LMFDB - Embedded newform 121.2.e.a.23.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,2,Mod(12,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([18]))

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

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

chi := DirichletCharacter("121.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	121.e (of order $11$, degree $10$, 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:	$0.966189864457$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			23.7
Character	$\chi$	$=$	121.23
Dual form			121.2.e.a.100.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.333827 - 0.730979i) q^{2} +0.0294246 q^{3} +(0.886832 + 1.02346i) q^{4} +(0.779896 + 0.228998i) q^{5} +(0.00982271 - 0.0215087i) q^{6} +(0.0964221 + 0.670630i) q^{7} +(2.58627 - 0.759397i) q^{8} -2.99913 q^{9} +O(q^{10})$	\(q+(0.333827 - 0.730979i) q^{2} +0.0294246 q^{3} +(0.886832 + 1.02346i) q^{4} +(0.779896 + 0.228998i) q^{5} +(0.00982271 - 0.0215087i) q^{6} +(0.0964221 + 0.670630i) q^{7} +(2.58627 - 0.759397i) q^{8} -2.99913 q^{9} +(0.427743 - 0.493642i) q^{10} +(0.219276 - 3.30937i) q^{11} +(0.0260947 + 0.0301148i) q^{12} +(0.295853 + 0.341432i) q^{13} +(0.522405 + 0.153392i) q^{14} +(0.0229481 + 0.00673818i) q^{15} +(-0.0771914 + 0.536878i) q^{16} +(-4.29650 - 2.76119i) q^{17} +(-1.00119 + 2.19230i) q^{18} +(-0.330107 + 0.212147i) q^{19} +(0.457267 + 1.00127i) q^{20} +(0.00283718 + 0.0197330i) q^{21} +(-2.34588 - 1.26504i) q^{22} +(-0.883277 + 6.14333i) q^{23} +(0.0760999 - 0.0223449i) q^{24} +(-3.65047 - 2.34601i) q^{25} +(0.348343 - 0.102283i) q^{26} -0.176522 q^{27} +(-0.600852 + 0.693421i) q^{28} +(3.92166 - 2.52030i) q^{29} +(0.0125862 - 0.0145252i) q^{30} +(-5.66785 + 6.54105i) q^{31} +(4.90180 + 3.15019i) q^{32} +(0.00645211 - 0.0973768i) q^{33} +(-3.45266 + 2.21889i) q^{34} +(-0.0783739 + 0.545103i) q^{35} +(-2.65973 - 3.06949i) q^{36} +(-2.06499 + 2.38312i) q^{37} +(0.0448763 + 0.312121i) q^{38} +(0.00870535 + 0.0100465i) q^{39} +2.19092 q^{40} +(3.53512 - 7.74082i) q^{41} +(0.0153715 + 0.00451349i) q^{42} +(0.845214 - 0.248177i) q^{43} +(3.58146 - 2.71043i) q^{44} +(-2.33901 - 0.686796i) q^{45} +(4.19578 + 2.69646i) q^{46} +(-1.67980 - 3.67826i) q^{47} +(-0.00227133 + 0.0157974i) q^{48} +(6.27600 - 1.84280i) q^{49} +(-2.93351 + 1.88525i) q^{50} +(-0.126423 - 0.0812470i) q^{51} +(-0.0870702 + 0.605586i) q^{52} +(-0.438597 - 3.05051i) q^{53} +(-0.0589278 + 0.129034i) q^{54} +(0.928852 - 2.53075i) q^{55} +(0.758648 + 1.66121i) q^{56} +(-0.00971326 + 0.00624233i) q^{57} +(-0.533129 - 3.70799i) q^{58} +(3.61444 + 7.91452i) q^{59} +(0.0134549 + 0.0294621i) q^{60} +(-2.93172 - 6.41957i) q^{61} +(2.88929 + 6.32665i) q^{62} +(-0.289183 - 2.01131i) q^{63} +(3.02648 - 1.94500i) q^{64} +(0.152547 + 0.334032i) q^{65} +(-0.0690264 - 0.0372233i) q^{66} +(-1.05158 + 2.30263i) q^{67} +(-0.984307 - 6.84601i) q^{68} +(-0.0259901 + 0.180765i) q^{69} +(0.372295 + 0.239260i) q^{70} +(10.6095 - 6.81833i) q^{71} +(-7.75657 + 2.27753i) q^{72} +(-0.780694 + 5.42985i) q^{73} +(1.05266 + 2.30501i) q^{74} +(-0.107414 - 0.0690305i) q^{75} +(-0.509873 - 0.149712i) q^{76} +(2.24051 - 0.172043i) q^{77} +(0.0102499 - 0.00300963i) q^{78} +(13.2963 + 3.90413i) q^{79} +(-0.183145 + 0.401033i) q^{80} +8.99221 q^{81} +(-4.47826 - 5.16819i) q^{82} +(1.16440 + 8.09855i) q^{83} +(-0.0176798 + 0.0204036i) q^{84} +(-2.71852 - 3.13734i) q^{85} +(0.100743 - 0.700682i) q^{86} +(0.115393 - 0.0741587i) q^{87} +(-1.94602 - 8.72543i) q^{88} +(0.399545 + 0.256772i) q^{89} +(-1.28286 + 1.48050i) q^{90} +(-0.200448 + 0.231330i) q^{91} +(-7.07076 + 4.54410i) q^{92} +(-0.166774 + 0.192468i) q^{93} -3.24949 q^{94} +(-0.306030 + 0.0898586i) q^{95} +(0.144233 + 0.0926931i) q^{96} +(-11.6531 + 3.42164i) q^{97} +(0.748050 - 5.20280i) q^{98} +(-0.657639 + 9.92524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9}+O(q^{10}) $ 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9	\( 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9} - 13 q^{10} - 12 q^{11} - 51 q^{12} - 34 q^{13} - 17 q^{14} - 46 q^{15} + 10 q^{16} + 9 q^{17} - 31 q^{18} + 9 q^{19} + 21 q^{20} - 14 q^{21} - 20 q^{22} - 11 q^{23} - 72 q^{24} + 11 q^{25} + 33 q^{26} - 60 q^{27} + 49 q^{28} + 19 q^{29} + 26 q^{30} - 13 q^{31} + 44 q^{32} + q^{33} + 31 q^{34} + 39 q^{35} - 17 q^{36} - 16 q^{37} - 29 q^{38} + 16 q^{39} + 2 q^{40} + 39 q^{41} + 42 q^{42} + 39 q^{43} + 53 q^{44} - 33 q^{45} + 59 q^{46} + 21 q^{47} + 56 q^{48} - 11 q^{49} - 58 q^{50} - 139 q^{51} - 75 q^{52} - 73 q^{53} - 156 q^{54} - 34 q^{55} + 10 q^{56} - 41 q^{57} - 38 q^{58} + 33 q^{59} + 100 q^{60} + 39 q^{61} + 44 q^{62} - 76 q^{63} - 16 q^{64} + 36 q^{65} + 75 q^{66} - 4 q^{67} + 119 q^{68} + 32 q^{69} + 61 q^{70} + 5 q^{71} + 63 q^{72} + 37 q^{73} + 109 q^{74} + 58 q^{75} - 91 q^{76} - 53 q^{77} - 24 q^{78} - 9 q^{79} - 36 q^{80} + 28 q^{81} + 33 q^{82} + 79 q^{83} + 176 q^{84} - 11 q^{85} + 85 q^{86} + 76 q^{87} + 33 q^{88} - 48 q^{89} - 89 q^{90} - 14 q^{91} - 113 q^{92} + 31 q^{93} - 38 q^{94} + 21 q^{95} + 84 q^{96} + 40 q^{97} - 22 q^{98} - 53 q^{99}+O(q^{100}) \) 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9 - 13 * q^10 - 12 * q^11 - 51 * q^12 - 34 * q^13 - 17 * q^14 - 46 * q^15 + 10 * q^16 + 9 * q^17 - 31 * q^18 + 9 * q^19 + 21 * q^20 - 14 * q^21 - 20 * q^22 - 11 * q^23 - 72 * q^24 + 11 * q^25 + 33 * q^26 - 60 * q^27 + 49 * q^28 + 19 * q^29 + 26 * q^30 - 13 * q^31 + 44 * q^32 + q^33 + 31 * q^34 + 39 * q^35 - 17 * q^36 - 16 * q^37 - 29 * q^38 + 16 * q^39 + 2 * q^40 + 39 * q^41 + 42 * q^42 + 39 * q^43 + 53 * q^44 - 33 * q^45 + 59 * q^46 + 21 * q^47 + 56 * q^48 - 11 * q^49 - 58 * q^50 - 139 * q^51 - 75 * q^52 - 73 * q^53 - 156 * q^54 - 34 * q^55 + 10 * q^56 - 41 * q^57 - 38 * q^58 + 33 * q^59 + 100 * q^60 + 39 * q^61 + 44 * q^62 - 76 * q^63 - 16 * q^64 + 36 * q^65 + 75 * q^66 - 4 * q^67 + 119 * q^68 + 32 * q^69 + 61 * q^70 + 5 * q^71 + 63 * q^72 + 37 * q^73 + 109 * q^74 + 58 * q^75 - 91 * q^76 - 53 * q^77 - 24 * q^78 - 9 * q^79 - 36 * q^80 + 28 * q^81 + 33 * q^82 + 79 * q^83 + 176 * q^84 - 11 * q^85 + 85 * q^86 + 76 * q^87 + 33 * q^88 - 48 * q^89 - 89 * q^90 - 14 * q^91 - 113 * q^92 + 31 * q^93 - 38 * q^94 + 21 * q^95 + 84 * q^96 + 40 * q^97 - 22 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.333827	−	0.730979i	0.236051	−	0.516880i	−0.754121	−	0.656736i	$-0.771937\pi$
$2$	0.333827	−	0.730979i	0.236051	−	0.516880i	0.990172	+	0.139856i	$0.0446639\pi$
$3$	0.0294246			0.0169883			0.00849414	−	0.999964i	$-0.497296\pi$
$3$	0.0294246			0.0169883			0.00849414	+	0.999964i	$0.497296\pi$
$4$	0.886832	+	1.02346i	0.443416	+	0.511729i
$5$	0.779896	+	0.228998i	0.348780	+	0.102411i	0.451430	−	0.892306i	$-0.350914\pi$
$5$	0.779896	+	0.228998i	0.348780	+	0.102411i	−0.102650	+	0.994718i	$0.532732\pi$
$6$	0.00982271	−	0.0215087i	0.00401011	−	0.00878091i
$7$	0.0964221	+	0.670630i	0.0364441	+	0.253474i	0.999896	−	0.0144062i	$-0.00458580\pi$
$7$	0.0964221	+	0.670630i	0.0364441	+	0.253474i	−0.963452	+	0.267881i	$0.913677\pi$
$8$	2.58627	−	0.759397i	0.914384	−	0.268487i
$9$	−2.99913			−0.999711
$10$	0.427743	−	0.493642i	0.135264	−	0.156103i
$11$	0.219276	−	3.30937i	0.0661143	−	0.997812i
$11$	0.219276	−	3.30937i	0.0661143	−	0.997812i
$12$	0.0260947	+	0.0301148i	0.00753288	+	0.00869341i
$13$	0.295853	+	0.341432i	0.0820548	+	0.0946963i	0.795292	−	0.606226i	$-0.207317\pi$
$13$	0.295853	+	0.341432i	0.0820548	+	0.0946963i	−0.713238	+	0.700922i	$0.752772\pi$
$14$	0.522405	+	0.153392i	0.139619	+	0.0409957i
$15$	0.0229481	+	0.00673818i	0.00592518	+	0.00173979i
$16$	−0.0771914	+	0.536878i	−0.0192979	+	0.134220i
$17$	−4.29650	−	2.76119i	−1.04205	−	0.669688i	−0.0965606	−	0.995327i	$-0.530784\pi$
$17$	−4.29650	−	2.76119i	−1.04205	−	0.669688i	−0.945494	+	0.325639i	$0.894421\pi$
$18$	−1.00119	+	2.19230i	−0.235983	+	0.516731i
$19$	−0.330107	+	0.212147i	−0.0757317	+	0.0486698i	−0.577959	−	0.816066i	$-0.696151\pi$
$19$	−0.330107	+	0.212147i	−0.0757317	+	0.0486698i	0.502227	+	0.864736i	$0.332514\pi$
$20$	0.457267	+	1.00127i	0.102248	+	0.223892i
$21$	0.00283718	+	0.0197330i	0.000619123	+	0.00430610i
$22$	−2.34588	−	1.26504i	−0.500143	−	0.269708i
$23$	−0.883277	+	6.14333i	−0.184176	+	1.28097i	0.662580	+	0.748991i	$0.269461\pi$
$23$	−0.883277	+	6.14333i	−0.184176	+	1.28097i	−0.846756	+	0.531981i	$0.821448\pi$
$24$	0.0760999	−	0.0223449i	0.0155338	−	0.00456114i
$25$	−3.65047	−	2.34601i	−0.730094	−	0.469203i
$26$	0.348343	−	0.102283i	0.0683158	−	0.0200593i
$27$	−0.176522			−0.0339717
$28$	−0.600852	+	0.693421i	−0.113550	+	0.131044i
$29$	3.92166	−	2.52030i	0.728234	−	0.468008i	−0.123258	−	0.992375i	$-0.539334\pi$
$29$	3.92166	−	2.52030i	0.728234	−	0.468008i	0.851492	+	0.524367i	$0.175698\pi$
$30$	0.0125862	−	0.0145252i	0.00229791	−	0.00265193i
$31$	−5.66785	+	6.54105i	−1.01798	+	1.17481i	−0.0334724	+	0.999440i	$0.510657\pi$
$31$	−5.66785	+	6.54105i	−1.01798	+	1.17481i	−0.984503	+	0.175367i	$0.943889\pi$
$32$	4.90180	+	3.15019i	0.866523	+	0.556881i
$33$	0.00645211	−	0.0973768i	0.00112317	−	0.0169511i
$34$	−3.45266	+	2.21889i	−0.592126	+	0.380537i
$35$	−0.0783739	+	0.545103i	−0.0132476	+	0.0921392i
$36$	−2.65973	−	3.06949i	−0.443288	−	0.511582i
$37$	−2.06499	+	2.38312i	−0.339482	+	0.391783i	−0.899661	−	0.436588i	$-0.856187\pi$
$37$	−2.06499	+	2.38312i	−0.339482	+	0.391783i	0.560180	+	0.828371i	$0.310732\pi$
$38$	0.0448763	+	0.312121i	0.00727989	+	0.0506328i
$39$	0.00870535	+	0.0100465i	0.00139397	+	0.00160873i
$40$	2.19092			0.346415
$41$	3.53512	−	7.74082i	0.552092	−	1.20891i	−0.403706	−	0.914889i	$-0.632278\pi$
$41$	3.53512	−	7.74082i	0.552092	−	1.20891i	0.955798	−	0.294025i	$-0.0949948\pi$
$42$	0.0153715	+	0.00451349i	0.00237188	+	0.000696447i
$43$	0.845214	−	0.248177i	0.128894	−	0.0378467i	−0.216649	−	0.976249i	$-0.569513\pi$
$43$	0.845214	−	0.248177i	0.128894	−	0.0378467i	0.345543	+	0.938403i	$0.387695\pi$
$44$	3.58146	−	2.71043i	0.539926	−	0.408613i
$45$	−2.33901	−	0.686796i	−0.348680	−	0.102382i
$46$	4.19578	+	2.69646i	0.618634	+	0.397572i
