LMFDB - Embedded newform 144.3.o.b.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(31,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("144.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.o (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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.121550625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 4x^{6} - 9x^{5} + 23x^{4} + 18x^{3} - 16x^{2} + 8x + 16 $ x^8 - x^7 - 4x^6 - 9x^5 + 23x^4 + 18x^3 - 16x^2 + 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.3
Root			$-1.44918 + 1.77086i$ of defining polynomial
Character	$\chi$	$=$	144.31
Dual form			144.3.o.b.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.531407 + 2.95256i) q^{3} +(-3.31174 + 5.73610i) q^{5} +(8.46808 - 4.88905i) q^{7} +(-8.43521 + 3.13802i) q^{9} +O(q^{10})$	\(q+(0.531407 + 2.95256i) q^{3} +(-3.31174 + 5.73610i) q^{5} +(8.46808 - 4.88905i) q^{7} +(-8.43521 + 3.13802i) q^{9} +(-10.0623 + 5.80948i) q^{11} +(-8.93521 + 15.4762i) q^{13} +(-18.6961 - 6.72990i) q^{15} +2.37652 q^{17} -14.0337i q^{19} +(18.9352 + 22.4044i) q^{21} +(35.9635 + 20.7636i) q^{23} +(-9.43521 - 16.3423i) q^{25} +(-13.7477 - 23.2379i) q^{27} +(-5.68826 - 9.85236i) q^{29} +(18.0334 + 10.4116i) q^{31} +(-22.5000 - 26.6224i) q^{33} +64.7650i q^{35} +35.7409 q^{37} +(-50.4428 - 18.1576i) q^{39} +(-2.62957 + 4.55456i) q^{41} +(54.4939 - 31.4621i) q^{43} +(9.93521 - 58.7775i) q^{45} +(-4.28568 + 2.47434i) q^{47} +(23.3056 - 40.3666i) q^{49} +(1.26290 + 7.01683i) q^{51} +75.7409 q^{53} -76.9578i q^{55} +(41.4352 - 7.45759i) q^{57} +(-50.3115 - 29.0474i) q^{59} +(5.93521 + 10.2801i) q^{61} +(-56.0882 + 67.8132i) q^{63} +(-59.1822 - 102.507i) q^{65} +(20.6216 + 11.9059i) q^{67} +(-42.1944 + 117.218i) q^{69} +46.4758i q^{71} -104.352 q^{73} +(43.2376 - 36.5424i) q^{75} +(-56.8056 + 98.3903i) q^{77} +(18.0334 - 10.4116i) q^{79} +(61.3056 - 52.9398i) q^{81} +(24.4103 - 14.0933i) q^{83} +(-7.87043 + 13.6320i) q^{85} +(26.0669 - 22.0305i) q^{87} +73.0122 q^{89} +174.739i q^{91} +(-21.1578 + 58.7775i) q^{93} +(80.4984 + 46.4758i) q^{95} +(71.1113 + 123.168i) q^{97} +(66.6474 - 80.5799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q - 6 * q^5 - 6 * q^9	$ 8 q - 6 q^{5} - 6 q^{9} - 10 q^{13} + 60 q^{17} + 90 q^{21} - 14 q^{25} - 66 q^{29} - 180 q^{33} + 40 q^{37} - 144 q^{41} + 18 q^{45} + 2 q^{49} + 360 q^{53} + 270 q^{57} - 14 q^{61} - 330 q^{65} - 522 q^{69} - 220 q^{73} - 270 q^{77} + 306 q^{81} + 60 q^{85} + 912 q^{89} + 630 q^{93} + 200 q^{97}+O(q^{100}) $ 8 * q - 6 * q^5 - 6 * q^9 - 10 * q^13 + 60 * q^17 + 90 * q^21 - 14 * q^25 - 66 * q^29 - 180 * q^33 + 40 * q^37 - 144 * q^41 + 18 * q^45 + 2 * q^49 + 360 * q^53 + 270 * q^57 - 14 * q^61 - 330 * q^65 - 522 * q^69 - 220 * q^73 - 270 * q^77 + 306 * q^81 + 60 * q^85 + 912 * q^89 + 630 * q^93 + 200 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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
$3$	0.531407	+	2.95256i	0.177136	+	0.984186i
$3$	0.531407	+	2.95256i	0.177136	+	0.984186i
$4$		0			0
$5$	−3.31174	+	5.73610i	−0.662348	+	1.14722i	0.317650	+	0.948208i	$0.397106\pi$
$5$	−3.31174	+	5.73610i	−0.662348	+	1.14722i	−0.979997	+	0.199011i	$0.936227\pi$
$6$		0			0
$7$	8.46808	−	4.88905i	1.20973	−	0.698436i	0.247027	−	0.969009i	$-0.420546\pi$
$7$	8.46808	−	4.88905i	1.20973	−	0.698436i	0.962700	+	0.270573i	$0.0872131\pi$
$8$		0			0
$9$	−8.43521	+	3.13802i	−0.937246	+	0.348669i
$10$		0			0
$11$	−10.0623	+	5.80948i	−0.914755	+	0.528134i	−0.881958	−	0.471328i	$-0.843775\pi$
$11$	−10.0623	+	5.80948i	−0.914755	+	0.528134i	−0.0327970	+	0.999462i	$0.510441\pi$
$12$		0			0
$13$	−8.93521	+	15.4762i	−0.687324	+	1.19048i	0.285376	+	0.958416i	$0.407881\pi$
$13$	−8.93521	+	15.4762i	−0.687324	+	1.19048i	−0.972700	+	0.232065i	$0.925452\pi$
$14$		0			0
$15$	−18.6961	−	6.72990i	−1.24640	−	0.448660i
$16$		0			0
$17$	2.37652			0.139796			0.0698978	−	0.997554i	$-0.477733\pi$
$17$	2.37652			0.139796			0.0698978	+	0.997554i	$0.477733\pi$
$18$		0			0
$19$		−	14.0337i		−	0.738614i	−0.929308	−	0.369307i	$-0.879595\pi$
$19$		−	14.0337i		−	0.738614i	0.929308	−	0.369307i	$-0.120405\pi$
$20$		0			0
$21$	18.9352	+	22.4044i	0.901677	+	1.06688i
$22$		0			0
$23$	35.9635	+	20.7636i	1.56363	+	0.902763i	0.996885	+	0.0788718i	$0.0251318\pi$
$23$	35.9635	+	20.7636i	1.56363	+	0.902763i	0.566747	+	0.823892i	$0.308202\pi$
$24$		0			0
$25$	−9.43521	−	16.3423i	−0.377409	−	0.653691i
$26$		0			0
$27$	−13.7477	−	23.2379i	−0.509175	−	0.860663i
$28$		0			0
$29$	−5.68826	−	9.85236i	−0.196147	−	0.339737i	0.751129	−	0.660156i	$-0.229510\pi$
$29$	−5.68826	−	9.85236i	−0.196147	−	0.339737i	−0.947276	+	0.320419i	$0.896176\pi$
$30$		0			0
$31$	18.0334	+	10.4116i	0.581723	+	0.335858i	0.761818	−	0.647791i	$-0.224307\pi$
$31$	18.0334	+	10.4116i	0.581723	+	0.335858i	−0.180095	+	0.983649i	$0.557640\pi$
$32$		0			0
$33$	−22.5000	−	26.6224i	−0.681818	−	0.806738i
$34$		0			0
$35$			64.7650i			1.85043i
$36$		0			0
$37$	35.7409			0.965969			0.482984	−	0.875629i	$-0.339553\pi$
$37$	35.7409			0.965969			0.482984	+	0.875629i	$0.339553\pi$
$38$		0			0
$39$	−50.4428	−	18.1576i	−1.29340	−	0.465579i
$40$		0			0
$41$	−2.62957	+	4.55456i	−0.0641359	+	0.111087i	−0.896310	−	0.443427i	$-0.853762\pi$
$41$	−2.62957	+	4.55456i	−0.0641359	+	0.111087i	0.832174	+	0.554514i	$0.187096\pi$
$42$		0			0
$43$	54.4939	−	31.4621i	1.26730	−	0.731676i	0.292824	−	0.956166i	$-0.405405\pi$
$43$	54.4939	−	31.4621i	1.26730	−	0.731676i	0.974476	+	0.224490i	$0.0720716\pi$
$44$		0			0
$45$	9.93521	−	58.7775i	0.220783	−	1.30617i
$46$		0			0
$47$	−4.28568	+	2.47434i	−0.0911848	+	0.0526456i	−0.544899	−	0.838502i	$-0.683432\pi$
$47$	−4.28568	+	2.47434i	−0.0911848	+	0.0526456i	0.453714	+	0.891147i	$0.350099\pi$
$48$		0			0
$49$	23.3056	−	40.3666i	0.475625	−	0.823807i
$50$		0			0
$51$	1.26290	+	7.01683i	0.0247628	+	0.137585i
$52$		0			0
$53$	75.7409			1.42907			0.714536	−	0.699598i	$-0.246638\pi$
$53$	75.7409			1.42907			0.714536	+	0.699598i	$0.246638\pi$
$54$		0			0
$55$		−	76.9578i		−	1.39923i
$56$		0			0
$57$	41.4352	−	7.45759i	0.726934	−	0.130835i
$58$		0			0
$59$	−50.3115	−	29.0474i	−0.852738	−	0.492328i	0.00883587	−	0.999961i	$-0.497187\pi$
$59$	−50.3115	−	29.0474i	−0.852738	−	0.492328i	−0.861574	+	0.507633i	$0.830521\pi$
$60$		0			0
$61$	5.93521	+	10.2801i	0.0972986	+	0.168526i	0.910566	−	0.413365i	$-0.135646\pi$
$61$	5.93521	+	10.2801i	0.0972986	+	0.168526i	−0.813267	+	0.581891i	$0.802313\pi$
$62$		0			0
$63$	−56.0882	+	67.8132i	−0.890288	+	1.07640i
$64$		0			0
$65$	−59.1822	−	102.507i	−0.910495	−	1.57702i
$66$		0			0
$67$	20.6216	+	11.9059i	0.307785	+	0.177700i	0.645935	−	0.763393i	$-0.276468\pi$
$67$	20.6216	+	11.9059i	0.307785	+	0.177700i	−0.338150	+	0.941092i	$0.609801\pi$
