LMFDB - Embedded newform 81.2.g.a.25.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,2,Mod(4,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	81.25
Dual form			81.2.g.a.13.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.744407 - 0.373855i) q^{2} +(0.703902 - 1.58257i) q^{3} +(-0.779943 + 1.04765i) q^{4} +(0.345929 - 1.15548i) q^{5} +(-0.0676620 - 1.44123i) q^{6} +(-0.520803 + 1.20736i) q^{7} +(-0.478230 + 2.71217i) q^{8} +(-2.00904 - 2.22795i) q^{9} +(-0.174471 - 0.989477i) q^{10} +(2.11479 + 0.501215i) q^{11} +(1.10897 + 1.97175i) q^{12} +(-3.80561 + 2.50299i) q^{13} +(0.0636874 + 1.09347i) q^{14} +(-1.58513 - 1.36080i) q^{15} +(-0.0912185 - 0.304691i) q^{16} +(3.54217 + 1.28924i) q^{17} +(-2.32848 - 0.907406i) q^{18} +(-2.50517 + 0.911807i) q^{19} +(0.940731 + 1.26362i) q^{20} +(1.54413 + 1.67407i) q^{21} +(1.76165 - 0.417519i) q^{22} +(-2.38967 - 5.53988i) q^{23} +(3.95557 + 2.66594i) q^{24} +(2.96197 + 1.94812i) q^{25} +(-1.89717 + 3.28599i) q^{26} +(-4.94005 + 1.61120i) q^{27} +(-0.858686 - 1.48729i) q^{28} +(0.241756 - 4.15079i) q^{29} +(-1.68873 - 0.420381i) q^{30} +(-7.40674 - 0.865723i) q^{31} +(-3.96165 - 4.19911i) q^{32} +(2.28181 - 2.99400i) q^{33} +(3.11881 - 0.364536i) q^{34} +(1.21492 + 1.01944i) q^{35} +(3.90104 - 0.367096i) q^{36} +(7.47819 - 6.27494i) q^{37} +(-1.52398 + 1.61533i) q^{38} +(1.28237 + 7.78449i) q^{39} +(2.96844 + 1.49081i) q^{40} +(5.17242 + 2.59769i) q^{41} +(1.77532 + 0.668906i) q^{42} +(3.46904 - 3.67697i) q^{43} +(-2.17451 + 1.82463i) q^{44} +(-3.26934 + 1.55071i) q^{45} +(-3.85000 - 3.23053i) q^{46} +(2.97767 - 0.348040i) q^{47} +(-0.546403 - 0.0701130i) q^{48} +(3.61722 + 3.83402i) q^{49} +(2.93322 + 0.342844i) q^{50} +(4.53365 - 4.69822i) q^{51} +(0.345914 - 5.93911i) q^{52} +(-6.22987 - 10.7905i) q^{53} +(-3.07505 + 3.04625i) q^{54} +(1.31071 - 2.27022i) q^{55} +(-3.02550 - 1.98990i) q^{56} +(-0.320396 + 4.60642i) q^{57} +(-1.37183 - 3.18026i) q^{58} +(-10.6138 + 2.51552i) q^{59} +(2.66195 - 0.599306i) q^{60} +(7.04237 + 9.45955i) q^{61} +(-5.83728 + 2.12460i) q^{62} +(3.73624 - 1.26531i) q^{63} +(-3.92120 - 1.42720i) q^{64} +(1.57569 + 5.26317i) q^{65} +(0.579276 - 3.08182i) q^{66} +(0.0482665 + 0.828703i) q^{67} +(-4.11336 + 2.70540i) q^{68} +(-10.4493 - 0.117714i) q^{69} +(1.28552 + 0.304673i) q^{70} +(1.25916 + 7.14107i) q^{71} +(7.00336 - 4.38341i) q^{72} +(-1.41006 + 7.99685i) q^{73} +(3.22089 - 7.46687i) q^{74} +(5.16796 - 3.31623i) q^{75} +(0.998639 - 3.33569i) q^{76} +(-1.70654 + 2.29228i) q^{77} +(3.86488 + 5.31541i) q^{78} +(-10.2764 + 5.16099i) q^{79} -0.383620 q^{80} +(-0.927480 + 8.95208i) q^{81} +4.82155 q^{82} +(-4.26695 + 2.14294i) q^{83} +(-2.95816 + 0.312025i) q^{84} +(2.71504 - 3.64693i) q^{85} +(1.20772 - 4.03408i) q^{86} +(-6.39873 - 3.30434i) q^{87} +(-2.37074 + 5.49599i) q^{88} +(0.578632 - 3.28158i) q^{89} +(-1.85398 + 2.37662i) q^{90} +(-1.04003 - 5.89829i) q^{91} +(7.66763 + 1.81726i) q^{92} +(-6.58368 + 11.1123i) q^{93} +(2.08648 - 1.37230i) q^{94} +(0.186967 + 3.21010i) q^{95} +(-9.43399 + 3.31383i) q^{96} +(-0.390985 - 1.30598i) q^{97} +(4.12605 + 1.50176i) q^{98} +(-3.13203 - 5.71861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	0.744407	−	0.373855i	0.526375	−	0.264356i	−0.165706	−	0.986175i	$-0.552990\pi$
$2$	0.744407	−	0.373855i	0.526375	−	0.264356i	0.692081	+	0.721820i	$0.256694\pi$
$3$	0.703902	−	1.58257i	0.406398	−	0.913696i
$3$	0.703902	−	1.58257i	0.406398	−	0.913696i
$4$	−0.779943	+	1.04765i	−0.389972	+	0.523823i
$5$	0.345929	−	1.15548i	0.154704	−	0.516747i	−0.845137	−	0.534549i	$-0.820482\pi$
$5$	0.345929	−	1.15548i	0.154704	−	0.516747i	0.999842	+	0.0178015i	$0.00566669\pi$
$6$	−0.0676620	−	1.44123i	−0.0276229	−	0.588381i
$7$	−0.520803	+	1.20736i	−0.196845	+	0.456338i	−0.987838	−	0.155487i	$-0.950305\pi$
$7$	−0.520803	+	1.20736i	−0.196845	+	0.456338i	0.790993	+	0.611825i	$0.209565\pi$
$8$	−0.478230	+	2.71217i	−0.169080	+	0.958899i
$9$	−2.00904	−	2.22795i	−0.669682	−	0.742648i
$10$	−0.174471	−	0.989477i	−0.0551727	−	0.312900i
$11$	2.11479	+	0.501215i	0.637634	+	0.151122i	0.536703	−	0.843771i	$-0.319670\pi$
$11$	2.11479	+	0.501215i	0.637634	+	0.151122i	0.100931	+	0.994893i	$0.467818\pi$
$12$	1.10897	+	1.97175i	0.320131	+	0.569196i
$13$	−3.80561	+	2.50299i	−1.05549	+	0.694204i	−0.953748	−	0.300607i	$-0.902811\pi$
$13$	−3.80561	+	2.50299i	−1.05549	+	0.694204i	−0.101738	+	0.994811i	$0.532440\pi$
$14$	0.0636874	+	1.09347i	0.0170212	+	0.292242i
$15$	−1.58513	−	1.36080i	−0.409279	−	0.351358i
$16$	−0.0912185	−	0.304691i	−0.0228046	−	0.0761727i
$17$	3.54217	+	1.28924i	0.859102	+	0.312688i	0.733746	−	0.679424i	$-0.237770\pi$
$17$	3.54217	+	1.28924i	0.859102	+	0.312688i	0.125356	+	0.992112i	$0.459993\pi$
$18$	−2.32848	−	0.907406i	−0.548827	−	0.213878i
$19$	−2.50517	+	0.911807i	−0.574725	+	0.209183i	−0.612998	−	0.790084i	$-0.710037\pi$
$19$	−2.50517	+	0.911807i	−0.574725	+	0.209183i	0.0382728	+	0.999267i	$0.487814\pi$
$20$	0.940731	+	1.26362i	0.210354	+	0.282554i
$21$	1.54413	+	1.67407i	0.336957	+	0.365311i
$22$	1.76165	−	0.417519i	0.375585	−	0.0890153i
$23$	−2.38967	−	5.53988i	−0.498281	−	1.15514i	−0.962955	−	0.269663i	$-0.913088\pi$
$23$	−2.38967	−	5.53988i	−0.498281	−	1.15514i	0.464674	−	0.885482i	$-0.346171\pi$
$24$	3.95557	+	2.66594i	0.807428	+	0.544182i
$25$	2.96197	+	1.94812i	0.592393	+	0.389623i
$26$	−1.89717	+	3.28599i	−0.372065	+	0.644435i
$27$	−4.94005	+	1.61120i	−0.950712	+	0.310075i
$28$	−0.858686	−	1.48729i	−0.162276	−	0.281071i
$29$	0.241756	−	4.15079i	0.0448929	−	0.770782i	−0.898473	−	0.439028i	$-0.855323\pi$
$29$	0.241756	−	4.15079i	0.0448929	−	0.770782i	0.943366	−	0.331753i	$-0.107640\pi$
$30$	−1.68873	−	0.420381i	−0.308318	−	0.0767508i
$31$	−7.40674	−	0.865723i	−1.33029	−	0.155488i	−0.578927	−	0.815379i	$-0.696529\pi$
$31$	−7.40674	−	0.865723i	−1.33029	−	0.155488i	−0.751362	+	0.659891i	$0.770603\pi$
$32$	−3.96165	−	4.19911i	−0.700328	−	0.742304i
$33$	2.28181	−	2.99400i	0.397213	−	0.521188i
$34$	3.11881	−	0.364536i	0.534871	−	0.0625174i
$35$	1.21492	+	1.01944i	0.205359	+	0.172317i
$36$	3.90104	−	0.367096i	0.650173	−	0.0611826i
$37$	7.47819	−	6.27494i	1.22941	−	1.03159i	0.231129	−	0.972923i	$-0.425758\pi$
$37$	7.47819	−	6.27494i	1.22941	−	1.03159i	0.998277	−	0.0586711i	$-0.0186863\pi$
$38$	−1.52398	+	1.61533i	−0.247222	+	0.262040i
$39$	1.28237	+	7.78449i	0.205344	+	1.24652i
$40$	2.96844	+	1.49081i	0.469351	+	0.235717i
$41$	5.17242	+	2.59769i	0.807797	+	0.405691i	0.804241	−	0.594303i	$-0.202572\pi$
$41$	5.17242	+	2.59769i	0.807797	+	0.405691i	0.00355548	+	0.999994i	$0.498868\pi$
$42$	1.77532	+	0.668906i	0.273938	+	0.103214i
$43$	3.46904	−	3.67697i	0.529024	−	0.560732i	−0.406657	−	0.913581i	$-0.633305\pi$
$43$	3.46904	−	3.67697i	0.529024	−	0.560732i	0.935680	+	0.352849i	$0.114787\pi$
$44$	−2.17451	+	1.82463i	−0.327820	+	0.275074i
$45$	−3.26934	+	1.55071i	−0.487364	+	0.231166i
$46$	−3.85000	−	3.23053i	−0.567652	−	0.476316i
$47$	2.97767	−	0.348040i	0.434338	−	0.0507669i	0.103885	−	0.994589i	$-0.466873\pi$
$47$	2.97767	−	0.348040i	0.434338	−	0.0507669i	0.330453	+	0.943822i	$0.392798\pi$
$48$	−0.546403	−	0.0701130i	−0.0788665	−	0.0101199i
$49$	3.61722	+	3.83402i	0.516745	+	0.547718i
$50$	2.93322	+	0.342844i	0.414820	+	0.0484855i
$51$	4.53365	−	4.69822i	0.634839	−	0.657883i
$52$	0.345914	−	5.93911i	0.0479696	−	0.823607i
$53$	−6.22987	−	10.7905i	−0.855739	−	1.48218i	−0.875958	−	0.482388i	$-0.839770\pi$
$53$	−6.22987	−	10.7905i	−0.855739	−	1.48218i	0.0202187	−	0.999796i	$-0.493564\pi$
$54$	−3.07505	+	3.04625i	−0.418461	+	0.414542i
$55$	1.31071	−	2.27022i	0.176737	−	0.306117i
$56$	−3.02550	−	1.98990i	−0.404300	−	0.265912i
$57$	−0.320396	+	4.60642i	−0.0424375	+	0.610136i
$58$	−1.37183	−	3.18026i	−0.180130	−	0.417588i
$59$	−10.6138	+	2.51552i	−1.38180	+	0.327493i	−0.853292	−	0.521434i	$-0.825397\pi$
$59$	−10.6138	+	2.51552i	−1.38180	+	0.327493i	−0.528510	+	0.848927i	$0.677249\pi$
$60$	2.66195	−	0.599306i	0.343656	−	0.0773701i
$61$	7.04237	+	9.45955i	0.901684	+	1.21117i	0.976834	+	0.213999i	$0.0686490\pi$
$61$	7.04237	+	9.45955i	0.901684	+	1.21117i	−0.0751502	+	0.997172i	$0.523944\pi$
$62$	−5.83728	+	2.12460i	−0.741336	+	0.269824i
$63$	3.73624	−	1.26531i	0.470722	−	0.159415i
$64$	−3.92120	−	1.42720i	−0.490150	−	0.178400i
$65$	1.57569	+	5.26317i	0.195440	+	0.652816i
$66$	0.579276	−	3.08182i	0.0713040	−	0.379346i
$67$	0.0482665	+	0.828703i	0.00589669	+	0.101242i	0.999972	−	0.00744893i	$-0.00237109\pi$
$67$	0.0482665	+	0.828703i	0.00589669	+	0.101242i	−0.994076	+	0.108691i	$0.965334\pi$
$68$	−4.11336	+	2.70540i	−0.498818	+	0.328078i
$69$	−10.4493	−	0.117714i	−1.25795	−	0.0141711i
$70$	1.28552	+	0.304673i	0.153649	+	0.0364154i
$71$	1.25916	+	7.14107i	0.149435	+	0.847489i	0.963698	+	0.266993i	$0.0860301\pi$
$71$	1.25916	+	7.14107i	0.149435	+	0.847489i	−0.814263	+	0.580496i	$0.802859\pi$
$72$	7.00336	−	4.38341i	0.825354	−	0.516590i
$73$	−1.41006	+	7.99685i	−0.165035	+	0.935960i	0.783993	+	0.620769i	$0.213180\pi$
$73$	−1.41006	+	7.99685i	−0.165035	+	0.935960i	−0.949028	+	0.315191i	$0.897931\pi$
$74$	3.22089	−	7.46687i	0.374421	−	0.868006i
$75$	5.16796	−	3.31623i	0.596745	−	0.382925i
$76$	0.998639	−	3.33569i	0.114552	−	0.382629i
$77$	−1.70654	+	2.29228i	−0.194478	+	0.261229i
$78$	3.86488	+	5.31541i	0.437612	+	0.601851i
$79$	−10.2764	+	5.16099i	−1.15618	+	0.580657i	−0.920334	−	0.391133i	$-0.872083\pi$