$47$	−1.67980	−	3.67826i	−0.245024	−	0.536529i	0.746662	−	0.665203i	$-0.231655\pi$
$47$	−1.67980	−	3.67826i	−0.245024	−	0.536529i	−0.991687	+	0.128674i	$0.958928\pi$
$48$	−0.00227133	+	0.0157974i	−0.000327838	+	0.00228016i
$49$	6.27600	−	1.84280i	0.896572	−	0.263257i
$50$	−2.93351	+	1.88525i	−0.414861	+	0.266615i
$51$	−0.126423	−	0.0812470i	−0.0177027	−	0.0113769i
$52$	−0.0870702	+	0.605586i	−0.0120745	+	0.0839797i
$53$	−0.438597	−	3.05051i	−0.0602460	−	0.419020i	−0.997517	−	0.0704197i	$-0.977566\pi$
$53$	−0.438597	−	3.05051i	−0.0602460	−	0.419020i	0.937271	−	0.348600i	$-0.113343\pi$
$54$	−0.0589278	+	0.129034i	−0.00801905	+	0.0175593i
$55$	0.928852	−	2.53075i	0.125246	−	0.341246i
$56$	0.758648	+	1.66121i	0.101379	+	0.221988i
$57$	−0.00971326	+	0.00624233i	−0.00128655	+	0.000826817i
$58$	−0.533129	−	3.70799i	−0.0700033	−	0.486883i
$59$	3.61444	+	7.91452i	0.470560	+	1.03038i	0.984952	+	0.172828i	$0.0552904\pi$
$59$	3.61444	+	7.91452i	0.470560	+	1.03038i	−0.514392	+	0.857555i	$0.671982\pi$
$60$	0.0134549	+	0.0294621i	0.00173702	+	0.00380354i
$61$	−2.93172	−	6.41957i	−0.375368	−	0.821942i	−0.999185	−	0.0403710i	$-0.987146\pi$
$61$	−2.93172	−	6.41957i	−0.375368	−	0.821942i	0.623816	−	0.781571i	$-0.285581\pi$
$62$	2.88929	+	6.32665i	0.366940	+	0.803486i
$63$	−0.289183	−	2.01131i	−0.0364336	−	0.253401i
$64$	3.02648	−	1.94500i	0.378311	−	0.243125i
$65$	0.152547	+	0.334032i	0.0189211	+	0.0414315i
$66$	−0.0690264	−	0.0372233i	−0.00849657	−	0.00458187i
$67$	−1.05158	+	2.30263i	−0.128471	+	0.281311i	−0.962927	−	0.269763i	$-0.913055\pi$
$67$	−1.05158	+	2.30263i	−0.128471	+	0.281311i	0.834456	+	0.551074i	$0.185782\pi$
$68$	−0.984307	−	6.84601i	−0.119365	−	0.830200i
$69$	−0.0259901	+	0.180765i	−0.00312883	+	0.0217615i
$70$	0.372295	+	0.239260i	0.0444978	+	0.0285970i
$71$	10.6095	−	6.81833i	1.25912	−	0.809187i	0.270957	−	0.962592i	$-0.412660\pi$
$71$	10.6095	−	6.81833i	1.25912	−	0.809187i	0.988164	+	0.153404i	$0.0490236\pi$
$72$	−7.75657	+	2.27753i	−0.914120	+	0.268410i
$73$	−0.780694	+	5.42985i	−0.0913733	+	0.635515i	0.891744	+	0.452540i	$0.149482\pi$
$73$	−0.780694	+	5.42985i	−0.0913733	+	0.635515i	−0.983117	+	0.182975i	$0.941427\pi$
$74$	1.05266	+	2.30501i	0.122370	+	0.267952i
$75$	−0.107414	−	0.0690305i	−0.0124030	−	0.00797095i
$76$	−0.509873	−	0.149712i	−0.0584864	−	0.0171732i
$77$	2.24051	−	0.172043i	0.255329	−	0.0196061i
$78$	0.0102499	−	0.00300963i	0.00116057	−	0.000340773i
$79$	13.2963	+	3.90413i	1.49595	+	0.439249i	0.924433	−	0.381344i	$-0.124539\pi$
$79$	13.2963	+	3.90413i	1.49595	+	0.439249i	0.571513	+	0.820593i	$0.306357\pi$
$80$	−0.183145	+	0.401033i	−0.0204763	+	0.0448368i
$81$	8.99221			0.999134
$82$	−4.47826	−	5.16819i	−0.494541	−	0.570731i
$83$	1.16440	+	8.09855i	0.127809	+	0.888931i	0.948323	+	0.317305i	$0.102778\pi$
$83$	1.16440	+	8.09855i	0.127809	+	0.888931i	−0.820514	+	0.571626i	$0.806313\pi$
$84$	−0.0176798	+	0.0204036i	−0.00192903	+	0.00222622i
$85$	−2.71852	−	3.13734i	−0.294865	−	0.340292i
$86$	0.100743	−	0.700682i	0.0108634	−	0.0755564i
$87$	0.115393	−	0.0741587i	0.0123715	−	0.00795065i
$88$	−1.94602	−	8.72543i	−0.207446	−	0.930134i
$89$	0.399545	+	0.256772i	0.0423517	+	0.0272178i	0.561645	−	0.827378i	$-0.310169\pi$
$89$	0.399545	+	0.256772i	0.0423517	+	0.0272178i	−0.519294	+	0.854596i	$0.673805\pi$
$90$	−1.28286	+	1.48050i	−0.135225	+	0.156058i
$91$	−0.200448	+	0.231330i	−0.0210127	+	0.0242499i
$92$	−7.07076	+	4.54410i	−0.737178	+	0.473755i
$93$	−0.166774	+	0.192468i	−0.0172937	+	0.0199580i
$94$	−3.24949			−0.335159
$95$	−0.306030	+	0.0898586i	−0.0313981	+	0.00921930i
$96$	0.144233	+	0.0926931i	0.0147208	+	0.00946045i
$97$	−11.6531	+	3.42164i	−1.18319	+	0.347415i	−0.813402	−	0.581702i	$-0.802387\pi$
$97$	−11.6531	+	3.42164i	−1.18319	+	0.347415i	−0.369786	+	0.929117i	$0.620569\pi$
$98$	0.748050	−	5.20280i	0.0755644	−	0.525562i
$99$	−0.657639	+	9.92524i	−0.0660952	+	0.997524i
$100$	−0.836305	−	5.81663i	−0.0836305	−	0.581663i
$101$	−0.697610	−	1.52755i	−0.0694148	−	0.151997i	0.871744	−	0.489961i	$-0.162989\pi$
$101$	−0.697610	−	1.52755i	−0.0694148	−	0.151997i	−0.941159	+	0.337964i	$0.890262\pi$
$102$	−0.101593	+	0.0652899i	−0.0100592	+	0.00646467i
$103$	−4.45769	+	9.76098i	−0.439229	+	0.961778i	0.552510	+	0.833507i	$0.313670\pi$
$103$	−4.45769	+	9.76098i	−0.439229	+	0.961778i	−0.991739	+	0.128272i	$0.959057\pi$
$104$	1.02444	+	0.658366i	0.100454	+	0.0645581i
$105$	−0.00230612	+	0.0160394i	−0.000225054	+	0.00156529i
$106$	−2.37627	−	0.697737i	−0.230804	−	0.0677702i
$107$	−9.78590	−	2.87340i	−0.946038	−	0.277782i	−0.227902	−	0.973684i	$-0.573187\pi$
$107$	−9.78590	−	2.87340i	−0.946038	−	0.277782i	−0.718137	+	0.695902i	$0.755005\pi$
$108$	−0.156545	−	0.180663i	−0.0150636	−	0.0173843i
$109$	7.84283	+	9.05111i	0.751207	+	0.866939i	0.994685	−	0.102967i	$-0.0328337\pi$
$109$	7.84283	+	9.05111i	0.751207	+	0.866939i	−0.243478	+	0.969907i	$0.578288\pi$
$110$	−1.53985	−	1.52380i	−0.146819	−	0.145289i
$111$	−0.0607613	+	0.0701223i	−0.00576721	+	0.00665572i
$112$	−0.367490			−0.0347245
$113$	3.09074	−	0.907522i	0.290752	−	0.0853725i	−0.133104	−	0.991102i	$-0.542494\pi$
$113$	3.09074	−	0.907522i	0.290752	−	0.0853725i	0.423856	+	0.905730i	$0.360676\pi$
$114$	0.00132047	+	0.00918404i	0.000123673	+	0.000860164i
$115$	−2.09567	+	4.58889i	−0.195423	+	0.427916i
$116$	6.05728	+	1.77858i	0.562404	+	0.165137i
$117$	−0.887302	−	1.02400i	−0.0820311	−	0.0946690i
$118$	6.99194			0.643661
$119$	1.43746	−	3.14760i	0.131772	−	0.288540i
$120$	0.0644670			0.00588500
$121$	−10.9038	−	1.45133i	−0.991258	−	0.131939i
$122$	−5.67126			−0.513451
$123$	0.104019	−	0.227770i	0.00937910	−	0.0205374i
$124$	−11.7209			−1.05257
$125$	−4.97118	−	5.73705i	−0.444636	−	0.513137i
$126$	−1.56676	−	0.460043i	−0.139578	−	0.0409839i
$127$	4.45831	−	9.76234i	0.395611	−	0.866268i	−0.602085	−	0.798432i	$-0.705663\pi$
$127$	4.45831	−	9.76234i	0.395611	−	0.866268i	0.997696	−	0.0678359i	$-0.0216094\pi$
$128$	1.24704	+	8.67335i	0.110224	+	0.766623i
$129$	0.0248701	−	0.00730251i	0.00218969	−	0.000642950i
$130$	0.295094			0.0258815
$131$	−9.66367	+	11.1525i	−0.844319	+	0.974396i	−0.999910	−	0.0134260i	$-0.995726\pi$
$131$	−9.66367	+	11.1525i	−0.844319	+	0.974396i	0.155591	+	0.987822i	$0.450272\pi$
$132$	0.105383	−	0.0797534i	0.00917242	−	0.00694164i
$133$	−0.174102	−	0.200924i	−0.0150965	−	0.0174223i
$134$	1.33213	+	1.53736i	0.115079	+	0.132808i
$135$	−0.137669	−	0.0404232i	−0.0118486	−	0.00347908i
$136$	−13.2087	−	3.87844i	−1.13264	−	0.332573i
$137$	0.465301	−	3.23624i	0.0397533	−	0.276490i	−0.960243	−	0.279165i	$-0.909942\pi$
$137$	0.465301	−	3.23624i	0.0397533	−	0.276490i	0.999996	+	0.00267477i	$0.000851407\pi$
$138$	0.123459	+	0.0793423i	0.0105095	+	0.00675406i
$139$	4.10711	−	8.99333i	0.348361	−	0.762804i	−0.651630	−	0.758537i	$-0.725914\pi$
$139$	4.10711	−	8.99333i	0.348361	−	0.762804i	0.999991	−	0.00426699i	$-0.00135823\pi$
$140$	−0.627395	+	0.403202i	−0.0530245	+	0.0340768i
$141$	−0.0494275	−	0.108231i	−0.00416255	−	0.00911470i
$142$	−1.44231	−	10.0315i	−0.121036	−	0.841824i
$143$	1.19480	−	0.904218i	0.0999141	−	0.0756145i
$144$	0.231507	−	1.61017i	0.0192923	−	0.134181i
$145$	3.63563	−	1.06752i	0.301923	−	0.0886526i
$146$	3.70848	+	2.38330i	0.306916	+	0.197243i
$147$	0.184669	−	0.0542236i	0.0152312	−	0.00447229i
$148$	−4.27032			−0.351018
$149$	2.75615	−	3.18076i	0.225792	−	0.260578i	−0.631538	−	0.775345i	$-0.717576\pi$
$149$	2.75615	−	3.18076i	0.225792	−	0.260578i	0.857330	+	0.514767i	$0.172121\pi$
$150$	−0.0863173	+	0.0554728i	−0.00704778	+	0.00452933i
$151$	−2.94390	+	3.39744i	−0.239571	+	0.276480i	−0.862784	−	0.505572i	$-0.831281\pi$
$151$	−2.94390	+	3.39744i	−0.239571	+	0.276480i	0.623213	+	0.782052i	$0.285827\pi$
$152$	−0.692641	+	0.799351i	−0.0561806	+	0.0648359i
$153$	12.8858	+	8.28119i	1.04175	+	0.669495i
$154$	0.622181	−	1.69519i	0.0501368	−	0.136603i
$155$	−5.91822	+	3.80341i	−0.475363	+	0.305497i
$156$	−0.00256200	+	0.0178191i	−0.000205124	+	0.00142667i
$157$	12.2971	+	14.1916i	0.981418	+	1.13262i	0.991161	+	0.132664i	$0.0423532\pi$
$157$	12.2971	+	14.1916i	0.981418	+	1.13262i	−0.00974308	+	0.999953i	$0.503101\pi$
$158$	7.29249	−	8.41598i	0.580159	−	0.669539i
$159$	−0.0129055	−	0.0897600i	−0.00102348	−	0.00711843i
$160$	3.10150	+	3.57933i	0.245195	+	0.282971i
$161$	−4.20507			−0.331406
$162$	3.00184	−	6.57311i	0.235847	−	0.516432i
$163$	15.4697	+	4.54231i	1.21168	+	0.355781i	0.824308	−	0.566142i	$-0.191565\pi$
$163$	15.4697	+	4.54231i	1.21168	+	0.355781i	0.387372	+	0.921923i	$0.373383\pi$
$164$	11.0575	−	3.24677i	0.863443	−	0.253530i
$165$	0.0273311	−	0.0744663i	0.00212772	−	0.00579719i
$166$	6.30857	+	1.85236i	0.489640	+	0.143771i
$167$	−3.23297	−	2.07770i	−0.250175	−	0.160778i	0.409544	−	0.912291i	$-0.365688\pi$
$167$	−3.23297	−	2.07770i	−0.250175	−	0.160778i	−0.659718	+	0.751513i	$0.729324\pi$
$168$	0.0223229	+	0.0488803i	0.00172225	+	0.00377120i
$169$	1.82105	−	12.6657i	0.140080	−	0.974281i
$170$	−3.20084	+	0.939851i	−0.245493	+	0.0720833i
$171$	0.990035	−	0.636257i	0.0757099	−	0.0486558i
$172$	1.00356	+	0.644950i	0.0765209	+	0.0491770i
$173$	1.19348	−	8.30082i	0.0907384	−	0.631099i	−0.892807	−	0.450439i	$-0.851267\pi$
$173$	1.19348	−	8.30082i	0.0907384	−	0.631099i	0.983546	−	0.180660i	$-0.0578235\pi$
$174$	−0.0156871	−	0.109106i	−0.00118924	−	0.00827132i
$175$	1.22132	−	2.67432i	0.0923233	−	0.202160i
$176$	1.75980	+	0.373179i	0.132650	+	0.0281295i
$177$	0.106353	+	0.232881i	0.00799401	+	0.0175044i
$178$	0.321074	−	0.206342i	0.0240655	−	0.0154660i
$179$	1.06277	+	7.39172i	0.0794351	+	0.552483i	0.990211	+	0.139581i	$0.0445757\pi$
$179$	1.06277	+	7.39172i	0.0794351	+	0.552483i	−0.910776	+	0.412902i	$0.864515\pi$
$180$	−1.37140	−	3.00296i	−0.102218	−	0.223827i
$181$	−2.73165	−	5.98148i	−0.203042	−	0.444600i	0.780530	−	0.625119i	$-0.214950\pi$
$181$	−2.73165	−	5.98148i	−0.203042	−	0.444600i	−0.983572	+	0.180519i	$0.942222\pi$
$182$	0.102182	+	0.223747i	0.00757423	+	0.0165853i
$183$	−0.0862646	−	0.188893i	−0.00637686	−	0.0139634i
$184$	2.38083	+	16.5590i	0.175517	+	1.22075i
