LMFDB - Embedded newform 684.3.m.a.353.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(353,684)]

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, 4]))

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

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.m (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			353.33
Character	$\chi$	$=$	684.353
Dual form			684.3.m.a.653.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.48438 + 1.68163i) q^{3} +9.01704i q^{5} +(-2.96809 + 5.14088i) q^{7} +(3.34426 + 8.35559i) q^{9} +O(q^{10})$	\(q+(2.48438 + 1.68163i) q^{3} +9.01704i q^{5} +(-2.96809 + 5.14088i) q^{7} +(3.34426 + 8.35559i) q^{9} +(-12.6334 - 7.29387i) q^{11} +(5.07944 - 8.79786i) q^{13} +(-15.1633 + 22.4017i) q^{15} +(8.78209 + 5.07034i) q^{17} +(-11.4499 + 15.1624i) q^{19} +(-16.0189 + 7.78067i) q^{21} +(31.6054 + 18.2474i) q^{23} -56.3071 q^{25} +(-5.74257 + 26.3822i) q^{27} -42.7558i q^{29} +(6.00654 + 10.4036i) q^{31} +(-19.1204 - 39.3653i) q^{33} +(-46.3555 - 26.7634i) q^{35} -3.36324 q^{37} +(27.4140 - 13.3155i) q^{39} -49.5225i q^{41} +(-23.9599 - 41.4997i) q^{43} +(-75.3427 + 30.1554i) q^{45} +19.0892i q^{47} +(6.88091 + 11.9181i) q^{49} +(13.2916 + 27.3648i) q^{51} +(18.0739 - 10.4350i) q^{53} +(65.7691 - 113.915i) q^{55} +(-53.9435 + 18.4148i) q^{57} +88.5735i q^{59} -90.7807 q^{61} +(-52.8811 - 7.60767i) q^{63} +(79.3306 + 45.8016i) q^{65} +(6.87740 - 11.9120i) q^{67} +(47.8345 + 98.4819i) q^{69} +(-47.2523 - 27.2811i) q^{71} +(-3.72907 + 6.45893i) q^{73} +(-139.888 - 94.6874i) q^{75} +(74.9938 - 43.2977i) q^{77} +(41.3420 + 71.6065i) q^{79} +(-58.6318 + 55.8866i) q^{81} +(131.072 + 75.6747i) q^{83} +(-45.7195 + 79.1885i) q^{85} +(71.8994 - 106.222i) q^{87} +(-29.6962 + 17.1451i) q^{89} +(30.1525 + 52.2256i) q^{91} +(-2.57251 + 35.9473i) q^{93} +(-136.720 - 103.244i) q^{95} +(68.4432 + 118.547i) q^{97} +(18.6953 - 129.952i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	2.48438	+	1.68163i	0.828126	+	0.560542i
$3$	2.48438	+	1.68163i	0.828126	+	0.560542i
$4$		0			0
$5$			9.01704i			1.80341i	0.432353	+	0.901704i	$0.357683\pi$
$5$			9.01704i			1.80341i	−0.432353	+	0.901704i	$0.642317\pi$
$6$		0			0
$7$	−2.96809	+	5.14088i	−0.424013	+	0.734411i	−0.996328	−	0.0856225i	$-0.972712\pi$
$7$	−2.96809	+	5.14088i	−0.424013	+	0.734411i	0.572315	+	0.820034i	$0.306045\pi$
$8$		0			0
$9$	3.34426	+	8.35559i	0.371585	+	0.928399i
$10$		0			0
$11$	−12.6334	−	7.29387i	−1.14849	−	0.663079i	−0.199968	−	0.979802i	$-0.564084\pi$
$11$	−12.6334	−	7.29387i	−1.14849	−	0.663079i	−0.948518	+	0.316723i	$0.897417\pi$
$12$		0			0
$13$	5.07944	−	8.79786i	0.390726	−	0.676758i	−0.601819	−	0.798632i	$-0.705557\pi$
$13$	5.07944	−	8.79786i	0.390726	−	0.676758i	0.992546	+	0.121874i	$0.0388905\pi$
$14$		0			0
$15$	−15.1633	+	22.4017i	−1.01089	+	1.49345i
$16$		0			0
$17$	8.78209	+	5.07034i	0.516593	+	0.298255i	0.735540	−	0.677482i	$-0.236929\pi$
$17$	8.78209	+	5.07034i	0.516593	+	0.298255i	−0.218946	+	0.975737i	$0.570262\pi$
$18$		0			0
$19$	−11.4499	+	15.1624i	−0.602627	+	0.798023i
$19$	−11.4499	+	15.1624i	−0.602627	+	0.798023i
$20$		0			0
$21$	−16.0189	+	7.78067i	−0.762804	+	0.370508i
$22$		0			0
$23$	31.6054	+	18.2474i	1.37415	+	0.793365i	0.991447	−	0.130507i	$-0.0416606\pi$
$23$	31.6054	+	18.2474i	1.37415	+	0.793365i	0.382701	+	0.923872i	$0.374994\pi$
$24$		0			0
$25$	−56.3071			−2.25228
$26$		0			0
$27$	−5.74257	+	26.3822i	−0.212688	+	0.977120i
$28$		0			0
$29$		−	42.7558i		−	1.47434i	−0.675708	−	0.737170i	$-0.736162\pi$
$29$		−	42.7558i		−	1.47434i	0.675708	−	0.737170i	$-0.263838\pi$
$30$		0			0
$31$	6.00654	+	10.4036i	0.193759	+	0.335601i	0.946493	−	0.322724i	$-0.104599\pi$
$31$	6.00654	+	10.4036i	0.193759	+	0.335601i	−0.752734	+	0.658325i	$0.771265\pi$
$32$		0			0
$33$	−19.1204	−	39.3653i	−0.579408	−	1.19289i
$34$		0			0
$35$	−46.3555	−	26.7634i	−1.32444	−	0.764668i
$36$		0			0
$37$	−3.36324			−0.0908985			−0.0454492	−	0.998967i	$-0.514472\pi$
$37$	−3.36324			−0.0908985			−0.0454492	+	0.998967i	$0.514472\pi$
$38$		0			0
$39$	27.4140	−	13.3155i	0.702922	−	0.341422i
$40$		0			0
$41$		−	49.5225i		−	1.20787i	−0.797035	−	0.603933i	$-0.793599\pi$
$41$		−	49.5225i		−	1.20787i	0.797035	−	0.603933i	$-0.206401\pi$
$42$		0			0
$43$	−23.9599	−	41.4997i	−0.557207	−	0.965110i	−0.997728	−	0.0673683i	$-0.978540\pi$
$43$	−23.9599	−	41.4997i	−0.557207	−	0.965110i	0.440521	−	0.897742i	$-0.354794\pi$
$44$		0			0
$45$	−75.3427	+	30.1554i	−1.67428	+	0.670119i
$46$		0			0
$47$			19.0892i			0.406153i	0.979163	+	0.203077i	$0.0650940\pi$
$47$			19.0892i			0.406153i	−0.979163	+	0.203077i	$0.934906\pi$
$48$		0			0
$49$	6.88091	+	11.9181i	0.140427	+	0.243226i
$50$		0			0
$51$	13.2916	+	27.3648i	0.260620	+	0.536565i
$52$		0			0
$53$	18.0739	−	10.4350i	0.341017	−	0.196886i	−0.319705	−	0.947517i	$-0.603584\pi$
$53$	18.0739	−	10.4350i	0.341017	−	0.196886i	0.660722	+	0.750631i	$0.270250\pi$
$54$		0			0
$55$	65.7691	−	113.915i	1.19580	−	2.07119i
$56$		0			0
$57$	−53.9435	+	18.4148i	−0.946376	+	0.323066i
$58$		0			0
$59$			88.5735i			1.50125i	0.660731	+	0.750623i	$0.270247\pi$
$59$			88.5735i			1.50125i	−0.660731	+	0.750623i	$0.729753\pi$
$60$		0			0
$61$	−90.7807			−1.48821			−0.744105	−	0.668063i	$-0.767124\pi$
$61$	−90.7807			−1.48821			−0.744105	+	0.668063i	$0.767124\pi$
$62$		0			0
$63$	−52.8811	−	7.60767i	−0.839383	−	0.120757i
$64$		0			0
$65$	79.3306	+	45.8016i	1.22047	+	0.704639i
$66$		0			0
$67$	6.87740	−	11.9120i	0.102648	−	0.177791i	−0.810127	−	0.586254i	$-0.800602\pi$
$67$	6.87740	−	11.9120i	0.102648	−	0.177791i	0.912775	+	0.408463i	$0.133935\pi$
$68$		0			0
$69$	47.8345	+	98.4819i	0.693253	+	1.42727i
$70$		0			0
$71$	−47.2523	−	27.2811i	−0.665525	−	0.384241i	0.128854	−	0.991664i	$-0.458870\pi$
$71$	−47.2523	−	27.2811i	−0.665525	−	0.384241i	−0.794379	+	0.607423i	$0.792203\pi$
$72$		0			0
$73$	−3.72907	+	6.45893i	−0.0510831	+	0.0884785i	−0.890436	−	0.455108i	$-0.849601\pi$
$73$	−3.72907	+	6.45893i	−0.0510831	+	0.0884785i	0.839353	+	0.543586i	$0.182934\pi$
$74$		0			0
$75$	−139.888	−	94.6874i	−1.86517	−	1.26250i
$76$		0			0
$77$	74.9938	−	43.2977i	0.973945	−	0.562308i
$78$		0			0
$79$	41.3420	+	71.6065i	0.523317	+	0.906411i	0.999632	+	0.0271365i	$0.00863888\pi$
$79$	41.3420	+	71.6065i	0.523317	+	0.906411i	−0.476315	+	0.879275i	$0.658028\pi$
$80$		0			0
$81$	−58.6318	+	55.8866i	−0.723849	+	0.689958i
$82$		0			0
$83$	131.072	+	75.6747i	1.57919	+	0.911743i	0.994973	+	0.100142i	$0.0319297\pi$
