LMFDB - Embedded newform 418.2.n.d.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	418.49
Dual form			418.2.n.d.273.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(-0.690099 + 0.307252i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.78499 - 3.09304i) q^{5} +(-0.738900 + 0.157058i) q^{6} +(1.79660 - 1.30531i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.62556 + 1.80537i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(-0.690099 + 0.307252i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.78499 - 3.09304i) q^{5} +(-0.738900 + 0.157058i) q^{6} +(1.79660 - 1.30531i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.62556 + 1.80537i) q^{9} +(-2.08105 - 3.60448i) q^{10} +(-2.71302 - 1.90776i) q^{11} -0.755407 q^{12} +(3.57339 - 3.96865i) q^{13} +(2.02873 - 0.903249i) q^{14} +(2.87226 + 1.27881i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-2.06907 - 2.29793i) q^{17} +(-1.96539 + 1.42794i) q^{18} +(-0.613896 - 4.31545i) q^{19} +(-1.28616 - 3.95839i) q^{20} +(-0.838775 + 1.45280i) q^{21} +(-2.25709 - 2.43014i) q^{22} +(-3.27816 - 5.67793i) q^{23} +(-0.738900 - 0.157058i) q^{24} +(-1.28811 + 12.2555i) q^{25} +(4.32043 - 3.13898i) q^{26} +(1.26740 - 3.90064i) q^{27} +(2.17219 - 0.461714i) q^{28} +(4.35534 + 1.93912i) q^{29} +(2.54361 + 1.84804i) q^{30} +(2.93603 + 9.03617i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.45841 + 0.482962i) q^{33} +(-1.54609 - 2.67790i) q^{34} +(-9.04088 - 1.92170i) q^{35} +(-2.21933 + 0.988110i) q^{36} +(1.55807 - 1.13201i) q^{37} +(0.296752 - 4.34879i) q^{38} +(-1.24662 + 3.83669i) q^{39} +(-0.435057 - 4.13930i) q^{40} +(5.30298 - 2.36104i) q^{41} +(-1.12250 + 1.24666i) q^{42} +(0.172924 - 0.299514i) q^{43} +(-1.70251 - 2.84631i) q^{44} +10.1112 q^{45} +(-2.02601 - 6.23542i) q^{46} +(-0.225823 + 2.14857i) q^{47} +(-0.690099 - 0.307252i) q^{48} +(-0.639168 + 1.96716i) q^{49} +(-3.80803 + 11.7199i) q^{50} +(2.13391 + 0.950076i) q^{51} +(4.87865 - 2.17211i) q^{52} +(-2.36941 + 2.63150i) q^{53} +(2.05069 - 3.55190i) q^{54} +(1.65495 + 13.7045i) q^{55} +2.22072 q^{56} +(1.74958 + 2.78947i) q^{57} +(3.85700 + 2.80227i) q^{58} +(0.703551 + 6.69384i) q^{59} +(2.10380 + 2.33650i) q^{60} +(1.45800 - 0.309909i) q^{61} +(0.993145 + 9.44915i) q^{62} +(-0.563924 + 5.36538i) q^{63} +(0.309017 + 0.951057i) q^{64} -22.2270 q^{65} +(2.30428 + 0.983540i) q^{66} +(-0.202754 - 0.351181i) q^{67} +(-0.955534 - 2.94083i) q^{68} +(4.00681 + 2.91111i) q^{69} +(-8.44377 - 3.75941i) q^{70} +(1.94836 + 2.16387i) q^{71} +(-2.37627 + 0.505092i) q^{72} +(-1.37524 - 13.0845i) q^{73} +(1.75938 - 0.783327i) q^{74} +(-2.87661 - 8.85330i) q^{75} +(1.19443 - 4.19206i) q^{76} +(-7.36442 + 0.113842i) q^{77} +(-2.01707 + 3.49366i) q^{78} +(-9.38302 - 1.99442i) q^{79} +(0.435057 - 4.13930i) q^{80} +(-0.437961 - 4.16692i) q^{81} +(5.67798 - 1.20689i) q^{82} +(-2.21429 + 6.81490i) q^{83} +(-1.35717 + 0.986039i) q^{84} +(-1.34527 + 12.7994i) q^{85} +(0.231418 - 0.257016i) q^{86} -3.60141 q^{87} +(-1.07353 - 3.13808i) q^{88} +(0.0638976 + 0.110674i) q^{89} +(9.89027 + 2.10224i) q^{90} +(1.23965 - 11.7945i) q^{91} +(-0.685321 - 6.52039i) q^{92} +(-4.80253 - 5.33375i) q^{93} +(-0.667601 + 2.05466i) q^{94} +(-11.6382 + 13.9173i) q^{95} +(-0.611137 - 0.444017i) q^{96} +(10.5100 + 2.23396i) q^{97} +(-1.03419 + 1.79128i) q^{98} +(7.85437 - 1.79682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$3$	−0.690099	+	0.307252i	−0.398429	+	0.177392i	−0.596162	−	0.802864i	$-0.703309\pi$
$3$	−0.690099	+	0.307252i	−0.398429	+	0.177392i	0.197734	+	0.980256i	$0.436642\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	−2.78499	−	3.09304i	−1.24548	−	1.38325i	−0.894623	−	0.446822i	$-0.852556\pi$
$5$	−2.78499	−	3.09304i	−1.24548	−	1.38325i	−0.350861	−	0.936428i	$-0.614111\pi$
$6$	−0.738900	+	0.157058i	−0.301655	+	0.0641187i
$7$	1.79660	−	1.30531i	0.679052	−	0.493360i	−0.193991	−	0.981003i	$-0.562143\pi$
$7$	1.79660	−	1.30531i	0.679052	−	0.493360i	0.873043	+	0.487643i	$0.162143\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−1.62556	+	1.80537i	−0.541853	+	0.601789i
$10$	−2.08105	−	3.60448i	−0.658085	−	1.13984i
$11$	−2.71302	−	1.90776i	−0.818005	−	0.575210i
$11$	−2.71302	−	1.90776i	−0.818005	−	0.575210i
$12$	−0.755407			−0.218067
$13$	3.57339	−	3.96865i	0.991080	−	1.10071i	−0.00383587	−	0.999993i	$-0.501221\pi$
$13$	3.57339	−	3.96865i	0.991080	−	1.10071i	0.994916	−	0.100713i	$-0.0321123\pi$
$14$	2.02873	−	0.903249i	0.542201	−	0.241404i
$15$	2.87226	+	1.27881i	0.741614	+	0.330188i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−2.06907	−	2.29793i	−0.501823	−	0.557331i	0.438008	−	0.898971i	$-0.355684\pi$
$17$	−2.06907	−	2.29793i	−0.501823	−	0.557331i	−0.939831	+	0.341640i	$0.889017\pi$
$18$	−1.96539	+	1.42794i	−0.463248	+	0.336569i
$19$	−0.613896	−	4.31545i	−0.140838	−	0.990033i
$19$	−0.613896	−	4.31545i	−0.140838	−	0.990033i
$20$	−1.28616	−	3.95839i	−0.287594	−	0.885123i
$21$	−0.838775	+	1.45280i	−0.183036	+	0.317027i
$22$	−2.25709	−	2.43014i	−0.481212	−	0.518107i
$23$	−3.27816	−	5.67793i	−0.683543	−	1.18393i	−0.973892	−	0.227010i	$-0.927105\pi$
$23$	−3.27816	−	5.67793i	−0.683543	−	1.18393i	0.290350	−	0.956921i	$-0.406228\pi$
$24$	−0.738900	−	0.157058i	−0.150827	−	0.0320593i
$25$	−1.28811	+	12.2555i	−0.257622	+	2.45111i
$26$	4.32043	−	3.13898i	0.847306	−	0.615604i
$27$	1.26740	−	3.90064i	0.243910	−	0.750679i
$28$	2.17219	−	0.461714i	0.410506	−	0.0872558i
$29$	4.35534	+	1.93912i	0.808766	+	0.360086i	0.769101	−	0.639127i	$-0.220704\pi$
$29$	4.35534	+	1.93912i	0.808766	+	0.360086i	0.0396650	+	0.999213i	$0.487371\pi$
$30$	2.54361	+	1.84804i	0.464398	+	0.337405i
$31$	2.93603	+	9.03617i	0.527327	+	1.62294i	0.759668	+	0.650311i	$0.225361\pi$
$31$	2.93603	+	9.03617i	0.527327	+	1.62294i	−0.232342	+	0.972634i	$0.574639\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.45841	+	0.482962i	0.427955	+	0.0840728i
$34$	−1.54609	−	2.67790i	−0.265152	−	0.459256i
$35$	−9.04088	−	1.92170i	−1.52819	−	0.324826i
$36$	−2.21933	+	0.988110i	−0.369888	+	0.164685i
$37$	1.55807	−	1.13201i	0.256145	−	0.186101i	−0.452301	−	0.891866i	$-0.649397\pi$
$37$	1.55807	−	1.13201i	0.256145	−	0.186101i	0.708446	+	0.705765i	$0.249397\pi$
$38$	0.296752	−	4.34879i	0.0481395	−	0.705466i
$39$	−1.24662	+	3.83669i	−0.199618	+	0.614362i
$40$	−0.435057	−	4.13930i	−0.0687886	−	0.654480i
$41$	5.30298	−	2.36104i	0.828186	−	0.368732i	0.0515409	−	0.998671i	$-0.483587\pi$
$41$	5.30298	−	2.36104i	0.828186	−	0.368732i	0.776645	+	0.629939i	$0.216920\pi$
$42$	−1.12250	+	1.24666i	−0.173206	+	0.192364i
$43$	0.172924	−	0.299514i	0.0263707	−	0.0456754i	−0.852539	−	0.522664i	$-0.824938\pi$
$43$	0.172924	−	0.299514i	0.0263707	−	0.0456754i	0.878910	+	0.476988i	$0.158272\pi$
$44$	−1.70251	−	2.84631i	−0.256663	−	0.429097i
$45$	10.1112			1.50729
$46$	−2.02601	−	6.23542i	−0.298719	−	0.919363i
$47$	−0.225823	+	2.14857i	−0.0329397	+	0.313401i	0.965629	+	0.259923i	$0.0836972\pi$
$47$	−0.225823	+	2.14857i	−0.0329397	+	0.313401i	−0.998569	+	0.0534775i	$0.982969\pi$
$48$	−0.690099	−	0.307252i	−0.0996072	−	0.0443480i
$49$	−0.639168	+	1.96716i	−0.0913097	+	0.281022i
$50$	−3.80803	+	11.7199i	−0.538537	+	1.65745i
$51$	2.13391	+	0.950076i	0.298807	+	0.133037i
$52$	4.87865	−	2.17211i	0.676547	−	0.301218i
$53$	−2.36941	+	2.63150i	−0.325464	+	0.361464i	−0.883565	−	0.468309i	$-0.844864\pi$
$53$	−2.36941	+	2.63150i	−0.325464	+	0.361464i	0.558101	+	0.829773i	$0.311530\pi$
$54$	2.05069	−	3.55190i	0.279063	−	0.483352i
$55$	1.65495	+	13.7045i	0.223153	+	1.84792i
$56$	2.22072			0.296757
$57$	1.74958	+	2.78947i	0.231737	+	0.369474i
$58$	3.85700	+	2.80227i	0.506449	+	0.367956i
$59$	0.703551	+	6.69384i	0.0915945	+	0.871464i	0.939784	+	0.341770i	$0.111026\pi$
$59$	0.703551	+	6.69384i	0.0915945	+	0.871464i	−0.848189	+	0.529694i	$0.822307\pi$
$60$	2.10380	+	2.33650i	0.271599	+	0.301641i
$61$	1.45800	−	0.309909i	0.186678	−	0.0396797i	−0.113624	−	0.993524i	$-0.536246\pi$
$61$	1.45800	−	0.309909i	0.186678	−	0.0396797i	0.300302	+	0.953844i	$0.402912\pi$
$62$	0.993145	+	9.44915i	0.126130	+	1.20004i
$63$	−0.563924	+	5.36538i	−0.0710478	+	0.675975i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−22.2270			−2.75692
$66$	2.30428	+	0.983540i	0.283637	+	0.121065i
$67$	−0.202754	−	0.351181i	−0.0247704	−	0.0429036i	0.853374	−	0.521298i	$-0.174552\pi$
$67$	−0.202754	−	0.351181i	−0.0247704	−	0.0429036i	−0.878145	+	0.478395i	$0.841219\pi$
$68$	−0.955534	−	2.94083i	−0.115876	−	0.356628i
$69$	4.00681	+	2.91111i	0.482363	+	0.350457i
$70$	−8.44377	−	3.75941i	−1.00922	−	0.449336i
$71$	1.94836	+	2.16387i	0.231227	+	0.256804i	0.847582	−	0.530665i	$-0.178058\pi$
$71$	1.94836	+	2.16387i	0.231227	+	0.256804i	−0.616354	+	0.787469i	$0.711391\pi$
$72$	−2.37627	+	0.505092i	−0.280046	+	0.0595257i
$73$	−1.37524	−	13.0845i	−0.160959	−	1.53143i	−0.715111	−	0.699011i	$-0.753624\pi$
$73$	−1.37524	−	13.0845i	−0.160959	−	1.53143i	0.554152	−	0.832416i	$-0.313043\pi$
$74$	1.75938	−	0.783327i	0.204524	−	0.0910599i
$75$	−2.87661	−	8.85330i	−0.332163	−	1.02229i
$76$	1.19443	−	4.19206i	0.137011	−	0.480862i
$77$	−7.36442	+	0.113842i	−0.839254	+	0.0129735i
$78$	−2.01707	+	3.49366i	−0.228388	+	0.395580i
$79$	−9.38302	−	1.99442i	−1.05567	−	0.224390i	−0.352794	−	0.935701i	$-0.614768\pi$
