LMFDB - Embedded newform 324.3.o.a.65.11

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			65.11
Character	$\chi$	$=$	324.65
Dual form			324.3.o.a.5.11

$q$-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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{31}{54}\right)$

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	0.384982	−	0.922924i	$-0.374208\pi$
$5$	−1.94378	−	1.44709i	−0.388755	−	0.289418i	−0.773737	+	0.633506i	$0.781615\pi$
$6$		0			0
$7$	9.49800	+	6.24693i	1.35686	+	0.892419i	0.999142	−	0.0414120i	$-0.0131856\pi$
$7$	9.49800	+	6.24693i	1.35686	+	0.892419i	0.357715	+	0.933831i	$0.383556\pi$
$8$		0			0
$9$	−7.38815	−	5.13957i	−0.820906	−	0.571064i
$10$		0			0
$11$	−2.00071	−	17.1171i	−0.181882	−	1.55610i	−0.708321	−	0.705890i	$-0.750547\pi$
$11$	−2.00071	−	17.1171i	−0.181882	−	1.55610i	0.526439	−	0.850213i	$-0.323527\pi$
$12$		0			0
$13$	2.68685	−	8.97472i	0.206681	−	0.690363i	−0.790300	−	0.612720i	$-0.790075\pi$
$13$	2.68685	−	8.97472i	0.206681	−	0.690363i	0.996981	−	0.0776429i	$-0.0247394\pi$
$14$		0			0
$15$	−5.88732	+	4.26502i	−0.392488	+	0.284335i
$16$		0			0
$17$	25.0778	−	4.42190i	1.47517	−	0.260112i	0.622522	−	0.782603i	$-0.286108\pi$
$17$	25.0778	−	4.42190i	1.47517	−	0.260112i	0.852645	+	0.522491i	$0.174997\pi$
$18$		0			0
$19$	−5.00224	+	28.3691i	−0.263276	+	1.49311i	0.510625	+	0.859804i	$0.329414\pi$
$19$	−5.00224	+	28.3691i	−0.263276	+	1.49311i	−0.773900	+	0.633307i	$0.781697\pi$
$20$		0			0
$21$	26.4087	−	21.5802i	1.25756	−	1.02763i
$22$		0			0
$23$	−15.6168	−	23.7441i	−0.678990	−	1.03235i	−0.996459	−	0.0840855i	$-0.973203\pi$
$23$	−15.6168	−	23.7441i	−0.678990	−	1.03235i	0.317468	−	0.948269i	$-0.397167\pi$
$24$		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	0.344607	−	0.938747i	$-0.388012\pi$
$29$	−16.6029	−	15.6641i	−0.572515	−	0.540140i	−0.917122	+	0.398607i	$0.869494\pi$
$30$		0			0
$31$	−1.00203	−	17.2041i	−0.0323235	−	0.554972i	−0.975130	−	0.221633i	$-0.928861\pi$
$31$	−1.00203	−	17.2041i	−0.0323235	−	0.554972i	0.942807	−	0.333340i	$-0.108176\pi$
$32$		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	−0.260797	−	0.965394i	$-0.583985\pi$
$37$	−40.0015	−	14.5594i	−1.08112	−	0.393496i	−0.820325	+	0.571898i	$0.806207\pi$
$38$		0			0
$39$	−23.2783	−	15.7481i	−0.596880	−	0.403797i
$40$		0			0
$41$	13.8323	+	58.3631i	0.337373	+	1.42349i	0.832189	+	0.554492i	$0.187087\pi$
$41$	13.8323	+	58.3631i	0.337373	+	1.42349i	−0.494816	+	0.868998i	$0.664764\pi$
$42$		0			0
$43$	20.8820	−	48.4098i	0.485627	−	1.12581i	−0.482623	−	0.875828i	$-0.660316\pi$
$43$	20.8820	−	48.4098i	0.485627	−	1.12581i	0.968250	−	0.249982i	$-0.0804247\pi$
$44$		0			0
$45$	6.92350	+	20.6815i	0.153856	+	0.459589i
$46$		0			0
$47$	60.7845	+	3.54029i	1.29329	+	0.0753254i	0.690942	−	0.722910i	$-0.257196\pi$
$47$	60.7845	+	3.54029i	1.29329	+	0.0753254i	0.602345	+	0.798236i	$0.294233\pi$
$48$		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	−0.300491	−	0.953785i	$-0.597150\pi$
$53$	19.8891	−	11.4830i	0.375266	−	0.216660i	0.675757	+	0.737125i	$0.263817\pi$
$54$		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	−0.987584	−	0.157090i	$-0.949789\pi$
$59$	0.566813	−	4.84939i	0.00960700	−	0.0821931i	0.997191	+	0.0748969i	$0.0238628\pi$
$60$		0			0
$61$	−36.6054	+	18.3839i	−0.600088	+	0.301376i	−0.722790	−	0.691068i	$-0.757141\pi$
$61$	−36.6054	+	18.3839i	−0.600088	+	0.301376i	0.122702	+	0.992444i	$0.460844\pi$
$62$		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	0.981951	−	0.189137i	$-0.0605691\pi$
$67$	49.3145	+	52.2704i	0.736038	+	0.780155i	−0.245913	+	0.969292i	$0.579088\pi$
$68$		0			0
$69$	−81.9880	+	23.3876i	−1.18823	+	0.338950i
$70$		0			0
$71$	10.8606	+	12.9431i	0.152966	+	0.182297i	0.837085	−	0.547072i	$-0.184258\pi$
$71$	10.8606	+	12.9431i	0.152966	+	0.182297i	−0.684120	+	0.729370i	$0.739813\pi$
$72$		0			0
$73$	106.603	+	89.4502i	1.46031	+	1.22535i	0.924598	+	0.380944i	$0.124401\pi$
$73$	106.603	+	89.4502i	1.46031	+	1.22535i	0.535712	+	0.844401i	$0.320043\pi$
