LMFDB - Embedded newform 405.2.r.a.368.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			368.7
Character	$\chi$	$=$	405.368
Dual form			405.2.r.a.197.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.160295 - 0.0140240i) q^{2} +(-1.94412 - 0.342800i) q^{4} +(0.476055 + 2.18480i) q^{5} +(-2.37204 - 1.66092i) q^{7} +(0.617675 + 0.165506i) q^{8} +O(q^{10})$	\(q+(-0.160295 - 0.0140240i) q^{2} +(-1.94412 - 0.342800i) q^{4} +(0.476055 + 2.18480i) q^{5} +(-2.37204 - 1.66092i) q^{7} +(0.617675 + 0.165506i) q^{8} +(-0.0456696 - 0.356890i) q^{10} +(1.48958 - 4.09258i) q^{11} +(-0.412163 - 4.71104i) q^{13} +(0.356933 + 0.299503i) q^{14} +(3.61342 + 1.31518i) q^{16} +(5.66739 - 1.51857i) q^{17} +(0.695229 - 0.401391i) q^{19} +(-0.176555 - 4.41071i) q^{20} +(-0.296167 + 0.635132i) q^{22} +(-1.52888 - 2.18347i) q^{23} +(-4.54674 + 2.08017i) q^{25} +0.760939i q^{26} +(4.04215 + 4.04215i) q^{28} +(-2.06994 + 1.73689i) q^{29} +(1.27517 - 7.23183i) q^{31} +(-1.71987 - 0.801990i) q^{32} +(-0.929752 + 0.163940i) q^{34} +(2.49956 - 5.97312i) q^{35} +(-0.841448 - 3.14033i) q^{37} +(-0.117071 + 0.0545912i) q^{38} +(-0.0675500 + 1.42829i) q^{40} +(-2.88706 + 3.44066i) q^{41} +(-2.90471 - 6.22917i) q^{43} +(-4.29885 + 7.44583i) q^{44} +(0.214452 + 0.371442i) q^{46} +(-3.17114 + 4.52886i) q^{47} +(0.473765 + 1.30166i) q^{49} +(0.757994 - 0.269679i) q^{50} +(-0.813654 + 9.30011i) q^{52} +(1.70331 - 1.70331i) q^{53} +(9.65061 + 1.30614i) q^{55} +(-1.19026 - 1.41849i) q^{56} +(0.356161 - 0.249386i) q^{58} +(4.31439 - 1.57031i) q^{59} +(2.10123 + 11.9167i) q^{61} +(-0.305823 + 1.14135i) q^{62} +(-6.39585 - 3.69265i) q^{64} +(10.0965 - 3.14321i) q^{65} +(-6.65253 + 0.582021i) q^{67} +(-11.5386 + 1.00950i) q^{68} +(-0.484435 + 0.922410i) q^{70} +(5.61473 + 3.24167i) q^{71} +(2.49666 - 9.31768i) q^{73} +(0.0908402 + 0.515180i) q^{74} +(-1.48920 + 0.542026i) q^{76} +(-10.3308 + 7.23368i) q^{77} +(-0.322504 - 0.384345i) q^{79} +(-1.15322 + 8.52072i) q^{80} +(0.511034 - 0.511034i) q^{82} +(0.780495 - 8.92110i) q^{83} +(6.01577 + 11.6592i) q^{85} +(0.378253 + 1.03924i) q^{86} +(1.59742 - 2.28135i) q^{88} +(6.84734 + 11.8599i) q^{89} +(-6.84699 + 11.8593i) q^{91} +(2.22384 + 4.76903i) q^{92} +(0.571832 - 0.681483i) q^{94} +(1.20793 + 1.32786i) q^{95} +(6.60652 - 3.08067i) q^{97} +(-0.0576878 - 0.215294i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	−0.160295	−	0.0140240i	−0.113346	−	0.00991648i	0.0303416	−	0.999540i	$-0.490340\pi$
$2$	−0.160295	−	0.0140240i	−0.113346	−	0.00991648i	−0.143688	+	0.989623i	$0.545896\pi$
$3$		0			0
$3$		0			0
$4$	−1.94412	−	0.342800i	−0.972059	−	0.171400i
$5$	0.476055	+	2.18480i	0.212898	+	0.977074i
$5$	0.476055	+	2.18480i	0.212898	+	0.977074i
$6$		0			0
$7$	−2.37204	−	1.66092i	−0.896545	−	0.627768i	0.0317971	−	0.999494i	$-0.489877\pi$
$7$	−2.37204	−	1.66092i	−0.896545	−	0.627768i	−0.928342	+	0.371727i	$0.878766\pi$
$8$	0.617675	+	0.165506i	0.218381	+	0.0585151i
$9$		0			0
$10$	−0.0456696	−	0.356890i	−0.0144420	−	0.112859i
$11$	1.48958	−	4.09258i	0.449125	−	1.23396i	−0.484210	−	0.874952i	$-0.660893\pi$
$11$	1.48958	−	4.09258i	0.449125	−	1.23396i	0.933335	−	0.359008i	$-0.116885\pi$
$12$		0			0
$13$	−0.412163	−	4.71104i	−0.114313	−	1.30661i	−0.809219	−	0.587507i	$-0.800109\pi$
$13$	−0.412163	−	4.71104i	−0.114313	−	1.30661i	0.694905	−	0.719101i	$-0.255446\pi$
$14$	0.356933	+	0.299503i	0.0953945	+	0.0800455i
$15$		0			0
$16$	3.61342	+	1.31518i	0.903355	+	0.328794i
$17$	5.66739	−	1.51857i	1.37454	−	0.368308i	0.505407	−	0.862881i	$-0.331342\pi$
$17$	5.66739	−	1.51857i	1.37454	−	0.368308i	0.869136	+	0.494573i	$0.164676\pi$
$18$		0			0
$19$	0.695229	−	0.401391i	0.159497	−	0.0920854i	−0.418127	−	0.908388i	$-0.637313\pi$
$19$	0.695229	−	0.401391i	0.159497	−	0.0920854i	0.577624	+	0.816303i	$0.303980\pi$
$20$	−0.176555	−	4.41071i	−0.0394789	−	0.986265i
$21$		0			0
$22$	−0.296167	+	0.635132i	−0.0631430	+	0.135411i
$23$	−1.52888	−	2.18347i	−0.318794	−	0.455286i	0.627488	−	0.778626i	$-0.284083\pi$
$23$	−1.52888	−	2.18347i	−0.318794	−	0.455286i	−0.946283	+	0.323340i	$0.895194\pi$
$24$		0			0
$25$	−4.54674	+	2.08017i	−0.909349	+	0.416035i
$26$			0.760939i			0.149232i
$27$		0			0
$28$	4.04215	+	4.04215i	0.763895	+	0.763895i
$29$	−2.06994	+	1.73689i	−0.384379	+	0.322532i	−0.814419	−	0.580278i	$-0.802944\pi$
$29$	−2.06994	+	1.73689i	−0.384379	+	0.322532i	0.430040	+	0.902810i	$0.358500\pi$
$30$		0			0
$31$	1.27517	−	7.23183i	0.229027	−	1.29887i	−0.625809	−	0.779976i	$-0.715231\pi$
$31$	1.27517	−	7.23183i	0.229027	−	1.29887i	0.854836	−	0.518899i	$-0.173658\pi$
$32$	−1.71987	−	0.801990i	−0.304034	−	0.141773i
$33$		0			0
$34$	−0.929752	+	0.163940i	−0.159451	+	0.0281155i
$35$	2.49956	−	5.97312i	0.422503	−	1.00964i
$36$		0			0
$37$	−0.841448	−	3.14033i	−0.138333	−	0.516266i	−0.999962	−	0.00872734i	$-0.997222\pi$
$37$	−0.841448	−	3.14033i	−0.138333	−	0.516266i	0.861629	−	0.507539i	$-0.169445\pi$
$38$	−0.117071	+	0.0545912i	−0.0189914	+	0.00885586i
$39$		0			0
$40$	−0.0675500	+	1.42829i	−0.0106806	+	0.225832i
$41$	−2.88706	+	3.44066i	−0.450883	+	0.537341i	−0.942826	−	0.333286i	$-0.891842\pi$
$41$	−2.88706	+	3.44066i	−0.450883	+	0.537341i	0.491943	+	0.870628i	$0.336287\pi$
$42$		0			0
$43$	−2.90471	−	6.22917i	−0.442964	−	0.949940i	−0.993361	−	0.115037i	$-0.963301\pi$
$43$	−2.90471	−	6.22917i	−0.442964	−	0.949940i	0.550397	−	0.834903i	$-0.314476\pi$
$44$	−4.29885	+	7.44583i	−0.648076	+	1.12250i
$45$		0			0
$46$	0.214452	+	0.371442i	0.0316192	+	0.0547661i
$47$	−3.17114	+	4.52886i	−0.462558	+	0.660602i	−0.980887	−	0.194580i	$-0.937666\pi$
$47$	−3.17114	+	4.52886i	−0.462558	+	0.660602i	0.518328	+	0.855182i	$0.326555\pi$
$48$		0			0
$49$	0.473765	+	1.30166i	0.0676807	+	0.185951i
$50$	0.757994	−	0.269679i	0.107197	−	0.0381383i
$51$		0			0
$52$	−0.813654	+	9.30011i	−0.112834	+	1.28969i
$53$	1.70331	−	1.70331i	0.233968	−	0.233968i	−0.580379	−	0.814347i	$-0.697095\pi$
$53$	1.70331	−	1.70331i	0.233968	−	0.233968i	0.814347	+	0.580379i	$0.197095\pi$
$54$		0			0
$55$	9.65061	+	1.30614i	1.30129	+	0.176120i
$56$	−1.19026	−	1.41849i	−0.159055	−	0.189554i
$57$		0			0