$79$	−10.2764	+	5.16099i	−1.15618	+	0.580657i	−0.235849	+	0.971790i	$0.575787\pi$
$80$	−0.383620			−0.0428900
$81$	−0.927480	+	8.95208i	−0.103053	+	0.994676i
$82$	4.82155			0.532451
$83$	−4.26695	+	2.14294i	−0.468358	+	0.235218i	−0.667294	−	0.744794i	$-0.732548\pi$
$83$	−4.26695	+	2.14294i	−0.468358	+	0.235218i	0.198936	+	0.980012i	$0.436251\pi$
$84$	−2.95816	+	0.312025i	−0.322762	+	0.0340447i
$85$	2.71504	−	3.64693i	0.294487	−	0.395565i
$86$	1.20772	−	4.03408i	0.130232	−	0.435006i
$87$	−6.39873	−	3.30434i	−0.686016	−	0.354262i
$88$	−2.37074	+	5.49599i	−0.252722	+	0.585875i
$89$	0.578632	−	3.28158i	0.0613348	−	0.347847i	−0.938661	−	0.344842i	$-0.887932\pi$
$89$	0.578632	−	3.28158i	0.0613348	−	0.347847i	0.999995	−	0.00300484i	$-0.000956472\pi$
$90$	−1.85398	+	2.37662i	−0.195427	+	0.250517i
$91$	−1.04003	−	5.89829i	−0.109025	−	0.618309i
$92$	7.66763	+	1.81726i	0.799406	+	0.189463i
$93$	−6.58368	+	11.1123i	−0.682696	+	1.15229i
$94$	2.08648	−	1.37230i	0.215204	−	0.141542i
$95$	0.186967	+	3.21010i	0.0191824	+	0.329349i
$96$	−9.43399	+	3.31383i	−0.962852	+	0.338216i
$97$	−0.390985	−	1.30598i	−0.0396985	−	0.132602i	0.935843	−	0.352417i	$-0.114640\pi$
$97$	−0.390985	−	1.30598i	−0.0396985	−	0.132602i	−0.975542	+	0.219814i	$0.929455\pi$
$98$	4.12605	+	1.50176i	0.416794	+	0.151701i
$99$	−3.13203	−	5.71861i	−0.314781	−	0.574742i
$100$	−4.35110	+	1.58367i	−0.435110	+	0.158367i
$101$	1.38233	+	1.85679i	0.137547	+	0.184757i	0.865559	−	0.500807i	$-0.166963\pi$
$101$	1.38233	+	1.85679i	0.137547	+	0.184757i	−0.728013	+	0.685564i	$0.759556\pi$
$102$	1.61843	−	5.19232i	0.160248	−	0.514116i
$103$	4.42692	−	1.04920i	0.436198	−	0.103381i	−0.00664935	−	0.999978i	$-0.502117\pi$
$103$	4.42692	−	1.04920i	0.436198	−	0.103381i	0.442847	+	0.896597i	$0.353968\pi$
$104$	−4.96858	−	11.5185i	−0.487210	−	1.12948i
$105$	2.46852	−	1.20511i	0.240902	−	0.117607i
$106$	−8.67163	−	5.70342i	−0.842263	−	0.553965i
$107$	6.14665	−	10.6463i	0.594219	−	1.02922i	−0.399438	−	0.916760i	$-0.630795\pi$
$107$	6.14665	−	10.6463i	0.594219	−	1.02922i	0.993657	−	0.112457i	$-0.0358721\pi$
$108$	2.16499	−	6.43206i	0.208327	−	0.618925i
$109$	4.45327	+	7.71330i	0.426546	+	0.738800i	0.996563	−	0.0828329i	$-0.0263968\pi$
$109$	4.45327	+	7.71330i	0.426546	+	0.738800i	−0.570017	+	0.821633i	$0.693063\pi$
$110$	0.126970	−	2.17999i	0.0121061	−	0.207854i
$111$	−4.66662	−	16.2517i	−0.442936	−	1.54254i
$112$	0.415378	+	0.0485507i	0.0392495	+	0.00458761i
$113$	11.9342	+	12.6496i	1.12268	+	1.18997i	0.979747	+	0.200238i	$0.0641716\pi$
$113$	11.9342	+	12.6496i	1.12268	+	1.18997i	0.142932	+	0.989733i	$0.454347\pi$
$114$	1.48363	+	3.54884i	0.138955	+	0.332379i
$115$	−7.22789	+	0.844819i	−0.674004	+	0.0787798i
$116$	4.16000	+	3.49065i	0.386246	+	0.324099i
$117$	13.2222	+	3.45007i	1.22239	+	0.318959i
$118$	−6.96056	+	5.84061i	−0.640772	+	0.537671i
$119$	−3.40135	+	3.60522i	−0.311801	+	0.330490i
$120$	4.44879	−	3.64837i	0.406117	−	0.333049i
$121$	−5.60882	−	2.81686i	−0.509893	−	0.256078i
$122$	8.77890	+	4.40893i	0.794804	+	0.399166i
$123$	7.75190	−	6.35720i	0.698965	−	0.573209i
$124$	6.68380	−	7.08442i	0.600223	−	0.636199i
$125$	7.89548	−	6.62509i	0.706193	−	0.592566i
$126$	2.30824	−	2.33872i	0.205634	−	0.208350i
$127$	4.35255	+	3.65222i	0.386226	+	0.324082i	0.815141	−	0.579263i	$-0.196660\pi$
$127$	4.35255	+	3.65222i	0.386226	+	0.324082i	−0.428915	+	0.903345i	$0.641104\pi$
$128$	8.01534	−	0.936859i	0.708462	−	0.0828074i
$129$	−3.37719	−	8.07822i	−0.297345	−	0.711247i
$130$	3.14062	+	3.32886i	0.275450	+	0.291960i
$131$	19.3865	+	2.26596i	1.69381	+	0.197978i	0.907556	−	0.419931i	$-0.137946\pi$
$131$	19.3865	+	2.26596i	1.69381	+	0.197978i	0.786250	+	0.617909i	$0.212020\pi$
$132$	1.35696	+	4.72568i	0.118109	+	0.411318i
$133$	0.203823	−	3.49951i	0.0176737	−	0.303446i
$134$	0.345745	+	0.598848i	0.0298678	+	0.0517326i
$135$	0.152805	+	6.26550i	0.0131513	+	0.539248i
$136$	−5.19062	+	8.99042i	−0.445092	+	0.770922i
$137$	−13.2460	−	8.71204i	−1.13168	−	0.744320i	−0.161543	−	0.986866i	$-0.551647\pi$
$137$	−13.2460	−	8.71204i	−1.13168	−	0.744320i	−0.970140	+	0.242546i	$0.922018\pi$
$138$	−7.82256	+	3.81891i	−0.665901	+	0.325087i
$139$	−4.13477	−	9.58547i	−0.350707	−	0.813029i	−0.998680	−	0.0513663i	$-0.983642\pi$
$139$	−4.13477	−	9.58547i	−0.350707	−	0.813029i	0.647973	−	0.761663i	$-0.275617\pi$
$140$	−2.01558	+	0.477701i	−0.170347	+	0.0403731i
$141$	1.54519	−	4.95736i	0.130129	−	0.417485i
$142$	3.60706	+	4.84512i	0.302697	+	0.406593i
$143$	−9.30261	+	3.38587i	−0.777923	+	0.283141i
$144$	−0.495573	+	0.815367i	−0.0412977	+	0.0679473i
$145$	−4.71253	−	1.71522i	−0.391354	−	0.142441i
$146$	1.94001	+	6.48007i	0.160556	+	0.536294i
$147$	8.61377	−	3.02571i	0.710452	−	0.249557i
$148$	0.741356	+	12.7286i	0.0609391	+	1.04628i
$149$	2.43554	−	1.60188i	0.199527	−	0.131231i	−0.445814	−	0.895126i	$-0.647086\pi$
$149$	2.43554	−	1.60188i	0.199527	−	0.131231i	0.645341	+	0.763895i	$0.276715\pi$
$150$	2.60727	−	4.40069i	0.212883	−	0.359315i
$151$	−12.4159	−	2.94262i	−1.01039	−	0.239467i	−0.308098	−	0.951355i	$-0.599692\pi$
$151$	−12.4159	−	2.94262i	−1.01039	−	0.239467i	−0.702293	+	0.711888i	$0.747840\pi$
$152$	−1.27493	−	7.23051i	−0.103411	−	0.586472i
$153$	−4.24401	−	10.4819i	−0.343108	−	0.847412i
$154$	−0.413378	+	2.34439i	−0.0333110	+	0.188916i
$155$	−3.56253	+	8.25887i	−0.286149	+	0.663369i
$156$	−9.15556	−	4.72799i	−0.733032	−	0.378542i
$157$	0.364422	−	1.21726i	0.0290841	−	0.0971476i	−0.942215	−	0.335008i	$-0.891261\pi$
$157$	0.364422	−	1.21726i	0.0290841	−	0.0971476i	0.971299	+	0.237861i	$0.0764461\pi$
$158$	−5.72035	+	7.68376i	−0.455086	+	0.611287i
$159$	−21.4619	+	2.26378i	−1.70204	+	0.179529i
$160$	−6.22244	+	3.12503i	−0.491927	+	0.247055i
$161$	7.93316			0.625221
$162$	2.65636	+	7.01074i	0.208703	+	0.550816i
$163$	12.3636			0.968391			0.484195	−	0.874960i	$-0.339112\pi$
$163$	12.3636			0.968391			0.484195	+	0.874960i	$0.339112\pi$
$164$	−6.75565	+	3.39282i	−0.527528	+	0.264934i
$165$	−2.67017	−	3.67231i	−0.207872	−	0.285889i
$166$	−2.37520	+	3.19044i	−0.184351	+	0.247626i
$167$	−1.09374	+	3.65334i	−0.0846359	+	0.282704i	−0.989822	−	0.142312i	$-0.954546\pi$
$167$	−1.09374	+	3.65334i	−0.0846359	+	0.282704i	0.905186	+	0.425016i	$0.139731\pi$
$168$	−5.27881	+	3.38737i	−0.407269	+	0.261341i
$169$	3.06867	−	7.11397i	0.236051	−	0.547228i
$170$	0.657669	−	3.72983i	0.0504409	−	0.286065i
$171$	7.06445	+	3.74952i	0.540232	+	0.286733i
$172$	1.14650	+	6.50215i	0.0874201	+	0.495784i
$173$	−23.4213	−	5.55096i	−1.78069	−	0.422031i	−0.797307	−	0.603574i	$-0.793743\pi$
$173$	−23.4213	−	5.55096i	−1.78069	−	0.422031i	−0.983383	+	0.181542i	$0.941891\pi$
$174$	−5.99861	−	0.0675756i	−0.454753	−	0.00512289i
$175$	−3.89467	+	2.56157i	−0.294410	+	0.193636i
$176$	−0.0401925	−	0.690078i	−0.00302962	−	0.0520166i
$177$	−3.49010	+	18.5678i	−0.262332	+	1.39564i
$178$	−0.796100	−	2.65916i	−0.0596702	−	0.199312i
$179$	5.95691	+	2.16814i	0.445240	+	0.162054i	0.554904	−	0.831915i	$-0.312755\pi$
$179$	5.95691	+	2.16814i	0.445240	+	0.162054i	−0.109664	+	0.993969i	$0.534977\pi$
$180$	0.925308	−	4.63457i	0.0689684	−	0.345440i
$181$	−5.82014	+	2.11836i	−0.432608	+	0.157456i	−0.549140	−	0.835731i	$-0.685045\pi$
$181$	−5.82014	+	2.11836i	−0.432608	+	0.157456i	0.116532	+	0.993187i	$0.462822\pi$
$182$	−2.97931	−	4.00191i	−0.220841	−	0.296641i
$183$	19.9275	−	4.48644i	1.47309	−	0.331647i
$184$	16.1679	−	3.83187i	1.19192	−	0.282489i
$185$	−4.66367	−	10.8116i	−0.342880	−	0.794884i
$186$	−0.746554	+	10.7334i	−0.0547400	+	0.787011i
$187$	6.84476	+	4.50187i	0.500539	+	0.329210i
$188$	−1.95779	+	3.39100i	−0.142787	+	0.247314i
$189$	0.627502	−	6.80352i	0.0456441	−	0.494883i
$190$	1.33929	+	2.31972i	0.0971625	+	0.168290i
$191$	−0.392632	+	6.74123i	−0.0284098	+	0.487778i	0.953854	+	0.300272i	$0.0970774\pi$
$191$	−0.392632	+	6.74123i	−0.0284098	+	0.487778i	−0.982263	+	0.187506i	$0.939960\pi$
$192$	−5.01878	+	5.20095i	−0.362199	+	0.375347i
$193$	15.8040	+	1.84722i	1.13759	+	0.132966i	0.663969	−	0.747761i	$-0.268871\pi$
$193$	15.8040	+	1.84722i	1.13759	+	0.132966i	0.473626	+	0.880726i	$0.342945\pi$
$194$	−0.779300	−	0.826010i	−0.0559505	−	0.0593041i
$195$	9.43845	+	1.21112i	0.675902	+	0.0867300i
$196$	−6.83792	+	0.799238i	−0.488423	+	0.0570884i
$197$	−8.88023	−	7.45140i	−0.632690	−	0.530890i	0.269073	−	0.963120i	$-0.413283\pi$
$197$	−8.88023	−	7.45140i	−0.632690	−	0.530890i	−0.901764	+	0.432229i	$0.857727\pi$
$198$	−4.46944	−	3.08604i	−0.317629	−	0.219316i
$199$	3.29385	−	2.76387i	0.233495	−	0.195925i	−0.518531	−	0.855059i	$-0.673521\pi$
$199$	3.29385	−	2.76387i	0.233495	−	0.195925i	0.752026	+	0.659133i	$0.229077\pi$
$200$	−6.70013	+	7.10172i	−0.473771	+	0.502168i
$201$	1.34545	+	0.506941i	0.0949010	+	0.0357568i
$202$	1.72318	+	0.865416i	0.121243	+	0.0608904i
$203$	4.88558	+	2.45363i	0.342900	+	0.172211i
$204$	1.38608	+	8.41401i	0.0970448	+	0.589098i
$205$	4.79087	−	5.07803i	0.334609	−	0.354665i
$206$	2.90318	−	2.43606i	0.202274	−	0.169728i
$207$	−7.54159	+	16.4539i	−0.524177	+	1.14363i
$208$	1.10978	+	0.931215i	0.0769493	+	0.0645682i
$209$	−5.75493	+	0.672654i	−0.398077	+	0.0465285i
$210$	1.38704	−	1.81996i	0.0957151	−	0.125589i
$211$	−9.80038	−	10.3878i	−0.674686	−	0.715126i	0.296077	−	0.955164i	$-0.404321\pi$
$211$	−9.80038	−	10.3878i	−0.674686	−	0.715126i	−0.970763	+	0.240038i	$0.922840\pi$
$212$	16.1635	+	1.88924i	1.11012	+	0.129754i
