LMFDB - Embedded newform 108.3.k.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, degree $6$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	108.5
Dual form			108.3.k.a.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95183 + 2.27824i) q^{3} +(-3.25030 - 8.93012i) q^{5} +(0.410040 + 2.32545i) q^{7} +(-1.38071 - 8.89346i) q^{9} +O(q^{10})$	\(q+(-1.95183 + 2.27824i) q^{3} +(-3.25030 - 8.93012i) q^{5} +(0.410040 + 2.32545i) q^{7} +(-1.38071 - 8.89346i) q^{9} +(4.40911 - 12.1139i) q^{11} +(-12.2099 - 10.2453i) q^{13} +(26.6889 + 10.0251i) q^{15} +(12.2018 + 7.04474i) q^{17} +(-3.29274 - 5.70319i) q^{19} +(-6.09825 - 3.60472i) q^{21} +(-25.9779 - 4.58061i) q^{23} +(-50.0315 + 41.9814i) q^{25} +(22.9563 + 14.2129i) q^{27} +(0.977913 + 1.16543i) q^{29} +(-0.620995 + 3.52184i) q^{31} +(18.9925 + 33.6893i) q^{33} +(19.4338 - 11.2201i) q^{35} +(-11.0926 + 19.2129i) q^{37} +(47.1730 - 7.81990i) q^{39} +(31.4714 - 37.5062i) q^{41} +(78.8159 + 28.6866i) q^{43} +(-74.9319 + 41.2363i) q^{45} +(-34.9622 + 6.16478i) q^{47} +(40.8053 - 14.8519i) q^{49} +(-39.8655 + 14.0485i) q^{51} -65.8880i q^{53} -122.510 q^{55} +(19.4201 + 3.63003i) q^{57} +(-17.2513 - 47.3976i) q^{59} +(-11.5793 - 65.6697i) q^{61} +(20.1152 - 6.85745i) q^{63} +(-51.8062 + 142.336i) q^{65} +(72.5027 + 60.8370i) q^{67} +(61.1402 - 50.2432i) q^{69} +(71.8787 + 41.4992i) q^{71} +(-47.8713 - 82.9155i) q^{73} +(2.00947 - 195.924i) q^{75} +(29.9782 + 5.28597i) q^{77} +(-25.9904 + 21.8086i) q^{79} +(-77.1873 + 24.5587i) q^{81} +(7.14066 + 8.50991i) q^{83} +(23.2507 - 131.861i) q^{85} +(-4.56385 - 0.0468084i) q^{87} +(-8.83930 + 5.10337i) q^{89} +(18.8185 - 32.5945i) q^{91} +(-6.81149 - 8.28880i) q^{93} +(-40.2278 + 47.9416i) q^{95} +(66.7584 + 24.2981i) q^{97} +(-113.822 - 22.4863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.95183	+	2.27824i	−0.650610	+	0.759412i
$3$	−1.95183	+	2.27824i	−0.650610	+	0.759412i
$4$		0			0
$5$	−3.25030	−	8.93012i	−0.650060	−	1.78602i	−0.617522	−	0.786553i	$-0.711863\pi$
$5$	−3.25030	−	8.93012i	−0.650060	−	1.78602i	−0.0325374	−	0.999471i	$-0.510359\pi$
$6$		0			0
$7$	0.410040	+	2.32545i	0.0585771	+	0.332207i	0.999987	−	0.00505674i	$-0.00160962\pi$
$7$	0.410040	+	2.32545i	0.0585771	+	0.332207i	−0.941410	+	0.337264i	$0.890499\pi$
$8$		0			0
$9$	−1.38071	−	8.89346i	−0.153413	−	0.988162i
$10$		0			0
$11$	4.40911	−	12.1139i	0.400828	−	1.10127i	−0.561049	−	0.827783i	$-0.689602\pi$
$11$	4.40911	−	12.1139i	0.400828	−	1.10127i	0.961877	−	0.273483i	$-0.0881757\pi$
$12$		0			0
$13$	−12.2099	−	10.2453i	−0.939224	−	0.788103i	0.0382260	−	0.999269i	$-0.487829\pi$
$13$	−12.2099	−	10.2453i	−0.939224	−	0.788103i	−0.977450	+	0.211166i	$0.932274\pi$
$14$		0			0
$15$	26.6889	+	10.0251i	1.77926	+	0.668343i
$16$		0			0
$17$	12.2018	+	7.04474i	0.717755	+	0.414396i	0.813926	−	0.580969i	$-0.197326\pi$
$17$	12.2018	+	7.04474i	0.717755	+	0.414396i	−0.0961707	+	0.995365i	$0.530659\pi$
$18$		0			0
$19$	−3.29274	−	5.70319i	−0.173302	−	0.300168i	0.766270	−	0.642518i	$-0.222110\pi$
$19$	−3.29274	−	5.70319i	−0.173302	−	0.300168i	−0.939572	+	0.342350i	$0.888777\pi$
$20$		0			0
$21$	−6.09825	−	3.60472i	−0.290393	−	0.171653i
$22$		0			0
$23$	−25.9779	−	4.58061i	−1.12947	−	0.199157i	−0.422477	−	0.906374i	$-0.638839\pi$
$23$	−25.9779	−	4.58061i	−1.12947	−	0.199157i	−0.706997	+	0.707217i	$0.749950\pi$
$24$		0			0
$25$	−50.0315	+	41.9814i	−2.00126	+	1.67926i
$26$		0			0
$27$	22.9563	+	14.2129i	0.850234	+	0.526405i
$28$		0			0
$29$	0.977913	+	1.16543i	0.0337211	+	0.0401873i	0.782641	−	0.622473i	$-0.213872\pi$
$29$	0.977913	+	1.16543i	0.0337211	+	0.0401873i	−0.748920	+	0.662660i	$0.769427\pi$
$30$		0			0
$31$	−0.620995	+	3.52184i	−0.0200321	+	0.113608i	−0.993184	−	0.116555i	$-0.962815\pi$
$31$	−0.620995	+	3.52184i	−0.0200321	+	0.113608i	0.973152	+	0.230163i	$0.0739259\pi$
$32$		0			0
$33$	18.9925	+	33.6893i	0.575531	+	1.02089i
$34$		0			0
$35$	19.4338	−	11.2201i	0.555252	−	0.320575i
$36$		0			0
$37$	−11.0926	+	19.2129i	−0.299800	+	0.519269i	−0.976090	−	0.217367i	$-0.930253\pi$
$37$	−11.0926	+	19.2129i	−0.299800	+	0.519269i	0.676290	+	0.736635i	$0.263587\pi$
$38$		0			0
$39$	47.1730	−	7.81990i	1.20956	−	0.200510i
$40$		0			0
$41$	31.4714	−	37.5062i	0.767595	−	0.914784i	−0.230707	−	0.973023i	$-0.574104\pi$
$41$	31.4714	−	37.5062i	0.767595	−	0.914784i	0.998303	+	0.0582388i	$0.0185485\pi$
$42$		0			0
$43$	78.8159	+	28.6866i	1.83293	+	0.667131i	0.992040	+	0.125921i	$0.0401887\pi$
$43$	78.8159	+	28.6866i	1.83293	+	0.667131i	0.840888	+	0.541210i	$0.182033\pi$
$44$		0			0
$45$	−74.9319	+	41.2363i	−1.66515	+	0.916363i
$46$		0			0
$47$	−34.9622	+	6.16478i	−0.743877	+	0.131166i	−0.532726	−	0.846288i	$-0.678832\pi$
$47$	−34.9622	+	6.16478i	−0.743877	+	0.131166i	−0.211151	+	0.977453i	$0.567721\pi$
$48$		0			0
$49$	40.8053	−	14.8519i	0.832762	−	0.303101i
$50$		0			0
$51$	−39.8655	+	14.0485i	−0.781676	+	0.275461i
$52$		0			0
$53$		−	65.8880i		−	1.24317i	−0.783347	−	0.621585i	$-0.786489\pi$
$53$		−	65.8880i		−	1.24317i	0.783347	−	0.621585i	$-0.213511\pi$
$54$		0			0
$55$	−122.510			−2.22745
$56$		0			0
$57$	19.4201	+	3.63003i	0.340703	+	0.0636847i
$58$		0			0
$59$	−17.2513	−	47.3976i	−0.292395	−	0.803349i	−0.995715	−	0.0924754i	$-0.970522\pi$
$59$	−17.2513	−	47.3976i	−0.292395	−	0.803349i	0.703320	−	0.710874i	$-0.251700\pi$
$60$		0			0
$61$	−11.5793	−	65.6697i	−0.189825	−	1.07655i	−0.919597	−	0.392862i	$-0.871485\pi$
$61$	−11.5793	−	65.6697i	−0.189825	−	1.07655i	0.729772	−	0.683690i	$-0.239626\pi$
$62$		0			0
$63$	20.1152	−	6.85745i	0.319288	−	0.108848i
$64$		0			0
$65$	−51.8062	+	142.336i	−0.797019	+	2.18979i
$66$		0			0
$67$	72.5027	+	60.8370i	1.08213	+	0.908015i	0.996096	−	0.0882774i	$-0.0281362\pi$
$67$	72.5027	+	60.8370i	1.08213	+	0.908015i	0.0860340	+	0.996292i	$0.472581\pi$
$68$		0			0
$69$	61.1402	−	50.2432i	0.886089	−	0.728163i
$70$		0			0
$71$	71.8787	+	41.4992i	1.01238	+	0.584496i	0.911887	−	0.410442i	$-0.134626\pi$
$71$	71.8787	+	41.4992i	1.01238	+	0.584496i	0.100490	+	0.994938i	$0.467959\pi$
$72$		0			0
$73$	−47.8713	−	82.9155i	−0.655771	−	1.13583i	−0.981700	−	0.190434i	$-0.939010\pi$
$73$	−47.8713	−	82.9155i	−0.655771	−	1.13583i	0.325929	−	0.945394i	$-0.394323\pi$
$74$		0			0
$75$	2.00947	−	195.924i	0.0267929	−	2.61232i
$76$		0			0
$77$	29.9782	+	5.28597i	0.389328	+	0.0686490i
$78$		0			0
$79$	−25.9904	+	21.8086i	−0.328993	+	0.276058i	−0.792289	−	0.610146i	$-0.791111\pi$
$79$	−25.9904	+	21.8086i	−0.328993	+	0.276058i	0.463296	+	0.886203i	$0.346667\pi$
$80$		0			0
$81$	−77.1873	+	24.5587i	−0.952929	+	0.303193i
$82$		0			0
$83$	7.14066	+	8.50991i	0.0860321	+	0.102529i	0.807343	−	0.590082i	$-0.200905\pi$
