LMFDB - Embedded newform 405.2.r.a.197.7

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			197.7
Character	$\chi$	$=$	405.197
Dual form			405.2.r.a.368.7

$q$-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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

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	−0.143688	−	0.989623i	$-0.545896\pi$
$2$	−0.160295	+	0.0140240i	−0.113346	+	0.00991648i	0.0303416	+	0.999540i	$0.490340\pi$
$3$		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	−0.928342	−	0.371727i	$-0.878766\pi$
$7$	−2.37204	+	1.66092i	−0.896545	+	0.627768i	0.0317971	+	0.999494i	$0.489877\pi$
$8$	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	0.933335	+	0.359008i	$0.116885\pi$
$11$	1.48958	+	4.09258i	0.449125	+	1.23396i	−0.484210	+	0.874952i	$0.660893\pi$
$12$		0			0
$13$	−0.412163	+	4.71104i	−0.114313	+	1.30661i	0.694905	+	0.719101i	$0.255446\pi$
$13$	−0.412163	+	4.71104i	−0.114313	+	1.30661i	−0.809219	+	0.587507i	$0.800109\pi$
$14$	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	0.869136	−	0.494573i	$-0.164676\pi$
$17$	5.66739	+	1.51857i	1.37454	+	0.368308i	0.505407	+	0.862881i	$0.331342\pi$
$18$		0			0
$19$	0.695229	+	0.401391i	0.159497	+	0.0920854i	0.577624	−	0.816303i	$-0.303980\pi$
$19$	0.695229	+	0.401391i	0.159497	+	0.0920854i	−0.418127	+	0.908388i	$0.637313\pi$
$20$	−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	−0.946283	−	0.323340i	$-0.895194\pi$
$23$	−1.52888	+	2.18347i	−0.318794	+	0.455286i	0.627488	+	0.778626i	$0.284083\pi$
$24$		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	0.430040	−	0.902810i	$-0.358500\pi$
$29$	−2.06994	−	1.73689i	−0.384379	−	0.322532i	−0.814419	+	0.580278i	$0.802944\pi$
$30$		0			0
$31$	1.27517	+	7.23183i	0.229027	+	1.29887i	0.854836	+	0.518899i	$0.173658\pi$
$31$	1.27517	+	7.23183i	0.229027	+	1.29887i	−0.625809	+	0.779976i	$0.715231\pi$
$32$	−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	0.861629	+	0.507539i	$0.169445\pi$
$37$	−0.841448	+	3.14033i	−0.138333	+	0.516266i	−0.999962	+	0.00872734i	$0.997222\pi$
$38$	−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	0.491943	−	0.870628i	$-0.336287\pi$
$41$	−2.88706	−	3.44066i	−0.450883	−	0.537341i	−0.942826	+	0.333286i	$0.891842\pi$
$42$		0			0
$43$	−2.90471	+	6.22917i	−0.442964	+	0.949940i	0.550397	+	0.834903i	$0.314476\pi$
$43$	−2.90471	+	6.22917i	−0.442964	+	0.949940i	−0.993361	+	0.115037i	$0.963301\pi$
$44$	−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	0.518328	−	0.855182i	$-0.326555\pi$
$47$	−3.17114	−	4.52886i	−0.462558	−	0.660602i	−0.980887	+	0.194580i	$0.937666\pi$
$48$		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	0.814347	−	0.580379i	$-0.197095\pi$
$53$	1.70331	+	1.70331i	0.233968	+	0.233968i	−0.580379	+	0.814347i	$0.697095\pi$
$54$		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	0.607231	−	0.794525i	$-0.292280\pi$
$59$	4.31439	+	1.57031i	0.561686	+	0.204437i	−0.0455453	+	0.998962i	$0.514503\pi$
$60$		0			0
$61$	2.10123	−	11.9167i	0.269035	−	1.52577i	−0.488259	−	0.872699i	$-0.662368\pi$
$61$	2.10123	−	11.9167i	0.269035	−	1.52577i	0.757294	−	0.653074i	$-0.226521\pi$
$62$	−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	−0.326793	−	0.945096i	$-0.605968\pi$
$67$	−6.65253	−	0.582021i	−0.812736	−	0.0711052i	−0.485943	+	0.873991i	$0.661524\pi$
$68$	−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	−0.128345	−	0.991730i	$-0.540966\pi$
$71$	5.61473	−	3.24167i	0.666346	−	0.384715i	0.794691	+	0.607014i	$0.207633\pi$
$72$		0			0
$73$	2.49666	+	9.31768i	0.292212	+	1.09055i	0.943406	+	0.331640i	$0.107602\pi$
$73$	2.49666	+	9.31768i	0.292212	+	1.09055i	−0.651194	+	0.758912i	$0.725731\pi$
$74$	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	−0.783882	−	0.620910i	$-0.786763\pi$
$79$	−0.322504	+	0.384345i	−0.0362845	+	0.0432422i	0.747597	+	0.664153i	$0.231208\pi$
$80$	−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	0.910411	+	0.413706i	$0.135766\pi$
$83$	0.780495	+	8.92110i	0.0856704	+	0.979218i	−0.824740	+	0.565512i	$0.808679\pi$
$84$		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	−0.232821	−	0.972520i	$-0.574796\pi$
$89$	6.84734	−	11.8599i	0.725816	−	1.25715i	0.958637	−	0.284631i	$-0.0918711\pi$
$90$		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	0.728010	−	0.685567i	$-0.240446\pi$
$97$	6.60652	+	3.08067i	0.670790	+	0.312795i	−0.0572192	+	0.998362i	$0.518223\pi$
$98$	−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	−0.0900315	−	0.995939i	$-0.528697\pi$
$101$	−5.17835	−	0.913082i	−0.515265	−	0.0908551i	−0.425233	+	0.905084i	$0.639808\pi$
$102$		0			0
