LMFDB - Embedded newform 180.3.m.c.107.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,3,Mod(107,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("180.107");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	180.m (of order $4$, 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:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.6
Character	$\chi$	$=$	180.107
Dual form			180.3.m.c.143.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34709 - 1.47830i) q^{2} +(-0.370713 + 3.98278i) q^{4} +(-4.91198 - 0.934037i) q^{5} +(6.91072 - 6.91072i) q^{7} +(6.38711 - 4.81713i) q^{8} +(5.23609 + 8.51959i) q^{10} -11.7722 q^{11} +(-15.8648 + 15.8648i) q^{13} +(-19.5254 - 0.906743i) q^{14} +(-15.7251 - 2.95294i) q^{16} +(2.08802 - 2.08802i) q^{17} -25.8603 q^{19} +(5.54100 - 19.2171i) q^{20} +(15.8582 + 17.4028i) q^{22} +(-16.6596 + 16.6596i) q^{23} +(23.2552 + 9.17595i) q^{25} +(44.8240 + 2.08159i) q^{26} +(24.9620 + 30.0858i) q^{28} -16.1888 q^{29} -24.3646i q^{31} +(16.8178 + 27.2243i) q^{32} +(-5.89944 - 0.273965i) q^{34} +(-40.4002 + 27.4905i) q^{35} +(-17.7235 - 17.7235i) q^{37} +(34.8361 + 38.2292i) q^{38} +(-35.8728 + 17.6959i) q^{40} -4.72832i q^{41} +(-29.6654 - 29.6654i) q^{43} +(4.36410 - 46.8861i) q^{44} +(47.0698 + 2.18588i) q^{46} +(10.1392 + 10.1392i) q^{47} -46.5162i q^{49} +(-17.7620 - 46.7388i) q^{50} +(-57.3047 - 69.0672i) q^{52} +(47.9481 + 47.9481i) q^{53} +(57.8248 + 10.9957i) q^{55} +(10.8497 - 77.4294i) q^{56} +(21.8078 + 23.9319i) q^{58} -45.7297i q^{59} +26.7308 q^{61} +(-36.0181 + 32.8213i) q^{62} +(17.5904 - 61.5352i) q^{64} +(92.7457 - 63.1092i) q^{65} +(41.7043 - 41.7043i) q^{67} +(7.54206 + 9.09017i) q^{68} +(95.0617 + 22.6914i) q^{70} -68.0054 q^{71} +(22.7380 - 22.7380i) q^{73} +(-2.32547 + 50.0758i) q^{74} +(9.58676 - 102.996i) q^{76} +(-81.3543 + 81.3543i) q^{77} -102.115 q^{79} +(74.4835 + 29.1927i) q^{80} +(-6.98985 + 6.36945i) q^{82} +(79.1393 - 79.1393i) q^{83} +(-12.2066 + 8.30601i) q^{85} +(-3.89235 + 83.8162i) q^{86} +(-75.1903 + 56.7082i) q^{88} -87.2500 q^{89} +219.274i q^{91} +(-60.1757 - 72.5275i) q^{92} +(1.33035 - 28.6471i) q^{94} +(127.026 + 24.1545i) q^{95} +(-22.6466 - 22.6466i) q^{97} +(-68.7646 + 62.6613i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 16 q^{10} - 40 q^{13} + 184 q^{16} + 112 q^{22} + 32 q^{28} - 264 q^{37} + 40 q^{40} - 160 q^{46} - 328 q^{52} - 720 q^{58} - 128 q^{61} + 464 q^{70} - 664 q^{73} + 576 q^{76} + 320 q^{82} + 608 q^{85}+ \cdots + 360 q^{97}+O(q^{100}) $ 40 * q + 16 * q^10 - 40 * q^13 + 184 * q^16 + 112 * q^22 + 32 * q^28 - 264 * q^37 + 40 * q^40 - 160 * q^46 - 328 * q^52 - 720 * q^58 - 128 * q^61 + 464 * q^70 - 664 * q^73 + 576 * q^76 + 320 * q^82 + 608 * q^85 + 544 * q^88 + 360 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	−1.34709	−	1.47830i	−0.673544	−	0.739148i
$2$	−1.34709	−	1.47830i	−0.673544	−	0.739148i
$3$		0			0
$3$		0			0
$4$	−0.370713	+	3.98278i	−0.0926783	+	0.995696i
$5$	−4.91198	−	0.934037i	−0.982397	−	0.186807i
$5$	−4.91198	−	0.934037i	−0.982397	−	0.186807i
$6$		0			0
$7$	6.91072	−	6.91072i	0.987246	−	0.987246i	−0.0126736	−	0.999920i	$-0.504034\pi$
$7$	6.91072	−	6.91072i	0.987246	−	0.987246i	0.999920	+	0.0126736i	$0.00403425\pi$
$8$	6.38711	−	4.81713i	0.798389	−	0.602142i
$9$		0			0
$10$	5.23609	+	8.51959i	0.523609	+	0.851959i
$11$	−11.7722			−1.07020			−0.535099	−	0.844789i	$-0.679726\pi$
$11$	−11.7722			−1.07020			−0.535099	+	0.844789i	$0.679726\pi$
$12$		0			0
$13$	−15.8648	+	15.8648i	−1.22037	+	1.22037i	−0.252865	+	0.967502i	$0.581373\pi$
$13$	−15.8648	+	15.8648i	−1.22037	+	1.22037i	−0.967502	+	0.252865i	$0.918627\pi$
$14$	−19.5254	−	0.906743i	−1.39467	−	0.0647673i
$15$		0			0
$16$	−15.7251	−	2.95294i	−0.982821	−	0.184559i
$17$	2.08802	−	2.08802i	0.122824	−	0.122824i	−0.643023	−	0.765847i	$-0.722320\pi$
$17$	2.08802	−	2.08802i	0.122824	−	0.122824i	0.765847	+	0.643023i	$0.222320\pi$
$18$		0			0
$19$	−25.8603			−1.36107			−0.680535	−	0.732715i	$-0.738253\pi$
$19$	−25.8603			−1.36107			−0.680535	+	0.732715i	$0.738253\pi$
$20$	5.54100	−	19.2171i	0.277050	−	0.960855i
$21$		0			0
$22$	15.8582	+	17.4028i	0.720825	+	0.791034i
$23$	−16.6596	+	16.6596i	−0.724331	+	0.724331i	−0.969484	−	0.245154i	$-0.921162\pi$
$23$	−16.6596	+	16.6596i	−0.724331	+	0.724331i	0.245154	+	0.969484i	$0.421162\pi$
$24$		0			0
$25$	23.2552	+	9.17595i	0.930206	+	0.367038i
$26$	44.8240	+	2.08159i	1.72400	+	0.0800610i
$27$		0			0
$28$	24.9620	+	30.0858i	0.891501	+	1.07449i
$29$	−16.1888			−0.558236			−0.279118	−	0.960257i	$-0.590042\pi$
$29$	−16.1888			−0.558236			−0.279118	+	0.960257i	$0.590042\pi$
$30$		0			0
$31$		−	24.3646i		−	0.785955i	−0.919548	−	0.392978i	$-0.871445\pi$
$31$		−	24.3646i		−	0.785955i	0.919548	−	0.392978i	$-0.128555\pi$
$32$	16.8178	+	27.2243i	0.525557	+	0.850758i
$33$		0			0
$34$	−5.89944	−	0.273965i	−0.173513	−	0.00805778i
$35$	−40.4002	+	27.4905i	−1.15429	+	0.785442i
$36$		0			0
$37$	−17.7235	−	17.7235i	−0.479015	−	0.479015i	0.425802	−	0.904817i	$-0.359992\pi$
$37$	−17.7235	−	17.7235i	−0.479015	−	0.479015i	−0.904817	+	0.425802i	$0.859992\pi$
$38$	34.8361	+	38.2292i	0.916740	+	1.00603i
$39$		0			0
$40$	−35.8728	+	17.6959i	−0.896819	+	0.442397i
$41$		−	4.72832i		−	0.115325i	−0.998336	−	0.0576624i	$-0.981635\pi$
$41$		−	4.72832i		−	0.115325i	0.998336	−	0.0576624i	$-0.0183647\pi$
$42$		0			0
$43$	−29.6654	−	29.6654i	−0.689894	−	0.689894i	0.272314	−	0.962208i	$-0.412211\pi$
$43$	−29.6654	−	29.6654i	−0.689894	−	0.689894i	−0.962208	+	0.272314i	$0.912211\pi$
$44$	4.36410	−	46.8861i	0.0991841	−	1.06559i
$45$		0			0
$46$	47.0698	+	2.18588i	1.02326	+	0.0475190i
$47$	10.1392	+	10.1392i	0.215728	+	0.215728i	0.806695	−	0.590968i	$-0.201254\pi$
$47$	10.1392	+	10.1392i	0.215728	+	0.215728i	−0.590968	+	0.806695i	$0.701254\pi$
$48$		0			0
$49$		−	46.5162i		−	0.949310i
$50$	−17.7620	−	46.7388i	−0.355239	−	0.934775i
$51$		0			0
$52$	−57.3047	−	69.0672i	−1.10201	−	1.32822i
$53$	47.9481	+	47.9481i	0.904682	+	0.904682i	0.995837	−	0.0911547i	$-0.0290558\pi$
$53$	47.9481	+	47.9481i	0.904682	+	0.904682i	−0.0911547	+	0.995837i	$0.529056\pi$
$54$		0			0
$55$	57.8248	+	10.9957i	1.05136	+	0.199921i
$56$	10.8497	−	77.4294i	0.193745	−	1.38267i
$57$		0			0
$58$	21.8078	+	23.9319i	0.375996	+	0.412618i
$59$		−	45.7297i		−	0.775079i	−0.921853	−	0.387540i	$-0.873325\pi$
$59$		−	45.7297i		−	0.775079i	0.921853	−	0.387540i	$-0.126675\pi$
$60$		0			0
$61$	26.7308			0.438210			0.219105	−	0.975701i	$-0.429686\pi$
$61$	26.7308			0.438210			0.219105	+	0.975701i	$0.429686\pi$
$62$	−36.0181	+	32.8213i	−0.580937	+	0.529375i
$63$		0			0
$64$	17.5904	−	61.5352i	0.274851	−	0.961487i
$65$	92.7457	−	63.1092i	1.42686	−	0.970910i
$66$		0			0
$67$	41.7043	−	41.7043i	0.622453	−	0.622453i	−0.323705	−	0.946158i	$-0.604929\pi$
$67$	41.7043	−	41.7043i	0.622453	−	0.622453i	0.946158	+	0.323705i	$0.104929\pi$
$68$	7.54206	+	9.09017i	0.110913	+	0.133679i
$69$		0			0
$70$	95.0617	+	22.6914i	1.35802	+	0.324163i
$71$	−68.0054			−0.957823			−0.478911	−	0.877863i	$-0.658969\pi$
$71$	−68.0054			−0.957823			−0.478911	+	0.877863i	$0.658969\pi$
$72$		0			0
$73$	22.7380	−	22.7380i	0.311479	−	0.311479i	−0.534003	−	0.845482i	$-0.679313\pi$
$73$	22.7380	−	22.7380i	0.311479	−	0.311479i	0.845482	+	0.534003i	$0.179313\pi$
