$	936.819	−	126.456i	1.17987	−	0.159265i
$795$		0			0
$796$	231.447	+	841.689i	0.290763	+	1.05740i
$797$	68.7432			0.0862524			0.0431262	−	0.999070i	$-0.486268\pi$
$797$	68.7432			0.0862524			0.0431262	+	0.999070i	$0.486268\pi$
$798$		0			0
$799$		−	15.1858i		−	0.0190061i
$800$	−103.252	+	81.9477i	−0.129065	+	0.102435i
$801$		0			0
$802$	951.349	−	128.418i	1.18622	−	0.160122i
$803$	24.6244			0.0306655
$804$		0			0
$805$	1282.63			1.59333
$806$	−15.5382	−	115.111i	−0.0192782	−	0.142817i
$807$		0			0
$808$	−106.429	−	249.969i	−0.131719	−	0.309368i
$809$			1398.49i			1.72866i	0.502924	+	0.864331i	$0.332258\pi$
$809$			1398.49i			1.72866i	−0.502924	+	0.864331i	$0.667742\pi$
$810$		0			0
$811$	−650.999			−0.802712			−0.401356	−	0.915922i	$-0.631461\pi$
$811$	−650.999			−0.802712			−0.401356	+	0.915922i	$0.631461\pi$
$812$	−106.292	−	386.546i	−0.130902	−	0.476042i
$813$		0			0
$814$	−19.9477	−	147.778i	−0.0245058	−	0.181545i
$815$	343.181			0.421080
$816$		0			0
$817$	436.195	+	232.238i	0.533898	+	0.284257i
$818$	−96.8338	−	717.369i	−0.118379	−	0.876979i
$819$		0			0
$820$	−7.09154	−	25.7893i	−0.00864822	−	0.0314504i
$821$		−	682.984i		−	0.831893i	−0.909389	−	0.415947i	$-0.863450\pi$
$821$		−	682.984i		−	0.831893i	0.909389	−	0.415947i	$-0.136550\pi$
$822$		0			0
$823$			277.691i			0.337414i	0.985666	+	0.168707i	$0.0539591\pi$
$823$			277.691i			0.337414i	−0.985666	+	0.168707i	$0.946041\pi$
$824$	1068.73	−	455.030i	1.29700	−	0.552221i
$825$		0			0
$826$	−1098.51	+	148.282i	−1.32991	+	0.179518i
$827$		−	695.454i		−	0.840936i	−0.907307	−	0.420468i	$-0.861866\pi$
$827$		−	695.454i		−	0.840936i	0.907307	−	0.420468i	$-0.138134\pi$
$828$		0			0
$829$		−	1116.30i		−	1.34657i	−0.739385	−	0.673283i	$-0.764884\pi$
$829$		−	1116.30i		−	1.34657i	0.739385	−	0.673283i	$-0.235116\pi$
$830$	−83.7859	−	620.707i	−0.100947	−	0.747839i
$831$		0			0
$832$	−665.548	−	639.900i	−0.799937	−	0.769111i
$833$			110.051i			0.132114i
$834$		0			0
$835$	−1085.32			−1.29979
$836$	37.6195	−	167.524i	0.0449994	−	0.200387i
$837$		0			0
$838$	757.493	−	102.250i	0.903929	−	0.122017i
$839$			18.3244i			0.0218407i	0.999940	+	0.0109204i	$0.00347613\pi$
$839$			18.3244i			0.0218407i	−0.999940	+	0.0109204i	$0.996524\pi$
$840$		0			0
$841$	−733.601			−0.872296
$842$	−133.565	−	989.483i	−0.158628	−	1.17516i
$843$		0			0
$844$	640.865	−	176.225i	0.759319	−	0.208797i
$845$			178.723i			0.211507i
$846$		0			0
$847$			1120.83i			1.32329i
$848$	−225.582	+	134.209i	−0.266017	+	0.158265i
$849$		0			0
$850$	2.72387	+	20.1791i	0.00320456	+	0.0237401i
$851$		−	957.883i		−	1.12560i
$852$		0			0
$853$	131.970			0.154713			0.0773566	−	0.997003i	$-0.475352\pi$
$853$	131.970			0.154713			0.0773566	+	0.997003i	$0.475352\pi$
$854$	244.202	+	1809.11i	0.285951	+	2.11840i
$855$		0			0
$856$	67.0210	+	157.412i	0.0782955	+	0.183892i
$857$	−53.1058			−0.0619671			−0.0309836	−	0.999520i	$-0.509864\pi$
$857$	−53.1058			−0.0619671			−0.0309836	+	0.999520i	$0.509864\pi$
$858$		0			0
$859$		−	448.972i		−	0.522669i	−0.965248	−	0.261334i	$-0.915837\pi$
