LMFDB - Embedded newform 684.3.t.a.265.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(265,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("684.265");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			265.16
Character	$\chi$	$=$	684.265
Dual form			684.3.t.a.493.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05443 - 2.80859i) q^{3} +(-1.91223 + 3.31208i) q^{5} +(-5.72810 - 9.92136i) q^{7} +(-6.77637 + 5.92290i) q^{9} +O(q^{10})$	\(q+(-1.05443 - 2.80859i) q^{3} +(-1.91223 + 3.31208i) q^{5} +(-5.72810 - 9.92136i) q^{7} +(-6.77637 + 5.92290i) q^{9} +(-4.79772 - 8.30989i) q^{11} +(-7.74438 - 4.47122i) q^{13} +(11.3186 + 1.87833i) q^{15} +21.3706 q^{17} +(-10.1294 + 16.0747i) q^{19} +(-21.8252 + 26.5492i) q^{21} +(9.24246 - 16.0084i) q^{23} +(5.18675 + 8.98371i) q^{25} +(23.7802 + 12.7868i) q^{27} +(-19.3970 + 11.1989i) q^{29} +(-0.0307992 - 0.0177819i) q^{31} +(-18.2803 + 22.2370i) q^{33} +43.8138 q^{35} +70.0965i q^{37} +(-4.39196 + 26.4654i) q^{39} +(-14.9753 - 8.64601i) q^{41} +(-10.7226 - 18.5720i) q^{43} +(-6.65914 - 33.7698i) q^{45} +(-1.29232 - 2.23837i) q^{47} +(-41.1223 + 71.2259i) q^{49} +(-22.5337 - 60.0212i) q^{51} +11.4190i q^{53} +36.6974 q^{55} +(55.8279 + 11.4997i) q^{57} +(-48.4874 - 27.9942i) q^{59} +(34.5169 + 59.7850i) q^{61} +(97.5790 + 33.3039i) q^{63} +(29.6181 - 17.1000i) q^{65} +(20.5989 + 11.8928i) q^{67} +(-54.7065 - 9.07861i) q^{69} +103.587i q^{71} +31.3012 q^{73} +(19.7625 - 24.0401i) q^{75} +(-54.9636 + 95.1998i) q^{77} +(28.5508 - 16.4838i) q^{79} +(10.8385 - 80.2716i) q^{81} +(-1.38498 - 2.39885i) q^{83} +(-40.8654 + 70.7810i) q^{85} +(51.9058 + 42.6700i) q^{87} +112.225i q^{89} +102.446i q^{91} +(-0.0174667 + 0.105252i) q^{93} +(-33.8709 - 64.2878i) q^{95} +(49.1372 - 28.3694i) q^{97} +(81.7298 + 27.8945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 2 * q^7 + 4 * q^9	$ 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) $ 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.05443	−	2.80859i	−0.351475	−	0.936197i
$3$	−1.05443	−	2.80859i	−0.351475	−	0.936197i
$4$		0			0
$5$	−1.91223	+	3.31208i	−0.382446	+	0.662416i	−0.991411	−	0.130781i	$-0.958252\pi$
$5$	−1.91223	+	3.31208i	−0.382446	+	0.662416i	0.608965	+	0.793197i	$0.291585\pi$
$6$		0			0
$7$	−5.72810	−	9.92136i	−0.818300	−	1.41734i	−0.906934	−	0.421273i	$-0.861583\pi$
$7$	−5.72810	−	9.92136i	−0.818300	−	1.41734i	0.0886333	−	0.996064i	$-0.471750\pi$
$8$		0			0
$9$	−6.77637	+	5.92290i	−0.752930	+	0.658100i
$10$		0			0
$11$	−4.79772	−	8.30989i	−0.436156	−	0.755445i	0.561233	−	0.827658i	$-0.310327\pi$
$11$	−4.79772	−	8.30989i	−0.436156	−	0.755445i	−0.997389	+	0.0722131i	$0.976994\pi$
$12$		0			0
$13$	−7.74438	−	4.47122i	−0.595722	−	0.343940i	0.171635	−	0.985161i	$-0.445095\pi$
$13$	−7.74438	−	4.47122i	−0.595722	−	0.343940i	−0.767357	+	0.641221i	$0.778428\pi$
$14$		0			0
$15$	11.3186	+	1.87833i	0.754572	+	0.125222i
$16$		0			0
$17$	21.3706			1.25709			0.628546	−	0.777772i	$-0.283650\pi$
$17$	21.3706			1.25709			0.628546	+	0.777772i	$0.283650\pi$
$18$		0			0
$19$	−10.1294	+	16.0747i	−0.533125	+	0.846036i
$19$	−10.1294	+	16.0747i	−0.533125	+	0.846036i
$20$		0			0
$21$	−21.8252	+	26.5492i	−1.03930	+	1.26425i
$22$		0			0
$23$	9.24246	−	16.0084i	0.401846	−	0.696018i	−0.592103	−	0.805862i	$-0.701702\pi$
$23$	9.24246	−	16.0084i	0.401846	−	0.696018i	0.993949	+	0.109845i	$0.0350354\pi$
$24$		0			0
$25$	5.18675	+	8.98371i	0.207470	+	0.359348i
$26$		0			0
$27$	23.7802	+	12.7868i	0.880748	+	0.473585i
$28$		0			0
$29$	−19.3970	+	11.1989i	−0.668863	+	0.386168i	−0.795646	−	0.605762i	$-0.792868\pi$
$29$	−19.3970	+	11.1989i	−0.668863	+	0.386168i	0.126783	+	0.991931i	$0.459535\pi$
$30$		0			0
$31$	−0.0307992	−	0.0177819i	−0.000993522	−	0.000573610i	0.499503	−	0.866312i	$-0.333516\pi$
$31$	−0.0307992	−	0.0177819i	−0.000993522	−	0.000573610i	−0.500497	+	0.865738i	$0.666849\pi$
$32$		0			0
$33$	−18.2803	+	22.2370i	−0.553947	+	0.673848i
$34$		0			0
$35$	43.8138			1.25182
$36$		0			0
$37$			70.0965i			1.89450i	0.320496	+	0.947250i	$0.396150\pi$
$37$			70.0965i			1.89450i	−0.320496	+	0.947250i	$0.603850\pi$
$38$		0			0
$39$	−4.39196	+	26.4654i	−0.112614	+	0.678599i
$40$		0			0
$41$	−14.9753	−	8.64601i	−0.365252	−	0.210878i	0.306130	−	0.951990i	$-0.400966\pi$
$41$	−14.9753	−	8.64601i	−0.365252	−	0.210878i	−0.671382	+	0.741111i	$0.734299\pi$
$42$		0			0
$43$	−10.7226	−	18.5720i	−0.249362	−	0.431908i	0.713987	−	0.700159i	$-0.246888\pi$
$43$	−10.7226	−	18.5720i	−0.249362	−	0.431908i	−0.963349	+	0.268251i	$0.913554\pi$
$44$		0			0
$45$	−6.65914	−	33.7698i	−0.147981	−	0.750441i
$46$		0			0
$47$	−1.29232	−	2.23837i	−0.0274962	−	0.0476249i	0.851950	−	0.523623i	$-0.175420\pi$
$47$	−1.29232	−	2.23837i	−0.0274962	−	0.0476249i	−0.879446	+	0.475999i	$0.842087\pi$
$48$		0			0
$49$	−41.1223	+	71.2259i	−0.839231	+	1.45359i
$50$		0			0
$51$	−22.5337	−	60.0212i	−0.441837	−	1.17689i
$52$		0			0
$53$			11.4190i			0.215453i	0.994181	+	0.107726i	$0.0343570\pi$
$53$			11.4190i			0.215453i	−0.994181	+	0.107726i	$0.965643\pi$
$54$		0			0
$55$	36.6974			0.667225
$56$		0			0
$57$	55.8279	+	11.4997i	0.979437	+	0.201750i
$58$		0			0
$59$	−48.4874	−	27.9942i	−0.821820	−	0.474478i	0.0292236	−	0.999573i	$-0.490697\pi$
$59$	−48.4874	−	27.9942i	−0.821820	−	0.474478i	−0.851044	+	0.525095i	$0.824030\pi$
$60$		0			0
$61$	34.5169	+	59.7850i	0.565850	+	0.980082i	0.996970	+	0.0777868i	$0.0247853\pi$
$61$	34.5169	+	59.7850i	0.565850	+	0.980082i	−0.431120	+	0.902295i	$0.641881\pi$
$62$		0			0
$63$	97.5790	+	33.3039i	1.54887	+	0.528633i
$64$		0			0
$65$	29.6181	−	17.1000i	0.455663	−	0.263077i
$66$		0			0
$67$	20.5989	+	11.8928i	0.307446	+	0.177504i	0.645783	−	0.763521i	$-0.276531\pi$
$67$	20.5989	+	11.8928i	0.307446	+	0.177504i	−0.338337	+	0.941025i	$0.609864\pi$
$68$		0			0
$69$	−54.7065	−	9.07861i	−0.792849	−	0.131574i
$70$		0			0
$71$			103.587i			1.45897i	0.683999	+	0.729483i	$0.260239\pi$
$71$			103.587i			1.45897i	−0.683999	+	0.729483i	$0.739761\pi$
$72$		0			0
$73$	31.3012			0.428784			0.214392	−	0.976748i	$-0.431223\pi$
$73$	31.3012			0.428784			0.214392	+	0.976748i	$0.431223\pi$
$74$		0			0
$75$	19.7625	−	24.0401i	0.263500	−	0.320535i
$76$		0			0
$77$	−54.9636	+	95.1998i	−0.713814	+	1.23636i
$78$		0			0
$79$	28.5508	−	16.4838i	0.361403	−	0.208656i	−0.308293	−	0.951291i	$-0.599758\pi$
$79$	28.5508	−	16.4838i	0.361403	−	0.208656i	0.669696	+	0.742635i	$0.266424\pi$
$80$		0			0
$81$	10.8385	−	80.2716i	0.133808	−	0.991007i