$103$	−3.40559	+	1.58805i	−0.335562	+	0.156475i	−0.583094	−	0.812404i	$-0.698158\pi$
$103$	−3.40559	+	1.58805i	−0.335562	+	0.156475i	0.247532	+	0.968880i	$0.420380\pi$
$104$	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	−0.926512	−	0.376266i	$-0.877208\pi$
$107$	−5.69179	+	5.69179i	−0.550246	+	0.550246i	0.376266	+	0.926512i	$0.377208\pi$
$108$		0			0
$109$		−	12.1610i		−	1.16481i	−0.812899	−	0.582405i	$-0.802112\pi$
$109$		−	12.1610i		−	1.16481i	0.812899	−	0.582405i	$-0.197888\pi$
$110$	−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	0.970469	−	0.241225i	$-0.0775490\pi$
$113$	1.72075	+	3.69017i	0.161875	+	0.347142i	−0.808594	+	0.588366i	$0.799771\pi$
$114$		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	−0.225441	−	0.974257i	$-0.572382\pi$
$127$	0.748856	−	0.200655i	0.0664502	−	0.0178053i	0.291891	+	0.956452i	$0.405716\pi$
$128$	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	0.162481	−	0.986712i	$-0.448050\pi$
$131$	7.46979	−	1.31713i	0.652639	−	0.115078i	0.490158	+	0.871634i	$0.336939\pi$
$132$		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	−0.500431	−	0.865776i	$-0.666825\pi$
$137$	−9.86611	+	0.863173i	−0.842919	+	0.0737459i	−0.342488	+	0.939522i	$0.611270\pi$
$138$		0			0
$139$	14.8464	−	2.61782i	1.25926	−	0.222041i	0.496105	−	0.868262i	$-0.334763\pi$
$139$	14.8464	−	2.61782i	1.25926	−	0.222041i	0.763150	+	0.646222i	$0.223652\pi$
$140$	−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	−0.0487579	−	0.998811i	$-0.515526\pi$
$149$	11.3083	−	9.48879i	0.926412	−	0.777352i	0.975170	+	0.221459i	$0.0710818\pi$
$150$		0			0
$151$	−2.23835	+	0.814693i	−0.182154	+	0.0662987i	−0.431487	−	0.902119i	$-0.642011\pi$
$151$	−2.23835	+	0.814693i	−0.182154	+	0.0662987i	0.249333	+	0.968418i	$0.419789\pi$
$152$	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	0.993038	−	0.117794i	$-0.0375824\pi$
$157$	3.31405	+	7.10700i	0.264490	+	0.567200i	−0.728548	+	0.684995i	$0.759805\pi$
$158$	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	−0.184210	−	0.982887i	$-0.558973\pi$
$163$	10.1968	−	10.1968i	0.798677	−	0.798677i	0.982887	+	0.184210i	$0.0589726\pi$
$164$	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	−0.181477	−	0.983395i	$-0.558088\pi$
$167$	5.88244	−	2.74303i	0.455197	−	0.212262i	0.636673	+	0.771133i	$0.280310\pi$
$168$		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	−0.0201240	−	0.999797i	$-0.506406\pi$
$173$	−10.5085	−	4.90021i	−0.798949	−	0.372556i	−0.778825	+	0.627242i	$0.784184\pi$
$174$		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	0.965074	−	0.261977i	$-0.0843744\pi$
$179$	3.42048	+	5.92444i	0.255658	+	0.442813i	−0.709416	+	0.704790i	$0.751041\pi$
$180$		0			0
$181$	−8.12103	+	14.0660i	−0.603631	+	1.04552i	0.388635	+	0.921392i	$0.372947\pi$
$181$	−8.12103	+	14.0660i	−0.603631	+	1.04552i	−0.992266	+	0.124128i	$0.960387\pi$
$182$	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	−0.0387846	−	0.999248i	$-0.512349\pi$
$191$	13.1571	−	15.6801i	0.952017	−	1.13457i	0.990802	−	0.135322i	$-0.0432069\pi$
$192$		0			0
$193$	−6.37883	−	4.46650i	−0.459158	−	0.321506i	0.321010	−	0.947076i	$-0.395978\pi$
$193$	−6.37883	−	4.46650i	−0.459158	−	0.321506i	−0.780168	+	0.625570i	$0.784867\pi$
$194$	−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	0.997406	−	0.0719752i	$-0.0229303\pi$
$197$	1.37044	+	5.11454i	0.0976395	+	0.364396i	−0.899767	+	0.436371i	$0.856264\pi$
$198$		0			0
$199$	−24.0896	+	13.9081i	−1.70766	+	0.985920i	−0.770225	+	0.637773i	$0.779856\pi$
$199$	−24.0896	+	13.9081i	−1.70766	+	0.985920i	−0.937440	+	0.348148i	$0.886811\pi$
$200$	−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	0.628306	−	0.777966i	$-0.283749\pi$
$211$	8.85421	+	3.22267i	0.609549	+	0.221858i	−0.0187568	+	0.999824i	$0.505971\pi$
$212$	−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	0.967462	−	0.253017i	$-0.0814230\pi$
$223$	5.95553	+	8.50538i	0.398812	+	0.569562i	−0.568650	+	0.822580i	$0.692534\pi$
$224$	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	−0.572966	−	0.819579i	$-0.694207\pi$
$227$	6.37560	−	13.6725i	0.423164	−	0.907477i	0.996129	−	0.0878980i	$-0.0280150\pi$
$228$		0			0
$229$	0.604581	+	0.720511i	0.0399518	+	0.0476127i	0.785650	−	0.618671i	$-0.212329\pi$
$229$	0.604581	+	0.720511i	0.0399518	+	0.0476127i	−0.745699	+	0.666284i	$0.767884\pi$
$230$	−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	−0.901813	−	0.432126i	$-0.857764\pi$
$233$	1.45382	−	5.42572i	0.0952427	−	0.355451i	0.997056	+	0.0766749i	$0.0244304\pi$
$234$		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	0.939127	+	0.343571i	$0.111637\pi$
