LMFDB - Embedded newform 684.3.be.a.425.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(425,684)]

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, 1, 2]))

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

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

chi := DirichletCharacter("684.425");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.be (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			425.12
Character	$\chi$	$=$	684.425
Dual form			684.3.be.a.581.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76470 - 2.42608i) q^{3} +(2.53393 + 1.46297i) q^{5} +(-2.71227 + 4.69779i) q^{7} +(-2.77170 + 8.56257i) q^{9} +O(q^{10})$	\(q+(-1.76470 - 2.42608i) q^{3} +(2.53393 + 1.46297i) q^{5} +(-2.71227 + 4.69779i) q^{7} +(-2.77170 + 8.56257i) q^{9} +(9.00863 + 5.20114i) q^{11} -24.4777 q^{13} +(-0.922349 - 8.72920i) q^{15} +(19.6840 - 11.3645i) q^{17} +(-5.11536 - 18.2984i) q^{19} +(16.1835 - 1.70999i) q^{21} -29.3354i q^{23} +(-8.21946 - 14.2365i) q^{25} +(25.6647 - 8.38598i) q^{27} +(-26.6384 + 15.3797i) q^{29} +(-8.67884 - 15.0322i) q^{31} +(-3.27913 - 31.0341i) q^{33} +(-13.7454 + 7.93593i) q^{35} +47.8168 q^{37} +(43.1957 + 59.3848i) q^{39} +(-66.1461 - 38.1895i) q^{41} -6.25697 q^{43} +(-19.5501 + 17.6421i) q^{45} +(-15.3230 + 8.84672i) q^{47} +(9.78715 + 16.9518i) q^{49} +(-62.3075 - 27.6999i) q^{51} +(-12.9368 - 7.46908i) q^{53} +(15.2182 + 26.3586i) q^{55} +(-35.3664 + 44.7014i) q^{57} +(-18.8486 - 10.8822i) q^{59} +(-56.0166 - 97.0236i) q^{61} +(-32.7076 - 36.2449i) q^{63} +(-62.0248 - 35.8100i) q^{65} +21.1644 q^{67} +(-71.1700 + 51.7681i) q^{69} +(43.5246 - 25.1289i) q^{71} +(-6.91001 - 11.9685i) q^{73} +(-20.0341 + 45.0642i) q^{75} +(-48.8677 + 28.2138i) q^{77} +1.30487 q^{79} +(-65.6354 - 47.4658i) q^{81} +(66.2341 + 38.2403i) q^{83} +66.5038 q^{85} +(84.3210 + 37.4863i) q^{87} +(-123.051 - 71.0438i) q^{89} +(66.3902 - 114.991i) q^{91} +(-21.1537 + 47.5828i) q^{93} +(13.8080 - 53.8506i) q^{95} -184.984 q^{97} +(-69.5043 + 62.7211i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.76470	−	2.42608i	−0.588232	−	0.808692i
$3$	−1.76470	−	2.42608i	−0.588232	−	0.808692i
$4$		0			0
$5$	2.53393	+	1.46297i	0.506786	+	0.292593i	0.731512	−	0.681829i	$-0.238815\pi$
$5$	2.53393	+	1.46297i	0.506786	+	0.292593i	−0.224725	+	0.974422i	$0.572149\pi$
$6$		0			0
$7$	−2.71227	+	4.69779i	−0.387468	+	0.671114i	−0.992108	−	0.125385i	$-0.959983\pi$
$7$	−2.71227	+	4.69779i	−0.387468	+	0.671114i	0.604641	+	0.796498i	$0.293317\pi$
$8$		0			0
$9$	−2.77170	+	8.56257i	−0.307967	+	0.951397i
$10$		0			0
$11$	9.00863	+	5.20114i	0.818966	+	0.472830i	0.850060	−	0.526686i	$-0.176566\pi$
$11$	9.00863	+	5.20114i	0.818966	+	0.472830i	−0.0310935	+	0.999516i	$0.509899\pi$
$12$		0			0
$13$	−24.4777			−1.88290			−0.941450	−	0.337153i	$-0.890536\pi$
$13$	−24.4777			−1.88290			−0.941450	+	0.337153i	$0.890536\pi$
$14$		0			0
$15$	−0.922349	−	8.72920i	−0.0614899	−	0.581947i
$16$		0			0
$17$	19.6840	−	11.3645i	1.15788	−	0.668503i	0.207086	−	0.978323i	$-0.433602\pi$
$17$	19.6840	−	11.3645i	1.15788	−	0.668503i	0.950795	+	0.309820i	$0.100269\pi$
$18$		0			0
$19$	−5.11536	−	18.2984i	−0.269230	−	0.963076i
$19$	−5.11536	−	18.2984i	−0.269230	−	0.963076i
$20$		0			0
$21$	16.1835	−	1.70999i	0.770645	−	0.0814283i
$22$		0			0
$23$		−	29.3354i		−	1.27545i	−0.770263	−	0.637727i	$-0.779875\pi$
$23$		−	29.3354i		−	1.27545i	0.770263	−	0.637727i	$-0.220125\pi$
$24$		0			0
$25$	−8.21946	−	14.2365i	−0.328778	−	0.569461i
$26$		0			0
$27$	25.6647	−	8.38598i	0.950543	−	0.310592i
$28$		0			0
$29$	−26.6384	+	15.3797i	−0.918566	+	0.530334i	−0.883177	−	0.469040i	$-0.844600\pi$
$29$	−26.6384	+	15.3797i	−0.918566	+	0.530334i	−0.0353884	+	0.999374i	$0.511267\pi$
$30$		0			0
$31$	−8.67884	−	15.0322i	−0.279962	−	0.484909i	0.691413	−	0.722460i	$-0.256989\pi$
$31$	−8.67884	−	15.0322i	−0.279962	−	0.484909i	−0.971375	+	0.237551i	$0.923655\pi$
$32$		0			0
$33$	−3.27913	−	31.0341i	−0.0993677	−	0.940426i
$34$		0			0
$35$	−13.7454	+	7.93593i	−0.392726	+	0.226741i
$36$		0			0
$37$	47.8168			1.29234			0.646172	−	0.763192i	$-0.276369\pi$
$37$	47.8168			1.29234			0.646172	+	0.763192i	$0.276369\pi$
$38$		0			0
$39$	43.1957	+	59.3848i	1.10758	+	1.52269i
$40$		0			0
$41$	−66.1461	−	38.1895i	−1.61332	−	0.931451i	−0.988594	−	0.150608i	$-0.951877\pi$
$41$	−66.1461	−	38.1895i	−1.61332	−	0.931451i	−0.624727	−	0.780843i	$-0.714790\pi$
$42$		0			0
$43$	−6.25697			−0.145511			−0.0727554	−	0.997350i	$-0.523179\pi$
$43$	−6.25697			−0.145511			−0.0727554	+	0.997350i	$0.523179\pi$
$44$		0			0
$45$	−19.5501	+	17.6421i	−0.434446	+	0.392046i
$46$		0			0
$47$	−15.3230	+	8.84672i	−0.326021	+	0.188228i	−0.654073	−	0.756431i	$-0.726941\pi$
$47$	−15.3230	+	8.84672i	−0.326021	+	0.188228i	0.328052	+	0.944660i	$0.393608\pi$
$48$		0			0
$49$	9.78715	+	16.9518i	0.199738	+	0.345956i
$50$		0			0
$51$	−62.3075	−	27.6999i	−1.22172	−	0.543135i
$52$		0			0
$53$	−12.9368	−	7.46908i	−0.244091	−	0.140926i	0.372964	−	0.927846i	$-0.378341\pi$
$53$	−12.9368	−	7.46908i	−0.244091	−	0.140926i	−0.617056	+	0.786920i	$0.711675\pi$
$54$		0			0
$55$	15.2182	+	26.3586i	0.276694	+	0.479248i
$56$		0			0
$57$	−35.3664	+	44.7014i	−0.620463	+	0.784236i
$58$		0			0
$59$	−18.8486	−	10.8822i	−0.319468	−	0.184445i	0.331688	−	0.943389i	$-0.392382\pi$
$59$	−18.8486	−	10.8822i	−0.319468	−	0.184445i	−0.651155	+	0.758945i	$0.725715\pi$
$60$		0			0
$61$	−56.0166	−	97.0236i	−0.918305	−	1.59055i	−0.801989	−	0.597339i	$-0.796225\pi$
$61$	−56.0166	−	97.0236i	−0.918305	−	1.59055i	−0.116316	−	0.993212i	$-0.537109\pi$
$62$		0			0
$63$	−32.7076	−	36.2449i	−0.519168	−	0.575316i
$64$		0			0
$65$	−62.0248	−	35.8100i	−0.954228	−	0.550924i
$66$		0			0
$67$	21.1644			0.315887			0.157943	−	0.987448i	$-0.449514\pi$
$67$	21.1644			0.315887			0.157943	+	0.987448i	$0.449514\pi$
$68$		0			0
$69$	−71.1700	+	51.7681i	−1.03145	+	0.750262i
$70$		0			0
$71$	43.5246	−	25.1289i	0.613023	−	0.353929i	−0.161125	−	0.986934i	$-0.551512\pi$
$71$	43.5246	−	25.1289i	0.613023	−	0.353929i	0.774147	+	0.633005i	$0.218179\pi$
$72$		0			0
$73$	−6.91001	−	11.9685i	−0.0946577	−	0.163952i	0.814808	−	0.579731i	$-0.196842\pi$
$73$	−6.91001	−	11.9685i	−0.0946577	−	0.163952i	−0.909466	+	0.415779i	$0.863509\pi$
$74$		0			0
$75$	−20.0341	+	45.0642i	−0.267121	+	0.600856i
$76$		0			0
$77$	−48.8677	+	28.2138i	−0.634646	+	0.366413i
$78$		0			0
$79$	1.30487			0.0165174			0.00825868	−	0.999966i	$-0.497371\pi$
