LMFDB - Embedded newform 324.3.o.a.5.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(5,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("324.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.o (of order $54$, degree $18$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$18$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	324.5
Dual form			324.3.o.a.65.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.897733 + 2.86253i) q^{3} +(-1.94378 + 1.44709i) q^{5} +(9.49800 - 6.24693i) q^{7} +(-7.38815 + 5.13957i) q^{9} +O(q^{10})$	\(q+(0.897733 + 2.86253i) q^{3} +(-1.94378 + 1.44709i) q^{5} +(9.49800 - 6.24693i) q^{7} +(-7.38815 + 5.13957i) q^{9} +(-2.00071 + 17.1171i) q^{11} +(2.68685 + 8.97472i) q^{13} +(-5.88732 - 4.26502i) q^{15} +(25.0778 + 4.42190i) q^{17} +(-5.00224 - 28.3691i) q^{19} +(26.4087 + 21.5802i) q^{21} +(-15.6168 + 23.7441i) q^{23} +(-5.48588 + 18.3241i) q^{25} +(-21.3448 - 16.5348i) q^{27} +(-16.6029 + 15.6641i) q^{29} +(-1.00203 + 17.2041i) q^{31} +(-50.7944 + 9.63953i) q^{33} +(-9.42213 + 25.8871i) q^{35} +(-40.0015 + 14.5594i) q^{37} +(-23.2783 + 15.7481i) q^{39} +(13.8323 - 58.3631i) q^{41} +(20.8820 + 48.4098i) q^{43} +(6.92350 - 20.6815i) q^{45} +(60.7845 - 3.54029i) q^{47} +(31.7799 - 73.6741i) q^{49} +(9.85538 + 75.7557i) q^{51} +(19.8891 + 11.4830i) q^{53} +(-20.8811 - 36.1671i) q^{55} +(76.7167 - 39.7869i) q^{57} +(0.566813 + 4.84939i) q^{59} +(-36.6054 - 18.3839i) q^{61} +(-38.0661 + 94.9689i) q^{63} +(-18.2098 - 13.5567i) q^{65} +(49.3145 - 52.2704i) q^{67} +(-81.9880 - 23.3876i) q^{69} +(10.8606 - 12.9431i) q^{71} +(106.603 - 89.4502i) q^{73} +(-57.3781 + 0.746666i) q^{75} +(87.9269 + 175.077i) q^{77} +(-41.3713 + 9.80519i) q^{79} +(28.1696 - 75.9439i) q^{81} +(19.1145 + 80.6503i) q^{83} +(-55.1446 + 27.6946i) q^{85} +(-59.7439 - 33.4643i) q^{87} +(-80.2312 - 95.6158i) q^{89} +(81.5842 + 68.4572i) q^{91} +(-50.1469 + 12.5764i) q^{93} +(50.7758 + 47.9045i) q^{95} +(71.9647 - 96.6654i) q^{97} +(-73.1933 - 136.747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q+O(q^{10}) $ 324 * q	$ 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) $ 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{23}{54}\right)$

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
$3$	0.897733	+	2.86253i	0.299244	+	0.954177i
$3$	0.897733	+	2.86253i	0.299244	+	0.954177i
$4$		0			0
$5$	−1.94378	+	1.44709i	−0.388755	+	0.289418i	−0.773737	−	0.633506i	$-0.781615\pi$
$5$	−1.94378	+	1.44709i	−0.388755	+	0.289418i	0.384982	+	0.922924i	$0.374208\pi$
$6$		0			0
$7$	9.49800	−	6.24693i	1.35686	−	0.892419i	0.357715	−	0.933831i	$-0.383556\pi$
$7$	9.49800	−	6.24693i	1.35686	−	0.892419i	0.999142	+	0.0414120i	$0.0131856\pi$
$8$		0			0
$9$	−7.38815	+	5.13957i	−0.820906	+	0.571064i
$10$		0			0
$11$	−2.00071	+	17.1171i	−0.181882	+	1.55610i	0.526439	+	0.850213i	$0.323527\pi$
$11$	−2.00071	+	17.1171i	−0.181882	+	1.55610i	−0.708321	+	0.705890i	$0.750547\pi$
$12$		0			0
$13$	2.68685	+	8.97472i	0.206681	+	0.690363i	0.996981	+	0.0776429i	$0.0247394\pi$
$13$	2.68685	+	8.97472i	0.206681	+	0.690363i	−0.790300	+	0.612720i	$0.790075\pi$
$14$		0			0
$15$	−5.88732	−	4.26502i	−0.392488	−	0.284335i
$16$		0			0
$17$	25.0778	+	4.42190i	1.47517	+	0.260112i	0.852645	−	0.522491i	$-0.174997\pi$
$17$	25.0778	+	4.42190i	1.47517	+	0.260112i	0.622522	+	0.782603i	$0.286108\pi$
$18$		0			0
$19$	−5.00224	−	28.3691i	−0.263276	−	1.49311i	−0.773900	−	0.633307i	$-0.781697\pi$
$19$	−5.00224	−	28.3691i	−0.263276	−	1.49311i	0.510625	−	0.859804i	$-0.329414\pi$
$20$		0			0
$21$	26.4087	+	21.5802i	1.25756	+	1.02763i
$22$		0			0
$23$	−15.6168	+	23.7441i	−0.678990	+	1.03235i	0.317468	+	0.948269i	$0.397167\pi$
$23$	−15.6168	+	23.7441i	−0.678990	+	1.03235i	−0.996459	+	0.0840855i	$0.973203\pi$
$24$		0			0
$25$	−5.48588	+	18.3241i	−0.219435	+	0.732964i
$26$		0			0
$27$	−21.3448	−	16.5348i	−0.790547	−	0.612401i
$28$		0			0
$29$	−16.6029	+	15.6641i	−0.572515	+	0.540140i	−0.917122	−	0.398607i	$-0.869494\pi$
$29$	−16.6029	+	15.6641i	−0.572515	+	0.540140i	0.344607	+	0.938747i	$0.388012\pi$
$30$		0			0
$31$	−1.00203	+	17.2041i	−0.0323235	+	0.554972i	0.942807	+	0.333340i	$0.108176\pi$
$31$	−1.00203	+	17.2041i	−0.0323235	+	0.554972i	−0.975130	+	0.221633i	$0.928861\pi$
$32$		0			0
$33$	−50.7944	+	9.63953i	−1.53922	+	0.292107i
$34$		0			0
$35$	−9.42213	+	25.8871i	−0.269204	+	0.739631i
$36$		0			0
$37$	−40.0015	+	14.5594i	−1.08112	+	0.393496i	−0.820325	−	0.571898i	$-0.806207\pi$
$37$	−40.0015	+	14.5594i	−1.08112	+	0.393496i	−0.260797	+	0.965394i	$0.583985\pi$
$38$		0			0
$39$	−23.2783	+	15.7481i	−0.596880	+	0.403797i
$40$		0			0
$41$	13.8323	−	58.3631i	0.337373	−	1.42349i	−0.494816	−	0.868998i	$-0.664764\pi$
$41$	13.8323	−	58.3631i	0.337373	−	1.42349i	0.832189	−	0.554492i	$-0.187087\pi$
$42$		0			0
$43$	20.8820	+	48.4098i	0.485627	+	1.12581i	0.968250	+	0.249982i	$0.0804247\pi$
$43$	20.8820	+	48.4098i	0.485627	+	1.12581i	−0.482623	+	0.875828i	$0.660316\pi$
$44$		0			0
$45$	6.92350	−	20.6815i	0.153856	−	0.459589i
$46$		0			0
$47$	60.7845	−	3.54029i	1.29329	−	0.0753254i	0.602345	−	0.798236i	$-0.294233\pi$
$47$	60.7845	−	3.54029i	1.29329	−	0.0753254i	0.690942	+	0.722910i	$0.257196\pi$
$48$		0			0
$49$	31.7799	−	73.6741i	0.648570	−	1.50355i
$50$		0			0
$51$	9.85538	+	75.7557i	0.193243	+	1.48541i
$52$		0			0
$53$	19.8891	+	11.4830i	0.375266	+	0.216660i	0.675757	−	0.737125i	$-0.263817\pi$
$53$	19.8891	+	11.4830i	0.375266	+	0.216660i	−0.300491	+	0.953785i	$0.597150\pi$
$54$		0			0
$55$	−20.8811	−	36.1671i	−0.379656	−	0.657583i
$56$		0			0
$57$	76.7167	−	39.7869i	1.34591	−	0.698017i
$58$		0			0
$59$	0.566813	+	4.84939i	0.00960700	+	0.0821931i	0.997191	−	0.0748969i	$-0.0238628\pi$
$59$	0.566813	+	4.84939i	0.00960700	+	0.0821931i	−0.987584	+	0.157090i	$0.949789\pi$
$60$		0			0
$61$	−36.6054	−	18.3839i	−0.600088	−	0.301376i	0.122702	−	0.992444i	$-0.460844\pi$
$61$	−36.6054	−	18.3839i	−0.600088	−	0.301376i	−0.722790	+	0.691068i	$0.757141\pi$
$62$		0			0
$63$	−38.0661	+	94.9689i	−0.604224	+	1.50744i
$64$		0			0
$65$	−18.2098	−	13.5567i	−0.280151	−	0.208565i
$66$		0			0
$67$	49.3145	−	52.2704i	0.736038	−	0.780155i	−0.245913	−	0.969292i	$-0.579088\pi$
$67$	49.3145	−	52.2704i	0.736038	−	0.780155i	0.981951	+	0.189137i	$0.0605691\pi$
$68$		0			0
$69$	−81.9880	−	23.3876i	−1.18823	−	0.338950i
$70$		0			0
$71$	10.8606	−	12.9431i	0.152966	−	0.182297i	−0.684120	−	0.729370i	$-0.739813\pi$
$71$	10.8606	−	12.9431i	0.152966	−	0.182297i	0.837085	+	0.547072i	$0.184258\pi$
$72$		0			0
$73$	106.603	−	89.4502i	1.46031	−	1.22535i	0.535712	−	0.844401i	$-0.320043\pi$
$73$	106.603	−	89.4502i	1.46031	−	1.22535i	0.924598	−	0.380944i	$-0.124401\pi$
$74$		0			0
$75$	−57.3781	+	0.746666i	−0.765042	+	0.00995555i
$76$		0			0
$77$	87.9269	+	175.077i	1.14191	+	2.27372i
