LMFDB - Embedded newform 324.3.j.a.307.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			307.5
Character	$\chi$	$=$	324.307
Dual form			324.3.j.a.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70561 - 1.04446i) q^{2} +(1.81819 + 3.56289i) q^{4} +(0.00321173 - 0.0182146i) q^{5} +(-0.446686 - 0.532339i) q^{7} +(0.620191 - 7.97592i) q^{8} +O(q^{10})$	\(q+(-1.70561 - 1.04446i) q^{2} +(1.81819 + 3.56289i) q^{4} +(0.00321173 - 0.0182146i) q^{5} +(-0.446686 - 0.532339i) q^{7} +(0.620191 - 7.97592i) q^{8} +(-0.0245024 + 0.0277124i) q^{10} +(-5.71885 + 1.00839i) q^{11} +(6.99816 - 2.54712i) q^{13} +(0.205861 + 1.37451i) q^{14} +(-9.38837 + 12.9560i) q^{16} +(4.38388 - 7.59310i) q^{17} +(17.1217 - 9.88523i) q^{19} +(0.0707361 - 0.0216746i) q^{20} +(10.8073 + 4.25322i) q^{22} +(-7.15027 + 8.52136i) q^{23} +(23.4920 + 8.55039i) q^{25} +(-14.5965 - 2.96494i) q^{26} +(1.08451 - 2.55939i) q^{28} +(21.1363 + 7.69297i) q^{29} +(20.2667 - 24.1529i) q^{31} +(29.5450 - 12.2921i) q^{32} +(-15.4079 + 8.37204i) q^{34} +(-0.0111310 + 0.00642647i) q^{35} +(26.7594 - 46.3486i) q^{37} +(-39.5277 - 1.02270i) q^{38} +(-0.143286 - 0.0369130i) q^{40} +(52.8679 - 19.2423i) q^{41} +(-70.5871 + 12.4464i) q^{43} +(-13.9907 - 18.5422i) q^{44} +(21.0958 - 7.06589i) q^{46} +(-43.9159 - 52.3369i) q^{47} +(8.42490 - 47.7800i) q^{49} +(-31.1375 - 39.1201i) q^{50} +(21.7991 + 20.3025i) q^{52} +41.1446 q^{53} +0.107405i q^{55} +(-4.52293 + 3.23258i) q^{56} +(-28.0151 - 35.1972i) q^{58} +(50.0926 + 8.83268i) q^{59} +(28.9297 - 24.2749i) q^{61} +(-59.7939 + 20.0275i) q^{62} +(-63.2307 - 9.89320i) q^{64} +(-0.0239186 - 0.135649i) q^{65} +(-14.8206 - 40.7193i) q^{67} +(35.0241 + 1.81357i) q^{68} +(0.0256973 + 0.000664867i) q^{70} +(49.5059 + 28.5822i) q^{71} +(14.6051 + 25.2968i) q^{73} +(-94.0505 + 51.1033i) q^{74} +(66.3505 + 43.0296i) q^{76} +(3.09133 + 2.59394i) q^{77} +(-46.0077 + 126.405i) q^{79} +(0.205836 + 0.212617i) q^{80} +(-110.270 - 22.3987i) q^{82} +(49.0991 - 134.899i) q^{83} +(-0.124225 - 0.104237i) q^{85} +(133.394 + 52.4970i) q^{86} +(4.49604 + 46.2385i) q^{88} +(29.5539 + 51.1889i) q^{89} +(-4.48191 - 2.58763i) q^{91} +(-43.3612 - 9.98217i) q^{92} +(20.2392 + 135.135i) q^{94} +(-0.125065 - 0.343614i) q^{95} +(6.63733 + 37.6422i) q^{97} +(-64.2741 + 72.6944i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−1.70561	−	1.04446i	−0.852803	−	0.522232i
$2$	−1.70561	−	1.04446i	−0.852803	−	0.522232i
$3$		0			0
$3$		0			0
$4$	1.81819	+	3.56289i	0.454548	+	0.890722i
$5$	0.00321173	−	0.0182146i	0.000642345	−	0.00364292i	−0.984485	−	0.175469i	$-0.943856\pi$
$5$	0.00321173	−	0.0182146i	0.000642345	−	0.00364292i	0.985127	+	0.171826i	$0.0549668\pi$
$6$		0			0
$7$	−0.446686	−	0.532339i	−0.0638123	−	0.0760485i	0.733194	−	0.680019i	$-0.238029\pi$
$7$	−0.446686	−	0.532339i	−0.0638123	−	0.0760485i	−0.797006	+	0.603971i	$0.793584\pi$
$8$	0.620191	−	7.97592i	0.0775239	−	0.996990i
$9$		0			0
$10$	−0.0245024	+	0.0277124i	−0.00245024	+	0.00277124i
$11$	−5.71885	+	1.00839i	−0.519896	+	0.0916716i	−0.427437	−	0.904045i	$-0.640584\pi$
$11$	−5.71885	+	1.00839i	−0.519896	+	0.0916716i	−0.0924582	+	0.995717i	$0.529472\pi$
$12$		0			0
$13$	6.99816	−	2.54712i	0.538320	−	0.195933i	−0.0585294	−	0.998286i	$-0.518641\pi$
$13$	6.99816	−	2.54712i	0.538320	−	0.195933i	0.596850	+	0.802353i	$0.296419\pi$
$14$	0.205861	+	1.37451i	0.0147044	+	0.0981792i
$15$		0			0
$16$	−9.38837	+	12.9560i	−0.586773	+	0.809752i
$17$	4.38388	−	7.59310i	0.257875	−	0.446653i	−0.707797	−	0.706416i	$-0.750311\pi$
$17$	4.38388	−	7.59310i	0.257875	−	0.446653i	0.965672	+	0.259763i	$0.0836444\pi$
$18$		0			0
$19$	17.1217	−	9.88523i	0.901143	−	0.520275i	0.0235724	−	0.999722i	$-0.492496\pi$
$19$	17.1217	−	9.88523i	0.901143	−	0.520275i	0.877571	+	0.479447i	$0.159163\pi$
$20$	0.0707361	−	0.0216746i	0.00353681	−	0.00108373i
$21$		0			0
$22$	10.8073	+	4.25322i	0.491243	+	0.193328i
$23$	−7.15027	+	8.52136i	−0.310881	+	0.370494i	−0.898749	−	0.438463i	$-0.855523\pi$
$23$	−7.15027	+	8.52136i	−0.310881	+	0.370494i	0.587868	+	0.808957i	$0.299967\pi$
$24$		0			0
$25$	23.4920	+	8.55039i	0.939680	+	0.342015i
$26$	−14.5965	−	2.96494i	−0.561404	−	0.114036i
$27$		0			0
$28$	1.08451	−	2.55939i	0.0387324	−	0.0914067i
$29$	21.1363	+	7.69297i	0.728837	+	0.265275i	0.679672	−	0.733516i	$-0.262122\pi$
$29$	21.1363	+	7.69297i	0.728837	+	0.265275i	0.0491643	+	0.998791i	$0.484344\pi$
$30$		0			0
$31$	20.2667	−	24.1529i	0.653765	−	0.779126i	−0.332712	−	0.943029i	$-0.607964\pi$
$31$	20.2667	−	24.1529i	0.653765	−	0.779126i	0.986477	+	0.163902i	$0.0524081\pi$
$32$	29.5450	−	12.2921i	0.923280	−	0.384127i
$33$		0			0
$34$	−15.4079	+	8.37204i	−0.453173	+	0.246236i
$35$	−0.0111310	+	0.00642647i	−0.000318028	+	0.000183614i
$36$		0			0
$37$	26.7594	−	46.3486i	0.723227	−	1.25267i	−0.236473	−	0.971638i	$-0.575991\pi$
$37$	26.7594	−	46.3486i	0.723227	−	1.25267i	0.959700	−	0.281028i	$-0.0906753\pi$
$38$	−39.5277	−	1.02270i	−1.04020	−	0.0269132i
$39$		0			0
$40$	−0.143286	−	0.0369130i	−0.00358216	−	0.000922825i
$41$	52.8679	−	19.2423i	1.28946	−	0.469325i	0.395910	−	0.918289i	$-0.370429\pi$
$41$	52.8679	−	19.2423i	1.28946	−	0.469325i	0.893550	+	0.448964i	$0.148207\pi$
$42$		0			0
$43$	−70.5871	+	12.4464i	−1.64156	+	0.289452i	−0.916740	−	0.399485i	$-0.869189\pi$
$43$	−70.5871	+	12.4464i	−1.64156	+	0.289452i	−0.724822	+	0.688936i	$0.758078\pi$
$44$	−13.9907	−	18.5422i	−0.317971	−	0.421414i
$45$		0			0
$46$	21.0958	−	7.06589i	0.458605	−	0.153606i
$47$	−43.9159	−	52.3369i	−0.934381	−	1.11355i	−0.993332	−	0.115291i	$-0.963220\pi$
$47$	−43.9159	−	52.3369i	−0.934381	−	1.11355i	0.0589506	−	0.998261i	$-0.481225\pi$
$48$		0			0
$49$	8.42490	−	47.7800i	0.171937	−	0.975102i
$50$	−31.1375	−	39.1201i	−0.622751	−	0.782403i
$51$		0			0
$52$	21.7991	+	20.3025i	0.419214	+	0.390433i
$53$	41.1446			0.776313			0.388156	−	0.921594i	$-0.373112\pi$
$53$	41.1446			0.776313			0.388156	+	0.921594i	$0.373112\pi$
$54$		0			0
$55$			0.107405i			0.00195282i
$56$	−4.52293	+	3.23258i	−0.0807666	+	0.0577246i
$57$		0			0
$58$	−28.0151	−	35.1972i	−0.483019	−	0.606849i
$59$	50.0926	+	8.83268i	0.849027	+	0.149706i	0.581200	−	0.813761i	$-0.302583\pi$
$59$	50.0926	+	8.83268i	0.849027	+	0.149706i	0.267827	+	0.963467i	$0.413694\pi$
$60$		0			0
$61$	28.9297	−	24.2749i	0.474258	−	0.397949i	−0.374087	−	0.927394i	$-0.622044\pi$
$61$	28.9297	−	24.2749i	0.474258	−	0.397949i	0.848345	+	0.529444i	$0.177599\pi$
$62$	−59.7939	+	20.0275i	−0.964417	+	0.323025i
$63$		0			0
$64$	−63.2307	−	9.89320i	−0.987980	−	0.154581i
$65$	−0.0239186	−	0.135649i	−0.000367979	−	0.00208691i
$66$		0			0
$67$	−14.8206	−	40.7193i	−0.221203	−	0.607751i	0.778601	−	0.627519i	$-0.215930\pi$
$67$	−14.8206	−	40.7193i	−0.221203	−	0.607751i	−0.999805	+	0.0197678i	$0.993707\pi$
$68$	35.0241	+	1.81357i	0.515060	+	0.0266702i
$69$		0			0
$70$	0.0256973		0.000664867i	0.000367104		9.49810e-6i
$71$	49.5059	+	28.5822i	0.697266	+	0.402567i	0.806328	−	0.591468i	$-0.201451\pi$
$71$	49.5059	+	28.5822i	0.697266	+	0.402567i	−0.109062	+	0.994035i	$0.534785\pi$
$72$		0			0
$73$	14.6051	+	25.2968i	0.200070	+	0.346532i	0.948551	−	0.316625i	$-0.102550\pi$
$73$	14.6051	+	25.2968i	0.200070	+	0.346532i	−0.748481	+	0.663157i	$0.769216\pi$
$74$	−94.0505	+	51.1033i	−1.27095	+	0.690586i
$75$		0			0
$76$	66.3505	+	43.0296i	0.873033	+	0.566179i
$77$	3.09133	+	2.59394i	0.0401472	+	0.0336875i
$78$		0			0
$79$	−46.0077	+	126.405i	−0.582376	+	1.60007i	0.201731	+	0.979441i	$0.435343\pi$
$79$	−46.0077	+	126.405i	−0.582376	+	1.60007i	−0.784107	+	0.620625i	$0.786879\pi$
$80$	0.205836	+	0.212617i	0.00257295	+	0.00265771i
$81$		0			0