$83$	7.14066	+	8.50991i	0.0860321	+	0.102529i	−0.721311	+	0.692611i	$0.756460\pi$
$84$		0			0
$85$	23.2507	−	131.861i	0.273538	−	1.55131i
$86$		0			0
$87$	−4.56385	−	0.0468084i	−0.0524580	−	0.000538028i
$88$		0			0
$89$	−8.83930	+	5.10337i	−0.0993180	+	0.0573412i	−0.548836	−	0.835930i	$-0.684929\pi$
$89$	−8.83930	+	5.10337i	−0.0993180	+	0.0573412i	0.449518	+	0.893271i	$0.351596\pi$
$90$		0			0
$91$	18.8185	−	32.5945i	0.206796	−	0.358182i
$92$		0			0
$93$	−6.81149	−	8.28880i	−0.0732419	−	0.0891269i
$94$		0			0
$95$	−40.2278	+	47.9416i	−0.423450	+	0.504648i
$96$		0			0
$97$	66.7584	+	24.2981i	0.688231	+	0.250496i	0.662378	−	0.749170i	$-0.269547\pi$
$97$	66.7584	+	24.2981i	0.688231	+	0.250496i	0.0258533	+	0.999666i	$0.491770\pi$
$98$		0			0
$99$	−113.822	−	22.4863i	−1.14972	−	0.227135i
$100$		0			0
$101$	−60.9870	+	10.7536i	−0.603831	+	0.106472i	−0.467202	−	0.884151i	$-0.654738\pi$
$101$	−60.9870	+	10.7536i	−0.603831	+	0.106472i	−0.136629	+	0.990622i	$0.543627\pi$
$102$		0			0
$103$	98.6549	−	35.9074i	0.957814	−	0.348616i	0.184638	−	0.982807i	$-0.440889\pi$
$103$	98.6549	−	35.9074i	0.957814	−	0.348616i	0.773177	+	0.634191i	$0.218667\pi$
$104$		0			0
$105$	−12.3694	+	66.1745i	−0.117804	+	0.630234i
$106$		0			0
$107$			20.2740i			0.189477i	0.995502	+	0.0947385i	$0.0302015\pi$
$107$			20.2740i			0.189477i	−0.995502	+	0.0947385i	$0.969799\pi$
$108$		0			0
$109$	145.914			1.33866			0.669328	−	0.742967i	$-0.266582\pi$
$109$	145.914			1.33866			0.669328	+	0.742967i	$0.266582\pi$
$110$		0			0
$111$	−22.1207	−	62.7719i	−0.199286	−	0.565513i
$112$		0			0
$113$	−22.6555	−	62.2454i	−0.200491	−	0.550844i	0.798178	−	0.602422i	$-0.205797\pi$
$113$	−22.6555	−	62.2454i	−0.200491	−	0.550844i	−0.998669	+	0.0515773i	$0.983575\pi$
$114$		0			0
$115$	43.5306	+	246.874i	0.378527	+	2.14673i
$116$		0			0
$117$	−74.2581	+	122.734i	−0.634684	+	1.04901i
$118$		0			0
$119$	−11.3789	+	31.2634i	−0.0956214	+	0.262718i
$120$		0			0
$121$	−34.6155	−	29.0458i	−0.286078	−	0.240048i
$122$		0			0
$123$	24.0210	+	144.905i	0.195293	+	1.17809i
$124$		0			0
$125$	331.765	+	191.545i	2.65412	+	1.53236i
$126$		0			0
$127$	19.5642	+	33.8862i	0.154049	+	0.266820i	0.932712	−	0.360621i	$-0.117435\pi$
$127$	19.5642	+	33.8862i	0.154049	+	0.266820i	−0.778663	+	0.627442i	$0.784102\pi$
$128$		0			0
$129$	−219.190	+	123.570i	−1.69915	+	0.957905i
$130$		0			0
$131$	−225.050	−	39.6824i	−1.71794	−	0.302919i	−0.774036	−	0.633142i	$-0.781765\pi$
$131$	−225.050	−	39.6824i	−1.71794	−	0.302919i	−0.943903	+	0.330223i	$0.892876\pi$
$132$		0			0
$133$	11.9123	−	9.99563i	0.0895664	−	0.0751551i
$134$		0			0
$135$	52.3083	−	251.199i	0.387469	−	1.86073i
$136$		0			0
$137$	90.7406	+	108.140i	0.662340	+	0.789346i	0.987720	−	0.156237i	$-0.0499364\pi$
$137$	90.7406	+	108.140i	0.662340	+	0.789346i	−0.325379	+	0.945584i	$0.605492\pi$
$138$		0			0
$139$	15.8432	−	89.8510i	0.113980	−	0.646410i	−0.873271	−	0.487235i	$-0.838005\pi$
$139$	15.8432	−	89.8510i	0.113980	−	0.646410i	0.987250	−	0.159175i	$-0.0508835\pi$
$140$		0			0
$141$	54.1955	−	91.6847i	0.384365	−	0.650246i
$142$		0			0
$143$	−177.946	+	102.737i	−1.24438	+	0.718442i
$144$		0			0
$145$	7.22893	−	12.5209i	0.0498547	−	0.0863509i
$146$		0			0
$147$	−45.8089	+	121.953i	−0.311625	+	0.829610i
$148$		0			0
$149$	20.1684	−	24.0358i	0.135358	−	0.161314i	−0.694107	−	0.719872i	$-0.744201\pi$
$149$	20.1684	−	24.0358i	0.135358	−	0.161314i	0.829466	+	0.558558i	$0.188645\pi$
$150$		0			0
$151$	−91.3198	−	33.2377i	−0.604767	−	0.220117i	0.0214449	−	0.999770i	$-0.493173\pi$
$151$	−91.3198	−	33.2377i	−0.604767	−	0.220117i	−0.626212	+	0.779653i	$0.715396\pi$
$152$		0			0
$153$	45.8048	−	118.243i	0.299378	−	0.772832i
$154$		0			0
$155$	33.4688	−	5.90146i	0.215928	−	0.0380739i
$156$		0			0
$157$	11.8874	−	4.32668i	0.0757162	−	0.0275584i	−0.303884	−	0.952709i	$-0.598284\pi$
$157$	11.8874	−	4.32668i	0.0757162	−	0.0275584i	0.379601	+	0.925150i	$0.376061\pi$
$158$		0			0
$159$	150.108	+	128.602i	0.944078	+	0.808819i
$160$		0			0
$161$		−	62.2886i		−	0.386885i
$162$		0			0
$163$	−167.367			−1.02679			−0.513397	−	0.858151i	$-0.671613\pi$
$163$	−167.367			−1.02679			−0.513397	+	0.858151i	$0.671613\pi$
$164$		0			0
$165$	239.118	−	279.106i	1.44920	−	1.69155i
$166$		0			0
$167$	6.44485	+	17.7071i	0.0385919	+	0.106030i	0.957492	−	0.288460i	$-0.0931433\pi$
$167$	6.44485	+	17.7071i	0.0385919	+	0.106030i	−0.918900	+	0.394491i	$0.870921\pi$
$168$		0			0
$169$	14.7686	+	83.7568i	0.0873881	+	0.495602i
$170$		0			0
$171$	−46.1748	+	37.1583i	−0.270028	+	0.217300i
$172$		0			0
$173$	70.3332	−	193.239i	0.406550	−	1.11699i	−0.552441	−	0.833552i	$-0.686303\pi$
$173$	70.3332	−	193.239i	0.406550	−	1.11699i	0.958991	−	0.283436i	$-0.0914743\pi$
$174$		0			0
$175$	−118.141	−	99.1317i	−0.675089	−	0.566467i
$176$		0			0
$177$	141.655	+	53.2095i	0.800308	+	0.300619i
$178$		0			0
$179$	−125.847	−	72.6580i	−0.703058	−	0.405911i	0.105427	−	0.994427i	$-0.466379\pi$
$179$	−125.847	−	72.6580i	−0.703058	−	0.405911i	−0.808485	+	0.588516i	$0.799712\pi$
$180$		0			0
$181$	−60.7901	−	105.292i	−0.335857	−	0.581721i	0.647792	−	0.761817i	$-0.275693\pi$
$181$	−60.7901	−	105.292i	−0.335857	−	0.581721i	−0.983649	+	0.180096i	$0.942359\pi$
$182$		0			0
$183$	172.212	+	101.796i	0.941049	+	0.556260i
$184$		0			0
$185$	207.628	+	36.6104i	1.12231	+	0.197894i
$186$		0			0
$187$	139.139	−	116.751i	0.744057	−	0.624338i
$188$		0			0
$189$	−23.6385	+	59.2117i	−0.125071	+	0.313289i
$190$		0			0
$191$	−58.7864	−	70.0589i	−0.307782	−	0.366801i	0.589875	−	0.807494i	$-0.299177\pi$
$191$	−58.7864	−	70.0589i	−0.307782	−	0.366801i	−0.897658	+	0.440694i	$0.854732\pi$
$192$		0			0
$193$	−56.8849	+	322.610i	−0.294740	+	1.67156i	0.373515	+	0.927624i	$0.378152\pi$
$193$	−56.8849	+	322.610i	−0.294740	+	1.67156i	−0.668256	+	0.743932i	$0.732959\pi$
$194$		0			0
$195$	−223.159	−	395.843i	−1.14440	−	2.02997i
$196$		0			0
$197$	−43.6830	+	25.2204i	−0.221741	+	0.128022i	−0.606756	−	0.794888i	$-0.707530\pi$
$197$	−43.6830	+	25.2204i	−0.221741	+	0.128022i	0.385015	+	0.922910i	$0.374196\pi$
$198$		0			0
$199$	−3.02449	+	5.23856i	−0.0151984	+	0.0263244i	−0.873525	−	0.486780i	$-0.838171\pi$
$199$	−3.02449	+	5.23856i	−0.0151984	+	0.0263244i	0.858326	+	0.513104i	$0.171505\pi$
$200$		0			0
$201$	−280.114	+	46.4347i	−1.39360	+	0.231019i
$202$		0			0
$203$	−2.30917	+	2.75196i	−0.0113752	+	0.0135565i
$204$		0			0
$205$	−437.226	−	159.137i	−2.13281	−	0.776279i
$206$		0			0
$207$	−4.86937	+	237.358i	−0.0235235	+	1.14666i
$208$		0			0
$209$	−83.6060	+	14.7420i	−0.400029	+	0.0705359i
$210$		0			0
$211$	18.4132	−	6.70185i	0.0872663	−	0.0317623i	−0.298018	−	0.954560i	$-0.596326\pi$