$213$	12.1876	+	3.03390i	0.835077	+	0.207879i
$214$	0.595430	−	10.2231i	0.0407028	−	0.698840i
$215$	−3.04863	−	5.28038i	−0.207915	−	0.360119i
$216$	−2.00737	−	14.1688i	−0.136584	−	0.964064i
$217$	4.90269	−	8.49171i	0.332816	−	0.576455i
$218$	6.19871	+	4.07695i	0.419829	+	0.276126i
$219$	11.6630	+	7.86051i	0.788113	+	0.531164i
$220$	1.35611	+	3.14381i	0.0914286	+	0.211955i
$221$	−16.7071	+	3.95965i	−1.12384	+	0.266355i
$222$	−9.54964	−	10.3532i	−0.640930	−	0.694863i
$223$	−12.0568	−	16.1950i	−0.807381	−	1.08450i	−0.994762	−	0.102214i	$-0.967408\pi$
$223$	−12.0568	−	16.1950i	−0.807381	−	1.08450i	0.187382	−	0.982287i	$-0.440000\pi$
$224$	7.13306	−	2.59622i	0.476598	−	0.173467i
$225$	−1.61043	−	10.5129i	−0.107362	−	0.700863i
$226$	13.6130	+	4.95474i	0.905526	+	0.329585i
$227$	−0.781091	−	2.60903i	−0.0518428	−	0.173167i	0.928147	−	0.372213i	$-0.121401\pi$
$227$	−0.781091	−	2.60903i	−0.0518428	−	0.173167i	−0.979990	+	0.199046i	$0.936216\pi$
$228$	−4.57601	−	3.92841i	−0.303053	−	0.260165i
$229$	−0.0887613	−	1.52397i	−0.00586551	−	0.100707i	0.994105	−	0.108424i	$-0.0345805\pi$
$229$	−0.0887613	−	1.52397i	−0.00586551	−	0.100707i	−0.999970	+	0.00771732i	$0.997543\pi$
$230$	−5.06465	+	3.33107i	−0.333953	+	0.219645i
$231$	2.42645	+	4.31425i	0.159649	+	0.283857i
$232$	11.1420	+	2.64071i	0.731511	+	0.173371i
$233$	−1.13347	−	6.42825i	−0.0742563	−	0.421128i	−0.999162	−	0.0409317i	$-0.986967\pi$
$233$	−1.13347	−	6.42825i	−0.0742563	−	0.421128i	0.924906	−	0.380197i	$-0.124144\pi$
$234$	11.1325	−	2.37491i	0.727754	−	0.155253i
$235$	0.627909	−	3.56105i	0.0409602	−	0.232297i
$236$	5.64280	−	13.0815i	0.367315	−	0.851532i
$237$	0.934060	+	19.8959i	0.0606737	+	1.29238i
$238$	−1.18416	+	3.95536i	−0.0767576	+	0.256388i
$239$	−10.0905	+	13.5539i	−0.652702	+	0.876731i	−0.998093	−	0.0617275i	$-0.980339\pi$
$239$	−10.0905	+	13.5539i	−0.652702	+	0.876731i	0.345391	+	0.938459i	$0.387746\pi$
$240$	−0.270031	+	0.607105i	−0.0174304	+	0.0391885i
$241$	−11.2588	+	5.65439i	−0.725244	+	0.364231i	−0.772811	−	0.634637i	$-0.781150\pi$
$241$	−11.2588	+	5.65439i	−0.725244	+	0.364231i	0.0475663	+	0.998868i	$0.484853\pi$
$242$	−5.22835			−0.336091
$243$	13.5144	+	7.76919i	0.866951	+	0.498394i
$244$	−15.4029			−0.986070
$245$	5.68145	−	2.85333i	0.362974	−	0.182293i
$246$	3.39390	−	7.63043i	0.216387	−	0.486498i
$247$	7.25145	−	9.74038i	0.461399	−	0.619766i
$248$	5.89011	−	19.6743i	0.374023	−	1.24932i
$249$	0.387839	+	8.26115i	0.0245783	+	0.523529i
$250$	3.40062	−	7.88353i	0.215074	−	0.498598i
$251$	−4.48052	+	25.4103i	−0.282808	+	1.60388i	0.430204	+	0.902732i	$0.358442\pi$
$251$	−4.48052	+	25.4103i	−0.282808	+	1.60388i	−0.713012	+	0.701152i	$0.752669\pi$
$252$	−1.58846	+	4.90113i	−0.100063	+	0.308742i
$253$	−2.27699	−	12.9134i	−0.143153	−	0.811861i
$254$	4.60547	+	1.09152i	0.288973	+	0.0684878i
$255$	−3.86039	−	6.86381i	−0.241747	−	0.429828i
$256$	12.5892	−	8.28002i	0.786822	−	0.517501i
$257$	−0.841489	−	14.4478i	−0.0524906	−	0.901229i	−0.917068	−	0.398730i	$-0.869451\pi$
$257$	−0.841489	−	14.4478i	−0.0524906	−	0.901229i	0.864578	−	0.502499i	$-0.167586\pi$
$258$	−5.53409	−	4.75090i	−0.344537	−	0.295778i
$259$	3.68144	+	12.2969i	0.228753	+	0.764089i
$260$	−6.74288	−	2.45421i	−0.418176	−	0.152204i
$261$	−9.73342	+	7.80050i	−0.602484	+	0.482839i
$262$	15.2786	−	5.56095i	0.943914	−	0.343557i
$263$	−6.24306	−	8.38588i	−0.384963	−	0.517096i	0.566830	−	0.823835i	$-0.308170\pi$
$263$	−6.24306	−	8.38588i	−0.384963	−	0.517096i	−0.951794	+	0.306739i	$0.900762\pi$
$264$	7.02902	+	7.62050i	0.432606	+	0.469009i
$265$	−14.6233	+	3.46578i	−0.898301	+	0.212901i
$266$	−1.15658	−	2.68126i	−0.0709146	−	0.164398i
$267$	−4.78603	−	3.22564i	−0.292900	−	0.197406i
$268$	−0.905832	−	0.595775i	−0.0553325	−	0.0363928i
$269$	0.105374	−	0.182513i	0.00642476	−	0.0111280i	−0.862795	−	0.505554i	$-0.831288\pi$
$269$	0.105374	−	0.182513i	0.00642476	−	0.0111280i	0.869220	+	0.494426i	$0.164622\pi$
$270$	2.45614	+	4.60695i	0.149476	+	0.280370i
$271$	5.70846	+	9.88735i	0.346765	+	0.600614i	0.985673	−	0.168669i	$-0.0539470\pi$
$271$	5.70846	+	9.88735i	0.346765	+	0.600614i	−0.638908	+	0.769283i	$0.720614\pi$
$272$	0.0697097	−	1.19687i	0.00422677	−	0.0725708i
$273$	−10.0665	−	2.50590i	−0.609254	−	0.151664i
$274$	−13.1175	−	1.53321i	−0.792455	−	0.0926247i
$275$	5.28752	+	5.60444i	0.318850	+	0.337961i
$276$	8.27320	−	10.8554i	0.497988	−	0.653417i
$277$	11.0740	−	1.29437i	0.665375	−	0.0777712i	0.223301	−	0.974750i	$-0.428317\pi$
$277$	11.0740	−	1.29437i	0.665375	−	0.0777712i	0.442074	+	0.896978i	$0.354243\pi$
$278$	−6.66153	−	5.58969i	−0.399532	−	0.335247i
$279$	12.9517	+	18.2411i	0.775397	+	1.09206i
$280$	−3.34591	+	2.80755i	−0.199956	+	0.167783i
$281$	14.8936	−	15.7863i	0.888478	−	0.941732i	−0.110159	−	0.993914i	$-0.535136\pi$
$281$	14.8936	−	15.7863i	0.888478	−	0.941732i	0.998638	+	0.0521821i	$0.0166176\pi$
$282$	−0.703082	−	4.26797i	−0.0418679	−	0.254154i
$283$	−0.264982	−	0.133079i	−0.0157515	−	0.00791072i	0.440906	−	0.897553i	$-0.354657\pi$
$283$	−0.264982	−	0.133079i	−0.0157515	−	0.00791072i	−0.456658	+	0.889643i	$0.650954\pi$
$284$	−8.46338	−	4.25047i	−0.502209	−	0.252219i
$285$	5.21181	+	1.96371i	0.308721	+	0.116320i
$286$	−5.65910	+	5.99830i	−0.334630	+	0.354687i
$287$	−5.83015	+	4.89208i	−0.344143	+	0.288770i
$288$	−1.39624	+	17.2625i	−0.0822744	+	1.01720i
$289$	−2.13795	−	1.79396i	−0.125762	−	0.105527i
$290$	−4.14929	+	0.484982i	−0.243654	+	0.0284791i
$291$	−2.34202	−	0.300522i	−0.137292	−	0.0176169i
$292$	−7.27809	−	7.71433i	−0.425918	−	0.451447i
$293$	14.4085	+	1.68412i	0.841755	+	0.0983871i	0.526032	−	0.850464i	$-0.323679\pi$
$293$	14.4085	+	1.68412i	0.841755	+	0.0983871i	0.315723	+	0.948852i	$0.397753\pi$
$294$	5.28097	−	5.47267i	0.307993	−	0.319172i
$295$	−0.764985	+	13.1343i	−0.0445391	+	0.764707i
$296$	13.4425	+	23.2830i	0.781327	+	1.35330i
$297$	−11.2547	+	0.931320i	−0.653066	+	0.0540407i
$298$	1.21416	−	2.10299i	0.0703346	−	0.121823i
$299$	22.9604	+	15.1013i	1.32783	+	0.873330i
$300$	−0.556480	+	8.00066i	−0.0321284	+	0.461918i
$301$	2.63273	+	6.10335i	0.151748	+	0.351791i
$302$	−10.3426	+	2.45124i	−0.595149	+	0.141053i
$303$	3.91152	−	0.880631i	0.224711	−	0.0505909i
$304$	0.506337	+	0.680128i	0.0290404	+	0.0390080i
$305$	13.3665	−	4.86501i	0.765364	−	0.278570i
$306$	−7.07799	−	6.21616i	−0.404621	−	0.355354i
$307$	−3.56052	−	1.29592i	−0.203210	−	0.0739622i	0.238410	−	0.971165i	$-0.423374\pi$
$307$	−3.56052	−	1.29592i	−0.203210	−	0.0739622i	−0.441620	+	0.897202i	$0.645596\pi$
$308$	−1.07049	−	3.57569i	−0.0609969	−	0.203744i
$309$	1.45569	−	7.74444i	0.0828112	−	0.440566i
$310$	0.435651	+	7.47984i	0.0247433	+	0.424826i
$311$	−10.3012	+	6.77519i	−0.584126	+	0.384186i	−0.806903	−	0.590684i	$-0.798858\pi$
$311$	−10.3012	+	6.77519i	−0.584126	+	0.384186i	0.222777	+	0.974869i	$0.428488\pi$
$312$	−21.7262	−	0.244750i	−1.23000	−	0.0138562i
$313$	6.62237	+	1.56953i	0.374319	+	0.0887151i	0.413469	−	0.910518i	$-0.364317\pi$
$313$	6.62237	+	1.56953i	0.374319	+	0.0887151i	−0.0391504	+	0.999233i	$0.512465\pi$
$314$	−0.183799	−	1.04238i	−0.0103724	−	0.0588246i
$315$	−0.169574	−	4.75487i	−0.00955443	−	0.267907i
$316$	2.60810	−	14.7913i	0.146717	−	0.832074i
$317$	−5.91605	+	13.7150i	−0.332279	+	0.770309i	0.667394	+	0.744705i	$0.267410\pi$
$317$	−5.91605	+	13.7150i	−0.332279	+	0.770309i	−0.999672	+	0.0256033i	$0.991849\pi$
$318$	−15.1300	+	9.70880i	−0.848450	+	0.544443i
$319$	2.59170	−	8.65688i	0.145107	−	0.484692i
$320$	−3.00556	+	4.03717i	−0.168016	+	0.225684i
$321$	−12.5219	−	17.2214i	−0.698903	−	0.961207i
$322$	5.90550	−	2.96585i	0.329101	−	0.165281i
$323$	−10.0493			−0.559156
$324$	−8.65523	−	7.95378i	−0.480846	−	0.441877i
$325$	−16.1482			−0.895740
$326$	9.20354	−	4.62219i	0.509737	−	0.256000i
$327$	15.3415	−	1.61821i	0.848386	−	0.0894870i
$328$	−9.51899	+	12.7862i	−0.525598	+	0.706001i
$329$	−1.13057	+	3.77638i	−0.0623305	+	0.208198i
$330$	−3.36060	−	1.73543i	−0.184995	−	0.0955325i
$331$	−1.46304	+	3.39172i	−0.0804162	+	0.186426i	−0.953681	−	0.300821i	$-0.902739\pi$
$331$	−1.46304	+	3.39172i	−0.0804162	+	0.186426i	0.873265	+	0.487246i	$0.161999\pi$
$332$	1.08293	−	6.14162i	0.0594337	−	0.337065i
$333$	−29.0042	−	4.05435i	−1.58942	−	0.222177i
$334$	0.551633	+	3.12847i	0.0301840	+	0.171182i
$335$	0.974249	+	0.230901i	0.0532289	+	0.0126155i
$336$	0.369220	−	0.623189i	0.0201426	−	0.0339977i
$337$	−15.4103	+	10.1355i	−0.839450	+	0.552115i	−0.894859	−	0.446349i	$-0.852724\pi$
$337$	−15.4103	+	10.1355i	−0.839450	+	0.552115i	0.0554092	+	0.998464i	$0.482354\pi$
$338$	−0.375258	−	6.44292i	−0.0204113	−	0.350449i
$339$	28.4193	−	9.98271i	1.54353	−	0.542186i
$340$	1.70311	+	5.68879i	0.0923642	+	0.308518i
$341$	−15.2298	−	5.54319i	−0.824740	−	0.300181i
$342$	6.66060	+	0.150085i	0.360164	+	0.00811568i
$343$	−15.1621	+	5.51854i	−0.818675	+	0.297973i
$344$	8.31358	+	11.1671i	0.448238	+	0.602089i
$345$	−3.75074	+	12.0333i	−0.201933	+	0.647851i
$346$	−19.5103	+	4.62402i	−1.04888	+	0.248589i
$347$	−13.3067	−	30.8484i	−0.714341	−	1.65603i	−0.754049	−	0.656818i	$-0.771902\pi$
$347$	−13.3067	−	30.8484i	−0.714341	−	1.65603i	0.0397080	−	0.999211i	$-0.487357\pi$
$348$	8.45242	−	4.12640i	0.453097	−	0.221198i
$349$	27.5190	+	18.0995i	1.47306	+	0.968844i	0.995941	+	0.0900033i	$0.0286878\pi$
$349$	27.5190	+	18.0995i	1.47306	+	0.968844i	0.477115	+	0.878841i	$0.341683\pi$
