LMFDB - Embedded newform 684.3.s.a.445.26

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			445.26
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44572 + 2.62867i) q^{3} +(-1.78673 - 3.09471i) q^{5} +(2.11933 + 3.67079i) q^{7} +(-4.81977 + 7.60065i) q^{9} +O(q^{10})$	\(q+(1.44572 + 2.62867i) q^{3} +(-1.78673 - 3.09471i) q^{5} +(2.11933 + 3.67079i) q^{7} +(-4.81977 + 7.60065i) q^{9} +(-8.61085 - 14.9144i) q^{11} -19.3844i q^{13} +(5.55184 - 9.17081i) q^{15} +(-16.5029 + 28.5838i) q^{17} +(-0.306057 + 18.9975i) q^{19} +(-6.58532 + 10.8780i) q^{21} -33.6031 q^{23} +(6.11519 - 10.5918i) q^{25} +(-26.9476 - 1.68114i) q^{27} +(0.310233 + 0.179113i) q^{29} +(-43.6395 - 25.1953i) q^{31} +(26.7562 - 44.1972i) q^{33} +(7.57335 - 13.1174i) q^{35} -26.4325i q^{37} +(50.9550 - 28.0244i) q^{39} +(-34.5685 + 19.9581i) q^{41} +19.8505 q^{43} +(32.1334 + 1.33548i) q^{45} +(-2.57889 + 4.46676i) q^{47} +(15.5169 - 26.8760i) q^{49} +(-98.9960 - 2.05627i) q^{51} +(20.3465 - 11.7470i) q^{53} +(-30.7706 + 53.2962i) q^{55} +(-50.3806 + 26.6606i) q^{57} +(-23.0105 + 13.2851i) q^{59} +(22.5456 - 39.0500i) q^{61} +(-38.1151 - 1.58408i) q^{63} +(-59.9890 + 34.6347i) q^{65} +79.5824i q^{67} +(-48.5808 - 88.3314i) q^{69} +(-1.79086 - 1.03395i) q^{71} +(18.0979 - 31.3466i) q^{73} +(36.6832 + 0.761956i) q^{75} +(36.4985 - 63.2173i) q^{77} +71.7472i q^{79} +(-34.5396 - 73.2667i) q^{81} +(-63.8891 - 110.659i) q^{83} +117.945 q^{85} +(-0.0223176 + 1.07445i) q^{87} +(-35.6570 + 20.5866i) q^{89} +(71.1560 - 41.0819i) q^{91} +(3.13935 - 151.139i) q^{93} +(59.3387 - 32.9963i) q^{95} +50.6357i q^{97} +(154.862 + 6.43612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.44572	+	2.62867i	0.481908	+	0.876222i
$3$	1.44572	+	2.62867i	0.481908	+	0.876222i
$4$		0			0
$5$	−1.78673	−	3.09471i	−0.357346	−	0.618942i	0.630170	−	0.776457i	$-0.282985\pi$
$5$	−1.78673	−	3.09471i	−0.357346	−	0.618942i	−0.987517	+	0.157515i	$0.949652\pi$
$6$		0			0
$7$	2.11933	+	3.67079i	0.302762	+	0.524399i	0.976760	−	0.214334i	$-0.0687580\pi$
$7$	2.11933	+	3.67079i	0.302762	+	0.524399i	−0.673999	+	0.738733i	$0.735425\pi$
$8$		0			0
$9$	−4.81977	+	7.60065i	−0.535530	+	0.844516i
$10$		0			0
$11$	−8.61085	−	14.9144i	−0.782805	−	1.35586i	−0.930302	−	0.366795i	$-0.880455\pi$
$11$	−8.61085	−	14.9144i	−0.782805	−	1.35586i	0.147497	−	0.989063i	$-0.452878\pi$
$12$		0			0
$13$		−	19.3844i		−	1.49111i	−0.666446	−	0.745553i	$-0.732186\pi$
$13$		−	19.3844i		−	1.49111i	0.666446	−	0.745553i	$-0.267814\pi$
$14$		0			0
$15$	5.55184	−	9.17081i	0.370122	−	0.611387i
$16$		0			0
$17$	−16.5029	+	28.5838i	−0.970758	+	1.68140i	−0.277481	+	0.960731i	$0.589500\pi$
$17$	−16.5029	+	28.5838i	−0.970758	+	1.68140i	−0.693277	+	0.720671i	$0.743834\pi$
$18$		0			0
$19$	−0.306057	+	18.9975i	−0.0161083	+	0.999870i
$19$	−0.306057	+	18.9975i	−0.0161083	+	0.999870i
$20$		0			0
$21$	−6.58532	+	10.8780i	−0.313587	+	0.517998i
$22$		0			0
$23$	−33.6031			−1.46100			−0.730502	−	0.682910i	$-0.760714\pi$
$23$	−33.6031			−1.46100			−0.730502	+	0.682910i	$0.760714\pi$
$24$		0			0
$25$	6.11519	−	10.5918i	0.244608	−	0.423673i
$26$		0			0
$27$	−26.9476	−	1.68114i	−0.998060	−	0.0622645i
$28$		0			0
$29$	0.310233	+	0.179113i	0.0106977	+	0.00617632i	0.505339	−	0.862921i	$-0.331367\pi$
$29$	0.310233	+	0.179113i	0.0106977	+	0.00617632i	−0.494642	+	0.869097i	$0.664701\pi$
$30$		0			0
$31$	−43.6395	−	25.1953i	−1.40773	−	0.812751i	−0.412558	−	0.910931i	$-0.635364\pi$
$31$	−43.6395	−	25.1953i	−1.40773	−	0.812751i	−0.995169	+	0.0981804i	$0.968698\pi$
$32$		0			0
$33$	26.7562	−	44.1972i	0.810793	−	1.33931i
$34$		0			0
$35$	7.57335	−	13.1174i	0.216381	−	0.374784i
$36$		0			0
$37$		−	26.4325i		−	0.714391i	−0.934030	−	0.357196i	$-0.883733\pi$
$37$		−	26.4325i		−	0.714391i	0.934030	−	0.357196i	$-0.116267\pi$
$38$		0			0
$39$	50.9550	−	28.0244i	1.30654	−	0.718575i
$40$		0			0
$41$	−34.5685	+	19.9581i	−0.843134	+	0.486784i	−0.858328	−	0.513101i	$-0.828497\pi$
$41$	−34.5685	+	19.9581i	−0.843134	+	0.486784i	0.0151941	+	0.999885i	$0.495163\pi$
$42$		0			0
$43$	19.8505			0.461640			0.230820	−	0.972996i	$-0.425859\pi$
$43$	19.8505			0.461640			0.230820	+	0.972996i	$0.425859\pi$
$44$		0			0
$45$	32.1334	+	1.33548i	0.714076	+	0.0296773i
$46$		0			0
$47$	−2.57889	+	4.46676i	−0.0548699	+	0.0950375i	−0.892156	−	0.451728i	$-0.850808\pi$
$47$	−2.57889	+	4.46676i	−0.0548699	+	0.0950375i	0.837286	+	0.546766i	$0.184141\pi$
$48$		0			0
$49$	15.5169	−	26.8760i	0.316671	−	0.548490i
$50$		0			0
$51$	−98.9960	−	2.05627i	−1.94110	−	0.0403190i
$52$		0			0
$53$	20.3465	−	11.7470i	0.383896	−	0.221642i	−0.295616	−	0.955307i	$-0.595525\pi$
$53$	20.3465	−	11.7470i	0.383896	−	0.221642i	0.679512	+	0.733664i	$0.262192\pi$
$54$		0			0
$55$	−30.7706	+	53.2962i	−0.559465	+	0.969021i
$56$		0			0
$57$	−50.3806	+	26.6606i	−0.883871	+	0.467731i
$58$		0			0
$59$	−23.0105	+	13.2851i	−0.390008	+	0.225171i	−0.682164	−	0.731200i	$-0.738961\pi$
$59$	−23.0105	+	13.2851i	−0.390008	+	0.225171i	0.292156	+	0.956371i	$0.405627\pi$
$60$		0			0
$61$	22.5456	−	39.0500i	0.369599	−	0.640165i	−0.619904	−	0.784678i	$-0.712828\pi$
$61$	22.5456	−	39.0500i	0.369599	−	0.640165i	0.989503	+	0.144513i	$0.0461616\pi$
$62$		0			0
$63$	−38.1151	−	1.58408i	−0.605001	−	0.0251441i
$64$		0			0
$65$	−59.9890	+	34.6347i	−0.922907	+	0.532841i
$66$		0			0
$67$			79.5824i			1.18780i	0.804540	+	0.593899i	$0.202412\pi$
$67$			79.5824i			1.18780i	−0.804540	+	0.593899i	$0.797588\pi$
$68$		0			0
$69$	−48.5808	−	88.3314i	−0.704069	−	1.28016i
$70$		0			0
$71$	−1.79086	−	1.03395i	−0.0252234	−	0.0145627i	0.487335	−	0.873215i	$-0.337969\pi$
$71$	−1.79086	−	1.03395i	−0.0252234	−	0.0145627i	−0.512559	+	0.858652i	$0.671302\pi$
$72$		0			0
$73$	18.0979	−	31.3466i	0.247917	−	0.429405i	−0.715031	−	0.699093i	$-0.753587\pi$
$73$	18.0979	−	31.3466i	0.247917	−	0.429405i	0.962948	+	0.269688i	$0.0869206\pi$
$74$		0			0
$75$	36.6832	+	0.761956i	0.489110	+	0.0101594i
$76$		0			0
$77$	36.4985	−	63.2173i	0.474007	−	0.821004i
$78$		0			0
$79$			71.7472i			0.908192i	0.890953	+	0.454096i	$0.150038\pi$
$79$			71.7472i			0.908192i	−0.890953	+	0.454096i	$0.849962\pi$
$80$		0			0
$81$	−34.5396	−	73.2667i	−0.426415	−	0.904528i
$82$		0			0
$83$	−63.8891	−	110.659i	−0.769748	−	1.33324i	−0.937699	−	0.347447i	$-0.887049\pi$
$83$	−63.8891	−	110.659i	−0.769748	−	1.33324i	0.167951	−	0.985795i	$-0.446285\pi$
$84$		0			0
$85$	117.945			1.38759
$86$		0			0