$74$		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	−0.0397347	−	0.999210i	$-0.512651\pi$
$79$	−41.3713	−	9.80519i	−0.523688	−	0.124116i	−0.483953	+	0.875094i	$0.660799\pi$
$80$		0			0
$81$	28.1696	+	75.9439i	0.347772	+	0.937579i
$82$		0			0
$83$	19.1145	−	80.6503i	0.230295	−	0.971690i	−0.727925	−	0.685657i	$-0.759515\pi$
$83$	19.1145	−	80.6503i	0.230295	−	0.971690i	0.958220	−	0.286033i	$-0.0923367\pi$
$84$		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	0.0954092	+	0.995438i	$0.469584\pi$
$89$	−80.2312	+	95.6158i	−0.901474	+	1.07433i	−0.996883	+	0.0788963i	$0.974860\pi$
$90$		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	0.999541	+	0.0303084i	$0.00964895\pi$
$97$	71.9647	+	96.6654i	0.741904	+	0.996550i	−0.257636	+	0.966242i	$0.582944\pi$
$98$		0			0
$99$	−73.1933	+	136.747i	−0.739326	+	1.38128i
$100$		0			0
$101$	−7.90639	−	15.7429i	−0.0782811	−	0.155870i	0.851087	−	0.525024i	$-0.175944\pi$
$101$	−7.90639	−	15.7429i	−0.0782811	−	0.155870i	−0.929368	+	0.369154i	$0.879648\pi$
$102$		0			0
$103$	111.355	+	13.0155i	1.08112	+	0.126364i	0.637952	−	0.770076i	$-0.279782\pi$
$103$	111.355	+	13.0155i	1.08112	+	0.126364i	0.443164	+	0.896440i	$0.353856\pi$
$104$		0			0
$105$	−82.5611	+	3.73143i	−0.786296	+	0.0355375i
$106$		0			0
$107$	−6.66597	−	3.84860i	−0.0622987	−	0.0359682i	0.468527	−	0.883449i	$-0.344785\pi$
$107$	−6.66597	−	3.84860i	−0.0622987	−	0.0359682i	−0.530826	+	0.847481i	$0.678118\pi$
$108$		0			0
$109$	98.6717	+	170.904i	0.905245	+	1.56793i	0.820588	+	0.571520i	$0.193646\pi$
$109$	98.6717	+	170.904i	0.905245	+	1.56793i	0.0846573	+	0.996410i	$0.473020\pi$
$110$		0			0
$111$	−77.5873	+	101.435i	−0.698984	+	0.913830i
$112$		0			0
$113$	141.662	−	61.1071i	1.25365	−	0.540771i	0.337392	−	0.941364i	$-0.390455\pi$
$113$	141.662	−	61.1071i	1.25365	−	0.540771i	0.916256	+	0.400594i	$0.131196\pi$
$114$		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	−0.741282	−	0.671194i	$-0.765782\pi$
$127$	−111.468	+	40.5711i	−0.877702	+	0.319458i	−0.136420	+	0.990651i	$0.543560\pi$
$128$		0			0
$129$	−119.828	−	103.234i	−0.928900	−	0.800266i
$130$		0			0
$131$	−105.246	+	6.12988i	−0.803404	+	0.0467930i	−0.454932	−	0.890526i	$-0.650336\pi$
$131$	−105.246	+	6.12988i	−0.803404	+	0.0467930i	−0.348472	+	0.937319i	$0.613299\pi$
$132$		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	−0.623406	−	0.781898i	$-0.714252\pi$
$137$	−97.8994	+	29.3092i	−0.714594	+	0.213935i	−0.0911881	+	0.995834i	$0.529066\pi$
$138$		0			0
$139$	111.430	−	73.2885i	0.801653	−	0.527255i	−0.0813154	−	0.996688i	$-0.525912\pi$
$139$	111.430	−	73.2885i	0.801653	−	0.527255i	0.882968	+	0.469433i	$0.155542\pi$
$140$		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	0.143288	−	0.989681i	$-0.454232\pi$
$149$	−41.8444	−	12.5274i	−0.280835	−	0.0840765i	−0.424123	+	0.905605i	$0.639418\pi$
$150$		0			0
$151$	−76.1921	+	8.90557i	−0.504583	+	0.0589773i	−0.364577	−	0.931173i	$-0.618786\pi$
$151$	−76.1921	+	8.90557i	−0.504583	+	0.0589773i	−0.140006	+	0.990151i	$0.544712\pi$
$152$		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	0.0320951	−	0.999485i	$-0.489782\pi$
$157$	153.921	−	206.751i	0.980386	−	1.31689i	0.948291	−	0.317402i	$-0.102811\pi$
$158$		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	0.162242	−	0.986751i	$-0.448127\pi$
$167$	−122.999	−	91.5696i	−0.736523	−	0.548321i	−0.898765	+	0.438430i	$0.855535\pi$
$168$		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	0.637995	+	0.770040i	$0.279764\pi$
$173$	33.6971	+	288.297i	0.194781	+	1.66646i	−0.443214	+	0.896416i	$0.646162\pi$
$174$		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	−0.346728	−	0.937966i	$-0.612707\pi$
$179$	−62.9620	+	11.1019i	−0.351743	+	0.0620218i	−0.00501485	+	0.999987i	$0.501596\pi$
$180$		0			0
$181$	−21.4979	+	121.921i	−0.118773	+	0.673595i	0.866040	+	0.499975i	$0.166658\pi$
$181$	−21.4979	+	121.921i	−0.118773	+	0.673595i	−0.984813	+	0.173620i	$0.944454\pi$
$182$		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	0.955919	−	0.293632i	$-0.0948640\pi$
$191$	137.208	+	129.449i	0.718365	+	0.677743i	−0.237553	+	0.971375i	$0.576345\pi$