$58$	0.356161	−	0.249386i	0.0467662	−	0.0327460i
$59$	4.31439	−	1.57031i	0.561686	−	0.204437i	−0.0455453	−	0.998962i	$-0.514503\pi$
$59$	4.31439	−	1.57031i	0.561686	−	0.204437i	0.607231	+	0.794525i	$0.292280\pi$
$60$		0			0
$61$	2.10123	+	11.9167i	0.269035	+	1.52577i	0.757294	+	0.653074i	$0.226521\pi$
$61$	2.10123	+	11.9167i	0.269035	+	1.52577i	−0.488259	+	0.872699i	$0.662368\pi$
$62$	−0.305823	+	1.14135i	−0.0388395	+	0.144951i
$63$		0			0
$64$	−6.39585	−	3.69265i	−0.799482	−	0.461581i
$65$	10.0965	−	3.14321i	1.25232	−	0.389867i
$66$		0			0
$67$	−6.65253	+	0.582021i	−0.812736	+	0.0711052i	−0.485943	−	0.873991i	$-0.661524\pi$
$67$	−6.65253	+	0.582021i	−0.812736	+	0.0711052i	−0.326793	+	0.945096i	$0.605968\pi$
$68$	−11.5386	+	1.00950i	−1.39926	+	0.122420i
$69$		0			0
$70$	−0.484435	+	0.922410i	−0.0579011	+	0.110249i
$71$	5.61473	+	3.24167i	0.666346	+	0.384715i	0.794691	−	0.607014i	$-0.207633\pi$
$71$	5.61473	+	3.24167i	0.666346	+	0.384715i	−0.128345	+	0.991730i	$0.540966\pi$
$72$		0			0
$73$	2.49666	−	9.31768i	0.292212	−	1.09055i	−0.651194	−	0.758912i	$-0.725731\pi$
$73$	2.49666	−	9.31768i	0.292212	−	1.09055i	0.943406	−	0.331640i	$-0.107602\pi$
$74$	0.0908402	+	0.515180i	0.0105600	+	0.0598885i
$75$		0			0
$76$	−1.48920	+	0.542026i	−0.170823	+	0.0621747i
$77$	−10.3308	+	7.23368i	−1.17730	+	0.824355i
$78$		0			0
$79$	−0.322504	−	0.384345i	−0.0362845	−	0.0432422i	0.747597	−	0.664153i	$-0.231208\pi$
$79$	−0.322504	−	0.384345i	−0.0362845	−	0.0432422i	−0.783882	+	0.620910i	$0.786763\pi$
$80$	−1.15322	+	8.52072i	−0.128934	+	0.952645i
$81$		0			0
$82$	0.511034	−	0.511034i	0.0564343	−	0.0564343i
$83$	0.780495	−	8.92110i	0.0856704	−	0.979218i	−0.824740	−	0.565512i	$-0.808679\pi$
$83$	0.780495	−	8.92110i	0.0856704	−	0.979218i	0.910411	−	0.413706i	$-0.135766\pi$
$84$		0			0
$85$	6.01577	+	11.6592i	0.652502	+	1.26462i
$86$	0.378253	+	1.03924i	0.0407881	+	0.112064i
$87$		0			0
$88$	1.59742	−	2.28135i	0.170286	−	0.243193i
$89$	6.84734	+	11.8599i	0.725816	+	1.25715i	0.958637	+	0.284631i	$0.0918711\pi$
$89$	6.84734	+	11.8599i	0.725816	+	1.25715i	−0.232821	+	0.972520i	$0.574796\pi$
$90$		0			0
$91$	−6.84699	+	11.8593i	−0.717759	+	1.24320i
$92$	2.22384	+	4.76903i	0.231851	+	0.497206i
$93$		0			0
$94$	0.571832	−	0.681483i	0.0589800	−	0.0702896i
$95$	1.20793	+	1.32786i	0.123931	+	0.136235i
$96$		0			0
$97$	6.60652	−	3.08067i	0.670790	−	0.312795i	−0.0572192	−	0.998362i	$-0.518223\pi$
$97$	6.60652	−	3.08067i	0.670790	−	0.312795i	0.728010	+	0.685567i	$0.240446\pi$
$98$	−0.0576878	−	0.215294i	−0.00582735	−	0.0217480i
$99$		0			0
$100$	9.55249	−	2.48548i	0.955249	−	0.248548i
$101$	−5.17835	+	0.913082i	−0.515265	+	0.0908551i	−0.425233	−	0.905084i	$-0.639808\pi$
$101$	−5.17835	+	0.913082i	−0.515265	+	0.0908551i	−0.0900315	+	0.995939i	$0.528697\pi$
$102$		0			0
$103$	−3.40559	−	1.58805i	−0.335562	−	0.156475i	0.247532	−	0.968880i	$-0.420380\pi$
$103$	−3.40559	−	1.58805i	−0.335562	−	0.156475i	−0.583094	+	0.812404i	$0.698158\pi$
$104$	0.525121	−	2.97811i	0.0514924	−	0.292028i
$105$		0			0
$106$	−0.296920	+	0.249146i	−0.0288395	+	0.0241992i
$107$	−5.69179	−	5.69179i	−0.550246	−	0.550246i	0.376266	−	0.926512i	$-0.377208\pi$
$107$	−5.69179	−	5.69179i	−0.550246	−	0.550246i	−0.926512	+	0.376266i	$0.877208\pi$
$108$		0			0
$109$			12.1610i			1.16481i	0.812899	+	0.582405i	$0.197888\pi$
$109$			12.1610i			1.16481i	−0.812899	+	0.582405i	$0.802112\pi$
$110$	−1.52863	−	0.344709i	−0.145749	−	0.0328667i
$111$		0			0
$112$	−6.38676	−	9.12124i	−0.603492	−	0.861876i
$113$	1.72075	−	3.69017i	0.161875	−	0.347142i	−0.808594	−	0.588366i	$-0.799771\pi$
$113$	1.72075	−	3.69017i	0.161875	−	0.347142i	0.970469	+	0.241225i	$0.0775490\pi$
$114$		0			0
$115$	4.04263	−	4.37977i	0.376977	−	0.408415i
$116$	4.61962	−	2.66714i	0.428921	−	0.247638i
$117$		0			0
$118$	−0.713599	+	0.191208i	−0.0656921	+	0.0176021i
$119$	−15.9655	−	5.81095i	−1.46355	−	0.532689i
$120$		0			0
$121$	−6.10389	−	5.12177i	−0.554899	−	0.465616i
$122$	−0.169698	−	1.93965i	−0.0153637	−	0.175608i
$123$		0			0
$124$	−4.95815	+	13.6224i	−0.445255	+	1.22333i
$125$	−6.70927	−	8.94347i	−0.600096	−	0.799928i
$126$		0			0
$127$	0.748856	+	0.200655i	0.0664502	+	0.0178053i	0.291891	−	0.956452i	$-0.405716\pi$
$127$	0.748856	+	0.200655i	0.0664502	+	0.0178053i	−0.225441	+	0.974257i	$0.572382\pi$
$128$	4.08240	+	2.85853i	0.360837	+	0.252661i
$129$		0			0
$130$	−1.66250	+	0.362249i	−0.145811	+	0.0317713i
$131$	7.46979	+	1.31713i	0.652639	+	0.115078i	0.490158	−	0.871634i	$-0.336939\pi$
$131$	7.46979	+	1.31713i	0.652639	+	0.115078i	0.162481	+	0.986712i	$0.448050\pi$
$132$		0			0
$133$	−2.31579	−	0.202605i	−0.200804	−	0.0175681i
$134$	1.07453			0.0928254
$135$		0			0
$136$	3.75194			0.321726
$137$	−9.86611	−	0.863173i	−0.842919	−	0.0737459i	−0.342488	−	0.939522i	$-0.611270\pi$
$137$	−9.86611	−	0.863173i	−0.842919	−	0.0737459i	−0.500431	+	0.865776i	$0.666825\pi$
$138$		0			0
$139$	14.8464	+	2.61782i	1.25926	+	0.222041i	0.763150	−	0.646222i	$-0.223652\pi$
$139$	14.8464	+	2.61782i	1.25926	+	0.222041i	0.496105	+	0.868262i	$0.334763\pi$
$140$	−6.90703	+	10.7556i	−0.583750	+	0.909014i
$141$		0			0
$142$	−0.854554	−	0.598365i	−0.0717126	−	0.0502137i
$143$	−19.8943	−	5.33066i	−1.66364	−	0.445772i
$144$		0			0
$145$	−4.78017	−	3.69557i	−0.396972	−	0.306900i
$146$	−0.530875	+	1.45857i	−0.0439355	+	0.120712i
$147$		0			0
$148$	0.559369	+	6.39361i	0.0459798	+	0.525552i
$149$	11.3083	+	9.48879i	0.926412	+	0.777352i	0.975170	−	0.221459i	$-0.0710818\pi$
$149$	11.3083	+	9.48879i	0.926412	+	0.777352i	−0.0487579	+	0.998811i	$0.515526\pi$
$150$		0			0
$151$	−2.23835	−	0.814693i	−0.182154	−	0.0662987i	0.249333	−	0.968418i	$-0.419789\pi$
$151$	−2.23835	−	0.814693i	−0.182154	−	0.0662987i	−0.431487	+	0.902119i	$0.642011\pi$
$152$	0.495858	−	0.132865i	0.0402194	−	0.0107768i
$153$		0			0
$154$	1.75742	−	1.01465i	0.141617	−	0.0817626i
$155$	16.4072	−	0.656758i	1.31786	−	0.0527521i
$156$		0			0
$157$	3.31405	−	7.10700i	0.264490	−	0.567200i	−0.728548	−	0.684995i	$-0.759805\pi$
$157$	3.31405	−	7.10700i	0.264490	−	0.567200i	0.993038	+	0.117794i	$0.0375824\pi$
$158$	0.0463058	+	0.0661316i	0.00368389	+	0.00526114i