$350$	−1.94157	+	3.36289i	−0.103781	+	0.179754i
$351$	14.7671	−	18.4964i	0.788208	−	0.987267i
$352$	−6.27342	−	10.8659i	−0.334374	−	0.579154i
$353$	−0.775734	+	13.3188i	−0.0412881	+	0.708890i	0.912623	+	0.408802i	$0.134053\pi$
$353$	−0.775734	+	13.3188i	−0.0412881	+	0.708890i	−0.953911	+	0.300088i	$0.902984\pi$
$354$	4.34361	+	15.1268i	0.230860	+	0.803979i
$355$	8.68696	+	1.01536i	0.461056	+	0.0538897i
$356$	2.98664	+	3.16565i	0.158291	+	0.167779i
$357$	3.31129	+	7.92059i	0.175252	+	0.419202i
$358$	5.24493	−	0.613045i	0.277203	−	0.0324004i
$359$	6.91454	+	5.80199i	0.364936	+	0.306217i	0.806754	−	0.590887i	$-0.201222\pi$
$359$	6.91454	+	5.80199i	0.364936	+	0.306217i	−0.441819	+	0.897104i	$0.645667\pi$
$360$	−2.64229	−	9.60861i	−0.139261	−	0.506418i
$361$	−9.11037	+	7.64450i	−0.479493	+	0.402342i
$362$	−3.54060	+	3.75281i	−0.186090	+	0.197243i
$363$	−8.40593	+	6.89356i	−0.441197	+	0.361818i
$364$	6.99048	+	3.51075i	0.366401	+	0.184013i
$365$	8.75244	+	4.39564i	0.458124	+	0.230078i
$366$	13.1569	−	10.7898i	0.687723	−	0.563989i
$367$	−17.5705	+	18.6236i	−0.917171	+	0.972145i	−0.999701	−	0.0244437i	$-0.992219\pi$
$367$	−17.5705	+	18.6236i	−0.917171	+	0.972145i	0.0825298	+	0.996589i	$0.473700\pi$
$368$	−1.46997	+	1.23345i	−0.0766274	+	0.0642980i
$369$	−4.60412	−	16.7427i	−0.239681	−	0.871593i
$370$	−7.51364	−	6.30469i	−0.390616	−	0.327765i
$371$	16.2725	−	1.90198i	0.844825	−	0.0987459i
$372$	−6.50683	−	15.5643i	−0.337364	−	0.806972i
$373$	15.0065	+	15.9060i	0.777008	+	0.823580i	0.988088	−	0.153888i	$-0.0491796\pi$
$373$	15.0065	+	15.9060i	0.777008	+	0.823580i	−0.211080	+	0.977469i	$0.567698\pi$
$374$	6.77834	+	0.792274i	0.350500	+	0.0409675i
$375$	−4.92702	−	17.1585i	−0.254430	−	0.886064i
$376$	−0.480066	+	8.24241i	−0.0247575	+	0.425070i
$377$	9.46934	+	16.4014i	0.487696	+	0.844714i
$378$	−2.07641	−	5.29918i	−0.106799	−	0.272560i
$379$	−5.26717	+	9.12300i	−0.270556	+	0.468617i	−0.969004	−	0.247043i	$-0.920541\pi$
$379$	−5.26717	+	9.12300i	−0.270556	+	0.468617i	0.698448	+	0.715661i	$0.253874\pi$
$380$	−3.50887	−	2.30782i	−0.180001	−	0.118389i
$381$	8.84365	−	4.31740i	0.453074	−	0.221187i
$382$	2.22797	+	5.16500i	0.113993	+	0.264265i
$383$	21.2791	−	5.04324i	1.08731	−	0.257698i	0.352393	−	0.935852i	$-0.385368\pi$
$383$	21.2791	−	5.04324i	1.08731	−	0.257698i	0.734919	+	0.678154i	$0.237220\pi$
$384$	4.15937	−	13.3443i	0.212257	−	0.680972i
$385$	2.05835	+	2.76484i	0.104903	+	0.140909i
$386$	12.4552	−	4.53331i	0.633952	−	0.230740i
$387$	−15.1615	−	0.341639i	−0.770704	−	0.0173665i
$388$	1.67315	+	0.608977i	0.0849414	+	0.0309161i
$389$	−6.99531	−	23.3660i	−0.354676	−	1.18470i	−0.930242	−	0.366946i	$-0.880403\pi$
$389$	−6.99531	−	23.3660i	−0.354676	−	1.18470i	0.575566	−	0.817755i	$-0.304782\pi$
$390$	7.47883	−	2.62705i	0.378706	−	0.133026i
$391$	−1.32236	−	22.7040i	−0.0668746	−	1.14819i
$392$	−12.1284	+	7.97698i	−0.612577	+	0.402898i
$393$	17.2322	−	29.0854i	0.869250	−	1.46717i
$394$	−9.39625	−	2.22695i	−0.473376	−	0.112192i
$395$	2.40854	+	13.6595i	0.121187	+	0.687285i
$396$	8.43388	+	1.17893i	0.423818	+	0.0592433i
$397$	4.16728	−	23.6338i	0.209150	−	1.18615i	−0.681625	−	0.731702i	$-0.738726\pi$
$397$	4.16728	−	23.6338i	0.209150	−	1.18615i	0.890775	−	0.454445i	$-0.150163\pi$
$398$	1.41868	−	3.28887i	0.0711119	−	0.164856i
$399$	−5.39474	−	2.78587i	−0.270075	−	0.139468i
$400$	0.323387	−	1.08019i	0.0161694	−	0.0540094i
$401$	−22.0434	+	29.6094i	−1.10079	+	1.47862i	−0.239235	+	0.970962i	$0.576897\pi$
$401$	−22.0434	+	29.6094i	−1.10079	+	1.47862i	−0.861558	+	0.507660i	$0.830511\pi$
$402$	1.19109	−	0.125635i	0.0594061	−	0.00626610i
$403$	30.3540	−	15.2444i	1.51204	−	0.759376i
$404$	−3.02339			−0.150419
$405$	10.0231	+	4.16847i	0.498053	+	0.207133i
$406$	4.55416			0.226019
$407$	18.9599	−	9.52203i	0.939808	−	0.471989i
$408$	10.5743	+	14.5429i	0.523504	+	0.719980i
$409$	−1.70501	+	2.29023i	−0.0843075	+	0.113245i	−0.842276	−	0.539047i	$-0.818785\pi$
$409$	−1.70501	+	2.29023i	−0.0843075	+	0.113245i	0.757968	+	0.652291i	$0.226192\pi$
$410$	1.66791	−	5.57121i	0.0823723	−	0.275143i
$411$	−23.1113	+	14.8303i	−1.14000	+	0.731525i
$412$	−2.35356	+	5.45616i	−0.115952	+	0.268806i
$413$	2.49058	−	14.1248i	0.122553	−	0.695035i
$414$	0.537370	+	15.0679i	0.0264103	+	0.740546i
$415$	1.00007	+	5.67169i	0.0490916	+	0.278412i
$416$	25.5868	+	6.06418i	1.25450	+	0.297321i
$417$	−18.0801	−	0.203677i	−0.885388	−	0.00997409i
$418$	−4.03253	+	2.65224i	−0.197238	+	0.129725i
$419$	−1.99872	−	34.3166i	−0.0976437	−	1.67648i	−0.591016	−	0.806660i	$-0.701273\pi$
$419$	−1.99872	−	34.3166i	−0.0976437	−	1.67648i	0.493372	−	0.869818i	$-0.335764\pi$
$420$	−0.662775	+	3.52604i	−0.0323401	+	0.172053i
$421$	−1.79299	−	5.98899i	−0.0873849	−	0.291886i	0.903115	−	0.429398i	$-0.141274\pi$
$421$	−1.79299	−	5.98899i	−0.0873849	−	0.291886i	−0.990500	+	0.137513i	$0.956089\pi$
$422$	−11.1790	−	4.06883i	−0.544186	−	0.198067i
$423$	−6.75769	−	5.93486i	−0.328570	−	0.288563i
$424$	32.2449	−	11.7362i	1.56595	−	0.569960i
$425$	7.98018	+	10.7192i	0.387096	+	0.519960i
$426$	10.2067	−	2.29793i	0.494518	−	0.111335i
$427$	−15.0887	+	3.57610i	−0.730196	+	0.173060i
$428$	6.35952	+	14.7430i	0.307399	+	0.712631i
$429$	−1.18975	+	17.1053i	−0.0574416	+	0.825853i
$430$	−4.24352	−	2.79101i	−0.204641	−	0.134594i
$431$	−1.50862	+	2.61301i	−0.0726679	+	0.125864i	−0.900070	−	0.435746i	$-0.856485\pi$
$431$	−1.50862	+	2.61301i	−0.0726679	+	0.125864i	0.827402	+	0.561610i	$0.189818\pi$
$432$	0.941540	+	1.35822i	0.0452999	+	0.0653472i
$433$	−15.3659	−	26.6146i	−0.738439	−	1.27901i	−0.953198	−	0.302347i	$-0.902230\pi$
$433$	−15.3659	−	26.6146i	−0.738439	−	1.27901i	0.214759	−	0.976667i	$-0.431104\pi$
$434$	0.474927	−	8.15418i	0.0227972	−	0.391413i
$435$	−6.03161	+	6.25055i	−0.289194	+	0.299691i
$436$	−11.5541	−	1.35048i	−0.553341	−	0.0646763i
$437$	11.0378	+	11.6994i	0.528011	+	0.559659i
$438$	11.6207	+	1.49114i	0.555260	+	0.0712495i
$439$	−0.454536	+	0.0531276i	−0.0216938	+	0.00253564i	−0.126933	−	0.991911i	$-0.540513\pi$
$439$	−0.454536	+	0.0531276i	−0.0216938	+	0.00253564i	0.105239	+	0.994447i	$0.466439\pi$
$440$	5.53042	+	4.64057i	0.263652	+	0.221231i
$441$	1.27485	−	15.7617i	0.0607071	−	0.750556i
$442$	−10.9565	+	9.19361i	−0.521148	+	0.437296i
$443$	23.9557	−	25.3916i	1.13817	−	1.20639i	0.162602	−	0.986692i	$-0.448011\pi$
$443$	23.9557	−	25.3916i	1.13817	−	1.20639i	0.975568	−	0.219698i	$-0.0705072\pi$
$444$	20.6657	+	7.78643i	0.980750	+	0.369527i
$445$	−3.59165	−	1.80379i	−0.170260	−	0.0855080i
$446$	−15.0297	−	7.54822i	−0.711679	−	0.357419i
$447$	−0.820704	−	4.98198i	−0.0388180	−	0.235640i
$448$	3.76531	−	3.99100i	0.177894	−	0.188557i
$449$	−5.48196	+	4.59991i	−0.258710	+	0.217083i	−0.762912	−	0.646502i	$-0.776231\pi$
$449$	−5.48196	+	4.59991i	−0.258710	+	0.217083i	0.504202	+	0.863586i	$0.331787\pi$
$450$	−5.12913	−	7.22385i	−0.241790	−	0.340535i
$451$	9.63661	+	8.08607i	0.453770	+	0.380758i
$452$	−22.5603	+	2.63692i	−1.06115	+	0.124030i
$453$	−13.3965	+	17.5777i	−0.629421	+	0.825871i
$454$	−1.55685	−	1.65016i	−0.0730665	−	0.0774459i
$455$	−7.17515	−	0.838655i	−0.336376	−	0.0393167i
$456$	−12.3402	−	3.07190i	−0.577883	−	0.143855i
$457$	0.737417	−	12.6610i	0.0344949	−	0.592255i	−0.936130	−	0.351655i	$-0.885619\pi$
$457$	0.737417	−	12.6610i	0.0344949	−	0.592255i	0.970625	−	0.240599i	$-0.0773440\pi$
$458$	−0.635820	−	1.10127i	−0.0297099	−	0.0514591i
$459$	−19.5757	−	0.661797i	−0.913715	−	0.0308900i
$460$	4.75227	−	8.23117i	0.221576	−	0.383780i
$461$	−0.385841	−	0.253772i	−0.0179704	−	0.0118193i	0.540492	−	0.841349i	$-0.318238\pi$
$461$	−0.385841	−	0.253772i	−0.0179704	−	0.0118193i	−0.558462	+	0.829530i	$0.688608\pi$
$462$	3.41917	+	2.30442i	0.159074	+	0.107211i
$463$	14.6949	+	34.0667i	0.682931	+	1.58321i	0.806740	+	0.590906i	$0.201230\pi$
$463$	14.6949	+	34.0667i	0.682931	+	1.58321i	−0.123809	+	0.992306i	$0.539511\pi$
$464$	−1.28676	+	0.304968i	−0.0597363	+	0.0141578i
$465$	10.5626	+	11.4514i	0.489827	+	0.531045i
$466$	−3.24700	−	4.36148i	−0.150414	−	0.202042i
$467$	−25.8480	+	9.40792i	−1.19611	+	0.435347i	−0.861863	−	0.507141i	$-0.830702\pi$
$467$	−25.8480	+	9.40792i	−1.19611	+	0.435347i	−0.334242	+	0.942487i	$0.608480\pi$
$468$	−13.9270	+	11.1613i	−0.643775	+	0.515930i
$469$	−1.02568	−	0.373316i	−0.0473614	−	0.0172381i
$470$	−0.863897	−	2.88562i	−0.0398486	−	0.133104i
$471$	−1.66987	−	1.43355i	−0.0769437	−	0.0660546i
$472$	−1.74669	−	29.9895i	−0.0803980	−	1.38038i
$473$	9.17926	−	6.03729i	0.422063	−	0.277595i
$474$	8.13351	+	14.4614i	0.373584	+	0.664236i
$475$	−9.19653	−	2.17962i	−0.421966	−	0.100008i
$476$	−1.12413	−	6.37527i	−0.0515245	−	0.292210i
$477$	−11.5245	+	35.5583i	−0.527669	+	1.62810i
$478$	−2.44425	+	13.8620i	−0.111798	+	0.634035i
$479$	−5.64829	+	13.0942i	−0.258077	+	0.598290i	−0.997159	−	0.0753257i	$-0.976000\pi$
$479$	−5.64829	+	13.0942i	−0.258077	+	0.598290i	0.739082	+	0.673616i	$0.235260\pi$
$480$	0.565582	+	12.0472i	0.0258152	+	0.549875i
$481$	−12.7529	+	42.5978i	−0.581484	+	1.94229i
$482$	−6.26722	+	8.41834i	−0.285464	+	0.383445i
$483$	5.58417	−	12.5548i	0.254088	−	0.571262i
$484$	7.32563	−	3.67907i	0.332983	−	0.167230i
$485$	−1.64429			−0.0746634
$486$	12.9648	+	0.730998i	0.588095	+	0.0331587i
$487$	9.07752			0.411342			0.205671	−	0.978621i	$-0.434062\pi$
$487$	9.07752			0.411342			0.205671	+	0.978621i	$0.434062\pi$
$488$	−29.0238	+	14.5763i	−1.31385	+	0.659839i
