LMFDB - Embedded newform 684.3.bl.a.373.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(373,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("684.373");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.bl (of order $6$, degree $2$, 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:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.9
Character	$\chi$	$=$	684.373
Dual form			684.3.bl.a.673.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.51806 + 1.63076i) q^{3} -7.88879 q^{5} +(6.38121 + 11.0526i) q^{7} +(3.68127 - 8.21269i) q^{9} +O(q^{10})$	\(q+(-2.51806 + 1.63076i) q^{3} -7.88879 q^{5} +(6.38121 + 11.0526i) q^{7} +(3.68127 - 8.21269i) q^{9} +(6.96387 + 12.0618i) q^{11} +(-12.8183 + 7.40066i) q^{13} +(19.8645 - 12.8647i) q^{15} +(0.670914 + 1.16206i) q^{17} +(-2.88756 + 18.7793i) q^{19} +(-34.0923 - 17.4249i) q^{21} +(12.6296 + 21.8751i) q^{23} +37.2330 q^{25} +(4.12322 + 26.6833i) q^{27} -12.5804i q^{29} +(28.7857 + 16.6194i) q^{31} +(-37.2052 - 19.0159i) q^{33} +(-50.3400 - 87.1915i) q^{35} -19.5864i q^{37} +(20.2086 - 39.5389i) q^{39} -69.5993i q^{41} +(-27.6486 + 47.8889i) q^{43} +(-29.0408 + 64.7882i) q^{45} -71.1152 q^{47} +(-56.9397 + 98.6224i) q^{49} +(-3.58443 - 1.83203i) q^{51} +(-48.4471 - 27.9709i) q^{53} +(-54.9365 - 95.1528i) q^{55} +(-23.3534 - 51.9963i) q^{57} -69.3051i q^{59} -79.6978 q^{61} +(114.262 - 11.7194i) q^{63} +(101.121 - 58.3822i) q^{65} +(43.2999 - 24.9992i) q^{67} +(-67.4749 - 34.4870i) q^{69} +(-14.7531 + 8.51773i) q^{71} +(-5.02237 - 8.69900i) q^{73} +(-93.7550 + 60.7179i) q^{75} +(-88.8758 + 153.937i) q^{77} +(43.7062 + 25.2338i) q^{79} +(-53.8965 - 60.4663i) q^{81} +(-35.6125 - 61.6827i) q^{83} +(-5.29270 - 9.16722i) q^{85} +(20.5156 + 31.6783i) q^{87} +(39.8612 + 23.0138i) q^{89} +(-163.593 - 94.4503i) q^{91} +(-99.5865 + 5.09370i) q^{93} +(22.7793 - 148.146i) q^{95} +(118.975 + 68.6905i) q^{97} +(124.695 - 12.7894i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−2.51806	+	1.63076i	−0.839354	+	0.543585i
$3$	−2.51806	+	1.63076i	−0.839354	+	0.543585i
$4$		0			0
$5$	−7.88879			−1.57776			−0.788879	−	0.614549i	$-0.789338\pi$
$5$	−7.88879			−1.57776			−0.788879	+	0.614549i	$0.789338\pi$
$6$		0			0
$7$	6.38121	+	11.0526i	0.911601	+	1.57894i	0.811803	+	0.583932i	$0.198487\pi$
$7$	6.38121	+	11.0526i	0.911601	+	1.57894i	0.0997987	+	0.995008i	$0.468180\pi$
$8$		0			0
$9$	3.68127	−	8.21269i	0.409030	−	0.912521i
$10$		0			0
$11$	6.96387	+	12.0618i	0.633079	+	1.09652i	0.986919	+	0.161219i	$0.0515424\pi$
$11$	6.96387	+	12.0618i	0.633079	+	1.09652i	−0.353840	+	0.935306i	$0.615124\pi$
$12$		0			0
$13$	−12.8183	+	7.40066i	−0.986024	+	0.569281i	−0.904084	−	0.427356i	$-0.859445\pi$
$13$	−12.8183	+	7.40066i	−0.986024	+	0.569281i	−0.0819408	+	0.996637i	$0.526112\pi$
$14$		0			0
$15$	19.8645	−	12.8647i	1.32430	−	0.857646i
$16$		0			0
$17$	0.670914	+	1.16206i	0.0394655	+	0.0683563i	0.885083	−	0.465432i	$-0.154101\pi$
$17$	0.670914	+	1.16206i	0.0394655	+	0.0683563i	−0.845618	+	0.533789i	$0.820768\pi$
$18$		0			0
$19$	−2.88756	+	18.7793i	−0.151977	+	0.988384i
$19$	−2.88756	+	18.7793i	−0.151977	+	0.988384i
$20$		0			0
$21$	−34.0923	−	17.4249i	−1.62344	−	0.829756i
$22$		0			0
$23$	12.6296	+	21.8751i	0.549112	+	0.951090i	0.998336	+	0.0576704i	$0.0183673\pi$
$23$	12.6296	+	21.8751i	0.549112	+	0.951090i	−0.449224	+	0.893419i	$0.648299\pi$
$24$		0			0
$25$	37.2330			1.48932
$26$		0			0
$27$	4.12322	+	26.6833i	0.152712	+	0.988271i
$28$		0			0
$29$		−	12.5804i		−	0.433808i	−0.976193	−	0.216904i	$-0.930404\pi$
$29$		−	12.5804i		−	0.433808i	0.976193	−	0.216904i	$-0.0695959\pi$
$30$		0			0
$31$	28.7857	+	16.6194i	0.928572	+	0.536111i	0.886360	−	0.462998i	$-0.153226\pi$
$31$	28.7857	+	16.6194i	0.928572	+	0.536111i	0.0422122	+	0.999109i	$0.486559\pi$
$32$		0			0
$33$	−37.2052	−	19.0159i	−1.12743	−	0.576240i
$34$		0			0
$35$	−50.3400	−	87.1915i	−1.43829	−	2.49118i
$36$		0			0
$37$		−	19.5864i		−	0.529361i	−0.964336	−	0.264681i	$-0.914733\pi$
$37$		−	19.5864i		−	0.529361i	0.964336	−	0.264681i	$-0.0852666\pi$
$38$		0			0
$39$	20.2086	−	39.5389i	0.518170	−	1.01382i
$40$		0			0
$41$		−	69.5993i		−	1.69754i	−0.528759	−	0.848772i	$-0.677342\pi$
$41$		−	69.5993i		−	1.69754i	0.528759	−	0.848772i	$-0.322658\pi$
$42$		0			0
$43$	−27.6486	+	47.8889i	−0.642992	+	1.11369i	0.341770	+	0.939784i	$0.388974\pi$
$43$	−27.6486	+	47.8889i	−0.642992	+	1.11369i	−0.984761	+	0.173911i	$0.944360\pi$
$44$		0			0
$45$	−29.0408	+	64.7882i	−0.645350	+	1.43974i
$46$		0			0
$47$	−71.1152			−1.51309			−0.756544	−	0.653942i	$-0.773114\pi$
$47$	−71.1152			−1.51309			−0.756544	+	0.653942i	$0.773114\pi$
$48$		0			0
$49$	−56.9397	+	98.6224i	−1.16203	+	2.01270i
$50$		0			0
$51$	−3.58443	−	1.83203i	−0.0702830	−	0.0359222i
$52$		0			0
$53$	−48.4471	−	27.9709i	−0.914096	−	0.527753i	−0.0323489	−	0.999477i	$-0.510299\pi$
$53$	−48.4471	−	27.9709i	−0.914096	−	0.527753i	−0.881747	+	0.471723i	$0.843632\pi$
$54$		0			0
$55$	−54.9365	−	95.1528i	−0.998845	−	1.73005i
$56$		0			0
$57$	−23.3534	−	51.9963i	−0.409709	−	0.912216i
$58$		0			0
$59$		−	69.3051i		−	1.17466i	−0.809346	−	0.587332i	$-0.800178\pi$
$59$		−	69.3051i		−	1.17466i	0.809346	−	0.587332i	$-0.199822\pi$
$60$		0			0
$61$	−79.6978			−1.30652			−0.653261	−	0.757133i	$-0.726600\pi$
$61$	−79.6978			−1.30652			−0.653261	+	0.757133i	$0.726600\pi$
$62$		0			0
$63$	114.262	−	11.7194i	1.81369	−	0.186021i
$64$		0			0
$65$	101.121	−	58.3822i	1.55571	−	0.898188i
$66$		0			0
$67$	43.2999	−	24.9992i	0.646266	−	0.373122i	−0.140758	−	0.990044i	$-0.544954\pi$
$67$	43.2999	−	24.9992i	0.646266	−	0.373122i	0.787024	+	0.616922i	$0.211621\pi$
$68$		0			0
$69$	−67.4749	−	34.4870i	−0.977898	−	0.499812i
$70$		0			0
$71$	−14.7531	+	8.51773i	−0.207791	+	0.119968i	−0.600284	−	0.799787i	$-0.704946\pi$
$71$	−14.7531	+	8.51773i	−0.207791	+	0.119968i	0.392494	+	0.919755i	$0.371613\pi$
$72$		0			0
$73$	−5.02237	−	8.69900i	−0.0687996	−	0.119164i	0.829574	−	0.558397i	$-0.188584\pi$
$73$	−5.02237	−	8.69900i	−0.0687996	−	0.119164i	−0.898373	+	0.439233i	$0.855250\pi$
$74$		0			0
$75$	−93.7550	+	60.7179i	−1.25007	+	0.809572i
$76$		0			0
$77$	−88.8758	+	153.937i	−1.15423	+	1.99919i
$78$		0			0
$79$	43.7062	+	25.2338i	0.553243	+	0.319415i	0.750429	−	0.660951i	$-0.229847\pi$
$79$	43.7062	+	25.2338i	0.553243	+	0.319415i	−0.197186	+	0.980366i	$0.563180\pi$
$80$		0			0
$81$	−53.8965	−	60.4663i	−0.665389	−	0.746497i
$82$		0			0