$211$	18.4132	−	6.70185i	0.0872663	−	0.0317623i	0.385284	+	0.922798i	$0.374103\pi$
$212$		0			0
$213$	−234.840	+	82.7573i	−1.10254	+	0.388532i
$214$		0			0
$215$		−	797.076i		−	3.70733i
$216$		0			0
$217$	−8.44449			−0.0389147
$218$		0			0
$219$	282.338	+	52.7749i	1.28921	+	0.240981i
$220$		0			0
$221$	−76.8077	−	211.028i	−0.347546	−	0.954876i
$222$		0			0
$223$	17.4949	+	99.2183i	0.0784523	+	0.444925i	0.998578	+	0.0533028i	$0.0169748\pi$
$223$	17.4949	+	99.2183i	0.0784523	+	0.444925i	−0.920126	+	0.391622i	$0.871914\pi$
$224$		0			0
$225$	442.439	+	386.989i	1.96640	+	1.71995i
$226$		0			0
$227$	−12.2532	+	33.6653i	−0.0539787	+	0.148305i	−0.963752	−	0.266801i	$-0.914033\pi$
$227$	−12.2532	+	33.6653i	−0.0539787	+	0.148305i	0.909773	+	0.415106i	$0.136256\pi$
$228$		0			0
$229$	131.729	+	110.534i	0.575235	+	0.482679i	0.883378	−	0.468661i	$-0.155263\pi$
$229$	131.729	+	110.534i	0.575235	+	0.482679i	−0.308144	+	0.951340i	$0.599708\pi$
$230$		0			0
$231$	−70.5551	+	57.9802i	−0.305433	+	0.250996i
$232$		0			0
$233$	110.221	+	63.6363i	0.473053	+	0.273117i	0.717517	−	0.696541i	$-0.245279\pi$
$233$	110.221	+	63.6363i	0.473053	+	0.273117i	−0.244464	+	0.969658i	$0.578612\pi$
$234$		0			0
$235$	168.690	+	292.179i	0.717829	+	1.24332i
$236$		0			0
$237$	1.04388	−	101.779i	0.00440456	−	0.429447i
$238$		0			0
$239$	343.656	+	60.5957i	1.43789	+	0.253539i	0.837617	−	0.546257i	$-0.183948\pi$
$239$	343.656	+	60.5957i	1.43789	+	0.253539i	0.600272	+	0.799796i	$0.295059\pi$
$240$		0			0
$241$	361.538	−	303.367i	1.50016	−	1.25878i	0.619532	−	0.784971i	$-0.287322\pi$
$241$	361.538	−	303.367i	1.50016	−	1.25878i	0.880626	−	0.473811i	$-0.157122\pi$
$242$		0			0
$243$	94.7061	−	223.785i	0.389737	−	0.920926i
$244$		0			0
$245$	−265.259	−	316.123i	−1.08269	−	1.29030i
$246$		0			0
$247$	−18.2270	+	103.371i	−0.0737937	+	0.418505i
$248$		0			0
$249$	−33.3249	−	0.341792i	−0.133835	−	0.00137266i
$250$		0			0
$251$	−321.947	+	185.876i	−1.28266	+	0.740542i	−0.977333	−	0.211707i	$-0.932098\pi$
$251$	−321.947	+	185.876i	−1.28266	+	0.740542i	−0.305323	+	0.952249i	$0.598764\pi$
$252$		0			0
$253$	−170.028	+	294.498i	−0.672049	+	1.16402i
$254$		0			0
$255$	255.030	+	310.342i	1.00012	+	1.21703i
$256$		0			0
$257$	65.9115	−	78.5502i	0.256465	−	0.305643i	−0.622414	−	0.782688i	$-0.713848\pi$
$257$	65.9115	−	78.5502i	0.256465	−	0.305643i	0.878879	+	0.477045i	$0.158292\pi$
$258$		0			0
$259$	−49.2271	−	17.9172i	−0.190066	−	0.0691784i
$260$		0			0
$261$	9.01450	−	10.3062i	0.0345383	−	0.0394872i
$262$		0			0
$263$	225.681	−	39.7937i	0.858103	−	0.151307i	0.272750	−	0.962085i	$-0.412067\pi$
$263$	225.681	−	39.7937i	0.858103	−	0.151307i	0.585353	+	0.810778i	$0.300956\pi$
$264$		0			0
$265$	−588.388	+	214.156i	−2.22033	+	0.808134i
$266$		0			0
$267$	5.62613	−	30.0989i	0.0210717	−	0.112730i
$268$		0			0
$269$			111.782i			0.415546i	0.978177	+	0.207773i	$0.0666215\pi$
$269$			111.782i			0.415546i	−0.978177	+	0.207773i	$0.933378\pi$
$270$		0			0
$271$	−107.229			−0.395680			−0.197840	−	0.980234i	$-0.563393\pi$
$271$	−107.229			−0.395680			−0.197840	+	0.980234i	$0.563393\pi$
$272$		0			0
$273$	37.5276	+	106.492i	0.137464	+	0.390080i
$274$		0			0
$275$	287.965	+	791.178i	1.04715	+	2.87701i
$276$		0			0
$277$	−74.3484	−	421.651i	−0.268406	−	1.52221i	−0.759158	−	0.650906i	$-0.774389\pi$
$277$	−74.3484	−	421.651i	−0.268406	−	1.52221i	0.490752	−	0.871299i	$-0.336722\pi$
$278$		0			0
$279$	32.1787	+	0.660142i	0.115336	+	0.00236610i
$280$		0			0
$281$	−46.0248	+	126.452i	−0.163789	+	0.450007i	−0.994252	−	0.107067i	$-0.965854\pi$
$281$	−46.0248	+	126.452i	−0.163789	+	0.450007i	0.830463	+	0.557074i	$0.188076\pi$
$282$		0			0
$283$	−0.267348	−	0.224332i	−0.000944693	−	0.000792692i	0.642315	−	0.766441i	$-0.277974\pi$
$283$	−0.267348	−	0.224332i	−0.000944693	−	0.000792692i	−0.643260	+	0.765648i	$0.722418\pi$
$284$		0			0
$285$	−30.7045	−	185.222i	−0.107735	−	0.649903i
$286$		0			0
$287$	100.123	+	57.8062i	0.348862	+	0.201415i
$288$		0			0
$289$	−45.2434	−	78.3639i	−0.156552	−	0.271155i
$290$		0			0
$291$	−185.658	+	104.666i	−0.637999	+	0.359676i
$292$		0			0
$293$	−454.925	−	80.2156i	−1.55265	−	0.273773i	−0.669478	−	0.742832i	$-0.733482\pi$
$293$	−454.925	−	80.2156i	−1.55265	−	0.273773i	−0.883167	+	0.469059i	$0.844593\pi$
$294$		0			0
$295$	−367.194	+	308.113i	−1.24473	+	1.04445i
$296$		0			0
$297$	273.391	−	215.425i	0.920509	−	0.725336i
$298$		0			0
$299$	270.258	+	322.081i	0.903873	+	1.07719i
$300$		0			0
$301$	−34.3917	+	195.045i	−0.114258	+	0.647991i
$302$		0			0
$303$	94.5369	−	159.932i	0.312003	−	0.527828i
$304$		0			0
$305$	−548.802	+	316.851i	−1.79935	+	1.03886i
$306$		0			0
$307$	164.184	−	284.376i	0.534803	−	0.926305i	−0.464370	−	0.885641i	$-0.653719\pi$
$307$	164.184	−	284.376i	0.534803	−	0.926305i	0.999173	−	0.0406640i	$-0.0129473\pi$
$308$		0			0
$309$	−110.752	+	294.844i	−0.358421	+	0.954188i
$310$		0			0
$311$	104.035	−	123.985i	0.334519	−	0.398664i	−0.572396	−	0.819977i	$-0.693986\pi$
$311$	104.035	−	123.985i	0.334519	−	0.398664i	0.906915	+	0.421313i	$0.138431\pi$
$312$		0			0
$313$	219.058	+	79.7305i	0.699865	+	0.254730i	0.667353	−	0.744741i	$-0.267427\pi$
$313$	219.058	+	79.7305i	0.699865	+	0.254730i	0.0325118	+	0.999471i	$0.489649\pi$
$314$		0			0
$315$	−126.618	−	157.342i	−0.401962	−	0.499498i
$316$		0			0
$317$	391.166	−	68.9732i	1.23396	−	0.217581i	0.481636	−	0.876371i	$-0.340043\pi$
$317$	391.166	−	68.9732i	1.23396	−	0.217581i	0.752327	+	0.658790i	$0.228932\pi$
$318$		0			0
$319$	18.4297	−	6.70785i	0.0577732	−	0.0210277i
$320$		0			0
$321$	−46.1890	−	39.5715i	−0.143891	−	0.123276i
$322$		0			0
$323$		−	92.7859i		−	0.287263i
$324$		0			0
$325$	1040.99			3.20306
$326$		0			0
$327$	−284.799	+	332.425i	−0.870944	+	1.01659i
$328$		0			0
$329$	−28.6718	−	78.7751i	−0.0871483	−	0.239438i
$330$		0			0
$331$	−60.1296	−	341.012i	−0.181660	−	1.03025i	−0.930172	−	0.367125i	$-0.880342\pi$
$331$	−60.1296	−	341.012i	−0.181660	−	1.03025i	0.748511	−	0.663122i	$-0.230769\pi$
$332$		0			0
$333$	186.185	+	72.1240i	0.559115	+	0.216588i
$334$		0			0
$335$	307.626	−	845.196i	0.918287	−	2.52297i
$336$		0			0
$337$	−27.9604	−	23.4615i	−0.0829685	−	0.0696188i	0.600360	−	0.799730i	$-0.295024\pi$
$337$	−27.9604	−	23.4615i	−0.0829685	−	0.0696188i	−0.683329	+	0.730111i	$0.739468\pi$
$338$		0			0
$339$	186.029	+	69.8780i	0.548759	+	0.206130i
$340$		0			0
$341$	39.9252	+	23.0508i	0.117083	+	0.0675977i
$342$		0			0
$343$	109.122	+	189.004i	0.318139	+	0.551033i
$344$		0			0
$345$	−647.402	−	382.684i	−1.87653	−	1.10923i
$346$		0			0
$347$	33.2515	+	5.86314i	0.0958257	+	0.0168967i	0.221355	−	0.975193i	$-0.428952\pi$
$347$	33.2515	+	5.86314i	0.0958257	+	0.0168967i	−0.125530	+	0.992090i	$0.540063\pi$