$185$	−2.15621	+	1.38571i	−0.158527	+	0.101879i
$186$	0.0850160	+	0.186159i	0.00623368	+	0.0136498i
$187$	−10.0799	+	13.6132i	−0.737117	+	0.995499i
$188$	2.27484	−	4.98120i	0.165910	−	0.363292i
$189$	−0.0170206	−	0.118381i	−0.00123807	−	0.00861095i
$190$	−0.0364764	+	0.253699i	−0.00264628	+	0.0184053i
$191$	7.85462	+	5.04786i	0.568340	+	0.365250i	0.793032	−	0.609180i	$-0.208501\pi$
$191$	7.85462	+	5.04786i	0.568340	+	0.365250i	−0.224692	+	0.974430i	$0.572138\pi$
$192$	0.0890530	−	0.0572309i	0.00642685	−	0.00413029i
$193$	18.2301	−	5.35284i	1.31223	−	0.385306i	0.450547	−	0.892753i	$-0.351229\pi$
$193$	18.2301	−	5.35284i	1.31223	−	0.385306i	0.861683	+	0.507447i	$0.169411\pi$
$194$	−1.38895	+	9.66037i	−0.0997209	+	0.693574i
$195$	0.00448864	+	0.00982874i	0.000321438	+	0.000703851i
$196$	7.45179	+	4.78898i	0.532271	+	0.342070i
$197$	−20.3045	−	5.96193i	−1.44663	−	0.424770i	−0.538207	−	0.842813i	$-0.680898\pi$
$197$	−20.3045	−	5.96193i	−1.44663	−	0.424770i	−0.908427	+	0.418043i	$0.862716\pi$
$198$	7.03560	+	3.79403i	0.499998	+	0.269630i
$199$	12.9637	−	3.80649i	0.918973	−	0.269835i	0.212160	−	0.977235i	$-0.431950\pi$
$199$	12.9637	−	3.80649i	0.918973	−	0.269835i	0.706813	+	0.707400i	$0.250132\pi$
$200$	−11.2226	−	3.29527i	−0.793561	−	0.233011i
$201$	−0.0309422	+	0.0677540i	−0.00218250	+	0.00477900i
$202$	−1.34949			−0.0949497
$203$	2.06832	+	2.38697i	0.145168	+	0.167533i
$204$	−0.0289628	−	0.201441i	−0.00202780	−	0.0141037i
$205$	4.52966	−	5.22750i	0.316365	−	0.365105i
$206$	5.64697	+	6.51696i	0.393443	+	0.454058i
$207$	2.64907	−	18.4247i	0.184123	−	1.28060i
$208$	−0.206145	+	0.132481i	−0.0142936	+	0.00918592i
$209$	0.629687	+	1.13896i	0.0435564	+	0.0787838i
$210$	0.0109546	+	0.00704011i	0.000755941	+	0.000485814i
$211$	3.22174	−	3.71809i	0.221794	−	0.255964i	−0.633937	−	0.773384i	$-0.718562\pi$
$211$	3.22174	−	3.71809i	0.221794	−	0.255964i	0.855731	+	0.517421i	$0.173108\pi$
$212$	2.73311	−	3.15418i	0.187711	−	0.216630i
$213$	0.312181	−	0.200627i	0.0213903	−	0.0137467i
$214$	−5.36719	+	6.19406i	−0.366893	+	0.423418i
$215$	0.716011			0.0488316
$216$	−0.456533	+	0.134050i	−0.0310632	+	0.00912097i
$217$	−4.93313	−	3.17033i	−0.334883	−	0.215216i
$218$	9.23432	−	2.71144i	0.625427	−	0.183642i
$219$	−0.0229716	+	0.159771i	−0.00155228	+	0.0107963i
$220$	3.41385	−	1.29371i	0.230162	−	0.0872218i
$221$	−0.328371	−	2.28387i	−0.0220886	−	0.153630i
$222$	0.0309742	+	0.0678240i	0.00207885	+	0.00455205i
$223$	−4.71553	+	3.03049i	−0.315775	+	0.202936i	−0.688921	−	0.724836i	$-0.741915\pi$
$223$	−4.71553	+	3.03049i	−0.315775	+	0.202936i	0.373146	+	0.927773i	$0.378279\pi$
$224$	−1.63997	+	3.59104i	−0.109575	+	0.239937i
$225$	10.9482	+	7.03601i	0.729883	+	0.469067i
$226$	0.368391	−	2.56222i	0.0245050	−	0.170436i
$227$	−28.5868	−	8.39386i	−1.89738	−	0.557120i	−0.990850	−	0.134969i	$-0.956906\pi$
$227$	−28.5868	−	8.39386i	−1.89738	−	0.557120i	−0.906526	−	0.422150i	$-0.861275\pi$
$228$	−0.0150028	−	0.00440522i	−0.000993584	−	0.000291743i
$229$	−12.8244	−	14.8001i	−0.847458	−	0.978019i	0.152489	−	0.988305i	$-0.451271\pi$
$229$	−12.8244	−	14.8001i	−0.847458	−	0.978019i	−0.999947	+	0.0102860i	$0.996726\pi$
$230$	2.65479	+	3.06379i	0.175051	+	0.202020i
$231$	0.0659259	−	0.00506229i	0.00433761	−	0.000333074i
$232$	8.22856	−	9.49627i	0.540232	−	0.623460i
$233$	−20.8703			−1.36726			−0.683629	−	0.729829i	$-0.739599\pi$
$233$	−20.8703			−1.36726			−0.683629	+	0.729829i	$0.739599\pi$
$234$	−1.04473	+	0.306760i	−0.0682960	+	0.0200535i
$235$	−0.467758	−	3.25333i	−0.0305132	−	0.212224i
$236$	−4.89478	+	10.7181i	−0.318623	+	0.697688i
$237$	0.391237	+	0.114878i	0.0254136	+	0.00746210i
$238$	−1.82097	−	2.10151i	−0.118036	−	0.136221i
$239$	−1.77550			−0.114848			−0.0574238	−	0.998350i	$-0.518289\pi$
$239$	−1.77550			−0.114848			−0.0574238	+	0.998350i	$0.518289\pi$
$240$	−0.00538898	+	0.0118002i	−0.000347857	+	0.000761701i
$241$	−24.0819			−1.55125			−0.775625	−	0.631194i	$-0.782565\pi$
$241$	−24.0819			−1.55125			−0.775625	+	0.631194i	$0.782565\pi$
$242$	−4.70088	+	7.48598i	−0.302184	+	0.481217i
$243$	0.794158			0.0509453
$244$	3.97022	−	8.69358i	0.254167	−	0.556549i
$245$	5.31663			0.339667
$246$	−0.131771	−	0.152072i	−0.00840141	−	0.00969574i
$247$	−0.170097	−	0.0499449i	−0.0108230	−	0.00317792i
$248$	−9.69133	+	21.2210i	−0.615400	+	1.34754i
$249$	0.0342618	+	0.238296i	0.00217126	+	0.0151014i
$250$	−5.85317	+	1.71865i	−0.370187	+	0.108697i
$251$	−13.2171			−0.834255			−0.417128	−	0.908848i	$-0.636963\pi$
$251$	−13.2171			−0.834255			−0.417128	+	0.908848i	$0.636963\pi$
$252$	1.80204	−	2.07966i	0.113518	−	0.131006i
$253$	20.1368	+	4.27017i	1.26599	+	0.268463i
$254$	−5.64776	−	6.51786i	−0.354372	−	0.408967i
$255$	−0.0799912	−	0.0923148i	−0.00500925	−	0.00578098i
$256$	13.6600	+	4.01095i	0.853753	+	0.250685i
$257$	0.412875	+	0.121231i	0.0257544	+	0.00756218i	0.294584	−	0.955625i	$-0.404819\pi$
$257$	0.412875	+	0.121231i	0.0257544	+	0.00756218i	−0.268830	+	0.963188i	$0.586637\pi$
$258$	0.00296431	−	0.0206173i	0.000184550	−	0.00128357i
$259$	−1.79730	−	1.15506i	−0.111679	−	0.0717717i
$260$	−0.206584	+	0.452356i	−0.0128118	+	0.0280539i
$261$	−11.7616	+	7.55871i	−0.728024	+	0.467873i
$262$	4.92622	+	10.7869i	0.304343	+	0.666418i
$263$	−2.19009	−	15.2324i	−0.135047	−	0.939271i	−0.938838	−	0.344359i	$-0.888096\pi$
$263$	−2.19009	−	15.2324i	−0.135047	−	0.939271i	0.803791	−	0.594912i	$-0.202813\pi$
$264$	−0.0572607	−	0.256742i	−0.00352415	−	0.0158014i
$265$	0.356501	−	2.47952i	0.0218997	−	0.152316i
$266$	−0.204991	+	0.0601908i	−0.0125688	+	0.00369053i
$267$	0.0117565	+	0.00755541i	0.000719483	+	0.000462384i
$268$	−3.28922	+	0.965803i	−0.200921	+	0.0589958i
$269$	−25.4699			−1.55293			−0.776464	−	0.630161i	$-0.782989\pi$
$269$	−25.4699			−1.55293			−0.776464	+	0.630161i	$0.782989\pi$
$270$	−0.0755061	+	0.0871386i	−0.00459515	+	0.00530309i
$271$	18.1638	−	11.6732i	1.10337	−	0.709094i	0.143533	−	0.989645i	$-0.454154\pi$
$271$	18.1638	−	11.6732i	1.10337	−	0.709094i	0.959839	+	0.280551i	$0.0905172\pi$
$272$	1.81408	−	2.09356i	0.109995	−	0.126941i
$273$	−0.00589810	+	0.00680677i	−0.000356969	+	0.000411965i
$274$	−2.21029	−	1.42047i	−0.133528	−	0.0858136i
$275$	−8.56429	+	11.5663i	−0.516446	+	0.697476i
$276$	−0.208054	+	0.133708i	−0.0125234	+	0.00804829i
$277$	−4.16055	+	28.9372i	−0.249983	+	1.73867i	0.348298	+	0.937384i	$0.386760\pi$
$277$	−4.16055	+	28.9372i	−0.249983	+	1.73867i	−0.598281	+	0.801286i	$0.704150\pi$
$278$	−5.20286	−	6.00443i	−0.312047	−	0.360122i
$279$	16.9986	−	19.6175i	1.01768	−	1.17447i
$280$	0.211253	+	1.46930i	0.0126248	+	0.0878074i
$281$	9.71091	+	11.2070i	0.579304	+	0.668553i	0.967455	−	0.253043i	$-0.0814315\pi$
$281$	9.71091	+	11.2070i	0.579304	+	0.668553i	−0.388151	+	0.921596i	$0.626886\pi$
$282$	−0.0956149			−0.00569378
$283$	−10.9689	+	24.0186i	−0.652035	+	1.42776i	0.237726	+	0.971332i	$0.423598\pi$
$283$	−10.9689	+	24.0186i	−0.652035	+	1.42776i	−0.889761	+	0.456426i	$0.849129\pi$
$284$	16.3872	+	4.81170i	0.972399	+	0.285522i
$285$	−0.00900482	+	0.00264405i	−0.000533399	+	0.000156620i
$286$	−0.262108	−	1.17522i	−0.0154988	−	0.0694925i
$287$	5.53209	+	1.62437i	0.326549	+	0.0958835i
$288$	−14.7011	−	9.44785i	−0.866273	−	0.556720i
$289$	3.77368	+	8.26321i	0.221981	+	0.486071i
$290$	0.433339	−	3.01394i	0.0254465	−	0.176984i
$291$	−0.342886	+	0.100680i	−0.0201003	+	0.00590199i
$292$	−6.24957	+	4.01635i	−0.365728	+	0.235039i
$293$	−21.9218	−	14.0883i	−1.28069	−	0.823048i	−0.289715	−	0.957113i	$-0.593560\pi$
$293$	−21.9218	−	14.0883i	−1.28069	−	0.823048i	−0.990972	+	0.134065i	$0.957197\pi$
$294$	0.0220110	−	0.153090i	0.00128371	−	0.00892840i
$295$	1.00648	+	7.00021i	0.0585994	+	0.407568i
$296$	−3.53087	+	7.73153i	−0.205228	+	0.449386i
$297$	−0.0387071	+	0.584176i	−0.00224601	+	0.0338973i
$298$	−1.40499	−	3.07651i	−0.0813891	−	0.178217i
$299$	−2.35885	+	1.51594i	−0.136416	+	0.0876691i
$300$	−0.0246079	−	0.171152i	−0.00142074	−	0.00988145i
$301$	0.247933	+	0.542896i	0.0142906	+	0.0312920i
$302$	1.50071	+	3.28609i	0.0863559	+	0.189093i
$303$	−0.0205269	−	0.0449476i	−0.00117924	−	0.00258217i
$304$	−0.0884156	−	0.193603i	−0.00507098	−	0.0111039i
$305$	−0.816367	−	5.67796i	−0.0467450	−	0.325119i
$306$	10.3550	−	6.65475i	0.591956	−	0.380427i
$307$	−9.27548	−	20.3105i	−0.529380	−	1.15918i	−0.965765	−	0.259420i	$-0.916469\pi$
$307$	−9.27548	−	20.3105i	−0.529380	−	1.15918i	0.436385	−	0.899760i	$-0.356259\pi$
$308$	2.16303	+	2.14049i	0.123250	+	0.121966i
$309$	−0.131166	+	0.287213i	−0.00746176	+	0.0163390i
$310$	0.804551	+	5.59577i	0.0456954	+	0.317819i
$311$	1.15552	−	8.03679i	0.0655233	−	0.455724i	−0.930475	−	0.366355i	$-0.880606\pi$
$311$	1.15552	−	8.03679i	0.0655233	−	0.455724i	0.995999	−	0.0893696i	$-0.0284852\pi$
$312$	0.0301436	+	0.0193721i	0.00170655	+	0.00109673i
$313$	−0.814355	+	0.523354i	−0.0460300	+	0.0295817i	−0.563453	−	0.826148i	$-0.690528\pi$
$313$	−0.814355	+	0.523354i	−0.0460300	+	0.0295817i	0.517423	+	0.855730i	$0.326891\pi$
$314$	14.4789	−	4.25139i	0.817092	−	0.239920i
$315$	0.235054	−	1.63484i	0.0132438	−	0.0921126i
$316$	7.79583	+	17.0705i	0.438550	+	0.960290i
$317$	18.1890	+	11.6894i	1.02160	+	0.656541i	0.940369	−	0.340155i	$-0.110480\pi$
$317$	18.1890	+	11.6894i	1.02160	+	0.656541i	0.0812277	+	0.996696i	$0.474116\pi$
$318$	−0.0699209	−	0.0205306i	−0.00392097	−	0.00115130i
$319$	−7.48067	−	13.5309i	−0.418837	−	0.757583i
$320$	2.80575	−	0.823842i	0.156846	−	0.0460541i
$321$	−0.287946	−	0.0845486i	−0.0160716	−	0.00471904i
$322$	−1.40376	+	3.07381i	−0.0782287	+	0.171297i
$323$	2.00408			0.111510
$324$	7.97458	+	9.20315i	0.443032	+	0.511286i
$325$	−0.278997	−	1.94046i	−0.0154759	−	0.107638i
$326$	8.48453	−	9.79167i	0.469915	−	0.542310i
$327$	0.230772	+	0.266325i	0.0127617	+	0.0147278i
$328$	3.26440	−	22.7044i	0.180246	−	1.25364i
$329$	2.30478	−	1.48119i	0.127067	−	0.0816608i
$330$	−0.0453094	−	0.0448373i	−0.00249420	−	0.00246821i
$331$	0.0475115	+	0.0305338i	0.00261147	+	0.00167829i	0.541946	−	0.840413i	$-0.317688\pi$
$331$	0.0475115	+	0.0305338i	0.00261147	+	0.00167829i	−0.539334	+	0.842092i	$0.681324\pi$