$159$		0			0
$160$	0.933438	−	4.13938i	0.0737947	−	0.327247i
$161$			7.71863i			0.608313i
$162$		0			0
$163$	10.1968	+	10.1968i	0.798677	+	0.798677i	0.982887	−	0.184210i	$-0.0589726\pi$
$163$	10.1968	+	10.1968i	0.798677	+	0.798677i	−0.184210	+	0.982887i	$0.558973\pi$
$164$	6.79225	−	5.69937i	0.530385	−	0.445046i
$165$		0			0
$166$	−0.250219	+	1.41906i	−0.0194208	+	0.110141i
$167$	5.88244	+	2.74303i	0.455197	+	0.212262i	0.636673	−	0.771133i	$-0.280310\pi$
$167$	5.88244	+	2.74303i	0.455197	+	0.212262i	−0.181477	+	0.983395i	$0.558088\pi$
$168$		0			0
$169$	−9.22155	+	1.62601i	−0.709350	+	0.125078i
$170$	−0.800791	−	1.95328i	−0.0614178	−	0.149810i
$171$		0			0
$172$	3.51174	+	13.1060i	0.267767	+	0.999321i
$173$	−10.5085	+	4.90021i	−0.798949	+	0.372556i	−0.778825	−	0.627242i	$-0.784184\pi$
$173$	−10.5085	+	4.90021i	−0.798949	+	0.372556i	−0.0201240	+	0.999797i	$0.506406\pi$
$174$		0			0
$175$	14.2400	+	2.61752i	1.07645	+	0.197866i
$176$	10.7649	−	12.8292i	0.811438	−	0.967034i
$177$		0			0
$178$	−0.931272	−	1.99712i	−0.0698018	−	0.149690i
$179$	3.42048	−	5.92444i	0.255658	−	0.442813i	−0.709416	−	0.704790i	$-0.751041\pi$
$179$	3.42048	−	5.92444i	0.255658	−	0.442813i	0.965074	+	0.261977i	$0.0843744\pi$
$180$		0			0
$181$	−8.12103	−	14.0660i	−0.603631	−	1.04552i	−0.992266	−	0.124128i	$-0.960387\pi$
$181$	−8.12103	−	14.0660i	−0.603631	−	1.04552i	0.388635	−	0.921392i	$-0.372947\pi$
$182$	1.26386	−	1.80497i	0.0936832	−	0.133794i
$183$		0			0
$184$	−0.582977	−	1.60172i	−0.0429776	−	0.118080i
$185$	6.46042	−	3.33337i	0.474980	−	0.245074i
$186$		0			0
$187$	2.22713	−	25.4563i	0.162864	−	1.86155i
$188$	7.71757	−	7.71757i	0.562861	−	0.562861i
$189$		0			0
$190$	−0.175003	−	0.229789i	−0.0126961	−	0.0166707i
$191$	13.1571	+	15.6801i	0.952017	+	1.13457i	0.990802	+	0.135322i	$0.0432069\pi$
$191$	13.1571	+	15.6801i	0.952017	+	1.13457i	−0.0387846	+	0.999248i	$0.512349\pi$
$192$		0			0
$193$	−6.37883	+	4.46650i	−0.459158	+	0.321506i	−0.780168	−	0.625570i	$-0.784867\pi$
$193$	−6.37883	+	4.46650i	−0.459158	+	0.321506i	0.321010	+	0.947076i	$0.395978\pi$
$194$	−1.10220	+	0.401167i	−0.0791332	+	0.0288021i
$195$		0			0
$196$	−0.474846	−	2.69298i	−0.0339176	−	0.192356i
$197$	1.37044	−	5.11454i	0.0976395	−	0.364396i	−0.899767	−	0.436371i	$-0.856264\pi$
$197$	1.37044	−	5.11454i	0.0976395	−	0.364396i	0.997406	+	0.0719752i	$0.0229303\pi$
$198$		0			0
$199$	−24.0896	−	13.9081i	−1.70766	−	0.985920i	−0.937440	−	0.348148i	$-0.886811\pi$
$199$	−24.0896	−	13.9081i	−1.70766	−	0.985920i	−0.770225	−	0.637773i	$-0.779856\pi$
$200$	−3.15269	+	0.532361i	−0.222929	+	0.0376436i
$201$		0			0
$202$	0.842870	−	0.0737416i	0.0593041	−	0.00518844i
$203$	7.79481	−	0.681958i	0.547088	−	0.0478640i
$204$		0			0
$205$	−8.89158	−	4.66972i	−0.621015	−	0.326147i
$206$	0.523629	+	0.302317i	0.0364829	+	0.0210634i
$207$		0			0
$208$	4.70654	−	17.5651i	0.326340	−	1.21792i
$209$	−0.607127	−	3.44319i	−0.0419958	−	0.238170i
$210$		0			0
$211$	8.85421	−	3.22267i	0.609549	−	0.221858i	−0.0187568	−	0.999824i	$-0.505971\pi$
$211$	8.85421	−	3.22267i	0.609549	−	0.221858i	0.628306	+	0.777966i	$0.283749\pi$
$212$	−3.89534	+	2.72754i	−0.267533	+	0.187328i
$213$		0			0
$214$	0.832546	+	0.992189i	0.0569116	+	0.0678247i
$215$	12.2267	−	9.31165i	0.833855	−	0.635049i
$216$		0			0
$217$	−15.0362	+	15.0362i	−1.02072	+	1.02072i
$218$	0.170546	−	1.94935i	0.0115508	−	0.132026i
$219$		0			0
$220$	−18.3142	−	5.84753i	−1.23474	−	0.394240i
$221$	−9.48994	−	26.0734i	−0.638363	−	1.75389i
$222$		0			0
$223$	5.95553	−	8.50538i	0.398812	−	0.569562i	−0.568650	−	0.822580i	$-0.692534\pi$
$223$	5.95553	−	8.50538i	0.398812	−	0.569562i	0.967462	+	0.253017i	$0.0814230\pi$
$224$	2.74756	+	4.75892i	0.183579	+	0.317969i
$225$		0			0
$226$	−0.327580	+	0.567385i	−0.0217903	+	0.0377419i
$227$	6.37560	+	13.6725i	0.423164	+	0.907477i	0.996129	+	0.0878980i	$0.0280150\pi$
$227$	6.37560	+	13.6725i	0.423164	+	0.907477i	−0.572966	+	0.819579i	$0.694207\pi$
$228$		0			0
$229$	0.604581	−	0.720511i	0.0399518	−	0.0476127i	−0.745699	−	0.666284i	$-0.767884\pi$
$229$	0.604581	−	0.720511i	0.0399518	−	0.0476127i	0.785650	+	0.618671i	$0.212329\pi$
$230$	−0.709437	+	0.645362i	−0.0467789	+	0.0425539i
$231$		0			0
$232$	−1.56602	+	0.730246i	−0.102814	+	0.0479430i
$233$	1.45382	+	5.42572i	0.0952427	+	0.355451i	0.997056	−	0.0766749i	$-0.0244304\pi$
$233$	1.45382	+	5.42572i	0.0952427	+	0.355451i	−0.901813	+	0.432126i	$0.857764\pi$
$234$		0			0
$235$	−11.4043	−	4.77234i	−0.743935	−	0.311313i
$236$	−8.92598	+	1.57389i	−0.581032	+	0.102452i
$237$		0			0
$238$	2.47770	+	1.15537i	0.160605	+	0.0748914i
$239$	2.69221	−	15.2683i	0.174144	−	0.987622i	−0.764982	−	0.644051i	$-0.777252\pi$
$239$	2.69221	−	15.2683i	0.174144	−	0.987622i	0.939127	−	0.343571i	$-0.111637\pi$
$240$		0			0
$241$	14.6302	−	12.2762i	0.942414	−	0.790779i	−0.0355896	−	0.999366i	$-0.511331\pi$
$241$	14.6302	−	12.2762i	0.942414	−	0.790779i	0.978004	+	0.208587i	$0.0668865\pi$
$242$	0.906597	+	0.906597i	0.0582783	+	0.0582783i
$243$		0			0
$244$		−	23.8877i		−	1.52925i
$245$	−2.61833	+	1.65475i	−0.167279	+	0.105718i
$246$		0			0
$247$	−2.17752	−	3.10982i	−0.138552	−	0.197873i
$248$	1.98455	−	4.25587i	0.126019	−	0.270248i
$249$		0			0
$250$	0.950042	+	1.52769i	0.0600859	+	0.0966194i
$251$	10.8992	−	6.29267i	0.687953	−	0.397190i	−0.114892	−	0.993378i	$-0.536652\pi$
$251$	10.8992	−	6.29267i	0.687953	−	0.397190i	0.802845	+	0.596188i	$0.203319\pi$
$252$		0			0
$253$	−11.2134	+	3.00463i	−0.704983	+	0.188900i
$254$	−0.117224	−	0.0426661i	−0.00735529	−	0.00267711i
$255$		0			0
$256$	10.7006	+	8.97889i	0.668789	+	0.561181i
$257$	−2.58192	−	29.5115i	−0.161056	−	1.84088i	−0.461576	−	0.887100i	$-0.652716\pi$
$257$	−2.58192	−	29.5115i	−0.161056	−	1.84088i	0.300521	−	0.953775i	$-0.402840\pi$
$258$		0			0
$259$	−3.21988	+	8.84654i	−0.200073	+	0.549697i
$260$	−20.7063	+	2.64969i	−1.28415	+	0.164327i
$261$		0			0
$262$	−1.17890	−	0.315886i	−0.0728328	−	0.0195155i
$263$	−0.484194	−	0.339036i	−0.0298567	−	0.0209059i	0.558553	−	0.829469i	$-0.311357\pi$
$263$	−0.484194	−	0.339036i	−0.0298567	−	0.0209059i	−0.588410	+	0.808563i	$0.700246\pi$