$82$	−110.270	−	22.3987i	−1.34475	−	0.273155i
$83$	49.0991	−	134.899i	0.591555	−	1.62528i	−0.176064	−	0.984379i	$-0.556337\pi$
$83$	49.0991	−	134.899i	0.591555	−	1.62528i	0.767619	−	0.640906i	$-0.221441\pi$
$84$		0			0
$85$	−0.124225	−	0.104237i	−0.00146148	−	0.00122632i
$86$	133.394	+	52.4970i	1.55109	+	0.610431i
$87$		0			0
$88$	4.49604	+	46.2385i	0.0510914	+	0.525438i
$89$	29.5539	+	51.1889i	0.332067	+	0.575156i	0.982917	−	0.184050i	$-0.0589208\pi$
$89$	29.5539	+	51.1889i	0.332067	+	0.575156i	−0.650850	+	0.759206i	$0.725587\pi$
$90$		0			0
$91$	−4.48191	−	2.58763i	−0.0492518	−	0.0284355i
$92$	−43.3612	−	9.98217i	−0.471318	−	0.108502i
$93$		0			0
$94$	20.2392	+	135.135i	0.215311	+	1.43760i
$95$	−0.125065	−	0.343614i	−0.00131648	−	0.00361699i
$96$		0			0
$97$	6.63733	+	37.6422i	0.0684261	+	0.388064i	0.999717	+	0.0237874i	$0.00757248\pi$
$97$	6.63733	+	37.6422i	0.0684261	+	0.388064i	−0.931291	+	0.364276i	$0.881316\pi$
$98$	−64.2741	+	72.6944i	−0.655858	+	0.741780i
$99$		0			0
$100$	12.2488	+	99.2456i	0.122488	+	0.992456i
$101$	−103.239	+	86.6279i	−1.02217	+	0.857702i	−0.989899	−	0.141777i	$-0.954718\pi$
$101$	−103.239	+	86.6279i	−1.02217	+	0.857702i	−0.0322707	+	0.999479i	$0.510274\pi$
$102$		0			0
$103$	48.5344	+	8.55793i	0.471208	+	0.0830867i	0.404210	−	0.914666i	$-0.367547\pi$
$103$	48.5344	+	8.55793i	0.471208	+	0.0830867i	0.0669984	+	0.997753i	$0.478658\pi$
$104$	−15.9755	−	57.3965i	−0.153610	−	0.551890i
$105$		0			0
$106$	−70.1765	−	42.9740i	−0.662042	−	0.405415i
$107$			171.403i			1.60189i	0.598736	+	0.800946i	$0.295670\pi$
$107$			171.403i			1.60189i	−0.598736	+	0.800946i	$0.704330\pi$
$108$		0			0
$109$	−117.306			−1.07620			−0.538100	−	0.842881i	$-0.680858\pi$
$109$	−117.306			−1.07620			−0.538100	+	0.842881i	$0.680858\pi$
$110$	0.112181	−	0.183191i	0.00101983	−	0.00166537i
$111$		0			0
$112$	11.0907	−	0.789474i	0.0990237	−	0.00704888i
$113$	−5.87247	+	33.3044i	−0.0519687	+	0.294729i	−0.999704	−	0.0243284i	$-0.992255\pi$
$113$	−5.87247	+	33.3044i	−0.0519687	+	0.294729i	0.947735	+	0.319058i	$0.103366\pi$
$114$		0			0
$115$	0.132248	+	0.157608i	0.00114999	+	0.00137050i
$116$	11.0205	+	89.2934i	0.0950047	+	0.769771i
$117$		0			0
$118$	−76.2129	−	67.3850i	−0.645872	−	0.571059i
$119$	−6.00032	+	1.05802i	−0.0504229	+	0.00889091i
$120$		0			0
$121$	−82.0144	+	29.8508i	−0.677805	+	0.246701i
$122$	−74.6970	+	11.1874i	−0.612270	+	0.0917002i
$123$		0			0
$124$	122.903	+	28.2934i	0.991153	+	0.228173i
$125$	0.462387	−	0.800877i	0.00369909	−	0.00640702i
$126$		0			0
$127$	168.353	−	97.1989i	1.32562	−	0.765346i	0.340999	−	0.940064i	$-0.389235\pi$
$127$	168.353	−	97.1989i	1.32562	−	0.765346i	0.984618	+	0.174718i	$0.0559014\pi$
$128$	97.5137	+	82.9161i	0.761826	+	0.647782i
$129$		0			0
$130$	−0.100885	+	0.256347i	−0.000776039	+	0.00197190i
$131$	−57.8214	+	68.9089i	−0.441385	+	0.526022i	−0.940171	−	0.340703i	$-0.889335\pi$
$131$	−57.8214	+	68.9089i	−0.441385	+	0.526022i	0.498786	+	0.866725i	$0.333779\pi$
$132$		0			0
$133$	−12.9103	−	4.69897i	−0.0970701	−	0.0353306i
$134$	−17.2517	+	84.9308i	−0.128744	+	0.633812i
$135$		0			0
$136$	−57.8431	−	39.6746i	−0.425317	−	0.291725i
$137$	56.4129	+	20.5326i	0.411773	+	0.149873i	0.539596	−	0.841924i	$-0.318577\pi$
$137$	56.4129	+	20.5326i	0.411773	+	0.149873i	−0.127823	+	0.991797i	$0.540799\pi$
$138$		0			0
$139$	57.0172	−	67.9505i	0.410196	−	0.488852i	−0.520905	−	0.853615i	$-0.674405\pi$
$139$	57.0172	−	67.9505i	0.410196	−	0.488852i	0.931101	+	0.364762i	$0.118850\pi$
$140$	−0.0431351	−	0.0279739i	−0.000308108	−	0.000199814i
$141$		0			0
$142$	−54.5845	−	100.457i	−0.384398	−	0.707445i
$143$	−37.4530	+	21.6235i	−0.261909	+	0.151213i
$144$		0			0
$145$	0.208008	−	0.360281i	0.00143454	−	0.00248470i
$146$	1.51101	−	58.4009i	0.0103494	−	0.400006i
$147$		0			0
$148$	213.789	+	11.0701i	1.44452	+	0.0747982i
$149$	−132.507	+	48.2287i	−0.889310	+	0.323682i	−0.745961	−	0.665990i	$-0.768009\pi$
$149$	−132.507	+	48.2287i	−0.889310	+	0.323682i	−0.143349	+	0.989672i	$0.545787\pi$
$150$		0			0
$151$	−94.7076	+	16.6995i	−0.627203	+	0.110593i	−0.478210	−	0.878246i	$-0.658714\pi$
$151$	−94.7076	+	16.6995i	−0.627203	+	0.110593i	−0.148993	+	0.988838i	$0.547603\pi$
$152$	−68.2251	−	142.692i	−0.448849	−	0.938765i
$153$		0			0
$154$	−2.56333	−	7.65302i	−0.0166450	−	0.0496950i
$155$	−0.374845	−	0.446722i	−0.00241835	−	0.00288208i
$156$		0			0
$157$	14.7220	−	83.4925i	0.0937706	−	0.531799i	−0.901347	−	0.433099i	$-0.857420\pi$
$157$	14.7220	−	83.4925i	0.0937706	−	0.531799i	0.995117	−	0.0987008i	$-0.0314687\pi$
$158$	210.497	−	167.544i	1.33226	−	1.06041i
$159$		0			0
$160$	−0.129005	−	0.577628i	−0.000806281	−	0.00361018i
$161$	7.73018			0.0480135
$162$		0			0
$163$			61.7577i			0.378882i	0.981892	+	0.189441i	$0.0606675\pi$
$163$			61.7577i			0.378882i	−0.981892	+	0.189441i	$0.939332\pi$
$164$	164.682	+	153.376i	1.00416	+	0.935220i
$165$		0			0
$166$	−224.640	+	178.802i	−1.35326	+	1.07712i
$167$	−295.731	−	52.1454i	−1.77085	−	0.312248i	−0.809404	−	0.587252i	$-0.800210\pi$
$167$	−295.731	−	52.1454i	−1.77085	−	0.312248i	−0.961443	+	0.275004i	$0.911321\pi$
$168$		0			0
$169$	−86.9751	+	72.9808i	−0.514645	+	0.431839i
$170$	0.103007	+	0.307537i	0.000605926	+	0.00180904i
$171$		0			0
$172$	−172.686	−	228.864i	−1.00399	−	1.33061i
$173$	−53.1023	−	301.158i	−0.306950	−	1.74080i	−0.614183	−	0.789163i	$-0.710514\pi$
$173$	−53.1023	−	301.158i	−0.306950	−	1.74080i	0.307234	−	0.951634i	$-0.400597\pi$
$174$		0			0
$175$	−5.94183	−	16.3250i	−0.0339533	−	0.0932860i
$176$	40.6260	−	83.5607i	0.230829	−	0.474777i
$177$		0			0
$178$	3.05758	−	118.176i	0.0171774	−	0.663911i
$179$	187.706	+	108.372i	1.04864	+	0.605431i	0.922267	−	0.386553i	$-0.126334\pi$
$179$	187.706	+	108.372i	1.04864	+	0.605431i	0.126369	+	0.991983i	$0.459668\pi$
$180$		0			0
$181$	15.1790	+	26.2908i	0.0838619	+	0.145253i	0.904906	−	0.425612i	$-0.139941\pi$
$181$	15.1790	+	26.2908i	0.0838619	+	0.145253i	−0.821044	+	0.570865i	$0.806608\pi$
$182$	4.94169	+	9.09468i	0.0271522	+	0.0499708i
$183$		0			0
$184$	63.5312	+	62.3149i	0.345278	+	0.338668i
$185$	−0.758278	−	0.636271i	−0.00409880	−	0.00343930i
$186$		0			0
$187$	−17.4140	+	47.8444i	−0.0931227	+	0.255853i
$188$	106.623	−	251.626i	0.567145	−	1.33844i
$189$		0			0
$190$	−0.145580	+	0.716697i	−0.000766212	+	0.00377209i
$191$	93.0062	−	255.533i	0.486944	−	1.33787i	−0.416491	−	0.909140i	$-0.636740\pi$
$191$	93.0062	−	255.533i	0.486944	−	1.33787i	0.903434	−	0.428727i	$-0.141038\pi$
$192$		0			0
$193$	203.137	+	170.452i	1.05252	+	0.883172i	0.993357	−	0.115076i	$-0.0367113\pi$
$193$	203.137	+	170.452i	1.05252	+	0.883172i	0.0591665	+	0.998248i	$0.481156\pi$
$194$	27.9952	−	71.1352i	0.144305	−	0.366676i
$195$		0			0
$196$	185.553	−	56.8561i	0.946699	−	0.290082i
$197$	−84.4497	−	146.271i	−0.428678	−	0.742493i	0.568078	−	0.822975i	$-0.307687\pi$
$197$	−84.4497	−	146.271i	−0.428678	−	0.742493i	−0.996756	+	0.0804822i	$0.974354\pi$
$198$		0			0
$199$	104.097	+	60.1006i	0.523102	+	0.302013i	0.738203	−	0.674579i	$-0.235675\pi$
$199$	104.097	+	60.1006i	0.523102	+	0.302013i	−0.215101	+	0.976592i	$0.569008\pi$
$200$	82.7668	−	182.067i	0.413834	−	0.910337i
$201$		0			0
$202$	266.565	−	39.9236i	1.31963	−	0.197642i
$203$	−5.34600	−	14.6880i	−0.0263350	−	0.0723547i
$204$		0			0
$205$	−0.180694	−	1.02477i	−0.000881435	−	0.00499887i
$206$	−73.8422	−	65.2889i	−0.358457	−	0.316936i
$207$		0			0
$208$	−32.7007	+	114.582i	−0.157215	+	0.550873i
$209$	−87.9484	+	73.7975i	−0.420806	+	0.353098i
$210$		0			0
$211$	−273.456	−	48.2177i	−1.29600	−	0.228520i	−0.517239	−	0.855841i	$-0.673040\pi$