$83$	−35.6125	−	61.6827i	−0.429067	−	0.743165i	0.567724	−	0.823219i	$-0.307824\pi$
$83$	−35.6125	−	61.6827i	−0.429067	−	0.743165i	−0.996791	+	0.0800539i	$0.974491\pi$
$84$		0			0
$85$	−5.29270	−	9.16722i	−0.0622670	−	0.107850i
$86$		0			0
$87$	20.5156	+	31.6783i	0.235812	+	0.364119i
$88$		0			0
$89$	39.8612	+	23.0138i	0.447878	+	0.258583i	0.706934	−	0.707280i	$-0.250078\pi$
$89$	39.8612	+	23.0138i	0.447878	+	0.258583i	−0.259056	+	0.965862i	$0.583411\pi$
$90$		0			0
$91$	−163.593	−	94.4503i	−1.79772	−	1.03792i
$92$		0			0
$93$	−99.5865	+	5.09370i	−1.07082	+	0.0547710i
$94$		0			0
$95$	22.7793	−	148.146i	0.239782	−	1.55943i
$96$		0			0
$97$	118.975	+	68.6905i	1.22655	+	0.708149i	0.966307	−	0.257394i	$-0.0828638\pi$
$97$	118.975	+	68.6905i	1.22655	+	0.708149i	0.260243	+	0.965543i	$0.416197\pi$
$98$		0			0
$99$	124.695	−	12.7894i	1.25955	−	0.129186i
$100$		0			0
$101$	65.6530			0.650030			0.325015	−	0.945709i	$-0.394631\pi$
$101$	65.6530			0.650030			0.325015	+	0.945709i	$0.394631\pi$
$102$		0			0
$103$	−44.7353	−	25.8280i	−0.434324	−	0.250757i	0.266863	−	0.963734i	$-0.414013\pi$
$103$	−44.7353	−	25.8280i	−0.434324	−	0.250757i	−0.701187	+	0.712978i	$0.747346\pi$
$104$		0			0
$105$	268.947	+	137.461i	2.56140	+	1.30915i
$106$		0			0
$107$			139.691i			1.30553i	0.757562	+	0.652763i	$0.226390\pi$
$107$			139.691i			1.30553i	−0.757562	+	0.652763i	$0.773610\pi$
$108$		0			0
$109$	114.708	−	66.2264i	1.05236	−	0.607582i	0.129053	−	0.991638i	$-0.458806\pi$
$109$	114.708	−	66.2264i	1.05236	−	0.607582i	0.923310	+	0.384056i	$0.125473\pi$
$110$		0			0
$111$	31.9406	+	49.3197i	0.287753	+	0.444322i
$112$		0			0
$113$	30.0856	+	17.3699i	0.266245	+	0.153716i	0.627180	−	0.778875i	$-0.284209\pi$
$113$	30.0856	+	17.3699i	0.266245	+	0.153716i	−0.360935	+	0.932591i	$0.617542\pi$
$114$		0			0
$115$	−99.6320	−	172.568i	−0.866366	−	1.50059i
$116$		0			0
$117$	13.5916	+	132.517i	0.116168	+	1.13262i
$118$		0			0
$119$	−8.56248	+	14.8307i	−0.0719536	+	0.124627i
$120$		0			0
$121$	−36.4909	+	63.2040i	−0.301577	+	0.522347i
$122$		0			0
$123$	113.499	+	175.255i	0.922760	+	1.42484i
$124$		0			0
$125$	−96.5035			−0.772028
$126$		0			0
$127$	−6.36484	−	3.67474i	−0.0501168	−	0.0289350i	0.474732	−	0.880130i	$-0.342545\pi$
$127$	−6.36484	−	3.67474i	−0.0501168	−	0.0289350i	−0.524849	+	0.851195i	$0.675878\pi$
$128$		0			0
$129$	−8.47404	−	165.675i	−0.0656902	−	1.28430i
$130$		0			0
$131$	17.8077			0.135937			0.0679683	−	0.997687i	$-0.478348\pi$
$131$	17.8077			0.135937			0.0679683	+	0.997687i	$0.478348\pi$
$132$		0			0
$133$	−225.986	+	87.9197i	−1.69914	+	0.661050i
$134$		0			0
$135$	−32.5272	−	210.499i	−0.240942	−	1.55925i
$136$		0			0
$137$	165.531			1.20825			0.604127	−	0.796888i	$-0.293522\pi$
$137$	165.531			1.20825			0.604127	+	0.796888i	$0.293522\pi$
$138$		0			0
$139$	4.09692	+	7.09607i	0.0294743	+	0.0510509i	0.880386	−	0.474257i	$-0.157283\pi$
$139$	4.09692	+	7.09607i	0.0294743	+	0.0510509i	−0.850912	+	0.525308i	$0.823950\pi$
$140$		0			0
$141$	179.072	−	115.971i	1.27002	−	0.822493i
$142$		0			0
$143$	−178.530	−	103.074i	−1.24846	−	0.720800i
$144$		0			0
$145$			99.2444i			0.684444i
$146$		0			0
$147$	−17.4514	−	341.192i	−0.118717	−	2.32103i
$148$		0			0
$149$	223.858			1.50240			0.751201	−	0.660073i	$-0.229475\pi$
$149$	223.858			1.50240			0.751201	+	0.660073i	$0.229475\pi$
$150$		0			0
$151$	−203.065	+	117.240i	−1.34480	+	0.776421i	−0.987508	−	0.157571i	$-0.949634\pi$
$151$	−203.065	+	117.240i	−1.34480	+	0.776421i	−0.357293	+	0.933992i	$0.616300\pi$
$152$		0			0
$153$	12.0134	−	1.23216i	0.0785191	−	0.00805334i
$154$		0			0
$155$	−227.085	−	131.107i	−1.46506	−	0.845854i
$156$		0			0
$157$	−283.638			−1.80661			−0.903305	−	0.428999i	$-0.858866\pi$
$157$	−283.638			−1.80661			−0.903305	+	0.428999i	$0.858866\pi$
$158$		0			0
$159$	167.606	−	8.57282i	1.05413	−	0.0539171i
$160$		0			0
$161$	−161.184	+	279.179i	−1.00114	+	1.73403i
$162$		0			0
$163$	147.433			0.904494			0.452247	−	0.891893i	$-0.350623\pi$
$163$	147.433			0.904494			0.452247	+	0.891893i	$0.350623\pi$
$164$		0			0
$165$	293.504	+	150.013i	1.77881	+	0.909167i
$166$		0			0
$167$	−145.747	+	84.1470i	−0.872736	+	0.503874i	−0.868257	−	0.496116i	$-0.834759\pi$
$167$	−145.747	+	84.1470i	−0.872736	+	0.503874i	−0.00447964	+	0.999990i	$0.501426\pi$
$168$		0			0
$169$	25.0395	−	43.3697i	0.148163	−	0.256625i
$170$		0			0
$171$	143.599	+	92.8463i	0.839758	+	0.542961i
$172$		0			0
$173$	−96.2318	−	55.5594i	−0.556253	−	0.321153i	0.195387	−	0.980726i	$-0.437404\pi$
$173$	−96.2318	−	55.5594i	−0.556253	−	0.321153i	−0.751640	+	0.659573i	$0.770737\pi$
$174$		0			0
$175$	237.591	+	411.521i	1.35767	+	2.35155i
$176$		0			0
$177$	113.020	+	174.515i	0.638530	+	0.985958i
$178$		0			0
$179$			26.2293i			0.146533i	0.997312	+	0.0732663i	$0.0233423\pi$
$179$			26.2293i			0.146533i	−0.997312	+	0.0732663i	$0.976658\pi$
$180$		0			0
$181$	10.5439	+	6.08750i	0.0582534	+	0.0336326i	0.528844	−	0.848719i	$-0.322626\pi$
$181$	10.5439	+	6.08750i	0.0582534	+	0.0336326i	−0.470590	+	0.882352i	$0.655959\pi$
$182$		0			0
$183$	200.684	−	129.968i	1.09663	−	0.710206i
$184$		0			0
$185$			154.513i			0.835204i
$186$		0			0
$187$	−9.34431	+	16.1848i	−0.0499696	+	0.0865498i
$188$		0			0
$189$	−268.608	+	215.844i	−1.42121	+	1.14203i
$190$		0			0
$191$	−182.299	−	315.750i	−0.954443	−	1.65314i	−0.735638	−	0.677375i	$-0.763117\pi$
$191$	−182.299	−	315.750i	−0.954443	−	1.65314i	−0.218805	−	0.975769i	$-0.570216\pi$
$192$		0			0
$193$		−	56.9406i		−	0.295029i	−0.989060	−	0.147515i	$-0.952873\pi$
$193$		−	56.9406i		−	0.295029i	0.989060	−	0.147515i	$-0.0471273\pi$
$194$		0			0
$195$	−159.422	+	311.914i	−0.817547	+	1.59956i
$196$		0			0
$197$	34.5922			0.175595			0.0877975	−	0.996138i	$-0.472017\pi$
$197$	34.5922			0.175595			0.0877975	+	0.996138i	$0.472017\pi$
$198$		0			0
$199$	157.262	−	272.386i	0.790262	−	1.36877i	−0.135543	−	0.990772i	$-0.543278\pi$
$199$	157.262	−	272.386i	0.790262	−	1.36877i	0.925805	−	0.378002i	$-0.123389\pi$
$200$		0			0
$201$	−68.2641	+	133.561i	−0.339623	+	0.664482i
$202$		0			0
$203$	139.046	−	80.2784i	0.684957	−	0.395460i
$204$		0			0
$205$			549.054i			2.67831i
$206$		0			0
$207$	226.146	−	23.1947i	1.09249	−	0.112052i
$208$		0			0
$209$	−246.620	+	95.9475i	−1.18000	+	0.459079i
$210$		0			0
$211$			244.293i			1.15779i	0.815403	+	0.578894i	$0.196515\pi$
$211$			244.293i			1.15779i	−0.815403	+	0.578894i	$0.803485\pi$
$212$		0			0