$82$		0			0
$83$	−1.38498	−	2.39885i	−0.0166865	−	0.0289019i	0.857562	−	0.514381i	$-0.171978\pi$
$83$	−1.38498	−	2.39885i	−0.0166865	−	0.0289019i	−0.874248	+	0.485479i	$0.838645\pi$
$84$		0			0
$85$	−40.8654	+	70.7810i	−0.480770	+	0.832718i
$86$		0			0
$87$	51.9058	+	42.6700i	0.596619	+	0.490459i
$88$		0			0
$89$			112.225i			1.26096i	0.776207	+	0.630478i	$0.217141\pi$
$89$			112.225i			1.26096i	−0.776207	+	0.630478i	$0.782859\pi$
$90$		0			0
$91$			102.446i			1.12578i
$92$		0			0
$93$	−0.0174667	+	0.105252i	−0.000187814	+	0.00113174i
$94$		0			0
$95$	−33.8709	−	64.2878i	−0.356536	−	0.676714i
$96$		0			0
$97$	49.1372	−	28.3694i	0.506569	−	0.292468i	−0.224853	−	0.974393i	$-0.572190\pi$
$97$	49.1372	−	28.3694i	0.506569	−	0.292468i	0.731422	+	0.681925i	$0.238857\pi$
$98$		0			0
$99$	81.7298	+	27.8945i	0.825554	+	0.281763i
$100$		0			0
$101$	−51.8098	−	89.7372i	−0.512968	−	0.888487i	−0.999887	−	0.0150400i	$-0.995212\pi$
$101$	−51.8098	−	89.7372i	−0.512968	−	0.888487i	0.486918	−	0.873447i	$-0.338121\pi$
$102$		0			0
$103$	43.8611	+	25.3232i	0.425836	+	0.245856i	0.697571	−	0.716516i	$-0.254264\pi$
$103$	43.8611	+	25.3232i	0.425836	+	0.245856i	−0.271735	+	0.962372i	$0.587598\pi$
$104$		0			0
$105$	−46.1984	−	123.055i	−0.439985	−	1.17195i
$106$		0			0
$107$			119.244i			1.11443i	0.830367	+	0.557216i	$0.188131\pi$
$107$			119.244i			1.11443i	−0.830367	+	0.557216i	$0.811869\pi$
$108$		0			0
$109$		−	76.7629i		−	0.704247i	−0.935954	−	0.352123i	$-0.885460\pi$
$109$		−	76.7629i		−	0.704247i	0.935954	−	0.352123i	$-0.114540\pi$
$110$		0			0
$111$	196.872	−	73.9115i	1.77363	−	0.665870i
$112$		0			0
$113$	−4.59271	−	2.65161i	−0.0406435	−	0.0234655i	0.479541	−	0.877520i	$-0.340803\pi$
$113$	−4.59271	−	2.65161i	−0.0406435	−	0.0234655i	−0.520184	+	0.854054i	$0.674137\pi$
$114$		0			0
$115$	35.3474	+	61.2235i	0.307369	+	0.532378i
$116$		0			0
$117$	78.9614	−	15.5706i	0.674884	−	0.133082i
$118$		0			0
$119$	−122.413	−	212.025i	−1.02868	−	1.78172i
$120$		0			0
$121$	14.4638	−	25.0520i	0.119535	−	0.207042i
$122$		0			0
$123$	−8.49274	+	51.1762i	−0.0690467	+	0.416066i
$124$		0			0
$125$	−135.285			−1.08228
$126$		0			0
$127$			56.5145i			0.444996i	0.974933	+	0.222498i	$0.0714211\pi$
$127$			56.5145i			0.444996i	−0.974933	+	0.222498i	$0.928579\pi$
$128$		0			0
$129$	−40.8551	+	49.6981i	−0.316706	+	0.385257i
$130$		0			0
$131$	11.9870	−	20.7620i	0.0915035	−	0.158489i	−0.816640	−	0.577147i	$-0.804166\pi$
$131$	11.9870	−	20.7620i	0.0915035	−	0.158489i	0.908144	+	0.418658i	$0.137499\pi$
$132$		0			0
$133$	217.505	+	8.41983i	1.63538	+	0.0633070i
$134$		0			0
$135$	−87.8241	+	54.3106i	−0.650549	+	0.402301i
$136$		0			0
$137$	−70.2838	−	121.735i	−0.513021	−	0.888578i	−0.999886	−	0.0151009i	$-0.995193\pi$
$137$	−70.2838	−	121.735i	−0.513021	−	0.888578i	0.486865	−	0.873477i	$-0.338140\pi$
$138$		0			0
$139$	−86.0899	+	149.112i	−0.619351	+	1.07275i	0.370253	+	0.928931i	$0.379271\pi$
$139$	−86.0899	+	149.112i	−0.619351	+	1.07275i	−0.989604	+	0.143817i	$0.954062\pi$
$140$		0			0
$141$	−4.92401	+	5.98980i	−0.0349220	+	0.0424809i
$142$		0			0
$143$			85.8066i			0.600046i
$144$		0			0
$145$		−	85.6594i		−	0.590754i
$146$		0			0
$147$	243.405	+	40.3933i	1.65582	+	0.274785i
$148$		0			0
$149$	75.7205	−	131.152i	0.508191	−	0.880213i	−0.491764	−	0.870729i	$-0.663648\pi$
$149$	75.7205	−	131.152i	0.508191	−	0.880213i	0.999955	−	0.00948453i	$-0.00301906\pi$
$150$		0			0
$151$	−191.195	+	110.386i	−1.26619	+	0.731035i	−0.974265	−	0.225407i	$-0.927629\pi$
$151$	−191.195	+	110.386i	−1.26619	+	0.731035i	−0.291924	+	0.956441i	$0.594296\pi$
$152$		0			0
$153$	−144.815	+	126.576i	−0.946503	+	0.827292i
$154$		0			0
$155$	0.117790	−	0.0680063i	0.000759938	−	0.000438750i
$156$		0			0
$157$	3.18306	−	5.51322i	0.0202743	−	0.0351160i	−0.855710	−	0.517455i	$-0.826879\pi$
$157$	3.18306	−	5.51322i	0.0202743	−	0.0351160i	0.875985	+	0.482339i	$0.160213\pi$
$158$		0			0
$159$	32.0713	−	12.0405i	0.201706	−	0.0757262i
$160$		0			0
$161$	−211.767			−1.31532
$162$		0			0
$163$	−184.645			−1.13279			−0.566395	−	0.824134i	$-0.691662\pi$
$163$	−184.645			−1.13279			−0.566395	+	0.824134i	$0.691662\pi$
$164$		0			0
$165$	−38.6947	−	103.068i	−0.234513	−	0.624654i
$166$		0			0
$167$	−170.755	−	98.5855i	−1.02249	−	0.590332i	−0.107663	−	0.994187i	$-0.534337\pi$
$167$	−170.755	−	98.5855i	−1.02249	−	0.590332i	−0.914823	+	0.403855i	$0.867670\pi$
$168$		0			0
$169$	−44.5164	−	77.1046i	−0.263411	−	0.456240i
$170$		0			0
$171$	−26.5683	−	168.923i	−0.155370	−	0.987856i
$172$		0			0
$173$	−237.112	+	136.897i	−1.37059	+	0.791310i	−0.991002	−	0.133846i	$-0.957267\pi$
$173$	−237.112	+	136.897i	−1.37059	+	0.791310i	−0.379587	+	0.925156i	$0.623934\pi$
$174$		0			0
$175$	59.4204	−	102.919i	0.339545	−	0.588110i
$176$		0			0
$177$	−27.4979	+	165.699i	−0.155356	+	0.936153i
$178$		0			0
$179$		−	235.524i		−	1.31578i	−0.753115	−	0.657889i	$-0.771449\pi$
$179$		−	235.524i		−	1.31578i	0.753115	−	0.657889i	$-0.228551\pi$
$180$		0			0
$181$			19.1952i			0.106051i	0.998593	+	0.0530255i	$0.0168865\pi$
$181$			19.1952i			0.106051i	−0.998593	+	0.0530255i	$0.983114\pi$
$182$		0			0
$183$	131.516	−	159.983i	0.718667	−	0.874222i
$184$		0			0
$185$	−232.165	−	134.041i	−1.25495	−	0.724544i
$186$		0			0
$187$	−102.530	−	177.587i	−0.548288	−	0.949663i
$188$		0			0
$189$	−9.35284	−	309.176i	−0.0494859	−	1.63585i
$190$		0			0
$191$	50.2350	+	87.0097i	0.263011	+	0.455548i	0.967041	−	0.254622i	$-0.0819512\pi$
$191$	50.2350	+	87.0097i	0.263011	+	0.455548i	−0.704030	+	0.710170i	$0.748618\pi$
$192$		0			0
$193$	−17.3894	−	10.0398i	−0.0901004	−	0.0520195i	0.454273	−	0.890863i	$-0.349899\pi$
$193$	−17.3894	−	10.0398i	−0.0901004	−	0.0520195i	−0.544373	+	0.838843i	$0.683232\pi$
$194$		0			0
$195$	−79.2570	−	65.1544i	−0.406446	−	0.334125i
$196$		0			0
$197$	−16.8259			−0.0854108			−0.0427054	−	0.999088i	$-0.513598\pi$
$197$	−16.8259			−0.0854108			−0.0427054	+	0.999088i	$0.513598\pi$
$198$		0			0
$199$	−360.537			−1.81175			−0.905873	−	0.423550i	$-0.860784\pi$
$199$	−360.537			−1.81175			−0.905873	+	0.423550i	$0.860784\pi$
$200$		0			0
$201$	11.6819	−	70.3939i	0.0581191	−	0.350218i
$202$		0			0
$203$	222.216	+	128.297i	1.09466	+	0.632003i
$204$		0			0
$205$	57.2726	−	33.0663i	0.279378	−	0.161299i
$206$		0			0
$207$	32.1859	+	163.221i	0.155487	+	0.788508i
$208$		0			0
$209$	182.177	+	7.05224i	0.871660	+	0.0337428i
$210$		0			0
$211$	252.579	+	145.827i	1.19706	+	0.691122i	0.959898	−	0.280348i	$-0.0904499\pi$