$192$		0			0
$193$	3.28408	+	56.3855i	0.0170160	+	0.292153i	0.996071	+	0.0885574i	$0.0282257\pi$
$193$	3.28408	+	56.3855i	0.0170160	+	0.292153i	−0.979055	+	0.203595i	$0.934737\pi$
$194$		0			0
$195$	22.4590	+	64.2965i	0.115174	+	0.329726i
$196$		0			0
$197$	20.2973	+	55.7663i	0.103032	+	0.283078i	0.980488	−	0.196579i	$-0.0629833\pi$
$197$	20.2973	+	55.7663i	0.103032	+	0.283078i	−0.877456	+	0.479657i	$0.840761\pi$
$198$		0			0
$199$	151.646	+	55.1945i	0.762038	+	0.277359i	0.693662	−	0.720300i	$-0.255996\pi$
$199$	151.646	+	55.1945i	0.762038	+	0.277359i	0.0683760	+	0.997660i	$0.478218\pi$
$200$		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	0.729071	−	0.684438i	$-0.239952\pi$
$211$	−56.7781	−	131.626i	−0.269090	−	0.623822i	−0.998161	+	0.0606168i	$0.980693\pi$
$212$		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	−0.630488	−	0.776199i	$-0.717145\pi$
$223$	−85.7173	+	43.0489i	−0.384383	+	0.193044i	0.246106	+	0.969243i	$0.420849\pi$
$224$		0			0
$225$	−53.6476	+	163.576i	−0.238434	+	0.727006i
$226$		0			0
$227$	−136.664	+	101.742i	−0.602043	+	0.448204i	−0.854534	−	0.519395i	$-0.826157\pi$
$227$	−136.664	+	101.742i	−0.602043	+	0.448204i	0.252492	+	0.967599i	$0.418750\pi$
$228$		0			0
$229$	−63.0448	−	66.8236i	−0.275305	−	0.291806i	0.574938	−	0.818197i	$-0.305026\pi$
$229$	−63.0448	−	66.8236i	−0.275305	−	0.291806i	−0.850243	+	0.526391i	$0.823545\pi$
$230$		0			0
$231$	−422.228	−	408.865i	−1.82783	−	1.76998i
$232$		0			0
$233$	−63.5116	−	75.6902i	−0.272582	−	0.324851i	0.612336	−	0.790598i	$-0.290230\pi$
$233$	−63.5116	−	75.6902i	−0.272582	−	0.324851i	−0.884918	+	0.465747i	$0.845786\pi$
$234$		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	−0.986038	−	0.166521i	$-0.946747\pi$
$239$	−63.0115	+	125.466i	−0.263647	+	0.524964i	0.722391	+	0.691484i	$0.243043\pi$
$240$		0			0
$241$	−2.35460	−	0.558049i	−0.00977011	−	0.00231556i	0.225728	−	0.974190i	$-0.427524\pi$
$241$	−2.35460	−	0.558049i	−0.00977011	−	0.00231556i	−0.235498	+	0.971875i	$0.575672\pi$
$242$		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	−0.738832	−	0.673890i	$-0.764622\pi$
$251$	13.3323	−	15.8888i	0.0531166	−	0.0633018i	0.791949	+	0.610588i	$0.209067\pi$
$252$		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	−0.448043	−	0.894012i	$-0.647879\pi$
$257$	107.530	−	101.450i	0.418406	−	0.394745i	0.866448	+	0.499267i	$0.166397\pi$
$258$		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	−0.799690	−	0.600413i	$-0.795003\pi$
$263$	−211.387	−	420.906i	−0.803753	−	1.60040i	−0.00406289	−	0.999992i	$-0.501293\pi$
$264$		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	0.353736	−	0.935345i	$-0.384911\pi$
$269$	−75.1666	−	43.3974i	−0.279430	−	0.161329i	−0.633165	+	0.774017i	$0.718245\pi$
$270$		0			0
$271$	−100.669	−	174.364i	−0.371473	−	0.643409i	0.618320	−	0.785927i	$-0.287814\pi$
$271$	−100.669	−	174.364i	−0.371473	−	0.643409i	−0.989792	+	0.142517i	$0.954480\pi$
$272$		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	−0.986794	−	0.161981i	$-0.948212\pi$
$277$	3.36070	−	57.7010i	0.0121325	−	0.208307i	0.998926	−	0.0463259i	$-0.0147513\pi$
$278$		0			0
$279$	−81.0188	+	132.257i	−0.290390	+	0.474039i
$280$		0			0
$281$	−42.1834	−	18.1962i	−0.150119	−	0.0647550i	0.319695	−	0.947521i	$-0.396420\pi$
$281$	−42.1834	−	18.1962i	−0.150119	−	0.0647550i	−0.469814	+	0.882766i	$0.655679\pi$
$282$		0			0
$283$	246.202	−	58.3509i	0.869971	−	0.206187i	0.228696	−	0.973498i	$-0.426554\pi$
$283$	246.202	−	58.3509i	0.869971	−	0.206187i	0.641275	+	0.767311i	$0.278406\pi$
$284$		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	−0.289856	−	0.957070i	$-0.593607\pi$
$293$	−136.726	+	7.96340i	−0.466642	+	0.0271788i	−0.176787	+	0.984249i	$0.556570\pi$
$294$		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	0.988253	+	0.152829i	$0.0488384\pi$
$307$	34.3440	+	194.774i	0.111870	+	0.634444i	−0.876383	+	0.481615i	$0.840050\pi$
$308$		0			0
$309$	137.224	−	307.073i	0.444092	−	0.993762i
$310$		0			0
$311$	−49.3948	−	14.7878i	−0.158826	−	0.0475493i	0.206403	−	0.978467i	$-0.433824\pi$