$332$	−7.25591	+	8.37376i	−0.398220	+	0.459570i
$333$	6.19317	−	7.14730i	0.339384	−	0.391670i
$334$	−2.59801	+	1.66964i	−0.142157	+	0.0913586i
$335$	−1.34742	+	1.55501i	−0.0736174	+	0.0849591i
$336$	−0.0108132			−0.000589910
$337$	27.3618	−	8.03416i	1.49049	−	0.437648i	0.567795	−	0.823170i	$-0.307797\pi$
$337$	27.3618	−	8.03416i	1.49049	−	0.437648i	0.922699	+	0.385522i	$0.125979\pi$
$338$	−8.65041	−	5.55928i	−0.470520	−	0.302385i
$339$	0.0909436	−	0.0267035i	0.00493938	−	0.00145033i
$340$	0.800066	−	5.56458i	0.0433897	−	0.301782i
$341$	20.4039	+	20.1913i	1.10493	+	1.09342i
$342$	−0.134590	−	0.936094i	−0.00727779	−	0.0506182i
$343$	3.81117	+	8.34529i	0.205784	+	0.450603i
$344$	1.99749	−	1.28371i	0.107697	−	0.0692128i
$345$	−0.0616644	+	0.135026i	−0.00331990	+	0.00726956i
$346$	−5.66930	−	3.64344i	−0.304784	−	0.195873i
$347$	3.00031	−	20.8676i	0.161065	−	1.12023i	−0.735566	−	0.677453i	$-0.763084\pi$
$347$	3.00031	−	20.8676i	0.161065	−	1.12023i	0.896631	−	0.442779i	$-0.146007\pi$
$348$	0.178233	+	0.0523339i	0.00955428	+	0.00280539i
$349$	25.9264	+	7.61267i	1.38781	+	0.407497i	0.888479	−	0.458917i	$-0.151762\pi$
$349$	25.9264	+	7.61267i	1.38781	+	0.407497i	0.499327	+	0.866414i	$0.333581\pi$
$350$	−1.54716	−	1.78552i	−0.0826993	−	0.0954401i
$351$	−0.0522245	−	0.0602703i	−0.00278754	−	0.00321699i
$352$	11.5000	−	15.5311i	0.612952	−	0.827810i
$353$	−9.83668	+	11.3521i	−0.523554	+	0.604213i	−0.954517	−	0.298156i	$-0.903628\pi$
$353$	−9.83668	+	11.3521i	−0.523554	+	0.604213i	0.430963	+	0.902369i	$0.358174\pi$
$354$	0.205735			0.0109347
$355$	9.83572	−	2.88803i	0.522026	−	0.153281i
$356$	0.0915339	+	0.636632i	0.00485128	+	0.0337414i
$357$	0.0422967	−	0.0926170i	0.00223858	−	0.00490181i
$358$	5.75797	+	1.69069i	0.304318	+	0.0893559i
$359$	−14.8378	−	17.1237i	−0.783109	−	0.903756i	0.214221	−	0.976785i	$-0.431279\pi$
$359$	−14.8378	−	17.1237i	−0.783109	−	0.903756i	−0.997330	+	0.0730296i	$0.976733\pi$
$360$	−6.57087			−0.346315
$361$	−7.82892	+	17.1429i	−0.412048	+	0.902260i
$362$	−5.28423			−0.277733
$363$	−0.320841	−	0.0427048i	−0.0168398	−	0.00224142i
$364$	−0.414520			−0.0217268
$365$	−1.85229	+	4.05594i	−0.0969530	+	0.212298i
$366$	−0.166874			−0.00872266
$367$	−16.0500	−	18.5227i	−0.837804	−	0.966877i	0.161998	−	0.986791i	$-0.448206\pi$
$367$	−16.0500	−	18.5227i	−0.837804	−	0.966877i	−0.999802	+	0.0199139i	$0.993661\pi$
$368$	−3.23004	−	0.948424i	−0.168377	−	0.0494400i
$369$	−10.6023	+	23.2158i	−0.551933	+	1.20856i
$370$	0.293125	+	2.03873i	0.0152388	+	0.105988i
$371$	2.00348	−	0.588273i	0.104015	−	0.0305416i
$372$	−0.344883			−0.0178814
$373$	−14.5141	+	16.7502i	−0.751513	+	0.867293i	−0.994714	−	0.102683i	$-0.967257\pi$
$373$	−14.5141	+	16.7502i	−0.751513	+	0.867293i	0.243201	+	0.969976i	$0.421803\pi$
$374$	6.58604	+	11.9127i	0.340556	+	0.615990i
$375$	−0.146275	−	0.168810i	−0.00755360	−	0.00871732i
$376$	−7.13768	−	8.23732i	−0.368098	−	0.424807i
$377$	2.02075	+	0.593345i	0.104074	+	0.0305588i
$378$	−0.0922159	−	0.0270770i	−0.00474308	−	0.00139269i
$379$	−0.856745	+	5.95879i	−0.0440080	+	0.306082i	0.955915	+	0.293645i	$0.0948683\pi$
$379$	−0.856745	+	5.95879i	−0.0440080	+	0.306082i	−0.999923	+	0.0124378i	$0.996041\pi$
$380$	−0.363364	−	0.233520i	−0.0186402	−	0.0119793i
$381$	0.131184	−	0.287253i	0.00672076	−	0.0147164i
$382$	6.31196	−	4.05645i	0.322948	−	0.207546i
$383$	1.67653	+	3.67108i	0.0856665	+	0.187584i	0.947617	−	0.319409i	$-0.103484\pi$
$383$	1.67653	+	3.67108i	0.0856665	+	0.187584i	−0.861950	+	0.506993i	$0.830757\pi$
$384$	0.0366936	+	0.255210i	0.00187251	+	0.0130236i
$385$	1.78676	+	0.378896i	0.0910617	+	0.0193103i
$386$	2.17288	−	15.1127i	0.110597	−	0.769217i
$387$	−2.53491	+	0.744317i	−0.128857	+	0.0378358i
$388$	−13.8362	−	8.89199i	−0.702427	−	0.451423i
$389$	8.28945	−	2.43400i	0.420292	−	0.123409i	−0.0647465	−	0.997902i	$-0.520624\pi$
$389$	8.28945	−	2.43400i	0.420292	−	0.123409i	0.485038	+	0.874493i	$0.338806\pi$
$390$	0.00868303			0.000439682
$391$	20.7579	−	23.9559i	1.04977	−	1.21150i
$392$	14.8320	−	9.53195i	0.749130	−	0.481436i
$393$	−0.284349	+	0.328157i	−0.0143435	+	0.0165533i
$394$	−11.1362	+	12.8519i	−0.561035	+	0.647469i
$395$	9.47567	+	6.08964i	0.476772	+	0.306403i
$396$	−10.7413	+	8.12895i	−0.539770	+	0.408495i
$397$	30.6507	−	19.6980i	1.53832	−	0.988615i	0.550177	−	0.835048i	$-0.314560\pi$
$397$	30.6507	−	19.6980i	1.53832	−	0.988615i	0.988138	−	0.153567i	$-0.0490761\pi$
$398$	1.54517	−	10.7469i	0.0774524	−	0.538693i
$399$	−0.00512287	−	0.00591211i	−0.000256464	−	0.000295976i
$400$	1.54131	−	1.77876i	0.0770654	−	0.0889382i
$401$	−3.03912	−	21.1375i	−0.151766	−	1.05556i	−0.913258	−	0.407382i	$-0.866442\pi$
$401$	−3.03912	−	21.1375i	−0.151766	−	1.05556i	0.761492	−	0.648175i	$-0.224467\pi$
$402$	0.0391974	+	0.0452362i	0.00195499	+	0.00225618i
$403$	−3.91017			−0.194780
$404$	0.944724	−	2.06866i	0.0470018	−	0.102920i
$405$	7.01299	+	2.05920i	0.348478	+	0.102322i
$406$	2.43529	−	0.715065i	0.120861	−	0.0354881i
$407$	7.43382	+	7.35636i	0.368481	+	0.364641i
$408$	−0.388662	−	0.114121i	−0.0192416	−	0.00564985i
$409$	−2.60666	−	1.67520i	−0.128891	−	0.0828334i	0.474606	−	0.880198i	$-0.342590\pi$
$409$	−2.60666	−	1.67520i	−0.128891	−	0.0828334i	−0.603498	+	0.797365i	$0.706227\pi$
$410$	−2.30907	−	5.05616i	−0.114037	−	0.249706i
$411$	0.0136913	−	0.0952249i	0.000675341	−	0.00469710i
$412$	−13.9432	+	4.09409i	−0.686932	+	0.201701i
$413$	−4.95921	+	3.18709i	−0.244027	+	0.156826i
$414$	−12.5837	−	8.08705i	−0.618455	−	0.397457i
$415$	−0.946445	+	6.58267i	−0.0464592	+	0.323131i
$416$	0.374632	+	2.60563i	0.0183679	+	0.127751i
$417$	0.120850	−	0.264625i	0.00591806	−	0.0129587i
$418$	1.04276	−	0.0800713i	0.0510033	−	0.00391642i
$419$	11.8742	+	26.0009i	0.580093	+	1.27023i	0.941246	+	0.337721i	$0.109656\pi$
$419$	11.8742	+	26.0009i	0.580093	+	1.27023i	−0.361153	+	0.932506i	$0.617617\pi$
$420$	−0.0184608	+	0.0118641i	−0.000900796	+	0.000578906i
$421$	3.04612	+	21.1862i	0.148459	+	1.03255i	0.918744	+	0.394853i	$0.129205\pi$
$421$	3.04612	+	21.1862i	0.148459	+	1.03255i	−0.770286	+	0.637699i	$0.779886\pi$
$422$	−1.64234	−	3.59622i	−0.0799479	−	0.175061i
$423$	5.03795	+	11.0316i	0.244954	+	0.536374i
$424$	−3.45088	−	7.55637i	−0.167590	−	0.366970i
$425$	9.20645	+	20.1593i	0.446578	+	0.977870i
$426$	−0.0424394	−	0.295172i	−0.00205619	−	0.0143011i
$427$	4.02248	−	2.58509i	0.194661	−	0.125101i
$428$	−5.73764	−	12.5637i	−0.277339	−	0.607289i
$429$	0.0351565	−	0.0266062i	0.00169737	−	0.00128456i
$430$	0.239024	−	0.523389i	0.0115267	−	0.0252401i
$431$	−2.04394	−	14.2159i	−0.0984534	−	0.684758i	−0.977948	−	0.208849i	$-0.933028\pi$
$431$	−2.04394	−	14.2159i	−0.0984534	−	0.684758i	0.879495	−	0.475909i	$-0.157881\pi$
$432$	0.0136260	−	0.0947708i	0.000655580	−	0.00455966i
$433$	32.0010	+	20.5658i	1.53787	+	0.988328i	0.988238	+	0.152921i	$0.0488679\pi$
$433$	32.0010	+	20.5658i	1.53787	+	0.988328i	0.549631	+	0.835408i	$0.314768\pi$
$434$	−3.96425	+	2.54767i	−0.190290	+	0.122292i
$435$	0.106977	−	0.0314113i	0.00512915	−	0.00150606i
$436$	−2.30816	+	16.0536i	−0.110541	+	0.768830i
$437$	−1.01171	−	2.21534i	−0.0483967	−	0.105974i
$438$	0.109121	+	0.0701276i	0.00521398	+	0.00335082i
$439$	−33.2454	−	9.76172i	−1.58672	−	0.465902i	−0.634905	−	0.772590i	$-0.718961\pi$
$439$	−33.2454	−	9.76172i	−1.58672	−	0.465902i	−0.951810	+	0.306688i	$0.900779\pi$
$440$	0.480417	−	7.25057i	0.0229030	−	0.345657i
$441$	−18.8226	+	5.52681i	−0.896313	+	0.263181i
$442$	−1.77908	−	0.522385i	−0.0846222	−	0.0248473i
$443$	−4.16774	+	9.12607i	−0.198015	+	0.433593i	−0.982427	−	0.186648i	$-0.940238\pi$
$443$	−4.16774	+	9.12607i	−0.198015	+	0.433593i	0.784412	+	0.620240i	$0.212965\pi$
$444$	−0.125652			−0.00596320
$445$	0.252804	+	0.291751i	0.0119840	+	0.0138303i
$446$	0.641051	+	4.45861i	0.0303547	+	0.211121i
$447$	0.0810985	−	0.0935926i	0.00383583	−	0.00442678i
$448$	1.59620	+	1.84211i	0.0754133	+	0.0870316i
$449$	5.59511	−	38.9148i	0.264049	−	1.83650i	−0.237514	−	0.971384i	$-0.576333\pi$
$449$	5.59511	−	38.9148i	0.264049	−	1.83650i	0.501564	−	0.865121i	$-0.332758\pi$
$450$	8.79799	−	5.65413i	0.414741	−	0.266538i
$451$	−24.8421	−	13.3964i	−1.16977	−	0.630811i
$452$	3.66977	+	2.35842i	0.172612	+	0.110931i
$453$	−0.0866231	+	0.0999683i	−0.00406991	+	0.00469692i
$454$	−15.6788	+	18.0943i	−0.735842	+	0.849207i
$455$	−0.209303	+	0.134511i	−0.00981227	+	0.00630596i
$456$	−0.0203807	+	0.0235206i	−0.000954413	+	0.00110145i
$457$	−39.3932			−1.84273			−0.921367	−	0.388693i	$-0.872927\pi$
$457$	−39.3932			−1.84273			−0.921367	+	0.388693i	$0.872927\pi$
$458$	−15.0997	+	4.43367i	−0.705562	+	0.207172i
$459$	0.758427	+	0.487412i	0.0354003	+	0.0227504i
$460$	−6.55505	+	1.92474i	−0.305631	+	0.0897413i
$461$	0.236365	−	1.64395i	0.0110086	−	0.0765665i	−0.983577	−	0.180492i	$-0.942231\pi$
$461$	0.236365	−	1.64395i	0.0110086	−	0.0765665i	0.994585	+	0.103925i	$0.0331402\pi$
$462$	0.0183074	−	0.0498804i	0.000851738	−	0.00232065i
$463$	0.668228	+	4.64762i	0.0310552	+	0.215993i	0.999440	−	0.0334685i	$-0.0106553\pi$
$463$	0.668228	+	4.64762i	0.0310552	+	0.215993i	−0.968385	+	0.249462i	$0.919746\pi$
$464$	1.05037	+	2.30000i	0.0487624	+	0.106775i
$465$	−0.174141	+	0.111914i	−0.00807560	+	0.00518988i
$466$	−6.96706	+	15.2557i	−0.322743	+	0.706709i
$467$	22.3874	+	14.3875i	1.03597	+	0.665775i	0.943986	−	0.329985i	$-0.107044\pi$
$467$	22.3874	+	14.3875i	1.03597	+	0.665775i	0.0919807	+	0.995761i	$0.470680\pi$
$468$	0.261135	−	1.81623i	0.0120710	−	0.0839555i
$469$	−1.64561	−	0.483195i	−0.0759873	−	0.0223119i
$470$	−2.53426	−	0.744127i	−0.116897	−	0.0343240i
$471$	0.361838	+	0.417583i	0.0166726	+	0.0192412i
$472$	15.3582	+	17.7243i	0.706917	+	0.815826i
$473$	−0.635975	−	2.85154i	−0.0292421	−	0.131114i
$474$	0.214578	−	0.247637i	0.00985591	−	0.0113743i
$475$	1.70274			0.0781273
$476$	4.49623	−	1.32021i	0.206084	−	0.0605119i
$477$	1.31541	+	9.14889i	0.0602286	+	0.418899i
$478$	−0.592709	+	1.29785i	−0.0271099	+	0.0593624i
$479$	8.97340	+	2.63483i	0.410005	+	0.120388i	0.480230	−	0.877143i	$-0.340553\pi$