$68$		0			0
$69$	−42.1944	+	117.218i	−0.611512	+	1.69882i
$70$		0			0
$71$			46.4758i			0.654589i	0.944922	+	0.327294i	$0.106137\pi$
$71$			46.4758i			0.654589i	−0.944922	+	0.327294i	$0.893863\pi$
$72$		0			0
$73$	−104.352			−1.42948			−0.714741	−	0.699390i	$-0.753455\pi$
$73$	−104.352			−1.42948			−0.714741	+	0.699390i	$0.753455\pi$
$74$		0			0
$75$	43.2376	−	36.5424i	0.576501	−	0.487232i
$76$		0			0
$77$	−56.8056	+	98.3903i	−0.737736	+	1.27780i
$78$		0			0
$79$	18.0334	−	10.4116i	0.228271	−	0.131792i	−0.381503	−	0.924368i	$-0.624593\pi$
$79$	18.0334	−	10.4116i	0.228271	−	0.131792i	0.609774	+	0.792575i	$0.291260\pi$
$80$		0			0
$81$	61.3056	−	52.9398i	0.756860	−	0.653577i
$82$		0			0
$83$	24.4103	−	14.0933i	0.294100	−	0.169799i	−0.345689	−	0.938349i	$-0.612355\pi$
$83$	24.4103	−	14.0933i	0.294100	−	0.169799i	0.639789	+	0.768550i	$0.279022\pi$
$84$		0			0
$85$	−7.87043	+	13.6320i	−0.0925932	+	0.160376i
$86$		0			0
$87$	26.0669	−	22.0305i	0.299619	−	0.253225i
$88$		0			0
$89$	73.0122			0.820362			0.410181	−	0.912004i	$-0.365466\pi$
$89$	73.0122			0.820362			0.410181	+	0.912004i	$0.365466\pi$
$90$		0			0
$91$			174.739i			1.92021i
$92$		0			0
$93$	−21.1578	+	58.7775i	−0.227503	+	0.632016i
$94$		0			0
$95$	80.4984	+	46.4758i	0.847352	+	0.489219i
$96$		0			0
$97$	71.1113	+	123.168i	0.733106	+	1.26978i	0.955549	+	0.294831i	$0.0952634\pi$
$97$	71.1113	+	123.168i	0.733106	+	1.26978i	−0.222443	+	0.974946i	$0.571403\pi$
$98$		0			0
$99$	66.6474	−	80.5799i	0.673206	−	0.813938i
$100$		0			0
$101$	13.6761	+	23.6876i	0.135407	+	0.234531i	0.925753	−	0.378130i	$-0.123433\pi$
$101$	13.6761	+	23.6876i	0.135407	+	0.234531i	−0.790346	+	0.612661i	$0.790099\pi$
$102$		0			0
$103$	−127.021	−	73.3358i	−1.23322	−	0.711998i	−0.265517	−	0.964106i	$-0.585543\pi$
$103$	−127.021	−	73.3358i	−1.23322	−	0.711998i	−0.967699	+	0.252108i	$0.918876\pi$
$104$		0			0
$105$	−191.223	+	34.4166i	−1.82117	+	0.327777i
$106$		0			0
$107$		−	192.573i		−	1.79975i	−0.436146	−	0.899876i	$-0.643657\pi$
$107$		−	192.573i		−	1.79975i	0.436146	−	0.899876i	$-0.356343\pi$
$108$		0			0
$109$	0.259148			0.00237750			0.00118875	−	0.999999i	$-0.499622\pi$
$109$	0.259148			0.00237750			0.00118875	+	0.999999i	$0.499622\pi$
$110$		0			0
$111$	18.9929	+	105.527i	0.171108	+	0.950694i
$112$		0			0
$113$	−99.4291	+	172.216i	−0.879904	+	1.52404i	−0.0284580	+	0.999595i	$0.509060\pi$
$113$	−99.4291	+	172.216i	−0.879904	+	1.52404i	−0.851446	+	0.524443i	$0.824274\pi$
$114$		0			0
$115$	−238.204	+	137.527i	−2.07134	+	1.19589i
$116$		0			0
$117$	26.8056	−	158.584i	0.229108	−	1.35542i
$118$		0			0
$119$	20.1246	−	11.6190i	0.169114	−	0.0976382i
$120$		0			0
$121$	7.00000	−	12.1244i	0.0578512	−	0.100201i
$122$		0			0
$123$	−14.8450	−	5.34365i	−0.120691	−	0.0434443i
$124$		0			0
$125$	−40.5991			−0.324793
$126$		0			0
$127$		−	72.2477i		−	0.568879i	−0.958694	−	0.284440i	$-0.908192\pi$
$127$		−	72.2477i		−	0.568879i	0.958694	−	0.284440i	$-0.0918075\pi$
$128$		0			0
$129$	121.852	+	144.177i	0.944590	+	1.11765i
$130$		0			0
$131$	−159.693	−	92.1988i	−1.21903	−	0.703808i	−0.254320	−	0.967120i	$-0.581852\pi$
$131$	−159.693	−	92.1988i	−1.21903	−	0.703808i	−0.964711	+	0.263312i	$0.915185\pi$
$132$		0			0
$133$	−68.6113	−	118.838i	−0.515874	−	0.893520i
$134$		0			0
$135$	178.824	−	1.90048i	1.32462	−	0.0140776i
$136$		0			0
$137$	−69.8765	−	121.030i	−0.510048	−	0.883428i	−0.999932	−	0.0116411i	$-0.996294\pi$
$137$	−69.8765	−	121.030i	−0.510048	−	0.883428i	0.489885	−	0.871787i	$-0.337039\pi$
$138$		0			0
$139$	151.722	+	87.5967i	1.09153	+	0.630192i	0.933982	−	0.357320i	$-0.116309\pi$
$139$	151.722	+	87.5967i	1.09153	+	0.630192i	0.157543	+	0.987512i	$0.449643\pi$
$140$		0			0
$141$	−9.58308	−	11.3389i	−0.0679651	−	0.0804174i
$142$		0			0
$143$		−	207.636i		−	1.45200i
$144$		0			0
$145$	75.3521			0.519670
$146$		0			0
$147$	131.569	+	47.3602i	0.895030	+	0.322178i
$148$		0			0
$149$	95.5343	−	165.470i	0.641170	−	1.11054i	−0.344002	−	0.938969i	$-0.611783\pi$
$149$	95.5343	−	165.470i	0.641170	−	1.11054i	0.985172	−	0.171570i	$-0.0548839\pi$
$150$		0			0
$151$	−6.27360	+	3.62206i	−0.0415470	+	0.0239872i	−0.520630	−	0.853783i	$-0.674303\pi$
$151$	−6.27360	+	3.62206i	−0.0415470	+	0.0239872i	0.479083	+	0.877770i	$0.340969\pi$
$152$		0			0
$153$	−20.0465	+	7.45759i	−0.131023	+	0.0487424i
$154$		0			0
$155$	−119.444	+	68.9609i	−0.770606	+	0.444909i
$156$		0			0
$157$	−36.0648	+	62.4660i	−0.229712	+	0.397873i	−0.957723	−	0.287693i	$-0.907112\pi$
$157$	−36.0648	+	62.4660i	−0.229712	+	0.397873i	0.728011	+	0.685566i	$0.240445\pi$
$158$		0			0
$159$	40.2492	+	223.629i	0.253140	+	1.40647i
$160$		0			0
$161$	406.056			2.52209
$162$		0			0
$163$			112.269i			0.688769i	0.938829	+	0.344384i	$0.111912\pi$
$163$			112.269i			0.688769i	−0.938829	+	0.344384i	$0.888088\pi$
$164$		0			0
$165$	227.223	−	40.8959i	1.37711	−	0.247854i
$166$		0			0
$167$	−15.8389	−	9.14461i	−0.0948439	−	0.0547581i	0.451828	−	0.892105i	$-0.350772\pi$
$167$	−15.8389	−	9.14461i	−0.0948439	−	0.0547581i	−0.546672	+	0.837347i	$0.684105\pi$
$168$		0			0
$169$	−75.1761	−	130.209i	−0.444829	−	0.770466i
$170$		0			0
$171$	44.0379	+	118.377i	0.257532	+	0.692263i
$172$		0			0
$173$	−146.652	−	254.008i	−0.847698	−	1.46826i	−0.883258	−	0.468888i	$-0.844655\pi$
$173$	−146.652	−	254.008i	−0.847698	−	1.46826i	0.0355603	−	0.999368i	$-0.488678\pi$
$174$		0			0
$175$	−159.796	−	92.2585i	−0.913122	−	0.527191i
$176$		0			0
$177$	59.0282	−	163.984i	0.333493	−	0.926462i
$178$		0			0
$179$		−	92.9516i		−	0.519283i	−0.965705	−	0.259641i	$-0.916396\pi$
$179$		−	92.9516i		−	0.519283i	0.965705	−	0.259641i	$-0.0836043\pi$
$180$		0			0
$181$	128.445			0.709642			0.354821	−	0.934934i	$-0.384542\pi$
$181$	128.445			0.709642			0.354821	+	0.934934i	$0.384542\pi$
$182$		0			0
$183$	−27.1986	+	22.9870i	−0.148626	+	0.125612i
$184$		0			0
$185$	−118.364	+	205.013i	−0.639807	+	1.10818i
$186$		0			0
$187$	−23.9133	+	13.8064i	−0.127879	+	0.0738308i
$188$		0			0
$189$	−230.028	−	129.567i	−1.21708	−	0.685541i
$190$		0			0
$191$	260.316	−	150.294i	1.36291	−	0.786877i	0.372901	−	0.927871i	$-0.378363\pi$
$191$	260.316	−	150.294i	1.36291	−	0.786877i	0.990011	+	0.140994i	$0.0450297\pi$
$192$		0			0
$193$	19.6296	−	33.9994i	0.101708	−	0.176163i	−0.810681	−	0.585489i	$-0.800903\pi$
$193$	19.6296	−	33.9994i	0.101708	−	0.176163i	0.912388	+	0.409326i	$0.134236\pi$
$194$		0			0
$195$	271.207	−	229.212i	1.39080	−	1.17544i
$196$		0			0
$197$	−94.7530			−0.480980			−0.240490	−	0.970652i	$-0.577308\pi$
$197$	−94.7530			−0.480980			−0.240490	+	0.970652i	$0.577308\pi$
$198$		0			0
$199$			111.360i			0.559598i	0.960059	+	0.279799i	$0.0902679\pi$
$199$			111.360i			0.559598i	−0.960059	+	0.279799i	$0.909732\pi$