$311$	−49.3948	−	14.7878i	−0.158826	−	0.0475493i	−0.365229	+	0.930918i	$0.619009\pi$
$312$		0			0
$313$	−401.918	+	46.9775i	−1.28408	+	0.150088i	−0.730620	−	0.682785i	$-0.760769\pi$
$313$	−401.918	+	46.9775i	−1.28408	+	0.150088i	−0.553465	+	0.832873i	$0.686695\pi$
$314$		0			0
$315$	−63.4365	+	239.683i	−0.201386	+	0.760900i
$316$		0			0
$317$	−272.816	+	414.796i	−0.860617	+	1.30851i	0.0893003	+	0.996005i	$0.471537\pi$
$317$	−272.816	+	414.796i	−0.860617	+	1.30851i	−0.949918	+	0.312500i	$0.898833\pi$
$318$		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	0.766272	−	0.642516i	$-0.222109\pi$
$331$	158.817	+	104.455i	0.479809	+	0.315575i	−0.286463	+	0.958091i	$0.592480\pi$
$332$		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	−0.818409	−	0.574636i	$-0.805144\pi$
$337$	61.0407	−	203.890i	0.181130	−	0.605015i	0.999538	−	0.0303785i	$-0.00967127\pi$
$338$		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	0.711030	−	0.703162i	$-0.248229\pi$
$347$	−75.0383	−	114.090i	−0.216249	−	0.328790i	−0.927279	+	0.374371i	$0.877859\pi$
$348$		0			0
$349$	−175.437	−	586.000i	−0.502684	−	1.67908i	−0.712768	−	0.701400i	$-0.752559\pi$
$349$	−175.437	−	586.000i	−0.502684	−	1.67908i	0.210084	−	0.977683i	$-0.432626\pi$
$350$		0			0
$351$	91.0452	+	235.990i	0.259388	+	0.672336i
$352$		0			0
$353$	366.717	+	345.979i	1.03886	+	0.980112i	0.999817	−	0.0191259i	$-0.00608832\pi$
$353$	366.717	+	345.979i	1.03886	+	0.980112i	0.0390407	+	0.999238i	$0.487570\pi$
$354$		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	−0.970080	−	0.242787i	$-0.921938\pi$
$359$	−137.503	−	377.786i	−0.383016	−	1.05233i	0.587063	−	0.809541i	$-0.300284\pi$
$360$		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	−0.745649	−	0.666339i	$-0.767860\pi$
$367$	92.0158	−	213.317i	0.250724	−	0.581244i	0.996373	+	0.0850954i	$0.0271195\pi$
$368$		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	0.969315	−	0.245821i	$-0.0790576\pi$
$373$	46.7469	+	108.372i	0.125327	+	0.290540i	−0.843988	+	0.536362i	$0.819798\pi$
$374$		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	−0.719496	−	0.694496i	$-0.755627\pi$
$379$	91.6055	−	158.665i	0.241703	−	0.418642i	0.961200	+	0.275854i	$0.0889607\pi$
$380$		0			0
$381$	16.0673	+	355.503i	0.0421715	+	0.933079i
$382$		0			0
$383$	9.72594	−	83.2108i	0.0253941	−	0.217260i	−0.974583	−	0.224027i	$-0.928080\pi$
$383$	9.72594	−	83.2108i	0.0253941	−	0.217260i	0.999977	+	0.00676626i	$0.00215378\pi$
$384$		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	−0.646615	−	0.762817i	$-0.723816\pi$
$389$	−39.4038	+	29.3350i	−0.101295	+	0.0754114i	0.545319	+	0.838228i	$0.316408\pi$
$390$		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	0.987066	+	0.160317i	$0.0512518\pi$
$397$	522.591	+	438.506i	1.31635	+	1.10455i	0.329284	+	0.944231i	$0.393193\pi$
$398$		0			0
$399$	480.109	+	857.141i	1.20328	+	2.14822i
$400$		0			0
$401$	−253.522	+	504.803i	−0.632223	+	1.25886i	0.318236	+	0.948012i	$0.396910\pi$
$401$	−253.522	+	504.803i	−0.632223	+	1.25886i	−0.950459	+	0.310849i	$0.899387\pi$
$402$		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	0.837261	−	0.546803i	$-0.184156\pi$
$409$	367.542	+	184.586i	0.898635	+	0.451311i	0.0613738	+	0.998115i	$0.480452\pi$
$410$		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	−0.445509	−	0.895277i	$-0.646977\pi$
$419$	176.964	−	166.957i	0.422349	−	0.398466i	0.867859	+	0.496811i	$0.165496\pi$
$420$		0			0
$421$	258.380	+	347.064i	0.613728	+	0.824380i	0.994978	−	0.100092i	$-0.0319136\pi$
$421$	258.380	+	347.064i	0.613728	+	0.824380i	−0.381250	+	0.924472i	$0.624506\pi$
$422$		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	0.686957	−	0.726698i	$-0.258946\pi$
$431$	172.873	+	99.8080i	0.401096	+	0.231573i	−0.285861	+	0.958271i	$0.592279\pi$
$432$		0			0
$433$	−3.08649	−	5.34596i	−0.00712815	−	0.0123463i	0.862439	−	0.506160i	$-0.168936\pi$
$433$	−3.08649	−	5.34596i	−0.00712815	−	0.0123463i	−0.869567	+	0.493814i	$0.835602\pi$
$434$		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	−0.937842	−	0.347063i	$-0.887179\pi$