$211$	252.579	+	145.827i	1.19706	+	0.691122i	0.237161	+	0.971470i	$0.423783\pi$
$212$		0			0
$213$	290.932	−	109.224i	1.36588	−	0.512790i
$214$		0			0
$215$	82.0160			0.381470
$216$		0			0
$217$			0.407427i			0.00187754i
$218$		0			0
$219$	−33.0048	−	87.9124i	−0.150707	−	0.401427i
$220$		0			0
$221$	−165.502	−	95.5525i	−0.748877	−	0.432364i
$222$		0			0
$223$	−297.509	+	171.767i	−1.33412	+	0.770256i	−0.985929	−	0.167166i	$-0.946538\pi$
$223$	−297.509	+	171.767i	−1.33412	+	0.770256i	−0.348194	+	0.937422i	$0.613205\pi$
$224$		0			0
$225$	−88.3570	−	30.1564i	−0.392698	−	0.134028i
$226$		0			0
$227$	334.023	−	192.848i	1.47147	−	0.849553i	0.471982	−	0.881608i	$-0.343539\pi$
$227$	334.023	−	192.848i	1.47147	−	0.849553i	0.999486	+	0.0320556i	$0.0102054\pi$
$228$		0			0
$229$	−215.740	+	373.673i	−0.942097	+	1.63176i	−0.180635	+	0.983550i	$0.557815\pi$
$229$	−215.740	+	373.673i	−0.942097	+	1.63176i	−0.761462	+	0.648209i	$0.775518\pi$
$230$		0			0
$231$	325.333	+	53.9893i	1.40837	+	0.233720i
$232$		0			0
$233$	57.6767			0.247539			0.123770	−	0.992311i	$-0.460502\pi$
$233$	57.6767			0.247539			0.123770	+	0.992311i	$0.460502\pi$
$234$		0			0
$235$	9.88488			0.0420633
$236$		0			0
$237$	−76.4010	−	62.8066i	−0.322367	−	0.265007i
$238$		0			0
$239$	21.3107	−	36.9112i	0.0891661	−	0.154440i	−0.817993	−	0.575229i	$-0.804913\pi$
$239$	21.3107	−	36.9112i	0.0891661	−	0.154440i	0.907159	+	0.420788i	$0.138246\pi$
$240$		0			0
$241$	64.4105	−	37.1874i	0.267264	−	0.154305i	−0.360380	−	0.932806i	$-0.617353\pi$
$241$	64.4105	−	37.1874i	0.267264	−	0.154305i	0.627643	+	0.778501i	$0.284020\pi$
$242$		0			0
$243$	−236.878	+	54.1996i	−0.974808	+	0.223044i
$244$		0			0
$245$	−157.271	−	272.401i	−0.641921	−	1.11184i
$246$		0			0
$247$	150.319	−	79.1978i	0.608580	−	0.320639i
$248$		0			0
$249$	−5.27704	+	6.41925i	−0.0211929	+	0.0257801i
$250$		0			0
$251$	312.551			1.24522			0.622612	−	0.782531i	$-0.286071\pi$
$251$	312.551			1.24522			0.622612	+	0.782531i	$0.286071\pi$
$252$		0			0
$253$	−177.371			−0.701070
$254$		0			0
$255$	241.885	+	40.1410i	0.948567	+	0.157416i
$256$		0			0
$257$	382.713	+	220.960i	1.48916	+	0.859765i	0.999923	−	0.0123878i	$-0.00394326\pi$
$257$	382.713	+	220.960i	1.48916	+	0.859765i	0.489233	+	0.872153i	$0.337277\pi$
$258$		0			0
$259$	695.453	−	401.520i	2.68515	−	1.55027i
$260$		0			0
$261$	65.1117	−	190.775i	0.249470	−	0.730937i
$262$		0			0
$263$	−188.811	−	327.031i	−0.717913	−	1.24346i	−0.961825	−	0.273665i	$-0.911764\pi$
$263$	−188.811	−	327.031i	−0.717913	−	1.24346i	0.243912	−	0.969797i	$-0.421569\pi$
$264$		0			0
$265$	−37.8206	−	21.8357i	−0.142719	−	0.0823990i
$266$		0			0
$267$	315.194	−	118.333i	1.18050	−	0.443195i
$268$		0			0
$269$		−	512.749i		−	1.90613i	−0.302763	−	0.953066i	$-0.597909\pi$
$269$		−	512.749i		−	1.90613i	0.302763	−	0.953066i	$-0.402091\pi$
$270$		0			0
$271$	110.311			0.407050			0.203525	−	0.979070i	$-0.434760\pi$
$271$	110.311			0.407050			0.203525	+	0.979070i	$0.434760\pi$
$272$		0			0
$273$	287.730	−	108.022i	1.05396	−	0.395686i
$274$		0			0
$275$	49.7691	−	86.2026i	0.180979	−	0.313464i
$276$		0			0
$277$	131.806	+	228.294i	0.475833	+	0.824167i	0.999617	−	0.0276842i	$-0.00881327\pi$
$277$	131.806	+	228.294i	0.475833	+	0.824167i	−0.523784	+	0.851851i	$0.675480\pi$
$278$		0			0
$279$	0.314027	−	0.0619237i	0.00112555	−	0.000221949i
$280$		0			0
$281$	64.0202	−	36.9621i	0.227830	−	0.131538i	−0.381741	−	0.924269i	$-0.624675\pi$
$281$	64.0202	−	36.9621i	0.227830	−	0.131538i	0.609570	+	0.792732i	$0.291342\pi$
$282$		0			0
$283$	−221.009	+	382.798i	−0.780950	+	1.35264i	0.150440	+	0.988619i	$0.451931\pi$
$283$	−221.009	+	382.798i	−0.780950	+	1.35264i	−0.931389	+	0.364025i	$0.881402\pi$
$284$		0			0
$285$	−144.844	+	162.916i	−0.508224	+	0.571637i
$286$		0			0
$287$			198.101i			0.690247i
$288$		0			0
$289$	167.701			0.580280
$290$		0			0
$291$	−131.490	−	108.093i	−0.451854	−	0.371454i
$292$		0			0
$293$	−305.135	−	176.170i	−1.04142	−	0.601261i	−0.121182	−	0.992630i	$-0.538668\pi$
$293$	−305.135	−	176.170i	−1.04142	−	0.601261i	−0.920234	+	0.391369i	$0.872002\pi$
$294$		0			0
$295$	185.438	−	107.063i	0.628604	−	0.362925i
$296$		0			0
$297$	−7.83371	−	258.958i	−0.0263761	−	0.871914i
$298$		0			0
$299$	−143.154	+	82.6501i	−0.478777	+	0.276422i
$300$		0			0
$301$	−122.840	+	212.765i	−0.408106	+	0.706860i
$302$		0			0
$303$	−197.406	+	240.134i	−0.651504	+	0.792521i
$304$		0			0
$305$	−264.017			−0.865629
$306$		0			0
$307$		−	76.9855i		−	0.250767i	−0.992108	−	0.125384i	$-0.959984\pi$
$307$		−	76.9855i		−	0.250767i	0.992108	−	0.125384i	$-0.0400162\pi$
$308$		0			0
$309$	24.8743	−	149.889i	0.0804993	−	0.485079i
$310$		0			0
$311$	85.3473	−	147.826i	0.274429	−	0.475324i	−0.695562	−	0.718466i	$-0.744845\pi$
$311$	85.3473	−	147.826i	0.274429	−	0.475324i	0.969991	+	0.243142i	$0.0781780\pi$
$312$		0			0
$313$	5.47062	+	9.47539i	0.0174780	+	0.0302728i	0.874632	−	0.484787i	$-0.161103\pi$
$313$	5.47062	+	9.47539i	0.0174780	+	0.0302728i	−0.857154	+	0.515060i	$0.827770\pi$
$314$		0			0
$315$	−296.899	+	259.505i	−0.942536	+	0.823825i
$316$		0			0
$317$	−472.712	+	272.920i	−1.49120	+	0.860947i	−0.999949	−	0.0100689i	$-0.996795\pi$
$317$	−472.712	+	272.920i	−1.49120	+	0.860947i	−0.491255	+	0.871016i	$0.663462\pi$
$318$		0			0
$319$	186.123	+	107.458i	0.583458	+	0.336859i
$320$		0			0
$321$	334.908	−	125.734i	1.04333	−	0.391695i
$322$		0			0
$323$	−216.471	+	343.525i	−0.670188	+	1.06355i
$324$		0			0
$325$		−	92.7644i		−	0.285429i
$326$		0			0
$327$	−215.596	+	80.9408i	−0.659314	+	0.247525i
$328$		0			0
$329$	−14.8051	+	25.6432i	−0.0450004	+	0.0779429i
$330$		0			0
$331$	−276.390	+	159.574i	−0.835014	+	0.482096i	−0.855566	−	0.517693i	$-0.826791\pi$
$331$	−276.390	+	159.574i	−0.835014	+	0.482096i	0.0205521	+	0.999789i	$0.493458\pi$
$332$		0			0
$333$	−415.175	−	475.000i	−1.24677	−	1.42643i
$334$		0			0
$335$	−78.7796	+	45.4835i	−0.235163	+	0.135771i
$336$		0			0
$337$	−348.668	−	201.303i	−1.03462	−	0.597339i	−0.116317	−	0.993212i	$-0.537109\pi$
$337$	−348.668	−	201.303i	−1.03462	−	0.597339i	−0.918305	+	0.395873i	$0.870442\pi$
$338$		0			0
$339$	−2.60460	+	15.6950i	−0.00768318	+	0.0462979i
$340$		0			0
$341$			0.341251i			0.00100074i
$342$		0			0
$343$	380.857			1.11037
$344$		0			0
$345$	134.681	−	163.832i	0.390379	−	0.474876i
$346$		0			0
$347$	−272.973	+	472.803i	−0.786665	+	1.36254i	0.141334	+	0.989962i	$0.454861\pi$