$83$	131.072	+	75.6747i	1.57919	+	0.911743i	0.584212	+	0.811601i	$0.301404\pi$
$84$		0			0
$85$	−45.7195	+	79.1885i	−0.537876	+	0.931629i
$86$		0			0
$87$	71.8994	−	106.222i	0.826430	−	1.22094i
$88$		0			0
$89$	−29.6962	+	17.1451i	−0.333665	+	0.192642i	−0.657467	−	0.753483i	$-0.728372\pi$
$89$	−29.6962	+	17.1451i	−0.333665	+	0.192642i	0.323802	+	0.946125i	$0.395039\pi$
$90$		0			0
$91$	30.1525	+	52.2256i	0.331346	+	0.573908i
$92$		0			0
$93$	−2.57251	+	35.9473i	−0.0276614	+	0.386530i
$94$		0			0
$95$	−136.720	−	103.244i	−1.43916	−	1.08678i
$96$		0			0
$97$	68.4432	+	118.547i	0.705600	+	1.22213i	0.966475	+	0.256762i	$0.0826557\pi$
$97$	68.4432	+	118.547i	0.705600	+	1.22213i	−0.260875	+	0.965373i	$0.584011\pi$
$98$		0			0
$99$	18.6953	−	129.952i	0.188842	−	1.31264i
$100$		0			0
$101$		−	93.2708i		−	0.923473i	−0.887017	−	0.461737i	$-0.847227\pi$
$101$		−	93.2708i		−	0.923473i	0.887017	−	0.461737i	$-0.152773\pi$
$102$		0			0
$103$	−5.07145	−	8.78401i	−0.0492374	−	0.0852816i	0.840356	−	0.542034i	$-0.182346\pi$
$103$	−5.07145	−	8.78401i	−0.0492374	−	0.0852816i	−0.889594	+	0.456753i	$0.849012\pi$
$104$		0			0
$105$	−70.1586	−	144.443i	−0.668177	−	1.37565i
$106$		0			0
$107$			2.45423i			0.0229367i	0.999934	+	0.0114684i	$0.00365058\pi$
$107$			2.45423i			0.0229367i	−0.999934	+	0.0114684i	$0.996349\pi$
$108$		0			0
$109$	−60.6982	+	105.132i	−0.556864	+	0.964518i	0.440891	+	0.897560i	$0.354662\pi$
$109$	−60.6982	+	105.132i	−0.556864	+	0.964518i	−0.997756	+	0.0669571i	$0.978671\pi$
$110$		0			0
$111$	−8.35557	−	5.65572i	−0.0752754	−	0.0509524i
$112$		0			0
$113$	83.7910	−	48.3767i	0.741513	−	0.428113i	−0.0811061	−	0.996705i	$-0.525845\pi$
$113$	83.7910	−	48.3767i	0.741513	−	0.428113i	0.822619	+	0.568593i	$0.192512\pi$
$114$		0			0
$115$	−164.538	+	284.987i	−1.43076	+	2.47815i
$116$		0			0
$117$	90.4983	+	13.0194i	0.773490	+	0.111277i
$118$		0			0
$119$	−52.1320	+	30.0984i	−0.438084	+	0.252928i
$120$		0			0
$121$	45.9010	+	79.5029i	0.379347	+	0.657049i
$122$		0			0
$123$	83.2784	−	123.033i	0.677060	−	1.00027i
$124$		0			0
$125$		−	282.297i		−	2.25838i
$126$		0			0
$127$	60.5677	+	104.906i	0.476911	+	0.826034i	0.999650	−	0.0264586i	$-0.00842302\pi$
$127$	60.5677	+	104.906i	0.476911	+	0.826034i	−0.522739	+	0.852493i	$0.675090\pi$
$128$		0			0
$129$	10.2617	−	143.393i	0.0795478	−	1.11157i
$130$		0			0
$131$			209.768i			1.60128i	0.599144	+	0.800641i	$0.295508\pi$
$131$			209.768i			1.60128i	−0.599144	+	0.800641i	$0.704492\pi$
$132$		0			0
$133$	−43.9639	−	103.866i	−0.330556	−	0.780948i
$134$		0			0
$135$	−237.890	−	51.7810i	−1.76215	−	0.383563i
$136$		0			0
$137$			93.7450i			0.684270i	0.939651	+	0.342135i	$0.111150\pi$
$137$			93.7450i			0.684270i	−0.939651	+	0.342135i	$0.888850\pi$
$138$		0			0
$139$	−24.8326	+	43.0112i	−0.178651	+	0.309433i	−0.941419	−	0.337239i	$-0.890507\pi$
$139$	−24.8326	+	43.0112i	−0.178651	+	0.309433i	0.762767	+	0.646673i	$0.223840\pi$
$140$		0			0
$141$	−32.1009	+	47.4248i	−0.227666	+	0.336346i
$142$		0			0
$143$	−128.341	+	74.0976i	−0.897488	+	0.518165i
$144$		0			0
$145$	385.531			2.65884
$146$		0			0
$147$	−2.94699	+	41.1802i	−0.0200476	+	0.280137i
$148$		0			0
$149$		−	182.398i		−	1.22415i	−0.790800	−	0.612075i	$-0.790335\pi$
$149$		−	182.398i		−	1.22415i	0.790800	−	0.612075i	$-0.209665\pi$
$150$		0			0
$151$	−93.8272	+	162.514i	−0.621372	+	1.07625i	0.367858	+	0.929882i	$0.380091\pi$
$151$	−93.8272	+	162.514i	−0.621372	+	1.07625i	−0.989230	+	0.146367i	$0.953242\pi$
$152$		0			0
$153$	−12.9961	+	90.3361i	−0.0849417	+	0.590432i
$154$		0			0
$155$	−93.8100	+	54.1612i	−0.605225	+	0.349427i
$156$		0			0
$157$	−186.902			−1.19046			−0.595230	−	0.803555i	$-0.702939\pi$
$157$	−186.902			−1.19046			−0.595230	+	0.803555i	$0.702939\pi$
$158$		0			0
$159$	62.4501	+	4.46914i	0.392768	+	0.0281078i
$160$		0			0
$161$	−187.615	+	108.320i	−1.16531	+	0.672793i
$162$		0			0
$163$	174.970			1.07343			0.536717	−	0.843763i	$-0.319664\pi$
$163$	174.970			1.07343			0.536717	+	0.843763i	$0.319664\pi$
$164$		0			0
$165$	354.959	−	172.410i	2.15126	−	1.04491i
$166$		0			0
$167$	172.723	+	99.7216i	1.03427	+	0.597135i	0.918205	−	0.396107i	$-0.129639\pi$
$167$	172.723	+	99.7216i	1.03427	+	0.597135i	0.116064	+	0.993242i	$0.462972\pi$
$168$		0			0
$169$	32.8985	+	56.9819i	0.194666	+	0.337171i
$170$		0			0
$171$	−164.983	−	44.9636i	−0.964811	−	0.262945i
$172$		0			0
$173$	254.581	−	146.982i	1.47157	−	0.849609i	0.472077	−	0.881557i	$-0.343504\pi$
$173$	254.581	−	146.982i	1.47157	−	0.849609i	0.999490	+	0.0319481i	$0.0101711\pi$
$174$		0			0
$175$	167.124	−	289.468i	0.954996	−	1.65410i
$176$		0			0
$177$	−148.948	+	220.050i	−0.841512	+	1.24322i
$178$		0			0
$179$		−	252.892i		−	1.41281i	−0.707810	−	0.706403i	$-0.750317\pi$
$179$		−	252.892i		−	1.41281i	0.707810	−	0.706403i	$-0.249683\pi$
$180$		0			0
$181$	24.0112	+	41.5885i	0.132658	+	0.229771i	0.924700	−	0.380695i	$-0.124315\pi$
$181$	24.0112	+	41.5885i	0.132658	+	0.229771i	−0.792042	+	0.610466i	$0.790982\pi$
$182$		0			0
$183$	−225.534	−	152.659i	−1.23242	−	0.834204i
$184$		0			0
$185$		−	30.3265i		−	0.163927i
$186$		0			0
$187$	−73.9648	−	128.111i	−0.395534	−	0.685084i
$188$		0			0
$189$	−118.583	−	107.827i	−0.627426	−	0.570512i
$190$		0			0
$191$	−251.753	−	145.350i	−1.31808	−	0.760993i	−0.334660	−	0.942339i	$-0.608621\pi$
$191$	−251.753	−	145.350i	−1.31808	−	0.760993i	−0.983419	+	0.181346i	$0.941955\pi$
$192$		0			0
$193$	−156.633			−0.811567			−0.405784	−	0.913969i	$-0.633001\pi$
$193$	−156.633			−0.811567			−0.405784	+	0.913969i	$0.633001\pi$
$194$		0			0
$195$	120.066	+	247.193i	0.615724	+	1.26766i
$196$		0			0
$197$		−	81.8833i		−	0.415651i	−0.978166	−	0.207826i	$-0.933361\pi$
$197$		−	81.8833i		−	0.415651i	0.978166	−	0.207826i	$-0.0666386\pi$
$198$		0			0
$199$	13.2629	+	22.9721i	0.0666479	+	0.115438i	0.897424	−	0.441170i	$-0.145436\pi$
$199$	13.2629	+	22.9721i	0.0666479	+	0.115438i	−0.830776	+	0.556607i	$0.812103\pi$
$200$		0			0
$201$	37.1176	−	18.0287i	0.184665	−	0.0896950i
$202$		0			0
$203$	219.803	+	126.903i	1.08277	+	0.625138i
$204$		0			0
$205$	446.547			2.17828
$206$		0			0
$207$	−46.7709	+	325.106i	−0.225947	+	1.57056i
$208$		0			0
$209$	255.244	−	108.038i	1.22126	−	0.516930i
$210$		0			0
$211$	300.488			1.42411			0.712056	−	0.702123i	$-0.247764\pi$
$211$	300.488			1.42411			0.712056	+	0.702123i	$0.247764\pi$
$212$		0			0
$213$	−71.5158	−	147.237i	−0.335755	−	0.691254i