$213$	23.2590	−	45.5069i	0.109197	−	0.213648i
$214$		0			0
$215$	218.114	−	377.785i	1.01449	−	1.75714i
$216$		0			0
$217$			424.209i			1.95488i
$218$		0			0
$219$	26.8326	+	13.7144i	0.122523	+	0.0626226i
$220$		0			0
$221$	−17.2000	−	9.93041i	−0.0778279	−	0.0449340i
$222$		0			0
$223$	340.289	+	196.466i	1.52596	+	0.881014i	0.999526	+	0.0307992i	$0.00980524\pi$
$223$	340.289	+	196.466i	1.52596	+	0.881014i	0.526436	+	0.850215i	$0.323528\pi$
$224$		0			0
$225$	137.065	−	305.783i	0.609176	−	1.35904i
$226$		0			0
$227$	−176.235	+	101.749i	−0.776364	+	0.448234i	−0.835140	−	0.550037i	$-0.814614\pi$
$227$	−176.235	+	101.749i	−0.776364	+	0.448234i	0.0587761	+	0.998271i	$0.481280\pi$
$228$		0			0
$229$	−55.3045	+	95.7901i	−0.241504	+	0.418297i	−0.961143	−	0.276051i	$-0.910974\pi$
$229$	−55.3045	+	95.7901i	−0.241504	+	0.418297i	0.719639	+	0.694349i	$0.244307\pi$
$230$		0			0
$231$	−27.2396	−	532.558i	−0.117920	−	2.30545i
$232$		0			0
$233$	−97.6118	−	169.069i	−0.418935	−	0.725616i	0.576898	−	0.816816i	$-0.304263\pi$
$233$	−97.6118	−	169.069i	−0.418935	−	0.725616i	−0.995833	+	0.0912002i	$0.970930\pi$
$234$		0			0
$235$	561.013			2.38729
$236$		0			0
$237$	−151.205	+	7.73390i	−0.637995	+	0.0326325i
$238$		0			0
$239$	−64.7106	+	112.082i	−0.270756	+	0.468962i	−0.969056	−	0.246843i	$-0.920607\pi$
$239$	−64.7106	+	112.082i	−0.270756	+	0.468962i	0.698300	+	0.715805i	$0.253940\pi$
$240$		0			0
$241$		−	401.949i		−	1.66784i	−0.551888	−	0.833919i	$-0.686092\pi$
$241$		−	401.949i		−	1.66784i	0.551888	−	0.833919i	$-0.313908\pi$
$242$		0			0
$243$	234.320	+	64.3657i	0.964282	+	0.264880i
$244$		0			0
$245$	449.185	−	778.011i	1.83341	−	3.17556i
$246$		0			0
$247$	−101.966	−	262.089i	−0.412816	−	1.06109i
$248$		0			0
$249$	190.264	+	97.2455i	0.764112	+	0.390544i
$250$		0			0
$251$	−34.7880	+	60.2547i	−0.138598	+	0.240058i	−0.926966	−	0.375145i	$-0.877593\pi$
$251$	−34.7880	+	60.2547i	−0.138598	+	0.240058i	0.788368	+	0.615204i	$0.210926\pi$
$252$		0			0
$253$	−175.901	+	304.670i	−0.695262	+	1.20423i
$254$		0			0
$255$	28.2768	+	14.4525i	0.110890	+	0.0566766i
$256$		0			0
$257$	−76.4556	+	44.1417i	−0.297493	+	0.171757i	−0.641316	−	0.767277i	$-0.721611\pi$
$257$	−76.4556	+	44.1417i	−0.297493	+	0.171757i	0.343823	+	0.939034i	$0.388278\pi$
$258$		0			0
$259$	216.480	−	124.985i	0.835830	−	0.482567i
$260$		0			0
$261$	−103.319	−	46.3120i	−0.395859	−	0.177441i
$262$		0			0
$263$	−112.613	+	195.051i	−0.428186	+	0.741640i	−0.996712	−	0.0810252i	$-0.974181\pi$
$263$	−112.613	+	195.051i	−0.428186	+	0.741640i	0.568526	+	0.822665i	$0.307514\pi$
$264$		0			0
$265$	382.189	+	220.657i	1.44222	+	0.832667i
$266$		0			0
$267$	−137.903	+	7.05352i	−0.516490	+	0.0264177i
$268$		0			0
$269$	217.376	−	125.502i	0.808090	−	0.466551i	−0.0382019	−	0.999270i	$-0.512163\pi$
$269$	217.376	−	125.502i	0.808090	−	0.466551i	0.846292	+	0.532719i	$0.178830\pi$
$270$		0			0
$271$	−166.275	−	287.996i	−0.613559	−	1.06272i	−0.990635	−	0.136534i	$-0.956404\pi$
$271$	−166.275	−	287.996i	−0.613559	−	1.06272i	0.377076	−	0.926182i	$-0.376930\pi$
$272$		0			0
$273$	565.962	−	28.9481i	2.07312	−	0.106037i
$274$		0			0
$275$	259.286	+	449.096i	0.942857	+	1.63308i
$276$		0			0
$277$	56.4817	+	97.8292i	0.203905	+	0.353174i	0.949783	−	0.312908i	$-0.101303\pi$
$277$	56.4817	+	97.8292i	0.203905	+	0.353174i	−0.745878	+	0.666082i	$0.767970\pi$
$278$		0			0
$279$	242.458	−	175.228i	0.869026	−	0.628056i
$280$		0			0
$281$		−	239.488i		−	0.852271i	−0.904659	−	0.426136i	$-0.859875\pi$
$281$		−	239.488i		−	0.852271i	0.904659	−	0.426136i	$-0.140125\pi$
$282$		0			0
$283$	−153.544			−0.542560			−0.271280	−	0.962500i	$-0.587447\pi$
$283$	−153.544			−0.542560			−0.271280	+	0.962500i	$0.587447\pi$
$284$		0			0
$285$	184.230	+	410.188i	0.646421	+	1.43926i
$286$		0			0
$287$	769.252	−	444.128i	2.68032	−	1.54748i
$288$		0			0
$289$	143.600	−	248.722i	0.496885	−	0.860630i
$290$		0			0
$291$	−411.605	+	21.0530i	−1.41445	+	0.0723469i
$292$		0			0
$293$	−98.9313	−	57.1180i	−0.337649	−	0.194942i	0.321583	−	0.946881i	$-0.395785\pi$
$293$	−98.9313	−	57.1180i	−0.337649	−	0.194942i	−0.659232	+	0.751940i	$0.729119\pi$
$294$		0			0
$295$			546.734i			1.85333i
$296$		0			0
$297$	−293.134	+	235.552i	−0.986984	+	0.793106i
$298$		0			0
$299$	−323.780	−	186.934i	−1.08288	−	0.625198i
$300$		0			0
$301$	−705.727			−2.34461
$302$		0			0
$303$	−165.318	+	107.064i	−0.545605	+	0.353347i
$304$		0			0
$305$	628.719			2.06138
$306$		0			0
$307$	−265.835	+	153.480i	−0.865911	+	0.499934i	−0.865987	−	0.500066i	$-0.833309\pi$
$307$	−265.835	+	153.480i	−0.865911	+	0.499934i	7.61808e−5		1.00000i	$0.499976\pi$
$308$		0			0
$309$	154.765	−	7.91602i	0.500859	−	0.0256182i
$310$		0			0
$311$	−292.504	+	506.631i	−0.940526	+	1.62904i	−0.176055	+	0.984380i	$0.556334\pi$
$311$	−292.504	+	506.631i	−0.940526	+	1.62904i	−0.764471	+	0.644658i	$0.777000\pi$
$312$		0			0
$313$	−55.0069			−0.175741			−0.0878704	−	0.996132i	$-0.528006\pi$
$313$	−55.0069			−0.175741			−0.0878704	+	0.996132i	$0.528006\pi$
$314$		0			0
$315$	−901.391	+	92.4515i	−2.86156	+	0.293497i
$316$		0			0
$317$			168.328i			0.531004i	0.964110	+	0.265502i	$0.0855377\pi$
$317$			168.328i			0.531004i	−0.964110	+	0.265502i	$0.914462\pi$
$318$		0			0
$319$	151.742	−	87.6085i	0.475681	−	0.274635i
$320$		0			0
$321$	−227.802	−	351.751i	−0.709664	−	1.09580i
$322$		0			0
$323$	−23.7599	+	9.24379i	−0.0735601	+	0.0286185i
$324$		0			0
$325$	−477.264	+	275.549i	−1.46851	+	0.847842i
$326$		0			0
$327$	−180.842	+	353.822i	−0.553032	+	1.08203i
$328$		0			0
$329$	−453.801	−	786.006i	−1.37933	−	2.38908i
$330$		0			0
$331$	484.892	−	279.952i	1.46493	−	0.845778i	0.465697	−	0.884944i	$-0.345804\pi$
$331$	484.892	−	279.952i	1.46493	−	0.845778i	0.999233	+	0.0391662i	$0.0124702\pi$
$332$		0			0
$333$	−160.857	−	72.1027i	−0.483053	−	0.216525i
$334$		0			0
$335$	−341.583	+	197.213i	−1.01965	+	0.588696i
$336$		0			0
$337$		−	366.696i		−	1.08812i	−0.839046	−	0.544060i	$-0.816886\pi$
$337$		−	366.696i		−	1.08812i	0.839046	−	0.544060i	$-0.183114\pi$
$338$		0			0
$339$	−104.084	+	5.32372i	−0.307031	+	0.0157042i
$340$		0			0
$341$			462.942i			1.35760i
$342$		0			0
$343$	−828.017			−2.41404
$344$		0			0
$345$	532.295	+	272.061i	1.54289	+	0.788582i
$346$		0			0
$347$	308.988			0.890454			0.445227	−	0.895418i	$-0.353123\pi$
$347$	308.988			0.890454			0.445227	+	0.895418i	$0.353123\pi$
$348$		0			0
$349$	110.184	+	190.844i	0.315714	+	0.546832i	0.979589	−	0.201011i	$-0.0644227\pi$
