LMFDB - Embedded newform 324.2.p.a.311.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			311.35
Character	$\chi$	$=$	324.311
Dual form			324.2.p.a.299.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.621813 + 1.27018i) q^{2} +(-0.0272775 - 1.73184i) q^{3} +(-1.22670 + 1.57962i) q^{4} +(0.720383 - 0.215669i) q^{5} +(2.18278 - 1.11153i) q^{6} +(2.05588 - 0.886819i) q^{7} +(-2.76918 - 0.575890i) q^{8} +(-2.99851 + 0.0944802i) q^{9} +O(q^{10})$	\(q+(0.621813 + 1.27018i) q^{2} +(-0.0272775 - 1.73184i) q^{3} +(-1.22670 + 1.57962i) q^{4} +(0.720383 - 0.215669i) q^{5} +(2.18278 - 1.11153i) q^{6} +(2.05588 - 0.886819i) q^{7} +(-2.76918 - 0.575890i) q^{8} +(-2.99851 + 0.0944802i) q^{9} +(0.721881 + 0.780908i) q^{10} +(4.86915 - 1.15401i) q^{11} +(2.76911 + 2.08135i) q^{12} +(3.66469 + 2.41030i) q^{13} +(2.40479 + 2.05989i) q^{14} +(-0.393153 - 1.24170i) q^{15} +(-0.990430 - 3.87544i) q^{16} +(-0.0735547 - 0.202090i) q^{17} +(-1.98452 - 3.74989i) q^{18} +(0.348737 - 0.958146i) q^{19} +(-0.543016 + 1.40249i) q^{20} +(-1.59190 - 3.53625i) q^{21} +(4.49349 + 5.46710i) q^{22} +(2.12258 - 4.92069i) q^{23} +(-0.921810 + 4.81147i) q^{24} +(-3.70500 + 2.43682i) q^{25} +(-0.782759 + 6.15355i) q^{26} +(0.245416 + 5.19035i) q^{27} +(-1.12110 + 4.33537i) q^{28} +(-6.14834 + 0.358100i) q^{29} +(1.33271 - 1.27148i) q^{30} +(0.372752 + 3.18910i) q^{31} +(4.30663 - 3.66782i) q^{32} +(-2.13137 - 8.40108i) q^{33} +(0.210953 - 0.219090i) q^{34} +(1.28976 - 1.08224i) q^{35} +(3.52902 - 4.85242i) q^{36} +(2.60129 + 2.18274i) q^{37} +(1.43386 - 0.152831i) q^{38} +(4.07428 - 6.41238i) q^{39} +(-2.11907 + 0.182363i) q^{40} +(0.104706 + 0.208487i) q^{41} +(3.50180 - 4.22089i) q^{42} +(-4.41820 + 4.16836i) q^{43} +(-4.15006 + 9.10704i) q^{44} +(-2.13970 + 0.714747i) q^{45} +(7.56999 - 0.363700i) q^{46} +(-5.38625 - 0.629562i) q^{47} +(-6.68461 + 1.82097i) q^{48} +(-1.36351 + 1.44523i) q^{49} +(-5.39901 - 3.19076i) q^{50} +(-0.347980 + 0.132897i) q^{51} +(-8.30283 + 2.83212i) q^{52} +(-6.49329 - 3.74890i) q^{53} +(-6.44006 + 3.53915i) q^{54} +(3.25877 - 1.88145i) q^{55} +(-6.20380 + 1.27180i) q^{56} +(-1.66886 - 0.577819i) q^{57} +(-4.27797 - 7.58680i) q^{58} +(-12.7178 - 3.01418i) q^{59} +(2.44370 + 0.902158i) q^{60} +(0.198645 - 0.266826i) q^{61} +(-3.81893 + 2.45648i) q^{62} +(-6.08079 + 2.85338i) q^{63} +(7.33670 + 3.18948i) q^{64} +(3.15980 + 0.945983i) q^{65} +(9.34554 - 7.93112i) q^{66} +(2.69719 + 0.157093i) q^{67} +(0.409455 + 0.131714i) q^{68} +(-8.57972 - 3.54173i) q^{69} +(2.17662 + 0.965274i) q^{70} +(-0.104771 + 0.594186i) q^{71} +(8.35783 + 1.46518i) q^{72} +(2.29264 + 13.0022i) q^{73} +(-1.15495 + 4.66136i) q^{74} +(4.32123 + 6.34998i) q^{75} +(1.08572 + 1.72623i) q^{76} +(8.98697 - 6.69055i) q^{77} +(10.6783 + 1.18776i) q^{78} +(6.90321 - 13.7454i) q^{79} +(-1.54930 - 2.57820i) q^{80} +(8.98215 - 0.566600i) q^{81} +(-0.199708 + 0.262635i) q^{82} +(-15.1702 - 7.61877i) q^{83} +(7.53874 + 1.82330i) q^{84} +(-0.0965720 - 0.129719i) q^{85} +(-8.04185 - 3.01996i) q^{86} +(0.787881 + 10.6381i) q^{87} +(-14.1481 + 0.391565i) q^{88} +(13.6831 - 2.41271i) q^{89} +(-2.23835 - 2.27336i) q^{90} +(9.67165 + 1.70537i) q^{91} +(5.16908 + 9.38907i) q^{92} +(5.51282 - 0.732536i) q^{93} +(-2.54958 - 7.23296i) q^{94} +(0.0445820 - 0.765444i) q^{95} +(-6.46954 - 7.35833i) q^{96} +(3.45912 - 11.5543i) q^{97} +(-2.68355 - 0.833229i) q^{98} +(-14.4912 + 3.92035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{35}{54}\right)$

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 $

$2$	0.621813	+	1.27018i	0.439688	+	0.898150i
$2$	0.621813	+	1.27018i	0.439688	+	0.898150i
$3$	−0.0272775	−	1.73184i	−0.0157487	−	0.999876i
$3$	−0.0272775	−	1.73184i	−0.0157487	−	0.999876i
$4$	−1.22670	+	1.57962i	−0.613348	+	0.789812i
$5$	0.720383	−	0.215669i	0.322165	−	0.0964499i	−0.121637	−	0.992575i	$-0.538814\pi$
$5$	0.720383	−	0.215669i	0.322165	−	0.0964499i	0.443802	+	0.896125i	$0.353629\pi$
$6$	2.18278	−	1.11153i	0.891115	−	0.453778i
$7$	2.05588	−	0.886819i	0.777049	−	0.335186i	0.0296487	−	0.999560i	$-0.490561\pi$
$7$	2.05588	−	0.886819i	0.777049	−	0.335186i	0.747400	+	0.664374i	$0.231302\pi$
$8$	−2.76918	−	0.575890i	−0.979053	−	0.203608i
$9$	−2.99851	+	0.0944802i	−0.999504	+	0.0314934i
$10$	0.721881	+	0.780908i	0.228279	+	0.246945i
$11$	4.86915	−	1.15401i	1.46810	−	0.347947i	0.582668	−	0.812710i	$-0.302009\pi$
$11$	4.86915	−	1.15401i	1.46810	−	0.347947i	0.885435	+	0.464764i	$0.153861\pi$
$12$	2.76911	+	2.08135i	0.799374	+	0.600834i
$13$	3.66469	+	2.41030i	1.01640	+	0.668497i	0.944363	−	0.328905i	$-0.106679\pi$
$13$	3.66469	+	2.41030i	1.01640	+	0.668497i	0.0720376	+	0.997402i	$0.477050\pi$
$14$	2.40479	+	2.05989i	0.642707	+	0.550529i
$15$	−0.393153	−	1.24170i	−0.101512	−	0.320606i
$16$	−0.990430	−	3.87544i	−0.247608	−	0.968860i
$17$	−0.0735547	−	0.202090i	−0.0178396	−	0.0490140i	0.930453	−	0.366411i	$-0.119414\pi$
$17$	−0.0735547	−	0.202090i	−0.0178396	−	0.0490140i	−0.948293	+	0.317397i	$0.897191\pi$
$18$	−1.98452	−	3.74989i	−0.467756	−	0.883858i
$19$	0.348737	−	0.958146i	0.0800057	−	0.219814i	−0.893240	−	0.449580i	$-0.851574\pi$
$19$	0.348737	−	0.958146i	0.0800057	−	0.219814i	0.973246	+	0.229766i	$0.0737960\pi$
$20$	−0.543016	+	1.40249i	−0.121422	+	0.313607i
$21$	−1.59190	−	3.53625i	−0.347382	−	0.771674i
$22$	4.49349	+	5.46710i	0.958016	+	1.16559i
$23$	2.12258	−	4.92069i	0.442588	−	1.02603i	−0.540240	−	0.841511i	$-0.681667\pi$
$23$	2.12258	−	4.92069i	0.442588	−	1.02603i	0.982828	−	0.184524i	$-0.0590742\pi$
$24$	−0.921810	+	4.81147i	−0.188164	+	0.982138i
$25$	−3.70500	+	2.43682i	−0.741000	+	0.487363i
$26$	−0.782759	+	6.15355i	−0.153512	+	1.20681i
$27$	0.245416	+	5.19035i	0.0472303	+	0.998884i
$28$	−1.12110	+	4.33537i	−0.211867	+	0.819309i
$29$	−6.14834	+	0.358100i	−1.14172	+	0.0664975i	−0.618559	−	0.785738i	$-0.712283\pi$
$29$	−6.14834	+	0.358100i	−1.14172	+	0.0664975i	−0.523158	+	0.852236i	$0.675246\pi$
$30$	1.33271	−	1.27148i	0.243319	−	0.232139i
$31$	0.372752	+	3.18910i	0.0669482	+	0.572779i	0.984528	+	0.175227i	$0.0560660\pi$
$31$	0.372752	+	3.18910i	0.0669482	+	0.572779i	−0.917580	+	0.397552i	$0.869860\pi$
$32$	4.30663	−	3.66782i	0.761312	−	0.648385i
$33$	−2.13137	−	8.40108i	−0.371024	−	1.46244i
$34$	0.210953	−	0.219090i	0.0361781	−	0.0375736i
$35$	1.28976	−	1.08224i	0.218009	−	0.182932i
$36$	3.52902	−	4.85242i	0.588170	−	0.808737i
$37$	2.60129	+	2.18274i	0.427650	+	0.358841i	0.831064	−	0.556176i	$-0.187732\pi$
$37$	2.60129	+	2.18274i	0.427650	+	0.358841i	−0.403414	+	0.915018i	$0.632177\pi$
$38$	1.43386	−	0.152831i	0.232603	−	0.0247924i
$39$	4.07428	−	6.41238i	0.652407	−	1.02680i
$40$	−2.11907	+	0.182363i	−0.335054	+	0.0288342i
$41$	0.104706	+	0.208487i	0.0163524	+	0.0325602i	0.901661	−	0.432445i	$-0.142349\pi$
$41$	0.104706	+	0.208487i	0.0163524	+	0.0325602i	−0.885308	+	0.465005i	$0.846053\pi$
$42$	3.50180	−	4.22089i	0.540339	−	0.651297i
$43$	−4.41820	+	4.16836i	−0.673770	+	0.635669i	−0.945086	−	0.326821i	$-0.894022\pi$
$43$	−4.41820	+	4.16836i	−0.673770	+	0.635669i	0.271317	+	0.962490i	$0.412541\pi$
$44$	−4.15006	+	9.10704i	−0.625646	+	1.37294i
$45$	−2.13970	+	0.714747i	−0.318968	+	0.106548i
$46$	7.56999	−	0.363700i	1.11613	−	0.0536247i
$47$	−5.38625	−	0.629562i	−0.785665	−	0.0918311i	−0.286205	−	0.958168i	$-0.592394\pi$
$47$	−5.38625	−	0.629562i	−0.785665	−	0.0918311i	−0.499460	+	0.866337i	$0.666468\pi$
$48$	−6.68461	+	1.82097i	−0.964841	+	0.262835i
$49$	−1.36351	+	1.44523i	−0.194787	+	0.206462i
$50$	−5.39901	−	3.19076i	−0.763535	−	0.451242i
$51$	−0.347980	+	0.132897i	−0.0487270	+	0.0186093i
$52$	−8.30283	+	2.83212i	−1.15140	+	0.392744i
$53$	−6.49329	−	3.74890i	−0.891922	−	0.514951i	−0.0173514	−	0.999849i	$-0.505523\pi$
$53$	−6.49329	−	3.74890i	−0.891922	−	0.514951i	−0.874571	+	0.484898i	$0.838857\pi$
$54$	−6.44006	+	3.53915i	−0.876381	+	0.481618i
$55$	3.25877	−	1.88145i	0.439412	−	0.253695i
$56$	−6.20380	+	1.27180i	−0.829018	+	0.169952i
$57$	−1.66886	−	0.577819i	−0.221047	−	0.0765340i
$58$	−4.27797	−	7.58680i	−0.561724	−	0.996196i
$59$	−12.7178	−	3.01418i	−1.65572	−	0.392412i	−0.706670	−	0.707543i	$-0.749803\pi$
$59$	−12.7178	−	3.01418i	−1.65572	−	0.392412i	−0.949048	+	0.315131i	$0.897952\pi$
$60$	2.44370	+	0.902158i	0.315481	+	0.116468i
$61$	0.198645	−	0.266826i	0.0254338	−	0.0341636i	−0.789224	−	0.614105i	$-0.789517\pi$
$61$	0.198645	−	0.266826i	0.0254338	−	0.0341636i	0.814658	+	0.579941i	$0.196925\pi$
$62$	−3.81893	+	2.45648i	−0.485005	+	0.311974i
$63$	−6.08079	+	2.85338i	−0.766107	+	0.359492i
$64$	7.33670	+	3.18948i	0.917088	+	0.398685i
$65$	3.15980	+	0.945983i	0.391925	+	0.117335i
$66$	9.34554	−	7.93112i	1.15036	−	0.976254i
$67$	2.69719	+	0.157093i	0.329514	+	0.0191920i	0.222104	−	0.975023i	$-0.428707\pi$
$67$	2.69719	+	0.157093i	0.329514	+	0.0191920i	0.107409	+	0.994215i	$0.465744\pi$
$68$	0.409455	+	0.131714i	0.0496538	+	0.0159727i
$69$	−8.57972	−	3.54173i	−1.03288	−	0.426375i
$70$	2.17662	+	0.965274i	0.260156	+	0.115372i
$71$	−0.104771	+	0.594186i	−0.0124340	+	0.0705169i	−0.990393	−	0.138278i	$-0.955843\pi$
$71$	−0.104771	+	0.594186i	−0.0124340	+	0.0705169i	0.977959	+	0.208795i	$0.0669542\pi$
$72$	8.35783	+	1.46518i	0.984979	+	0.172673i
$73$	2.29264	+	13.0022i	0.268334	+	1.52180i	0.759371	+	0.650658i	$0.225507\pi$
$73$	2.29264	+	13.0022i	0.268334	+	1.52180i	−0.491037	+	0.871138i	$0.663382\pi$
$74$	−1.15495	+	4.66136i	−0.134260	+	0.541872i
$75$	4.32123	+	6.34998i	0.498973	+	0.733233i