$79$	1.30487			0.0165174			0.00825868	+	0.999966i	$0.497371\pi$
$80$		0			0
$81$	−65.6354	−	47.4658i	−0.810313	−	0.585997i
$82$		0			0
$83$	66.2341	+	38.2403i	0.798002	+	0.460726i	0.842772	−	0.538271i	$-0.180922\pi$
$83$	66.2341	+	38.2403i	0.798002	+	0.460726i	−0.0447703	+	0.998997i	$0.514256\pi$
$84$		0			0
$85$	66.5038			0.782398
$86$		0			0
$87$	84.3210	+	37.4863i	0.969207	+	0.430878i
$88$		0			0
$89$	−123.051	−	71.0438i	−1.38260	−	0.798244i	−0.390133	−	0.920758i	$-0.627571\pi$
$89$	−123.051	−	71.0438i	−1.38260	−	0.798244i	−0.992467	+	0.122514i	$0.960904\pi$
$90$		0			0
$91$	66.3902	−	114.991i	0.729563	−	1.26364i
$92$		0			0
$93$	−21.1537	+	47.5828i	−0.227460	+	0.511643i
$94$		0			0
$95$	13.8080	−	53.8506i	0.145348	−	0.566848i
$96$		0			0
$97$	−184.984			−1.90705			−0.953524	−	0.301317i	$-0.902574\pi$
$97$	−184.984			−1.90705			−0.953524	+	0.301317i	$0.902574\pi$
$98$		0			0
$99$	−69.5043	+	62.7211i	−0.702064	+	0.633546i
$100$		0			0
$101$	−51.2365	+	29.5814i	−0.507292	+	0.292885i	−0.731720	−	0.681605i	$-0.761282\pi$
$101$	−51.2365	+	29.5814i	−0.507292	+	0.292885i	0.224428	+	0.974491i	$0.427949\pi$
$102$		0			0
$103$	84.6622	+	146.639i	0.821963	+	1.42368i	0.904218	+	0.427070i	$0.140454\pi$
$103$	84.6622	+	146.639i	0.821963	+	1.42368i	−0.0822557	+	0.996611i	$0.526212\pi$
$104$		0			0
$105$	43.5097	+	19.3430i	0.414378	+	0.184219i
$106$		0			0
$107$		−	131.165i		−	1.22584i	−0.790144	−	0.612921i	$-0.789994\pi$
$107$		−	131.165i		−	1.22584i	0.790144	−	0.612921i	$-0.210006\pi$
$108$		0			0
$109$	−7.82050	−	13.5455i	−0.0717477	−	0.124271i	0.827920	−	0.560847i	$-0.189524\pi$
$109$	−7.82050	−	13.5455i	−0.0717477	−	0.124271i	−0.899667	+	0.436576i	$0.856191\pi$
$110$		0			0
$111$	−84.3820	−	116.007i	−0.760198	−	1.04511i
$112$		0			0
$113$	−20.4851	+	11.8271i	−0.181284	+	0.104665i	−0.587896	−	0.808937i	$-0.700044\pi$
$113$	−20.4851	+	11.8271i	−0.181284	+	0.104665i	0.406612	+	0.913601i	$0.366710\pi$
$114$		0			0
$115$	42.9167	−	74.3339i	0.373189	−	0.646382i
$116$		0			0
$117$	67.8448	−	209.592i	0.579870	−	1.79139i
$118$		0			0
$119$			123.295i			1.03609i
$120$		0			0
$121$	−6.39638	−	11.0789i	−0.0528627	−	0.0915608i
$122$		0			0
$123$	24.0771	+	227.868i	0.195749	+	1.85259i
$124$		0			0
$125$		−	121.247i		−	0.969980i
$126$		0			0
$127$	−41.1013	+	71.1895i	−0.323632	+	0.560547i	−0.981235	−	0.192818i	$-0.938237\pi$
$127$	−41.1013	+	71.1895i	−0.323632	+	0.560547i	0.657603	+	0.753365i	$0.271571\pi$
$128$		0			0
$129$	11.0416	+	15.1799i	0.0855941	+	0.117673i
$130$		0			0
$131$	−68.7184	−	39.6746i	−0.524568	−	0.302860i	0.214233	−	0.976782i	$-0.431275\pi$
$131$	−68.7184	−	39.6746i	−0.524568	−	0.302860i	−0.738802	+	0.673923i	$0.764608\pi$
$132$		0			0
$133$	99.8366	+	25.5995i	0.750651	+	0.192477i
$134$		0			0
$135$	77.3009	+	16.2970i	0.572599	+	0.120719i
$136$		0			0
$137$	−40.3121	+	23.2742i	−0.294249	+	0.169885i	−0.639856	−	0.768495i	$-0.721006\pi$
$137$	−40.3121	+	23.2742i	−0.294249	+	0.169885i	0.345608	+	0.938379i	$0.387673\pi$
$138$		0			0
$139$	73.9559			0.532057			0.266028	−	0.963965i	$-0.414289\pi$
$139$	73.9559			0.532057			0.266028	+	0.963965i	$0.414289\pi$
$140$		0			0
$141$	48.5032	+	21.5629i	0.343994	+	0.152929i
$142$		0			0
$143$	−220.511	−	127.312i	−1.54203	−	0.890292i
$144$		0			0
$145$	−89.9998			−0.620689
$146$		0			0
$147$	23.8551	−	53.6592i	0.162280	−	0.365029i
$148$		0			0
$149$	170.929	+	98.6858i	1.14717	+	0.662321i	0.948197	−	0.317683i	$-0.102905\pi$
$149$	170.929	+	98.6858i	1.14717	+	0.662321i	0.198976	+	0.980004i	$0.436238\pi$
$150$		0			0
$151$	104.491	−	180.983i	0.691992	−	1.19856i	−0.279193	−	0.960235i	$-0.590067\pi$
$151$	104.491	−	180.983i	0.691992	−	1.19856i	0.971184	−	0.238330i	$-0.0765998\pi$
$152$		0			0
$153$	42.7517	+	200.045i	0.279423	+	1.30748i
$154$		0			0
$155$		−	50.7874i		−	0.327660i
$156$		0			0
$157$	21.7121	−	37.6065i	0.138294	−	0.239532i	−0.788557	−	0.614962i	$-0.789171\pi$
$157$	21.7121	−	37.6065i	0.138294	−	0.239532i	0.926851	+	0.375430i	$0.122505\pi$
$158$		0			0
$159$	4.70900	+	44.5664i	0.0296163	+	0.280292i
$160$		0			0
$161$	137.812	+	79.5657i	0.855974	+	0.494197i
$162$		0			0
$163$	268.887			1.64962			0.824808	−	0.565413i	$-0.191283\pi$
$163$	268.887			1.64962			0.824808	+	0.565413i	$0.191283\pi$
$164$		0			0
$165$	37.0927	−	83.4354i	0.224804	−	0.505669i
$166$		0			0
$167$			322.085i			1.92865i	0.264713	+	0.964327i	$0.414723\pi$
$167$			322.085i			1.92865i	−0.264713	+	0.964327i	$0.585277\pi$
$168$		0			0
$169$	430.158			2.54531
$170$		0			0
$171$	170.860	+	6.91712i	0.999182	+	0.0404510i
$172$		0			0
$173$			35.5104i			0.205262i	0.994719	+	0.102631i	$0.0327261\pi$
$173$			35.5104i			0.205262i	−0.994719	+	0.102631i	$0.967274\pi$
$174$		0			0
$175$	89.1737			0.509564
$176$		0			0
$177$	6.86087	+	64.9320i	0.0387620	+	0.366847i
$178$		0			0
$179$		−	214.059i		−	1.19586i	−0.801549	−	0.597930i	$-0.795990\pi$
$179$		−	214.059i		−	1.19586i	0.801549	−	0.597930i	$-0.204010\pi$
$180$		0			0
$181$	40.8818	−	70.8094i	0.225866	−	0.391212i	−0.730713	−	0.682685i	$-0.760812\pi$
$181$	40.8818	−	70.8094i	0.225866	−	0.391212i	0.956579	+	0.291473i	$0.0941454\pi$
$182$		0			0
$183$	−136.535	+	307.118i	−0.746090	+	1.67824i
$184$		0			0
$185$	121.164	+	69.9543i	0.654943	+	0.378131i
$186$		0			0
$187$	236.434			1.26435
$188$		0			0
$189$	−30.2140	+	143.312i	−0.159862	+	0.758267i
$190$		0			0
$191$	−284.070	−	164.008i	−1.48728	−	0.858681i	−0.487384	−	0.873188i	$-0.662049\pi$
$191$	−284.070	−	164.008i	−1.48728	−	0.858681i	−0.999895	+	0.0145071i	$0.995382\pi$
$192$		0			0
$193$	−109.833	+	190.236i	−0.569083	+	0.985680i	0.427574	+	0.903980i	$0.359368\pi$
$193$	−109.833	+	190.236i	−0.569083	+	0.985680i	−0.996657	+	0.0817000i	$0.973965\pi$
$194$		0			0
$195$	22.5770	+	213.671i	0.115779	+	1.09575i
$196$		0			0
$197$			161.830i			0.821470i	0.911755	+	0.410735i	$0.134728\pi$
$197$			161.830i			0.821470i	−0.911755	+	0.410735i	$0.865272\pi$
$198$		0			0
$199$	37.0576	−	64.1857i	0.186219	−	0.322541i	−0.757767	−	0.652525i	$-0.773710\pi$
$199$	37.0576	−	64.1857i	0.186219	−	0.322541i	0.943987	+	0.329984i	$0.107043\pi$
$200$		0			0
$201$	−37.3488	−	51.3465i	−0.185815	−	0.255455i
$202$		0			0
$203$		−	166.856i		−	0.821949i
$204$		0			0
$205$	−111.740	−	193.539i	−0.545072	−	0.944093i
$206$		0			0
$207$	251.187	+	81.3090i	1.21346	+	0.392797i
$208$		0			0
$209$	49.0903	−	191.450i	0.234882	−	0.916027i
$210$		0			0
$211$	62.2388	−	107.801i	0.294970	−	0.510904i	−0.680008	−	0.733205i	$-0.738024\pi$