$348$		0			0
$349$	−128.274	+	107.635i	−0.367548	+	0.308410i	−0.807791	−	0.589469i	$-0.799337\pi$
$349$	−128.274	+	107.635i	−0.367548	+	0.308410i	0.440242	+	0.897879i	$0.354893\pi$
$350$		0			0
$351$	−134.678	−	408.734i	−0.383699	−	1.16448i
$352$		0			0
$353$	−249.417	−	297.244i	−0.706564	−	0.842050i	0.286689	−	0.958024i	$-0.407445\pi$
$353$	−249.417	−	297.244i	−0.706564	−	0.842050i	−0.993252	+	0.115974i	$0.963001\pi$
$354$		0			0
$355$	136.966	−	776.771i	0.385819	−	2.18809i
$356$		0			0
$357$	−49.0156	−	86.9448i	−0.137299	−	0.243543i
$358$		0			0
$359$	−309.401	+	178.633i	−0.861841	+	0.497584i	−0.864628	−	0.502412i	$-0.832446\pi$
$359$	−309.401	+	178.633i	−0.861841	+	0.497584i	0.00278752	+	0.999996i	$0.499113\pi$
$360$		0			0
$361$	158.816	−	275.077i	0.439933	−	0.761986i
$362$		0			0
$363$	133.737	−	22.1697i	0.368421	−	0.0610735i
$364$		0			0
$365$	−584.849	+	696.996i	−1.60233	+	1.90958i
$366$		0			0
$367$	530.990	+	193.265i	1.44684	+	0.526606i	0.941707	−	0.336435i	$-0.109221\pi$
$367$	530.990	+	193.265i	1.44684	+	0.526606i	0.505133	+	0.863042i	$0.331444\pi$
$368$		0			0
$369$	−377.013	−	228.104i	−1.02171	−	0.618169i
$370$		0			0
$371$	153.219	−	27.0167i	0.412990	−	0.0728213i
$372$		0			0
$373$	−68.7050	+	25.0066i	−0.184196	+	0.0670417i	−0.432471	−	0.901648i	$-0.642358\pi$
$373$	−68.7050	+	25.0066i	−0.184196	+	0.0670417i	0.248276	+	0.968689i	$0.420136\pi$
$374$		0			0
$375$	−1083.93	+	381.976i	−2.89049	+	1.01860i
$376$		0			0
$377$		−	24.2489i		−	0.0643206i
$378$		0			0
$379$	63.3568			0.167168			0.0835841	−	0.996501i	$-0.473363\pi$
$379$	63.3568			0.167168			0.0835841	+	0.996501i	$0.473363\pi$
$380$		0			0
$381$	−115.387	−	21.5682i	−0.302852	−	0.0566095i
$382$		0			0
$383$	−21.5538	−	59.2185i	−0.0562762	−	0.154618i	0.908369	−	0.418169i	$-0.137328\pi$
$383$	−21.5538	−	59.2185i	−0.0562762	−	0.154618i	−0.964645	+	0.263552i	$0.915106\pi$
$384$		0			0
$385$	−50.2338	−	284.890i	−0.130477	−	0.739975i
$386$		0			0
$387$	146.301	−	740.554i	0.378039	−	1.91358i
$388$		0			0
$389$	10.7172	−	29.4454i	0.0275508	−	0.0756951i	−0.925155	−	0.379590i	$-0.876065\pi$
$389$	10.7172	−	29.4454i	0.0275508	−	0.0756951i	0.952706	+	0.303895i	$0.0982872\pi$
$390$		0			0
$391$	−284.709	−	238.899i	−0.728156	−	0.610996i
$392$		0			0
$393$	529.665	−	435.264i	1.34775	−	1.10754i
$394$		0			0
$395$	279.230	+	161.213i	0.706911	+	0.408135i
$396$		0			0
$397$	247.263	+	428.273i	0.622830	+	1.07877i	0.988956	+	0.148208i	$0.0473505\pi$
$397$	247.263	+	428.273i	0.622830	+	1.07877i	−0.366126	+	0.930565i	$0.619316\pi$
$398$		0			0
$399$	−0.478447	+	46.6489i	−0.00119912	+	0.116914i
$400$		0			0
$401$	671.249	+	118.359i	1.67394	+	0.295160i	0.928477	−	0.371390i	$-0.121119\pi$
$401$	671.249	+	118.359i	1.67394	+	0.295160i	0.745460	+	0.666550i	$0.232230\pi$
$402$		0			0
$403$	43.6647	−	36.6390i	0.108349	−	0.0909157i
$404$		0			0
$405$	470.193	+	609.469i	1.16097	+	1.50486i
$406$		0			0
$407$	183.836	+	219.087i	0.451684	+	0.538297i
$408$		0			0
$409$	−82.5079	+	467.926i	−0.201731	+	1.14407i	0.700771	+	0.713386i	$0.252840\pi$
$409$	−82.5079	+	467.926i	−0.201731	+	1.14407i	−0.902502	+	0.430686i	$0.858272\pi$
$410$		0			0
$411$	−423.480	−	4.34336i	−1.03036	−	0.0105678i
$412$		0			0
$413$	103.147	−	59.5520i	0.249751	−	0.144194i
$414$		0			0
$415$	52.7852	−	91.4267i	0.127193	−	0.220305i
$416$		0			0
$417$	173.779	+	211.468i	0.416735	+	0.507119i
$418$		0			0
$419$	−150.860	+	179.788i	−0.360048	+	0.429088i	−0.915411	−	0.402519i	$-0.868135\pi$
$419$	−150.860	+	179.788i	−0.360048	+	0.429088i	0.555364	+	0.831608i	$0.312579\pi$
$420$		0			0
$421$	−121.158	−	44.0979i	−0.287786	−	0.104746i	0.194094	−	0.980983i	$-0.437823\pi$
$421$	−121.158	−	44.0979i	−0.287786	−	0.104746i	−0.481879	+	0.876238i	$0.660046\pi$
$422$		0			0
$423$	103.099	+	302.423i	0.243733	+	0.714948i
$424$		0			0
$425$	−906.224	+	159.792i	−2.13229	+	0.375981i
$426$		0			0
$427$	147.964	−	53.8544i	0.346519	−	0.126123i
$428$		0			0
$429$	113.261	−	605.928i	0.264012	−	1.41242i
$430$		0			0
$431$			270.719i			0.628119i	0.949403	+	0.314059i	$0.101689\pi$
$431$			270.719i			0.628119i	−0.949403	+	0.314059i	$0.898311\pi$
$432$		0			0
$433$	−89.2999			−0.206235			−0.103118	−	0.994669i	$-0.532882\pi$
$433$	−89.2999			−0.206235			−0.103118	+	0.994669i	$0.532882\pi$
$434$		0			0
$435$	14.4159	+	40.9078i	0.0331399	+	0.0940410i
$436$		0			0
$437$	59.4144	+	163.240i	0.135960	+	0.373546i
$438$		0			0
$439$	−108.018	−	612.599i	−0.246054	−	1.39544i	−0.818032	−	0.575172i	$-0.804935\pi$
$439$	−108.018	−	612.599i	−0.246054	−	1.39544i	0.571978	−	0.820269i	$-0.306176\pi$
$440$		0			0
$441$	−188.426	−	342.394i	−0.427269	−	0.776405i
$442$		0			0
$443$	−213.946	+	587.813i	−0.482949	+	1.32689i	0.424005	+	0.905660i	$0.360624\pi$
$443$	−213.946	+	587.813i	−0.482949	+	1.32689i	−0.906953	+	0.421231i	$0.861598\pi$
$444$		0			0
$445$	74.3041	+	62.3485i	0.166975	+	0.140109i
$446$		0			0
$447$	15.3938	+	92.8621i	0.0344381	+	0.207745i
$448$		0			0
$449$	86.6015	+	49.9994i	0.192876	+	0.111357i	0.593328	−	0.804960i	$-0.297814\pi$
$449$	86.6015	+	49.9994i	0.192876	+	0.111357i	−0.400452	+	0.916318i	$0.631147\pi$
$450$		0			0
$451$	−315.586	−	546.611i	−0.699747	−	1.21200i
$452$		0			0
$453$	253.964	−	143.174i	0.560627	−	0.316057i
$454$		0			0
$455$	−352.239	−	62.1092i	−0.774151	−	0.136504i
$456$		0			0
$457$	−134.065	+	112.494i	−0.293359	+	0.246158i	−0.777574	−	0.628792i	$-0.783550\pi$
$457$	−134.065	+	112.494i	−0.293359	+	0.246158i	0.484214	+	0.874949i	$0.339105\pi$
$458$		0			0
$459$	179.983	+	335.145i	0.392120	+	0.730164i
$460$		0			0
$461$	494.766	+	589.639i	1.07325	+	1.27904i	0.958328	+	0.285669i	$0.0922159\pi$
$461$	494.766	+	589.639i	1.07325	+	1.27904i	0.114917	+	0.993375i	$0.463340\pi$
$462$		0			0
$463$	−86.2655	+	489.236i	−0.186319	+	1.05667i	0.737931	+	0.674876i	$0.235803\pi$
$463$	−86.2655	+	489.236i	−0.186319	+	1.05667i	−0.924249	+	0.381789i	$0.875308\pi$
$464$		0			0
$465$	−51.8806	+	87.7685i	−0.111571	+	0.188750i
$466$		0			0
$467$	−368.842	+	212.951i	−0.789811	+	0.455997i	−0.839896	−	0.542748i	$-0.817384\pi$
$467$	−368.842	+	212.951i	−0.789811	+	0.455997i	0.0500853	+	0.998745i	$0.484051\pi$
$468$		0			0
$469$	−111.744	+	193.547i	−0.238261	+	0.412680i
$470$		0			0
$471$	−13.3451	+	35.5273i	−0.0283335	+	0.0754296i
$472$		0			0
$473$	695.015	−	828.287i	1.46938	−	1.75114i
$474$		0			0
$475$	404.169	+	147.105i	0.850881	+	0.309695i
$476$		0			0
$477$	−585.972	+	90.9725i	−1.22845	+	0.190718i
$478$		0			0
$479$	696.066	−	122.735i	1.45316	−	0.256232i	0.609365	−	0.792890i	$-0.291424\pi$
$479$	696.066	−	122.735i	1.45316	−	0.256232i	0.843800	+	0.536658i	$0.180313\pi$
$480$		0			0