$211$	−273.456	−	48.2177i	−1.29600	−	0.228520i	−0.778761	+	0.627321i	$0.784151\pi$
$212$	74.8087	+	146.594i	0.352871	+	0.691479i
$213$		0			0
$214$	179.024	−	292.345i	0.836559	−	1.36610i
$215$			1.32569i			0.00616600i
$216$		0			0
$217$	−21.9104			−0.100970
$218$	200.078	+	122.522i	0.917788	+	0.562026i
$219$		0			0
$220$	−0.382673	+	0.195283i	−0.00173942	+	0.000887651i
$221$	11.3385	−	64.3040i	0.0513056	−	0.290968i
$222$		0			0
$223$	23.5366	+	28.0498i	0.105545	+	0.125784i	0.816231	−	0.577726i	$-0.196060\pi$
$223$	23.5366	+	28.0498i	0.105545	+	0.125784i	−0.710686	+	0.703510i	$0.751615\pi$
$224$	−19.7409	−	10.2373i	−0.0881289	−	0.0457020i
$225$		0			0
$226$	44.8014	−	50.6707i	0.198236	−	0.224206i
$227$	−33.4702	+	5.90171i	−0.147446	+	0.0259987i	−0.246884	−	0.969045i	$-0.579407\pi$
$227$	−33.4702	+	5.90171i	−0.147446	+	0.0259987i	0.0994379	+	0.995044i	$0.468296\pi$
$228$		0			0
$229$	−285.636	+	103.963i	−1.24732	+	0.453986i	−0.879494	−	0.475909i	$-0.842119\pi$
$229$	−285.636	+	103.963i	−1.24732	+	0.453986i	−0.367823	+	0.929896i	$0.619897\pi$
$230$	−0.0609485	−	0.406945i	−0.000264993	−	0.00176933i
$231$		0			0
$232$	74.4671	−	163.810i	0.320979	−	0.706078i
$233$	49.9878	−	86.5815i	0.214540	−	0.371594i	−0.738590	−	0.674155i	$-0.764508\pi$
$233$	49.9878	−	86.5815i	0.214540	−	0.371594i	0.953130	+	0.302560i	$0.0978414\pi$
$234$		0			0
$235$	−1.09434	+	0.631819i	−0.00465678	+	0.00268859i
$236$	59.6081	+	194.534i	0.252577	+	0.824297i
$237$		0			0
$238$	11.3392	+	4.46255i	0.0476439	+	0.0187502i
$239$	−83.2205	+	99.1783i	−0.348203	+	0.414972i	−0.911511	−	0.411275i	$-0.865084\pi$
$239$	−83.2205	+	99.1783i	−0.348203	+	0.414972i	0.563309	+	0.826247i	$0.309528\pi$
$240$		0			0
$241$	55.8840	+	20.3401i	0.231884	+	0.0843987i	0.455349	−	0.890313i	$-0.349515\pi$
$241$	55.8840	+	20.3401i	0.231884	+	0.0843987i	−0.223465	+	0.974712i	$0.571737\pi$
$242$	171.062	+	34.7473i	0.706869	+	0.143584i
$243$		0			0
$244$	139.089	+	58.9370i	0.570035	+	0.241545i
$245$	−0.843235	−	0.306912i	−0.00344178	−	0.00125270i
$246$		0			0
$247$	94.6417	−	112.790i	0.383165	−	0.456638i
$248$	−180.073	−	176.625i	−0.726099	−	0.712198i
$249$		0			0
$250$	−1.62514	+	0.883035i	−0.00650055	+	0.00353214i
$251$	178.915	−	103.297i	0.712810	−	0.411541i	−0.0992905	−	0.995058i	$-0.531657\pi$
$251$	178.915	−	103.297i	0.712810	−	0.411541i	0.812101	+	0.583517i	$0.198324\pi$
$252$		0			0
$253$	32.2985	−	55.9427i	0.127662	−	0.221117i
$254$	−388.665	−	10.0560i	−1.53018	−	0.0395904i
$255$		0			0
$256$	−79.7171	−	243.272i	−0.311395	−	0.950281i
$257$	−5.94379	+	2.16336i	−0.0231276	+	0.00841775i	−0.353558	−	0.935413i	$-0.615028\pi$
$257$	−5.94379	+	2.16336i	−0.0231276	+	0.00841775i	0.330430	+	0.943830i	$0.392806\pi$
$258$		0			0
$259$	−36.6262	+	6.45820i	−0.141414	+	0.0249351i
$260$	0.439815	−	0.331856i	0.00169160	−	0.00127637i
$261$		0			0
$262$	170.593	−	57.1391i	0.651120	−	0.218088i
$263$	110.483	+	131.668i	0.420087	+	0.500640i	0.934035	−	0.357181i	$-0.116262\pi$
$263$	110.483	+	131.668i	0.420087	+	0.500640i	−0.513948	+	0.857821i	$0.671818\pi$
$264$		0			0
$265$	0.132145	−	0.749432i	0.000498661	−	0.00282805i
$266$	17.1120	+	21.4990i	0.0643310	+	0.0808232i
$267$		0			0
$268$	118.132	−	126.840i	0.440790	−	0.473283i
$269$	−219.984			−0.817785			−0.408893	−	0.912582i	$-0.634085\pi$
$269$	−219.984			−0.817785			−0.408893	+	0.912582i	$0.634085\pi$
$270$		0			0
$271$			250.774i			0.925365i	0.886524	+	0.462682i	$0.153113\pi$
$271$			250.774i			0.925365i	−0.886524	+	0.462682i	$0.846887\pi$
$272$	57.2189	+	128.084i	0.210364	+	0.470898i
$273$		0			0
$274$	−74.7727	−	93.9419i	−0.272893	−	0.342853i
$275$	−142.969	−	25.2094i	−0.519889	−	0.0916704i
$276$		0			0
$277$	25.4939	−	21.3919i	0.0920358	−	0.0772272i	−0.595609	−	0.803275i	$-0.703089\pi$
$277$	25.4939	−	21.3919i	0.0920358	−	0.0772272i	0.687645	+	0.726047i	$0.258645\pi$
$278$	−168.221	+	56.3444i	−0.605111	+	0.202678i
$279$		0			0
$280$	0.0443537	+	0.0927655i	0.000158406	+	0.000331305i
$281$	−27.5612	−	156.307i	−0.0980826	−	0.556254i	−0.993759	−	0.111548i	$-0.964419\pi$
$281$	−27.5612	−	156.307i	−0.0980826	−	0.556254i	0.895677	−	0.444706i	$-0.146692\pi$
$282$		0			0
$283$	−120.497	−	331.063i	−0.425785	−	1.16984i	−0.948347	−	0.317234i	$-0.897246\pi$
$283$	−120.497	−	331.063i	−0.425785	−	1.16984i	0.522562	−	0.852601i	$-0.324976\pi$
$284$	−11.8242	+	228.352i	−0.0416346	+	0.804056i
$285$		0			0
$286$	86.4650	+	2.23711i	0.302325	+	0.00782207i
$287$	−33.8588	−	19.5484i	−0.117975	−	0.0681128i
$288$		0			0
$289$	106.063	+	183.707i	0.367001	+	0.635664i
$290$	−0.731081	+	0.397240i	−0.00252097	+	0.00136979i
$291$		0			0
$292$	−63.5748	+	98.0308i	−0.217722	+	0.335722i
$293$	−21.2865	−	17.8615i	−0.0726503	−	0.0609608i	0.605739	−	0.795663i	$-0.292877\pi$
$293$	−21.2865	−	17.8615i	−0.0726503	−	0.0609608i	−0.678390	+	0.734702i	$0.737322\pi$
$294$		0			0
$295$	0.321767	−	0.884049i	0.00109074	−	0.00299678i
$296$	−353.077	−	242.176i	−1.19283	−	0.818162i
$297$		0			0
$298$	276.378	+	56.1398i	0.927444	+	0.188389i
$299$	−28.3338	+	77.8465i	−0.0947619	+	0.260356i
$300$		0			0
$301$	38.1560	+	32.0167i	0.126764	+	0.106368i
$302$	178.976	+	70.4359i	0.592636	+	0.233231i
$303$		0			0
$304$	−32.6717	+	314.636i	−0.107473	+	1.03499i
$305$	−0.349243	−	0.604907i	−0.00114506	−	0.00198330i
$306$		0			0
$307$	345.391	+	199.412i	1.12505	+	0.649549i	0.942686	−	0.333681i	$-0.108291\pi$
$307$	345.391	+	199.412i	1.12505	+	0.649549i	0.182366	+	0.983231i	$0.441624\pi$
$308$	−3.62128	+	15.7304i	−0.0117574	+	0.0510726i
$309$		0			0
$310$	0.172752	+	1.15344i	0.000557265	+	0.00372079i
$311$	82.2845	+	226.075i	0.264580	+	0.726928i	0.998844	+	0.0480643i	$0.0153052\pi$
$311$	82.2845	+	226.075i	0.264580	+	0.726928i	−0.734264	+	0.678864i	$0.762473\pi$
$312$		0			0
$313$	21.6287	+	122.662i	0.0691012	+	0.391892i	0.999668	+	0.0257700i	$0.00820376\pi$
$313$	21.6287	+	122.662i	0.0691012	+	0.391892i	−0.930567	+	0.366122i	$0.880685\pi$
$314$	−112.315	+	127.029i	−0.357690	+	0.404550i
$315$		0			0
$316$	−534.019	+	65.9083i	−1.68993	+	0.208570i
$317$	−300.212	+	251.908i	−0.947043	+	0.794663i	−0.978797	−	0.204833i	$-0.934335\pi$
$317$	−300.212	+	251.908i	−0.947043	+	0.794663i	0.0317545	+	0.999496i	$0.489891\pi$
$318$		0			0
$319$	−128.633	−	22.6814i	−0.403237	−	0.0711016i
$320$	−0.383280	+	1.11995i	−0.00119775	+	0.00349984i
$321$		0			0
$322$	−13.1847	−	8.07390i	−0.0409461	−	0.0250742i
$323$		−	173.343i		−	0.536664i
$324$		0			0
$325$	186.180			0.572861
$326$	64.5037	−	105.334i	0.197864	−	0.323112i
$327$		0			0
$328$	−120.687	−	433.604i	−0.367949	−	1.32196i
$329$	−8.24440	+	46.7563i	−0.0250590	+	0.142117i
$330$		0			0
$331$	30.9734	+	36.9126i	0.0935751	+	0.111518i	0.810800	−	0.585323i	$-0.199032\pi$
$331$	30.9734	+	36.9126i	0.0935751	+	0.111518i	−0.717225	+	0.696842i	$0.754588\pi$
$332$	569.900	−	70.3368i	1.71657	−	0.211858i
$333$		0			0
$334$	449.938	+	397.820i	1.34712	+	1.19108i
$335$	−0.789286	+	0.139172i	−0.00235608	+	0.000415440i
$336$		0			0
$337$	−534.338	+	194.483i	−1.58557	+	0.577101i	−0.976406	−	0.215941i	$-0.930718\pi$
$337$	−534.338	+	194.483i	−1.58557	+	0.577101i	−0.609166	+	0.793043i	$0.708496\pi$
$338$	224.571	−	33.6342i	0.664411	−	0.0995093i
$339$		0			0
$340$	0.145521	−	0.632125i	0.000428004	−	0.00185919i
$341$	−91.5468	+	158.564i	−0.268466	+	0.464996i
$342$		0			0
$343$	−58.6875	+	33.8833i	−0.171101	+	0.0987850i
$344$	55.4942	+	570.717i	0.161320	+	1.65906i
$345$		0			0
$346$	−223.977	+	569.121i	−0.647332	+	1.64486i
$347$	−74.5764	+	88.8767i	−0.214918	+	0.256129i	−0.862723	−	0.505677i	$-0.831243\pi$
$347$	−74.5764	+	88.8767i	−0.214918	+	0.256129i	0.647805	+	0.761806i	$0.275687\pi$