$74$	−2.32547	+	50.0758i	−0.0314253	+	0.676700i
$75$		0			0
$76$	9.58676	−	102.996i	0.126142	−	1.35521i
$77$	−81.3543	+	81.3543i	−1.05655	+	1.05655i
$78$		0			0
$79$	−102.115			−1.29259			−0.646297	−	0.763086i	$-0.723683\pi$
$79$	−102.115			−1.29259			−0.646297	+	0.763086i	$0.723683\pi$
$80$	74.4835	+	29.1927i	0.931044	+	0.364908i
$81$		0			0
$82$	−6.98985	+	6.36945i	−0.0852420	+	0.0776763i
$83$	79.1393	−	79.1393i	0.953486	−	0.953486i	−0.0454796	−	0.998965i	$-0.514482\pi$
$83$	79.1393	−	79.1393i	0.953486	−	0.953486i	0.998965	+	0.0454796i	$0.0144816\pi$
$84$		0			0
$85$	−12.2066	+	8.30601i	−0.143607	+	0.0977178i
$86$	−3.89235	+	83.8162i	−0.0452599	+	0.974607i
$87$		0			0
$88$	−75.1903	+	56.7082i	−0.854435	+	0.644411i
$89$	−87.2500			−0.980337			−0.490168	−	0.871628i	$-0.663065\pi$
$89$	−87.2500			−0.980337			−0.490168	+	0.871628i	$0.663065\pi$
$90$		0			0
$91$			219.274i			2.40960i
$92$	−60.1757	−	72.5275i	−0.654084	−	0.788343i
$93$		0			0
$94$	1.33035	−	28.6471i	0.0141526	−	0.304757i
$95$	127.026	+	24.1545i	1.33711	+	0.254258i
$96$		0			0
$97$	−22.6466	−	22.6466i	−0.233470	−	0.233470i	0.580669	−	0.814140i	$-0.302791\pi$
$97$	−22.6466	−	22.6466i	−0.233470	−	0.233470i	−0.814140	+	0.580669i	$0.802791\pi$
$98$	−68.7646	+	62.6613i	−0.701680	+	0.639401i
$99$		0			0
$100$	−45.1668	+	89.2186i	−0.451668	+	0.892186i
$101$		−	135.581i		−	1.34238i	−0.741284	−	0.671191i	$-0.765783\pi$
$101$		−	135.581i		−	1.34238i	0.741284	−	0.671191i	$-0.234217\pi$
$102$		0			0
$103$	10.3775	+	10.3775i	0.100753	+	0.100753i	0.755686	−	0.654934i	$-0.227303\pi$
$103$	10.3775	+	10.3775i	0.100753	+	0.100753i	−0.654934	+	0.755686i	$0.727303\pi$
$104$	−24.9074	+	177.753i	−0.239494	+	1.70916i
$105$		0			0
$106$	6.29119	−	135.472i	0.0593508	−	1.27804i
$107$	84.1811	+	84.1811i	0.786739	+	0.786739i	0.980958	−	0.194219i	$-0.0622172\pi$
$107$	84.1811	+	84.1811i	0.786739	+	0.786739i	−0.194219	+	0.980958i	$0.562217\pi$
$108$		0			0
$109$			110.196i			1.01097i	0.862835	+	0.505486i	$0.168687\pi$
$109$			110.196i			1.01097i	−0.862835	+	0.505486i	$0.831313\pi$
$110$	−61.6402	−	100.294i	−0.560365	−	0.911765i
$111$		0			0
$112$	−129.079	+	88.2652i	−1.15249	+	0.788082i
$113$	82.8202	+	82.8202i	0.732922	+	0.732922i	0.971198	−	0.238276i	$-0.0765821\pi$
$113$	82.8202	+	82.8202i	0.732922	+	0.732922i	−0.238276	+	0.971198i	$0.576582\pi$
$114$		0			0
$115$	97.3924	−	66.2710i	0.846890	−	0.576270i
$116$	6.00141	−	64.4766i	0.0517363	−	0.555833i
$117$		0			0
$118$	−67.6020	+	61.6019i	−0.572898	+	0.522050i
$119$		−	28.8594i		−	0.242516i
$120$		0			0
$121$	17.5843			0.145324
$122$	−36.0087	−	39.5160i	−0.295153	−	0.323902i
$123$		0			0
$124$	97.0390	+	9.03228i	0.782573	+	0.0728410i
$125$	−105.658	−	66.7933i	−0.845266	−	0.534346i
$126$		0			0
$127$	−34.4553	+	34.4553i	−0.271302	+	0.271302i	−0.829624	−	0.558322i	$-0.811445\pi$
$127$	−34.4553	+	34.4553i	−0.271302	+	0.271302i	0.558322	+	0.829624i	$0.311445\pi$
$128$	−114.663	+	56.8894i	−0.895805	+	0.444448i
$129$		0			0
$130$	−218.231	−	52.0920i	−1.67870	−	0.400708i
$131$	26.7519			0.204213			0.102106	−	0.994773i	$-0.467442\pi$
$131$	26.7519			0.204213			0.102106	+	0.994773i	$0.467442\pi$
$132$		0			0
$133$	−178.714	+	178.714i	−1.34371	+	1.34371i
$134$	−117.831	−	5.47195i	−0.879334	−	0.0408354i
$135$		0			0
$136$	3.27814	−	23.3946i	0.0241040	−	0.172019i
$137$	32.5529	−	32.5529i	0.237612	−	0.237612i	−0.578248	−	0.815861i	$-0.696264\pi$
$137$	32.5529	−	32.5529i	0.237612	−	0.237612i	0.815861	+	0.578248i	$0.196264\pi$
$138$		0			0
$139$	184.999			1.33093			0.665464	−	0.746430i	$-0.268234\pi$
$139$	184.999			1.33093			0.665464	+	0.746430i	$0.268234\pi$
$140$	−94.5118	−	171.096i	−0.675084	−	1.22212i
$141$		0			0
$142$	91.6092	+	100.532i	0.645135	+	0.707972i
$143$	186.763	−	186.763i	1.30603	−	1.30603i
$144$		0			0
$145$	79.5193	+	15.1210i	0.548409	+	0.104283i
$146$	−64.2435	−	2.98341i	−0.440024	−	0.0204343i
$147$		0			0
$148$	77.1594	−	64.0187i	0.521347	−	0.432559i
$149$	−34.5249			−0.231711			−0.115855	−	0.993266i	$-0.536961\pi$
$149$	−34.5249			−0.231711			−0.115855	+	0.993266i	$0.536961\pi$
$150$		0			0
$151$			254.057i			1.68250i	0.540648	+	0.841249i	$0.318179\pi$
$151$			254.057i			1.68250i	−0.540648	+	0.841249i	$0.681821\pi$
$152$	−165.173	+	124.573i	−1.08666	+	0.819557i
$153$		0			0
$154$	229.857	+	10.6743i	1.49258	+	0.0693139i
$155$	−22.7574	+	119.679i	−0.146822	+	0.772120i
$156$		0			0
$157$	66.8034	+	66.8034i	0.425500	+	0.425500i	0.887092	−	0.461592i	$-0.152722\pi$
$157$	66.8034	+	66.8034i	0.425500	+	0.425500i	−0.461592	+	0.887092i	$0.652722\pi$
$158$	137.558	+	150.956i	0.870618	+	0.955417i
$159$		0			0
$160$	−57.1804	−	149.434i	−0.357377	−	0.933960i
$161$			230.260i			1.43019i
$162$		0			0
$163$	−195.020	−	195.020i	−1.19644	−	1.19644i	−0.975224	−	0.221218i	$-0.928997\pi$
$163$	−195.020	−	195.020i	−1.19644	−	1.19644i	−0.221218	−	0.975224i	$-0.571003\pi$
$164$	18.8319	+	1.75285i	0.114828	+	0.0106881i
$165$		0			0
$166$	−223.599	−	10.3837i	−1.34698	−	0.0625525i
$167$	−109.011	−	109.011i	−0.652759	−	0.652759i	0.300898	−	0.953656i	$-0.402714\pi$
$167$	−109.011	−	109.011i	−0.652759	−	0.652759i	−0.953656	+	0.300898i	$0.902714\pi$
$168$		0			0
$169$		−	334.381i		−	1.97859i
$170$	28.7221	+	6.85601i	0.168953	+	0.0403294i
$171$		0			0
$172$	129.148	−	107.154i	0.750863	−	0.622987i
$173$	−188.178	−	188.178i	−1.08773	−	1.08773i	−0.995762	−	0.0919721i	$-0.970683\pi$
$173$	−188.178	−	188.178i	−1.08773	−	1.08773i	−0.0919721	−	0.995762i	$-0.529317\pi$
$174$		0			0
$175$	224.122	−	97.2975i	1.28070	−	0.555986i
$176$	185.119	+	34.7625i	1.05181	+	0.197514i
$177$		0			0
$178$	117.533	+	128.981i	0.660299	+	0.724613i
$179$		−	117.394i		−	0.655830i	−0.944707	−	0.327915i	$-0.893654\pi$
$179$		−	117.394i		−	0.655830i	0.944707	−	0.327915i	$-0.106346\pi$
$180$		0			0
$181$	−3.27275			−0.0180815			−0.00904073	−	0.999959i	$-0.502878\pi$
$181$	−3.27275			−0.0180815			−0.00904073	+	0.999959i	$0.502878\pi$
$182$	324.152	−	295.381i	1.78105	−	1.62297i
$183$		0			0
$184$	−26.1552	+	186.658i	−0.142148	+	1.01445i
$185$	70.5033	+	103.612i	0.381099	+	0.560066i
$186$		0			0
$187$	−24.5805	+	24.5805i	−0.131447	+	0.131447i
$188$	−44.1410	+	36.6235i	−0.234792	+	0.194806i
$189$		0			0
$190$	−135.407	−	220.319i	−0.712668	−	1.15958i
$191$	−309.425			−1.62002			−0.810012	−	0.586413i	$-0.800539\pi$
$191$	−309.425			−1.62002			−0.810012	+	0.586413i	$0.800539\pi$
$192$		0			0
$193$	132.348	−	132.348i	0.685740	−	0.685740i	−0.275548	−	0.961287i	$-0.588859\pi$
$193$	132.348	−	132.348i	0.685740	−	0.685740i	0.961287	+	0.275548i	$0.0888592\pi$
$194$	−2.97142	+	63.9854i	−0.0153166	+	0.329822i
$195$		0			0
$196$	185.264	+	17.2442i	0.945224	+	0.0879804i
$197$	154.159	−	154.159i	0.782534	−	0.782534i	−0.197724	−	0.980258i	$-0.563355\pi$
$197$	154.159	−	154.159i	0.782534	−	0.782534i	0.980258	+	0.197724i	$0.0633550\pi$
$198$		0			0
$199$	−350.828			−1.76296			−0.881478	−	0.472226i	$-0.843451\pi$
$199$	−350.828			−1.76296			−0.881478	+	0.472226i	$0.843451\pi$
$200$	192.735	−	53.4154i	0.963675	−	0.267077i
$201$		0			0
$202$	−200.428	+	182.639i	−0.992218	+	0.904153i
$203$	−111.877	+	111.877i	−0.551116	+	0.551116i
$204$		0			0
$205$	−4.41642	+	23.2254i	−0.0215435	+	0.113295i
