LMFDB - Embedded newform 122.2.i.a.15.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(15,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("122.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.i (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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			15.2
Root			$2.52368i$ of defining polynomial
Character	$\chi$	$=$	122.15
Dual form			122.2.i.a.57.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 + 0.994522i) q^{2} +(2.50985 - 1.82351i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.320145 + 0.355557i) q^{5} +(2.07588 + 2.30549i) q^{6} +(-3.17717 + 1.41457i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.04710 - 6.30034i) q^{9} +O(q^{10})$	\(q+(0.104528 + 0.994522i) q^{2} +(2.50985 - 1.82351i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.320145 + 0.355557i) q^{5} +(2.07588 + 2.30549i) q^{6} +(-3.17717 + 1.41457i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.04710 - 6.30034i) q^{9} +(-0.320145 + 0.355557i) q^{10} +1.19532 q^{11} +(-2.07588 + 2.30549i) q^{12} +(-1.03054 + 1.78495i) q^{13} +(-1.73892 - 3.01190i) q^{14} +(1.45188 + 0.308606i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-7.31827 + 1.55555i) q^{17} +(6.47981 + 1.37733i) q^{18} +(4.69556 + 2.09060i) q^{19} +(-0.387073 - 0.281225i) q^{20} +(-5.39475 + 9.34398i) q^{21} +(0.124945 + 1.18877i) q^{22} +(-1.46962 + 4.52302i) q^{23} +(-2.50985 - 1.82351i) q^{24} +(0.498714 - 4.74495i) q^{25} +(-1.88289 - 0.838319i) q^{26} +(-3.47480 - 10.6943i) q^{27} +(2.81364 - 2.04423i) q^{28} +(-0.136165 - 0.235845i) q^{29} +(-0.155153 + 1.47618i) q^{30} +(0.872224 - 8.29866i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00008 - 2.17968i) q^{33} +(-2.31199 - 7.11558i) q^{34} +(-1.52011 - 0.676798i) q^{35} +(-0.692456 + 6.58828i) q^{36} +(1.29110 + 0.938039i) q^{37} +(-1.58833 + 4.88837i) q^{38} +(0.668376 + 6.35918i) q^{39} +(0.239224 - 0.414349i) q^{40} +(-5.35315 - 3.88929i) q^{41} +(-9.85669 - 4.38848i) q^{42} +(4.46073 + 0.948156i) q^{43} +(-1.16920 + 0.248521i) q^{44} +(2.89550 - 1.28916i) q^{45} +(-4.65186 - 0.988784i) q^{46} +(4.59378 + 7.95667i) q^{47} +(1.55117 - 2.68671i) q^{48} +(3.40950 - 3.78663i) q^{49} +4.77109 q^{50} +(-15.5312 + 17.2492i) q^{51} +(0.636910 - 1.96021i) q^{52} +(-3.83265 - 11.7957i) q^{53} +(10.2725 - 4.57362i) q^{54} +(0.382675 + 0.425004i) q^{55} +(2.32713 + 2.58454i) q^{56} +(15.5974 - 3.31533i) q^{57} +(0.220319 - 0.160071i) q^{58} +(0.251433 + 2.39223i) q^{59} -1.48431 q^{60} +(6.14931 + 4.81518i) q^{61} +8.34437 q^{62} +(2.40826 + 22.9130i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.964574 + 0.205027i) q^{65} +(2.48134 + 2.75580i) q^{66} +(5.78253 + 6.42215i) q^{67} +(6.83493 - 3.04311i) q^{68} +(4.55927 + 14.0320i) q^{69} +(0.514195 - 1.58253i) q^{70} +(2.72458 - 3.02595i) q^{71} -6.62457 q^{72} +(11.0836 - 12.3096i) q^{73} +(-0.797944 + 1.38208i) q^{74} +(-7.40079 - 12.8185i) q^{75} +(-5.02761 - 1.06865i) q^{76} +(-3.79774 + 1.69086i) q^{77} +(-6.25448 + 1.32943i) q^{78} +(-9.18923 - 1.95323i) q^{79} +(0.437085 + 0.194603i) q^{80} +(-12.1443 - 8.82336i) q^{81} +(3.30843 - 5.73037i) q^{82} +(0.654654 + 6.22862i) q^{83} +(3.33414 - 10.2614i) q^{84} +(-2.89599 - 2.10406i) q^{85} +(-0.476690 + 4.53540i) q^{86} +(-0.771820 - 0.343636i) q^{87} +(-0.369374 - 1.13682i) q^{88} +(1.85050 - 1.34447i) q^{89} +(1.58476 + 2.74488i) q^{90} +(0.749274 - 7.12887i) q^{91} +(0.497115 - 4.72973i) q^{92} +(-12.9436 - 22.4189i) q^{93} +(-7.43290 + 5.40032i) q^{94} +(0.759933 + 2.33883i) q^{95} +(2.83414 + 1.26184i) q^{96} +(-1.07950 + 10.2708i) q^{97} +(4.12228 + 2.99501i) q^{98} +(2.44695 - 7.53092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9} - 6 q^{10} - 2 q^{11} + q^{12} - 9 q^{13} - 10 q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 24 q^{18} + 10 q^{19} - 7 q^{20} - 6 q^{21} - 11 q^{22} - 11 q^{23} - 3 q^{24} - 28 q^{25} + 4 q^{26} - 33 q^{27} + 5 q^{28} + 15 q^{29} - 12 q^{30} - 12 q^{31} + 8 q^{32} + 15 q^{33} - 11 q^{34} + 19 q^{35} + q^{36} + 16 q^{37} - 10 q^{38} + 24 q^{39} + 4 q^{40} - 20 q^{41} - 19 q^{42} - 21 q^{43} - 4 q^{44} + 17 q^{45} + 2 q^{46} - 11 q^{47} + q^{48} - 10 q^{49} + 4 q^{50} - 56 q^{51} - 2 q^{52} - 8 q^{53} + 41 q^{54} + 35 q^{55} + 10 q^{56} + 49 q^{57} - 10 q^{58} + 35 q^{59} + 6 q^{60} + 15 q^{61} + 16 q^{62} - 26 q^{63} - 4 q^{64} + 24 q^{65} + 10 q^{66} + 22 q^{67} + 12 q^{68} + 46 q^{69} + 28 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 7 q^{74} - 15 q^{75} - 20 q^{76} + 2 q^{77} + 11 q^{78} + 10 q^{79} - 4 q^{80} - 27 q^{81} + 15 q^{82} - 45 q^{83} + 17 q^{84} + 2 q^{85} + 11 q^{86} - 9 q^{87} - 8 q^{88} - 26 q^{89} + 8 q^{90} - 84 q^{91} - 47 q^{92} - 33 q^{93} - 2 q^{94} + 37 q^{95} + 9 q^{96} - 41 q^{97} - 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9 - 6 * q^10 - 2 * q^11 + q^12 - 9 * q^13 - 10 * q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 24 * q^18 + 10 * q^19 - 7 * q^20 - 6 * q^21 - 11 * q^22 - 11 * q^23 - 3 * q^24 - 28 * q^25 + 4 * q^26 - 33 * q^27 + 5 * q^28 + 15 * q^29 - 12 * q^30 - 12 * q^31 + 8 * q^32 + 15 * q^33 - 11 * q^34 + 19 * q^35 + q^36 + 16 * q^37 - 10 * q^38 + 24 * q^39 + 4 * q^40 - 20 * q^41 - 19 * q^42 - 21 * q^43 - 4 * q^44 + 17 * q^45 + 2 * q^46 - 11 * q^47 + q^48 - 10 * q^49 + 4 * q^50 - 56 * q^51 - 2 * q^52 - 8 * q^53 + 41 * q^54 + 35 * q^55 + 10 * q^56 + 49 * q^57 - 10 * q^58 + 35 * q^59 + 6 * q^60 + 15 * q^61 + 16 * q^62 - 26 * q^63 - 4 * q^64 + 24 * q^65 + 10 * q^66 + 22 * q^67 + 12 * q^68 + 