$264$		0			0
$265$	4.53228	+	2.91054i	0.278416	+	0.178793i
$266$	0.368368	+	0.0649533i	0.0225861	+	0.00398254i
$267$		0			0
$268$	13.1328	+	1.14897i	0.802215	+	0.0701847i
$269$	−29.5187			−1.79979			−0.899894	−	0.436108i	$-0.856357\pi$
$269$	−29.5187			−1.79979			−0.899894	+	0.436108i	$0.856357\pi$
$270$		0			0
$271$	−9.45815			−0.574542			−0.287271	−	0.957849i	$-0.592748\pi$
$271$	−9.45815			−0.574542			−0.287271	+	0.957849i	$0.592748\pi$
$272$	22.4758	+	1.96638i	1.36280	+	0.119229i
$273$		0			0
$274$	1.56939	+	0.276725i	0.0948101	+	0.0167176i
$275$	1.74055	+	21.7065i	0.104959	+	1.30895i
$276$		0			0
$277$	16.7047	+	11.6968i	1.00369	+	0.702792i	0.955178	−	0.296031i	$-0.0956631\pi$
$277$	16.7047	+	11.6968i	1.00369	+	0.702792i	0.0485123	+	0.998823i	$0.484552\pi$
$278$	−2.34310	−	0.627831i	−0.140530	−	0.0376548i
$279$		0			0
$280$	2.53250	−	3.27576i	0.151346	−	0.195764i
$281$	−7.06656	+	19.4152i	−0.421555	+	1.15821i	0.529261	+	0.848459i	$0.322469\pi$
$281$	−7.06656	+	19.4152i	−0.421555	+	1.15821i	−0.950816	+	0.309755i	$0.899753\pi$
$282$		0			0
$283$	1.12399	+	12.8473i	0.0668145	+	0.763693i	0.953514	+	0.301348i	$0.0974364\pi$
$283$	1.12399	+	12.8473i	0.0668145	+	0.763693i	−0.886700	+	0.462345i	$0.847008\pi$
$284$	−9.80446	−	8.22692i	−0.581787	−	0.488178i
$285$		0			0
$286$	3.11420	+	1.13348i	0.184147	+	0.0670239i
$287$	12.5629	−	3.36621i	0.741563	−	0.198701i
$288$		0			0
$289$	15.0908	−	8.71266i	0.887692	−	0.512509i
$290$	0.714413	+	0.659420i	0.0419518	+	0.0387225i
$291$		0			0
$292$	−8.04791	+	17.2588i	−0.470968	+	1.01000i
$293$	19.3518	+	27.6373i	1.13055	+	1.61459i	0.704153	+	0.710048i	$0.251327\pi$
$293$	19.3518	+	27.6373i	1.13055	+	1.61459i	0.426392	+	0.904538i	$0.359784\pi$
$294$		0			0
$295$	5.48471	+	8.67854i	0.319332	+	0.505284i
$296$		−	2.07897i		−	0.120837i
$297$		0			0
$298$	−1.67960	−	1.67960i	−0.0972964	−	0.0972964i
$299$	−9.65629	+	8.10259i	−0.558438	+	0.468585i
$300$		0			0
$301$	−3.45606	+	19.6003i	−0.199204	+	1.12974i
$302$	0.347372	+	0.161982i	0.0199890	+	0.00932102i
$303$		0			0
$304$	3.04006	−	0.536044i	0.174359	−	0.0307442i
$305$	−25.0353	+	10.2638i	−1.43352	+	0.587702i
$306$		0			0
$307$	2.60886	+	9.73639i	0.148895	+	0.555685i	0.999551	+	0.0299620i	$0.00953863\pi$
$307$	2.60886	+	9.73639i	0.148895	+	0.555685i	−0.850656	+	0.525723i	$0.823795\pi$
$308$	22.5639	−	10.5217i	1.28570	−	0.599532i
$309$		0			0
$310$	−2.63921	−	0.124819i	−0.149897	−	0.00708927i
$311$	−16.5976	+	19.7803i	−0.941166	+	1.12164i	0.0512465	+	0.998686i	$0.483681\pi$
$311$	−16.5976	+	19.7803i	−0.941166	+	1.12164i	−0.992413	+	0.122952i	$0.960764\pi$
$312$		0			0
$313$	2.37968	+	5.10324i	0.134508	+	0.288452i	0.962012	−	0.273007i	$-0.0880181\pi$
$313$	2.37968	+	5.10324i	0.134508	+	0.288452i	−0.827505	+	0.561459i	$0.810240\pi$
$314$	−0.630895	+	1.09274i	−0.0356035	+	0.0616670i
$315$		0			0
$316$	0.495232	+	0.857767i	0.0278590	+	0.0482532i
$317$	1.06328	−	1.51852i	0.0597197	−	0.0852886i	−0.788181	−	0.615443i	$-0.788977\pi$
$317$	1.06328	−	1.51852i	0.0597197	−	0.0852886i	0.847901	+	0.530154i	$0.177866\pi$
$318$		0			0
$319$	4.02502	+	11.0586i	0.225358	+	0.619165i
$320$	5.02294	−	15.7316i	0.280791	−	0.879423i
$321$		0			0
$322$	0.108246	−	1.23726i	0.00603233	−	0.0689498i
$323$	3.33059	−	3.33059i	0.185319	−	0.185319i
$324$		0			0
$325$	11.6738	+	20.5625i	0.647545	+	1.14060i
$326$	−1.49150	−	1.77750i	−0.0826067	−	0.0984469i
$327$		0			0
$328$	−2.35271	+	1.64739i	−0.129907	+	0.0909618i
$329$	15.0441	−	5.47561i	0.829409	−	0.301880i
$330$		0			0
$331$	−3.34434	−	18.9667i	−0.183822	−	1.04251i	−0.927460	−	0.373923i	$-0.878012\pi$
$331$	−3.34434	−	18.9667i	−0.183822	−	1.04251i	0.743638	−	0.668583i	$-0.233099\pi$
$332$	−4.57553	+	17.0761i	−0.251115	+	0.937173i
$333$		0			0
$334$	−0.904459	−	0.522190i	−0.0494898	−	0.0285730i
$335$	−4.43857	−	14.2574i	−0.242505	−	0.778965i
$336$		0			0
$337$	3.43672	−	0.300674i	0.187210	−	0.0163788i	0.00683487	−	0.999977i	$-0.497824\pi$
$337$	3.43672	−	0.300674i	0.187210	−	0.0163788i	0.180375	+	0.983598i	$0.442269\pi$
$338$	1.50097	−	0.131318i	0.0816423	−	0.00714277i
$339$		0			0
$340$	−7.69858	−	24.7291i	−0.417514	−	1.34112i
$341$	−27.6974	−	15.9911i	−1.49990	−	0.865966i
$342$		0			0
$343$	−4.20811	+	15.7049i	−0.227217	+	0.847984i
$344$	−0.763205	−	4.32835i	−0.0411493	−	0.233369i
$345$		0			0
$346$	1.75319	−	0.638109i	0.0942520	−	0.0343049i
$347$	−7.09044	+	4.96478i	−0.380635	+	0.266523i	−0.748198	−	0.663475i	$-0.769081\pi$
$347$	−7.09044	+	4.96478i	−0.380635	+	0.266523i	0.367564	+	0.929998i	$0.380192\pi$
$348$		0			0
$349$	6.93929	+	8.26992i	0.371452	+	0.442679i	0.919097	−	0.394032i	$-0.128920\pi$
$349$	6.93929	+	8.26992i	0.371452	+	0.442679i	−0.547645	+	0.836711i	$0.684476\pi$
$350$	−2.24590	−	0.619278i	−0.120049	−	0.0331018i
$351$		0			0
$352$	−5.84410	+	5.84410i	−0.311491	+	0.311491i
$353$	−2.33150	+	26.6492i	−0.124093	+	1.41839i	0.637555	+	0.770405i	$0.279946\pi$
$353$	−2.33150	+	26.6492i	−0.124093	+	1.41839i	−0.761649	+	0.647990i	$0.775610\pi$
$354$		0			0
$355$	−4.40949	+	13.8103i	−0.234031	+	0.732975i
$356$	−9.24644	−	25.4044i	−0.490060	−	1.34643i
$357$		0			0
$358$	−0.631371	+	0.901691i	−0.0333690	+	0.0476559i
$359$	6.82588	+	11.8228i	0.360256	+	0.623982i	0.988003	−	0.154436i	$-0.0493560\pi$
$359$	6.82588	+	11.8228i	0.360256	+	0.623982i	−0.627747	+	0.778418i	$0.716023\pi$
$360$		0			0
$361$	−9.17777	+	15.8964i	−0.483041	+	0.836651i
$362$	1.10450	+	2.36861i	0.0580513	+	0.124491i
$363$		0			0
$364$	17.3767	−	20.7088i	0.910788	−	1.08544i
$365$	21.5459	+	1.01900i	1.12776	+	0.0533367i
$366$		0			0
$367$	11.8122	−	5.50814i	0.616594	−	0.287523i	−0.0891181	−	0.996021i	$-0.528405\pi$
$367$	11.8122	−	5.50814i	0.616594	−	0.287523i	0.705712	+	0.708498i	$0.250627\pi$
$368$	−2.65285	−	9.90056i	−0.138289	−	0.516103i
$369$		0			0
$370$	−1.08232	+	0.443722i	−0.0562673	+	0.0230680i
$371$	−6.86938	+	1.21126i	−0.356640	+	0.0628853i
$372$		0			0
$373$	−1.71551	−	0.799956i	−0.0888258	−	0.0414201i	0.377698	−	0.925929i	$-0.376716\pi$
$373$	−1.71551	−	0.799956i	−0.0888258	−	0.0414201i	−0.466523	+	0.884509i	$0.654494\pi$
$374$	−0.713999	+	4.04929i	−0.0369200	+	0.209384i