$206$	1.36161	−	29.3204i	0.00660977	−	0.142332i
$207$		0			0
$208$	296.323	−	202.628i	1.42463	−	0.974173i
$209$	304.433			1.45662
$210$		0			0
$211$			54.5636i			0.258595i	0.991606	+	0.129298i	$0.0412723\pi$
$211$			54.5636i			0.258595i	−0.991606	+	0.129298i	$0.958728\pi$
$212$	−208.742	+	173.192i	−0.984633	+	0.816944i
$213$		0			0
$214$	11.0452	−	237.844i	0.0516133	−	1.11142i
$215$	118.008	+	173.425i	0.548872	+	0.806627i
$216$		0			0
$217$	−168.377	−	168.377i	−0.775931	−	0.775931i
$218$	162.902	−	148.444i	0.747258	−	0.680934i
$219$		0			0
$220$	−65.2297	+	226.227i	−0.296499	+	1.02831i
$221$			66.2518i			0.299782i
$222$		0			0
$223$	−106.514	−	106.514i	−0.477642	−	0.477642i	0.426735	−	0.904377i	$-0.359664\pi$
$223$	−106.514	−	106.514i	−0.477642	−	0.477642i	−0.904377	+	0.426735i	$0.859664\pi$
$224$	304.363	+	71.9161i	1.35876	+	0.321054i
$225$		0			0
$226$	10.8667	−	233.999i	0.0480827	−	1.03539i
$227$	140.653	+	140.653i	0.619619	+	0.619619i	0.945434	−	0.325815i	$-0.105639\pi$
$227$	140.653	+	140.653i	0.619619	+	0.619619i	−0.325815	+	0.945434i	$0.605639\pi$
$228$		0			0
$229$			297.192i			1.29778i	0.760882	+	0.648890i	$0.224766\pi$
$229$			297.192i			1.29778i	−0.760882	+	0.648890i	$0.775234\pi$
$230$	−229.164	−	54.7019i	−0.996366	−	0.237834i
$231$		0			0
$232$	−103.400	+	77.9838i	−0.445689	+	0.336137i
$233$	83.8970	+	83.8970i	0.360073	+	0.360073i	0.863840	−	0.503767i	$-0.168053\pi$
$233$	83.8970	+	83.8970i	0.360073	+	0.360073i	−0.503767	+	0.863840i	$0.668053\pi$
$234$		0			0
$235$	−40.3332	−	59.2740i	−0.171631	−	0.252230i
$236$	182.131	+	16.9526i	0.771744	+	0.0718330i
$237$		0			0
$238$	−42.6627	+	38.8761i	−0.179255	+	0.163345i
$239$			245.015i			1.02517i	0.858638	+	0.512583i	$0.171311\pi$
$239$			245.015i			1.02517i	−0.858638	+	0.512583i	$0.828689\pi$
$240$		0			0
$241$	75.3232			0.312545			0.156272	−	0.987714i	$-0.450052\pi$
$241$	75.3232			0.312545			0.156272	+	0.987714i	$0.450052\pi$
$242$	−23.6875	−	25.9947i	−0.0978823	−	0.107416i
$243$		0			0
$244$	−9.90946	+	106.463i	−0.0406125	+	0.436324i
$245$	−43.4478	+	228.487i	−0.177338	+	0.932598i
$246$		0			0
$247$	410.268	−	410.268i	1.66100	−	1.66100i
$248$	−117.368	−	155.620i	−0.473256	−	0.627498i
$249$		0			0
$250$	43.5907	+	246.170i	0.174363	+	0.984681i
$251$	−354.214			−1.41121			−0.705605	−	0.708605i	$-0.749325\pi$
$251$	−354.214			−1.41121			−0.705605	+	0.708605i	$0.749325\pi$
$252$		0			0
$253$	196.120	−	196.120i	0.775177	−	0.775177i
$254$	97.3494	+	4.52081i	0.383265	+	0.0177985i
$255$		0			0
$256$	238.560	+	92.8708i	0.931876	+	0.362777i
$257$	−81.5733	+	81.5733i	−0.317406	+	0.317406i	−0.847770	−	0.530364i	$-0.822055\pi$
$257$	−81.5733	+	81.5733i	−0.317406	+	0.317406i	0.530364	+	0.847770i	$0.322055\pi$
$258$		0			0
$259$	−244.965			−0.945811
$260$	216.968	+	392.782i	0.834493	+	1.51070i
$261$		0			0
$262$	−36.0371	−	39.5472i	−0.137546	−	0.150944i
$263$	−165.965	+	165.965i	−0.631045	+	0.631045i	−0.948330	−	0.317285i	$-0.897229\pi$
$263$	−165.965	+	165.965i	−0.631045	+	0.631045i	0.317285	+	0.948330i	$0.397229\pi$
$264$		0			0
$265$	−190.735	−	280.306i	−0.719755	−	1.05776i
$266$	504.934	+	23.4487i	1.89825	+	0.0881529i
$267$		0			0
$268$	150.639	+	181.560i	0.562086	+	0.677462i
$269$	−54.9394			−0.204236			−0.102118	−	0.994772i	$-0.532562\pi$
$269$	−54.9394			−0.204236			−0.102118	+	0.994772i	$0.532562\pi$
$270$		0			0
$271$		−	188.837i		−	0.696815i	−0.937343	−	0.348408i	$-0.886722\pi$
$271$		−	188.837i		−	0.696815i	0.937343	−	0.348408i	$-0.113278\pi$
$272$	−39.0001	+	26.6686i	−0.143383	+	0.0980462i
$273$		0			0
$274$	−91.9743	−	4.27120i	−0.335673	−	0.0155883i
$275$	−273.764	−	108.021i	−0.995505	−	0.392803i
$276$		0			0
$277$	255.844	+	255.844i	0.923624	+	0.923624i	0.997283	−	0.0736592i	$-0.0234677\pi$
$277$	255.844	+	255.844i	0.923624	+	0.923624i	−0.0736592	+	0.997283i	$0.523468\pi$
$278$	−249.210	−	273.483i	−0.896437	−	0.983752i
$279$		0			0
$280$	−125.615	+	370.198i	−0.448627	+	1.32214i
$281$		−	294.157i		−	1.04682i	−0.852080	−	0.523411i	$-0.824659\pi$
$281$		−	294.157i		−	1.04682i	0.852080	−	0.523411i	$-0.175341\pi$
$282$		0			0
$283$	−11.2182	−	11.2182i	−0.0396404	−	0.0396404i	0.687009	−	0.726649i	$-0.258923\pi$
$283$	−11.2182	−	11.2182i	−0.0396404	−	0.0396404i	−0.726649	+	0.687009i	$0.758923\pi$
$284$	25.2105	−	270.851i	0.0887694	−	0.953701i
$285$		0			0
$286$	−527.676	−	24.5048i	−1.84502	−	0.0856811i
$287$	−32.6761	−	32.6761i	−0.113854	−	0.113854i
$288$		0			0
$289$			280.280i			0.969828i
$290$	−84.7661	−	137.922i	−0.292297	−	0.475594i
$291$		0			0
$292$	82.1312	+	98.9898i	0.281271	+	0.339006i
$293$	−365.061	−	365.061i	−1.24594	−	1.24594i	−0.957496	−	0.288447i	$-0.906861\pi$
$293$	−365.061	−	365.061i	−1.24594	−	1.24594i	−0.288447	−	0.957496i	$-0.593139\pi$
$294$		0			0
$295$	−42.7132	+	224.623i	−0.144791	+	0.761435i
$296$	−198.579	−	27.8256i	−0.670875	−	0.0940054i
$297$		0			0
$298$	46.5081	+	51.0380i	0.156067	+	0.171268i
$299$		−	528.601i		−	1.76790i
$300$		0			0
$301$	−410.019			−1.36219
$302$	375.571	−	342.237i	1.24361	−	1.13324i
$303$		0			0
$304$	406.658	+	76.3640i	1.33769	+	0.251197i
$305$	−131.301	−	24.9676i	−0.430496	−	0.0818608i
$306$		0			0
$307$	−169.301	+	169.301i	−0.551470	+	0.551470i	−0.926865	−	0.375395i	$-0.877507\pi$
$307$	−169.301	+	169.301i	−0.551470	+	0.551470i	0.375395	+	0.926865i	$0.377507\pi$
$308$	−293.857	−	354.176i	−0.954083	−	1.14992i
$309$		0			0
$310$	207.576	−	127.575i	0.669602	−	0.411533i
$311$	256.859			0.825912			0.412956	−	0.910751i	$-0.364496\pi$
$311$	256.859			0.825912			0.412956	+	0.910751i	$0.364496\pi$
$312$		0			0
$313$	93.6725	−	93.6725i	0.299273	−	0.299273i	−0.541456	−	0.840729i	$-0.682127\pi$
$313$	93.6725	−	93.6725i	0.299273	−	0.299273i	0.840729	+	0.541456i	$0.182127\pi$
$314$	8.76515	−	188.745i	0.0279145	−	0.601100i
$315$		0			0
$316$	37.8553	−	406.702i	0.119795	−	1.28703i
$317$	−70.8818	+	70.8818i	−0.223602	+	0.223602i	−0.810013	−	0.586411i	$-0.800540\pi$
$317$	−70.8818	+	70.8818i	−0.223602	+	0.223602i	0.586411	+	0.810013i	$0.300540\pi$
$318$		0			0
$319$	190.578			0.597423
$320$	−143.880	+	285.830i	−0.449625	+	0.893217i
$321$		0			0
$322$	340.392	−	310.180i	1.05712	−	0.963292i
$323$	−53.9968	+	53.9968i	−0.167173	+	0.167173i
$324$		0			0
$325$	−514.512	+	223.363i	−1.58311	+	0.687272i
$326$	−25.5882	+	551.006i	−0.0784915	+	1.69020i
$327$		0			0
$328$	−22.7769	−	30.2003i	−0.0694419	−	0.0920741i
$329$	140.138			0.425953
$330$		0			0
$331$		−	130.072i		−	0.392967i	−0.980507	−	0.196483i	$-0.937048\pi$
$331$		−	130.072i		−	0.392967i	0.980507	−	0.196483i	$-0.0629522\pi$
$332$	285.857	+	344.533i	0.861015	+	1.03775i
$333$		0			0
$334$	−14.3031	+	307.997i	−0.0428236	+	0.922147i
$335$	−243.804	+	165.898i	−0.727774	+	0.495217i
$336$		0			0
$337$	127.319	+	127.319i	0.377802	+	0.377802i	0.870309	−	0.492507i	$-0.163919\pi$
$337$	127.319	+	127.319i	0.377802	+	0.377802i	−0.492507	+	0.870309i	$0.663919\pi$
$338$	−494.314	+	450.441i	−1.46247	+	1.33267i
$339$		0			0
$340$	−28.5559	−	51.6953i	−0.0839880	−	0.152045i
$341$			286.825i			0.841128i
$342$		0			0
$343$	17.1651	+	17.1651i	0.0500439	+	0.0500439i
$344$	−332.379	−	46.5741i	−0.966218	−	0.135390i
$345$		0			0
$346$	−24.6905	+	531.675i	−0.0713597	+	1.53663i