$479$	8.97340	+	2.63483i	0.410005	+	0.120388i	−0.0702245	+	0.997531i	$0.522372\pi$
$480$	0.0912605	+	0.105320i	0.00416545	+	0.00480719i
$481$	−1.42461			−0.0649565
$482$	−8.03917	+	17.6033i	−0.366174	+	0.801810i
$483$	−0.123732			−0.00563002
$484$	−8.18449	−	12.4467i	−0.372022	−	0.565760i
$485$	−9.87172			−0.448252
$486$	0.265111	−	0.580512i	0.0120257	−	0.0263326i
$487$	14.4101			0.652984			0.326492	−	0.945200i	$-0.394133\pi$
$487$	14.4101			0.652984			0.326492	+	0.945200i	$0.394133\pi$
$488$	−12.4572	−	14.3764i	−0.563912	−	0.650789i
$489$	0.455189	+	0.133656i	0.0205844	+	0.00604412i
$490$	1.77483	−	3.88634i	0.0801788	−	0.175567i
$491$	3.63945	+	25.3130i	0.164246	+	1.14236i	0.890517	+	0.454949i	$0.150343\pi$
$491$	3.63945	+	25.3130i	0.164246	+	1.14236i	−0.726271	+	0.687408i	$0.758748\pi$
$492$	0.325361	−	0.0955347i	0.0146684	−	0.00430704i
$493$	−23.8085			−1.07228
$494$	−0.0932916	+	0.107664i	−0.00419739	+	0.00484404i
$495$	−2.78575	+	7.59006i	−0.125210	+	0.341148i
$496$	−3.07423	−	3.54786i	−0.138037	−	0.159303i
$497$	5.59558	+	6.45764i	0.250996	+	0.289665i
$498$	0.185627	+	0.0545050i	0.00831815	+	0.00244243i
$499$	−28.6108	−	8.40088i	−1.28079	−	0.376075i	−0.430599	−	0.902543i	$-0.641698\pi$
$499$	−28.6108	−	8.40088i	−1.28079	−	0.376075i	−0.850195	+	0.526469i	$0.823516\pi$
$500$	1.46303	−	10.1756i	0.0654287	−	0.455066i
$501$	−0.0951288	−	0.0611355i	−0.00425004	−	0.00273133i
$502$	−4.41222	+	9.66141i	−0.196927	+	0.431210i
$503$	8.31375	−	5.34293i	0.370692	−	0.238229i	−0.342010	−	0.939696i	$-0.611108\pi$
$503$	8.31375	−	5.34293i	0.370692	−	0.238229i	0.712702	+	0.701467i	$0.247471\pi$
$504$	−2.27529	−	4.98218i	−0.101349	−	0.221924i
$505$	−0.194257	−	1.35108i	−0.00864430	−	0.0601224i
$506$	9.84362	−	13.2941i	0.437602	−	0.590995i
$507$	0.0535835	−	0.372681i	0.00237973	−	0.0165514i
$508$	13.9451	−	4.09466i	0.618715	−	0.181671i
$509$	7.53089	+	4.83981i	0.333801	+	0.214521i	0.696795	−	0.717271i	$-0.254609\pi$
$509$	7.53089	+	4.83981i	0.333801	+	0.214521i	−0.362994	+	0.931792i	$0.618245\pi$
$510$	−0.0941834	+	0.0276547i	−0.00417051	+	0.00122457i
$511$	−3.71670			−0.164417
$512$	−3.98447	+	4.59833i	−0.176091	+	0.203219i
$513$	0.0582711	−	0.0374486i	0.00257273	−	0.00165340i
$514$	0.226446	−	0.261333i	0.00998810	−	0.0115269i
$515$	−5.71179	+	6.59175i	−0.251691	+	0.290467i
$516$	0.0295294	+	0.0189774i	0.00129996	+	0.000835433i
$517$	−12.5410	+	4.75253i	−0.551554	+	0.209016i
$518$	−1.44431	+	0.928202i	−0.0634593	+	0.0407828i
$519$	0.0351176	−	0.244248i	0.00154149	−	0.0107213i
$520$	0.648190	+	0.748052i	0.0284250	+	0.0328042i
$521$	15.5084	−	17.8976i	0.679434	−	0.784109i	−0.306387	−	0.951907i	$-0.599120\pi$
$521$	15.5084	−	17.8976i	0.679434	−	0.784109i	0.985821	+	0.167798i	$0.0536656\pi$
$522$	1.59893	+	11.1208i	0.0699831	+	0.486743i
$523$	0.0287283	+	0.0331542i	0.00125620	+	0.00144973i	0.756377	−	0.654136i	$-0.226967\pi$
$523$	0.0287283	+	0.0331542i	0.00125620	+	0.00144973i	−0.755121	+	0.655585i	$0.772422\pi$
$524$	−19.9841			−0.873011
$525$	0.0359369	−	0.0786908i	0.00156842	−	0.00343435i
$526$	−11.8657	−	3.48408i	−0.517368	−	0.151913i
$527$	42.4130	−	12.4536i	1.84754	−	0.542487i
$528$	0.0517814	+	0.0109806i	0.00225350	+	0.000477871i
$529$	−14.8919	−	4.37267i	−0.647475	−	0.190116i
$530$	−1.69347	−	1.08833i	−0.0735595	−	0.0472738i
$531$	−10.8402	−	23.7367i	−0.470424	−	1.03009i
$532$	0.0512385	−	0.356372i	0.00222147	−	0.0154507i
$533$	3.68884	−	1.08314i	0.159781	−	0.0469161i
$534$	0.00944746	−	0.00607152i	0.000408832	−	0.000262740i
$535$	−6.97398	−	4.48191i	−0.301512	−	0.193770i
$536$	−0.971049	+	6.75379i	−0.0419429	+	0.291719i
$537$	0.0312715	+	0.217498i	0.00134947	+	0.00938574i
$538$	−8.50254	+	18.6180i	−0.366571	+	0.802678i
$539$	−4.72233	−	21.1737i	−0.203405	−	0.912015i
$540$	−0.0807177	−	0.176747i	−0.00347353	−	0.00760598i
$541$	1.75617	−	1.12862i	0.0755037	−	0.0485233i	−0.502344	−	0.864668i	$-0.667529\pi$
$541$	1.75617	−	1.12862i	0.0755037	−	0.0485233i	0.577848	+	0.816144i	$0.303893\pi$
$542$	−2.46927	−	17.1742i	−0.106064	−	0.737694i
$543$	−0.0803777	−	0.176003i	−0.00344934	−	0.00755299i
$544$	−12.3623	−	27.0696i	−0.530029	−	1.16060i
$545$	4.04391	+	8.85492i	0.173222	+	0.379303i
$546$	0.00300666	+	0.00658367i	0.000128673	+	0.000281755i
$547$	−3.40015	−	23.6486i	−0.145380	−	1.01114i	−0.923657	−	0.383220i	$-0.874815\pi$
$547$	−3.40015	−	23.6486i	−0.145380	−	1.01114i	0.778277	−	0.627921i	$-0.216094\pi$
$548$	3.72480	−	2.39378i	0.159115	−	0.102257i
$549$	8.79262	+	19.2532i	0.375260	+	0.821705i
$550$	5.59575	+	10.1215i	0.238603	+	0.431580i
$551$	−0.759894	+	1.66394i	−0.0323726	+	0.0708861i
$552$	0.0700550	+	0.487243i	0.00298174	+	0.0207384i
$553$	−1.33618	+	9.29332i	−0.0568201	+	0.395192i
$554$	19.7636	+	12.7013i	0.839675	+	0.539626i
$555$	−0.0634454	+	0.0407739i	−0.00269311	+	0.00173076i
$556$	12.8466	−	3.77211i	0.544818	−	0.159973i
$557$	−1.13171	+	7.87121i	−0.0479521	+	0.333514i	0.951697	+	0.307038i	$0.0993377\pi$
$557$	−1.13171	+	7.87121i	−0.0479521	+	0.333514i	−0.999649	+	0.0264763i	$0.991571\pi$
$558$	−8.66535	−	18.9745i	−0.366834	−	0.803254i
$559$	0.334795	+	0.215160i	0.0141603	+	0.00910028i
$560$	−0.286604	−	0.0841545i	−0.0121112	−	0.00355618i
$561$	−0.296598	+	0.400564i	−0.0125224	+	0.0169118i
$562$	11.4338	−	3.35727i	0.482307	−	0.141618i
$563$	23.6231	+	6.93636i	0.995594	+	0.292333i	0.738647	−	0.674093i	$-0.235465\pi$
$563$	23.6231	+	6.93636i	0.995594	+	0.292333i	0.256947	+	0.966426i	$0.417283\pi$
$564$	0.0669362	−	0.146570i	0.00281852	−	0.00617170i
$565$	2.61827			0.110152
$566$	13.8954	+	16.0361i	0.584066	+	0.674048i
$567$	0.867048	+	6.03045i	0.0364126	+	0.253255i
$568$	22.2613	−	25.6909i	0.934063	−	1.07797i
$569$	−13.0541	−	15.0652i	−0.547255	−	0.631566i	0.412986	−	0.910737i	$-0.364486\pi$
$569$	−13.0541	−	15.0652i	−0.547255	−	0.631566i	−0.960241	+	0.279171i	$0.909940\pi$
$570$	−0.00107330	+	0.00746498i	−4.49557e−5	+	0.000312674i
$571$	28.2500	−	18.1552i	1.18223	−	0.759770i	0.206431	−	0.978461i	$-0.433815\pi$
$571$	28.2500	−	18.1552i	1.18223	−	0.759770i	0.975794	+	0.218691i	$0.0701786\pi$
$572$	1.98502	+	0.420938i	0.0829977	+	0.0176003i
$573$	0.231119	+	0.148531i	0.00965513	+	0.00620498i
$574$	3.03414	−	3.50158i	0.126643	−	0.146153i
$575$	17.6367	−	20.3538i	0.735501	−	0.848814i
$576$	−9.07683	+	5.83333i	−0.378201	+	0.243055i
$577$	8.47073	−	9.77574i	0.352641	−	0.406969i	−0.551520	−	0.834162i	$-0.685952\pi$
$577$	8.47073	−	9.77574i	0.352641	−	0.406969i	0.904161	+	0.427192i	$0.140497\pi$
$578$	7.29998			0.303639
$579$	0.536413	−	0.157505i	0.0222925	−	0.00654568i
$580$	4.31676	+	2.77421i	0.179244	+	0.115193i
$581$	−5.31886	+	1.56176i	−0.220663	+	0.0647926i
$582$	−0.0408693	+	0.284252i	−0.00169409	+	0.0117826i
$583$	−10.1914	+	0.782576i	−0.422086	+	0.0324110i
$584$	2.10432	+	14.6359i	0.0870775	+	0.605638i
$585$	−0.457509	−	1.00181i	−0.0189157	−	0.0414196i
$586$	−17.6163	+	11.3213i	−0.727724	+	0.467680i
$587$	−17.4801	+	38.2760i	−0.721480	+	1.57982i	0.0903378	+	0.995911i	$0.471205\pi$
$587$	−17.4801	+	38.2760i	−0.721480	+	1.57982i	−0.811818	+	0.583910i	$0.801522\pi$
$588$	0.219266	+	0.140914i	0.00904237	+	0.00581118i
$589$	0.483334	−	3.36166i	0.0199154	−	0.138515i
$590$	5.45299	+	1.60114i	0.224496	+	0.0659180i
$591$	−0.597451	−	0.175427i	−0.0245758	−	0.00721612i
$592$	−1.12005	−	1.29260i	−0.0460336	−	0.0531256i
$593$	24.2640	+	28.0022i	0.996404	+	1.14991i	0.988695	+	0.149941i	$0.0479083\pi$
$593$	24.2640	+	28.0022i	0.996404	+	1.14991i	0.00770864	+	0.999970i	$0.497546\pi$
$594$	0.414099	+	0.223308i	0.0169907	+	0.00916243i
$595$	1.84187	−	2.12563i	0.0755092	−	0.0871423i
$596$	5.69962			0.233466
$597$	0.381452	−	0.112004i	0.0156118	−	0.00458403i
$598$	0.320673	+	2.23033i	0.0131133	+	0.0912050i
$599$	5.71580	−	12.5159i	0.233541	−	0.511384i	−0.756185	−	0.654358i	$-0.772939\pi$
$599$	5.71580	−	12.5159i	0.233541	−	0.511384i	0.989727	+	0.142973i	$0.0456663\pi$
$600$	−0.330222	−	0.0969619i	−0.0134812	−	0.00395845i
$601$	15.9255	+	18.3790i	0.649614	+	0.749695i	0.981044	−	0.193785i	$-0.0620764\pi$
$601$	15.9255	+	18.3790i	0.649614	+	0.749695i	−0.331430	+	0.943480i	$0.607531\pi$
$602$	0.479612			0.0195475
$603$	3.15382	−	6.90591i	0.128434	−	0.281230i
$604$	−6.08789			−0.247713
$605$	−8.17151	−	3.62885i	−0.332219	−	0.147534i
$606$	−0.0397081			−0.00161303
$607$	9.09516	−	19.9156i	0.369161	−	0.808350i	−0.630326	−	0.776330i	$-0.717079\pi$
$607$	9.09516	−	19.9156i	0.369161	−	0.808350i	0.999487	−	0.0320197i	$-0.0101939\pi$
$608$	−2.28642			−0.0927266
$609$	0.0608596	+	0.0702357i	0.00246615	+	0.00284609i
$610$	−4.42299	−	1.29871i	−0.179082	−	0.0525831i
$611$	0.758901	−	1.66176i	0.0307019	−	0.0672277i
$612$	2.95207	+	20.5321i	0.119330	+	0.829961i
$613$	9.60554	−	2.82044i	0.387964	−	0.113917i	−0.0819327	−	0.996638i	$-0.526109\pi$
$613$	9.60554	−	2.82044i	0.387964	−	0.113917i	0.469897	+	0.882721i	$0.344291\pi$
$614$	−17.9429			−0.724117
$615$	0.133283	−	0.153817i	0.00537450	−	0.00620251i
$616$	5.66390	−	2.14638i	0.228205	−	0.0864802i
$617$	6.45251	+	7.44660i	0.259768	+	0.299789i	0.870620	−	0.491957i	$-0.163718\pi$
$617$	6.45251	+	7.44660i	0.259768	+	0.299789i	−0.610851	+	0.791745i	$0.709173\pi$
$618$	0.166160	+	0.191759i	0.00668393	+	0.00771367i
$619$	−22.7764	−	6.68776i	−0.915461	−	0.268804i	−0.210123	−	0.977675i	$-0.567387\pi$
$619$	−22.7764	−	6.68776i	−0.915461	−	0.268804i	−0.705338	+	0.708871i	$0.749205\pi$
$620$	−9.14110	−	2.68407i	−0.367116	−	0.107795i
$621$	0.155918	−	1.08443i	0.00625677	−	0.0435168i
$622$	−5.48898	−	3.52755i	−0.220088	−	0.141442i
$623$	−0.133674	+	0.292706i	−0.00535554	+	0.0117270i
$624$	−0.00606573	+	0.00389821i	−0.000242823	+	0.000156053i
$625$	6.44987	+	14.1232i	0.257995	+	0.564929i
$626$	0.110707	+	0.769985i	0.00442475	+	0.0307748i
$627$	0.0185283	+	0.0335135i	0.000739948	+	0.00133840i
$628$	−3.61907	+	25.1712i	−0.144417	+	1.00444i
$629$	15.4525	−	4.53726i	0.616131	−	0.180912i
$630$	−1.11656	−	0.717571i	−0.0444849	−	0.0285887i
$631$	−10.7554	+	3.15808i	−0.428167	+	0.125721i	−0.488714	−	0.872444i	$-0.662534\pi$