$76$	1.08572	+	1.72623i	0.124540	+	0.198012i
$77$	8.98697	−	6.69055i	1.02416	−	0.762459i
$78$	10.6783	+	1.18776i	1.20908	+	0.134487i
$79$	6.90321	−	13.7454i	0.776672	−	1.54648i	−0.0596355	−	0.998220i	$-0.518994\pi$
$79$	6.90321	−	13.7454i	0.776672	−	1.54648i	0.836307	−	0.548261i	$-0.184710\pi$
$80$	−1.54930	−	2.57820i	−0.173217	−	0.288251i
$81$	8.98215	−	0.566600i	0.998016	−	0.0629556i
$82$	−0.199708	+	0.262635i	−0.0220540	+	0.0290032i
$83$	−15.1702	−	7.61877i	−1.66515	−	0.836269i	−0.995621	−	0.0934823i	$-0.970200\pi$
$83$	−15.1702	−	7.61877i	−1.66515	−	0.836269i	−0.669528	−	0.742787i	$-0.733504\pi$
$84$	7.53874	+	1.82330i	0.822544	+	0.198938i
$85$	−0.0965720	−	0.129719i	−0.0104747	−	0.0140700i
$86$	−8.04185	−	3.01996i	−0.867175	−	0.325650i
$87$	0.787881	+	10.6381i	0.0844697	+	1.14053i
$88$	−14.1481	+	0.391565i	−1.50819	+	0.0417410i
$89$	13.6831	−	2.41271i	1.45041	−	0.255747i	0.607723	−	0.794149i	$-0.292083\pi$
$89$	13.6831	−	2.41271i	1.45041	−	0.255747i	0.842688	+	0.538403i	$0.180972\pi$
$90$	−2.23835	−	2.27336i	−0.235943	−	0.239633i
$91$	9.67165	+	1.70537i	1.01386	+	0.178772i
$92$	5.16908	+	9.38907i	0.538914	+	0.978878i
$93$	5.51282	−	0.732536i	0.571653	−	0.0759604i
$94$	−2.54958	−	7.23296i	−0.262970	−	0.746022i
$95$	0.0445820	−	0.765444i	0.00457402	−	0.0785329i
$96$	−6.46954	−	7.35833i	−0.660295	−	0.751007i
$97$	3.45912	−	11.5543i	0.351221	−	1.17316i	−0.581799	−	0.813333i	$-0.697651\pi$
$97$	3.45912	−	11.5543i	0.351221	−	1.17316i	0.933019	−	0.359826i	$-0.117164\pi$
$98$	−2.68355	−	0.833229i	−0.271079	−	0.0841689i
$99$	−14.4912	+	3.92035i	−1.45642	+	0.394010i
$100$	0.695655	−	8.84175i	0.0695655	−	0.884175i
$101$	−2.25486	−	1.67868i	−0.224367	−	0.167035i	0.479106	−	0.877757i	$-0.340961\pi$
$101$	−2.25486	−	1.67868i	−0.224367	−	0.167035i	−0.703473	+	0.710722i	$0.748368\pi$
$102$	−0.385181	−	0.359359i	−0.0381386	−	0.0355818i
$103$	−3.00745	+	12.6894i	−0.296333	+	1.25033i	0.597479	+	0.801884i	$0.296169\pi$
$103$	−3.00745	+	12.6894i	−0.296333	+	1.25033i	−0.893812	+	0.448442i	$0.851979\pi$
$104$	−8.76010	−	8.78501i	−0.858999	−	0.861441i
$105$	−1.90944	−	2.20413i	−0.186342	−	0.215101i
$106$	0.724155	−	10.5787i	0.0703362	−	1.02750i
$107$	5.05327	+	8.75252i	0.488518	+	0.846138i	0.999913	−	0.0132077i	$-0.00420426\pi$
$107$	5.05327	+	8.75252i	0.488518	+	0.846138i	−0.511395	+	0.859346i	$0.670871\pi$
$108$	−8.49986	−	5.97932i	−0.817900	−	0.575361i
$109$	−9.22908	+	15.9852i	−0.883986	+	1.53111i	−0.0371145	+	0.999311i	$0.511817\pi$
$109$	−9.22908	+	15.9852i	−0.883986	+	1.53111i	−0.846871	+	0.531798i	$0.821517\pi$
$110$	4.41612	+	2.96930i	0.421060	+	0.283112i
$111$	3.70920	−	4.56455i	0.352062	−	0.433248i
$112$	−5.47302	−	7.08910i	−0.517152	−	0.669857i
$113$	9.30887	+	8.78247i	0.875705	+	0.826185i	0.985833	−	0.167732i	$-0.0536444\pi$
$113$	9.30887	+	8.78247i	0.875705	+	0.826185i	−0.110127	+	0.993917i	$0.535126\pi$
$114$	−0.303790	−	2.47905i	−0.0284525	−	0.232184i
$115$	0.467831	−	4.00255i	0.0436255	−	0.373240i
$116$	6.97648	−	10.1513i	0.647750	−	0.942529i
$117$	−11.2163	−	6.88108i	−1.03695	−	0.636156i
$118$	−4.07957	−	18.0281i	−0.375555	−	1.65962i
$119$	−0.330437	−	0.350242i	−0.0302911	−	0.0321067i
$120$	0.373627	+	3.66491i	0.0341073	+	0.334559i
$121$	12.5469	−	6.30129i	1.14063	−	0.572844i
$122$	0.462436	+	0.0863978i	0.0418670	+	0.00782209i
$123$	0.358209	−	0.187021i	0.0322986	−	0.0168631i
$124$	−5.49483	−	3.32325i	−0.493450	−	0.298436i
$125$	−4.56027	+	5.43472i	−0.407883	+	0.486096i
$126$	−7.40541	−	5.94941i	−0.659726	−	0.530015i
$127$	−10.6562	−	12.6995i	−0.945581	−	1.12690i	−0.991778	−	0.127967i	$-0.959155\pi$
$127$	−10.6562	−	12.6995i	−0.945581	−	1.12690i	0.0461978	−	0.998932i	$-0.485290\pi$
$128$	0.510851	+	11.3022i	0.0451533	+	0.998980i
$129$	7.33943	+	7.53790i	0.646201	+	0.663675i
$130$	0.763242	+	4.60173i	0.0669407	+	0.403599i
$131$	−1.81418	+	0.212047i	−0.158505	+	0.0185266i	−0.194975	−	0.980808i	$-0.562463\pi$
$131$	−1.81418	+	0.212047i	−0.158505	+	0.0185266i	0.0364701	+	0.999335i	$0.488389\pi$
$132$	15.8851	+	6.93881i	1.38262	+	0.603946i
$133$	−0.132742	−	2.27910i	−0.0115102	−	0.197623i
$134$	1.47761	+	3.52358i	0.127646	+	0.304391i
$135$	1.29619	+	3.68611i	0.111558	+	0.317250i
$136$	0.0873046	+	0.601982i	0.00748631	+	0.0516196i
$137$	8.36626	+	12.7203i	0.714778	+	1.08677i	0.992034	+	0.125971i	$0.0402045\pi$
$137$	8.36626	+	12.7203i	0.714778	+	1.08677i	−0.277256	+	0.960796i	$0.589425\pi$
$138$	−0.836360	−	13.1001i	−0.0711957	−	1.11515i
$139$	7.65921	+	3.30386i	0.649646	+	0.280230i	0.695292	−	0.718728i	$-0.255275\pi$
$139$	7.65921	+	3.30386i	0.649646	+	0.280230i	−0.0456456	+	0.998958i	$0.514534\pi$
$140$	0.127384	+	3.36492i	0.0107660	+	0.284387i
$141$	−0.943375	+	9.34527i	−0.0794465	+	0.787014i
$142$	−0.819869	+	0.236395i	−0.0688019	+	0.0198378i
$143$	20.6254	+	7.50703i	1.72478	+	0.627769i
$144$	3.33597	+	11.5270i	0.277997	+	0.960582i
$145$	−4.35193	+	1.58397i	−0.361408	+	0.131542i
$146$	−15.0895	+	10.9970i	−1.24882	+	0.910120i
$147$	2.54010	+	2.32195i	0.209504	+	0.191511i
$148$	−6.63892	+	1.43150i	−0.545716	+	0.117669i
$149$	−0.329922	+	0.501623i	−0.0270283	+	0.0410945i	−0.848749	−	0.528796i	$-0.822644\pi$
$149$	−0.329922	+	0.501623i	−0.0270283	+	0.0410945i	0.821721	+	0.569890i	$0.193014\pi$
$150$	−5.37860	+	9.43723i	−0.439161	+	0.770546i
$151$	−0.424926	−	1.79291i	−0.0345800	−	0.145905i	0.953016	−	0.302919i	$-0.0979612\pi$
$151$	−0.424926	−	1.79291i	−0.0345800	−	0.145905i	−0.987596	+	0.157015i	$0.949813\pi$
$152$	−1.51750	+	2.45244i	−0.123086	+	0.198919i
$153$	0.239648	+	0.599019i	0.0193744	+	0.0484278i
$154$	14.0864	+	7.25477i	1.13511	+	0.584606i
$155$	0.956312	+	2.21698i	0.0768128	+	0.178072i
$156$	5.13125	+	14.3019i	0.410829	+	1.14507i
$157$	2.56168	+	8.55660i	0.204444	+	0.682891i	0.997297	+	0.0734777i	$0.0234098\pi$
$157$	2.56168	+	8.55660i	0.204444	+	0.682891i	−0.792853	+	0.609413i	$0.791405\pi$
$158$	21.7516	+	0.221211i	1.73047	+	0.0175986i
$159$	−6.31537	+	11.3476i	−0.500841	+	0.899921i
$160$	2.31139	−	3.57104i	0.182732	−	0.282316i
$161$		−	11.9987i		−	0.945628i
$162$	6.30490	+	11.0566i	0.495360	+	0.868688i
$163$			15.1388i			1.18576i	0.805289	+	0.592882i	$0.202010\pi$
$163$			15.1388i			1.18576i	−0.805289	+	0.592882i	$0.797990\pi$
$164$	−0.457774	−	0.0903540i	−0.0357462	−	0.00705546i
$165$	−3.34725	−	5.59233i	−0.260583	−	0.435362i
$166$	0.244141	−	24.0063i	0.0189490	−	1.86325i
$167$	−4.16068	−	13.8976i	−0.321963	−	1.07543i	−0.953828	−	0.300353i	$-0.902895\pi$
$167$	−4.16068	−	13.8976i	−0.321963	−	1.07543i	0.631865	−	0.775079i	$-0.282290\pi$
$168$	2.37178	+	10.7093i	0.182986	+	0.826239i
$169$	2.47133	+	5.72918i	0.190102	+	0.440706i
$170$	0.104716	−	0.203324i	0.00803134	−	0.0155943i
$171$	−0.955165	+	2.90596i	−0.0730433	+	0.222224i
$172$	−1.16465	−	12.0924i	−0.0888037	−	0.922038i
$173$	−4.89097	−	20.6366i	−0.371854	−	1.56897i	−0.761597	−	0.648050i	$-0.775585\pi$
$173$	−4.89097	−	20.6366i	−0.371854	−	1.56897i	0.389744	−	0.920923i	$-0.372564\pi$
$174$	−13.0224	+	7.61568i	−0.987226	+	0.577344i
$175$	−5.45601	+	8.29546i	−0.412436	+	0.627078i
$176$	−9.29484	−	17.7271i	−0.700625	−	1.33623i
$177$	−4.87315	+	22.1074i	−0.366288	+	1.66169i
$178$	11.5729	+	15.8798i	0.867427	+	1.19024i
$179$	7.58031	−	2.75901i	0.566579	−	0.206218i	−0.0428185	−	0.999083i	$-0.513634\pi$
$179$	7.58031	−	2.75901i	0.566579	−	0.206218i	0.609397	+	0.792865i	$0.291411\pi$
$180$	1.49573	−	4.25670i	0.111485	−	0.317276i
$181$	−8.88347	−	3.23332i	−0.660303	−	0.240331i	−0.00993597	−	0.999951i	$-0.503163\pi$
$181$	−8.88347	−	3.23332i	−0.660303	−	0.240331i	−0.650367	+	0.759620i	$0.725385\pi$
$182$	3.84783	+	13.3451i	0.285220	+	0.989206i
$183$	−0.467518	−	0.336742i	−0.0345599	−	0.0248927i
$184$	−8.71157	+	12.4039i	−0.642226	+	0.914427i
$185$	2.34468	+	1.01140i	0.172384	+	0.0743592i
$186$	4.35840	+	6.54676i	0.319573	+	0.480032i
$187$	−0.591362	−	0.899122i	−0.0432447	−	0.0657503i
$188$	7.60176	−	7.73597i	0.554416	−	0.564204i
$189$	5.10745	+	10.4531i	0.371512	+	0.760351i
$190$	0.999970	−	0.419336i	0.0725455	−	0.0304218i
$191$	0.251025	+	4.30994i	0.0181636	+	0.311856i	0.995137	+	0.0984969i	$0.0314035\pi$
$191$	0.251025	+	4.30994i	0.0181636	+	0.311856i	−0.976974	+	0.213359i	$0.931560\pi$
$192$	5.32354	−	12.7930i	0.384193	−	0.923253i
$193$	−7.02782	+	0.821435i	−0.505874	+	0.0591282i	−0.365202	−	0.930928i	$-0.619000\pi$
$193$	−7.02782	+	0.821435i	−0.505874	+	0.0591282i	−0.140671	+	0.990056i	$0.544926\pi$
$194$	16.8269	−	2.79090i	1.20810	−	0.200375i
$195$	1.55210	−	5.49806i	0.111148	−	0.393725i
$196$	−0.610316	−	3.92669i	−0.0435940	−	0.280478i
$197$	1.44834	+	1.72607i	0.103190	+	0.122977i	0.815168	−	0.579225i	$-0.196645\pi$
$197$	1.44834	+	1.72607i	0.103190	+	0.122977i	−0.711978	+	0.702202i	$0.752200\pi$
$198$	−13.9903	−	15.9686i	−0.994249	−	1.13484i
$199$	6.19515	−	7.38309i	0.439162	−	0.523373i	−0.500380	−	0.865806i	$-0.666806\pi$
$199$	6.19515	−	7.38309i	0.439162	−	0.523373i	0.939542	+	0.342433i	$0.111251\pi$
$200$	11.6631	−	4.61431i	0.824709	−	0.326281i
$201$	0.198487	−	4.67537i	0.0140002	−	0.329775i
$202$	0.730120	−	3.90790i	0.0513711	−	0.274959i
$203$	−12.3227	+	6.18867i	−0.864881	+	0.434360i
$204$	0.216938	−	0.712703i	0.0151887	−	0.0498992i
$205$	0.120393	+	0.127609i	0.00840859	+	0.00891258i
$206$	−17.9879	+	4.07046i	−1.25328	+	0.283602i
$207$	−5.89967	+	14.9553i	−0.410055	+	1.03946i
$208$	5.71137	−	16.5895i	0.396012	−	1.15028i
$209$	0.592341	−	5.06780i	0.0409731	−	0.350547i