$347$	−18.7320	−	18.7320i	−0.0539827	−	0.0539827i	0.679600	−	0.733583i	$-0.262153\pi$
$347$	−18.7320	−	18.7320i	−0.0539827	−	0.0539827i	−0.733583	+	0.679600i	$0.762153\pi$
$348$		0			0
$349$			468.267i			1.34174i	0.741575	+	0.670870i	$0.234079\pi$
$349$			468.267i			1.34174i	−0.741575	+	0.670870i	$0.765921\pi$
$350$	−445.747	−	200.251i	−1.27356	−	0.572145i
$351$		0			0
$352$	−197.982	−	320.489i	−0.562450	−	0.910480i
$353$	196.998	+	196.998i	0.558068	+	0.558068i	0.928757	−	0.370689i	$-0.120878\pi$
$353$	196.998	+	196.998i	0.558068	+	0.558068i	−0.370689	+	0.928757i	$0.620878\pi$
$354$		0			0
$355$	334.041	+	63.5196i	0.940962	+	0.178928i
$356$	32.3447	−	347.498i	0.0908559	−	0.976117i
$357$		0			0
$358$	−173.542	+	158.139i	−0.484755	+	0.441730i
$359$		−	34.7036i		−	0.0966673i	−0.998831	−	0.0483336i	$-0.984609\pi$
$359$		−	34.7036i		−	0.0966673i	0.998831	−	0.0483336i	$-0.0153911\pi$
$360$		0			0
$361$	307.757			0.852513
$362$	4.40867	+	4.83808i	0.0121787	+	0.0133649i
$363$		0			0
$364$	−873.321	−	81.2877i	−2.39923	−	0.223318i
$365$	−132.927	+	90.4505i	−0.364183	+	0.247810i
$366$		0			0
$367$	−172.175	+	172.175i	−0.469143	+	0.469143i	−0.901637	−	0.432494i	$-0.857634\pi$
$367$	−172.175	+	172.175i	−0.469143	+	0.469143i	0.432494	+	0.901637i	$0.357634\pi$
$368$	311.170	−	212.780i	0.845569	−	0.578206i
$369$		0			0
$370$	58.1953	−	243.799i	0.157285	−	0.658917i
$371$	662.713			1.78629
$372$		0			0
$373$	−64.3314	+	64.3314i	−0.172470	+	0.172470i	−0.788064	−	0.615594i	$-0.788916\pi$
$373$	−64.3314	+	64.3314i	−0.172470	+	0.172470i	0.615594	+	0.788064i	$0.288916\pi$
$374$	69.4493	+	3.22516i	0.185693	+	0.00862342i
$375$		0			0
$376$	113.602	+	15.9183i	0.302133	+	0.0423360i
$377$	256.832	−	256.832i	0.681252	−	0.681252i
$378$		0			0
$379$	−103.138			−0.272132			−0.136066	−	0.990700i	$-0.543446\pi$
$379$	−103.138			−0.272132			−0.136066	+	0.990700i	$0.543446\pi$
$380$	−143.292	+	496.961i	−0.377085	+	1.30779i
$381$		0			0
$382$	416.822	+	457.421i	1.09116	+	1.19744i
$383$	278.067	−	278.067i	0.726022	−	0.726022i	−0.243803	−	0.969825i	$-0.578395\pi$
$383$	278.067	−	278.067i	0.726022	−	0.726022i	0.969825	+	0.243803i	$0.0783949\pi$
$384$		0			0
$385$	475.599	−	323.623i	1.23532	−	0.840579i
$386$	−373.933	−	17.3651i	−0.968738	−	0.0449873i
$387$		0			0
$388$	98.5920	−	81.8012i	0.254103	−	0.210828i
$389$	−237.818			−0.611358			−0.305679	−	0.952135i	$-0.598883\pi$
$389$	−237.818			−0.611358			−0.305679	+	0.952135i	$0.598883\pi$
$390$		0			0
$391$			69.5710i			0.177931i
$392$	−224.075	−	297.104i	−0.571619	−	0.757919i
$393$		0			0
$394$	−435.558	−	20.2269i	−1.10548	−	0.0513374i
$395$	501.587	+	95.3791i	1.26984	+	0.241466i
$396$		0			0
$397$	−29.8329	−	29.8329i	−0.0751459	−	0.0751459i	0.668535	−	0.743681i	$-0.266922\pi$
$397$	−29.8329	−	29.8329i	−0.0751459	−	0.0751459i	−0.743681	+	0.668535i	$0.766922\pi$
$398$	472.596	+	518.627i	1.18743	+	1.30308i
$399$		0			0
$400$	−338.595	−	212.964i	−0.846486	−	0.532410i
$401$		−	23.2038i		−	0.0578647i	−0.999581	−	0.0289324i	$-0.990789\pi$
$401$		−	23.2038i		−	0.0578647i	0.999581	−	0.0289324i	$-0.00921074\pi$
$402$		0			0
$403$	386.539	+	386.539i	0.959153	+	0.959153i
$404$	539.988	+	50.2615i	1.33660	+	0.124410i
$405$		0			0
$406$	316.094	+	14.6791i	0.778556	+	0.0361554i
$407$	208.645	+	208.645i	0.512641	+	0.512641i
$408$		0			0
$409$		−	725.927i		−	1.77488i	−0.460920	−	0.887442i	$-0.652480\pi$
$409$		−	725.927i		−	1.77488i	0.460920	−	0.887442i	$-0.347520\pi$
$410$	40.2833	−	24.7579i	0.0982520	−	0.0603851i
$411$		0			0
$412$	−45.1785	+	37.4843i	−0.109656	+	0.0909813i
$413$	−316.025	−	316.025i	−0.765194	−	0.765194i
$414$		0			0
$415$	−462.650	+	314.812i	−1.11482	+	0.758583i
$416$	−698.717	−	165.096i	−1.67961	−	0.396865i
$417$		0			0
$418$	−410.097	−	450.041i	−0.981094	−	1.07665i
$419$			635.614i			1.51698i	0.651685	+	0.758489i	$0.274062\pi$
$419$			635.614i			1.51698i	−0.651685	+	0.758489i	$0.725938\pi$
$420$		0			0
$421$	−572.425			−1.35968			−0.679839	−	0.733361i	$-0.737950\pi$
$421$	−572.425			−1.35968			−0.679839	+	0.733361i	$0.737950\pi$
$422$	80.6611	−	73.5019i	0.191140	−	0.174175i
$423$		0			0
$424$	537.223	+	75.2776i	1.26704	+	0.177542i
$425$	67.7166	−	29.3976i	0.159333	−	0.0691708i
$426$		0			0
$427$	184.729	−	184.729i	0.432621	−	0.432621i
$428$	−366.482	+	304.068i	−0.856267	+	0.710440i
$429$		0			0
$430$	97.4066	−	408.068i	0.226527	−	0.948996i
$431$	105.968			0.245866			0.122933	−	0.992415i	$-0.460770\pi$
$431$	105.968			0.245866			0.122933	+	0.992415i	$0.460770\pi$
$432$		0			0
$433$	10.8467	−	10.8467i	0.0250502	−	0.0250502i	−0.694471	−	0.719521i	$-0.744361\pi$
$433$	10.8467	−	10.8467i	0.0250502	−	0.0250502i	0.719521	+	0.694471i	$0.244361\pi$
$434$	−22.0924	+	475.730i	−0.0509042	+	1.09615i
$435$		0			0
$436$	−438.887	−	40.8511i	−1.00662	−	0.0936951i
$437$	430.823	−	430.823i	0.985865	−	0.985865i
$438$		0			0
$439$	425.479			0.969201			0.484601	−	0.874736i	$-0.338965\pi$
$439$	425.479			0.969201			0.484601	+	0.874736i	$0.338965\pi$
$440$	422.301	−	208.319i	0.959774	−	0.473453i
$441$		0			0
$442$	97.9396	−	89.2469i	0.221583	−	0.201916i
$443$	140.068	−	140.068i	0.316181	−	0.316181i	−0.531117	−	0.847298i	$-0.678228\pi$
$443$	140.068	−	140.068i	0.316181	−	0.316181i	0.847298	+	0.531117i	$0.178228\pi$
$444$		0			0
$445$	428.570	+	81.4947i	0.963079	+	0.183134i
$446$	−13.9755	+	300.943i	−0.0313353	+	0.674761i
$447$		0			0
$448$	−303.690	−	546.815i	−0.677879	−	1.22057i
$449$	211.838			0.471799			0.235899	−	0.971777i	$-0.424196\pi$
$449$	211.838			0.471799			0.235899	+	0.971777i	$0.424196\pi$
$450$		0			0
$451$			55.6626i			0.123420i
$452$	−360.558	+	299.152i	−0.797694	+	0.661842i
$453$		0			0
$454$	18.4549	−	397.400i	0.0406495	−	0.875330i
$455$	204.810	−	1077.07i	0.450132	−	2.36719i
$456$		0			0
$457$	−201.239	−	201.239i	−0.440348	−	0.440348i	0.451781	−	0.892129i	$-0.350789\pi$
$457$	−201.239	−	201.239i	−0.440348	−	0.440348i	−0.892129	+	0.451781i	$0.850789\pi$
$458$	439.337	−	400.343i	0.959251	−	0.874111i
$459$		0			0
$460$	227.839	+	412.460i	0.495301	+	0.896653i
$461$			779.493i			1.69087i	0.534075	+	0.845437i	$0.320660\pi$
$461$			779.493i			1.69087i	−0.534075	+	0.845437i	$0.679340\pi$
$462$		0			0
$463$	291.584	+	291.584i	0.629770	+	0.629770i	0.948010	−	0.318240i	$-0.103092\pi$
$463$	291.584	+	291.584i	0.629770	+	0.629770i	−0.318240	+	0.948010i	$0.603092\pi$
$464$	254.572	+	47.8047i	0.548646	+	0.103027i
$465$		0			0
$466$	11.0080	−	237.041i	0.0236222	−	0.508672i
$467$	−384.406	−	384.406i	−0.823140	−	0.823140i	0.163418	−	0.986557i	$-0.447748\pi$
$467$	−384.406	−	384.406i	−0.823140	−	0.823140i	−0.986557	+	0.163418i	$0.947748\pi$
$468$		0			0
$469$		−	576.414i		−	1.22903i
$470$	−33.2921	+	139.472i	−0.0708342	+	0.296748i
$471$		0			0
$472$	−220.286	−	292.081i	−0.466708	−	0.618815i
$473$	349.227	+	349.227i	0.738324	+	0.738324i
$474$		0			0
$475$	−601.386	−	237.293i	−1.26608	−	0.499564i
$476$	114.941	+	10.6986i	0.241472	+	0.0224760i
$477$		0			0
$478$	362.204	−	330.056i	0.757749	−	0.690494i
$479$		−	386.754i		−	0.807420i	−0.914887	−	0.403710i	$-0.867720\pi$
$479$		−	386.754i		−	0.807420i	0.914887	−	0.403710i	$-0.132280\pi$
$480$		0			0
$481$	562.360			1.16915
$482$	−101.467	−	111.350i	−0.210512	−	0.231017i
$483$		0			0
$484$	−6.51871	+	70.0343i	−0.0134684	+	0.144699i