$489$	8.70275	−	19.5662i	0.393552	−	0.884815i
$490$	3.16258	−	4.24808i	0.142871	−	0.191909i
$491$	7.99691	−	26.7115i	0.360896	−	1.20548i	−0.564167	−	0.825661i	$-0.690803\pi$
$491$	7.99691	−	26.7115i	0.360896	−	1.20548i	0.925063	−	0.379815i	$-0.124012\pi$
$492$	0.614047	+	13.0795i	0.0276834	+	0.589669i
$493$	6.20771	−	14.3911i	0.279581	−	0.648142i
$494$	1.75653	−	9.96180i	0.0790302	−	0.448203i
$495$	−7.69121	+	1.64078i	−0.345694	+	0.0737476i
$496$	0.411853	+	2.33573i	0.0184927	+	0.104878i
$497$	−9.27760	−	2.19883i	−0.416157	−	0.0986310i
$498$	3.37719	+	6.00467i	0.151335	+	0.269075i
$499$	19.8773	−	13.0735i	0.889828	−	0.585249i	−0.0202000	−	0.999796i	$-0.506430\pi$
$499$	19.8773	−	13.0735i	0.889828	−	0.585249i	0.910028	+	0.414547i	$0.136060\pi$
$500$	0.782724	+	13.4389i	0.0350045	+	0.601004i
$501$	5.01177	+	4.30250i	0.223909	+	0.192222i
$502$	6.16444	+	20.5907i	0.275133	+	0.919007i
$503$	7.57016	+	2.75531i	0.337537	+	0.122853i	0.505227	−	0.862986i	$-0.331409\pi$
$503$	7.57016	+	2.75531i	0.337537	+	0.122853i	−0.167690	+	0.985840i	$0.553631\pi$
$504$	1.64497	+	10.7385i	0.0732728	+	0.478329i
$505$	2.62367	−	0.954939i	0.116752	−	0.0424942i
$506$	−6.52276	−	8.76159i	−0.289972	−	0.389500i
$507$	−9.09830	−	9.86390i	−0.404070	−	0.438071i
$508$	−7.22097	+	1.71140i	−0.320379	+	0.0759311i
$509$	−7.64624	−	17.7260i	−0.338914	−	0.785690i	−0.999393	−	0.0348457i	$-0.988906\pi$
$509$	−7.64624	−	17.7260i	−0.338914	−	0.785690i	0.660479	−	0.750844i	$-0.270353\pi$
$510$	−5.43977	−	3.66624i	−0.240877	−	0.162344i
$511$	−8.92069	−	5.86723i	−0.394628	−	0.259551i
$512$	−1.79397	+	3.10725i	−0.0792832	+	0.137323i
$513$	10.9065	−	8.54068i	0.481536	−	0.377080i
$514$	−6.02780	−	10.4405i	−0.265875	−	0.460509i
$515$	0.319068	−	5.47818i	0.0140598	−	0.241398i
$516$	11.0971	+	2.76245i	0.488524	+	0.121610i
$517$	6.47161	+	0.756422i	0.284621	+	0.0332674i
$518$	7.33773	+	7.77754i	0.322401	+	0.341725i
$519$	−25.2711	+	33.1585i	−1.10928	+	1.45550i
$520$	−15.0282	+	1.75654i	−0.659029	+	0.0770294i
$521$	2.04454	+	1.71557i	0.0895727	+	0.0751604i	0.686474	−	0.727154i	$-0.259157\pi$
$521$	2.04454	+	1.71557i	0.0895727	+	0.0751604i	−0.596902	+	0.802314i	$0.703602\pi$
$522$	−4.32937	+	9.44564i	−0.189491	+	0.413424i
$523$	11.7693	−	9.87562i	0.514636	−	0.431831i	−0.348121	−	0.937450i	$-0.613180\pi$
$523$	11.7693	−	9.87562i	0.514636	−	0.431831i	0.862757	+	0.505619i	$0.168736\pi$
$524$	−17.4943	+	18.5429i	−0.764241	+	0.810048i
$525$	1.31239	+	7.96668i	0.0572773	+	0.347694i
$526$	−7.78248	−	3.90851i	−0.339332	−	0.170419i
$527$	−25.1198	−	12.6156i	−1.09423	−	0.549545i
$528$	−1.12039	−	0.422140i	−0.0487586	−	0.0183713i
$529$	−9.19617	+	9.74738i	−0.399834	+	0.423799i
$530$	−9.58997	+	8.04694i	−0.416562	+	0.349537i
$531$	26.9281	+	18.5932i	1.16858	+	0.806877i
$532$	3.50727	+	2.94295i	0.152059	+	0.127593i
$533$	−26.1862	+	3.06073i	−1.13425	+	0.132575i
$534$	−4.76867	−	0.611904i	−0.206361	−	0.0264797i
$535$	−10.1753	−	10.7852i	−0.439917	−	0.466285i
$536$	−2.27067	−	0.265403i	−0.0980780	−	0.0114637i
$537$	7.62430	−	7.90105i	0.329013	−	0.340956i
$538$	0.0102077	−	0.175259i	0.000440083	−	0.00755594i
$539$	5.72799	+	9.92117i	0.246722	+	0.427335i
$540$	−6.68320	−	4.72664i	−0.287599	−	0.203402i
$541$	9.39421	−	16.2713i	0.403889	−	0.699556i	−0.590303	−	0.807182i	$-0.700992\pi$
$541$	9.39421	−	16.2713i	0.403889	−	0.699556i	0.994191	+	0.107626i	$0.0343250\pi$
$542$	7.94586	+	5.22607i	0.341304	+	0.224479i
$543$	−0.744362	+	10.7019i	−0.0319436	+	0.459262i
$544$	−8.61917	−	19.9815i	−0.369544	−	0.856699i
$545$	10.4531	−	2.47743i	0.447761	−	0.106121i
$546$	−8.43044	+	1.89801i	−0.360790	+	0.0812274i
$547$	−6.84395	−	9.19302i	−0.292626	−	0.393065i	0.631361	−	0.775489i	$-0.282497\pi$
$547$	−6.84395	−	9.19302i	−0.292626	−	0.393065i	−0.923987	+	0.382424i	$0.875089\pi$
$548$	19.4583	−	7.08223i	0.831216	−	0.302538i
$549$	6.92692	−	34.6947i	0.295634	−	1.48073i
$550$	6.03132	+	2.19522i	0.257176	+	0.0936045i
$551$	3.17908	+	10.6189i	0.135433	+	0.452378i
$552$	5.31644	−	28.2841i	0.226283	−	1.20385i
$553$	−0.879191	−	15.0951i	−0.0373870	−	0.641910i
$554$	7.75969	−	5.10363i	0.329678	−	0.216832i
$555$	−20.3929	−	0.229730i	−0.865628	−	0.00975149i
$556$	13.2671	+	3.14435i	0.562649	+	0.133350i
$557$	4.33665	+	24.5943i	0.183750	+	1.04210i	0.927551	+	0.373695i	$0.121909\pi$
$557$	4.33665	+	24.5943i	0.183750	+	1.04210i	−0.743802	+	0.668400i	$0.766979\pi$
$558$	16.4608	+	8.73673i	0.696843	+	0.369855i
$559$	−3.99840	+	22.6761i	−0.169114	+	0.959095i
$560$	0.199791	−	0.463167i	0.00844269	−	0.0195724i
$561$	11.9426	−	7.66343i	0.504215	−	0.323550i
$562$	5.18511	−	17.3195i	0.218721	−	0.730579i
$563$	−10.4988	+	14.1023i	−0.442471	+	0.594341i	−0.966280	−	0.257494i	$-0.917103\pi$
$563$	−10.4988	+	14.1023i	−0.442471	+	0.594341i	0.523809	+	0.851836i	$0.324511\pi$
$564$	3.98839	+	5.48527i	0.167942	+	0.230972i
$565$	18.7447	−	9.41396i	0.788597	−	0.396048i
$566$	−0.247007			−0.0103825
$567$	−10.3253	−	5.78207i	−0.433623	−	0.242824i
$568$	−19.9700			−0.837922
$569$	14.2884	−	7.17589i	0.599000	−	0.300829i	−0.123343	−	0.992364i	$-0.539362\pi$
$569$	14.2884	−	7.17589i	0.599000	−	0.300829i	0.722343	+	0.691535i	$0.243065\pi$
$570$	4.61385	−	0.486665i	0.193253	−	0.0203841i
$571$	6.16873	−	8.28604i	0.258153	−	0.346760i	−0.654084	−	0.756422i	$-0.726946\pi$
$571$	6.16873	−	8.28604i	0.258153	−	0.346760i	0.912238	+	0.409662i	$0.134353\pi$
$572$	3.70831	−	12.3866i	0.155052	−	0.517911i
$573$	10.3921	+	5.36653i	0.434135	+	0.224190i
$574$	−2.51108	+	5.82133i	−0.104810	+	0.242978i
$575$	3.71420	−	21.0643i	0.154893	−	0.878441i
$576$	4.69814	+	11.6035i	0.195756	+	0.483480i
$577$	6.79785	+	38.5525i	0.282998	+	1.60496i	0.712349	+	0.701825i	$0.247631\pi$
$577$	6.79785	+	38.5525i	0.282998	+	1.60496i	−0.429351	+	0.903138i	$0.641258\pi$
$578$	−2.26219	−	0.536148i	−0.0940946	−	0.0223008i
$579$	14.0478	−	23.7106i	0.583806	−	0.985379i
$580$	5.47245	−	3.59929i	0.227231	−	0.149452i
$581$	−0.365057	−	6.26778i	−0.0151451	−	0.260031i
$582$	−1.85577	+	0.651866i	−0.0769241	+	0.0270207i
$583$	−7.76656	−	25.9421i	−0.321658	−	1.07441i
$584$	−21.0145	−	7.64866i	−0.869587	−	0.316504i
$585$	8.56042	−	14.0845i	0.353930	−	0.582322i
$586$	11.3554	−	4.13304i	0.469088	−	0.170734i
$587$	−10.6305	−	14.2792i	−0.438766	−	0.589365i	0.526649	−	0.850083i	$-0.323448\pi$
$587$	−10.6305	−	14.2792i	−0.438766	−	0.589365i	−0.965415	+	0.260718i	$0.916041\pi$
$588$	−3.54837	+	11.3841i	−0.146333	+	0.469471i
$589$	19.3445	−	4.58473i	0.797076	−	0.188910i
$590$	4.34086	+	10.0632i	0.178710	+	0.414297i
$591$	−18.0432	+	8.80852i	−0.742196	+	0.362334i
$592$	−2.59407	−	1.70614i	−0.106615	−	0.0701221i
$593$	6.92687	−	11.9977i	0.284452	−	0.492686i	−0.688024	−	0.725688i	$-0.741522\pi$
$593$	6.92687	−	11.9977i	0.284452	−	0.492686i	0.972476	+	0.233002i	$0.0748549\pi$
$594$	−8.02992	+	4.90092i	−0.329472	+	0.201087i
$595$	2.98914	+	5.17735i	0.122543	+	0.212251i
$596$	−0.221381	+	3.80096i	−0.00906811	+	0.155693i
$597$	−2.05546	−	7.15823i	−0.0841245	−	0.292967i
$598$	22.7376	+	2.65764i	0.929809	+	0.108679i
$599$	−2.48356	−	2.63242i	−0.101475	−	0.107558i	0.674645	−	0.738142i	$-0.264297\pi$
$599$	−2.48356	−	2.63242i	−0.101475	−	0.107558i	−0.776121	+	0.630585i	$0.782815\pi$
$600$	6.52273	+	15.6023i	0.266289	+	0.636962i
$601$	10.3128	−	1.20539i	0.420667	−	0.0491689i	0.0968736	−	0.995297i	$-0.469116\pi$
$601$	10.3128	−	1.20539i	0.420667	−	0.0491689i	0.323794	+	0.946128i	$0.395042\pi$
$602$	4.24159	+	3.55912i	0.172874	+	0.145059i
$603$	1.74934	−	1.77244i	0.0712385	−	0.0721792i
$604$	12.7665	−	10.7124i	0.519462	−	0.435880i
$605$	−5.19508	+	5.50647i	−0.211210	+	0.223870i
$606$	2.58253	−	2.11789i	0.104908	−	0.0860334i
$607$	12.0040	+	6.02866i	0.487229	+	0.244696i	0.675415	−	0.737438i	$-0.263964\pi$
$607$	12.0040	+	6.02866i	0.487229	+	0.244696i	−0.188186	+	0.982133i	$0.560261\pi$
$608$	13.7534	+	6.90721i	0.557773	+	0.280124i
$609$	7.32200	−	6.00464i	0.296702	−	0.243320i
$610$	8.13131	−	8.61869i	0.329227	−	0.348960i
$611$	−10.4607	+	8.77758i	−0.423195	+	0.355103i
$612$	14.2914	+	3.72907i	0.577696	+	0.150739i
$613$	22.2652	+	18.6827i	0.899281	+	0.754587i	0.970050	−	0.242906i	$-0.0781007\pi$
$613$	22.2652	+	18.6827i	0.899281	+	0.754587i	−0.0707686	+	0.997493i	$0.522545\pi$
$614$	−3.13496	+	0.366425i	−0.126517	+	0.0147877i
$615$	−4.66402	−	11.1563i	−0.188072	−	0.449866i
$616$	−5.40094	−	5.72466i	−0.217610	−	0.230653i
$617$	−12.3463	−	1.44308i	−0.497044	−	0.0580961i	−0.136122	−	0.990692i	$-0.543464\pi$
$617$	−12.3463	−	1.44308i	−0.497044	−	0.0580961i	−0.360922	+	0.932596i	$0.617538\pi$
$618$	−1.81168	−	6.30924i	−0.0728763	−	0.253795i
$619$	−2.00980	+	34.5070i	−0.0807807	+	1.38695i	0.677739	+	0.735302i	$0.262960\pi$
$619$	−2.00980	+	34.5070i	−0.0807807	+	1.38695i	−0.758520	+	0.651650i	$0.774077\pi$
$620$	−5.87380	−	10.1737i	−0.235898	−	0.408586i
$621$	20.7309	+	23.5170i	0.831903	+	0.943706i
$622$	−5.13533	+	8.89464i	−0.205908	+	0.356643i
$623$	3.66069	+	2.40767i	0.146662	+	0.0964614i
$624$	2.25489	−	1.10082i	0.0902677	−	0.0440679i
$625$	2.09699	+	4.86137i	0.0838796	+	0.194455i
$626$	5.51652	−	1.30744i	0.220484	−	0.0522558i
$627$	−2.98638	+	9.58105i	−0.119265	+	0.382630i
$628$	0.991023	+	1.33118i	0.0395461	+	0.0531197i
$629$	34.5789	−	12.5857i	1.37875	−	0.501825i
$630$	−1.90387	−	3.47616i	−0.0758519	−	0.138494i
$631$	12.4258	+	4.52262i	0.494663	+	0.180042i	0.577292	−	0.816538i	$-0.304109\pi$