$79$	−9.38302	−	1.99442i	−1.05567	−	0.224390i	−0.702877	+	0.711311i	$0.748102\pi$
$80$	0.435057	−	4.13930i	0.0486409	−	0.462787i
$81$	−0.437961	−	4.16692i	−0.0486623	−	0.462991i
$82$	5.67798	−	1.20689i	0.627028	−	0.133279i
$83$	−2.21429	+	6.81490i	−0.243050	+	0.748032i	0.752901	+	0.658134i	$0.228654\pi$
$83$	−2.21429	+	6.81490i	−0.243050	+	0.748032i	−0.995951	+	0.0898979i	$0.971346\pi$
$84$	−1.35717	+	0.986039i	−0.148079	+	0.107586i
$85$	−1.34527	+	12.7994i	−0.145915	+	1.38829i
$86$	0.231418	−	0.257016i	0.0249544	−	0.0277147i
$87$	−3.60141			−0.386112
$88$	−1.07353	−	3.13808i	−0.114438	−	0.334520i
$89$	0.0638976	+	0.110674i	0.00677313	+	0.0117314i	0.869392	−	0.494123i	$-0.164511\pi$
$89$	0.0638976	+	0.110674i	0.00677313	+	0.0117314i	−0.862619	+	0.505854i	$0.831177\pi$
$90$	9.89027	+	2.10224i	1.04253	+	0.221596i
$91$	1.23965	−	11.7945i	0.129950	−	1.23640i
$92$	−0.685321	−	6.52039i	−0.0714497	−	0.679798i
$93$	−4.80253	−	5.33375i	−0.497999	−	0.553084i
$94$	−0.667601	+	2.05466i	−0.0688577	+	0.211922i
$95$	−11.6382	+	13.9173i	−1.19405	+	1.42788i
$96$	−0.611137	−	0.444017i	−0.0623739	−	0.0453173i
$97$	10.5100	+	2.23396i	1.06712	+	0.226824i	0.707818	−	0.706395i	$-0.249680\pi$
$97$	10.5100	+	2.23396i	1.06712	+	0.226824i	0.359307	+	0.933220i	$0.383013\pi$
$98$	−1.03419	+	1.79128i	−0.104469	+	0.180946i
$99$	7.85437	−	1.79682i	0.789394	−	0.180587i
$100$	−6.16152	+	10.6721i	−0.616152	+	1.06721i
$101$	10.3521	−	11.4972i	1.03007	−	1.14401i	0.0406182	−	0.999175i	$-0.487067\pi$
$101$	10.3521	−	11.4972i	1.03007	−	1.14401i	0.989455	−	0.144838i	$-0.0462661\pi$
$102$	1.88974	+	1.37298i	0.187112	+	0.135945i
$103$	5.82684	−	4.23345i	0.574135	−	0.417134i	−0.262470	−	0.964940i	$-0.584537\pi$
$103$	5.82684	−	4.23345i	0.574135	−	0.417134i	0.836605	+	0.547806i	$0.184537\pi$
$104$	5.22365	−	1.11032i	0.512221	−	0.108876i
$105$	6.82955	−	1.45167i	0.666496	−	0.141668i
$106$	−2.86476	+	2.08137i	−0.278250	+	0.202160i
$107$	2.46545	+	1.79126i	0.238344	+	0.173167i	0.700545	−	0.713608i	$-0.252940\pi$
$107$	2.46545	+	1.79126i	0.238344	+	0.173167i	−0.462201	+	0.886775i	$0.652940\pi$
$108$	2.74436	−	3.04792i	0.264076	−	0.293286i
$109$	7.61223	−	13.1848i	0.729119	−	1.26287i	−0.228136	−	0.973629i	$-0.573263\pi$
$109$	7.61223	−	13.1848i	0.729119	−	1.26287i	0.957256	−	0.289243i	$-0.0934034\pi$
$110$	−1.23056	+	13.7492i	−0.117329	+	1.31093i
$111$	−0.727413	+	1.25992i	−0.0690430	+	0.119586i
$112$	2.17219	+	0.461714i	0.205253	+	0.0436279i
$113$	−5.83454	−	4.23904i	−0.548867	−	0.398775i	0.278501	−	0.960436i	$-0.410163\pi$
$113$	−5.83454	−	4.23904i	−0.548867	−	0.398775i	−0.827368	+	0.561661i	$0.810163\pi$
$114$	1.13138	+	3.09227i	0.105964	+	0.289618i
$115$	−8.43245	+	25.9524i	−0.786330	+	2.42008i
$116$	3.19009	+	3.54295i	0.296192	+	0.328955i
$117$	1.35611	+	12.9026i	0.125373	+	1.19284i
$118$	−0.703551	+	6.69384i	−0.0647671	+	0.616218i
$119$	−6.71680	−	1.42770i	−0.615728	−	0.130877i
$120$	1.57204	+	2.72285i	0.143507	+	0.248561i
$121$	3.72093	+	10.3516i	0.338266	+	0.941051i
$122$	1.49058			0.134951
$123$	−2.93414	+	3.25870i	−0.264563	+	0.293827i
$124$	−0.993145	+	9.44915i	−0.0891871	+	0.848559i
$125$	24.6582	−	17.9152i	2.20550	−	1.60239i
$126$	−1.66713	+	5.13089i	−0.148519	+	0.457096i
$127$	8.55179	−	1.81774i	0.758848	−	0.161298i	0.187792	−	0.982209i	$-0.439867\pi$
$127$	8.55179	−	1.81774i	0.758848	−	0.161298i	0.571057	+	0.820911i	$0.306534\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	−0.0273088	+	0.259826i	−0.00240440	+	0.0228764i
$130$	−21.7413	−	4.62126i	−1.90684	−	0.405311i
$131$	1.21127	−	2.09798i	0.105829	−	0.183301i	−0.808248	−	0.588843i	$-0.799584\pi$
$131$	1.21127	−	2.09798i	0.105829	−	0.183301i	0.914077	+	0.405542i	$0.132917\pi$
$132$	2.04943	+	1.44113i	0.178380	+	0.125435i
$133$	−6.73592	−	6.95183i	−0.584079	−	0.602800i
$134$	−0.125309	−	0.385662i	−0.0108251	−	0.0333161i
$135$	−15.5945	+	6.94313i	−1.34216	+	0.597569i
$136$	−0.323220	−	3.07523i	−0.0277159	−	0.263699i
$137$	16.7844	−	3.56764i	1.43399	−	0.304804i	0.575571	−	0.817752i	$-0.304780\pi$
$137$	16.7844	−	3.56764i	1.43399	−	0.304804i	0.858420	+	0.512948i	$0.171447\pi$
$138$	3.31399	+	3.68056i	0.282106	+	0.313310i
$139$	−3.37042	−	1.50061i	−0.285875	−	0.127280i	0.258790	−	0.965934i	$-0.416676\pi$
$139$	−3.37042	−	1.50061i	−0.285875	−	0.127280i	−0.544665	+	0.838654i	$0.683343\pi$
$140$	−7.47763	−	5.43282i	−0.631975	−	0.459157i
$141$	−0.504310	−	1.55211i	−0.0424706	−	0.130711i
$142$	1.45589	+	2.52167i	0.122175	+	0.211614i
$143$	−17.2659	+	3.94986i	−1.44385	+	0.330304i
$144$	−2.42936			−0.202447
$145$	−6.13177	−	18.8717i	−0.509216	−	1.56721i
$146$	1.37524	−	13.0845i	0.113815	−	1.08288i
$147$	−0.163323	−	1.55392i	−0.0134707	−	0.128165i
$148$	1.88380	−	0.400413i	0.154847	−	0.0329138i
$149$	14.4026	+	15.9957i	1.17990	+	1.31042i	0.940618	+	0.339468i	$0.110247\pi$
$149$	14.4026	+	15.9957i	1.17990	+	1.31042i	0.239287	+	0.970949i	$0.423086\pi$
$150$	−0.973047	−	9.25792i	−0.0794489	−	0.755906i
$151$	6.18935	+	4.49683i	0.503682	+	0.365947i	0.810422	−	0.585847i	$-0.199238\pi$
$151$	6.18935	+	4.49683i	0.503682	+	0.365947i	−0.306739	+	0.951794i	$0.599238\pi$
$152$	2.03991	−	3.85211i	0.165458	−	0.312448i
$153$	7.51200			0.607310
$154$	−7.22716	−	1.41980i	−0.582381	−	0.114410i
$155$	19.7724	−	34.2469i	1.58816	−	2.75078i
$156$	−2.69936	+	2.99795i	−0.216122	+	0.240028i
$157$	0.505755	−	0.225177i	0.0403636	−	0.0179710i	−0.386456	−	0.922308i	$-0.626301\pi$
$157$	0.505755	−	0.225177i	0.0403636	−	0.0179710i	0.426819	+	0.904337i	$0.359634\pi$
$158$	−8.76331	−	3.90168i	−0.697172	−	0.310401i
$159$	0.826596	−	2.54400i	0.0655534	−	0.201752i
$160$	1.28616	−	3.95839i	0.101680	−	0.312938i
$161$	−13.3010	−	5.92198i	−1.04827	−	0.466718i
$162$	0.437961	−	4.16692i	0.0344094	−	0.327384i
$163$	0.0373625	+	0.114990i	0.00292646	+	0.00900672i	0.952509	−	0.304510i	$-0.0984928\pi$
$163$	0.0373625	+	0.114990i	0.00292646	+	0.00900672i	−0.949583	+	0.313517i	$0.898493\pi$
$164$	5.80483			0.453281
$165$	−5.35282	−	8.94901i	−0.416717	−	0.696679i
$166$	−3.58280	+	6.20560i	−0.278080	+	0.481648i
$167$	−4.68800	+	5.20655i	−0.362768	+	0.402895i	−0.896704	−	0.442630i	$-0.854046\pi$
$167$	−4.68800	+	5.20655i	−0.362768	+	0.402895i	0.533936	+	0.845525i	$0.320712\pi$
$168$	−1.53252	+	0.682321i	−0.118236	+	0.0526422i
$169$	−1.62221	−	15.4343i	−0.124785	−	1.18725i
$170$	−3.97703	+	12.2400i	−0.305024	+	0.938767i
$171$	8.78890	+	5.90672i	0.672104	+	0.451698i
$172$	0.279798	−	0.203285i	0.0213344	−	0.0155003i
$173$	10.4065	−	4.63325i	0.791188	−	0.352260i	0.0289704	−	0.999580i	$-0.490777\pi$
$173$	10.4065	−	4.63325i	0.791188	−	0.352260i	0.762218	+	0.647321i	$0.224110\pi$
$174$	−3.52271	−	0.748776i	−0.267056	−	0.0567645i
$175$	13.6830	+	23.6997i	1.03434	+	1.79153i
$176$	−0.397623	−	3.29270i	−0.0299720	−	0.248197i
$177$	−2.54221	−	4.40324i	−0.191084	−	0.330968i
$178$	0.0394909	+	0.121540i	0.00295997	+	0.00910984i
$179$	−15.8751	−	11.5340i	−1.18656	−	0.862088i	−0.193666	−	0.981067i	$-0.562038\pi$
$179$	−15.8751	−	11.5340i	−1.18656	−	0.862088i	−0.992897	+	0.118979i	$0.962038\pi$
$180$	9.23707	+	4.11261i	0.688490	+	0.306536i
$181$	−16.8030	+	3.57159i	−1.24896	+	0.265474i	−0.784504	−	0.620123i	$-0.787083\pi$
$181$	−16.8030	+	3.57159i	−1.24896	+	0.265474i	−0.464453	+	0.885598i	$0.653749\pi$
$182$	3.66476	−	11.2790i	0.271650	−	0.836054i
$183$	−0.910948	+	0.661842i	−0.0673392	+	0.0489248i
$184$	0.685321	−	6.52039i	0.0505225	−	0.480690i
$185$	−7.84054	−	1.66656i	−0.576448	−	0.122528i
$186$	−3.58864	−	6.21570i	−0.263132	−	0.455757i
$187$	1.22952	+	10.1816i	0.0899114	+	0.744553i
$188$	−1.08020	+	1.87096i	−0.0787817	+	0.136454i
$189$	−2.81453	−	8.66224i	−0.204727	−	0.630086i
$190$	−14.2774	+	11.1934i	−1.03579	+	0.812058i
$191$	−20.0450	+	14.5635i	−1.45040	+	1.05378i	−0.464667	+	0.885485i	$0.653826\pi$
$191$	−20.0450	+	14.5635i	−1.45040	+	1.05378i	−0.985737	+	0.168295i	$0.946174\pi$
$192$	−0.505466	−	0.561377i	−0.0364789	−	0.0405139i
$193$	−10.1299	−	11.2504i	−0.729166	−	0.809820i	0.258564	−	0.965994i	$-0.416751\pi$
$193$	−10.1299	−	11.2504i	−0.729166	−	0.809820i	−0.987730	+	0.156174i	$0.950084\pi$
$194$	9.81582	+	4.37029i	0.704735	+	0.313768i
$195$	15.3388	−	6.82929i	1.09844	−	0.489056i
$196$	−1.38402	+	1.53711i	−0.0988588	+	0.109794i
$197$	10.5835			0.754041			0.377020	−	0.926205i	$-0.376949\pi$
$197$	10.5835			0.754041			0.377020	+	0.926205i	$0.376949\pi$
$198$	8.05631	−	0.124538i	0.572537	−	0.00885050i
$199$	3.53822	+	6.12838i	0.250818	+	0.434429i	0.963751	−	0.266802i	$-0.0859671\pi$
$199$	3.53822	+	6.12838i	0.250818	+	0.434429i	−0.712933	+	0.701232i	$0.752634\pi$
$200$	−8.24573	+	9.15781i	−0.583061	+	0.647555i
$201$	0.247822	+	0.180053i	0.0174800	+	0.0127000i
$202$	12.5163	−	9.09362i	0.880643	−	0.639825i
$203$	10.3560	−	2.20123i	0.726846	−	0.154496i
$204$	1.56299	+	1.73588i	0.109431	+	0.121536i
$205$	−22.0715	−	9.82686i	−1.54154	−	0.686338i
$206$	6.57969	−	2.92947i	0.458429	−	0.204106i
$207$	15.5796	+	3.31154i	1.08286	+	0.230168i
$208$	5.34035			0.370286
$209$	−6.56732	+	12.8791i	−0.454271	+	0.890863i
$210$	6.98212			0.481812
$211$	8.58146	+	1.82405i	0.590772	+	0.125572i	0.493591	−	0.869694i	$-0.335684\pi$
$211$	8.58146	+	1.82405i	0.590772	+	0.125572i	0.0971811	+	0.995267i	$0.469017\pi$