$200$		0			0
$201$	−24.1944	+	67.2133i	−0.120370	+	0.334395i
$202$		0			0
$203$	−96.3374	−	55.6204i	−0.474568	−	0.273992i
$204$		0			0
$205$	−17.4169	−	30.1670i	−0.0849606	−	0.147156i
$206$		0			0
$207$	−368.517	−	62.2907i	−1.78027	−	0.300921i
$208$		0			0
$209$	81.5282	+	141.211i	0.390087	+	0.675651i
$210$		0			0
$211$	−102.714	−	59.3021i	−0.486797	−	0.281053i	0.236447	−	0.971644i	$-0.424017\pi$
$211$	−102.714	−	59.3021i	−0.486797	−	0.281053i	−0.723245	+	0.690592i	$0.757350\pi$
$212$		0			0
$213$	−137.223	+	24.6976i	−0.644237	+	0.115951i
$214$		0			0
$215$			416.777i			1.93850i
$216$		0			0
$217$	203.611			0.938301
$218$		0			0
$219$	−55.4535	−	308.106i	−0.253212	−	1.40688i
$220$		0			0
$221$	−21.2348	+	36.7797i	−0.0960849	+	0.166424i
$222$		0			0
$223$	−21.0153	+	12.1332i	−0.0942389	+	0.0544089i	−0.546379	−	0.837538i	$-0.683994\pi$
$223$	−21.0153	+	12.1332i	−0.0942389	+	0.0544089i	0.452140	+	0.891947i	$0.350661\pi$
$224$		0			0
$225$	130.870	+	108.243i	0.581646	+	0.481078i
$226$		0			0
$227$	−10.0623	+	5.80948i	−0.0443273	+	0.0255924i	−0.522000	−	0.852946i	$-0.674814\pi$
$227$	−10.0623	+	5.80948i	−0.0443273	+	0.0255924i	0.477673	+	0.878538i	$0.341481\pi$
$228$		0			0
$229$	9.06479	−	15.7007i	0.0395842	−	0.0685619i	−0.845555	−	0.533889i	$-0.820730\pi$
$229$	9.06479	−	15.7007i	0.0395842	−	0.0685619i	0.885139	+	0.465327i	$0.154063\pi$
$230$		0			0
$231$	−320.690	−	115.437i	−1.38827	−	0.499726i
$232$		0			0
$233$	−219.785			−0.943283			−0.471642	−	0.881790i	$-0.656338\pi$
$233$	−219.785			−0.943283			−0.471642	+	0.881790i	$0.656338\pi$
$234$		0			0
$235$		−	32.7775i		−	0.139479i
$236$		0			0
$237$	40.3239	+	47.7119i	0.170143	+	0.201316i
$238$		0			0
$239$	139.568	+	80.5799i	0.583968	+	0.337154i	0.762709	−	0.646742i	$-0.223869\pi$
$239$	139.568	+	80.5799i	0.583968	+	0.337154i	−0.178740	+	0.983896i	$0.557202\pi$
$240$		0			0
$241$	84.5930	+	146.519i	0.351008	+	0.607964i	0.986426	−	0.164204i	$-0.0525056\pi$
$241$	84.5930	+	146.519i	0.351008	+	0.607964i	−0.635418	+	0.772168i	$0.719172\pi$
$242$		0			0
$243$	188.886	+	152.876i	0.777309	+	0.629119i
$244$		0			0
$245$	154.364	+	267.367i	0.630058	+	1.09129i
$246$		0			0
$247$	217.188	+	125.394i	0.879305	+	0.507667i
$248$		0			0
$249$	54.5831	+	64.5836i	0.219209	+	0.259372i
$250$		0			0
$251$			219.255i			0.873524i	0.899577	+	0.436762i	$0.143875\pi$
$251$			219.255i			0.873524i	−0.899577	+	0.436762i	$0.856125\pi$
$252$		0			0
$253$	−482.502			−1.90712
$254$		0			0
$255$	−44.4316	−	15.9938i	−0.174242	−	0.0627207i
$256$		0			0
$257$	88.7348	−	153.693i	0.345271	−	0.598028i	−0.640132	−	0.768265i	$-0.721120\pi$
$257$	88.7348	−	153.693i	0.345271	−	0.598028i	0.985403	+	0.170238i	$0.0544535\pi$
$258$		0			0
$259$	302.657	−	174.739i	1.16856	−	0.674667i
$260$		0			0
$261$	78.8986	+	65.2569i	0.302294	+	0.250026i
$262$		0			0
$263$	59.0700	−	34.1041i	0.224601	−	0.129673i	−0.383478	−	0.923550i	$-0.625274\pi$
$263$	59.0700	−	34.1041i	0.224601	−	0.129673i	0.608079	+	0.793877i	$0.291940\pi$
$264$		0			0
$265$	−250.834	+	434.457i	−0.946543	+	1.63946i
$266$		0			0
$267$	38.7992	+	215.573i	0.145315	+	0.807389i
$268$		0			0
$269$	−77.7652			−0.289090			−0.144545	−	0.989498i	$-0.546172\pi$
$269$	−77.7652			−0.289090			−0.144545	+	0.989498i	$0.546172\pi$
$270$		0			0
$271$		−	447.259i		−	1.65040i	−0.564840	−	0.825201i	$-0.691062\pi$
$271$		−	447.259i		−	1.65040i	0.564840	−	0.825201i	$-0.308938\pi$
$272$		0			0
$273$	−515.927	+	92.8575i	−1.88984	+	0.340137i
$274$		0			0
$275$	189.880	+	109.627i	0.690473	+	0.398645i
$276$		0			0
$277$	84.0282	+	145.541i	0.303351	+	0.525419i	0.976893	−	0.213730i	$-0.0685612\pi$
$277$	84.0282	+	145.541i	0.303351	+	0.525419i	−0.673542	+	0.739149i	$0.735228\pi$
$278$		0			0
$279$	−184.787	−	31.2348i	−0.662321	−	0.111953i
$280$		0			0
$281$	−103.170	−	178.696i	−0.367153	−	0.635927i	0.621966	−	0.783044i	$-0.286334\pi$
$281$	−103.170	−	178.696i	−0.367153	−	0.635927i	−0.989119	+	0.147117i	$0.953001\pi$
$282$		0			0
$283$	172.653	+	99.6815i	0.610083	+	0.352231i	0.772998	−	0.634409i	$-0.218756\pi$
$283$	172.653	+	99.6815i	0.610083	+	0.352231i	−0.162915	+	0.986640i	$0.552090\pi$
$284$		0			0
$285$	−94.4451	+	262.374i	−0.331386	+	0.920611i
$286$		0			0
$287$			51.4245i			0.179179i
$288$		0			0
$289$	−283.352			−0.980457
$290$		0			0
$291$	−325.873	+	275.413i	−1.11984	+	0.946436i
$292$		0			0
$293$	28.5953	−	49.5285i	0.0975948	−	0.169039i	−0.813094	−	0.582133i	$-0.802218\pi$
$293$	28.5953	−	49.5285i	0.0975948	−	0.169039i	0.910689	+	0.413094i	$0.135552\pi$
$294$		0			0
$295$	333.237	−	192.395i	1.12962	−	0.652185i
$296$		0			0
$297$	273.334	+	153.960i	0.920316	+	0.518383i
$298$		0			0
$299$	−642.684	+	371.054i	−2.14944	+	1.24098i
$300$		0			0
$301$	307.639	−	532.847i	1.02206	−	1.77026i
$302$		0			0
$303$	−62.6716	+	52.9672i	−0.206837	+	0.174809i
$304$		0			0
$305$	−78.6235			−0.257782
$306$		0			0
$307$		−	276.775i		−	0.901549i	−0.892638	−	0.450774i	$-0.851148\pi$
$307$		−	276.775i		−	0.901549i	0.892638	−	0.450774i	$-0.148852\pi$
$308$		0			0
$309$	149.028	−	414.009i	0.482292	−	1.33983i
$310$		0			0
$311$	−21.4284	−	12.3717i	−0.0689017	−	0.0397804i	0.465153	−	0.885230i	$-0.345999\pi$
$311$	−21.4284	−	12.3717i	−0.0689017	−	0.0397804i	−0.534055	+	0.845450i	$0.679333\pi$
$312$		0			0
$313$	32.4070	+	56.1306i	0.103537	+	0.179331i	0.913139	−	0.407647i	$-0.133651\pi$
$313$	32.4070	+	56.1306i	0.103537	+	0.179331i	−0.809603	+	0.586978i	$0.800317\pi$
$314$		0			0
$315$	−203.234	−	546.307i	−0.645187	−	1.73431i
$316$		0			0
$317$	227.300	+	393.694i	0.717033	+	1.24194i	0.962170	+	0.272450i	$0.0878338\pi$
$317$	227.300	+	393.694i	0.717033	+	1.24194i	−0.245137	+	0.969488i	$0.578833\pi$
$318$		0			0
$319$	114.474	+	66.0916i	0.358853	+	0.207184i
$320$		0			0
$321$	568.585	−	102.335i	1.77129	−	0.318800i
$322$		0			0
$323$		−	33.3513i		−	0.103255i
$324$		0			0
$325$	337.223			1.03761
$326$		0			0
$327$	0.137713	+	0.765149i	0.000421140	+	0.00233991i
$328$		0			0
$329$	−24.1944	+	41.9059i	−0.0735391	+	0.127373i
$330$		0			0
$331$	236.009	−	136.260i	0.713019	−	0.411661i	−0.0991592	−	0.995072i	$-0.531615\pi$
$331$	236.009	−	136.260i	0.713019	−	0.411661i	0.812178	+	0.583410i	$0.198282\pi$
$332$		0			0
$333$	−301.482	+	112.156i	−0.905350	+	0.336804i
$334$		0			0
$335$	−136.587	+	78.8583i	−0.407721	+	0.235398i
$336$		0			0
$337$	246.945	−	427.721i	0.732775	−	1.26920i	−0.222918	−	0.974837i	$-0.571558\pi$
$337$	246.945	−	427.721i	0.732775	−	1.26920i	0.955693	−	0.294366i	$-0.0951085\pi$
$338$		0			0
$339$	−561.316	−	202.053i	−1.65580	−	0.596028i
$340$		0			0
$341$	−241.944			−0.709512
$342$		0			0
$343$			23.3572i			0.0680967i
$344$		0			0
$345$	−532.639	−	630.228i	−1.54388	−	1.82675i