$211$	62.2388	−	107.801i	0.294970	−	0.510904i	0.974978	+	0.222301i	$0.0713568\pi$
$212$		0			0
$213$	−137.772	−	61.2491i	−0.646819	−	0.287554i
$214$		0			0
$215$	−15.8547	−	9.15373i	−0.0737429	−	0.0425755i
$216$		0			0
$217$	94.1575			0.433906
$218$		0			0
$219$	−16.8424	+	37.8850i	−0.0769060	+	0.172991i
$220$		0			0
$221$	−481.818	+	278.178i	−2.18017	+	1.25872i
$222$		0			0
$223$	−320.431			−1.43691			−0.718456	−	0.695572i	$-0.755151\pi$
$223$	−320.431			−1.43691			−0.718456	+	0.695572i	$0.755151\pi$
$224$		0			0
$225$	144.683	−	30.9204i	0.643036	−	0.137424i
$226$		0			0
$227$	−137.264	−	79.2492i	−0.604685	−	0.349115i	0.166197	−	0.986093i	$-0.446851\pi$
$227$	−137.264	−	79.2492i	−0.604685	−	0.349115i	−0.770883	+	0.636977i	$0.780184\pi$
$228$		0			0
$229$	−124.132	−	215.003i	−0.542061	−	0.938876i	−0.998786	−	0.0492684i	$-0.984311\pi$
$229$	−124.132	−	215.003i	−0.542061	−	0.938876i	0.456725	−	0.889608i	$-0.349022\pi$
$230$		0			0
$231$	154.686	+	68.7681i	0.669634	+	0.297698i
$232$		0			0
$233$	277.122	−	159.996i	1.18936	−	0.686680i	0.231202	−	0.972906i	$-0.425734\pi$
$233$	277.122	−	159.996i	1.18936	−	0.686680i	0.958162	+	0.286226i	$0.0924008\pi$
$234$		0			0
$235$	−51.7698			−0.220297
$236$		0			0
$237$	−2.30270	−	3.16572i	−0.00971603	−	0.0133575i
$238$		0			0
$239$	13.0028	−	7.50716i	0.0544049	−	0.0314107i	−0.472551	−	0.881303i	$-0.656667\pi$
$239$	13.0028	−	7.50716i	0.0544049	−	0.0314107i	0.526956	+	0.849893i	$0.323333\pi$
$240$		0			0
$241$	22.8860	+	39.6396i	0.0949625	+	0.164480i	0.909593	−	0.415501i	$-0.136394\pi$
$241$	22.8860	+	39.6396i	0.0949625	+	0.164480i	−0.814630	+	0.579980i	$0.803060\pi$
$242$		0			0
$243$	0.670797	+	242.999i	0.00276048	+	0.999996i
$244$		0			0
$245$			57.2731i			0.233768i
$246$		0			0
$247$	125.212	+	447.904i	0.506932	+	1.81338i
$248$		0			0
$249$	−24.1092	−	228.172i	−0.0968240	−	0.916352i
$250$		0			0
$251$	306.214	+	176.793i	1.21997	+	0.704353i	0.964912	−	0.262572i	$-0.0845707\pi$
$251$	306.214	+	176.793i	1.21997	+	0.704353i	0.255062	+	0.966925i	$0.417904\pi$
$252$		0			0
$253$	152.578	−	264.272i	0.603073	−	1.04455i
$254$		0			0
$255$	−117.359	−	161.343i	−0.460231	−	0.632719i
$256$		0			0
$257$		−	157.838i		−	0.614157i	−0.951684	−	0.307079i	$-0.900649\pi$
$257$		−	157.838i		−	0.614157i	0.951684	−	0.307079i	$-0.0993515\pi$
$258$		0			0
$259$	−129.692	+	224.633i	−0.500742	+	0.867310i
$260$		0			0
$261$	−57.8561	−	270.721i	−0.221671	−	1.03725i
$262$		0			0
$263$			280.562i			1.06678i	0.845870	+	0.533389i	$0.179082\pi$
$263$			280.562i			1.06678i	−0.845870	+	0.533389i	$0.820918\pi$
$264$		0			0
$265$	−21.8540	−	37.8523i	−0.0824680	−	0.142839i
$266$		0			0
$267$	44.7906	+	423.903i	0.167755	+	1.58765i
$268$		0			0
$269$	−293.137	+	169.243i	−1.08973	+	0.629156i	−0.933505	−	0.358566i	$-0.883266\pi$
$269$	−293.137	+	169.243i	−1.08973	+	0.629156i	−0.156225	+	0.987721i	$0.549933\pi$
$270$		0			0
$271$	144.466	+	250.222i	0.533084	+	0.923329i	0.999253	+	0.0386333i	$0.0123004\pi$
$271$	144.466	+	250.222i	0.533084	+	0.923329i	−0.466169	+	0.884696i	$0.654366\pi$
$272$		0			0
$273$	−396.136	+	41.8567i	−1.45105	+	0.153321i
$274$		0			0
$275$		−	171.002i		−	0.621826i
$276$		0			0
$277$	−254.832	+	441.382i	−0.919971	+	1.59344i	−0.120515	+	0.992712i	$0.538454\pi$
$277$	−254.832	+	441.382i	−0.919971	+	1.59344i	−0.799456	+	0.600725i	$0.794879\pi$
$278$		0			0
$279$	152.769	−	32.6485i	0.547560	−	0.117020i
$280$		0			0
$281$	−350.515	+	202.370i	−1.24738	+	0.720178i	−0.970587	−	0.240751i	$-0.922606\pi$
$281$	−350.515	+	202.370i	−1.24738	+	0.720178i	−0.276797	+	0.960928i	$0.589273\pi$
$282$		0			0
$283$	184.711	−	319.929i	0.652689	−	1.13049i	−0.329779	−	0.944058i	$-0.606974\pi$
$283$	184.711	−	319.929i	0.652689	−	1.13049i	0.982468	−	0.186432i	$-0.0596925\pi$
$284$		0			0
$285$	−155.013	+	61.5306i	−0.543904	+	0.215897i
$286$		0			0
$287$	358.813	−	207.161i	1.25022	−	0.721814i
$288$		0			0
$289$	113.806	−	197.118i	0.393792	−	0.682068i
$290$		0			0
$291$	326.440	+	448.785i	1.12179	+	1.54222i
$292$		0			0
$293$	115.170	−	66.4934i	0.393071	−	0.226940i	−0.290419	−	0.956900i	$-0.593795\pi$
$293$	115.170	−	66.4934i	0.393071	−	0.226940i	0.683490	+	0.729960i	$0.260461\pi$
$294$		0			0
$295$	−31.8407	−	55.1497i	−0.107935	−	0.186948i
$296$		0			0
$297$	274.820	+	57.9392i	0.925320	+	0.195082i
$298$		0			0
$299$			718.064i			2.40155i
$300$		0			0
$301$	16.9706	−	29.3939i	0.0563807	−	0.0976543i
$302$		0			0
$303$	162.184	+	72.1015i	0.535260	+	0.237959i
$304$		0			0
$305$		−	327.802i		−	1.07476i
$306$		0			0
$307$	−49.3725	−	85.5156i	−0.160822	−	0.278552i	0.774341	−	0.632768i	$-0.218081\pi$
$307$	−49.3725	−	85.5156i	−0.160822	−	0.278552i	−0.935164	+	0.354215i	$0.884748\pi$
$308$		0			0
$309$	206.355	−	464.170i	0.667816	−	1.50217i
$310$		0			0
$311$	102.641	−	59.2596i	0.330034	−	0.190545i	−0.325822	−	0.945431i	$-0.605641\pi$
$311$	102.641	−	59.2596i	0.330034	−	0.190545i	0.655856	+	0.754886i	$0.272308\pi$
$312$		0			0
$313$	19.5446	+	33.8523i	0.0624429	+	0.108154i	0.895557	−	0.444947i	$-0.146778\pi$
$313$	19.5446	+	33.8523i	0.0624429	+	0.108154i	−0.833114	+	0.553101i	$0.813444\pi$
$314$		0			0
$315$	−29.8538	−	139.692i	−0.0947738	−	0.443467i
$316$		0			0
$317$	487.762	−	281.609i	1.53868	−	0.888358i	0.539764	−	0.841816i	$-0.318513\pi$
$317$	487.762	−	281.609i	1.53868	−	0.888358i	0.998916	−	0.0465417i	$-0.0148200\pi$
$318$		0			0
$319$	−319.967			−1.00303
$320$		0			0
$321$	−318.217	+	231.466i	−0.991329	+	0.721079i
$322$		0			0
$323$	−308.644	−	302.052i	−0.955555	−	0.935147i
$324$		0			0
$325$	201.193	+	348.477i	0.619057	+	1.07224i
$326$		0			0
$327$	−19.0616	+	42.8768i	−0.0582924	+	0.131122i
$328$		0			0
$329$		−	95.9789i		−	0.291729i
$330$		0			0
$331$	275.829	−	477.751i	0.833322	−	1.44336i	−0.0620679	−	0.998072i	$-0.519770\pi$
$331$	275.829	−	477.751i	0.833322	−	1.44336i	0.895390	−	0.445284i	$-0.146897\pi$
$332$		0			0
$333$	−132.534	+	409.435i	−0.397999	+	1.22953i
$334$		0			0
$335$	53.6292	+	30.9628i	0.160087	+	0.0924263i
$336$		0			0
$337$	−94.2874	+	163.311i	−0.279785	+	0.484601i	−0.971331	−	0.237731i	$-0.923596\pi$
$337$	−94.2874	+	163.311i	−0.279785	+	0.484601i	0.691546	+	0.722332i	$0.256930\pi$
$338$		0			0
$339$	64.8434	+	28.8273i	0.191279	+	0.0850362i
$340$		0			0
$341$		−	180.559i		−	0.529499i
$342$		0			0
$343$	−371.984			−1.08450
$344$		0			0
$345$	−256.075	+	27.0575i	−0.742246	+	0.0784275i
$346$		0			0