$214$		0			0
$215$	374.205	−	216.047i	1.74049	−	1.00487i
$216$		0			0
$217$	−71.3117			−0.328625
$218$		0			0
$219$	−20.1259	+	9.77553i	−0.0918992	+	0.0446371i
$220$		0			0
$221$	89.2163	−	51.5090i	0.403693	−	0.233073i
$222$		0			0
$223$	153.653	+	266.135i	0.689026	+	1.19343i	0.972153	+	0.234346i	$0.0752949\pi$
$223$	153.653	+	266.135i	0.689026	+	1.19343i	−0.283127	+	0.959082i	$0.591372\pi$
$224$		0			0
$225$	−188.306	−	470.479i	−0.836914	−	2.09102i
$226$		0			0
$227$	220.586	+	127.355i	0.971744	+	0.561037i	0.899768	−	0.436369i	$-0.143736\pi$
$227$	220.586	+	127.355i	0.971744	+	0.561037i	0.0719768	+	0.997406i	$0.477069\pi$
$228$		0			0
$229$	125.306	+	217.037i	0.547189	+	0.947760i	0.998466	+	0.0553756i	$0.0176356\pi$
$229$	125.306	+	217.037i	0.547189	+	0.947760i	−0.451276	+	0.892384i	$0.649031\pi$
$230$		0			0
$231$	259.123	+	18.5438i	1.12175	+	0.0802760i
$232$		0			0
$233$	−24.4004	−	14.0876i	−0.104723	−	0.0604617i	0.446724	−	0.894672i	$-0.352591\pi$
$233$	−24.4004	−	14.0876i	−0.104723	−	0.0604617i	−0.551447	+	0.834210i	$0.685924\pi$
$234$		0			0
$235$	−172.128			−0.732460
$236$		0			0
$237$	−17.7062	+	247.419i	−0.0747096	+	1.04396i
$238$		0			0
$239$	74.6979	−	43.1268i	0.312543	−	0.180447i	−0.335521	−	0.942033i	$-0.608912\pi$
$239$	74.6979	−	43.1268i	0.312543	−	0.180447i	0.648064	+	0.761586i	$0.275579\pi$
$240$		0			0
$241$	−101.626			−0.421683			−0.210841	−	0.977520i	$-0.567620\pi$
$241$	−101.626			−0.421683			−0.210841	+	0.977520i	$0.567620\pi$
$242$		0			0
$243$	−239.644	+	40.2466i	−0.986189	+	0.165624i
$244$		0			0
$245$	−107.466	+	62.0455i	−0.438636	+	0.253247i
$246$		0			0
$247$	75.2378	+	177.751i	0.304606	+	0.719641i
$248$		0			0
$249$	198.377	+	408.419i	0.796694	+	1.64024i
$250$		0			0
$251$	46.5824	−	26.8944i	0.185587	−	0.107149i	−0.404328	−	0.914614i	$-0.632495\pi$
$251$	46.5824	−	26.8944i	0.185587	−	0.107149i	0.589915	+	0.807465i	$0.299161\pi$
$252$		0			0
$253$	−266.188	−	461.051i	−1.05213	−	1.82234i
$254$		0			0
$255$	−246.750	+	119.851i	−0.967647	+	0.470004i
$256$		0			0
$257$	−119.021	−	68.7170i	−0.463118	−	0.267381i	0.250236	−	0.968185i	$-0.419492\pi$
$257$	−119.021	−	68.7170i	−0.463118	−	0.267381i	−0.713354	+	0.700803i	$0.752825\pi$
$258$		0			0
$259$	9.98240	−	17.2900i	0.0385421	−	0.0667569i
$260$		0			0
$261$	357.250	−	142.987i	1.36878	−	0.547842i
$262$		0			0
$263$	−214.220	+	123.680i	−0.814526	+	0.470267i	−0.848525	−	0.529155i	$-0.822509\pi$
$263$	−214.220	+	123.680i	−0.814526	+	0.470267i	0.0339991	+	0.999422i	$0.489176\pi$
$264$		0			0
$265$	94.0926	+	162.973i	0.355066	+	0.614993i
$266$		0			0
$267$	−102.608	−	7.34299i	−0.384300	−	0.0275019i
$268$		0			0
$269$	446.055	+	257.530i	1.65820	+	0.957361i	0.973546	+	0.228490i	$0.0733789\pi$
$269$	446.055	+	257.530i	1.65820	+	0.957361i	0.684652	+	0.728871i	$0.259954\pi$
$270$		0			0
$271$	92.4731	−	160.168i	0.341229	−	0.591026i	−0.643432	−	0.765503i	$-0.722490\pi$
$271$	92.4731	−	160.168i	0.341229	−	0.591026i	0.984661	+	0.174477i	$0.0558234\pi$
$272$		0			0
$273$	−12.9139	+	180.453i	−0.0473035	+	0.661001i
$274$		0			0
$275$	711.347	+	410.696i	2.58672	+	1.49344i
$276$		0			0
$277$	168.796	−	292.363i	0.609371	−	1.05546i	−0.381973	−	0.924173i	$-0.624755\pi$
$277$	168.796	−	292.363i	0.609371	−	1.05546i	0.991344	−	0.131288i	$-0.0419114\pi$
$278$		0			0
$279$	−66.8410	+	84.9806i	−0.239574	+	0.304590i
$280$		0			0
$281$		−	4.16769i		−	0.0148316i	−0.999973	−	0.00741582i	$-0.997639\pi$
$281$		−	4.16769i		−	0.0148316i	0.999973	−	0.00741582i	$-0.00236055\pi$
$282$		0			0
$283$	−206.565			−0.729911			−0.364956	−	0.931025i	$-0.618916\pi$
$283$	−206.565			−0.729911			−0.364956	+	0.931025i	$0.618916\pi$
$284$		0			0
$285$	−166.047	−	486.410i	−0.582620	−	1.70670i
$286$		0			0
$287$	254.589	+	146.987i	0.887071	+	0.512150i
$288$		0			0
$289$	−93.0833	−	161.225i	−0.322087	−	0.557872i
$290$		0			0
$291$	−29.3132	+	409.612i	−0.100733	+	1.40760i
$292$		0			0
$293$	93.2526	−	53.8394i	0.318268	−	0.183752i	−0.332352	−	0.943155i	$-0.607842\pi$
$293$	93.2526	−	53.8394i	0.318268	−	0.183752i	0.650620	+	0.759403i	$0.274509\pi$
$294$		0			0
$295$	−798.671			−2.70736
$296$		0			0
$297$	264.977	−	291.411i	0.892177	−	0.981180i
$298$		0			0
$299$	321.076	−	185.373i	1.07383	−	0.619977i
$300$		0			0
$301$	284.460			0.945051
$302$		0			0
$303$	156.847	−	231.720i	0.517646	−	0.764752i
$304$		0			0
$305$		−	818.574i		−	2.68385i
$306$		0			0
$307$	92.3349	−	159.929i	0.300765	−	0.520940i	−0.675544	−	0.737319i	$-0.736091\pi$
$307$	92.3349	−	159.929i	0.300765	−	0.520940i	0.976309	+	0.216379i	$0.0694247\pi$
$308$		0			0
$309$	2.17203	−	30.3511i	0.00702921	−	0.0982235i
$310$		0			0
$311$	−173.750	+	100.315i	−0.558681	+	0.322555i	−0.752616	−	0.658460i	$-0.771208\pi$
$311$	−173.750	+	100.315i	−0.558681	+	0.322555i	0.193935	+	0.981014i	$0.437875\pi$
$312$		0			0
$313$	121.810			0.389169			0.194585	−	0.980886i	$-0.437664\pi$
$313$	121.810			0.389169			0.194585	+	0.980886i	$0.437664\pi$
$314$		0			0
$315$	68.5987	−	476.832i	0.217774	−	1.51375i
$316$		0			0
$317$		−	620.020i		−	1.95590i	−0.208840	−	0.977950i	$-0.566969\pi$
$317$		−	620.020i		−	1.95590i	0.208840	−	0.977950i	$-0.433031\pi$
$318$		0			0
$319$	−311.856	+	540.150i	−0.977603	+	1.69326i
$320$		0			0
$321$	−4.12710	+	6.09724i	−0.0128570	+	0.0189945i
$322$		0			0
$323$	−177.433	+	75.1029i	−0.549328	+	0.232517i
$324$		0			0
$325$	−286.009	+	495.381i	−0.880026	+	1.52425i
$326$		0			0
$327$	−327.591	+	159.117i	−1.00181	+	0.486596i
$328$		0			0
$329$	−98.1353	−	56.6584i	−0.298283	−	0.172214i
$330$		0			0
$331$	34.1839	−	59.2083i	0.103275	−	0.178877i	−0.809757	−	0.586765i	$-0.800401\pi$
$331$	34.1839	−	59.2083i	0.103275	−	0.178877i	0.913032	+	0.407888i	$0.133735\pi$
$332$		0			0
$333$	−11.2476	−	28.1019i	−0.0337765	−	0.0843901i
$334$		0			0
$335$	107.411	+	62.0138i	0.320630	+	0.185116i
$336$		0			0
$337$	317.779			0.942964			0.471482	−	0.881876i	$-0.343719\pi$
$337$	317.779			0.942964			0.471482	+	0.881876i	$0.343719\pi$
$338$		0			0
$339$	289.520	+	20.7190i	0.854041	+	0.0611181i
$340$		0			0
$341$		−	175.244i		−	0.513911i
$342$		0			0
$343$	−372.565			−1.08620
$344$		0			0
$345$	−888.016	+	431.325i	−2.57396	+	1.25022i
$346$		0			0
$347$		−	231.865i		−	0.668200i	−0.942538	−	0.334100i	$-0.891568\pi$
$347$		−	231.865i		−	0.668200i	0.942538	−	0.334100i	$-0.108432\pi$
$348$		0			0
$349$	91.7068	−	158.841i	0.262770	−	0.455132i	−0.704207	−	0.709995i	$-0.748697\pi$