$485$	90.0871	+	132.393i	0.185747	+	0.272974i
$486$		0			0
$487$	−461.061	+	461.061i	−0.946738	+	0.946738i	−0.998652	−	0.0519138i	$-0.983468\pi$
$487$	−461.061	+	461.061i	−0.946738	+	0.946738i	0.0519138	+	0.998652i	$0.483468\pi$
$488$	170.733	−	128.766i	0.349862	−	0.263864i
$489$		0			0
$490$	396.299	−	243.563i	0.808773	−	0.497067i
$491$	114.698			0.233601			0.116800	−	0.993155i	$-0.462736\pi$
$491$	114.698			0.233601			0.116800	+	0.993155i	$0.462736\pi$
$492$		0			0
$493$	−33.8025	+	33.8025i	−0.0685650	+	0.0685650i
$494$	−1159.16	−	53.8305i	−2.34649	−	0.108969i
$495$		0			0
$496$	−71.9472	+	383.137i	−0.145055	+	0.772454i
$497$	−469.967	+	469.967i	−0.945607	+	0.945607i
$498$		0			0
$499$	478.364			0.958646			0.479323	−	0.877639i	$-0.340882\pi$
$499$	478.364			0.958646			0.479323	+	0.877639i	$0.340882\pi$
$500$	305.192	−	396.053i	0.610384	−	0.792106i
$501$		0			0
$502$	477.157	+	523.633i	0.950512	+	1.04309i
$503$	−202.334	+	202.334i	−0.402254	+	0.402254i	−0.879026	−	0.476773i	$-0.841806\pi$
$503$	−202.334	+	202.334i	−0.402254	+	0.402254i	0.476773	+	0.879026i	$0.341806\pi$
$504$		0			0
$505$	−126.637	+	665.969i	−0.250767	+	1.31875i
$506$	−554.114	−	25.7325i	−1.09509	−	0.0508548i
$507$		0			0
$508$	−124.455	−	150.001i	−0.244990	−	0.295278i
$509$	547.761			1.07615			0.538076	−	0.842896i	$-0.319151\pi$
$509$	547.761			1.07615			0.538076	+	0.842896i	$0.319151\pi$
$510$		0			0
$511$		−	314.272i		−	0.615014i
$512$	−184.071	−	477.768i	−0.359514	−	0.933140i
$513$		0			0
$514$	230.476	+	10.7031i	0.448396	+	0.0208231i
$515$	−41.2812	−	60.6671i	−0.0801576	−	0.117800i
$516$		0			0
$517$	−119.361	−	119.361i	−0.230871	−	0.230871i
$518$	329.989	+	362.131i	0.637045	+	0.699094i
$519$		0			0
$520$	288.372	−	849.854i	0.554562	−	1.63433i
$521$		−	954.085i		−	1.83126i	−0.402024	−	0.915629i	$-0.631693\pi$
$521$		−	954.085i		−	1.83126i	0.402024	−	0.915629i	$-0.368307\pi$
$522$		0			0
$523$	344.965	+	344.965i	0.659590	+	0.659590i	0.955283	−	0.295693i	$-0.0955506\pi$
$523$	344.965	+	344.965i	0.659590	+	0.659590i	−0.295693	+	0.955283i	$0.595551\pi$
$524$	−9.91728	+	106.547i	−0.0189261	+	0.203334i
$525$		0			0
$526$	468.914	+	21.7759i	0.891471	+	0.0413991i
$527$	−50.8737	−	50.8737i	−0.0965345	−	0.0965345i
$528$		0			0
$529$		−	26.0849i		−	0.0493098i
$530$	−157.438	+	659.559i	−0.297053	+	1.24445i
$531$		0			0
$532$	−645.526	−	778.029i	−1.21340	−	1.46246i
$533$	75.0136	+	75.0136i	0.140739	+	0.140739i
$534$		0			0
$535$	−334.868	−	492.124i	−0.625921	−	0.919859i
$536$	65.4750	−	467.266i	0.122155	−	0.871765i
$537$		0			0
$538$	74.0081	+	81.2166i	0.137562	+	0.150960i
$539$			547.597i			1.01595i
$540$		0			0
$541$	930.699			1.72033			0.860166	−	0.510015i	$-0.170360\pi$
$541$	930.699			1.72033			0.860166	+	0.510015i	$0.170360\pi$
$542$	−279.157	+	254.380i	−0.515049	+	0.469335i
$543$		0			0
$544$	91.9606	+	21.7288i	0.169045	+	0.0399427i
$545$	102.927	−	541.281i	0.188857	−	0.993176i
$546$		0			0
$547$	−217.652	+	217.652i	−0.397901	+	0.397901i	−0.877492	−	0.479591i	$-0.840785\pi$
$547$	−217.652	+	217.652i	−0.397901	+	0.397901i	0.479591	+	0.877492i	$0.340785\pi$
$548$	117.583	+	141.719i	0.214568	+	0.258611i
$549$		0			0
$550$	209.097	+	550.217i	0.380176	+	1.00040i
$551$	418.649			0.759798
$552$		0			0
$553$	−705.688	+	705.688i	−1.27611	+	1.27611i
$554$	33.5688	−	722.857i	0.0605935	−	1.30480i
$555$		0			0
$556$	−68.5815	+	736.811i	−0.123348	+	1.32520i
$557$	−605.625	+	605.625i	−1.08730	+	1.08730i	−0.0914918	+	0.995806i	$0.529164\pi$
$557$	−605.625	+	605.625i	−1.08730	+	1.08730i	−0.995806	+	0.0914918i	$0.970836\pi$
$558$		0			0
$559$	941.271			1.68385
$560$	716.477	−	312.992i	1.27942	−	0.558915i
$561$		0			0
$562$	−434.851	+	396.255i	−0.773757	+	0.705081i
$563$	−364.086	+	364.086i	−0.646689	+	0.646689i	−0.952191	−	0.305503i	$-0.901176\pi$
$563$	−364.086	+	364.086i	−0.646689	+	0.646689i	0.305503	+	0.952191i	$0.401176\pi$
$564$		0			0
$565$	−329.454	−	484.168i	−0.583105	−	0.856935i
$566$	−1.47192	+	31.6958i	−0.00260057	+	0.0559997i
$567$		0			0
$568$	−434.358	+	327.591i	−0.764715	+	0.576745i
$569$	−1036.61			−1.82182			−0.910909	−	0.412608i	$-0.864618\pi$
$569$	−1036.61			−1.82182			−0.910909	+	0.412608i	$0.864618\pi$
$570$		0			0
$571$		−	948.829i		−	1.66170i	−0.556499	−	0.830848i	$-0.687856\pi$
$571$		−	948.829i		−	1.66170i	0.556499	−	0.830848i	$-0.312144\pi$
$572$	674.601	+	813.072i	1.17937	+	1.42145i
$573$		0			0
$574$	−4.28737	+	92.3224i	−0.00746928	+	0.160840i
$575$	−540.289	+	234.554i	−0.939633	+	0.407920i
$576$		0			0
$577$	−413.427	−	413.427i	−0.716511	−	0.716511i	0.251378	−	0.967889i	$-0.419116\pi$
$577$	−413.427	−	413.427i	−0.716511	−	0.716511i	−0.967889	+	0.251378i	$0.919116\pi$
$578$	414.337	−	377.562i	0.716846	−	0.653222i
$579$		0			0
$580$	−89.7024	+	311.103i	−0.154659	+	0.536384i
$581$		−	1093.82i		−	1.88265i
$582$		0			0
$583$	−564.454	−	564.454i	−0.968189	−	0.968189i
$584$	35.6982	−	254.762i	0.0611270	−	0.436236i
$585$		0			0
$586$	−47.8990	+	1031.44i	−0.0817389	+	1.76013i
$587$	−173.216	−	173.216i	−0.295087	−	0.295087i	0.543999	−	0.839086i	$-0.316910\pi$
$587$	−173.216	−	173.216i	−0.295087	−	0.295087i	−0.839086	+	0.543999i	$0.816910\pi$
$588$		0			0
$589$			630.077i			1.06974i
$590$	389.598	−	239.445i	0.660336	−	0.405838i
$591$		0			0
$592$	226.369	+	331.042i	0.382380	+	0.559192i
$593$	304.478	+	304.478i	0.513453	+	0.513453i	0.915583	−	0.402130i	$-0.131730\pi$
$593$	304.478	+	304.478i	0.513453	+	0.513453i	−0.402130	+	0.915583i	$0.631730\pi$
$594$		0			0
$595$	−26.9557	+	141.757i	−0.0453038	+	0.238247i
$596$	12.7988	−	137.505i	0.0214745	−	0.230714i
$597$		0			0
$598$	−781.429	+	712.072i	−1.30674	+	1.19076i
$599$			805.100i			1.34407i	0.740518	+	0.672037i	$0.234580\pi$
$599$			805.100i			1.34407i	−0.740518	+	0.672037i	$0.765420\pi$
$600$		0			0
$601$	−878.614			−1.46192			−0.730960	−	0.682420i	$-0.760927\pi$
$601$	−878.614			−1.46192			−0.730960	+	0.682420i	$0.760927\pi$
$602$	552.332	+	606.130i	0.917495	+	1.00686i
$603$		0			0
$604$	−1011.85	−	94.1823i	−1.67526	−	0.155931i
$605$	−86.3735	−	16.4243i	−0.142766	−	0.0271477i
$606$		0			0
$607$	−586.644	+	586.644i	−0.966464	+	0.966464i	−0.999456	−	0.0329916i	$-0.989497\pi$
$607$	−586.644	+	586.644i	−0.966464	+	0.966464i	0.0329916	+	0.999456i	$0.489497\pi$
$608$	−434.915	−	704.029i	−0.715320	−	1.15794i
$609$		0			0
$610$	139.965	+	227.735i	0.229451	+	0.373337i
$611$	−321.712			−0.526534
$612$		0			0
$613$	304.685	−	304.685i	0.497039	−	0.497039i	−0.413476	−	0.910515i	$-0.635686\pi$
$613$	304.685	−	304.685i	0.497039	−	0.497039i	0.910515	+	0.413476i	$0.135686\pi$
$614$	478.341	+	22.2137i	0.779057	+	0.0361787i
$615$		0			0
$616$	−127.725	+	911.513i	−0.207345	+	1.47973i
$617$	−376.724	+	376.724i	−0.610574	+	0.610574i	−0.943096	−	0.332522i	$-0.892100\pi$
$617$	−376.724	+	376.724i	−0.610574	+	0.610574i	0.332522	+	0.943096i	$0.392100\pi$
$618$		0			0
$619$	−105.200			−0.169952			−0.0849761	−	0.996383i	$-0.527081\pi$
$619$	−105.200			−0.169952			−0.0849761	+	0.996383i	$0.527081\pi$
$620$	−468.217	−	135.004i	−0.755189	−	0.217749i
$621$		0			0
$622$	−346.011	−	379.713i	−0.556288	−	0.610471i
$623$	−602.960	+	602.960i	−0.967834	+	0.967834i
$624$		0			0
$625$	456.604	+	426.776i	0.730566	+	0.682842i