$375$		0			0
$376$	−2.70829	+	2.27252i	−0.139669	+	0.117196i
$377$	9.03572	+	9.03572i	0.465363	+	0.465363i
$378$		0			0
$379$		−	8.64900i		−	0.444270i	−0.975016	−	0.222135i	$-0.928698\pi$
$379$		−	8.64900i		−	0.444270i	0.975016	−	0.222135i	$-0.0713025\pi$
$380$	−1.89316	−	2.99559i	−0.0971173	−	0.153670i
$381$		0			0
$382$	−1.88913	−	2.69796i	−0.0966563	−	0.138040i
$383$	−7.21777	+	15.4786i	−0.368811	+	0.790917i	0.631074	+	0.775723i	$0.282614\pi$
$383$	−7.21777	+	15.4786i	−0.368811	+	0.790917i	−0.999885	+	0.0151943i	$0.995163\pi$
$384$		0			0
$385$	−20.7222	−	19.1271i	−1.05610	−	0.974806i
$386$	1.08513	−	0.626503i	0.0552319	−	0.0318881i
$387$		0			0
$388$	−13.8999	+	3.72447i	−0.705661	+	0.189081i
$389$	0.823821	+	0.299846i	0.0417694	+	0.0152028i	0.362820	−	0.931859i	$-0.381814\pi$
$389$	0.823821	+	0.299846i	0.0417694	+	0.0152028i	−0.321051	+	0.947062i	$0.604036\pi$
$390$		0			0
$391$	−11.9805	−	10.0529i	−0.605882	−	0.508395i
$392$	0.0772012	+	0.882413i	0.00389925	+	0.0445686i
$393$		0			0
$394$	−0.291401	+	0.800617i	−0.0146806	+	0.0403345i
$395$	0.686190	−	0.887578i	0.0345260	−	0.0446589i
$396$		0			0
$397$	2.23467	+	0.598779i	0.112155	+	0.0300519i	0.314460	−	0.949271i	$-0.398177\pi$
$397$	2.23467	+	0.598779i	0.112155	+	0.0300519i	−0.202305	+	0.979323i	$0.564843\pi$
$398$	3.66640	+	2.56724i	0.183780	+	0.128684i
$399$		0			0
$400$	−19.1651	+	1.53677i	−0.958255	+	0.0768385i
$401$	−6.34251	−	1.11835i	−0.316730	−	0.0558480i	0.0130235	−	0.999915i	$-0.495854\pi$
$401$	−6.34251	−	1.11835i	−0.316730	−	0.0558480i	−0.329753	+	0.944067i	$0.606965\pi$
$402$		0			0
$403$	−34.5950	−	3.02667i	−1.72330	−	0.150769i
$404$	10.3803			0.516440
$405$		0			0
$406$	−1.25904			−0.0624849
$407$	−14.1054	−	1.23407i	−0.699181	−	0.0611704i
$408$		0			0
$409$	27.7142	+	4.88676i	1.37038	+	0.241635i	0.809916	−	0.586546i	$-0.199513\pi$
$409$	27.7142	+	4.88676i	1.37038	+	0.241635i	0.560462	+	0.828180i	$0.310624\pi$
$410$	1.35979	+	0.873230i	0.0671553	+	0.0431257i
$411$		0			0
$412$	6.07648	+	4.25479i	0.299367	+	0.209619i
$413$	−12.8420	−	3.44101i	−0.631915	−	0.169321i
$414$		0			0
$415$	19.8624	−	2.54170i	0.975008	−	0.124767i
$416$	−3.06934	+	8.43295i	−0.150487	+	0.413459i
$417$		0			0
$418$	0.0490322	+	0.560441i	0.00239824	+	0.0274121i
$419$	28.5256	+	23.9358i	1.39357	+	1.16934i	0.963872	+	0.266365i	$0.0858226\pi$
$419$	28.5256	+	23.9358i	1.39357	+	1.16934i	0.429693	+	0.902975i	$0.358622\pi$
$420$		0			0
$421$	27.5767	+	10.0371i	1.34400	+	0.489178i	0.911071	−	0.412249i	$-0.135256\pi$
$421$	27.5767	+	10.0371i	1.34400	+	0.489178i	0.432933	+	0.901426i	$0.357479\pi$
$422$	−1.46448	+	0.392407i	−0.0712900	+	0.0191021i
$423$		0			0
$424$	1.33400	−	0.770186i	0.0647849	−	0.0374036i
$425$	−22.6093	+	18.6937i	−1.09671	+	0.906778i
$426$		0			0
$427$	14.8084	−	31.7567i	0.716629	−	1.53682i
$428$	9.11436	+	13.0167i	0.440559	+	0.629184i
$429$		0			0
$430$	−2.09047	+	1.32115i	−0.100812	+	0.0637113i
$431$		−	0.480686i		−	0.0231538i	−0.999933	−	0.0115769i	$-0.996315\pi$
$431$		−	0.480686i		−	0.0231538i	0.999933	−	0.0115769i	$-0.00368513\pi$
$432$		0			0
$433$	−5.55599	−	5.55599i	−0.267004	−	0.267004i	0.560888	−	0.827892i	$-0.310460\pi$
$433$	−5.55599	−	5.55599i	−0.267004	−	0.267004i	−0.827892	+	0.560888i	$0.810460\pi$
$434$	2.62110	−	2.19937i	0.125817	−	0.105573i
$435$		0			0
$436$	4.16878	−	23.6423i	0.199648	−	1.13226i
$437$	−1.93935	−	0.904335i	−0.0927718	−	0.0432602i
$438$		0			0
$439$	−12.2268	+	2.15591i	−0.583551	+	0.102896i	−0.457627	−	0.889144i	$-0.651301\pi$
$439$	−12.2268	+	2.15591i	−0.583551	+	0.102896i	−0.125924	+	0.992040i	$0.540190\pi$
$440$	5.74477	+	2.40400i	0.273871	+	0.114606i
$441$		0			0
$442$	1.15554	+	4.31253i	0.0549634	+	0.205126i
$443$	16.1231	−	7.51833i	0.766033	−	0.357207i	−7.21597e−6	−	1.00000i	$-0.500002\pi$
$443$	16.1231	−	7.51833i	0.766033	−	0.357207i	0.766040	+	0.642793i	$0.222225\pi$
$444$		0			0
$445$	−22.6519	+	20.6061i	−1.07380	+	0.976822i
$446$	−1.07392	+	1.27985i	−0.0508517	+	0.0606028i
$447$		0			0
$448$	9.03801	+	19.3821i	0.427006	+	0.915717i
$449$	−1.91039	+	3.30889i	−0.0901568	+	0.156156i	−0.907577	−	0.419886i	$-0.862070\pi$
$449$	−1.91039	+	3.30889i	−0.0901568	+	0.156156i	0.817420	+	0.576042i	$0.195403\pi$
$450$		0			0
$451$	9.78070	+	16.9407i	0.460555	+	0.797705i
$452$	−4.61034	+	6.58425i	−0.216852	+	0.309697i
$453$		0			0
$454$	−0.830236	−	2.28105i	−0.0389649	−	0.107055i
$455$	−29.1699	−	9.31364i	−1.36750	−	0.436630i
$456$		0			0
$457$	−1.92516	+	22.0047i	−0.0900553	+	1.02934i	0.807920	+	0.589292i	$0.200593\pi$
$457$	−1.92516	+	22.0047i	−0.0900553	+	1.02934i	−0.897976	+	0.440045i	$0.854962\pi$
$458$	−0.107016	+	0.107016i	−0.00500053	+	0.00500053i
$459$		0			0
$460$	−9.36073	+	7.12897i	−0.436446	+	0.332390i
$461$	−4.15610	−	4.95304i	−0.193569	−	0.230686i	0.660527	−	0.750803i	$-0.270333\pi$
$461$	−4.15610	−	4.95304i	−0.193569	−	0.230686i	−0.854095	+	0.520116i	$0.825889\pi$
$462$		0			0
$463$	0.251426	−	0.176051i	0.0116848	−	0.00818177i	−0.567719	−	0.823222i	$-0.692174\pi$
$463$	0.251426	−	0.176051i	0.0116848	−	0.00818177i	0.579404	+	0.815040i	$0.303285\pi$
$464$	−9.76390	+	3.55377i	−0.453278	+	0.164980i
$465$		0			0
$466$	−0.156950	−	0.890106i	−0.00727056	−	0.0412334i
$467$	11.0784	−	41.3450i	0.512645	−	1.91322i	0.122489	−	0.992470i	$-0.460912\pi$
$467$	11.0784	−	41.3450i	0.512645	−	1.91322i	0.390156	−	0.920749i	$-0.372421\pi$
$468$		0			0
$469$	16.7467	+	9.66873i	0.773292	+	0.446460i
$470$	1.76113	+	0.924918i	0.0812349	+	0.0426633i
$471$		0			0
$472$	2.92479	−	0.255886i	0.134624	−	0.0117781i
$473$	−29.8202	+	2.60893i	−1.37113	+	0.119959i
$474$		0			0
$475$	−2.32607	+	3.27122i	−0.106727	+	0.150094i
$476$	29.0467	+	16.7701i	1.33135	+	0.768658i
$477$		0			0
$478$	−0.645671	+	2.40968i	−0.0295323	+	0.110216i
$479$	−7.22789	−	40.9914i	−0.330251	−	1.87295i	−0.469863	−	0.882740i	$-0.655697\pi$
$479$	−7.22789	−	40.9914i	−0.330251	−	1.87295i	0.139612	−	0.990206i	$-0.455415\pi$
$480$		0			0
$481$	−14.4474	+	5.25842i	−0.658745	+	0.239763i
$482$	−2.51732	+	1.76264i	−0.114661	+	0.0802862i
$483$		0			0
$484$	10.1109	+	12.0497i	0.459588	+	0.547716i
$485$	9.87573	+	12.9674i	0.448434	+	0.588819i