$346$		0			0
$347$	450.196	+	259.921i	1.29740	+	0.749051i	0.979954	−	0.199226i	$-0.0638429\pi$
$347$	450.196	+	259.921i	1.29740	+	0.749051i	0.317442	+	0.948278i	$0.397176\pi$
$348$		0			0
$349$	120.639	+	208.954i	0.345672	+	0.598721i	0.985476	−	0.169817i	$-0.0543177\pi$
$349$	120.639	+	208.954i	0.345672	+	0.598721i	−0.639804	+	0.768538i	$0.720984\pi$
$350$		0			0
$351$	482.474	−	5.12758i	1.37457	−	0.0146085i
$352$		0			0
$353$	−100.463	−	174.008i	−0.284599	−	0.492940i	0.687913	−	0.725793i	$-0.258527\pi$
$353$	−100.463	−	174.008i	−0.284599	−	0.492940i	−0.972512	+	0.232853i	$0.925194\pi$
$354$		0			0
$355$	−266.590	−	153.916i	−0.750957	−	0.433565i
$356$		0			0
$357$	45.0000	+	53.2447i	0.126050	+	0.149145i
$358$		0			0
$359$			159.654i			0.444719i	0.974965	+	0.222360i	$0.0713759\pi$
$359$			159.654i			0.444719i	−0.974965	+	0.222360i	$0.928624\pi$
$360$		0			0
$361$	164.056			0.454450
$362$		0			0
$363$	39.5177	+	14.2249i	0.108864	+	0.0391872i
$364$		0			0
$365$	345.587	−	598.574i	0.946813	−	1.63993i
$366$		0			0
$367$	−320.690	+	185.150i	−0.873815	+	0.504497i	−0.868614	−	0.495489i	$-0.834989\pi$
$367$	−320.690	+	185.150i	−0.873815	+	0.504497i	−0.00520064	+	0.999986i	$0.501655\pi$
$368$		0			0
$369$	7.88872	−	46.6703i	0.0213786	−	0.126478i
$370$		0			0
$371$	641.380	−	370.301i	1.72879	−	0.998116i
$372$		0			0
$373$	−163.194	+	282.661i	−0.437518	+	0.757804i	−0.997497	−	0.0707027i	$-0.977476\pi$
$373$	−163.194	+	282.661i	−0.437518	+	0.757804i	0.559979	+	0.828507i	$0.310809\pi$
$374$		0			0
$375$	−21.5746	−	119.871i	−0.0575324	−	0.319657i
$376$		0			0
$377$	203.303			0.539266
$378$		0			0
$379$			348.114i			0.918506i	0.888305	+	0.459253i	$0.151883\pi$
$379$			348.114i			0.918506i	−0.888305	+	0.459253i	$0.848117\pi$
$380$		0			0
$381$	213.316	−	38.3929i	0.559883	−	0.100769i
$382$		0			0
$383$	202.550	+	116.942i	0.528851	+	0.305332i	0.740548	−	0.672003i	$-0.234566\pi$
$383$	202.550	+	116.942i	0.528851	+	0.305332i	−0.211697	+	0.977335i	$0.567899\pi$
$384$		0			0
$385$	−376.251	−	651.685i	−0.977275	−	1.69269i
$386$		0			0
$387$	−360.939	+	436.393i	−0.932659	+	1.12763i
$388$		0			0
$389$	218.806	+	378.982i	0.562482	+	0.974248i	0.997279	+	0.0737194i	$0.0234869\pi$
$389$	218.806	+	378.982i	0.562482	+	0.974248i	−0.434797	+	0.900529i	$0.643180\pi$
$390$		0			0
$391$	85.4682	+	49.3451i	0.218589	+	0.126202i
$392$		0			0
$393$	187.361	−	520.498i	0.476744	−	1.32442i
$394$		0			0
$395$			137.922i			0.349169i
$396$		0			0
$397$	−324.259			−0.816774			−0.408387	−	0.912809i	$-0.633909\pi$
$397$	−324.259			−0.816774			−0.408387	+	0.912809i	$0.633909\pi$
$398$		0			0
$399$	314.416	−	265.730i	0.788011	−	0.665991i
$400$		0			0
$401$	197.087	−	341.364i	0.491488	−	0.851283i	−0.508463	−	0.861084i	$-0.669786\pi$
$401$	197.087	−	341.364i	0.491488	−	0.851283i	0.999952	+	0.00980052i	$0.00311965\pi$
$402$		0			0
$403$	−322.265	+	186.060i	−0.799664	+	0.461686i
$404$		0			0
$405$	100.639	+	526.978i	0.248493	+	1.30118i
$406$		0			0
$407$	−359.635	+	207.636i	−0.883625	+	0.510161i
$408$		0			0
$409$	14.1479	−	24.5048i	0.0345914	−	0.0599140i	−0.848211	−	0.529658i	$-0.822320\pi$
$409$	14.1479	−	24.5048i	0.0345914	−	0.0599140i	0.882803	+	0.469744i	$0.155654\pi$
$410$		0			0
$411$	320.214	−	270.631i	0.779111	−	0.658469i
$412$		0			0
$413$	−568.056			−1.37544
$414$		0			0
$415$			186.693i			0.449863i
$416$		0			0
$417$	−178.008	+	494.518i	−0.426879	+	1.18589i
$418$		0			0
$419$	−280.441	−	161.913i	−0.669310	−	0.386426i	0.126505	−	0.991966i	$-0.459624\pi$
$419$	−280.441	−	161.913i	−0.669310	−	0.386426i	−0.795815	+	0.605540i	$0.792957\pi$
$420$		0			0
$421$	215.676	+	373.562i	0.512295	+	0.887320i	0.999898	+	0.0142554i	$0.00453777\pi$
$421$	215.676	+	373.562i	0.512295	+	0.887320i	−0.487604	+	0.873065i	$0.662129\pi$
$422$		0			0
$423$	28.3861	−	34.3202i	0.0671067	−	0.0811351i
$424$		0			0
$425$	−22.4230	−	38.8378i	−0.0527600	−	0.0913831i
$426$		0			0
$427$	100.520	+	58.0351i	0.235409	+	0.135914i
$428$		0			0
$429$	613.056	−	110.339i	1.42904	−	0.257201i
$430$		0			0
$431$		−	345.557i		−	0.801757i	−0.916131	−	0.400879i	$-0.868705\pi$
$431$		−	345.557i		−	0.801757i	0.916131	−	0.400879i	$-0.131295\pi$
$432$		0			0
$433$	369.907			0.854289			0.427144	−	0.904183i	$-0.359520\pi$
$433$	369.907			0.854289			0.427144	+	0.904183i	$0.359520\pi$
$434$		0			0
$435$	40.0427	+	222.482i	0.0920521	+	0.511452i
$436$		0			0
$437$	291.389	−	504.700i	0.666793	−	1.15492i
$438$		0			0
$439$	358.332	−	206.883i	0.816245	−	0.471259i	−0.0328748	−	0.999459i	$-0.510466\pi$
$439$	358.332	−	206.883i	0.816245	−	0.471259i	0.849120	+	0.528200i	$0.177133\pi$
$440$		0			0
$441$	−69.9169	+	413.634i	−0.158542	+	0.937946i
$442$		0			0
$443$	467.339	−	269.818i	1.05494	−	0.609070i	0.130912	−	0.991394i	$-0.458209\pi$
$443$	467.339	−	269.818i	1.05494	−	0.609070i	0.924029	+	0.382323i	$0.124876\pi$
$444$		0			0
$445$	−241.797	+	418.805i	−0.543365	+	0.941135i
$446$		0			0
$447$	539.328	+	194.139i	1.20655	+	0.434315i
$448$		0			0
$449$	−325.056			−0.723956			−0.361978	−	0.932187i	$-0.617899\pi$
$449$	−325.056			−0.723956			−0.361978	+	0.932187i	$0.617899\pi$
$450$		0			0
$451$		−	61.1058i		−	0.135490i
$452$		0			0
$453$	−14.0282	−	16.5984i	−0.0309673	−	0.0366410i
$454$		0			0
$455$	−1002.32	−	578.689i	−2.20290	−	1.27184i
$456$		0			0
$457$	−309.075	−	535.333i	−0.676312	−	1.17141i	−0.976083	−	0.217396i	$-0.930244\pi$
$457$	−309.075	−	535.333i	−0.676312	−	1.17141i	0.299771	−	0.954011i	$-0.403090\pi$
$458$		0			0
$459$	−32.6718	−	55.2254i	−0.0711804	−	0.120317i
$460$		0			0
$461$	424.992	+	736.107i	0.921891	+	1.59676i	0.796487	+	0.604656i	$0.206689\pi$
$461$	424.992	+	736.107i	0.921891	+	1.59676i	0.125404	+	0.992106i	$0.459977\pi$
$462$		0			0
$463$	−706.453	−	407.871i	−1.52582	−	0.880930i	−0.999531	−	0.0306215i	$-0.990251\pi$
$463$	−706.453	−	407.871i	−1.52582	−	0.880930i	−0.526285	−	0.850309i	$-0.676415\pi$
$464$		0			0
$465$	−267.085	−	316.019i	−0.574375	−	0.679610i
$466$		0			0
$467$		−	378.909i		−	0.811368i	−0.914013	−	0.405684i	$-0.867033\pi$
$467$		−	378.909i		−	0.811368i	0.914013	−	0.405684i	$-0.132967\pi$
$468$		0			0
$469$	232.834			0.496447
$470$		0			0
$471$	−203.600	−	73.2885i	−0.432271	−	0.155602i
$472$		0			0
$473$	−365.556	+	633.162i	−0.772846	+	1.33861i
$474$		0			0
$475$	−229.342	+	132.411i	−0.482825	+	0.278759i
$476$		0			0
$477$	−638.890	+	237.676i	−1.33939	+	0.498273i
$478$		0			0
$479$	−297.958	+	172.026i	−0.622041	+	0.359136i	−0.777663	−	0.628681i	$-0.783595\pi$
$479$	−297.958	+	172.026i	−0.622041	+	0.359136i	0.155622	+	0.987817i	$0.450262\pi$
$480$		0			0
$481$	−319.352	+	553.134i	−0.663934	+	1.14997i
$482$		0			0
$483$	215.781	+	1198.91i	0.446752	+	2.48221i
$484$		0			0
$485$	−942.008			−1.94228