$87$	−0.0223176	+	1.07445i	−0.000256524	+	0.0123500i
$88$		0			0
$89$	−35.6570	+	20.5866i	−0.400640	+	0.231310i	−0.686760	−	0.726884i	$-0.740968\pi$
$89$	−35.6570	+	20.5866i	−0.400640	+	0.231310i	0.286120	+	0.958194i	$0.407634\pi$
$90$		0			0
$91$	71.1560	−	41.0819i	0.781934	−	0.451450i
$92$		0			0
$93$	3.13935	−	151.139i	0.0337564	−	1.62515i
$94$		0			0
$95$	59.3387	−	32.9963i	0.624617	−	0.347330i
$96$		0			0
$97$			50.6357i			0.522017i	0.965336	+	0.261009i	$0.0840551\pi$
$97$			50.6357i			0.522017i	−0.965336	+	0.261009i	$0.915945\pi$
$98$		0			0
$99$	154.862	+	6.43612i	1.56426	+	0.0650113i
$100$		0			0
$101$	72.5178	−	125.605i	0.717998	−	1.24361i	−0.243794	−	0.969827i	$-0.578392\pi$
$101$	72.5178	−	125.605i	0.717998	−	1.24361i	0.961792	−	0.273782i	$-0.0882747\pi$
$102$		0			0
$103$	−120.942	−	69.8258i	−1.17419	−	0.677920i	−0.219528	−	0.975606i	$-0.570452\pi$
$103$	−120.942	−	69.8258i	−1.17419	−	0.677920i	−0.954664	+	0.297686i	$0.903785\pi$
$104$		0			0
$105$	45.4303	+	0.943644i	0.432670	+	0.00898709i
$106$		0			0
$107$		−	24.8950i		−	0.232664i	−0.993210	−	0.116332i	$-0.962886\pi$
$107$		−	24.8950i		−	0.232664i	0.993210	−	0.116332i	$-0.0371136\pi$
$108$		0			0
$109$	−35.6302	−	20.5711i	−0.326882	−	0.188726i	0.327574	−	0.944826i	$-0.393769\pi$
$109$	−35.6302	−	20.5711i	−0.326882	−	0.188726i	−0.654456	+	0.756100i	$0.727102\pi$
$110$		0			0
$111$	69.4822	−	38.2140i	0.625965	−	0.344271i
$112$		0			0
$113$	65.6579	+	37.9076i	0.581043	+	0.335465i	0.761548	−	0.648109i	$-0.224440\pi$
$113$	65.6579	+	37.9076i	0.581043	+	0.335465i	−0.180505	+	0.983574i	$0.557773\pi$
$114$		0			0
$115$	60.0397	+	103.992i	0.522084	+	0.904277i
$116$		0			0
$117$	147.334	+	93.4282i	1.25926	+	0.798532i
$118$		0			0
$119$	−139.900			−1.17563
$120$		0			0
$121$	−87.7936	+	152.063i	−0.725567	+	1.25672i
$122$		0			0
$123$	−102.440	−	62.0151i	−0.832844	−	0.504188i
$124$		0			0
$125$	−133.041			−1.06433
$126$		0			0
$127$	−6.68080	+	3.85716i	−0.0526047	+	0.0303714i	−0.526072	−	0.850440i	$-0.676336\pi$
$127$	−6.68080	+	3.85716i	−0.0526047	+	0.0303714i	0.473467	+	0.880812i	$0.343002\pi$
$128$		0			0
$129$	28.6984	+	52.1804i	0.222468	+	0.404499i
$130$		0			0
$131$	52.3204	+	90.6216i	0.399392	+	0.691768i	0.993651	−	0.112506i	$-0.0358878\pi$
$131$	52.3204	+	90.6216i	0.399392	+	0.691768i	−0.594259	+	0.804274i	$0.702555\pi$
$132$		0			0
$133$	−70.3846	+	39.1386i	−0.529208	+	0.294275i
$134$		0			0
$135$	42.9455	+	86.3987i	0.318115	+	0.639991i
$136$		0			0
$137$	−113.046	+	195.802i	−0.825154	+	1.42921i	0.0766467	+	0.997058i	$0.475579\pi$
$137$	−113.046	+	195.802i	−0.825154	+	1.42921i	−0.901801	+	0.432151i	$0.857755\pi$
$138$		0			0
$139$	−108.727			−0.782211			−0.391106	−	0.920346i	$-0.627907\pi$
$139$	−108.727			−0.782211			−0.391106	+	0.920346i	$0.627907\pi$
$140$		0			0
$141$	−15.4700	−	0.321331i	−0.109716	−	0.00227894i
$142$		0			0
$143$	−289.107	+	166.916i	−2.02173	+	1.16725i
$144$		0			0
$145$		−	1.28011i		−	0.00882834i
$146$		0			0
$147$	93.0811	+	1.93341i	0.633205	+	0.0131525i
$148$		0			0
$149$	−42.2582	−	73.1934i	−0.283612	−	0.491231i	0.688660	−	0.725085i	$-0.258199\pi$
$149$	−42.2582	−	73.1934i	−0.283612	−	0.491231i	−0.972272	+	0.233854i	$0.924866\pi$
$150$		0			0
$151$	129.120	−	74.5477i	0.855102	−	0.493694i	−0.00726680	−	0.999974i	$-0.502313\pi$
$151$	129.120	−	74.5477i	0.855102	−	0.493694i	0.862369	+	0.506280i	$0.168980\pi$
$152$		0			0
$153$	−137.715	−	263.200i	−0.900101	−	1.72026i
$154$		0			0
$155$			180.069i			1.16173i
$156$		0			0
$157$	111.891	+	193.800i	0.712680	+	1.23440i	0.963848	+	0.266454i	$0.0858520\pi$
$157$	111.891	+	193.800i	0.712680	+	1.23440i	−0.251168	+	0.967943i	$0.580815\pi$
$158$		0			0
$159$	60.2944	+	36.5011i	0.379210	+	0.229567i
$160$		0			0
$161$	−71.2162	−	123.350i	−0.442336	−	0.766149i
$162$		0			0
$163$	280.953			1.72364			0.861818	−	0.507218i	$-0.169326\pi$
$163$	280.953			1.72364			0.861818	+	0.507218i	$0.169326\pi$
$164$		0			0
$165$	−184.583	−	3.83403i	−1.11869	−	0.0232365i
$166$		0			0
$167$		−	90.9975i		−	0.544895i	−0.962171	−	0.272448i	$-0.912167\pi$
$167$		−	90.9975i		−	0.544895i	0.962171	−	0.272448i	$-0.0878331\pi$
$168$		0			0
$169$	−206.754			−1.22340
$170$		0			0
$171$	−142.918	−	93.8900i	−0.835780	−	0.549064i
$172$		0			0
$173$		−	181.582i		−	1.04961i	−0.851224	−	0.524803i	$-0.824139\pi$
$173$		−	181.582i		−	1.04961i	0.851224	−	0.524803i	$-0.175861\pi$
$174$		0			0
$175$	51.8405			0.296231
$176$		0			0
$177$	−68.1889	−	41.2803i	−0.385248	−	0.233222i
$178$		0			0
$179$			285.526i			1.59512i	0.603241	+	0.797559i	$0.293876\pi$
$179$			285.526i			1.59512i	−0.603241	+	0.797559i	$0.706124\pi$
$180$		0			0
$181$	−44.5028	+	25.6937i	−0.245872	+	0.141954i	−0.617873	−	0.786278i	$-0.712005\pi$
$181$	−44.5028	+	25.6937i	−0.245872	+	0.141954i	0.372001	+	0.928232i	$0.378672\pi$
$182$		0			0
$183$	135.244	+	2.80919i	0.739039	+	0.0153508i
$184$		0			0
$185$	−81.8008	+	47.2277i	−0.442166	+	0.255285i
$186$		0			0
$187$	568.416			3.03966
$188$		0			0
$189$	−50.9398	−	102.482i	−0.269523	−	0.542233i
$190$		0			0
$191$	186.020	+	322.197i	0.973929	+	1.68689i	0.683424	+	0.730021i	$0.260490\pi$
$191$	186.020	+	322.197i	0.973929	+	1.68689i	0.290505	+	0.956874i	$0.406177\pi$
$192$		0			0
$193$	72.0574	−	41.6024i	0.373355	−	0.215556i	−0.301568	−	0.953445i	$-0.597510\pi$
$193$	72.0574	−	41.6024i	0.373355	−	0.215556i	0.674923	+	0.737888i	$0.264177\pi$
$194$		0			0
$195$	−177.770	−	107.619i	−0.911643	−	0.551892i
$196$		0			0
$197$	−211.557			−1.07390			−0.536948	−	0.843615i	$-0.680423\pi$
$197$	−211.557			−1.07390			−0.536948	+	0.843615i	$0.680423\pi$
$198$		0			0
$199$	137.799	+	238.674i	0.692456	+	1.19937i	0.971031	+	0.238954i	$0.0768046\pi$
$199$	137.799	+	238.674i	0.692456	+	1.19937i	−0.278575	+	0.960415i	$0.589862\pi$
$200$		0			0
$201$	−209.196	+	115.054i	−1.04077	+	0.572409i
$202$		0			0
$203$			1.51840i			0.00747982i
$204$		0			0
$205$	123.529	+	71.3196i	0.602581	+	0.347901i
$206$		0			0
$207$	161.959	−	255.405i	0.782412	−	1.23384i
$208$		0			0
$209$	285.973	−	159.020i	1.36829	−	0.760863i
$210$		0			0
$211$	−301.051	+	173.812i	−1.42678	+	0.823753i	−0.996865	−	0.0791156i	$-0.974790\pi$
$211$	−301.051	+	173.812i	−1.42678	+	0.823753i	−0.429917	+	0.902869i	$0.641457\pi$
$212$		0			0
$213$	0.128831	−	6.20238i	0.000604841	−	0.0291191i
$214$		0			0
$215$	−35.4675	−	61.4316i	−0.164965	−	0.285728i
$216$		0			0
$217$		−	213.589i		−	0.984280i
$218$		0			0