$486$		0			0
$487$	16.8595	−	16.8595i	0.763975	−	0.763975i	−0.213064	−	0.977038i	$-0.568344\pi$
$487$	16.8595	−	16.8595i	0.763975	−	0.763975i	0.977038	+	0.213064i	$0.0683442\pi$
$488$	−0.674397	+	7.70840i	−0.0305285	+	0.348943i
$489$		0			0
$490$	0.442913	−	0.228528i	0.0200088	−	0.0103239i
$491$	5.41828	+	14.8866i	0.244524	+	0.671823i	0.999864	+	0.0164907i	$0.00524938\pi$
$491$	5.41828	+	14.8866i	0.244524	+	0.671823i	−0.755340	+	0.655333i	$0.772528\pi$
$492$		0			0
$493$	−9.09358	+	12.9870i	−0.409554	+	0.584904i
$494$	0.305434	+	0.529027i	0.0137421	+	0.0238020i
$495$		0			0
$496$	14.1189	−	24.4546i	0.633955	−	1.09804i
$497$	−7.93420	−	17.0150i	−0.355898	−	0.763225i
$498$		0			0
$499$	−0.350248	+	0.417409i	−0.0156792	+	0.0186858i	−0.773827	−	0.633397i	$-0.781660\pi$
$499$	−0.350248	+	0.417409i	−0.0156792	+	0.0186858i	0.758148	+	0.652083i	$0.226105\pi$
$500$	9.97779	+	19.6871i	0.446220	+	0.880434i
$501$		0			0
$502$	−1.83534	+	0.855835i	−0.0819154	+	0.0381978i
$503$	5.01841	+	18.7290i	0.223760	+	0.835083i	0.982898	+	0.184153i	$0.0589542\pi$
$503$	5.01841	+	18.7290i	0.223760	+	0.835083i	−0.759138	+	0.650930i	$0.774379\pi$
$504$		0			0
$505$	−4.46008	−	10.8790i	−0.198471	−	0.484109i
$506$	1.83960	−	0.324371i	0.0817801	−	0.0144200i
$507$		0			0
$508$	−1.38708	−	0.646805i	−0.0615417	−	0.0286974i
$509$	4.57685	−	25.9566i	0.202865	−	1.15051i	−0.697898	−	0.716197i	$-0.745881\pi$
$509$	4.57685	−	25.9566i	0.202865	−	1.15051i	0.900764	−	0.434310i	$-0.143008\pi$
$510$		0			0
$511$	−21.3981	+	17.9551i	−0.946595	+	0.794287i
$512$	−8.63735	−	8.63735i	−0.381720	−	0.381720i
$513$		0			0
$514$			4.76676i			0.210253i
$515$	1.84834	−	8.19654i	0.0814474	−	0.361183i
$516$		0			0
$517$	13.8111	+	19.7242i	0.607410	+	0.867471i
$518$	0.640195	−	1.37290i	0.0281286	−	0.0603219i
$519$		0			0
$520$	6.75658	−	0.270457i	0.296295	−	0.0118603i
$521$	6.99745	−	4.03998i	0.306564	−	0.176995i	−0.338824	−	0.940850i	$-0.610029\pi$
$521$	6.99745	−	4.03998i	0.306564	−	0.176995i	0.645388	+	0.763855i	$0.276696\pi$
$522$		0			0
$523$	34.5655	−	9.26181i	1.51145	−	0.404991i	0.594530	−	0.804073i	$-0.297338\pi$
$523$	34.5655	−	9.26181i	1.51145	−	0.404991i	0.916915	+	0.399083i	$0.130671\pi$
$524$	−14.0706	−	5.12130i	−0.614679	−	0.223725i
$525$		0			0
$526$	0.0728594	+	0.0611363i	0.00317682	+	0.00266567i
$527$	−3.75519	−	42.9220i	−0.163579	−	1.86971i
$528$		0			0
$529$	5.43640	−	14.9364i	0.236365	−	0.649408i
$530$	−0.685685	−	0.530106i	−0.0297843	−	0.0230263i
$531$		0			0
$532$	4.43271	+	1.18774i	0.192182	+	0.0514951i
$533$	17.3991	+	12.1830i	0.753637	+	0.527702i
$534$		0			0
$535$	9.72584	−	15.1451i	0.420485	−	0.654778i
$536$	−4.20543	−	0.741531i	−0.181647	−	0.0320293i
$537$		0			0
$538$	4.73172	+	0.413971i	0.203999	+	0.0178476i
$539$	6.03285			0.259853
$540$		0			0
$541$	−6.99126			−0.300578			−0.150289	−	0.988642i	$-0.548020\pi$
$541$	−6.99126			−0.300578			−0.150289	+	0.988642i	$0.548020\pi$
$542$	1.51610	+	0.132641i	0.0651220	+	0.00569743i
$543$		0			0
$544$	−10.9651	−	1.93344i	−0.470123	−	0.0828954i
$545$	−26.5693	+	5.78929i	−1.13811	+	0.247986i
$546$		0			0
$547$	−9.60101	−	6.72270i	−0.410509	−	0.287442i	0.350024	−	0.936741i	$-0.386174\pi$
$547$	−9.60101	−	6.72270i	−0.410509	−	0.287442i	−0.760533	+	0.649299i	$0.775062\pi$
$548$	18.8850	+	5.06022i	0.806727	+	0.216162i
$549$		0			0
$550$	0.0254097	−	3.50386i	0.00108347	−	0.149405i
$551$	−0.741915	+	2.03839i	−0.0316066	+	0.0868385i
$552$		0			0
$553$	0.126625	+	1.44733i	0.00538465	+	0.0615469i
$554$	−2.51366	−	2.10921i	−0.106795	−	0.0896117i
$555$		0			0
$556$	−27.9658	−	10.1787i	−1.18601	−	0.431673i
$557$	11.5536	−	3.09577i	0.489541	−	0.131172i	−0.00560082	−	0.999984i	$-0.501783\pi$
$557$	11.5536	−	3.09577i	0.489541	−	0.131172i	0.495142	+	0.868812i	$0.335116\pi$
$558$		0			0
$559$	−28.1487	+	16.2516i	−1.19056	+	0.687371i
$560$	16.8877	−	18.2960i	0.713635	−	0.773149i
$561$		0			0
$562$	1.40502	−	3.01306i	0.0592670	−	0.127098i
$563$	−4.83500	−	6.90509i	−0.203771	−	0.291015i	0.704240	−	0.709962i	$-0.251288\pi$
$563$	−4.83500	−	6.90509i	−0.203771	−	0.291015i	−0.908010	+	0.418947i	$0.862399\pi$
$564$		0			0
$565$	8.88147	+	2.00279i	0.373646	+	0.0842579i
$566$		−	2.07513i		−	0.0872241i
$567$		0			0
$568$	2.93157	+	2.93157i	0.123006	+	0.123006i
$569$	9.07677	−	7.61631i	0.380518	−	0.319292i	−0.432388	−	0.901688i	$-0.642329\pi$
$569$	9.07677	−	7.61631i	0.380518	−	0.319292i	0.812906	+	0.582395i	$0.197884\pi$
$570$		0			0
$571$	5.84395	−	33.1427i	0.244562	−	1.38698i	−0.576946	−	0.816782i	$-0.695756\pi$
$571$	5.84395	−	33.1427i	0.244562	−	1.38698i	0.821508	−	0.570197i	$-0.193133\pi$
$572$	36.8495	+	17.1832i	1.54075	+	0.718465i
$573$		0			0
$574$	−2.06098	+	0.363406i	−0.0860235	+	0.0151683i
$575$	11.4935	+	6.74735i	0.479310	+	0.281384i
$576$		0			0
$577$	−7.63587	−	28.4975i	−0.317886	−	1.18637i	−0.921273	−	0.388917i	$-0.872849\pi$
$577$	−7.63587	−	28.4975i	−0.317886	−	1.18637i	0.603387	−	0.797448i	$-0.293817\pi$
$578$	−2.54117	+	1.18497i	−0.105699	+	0.0492881i
$579$		0			0
$580$	8.02637	+	8.82327i	0.333277	+	0.366366i
$581$	−16.6686	+	19.8648i	−0.691529	+	0.824132i
$582$		0			0
$583$	−4.43373	−	9.50816i	−0.183626	−	0.393788i
$584$	3.08426	−	5.34209i	0.127627	−	0.221057i
$585$		0			0
$586$	−2.71442	−	4.70152i	−0.112132	−	0.194218i
$587$	−13.0366	+	18.6182i	−0.538077	+	0.768453i	−0.992488	−	0.122338i	$-0.960961\pi$
$587$	−13.0366	+	18.6182i	−0.538077	+	0.768453i	0.454412	+	0.890792i	$0.349850\pi$
$588$		0			0
$589$	−2.01626	−	5.53962i	−0.0830784	−	0.228256i
$590$	−0.757465	−	1.46805i	−0.0311843	−	0.0604386i
$591$		0			0
$592$	1.08958	−	12.4540i	0.0447815	−	0.511855i
$593$	−9.57575	+	9.57575i	−0.393229	+	0.393229i	−0.875837	−	0.482608i	$-0.839690\pi$
$593$	−9.57575	+	9.57575i	−0.393229	+	0.393229i	0.482608	+	0.875837i	$0.339690\pi$
$594$		0			0
$595$	5.09536	−	37.6477i	0.208889	−	1.54341i
$596$	−18.7319	−	22.3238i	−0.767288	−	0.914419i
$597$		0			0
$598$	1.66149	−	1.16339i	0.0679433	−	0.0475744i
$599$	−13.5529	+	4.93284i	−0.553755	+	0.201550i	−0.603714	−	0.797201i	$-0.706313\pi$
$599$	−13.5529	+	4.93284i	−0.553755	+	0.201550i	0.0499591	+	0.998751i	$0.484091\pi$
