LMFDB - Embedded newform 684.3.s.a.445.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (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			445.32
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29742 - 1.92921i) q^{3} +(-2.38274 - 4.12702i) q^{5} +(3.51868 + 6.09454i) q^{7} +(1.55627 - 8.86442i) q^{9} +O(q^{10})$	\(q+(2.29742 - 1.92921i) q^{3} +(-2.38274 - 4.12702i) q^{5} +(3.51868 + 6.09454i) q^{7} +(1.55627 - 8.86442i) q^{9} +(2.56395 + 4.44089i) q^{11} -18.0658i q^{13} +(-13.4361 - 4.88469i) q^{15} +(-0.508862 + 0.881376i) q^{17} +(-0.399427 - 18.9958i) q^{19} +(19.8415 + 7.21341i) q^{21} -23.4146 q^{23} +(1.14513 - 1.98342i) q^{25} +(-13.5260 - 23.3677i) q^{27} +(39.6810 + 22.9099i) q^{29} +(-2.83600 - 1.63736i) q^{31} +(14.4579 + 5.25617i) q^{33} +(16.7682 - 29.0434i) q^{35} -57.4081i q^{37} +(-34.8528 - 41.5048i) q^{39} +(48.8958 - 28.2300i) q^{41} -79.4452 q^{43} +(-40.2918 + 14.6988i) q^{45} +(-33.1039 + 57.3376i) q^{47} +(-0.262246 + 0.454223i) q^{49} +(0.531292 + 3.00659i) q^{51} +(-36.1806 + 20.8889i) q^{53} +(12.2184 - 21.1629i) q^{55} +(-37.5646 - 42.8707i) q^{57} +(14.3969 - 8.31204i) q^{59} +(39.3248 - 68.1126i) q^{61} +(59.5006 - 21.7064i) q^{63} +(-74.5581 + 43.0461i) q^{65} -120.159i q^{67} +(-53.7932 + 45.1718i) q^{69} +(-40.9176 - 23.6238i) q^{71} +(-47.5240 + 82.3140i) q^{73} +(-1.19560 - 6.76595i) q^{75} +(-18.0434 + 31.2521i) q^{77} +117.643i q^{79} +(-76.1561 - 27.5909i) q^{81} +(13.8505 + 23.9898i) q^{83} +4.84994 q^{85} +(135.362 - 23.9197i) q^{87} +(24.4672 - 14.1261i) q^{89} +(110.103 - 63.5679i) q^{91} +(-9.67429 + 1.70953i) q^{93} +(-77.4443 + 46.9104i) q^{95} +101.458i q^{97} +(43.3561 - 15.8167i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	2.29742	−	1.92921i	0.765806	−	0.643071i
$3$	2.29742	−	1.92921i	0.765806	−	0.643071i
$4$		0			0
$5$	−2.38274	−	4.12702i	−0.476547	−	0.825404i	0.523091	−	0.852277i	$-0.324779\pi$
$5$	−2.38274	−	4.12702i	−0.476547	−	0.825404i	−0.999639	+	0.0268723i	$0.991445\pi$
$6$		0			0
$7$	3.51868	+	6.09454i	0.502669	+	0.870648i	0.999995	+	0.00308448i	$0.000981821\pi$
$7$	3.51868	+	6.09454i	0.502669	+	0.870648i	−0.497326	+	0.867564i	$0.665685\pi$
$8$		0			0
$9$	1.55627	−	8.86442i	0.172919	−	0.984936i
$10$		0			0
$11$	2.56395	+	4.44089i	0.233086	+	0.403717i	0.958715	−	0.284370i	$-0.0917843\pi$
$11$	2.56395	+	4.44089i	0.233086	+	0.403717i	−0.725629	+	0.688086i	$0.758451\pi$
$12$		0			0
$13$		−	18.0658i		−	1.38968i	−0.719165	−	0.694840i	$-0.755475\pi$
$13$		−	18.0658i		−	1.38968i	0.719165	−	0.694840i	$-0.244525\pi$
$14$		0			0
$15$	−13.4361	−	4.88469i	−0.895737	−	0.325646i
$16$		0			0
$17$	−0.508862	+	0.881376i	−0.0299331	+	0.0518456i	−0.880604	−	0.473853i	$-0.842863\pi$
$17$	−0.508862	+	0.881376i	−0.0299331	+	0.0518456i	0.850671	+	0.525699i	$0.176196\pi$
$18$		0			0
$19$	−0.399427	−	18.9958i	−0.0210225	−	0.999779i
$19$	−0.399427	−	18.9958i	−0.0210225	−	0.999779i
$20$		0			0
$21$	19.8415	+	7.21341i	0.944836	+	0.343496i
$22$		0			0
$23$	−23.4146			−1.01803			−0.509014	−	0.860758i	$-0.669990\pi$
$23$	−23.4146			−1.01803			−0.509014	+	0.860758i	$0.669990\pi$
$24$		0			0
$25$	1.14513	−	1.98342i	0.0458052	−	0.0793369i
$26$		0			0
$27$	−13.5260	−	23.3677i	−0.500962	−	0.865469i
$28$		0			0
$29$	39.6810	+	22.9099i	1.36831	+	0.789995i	0.990712	−	0.135974i	$-0.0434165\pi$
$29$	39.6810	+	22.9099i	1.36831	+	0.789995i	0.377599	+	0.925969i	$0.376750\pi$
$30$		0			0
$31$	−2.83600	−	1.63736i	−0.0914837	−	0.0528181i	0.453560	−	0.891226i	$-0.350154\pi$
$31$	−2.83600	−	1.63736i	−0.0914837	−	0.0528181i	−0.545044	+	0.838407i	$0.683487\pi$
$32$		0			0
$33$	14.4579	+	5.25617i	0.438117	+	0.159278i
$34$		0			0
$35$	16.7682	−	29.0434i	0.479091	−	0.829810i
$36$		0			0
$37$		−	57.4081i		−	1.55157i	−0.630997	−	0.775786i	$-0.717354\pi$
$37$		−	57.4081i		−	1.55157i	0.630997	−	0.775786i	$-0.282646\pi$
$38$		0			0
$39$	−34.8528	−	41.5048i	−0.893663	−	1.06423i
$40$		0			0
$41$	48.8958	−	28.2300i	1.19258	−	0.688536i	0.233689	−	0.972311i	$-0.424920\pi$
$41$	48.8958	−	28.2300i	1.19258	−	0.688536i	0.958891	+	0.283775i	$0.0915869\pi$
$42$		0			0
$43$	−79.4452			−1.84756			−0.923782	−	0.382919i	$-0.874919\pi$
$43$	−79.4452			−1.84756			−0.923782	+	0.382919i	$0.874919\pi$
$44$		0			0
$45$	−40.2918	+	14.6988i	−0.895374	+	0.326641i
$46$		0			0
$47$	−33.1039	+	57.3376i	−0.704337	+	1.21995i	0.262593	+	0.964907i	$0.415422\pi$
$47$	−33.1039	+	57.3376i	−0.704337	+	1.21995i	−0.966930	+	0.255041i	$0.917911\pi$
$48$		0			0
$49$	−0.262246	+	0.454223i	−0.00535196	+	0.00926986i
$50$		0			0
$51$	0.531292	+	3.00659i	0.0104175	+	0.0589528i
$52$		0			0
$53$	−36.1806	+	20.8889i	−0.682653	+	0.394130i	−0.800854	−	0.598860i	$-0.795621\pi$
$53$	−36.1806	+	20.8889i	−0.682653	+	0.394130i	0.118201	+	0.992990i	$0.462287\pi$
$54$		0			0
$55$	12.2184	−	21.1629i	0.222153	−	0.384780i
$56$		0			0
$57$	−37.5646	−	42.8707i	−0.659028	−	0.752118i
$58$		0			0
$59$	14.3969	−	8.31204i	0.244015	−	0.140882i	−0.373006	−	0.927829i	$-0.621673\pi$
$59$	14.3969	−	8.31204i	0.244015	−	0.140882i	0.617021	+	0.786947i	$0.288339\pi$
$60$		0			0
$61$	39.3248	−	68.1126i	0.644669	−	1.11660i	−0.339708	−	0.940531i	$-0.610328\pi$
$61$	39.3248	−	68.1126i	0.644669	−	1.11660i	0.984378	−	0.176069i	$-0.0563383\pi$
$62$		0			0
$63$	59.5006	−	21.7064i	0.944454	−	0.344545i
$64$		0			0
$65$	−74.5581	+	43.0461i	−1.14705	+	0.662248i
$66$		0			0
$67$		−	120.159i		−	1.79342i	−0.442616	−	0.896711i	$-0.645949\pi$
$67$		−	120.159i		−	1.79342i	0.442616	−	0.896711i	$-0.354051\pi$
$68$		0			0
$69$	−53.7932	+	45.1718i	−0.779612	+	0.654664i
$70$		0			0
$71$	−40.9176	−	23.6238i	−0.576304	−	0.332729i	0.183359	−	0.983046i	$-0.441303\pi$
$71$	−40.9176	−	23.6238i	−0.576304	−	0.332729i	−0.759663	+	0.650317i	$0.774636\pi$
$72$		0			0
$73$	−47.5240	+	82.3140i	−0.651014	+	1.12759i	0.331863	+	0.943328i	$0.392323\pi$
$73$	−47.5240	+	82.3140i	−0.651014	+	1.12759i	−0.982877	+	0.184262i	$0.941010\pi$
$74$		0			0
$75$	−1.19560	−	6.76595i	−0.0159414	−	0.0902127i
$76$		0			0
$77$	−18.0434	+	31.2521i	−0.234330	+	0.405872i
$78$		0			0
$79$			117.643i			1.48915i	0.667539	+	0.744575i	$0.267348\pi$
$79$			117.643i			1.48915i	−0.667539	+	0.744575i	$0.732652\pi$
$80$		0			0
$81$	−76.1561	−	27.5909i	−0.940198	−	0.340628i
$82$		0			0
$83$	13.8505	+	23.9898i	0.166874	+	0.289034i	0.937319	−	0.348472i	$-0.113299\pi$
$83$	13.8505	+	23.9898i	0.166874	+	0.289034i	−0.770445	+	0.637506i	$0.779966\pi$
$84$		0			0