$212$	−3.23489	+	1.44027i	−0.222173	+	0.0989180i
$213$	−2.00941	−	0.894648i	−0.137683	−	0.0613003i
$214$	2.03915	+	2.26471i	0.139394	+	0.154812i
$215$	−1.40800	+	0.299280i	−0.0960248	+	0.0204107i
$216$	3.31808	−	2.41073i	0.225767	−	0.164029i
$217$	17.0699	+	12.4020i	1.15878	+	0.841902i
$218$	10.1872	−	11.3140i	0.689961	−	0.766279i
$219$	4.96929	+	8.60706i	0.335793	+	0.581611i
$220$	−4.06227	+	13.1929i	−0.273878	+	0.889462i
$221$	−16.5133			−1.11080
$222$	−0.973468	+	1.08115i	−0.0653349	+	0.0725618i
$223$	−13.9937	+	6.23040i	−0.937088	+	0.417218i	−0.817710	−	0.575631i	$-0.804757\pi$
$223$	−13.9937	+	6.23040i	−0.937088	+	0.417218i	−0.119378	+	0.992849i	$0.538090\pi$
$224$	2.02873	+	0.903249i	0.135550	+	0.0603509i
$225$	−20.0318	−	22.2476i	−1.33546	−	1.48317i
$226$	−4.82569	−	5.35947i	−0.321000	−	0.356507i
$227$	22.9125	−	16.6469i	1.52075	−	1.10489i	0.559640	−	0.828736i	$-0.310939\pi$
$227$	22.9125	−	16.6469i	1.52075	−	1.10489i	0.961113	−	0.276156i	$-0.0890607\pi$
$228$	0.463742	+	3.25992i	0.0307121	+	0.215894i
$229$	−7.93686	−	24.4271i	−0.524483	−	1.61419i	−0.765337	−	0.643630i	$-0.777428\pi$
$229$	−7.93686	−	24.4271i	−0.524483	−	1.61419i	0.240854	−	0.970561i	$-0.422572\pi$
$230$	−13.6440	+	23.6321i	−0.899658	+	1.55825i
$231$	5.04720	−	2.34129i	0.332082	−	0.154046i
$232$	2.38376	+	4.12879i	0.156501	+	0.271068i
$233$	−2.60093	−	0.552845i	−0.170393	−	0.0362181i	0.121925	−	0.992539i	$-0.461093\pi$
$233$	−2.60093	−	0.552845i	−0.170393	−	0.0362181i	−0.292318	+	0.956321i	$0.594427\pi$
$234$	−1.35611	+	12.9026i	−0.0886519	+	0.843466i
$235$	7.27451	−	5.28524i	0.474537	−	0.344771i
$236$	−2.07990	+	6.40129i	−0.135390	+	0.416688i
$237$	7.08800	−	1.50660i	0.460415	−	0.0978642i
$238$	−6.27319	−	2.79300i	−0.406631	−	0.181044i
$239$	−12.2233	−	8.88078i	−0.790662	−	0.574450i	0.117498	−	0.993073i	$-0.462513\pi$
$239$	−12.2233	−	8.88078i	−0.790662	−	0.574450i	−0.908160	+	0.418623i	$0.862513\pi$
$240$	0.971573	+	2.99020i	0.0627148	+	0.193016i
$241$	−1.08593	−	1.88088i	−0.0699507	−	0.121158i	0.828929	−	0.559354i	$-0.188951\pi$
$241$	−1.08593	−	1.88088i	−0.0699507	−	0.121158i	−0.898879	+	0.438196i	$0.855618\pi$
$242$	1.48740	+	10.8990i	0.0956140	+	0.700613i
$243$	7.73460	+	13.3967i	0.496175	+	0.859399i
$244$	1.45800	+	0.309909i	0.0933392	+	0.0198399i
$245$	7.86456	−	3.50153i	0.502449	−	0.223705i
$246$	−3.54755	+	2.57744i	−0.226183	+	0.164332i
$247$	−19.3202	−	12.9844i	−1.22932	−	0.826181i
$248$	−2.93603	+	9.03617i	−0.186438	+	0.573798i
$249$	−0.565807	−	5.38330i	−0.0358566	−	0.341153i
$250$	27.8441	−	12.3970i	1.76102	−	0.784056i
$251$	−2.15862	+	2.39739i	−0.136251	+	0.151322i	−0.807409	−	0.589993i	$-0.799131\pi$
$251$	−2.15862	+	2.39739i	−0.136251	+	0.151322i	0.671158	+	0.741315i	$0.265797\pi$
$252$	−2.69747	+	4.67215i	−0.169924	+	0.294318i
$253$	−1.93842	+	21.6582i	−0.121868	+	1.36164i
$254$	8.74284			0.548574
$255$	−3.00427	−	9.24620i	−0.188135	−	0.579020i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	22.0270	+	9.80704i	1.37400	+	0.611746i	0.955100	−	0.296284i	$-0.0957474\pi$
$257$	22.0270	+	9.80704i	1.37400	+	0.611746i	0.418905	+	0.908030i	$0.362414\pi$
$258$	−0.0807328	+	0.248470i	−0.00502620	+	0.0154691i
$259$	1.32162	−	4.06753i	0.0821214	−	0.252744i
$260$	−20.3054	−	9.04055i	−1.25929	−	0.560671i
$261$	−10.5807	+	4.71082i	−0.654928	+	0.291593i
$262$	1.62099	−	1.80030i	0.100145	−	0.111223i
$263$	12.4545	−	21.5718i	0.767977	−	1.33017i	−0.170682	−	0.985326i	$-0.554597\pi$
$263$	12.4545	−	21.5718i	0.767977	−	1.33017i	0.938658	−	0.344849i	$-0.112070\pi$
$264$	1.70502	+	1.83574i	0.104937	+	0.112982i
$265$	14.7381			0.905356
$266$	−5.14336	−	8.20039i	−0.315360	−	0.502798i
$267$	−0.0781004	−	0.0567432i	−0.00477966	−	0.00347263i
$268$	−0.0423872	−	0.403287i	−0.00258921	−	0.0246347i
$269$	3.57851	+	3.97434i	0.218186	+	0.242320i	0.842294	−	0.539018i	$-0.181204\pi$
$269$	3.57851	+	3.97434i	0.218186	+	0.242320i	−0.624109	+	0.781338i	$0.714538\pi$
$270$	−16.6973	+	3.54912i	−1.01617	+	0.215993i
$271$	2.26792	+	21.5778i	0.137766	+	1.31076i	0.816916	+	0.576757i	$0.195682\pi$
$271$	2.26792	+	21.5778i	0.137766	+	1.31076i	−0.679150	+	0.734000i	$0.737651\pi$
$272$	0.323220	−	3.07523i	0.0195981	−	0.186463i
$273$	2.76839	+	8.52023i	0.167551	+	0.515668i
$274$	17.1594			1.03664
$275$	26.8752	−	30.7921i	1.62064	−	1.85683i
$276$	2.47634	+	4.28915i	0.149058	+	0.258176i
$277$	2.97146	+	9.14520i	0.178538	+	0.549482i	0.999777	−	0.0211012i	$-0.00671721\pi$
$277$	2.97146	+	9.14520i	0.178538	+	0.549482i	−0.821240	+	0.570583i	$0.806717\pi$
$278$	−2.98477	−	2.16856i	−0.179015	−	0.130062i
$279$	−21.0863	−	9.38822i	−1.26240	−	0.562058i
$280$	−6.18468	−	6.86878i	−0.369605	−	0.410488i
$281$	8.86898	−	1.88516i	0.529079	−	0.112459i	0.0643757	−	0.997926i	$-0.479494\pi$
$281$	8.86898	−	1.88516i	0.529079	−	0.112459i	0.464703	+	0.885467i	$0.346161\pi$
$282$	−0.170589	−	1.62304i	−0.0101584	−	0.0966507i
$283$	−6.01595	+	2.67847i	−0.357611	+	0.159219i	−0.577675	−	0.816267i	$-0.696040\pi$
$283$	−6.01595	+	2.67847i	−0.357611	+	0.159219i	0.220064	+	0.975485i	$0.429373\pi$
$284$	0.899788	+	2.76926i	0.0533926	+	0.164325i
$285$	3.75538	−	13.1801i	0.222450	−	0.780725i
$286$	−17.7098	+	0.273765i	−1.04720	+	0.0161881i
$287$	6.44546	−	11.1639i	0.380463	−	0.658982i
$288$	−2.37627	−	0.505092i	−0.140023	−	0.0297629i
$289$	0.777531	−	7.39771i	0.0457371	−	0.435160i
$290$	−2.07414	−	19.7341i	−0.121798	−	1.15883i
$291$	−7.93930	+	1.68755i	−0.465410	+	0.0989259i
$292$	4.06561	−	12.5127i	0.237922	−	0.732248i
$293$	−14.8286	+	10.7736i	−0.866293	+	0.629399i	−0.929590	−	0.368596i	$-0.879839\pi$
$293$	−14.8286	+	10.7736i	−0.866293	+	0.629399i	0.0632965	+	0.997995i	$0.479839\pi$
$294$	0.163323	−	1.55392i	0.00952521	−	0.0906263i
$295$	18.7449	−	20.8184i	1.09137	−	1.21209i
$296$	1.92588			0.111940
$297$	−10.8799	+	8.16463i	−0.631318	+	0.473760i
$298$	10.7622	+	18.6406i	0.623435	+	1.07982i
$299$	−34.2478	−	7.27960i	−1.98060	−	0.420990i
$300$	0.973047	−	9.25792i	0.0561789	−	0.534506i
$301$	−0.0802815	−	0.763827i	−0.00462735	−	0.0440263i
$302$	5.11916	+	5.68540i	0.294574	+	0.327158i
$303$	−3.61145	+	11.1149i	−0.207472	+	0.638534i
$304$	2.79623	−	3.34382i	0.160375	−	0.191781i
$305$	−5.01908	−	3.64658i	−0.287392	−	0.208802i
$306$	7.34785	+	1.56183i	0.420049	+	0.0892841i
$307$	2.81014	−	4.86731i	0.160383	−	0.277792i	−0.774623	−	0.632423i	$-0.782060\pi$
$307$	2.81014	−	4.86731i	0.160383	−	0.277792i	0.935006	+	0.354631i	$0.115394\pi$
$308$	−6.77404	−	2.89138i	−0.385987	−	0.164752i
$309$	−2.72036	+	4.71180i	−0.154756	+	0.268045i
$310$	26.4607	−	29.3876i	1.50287	−	1.66910i
$311$	−22.9886	−	16.7022i	−1.30356	−	0.947095i	−0.303580	−	0.952806i	$-0.598182\pi$
$311$	−22.9886	−	16.7022i	−1.30356	−	0.947095i	−0.999984	+	0.00571134i	$0.998182\pi$
$312$	−3.26368	+	2.37121i	−0.184770	+	0.134243i
$313$	13.8610	−	2.94626i	0.783472	−	0.166532i	0.201226	−	0.979545i	$-0.435507\pi$
$313$	13.8610	−	2.94626i	0.783472	−	0.166532i	0.582246	+	0.813013i	$0.302174\pi$
$314$	0.541520	−	0.115104i	0.0305597	−	0.00649567i
$315$	18.1659	−	13.1983i	1.02353	−	0.743638i
$316$	−7.76061	−	5.63841i	−0.436568	−	0.317185i
$317$	−12.1404	+	13.4833i	−0.681872	+	0.757296i	−0.980381	−	0.197111i	$-0.936844\pi$
$317$	−12.1404	+	13.4833i	−0.681872	+	0.757296i	0.298509	+	0.954407i	$0.403511\pi$
$318$	1.33746	−	2.31655i	0.0750011	−	0.129906i
$319$	−8.11674	−	13.5698i	−0.454450	−	0.759763i
$320$	2.08105	−	3.60448i	0.116334	−	0.201497i
$321$	−2.25177	−	0.478629i	−0.125682	−	0.0267145i
$322$	−11.7791	−	8.55801i	−0.656423	−	0.476919i
$323$	−8.64643	+	10.3397i	−0.481100	+	0.575314i
$324$	1.29474	−	3.98480i	0.0719301	−	0.221378i
$325$	44.0350	+	48.9058i	2.44262	+	2.71281i
$326$	0.0126383	+	0.120245i	0.000699971	+	0.00665978i
$327$	−1.20215	+	11.4377i	−0.0664789	+	0.632504i
$328$	5.67798	+	1.20689i	0.313514	+	0.0666395i
$329$	2.39883	+	4.15489i	0.132252	+	0.229066i
$330$	−3.37525	−	9.86636i	−0.185801	−	0.543125i
$331$	−26.4436			−1.45347			−0.726735	−	0.686918i	$-0.758963\pi$
$331$	−26.4436			−1.45347			−0.726735	+	0.686918i	$0.758963\pi$
$332$	−4.79473	+	5.32508i	−0.263145	+	0.292252i
$333$	−0.489053	+	4.65303i	−0.0268000	+	0.254985i
$334$	−5.66806	+	4.11808i	−0.310142	+	0.225331i
$335$	−0.521549	+	1.60516i	−0.0284952	+	0.0876993i
$336$	−1.64089	+	0.348782i	−0.0895180	+	0.0190276i
$337$	3.17803	+	30.2370i	0.173118	+	1.64711i	0.644080	+	0.764958i	$0.277240\pi$
$337$	3.17803	+	30.2370i	0.173118	+	1.64711i	−0.470962	+	0.882154i	$0.656093\pi$
$338$	1.62221	−	15.4343i	0.0882365	−	0.839514i
$339$	5.32886	+	1.13268i	0.289424	+	0.0615189i
$340$	−6.43496	+	11.1457i	−0.348985	+	0.604459i
$341$	9.27332	−	30.1165i	0.502179	−	1.63090i
$342$	7.36876	+	7.60495i	0.398457	+	0.411229i
$343$	6.22310	+	19.1527i	0.336016	+	1.03415i
$344$	0.315949	−	0.140669i	0.0170348	−	0.00758439i
$345$	−2.15470	−	20.5006i	−0.116005	−	1.10372i
$346$	11.1424	−	2.36838i	0.599017	−	0.127325i
$347$	−10.6546	−	11.8331i	−0.571969	−	0.635236i	0.385866	−	0.922555i	$-0.373903\pi$
$347$	−10.6546	−	11.8331i	−0.571969	−	0.635236i	−0.957835	+	0.287319i	$0.907236\pi$
$348$	−3.29005	−	1.46483i	−0.176365	−	0.0785229i
$349$	11.4538	+	8.32167i	0.613108	+	0.445449i	0.850507	−	0.525963i	$-0.176295\pi$