$219$	108.564	+	2.25501i	0.495727	+	0.0102969i
$220$		0			0
$221$	554.080	+	319.898i	2.50715	+	1.44750i
$222$		0			0
$223$		−	132.591i		−	0.594577i	−0.954788	−	0.297289i	$-0.903918\pi$
$223$		−	132.591i		−	0.594577i	0.954788	−	0.297289i	$-0.0960824\pi$
$224$		0			0
$225$	51.0308	+	97.5295i	0.226804	+	0.433465i
$226$		0			0
$227$	146.854	−	84.7865i	0.646936	−	0.373509i	−0.140345	−	0.990103i	$-0.544821\pi$
$227$	146.854	−	84.7865i	0.646936	−	0.373509i	0.787281	+	0.616594i	$0.211488\pi$
$228$		0			0
$229$	−195.308	+	338.283i	−0.852872	+	1.47722i	0.0257340	+	0.999669i	$0.491808\pi$
$229$	−195.308	+	338.283i	−0.852872	+	1.47722i	−0.878606	+	0.477548i	$0.841526\pi$
$230$		0			0
$231$	218.944	+	4.54774i	0.947809	+	0.0196872i
$232$		0			0
$233$	−55.9875	+	96.9731i	−0.240290	+	0.416194i	−0.960797	−	0.277254i	$-0.910576\pi$
$233$	−55.9875	+	96.9731i	−0.240290	+	0.416194i	0.720507	+	0.693447i	$0.243909\pi$
$234$		0			0
$235$	18.4311			0.0784302
$236$		0			0
$237$	−188.599	+	103.727i	−0.795778	+	0.437665i
$238$		0			0
$239$	−78.8759	+	136.617i	−0.330025	+	0.571619i	−0.982516	−	0.186177i	$-0.940390\pi$
$239$	−78.8759	+	136.617i	−0.330025	+	0.571619i	0.652492	+	0.757796i	$0.273724\pi$
$240$		0			0
$241$	312.571	+	180.463i	1.29697	+	0.748808i	0.979880	−	0.199586i	$-0.0639597\pi$
$241$	312.571	+	180.463i	1.29697	+	0.748808i	0.317094	+	0.948394i	$0.397293\pi$
$242$		0			0
$243$	142.659	−	196.717i	0.587074	−	0.809533i
$244$		0			0
$245$	−110.898			−0.452644
$246$		0			0
$247$	368.255	+	5.93272i	1.49091	+	0.0240191i
$248$		0			0
$249$	198.520	−	327.926i	0.797269	−	1.31697i
$250$		0			0
$251$	−95.8755	−	166.061i	−0.381974	−	0.661598i	0.609370	−	0.792886i	$-0.291422\pi$
$251$	−95.8755	−	166.061i	−0.381974	−	0.661598i	−0.991344	+	0.131287i	$0.958089\pi$
$252$		0			0
$253$	289.352	+	501.172i	1.14368	+	1.98092i
$254$		0			0
$255$	170.516	+	310.038i	0.668688	+	1.21583i
$256$		0			0
$257$		−	289.983i		−	1.12834i	−0.825660	−	0.564169i	$-0.809197\pi$
$257$		−	289.983i		−	1.12834i	0.825660	−	0.564169i	$-0.190803\pi$
$258$		0			0
$259$	97.0281	−	56.0192i	0.374626	−	0.216290i
$260$		0			0
$261$	−2.85663	+	1.49469i	−0.0109449	+	0.00572678i
$262$		0			0
$263$	58.9700			0.224221			0.112110	−	0.993696i	$-0.464239\pi$
$263$	58.9700			0.224221			0.112110	+	0.993696i	$0.464239\pi$
$264$		0			0
$265$	−72.7073	−	41.9776i	−0.274367	−	0.158406i
$266$		0			0
$267$	−105.665	−	63.9678i	−0.395750	−	0.239580i
$268$		0			0
$269$	−58.1708	−	33.5849i	−0.216248	−	0.124851i	0.387964	−	0.921675i	$-0.373179\pi$
$269$	−58.1708	−	33.5849i	−0.216248	−	0.124851i	−0.604212	+	0.796824i	$0.706512\pi$
$270$		0			0
$271$	−20.1126	+	34.8360i	−0.0742162	+	0.128546i	−0.900745	−	0.434348i	$-0.856979\pi$
$271$	−20.1126	+	34.8360i	−0.0742162	+	0.128546i	0.826529	+	0.562894i	$0.190312\pi$
$272$		0			0
$273$	210.863	+	127.652i	0.772390	+	0.467591i
$274$		0			0
$275$	−210.628			−0.765920
$276$		0			0
$277$	−62.3160	−	107.935i	−0.224968	−	0.389655i	0.731342	−	0.682011i	$-0.238894\pi$
$277$	−62.3160	−	107.935i	−0.224968	−	0.389655i	−0.956310	+	0.292355i	$0.905561\pi$
$278$		0			0
$279$	401.833	−	210.253i	1.44026	−	0.753595i
$280$		0			0
$281$	−434.977	−	251.134i	−1.54796	−	0.893715i	−0.998298	−	0.0583272i	$-0.981423\pi$
$281$	−434.977	−	251.134i	−1.54796	−	0.893715i	−0.549662	−	0.835387i	$-0.685243\pi$
$282$		0			0
$283$	125.492	+	217.359i	0.443435	+	0.768052i	0.997942	−	0.0641272i	$-0.0204263\pi$
$283$	125.492	+	217.359i	0.443435	+	0.768052i	−0.554507	+	0.832179i	$0.687093\pi$
$284$		0			0
$285$	172.524	+	108.278i	0.605346	+	0.379923i
$286$		0			0
$287$	−146.524	−	84.5958i	−0.510538	−	0.294759i
$288$		0			0
$289$	−400.191	−	693.150i	−1.38474	−	2.39844i
$290$		0			0
$291$	−133.104	+	73.2051i	−0.457403	+	0.251564i
$292$		0			0
$293$	29.5654	+	17.0696i	0.100906	+	0.0582580i	0.549604	−	0.835426i	$-0.314779\pi$
$293$	29.5654	+	17.0696i	0.100906	+	0.0582580i	−0.448698	+	0.893684i	$0.648112\pi$
$294$		0			0
$295$	82.2270	+	47.4738i	0.278736	+	0.160928i
$296$		0			0
$297$	206.969	+	416.385i	0.696864	+	1.40197i
$298$		0			0
$299$			651.375i			2.17851i
$300$		0			0
$301$	42.0699	+	72.8671i	0.139767	+	0.242083i
$302$		0			0
$303$	435.013	+	9.03576i	1.43569	+	0.0298210i
$304$		0			0
$305$	−161.131			−0.528299
$306$		0			0
$307$	−174.403	−	100.692i	−0.568088	−	0.327986i	0.188297	−	0.982112i	$-0.439703\pi$
$307$	−174.403	−	100.692i	−0.568088	−	0.327986i	−0.756385	+	0.654126i	$0.773036\pi$
$308$		0			0
$309$	8.70033	−	418.864i	0.0281564	−	1.35555i
$310$		0			0
$311$	15.4402	−	26.7432i	0.0496470	−	0.0859911i	−0.840134	−	0.542379i	$-0.817524\pi$
$311$	15.4402	−	26.7432i	0.0496470	−	0.0859911i	0.889781	+	0.456388i	$0.150857\pi$
$312$		0			0
$313$	31.8993	−	55.2512i	0.101915	−	0.176522i	−0.810559	−	0.585657i	$-0.800836\pi$
$313$	31.8993	−	55.2512i	0.101915	−	0.176522i	0.912474	+	0.409136i	$0.134170\pi$
$314$		0			0
$315$	63.1991	+	120.785i	0.200632	+	0.383446i
$316$		0			0
$317$	273.272	+	157.774i	0.862056	+	0.497708i	0.864700	−	0.502288i	$-0.167508\pi$
$317$	273.272	+	157.774i	0.862056	+	0.497708i	−0.00264414	+	0.999997i	$0.500842\pi$
$318$		0			0
$319$		−	6.16927i		−	0.0193394i
$320$		0			0
$321$	65.4407	−	35.9913i	0.203865	−	0.112122i
$322$		0			0
$323$	−537.972	−	322.262i	−1.66555	−	0.997717i
$324$		0			0
$325$	−205.316	−	118.539i	−0.631741	−	0.364736i
$326$		0			0
$327$	2.56317	−	123.400i	0.00783844	−	0.377370i
$328$		0			0
$329$	−21.8621			−0.0664501
$330$		0			0
$331$	−67.2074	+	38.8022i	−0.203044	+	0.117227i	−0.598074	−	0.801441i	$-0.704067\pi$
$331$	−67.2074	+	38.8022i	−0.203044	+	0.117227i	0.395031	+	0.918668i	$0.370734\pi$
$332$		0			0
$333$	200.904	+	127.398i	0.603315	+	0.382578i
$334$		0			0
$335$	246.284	−	142.192i	0.735177	−	0.424455i
$336$		0			0
$337$	244.336	−	141.068i	0.725033	−	0.418598i	−0.0915692	−	0.995799i	$-0.529188\pi$
$337$	244.336	−	141.068i	0.725033	−	0.418598i	0.816602	+	0.577201i	$0.195855\pi$
$338$		0			0
$339$	−4.72331	+	227.397i	−0.0139331	+	0.670786i
$340$		0			0
$341$			867.812i			2.54490i
$342$		0			0
$343$	339.236			0.989027
$344$		0			0
$345$	−186.559	+	308.168i	−0.540751	+	0.893240i
$346$		0			0
$347$	−145.454	−	251.933i	−0.419175	−	0.726033i	0.576681	−	0.816969i	$-0.304347\pi$
$347$	−145.454	−	251.933i	−0.419175	−	0.726033i	−0.995857	+	0.0909362i	$0.971014\pi$
$348$		0			0
$349$	−195.221	−	338.133i	−0.559373	−	0.968863i	−0.997549	−	0.0699734i	$-0.977709\pi$