$631$	−10.7554	+	3.15808i	−0.428167	+	0.125721i	0.0605466	+	0.998165i	$0.480716\pi$
$632$	37.3525			1.48580
$633$	0.0947984	−	0.109403i	0.00376790	−	0.00434839i
$634$	14.6167	−	9.39356i	0.580502	−	0.373066i
$635$	5.71258	−	6.59267i	0.226697	−	0.261622i
$636$	0.0804206	−	0.0928104i	0.00318889	−	0.00368017i
$637$	2.48597	+	1.59763i	0.0984975	+	0.0633005i
$638$	−12.3880	+	0.951245i	−0.490446	+	0.0376602i
$639$	−31.8194	+	20.4491i	−1.25876	+	0.808954i
$640$	−1.01362	+	7.04988i	−0.0400668	+	0.278671i
$641$	−5.80149	−	6.69528i	−0.229145	−	0.264448i	0.629520	−	0.776984i	$-0.283251\pi$
$641$	−5.80149	−	6.69528i	−0.229145	−	0.264448i	−0.858666	+	0.512536i	$0.828706\pi$
$642$	−0.157927	+	0.182258i	−0.00623289	+	0.00719314i
$643$	−4.30176	−	29.9194i	−0.169645	−	1.17991i	−0.879619	−	0.475678i	$-0.842203\pi$
$643$	−4.30176	−	29.9194i	−0.169645	−	1.17991i	0.709974	−	0.704228i	$-0.248707\pi$
$644$	−3.72919	−	4.30371i	−0.146951	−	0.169590i
$645$	0.0210683			0.000829565
$646$	0.669017	−	1.46494i	0.0263221	−	0.0576374i
$647$	47.7917	+	14.0329i	1.87889	+	0.551691i	0.996737	+	0.0807224i	$0.0257227\pi$
$647$	47.7917	+	14.0329i	1.87889	+	0.551691i	0.882150	+	0.470969i	$0.156095\pi$
$648$	23.2563	−	6.82866i	0.913592	−	0.268255i
$649$	26.9846	−	10.2260i	1.05924	−	0.401408i
$650$	−1.51157	−	0.443838i	−0.0592888	−	0.0174088i
$651$	−0.145155	−	0.0932856i	−0.00568908	−	0.00365615i
$652$	9.07015	+	19.8609i	0.355215	+	0.777811i
$653$	5.17720	−	36.0082i	0.202599	−	1.40911i	−0.593933	−	0.804514i	$-0.702426\pi$
$653$	5.17720	−	36.0082i	0.202599	−	1.40911i	0.796533	−	0.604596i	$-0.206665\pi$
$654$	0.271716	−	0.0797830i	0.0106249	−	0.00311976i
$655$	−10.0906	+	6.48480i	−0.394271	+	0.253382i
$656$	3.88300	+	2.49545i	0.151606	+	0.0974310i
$657$	2.34141	−	16.2848i	0.0913469	−	0.635332i
$658$	−0.313323	−	2.17921i	−0.0122146	−	0.0849543i
$659$	−13.0594	+	28.5962i	−0.508724	+	1.11395i	0.464811	+	0.885410i	$0.346122\pi$
$659$	−13.0594	+	28.5962i	−0.508724	+	1.11395i	−0.973535	+	0.228540i	$0.926605\pi$
$660$	0.100451	−	0.0380668i	0.00391006	−	0.00148175i
$661$	−16.5113	−	36.1547i	−0.642215	−	1.40625i	−0.898206	−	0.439575i	$-0.855129\pi$
$661$	−16.5113	−	36.1547i	−0.642215	−	1.40625i	0.255991	−	0.966679i	$-0.417598\pi$
$662$	0.0381802	−	0.0245369i	0.00148391	−	0.000953654i
$663$	−0.00966219	−	0.0672020i	−0.000375248	−	0.00260991i
$664$	9.16145	+	20.0608i	0.355533	+	0.778509i
$665$	−0.0897700	−	0.196569i	−0.00348113	−	0.00762262i
$666$	−3.15708	−	6.91303i	−0.122334	−	0.267875i
$667$	12.0191	+	26.3182i	0.465382	+	1.01904i
$668$	−0.740657	−	5.15138i	−0.0286569	−	0.199313i
$669$	−0.138753	+	0.0891708i	−0.00536448	+	0.00344754i
$670$	0.686871	+	1.50404i	0.0265362	+	0.0581061i
$671$	−21.8876	+	8.29448i	−0.844961	+	0.320205i
$672$	−0.0482555	+	0.105665i	−0.00186150	+	0.00407611i
$673$	2.80082	+	19.4802i	0.107964	+	0.750905i	0.969832	+	0.243773i	$0.0783852\pi$
$673$	2.80082	+	19.4802i	0.107964	+	0.750905i	−0.861869	+	0.507132i	$0.830706\pi$
$674$	3.26131	−	22.6829i	0.125621	−	0.873714i
$675$	0.644388	+	0.414123i	0.0248025	+	0.0159396i
$676$	14.5777	−	9.36854i	0.560682	−	0.360328i
$677$	−20.8017	+	6.10792i	−0.799473	+	0.234747i	−0.655855	−	0.754887i	$-0.727692\pi$
$677$	−20.8017	+	6.10792i	−0.799473	+	0.234747i	−0.143618	+	0.989633i	$0.545874\pi$
$678$	0.0108398	−	0.0753922i	0.000416298	−	0.00289542i
$679$	−3.41827	−	7.48497i	−0.131181	−	0.287247i
$680$	−9.41330	−	6.04956i	−0.360984	−	0.231990i
$681$	−0.841156	−	0.246986i	−0.0322332	−	0.00946451i
$682$	21.5708	−	8.17442i	0.825988	−	0.313015i
$683$	−34.9383	+	10.2588i	−1.33688	+	0.392542i	−0.870554	−	0.492073i	$-0.836239\pi$
$683$	−34.9383	+	10.2588i	−1.33688	+	0.392542i	−0.466321	+	0.884615i	$0.654421\pi$
$684$	1.52918	+	0.449007i	0.0584696	+	0.0171682i
$685$	1.10398	−	2.41738i	0.0421809	−	0.0923632i
$686$	7.37250			0.281483
$687$	−0.377352	−	0.435487i	−0.0143969	−	0.0166149i
$688$	0.0679977	+	0.472934i	0.00259239	+	0.0180304i
$689$	0.911783	−	1.05225i	0.0347362	−	0.0400877i
$690$	0.0781160	+	0.0901506i	0.00297382	+	0.00343198i
$691$	−1.21876	+	8.47664i	−0.0463637	+	0.322467i	0.953420	+	0.301647i	$0.0975365\pi$
$691$	−1.21876	+	8.47664i	−0.0463637	+	0.322467i	−0.999783	+	0.0208193i	$0.993373\pi$
$692$	9.55396	−	6.13996i	0.363187	−	0.233406i
$693$	−6.71958	+	0.515980i	−0.255256	+	0.0196005i
$694$	−14.2522	−	9.15933i	−0.541006	−	0.347683i
$695$	5.26258	−	6.07334i	0.199621	−	0.230375i
$696$	0.242122	−	0.279424i	0.00917761	−	0.0105915i
$697$	−36.5625	+	23.4973i	−1.38491	+	0.890025i
$698$	14.2196	−	16.4103i	0.538220	−	0.621139i
$699$	−0.614100			−0.0232274
$700$	3.82017	−	1.12170i	0.144389	−	0.0423964i
$701$	12.4004	+	7.96923i	0.468356	+	0.300994i	0.753450	−	0.657506i	$-0.228388\pi$
$701$	12.4004	+	7.96923i	0.468356	+	0.300994i	−0.285094	+	0.958500i	$0.592025\pi$
$702$	−0.0614903	+	0.0180552i	−0.00232080	+	0.000681449i
$703$	0.176095	−	1.22476i	0.00664153	−	0.0461929i
$704$	−5.77310	−	10.4422i	−0.217582	−	0.393557i
$705$	−0.0137636	−	0.0957279i	−0.000518367	−	0.00360532i
$706$	5.01442	+	10.9800i	0.188720	+	0.413240i
$707$	0.957158	−	0.615128i	0.0359976	−	0.0231343i
$708$	−0.144027	+	0.315375i	−0.00541287	+	0.0118525i
$709$	−32.5770	−	20.9360i	−1.22346	−	0.786268i	−0.240597	−	0.970625i	$-0.577343\pi$
$709$	−32.5770	−	20.9360i	−1.22346	−	0.786268i	−0.982859	+	0.184357i	$0.940980\pi$
$710$	1.17234	−	8.15381i	0.0439971	−	0.306007i
$711$	−39.8773	−	11.7090i	−1.49551	−	0.439123i
$712$	1.22832	+	0.360668i	0.0460334	+	0.0135166i
$713$	−35.1775	−	40.5970i	−1.31741	−	1.52037i
$714$	−0.0535812	−	0.0618360i	−0.00200523	−	0.00231416i
$715$	1.13888	−	0.431589i	0.0425918	−	0.0161405i
$716$	−6.62262	+	7.64291i	−0.247499	+	0.285629i
$717$	−0.0522433			−0.00195106
$718$	−17.4703	+	5.12975i	−0.651987	+	0.191441i
$719$	5.52403	+	38.4205i	0.206012	+	1.43284i	0.786004	+	0.618221i	$0.212146\pi$
$719$	5.52403	+	38.4205i	0.206012	+	1.43284i	−0.579993	+	0.814622i	$0.696945\pi$
$720$	0.549278	−	1.20275i	0.0204704	−	0.0448239i
$721$	−6.97583	−	2.04829i	−0.259794	−	0.0762823i
$722$	9.91762	+	11.4455i	0.369096	+	0.425959i
$723$	−0.708599			−0.0263531
$724$	3.69928	−	8.10030i	0.137483	−	0.301045i
$725$	−20.2286			−0.751270
$726$	−0.138322	+	0.220272i	−0.00513359	+	0.00817505i
$727$	28.7519			1.06635			0.533175	−	0.846005i	$-0.320999\pi$
$727$	28.7519			1.06635			0.533175	+	0.846005i	$0.320999\pi$
$728$	−0.342742	+	0.750500i	−0.0127029	+	0.0278154i
$729$	−26.9533			−0.998269
$730$	2.34646	+	2.70796i	0.0868465	+	0.100226i
$731$	−4.31673	−	1.26751i	−0.159660	−	0.0468804i
$732$	0.116822	−	0.255805i	0.00431787	−	0.00945482i
$733$	6.66754	+	46.3738i	0.246271	+	1.71285i	0.619401	+	0.785075i	$0.287376\pi$
$733$	6.66754	+	46.3738i	0.246271	+	1.71285i	−0.373130	+	0.927779i	$0.621715\pi$
$734$	−18.8976	+	5.54884i	−0.697524	+	0.204812i
$735$	0.156440			0.00577036
$736$	−23.6823	+	27.3308i	−0.872941	+	1.00743i
$737$	7.38968	+	3.98497i	0.272202	+	0.146788i
$738$	13.4309	+	15.5001i	0.494398	+	0.570566i
$739$	12.7355	+	14.6976i	0.468483	+	0.540658i	0.939989	−	0.341205i	$-0.110835\pi$
$739$	12.7355	+	14.6976i	0.468483	+	0.540658i	−0.471506	+	0.881863i	$0.656289\pi$
$740$	−3.33041	−	0.977896i	−0.122428	−	0.0359482i
$741$	−0.00500503	−	0.00146961i	−0.000183864	−	5.39874e-5i
$742$	0.238798	−	1.66088i	0.00876656	−	0.0609728i
$743$	−34.8757	−	22.4133i	−1.27947	−	0.822263i	−0.288645	−	0.957436i	$-0.593205\pi$
$743$	−34.8757	−	22.4133i	−1.27947	−	0.822263i	−0.990822	+	0.135173i	$0.956841\pi$
$744$	−0.285163	+	0.624420i	−0.0104546	+	0.0228924i
$745$	2.87790	−	1.84951i	0.105438	−	0.0677609i
$746$	7.39883	+	16.2012i	0.270891	+	0.593168i
$747$	−3.49218	−	24.2886i	−0.127772	−	0.888675i
$748$	−22.8718	+	1.75627i	−0.836276	+	0.0642155i
$749$	0.983412	−	6.83978i	0.0359331	−	0.249920i
$750$	−0.172227	+	0.0505704i	−0.00628884	+	0.00184657i
$751$	−15.9826	−	10.2714i	−0.583215	−	0.374810i	0.215514	−	0.976501i	$-0.430857\pi$
$751$	−15.9826	−	10.2714i	−0.583215	−	0.374810i	−0.798729	+	0.601691i	$0.794494\pi$
$752$	2.10444	−	0.617920i	0.0767411	−	0.0225332i
$753$	−0.388907			−0.0141726
$754$	1.10830	−	1.27905i	0.0403620	−	0.0465802i
$755$	−3.07395	+	1.97551i	−0.111872	+	0.0718960i
$756$	0.106064	−	0.122404i	0.00385750	−	0.00445179i
$757$	−21.7651	+	25.1183i	−0.791066	+	0.912939i	−0.997856	−	0.0654467i	$-0.979153\pi$
$757$	−21.7651	+	25.1183i	−0.791066	+	0.912939i	0.206790	+	0.978385i	$0.433698\pi$
$758$	4.06974	+	2.61547i	0.147820	+	0.0949980i
$759$	0.592518	+	0.125648i	0.0215070	+	0.00456074i
$760$	−0.723238	+	0.464797i	−0.0262346	+	0.0168600i
$761$	4.35162	−	30.2662i	0.157746	−	1.09715i	−0.745028	−	0.667033i	$-0.767564\pi$
$761$	4.35162	−	30.2662i	0.157746	−	1.09715i	0.902774	−	0.430115i	$-0.141527\pi$
$762$	−0.166183	−	0.191785i	−0.00602017	−	0.00694765i
$763$	−5.31373	+	6.13237i	−0.192370	+	0.222007i
$764$	1.79945	+	12.5155i	0.0651020	+	0.452794i
$765$	8.15320	+	9.40929i	0.294780	+	0.340194i
$766$	3.24315			0.117180
$767$	−1.63293	+	3.57562i	−0.0589617	+	0.129108i
$768$	0.401941	+	0.118021i	0.0145038	+	0.00425870i
$769$	16.0437	−	4.71087i	0.578552	−	0.169878i	0.0206527	−	0.999787i	$-0.493426\pi$
$769$	16.0437	−	4.71087i	0.578552	−	0.169878i	0.557900	+	0.829908i	$0.311607\pi$
$770$	0.873433	−	1.17960i	0.0314763	−	0.0425097i
$771$	0.0121487	+	0.00356717i	0.000437524	+	0.000128469i
$772$	21.6454	+	13.9107i	0.779036	+	0.500656i
$773$	−2.95927	−	6.47990i	−0.106438	−	0.233066i	0.848918	−	0.528525i	$-0.177255\pi$
$773$	−2.95927	−	6.47990i	−0.106438	−	0.233066i	−0.955355	+	0.295459i	$0.904527\pi$
$774$	−0.302141	+	2.10144i	−0.0108602	+	0.0755346i
$775$	36.0357	−	10.5810i	1.29444	−	0.380082i
$776$	−27.5395	+	17.6986i	−0.988612	+	0.635342i
$777$	−0.0528849	−	0.0339871i	−0.00189724	−	0.00121928i
$778$	0.988036	−	6.87194i	0.0354228	−	0.246371i
$779$	0.475225	+	3.30526i	0.0170267	+	0.118423i
$780$	−0.00607865	+	0.0133104i	−0.000217650	+	0.000476588i
$781$	−20.2380	−	36.6060i	−0.724171	−	1.30986i
$782$	−10.5817	−	23.1707i	−0.378401	−	0.828583i
$783$	−0.692260	+	0.444888i	−0.0247393	+	0.0158990i
$784$	0.504906	+	3.51170i	0.0180323	+	0.125418i