$859$		−	448.972i		−	0.522669i	0.965248	−	0.261334i	$-0.0841625\pi$
$860$	458.378	−	126.045i	0.532998	−	0.146564i
$861$		0			0
$862$	186.698	+	1383.10i	0.216587	+	1.60453i
$863$		−	1355.28i		−	1.57042i	−0.619228	−	0.785212i	$-0.712554\pi$
$863$		−	1355.28i		−	1.57042i	0.619228	−	0.785212i	$-0.287446\pi$
$864$		0			0
$865$			709.809i			0.820588i
$866$	130.313	+	965.387i	0.150476	+	1.11477i
$867$		0			0
$868$	41.2916	+	150.162i	0.0475709	+	0.172998i
$869$	−122.196			−0.140616
$870$		0			0
$871$			1734.98i			1.99194i
$872$	573.131	+	1346.11i	0.657260	+	1.54370i
$873$		0			0
$874$	383.436	−	1034.12i	0.438714	−	1.18320i
$875$	−1286.84			−1.47067
$876$		0			0
$877$			797.110i			0.908905i	0.890771	+	0.454453i	$0.150165\pi$
$877$			797.110i			0.908905i	−0.890771	+	0.454453i	$0.849835\pi$
$878$	−1408.38	+	190.109i	−1.60407	+	0.216525i
$879$		0			0
$880$	−84.4525	−	141.950i	−0.0959688	−	0.161307i
$881$		−	1459.02i		−	1.65609i	−0.560659	−	0.828047i	$-0.689452\pi$
$881$		−	1459.02i		−	1.65609i	0.560659	−	0.828047i	$-0.310548\pi$
$882$		0			0
$883$		−	643.055i		−	0.728262i	−0.931348	−	0.364131i	$-0.881366\pi$
$883$		−	643.055i		−	0.728262i	0.931348	−	0.364131i	$-0.118634\pi$
$884$	−137.513	+	37.8133i	−0.155558	+	0.0427752i
$885$		0			0
$886$	455.504	−	61.4861i	0.514113	−	0.0693974i
$887$			819.588i			0.924001i	0.886880	+	0.462000i	$0.152868\pi$
$887$			819.588i			0.924001i	−0.886880	+	0.462000i	$0.847132\pi$
$888$		0			0
$889$			1771.34i			1.99251i
$890$	8.56364	+	63.4416i	0.00962207	+	0.0712827i
$891$		0			0
$892$	250.924	−	68.9990i	0.281305	−	0.0773531i
$893$	54.8642	−	103.047i	0.0614381	−	0.115394i
$894$		0			0
$895$	−1573.00			−1.75754
$896$	999.091	+	730.873i	1.11506	+	0.815707i
$897$		0			0
$898$	−1023.37	+	138.140i	−1.13961	+	0.153830i
$899$	−41.7213			−0.0464086
$900$		0			0
$901$			40.5463i			0.0450015i
$902$	−6.55226	+	0.884455i	−0.00726415	+	0.000980549i
$903$		0			0
$904$	−1376.20	+	585.941i	−1.52234	+	0.648165i
$905$	1180.66			1.30459
$906$		0			0
$907$	362.829			0.400032			0.200016	−	0.979793i	$-0.435901\pi$
$907$	362.829			0.400032			0.200016	+	0.979793i	$0.435901\pi$
$908$	238.327	+	866.708i	0.262475	+	0.954524i
$909$		0			0
$910$	−170.563	−	1263.57i	−0.187432	−	1.38854i
$911$		−	1430.96i		−	1.57076i	−0.619016	−	0.785378i	$-0.712469\pi$
$911$		−	1430.96i		−	1.57076i	0.619016	−	0.785378i	$-0.287531\pi$
$912$		0			0
$913$	−154.829			−0.169583
$914$	−1039.39	+	140.302i	−1.13719	+	0.153503i
$915$		0			0
$916$	−210.607	+	57.9126i	−0.229920	+	0.0632234i
$917$			1138.80i			1.24187i
$918$		0			0
$919$			622.857i			0.677755i	0.940831	+	0.338877i	$0.110047\pi$
$919$			622.857i			0.677755i	−0.940831	+	0.338877i	$0.889953\pi$
$920$	−415.640	−	976.213i	−0.451783	−	1.06110i
$921$		0			0
$922$	98.3163	+	728.351i	0.106634	+	0.789969i
$923$	−1472.49			−1.59533
$924$		0			0
$925$			135.951i			0.146974i
$926$	56.1121	+	415.693i	0.0605963	+	0.448912i
$927$		0			0
$928$	−259.757	+	206.161i	−0.279911	+	0.222157i
$929$			1500.02i			1.61466i	0.590098	+	0.807331i	$0.299089\pi$