$439$	14.9041	−	255.894i	0.0339502	−	0.582902i	0.971792	−	0.235839i	$-0.0757838\pi$
$440$		0			0
$441$	143.859	−	707.651i	0.326210	−	1.60465i
$442$		0			0
$443$	657.070	+	283.432i	1.48323	+	0.639802i	0.975157	−	0.221513i	$-0.0710996\pi$
$443$	657.070	+	283.432i	1.48323	+	0.639802i	0.508071	+	0.861315i	$0.330359\pi$
$444$		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	−0.883990	−	0.467506i	$-0.845153\pi$
$449$	42.0679	−	115.581i	0.0936924	−	0.257418i	0.977683	+	0.210088i	$0.0673750\pi$
$450$		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	−0.803174	−	0.595744i	$-0.796857\pi$
$457$	−73.9143	+	78.3445i	−0.161738	+	0.171432i	0.641436	+	0.767176i	$0.278339\pi$
$458$		0			0
$459$	−462.165	+	509.042i	−1.00690	+	1.10902i
$460$		0			0
$461$	−25.4979	+	7.63356i	−0.0553099	+	0.0165587i	−0.314339	−	0.949311i	$-0.601783\pi$
$461$	−25.4979	+	7.63356i	−0.0553099	+	0.0165587i	0.259029	+	0.965870i	$0.416598\pi$
$462$		0			0
$463$	−271.756	+	178.737i	−0.586946	+	0.386041i	−0.807966	−	0.589229i	$-0.799432\pi$
$463$	−271.756	+	178.737i	−0.586946	+	0.386041i	0.221020	+	0.975269i	$0.429061\pi$
$464$		0			0
$465$	79.2753	+	97.0127i	0.170484	+	0.208629i
$466$		0			0
$467$	−686.646	−	121.074i	−1.47033	−	0.259260i	−0.619625	−	0.784898i	$-0.712715\pi$
$467$	−686.646	−	121.074i	−1.47033	−	0.259260i	−0.850708	+	0.525638i	$0.823827\pi$
$468$		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	−0.937671	−	0.347524i	$-0.887023\pi$
$479$	−118.398	+	180.015i	−0.247177	+	0.375814i	0.690495	+	0.723338i	$0.257393\pi$
$480$		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	0.992608	−	0.121367i	$-0.0387279\pi$
$491$	570.062	+	424.395i	1.16102	+	0.864349i	0.168414	+	0.985716i	$0.446135\pi$
$492$		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	−0.866630	−	0.498951i	$-0.833719\pi$
$499$	65.6719	−	219.360i	0.131607	−	0.439598i	0.998237	+	0.0593531i	$0.0189038\pi$
$500$		0			0
$501$	−372.541	+	269.884i	−0.743595	+	0.538691i
$502$		0			0
$503$	−666.492	+	117.521i	−1.32503	+	0.233639i	−0.790996	−	0.611821i	$-0.790437\pi$
$503$	−666.492	+	117.521i	−1.32503	+	0.233639i	−0.534038	+	0.845460i	$0.679326\pi$
$504$		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	0.436437	−	0.899735i	$-0.356240\pi$
$509$	−286.352	−	435.378i	−0.562578	−	0.855359i	−0.999015	+	0.0443764i	$0.985870\pi$
$510$		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	0.810222	−	0.586124i	$-0.199347\pi$
$521$	−97.5297	−	267.961i	−0.187197	−	0.514320i	−0.997419	+	0.0718036i	$0.977125\pi$
$522$		0			0
$523$	−72.7892	−	26.4931i	−0.139176	−	0.0506560i	0.271493	−	0.962440i	$-0.412483\pi$
$523$	−72.7892	−	26.4931i	−0.139176	−	0.0506560i	−0.410669	+	0.911784i	$0.634705\pi$
$524$		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	−0.667784	−	0.744355i	$-0.732757\pi$
$541$	168.110	−	291.174i	0.310739	−	0.538215i	0.978522	+	0.206140i	$0.0660903\pi$
$542$		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	0.206573	−	0.978431i	$-0.433769\pi$
$547$	609.769	−	306.238i	1.11475	−	0.559849i	0.908179	+	0.418582i	$0.137473\pi$
$548$		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	0.906144	−	0.422969i	$-0.139012\pi$
$557$	185.064	+	220.550i	0.332251	+	0.395961i	−0.573894	+	0.818930i	$0.694568\pi$
$558$		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	−0.986851	−	0.161633i	$-0.948324\pi$
$563$	−150.825	+	300.316i	−0.267894	+	0.533422i	0.718956	+	0.695055i	$0.244620\pi$
$564$		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	−0.816040	−	0.577995i	$-0.803835\pi$
$569$	98.2115	−	414.387i	0.172604	−	0.728272i	0.988644	−	0.150277i	$-0.0480166\pi$
$570$		0			0
$571$	339.515	+	170.511i	0.594597	+	0.298618i	0.720533	−	0.693420i	$-0.243897\pi$
$571$	339.515	+	170.511i	0.594597	+	0.298618i	−0.125936	+	0.992038i	$0.540193\pi$
$572$		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	−0.672518	−	0.740081i	$-0.734787\pi$
$577$	−34.8869	+	29.2736i	−0.0604625	+	0.0507341i	0.612056	+	0.790815i	$0.290343\pi$