$785$	6.34063	+	13.8840i	0.226307	+	0.495542i
$786$	0.144952	+	0.317401i	0.00517027	+	0.0113213i
$787$	−10.0500	−	22.0064i	−0.358244	−	0.784445i	−0.999848	−	0.0174092i	$-0.994458\pi$
$787$	−10.0500	−	22.0064i	−0.358244	−	0.784445i	0.641605	−	0.767036i	$-0.278269\pi$
$788$	−11.9049	−	26.0680i	−0.424093	−	0.928635i
$789$	−0.0644425	−	0.448207i	−0.00229421	−	0.0159566i
$790$	7.61463	−	4.89362i	0.270916	−	0.174107i
$791$	0.906627	+	1.98524i	0.0322359	+	0.0705869i
$792$	5.83637	+	26.1687i	0.207386	+	0.929866i
$793$	1.32449	−	2.90023i	0.0470341	−	0.102990i
$794$	−4.16680	−	28.9807i	−0.147874	−	1.02849i
$795$	0.0104899	−	0.0729589i	0.000372038	−	0.00258758i
$796$	15.3924	+	9.89210i	0.545570	+	0.350616i
$797$	1.21086	−	0.778174i	0.0428909	−	0.0275643i	−0.519020	−	0.854762i	$-0.673703\pi$
$797$	1.21086	−	0.778174i	0.0428909	−	0.0275643i	0.561911	+	0.827198i	$0.310066\pi$
$798$	−0.00603177	+	0.00177109i	−0.000213522	+	6.26959e-5i
$799$	−2.93910	+	20.4419i	−0.103978	+	0.723182i
$800$	−10.5035	−	22.9994i	−0.371353	−	0.813151i
$801$	−1.19829	−	0.770094i	−0.0423395	−	0.0272099i
$802$	−16.4656	−	4.83474i	−0.581421	−	0.170721i
$803$	17.7982	+	3.77424i	0.628084	+	0.133190i
$804$	−0.0967840	+	0.0284184i	−0.00341331	+	0.00100224i
$805$	−3.27952	−	0.962953i	−0.115588	−	0.0339396i
$806$	−1.30532	+	2.85825i	−0.0459780	+	0.100678i
$807$	−0.749442			−0.0263816
$808$	−2.96422	−	3.42090i	−0.104281	−	0.120347i
$809$	5.44711	+	37.8855i	0.191510	+	1.33198i	0.828013	+	0.560709i	$0.189471\pi$
$809$	5.44711	+	37.8855i	0.191510	+	1.33198i	−0.636503	+	0.771275i	$0.719620\pi$
$810$	3.84635	−	4.43893i	0.135147	−	0.155968i
$811$	14.6379	+	16.8930i	0.514006	+	0.593195i	0.952120	−	0.305725i	$-0.0988988\pi$
$811$	14.6379	+	16.8930i	0.514006	+	0.593195i	−0.438114	+	0.898920i	$0.644353\pi$
$812$	−0.608712	+	4.23369i	−0.0213616	+	0.148573i
$813$	0.534462	−	0.343478i	0.0187444	−	0.0120463i
$814$	7.85895	−	2.97822i	0.275456	−	0.104386i
$815$	11.0246	+	7.08507i	0.386174	+	0.248179i
$816$	0.0533785	−	0.0616020i	0.00186862	−	0.00215650i
$817$	−0.226361	+	0.261234i	−0.00791937	+	0.00913944i
$818$	−2.09471	+	1.34619i	−0.0732399	+	0.0470684i
$819$	0.601171	−	0.693788i	0.0210066	−	0.0242429i
$820$	9.36718			0.327116
$821$	52.4331	−	15.3958i	1.82993	−	0.537316i	0.830134	−	0.557564i	$-0.188264\pi$
$821$	52.4331	−	15.3958i	1.82993	−	0.537316i	0.999795	+	0.0202480i	$0.00644559\pi$
$822$	−0.0650369	−	0.0417966i	−0.00226842	−	0.00145783i
$823$	−24.5860	+	7.21911i	−0.857015	+	0.251642i	−0.680583	−	0.732671i	$-0.738274\pi$
$823$	−24.5860	+	7.21911i	−0.857015	+	0.251642i	−0.176431	+	0.984313i	$0.556455\pi$
$824$	−4.11633	+	28.6297i	−0.143399	+	0.997362i
$825$	−0.252001	+	0.340334i	−0.00877353	+	0.0118489i
$826$	0.674178	+	4.68901i	0.0234576	+	0.163151i
$827$	2.31815	+	5.07605i	0.0806101	+	0.176511i	0.945645	−	0.325199i	$-0.105431\pi$
$827$	2.31815	+	5.07605i	0.0806101	+	0.176511i	−0.865035	+	0.501711i	$0.832704\pi$
$828$	21.2062	−	13.6284i	0.736965	−	0.473618i
$829$	−1.81169	+	3.96706i	−0.0629228	+	0.137782i	−0.938481	−	0.345331i	$-0.887767\pi$
$829$	−1.81169	+	3.96706i	−0.0629228	+	0.137782i	0.875558	+	0.483113i	$0.160494\pi$
$830$	4.49584	+	2.88930i	0.156053	+	0.100289i
$831$	−0.122422	+	0.851466i	−0.00424678	+	0.0295370i
$832$	1.55948	+	0.457905i	0.0540653	+	0.0158750i
$833$	−32.0532	−	9.41167i	−1.11058	−	0.326095i
$834$	−0.153092	−	0.176678i	−0.00530115	−	0.00611785i
$835$	−2.04559	−	2.36074i	−0.0707906	−	0.0816967i
$836$	−0.607256	+	1.65453i	−0.0210024	+	0.0572231i
$837$	1.00050	−	1.15464i	0.0345823	−	0.0399101i
$838$	22.9700			0.793487
$839$	−18.7711	+	5.51170i	−0.648051	+	0.190285i	−0.589207	−	0.807982i	$-0.700560\pi$
$839$	−18.7711	+	5.51170i	−0.648051	+	0.190285i	−0.0588442	+	0.998267i	$0.518742\pi$
$840$	0.00621604	+	0.0432335i	0.000214474	+	0.00149170i
$841$	−3.01951	+	6.61181i	−0.104121	+	0.227993i
$842$	16.5035	+	4.84588i	0.568749	+	0.167000i
$843$	0.285739	+	0.329761i	0.00984139	+	0.0113576i
$844$	6.66246			0.229331
$845$	4.32064	−	9.46088i	0.148634	−	0.325464i
$846$	9.74565			0.335062
$847$	−0.0780638	−	7.45238i	−0.00268230	−	0.256067i
$848$	1.67161			0.0574033
$849$	−0.322756	+	0.706737i	−0.0110770	+	0.0242552i
$850$	17.8094			0.610857
$851$	−12.8163	−	14.7908i	−0.439338	−	0.507023i
$852$	0.482185	+	0.141582i	0.0165194	+	0.00485053i
$853$	−1.35726	+	2.97199i	−0.0464718	+	0.101759i	−0.931444	−	0.363885i	$-0.881450\pi$
$853$	−1.35726	+	2.97199i	−0.0464718	+	0.101759i	0.884972	+	0.465644i	$0.154177\pi$
$854$	−0.546834	−	3.80332i	−0.0187123	−	0.130147i
$855$	0.917826	−	0.269498i	0.0313890	−	0.00921664i
$856$	−27.4910			−0.939623
$857$	30.2534	−	34.9143i	1.03344	−	1.19265i	0.0524408	−	0.998624i	$-0.483300\pi$
$857$	30.2534	−	34.9143i	1.03344	−	1.19265i	0.980996	−	0.194026i	$-0.0621546\pi$
$858$	−0.00771242	−	0.0345805i	−0.000263298	−	0.00118056i
$859$	7.74691	+	8.94041i	0.264321	+	0.305043i	0.872360	−	0.488865i	$-0.162589\pi$
$859$	7.74691	+	8.94041i	0.264321	+	0.305043i	−0.608039	+	0.793908i	$0.708043\pi$
$860$	0.634982	+	0.732808i	0.0216527	+	0.0249886i
$861$	0.162780	+	0.0477964i	0.00554751	+	0.00162890i
$862$	−11.0739	−	3.25158i	−0.377178	−	0.110749i
$863$	−7.66647	+	53.3215i	−0.260970	+	1.81508i	0.264628	+	0.964350i	$0.414751\pi$
$863$	−7.66647	+	53.3215i	−0.260970	+	1.81508i	−0.525598	+	0.850733i	$0.676158\pi$
$864$	−0.865275	−	0.556078i	−0.0294373	−	0.0189182i
$865$	2.83166	−	6.20047i	0.0962794	−	0.210822i
$866$	25.7159	−	16.5266i	0.873863	−	0.561598i
$867$	0.111039	+	0.243141i	0.00377108	+	0.00825751i
$868$	−1.13016	−	7.86041i	−0.0383600	−	0.266800i
$869$	15.8358	−	43.1461i	0.537192	−	1.46363i
$870$	0.0127508	−	0.0886838i	0.000432293	−	0.00300666i
$871$	−1.09731	+	0.322198i	−0.0371808	+	0.0109173i
$872$	27.1571	+	17.4528i	0.919654	+	0.591026i
$873$	34.9491	−	10.2620i	1.18285	−	0.347315i
$874$	−1.95710			−0.0661999
$875$	3.36811	−	3.88700i	0.113863	−	0.131405i
$876$	−0.183891	+	0.118180i	−0.00621310	+	0.00399292i
$877$	5.90734	−	6.81743i	0.199477	−	0.230208i	−0.647194	−	0.762325i	$-0.724058\pi$
$877$	5.90734	−	6.81743i	0.199477	−	0.230208i	0.846671	+	0.532117i	$0.178603\pi$
$878$	−18.2338	+	21.0429i	−0.615361	+	0.710165i
$879$	−0.645041	−	0.414542i	−0.0217567	−	0.0139822i
$880$	1.28700	+	0.694033i	0.0433849	+	0.0233958i
$881$	1.82025	−	1.16980i	0.0613258	−	0.0394117i	−0.509619	−	0.860400i	$-0.670214\pi$
$881$	1.82025	−	1.16980i	0.0613258	−	0.0394117i	0.570944	+	0.820989i	$0.306577\pi$
$882$	−2.24350	+	15.6039i	−0.0755426	+	0.525410i
$883$	6.37562	+	7.35785i	0.214557	+	0.247611i	0.852818	−	0.522208i	$-0.174892\pi$
$883$	6.37562	+	7.35785i	0.214557	+	0.247611i	−0.638262	+	0.769820i	$0.720346\pi$
$884$	2.04624	−	2.36149i	0.0688225	−	0.0794254i
$885$	0.0296152	+	0.205978i	0.000995504	+	0.00692388i
$886$	5.27966	+	6.09305i	0.177374	+	0.204700i
$887$	6.92647			0.232568			0.116284	−	0.993216i	$-0.462902\pi$
$887$	6.92647			0.232568			0.116284	+	0.993216i	$0.462902\pi$
$888$	−0.103894	+	0.227497i	−0.00348647	+	0.00763430i
$889$	6.97680	+	2.04857i	0.233994	+	0.0687070i
$890$	0.297656	−	0.0873997i	0.00997746	−	0.00292965i
$891$	1.97178	−	29.7585i	0.0660570	−	0.996948i
$892$	−7.28346	−	2.13862i	−0.243868	−	0.0716062i
$893$	1.33484	+	0.857853i	0.0446689	+	0.0287069i
$894$	−0.0413414	−	0.0905250i	−0.00138266	−	0.00302761i
$895$	−0.863841	+	6.00815i	−0.0288750	+	0.200830i
$896$	−5.69637	+	1.67260i	−0.190302	+	0.0558778i
$897$	−0.0694082	+	0.0446059i	−0.00231747	+	0.00148935i
$898$	−26.5781	−	17.0807i	−0.886923	−	0.569991i
$899$	−5.74199	+	39.9364i	−0.191506	+	1.33195i
$900$	2.50819	+	17.4448i	0.0836063	+	0.581495i
$901$	−6.53862	+	14.3176i	−0.217833	+	0.476988i
$902$	−18.0854	+	13.6870i	−0.602178	+	0.455726i
$903$	0.00729531	+	0.0159745i	0.000242773	+	0.000531598i
$904$	7.30430	−	4.69419i	0.242937	−	0.156126i
$905$	−0.760656	−	5.29048i	−0.0252851	−	0.175861i
$906$	0.0441576	+	0.0966917i	0.00146704	+	0.00321237i
$907$	5.70410	+	12.4902i	0.189402	+	0.414732i	0.980381	−	0.197111i	$-0.0631559\pi$
$907$	5.70410	+	12.4902i	0.189402	+	0.414732i	−0.790980	+	0.611843i	$0.790429\pi$
$908$	−16.7610	−	36.7014i	−0.556232	−	1.21798i
$909$	2.09223	+	4.58133i	0.0693947	+	0.151953i
$910$	0.0284536	+	0.197899i	0.000943228	+	0.00656029i
$911$	43.6857	−	28.0751i	1.44737	−	0.930169i	0.448025	−	0.894021i	$-0.352128\pi$
$911$	43.6857	−	28.0751i	1.44737	−	0.930169i	0.999346	−	0.0361482i	$-0.0115088\pi$
$912$	−0.00260159	−	0.00569669i	−8.61473e−5	−	0.000188636i
$913$	27.0564	−	2.07759i	0.895436	−	0.0687583i
$914$	−13.1505	+	28.7956i	−0.434980	+	0.952473i
$915$	−0.0240213	−	0.167072i	−0.000794118	−	0.00552322i
$916$	3.77424	−	26.2504i	0.124704	−	0.867339i
$917$	−8.41097	−	5.40540i	−0.277755	−	0.178502i
$918$	0.609471	−	0.391683i	0.0201155	−	0.0129275i
$919$	15.1036	−	4.43483i	0.498223	−	0.146292i	−0.0229598	−	0.999736i	$-0.507309\pi$
$919$	15.1036	−	4.43483i	0.498223	−	0.146292i	0.521183	+	0.853445i	$0.325491\pi$
$920$	−1.93519	+	13.4595i	−0.0638013	+	0.443748i
$921$	−0.272927	−	0.597627i	−0.00899325	−	0.0196925i
$922$	−1.12279	−	0.721573i	−0.0369771	−	0.0237637i
$923$	5.46686	+	1.60522i	0.179944	+	0.0528363i
$924$	0.0636463	+	0.0629831i	0.00209381	+	0.00207199i
$925$	13.1290	−	3.85502i	0.431679	−	0.126752i
$926$	3.62039	+	1.06304i	0.118973	+	0.0349337i
$927$	13.3692	−	29.2745i	0.439103	−	0.961501i
$928$	27.1626			0.891657
$929$	−16.0629	−	18.5376i	−0.527007	−	0.608198i	0.428364	−	0.903606i	$-0.359090\pi$
$929$	−16.0629	−	18.5376i	−0.527007	−	0.608198i	−0.955371	+	0.295408i	$0.904545\pi$
$930$	0.0236736	+	0.164653i	0.000776287	+	0.00539919i
$931$	−1.68081	+	1.93976i	−0.0550862	+	0.0635729i
$932$	−18.5084	−	21.3599i	−0.606264	−	0.699666i
$933$	0.0340006	−	0.236479i	0.00111313	−	0.00774198i
$934$	17.9905	−	11.5618i	0.588667	−	0.378313i
$935$	−10.9787	+	8.30863i	−0.359042	+	0.271721i
$936$	−3.07243	−	1.97453i	−0.100425	−	0.0645395i
$937$	−27.9185	+	32.2197i	−0.912059	+	1.05257i	0.0863546	+	0.996264i	$0.472478\pi$
$937$	−27.9185	+	32.2197i	−0.912059	+	1.05257i	−0.998413	+	0.0563076i	$0.982067\pi$