$481$	332.283	−	120.941i	0.690816	−	0.251437i
$482$		0			0
$483$	141.908	+	121.577i	0.293805	+	0.251712i
$484$		0			0
$485$		−	675.136i		−	1.39203i
$486$		0			0
$487$	−835.437			−1.71548			−0.857738	−	0.514087i	$-0.828131\pi$
$487$	−835.437			−1.71548			−0.857738	+	0.514087i	$0.828131\pi$
$488$		0			0
$489$	326.673	−	381.302i	0.668042	−	0.779759i
$490$		0			0
$491$	218.847	+	601.277i	0.445717	+	1.22460i	0.935679	+	0.352854i	$0.114789\pi$
$491$	218.847	+	601.277i	0.445717	+	1.22460i	−0.489961	+	0.871744i	$0.662989\pi$
$492$		0			0
$493$	3.72218	+	21.1095i	0.00755007	+	0.0428185i
$494$		0			0
$495$	169.151	+	1089.53i	0.341719	+	2.20108i
$496$		0			0
$497$	−67.0312	+	184.167i	−0.134872	+	0.370557i
$498$		0			0
$499$	517.161	+	433.949i	1.03639	+	0.869638i	0.991598	−	0.129358i	$-0.0412917\pi$
$499$	517.161	+	433.949i	1.03639	+	0.869638i	0.0447962	+	0.998996i	$0.485736\pi$
$500$		0			0
$501$	−52.9201	−	19.8783i	−0.105629	−	0.0396773i
$502$		0			0
$503$	−530.717	−	306.409i	−1.05510	−	0.609164i	−0.131029	−	0.991378i	$-0.541828\pi$
$503$	−530.717	−	306.409i	−1.05510	−	0.609164i	−0.924074	+	0.382215i	$0.875162\pi$
$504$		0			0
$505$	294.257	+	509.668i	0.582687	+	1.00924i
$506$		0			0
$507$	−219.643	−	129.833i	−0.433222	−	0.256080i
$508$		0			0
$509$	473.492	+	83.4894i	0.930239	+	0.164026i	0.618180	−	0.786036i	$-0.287870\pi$
$509$	473.492	+	83.4894i	0.930239	+	0.164026i	0.312059	+	0.950063i	$0.398981\pi$
$510$		0			0
$511$	173.187	−	145.321i	0.338917	−	0.284385i
$512$		0			0
$513$	5.46993	−	177.724i	0.0106626	−	0.346440i
$514$		0			0
$515$	−641.315	−	764.290i	−1.24527	−	1.48406i
$516$		0			0
$517$	−79.4724	+	450.711i	−0.153718	+	0.871781i
$518$		0			0
$519$	302.965	+	537.405i	0.583748	+	1.03546i
$520$		0			0
$521$	194.362	−	112.215i	0.373055	−	0.215383i	−0.301737	−	0.953391i	$-0.597567\pi$
$521$	194.362	−	112.215i	0.373055	−	0.215383i	0.674792	+	0.738008i	$0.264233\pi$
$522$		0			0
$523$	−317.364	+	549.691i	−0.606815	+	1.05104i	0.384946	+	0.922939i	$0.374220\pi$
$523$	−317.364	+	549.691i	−0.606815	+	1.05104i	−0.991762	+	0.128096i	$0.959113\pi$
$524$		0			0
$525$	456.436	−	75.6638i	0.869402	−	0.144121i
$526$		0			0
$527$	−32.3877	+	38.5981i	−0.0614567	+	0.0732412i
$528$		0			0
$529$	156.772	+	57.0604i	0.296355	+	0.107865i
$530$		0			0
$531$	−397.709	+	218.866i	−0.748982	+	0.412178i
$532$		0			0
$533$	−768.526	+	135.512i	−1.44189	+	0.254244i
$534$		0			0
$535$	181.050	−	65.8967i	0.338410	−	0.123171i
$536$		0			0
$537$	411.165	−	144.894i	0.765670	−	0.269821i
$538$		0			0
$539$		−	559.797i		−	1.03858i
$540$		0			0
$541$	−322.531			−0.596176			−0.298088	−	0.954538i	$-0.596349\pi$
$541$	−322.531			−0.596176			−0.298088	+	0.954538i	$0.596349\pi$
$542$		0			0
$543$	358.531	+	67.0171i	0.660278	+	0.123420i
$544$		0			0
$545$	−474.263	−	1303.03i	−0.870207	−	2.39087i
$546$		0			0
$547$	63.9102	+	362.453i	0.116838	+	0.662619i	0.985824	+	0.167783i	$0.0536608\pi$
$547$	63.9102	+	362.453i	0.116838	+	0.662619i	−0.868986	+	0.494836i	$0.835228\pi$
$548$		0			0
$549$	−568.043	+	193.651i	−1.03469	+	0.352735i
$550$		0			0
$551$	3.42666	−	9.41468i	0.00621899	−	0.0170865i
$552$		0			0
$553$	−61.3719	−	51.4971i	−0.110980	−	0.0931232i
$554$		0			0
$555$	−488.662	+	401.568i	−0.880472	+	0.723546i
$556$		0			0
$557$	218.606	+	126.212i	0.392470	+	0.226593i	0.683230	−	0.730203i	$-0.260575\pi$
$557$	218.606	+	126.212i	0.392470	+	0.226593i	−0.290760	+	0.956796i	$0.593908\pi$
$558$		0			0
$559$	−668.431	−	1157.76i	−1.19576	−	2.07112i
$560$		0			0
$561$	−5.58837	+	544.869i	−0.00996144	+	0.971246i
$562$		0			0
$563$	−654.162	−	115.346i	−1.16192	−	0.204878i	−0.440747	−	0.897631i	$-0.645287\pi$
$563$	−654.162	−	115.346i	−1.16192	−	0.204878i	−0.721175	+	0.692753i	$0.756398\pi$
$564$		0			0
$565$	−482.222	+	404.632i	−0.853490	+	0.716163i
$566$		0			0
$567$	−88.7598	−	169.425i	−0.156543	−	0.298810i
$568$		0			0
$569$	−173.933	−	207.286i	−0.305682	−	0.364298i	0.591233	−	0.806501i	$-0.298641\pi$
$569$	−173.933	−	207.286i	−0.305682	−	0.364298i	−0.896915	+	0.442203i	$0.854197\pi$
$570$		0			0
$571$	64.4159	−	365.321i	0.112812	−	0.639791i	−0.874998	−	0.484127i	$-0.839137\pi$
$571$	64.4159	−	365.321i	0.112812	−	0.639791i	0.987810	−	0.155664i	$-0.0497517\pi$
$572$		0			0
$573$	274.352	+	2.81385i	0.478799	+	0.00491073i
$574$		0			0
$575$	1492.01	−	861.414i	2.59481	−	1.49811i
$576$		0			0
$577$	172.890	−	299.454i	0.299636	−	0.518985i	−0.676417	−	0.736519i	$-0.736468\pi$
$577$	172.890	−	299.454i	0.299636	−	0.518985i	0.976053	+	0.217535i	$0.0698015\pi$
$578$		0			0
$579$	−623.953	−	759.278i	−1.07764	−	1.31136i
$580$		0			0
$581$	−16.8614	+	20.0947i	−0.0290214	+	0.0345863i
$582$		0			0
$583$	−798.162	−	290.507i	−1.36906	−	0.498297i
$584$		0			0
$585$	1337.39	+	264.211i	2.28614	+	0.451642i
$586$		0			0
$587$	390.919	−	68.9295i	0.665960	−	0.117427i	0.169559	−	0.985520i	$-0.445766\pi$
$587$	390.919	−	68.9295i	0.665960	−	0.117427i	0.496401	+	0.868093i	$0.334655\pi$
$588$		0			0
$589$	22.1305	−	8.05483i	0.0375730	−	0.0136754i
$590$		0			0
$591$	27.8038	−	148.746i	0.0470454	−	0.251685i
$592$		0			0
$593$			453.585i			0.764899i	0.923976	+	0.382449i	$0.124919\pi$
$593$			453.585i			0.764899i	−0.923976	+	0.382449i	$0.875081\pi$
$594$		0			0
$595$	316.171			0.531380
$596$		0			0
$597$	−6.03140	−	17.1153i	−0.0101028	−	0.0286688i
$598$		0			0
$599$	−127.690	−	350.827i	−0.213173	−	0.585687i	0.786310	−	0.617832i	$-0.211989\pi$
$599$	−127.690	−	350.827i	−0.213173	−	0.585687i	−0.999483	+	0.0321442i	$0.989766\pi$
$600$		0			0
$601$	162.521	+	921.701i	0.270417	+	1.53361i	0.753153	+	0.657846i	$0.228532\pi$
$601$	162.521	+	921.701i	0.270417	+	1.53361i	−0.482736	+	0.875766i	$0.660357\pi$
$602$		0			0
$603$	440.946	−	728.798i	0.731253	−	1.20862i
$604$		0			0
$605$	−146.872	+	403.528i	−0.242764	+	0.666989i
$606$		0			0
$607$	−825.430	−	692.618i	−1.35985	−	1.14105i	−0.976028	−	0.217645i	$-0.930163\pi$
$607$	−825.430	−	692.618i	−1.35985	−	1.14105i	−0.383824	−	0.923406i	$-0.625393\pi$
$608$		0			0
$609$	−1.76251	−	10.6322i	−0.00289410	−	0.0174585i
$610$		0			0
$611$	490.046	+	282.928i	0.802039	+	0.463057i
$612$		0			0
$613$	51.2650	+	88.7935i	0.0836296	+	0.144851i	0.904806	−	0.425823i	$-0.140015\pi$
$613$	51.2650	+	88.7935i	0.0836296	+	0.144851i	−0.821177	+	0.570674i	$0.806682\pi$
$614$		0			0
$615$	1215.94	−	685.495i	1.97714	−	1.11463i
$616$		0			0
$617$	−104.533	−	18.4319i	−0.169421	−	0.0298735i	0.0882941	−	0.996094i	$-0.471858\pi$
$617$	−104.533	−	18.4319i	−0.169421	−	0.0298735i	−0.257715	+	0.966221i	$0.582970\pi$
$618$		0			0
$619$	59.1978	−	49.6728i	0.0956345	−	0.0802469i	−0.593717	−	0.804674i	$-0.702340\pi$
$619$	59.1978	−	49.6728i	0.0956345	−	0.0802469i	0.689351	+	0.724427i	$0.257896\pi$