$347$	−578.131	−	333.784i	−1.66608	−	0.961914i	−0.969718	−	0.244226i	$-0.921466\pi$
$347$	−578.131	−	333.784i	−1.66608	−	0.961914i	−0.696365	−	0.717688i	$-0.745201\pi$
$348$		0			0
$349$	41.5364	−	71.9431i	0.119015	−	0.206141i	−0.800362	−	0.599517i	$-0.795360\pi$
$349$	41.5364	−	71.9431i	0.119015	−	0.206141i	0.919378	+	0.393376i	$0.128693\pi$
$350$		0			0
$351$	−628.212	+	205.269i	−1.78978	+	0.584813i
$352$		0			0
$353$	−220.283	−	127.181i	−0.624032	−	0.360285i	0.154405	−	0.988008i	$-0.450654\pi$
$353$	−220.283	−	127.181i	−0.624032	−	0.360285i	−0.778437	+	0.627722i	$0.783987\pi$
$354$		0			0
$355$	147.051			0.414229
$356$		0			0
$357$	299.123	−	217.578i	0.837880	−	0.609463i
$358$		0			0
$359$	−165.360	+	95.4709i	−0.460614	+	0.265936i	−0.712302	−	0.701873i	$-0.752347\pi$
$359$	−165.360	+	95.4709i	−0.460614	+	0.265936i	0.251688	+	0.967808i	$0.419014\pi$
$360$		0			0
$361$	−308.666	+	187.206i	−0.855031	+	0.518577i
$362$		0			0
$363$	−15.5905	+	35.0689i	−0.0429490	+	0.0966086i
$364$		0			0
$365$		−	40.4364i		−	0.110785i
$366$		0			0
$367$	−84.5427	−	146.432i	−0.230362	−	0.398998i	0.727553	−	0.686052i	$-0.240658\pi$
$367$	−84.5427	−	146.432i	−0.230362	−	0.398998i	−0.957915	+	0.287053i	$0.907324\pi$
$368$		0			0
$369$	510.338	−	460.531i	1.38303	−	1.24805i
$370$		0			0
$371$	70.1765	−	40.5164i	0.189155	−	0.109209i
$372$		0			0
$373$	188.822	+	327.049i	0.506225	+	0.876808i	0.999974	+	0.00720342i	$0.00229294\pi$
$373$	188.822	+	327.049i	0.506225	+	0.876808i	−0.493749	+	0.869605i	$0.664374\pi$
$374$		0			0
$375$	−294.156	+	213.965i	−0.784415	+	0.570573i
$376$		0			0
$377$	652.047	−	376.459i	1.72957	−	0.998566i
$378$		0			0
$379$	673.545			1.77716			0.888581	−	0.458719i	$-0.151692\pi$
$379$	673.545			1.77716			0.888581	+	0.458719i	$0.151692\pi$
$380$		0			0
$381$	245.242	−	25.9129i	0.643681	−	0.0680129i
$382$		0			0
$383$	45.6149	+	26.3358i	0.119099	+	0.0687618i	0.558366	−	0.829595i	$-0.311428\pi$
$383$	45.6149	+	26.3358i	0.119099	+	0.0687618i	−0.439267	+	0.898357i	$0.644762\pi$
$384$		0			0
$385$	−165.103			−0.428840
$386$		0			0
$387$	17.3424	−	53.5757i	0.0448125	−	0.138439i
$388$		0			0
$389$	76.4930	−	44.1633i	0.196640	−	0.113530i	−0.398447	−	0.917191i	$-0.630451\pi$
$389$	76.4930	−	44.1633i	0.196640	−	0.113530i	0.595087	+	0.803661i	$0.297117\pi$
$390$		0			0
$391$	−333.384	−	577.438i	−0.852644	−	1.47682i
$392$		0			0
$393$	25.0135	+	236.730i	0.0636475	+	0.602366i
$394$		0			0
$395$	3.30645	+	1.90898i	0.00837077	+	0.00483287i
$396$		0			0
$397$	50.6046	+	87.6498i	0.127468	+	0.220780i	0.922695	−	0.385531i	$-0.125982\pi$
$397$	50.6046	+	87.6498i	0.127468	+	0.220780i	−0.795227	+	0.606312i	$0.792648\pi$
$398$		0			0
$399$	−114.075	−	287.387i	−0.285902	−	0.720267i
$400$		0			0
$401$	−34.5487	−	19.9467i	−0.0861563	−	0.0497423i	0.456303	−	0.889825i	$-0.349173\pi$
$401$	−34.5487	−	19.9467i	−0.0861563	−	0.0497423i	−0.542459	+	0.840082i	$0.682507\pi$
$402$		0			0
$403$	212.438	+	367.953i	0.527141	+	0.913035i
$404$		0			0
$405$	−96.8747	−	216.297i	−0.239197	−	0.534067i
$406$		0			0
$407$	430.763	+	248.701i	1.05839	+	0.611060i
$408$		0			0
$409$	136.057			0.332657			0.166329	−	0.986070i	$-0.446809\pi$
$409$	136.057			0.332657			0.166329	+	0.986070i	$0.446809\pi$
$410$		0			0
$411$	127.603	+	56.7283i	0.310471	+	0.138025i
$412$		0			0
$413$	102.245	−	59.0312i	0.247567	−	0.142933i
$414$		0			0
$415$	111.888	+	193.797i	0.269611	+	0.466980i
$416$		0			0
$417$	−130.510	−	179.423i	−0.312973	−	0.430270i
$418$		0			0
$419$	−434.800	+	251.032i	−1.03771	+	0.599122i	−0.919184	−	0.393830i	$-0.871150\pi$
$419$	−434.800	+	251.032i	−1.03771	+	0.599122i	−0.118525	+	0.992951i	$0.537817\pi$
$420$		0			0
$421$	−176.166			−0.418446			−0.209223	−	0.977868i	$-0.567093\pi$
$421$	−176.166			−0.418446			−0.209223	+	0.977868i	$0.567093\pi$
$422$		0			0
$423$	−33.2800	−	155.725i	−0.0786762	−	0.368143i
$424$		0			0
$425$	−323.583	−	186.821i	−0.761373	−	0.439579i
$426$		0			0
$427$	607.729			1.42325
$428$		0			0
$429$	80.2657	+	759.642i	0.187099	+	1.77073i
$430$		0			0
$431$	−168.235	−	97.1304i	−0.390336	−	0.225361i	0.291970	−	0.956428i	$-0.405689\pi$
$431$	−168.235	−	97.1304i	−0.390336	−	0.225361i	−0.682306	+	0.731067i	$0.739023\pi$
$432$		0			0
$433$	306.183	−	530.324i	0.707120	−	1.22477i	−0.258802	−	0.965931i	$-0.583328\pi$
$433$	306.183	−	530.324i	0.707120	−	1.22477i	0.965921	−	0.258837i	$-0.0833391\pi$
$434$		0			0
$435$	158.822	+	218.347i	0.365109	+	0.501946i
$436$		0			0
$437$	−536.793	+	150.061i	−1.22836	+	0.343390i
$438$		0			0
$439$	−171.777			−0.391292			−0.195646	−	0.980675i	$-0.562680\pi$
$439$	−171.777			−0.391292			−0.195646	+	0.980675i	$0.562680\pi$
$440$		0			0
$441$	−172.278	+	36.8178i	−0.390654	+	0.0834870i
$442$		0			0
$443$	199.252	−	115.038i	0.449780	−	0.259680i	−0.257957	−	0.966156i	$-0.583049\pi$
$443$	199.252	−	115.038i	0.449780	−	0.259680i	0.707737	+	0.706476i	$0.249716\pi$
$444$		0			0
$445$	−207.869	−	360.040i	−0.467122	−	0.809079i
$446$		0			0
$447$	−62.2180	−	588.837i	−0.139190	−	1.31731i
$448$		0			0
$449$			443.639i			0.988061i	0.869445	+	0.494031i	$0.164477\pi$
$449$			443.639i			0.988061i	−0.869445	+	0.494031i	$0.835523\pi$
$450$		0			0
$451$	−397.257	−	688.070i	−0.880837	−	1.52565i
$452$		0			0
$453$	−623.474	+	65.8778i	−1.37632	+	0.145426i
$454$		0			0
$455$	336.456	−	194.253i	0.739465	−	0.426930i
$456$		0			0
$457$	372.974	−	646.009i	0.816135	−	1.41359i	−0.0923753	−	0.995724i	$-0.529446\pi$
$457$	372.974	−	646.009i	0.816135	−	1.41359i	0.908510	−	0.417863i	$-0.137221\pi$
$458$		0			0
$459$	409.880	−	456.737i	0.892985	−	0.995069i
$460$		0			0
$461$			250.804i			0.544043i	0.962291	+	0.272021i	$0.0876921\pi$
$461$			250.804i			0.544043i	−0.962291	+	0.272021i	$0.912308\pi$
$462$		0			0
$463$	83.5338	+	144.685i	0.180419	+	0.312494i	0.942023	−	0.335548i	$-0.108921\pi$
$463$	83.5338	+	144.685i	0.180419	+	0.312494i	−0.761605	+	0.648042i	$0.775588\pi$
$464$		0			0
$465$	−123.214	+	89.6242i	−0.264976	+	0.192740i
$466$		0			0
$467$			438.133i			0.938186i	0.883149	+	0.469093i	$0.155419\pi$
$467$			438.133i			0.938186i	−0.883149	+	0.469093i	$0.844581\pi$
$468$		0			0
$469$	−57.4037	+	99.4261i	−0.122396	+	0.211996i
$470$		0			0
$471$	−129.552	+	13.6887i	−0.275057	+	0.0290632i
$472$		0			0
$473$	−56.3667	−	32.5433i	−0.119168	−	0.0688020i
$474$		0			0
$475$	−218.461	+	223.228i	−0.459917	+	0.469954i
$476$		0			0
$477$	99.8116	−	90.0705i	0.209249	−	0.188827i
$478$		0			0