$85$	4.84994			0.0570581
$86$		0			0
$87$	135.362	−	23.9197i	1.55588	−	0.274939i
$88$		0			0
$89$	24.4672	−	14.1261i	0.274912	−	0.158721i	−0.356206	−	0.934408i	$-0.615930\pi$
$89$	24.4672	−	14.1261i	0.274912	−	0.158721i	0.631118	+	0.775687i	$0.282596\pi$
$90$		0			0
$91$	110.103	−	63.5679i	1.20992	−	0.698548i
$92$		0			0
$93$	−9.67429	+	1.70953i	−0.104025	+	0.0183821i
$94$		0			0
$95$	−77.4443	+	46.9104i	−0.815204	+	0.493794i
$96$		0			0
$97$			101.458i			1.04596i	0.852344	+	0.522981i	$0.175180\pi$
$97$			101.458i			1.04596i	−0.852344	+	0.522981i	$0.824820\pi$
$98$		0			0
$99$	43.3561	−	15.8167i	0.437940	−	0.159765i
$100$		0			0
$101$	82.6533	−	143.160i	0.818349	−	1.41742i	−0.0885488	−	0.996072i	$-0.528223\pi$
$101$	82.6533	−	143.160i	0.818349	−	1.41742i	0.906898	−	0.421350i	$-0.138444\pi$
$102$		0			0
$103$	51.6210	+	29.8034i	0.501174	+	0.289353i	0.729198	−	0.684302i	$-0.239893\pi$
$103$	51.6210	+	29.8034i	0.501174	+	0.289353i	−0.228024	+	0.973656i	$0.573226\pi$
$104$		0			0
$105$	−17.5073	−	99.0742i	−0.166736	−	0.943563i
$106$		0			0
$107$			112.820i			1.05439i	0.849744	+	0.527195i	$0.176756\pi$
$107$			112.820i			1.05439i	−0.849744	+	0.527195i	$0.823244\pi$
$108$		0			0
$109$	77.6418	+	44.8265i	0.712310	+	0.411252i	0.811916	−	0.583775i	$-0.198425\pi$
$109$	77.6418	+	44.8265i	0.712310	+	0.411252i	−0.0996059	+	0.995027i	$0.531758\pi$
$110$		0			0
$111$	−110.753	−	131.891i	−0.997771	−	1.18820i
$112$		0			0
$113$	−44.8713	−	25.9065i	−0.397091	−	0.229261i	0.288137	−	0.957589i	$-0.406964\pi$
$113$	−44.8713	−	25.9065i	−0.397091	−	0.229261i	−0.685228	+	0.728328i	$0.740298\pi$
$114$		0			0
$115$	55.7909	+	96.6327i	0.485138	+	0.840284i
$116$		0			0
$117$	−160.143	−	28.1153i	−1.36875	−	0.240302i
$118$		0			0
$119$	−7.16210			−0.0601857
$120$		0			0
$121$	47.3524	−	82.0167i	0.391342	−	0.677824i
$122$		0			0
$123$	57.8724	−	159.187i	0.470507	−	1.29420i
$124$		0			0
$125$	−130.051			−1.04041
$126$		0			0
$127$	128.735	−	74.3249i	1.01366	−	0.585236i	0.101398	−	0.994846i	$-0.467669\pi$
$127$	128.735	−	74.3249i	1.01366	−	0.585236i	0.912261	+	0.409610i	$0.134335\pi$
$128$		0			0
$129$	−182.519	+	153.267i	−1.41488	+	1.18812i
$130$		0			0
$131$	55.9220	+	96.8597i	0.426885	+	0.739387i	0.996594	−	0.0824594i	$-0.0262775\pi$
$131$	55.9220	+	96.8597i	0.426885	+	0.739387i	−0.569709	+	0.821846i	$0.692944\pi$
$132$		0			0
$133$	114.365	−	69.2745i	0.859888	−	0.520861i
$134$		0			0
$135$	−64.2101	+	111.501i	−0.475630	+	0.825933i
$136$		0			0
$137$	117.842	−	204.108i	0.860158	−	1.48984i	−0.0116180	−	0.999933i	$-0.503698\pi$
$137$	117.842	−	204.108i	0.860158	−	1.48984i	0.871776	−	0.489905i	$-0.162968\pi$
$138$		0			0
$139$	14.7457			0.106084			0.0530420	−	0.998592i	$-0.483108\pi$
$139$	14.7457			0.106084			0.0530420	+	0.998592i	$0.483108\pi$
$140$		0			0
$141$	34.5630	+	195.593i	0.245127	+	1.38718i
$142$		0			0
$143$	80.2283	−	46.3198i	0.561037	−	0.323915i
$144$		0			0
$145$		−	218.353i		−	1.50588i
$146$		0			0
$147$	0.273805	+	1.54947i	0.00186262	+	0.0105406i
$148$		0			0
$149$	74.2641	+	128.629i	0.498417	+	0.863283i	0.999998	−	0.00182699i	$-0.000581551\pi$
$149$	74.2641	+	128.629i	0.498417	+	0.863283i	−0.501581	+	0.865110i	$0.667248\pi$
$150$		0			0
$151$	7.73412	−	4.46529i	0.0512193	−	0.0295715i	−0.474172	−	0.880432i	$-0.657252\pi$
$151$	7.73412	−	4.46529i	0.0512193	−	0.0295715i	0.525391	+	0.850861i	$0.323919\pi$
$152$		0			0
$153$	7.02096	+	5.88243i	0.0458886	+	0.0384473i
$154$		0			0
$155$			15.6056i			0.100681i
$156$		0			0
$157$	10.0063	+	17.3314i	0.0637342	+	0.110391i	0.896132	−	0.443788i	$-0.146366\pi$
$157$	10.0063	+	17.3314i	0.0637342	+	0.110391i	−0.832398	+	0.554179i	$0.813032\pi$
$158$		0			0
$159$	−42.8229	+	117.791i	−0.269327	+	0.740822i
$160$		0			0
$161$	−82.3887	−	142.701i	−0.511731	−	0.886344i
$162$		0			0
$163$	28.7108			0.176140			0.0880701	−	0.996114i	$-0.471930\pi$
$163$	28.7108			0.176140			0.0880701	+	0.996114i	$0.471930\pi$
$164$		0			0
$165$	−12.7570	−	72.1920i	−0.0773150	−	0.437528i
$166$		0			0
$167$			185.248i			1.10927i	0.832094	+	0.554635i	$0.187142\pi$
$167$			185.248i			1.10927i	−0.832094	+	0.554635i	$0.812858\pi$
$168$		0			0
$169$	−157.374			−0.931208
$170$		0			0
$171$	−169.008	−	26.0219i	−0.988354	−	0.152175i
$172$		0			0
$173$			282.744i			1.63436i	0.576383	+	0.817180i	$0.304464\pi$
$173$			282.744i			1.63436i	−0.576383	+	0.817180i	$0.695536\pi$
$174$		0			0
$175$	16.1174			0.0920994
$176$		0			0
$177$	17.0400	−	46.8709i	0.0962709	−	0.264807i
$178$		0			0
$179$		−	11.5013i		−	0.0642530i	−0.999484	−	0.0321265i	$-0.989772\pi$
$179$		−	11.5013i		−	0.0642530i	0.999484	−	0.0321265i	$-0.0102279\pi$
$180$		0			0
$181$	70.0041	−	40.4169i	0.386763	−	0.223298i	−0.293994	−	0.955807i	$-0.594984\pi$
$181$	70.0041	−	40.4169i	0.386763	−	0.223298i	0.680757	+	0.732510i	$0.261651\pi$
$182$		0			0
$183$	−41.0582	−	232.349i	−0.224362	−	1.26967i
$184$		0			0
$185$	−236.925	+	136.788i	−1.28067	+	0.739397i
$186$		0			0
$187$	−5.21878			−0.0279079
$188$		0			0
$189$	94.8215	−	164.658i	0.501701	−	0.871206i
$190$		0			0
$191$	−12.8496	−	22.2562i	−0.0672756	−	0.116525i	0.830426	−	0.557130i	$-0.188097\pi$
$191$	−12.8496	−	22.2562i	−0.0672756	−	0.116525i	−0.897701	+	0.440605i	$0.854764\pi$
$192$		0			0
$193$	229.650	−	132.588i	1.18989	−	0.686986i	0.231611	−	0.972808i	$-0.425600\pi$
$193$	229.650	−	132.588i	1.18989	−	0.686986i	0.958283	+	0.285823i	$0.0922669\pi$
$194$		0			0
$195$	−88.2460	+	242.733i	−0.452543	+	1.24479i
$196$		0			0
$197$	333.924			1.69505			0.847523	−	0.530759i	$-0.178093\pi$
$197$	333.924			1.69505			0.847523	+	0.530759i	$0.178093\pi$
$198$		0			0
$199$	44.0469	+	76.2915i	0.221341	+	0.383374i	0.955215	−	0.295911i	$-0.0956232\pi$
$199$	44.0469	+	76.2915i	0.221341	+	0.383374i	−0.733874	+	0.679285i	$0.762290\pi$
$200$		0			0
$201$	−231.813	−	276.056i	−1.15330	−	1.37341i
$202$		0			0
$203$			322.450i			1.58842i
$204$		0			0
$205$	−233.012	−	134.529i	−1.13664	−	0.656240i
$206$		0			0
$207$	−36.4395	+	207.557i	−0.176036	+	1.00269i
$208$		0			0
$209$	83.3341	−	50.4780i	0.398728	−	0.241522i
$210$		0			0
$211$	143.410	−	82.7979i	0.679669	−	0.392407i	−0.120062	−	0.992766i	$-0.538309\pi$
$211$	143.410	−	82.7979i	0.679669	−	0.392407i	0.799730	+	0.600360i	$0.204976\pi$
$212$		0			0
$213$	−139.580	+	24.6650i	−0.655306	+	0.115798i
$214$		0			0
$215$	189.297	+	327.872i	0.880452	+	1.52499i
$216$		0			0
$217$		−	23.0454i		−	0.106200i
$218$		0			0