$626$	−264.661	−	12.2906i	−0.422780	−	0.0196335i
$627$		0			0
$628$	−290.829	+	241.299i	−0.463103	+	0.384234i
$629$	−74.0141			−0.117669
$630$		0			0
$631$		−	478.074i		−	0.757646i	−0.925469	−	0.378823i	$-0.876329\pi$
$631$		−	478.074i		−	0.757646i	0.925469	−	0.378823i	$-0.123671\pi$
$632$	−652.219	+	491.901i	−1.03199	+	0.778324i
$633$		0			0
$634$	200.268	+	9.30027i	0.315881	+	0.0146692i
$635$	201.426	−	137.061i	0.317207	−	0.215845i
$636$		0			0
$637$	737.968	+	737.968i	1.15851	+	1.15851i
$638$	−256.725	−	281.730i	−0.402390	−	0.441584i
$639$		0			0
$640$	616.359	−	172.340i	0.963062	−	0.269281i
$641$			772.513i			1.20517i	0.798055	+	0.602584i	$0.205862\pi$
$641$			772.513i			1.20517i	−0.798055	+	0.602584i	$0.794138\pi$
$642$		0			0
$643$	−134.656	−	134.656i	−0.209419	−	0.209419i	0.594601	−	0.804021i	$-0.297310\pi$
$643$	−134.656	−	134.656i	−0.209419	−	0.209419i	−0.804021	+	0.594601i	$0.797310\pi$
$644$	−917.075	−	85.3603i	−1.42403	−	0.132547i
$645$		0			0
$646$	152.562	+	7.08482i	0.236163	+	0.0109672i
$647$	17.3600	+	17.3600i	0.0268316	+	0.0268316i	0.720395	−	0.693564i	$-0.243960\pi$
$647$	17.3600	+	17.3600i	0.0268316	+	0.0268316i	−0.693564	+	0.720395i	$0.743960\pi$
$648$		0			0
$649$			538.338i			0.829489i
$650$	1023.29	+	459.710i	1.57429	+	0.707247i
$651$		0			0
$652$	849.019	−	704.426i	1.30218	−	1.08041i
$653$	334.887	+	334.887i	0.512844	+	0.512844i	0.915397	−	0.402553i	$-0.131877\pi$
$653$	334.887	+	334.887i	0.512844	+	0.512844i	−0.402553	+	0.915397i	$0.631877\pi$
$654$		0			0
$655$	−131.405	−	24.9873i	−0.200618	−	0.0381485i
$656$	−13.9624	+	74.3535i	−0.0212842	+	0.113344i
$657$		0			0
$658$	−188.779	−	207.166i	−0.286898	−	0.314842i
$659$			470.785i			0.714392i	0.934029	+	0.357196i	$0.116267\pi$
$659$			470.785i			0.714392i	−0.934029	+	0.357196i	$0.883733\pi$
$660$		0			0
$661$	−463.127			−0.700645			−0.350323	−	0.936629i	$-0.613928\pi$
$661$	−463.127			−0.700645			−0.350323	+	0.936629i	$0.613928\pi$
$662$	−192.285	+	175.218i	−0.290460	+	0.264680i
$663$		0			0
$664$	124.247	−	886.696i	0.187119	−	1.33539i
$665$	1044.76	−	710.913i	1.57107	−	1.06904i
$666$		0			0
$667$	269.700	−	269.700i	0.404347	−	0.404347i
$668$	474.578	−	393.755i	0.710446	−	0.589453i
$669$		0			0
$670$	573.671	+	136.936i	0.856226	+	0.204383i
$671$	−314.680			−0.468972
$672$		0			0
$673$	−182.313	+	182.313i	−0.270896	+	0.270896i	−0.829461	−	0.558565i	$-0.811352\pi$
$673$	−182.313	+	182.313i	−0.270896	+	0.270896i	0.558565	+	0.829461i	$0.311352\pi$
$674$	16.7053	−	359.726i	0.0247853	−	0.533718i
$675$		0			0
$676$	1331.77	+	123.960i	1.97007	+	0.183372i
$677$	527.583	−	527.583i	0.779296	−	0.779296i	−0.200415	−	0.979711i	$-0.564229\pi$
$677$	527.583	−	527.583i	0.779296	−	0.779296i	0.979711	+	0.200415i	$0.0642291\pi$
$678$		0			0
$679$	−313.009			−0.460985
$680$	−37.9536	+	111.852i	−0.0558142	+	0.164489i
$681$		0			0
$682$	424.011	−	386.378i	0.621718	−	0.566536i
$683$	211.561	−	211.561i	0.309752	−	0.309752i	−0.535061	−	0.844813i	$-0.679712\pi$
$683$	211.561	−	211.561i	0.309752	−	0.309752i	0.844813	+	0.535061i	$0.179712\pi$
$684$		0			0
$685$	−190.305	+	129.494i	−0.277817	+	0.189042i
$686$	2.25219	−	48.4978i	0.00328308	−	0.0706966i
$687$		0			0
$688$	378.893	+	554.094i	0.550717	+	0.805369i
$689$	−1521.37			−2.20809
$690$		0			0
$691$		−	745.870i		−	1.07941i	−0.841855	−	0.539703i	$-0.818536\pi$
$691$		−	745.870i		−	1.07941i	0.841855	−	0.539703i	$-0.181464\pi$
$692$	819.232	−	679.712i	1.18386	−	0.982243i
$693$		0			0
$694$	−2.45779	+	52.9251i	−0.00354148	+	0.0762609i
$695$	−908.711	−	172.796i	−1.30750	−	0.248627i
$696$		0			0
$697$	−9.87280	−	9.87280i	−0.0141647	−	0.0141647i
$698$	692.237	−	630.797i	0.991744	−	0.903720i
$699$		0			0
$700$	304.430	+	928.700i	0.434900	+	1.32671i
$701$		−	245.533i		−	0.350260i	−0.984545	−	0.175130i	$-0.943965\pi$
$701$		−	245.533i		−	0.350260i	0.984545	−	0.175130i	$-0.0560346\pi$
$702$		0			0
$703$	458.337	+	458.337i	0.651973	+	0.651973i
$704$	−207.078	+	724.403i	−0.294145	+	1.02898i
$705$		0			0
$706$	25.8478	−	556.595i	0.0366116	−	0.788378i
$707$	−936.960	−	936.960i	−1.32526	−	1.32526i
$708$		0			0
$709$		−	764.942i		−	1.07890i	−0.842017	−	0.539451i	$-0.818632\pi$
$709$		−	764.942i		−	1.07890i	0.842017	−	0.539451i	$-0.181368\pi$
$710$	−356.082	−	579.378i	−0.501524	−	0.816026i
$711$		0			0
$712$	−557.275	+	420.295i	−0.782690	+	0.590302i
$713$	405.905	+	405.905i	0.569291	+	0.569291i
$714$		0			0
$715$	−1091.82	+	742.933i	−1.52702	+	1.03907i
$716$	467.553	+	43.5193i	0.653007	+	0.0607812i
$717$		0			0
$718$	−51.3021	+	46.7487i	−0.0714514	+	0.0651096i
$719$		−	419.847i		−	0.583932i	−0.956429	−	0.291966i	$-0.905691\pi$
$719$		−	419.847i		−	0.583932i	0.956429	−	0.291966i	$-0.0943093\pi$
$720$		0			0
$721$	143.432			0.198935
$722$	−414.576	−	454.956i	−0.574205	−	0.630133i
$723$		0			0
$724$	1.21325	−	13.0346i	0.00167576	−	0.0180036i
$725$	−376.474	−	148.548i	−0.519274	−	0.204894i
$726$		0			0
$727$	822.560	−	822.560i	1.13144	−	1.13144i	0.141508	−	0.989937i	$-0.454805\pi$
$727$	822.560	−	822.560i	1.13144	−	1.13144i	0.989937	−	0.141508i	$-0.0451950\pi$
$728$	1056.27	+	1400.53i	1.45092	+	1.92380i
$729$		0			0
$730$	312.776	+	74.6603i	0.428461	+	0.102274i
$731$	−123.884			−0.169472
$732$		0			0
$733$	556.245	−	556.245i	0.758861	−	0.758861i	−0.217254	−	0.976115i	$-0.569710\pi$
$733$	556.245	−	556.245i	0.758861	−	0.758861i	0.976115	+	0.217254i	$0.0697100\pi$
$734$	486.461	+	22.5908i	0.662754	+	0.0307777i
$735$		0			0
$736$	−733.724	−	173.367i	−0.996907	−	0.235553i
$737$	−490.951	+	490.951i	−0.666148	+	0.666148i
$738$		0			0
$739$	−478.496			−0.647492			−0.323746	−	0.946144i	$-0.604942\pi$
$739$	−478.496			−0.647492			−0.323746	+	0.946144i	$0.604942\pi$
$740$	−438.802	+	242.389i	−0.592975	+	0.327553i
$741$		0			0
$742$	−892.732	−	979.685i	−1.20314	−	1.32033i
$743$	−455.930	+	455.930i	−0.613635	+	0.613635i	−0.943891	−	0.330257i	$-0.892865\pi$
$743$	−455.930	+	455.930i	−0.613635	+	0.613635i	0.330257	+	0.943891i	$0.392865\pi$
$744$		0			0
$745$	169.586	+	32.2475i	0.227632	+	0.0432853i
$746$	181.761	+	8.44080i	0.243647	+	0.0113147i
$747$		0			0
$748$	−88.7865	−	107.011i	−0.118699	−	0.143063i
$749$	1163.50			1.55341
$750$		0			0
$751$		−	414.547i		−	0.551993i	−0.961159	−	0.275996i	$-0.910992\pi$
$751$		−	414.547i		−	0.551993i	0.961159	−	0.275996i	$-0.0890078\pi$
$752$	−129.500	−	189.381i	−0.172207	−	0.251836i
$753$		0			0
$754$	−725.648	−	33.6984i	−0.962399	−	0.0446929i
$755$	237.299	−	1247.92i	0.314303	−	1.65288i
$756$		0			0
$757$	−883.323	−	883.323i	−1.16687	−	1.16687i	−0.982938	−	0.183935i	$-0.941116\pi$
$757$	−883.323	−	883.323i	−1.16687	−	1.16687i	−0.183935	−	0.982938i	$-0.558884\pi$
$758$	138.936	+	152.468i	0.183292	+	0.201145i
$759$		0			0
$760$	927.682	−	457.621i	1.22063	−	0.602134i
$761$			631.882i			0.830331i	0.909746	+	0.415166i	$0.136276\pi$
$761$			631.882i			0.830331i	−0.909746	+	0.415166i	$0.863724\pi$
$762$		0			0
$763$	761.534	+	761.534i	0.998078	+	0.998078i
$764$	114.708	−	1232.37i	0.150141	−	1.61305i
$765$		0			0
$766$	−785.644	−	36.4846i	−1.02565	−	0.0476300i
$767$	725.491	+	725.491i	0.945881	+	0.945881i
$768$		0			0
$769$		−	1160.04i		−	1.50851i	−0.656582	−	0.754255i	$-0.727998\pi$
$769$		−	1160.04i		−	1.50851i	0.656582	−	0.754255i	$-0.272002\pi$