$479$	−20.0713	+	11.5882i	−0.0419025	+	0.0241924i	−0.520805	−	0.853676i	$-0.674368\pi$
$479$	−20.0713	+	11.5882i	−0.0419025	+	0.0241924i	0.478902	+	0.877868i	$0.341035\pi$
$480$		0			0
$481$	−1170.44			−2.43336
$482$		0			0
$483$	−50.1634	−	474.751i	−0.103858	−	0.982922i
$484$		0			0
$485$	−468.736	−	270.625i	−0.966466	−	0.557989i
$486$		0			0
$487$	−412.683			−0.847399			−0.423700	−	0.905803i	$-0.639269\pi$
$487$	−412.683			−0.847399			−0.423700	+	0.905803i	$0.639269\pi$
$488$		0			0
$489$	−474.504	−	652.342i	−0.970357	−	1.33403i
$490$		0			0
$491$	218.449	+	126.121i	0.444905	+	0.256866i	0.705676	−	0.708535i	$-0.250643\pi$
$491$	218.449	+	126.121i	0.444905	+	0.256866i	−0.260771	+	0.965401i	$0.583977\pi$
$492$		0			0
$493$	−349.566	+	605.467i	−0.709060	+	1.22813i
$494$		0			0
$495$	−267.878	+	57.2485i	−0.541168	+	0.115653i
$496$		0			0
$497$			272.626i			0.548544i
$498$		0			0
$499$	−139.364	+	241.385i	−0.279286	+	0.483738i	−0.971207	−	0.238235i	$-0.923431\pi$
$499$	−139.364	+	241.385i	−0.279286	+	0.483738i	0.691921	+	0.721973i	$0.256764\pi$
$500$		0			0
$501$	781.404	−	568.382i	1.55969	−	1.13450i
$502$		0			0
$503$	−397.715	−	229.621i	−0.790685	−	0.456502i	0.0495184	−	0.998773i	$-0.484231\pi$
$503$	−397.715	−	229.621i	−0.790685	−	0.456502i	−0.840204	+	0.542271i	$0.817565\pi$
$504$		0			0
$505$	−173.106			−0.342785
$506$		0			0
$507$	−759.097	−	1043.60i	−1.49723	−	2.05837i
$508$		0			0
$509$			116.649i			0.229173i	0.993413	+	0.114586i	$0.0365543\pi$
$509$			116.649i			0.229173i	−0.993413	+	0.114586i	$0.963446\pi$
$510$		0			0
$511$	74.9674			0.146707
$512$		0			0
$513$	−284.734	−	426.726i	−0.555038	−	0.831825i
$514$		0			0
$515$			495.431i			0.962003i
$516$		0			0
$517$	−184.052			−0.356000
$518$		0			0
$519$	86.1509	−	62.6650i	0.165994	−	0.120742i
$520$		0			0
$521$		−	280.254i		−	0.537916i	−0.963152	−	0.268958i	$-0.913321\pi$
$521$		−	280.254i		−	0.537916i	0.963152	−	0.268958i	$-0.0866793\pi$
$522$		0			0
$523$	51.0370	−	88.3987i	0.0975851	−	0.169022i	−0.813099	−	0.582125i	$-0.802222\pi$
$523$	51.0370	−	88.3987i	0.0975851	−	0.169022i	0.910685	+	0.413102i	$0.135555\pi$
$524$		0			0
$525$	−157.364	−	216.342i	−0.299742	−	0.412081i
$526$		0			0
$527$	−341.668	−	197.262i	−0.648326	−	0.374311i
$528$		0			0
$529$	−331.567			−0.626781
$530$		0			0
$531$	145.423	−	131.230i	0.273866	−	0.247138i
$532$		0			0
$533$	1619.11	+	934.791i	3.03772	+	1.75383i
$534$		0			0
$535$	191.890	−	332.363i	0.358673	−	0.621240i
$536$		0			0
$537$	−519.323	+	377.749i	−0.967082	+	0.703443i
$538$		0			0
$539$			203.617i			0.377768i
$540$		0			0
$541$	−376.134	+	651.483i	−0.695257	+	1.20422i	0.274837	+	0.961491i	$0.411376\pi$
$541$	−376.134	+	651.483i	−0.695257	+	1.20422i	−0.970094	+	0.242729i	$0.921957\pi$
$542$		0			0
$543$	−243.933	+	25.7746i	−0.449232	+	0.0474670i
$544$		0			0
$545$		−	45.7645i		−	0.0839715i
$546$		0			0
$547$	327.909	+	567.955i	0.599468	+	1.03831i	0.992900	+	0.118955i	$0.0379545\pi$
$547$	327.909	+	567.955i	0.599468	+	1.03831i	−0.393431	+	0.919354i	$0.628712\pi$
$548$		0			0
$549$	986.033	−	210.726i	1.79605	−	0.383836i
$550$		0			0
$551$	417.689	+	408.769i	0.758057	+	0.741867i
$552$		0			0
$553$	−3.53917	+	6.13002i	−0.00639994	+	0.0110850i
$554$		0			0
$555$	−44.1037	−	417.402i	−0.0794662	−	0.752076i
$556$		0			0
$557$	497.328	+	287.133i	0.892870	+	0.515498i	0.874880	−	0.484340i	$-0.160940\pi$
$557$	497.328	+	287.133i	0.892870	+	0.515498i	0.0179895	+	0.999838i	$0.494273\pi$
$558$		0			0
$559$	153.156			0.273982
$560$		0			0
$561$	−417.234	−	573.608i	−0.743733	−	1.02247i
$562$		0			0
$563$	−773.883	+	446.801i	−1.37457	+	0.793608i	−0.991499	−	0.130111i	$-0.958467\pi$
$563$	−773.883	+	446.801i	−1.37457	+	0.793608i	−0.383070	+	0.923719i	$0.625133\pi$
$564$		0			0
$565$	−69.2105			−0.122497
$566$		0			0
$567$	401.005	−	179.601i	0.707241	−	0.316757i
$568$		0			0
$569$	−337.331	−	194.758i	−0.592848	−	0.342281i	0.173375	−	0.984856i	$-0.444533\pi$
$569$	−337.331	−	194.758i	−0.592848	−	0.342281i	−0.766223	+	0.642575i	$0.777866\pi$
$570$		0			0
$571$	61.1358	+	105.890i	0.107068	+	0.185447i	0.914581	−	0.404402i	$-0.132520\pi$
$571$	61.1358	+	105.890i	0.107068	+	0.185447i	−0.807513	+	0.589849i	$0.799187\pi$
$572$		0			0
$573$	103.401	+	978.600i	0.180456	+	1.70785i
$574$		0			0
$575$	−417.634	+	241.121i	−0.726321	+	0.419342i
$576$		0			0
$577$	−927.013			−1.60661			−0.803304	−	0.595569i	$-0.796926\pi$
$577$	−927.013			−1.60661			−0.803304	+	0.595569i	$0.796926\pi$
$578$		0			0
$579$	655.350	−	69.2459i	1.13186	−	0.119596i
$580$		0			0
$581$	−359.290	+	207.436i	−0.618399	+	0.357033i
$582$		0			0
$583$	−77.6954	−	134.572i	−0.133268	−	0.230828i
$584$		0			0
$585$	478.540	−	431.837i	0.818017	−	0.738183i
$586$		0			0
$587$		−	530.684i		−	0.904062i	−0.892002	−	0.452031i	$-0.850700\pi$
$587$		−	530.684i		−	0.904062i	0.892002	−	0.452031i	$-0.149300\pi$
$588$		0			0
$589$	−230.670	+	235.704i	−0.391630	+	0.400177i
$590$		0			0
$591$	392.611	−	285.580i	0.664317	−	0.483215i
$592$		0			0
$593$	486.494	+	280.878i	0.820395	+	0.473655i	0.850553	−	0.525890i	$-0.176268\pi$
$593$	486.494	+	280.878i	0.820395	+	0.473655i	−0.0301577	+	0.999545i	$0.509601\pi$
$594$		0			0
$595$	−180.376	+	312.421i	−0.303154	+	0.525078i
$596$		0			0
$597$	−221.115	+	23.3635i	−0.370377	+	0.0391349i
$598$		0			0
$599$		−	639.542i		−	1.06768i	−0.845584	−	0.533842i	$-0.820748\pi$
$599$		−	639.542i		−	1.06768i	0.845584	−	0.533842i	$-0.179252\pi$
$600$		0			0
$601$	−248.581	+	430.555i	−0.413612	+	0.716397i	−0.995282	−	0.0970281i	$-0.969066\pi$
$601$	−248.581	+	430.555i	−0.413612	+	0.716397i	0.581670	+	0.813425i	$0.302400\pi$
$602$		0			0
$603$	−58.6614	+	181.222i	−0.0972826	+	0.300534i
$604$		0			0
$605$		−	37.4308i		−	0.0618690i
$606$		0			0
$607$	55.0624	+	95.3708i	0.0907123	+	0.157118i	0.907811	−	0.419379i	$-0.137752\pi$
$607$	55.0624	+	95.3708i	0.0907123	+	0.157118i	−0.817099	+	0.576498i	$0.804419\pi$
$608$		0			0
$609$	−404.805	+	294.449i	−0.664704	+	0.483497i
$610$		0			0
$611$	375.071	−	216.547i	0.613864	−	0.354415i
$612$		0			0
$613$	−51.6325	−	89.4302i	−0.0842293	−	0.145889i	0.820833	−	0.571168i	$-0.193509\pi$
$613$	−51.6325	−	89.4302i	−0.0842293	−	0.145889i	−0.905063	+	0.425279i	$0.860176\pi$
$614$		0			0
$615$	−272.354	+	612.627i	−0.442852	+	0.996142i
$616$		0			0
$617$			109.410i			0.177325i	0.996062	+	0.0886627i	$0.0282593\pi$
$617$			109.410i			0.177325i	−0.996062	+	0.0886627i	$0.971741\pi$
$618$		0			0
$619$	−280.995	+	486.697i	−0.453950	+	0.786264i	−0.998627	−	0.0523816i	$-0.983319\pi$