$239$	2.69221	+	15.2683i	0.174144	+	0.987622i	−0.764982	+	0.644051i	$0.777252\pi$
$240$		0			0
$241$	14.6302	+	12.2762i	0.942414	+	0.790779i	0.978004	−	0.208587i	$-0.0668865\pi$
$241$	14.6302	+	12.2762i	0.942414	+	0.790779i	−0.0355896	+	0.999366i	$0.511331\pi$
$242$	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	0.802845	−	0.596188i	$-0.203319\pi$
$251$	10.8992	+	6.29267i	0.687953	+	0.397190i	−0.114892	+	0.993378i	$0.536652\pi$
$252$		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	0.300521	+	0.953775i	$0.402840\pi$
$257$	−2.58192	+	29.5115i	−0.161056	+	1.84088i	−0.461576	+	0.887100i	$0.652716\pi$
$258$		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	−0.588410	−	0.808563i	$-0.700246\pi$
$263$	−0.484194	+	0.339036i	−0.0298567	+	0.0209059i	0.558553	+	0.829469i	$0.311357\pi$
$264$		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	0.0485123	−	0.998823i	$-0.484552\pi$
$277$	16.7047	−	11.6968i	1.00369	−	0.702792i	0.955178	+	0.296031i	$0.0956631\pi$
$278$	−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	−0.950816	−	0.309755i	$-0.899753\pi$
$281$	−7.06656	−	19.4152i	−0.421555	−	1.15821i	0.529261	−	0.848459i	$-0.322469\pi$
$282$		0			0
$283$	1.12399	−	12.8473i	0.0668145	−	0.763693i	−0.886700	−	0.462345i	$-0.847008\pi$
$283$	1.12399	−	12.8473i	0.0668145	−	0.763693i	0.953514	−	0.301348i	$-0.0974364\pi$
$284$	−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	0.426392	−	0.904538i	$-0.359784\pi$
$293$	19.3518	−	27.6373i	1.13055	−	1.61459i	0.704153	−	0.710048i	$-0.251327\pi$
$294$		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	−0.850656	−	0.525723i	$-0.823795\pi$
$307$	2.60886	−	9.73639i	0.148895	−	0.555685i	0.999551	−	0.0299620i	$-0.00953863\pi$
$308$	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	−0.992413	−	0.122952i	$-0.960764\pi$
$311$	−16.5976	−	19.7803i	−0.941166	−	1.12164i	0.0512465	−	0.998686i	$-0.483681\pi$
$312$		0			0
$313$	2.37968	−	5.10324i	0.134508	−	0.288452i	−0.827505	−	0.561459i	$-0.810240\pi$
$313$	2.37968	−	5.10324i	0.134508	−	0.288452i	0.962012	+	0.273007i	$0.0880181\pi$
$314$	−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	0.847901	−	0.530154i	$-0.177866\pi$
$317$	1.06328	+	1.51852i	0.0597197	+	0.0852886i	−0.788181	+	0.615443i	$0.788977\pi$
$318$		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	0.743638	+	0.668583i	$0.233099\pi$
$331$	−3.34434	+	18.9667i	−0.183822	+	1.04251i	−0.927460	+	0.373923i	$0.878012\pi$
$332$	−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	0.180375	−	0.983598i	$-0.442269\pi$
$337$	3.43672	+	0.300674i	0.187210	+	0.0163788i	0.00683487	+	0.999977i	$0.497824\pi$
$338$	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	0.367564	−	0.929998i	$-0.380192\pi$
$347$	−7.09044	−	4.96478i	−0.380635	−	0.266523i	−0.748198	+	0.663475i	$0.769081\pi$
$348$		0			0
$349$	6.93929	−	8.26992i	0.371452	−	0.442679i	−0.547645	−	0.836711i	$-0.684476\pi$
$349$	6.93929	−	8.26992i	0.371452	−	0.442679i	0.919097	+	0.394032i	$0.128920\pi$
$350$	−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	−0.761649	−	0.647990i	$-0.775610\pi$
$353$	−2.33150	−	26.6492i	−0.124093	−	1.41839i	0.637555	−	0.770405i	$-0.279946\pi$
$354$		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	−0.627747	−	0.778418i	$-0.716023\pi$
$359$	6.82588	−	11.8228i	0.360256	−	0.623982i	0.988003	+	0.154436i	$0.0493560\pi$
$360$		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	0.705712	−	0.708498i	$-0.250627\pi$
$367$	11.8122	+	5.50814i	0.616594	+	0.287523i	−0.0891181	+	0.996021i	$0.528405\pi$
$368$	−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	−0.466523	−	0.884509i	$-0.654494\pi$
$373$	−1.71551	+	0.799956i	−0.0888258	+	0.0414201i	0.377698	+	0.925929i	$0.376716\pi$
$374$	−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	$0.0713025\pi$
$379$			8.64900i			0.444270i	−0.975016	+	0.222135i	$0.928698\pi$
$380$	−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	−0.999885	−	0.0151943i	$-0.995163\pi$
$383$	−7.21777	−	15.4786i	−0.368811	−	0.790917i	0.631074	−	0.775723i	$-0.282614\pi$
$384$		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	−0.321051	−	0.947062i	$-0.604036\pi$
$389$	0.823821	−	0.299846i	0.0417694	−	0.0152028i	0.362820	+	0.931859i	$0.381814\pi$
$390$		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	−0.202305	−	0.979323i	$-0.564843\pi$
$397$	2.23467	−	0.598779i	0.112155	−	0.0300519i	0.314460	+	0.949271i	$0.398177\pi$
$398$	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	−0.329753	−	0.944067i	$-0.606965\pi$
$401$	−6.34251	+	1.11835i	−0.316730	+	0.0558480i	0.0130235	+	0.999915i	$0.495854\pi$