$349$	−195.221	−	338.133i	−0.559373	−	0.968863i	0.438176	−	0.898889i	$-0.355625\pi$
$350$		0			0
$351$	−32.5879	+	522.363i	−0.0928429	+	1.48821i
$352$		0			0
$353$	−229.262	−	397.093i	−0.649467	−	1.12491i	−0.983250	−	0.182260i	$-0.941659\pi$
$353$	−229.262	−	397.093i	−0.649467	−	1.12491i	0.333784	−	0.942650i	$-0.391675\pi$
$354$		0			0
$355$			7.38958i			0.0208157i
$356$		0			0
$357$	−202.257	−	367.751i	−0.566547	−	1.03012i
$358$		0			0
$359$	−34.1410	+	59.1339i	−0.0951002	+	0.164718i	−0.909650	−	0.415375i	$-0.863650\pi$
$359$	−34.1410	+	59.1339i	−0.0951002	+	0.164718i	0.814550	+	0.580093i	$0.196984\pi$
$360$		0			0
$361$	−360.813	−	11.6287i	−0.999481	−	0.0322123i
$362$		0			0
$363$	−526.648	−	10.9391i	−1.45082	−	0.0301354i
$364$		0			0
$365$	−129.345			−0.354369
$366$		0			0
$367$	−226.321	+	391.999i	−0.616678	+	1.06812i	0.373410	+	0.927666i	$0.378189\pi$
$367$	−226.321	+	391.999i	−0.616678	+	1.06812i	−0.990088	+	0.140451i	$0.955145\pi$
$368$		0			0
$369$	14.9176	−	358.937i	0.0404270	−	0.972728i
$370$		0			0
$371$	86.2419	+	49.7918i	0.232458	+	0.134210i
$372$		0			0
$373$	−180.571	−	104.253i	−0.484105	−	0.279498i	0.238021	−	0.971260i	$-0.423501\pi$
$373$	−180.571	−	104.253i	−0.484105	−	0.279498i	−0.722126	+	0.691762i	$0.756835\pi$
$374$		0			0
$375$	−192.341	−	349.721i	−0.512909	−	0.932590i
$376$		0			0
$377$	3.47200	−	6.01368i	0.00920955	−	0.0159514i
$378$		0			0
$379$			26.5246i			0.0699858i	0.999388	+	0.0349929i	$0.0111409\pi$
$379$			26.5246i			0.0699858i	−0.999388	+	0.0349929i	$0.988859\pi$
$380$		0			0
$381$	−19.7978	−	11.9852i	−0.0519627	−	0.0314572i
$382$		0			0
$383$	99.1329	−	57.2344i	0.258833	−	0.149437i	−0.364969	−	0.931020i	$-0.618921\pi$
$383$	99.1329	−	57.2344i	0.258833	−	0.149437i	0.623802	+	0.781583i	$0.285587\pi$
$384$		0			0
$385$	−260.852			−0.677538
$386$		0			0
$387$	−95.6750	+	150.877i	−0.247222	+	0.389863i
$388$		0			0
$389$	−58.7477	+	101.754i	−0.151022	+	0.261579i	−0.931604	−	0.363476i	$-0.881590\pi$
$389$	−58.7477	+	101.754i	−0.151022	+	0.261579i	0.780581	+	0.625054i	$0.214923\pi$
$390$		0			0
$391$	554.548	−	960.506i	1.41828	−	2.45654i
$392$		0			0
$393$	−162.573	+	268.546i	−0.413672	+	0.683324i
$394$		0			0
$395$	222.036	−	128.193i	0.562118	−	0.324539i
$396$		0			0
$397$	281.926	−	488.311i	0.710142	−	1.23000i	−0.254662	−	0.967030i	$-0.581964\pi$
$397$	281.926	−	488.311i	0.710142	−	1.23000i	0.964804	−	0.262971i	$-0.0847024\pi$
$398$		0			0
$399$	−204.639	−	128.434i	−0.512880	−	0.321890i
$400$		0			0
$401$	491.130	−	283.554i	1.22476	−	0.707117i	0.258833	−	0.965922i	$-0.416662\pi$
$401$	491.130	−	283.554i	1.22476	−	0.707117i	0.965929	+	0.258805i	$0.0833288\pi$
$402$		0			0
$403$	−488.395	+	845.925i	−1.21190	+	2.09907i
$404$		0			0
$405$	−165.026	+	237.798i	−0.407472	+	0.587155i
$406$		0			0
$407$	−394.226	+	227.606i	−0.968613	+	0.559229i
$408$		0			0
$409$		−	175.230i		−	0.428434i	−0.976786	−	0.214217i	$-0.931280\pi$
$409$		−	175.230i		−	0.428434i	0.976786	−	0.214217i	$-0.0687200\pi$
$410$		0			0
$411$	−678.131	−	14.0856i	−1.64995	−	0.0342716i
$412$		0			0
$413$	−97.5337	−	56.3111i	−0.236159	−	0.136346i
$414$		0			0
$415$	−228.305	+	395.436i	−0.550133	+	0.952858i
$416$		0			0
$417$	−157.190	−	285.808i	−0.376954	−	0.685391i
$418$		0			0
$419$	37.2462	−	64.5122i	0.0888930	−	0.153967i	−0.818150	−	0.575004i	$-0.805000\pi$
$419$	37.2462	−	64.5122i	0.0888930	−	0.153967i	0.907043	+	0.421037i	$0.138334\pi$
$420$		0			0
$421$			61.2336i			0.145448i	0.997352	+	0.0727240i	$0.0231692\pi$
$421$			61.2336i			0.145448i	−0.997352	+	0.0727240i	$0.976831\pi$
$422$		0			0
$423$	−21.5206	−	41.1300i	−0.0508762	−	0.0972340i
$424$		0			0
$425$	201.837	+	349.591i	0.474910	+	0.822567i
$426$		0			0
$427$	191.126			0.447602
$428$		0			0
$429$	−856.735	−	518.652i	−1.99705	−	1.20898i
$430$		0			0
$431$	462.163	−	266.830i	1.07230	−	0.619095i	0.143494	−	0.989651i	$-0.454166\pi$
$431$	462.163	−	266.830i	1.07230	−	0.619095i	0.928810	+	0.370557i	$0.120833\pi$
$432$		0			0
$433$	−338.448	+	195.403i	−0.781635	+	0.451277i	−0.837010	−	0.547188i	$-0.815698\pi$
$433$	−338.448	+	195.403i	−0.781635	+	0.451277i	0.0553741	+	0.998466i	$0.482365\pi$
$434$		0			0
$435$	3.36498	−	1.85068i	0.00773558	−	0.00425444i
$436$		0			0
$437$	10.2845	−	638.376i	0.0235343	−	1.46082i
$438$		0			0
$439$			788.021i			1.79504i	0.440976	+	0.897519i	$0.354632\pi$
$439$			788.021i			1.79504i	−0.440976	+	0.897519i	$0.645368\pi$
$440$		0			0
$441$	129.487	+	247.474i	0.293622	+	0.561166i
$442$		0			0
$443$	−255.045	+	441.750i	−0.575721	+	0.997179i	0.420241	+	0.907412i	$0.361945\pi$
$443$	−255.045	+	441.750i	−0.575721	+	0.997179i	−0.995963	+	0.0897663i	$0.971388\pi$
$444$		0			0
$445$	127.419	+	73.5652i	0.286334	+	0.165315i
$446$		0			0
$447$	131.307	−	216.900i	0.293752	−	0.485235i
$448$		0			0
$449$		−	3.02812i		−	0.00674414i	−0.999994	−	0.00337207i	$-0.998927\pi$
$449$		−	3.02812i		−	0.00674414i	0.999994	−	0.00337207i	$-0.00107336\pi$
$450$		0			0
$451$	595.329	+	343.713i	1.32002	+	0.762114i
$452$		0			0
$453$	382.633	+	231.639i	0.844666	+	0.511345i
$454$		0			0
$455$	−254.273	−	146.805i	−0.558842	−	0.322648i
$456$		0			0
$457$	−431.036	−	746.576i	−0.943186	−	1.63365i	−0.759343	−	0.650691i	$-0.774479\pi$
$457$	−431.036	−	746.576i	−0.943186	−	1.63365i	−0.183843	−	0.982956i	$-0.558854\pi$
$458$		0			0
$459$	492.767	−	742.522i	1.07357	−	1.61770i
$460$		0			0
$461$	394.550			0.855856			0.427928	−	0.903813i	$-0.359244\pi$
$461$	394.550			0.855856			0.427928	+	0.903813i	$0.359244\pi$
$462$		0			0
$463$	−64.8349	+	112.297i	−0.140032	+	0.242543i	−0.927509	−	0.373802i	$-0.878054\pi$
$463$	−64.8349	+	112.297i	−0.140032	+	0.242543i	0.787476	+	0.616345i	$0.211387\pi$
$464$		0			0
$465$	−473.341	+	260.329i	−1.01794	+	0.559848i
$466$		0			0
$467$	126.290			0.270428			0.135214	−	0.990816i	$-0.456828\pi$
$467$	126.290			0.270428			0.135214	+	0.990816i	$0.456828\pi$
$468$		0			0
$469$	−292.130	+	168.662i	−0.622879	+	0.359620i
$470$		0			0
$471$	−347.674	+	574.305i	−0.738160	+	1.21933i
$472$		0			0
$473$	−170.930	−	296.059i	−0.361374	−	0.625918i
$474$		0			0
$475$	199.347	+	119.415i	0.419678	+	0.251400i
$476$		0			0
$477$	−8.78024	+	211.264i	−0.0184072	+	0.442902i
$478$		0			0
$479$	140.257	−	242.932i	0.292811	−	0.507164i	−0.681662	−	0.731667i	$-0.738743\pi$
$479$	140.257	−	242.932i	0.292811	−	0.507164i	0.974473	+	0.224503i	$0.0720759\pi$
$480$		0			0
$481$	−512.377			−1.06523
$482$		0			0