$619$	−280.995	+	486.697i	−0.453950	+	0.786264i	0.544677	+	0.838646i	$0.316652\pi$
$620$		0			0
$621$	−246.006	−	752.884i	−0.396145	−	1.21237i
$622$		0			0
$623$	667.498	−	385.380i	1.07143	−	0.618588i
$624$		0			0
$625$	−28.1056	+	48.6804i	−0.0449690	+	0.0778887i
$626$		0			0
$627$	−551.101	+	218.753i	−0.878949	+	0.348889i
$628$		0			0
$629$	941.224	−	543.416i	1.49638	−	0.863936i
$630$		0			0
$631$	−310.083	+	537.079i	−0.491415	+	0.851155i	−0.999951	−	0.00988537i	$-0.996853\pi$
$631$	−310.083	+	537.079i	−0.491415	+	0.851155i	0.508537	+	0.861040i	$0.330187\pi$
$632$		0			0
$633$	−371.365	+	39.2394i	−0.586675	+	0.0619895i
$634$		0			0
$635$	−208.296	+	120.259i	−0.328024	+	0.189385i
$636$		0			0
$637$	−239.567	−	414.942i	−0.376086	−	0.651400i
$638$		0			0
$639$	94.5313	+	442.332i	0.147936	+	0.692226i
$640$		0			0
$641$		−	150.952i		−	0.235495i	−0.993044	−	0.117748i	$-0.962433\pi$
$641$		−	150.952i		−	0.235495i	0.993044	−	0.117748i	$-0.0375673\pi$
$642$		0			0
$643$	23.7325	−	41.1058i	0.0369089	−	0.0639282i	−0.846981	−	0.531623i	$-0.821582\pi$
$643$	23.7325	−	41.1058i	0.0369089	−	0.0639282i	0.883890	+	0.467695i	$0.154916\pi$
$644$		0			0
$645$	5.77111	+	54.6183i	0.00894745	+	0.0846796i
$646$		0			0
$647$			36.8284i			0.0569218i	0.999595	+	0.0284609i	$0.00906061\pi$
$647$			36.8284i			0.0569218i	−0.999595	+	0.0284609i	$0.990939\pi$
$648$		0			0
$649$	−113.200	−	196.068i	−0.174422	−	0.302108i
$650$		0			0
$651$	−166.159	−	228.433i	−0.255237	−	0.350896i
$652$		0			0
$653$	−336.741	+	194.418i	−0.515684	+	0.297730i	−0.735167	−	0.677886i	$-0.762896\pi$
$653$	−336.741	+	194.418i	−0.515684	+	0.297730i	0.219483	+	0.975616i	$0.429563\pi$
$654$		0			0
$655$	−116.085	−	201.065i	−0.177229	−	0.306970i
$656$		0			0
$657$	121.634	−	25.9944i	0.185135	−	0.0395653i
$658$		0			0
$659$	−27.7225	+	16.0056i	−0.0420676	+	0.0242877i	−0.520886	−	0.853626i	$-0.674398\pi$
$659$	−27.7225	+	16.0056i	−0.0420676	+	0.0242877i	0.478819	+	0.877914i	$0.341065\pi$
$660$		0			0
$661$	49.2240			0.0744690			0.0372345	−	0.999307i	$-0.488145\pi$
$661$	49.2240			0.0744690			0.0372345	+	0.999307i	$0.488145\pi$
$662$		0			0
$663$	1525.14	+	678.029i	2.30037	+	1.02267i
$664$		0			0
$665$	215.528	+	210.925i	0.324102	+	0.317180i
$666$		0			0
$667$	451.170	+	781.449i	0.676416	+	1.17159i
$668$		0			0
$669$	565.464	+	777.391i	0.845238	+	1.16202i
$670$		0			0
$671$		−	1165.40i		−	1.73681i
$672$		0			0
$673$	386.780	−	669.922i	0.574710	−	0.995426i	−0.421363	−	0.906892i	$-0.638448\pi$
$673$	386.780	−	669.922i	0.574710	−	0.995426i	0.996073	−	0.0885345i	$-0.0282184\pi$
$674$		0			0
$675$	−330.337	−	296.448i	−0.489388	−	0.439182i
$676$		0			0
$677$	1071.11	+	618.403i	1.58214	+	0.913446i	0.994547	+	0.104286i	$0.0332556\pi$
$677$	1071.11	+	618.403i	1.58214	+	0.913446i	0.587588	+	0.809160i	$0.300078\pi$
$678$		0			0
$679$	501.726	−	869.015i	0.738919	−	1.27985i
$680$		0			0
$681$	49.9638	+	472.863i	0.0733683	+	0.694365i
$682$		0			0
$683$		−	234.238i		−	0.342955i	−0.985188	−	0.171478i	$-0.945146\pi$
$683$		−	234.238i		−	0.342955i	0.985188	−	0.171478i	$-0.0548541\pi$
$684$		0			0
$685$	−136.197			−0.198828
$686$		0			0
$687$	−302.558	+	680.568i	−0.440405	+	0.990637i
$688$		0			0
$689$	316.664	+	182.826i	0.459599	+	0.265350i
$690$		0			0
$691$	284.313	−	492.445i	0.411452	−	0.712655i	−0.583597	−	0.812043i	$-0.698355\pi$
$691$	284.313	−	492.445i	0.411452	−	0.712655i	0.995049	+	0.0993883i	$0.0316886\pi$
$692$		0			0
$693$	−106.136	−	496.634i	−0.153154	−	0.716643i
$694$		0			0
$695$	187.399	+	108.195i	0.269639	+	0.155676i
$696$		0			0
$697$	−1736.03			−2.49071
$698$		0			0
$699$	−877.199	−	389.974i	−1.25493	−	0.557903i
$700$		0			0
$701$	1031.29	−	595.416i	1.47117	−	0.849381i	0.471696	−	0.881761i	$-0.343642\pi$
$701$	1031.29	−	595.416i	1.47117	−	0.849381i	0.999476	+	0.0323797i	$0.0103086\pi$
$702$		0			0
$703$	−244.600	−	874.972i	−0.347937	−	1.24463i
$704$		0			0
$705$	91.3580	+	125.598i	0.129586	+	0.178153i
$706$		0			0
$707$		−	320.932i		−	0.453934i
$708$		0			0
$709$	599.530	+	1038.42i	0.845599	+	1.46462i	0.885100	+	0.465401i	$0.154090\pi$
$709$	599.530	+	1038.42i	0.845599	+	1.46462i	−0.0395008	+	0.999220i	$0.512577\pi$
$710$		0			0
$711$	−3.61671	+	11.1731i	−0.00508679	+	0.0157146i
$712$		0			0
$713$	−440.976	+	254.597i	−0.618479	+	0.357079i
$714$		0			0
$715$	−372.506	−	645.199i	−0.520987	−	0.902376i
$716$		0			0
$717$	−41.1589	−	18.2979i	−0.0574043	−	0.0255201i
$718$		0			0
$719$	−911.986	+	526.535i	−1.26841	+	0.732316i	−0.974687	−	0.223574i	$-0.928227\pi$
$719$	−911.986	+	526.535i	−1.26841	+	0.732316i	−0.293722	+	0.955891i	$0.594894\pi$
$720$		0			0
$721$	−918.508			−1.27394
$722$		0			0
$723$	55.7821	−	125.475i	0.0771536	−	0.173548i
$724$		0			0
$725$	437.907	+	252.826i	0.604009	+	0.348725i
$726$		0			0
$727$	876.971			1.20629			0.603143	−	0.797633i	$-0.293915\pi$
$727$	876.971			1.20629			0.603143	+	0.797633i	$0.293915\pi$
$728$		0			0
$729$	588.351	−	430.447i	0.807065	−	0.590462i
$730$		0			0
$731$	−123.162	+	71.1076i	−0.168484	+	0.0972744i
$732$		0			0
$733$	517.161	+	895.748i	0.705540	+	1.22203i	0.966496	+	0.256680i	$0.0826287\pi$
$733$	517.161	+	895.748i	0.705540	+	1.22203i	−0.260957	+	0.965351i	$0.584038\pi$
$734$		0			0
$735$	138.949	−	101.070i	0.189046	−	0.137510i
$736$		0			0
$737$	190.662	+	110.079i	0.258701	+	0.149361i
$738$		0			0
$739$	−349.864	−	605.982i	−0.473429	−	0.820003i	0.526108	−	0.850418i	$-0.323651\pi$
$739$	−349.864	−	605.982i	−0.473429	−	0.820003i	−0.999537	+	0.0304143i	$0.990317\pi$
$740$		0			0
$741$	865.687	−	1094.19i	1.16827	−	1.47664i
$742$		0			0
$743$	−766.665	−	442.634i	−1.03185	−	0.595739i	−0.114336	−	0.993442i	$-0.536474\pi$
$743$	−766.665	−	442.634i	−1.03185	−	0.595739i	−0.917514	+	0.397703i	$0.869808\pi$
$744$		0			0
$745$	288.748	+	500.126i	0.387581	+	0.671310i
$746$		0			0
$747$	−511.016	+	461.144i	−0.684092	+	0.617328i
$748$		0			0
$749$	616.187	+	355.756i	0.822679	+	0.474974i
$750$		0			0
$751$	1294.48			1.72368			0.861840	−	0.507181i	$-0.169312\pi$
$751$	1294.48			1.72368			0.861840	+	0.507181i	$0.169312\pi$
$752$		0			0
$753$	−111.462	−	1054.88i	−0.148023	−	1.40091i
$754$		0			0
$755$	529.545	−	305.733i	0.701384	−	0.404944i
$756$		0			0
$757$	−80.2906	−	139.067i	−0.106064	−	0.183708i	0.808108	−	0.589034i	$-0.200492\pi$
$757$	−80.2906	−	139.067i	−0.106064	−	0.183708i	−0.914172	+	0.405325i	$0.867158\pi$
$758$		0			0