$770$	−1119.08	−	267.127i	−1.45335	−	0.346918i
$771$		0			0
$772$	478.049	+	576.176i	0.619235	+	0.746341i
$773$	−27.8223	−	27.8223i	−0.0359926	−	0.0359926i	0.688881	−	0.724874i	$-0.258102\pi$
$773$	−27.8223	−	27.8223i	−0.0359926	−	0.0359926i	−0.724874	+	0.688881i	$0.758102\pi$
$774$		0			0
$775$	223.568	−	566.603i	0.288475	−	0.731100i
$776$	−253.738	−	35.5547i	−0.326982	−	0.0458180i
$777$		0			0
$778$	320.362	+	351.565i	0.411776	+	0.451884i
$779$			122.276i			0.156965i
$780$		0			0
$781$	800.572			1.02506
$782$	102.847	−	93.7182i	0.131517	−	0.119844i
$783$		0			0
$784$	−137.359	+	731.473i	−0.175203	+	0.933002i
$785$	−265.740	−	390.534i	−0.338523	−	0.497496i
$786$		0			0
$787$	−215.803	+	215.803i	−0.274209	+	0.274209i	−0.830792	−	0.556583i	$-0.812112\pi$
$787$	−215.803	+	215.803i	−0.274209	+	0.274209i	0.556583	+	0.830792i	$0.312112\pi$
$788$	556.834	+	671.131i	0.706642	+	0.851690i
$789$		0			0
$790$	−534.682	−	869.977i	−0.676813	−	1.10124i
$791$	1144.69			1.44715
$792$		0			0
$793$	−424.078	+	424.078i	−0.534777	+	0.534777i
$794$	−3.91432	+	84.2894i	−0.00492988	+	0.106158i
$795$		0			0
$796$	130.057	−	1397.27i	0.163388	−	1.75537i
$797$	583.750	−	583.750i	0.732434	−	0.732434i	−0.238667	−	0.971101i	$-0.576711\pi$
$797$	583.750	−	583.750i	0.732434	−	0.732434i	0.971101	+	0.238667i	$0.0767106\pi$
$798$		0			0
$799$	42.3416			0.0529933
$800$	141.293	+	787.424i	0.176616	+	0.984280i
$801$		0			0
$802$	−34.3020	+	31.2575i	−0.0427706	+	0.0389744i
$803$	−267.676	+	267.676i	−0.333345	+	0.333345i
$804$		0			0
$805$	215.071	−	1131.03i	0.267169	−	1.40501i
$806$	50.7170	−	1092.12i	0.0629243	−	1.35499i
$807$		0			0
$808$	−653.110	−	865.969i	−0.808304	−	1.07174i
$809$	185.805			0.229673			0.114836	−	0.993384i	$-0.463366\pi$
$809$	185.805			0.229673			0.114836	+	0.993384i	$0.463366\pi$
$810$		0			0
$811$		−	202.958i		−	0.250257i	−0.992141	−	0.125128i	$-0.960066\pi$
$811$		−	202.958i		−	0.250257i	0.992141	−	0.125128i	$-0.0399343\pi$
$812$	−404.106	−	487.054i	−0.497667	−	0.599820i
$813$		0			0
$814$	27.3759	−	589.501i	0.0336313	−	0.724203i
$815$	775.779	+	1140.09i	0.951877	+	1.39888i
$816$		0			0
$817$	767.159	+	767.159i	0.938995	+	0.938995i
$818$	−1073.14	+	977.888i	−1.31190	+	1.19546i
$819$		0			0
$820$	−90.8646	−	26.1996i	−0.110810	−	0.0319508i
$821$			71.5435i			0.0871419i	0.999050	+	0.0435710i	$0.0138735\pi$
$821$			71.5435i			0.0871419i	−0.999050	+	0.0435710i	$0.986127\pi$
$822$		0			0
$823$	556.952	+	556.952i	0.676734	+	0.676734i	0.959260	−	0.282526i	$-0.0911723\pi$
$823$	556.952	+	556.952i	0.676734	+	0.676734i	−0.282526	+	0.959260i	$0.591172\pi$
$824$	116.272	+	16.2925i	0.141107	+	0.0197724i
$825$		0			0
$826$	−41.4651	+	892.892i	−0.0501998	+	1.08098i
$827$	993.891	+	993.891i	1.20180	+	1.20180i	0.973618	+	0.228185i	$0.0732791\pi$
$827$	993.891	+	993.891i	1.20180	+	1.20180i	0.228185	+	0.973618i	$0.426721\pi$
$828$		0			0
$829$			62.8289i			0.0757887i	0.999282	+	0.0378944i	$0.0120650\pi$
$829$			62.8289i			0.0757887i	−0.999282	+	0.0378944i	$0.987935\pi$
$830$	1088.61	+	259.854i	1.31158	+	0.313077i
$831$		0			0
$832$	697.173	+	1255.31i	0.837948	+	1.50878i
$833$	−97.1265	−	97.1265i	−0.116598	−	0.116598i
$834$		0			0
$835$	433.639	+	637.279i	0.519328	+	0.763208i
$836$	−112.857	+	1212.49i	−0.134997	+	1.45035i
$837$		0			0
$838$	939.625	−	856.227i	1.12127	−	1.02175i
$839$		−	1639.90i		−	1.95459i	−0.211882	−	0.977295i	$-0.567959\pi$
$839$		−	1639.90i		−	1.95459i	0.211882	−	0.977295i	$-0.432041\pi$
$840$		0			0
$841$	−578.922			−0.688373
$842$	771.106	+	846.213i	0.915803	+	1.00500i
$843$		0			0
$844$	−217.315	−	20.2274i	−0.257482	−	0.0239662i
$845$	−312.325	+	1642.48i	−0.369615	+	1.94376i
$846$		0			0
$847$	121.520	−	121.520i	0.143471	−	0.143471i
$848$	−612.404	−	895.580i	−0.722174	−	1.05611i
$849$		0			0
$850$	−134.679	−	60.5041i	−0.158445	−	0.0711812i
$851$	590.535			0.693930
$852$		0			0
$853$	107.337	−	107.337i	0.125835	−	0.125835i	−0.641384	−	0.767220i	$-0.721640\pi$
$853$	107.337	−	107.337i	0.125835	−	0.125835i	0.767220	+	0.641384i	$0.221640\pi$
$854$	−521.931	−	24.2380i	−0.611160	−	0.0283817i
$855$		0			0
$856$	943.186	+	132.163i	1.10185	+	0.154396i
$857$	554.853	−	554.853i	0.647436	−	0.647436i	−0.304936	−	0.952373i	$-0.598635\pi$
$857$	554.853	−	554.853i	0.647436	−	0.647436i	0.952373	+	0.304936i	$0.0986352\pi$
$858$		0			0
$859$	−339.135			−0.394802			−0.197401	−	0.980323i	$-0.563250\pi$
$859$	−339.135			−0.394802			−0.197401	+	0.980323i	$0.563250\pi$
$860$	−734.461	+	405.708i	−0.854024	+	0.471753i
$861$		0			0
$862$	−142.748	−	156.652i	−0.165601	−	0.181731i
$863$	649.664	−	649.664i	0.752797	−	0.752797i	−0.222203	−	0.975000i	$-0.571325\pi$
$863$	649.664	−	649.664i	0.752797	−	0.752797i	0.975000	+	0.222203i	$0.0713249\pi$
$864$		0			0
$865$	748.562	+	1100.09i	0.865389	+	1.27178i
$866$	−30.6462	−	1.42318i	−0.0353882	−	0.00164339i
$867$		0			0
$868$	733.029	−	608.190i	0.844504	−	0.700680i
$869$	1202.11			1.38333
$870$		0			0
$871$			1323.26i			1.51924i
$872$	530.829	+	703.834i	0.608749	+	0.807149i
$873$		0			0
$874$	−1217.24	−	56.5275i	−1.39272	−	0.0646767i
$875$	−1191.76	+	268.585i	−1.36202	+	0.306954i
$876$		0			0
$877$	−35.1088	−	35.1088i	−0.0400328	−	0.0400328i	0.686807	−	0.726840i	$-0.259012\pi$
$877$	−35.1088	−	35.1088i	−0.0400328	−	0.0400328i	−0.726840	+	0.686807i	$0.759012\pi$
$878$	−573.158	−	628.984i	−0.652799	−	0.716383i
$879$		0			0
$880$	−876.833	−	343.661i	−0.996401	−	0.390524i
$881$		−	622.062i		−	0.706086i	−0.935607	−	0.353043i	$-0.885147\pi$
$881$		−	622.062i		−	0.706086i	0.935607	−	0.353043i	$-0.114853\pi$
$882$		0			0
$883$	−1041.39	−	1041.39i	−1.17938	−	1.17938i	−0.979903	−	0.199472i	$-0.936077\pi$
$883$	−1041.39	−	1041.39i	−1.17938	−	1.17938i	−0.199472	−	0.979903i	$-0.563923\pi$
$884$	−263.866	−	24.5604i	−0.298491	−	0.0277832i
$885$		0			0
$886$	−395.746	−	18.3781i	−0.446666	−	0.0207427i
$887$	−501.698	−	501.698i	−0.565612	−	0.565612i	0.365284	−	0.930896i	$-0.380972\pi$
$887$	−501.698	−	501.698i	−0.565612	−	0.565612i	−0.930896	+	0.365284i	$0.880972\pi$
$888$		0			0
$889$			476.222i			0.535683i
$890$	−456.848	−	743.334i	−0.513313	−	0.835207i
$891$		0			0
$892$	463.709	−	384.737i	0.519853	−	0.431319i
$893$	−262.203	−	262.203i	−0.293621	−	0.293621i
$894$		0			0
$895$	−109.650	+	576.635i	−0.122514	+	0.644285i
$896$	−399.257	+	1185.55i	−0.445600	+	1.32316i
$897$		0			0
$898$	−285.364	−	313.159i	−0.317777	−	0.348729i
$899$			394.435i			0.438748i
$900$		0			0
$901$	200.233			0.222234
$902$	82.2858	−	74.9824i	0.0912259	−	0.0831290i
$903$		0			0
$904$	927.938	+	130.026i	1.02648	+	0.143834i
$905$	16.0757	+	3.05686i	0.0177632	+	0.00337775i
$906$		0			0
$907$	−387.039	+	387.039i	−0.426725	+	0.426725i	−0.887511	−	0.460786i	$-0.847567\pi$
$907$	−387.039	+	387.039i	−0.426725	+	0.426725i	0.460786	+	0.887511i	$0.347567\pi$
$908$	−612.335	+	508.050i	−0.674377	+	0.559527i
$909$		0			0
$910$	−1868.12	+	1148.14i	−2.05288	+	1.26169i
$911$	1306.68			1.43434			0.717168	−	0.696900i	$-0.245438\pi$
$911$	1306.68			1.43434			0.717168	+	0.696900i	$0.245438\pi$
$912$		0			0
$913$	−931.642	+	931.642i	−1.02042	+	1.02042i
$914$	−26.4042	+	568.577i	−0.0288886	+	0.622075i
$915$		0			0
$916$	−1183.65	−	110.173i	−1.29219	−	0.120276i