46 * q^69 + 28 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 7 * q^74 - 15 * q^75 - 20 * q^76 + 2 * q^77 + 11 * q^78 + 10 * q^79 - 4 * q^80 - 27 * q^81 + 15 * q^82 - 45 * q^83 + 17 * q^84 + 2 * q^85 + 11 * q^86 - 9 * q^87 - 8 * q^88 - 26 * q^89 + 8 * q^90 - 84 * q^91 - 47 * q^92 - 33 * q^93 - 2 * q^94 + 37 * q^95 + 9 * q^96 - 41 * q^97 - 5 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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 $

$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$3$	2.50985	−	1.82351i	1.44906	−	1.05281i	0.463016	−	0.886350i	$-0.346767\pi$
$3$	2.50985	−	1.82351i	1.44906	−	1.05281i	0.986049	−	0.166457i	$-0.0532326\pi$
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	0.320145	+	0.355557i	0.143173	+	0.159010i	0.810466	−	0.585785i	$-0.199214\pi$
$5$	0.320145	+	0.355557i	0.143173	+	0.159010i	−0.667293	+	0.744795i	$0.732547\pi$
$6$	2.07588	+	2.30549i	0.847473	+	0.941214i
$7$	−3.17717	+	1.41457i	−1.20086	+	0.534656i	−0.906975	−	0.421185i	$-0.861614\pi$
$7$	−3.17717	+	1.41457i	−1.20086	+	0.534656i	−0.293883	+	0.955841i	$0.594948\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	2.04710	−	6.30034i	0.682368	−	2.10011i
$10$	−0.320145	+	0.355557i	−0.101239	+	0.112437i
$11$	1.19532			0.360403			0.180201	−	0.983630i	$-0.442325\pi$
$11$	1.19532			0.360403			0.180201	+	0.983630i	$0.442325\pi$
$12$	−2.07588	+	2.30549i	−0.599254	+	0.665539i
$13$	−1.03054	+	1.78495i	−0.285821	+	0.495057i	−0.972808	−	0.231613i	$-0.925600\pi$
$13$	−1.03054	+	1.78495i	−0.285821	+	0.495057i	0.686987	+	0.726670i	$0.258933\pi$
$14$	−1.73892	−	3.01190i	−0.464747	−	0.804965i
$15$	1.45188	+	0.308606i	0.374874	+	0.0796818i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	−7.31827	+	1.55555i	−1.77494	+	0.377275i	−0.974895	−	0.222663i	$-0.928525\pi$
$17$	−7.31827	+	1.55555i	−1.77494	+	0.377275i	−0.800046	+	0.599939i	$0.795192\pi$
$18$	6.47981	+	1.37733i	1.52730	+	0.324639i
$19$	4.69556	+	2.09060i	1.07724	+	0.479616i	0.867140	−	0.498064i	$-0.165956\pi$
$19$	4.69556	+	2.09060i	1.07724	+	0.479616i	0.210096	+	0.977681i	$0.432622\pi$
$20$	−0.387073	−	0.281225i	−0.0865522	−	0.0628838i
$21$	−5.39475	+	9.34398i	−1.17723	+	2.03902i
$22$	0.124945	+	1.18877i	0.0266384	+	0.253447i
$23$	−1.46962	+	4.52302i	−0.306437	+	0.943115i	0.672701	+	0.739915i	$0.265134\pi$
$23$	−1.46962	+	4.52302i	−0.306437	+	0.943115i	−0.979137	+	0.203200i	$0.934866\pi$
$24$	−2.50985	−	1.82351i	−0.512322	−	0.372223i
$25$	0.498714	−	4.74495i	0.0997429	−	0.948990i
$26$	−1.88289	−	0.838319i	−0.369266	−	0.164408i
$27$	−3.47480	−	10.6943i	−0.668725	−	2.05812i
$28$	2.81364	−	2.04423i	0.531727	−	0.386323i
$29$	−0.136165	−	0.235845i	−0.0252852	−	0.0437952i	0.853106	−	0.521738i	$-0.174716\pi$