$349$	110.184	+	190.844i	0.315714	+	0.546832i	−0.663875	+	0.747843i	$0.731089\pi$
$350$		0			0
$351$	−250.327	−	311.521i	−0.713182	−	0.887523i
$352$		0			0
$353$	−35.8793	−	62.1448i	−0.101641	−	0.176048i	0.810720	−	0.585434i	$-0.199076\pi$
$353$	−35.8793	−	62.1448i	−0.101641	−	0.176048i	−0.912361	+	0.409387i	$0.865743\pi$
$354$		0			0
$355$	116.384	−	67.1945i	0.327843	−	0.189280i
$356$		0			0
$357$	−2.62432	−	51.3078i	−0.00735103	−	0.143719i
$358$		0			0
$359$	181.655	+	314.635i	0.506002	+	0.876422i	0.999976	+	0.00694495i	$0.00221067\pi$
$359$	181.655	+	314.635i	0.506002	+	0.876422i	−0.493973	+	0.869477i	$0.664456\pi$
$360$		0			0
$361$	−344.324	−	108.453i	−0.953806	−	0.300423i
$362$		0			0
$363$	−11.1841	−	218.659i	−0.0308102	−	0.602367i
$364$		0			0
$365$	39.6204	+	68.6245i	0.108549	+	0.188012i
$366$		0			0
$367$	−198.432			−0.540686			−0.270343	−	0.962764i	$-0.587137\pi$
$367$	−198.432			−0.540686			−0.270343	+	0.962764i	$0.587137\pi$
$368$		0			0
$369$	−571.597	−	256.214i	−1.54904	−	0.694346i
$370$		0			0
$371$		−	713.953i		−	1.92440i
$372$		0			0
$373$	382.831	+	221.027i	1.02636	+	0.592567i	0.915939	−	0.401319i	$-0.131448\pi$
$373$	382.831	+	221.027i	1.02636	+	0.592567i	0.110417	+	0.993885i	$0.464781\pi$
$374$		0			0
$375$	243.002	−	157.374i	0.648005	−	0.419663i
$376$		0			0
$377$	93.1035	+	161.260i	0.246959	+	0.427745i
$378$		0			0
$379$			362.393i			0.956183i	0.878310	+	0.478092i	$0.158671\pi$
$379$			362.393i			0.956183i	−0.878310	+	0.478092i	$0.841329\pi$
$380$		0			0
$381$	22.0197	−	1.12627i	0.0577944	−	0.00295609i
$382$		0			0
$383$			656.847i			1.71501i	0.514479	+	0.857503i	$0.327985\pi$
$383$			656.847i			1.71501i	−0.514479	+	0.857503i	$0.672015\pi$
$384$		0			0
$385$	701.122	−	1214.38i	1.82110	−	3.15423i
$386$		0			0
$387$	291.514	+	403.362i	0.753266	+	1.04228i
$388$		0			0
$389$	−444.122			−1.14170			−0.570851	−	0.821053i	$-0.693387\pi$
$389$	−444.122			−1.14170			−0.570851	+	0.821053i	$0.693387\pi$
$390$		0			0
$391$	−16.9467	+	29.3526i	−0.0433420	+	0.0750705i
$392$		0			0
$393$	−44.8409	+	29.0400i	−0.114099	+	0.0738932i
$394$		0			0
$395$	−344.789	−	199.064i	−0.872883	−	0.503959i
$396$		0			0
$397$	−41.6668	−	72.1690i	−0.104954	−	0.181786i	0.808765	−	0.588131i	$-0.200136\pi$
$397$	−41.6668	−	72.1690i	−0.104954	−	0.181786i	−0.913719	+	0.406346i	$0.866803\pi$
$398$		0			0
$399$	425.671	−	589.915i	1.06684	−	1.47848i
$400$		0			0
$401$			103.439i			0.257952i	0.991648	+	0.128976i	$0.0411690\pi$
$401$			103.439i			0.257952i	−0.991648	+	0.128976i	$0.958831\pi$
$402$		0			0
$403$	−491.979			−1.22079
$404$		0			0
$405$	425.178	+	477.006i	1.04982	+	1.17779i
$406$		0			0
$407$	236.246	−	136.397i	0.580458	−	0.335127i
$408$		0			0
$409$	−179.646	+	103.718i	−0.439232	+	0.253590i	−0.703272	−	0.710921i	$-0.748278\pi$
$409$	−179.646	+	103.718i	−0.439232	+	0.253590i	0.264040	+	0.964512i	$0.414945\pi$
$410$		0			0
$411$	−416.817	+	269.940i	−1.01415	+	0.656789i
$412$		0			0
$413$	766.001	−	442.251i	1.85472	−	1.07082i
$414$		0			0
$415$	280.940	+	486.602i	0.676963	+	1.17253i
$416$		0			0
$417$	−21.8883	−	11.1873i	−0.0524898	−	0.0268280i
$418$		0			0
$419$	42.1930	−	73.0805i	0.100699	−	0.174416i	−0.811274	−	0.584667i	$-0.801225\pi$
$419$	42.1930	−	73.0805i	0.100699	−	0.174416i	0.911973	+	0.410250i	$0.134559\pi$
$420$		0			0
$421$	−541.371	−	312.561i	−1.28592	−	0.742425i	−0.307994	−	0.951388i	$-0.599658\pi$
$421$	−541.371	−	312.561i	−1.28592	−	0.742425i	−0.977923	+	0.208964i	$0.932991\pi$
$422$		0			0
$423$	−261.794	+	584.047i	−0.618899	+	1.38073i
$424$		0			0
$425$	24.9801	+	43.2669i	0.0587768	+	0.101804i
$426$		0			0
$427$	−508.569	−	880.867i	−1.19103	−	2.06292i
$428$		0			0
$429$	617.639	−	31.5913i	1.43972	−	0.0736394i
$430$		0			0
$431$	−55.1286	−	31.8285i	−0.127909	−	0.0738481i	0.434680	−	0.900585i	$-0.356861\pi$
$431$	−55.1286	−	31.8285i	−0.127909	−	0.0738481i	−0.562589	+	0.826737i	$0.690195\pi$
$432$		0			0
$433$	217.312	+	125.465i	0.501875	+	0.289758i	0.729488	−	0.683994i	$-0.239759\pi$
$433$	217.312	+	125.465i	0.501875	+	0.289758i	−0.227612	+	0.973752i	$0.573092\pi$
$434$		0			0
$435$	−161.843	−	249.903i	−0.372054	−	0.574491i
$436$		0			0
$437$	−447.267	+	174.009i	−1.02349	+	0.398190i
$438$		0			0
$439$	337.659	+	194.947i	0.769154	+	0.444071i	0.832573	−	0.553916i	$-0.186867\pi$
$439$	337.659	+	194.947i	0.769154	+	0.444071i	−0.0634185	+	0.997987i	$0.520200\pi$
$440$		0			0
$441$	600.345	+	830.683i	1.36133	+	1.88364i
$442$		0			0
$443$	−132.571			−0.299257			−0.149629	−	0.988742i	$-0.547808\pi$
$443$	−132.571			−0.299257			−0.149629	+	0.988742i	$0.547808\pi$
$444$		0			0
$445$	−314.456	−	181.551i	−0.706643	−	0.407981i
$446$		0			0
$447$	−563.688	+	365.058i	−1.26105	+	0.816684i
$448$		0			0
$449$		−	213.939i		−	0.476479i	−0.971206	−	0.238240i	$-0.923430\pi$
$449$		−	213.939i		−	0.476479i	0.971206	−	0.238240i	$-0.0765703\pi$
$450$		0			0
$451$	839.491	−	484.680i	1.86140	−	1.07468i
$452$		0			0
$453$	320.141	−	626.366i	0.706713	−	1.38271i
$454$		0			0
$455$	1290.55	+	745.098i	2.83637	+	1.63758i
$456$		0			0
$457$	93.5783	+	162.082i	0.204766	+	0.354666i	0.950058	−	0.312072i	$-0.101023\pi$
$457$	93.5783	+	162.082i	0.204766	+	0.354666i	−0.745292	+	0.666738i	$0.767690\pi$
$458$		0			0
$459$	−28.2412	+	22.6936i	−0.0615277	+	0.0494414i
$460$		0			0
$461$	−142.711	+	247.182i	−0.309568	+	0.536187i	−0.978268	−	0.207345i	$-0.933518\pi$
$461$	−142.711	+	247.182i	−0.309568	+	0.536187i	0.668700	+	0.743532i	$0.266851\pi$
$462$		0			0
$463$	57.3059	−	99.2568i	0.123771	−	0.214378i	−0.797481	−	0.603344i	$-0.793835\pi$
$463$	57.3059	−	99.2568i	0.123771	−	0.214378i	0.921252	+	0.388967i	$0.127168\pi$
$464$		0			0
$465$	785.617	−	40.1831i	1.68950	−	0.0864153i
$466$		0			0
$467$	−182.405			−0.390590			−0.195295	−	0.980745i	$-0.562566\pi$
$467$	−182.405			−0.390590			−0.195295	+	0.980745i	$0.562566\pi$
$468$		0			0
$469$	552.611	+	319.050i	1.17827	+	0.680277i
$470$		0			0
$471$	714.217	−	462.544i	1.51638	−	0.982046i
$472$		0			0
$473$	−770.166			−1.62826
$474$		0			0
$475$	−107.512	+	699.209i	−0.226342	+	1.47202i
$476$		0			0
$477$	−408.063	+	294.912i	−0.855478	+	0.618264i
$478$		0			0
$479$	43.9323			0.0917167			0.0458584	−	0.998948i	$-0.485398\pi$
$479$	43.9323			0.0917167			0.0458584	+	0.998948i	$0.485398\pi$
$480$		0			0
$481$	144.952	+	251.064i	0.301356	+	0.521963i
$482$		0			0
$483$	−49.4013	−	965.841i	−0.102280	−	1.99967i