$486$		0			0
$487$			587.595i			1.20656i	0.797529	+	0.603281i	$0.206140\pi$
$487$			587.595i			1.20656i	−0.797529	+	0.603281i	$0.793860\pi$
$488$		0			0
$489$	−331.482	+	59.6607i	−0.677877	+	0.122005i
$490$		0			0
$491$	−430.072	−	248.302i	−0.875909	−	0.505707i	−0.00660193	−	0.999978i	$-0.502101\pi$
$491$	−430.072	−	248.302i	−0.875909	−	0.505707i	−0.869307	+	0.494272i	$0.835435\pi$
$492$		0			0
$493$	−13.5183	−	23.4144i	−0.0274205	−	0.0474937i
$494$		0			0
$495$	241.495	+	649.156i	0.487869	+	1.31143i
$496$		0			0
$497$	227.223	+	393.561i	0.457188	+	0.791873i
$498$		0			0
$499$	30.1869	+	17.4284i	0.0604948	+	0.0349267i	0.529942	−	0.848034i	$-0.322214\pi$
$499$	30.1869	+	17.4284i	0.0604948	+	0.0349267i	−0.469448	+	0.882960i	$0.655547\pi$
$500$		0			0
$501$	18.5831	−	51.6249i	0.0370920	−	0.103044i
$502$		0			0
$503$		−	630.866i		−	1.25421i	−0.778936	−	0.627104i	$-0.784240\pi$
$503$		−	630.866i		−	1.25421i	0.778936	−	0.627104i	$-0.215760\pi$
$504$		0			0
$505$	−181.166			−0.358745
$506$		0			0
$507$	344.500	−	291.156i	0.679487	−	0.574271i
$508$		0			0
$509$	−41.0282	+	71.0629i	−0.0806055	+	0.139613i	−0.903510	−	0.428567i	$-0.859019\pi$
$509$	−41.0282	+	71.0629i	−0.0806055	+	0.139613i	0.822905	+	0.568179i	$0.192352\pi$
$510$		0			0
$511$	−883.663	+	510.183i	−1.72928	+	0.998401i
$512$		0			0
$513$	−326.113	+	192.931i	−0.635697	+	0.376084i
$514$		0			0
$515$	841.322	−	485.738i	1.63364	−	0.943180i
$516$		0			0
$517$	28.7492	−	49.7952i	0.0556078	−	0.0963156i
$518$		0			0
$519$	672.042	−	567.979i	1.29488	−	1.09437i
$520$		0			0
$521$	562.797			1.08023			0.540113	−	0.841593i	$-0.318382\pi$
$521$	562.797			1.08023			0.540113	+	0.841593i	$0.318382\pi$
$522$		0			0
$523$		−	909.721i		−	1.73943i	−0.493555	−	0.869714i	$-0.664303\pi$
$523$		−	909.721i		−	1.73943i	0.493555	−	0.869714i	$-0.335697\pi$
$524$		0			0
$525$	187.482	−	520.835i	0.357108	−	0.992067i
$526$		0			0
$527$	42.8568	+	24.7434i	0.0813223	+	0.0469514i
$528$		0			0
$529$	597.751	+	1035.33i	1.12996	+	1.95715i
$530$		0			0
$531$	515.540	+	87.1421i	0.970885	+	0.164109i
$532$		0			0
$533$	−46.9916	−	81.3918i	−0.0881644	−	0.152705i
$534$		0			0
$535$	1104.62	+	637.753i	2.06471	+	1.19206i
$536$		0			0
$537$	274.445	−	49.3951i	0.511071	−	0.0919835i
$538$		0			0
$539$			541.574i			1.00478i
$540$		0			0
$541$	468.259			0.865544			0.432772	−	0.901503i	$-0.357536\pi$
$541$	468.259			0.865544			0.432772	+	0.901503i	$0.357536\pi$
$542$		0			0
$543$	68.2566	+	379.242i	0.125703	+	0.698420i
$544$		0			0
$545$	−0.858229	+	1.48650i	−0.00157473	+	0.00272752i
$546$		0			0
$547$	−271.063	+	156.498i	−0.495544	+	0.286102i	−0.726872	−	0.686773i	$-0.759026\pi$
$547$	−271.063	+	156.498i	−0.495544	+	0.286102i	0.231328	+	0.972876i	$0.425693\pi$
$548$		0			0
$549$	−82.3239	−	68.0899i	−0.149953	−	0.124025i
$550$		0			0
$551$	−138.265	+	79.8271i	−0.250934	+	0.144877i
$552$		0			0
$553$	101.806	−	176.333i	0.184097	−	0.318865i
$554$		0			0
$555$	−668.213	−	240.532i	−1.20399	−	0.433392i
$556$		0			0
$557$	382.841			0.687328			0.343664	−	0.939093i	$-0.388332\pi$
$557$	382.841			0.687328			0.343664	+	0.939093i	$0.388332\pi$
$558$		0			0
$559$			1124.48i			2.01160i
$560$		0			0
$561$	−53.4718	−	63.2687i	−0.0953152	−	0.112778i
$562$		0			0
$563$	518.767	+	299.510i	0.921434	+	0.531990i	0.884092	−	0.467313i	$-0.154778\pi$
$563$	518.767	+	299.510i	0.921434	+	0.531990i	0.0373414	+	0.999303i	$0.488111\pi$
$564$		0			0
$565$	−658.566	−	1140.67i	−1.16560	−	2.01889i
$566$		0			0
$567$	260.316	−	748.025i	0.459111	−	1.31927i
$568$		0			0
$569$	−422.087	−	731.076i	−0.741805	−	1.28484i	−0.951673	−	0.307114i	$-0.900637\pi$
$569$	−422.087	−	731.076i	−0.741805	−	1.28484i	0.209868	−	0.977730i	$-0.432697\pi$
$570$		0			0
$571$	−672.354	−	388.184i	−1.17750	−	0.679832i	−0.222067	−	0.975031i	$-0.571281\pi$
$571$	−672.354	−	388.184i	−1.17750	−	0.679832i	−0.955436	+	0.295200i	$0.904614\pi$
$572$		0			0
$573$	582.085	+	688.732i	1.01585	+	1.20198i
$574$		0			0
$575$		−	783.634i		−	1.36284i
$576$		0			0
$577$	−487.316			−0.844568			−0.422284	−	0.906464i	$-0.638771\pi$
$577$	−487.316			−0.844568			−0.422284	+	0.906464i	$0.638771\pi$
$578$		0			0
$579$	110.817	+	39.8899i	0.191393	+	0.0688946i
$580$		0			0
$581$	137.806	−	238.686i	0.237187	−	0.410820i
$582$		0			0
$583$	−762.128	+	440.015i	−1.30725	+	0.754742i
$584$		0			0
$585$	820.882	+	678.949i	1.40322	+	1.16060i
$586$		0			0
$587$	−487.463	+	281.437i	−0.830432	+	0.479450i	−0.854001	−	0.520272i	$-0.825830\pi$
$587$	−487.463	+	281.437i	−0.830432	+	0.479450i	0.0235687	+	0.999722i	$0.492497\pi$
$588$		0			0
$589$	146.113	−	253.075i	0.248069	−	0.429669i
$590$		0			0
$591$	−50.3524	−	279.764i	−0.0851987	−	0.473374i
$592$		0			0
$593$	−316.915			−0.534426			−0.267213	−	0.963637i	$-0.586103\pi$
$593$	−316.915			−0.534426			−0.267213	+	0.963637i	$0.586103\pi$
$594$		0			0
$595$			153.916i			0.258682i
$596$		0			0
$597$	−328.797	+	59.1775i	−0.550749	+	0.0991248i
$598$		0			0
$599$	76.5870	+	44.2175i	0.127858	+	0.0738189i	0.562565	−	0.826753i	$-0.309815\pi$
$599$	76.5870	+	44.2175i	0.127858	+	0.0738189i	−0.434707	+	0.900572i	$0.643148\pi$
$600$		0			0
$601$	55.9085	+	96.8364i	0.0930258	+	0.161125i	0.908783	−	0.417269i	$-0.137013\pi$
$601$	55.9085	+	96.8364i	0.0930258	+	0.161125i	−0.815757	+	0.578395i	$0.803679\pi$
$602$		0			0
$603$	−211.308	−	35.7176i	−0.350429	−	0.0592332i
$604$		0			0
$605$	46.3643	+	80.3054i	0.0766353	+	0.132736i
$606$		0			0
$607$	−596.058	−	344.134i	−0.981973	−	0.566942i	−0.0791078	−	0.996866i	$-0.525207\pi$
$607$	−596.058	−	344.134i	−0.981973	−	0.566942i	−0.902865	+	0.429924i	$0.858540\pi$
$608$		0			0
$609$	113.028	−	313.999i	0.185596	−	0.515598i
$610$		0			0
$611$		−	88.4351i		−	0.144738i
$612$		0			0
$613$	−1021.67			−1.66667			−0.833334	−	0.552770i	$-0.813571\pi$
$613$	−1021.67			−1.66667			−0.833334	+	0.552770i	$0.813571\pi$
$614$		0			0
$615$	79.8143	−	67.4554i	0.129779	−	0.109684i
$616$		0			0
$617$	381.884	−	661.443i	0.618937	−	1.07203i	−0.370743	−	0.928735i	$-0.620897\pi$
$617$	381.884	−	661.443i	0.618937	−	1.07203i	0.989680	−	0.143295i	$-0.0457697\pi$
$618$		0			0
$619$	661.382	−	381.849i	1.06847	−	0.616880i	0.140706	−	0.990051i	$-0.455063\pi$
$619$	661.382	−	381.849i	1.06847	−	0.616880i	0.927763	+	0.373171i	$0.121730\pi$
$620$		0			0
$621$	−11.9154	−	1121.17i	−0.0191875	−	1.80542i
$622$		0			0
$623$	618.273	−	356.960i	0.992413	−	0.572970i
$624$		0			0
$625$	370.334	−	641.437i	0.592534	−	1.02630i
$626$		0			0
$627$	−373.609	+	315.757i	−0.595868	+	0.503600i
$628$		0			0
$629$	84.9390			0.135038
$630$		0			0
$631$			166.586i			0.264002i	0.991250	+	0.132001i	$0.0421403\pi$
$631$			166.586i			0.264002i	−0.991250	+	0.132001i	$0.957860\pi$
$632$		0			0