$348$		0			0
$349$	−155.510	−	56.6009i	−0.445587	−	0.162180i	0.109475	−	0.993990i	$-0.465083\pi$
$349$	−155.510	−	56.6009i	−0.445587	−	0.162180i	−0.555062	+	0.831809i	$0.687305\pi$
$350$	−6.91649	+	34.0501i	−0.0197614	+	0.0972861i
$351$		0			0
$352$	−156.568	+	100.089i	−0.444796	+	0.284345i
$353$	603.473	+	219.646i	1.70956	+	0.622227i	0.996855	−	0.0792417i	$-0.0252499\pi$
$353$	603.473	+	219.646i	1.70956	+	0.622227i	0.712700	+	0.701469i	$0.247472\pi$
$354$		0			0
$355$	0.679613	−	0.809932i	0.00191440	−	0.00228150i
$356$	−128.646	+	198.369i	−0.361365	+	0.557215i
$357$		0			0
$358$	−206.962	−	380.892i	−0.578106	−	1.06394i
$359$	284.704	−	164.374i	0.793046	−	0.457866i	−0.0479875	−	0.998848i	$-0.515281\pi$
$359$	284.704	−	164.374i	0.793046	−	0.457866i	0.841034	+	0.540982i	$0.181947\pi$
$360$		0			0
$361$	14.9356	−	25.8692i	0.0413728	−	0.0716599i
$362$	1.57038	−	60.6957i	0.00433807	−	0.167668i
$363$		0			0
$364$	1.07048	−	20.6734i	0.00294089	−	0.0567950i
$365$	0.507679	−	0.184780i	0.00139090	−	0.000506246i
$366$		0			0
$367$	108.149	−	19.0695i	0.294683	−	0.0519605i	−0.0243522	−	0.999703i	$-0.507752\pi$
$367$	108.149	−	19.0695i	0.294683	−	0.0519605i	0.319035	+	0.947743i	$0.396641\pi$
$368$	−43.2736	−	172.641i	−0.117591	−	0.469133i
$369$		0			0
$370$	0.628762	+	1.87722i	0.00169936	+	0.00507357i
$371$	−18.3787	−	21.9029i	−0.0495383	−	0.0590374i
$372$		0			0
$373$	121.587	−	689.555i	0.325971	−	1.84867i	−0.176792	−	0.984248i	$-0.556572\pi$
$373$	121.587	−	689.555i	0.325971	−	1.84867i	0.502763	−	0.864425i	$-0.332317\pi$
$374$	79.6732	−	63.4156i	0.213030	−	0.169560i
$375$		0			0
$376$	−444.672	+	317.811i	−1.18264	+	0.845242i
$377$	167.510			0.444323
$378$		0			0
$379$			138.113i			0.364413i	0.983260	+	0.182207i	$0.0583239\pi$
$379$			138.113i			0.364413i	−0.983260	+	0.182207i	$0.941676\pi$
$380$	0.996866	−	1.07035i	0.00262333	−	0.00281671i
$381$		0			0
$382$	−425.527	+	338.696i	−1.11394	+	0.886640i
$383$	−37.4599	−	6.60520i	−0.0978067	−	0.0172460i	0.124531	−	0.992216i	$-0.460257\pi$
$383$	−37.4599	−	6.60520i	−0.0978067	−	0.0172460i	−0.222337	+	0.974970i	$0.571369\pi$
$384$		0			0
$385$	0.0571760	−	0.0479764i	0.000148509	−	0.000124614i
$386$	−168.441	−	502.894i	−0.436375	−	1.30283i
$387$		0			0
$388$	−122.047	+	92.0887i	−0.314554	+	0.237342i
$389$	7.82254	+	44.3639i	0.0201094	+	0.114046i	0.993210	−	0.116334i	$-0.0371143\pi$
$389$	7.82254	+	44.3639i	0.0201094	+	0.114046i	−0.973101	+	0.230380i	$0.926003\pi$
$390$		0			0
$391$	33.3576	+	91.6493i	0.0853136	+	0.234397i
$392$	−375.865	−	96.8291i	−0.958838	−	0.247013i
$393$		0			0
$394$	−8.73695	+	337.686i	−0.0221750	+	0.857070i
$395$	2.15466	+	1.24399i	0.00545483	+	0.00314935i
$396$		0			0
$397$	−348.887	−	604.290i	−0.878809	−	1.52214i	−0.852649	−	0.522484i	$-0.825006\pi$
$397$	−348.887	−	604.290i	−0.878809	−	1.52214i	−0.0261596	−	0.999658i	$-0.508328\pi$
$398$	−114.776	−	211.234i	−0.288382	−	0.530738i
$399$		0			0
$400$	−331.330	+	224.089i	−0.828326	+	0.560222i
$401$	462.311	+	387.925i	1.15289	+	0.967394i	0.999783	−	0.0208151i	$-0.00662614\pi$
$401$	462.311	+	387.925i	1.15289	+	0.967394i	0.153112	+	0.988209i	$0.451071\pi$
$402$		0			0
$403$	80.3092	−	220.648i	0.199279	−	0.547513i
$404$	−496.354	−	210.324i	−1.22860	−	0.520603i
$405$		0			0
$406$	−6.22292	+	30.6357i	−0.0153274	+	0.0754573i
$407$	−106.296	+	292.045i	−0.261169	+	0.717555i
$408$		0			0
$409$	512.307	+	429.876i	1.25258	+	1.05104i	0.996431	+	0.0844058i	$0.0268992\pi$
$409$	512.307	+	429.876i	1.25258	+	1.05104i	0.256152	+	0.966637i	$0.417545\pi$
$410$	−0.762140	+	1.93658i	−0.00185888	+	0.00472337i
$411$		0			0
$412$	57.7539	+	188.483i	0.140179	+	0.457482i
$413$	−17.6737	−	30.6117i	−0.0427934	−	0.0741204i
$414$		0			0
$415$	−2.29943	−	1.32758i	−0.00554080	−	0.00319898i
$416$	175.451	−	161.277i	0.421757	−	0.387684i
$417$		0			0
$418$	227.084	−	34.0106i	0.543264	−	0.0813650i
$419$	−114.302	−	314.043i	−0.272798	−	0.749507i	−0.998131	−	0.0611085i	$-0.980536\pi$
$419$	−114.302	−	314.043i	−0.272798	−	0.749507i	0.725333	−	0.688398i	$-0.241686\pi$
$420$		0			0
$421$	−86.2197	−	488.976i	−0.204797	−	1.16146i	−0.897758	−	0.440488i	$-0.854805\pi$
$421$	−86.2197	−	488.976i	−0.204797	−	1.16146i	0.692961	−	0.720975i	$-0.256306\pi$
$422$	416.047	+	367.855i	0.985893	+	0.871695i
$423$		0			0
$424$	25.5175	−	328.166i	0.0601828	−	0.773977i
$425$	167.910	−	140.893i	0.395082	−	0.331513i
$426$		0			0
$427$	−25.8450	−	4.55717i	−0.0605269	−	0.0106725i
$428$	−610.688	+	311.642i	−1.42684	+	0.728136i
$429$		0			0
$430$	1.38464	−	2.26111i	0.00322008	−	0.00525839i
$431$		−	406.367i		−	0.942847i	−0.881907	−	0.471424i	$-0.843740\pi$
$431$		−	406.367i		−	0.942847i	0.881907	−	0.471424i	$-0.156260\pi$
$432$		0			0
$433$	313.745			0.724584			0.362292	−	0.932065i	$-0.381994\pi$
$433$	313.745			0.724584			0.362292	+	0.932065i	$0.381994\pi$
$434$	37.3705	+	22.8846i	0.0861072	+	0.0527295i
$435$		0			0
$436$	−213.284	−	417.948i	−0.489184	−	0.958596i
$437$	−38.1893	+	216.583i	−0.0873898	+	0.495612i
$438$		0			0
$439$	−291.034	−	346.841i	−0.662948	−	0.790070i	0.324858	−	0.945763i	$-0.394683\pi$
$439$	−291.034	−	346.841i	−0.662948	−	0.790070i	−0.987806	+	0.155693i	$0.950239\pi$
$440$	0.856656	+	0.0666118i	0.00194695	+	0.000151390i
$441$		0			0
$442$	−86.5023	+	97.8347i	−0.195706	+	0.221345i
$443$	−230.762	+	40.6896i	−0.520908	+	0.0918502i	−0.427919	−	0.903817i	$-0.640753\pi$
$443$	−230.762	+	40.6896i	−0.520908	+	0.0918502i	−0.0929890	+	0.995667i	$0.529642\pi$
$444$		0			0
$445$	1.02730	−	0.373908i	0.00230855	−	0.000840243i
$446$	−10.8472	−	72.4251i	−0.0243210	−	0.162388i
$447$		0			0
$448$	22.9777	+	38.0794i	0.0512896	+	0.0849986i
$449$	80.2533	−	139.003i	0.178738	−	0.309583i	−0.762711	−	0.646740i	$-0.776132\pi$
$449$	80.2533	−	139.003i	0.178738	−	0.309583i	0.941449	+	0.337157i	$0.109465\pi$
$450$		0			0
$451$	−282.940	+	163.355i	−0.627361	+	0.362207i
$452$	−129.337	+	39.6308i	−0.286144	+	0.0876788i
$453$		0			0
$454$	63.2512	+	24.8925i	0.139320	+	0.0548292i
$455$	−0.0615274	+	0.0733255i	−0.000135225	+	0.000161155i
$456$		0			0
$457$	85.8747	+	31.2559i	0.187910	+	0.0683935i	0.434261	−	0.900787i	$-0.357010\pi$
$457$	85.8747	+	31.2559i	0.187910	+	0.0683935i	−0.246351	+	0.969181i	$0.579232\pi$
$458$	595.768	+	121.016i	1.30080	+	0.264228i
$459$		0			0
$460$	−0.321086	+	0.757747i	−0.000698012	+	0.00164728i
$461$	124.007	+	45.1350i	0.268997	+	0.0979068i	0.472997	−	0.881064i	$-0.343172\pi$
$461$	124.007	+	45.1350i	0.268997	+	0.0979068i	−0.204000	+	0.978971i	$0.565394\pi$
$462$		0			0
$463$	−143.224	+	170.688i	−0.309339	+	0.368656i	−0.898207	−	0.439574i	$-0.855130\pi$
$463$	−143.224	+	170.688i	−0.309339	+	0.368656i	0.588867	+	0.808230i	$0.299574\pi$
$464$	−298.105	+	201.617i	−0.642468	+	0.434520i
$465$		0			0
$466$	−175.691	+	95.4635i	−0.377019	+	0.204857i
$467$	−385.006	+	222.284i	−0.824425	+	0.475982i	−0.851940	−	0.523639i	$-0.824574\pi$
$467$	−385.006	+	222.284i	−0.824425	+	0.475982i	0.0275151	+	0.999621i	$0.491241\pi$
$468$		0			0
$469$	−15.0563	+	26.0783i	−0.0321031	+	0.0556042i
$470$	2.52643	+	0.0653664i	0.00537538	+	0.000139077i
$471$		0			0
$472$	101.516	−	394.057i	0.215076	−	0.834866i
$473$	391.127	−	142.358i	0.826906	−	0.300969i
$474$		0			0
$475$	486.746	−	85.8264i	1.02473	−	0.180687i
$476$	−14.6793	−	19.4548i	−0.0308389	−	0.0408714i
$477$		0			0
$478$	245.530	−	82.2384i	0.513660	−	0.172047i
$479$	365.461	+	435.539i	0.762966	+	0.909268i	0.998032	−	0.0627117i	$-0.0199749\pi$
$479$	365.461	+	435.539i	0.762966	+	0.909268i	−0.235065	+	0.971980i	$0.575530\pi$
$480$		0			0
$481$	69.2109	−	392.515i	0.143890	−	0.816039i