$484$		0			0
$485$	−938.571	−	541.884i	−1.93520	−	1.11729i
$486$		0			0
$487$		−	577.322i		−	1.18547i	−0.805399	−	0.592733i	$-0.798049\pi$
$487$		−	577.322i		−	1.18547i	0.805399	−	0.592733i	$-0.201951\pi$
$488$		0			0
$489$	−371.244	+	240.427i	−0.759191	+	0.491670i
$490$		0			0
$491$	−152.349			−0.310284			−0.155142	−	0.987892i	$-0.549583\pi$
$491$	−152.349			−0.310284			−0.155142	+	0.987892i	$0.549583\pi$
$492$		0			0
$493$	14.6192	−	8.44039i	0.0296535	−	0.0171205i
$494$		0			0
$495$	−983.696	+	100.893i	−1.98726	+	0.203824i
$496$		0			0
$497$	−188.286	−	108.707i	−0.378844	−	0.218726i
$498$		0			0
$499$	265.373			0.531809			0.265905	−	0.963999i	$-0.414329\pi$
$499$	265.373			0.531809			0.265905	+	0.963999i	$0.414329\pi$
$500$		0			0
$501$	229.777	−	449.565i	0.458636	−	0.897336i
$502$		0			0
$503$	−297.421	+	515.149i	−0.591295	+	1.02415i	0.402763	+	0.915304i	$0.368050\pi$
$503$	−297.421	+	515.149i	−0.591295	+	1.02415i	−0.994058	+	0.108849i	$0.965284\pi$
$504$		0			0
$505$	−517.923			−1.02559
$506$		0			0
$507$	7.67436	+	150.041i	0.0151368	+	0.295938i
$508$		0			0
$509$	−278.140	+	160.584i	−0.546445	+	0.315490i	−0.747687	−	0.664052i	$-0.768836\pi$
$509$	−278.140	+	160.584i	−0.546445	+	0.315490i	0.201242	+	0.979542i	$0.435502\pi$
$510$		0			0
$511$	64.0976	−	111.020i	0.125436	−	0.217261i
$512$		0			0
$513$	−513.000	+	0.381667i	−1.00000	+	0.000743990i
$514$		0			0
$515$	352.908	+	203.751i	0.685258	+	0.395634i
$516$		0			0
$517$	−495.237	−	857.775i	−0.957904	−	1.65914i
$518$		0			0
$519$	332.921	−	17.0284i	0.641467	−	0.0328101i
$520$		0			0
$521$			474.505i			0.910757i	0.890298	+	0.455379i	$0.150496\pi$
$521$			474.505i			0.910757i	−0.890298	+	0.455379i	$0.849504\pi$
$522$		0			0
$523$	−301.250	−	173.927i	−0.576004	−	0.332556i	0.183540	−	0.983012i	$-0.441244\pi$
$523$	−301.250	−	173.927i	−0.576004	−	0.332556i	−0.759544	+	0.650456i	$0.774578\pi$
$524$		0			0
$525$	−1269.36	−	648.780i	−2.41783	−	1.23577i
$526$		0			0
$527$			44.6009i			0.0846316i
$528$		0			0
$529$	−54.5122	+	94.4180i	−0.103048	+	0.178484i
$530$		0			0
$531$	−569.182	−	255.131i	−1.07191	−	0.480473i
$532$		0			0
$533$	515.081	+	892.146i	0.966380	+	1.67382i
$534$		0			0
$535$		−	1101.99i		−	2.05980i
$536$		0			0
$537$	−42.7737	−	66.0471i	−0.0796530	−	0.122993i
$538$		0			0
$539$	−1586.08			−2.94264
$540$		0			0
$541$	−432.627	+	749.332i	−0.799681	+	1.38509i	0.120144	+	0.992757i	$0.461664\pi$
$541$	−432.627	+	749.332i	−0.799681	+	1.38509i	−0.919824	+	0.392331i	$0.871669\pi$
$542$		0			0
$543$	−36.4773	+	1.86576i	−0.0671774	+	0.00343602i
$544$		0			0
$545$	−904.903	+	522.446i	−1.66037	+	0.958617i
$546$		0			0
$547$			240.745i			0.440119i	0.975486	+	0.220060i	$0.0706252\pi$
$547$			240.745i			0.440119i	−0.975486	+	0.220060i	$0.929375\pi$
$548$		0			0
$549$	−293.389	+	654.534i	−0.534407	+	1.19223i
$550$		0			0
$551$	236.252	+	36.3267i	0.428769	+	0.0659287i
$552$		0			0
$553$			644.088i			1.16472i
$554$		0			0
$555$	−251.973	−	389.073i	−0.454005	−	0.701032i
$556$		0			0
$557$	362.318	−	627.554i	0.650482	−	1.12667i	−0.332524	−	0.943095i	$-0.607900\pi$
$557$	362.318	−	627.554i	0.650482	−	1.12667i	0.983006	−	0.183573i	$-0.0587663\pi$
$558$		0			0
$559$		−	818.473i		−	1.46417i
$560$		0			0
$561$	−2.86394	−	55.9927i	−0.00510506	−	0.0998087i
$562$		0			0
$563$	−84.3451	−	48.6967i	−0.149814	−	0.0864949i	0.423219	−	0.906027i	$-0.360900\pi$
$563$	−84.3451	−	48.6967i	−0.149814	−	0.0864949i	−0.573033	+	0.819532i	$0.694233\pi$
$564$		0			0
$565$	−237.339	−	137.028i	−0.420069	−	0.242527i
$566$		0			0
$567$	324.383	−	981.543i	0.572104	−	1.73112i
$568$		0			0
$569$	−313.132	+	180.787i	−0.550320	+	0.317727i	−0.749251	−	0.662286i	$-0.769586\pi$
$569$	−313.132	+	180.787i	−0.550320	+	0.317727i	0.198931	+	0.980013i	$0.436253\pi$
$570$		0			0
$571$	450.487	−	780.266i	0.788944	−	1.36649i	−0.137671	−	0.990478i	$-0.543962\pi$
$571$	450.487	−	780.266i	0.788944	−	1.36649i	0.926614	−	0.376013i	$-0.122705\pi$
$572$		0			0
$573$	973.951	+	497.795i	1.69974	+	0.868752i
$574$		0			0
$575$	470.237	+	814.474i	0.817803	+	1.41648i
$576$		0			0
$577$	721.069			1.24969			0.624843	−	0.780750i	$-0.285163\pi$
$577$	721.069			1.24969			0.624843	+	0.780750i	$0.285163\pi$
$578$		0			0
$579$	92.8563	+	143.380i	0.160373	+	0.247634i
$580$		0			0
$581$	454.502	−	787.220i	0.782275	−	1.35494i
$582$		0			0
$583$		−	779.143i		−	1.33644i
$584$		0			0
$585$	−107.221	−	1045.40i	−0.183284	−	1.78700i
$586$		0			0
$587$	−65.3830	+	113.247i	−0.111385	+	0.192924i	−0.916329	−	0.400426i	$-0.868862\pi$
$587$	−65.3830	+	113.247i	−0.111385	+	0.192924i	0.804944	+	0.593351i	$0.202195\pi$
$588$		0			0
$589$	−395.222	+	492.586i	−0.671005	+	0.836309i
$590$		0			0
$591$	−87.1054	+	56.4115i	−0.147386	+	0.0954509i
$592$		0			0
$593$	−109.685	+	189.979i	−0.184965	+	0.320370i	−0.943565	−	0.331188i	$-0.892551\pi$
$593$	−109.685	+	189.979i	−0.184965	+	0.320370i	0.758599	+	0.651557i	$0.225884\pi$
$594$		0			0
$595$	67.5476	−	116.996i	0.113525	−	0.196632i
$596$		0			0
$597$	48.1993	+	942.341i	0.0807359	+	1.57846i
$598$		0			0
$599$	−958.654	+	553.479i	−1.60042	+	0.924005i	−0.609022	+	0.793153i	$0.708438\pi$
$599$	−958.654	+	553.479i	−1.60042	+	0.924005i	−0.991402	+	0.130852i	$0.958229\pi$
$600$		0			0
$601$	626.086	−	361.471i	1.04174	−	0.601449i	0.121415	−	0.992602i	$-0.461257\pi$
$601$	626.086	−	361.471i	1.04174	−	0.601449i	0.920326	+	0.391153i	$0.127924\pi$
$602$		0			0
$603$	−45.9120	−	447.637i	−0.0761393	−	0.742350i
$604$		0			0
$605$	287.869	−	498.603i	0.475816	−	0.824138i
$606$		0			0
$607$	719.925	+	415.649i	1.18604	+	0.684759i	0.957404	−	0.288753i	$-0.0932406\pi$
$607$	719.925	+	415.649i	1.18604	+	0.684759i	0.228634	+	0.973512i	$0.426574\pi$
$608$		0			0
$609$	−219.213	+	428.896i	−0.359955	+	0.704263i
$610$		0			0
$611$	911.577	−	526.299i	1.49194	−	0.861373i
$612$		0			0
$613$	60.6336	+	105.020i	0.0989128	+	0.171322i	0.911235	−	0.411887i	$-0.135130\pi$
$613$	60.6336	+	105.020i	0.0989128	+	0.171322i	−0.812322	+	0.583209i	$0.801797\pi$
$614$		0			0
$615$	−895.373	−	1382.55i	−1.45589	−	2.24805i
$616$		0			0
$617$	130.423	+	225.900i	0.211383	+	0.366126i	0.952148	−	0.305639i	$-0.0988700\pi$
$617$	130.423	+	225.900i	0.211383	+	0.366126i	−0.740765	+	0.671765i	$0.765537\pi$
$618$		0			0
$619$	31.5546	+	54.6542i	0.0509767	+	0.0882943i	0.890388	−	0.455203i	$-0.150433\pi$
$619$	31.5546	+	54.6542i	0.0509767	+	0.0882943i	−0.839411	+	0.543497i	$0.817100\pi$