$620$		0			0
$621$	−531.253	−	474.376i	−0.855480	−	0.763891i
$622$		0			0
$623$	−15.4921	−	18.4628i	−0.0248669	−	0.0296353i
$624$		0			0
$625$	348.651	−	1977.30i	0.557842	−	3.16368i
$626$		0			0
$627$	129.599	−	219.248i	0.206697	−	0.349678i
$628$		0			0
$629$	−270.700	+	156.289i	−0.430366	+	0.248472i
$630$		0			0
$631$	−489.646	+	848.091i	−0.775983	+	1.34404i	0.158257	+	0.987398i	$0.449413\pi$
$631$	−489.646	+	848.091i	−0.775983	+	1.34404i	−0.934240	+	0.356645i	$0.883921\pi$
$632$		0			0
$633$	−20.6710	+	55.0304i	−0.0326556	+	0.0869359i
$634$		0			0
$635$	239.018	−	284.851i	0.376407	−	0.448584i
$636$		0			0
$637$	−650.393	−	236.724i	−1.02102	−	0.371623i
$638$		0			0
$639$	269.828	−	696.549i	0.422265	−	1.09006i
$640$		0			0
$641$	489.106	−	86.2426i	0.763036	−	0.134544i	0.221430	−	0.975176i	$-0.428928\pi$
$641$	489.106	−	86.2426i	0.763036	−	0.134544i	0.541606	+	0.840633i	$0.317817\pi$
$642$		0			0
$643$	−789.739	+	287.442i	−1.22821	+	0.447032i	−0.872984	−	0.487748i	$-0.837818\pi$
$643$	−789.739	+	287.442i	−1.22821	+	0.447032i	−0.355226	+	0.934780i	$0.615596\pi$
$644$		0			0
$645$	1815.93	+	1555.76i	2.81539	+	2.41203i
$646$		0			0
$647$			1032.02i			1.59508i	0.603263	+	0.797542i	$0.293867\pi$
$647$			1032.02i			1.59508i	−0.603263	+	0.797542i	$0.706133\pi$
$648$		0			0
$649$	−650.234			−1.00190
$650$		0			0
$651$	16.4822	−	19.2385i	0.0253183	−	0.0295523i
$652$		0			0
$653$	−318.739	−	875.728i	−0.488115	−	1.34108i	−0.902385	−	0.430930i	$-0.858185\pi$
$653$	−318.739	−	875.728i	−0.488115	−	1.34108i	0.414270	−	0.910154i	$-0.364037\pi$
$654$		0			0
$655$	377.111	+	2138.70i	0.575742	+	3.26519i
$656$		0			0
$657$	−671.309	+	540.224i	−1.02178	+	0.822258i
$658$		0			0
$659$	137.332	−	377.318i	0.208395	−	0.572561i	−0.790825	−	0.612042i	$-0.790348\pi$
$659$	137.332	−	377.318i	0.208395	−	0.572561i	0.999220	+	0.0394813i	$0.0125705\pi$
$660$		0			0
$661$	−51.6587	−	43.3468i	−0.0781523	−	0.0655776i	0.602875	−	0.797836i	$-0.294022\pi$
$661$	−51.6587	−	43.3468i	−0.0781523	−	0.0655776i	−0.681027	+	0.732258i	$0.738466\pi$
$662$		0			0
$663$	630.686	+	236.904i	0.951261	+	0.357321i
$664$		0			0
$665$	−127.981	−	73.8898i	−0.192452	−	0.111112i
$666$		0			0
$667$	−20.0657	−	34.7549i	−0.0300836	−	0.0521063i
$668$		0			0
$669$	−260.190	−	153.800i	−0.388923	−	0.229895i
$670$		0			0
$671$	−846.572	−	149.273i	−1.26166	−	0.222464i
$672$		0			0
$673$	14.3494	−	12.0405i	0.0213215	−	0.0178909i	−0.632065	−	0.774916i	$-0.717792\pi$
$673$	14.3494	−	12.0405i	0.0213215	−	0.0178909i	0.653386	+	0.757025i	$0.273348\pi$
$674$		0			0
$675$	−1745.22	+	252.644i	−2.58551	+	0.374288i
$676$		0			0
$677$	165.239	+	196.924i	0.244075	+	0.290877i	0.874149	−	0.485658i	$-0.161420\pi$
$677$	165.239	+	196.924i	0.244075	+	0.290877i	−0.630074	+	0.776535i	$0.716975\pi$
$678$		0			0
$679$	−29.1304	+	165.207i	−0.0429019	+	0.243309i
$680$		0			0
$681$	−52.7813	−	93.6245i	−0.0775056	−	0.137481i
$682$		0			0
$683$	266.287	−	153.741i	0.389879	−	0.225097i	−0.292229	−	0.956348i	$-0.594397\pi$
$683$	266.287	−	153.741i	0.389879	−	0.225097i	0.682108	+	0.731252i	$0.261064\pi$
$684$		0			0
$685$	670.773	−	1161.81i	0.979231	−	1.69608i
$686$		0			0
$687$	−508.934	+	84.3664i	−0.740806	+	0.122804i
$688$		0			0
$689$	−675.044	+	804.487i	−0.979745	+	1.16761i
$690$		0			0
$691$	280.337	+	102.034i	0.405697	+	0.147662i	0.536805	−	0.843707i	$-0.319631\pi$
$691$	280.337	+	102.034i	0.405697	+	0.147662i	−0.131108	+	0.991368i	$0.541853\pi$
$692$		0			0
$693$	5.61920	−	273.909i	0.00810851	−	0.395251i
$694$		0			0
$695$	−853.876	+	150.561i	−1.22860	+	0.216635i
$696$		0			0
$697$	648.230	−	235.936i	0.930029	−	0.338503i
$698$		0			0
$699$	−360.112	+	126.903i	−0.515181	+	0.181549i
$700$		0			0
$701$			274.104i			0.391019i	0.980702	+	0.195510i	$0.0626361\pi$
$701$			274.104i			0.391019i	−0.980702	+	0.195510i	$0.937364\pi$
$702$		0			0
$703$	146.100			0.207824
$704$		0			0
$705$	−994.907	−	185.969i	−1.41122	−	0.263786i
$706$		0			0
$707$	−50.0142	−	137.413i	−0.0707414	−	0.194360i
$708$		0			0
$709$	68.7370	+	389.827i	0.0969492	+	0.549826i	0.994133	+	0.108168i	$0.0344985\pi$
$709$	68.7370	+	389.827i	0.0969492	+	0.549826i	−0.897183	+	0.441658i	$0.854390\pi$
$710$		0			0
$711$	229.839	+	201.034i	0.323262	+	0.282748i
$712$		0			0
$713$	32.2643	−	88.6454i	0.0452514	−	0.124327i
$714$		0			0
$715$	1495.83	+	1255.15i	2.09207	+	1.75546i
$716$		0			0
$717$	−808.809	+	664.656i	−1.12805	+	0.926995i
$718$		0			0
$719$	80.2851	+	46.3526i	0.111662	+	0.0644682i	0.554791	−	0.831990i	$-0.312798\pi$
$719$	80.2851	+	46.3526i	0.111662	+	0.0644682i	−0.443129	+	0.896458i	$0.646132\pi$
$720$		0			0
$721$	123.953	+	214.694i	0.171919	+	0.297772i
$722$		0			0
$723$	−14.5208	+	1415.79i	−0.0200841	+	1.95821i
$724$		0			0
$725$	−97.8529	−	17.2541i	−0.134970	−	0.0237988i
$726$		0			0
$727$	458.479	−	384.709i	0.630645	−	0.529174i	−0.270484	−	0.962724i	$-0.587184\pi$
$727$	458.479	−	384.709i	0.630645	−	0.529174i	0.901129	+	0.433550i	$0.142739\pi$
$728$		0			0
$729$	324.985	+	652.553i	0.445796	+	0.895135i
$730$		0			0
$731$	759.609	+	905.267i	1.03914	+	1.23840i
$732$		0			0
$733$	−127.319	+	722.063i	−0.173696	+	0.985079i	0.765942	+	0.642910i	$0.222273\pi$
$733$	−127.319	+	722.063i	−0.173696	+	0.985079i	−0.939638	+	0.342170i	$0.888838\pi$
$734$		0			0
$735$	1237.94	+	12.6968i	1.68428	+	0.0172746i
$736$		0			0
$737$	1056.65	−	610.055i	1.43371	−	0.827755i
$738$		0			0
$739$	208.119	−	360.472i	0.281622	−	0.487784i	−0.690162	−	0.723655i	$-0.742461\pi$
$739$	208.119	−	360.472i	0.281622	−	0.487784i	0.971784	+	0.235871i	$0.0757942\pi$
$740$		0			0
$741$	−199.927	−	243.287i	−0.269806	−	0.328323i
$742$		0			0
$743$	852.915	−	1016.46i	1.14793	−	1.36805i	0.229104	−	0.973402i	$-0.426420\pi$
$743$	852.915	−	1016.46i	1.14793	−	1.36805i	0.918830	−	0.394653i	$-0.129135\pi$
$744$		0			0
$745$	−280.196	−	101.983i	−0.376101	−	0.136890i
$746$		0			0
$747$	65.8233	−	75.2550i	0.0881169	−	0.100743i
$748$		0			0
$749$	−47.1463	+	8.31316i	−0.0629456	+	0.0110990i
$750$		0			0
$751$	1209.13	−	440.087i	1.61002	−	0.586001i	0.628579	−	0.777745i	$-0.283637\pi$
$751$	1209.13	−	440.087i	1.61002	−	0.586001i	0.981445	+	0.191744i	$0.0614145\pi$
$752$		0			0
$753$	204.916	−	1096.27i	0.272133	−	1.45587i
$754$		0			0
$755$			923.530i			1.22322i
$756$		0			0
$757$	−519.945			−0.686849			−0.343425	−	0.939180i	$-0.611587\pi$
$757$	−519.945			−0.686849			−0.343425	+	0.939180i	$0.611587\pi$
$758$		0			0
$759$	−339.069	−	962.175i	−0.446731	−	1.26769i
$760$		0			0
$761$	129.215	+	355.015i	0.169796	+	0.466511i	0.995180	−	0.0980603i	$-0.0312638\pi$
$761$	129.215	+	355.015i	0.169796	+	0.466511i	−0.825384	+	0.564571i	$0.809042\pi$