$349$	11.4538	+	8.32167i	0.613108	+	0.445449i	−0.237399	+	0.971412i	$0.576295\pi$
$350$	8.45658	+	26.0267i	0.452023	+	1.39118i
$351$	−10.9514	−	18.9684i	−0.584542	−	1.01246i
$352$	0.295658	−	3.30342i	0.0157586	−	0.176073i
$353$	−20.8820			−1.11144			−0.555719	−	0.831370i	$-0.687557\pi$
$353$	−20.8820			−1.11144			−0.555719	+	0.831370i	$0.687557\pi$
$354$	−1.57117	−	4.83558i	−0.0835070	−	0.257008i
$355$	1.26679	−	12.0527i	0.0672342	−	0.639691i
$356$	0.0133582	+	0.127095i	0.000707985	+	0.00673602i
$357$	5.07392	−	1.07850i	0.268540	−	0.0570800i
$358$	−13.1302	−	14.5825i	−0.693951	−	0.770711i
$359$	0.935041	+	8.89632i	0.0493496	+	0.469530i	0.991090	+	0.133191i	$0.0425222\pi$
$359$	0.935041	+	8.89632i	0.0493496	+	0.469530i	−0.941741	+	0.336339i	$0.890811\pi$
$360$	8.18016	+	5.94323i	0.431132	+	0.313236i
$361$	−18.2463	+	5.29848i	−0.960330	+	0.278867i
$362$	−17.1784			−0.902876
$363$	−5.74834	−	6.00034i	−0.301710	−	0.314936i
$364$	5.92971	−	10.2706i	0.310801	−	0.538324i
$365$	−36.6409	+	40.6938i	−1.91787	+	2.13001i
$366$	−1.02865	+	0.457983i	−0.0537682	+	0.0239391i
$367$	18.2620	+	8.13076i	0.953267	+	0.424422i	0.823622	−	0.567138i	$-0.191950\pi$
$367$	18.2620	+	8.13076i	0.953267	+	0.424422i	0.129645	+	0.991560i	$0.458616\pi$
$368$	2.02601	−	6.23542i	0.105613	−	0.325044i
$369$	−4.35776	+	13.4118i	−0.226856	+	0.698191i
$370$	−7.32271	−	3.26028i	−0.380690	−	0.169494i
$371$	−0.821976	+	7.82058i	−0.0426748	+	0.406024i
$372$	−2.21790	−	6.82599i	−0.114993	−	0.353911i
$373$	−20.6017			−1.06672			−0.533359	−	0.845889i	$-0.679070\pi$
$373$	−20.6017			−1.06672			−0.533359	+	0.845889i	$0.679070\pi$
$374$	−0.914225	+	10.2148i	−0.0472734	+	0.528192i
$375$	−11.5121	+	19.9396i	−0.594483	+	1.02967i
$376$	−1.44559	+	1.60549i	−0.0745506	+	0.0827969i
$377$	23.2590	−	10.3556i	1.19790	−	0.533339i
$378$	−0.952048	−	9.05813i	−0.0489680	−	0.465900i
$379$	−6.93233	+	21.3355i	−0.356090	+	1.09593i	0.599285	+	0.800536i	$0.295452\pi$
$379$	−6.93233	+	21.3355i	−0.356090	+	1.09593i	−0.955375	+	0.295396i	$0.904548\pi$
$380$	−16.2927	+	7.98040i	−0.835796	+	0.409386i
$381$	−5.34307	+	3.88197i	−0.273734	+	0.198879i
$382$	−22.6349	+	10.0777i	−1.15810	+	0.515620i
$383$	−13.9193	−	2.95863i	−0.711241	−	0.151179i	−0.161936	−	0.986801i	$-0.551774\pi$
$383$	−13.9193	−	2.95863i	−0.711241	−	0.151179i	−0.549304	+	0.835622i	$0.685107\pi$
$384$	−0.377704	−	0.654202i	−0.0192746	−	0.0333846i
$385$	20.8619	+	22.4614i	1.06322	+	1.14474i
$386$	−7.56944	−	13.1107i	−0.385275	−	0.667315i
$387$	0.259633	+	0.799069i	0.0131979	+	0.0406190i
$388$	8.69269	+	6.31561i	0.441304	+	0.320626i
$389$	7.95725	+	3.54280i	0.403448	+	0.179627i	0.598421	−	0.801182i	$-0.295795\pi$
$389$	7.95725	+	3.54280i	0.403448	+	0.179627i	−0.194972	+	0.980809i	$0.562462\pi$
$390$	16.4235	−	3.49093i	0.831639	−	0.176770i
$391$	−6.26478	+	19.2810i	−0.316824	+	0.975082i
$392$	−1.67336	+	1.21577i	−0.0845176	+	0.0614056i
$393$	−0.191287	+	1.81998i	−0.00964916	+	0.0918057i
$394$	10.3522	+	2.20043i	0.521536	+	0.110856i
$395$	19.9627	+	34.5765i	1.00443	+	1.73973i
$396$	7.90616	+	1.55319i	0.397299	+	0.0780505i
$397$	16.0923	−	27.8727i	0.807651	−	1.39889i	−0.106836	−	0.994277i	$-0.534072\pi$
$397$	16.0923	−	27.8727i	0.807651	−	1.39889i	0.914487	−	0.404616i	$-0.132595\pi$
$398$	2.18674	+	6.73010i	0.109611	+	0.337349i
$399$	6.78441	+	2.72782i	0.339646	+	0.136562i
$400$	−9.96955	+	7.24330i	−0.498478	+	0.362165i
$401$	16.5988	+	18.4348i	0.828904	+	0.920592i	0.997883	−	0.0650281i	$-0.0207137\pi$
$401$	16.5988	+	18.4348i	0.828904	+	0.920592i	−0.168979	+	0.985620i	$0.554047\pi$
$402$	0.204971	+	0.227643i	0.0102230	+	0.0113538i
$403$	46.3530	+	20.6377i	2.30901	+	1.02804i
$404$	14.1335	−	6.29262i	0.703165	−	0.313069i
$405$	−11.6687	+	12.9594i	−0.579824	+	0.643960i
$406$	10.5873			0.525440
$407$	−6.38667	+	0.0987276i	−0.316575	+	0.00489374i
$408$	1.16793	+	2.02291i	0.0578209	+	0.100149i
$409$	−11.5643	+	12.8435i	−0.571820	+	0.635071i	−0.957800	−	0.287437i	$-0.907197\pi$
$409$	−11.5643	+	12.8435i	−0.571820	+	0.635071i	0.385979	+	0.922507i	$0.373864\pi$
$410$	−19.5461	−	14.2010i	−0.965311	−	0.701339i
$411$	−10.4867	+	7.61907i	−0.517273	+	0.375821i
$412$	7.04498	−	1.49746i	0.347081	−	0.0737744i
$413$	10.0015	+	11.1078i	0.492143	+	0.546580i
$414$	14.5506	+	6.47835i	0.715124	+	0.318394i
$415$	27.2455	−	12.1305i	1.33743	−	0.595462i
$416$	5.22365	+	1.11032i	0.256110	+	0.0544379i
$417$	2.78698			0.136479
$418$	−9.10152	+	11.2322i	−0.445170	+	0.549385i
$419$	6.28016			0.306806			0.153403	−	0.988164i	$-0.450977\pi$
$419$	6.28016			0.306806			0.153403	+	0.988164i	$0.450977\pi$
$420$	6.82955	+	1.45167i	0.333248	+	0.0708340i
$421$	14.5437	−	6.47529i	0.708818	−	0.315586i	−0.0204724	−	0.999790i	$-0.506517\pi$
$421$	14.5437	−	6.47529i	0.708818	−	0.315586i	0.729290	+	0.684204i	$0.239850\pi$
$422$	8.01469	+	3.56837i	0.390149	+	0.173706i
$423$	−3.51186	−	3.90031i	−0.170752	−	0.189640i
$424$	−3.46365	+	0.736222i	−0.168210	+	0.0357541i
$425$	30.8276	−	22.3976i	1.49536	−	1.08644i
$426$	−1.77949	−	1.29288i	−0.0862167	−	0.0626401i
$427$	2.21493	−	2.45993i	0.107188	−	0.119044i
$428$	1.52373	+	2.63918i	0.0736524	+	0.127570i
$429$	10.7016	−	8.03077i	0.516676	−	0.387729i
$430$	−1.43946			−0.0694167
$431$	−16.0945	+	17.8748i	−0.775247	+	0.860999i	−0.993375	−	0.114921i	$-0.963338\pi$
$431$	−16.0945	+	17.8748i	−0.775247	+	0.860999i	0.218128	+	0.975920i	$0.430005\pi$
$432$	3.74679	−	1.66818i	0.180268	−	0.0802604i
$433$	22.2758	+	9.91784i	1.07051	+	0.476621i	0.864864	−	0.502006i	$-0.167404\pi$
$433$	22.2758	+	9.91784i	1.07051	+	0.476621i	0.205644	+	0.978627i	$0.434071\pi$
$434$	14.1183	+	15.6800i	0.677702	+	0.752664i
$435$	10.0299	+	11.1393i	0.480896	+	0.534089i
$436$	12.3168	−	8.94871i	0.589870	−	0.428566i
$437$	−22.4904	+	17.6324i	−1.07586	+	0.843471i
$438$	3.07119	+	9.45215i	0.146747	+	0.451641i
$439$	9.55875	−	16.5562i	0.456214	−	0.790187i	−0.542543	−	0.840028i	$-0.682538\pi$
$439$	9.55875	−	16.5562i	0.456214	−	0.790187i	0.998757	+	0.0498416i	$0.0158717\pi$
$440$	−6.71645	+	12.0600i	−0.320194	+	0.574936i
$441$	−2.51243	−	4.35166i	−0.119640	−	0.207222i
$442$	−16.1524	−	3.43330i	−0.768292	−	0.163306i
$443$	−3.63132	+	34.5497i	−0.172529	+	1.64151i	0.475373	+	0.879784i	$0.342313\pi$
$443$	−3.63132	+	34.5497i	−0.172529	+	1.64151i	−0.647902	+	0.761723i	$0.724354\pi$
$444$	−1.17698	+	0.855125i	−0.0558569	+	0.0405824i
$445$	0.164365	−	0.505863i	0.00779164	−	0.0239802i
$446$	−14.9833	+	3.18479i	−0.709479	+	0.150804i
$447$	−14.8539	−	6.61338i	−0.702565	−	0.312802i
$448$	1.79660	+	1.30531i	0.0848815	+	0.0616700i
$449$	−1.38286	−	4.25601i	−0.0652613	−	0.200854i	0.913109	−	0.407716i	$-0.133675\pi$
$449$	−1.38286	−	4.25601i	−0.0652613	−	0.200854i	−0.978370	+	0.206863i	$0.933675\pi$
$450$	−14.9686	−	25.9263i	−0.705624	−	1.22218i
$451$	−18.8913	−	3.71126i	−0.889559	−	0.174756i
$452$	−3.60594	−	6.24567i	−0.169609	−	0.293772i
$453$	−5.65292	−	1.20157i	−0.265598	−	0.0564545i
$454$	25.8728	−	11.5193i	1.21427	−	0.540629i
$455$	−39.9331	+	29.0131i	−1.87209	+	1.36016i
$456$	−0.224168	+	3.28510i	−0.0104976	+	0.153839i
$457$	1.37148	−	4.22099i	0.0641552	−	0.197449i	−0.913841	−	0.406072i	$-0.866898\pi$
$457$	1.37148	−	4.22099i	0.0641552	−	0.197449i	0.977996	+	0.208623i	$0.0668981\pi$
$458$	−2.68473	−	25.5435i	−0.125449	−	1.19357i
$459$	−11.5857	+	5.15830i	−0.540776	+	0.240769i
$460$	−18.2592	+	20.2789i	−0.851341	+	0.945510i
$461$	0.0100647	−	0.0174327i	0.000468762	−	0.000811920i	−0.865791	−	0.500406i	$-0.833184\pi$
$461$	0.0100647	−	0.0174327i	0.000468762	−	0.000811920i	0.866260	+	0.499594i	$0.166517\pi$
$462$	5.42369	−	1.24076i	0.252333	−	0.0577254i
$463$	12.6734			0.588983			0.294491	−	0.955654i	$-0.404850\pi$
$463$	12.6734			0.588983			0.294491	+	0.955654i	$0.404850\pi$
$464$	1.47324	+	4.53417i	0.0683935	+	0.210494i
$465$	−3.12253	+	29.7089i	−0.144804	+	1.37771i
$466$	−2.42915	−	1.08153i	−0.112528	−	0.0501008i
$467$	7.21861	−	22.2166i	0.334037	−	1.02806i	−0.633157	−	0.774023i	$-0.718241\pi$
$467$	7.21861	−	22.2166i	0.334037	−	1.02806i	0.967194	−	0.254038i	$-0.0817587\pi$
$468$	−4.00907	+	12.3386i	−0.185319	+	0.570354i
$469$	−0.822668	−	0.366276i	−0.0379873	−	0.0169130i
$470$	8.21441	−	3.65729i	0.378903	−	0.168698i
$471$	−0.279835	+	0.310788i	−0.0128941	+	0.0143204i
$472$	−3.36535	+	5.82897i	−0.154903	+	0.268300i
$473$	−1.04055	+	0.482689i	−0.0478444	+	0.0221940i
$474$	7.24635			0.332836
$475$	53.6790	−	1.96486i	2.46296	−	0.0901539i
$476$	−5.55541	−	4.03624i	−0.254632	−	0.185001i
$477$	−0.899200	−	8.55532i	−0.0411716	−	0.391721i
$478$	−10.1098	−	11.2281i	−0.462412	−	0.513561i
$479$	2.96671	−	0.630593i	0.135552	−	0.0288125i	−0.139636	−	0.990203i	$-0.544593\pi$
$479$	2.96671	−	0.630593i	0.135552	−	0.0288125i	0.275188	+	0.961390i	$0.411260\pi$
$480$	0.328646	+	3.12685i	0.0150005	+	0.142721i
$481$	1.07506	−	10.2285i	0.0490186	−	0.466381i
$482$	−0.671139	−	2.06555i	−0.0305696	−	0.0940834i
$483$	10.9985			0.500451
$484$	−0.811123	+	10.9701i	−0.0368692	+	0.498639i
$485$	−22.3604	−	38.7293i	−1.01533	−	1.75861i
$486$	4.78024	+	14.7121i	0.216836	+	0.667353i
$487$	−5.87128	−	4.26574i	−0.266053	−	0.193299i	0.446758	−	0.894655i	$-0.352578\pi$
$487$	−5.87128	−	4.26574i	−0.266053	−	0.193299i	−0.712811	+	0.701356i	$0.752578\pi$