$620$		0			0
$621$	−531.625	+	427.195i	−0.856078	+	0.687914i
$622$		0			0
$623$			587.425i			0.942897i
$624$		0			0
$625$	−169.529			−0.271247
$626$		0			0
$627$	464.538	−	643.779i	0.740890	−	1.02676i
$628$		0			0
$629$	22.7605	−	13.1408i	0.0361852	−	0.0208915i
$630$		0			0
$631$	−541.477	+	937.865i	−0.858124	+	1.48632i	0.0155914	+	0.999878i	$0.495037\pi$
$631$	−541.477	+	937.865i	−0.858124	+	1.48632i	−0.873716	+	0.486437i	$0.838296\pi$
$632$		0			0
$633$	−398.382	−	615.145i	−0.629356	−	0.971793i
$634$		0			0
$635$	50.2109	+	28.9892i	0.0790722	+	0.0456524i
$636$		0			0
$637$		−	1685.56i		−	2.64610i
$638$		0			0
$639$	15.6432	+	152.519i	0.0244807	+	0.238684i
$640$		0			0
$641$	−149.542	−	86.3383i	−0.233295	−	0.134693i	0.378796	−	0.925480i	$-0.376338\pi$
$641$	−149.542	−	86.3383i	−0.233295	−	0.134693i	−0.612091	+	0.790787i	$0.709672\pi$
$642$		0			0
$643$	−739.425			−1.14996			−0.574981	−	0.818167i	$-0.694990\pi$
$643$	−739.425			−1.14996			−0.574981	+	0.818167i	$0.694990\pi$
$644$		0			0
$645$	66.8499	+	1306.98i	0.103643	+	2.02632i
$646$		0			0
$647$	708.194			1.09458			0.547290	−	0.836943i	$-0.315659\pi$
$647$	708.194			1.09458			0.547290	+	0.836943i	$0.315659\pi$
$648$		0			0
$649$	835.943	−	482.632i	1.28805	−	0.743655i
$650$		0			0
$651$	−691.781	−	1068.18i	−1.06264	−	1.64083i
$652$		0			0
$653$	547.163	−	947.714i	0.837922	−	1.45132i	−0.0537078	−	0.998557i	$-0.517104\pi$
$653$	547.163	−	947.714i	0.837922	−	1.45132i	0.891629	−	0.452766i	$-0.149563\pi$
$654$		0			0
$655$	−140.481			−0.214475
$656$		0			0
$657$	−89.9308	+	9.22378i	−0.136881	+	0.0140392i
$658$		0			0
$659$			60.7946i			0.0922528i	0.998936	+	0.0461264i	$0.0146877\pi$
$659$			60.7946i			0.0922528i	−0.998936	+	0.0461264i	$0.985312\pi$
$660$		0			0
$661$	1117.12	−	644.967i	1.69004	−	0.975744i	0.735563	−	0.677456i	$-0.236918\pi$
$661$	1117.12	−	644.967i	1.69004	−	0.975744i	0.954476	−	0.298288i	$-0.0964156\pi$
$662$		0			0
$663$	59.5047	−	3.04357i	0.0897506	−	0.00459061i
$664$		0			0
$665$	1782.75	−	693.580i	2.68083	−	1.04298i
$666$		0			0
$667$	275.198	−	158.886i	0.412590	−	0.238209i
$668$		0			0
$669$	−1177.26	+	60.2150i	−1.75973	+	0.0900074i
$670$		0			0
$671$	−555.005	−	961.297i	−0.827131	−	1.43263i
$672$		0			0
$673$	−619.674	+	357.769i	−0.920764	+	0.531604i	−0.883879	−	0.467716i	$-0.845077\pi$
$673$	−619.674	+	357.769i	−0.920764	+	0.531604i	−0.0368856	+	0.999319i	$0.511744\pi$
$674$		0			0
$675$	153.520	+	993.499i	0.227437	+	1.47185i
$676$		0			0
$677$	475.400	−	274.472i	0.702215	−	0.405424i	−0.105957	−	0.994371i	$-0.533791\pi$
$677$	475.400	−	274.472i	0.702215	−	0.405424i	0.808172	+	0.588947i	$0.200457\pi$
$678$		0			0
$679$			1753.31i			2.58220i
$680$		0			0
$681$	277.842	−	543.606i	0.407991	−	0.798247i
$682$		0			0
$683$			568.265i			0.832013i	0.909362	+	0.416007i	$0.136571\pi$
$683$			568.265i			0.832013i	−0.909362	+	0.416007i	$0.863429\pi$
$684$		0			0
$685$	−1305.84			−1.90633
$686$		0			0
$687$	−16.9503	−	331.394i	−0.0246729	−	0.482378i
$688$		0			0
$689$	828.013			1.20176
$690$		0			0
$691$	−314.474	−	544.685i	−0.455100	−	0.788256i	0.543594	−	0.839348i	$-0.317063\pi$
$691$	−314.474	−	544.685i	−0.455100	−	0.788256i	−0.998694	+	0.0510924i	$0.983730\pi$
$692$		0			0
$693$	937.064	+	1296.59i	1.35218	+	1.87099i
$694$		0			0
$695$	−32.3197	−	55.9794i	−0.0465032	−	0.0805460i
$696$		0			0
$697$	80.8783	−	46.6951i	0.116038	−	0.0669945i
$698$		0			0
$699$	521.502	+	266.544i	0.746069	+	0.381322i
$700$		0			0
$701$	−124.893	−	216.320i	−0.178163	−	0.308588i	0.763088	−	0.646294i	$-0.223682\pi$
$701$	−124.893	−	216.320i	−0.178163	−	0.308588i	−0.941251	+	0.337706i	$0.890349\pi$
$702$		0			0
$703$	367.818	+	56.5568i	0.523212	+	0.0804506i
$704$		0			0
$705$	−1412.66	+	914.875i	−2.00378	+	1.29769i
$706$		0			0
$707$	418.946	+	725.635i	0.592568	+	1.02636i
$708$		0			0
$709$	−334.091			−0.471214			−0.235607	−	0.971848i	$-0.575708\pi$
$709$	−334.091			−0.471214			−0.235607	+	0.971848i	$0.575708\pi$
$710$		0			0
$711$	368.131	−	266.053i	0.517765	−	0.374195i
$712$		0			0
$713$			839.586i			1.17754i
$714$		0			0
$715$	1408.39	+	813.132i	1.96977	+	1.13725i
$716$		0			0
$717$	−19.8332	−	387.757i	−0.0276613	−	0.540804i
$718$		0			0
$719$	566.067	+	980.456i	0.787297	+	1.36364i	0.927617	+	0.373533i	$0.121854\pi$
$719$	566.067	+	980.456i	0.787297	+	1.36364i	−0.140320	+	0.990106i	$0.544813\pi$
$720$		0			0
$721$		−	659.254i		−	0.914361i
$722$		0			0
$723$	655.480	+	1012.13i	0.906612	+	1.39991i
$724$		0			0
$725$		−	468.407i		−	0.646079i
$726$		0			0
$727$	−146.646	+	253.998i	−0.201714	+	0.349379i	−0.949081	−	0.315033i	$-0.897984\pi$
$727$	−146.646	+	253.998i	−0.201714	+	0.349379i	0.747367	+	0.664412i	$0.231318\pi$
$728$		0			0
$729$	−694.998	+	220.042i	−0.953358	+	0.301842i
$730$		0			0
$731$	−74.1994			−0.101504
$732$		0			0
$733$	109.477	−	189.620i	0.149355	−	0.258690i	−0.781634	−	0.623737i	$-0.785614\pi$
$733$	109.477	−	189.620i	0.149355	−	0.258690i	0.930989	+	0.365047i	$0.118947\pi$
$734$		0			0
$735$	137.671	+	2691.59i	0.187307	+	3.66203i
$736$		0			0
$737$	603.069	+	348.182i	0.818275	+	0.472431i
$738$		0			0
$739$	86.1395	+	149.198i	0.116562	+	0.201892i	0.918403	−	0.395646i	$-0.129479\pi$
$739$	86.1395	+	149.198i	0.116562	+	0.201892i	−0.801841	+	0.597538i	$0.796146\pi$
$740$		0			0
$741$	684.158	+	493.675i	0.923291	+	0.666228i
$742$		0			0
$743$		−	217.534i		−	0.292778i	−0.989227	−	0.146389i	$-0.953235\pi$
$743$		−	217.534i		−	0.292778i	0.989227	−	0.146389i	$-0.0467651\pi$
$744$		0			0
$745$	−1765.97			−2.37043
$746$		0			0
$747$	−637.680	+	65.4039i	−0.853655	+	0.0875554i
$748$		0			0
$749$	−1543.95	+	891.399i	−2.06135	+	1.19012i
$750$		0			0
$751$	28.8622	−	16.6636i	0.0384318	−	0.0221886i	−0.480661	−	0.876906i	$-0.659603\pi$
$751$	28.8622	−	16.6636i	0.0384318	−	0.0221886i	0.519093	+	0.854718i	$0.326270\pi$
$752$		0			0
$753$	−10.6622	−	208.456i	−0.0141596	−	0.276834i
$754$		0			0
$755$	1601.94	−	924.879i	2.12177	−	1.22500i
$756$		0			0
$757$	−24.2338	−	41.9742i	−0.0320129	−	0.0554480i	0.849575	−	0.527468i	$-0.176858\pi$
$757$	−24.2338	−	41.9742i	−0.0320129	−	0.0554480i	−0.881588	+	0.472020i	$0.843525\pi$
$758$		0			0
$759$	−53.9120	−	1054.03i	−0.0710304	−	1.38871i
$760$		0			0
$761$	−336.297	+	582.483i	−0.441915	+	0.765418i	−0.997832	−	0.0658193i	$-0.979034\pi$
$761$	−336.297	+	582.483i	−0.441915	+	0.765418i	0.555917	+	0.831238i	$0.312367\pi$
$762$		0			0