$78$		0			0
$79$	−41.3713	+	9.80519i	−0.523688	+	0.124116i	−0.483953	−	0.875094i	$-0.660799\pi$
$79$	−41.3713	+	9.80519i	−0.523688	+	0.124116i	−0.0397347	+	0.999210i	$0.512651\pi$
$80$		0			0
$81$	28.1696	−	75.9439i	0.347772	−	0.937579i
$82$		0			0
$83$	19.1145	+	80.6503i	0.230295	+	0.971690i	0.958220	+	0.286033i	$0.0923367\pi$
$83$	19.1145	+	80.6503i	0.230295	+	0.971690i	−0.727925	+	0.685657i	$0.759515\pi$
$84$		0			0
$85$	−55.1446	+	27.6946i	−0.648760	+	0.325819i
$86$		0			0
$87$	−59.7439	−	33.4643i	−0.686711	−	0.384647i
$88$		0			0
$89$	−80.2312	−	95.6158i	−0.901474	−	1.07433i	−0.996883	−	0.0788963i	$-0.974860\pi$
$89$	−80.2312	−	95.6158i	−0.901474	−	1.07433i	0.0954092	−	0.995438i	$-0.469584\pi$
$90$		0			0
$91$	81.5842	+	68.4572i	0.896529	+	0.752277i
$92$		0			0
$93$	−50.1469	+	12.5764i	−0.539214	+	0.135230i
$94$		0			0
$95$	50.7758	+	47.9045i	0.534483	+	0.504258i
$96$		0			0
$97$	71.9647	−	96.6654i	0.741904	−	0.996550i	−0.257636	−	0.966242i	$-0.582944\pi$
$97$	71.9647	−	96.6654i	0.741904	−	0.996550i	0.999541	−	0.0303084i	$-0.00964895\pi$
$98$		0			0
$99$	−73.1933	−	136.747i	−0.739326	−	1.38128i
$100$		0			0
$101$	−7.90639	+	15.7429i	−0.0782811	+	0.155870i	−0.929368	−	0.369154i	$-0.879648\pi$
$101$	−7.90639	+	15.7429i	−0.0782811	+	0.155870i	0.851087	+	0.525024i	$0.175944\pi$
$102$		0			0
$103$	111.355	−	13.0155i	1.08112	−	0.126364i	0.443164	−	0.896440i	$-0.353856\pi$
$103$	111.355	−	13.0155i	1.08112	−	0.126364i	0.637952	+	0.770076i	$0.279782\pi$
$104$		0			0
$105$	−82.5611	−	3.73143i	−0.786296	−	0.0355375i
$106$		0			0
$107$	−6.66597	+	3.84860i	−0.0622987	+	0.0359682i	−0.530826	−	0.847481i	$-0.678118\pi$
$107$	−6.66597	+	3.84860i	−0.0622987	+	0.0359682i	0.468527	+	0.883449i	$0.344785\pi$
$108$		0			0
$109$	98.6717	−	170.904i	0.905245	−	1.56793i	0.0846573	−	0.996410i	$-0.473020\pi$
$109$	98.6717	−	170.904i	0.905245	−	1.56793i	0.820588	−	0.571520i	$-0.193646\pi$
$110$		0			0
$111$	−77.5873	−	101.435i	−0.698984	−	0.913830i
$112$		0			0
$113$	141.662	+	61.1071i	1.25365	+	0.540771i	0.916256	−	0.400594i	$-0.131196\pi$
$113$	141.662	+	61.1071i	1.25365	+	0.540771i	0.337392	+	0.941364i	$0.390455\pi$
$114$		0			0
$115$	−4.00436	−	68.7522i	−0.0348205	−	0.597845i
$116$		0			0
$117$	−65.9771	−	52.4973i	−0.563907	−	0.448695i
$118$		0			0
$119$	265.812	−	114.660i	2.23372	−	0.963532i
$120$		0			0
$121$	−171.255	−	40.5882i	−1.41533	−	0.335439i
$122$		0			0
$123$	179.484	−	12.7991i	1.45922	−	0.104058i
$124$		0			0
$125$	−36.5736	−	100.485i	−0.292589	−	0.803882i
$126$		0			0
$127$	−111.468	−	40.5711i	−0.877702	−	0.319458i	−0.136420	−	0.990651i	$-0.543560\pi$
$127$	−111.468	−	40.5711i	−0.877702	−	0.319458i	−0.741282	+	0.671194i	$0.765782\pi$
$128$		0			0
$129$	−119.828	+	103.234i	−0.928900	+	0.800266i
$130$		0			0
$131$	−105.246	−	6.12988i	−0.803404	−	0.0467930i	−0.348472	−	0.937319i	$-0.613299\pi$
$131$	−105.246	−	6.12988i	−0.803404	−	0.0467930i	−0.454932	+	0.890526i	$0.650336\pi$
$132$		0			0
$133$	−224.731	−	238.201i	−1.68971	−	1.79099i
$134$		0			0
$135$	65.4168	+	1.25227i	0.484569	+	0.00927608i
$136$		0			0
$137$	−97.8994	−	29.3092i	−0.714594	−	0.213935i	−0.0911881	−	0.995834i	$-0.529066\pi$
$137$	−97.8994	−	29.3092i	−0.714594	−	0.213935i	−0.623406	+	0.781898i	$0.714252\pi$
$138$		0			0
$139$	111.430	+	73.2885i	0.801653	+	0.527255i	0.882968	−	0.469433i	$-0.155542\pi$
$139$	111.430	+	73.2885i	0.801653	+	0.527255i	−0.0813154	+	0.996688i	$0.525912\pi$
$140$		0			0
$141$	64.7025	+	170.819i	0.458883	+	1.21148i
$142$		0			0
$143$	−158.997	+	28.0355i	−1.11187	+	0.196052i
$144$		0			0
$145$	9.60512	−	54.4734i	0.0662422	−	0.375678i
$146$		0			0
$147$	239.424	+	24.8313i	1.62874	+	0.168920i
$148$		0			0
$149$	−41.8444	+	12.5274i	−0.280835	+	0.0840765i	−0.424123	−	0.905605i	$-0.639418\pi$
$149$	−41.8444	+	12.5274i	−0.280835	+	0.0840765i	0.143288	+	0.989681i	$0.454232\pi$
$150$		0			0
$151$	−76.1921	−	8.90557i	−0.504583	−	0.0589773i	−0.140006	−	0.990151i	$-0.544712\pi$
$151$	−76.1921	−	8.90557i	−0.504583	−	0.0589773i	−0.364577	+	0.931173i	$0.618786\pi$
$152$		0			0
$153$	−208.005	+	96.2197i	−1.35951	+	0.628887i
$154$		0			0
$155$	−22.9482	−	34.8910i	−0.148053	−	0.225103i
$156$		0			0
$157$	153.921	+	206.751i	0.980386	+	1.31689i	0.948291	+	0.317402i	$0.102811\pi$
$157$	153.921	+	206.751i	0.980386	+	1.31689i	0.0320951	+	0.999485i	$0.489782\pi$
$158$		0			0
$159$	−15.0153	+	67.2418i	−0.0944356	+	0.422904i
$160$		0			0
$161$			323.079i			2.00670i
$162$		0			0
$163$	−24.1259			−0.148011			−0.0740057	−	0.997258i	$-0.523578\pi$
$163$	−24.1259			−0.148011			−0.0740057	+	0.997258i	$0.523578\pi$
$164$		0			0
$165$	84.7837	−	92.2411i	0.513841	−	0.559037i
$166$		0			0
$167$	−122.999	+	91.5696i	−0.736523	+	0.548321i	−0.898765	−	0.438430i	$-0.855535\pi$
$167$	−122.999	+	91.5696i	−0.736523	+	0.548321i	0.162242	+	0.986751i	$0.448127\pi$
$168$		0			0
$169$	67.8711	−	44.6395i	0.401604	−	0.264139i
$170$		0			0
$171$	182.762	+	183.886i	1.06879	+	1.07536i
$172$		0			0
$173$	33.6971	−	288.297i	0.194781	−	1.66646i	−0.443214	−	0.896416i	$-0.646162\pi$
$173$	33.6971	−	288.297i	0.194781	−	1.66646i	0.637995	−	0.770040i	$-0.279764\pi$
$174$		0			0
$175$	62.3646	+	208.312i	0.356369	+	1.19036i
$176$		0			0
$177$	−13.3727	+	5.97598i	−0.0755519	+	0.0337626i
$178$		0			0
$179$	−62.9620	−	11.1019i	−0.351743	−	0.0620218i	−0.00501485	−	0.999987i	$-0.501596\pi$
$179$	−62.9620	−	11.1019i	−0.351743	−	0.0620218i	−0.346728	+	0.937966i	$0.612707\pi$
$180$		0			0
$181$	−21.4979	−	121.921i	−0.118773	−	0.673595i	−0.984813	−	0.173620i	$-0.944454\pi$
$181$	−21.4979	−	121.921i	−0.118773	−	0.673595i	0.866040	−	0.499975i	$-0.166658\pi$
$182$		0			0
$183$	19.7626	−	121.288i	0.107993	−	0.662775i
$184$		0			0
$185$	56.6853	−	86.1858i	0.306407	−	0.465869i
$186$		0			0
$187$	−125.864	+	420.414i	−0.673067	+	2.24820i
$188$		0			0
$189$	−306.025	−	23.7085i	−1.61918	−	0.125442i
$190$		0			0
$191$	137.208	−	129.449i	0.718365	−	0.677743i	−0.237553	−	0.971375i	$-0.576345\pi$
$191$	137.208	−	129.449i	0.718365	−	0.677743i	0.955919	+	0.293632i	$0.0948640\pi$
$192$		0			0
$193$	3.28408	−	56.3855i	0.0170160	−	0.292153i	−0.979055	−	0.203595i	$-0.934737\pi$
$193$	3.28408	−	56.3855i	0.0170160	−	0.292153i	0.996071	−	0.0885574i	$-0.0282257\pi$
$194$		0			0
$195$	22.4590	−	64.2965i	0.115174	−	0.329726i
$196$		0			0
$197$	20.2973	−	55.7663i	0.103032	−	0.283078i	−0.877456	−	0.479657i	$-0.840761\pi$
$197$	20.2973	−	55.7663i	0.103032	−	0.283078i	0.980488	+	0.196579i	$0.0629833\pi$
$198$		0			0
$199$	151.646	−	55.1945i	0.762038	−	0.277359i	0.0683760	−	0.997660i	$-0.478218\pi$
$199$	151.646	−	55.1945i	0.762038	−	0.277359i	0.693662	+	0.720300i	$0.255996\pi$
$200$		0			0
$201$	193.897	+	94.2395i	0.964660	+	0.468853i
$202$		0			0
$203$	−59.8424	+	252.495i	−0.294790	+	1.24382i
$204$		0			0