$349$	91.7068	−	158.841i	0.262770	−	0.455132i	0.966977	+	0.254863i	$0.0820305\pi$
$350$		0			0
$351$	202.938	+	184.529i	0.578171	+	0.525725i
$352$		0			0
$353$	447.875	+	258.581i	1.26877	+	0.732523i	0.974755	−	0.223279i	$-0.0716759\pi$
$353$	447.875	+	258.581i	1.26877	+	0.732523i	0.294012	+	0.955802i	$0.405009\pi$
$354$		0			0
$355$	245.995	−	426.076i	0.692943	−	1.20021i
$356$		0			0
$357$	−180.130	−	12.8907i	−0.504566	−	0.0361085i
$358$		0			0
$359$	−218.412	−	126.100i	−0.608389	−	0.351254i	0.163945	−	0.986469i	$-0.447578\pi$
$359$	−218.412	−	126.100i	−0.608389	−	0.351254i	−0.772335	+	0.635216i	$0.780911\pi$
$360$		0			0
$361$	−98.7992	−	347.217i	−0.273682	−	0.961820i
$362$		0			0
$363$	−19.6587	+	274.704i	−0.0541563	+	0.756759i
$364$		0			0
$365$	−58.2405	−	33.6251i	−0.159563	−	0.0921237i
$366$		0			0
$367$	−358.947			−0.978058			−0.489029	−	0.872267i	$-0.662649\pi$
$367$	−358.947			−0.978058			−0.489029	+	0.872267i	$0.662649\pi$
$368$		0			0
$369$	413.790	−	165.616i	1.12138	−	0.448825i
$370$		0			0
$371$			123.888i			0.333929i
$372$		0			0
$373$	−38.7709	−	67.1531i	−0.103943	−	0.180035i	0.809363	−	0.587309i	$-0.199813\pi$
$373$	−38.7709	−	67.1531i	−0.103943	−	0.180035i	−0.913306	+	0.407274i	$0.866479\pi$
$374$		0			0
$375$	474.718	−	701.332i	1.26592	−	1.87022i
$376$		0			0
$377$	−376.160	−	217.176i	−0.997771	−	0.576063i
$378$		0			0
$379$	413.971			1.09227			0.546136	−	0.837696i	$-0.316098\pi$
$379$	413.971			1.09227			0.546136	+	0.837696i	$0.316098\pi$
$380$		0			0
$381$	−25.9403	+	362.479i	−0.0680847	+	0.951389i
$382$		0			0
$383$			39.7260i			0.103723i	0.998654	+	0.0518617i	$0.0165155\pi$
$383$			39.7260i			0.103723i	−0.998654	+	0.0518617i	$0.983485\pi$
$384$		0			0
$385$	390.417	+	676.222i	1.01407	+	1.75642i
$386$		0			0
$387$	266.627	−	338.985i	0.688958	−	0.875931i
$388$		0			0
$389$			265.449i			0.682389i	0.939993	+	0.341194i	$0.110831\pi$
$389$			265.449i			0.682389i	−0.939993	+	0.341194i	$0.889169\pi$
$390$		0			0
$391$	185.041	+	320.500i	0.473251	+	0.819694i
$392$		0			0
$393$	−352.752	+	521.143i	−0.897587	+	1.32606i
$394$		0			0
$395$	−645.679	+	372.783i	−1.63463	+	0.943754i
$396$		0			0
$397$	−0.280988	+	0.486685i	−0.000707777	+	0.00122591i	−0.866379	−	0.499387i	$-0.833559\pi$
$397$	−0.280988	+	0.486685i	−0.000707777	+	0.00122591i	0.865671	+	0.500613i	$0.166892\pi$
$398$		0			0
$399$	65.4409	−	331.973i	0.164012	−	0.832013i
$400$		0			0
$401$			448.709i			1.11897i	0.828839	+	0.559487i	$0.189002\pi$
$401$			448.709i			1.11897i	−0.828839	+	0.559487i	$0.810998\pi$
$402$		0			0
$403$	122.039			0.302827
$404$		0			0
$405$	−503.932	−	528.685i	−1.24428	−	1.30540i
$406$		0			0
$407$	42.4890	+	24.5311i	0.104396	+	0.0602729i
$408$		0			0
$409$	−364.310	+	631.004i	−0.890734	+	1.54280i	−0.0517361	+	0.998661i	$0.516475\pi$
$409$	−364.310	+	631.004i	−0.890734	+	1.54280i	−0.838998	+	0.544135i	$0.816858\pi$
$410$		0			0
$411$	−157.644	+	232.898i	−0.383562	+	0.566662i
$412$		0			0
$413$	−455.346	−	262.894i	−1.10253	−	0.636547i
$414$		0			0
$415$	−682.362	+	1181.89i	−1.64425	+	2.84792i
$416$		0			0
$417$	−134.022	+	65.0971i	−0.321396	+	0.156108i
$418$		0			0
$419$	−269.895	+	155.824i	−0.644141	+	0.371895i	−0.786208	−	0.617962i	$-0.787959\pi$
$419$	−269.895	+	155.824i	−0.644141	+	0.371895i	0.142067	+	0.989857i	$0.454625\pi$
$420$		0			0
$421$	−361.904	−	626.836i	−0.859629	−	1.48892i	−0.872283	−	0.489001i	$-0.837361\pi$
$421$	−361.904	−	626.836i	−0.859629	−	1.48892i	0.0126544	−	0.999920i	$-0.495972\pi$
$422$		0			0
$423$	−159.502	+	63.8393i	−0.377072	+	0.150920i
$424$		0			0
$425$	−494.494	−	285.496i	−1.16351	−	0.671755i
$426$		0			0
$427$	269.445	−	466.693i	0.631019	−	1.09296i
$428$		0			0
$429$	−443.451	−	31.7349i	−1.03369	−	0.0739741i
$430$		0			0
$431$	−315.537	+	182.176i	−0.732105	+	0.422681i	−0.819192	−	0.573520i	$-0.805578\pi$
$431$	−315.537	+	182.176i	−0.732105	+	0.422681i	0.0870866	+	0.996201i	$0.472244\pi$
$432$		0			0
$433$	−261.870	−	453.572i	−0.604781	−	1.04751i	−0.992086	−	0.125559i	$-0.959927\pi$
$433$	−261.870	−	453.572i	−0.604781	−	1.04751i	0.387306	−	0.921951i	$-0.373406\pi$
$434$		0			0
$435$	957.805	+	648.320i	2.20185	+	1.49039i
$436$		0			0
$437$	−638.554	+	270.284i	−1.46122	+	0.618499i
$438$		0			0
$439$	−263.689	−	456.723i	−0.600658	−	1.04037i	−0.992722	−	0.120432i	$-0.961572\pi$
$439$	−263.689	−	456.723i	−0.600658	−	1.04037i	0.392063	−	0.919938i	$-0.371761\pi$
$440$		0			0
$441$	−76.5711	+	97.3513i	−0.173631	+	0.220751i
$442$		0			0
$443$			785.142i			1.77233i	0.463370	+	0.886165i	$0.346640\pi$
$443$			785.142i			1.77233i	−0.463370	+	0.886165i	$0.653360\pi$
$444$		0			0
$445$	−154.598	−	267.772i	−0.347411	−	0.601734i
$446$		0			0
$447$	306.726	−	453.147i	0.686188	−	1.01375i
$448$		0			0
$449$			182.063i			0.405485i	0.979232	+	0.202742i	$0.0649854\pi$
$449$			182.063i			0.405485i	−0.979232	+	0.202742i	$0.935015\pi$
$450$		0			0
$451$	−361.211	+	625.635i	−0.800911	+	1.38722i
$452$		0			0
$453$	−506.389	+	245.963i	−1.11786	+	0.542964i
$454$		0			0
$455$	−470.921	+	271.886i	−1.03499	+	0.597552i
$456$		0			0
$457$	236.424	−	409.498i	0.517339	−	0.896057i	−0.482458	−	0.875919i	$-0.660256\pi$
$457$	236.424	−	409.498i	0.517339	−	0.896057i	0.999797	−	0.0201383i	$-0.00641066\pi$
$458$		0			0
$459$	−184.199	+	202.574i	−0.401304	+	0.441339i
$460$		0			0
$461$	562.770	−	324.916i	1.22076	−	0.704806i	0.255680	−	0.966761i	$-0.417701\pi$
$461$	562.770	−	324.916i	1.22076	−	0.704806i	0.965080	+	0.261955i	$0.0843673\pi$
$462$		0			0
$463$	381.353	+	660.522i	0.823656	+	1.42661i	0.902942	+	0.429762i	$0.141402\pi$
$463$	381.353	+	660.522i	0.823656	+	1.42661i	−0.0792867	+	0.996852i	$0.525264\pi$
$464$		0			0
$465$	−324.138	−	23.1964i	−0.697072	−	0.0498848i
$466$		0			0
$467$			642.808i			1.37646i	0.725491	+	0.688231i	$0.241613\pi$
$467$			642.808i			1.37646i	−0.725491	+	0.688231i	$0.758387\pi$
$468$		0			0
$469$	40.8254	+	70.7117i	0.0870479	+	0.150771i
$470$		0			0
$471$	−464.336	−	314.300i	−0.985851	−	0.667303i
$472$		0			0
$473$			699.041i			1.47789i
$474$		0			0
$475$	644.711	−	853.752i	1.35729	−	1.79737i
$476$		0			0
$477$	147.634	+	116.121i	0.309506	+	0.243440i
$478$		0			0
$479$		−	797.617i		−	1.66517i	−0.553896	−	0.832586i	$-0.686859\pi$
$479$		−	797.617i		−	1.66517i	0.553896	−	0.832586i	$-0.313141\pi$
$480$		0			0
$481$	−17.0834	+	29.5893i	−0.0355164	+	0.0615163i
$482$		0			0
$483$	−648.260	−	46.3917i	−1.34215	−	0.0960492i