$488$	1.36171	+	0.606273i	0.0616417	+	0.0274447i
$489$	−0.0611147	−	0.0678748i	−0.00276370	−	0.00306940i
$490$	8.42071	−	1.78988i	0.380409	−	0.0808584i
$491$	1.46130	+	13.9034i	0.0659476	+	0.627450i	0.976717	+	0.214533i	$0.0688231\pi$
$491$	1.46130	+	13.9034i	0.0659476	+	0.627450i	−0.910769	+	0.412916i	$0.864510\pi$
$492$	−4.00591	+	1.78354i	−0.180600	+	0.0804084i
$493$	−4.55552	−	14.0205i	−0.205170	−	0.631449i
$494$	−16.1984	−	16.7176i	−0.728800	−	0.752161i
$495$	−27.4319	−	19.2898i	−1.23297	−	0.867011i
$496$	−4.75060	+	8.22828i	−0.213308	+	0.369461i
$497$	6.32494	+	1.34441i	0.283712	+	0.0603049i
$498$	0.565807	−	5.38330i	0.0253544	−	0.241231i
$499$	0.0897583	+	0.853993i	0.00401813	+	0.0382300i	0.996347	−	0.0853942i	$-0.0272150\pi$
$499$	0.0897583	+	0.853993i	0.00401813	+	0.0382300i	−0.992329	+	0.123624i	$0.960548\pi$
$500$	29.8132	−	6.33698i	1.33329	−	0.283399i
$501$	1.63546	−	5.03343i	0.0730670	−	0.224877i
$502$	−2.60990	+	1.89620i	−0.116485	+	0.0846316i
$503$	−0.764719	+	7.27582i	−0.0340971	+	0.324413i	0.964156	+	0.265335i	$0.0854826\pi$
$503$	−0.764719	+	7.27582i	−0.0340971	+	0.324413i	−0.998253	+	0.0590776i	$0.981184\pi$
$504$	−3.60992	+	4.00922i	−0.160798	+	0.178585i
$505$	−64.3917			−2.86539
$506$	−6.39907	+	20.7819i	−0.284473	+	0.923870i
$507$	5.86169	+	10.1527i	0.260327	+	0.450899i
$508$	8.55179	+	1.81774i	0.379424	+	0.0806491i
$509$	−3.38855	+	32.2399i	−0.150195	+	1.42901i	0.616680	+	0.787214i	$0.288477\pi$
$509$	−3.38855	+	32.2399i	−0.150195	+	1.42901i	−0.766875	+	0.641796i	$0.778189\pi$
$510$	−1.01623	−	9.66878i	−0.0449994	−	0.428141i
$511$	−19.5501	−	21.7126i	−0.864844	−	0.960507i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−17.6111	−	3.07479i	−0.777548	−	0.135755i
$514$	19.5066	+	14.1724i	0.860401	+	0.625118i
$515$	−29.3219	−	6.23256i	−1.29208	−	0.274639i
$516$	−0.130628	+	0.226255i	−0.00575059	+	0.00996032i
$517$	4.71160	−	5.39828i	0.207216	−	0.237416i
$518$	2.13843	−	3.70386i	0.0939570	−	0.162738i
$519$	−5.75791	+	6.39480i	−0.252744	+	0.280701i
$520$	−17.9820	−	13.0647i	−0.788565	−	0.572926i
$521$	26.4120	−	19.1894i	1.15713	−	0.840704i	0.167718	−	0.985835i	$-0.446360\pi$
$521$	26.4120	−	19.1894i	1.15713	−	0.840704i	0.989413	+	0.145131i	$0.0463602\pi$
$522$	−11.3289	+	2.40803i	−0.495853	+	0.105397i
$523$	−20.4763	+	4.35238i	−0.895367	+	0.190316i	−0.632541	−	0.774527i	$-0.717988\pi$
$523$	−20.4763	+	4.35238i	−0.895367	+	0.190316i	−0.262826	+	0.964843i	$0.584655\pi$
$524$	1.95987	−	1.42393i	0.0856174	−	0.0622047i
$525$	−16.7244	−	12.1510i	−0.729914	−	0.530313i
$526$	16.6674	−	18.5110i	0.726731	−	0.807117i
$527$	14.6897	−	25.4433i	0.639892	−	1.10833i
$528$	1.28609	+	2.15012i	0.0559698	+	0.0935720i
$529$	−9.99260	+	17.3077i	−0.434461	+	0.752508i
$530$	14.4161	+	3.06423i	0.626193	+	0.133102i
$531$	−13.2285	−	9.61106i	−0.574068	−	0.417085i
$532$	−3.32601	−	9.09056i	−0.144201	−	0.394126i
$533$	9.57946	−	29.4826i	0.414933	−	1.27703i
$534$	−0.0645961	−	0.0717412i	−0.00279535	−	0.00310455i
$535$	−1.32582	−	12.6144i	−0.0573203	−	0.545366i
$536$	0.0423872	−	0.403287i	0.00183085	−	0.0174194i
$537$	14.4992	+	3.08191i	0.625688	+	0.132994i
$538$	2.67400	+	4.63151i	0.115284	+	0.199678i
$539$	5.48693	−	4.11755i	0.236339	−	0.177355i
$540$	−17.0703			−0.734590
$541$	15.7548	−	17.4975i	0.677354	−	0.752277i	−0.302247	−	0.953229i	$-0.597737\pi$
$541$	15.7548	−	17.4975i	0.677354	−	0.752277i	0.979601	+	0.200952i	$0.0644036\pi$
$542$	−2.26792	+	21.5778i	−0.0974153	+	0.926845i
$543$	10.4984	−	7.62750i	0.450528	−	0.327327i
$544$	0.955534	−	2.94083i	0.0409682	−	0.126087i
$545$	−61.9810	+	13.1745i	−2.65497	+	0.564332i
$546$	0.936439	+	8.90962i	0.0400759	+	0.381297i
$547$	−1.86888	+	17.7812i	−0.0799075	+	0.760269i	0.879052	+	0.476726i	$0.158177\pi$
$547$	−1.86888	+	17.7812i	−0.0799075	+	0.760269i	−0.958959	+	0.283543i	$0.908490\pi$
$548$	16.7844	+	3.56764i	0.716995	+	0.152402i
$549$	−1.81057	+	3.13601i	−0.0772735	+	0.133842i
$550$	32.6900	−	24.5315i	1.39391	−	1.04603i
$551$	5.69446	−	19.9857i	0.242592	−	0.851418i
$552$	1.53046	+	4.71028i	0.0651408	+	0.200483i
$553$	−19.4609	+	8.66454i	−0.827561	+	0.368454i
$554$	1.00513	+	9.56316i	0.0427038	+	0.406300i
$555$	5.92280	−	1.25893i	0.251409	−	0.0534386i
$556$	−2.46868	−	2.74174i	−0.104695	−	0.116276i
$557$	15.6667	+	6.97524i	0.663818	+	0.295551i	0.710851	−	0.703343i	$-0.248310\pi$
$557$	15.6667	+	6.97524i	0.663818	+	0.295551i	−0.0470334	+	0.998893i	$0.514977\pi$
$558$	−18.6736	−	13.5672i	−0.790516	−	0.574344i
$559$	−0.570740	−	1.75656i	−0.0241397	−	0.0742944i
$560$	−4.62143	−	8.00455i	−0.195291	−	0.338254i
$561$	−3.97681	−	6.64855i	−0.167901	−	0.280702i
$562$	9.06711			0.382473
$563$	−6.63993	−	20.4356i	−0.279840	−	0.861258i	−0.987898	−	0.155104i	$-0.950429\pi$
$563$	−6.63993	−	20.4356i	−0.279840	−	0.861258i	0.708058	−	0.706154i	$-0.249571\pi$
$564$	0.170589	−	1.62304i	0.00718308	−	0.0683424i
$565$	3.13758	+	29.8521i	0.131999	+	1.25589i
$566$	−6.44137	+	1.36916i	−0.270751	+	0.0575499i
$567$	−6.22595	−	6.91462i	−0.261465	−	0.290387i
$568$	0.304363	+	2.89582i	0.0127708	+	0.121506i
$569$	−6.95704	−	5.05459i	−0.291654	−	0.211899i	0.432330	−	0.901715i	$-0.357691\pi$
$569$	−6.95704	−	5.05459i	−0.291654	−	0.211899i	−0.723985	+	0.689816i	$0.757691\pi$
$570$	6.41362	−	12.1113i	0.268637	−	0.507288i
$571$	−0.814236			−0.0340747			−0.0170373	−	0.999855i	$-0.505423\pi$
$571$	−0.814236			−0.0340747			−0.0170373	+	0.999855i	$0.505423\pi$
$572$	−17.3797	−	3.41429i	−0.726683	−	0.142759i
$573$	9.35835	−	16.2091i	0.390951	−	0.677146i
$574$	8.62571	−	9.57982i	0.360030	−	0.399854i
$575$	73.8087	−	32.8618i	3.07804	−	1.37043i
$576$	−2.21933	−	0.988110i	−0.0924721	−	0.0411712i
$577$	−5.61995	+	17.2964i	−0.233962	+	0.720060i	0.763296	+	0.646049i	$0.223580\pi$
$577$	−5.61995	+	17.2964i	−0.233962	+	0.720060i	−0.997257	+	0.0740109i	$0.976420\pi$
$578$	2.29861	−	7.07440i	0.0956096	−	0.294256i
$579$	10.4473	+	4.65145i	0.434176	+	0.193308i
$580$	2.07414	−	19.7341i	0.0861240	−	0.819416i
$581$	4.91733	+	15.1340i	0.204005	+	0.627864i
$582$	−8.11666			−0.336447
$583$	11.4485	−	2.61904i	0.474149	−	0.108470i
$584$	6.57829	−	11.3939i	0.272212	−	0.471484i
$585$	36.1314	−	40.1279i	1.49385	−	1.65909i
$586$	−16.7445	+	7.45512i	−0.691707	+	0.307968i
$587$	−0.823766	−	7.83761i	−0.0340005	−	0.323493i	−0.998281	−	0.0586097i	$-0.981333\pi$
$587$	−0.823766	−	7.83761i	−0.0340005	−	0.323493i	0.964281	−	0.264883i	$-0.0853334\pi$
$588$	0.482832	−	1.48600i	0.0199116	−	0.0612817i
$589$	37.1928	−	18.2176i	1.53250	−	0.750642i
$590$	22.6637	−	16.4661i	0.933049	−	0.677900i
$591$	−7.30363	+	3.25179i	−0.300431	+	0.133761i
$592$	1.88380	+	0.400413i	0.0774236	+	0.0164569i
$593$	9.33780	+	16.1735i	0.383457	+	0.664168i	0.991554	−	0.129695i	$-0.0414000\pi$
$593$	9.33780	+	16.1735i	0.383457	+	0.664168i	−0.608097	+	0.793863i	$0.708067\pi$
$594$	−12.3397	+	5.72414i	−0.506304	+	0.234864i
$595$	14.2903	+	24.7515i	0.585844	+	1.01471i
$596$	6.65138	+	20.4708i	0.272451	+	0.838518i
$597$	−4.32468	−	3.14206i	−0.176997	−	0.128596i
$598$	−31.9859	−	14.2411i	−1.30800	−	0.582360i
$599$	23.2984	−	4.95223i	0.951947	−	0.202343i	0.294338	−	0.955702i	$-0.404901\pi$
$599$	23.2984	−	4.95223i	0.951947	−	0.202343i	0.657610	+	0.753359i	$0.271568\pi$
$600$	2.87661	−	8.85330i	0.117437	−	0.361435i
$601$	14.7921	−	10.7471i	0.603383	−	0.438383i	−0.243695	−	0.969852i	$-0.578360\pi$
$601$	14.7921	−	10.7471i	0.603383	−	0.438383i	0.847078	+	0.531469i	$0.178360\pi$
$602$	0.0802815	−	0.763827i	0.00327203	−	0.0311313i
$603$	0.963599	+	0.204819i	0.0392408	+	0.00834089i
$604$	3.82523	+	6.62549i	0.155646	+	0.269588i
$605$	21.6551	−	40.3379i	0.880403	−	1.63997i
$606$	−5.84345	+	10.1211i	−0.237374	+	0.411144i
$607$	8.45422	+	26.0194i	0.343146	+	1.05609i	0.962569	+	0.271037i	$0.0873667\pi$
$607$	8.45422	+	26.0194i	0.343146	+	1.05609i	−0.619423	+	0.785058i	$0.712633\pi$
$608$	3.43034	−	2.68938i	0.139119	−	0.109069i
$609$	−6.47031	+	4.70095i	−0.262190	+	0.190492i
$610$	−4.15124	−	4.61042i	−0.168079	−	0.186670i
$611$	7.71995	+	8.57387i	0.312316	+	0.346862i
$612$	6.86256	+	3.05541i	0.277402	+	0.123508i
$613$	−38.5198	+	17.1501i	−1.55580	+	0.692687i	−0.991163	−	0.132652i	$-0.957651\pi$
$613$	−38.5198	+	17.1501i	−1.55580	+	0.692687i	−0.564638	+	0.825339i	$0.690984\pi$
$614$	3.76071	−	4.17669i	0.151770	−	0.168557i
$615$	18.2508			0.735945
$616$	−6.02486	−	4.23660i	−0.242749	−	0.170697i
$617$	20.9170	+	36.2293i	0.842085	+	1.45853i	0.888128	+	0.459595i	$0.152006\pi$
$617$	20.9170	+	36.2293i	0.842085	+	1.45853i	−0.0460429	+	0.998939i	$0.514661\pi$
$618$	−3.64055	+	4.04324i	−0.146444	+	0.162643i
$619$	27.7622	+	20.1704i	1.11586	+	0.810716i	0.983576	−	0.180496i	$-0.0577703\pi$
$619$	27.7622	+	20.1704i	1.11586	+	0.810716i	0.132280	+	0.991212i	$0.457770\pi$
$620$	31.9925	−	23.2439i	1.28485	−	0.933498i
$621$	−26.3023	+	5.59073i	−1.05547	+	0.224348i
$622$	−19.0137	−	21.1168i	−0.762378	−	0.846707i
$623$	0.259262	+	0.115431i	0.0103871	+	0.00462464i
$624$	−3.68537	+	1.64083i	−0.147533	+	0.0656858i
$625$	−63.8165	−	13.5646i	−2.55266	−	0.542584i
$626$	14.1707			0.566375
$627$	0.574987	−	10.9056i	0.0229628	−	0.435530i
$628$	0.553618			0.0220917
$629$	−5.82503	−	1.23815i	−0.232259	−	0.0493682i
$630$	20.5130	−	9.13296i	0.817256	−	0.363866i