$219$	49.6188	+	280.794i	0.226570	+	1.28216i
$220$		0			0
$221$	15.9228	+	9.19302i	0.0720488	+	0.0415974i
$222$		0			0
$223$			12.0348i			0.0539679i	0.999636	+	0.0269840i	$0.00859030\pi$
$223$			12.0348i			0.0539679i	−0.999636	+	0.0269840i	$0.991410\pi$
$224$		0			0
$225$	−15.7998	−	13.2377i	−0.0702212	−	0.0588340i
$226$		0			0
$227$	350.478	−	202.349i	1.54396	−	0.891404i	0.545374	−	0.838193i	$-0.316388\pi$
$227$	350.478	−	202.349i	1.54396	−	0.891404i	0.998583	−	0.0532114i	$-0.0169457\pi$
$228$		0			0
$229$	−124.232	+	215.175i	−0.542496	+	0.939630i	0.456264	+	0.889844i	$0.349187\pi$
$229$	−124.232	+	215.175i	−0.542496	+	0.939630i	−0.998760	+	0.0497858i	$0.984146\pi$
$230$		0			0
$231$	18.8387	+	106.609i	0.0815529	+	0.461510i
$232$		0			0
$233$	−112.559	+	194.958i	−0.483086	+	0.836729i	−0.999811	−	0.0194221i	$-0.993817\pi$
$233$	−112.559	+	194.958i	−0.483086	+	0.836729i	0.516726	+	0.856151i	$0.327151\pi$
$234$		0			0
$235$	315.511			1.34260
$236$		0			0
$237$	226.958	+	270.275i	0.957629	+	1.14040i
$238$		0			0
$239$	−228.602	+	395.950i	−0.956494	+	1.65670i	−0.225582	+	0.974224i	$0.572428\pi$
$239$	−228.602	+	395.950i	−0.956494	+	1.65670i	−0.730912	+	0.682472i	$0.760905\pi$
$240$		0			0
$241$	319.565	+	184.501i	1.32600	+	0.765564i	0.984678	−	0.174383i	$-0.0557932\pi$
$241$	319.565	+	184.501i	1.32600	+	0.765564i	0.341318	+	0.939948i	$0.389127\pi$
$242$		0			0
$243$	−228.191	+	83.5336i	−0.939058	+	0.343760i
$244$		0			0
$245$	2.49945			0.0102018
$246$		0			0
$247$	−343.175	+	7.21597i	−1.38937	+	0.0292145i
$248$		0			0
$249$	78.1018	+	28.3940i	0.313662	+	0.114032i
$250$		0			0
$251$	50.8316	+	88.0429i	0.202516	+	0.350769i	0.949339	−	0.314255i	$-0.101755\pi$
$251$	50.8316	+	88.0429i	0.202516	+	0.350769i	−0.746822	+	0.665024i	$0.768421\pi$
$252$		0			0
$253$	−60.0339	−	103.982i	−0.237288	−	0.410995i
$254$		0			0
$255$	11.1423	−	9.35657i	0.0436955	−	0.0366924i
$256$		0			0
$257$			62.5439i			0.243362i	0.992569	+	0.121681i	$0.0388284\pi$
$257$			62.5439i			0.243362i	−0.992569	+	0.121681i	$0.961172\pi$
$258$		0			0
$259$	349.876	−	202.001i	1.35087	−	0.779926i
$260$		0			0
$261$	264.837	−	316.096i	1.01470	−	1.21109i
$262$		0			0
$263$	189.113			0.719062			0.359531	−	0.933133i	$-0.382937\pi$
$263$	189.113			0.719062			0.359531	+	0.933133i	$0.382937\pi$
$264$		0			0
$265$	172.418	+	99.5455i	0.650633	+	0.375643i
$266$		0			0
$267$	28.9590	−	79.6561i	0.108461	−	0.298337i
$268$		0			0
$269$	−109.722	−	63.3477i	−0.407887	−	0.235493i	0.281995	−	0.959416i	$-0.409004\pi$
$269$	−109.722	−	63.3477i	−0.407887	−	0.235493i	−0.689881	+	0.723923i	$0.742337\pi$
$270$		0			0
$271$	−142.679	+	247.128i	−0.526492	+	0.911911i	0.473031	+	0.881046i	$0.343160\pi$
$271$	−142.679	+	247.128i	−0.526492	+	0.911911i	−0.999524	+	0.0308656i	$0.990174\pi$
$272$		0			0
$273$	130.316	−	358.454i	0.477349	−	1.31302i
$274$		0			0
$275$	11.7442			0.0427062
$276$		0			0
$277$	119.422	+	206.845i	0.431127	+	0.746735i	0.996971	−	0.0777783i	$-0.0247826\pi$
$277$	119.422	+	206.845i	0.431127	+	0.746735i	−0.565843	+	0.824513i	$0.691449\pi$
$278$		0			0
$279$	−18.9278	+	22.5913i	−0.0678417	+	0.0809724i
$280$		0			0
$281$	−137.190	−	79.2065i	−0.488220	−	0.281874i	0.235616	−	0.971846i	$-0.424289\pi$
$281$	−137.190	−	79.2065i	−0.488220	−	0.281874i	−0.723836	+	0.689972i	$0.757623\pi$
$282$		0			0
$283$	−13.8579	−	24.0027i	−0.0489680	−	0.0848151i	0.840502	−	0.541808i	$-0.182260\pi$
$283$	−13.8579	−	24.0027i	−0.0489680	−	0.0848151i	−0.889470	+	0.456993i	$0.848927\pi$
$284$		0			0
$285$	−87.4219	+	257.180i	−0.306743	+	0.902385i
$286$		0			0
$287$	344.097	+	198.665i	1.19895	+	0.692212i
$288$		0			0
$289$	143.982	+	249.384i	0.498208	+	0.862922i
$290$		0			0
$291$	195.735	+	233.092i	0.672628	+	0.801005i
$292$		0			0
$293$	296.143	+	170.978i	1.01073	+	0.583543i	0.911404	−	0.411512i	$-0.134999\pi$
$293$	296.143	+	170.978i	1.01073	+	0.583543i	0.0993218	+	0.995055i	$0.468333\pi$
$294$		0			0
$295$	−68.6079	−	39.6108i	−0.232569	−	0.134274i
$296$		0			0
$297$	69.0933	−	119.981i	0.232637	−	0.403976i
$298$		0			0
$299$			423.005i			1.41473i
$300$		0			0
$301$	−279.543	−	484.182i	−0.928713	−	1.60858i
$302$		0			0
$303$	−86.2964	−	488.354i	−0.284807	−	1.61173i
$304$		0			0
$305$	−374.803			−1.22886
$306$		0			0
$307$	−246.917	−	142.558i	−0.804292	−	0.464358i	0.0406781	−	0.999172i	$-0.487048\pi$
$307$	−246.917	−	142.558i	−0.804292	−	0.464358i	−0.844970	+	0.534814i	$0.820382\pi$
$308$		0			0
$309$	176.092	−	31.1170i	0.569877	−	0.100702i
$310$		0			0
$311$	−158.490	+	274.513i	−0.509615	+	0.882678i	0.490323	+	0.871541i	$0.336879\pi$
$311$	−158.490	+	274.513i	−0.509615	+	0.882678i	−0.999938	+	0.0111378i	$0.996455\pi$
$312$		0			0
$313$	23.5165	−	40.7317i	0.0751325	−	0.130133i	−0.826011	−	0.563653i	$-0.809395\pi$
$313$	23.5165	−	40.7317i	0.0751325	−	0.130133i	0.901144	+	0.433520i	$0.142729\pi$
$314$		0			0
$315$	−231.357	−	193.840i	−0.734466	−	0.615364i
$316$		0			0
$317$	−448.669	−	259.039i	−1.41536	−	0.817159i	−0.419474	−	0.907767i	$-0.637785\pi$
$317$	−448.669	−	259.039i	−1.41536	−	0.817159i	−0.995887	+	0.0906088i	$0.971119\pi$
$318$		0			0
$319$			234.958i			0.736547i
$320$		0			0
$321$	217.653	+	259.194i	0.678048	+	0.807459i
$322$		0			0
$323$	16.9457	+	9.31420i	0.0524634	+	0.0288365i
$324$		0			0
$325$	−35.8322	−	20.6877i	−0.110253	−	0.0636545i
$326$		0			0
$327$	264.856	−	46.8023i	0.809956	−	0.143126i
$328$		0			0
$329$	−465.928			−1.41619
$330$		0			0
$331$	−1.17840	+	0.680349i	−0.00356012	+	0.00205544i	−0.501779	−	0.864996i	$-0.667321\pi$
$331$	−1.17840	+	0.680349i	−0.00356012	+	0.00205544i	0.498219	+	0.867051i	$0.333988\pi$
$332$		0			0
$333$	−508.890	−	89.3425i	−1.52820	−	0.268296i
$334$		0			0
$335$	−495.900	+	286.308i	−1.48030	+	0.854651i
$336$		0			0
$337$	−298.578	+	172.384i	−0.885988	+	0.511525i	−0.872628	−	0.488386i	$-0.837586\pi$
$337$	−298.578	+	172.384i	−0.885988	+	0.511525i	−0.0133597	+	0.999911i	$0.504253\pi$
$338$		0			0
$339$	−153.067	+	27.0484i	−0.451526	+	0.0797887i
$340$		0			0
$341$		−	16.7924i		−	0.0492447i
$342$		0			0
$343$	341.140			0.994577
$344$		0			0
$345$	314.600	+	114.373i	0.911885	+	0.331517i
$346$		0			0
$347$	−125.763	−	217.828i	−0.362430	−	0.627747i	0.625930	−	0.779879i	$-0.284719\pi$
$347$	−125.763	−	217.828i	−0.362430	−	0.627747i	−0.988360	+	0.152132i	$0.951386\pi$
$348$		0			0
$349$	−91.0768	−	157.750i	−0.260965	−	0.452005i	0.705534	−	0.708676i	$-0.250707\pi$