$210$	1.61232	−	3.79588i	0.111261	−	0.261941i
$211$	16.5662	+	15.6294i	1.14047	+	1.07597i	0.996258	+	0.0864264i	$0.0275447\pi$
$211$	16.5662	+	15.6294i	1.14047	+	1.07597i	0.144207	+	0.989547i	$0.453937\pi$
$212$	13.8872	−	5.65820i	0.953774	−	0.388607i
$213$	1.03189	+	0.165238i	0.0707040	+	0.0113219i
$214$	−7.97506	+	11.8610i	−0.545164	+	0.810800i
$215$	−2.28381	+	3.95568i	−0.155755	+	0.269775i
$216$	2.30947	−	14.5143i	0.157140	−	0.987576i
$217$	3.59448	+	6.22583i	0.244009	+	0.422637i
$218$	−26.0428	−	1.78273i	−1.76384	−	0.120742i
$219$	22.4552	−	4.32515i	1.51738	−	0.292267i
$220$	−1.02553	+	7.45560i	−0.0691415	+	0.502656i
$221$	0.217543	−	0.917885i	0.0146335	−	0.0617436i
$222$	8.10422	+	1.87304i	0.543920	+	0.125710i
$223$	−10.9371	−	8.14240i	−0.732405	−	0.545255i	0.165091	−	0.986278i	$-0.447208\pi$
$223$	−10.9371	−	8.14240i	−0.732405	−	0.545255i	−0.897496	+	0.441023i	$0.854616\pi$
$224$	5.60122	−	11.3598i	0.374247	−	0.759008i
$225$	10.8793	−	7.65687i	0.725284	−	0.510458i
$226$	−5.36691	+	17.2850i	−0.357001	+	1.14978i
$227$	−0.747433	+	2.49660i	−0.0496089	+	0.165705i	−0.979204	−	0.202876i	$-0.934971\pi$
$227$	−0.747433	+	2.49660i	−0.0496089	+	0.165705i	0.929596	+	0.368581i	$0.120156\pi$
$228$	2.95993	−	1.92737i	0.196026	−	0.127643i
$229$	0.917811	−	15.7582i	0.0606506	−	1.04133i	−0.821453	−	0.570276i	$-0.806836\pi$
$229$	0.917811	−	15.7582i	0.0606506	−	1.04133i	0.882104	−	0.471055i	$-0.156127\pi$
$230$	5.37485	−	1.89461i	0.354407	−	0.124927i
$231$	−11.8321	−	15.3815i	−0.778494	−	1.01203i
$232$	17.2321	+	2.54912i	1.13134	+	0.167358i
$233$	13.2982	+	2.34482i	0.871191	+	0.153614i	0.591334	−	0.806427i	$-0.298602\pi$
$233$	13.2982	+	2.34482i	0.871191	+	0.153614i	0.279857	+	0.960042i	$0.409713\pi$
$234$	1.76572	−	18.5255i	0.115429	−	1.21105i
$235$	−4.01594	+	0.708118i	−0.261971	+	0.0461925i
$236$	20.3622	−	16.3919i	1.32546	−	1.06702i
$237$	−23.9931	−	11.5803i	−1.55852	−	0.752221i
$238$	0.239400	−	0.637498i	0.0155180	−	0.0413229i
$239$	3.54502	+	4.76179i	0.229309	+	0.308015i	0.901854	−	0.432041i	$-0.142206\pi$
$239$	3.54502	+	4.76179i	0.229309	+	0.308015i	−0.672545	+	0.740056i	$0.734799\pi$
$240$	−4.42275	+	2.75346i	−0.285488	+	0.177735i
$241$	−9.43477	−	4.73832i	−0.607747	−	0.305222i	0.118182	−	0.992992i	$-0.462293\pi$
$241$	−9.43477	−	4.73832i	−0.607747	−	0.305222i	−0.725929	+	0.687770i	$0.758590\pi$
$242$	15.8056	+	12.0185i	1.01602	+	0.772581i
$243$	−1.22627	−	15.5402i	−0.0786652	−	0.996901i
$244$	0.177808	+	0.641099i	0.0113830	+	0.0410421i
$245$	−0.670556	+	1.33519i	−0.0428402	+	0.0853019i
$246$	0.460289	+	0.338697i	0.0293469	+	0.0215945i
$247$	3.58743	−	2.67074i	0.228263	−	0.169935i
$248$	0.804351	−	9.04584i	0.0510764	−	0.574412i
$249$	−12.7807	+	26.4802i	−0.809942	+	1.67811i
$250$	−9.73869	−	2.41297i	−0.615929	−	0.152610i
$251$	1.08583	+	6.15806i	0.0685372	+	0.388694i	0.999709	+	0.0241136i	$0.00767633\pi$
$251$	1.08583	+	6.15806i	0.0685372	+	0.388694i	−0.931172	+	0.364580i	$0.881213\pi$
$252$	2.95202	−	13.1056i	0.185959	−	0.825575i
$253$	4.65662	−	26.4090i	0.292759	−	1.66032i
$254$	9.50448	−	21.4319i	0.596364	−	1.34476i
$255$	−0.222017	+	0.170785i	−0.0139033	+	0.0106950i
$256$	−14.0381	+	7.67671i	−0.877381	+	0.479794i
$257$	−16.9111	−	0.984958i	−1.05488	−	0.0614400i	−0.478075	−	0.878319i	$-0.658665\pi$
$257$	−16.9111	−	0.984958i	−1.05488	−	0.0614400i	−0.576809	+	0.816879i	$0.695702\pi$
$258$	−5.01071	+	14.0095i	−0.311953	+	0.872196i
$259$	7.28364	+	2.18058i	0.452584	+	0.135495i
$260$	−5.37042	+	3.83087i	−0.333059	+	0.237580i
$261$	18.4020	−	1.65466i	1.13906	−	0.102421i
$262$	−1.39742	−	2.17247i	−0.0863326	−	0.134216i
$263$	8.99227	−	12.0787i	0.554487	−	0.744805i	−0.433192	−	0.901302i	$-0.642613\pi$
$263$	8.99227	−	12.0787i	0.554487	−	0.744805i	0.987678	+	0.156497i	$0.0500200\pi$
$264$	1.06405	+	24.4915i	0.0654879	+	1.50735i
$265$	−5.48618	−	1.30025i	−0.337013	−	0.0798736i
$266$	2.81232	−	1.58578i	0.172434	−	0.0972304i
$267$	−4.55166	−	23.6312i	−0.278557	−	1.44620i
$268$	−3.55678	+	4.06784i	−0.217265	+	0.248483i
$269$	19.9435	−	11.5144i	1.21598	−	0.702045i	0.251922	−	0.967747i	$-0.418937\pi$
$269$	19.9435	−	11.5144i	1.21598	−	0.702045i	0.964055	+	0.265703i	$0.0856040\pi$
$270$	−3.87603	+	3.93846i	−0.235888	+	0.239687i
$271$	−10.2081	−	5.89367i	−0.620100	−	0.358015i	0.156808	−	0.987629i	$-0.449880\pi$
$271$	−10.2081	−	5.89367i	−0.620100	−	0.358015i	−0.776908	+	0.629614i	$0.783213\pi$
$272$	−0.710337	+	0.485213i	−0.0430705	+	0.0294203i
$273$	2.68961	−	16.7962i	0.162782	−	1.01655i
$274$	−10.9547	+	18.5363i	−0.661801	+	1.11982i
$275$	−15.2281	+	16.1408i	−0.918288	+	0.973328i
$276$	16.1193	−	9.20811i	0.970270	−	0.554263i
$277$	−30.5323	−	3.56871i	−1.83451	−	0.214423i	−0.872719	−	0.488223i	$-0.837645\pi$
$277$	−30.5323	−	3.56871i	−1.83451	−	0.214423i	−0.961787	+	0.273801i	$0.911719\pi$
$278$	0.566112	+	11.7829i	0.0339531	+	0.706694i
$279$	−1.41901	−	9.52733i	−0.0849538	−	0.570386i
$280$	−4.19483	+	2.25415i	−0.250689	+	0.134711i
$281$	15.4767	−	14.6016i	0.923265	−	0.871056i	−0.0686910	−	0.997638i	$-0.521882\pi$
$281$	15.4767	−	14.6016i	0.923265	−	0.871056i	0.991956	+	0.126582i	$0.0404008\pi$
$282$	−12.4567	+	4.61276i	−0.741788	+	0.274686i
$283$	−3.26042	−	6.49203i	−0.193812	−	0.385911i	0.775646	−	0.631168i	$-0.217424\pi$
$283$	−3.26042	−	6.49203i	−0.193812	−	0.385911i	−0.969458	+	0.245257i	$0.921128\pi$
$284$	−0.810069	−	0.894385i	−0.0480688	−	0.0530720i
$285$	−1.32684	−	0.0563294i	−0.0785952	−	0.00333666i
$286$	3.28989	+	30.8659i	0.194535	+	1.82514i
$287$	0.400153	+	0.335769i	0.0236203	+	0.0198198i
$288$	−12.5670	+	11.4049i	−0.740515	+	0.672040i
$289$	12.9873	−	10.8977i	0.763960	−	0.641039i
$290$	−4.71801	−	4.54278i	−0.277051	−	0.266761i
$291$	−20.1045	−	5.67546i	−1.17854	−	0.332702i
$292$	−23.3510	−	12.3283i	−1.36652	−	0.721458i
$293$	2.78728	+	23.8467i	0.162834	+	1.39314i	0.789453	+	0.613811i	$0.210364\pi$
$293$	2.78728	+	23.8467i	0.162834	+	1.39314i	−0.626619	+	0.779326i	$0.715562\pi$
$294$	−1.36982	+	4.67019i	−0.0798893	+	0.272371i
$295$	−9.81176	+	0.571470i	−0.571263	+	0.0332723i
$296$	−5.94643	−	7.54247i	−0.345629	−	0.438397i
$297$	7.18468	+	24.9894i	0.416897	+	1.45003i
$298$	−0.842299	−	0.107144i	−0.0487931	−	0.00620669i
$299$	19.6389	−	12.9167i	1.13575	−	0.746993i
$300$	−15.3314	−	0.963579i	−0.885161	−	0.0556323i
$301$	−5.38670	+	12.4878i	−0.310484	+	0.719784i
$302$	2.01308	−	1.65458i	0.115840	−	0.0952106i
$303$	−2.84569	+	3.95084i	−0.163481	+	0.226970i
$304$	−4.05864	−	0.402532i	−0.232779	−	0.0230868i
$305$	0.0855543	−	0.235058i	0.00489882	−	0.0134594i
$306$	−0.611844	+	0.676874i	−0.0349768	+	0.0386943i
$307$	−9.21097	−	25.3069i	−0.525698	−	1.44434i	−0.864090	−	0.503338i	$-0.832105\pi$
$307$	−9.21097	−	25.3069i	−0.525698	−	1.44434i	0.338392	−	0.941005i	$-0.390117\pi$
$308$	−0.455725	+	22.4033i	−0.0259673	+	1.27655i
$309$	22.0580	+	4.86227i	1.25484	+	0.276605i
$310$	−2.22131	+	2.59323i	−0.126162	+	0.147286i
$311$	7.43273	+	4.88858i	0.421471	+	0.277206i	0.742477	−	0.669871i	$-0.233651\pi$
$311$	7.43273	+	4.88858i	0.421471	+	0.277206i	−0.321006	+	0.947077i	$0.604021\pi$
$312$	−14.9752	+	15.4107i	−0.847806	+	0.872459i
$313$	24.7883	−	5.87493i	1.40112	−	0.332071i	0.540509	−	0.841338i	$-0.318232\pi$
$313$	24.7883	−	5.87493i	1.40112	−	0.332071i	0.860608	+	0.509267i	$0.170084\pi$
$314$	−9.27551	+	8.57439i	−0.523447	+	0.483881i
$315$	−3.76511	+	3.36696i	−0.212140	+	0.189707i
$316$	13.2445	+	27.7660i	0.745060	+	1.56196i
$317$	−28.2663	+	12.1929i	−1.58759	+	0.684821i	−0.992880	−	0.119118i	$-0.961993\pi$
$317$	−28.2663	+	12.1929i	−1.58759	+	0.684821i	−0.594713	+	0.803938i	$0.702734\pi$
$318$	−18.3404	−	0.965556i	−1.02848	−	0.0541457i
$319$	−29.5239	+	8.83887i	−1.65302	+	0.494882i
$320$	5.97311	+	0.715354i	0.333907	+	0.0399895i
$321$	15.0201	−	8.99018i	0.838340	−	0.501783i
$322$	15.2404	−	7.46094i	0.849316	−	0.415782i
$323$	−0.219283			−0.0122012
$324$	−10.1234	+	14.8835i	−0.562409	+	0.826859i
$325$	−19.4511			−1.07895
$326$	−19.2290	+	9.41352i	−1.06499	+	0.521367i
$327$	27.9356	+	15.5472i	1.54484	+	0.859763i
$328$	−0.169884	−	0.637637i	−0.00938030	−	0.0352076i
$329$	−11.6318	+	3.48232i	−0.641281	+	0.191987i
$330$	5.02188	−	7.72899i	0.276445	−	0.425467i
$331$	21.4692	−	9.26092i	1.18006	−	0.509026i	0.286544	−	0.958067i	$-0.407494\pi$
$331$	21.4692	−	9.26092i	1.18006	−	0.509026i	0.893511	+	0.449041i	$0.148234\pi$
$332$	30.6441	−	14.6173i	1.68181	−	0.802231i
$333$	−8.00624	−	6.29922i	−0.438739	−	0.345195i
$334$	15.0653	−	13.9265i	0.824336	−	0.762026i
$335$	1.97689	−	0.468531i	0.108009	−	0.0255986i
$336$	−12.1279	+	9.67174i	−0.661630	+	0.527637i
$337$	−0.626216	−	0.411869i	−0.0341121	−	0.0224359i	0.532338	−	0.846532i	$-0.321313\pi$
$337$	−0.626216	−	0.411869i	−0.0341121	−	0.0224359i	−0.566451	+	0.824096i	$0.691684\pi$
$338$	−5.74037	+	6.70150i	−0.312235	+	0.364514i
$339$	14.9559	−	16.3610i	0.812292	−	0.888608i
$340$	0.323371	+	0.00657797i	0.0175373	+	0.000356741i
$341$	5.49523	+	15.0980i	0.297583	+	0.817604i
$342$	−4.28502	+	0.593737i	−0.231707	+	0.0321056i
$343$	−6.88200	+	18.9081i	−0.371593	+	1.02094i
$344$	14.6353	−	8.99853i	0.789083	−	0.485168i
$345$	−6.94453	−	0.701028i	−0.373881	−	0.0377421i
$346$	23.1709	−	19.0445i	1.24567	−	1.02384i
$347$	2.69985	−	6.25896i	0.144936	−	0.335999i	−0.830249	−	0.557393i	$-0.811802\pi$
$347$	2.69985	−	6.25896i	0.144936	−	0.335999i	0.975184	+	0.221395i	$0.0710609\pi$
$348$	−17.7708	−	11.8052i	−0.952613	−	0.632826i