$938$	−0.902554	+	1.04160i	−0.0294694	+	0.0340096i
$939$	−0.0239620	+	0.0153995i	−0.000781972	+	0.000502543i
$940$	2.91483	−	3.36389i	0.0950711	−	0.109718i
$941$	−16.3824			−0.534051			−0.267026	−	0.963689i	$-0.586041\pi$
$941$	−16.3824			−0.534051			−0.267026	+	0.963689i	$0.586041\pi$
$942$	0.426036	−	0.125095i	0.0138810	−	0.00407583i
$943$	44.4319	+	28.5547i	1.44690	+	0.929868i
$944$	−4.52814	+	1.32958i	−0.147378	+	0.0432742i
$945$	0.0138347	−	0.0962226i	0.000450044	−	0.00313012i
$946$	−2.29672	−	0.487038i	−0.0746729	−	0.0158350i
$947$	1.88492	+	13.1099i	0.0612518	+	0.426016i	0.997256	+	0.0740274i	$0.0235852\pi$
$947$	1.88492	+	13.1099i	0.0612518	+	0.426016i	−0.936004	+	0.351988i	$0.885506\pi$
$948$	0.229389	+	0.502292i	0.00745021	+	0.0163137i
$949$	−2.08490	+	1.33988i	−0.0676786	+	0.0434944i
$950$	0.568422	−	1.24467i	0.0184420	−	0.0403824i
$951$	0.535204	+	0.343955i	0.0173552	+	0.0111535i
$952$	1.32738	−	9.23216i	0.0430207	−	0.299216i
$953$	−11.3170	−	3.32298i	−0.366595	−	0.107642i	0.0932464	−	0.995643i	$-0.470276\pi$
$953$	−11.3170	−	3.32298i	−0.366595	−	0.107642i	−0.459841	+	0.888001i	$0.652094\pi$
$954$	7.12677	+	2.09261i	0.230738	+	0.0677507i
$955$	4.96984	+	5.73550i	0.160820	+	0.185596i
$956$	−1.57457	−	1.81715i	−0.0509252	−	0.0587708i
$957$	−0.220116	−	0.398140i	−0.00711533	−	0.0128700i
$958$	4.92156	−	5.67979i	0.159008	−	0.183506i
$959$	2.21518			0.0715320
$960$	0.0825579	−	0.0242412i	0.00266455	−	0.000782381i
$961$	−6.24901	−	43.4628i	−0.201581	−	1.40203i
$962$	−0.475572	+	1.04136i	−0.0153331	+	0.0335747i
$963$	29.3492	+	8.61771i	0.945765	+	0.277702i
$964$	−21.3566	−	24.6468i	−0.687849	−	0.793820i
$965$	15.4434			0.497140
$966$	−0.0413052	+	0.0904457i	−0.00132897	+	0.00291004i
$967$	5.54824			0.178419			0.0892097	−	0.996013i	$-0.471566\pi$
$967$	5.54824			0.178419			0.0892097	+	0.996013i	$0.471566\pi$
$968$	−29.3024	+	4.52681i	−0.941814	+	0.145497i
$969$	0.0589693			0.00189437
$970$	−3.29545	+	7.21602i	−0.105810	+	0.231692i
$971$	−25.5694			−0.820560			−0.410280	−	0.911960i	$-0.634569\pi$
$971$	−25.5694			−0.820560			−0.410280	+	0.911960i	$0.634569\pi$
$972$	0.704285	+	0.812788i	0.0225899	+	0.0260702i
$973$	6.42721	+	1.88720i	0.206047	+	0.0605009i
$974$	4.81047	−	10.5335i	0.154138	−	0.337514i
$975$	−0.00820936	−	0.0570973i	−0.000262910	−	0.00182858i
$976$	3.67283	−	1.07844i	0.117564	−	0.0345200i
$977$	−12.5898			−0.402782			−0.201391	−	0.979511i	$-0.564546\pi$
$977$	−12.5898			−0.402782			−0.201391	+	0.979511i	$0.564546\pi$
$978$	0.249654	−	0.288116i	0.00798305	−	0.00921293i
$979$	0.937364	−	1.26594i	0.0299583	−	0.0404596i
$980$	4.71496	+	5.44135i	0.150614	+	0.173818i
$981$	−23.5217	−	27.1455i	−0.750990	−	0.866689i
$982$	19.7182	+	5.78978i	0.629232	+	0.184759i
$983$	−14.1916	−	4.16703i	−0.452642	−	0.132908i	0.0474622	−	0.998873i	$-0.484887\pi$
$983$	−14.1916	−	4.16703i	−0.452642	−	0.132908i	−0.500104	+	0.865965i	$0.666705\pi$
$984$	0.0960536	−	0.668068i	0.00306208	−	0.0212972i
$985$	−14.4701	−	9.29938i	−0.461056	−	0.296303i
$986$	−7.94790	+	17.4035i	−0.253113	+	0.554240i
$987$	0.0678172	−	0.0435835i	0.00215864	−	0.00138728i
$988$	−0.0997308	−	0.218380i	−0.00317286	−	0.00694759i
$989$	0.778076	+	5.41163i	0.0247414	+	0.172080i
$990$	4.61821	+	4.57009i	0.146776	+	0.145247i
$991$	−0.660306	+	4.59253i	−0.0209753	+	0.145887i	−0.997618	−	0.0689846i	$-0.978024\pi$
$991$	−0.660306	+	4.59253i	−0.0209753	+	0.145887i	0.976642	+	0.214871i	$0.0689332\pi$
$992$	−48.3882	+	14.2081i	−1.53633	+	0.451106i
$993$	0.00139801		0.000898445i	4.43644e−5		2.85113e-5i
$994$	6.58835	−	1.93451i	0.208970	−	0.0613590i
$995$	10.9820			0.348154
$996$	−0.213502	+	0.246394i	−0.00676507	+	0.00780731i
$997$	27.2032	−	17.4824i	0.861534	−	0.553674i	−0.0336183	−	0.999435i	$-0.510703\pi$
$997$	27.2032	−	17.4824i	0.861534	−	0.553674i	0.895152	+	0.445760i	$0.147067\pi$
$998$	−15.6919	+	18.1094i	−0.496718	+	0.573243i
$999$	0.364515	−	0.420673i	0.0115328	−	0.0133095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.2.e.a.23.7	✓	100
121.100	even	11	inner	121.2.e.a.100.7	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.2.e.a.23.7	✓	100	1.1	even	1	trivial
121.2.e.a.100.7	yes	100	121.100	even	11	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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.333827 - 0.730979i) q^{2} +0.0294246 q^{3} +(0.886832 + 1.02346i) q^{4} +(0.779896 + 0.228998i) q^{5} +(0.00982271 - 0.0215087i) q^{6} +(0.0964221 + 0.670630i) q^{7} +(2.58627 - 0.759397i) q^{8} -2.99913 q^{9} +O(q^{10})\)	\(q+(0.333827 - 0.730979i) q^{2} +0.0294246 q^{3} +(0.886832 + 1.02346i) q^{4} +(0.779896 + 0.228998i) q^{5} +(0.00982271 - 0.0215087i) q^{6} +(0.0964221 + 0.670630i) q^{7} +(2.58627 - 0.759397i) q^{8} -2.99913 q^{9} +(0.427743 - 0.493642i) q^{10} +(0.219276 - 3.30937i) q^{11} +(0.0260947 + 0.0301148i) q^{12} +(0.295853 + 0.341432i) q^{13} +(0.522405 + 0.153392i) q^{14} +(0.0229481 + 0.00673818i) q^{15} +(-0.0771914 + 0.536878i) q^{16} +(-4.29650 - 2.76119i) q^{17} +(-1.00119 + 2.19230i) q^{18} +(-0.330107 + 0.212147i) q^{19} +(0.457267 + 1.00127i) q^{20} +(0.00283718 + 0.0197330i) q^{21} +(-2.34588 - 1.26504i) q^{22} +(-0.883277 + 6.14333i) q^{23} +(0.0760999 - 0.0223449i) q^{24} +(-3.65047 - 2.34601i) q^{25} +(0.348343 - 0.102283i) q^{26} -0.176522 q^{27} +(-0.600852 + 0.693421i) q^{28} +(3.92166 - 2.52030i) q^{29} +(0.0125862 - 0.0145252i) q^{30} +(-5.66785 + 6.54105i) q^{31} +(4.90180 + 3.15019i) q^{32} +(0.00645211 - 0.0973768i) q^{33} +(-3.45266 + 2.21889i) q^{34} +(-0.0783739 + 0.545103i) q^{35} +(-2.65973 - 3.06949i) q^{36} +(-2.06499 + 2.38312i) q^{37} +(0.0448763 + 0.312121i) q^{38} +(0.00870535 + 0.0100465i) q^{39} +2.19092 q^{40} +(3.53512 - 7.74082i) q^{41} +(0.0153715 + 0.00451349i) q^{42} +(0.845214 - 0.248177i) q^{43} +(3.58146 - 2.71043i) q^{44} +(-2.33901 - 0.686796i) q^{45} +(4.19578 + 2.69646i) q^{46} +(-1.67980 - 3.67826i) q^{47} +(-0.00227133 + 0.0157974i) q^{48} +(6.27600 - 1.84280i) q^{49} +(-2.93351 + 1.88525i) q^{50} +(-0.126423 - 0.0812470i) q^{51} +(-0.0870702 + 0.605586i) q^{52} +(-0.438597 - 3.05051i) q^{53} +(-0.0589278 + 0.129034i) q^{54} +(0.928852 - 2.53075i) q^{55} +(0.758648 + 1.66121i) q^{56} +(-0.00971326 + 0.00624233i) q^{57} +(-0.533129 - 3.70799i) q^{58} +(3.61444 + 7.91452i) q^{59} +(0.0134549 + 0.0294621i) q^{60} +(-2.93172 - 6.41957i) q^{61} +(2.88929 + 6.32665i) q^{62} +(-0.289183 - 2.01131i) q^{63} +(3.02648 - 1.94500i) q^{64} +(0.152547 + 0.334032i) q^{65} +(-0.0690264 - 0.0372233i) q^{66} +(-1.05158 + 2.30263i) q^{67} +(-0.984307 - 6.84601i) q^{68} +(-0.0259901 + 0.180765i) q^{69} +(0.372295 + 0.239260i) q^{70} +(10.6095 - 6.81833i) q^{71} +(-7.75657 + 2.27753i) q^{72} +(-0.780694 + 5.42985i) q^{73} +(1.05266 + 2.30501i) q^{74} +(-0.107414 - 0.0690305i) q^{75} +(-0.509873 - 0.149712i) q^{76} +(2.24051 - 0.172043i) q^{77} +(0.0102499 - 0.00300963i) q^{78} +(13.2963 + 3.90413i) q^{79} +(-0.183145 + 0.401033i) q^{80} +8.99221 q^{81} +(-4.47826 - 5.16819i) q^{82} +(1.16440 + 8.09855i) q^{83} +(-0.0176798 + 0.0204036i) q^{84} +(-2.71852 - 3.13734i) q^{85} +(0.100743 - 0.700682i) q^{86} +(0.115393 - 0.0741587i) q^{87} +(-1.94602 - 8.72543i) q^{88} +(0.399545 + 0.256772i) q^{89} +(-1.28286 + 1.48050i) q^{90} +(-0.200448 + 0.231330i) q^{91} +(-7.07076 + 4.54410i) q^{92} +(-0.166774 + 0.192468i) q^{93} -3.24949 q^{94} +(-0.306030 + 0.0898586i) q^{95} +(0.144233 + 0.0926931i) q^{96} +(-11.6531 + 3.42164i) q^{97} +(0.748050 - 5.20280i) q^{98} +(-0.657639 + 9.92524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9}+O(q^{10}) \) 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9	\( 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9} - 13 q^{10} - 12 q^{11} - 51 q^{12} - 34 q^{13} - 17 q^{14} - 46 q^{15} + 10 q^{16} + 9 q^{17} - 31 q^{18} + 9 q^{19} + 21 q^{20} - 14 q^{21} - 20 q^{22} - 11 q^{23} - 72 q^{24} + 11 q^{25} + 33 q^{26} - 60 q^{27} + 49 q^{28} + 19 q^{29} + 26 q^{30} - 13 q^{31} + 44 q^{32} + q^{33} + 31 q^{34} + 39 q^{35} - 17 q^{36} - 16 q^{37} - 29 q^{38} + 16 q^{39} + 2 q^{40} + 39 q^{41} + 42 q^{42} + 39 q^{43} + 53 q^{44} - 33 q^{45} + 59 q^{46} + 21 q^{47} + 56 q^{48} - 11 q^{49} - 58 q^{50} - 139 q^{51} - 75 q^{52} - 73 q^{53} - 156 q^{54} - 34 q^{55} + 10 q^{56} - 41 q^{57} - 38 q^{58} + 33 q^{59} + 100 q^{60} + 39 q^{61} + 44 q^{62} - 76 q^{63} - 16 q^{64} + 36 q^{65} + 75 q^{66} - 4 q^{67} + 119 q^{68} + 32 q^{69} + 61 q^{70} + 5 q^{71} + 63 q^{72} + 37 q^{73} + 109 q^{74} + 58 q^{75} - 91 q^{76} - 53 q^{77} - 24 q^{78} - 9 q^{79} - 36 q^{80} + 28 q^{81} + 33 q^{82} + 79 q^{83} + 176 q^{84} - 11 q^{85} + 85 q^{86} + 76 q^{87} + 33 q^{88} - 48 q^{89} - 89 q^{90} - 14 q^{91} - 113 q^{92} + 31 q^{93} - 38 q^{94} + 21 q^{95} + 84 q^{96} + 40 q^{97} - 22 q^{98} - 53 q^{99}+O(q^{100}) \) 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9 - 13 * q^10 - 12 * q^11 - 51 * q^12 - 34 * q^13 - 17 * q^14 - 46 * q^15 + 10 * q^16 + 9 * q^17 - 31 * q^18 + 9 * q^19 + 21 * q^20 - 14 * q^21 - 20 * q^22 - 11 * q^23 - 72 * q^24 + 11 * q^25 + 33 * q^26 - 60 * q^27 + 49 * q^28 + 19 * q^29 + 26 * q^30 - 13 * q^31 + 44 * q^32 + q^33 + 31 * q^34 + 39 * q^35 - 17 * q^36 - 16 * q^37 - 29 * q^38 + 16 * q^39 + 2 * q^40 + 39 * q^41 + 42 * q^42 + 39 * q^43 + 53 * q^44 - 33 * q^45 + 59 * q^46 + 21 * q^47 + 56 * q^48 - 11 * q^49 - 58 * q^50 - 139 * q^51 - 75 * q^52 - 73 * q^53 - 156 * q^54 - 34 * q^55 + 10 * q^56 - 41 * q^57 - 38 * q^58 + 33 * q^59 + 100 * q^60 + 39 * q^61 + 44 * q^62 - 76 * q^63 - 16 * q^64 + 36 * q^65 + 75 * q^66 - 4 * q^67 + 119 * q^68 + 32 * q^69 + 61 * q^70 + 5 * q^71 + 63 * q^72 + 37 * q^73 + 109 * q^74 + 58 * q^75 - 91 * q^76 - 53 * q^77 - 24 * q^78 - 9 * q^79 - 36 * q^80 + 28 * q^81 + 33 * q^82 + 79 * q^83 + 176 * q^84 - 11 * q^85 + 85 * q^86 + 76 * q^87 + 33 * q^88 - 48 * q^89 - 89 * q^90 - 14 * q^91 - 113 * q^92 + 31 * q^93 - 38 * q^94 + 21 * q^95 + 84 * q^96 + 40 * q^97 - 22 * q^98 - 53 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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