$633$	120.510	−	334.783i	0.190379	−	0.528884i
$634$		0			0
$635$	414.420	+	239.265i	0.652629	+	0.376796i
$636$		0			0
$637$	416.482	+	721.367i	0.653817	+	1.13245i
$638$		0			0
$639$	−145.842	−	392.033i	−0.228235	−	0.613511i
$640$		0			0
$641$	−102.136	−	176.904i	−0.159338	−	0.275982i	0.775292	−	0.631603i	$-0.217603\pi$
$641$	−102.136	−	176.904i	−0.159338	−	0.275982i	−0.934630	+	0.355621i	$0.884269\pi$
$642$		0			0
$643$	−826.974	−	477.454i	−1.28612	−	0.742541i	−0.308159	−	0.951335i	$-0.599713\pi$
$643$	−826.974	−	477.454i	−1.28612	−	0.742541i	−0.977960	+	0.208794i	$0.933046\pi$
$644$		0			0
$645$	−1230.56	+	221.478i	−1.90784	+	0.343377i
$646$		0			0
$647$		−	424.736i		−	0.656470i	−0.944596	−	0.328235i	$-0.893546\pi$
$647$		−	424.736i		−	0.656470i	0.944596	−	0.328235i	$-0.106454\pi$
$648$		0			0
$649$	675.000			1.04006
$650$		0			0
$651$	108.200	+	601.174i	0.166207	+	0.923463i
$652$		0			0
$653$	307.178	−	532.047i	0.470410	−	0.814774i	−0.529018	−	0.848611i	$-0.677439\pi$
$653$	307.178	−	532.047i	0.470410	−	0.814774i	0.999427	+	0.0338373i	$0.0107728\pi$
$654$		0			0
$655$	1057.72	−	610.677i	1.61484	−	0.932331i
$656$		0			0
$657$	880.232	−	327.459i	1.33978	−	0.498416i
$658$		0			0
$659$	−843.930	+	487.243i	−1.28062	+	0.739367i	−0.976962	−	0.213413i	$-0.931542\pi$
$659$	−843.930	+	487.243i	−1.28062	+	0.739367i	−0.303660	+	0.952780i	$0.598209\pi$
$660$		0			0
$661$	274.380	−	475.241i	0.415099	−	0.718972i	−0.580340	−	0.814374i	$-0.697080\pi$
$661$	274.380	−	475.241i	0.415099	−	0.718972i	0.995439	+	0.0954020i	$0.0304137\pi$
$662$		0			0
$663$	−119.878	−	43.1519i	−0.180812	−	0.0650858i
$664$		0			0
$665$	908.890			1.36675
$666$		0			0
$667$		−	472.434i		−	0.708297i
$668$		0			0
$669$	−46.9916	−	55.6012i	−0.0702416	−	0.0831109i
$670$		0			0
$671$	−119.444	−	68.9609i	−0.178009	−	0.102773i
$672$		0			0
$673$	186.992	+	323.879i	0.277848	+	0.481247i	0.970850	−	0.239689i	$-0.0770456\pi$
$673$	186.992	+	323.879i	0.277848	+	0.481247i	−0.693002	+	0.720936i	$0.743712\pi$
$674$		0			0
$675$	−250.047	+	443.924i	−0.370440	+	0.657665i
$676$		0			0
$677$	120.972	+	209.529i	0.178688	+	0.309497i	0.941431	−	0.337205i	$-0.109481\pi$
$677$	120.972	+	209.529i	0.178688	+	0.309497i	−0.762743	+	0.646701i	$0.776148\pi$
$678$		0			0
$679$	1204.35	+	695.333i	1.77372	+	1.02405i
$680$		0			0
$681$	−22.5000	−	26.6224i	−0.0330396	−	0.0390930i
$682$		0			0
$683$			524.358i			0.767728i	0.923390	+	0.383864i	$0.125407\pi$
$683$			524.358i			0.767728i	−0.923390	+	0.383864i	$0.874593\pi$
$684$		0			0
$685$	925.651			1.35132
$686$		0			0
$687$	51.1743	+	18.4209i	0.0744895	+	0.0268135i
$688$		0			0
$689$	−676.761	+	1172.18i	−0.982236	+	1.70128i
$690$		0			0
$691$	306.568	−	176.997i	0.443658	−	0.256146i	−0.261490	−	0.965206i	$-0.584214\pi$
$691$	306.568	−	176.997i	0.443658	−	0.256146i	0.705148	+	0.709060i	$0.250880\pi$
$692$		0			0
$693$	170.417	−	1008.20i	0.245912	−	1.45483i
$694$		0			0
$695$	−1004.93	+	580.195i	−1.44594	+	0.834813i
$696$		0			0
$697$	−6.24925	+	10.8240i	−0.00896592	+	0.0155294i
$698$		0			0
$699$	−116.795	−	648.928i	−0.167089	−	0.928367i
$700$		0			0
$701$	−621.287			−0.886286			−0.443143	−	0.896451i	$-0.646137\pi$
$701$	−621.287			−0.886286			−0.443143	+	0.896451i	$0.646137\pi$
$702$		0			0
$703$		−	501.575i		−	0.713478i
$704$		0			0
$705$	96.7774	−	17.4182i	0.137273	−	0.0247066i
$706$		0			0
$707$	231.620	+	133.726i	0.327610	+	0.189146i
$708$		0			0
$709$	−393.992	−	682.413i	−0.555700	−	0.962501i	−0.997849	−	0.0655594i	$-0.979117\pi$
$709$	−393.992	−	682.413i	−0.555700	−	0.962501i	0.442148	−	0.896942i	$-0.354217\pi$
$710$		0			0
$711$	−119.444	+	144.413i	−0.167994	+	0.203113i
$712$		0			0
$713$	432.364	+	748.876i	0.606400	+	1.05032i
$714$		0			0
$715$	1191.02	+	687.635i	1.66576	+	0.961727i
$716$		0			0
$717$	−163.749	+	454.905i	−0.228381	+	0.634456i
$718$		0			0
$719$			1248.82i			1.73689i	0.495785	+	0.868445i	$0.334881\pi$
$719$			1248.82i			1.73689i	−0.495785	+	0.868445i	$0.665119\pi$
$720$		0			0
$721$	−1434.17			−1.98914
$722$		0			0
$723$	−387.654	+	327.627i	−0.536174	+	0.453150i
$724$		0			0
$725$	−107.340	+	185.918i	−0.148055	+	0.256439i
$726$		0			0
$727$	634.487	−	366.321i	0.872746	−	0.503880i	0.00448649	−	0.999990i	$-0.498572\pi$
$727$	634.487	−	366.321i	0.872746	−	0.503880i	0.868260	+	0.496110i	$0.165239\pi$
$728$		0			0
$729$	−351.000	+	638.937i	−0.481481	+	0.876456i
$730$		0			0
$731$	129.506	−	74.7704i	0.177163	−	0.102285i
$732$		0			0
$733$	182.361	−	315.858i	0.248787	−	0.430911i	−0.714403	−	0.699735i	$-0.753302\pi$
$733$	182.361	−	315.858i	0.248787	−	0.430911i	0.963189	+	0.268824i	$0.0866349\pi$
$734$		0			0
$735$	−707.386	+	597.850i	−0.962430	+	0.813402i
$736$		0			0
$737$	−276.668			−0.375397
$738$		0			0
$739$		−	1162.07i		−	1.57248i	−0.617918	−	0.786242i	$-0.712024\pi$
$739$		−	1162.07i		−	1.57248i	0.617918	−	0.786242i	$-0.287976\pi$
$740$		0			0
$741$	−254.817	+	707.897i	−0.343883	+	0.955326i
$742$		0			0
$743$	156.711	+	90.4773i	0.210917	+	0.121773i	0.601737	−	0.798694i	$-0.294475\pi$
$743$	156.711	+	90.4773i	0.210917	+	0.121773i	−0.390821	+	0.920467i	$0.627809\pi$
$744$		0			0
$745$	632.769	+	1095.99i	0.849354	+	1.47113i
$746$		0			0
$747$	−161.681	+	195.480i	−0.216440	+	0.261687i
$748$		0			0
$749$	−941.502	−	1630.73i	−1.25701	−	2.17721i
$750$		0			0
$751$	−152.903	−	88.2786i	−0.203599	−	0.117548i	0.394734	−	0.918795i	$-0.370837\pi$
$751$	−152.903	−	88.2786i	−0.203599	−	0.117548i	−0.598333	+	0.801247i	$0.704170\pi$
$752$		0			0
$753$	−647.362	+	116.513i	−0.859711	+	0.154732i
$754$		0			0
$755$		−	47.9813i		−	0.0635514i
$756$		0			0
$757$	146.665			0.193745			0.0968723	−	0.995297i	$-0.469116\pi$
$757$	146.665			0.193745			0.0968723	+	0.995297i	$0.469116\pi$
$758$		0			0
$759$	−256.405	−	1424.61i	−0.337819	−	1.87696i
$760$		0			0
$761$	−403.405	+	698.717i	−0.530098	+	0.918157i	0.469285	+	0.883047i	$0.344512\pi$
$761$	−403.405	+	698.717i	−0.530098	+	0.918157i	−0.999383	+	0.0351104i	$0.988822\pi$
$762$		0			0
$763$	2.19448	−	1.26699i	0.00287613	−	0.00166053i
$764$		0			0
$765$	23.6113	−	139.686i	0.0308644	−	0.182596i
$766$		0			0
$767$	899.088	−	519.089i	1.17221	−	0.676778i
$768$		0			0
$769$	−275.566	+	477.295i	−0.358344	+	0.620669i	−0.987684	−	0.156460i	$-0.949992\pi$
$769$	−275.566	+	477.295i	−0.358344	+	0.620669i	0.629341	+	0.777130i	$0.283325\pi$
$770$		0			0
$771$	500.942	+	180.321i	0.649731	+	0.233879i
$772$		0			0
$773$	856.915			1.10856			0.554279	−	0.832331i	$-0.312994\pi$
$773$	856.915			1.10856			0.554279	+	0.832331i	$0.312994\pi$
$774$		0			0
$775$		−	392.942i		−	0.507023i
$776$		0			0
$777$	676.761	+	800.754i	0.870992	+	1.03057i
$778$		0			0
$779$	63.9171	+	36.9025i	0.0820502	+	0.0473717i
$780$		0			0
$781$	−270.000	−	467.654i	−0.345711	−	0.598788i