$349$	−19.0748	+	12.5457i	−1.02105	+	0.671555i	−0.945512	−	0.325588i	$-0.894438\pi$
$349$	−19.0748	+	12.5457i	−1.02105	+	0.671555i	−0.0755382	+	0.997143i	$0.524067\pi$
$350$	−13.9293	−	1.77187i	−0.744554	−	0.0947104i
$351$	−11.6109	+	19.6125i	−0.619746	+	1.04684i
$352$	16.7369	−	22.8291i	0.892081	−	1.21679i
$353$	−33.6818	+	1.96174i	−1.79270	+	0.104413i	−0.921949	−	0.387312i	$-0.873403\pi$
$353$	−33.6818	+	1.96174i	−1.79270	+	0.104413i	−0.870750	+	0.491725i	$0.836366\pi$
$354$	−31.1105	+	7.55690i	−1.65350	+	0.401645i
$355$	0.0526720	+	0.450638i	0.00279554	+	0.0239174i
$356$	−12.9739	+	24.5739i	−0.687615	+	1.30241i
$357$	−0.597549	+	0.581816i	−0.0316256	+	0.0307930i
$358$	8.21796	+	7.91274i	0.434333	+	0.418201i
$359$	12.3679	−	10.3779i	0.652754	−	0.547726i	−0.255151	−	0.966901i	$-0.582125\pi$
$359$	12.3679	−	10.3779i	0.652754	−	0.547726i	0.907905	+	0.419175i	$0.137681\pi$
$360$	6.33683	−	0.747029i	0.333980	−	0.0393719i
$361$	13.7584	+	11.5447i	0.724127	+	0.607615i
$362$	−1.41697	−	13.2941i	−0.0744745	−	0.698722i
$363$	−11.2550	−	21.5573i	−0.590736	−	1.13146i
$364$	−14.5580	+	13.1856i	−0.763048	+	0.691113i
$365$	4.45575	+	8.87214i	0.233225	+	0.464389i
$366$	0.137013	−	0.803220i	0.00716177	−	0.0419850i
$367$	19.7286	−	18.6130i	1.02983	−	0.971590i	0.0302161	−	0.999543i	$-0.490380\pi$
$367$	19.7286	−	18.6130i	1.02983	−	0.971590i	0.999609	+	0.0279533i	$0.00889899\pi$
$368$	−21.1721	−	3.35233i	−1.10367	−	0.174752i
$369$	−0.333661	−	0.615258i	−0.0173697	−	0.0320291i
$370$	0.173301	+	3.60705i	0.00900949	+	0.187522i
$371$	−16.6740	−	1.94891i	−0.865672	−	0.101182i
$372$	−5.60543	+	9.60679i	−0.290628	+	0.498089i
$373$	16.0053	−	16.9646i	0.828722	−	0.878394i	−0.165448	−	0.986219i	$-0.552907\pi$
$373$	16.0053	−	16.9646i	0.828722	−	0.878394i	0.994170	+	0.107824i	$0.0343884\pi$
$374$	0.774327	−	1.31022i	0.0400395	−	0.0677499i
$375$	9.53644	+	7.74940i	0.492459	+	0.400177i
$376$	14.5529	+	4.84526i	0.750510	+	0.249875i
$377$	−23.3948	−	13.5070i	−1.20490	−	0.695647i
$378$	−10.1014	+	12.9872i	−0.519560	+	0.667991i
$379$	−14.5528	+	8.40207i	−0.747528	+	0.431585i	−0.824800	−	0.565425i	$-0.808712\pi$
$379$	−14.5528	+	8.40207i	−0.747528	+	0.431585i	0.0772721	+	0.997010i	$0.475379\pi$
$380$	1.15443	+	1.00939i	0.0592208	+	0.0517806i
$381$	−21.7028	+	18.8011i	−1.11187	+	0.963211i
$382$	−5.31829	+	2.99882i	−0.272107	+	0.153433i
$383$	4.71180	+	1.11672i	0.240762	+	0.0570616i	0.349225	−	0.937039i	$-0.386445\pi$
$383$	4.71180	+	1.11672i	0.240762	+	0.0570616i	−0.108463	+	0.994100i	$0.534593\pi$
$384$	19.5596	−	1.19300i	0.998145	−	0.0608803i
$385$	5.03112	−	6.75797i	0.256410	−	0.344418i
$386$	−5.41336	−	8.41580i	−0.275533	−	0.428353i
$387$	12.8542	−	12.9163i	0.653416	−	0.656573i
$388$	14.0081	+	19.6377i	0.711155	+	0.996954i
$389$	−16.2439	−	4.86310i	−0.823598	−	0.246569i	−0.152845	−	0.988250i	$-0.548844\pi$
$389$	−16.2439	−	4.86310i	−0.823598	−	0.246569i	−0.670753	+	0.741681i	$0.734029\pi$
$390$	7.94863	−	1.44733i	0.402494	−	0.0732886i
$391$	−1.15055	−	0.0670117i	−0.0581857	−	0.00338893i
$392$	4.60809	−	3.21688i	0.232744	−	0.162477i
$393$	0.416716	+	3.13607i	0.0210206	+	0.158194i
$394$	−1.29181	+	2.91294i	−0.0650805	+	0.146752i
$395$	2.00850	−	11.3908i	0.101059	−	0.573132i
$396$	11.5836	−	27.6997i	0.582097	−	1.39196i
$397$	−2.24318	−	12.7217i	−0.112582	−	0.638483i	−0.987919	−	0.154970i	$-0.950472\pi$
$397$	−2.24318	−	12.7217i	−0.112582	−	0.638483i	0.875337	−	0.483513i	$-0.160639\pi$
$398$	13.2300	+	3.27803i	0.663162	+	0.164313i
$399$	−3.94340	+	0.292056i	−0.197417	+	0.0146211i
$400$	13.1133	+	11.9450i	0.655664	+	0.597251i
$401$	12.4360	−	9.25827i	0.621025	−	0.462336i	−0.240087	−	0.970751i	$-0.577176\pi$
$401$	12.4360	−	9.25827i	0.621025	−	0.462336i	0.861112	+	0.508415i	$0.169769\pi$
$402$	6.06196	−	2.65509i	0.302343	−	0.132424i
$403$	−6.32066	+	12.5855i	−0.314855	+	0.626927i
$404$	5.41772	−	1.50260i	0.269542	−	0.0747572i
$405$	6.34839	−	2.34534i	0.315454	−	0.116541i
$406$	−15.5231	−	11.8038i	−0.770398	−	0.585810i
$407$	15.1850	+	7.62619i	0.752692	+	0.378016i
$408$	1.04015	−	0.167618i	0.0514953	−	0.00829832i
$409$	0.582865	+	0.782923i	0.0288208	+	0.0387131i	0.816300	−	0.577628i	$-0.196022\pi$
$409$	0.582865	+	0.782923i	0.0288208	+	0.0387131i	−0.787479	+	0.616341i	$0.788614\pi$
$410$	−0.0872239	+	0.232269i	−0.00430768	+	0.0114709i
$411$	21.8012	−	14.8360i	1.07538	−	0.731804i
$412$	−16.3553	−	20.3167i	−0.805768	−	1.00093i
$413$	−28.8193	+	5.08162i	−1.41810	+	0.250050i
$414$	−22.6643	+	1.80577i	−1.11389	+	0.0887490i
$415$	−12.5715	−	2.21670i	−0.617111	−	0.108813i
$416$	24.6230	−	3.06113i	1.20724	−	0.150084i
$417$	5.51282	−	13.3546i	0.269964	−	0.653979i
$418$	6.80532	−	2.39885i	0.332859	−	0.117331i
$419$	−1.40369	+	24.1005i	−0.0685749	+	1.17739i	0.771975	+	0.635653i	$0.219269\pi$
$419$	−1.40369	+	24.1005i	−0.0685749	+	1.17739i	−0.840550	+	0.541734i	$0.817768\pi$
$420$	5.82401	−	0.312395i	0.284182	−	0.0152433i
$421$	8.46265	−	28.2672i	0.412444	−	1.37766i	−0.459553	−	0.888150i	$-0.651991\pi$
$421$	8.46265	−	28.2672i	0.412444	−	1.37766i	0.871998	−	0.489510i	$-0.162824\pi$
$422$	−9.55103	+	30.7606i	−0.464937	+	1.49740i
$423$	16.2102	+	1.37886i	0.788167	+	0.0670422i
$424$	15.8221	+	14.1208i	0.768391	+	0.685767i
$425$	0.764976	+	0.569504i	0.0371068	+	0.0276250i
$426$	0.431762	+	1.41343i	0.0209189	+	0.0684810i
$427$	0.171763	−	0.724724i	0.00831218	−	0.0350718i
$428$	−20.0245	−	2.75442i	−0.967922	−	0.133140i
$429$	12.4383	−	35.9246i	0.600529	−	1.73446i
$430$	−6.44452	−	0.441152i	−0.310782	−	0.0212742i
$431$	6.64092	+	11.5024i	0.319882	+	0.554052i	0.980463	−	0.196703i	$-0.0630234\pi$
$431$	6.64092	+	11.5024i	0.319882	+	0.554052i	−0.660581	+	0.750755i	$0.729690\pi$
$432$	19.8718	−	6.09178i	0.956085	−	0.293091i
$433$	−1.36282	+	2.36047i	−0.0654930	+	0.113437i	−0.896913	−	0.442208i	$-0.854195\pi$
$433$	−1.36282	+	2.36047i	−0.0654930	+	0.113437i	0.831420	+	0.555645i	$0.187529\pi$
$434$	−5.67280	+	8.43693i	−0.272303	+	0.404986i
$435$	2.86189	+	7.49362i	0.137217	+	0.359291i
$436$	−13.9294	−	34.1875i	−0.667097	−	1.63729i
$437$	−3.97452	−	3.74976i	−0.190127	−	0.179376i
$438$	19.4566	+	25.8326i	0.929674	+	1.23433i
$439$	1.64099	−	14.0395i	0.0783200	−	0.670070i	−0.895866	−	0.444324i	$-0.853444\pi$
$439$	1.64099	−	14.0395i	0.0783200	−	0.670070i	0.974186	−	0.225746i	$-0.0724820\pi$
$440$	−10.1076	+	3.33338i	−0.481862	+	0.158913i
$441$	3.95194	−	4.46237i	0.188188	−	0.212494i
$442$	1.30115	−	0.294435i	0.0618892	−	0.0140049i
$443$	−22.6690	−	24.0277i	−1.07704	−	1.14159i	−0.989367	−	0.145443i	$-0.953539\pi$
$443$	−22.6690	−	24.0277i	−1.07704	−	1.14159i	−0.0876700	−	0.996150i	$-0.527942\pi$
$444$	2.66022	+	11.4585i	0.126249	+	0.543795i
$445$	9.33676	−	4.68910i	0.442605	−	0.222285i
$446$	3.54143	−	18.9551i	0.167691	−	0.897552i
$447$	0.877728	+	0.557688i	0.0415151	+	0.0263778i
$448$	17.9119	+	0.0508606i	0.846256	+	0.00240294i
$449$	5.38171	−	6.41367i	0.253978	−	0.302680i	−0.623957	−	0.781459i	$-0.714476\pi$
$449$	5.38171	−	6.41367i	0.253978	−	0.302680i	0.877936	+	0.478779i	$0.158920\pi$
$450$	16.4904	+	9.05743i	0.777367	+	0.426971i
$451$	0.750426	+	0.894322i	0.0353362	+	0.0421120i
$452$	−25.2922	+	3.93110i	−1.18964	+	0.184904i
$453$	−3.09343	+	0.784809i	−0.145342	+	0.0368735i
$454$	−3.63589	+	0.603047i	−0.170641	+	0.0283024i
$455$	7.33508	−	0.857348i	0.343874	−	0.0401931i
$456$	4.28862	+	2.56117i	0.200833	+	0.119938i
$457$	0.824101	+	14.1493i	0.0385498	+	0.661875i	0.961135	+	0.276080i	$0.0890356\pi$
$457$	0.824101	+	14.1493i	0.0385498	+	0.661875i	−0.922585	+	0.385794i	$0.873927\pi$
$458$	20.5864	−	8.63288i	0.961939	−	0.403388i
$459$	1.03087	−	0.431371i	0.0481167	−	0.0201347i
$460$	5.74865	+	5.64892i	0.268032	+	0.263382i
$461$	3.77372	+	5.73766i	0.175760	+	0.267229i	0.912614	−	0.408822i	$-0.134060\pi$
$461$	3.77372	+	5.73766i	0.175760	+	0.267229i	−0.736855	+	0.676051i	$0.763690\pi$
$462$	12.1798	−	24.5932i	0.566657	−	1.14418i
$463$	15.4362	+	6.65853i	0.717382	+	0.309448i	0.723300	−	0.690534i	$-0.242624\pi$
$463$	15.4362	+	6.65853i	0.717382	+	0.309448i	−0.00591795	+	0.999982i	$0.501884\pi$
$464$	7.47729	+	23.4728i	0.347125	+	1.08970i
$465$	3.81336	−	1.71665i	0.176840	−	0.0796077i
$466$	5.29063	+	18.3490i	0.245084	+	0.850003i
$467$	−12.0220	−	4.37566i	−0.556313	−	0.202481i	0.0485362	−	0.998821i	$-0.484544\pi$
$467$	−12.0220	−	4.37566i	−0.556313	−	0.202481i	−0.604849	+	0.796340i	$0.706767\pi$
$468$	24.6286	−	9.27660i	1.13846	−	0.428811i
$469$	5.68440	−	2.06895i	0.262481	−	0.0955353i
$470$	−3.39660	−	4.66063i	−0.156673	−	0.214979i
$471$	14.7488	−	4.66981i	0.679587	−	0.215173i
$472$	33.4821	+	15.6709i	1.54114	+	0.721309i
$473$	−16.7025	+	25.3950i	−0.767984	+	1.16766i
$474$	−0.210228	−	37.6763i	−0.00965608	−	1.73053i
$475$	1.04276	+	4.39974i	0.0478450	+	0.201874i
$476$	0.958597	−	0.0923248i	0.0439372	−	0.00423170i
$477$	19.8244	+	10.6276i	0.907697	+	0.486606i
$478$	−3.84398	+	7.46375i	−0.175819	+	0.341384i
$479$	2.69070	+	6.23774i	0.122941	+	0.285009i	0.968561	−	0.248776i	$-0.0800283\pi$
$479$	2.69070	+	6.23774i	0.122941	+	0.285009i	−0.845620	+	0.533785i	$0.820769\pi$
$480$	−6.24751	−	3.90554i	−0.285158	−	0.178263i
$481$	4.27185	+	14.2690i	0.194780	+	0.650609i
$482$	0.151838	−	14.9302i	0.00691603	−	0.680051i
$483$	−20.7797	+	0.327294i	−0.945511	+	0.0148924i
$484$	−5.43756	+	27.5491i	−0.247162	+	1.25223i
$485$		−	9.06953i		−	0.411826i
$486$	18.9762	−	11.2206i	0.860779	−	0.508979i
$487$		−	19.2023i		−	0.870141i	−0.900396	−	0.435070i	$-0.856723\pi$