$347$	−272.973	+	472.803i	−0.786665	+	1.36254i	−0.927999	+	0.372582i	$0.878472\pi$
$348$		0			0
$349$	310.169	+	537.228i	0.888735	+	1.53934i	0.841371	+	0.540457i	$0.181749\pi$
$349$	310.169	+	537.228i	0.888735	+	1.53934i	0.0473641	+	0.998878i	$0.484918\pi$
$350$		0			0
$351$	−126.990	−	205.352i	−0.361796	−	0.585049i
$352$		0			0
$353$	128.114	+	221.900i	0.362929	+	0.628611i	0.988441	−	0.151603i	$-0.0484436\pi$
$353$	128.114	+	221.900i	0.362929	+	0.628611i	−0.625513	+	0.780214i	$0.715110\pi$
$354$		0			0
$355$	−343.087	−	198.081i	−0.966443	−	0.557976i
$356$		0			0
$357$	−466.417	+	567.372i	−1.30649	+	1.58928i
$358$		0			0
$359$	−39.6964			−0.110575			−0.0552875	−	0.998470i	$-0.517608\pi$
$359$	−39.6964			−0.110575			−0.0552875	+	0.998470i	$0.517608\pi$
$360$		0			0
$361$	−155.791	−	325.653i	−0.431555	−	0.902087i
$362$		0			0
$363$	−85.6119	−	14.2074i	−0.235845	−	0.0391388i
$364$		0			0
$365$	−59.8552	+	103.672i	−0.163987	+	0.284034i
$366$		0			0
$367$	106.807	+	184.996i	0.291028	+	0.504075i	0.974053	−	0.226320i	$-0.0726694\pi$
$367$	106.807	+	184.996i	0.291028	+	0.504075i	−0.683025	+	0.730395i	$0.739336\pi$
$368$		0			0
$369$	152.688	−	30.1088i	0.413788	−	0.0815957i
$370$		0			0
$371$	113.292	−	65.4091i	0.305369	−	0.176305i
$372$		0			0
$373$	486.381	+	280.812i	1.30397	+	0.752848i	0.981083	−	0.193589i	$-0.0620130\pi$
$373$	486.381	+	280.812i	1.30397	+	0.752848i	0.322888	+	0.946437i	$0.395346\pi$
$374$		0			0
$375$	142.648	+	379.959i	0.380393	+	1.01322i
$376$		0			0
$377$	200.291			0.531275
$378$		0			0
$379$			539.903i			1.42455i	0.701903	+	0.712273i	$0.252334\pi$
$379$			539.903i			1.42455i	−0.701903	+	0.712273i	$0.747666\pi$
$380$		0			0
$381$	158.726	−	59.5903i	0.416604	−	0.156405i
$382$		0			0
$383$	−309.262	−	178.553i	−0.807473	−	0.466195i	0.0386044	−	0.999255i	$-0.487709\pi$
$383$	−309.262	−	178.553i	−0.807473	−	0.466195i	−0.846078	+	0.533060i	$0.821042\pi$
$384$		0			0
$385$	−210.206	−	364.088i	−0.545990	−	0.945683i
$386$		0			0
$387$	182.660	+	62.3423i	0.471991	+	0.161091i
$388$		0			0
$389$	−386.403	−	669.270i	−0.993324	−	1.72049i	−0.596565	−	0.802565i	$-0.703468\pi$
$389$	−386.403	−	669.270i	−0.993324	−	1.72049i	−0.396759	−	0.917923i	$-0.629865\pi$
$390$		0			0
$391$	197.516	−	342.109i	0.505157	−	0.874958i
$392$		0			0
$393$	−70.9514	−	11.7745i	−0.180538	−	0.0299605i
$394$		0			0
$395$			126.083i			0.319199i
$396$		0			0
$397$	−256.074			−0.645023			−0.322512	−	0.946566i	$-0.604527\pi$
$397$	−256.074			−0.645023			−0.322512	+	0.946566i	$0.604527\pi$
$398$		0			0
$399$	−205.695	−	619.761i	−0.515526	−	1.55329i
$400$		0			0
$401$	−62.0407	−	35.8192i	−0.154715	−	0.0893247i	0.420644	−	0.907226i	$-0.361804\pi$
$401$	−62.0407	−	35.8192i	−0.154715	−	0.0893247i	−0.575359	+	0.817901i	$0.695138\pi$
$402$		0			0
$403$	0.159014	+	0.275420i	0.000394575	+	0.000683424i
$404$		0			0
$405$	245.140	+	189.396i	0.605285	+	0.467644i
$406$		0			0
$407$	582.494	−	336.303i	1.43119	−	0.826298i
$408$		0			0
$409$	572.451	+	330.505i	1.39964	+	0.808080i	0.994354	−	0.106112i	$-0.0338401\pi$
$409$	572.451	+	330.505i	1.39964	+	0.808080i	0.405282	+	0.914192i	$0.367173\pi$
$410$		0			0
$411$	−267.795	+	325.759i	−0.651570	+	0.792602i
$412$		0			0
$413$			641.415i			1.55306i
$414$		0			0
$415$	10.5936			0.0255267
$416$		0			0
$417$	509.570	+	84.5637i	1.22199	+	0.202791i
$418$		0			0
$419$	159.011	−	275.415i	0.379501	−	0.657316i	−0.611488	−	0.791253i	$-0.709429\pi$
$419$	159.011	−	275.415i	0.379501	−	0.657316i	0.990990	+	0.133938i	$0.0427622\pi$
$420$		0			0
$421$	−424.217	+	244.922i	−1.00764	+	0.581762i	−0.910500	−	0.413509i	$-0.864303\pi$
$421$	−424.217	+	244.922i	−1.00764	+	0.581762i	−0.0971407	+	0.995271i	$0.530970\pi$
$422$		0			0
$423$	22.0149	+	7.51372i	0.0520447	+	0.0177629i
$424$		0			0
$425$	110.844	+	191.987i	0.260809	+	0.451734i
$426$		0			0
$427$	395.432	−	684.909i	0.926071	−	1.60400i
$428$		0			0
$429$	240.996	−	90.4767i	0.561762	−	0.210901i
$430$		0			0
$431$			325.107i			0.754310i	0.926150	+	0.377155i	$0.123098\pi$
$431$			325.107i			0.754310i	−0.926150	+	0.377155i	$0.876902\pi$
$432$		0			0
$433$			538.799i			1.24434i	0.782882	+	0.622170i	$0.213749\pi$
$433$			538.799i			1.24434i	−0.782882	+	0.622170i	$0.786251\pi$
$434$		0			0
$435$	−240.582	+	90.3215i	−0.553063	+	0.207636i
$436$		0			0
$437$	163.710	+	310.725i	0.374622	+	0.711041i
$438$		0			0
$439$	−398.313	+	229.966i	−0.907319	+	0.523841i	−0.879567	−	0.475774i	$-0.842168\pi$
$439$	−398.313	+	229.966i	−0.907319	+	0.523841i	−0.0277512	+	0.999615i	$0.508835\pi$
$440$		0			0
$441$	−143.204	−	726.217i	−0.324726	−	1.64675i
$442$		0			0
$443$	288.684	+	500.015i	0.651657	+	1.12870i	0.982721	+	0.185094i	$0.0592591\pi$
$443$	288.684	+	500.015i	0.651657	+	1.12870i	−0.331064	+	0.943608i	$0.607408\pi$
$444$		0			0
$445$	−371.699	−	214.600i	−0.835278	−	0.482248i
$446$		0			0
$447$	−448.193	−	74.3782i	−1.00267	−	0.166394i
$448$		0			0
$449$			808.858i			1.80147i	0.434373	+	0.900733i	$0.356970\pi$
$449$			808.858i			1.80147i	−0.434373	+	0.900733i	$0.643030\pi$
$450$		0			0
$451$			165.924i			0.367904i
$452$		0			0
$453$	511.630	+	420.593i	1.12943	+	0.928462i
$454$		0			0
$455$	−339.311	−	195.901i	−0.745738	−	0.430552i
$456$		0			0
$457$	−166.118	−	287.724i	−0.363496	−	0.629594i	0.625037	−	0.780595i	$-0.285084\pi$
$457$	−166.118	−	287.724i	−0.363496	−	0.629594i	−0.988534	+	0.151001i	$0.951750\pi$
$458$		0			0
$459$	508.196	+	273.261i	1.10718	+	0.595340i
$460$		0			0
$461$	−40.4567	−	70.0731i	−0.0877586	−	0.152002i	0.818805	−	0.574072i	$-0.194637\pi$
$461$	−40.4567	−	70.0731i	−0.0877586	−	0.152002i	−0.906563	+	0.422070i	$0.861304\pi$
$462$		0			0
$463$	162.418	−	281.316i	0.350794	−	0.607593i	−0.635595	−	0.772023i	$-0.719245\pi$
$463$	162.418	−	281.316i	0.350794	−	0.607593i	0.986389	+	0.164430i	$0.0525784\pi$
$464$		0			0
$465$	−0.315203	−	0.259117i	−0.000677856	−	0.000557242i
$466$		0			0
$467$	261.167			0.559244			0.279622	−	0.960110i	$-0.409791\pi$
$467$	261.167			0.559244			0.279622	+	0.960110i	$0.409791\pi$
$468$		0			0
$469$		−	272.492i		−	0.581007i
$470$		0			0
$471$	−18.8407	−	3.12663i	−0.0400014	−	0.00663828i
$472$		0			0
$473$	−102.888	+	178.207i	−0.217522	+	0.376758i
$474$		0			0
$475$	−196.949	−	7.62408i	−0.414629	−	0.0160507i
$476$		0			0
$477$	−67.6335	−	77.3793i	−0.141789	−	0.162221i
$478$		0			0
$479$	107.772	+	186.666i	0.224993	+	0.389700i	0.956317	−	0.292330i	$-0.0944306\pi$
$479$	107.772	+	186.666i	0.224993	+	0.389700i	−0.731324	+	0.682030i	$0.761097\pi$