$483$	221.287	−	365.533i	0.458151	−	0.756798i
$484$		0			0
$485$	156.703	−	90.4723i	0.323098	−	0.186541i
$486$		0			0
$487$		−	783.264i		−	1.60835i	−0.594396	−	0.804173i	$-0.702609\pi$
$487$		−	783.264i		−	1.60835i	0.594396	−	0.804173i	$-0.297391\pi$
$488$		0			0
$489$	406.180	+	738.531i	0.830633	+	1.51029i
$490$		0			0
$491$	102.247	+	177.098i	0.208243	+	0.360688i	0.951161	−	0.308695i	$-0.0998921\pi$
$491$	102.247	+	177.098i	0.208243	+	0.360688i	−0.742918	+	0.669382i	$0.766559\pi$
$492$		0			0
$493$	−10.2395	+	5.91177i	−0.0207698	+	0.0119914i
$494$		0			0
$495$	−256.778	−	490.751i	−0.518744	−	0.991417i
$496$		0			0
$497$		−	8.76516i		−	0.0176361i
$498$		0			0
$499$	−252.619	−	437.549i	−0.506251	−	0.876852i	−0.999974	−	0.00723259i	$-0.997698\pi$
$499$	−252.619	−	437.549i	−0.506251	−	0.876852i	0.493723	−	0.869619i	$-0.335636\pi$
$500$		0			0
$501$	239.202	−	131.557i	0.477449	−	0.262589i
$502$		0			0
$503$	−340.083	−	589.040i	−0.676108	−	1.17105i	−0.976144	−	0.217126i	$-0.930332\pi$
$503$	−340.083	−	589.040i	−0.676108	−	1.17105i	0.300035	−	0.953928i	$-0.403002\pi$
$504$		0			0
$505$	−518.279			−1.02630
$506$		0			0
$507$	−298.909	−	543.487i	−0.589564	−	1.07197i
$508$		0			0
$509$		−	449.590i		−	0.883280i	−0.897192	−	0.441640i	$-0.854397\pi$
$509$		−	449.590i		−	0.883280i	0.897192	−	0.441640i	$-0.145603\pi$
$510$		0			0
$511$	153.422			0.300239
$512$		0			0
$513$	40.1850	−	511.424i	0.0783334	−	0.996927i
$514$		0			0
$515$			499.039i			0.969008i
$516$		0			0
$517$	88.8257			0.171810
$518$		0			0
$519$	477.318	−	262.517i	0.919688	−	0.505813i
$520$		0			0
$521$		−	725.604i		−	1.39271i	−0.717696	−	0.696357i	$-0.754803\pi$
$521$		−	725.604i		−	1.39271i	0.717696	−	0.696357i	$-0.245197\pi$
$522$		0			0
$523$	−456.195	+	263.384i	−0.872265	+	0.503602i	−0.868100	−	0.496389i	$-0.834659\pi$
$523$	−456.195	+	263.384i	−0.872265	+	0.503602i	−0.00416462	+	0.999991i	$0.501326\pi$
$524$		0			0
$525$	74.9470	+	136.271i	0.142756	+	0.259564i
$526$		0			0
$527$	1440.36	−	831.590i	2.73312	−	1.57797i
$528$		0			0
$529$	600.169			1.13454
$530$		0			0
$531$	9.92985	−	238.926i	0.0187003	−	0.449954i
$532$		0			0
$533$	386.876	+	670.089i	0.725846	+	1.25720i
$534$		0			0
$535$	−77.0428	+	44.4807i	−0.144005	+	0.0831415i
$536$		0			0
$537$	−750.553	+	412.792i	−1.39768	+	0.768699i
$538$		0			0
$539$	−534.454			−0.991565
$540$		0			0
$541$	−241.845	−	418.888i	−0.447034	−	0.774286i	0.551157	−	0.834401i	$-0.314186\pi$
$541$	−241.845	−	418.888i	−0.447034	−	0.774286i	−0.998191	+	0.0601157i	$0.980853\pi$
$542$		0			0
$543$	−131.879	−	79.8371i	−0.242871	−	0.147030i
$544$		0			0
$545$			147.020i			0.269761i
$546$		0			0
$547$	−901.020	−	520.204i	−1.64720	−	0.951013i	−0.978177	−	0.207774i	$-0.933378\pi$
$547$	−901.020	−	520.204i	−1.64720	−	0.951013i	−0.669026	−	0.743239i	$-0.733289\pi$
$548$		0			0
$549$	188.141	+	359.573i	0.342698	+	0.654960i
$550$		0			0
$551$	−3.49766	+	5.83885i	−0.00634784	+	0.0105968i
$552$		0			0
$553$	−263.369	+	152.056i	−0.476255	+	0.274966i
$554$		0			0
$555$	−242.407	−	146.749i	−0.436770	−	0.264412i
$556$		0			0
$557$	321.105	+	556.170i	0.576490	+	0.998510i	0.995878	+	0.0907030i	$0.0289114\pi$
$557$	321.105	+	556.170i	0.576490	+	0.998510i	−0.419388	+	0.907807i	$0.637755\pi$
$558$		0			0
$559$		−	384.790i		−	0.688354i
$560$		0			0
$561$	821.772	+	1494.18i	1.46483	+	2.66341i
$562$		0			0
$563$	−17.8501	−	10.3058i	−0.0317053	−	0.0183051i	0.484064	−	0.875033i	$-0.339160\pi$
$563$	−17.8501	−	10.3058i	−0.0317053	−	0.0183051i	−0.515769	+	0.856728i	$0.672494\pi$
$564$		0			0
$565$		−	270.923i		−	0.479509i
$566$		0			0
$567$	195.746	−	282.064i	0.345231	−	0.497468i
$568$		0			0
$569$	−414.099	+	239.080i	−0.727767	+	0.420176i	−0.817605	−	0.575780i	$-0.804698\pi$
$569$	−414.099	+	239.080i	−0.727767	+	0.420176i	0.0898379	+	0.995956i	$0.471365\pi$
$570$		0			0
$571$	−154.725	+	267.991i	−0.270972	+	0.469337i	−0.969111	−	0.246625i	$-0.920678\pi$
$571$	−154.725	+	267.991i	−0.270972	+	0.469337i	0.698139	+	0.715962i	$0.254012\pi$
$572$		0			0
$573$	−578.014	+	954.793i	−1.00875	+	1.66631i
$574$		0			0
$575$	−205.489	+	355.918i	−0.357373	+	0.618988i
$576$		0			0
$577$	684.624			1.18652			0.593262	−	0.805010i	$-0.297840\pi$
$577$	684.624			1.18652			0.593262	+	0.805010i	$0.297840\pi$
$578$		0			0
$579$	213.534	+	129.269i	0.368798	+	0.223263i
$580$		0			0
$581$	270.804	−	469.047i	0.466100	−	0.807310i
$582$		0			0
$583$	−350.401	−	202.304i	−0.601031	−	0.347005i
$584$		0			0
$585$	25.8874	−	622.886i	0.0442520	−	1.06476i
$586$		0			0
$587$	221.269			0.376949			0.188475	−	0.982078i	$-0.439646\pi$
$587$	221.269			0.376949			0.188475	+	0.982078i	$0.439646\pi$
$588$		0			0
$589$	492.004	−	821.332i	0.835322	−	1.39445i
$590$		0			0
$591$	−305.853	−	556.114i	−0.517519	−	0.940971i
$592$		0			0
$593$	−173.199	−	299.989i	−0.292072	−	0.505883i	0.682228	−	0.731140i	$-0.261011\pi$
$593$	−173.199	−	299.989i	−0.292072	−	0.505883i	−0.974299	+	0.225257i	$0.927678\pi$
$594$		0			0
$595$	249.964	+	432.951i	0.420108	+	0.727649i
$596$		0			0
$597$	−428.177	+	707.284i	−0.717214	+	1.18473i
$598$		0			0
$599$			1126.11i			1.87998i	0.341207	+	0.939988i	$0.389164\pi$
$599$			1126.11i			1.87998i	−0.341207	+	0.939988i	$0.610836\pi$
$600$		0			0
$601$	−14.5616	+	8.40717i	−0.0242290	+	0.0139886i	−0.512066	−	0.858946i	$-0.671120\pi$
$601$	−14.5616	+	8.40717i	−0.0242290	+	0.0139886i	0.487837	+	0.872935i	$0.337786\pi$
$602$		0			0
$603$	−604.878	−	383.569i	−1.00311	−	0.636101i
$604$		0			0
$605$	627.454			1.03711
$606$		0			0
$607$	−542.819	−	313.396i	−0.894265	−	0.516304i	−0.0189295	−	0.999821i	$-0.506026\pi$
$607$	−542.819	−	313.396i	−0.894265	−	0.516304i	−0.875335	+	0.483517i	$0.839359\pi$
$608$		0			0
$609$	−3.99137	+	2.19519i	−0.00655398	+	0.00360458i
$610$		0			0
$611$	86.5854	+	49.9901i	0.141711	+	0.0818169i
$612$		0			0
$613$	−127.095	+	220.136i	−0.207333	+	0.359112i	−0.950874	−	0.309579i	$-0.899812\pi$
$613$	−127.095	+	220.136i	−0.207333	+	0.359112i	0.743540	+	0.668691i	$0.233145\pi$
$614$		0			0
$615$	−8.88647	+	427.825i	−0.0144495	+	0.695651i
$616$		0			0
$617$	−617.018			−1.00003			−0.500015	−	0.866017i	$-0.666672\pi$
$617$	−617.018			−1.00003			−0.500015	+	0.866017i	$0.666672\pi$
$618$		0			0
$619$	−373.018	−	646.086i	−0.602614	−	1.04376i	−0.992424	−	0.122863i	$-0.960793\pi$
$619$	−373.018	−	646.086i	−0.602614	−	1.04376i	0.389810	−	0.920895i	$-0.372541\pi$
$620$		0			0
$621$	905.524	+	56.4916i	1.45817	+	0.0909687i