$631$	−30.9283	−	13.7702i	−1.23124	−	0.548182i	−0.315104	−	0.949057i	$-0.602039\pi$
$631$	−30.9283	−	13.7702i	−1.23124	−	0.548182i	−0.916133	+	0.400875i	$0.868706\pi$
$632$	−6.41873	−	7.12872i	−0.255323	−	0.283565i
$633$	−6.48250	+	1.37790i	−0.257656	+	0.0547665i
$634$	−14.6784	+	10.6645i	−0.582955	+	0.423541i
$635$	−29.4389	−	21.3886i	−1.16825	−	0.848782i
$636$	1.78987	−	1.98785i	0.0709730	−	0.0788236i
$637$	5.52296	+	9.56604i	0.218828	+	0.379020i
$638$	−5.11805	−	14.9608i	−0.202625	−	0.592305i
$639$	−7.07375			−0.279833
$640$	2.78499	−	3.09304i	0.110086	−	0.122263i
$641$	−3.46300	+	1.54183i	−0.136780	+	0.0608984i	−0.473985	−	0.880533i	$-0.657185\pi$
$641$	−3.46300	+	1.54183i	−0.136780	+	0.0608984i	0.337205	+	0.941431i	$0.390518\pi$
$642$	−2.10305	−	0.936339i	−0.0830009	−	0.0369544i
$643$	−26.4515	−	29.3773i	−1.04314	−	1.15853i	−0.987101	−	0.160101i	$-0.948818\pi$
$643$	−26.4515	−	29.3773i	−1.04314	−	1.15853i	−0.0560438	−	0.998428i	$-0.517849\pi$
$644$	−9.74237	−	10.8200i	−0.383903	−	0.426368i
$645$	0.879705	−	0.639143i	0.0346384	−	0.0251662i
$646$	−10.6072	+	8.31602i	−0.417335	+	0.327189i
$647$	10.9737	+	33.7736i	0.431421	+	1.32778i	0.896710	+	0.442618i	$0.145950\pi$
$647$	10.9737	+	33.7736i	0.431421	+	1.32778i	−0.465290	+	0.885159i	$0.654050\pi$
$648$	2.09494	−	3.62853i	0.0822968	−	0.142542i
$649$	10.8615	−	19.5027i	0.426350	−	0.765548i
$650$	32.9047	+	56.9925i	1.29063	+	2.23543i
$651$	−15.5904	−	3.31385i	−0.611037	−	0.129880i
$652$	−0.0126383	+	0.120245i	−0.000494954	+	0.00470917i
$653$	−21.1852	+	15.3919i	−0.829040	+	0.602333i	−0.919288	−	0.393586i	$-0.871234\pi$
$653$	−21.1852	+	15.3919i	−0.829040	+	0.602333i	0.0902473	+	0.995919i	$0.471234\pi$
$654$	−3.55390	+	10.9378i	−0.138969	+	0.427701i
$655$	−9.86249	+	2.09634i	−0.385360	+	0.0819107i
$656$	5.30298	+	2.36104i	0.207046	+	0.0921830i
$657$	25.8579	+	18.7868i	1.00881	+	0.732944i
$658$	1.48256	+	4.56284i	0.0577960	+	0.177878i
$659$	−9.33291	−	16.1651i	−0.363558	−	0.629702i	0.624985	−	0.780637i	$-0.285105\pi$
$659$	−9.33291	−	16.1651i	−0.363558	−	0.629702i	−0.988544	+	0.150935i	$0.951772\pi$
$660$	−1.25016	−	10.3525i	−0.0486623	−	0.402971i
$661$	−21.4586	−	37.1673i	−0.834642	−	1.44564i	−0.894322	−	0.447424i	$-0.852341\pi$
$661$	−21.4586	−	37.1673i	−0.834642	−	1.44564i	0.0596799	−	0.998218i	$-0.480992\pi$
$662$	−25.8657	−	5.49792i	−1.00530	−	0.213683i
$663$	11.3958	−	5.07373i	0.442576	−	0.197047i
$664$	−5.79710	+	4.21184i	−0.224971	+	0.163451i
$665$	−2.74283	+	40.1952i	−0.106363	+	1.55870i
$666$	−1.44579	+	4.44967i	−0.0560231	+	0.172421i
$667$	−3.26728	−	31.0861i	−0.126509	−	1.20366i
$668$	−6.40039	+	2.84964i	−0.247639	+	0.110256i
$669$	7.74274	−	8.59918i	0.299352	−	0.332464i
$670$	−0.843883	+	1.46165i	−0.0326021	+	0.0564684i
$671$	−4.54682	−	1.94073i	−0.175528	−	0.0749211i
$672$	−1.67755			−0.0647129
$673$	1.96225	+	6.03920i	0.0756394	+	0.232794i	0.981727	−	0.190297i	$-0.0609451\pi$
$673$	1.96225	+	6.03920i	0.0756394	+	0.232794i	−0.906087	+	0.423091i	$0.860945\pi$
$674$	−3.17803	+	30.2370i	−0.122413	+	1.16468i
$675$	46.1719	+	20.5571i	1.77716	+	0.791242i
$676$	4.79572	−	14.7597i	0.184451	−	0.567682i
$677$	2.30752	−	7.10183i	0.0886853	−	0.272945i	−0.896871	−	0.442292i	$-0.854166\pi$
$677$	2.30752	−	7.10183i	0.0886853	−	0.272945i	0.985557	+	0.169346i	$0.0541656\pi$
$678$	4.97691	+	2.21586i	0.191137	+	0.0850997i
$679$	21.7982	−	9.70519i	0.836539	−	0.372451i
$680$	−8.61166	+	9.56422i	−0.330242	+	0.366771i
$681$	−10.6971	+	18.5279i	−0.409913	+	0.709990i
$682$	15.3323	−	27.5304i	0.587103	−	1.05419i
$683$	23.6992			0.906826			0.453413	−	0.891301i	$-0.350206\pi$
$683$	23.6992			0.906826			0.453413	+	0.891301i	$0.350206\pi$
$684$	5.62658	+	8.97082i	0.215138	+	0.343008i
$685$	−57.7792	−	41.9791i	−2.20763	−	1.60394i
$686$	2.10503	+	20.0281i	0.0803706	+	0.764675i
$687$	12.9825	+	14.4185i	0.495313	+	0.550101i
$688$	0.338291	−	0.0719060i	0.0128972	−	0.00274139i
$689$	1.97667	+	18.8067i	0.0753051	+	0.716480i
$690$	2.15470	−	20.5006i	0.0820281	−	0.780445i
$691$	−0.286560	−	0.881940i	−0.0109012	−	0.0335506i	0.945458	−	0.325744i	$-0.105615\pi$
$691$	−0.286560	−	0.881940i	−0.0109012	−	0.0335506i	−0.956359	+	0.292194i	$0.905615\pi$
$692$	11.3913			0.433032
$693$	11.7658	−	13.4805i	0.446945	−	0.512083i
$694$	−7.96153	−	13.7898i	−0.302216	−	0.523453i
$695$	4.74513	+	14.6040i	0.179993	+	0.553961i
$696$	−2.91360	−	2.11686i	−0.110440	−	0.0802393i
$697$	−16.3977	−	7.30074i	−0.621108	−	0.276535i
$698$	9.47334	+	10.5212i	0.358571	+	0.398233i
$699$	1.96476	−	0.417623i	0.0743141	−	0.0157960i
$700$	2.86053	+	27.2161i	0.108118	+	1.02867i
$701$	6.04249	−	2.69029i	0.228222	−	0.101611i	−0.289440	−	0.957196i	$-0.593469\pi$
$701$	6.04249	−	2.69029i	0.228222	−	0.101611i	0.517662	+	0.855585i	$0.326802\pi$
$702$	−6.76833	−	20.8308i	−0.255454	−	0.786207i
$703$	−5.84161	−	6.02885i	−0.220320	−	0.227382i
$704$	0.976016	−	3.16976i	0.0367850	−	0.119465i
$705$	−3.39623	+	5.88245i	−0.127910	+	0.221546i
$706$	−20.4257	−	4.34162i	−0.768731	−	0.163399i
$707$	3.59126	−	34.1686i	0.135063	−	1.28504i
$708$	−0.531467	−	5.05657i	−0.0199738	−	0.190038i
$709$	8.34398	−	1.77357i	0.313365	−	0.0666078i	−0.0485446	−	0.998821i	$-0.515458\pi$
$709$	8.34398	−	1.77357i	0.313365	−	0.0666078i	0.361909	+	0.932213i	$0.382125\pi$
$710$	3.74500	−	11.5259i	0.140547	−	0.432561i
$711$	18.8533	−	13.6977i	0.707054	−	0.513705i
$712$	−0.0133582	+	0.127095i	−0.000500621	+	0.00476309i
$713$	41.6820	−	46.2926i	1.56100	−	1.73367i
$714$	5.18728			0.194129
$715$	60.3023	+	42.4038i	2.25518	+	1.58581i
$716$	−9.81137	−	16.9938i	−0.366668	−	0.635088i
$717$	11.1640	+	2.37297i	0.416925	+	0.0886202i
$718$	−0.935041	+	8.89632i	−0.0348954	+	0.332008i
$719$	−0.504542	−	4.80039i	−0.0188162	−	0.179024i	0.981077	−	0.193616i	$-0.0620217\pi$
$719$	−0.504542	−	4.80039i	−0.0188162	−	0.179024i	−0.999894	+	0.0145920i	$0.995355\pi$
$720$	6.76573	+	7.51411i	0.252144	+	0.280034i
$721$	4.94256	−	15.2116i	0.184071	−	0.566511i
$722$	−18.9492	+	1.38909i	−0.705214	+	0.0516964i
$723$	1.32730	+	0.964340i	0.0493628	+	0.0358642i
$724$	−16.8030	−	3.57159i	−0.624479	−	0.132737i
$725$	−29.3751	+	50.8792i	−1.09096	+	1.88961i
$726$	−4.37519	−	7.06436i	−0.162378	−	0.262183i
$727$	−5.56558	+	9.63986i	−0.206416	+	0.357523i	−0.950583	−	0.310471i	$-0.899513\pi$
$727$	−5.56558	+	9.63986i	−0.206416	+	0.357523i	0.744167	+	0.667993i	$0.232847\pi$
$728$	7.93551	−	8.81327i	0.294109	−	0.326642i
$729$	0.715230	+	0.519645i	0.0264900	+	0.0192461i
$730$	−44.3009	+	32.1865i	−1.63965	+	1.19128i
$731$	−1.04606	+	0.222346i	−0.0386898	+	0.00822376i
$732$	−1.10139	+	0.234107i	−0.0407084	+	0.00865285i
$733$	−38.7870	+	28.1804i	−1.43263	+	1.04087i	−0.443112	+	0.896466i	$0.646126\pi$
$733$	−38.7870	+	28.1804i	−1.43263	+	1.04087i	−0.989519	+	0.144402i	$0.953874\pi$
$734$	16.1724	+	11.7500i	0.596935	+	0.433699i
$735$	−4.35147	+	4.83280i	−0.160507	+	0.178261i
$736$	3.27816	−	5.67793i	0.120834	−	0.209291i
$737$	−0.119892	+	1.33957i	−0.00441627	+	0.0493436i
$738$	−7.05101	+	12.2127i	−0.259551	+	0.449556i
$739$	−38.4228	−	8.16702i	−1.41341	−	0.300429i	−0.562957	−	0.826486i	$-0.690336\pi$
$739$	−38.4228	−	8.16702i	−1.41341	−	0.300429i	−0.850449	+	0.526058i	$0.823670\pi$
$740$	−6.48484	−	4.71151i	−0.238388	−	0.173199i
$741$	17.3223	+	3.02438i	0.636352	+	0.111103i
$742$	−2.43000	+	7.47878i	−0.0892082	+	0.274555i
$743$	−0.240283	−	0.266861i	−0.00881512	−	0.00979019i	0.738721	−	0.674011i	$-0.235430\pi$
$743$	−0.240283	−	0.266861i	−0.00881512	−	0.00979019i	−0.747536	+	0.664221i	$0.768763\pi$
$744$	−0.750229	−	7.13795i	−0.0275047	−	0.261690i
$745$	9.36431	−	89.0955i	0.343082	−	3.26421i
$746$	−20.1515	−	4.28334i	−0.737800	−	0.156824i
$747$	−8.70392	−	15.0756i	−0.318460	−	0.551589i
$748$	−3.01801	+	9.80146i	−0.110349	+	0.358377i
$749$	6.76758			0.247282
$750$	−15.4062	+	17.1103i	−0.562555	+	0.624781i
$751$	−0.278498	+	2.64974i	−0.0101626	+	0.0966902i	−0.998427	−	0.0560598i	$-0.982146\pi$
$751$	−0.278498	+	2.64974i	−0.0101626	+	0.0966902i	0.988265	+	0.152750i	$0.0488129\pi$
$752$	−1.74780	+	1.26985i	−0.0637357	+	0.0463067i
$753$	0.753059	−	2.31768i	0.0274430	−	0.0844609i
$754$	24.9038	−	5.29346i	0.906943	−	0.192777i
$755$	−3.32839	−	31.6675i	−0.121133	−	1.15250i
$756$	0.952048	−	9.05813i	0.0346256	−	0.329441i
$757$	37.1915	+	7.90529i	1.35175	+	0.287323i	0.826169	−	0.563422i	$-0.190516\pi$
$757$	37.1915	+	7.90529i	1.35175	+	0.287323i	0.525578	+	0.850745i	$0.323849\pi$
$758$	−11.2167	+	19.4280i	−0.407411	+	0.705656i
$759$	−5.31683	−	15.5419i	−0.192989	−	0.564136i
$760$	−17.5959	+	4.41857i	−0.638269	+	0.160278i
$761$	3.86870	+	11.9066i	0.140240	+	0.431615i	0.996368	−	0.0851486i	$-0.0271365\pi$
$761$	3.86870	+	11.9066i	0.140240	+	0.431615i	−0.856128	+	0.516764i	$0.827137\pi$
$762$	−6.03342	+	2.68625i	−0.218568	+	0.0973127i
$763$	−3.53403	−	33.6241i	−0.127941	−	1.21727i
$764$	−24.2355	+	5.15142i	−0.876810	+	0.186372i
$765$	−20.9208	−	23.2349i	−0.756394	−	0.840061i
$766$	−12.9999	−	5.78795i	−0.469707	−	0.209127i
$767$	29.0796	+	21.1275i	1.05000	+	0.762871i
$768$	−0.233434	−	0.718435i	−0.00842331	−	0.0259243i
$769$	12.7193	+	22.0304i	0.458669	+	0.794438i	0.998891	−	0.0470848i	$-0.0149931\pi$
$769$	12.7193	+	22.0304i	0.458669	+	0.794438i	−0.540222	+	0.841522i	$0.681660\pi$