$480$		0			0
$481$	313.417	−	542.854i	0.651594	−	1.12859i
$482$		0			0
$483$	223.292	+	594.767i	0.462303	+	1.23140i
$484$		0			0
$485$			216.995i			0.447413i
$486$		0			0
$487$		−	835.680i		−	1.71598i	−0.513670	−	0.857988i	$-0.671714\pi$
$487$		−	835.680i		−	1.71598i	0.513670	−	0.857988i	$-0.328286\pi$
$488$		0			0
$489$	194.694	+	518.591i	0.398147	+	1.06051i
$490$		0			0
$491$	−271.039	+	469.453i	−0.552014	+	0.956117i	0.446115	+	0.894976i	$0.352807\pi$
$491$	−271.039	+	469.453i	−0.552014	+	0.956117i	−0.998129	+	0.0611409i	$0.980526\pi$
$492$		0			0
$493$	−414.525	+	239.326i	−0.840822	+	0.485449i
$494$		0			0
$495$	−248.675	+	217.355i	−0.502374	+	0.439101i
$496$		0			0
$497$	1027.72	−	593.355i	2.06785	−	1.19387i
$498$		0			0
$499$	−361.979	+	626.967i	−0.725410	+	1.25645i	0.233396	+	0.972382i	$0.425016\pi$
$499$	−361.979	+	626.967i	−0.725410	+	1.25645i	−0.958805	+	0.284064i	$0.908317\pi$
$500$		0			0
$501$	−96.8379	+	583.532i	−0.193289	+	1.16474i
$502$		0			0
$503$	619.749			1.23211			0.616053	−	0.787705i	$-0.288731\pi$
$503$	619.749			1.23211			0.616053	+	0.787705i	$0.288731\pi$
$504$		0			0
$505$	396.289			0.784731
$506$		0			0
$507$	−169.616	+	206.329i	−0.334549	+	0.406961i
$508$		0			0
$509$	−540.634	−	312.135i	−1.06215	−	0.613232i	−0.136123	−	0.990692i	$-0.543464\pi$
$509$	−540.634	−	312.135i	−1.06215	−	0.613232i	−0.926026	+	0.377460i	$0.876798\pi$
$510$		0			0
$511$	−179.297	−	310.551i	−0.350874	−	0.607732i
$512$		0			0
$513$	−446.423	+	252.737i	−0.870219	+	0.492664i
$514$		0			0
$515$	−167.745	+	96.8476i	−0.325718	+	0.188054i
$516$		0			0
$517$	−12.4004	+	21.4781i	−0.0239853	+	0.0415438i
$518$		0			0
$519$	634.503	+	521.603i	1.22255	+	1.00502i
$520$		0			0
$521$		−	909.509i		−	1.74570i	−0.487990	−	0.872849i	$-0.662270\pi$
$521$		−	909.509i		−	1.74570i	0.487990	−	0.872849i	$-0.337730\pi$
$522$		0			0
$523$		−	200.239i		−	0.382867i	−0.981506	−	0.191433i	$-0.938686\pi$
$523$		−	200.239i		−	0.382867i	0.981506	−	0.191433i	$-0.0613136\pi$
$524$		0			0
$525$	−351.713	−	58.3671i	−0.669929	−	0.111175i
$526$		0			0
$527$	−0.658196	−	0.380010i	−0.00124895	−	0.000721081i
$528$		0			0
$529$	93.6540	+	162.214i	0.177040	+	0.306642i
$530$		0			0
$531$	494.376	−	97.4868i	0.931027	−	0.183591i
$532$		0			0
$533$	77.3164	+	133.916i	0.145059	+	0.251250i
$534$		0			0
$535$	−394.947	−	228.023i	−0.738218	−	0.426210i
$536$		0			0
$537$	−661.492	+	248.343i	−1.23183	+	0.462464i
$538$		0			0
$539$	789.173			1.46414
$540$		0			0
$541$	−452.699			−0.836782			−0.418391	−	0.908267i	$-0.637406\pi$
$541$	−452.699			−0.836782			−0.418391	+	0.908267i	$0.637406\pi$
$542$		0			0
$543$	53.9116	−	20.2400i	0.0992847	−	0.0372743i
$544$		0			0
$545$	254.245	+	146.788i	0.466504	+	0.269336i
$546$		0			0
$547$	−721.135	+	416.348i	−1.31835	+	0.761148i	−0.983463	−	0.181112i	$-0.942030\pi$
$547$	−721.135	+	416.348i	−1.31835	+	0.761148i	−0.334884	+	0.942259i	$0.608697\pi$
$548$		0			0
$549$	−588.000	−	200.685i	−1.07104	−	0.365547i
$550$		0			0
$551$	16.4614	−	425.239i	0.0298755	−	0.771759i
$552$		0			0
$553$	−327.084	−	188.842i	−0.591472	−	0.341487i
$554$		0			0
$555$	−131.664	+	793.393i	−0.237233	+	1.42954i
$556$		0			0
$557$	758.522			1.36180			0.680899	−	0.732377i	$-0.261589\pi$
$557$	758.522			1.36180			0.680899	+	0.732377i	$0.261589\pi$
$558$		0			0
$559$			191.772i			0.343062i
$560$		0			0
$561$	−390.659	+	475.217i	−0.696362	+	0.847089i
$562$		0			0
$563$	143.945	+	83.1064i	0.255674	+	0.147614i	0.622360	−	0.782731i	$-0.286174\pi$
$563$	143.945	+	83.1064i	0.255674	+	0.147614i	−0.366686	+	0.930345i	$0.619507\pi$
$564$		0			0
$565$	17.5647	−	10.1410i	0.0310879	−	0.0179486i
$566$		0			0
$567$	−858.487	+	352.271i	−1.51409	+	0.621290i
$568$		0			0
$569$	−228.473	+	131.909i	−0.401534	+	0.231826i	−0.687146	−	0.726519i	$-0.741137\pi$
$569$	−228.473	+	131.909i	−0.401534	+	0.231826i	0.285611	+	0.958346i	$0.407803\pi$
$570$		0			0
$571$	500.217	−	866.402i	0.876037	−	1.51734i	0.0203836	−	0.999792i	$-0.493511\pi$
$571$	500.217	−	866.402i	0.876037	−	1.51734i	0.855654	−	0.517549i	$-0.173155\pi$
$572$		0			0
$573$	191.405	−	232.835i	0.334041	−	0.406344i
$574$		0			0
$575$	191.753			0.333484
$576$		0			0
$577$	447.404			0.775397			0.387699	−	0.921786i	$-0.373270\pi$
$577$	447.404			0.775397			0.387699	+	0.921786i	$0.373270\pi$
$578$		0			0
$579$	−9.86179	+	59.4259i	−0.0170324	+	0.102635i
$580$		0			0
$581$	−15.8666	+	27.4818i	−0.0273091	+	0.0473008i
$582$		0			0
$583$	94.8905	−	54.7851i	0.162762	−	0.0939710i
$584$		0			0
$585$	−99.4215	+	291.301i	−0.169951	+	0.497951i
$586$		0			0
$587$	400.936	+	694.442i	0.683026	+	1.18304i	0.974053	+	0.226321i	$0.0726699\pi$
$587$	400.936	+	694.442i	0.683026	+	1.18304i	−0.291026	+	0.956715i	$0.593997\pi$
$588$		0			0
$589$	0.597816	−	0.314968i	0.00101497	−	0.000534750i
$590$		0			0
$591$	17.7417	+	47.2572i	0.0300198	+	0.0799614i
$592$		0			0
$593$	268.667			0.453064			0.226532	−	0.974004i	$-0.427261\pi$
$593$	268.667			0.453064			0.226532	+	0.974004i	$0.427261\pi$
$594$		0			0
$595$	936.326			1.57366
$596$		0			0
$597$	380.160	+	1012.60i	0.636784	+	1.69615i
$598$		0			0
$599$	−862.258	−	497.825i	−1.43950	−	0.831093i	−0.441682	−	0.897172i	$-0.645618\pi$
$599$	−862.258	−	497.825i	−1.43950	−	0.831093i	−0.997814	+	0.0660785i	$0.978951\pi$
$600$		0			0
$601$	555.856	−	320.923i	0.924885	−	0.533982i	0.0396946	−	0.999212i	$-0.487361\pi$
$601$	555.856	−	320.923i	0.924885	−	0.533982i	0.885190	+	0.465229i	$0.154028\pi$
$602$		0			0
$603$	−210.025	+	41.4153i	−0.348301	+	0.0686821i
$604$		0			0
$605$	55.3162	+	95.8105i	0.0914318	+	0.158364i
$606$		0			0
$607$	−28.4848	−	16.4457i	−0.0469272	−	0.0270935i	0.476353	−	0.879254i	$-0.341959\pi$
$607$	−28.4848	−	16.4457i	−0.0469272	−	0.0270935i	−0.523280	+	0.852161i	$0.675292\pi$
$608$		0			0
$609$	126.022	−	759.394i	0.206933	−	1.24695i
$610$		0			0
$611$			23.1130i			0.0378282i
$612$		0			0
$613$	633.976			1.03422			0.517110	−	0.855919i	$-0.327008\pi$
$613$	633.976			1.03422			0.517110	+	0.855919i	$0.327008\pi$
$614$		0			0
$615$	−153.259	−	125.989i	−0.249202	−	0.204861i
$616$		0			0
$617$	−491.645	+	851.555i	−0.796832	+	1.38015i	0.124837	+	0.992177i	$0.460159\pi$
$617$	−491.645	+	851.555i	−0.796832	+	1.38015i	−0.921669	+	0.387976i	$0.873174\pi$
$618$		0			0
$619$	−354.259	−	613.594i	−0.572308	−	0.991266i	−0.996328	−	0.0856137i	$-0.972715\pi$
$619$	−354.259	−	613.594i	−0.572308	−	0.991266i	0.424021	−	0.905653i	$-0.360618\pi$
$620$		0			0