$205$	57.5696	+	133.461i	0.280827	+	0.651031i
$206$		0			0
$207$	−6.65573	−	255.689i	−0.0321533	−	1.23521i
$208$		0			0
$209$	495.606	−	28.8658i	2.37132	−	0.138114i
$210$		0			0
$211$	−56.7781	+	131.626i	−0.269090	+	0.623822i	−0.998161	−	0.0606168i	$-0.980693\pi$
$211$	−56.7781	+	131.626i	−0.269090	+	0.623822i	0.729071	+	0.684438i	$0.239952\pi$
$212$		0			0
$213$	46.7999	+	19.4692i	0.219718	+	0.0914048i
$214$		0			0
$215$	−110.643	−	63.8799i	−0.514619	−	0.297116i
$216$		0			0
$217$	97.9558	+	169.664i	0.451409	+	0.781864i
$218$		0			0
$219$	351.755	+	224.851i	1.60619	+	1.02672i
$220$		0			0
$221$	27.6952	+	236.947i	0.125318	+	1.07216i
$222$		0			0
$223$	−85.7173	−	43.0489i	−0.384383	−	0.193044i	0.246106	−	0.969243i	$-0.420849\pi$
$223$	−85.7173	−	43.0489i	−0.384383	−	0.193044i	−0.630488	+	0.776199i	$0.717145\pi$
$224$		0			0
$225$	−53.6476	−	163.576i	−0.238434	−	0.727006i
$226$		0			0
$227$	−136.664	−	101.742i	−0.602043	−	0.448204i	0.252492	−	0.967599i	$-0.418750\pi$
$227$	−136.664	−	101.742i	−0.602043	−	0.448204i	−0.854534	+	0.519395i	$0.826157\pi$
$228$		0			0
$229$	−63.0448	+	66.8236i	−0.275305	+	0.291806i	−0.850243	−	0.526391i	$-0.823545\pi$
$229$	−63.0448	+	66.8236i	−0.275305	+	0.291806i	0.574938	+	0.818197i	$0.305026\pi$
$230$		0			0
$231$	−422.228	+	408.865i	−1.82783	+	1.76998i
$232$		0			0
$233$	−63.5116	+	75.6902i	−0.272582	+	0.324851i	−0.884918	−	0.465747i	$-0.845786\pi$
$233$	−63.5116	+	75.6902i	−0.272582	+	0.324851i	0.612336	+	0.790598i	$0.290230\pi$
$234$		0			0
$235$	−113.028	+	94.8421i	−0.480972	+	0.403583i
$236$		0			0
$237$	−65.2080	−	109.624i	−0.275139	−	0.462549i
$238$		0			0
$239$	−63.0115	−	125.466i	−0.263647	−	0.524964i	0.722391	−	0.691484i	$-0.243043\pi$
$239$	−63.0115	−	125.466i	−0.263647	−	0.524964i	−0.986038	+	0.166521i	$0.946747\pi$
$240$		0			0
$241$	−2.35460	+	0.558049i	−0.00977011	+	0.00231556i	−0.235498	−	0.971875i	$-0.575672\pi$
$241$	−2.35460	+	0.558049i	−0.00977011	+	0.00231556i	0.225728	+	0.974190i	$0.427524\pi$
$242$		0			0
$243$	242.680	+	12.4589i	0.998685	+	0.0512711i
$244$		0			0
$245$	44.8399	+	189.194i	0.183020	+	0.772222i
$246$		0			0
$247$	241.164	−	121.117i	0.976374	−	0.490353i
$248$		0			0
$249$	−213.704	+	127.118i	−0.858249	+	0.510514i
$250$		0			0
$251$	13.3323	+	15.8888i	0.0531166	+	0.0633018i	0.791949	−	0.610588i	$-0.209067\pi$
$251$	13.3323	+	15.8888i	0.0531166	+	0.0633018i	−0.738832	+	0.673890i	$0.764622\pi$
$252$		0			0
$253$	−375.187	−	314.819i	−1.48295	−	1.24435i
$254$		0			0
$255$	−128.782	−	132.991i	−0.505027	−	0.521532i
$256$		0			0
$257$	107.530	+	101.450i	0.418406	+	0.394745i	0.866448	−	0.499267i	$-0.166397\pi$
$257$	107.530	+	101.450i	0.418406	+	0.394745i	−0.448043	+	0.894012i	$0.647879\pi$
$258$		0			0
$259$	−288.983	+	388.171i	−1.11576	+	1.49873i
$260$		0			0
$261$	42.1584	−	201.061i	0.161526	−	0.770347i
$262$		0			0
$263$	−211.387	+	420.906i	−0.803753	+	1.60040i	−0.00406289	+	0.999992i	$0.501293\pi$
$263$	−211.387	+	420.906i	−0.803753	+	1.60040i	−0.799690	+	0.600413i	$0.795003\pi$
$264$		0			0
$265$	−55.2768	+	6.46094i	−0.208592	+	0.0243809i
$266$		0			0
$267$	201.677	−	315.501i	0.755344	−	1.18165i
$268$		0			0
$269$	−75.1666	+	43.3974i	−0.279430	+	0.161329i	−0.633165	−	0.774017i	$-0.718245\pi$
$269$	−75.1666	+	43.3974i	−0.279430	+	0.161329i	0.353736	+	0.935345i	$0.384911\pi$
$270$		0			0
$271$	−100.669	+	174.364i	−0.371473	+	0.643409i	−0.989792	−	0.142517i	$-0.954480\pi$
$271$	−100.669	+	174.364i	−0.371473	+	0.643409i	0.618320	+	0.785927i	$0.287814\pi$
$272$		0			0
$273$	−122.720	+	294.993i	−0.449524	+	1.08056i
$274$		0			0
$275$	−302.681	−	130.564i	−1.10066	−	0.474777i
$276$		0			0
$277$	3.36070	+	57.7010i	0.0121325	+	0.208307i	0.998926	+	0.0463259i	$0.0147513\pi$
$277$	3.36070	+	57.7010i	0.0121325	+	0.208307i	−0.986794	+	0.161981i	$0.948212\pi$
$278$		0			0
$279$	−81.0188	−	132.257i	−0.290390	−	0.474039i
$280$		0			0
$281$	−42.1834	+	18.1962i	−0.150119	+	0.0647550i	−0.469814	−	0.882766i	$-0.655679\pi$
$281$	−42.1834	+	18.1962i	−0.150119	+	0.0647550i	0.319695	+	0.947521i	$0.396420\pi$
$282$		0			0
$283$	246.202	+	58.3509i	0.869971	+	0.206187i	0.641275	−	0.767311i	$-0.278406\pi$
$283$	246.202	+	58.3509i	0.869971	+	0.206187i	0.228696	+	0.973498i	$0.426554\pi$
$284$		0			0
$285$	−91.5450	+	188.353i	−0.321211	+	0.660887i
$286$		0			0
$287$	−233.211	−	640.742i	−0.812582	−	2.23255i
$288$		0			0
$289$	337.773	+	122.939i	1.16877	+	0.425396i
$290$		0			0
$291$	341.313	+	119.221i	1.17290	+	0.409696i
$292$		0			0
$293$	−136.726	−	7.96340i	−0.466642	−	0.0271788i	−0.176787	−	0.984249i	$-0.556570\pi$
$293$	−136.726	−	7.96340i	−0.466642	−	0.0271788i	−0.289856	+	0.957070i	$0.593607\pi$
$294$		0			0
$295$	−8.11926	−	8.60591i	−0.0275229	−	0.0291726i
$296$		0			0
$297$	325.734	−	332.280i	1.09675	−	1.11879i
$298$		0			0
$299$	−255.057	−	76.3590i	−0.853033	−	0.255381i
$300$		0			0
$301$	500.750	+	329.348i	1.66362	+	1.09418i
$302$		0			0
$303$	−52.1624	−	8.49934i	−0.172153	−	0.0280506i
$304$		0			0
$305$	97.7558	−	17.2370i	0.320511	−	0.0565147i
$306$		0			0
$307$	34.3440	−	194.774i	0.111870	−	0.634444i	−0.876383	−	0.481615i	$-0.840050\pi$
$307$	34.3440	−	194.774i	0.111870	−	0.634444i	0.988253	−	0.152829i	$-0.0488384\pi$
$308$		0			0
$309$	137.224	+	307.073i	0.444092	+	0.993762i
$310$		0			0
$311$	−49.3948	+	14.7878i	−0.158826	+	0.0475493i	−0.365229	−	0.930918i	$-0.619009\pi$
$311$	−49.3948	+	14.7878i	−0.158826	+	0.0475493i	0.206403	+	0.978467i	$0.433824\pi$
$312$		0			0
$313$	−401.918	−	46.9775i	−1.28408	−	0.150088i	−0.553465	−	0.832873i	$-0.686695\pi$
$313$	−401.918	−	46.9775i	−1.28408	−	0.150088i	−0.730620	+	0.682785i	$0.760769\pi$
$314$		0			0
$315$	−63.4365	−	239.683i	−0.201386	−	0.760900i
$316$		0			0
$317$	−272.816	−	414.796i	−0.860617	−	1.30851i	−0.949918	−	0.312500i	$-0.898833\pi$
$317$	−272.816	−	414.796i	−0.860617	−	1.30851i	0.0893003	−	0.996005i	$-0.471537\pi$
$318$		0			0
$319$	−234.906	−	315.534i	−0.736383	−	0.989135i
$320$		0			0
$321$	−17.0010	−	15.6265i	−0.0529626	−	0.0486807i
$322$		0			0
$323$		−	733.555i		−	2.27107i
$324$		0			0
$325$	−179.193			−0.551364
$326$		0			0
$327$	577.800	+	129.024i	1.76697	+	0.394569i
$328$		0			0
$329$	555.215	−	413.342i	1.68758	−	1.25636i
$330$		0			0
$331$	158.817	−	104.455i	0.479809	−	0.315575i	−0.286463	−	0.958091i	$-0.592480\pi$
$331$	158.817	−	104.455i	0.479809	−	0.315575i	0.766272	+	0.642516i	$0.222109\pi$
$332$		0			0
$333$	220.708	−	313.157i	0.662788	−	0.940413i
$334$		0			0
$335$	−20.2166	+	172.964i	−0.0603482	+	0.516312i
$336$		0			0
$337$	61.0407	+	203.890i	0.181130	+	0.605015i	0.999538	+	0.0303785i	$0.00967127\pi$
$337$	61.0407	+	203.890i	0.181130	+	0.605015i	−0.818409	+	0.574636i	$0.805144\pi$
$338$		0			0
$339$	−47.7461	+	460.370i	−0.140844	+	1.35802i
$340$		0			0