$402$		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	0.560462	−	0.828180i	$-0.310624\pi$
$409$	27.7142	−	4.88676i	1.37038	−	0.241635i	0.809916	+	0.586546i	$0.199513\pi$
$410$	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	0.429693	−	0.902975i	$-0.358622\pi$
$419$	28.5256	−	23.9358i	1.39357	−	1.16934i	0.963872	−	0.266365i	$-0.0858226\pi$
$420$		0			0
$421$	27.5767	−	10.0371i	1.34400	−	0.489178i	0.432933	−	0.901426i	$-0.357479\pi$
$421$	27.5767	−	10.0371i	1.34400	−	0.489178i	0.911071	+	0.412249i	$0.135256\pi$
$422$	−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	$0.00368513\pi$
$431$			0.480686i			0.0231538i	−0.999933	+	0.0115769i	$0.996315\pi$
$432$		0			0
$433$	−5.55599	+	5.55599i	−0.267004	+	0.267004i	−0.827892	−	0.560888i	$-0.810460\pi$
$433$	−5.55599	+	5.55599i	−0.267004	+	0.267004i	0.560888	+	0.827892i	$0.310460\pi$
$434$	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	−0.125924	−	0.992040i	$-0.540190\pi$
$439$	−12.2268	−	2.15591i	−0.583551	−	0.102896i	−0.457627	+	0.889144i	$0.651301\pi$
$440$	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	0.766040	−	0.642793i	$-0.222225\pi$
$443$	16.1231	+	7.51833i	0.766033	+	0.357207i	−7.21597e−6		1.00000i	$0.500002\pi$
$444$		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	0.817420	−	0.576042i	$-0.195403\pi$
$449$	−1.91039	−	3.30889i	−0.0901568	−	0.156156i	−0.907577	+	0.419886i	$0.862070\pi$
$450$		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	−0.897976	−	0.440045i	$-0.854962\pi$
$457$	−1.92516	−	22.0047i	−0.0900553	−	1.02934i	0.807920	−	0.589292i	$-0.200593\pi$
$458$	−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	−0.854095	−	0.520116i	$-0.825889\pi$
$461$	−4.15610	+	4.95304i	−0.193569	+	0.230686i	0.660527	+	0.750803i	$0.270333\pi$
$462$		0			0
$463$	0.251426	+	0.176051i	0.0116848	+	0.00818177i	0.579404	−	0.815040i	$-0.303285\pi$
$463$	0.251426	+	0.176051i	0.0116848	+	0.00818177i	−0.567719	+	0.823222i	$0.692174\pi$
$464$	−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	0.390156	+	0.920749i	$0.372421\pi$
$467$	11.0784	+	41.3450i	0.512645	+	1.91322i	0.122489	+	0.992470i	$0.460912\pi$
$468$		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	0.139612	+	0.990206i	$0.455415\pi$
$479$	−7.22789	+	40.9914i	−0.330251	+	1.87295i	−0.469863	+	0.882740i	$0.655697\pi$
$480$		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	0.977038	−	0.213064i	$-0.0683442\pi$
$487$	16.8595	+	16.8595i	0.763975	+	0.763975i	−0.213064	+	0.977038i	$0.568344\pi$
$488$	−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	−0.755340	−	0.655333i	$-0.772528\pi$
$491$	5.41828	−	14.8866i	0.244524	−	0.671823i	0.999864	−	0.0164907i	$-0.00524938\pi$
$492$		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	0.758148	−	0.652083i	$-0.226105\pi$
$499$	−0.350248	−	0.417409i	−0.0156792	−	0.0186858i	−0.773827	+	0.633397i	$0.781660\pi$
$500$	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	−0.759138	−	0.650930i	$-0.774379\pi$
$503$	5.01841	−	18.7290i	0.223760	−	0.835083i	0.982898	−	0.184153i	$-0.0589542\pi$
$504$		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	0.900764	+	0.434310i	$0.143008\pi$
$509$	4.57685	+	25.9566i	0.202865	+	1.15051i	−0.697898	+	0.716197i	$0.745881\pi$
$510$		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	0.645388	−	0.763855i	$-0.276696\pi$
$521$	6.99745	+	4.03998i	0.306564	+	0.176995i	−0.338824	+	0.940850i	$0.610029\pi$
$522$		0			0
$523$	34.5655	+	9.26181i	1.51145	+	0.404991i	0.916915	−	0.399083i	$-0.130671\pi$
$523$	34.5655	+	9.26181i	1.51145	+	0.404991i	0.594530	+	0.804073i	$0.297338\pi$
$524$	−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	−0.760533	−	0.649299i	$-0.775062\pi$
$547$	−9.60101	+	6.72270i	−0.410509	+	0.287442i	0.350024	+	0.936741i	$0.386174\pi$
$548$	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	0.495142	−	0.868812i	$-0.335116\pi$
$557$	11.5536	+	3.09577i	0.489541	+	0.131172i	−0.00560082	+	0.999984i	$0.501783\pi$
$558$		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	−0.908010	−	0.418947i	$-0.862399\pi$
$563$	−4.83500	+	6.90509i	−0.203771	+	0.291015i	0.704240	+	0.709962i	$0.251288\pi$
$564$		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	0.812906	−	0.582395i	$-0.197884\pi$
$569$	9.07677	+	7.61631i	0.380518	+	0.319292i	−0.432388	+	0.901688i	$0.642329\pi$
$570$		0			0
$571$	5.84395	+	33.1427i	0.244562	+	1.38698i	0.821508	+	0.570197i	$0.193133\pi$
$571$	5.84395	+	33.1427i	0.244562	+	1.38698i	−0.576946	+	0.816782i	$0.695756\pi$
$572$	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	0.603387	+	0.797448i	$0.293817\pi$