$631$	12.4258	+	4.52262i	0.494663	+	0.180042i	−0.0826292	+	0.996580i	$0.526332\pi$
$632$	−9.08304	−	30.3395i	−0.361304	−	1.20684i
$633$	−23.3379	+	8.19779i	−0.927599	+	0.325833i
$634$	0.723456	+	12.4213i	0.0287321	+	0.493311i
$635$	5.72575	−	3.76588i	0.227219	−	0.149445i
$636$	14.3674	−	24.2500i	0.569704	−	0.961576i
$637$	−23.3622	−	5.53695i	−0.925645	−	0.219382i
$638$	−1.30714	−	7.41317i	−0.0517502	−	0.293490i
$639$	13.3802	−	17.1521i	0.529312	−	0.678525i
$640$	1.69021	−	9.58567i	0.0668115	−	0.378907i
$641$	−2.08848	+	4.84165i	−0.0824901	+	0.191234i	−0.954469	−	0.298310i	$-0.903577\pi$
$641$	−2.08848	+	4.84165i	−0.0824901	+	0.191234i	0.871979	+	0.489543i	$0.162836\pi$
$642$	−15.7597	−	8.13840i	−0.621986	−	0.321197i
$643$	−1.25523	+	4.19275i	−0.0495013	+	0.165346i	−0.979166	−	0.203060i	$-0.934911\pi$
$643$	−1.25523	+	4.19275i	−0.0495013	+	0.165346i	0.929665	+	0.368406i	$0.120096\pi$
$644$	−6.18741	+	8.31114i	−0.243818	+	0.327505i
$645$	−10.5025	+	1.10780i	−0.413536	+	0.0436194i
$646$	−7.48075	+	3.75697i	−0.294326	+	0.147816i
$647$	5.42624			0.213327			0.106664	−	0.994295i	$-0.465983\pi$
$647$	5.42624			0.213327			0.106664	+	0.994295i	$0.465983\pi$
$648$	−23.8361	−	6.79664i	−0.936369	−	0.266997i
$649$	−23.7069			−0.930576
$650$	−12.0208	+	6.03709i	−0.471496	+	0.236794i
$651$	−9.98769	−	13.7362i	−0.391449	−	0.538363i
$652$	−9.64289	+	12.9527i	−0.377645	+	0.507265i
$653$	−3.18380	+	10.6346i	−0.124592	+	0.416166i	−0.997414	−	0.0718731i	$-0.977102\pi$
$653$	−3.18380	+	10.6346i	−0.124592	+	0.416166i	0.872822	+	0.488039i	$0.162288\pi$
$654$	10.8153	−	6.94010i	0.422913	−	0.271379i
$655$	9.32462	−	21.6169i	0.364343	−	0.844642i
$656$	0.319672	−	1.81295i	0.0124811	−	0.0707837i
$657$	20.6494	−	12.9245i	0.805610	−	0.504232i
$658$	0.570212	+	3.23383i	0.0222292	+	0.126068i
$659$	−7.23488	−	1.71470i	−0.281831	−	0.0667951i	0.0872694	−	0.996185i	$-0.472186\pi$
$659$	−7.23488	−	1.71470i	−0.281831	−	0.0667951i	−0.369100	+	0.929390i	$0.620334\pi$
$660$	5.92985	+	0.0668011i	0.230819	+	0.00260023i
$661$	3.20127	−	2.10551i	0.124515	−	0.0818948i	−0.485724	−	0.874112i	$-0.661444\pi$
$661$	3.20127	−	2.10551i	0.124515	−	0.0818948i	0.610239	+	0.792218i	$0.291074\pi$
$662$	0.178911	+	3.07178i	0.00695358	+	0.119388i
$663$	−5.49372	+	29.2273i	−0.213358	+	1.13509i
$664$	−3.77145	−	12.5975i	−0.146361	−	0.488879i
$665$	−3.97311	−	1.44609i	−0.154071	−	0.0560771i
$666$	−23.1067	+	7.82530i	−0.895366	+	0.303224i
$667$	−23.5726	+	8.57971i	−0.912733	+	0.332208i
$668$	−2.97435	−	3.99524i	−0.115081	−	0.154581i
$669$	−34.1166	+	7.68093i	−1.31902	+	0.296962i
$670$	0.811561	−	0.192344i	0.0313533	−	0.00743088i
$671$	10.1519	+	23.5347i	0.391910	+	0.908549i
$672$	0.912276	−	13.1160i	0.0351918	−	0.505962i
$673$	−35.1668	−	23.1295i	−1.35558	−	0.891578i	−0.356492	−	0.934298i	$-0.616027\pi$
$673$	−35.1668	−	23.1295i	−1.35558	−	0.891578i	−0.999087	+	0.0427202i	$0.986398\pi$
$674$	−7.68230	+	13.3061i	−0.295911	+	0.512533i
$675$	−17.7710	−	4.85147i	−0.684008	−	0.186733i
$676$	5.05953	+	8.76336i	0.194597	+	0.337052i
$677$	0.144919	−	2.48817i	0.00556970	−	0.0956281i	−0.994378	−	0.105892i	$-0.966230\pi$
$677$	0.144919	−	2.48817i	0.00556970	−	0.0956281i	0.999947	+	0.0102640i	$0.00326720\pi$
$678$	17.4235	−	18.0559i	0.669144	−	0.693433i
$679$	1.78041	+	0.208100i	0.0683260	+	0.00798616i
$680$	8.59269	+	9.10772i	0.329515	+	0.349265i
$681$	−4.67877	−	0.600368i	−0.179291	−	0.0230061i
$682$	−13.4095	+	1.56735i	−0.513477	+	0.0600169i
$683$	−11.7411	−	9.85194i	−0.449260	−	0.376974i	0.389901	−	0.920857i	$-0.372509\pi$
$683$	−11.7411	−	9.85194i	−0.449260	−	0.376974i	−0.839161	+	0.543883i	$0.816954\pi$
$684$	−9.43803	+	4.47663i	−0.360872	+	0.171168i
$685$	−14.6488	+	12.2918i	−0.559701	+	0.469645i
$686$	−9.22362	+	9.77646i	−0.352159	+	0.373267i
$687$	−2.47427	−	0.932257i	−0.0943993	−	0.0355678i
$688$	−1.43678	−	0.721578i	−0.0547767	−	0.0275099i
$689$	50.7168	+	25.4710i	1.93216	+	0.970366i
$690$	1.70663	+	10.3599i	0.0649705	+	0.394395i
$691$	−25.4658	+	26.9922i	−0.968765	+	1.02683i	0.0308620	+	0.999524i	$0.490175\pi$
$691$	−25.4658	+	26.9922i	−0.968765	+	1.02683i	−0.999627	+	0.0273073i	$0.991307\pi$
$692$	24.0827	−	20.2078i	0.915488	−	0.768186i
$693$	8.53558	−	0.803216i	0.324240	−	0.0305116i
$694$	−21.4384	−	17.9890i	−0.813792	−	0.682853i
$695$	−12.5062	+	1.46176i	−0.474387	+	0.0554478i
$696$	12.0220	−	15.7742i	0.455693	−	0.597921i
$697$	14.9725	+	15.8700i	0.567125	+	0.601118i
$698$	27.2519	+	3.18529i	1.03150	+	0.120565i
$699$	−10.9710	−	2.73105i	−0.414961	−	0.103298i
$700$	0.354010	−	6.07811i	0.0133803	−	0.229731i
$701$	−3.35489	−	5.81083i	−0.126712	−	0.219472i	0.795689	−	0.605706i	$-0.207109\pi$
$701$	−3.35489	−	5.81083i	−0.126712	−	0.219472i	−0.922401	+	0.386234i	$0.873776\pi$
$702$	4.07772	−	19.2896i	0.153904	−	0.728040i
$703$	−13.0126	+	22.5385i	−0.490779	+	0.850054i
$704$	−7.57719	−	4.98360i	−0.285576	−	0.187826i
$705$	−5.19361	−	3.50034i	−0.195603	−	0.131830i
$706$	4.40186	+	10.2046i	0.165666	+	0.384057i
$707$	−2.96173	+	0.701942i	−0.111387	+	0.0263993i
$708$	−16.7304	−	18.1382i	−0.628766	−	0.681675i
$709$	−14.2011	−	19.0753i	−0.533332	−	0.716389i	0.451037	−	0.892505i	$-0.351054\pi$
$709$	−14.2011	−	19.0753i	−0.533332	−	0.716389i	−0.984369	+	0.176116i	$0.943647\pi$
$710$	6.84623	−	2.49182i	0.256934	−	0.0935165i
$711$	32.1441	+	12.5265i	1.20550	+	0.469782i
$712$	8.62351	+	3.13870i	0.323180	+	0.117628i
$713$	12.9037	+	43.1012i	0.483246	+	1.61415i
$714$	5.42610	+	4.65820i	0.203067	+	0.174329i
$715$	0.694277	+	11.9203i	0.0259645	+	0.445793i
$716$	−6.91748	+	4.54970i	−0.258519	+	0.170030i
$717$	14.3473	+	25.5096i	0.535809	+	0.952674i
$718$	7.31634	+	1.73400i	0.273043	+	0.0647125i
$719$	−7.41202	−	42.0356i	−0.276422	−	1.56766i	−0.734410	−	0.678706i	$-0.762541\pi$
$719$	−7.41202	−	42.0356i	−0.276422	−	1.56766i	0.457988	−	0.888958i	$-0.348570\pi$
$720$	0.770710	+	0.854684i	0.0287227	+	0.0318522i
$721$	−1.03880	+	5.89131i	−0.0386868	+	0.219404i
$722$	−3.92388	+	9.09658i	−0.146032	+	0.338540i
$723$	1.02336	+	21.7980i	0.0380591	+	0.810676i
$724$	2.32009	−	7.74965i	0.0862255	−	0.288013i
$725$	8.80228	−	11.8235i	0.326909	−	0.439114i
$726$	−3.68024	+	8.27421i	−0.136587	+	0.307085i
$727$	17.0289	−	8.55222i	0.631565	−	0.317184i	−0.104062	−	0.994571i	$-0.533184\pi$
$727$	17.0289	−	8.55222i	0.631565	−	0.317184i	0.735627	+	0.677387i	$0.236888\pi$
$728$	16.4946			0.611329
$729$	21.8081	−	15.9188i	0.807707	−	0.589584i
$730$	8.15871			0.301967
$731$	17.0284	−	8.55200i	0.629819	−	0.316307i
$732$	−10.8421	+	24.3761i	−0.400737	+	0.900968i
$733$	−10.7269	+	14.4087i	−0.396207	+	0.532199i	−0.954802	−	0.297242i	$-0.903933\pi$
$733$	−10.7269	+	14.4087i	−0.396207	+	0.532199i	0.558595	+	0.829441i	$0.311341\pi$
$734$	−6.11705	+	20.4324i	−0.225784	+	0.754173i
$735$	−0.516409	−	10.9997i	−0.0190480	−	0.405732i
$736$	−13.7955	+	31.9816i	−0.508509	+	1.17886i
$737$	−0.313285	+	1.77673i	−0.0115400	+	0.0654466i
$738$	−9.68671	−	10.7421i	−0.356573	−	0.395424i
$739$	2.16602	+	12.2841i	0.0796782	+	0.451878i	0.998379	+	0.0569224i	$0.0181288\pi$
$739$	2.16602	+	12.2841i	0.0796782	+	0.451878i	−0.918700	+	0.394955i	$0.870760\pi$
$740$	14.9641	+	3.54656i	0.550092	+	0.130374i
$741$	−10.3105	−	18.3322i	−0.378766	−	0.673450i
$742$	11.4023	−	7.49940i	0.418591	−	0.275312i
$743$	1.50694	+	25.8731i	0.0552842	+	0.949193i	0.905923	+	0.423443i	$0.139179\pi$
$743$	1.50694	+	25.8731i	0.0552842	+	0.949193i	−0.850639	+	0.525751i	$0.823784\pi$
$744$	−26.9899	−	23.1703i	−0.989499	−	0.849465i
$745$	−1.00842	−	3.36836i	−0.0369457	−	0.123407i
$746$	17.1175	+	6.23026i	0.626716	+	0.228106i
$747$	13.3468	+	5.20126i	0.488335	+	0.190304i
$748$	−10.0549	+	3.65968i	−0.367643	+	0.133811i
$749$	9.65270	+	12.9658i	0.352702	+	0.473761i
$750$	−10.0825	−	10.9310i	−0.368162	−	0.399142i
$751$	10.2130	−	2.42053i	0.372679	−	0.0883265i	−0.0400083	−	0.999199i	$-0.512738\pi$
$751$	10.2130	−	2.42053i	0.372679	−	0.0883265i	0.412687	+	0.910873i	$0.364590\pi$
$752$	−0.377663	−	0.875522i	−0.0137720	−	0.0319270i
$753$	37.0597	+	24.9771i	1.35053	+	0.910216i
$754$	13.1808	+	8.66914i	0.480016	+	0.315711i
$755$	−7.69516	+	13.3284i	−0.280056	+	0.485070i
$756$	6.63826	+	5.96375i	0.241431	+	0.216900i
$757$	−0.0864170	−	0.149679i	−0.00314088	−	0.00544016i	0.864451	−	0.502718i	$-0.167666\pi$
$757$	−0.0864170	−	0.149679i	−0.00314088	−	0.00544016i	−0.867592	+	0.497277i	$0.834333\pi$
$758$	−0.510234	+	8.76039i	−0.0185326	+	0.318192i
$759$	−22.0392	−	5.48630i	−0.799971	−	0.199140i
$760$	−8.79576	−	1.02808i	−0.319056	−	0.0372923i
$761$	−1.28543	−	1.36248i	−0.0465968	−	0.0493897i	0.703656	−	0.710541i	$-0.251550\pi$
$761$	−1.28543	−	1.36248i	−0.0465968	−	0.0493897i	−0.750253	+	0.661151i	$0.770068\pi$
$762$	4.96920	−	6.52015i	0.180015	−	0.236200i
$763$	−11.6320	+	1.35958i	−0.421106	+	0.0492203i
$764$	−6.75618	−	5.66911i	−0.244430	−	0.205101i
$765$	−13.5798	+	1.27789i	−0.490978	+	0.0462021i
$766$	13.9549	−	11.7095i	0.504211	−	0.423083i
$767$	34.0957	−	36.1394i	1.23113	−	1.30492i
$768$	−4.24217	−	25.7515i	−0.153076	−	0.929228i
$769$	−24.9413	−	12.5260i	−0.899405	−	0.451698i	−0.0618716	−	0.998084i	$-0.519707\pi$
$769$	−24.9413	−	12.5260i	−0.899405	−	0.451698i	−0.837534	+	0.546386i	$0.816003\pi$
$770$	2.56590	+	1.28864i	0.0924685	+	0.0464394i
$771$	−23.4570	−	8.83812i	−0.844782	−	0.318297i
$772$	−14.2614	+	15.1162i	−0.513280	+	0.544045i