$341$	−292.481	−	51.5723i	−0.857715	−	0.151238i
$342$		0			0
$343$	−61.6623	−	349.704i	−0.179773	−	1.01955i
$344$		0			0
$345$	193.210	−	73.1837i	0.560030	−	0.212127i
$346$		0			0
$347$	−75.0383	+	114.090i	−0.216249	+	0.328790i	−0.927279	−	0.374371i	$-0.877859\pi$
$347$	−75.0383	+	114.090i	−0.216249	+	0.328790i	0.711030	+	0.703162i	$0.248229\pi$
$348$		0			0
$349$	−175.437	+	586.000i	−0.502684	+	1.67908i	0.210084	+	0.977683i	$0.432626\pi$
$349$	−175.437	+	586.000i	−0.502684	+	1.67908i	−0.712768	+	0.701400i	$0.752559\pi$
$350$		0			0
$351$	91.0452	−	235.990i	0.259388	−	0.672336i
$352$		0			0
$353$	366.717	−	345.979i	1.03886	−	0.980112i	0.0390407	−	0.999238i	$-0.487570\pi$
$353$	366.717	−	345.979i	1.03886	−	0.980112i	0.999817	+	0.0191259i	$0.00608832\pi$
$354$		0			0
$355$	−2.38068	+	40.8747i	−0.00670615	+	0.115140i
$356$		0			0
$357$	566.847	+	657.962i	1.58781	+	1.84303i
$358$		0			0
$359$	−137.503	+	377.786i	−0.383016	+	1.05233i	0.587063	+	0.809541i	$0.300284\pi$
$359$	−137.503	+	377.786i	−0.383016	+	1.05233i	−0.970080	+	0.242787i	$0.921938\pi$
$360$		0			0
$361$	−440.555	+	160.349i	−1.22037	+	0.444180i
$362$		0			0
$363$	−37.5564	−	526.660i	−0.103461	−	1.45085i
$364$		0			0
$365$	−77.7693	+	328.135i	−0.213067	+	0.898999i
$366$		0			0
$367$	92.0158	+	213.317i	0.250724	+	0.581244i	0.996373	−	0.0850954i	$-0.0271195\pi$
$367$	92.0158	+	213.317i	0.250724	+	0.581244i	−0.745649	+	0.666339i	$0.767860\pi$
$368$		0			0
$369$	197.766	+	502.288i	0.535952	+	1.36121i
$370$		0			0
$371$	260.640	−	15.1805i	0.702534	−	0.0409179i
$372$		0			0
$373$	46.7469	−	108.372i	0.125327	−	0.290540i	−0.843988	−	0.536362i	$-0.819798\pi$
$373$	46.7469	−	108.372i	0.125327	−	0.290540i	0.969315	+	0.245821i	$0.0790576\pi$
$374$		0			0
$375$	254.809	−	194.902i	0.679489	−	0.519738i
$376$		0			0
$377$	−185.190	−	106.920i	−0.491221	−	0.283606i
$378$		0			0
$379$	91.6055	+	158.665i	0.241703	+	0.418642i	0.961200	−	0.275854i	$-0.0889607\pi$
$379$	91.6055	+	158.665i	0.241703	+	0.418642i	−0.719496	+	0.694496i	$0.755627\pi$
$380$		0			0
$381$	16.0673	−	355.503i	0.0421715	−	0.933079i
$382$		0			0
$383$	9.72594	+	83.2108i	0.0253941	+	0.217260i	0.999977	−	0.00676626i	$-0.00215378\pi$
$383$	9.72594	+	83.2108i	0.0253941	+	0.217260i	−0.974583	+	0.224027i	$0.928080\pi$
$384$		0			0
$385$	−424.262	−	213.072i	−1.10198	−	0.553434i
$386$		0			0
$387$	−403.085	−	250.335i	−1.04156	−	0.646860i
$388$		0			0
$389$	−39.4038	−	29.3350i	−0.101295	−	0.0754114i	0.545319	−	0.838228i	$-0.316408\pi$
$389$	−39.4038	−	29.3350i	−0.101295	−	0.0754114i	−0.646615	+	0.762817i	$0.723816\pi$
$390$		0			0
$391$	−496.629	+	526.396i	−1.27015	+	1.34628i
$392$		0			0
$393$	−76.9358	−	306.773i	−0.195765	−	0.780592i
$394$		0			0
$395$	66.2277	−	78.9271i	0.167665	−	0.199815i
$396$		0			0
$397$	522.591	−	438.506i	1.31635	−	1.10455i	0.329284	−	0.944231i	$-0.393193\pi$
$397$	522.591	−	438.506i	1.31635	−	1.10455i	0.987066	−	0.160317i	$-0.0512518\pi$
$398$		0			0
$399$	480.109	−	857.141i	1.20328	−	2.14822i
$400$		0			0
$401$	−253.522	−	504.803i	−0.632223	−	1.25886i	−0.950459	−	0.310849i	$-0.899387\pi$
$401$	−253.522	−	504.803i	−0.632223	−	1.25886i	0.318236	−	0.948012i	$-0.396910\pi$
$402$		0			0
$403$	−157.095	+	37.2321i	−0.389813	+	0.0923873i
$404$		0			0
$405$	55.1422	+	188.382i	0.136154	+	0.465140i
$406$		0			0
$407$	−169.183	−	713.840i	−0.415684	−	1.75391i
$408$		0			0
$409$	367.542	−	184.586i	0.898635	−	0.451311i	0.0613738	−	0.998115i	$-0.480452\pi$
$409$	367.542	−	184.586i	0.898635	−	0.451311i	0.837261	+	0.546803i	$0.184156\pi$
$410$		0			0
$411$	−3.98918	−	306.552i	−0.00970604	−	0.745868i
$412$		0			0
$413$	35.6774	+	42.5187i	0.0863860	+	0.102951i
$414$		0			0
$415$	−153.862	−	129.106i	−0.370752	−	0.311098i
$416$		0			0
$417$	−109.756	+	384.764i	−0.263205	+	0.922696i
$418$		0			0
$419$	176.964	+	166.957i	0.422349	+	0.398466i	0.867859	−	0.496811i	$-0.165496\pi$
$419$	176.964	+	166.957i	0.422349	+	0.398466i	−0.445509	+	0.895277i	$0.646977\pi$
$420$		0			0
$421$	258.380	−	347.064i	0.613728	−	0.824380i	−0.381250	−	0.924472i	$-0.624506\pi$
$421$	258.380	−	347.064i	0.613728	−	0.824380i	0.994978	+	0.100092i	$0.0319136\pi$
$422$		0			0
$423$	−430.890	+	338.563i	−1.01865	+	0.800385i
$424$		0			0
$425$	−218.601	+	435.271i	−0.514356	+	1.02417i
$426$		0			0
$427$	−462.521	+	54.0609i	−1.08319	+	0.126606i
$428$		0			0
$429$	−222.989	−	429.965i	−0.519788	−	1.00225i
$430$		0			0
$431$	172.873	−	99.8080i	0.401096	−	0.231573i	−0.285861	−	0.958271i	$-0.592279\pi$
$431$	172.873	−	99.8080i	0.401096	−	0.231573i	0.686957	+	0.726698i	$0.258946\pi$
$432$		0			0
$433$	−3.08649	+	5.34596i	−0.00712815	+	0.0123463i	−0.869567	−	0.493814i	$-0.835602\pi$
$433$	−3.08649	+	5.34596i	−0.00712815	+	0.0123463i	0.862439	+	0.506160i	$0.168936\pi$
$434$		0			0
$435$	164.554	−	21.4076i	0.378286	−	0.0492128i
$436$		0			0
$437$	751.719	+	324.260i	1.72018	+	0.742014i
$438$		0			0
$439$	14.9041	+	255.894i	0.0339502	+	0.582902i	0.971792	+	0.235839i	$0.0757838\pi$
$439$	14.9041	+	255.894i	0.0339502	+	0.582902i	−0.937842	+	0.347063i	$0.887179\pi$
$440$		0			0
$441$	143.859	+	707.651i	0.326210	+	1.60465i
$442$		0			0
$443$	657.070	−	283.432i	1.48323	−	0.639802i	0.508071	−	0.861315i	$-0.330359\pi$
$443$	657.070	−	283.432i	1.48323	−	0.639802i	0.975157	+	0.221513i	$0.0710996\pi$
$444$		0			0
$445$	294.316	+	69.7541i	0.661384	+	0.156751i
$446$		0			0
$447$	−73.4251	−	108.535i	−0.164262	−	0.242807i
$448$		0			0
$449$	42.0679	+	115.581i	0.0936924	+	0.257418i	0.977683	−	0.210088i	$-0.0673750\pi$
$449$	42.0679	+	115.581i	0.0936924	+	0.257418i	−0.883990	+	0.467506i	$0.845153\pi$
$450$		0			0
$451$	971.334	+	353.537i	2.15373	+	0.783895i
$452$		0			0
$453$	−42.9076	−	226.097i	−0.0947189	−	0.499110i
$454$		0			0
$455$	−257.645	−	15.0061i	−0.566253	−	0.0329805i
$456$		0			0
$457$	−73.9143	−	78.3445i	−0.161738	−	0.171432i	0.641436	−	0.767176i	$-0.278339\pi$
$457$	−73.9143	−	78.3445i	−0.161738	−	0.171432i	−0.803174	+	0.595744i	$0.796857\pi$
$458$		0			0
$459$	−462.165	−	509.042i	−1.00690	−	1.10902i
$460$		0			0
$461$	−25.4979	−	7.63356i	−0.0553099	−	0.0165587i	0.259029	−	0.965870i	$-0.416598\pi$
$461$	−25.4979	−	7.63356i	−0.0553099	−	0.0165587i	−0.314339	+	0.949311i	$0.601783\pi$
$462$		0			0
$463$	−271.756	−	178.737i	−0.586946	−	0.386041i	0.221020	−	0.975269i	$-0.429061\pi$
$463$	−271.756	−	178.737i	−0.586946	−	0.386041i	−0.807966	+	0.589229i	$0.799432\pi$
$464$		0			0
$465$	79.2753	−	97.0127i	0.170484	−	0.208629i
$466$		0			0
$467$	−686.646	+	121.074i	−1.47033	+	0.259260i	−0.850708	−	0.525638i	$-0.823827\pi$
$467$	−686.646	+	121.074i	−1.47033	+	0.259260i	−0.619625	+	0.784898i	$0.712715\pi$
$468$		0			0
$469$	141.860	−	804.528i	0.302474	−	1.71541i
$470$		0			0
$471$	−453.652	+	626.210i	−0.963168	+	1.32953i
$472$		0			0