$484$		0			0
$485$	−1068.94	+	617.155i	−2.20401	+	1.27248i
$486$		0			0
$487$	270.271			0.554971			0.277486	−	0.960730i	$-0.410499\pi$
$487$	270.271			0.554971			0.277486	+	0.960730i	$0.410499\pi$
$488$		0			0
$489$	434.690	+	294.234i	0.888938	+	0.601705i
$490$		0			0
$491$		−	577.156i		−	1.17547i	−0.809053	−	0.587735i	$-0.800020\pi$
$491$		−	577.156i		−	1.17547i	0.809053	−	0.587735i	$-0.199980\pi$
$492$		0			0
$493$	216.787	−	375.486i	0.439730	−	0.761634i
$494$		0			0
$495$	1171.78	+	168.577i	2.36723	+	0.340559i
$496$		0			0
$497$	280.498	−	161.945i	0.564382	−	0.325846i
$498$		0			0
$499$	−911.776			−1.82721			−0.913604	−	0.406606i	$-0.866712\pi$
$499$	−911.776			−1.82721			−0.913604	+	0.406606i	$0.866712\pi$
$500$		0			0
$501$	261.414	+	538.201i	0.521785	+	1.07425i
$502$		0			0
$503$	453.750	−	261.973i	0.902087	−	0.520820i	0.0242104	−	0.999707i	$-0.492293\pi$
$503$	453.750	−	261.973i	0.902087	−	0.520820i	0.877877	+	0.478887i	$0.158960\pi$
$504$		0			0
$505$	841.027			1.66540
$506$		0			0
$507$	−14.0899	+	196.887i	−0.0277908	+	0.388338i
$508$		0			0
$509$	531.050	+	306.602i	1.04332	+	0.602361i	0.920772	−	0.390102i	$-0.127560\pi$
$509$	531.050	+	306.602i	1.04332	+	0.602361i	0.122548	+	0.992463i	$0.460894\pi$
$510$		0			0
$511$	−22.1364	−	38.3414i	−0.0433197	−	0.0750320i
$512$		0			0
$513$	−334.267	−	389.146i	−0.651593	−	0.758569i
$514$		0			0
$515$	79.2058	−	45.7295i	0.153798	−	0.0887951i
$516$		0			0
$517$	139.234	−	241.161i	0.269312	−	0.466461i
$518$		0			0
$519$	879.645	+	62.9504i	1.69488	+	0.121292i
$520$		0			0
$521$			828.098i			1.58944i	0.606977	+	0.794719i	$0.292382\pi$
$521$			828.098i			1.58944i	−0.606977	+	0.794719i	$0.707618\pi$
$522$		0			0
$523$	71.0073	+	122.988i	0.135769	+	0.235159i	0.925891	−	0.377791i	$-0.123316\pi$
$523$	71.0073	+	122.988i	0.135769	+	0.235159i	−0.790122	+	0.612950i	$0.789983\pi$
$524$		0			0
$525$	901.976	−	438.106i	1.71805	−	0.834489i
$526$		0			0
$527$			121.821i			0.231159i
$528$		0			0
$529$	401.435	+	695.305i	0.758856	+	1.31438i
$530$		0			0
$531$	−740.084	+	296.213i	−1.39376	+	0.557840i
$532$		0			0
$533$	−435.692	−	251.547i	−0.817433	−	0.471945i
$534$		0			0
$535$	−22.1299			−0.0413643
$536$		0			0
$537$	425.270	−	628.279i	0.791937	−	1.16998i
$538$		0			0
$539$		−	200.754i		−	0.372456i
$540$		0			0
$541$	−155.307	−	268.999i	−0.287073	−	0.497226i	0.686036	−	0.727567i	$-0.259349\pi$
$541$	−155.307	−	268.999i	−0.287073	−	0.497226i	−0.973110	+	0.230341i	$0.926016\pi$
$542$		0			0
$543$	−10.2836	+	143.699i	−0.0189385	+	0.264640i
$544$		0			0
$545$	−947.983	−	547.318i	−1.73942	−	1.00425i
$546$		0			0
$547$	−12.7304			−0.0232731			−0.0116366	−	0.999932i	$-0.503704\pi$
$547$	−12.7304			−0.0232731			−0.0116366	+	0.999932i	$0.503704\pi$
$548$		0			0
$549$	−303.595	−	758.527i	−0.552996	−	1.38165i
$550$		0			0
$551$	648.283	+	489.551i	1.17656	+	0.888476i
$552$		0			0
$553$	−490.827			−0.887571
$554$		0			0
$555$	50.9979	−	75.3425i	0.0918881	−	0.135752i
$556$		0			0
$557$	34.2301	−	19.7628i	0.0614544	−	0.0354807i	−0.468958	−	0.883220i	$-0.655370\pi$
$557$	34.2301	−	19.7628i	0.0614544	−	0.0354807i	0.530412	+	0.847740i	$0.322037\pi$
$558$		0			0
$559$	−486.812			−0.870862
$560$		0			0
$561$	31.6780	−	442.657i	0.0564671	−	0.789049i
$562$		0			0
$563$	−78.3632	+	45.2430i	−0.139189	+	0.0803606i	−0.567977	−	0.823044i	$-0.692274\pi$
$563$	−78.3632	+	45.2430i	−0.139189	+	0.0803606i	0.428789	+	0.903405i	$0.358941\pi$
$564$		0			0
$565$	436.215	+	755.547i	0.772062	+	1.33725i
$566$		0			0
$567$	−113.282	−	467.295i	−0.199792	−	0.824154i
$568$		0			0
$569$	−59.5082	−	34.3571i	−0.104584	−	0.0603815i	0.446796	−	0.894636i	$-0.352565\pi$
$569$	−59.5082	−	34.3571i	−0.104584	−	0.0603815i	−0.551380	+	0.834254i	$0.685898\pi$
$570$		0			0
$571$	−141.927	−	245.824i	−0.248558	−	0.430515i	0.714568	−	0.699566i	$-0.246623\pi$
$571$	−141.927	−	245.824i	−0.248558	−	0.430515i	−0.963126	+	0.269051i	$0.913290\pi$
$572$		0			0
$573$	−381.026	−	784.458i	−0.664966	−	1.36904i
$574$		0			0
$575$	−1779.61	−	1027.46i	−3.09497	−	1.78688i
$576$		0			0
$577$	680.850			1.17998			0.589991	−	0.807410i	$-0.299131\pi$
$577$	680.850			1.17998			0.589991	+	0.807410i	$0.299131\pi$
$578$		0			0
$579$	−389.134	−	263.397i	−0.672080	−	0.454918i
$580$		0			0
$581$	−778.069	+	449.218i	−1.33919	+	0.773181i
$582$		0			0
$583$	−304.445			−0.522204
$584$		0			0
$585$	−117.397	+	816.027i	−0.200678	+	1.39492i
$586$		0			0
$587$	694.362	−	400.890i	1.18290	−	0.682947i	0.226216	−	0.974077i	$-0.427365\pi$
$587$	694.362	−	400.890i	1.18290	−	0.682947i	0.956684	+	0.291130i	$0.0940312\pi$
$588$		0			0
$589$	−226.519	−	28.0468i	−0.384582	−	0.0476177i
$590$		0			0
$591$	137.697	−	203.429i	0.232990	−	0.344211i
$592$		0			0
$593$	241.902	−	139.662i	0.407929	−	0.235518i	−0.281971	−	0.959423i	$-0.590988\pi$
$593$	241.902	−	139.662i	0.407929	−	0.235518i	0.689899	+	0.723905i	$0.257655\pi$
$594$		0			0
$595$	−271.399	−	470.077i	−0.456133	−	0.790045i
$596$		0			0
$597$	−5.68032	+	79.3746i	−0.00951477	+	0.132956i
$598$		0			0
$599$	−777.028	−	448.617i	−1.29721	−	0.748943i	−0.317287	−	0.948330i	$-0.602772\pi$
$599$	−777.028	−	448.617i	−1.29721	−	0.748943i	−0.979921	+	0.199386i	$0.936105\pi$
$600$		0			0
$601$	247.830	−	429.254i	0.412362	−	0.714232i	−0.582785	−	0.812626i	$-0.698037\pi$
$601$	247.830	−	429.254i	0.412362	−	0.714232i	0.995148	+	0.0983938i	$0.0313705\pi$
$602$		0			0
$603$	122.532	+	17.6279i	0.203203	+	0.0292336i
$604$		0			0
$605$	−716.881	+	413.892i	−1.18493	+	0.684118i
$606$		0			0
$607$	−537.759	−	931.426i	−0.885929	−	1.53447i	−0.844645	−	0.535327i	$-0.820188\pi$
$607$	−537.759	−	931.426i	−0.885929	−	1.53447i	−0.0412846	−	0.999147i	$-0.513145\pi$
$608$		0			0
$609$	332.669	+	684.901i	0.546255	+	1.12463i
$610$		0			0
$611$	167.944	+	96.9625i	0.274867	+	0.158695i
$612$		0			0
$613$	−393.213	+	681.066i	−0.641457	+	1.11104i	0.343650	+	0.939098i	$0.388337\pi$
$613$	−393.213	+	681.066i	−0.641457	+	1.11104i	−0.985108	+	0.171939i	$0.944997\pi$
$614$		0			0
$615$	1109.39	+	750.925i	1.80389	+	1.22102i
$616$		0			0
$617$	−2.58832	−	1.49437i	−0.00419502	−	0.00242199i	0.497901	−	0.867234i	$-0.334104\pi$
$617$	−2.58832	−	1.49437i	−0.00419502	−	0.00242199i	−0.502096	+	0.864812i	$0.667438\pi$
$618$		0			0
$619$	410.833	−	711.584i	0.663705	−	1.14957i	−0.315930	−	0.948783i	$-0.602316\pi$
$619$	410.833	−	711.584i	0.663705	−	1.14957i	0.979635	−	0.200788i	$-0.0643503\pi$
$620$		0			0