$773$	0.0418155	−	0.0350873i	0.00150400	−	0.00126200i	−0.642035	−	0.766675i	$-0.721910\pi$
$773$	0.0418155	−	0.0350873i	0.00150400	−	0.00126200i	0.643539	+	0.765413i	$0.277465\pi$
$774$	−11.4141	+	5.41390i	−0.410271	+	0.194599i
$775$	−20.2520	−	16.9934i	−0.727472	−	0.610422i
$776$	3.72903	−	0.435861i	0.133864	−	0.0156465i
$777$	22.0520	+	2.82965i	0.791110	+	0.101513i
$778$	−13.9429	−	14.7786i	−0.499875	−	0.529837i
$779$	−15.3264	−	1.79140i	−0.549125	−	0.0641835i
$780$	−8.63028	+	8.94355i	−0.309014	+	0.320230i
$781$	−0.916342	+	15.7330i	−0.0327893	+	0.562971i
$782$	−9.47240	−	16.4067i	−0.338732	−	0.586702i
$783$	5.49344	+	20.8946i	0.196320	+	0.746712i
$784$	0.838235	−	1.45187i	0.0299370	−	0.0518524i
$785$	−1.28045	−	0.842167i	−0.0457013	−	0.0300582i
$786$	1.95404	−	28.0938i	0.0696983	−	1.00207i
$787$	−13.4349	−	31.1455i	−0.478901	−	1.11022i	−0.970871	−	0.239604i	$-0.922982\pi$
$787$	−13.4349	−	31.1455i	−0.478901	−	1.11022i	0.491970	−	0.870612i	$-0.336277\pi$
$788$	14.7325	−	3.49167i	0.524824	−	0.124385i
$789$	−17.6657	+	3.97723i	−0.628917	+	0.141593i
$790$	6.89962	+	9.26779i	0.245477	+	0.329733i
$791$	−21.4879	+	7.82097i	−0.764023	+	0.278082i
$792$	17.0077	−	5.75982i	0.604342	−	0.204666i
$793$	−50.4776	−	18.3724i	−1.79251	−	0.652422i
$794$	−5.73347	−	19.1511i	−0.203473	−	0.679648i
$795$	−4.80852	+	25.5819i	−0.170541	+	0.907297i
$796$	0.326538	+	5.60645i	0.0115738	+	0.198715i
$797$	−12.1670	+	8.00239i	−0.430979	+	0.283459i	−0.746406	−	0.665491i	$-0.768222\pi$
$797$	−12.1670	+	8.00239i	−0.430979	+	0.283459i	0.315428	+	0.948950i	$0.397852\pi$
$798$	−5.05739	−	0.0569726i	−0.179030	−	0.00201681i
$799$	10.9961	+	2.60613i	0.389015	+	0.0921982i
$800$	−3.55394	−	20.1554i	−0.125651	−	0.712600i
$801$	−8.47368	+	5.30369i	−0.299403	+	0.187397i
$802$	−5.33961	+	30.2825i	−0.188548	+	1.06931i
$803$	−6.99013	+	16.2049i	−0.246676	+	0.571860i
$804$	−1.58047	+	1.01417i	−0.0557389	+	0.0357672i
$805$	2.74431	−	9.16663i	0.0967242	−	0.323081i
$806$	16.8966	−	22.6960i	0.595156	−	0.799433i
$807$	−0.214666	−	0.295233i	−0.00755662	−	0.0103927i
$808$	−5.69700	+	2.86114i	−0.200420	+	0.100655i
$809$	28.0189			0.985092			0.492546	−	0.870286i	$-0.336066\pi$
$809$	28.0189			0.985092			0.492546	+	0.870286i	$0.336066\pi$
$810$	9.01970	−	0.644163i	0.316920	−	0.0226336i
$811$	29.1924			1.02508			0.512542	−	0.858662i	$-0.328704\pi$
$811$	29.1924			1.02508			0.512542	+	0.858662i	$0.328704\pi$
$812$	−6.38100	+	3.20466i	−0.223929	+	0.112462i
$813$	19.6656	−	2.07431i	0.689703	−	0.0727493i
$814$	10.5540	−	14.1765i	0.369919	−	0.496887i
$815$	4.27692	−	14.2859i	0.149814	−	0.500413i
$816$	−1.84506	−	0.952798i	−0.0645900	−	0.0333546i
$817$	−5.33785	+	12.3745i	−0.186748	+	0.432930i
$818$	−0.413009	+	2.34229i	−0.0144405	+	0.0818964i
$819$	−11.0516	+	14.1671i	−0.386174	+	0.495037i
$820$	1.58337	+	8.97971i	0.0552935	+	0.313585i
$821$	−29.0511	−	6.88525i	−1.01389	−	0.240297i	−0.310101	−	0.950704i	$-0.600363\pi$
$821$	−29.0511	−	6.88525i	−1.01389	−	0.240297i	−0.703791	+	0.710407i	$0.748511\pi$
$822$	−11.6598	+	19.6801i	−0.406683	+	0.686421i
$823$	33.5799	−	22.0858i	1.17052	−	0.769864i	0.193103	−	0.981178i	$-0.438145\pi$
$823$	33.5799	−	22.0858i	1.17052	−	0.769864i	0.977418	+	0.211315i	$0.0677745\pi$
$824$	0.728528	+	12.5084i	0.0253795	+	0.435749i
$825$	12.5913	−	4.42288i	0.438373	−	0.153985i
$826$	−3.42662	−	11.4457i	−0.119227	−	0.398247i
$827$	39.9498	+	14.5405i	1.38919	+	0.505623i	0.924951	−	0.380087i	$-0.124106\pi$
$827$	39.9498	+	14.5405i	1.38919	+	0.505623i	0.464238	+	0.885710i	$0.346328\pi$
$828$	−11.3559	−	20.7340i	−0.394643	−	0.720557i
$829$	5.90599	−	2.14960i	0.205124	−	0.0746589i	−0.237415	−	0.971408i	$-0.576300\pi$
$829$	5.90599	−	2.14960i	0.205124	−	0.0746589i	0.442539	+	0.896749i	$0.354078\pi$
$830$	2.86485	+	3.84816i	0.0994404	+	0.133572i
$831$	5.74661	−	18.4365i	0.199348	−	0.639557i
$832$	18.4948	−	4.38335i	0.641192	−	0.151965i
$833$	7.86979	+	18.2442i	0.272672	+	0.632125i
$834$	−13.5351	+	6.60774i	−0.468683	+	0.228807i
$835$	3.84301	+	2.52759i	0.132993	+	0.0874708i
$836$	3.78381	−	6.55375i	0.130866	−	0.226666i
$837$	37.9845	−	7.65699i	1.31293	−	0.264664i
$838$	−14.3173	−	24.7983i	−0.494584	−	0.856644i
$839$	−0.963006	+	16.5342i	−0.0332466	+	0.570823i	0.940016	+	0.341129i	$0.110809\pi$
$839$	−0.963006	+	16.5342i	−0.0332466	+	0.570823i	−0.973263	+	0.229694i	$0.926228\pi$
$840$	2.08795	+	7.27136i	0.0720410	+	0.250886i
$841$	11.6333	+	1.35974i	0.401149	+	0.0468876i
$842$	−3.57373	−	3.78793i	−0.123159	−	0.130541i
$843$	−14.4993	−	34.6822i	−0.499381	−	1.19452i
$844$	18.5265	−	2.16543i	0.637707	−	0.0745373i
$845$	−7.15852	−	6.00671i	−0.246261	−	0.206637i
$846$	−7.24926	−	1.89156i	−0.249235	−	0.0650330i
$847$	6.32205	−	5.30483i	0.217228	−	0.182276i
$848$	−2.71947	+	2.88247i	−0.0933871	+	0.0989846i
$849$	−0.397128	+	0.325677i	−0.0136294	+	0.0111772i
$850$	9.94795	+	4.99605i	0.341212	+	0.171363i
$851$	−52.6328	−	26.4332i	−1.80423	−	0.906118i
$852$	−12.6840	+	10.4020i	−0.434548	+	0.356365i
$853$	35.7674	−	37.9112i	1.22465	−	1.29806i	0.283943	−	0.958841i	$-0.408357\pi$
$853$	35.7674	−	37.9112i	1.22465	−	1.29806i	0.940709	−	0.339214i	$-0.110161\pi$
$854$	−9.89523	+	8.30308i	−0.338608	+	0.284126i
$855$	6.77630	−	6.86578i	0.231745	−	0.234805i
$856$	25.9351	+	21.7622i	0.886445	+	0.743815i
$857$	38.6194	−	4.51396i	1.31921	−	0.154194i	0.572811	−	0.819687i	$-0.305853\pi$
$857$	38.6194	−	4.51396i	1.31921	−	0.154194i	0.746404	+	0.665493i	$0.231779\pi$
$858$	5.50926	+	13.1781i	0.188083	+	0.449894i
$859$	14.8940	+	15.7867i	0.508177	+	0.538637i	0.929766	−	0.368151i	$-0.120009\pi$
$859$	14.8940	+	15.7867i	0.508177	+	0.538637i	−0.421589	+	0.906787i	$0.638527\pi$
$860$	7.90973	+	0.924515i	0.269720	+	0.0315257i
$861$	3.63819	+	12.6702i	0.123989	+	0.431798i
$862$	−0.146142	+	2.50915i	−0.00497760	+	0.0854621i
$863$	−21.9404	−	38.0020i	−0.746861	−	1.29360i	−0.949320	−	0.314311i	$-0.898227\pi$
$863$	−21.9404	−	38.0020i	−0.746861	−	1.29360i	0.202459	−	0.979291i	$-0.435107\pi$
$864$	26.3363	+	14.3608i	0.895980	+	0.488564i
$865$	−14.5161	+	25.1427i	−0.493564	+	0.854877i
$866$	−21.3885	−	14.0674i	−0.726811	−	0.478031i
$867$	−4.34397	+	2.12069i	−0.147529	+	0.0720223i
$868$	5.07248	+	11.7593i	0.172171	+	0.399138i
$869$	−24.3192	+	5.76375i	−0.824972	+	0.195522i
$870$	−2.15317	+	6.90791i	−0.0729994	+	0.234200i
$871$	−2.25792	−	3.03291i	−0.0765066	−	0.102766i
$872$	−23.0495	+	8.38933i	−0.780554	+	0.284099i
$873$	−2.12415	+	3.49487i	−0.0718915	+	0.118283i
$874$	12.5905	+	4.58258i	0.425881	+	0.155008i
$875$	3.88687	+	12.9830i	0.131400	+	0.438907i
$876$	−17.3315	+	6.08795i	−0.585578	+	0.205693i
$877$	1.46065	+	25.0784i	0.0493226	+	0.846837i	0.928728	+	0.370763i	$0.120904\pi$
$877$	1.46065	+	25.0784i	0.0493226	+	0.846837i	−0.879405	+	0.476074i	$0.842059\pi$
$878$	−0.318498	+	0.209479i	−0.0107488	+	0.00706958i
$879$	12.8074	−	21.6170i	0.431983	−	0.729124i
$880$	−0.811277	−	0.192276i	−0.0273481	−	0.00648163i
$881$	0.463850	+	2.63063i	0.0156275	+	0.0886281i	0.991624	−	0.129158i	$-0.0412275\pi$
$881$	0.463850	+	2.63063i	0.0156275	+	0.0886281i	−0.975996	+	0.217786i	$0.930116\pi$
$882$	−4.94358	−	12.2097i	−0.166459	−	0.411123i
$883$	6.82642	−	38.7145i	0.229727	−	1.30285i	−0.623711	−	0.781655i	$-0.714376\pi$
$883$	6.82642	−	38.7145i	0.229727	−	1.30285i	0.853439	−	0.521193i	$-0.174513\pi$
$884$	8.88225	−	20.5914i	0.298742	−	0.692563i
$885$	20.2474	+	10.4559i	0.680610	+	0.351471i
$886$	8.34003	−	27.8576i	0.280189	−	0.935895i
$887$	19.9569	−	26.8067i	0.670086	−	0.900081i	−0.328934	−	0.944353i	$-0.606689\pi$
$887$	19.9569	−	26.8067i	0.670086	−	0.900081i	0.999020	+	0.0442716i	$0.0140967\pi$
$888$	46.3091	−	4.88465i	1.55403	−	0.163918i
$889$	−6.67635	+	3.35299i	−0.223918	+	0.112456i
$890$	−3.34800			−0.112225
$891$	−6.44835	+	18.4669i	−0.216028	+	0.618666i
$892$	26.3703			0.882942
$893$	−7.14223	+	3.58696i	−0.239006	+	0.120033i
$894$	−2.47348	−	3.40180i	−0.0827254	−	0.113773i
$895$	4.56591	−	6.13308i	0.152621	−	0.205006i
$896$	−3.04329	+	10.1653i	−0.101669	+	0.339599i
$897$	40.0607	−	25.7066i	1.33759	−	0.858317i
$898$	−2.36111	+	5.47367i	−0.0787912	+	0.182659i
$899$	−5.38405	+	30.5345i	−0.179568	+	1.01838i
$900$	12.2699	+	6.51235i	0.408996	+	0.217078i
$901$	−8.15573	−	46.2534i	−0.271707	−	1.54093i
$902$	10.1966	+	2.41663i	0.339509	+	0.0804651i
$903$	11.5121	+	0.129687i	0.383100	+	0.00431571i
$904$	−40.0151	+	26.3184i	−1.33088	+	0.875336i
$905$	0.434372	+	7.45788i	0.0144390	+	0.247908i
$906$	−3.40092	+	18.0933i	−0.112988	+	0.601109i
$907$	3.52864	+	11.7865i	0.117167	+	0.391364i	0.996375	−	0.0850742i	$-0.0271127\pi$
$907$	3.52864	+	11.7865i	0.117167	+	0.391364i	−0.879208	+	0.476438i	$0.841928\pi$
$908$	3.34254	+	1.21658i	0.110926	+	0.0403738i
$909$	1.35966	−	6.81012i	0.0450972	−	0.225877i
$910$	−5.65477	+	2.05817i	−0.187454	+	0.0682276i
$911$	−13.0498	−	17.5289i	−0.432359	−	0.580759i	0.531538	−	0.847034i	$-0.321614\pi$
$911$	−13.0498	−	17.5289i	−0.432359	−	0.580759i	−0.963897	+	0.266276i	$0.914207\pi$
$912$	1.43276	−	0.322569i	0.0474435	−	0.0106813i
$913$	−10.0978	+	2.39322i	−0.334188	+	0.0792040i
$914$	−4.18443	−	9.70059i	−0.138409	−	0.320867i
$915$	1.70950	−	24.5779i	0.0565142	−	0.812520i
$916$	1.66581	+	1.09562i	0.0550400	+	0.0362004i
$917$	−12.8324	+	22.2263i	−0.423762	+	0.733977i
$918$	−14.8197	+	6.82583i	−0.489123	+	0.225286i