$917$	184.875	−	184.875i	0.201608	−	0.201608i
$918$		0			0
$919$	166.211			0.180860			0.0904302	−	0.995903i	$-0.471176\pi$
$919$	166.211			0.180860			0.0904302	+	0.995903i	$0.471176\pi$
$920$	302.820	−	892.433i	0.329152	−	0.970035i
$921$		0			0
$922$	1152.32	−	1050.04i	1.24981	−	1.13888i
$923$	1078.89	−	1078.89i	1.16889	−	1.16889i
$924$		0			0
$925$	−249.533	−	574.794i	−0.269766	−	0.621399i
$926$	38.2581	−	823.835i	0.0413155	−	0.889671i
$927$		0			0
$928$	−272.261	−	440.729i	−0.293385	−	0.474924i
$929$	−1196.27			−1.28769			−0.643847	−	0.765155i	$-0.722662\pi$
$929$	−1196.27			−1.28769			−0.643847	+	0.765155i	$0.722662\pi$
$930$		0			0
$931$			1202.92i			1.29208i
$932$	−365.245	+	303.042i	−0.391894	+	0.325152i
$933$		0			0
$934$	−50.4372	+	1086.09i	−0.0540013	+	1.16284i
$935$	143.698	−	97.7799i	0.153688	−	0.104577i
$936$		0			0
$937$	−1083.03	−	1083.03i	−1.15585	−	1.15585i	−0.985360	−	0.170488i	$-0.945466\pi$
$937$	−1083.03	−	1083.03i	−1.15585	−	1.15585i	−0.170488	−	0.985360i	$-0.554534\pi$
$938$	−852.110	+	776.480i	−0.908433	+	0.827804i
$939$		0			0
$940$	251.027	−	138.665i	0.267051	−	0.147516i
$941$			1346.48i			1.43090i	0.698664	+	0.715450i	$0.253778\pi$
$941$			1346.48i			1.43090i	−0.698664	+	0.715450i	$0.746222\pi$
$942$		0			0
$943$	78.7719	+	78.7719i	0.0835333	+	0.0835333i
$944$	−135.037	+	719.106i	−0.143048	+	0.761765i
$945$		0			0
$946$	45.8214	−	986.700i	0.0484370	−	1.04302i
$947$	720.862	+	720.862i	0.761206	+	0.761206i	0.976540	−	0.215334i	$-0.0690841\pi$
$947$	720.862	+	720.862i	0.761206	+	0.761206i	−0.215334	+	0.976540i	$0.569084\pi$
$948$		0			0
$949$			721.466i			0.760238i
$950$	459.330	+	1208.68i	0.483506	+	1.27230i
$951$		0			0
$952$	−139.020	−	184.328i	−0.146029	−	0.193622i
$953$	−1252.57	−	1252.57i	−1.31434	−	1.31434i	−0.918179	−	0.396165i	$-0.870341\pi$
$953$	−1252.57	−	1252.57i	−1.31434	−	1.31434i	−0.396165	−	0.918179i	$-0.629659\pi$
$954$		0			0
$955$	1519.89	+	289.014i	1.59151	+	0.302632i
$956$	−975.840	−	90.8301i	−1.02075	−	0.0950106i
$957$		0			0
$958$	−571.737	+	520.992i	−0.596803	+	0.543833i
$959$		−	449.928i		−	0.469164i
$960$		0			0
$961$	367.366			0.382274
$962$	−757.548	−	831.334i	−0.787471	−	0.864172i
$963$		0			0
$964$	−27.9233	+	299.996i	−0.0289661	+	0.311199i
$965$	−773.707	+	526.472i	−0.801769	+	0.545567i
$966$		0			0
$967$	−1073.52	+	1073.52i	−1.11016	+	1.11016i	−0.117031	+	0.993128i	$0.537338\pi$
$967$	−1073.52	+	1073.52i	−1.11016	+	1.11016i	−0.993128	+	0.117031i	$0.962662\pi$
$968$	112.313	−	84.7057i	0.116025	−	0.0875059i
$969$		0			0
$970$	74.3603	−	311.520i	0.0766601	−	0.321154i
$971$	−1157.66			−1.19223			−0.596117	−	0.802897i	$-0.703291\pi$
$971$	−1157.66			−1.19223			−0.596117	+	0.802897i	$0.703291\pi$
$972$		0			0
$973$	1278.48	−	1278.48i	1.31395	−	1.31395i
$974$	1302.67	+	60.4950i	1.33745	+	0.0621098i
$975$		0			0
$976$	−420.346	−	78.9345i	−0.430682	−	0.0808755i
$977$	−813.236	+	813.236i	−0.832381	+	0.832381i	−0.987842	−	0.155461i	$-0.950314\pi$
$977$	−813.236	+	813.236i	−0.832381	+	0.832381i	0.155461	+	0.987842i	$0.450314\pi$
$978$		0			0
$979$	1027.12			1.04915
$980$	−893.906	−	257.746i	−0.912149	−	0.263006i
$981$		0			0
$982$	−154.508	−	169.558i	−0.157340	−	0.172666i
$983$	343.132	−	343.132i	0.349066	−	0.349066i	−0.510696	−	0.859762i	$-0.670612\pi$
$983$	343.132	−	343.132i	0.349066	−	0.349066i	0.859762	+	0.510696i	$0.170612\pi$
$984$		0			0
$985$	−901.217	+	613.237i	−0.914941	+	0.622575i
$986$	95.5051	+	4.43517i	0.0968611	+	0.00449814i
$987$		0			0
$988$	1481.92	+	1786.10i	1.49992	+	1.80779i
$989$	988.429			0.999423
$990$		0			0
$991$		−	473.847i		−	0.478150i	−0.971001	−	0.239075i	$-0.923156\pi$
$991$		−	473.847i		−	0.478150i	0.971001	−	0.239075i	$-0.0768442\pi$
$992$	663.309	−	409.760i	0.668658	−	0.413064i
$993$		0			0
$994$	1327.84	+	61.6634i	1.33585	+	0.0620356i
$995$	1723.26	+	327.686i	1.73192	+	0.329333i
$996$		0			0
$997$	199.018	+	199.018i	0.199617	+	0.199617i	0.799836	−	0.600219i	$-0.204920\pi$
$997$	199.018	+	199.018i	0.199617	+	0.199617i	−0.600219	+	0.799836i	$0.704920\pi$
$998$	−644.398	−	707.164i	−0.645690	−	0.708581i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.m.c.107.6	yes	40
3.2	odd	2	inner	180.3.m.c.107.15	yes	40
4.3	odd	2	inner	180.3.m.c.107.16	yes	40
5.3	odd	4	inner	180.3.m.c.143.5	yes	40
12.11	even	2	inner	180.3.m.c.107.5	✓	40
15.8	even	4	inner	180.3.m.c.143.16	yes	40
20.3	even	4	inner	180.3.m.c.143.15	yes	40
60.23	odd	4	inner	180.3.m.c.143.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.m.c.107.5	✓	40	12.11	even	2	inner
180.3.m.c.107.6	yes	40	1.1	even	1	trivial
180.3.m.c.107.15	yes	40	3.2	odd	2	inner
180.3.m.c.107.16	yes	40	4.3	odd	2	inner
180.3.m.c.143.5	yes	40	5.3	odd	4	inner
180.3.m.c.143.6	yes	40	60.23	odd	4	inner
180.3.m.c.143.15	yes	40	20.3	even	4	inner
180.3.m.c.143.16	yes	40	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34709 - 1.47830i) q^{2} +(-0.370713 + 3.98278i) q^{4} +(-4.91198 - 0.934037i) q^{5} +(6.91072 - 6.91072i) q^{7} +(6.38711 - 4.81713i) q^{8} +(5.23609 + 8.51959i) q^{10} -11.7722 q^{11} +(-15.8648 + 15.8648i) q^{13} +(-19.5254 - 0.906743i) q^{14} +(-15.7251 - 2.95294i) q^{16} +(2.08802 - 2.08802i) q^{17} -25.8603 q^{19} +(5.54100 - 19.2171i) q^{20} +(15.8582 + 17.4028i) q^{22} +(-16.6596 + 16.6596i) q^{23} +(23.2552 + 9.17595i) q^{25} +(44.8240 + 2.08159i) q^{26} +(24.9620 + 30.0858i) q^{28} -16.1888 q^{29} -24.3646i q^{31} +(16.8178 + 27.2243i) q^{32} +(-5.89944 - 0.273965i) q^{34} +(-40.4002 + 27.4905i) q^{35} +(-17.7235 - 17.7235i) q^{37} +(34.8361 + 38.2292i) q^{38} +(-35.8728 + 17.6959i) q^{40} -4.72832i q^{41} +(-29.6654 - 29.6654i) q^{43} +(4.36410 - 46.8861i) q^{44} +(47.0698 + 2.18588i) q^{46} +(10.1392 + 10.1392i) q^{47} -46.5162i q^{49} +(-17.7620 - 46.7388i) q^{50} +(-57.3047 - 69.0672i) q^{52} +(47.9481 + 47.9481i) q^{53} +(57.8248 + 10.9957i) q^{55} +(10.8497 - 77.4294i) q^{56} +(21.8078 + 23.9319i) q^{58} -45.7297i q^{59} +26.7308 q^{61} +(-36.0181 + 32.8213i) q^{62} +(17.5904 - 61.5352i) q^{64} +(92.7457 - 63.1092i) q^{65} +(41.7043 - 41.7043i) q^{67} +(7.54206 + 9.09017i) q^{68} +(95.0617 + 22.6914i) q^{70} -68.0054 q^{71} +(22.7380 - 22.7380i) q^{73} +(-2.32547 + 50.0758i) q^{74} +(9.58676 - 102.996i) q^{76} +(-81.3543 + 81.3543i) q^{77} -102.115 q^{79} +(74.4835 + 29.1927i) q^{80} +(-6.98985 + 6.36945i) q^{82} +(79.1393 - 79.1393i) q^{83} +(-12.2066 + 8.30601i) q^{85} +(-3.89235 + 83.8162i) q^{86} +(-75.1903 + 56.7082i) q^{88} -87.2500 q^{89} +219.274i q^{91} +(-60.1757 - 72.5275i) q^{92} +(1.33035 - 28.6471i) q^{94} +(127.026 + 24.1545i) q^{95} +(-22.6466 - 22.6466i) q^{97} +(-68.7646 + 62.6613i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 16 q^{10} - 40 q^{13} + 184 q^{16} + 112 q^{22} + 32 q^{28} - 264 q^{37} + 40 q^{40} - 160 q^{46} - 328 q^{52} - 720 q^{58} - 128 q^{61} + 464 q^{70} - 664 q^{73} + 576 q^{76} + 320 q^{82} + 608 q^{85}+ \cdots + 360 q^{97}+O(q^{100}) \) 40 * q + 16 * q^10 - 40 * q^13 + 184 * q^16 + 112 * q^22 + 32 * q^28 - 264 * q^37 + 40 * q^40 - 160 * q^46 - 328 * q^52 - 720 * q^58 - 128 * q^61 + 464 * q^70 - 664 * q^73 + 576 * q^76 + 320 * q^82 + 608 * q^85 + 544 * q^88 + 360 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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