$577$	−7.63587	+	28.4975i	−0.317886	+	1.18637i	−0.921273	+	0.388917i	$0.872849\pi$
$578$	−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	0.454412	−	0.890792i	$-0.349850\pi$
$587$	−13.0366	−	18.6182i	−0.538077	−	0.768453i	−0.992488	+	0.122338i	$0.960961\pi$
$588$		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	0.482608	−	0.875837i	$-0.339690\pi$
$593$	−9.57575	−	9.57575i	−0.393229	−	0.393229i	−0.875837	+	0.482608i	$0.839690\pi$
$594$		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	0.0499591	−	0.998751i	$-0.484091\pi$
$599$	−13.5529	−	4.93284i	−0.553755	−	0.201550i	−0.603714	+	0.797201i	$0.706313\pi$
$600$		0			0
$601$	4.30406	−	24.4095i	0.175566	−	0.995686i	−0.761922	−	0.647669i	$-0.775744\pi$
$601$	4.30406	−	24.4095i	0.175566	−	0.995686i	0.937488	−	0.348017i	$-0.113145\pi$
$602$	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	−0.491789	−	0.870714i	$-0.663657\pi$
$607$	−27.7738	−	2.42989i	−1.12730	−	0.0986264i	−0.635516	+	0.772088i	$0.719212\pi$
$608$	−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	−0.885464	−	0.464708i	$-0.846159\pi$
$613$	−8.68995	−	32.4313i	−0.350984	−	1.30989i	0.534480	−	0.845181i	$-0.320507\pi$
$614$	−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	0.00222854	−	0.999998i	$-0.499291\pi$
$617$	−23.2671	−	16.2918i	−0.936700	−	0.655884i	−0.938928	+	0.344113i	$0.888180\pi$
$618$		0			0
$619$	−16.2376	+	19.3513i	−0.652646	+	0.777793i	−0.986310	−	0.164899i	$-0.947270\pi$
$619$	−16.2376	+	19.3513i	−0.652646	+	0.777793i	0.333665	+	0.942692i	$0.391715\pi$
$620$	−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	0.915724	−	0.401807i	$-0.131618\pi$
$631$	2.76033	+	4.78103i	0.109887	+	0.190330i	−0.805837	+	0.592137i	$0.798284\pi$
$632$	−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	0.963699	−	0.266991i	$-0.0860295\pi$
$641$	45.0144	+	7.93726i	1.77796	+	0.313503i	0.814264	+	0.580494i	$0.197141\pi$
$642$		0			0
$643$	14.3424	−	6.68798i	0.565610	−	0.263748i	−0.118711	−	0.992929i	$-0.537876\pi$
$643$	14.3424	−	6.68798i	0.565610	−	0.263748i	0.684321	+	0.729181i	$0.260099\pi$
$644$	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	−0.525564	−	0.850754i	$-0.676146\pi$
$647$	8.27160	−	8.27160i	0.325190	−	0.325190i	0.850754	+	0.525564i	$0.176146\pi$
$648$		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	0.639316	+	0.768944i	$0.279217\pi$
$653$	20.8882	+	44.7948i	0.817417	+	1.75296i	0.178100	+	0.984012i	$0.443005\pi$
$654$		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	0.196087	−	0.980586i	$-0.437176\pi$
$659$	25.0705	−	9.12491i	0.976607	−	0.355456i	0.780520	+	0.625130i	$0.214954\pi$
$660$		0			0
$661$	−33.2465	+	27.8971i	−1.29314	+	1.08507i	−0.301851	+	0.953355i	$0.597604\pi$
$661$	−33.2465	+	27.8971i	−1.29314	+	1.08507i	−0.991287	+	0.131716i	$0.957951\pi$
$662$	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	0.106820	−	0.994278i	$-0.465933\pi$
$673$	9.97924	−	0.873070i	0.384671	−	0.0336544i	0.277852	+	0.960624i	$0.410378\pi$
$674$	−0.555107			−0.0213819
$675$		0			0
$676$	18.4852			0.710968
$677$	35.9148	−	3.14213i	1.38032	−	0.120762i	0.627307	−	0.778772i	$-0.284157\pi$
$677$	35.9148	−	3.14213i	1.38032	−	0.120762i	0.753009	+	0.658010i	$0.228602\pi$
$678$		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	0.628871	−	0.777510i	$-0.283517\pi$
$683$	40.8281	−	10.9399i	1.56224	−	0.418602i	0.933373	+	0.358908i	$0.116851\pi$
$684$		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	−0.437227	−	0.899351i	$-0.644040\pi$
$691$	−5.10153	+	1.85681i	−0.194071	+	0.0706362i	0.243156	+	0.969987i	$0.421817\pi$
$692$	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	$0.0505647\pi$
$701$			8.37641i			0.316373i	−0.987409	+	0.158186i	$0.949435\pi$
$702$		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	0.659599	−	0.751617i	$-0.270726\pi$
$709$	27.2222	+	4.80001i	1.02235	+	0.180268i	0.362752	+	0.931886i	$0.381837\pi$
$710$	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	−0.999999	−	0.00158362i	$-0.999496\pi$
$719$	−13.4438	−	23.2854i	−0.501371	−	0.868400i	0.498628	−	0.866816i	$-0.333837\pi$
$720$		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	−0.962141	−	0.272553i	$-0.912132\pi$
$727$	−1.67023	−	19.0908i	−0.0619455	−	0.708040i	0.900195	−	0.435487i	$-0.143424\pi$
$728$	−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	−0.100699	−	0.994917i	$-0.532108\pi$
$733$	−28.9707	−	20.2855i	−1.07006	−	0.749261i	−0.969357	+	0.245656i	$0.920997\pi$
$734$	−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	−0.157484	−	0.987522i	$-0.550338\pi$
$739$	16.8271	−	9.71511i	0.618993	−	0.357376i	0.776477	+	0.630146i	$0.217005\pi$