$919$	27.9349	+	48.3846i	0.921487	+	1.59606i	0.797116	+	0.603826i	$0.206358\pi$
$919$	27.9349	+	48.3846i	0.921487	+	1.59606i	0.124370	+	0.992236i	$0.460309\pi$
$920$	1.16529	−	20.0073i	0.0384186	−	0.659622i
$921$	−4.55714	+	4.72256i	−0.150163	+	0.155614i
$922$	−0.382097	−	0.0446607i	−0.0125837	−	0.00147082i
$923$	−22.6659	−	24.0244i	−0.746056	−	0.790774i
$924$	−6.41230	−	0.822809i	−0.210949	−	0.0270684i
$925$	34.3744	−	4.01780i	1.13022	−	0.132104i
$926$	23.6750	+	19.8657i	0.778009	+	0.652827i
$927$	−11.2314	−	7.75505i	−0.368889	−	0.254709i
$928$	−18.3873	+	15.4288i	−0.603594	+	0.506476i
$929$	−29.4428	+	31.2075i	−0.965986	+	1.02389i	0.0337151	+	0.999431i	$0.489266\pi$
$929$	−29.4428	+	31.2075i	−0.965986	+	1.02389i	−0.999701	+	0.0244537i	$0.992215\pi$
$930$	12.1440	+	4.57562i	0.398218	+	0.150041i
$931$	−12.5576	−	6.30668i	−0.411560	−	0.206693i
$932$	7.61857	+	3.82619i	0.249554	+	0.125331i
$933$	3.47118	+	21.0714i	0.113641	+	0.689846i
$934$	−15.7243	+	16.6668i	−0.514514	+	0.545353i
$935$	7.56964	−	6.35168i	0.247554	−	0.207722i
$936$	−15.6804	+	34.2109i	−0.512531	+	1.11822i
$937$	−10.4519	−	8.77015i	−0.341447	−	0.286508i	0.455898	−	0.890032i	$-0.349318\pi$
$937$	−10.4519	−	8.77015i	−0.341447	−	0.286508i	−0.797345	+	0.603524i	$0.793763\pi$
$938$	−0.903088	+	0.105556i	−0.0294869	+	0.00344652i
$939$	7.14539	−	9.37556i	0.233181	−	0.305960i
$940$	3.24098	+	3.43524i	0.105709	+	0.112045i
$941$	−44.1544	−	5.16091i	−1.43939	−	0.168241i	−0.639687	−	0.768635i	$-0.720936\pi$
$941$	−44.1544	−	5.16091i	−1.43939	−	0.168241i	−0.799704	+	0.600395i	$0.795010\pi$
$942$	−1.77901	−	0.442855i	−0.0579631	−	0.0144290i
$943$	2.03049	−	34.8622i	0.0661219	−	1.13527i
$944$	1.73463	+	3.00447i	0.0564575	+	0.0977873i
$945$	−7.64427	−	3.07860i	−0.248668	−	0.100147i
$946$	4.57603	−	7.92592i	0.148780	−	0.257694i
$947$	3.62204	+	2.38225i	0.117700	+	0.0774128i	0.606994	−	0.794706i	$-0.292375\pi$
$947$	3.62204	+	2.38225i	0.117700	+	0.0774128i	−0.489294	+	0.872119i	$0.662745\pi$
$948$	−21.5724	−	14.5391i	−0.700638	−	0.472208i
$949$	−14.6499	−	33.9622i	−0.475555	−	1.10246i
$950$	−7.66082	+	1.81565i	−0.248550	+	0.0589074i
$951$	17.5405	+	19.0165i	0.568791	+	0.616653i
$952$	−8.15136	−	10.9492i	−0.264187	−	0.354865i
$953$	−34.6339	+	12.6057i	−1.12190	+	0.408339i	−0.835346	−	0.549724i	$-0.814733\pi$
$953$	−34.6339	+	12.6057i	−1.12190	+	0.408339i	−0.286556	+	0.958063i	$0.592511\pi$
$954$	4.71478	+	30.7784i	0.152647	+	0.996486i
$955$	7.65355	+	2.78566i	0.247663	+	0.0901419i
$956$	−6.32968	−	21.1426i	−0.204716	−	0.683801i
$957$	−11.8758	−	10.1951i	−0.383890	−	0.329562i
$958$	0.690712	+	11.8591i	0.0223159	+	0.383149i
$959$	17.4171	−	11.4554i	0.562428	−	0.369915i
$960$	4.27347	+	7.59827i	0.137926	+	0.245233i
$961$	23.9459	+	5.67527i	0.772447	+	0.183073i
$962$	6.43203	+	36.4778i	0.207377	+	1.17609i
$963$	−36.0683	+	7.69451i	−1.16228	+	0.247952i
$964$	2.85744	−	16.2054i	0.0920320	−	0.521939i
$965$	7.60147	−	17.6222i	0.244700	−	0.567279i
$966$	−0.536774	−	11.4335i	−0.0172704	−	0.367868i
$967$	2.93507	−	9.80383i	0.0943856	−	0.315270i	−0.897738	−	0.440529i	$-0.854791\pi$
$967$	2.93507	−	9.80383i	0.0943856	−	0.315270i	0.992124	+	0.125259i	$0.0399761\pi$
$968$	10.3221	−	13.8650i	0.331765	−	0.445638i
$969$	−7.07370	+	15.9037i	−0.227240	+	0.510899i
$970$	−1.22402	+	0.614727i	−0.0393010	+	0.0197377i
$971$	−43.9486			−1.41038			−0.705188	−	0.709020i	$-0.749138\pi$
$971$	−43.9486			−1.41038			−0.705188	+	0.709020i	$0.749138\pi$
$972$	−18.6798	+	8.09880i	−0.599156	+	0.259769i
$973$	13.7265			0.440051
$974$	6.75737	−	3.39368i	0.216520	−	0.108740i
$975$	−11.3667	+	25.5556i	−0.364027	+	0.818435i
$976$	2.23984	−	3.00863i	0.0716957	−	0.0963040i
$977$	−16.9236	+	56.5287i	−0.541433	+	1.80851i	0.0456115	+	0.998959i	$0.485476\pi$
$977$	−16.9236	+	56.5287i	−0.541433	+	1.80851i	−0.587045	+	0.809554i	$0.699709\pi$
$978$	−0.836545	−	17.8188i	−0.0267498	−	0.569782i
$979$	2.86847	−	6.64985i	0.0916766	−	0.212530i
$980$	−1.44193	+	8.17758i	−0.0460607	+	0.261223i
$981$	8.23798	−	25.4180i	0.263018	−	0.811535i
$982$	−4.03329	−	22.8740i	−0.128708	−	0.729937i
$983$	−26.0666	−	6.17791i	−0.831397	−	0.197045i	−0.207187	−	0.978301i	$-0.566431\pi$
$983$	−26.0666	−	6.17791i	−0.831397	−	0.197045i	−0.624210	+	0.781257i	$0.714579\pi$
$984$	13.5346	+	24.0647i	0.431468	+	0.767155i
$985$	−11.6819	+	7.68330i	−0.372216	+	0.244810i
$986$	−0.759122	−	13.0336i	−0.0241754	−	0.415075i
$987$	5.18056	+	4.44741i	0.164899	+	0.141563i
$988$	4.54875	+	15.1939i	0.144715	+	0.483382i
$989$	−28.6598	−	10.4313i	−0.911329	−	0.331697i
$990$	−5.11198	+	4.09681i	−0.162469	+	0.130205i
$991$	8.60252	−	3.13106i	0.273268	−	0.0994614i	−0.201751	−	0.979437i	$-0.564663\pi$
$991$	8.60252	−	3.13106i	0.273268	−	0.0994614i	0.475019	+	0.879975i	$0.342441\pi$
$992$	25.7076	+	34.5314i	0.816219	+	1.09637i
$993$	4.33778	+	4.70280i	0.137655	+	0.149239i
$994$	−7.72835	+	1.83165i	−0.245128	+	0.0580965i
$995$	−2.05416	−	4.76209i	−0.0651214	−	0.150968i
$996$	−8.95725	−	6.03691i	−0.283821	−	0.191287i
$997$	−35.3642	−	23.2594i	−1.12000	−	0.736633i	−0.152195	−	0.988350i	$-0.548634\pi$
$997$	−35.3642	−	23.2594i	−1.12000	−	0.736633i	−0.967801	+	0.251718i	$0.919005\pi$
$998$	9.90918	−	17.1632i	0.313670	−	0.543292i
$999$	−26.8324	+	43.0473i	−0.848940	+	1.36196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.25.6	yes	144
3.2	odd	2		243.2.g.a.73.3		144
9.2	odd	6		729.2.g.b.703.6		144
9.4	even	3		729.2.g.d.217.3		144
9.5	odd	6		729.2.g.a.217.6		144
9.7	even	3		729.2.g.c.703.3		144
81.13	even	27	inner	81.2.g.a.13.6	✓	144
81.14	odd	54		729.2.g.a.514.6		144
81.16	even	27		6561.2.a.c.1.49		72
81.40	even	27		729.2.g.c.28.3		144
81.41	odd	54		729.2.g.b.28.6		144
81.65	odd	54		6561.2.a.d.1.24		72
81.67	even	27		729.2.g.d.514.3		144
81.68	odd	54		243.2.g.a.10.3		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.6	✓	144	81.13	even	27	inner
81.2.g.a.25.6	yes	144	1.1	even	1	trivial
243.2.g.a.10.3		144	81.68	odd	54
243.2.g.a.73.3		144	3.2	odd	2
729.2.g.a.217.6		144	9.5	odd	6
729.2.g.a.514.6		144	81.14	odd	54
729.2.g.b.28.6		144	81.41	odd	54
729.2.g.b.703.6		144	9.2	odd	6
729.2.g.c.28.3		144	81.40	even	27
729.2.g.c.703.3		144	9.7	even	3
729.2.g.d.217.3		144	9.4	even	3
729.2.g.d.514.3		144	81.67	even	27
6561.2.a.c.1.49		72	81.16	even	27
6561.2.a.d.1.24		72	81.65	odd	54

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.744407 - 0.373855i) q^{2} +(0.703902 - 1.58257i) q^{3} +(-0.779943 + 1.04765i) q^{4} +(0.345929 - 1.15548i) q^{5} +(-0.0676620 - 1.44123i) q^{6} +(-0.520803 + 1.20736i) q^{7} +(-0.478230 + 2.71217i) q^{8} +(-2.00904 - 2.22795i) q^{9} +(-0.174471 - 0.989477i) q^{10} +(2.11479 + 0.501215i) q^{11} +(1.10897 + 1.97175i) q^{12} +(-3.80561 + 2.50299i) q^{13} +(0.0636874 + 1.09347i) q^{14} +(-1.58513 - 1.36080i) q^{15} +(-0.0912185 - 0.304691i) q^{16} +(3.54217 + 1.28924i) q^{17} +(-2.32848 - 0.907406i) q^{18} +(-2.50517 + 0.911807i) q^{19} +(0.940731 + 1.26362i) q^{20} +(1.54413 + 1.67407i) q^{21} +(1.76165 - 0.417519i) q^{22} +(-2.38967 - 5.53988i) q^{23} +(3.95557 + 2.66594i) q^{24} +(2.96197 + 1.94812i) q^{25} +(-1.89717 + 3.28599i) q^{26} +(-4.94005 + 1.61120i) q^{27} +(-0.858686 - 1.48729i) q^{28} +(0.241756 - 4.15079i) q^{29} +(-1.68873 - 0.420381i) q^{30} +(-7.40674 - 0.865723i) q^{31} +(-3.96165 - 4.19911i) q^{32} +(2.28181 - 2.99400i) q^{33} +(3.11881 - 0.364536i) q^{34} +(1.21492 + 1.01944i) q^{35} +(3.90104 - 0.367096i) q^{36} +(7.47819 - 6.27494i) q^{37} +(-1.52398 + 1.61533i) q^{38} +(1.28237 + 7.78449i) q^{39} +(2.96844 + 1.49081i) q^{40} +(5.17242 + 2.59769i) q^{41} +(1.77532 + 0.668906i) q^{42} +(3.46904 - 3.67697i) q^{43} +(-2.17451 + 1.82463i) q^{44} +(-3.26934 + 1.55071i) q^{45} +(-3.85000 - 3.23053i) q^{46} +(2.97767 - 0.348040i) q^{47} +(-0.546403 - 0.0701130i) q^{48} +(3.61722 + 3.83402i) q^{49} +(2.93322 + 0.342844i) q^{50} +(4.53365 - 4.69822i) q^{51} +(0.345914 - 5.93911i) q^{52} +(-6.22987 - 10.7905i) q^{53} +(-3.07505 + 3.04625i) q^{54} +(1.31071 - 2.27022i) q^{55} +(-3.02550 - 1.98990i) q^{56} +(-0.320396 + 4.60642i) q^{57} +(-1.37183 - 3.18026i) q^{58} +(-10.6138 + 2.51552i) q^{59} +(2.66195 - 0.599306i) q^{60} +(7.04237 + 9.45955i) q^{61} +(-5.83728 + 2.12460i) q^{62} +(3.73624 - 1.26531i) q^{63} +(-3.92120 - 1.42720i) q^{64} +(1.57569 + 5.26317i) q^{65} +(0.579276 - 3.08182i) q^{66} +(0.0482665 + 0.828703i) q^{67} +(-4.11336 + 2.70540i) q^{68} +(-10.4493 - 0.117714i) q^{69} +(1.28552 + 0.304673i) q^{70} +(1.25916 + 7.14107i) q^{71} +(7.00336 - 4.38341i) q^{72} +(-1.41006 + 7.99685i) q^{73} +(3.22089 - 7.46687i) q^{74} +(5.16796 - 3.31623i) q^{75} +(0.998639 - 3.33569i) q^{76} +(-1.70654 + 2.29228i) q^{77} +(3.86488 + 5.31541i) q^{78} +(-10.2764 + 5.16099i) q^{79} -0.383620 q^{80} +(-0.927480 + 8.95208i) q^{81} +4.82155 q^{82} +(-4.26695 + 2.14294i) q^{83} +(-2.95816 + 0.312025i) q^{84} +(2.71504 - 3.64693i) q^{85} +(1.20772 - 4.03408i) q^{86} +(-6.39873 - 3.30434i) q^{87} +(-2.37074 + 5.49599i) q^{88} +(0.578632 - 3.28158i) q^{89} +(-1.85398 + 2.37662i) q^{90} +(-1.04003 - 5.89829i) q^{91} +(7.66763 + 1.81726i) q^{92} +(-6.58368 + 11.1123i) q^{93} +(2.08648 - 1.37230i) q^{94} +(0.186967 + 3.21010i) q^{95} +(-9.43399 + 3.31383i) q^{96} +(-0.390985 - 1.30598i) q^{97} +(4.12605 + 1.50176i) q^{98} +(-3.13203 - 5.71861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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