$349$	−91.0768	−	157.750i	−0.260965	−	0.452005i	−0.966499	+	0.256672i	$0.917374\pi$
$350$		0			0
$351$	−422.156	+	244.358i	−1.20272	+	0.696176i
$352$		0			0
$353$	−187.453	−	324.678i	−0.531028	−	0.919768i	−0.999344	−	0.0362067i	$-0.988473\pi$
$353$	−187.453	−	324.678i	−0.531028	−	0.919768i	0.468316	−	0.883561i	$-0.344861\pi$
$354$		0			0
$355$			225.157i			0.634245i
$356$		0			0
$357$	−16.4543	+	13.8172i	−0.0460906	+	0.0387037i
$358$		0			0
$359$	−15.9655	+	27.6530i	−0.0444720	+	0.0770278i	−0.887405	−	0.460991i	$-0.847494\pi$
$359$	−15.9655	+	27.6530i	−0.0444720	+	0.0770278i	0.842933	+	0.538019i	$0.180827\pi$
$360$		0			0
$361$	−360.681	+	15.1749i	−0.999116	+	0.0420356i
$362$		0			0
$363$	−49.4395	−	279.780i	−0.136197	−	0.770743i
$364$		0			0
$365$	452.949			1.24096
$366$		0			0
$367$	0.630275	−	1.09167i	0.00171737	−	0.00297457i	−0.865165	−	0.501487i	$-0.832787\pi$
$367$	0.630275	−	1.09167i	0.00171737	−	0.00297457i	0.866883	+	0.498512i	$0.166120\pi$
$368$		0			0
$369$	−174.148	−	477.366i	−0.471945	−	1.29368i
$370$		0			0
$371$	−254.616	−	147.003i	−0.686297	−	0.396234i
$372$		0			0
$373$	119.825	+	69.1813i	0.321248	+	0.185473i	0.651949	−	0.758263i	$-0.273952\pi$
$373$	119.825	+	69.1813i	0.321248	+	0.185473i	−0.330701	+	0.943736i	$0.607285\pi$
$374$		0			0
$375$	−298.782	+	250.896i	−0.796751	+	0.669057i
$376$		0			0
$377$	413.885	−	716.871i	1.09784	−	1.90151i
$378$		0			0
$379$		−	282.758i		−	0.746064i	−0.927818	−	0.373032i	$-0.878318\pi$
$379$		−	282.758i		−	0.746064i	0.927818	−	0.373032i	$-0.121682\pi$
$380$		0			0
$381$	152.369	−	419.112i	0.399918	−	1.10003i
$382$		0			0
$383$	−379.768	+	219.259i	−0.991560	+	0.572478i	−0.905740	−	0.423833i	$-0.860684\pi$
$383$	−379.768	+	219.259i	−0.991560	+	0.572478i	−0.0858200	+	0.996311i	$0.527351\pi$
$384$		0			0
$385$	171.971			0.446678
$386$		0			0
$387$	−123.638	+	704.236i	−0.319478	+	1.81973i
$388$		0			0
$389$	359.122	−	622.018i	0.923193	−	1.59902i	0.128752	−	0.991677i	$-0.458903\pi$
$389$	359.122	−	622.018i	0.923193	−	1.59902i	0.794442	−	0.607341i	$-0.207764\pi$
$390$		0			0
$391$	11.9148	−	20.6371i	0.0304727	−	0.0527803i
$392$		0			0
$393$	315.339	+	114.642i	0.802390	+	0.291710i
$394$		0			0
$395$	485.514	−	280.312i	1.22915	−	0.709650i
$396$		0			0
$397$	−127.044	+	220.047i	−0.320011	+	0.554275i	−0.980490	−	0.196569i	$-0.937020\pi$
$397$	−127.044	+	220.047i	−0.320011	+	0.554275i	0.660479	+	0.750844i	$0.270353\pi$
$398$		0			0
$399$	129.099	−	379.787i	0.323557	−	0.951848i
$400$		0			0
$401$	427.982	−	247.096i	1.06729	−	0.616199i	0.139848	−	0.990173i	$-0.455338\pi$
$401$	427.982	−	247.096i	1.06729	−	0.616199i	0.927439	+	0.373974i	$0.122005\pi$
$402$		0			0
$403$	−29.5803	+	51.2346i	−0.0734003	+	0.127133i
$404$		0			0
$405$	67.5918	+	380.039i	0.166893	+	0.938369i
$406$		0			0
$407$	254.943	−	147.191i	0.626395	−	0.361650i
$408$		0			0
$409$		−	695.992i		−	1.70169i	−0.525415	−	0.850846i	$-0.676090\pi$
$409$		−	695.992i		−	1.70169i	0.525415	−	0.850846i	$-0.323910\pi$
$410$		0			0
$411$	−123.036	−	696.263i	−0.299357	−	1.69407i
$412$		0			0
$413$	101.316	+	58.4949i	0.245317	+	0.141634i
$414$		0			0
$415$	66.0042	−	114.323i	0.159046	−	0.275476i
$416$		0			0
$417$	33.8770	−	28.4476i	0.0812398	−	0.0682196i
$418$		0			0
$419$	189.788	−	328.722i	0.452955	−	0.784540i	−0.545613	−	0.838037i	$-0.683703\pi$
$419$	189.788	−	328.722i	0.452955	−	0.784540i	0.998568	+	0.0534967i	$0.0170366\pi$
$420$		0			0
$421$			523.193i			1.24274i	0.783518	+	0.621370i	$0.213423\pi$
$421$			523.193i			1.24274i	−0.783518	+	0.621370i	$0.786577\pi$
$422$		0			0
$423$	456.746	+	382.679i	1.07978	+	0.904679i
$424$		0			0
$425$	1.16543	+	2.01858i	0.00274218	+	0.00474960i
$426$		0			0
$427$	553.486			1.29622
$428$		0			0
$429$	94.9571	−	261.194i	0.221345	−	0.608843i
$430$		0			0
$431$	222.148	−	128.257i	0.515426	−	0.297581i	−0.219635	−	0.975582i	$-0.570487\pi$
$431$	222.148	−	128.257i	0.515426	−	0.297581i	0.735061	+	0.678001i	$0.237153\pi$
$432$		0			0
$433$	−234.232	+	135.234i	−0.540951	+	0.312318i	−0.745464	−	0.666545i	$-0.767772\pi$
$433$	−234.232	+	135.234i	−0.540951	+	0.312318i	0.204513	+	0.978864i	$0.434439\pi$
$434$		0			0
$435$	−421.249	−	501.647i	−0.968388	−	1.15321i
$436$		0			0
$437$	9.35243	+	444.780i	0.0214014	+	1.01780i
$438$		0			0
$439$		−	635.775i		−	1.44823i	−0.689677	−	0.724117i	$-0.742247\pi$
$439$		−	635.775i		−	1.44823i	0.689677	−	0.724117i	$-0.257753\pi$
$440$		0			0
$441$	3.61830	+	3.03155i	0.00820477	+	0.00687427i
$442$		0			0
$443$	−24.4107	+	42.2805i	−0.0551031	+	0.0954413i	−0.892261	−	0.451520i	$-0.850882\pi$
$443$	−24.4107	+	42.2805i	−0.0551031	+	0.0954413i	0.837158	+	0.546961i	$0.184215\pi$
$444$		0			0
$445$	−116.598	−	67.3177i	−0.262017	−	0.151276i
$446$		0			0
$447$	418.769	+	152.244i	0.936844	+	0.340590i
$448$		0			0
$449$			11.4958i			0.0256031i	0.999918	+	0.0128015i	$0.00407497\pi$
$449$			11.4958i			0.0256031i	−0.999918	+	0.0128015i	$0.995925\pi$
$450$		0			0
$451$	250.732	+	144.760i	0.555947	+	0.320976i
$452$		0			0
$453$	9.15400	−	25.1794i	0.0202075	−	0.0555837i
$454$		0			0
$455$	−524.692	−	302.931i	−1.15317	−	0.665783i
$456$		0			0
$457$	−168.104	−	291.165i	−0.367842	−	0.637122i	0.621386	−	0.783505i	$-0.286570\pi$
$457$	−168.104	−	291.165i	−0.367842	−	0.637122i	−0.989228	+	0.146383i	$0.953237\pi$
$458$		0			0
$459$	27.4786	−	0.0305279i	0.0598661	−	6.65096e-5i
$460$		0			0
$461$	−391.668			−0.849605			−0.424803	−	0.905286i	$-0.639657\pi$
$461$	−391.668			−0.849605			−0.424803	+	0.905286i	$0.639657\pi$
$462$		0			0
$463$	217.097	−	376.022i	0.468891	−	0.812143i	−0.530477	−	0.847700i	$-0.677987\pi$
$463$	217.097	−	376.022i	0.468891	−	0.812143i	0.999368	+	0.0355563i	$0.0113203\pi$
$464$		0			0
$465$	30.1066	+	35.8526i	0.0647453	+	0.0771025i
$466$		0			0
$467$	−176.659			−0.378286			−0.189143	−	0.981950i	$-0.560571\pi$
$467$	−176.659			−0.378286			−0.189143	+	0.981950i	$0.560571\pi$
$468$		0			0
$469$	732.315	−	422.802i	1.56144	−	0.901498i
$470$		0			0
$471$	56.4245	+	20.5132i	0.119797	+	0.0435524i
$472$		0			0
$473$	−203.693	−	352.807i	−0.430641	−	0.745893i
$474$		0			0
$475$	−38.1341	−	20.9604i	−0.0802823	−	0.0441272i
$476$		0			0
$477$	128.861	+	353.229i	0.270149	+	0.740523i
$478$		0			0
$479$	−132.451	+	229.412i	−0.276516	+	0.478940i	−0.970517	−	0.241035i	$-0.922513\pi$
$479$	−132.451	+	229.412i	−0.276516	+	0.478940i	0.694000	+	0.719975i	$0.255847\pi$
$480$		0			0
$481$	−1037.13			−2.15619
$482$		0			0