$759$	−910.397	+	96.1948i	−1.19947	+	0.126739i
$760$		0			0
$761$	−396.859	+	229.127i	−0.521497	+	0.301087i	−0.737547	−	0.675296i	$-0.764016\pi$
$761$	−396.859	+	229.127i	−0.521497	+	0.301087i	0.216050	+	0.976382i	$0.430683\pi$
$762$		0			0
$763$	84.8453			0.111200
$764$		0			0
$765$	−184.329	+	569.444i	−0.240952	+	0.744371i
$766$		0			0
$767$	461.370	+	266.372i	0.601526	+	0.347291i
$768$		0			0
$769$	175.710			0.228492			0.114246	−	0.993453i	$-0.463555\pi$
$769$	175.710			0.228492			0.114246	+	0.993453i	$0.463555\pi$
$770$		0			0
$771$	−382.928	+	278.537i	−0.496664	+	0.361267i
$772$		0			0
$773$	936.670	+	540.787i	1.21173	+	0.699595i	0.963137	−	0.269012i	$-0.0866971\pi$
$773$	936.670	+	540.787i	1.21173	+	0.699595i	0.248597	+	0.968607i	$0.420030\pi$
$774$		0			0
$775$	−142.671	+	247.113i	−0.184091	+	0.318855i
$776$		0			0
$777$	773.845	−	81.7663i	0.995939	−	0.105233i
$778$		0			0
$779$	−360.447	+	1405.72i	−0.462705	+	1.80452i
$780$		0			0
$781$	522.796			0.669393
$782$		0			0
$783$	−554.692	+	618.104i	−0.708419	+	0.789404i
$784$		0			0
$785$	110.034	−	63.5282i	0.140171	−	0.0809277i
$786$		0			0
$787$	143.087	+	247.834i	0.181813	+	0.314910i	0.942498	−	0.334212i	$-0.108470\pi$
$787$	143.087	+	247.834i	0.181813	+	0.314910i	−0.760685	+	0.649121i	$0.775137\pi$
$788$		0			0
$789$	680.666	−	495.107i	0.862695	−	0.627512i
$790$		0			0
$791$		−	128.313i		−	0.162216i
$792$		0			0
$793$	1371.16	+	2374.91i	1.72908	+	2.99485i
$794$		0			0
$795$	−53.2669	+	119.817i	−0.0670024	+	0.150714i
$796$		0			0
$797$	207.738	−	119.938i	0.260650	−	0.150487i	−0.363981	−	0.931406i	$-0.618583\pi$
$797$	207.738	−	119.938i	0.260650	−	0.150487i	0.624631	+	0.780920i	$0.285249\pi$
$798$		0			0
$799$	−201.078	+	348.277i	−0.251662	+	0.435892i
$800$		0			0
$801$	949.379	−	856.725i	1.18524	−	1.06957i
$802$		0			0
$803$		−	143.760i		−	0.179028i
$804$		0			0
$805$	232.804	+	403.228i	0.289197	+	0.500904i
$806$		0			0
$807$	927.894	+	412.512i	1.14981	+	0.511167i
$808$		0			0
$809$			69.4467i			0.0858426i	0.999078	+	0.0429213i	$0.0136665\pi$
$809$			69.4467i			0.0858426i	−0.999078	+	0.0429213i	$0.986334\pi$
$810$		0			0
$811$	−5.39295	+	9.34086i	−0.00664975	+	0.0115177i	−0.869331	−	0.494230i	$-0.835450\pi$
$811$	−5.39295	+	9.34086i	−0.00664975	+	0.0115177i	0.862681	+	0.505748i	$0.168783\pi$
$812$		0			0
$813$	352.120	−	792.051i	0.433112	−	0.974232i
$814$		0			0
$815$	681.342	+	393.373i	0.836003	+	0.482666i
$816$		0			0
$817$	32.0066	+	114.493i	0.0391758	+	0.140138i
$818$		0			0
$819$	800.607	+	887.192i	0.977542	+	1.08326i
$820$		0			0
$821$	−383.062	+	221.161i	−0.466580	+	0.269380i	−0.714807	−	0.699322i	$-0.753485\pi$
$821$	−383.062	+	221.161i	−0.466580	+	0.269380i	0.248227	+	0.968702i	$0.420152\pi$
$822$		0			0
$823$	−21.7579			−0.0264374			−0.0132187	−	0.999913i	$-0.504208\pi$
$823$	−21.7579			−0.0264374			−0.0132187	+	0.999913i	$0.504208\pi$
$824$		0			0
$825$	−414.864	+	301.767i	−0.502866	+	0.365778i
$826$		0			0
$827$	−556.307	−	321.184i	−0.672681	−	0.388372i	0.124411	−	0.992231i	$-0.460296\pi$
$827$	−556.307	−	321.184i	−0.672681	−	0.388372i	−0.797092	+	0.603858i	$0.793629\pi$
$828$		0			0
$829$	−540.967			−0.652554			−0.326277	−	0.945274i	$-0.605794\pi$
$829$	−540.967			−0.652554			−0.326277	+	0.945274i	$0.605794\pi$
$830$		0			0
$831$	1520.53	−	160.663i	1.82976	−	0.193336i
$832$		0			0
$833$	385.300	+	222.453i	0.462545	+	0.267051i
$834$		0			0
$835$	−471.200	+	816.142i	−0.564311	+	0.977416i
$836$		0			0
$837$	−348.799	−	313.016i	−0.416725	−	0.373973i
$838$		0			0
$839$		−	1098.29i		−	1.30905i	−0.756042	−	0.654523i	$-0.772870\pi$
$839$		−	1098.29i		−	1.30905i	0.756042	−	0.654523i	$-0.227130\pi$
$840$		0			0
$841$	52.5696	−	91.0532i	0.0625084	−	0.108268i
$842$		0			0
$843$	1109.52	+	493.255i	1.31615	+	0.585119i
$844$		0			0
$845$	1089.99	+	629.306i	1.28993	+	0.744741i
$846$		0			0
$847$	69.3949			0.0819303
$848$		0			0
$849$	−1102.13	+	116.454i	−1.29815	+	0.137166i
$850$		0			0
$851$		−	1402.72i		−	1.64833i
$852$		0			0
$853$	−272.054			−0.318938			−0.159469	−	0.987203i	$-0.550978\pi$
$853$	−272.054			−0.318938			−0.159469	+	0.987203i	$0.550978\pi$
$854$		0			0
$855$	422.828	+	267.490i	0.494536	+	0.312854i
$856$		0			0
$857$			1043.71i			1.21787i	0.793220	+	0.608935i	$0.208403\pi$
$857$			1043.71i			1.21787i	−0.793220	+	0.608935i	$0.791597\pi$
$858$		0			0
$859$	−1078.69			−1.25576			−0.627878	−	0.778312i	$-0.716076\pi$
$859$	−1078.69			−1.25576			−0.627878	+	0.778312i	$0.716076\pi$
$860$		0			0
$861$	−1135.78	−	504.932i	−1.31914	−	0.586448i
$862$		0			0
$863$		−	613.165i		−	0.710504i	−0.934771	−	0.355252i	$-0.884395\pi$
$863$		−	613.165i		−	0.710504i	0.934771	−	0.355252i	$-0.115605\pi$
$864$		0			0
$865$	−51.9505	+	89.9809i	−0.0600583	+	0.104024i
$866$		0			0
$867$	−679.056	+	71.7507i	−0.783225	+	0.0827574i
$868$		0			0
$869$	11.7551	+	6.78681i	0.0135272	+	0.00780991i
$870$		0			0
$871$	−518.056			−0.594783
$872$		0			0
$873$	512.719	−	1583.94i	0.587307	−	1.81436i
$874$		0			0
$875$	569.596	+	328.856i	0.650967	+	0.375836i
$876$		0			0
$877$	−172.712	+	299.146i	−0.196935	+	0.341102i	−0.947533	−	0.319657i	$-0.896432\pi$
$877$	−172.712	+	299.146i	−0.196935	+	0.341102i	0.750598	+	0.660759i	$0.229766\pi$
$878$		0			0
$879$	−364.558	−	162.071i	−0.414742	−	0.184381i
$880$		0			0
$881$		−	452.169i		−	0.513245i	−0.966512	−	0.256623i	$-0.917390\pi$
$881$		−	452.169i		−	0.513245i	0.966512	−	0.256623i	$-0.0826098\pi$
$882$		0			0
$883$	40.2017	−	69.6314i	0.0455285	−	0.0788577i	−0.842363	−	0.538910i	$-0.818836\pi$
$883$	40.2017	−	69.6314i	0.0455285	−	0.0788577i	0.887892	+	0.460053i	$0.152169\pi$
$884$		0			0
$885$	−77.6083	+	174.570i	−0.0876930	+	0.197255i
$886$		0			0
$887$			1446.02i			1.63024i	0.579290	+	0.815121i	$0.303330\pi$
$887$			1446.02i			1.63024i	−0.579290	+	0.815121i	$0.696670\pi$
$888$		0			0
$889$	−222.956	−	386.171i	−0.250794	−	0.434388i
$890$		0			0
$891$	−344.409	−	768.980i	−0.386542	−	0.863053i
$892$		0			0
$893$	240.264	+	235.132i	0.269052	+	0.263306i
$894$		0			0
$895$	313.161	−	542.410i	0.349900	−	0.606045i
$896$		0			0
$897$	1742.08	−	1267.16i	1.94212	−	1.41267i
$898$		0			0
$899$	462.381	+	266.956i	0.514328	+	0.296947i
$900$		0			0
$901$	−339.531			−0.376838
$902$		0			0
$903$	−101.260	+	10.6994i	−0.112137	+	0.0118487i
$904$		0			0
$905$	207.183	−	119.617i	0.228932	−	0.132174i
$906$		0			0
$907$	1675.42			1.84721			0.923606	−	0.383344i	$-0.125228\pi$
$907$	1675.42			1.84721			0.923606	+	0.383344i	$0.125228\pi$