$622$		0			0
$623$	−151.138	−	87.2595i	−0.242597	−	0.140063i
$624$		0			0
$625$	84.8292	+	146.928i	0.135727	+	0.235086i
$626$		0			0
$627$	831.449	+	521.828i	1.32608	+	0.832262i
$628$		0			0
$629$	755.542	+	436.212i	1.20118	+	0.693501i
$630$		0			0
$631$	423.895	+	734.207i	0.671782	+	1.16356i	0.977398	+	0.211406i	$0.0678043\pi$
$631$	423.895	+	734.207i	0.671782	+	1.16356i	−0.305616	+	0.952155i	$0.598862\pi$
$632$		0			0
$633$	−892.130	−	540.079i	−1.40937	−	0.853205i
$634$		0			0
$635$	23.8736	+	13.7834i	0.0375962	+	0.0217062i
$636$		0			0
$637$	−520.974	−	300.785i	−0.817856	−	0.472189i
$638$		0			0
$639$	16.4902	−	8.62827i	0.0258063	−	0.0135028i
$640$		0			0
$641$		−	736.317i		−	1.14870i	−0.818609	−	0.574351i	$-0.805255\pi$
$641$		−	736.317i		−	1.14870i	0.818609	−	0.574351i	$-0.194745\pi$
$642$		0			0
$643$	130.195	+	225.505i	0.202481	+	0.350708i	0.949327	−	0.314289i	$-0.101766\pi$
$643$	130.195	+	225.505i	0.202481	+	0.350708i	−0.746846	+	0.664997i	$0.768433\pi$
$644$		0			0
$645$	110.207	−	182.045i	0.170863	−	0.282241i
$646$		0			0
$647$	−692.664			−1.07058			−0.535289	−	0.844669i	$-0.679797\pi$
$647$	−692.664			−1.07058			−0.535289	+	0.844669i	$0.679797\pi$
$648$		0			0
$649$	396.280	+	228.792i	0.610600	+	0.352530i
$650$		0			0
$651$	561.453	−	308.790i	0.862448	−	0.474332i
$652$		0			0
$653$	316.724	−	548.582i	0.485029	−	0.840095i	−0.514823	−	0.857296i	$-0.672142\pi$
$653$	316.724	−	548.582i	0.485029	−	0.840095i	0.999852	+	0.0172016i	$0.00547572\pi$
$654$		0			0
$655$	186.965	−	323.833i	0.285442	−	0.494401i
$656$		0			0
$657$	151.026	+	288.639i	0.229872	+	0.439329i
$658$		0			0
$659$	577.022	+	333.144i	0.875602	+	0.505529i	0.869206	−	0.494450i	$-0.164631\pi$
$659$	577.022	+	333.144i	0.875602	+	0.505529i	0.00639647	+	0.999980i	$0.497964\pi$
$660$		0			0
$661$		−	46.6295i		−	0.0705438i	−0.999378	−	0.0352719i	$-0.988770\pi$
$661$		−	46.6295i		−	0.0705438i	0.999378	−	0.0352719i	$-0.0112297\pi$
$662$		0			0
$663$	−39.8595	+	1918.97i	−0.0601199	+	2.89438i
$664$		0			0
$665$	246.881	+	147.890i	0.371249	+	0.222390i
$666$		0			0
$667$	−10.4248	−	6.01876i	−0.0156294	−	0.00902364i
$668$		0			0
$669$	348.537	−	191.689i	0.520982	−	0.286531i
$670$		0			0
$671$	−776.546			−1.15730
$672$		0			0
$673$	17.1127	−	9.88002i	0.0254275	−	0.0146806i	−0.487232	−	0.873272i	$-0.661994\pi$
$673$	17.1127	−	9.88002i	0.0254275	−	0.0146806i	0.512660	+	0.858592i	$0.328660\pi$
$674$		0			0
$675$	−182.596	+	275.144i	−0.270513	+	0.407620i
$676$		0			0
$677$	−37.4947	+	21.6476i	−0.0553836	+	0.0319757i	−0.527436	−	0.849595i	$-0.676847\pi$
$677$	−37.4947	+	21.6476i	−0.0553836	+	0.0319757i	0.472053	+	0.881570i	$0.343513\pi$
$678$		0			0
$679$	−185.873	+	107.314i	−0.273745	+	0.158047i
$680$		0			0
$681$	435.186	+	263.454i	0.639040	+	0.386863i
$682$		0			0
$683$		−	1317.95i		−	1.92965i	−0.262895	−	0.964825i	$-0.584677\pi$
$683$		−	1317.95i		−	1.92965i	0.262895	−	0.964825i	$-0.415323\pi$
$684$		0			0
$685$	807.932			1.17946
$686$		0			0
$687$	−1171.59	−	24.3355i	−1.70538	−	0.0354228i
$688$		0			0
$689$	−227.709	−	394.404i	−0.330492	−	0.572429i
$690$		0			0
$691$	−556.438	−	963.778i	−0.805264	−	1.39476i	−0.916113	−	0.400921i	$-0.868690\pi$
$691$	−556.438	−	963.778i	−0.805264	−	1.39476i	0.110848	−	0.993837i	$-0.464643\pi$
$692$		0			0
$693$	304.578	+	582.105i	0.439506	+	0.839979i
$694$		0			0
$695$	194.267	+	336.480i	0.279520	+	0.484143i
$696$		0			0
$697$		−	1317.47i		−	1.89020i
$698$		0			0
$699$	−335.852	−	6.97607i	−0.480475	−	0.00998008i
$700$		0			0
$701$	−312.796	+	541.779i	−0.446214	+	0.772866i	−0.998136	−	0.0610303i	$-0.980561\pi$
$701$	−312.796	+	541.779i	−0.446214	+	0.772866i	0.551922	+	0.833896i	$0.313895\pi$
$702$		0			0
$703$	502.152	+	8.08985i	0.714299	+	0.0115076i
$704$		0			0
$705$	26.6463	+	48.4492i	0.0377961	+	0.0687223i
$706$		0			0
$707$	614.757			0.869529
$708$		0			0
$709$	658.564	−	1140.67i	0.928863	−	1.60884i	0.143635	−	0.989631i	$-0.454121\pi$
$709$	658.564	−	1140.67i	0.928863	−	1.60884i	0.785228	−	0.619207i	$-0.212546\pi$
$710$		0			0
$711$	−545.325	−	345.805i	−0.766983	−	0.486364i
$712$		0			0
$713$	1466.42	+	846.640i	2.05669	+	1.18743i
$714$		0			0
$715$	1033.11	+	596.468i	1.44491	+	0.834221i
$716$		0			0
$717$	−473.153	−	9.82798i	−0.659907	−	0.0137071i
$718$		0			0
$719$	189.686	−	328.545i	0.263819	−	0.456947i	−0.703435	−	0.710760i	$-0.748351\pi$
$719$	189.686	−	328.545i	0.263819	−	0.456947i	0.967253	+	0.253812i	$0.0816846\pi$
$720$		0			0
$721$		−	591.936i		−	0.820993i
$722$		0			0
$723$	−22.4858	+	1082.54i	−0.0311007	+	1.49729i
$724$		0			0
$725$	3.79427	−	2.19062i	0.00523348	−	0.00302155i
$726$		0			0
$727$	−559.070			−0.769010			−0.384505	−	0.923123i	$-0.625628\pi$
$727$	−559.070			−0.769010			−0.384505	+	0.923123i	$0.625628\pi$
$728$		0			0
$729$	723.348	+	90.6055i	0.992246	+	0.124287i
$730$		0			0
$731$	−327.591	+	567.404i	−0.448141	+	0.776203i
$732$		0			0
$733$	−700.738	+	1213.71i	−0.955986	+	1.65582i	−0.223891	+	0.974614i	$0.571876\pi$
$733$	−700.738	+	1213.71i	−0.955986	+	1.65582i	−0.732095	+	0.681202i	$0.761457\pi$
$734$		0			0
$735$	−160.327	−	291.513i	−0.218133	−	0.396617i
$736$		0			0
$737$	1186.93	−	685.273i	1.61048	−	0.929814i
$738$		0			0
$739$	−149.513	+	258.964i	−0.202318	+	0.350425i	−0.949275	−	0.314448i	$-0.898181\pi$
$739$	−149.513	+	258.964i	−0.202318	+	0.350425i	0.746957	+	0.664872i	$0.231514\pi$
$740$		0			0
$741$	516.800	+	976.597i	0.697436	+	1.31795i
$742$		0			0
$743$	177.589	−	102.531i	0.239016	−	0.137996i	−0.375709	−	0.926738i	$-0.622601\pi$
$743$	177.589	−	102.531i	0.239016	−	0.137996i	0.614724	+	0.788742i	$0.289267\pi$
$744$		0			0
$745$	−151.008	+	261.554i	−0.202695	+	0.351079i
$746$		0			0
$747$	1149.01	+	47.7534i	1.53817	+	0.0639269i
$748$		0			0
$749$	91.3844	−	52.7608i	0.122009	−	0.0704417i
$750$		0			0
$751$		−	305.332i		−	0.406567i	−0.979120	−	0.203284i	$-0.934839\pi$
$751$		−	305.332i		−	0.406567i	0.979120	−	0.203284i	$-0.0651613\pi$
$752$		0			0
$753$	297.910	−	492.103i	0.395631	−	0.653523i
$754$		0			0
$755$	−461.407	−	266.393i	−0.611135	−	0.352839i
$756$		0			0
$757$	−178.879	+	309.827i	−0.236300	+	0.409283i	−0.959650	−	0.281199i	$-0.909268\pi$
$757$	−178.879	+	309.827i	−0.236300	+	0.409283i	0.723350	+	0.690482i	$0.242601\pi$
$758$		0			0
$759$	−899.090	+	1485.16i	−1.18457	+	1.95674i
$760$		0			0
$761$	−133.599	+	231.399i	−0.175557	+	0.304073i	−0.940354	−	0.340198i	$-0.889506\pi$