$770$	15.7361	+	26.3080i	0.567088	+	0.948075i
$771$	−18.2140			−0.655962
$772$	−4.67817	−	14.3979i	−0.168371	−	0.518193i
$773$	4.00238	−	38.0801i	0.143956	−	1.36965i	−0.649195	−	0.760622i	$-0.724894\pi$
$773$	4.00238	−	38.0801i	0.143956	−	1.36965i	0.793151	−	0.609025i	$-0.208439\pi$
$774$	0.0878239	+	0.835589i	0.00315677	+	0.0300346i
$775$	−114.525	+	24.3431i	−4.11386	+	0.874429i
$776$	7.18964	+	7.98491i	0.258093	+	0.286642i
$777$	0.337707	+	3.21307i	0.0121152	+	0.115268i
$778$	7.04677	+	5.11978i	0.252639	+	0.183553i
$779$	−13.4444	−	21.4353i	−0.481696	−	0.768000i
$780$	16.7905			0.601195
$781$	−1.15779	−	9.58761i	−0.0414289	−	0.343072i
$782$	−10.1366	+	17.5572i	−0.362485	+	0.627842i
$783$	13.0838	−	14.5310i	0.467575	−	0.519295i
$784$	−1.88957	+	0.841290i	−0.0674846	+	0.0300461i
$785$	−2.10500	−	0.937207i	−0.0751307	−	0.0334503i
$786$	−0.565501	+	1.74043i	−0.0201708	+	0.0620792i
$787$	7.04507	−	21.6825i	0.251130	−	0.772898i	−0.743438	−	0.668805i	$-0.766806\pi$
$787$	7.04507	−	21.6825i	0.251130	−	0.772898i	0.994568	−	0.104093i	$-0.0331939\pi$
$788$	9.66847	+	4.30468i	0.344425	+	0.153348i
$789$	−1.96685	+	18.7133i	−0.0700218	+	0.666213i
$790$	12.3377	+	37.9714i	0.438954	+	1.35096i
$791$	−16.0156			−0.569449
$792$	7.41046	+	3.16303i	0.263319	+	0.112393i
$793$	3.98010	−	6.89374i	0.141337	−	0.244804i
$794$	21.5357	−	23.9179i	0.764275	−	0.848813i
$795$	−10.1708	+	4.52831i	−0.360720	+	0.160603i
$796$	0.739690	+	7.03768i	0.0262176	+	0.249444i
$797$	−4.51744	+	13.9033i	−0.160016	+	0.492479i	−0.998635	−	0.0522406i	$-0.983364\pi$
$797$	−4.51744	+	13.9033i	−0.160016	+	0.492479i	0.838619	+	0.544719i	$0.183364\pi$
$798$	6.06901	+	4.07877i	0.214841	+	0.144387i
$799$	5.40450	−	3.92660i	0.191198	−	0.138913i
$800$	−11.2577	+	5.01223i	−0.398018	+	0.177209i
$801$	−0.303676	−	0.0645483i	−0.0107299	−	0.00228070i
$802$	12.4033	+	21.4831i	0.437974	+	0.758594i
$803$	−21.2310	+	38.1221i	−0.749227	+	1.34530i
$804$	0.153162	+	0.265285i	0.00540161	+	0.00935587i
$805$	18.7261	+	57.6331i	0.660010	+	2.03130i
$806$	41.0493	+	29.8240i	1.44590	+	1.05051i
$807$	−3.69065	−	1.64318i	−0.129917	−	0.0578428i
$808$	15.1329	−	3.21660i	0.532374	−	0.113160i
$809$	7.43677	−	22.8880i	0.261463	−	0.804701i	−0.731024	−	0.682352i	$-0.760957\pi$
$809$	7.43677	−	22.8880i	0.261463	−	0.804701i	0.992487	−	0.122349i	$-0.0390427\pi$
$810$	−14.1082	+	10.2502i	−0.495710	+	0.360154i
$811$	−0.127769	+	1.21564i	−0.00448658	+	0.0426870i	−0.996536	−	0.0831609i	$-0.973498\pi$
$811$	−0.127769	+	1.21564i	−0.00448658	+	0.0426870i	0.992050	+	0.125848i	$0.0401651\pi$
$812$	10.3560	+	2.20123i	0.363423	+	0.0772480i
$813$	−8.19490	−	14.1940i	−0.287408	−	0.497804i
$814$	−6.26763	−	1.23129i	−0.219680	−	0.0431568i
$815$	0.251615	−	0.435810i	0.00881368	−	0.0152657i
$816$	0.721817	+	2.22153i	0.0252687	+	0.0777690i
$817$	−1.39870	−	0.562377i	−0.0489342	−	0.0196751i
$818$	−13.9820	+	10.1585i	−0.488868	+	0.355183i
$819$	19.2782	+	21.4106i	0.673635	+	0.748147i
$820$	−16.1664	−	17.9546i	−0.564554	−	0.627001i
$821$	30.5205	+	13.5886i	1.06517	+	0.474246i	0.863052	−	0.505114i	$-0.168550\pi$
$821$	30.5205	+	13.5886i	1.06517	+	0.474246i	0.202122	+	0.979360i	$0.435216\pi$
$822$	−11.8417	+	5.27226i	−0.413026	+	0.183891i
$823$	−1.50945	+	1.67641i	−0.0526160	+	0.0584360i	−0.768878	−	0.639395i	$-0.779185\pi$
$823$	−1.50945	+	1.67641i	−0.0526160	+	0.0584360i	0.716262	+	0.697831i	$0.245851\pi$
$824$	7.20237			0.250906
$825$	−9.08565	+	29.5070i	−0.316322	+	1.02730i
$826$	7.47352	+	12.9445i	0.260037	+	0.450397i
$827$	13.9988	−	15.5473i	0.486786	−	0.540631i	−0.448845	−	0.893610i	$-0.648164\pi$
$827$	13.9988	−	15.5473i	0.486786	−	0.540631i	0.935631	+	0.352979i	$0.114831\pi$
$828$	12.8857	+	9.36203i	0.447810	+	0.325353i
$829$	25.6462	−	18.6330i	0.890729	−	0.647152i	−0.0453391	−	0.998972i	$-0.514437\pi$
$829$	25.6462	−	18.6330i	0.890729	−	0.647152i	0.936068	+	0.351819i	$0.114437\pi$
$830$	29.1722	−	6.20075i	1.01258	−	0.215231i
$831$	−4.86048	−	5.39811i	−0.168608	−	0.187258i
$832$	4.87865	+	2.17211i	0.169137	+	0.0753045i
$833$	5.84287	−	2.60141i	0.202444	−	0.0901337i
$834$	2.72608	+	0.579446i	0.0943965	+	0.0200646i
$835$	29.1601			1.00913
$836$	−11.2379	+	9.09444i	−0.388672	+	0.314538i
$837$	38.9680			1.34693
$838$	6.14293	+	1.30572i	0.212204	+	0.0451053i
$839$	17.3453	−	7.72263i	0.598827	−	0.266615i	−0.0848571	−	0.996393i	$-0.527043\pi$
$839$	17.3453	−	7.72263i	0.598827	−	0.266615i	0.683684	+	0.729778i	$0.260377\pi$
$840$	6.37849	+	2.83989i	0.220079	+	0.0979854i
$841$	−4.19601	−	4.66014i	−0.144690	−	0.160694i
$842$	15.5722	−	3.30997i	0.536654	−	0.114069i
$843$	−5.54125	+	4.02595i	−0.190851	+	0.138661i
$844$	7.09765	+	5.15674i	0.244311	+	0.177502i
$845$	−43.2210	+	48.0018i	−1.48685	+	1.65131i
$846$	−2.62420	−	4.54524i	−0.0902217	−	0.156269i
$847$	20.1970	+	13.7407i	0.693977	+	0.472135i
$848$	−3.54103			−0.121600
$849$	3.32863	−	3.69682i	0.114238	−	0.126875i
$850$	34.8106	−	15.4987i	1.19400	−	0.531601i
$851$	−11.5350	−	5.13573i	−0.395416	−	0.176051i
$852$	−1.47180	−	1.63460i	−0.0504231	−	0.0560006i
$853$	−0.0525253	−	0.0583353i	−0.00179843	−	0.00199736i	0.742245	−	0.670129i	$-0.233761\pi$
$853$	−0.0525253	−	0.0583353i	−0.00179843	−	0.00199736i	−0.744043	+	0.668131i	$0.767094\pi$
$854$	2.67798	−	1.94566i	0.0916384	−	0.0665792i
$855$	−6.20725	−	43.6345i	−0.212283	−	1.49227i
$856$	0.941719	+	2.89831i	0.0321873	+	0.0990623i
$857$	1.78802	−	3.09694i	0.0610775	−	0.105789i	−0.833870	−	0.551961i	$-0.813880\pi$
$857$	1.78802	−	3.09694i	0.0610775	−	0.105789i	0.894947	+	0.446172i	$0.147213\pi$
$858$	12.1374	−	5.63029i	0.414364	−	0.192215i
$859$	−0.339008	−	0.587179i	−0.0115668	−	0.0200343i	0.860184	−	0.509984i	$-0.170349\pi$
$859$	−0.339008	−	0.587179i	−0.0115668	−	0.0200343i	−0.871751	+	0.489949i	$0.837015\pi$
$860$	−1.40800	−	0.299280i	−0.0480124	−	0.0102054i
$861$	−1.01789	+	9.68455i	−0.0346895	+	0.330048i
$862$	−19.4592	+	14.1380i	−0.662784	+	0.481541i
$863$	−0.483143	+	1.48696i	−0.0164464	+	0.0506167i	−0.958943	−	0.283599i	$-0.908471\pi$
$863$	−0.483143	+	1.48696i	−0.0164464	+	0.0506167i	0.942497	+	0.334216i	$0.108471\pi$
$864$	4.01175	−	0.852724i	0.136483	−	0.0290103i
$865$	−43.3127	−	19.2840i	−1.47268	−	0.655677i
$866$	19.7270	+	14.3325i	0.670351	+	0.487039i
$867$	1.73639	+	5.34405i	0.0589708	+	0.181493i
$868$	10.5498	+	18.2727i	0.358082	+	0.620217i
$869$	21.6514	+	23.3114i	0.734474	+	0.790786i
$870$	7.49471	+	12.9812i	0.254095	+	0.440105i
$871$	−2.11823	−	0.450245i	−0.0717736	−	0.0152560i
$872$	13.9082	−	6.19235i	0.470992	−	0.209699i
$873$	−21.1177	+	15.3429i	−0.714725	+	0.519278i
$874$	−25.6649	+	12.5711i	−0.868128	+	0.425222i
$875$	20.9161	−	64.3731i	0.707093	−	2.17621i
$876$	1.03886	+	9.88413i	0.0351000	+	0.333954i
$877$	−50.6070	+	22.5317i	−1.70888	+	0.760841i	−0.710512	+	0.703685i	$0.751536\pi$
$877$	−50.6070	+	22.5317i	−1.70888	+	0.760841i	−0.998365	+	0.0571555i	$0.981797\pi$
$878$	12.7921	−	14.2071i	0.431713	−	0.479466i
$879$	6.92297	−	11.9909i	0.233506	−	0.404444i
$880$	−9.07709	+	10.4000i	−0.305989	+	0.350584i
$881$	−26.4871			−0.892373			−0.446187	−	0.894940i	$-0.647218\pi$
$881$	−26.4871			−0.892373			−0.446187	+	0.894940i	$0.647218\pi$
$882$	−1.55277	−	4.77893i	−0.0522844	−	0.160915i
$883$	0.381487	−	3.62961i	0.0128381	−	0.122146i	−0.986226	−	0.165404i	$-0.947107\pi$
$883$	0.381487	−	3.62961i	0.0128381	−	0.122146i	0.999064	+	0.0432581i	$0.0137738\pi$
$884$	−15.0856	−	6.71655i	−0.507385	−	0.225902i
$885$	−6.53938	+	20.1261i	−0.219819	+	0.676533i
$886$	−10.7353	+	33.0398i	−0.360658	+	1.10999i
$887$	−24.0602	−	10.7123i	−0.807861	−	0.359683i	−0.0391132	−	0.999235i	$-0.512453\pi$
$887$	−24.0602	−	10.7123i	−0.807861	−	0.359683i	−0.768748	+	0.639552i	$0.779120\pi$
$888$	−1.32905	+	0.591731i	−0.0446000	+	0.0198572i
$889$	12.9915	−	14.4285i	0.435719	−	0.483915i
$890$	0.265948	−	0.460635i	0.00891459	−	0.0154405i
$891$	−6.76127	+	12.1404i	−0.226511	+	0.406720i
$892$	−15.3180			−0.512885
$893$	9.41067	−	0.344467i	0.314916	−	0.0115271i
$894$	−13.1543	−	9.55716i	−0.439946	−	0.319639i
$895$	8.53702	+	81.2243i	0.285361	+	2.71503i
$896$	1.48595	+	1.65032i	0.0496422	+	0.0551333i
$897$	25.8711	−	5.49906i	0.863810	−	0.183608i
$898$	−0.467769	−	4.45052i	−0.0156096	−	0.148516i
$899$	−4.73483	+	45.0489i	−0.157915	+	1.50247i
$900$	−9.25108	−	28.4719i	−0.308369	−	0.949063i
$901$	10.9495			0.364780
$902$	−17.7069	−	7.55789i	−0.589576	−	0.251650i
$903$	0.290089	+	0.502450i	0.00965357	+	0.0167205i
$904$	−2.22859	−	6.85891i	−0.0741219	−	0.228124i
$905$	57.8432	+	42.0255i	1.92277	+	1.39698i
$906$	−5.27957	−	2.35062i	−0.175402	−	0.0780940i
$907$	4.77830	+	5.30684i	0.158661	+	0.176211i	0.817234	−	0.576306i	$-0.195506\pi$
$907$	4.77830	+	5.30684i	0.158661	+	0.176211i	−0.658573	+	0.752517i	$0.728840\pi$
$908$	27.7025	−	5.88834i	0.919338	−	0.195411i
$909$	3.92866	+	37.3787i	0.130305	+	1.23977i
$910$	−45.0927	+	20.0766i	−1.49481	+	0.665531i
$911$	14.3326	+	44.1111i	0.474859	+	1.46147i	0.846148	+	0.532948i	$0.178916\pi$
$911$	14.3326	+	44.1111i	0.474859	+	1.46147i	−0.371289	+	0.928517i	$0.621084\pi$
$912$	−0.902281	+	3.16671i	−0.0298775	+	0.104860i
$913$	19.0086	−	14.2646i	0.629092	−	0.472089i
$914$	2.21910	−	3.84360i	0.0734014	−	0.127135i