$763$	1463.95	+	845.209i	1.91867	+	1.10774i
$764$		0			0
$765$	−94.7714	+	9.72026i	−0.123884	+	0.0127062i
$766$		0			0
$767$	512.904	+	888.375i	0.668714	+	1.15825i
$768$		0			0
$769$	435.742	+	754.727i	0.566634	+	0.981440i	0.996896	+	0.0787352i	$0.0250882\pi$
$769$	435.742	+	754.727i	0.566634	+	0.981440i	−0.430261	+	0.902704i	$0.641578\pi$
$770$		0			0
$771$	120.536	−	235.832i	0.156337	−	0.305878i
$772$		0			0
$773$	1110.37	+	641.073i	1.43644	+	0.829331i	0.997600	−	0.0692334i	$-0.0220553\pi$
$773$	1110.37	+	641.073i	1.43644	+	0.829331i	0.438842	+	0.898564i	$0.355389\pi$
$774$		0			0
$775$	1071.78	+	618.792i	1.38294	+	0.798441i
$776$		0			0
$777$	−341.290	+	667.745i	−0.439241	+	0.859389i
$778$		0			0
$779$	1307.03	+	200.972i	1.67783	+	0.257987i
$780$		0			0
$781$	−205.478	−	118.633i	−0.263096	−	0.151898i
$782$		0			0
$783$	335.688	−	51.8719i	0.428720	−	0.0662477i
$784$		0			0
$785$	2237.56			2.85039
$786$		0			0
$787$	745.350	+	430.328i	0.947078	+	0.546796i	0.892172	−	0.451696i	$-0.149181\pi$
$787$	745.350	+	430.328i	0.947078	+	0.546796i	0.0549061	+	0.998492i	$0.482514\pi$
$788$		0			0
$789$	−34.5148	−	674.796i	−0.0437450	−	0.855254i
$790$		0			0
$791$			443.365i			0.560512i
$792$		0			0
$793$	1021.59	−	589.817i	1.28826	−	0.743779i
$794$		0			0
$795$	−1322.21	+	67.6291i	−1.66316	+	0.0850681i
$796$		0			0
$797$	394.775	+	227.924i	0.495327	+	0.285977i	0.726782	−	0.686869i	$-0.241015\pi$
$797$	394.775	+	227.924i	0.495327	+	0.285977i	−0.231455	+	0.972846i	$0.574349\pi$
$798$		0			0
$799$	−47.7122	−	82.6399i	−0.0597148	−	0.103429i
$800$		0			0
$801$	335.745	−	242.647i	0.419158	−	0.302930i
$802$		0			0
$803$	69.9502	−	121.157i	0.0871111	−	0.150881i
$804$		0			0
$805$	1271.55	−	2202.38i	1.57956	−	2.73588i
$806$		0			0
$807$	−342.703	+	670.510i	−0.424663	+	0.830868i
$808$		0			0
$809$	979.177			1.21035			0.605177	−	0.796091i	$-0.293102\pi$
$809$	979.177			1.21035			0.605177	+	0.796091i	$0.293102\pi$
$810$		0			0
$811$	121.600	+	70.2060i	0.149939	+	0.0865672i	0.573092	−	0.819491i	$-0.305744\pi$
$811$	121.600	+	70.2060i	0.149939	+	0.0865672i	−0.423154	+	0.906058i	$0.639077\pi$
$812$		0			0
$813$	888.341	+	454.039i	1.09267	+	0.558473i
$814$		0			0
$815$	−1163.06			−1.42707
$816$		0			0
$817$	−819.482	−	657.504i	−1.00304	−	0.804778i
$818$		0			0
$819$	−1377.92	+	995.839i	−1.68244	+	1.21592i
$820$		0			0
$821$	−1222.31			−1.48881			−0.744404	−	0.667730i	$-0.767266\pi$
$821$	−1222.31			−1.48881			−0.744404	+	0.667730i	$0.767266\pi$
$822$		0			0
$823$	604.648	+	1047.28i	0.734687	+	1.27252i	0.954860	+	0.297055i	$0.0960044\pi$
$823$	604.648	+	1047.28i	0.734687	+	1.27252i	−0.220173	+	0.975461i	$0.570662\pi$
$824$		0			0
$825$	−1385.26	−	708.019i	−1.67911	−	0.858205i
$826$		0			0
$827$	−858.762	−	495.806i	−1.03841	−	0.599524i	−0.119025	−	0.992891i	$-0.537977\pi$
$827$	−858.762	−	495.806i	−1.03841	−	0.599524i	−0.919381	+	0.393367i	$0.871310\pi$
$828$		0			0
$829$		−	468.309i		−	0.564909i	−0.959281	−	0.282454i	$-0.908851\pi$
$829$		−	468.309i		−	0.564909i	0.959281	−	0.282454i	$-0.0911486\pi$
$830$		0			0
$831$	−301.760	−	154.232i	−0.363129	−	0.185598i
$832$		0			0
$833$	−152.806			−0.183441
$834$		0			0
$835$	1149.77	−	663.818i	1.37697	−	0.794992i
$836$		0			0
$837$	−324.772	+	836.624i	−0.388019	+	0.999551i
$838$		0			0
$839$	−1154.42	−	666.504i	−1.37595	−	0.794403i	−0.384277	−	0.923218i	$-0.625549\pi$
$839$	−1154.42	−	666.504i	−1.37595	−	0.794403i	−0.991669	+	0.128815i	$0.958883\pi$
$840$		0			0
$841$	682.733			0.811811
$842$		0			0
$843$	390.547	+	603.046i	0.463282	+	0.715357i
$844$		0			0
$845$	−197.531	+	342.134i	−0.233765	+	0.404892i
$846$		0			0
$847$	−931.423			−1.09967
$848$		0			0
$849$	386.634	−	250.394i	0.455400	−	0.294928i
$850$		0			0
$851$	428.453	−	247.368i	0.503470	−	0.290679i
$852$		0			0
$853$	−827.261	+	1432.86i	−0.969825	+	1.67979i	−0.273773	+	0.961794i	$0.588272\pi$
$853$	−827.261	+	1432.86i	−0.969825	+	1.67979i	−0.696052	+	0.717991i	$0.745062\pi$
$854$		0			0
$855$	−1132.82	−	732.445i	−1.32493	−	0.856660i
$856$		0			0
$857$	439.942	+	254.001i	0.513352	+	0.296384i	0.734210	−	0.678922i	$-0.237553\pi$
$857$	439.942	+	254.001i	0.513352	+	0.296384i	−0.220859	+	0.975306i	$0.570886\pi$
$858$		0			0
$859$	−9.19596	−	15.9279i	−0.0107054	−	0.0185423i	0.860623	−	0.509243i	$-0.170074\pi$
$859$	−9.19596	−	15.9279i	−0.0107054	−	0.0185423i	−0.871328	+	0.490700i	$0.836741\pi$
$860$		0			0
$861$	−1212.76	+	2372.80i	−1.40855	+	2.75587i
$862$		0			0
$863$		−	524.536i		−	0.607806i	−0.952703	−	0.303903i	$-0.901710\pi$
$863$		−	524.536i		−	0.607806i	0.952703	−	0.303903i	$-0.0982898\pi$
$864$		0			0
$865$	759.152	+	438.297i	0.877633	+	0.506701i
$866$		0			0
$867$	44.0119	+	860.474i	0.0507635	+	0.992473i
$868$		0			0
$869$			702.898i			0.808859i
$870$		0			0
$871$	−370.021	+	640.895i	−0.424823	+	0.735815i
$872$		0			0
$873$	1002.11	−	724.239i	1.14790	−	0.829598i
$874$		0			0
$875$	−615.809	−	1066.61i	−0.703781	−	1.21899i
$876$		0			0
$877$			50.3659i			0.0574297i	0.999588	+	0.0287149i	$0.00914148\pi$
$877$			50.3659i			0.0574297i	−0.999588	+	0.0287149i	$0.990859\pi$
$878$		0			0
$879$	342.261	−	17.5061i	0.389375	−	0.0199159i
$880$		0			0
$881$	−405.134			−0.459857			−0.229928	−	0.973208i	$-0.573849\pi$
$881$	−405.134			−0.459857			−0.229928	+	0.973208i	$0.573849\pi$
$882$		0			0
$883$	644.236	−	1115.85i	0.729599	−	1.26370i	−0.227454	−	0.973789i	$-0.573040\pi$
$883$	644.236	−	1115.85i	0.729599	−	1.26370i	0.957053	−	0.289913i	$-0.0936265\pi$
$884$		0			0
$885$	−891.589	−	1376.71i	−1.00745	−	1.55560i
$886$		0			0
$887$	26.6975	−	15.4138i	0.0300987	−	0.0173775i	−0.484875	−	0.874583i	$-0.661135\pi$
$887$	26.6975	−	15.4138i	0.0300987	−	0.0173775i	0.514974	+	0.857206i	$0.327802\pi$
$888$		0			0
$889$		−	93.7971i		−	0.105509i
$890$		0			0
$891$	354.002	−	1071.17i	0.397309	−	1.20221i
$892$		0			0
$893$	205.349	−	1335.49i	0.229954	−	1.49551i
$894$		0			0
$895$		−	206.918i		−	0.231193i
$896$		0			0
$897$	1120.14	−	57.2935i	1.24876	−	0.0638724i
$898$		0			0
$899$	209.080	−	362.137i	0.232569	−	0.402822i
$900$		0			0
$901$		−	75.0643i		−	0.0833122i
$902$		0			0
$903$	1777.06	−	1150.87i	1.96796	−	1.27449i
$904$		0			0
$905$	−83.1783	−	48.0230i	−0.0919097	−	0.0530641i
$906$		0			0
$907$	244.973	+	141.435i	0.270092	+	0.155937i	0.628929	−	0.777463i	$-0.283494\pi$
$907$	244.973	+	141.435i	0.270092	+	0.155937i	−0.358838	+	0.933400i	$0.616827\pi$
$908$		0			0
$909$	241.687	−	539.188i	0.265882	−	0.593166i