$740$	−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	−0.499796	−	0.866143i	$-0.666592\pi$
$743$	−31.1397	−	2.72437i	−1.14240	−	0.0999474i	−0.642608	+	0.766195i	$0.722147\pi$
$744$		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	0.705436	−	0.708774i	$-0.250751\pi$
$751$	21.6560	+	7.88215i	0.790240	+	0.287624i	0.0848041	+	0.996398i	$0.472974\pi$
$752$	−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	0.875410	−	0.483381i	$-0.160592\pi$
$757$	10.7861	+	10.7861i	0.392029	+	0.392029i	−0.483381	+	0.875410i	$0.660592\pi$
$758$	−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	−0.984007	−	0.178131i	$-0.942995\pi$
$761$	−3.19211	+	8.77024i	−0.115714	+	0.317921i	0.868293	+	0.496051i	$0.165217\pi$
$762$		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	0.607465	−	0.794346i	$-0.292186\pi$
$769$	−7.77292	−	9.26340i	−0.280299	−	0.334047i	−0.887764	+	0.460300i	$0.847742\pi$
$770$	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	−0.956776	−	0.290825i	$-0.906070\pi$
$773$	0.479004	−	1.78767i	0.0172286	−	0.0642980i	0.974005	+	0.226527i	$0.0727370\pi$
$774$		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	−	1.77944i	0.0636327	−	0.0636327i
$783$		0			0
$784$		−	5.32653i		−	0.190233i
$785$	17.1051	−	3.85723i	0.610506	−	0.137670i
$786$		0			0
$787$	9.79291	−	13.9857i	0.349080	−	0.498537i	−0.605765	−	0.795644i	$-0.707133\pi$
$787$	9.79291	−	13.9857i	0.349080	−	0.498537i	0.954844	+	0.297106i	$0.0960216\pi$
$788$	−4.41755	−	9.47347i	−0.157369	−	0.337479i
$789$		0			0
$790$	−0.122440	−	0.132651i	−0.00435624	−	0.00471953i
$791$	−10.2108	−	5.89518i	−0.363053	−	0.209609i
$792$		0			0
$793$	55.2739	+	14.8106i	1.96283	+	0.525940i
$794$	−0.349811	+	0.127321i	−0.0124143	+	0.00451844i
$795$		0			0
$796$	42.0652	−	35.2969i	1.49096	−	1.25107i
$797$	1.47293	−	16.8357i	0.0521739	−	0.596350i	−0.924437	−	0.381335i	$-0.875464\pi$
$797$	1.47293	−	16.8357i	0.0521739	−	0.596350i	0.976611	−	0.215015i	$-0.0689800\pi$
$798$		0			0
$799$	−11.0947	−	30.4824i	−0.392502	−	1.07839i
$800$	9.48810	−	0.0688069i	0.335455	−	0.00243269i
$801$		0			0
$802$	1.00099	−	0.268215i	0.0353462	−	0.00947098i
$803$	−34.4144	+	24.0972i	−1.21446	+	0.850372i
$804$		0			0
$805$	−16.8637	−	3.67449i	−0.594367	−	0.129509i
$806$	5.50298	−	0.970323i	0.193834	−	0.0341782i
$807$		0			0
$808$	−3.34966	+	0.293057i	−0.117841	+	0.0103097i
$809$	47.0271			1.65338			0.826692	−	0.562654i	$-0.190220\pi$
$809$	47.0271			1.65338			0.826692	+	0.562654i	$0.190220\pi$
$810$		0			0
$811$	−46.5510			−1.63463			−0.817314	−	0.576192i	$-0.804538\pi$
$811$	−46.5510			−1.63463			−0.817314	+	0.576192i	$0.804538\pi$
$812$	−15.3878	+	1.34626i	−0.540006	+	0.0472444i
$813$		0			0
$814$	2.24373	−	0.395630i	0.0786427	−	0.0138668i
$815$	−17.4238	−	27.1323i	−0.610330	−	0.950404i
$816$		0			0
$817$	−4.51977	+	3.16478i	−0.158127	+	0.110722i
$818$	−4.37392	+	1.17199i	−0.152931	+	0.0409776i
$819$		0			0
$820$	15.6855	−	12.1265i	0.547761	−	0.423476i
$821$	11.2400	+	30.8817i	0.392280	+	1.07778i	0.965958	+	0.258699i	$0.0832938\pi$
$821$	11.2400	+	30.8817i	0.392280	+	1.07778i	−0.573678	+	0.819081i	$0.694484\pi$
$822$		0			0
$823$	0.780841	−	8.92506i	0.0272184	−	0.311108i	−0.970366	−	0.241641i	$-0.922314\pi$
$823$	0.780841	−	8.92506i	0.0272184	−	0.311108i	0.997584	−	0.0694673i	$-0.0221299\pi$
$824$	−1.84072	+	1.54454i	−0.0641244	+	0.0538067i
$825$		0			0
$826$	2.01026	−	0.731675i	0.0699460	−	0.0254582i
$827$	−49.8029	−	13.3446i	−1.73182	−	0.464039i	−0.751216	−	0.660057i	$-0.770532\pi$
$827$	−49.8029	−	13.3446i	−1.73182	−	0.464039i	−0.980600	+	0.196018i	$0.937199\pi$
$828$		0			0
$829$	6.07560	+	3.50775i	0.211014	+	0.121829i	0.601783	−	0.798660i	$-0.294457\pi$
$829$	6.07560	+	3.50775i	0.211014	+	0.121829i	−0.390768	+	0.920489i	$0.627791\pi$
$830$	−3.21950	−	0.128872i	−0.111750	−	0.00447322i
$831$		0			0
$832$	−14.7601	−	31.6531i	−0.511714	−	1.09737i
$833$	4.66167	−	6.65756i	0.161517	−	0.230671i
$834$		0			0
$835$	−3.19261	−	14.1578i	−0.110485	−	0.489951i
$836$		−	6.90208i		−	0.238713i
$837$		0			0
$838$	−4.23684	+	4.23684i	−0.146359	+	0.146359i
$839$	2.86722	+	2.40588i	0.0989873	+	0.0830602i	0.690938	−	0.722914i	$-0.257198\pi$
$839$	2.86722	+	2.40588i	0.0989873	+	0.0830602i	−0.591951	+	0.805974i	$0.701642\pi$
$840$		0			0
$841$	−3.76791	−	21.3689i	−0.129928	−	0.736858i
$842$	−4.27965	+	1.99563i	−0.147487	+	0.0687741i
$843$		0			0
$844$	−18.3184	−	3.23002i	−0.630544	−	0.111182i
$845$	−7.94248	+	19.3732i	−0.273229	+	0.666459i
$846$		0			0
$847$	5.97181	−	22.2871i	0.205194	−	0.765793i
$848$	8.39495	+	3.91463i	0.288284	+	0.134429i