$761$	−133.599	+	231.399i	−0.175557	+	0.304073i	0.764797	+	0.644271i	$0.222839\pi$
$762$		0			0
$763$		−	174.388i		−	0.228556i
$764$		0			0
$765$	−568.467	+	896.457i	−0.743094	+	1.17184i
$766$		0			0
$767$	257.523	+	446.044i	0.335754	+	0.581543i
$768$		0			0
$769$	−791.594			−1.02938			−0.514691	−	0.857376i	$-0.672093\pi$
$769$	−791.594			−1.02938			−0.514691	+	0.857376i	$0.672093\pi$
$770$		0			0
$771$	762.268	−	419.235i	0.988674	−	0.543754i
$772$		0			0
$773$	−232.793	+	134.403i	−0.301155	+	0.173872i	−0.642962	−	0.765898i	$-0.722295\pi$
$773$	−232.793	+	134.403i	−0.301155	+	0.173872i	0.341807	+	0.939770i	$0.388961\pi$
$774$		0			0
$775$	−533.728	+	308.148i	−0.688681	+	0.397610i
$776$		0			0
$777$	287.532	+	174.066i	0.370053	+	0.224023i
$778$		0			0
$779$	−368.575	−	662.825i	−0.473139	−	0.850866i
$780$		0			0
$781$			35.6129i			0.0455991i
$782$		0			0
$783$	−8.05893	−	5.34822i	−0.0102924	−	0.00683042i
$784$		0			0
$785$	399.837	−	692.538i	0.509347	−	0.882214i
$786$		0			0
$787$	659.045	+	380.500i	0.837414	+	0.483481i	0.856384	−	0.516339i	$-0.172706\pi$
$787$	659.045	+	380.500i	0.837414	+	0.483481i	−0.0189706	+	0.999820i	$0.506039\pi$
$788$		0			0
$789$	85.2543	+	155.013i	0.108054	+	0.196467i
$790$		0			0
$791$			321.355i			0.406264i
$792$		0			0
$793$	−756.961	−	437.031i	−0.954553	−	0.551112i
$794$		0			0
$795$	5.23044	−	251.811i	0.00657916	−	0.316744i
$796$		0			0
$797$	69.0764	+	39.8813i	0.0866705	+	0.0500392i	0.542709	−	0.839921i	$-0.317399\pi$
$797$	69.0764	+	39.8813i	0.0866705	+	0.0500392i	−0.456038	+	0.889960i	$0.650732\pi$
$798$		0			0
$799$	−85.1182	−	147.429i	−0.106531	−	0.184517i
$800$		0			0
$801$	15.3873	−	370.238i	0.0192101	−	0.462220i
$802$		0			0
$803$	−623.355			−0.776283
$804$		0			0
$805$	−254.488	+	440.786i	−0.316134	+	0.547561i
$806$		0			0
$807$	4.18470	−	201.466i	0.00518550	−	0.249648i
$808$		0			0
$809$	783.760			0.968800			0.484400	−	0.874847i	$-0.339038\pi$
$809$	783.760			0.968800			0.484400	+	0.874847i	$0.339038\pi$
$810$		0			0
$811$	−1171.15	+	676.163i	−1.44408	+	0.833740i	−0.998119	−	0.0613126i	$-0.980471\pi$
$811$	−1171.15	+	676.163i	−1.44408	+	0.833740i	−0.445961	+	0.895052i	$0.647138\pi$
$812$		0			0
$813$	−120.649	−	2.50604i	−0.148400	−	0.00308246i
$814$		0			0
$815$	−501.987	−	869.466i	−0.615934	−	1.06683i
$816$		0			0
$817$	−6.07539	+	377.111i	−0.00743622	+	0.461580i
$818$		0			0
$819$	−30.7064	+	738.837i	−0.0374925	+	0.902121i
$820$		0			0
$821$	−355.115	+	615.078i	−0.432540	+	0.749181i	−0.997091	−	0.0762166i	$-0.975716\pi$
$821$	−355.115	+	615.078i	−0.432540	+	0.749181i	0.564551	+	0.825398i	$0.309049\pi$
$822$		0			0
$823$	−649.981			−0.789770			−0.394885	−	0.918731i	$-0.629216\pi$
$823$	−649.981			−0.789770			−0.394885	+	0.918731i	$0.629216\pi$
$824$		0			0
$825$	−304.510	−	553.671i	−0.369103	−	0.671116i
$826$		0			0
$827$	414.480	−	239.300i	0.501185	−	0.289359i	−0.228018	−	0.973657i	$-0.573224\pi$
$827$	414.480	−	239.300i	0.501185	−	0.289359i	0.729203	+	0.684298i	$0.239891\pi$
$828$		0			0
$829$			446.712i			0.538857i	0.963020	+	0.269429i	$0.0868348\pi$
$829$			446.712i			0.538857i	−0.963020	+	0.269429i	$0.913165\pi$
$830$		0			0
$831$	193.632	−	319.851i	0.233011	−	0.384899i
$832$		0			0
$833$	512.146	+	887.063i	0.614821	+	1.06490i
$834$		0			0
$835$	−281.611	+	162.588i	−0.337258	+	0.194716i
$836$		0			0
$837$	1133.62	+	752.317i	1.35439	+	0.898826i
$838$		0			0
$839$			718.499i			0.856375i	0.903690	+	0.428187i	$0.140848\pi$
$839$			718.499i			0.856375i	−0.903690	+	0.428187i	$0.859152\pi$
$840$		0			0
$841$	−420.436	−	728.216i	−0.499924	−	0.865893i
$842$		0			0
$843$	31.2914	−	1506.48i	0.0371191	−	1.78704i
$844$		0			0
$845$	369.414	+	639.843i	0.437176	+	0.757211i
$846$		0			0
$847$	−744.256			−0.878696
$848$		0			0
$849$	−389.937	+	644.117i	−0.459289	+	0.758678i
$850$		0			0
$851$			888.214i			1.04373i
$852$		0			0
$853$	−16.9836			−0.0199104			−0.00995519	−	0.999950i	$-0.503169\pi$
$853$	−16.9836			−0.0199104			−0.00995519	+	0.999950i	$0.503169\pi$
$854$		0			0
$855$	−35.2055	+	610.047i	−0.0411760	+	0.713505i
$856$		0			0
$857$			658.355i			0.768209i	0.923290	+	0.384105i	$0.125490\pi$
$857$			658.355i			0.768209i	−0.923290	+	0.384105i	$0.874510\pi$
$858$		0			0
$859$	795.978			0.926633			0.463317	−	0.886193i	$-0.346659\pi$
$859$	795.978			0.926633			0.463317	+	0.886193i	$0.346659\pi$
$860$		0			0
$861$	10.5407	−	507.466i	0.0122424	−	0.589391i
$862$		0			0
$863$			540.003i			0.625727i	0.949798	+	0.312864i	$0.101288\pi$
$863$			540.003i			0.625727i	−0.949798	+	0.312864i	$0.898712\pi$
$864$		0			0
$865$	−561.943	+	324.438i	−0.649645	+	0.375073i
$866$		0			0
$867$	1243.50	−	2054.07i	1.43425	−	2.36917i
$868$		0			0
$869$	1070.07	−	617.804i	1.23138	−	0.710937i
$870$		0			0
$871$	1542.66			1.77113
$872$		0			0
$873$	−384.864	−	244.052i	−0.440852	−	0.279556i
$874$		0			0
$875$	−281.959	−	488.367i	−0.322239	−	0.558133i
$876$		0			0
$877$	986.530	−	569.573i	1.12489	−	0.649457i	0.182246	−	0.983253i	$-0.441663\pi$
$877$	986.530	−	569.573i	1.12489	−	0.649457i	0.942645	+	0.333796i	$0.108330\pi$
$878$		0			0
$879$	−2.12688	+	102.396i	−0.00241966	+	0.116491i
$880$		0			0
$881$	168.246			0.190972			0.0954861	−	0.995431i	$-0.469559\pi$
$881$	168.246			0.190972			0.0954861	+	0.995431i	$0.469559\pi$
$882$		0			0
$883$	−301.318	−	521.897i	−0.341243	−	0.591050i	0.643421	−	0.765513i	$-0.277515\pi$
$883$	−301.318	−	521.897i	−0.341243	−	0.591050i	−0.984664	+	0.174463i	$0.944181\pi$
$884$		0			0
$885$	−5.91526	+	284.781i	−0.00668391	+	0.321787i
$886$		0			0
$887$			1187.26i			1.33851i	0.743033	+	0.669255i	$0.233387\pi$
$887$			1187.26i			1.33851i	−0.743033	+	0.669255i	$0.766613\pi$
$888$		0			0
$889$	−28.3177	−	16.3492i	−0.0318534	−	0.0183906i
$890$		0			0
$891$	−795.317	+	1146.03i	−0.892611	+	1.28623i
$892$		0			0
$893$	−84.0682	−	50.3596i	−0.0941413	−	0.0563937i
$894$		0			0
$895$	883.620	−	510.158i	0.987285	−	0.570009i
$896$		0			0
$897$	−1712.25	+	941.708i	−1.90886	+	1.04984i
$898$		0			0
$899$	−9.02562	−	15.6328i	−0.0100396	−	0.0173891i
$900$		0			0
$901$			775.441i			0.860644i
$902$		0			0
$903$	−130.722	+	215.933i	−0.144764	+	0.239129i
$904$		0			0
$905$	159.029	+	91.8155i	0.175723	+	0.101454i
$906$		0			0
$907$			1006.71i			1.10993i	0.831873	+	0.554966i	$0.187269\pi$
$907$			1006.71i			1.10993i	−0.831873	+	0.554966i	$0.812731\pi$
$908$		0			0
$909$	605.156	+	1156.57i	0.665738	+	1.27235i
$910$		0			0