$487$		−	19.2023i		−	0.870141i	0.900396	−	0.435070i	$-0.143277\pi$
$488$	−0.703745	+	0.624492i	−0.0318570	+	0.0282694i
$489$	26.2180	−	0.412949i	1.18562	−	0.0186742i
$490$	−2.11288	−	0.0214877i	−0.0954503	−	0.000970717i
$491$	1.88563	+	6.29845i	0.0850973	+	0.284245i	0.989937	−	0.141507i	$-0.0451948\pi$
$491$	1.88563	+	6.29845i	0.0850973	+	0.284245i	−0.904840	+	0.425752i	$0.860010\pi$
$492$	−0.143991	+	0.795254i	−0.00649163	+	0.0358528i
$493$	0.524607	+	1.21618i	0.0236271	+	0.0547738i
$494$	5.62303	+	2.89597i	0.252992	+	0.130296i
$495$	−9.59369	+	5.94944i	−0.431204	+	0.267407i
$496$	11.9900	−	4.60316i	0.538366	−	0.206688i
$497$	0.311539	+	1.31449i	0.0139744	+	0.0589628i
$498$	−41.5817	+	0.232019i	−1.86332	+	0.0103970i
$499$	−5.53642	+	8.41771i	−0.247844	+	0.376829i	−0.937888	−	0.346939i	$-0.887221\pi$
$499$	−5.53642	+	8.41771i	−0.247844	+	0.376829i	0.690044	+	0.723768i	$0.257591\pi$
$500$	−2.99075	−	13.8703i	−0.133750	−	0.620297i
$501$	−23.9550	+	7.58471i	−1.07023	+	0.338860i
$502$	−7.14664	+	5.20837i	−0.318970	+	0.232461i
$503$	−17.3699	+	6.32212i	−0.774484	+	0.281889i	−0.698871	−	0.715248i	$-0.746314\pi$
$503$	−17.3699	+	6.32212i	−0.774484	+	0.281889i	−0.0756135	+	0.997137i	$0.524092\pi$
$504$	18.4820	−	4.39965i	0.823254	−	0.195976i
$505$	−1.98640	−	0.722991i	−0.0883938	−	0.0321727i
$506$	36.4397	−	10.5067i	1.61994	−	0.467082i
$507$	9.85459	−	4.43621i	0.437658	−	0.197019i
$508$	33.1323	−	1.25428i	1.47001	−	0.0556497i
$509$	17.9996	+	7.76428i	0.797819	+	0.344145i	0.755659	−	0.654965i	$-0.227317\pi$
$509$	17.9996	+	7.76428i	0.797819	+	0.344145i	0.0421600	+	0.999111i	$0.486576\pi$
$510$	−0.354981	−	0.175805i	−0.0157188	−	0.00778476i
$511$	16.2440	+	24.6978i	0.718593	+	1.09257i
$512$	−18.4798	−	13.0574i	−0.816702	−	0.577060i
$513$	5.05870	+	1.57492i	0.223347	+	0.0695345i
$514$	−9.26446	−	22.0925i	−0.408638	−	0.974459i
$515$	0.570194	+	9.78986i	0.0251258	+	0.431393i
$516$	−20.9103	+	2.34683i	−0.920525	+	0.103314i
$517$	−26.9530	+	3.15035i	−1.18539	+	0.138552i
$518$	1.75934	+	10.6074i	0.0773011	+	0.466063i
$519$	−35.6058	+	9.03327i	−1.56292	+	0.396517i
$520$	−8.20528	−	4.43929i	−0.359825	−	0.194676i
$521$	16.6238	+	19.8114i	0.728301	+	0.867955i	0.995409	−	0.0957115i	$-0.0305126\pi$
$521$	16.6238	+	19.8114i	0.728301	+	0.867955i	−0.267108	+	0.963666i	$0.586068\pi$
$522$	13.5443	+	22.3449i	0.592819	+	0.978011i
$523$	−0.411866	+	0.490843i	−0.0180096	+	0.0214631i	−0.774974	−	0.631993i	$-0.782237\pi$
$523$	−0.411866	+	0.490843i	−0.0180096	+	0.0214631i	0.756964	+	0.653456i	$0.226682\pi$
$524$	1.89049	−	3.12584i	0.0825864	−	0.136553i
$525$	14.5152	+	9.22264i	0.633496	+	0.402509i
$526$	20.9336	+	3.91106i	0.912749	+	0.170531i
$527$	0.617066	−	0.309902i	0.0268798	−	0.0134996i
$528$	−30.4469	+	16.5807i	−1.32503	+	0.721582i
$529$	−3.92428	−	4.15950i	−0.170621	−	0.180848i
$530$	−1.75983	−	7.77692i	−0.0764423	−	0.337808i
$531$	38.4193	+	7.83646i	1.66726	+	0.340074i
$532$	3.76295	+	2.58608i	0.163145	+	0.112121i
$533$	−0.118802	+	1.01641i	−0.00514587	+	0.0440257i
$534$	27.1855	−	20.4756i	1.17643	−	0.886065i
$535$	5.52793	+	5.21534i	0.238993	+	0.225479i
$536$	−7.37852	−	1.98830i	−0.318704	−	0.0858815i
$537$	−4.98492	−	13.0526i	−0.215115	−	0.563261i
$538$	27.0264	+	18.1720i	1.16519	+	0.783450i
$539$	−4.97130	+	8.61054i	−0.214129	+	0.370882i
$540$	−7.41271	−	2.47425i	−0.318992	−	0.106475i
$541$	16.4588	+	28.5075i	0.707619	+	1.22563i	0.965738	+	0.259519i	$0.0835642\pi$
$541$	16.4588	+	28.5075i	0.707619	+	1.22563i	−0.258118	+	0.966113i	$0.583102\pi$
$542$	1.13845	−	16.6309i	0.0489005	−	0.714358i
$543$	−5.35726	+	15.4729i	−0.229902	+	0.664006i
$544$	−1.05800	−	0.600541i	−0.0453615	−	0.0257480i
$545$	−3.20096	+	13.5059i	−0.137114	+	0.578530i
$546$	23.0066	−	7.02784i	0.984592	−	0.300764i
$547$	13.2226	+	9.84385i	0.565357	+	0.420892i	0.841526	−	0.540217i	$-0.181658\pi$
$547$	13.2226	+	9.84385i	0.565357	+	0.420892i	−0.276169	+	0.961109i	$0.589065\pi$
$548$	−30.3561	−	2.38837i	−1.29675	−	0.102026i
$549$	−0.570429	+	0.818849i	−0.0243453	+	0.0349476i
$550$	−29.9707	−	9.30577i	−1.27796	−	0.396800i
$551$	−1.80104	+	6.01589i	−0.0767268	+	0.256285i
$552$	21.7191	+	14.7487i	0.924428	+	0.627745i
$553$	2.00245	−	34.3808i	0.0851530	−	1.46202i
$554$	−14.4525	−	41.0004i	−0.614026	−	1.74194i
$555$	1.68761	−	4.08818i	0.0716352	−	0.173534i
$556$	−14.6144	+	8.04585i	−0.619788	+	0.341220i
$557$	8.10041	+	1.42832i	0.343226	+	0.0605199i	0.342604	−	0.939480i	$-0.388691\pi$
$557$	8.10041	+	1.42832i	0.343226	+	0.0605199i	0.000621455		1.00000i	$0.499802\pi$
$558$	11.2190	−	7.72661i	0.474939	−	0.327093i
$559$	−26.2383	+	4.62652i	−1.10976	+	0.195681i
$560$	−5.47157	−	3.92651i	−0.231216	−	0.165925i
$561$	−1.54100	+	1.04867i	−0.0650611	+	0.0442748i
$562$	28.1702	+	10.5788i	1.18829	+	0.446238i
$563$	7.20858	+	9.68280i	0.303805	+	0.408081i	0.927640	−	0.373475i	$-0.121834\pi$
$563$	7.20858	+	9.68280i	0.303805	+	0.408081i	−0.623835	+	0.781556i	$0.714426\pi$
$564$	−13.6048	−	12.9540i	−0.572865	−	0.545461i
$565$	8.60006	+	4.31911i	0.361807	+	0.181706i
$566$	6.21865	−	8.17814i	0.261390	−	0.343753i
$567$	17.9637	−	9.13040i	0.754406	−	0.383441i
$568$	0.632316	−	1.58507i	0.0265314	−	0.0665081i
$569$	−17.6646	+	35.1732i	−0.740540	+	1.47454i	0.134720	+	0.990884i	$0.456987\pi$
$569$	−17.6646	+	35.1732i	−0.740540	+	1.47454i	−0.875260	+	0.483653i	$0.839310\pi$
$570$	−0.753498	−	1.72035i	−0.0315605	−	0.0720574i
$571$	9.76246	−	7.26788i	0.408546	−	0.304151i	−0.373197	−	0.927752i	$-0.621738\pi$
$571$	9.76246	−	7.26788i	0.408546	−	0.304151i	0.781743	+	0.623601i	$0.214331\pi$
$572$	−37.1594	+	23.3715i	−1.55371	+	0.977213i
$573$	7.45726	−	0.552299i	0.311531	−	0.0230726i
$574$	−0.177665	+	0.717051i	−0.00741558	+	0.0299291i
$575$	4.12667	+	23.4035i	0.172094	+	0.975993i
$576$	−22.3005	−	8.87053i	−0.929189	−	0.369605i
$577$	−0.389719	+	2.21021i	−0.0162242	+	0.0920121i	−0.991845	−	0.127453i	$-0.959320\pi$
$577$	−0.389719	+	2.21021i	−0.0162242	+	0.0920121i	0.975620	+	0.219465i	$0.0704311\pi$
$578$	21.9176	+	9.71989i	0.911654	+	0.404294i
$579$	1.61429	+	12.1486i	0.0670877	+	0.504880i
$580$	2.83641	−	8.81746i	0.117776	−	0.366125i
$581$	−37.9446	−	2.21002i	−1.57421	−	0.0916872i
$582$	−5.29238	−	29.0653i	−0.219376	−	1.20480i
$583$	−35.9431	−	10.7606i	−1.48861	−	0.445660i
$584$	1.13911	−	37.3258i	0.0471367	−	1.54455i
$585$	−9.56408	−	2.53800i	−0.395426	−	0.104933i
$586$	−28.5563	+	18.3685i	−1.17965	+	0.758796i
$587$	−5.54451	+	7.44757i	−0.228847	+	0.307394i	−0.901684	−	0.432396i	$-0.857668\pi$
$587$	−5.54451	+	7.44757i	−0.228847	+	0.307394i	0.672837	+	0.739791i	$0.265076\pi$
$588$	−6.78373	+	1.16408i	−0.279757	+	0.0480058i
$589$	3.18561	+	0.755004i	0.131261	+	0.0311094i
$590$	−6.82695	−	12.1073i	−0.281061	−	0.498450i
$591$	2.94975	−	2.55537i	0.121337	−	0.105114i
$592$	5.88270	−	12.2430i	0.241777	−	0.503185i
$593$	−25.8284	+	14.9120i	−1.06064	+	0.612363i	−0.925610	−	0.378478i	$-0.876447\pi$
$593$	−25.8284	+	14.9120i	−1.06064	+	0.612363i	−0.135033	+	0.990841i	$0.543114\pi$
$594$	−27.2734	+	24.6645i	−1.11904	+	1.01200i
$595$	−0.313577	−	0.181044i	−0.0128554	−	0.00742207i
$596$	−0.387661	−	1.13649i	−0.0158792	−	0.0465525i
$597$	−12.9553	−	10.5276i	−0.530224	−	0.430865i
$598$	28.6183	+	16.9131i	1.17029	+	0.691628i
$599$	−2.78371	+	2.95056i	−0.113739	+	0.120557i	−0.781741	−	0.623603i	$-0.785668\pi$
$599$	−2.78371	+	2.95056i	−0.113739	+	0.120557i	0.668002	+	0.744160i	$0.267150\pi$
$600$	−8.30937	−	20.0728i	−0.339229	−	0.819468i
$601$	36.2426	+	4.23615i	1.47837	+	0.172796i	0.816726	−	0.577026i	$-0.195787\pi$
$601$	36.2426	+	4.23615i	1.47837	+	0.172796i	0.661640	+	0.749822i	$0.269861\pi$
$602$	−19.2112	+	0.923003i	−0.782991	+	0.0376188i
$603$	−8.10239	−	0.216215i	−0.329955	−	0.00880496i
$604$	3.35337	+	1.52813i	0.136447	+	0.0621786i
$605$	7.67958	−	7.24531i	0.312219	−	0.294564i
$606$	−6.78775	−	1.15785i	−0.275734	−	0.0470345i
$607$	−17.5718	−	34.9884i	−0.713218	−	1.42013i	−0.899181	−	0.437577i	$-0.855837\pi$
$607$	−17.5718	−	34.9884i	−0.713218	−	1.42013i	0.185963	−	0.982557i	$-0.440460\pi$
$608$	−2.01243	−	5.40549i	−0.0816148	−	0.219221i
$609$	11.0539	+	21.1720i	0.447926	+	0.857933i
$610$	0.351764	−	0.0374934i	0.0142425	−	0.00151806i
$611$	−18.2215	−	15.2896i	−0.737162	−	0.618552i
$612$	−1.24020	−	0.356261i	−0.0501322	−	0.0144010i
$613$	30.3551	−	25.4710i	1.22603	−	1.02876i	0.227544	−	0.973768i	$-0.426930\pi$
$613$	30.3551	−	25.4710i	1.22603	−	1.02876i	0.998487	−	0.0549943i	$-0.0175141\pi$
$614$	26.4168	−	27.4357i	1.06609	−	1.10722i
$615$	0.217713	−	0.211981i	0.00877905	−	0.00854790i
$616$	−28.7396	+	13.3518i	−1.15795	+	0.537961i
$617$	0.103191	+	0.882853i	0.00415430	+	0.0355423i	0.995157	−	0.0983032i	$-0.0313415\pi$
$617$	0.103191	+	0.882853i	0.00415430	+	0.0355423i	−0.991002	+	0.133845i	$0.957267\pi$
$618$	7.54003	+	31.0410i	0.303305	+	1.24865i
$619$	20.1349	−	1.17272i	0.809290	−	0.0471358i	0.351491	−	0.936191i	$-0.385675\pi$
$619$	20.1349	−	1.17272i	0.809290	−	0.0471358i	0.457799	+	0.889056i	$0.348638\pi$
$620$	−4.67510	−	1.20895i	−0.187757	−	0.0485525i
$621$	26.0610	+	9.80931i	1.04579	+	0.393634i
$622$	−1.58759	+	12.4807i	−0.0636567	+	0.500429i
$623$	25.9912	−	17.0947i	1.04132	−	0.684885i
$624$	−28.8861	−	9.43863i	−1.15637	−	0.377848i
$625$	6.66910	−	15.4607i	0.266764	−	0.618429i
$626$	22.8759	+	27.8324i	0.914305	+	1.11241i
$627$	−8.79275	−	0.887600i	−0.351149	−	0.0354473i
$628$	−16.6586	−	6.44986i	−0.664751	−	0.257378i