$482$	−74.0716	−	93.0610i	−0.153675	−	0.193073i
$483$		0			0
$484$	−255.473	−	237.934i	−0.527837	−	0.491599i
$485$	0.706954			0.00145764
$486$		0			0
$487$		−	927.501i		−	1.90452i	−0.305288	−	0.952260i	$-0.598753\pi$
$487$		−	927.501i		−	1.90452i	0.305288	−	0.952260i	$-0.401247\pi$
$488$	−175.673	−	245.796i	−0.359985	−	0.503681i
$489$		0			0
$490$	1.11767	+	1.40420i	0.00228096	+	0.00286572i
$491$	538.209	+	94.9007i	1.09615	+	0.193281i	0.692346	−	0.721566i	$-0.256577\pi$
$491$	538.209	+	94.9007i	1.09615	+	0.193281i	0.403802	+	0.914846i	$0.367688\pi$
$492$		0			0
$493$	151.072	−	126.765i	0.306435	−	0.257129i
$494$	−279.226	+	93.5249i	−0.565235	+	0.189322i
$495$		0			0
$496$	122.655	+	489.332i	0.247287	+	0.986557i
$497$	−6.89813	−	39.1212i	−0.0138795	−	0.0787147i
$498$		0			0
$499$	263.489	+	723.929i	0.528034	+	1.45076i	0.861382	+	0.507957i	$0.169599\pi$
$499$	263.489	+	723.929i	0.528034	+	1.45076i	−0.333349	+	0.942804i	$0.608179\pi$
$500$	3.69414	+	0.191285i	0.00738829	+	0.000382571i
$501$		0			0
$502$	−413.049	−	10.6868i	−0.822807	−	0.0212885i
$503$	−367.090	−	211.939i	−0.729801	−	0.421351i	0.0885483	−	0.996072i	$-0.471777\pi$
$503$	−367.090	−	211.939i	−0.729801	−	0.421351i	−0.818349	+	0.574721i	$0.805111\pi$
$504$		0			0
$505$	1.24632	+	2.15868i	0.00246795	+	0.00427462i
$506$	−113.519	+	61.6816i	−0.224345	+	0.121900i
$507$		0			0
$508$	652.407	+	423.099i	1.28427	+	0.832871i
$509$	−530.899	−	445.477i	−1.04302	−	0.875200i	−0.0506806	−	0.998715i	$-0.516139\pi$
$509$	−530.899	−	445.477i	−1.04302	−	0.875200i	−0.992343	+	0.123514i	$0.960583\pi$
$510$		0			0
$511$	6.94259	−	19.0746i	0.0135863	−	0.0373280i
$512$	−118.123	+	498.188i	−0.230708	+	0.973023i
$513$		0			0
$514$	12.3973	+	2.51823i	0.0241193	+	0.00489928i
$515$	0.311758	−	0.856549i	0.000605356	−	0.00166320i
$516$		0			0
$517$	303.925	+	255.023i	0.587862	+	0.493275i
$518$	69.2153	+	27.2396i	0.133620	+	0.0525862i
$519$		0			0
$520$	−1.09676	+	0.106645i	−0.00210916	+	0.000205086i
$521$	304.376	+	527.195i	0.584215	+	1.01189i	0.994973	+	0.100145i	$0.0319308\pi$
$521$	304.376	+	527.195i	0.584215	+	1.01189i	−0.410758	+	0.911744i	$0.634736\pi$
$522$		0			0
$523$	−522.353	−	301.581i	−0.998762	−	0.576636i	−0.0908806	−	0.995862i	$-0.528968\pi$
$523$	−522.353	−	301.581i	−0.998762	−	0.576636i	−0.907882	+	0.419226i	$0.862301\pi$
$524$	−350.645	−	80.7218i	−0.669170	−	0.154049i
$525$		0			0
$526$	−50.9175	−	339.970i	−0.0968013	−	0.646330i
$527$	−94.5487	−	259.770i	−0.179409	−	0.492923i
$528$		0			0
$529$	70.3727	+	399.103i	0.133030	+	0.754448i
$530$	−1.00814	+	1.14022i	−0.00190216	+	0.00215135i
$531$		0			0
$532$	−6.73150	−	54.5417i	−0.0126532	−	0.102522i
$533$	320.965	−	269.322i	0.602186	−	0.505294i
$534$		0			0
$535$	3.12203	+	0.550498i	0.00583557	+	0.00102897i
$536$	−333.966	+	92.9544i	−0.623071	+	0.173422i
$537$		0			0
$538$	375.207	+	229.766i	0.697410	+	0.427074i
$539$			281.742i			0.522713i
$540$		0			0
$541$	406.606			0.751582			0.375791	−	0.926705i	$-0.377371\pi$
$541$	406.606			0.751582			0.375791	+	0.926705i	$0.377371\pi$
$542$	261.924	−	427.722i	0.483255	−	0.789154i
$543$		0			0
$544$	36.1866	−	278.225i	0.0665194	−	0.511442i
$545$	−0.376754	+	2.13668i	−0.000691292	+	0.00392051i
$546$		0			0
$547$	342.420	+	408.080i	0.625996	+	0.746032i	0.982089	−	0.188418i	$-0.0603359\pi$
$547$	342.420	+	408.080i	0.625996	+	0.746032i	−0.356093	+	0.934450i	$0.615892\pi$
$548$	29.4140	+	238.325i	0.0536751	+	0.434900i
$549$		0			0
$550$	217.519	+	192.324i	0.395490	+	0.349679i
$551$	437.936	−	77.2199i	0.794802	−	0.140145i
$552$		0			0
$553$	87.8415	−	31.9717i	0.158845	−	0.0578150i
$554$	−65.8257	+	9.85876i	−0.118819	+	0.0177956i
$555$		0			0
$556$	345.768	+	79.5992i	0.621885	+	0.143164i
$557$	−42.5317	+	73.6671i	−0.0763586	+	0.132257i	−0.901676	−	0.432412i	$-0.857663\pi$
$557$	−42.5317	+	73.6671i	−0.0763586	+	0.132257i	0.825318	+	0.564669i	$0.190996\pi$
$558$		0			0
$559$	−462.278	+	266.896i	−0.826973	+	0.477453i
$560$	0.0212402	−	0.204547i	3.79289e−5	−	0.000365263i
$561$		0			0
$562$	−116.249	+	295.386i	−0.206848	+	0.525597i
$563$	670.430	−	798.988i	1.19082	−	1.41916i	0.306758	−	0.951788i	$-0.400756\pi$
$563$	670.430	−	798.988i	1.19082	−	1.41916i	0.884060	−	0.467373i	$-0.154800\pi$
$564$		0			0
$565$	0.587766	+	0.213929i	0.00104029	+	0.000378636i
$566$	−140.263	+	690.519i	−0.247814	+	1.22000i
$567$		0			0
$568$	258.673	−	377.129i	0.455410	−	0.663959i
$569$	−233.686	−	85.0548i	−0.410696	−	0.149481i	0.128406	−	0.991722i	$-0.459014\pi$
$569$	−233.686	−	85.0548i	−0.410696	−	0.149481i	−0.539102	+	0.842241i	$0.681236\pi$
$570$		0			0
$571$	4.43075	−	5.28036i	0.00775963	−	0.00924757i	−0.762151	−	0.647400i	$-0.775856\pi$
$571$	4.43075	−	5.28036i	0.00775963	−	0.00924757i	0.769910	+	0.638152i	$0.220301\pi$
$572$	−145.139	−	94.1252i	−0.253739	−	0.164555i
$573$		0			0
$574$	37.3322	+	68.7061i	0.0650387	+	0.119697i
$575$	−240.835	+	139.046i	−0.418844	+	0.241819i
$576$		0			0
$577$	−489.126	+	847.191i	−0.847705	+	1.46827i	0.0355453	+	0.999368i	$0.488683\pi$
$577$	−489.126	+	847.191i	−0.847705	+	1.46827i	−0.883251	+	0.468901i	$0.844650\pi$
$578$	10.9730	−	424.111i	0.0189845	−	0.733756i
$579$		0			0
$580$	1.66184	+	0.0860512i	0.00286524	+	0.000148364i
$581$	−93.7437	+	34.1199i	−0.161349	+	0.0587262i
$582$		0			0
$583$	−235.300	+	41.4897i	−0.403602	+	0.0711659i
$584$	210.823	−	100.800i	0.360999	−	0.172604i
$585$		0			0
$586$	17.6508	+	52.6978i	0.0301207	+	0.0899279i
$587$	−222.285	−	264.909i	−0.378680	−	0.451293i	0.542717	−	0.839915i	$-0.317395\pi$
$587$	−222.285	−	264.909i	−0.378680	−	0.451293i	−0.921397	+	0.388623i	$0.872951\pi$
$588$		0			0
$589$	108.244	−	613.881i	0.183775	−	1.04224i
$590$	−1.47217	+	1.17177i	−0.00249520	+	0.00198604i
$591$		0			0
$592$	349.267	+	781.833i	0.589978	+	1.32066i
$593$	555.768			0.937214			0.468607	−	0.883407i	$-0.344756\pi$
$593$	555.768			0.937214			0.468607	+	0.883407i	$0.344756\pi$
$594$		0			0
$595$			0.112691i			0.000189397i
$596$	−412.757	−	384.420i	−0.692545	−	0.644999i
$597$		0			0
$598$	129.634	−	103.182i	0.216780	−	0.172545i
$599$	873.003	+	153.934i	1.45743	+	0.256985i	0.845522	−	0.533941i	$-0.179290\pi$
$599$	873.003	+	153.934i	1.45743	+	0.256985i	0.611912	+	0.790926i	$0.290401\pi$
$600$		0			0
$601$	417.266	−	350.128i	0.694287	−	0.582576i	−0.225855	−	0.974161i	$-0.572518\pi$
$601$	417.266	−	350.128i	0.694287	−	0.582576i	0.920142	+	0.391585i	$0.128073\pi$
$602$	−31.6389	−	94.4604i	−0.0525563	−	0.156911i
$603$		0			0
$604$	−231.695	−	307.070i	−0.383601	−	0.508394i
$605$	0.280313	+	1.58973i	0.000463327	+	0.00262766i
$606$		0			0
$607$	334.605	+	919.318i	0.551243	+	1.51453i	0.832015	+	0.554753i	$0.187187\pi$
$607$	334.605	+	919.318i	0.551243	+	1.51453i	−0.280772	+	0.959775i	$0.590590\pi$
$608$	384.351	−	502.520i	0.632156	−	0.826514i
$609$		0			0
$610$	−0.0361319	+	1.39651i	−5.92326e−5	+	0.00228935i
$611$	−440.639	−	254.403i	−0.721177	−	0.416372i
$612$		0			0
$613$	113.985	+	197.428i	0.185947	+	0.322069i	0.943895	−	0.330245i	$-0.107132\pi$
$613$	113.985	+	197.428i	0.185947	+	0.322069i	−0.757949	+	0.652314i	$0.773798\pi$
$614$	−380.823	−	700.866i	−0.620233	−	1.14148i
$615$		0			0
$616$	22.6063	−	23.0475i	0.0366985	−	0.0374148i
$617$	−490.000	−	411.159i	−0.794165	−	0.666384i	0.152607	−	0.988287i	$-0.451233\pi$
$617$	−490.000	−	411.159i	−0.794165	−	0.666384i	−0.946773	+	0.321903i	$0.895677\pi$
$618$		0			0
$619$	294.399	−	808.856i	0.475605	−	1.30671i	−0.437584	−	0.899178i	$-0.644166\pi$
$619$	294.399	−	808.856i	0.475605	−	1.30671i	0.913189	−	0.407536i	$-0.133612\pi$
$620$	0.910084	−	2.14776i	0.00146788	−	0.00346412i
$621$		0			0