$473$	−870.416	+	260.585i	−1.84020	+	0.550921i
$474$		0			0
$475$	547.280	+	63.9679i	1.15217	+	0.134669i
$476$		0			0
$477$	−205.961	+	17.3835i	−0.431785	+	0.0364434i
$478$		0			0
$479$	−118.398	−	180.015i	−0.247177	−	0.375814i	0.690495	−	0.723338i	$-0.257393\pi$
$479$	−118.398	−	180.015i	−0.247177	−	0.375814i	−0.937671	+	0.347524i	$0.887023\pi$
$480$		0			0
$481$	−238.144	−	319.883i	−0.495102	−	0.665038i
$482$		0			0
$483$	−924.823	+	290.038i	−1.91475	+	0.600494i
$484$		0			0
$485$			292.035i			0.602134i
$486$		0			0
$487$	−99.8495			−0.205030			−0.102515	−	0.994731i	$-0.532689\pi$
$487$	−99.8495			−0.205030			−0.102515	+	0.994731i	$0.532689\pi$
$488$		0			0
$489$	−21.6586	−	69.0610i	−0.0442916	−	0.141229i
$490$		0			0
$491$	570.062	−	424.395i	1.16102	−	0.864349i	0.168414	−	0.985716i	$-0.446135\pi$
$491$	570.062	−	424.395i	1.16102	−	0.864349i	0.992608	+	0.121367i	$0.0387279\pi$
$492$		0			0
$493$	−485.631	+	319.404i	−0.985052	+	0.647879i
$494$		0			0
$495$	340.156	+	159.888i	0.687184	+	0.323006i
$496$		0			0
$497$	22.2989	−	190.779i	0.0448669	−	0.383861i
$498$		0			0
$499$	65.6719	+	219.360i	0.131607	+	0.439598i	0.998237	−	0.0593531i	$-0.0189038\pi$
$499$	65.6719	+	219.360i	0.131607	+	0.439598i	−0.866630	+	0.498951i	$0.833719\pi$
$500$		0			0
$501$	−372.541	−	269.884i	−0.743595	−	0.538691i
$502$		0			0
$503$	−666.492	−	117.521i	−1.32503	−	0.233639i	−0.534038	−	0.845460i	$-0.679326\pi$
$503$	−666.492	−	117.521i	−1.32503	−	0.233639i	−0.790996	+	0.611821i	$0.790437\pi$
$504$		0			0
$505$	−7.41313	−	42.0419i	−0.0146795	−	0.0832514i
$506$		0			0
$507$	188.712	+	154.209i	0.372213	+	0.304159i
$508$		0			0
$509$	−286.352	+	435.378i	−0.562578	+	0.855359i	−0.999015	−	0.0443764i	$-0.985870\pi$
$509$	−286.352	+	435.378i	−0.562578	+	0.855359i	0.436437	+	0.899735i	$0.356240\pi$
$510$		0			0
$511$	453.722	−	1515.54i	0.887910	−	2.96583i
$512$		0			0
$513$	−362.307	+	688.243i	−0.706251	+	1.34160i
$514$		0			0
$515$	−197.615	+	186.440i	−0.383718	+	0.362019i
$516$		0			0
$517$	−61.0122	+	1047.54i	−0.118012	+	2.02619i
$518$		0			0
$519$	855.509	−	162.355i	1.64838	−	0.312822i
$520$		0			0
$521$	−97.5297	+	267.961i	−0.187197	+	0.514320i	−0.997419	−	0.0718036i	$-0.977125\pi$
$521$	−97.5297	+	267.961i	−0.187197	+	0.514320i	0.810222	+	0.586124i	$0.199347\pi$
$522$		0			0
$523$	−72.7892	+	26.4931i	−0.139176	+	0.0506560i	−0.410669	−	0.911784i	$-0.634705\pi$
$523$	−72.7892	+	26.4931i	−0.139176	+	0.0506560i	0.271493	+	0.962440i	$0.412483\pi$
$524$		0			0
$525$	−540.313	+	365.529i	−1.02917	+	0.696246i
$526$		0			0
$527$	−101.204	+	427.012i	−0.192037	+	0.810269i
$528$		0			0
$529$	−110.375	−	255.878i	−0.208648	−	0.483701i
$530$		0			0
$531$	−29.1115	−	32.9149i	−0.0548239	−	0.0619866i
$532$		0			0
$533$	560.958	−	32.6721i	1.05245	−	0.0612984i
$534$		0			0
$535$	7.38789	−	17.1271i	0.0138091	−	0.0320132i
$536$		0			0
$537$	−24.7435	−	190.197i	−0.0460774	−	0.354185i
$538$		0			0
$539$	1197.51	+	691.381i	2.22172	+	1.28271i
$540$		0			0
$541$	168.110	+	291.174i	0.310739	+	0.538215i	0.978522	−	0.206140i	$-0.0660903\pi$
$541$	168.110	+	291.174i	0.310739	+	0.538215i	−0.667784	+	0.744355i	$0.732757\pi$
$542$		0			0
$543$	329.702	−	170.991i	0.607187	−	0.314900i
$544$		0			0
$545$	55.5180	+	474.987i	0.101868	+	0.871535i
$546$		0			0
$547$	609.769	+	306.238i	1.11475	+	0.559849i	0.908179	−	0.418582i	$-0.137473\pi$
$547$	609.769	+	306.238i	1.11475	+	0.559849i	0.206573	+	0.978431i	$0.433769\pi$
$548$		0			0
$549$	364.932	−	52.3129i	0.664721	−	0.0952877i
$550$		0			0
$551$	527.428	+	392.655i	0.957219	+	0.712623i
$552$		0			0
$553$	−331.693	+	351.574i	−0.599806	+	0.635757i
$554$		0			0
$555$	297.598	+	84.8915i	0.536212	+	0.152958i
$556$		0			0
$557$	185.064	−	220.550i	0.332251	−	0.395961i	−0.573894	−	0.818930i	$-0.694568\pi$
$557$	185.064	−	220.550i	0.332251	−	0.395961i	0.906144	+	0.422969i	$0.139012\pi$
$558$		0			0
$559$	−378.358	+	317.480i	−0.676847	+	0.567942i
$560$		0			0
$561$	−1316.44	+	17.1309i	−2.34659	+	0.0305364i
$562$		0			0
$563$	−150.825	−	300.316i	−0.267894	−	0.533422i	0.718956	−	0.695055i	$-0.244620\pi$
$563$	−150.825	−	300.316i	−0.267894	−	0.533422i	−0.986851	+	0.161633i	$0.948324\pi$
$564$		0			0
$565$	−363.787	+	86.2191i	−0.643871	+	0.152600i
$566$		0			0
$567$	−206.862	−	897.288i	−0.364836	−	1.58252i
$568$		0			0
$569$	98.2115	+	414.387i	0.172604	+	0.728272i	0.988644	+	0.150277i	$0.0480166\pi$
$569$	98.2115	+	414.387i	0.172604	+	0.728272i	−0.816040	+	0.577995i	$0.803835\pi$
$570$		0			0
$571$	339.515	−	170.511i	0.594597	−	0.298618i	−0.125936	−	0.992038i	$-0.540193\pi$
$571$	339.515	−	170.511i	0.594597	−	0.298618i	0.720533	+	0.693420i	$0.243897\pi$
$572$		0			0
$573$	493.727	+	276.551i	0.861653	+	0.482637i
$574$		0			0
$575$	−349.419	−	416.421i	−0.607685	−	0.724210i
$576$		0			0
$577$	−34.8869	−	29.2736i	−0.0604625	−	0.0507341i	0.612056	−	0.790815i	$-0.290343\pi$
$577$	−34.8869	−	29.2736i	−0.0604625	−	0.0507341i	−0.672518	+	0.740081i	$0.734787\pi$
$578$		0			0
$579$	164.353	−	41.2183i	0.283857	−	0.0711888i
$580$		0			0
$581$	685.366	+	646.609i	1.17963	+	1.11292i
$582$		0			0
$583$	−236.348	+	317.470i	−0.405399	+	0.544546i
$584$		0			0
$585$	204.213	+	6.56831i	0.349082	+	0.0112279i
$586$		0			0
$587$	−20.5606	+	40.9395i	−0.0350266	+	0.0697436i	−0.910465	−	0.413586i	$-0.864276\pi$
$587$	−20.5606	+	40.9395i	−0.0350266	+	0.0697436i	0.875439	+	0.483329i	$0.160573\pi$
$588$		0			0
$589$	493.079	−	57.6326i	0.837145	−	0.0978482i
$590$		0			0
$591$	177.854	+	8.03831i	0.300938	+	0.0136012i
$592$		0			0
$593$	873.326	−	504.215i	1.47273	−	0.850278i	0.473196	−	0.880957i	$-0.343100\pi$
$593$	873.326	−	504.215i	1.47273	−	0.850278i	0.999529	+	0.0306787i	$0.00976687\pi$
$594$		0			0
$595$	−350.757	+	607.528i	−0.589507	+	1.02106i
$596$		0			0
$597$	294.133	+	384.540i	0.492685	+	0.644121i
$598$		0			0
$599$	−511.569	−	220.669i	−0.854039	−	0.368396i	−0.0763767	−	0.997079i	$-0.524335\pi$
$599$	−511.569	−	220.669i	−0.854039	−	0.368396i	−0.777662	+	0.628683i	$0.783594\pi$
$600$		0			0
$601$	−39.7856	−	683.092i	−0.0661989	−	1.13659i	−0.853867	−	0.520492i	$-0.825749\pi$
$601$	−39.7856	−	683.092i	−0.0661989	−	1.13659i	0.787668	−	0.616100i	$-0.211288\pi$
$602$		0			0
$603$	−95.6959	+	639.637i	−0.158700	+	1.06076i
$604$		0			0
$605$	391.616	−	168.927i	0.647299	−	0.279218i
$606$		0			0
$607$	143.441	+	33.9962i	0.236312	+	0.0560069i	0.347065	−	0.937841i	$-0.387178\pi$
$607$	143.441	+	33.9962i	0.236312	+	0.0560069i	−0.110753	+	0.993848i	$0.535326\pi$
$608$		0			0
$609$	−776.496	+	55.3723i	−1.27503	+	0.0909234i
$610$		0			0
$611$	195.092	+	536.011i	0.319300	+	0.877269i
$612$		0			0
$613$	−457.443	−	166.496i	−0.746237	−	0.271608i	−0.0592158	−	0.998245i	$-0.518860\pi$
$613$	−457.443	−	166.496i	−0.746237	−	0.271608i	−0.687022	+	0.726637i	$0.741082\pi$
$614$		0			0