$629$	0.249773	−	0.686246i	0.00995911	−	0.0273624i
$630$	−6.61783	−	2.68874i	−0.263661	−	0.107122i
$631$	11.9685	+	32.8832i	0.476459	+	1.30906i	0.912479	+	0.409123i	$0.134165\pi$
$631$	11.9685	+	32.8832i	0.476459	+	1.30906i	−0.436020	+	0.899937i	$0.643612\pi$
$632$	−27.0321	+	34.0880i	−1.07528	+	1.35595i
$633$	26.6157	−	29.1163i	1.05788	−	1.15727i
$634$	−33.0635	−	28.3215i	−1.31312	−	1.12479i
$635$	−10.4154	−	6.85031i	−0.413322	−	0.271846i
$636$	−10.1779	−	23.8959i	−0.403579	−	0.947536i
$637$	−8.48027	+	2.00986i	−0.336000	+	0.0796335i
$638$	−29.5853	−	32.0044i	−1.17129	−	1.26707i
$639$	0.258018	−	1.79157i	0.0102071	−	0.0708735i
$640$	2.80553	+	8.03172i	0.110898	+	0.317481i
$641$	23.6232	−	10.1900i	0.933059	−	0.402483i	0.125383	−	0.992108i	$-0.459984\pi$
$641$	23.6232	−	10.1900i	0.933059	−	0.402483i	0.807676	+	0.589626i	$0.200725\pi$
$642$	20.7588	+	13.4880i	0.819285	+	0.532327i
$643$	−21.3040	+	6.37800i	−0.840148	+	0.251524i	−0.677834	−	0.735215i	$-0.737081\pi$
$643$	−21.3040	+	6.37800i	−0.840148	+	0.251524i	−0.162314	+	0.986739i	$0.551896\pi$
$644$	18.9534	+	14.7187i	0.746869	+	0.580000i
$645$	6.91289	+	3.84729i	0.272195	+	0.151487i
$646$	−0.136353	−	0.278528i	−0.00536473	−	0.0109585i
$647$	−6.20780			−0.244054			−0.122027	−	0.992527i	$-0.538939\pi$
$647$	−6.20780			−0.244054			−0.122027	+	0.992527i	$0.538939\pi$
$648$	−25.1995	−	3.60371i	−0.989929	−	0.141567i
$649$	−65.4033			−2.56730
$650$	−12.0950	−	24.7064i	−0.474404	−	0.969063i
$651$	10.6841	−	6.39488i	0.418742	−	0.250635i
$652$	−23.9137	−	18.5707i	−0.936531	−	0.727287i
$653$	13.8483	−	4.14591i	0.541926	−	0.162242i	−0.00412854	−	0.999991i	$-0.501314\pi$
$653$	13.8483	−	4.14591i	0.541926	−	0.162242i	0.546055	+	0.837749i	$0.316129\pi$
$654$	−2.37702	+	45.1506i	−0.0929487	+	1.76553i
$655$	−1.26117	+	0.544016i	−0.0492780	+	0.0212565i
$656$	0.704275	−	0.612275i	0.0274973	−	0.0239053i
$657$	−8.10298	−	38.7707i	−0.316127	−	1.51259i
$658$	−11.6560	−	12.6091i	−0.454397	−	0.491552i
$659$	38.7774	−	9.19041i	1.51055	−	0.358008i	0.609876	−	0.792497i	$-0.291219\pi$
$659$	38.7774	−	9.19041i	1.51055	−	0.358008i	0.900677	+	0.434489i	$0.143071\pi$
$660$	12.9398	+	1.57269i	0.503683	+	0.0612167i
$661$	33.4119	+	21.9753i	1.29957	+	0.854742i	0.995205	−	0.0978130i	$-0.0311847\pi$
$661$	33.4119	+	21.9753i	1.29957	+	0.854742i	0.304367	+	0.952555i	$0.401555\pi$
$662$	25.1128	+	21.5111i	0.976038	+	0.836054i
$663$	−1.59556	−	0.351711i	−0.0619664	−	0.0136593i
$664$	37.6215	+	29.8341i	1.46000	+	1.15779i
$665$	−0.587155	−	1.61319i	−0.0227689	−	0.0625570i
$666$	3.02273	−	14.0863i	0.117128	−	0.545832i
$667$	−11.2882	+	31.0141i	−0.437082	+	1.20087i
$668$	27.0570	+	10.4759i	1.04687	+	0.405324i
$669$	−13.8030	+	19.1634i	−0.533653	+	0.740901i
$670$	1.82437	+	2.21966i	0.0704816	+	0.0857528i
$671$	0.659310	−	1.52845i	0.0254524	−	0.0590053i
$672$	−19.8261	−	9.39052i	−0.764808	−	0.362247i
$673$	−32.6532	+	21.4763i	−1.25869	+	0.827851i	−0.990765	−	0.135590i	$-0.956707\pi$
$673$	−32.6532	+	21.4763i	−1.25869	+	0.827851i	−0.267921	+	0.963441i	$0.586337\pi$
$674$	0.133757	−	1.05151i	0.00515211	−	0.0405026i
$675$	−13.5572	−	18.6322i	−0.521817	−	0.717155i
$676$	−12.0815	−	3.12420i	−0.464674	−	0.120161i
$677$	12.9338	−	0.753309i	0.497087	−	0.0289520i	0.192230	−	0.981350i	$-0.438428\pi$
$677$	12.9338	−	0.753309i	0.497087	−	0.0289520i	0.304858	+	0.952398i	$0.401391\pi$
$678$	30.0811	+	8.82311i	1.15526	+	0.338850i
$679$	−3.13502	−	26.8218i	−0.120311	−	1.02933i
$680$	0.192721	+	0.414829i	0.00739053	+	0.0159080i
$681$	4.34409	+	1.22633i	0.166466	+	0.0469931i
$682$	−15.7601	+	16.3681i	−0.603487	+	0.626765i
$683$	−24.9424	+	20.9292i	−0.954395	+	0.800833i	−0.980032	−	0.198839i	$-0.936283\pi$
$683$	−24.9424	+	20.9292i	−0.954395	+	0.800833i	0.0256370	+	0.999671i	$0.491839\pi$
$684$	−3.41863	−	5.07354i	−0.130715	−	0.193991i
$685$	8.77027	+	7.35913i	0.335095	+	0.281178i
$686$	−28.2960	+	3.01598i	−1.08035	+	0.115151i
$687$	−27.3157	−	1.15965i	−1.04216	−	0.0442435i
$688$	20.5302	+	12.9940i	0.782705	+	0.495392i
$689$	−14.7599	−	29.3893i	−0.562307	−	1.11964i
$690$	−3.42777	−	9.25668i	−0.130493	−	0.352396i
$691$	−15.5447	+	14.6657i	−0.591349	+	0.557909i	−0.922661	−	0.385612i	$-0.873990\pi$
$691$	−15.5447	+	14.6657i	−0.591349	+	0.557909i	0.331312	+	0.943521i	$0.392509\pi$
$692$	38.5979	+	17.5890i	1.46727	+	0.668633i
$693$	−26.3154	+	20.9108i	−0.999640	+	0.794335i
$694$	9.62879	−	0.462616i	0.365504	−	0.0175606i
$695$	6.23011	+	0.728195i	0.236321	+	0.0276220i
$696$	3.94461	−	29.9126i	0.149520	−	1.13384i
$697$	0.0344315	−	0.0364953i	0.00130419	−	0.00138236i
$698$	−27.7962	−	16.4273i	−1.05210	−	0.621782i
$699$	3.69811	−	23.0942i	0.139875	−	0.873502i
$700$	−6.41085	−	18.7945i	−0.242307	−	0.710364i
$701$	−8.66549	−	5.00303i	−0.327291	−	0.188962i	0.327347	−	0.944904i	$-0.393846\pi$
$701$	−8.66549	−	5.00303i	−0.327291	−	0.188962i	−0.654638	+	0.755943i	$0.727179\pi$
$702$	−32.1312	−	2.55261i	−1.21271	−	0.0963422i
$703$	2.99855	−	1.73122i	0.113093	−	0.0652941i
$704$	39.4042	+	7.06344i	1.48510	+	0.266213i
$705$	1.33589	+	6.93563i	0.0503125	+	0.261211i
$706$	−23.4355	−	41.5619i	−0.882007	−	1.56420i
$707$	−6.12441	−	1.45151i	−0.230332	−	0.0545897i
$708$	−28.9435	−	34.8168i	−1.08776	−	1.30850i
$709$	12.6247	−	16.9579i	0.474129	−	0.636866i	−0.499143	−	0.866519i	$-0.666352\pi$
$709$	12.6247	−	16.9579i	0.474129	−	0.636866i	0.973272	+	0.229654i	$0.0737593\pi$
$710$	−0.539637	+	0.347115i	−0.0202522	+	0.0130270i
$711$	−19.4007	+	41.8680i	−0.727583	+	1.57017i
$712$	−39.2805	−	1.19876i	−1.47210	−	0.0449256i
$713$	16.4837	+	4.93491i	0.617321	+	0.184814i
$714$	−1.11057	−	0.397212i	−0.0415621	−	0.0148653i
$715$	16.4772	+	0.959689i	0.616213	+	0.0358903i
$716$	−4.94054	+	15.3585i	−0.184637	+	0.573974i
$717$	8.14995	−	6.26929i	0.304365	−	0.234131i
$718$	20.8723	+	9.25632i	0.778949	+	0.345443i
$719$	4.56424	−	25.8851i	0.170217	−	0.965350i	−0.773303	−	0.634036i	$-0.781397\pi$
$719$	4.56424	−	25.8851i	0.170217	−	0.965350i	0.943521	−	0.331314i	$-0.107492\pi$
$720$	4.88918	+	7.58438i	0.182209	+	0.282653i
$721$	5.07028	+	28.7550i	0.188827	+	1.07089i
$722$	−6.10862	+	24.6543i	−0.227339	+	0.917536i
$723$	−7.94864	+	16.4687i	−0.295613	+	0.612479i
$724$	16.0048	−	10.0663i	0.594812	−	0.374109i
$725$	21.9070	−	16.3091i	0.813604	−	0.605706i
$726$	20.3830	−	27.7005i	0.756484	−	1.02806i
$727$	−14.7647	+	29.3990i	−0.547593	+	1.09035i	0.434275	+	0.900780i	$0.357005\pi$
$727$	−14.7647	+	29.3990i	−0.547593	+	1.09035i	−0.981868	+	0.189567i	$0.939292\pi$
$728$	−25.8004	−	10.2923i	−0.956227	−	0.381457i
$729$	−26.8795	+	2.54759i	−0.995539	+	0.0943553i
$730$	−8.49853	+	11.1764i	−0.314545	+	0.413657i
$731$	1.16736	+	0.586271i	0.0431765	+	0.0216840i
$732$	1.10543	−	0.325423i	0.0408578	−	0.0120280i
$733$	24.2294	+	32.5457i	0.894933	+	1.20210i	0.978633	+	0.205612i	$0.0659186\pi$
$733$	24.2294	+	32.5457i	0.894933	+	1.20210i	−0.0837007	+	0.996491i	$0.526674\pi$
$734$	35.9093	+	13.4850i	1.32544	+	0.497741i
$735$	2.33061	+	1.12487i	0.0859660	+	0.0414915i
$736$	−8.90705	−	28.9768i	−0.328318	−	1.06810i
$737$	13.3143	−	2.34767i	0.490438	−	0.0864774i
$738$	0.574012	−	0.806384i	0.0211297	−	0.0296834i
$739$	−20.8090	−	3.66919i	−0.765471	−	0.134973i	−0.222738	−	0.974878i	$-0.571499\pi$
$739$	−20.8090	−	3.66919i	−0.765471	−	0.134973i	−0.542733	+	0.839905i	$0.682610\pi$
$740$	−4.47383	+	2.46304i	−0.164461	+	0.0905430i
$741$	−4.72315	−	6.13999i	−0.173509	−	0.225558i
$742$	−7.89266	−	22.3908i	−0.289749	−	0.821992i
$743$	−0.464481	+	7.97483i	−0.0170402	+	0.292568i	0.979012	+	0.203801i	$0.0653297\pi$
$743$	−0.464481	+	7.97483i	−0.0170402	+	0.292568i	−0.996052	+	0.0887669i	$0.971707\pi$
$744$	−15.6879	−	1.14626i	−0.575145	−	0.0420238i
$745$	−0.129486	+	0.432514i	−0.00474401	+	0.0158461i
$746$	31.5003	+	9.78072i	1.15331	+	0.358098i
$747$	46.2079	+	21.4117i	1.69066	+	0.783413i
$748$	2.14570	+	0.168820i	0.0784545	+	0.00617268i
$749$	18.1508	+	13.5128i	0.663216	+	0.493746i
$750$	−3.91322	+	16.9316i	−0.142891	+	0.618256i
$751$	9.96541	−	42.0474i	0.363643	−	1.53433i	−0.416739	−	0.909026i	$-0.636827\pi$
$751$	9.96541	−	42.0474i	0.363643	−	1.53433i	0.780382	−	0.625304i	$-0.215025\pi$
$752$	2.89487	+	21.4976i	0.105565	+	0.783938i
$753$	10.6351	−	2.04846i	0.387566	−	0.0746501i
$754$	2.60908	−	38.1144i	0.0950170	−	1.38805i
$755$	−0.692783	−	1.19994i	−0.0252130	−	0.0436701i
$756$	−22.7773	−	4.75492i	−0.828401	−	0.172935i
$757$	1.08003	−	1.87067i	0.0392545	−	0.0679908i	−0.845731	−	0.533610i	$-0.820835\pi$
$757$	1.08003	−	1.87067i	0.0392545	−	0.0679908i	0.884985	+	0.465619i	$0.154168\pi$
$758$	−19.7212	−	13.2601i	−0.716308	−	0.481629i
$759$	−45.8631	−	7.34414i	−1.66473	−	0.266575i
$760$	−0.564267	+	2.09398i	−0.0204681	+	0.0759565i
$761$	−4.27275	−	4.03113i	−0.154887	−	0.146128i	0.604898	−	0.796303i	$-0.293214\pi$
$761$	−4.27275	−	4.03113i	−0.154887	−	0.146128i	−0.759784	+	0.650175i	$0.774696\pi$
$762$	−37.3758	−	15.8756i	−1.35398	−	0.575112i
$763$	−4.79785	+	41.0482i	−0.173694	+	1.48605i
$764$	−7.11602	−	4.89046i	−0.257448	−	0.176931i
$765$	0.301828	+	0.379839i	0.0109126	+	0.0137331i
$766$	1.51143	+	6.67921i	0.0546103	+	0.241330i
$767$	−39.3417	−	41.6998i	−1.42055	−	1.50569i
$768$	13.6777	+	24.1023i	0.493552	+	0.869716i
$769$	13.9200	−	6.99087i	0.501967	−	0.252097i	−0.179751	−	0.983712i	$-0.557529\pi$
$769$	13.9200	−	6.99087i	0.501967	−	0.252097i	0.681718	+	0.731615i	$0.261233\pi$
$770$	11.7122	+	2.18822i	0.422079	+	0.0788579i