$910$		0			0
$911$	−1022.48	+	590.330i	−1.12237	+	0.648002i	−0.942005	−	0.335598i	$-0.891062\pi$
$911$	−1022.48	+	590.330i	−1.12237	+	0.648002i	−0.180366	+	0.983599i	$0.557728\pi$
$912$		0			0
$913$	496.002	−	859.100i	0.543266	−	0.940964i
$914$		0			0
$915$	−1583.15	+	1025.29i	−1.73022	+	1.12053i
$916$		0			0
$917$	113.635	+	196.821i	0.123920	+	0.214636i
$918$		0			0
$919$	−882.256			−0.960017			−0.480009	−	0.877264i	$-0.659366\pi$
$919$	−882.256			−0.960017			−0.480009	+	0.877264i	$0.659366\pi$
$920$		0			0
$921$	419.100	−	819.983i	0.455049	−	0.890318i
$922$		0			0
$923$	126.074	−	218.366i	0.136591	−	0.236583i
$924$		0			0
$925$		−	729.259i		−	0.788388i
$926$		0			0
$927$	−376.800	+	272.318i	−0.406472	+	0.293762i
$928$		0			0
$929$	−199.914	+	346.261i	−0.215192	+	0.372724i	−0.953332	−	0.301924i	$-0.902371\pi$
$929$	−199.914	+	346.261i	−0.215192	+	0.372724i	0.738140	+	0.674648i	$0.235705\pi$
$930$		0			0
$931$	−1687.64	−	1354.06i	−1.81272	−	1.45442i
$932$		0			0
$933$	−89.6495	−	1752.73i	−0.0960873	−	1.87860i
$934$		0			0
$935$	73.7153	−	127.679i	0.0788399	−	0.136555i
$936$		0			0
$937$	−17.0611	+	29.5506i	−0.0182082	+	0.0315375i	−0.874986	−	0.484148i	$-0.839129\pi$
$937$	−17.0611	+	29.5506i	−0.0182082	+	0.0315375i	0.856778	+	0.515686i	$0.172463\pi$
$938$		0			0
$939$	138.511	−	89.7028i	0.147509	−	0.0955301i
$940$		0			0
$941$	−1093.43	+	631.293i	−1.16199	+	0.670875i	−0.951780	−	0.306781i	$-0.900748\pi$
$941$	−1093.43	+	631.293i	−1.16199	+	0.670875i	−0.210210	+	0.977656i	$0.567415\pi$
$942$		0			0
$943$	1522.49	−	879.009i	1.61452	−	0.932142i
$944$		0			0
$945$	2118.99	−	1702.75i	2.24232	−	1.80185i
$946$		0			0
$947$	−495.256	+	857.808i	−0.522974	+	0.905817i	0.476669	+	0.879083i	$0.341844\pi$
$947$	−495.256	+	857.808i	−0.522974	+	0.905817i	−0.999643	+	0.0267339i	$0.991489\pi$
$948$		0			0
$949$	128.757	+	74.3377i	0.135676	+	0.0783326i
$950$		0			0
$951$	−274.502	−	423.861i	−0.288646	−	0.445700i
$952$		0			0
$953$	231.077	−	133.412i	0.242473	−	0.139992i	−0.373840	−	0.927493i	$-0.621959\pi$
$953$	231.077	−	133.412i	0.242473	−	0.139992i	0.616313	+	0.787501i	$0.288626\pi$
$954$		0			0
$955$	1438.12	+	2490.89i	1.50588	+	2.60826i
$956$		0			0
$957$	−239.228	+	468.058i	−0.249978	+	0.489089i
$958$		0			0
$959$	1056.29	+	1829.54i	1.10145	+	1.90776i
$960$		0			0
$961$	71.9120	+	124.555i	0.0748304	+	0.129610i
$962$		0			0
$963$	1147.24	+	514.241i	1.19132	+	0.533999i
$964$		0			0
$965$			449.193i			0.465484i
$966$		0			0
$967$	−876.209			−0.906110			−0.453055	−	0.891482i	$-0.649666\pi$
$967$	−876.209			−0.906110			−0.453055	+	0.891482i	$0.649666\pi$
$968$		0			0
$969$	44.7546	−	62.0230i	0.0461864	−	0.0640073i
$970$		0			0
$971$	−1510.83	+	872.279i	−1.55595	+	0.898330i	−0.558316	+	0.829628i	$0.688552\pi$
$971$	−1510.83	+	872.279i	−1.55595	+	0.898330i	−0.997637	+	0.0687021i	$0.978114\pi$
$972$		0			0
$973$	−52.2866	+	90.5631i	−0.0537375	+	0.0930761i
$974$		0			0
$975$	752.428	−	1472.15i	0.771721	−	1.50990i
$976$		0			0
$977$	567.104	+	327.418i	0.580454	+	0.335126i	0.761314	−	0.648383i	$-0.224555\pi$
$977$	567.104	+	327.418i	0.580454	+	0.335126i	−0.180859	+	0.983509i	$0.557888\pi$
$978$		0			0
$979$			641.061i			0.654812i
$980$		0			0
$981$	−121.628	−	1185.85i	−0.123983	−	1.20882i
$982$		0			0
$983$	162.640	+	93.9004i	0.165453	+	0.0955243i	0.580440	−	0.814303i	$-0.302881\pi$
$983$	162.640	+	93.9004i	0.165453	+	0.0955243i	−0.414987	+	0.909827i	$0.636214\pi$
$984$		0			0
$985$	−272.891			−0.277047
$986$		0			0
$987$	2424.48	+	1239.17i	2.45642	+	1.25549i
$988$		0			0
$989$	−1396.76			−1.41230
$990$		0			0
$991$	−1265.75	+	730.783i	−1.27725	+	0.737420i	−0.976342	−	0.216234i	$-0.930623\pi$
$991$	−1265.75	+	730.783i	−1.27725	+	0.737420i	−0.300907	+	0.953654i	$0.597289\pi$
$992$		0			0
$993$	−764.454	+	1495.68i	−0.769842	+	1.50622i
$994$		0			0
$995$	−1240.61	+	2148.80i	−1.24684	+	2.15959i
$996$		0			0
$997$	−1224.51			−1.22820			−0.614098	−	0.789230i	$-0.710480\pi$
$997$	−1224.51			−1.22820			−0.614098	+	0.789230i	$0.710480\pi$
$998$		0			0
$999$	522.629	−	80.7590i	0.523152	−	0.0808398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.bl.a.373.9	yes	80
3.2	odd	2		2052.3.bl.a.145.37		80
9.2	odd	6		2052.3.s.a.829.4		80
9.7	even	3		684.3.s.a.601.7	yes	80
19.8	odd	6		684.3.s.a.445.7	✓	80
57.8	even	6		2052.3.s.a.901.4		80
171.65	even	6		2052.3.bl.a.1585.37		80
171.160	odd	6	inner	684.3.bl.a.673.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.7	✓	80	19.8	odd	6
684.3.s.a.601.7	yes	80	9.7	even	3
684.3.bl.a.373.9	yes	80	1.1	even	1	trivial
684.3.bl.a.673.9	yes	80	171.160	odd	6	inner
2052.3.s.a.829.4		80	9.2	odd	6
2052.3.s.a.901.4		80	57.8	even	6
2052.3.bl.a.145.37		80	3.2	odd	2
2052.3.bl.a.1585.37		80	171.65	even	6

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.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.51806 + 1.63076i) q^{3} -7.88879 q^{5} +(6.38121 + 11.0526i) q^{7} +(3.68127 - 8.21269i) q^{9} +O(q^{10})\)	\(q+(-2.51806 + 1.63076i) q^{3} -7.88879 q^{5} +(6.38121 + 11.0526i) q^{7} +(3.68127 - 8.21269i) q^{9} +(6.96387 + 12.0618i) q^{11} +(-12.8183 + 7.40066i) q^{13} +(19.8645 - 12.8647i) q^{15} +(0.670914 + 1.16206i) q^{17} +(-2.88756 + 18.7793i) q^{19} +(-34.0923 - 17.4249i) q^{21} +(12.6296 + 21.8751i) q^{23} +37.2330 q^{25} +(4.12322 + 26.6833i) q^{27} -12.5804i q^{29} +(28.7857 + 16.6194i) q^{31} +(-37.2052 - 19.0159i) q^{33} +(-50.3400 - 87.1915i) q^{35} -19.5864i q^{37} +(20.2086 - 39.5389i) q^{39} -69.5993i q^{41} +(-27.6486 + 47.8889i) q^{43} +(-29.0408 + 64.7882i) q^{45} -71.1152 q^{47} +(-56.9397 + 98.6224i) q^{49} +(-3.58443 - 1.83203i) q^{51} +(-48.4471 - 27.9709i) q^{53} +(-54.9365 - 95.1528i) q^{55} +(-23.3534 - 51.9963i) q^{57} -69.3051i q^{59} -79.6978 q^{61} +(114.262 - 11.7194i) q^{63} +(101.121 - 58.3822i) q^{65} +(43.2999 - 24.9992i) q^{67} +(-67.4749 - 34.4870i) q^{69} +(-14.7531 + 8.51773i) q^{71} +(-5.02237 - 8.69900i) q^{73} +(-93.7550 + 60.7179i) q^{75} +(-88.8758 + 153.937i) q^{77} +(43.7062 + 25.2338i) q^{79} +(-53.8965 - 60.4663i) q^{81} +(-35.6125 - 61.6827i) q^{83} +(-5.29270 - 9.16722i) q^{85} +(20.5156 + 31.6783i) q^{87} +(39.8612 + 23.0138i) q^{89} +(-163.593 - 94.4503i) q^{91} +(-99.5865 + 5.09370i) q^{93} +(22.7793 - 148.146i) q^{95} +(118.975 + 68.6905i) q^{97} +(124.695 - 12.7894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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