$578$		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	0.875439	−	0.483329i	$-0.160573\pi$
$587$	−20.5606	−	40.9395i	−0.0350266	−	0.0697436i	−0.910465	+	0.413586i	$0.864276\pi$
$588$		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	0.999529	−	0.0306787i	$-0.00976687\pi$
$593$	873.326	+	504.215i	1.47273	+	0.850278i	0.473196	+	0.880957i	$0.343100\pi$
$594$		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	−0.777662	−	0.628683i	$-0.783594\pi$
$599$	−511.569	+	220.669i	−0.854039	+	0.368396i	−0.0763767	+	0.997079i	$0.524335\pi$
$600$		0			0
$601$	−39.7856	+	683.092i	−0.0661989	+	1.13659i	0.787668	+	0.616100i	$0.211288\pi$
$601$	−39.7856	+	683.092i	−0.0661989	+	1.13659i	−0.853867	+	0.520492i	$0.825749\pi$
$602$		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	−0.110753	−	0.993848i	$-0.535326\pi$
$607$	143.441	−	33.9962i	0.236312	−	0.0560069i	0.347065	+	0.937841i	$0.387178\pi$
$608$		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	−0.687022	−	0.726637i	$-0.741082\pi$
$613$	−457.443	+	166.496i	−0.746237	+	0.271608i	−0.0592158	+	0.998245i	$0.518860\pi$
$614$		0			0
$615$	−330.355	−	284.607i	−0.537163	−	0.462776i
$616$		0			0
$617$	586.399	−	34.1538i	0.950403	−	0.0553547i	0.424066	−	0.905631i	$-0.360602\pi$
$617$	586.399	−	34.1538i	0.950403	−	0.0553547i	0.526336	+	0.850276i	$0.323565\pi$
$618$		0			0
$619$	−155.656	+	164.986i	−0.251464	+	0.266536i	−0.840793	−	0.541357i	$-0.817911\pi$
$619$	−155.656	+	164.986i	−0.251464	+	0.266536i	0.589329	+	0.807893i	$0.299392\pi$
$620$		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	−0.893357	−	0.449347i	$-0.851657\pi$
$631$	−130.972	−	742.777i	−0.207562	−	1.17714i	0.685795	−	0.727795i	$-0.259455\pi$
$632$		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	−0.344374	−	0.938833i	$-0.611909\pi$
$641$	419.263	−	637.459i	0.654077	−	0.994475i	0.998451	−	0.0556428i	$-0.0177208\pi$
$642$		0			0
$643$	−440.716	+	591.985i	−0.685406	+	0.920660i	−0.999588	−	0.0287026i	$-0.990862\pi$
$643$	−440.716	+	591.985i	−0.685406	+	0.920660i	0.314182	+	0.949363i	$0.398270\pi$
$644$		0			0
$645$	83.5300	+	374.066i	0.129504	+	0.579948i
$646$		0			0
$647$		−	250.378i		−	0.386982i	−0.981102	−	0.193491i	$-0.938019\pi$
$647$		−	250.378i		−	0.386982i	0.981102	−	0.193491i	$-0.0619811\pi$
$648$		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	0.972856	−	0.231409i	$-0.0743336\pi$
$653$	672.712	+	500.816i	1.03019	+	0.766946i	0.0573307	+	0.998355i	$0.481741\pi$
$654$		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	−0.988500	−	0.151224i	$-0.951679\pi$
$659$	−40.5416	−	346.855i	−0.0615198	−	0.526336i	0.926980	−	0.375111i	$-0.122396\pi$
$660$		0			0
$661$	−179.794	+	600.554i	−0.272003	+	0.908553i	0.707430	+	0.706783i	$0.249854\pi$
$661$	−179.794	+	600.554i	−0.272003	+	0.908553i	−0.979433	+	0.201770i	$0.935331\pi$
$662$		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	−0.998965	−	0.0454768i	$-0.985519\pi$
$673$	−127.420	−	425.614i	−0.189332	−	0.632413i	0.809634	−	0.586936i	$-0.199666\pi$
$674$		0			0
$675$	420.081	+	300.416i	0.622342	+	0.445060i
$676$		0			0
$677$	−874.762	−	825.296i	−1.29212	−	1.21905i	−0.961348	−	0.275336i	$-0.911211\pi$
$677$	−874.762	−	825.296i	−1.29212	−	1.21905i	−0.330767	−	0.943712i	$-0.607308\pi$
$678$		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	−0.999996	−	0.00279413i	$-0.999111\pi$
$683$	−161.018	−	442.393i	−0.235751	−	0.647720i	0.764245	−	0.644926i	$-0.223112\pi$
$684$		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	0.0538885	−	0.998547i	$-0.482838\pi$
$691$	513.568	−	1190.59i	0.743225	−	1.72299i	0.689336	−	0.724442i	$-0.257902\pi$
$692$		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	−0.559030	−	0.829147i	$-0.688826\pi$
$701$	−84.4585	+	48.7621i	−0.120483	+	0.0695608i	0.438547	+	0.898708i	$0.355493\pi$
$702$		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	−0.582659	−	0.812717i	$-0.697988\pi$
$709$	−197.598	+	99.2375i	−0.278700	+	0.139968i	0.303959	+	0.952685i	$0.401691\pi$
$710$		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	0.984405	−	0.175915i	$-0.0562883\pi$