$771$	−1.24449	+	29.3141i	−0.0448194	+	1.05572i
$772$	7.32345	−	12.1090i	0.263577	−	0.435812i
$773$	10.4262	−	12.4255i	0.375006	−	0.446914i	−0.545226	−	0.838289i	$-0.683556\pi$
$773$	10.4262	−	12.4255i	0.375006	−	0.446914i	0.920231	+	0.391375i	$0.128000\pi$
$774$	24.3989	+	8.29558i	0.877000	+	0.298178i
$775$	−9.15229	−	10.9073i	−0.328760	−	0.391801i
$776$	−16.2329	+	30.0038i	−0.582728	+	1.07707i
$777$	3.57773	−	12.6736i	0.128350	−	0.454661i
$778$	−3.92367	−	23.6565i	−0.140670	−	0.848128i
$779$	0.236276	−	0.0276167i	0.00846546	−	0.000989471i
$780$	6.78093	+	9.19619i	0.242796	+	0.329276i
$781$	0.175551	+	3.01409i	0.00628169	+	0.107852i
$782$	−0.630308	−	1.50307i	−0.0225398	−	0.0537495i
$783$	−3.36757	−	31.8242i	−0.120347	−	1.13730i
$784$	6.95137	+	3.85279i	0.248263	+	0.137600i
$785$	3.69078	+	5.61156i	0.131730	+	0.200285i
$786$	−3.72425	+	2.47935i	−0.132839	+	0.0884356i
$787$	17.8008	+	7.67851i	0.634529	+	0.273709i	0.688950	−	0.724809i	$-0.258072\pi$
$787$	17.8008	+	7.67851i	0.634529	+	0.273709i	−0.0544207	+	0.998518i	$0.517331\pi$
$788$	−4.50321	+	0.170477i	−0.160420	+	0.00607298i
$789$	−21.1636	−	15.2437i	−0.753445	−	0.542688i
$790$	15.7172	−	4.53178i	0.559193	−	0.161234i
$791$	26.9264	+	9.80040i	0.957391	+	0.348462i
$792$	42.3863	−	2.51083i	1.50613	−	0.0892185i
$793$	1.37110	−	0.499040i	0.0486892	−	0.0177214i
$794$	14.7639	−	10.7597i	0.523953	−	0.381849i
$795$	−2.10217	+	9.53663i	−0.0745562	+	0.338229i
$796$	4.06294	+	18.8428i	0.144007	+	0.667866i
$797$	0.655391	−	0.996474i	0.0232151	−	0.0352969i	−0.823694	−	0.567035i	$-0.808090\pi$
$797$	0.655391	−	0.996474i	0.0232151	−	0.0352969i	0.846909	+	0.531738i	$0.178461\pi$
$798$	−2.82302	−	4.82721i	−0.0999339	−	0.170881i
$799$	0.268956	+	1.13481i	0.00951497	+	0.0401468i
$800$	−7.01826	+	24.0838i	−0.248133	+	0.851489i
$801$	−40.8011	+	8.52732i	−1.44164	+	0.301298i
$802$	19.4925	+	10.0390i	0.688305	+	0.354490i
$803$	26.1679	+	60.6640i	0.923446	+	2.14079i
$804$	7.14184	+	6.04879i	0.251873	+	0.213325i
$805$	−2.58774	−	8.64364i	−0.0912057	−	0.304648i
$806$	−19.9161	−	0.202544i	−0.701513	−	0.00713430i
$807$	−20.4850	−	34.2248i	−0.721108	−	1.20477i
$808$	5.27738	+	5.94712i	0.185658	+	0.209219i
$809$		−	55.9656i		−	1.96764i	−0.179147	−	0.983822i	$-0.557334\pi$
$809$		−	55.9656i		−	1.96764i	0.179147	−	0.983822i	$-0.442666\pi$
$810$	6.92650	+	6.60521i	0.243372	+	0.232084i
$811$			11.7127i			0.411290i	0.978627	+	0.205645i	$0.0659292\pi$
$811$			11.7127i			0.411290i	−0.978627	+	0.205645i	$0.934071\pi$
$812$	5.34038	−	27.0568i	0.187411	−	0.949508i
$813$	−9.92842	+	17.8396i	−0.348205	+	0.625662i
$814$	−0.244379	+	24.0297i	−0.00856547	+	0.842240i
$815$	3.26497	+	10.9058i	0.114367	+	0.382012i
$816$	0.859685	+	1.21695i	0.0300950	+	0.0426018i
$817$	2.45311	+	5.68694i	0.0858234	+	0.198961i
$818$	−0.632018	+	1.22717i	−0.0220980	+	0.0429071i
$819$	−29.1617	−	4.19980i	−1.01899	−	0.146753i
$820$	−0.349259	+	0.0336380i	−0.0121967	+	0.00117469i
$821$	3.91626	+	16.5240i	0.136678	+	0.576691i	0.997679	+	0.0680878i	$0.0216898\pi$
$821$	3.91626	+	16.5240i	0.136678	+	0.576691i	−0.861001	+	0.508603i	$0.830162\pi$
$822$	32.4006	+	18.4662i	1.13010	+	0.644083i
$823$	16.5242	−	25.1238i	0.575998	−	0.875762i	−0.423549	−	0.905873i	$-0.639216\pi$
$823$	16.5242	−	25.1238i	0.575998	−	0.875762i	0.999547	+	0.0301114i	$0.00958621\pi$
$824$	15.6359	−	33.4073i	0.544702	−	1.16380i
$825$	28.3686	+	25.9323i	0.987669	+	0.902845i
$826$	−24.3748	−	33.4458i	−0.848107	−	1.16373i
$827$	−9.64656	+	3.51106i	−0.335444	+	0.122092i	−0.504250	−	0.863558i	$-0.668231\pi$
$827$	−9.64656	+	3.51106i	−0.335444	+	0.122092i	0.168806	+	0.985649i	$0.446009\pi$
$828$	−16.3866	−	27.6649i	−0.569475	−	0.961420i
$829$	−36.0765	−	13.1308i	−1.25299	−	0.456050i	−0.371578	−	0.928402i	$-0.621183\pi$
$829$	−36.0765	−	13.1308i	−1.25299	−	0.456050i	−0.881410	+	0.472352i	$0.843405\pi$
$830$	−5.00153	−	17.3464i	−0.173606	−	0.602102i
$831$	−5.34757	+	52.9742i	−0.185505	+	1.83765i
$832$	19.1991	+	29.3721i	0.665609	+	1.01829i
$833$	0.392359	+	0.169247i	0.0135944	+	0.00586407i
$834$	20.3907	−	1.30182i	0.706071	−	0.0450784i
$835$	−5.99457	−	9.11430i	−0.207451	−	0.315413i
$836$	7.27860	+	7.15233i	0.251736	+	0.247368i
$837$	−16.4611	+	2.71737i	−0.568977	+	0.0939260i
$838$	−31.4847	+	13.2031i	−1.08762	+	0.456092i
$839$	−2.52440	−	43.3422i	−0.0871519	−	1.49634i	−0.704530	−	0.709674i	$-0.748842\pi$
$839$	−2.52440	−	43.3422i	−0.0871519	−	1.49634i	0.617378	−	0.786666i	$-0.288195\pi$
$840$	4.01824	+	7.20326i	0.138642	+	0.248536i
$841$	8.86989	−	1.03674i	0.305858	−	0.0357497i
$842$	41.1665	−	6.82787i	1.41869	−	0.235304i
$843$	−25.7097	−	26.4049i	−0.885488	−	0.909433i
$844$	−45.0104	+	6.99585i	−1.54932	+	0.240807i
$845$	3.01591	+	3.59422i	0.103750	+	0.123645i
$846$	8.32833	+	21.4472i	0.286334	+	0.737371i
$847$	20.2068	−	24.0815i	0.694313	−	0.827450i
$848$	−8.09751	+	28.8774i	−0.278069	+	0.991654i
$849$	−11.1542	+	5.82360i	−0.382811	+	0.199865i
$850$	−0.247698	+	1.32578i	−0.00849597	+	0.0454739i
$851$	16.2621	−	8.16711i	0.557456	−	0.279965i
$852$	−1.52683	+	1.42730i	−0.0523084	+	0.0488986i
$853$	−11.2795	−	11.9556i	−0.386204	−	0.409352i	0.504881	−	0.863189i	$-0.331536\pi$
$853$	−11.2795	−	11.9556i	−0.386204	−	0.409352i	−0.891085	+	0.453837i	$0.850055\pi$
$854$	1.02733	−	0.232474i	0.0351546	−	0.00795509i
$855$	−0.0613604	+	2.29940i	−0.00209848	+	0.0786380i
$856$	−8.95292	−	27.1474i	−0.306005	−	0.927880i
$857$	−2.02807	+	17.3512i	−0.0692775	+	0.592707i	0.913358	+	0.407158i	$0.133480\pi$
$857$	−2.02807	+	17.3512i	−0.0692775	+	0.592707i	−0.982635	+	0.185549i	$0.940594\pi$
$858$	53.3649	−	6.53949i	1.82185	−	0.223255i
$859$	0.198297	+	0.187083i	0.00676580	+	0.00638320i	0.689617	−	0.724174i	$-0.257779\pi$
$859$	0.198297	+	0.187083i	0.00676580	+	0.00638320i	−0.682851	+	0.730557i	$0.739260\pi$
$860$	−3.44695	−	8.45999i	−0.117540	−	0.288483i
$861$	0.570581	−	0.702159i	0.0194453	−	0.0239295i
$862$	−10.4807	+	15.5875i	−0.356974	+	0.530912i
$863$	19.5197	−	33.8092i	0.664459	−	1.15088i	−0.314973	−	0.949101i	$-0.601995\pi$
$863$	19.5197	−	33.8092i	0.664459	−	1.15088i	0.979432	−	0.201776i	$-0.0646714\pi$
$864$	20.0942	+	21.4528i	0.683619	+	0.729839i
$865$	−7.97404	−	13.8114i	−0.271126	−	0.469603i
$866$	−3.84564	−	0.263248i	−0.130680	−	0.00894555i
$867$	−19.2272	−	22.1947i	−0.652991	−	0.753770i
$868$	−14.2438	−	1.95927i	−0.483467	−	0.0665019i
$869$	17.7504	−	74.8948i	0.602141	−	2.54063i
$870$	−7.73865	+	8.29473i	−0.262365	+	0.281218i
$871$	9.50569	+	7.07673i	0.322088	+	0.239786i
$872$	34.7627	−	38.9511i	1.17721	−	1.31905i
$873$	−9.28057	+	34.9725i	−0.314100	+	1.18364i
$874$	2.29145	−	7.37999i	0.0775096	−	0.249632i
$875$	−4.55575	+	15.2173i	−0.154012	+	0.514437i
$876$	−20.7136	+	40.7764i	−0.699848	+	1.37771i
$877$	−0.601468	+	10.3268i	−0.0203101	+	0.348712i	0.972809	+	0.231607i	$0.0743983\pi$
$877$	−0.601468	+	10.3268i	−0.0203101	+	0.348712i	−0.993120	+	0.117105i	$0.962639\pi$
$878$	18.8531	−	6.64562i	0.636260	−	0.224279i
$879$	41.2225	−	5.47758i	1.39040	−	0.184754i
$880$	−10.5190	−	10.7657i	−0.354596	−	0.362912i
$881$	−6.24872	−	1.10182i	−0.210525	−	0.0371212i	0.0673910	−	0.997727i	$-0.478533\pi$
$881$	−6.24872	−	1.10182i	−0.210525	−	0.0371212i	−0.277916	+	0.960605i	$0.589644\pi$
$882$	8.12537	+	2.24491i	0.273595	+	0.0755899i
$883$	26.5314	−	4.67820i	0.892852	−	0.157434i	0.291645	−	0.956527i	$-0.405798\pi$
$883$	26.5314	−	4.67820i	0.892852	−	0.157434i	0.601208	+	0.799093i	$0.294686\pi$
$884$	1.18305	+	1.46960i	0.0397904	+	0.0494281i
$885$	1.25733	+	16.9768i	0.0422648	+	0.570668i
$886$	16.4236	−	43.7344i	0.551761	−	1.46929i
$887$	−4.48340	−	6.02225i	−0.150538	−	0.202207i	0.720457	−	0.693500i	$-0.243932\pi$
$887$	−4.48340	−	6.02225i	−0.150538	−	0.202207i	−0.870995	+	0.491292i	$0.836525\pi$
$888$	−12.9001	+	10.5040i	−0.432900	+	0.352490i
$889$	−33.1699	−	16.6586i	−1.11248	−	0.558710i
$890$	11.7617	+	8.94359i	0.394253	+	0.299790i
$891$	43.0815	−	13.1243i	1.44329	−	0.439682i
$892$	26.2785	−	7.28832i	0.879869	−	0.244031i
$893$	−2.48159	+	4.94126i	−0.0830434	+	0.165353i
$894$	−0.162580	+	1.46165i	−0.00543750	+	0.0488848i
$895$	4.86569	−	3.62237i	0.162642	−	0.121083i
$896$	11.0732	+	22.7828i	0.369931	+	0.761121i
$897$	−22.9053	−	33.6591i	−0.764787	−	1.12384i
$898$	11.4929	+	2.84761i	0.383523	+	0.0950261i
$899$	−3.43382	−	19.4742i	−0.114524	−	0.649499i
$900$	−1.25056	+	26.5778i	−0.0416853	+	0.885927i
$901$	−0.280003	+	1.58798i	−0.00932826	+	0.0529032i
$902$	−0.669323	+	1.50927i	−0.0222860	+	0.0502533i
$903$	21.7737	+	8.98825i	0.724584	+	0.299110i
$904$	−20.7202	−	29.6811i	−0.689144	−	0.987179i
$905$	−7.09683	−	0.413343i	−0.235907	−	0.0137400i
$906$	−2.92038	−	3.44119i	−0.0970231	−	0.114326i
$907$	2.64388	+	0.791525i	0.0877885	+	0.0262822i	0.330396	−	0.943842i	$-0.392818\pi$
$907$	2.64388	+	0.791525i	0.0877885	+	0.0262822i	−0.242608	+	0.970124i	$0.578003\pi$
$908$	−3.02682	−	4.24324i	−0.100449	−	0.140817i
$909$	6.91983	+	4.82051i	0.229516	+	0.159886i
$910$	5.65004	+	8.78374i	0.187297	+	0.291178i
$911$	−9.87818	+	13.2687i	−0.327279	+	0.439611i	−0.935058	−	0.354494i	$-0.884653\pi$
$911$	−9.87818	+	13.2687i	−0.327279	+	0.439611i	0.607780	+	0.794106i	$0.292060\pi$
$912$	−0.586410	+	7.03988i	−0.0194180	+	0.233114i
$913$	−82.6582	−	19.5904i	−2.73559	−	0.648346i
$914$	−17.4596	+	9.84495i	−0.577513	+	0.325642i
$915$	−0.409416	−	0.141754i	−0.0135349	−	0.00468625i
$916$	23.7662	+	20.7803i	0.785256	+	0.686601i
$917$	−3.54168	+	2.04479i	−0.116957	+	0.0675249i