$622$	95.7819	−	471.538i	0.153990	−	0.758099i
$623$	14.0486	−	38.5981i	0.0225498	−	0.0619552i
$624$		0			0
$625$	478.758	+	401.726i	0.766013	+	0.642761i
$626$	91.2264	−	231.804i	0.145729	−	0.370294i
$627$		0			0
$628$	324.242	−	99.3525i	0.516309	−	0.158205i
$629$	−234.620	−	406.373i	−0.373004	−	0.646063i
$630$		0			0
$631$	−901.462	−	520.459i	−1.42862	−	0.824817i	−0.431612	−	0.902059i	$-0.642055\pi$
$631$	−901.462	−	520.459i	−1.42862	−	0.824817i	−0.997012	+	0.0772427i	$0.975388\pi$
$632$	979.665	+	445.350i	1.55010	+	0.704667i
$633$		0			0
$634$	775.154	−	116.095i	1.22264	−	0.183116i
$635$	−1.22973	−	3.37867i	−0.00193659	−	0.00532073i
$636$		0			0
$637$	−62.7427	−	355.831i	−0.0984972	−	0.558605i
$638$	195.707	+	173.038i	0.306750	+	0.271219i
$639$		0			0
$640$	1.82347	−	1.50987i	0.00284917	−	0.00235917i
$641$	−207.258	+	173.910i	−0.323336	+	0.271311i	−0.789978	−	0.613135i	$-0.789908\pi$
$641$	−207.258	+	173.910i	−0.323336	+	0.271311i	0.466642	+	0.884446i	$0.345464\pi$
$642$		0			0
$643$	326.145	+	57.5082i	0.507224	+	0.0894373i	0.421403	−	0.906873i	$-0.361538\pi$
$643$	326.145	+	57.5082i	0.507224	+	0.0894373i	0.0858206	+	0.996311i	$0.472649\pi$
$644$	14.0549	+	27.5418i	0.0218244	+	0.0427667i
$645$		0			0
$646$	−181.050	+	295.654i	−0.280263	+	0.457669i
$647$			302.985i			0.468293i	0.972201	+	0.234146i	$0.0752295\pi$
$647$			302.985i			0.468293i	−0.972201	+	0.234146i	$0.924771\pi$
$648$		0			0
$649$	−295.379			−0.455129
$650$	−317.549	−	194.458i	−0.488537	−	0.299166i
$651$		0			0
$652$	−220.036	+	112.287i	−0.337478	+	0.172220i
$653$	108.363	−	614.557i	0.165946	−	0.941129i	−0.782137	−	0.623107i	$-0.785870\pi$
$653$	108.363	−	614.557i	0.165946	−	0.941129i	0.948083	−	0.318022i	$-0.103019\pi$
$654$		0			0
$655$	1.06944	+	1.27451i	0.00163273	+	0.00194582i
$656$	−247.039	+	865.611i	−0.376584	+	1.31953i
$657$		0			0
$658$	62.8970	−	71.1370i	0.0955882	−	0.108111i
$659$	−969.694	+	170.983i	−1.47146	+	0.259459i	−0.851161	−	0.524904i	$-0.824101\pi$
$659$	−969.694	+	170.983i	−1.47146	+	0.259459i	−0.620302	+	0.784363i	$0.712990\pi$
$660$		0			0
$661$	−708.366	+	257.824i	−1.07166	+	0.390052i	−0.816797	−	0.576926i	$-0.804252\pi$
$661$	−708.366	+	257.824i	−1.07166	+	0.390052i	−0.254862	+	0.966978i	$0.582030\pi$
$662$	−14.2745	−	95.3090i	−0.0215627	−	0.143971i
$663$		0			0
$664$	−1045.49	−	475.274i	−1.57453	−	0.715773i
$665$	−0.127054	+	0.220065i	−0.000191059	+	0.000330924i
$666$		0			0
$667$	−216.685	+	125.103i	−0.324864	+	0.187561i
$668$	−351.908	−	1148.47i	−0.526808	−	1.71926i
$669$		0			0
$670$	1.49157	+	0.587007i	0.00222623	+	0.000876130i
$671$	−140.966	+	167.997i	−0.210084	+	0.250368i
$672$		0			0
$673$	120.292	+	43.7828i	0.178740	+	0.0650562i	0.429840	−	0.902905i	$-0.358570\pi$
$673$	120.292	+	43.7828i	0.178740	+	0.0650562i	−0.251100	+	0.967961i	$0.580792\pi$
$674$	1114.50	+	226.385i	1.65356	+	0.335883i
$675$		0			0
$676$	−418.160	−	177.190i	−0.618579	−	0.262115i
$677$	−795.059	−	289.378i	−1.17439	−	0.427441i	−0.320170	−	0.947360i	$-0.603740\pi$
$677$	−795.059	−	289.378i	−1.17439	−	0.427441i	−0.854216	+	0.519919i	$0.825962\pi$
$678$		0			0
$679$	17.0736	−	20.3475i	0.0251452	−	0.0299669i
$680$	−0.908434	+	0.926165i	−0.00133593	+	0.00136201i
$681$		0			0
$682$	321.757	−	174.830i	0.471784	−	0.256349i
$683$	−709.493	+	409.626i	−1.03879	+	0.599745i	−0.919490	−	0.393113i	$-0.871398\pi$
$683$	−709.493	+	409.626i	−1.03879	+	0.599745i	−0.119299	+	0.992858i	$0.538065\pi$
$684$		0			0
$685$	0.555176	−	0.961594i	0.000810476	−	0.00140379i
$686$	135.488	+	3.50548i	0.197504	+	0.00511003i
$687$		0			0
$688$	501.442	−	1031.38i	0.728840	−	1.49910i
$689$	287.936	−	104.800i	0.417905	−	0.152105i
$690$		0			0
$691$	540.831	−	95.3631i	0.782679	−	0.138007i	0.231990	−	0.972718i	$-0.425476\pi$
$691$	540.831	−	95.3631i	0.782679	−	0.138007i	0.550689	+	0.834711i	$0.314365\pi$
$692$	976.443	−	736.760i	1.41104	−	1.06468i
$693$		0			0
$694$	220.027	−	73.6964i	0.317041	−	0.106191i
$695$	−1.05457	−	1.25678i	−0.00151736	−	0.00180832i
$696$		0			0
$697$	85.6573	−	485.787i	0.122894	−	0.696968i
$698$	206.121	+	258.963i	0.295302	+	0.371008i
$699$		0			0
$700$	47.3610	−	50.8521i	0.0676585	−	0.0726459i
$701$	−378.016			−0.539253			−0.269626	−	0.962965i	$-0.586900\pi$
$701$	−378.016			−0.539253			−0.269626	+	0.962965i	$0.586900\pi$
$702$		0			0
$703$		−	1058.09i		−	1.50511i
$704$	371.583	−	7.18337i	0.527817	−	0.0102036i
$705$		0			0
$706$	−799.875	−	1004.94i	−1.13297	−	1.42342i
$707$	92.2309	+	16.2628i	0.130454	+	0.0230025i
$708$		0			0
$709$	−658.239	+	552.328i	−0.928404	+	0.779024i	−0.975530	−	0.219865i	$-0.929438\pi$
$709$	−658.239	+	552.328i	−0.928404	+	0.779024i	0.0471258	+	0.998889i	$0.484994\pi$
$710$	−2.00510	+	0.671594i	−0.00282408	+	0.000945906i
$711$		0			0
$712$	426.608	−	203.973i	0.599169	−	0.286479i
$713$	60.9033	+	345.400i	0.0854184	+	0.484432i
$714$		0			0
$715$	0.273574	+	0.751639i	0.000382621	+	0.00105124i
$716$	−44.8326	+	865.817i	−0.0626154	+	1.20924i
$717$		0			0
$718$	−657.275	−	17.0057i	−0.915425	−	0.0236848i
$719$	−464.412	−	268.129i	−0.645914	−	0.372919i	0.140975	−	0.990013i	$-0.454976\pi$
$719$	−464.412	−	268.129i	−0.645914	−	0.372919i	−0.786889	+	0.617094i	$0.788310\pi$
$720$		0			0
$721$	−17.1239	−	29.6595i	−0.0237502	−	0.0411366i
$722$	−52.4937	+	28.5230i	−0.0727060	+	0.0395056i
$723$		0			0
$724$	−66.0729	+	101.883i	−0.0912609	+	0.140722i
$725$	430.755	+	361.446i	0.594145	+	0.498547i
$726$		0			0
$727$	−169.632	+	466.059i	−0.233331	+	0.641071i	−1.00000		0.000971702i	$-0.999691\pi$
$727$	−169.632	+	466.059i	−0.233331	+	0.641071i	0.766669	+	0.642043i	$0.221913\pi$
$728$	−23.4184	+	34.1426i	−0.0321681	+	0.0468991i
$729$		0			0
$730$	−1.05890	−	0.215090i	−0.00145054	−	0.000294644i
$731$	−214.938	+	590.539i	−0.294033	+	0.807850i
$732$		0			0
$733$	246.754	+	207.051i	0.336635	+	0.282471i	0.795397	−	0.606089i	$-0.207262\pi$
$733$	246.754	+	207.051i	0.336635	+	0.282471i	−0.458762	+	0.888559i	$0.651707\pi$
$734$	−204.376	−	80.4322i	−0.278442	−	0.109581i
$735$		0			0
$736$	−106.509	+	339.655i	−0.144714	+	0.461488i
$737$	125.818	+	217.923i	0.170716	+	0.295689i
$738$		0			0
$739$	163.942	+	94.6517i	0.221842	+	0.128081i	0.606803	−	0.794852i	$-0.292452\pi$
$739$	163.942	+	94.6517i	0.221842	+	0.128081i	−0.384961	+	0.922933i	$0.625785\pi$
$740$	0.888269	−	3.85852i	0.00120036	−	0.00521422i
$741$		0			0
$742$	8.47007	+	56.5536i	0.0114152	+	0.0762178i
$743$	215.502	+	592.087i	0.290043	+	0.796886i	0.996059	+	0.0886907i	$0.0282683\pi$
$743$	215.502	+	592.087i	0.290043	+	0.796886i	−0.706016	+	0.708196i	$0.749509\pi$
$744$		0			0
$745$	0.452889	+	2.56846i	0.000607905	+	0.00344760i
$746$	−927.595	+	1049.12i	−1.24343	+	1.40632i
$747$		0			0
$748$	−202.126	+	24.9463i	−0.270222	+	0.0333507i
$749$	91.2443	−	76.5631i	0.121821	−	0.102220i
$750$		0			0
$751$	1238.93	+	218.457i	1.64971	+	0.290888i	0.919721	−	0.392572i	$-0.128415\pi$
$751$	1238.93	+	218.457i	1.64971	+	0.290888i	0.729988	+	0.683460i	$0.239526\pi$
$752$	1090.38	−	77.6172i	1.44997	−	0.103214i
$753$		0			0
$754$	−285.706	−	174.958i	−0.378921	−	0.232040i
$755$			1.77869i			0.00235589i
$756$		0			0
$757$	−1329.08			−1.75572			−0.877859	−	0.478919i	$-0.841029\pi$
$757$	−1329.08			−1.75572			−0.877859	+	0.478919i	$0.841029\pi$
$758$	144.254	−	235.566i	0.190308	−	0.310773i
$759$		0			0
$760$	−2.81820	+	0.784405i	−0.00370816	+	0.00103211i
$761$	−42.4342	+	240.656i	−0.0557611	+	0.316237i	−0.999912	−	0.0132768i	$-0.995774\pi$
$761$	−42.4342	+	240.656i	−0.0557611	+	0.316237i	0.944151	+	0.329514i	$0.106885\pi$
$762$		0			0
$763$	52.3989	+	62.4465i	0.0686748	+	0.0818434i
$764$	1079.54	−	133.236i	1.41301	−	0.174392i