$615$	−330.355	+	284.607i	−0.537163	+	0.462776i
$616$		0			0
$617$	586.399	+	34.1538i	0.950403	+	0.0553547i	0.526336	−	0.850276i	$-0.323565\pi$
$617$	586.399	+	34.1538i	0.950403	+	0.0553547i	0.424066	+	0.905631i	$0.360602\pi$
$618$		0			0
$619$	−155.656	−	164.986i	−0.251464	−	0.266536i	0.589329	−	0.807893i	$-0.299392\pi$
$619$	−155.656	−	164.986i	−0.251464	−	0.266536i	−0.840793	+	0.541357i	$0.817911\pi$
$620$		0			0
$621$	725.942	−	248.593i	1.16899	−	0.400310i
$622$		0			0
$623$	−1359.34	−	406.960i	−2.18193	−	0.653226i
$624$		0			0
$625$	−183.021	−	120.375i	−0.292834	−	0.192600i
$626$		0			0
$627$	527.551	+	1392.77i	0.841389	+	2.22133i
$628$		0			0
$629$	−1067.53	+	188.235i	−1.69719	+	0.299260i
$630$		0			0
$631$	−130.972	+	742.777i	−0.207562	+	1.17714i	0.685795	+	0.727795i	$0.259455\pi$
$631$	−130.972	+	742.777i	−0.207562	+	1.17714i	−0.893357	+	0.449347i	$0.851657\pi$
$632$		0			0
$633$	−427.756	−	44.3636i	−0.675760	−	0.0700847i
$634$		0			0
$635$	275.379	−	82.4431i	0.433668	−	0.129832i
$636$		0			0
$637$	746.592	+	87.2641i	1.17204	+	0.136992i
$638$		0			0
$639$	−13.7174	+	151.444i	−0.0214670	+	0.237002i
$640$		0			0
$641$	419.263	+	637.459i	0.654077	+	0.994475i	0.998451	+	0.0556428i	$0.0177208\pi$
$641$	419.263	+	637.459i	0.654077	+	0.994475i	−0.344374	+	0.938833i	$0.611909\pi$
$642$		0			0
$643$	−440.716	−	591.985i	−0.685406	−	0.920660i	0.314182	−	0.949363i	$-0.398270\pi$
$643$	−440.716	−	591.985i	−0.685406	−	0.920660i	−0.999588	+	0.0287026i	$0.990862\pi$
$644$		0			0
$645$	83.5300	−	374.066i	0.129504	−	0.579948i
$646$		0			0
$647$			250.378i			0.386982i	0.981102	+	0.193491i	$0.0619811\pi$
$647$			250.378i			0.386982i	−0.981102	+	0.193491i	$0.938019\pi$
$648$		0			0
$649$	−84.1417			−0.129648
$650$		0			0
$651$	−397.731	+	432.715i	−0.610955	+	0.664693i
$652$		0			0
$653$	672.712	−	500.816i	1.03019	−	0.766946i	0.0573307	−	0.998355i	$-0.481741\pi$
$653$	672.712	−	500.816i	1.03019	−	0.766946i	0.972856	+	0.231409i	$0.0743336\pi$
$654$		0			0
$655$	213.445	−	140.385i	0.325870	−	0.214328i
$656$		0			0
$657$	−327.860	+	1208.76i	−0.499026	+	1.83982i
$658$		0			0
$659$	−40.5416	+	346.855i	−0.0615198	+	0.526336i	0.926980	+	0.375111i	$0.122396\pi$
$659$	−40.5416	+	346.855i	−0.0615198	+	0.526336i	−0.988500	+	0.151224i	$0.951679\pi$
$660$		0			0
$661$	−179.794	−	600.554i	−0.272003	−	0.908553i	−0.979433	−	0.201770i	$-0.935331\pi$
$661$	−179.794	−	600.554i	−0.272003	−	0.908553i	0.707430	−	0.706783i	$-0.249854\pi$
$662$		0			0
$663$	−653.406	+	291.994i	−0.985529	+	0.440413i
$664$		0			0
$665$	781.525	+	137.804i	1.17523	+	0.207224i
$666$		0			0
$667$	−112.646	−	638.845i	−0.168884	−	0.957788i
$668$		0			0
$669$	46.2774	−	284.015i	0.0691740	−	0.424536i
$670$		0			0
$671$	387.917	−	589.798i	0.578117	−	0.878984i
$672$		0			0
$673$	−127.420	+	425.614i	−0.189332	+	0.632413i	0.809634	+	0.586936i	$0.199666\pi$
$673$	−127.420	+	425.614i	−0.189332	+	0.632413i	−0.998965	+	0.0454768i	$0.985519\pi$
$674$		0			0
$675$	420.081	−	300.416i	0.622342	−	0.445060i
$676$		0			0
$677$	−874.762	+	825.296i	−1.29212	+	1.21905i	−0.330767	+	0.943712i	$0.607308\pi$
$677$	−874.762	+	825.296i	−1.29212	+	1.21905i	−0.961348	+	0.275336i	$0.911211\pi$
$678$		0			0
$679$	79.6587	−	1367.69i	0.117318	−	2.01427i
$680$		0			0
$681$	168.553	−	482.541i	0.247508	−	0.708578i
$682$		0			0
$683$	−161.018	+	442.393i	−0.235751	+	0.647720i	0.764245	+	0.644926i	$0.223112\pi$
$683$	−161.018	+	442.393i	−0.235751	+	0.647720i	−0.999996	+	0.00279413i	$0.999111\pi$
$684$		0			0
$685$	232.708	−	84.6986i	0.339719	−	0.123648i
$686$		0			0
$687$	−247.882	−	120.478i	−0.360818	−	0.175368i
$688$		0			0
$689$	−49.6173	+	209.352i	−0.0720136	+	0.303849i
$690$		0			0
$691$	513.568	+	1190.59i	0.743225	+	1.72299i	0.689336	+	0.724442i	$0.257902\pi$
$691$	513.568	+	1190.59i	0.743225	+	1.72299i	0.0538885	+	0.998547i	$0.482838\pi$
$692$		0			0
$693$	−1549.44	−	841.587i	−2.23584	−	1.21441i
$694$		0			0
$695$	−322.649	+	18.7922i	−0.464244	+	0.0270391i
$696$		0			0
$697$	604.960	−	1402.45i	0.867948	−	2.01213i
$698$		0			0
$699$	−273.682	−	113.854i	−0.391534	−	0.162882i
$700$		0			0
$701$	−84.4585	−	48.7621i	−0.120483	−	0.0695608i	0.438547	−	0.898708i	$-0.355493\pi$
$701$	−84.4585	−	48.7621i	−0.120483	−	0.0695608i	−0.559030	+	0.829147i	$0.688826\pi$
$702$		0			0
$703$	613.133	+	1061.98i	0.872167	+	1.51064i
$704$		0			0
$705$	−372.958	−	238.404i	−0.529018	−	0.338162i
$706$		0			0
$707$	23.2500	+	198.917i	0.0328855	+	0.281353i
$708$		0			0
$709$	−197.598	−	99.2375i	−0.278700	−	0.139968i	0.303959	−	0.952685i	$-0.401691\pi$
$709$	−197.598	−	99.2375i	−0.278700	−	0.139968i	−0.582659	+	0.812717i	$0.697988\pi$
$710$		0			0
$711$	255.263	−	285.073i	0.359020	−	0.400947i
$712$		0			0
$713$	−392.849	−	292.465i	−0.550981	−	0.410190i
$714$		0			0
$715$	268.485	−	284.577i	0.375503	−	0.398010i
$716$		0			0
$717$	302.583	−	293.008i	0.422013	−	0.408658i
$718$		0			0
$719$	460.320	−	548.589i	0.640223	−	0.762988i	−0.344182	−	0.938903i	$-0.611844\pi$
$719$	460.320	−	548.589i	0.640223	−	0.762988i	0.984405	+	0.175915i	$0.0562883\pi$
$720$		0			0
$721$	976.343	−	819.249i	1.35415	−	1.13627i
$722$		0			0
$723$	−3.71123	−	6.23912i	−0.00513310	−	0.00862949i
$724$		0			0
$725$	−195.948	−	390.165i	−0.270274	−	0.538159i
$726$		0			0
$727$	−1172.89	+	277.981i	−1.61333	+	0.382367i	−0.935633	−	0.352974i	$-0.885171\pi$
$727$	−1172.89	+	277.981i	−1.61333	+	0.382367i	−0.677698	+	0.735340i	$0.737022\pi$
$728$		0			0
$729$	182.198	+	705.865i	0.249929	+	0.968264i
$730$		0			0
$731$	309.611	+	1306.35i	0.423544	+	1.78707i
$732$		0			0
$733$	85.3175	−	42.8480i	0.116395	−	0.0584557i	−0.389649	−	0.920963i	$-0.627404\pi$
$733$	85.3175	−	42.8480i	0.116395	−	0.0584557i	0.506044	+	0.862508i	$0.331107\pi$
$734$		0			0
$735$	−501.320	+	298.201i	−0.682068	+	0.405716i
$736$		0			0
$737$	796.055	+	948.701i	1.08013	+	1.28725i
$738$		0			0
$739$	−640.804	−	537.699i	−0.867124	−	0.727603i	0.0963669	−	0.995346i	$-0.469278\pi$
$739$	−640.804	−	537.699i	−0.867124	−	0.727603i	−0.963490	+	0.267743i	$0.913722\pi$
$740$		0			0
$741$	563.203	+	581.609i	0.760058	+	0.784898i
$742$		0			0
$743$	−464.350	−	438.092i	−0.624966	−	0.589625i	0.307205	−	0.951643i	$-0.400606\pi$
$743$	−464.350	−	438.092i	−0.624966	−	0.589625i	−0.932171	+	0.362018i	$0.882088\pi$
$744$		0			0
$745$	63.2080	−	84.9030i	0.0848429	−	0.113964i
$746$		0			0
$747$	−555.728	−	497.616i	−0.743947	−	0.666153i
$748$		0			0
$749$	−39.2714	+	78.1958i	−0.0524318	+	0.104400i
$750$		0			0
$751$	300.724	−	35.1496i	0.400432	−	0.0468038i	0.0865062	−	0.996251i	$-0.472430\pi$
$751$	300.724	−	35.1496i	0.400432	−	0.0468038i	0.313926	+	0.949448i	$0.398356\pi$
$752$		0			0
$753$	−33.5132	+	52.4278i	−0.0445063	+	0.0696253i
$754$		0			0
$755$	160.987	−	92.9462i	0.213228	−	0.123108i
$756$		0			0