$600$		0			0
$601$	4.30406	+	24.4095i	0.175566	+	0.995686i	0.937488	+	0.348017i	$0.113145\pi$
$601$	4.30406	+	24.4095i	0.175566	+	0.995686i	−0.761922	+	0.647669i	$0.775744\pi$
$602$	0.828865	−	3.09337i	0.0337820	−	0.126076i
$603$		0			0
$604$	4.07234	+	2.35117i	0.165701	+	0.0956676i
$605$	8.28429	−	15.7741i	0.336804	−	0.641307i
$606$		0			0
$607$	−27.7738	+	2.42989i	−1.12730	+	0.0986264i	−0.635516	−	0.772088i	$-0.719212\pi$
$607$	−27.7738	+	2.42989i	−1.12730	+	0.0986264i	−0.491789	+	0.870714i	$0.663657\pi$
$608$	−1.51762	+	0.132774i	−0.0615476	+	0.00538471i
$609$		0			0
$610$	4.15698	−	1.29414i	0.168311	−	0.0523981i
$611$	22.6427	+	13.0728i	0.916025	+	0.528867i
$612$		0			0
$613$	−8.68995	+	32.4313i	−0.350984	+	1.30989i	0.534480	+	0.845181i	$0.320507\pi$
$613$	−8.68995	+	32.4313i	−0.350984	+	1.30989i	−0.885464	+	0.464708i	$0.846159\pi$
$614$	−0.281645	−	1.59729i	−0.0113662	−	0.0644612i
$615$		0			0
$616$	−7.57828	+	2.75827i	−0.305337	+	0.111134i
$617$	−23.2671	+	16.2918i	−0.936700	+	0.655884i	−0.938928	−	0.344113i	$-0.888180\pi$
$617$	−23.2671	+	16.2918i	−0.936700	+	0.655884i	0.00222854	+	0.999998i	$0.499291\pi$
$618$		0			0
$619$	−16.2376	−	19.3513i	−0.652646	−	0.777793i	0.333665	−	0.942692i	$-0.391715\pi$
$619$	−16.2376	−	19.3513i	−0.652646	−	0.777793i	−0.986310	+	0.164899i	$0.947270\pi$
$620$	−32.1226	−	4.34757i	−1.29008	−	0.174603i
$621$		0			0
$622$	2.93792	−	2.93792i	0.117800	−	0.117800i
$623$	3.45624	−	39.5050i	0.138471	−	1.58274i
$624$		0			0
$625$	16.3458	−	18.9160i	0.653830	−	0.756641i
$626$	−0.309884	−	0.851399i	−0.0123854	−	0.0340287i
$627$		0			0
$628$	−8.87918	+	12.6808i	−0.354318	+	0.506018i
$629$	−9.53762	−	16.5196i	−0.380290	−	0.658681i
$630$		0			0
$631$	2.76033	−	4.78103i	0.109887	−	0.190330i	−0.805837	−	0.592137i	$-0.798284\pi$
$631$	2.76033	−	4.78103i	0.109887	−	0.190330i	0.915724	+	0.401807i	$0.131618\pi$
$632$	−0.135591	−	0.290777i	−0.00539354	−	0.0115665i
$633$		0			0
$634$	−0.191734	+	0.228500i	−0.00761475	+	0.00907490i
$635$	−0.0818961	+	1.73163i	−0.00324995	+	0.0687175i
$636$		0			0
$637$	5.93690	−	2.76842i	0.235229	−	0.109689i
$638$	−0.490105	−	1.82910i	−0.0194034	−	0.0724146i
$639$		0			0
$640$	−4.30188	+	10.2801i	−0.170047	+	0.406355i
$641$	45.0144	−	7.93726i	1.77796	−	0.313503i	0.814264	−	0.580494i	$-0.197141\pi$
$641$	45.0144	−	7.93726i	1.77796	−	0.313503i	0.963699	+	0.266991i	$0.0860295\pi$
$642$		0			0
$643$	14.3424	+	6.68798i	0.565610	+	0.263748i	0.684321	−	0.729181i	$-0.260099\pi$
$643$	14.3424	+	6.68798i	0.565610	+	0.263748i	−0.118711	+	0.992929i	$0.537876\pi$
$644$	2.64595	−	15.0059i	0.104265	−	0.591316i
$645$		0			0
$646$	−0.580587	+	0.487170i	−0.0228429	+	0.0191675i
$647$	8.27160	+	8.27160i	0.325190	+	0.325190i	0.850754	−	0.525564i	$-0.176146\pi$
$647$	8.27160	+	8.27160i	0.325190	+	0.325190i	−0.525564	+	0.850754i	$0.676146\pi$
$648$		0			0
$649$		−	19.9961i		−	0.784915i
$650$	−1.58288	−	3.45979i	−0.0620858	−	0.135704i
$651$		0			0
$652$	−16.3284	−	23.3193i	−0.639468	−	0.913255i
$653$	20.8882	−	44.7948i	0.817417	−	1.75296i	0.178100	−	0.984012i	$-0.443005\pi$
$653$	20.8882	−	44.7948i	0.817417	−	1.75296i	0.639316	−	0.768944i	$-0.279217\pi$
$654$		0			0
$655$	0.678369	+	16.9471i	0.0265061	+	0.662177i
$656$	−14.9572	+	8.63557i	−0.583982	+	0.337162i
$657$		0			0
$658$	−2.48829	+	0.666736i	−0.0970037	+	0.0259921i
$659$	25.0705	+	9.12491i	0.976607	+	0.355456i	0.780520	−	0.625130i	$-0.214954\pi$
$659$	25.0705	+	9.12491i	0.976607	+	0.355456i	0.196087	+	0.980586i	$0.437176\pi$
$660$		0			0
$661$	−33.2465	−	27.8971i	−1.29314	−	1.08507i	−0.991287	−	0.131716i	$-0.957951\pi$
$661$	−33.2465	−	27.8971i	−1.29314	−	1.08507i	−0.301851	−	0.953355i	$-0.597604\pi$
$662$	0.270093	+	3.08718i	0.0104975	+	0.119987i
$663$		0			0
$664$	1.95858	−	5.38117i	0.0760078	−	0.208830i
$665$	−0.659789	−	5.15599i	−0.0255855	−	0.199941i
$666$		0			0
$667$	6.95716	+	1.86416i	0.269382	+	0.0721808i
$668$	−10.4958	−	7.34927i	−0.406096	−	0.284352i
$669$		0			0
$670$	0.511536	+	2.34764i	0.0197624	+	0.0906974i
$671$	51.8999	+	9.15135i	2.00357	+	0.353284i
$672$		0			0
$673$	9.97924	+	0.873070i	0.384671	+	0.0336544i	0.277852	−	0.960624i	$-0.410378\pi$
$673$	9.97924	+	0.873070i	0.384671	+	0.0336544i	0.106820	+	0.994278i	$0.465933\pi$
$674$	−0.555107			−0.0213819
$675$		0			0
$676$	18.4852			0.710968
$677$	35.9148	+	3.14213i	1.38032	+	0.120762i	0.753009	−	0.658010i	$-0.228602\pi$
$677$	35.9148	+	3.14213i	1.38032	+	0.120762i	0.627307	+	0.778772i	$0.284157\pi$
$678$		0			0
$679$	−20.7876	−	3.66542i	−0.797756	−	0.140666i
$680$	1.78613	+	8.19725i	0.0684949	+	0.314350i
$681$		0			0
$682$	4.21550	+	2.95173i	0.161420	+	0.113027i
$683$	40.8281	+	10.9399i	1.56224	+	0.418602i	0.933373	−	0.358908i	$-0.116851\pi$
$683$	40.8281	+	10.9399i	1.56224	+	0.418602i	0.628871	+	0.777510i	$0.283517\pi$
$684$		0			0
$685$	−2.81095	−	21.9664i	−0.107401	−	0.839295i
$686$	0.894787	−	2.45841i	0.0341631	−	0.0938624i
$687$		0			0
$688$	−2.30347	−	26.3288i	−0.0878191	−	1.00378i
$689$	−8.72642	−	7.32234i	−0.332450	−	0.278959i
$690$		0			0
$691$	−5.10153	−	1.85681i	−0.194071	−	0.0706362i	0.243156	−	0.969987i	$-0.421817\pi$
$691$	−5.10153	−	1.85681i	−0.194071	−	0.0706362i	−0.437227	+	0.899351i	$0.644040\pi$
$692$	22.1096	−	5.92425i	0.840481	−	0.225206i
$693$		0			0
$694$	1.20619	−	0.696395i	0.0457864	−	0.0264348i
$695$	1.34827	+	33.6827i	0.0511430	+	1.27766i
$696$		0			0
$697$	−11.1372	+	23.8838i	−0.421851	+	0.904663i
$698$	−0.996358	−	1.42295i	−0.0377127	−	0.0538593i
$699$		0			0
$700$	−26.7870	−	9.97025i	−1.01245	−	0.376840i
$701$		−	8.37641i		−	0.316373i	−0.987409	−	0.158186i	$-0.949435\pi$
$701$		−	8.37641i		−	0.316373i	0.987409	−	0.158186i	$-0.0505647\pi$
$702$		0			0
$703$	−1.84550	−	1.84550i	−0.0696043	−	0.0696043i
$704$	−24.6396	+	20.6751i	−0.928639	+	0.779221i
$705$		0			0
$706$	0.747459	−	4.23905i	0.0281310	−	0.159539i
$707$	13.7998	+	6.43494i	0.518994	+	0.242011i
$708$		0			0
$709$	27.2222	−	4.80001i	1.02235	−	0.180268i	0.362752	−	0.931886i	$-0.381837\pi$
$709$	27.2222	−	4.80001i	1.02235	−	0.180268i	0.659599	+	0.751617i	$0.270726\pi$
$710$	0.900497	−	2.15189i	0.0337950	−	0.0807590i