$782$		0			0
$783$	−150.747	+	267.631i	−0.192525	+	0.341802i
$784$		0			0
$785$	−238.874	−	413.742i	−0.304298	−	0.527060i
$786$		0			0
$787$	−466.532	−	269.352i	−0.592798	−	0.342252i	0.173405	−	0.984851i	$-0.444523\pi$
$787$	−466.532	−	269.352i	−0.592798	−	0.342252i	−0.766203	+	0.642598i	$0.777856\pi$
$788$		0			0
$789$	132.085	+	156.285i	0.167408	+	0.198079i
$790$		0			0
$791$			1944.46i			2.45823i
$792$		0			0
$793$	−212.130			−0.267503
$794$		0			0
$795$	−1416.05	−	509.728i	−1.78120	−	0.641168i
$796$		0			0
$797$	−674.153	+	1167.67i	−0.845863	+	1.46508i	0.0390058	+	0.999239i	$0.487581\pi$
$797$	−674.153	+	1167.67i	−0.845863	+	1.46508i	−0.884869	+	0.465840i	$0.845752\pi$
$798$		0			0
$799$	−10.1850	+	5.88033i	−0.0127472	+	0.00735962i
$800$		0			0
$801$	−615.873	+	229.114i	−0.768881	+	0.286035i
$802$		0			0
$803$	1050.02	−	606.231i	1.30763	−	0.754958i
$804$		0			0
$805$	−1344.75	+	2329.18i	−1.67050	+	2.89339i
$806$		0			0
$807$	−41.3250	−	229.607i	−0.0512082	−	0.284519i
$808$		0			0
$809$	1163.88			1.43867			0.719334	−	0.694664i	$-0.244447\pi$
$809$	1163.88			1.43867			0.719334	+	0.694664i	$0.244447\pi$
$810$		0			0
$811$			627.878i			0.774202i	0.922037	+	0.387101i	$0.126524\pi$
$811$			627.878i			0.774202i	−0.922037	+	0.387101i	$0.873476\pi$
$812$		0			0
$813$	1320.56	−	237.676i	1.62430	−	0.292345i
$814$		0			0
$815$	−643.988	−	371.806i	−0.790169	−	0.456204i
$816$		0			0
$817$	−441.528	−	764.749i	−0.540426	−	0.936046i
$818$		0			0
$819$	−548.334	−	1473.96i	−0.669517	−	1.79971i
$820$		0			0
$821$	−32.1822	−	55.7411i	−0.0391987	−	0.0678942i	0.845760	−	0.533563i	$-0.179147\pi$
$821$	−32.1822	−	55.7411i	−0.0391987	−	0.0678942i	−0.884959	+	0.465669i	$0.845814\pi$
$822$		0			0
$823$	−817.183	−	471.801i	−0.992932	−	0.573269i	−0.0867825	−	0.996227i	$-0.527659\pi$
$823$	−817.183	−	471.801i	−0.992932	−	0.573269i	−0.906149	+	0.422958i	$0.860992\pi$
$824$		0			0
$825$	−222.777	+	618.889i	−0.270033	+	0.750168i
$826$		0			0
$827$			571.482i			0.691031i	0.938413	+	0.345515i	$0.112296\pi$
$827$			571.482i			0.691031i	−0.938413	+	0.345515i	$0.887704\pi$
$828$		0			0
$829$	−519.555			−0.626725			−0.313362	−	0.949634i	$-0.601455\pi$
$829$	−519.555			−0.626725			−0.313362	+	0.949634i	$0.601455\pi$
$830$		0			0
$831$	−385.066	+	325.440i	−0.463376	+	0.391624i
$832$		0			0
$833$	55.3864	−	95.9321i	0.0664903	−	0.115165i
$834$		0			0
$835$	104.909	−	60.5691i	0.125639	−	0.0725378i
$836$		0			0
$837$	−5.97482	−	562.194i	−0.00713837	−	0.671678i
$838$		0			0
$839$	−1039.96	+	600.422i	−1.23952	+	0.715640i	−0.968997	−	0.247073i	$-0.920531\pi$
$839$	−1039.96	+	600.422i	−1.23952	+	0.715640i	−0.270527	+	0.962712i	$0.587198\pi$
$840$		0			0
$841$	355.787	−	616.242i	0.423053	−	0.732749i
$842$		0			0
$843$	472.784	−	399.576i	0.560835	−	0.473992i
$844$		0			0
$845$	995.854			1.17853
$846$		0			0
$847$		−	136.893i		−	0.161622i
$848$		0			0
$849$	−202.566	+	562.741i	−0.238594	+	0.662828i
$850$		0			0
$851$	1285.37	+	742.107i	1.51042	+	0.872041i
$852$		0			0
$853$	299.583	+	518.893i	0.351211	+	0.608315i	0.986462	−	0.163990i	$-0.0524366\pi$
$853$	299.583	+	518.893i	0.351211	+	0.608315i	−0.635251	+	0.772306i	$0.719103\pi$
$854$		0			0
$855$	−824.864	−	139.427i	−0.964753	−	0.163073i
$856$		0			0
$857$	−345.664	−	598.707i	−0.403342	−	0.698608i	0.590785	−	0.806829i	$-0.298818\pi$
$857$	−345.664	−	598.707i	−0.403342	−	0.698608i	−0.994127	+	0.108221i	$0.965485\pi$
$858$		0			0
$859$	1215.72	+	701.896i	1.41527	+	0.817108i	0.995879	−	0.0906967i	$-0.0289094\pi$
$859$	1215.72	+	701.896i	1.41527	+	0.817108i	0.419394	+	0.907805i	$0.362243\pi$
$860$		0			0
$861$	−151.834	+	27.3273i	−0.176346	+	0.0317391i
$862$		0			0
$863$		−	253.038i		−	0.293207i	−0.989195	−	0.146604i	$-0.953166\pi$
$863$		−	253.038i		−	0.293207i	0.989195	−	0.146604i	$-0.0468342\pi$
$864$		0			0
$865$	1942.69			2.24588
$866$		0			0
$867$	−150.575	−	836.614i	−0.173674	−	0.964953i
$868$		0			0
$869$	−120.972	+	209.529i	−0.139208	+	0.241115i
$870$		0			0
$871$	−368.517	+	212.763i	−0.423096	+	0.244275i
$872$		0			0
$873$	−986.344	−	815.803i	−1.12983	−	0.934482i
$874$		0			0
$875$	−343.796	+	198.491i	−0.392910	+	0.226847i
$876$		0			0
$877$	53.9352	−	93.4185i	0.0614997	−	0.106521i	−0.833636	−	0.552314i	$-0.813745\pi$
$877$	53.9352	−	93.4185i	0.0614997	−	0.106521i	0.895136	+	0.445793i	$0.147078\pi$
$878$		0			0
$879$	161.431	+	58.1095i	0.183654	+	0.0661086i
$880$		0			0
$881$	−119.927			−0.136126			−0.0680629	−	0.997681i	$-0.521682\pi$
$881$	−119.927			−0.136126			−0.0680629	+	0.997681i	$0.521682\pi$
$882$		0			0
$883$			306.661i			0.347295i	0.984808	+	0.173647i	$0.0555553\pi$
$883$			306.661i			0.347295i	−0.984808	+	0.173647i	$0.944445\pi$
$884$		0			0
$885$	745.141	+	881.663i	0.841967	+	0.996229i
$886$		0			0
$887$	680.325	+	392.786i	0.766996	+	0.442825i	0.831802	−	0.555073i	$-0.187310\pi$
$887$	680.325	+	392.786i	0.766996	+	0.442825i	−0.0648060	+	0.997898i	$0.520643\pi$
$888$		0			0
$889$	−353.223	−	611.799i	−0.397326	−	0.688188i
$890$		0			0
$891$	−309.324	+	888.850i	−0.347165	+	0.997587i
$892$		0			0
$893$	34.7241	+	60.1438i	0.0388847	+	0.0673503i
$894$		0			0
$895$	533.179	+	307.831i	0.595731	+	0.343946i
$896$		0			0
$897$	−1437.08	−	1700.38i	−1.60210	−	1.89563i
$898$		0			0
$899$		−	236.896i		−	0.263510i
$900$		0			0
$901$	180.000			0.199778
$902$		0			0
$903$	1736.74	+	625.165i	1.92331	+	0.692320i
$904$		0			0
$905$	−425.377	+	736.774i	−0.470029	+	0.814115i
$906$		0			0
$907$	1055.14	−	609.182i	1.16332	−	0.671646i	0.211226	−	0.977437i	$-0.432254\pi$
$907$	1055.14	−	609.182i	1.16332	−	0.671646i	0.952098	+	0.305792i	$0.0989211\pi$
$908$		0			0
$909$	−189.693	−	156.895i	−0.208683	−	0.172601i
$910$		0			0
$911$	760.824	−	439.262i	0.835152	−	0.482175i	−0.0204612	−	0.999791i	$-0.506513\pi$
$911$	760.824	−	439.262i	0.835152	−	0.482175i	0.855614	+	0.517615i	$0.173180\pi$
$912$		0			0
$913$	−163.749	+	283.622i	−0.179353	+	0.310648i
$914$		0			0
$915$	−41.7811	−	232.140i	−0.0456624	−	0.253705i
$916$		0			0
$917$	−1803.06			−1.96626
$918$		0			0
$919$		−	1036.67i		−	1.12804i	−0.825760	−	0.564022i	$-0.809253\pi$
$919$		−	1036.67i		−	1.12804i	0.825760	−	0.564022i	$-0.190747\pi$
$920$		0			0
$921$	817.196	−	147.080i	0.887292	−	0.159696i
$922$		0			0
$923$	−719.271	−	415.271i	−0.779275	−	0.449915i
$924$		0			0
$925$	−337.223	−	584.087i	−0.364565	−	0.631445i
$926$		0			0
$927$	1301.58	+	220.007i	1.40408	+	0.237333i
$928$		0			0
$929$	−124.911	−	216.352i	−0.134457	−	0.232887i	0.790933	−	0.611903i	$-0.209596\pi$
$929$	−124.911	−	216.352i	−0.134457	−	0.232887i	−0.925390	+	0.379016i	$0.876262\pi$
$930$		0			0
$931$	−566.490	−	327.063i	−0.608475	−	0.351303i
$932$		0			0
$933$	25.1410	−	69.8431i	0.0269464	−	0.0748586i