$929$			1500.02i			1.61466i	−0.590098	+	0.807331i	$0.700911\pi$
$930$		0			0
$931$	−397.599	+	746.778i	−0.427066	+	0.802125i
$932$	375.414	+	1365.24i	0.402805	+	1.46485i
$933$		0			0
$934$	1250.74	−	168.831i	1.33912	−	0.180761i
$935$	−25.5142			−0.0272879
$936$		0			0
$937$	609.134			0.650089			0.325045	−	0.945699i	$-0.394621\pi$
$937$	609.134			0.650089			0.325045	+	0.945699i	$0.394621\pi$
$938$	−311.179	−	2305.29i	−0.331747	−	2.45767i
$939$		0			0
$940$	−29.7769	−	108.288i	−0.0316775	−	0.115200i
$941$	−355.623			−0.377920			−0.188960	−	0.981985i	$-0.560512\pi$
$941$	−355.623			−0.377920			−0.188960	+	0.981985i	$0.560512\pi$
$942$		0			0
$943$	−42.4712			−0.0450384
$944$	468.833	+	788.026i	0.496645	+	0.834773i
$945$		0			0
$946$	−15.7203	−	116.460i	−0.0166176	−	0.123107i
$947$	−1324.04			−1.39814			−0.699070	−	0.715053i	$-0.746402\pi$
$947$	−1324.04			−1.39814			−0.699070	+	0.715053i	$0.746402\pi$
$948$		0			0
$949$		−	157.242i		−	0.165692i
$950$	−54.4207	+	146.771i	−0.0572850	+	0.154496i
$951$		0			0
$952$	175.933	−	74.9068i	0.184804	−	0.0786836i
$953$	−679.988			−0.713523			−0.356762	−	0.934195i	$-0.616119\pi$
$953$	−679.988			−0.713523			−0.356762	+	0.934195i	$0.616119\pi$
$954$		0			0
$955$		−	1541.58i		−	1.61422i
$956$	1357.63	−	373.322i	1.42012	−	0.390504i
$957$		0			0
$958$	−1735.40	+	234.252i	−1.81148	+	0.244522i
$959$	195.447			0.203803
$960$		0			0
$961$	−944.792			−0.983135
$962$	−943.651	+	127.378i	−0.980926	+	0.132410i
$963$		0			0
$964$	219.734	+	799.092i	0.227940	+	0.828934i
$965$	−7.57561			−0.00785037
$966$		0			0
$967$			107.327i			0.110989i	0.998459	+	0.0554946i	$0.0176736\pi$
$967$			107.327i			0.110989i	−0.998459	+	0.0554946i	$0.982326\pi$
$968$	853.067	−	363.209i	0.881267	−	0.375216i
$969$		0			0
$970$	−263.020	+	35.5036i	−0.271154	+	0.0366017i
$971$		−	1424.28i		−	1.46681i	−0.679790	−	0.733407i	$-0.737929\pi$
$971$		−	1424.28i		−	1.46681i	0.679790	−	0.733407i	$-0.262071\pi$
$972$		0			0
$973$	1170.34			1.20281
$974$	−1218.76	+	164.514i	−1.25129	+	0.168906i
$975$		0			0
$976$	1297.79	−	772.112i	1.32970	−	0.791099i
$977$	129.650			0.132702			0.0663508	−	0.997796i	$-0.478864\pi$
$977$	129.650			0.132702			0.0663508	+	0.997796i	$0.478864\pi$
$978$		0			0
$979$	15.8248			0.0161643
$980$	215.792	+	784.756i	0.220196	+	0.800772i
$981$		0			0
$982$	−381.796	+	51.5366i	−0.388794	+	0.0524813i
$983$			955.633i			0.972159i	0.873914	+	0.486080i	$0.161574\pi$
$983$			955.633i			0.972159i	−0.873914	+	0.486080i	$0.838426\pi$
$984$		0			0
$985$	−253.336			−0.257194
$986$	6.85262	+	50.7659i	0.00694992	+	0.0514868i
$987$		0			0
$988$	−1069.74	−	240.223i	−1.08273	−	0.243141i
$989$		−	754.881i		−	0.763277i
$990$		0			0
$991$	369.630			0.372987			0.186494	−	0.982456i	$-0.440288\pi$
$991$	369.630			0.372987			0.186494	+	0.982456i	$0.440288\pi$
$992$	100.908	−	80.0877i	0.101722	−	0.0807336i
$993$		0			0
$994$	1956.52	−	264.100i	1.96833	−	0.265694i
$995$	997.221			1.00223
$996$		0			0
$997$	−1430.83			−1.43513			−0.717567	−	0.696490i	$-0.754744\pi$