$621$	424.484	−	262.501i	0.683549	−	0.422708i
$622$		0			0
$623$	1113.43	−	642.837i	1.78720	−	1.03184i
$624$		0			0
$625$	129.027	−	223.481i	0.206443	−	0.357569i
$626$		0			0
$627$	−172.285	−	519.096i	−0.274777	−	0.827905i
$628$		0			0
$629$			1498.00i			2.38156i
$630$		0			0
$631$	−344.066			−0.545271			−0.272636	−	0.962117i	$-0.587895\pi$
$631$	−344.066			−0.545271			−0.272636	+	0.962117i	$0.587895\pi$
$632$		0			0
$633$	143.242	−	863.156i	0.226290	−	1.36360i
$634$		0			0
$635$	−187.181	−	108.069i	−0.294773	−	0.170187i
$636$		0			0
$637$	636.934	−	367.734i	0.999896	−	0.577290i
$638$		0			0
$639$	−613.533	−	701.941i	−0.960146	−	1.09850i
$640$		0			0
$641$	453.035	−	261.560i	0.706763	−	0.408050i	−0.103098	−	0.994671i	$-0.532876\pi$
$641$	453.035	−	261.560i	0.706763	−	0.408050i	0.809861	+	0.586621i	$0.199542\pi$
$642$		0			0
$643$	110.396	−	191.211i	0.171689	−	0.297373i	−0.767322	−	0.641262i	$-0.778411\pi$
$643$	110.396	−	191.211i	0.171689	−	0.297373i	0.939010	+	0.343889i	$0.111744\pi$
$644$		0			0
$645$	−86.4798	−	230.350i	−0.134077	−	0.357131i
$646$		0			0
$647$	849.026			1.31225			0.656125	−	0.754652i	$-0.272194\pi$
$647$	849.026			1.31225			0.656125	+	0.754652i	$0.272194\pi$
$648$		0			0
$649$			537.233i			0.827786i
$650$		0			0
$651$	1.14430	−	0.429601i	0.00175775	−	0.000659910i
$652$		0			0
$653$	−602.652	+	1043.82i	−0.922898	+	1.59851i	−0.127991	+	0.991775i	$0.540853\pi$
$653$	−602.652	+	1043.82i	−0.922898	+	1.59851i	−0.794907	+	0.606731i	$0.792481\pi$
$654$		0			0
$655$	45.8437	+	79.4035i	0.0699903	+	0.121227i
$656$		0			0
$657$	−212.109	+	185.394i	−0.322845	+	0.282183i
$658$		0			0
$659$	373.829	−	215.830i	0.567266	−	0.327511i	−0.188790	−	0.982017i	$-0.560457\pi$
$659$	373.829	−	215.830i	0.567266	−	0.327511i	0.756057	+	0.654506i	$0.227123\pi$
$660$		0			0
$661$	−102.024	−	58.9036i	−0.154348	−	0.0891128i	0.420837	−	0.907136i	$-0.361737\pi$
$661$	−102.024	−	58.9036i	−0.154348	−	0.0891128i	−0.575185	+	0.818024i	$0.695070\pi$
$662$		0			0
$663$	−93.8586	+	565.580i	−0.141567	+	0.853062i
$664$		0			0
$665$	−443.807	+	704.293i	−0.667379	+	1.05909i
$666$		0			0
$667$			414.021i			0.620721i
$668$		0			0
$669$	796.125	+	654.467i	1.19002	+	0.978276i
$670$		0			0
$671$	331.204	−	573.663i	0.493598	−	0.854937i
$672$		0			0
$673$	188.742	−	108.970i	0.280448	−	0.161917i	−0.353178	−	0.935556i	$-0.614899\pi$
$673$	188.742	−	108.970i	0.280448	−	0.161917i	0.633626	+	0.773639i	$0.281566\pi$
$674$		0			0
$675$	8.46891	+	279.956i	0.0125465	+	0.414750i
$676$		0			0
$677$	322.990	−	186.479i	0.477091	−	0.275448i	−0.242113	−	0.970248i	$-0.577840\pi$
$677$	322.990	−	186.479i	0.477091	−	0.275448i	0.719203	+	0.694800i	$0.244507\pi$
$678$		0			0
$679$	−562.926	−	325.006i	−0.829052	−	0.478653i
$680$		0			0
$681$	−893.835	−	734.791i	−1.31253	−	1.07899i
$682$		0			0
$683$		−	581.301i		−	0.851100i	−0.904935	−	0.425550i	$-0.860081\pi$
$683$		−	581.301i		−	0.851100i	0.904935	−	0.425550i	$-0.139919\pi$
$684$		0			0
$685$	537.596			0.784811
$686$		0			0
$687$	1276.98	+	211.916i	1.85877	+	0.308465i
$688$		0			0
$689$	51.0568	−	88.4330i	0.0741027	−	0.128350i
$690$		0			0
$691$	119.093	+	206.276i	0.172349	+	0.298518i	0.939241	−	0.343259i	$-0.111531\pi$
$691$	119.093	+	206.276i	0.172349	+	0.298518i	−0.766892	+	0.641777i	$0.778198\pi$
$692$		0			0
$693$	−191.405	−	970.654i	−0.276198	−	1.40065i
$694$		0			0
$695$	−329.247	−	570.273i	−0.473737	−	0.820537i
$696$		0			0
$697$	−320.031	−	184.770i	−0.459155	−	0.265093i
$698$		0			0
$699$	−60.8157	−	161.990i	−0.0870039	−	0.231746i
$700$		0			0
$701$	−1291.97			−1.84303			−0.921517	−	0.388337i	$-0.873050\pi$
$701$	−1291.97			−1.84303			−0.921517	+	0.388337i	$0.873050\pi$
$702$		0			0
$703$	−1126.78	−	710.034i	−1.60282	−	1.01001i
$704$		0			0
$705$	−10.4229	−	27.7626i	−0.0147842	−	0.0393796i
$706$		0			0
$707$	−593.544	+	1028.05i	−0.839525	+	1.45410i
$708$		0			0
$709$	255.155	+	441.942i	0.359880	+	0.623331i	0.987941	−	0.154834i	$-0.0494842\pi$
$709$	255.155	+	441.942i	0.359880	+	0.623331i	−0.628060	+	0.778165i	$0.716151\pi$
$710$		0			0
$711$	−95.8389	+	280.804i	−0.134795	+	0.394943i
$712$		0			0
$713$	−0.569320	+	0.328697i	−0.000798486	+	0.000461006i
$714$		0			0
$715$	−284.198	−	164.082i	−0.397480	−	0.229485i
$716$		0			0
$717$	−126.139	−	20.9329i	−0.175926	−	0.0291951i
$718$		0			0
$719$	552.681			0.768680			0.384340	−	0.923192i	$-0.374429\pi$
$719$	552.681			0.768680			0.384340	+	0.923192i	$0.374429\pi$
$720$		0			0
$721$		−	580.216i		−	0.804737i
$722$		0			0
$723$	−172.360	−	141.692i	−0.238396	−	0.195977i
$724$		0			0
$725$	−201.215	−	116.172i	−0.277538	−	0.160237i
$726$		0			0
$727$	−522.246	−	904.557i	−0.718358	−	1.24423i	−0.961650	−	0.274279i	$-0.911561\pi$
$727$	−522.246	−	904.557i	−0.718358	−	1.24423i	0.243292	−	0.969953i	$-0.421773\pi$
$728$		0			0
$729$	401.995	+	608.145i	0.551434	+	0.834219i
$730$		0			0
$731$	−229.147	−	396.895i	−0.313471	−	0.542947i
$732$		0			0
$733$	−392.986	+	680.672i	−0.536134	+	0.928612i	0.462973	+	0.886372i	$0.346783\pi$
$733$	−392.986	+	680.672i	−0.536134	+	0.928612i	−0.999108	+	0.0422394i	$0.986551\pi$
$734$		0			0
$735$	−599.232	+	728.936i	−0.815282	+	0.991749i
$736$		0			0
$737$		−	228.233i		−	0.309678i
$738$		0			0
$739$	−74.2492			−0.100472			−0.0502362	−	0.998737i	$-0.515997\pi$
$739$	−74.2492			−0.100472			−0.0502362	+	0.998737i	$0.515997\pi$
$740$		0			0
$741$	−380.935	−	338.677i	−0.514082	−	0.457054i
$742$		0			0
$743$	−686.222	−	396.190i	−0.923583	−	0.533231i	−0.0388065	−	0.999247i	$-0.512356\pi$
$743$	−686.222	−	396.190i	−0.923583	−	0.533231i	−0.884776	+	0.466016i	$0.845689\pi$
$744$		0			0
$745$	289.590	+	501.585i	0.388712	+	0.673268i
$746$		0			0
$747$	23.5933	+	8.05243i	0.0315841	+	0.0107797i
$748$		0			0
$749$	1183.07	−	683.043i	1.57953	−	0.911940i
$750$		0			0
$751$	829.037	+	478.645i	1.10391	+	0.637343i	0.937245	−	0.348670i	$-0.113367\pi$
$751$	829.037	+	478.645i	1.10391	+	0.637343i	0.166666	+	0.986013i	$0.446700\pi$
$752$		0			0
$753$	−329.562	−	877.829i	−0.437665	−	1.16578i
$754$		0			0
$755$		−	844.336i		−	1.11833i
$756$		0			0
$757$	246.591			0.325748			0.162874	−	0.986647i	$-0.447924\pi$
$757$	246.591			0.325748			0.162874	+	0.986647i	$0.447924\pi$
$758$		0			0
$759$	187.024	+	498.162i	0.246409	+	0.656340i
$760$		0			0
$761$	332.807	−	576.439i	0.437328	−	0.757475i	−0.560154	−	0.828388i	$-0.689258\pi$
$761$	332.807	−	576.439i	0.437328	−	0.757475i	0.997482	+	0.0709134i	$0.0225914\pi$
$762$		0			0