$915$	4.58408	+	0.974376i	0.151545	+	0.0322119i
$916$	2.68473	−	25.5435i	0.0887061	−	0.843982i
$917$	−0.562340	−	5.35031i	−0.0185701	−	0.176683i
$918$	−12.4050	+	2.63677i	−0.409427	+	0.0870264i
$919$	15.8711	−	48.8464i	0.523541	−	1.61129i	−0.243643	−	0.969865i	$-0.578342\pi$
$919$	15.8711	−	48.8464i	0.523541	−	1.61129i	0.767184	−	0.641428i	$-0.221658\pi$
$920$	−22.0764	+	16.0395i	−0.727839	+	0.528806i
$921$	−0.443787	+	4.22235i	−0.0146233	+	0.139131i
$922$	0.0134693	−	0.0149591i	0.000443587	−	0.000492653i
$923$	15.5499			0.511831
$924$	5.56314	−	0.0859972i	0.183014	−	0.00282910i
$925$	11.8664	+	20.5531i	0.390164	+	0.675783i
$926$	12.3965	+	2.63495i	0.407373	+	0.0865897i
$927$	−1.82895	+	17.4013i	−0.0600706	+	0.571533i
$928$	0.498341	+	4.74139i	0.0163588	+	0.155644i
$929$	−11.7412	−	13.0400i	−0.385218	−	0.427828i	0.519083	−	0.854724i	$-0.326274\pi$
$929$	−11.7412	−	13.0400i	−0.385218	−	0.427828i	−0.904301	+	0.426896i	$0.859607\pi$
$930$	−9.23111	+	28.4104i	−0.302700	+	0.931615i
$931$	8.88155	+	1.55067i	0.291081	+	0.0508211i
$932$	−2.15121	−	1.56294i	−0.0704651	−	0.0511959i
$933$	20.9962	+	4.46288i	0.687384	+	0.146108i
$934$	11.6800	−	20.2303i	0.382180	−	0.661955i
$935$	28.0679	−	32.1586i	0.917920	−	1.05170i
$936$	−6.48681	+	11.2355i	−0.212028	+	0.367243i
$937$	22.5495	−	25.0438i	0.736661	−	0.818145i	−0.252092	−	0.967703i	$-0.581119\pi$
$937$	22.5495	−	25.0438i	0.736661	−	0.818145i	0.988753	+	0.149559i	$0.0477852\pi$
$938$	−0.728538	−	0.529314i	−0.0237876	−	0.0172827i
$939$	−8.66025	+	6.29204i	−0.282616	+	0.205333i
$940$	8.79530	−	1.86950i	0.286871	−	0.0609763i
$941$	−32.1407	+	6.83173i	−1.04776	+	0.222708i	−0.699457	−	0.714675i	$-0.746575\pi$
$941$	−32.1407	+	6.83173i	−1.04776	+	0.222708i	−0.348301	+	0.937383i	$0.613241\pi$
$942$	−0.338336	+	0.245816i	−0.0110236	+	0.00800911i
$943$	−30.7898	−	22.3701i	−1.00265	−	0.728470i
$944$	−4.50372	+	5.00189i	−0.146584	+	0.162798i
$945$	−18.9542	+	32.8297i	−0.616581	+	1.06795i
$946$	−1.11816	+	0.255799i	−0.0363547	+	0.00831674i
$947$	−11.2681	+	19.5169i	−0.366164	+	0.634215i	−0.988962	−	0.148168i	$-0.952663\pi$
$947$	−11.2681	+	19.5169i	−0.366164	+	0.634215i	0.622798	+	0.782383i	$0.285996\pi$
$948$	7.08800	+	1.50660i	0.230207	+	0.0489321i
$949$	−56.8421	−	41.2982i	−1.84517	−	1.34060i
$950$	52.9145	+	9.23856i	1.71677	+	0.299738i
$951$	4.23531	−	13.0349i	0.137339	−	0.422687i
$952$	−4.59483	−	5.10307i	−0.148919	−	0.165392i
$953$	0.157480	+	1.49832i	0.00510127	+	0.0485353i	0.996776	−	0.0802297i	$-0.0255654\pi$
$953$	0.157480	+	1.49832i	0.00510127	+	0.0485353i	−0.991675	+	0.128765i	$0.958899\pi$
$954$	0.899200	−	8.55532i	0.0291127	−	0.276989i
$955$	100.871	+	21.4407i	3.26410	+	0.693805i
$956$	−7.55444	−	13.0847i	−0.244328	−	0.423189i
$957$	9.77069	+	6.87062i	0.315842	+	0.222096i
$958$	3.03298			0.0979913
$959$	25.4981	−	28.3185i	0.823376	−	0.914451i
$960$	−0.328646	+	3.12685i	−0.0106070	+	0.100919i
$961$	−47.9526	+	34.8396i	−1.54686	+	1.12386i
$962$	3.17820	−	9.78150i	0.102469	−	0.315368i
$963$	−7.24161	+	1.53925i	−0.233358	+	0.0496017i
$964$	−0.227020	−	2.15996i	−0.00731184	−	0.0695675i
$965$	−6.58629	+	62.6643i	−0.212020	+	2.01724i
$966$	10.7582	+	2.28672i	0.346139	+	0.0735742i
$967$	−16.5341	+	28.6379i	−0.531701	+	0.920934i	0.467614	+	0.883933i	$0.345114\pi$
$967$	−16.5341	+	28.6379i	−0.531701	+	0.920934i	−0.999315	+	0.0370009i	$0.988220\pi$
$968$	−3.07420	+	10.5617i	−0.0988085	+	0.339466i
$969$	2.79001	−	9.79202i	0.0896281	−	0.314565i
$970$	−13.8195	−	42.5319i	−0.443716	−	1.36562i
$971$	15.7828	−	7.02693i	0.506493	−	0.225505i	−0.137550	−	0.990495i	$-0.543923\pi$
$971$	15.7828	−	7.02693i	0.506493	−	0.225505i	0.644042	+	0.764990i	$0.277256\pi$
$972$	1.61697	+	15.3844i	0.0518644	+	0.493456i
$973$	−8.01405	+	1.70344i	−0.256919	+	0.0546097i
$974$	−4.85608	−	5.39323i	−0.155599	−	0.172810i
$975$	−45.4149	−	20.2200i	−1.45444	−	0.647559i
$976$	1.20590	+	0.876140i	0.0386000	+	0.0280445i
$977$	−12.9606	−	39.8887i	−0.414647	−	1.27615i	−0.912566	−	0.408928i	$-0.865903\pi$
$977$	−12.9606	−	39.8887i	−0.414647	−	1.27615i	0.497920	−	0.867223i	$-0.334097\pi$
$978$	−0.0456673	−	0.0790980i	−0.00146028	−	0.00252928i
$979$	0.0377836	−	0.422161i	0.00120757	−	0.0134923i
$980$	8.60884			0.274999
$981$	11.4292	+	35.1755i	0.364907	+	1.12307i
$982$	−1.46130	+	13.9034i	−0.0466320	+	0.443674i
$983$	4.44478	+	42.2893i	0.141766	+	1.34882i	0.801805	+	0.597586i	$0.203873\pi$
$983$	4.44478	+	42.2893i	0.141766	+	1.34882i	−0.660038	+	0.751232i	$0.729460\pi$
$984$	−4.28919	+	0.911695i	−0.136734	+	0.0290638i
$985$	−29.4748	−	32.7351i	−0.939145	−	1.04303i
$986$	−1.54096	−	14.6612i	−0.0490740	−	0.466908i
$987$	−2.93202	−	2.13024i	−0.0933273	−	0.0678063i
$988$	−12.3686	−	19.7201i	−0.393499	−	0.627381i
$989$	−2.26749			−0.0721021
$990$	−22.8219	−	24.5717i	−0.725328	−	0.780939i
$991$	−2.30296	+	3.98884i	−0.0731559	+	0.126710i	−0.900283	−	0.435305i	$-0.856640\pi$
$991$	−2.30296	+	3.98884i	−0.0731559	+	0.126710i	0.827127	+	0.562015i	$0.189974\pi$
$992$	−6.35754	+	7.06077i	−0.201852	+	0.224180i
$993$	18.2487	−	8.12483i	0.579104	−	0.257834i
$994$	5.90721	+	2.63006i	0.187365	+	0.0834204i
$995$	9.10143	−	28.0113i	0.288535	−	0.888018i
$996$	1.67269	−	5.14802i	0.0530013	−	0.163121i
$997$	−22.4963	−	10.0160i	−0.712463	−	0.317209i	0.0183070	−	0.999832i	$-0.494172\pi$
$997$	−22.4963	−	10.0160i	−0.712463	−	0.317209i	−0.730770	+	0.682623i	$0.760839\pi$
$998$	−0.0897583	+	0.853993i	−0.00284125	+	0.0270327i
$999$	−2.44085	−	7.51218i	−0.0772252	−	0.237675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.d.49.5	✓	64
11.9	even	5	inner	418.2.n.d.163.4	yes	64
19.7	even	3	inner	418.2.n.d.159.4	yes	64
209.64	even	15	inner	418.2.n.d.273.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.d.49.5	✓	64	1.1	even	1	trivial
418.2.n.d.159.4	yes	64	19.7	even	3	inner
418.2.n.d.163.4	yes	64	11.9	even	5	inner
418.2.n.d.273.5	yes	64	209.64	even	15	inner

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(-0.690099 + 0.307252i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.78499 - 3.09304i) q^{5} +(-0.738900 + 0.157058i) q^{6} +(1.79660 - 1.30531i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.62556 + 1.80537i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(-0.690099 + 0.307252i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.78499 - 3.09304i) q^{5} +(-0.738900 + 0.157058i) q^{6} +(1.79660 - 1.30531i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.62556 + 1.80537i) q^{9} +(-2.08105 - 3.60448i) q^{10} +(-2.71302 - 1.90776i) q^{11} -0.755407 q^{12} +(3.57339 - 3.96865i) q^{13} +(2.02873 - 0.903249i) q^{14} +(2.87226 + 1.27881i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-2.06907 - 2.29793i) q^{17} +(-1.96539 + 1.42794i) q^{18} +(-0.613896 - 4.31545i) q^{19} +(-1.28616 - 3.95839i) q^{20} +(-0.838775 + 1.45280i) q^{21} +(-2.25709 - 2.43014i) q^{22} +(-3.27816 - 5.67793i) q^{23} +(-0.738900 - 0.157058i) q^{24} +(-1.28811 + 12.2555i) q^{25} +(4.32043 - 3.13898i) q^{26} +(1.26740 - 3.90064i) q^{27} +(2.17219 - 0.461714i) q^{28} +(4.35534 + 1.93912i) q^{29} +(2.54361 + 1.84804i) q^{30} +(2.93603 + 9.03617i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.45841 + 0.482962i) q^{33} +(-1.54609 - 2.67790i) q^{34} +(-9.04088 - 1.92170i) q^{35} +(-2.21933 + 0.988110i) q^{36} +(1.55807 - 1.13201i) q^{37} +(0.296752 - 4.34879i) q^{38} +(-1.24662 + 3.83669i) q^{39} +(-0.435057 - 4.13930i) q^{40} +(5.30298 - 2.36104i) q^{41} +(-1.12250 + 1.24666i) q^{42} +(0.172924 - 0.299514i) q^{43} +(-1.70251 - 2.84631i) q^{44} +10.1112 q^{45} +(-2.02601 - 6.23542i) q^{46} +(-0.225823 + 2.14857i) q^{47} +(-0.690099 - 0.307252i) q^{48} +(-0.639168 + 1.96716i) q^{49} +(-3.80803 + 11.7199i) q^{50} +(2.13391 + 0.950076i) q^{51} +(4.87865 - 2.17211i) q^{52} +(-2.36941 + 2.63150i) q^{53} +(2.05069 - 3.55190i) q^{54} +(1.65495 + 13.7045i) q^{55} +2.22072 q^{56} +(1.74958 + 2.78947i) q^{57} +(3.85700 + 2.80227i) q^{58} +(0.703551 + 6.69384i) q^{59} +(2.10380 + 2.33650i) q^{60} +(1.45800 - 0.309909i) q^{61} +(0.993145 + 9.44915i) q^{62} +(-0.563924 + 5.36538i) q^{63} +(0.309017 + 0.951057i) q^{64} -22.2270 q^{65} +(2.30428 + 0.983540i) q^{66} +(-0.202754 - 0.351181i) q^{67} +(-0.955534 - 2.94083i) q^{68} +(4.00681 + 2.91111i) q^{69} +(-8.44377 - 3.75941i) q^{70} +(1.94836 + 2.16387i) q^{71} +(-2.37627 + 0.505092i) q^{72} +(-1.37524 - 13.0845i) q^{73} +(1.75938 - 0.783327i) q^{74} +(-2.87661 - 8.85330i) q^{75} +(1.19443 - 4.19206i) q^{76} +(-7.36442 + 0.113842i) q^{77} +(-2.01707 + 3.49366i) q^{78} +(-9.38302 - 1.99442i) q^{79} +(0.435057 - 4.13930i) q^{80} +(-0.437961 - 4.16692i) q^{81} +(5.67798 - 1.20689i) q^{82} +(-2.21429 + 6.81490i) q^{83} +(-1.35717 + 0.986039i) q^{84} +(-1.34527 + 12.7994i) q^{85} +(0.231418 - 0.257016i) q^{86} -3.60141 q^{87} +(-1.07353 - 3.13808i) q^{88} +(0.0638976 + 0.110674i) q^{89} +(9.89027 + 2.10224i) q^{90} +(1.23965 - 11.7945i) q^{91} +(-0.685321 - 6.52039i) q^{92} +(-4.80253 - 5.33375i) q^{93} +(-0.667601 + 2.05466i) q^{94} +(-11.6382 + 13.9173i) q^{95} +(-0.611137 - 0.444017i) q^{96} +(10.5100 + 2.23396i) q^{97} +(-1.03419 + 1.79128i) q^{98} +(7.85437 - 1.79682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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