$934$		0			0
$935$		−	182.892i		−	0.195607i
$936$		0			0
$937$	190.744			0.203569			0.101784	−	0.994806i	$-0.467545\pi$
$937$	190.744			0.203569			0.101784	+	0.994806i	$0.467545\pi$
$938$		0			0
$939$	−148.508	+	125.512i	−0.158155	+	0.133665i
$940$		0			0
$941$	−141.150	+	244.479i	−0.150000	+	0.259808i	−0.931227	−	0.364439i	$-0.881261\pi$
$941$	−141.150	+	244.479i	−0.150000	+	0.259808i	0.781227	+	0.624247i	$0.214594\pi$
$942$		0			0
$943$	−189.138	+	109.199i	−0.200570	+	0.115799i
$944$		0			0
$945$	1505.00	−	890.372i	1.59260	−	0.942192i
$946$		0			0
$947$	−573.926	+	331.356i	−0.606046	+	0.349901i	−0.771416	−	0.636331i	$-0.780451\pi$
$947$	−573.926	+	331.356i	−0.606046	+	0.349901i	0.165370	+	0.986232i	$0.447118\pi$
$948$		0			0
$949$	932.409	−	1614.98i	0.982517	−	1.70177i
$950$		0			0
$951$	−1041.62	+	880.327i	−1.09529	+	0.925686i
$952$		0			0
$953$	1166.70			1.22424			0.612119	−	0.790765i	$-0.290317\pi$
$953$	1166.70			1.22424			0.612119	+	0.790765i	$0.290317\pi$
$954$		0			0
$955$			1990.93i			2.08475i
$956$		0			0
$957$	−134.307	+	373.113i	−0.140342	+	0.389878i
$958$		0			0
$959$	−1183.44	−	683.260i	−1.23404	−	0.712471i
$960$		0			0
$961$	−263.697	−	456.737i	−0.274399	−	0.475273i
$962$		0			0
$963$	604.300	+	1624.40i	0.627518	+	1.68681i
$964$		0			0
$965$	130.016	+	225.194i	0.134732	+	0.233362i
$966$		0			0
$967$	−1010.52	−	583.422i	−1.04500	−	0.603332i	−0.123756	−	0.992313i	$-0.539494\pi$
$967$	−1010.52	−	583.422i	−1.04500	−	0.603332i	−0.921246	+	0.388981i	$0.872827\pi$
$968$		0			0
$969$	98.4718	−	17.7231i	0.101622	−	0.0182901i
$970$		0			0
$971$		−	1481.20i		−	1.52544i	−0.646728	−	0.762721i	$-0.723863\pi$
$971$		−	1481.20i		−	1.52544i	0.646728	−	0.762721i	$-0.276137\pi$
$972$		0			0
$973$	1713.06			1.76060
$974$		0			0
$975$	179.202	+	995.670i	0.183797	+	1.02120i
$976$		0			0
$977$	592.779	−	1026.72i	0.606734	−	1.05089i	−0.385041	−	0.922899i	$-0.625813\pi$
$977$	592.779	−	1026.72i	0.606734	−	1.05089i	0.991775	−	0.127994i	$-0.0408539\pi$
$978$		0			0
$979$	−734.671	+	424.163i	−0.750430	+	0.433261i
$980$		0			0
$981$	−2.18597	+	0.813211i	−0.00222830	+	0.000828961i
$982$		0			0
$983$	−56.0882	+	32.3825i	−0.0570581	+	0.0329425i	−0.528258	−	0.849084i	$-0.677154\pi$
$983$	−56.0882	+	32.3825i	−0.0570581	+	0.0329425i	0.471200	+	0.882027i	$0.343821\pi$
$984$		0			0
$985$	313.797	−	543.513i	0.318576	−	0.551790i
$986$		0			0
$987$	−136.587	−	49.1662i	−0.138386	−	0.0498138i
$988$		0			0
$989$	2613.06			2.64212
$990$		0			0
$991$		−	1394.27i		−	1.40694i	−0.710727	−	0.703468i	$-0.751634\pi$
$991$		−	1394.27i		−	1.40694i	0.710727	−	0.703468i	$-0.248366\pi$
$992$		0			0
$993$	527.732	+	624.421i	0.531453	+	0.628823i
$994$		0			0
$995$	−638.772	−	368.795i	−0.641982	−	0.370649i
$996$		0			0
$997$	487.271	+	843.977i	0.488737	+	0.846517i	0.999916	−	0.0129572i	$-0.00412452\pi$
$997$	487.271	+	843.977i	0.488737	+	0.846517i	−0.511179	+	0.859474i	$0.670791\pi$
$998$		0			0
$999$	−491.355	−	830.542i	−0.491847	−	0.831374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.o.b.31.3	yes	8
3.2	odd	2		432.3.o.c.415.4		8
4.3	odd	2	inner	144.3.o.b.31.2	✓	8
8.3	odd	2		576.3.o.e.319.3		8
8.5	even	2		576.3.o.e.319.2		8
9.2	odd	6		432.3.o.c.127.3		8
9.4	even	3		1296.3.g.h.1135.4		4
9.5	odd	6		1296.3.g.d.1135.2		4
9.7	even	3	inner	144.3.o.b.79.2	yes	8
12.11	even	2		432.3.o.c.415.3		8
24.5	odd	2		1728.3.o.d.1279.2		8
24.11	even	2		1728.3.o.d.1279.1		8
36.7	odd	6	inner	144.3.o.b.79.3	yes	8
36.11	even	6		432.3.o.c.127.4		8
36.23	even	6		1296.3.g.d.1135.1		4
36.31	odd	6		1296.3.g.h.1135.3		4
72.11	even	6		1728.3.o.d.127.2		8
72.29	odd	6		1728.3.o.d.127.1		8
72.43	odd	6		576.3.o.e.511.2		8
72.61	even	6		576.3.o.e.511.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.b.31.2	✓	8	4.3	odd	2	inner
144.3.o.b.31.3	yes	8	1.1	even	1	trivial
144.3.o.b.79.2	yes	8	9.7	even	3	inner
144.3.o.b.79.3	yes	8	36.7	odd	6	inner
432.3.o.c.127.3		8	9.2	odd	6
432.3.o.c.127.4		8	36.11	even	6
432.3.o.c.415.3		8	12.11	even	2
432.3.o.c.415.4		8	3.2	odd	2
576.3.o.e.319.2		8	8.5	even	2
576.3.o.e.319.3		8	8.3	odd	2
576.3.o.e.511.2		8	72.43	odd	6
576.3.o.e.511.3		8	72.61	even	6
1296.3.g.d.1135.1		4	36.23	even	6
1296.3.g.d.1135.2		4	9.5	odd	6
1296.3.g.h.1135.3		4	36.31	odd	6
1296.3.g.h.1135.4		4	9.4	even	3
1728.3.o.d.127.1		8	72.29	odd	6
1728.3.o.d.127.2		8	72.11	even	6
1728.3.o.d.1279.1		8	24.11	even	2
1728.3.o.d.1279.2		8	24.5	odd	2

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.531407 + 2.95256i) q^{3} +(-3.31174 + 5.73610i) q^{5} +(8.46808 - 4.88905i) q^{7} +(-8.43521 + 3.13802i) q^{9} +O(q^{10})\)	\(q+(0.531407 + 2.95256i) q^{3} +(-3.31174 + 5.73610i) q^{5} +(8.46808 - 4.88905i) q^{7} +(-8.43521 + 3.13802i) q^{9} +(-10.0623 + 5.80948i) q^{11} +(-8.93521 + 15.4762i) q^{13} +(-18.6961 - 6.72990i) q^{15} +2.37652 q^{17} -14.0337i q^{19} +(18.9352 + 22.4044i) q^{21} +(35.9635 + 20.7636i) q^{23} +(-9.43521 - 16.3423i) q^{25} +(-13.7477 - 23.2379i) q^{27} +(-5.68826 - 9.85236i) q^{29} +(18.0334 + 10.4116i) q^{31} +(-22.5000 - 26.6224i) q^{33} +64.7650i q^{35} +35.7409 q^{37} +(-50.4428 - 18.1576i) q^{39} +(-2.62957 + 4.55456i) q^{41} +(54.4939 - 31.4621i) q^{43} +(9.93521 - 58.7775i) q^{45} +(-4.28568 + 2.47434i) q^{47} +(23.3056 - 40.3666i) q^{49} +(1.26290 + 7.01683i) q^{51} +75.7409 q^{53} -76.9578i q^{55} +(41.4352 - 7.45759i) q^{57} +(-50.3115 - 29.0474i) q^{59} +(5.93521 + 10.2801i) q^{61} +(-56.0882 + 67.8132i) q^{63} +(-59.1822 - 102.507i) q^{65} +(20.6216 + 11.9059i) q^{67} +(-42.1944 + 117.218i) q^{69} +46.4758i q^{71} -104.352 q^{73} +(43.2376 - 36.5424i) q^{75} +(-56.8056 + 98.3903i) q^{77} +(18.0334 - 10.4116i) q^{79} +(61.3056 - 52.9398i) q^{81} +(24.4103 - 14.0933i) q^{83} +(-7.87043 + 13.6320i) q^{85} +(26.0669 - 22.0305i) q^{87} +73.0122 q^{89} +174.739i q^{91} +(-21.1578 + 58.7775i) q^{93} +(80.4984 + 46.4758i) q^{95} +(71.1113 + 123.168i) q^{97} +(66.6474 - 80.5799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q - 6 * q^5 - 6 * q^9	\( 8 q - 6 q^{5} - 6 q^{9} - 10 q^{13} + 60 q^{17} + 90 q^{21} - 14 q^{25} - 66 q^{29} - 180 q^{33} + 40 q^{37} - 144 q^{41} + 18 q^{45} + 2 q^{49} + 360 q^{53} + 270 q^{57} - 14 q^{61} - 330 q^{65} - 522 q^{69} - 220 q^{73} - 270 q^{77} + 306 q^{81} + 60 q^{85} + 912 q^{89} + 630 q^{93} + 200 q^{97}+O(q^{100}) \) 8 * q - 6 * q^5 - 6 * q^9 - 10 * q^13 + 60 * q^17 + 90 * q^21 - 14 * q^25 - 66 * q^29 - 180 * q^33 + 40 * q^37 - 144 * q^41 + 18 * q^45 + 2 * q^49 + 360 * q^53 + 270 * q^57 - 14 * q^61 - 330 * q^65 - 522 * q^69 - 220 * q^73 - 270 * q^77 + 306 * q^81 + 60 * q^85 + 912 * q^89 + 630 * q^93 + 200 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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