$918$	1.18892	+	1.04115i	0.0392403	+	0.0343631i
$919$	40.1073	+	23.1560i	1.32302	+	0.763845i	0.984209	−	0.177010i	$-0.0566426\pi$
$919$	40.1073	+	23.1560i	1.32302	+	0.763845i	0.338809	+	0.940855i	$0.389976\pi$
$920$	−3.60054	+	10.8144i	−0.118706	+	0.356539i
$921$	−43.5762	+	16.6422i	−1.43588	+	0.548379i
$922$	−4.94129	+	8.36104i	−0.162733	+	0.275356i
$923$	−1.81612	+	1.92498i	−0.0597783	+	0.0633613i
$924$	38.8113	+	0.178135i	1.27680	+	0.00586021i
$925$	−14.9567	−	1.74819i	−0.491775	−	0.0574802i
$926$	1.14093	+	23.7471i	0.0374933	+	0.780378i
$927$	7.81897	−	38.3335i	0.256809	−	1.25904i
$928$	−25.1652	+	24.0932i	−0.826087	+	0.790898i
$929$	39.4296	−	37.1999i	1.29364	−	1.22049i	0.332928	−	0.942952i	$-0.391963\pi$
$929$	39.4296	−	37.1999i	1.29364	−	1.22049i	0.960715	−	0.277537i	$-0.0895182\pi$
$930$	4.55164	+	3.77621i	0.149254	+	0.123827i
$931$	0.909239	+	1.81044i	0.0297991	+	0.0593349i
$932$	−20.0167	+	18.1297i	−0.655670	+	0.593858i
$933$	8.26348	−	13.0056i	0.270534	−	0.425785i
$934$	−1.91759	−	17.9909i	−0.0627456	−	0.588681i
$935$	−0.619920	−	0.520174i	−0.0202735	−	0.0170115i
$936$	27.0973	+	25.5143i	0.885702	+	0.833961i
$937$	1.09270	−	0.916888i	0.0356971	−	0.0299534i	−0.624765	−	0.780813i	$-0.714805\pi$
$937$	1.09270	−	0.916888i	0.0356971	−	0.0299534i	0.660462	+	0.750860i	$0.270361\pi$
$938$	6.16257	+	5.93369i	0.201215	+	0.193742i
$939$	−10.8506	−	42.7690i	−0.354095	−	1.39571i
$940$	3.80778	−	7.21232i	0.124196	−	0.235240i
$941$	−1.68371	−	14.4050i	−0.0548873	−	0.469591i	−0.992531	−	0.121993i	$-0.961071\pi$
$941$	−1.68371	−	14.4050i	−0.0548873	−	0.469591i	0.937644	−	0.347598i	$-0.113003\pi$
$942$	15.1025	+	15.8298i	0.492064	+	0.515762i
$943$	1.24815	−	0.0726963i	0.0406453	−	0.00236732i
$944$	0.914838	+	52.2725i	0.0297755	+	1.70132i
$945$	5.93372	+	6.42871i	0.193024	+	0.209126i
$946$	−42.6420	−	5.42425i	−1.38641	−	0.176357i
$947$	−7.00254	+	4.60564i	−0.227552	+	0.149663i	−0.658166	−	0.752873i	$-0.728667\pi$
$947$	−7.00254	+	4.60564i	−0.227552	+	0.149663i	0.430614	+	0.902536i	$0.358297\pi$
$948$	47.7248	−	23.6946i	1.55003	−	0.769566i
$949$	−22.9375	+	53.1751i	−0.744582	+	1.72614i
$950$	−4.94004	+	4.06030i	−0.160276	+	0.131734i
$951$	21.8871	+	48.6200i	0.709738	+	1.57661i
$952$	0.713337	+	1.16018i	0.0231194	+	0.0376016i
$953$	−9.50762	+	26.1220i	−0.307982	+	0.846174i	0.685068	+	0.728479i	$0.259773\pi$
$953$	−9.50762	+	26.1220i	−0.307982	+	0.846174i	−0.993050	+	0.117695i	$0.962450\pi$
$954$	−1.17191	+	31.7889i	−0.0379418	+	1.02920i
$955$	1.11035	+	3.05067i	0.0359302	+	0.0987173i
$956$	−11.8705	−	0.241468i	−0.383920	−	0.00780964i
$957$	16.1128	+	50.8894i	0.520853	+	1.64502i
$958$	−6.24992	+	7.29637i	−0.201926	+	0.235735i
$959$	28.4806	+	18.7320i	0.919686	+	0.604887i
$960$	1.07594	−	10.3640i	0.0347260	−	0.334495i
$961$	20.1330	−	4.77161i	0.649452	−	0.153923i
$962$	−15.4678	+	14.2986i	−0.498703	+	0.461007i
$963$	−15.9792	−	25.7671i	−0.514924	−	0.830334i
$964$	19.0584	−	9.09092i	0.613829	−	0.292799i
$965$	−4.88557	+	2.10743i	−0.157272	+	0.0678405i
$966$	−13.3368	−	26.1904i	−0.429106	−	0.842663i
$967$	−11.3934	+	3.41097i	−0.366389	+	0.109690i	−0.464705	−	0.885466i	$-0.653840\pi$
$967$	−11.3934	+	3.41097i	−0.366389	+	0.109690i	0.0983162	+	0.995155i	$0.468654\pi$
$968$	−38.3734	+	10.2238i	−1.23337	+	0.328604i
$969$	0.00598148	+	0.379762i	0.000192153	+	0.0121997i
$970$	11.5199	−	5.63955i	0.369882	−	0.181075i
$971$	−57.5868			−1.84805			−0.924024	−	0.382335i	$-0.875120\pi$
$971$	−57.5868			−1.84805			−0.924024	+	0.382335i	$0.875120\pi$
$972$	26.0519	+	17.1260i	0.835614	+	0.549317i
$973$	18.6763			0.598736
$974$	24.3904	−	11.9403i	0.781517	−	0.382591i
$975$	0.530578	+	33.6862i	0.0169921	+	1.07882i
$976$	−1.23081	−	0.505563i	−0.0393974	−	0.0161827i
$977$	32.1049	−	9.61157i	1.02713	−	0.307501i	0.271454	−	0.962451i	$-0.412496\pi$
$977$	32.1049	−	9.61157i	1.02713	−	0.307501i	0.755672	+	0.654950i	$0.227310\pi$
$978$	16.8272	+	33.0447i	0.538074	+	1.05665i
$979$	63.8410	−	27.5383i	2.04037	−	0.880128i
$980$	−1.28652	−	2.69709i	−0.0410965	−	0.0861555i
$981$	26.1632	−	48.8039i	0.835328	−	1.55819i
$982$	−6.82763	+	6.31154i	−0.217878	+	0.201409i
$983$	51.8926	−	12.2988i	1.65512	−	0.392270i	0.706255	−	0.707958i	$-0.250383\pi$
$983$	51.8926	−	12.2988i	1.65512	−	0.392270i	0.948863	+	0.315688i	$0.102235\pi$
$984$	−1.09965	+	0.311605i	−0.0350555	+	0.00993361i
$985$	1.41562	+	0.931067i	0.0451053	+	0.0296662i
$986$	−1.21855	+	1.42258i	−0.0388066	+	0.0453041i
$987$	6.34810	+	20.0493i	0.202062	+	0.638177i
$988$	−0.181917	+	8.94299i	−0.00578755	+	0.284514i
$989$	11.1332	+	30.5883i	0.354016	+	0.972650i
$990$	−13.5223	−	8.48624i	−0.429768	−	0.269710i
$991$	6.41052	−	17.6128i	0.203637	−	0.559487i	−0.795269	−	0.606257i	$-0.792670\pi$
$991$	6.41052	−	17.6128i	0.203637	−	0.559487i	0.998906	+	0.0467693i	$0.0148926\pi$
$992$	13.3023	+	12.3671i	0.422350	+	0.392655i
$993$	−16.6240	−	36.9286i	−0.527547	−	1.17189i
$994$	−1.47591	+	1.21308i	−0.0468131	+	0.0384764i
$995$	2.87058	−	6.65475i	0.0910035	−	0.210970i
$996$	−26.1507	−	52.6718i	−0.828618	−	1.66897i
$997$	7.14921	−	4.70211i	0.226418	−	0.148917i	−0.431232	−	0.902241i	$-0.641921\pi$
$997$	7.14921	−	4.70211i	0.226418	−	0.148917i	0.657650	+	0.753324i	$0.271551\pi$
$998$	−14.1346	−	1.79798i	−0.447423	−	0.0569141i
$999$	−10.6908	+	14.0373i	−0.338243	+	0.444121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.311.35	yes	936
3.2	odd	2		972.2.p.a.719.18		936
4.3	odd	2	inner	324.2.p.a.311.2	yes	936
12.11	even	2		972.2.p.a.719.51		936
81.25	even	27		972.2.p.a.899.51		936
81.56	odd	54	inner	324.2.p.a.299.2	✓	936
324.187	odd	54		972.2.p.a.899.18		936
324.299	even	54	inner	324.2.p.a.299.35	yes	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.299.2	✓	936	81.56	odd	54	inner
324.2.p.a.299.35	yes	936	324.299	even	54	inner
324.2.p.a.311.2	yes	936	4.3	odd	2	inner
324.2.p.a.311.35	yes	936	1.1	even	1	trivial
972.2.p.a.719.18		936	3.2	odd	2
972.2.p.a.719.51		936	12.11	even	2
972.2.p.a.899.18		936	324.187	odd	54
972.2.p.a.899.51		936	81.25	even	27

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.621813 + 1.27018i) q^{2} +(-0.0272775 - 1.73184i) q^{3} +(-1.22670 + 1.57962i) q^{4} +(0.720383 - 0.215669i) q^{5} +(2.18278 - 1.11153i) q^{6} +(2.05588 - 0.886819i) q^{7} +(-2.76918 - 0.575890i) q^{8} +(-2.99851 + 0.0944802i) q^{9} +O(q^{10})\)	\(q+(0.621813 + 1.27018i) q^{2} +(-0.0272775 - 1.73184i) q^{3} +(-1.22670 + 1.57962i) q^{4} +(0.720383 - 0.215669i) q^{5} +(2.18278 - 1.11153i) q^{6} +(2.05588 - 0.886819i) q^{7} +(-2.76918 - 0.575890i) q^{8} +(-2.99851 + 0.0944802i) q^{9} +(0.721881 + 0.780908i) q^{10} +(4.86915 - 1.15401i) q^{11} +(2.76911 + 2.08135i) q^{12} +(3.66469 + 2.41030i) q^{13} +(2.40479 + 2.05989i) q^{14} +(-0.393153 - 1.24170i) q^{15} +(-0.990430 - 3.87544i) q^{16} +(-0.0735547 - 0.202090i) q^{17} +(-1.98452 - 3.74989i) q^{18} +(0.348737 - 0.958146i) q^{19} +(-0.543016 + 1.40249i) q^{20} +(-1.59190 - 3.53625i) q^{21} +(4.49349 + 5.46710i) q^{22} +(2.12258 - 4.92069i) q^{23} +(-0.921810 + 4.81147i) q^{24} +(-3.70500 + 2.43682i) q^{25} +(-0.782759 + 6.15355i) q^{26} +(0.245416 + 5.19035i) q^{27} +(-1.12110 + 4.33537i) q^{28} +(-6.14834 + 0.358100i) q^{29} +(1.33271 - 1.27148i) q^{30} +(0.372752 + 3.18910i) q^{31} +(4.30663 - 3.66782i) q^{32} +(-2.13137 - 8.40108i) q^{33} +(0.210953 - 0.219090i) q^{34} +(1.28976 - 1.08224i) q^{35} +(3.52902 - 4.85242i) q^{36} +(2.60129 + 2.18274i) q^{37} +(1.43386 - 0.152831i) q^{38} +(4.07428 - 6.41238i) q^{39} +(-2.11907 + 0.182363i) q^{40} +(0.104706 + 0.208487i) q^{41} +(3.50180 - 4.22089i) q^{42} +(-4.41820 + 4.16836i) q^{43} +(-4.15006 + 9.10704i) q^{44} +(-2.13970 + 0.714747i) q^{45} +(7.56999 - 0.363700i) q^{46} +(-5.38625 - 0.629562i) q^{47} +(-6.68461 + 1.82097i) q^{48} +(-1.36351 + 1.44523i) q^{49} +(-5.39901 - 3.19076i) q^{50} +(-0.347980 + 0.132897i) q^{51} +(-8.30283 + 2.83212i) q^{52} +(-6.49329 - 3.74890i) q^{53} +(-6.44006 + 3.53915i) q^{54} +(3.25877 - 1.88145i) q^{55} +(-6.20380 + 1.27180i) q^{56} +(-1.66886 - 0.577819i) q^{57} +(-4.27797 - 7.58680i) q^{58} +(-12.7178 - 3.01418i) q^{59} +(2.44370 + 0.902158i) q^{60} +(0.198645 - 0.266826i) q^{61} +(-3.81893 + 2.45648i) q^{62} +(-6.08079 + 2.85338i) q^{63} +(7.33670 + 3.18948i) q^{64} +(3.15980 + 0.945983i) q^{65} +(9.34554 - 7.93112i) q^{66} +(2.69719 + 0.157093i) q^{67} +(0.409455 + 0.131714i) q^{68} +(-8.57972 - 3.54173i) q^{69} +(2.17662 + 0.965274i) q^{70} +(-0.104771 + 0.594186i) q^{71} +(8.35783 + 1.46518i) q^{72} +(2.29264 + 13.0022i) q^{73} +(-1.15495 + 4.66136i) q^{74} +(4.32123 + 6.34998i) q^{75} +(1.08572 + 1.72623i) q^{76} +(8.98697 - 6.69055i) q^{77} +(10.6783 + 1.18776i) q^{78} +(6.90321 - 13.7454i) q^{79} +(-1.54930 - 2.57820i) q^{80} +(8.98215 - 0.566600i) q^{81} +(-0.199708 + 0.262635i) q^{82} +(-15.1702 - 7.61877i) q^{83} +(7.53874 + 1.82330i) q^{84} +(-0.0965720 - 0.129719i) q^{85} +(-8.04185 - 3.01996i) q^{86} +(0.787881 + 10.6381i) q^{87} +(-14.1481 + 0.391565i) q^{88} +(13.6831 - 2.41271i) q^{89} +(-2.23835 - 2.27336i) q^{90} +(9.67165 + 1.70537i) q^{91} +(5.16908 + 9.38907i) q^{92} +(5.51282 - 0.732536i) q^{93} +(-2.54958 - 7.23296i) q^{94} +(0.0445820 - 0.765444i) q^{95} +(-6.46954 - 7.35833i) q^{96} +(3.45912 - 11.5543i) q^{97} +(-2.68355 - 0.833229i) q^{98} +(-14.4912 + 3.92035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

Modular forms

Varieties

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