$483$	−464.583	−	168.899i	−0.961869	−	0.349688i
$484$		0			0
$485$	418.721	−	241.749i	0.863342	−	0.498451i
$486$		0			0
$487$			104.744i			0.215081i	0.994201	+	0.107540i	$0.0342975\pi$
$487$			104.744i			0.215081i	−0.994201	+	0.107540i	$0.965703\pi$
$488$		0			0
$489$	65.9608	−	55.3893i	0.134889	−	0.113271i
$490$		0			0
$491$	−285.529	−	494.550i	−0.581525	−	1.00723i	−0.995299	−	0.0968511i	$-0.969123\pi$
$491$	−285.529	−	494.550i	−0.581525	−	1.00723i	0.413774	−	0.910380i	$-0.364210\pi$
$492$		0			0
$493$	−40.3844	+	23.3159i	−0.0819155	+	0.0472940i
$494$		0			0
$495$	−168.582	−	141.244i	−0.340570	−	0.285342i
$496$		0			0
$497$		−	332.498i		−	0.669010i
$498$		0			0
$499$	88.1450	+	152.672i	0.176643	+	0.305955i	0.940729	−	0.339160i	$-0.110143\pi$
$499$	88.1450	+	152.672i	0.176643	+	0.305955i	−0.764085	+	0.645115i	$0.776809\pi$
$500$		0			0
$501$	357.383	+	425.593i	0.713340	+	0.849486i
$502$		0			0
$503$	277.472	+	480.596i	0.551635	+	0.955459i	0.998157	+	0.0606867i	$0.0193291\pi$
$503$	277.472	+	480.596i	0.551635	+	0.955459i	−0.446522	+	0.894773i	$0.647338\pi$
$504$		0			0
$505$	−787.764			−1.55993
$506$		0			0
$507$	−361.554	+	303.608i	−0.713125	+	0.598833i
$508$		0			0
$509$			714.626i			1.40398i	0.712186	+	0.701990i	$0.247705\pi$
$509$			714.626i			1.40398i	−0.712186	+	0.701990i	$0.752295\pi$
$510$		0			0
$511$	−668.888			−1.30898
$512$		0			0
$513$	−438.485	+	266.270i	−0.854747	+	0.519045i
$514$		0			0
$515$		−	284.054i		−	0.551562i
$516$		0			0
$517$	−339.506			−0.656685
$518$		0			0
$519$	545.474	+	649.582i	1.05101	+	1.25160i
$520$		0			0
$521$			327.567i			0.628728i	0.949303	+	0.314364i	$0.101791\pi$
$521$			327.567i			0.628728i	−0.949303	+	0.314364i	$0.898209\pi$
$522$		0			0
$523$	229.651	−	132.589i	0.439103	−	0.253516i	−0.264114	−	0.964492i	$-0.585079\pi$
$523$	229.651	−	132.589i	0.439103	−	0.253516i	0.703217	+	0.710975i	$0.251746\pi$
$524$		0			0
$525$	37.0284	−	31.0939i	0.0705303	−	0.0592264i
$526$		0			0
$527$	2.88626	−	1.66638i	0.00547678	−	0.00316202i
$528$		0			0
$529$	19.2452			0.0363804
$530$		0			0
$531$	−51.2761	−	140.556i	−0.0965651	−	0.264700i
$532$		0			0
$533$	−509.998	−	883.343i	−0.956845	−	1.65730i
$534$		0			0
$535$	465.610	−	268.820i	0.870298	−	0.502467i
$536$		0			0
$537$	−22.1884	−	26.4233i	−0.0413192	−	0.0492053i
$538$		0			0
$539$	−2.68954			−0.00498987
$540$		0			0
$541$	317.733	+	550.330i	0.587307	+	1.01725i	0.994584	+	0.103941i	$0.0331452\pi$
$541$	317.733	+	550.330i	0.587307	+	1.01725i	−0.407277	+	0.913305i	$0.633521\pi$
$542$		0			0
$543$	82.8560	−	227.907i	0.152589	−	0.419719i
$544$		0			0
$545$		−	427.239i		−	0.783925i
$546$		0			0
$547$	−81.7783	−	47.2147i	−0.149503	−	0.0863157i	0.423382	−	0.905951i	$-0.360843\pi$
$547$	−81.7783	−	47.2147i	−0.149503	−	0.0863157i	−0.572886	+	0.819635i	$0.694176\pi$
$548$		0			0
$549$	−542.579	−	454.594i	−0.988304	−	0.828039i
$550$		0			0
$551$	419.341	−	762.924i	0.761055	−	1.38462i
$552$		0			0
$553$	−716.978	+	413.948i	−1.29652	+	0.748549i
$554$		0			0
$555$	−280.421	+	771.339i	−0.505263	+	1.38980i
$556$		0			0
$557$	118.599	+	205.419i	0.212925	+	0.368796i	0.952629	−	0.304136i	$-0.0983678\pi$
$557$	118.599	+	205.419i	0.212925	+	0.368796i	−0.739704	+	0.672932i	$0.765034\pi$
$558$		0			0
$559$			1435.24i			2.56752i
$560$		0			0
$561$	−11.9897	+	10.0681i	−0.0213721	+	0.0179468i
$562$		0			0
$563$	−591.014	−	341.222i	−1.04976	−	0.606078i	−0.127176	−	0.991880i	$-0.540591\pi$
$563$	−591.014	−	341.222i	−1.04976	−	0.606078i	−0.922582	+	0.385802i	$0.873925\pi$
$564$		0			0
$565$			246.913i			0.437015i
$566$		0			0
$567$	−99.8155	−	561.219i	−0.176041	−	0.989805i
$568$		0			0
$569$	−60.1817	+	34.7459i	−0.105768	+	0.0610649i	−0.551951	−	0.833877i	$-0.686116\pi$
$569$	−60.1817	+	34.7459i	−0.105768	+	0.0610649i	0.446183	+	0.894942i	$0.352783\pi$
$570$		0			0
$571$	88.0919	−	152.580i	0.154277	−	0.267215i	−0.778519	−	0.627621i	$-0.784029\pi$
$571$	88.0919	−	152.580i	0.154277	−	0.267215i	0.932795	+	0.360406i	$0.117362\pi$
$572$		0			0
$573$	−72.4580	−	26.3422i	−0.126454	−	0.0459724i
$574$		0			0
$575$	−26.8128	+	46.4411i	−0.0466309	+	0.0807672i
$576$		0			0
$577$	−215.231			−0.373018			−0.186509	−	0.982453i	$-0.559717\pi$
$577$	−215.231			−0.373018			−0.186509	+	0.982453i	$0.559717\pi$
$578$		0			0
$579$	271.810	−	747.654i	0.469448	−	1.29128i
$580$		0			0
$581$	−97.4711	+	168.825i	−0.167764	+	0.290576i
$582$		0			0
$583$	−185.530	−	107.116i	−0.318234	−	0.183732i
$584$		0			0
$585$	265.547	+	727.906i	0.453926	+	1.24428i
$586$		0			0
$587$	130.209			0.221820			0.110910	−	0.993830i	$-0.464623\pi$
$587$	130.209			0.221820			0.110910	+	0.993830i	$0.464623\pi$
$588$		0			0
$589$	−29.9702	+	54.5260i	−0.0508833	+	0.0925739i
$590$		0			0
$591$	767.164	−	644.211i	1.29808	−	1.09004i
$592$		0			0
$593$	−388.044	−	672.113i	−0.654375	−	1.13341i	−0.982050	−	0.188620i	$-0.939598\pi$
$593$	−388.044	−	672.113i	−0.654375	−	1.13341i	0.327675	−	0.944790i	$-0.393735\pi$
$594$		0			0
$595$	17.0654	+	29.5581i	0.0286813	+	0.0496775i
$596$		0			0
$597$	248.377	+	90.2976i	0.416041	+	0.151252i
$598$		0			0
$599$		−	259.203i		−	0.432727i	−0.976313	−	0.216363i	$-0.930580\pi$
$599$		−	259.203i		−	0.432727i	0.976313	−	0.216363i	$-0.0694196\pi$
$600$		0			0
$601$	111.340	−	64.2824i	0.185259	−	0.106959i	−0.404502	−	0.914537i	$-0.632555\pi$
$601$	111.340	−	64.2824i	0.185259	−	0.106959i	0.589761	+	0.807578i	$0.299222\pi$
$602$		0			0
$603$	−1065.14	−	187.000i	−1.76641	−	0.310116i
$604$		0			0
$605$	−451.313			−0.745972
$606$		0			0
$607$	428.107	+	247.168i	0.705284	+	0.407196i	0.809312	−	0.587378i	$-0.199840\pi$
$607$	428.107	+	247.168i	0.705284	+	0.407196i	−0.104028	+	0.994574i	$0.533173\pi$
$608$		0			0
$609$	622.075	+	740.803i	1.02147	+	1.21642i
$610$		0			0
$611$	1035.85	+	598.049i	1.69534	+	0.978803i
$612$		0			0
$613$	−27.2301	+	47.1640i	−0.0444211	+	0.0769396i	−0.887381	−	0.461037i	$-0.847478\pi$
$613$	−27.2301	+	47.1640i	−0.0444211	+	0.0769396i	0.842960	+	0.537976i	$0.180811\pi$
$614$		0			0
$615$	−794.861	+	140.459i	−1.29246	+	0.228389i
$616$		0			0
$617$	−168.287			−0.272750			−0.136375	−	0.990657i	$-0.543545\pi$
$617$	−168.287			−0.272750			−0.136375	+	0.990657i	$0.543545\pi$
$618$		0			0
$619$	−226.776	−	392.788i	−0.366359	−	0.634553i	0.622634	−	0.782513i	$-0.286062\pi$
$619$	−226.776	−	392.788i	−0.366359	−	0.634553i	−0.988993	+	0.147961i	$0.952729\pi$
$620$		0			0
$621$	316.706	+	547.146i	0.509993	+	0.881072i