$765$		0			0
$766$	56.9931	+	50.3914i	0.0744035	+	0.0657852i
$767$	373.054	−	65.7795i	0.486381	−	0.0857621i
$768$		0			0
$769$	−706.569	+	257.170i	−0.918815	+	0.334421i	−0.757767	−	0.652525i	$-0.773710\pi$
$769$	−706.569	+	257.170i	−0.918815	+	0.334421i	−0.161048	+	0.986947i	$0.551487\pi$
$770$	−0.147629	+	0.0221106i	−0.000191727	+	2.87150e-5i
$771$		0			0
$772$	−237.961	+	1033.67i	−0.308239	+	1.33895i
$773$	−152.659	+	264.413i	−0.197489	+	0.342061i	−0.947714	−	0.319122i	$-0.896612\pi$
$773$	−152.659	+	264.413i	−0.197489	+	0.342061i	0.750225	+	0.661183i	$0.229945\pi$
$774$		0			0
$775$	682.622	−	394.112i	0.880803	−	0.508532i
$776$	304.348	−	29.5935i	0.392200	−	0.0381359i
$777$		0			0
$778$	32.9943	−	83.8377i	0.0424091	−	0.107760i
$779$	714.974	−	852.073i	0.917810	−	1.09380i
$780$		0			0
$781$	−311.939	−	113.536i	−0.399410	−	0.145373i
$782$	38.8294	−	191.159i	0.0496540	−	0.244448i
$783$		0			0
$784$	539.943	+	557.729i	0.688703	+	0.711390i
$785$	−1.47350	−	0.536310i	−0.00187707	−	0.000683197i
$786$		0			0
$787$	−160.331	+	191.075i	−0.203724	+	0.242789i	−0.858227	−	0.513271i	$-0.828434\pi$
$787$	−160.331	+	191.075i	−0.203724	+	0.242789i	0.654503	+	0.756060i	$0.272878\pi$
$788$	367.602	−	566.833i	0.466500	−	0.719332i
$789$		0			0
$790$	−2.37569	−	4.37222i	−0.00300721	−	0.00553446i
$791$	20.3524	−	11.7505i	0.0257300	−	0.0148552i
$792$		0			0
$793$	140.624	−	243.567i	0.177331	−	0.307147i
$794$	−36.0950	+	1395.08i	−0.0454597	+	1.75703i
$795$		0			0
$796$	−24.8631	+	480.162i	−0.0312351	+	0.603218i
$797$	−1423.05	+	517.950i	−1.78551	+	0.649874i	−0.786016	+	0.618207i	$0.787859\pi$
$797$	−1423.05	+	517.950i	−1.78551	+	0.649874i	−0.999498	+	0.0316673i	$0.989918\pi$
$798$		0			0
$799$	−589.921	+	104.019i	−0.738325	+	0.130187i
$800$	799.172	−	36.1445i	0.998965	−	0.0451806i
$801$		0			0
$802$	−383.347	−	1144.51i	−0.477989	−	1.42708i
$803$	−109.033	−	129.941i	−0.135783	−	0.161820i
$804$		0			0
$805$	0.0248272	−	0.140802i	3.08413e−5	−	0.000174910i
$806$	−367.435	+	292.458i	−0.455874	+	0.362852i
$807$		0			0
$808$	626.909	+	877.153i	0.775878	+	1.08559i
$809$	−1163.03			−1.43761			−0.718806	−	0.695211i	$-0.755311\pi$
$809$	−1163.03			−1.43761			−0.718806	+	0.695211i	$0.755311\pi$
$810$		0			0
$811$			888.115i			1.09509i	0.836777	+	0.547543i	$0.184437\pi$
$811$			888.115i			1.09509i	−0.836777	+	0.547543i	$0.815563\pi$
$812$	42.6117	−	45.7528i	0.0524775	−	0.0563458i
$813$		0			0
$814$	486.329	−	387.092i	0.597456	−	0.475543i
$815$	1.12489	+	0.198349i	0.00138024	+	0.000243373i
$816$		0			0
$817$	−1085.54	+	910.874i	−1.32869	+	1.11490i
$818$	−424.803	−	1268.29i	−0.519320	−	1.55047i
$819$		0			0
$820$	3.32260	−	2.50702i	0.00405195	−	0.00305734i
$821$	167.273	+	948.650i	0.203742	+	1.15548i	0.899406	+	0.437113i	$0.143999\pi$
$821$	167.273	+	948.650i	0.203742	+	1.15548i	−0.695664	+	0.718367i	$0.744890\pi$
$822$		0			0
$823$	228.127	+	626.774i	0.277189	+	0.761572i	0.997678	+	0.0681051i	$0.0216953\pi$
$823$	228.127	+	626.774i	0.277189	+	0.761572i	−0.720489	+	0.693467i	$0.756082\pi$
$824$	98.3580	−	381.799i	0.119366	−	0.463349i
$825$		0			0
$826$	−1.82847	+	70.6711i	−0.00221365	+	0.0855582i
$827$	537.817	+	310.509i	0.650322	+	0.375464i	0.788580	−	0.614933i	$-0.210817\pi$
$827$	537.817	+	310.509i	0.650322	+	0.375464i	−0.138257	+	0.990396i	$0.544150\pi$
$828$		0			0
$829$	155.530	+	269.386i	0.187612	+	0.324953i	0.944453	−	0.328645i	$-0.106592\pi$
$829$	155.530	+	269.386i	0.187612	+	0.324953i	−0.756842	+	0.653598i	$0.773259\pi$
$830$	2.53532	+	4.66600i	0.00305460	+	0.00562169i
$831$		0			0
$832$	−467.698	+	91.8222i	−0.562137	+	0.110363i
$833$	−325.864	−	273.433i	−0.391194	−	0.328251i
$834$		0			0
$835$	−1.89962	+	5.21915i	−0.00227499	+	0.00625048i
$836$	−422.839	−	179.173i	−0.505789	−	0.214321i
$837$		0			0
$838$	−133.052	+	655.019i	−0.158773	+	0.781646i
$839$	−413.494	+	1136.06i	−0.492841	+	1.35407i	0.405228	+	0.914216i	$0.367192\pi$
$839$	−413.494	+	1136.06i	−0.492841	+	1.35407i	−0.898069	+	0.439854i	$0.855030\pi$
$840$		0			0
$841$	−256.684	−	215.383i	−0.305212	−	0.256104i
$842$	−363.661	+	924.055i	−0.431901	+	1.09745i
$843$		0			0
$844$	−325.401	−	1061.96i	−0.385546	−	1.25825i
$845$	1.04998	+	1.81861i	0.00124257	+	0.00215220i
$846$		0			0
$847$	52.5254	+	30.3256i	0.0620135	+	0.0358035i
$848$	−386.280	+	533.070i	−0.455519	+	0.628621i
$849$		0			0
$850$	−433.546	+	64.9325i	−0.510054	+	0.0763912i
$851$	203.617	+	559.432i	0.239267	+	0.657382i
$852$		0			0
$853$	185.373	+	1051.30i	0.217319	+	1.23248i	0.876837	+	0.480787i	$0.159649\pi$
$853$	185.373	+	1051.30i	0.217319	+	1.23248i	−0.659519	+	0.751688i	$0.729240\pi$
$854$	39.3216	+	34.7669i	0.0460440	+	0.0407106i
$855$		0			0
$856$	1367.09	+	106.302i	1.59707	+	0.124185i
$857$	518.525	−	435.094i	0.605047	−	0.507695i	−0.288017	−	0.957625i	$-0.592996\pi$
$857$	518.525	−	435.094i	0.605047	−	0.507695i	0.893063	+	0.449931i	$0.148551\pi$
$858$		0			0
$859$	−931.954	−	164.329i	−1.08493	−	0.191302i	−0.397535	−	0.917587i	$-0.630134\pi$
$859$	−931.954	−	164.329i	−1.08493	−	0.191302i	−0.687394	+	0.726285i	$0.741245\pi$
$860$	−4.72329	+	2.41036i	−0.00549220	+	0.00280274i
$861$		0			0
$862$	−424.436	+	693.103i	−0.492385	+	0.804064i
$863$		−	1407.68i		−	1.63114i	−0.578657	−	0.815571i	$-0.696423\pi$
$863$		−	1407.68i		−	1.63114i	0.578657	−	0.815571i	$-0.303577\pi$
$864$		0			0
$865$	−5.65602			−0.00653875
$866$	−535.125	−	327.695i	−0.617928	−	0.378401i
$867$		0			0
$868$	−39.8373	−	78.0643i	−0.0458955	−	0.0899359i
$869$	135.646	−	769.286i	0.156094	−	0.885255i
$870$		0			0
$871$	−207.434	−	247.211i	−0.238156	−	0.283824i
$872$	−72.7521	+	935.623i	−0.0834313	+	1.07296i
$873$		0			0
$874$	291.349	−	329.517i	0.333351	−	0.377022i
$875$	−0.632880	+	0.111594i	−0.000723291	+	0.000127536i
$876$		0			0
$877$	−289.362	+	105.319i	−0.329946	+	0.120090i	−0.501681	−	0.865053i	$-0.667285\pi$
$877$	−289.362	+	105.319i	−0.329946	+	0.120090i	0.171735	+	0.985143i	$0.445063\pi$
$878$	134.127	+	895.548i	0.152764	+	1.01999i
$879$		0			0
$880$	−1.39155	−	1.00836i	−0.00158130	−	0.00114586i
$881$	−308.635	+	534.572i	−0.350324	+	0.606778i	−0.986306	−	0.164925i	$-0.947262\pi$
$881$	−308.635	+	534.572i	−0.350324	+	0.606778i	0.635982	+	0.771704i	$0.280595\pi$
$882$		0			0
$883$	−244.263	+	141.025i	−0.276629	+	0.159712i	−0.631896	−	0.775053i	$-0.717723\pi$
$883$	−244.263	+	141.025i	−0.276629	+	0.159712i	0.355268	+	0.934765i	$0.384390\pi$
$884$	249.724	−	76.5190i	0.282493	−	0.0865599i
$885$		0			0
$886$	436.089	+	171.622i	0.492200	+	0.193705i
$887$	−224.634	+	267.708i	−0.253251	+	0.301813i	−0.877659	−	0.479285i	$-0.840896\pi$
$887$	−224.634	+	267.708i	−0.253251	+	0.301813i	0.624408	+	0.781099i	$0.285340\pi$
$888$		0			0
$889$	−126.944	−	46.2038i	−0.142794	−	0.0519728i
$890$	−2.14271	−	0.435242i	−0.00240754	−	0.000489036i
$891$		0			0
$892$	−57.1444	+	134.858i	−0.0640633	+	0.151186i
$893$	−1269.28	−	461.980i	−1.42136	−	0.517335i
$894$		0			0
$895$	2.57681	−	3.07093i	0.00287912	−	0.00343120i
$896$	0.581539	−	88.9478i	0.000649039	−	0.0992721i
$897$		0			0
$898$	−282.064	+	153.263i	−0.314103	+	0.170671i
$899$	614.170	−	354.591i	0.683170	−	0.394429i
$900$		0			0
$901$	180.373	−	312.415i	0.200192	−	0.346742i
$902$	653.203	+	16.9003i	0.724172	+	0.0187365i
$903$		0			0
$904$	261.991	+	67.4934i	0.289813	+	0.0746609i
$905$	0.527627	−	0.192041i	0.000583014	−	0.000212200i
$906$		0			0
$907$	268.404	−	47.3268i	0.295925	−	0.0521795i	−0.0237146	−	0.999719i	$-0.507549\pi$
$907$	268.404	−	47.3268i	0.295925	−	0.0521795i	0.319639	+	0.947539i	$0.396438\pi$
$908$	−81.8824	−	108.520i	−0.0901789	−	0.119516i
$909$		0			0