$621$	−662.904	+	729.035i	−1.06748	+	1.17397i
$622$		0			0
$623$		−	203.553i		−	0.326730i
$624$		0			0
$625$	1137.81			1.82049
$626$		0			0
$627$	815.801	+	160.816i	1.30112	+	0.256486i
$628$		0			0
$629$	−29.5363	−	17.0528i	−0.0469576	−	0.0271110i
$630$		0			0
$631$	−229.749	−	397.937i	−0.364103	−	0.630646i	0.624528	−	0.781002i	$-0.285291\pi$
$631$	−229.749	−	397.937i	−0.364103	−	0.630646i	−0.988632	+	0.150356i	$0.951958\pi$
$632$		0			0
$633$	746.524	+	505.308i	1.17934	+	0.798275i
$634$		0			0
$635$	−945.945	+	546.142i	−1.48968	+	0.860066i
$636$		0			0
$637$	139.805			0.219474
$638$		0			0
$639$	69.9257	−	486.056i	0.109430	−	0.760650i
$640$		0			0
$641$	869.085	−	501.766i	1.35583	−	0.782787i	0.366768	−	0.930312i	$-0.380464\pi$
$641$	869.085	−	501.766i	1.35583	−	0.782787i	0.989058	+	0.147526i	$0.0471309\pi$
$642$		0			0
$643$	−294.626			−0.458205			−0.229103	−	0.973402i	$-0.573579\pi$
$643$	−294.626			−0.458205			−0.229103	+	0.973402i	$0.573579\pi$
$644$		0			0
$645$	1292.98	+	92.5299i	2.00462	+	0.143457i
$646$		0			0
$647$		−	808.604i		−	1.24977i	−0.780715	−	0.624887i	$-0.785145\pi$
$647$		−	808.604i		−	1.24977i	0.780715	−	0.624887i	$-0.214855\pi$
$648$		0			0
$649$	646.044	−	1118.98i	0.995445	−	1.72416i
$650$		0			0
$651$	−177.165	−	119.920i	−0.272143	−	0.184208i
$652$		0			0
$653$	−165.029	+	95.2793i	−0.252724	+	0.145910i	−0.621011	−	0.783802i	$-0.713278\pi$
$653$	−165.029	+	95.2793i	−0.252724	+	0.145910i	0.368287	+	0.929712i	$0.379944\pi$
$654$		0			0
$655$	−1891.49			−2.88777
$656$		0			0
$657$	−66.4392	−	9.55818i	−0.101125	−	0.0145482i
$658$		0			0
$659$			497.622i			0.755117i	0.925986	+	0.377559i	$0.123236\pi$
$659$			497.622i			0.755117i	−0.925986	+	0.377559i	$0.876764\pi$
$660$		0			0
$661$	53.1670	−	92.0879i	0.0804341	−	0.139316i	−0.823002	−	0.568038i	$-0.807703\pi$
$661$	53.1670	−	92.0879i	0.0804341	−	0.139316i	0.903436	+	0.428722i	$0.141036\pi$
$662$		0			0
$663$	308.266	+	22.0606i	0.464956	+	0.0332738i
$664$		0			0
$665$	936.565	−	396.425i	1.40837	−	0.596127i
$666$		0			0
$667$	780.183	−	1351.32i	1.16969	−	2.02596i
$668$		0			0
$669$	−65.8073	+	919.565i	−0.0983666	+	1.37454i
$670$		0			0
$671$	1146.87	+	662.143i	1.70919	+	0.986800i
$672$		0			0
$673$	−346.292	+	599.795i	−0.514550	+	0.891226i	0.485308	+	0.874343i	$0.338707\pi$
$673$	−346.292	+	599.795i	−0.514550	+	0.891226i	−0.999857	+	0.0168826i	$0.994626\pi$
$674$		0			0
$675$	323.347	−	1485.51i	0.479033	−	2.20075i
$676$		0			0
$677$	−281.840	−	162.720i	−0.416307	−	0.240355i	0.277189	−	0.960815i	$-0.410597\pi$
$677$	−281.840	−	162.720i	−0.416307	−	0.240355i	−0.693496	+	0.720461i	$0.743930\pi$
$678$		0			0
$679$	−812.581			−1.19673
$680$		0			0
$681$	333.855	+	687.342i	0.490242	+	1.00931i
$682$		0			0
$683$			12.7083i			0.0186066i	0.999957	+	0.00930332i	$0.00296138\pi$
$683$			12.7083i			0.0186066i	−0.999957	+	0.00930332i	$0.997039\pi$
$684$		0			0
$685$	−845.303			−1.23402
$686$		0			0
$687$	−53.6669	+	749.921i	−0.0781177	+	1.09159i
$688$		0			0
$689$		−	212.015i		−	0.307715i
$690$		0			0
$691$	105.337	−	182.449i	0.152442	−	0.264037i	−0.779683	−	0.626175i	$-0.784620\pi$
$691$	105.337	−	182.449i	0.152442	−	0.264037i	0.932125	+	0.362138i	$0.117953\pi$
$692$		0			0
$693$	612.577	+	481.819i	0.883949	+	0.695265i
$694$		0			0
$695$	−387.834	−	223.916i	−0.558035	−	0.322182i
$696$		0			0
$697$	251.096	−	434.911i	0.360253	−	0.623976i
$698$		0			0
$699$	−36.9298	−	76.0312i	−0.0528323	−	0.108771i
$700$		0			0
$701$	1164.83	+	672.516i	1.66167	+	0.959367i	0.971917	+	0.235323i	$0.0756149\pi$
$701$	1164.83	+	672.516i	1.66167	+	0.959367i	0.689754	+	0.724043i	$0.257718\pi$
$702$		0			0
$703$	38.5088	−	50.9950i	0.0547779	−	0.0725391i
$704$		0			0
$705$	−427.631	−	289.455i	−0.606569	−	0.410575i
$706$		0			0
$707$	479.494	+	276.836i	0.678209	+	0.391564i
$708$		0			0
$709$	−106.351			−0.150002			−0.0750008	−	0.997183i	$-0.523896\pi$
$709$	−106.351			−0.150002			−0.0750008	+	0.997183i	$0.523896\pi$
$710$		0			0
$711$	−460.056	+	584.908i	−0.647055	+	0.822655i
$712$		0			0
$713$			438.415i			0.614887i
$714$		0			0
$715$	−668.141	−	1157.25i	−0.934463	−	1.61854i
$716$		0			0
$717$	258.101	+	18.4706i	0.359973	+	0.0257609i
$718$		0			0
$719$	1101.59	+	636.001i	1.53211	+	0.884563i	0.999264	+	0.0383495i	$0.0122100\pi$
$719$	1101.59	+	636.001i	1.53211	+	0.884563i	0.532844	+	0.846214i	$0.321123\pi$
$720$		0			0
$721$	60.2100			0.0835090
$722$		0			0
$723$	−252.476	−	170.896i	−0.349206	−	0.236371i
$724$		0			0
$725$			2407.46i			3.32063i
$726$		0			0
$727$	505.833	+	876.129i	0.695781	+	1.20513i	0.969917	+	0.243437i	$0.0782751\pi$
$727$	505.833	+	876.129i	0.695781	+	1.20513i	−0.274135	+	0.961691i	$0.588392\pi$
$728$		0			0
$729$	−663.046	−	303.004i	−0.909528	−	0.415643i
$730$		0			0
$731$		−	485.939i		−	0.664760i
$732$		0			0
$733$	163.236	+	282.734i	0.222696	+	0.385721i	0.955626	−	0.294583i	$-0.0951808\pi$
$733$	163.236	+	282.734i	0.222696	+	0.385721i	−0.732930	+	0.680305i	$0.761848\pi$
$734$		0			0
$735$	−371.323	−	26.5732i	−0.505202	−	0.0361540i
$736$		0			0
$737$	−173.769	+	100.326i	−0.235779	+	0.136127i
$738$		0			0
$739$	−270.945	+	469.290i	−0.366637	+	0.635033i	−0.989037	−	0.147665i	$-0.952824\pi$
$739$	−270.945	+	469.290i	−0.366637	+	0.635033i	0.622401	+	0.782699i	$0.286157\pi$
$740$		0			0
$741$	−111.992	+	568.123i	−0.151137	+	0.766698i
$742$		0			0
$743$			513.938i			0.691707i	0.938289	+	0.345853i	$0.112411\pi$
$743$			513.938i			0.691707i	−0.938289	+	0.345853i	$0.887589\pi$
$744$		0			0
$745$	1644.69			2.20764
$746$		0			0
$747$	−193.966	+	1348.26i	−0.259660	+	1.80490i
$748$		0			0
$749$	−12.6169	−	7.28437i	−0.0168450	−	0.00972547i
$750$		0			0
$751$	591.224	−	1024.03i	0.787249	−	1.36356i	−0.140397	−	0.990095i	$-0.544838\pi$
$751$	591.224	−	1024.03i	0.787249	−	1.36356i	0.927646	−	0.373461i	$-0.121829\pi$
$752$		0			0
$753$	160.955	+	11.5185i	0.213751	+	0.0152968i
$754$		0			0
$755$	−1465.39	−	846.044i	−1.94092	−	1.12059i
$756$		0			0
$757$	−308.665	+	534.624i	−0.407748	+	0.706240i	−0.994637	−	0.103427i	$-0.967019\pi$
$757$	−308.665	+	534.624i	−0.407748	+	0.706240i	0.586889	+	0.809667i	$0.300352\pi$
$758$		0			0
$759$	114.004	−	1593.05i	0.150204	−	2.09889i
$760$		0			0
$761$	936.168	−	540.497i	1.23018	−	0.710246i	0.263114	−	0.964765i	$-0.415250\pi$
$761$	936.168	−	540.497i	1.23018	−	0.710246i	0.967068	+	0.254519i	$0.0819171\pi$
$762$		0			0
$763$	−360.315	−	624.084i	−0.472235	−	0.817935i
$764$		0			0