$622$		0			0
$623$	172.184	+	99.4107i	0.276380	+	0.159568i
$624$		0			0
$625$	281.249	+	487.138i	0.449999	+	0.779420i
$626$		0			0
$627$	94.0704	−	276.738i	0.150032	−	0.441369i
$628$		0			0
$629$	50.5981	+	29.2128i	0.0804422	+	0.0464433i
$630$		0			0
$631$	−394.174	−	682.730i	−0.624682	−	1.08198i	−0.988602	−	0.150551i	$-0.951895\pi$
$631$	−394.174	−	682.730i	−0.624682	−	1.08198i	0.363920	−	0.931430i	$-0.381438\pi$
$632$		0			0
$633$	169.738	−	466.890i	0.268149	−	0.737583i
$634$		0			0
$635$	−613.481	−	354.194i	−0.966112	−	0.557785i
$636$		0			0
$637$	8.20592	+	4.73769i	0.0128821	+	0.00743750i
$638$		0			0
$639$	−273.090	+	325.946i	−0.427371	+	0.510087i
$640$		0			0
$641$			526.655i			0.821614i	0.911722	+	0.410807i	$0.134753\pi$
$641$			526.655i			0.821614i	−0.911722	+	0.410807i	$0.865247\pi$
$642$		0			0
$643$	631.602	+	1093.97i	0.982273	+	1.70135i	0.653478	+	0.756945i	$0.273309\pi$
$643$	631.602	+	1093.97i	0.982273	+	1.70135i	0.328795	+	0.944401i	$0.393358\pi$
$644$		0			0
$645$	1067.43	+	388.065i	1.65493	+	0.601652i
$646$		0			0
$647$	498.316			0.770195			0.385098	−	0.922876i	$-0.374168\pi$
$647$	498.316			0.770195			0.385098	+	0.922876i	$0.374168\pi$
$648$		0			0
$649$	73.8256	+	42.6233i	0.113753	+	0.0656753i
$650$		0			0
$651$	−44.4596	−	52.9450i	−0.0682943	−	0.0813287i
$652$		0			0
$653$	406.675	−	704.382i	0.622779	−	1.07869i	−0.366186	−	0.930542i	$-0.619337\pi$
$653$	406.675	−	704.382i	0.622779	−	1.07869i	0.988966	−	0.148144i	$-0.0473299\pi$
$654$		0			0
$655$	266.495	−	461.582i	0.406862	−	0.704706i
$656$		0			0
$657$	655.706	+	549.376i	0.998031	+	0.836189i
$658$		0			0
$659$	−674.101	−	389.193i	−1.02292	−	0.590580i	−0.107968	−	0.994154i	$-0.534435\pi$
$659$	−674.101	−	389.193i	−1.02292	−	0.590580i	−0.914947	+	0.403574i	$0.867768\pi$
$660$		0			0
$661$		−	8.84755i		−	0.0133851i	−0.999978	−	0.00669255i	$-0.997870\pi$
$661$		−	8.84755i		−	0.0133851i	0.999978	−	0.00669255i	$-0.00213032\pi$
$662$		0			0
$663$	54.3166	−	9.59822i	0.0819255	−	0.0144770i
$664$		0			0
$665$	−558.399	−	306.924i	−0.839698	−	0.461541i
$666$		0			0
$667$	−929.117	−	536.426i	−1.39298	−	0.804237i
$668$		0			0
$669$	23.2178	+	27.6491i	0.0347052	+	0.0413290i
$670$		0			0
$671$	403.307			0.601054
$672$		0			0
$673$	−281.617	+	162.592i	−0.418451	+	0.241593i	−0.694414	−	0.719576i	$-0.744336\pi$
$673$	−281.617	+	162.592i	−0.418451	+	0.241593i	0.275964	+	0.961168i	$0.411003\pi$
$674$		0			0
$675$	−61.8370	+	0.0686992i	−0.0916103	+	0.000101777i
$676$		0			0
$677$	−109.957	+	63.4837i	−0.162418	+	0.0937721i	−0.579006	−	0.815323i	$-0.696559\pi$
$677$	−109.957	+	63.4837i	−0.162418	+	0.0937721i	0.416588	+	0.909095i	$0.363226\pi$
$678$		0			0
$679$	−618.342	+	357.000i	−0.910665	+	0.525773i
$680$		0			0
$681$	414.822	−	1141.03i	0.609136	−	1.67552i
$682$		0			0
$683$			1318.05i			1.92979i	0.262639	+	0.964894i	$0.415407\pi$
$683$			1318.05i			1.92979i	−0.262639	+	0.964894i	$0.584593\pi$
$684$		0			0
$685$	−1123.14			−1.63962
$686$		0			0
$687$	129.707	+	734.017i	0.188802	+	1.06844i
$688$		0			0
$689$	377.375	+	653.633i	0.547714	+	0.948669i
$690$		0			0
$691$	−7.62894	−	13.2137i	−0.0110404	−	0.0191226i	0.860452	−	0.509531i	$-0.170181\pi$
$691$	−7.62894	−	13.2137i	−0.0110404	−	0.0191226i	−0.871493	+	0.490408i	$0.836848\pi$
$692$		0			0
$693$	248.952	+	208.581i	0.359238	+	0.300983i
$694$		0			0
$695$	−35.1351	−	60.8557i	−0.0505541	−	0.0875622i
$696$		0			0
$697$			57.4607i			0.0824401i
$698$		0			0
$699$	117.520	+	665.050i	0.168126	+	0.951431i
$700$		0			0
$701$	195.166	−	338.037i	0.278411	−	0.482221i	−0.692579	−	0.721342i	$-0.743526\pi$
$701$	195.166	−	338.037i	0.278411	−	0.482221i	0.970990	+	0.239120i	$0.0768590\pi$
$702$		0			0
$703$	−1090.51	+	22.9303i	−1.55123	+	0.0326178i
$704$		0			0
$705$	724.861	−	608.688i	1.02817	−	0.863388i
$706$		0			0
$707$	1163.32			1.64543
$708$		0			0
$709$	−312.910	+	541.976i	−0.441340	+	0.764423i	−0.997789	−	0.0664584i	$-0.978830\pi$
$709$	−312.910	+	541.976i	−0.441340	+	0.764423i	0.556449	+	0.830882i	$0.312163\pi$
$710$		0			0
$711$	1042.84	+	183.084i	1.46672	+	0.257502i
$712$		0			0
$713$	66.4038	+	38.3382i	0.0931329	+	0.0537703i
$714$		0			0
$715$	−382.326	−	220.736i	−0.534721	−	0.308721i
$716$		0			0
$717$	238.678	+	1350.69i	0.332884	+	1.88380i
$718$		0			0
$719$	464.868	−	805.175i	0.646548	−	1.11985i	−0.337394	−	0.941364i	$-0.609545\pi$
$719$	464.868	−	805.175i	0.646548	−	1.11985i	0.983942	−	0.178490i	$-0.0571213\pi$
$720$		0			0
$721$			419.474i			0.581795i
$722$		0			0
$723$	1090.12	−	192.633i	1.50777	−	0.266436i
$724$		0			0
$725$	90.8798	−	52.4695i	0.125351	−	0.0723717i
$726$		0			0
$727$	800.752			1.10145			0.550723	−	0.834688i	$-0.314352\pi$
$727$	800.752			1.10145			0.550723	+	0.834688i	$0.314352\pi$
$728$		0			0
$729$	−363.096	+	632.141i	−0.498075	+	0.867134i
$730$		0			0
$731$	40.4267	−	70.0211i	0.0553033	−	0.0957881i
$732$		0			0
$733$	−453.750	+	785.917i	−0.619031	+	1.07219i	0.370632	+	0.928780i	$0.379141\pi$
$733$	−453.750	+	785.917i	−0.619031	+	1.07219i	−0.989663	+	0.143413i	$0.954192\pi$
$734$		0			0
$735$	5.74229	−	4.82198i	0.00781264	−	0.00656051i
$736$		0			0
$737$	533.614	−	308.082i	0.724035	−	0.418022i
$738$		0			0
$739$	469.579	−	813.334i	0.635424	−	1.10059i	−0.351001	−	0.936375i	$-0.614158\pi$
$739$	469.579	−	813.334i	0.635424	−	1.10059i	0.986425	−	0.164212i	$-0.0525082\pi$
$740$		0			0
$741$	−774.495	+	678.636i	−1.04520	+	0.915838i
$742$		0			0
$743$	−1013.53	+	585.160i	−1.36410	+	0.787563i	−0.990167	−	0.139892i	$-0.955324\pi$
$743$	−1013.53	+	585.160i	−1.36410	+	0.787563i	−0.373933	+	0.927456i	$0.621991\pi$
$744$		0			0
$745$	353.904	−	612.979i	0.475039	−	0.822791i
$746$		0			0
$747$	234.211	−	85.4422i	0.313535	−	0.114381i
$748$		0			0
$749$	−687.584	+	396.977i	−0.918003	+	0.530009i
$750$		0			0
$751$		−	734.947i		−	0.978625i	−0.872108	−	0.489313i	$-0.837248\pi$
$751$		−	734.947i		−	0.978625i	0.872108	−	0.489313i	$-0.162752\pi$
$752$		0			0
$753$	286.635	+	104.206i	0.380657	+	0.138388i
$754$		0			0
$755$	−36.8567	−	21.2792i	−0.0488169	−	0.0281844i
$756$		0			0
$757$	−159.609	+	276.450i	−0.210843	+	0.365192i	−0.951979	−	0.306164i	$-0.900954\pi$
$757$	−159.609	+	276.450i	−0.210843	+	0.365192i	0.741135	+	0.671356i	$0.234288\pi$
$758$		0			0
$759$	−338.526	−	123.071i	−0.446016	−	0.162149i
$760$		0			0
$761$	248.077	−	429.681i	0.325988	−	0.564627i	−0.655724	−	0.755001i	$-0.727637\pi$