$757$	353.782	−	612.769i	0.467348	−	0.809470i	−0.531956	−	0.846772i	$-0.678543\pi$
$757$	353.782	−	612.769i	0.467348	−	0.809470i	0.999304	+	0.0373019i	$0.0118763\pi$
$758$		0			0
$759$	564.362	−	1356.61i	0.743560	−	1.78736i
$760$		0			0
$761$	−1031.17	−	444.802i	−1.35502	−	0.584496i	−0.410168	−	0.912010i	$-0.634530\pi$
$761$	−1031.17	−	444.802i	−1.35502	−	0.584496i	−0.944847	+	0.327513i	$0.893789\pi$
$762$		0			0
$763$	−130.445	−	2239.65i	−0.170963	−	2.93532i
$764$		0			0
$765$	265.078	−	488.032i	0.346507	−	0.637950i
$766$		0			0
$767$	−41.9990	+	18.1166i	−0.0547575	+	0.0236201i
$768$		0			0
$769$	−436.895	−	103.546i	−0.568134	−	0.134650i	−0.0634974	−	0.997982i	$-0.520225\pi$
$769$	−436.895	−	103.546i	−0.568134	−	0.134650i	−0.504637	+	0.863332i	$0.668374\pi$
$770$		0			0
$771$	−193.869	+	398.883i	−0.251451	+	0.517358i
$772$		0			0
$773$	−18.9818	−	52.1520i	−0.0245560	−	0.0674670i	0.926809	−	0.375533i	$-0.122540\pi$
$773$	−18.9818	−	52.1520i	−0.0245560	−	0.0674670i	−0.951365	+	0.308066i	$0.900318\pi$
$774$		0			0
$775$	−309.753	−	112.741i	−0.399682	−	0.145472i
$776$		0			0
$777$	−1370.58	−	478.748i	−1.76394	−	0.616149i
$778$		0			0
$779$	−1724.90	−	100.464i	−2.21425	−	0.128965i
$780$		0			0
$781$	199.820	+	211.797i	0.255852	+	0.271187i
$782$		0			0
$783$	613.389	−	59.8190i	0.783383	−	0.0763971i
$784$		0			0
$785$	−598.375	−	179.142i	−0.762261	−	0.228206i
$786$		0			0
$787$	734.950	+	483.384i	0.933862	+	0.614211i	0.922613	−	0.385726i	$-0.126049\pi$
$787$	734.950	+	483.384i	0.933862	+	0.614211i	0.0112488	+	0.999937i	$0.496419\pi$
$788$		0			0
$789$	−1394.63	−	227.240i	−1.76759	−	0.288011i
$790$		0			0
$791$	1727.24	−	304.559i	2.18361	−	0.385030i
$792$		0			0
$793$	66.6371	−	377.918i	0.0840316	−	0.476567i
$794$		0			0
$795$	−68.1184	−	152.431i	−0.0856836	−	0.191738i
$796$		0			0
$797$	−110.704	+	33.1427i	−0.138901	+	0.0415843i	−0.355499	−	0.934677i	$-0.615689\pi$
$797$	−110.704	+	33.1427i	−0.138901	+	0.0415843i	0.216598	+	0.976261i	$0.430504\pi$
$798$		0			0
$799$	1540.00	+	180.000i	1.92741	+	0.225282i
$800$		0			0
$801$	1084.18	+	294.070i	1.35354	+	0.367128i
$802$		0			0
$803$	1317.85	+	2003.69i	1.64116	+	2.49526i
$804$		0			0
$805$	−467.523	−	627.993i	−0.580775	−	0.780116i
$806$		0			0
$807$	−191.706	−	176.207i	−0.237554	−	0.218349i
$808$		0			0
$809$			993.943i			1.22861i	0.789070	+	0.614303i	$0.210563\pi$
$809$			993.943i			1.22861i	−0.789070	+	0.614303i	$0.789437\pi$
$810$		0			0
$811$	−669.459			−0.825473			−0.412737	−	0.910850i	$-0.635427\pi$
$811$	−669.459			−0.825473			−0.412737	+	0.910850i	$0.635427\pi$
$812$		0			0
$813$	−589.496	−	131.636i	−0.725087	−	0.161914i
$814$		0			0
$815$	46.8953	−	34.9122i	0.0575402	−	0.0428371i
$816$		0			0
$817$	1268.89	−	834.560i	1.55311	−	1.02149i
$818$		0			0
$819$	−954.597	−	86.4646i	−1.16556	−	0.105573i
$820$		0			0
$821$	138.775	−	1187.29i	0.169031	−	1.44615i	−0.596426	−	0.802668i	$-0.703413\pi$
$821$	138.775	−	1187.29i	0.169031	−	1.44615i	0.765458	−	0.643486i	$-0.222513\pi$
$822$		0			0
$823$	14.4857	+	48.3857i	0.0176011	+	0.0587918i	0.966339	−	0.257272i	$-0.0828237\pi$
$823$	14.4857	+	48.3857i	0.0176011	+	0.0587918i	−0.948738	+	0.316064i	$0.897639\pi$
$824$		0			0
$825$	102.016	−	983.643i	0.123656	−	1.19229i
$826$		0			0
$827$	860.830	+	151.788i	1.04091	+	0.183540i	0.667871	−	0.744277i	$-0.267206\pi$
$827$	860.830	+	151.788i	1.04091	+	0.183540i	0.373036	+	0.927817i	$0.378317\pi$
$828$		0			0
$829$	237.360	+	1346.13i	0.286320	+	1.62380i	0.700530	+	0.713623i	$0.252947\pi$
$829$	237.360	+	1346.13i	0.286320	+	1.62380i	−0.414210	+	0.910181i	$0.635942\pi$
$830$		0			0
$831$	−162.154	+	61.4202i	−0.195131	+	0.0739111i
$832$		0			0
$833$	1122.75	−	1707.06i	1.34784	−	2.04929i
$834$		0			0
$835$	106.574	−	355.982i	0.127633	−	0.426325i
$836$		0			0
$837$	305.856	−	350.650i	0.365419	−	0.418937i
$838$		0			0
$839$	−29.4605	+	27.7945i	−0.0351138	+	0.0331282i	−0.703599	−	0.710598i	$-0.748425\pi$
$839$	−29.4605	+	27.7945i	−0.0351138	+	0.0331282i	0.668485	+	0.743726i	$0.266943\pi$
$840$		0			0
$841$	−18.6051	+	319.438i	−0.0221226	+	0.379831i
$842$		0			0
$843$	−89.9565	−	104.416i	−0.106710	−	0.123862i
$844$		0			0
$845$	−67.3289	+	184.985i	−0.0796792	+	0.218917i
$846$		0			0
$847$	−1880.13	+	684.312i	−2.21975	+	0.807924i
$848$		0			0
$849$	53.9923	+	757.144i	0.0635952	+	0.891807i
$850$		0			0
$851$	278.995	−	1177.17i	0.327844	−	1.38328i
$852$		0			0
$853$	138.171	+	320.316i	0.161982	+	0.375517i	0.979806	−	0.199953i	$-0.0640788\pi$
$853$	138.171	+	320.316i	0.161982	+	0.375517i	−0.817824	+	0.575469i	$0.804820\pi$
$854$		0			0
$855$	−621.348	−	92.9598i	−0.726723	−	0.108725i
$856$		0			0
$857$	663.836	−	38.6640i	0.774604	−	0.0451156i	0.333711	−	0.942675i	$-0.391699\pi$
$857$	663.836	−	38.6640i	0.774604	−	0.0451156i	0.440893	+	0.897560i	$0.354662\pi$
$858$		0			0
$859$	−24.2679	+	56.2593i	−0.0282513	+	0.0654939i	−0.931758	−	0.363081i	$-0.881725\pi$
$859$	−24.2679	+	56.2593i	−0.0282513	+	0.0654939i	0.903506	+	0.428575i	$0.140984\pi$
$860$		0			0
$861$	1624.78	−	1242.79i	1.88709	−	1.44342i
$862$		0			0
$863$	1247.51	+	720.249i	1.44555	+	0.834588i	0.998212	−	0.0597780i	$-0.0190393\pi$
$863$	1247.51	+	720.249i	1.44555	+	0.834588i	0.447337	+	0.894366i	$0.352373\pi$
$864$		0			0
$865$	351.691	+	609.147i	0.406580	+	0.704217i
$866$		0			0
$867$	−48.6875	+	1077.25i	−0.0561563	+	1.24251i
$868$		0			0
$869$	−85.0648	−	727.776i	−0.0978881	−	0.837487i
$870$		0			0
$871$	601.613	+	302.141i	0.690715	+	0.346890i
$872$		0			0
$873$	−34.8673	+	1084.05i	−0.0399396	+	1.24175i
$874$		0			0
$875$	−975.100	−	725.935i	−1.11440	−	0.829640i
$876$		0			0
$877$	−676.444	+	716.988i	−0.771315	+	0.817547i	−0.987303	−	0.158850i	$-0.949222\pi$
$877$	−676.444	+	716.988i	−0.771315	+	0.817547i	0.215987	+	0.976396i	$0.430703\pi$
$878$		0			0
$879$	−99.9482	−	398.532i	−0.113707	−	0.453392i
$880$		0			0
$881$	984.733	−	1173.56i	1.11774	−	1.33208i	0.180432	−	0.983587i	$-0.442250\pi$
$881$	984.733	−	1173.56i	1.11774	−	1.33208i	0.937313	−	0.348489i	$-0.113305\pi$
$882$		0			0
$883$	81.8590	−	68.6879i	0.0927056	−	0.0777892i	−0.595257	−	0.803535i	$-0.702950\pi$
$883$	81.8590	−	68.6879i	0.0927056	−	0.0777892i	0.687963	+	0.725746i	$0.258505\pi$
$884$		0			0
$885$	17.3457	−	30.9674i	0.0195997	−	0.0349914i
$886$		0			0
$887$	691.247	+	1376.39i	0.779309	+	1.55173i	0.833063	+	0.553178i	$0.186585\pi$
$887$	691.247	+	1376.39i	0.779309	+	1.55173i	−0.0537539	+	0.998554i	$0.517119\pi$
$888$		0			0
$889$	−1312.17	+	310.990i	−1.47601	+	0.349820i
$890$		0			0
$891$	1243.58	+	634.124i	1.39572	+	0.711699i
$892$		0			0
$893$	−404.494	−	1706.69i	−0.452960	−	1.91119i
$894$		0			0
$895$	138.450	−	69.5320i	0.154692	−	0.0776893i
$896$		0			0
$897$	−10.3930	−	798.658i	−0.0115864	−	0.890366i
$898$		0			0