$719$	460.320	+	548.589i	0.640223	+	0.762988i	−0.344182	+	0.938903i	$0.611844\pi$
$720$		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	−0.677698	−	0.735340i	$-0.737022\pi$
$727$	−1172.89	−	277.981i	−1.61333	−	0.382367i	−0.935633	+	0.352974i	$0.885171\pi$
$728$		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	0.506044	−	0.862508i	$-0.331107\pi$
$733$	85.3175	+	42.8480i	0.116395	+	0.0584557i	−0.389649	+	0.920963i	$0.627404\pi$
$734$		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	−0.963490	−	0.267743i	$-0.913722\pi$
$739$	−640.804	+	537.699i	−0.867124	+	0.727603i	0.0963669	+	0.995346i	$0.469278\pi$
$740$		0			0
$741$	563.203	−	581.609i	0.760058	−	0.784898i
$742$		0			0
$743$	−464.350	+	438.092i	−0.624966	+	0.589625i	−0.932171	−	0.362018i	$-0.882088\pi$
$743$	−464.350	+	438.092i	−0.624966	+	0.589625i	0.307205	+	0.951643i	$0.400606\pi$
$744$		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	0.313926	−	0.949448i	$-0.398356\pi$
$751$	300.724	+	35.1496i	0.400432	+	0.0468038i	0.0865062	+	0.996251i	$0.472430\pi$
$752$		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	0.999304	−	0.0373019i	$-0.0118763\pi$
$757$	353.782	+	612.769i	0.467348	+	0.809470i	−0.531956	+	0.846772i	$0.678543\pi$
$758$		0			0
$759$	564.362	+	1356.61i	0.743560	+	1.78736i
$760$		0			0
$761$	−1031.17	+	444.802i	−1.35502	+	0.584496i	−0.944847	−	0.327513i	$-0.893789\pi$
$761$	−1031.17	+	444.802i	−1.35502	+	0.584496i	−0.410168	+	0.912010i	$0.634530\pi$
$762$		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	−0.504637	−	0.863332i	$-0.668374\pi$
$769$	−436.895	+	103.546i	−0.568134	+	0.134650i	−0.0634974	+	0.997982i	$0.520225\pi$
$770$		0			0
$771$	−193.869	−	398.883i	−0.251451	−	0.517358i
$772$		0			0
$773$	−18.9818	+	52.1520i	−0.0245560	+	0.0674670i	−0.951365	−	0.308066i	$-0.900318\pi$
$773$	−18.9818	+	52.1520i	−0.0245560	+	0.0674670i	0.926809	+	0.375533i	$0.122540\pi$
$774$		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	0.0112488	−	0.999937i	$-0.496419\pi$
$787$	734.950	−	483.384i	0.933862	−	0.614211i	0.922613	+	0.385726i	$0.126049\pi$
$788$		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	0.216598	−	0.976261i	$-0.430504\pi$
$797$	−110.704	−	33.1427i	−0.138901	−	0.0415843i	−0.355499	+	0.934677i	$0.615689\pi$
$798$		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	$-0.789437\pi$
$809$		−	993.943i		−	1.22861i	0.789070	−	0.614303i	$-0.210563\pi$
$810$		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	0.765458	+	0.643486i	$0.222513\pi$
$821$	138.775	+	1187.29i	0.169031	+	1.44615i	−0.596426	+	0.802668i	$0.703413\pi$
$822$		0			0
$823$	14.4857	−	48.3857i	0.0176011	−	0.0587918i	−0.948738	−	0.316064i	$-0.897639\pi$
$823$	14.4857	−	48.3857i	0.0176011	−	0.0587918i	0.966339	+	0.257272i	$0.0828237\pi$
$824$		0			0
$825$	102.016	+	983.643i	0.123656	+	1.19229i
$826$		0			0
$827$	860.830	−	151.788i	1.04091	−	0.183540i	0.373036	−	0.927817i	$-0.378317\pi$
$827$	860.830	−	151.788i	1.04091	−	0.183540i	0.667871	+	0.744277i	$0.267206\pi$
$828$		0			0
$829$	237.360	−	1346.13i	0.286320	−	1.62380i	−0.414210	−	0.910181i	$-0.635942\pi$
$829$	237.360	−	1346.13i	0.286320	−	1.62380i	0.700530	−	0.713623i	$-0.252947\pi$
$830$		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	0.668485	−	0.743726i	$-0.266943\pi$
$839$	−29.4605	−	27.7945i	−0.0351138	−	0.0331282i	−0.703599	+	0.710598i	$0.748425\pi$
$840$		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	−0.817824	−	0.575469i	$-0.804820\pi$
$853$	138.171	−	320.316i	0.161982	−	0.375517i	0.979806	+	0.199953i	$0.0640788\pi$
$854$		0			0
$855$	−621.348	+	92.9598i	−0.726723	+	0.108725i
$856$		0			0
$857$	663.836	+	38.6640i	0.774604	+	0.0451156i	0.440893	−	0.897560i	$-0.354662\pi$
$857$	663.836	+	38.6640i	0.774604	+	0.0451156i	0.333711	+	0.942675i	$0.391699\pi$
$858$		0			0
$859$	−24.2679	−	56.2593i	−0.0282513	−	0.0654939i	0.903506	−	0.428575i	$-0.140984\pi$
$859$	−24.2679	−	56.2593i	−0.0282513	−	0.0654939i	−0.931758	+	0.363081i	$0.881725\pi$
$860$		0			0
$861$	1624.78	+	1242.79i	1.88709	+	1.44342i
$862$		0			0