$761$	248.077	−	429.681i	0.325988	−	0.564627i	0.981712	+	0.190373i	$0.0609699\pi$
$762$		0			0
$763$			630.921i			0.826895i
$764$		0			0
$765$	7.54781	−	42.9919i	0.00986642	−	0.0561986i
$766$		0			0
$767$	−150.164	−	260.092i	−0.195781	−	0.339102i
$768$		0			0
$769$	438.842			0.570666			0.285333	−	0.958428i	$-0.407896\pi$
$769$	438.842			0.570666			0.285333	+	0.958428i	$0.407896\pi$
$770$		0			0
$771$	120.661	+	143.690i	0.156499	+	0.186368i
$772$		0			0
$773$	−494.966	+	285.769i	−0.640319	+	0.369688i	−0.784737	−	0.619828i	$-0.787202\pi$
$773$	−494.966	+	285.769i	−0.640319	+	0.369688i	0.144418	+	0.989517i	$0.453869\pi$
$774$		0			0
$775$	−6.49516	+	3.74998i	−0.00838086	+	0.00483869i
$776$		0			0
$777$	414.109	−	1139.07i	0.532958	−	1.46598i
$778$		0			0
$779$	−555.782	−	917.539i	−0.713455	−	1.17784i
$780$		0			0
$781$		−	242.280i		−	0.310218i
$782$		0			0
$783$	−1.37442	−	1237.13i	−0.00175532	−	1.57999i
$784$		0			0
$785$	47.6846	−	82.5921i	0.0607447	−	0.105213i
$786$		0			0
$787$	648.532	+	374.430i	0.824056	+	0.475769i	0.851813	−	0.523846i	$-0.175503\pi$
$787$	648.532	+	374.430i	0.824056	+	0.475769i	−0.0277571	+	0.999615i	$0.508836\pi$
$788$		0			0
$789$	434.472	−	364.840i	0.550662	−	0.462408i
$790$		0			0
$791$		−	364.627i		−	0.460969i
$792$		0			0
$793$	−1230.51	−	710.436i	−1.55172	−	0.895884i
$794$		0			0
$795$	588.161	−	103.933i	0.739825	−	0.130734i
$796$		0			0
$797$	853.076	+	492.523i	1.07036	+	0.617972i	0.928279	−	0.371884i	$-0.121288\pi$
$797$	853.076	+	492.523i	1.07036	+	0.617972i	0.142079	+	0.989855i	$0.454621\pi$
$798$		0			0
$799$	−33.6906	−	58.3539i	−0.0421660	−	0.0730336i
$800$		0			0
$801$	−87.1425	−	238.872i	−0.108792	−	0.298217i
$802$		0			0
$803$	−487.396			−0.606969
$804$		0			0
$805$	−392.621	+	680.040i	−0.487728	+	0.844770i
$806$		0			0
$807$	−374.288	+	66.1399i	−0.463801	+	0.0819578i
$808$		0			0
$809$	1601.15			1.97917			0.989587	−	0.143939i	$-0.0459770\pi$
$809$	1601.15			1.97917			0.989587	+	0.143939i	$0.0459770\pi$
$810$		0			0
$811$	−715.560	+	413.129i	−0.882318	+	0.509406i	−0.871422	−	0.490534i	$-0.836802\pi$
$811$	−715.560	+	413.129i	−0.882318	+	0.509406i	−0.0108958	+	0.999941i	$0.503468\pi$
$812$		0			0
$813$	148.968	+	843.015i	0.183233	+	1.03692i
$814$		0			0
$815$	−68.4104	−	118.490i	−0.0839391	−	0.145387i
$816$		0			0
$817$	31.7325	+	1509.13i	0.0388403	+	1.84716i
$818$		0			0
$819$	−392.143	−	1074.93i	−0.478807	−	1.31249i
$820$		0			0
$821$	87.8076	−	152.087i	0.106952	−	0.185246i	−0.807582	−	0.589755i	$-0.799224\pi$
$821$	87.8076	−	152.087i	0.106952	−	0.185246i	0.914534	+	0.404509i	$0.132558\pi$
$822$		0			0
$823$	815.880			0.991348			0.495674	−	0.868509i	$-0.334921\pi$
$823$	815.880			0.991348			0.495674	+	0.868509i	$0.334921\pi$
$824$		0			0
$825$	26.9814	−	22.6571i	0.0327047	−	0.0274631i
$826$		0			0
$827$	−982.422	+	567.202i	−1.18793	+	0.685854i	−0.957837	−	0.287313i	$-0.907238\pi$
$827$	−982.422	+	567.202i	−1.18793	+	0.685854i	−0.230098	+	0.973167i	$0.573905\pi$
$828$		0			0
$829$			764.117i			0.921734i	0.887469	+	0.460867i	$0.152461\pi$
$829$			764.117i			0.921734i	−0.887469	+	0.460867i	$0.847539\pi$
$830$		0			0
$831$	673.412	+	244.820i	0.810364	+	0.294608i
$832$		0			0
$833$	−0.266894	−	0.462274i	−0.000320401	−	0.000554951i
$834$		0			0
$835$	764.523	−	441.398i	0.915596	−	0.528620i
$836$		0			0
$837$	0.0982294	+	88.4175i	0.000117359	+	0.105636i
$838$		0			0
$839$		−	121.498i		−	0.144813i	−0.997375	−	0.0724066i	$-0.976932\pi$
$839$		−	121.498i		−	0.144813i	0.997375	−	0.0724066i	$-0.0230679\pi$
$840$		0			0
$841$	629.222	+	1089.85i	0.748184	+	1.29589i
$842$		0			0
$843$	−467.989	+	82.6978i	−0.555147	+	0.0980993i
$844$		0			0
$845$	374.981	+	649.487i	0.443765	+	0.768623i
$846$		0			0
$847$	666.472			0.786861
$848$		0			0
$849$	−78.1438	−	28.4092i	−0.0920421	−	0.0334620i
$850$		0			0
$851$			1344.19i			1.57954i
$852$		0			0
$853$	−69.7227			−0.0817383			−0.0408691	−	0.999165i	$-0.513013\pi$
$853$	−69.7227			−0.0817383			−0.0408691	+	0.999165i	$0.513013\pi$
$854$		0			0
$855$	295.310	+	759.505i	0.345392	+	0.888310i
$856$		0			0
$857$		−	347.662i		−	0.405674i	−0.979213	−	0.202837i	$-0.934984\pi$
$857$		−	347.662i		−	0.405674i	0.979213	−	0.202837i	$-0.0650161\pi$
$858$		0			0
$859$	734.130			0.854633			0.427317	−	0.904102i	$-0.359459\pi$
$859$	734.130			0.854633			0.427317	+	0.904102i	$0.359459\pi$
$860$		0			0
$861$	1173.80	−	207.421i	1.36330	−	0.240907i
$862$		0			0
$863$		−	1462.37i		−	1.69452i	−0.531181	−	0.847258i	$-0.678252\pi$
$863$		−	1462.37i		−	1.69452i	0.531181	−	0.847258i	$-0.321748\pi$
$864$		0			0
$865$	1166.89	−	673.705i	1.34901	−	0.778850i
$866$		0			0
$867$	811.903	+	295.168i	0.936451	+	0.340448i
$868$		0			0
$869$	−522.438	+	301.630i	−0.601195	+	0.347100i
$870$		0			0
$871$	−2170.78			−2.49228
$872$		0			0
$873$	899.370	+	157.896i	1.03021	+	0.180866i
$874$		0			0
$875$	−457.608	−	792.601i	−0.522981	−	0.905829i
$876$		0			0
$877$	−1097.70	+	633.759i	−1.25166	+	0.722644i	−0.971438	−	0.237292i	$-0.923740\pi$
$877$	−1097.70	+	633.759i	−1.25166	+	0.722644i	−0.280218	+	0.959936i	$0.590407\pi$
$878$		0			0
$879$	1010.22	−	178.514i	1.14928	−	0.203088i
$880$		0			0
$881$	−1356.03			−1.53919			−0.769596	−	0.638531i	$-0.779542\pi$
$881$	−1356.03			−1.53919			−0.769596	+	0.638531i	$0.779542\pi$
$882$		0			0
$883$	276.740	+	479.328i	0.313409	+	0.542841i	0.979098	−	0.203389i	$-0.0651956\pi$
$883$	276.740	+	479.328i	0.313409	+	0.542841i	−0.665689	+	0.746229i	$0.731862\pi$
$884$		0			0
$885$	−234.039	+	41.3567i	−0.264451	+	0.0467308i
$886$		0			0
$887$			824.598i			0.929649i	0.885403	+	0.464824i	$0.153882\pi$
$887$			824.598i			0.929649i	−0.885403	+	0.464824i	$0.846118\pi$
$888$		0			0
$889$	905.952	+	523.052i	1.01907	+	0.588360i
$890$		0			0
$891$	−72.7322	−	408.942i	−0.0816299	−	0.458969i
$892$		0			0
$893$	1102.40	+	605.932i	1.23449	+	0.678535i
$894$		0			0
$895$	−47.4660	+	27.4045i	−0.0530347	+	0.0306196i
$896$		0			0
$897$	816.067	+	971.819i	0.909773	+	1.08341i
$898$		0			0
$899$	−75.0235	−	129.944i	−0.0834521	−	0.144543i
$900$		0			0
$901$		−	42.5183i		−	0.0471901i
$902$		0			0
$903$	−1576.32	−	573.071i	−1.74564	−	0.634630i
$904$		0			0
$905$	−333.603	−	192.606i	−0.368622	−	0.212824i
$906$		0			0
$907$		−	842.020i		−	0.928357i	−0.885742	−	0.464179i	$-0.846350\pi$
$907$		−	842.020i		−	0.928357i	0.885742	−	0.464179i	$-0.153650\pi$
$908$		0			0
$909$	−1140.40	−	955.469i	−1.25456	−	1.05112i
$910$		0			0