$908$		0			0
$909$	−111.281	−	520.707i	−0.122421	−	0.572835i
$910$		0			0
$911$	−51.2037	−	29.5624i	−0.0562060	−	0.0324505i	0.471634	−	0.881795i	$-0.343664\pi$
$911$	−51.2037	−	29.5624i	−0.0562060	−	0.0324505i	−0.527840	+	0.849344i	$0.676998\pi$
$912$		0			0
$913$	397.786	+	688.985i	0.435691	+	0.754639i
$914$		0			0
$915$	−795.272	+	578.470i	−0.869150	+	0.632208i
$916$		0			0
$917$	372.766	−	215.217i	0.406506	−	0.234697i
$918$		0			0
$919$	−811.809			−0.883361			−0.441680	−	0.897172i	$-0.645617\pi$
$919$	−811.809			−0.883361			−0.441680	+	0.897172i	$0.645617\pi$
$920$		0			0
$921$	−120.340	+	270.690i	−0.130662	+	0.293909i
$922$		0			0
$923$	−1065.38	+	615.099i	−1.15426	+	0.666412i
$924$		0			0
$925$	−393.028	−	680.744i	−0.424895	−	0.735940i
$926$		0			0
$927$	−1490.27	+	318.486i	−1.60762	+	0.343567i
$928$		0			0
$929$			1471.94i			1.58444i	0.610238	+	0.792218i	$0.291074\pi$
$929$			1471.94i			1.58444i	−0.610238	+	0.792218i	$0.708926\pi$
$930$		0			0
$931$	260.127	−	265.804i	0.279407	−	0.285504i
$932$		0			0
$933$	−324.898	−	144.439i	−0.348229	−	0.154811i
$934$		0			0
$935$	599.108	+	345.895i	0.640757	+	0.369941i
$936$		0			0
$937$	−292.962	+	507.425i	−0.312660	+	0.541543i	−0.978937	−	0.204161i	$-0.934553\pi$
$937$	−292.962	+	507.425i	−0.312660	+	0.541543i	0.666277	+	0.745704i	$0.267887\pi$
$938$		0			0
$939$	47.6379	−	107.156i	0.0507326	−	0.114117i
$940$		0			0
$941$		−	641.387i		−	0.681601i	−0.940136	−	0.340801i	$-0.889302\pi$
$941$		−	641.387i		−	0.681601i	0.940136	−	0.340801i	$-0.110698\pi$
$942$		0			0
$943$	−1120.31	+	1940.43i	−1.18802	+	2.05771i
$944$		0			0
$945$	−286.221	+	318.942i	−0.302880	+	0.337505i
$946$		0			0
$947$		−	1190.64i		−	1.25728i	−0.777697	−	0.628639i	$-0.783612\pi$
$947$		−	1190.64i		−	1.25728i	0.777697	−	0.628639i	$-0.216388\pi$
$948$		0			0
$949$	169.141	+	292.961i	0.178231	+	0.308705i
$950$		0			0
$951$	−1543.96	−	686.393i	−1.62351	−	0.721759i
$952$		0			0
$953$	−834.102	+	481.569i	−0.875238	+	0.505319i	−0.869085	−	0.494662i	$-0.835292\pi$
$953$	−834.102	+	481.569i	−0.875238	+	0.505319i	−0.00615290	+	0.999981i	$0.501959\pi$
$954$		0			0
$955$	−479.876	−	831.170i	−0.502488	−	0.870335i
$956$		0			0
$957$	564.645	+	776.265i	0.590016	+	0.811145i
$958$		0			0
$959$		−	252.504i		−	0.263299i
$960$		0			0
$961$	329.856	−	571.327i	0.343242	−	0.594513i
$962$		0			0
$963$	1123.11	+	363.550i	1.16626	+	0.377518i
$964$		0			0
$965$	−556.618	+	321.364i	−0.576807	+	0.333019i
$966$		0			0
$967$	677.770	−	1173.93i	0.700899	−	1.21399i	−0.267252	−	0.963627i	$-0.586116\pi$
$967$	677.770	−	1173.93i	0.700899	−	1.21399i	0.968151	−	0.250367i	$-0.0805512\pi$
$968$		0			0
$969$	−188.139	+	1281.83i	−0.194158	+	1.32283i
$970$		0			0
$971$	1057.02	−	610.270i	1.08859	−	0.628497i	0.155388	−	0.987853i	$-0.450337\pi$
$971$	1057.02	−	610.270i	1.08859	−	0.628497i	0.933200	+	0.359357i	$0.117004\pi$
$972$		0			0
$973$	−200.588	+	347.429i	−0.206155	+	0.357070i
$974$		0			0
$975$	490.388	−	1103.07i	0.502962	−	1.13135i
$976$		0			0
$977$	659.911	−	381.000i	0.675446	−	0.389969i	−0.122691	−	0.992445i	$-0.539152\pi$
$977$	659.911	−	381.000i	0.675446	−	0.389969i	0.798137	+	0.602476i	$0.205819\pi$
$978$		0			0
$979$	−739.016	−	1280.01i	−0.754869	−	1.30747i
$980$		0			0
$981$	137.660	−	29.4195i	0.140327	−	0.0299893i
$982$		0			0
$983$			1104.03i			1.12312i	0.827435	+	0.561562i	$0.189799\pi$
$983$			1104.03i			1.12312i	−0.827435	+	0.561562i	$0.810201\pi$
$984$		0			0
$985$	−236.751	+	410.065i	−0.240357	+	0.416310i
$986$		0			0
$987$	−232.852	+	169.374i	−0.235919	+	0.171604i
$988$		0			0
$989$			183.551i			0.185592i
$990$		0			0
$991$	−308.321	−	534.027i	−0.311121	−	0.538877i	0.667485	−	0.744624i	$-0.267371\pi$
$991$	−308.321	−	534.027i	−0.311121	−	0.538877i	−0.978605	+	0.205747i	$0.934038\pi$
$992$		0			0
$993$	−1645.81	+	173.901i	−1.65742	+	0.175127i
$994$		0			0
$995$	187.803	−	108.428i	0.188747	−	0.108973i
$996$		0			0
$997$	−290.261	−	502.746i	−0.291134	−	0.504259i	0.682944	−	0.730471i	$-0.260699\pi$
$997$	−290.261	−	502.746i	−0.291134	−	0.504259i	−0.974078	+	0.226212i	$0.927366\pi$
$998$		0			0
$999$	1227.20	−	400.990i	1.22843	−	0.401392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.be.a.425.12	yes	80
3.2	odd	2		2052.3.be.a.197.14		80
9.4	even	3		2052.3.m.a.881.14		80
9.5	odd	6		684.3.m.a.653.16	yes	80
19.11	even	3		684.3.m.a.353.16	✓	80
57.11	odd	6		2052.3.m.a.1493.27		80
171.49	even	3		2052.3.be.a.125.14		80
171.68	odd	6	inner	684.3.be.a.581.12	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.16	✓	80	19.11	even	3
684.3.m.a.653.16	yes	80	9.5	odd	6
684.3.be.a.425.12	yes	80	1.1	even	1	trivial
684.3.be.a.581.12	yes	80	171.68	odd	6	inner
2052.3.m.a.881.14		80	9.4	even	3
2052.3.m.a.1493.27		80	57.11	odd	6
2052.3.be.a.125.14		80	171.49	even	3
2052.3.be.a.197.14		80	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76470 - 2.42608i) q^{3} +(2.53393 + 1.46297i) q^{5} +(-2.71227 + 4.69779i) q^{7} +(-2.77170 + 8.56257i) q^{9} +O(q^{10})\)	\(q+(-1.76470 - 2.42608i) q^{3} +(2.53393 + 1.46297i) q^{5} +(-2.71227 + 4.69779i) q^{7} +(-2.77170 + 8.56257i) q^{9} +(9.00863 + 5.20114i) q^{11} -24.4777 q^{13} +(-0.922349 - 8.72920i) q^{15} +(19.6840 - 11.3645i) q^{17} +(-5.11536 - 18.2984i) q^{19} +(16.1835 - 1.70999i) q^{21} -29.3354i q^{23} +(-8.21946 - 14.2365i) q^{25} +(25.6647 - 8.38598i) q^{27} +(-26.6384 + 15.3797i) q^{29} +(-8.67884 - 15.0322i) q^{31} +(-3.27913 - 31.0341i) q^{33} +(-13.7454 + 7.93593i) q^{35} +47.8168 q^{37} +(43.1957 + 59.3848i) q^{39} +(-66.1461 - 38.1895i) q^{41} -6.25697 q^{43} +(-19.5501 + 17.6421i) q^{45} +(-15.3230 + 8.84672i) q^{47} +(9.78715 + 16.9518i) q^{49} +(-62.3075 - 27.6999i) q^{51} +(-12.9368 - 7.46908i) q^{53} +(15.2182 + 26.3586i) q^{55} +(-35.3664 + 44.7014i) q^{57} +(-18.8486 - 10.8822i) q^{59} +(-56.0166 - 97.0236i) q^{61} +(-32.7076 - 36.2449i) q^{63} +(-62.0248 - 35.8100i) q^{65} +21.1644 q^{67} +(-71.1700 + 51.7681i) q^{69} +(43.5246 - 25.1289i) q^{71} +(-6.91001 - 11.9685i) q^{73} +(-20.0341 + 45.0642i) q^{75} +(-48.8677 + 28.2138i) q^{77} +1.30487 q^{79} +(-65.6354 - 47.4658i) q^{81} +(66.2341 + 38.2403i) q^{83} +66.5038 q^{85} +(84.3210 + 37.4863i) q^{87} +(-123.051 - 71.0438i) q^{89} +(66.3902 - 114.991i) q^{91} +(-21.1537 + 47.5828i) q^{93} +(13.8080 - 53.8506i) q^{95} -184.984 q^{97} +(-69.5043 + 62.7211i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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