$849$		0			0
$850$	3.88632	+	2.67944i	0.133300	+	0.0919041i
$851$	−5.57034	−	6.63847i	−0.190949	−	0.227564i
$852$		0			0
$853$	−18.4044	+	39.4684i	−0.630155	+	1.35137i	0.288945	+	0.957346i	$0.406696\pi$
$853$	−18.4044	+	39.4684i	−0.630155	+	1.35137i	−0.919100	+	0.394025i	$0.871082\pi$
$854$	−2.81908	−	4.88278i	−0.0964668	−	0.167085i
$855$		0			0
$856$	−2.57365	+	4.45770i	−0.0879657	+	0.152361i
$857$	27.3168	+	39.0125i	0.933125	+	1.33264i	0.943036	+	0.332690i	$0.107956\pi$
$857$	27.3168	+	39.0125i	0.933125	+	1.33264i	−0.00991152	+	0.999951i	$0.503155\pi$
$858$		0			0
$859$	−14.5712	+	40.0340i	−0.497162	+	1.36594i	0.396844	+	0.917886i	$0.370105\pi$
$859$	−14.5712	+	40.0340i	−0.497162	+	1.36594i	−0.894006	+	0.448055i	$0.852117\pi$
$860$	−26.9622	−	13.9116i	−0.919404	−	0.474382i
$861$		0			0
$862$	−0.00674116	−	0.0770518i	−0.000229605	−	0.00262439i
$863$	−11.3790	−	11.3790i	−0.387346	−	0.387346i	0.486393	−	0.873740i	$-0.338312\pi$
$863$	−11.3790	−	11.3790i	−0.387346	−	0.387346i	−0.873740	+	0.486393i	$0.838312\pi$
$864$		0			0
$865$	−15.7086	+	20.6263i	−0.534110	+	0.701316i
$866$	0.812682	−	0.968517i	0.0276161	−	0.0329115i
$867$		0			0
$868$	34.3866	+	24.0777i	1.16716	+	0.817252i
$869$	−2.05336	−	0.747362i	−0.0696554	−	0.0253525i
$870$		0			0
$871$	5.48385	−	31.1005i	0.185813	−	1.05380i
$872$	−2.01271	−	7.51153i	−0.0681589	−	0.254372i
$873$		0			0
$874$	0.298187	−	0.172158i	0.0100863	−	0.00582334i
$875$	1.06028	−	32.3578i	0.0358439	−	1.09389i
$876$		0			0
$877$	24.8592	+	2.17490i	0.839435	+	0.0734411i	0.498760	−	0.866740i	$-0.333789\pi$
$877$	24.8592	+	2.17490i	0.839435	+	0.0734411i	0.340675	+	0.940181i	$0.389344\pi$
$878$	1.99013	+	0.174114i	0.0671635	+	0.00587605i
$879$		0			0
$880$	33.1539	−	17.4119i	1.11762	−	0.586956i
$881$	−19.2496	+	11.1138i	−0.648536	+	0.374432i	−0.787895	−	0.615810i	$-0.788829\pi$
$881$	−19.2496	+	11.1138i	−0.648536	+	0.374432i	0.139359	+	0.990242i	$0.455496\pi$
$882$		0			0
$883$	13.9173	+	51.9401i	0.468355	+	1.74792i	0.645521	+	0.763743i	$0.276640\pi$
$883$	13.9173	+	51.9401i	0.468355	+	1.74792i	−0.177166	+	0.984181i	$0.556693\pi$
$884$	9.51159	−	53.9429i	0.319909	−	1.81430i
$885$		0			0
$886$	−2.68990	−	0.979043i	−0.0903689	−	0.0328916i
$887$	−39.0601	−	27.3502i	−1.31151	−	0.918330i	−0.312015	−	0.950077i	$-0.601004\pi$
$887$	−39.0601	−	27.3502i	−1.31151	−	0.918330i	−0.999496	+	0.0317472i	$0.989893\pi$
$888$		0			0
$889$	−1.44304	+	1.71975i	−0.0483980	+	0.0576785i
$890$	3.91998	+	2.98539i	0.131398	+	0.100070i
$891$		0			0
$892$	−14.4939	−	14.4939i	−0.485292	−	0.485292i
$893$	−0.386828	−	4.42146i	−0.0129447	−	0.147959i
$894$		0			0
$895$	14.5721	−	4.65272i	0.487091	−	0.155523i
$896$	−4.93582	+	13.5611i	−0.164894	+	0.453043i
$897$		0			0
$898$	0.352630	+	0.503608i	0.0117674	+	0.0168056i
$899$	9.92137	−	17.1843i	0.330896	−	0.573129i
$900$		0			0
$901$	7.06673	+	12.2399i	0.235427	+	0.407771i
$902$	−1.33022	+	2.85267i	−0.0442916	+	0.0949837i
$903$		0			0
$904$	1.67361	+	1.99453i	0.0556635	+	0.0663371i
$905$	26.8655	+	24.4391i	0.893039	+	0.812382i
$906$		0			0
$907$	−32.6698	−	15.2342i	−1.08478	−	0.505842i	−0.203810	−	0.979010i	$-0.565332\pi$
$907$	−32.6698	−	15.2342i	−1.08478	−	0.505842i	−0.880972	+	0.473168i	$0.843110\pi$
$908$	−7.70797	+	28.7666i	−0.255798	+	0.954652i
$909$		0			0
$910$	4.54518	−	1.90201i	0.150671	−	0.0630511i
$911$	−35.2604	−	6.21737i	−1.16823	−	0.205991i	−0.444310	−	0.895873i	$-0.646551\pi$
$911$	−35.2604	−	6.21737i	−1.16823	−	0.205991i	−0.723921	+	0.689883i	$0.757662\pi$
$912$		0			0
$913$	−35.3477	+	16.4829i	−1.16984	+	0.545505i
$914$	0.617189	+	3.50025i	0.0204148	+	0.115778i
$915$		0			0
$916$	−1.42237	−	1.19351i	−0.0469964	−	0.0394346i
$917$	−15.5310	+	15.5310i	−0.512878	+	0.512878i
$918$		0			0
$919$		−	10.8922i		−	0.359301i	−0.983730	−	0.179651i	$-0.942503\pi$
$919$		−	10.8922i		−	0.359301i	0.983730	−	0.179651i	$-0.0574967\pi$
$920$	3.22191	+	2.03620i	0.106223	+	0.0671314i
$921$		0			0
$922$	0.596741	−	0.852235i	0.0196526	−	0.0280669i
$923$	12.9575	+	27.7873i	0.426500	+	0.914632i
$924$		0			0
$925$	10.3583	−	12.5279i	0.340578	−	0.411915i
$926$	−0.0427714	−	0.0246941i	−0.00140556	−	0.000811498i
$927$		0			0
$928$	4.95301	+	1.32716i	0.162591	+	0.0435660i
$929$	−0.624723	+	0.227381i	−0.0204965	+	0.00746012i	−0.352248	−	0.935907i	$-0.614583\pi$
$929$	−0.624723	+	0.227381i	−0.0204965	+	0.00746012i	0.331752	+	0.943367i	$0.392360\pi$
$930$		0			0
$931$	0.851849	−	0.714786i	0.0279182	−	0.0234262i
$932$	−0.966453	+	11.0466i	−0.0316572	+	0.361844i
$933$		0			0
$934$	−2.35563	−	6.47205i	−0.0770787	−	0.211772i