$997$	−1430.83			−1.43513			−0.717567	+	0.696490i	$0.754744\pi$
$998$	231.903	+	1718.00i	0.232368	+	1.72144i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.b.a.683.3	yes	80
3.2	odd	2	inner	684.3.b.a.683.77	yes	80
4.3	odd	2	inner	684.3.b.a.683.2	yes	80
12.11	even	2	inner	684.3.b.a.683.80	yes	80
19.18	odd	2	inner	684.3.b.a.683.78	yes	80
57.56	even	2	inner	684.3.b.a.683.4	yes	80
76.75	even	2	inner	684.3.b.a.683.79	yes	80
228.227	odd	2	inner	684.3.b.a.683.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.b.a.683.1	✓	80	228.227	odd	2	inner
684.3.b.a.683.2	yes	80	4.3	odd	2	inner
684.3.b.a.683.3	yes	80	1.1	even	1	trivial
684.3.b.a.683.4	yes	80	57.56	even	2	inner
684.3.b.a.683.77	yes	80	3.2	odd	2	inner
684.3.b.a.683.78	yes	80	19.18	odd	2	inner
684.3.b.a.683.79	yes	80	76.75	even	2	inner
684.3.b.a.683.80	yes	80	12.11	even	2	inner

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98202 + 0.267543i) q^{2} +(3.85684 - 1.06055i) q^{4} -4.56953i q^{5} -9.67098i q^{7} +(-7.36061 + 3.13391i) q^{8} +O(q^{10})\)	\(q+(-1.98202 + 0.267543i) q^{2} +(3.85684 - 1.06055i) q^{4} -4.56953i q^{5} -9.67098i q^{7} +(-7.36061 + 3.13391i) q^{8} +(1.22255 + 9.05693i) q^{10} +2.25916 q^{11} -14.4261i q^{13} +(2.58740 + 19.1681i) q^{14} +(13.7505 - 8.18077i) q^{16} -2.47152i q^{17} +(8.92923 - 16.7711i) q^{19} +(-4.84623 - 17.6240i) q^{20} +(-4.47770 + 0.604422i) q^{22} -29.0241 q^{23} +4.11936 q^{25} +(3.85960 + 28.5928i) q^{26} +(-10.2566 - 37.2994i) q^{28} +10.3633 q^{29} -4.02586 q^{31} +(-25.0650 + 19.8933i) q^{32} +(0.661237 + 4.89861i) q^{34} -44.1919 q^{35} +33.0030i q^{37} +(-13.2110 + 35.6296i) q^{38} +(14.3205 + 33.6346i) q^{40} +1.46331 q^{41} +26.0088i q^{43} +(8.71321 - 2.39596i) q^{44} +(57.5265 - 7.76519i) q^{46} +6.14434 q^{47} -44.5278 q^{49} +(-8.16467 + 1.10211i) q^{50} +(-15.2996 - 55.6391i) q^{52} -16.4054 q^{53} -10.3233i q^{55} +(30.3080 + 71.1843i) q^{56} +(-20.5404 + 2.77264i) q^{58} +57.3091i q^{59} +94.3814 q^{61} +(7.97935 - 1.07709i) q^{62} +(44.3572 - 46.1350i) q^{64} -65.9205 q^{65} -120.267 q^{67} +(-2.62118 - 9.53225i) q^{68} +(87.5893 - 11.8232i) q^{70} -102.072i q^{71} +10.8998 q^{73} +(-8.82973 - 65.4128i) q^{74} +(16.6520 - 74.1533i) q^{76} -21.8483i q^{77} -54.0890 q^{79} +(-37.3823 - 62.8332i) q^{80} +(-2.90031 + 0.391498i) q^{82} -68.5339 q^{83} -11.2937 q^{85} +(-6.95846 - 51.5500i) q^{86} +(-16.6288 + 7.08000i) q^{88} +7.00476 q^{89} -139.514 q^{91} +(-111.941 + 30.7816i) q^{92} +(-12.1782 + 1.64387i) q^{94} +(-76.6360 - 40.8024i) q^{95} +29.0407i q^{97} +(88.2551 - 11.9131i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{4}+O(q^{10}) \) 80 * q - 8 * q^4	\( 80 q - 8 q^{4} - 56 q^{16} - 400 q^{25} - 464 q^{49} - 272 q^{58} - 352 q^{61} - 200 q^{64} + 480 q^{73} + 152 q^{76} + 32 q^{82} + 704 q^{85}+O(q^{100}) \) 80 * q - 8 * q^4 - 56 * q^16 - 400 * q^25 - 464 * q^49 - 272 * q^58 - 352 * q^61 - 200 * q^64 + 480 * q^73 + 152 * q^76 + 32 * q^82 + 704 * q^85

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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