$765$	−814.564	−	117.186i	−1.06479	−	0.153185i
$766$		0			0
$767$	779.257	+	449.904i	1.01598	+	0.586577i
$768$		0			0
$769$	−122.791	+	212.680i	−0.159676	+	0.276568i	−0.934752	−	0.355301i	$-0.884378\pi$
$769$	−122.791	+	212.680i	−0.159676	+	0.276568i	0.775076	+	0.631869i	$0.217712\pi$
$770$		0			0
$771$	−180.138	−	370.869i	−0.233642	−	0.481023i
$772$		0			0
$773$	416.108	−	240.240i	0.538303	−	0.310789i	−0.206088	−	0.978533i	$-0.566073\pi$
$773$	416.108	−	240.240i	0.538303	−	0.310789i	0.744391	+	0.667744i	$0.232740\pi$
$774$		0			0
$775$	−338.210	−	585.798i	−0.436401	−	0.755868i
$776$		0			0
$777$	53.8754	−	26.1683i	0.0693378	−	0.0336786i
$778$		0			0
$779$	750.882	+	567.028i	0.963905	+	0.727893i
$780$		0			0
$781$	397.969	+	689.303i	0.509564	+	0.882591i
$782$		0			0
$783$	1128.00	+	245.529i	1.44061	+	0.313574i
$784$		0			0
$785$		−	1685.31i		−	2.14689i
$786$		0			0
$787$	304.506	+	527.420i	0.386920	+	0.670165i	0.992034	−	0.125974i	$-0.0402056\pi$
$787$	304.506	+	527.420i	0.386920	+	0.670165i	−0.605113	+	0.796139i	$0.706872\pi$
$788$		0			0
$789$	−740.188	−	52.9704i	−0.938135	−	0.0671361i
$790$		0			0
$791$			574.346i			0.726101i
$792$		0			0
$793$	−461.116	+	798.676i	−0.581483	+	1.00716i
$794$		0			0
$795$	−40.2985	+	563.115i	−0.0506899	+	0.708321i
$796$		0			0
$797$	−0.929930	+	0.536895i	−0.00116679	+	0.000673645i	−0.500583	−	0.865688i	$-0.666881\pi$
$797$	−0.929930	+	0.536895i	−0.00116679	+	0.000673645i	0.499416	+	0.866362i	$0.333548\pi$
$798$		0			0
$799$	−96.7888	+	167.643i	−0.121137	+	0.209816i
$800$		0			0
$801$	−242.569	−	190.791i	−0.302833	−	0.238192i
$802$		0			0
$803$	94.2212	−	54.3986i	0.117336	−	0.0677442i
$804$		0			0
$805$	−976.724	−	1691.73i	−1.21332	−	2.10153i
$806$		0			0
$807$	675.100	+	1389.90i	0.836555	+	1.72231i
$808$		0			0
$809$			318.162i			0.393278i	0.980476	+	0.196639i	$0.0630026\pi$
$809$			318.162i			0.393278i	−0.980476	+	0.196639i	$0.936997\pi$
$810$		0			0
$811$	−226.940	−	393.071i	−0.279827	−	0.484674i	0.691515	−	0.722362i	$-0.256944\pi$
$811$	−226.940	−	393.071i	−0.279827	−	0.484674i	−0.971342	+	0.237688i	$0.923610\pi$
$812$		0			0
$813$	499.081	−	242.413i	0.613876	−	0.298171i
$814$		0			0
$815$			1577.71i			1.93584i
$816$		0			0
$817$	903.576	+	111.878i	1.10597	+	0.136937i
$818$		0			0
$819$	−335.538	+	426.598i	−0.409692	+	0.520877i
$820$		0			0
$821$		−	693.941i		−	0.845239i	−0.906307	−	0.422619i	$-0.861111\pi$
$821$		−	693.941i		−	0.845239i	0.906307	−	0.422619i	$-0.138889\pi$
$822$		0			0
$823$	464.826	−	805.103i	0.564795	−	0.978254i	−0.432274	−	0.901742i	$-0.642289\pi$
$823$	464.826	−	805.103i	0.564795	−	0.978254i	0.997069	−	0.0765113i	$-0.0243781\pi$
$824$		0			0
$825$	1076.62	+	2216.54i	1.30499	+	2.68672i
$826$		0			0
$827$	−337.829	+	195.046i	−0.408500	+	0.235847i	−0.690145	−	0.723671i	$-0.742453\pi$
$827$	−337.829	+	195.046i	−0.408500	+	0.235847i	0.281645	+	0.959519i	$0.409120\pi$
$828$		0			0
$829$	1071.45			1.29246			0.646228	−	0.763145i	$-0.276346\pi$
$829$	1071.45			1.29246			0.646228	+	0.763145i	$0.276346\pi$
$830$		0			0
$831$	910.998	−	442.488i	1.09627	−	0.532477i
$832$		0			0
$833$			139.554i			0.167532i
$834$		0			0
$835$	−899.194	+	1557.45i	−1.07688	+	1.86521i
$836$		0			0
$837$	−308.964	+	98.7224i	−0.369133	+	0.117948i
$838$		0			0
$839$	−163.488	+	94.3898i	−0.194860	+	0.112503i	−0.594256	−	0.804276i	$-0.702553\pi$
$839$	−163.488	+	94.3898i	−0.194860	+	0.112503i	0.399396	+	0.916779i	$0.369220\pi$
$840$		0			0
$841$	−987.062			−1.17368
$842$		0			0
$843$	7.00850	−	10.3541i	0.00831376	−	0.0122825i
$844$		0			0
$845$	−513.808	+	296.647i	−0.608057	+	0.351062i
$846$		0			0
$847$	−544.953			−0.643392
$848$		0			0
$849$	−513.185	−	347.365i	−0.604458	−	0.409146i
$850$		0			0
$851$	−106.297	−	61.3704i	−0.124908	−	0.0721157i
$852$		0			0
$853$	−538.402	−	932.539i	−0.631186	−	1.09325i	−0.987310	−	0.158807i	$-0.949235\pi$
$853$	−538.402	−	932.539i	−0.631186	−	1.09325i	0.356124	−	0.934439i	$-0.384098\pi$
$854$		0			0
$855$	405.438	−	1487.66i	0.474197	−	1.73995i
$856$		0			0
$857$	713.131	−	411.726i	0.832124	−	0.480427i	−0.0224551	−	0.999748i	$-0.507148\pi$
$857$	713.131	−	411.726i	0.832124	−	0.480427i	0.854579	+	0.519321i	$0.173815\pi$
$858$		0			0
$859$	68.3289	−	118.349i	0.0795447	−	0.137775i	−0.823509	−	0.567303i	$-0.807987\pi$
$859$	68.3289	−	118.349i	0.0795447	−	0.137775i	0.903054	+	0.429528i	$0.141320\pi$
$860$		0			0
$861$	385.318	+	793.296i	0.447524	+	0.921366i
$862$		0			0
$863$		−	30.5304i		−	0.0353771i	−0.999844	−	0.0176885i	$-0.994369\pi$
$863$		−	30.5304i		−	0.0353771i	0.999844	−	0.0176885i	$-0.00563073\pi$
$864$		0			0
$865$	1325.35	+	2295.57i	1.53219	+	2.65384i
$866$		0			0
$867$	39.8662	−	557.075i	0.0459818	−	0.642532i
$868$		0			0
$869$		−	1206.17i		−	1.38800i
$870$		0			0
$871$	−69.8667	−	121.013i	−0.0802144	−	0.138935i
$872$		0			0
$873$	−761.639	+	968.336i	−0.872438	+	1.10920i
$874$		0			0
$875$	1451.25	+	837.882i	1.65858	+	0.957580i
$876$		0			0
$877$	−593.947			−0.677248			−0.338624	−	0.940922i	$-0.609961\pi$
$877$	−593.947			−0.677248			−0.338624	+	0.940922i	$0.609961\pi$
$878$		0			0
$879$	322.212	+	23.0586i	0.366567	+	0.0262328i
$880$		0			0
$881$			768.016i			0.871755i	0.900006	+	0.435878i	$0.143562\pi$
$881$			768.016i			0.871755i	−0.900006	+	0.435878i	$0.856438\pi$
$882$		0			0
$883$	95.8935	+	166.092i	0.108600	+	0.188100i	0.915203	−	0.402993i	$-0.132030\pi$
$883$	95.8935	+	166.092i	0.108600	+	0.188100i	−0.806604	+	0.591093i	$0.798697\pi$
$884$		0			0
$885$	−1984.20	−	1343.07i	−2.24204	−	1.51759i
$886$		0			0
$887$	−829.283	−	478.787i	−0.934930	−	0.539782i	−0.0465628	−	0.998915i	$-0.514827\pi$
$887$	−829.283	−	478.787i	−0.934930	−	0.539782i	−0.888367	+	0.459133i	$0.848160\pi$
$888$		0			0
$889$	−719.081			−0.808865
$890$		0			0
$891$	1148.35	−	278.382i	1.28883	−	0.312438i
$892$		0			0
$893$	−289.439	−	218.570i	−0.324120	−	0.244759i
$894$		0			0
$895$	2280.34			2.54786
$896$		0			0
$897$	1109.40	+	79.3926i	1.23679	+	0.0885091i
$898$		0			0
$899$	444.816	−	256.815i	0.494790	−	0.285667i
$900$		0			0
$901$	211.635			0.234889
$902$		0			0
$903$	706.707	+	478.356i	0.782621	+	0.529741i
$904$		0			0
$905$	−375.006	+	216.510i	−0.414371	+	0.239237i
$906$		0			0
$907$	−609.797	−	1056.20i	−0.672324	−	1.16450i	−0.977244	−	0.212121i	$-0.931963\pi$
$907$	−609.797	−	1056.20i	−0.672324	−	1.16450i	0.304920	−	0.952378i	$-0.401370\pi$
$908$		0			0
$909$	779.333	−	311.922i	0.857352	−	0.343149i