$935$	56.6772	+	7.25273i	1.85354	+	0.237190i
$936$		0			0
$937$	−30.5740	+	8.19227i	−0.998808	+	0.267630i	−0.720946	−	0.692991i	$-0.756292\pi$
$937$	−30.5740	+	8.19227i	−0.998808	+	0.267630i	−0.277862	+	0.960621i	$0.589626\pi$
$938$	−2.54883	+	1.78471i	−0.0832222	+	0.0582728i
$939$		0			0
$940$	20.5354	−	13.1874i	0.669790	−	0.430125i
$941$	−15.3045	+	2.69859i	−0.498911	+	0.0879715i	−0.417441	−	0.908704i	$-0.637073\pi$
$941$	−15.3045	+	2.69859i	−0.498911	+	0.0879715i	−0.0814707	+	0.996676i	$0.525962\pi$
$942$		0			0
$943$	11.9266	−	1.04344i	0.388383	−	0.0339791i
$944$	17.6549			0.574619
$945$		0			0
$946$	4.81662			0.156602
$947$	−26.0673	+	2.28059i	−0.847074	+	0.0741093i	−0.502423	−	0.864622i	$-0.667558\pi$
$947$	−26.0673	+	2.28059i	−0.847074	+	0.0741093i	−0.344650	+	0.938731i	$0.612003\pi$
$948$		0			0
$949$	−44.9250	+	7.92149i	−1.45833	+	0.257143i
$950$	0.418733	+	0.491740i	0.0135855	+	0.0159542i
$951$		0			0
$952$	−8.89972	+	6.23165i	−0.288442	+	0.201969i
$953$	37.4368	−	10.0312i	1.21270	−	0.324942i	0.404878	−	0.914371i	$-0.367314\pi$
$953$	37.4368	−	10.0312i	1.21270	−	0.324942i	0.807820	+	0.589429i	$0.200647\pi$
$954$		0			0
$955$	−27.9944	−	36.2103i	−0.905876	−	1.17174i
$956$	−10.4679	−	28.7604i	−0.338557	−	0.930178i
$957$		0			0
$958$	0.583733	−	6.67210i	0.0188596	−	0.215566i
$959$	21.9691	−	18.4343i	0.709420	−	0.595274i
$960$		0			0
$961$	−21.5428	+	7.84095i	−0.694930	+	0.252934i
$962$	2.38959	+	0.640290i	0.0770436	+	0.0206438i
$963$		0			0
$964$	−32.6511	−	18.8511i	−1.05162	−	0.607154i
$965$	−12.7951	+	11.8102i	−0.411889	+	0.380183i
$966$		0			0
$967$	14.1812	+	30.4117i	0.456036	+	0.977973i	0.991095	+	0.133158i	$0.0425118\pi$
$967$	14.1812	+	30.4117i	0.456036	+	0.977973i	−0.535058	+	0.844815i	$0.679710\pi$
$968$	−2.92254	+	4.17382i	−0.0939340	+	0.134152i
$969$		0			0
$970$	−1.40118	+	2.21711i	−0.0449891	+	0.0711871i
$971$		−	3.53962i		−	0.113592i	−0.998386	−	0.0567959i	$-0.981912\pi$
$971$		−	3.53962i		−	0.113592i	0.998386	−	0.0567959i	$-0.0180884\pi$
$972$		0			0
$973$	−30.8682	+	30.8682i	−0.989589	+	0.989589i
$974$	−2.93893	−	2.46605i	−0.0941694	−	0.0790175i
$975$		0			0
$976$	−8.07991	−	45.8234i	−0.258632	−	1.46677i
$977$	41.3945	−	19.3025i	1.32433	−	0.617543i	0.373604	−	0.927588i	$-0.378122\pi$
$977$	41.3945	−	19.3025i	1.32433	−	0.617543i	0.950722	+	0.310045i	$0.100344\pi$
$978$		0			0
$979$	58.7374	+	10.3570i	1.87726	+	0.331011i
$980$	5.65759	+	2.31945i	0.180725	+	0.0740922i
$981$		0			0
$982$	−0.659756	+	2.46224i	−0.0210536	+	0.0785733i
$983$	−29.5099	−	13.7607i	−0.941220	−	0.438898i	−0.109434	−	0.993994i	$-0.534904\pi$
$983$	−29.5099	−	13.7607i	−0.941220	−	0.438898i	−0.831786	+	0.555096i	$0.812682\pi$
$984$		0			0
$985$	11.8267	−	0.559334i	0.376829	−	0.0178219i
$986$	1.63979	+	1.95422i	0.0522215	+	0.0622352i
$987$		0			0
$988$	3.16730	−	6.79230i	0.100765	−	0.216092i
$989$	−9.16026	−	15.8660i	−0.291279	−	0.504511i
$990$		0			0
$991$	22.7542	−	39.4115i	0.722812	−	1.25195i	−0.237057	−	0.971496i	$-0.576183\pi$
$991$	22.7542	−	39.4115i	0.722812	−	1.25195i	0.959868	−	0.280451i	$-0.0904839\pi$
$992$	−7.99298	−	11.4152i	−0.253777	−	0.362432i
$993$		0			0
$994$	1.03320	−	2.83869i	0.0327710	−	0.0900377i
$995$	18.9186	+	59.2520i	0.599759	+	1.87842i
$996$		0			0
$997$	0.786008	+	8.98411i	0.0248931	+	0.284530i	0.998431	+	0.0560024i	$0.0178355\pi$
$997$	0.786008	+	8.98411i	0.0248931	+	0.284530i	−0.973538	+	0.228527i	$0.926609\pi$
$998$	0.0619968	+	0.0619968i	0.00196248	+	0.00196248i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.197.7		192
3.2	odd	2		135.2.q.a.92.10	yes	192
5.3	odd	4	inner	405.2.r.a.278.10		192
15.2	even	4		675.2.ba.b.443.10		192
15.8	even	4		135.2.q.a.38.7	yes	192
15.14	odd	2		675.2.ba.b.632.7		192
27.5	odd	18	inner	405.2.r.a.287.10		192
27.22	even	9		135.2.q.a.32.7	✓	192
135.22	odd	36		675.2.ba.b.518.7		192
135.49	even	18		675.2.ba.b.32.10		192
135.103	odd	36		135.2.q.a.113.10	yes	192
135.113	even	36	inner	405.2.r.a.368.7		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.7	✓	192	27.22	even	9
135.2.q.a.38.7	yes	192	15.8	even	4
135.2.q.a.92.10	yes	192	3.2	odd	2
135.2.q.a.113.10	yes	192	135.103	odd	36
405.2.r.a.197.7		192	1.1	even	1	trivial
405.2.r.a.278.10		192	5.3	odd	4	inner
405.2.r.a.287.10		192	27.5	odd	18	inner
405.2.r.a.368.7		192	135.113	even	36	inner
675.2.ba.b.32.10		192	135.49	even	18
675.2.ba.b.443.10		192	15.2	even	4
675.2.ba.b.518.7		192	135.22	odd	36
675.2.ba.b.632.7		192	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
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

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