$910$	0.181527	−	0.0608013i	0.000199481	−	6.68146e-5i
$911$	−31.4750	−	37.5105i	−0.0345500	−	0.0411750i	0.748493	−	0.663143i	$-0.230778\pi$
$911$	−31.4750	−	37.5105i	−0.0345500	−	0.0411750i	−0.783043	+	0.621968i	$0.786333\pi$
$912$		0			0
$913$	−144.760	+	820.976i	−0.158555	+	0.899207i
$914$	−113.823	−	143.003i	−0.124533	−	0.156459i
$915$		0			0
$916$	−889.748	−	828.664i	−0.971341	−	0.904655i
$917$	62.5109			0.0681689
$918$		0			0
$919$			710.873i			0.773529i	0.922179	+	0.386764i	$0.126407\pi$
$919$			710.873i			0.773529i	−0.922179	+	0.386764i	$0.873593\pi$
$920$	1.33909	−	0.957057i	0.00145553	−	0.00104028i
$921$		0			0
$922$	−164.366	−	206.504i	−0.178271	−	0.223974i
$923$	419.253	+	73.9256i	0.454228	+	0.0800927i
$924$		0			0
$925$	1024.93	−	860.019i	1.10803	−	0.929750i
$926$	422.561	−	141.534i	0.456329	−	0.152844i
$927$		0			0
$928$	719.033	−	32.5200i	0.774820	−	0.0350431i
$929$	147.173	+	834.661i	0.158421	+	0.898451i	0.955591	+	0.294696i	$0.0952184\pi$
$929$	147.173	+	834.661i	0.158421	+	0.898451i	−0.797170	+	0.603755i	$0.793670\pi$
$930$		0			0
$931$	−328.068	−	901.358i	−0.352382	−	0.968161i
$932$	399.368	+	20.6795i	0.428506	+	0.0221884i
$933$		0			0
$934$	888.837	+	22.9969i	0.951645	+	0.0246220i
$935$	0.815538	+	0.470851i	0.000872234	+	0.000503584i
$936$		0			0
$937$	330.059	+	571.679i	0.352251	+	0.610116i	0.986643	−	0.162895i	$-0.0520831\pi$
$937$	330.059	+	571.679i	0.352251	+	0.610116i	−0.634393	+	0.773011i	$0.718750\pi$
$938$	52.9181	−	28.7536i	0.0564159	−	0.0306542i
$939$		0			0
$940$	−4.24082	−	2.75025i	−0.00451151	−	0.00292580i
$941$	711.987	+	597.428i	0.756628	+	0.634886i	0.937247	−	0.348667i	$-0.113366\pi$
$941$	711.987	+	597.428i	0.756628	+	0.634886i	−0.180619	+	0.983553i	$0.557810\pi$
$942$		0			0
$943$	−214.049	+	588.094i	−0.226987	+	0.623642i
$944$	−584.724	+	566.077i	−0.619411	+	0.599658i
$945$		0			0
$946$	−815.797	−	165.710i	−0.862364	−	0.175169i
$947$	196.604	−	540.164i	0.207607	−	0.570395i	−0.791565	−	0.611085i	$-0.790733\pi$
$947$	196.604	−	540.164i	0.207607	−	0.570395i	0.999172	+	0.0406899i	$0.0129556\pi$
$948$		0			0
$949$	166.643	+	139.830i	0.175599	+	0.147345i
$950$	−919.840	−	362.002i	−0.968253	−	0.381055i
$951$		0			0
$952$	4.71733	+	48.5143i	0.00495518	+	0.0509604i
$953$	−747.116	−	1294.04i	−0.783962	−	1.35786i	−0.929617	−	0.368527i	$-0.879862\pi$
$953$	−747.116	−	1294.04i	−0.783962	−	1.35786i	0.145655	−	0.989335i	$-0.453471\pi$
$954$		0			0
$955$	−4.35571	−	2.51477i	−0.00456095	−	0.00263327i
$956$	−504.672	−	116.180i	−0.527900	−	0.121528i
$957$		0			0
$958$	−168.428	−	1124.57i	−0.175812	−	1.17387i
$959$	−14.2685	−	39.2025i	−0.0148785	−	0.0408785i
$960$		0			0
$961$	−5.74824	−	32.5999i	−0.00598152	−	0.0339229i
$962$	−528.014	+	597.188i	−0.548871	+	0.620777i
$963$		0			0
$964$	29.1382	+	236.091i	0.0302263	+	0.244907i
$965$	3.75714	−	3.15261i	0.00389341	−	0.00326696i
$966$		0			0
$967$	−40.1386	−	7.07751i	−0.0415083	−	0.00731904i	0.152855	−	0.988249i	$-0.451153\pi$
$967$	−40.1386	−	7.07751i	−0.0415083	−	0.00731904i	−0.194364	+	0.980930i	$0.562264\pi$
$968$	187.223	+	672.654i	0.193412	+	0.694890i
$969$		0			0
$970$	−1.20579	−	0.738388i	−0.00124308	−	0.000761225i
$971$			1253.25i			1.29068i	0.763895	+	0.645341i	$0.223285\pi$
$971$			1253.25i			1.29068i	−0.763895	+	0.645341i	$0.776715\pi$
$972$		0			0
$973$	−61.6415			−0.0633520
$974$	−968.742	+	1581.95i	−0.994601	+	1.62418i
$975$		0			0
$976$	42.9036	+	602.716i	0.0439586	+	0.617537i
$977$	−87.2483	+	494.810i	−0.0893023	+	0.506458i	0.907043	+	0.421039i	$0.138334\pi$
$977$	−87.2483	+	494.810i	−0.0893023	+	0.506458i	−0.996345	+	0.0854199i	$0.972777\pi$
$978$		0			0
$979$	−220.633	−	262.940i	−0.225366	−	0.268580i
$980$	−0.439667	−	3.56238i	−0.000448639	−	0.00363508i
$981$		0			0
$982$	−818.852	−	724.003i	−0.833862	−	0.737274i
$983$	964.524	−	170.072i	0.981204	−	0.173013i	0.340035	−	0.940413i	$-0.389561\pi$
$983$	964.524	−	170.072i	0.981204	−	0.173013i	0.641169	+	0.767400i	$0.278450\pi$
$984$		0			0
$985$	−2.93550	+	1.06843i	−0.00298020	+	0.00108470i
$986$	−390.071	+	58.4212i	−0.395609	+	0.0592507i
$987$		0			0
$988$	573.933	+	132.125i	0.580904	+	0.133730i
$989$	398.657	−	690.494i	0.403091	−	0.698174i
$990$		0			0
$991$	574.931	−	331.937i	0.580153	−	0.334951i	−0.181041	−	0.983475i	$-0.557947\pi$
$991$	574.931	−	331.937i	0.580153	−	0.334951i	0.761194	+	0.648524i	$0.224613\pi$
$992$	301.890	−	962.717i	0.304324	−	0.970481i
$993$		0			0
$994$	−29.0952	+	73.9303i	−0.0292708	+	0.0743765i
$995$	1.42904	−	1.70306i	0.00143622	−	0.00171162i
$996$		0			0
$997$	147.082	+	53.5333i	0.147524	+	0.0536944i	0.414727	−	0.909946i	$-0.363877\pi$
$997$	147.082	+	53.5333i	0.147524	+	0.0536944i	−0.267203	+	0.963640i	$0.586099\pi$
$998$	306.710	−	1509.94i	0.307325	−	1.51297i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.307.5		204
3.2	odd	2		108.3.j.a.31.30	yes	204
4.3	odd	2	inner	324.3.j.a.307.3		204
12.11	even	2		108.3.j.a.31.32	yes	204
27.7	even	9	inner	324.3.j.a.19.3		204
27.20	odd	18		108.3.j.a.7.32	yes	204
108.7	odd	18	inner	324.3.j.a.19.5		204
108.47	even	18		108.3.j.a.7.30	✓	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.30	✓	204	108.47	even	18
108.3.j.a.7.32	yes	204	27.20	odd	18
108.3.j.a.31.30	yes	204	3.2	odd	2
108.3.j.a.31.32	yes	204	12.11	even	2
324.3.j.a.19.3		204	27.7	even	9	inner
324.3.j.a.19.5		204	108.7	odd	18	inner
324.3.j.a.307.3		204	4.3	odd	2	inner
324.3.j.a.307.5		204	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70561 - 1.04446i) q^{2} +(1.81819 + 3.56289i) q^{4} +(0.00321173 - 0.0182146i) q^{5} +(-0.446686 - 0.532339i) q^{7} +(0.620191 - 7.97592i) q^{8} +O(q^{10})\)	\(q+(-1.70561 - 1.04446i) q^{2} +(1.81819 + 3.56289i) q^{4} +(0.00321173 - 0.0182146i) q^{5} +(-0.446686 - 0.532339i) q^{7} +(0.620191 - 7.97592i) q^{8} +(-0.0245024 + 0.0277124i) q^{10} +(-5.71885 + 1.00839i) q^{11} +(6.99816 - 2.54712i) q^{13} +(0.205861 + 1.37451i) q^{14} +(-9.38837 + 12.9560i) q^{16} +(4.38388 - 7.59310i) q^{17} +(17.1217 - 9.88523i) q^{19} +(0.0707361 - 0.0216746i) q^{20} +(10.8073 + 4.25322i) q^{22} +(-7.15027 + 8.52136i) q^{23} +(23.4920 + 8.55039i) q^{25} +(-14.5965 - 2.96494i) q^{26} +(1.08451 - 2.55939i) q^{28} +(21.1363 + 7.69297i) q^{29} +(20.2667 - 24.1529i) q^{31} +(29.5450 - 12.2921i) q^{32} +(-15.4079 + 8.37204i) q^{34} +(-0.0111310 + 0.00642647i) q^{35} +(26.7594 - 46.3486i) q^{37} +(-39.5277 - 1.02270i) q^{38} +(-0.143286 - 0.0369130i) q^{40} +(52.8679 - 19.2423i) q^{41} +(-70.5871 + 12.4464i) q^{43} +(-13.9907 - 18.5422i) q^{44} +(21.0958 - 7.06589i) q^{46} +(-43.9159 - 52.3369i) q^{47} +(8.42490 - 47.7800i) q^{49} +(-31.1375 - 39.1201i) q^{50} +(21.7991 + 20.3025i) q^{52} +41.1446 q^{53} +0.107405i q^{55} +(-4.52293 + 3.23258i) q^{56} +(-28.0151 - 35.1972i) q^{58} +(50.0926 + 8.83268i) q^{59} +(28.9297 - 24.2749i) q^{61} +(-59.7939 + 20.0275i) q^{62} +(-63.2307 - 9.89320i) q^{64} +(-0.0239186 - 0.135649i) q^{65} +(-14.8206 - 40.7193i) q^{67} +(35.0241 + 1.81357i) q^{68} +(0.0256973 + 0.000664867i) q^{70} +(49.5059 + 28.5822i) q^{71} +(14.6051 + 25.2968i) q^{73} +(-94.0505 + 51.1033i) q^{74} +(66.3505 + 43.0296i) q^{76} +(3.09133 + 2.59394i) q^{77} +(-46.0077 + 126.405i) q^{79} +(0.205836 + 0.212617i) q^{80} +(-110.270 - 22.3987i) q^{82} +(49.0991 - 134.899i) q^{83} +(-0.124225 - 0.104237i) q^{85} +(133.394 + 52.4970i) q^{86} +(4.49604 + 46.2385i) q^{88} +(29.5539 + 51.1889i) q^{89} +(-4.48191 - 2.58763i) q^{91} +(-43.3612 - 9.98217i) q^{92} +(20.2392 + 135.135i) q^{94} +(-0.125065 - 0.343614i) q^{95} +(6.63733 + 37.6422i) q^{97} +(-64.2741 + 72.6944i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more