$910$		0			0
$911$	307.278	+	177.407i	0.337297	+	0.194739i	0.659076	−	0.752076i	$-0.270947\pi$
$911$	307.278	+	177.407i	0.337297	+	0.194739i	−0.321779	+	0.946815i	$0.604281\pi$
$912$		0			0
$913$	−1103.92	−	1912.05i	−1.20912	−	2.09425i
$914$		0			0
$915$	1376.54	−	2033.65i	1.50441	−	2.22256i
$916$		0			0
$917$	−1078.39	−	622.610i	−1.17600	−	0.678964i
$918$		0			0
$919$	1258.56			1.36949			0.684744	−	0.728783i	$-0.259914\pi$
$919$	1258.56			1.36949			0.684744	+	0.728783i	$0.259914\pi$
$920$		0			0
$921$	498.335	−	242.050i	0.541080	−	0.262813i
$922$		0			0
$923$	−480.030	+	277.146i	−0.520076	+	0.300266i
$924$		0			0
$925$	189.374			0.204729
$926$		0			0
$927$	56.4353	−	71.7510i	0.0608795	−	0.0774013i
$928$		0			0
$929$	−949.455	+	548.168i	−1.02202	+	0.590063i	−0.914688	−	0.404161i	$-0.867564\pi$
$929$	−949.455	+	548.168i	−1.02202	+	0.590063i	−0.107331	+	0.994223i	$0.534230\pi$
$930$		0			0
$931$	−259.493	−	32.1296i	−0.278725	−	0.0345109i
$932$		0			0
$933$	−600.352	−	42.9632i	−0.643464	−	0.0460485i
$934$		0			0
$935$	1155.18	−	666.944i	1.23549	−	0.713309i
$936$		0			0
$937$	−284.246	−	492.329i	−0.303358	−	0.525431i	0.673537	−	0.739154i	$-0.264774\pi$
$937$	−284.246	−	492.329i	−0.303358	−	0.525431i	−0.976894	+	0.213723i	$0.931441\pi$
$938$		0			0
$939$	302.622	+	204.839i	0.322281	+	0.218146i
$940$		0			0
$941$	−81.4017	−	46.9973i	−0.0865055	−	0.0499440i	0.456123	−	0.889917i	$-0.349238\pi$
$941$	−81.4017	−	46.9973i	−0.0865055	−	0.0499440i	−0.542629	+	0.839973i	$0.682571\pi$
$942$		0			0
$943$	903.657	−	1565.18i	0.958279	−	1.65979i
$944$		0			0
$945$	972.278	−	1069.27i	1.02887	−	1.13150i
$946$		0			0
$947$	−112.608	+	65.0143i	−0.118910	+	0.0686529i	−0.558275	−	0.829656i	$-0.688537\pi$
$947$	−112.608	+	65.0143i	−0.118910	+	0.0686529i	0.439365	+	0.898309i	$0.355203\pi$
$948$		0			0
$949$	37.8832	+	65.6156i	0.0399190	+	0.0691418i
$950$		0			0
$951$	1042.64	−	1540.36i	1.09636	−	1.61973i
$952$		0			0
$953$	−782.954	−	452.039i	−0.821568	−	0.474332i	0.0293889	−	0.999568i	$-0.490644\pi$
$953$	−782.954	−	452.039i	−0.821568	−	0.474332i	−0.850957	+	0.525236i	$0.823977\pi$
$954$		0			0
$955$	1310.62	−	2270.07i	1.37238	−	2.37703i
$956$		0			0
$957$	−1683.10	+	817.511i	−1.75872	+	0.854243i
$958$		0			0
$959$	−481.932	−	278.243i	−0.502536	−	0.290139i
$960$		0			0
$961$	408.343	−	707.271i	0.424915	−	0.735974i
$962$		0			0
$963$	−20.5066	+	8.20760i	−0.0212945	+	0.00852295i
$964$		0			0
$965$		−	1412.36i		−	1.46359i
$966$		0			0
$967$	−405.876			−0.419727			−0.209864	−	0.977731i	$-0.567302\pi$
$967$	−405.876			−0.419727			−0.209864	+	0.977731i	$0.567302\pi$
$968$		0			0
$969$	−567.105	−	111.792i	−0.585248	−	0.115368i
$970$		0			0
$971$	−842.185	−	486.236i	−0.867338	−	0.500758i	−0.000875219	−	1.00000i	$-0.500279\pi$
$971$	−842.185	−	486.236i	−0.867338	−	0.500758i	−0.866463	+	0.499242i	$0.833612\pi$
$972$		0			0
$973$	−147.410	−	255.322i	−0.151501	−	0.262407i
$974$		0			0
$975$	−1543.60	+	749.755i	−1.58318	+	0.768979i
$976$		0			0
$977$	399.426	−	230.609i	0.408829	−	0.236038i	−0.281457	−	0.959574i	$-0.590818\pi$
$977$	399.426	−	230.609i	0.408829	−	0.236038i	0.690287	+	0.723536i	$0.257484\pi$
$978$		0			0
$979$	500.216			0.510946
$980$		0			0
$981$	−1081.43	−	155.579i	−1.10238	−	0.158592i
$982$		0			0
$983$	−1260.98	+	728.027i	−1.28279	+	0.740617i	−0.977357	−	0.211597i	$-0.932134\pi$
$983$	−1260.98	+	728.027i	−1.28279	+	0.740617i	−0.305430	+	0.952215i	$0.598800\pi$
$984$		0			0
$985$	738.345			0.749589
$986$		0			0
$987$	−148.527	−	305.788i	−0.150483	−	0.309815i
$988$		0			0
$989$		−	1748.82i		−	1.76827i
$990$		0			0
$991$	−102.030	+	176.722i	−0.102957	+	0.178327i	−0.912902	−	0.408180i	$-0.866164\pi$
$991$	−102.030	+	176.722i	−0.102957	+	0.178327i	0.809945	+	0.586506i	$0.199497\pi$
$992$		0			0
$993$	184.492	−	89.6111i	0.185792	−	0.0902428i
$994$		0			0
$995$	−207.140	+	119.592i	−0.208181	+	0.120193i
$996$		0			0
$997$	377.627			0.378763			0.189382	−	0.981904i	$-0.439352\pi$
$997$	377.627			0.378763			0.189382	+	0.981904i	$0.439352\pi$
$998$		0			0
$999$	19.3137	−	88.7299i	0.0193330	−	0.0888187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.353.33	✓	80
3.2	odd	2		2052.3.m.a.1493.3		80
9.4	even	3		2052.3.be.a.125.38		80
9.5	odd	6		684.3.be.a.581.6	yes	80
19.7	even	3		684.3.be.a.425.6	yes	80
57.26	odd	6		2052.3.be.a.197.38		80
171.121	even	3		2052.3.m.a.881.38		80
171.140	odd	6	inner	684.3.m.a.653.33	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.33	✓	80	1.1	even	1	trivial
684.3.m.a.653.33	yes	80	171.140	odd	6	inner
684.3.be.a.425.6	yes	80	19.7	even	3
684.3.be.a.581.6	yes	80	9.5	odd	6
2052.3.m.a.881.38		80	171.121	even	3
2052.3.m.a.1493.3		80	3.2	odd	2
2052.3.be.a.125.38		80	9.4	even	3
2052.3.be.a.197.38		80	57.26	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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.48438 + 1.68163i) q^{3} +9.01704i q^{5} +(-2.96809 + 5.14088i) q^{7} +(3.34426 + 8.35559i) q^{9} +O(q^{10})\)	\(q+(2.48438 + 1.68163i) q^{3} +9.01704i q^{5} +(-2.96809 + 5.14088i) q^{7} +(3.34426 + 8.35559i) q^{9} +(-12.6334 - 7.29387i) q^{11} +(5.07944 - 8.79786i) q^{13} +(-15.1633 + 22.4017i) q^{15} +(8.78209 + 5.07034i) q^{17} +(-11.4499 + 15.1624i) q^{19} +(-16.0189 + 7.78067i) q^{21} +(31.6054 + 18.2474i) q^{23} -56.3071 q^{25} +(-5.74257 + 26.3822i) q^{27} -42.7558i q^{29} +(6.00654 + 10.4036i) q^{31} +(-19.1204 - 39.3653i) q^{33} +(-46.3555 - 26.7634i) q^{35} -3.36324 q^{37} +(27.4140 - 13.3155i) q^{39} -49.5225i q^{41} +(-23.9599 - 41.4997i) q^{43} +(-75.3427 + 30.1554i) q^{45} +19.0892i q^{47} +(6.88091 + 11.9181i) q^{49} +(13.2916 + 27.3648i) q^{51} +(18.0739 - 10.4350i) q^{53} +(65.7691 - 113.915i) q^{55} +(-53.9435 + 18.4148i) q^{57} +88.5735i q^{59} -90.7807 q^{61} +(-52.8811 - 7.60767i) q^{63} +(79.3306 + 45.8016i) q^{65} +(6.87740 - 11.9120i) q^{67} +(47.8345 + 98.4819i) q^{69} +(-47.2523 - 27.2811i) q^{71} +(-3.72907 + 6.45893i) q^{73} +(-139.888 - 94.6874i) q^{75} +(74.9938 - 43.2977i) q^{77} +(41.3420 + 71.6065i) q^{79} +(-58.6318 + 55.8866i) q^{81} +(131.072 + 75.6747i) q^{83} +(-45.7195 + 79.1885i) q^{85} +(71.8994 - 106.222i) q^{87} +(-29.6962 + 17.1451i) q^{89} +(30.1525 + 52.2256i) q^{91} +(-2.57251 + 35.9473i) q^{93} +(-136.720 - 103.244i) q^{95} +(68.4432 + 118.547i) q^{97} +(18.6953 - 129.952i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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