$711$		0			0
$712$	2.26655	+	8.45886i	0.0849424	+	0.317009i
$713$	−17.7401	+	8.27234i	−0.664372	+	0.309802i
$714$		0			0
$715$	2.17567	−	46.0028i	0.0813655	−	1.72041i
$716$	−8.68071	+	10.3453i	−0.324413	+	0.386621i
$717$		0			0
$718$	−0.928354	−	1.99086i	−0.0346459	−	0.0742983i
$719$	−13.4438	+	23.2854i	−0.501371	+	0.868400i	0.498628	+	0.866816i	$0.333837\pi$
$719$	−13.4438	+	23.2854i	−0.501371	+	0.868400i	−0.999999	+	0.00158362i	$0.999496\pi$
$720$		0			0
$721$	5.44055	+	9.42331i	0.202617	+	0.350942i
$722$	1.69408	−	2.41940i	0.0630473	−	0.0900409i
$723$		0			0
$724$	10.9664	+	30.1299i	0.407563	+	1.11977i
$725$	5.79847	−	12.2030i	0.215350	−	0.453209i
$726$		0			0
$727$	−1.67023	+	19.0908i	−0.0619455	+	0.708040i	0.900195	+	0.435487i	$0.143424\pi$
$727$	−1.67023	+	19.0908i	−0.0619455	+	0.708040i	−0.962141	+	0.272553i	$0.912132\pi$
$728$	−6.19200	+	6.19200i	−0.229491	+	0.229491i
$729$		0			0
$730$	−3.43941	−	0.465500i	−0.127298	−	0.0172289i
$731$	−25.9216	−	30.8921i	−0.958743	−	1.14259i
$732$		0			0
$733$	−28.9707	+	20.2855i	−1.07006	+	0.749261i	−0.969357	−	0.245656i	$-0.920997\pi$
$733$	−28.9707	+	20.2855i	−1.07006	+	0.749261i	−0.100699	+	0.994917i	$0.532108\pi$
$734$	−1.97069	+	0.717274i	−0.0727397	+	0.0264751i
$735$		0			0
$736$	0.878364	+	4.98145i	0.0323769	+	0.183619i
$737$	−7.52749	+	28.0930i	−0.277279	+	1.03482i
$738$		0			0
$739$	16.8271	+	9.71511i	0.618993	+	0.357376i	0.776477	−	0.630146i	$-0.217005\pi$
$739$	16.8271	+	9.71511i	0.618993	+	0.357376i	−0.157484	+	0.987522i	$0.550338\pi$
$740$	−13.7025	+	4.26582i	−0.503714	+	0.156815i
$741$		0			0
$742$	1.11812	−	0.0978225i	0.0410473	−	0.00359118i
$743$	−31.1397	+	2.72437i	−1.14240	+	0.0999474i	−0.642608	−	0.766195i	$-0.722147\pi$
$743$	−31.1397	+	2.72437i	−1.14240	+	0.0999474i	−0.499796	+	0.866143i	$0.666592\pi$
$744$		0			0
$745$	−15.3478	+	29.2236i	−0.562299	+	1.07067i
$746$	0.263770	+	0.152288i	0.00965730	+	0.00557564i
$747$		0			0
$748$	−13.0562	+	48.7265i	−0.477383	+	1.78162i
$749$	4.04754	+	22.9547i	0.147894	+	0.838747i
$750$		0			0
$751$	21.6560	−	7.88215i	0.790240	−	0.287624i	0.0848041	−	0.996398i	$-0.472974\pi$
$751$	21.6560	−	7.88215i	0.790240	−	0.287624i	0.705436	+	0.708774i	$0.250751\pi$
$752$	−17.4149	+	12.1941i	−0.635057	+	0.444672i
$753$		0			0
$754$	−1.32167	−	1.57510i	−0.0481322	−	0.0573618i
$755$	0.714367	−	5.27819i	0.0259985	−	0.192093i
$756$		0			0
$757$	10.7861	−	10.7861i	0.392029	−	0.392029i	−0.483381	−	0.875410i	$-0.660592\pi$
$757$	10.7861	−	10.7861i	0.392029	−	0.392029i	0.875410	+	0.483381i	$0.160592\pi$
$758$	−0.121294	+	1.38640i	−0.00440559	+	0.0503561i
$759$		0			0
$760$	0.526340	+	1.02010i	0.0190923	+	0.0370030i
$761$	−3.19211	−	8.77024i	−0.115714	−	0.317921i	0.868293	−	0.496051i	$-0.165217\pi$
$761$	−3.19211	−	8.77024i	−0.115714	−	0.317921i	−0.984007	+	0.178131i	$0.942995\pi$
$762$		0			0
$763$	20.1984	−	28.8462i	0.731229	−	1.04430i
$764$	−20.2039	−	34.9942i	−0.730951	−	1.26604i
$765$		0			0
$766$	1.37405	−	2.37992i	0.0496463	−	0.0859899i
$767$	−9.17603	−	19.6781i	−0.331327	−	0.710533i
$768$		0			0
$769$	−7.77292	+	9.26340i	−0.280299	+	0.334047i	−0.887764	−	0.460300i	$-0.847742\pi$
$769$	−7.77292	+	9.26340i	−0.280299	+	0.334047i	0.607465	+	0.794346i	$0.292186\pi$
$770$	3.05343	+	3.35659i	0.110038	+	0.120963i
$771$		0			0
$772$	13.9323	−	6.49674i	0.501435	−	0.233823i
$773$	0.479004	+	1.78767i	0.0172286	+	0.0642980i	0.974005	−	0.226527i	$-0.0727370\pi$
$773$	0.479004	+	1.78767i	0.0172286	+	0.0642980i	−0.956776	+	0.290825i	$0.906070\pi$
$774$		0			0
$775$	9.24561	+	35.5338i	0.332112	+	1.27641i
$776$	4.59055	−	0.809438i	0.164791	−	0.0290571i
$777$		0			0
$778$	−0.127850	−	0.0596173i	−0.00458363	−	0.00213738i
$779$	−0.626118	+	3.55089i	−0.0224330	+	0.127224i
$780$		0			0
$781$	21.6304	−	18.1500i	0.773996	−	0.649459i
$782$	1.77944

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.160295 - 0.0140240i) q^{2} +(-1.94412 - 0.342800i) q^{4} +(0.476055 + 2.18480i) q^{5} +(-2.37204 - 1.66092i) q^{7} +(0.617675 + 0.165506i) q^{8} +O(q^{10})\)	\(q+(-0.160295 - 0.0140240i) q^{2} +(-1.94412 - 0.342800i) q^{4} +(0.476055 + 2.18480i) q^{5} +(-2.37204 - 1.66092i) q^{7} +(0.617675 + 0.165506i) q^{8} +(-0.0456696 - 0.356890i) q^{10} +(1.48958 - 4.09258i) q^{11} +(-0.412163 - 4.71104i) q^{13} +(0.356933 + 0.299503i) q^{14} +(3.61342 + 1.31518i) q^{16} +(5.66739 - 1.51857i) q^{17} +(0.695229 - 0.401391i) q^{19} +(-0.176555 - 4.41071i) q^{20} +(-0.296167 + 0.635132i) q^{22} +(-1.52888 - 2.18347i) q^{23} +(-4.54674 + 2.08017i) q^{25} +0.760939i q^{26} +(4.04215 + 4.04215i) q^{28} +(-2.06994 + 1.73689i) q^{29} +(1.27517 - 7.23183i) q^{31} +(-1.71987 - 0.801990i) q^{32} +(-0.929752 + 0.163940i) q^{34} +(2.49956 - 5.97312i) q^{35} +(-0.841448 - 3.14033i) q^{37} +(-0.117071 + 0.0545912i) q^{38} +(-0.0675500 + 1.42829i) q^{40} +(-2.88706 + 3.44066i) q^{41} +(-2.90471 - 6.22917i) q^{43} +(-4.29885 + 7.44583i) q^{44} +(0.214452 + 0.371442i) q^{46} +(-3.17114 + 4.52886i) q^{47} +(0.473765 + 1.30166i) q^{49} +(0.757994 - 0.269679i) q^{50} +(-0.813654 + 9.30011i) q^{52} +(1.70331 - 1.70331i) q^{53} +(9.65061 + 1.30614i) q^{55} +(-1.19026 - 1.41849i) q^{56} +(0.356161 - 0.249386i) q^{58} +(4.31439 - 1.57031i) q^{59} +(2.10123 + 11.9167i) q^{61} +(-0.305823 + 1.14135i) q^{62} +(-6.39585 - 3.69265i) q^{64} +(10.0965 - 3.14321i) q^{65} +(-6.65253 + 0.582021i) q^{67} +(-11.5386 + 1.00950i) q^{68} +(-0.484435 + 0.922410i) q^{70} +(5.61473 + 3.24167i) q^{71} +(2.49666 - 9.31768i) q^{73} +(0.0908402 + 0.515180i) q^{74} +(-1.48920 + 0.542026i) q^{76} +(-10.3308 + 7.23368i) q^{77} +(-0.322504 - 0.384345i) q^{79} +(-1.15322 + 8.52072i) q^{80} +(0.511034 - 0.511034i) q^{82} +(0.780495 - 8.92110i) q^{83} +(6.01577 + 11.6592i) q^{85} +(0.378253 + 1.03924i) q^{86} +(1.59742 - 2.28135i) q^{88} +(6.84734 + 11.8599i) q^{89} +(-6.84699 + 11.8593i) q^{91} +(2.22384 + 4.76903i) q^{92} +(0.571832 - 0.681483i) q^{94} +(1.20793 + 1.32786i) q^{95} +(6.60652 - 3.08067i) q^{97} +(-0.0576878 - 0.215294i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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