$899$	−252.850	−	301.335i	−0.281257	−	0.335189i
$900$		0			0
$901$	447.999	+	375.916i	0.497224	+	0.417220i
$902$		0			0
$903$	−493.230	+	1729.08i	−0.546212	+	1.91481i
$904$		0			0
$905$	218.217	+	205.877i	0.241124	+	0.227489i
$906$		0			0
$907$	−7.22826	+	9.70924i	−0.00796942	+	0.0107048i	−0.806090	−	0.591793i	$-0.798420\pi$
$907$	−7.22826	+	9.70924i	−0.00796942	+	0.0107048i	0.798121	+	0.602498i	$0.205828\pi$
$908$		0			0
$909$	−22.4983	−	156.946i	−0.0247506	−	0.172658i
$910$		0			0
$911$	−238.505	+	474.902i	−0.261806	+	0.521298i	−0.985678	−	0.168636i	$-0.946064\pi$
$911$	−238.505	+	474.902i	−0.261806	+	0.521298i	0.723873	+	0.689933i	$0.242360\pi$
$912$		0			0
$913$	−1418.74	+	165.827i	−1.55394	+	0.181629i
$914$		0			0
$915$	137.100	+	264.355i	0.149836	+	0.288912i
$916$		0			0
$917$	−1037.92	+	599.243i	−1.13186	+	0.653482i
$918$		0			0
$919$	−31.5108	+	54.5782i	−0.0342881	+	0.0593887i	−0.882660	−	0.470012i	$-0.844250\pi$
$919$	−31.5108	+	54.5782i	−0.0342881	+	0.0593887i	0.848372	+	0.529400i	$0.177583\pi$
$920$		0			0
$921$	588.379	−	76.5447i	0.638848	−	0.0831104i
$922$		0			0
$923$	145.342	+	62.6942i	0.157466	+	0.0679244i
$924$		0			0
$925$	−47.3439	−	812.863i	−0.0511826	−	0.878770i
$926$		0			0
$927$	−755.813	+	668.478i	−0.815333	+	0.721120i
$928$		0			0
$929$	−1173.03	+	505.997i	−1.26268	+	0.544669i	−0.918941	−	0.394395i	$-0.870954\pi$
$929$	−1173.03	+	505.997i	−1.26268	+	0.544669i	−0.343743	+	0.939064i	$0.611695\pi$
$930$		0			0
$931$	−2249.04	−	533.032i	−2.41572	−	0.572537i
$932$		0			0
$933$	−86.6739	−	128.119i	−0.0928981	−	0.137319i
$934$		0			0
$935$	−363.725	−	999.326i	−0.389011	−	1.06880i
$936$		0			0
$937$	−1126.63	−	410.059i	−1.20238	−	0.437629i	−0.338323	−	0.941030i	$-0.609860\pi$
$937$	−1126.63	−	410.059i	−1.20238	−	0.437629i	−0.864053	+	0.503401i	$0.832082\pi$
$938$		0			0
$939$	−226.341	−	1192.68i	−0.241045	−	1.27016i
$940$		0			0
$941$	−1077.40	−	62.7516i	−1.14495	−	0.0666860i	−0.524843	−	0.851199i	$-0.675876\pi$
$941$	−1077.40	−	62.7516i	−1.14495	−	0.0666860i	−0.620112	+	0.784513i	$0.712913\pi$
$942$		0			0
$943$	1169.77	+	1239.88i	1.24047	+	1.31482i
$944$		0			0
$945$	629.152	−	396.760i	0.665769	−	0.419852i
$946$		0			0
$947$	1481.61	+	443.564i	1.56453	+	0.468389i	0.947821	−	0.318803i	$-0.103281\pi$
$947$	1481.61	+	443.564i	1.56453	+	0.468389i	0.616707	+	0.787192i	$0.288466\pi$
$948$		0			0
$949$	1089.22	+	716.388i	1.14775	+	0.754888i
$950$		0			0
$951$	942.451	−	1153.32i	0.991010	−	1.21274i
$952$		0			0
$953$	−1627.55	+	286.981i	−1.70782	+	0.301134i	−0.940414	−	0.340031i	$-0.889562\pi$
$953$	−1627.55	+	286.981i	−1.70782	+	0.301134i	−0.767403	+	0.641166i	$0.778451\pi$
$954$		0			0
$955$	−79.3774	+	450.171i	−0.0831177	+	0.471384i
$956$		0			0
$957$	692.342	−	955.691i	0.723451	−	0.998633i
$958$		0			0
$959$	−1112.94	+	333.193i	−1.16052	+	0.347438i
$960$		0			0
$961$	659.524	+	77.0873i	0.686289	+	0.0802157i
$962$		0			0
$963$	29.4690	−	62.6942i	0.0306013	−	0.0651031i
$964$		0			0
$965$	75.2113	+	114.353i	0.0779391	+	0.118501i
$966$		0			0
$967$	−258.346	−	347.019i	−0.267163	−	0.358862i	0.648215	−	0.761457i	$-0.275516\pi$
$967$	−258.346	−	347.019i	−0.267163	−	0.358862i	−0.915378	+	0.402595i	$0.868108\pi$
$968$		0			0
$969$	2099.82	−	658.537i	2.16700	−	0.679604i
$970$		0			0
$971$		−	696.158i		−	0.716950i	−0.933539	−	0.358475i	$-0.883297\pi$
$971$		−	696.158i		−	0.716950i	0.933539	−	0.358475i	$-0.116703\pi$
$972$		0			0
$973$	1516.19			1.55826
$974$		0			0
$975$	−160.868	−	512.946i	−0.164993	−	0.526099i
$976$		0			0
$977$	1100.00	−	818.920i	1.12590	−	0.838198i	0.137561	−	0.990493i	$-0.456074\pi$
$977$	1100.00	−	818.920i	1.12590	−	0.838198i	0.988335	+	0.152295i	$0.0486664\pi$
$978$		0			0
$979$	1797.19	−	1182.03i	1.83574	−	1.20738i
$980$		0			0
$981$	149.374	+	1769.80i	0.152267	+	1.80408i
$982$		0			0
$983$	126.551	−	1082.71i	0.128739	−	1.10143i	−0.762209	−	0.647331i	$-0.775885\pi$
$983$	126.551	−	1082.71i	0.128739	−	1.10143i	0.890949	−	0.454104i	$-0.150041\pi$
$984$		0			0
$985$	41.2454	+	137.769i	0.0418735	+	0.139867i
$986$		0			0
$987$	1681.64	+	1218.25i	1.70379	+	1.23429i
$988$		0			0
$989$	−1475.56	−	260.181i	−1.49197	−	0.263075i
$990$		0			0
$991$	80.0598	+	454.042i	0.0807869	+	0.458165i	0.998186	+	0.0601979i	$0.0191732\pi$
$991$	80.0598	+	454.042i	0.0807869	+	0.458165i	−0.917400	+	0.397967i	$0.869716\pi$
$992$		0			0
$993$	441.582	+	360.845i	0.444695	+	0.363388i
$994$		0			0
$995$	−214.894	+	326.730i	−0.215974	+	0.328372i
$996$		0			0
$997$	−50.3762	+	168.268i	−0.0505278	+	0.168775i	−0.979529	−	0.201301i	$-0.935483\pi$
$997$	−50.3762	+	168.268i	−0.0505278	+	0.168775i	0.929002	+	0.370076i	$0.120668\pi$
$998$		0			0
$999$	1094.56	+	350.652i	1.09566	+	0.351003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.5.11	✓	324
81.65	odd	54	inner	324.3.o.a.65.11	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.11	✓	324	1.1	even	1	trivial
324.3.o.a.65.11	yes	324	81.65	odd	54	inner

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.o (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.897733 + 2.86253i) q^{3} +(-1.94378 + 1.44709i) q^{5} +(9.49800 - 6.24693i) q^{7} +(-7.38815 + 5.13957i) q^{9} +O(q^{10})\)	\(q+(0.897733 + 2.86253i) q^{3} +(-1.94378 + 1.44709i) q^{5} +(9.49800 - 6.24693i) q^{7} +(-7.38815 + 5.13957i) q^{9} +(-2.00071 + 17.1171i) q^{11} +(2.68685 + 8.97472i) q^{13} +(-5.88732 - 4.26502i) q^{15} +(25.0778 + 4.42190i) q^{17} +(-5.00224 - 28.3691i) q^{19} +(26.4087 + 21.5802i) q^{21} +(-15.6168 + 23.7441i) q^{23} +(-5.48588 + 18.3241i) q^{25} +(-21.3448 - 16.5348i) q^{27} +(-16.6029 + 15.6641i) q^{29} +(-1.00203 + 17.2041i) q^{31} +(-50.7944 + 9.63953i) q^{33} +(-9.42213 + 25.8871i) q^{35} +(-40.0015 + 14.5594i) q^{37} +(-23.2783 + 15.7481i) q^{39} +(13.8323 - 58.3631i) q^{41} +(20.8820 + 48.4098i) q^{43} +(6.92350 - 20.6815i) q^{45} +(60.7845 - 3.54029i) q^{47} +(31.7799 - 73.6741i) q^{49} +(9.85538 + 75.7557i) q^{51} +(19.8891 + 11.4830i) q^{53} +(-20.8811 - 36.1671i) q^{55} +(76.7167 - 39.7869i) q^{57} +(0.566813 + 4.84939i) q^{59} +(-36.6054 - 18.3839i) q^{61} +(-38.0661 + 94.9689i) q^{63} +(-18.2098 - 13.5567i) q^{65} +(49.3145 - 52.2704i) q^{67} +(-81.9880 - 23.3876i) q^{69} +(10.8606 - 12.9431i) q^{71} +(106.603 - 89.4502i) q^{73} +(-57.3781 + 0.746666i) q^{75} +(87.9269 + 175.077i) q^{77} +(-41.3713 + 9.80519i) q^{79} +(28.1696 - 75.9439i) q^{81} +(19.1145 + 80.6503i) q^{83} +(-55.1446 + 27.6946i) q^{85} +(-59.7439 - 33.4643i) q^{87} +(-80.2312 - 95.6158i) q^{89} +(81.5842 + 68.4572i) q^{91} +(-50.1469 + 12.5764i) q^{93} +(50.7758 + 47.9045i) q^{95} +(71.9647 - 96.6654i) q^{97} +(-73.1933 - 136.747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 324 * q	\( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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