$762$		0			0
$763$	59.8304	+	339.315i	0.0784146	+	0.444711i
$764$		0			0
$765$	−1204.81	−	24.7164i	−1.57491	−	0.0323091i
$766$		0			0
$767$	−274.967	+	755.466i	−0.358497	+	0.984962i
$768$		0			0
$769$	−176.852	−	148.396i	−0.229976	−	0.192973i	0.520517	−	0.853851i	$-0.325739\pi$
$769$	−176.852	−	148.396i	−0.229976	−	0.192973i	−0.750493	+	0.660879i	$0.770184\pi$
$770$		0			0
$771$	50.3079	+	303.479i	0.0652502	+	0.393617i
$772$		0			0
$773$	−184.241	−	106.372i	−0.238346	−	0.137609i	0.376070	−	0.926591i	$-0.377275\pi$
$773$	−184.241	−	106.372i	−0.238346	−	0.137609i	−0.614416	+	0.788982i	$0.710608\pi$
$774$		0			0
$775$	−116.782	−	202.273i	−0.150687	−	0.260997i
$776$		0			0
$777$	136.903	−	77.1797i	0.176194	−	0.0993303i
$778$		0			0
$779$	−317.532	−	55.9894i	−0.407615	−	0.0718735i
$780$		0			0
$781$	819.639	−	687.759i	1.04947	−	0.880613i
$782$		0			0
$783$	5.88508	+	40.6530i	0.00751607	+	0.0519196i
$784$		0			0
$785$	−77.2755	−	92.0933i	−0.0984401	−	0.117316i
$786$		0			0
$787$	106.636	−	604.766i	0.135497	−	0.768444i	−0.839015	−	0.544109i	$-0.816868\pi$
$787$	106.636	−	604.766i	0.135497	−	0.768444i	0.974512	−	0.224335i	$-0.0720211\pi$
$788$		0			0
$789$	−349.832	+	591.825i	−0.443387	+	0.750095i
$790$		0			0
$791$	135.459	−	78.2073i	0.171250	−	0.0988714i
$792$		0			0
$793$	−531.425	+	920.455i	−0.670145	+	1.16073i
$794$		0			0
$795$	660.536	−	1758.48i	0.830863	−	2.21193i
$796$		0			0
$797$	−71.3427	+	85.0229i	−0.0895141	+	0.106679i	−0.808942	−	0.587888i	$-0.799960\pi$
$797$	−71.3427	+	85.0229i	−0.0895141	+	0.106679i	0.719428	+	0.694567i	$0.244404\pi$
$798$		0			0
$799$	−470.032	−	171.078i	−0.588276	−	0.214115i
$800$		0			0
$801$	57.5912	+	71.5656i	0.0718991	+	0.0893454i
$802$		0			0
$803$	−1215.50	+	214.326i	−1.51370	+	0.266906i
$804$		0			0
$805$	−556.244	+	202.456i	−0.690987	+	0.251499i
$806$		0			0
$807$	−254.665	−	218.179i	−0.315570	−	0.270358i
$808$		0			0
$809$			1040.29i			1.28589i	0.765910	+	0.642947i	$0.222289\pi$
$809$			1040.29i			1.28589i	−0.765910	+	0.642947i	$0.777711\pi$
$810$		0			0
$811$	869.156			1.07171			0.535855	−	0.844310i	$-0.319989\pi$
$811$	869.156			1.07171			0.535855	+	0.844310i	$0.319989\pi$
$812$		0			0
$813$	209.293	−	244.293i	0.257433	−	0.300484i
$814$		0			0
$815$	543.994	+	1494.61i	0.667477	+	1.83388i
$816$		0			0
$817$	−95.9147	−	543.960i	−0.117399	−	0.665801i
$818$		0			0
$819$	−315.861	−	122.358i	−0.385667	−	0.149399i
$820$		0			0
$821$	−344.284	+	945.912i	−0.419347	+	1.15215i	0.532729	+	0.846286i	$0.321166\pi$
$821$	−344.284	+	945.912i	−0.419347	+	1.15215i	−0.952076	+	0.305861i	$0.901056\pi$
$822$		0			0
$823$	−681.106	−	571.516i	−0.827589	−	0.694430i	0.127147	−	0.991884i	$-0.459418\pi$
$823$	−681.106	−	571.516i	−0.827589	−	0.694430i	−0.954736	+	0.297454i	$0.903863\pi$
$824$		0			0
$825$	−2364.55	−	888.193i	−2.86612	−	1.07660i
$826$		0			0
$827$	−1179.72	−	681.112i	−1.42651	−	0.823594i	−0.429663	−	0.902989i	$-0.641368\pi$
$827$	−1179.72	−	681.112i	−1.42651	−	0.823594i	−0.996843	+	0.0793955i	$0.974701\pi$
$828$		0			0
$829$	−392.123	−	679.177i	−0.473007	−	0.819273i	0.526515	−	0.850166i	$-0.323498\pi$
$829$	−392.123	−	679.177i	−0.473007	−	0.819273i	−0.999523	+	0.0308929i	$0.990165\pi$
$830$		0			0
$831$	1105.74	+	653.608i	1.33061	+	0.786532i
$832$		0			0
$833$	602.528	+	106.242i	0.723323	+	0.127541i
$834$		0			0
$835$	137.179	−	115.107i	0.164286	−	0.137852i
$836$		0			0
$837$	−64.3114	+	72.0222i	−0.0768356	+	0.0860481i
$838$		0			0
$839$	170.797	+	203.547i	0.203572	+	0.242607i	0.858165	−	0.513374i	$-0.171605\pi$
$839$	170.797	+	203.547i	0.203572	+	0.242607i	−0.654593	+	0.755981i	$0.727160\pi$
$840$		0			0
$841$	145.636	−	825.944i	0.173170	−	0.982097i
$842$		0			0
$843$	−198.255	−	351.668i	−0.235178	−	0.417163i
$844$		0			0
$845$	699.956	−	404.120i	0.828350	−	0.478248i
$846$		0			0
$847$	53.3510	−	92.4066i	0.0629881	−	0.109099i
$848$		0			0
$849$	1.03290	−	0.171225i	0.00121661	−	0.000201678i
$850$		0			0
$851$	376.169	−	448.301i	0.442032	−	0.526793i
$852$		0			0
$853$	1525.03	+	555.065i	1.78784	+	0.650721i	0.999364	+	0.0356577i	$0.0113526\pi$
$853$	1525.03	+	555.065i	1.78784	+	0.650721i	0.788478	+	0.615063i	$0.210870\pi$
$854$		0			0
$855$	481.910	+	291.571i	0.563637	+	0.341018i
$856$		0			0
$857$	−153.201	+	27.0135i	−0.178764	+	0.0315210i	−0.262314	−	0.964983i	$-0.584485\pi$
$857$	−153.201	+	27.0135i	−0.178764	+	0.0315210i	0.0835493	+	0.996504i	$0.473374\pi$
$858$		0			0
$859$	1005.06	−	365.813i	1.17004	−	0.425860i	0.317366	−	0.948303i	$-0.397202\pi$
$859$	1005.06	−	365.813i	1.17004	−	0.425860i	0.852674	+	0.522443i	$0.174979\pi$
$860$		0			0
$861$	−327.120	+	115.276i	−0.379930	+	0.133887i
$862$		0			0
$863$		−	634.524i		−	0.735254i	−0.929973	−	0.367627i	$-0.880170\pi$
$863$		−	634.524i		−	0.735254i	0.929973	−	0.367627i	$-0.119830\pi$
$864$		0			0
$865$	−1954.25			−2.25925
$866$		0			0
$867$	266.839	+	49.8779i	0.307773	+	0.0575293i
$868$		0			0
$869$	149.593	+	411.002i	0.172143	+	0.472960i
$870$		0			0
$871$	−261.956	−	1485.63i	−0.300754	−	1.70566i
$872$		0			0
$873$	123.920	−	627.262i	0.141947	−	0.718513i
$874$		0			0
$875$	−309.391	+	850.045i	−0.353590	+	0.971480i
$876$		0			0
$877$	373.651	+	313.530i	0.426055	+	0.357503i	0.830461	−	0.557077i	$-0.188077\pi$
$877$	373.651	+	313.530i	0.426055	+	0.357503i	−0.404406	+	0.914580i	$0.632522\pi$
$878$		0			0
$879$	1070.69	−	879.859i	1.21807	−	1.00098i
$880$		0			0
$881$	481.009	+	277.711i	0.545981	+	0.315222i	0.747499	−	0.664262i	$-0.231254\pi$
$881$	481.009	+	277.711i	0.545981	+	0.315222i	−0.201518	+	0.979485i	$0.564588\pi$
$882$		0			0
$883$	348.544	+	603.697i	0.394728	+	0.683688i	0.993066	−	0.117555i	$-0.0375056\pi$
$883$	348.544	+	603.697i	0.394728	+	0.683688i	−0.598339	+	0.801243i	$0.704172\pi$
$884$		0			0
$885$	14.7480	−	1437.94i	0.0166644	−	1.62479i
$886$		0			0
$887$	210.497	+	37.1164i	0.237314	+	0.0418448i	0.291040	−	0.956711i	$-0.405999\pi$
$887$	210.497	+	37.1164i	0.237314	+	0.0418448i	−0.0537262	+	0.998556i	$0.517110\pi$
$888$		0			0
$889$	−70.7785	+	59.3902i	−0.0796159	+	0.0668057i
$890$		0			0
$891$	−42.8252	+	1043.32i	−0.0480642	+	1.17096i
$892$		0			0
$893$	150.280	+	179.097i	0.168287	+	0.200557i
$894$		0			0
$895$	−239.803	+	1359.99i	−0.267937	+	1.51954i
$896$		0			0
$897$	−1261.27	−	12.9361i	−1.40610	−	0.0144215i
$898$		0			0
$899$	−4.71174	+	2.72032i	−0.00524109	+	0.00302594i
$900$		0			0
$901$	464.163	−	803.955i	0.515165	−	0.892291i
$902$		0			0
$903$	−377.232	−	459.048i	−0.417754	−	0.508358i
$904$		0			0
$905$	−742.680	+	885.092i	−0.820641	+	0.978002i
$906$		0			0
$907$	−105.132	−	38.2650i	−0.115912	−	0.0421886i	0.283413	−	0.958998i	$-0.408533\pi$