$863$	1247.51	−	720.249i	1.44555	−	0.834588i	0.447337	−	0.894366i	$-0.352373\pi$
$863$	1247.51	−	720.249i	1.44555	−	0.834588i	0.998212	+	0.0597780i	$0.0190393\pi$
$864$		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	0.215987	−	0.976396i	$-0.430703\pi$
$877$	−676.444	−	716.988i	−0.771315	−	0.817547i	−0.987303	+	0.158850i	$0.949222\pi$
$878$		0			0
$879$	−99.9482	+	398.532i	−0.113707	+	0.453392i
$880$		0			0
$881$	984.733	+	1173.56i	1.11774	+	1.33208i	0.937313	+	0.348489i	$0.113305\pi$
$881$	984.733	+	1173.56i	1.11774	+	1.33208i	0.180432	+	0.983587i	$0.442250\pi$
$882$		0			0
$883$	81.8590	+	68.6879i	0.0927056	+	0.0777892i	0.687963	−	0.725746i	$-0.258505\pi$
$883$	81.8590	+	68.6879i	0.0927056	+	0.0777892i	−0.595257	+	0.803535i	$0.702950\pi$
$884$		0			0
$885$	17.3457	+	30.9674i	0.0195997	+	0.0349914i
$886$		0			0
$887$	691.247	−	1376.39i	0.779309	−	1.55173i	−0.0537539	−	0.998554i	$-0.517119\pi$
$887$	691.247	−	1376.39i	0.779309	−	1.55173i	0.833063	−	0.553178i	$-0.186585\pi$
$888$		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	0.798121	−	0.602498i	$-0.205828\pi$
$907$	−7.22826	−	9.70924i	−0.00796942	−	0.0107048i	−0.806090	+	0.591793i	$0.798420\pi$
$908$		0			0
$909$	−22.4983	+	156.946i	−0.0247506	+	0.172658i
$910$		0			0
$911$	−238.505	−	474.902i	−0.261806	−	0.521298i	0.723873	−	0.689933i	$-0.242360\pi$
$911$	−238.505	−	474.902i	−0.261806	−	0.521298i	−0.985678	+	0.168636i	$0.946064\pi$
$912$		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	0.848372	−	0.529400i	$-0.177583\pi$
$919$	−31.5108	−	54.5782i	−0.0342881	−	0.0593887i	−0.882660	+	0.470012i	$0.844250\pi$
$920$		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	−0.343743	−	0.939064i	$-0.611695\pi$
$929$	−1173.03	−	505.997i	−1.26268	−	0.544669i	−0.918941	+	0.394395i	$0.870954\pi$
$930$		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	−0.864053	−	0.503401i	$-0.832082\pi$
$937$	−1126.63	+	410.059i	−1.20238	+	0.437629i	−0.338323	+	0.941030i	$0.609860\pi$
$938$		0			0
$939$	−226.341	+	1192.68i	−0.241045	+	1.27016i
$940$		0			0
$941$	−1077.40	+	62.7516i	−1.14495	+	0.0666860i	−0.620112	−	0.784513i	$-0.712913\pi$
$941$	−1077.40	+	62.7516i	−1.14495	+	0.0666860i	−0.524843	+	0.851199i	$0.675876\pi$
$942$		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	0.616707	−	0.787192i	$-0.288466\pi$
$947$	1481.61	−	443.564i	1.56453	−	0.468389i	0.947821	+	0.318803i	$0.103281\pi$
$948$		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	−0.767403	−	0.641166i	$-0.778451\pi$
$953$	−1627.55	−	286.981i	−1.70782	−	0.301134i	−0.940414	+	0.340031i	$0.889562\pi$
$954$		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	−0.915378	−	0.402595i	$-0.868108\pi$
$967$	−258.346	+	347.019i	−0.267163	+	0.358862i	0.648215	+	0.761457i	$0.275516\pi$
$968$		0			0
$969$	2099.82	+	658.537i	2.16700	+	0.679604i
$970$		0			0
$971$			696.158i			0.716950i	0.933539	+	0.358475i	$0.116703\pi$
$971$			696.158i			0.716950i	−0.933539	+	0.358475i	$0.883297\pi$
$972$		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	0.988335	−	0.152295i	$-0.0486664\pi$
$977$	1100.00	+	818.920i	1.12590	+	0.838198i	0.137561	+	0.990493i	$0.456074\pi$
$978$		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	0.890949	+	0.454104i	$0.150041\pi$
$983$	126.551	+	1082.71i	0.128739	+	1.10143i	−0.762209	+	0.647331i	$0.775885\pi$
$984$		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	−0.917400	−	0.397967i	$-0.869716\pi$
$991$	80.0598	−	454.042i	0.0807869	−	0.458165i	0.998186	−	0.0601979i	$-0.0191732\pi$
$992$		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	0.929002	−	0.370076i	$-0.120668\pi$
$997$	−50.3762	−	168.268i	−0.0505278	−	0.168775i	−0.979529	+	0.201301i	$0.935483\pi$
$998$		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.65.11	yes	324
81.5	odd	54	inner	324.3.o.a.5.11	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.11	✓	324	81.5	odd	54	inner
324.3.o.a.65.11	yes	324	1.1	even	1	trivial

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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