$763$	−761.593	+	439.706i	−0.998156	+	0.576285i
$764$		0			0
$765$	−142.310	−	721.681i	−0.186026	−	0.943373i
$766$		0			0
$767$	250.337	+	433.596i	0.326384	+	0.565314i
$768$		0			0
$769$	126.903	−	219.802i	0.165023	−	0.285828i	−0.771641	−	0.636059i	$-0.780564\pi$
$769$	126.903	−	219.802i	0.165023	−	0.285828i	0.936663	+	0.350231i	$0.113897\pi$
$770$		0			0
$771$	217.043	−	1307.87i	0.281508	−	1.69633i
$772$		0			0
$773$			1252.35i			1.62011i	0.586351	+	0.810057i	$0.300564\pi$
$773$			1252.35i			1.62011i	−0.586351	+	0.810057i	$0.699436\pi$
$774$		0			0
$775$		−	0.368921i		−	0.000476028i
$776$		0			0
$777$	−1861.01	−	1529.87i	−2.39512	−	1.96894i
$778$		0			0
$779$	290.673	−	153.145i	0.373136	−	0.196592i
$780$		0			0
$781$	860.793	−	496.979i	1.10217	−	0.636337i
$782$		0			0
$783$	−604.463	+	18.2855i	−0.771984	+	0.0233531i
$784$		0			0
$785$	12.1735	+	21.0851i	0.0155076	+	0.0268600i
$786$		0			0
$787$	−97.4294	−	56.2509i	−0.123799	−	0.0714751i	0.436822	−	0.899548i	$-0.356104\pi$
$787$	−97.4294	−	56.2509i	−0.123799	−	0.0714751i	−0.560620	+	0.828073i	$0.689437\pi$
$788$		0			0
$789$	−719.408	+	875.123i	−0.911797	+	1.10915i
$790$		0			0
$791$			60.7547i			0.0768074i
$792$		0			0
$793$		−	617.330i		−	0.778474i
$794$		0			0
$795$	−21.4486	+	129.247i	−0.0269794	+	0.162575i
$796$		0			0
$797$	−229.396	−	132.442i	−0.287825	−	0.166176i	0.349136	−	0.937072i	$-0.386475\pi$
$797$	−229.396	−	132.442i	−0.287825	−	0.166176i	−0.636960	+	0.770897i	$0.719809\pi$
$798$		0			0
$799$	−27.6177	−	47.8352i	−0.0345653	−	0.0598689i
$800$		0			0
$801$	−664.698	−	760.479i	−0.829835	−	0.949412i
$802$		0			0
$803$	−150.175	−	260.110i	−0.187017	−	0.323923i
$804$		0			0
$805$	404.947	−	701.389i	0.503040	−	0.871291i
$806$		0			0
$807$	−1440.10	+	540.656i	−1.78452	+	0.669958i
$808$		0			0
$809$	−876.066			−1.08290			−0.541450	−	0.840733i	$-0.682124\pi$
$809$	−876.066			−1.08290			−0.541450	+	0.840733i	$0.682124\pi$
$810$		0			0
$811$		−	1129.00i		−	1.39211i	−0.717990	−	0.696053i	$-0.754938\pi$
$811$		−	1129.00i		−	1.39211i	0.717990	−	0.696053i	$-0.245062\pi$
$812$		0			0
$813$	−116.314	−	309.817i	−0.143068	−	0.381079i
$814$		0			0
$815$	353.083	−	611.558i	0.433231	−	0.750378i
$816$		0			0
$817$	407.152	+	15.7613i	0.498351	+	0.0192916i
$818$		0			0
$819$	−606.780	−	694.215i	−0.740879	−	0.847638i
$820$		0			0
$821$	−34.6415	−	60.0009i	−0.0421943	−	0.0730827i	0.844157	−	0.536096i	$-0.180102\pi$
$821$	−34.6415	−	60.0009i	−0.0421943	−	0.0730827i	−0.886351	+	0.463013i	$0.846768\pi$
$822$		0			0
$823$	−122.859	+	212.798i	−0.149282	+	0.258564i	−0.930962	−	0.365115i	$-0.881030\pi$
$823$	−122.859	+	212.798i	−0.149282	+	0.258564i	0.781680	+	0.623679i	$0.214363\pi$
$824$		0			0
$825$	−294.586	−	48.8868i	−0.357074	−	0.0592568i
$826$		0			0
$827$		−	1068.34i		−	1.29182i	−0.763412	−	0.645912i	$-0.776477\pi$
$827$		−	1068.34i		−	1.29182i	0.763412	−	0.645912i	$-0.223523\pi$
$828$		0			0
$829$			1619.42i			1.95347i	0.214458	+	0.976733i	$0.431201\pi$
$829$			1619.42i			1.95347i	−0.214458	+	0.976733i	$0.568799\pi$
$830$		0			0
$831$	502.206	−	610.908i	0.604339	−	0.735148i
$832$		0			0
$833$	−878.807	+	1522.14i	−1.05499	+	1.82730i
$834$		0			0
$835$	653.046	−	377.036i	0.782091	−	0.451541i
$836$		0			0
$837$	−0.505037	−	0.816681i	−0.000603389	−	0.000975724i
$838$		0			0
$839$	−2.69651	+	1.55683i	−0.00321396	+	0.00185558i	−0.501606	−	0.865096i	$-0.667257\pi$
$839$	−2.69651	+	1.55683i	−0.00321396	+	0.00185558i	0.498392	+	0.866952i	$0.333924\pi$
$840$		0			0
$841$	−169.670	+	293.877i	−0.201748	+	0.349438i
$842$		0			0
$843$	−171.316	−	140.833i	−0.203222	−	0.167061i
$844$		0			0
$845$	340.502			0.402961
$846$		0			0
$847$	−331.400			−0.391264
$848$		0			0
$849$	1308.16	+	217.091i	1.54083	+	0.255702i
$850$		0			0
$851$	1122.13	+	647.864i	1.31860	+	0.761297i
$852$		0			0
$853$	−729.162	−	1262.95i	−0.854820	−	1.48059i	−0.876812	−	0.480834i	$-0.840334\pi$
$853$	−729.162	−	1262.95i	−0.854820	−	1.48059i	0.0219912	−	0.999758i	$-0.492999\pi$
$854$		0			0
$855$	610.293	+	235.024i	0.713793	+	0.274882i
$856$		0			0
$857$	589.284	−	340.223i	0.687613	−	0.396993i	−0.115104	−	0.993353i	$-0.536720\pi$
$857$	589.284	−	340.223i	0.687613	−	0.396993i	0.802717	+	0.596360i	$0.203387\pi$
$858$		0			0
$859$	−194.397	+	336.706i	−0.226307	+	0.391975i	−0.956711	−	0.291041i	$-0.905999\pi$
$859$	−194.397	+	336.706i	−0.226307	+	0.391975i	0.730404	+	0.683015i	$0.239332\pi$
$860$		0			0
$861$	556.385	−	208.883i	0.646207	−	0.242605i
$862$		0			0
$863$		−	1347.92i		−	1.56190i	−0.624591	−	0.780952i	$-0.714734\pi$
$863$		−	1347.92i		−	1.56190i	0.624591	−	0.780952i	$-0.285266\pi$
$864$		0			0
$865$		−	1047.11i		−	1.21053i
$866$		0			0
$867$	−176.828	−	471.003i	−0.203954	−	0.543256i
$868$		0			0
$869$	−273.958	−	158.169i	−0.315256	−	0.182013i
$870$		0			0
$871$	−106.350	−	184.204i	−0.122102	−	0.211486i
$872$		0			0
$873$	−164.943	+	483.277i	−0.188938	+	0.553581i
$874$		0			0
$875$	774.924	+	1342.21i	0.885627	+	1.53395i
$876$		0			0
$877$	−581.597	−	335.785i	−0.663166	−	0.382879i	0.130316	−	0.991473i	$-0.458401\pi$
$877$	−581.597	−	335.785i	−0.663166	−	0.382879i	−0.793482	+	0.608593i	$0.791734\pi$
$878$		0			0
$879$	−173.047	+	1042.76i	−0.196868	+	1.18630i
$880$		0			0
$881$	1473.72			1.67278			0.836389	−	0.548136i	$-0.184662\pi$
$881$	1473.72			1.67278			0.836389	+	0.548136i	$0.184662\pi$
$882$		0			0
$883$	−1169.48			−1.32444			−0.662218	−	0.749311i	$-0.730385\pi$
$883$	−1169.48			−1.32444			−0.662218	+	0.749311i	$0.730385\pi$
$884$		0			0
$885$	−496.226	−	407.930i	−0.560708	−	0.460938i
$886$		0			0
$887$	85.8429	+	49.5614i	0.0967789	+	0.0558753i	0.547608	−	0.836735i	$-0.315538\pi$
$887$	85.8429	+	49.5614i	0.0967789	+	0.0558753i	−0.450829	+	0.892610i	$0.648872\pi$
$888$		0			0
$889$	560.701	−	323.721i	0.630710	−	0.364140i
$890$		0			0
$891$	−719.048	+	295.054i	−0.807013	+	0.331149i
$892$		0			0
$893$	49.0715	+	1.89961i	0.0549513	+	0.00212722i
$894$		0			0
$895$	780.076	+	450.377i	0.871593	+	0.503215i
$896$		0			0
$897$	383.076	+	314.913i	0.427063	+	0.351074i
$898$		0			0
$899$	0.796551			0.000886041
$900$		0			0
$901$			244.030i			0.270844i
$902$		0			0
$903$	727.095	+	120.662i	0.805200	+	0.133624i
$904$		0			0
$905$	−63.5762	−	36.7057i	−0.0702499	−	0.0405588i
$906$		0			0
$907$	−1009.86	+	583.043i	−1.11341	+	0.642826i	−0.939710	−	0.341973i	$-0.888905\pi$
$907$	−1009.86	+	583.043i	−1.11341	+	0.642826i	−0.173697	+	0.984799i	$0.555571\pi$
$908$		0			0