$907$	−105.132	−	38.2650i	−0.115912	−	0.0421886i	−0.399325	+	0.916809i	$0.630756\pi$
$908$		0			0
$909$	179.843	+	527.537i	0.197847	+	0.580349i
$910$		0			0
$911$	−782.305	+	137.941i	−0.858732	+	0.151418i	−0.585641	−	0.810571i	$-0.699157\pi$
$911$	−782.305	+	137.941i	−0.858732	+	0.151418i	−0.273091	+	0.961988i	$0.588046\pi$
$912$		0			0
$913$	134.572	−	48.9803i	0.147396	−	0.0536477i
$914$		0			0
$915$	349.307	−	1868.74i	0.381757	−	2.04234i
$916$		0			0
$917$		−	539.614i		−	0.588456i
$918$		0			0
$919$	1706.42			1.85682			0.928412	−	0.371553i	$-0.121175\pi$
$919$	1706.42			1.85682			0.928412	+	0.371553i	$0.121175\pi$
$920$		0			0
$921$	327.415	+	929.104i	0.355499	+	1.00880i
$922$		0			0
$923$	−452.460	−	1243.12i	−0.490206	−	1.34683i
$924$		0			0
$925$	−251.607	−	1426.93i	−0.272008	−	1.54263i
$926$		0			0
$927$	−455.555	−	827.805i	−0.491430	−	0.892994i
$928$		0			0
$929$	538.296	−	1478.96i	0.579436	−	1.59199i	−0.209699	−	0.977766i	$-0.567248\pi$
$929$	538.296	−	1478.96i	0.579436	−	1.59199i	0.789135	−	0.614220i	$-0.210529\pi$
$930$		0			0
$931$	−219.065	−	183.817i	−0.235300	−	0.197441i
$932$		0			0
$933$	79.4066	+	479.014i	0.0851089	+	0.513413i
$934$		0			0
$935$	−1494.84	−	863.048i	−1.59876	−	0.923046i
$936$		0			0
$937$	−570.487	−	988.113i	−0.608844	−	1.05455i	−0.991431	−	0.130630i	$-0.958300\pi$
$937$	−570.487	−	988.113i	−0.608844	−	1.05455i	0.382587	−	0.923920i	$-0.375033\pi$
$938$		0			0
$939$	−609.209	+	343.445i	−0.648784	+	0.365756i
$940$		0			0
$941$	1330.02	+	234.519i	1.41341	+	0.249223i	0.827643	−	0.561255i	$-0.189681\pi$
$941$	1330.02	+	234.519i	1.41341	+	0.249223i	0.585769	+	0.810478i	$0.300793\pi$
$942$		0			0
$943$	−989.362	+	830.173i	−1.04916	+	0.880353i
$944$		0			0
$945$	605.599	+	18.6389i	0.640846	+	0.0197238i
$946$		0			0
$947$	−842.221	−	1003.72i	−0.889357	−	1.05989i	−0.997833	−	0.0657950i	$-0.979042\pi$
$947$	−842.221	−	1003.72i	−0.889357	−	1.05989i	0.108476	−	0.994099i	$-0.465403\pi$
$948$		0			0
$949$	−264.993	+	1502.85i	−0.279234	+	1.58361i
$950$		0			0
$951$	−606.353	+	1025.79i	−0.637595	+	1.07865i
$952$		0			0
$953$	638.686	−	368.745i	0.670184	−	0.386931i	−0.125962	−	0.992035i	$-0.540202\pi$
$953$	638.686	−	368.745i	0.670184	−	0.386931i	0.796146	+	0.605104i	$0.206868\pi$
$954$		0			0
$955$	−434.561	+	752.682i	−0.455038	+	0.788149i
$956$		0			0
$957$	−20.6895	+	55.0797i	−0.0216191	+	0.0575546i
$958$		0			0
$959$	−214.268	+	255.355i	−0.223429	+	0.266272i
$960$		0			0
$961$	891.027	+	324.307i	0.927187	+	0.337469i
$962$		0			0
$963$	180.306	−	27.9927i	0.187234	−	0.0290682i
$964$		0			0
$965$	3065.84	−	540.591i	3.17704	−	0.560197i
$966$		0			0
$967$	468.930	−	170.677i	0.484933	−	0.176501i	−0.0879722	−	0.996123i	$-0.528039\pi$
$967$	468.930	−	170.677i	0.484933	−	0.176501i	0.572905	+	0.819622i	$0.305816\pi$
$968$		0			0
$969$	211.388	+	181.102i	0.218151	+	0.186896i
$970$		0			0
$971$			981.048i			1.01035i	0.863018	+	0.505174i	$0.168572\pi$
$971$			981.048i			1.01035i	−0.863018	+	0.505174i	$0.831428\pi$
$972$		0			0
$973$	215.441			0.221419
$974$		0			0
$975$	−2031.84	+	2371.63i	−2.08394	+	2.43244i
$976$		0			0
$977$	−118.283	−	324.980i	−0.121068	−	0.332630i	0.864324	−	0.502936i	$-0.167747\pi$
$977$	−118.283	−	324.980i	−0.121068	−	0.332630i	−0.985391	+	0.170305i	$0.945525\pi$
$978$		0			0
$979$	22.8484	+	129.580i	0.0233385	+	0.132359i
$980$		0			0
$981$	−201.465	−	1297.68i	−0.205367	−	1.32281i
$982$		0			0
$983$	67.6176	−	185.778i	0.0687870	−	0.188991i	−0.900536	−	0.434782i	$-0.856826\pi$
$983$	67.6176	−	185.778i	0.0687870	−	0.188991i	0.969323	+	0.245791i	$0.0790477\pi$
$984$		0			0
$985$	367.204	+	308.120i	0.372796	+	0.312813i
$986$		0			0
$987$	235.431	+	88.4345i	0.238532	+	0.0895993i
$988$		0			0
$989$	−1916.07	−	1106.24i	−1.93738	−	1.11855i
$990$		0			0
$991$	734.120	+	1271.53i	0.740787	+	1.28308i	0.952138	+	0.305670i	$0.0988804\pi$
$991$	734.120	+	1271.53i	0.740787	+	1.28308i	−0.211351	+	0.977410i	$0.567786\pi$
$992$		0			0
$993$	894.268	+	528.608i	0.900572	+	0.532334i
$994$		0			0
$995$	56.6115	+	9.98213i	0.0568960	+	0.0100323i
$996$		0			0
$997$	13.1521	−	11.0359i	0.0131917	−	0.0110691i	−0.636168	−	0.771551i	$-0.719481\pi$
$997$	13.1521	−	11.0359i	0.0131917	−	0.0110691i	0.649360	+	0.760481i	$0.275037\pi$
$998$		0			0
$999$	−527.717	+	283.400i	−0.528246	+	0.283684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.k.a.5.2	✓	36
3.2	odd	2		324.3.k.a.125.6		36
4.3	odd	2		432.3.bc.b.113.5		36
27.4	even	9		2916.3.c.b.1457.36		36
27.11	odd	18	inner	108.3.k.a.65.2	yes	36
27.16	even	9		324.3.k.a.197.6		36
27.23	odd	18		2916.3.c.b.1457.1		36
108.11	even	18		432.3.bc.b.65.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.5.2	✓	36	1.1	even	1	trivial
108.3.k.a.65.2	yes	36	27.11	odd	18	inner
324.3.k.a.125.6		36	3.2	odd	2
324.3.k.a.197.6		36	27.16	even	9
432.3.bc.b.65.5		36	108.11	even	18
432.3.bc.b.113.5		36	4.3	odd	2
2916.3.c.b.1457.1		36	27.23	odd	18
2916.3.c.b.1457.36		36	27.4	even	9

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95183 + 2.27824i) q^{3} +(-3.25030 - 8.93012i) q^{5} +(0.410040 + 2.32545i) q^{7} +(-1.38071 - 8.89346i) q^{9} +O(q^{10})\)	\(q+(-1.95183 + 2.27824i) q^{3} +(-3.25030 - 8.93012i) q^{5} +(0.410040 + 2.32545i) q^{7} +(-1.38071 - 8.89346i) q^{9} +(4.40911 - 12.1139i) q^{11} +(-12.2099 - 10.2453i) q^{13} +(26.6889 + 10.0251i) q^{15} +(12.2018 + 7.04474i) q^{17} +(-3.29274 - 5.70319i) q^{19} +(-6.09825 - 3.60472i) q^{21} +(-25.9779 - 4.58061i) q^{23} +(-50.0315 + 41.9814i) q^{25} +(22.9563 + 14.2129i) q^{27} +(0.977913 + 1.16543i) q^{29} +(-0.620995 + 3.52184i) q^{31} +(18.9925 + 33.6893i) q^{33} +(19.4338 - 11.2201i) q^{35} +(-11.0926 + 19.2129i) q^{37} +(47.1730 - 7.81990i) q^{39} +(31.4714 - 37.5062i) q^{41} +(78.8159 + 28.6866i) q^{43} +(-74.9319 + 41.2363i) q^{45} +(-34.9622 + 6.16478i) q^{47} +(40.8053 - 14.8519i) q^{49} +(-39.8655 + 14.0485i) q^{51} -65.8880i q^{53} -122.510 q^{55} +(19.4201 + 3.63003i) q^{57} +(-17.2513 - 47.3976i) q^{59} +(-11.5793 - 65.6697i) q^{61} +(20.1152 - 6.85745i) q^{63} +(-51.8062 + 142.336i) q^{65} +(72.5027 + 60.8370i) q^{67} +(61.1402 - 50.2432i) q^{69} +(71.8787 + 41.4992i) q^{71} +(-47.8713 - 82.9155i) q^{73} +(2.00947 - 195.924i) q^{75} +(29.9782 + 5.28597i) q^{77} +(-25.9904 + 21.8086i) q^{79} +(-77.1873 + 24.5587i) q^{81} +(7.14066 + 8.50991i) q^{83} +(23.2507 - 131.861i) q^{85} +(-4.56385 - 0.0468084i) q^{87} +(-8.83930 + 5.10337i) q^{89} +(18.8185 - 32.5945i) q^{91} +(-6.81149 - 8.28880i) q^{93} +(-40.2278 + 47.9416i) q^{95} +(66.7584 + 24.2981i) q^{97} +(-113.822 - 22.4863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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