$911$	316.343	−	182.641i	0.347248	−	0.200484i	−0.316224	−	0.948684i	$-0.602415\pi$
$911$	316.343	−	182.641i	0.347248	−	0.200484i	0.663473	+	0.748200i	$0.269082\pi$
$912$		0			0
$913$	−71.0239	+	123.017i	−0.0777918	+	0.134739i
$914$		0			0
$915$	−861.079	+	723.075i	−0.941070	+	0.790246i
$916$		0			0
$917$	−393.543	+	681.637i	−0.429164	+	0.743334i
$918$		0			0
$919$	−1460.11			−1.58880			−0.794400	−	0.607395i	$-0.792215\pi$
$919$	−1460.11			−1.58880			−0.794400	+	0.607395i	$0.792215\pi$
$920$		0			0
$921$	−842.298	+	148.841i	−0.914547	+	0.161609i
$922$		0			0
$923$	−426.783	+	739.210i	−0.462387	+	0.800877i
$924$		0			0
$925$	−113.865	−	65.7397i	−0.123097	−	0.0710700i
$926$		0			0
$927$	344.526	−	411.208i	0.371657	−	0.443590i
$928$		0			0
$929$	241.961			0.260453			0.130226	−	0.991484i	$-0.458430\pi$
$929$	241.961			0.260453			0.130226	+	0.991484i	$0.458430\pi$
$930$		0			0
$931$	8.73308	+	4.80014i	0.00938033	+	0.00515590i
$932$		0			0
$933$	165.476	+	936.433i	0.177359	+	1.00368i
$934$		0			0
$935$	12.4350	+	21.5380i	0.0132995	+	0.0230353i
$936$		0			0
$937$	−402.399	−	696.975i	−0.429454	−	0.743837i	0.567370	−	0.823463i	$-0.307961\pi$
$937$	−402.399	−	696.975i	−0.429454	−	0.743837i	−0.996825	+	0.0796259i	$0.974627\pi$
$938$		0			0
$939$	−24.5530	−	138.946i	−0.0261480	−	0.147972i
$940$		0			0
$941$		−	719.489i		−	0.764601i	−0.924038	−	0.382300i	$-0.875132\pi$
$941$		−	719.489i		−	0.764601i	0.924038	−	0.382300i	$-0.124868\pi$
$942$		0			0
$943$	−1144.88	+	660.995i	−1.21408	+	0.700949i
$944$		0			0
$945$	−905.482	+	1.00597i	−0.958182	+	0.00106451i
$946$		0			0
$947$	412.215			0.435285			0.217643	−	0.976029i	$-0.430163\pi$
$947$	412.215			0.435285			0.217643	+	0.976029i	$0.430163\pi$
$948$		0			0
$949$	1487.07	+	858.561i	1.56699	+	0.904701i
$950$		0			0
$951$	−1530.52	+	270.457i	−1.60938	+	0.284392i
$952$		0			0
$953$	−1176.65	−	679.339i	−1.23468	−	0.712843i	−0.266678	−	0.963786i	$-0.585926\pi$
$953$	−1176.65	−	679.339i	−1.23468	−	0.712843i	−0.968002	+	0.250943i	$0.919259\pi$
$954$		0			0
$955$	−61.2346	+	106.061i	−0.0641200	+	0.111059i
$956$		0			0
$957$	453.285	+	539.798i	0.473652	+	0.564052i
$958$		0			0
$959$	1658.59			1.72950
$960$		0			0
$961$	−475.138	−	822.963i	−0.494420	−	0.856361i
$962$		0			0
$963$	1000.08	+	175.578i	1.03851	+	0.182324i
$964$		0			0
$965$	−1094.39	−	631.846i	−1.13408	−	0.654762i
$966$		0			0
$967$	−448.377	−	776.611i	−0.463678	−	0.803114i	0.535463	−	0.844559i	$-0.320137\pi$
$967$	−448.377	−	776.611i	−0.463678	−	0.803114i	−0.999141	+	0.0414450i	$0.986804\pi$
$968$		0			0
$969$	56.9004	−	11.2932i	0.0587208	−	0.0116545i
$970$		0			0
$971$	952.730	+	550.059i	0.981184	+	0.566487i	0.902627	−	0.430423i	$-0.141636\pi$
$971$	952.730	+	550.059i	0.981184	+	0.566487i	0.0785567	+	0.996910i	$0.474969\pi$
$972$		0			0
$973$	51.8854	+	89.8681i	0.0533251	+	0.0923619i
$974$		0			0
$975$	−122.233	+	21.5996i	−0.125367	+	0.0221534i
$976$		0			0
$977$	−1.98302	−	1.14490i	−0.00202970	−	0.00117185i	0.498985	−	0.866611i	$-0.333706\pi$
$977$	−1.98302	−	1.14490i	−0.00202970	−	0.00117185i	−0.501015	+	0.865439i	$0.667040\pi$
$978$		0			0
$979$	125.465	+	72.4373i	0.128156	+	0.0739911i
$980$		0			0
$981$	518.193	−	618.488i	0.528229	−	0.630466i
$982$		0			0
$983$			656.624i			0.667979i	0.942577	+	0.333990i	$0.108395\pi$
$983$			656.624i			0.667979i	−0.942577	+	0.333990i	$0.891605\pi$
$984$		0			0
$985$	−795.653	−	1378.11i	−0.807770	−	1.39910i
$986$		0			0
$987$	−1070.43	+	898.874i	−1.08453	+	0.910713i
$988$		0			0
$989$	1860.18			1.88087
$990$		0			0
$991$	1396.56	+	806.305i	1.40924	+	0.813628i	0.995315	−	0.0966810i	$-0.0308227\pi$
$991$	1396.56	+	806.305i	1.40924	+	0.813628i	0.413930	+	0.910309i	$0.364156\pi$
$992$		0			0
$993$	−1.39474	+	3.83643i	−0.00140457	+	0.00386348i
$994$		0			0
$995$	209.904	−	363.565i	0.210959	−	0.365392i
$996$		0			0
$997$	−50.7545	+	87.9093i	−0.0509072	+	0.0881739i	−0.890356	−	0.455265i	$-0.849545\pi$
$997$	−50.7545	+	87.9093i	−0.0509072	+	0.0881739i	0.839449	+	0.543439i	$0.182878\pi$
$998$		0			0
$999$	−1341.49	+	776.501i	−1.34284	+	0.777278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.32	✓	80
3.2	odd	2		2052.3.s.a.901.31		80
9.2	odd	6		2052.3.bl.a.1585.10		80
9.7	even	3		684.3.bl.a.673.19	yes	80
19.12	odd	6		684.3.bl.a.373.19	yes	80
57.50	even	6		2052.3.bl.a.145.10		80
171.88	odd	6	inner	684.3.s.a.601.32	yes	80
171.164	even	6		2052.3.s.a.829.31		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.32	✓	80	1.1	even	1	trivial
684.3.s.a.601.32	yes	80	171.88	odd	6	inner
684.3.bl.a.373.19	yes	80	19.12	odd	6
684.3.bl.a.673.19	yes	80	9.7	even	3
2052.3.s.a.829.31		80	171.164	even	6
2052.3.s.a.901.31		80	3.2	odd	2
2052.3.bl.a.145.10		80	57.50	even	6
2052.3.bl.a.1585.10		80	9.2	odd	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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.29742 - 1.92921i) q^{3} +(-2.38274 - 4.12702i) q^{5} +(3.51868 + 6.09454i) q^{7} +(1.55627 - 8.86442i) q^{9} +O(q^{10})\)	\(q+(2.29742 - 1.92921i) q^{3} +(-2.38274 - 4.12702i) q^{5} +(3.51868 + 6.09454i) q^{7} +(1.55627 - 8.86442i) q^{9} +(2.56395 + 4.44089i) q^{11} -18.0658i q^{13} +(-13.4361 - 4.88469i) q^{15} +(-0.508862 + 0.881376i) q^{17} +(-0.399427 - 18.9958i) q^{19} +(19.8415 + 7.21341i) q^{21} -23.4146 q^{23} +(1.14513 - 1.98342i) q^{25} +(-13.5260 - 23.3677i) q^{27} +(39.6810 + 22.9099i) q^{29} +(-2.83600 - 1.63736i) q^{31} +(14.4579 + 5.25617i) q^{33} +(16.7682 - 29.0434i) q^{35} -57.4081i q^{37} +(-34.8528 - 41.5048i) q^{39} +(48.8958 - 28.2300i) q^{41} -79.4452 q^{43} +(-40.2918 + 14.6988i) q^{45} +(-33.1039 + 57.3376i) q^{47} +(-0.262246 + 0.454223i) q^{49} +(0.531292 + 3.00659i) q^{51} +(-36.1806 + 20.8889i) q^{53} +(12.2184 - 21.1629i) q^{55} +(-37.5646 - 42.8707i) q^{57} +(14.3969 - 8.31204i) q^{59} +(39.3248 - 68.1126i) q^{61} +(59.5006 - 21.7064i) q^{63} +(-74.5581 + 43.0461i) q^{65} -120.159i q^{67} +(-53.7932 + 45.1718i) q^{69} +(-40.9176 - 23.6238i) q^{71} +(-47.5240 + 82.3140i) q^{73} +(-1.19560 - 6.76595i) q^{75} +(-18.0434 + 31.2521i) q^{77} +117.643i q^{79} +(-76.1561 - 27.5909i) q^{81} +(13.8505 + 23.9898i) q^{83} +4.84994 q^{85} +(135.362 - 23.9197i) q^{87} +(24.4672 - 14.1261i) q^{89} +(110.103 - 63.5679i) q^{91} +(-9.67429 + 1.70953i) q^{93} +(-77.4443 + 46.9104i) q^{95} +101.458i q^{97} +(43.3561 - 15.8167i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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