$909$	882.588	+	301.229i	0.970943	+	0.331385i
$910$		0			0
$911$	−1015.56	+	586.332i	−1.11477	+	0.643614i	−0.940061	−	0.341006i	$-0.889232\pi$
$911$	−1015.56	+	586.332i	−1.11477	+	0.643614i	−0.174711	+	0.984620i	$0.555899\pi$
$912$		0			0
$913$	−13.2895	+	23.0180i	−0.0145558	+	0.0252114i
$914$		0			0
$915$	278.386	+	741.516i	0.304247	+	0.810400i
$916$		0			0
$917$	−274.650			−0.299509
$918$		0			0
$919$	−194.410			−0.211545			−0.105772	−	0.994390i	$-0.533732\pi$
$919$	−194.410			−0.211545			−0.105772	+	0.994390i	$0.533732\pi$
$920$		0			0
$921$	−216.221	+	81.1755i	−0.234768	+	0.0881385i
$922$		0			0
$923$	463.158	−	802.214i	0.501797	−	0.869138i
$924$		0			0
$925$	−629.727	+	363.573i	−0.680786	+	0.393052i
$926$		0			0
$927$	−447.206	+	88.1854i	−0.482423	+	0.0951299i
$928$		0			0
$929$	−426.376	−	738.504i	−0.458962	−	0.794946i	0.539944	−	0.841701i	$-0.318445\pi$
$929$	−426.376	−	738.504i	−0.458962	−	0.794946i	−0.998906	+	0.0467552i	$0.985112\pi$
$930$		0			0
$931$	−728.391	−	1382.50i	−0.782375	−	1.48497i
$932$		0			0
$933$	−505.175	−	83.8343i	−0.541452	−	0.0898546i
$934$		0			0
$935$	784.244			0.838763
$936$		0			0
$937$	1455.98			1.55388			0.776939	−	0.629576i	$-0.216771\pi$
$937$	1455.98			1.55388			0.776939	+	0.629576i	$0.216771\pi$
$938$		0			0
$939$	20.8441	−	25.3558i	0.0221982	−	0.0270030i
$940$		0			0
$941$	788.413	+	455.190i	0.837846	+	0.483731i	0.856531	−	0.516095i	$-0.172615\pi$
$941$	788.413	+	455.190i	0.837846	+	0.483731i	−0.0186855	+	0.999825i	$0.505948\pi$
$942$		0			0
$943$	−276.818	+	159.821i	−0.293550	+	0.169481i
$944$		0			0
$945$	1041.90	+	560.239i	1.10254	+	0.592845i
$946$		0			0
$947$	−111.173	−	192.557i	−0.117395	−	0.203333i	0.801340	−	0.598209i	$-0.204121\pi$
$947$	−111.173	−	192.557i	−0.117395	−	0.203333i	−0.918734	+	0.394876i	$0.870788\pi$
$948$		0			0
$949$	−242.409	−	139.955i	−0.255436	−	0.147476i
$950$		0			0
$951$	1264.96	+	1039.88i	1.33014	+	1.09346i
$952$		0			0
$953$			1266.57i			1.32903i	0.747274	+	0.664516i	$0.231362\pi$
$953$			1266.57i			1.32903i	−0.747274	+	0.664516i	$0.768638\pi$
$954$		0			0
$955$	−384.244			−0.402350
$956$		0			0
$957$	105.553	−	636.050i	0.110296	−	0.664629i
$958$		0			0
$959$	−805.186	+	1394.62i	−0.839610	+	1.45425i
$960$		0			0
$961$	−480.499	−	832.249i	−0.499999	−	0.866024i
$962$		0			0
$963$	−706.272	−	808.044i	−0.733408	−	0.839090i
$964$		0			0
$965$	66.5050	−	38.3967i	0.0689171	−	0.0397893i
$966$		0			0
$967$	296.636	−	513.789i	0.306759	−	0.531323i	−0.670892	−	0.741555i	$-0.734089\pi$
$967$	296.636	−	513.789i	0.306759	−	0.531323i	0.977652	+	0.210232i	$0.0674220\pi$
$968$		0			0
$969$	1193.07	+	245.756i	1.23124	+	0.253618i
$970$		0			0
$971$		−	1082.23i		−	1.11456i	−0.830326	−	0.557278i	$-0.811846\pi$
$971$		−	1082.23i		−	1.11456i	0.830326	−	0.557278i	$-0.188154\pi$
$972$		0			0
$973$	1972.53			2.02726
$974$		0			0
$975$	−260.537	+	97.8131i	−0.267218	+	0.100321i
$976$		0			0
$977$	−185.603	−	107.158i	−0.189972	−	0.109681i	0.401997	−	0.915641i	$-0.368316\pi$
$977$	−185.603	−	107.158i	−0.189972	−	0.109681i	−0.591970	+	0.805960i	$0.701649\pi$
$978$		0			0
$979$	932.578	−	538.424i	0.952583	−	0.549974i
$980$		0			0
$981$	454.659	+	520.174i	0.463465	+	0.530249i
$982$		0			0
$983$	−100.450	+	57.9949i	−0.102187	+	0.0589979i	−0.550223	−	0.835018i	$-0.685457\pi$
$983$	−100.450	+	57.9949i	−0.102187	+	0.0589979i	0.448035	+	0.894016i	$0.352124\pi$
$984$		0			0
$985$	32.1751	−	55.7288i	0.0326650	−	0.0565775i
$986$		0			0
$987$	87.6322	+	14.5427i	0.0887865	+	0.0147342i
$988$		0			0
$989$	−396.411			−0.400820
$990$		0			0
$991$		−	61.2610i		−	0.0618173i	−0.999522	−	0.0309087i	$-0.990160\pi$
$991$		−	61.2610i		−	0.0618173i	0.999522	−	0.0309087i	$-0.00984010\pi$
$992$		0			0
$993$	739.610	+	608.007i	0.744824	+	0.612293i
$994$		0			0
$995$	689.431	−	1194.13i	0.692895	−	1.20013i
$996$		0			0
$997$	36.9516	+	64.0020i	0.0370628	+	0.0641946i	0.883962	−	0.467559i	$-0.154867\pi$
$997$	36.9516	+	64.0020i	0.0370628	+	0.0641946i	−0.846899	+	0.531754i	$0.821533\pi$
$998$		0			0
$999$	−896.310	+	1666.91i	−0.897207	+	1.66858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.t.a.265.16	✓	80
3.2	odd	2		2052.3.t.a.37.29		80
9.2	odd	6		2052.3.t.a.721.30		80
9.7	even	3	inner	684.3.t.a.493.25	yes	80
19.18	odd	2	inner	684.3.t.a.265.25	yes	80
57.56	even	2		2052.3.t.a.37.30		80
171.56	even	6		2052.3.t.a.721.29		80
171.151	odd	6	inner	684.3.t.a.493.16	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.t.a.265.16	✓	80	1.1	even	1	trivial
684.3.t.a.265.25	yes	80	19.18	odd	2	inner
684.3.t.a.493.16	yes	80	171.151	odd	6	inner
684.3.t.a.493.25	yes	80	9.7	even	3	inner
2052.3.t.a.37.29		80	3.2	odd	2
2052.3.t.a.37.30		80	57.56	even	2
2052.3.t.a.721.29		80	171.56	even	6
2052.3.t.a.721.30		80	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05443 - 2.80859i) q^{3} +(-1.91223 + 3.31208i) q^{5} +(-5.72810 - 9.92136i) q^{7} +(-6.77637 + 5.92290i) q^{9} +O(q^{10})\)	\(q+(-1.05443 - 2.80859i) q^{3} +(-1.91223 + 3.31208i) q^{5} +(-5.72810 - 9.92136i) q^{7} +(-6.77637 + 5.92290i) q^{9} +(-4.79772 - 8.30989i) q^{11} +(-7.74438 - 4.47122i) q^{13} +(11.3186 + 1.87833i) q^{15} +21.3706 q^{17} +(-10.1294 + 16.0747i) q^{19} +(-21.8252 + 26.5492i) q^{21} +(9.24246 - 16.0084i) q^{23} +(5.18675 + 8.98371i) q^{25} +(23.7802 + 12.7868i) q^{27} +(-19.3970 + 11.1989i) q^{29} +(-0.0307992 - 0.0177819i) q^{31} +(-18.2803 + 22.2370i) q^{33} +43.8138 q^{35} +70.0965i q^{37} +(-4.39196 + 26.4654i) q^{39} +(-14.9753 - 8.64601i) q^{41} +(-10.7226 - 18.5720i) q^{43} +(-6.65914 - 33.7698i) q^{45} +(-1.29232 - 2.23837i) q^{47} +(-41.1223 + 71.2259i) q^{49} +(-22.5337 - 60.0212i) q^{51} +11.4190i q^{53} +36.6974 q^{55} +(55.8279 + 11.4997i) q^{57} +(-48.4874 - 27.9942i) q^{59} +(34.5169 + 59.7850i) q^{61} +(97.5790 + 33.3039i) q^{63} +(29.6181 - 17.1000i) q^{65} +(20.5989 + 11.8928i) q^{67} +(-54.7065 - 9.07861i) q^{69} +103.587i q^{71} +31.3012 q^{73} +(19.7625 - 24.0401i) q^{75} +(-54.9636 + 95.1998i) q^{77} +(28.5508 - 16.4838i) q^{79} +(10.8385 - 80.2716i) q^{81} +(-1.38498 - 2.39885i) q^{83} +(-40.8654 + 70.7810i) q^{85} +(51.9058 + 42.6700i) q^{87} +112.225i q^{89} +102.446i q^{91} +(-0.0174667 + 0.105252i) q^{93} +(-33.8709 - 64.2878i) q^{95} +(49.1372 - 28.3694i) q^{97} +(81.7298 + 27.8945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 2 * q^7 + 4 * q^9	\( 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) \) 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more