$911$	1111.24	−	641.574i	1.21980	−	0.704253i	0.254926	−	0.966961i	$-0.417949\pi$
$911$	1111.24	−	641.574i	1.21980	−	0.704253i	0.964875	+	0.262708i	$0.0846156\pi$
$912$		0			0
$913$	−1100.28	+	1905.74i	−1.20513	+	2.08734i
$914$		0			0
$915$	−232.951	−	423.560i	−0.254591	−	0.462908i
$916$		0			0
$917$	−221.769	+	384.114i	−0.241841	+	0.418882i
$918$		0			0
$919$	676.693			0.736336			0.368168	−	0.929759i	$-0.379985\pi$
$919$	676.693			0.736336			0.368168	+	0.929759i	$0.379985\pi$
$920$		0			0
$921$	12.5462	−	604.020i	0.0136224	−	0.655830i
$922$		0			0
$923$	−20.0425	+	34.7147i	−0.0217145	+	0.0376107i
$924$		0			0
$925$	−279.968	−	161.640i	−0.302668	−	0.174746i
$926$		0			0
$927$	1113.63	−	582.691i	1.20133	−	0.628577i
$928$		0			0
$929$	1699.03			1.82888			0.914440	−	0.404722i	$-0.132632\pi$
$929$	1699.03			1.82888			0.914440	+	0.404722i	$0.132632\pi$
$930$		0			0
$931$	505.829	+	303.008i	0.543317	+	0.325465i
$932$		0			0
$933$	92.6213	+	1.92386i	0.0992726	+	0.00206202i
$934$		0			0
$935$	−1015.61	−	1759.08i	−1.08621	−	1.88137i
$936$		0			0
$937$	−440.942	−	763.734i	−0.470589	−	0.815084i	0.528845	−	0.848718i	$-0.322625\pi$
$937$	−440.942	−	763.734i	−0.470589	−	0.815084i	−0.999434	+	0.0336344i	$0.989292\pi$
$938$		0			0
$939$	191.355	+	3.97468i	0.203786	+	0.00423288i
$940$		0			0
$941$		−	1098.42i		−	1.16729i	−0.812010	−	0.583644i	$-0.801626\pi$
$941$		−	1098.42i		−	1.16729i	0.812010	−	0.583644i	$-0.198374\pi$
$942$		0			0
$943$	1161.61	−	670.655i	1.23182	−	0.711193i
$944$		0			0
$945$	−226.136	+	340.751i	−0.239297	+	0.360584i
$946$		0			0
$947$	−337.114			−0.355981			−0.177990	−	0.984032i	$-0.556960\pi$
$947$	−337.114			−0.355981			−0.177990	+	0.984032i	$0.556960\pi$
$948$		0			0
$949$	−607.633	−	350.817i	−0.640288	−	0.369670i
$950$		0			0
$951$	−19.6587	+	946.437i	−0.0206716	+	0.995202i
$952$		0			0
$953$	−178.565	−	103.095i	−0.187372	−	0.108179i	0.403380	−	0.915033i	$-0.367835\pi$
$953$	−178.565	−	103.095i	−0.187372	−	0.108179i	−0.590752	+	0.806854i	$0.701169\pi$
$954$		0			0
$955$	664.737	−	1151.36i	0.696060	−	1.20561i
$956$		0			0
$957$	16.2170	−	8.91906i	0.0169456	−	0.00931981i
$958$		0			0
$959$	−958.330			−0.999301
$960$		0			0
$961$	789.105	+	1366.77i	0.821129	+	1.42224i
$962$		0			0
$963$	189.218	+	119.988i	0.196488	+	0.124598i
$964$		0			0
$965$	−257.494	−	148.664i	−0.266834	−	0.154056i
$966$		0			0
$967$	−395.091	−	684.318i	−0.408574	−	0.707671i	0.586156	−	0.810198i	$-0.300641\pi$
$967$	−395.091	−	684.318i	−0.408574	−	0.707671i	−0.994730	+	0.102527i	$0.967307\pi$
$968$		0			0
$969$	69.3625	−	1880.05i	0.0715815	−	1.94020i
$970$		0			0
$971$	−696.373	−	402.051i	−0.717171	−	0.414059i	0.0965395	−	0.995329i	$-0.469223\pi$
$971$	−696.373	−	402.051i	−0.717171	−	0.414059i	−0.813711	+	0.581270i	$0.802556\pi$
$972$		0			0
$973$	−230.429	−	399.116i	−0.236824	−	0.410191i
$974$		0			0
$975$	14.7700	−	711.081i	0.0151488	−	0.729314i
$976$		0			0
$977$	1248.86	+	721.028i	1.27826	+	0.738002i	0.976528	−	0.215391i	$-0.0691027\pi$
$977$	1248.86	+	721.028i	1.27826	+	0.738002i	0.301730	+	0.953394i	$0.402436\pi$
$978$		0			0
$979$	614.074	+	354.536i	0.627246	+	0.362141i
$980$		0			0
$981$	328.083	−	171.664i	0.334437	−	0.174989i
$982$		0			0
$983$		−	1749.25i		−	1.77950i	−0.456445	−	0.889751i	$-0.650878\pi$
$983$		−	1749.25i		−	1.77950i	0.456445	−	0.889751i	$-0.349122\pi$
$984$		0			0
$985$	377.996	+	654.708i	0.383752	+	0.664679i
$986$		0			0
$987$	−31.6065	−	57.4681i	−0.0320228	−	0.0582250i
$988$		0			0
$989$	−667.039			−0.674458
$990$		0			0
$991$	306.985	+	177.238i	0.309773	+	0.178847i	0.646825	−	0.762639i	$-0.276096\pi$
$991$	306.985	+	177.238i	0.309773	+	0.178847i	−0.337052	+	0.941486i	$0.609430\pi$
$992$		0			0
$993$	−199.161	−	120.569i	−0.200565	−	0.121419i
$994$		0			0
$995$	492.418	−	852.894i	0.494893	−	0.857180i
$996$		0			0
$997$	−640.147	+	1108.77i	−0.642073	+	1.11210i	0.342896	+	0.939373i	$0.388592\pi$
$997$	−640.147	+	1108.77i	−0.642073	+	1.11210i	−0.984969	+	0.172730i	$0.944741\pi$
$998$		0			0
$999$	−44.4367	+	712.292i	−0.0444812	+	0.713005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.26	✓	80
3.2	odd	2		2052.3.s.a.901.26		80
9.2	odd	6		2052.3.bl.a.1585.15		80
9.7	even	3		684.3.bl.a.673.40	yes	80
19.12	odd	6		684.3.bl.a.373.40	yes	80
57.50	even	6		2052.3.bl.a.145.15		80
171.88	odd	6	inner	684.3.s.a.601.26	yes	80
171.164	even	6		2052.3.s.a.829.26		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.26	✓	80	1.1	even	1	trivial
684.3.s.a.601.26	yes	80	171.88	odd	6	inner
684.3.bl.a.373.40	yes	80	19.12	odd	6
684.3.bl.a.673.40	yes	80	9.7	even	3
2052.3.s.a.829.26		80	171.164	even	6
2052.3.s.a.901.26		80	3.2	odd	2
2052.3.bl.a.145.15		80	57.50	even	6
2052.3.bl.a.1585.15		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)

\(f(q)\)	\(=\)	\(q+(1.44572 + 2.62867i) q^{3} +(-1.78673 - 3.09471i) q^{5} +(2.11933 + 3.67079i) q^{7} +(-4.81977 + 7.60065i) q^{9} +O(q^{10})\)	\(q+(1.44572 + 2.62867i) q^{3} +(-1.78673 - 3.09471i) q^{5} +(2.11933 + 3.67079i) q^{7} +(-4.81977 + 7.60065i) q^{9} +(-8.61085 - 14.9144i) q^{11} -19.3844i q^{13} +(5.55184 - 9.17081i) q^{15} +(-16.5029 + 28.5838i) q^{17} +(-0.306057 + 18.9975i) q^{19} +(-6.58532 + 10.8780i) q^{21} -33.6031 q^{23} +(6.11519 - 10.5918i) q^{25} +(-26.9476 - 1.68114i) q^{27} +(0.310233 + 0.179113i) q^{29} +(-43.6395 - 25.1953i) q^{31} +(26.7562 - 44.1972i) q^{33} +(7.57335 - 13.1174i) q^{35} -26.4325i q^{37} +(50.9550 - 28.0244i) q^{39} +(-34.5685 + 19.9581i) q^{41} +19.8505 q^{43} +(32.1334 + 1.33548i) q^{45} +(-2.57889 + 4.46676i) q^{47} +(15.5169 - 26.8760i) q^{49} +(-98.9960 - 2.05627i) q^{51} +(20.3465 - 11.7470i) q^{53} +(-30.7706 + 53.2962i) q^{55} +(-50.3806 + 26.6606i) q^{57} +(-23.0105 + 13.2851i) q^{59} +(22.5456 - 39.0500i) q^{61} +(-38.1151 - 1.58408i) q^{63} +(-59.9890 + 34.6347i) q^{65} +79.5824i q^{67} +(-48.5808 - 88.3314i) q^{69} +(-1.79086 - 1.03395i) q^{71} +(18.0979 - 31.3466i) q^{73} +(36.6832 + 0.761956i) q^{75} +(36.4985 - 63.2173i) q^{77} +71.7472i q^{79} +(-34.5396 - 73.2667i) q^{81} +(-63.8891 - 110.659i) q^{83} +117.945 q^{85} +(-0.0223176 + 1.07445i) q^{87} +(-35.6570 + 20.5866i) q^{89} +(71.1560 - 41.0819i) q^{91} +(3.13935 - 151.139i) q^{93} +(59.3387 - 32.9963i) q^{95} +50.6357i q^{97} +(154.862 + 6.43612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 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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