$29$	−0.136165	−	0.235845i	−0.0252852	−	0.0437952i	−0.878391	+	0.477943i	$0.841383\pi$
$30$	−0.155153	+	1.47618i	−0.0283270	+	0.269513i
$31$	0.872224	−	8.29866i	0.156656	−	1.49048i	−0.580223	−	0.814458i	$-0.697034\pi$
$31$	0.872224	−	8.29866i	0.156656	−	1.49048i	0.736879	−	0.676025i	$-0.236299\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.00008	−	2.17968i	0.522247	−	0.379434i
$34$	−2.31199	−	7.11558i	−0.396503	−	1.22031i
$35$	−1.52011	−	0.676798i	−0.256946	−	0.114400i
$36$	−0.692456	+	6.58828i	−0.115409	+	1.09805i
$37$	1.29110	+	0.938039i	0.212256	+	0.154213i	0.688834	−	0.724919i	$-0.258123\pi$
$37$	1.29110	+	0.938039i	0.212256	+	0.154213i	−0.476578	+	0.879132i	$0.658123\pi$
$38$	−1.58833	+	4.88837i	−0.257661	+	0.792998i
$39$	0.668376	+	6.35918i	0.107026	+	1.01828i
$40$	0.239224	−	0.414349i	0.0378247	−	0.0655143i
$41$	−5.35315	−	3.88929i	−0.836022	−	0.607406i	0.0852346	−	0.996361i	$-0.472836\pi$
$41$	−5.35315	−	3.88929i	−0.836022	−	0.607406i	−0.921257	+	0.388955i	$0.872836\pi$
$42$	−9.85669	−	4.38848i	−1.52092	−	0.677158i
$43$	4.46073	+	0.948156i	0.680254	+	0.144593i	0.535064	−	0.844811i	$-0.320287\pi$
$43$	4.46073	+	0.948156i	0.680254	+	0.144593i	0.145190	+	0.989404i	$0.453621\pi$
$44$	−1.16920	+	0.248521i	−0.176263	+	0.0374660i
$45$	2.89550	−	1.28916i	0.431635	−	0.192176i
$46$	−4.65186	−	0.988784i	−0.685879	−	0.145788i
$47$	4.59378	+	7.95667i	0.670072	+	1.16060i	0.977883	+	0.209152i	$0.0670702\pi$
$47$	4.59378	+	7.95667i	0.670072	+	1.16060i	−0.307811	+	0.951448i	$0.599596\pi$
$48$	1.55117	−	2.68671i	0.223893	−	0.387794i
$49$	3.40950	−	3.78663i	0.487071	−	0.540947i
$50$	4.77109			0.674734
$51$	−15.5312	+	17.2492i	−2.17481	+	2.41537i
$52$	0.636910	−	1.96021i	0.0883236	−	0.271832i
$53$	−3.83265	−	11.7957i	−0.526456	−	1.62026i	−0.761419	−	0.648260i	$-0.775497\pi$
$53$	−3.83265	−	11.7957i	−0.526456	−	1.62026i	0.234964	−	0.972004i	$-0.424503\pi$
$54$	10.2725	−	4.57362i	1.39791	−	0.622391i
$55$	0.382675	+	0.425004i	0.0515999	+	0.0573075i
$56$	2.32713	+	2.58454i	0.310976	+	0.345374i
$57$	15.5974	−	3.31533i	2.06593	−	0.439127i
$58$	0.220319	−	0.160071i	0.0289294	−	0.0210184i
$59$	0.251433	+	2.39223i	0.0327338	+	0.311441i	0.998622	+	0.0524816i	$0.0167131\pi$
$59$	0.251433	+	2.39223i	0.0327338	+	0.311441i	−0.965888	+	0.258960i	$0.916620\pi$
$60$	−1.48431			−0.191624
$61$	6.14931	+	4.81518i	0.787338	+	0.616521i
$61$	6.14931	+	4.81518i	0.787338	+	0.616521i
$62$	8.34437			1.05974
$63$	2.40826	+	22.9130i	0.303412	+	2.88677i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.964574	+	0.205027i	−0.119641	+	0.0254304i
$66$	2.48134	+	2.75580i	0.305431	+	0.339216i
$67$	5.78253	+	6.42215i	0.706449	+	0.784591i	0.984389	−	0.176008i	$-0.0563183\pi$
$67$	5.78253	+	6.42215i	0.706449	+	0.784591i	−0.277940	+	0.960598i	$0.589652\pi$
$68$	6.83493	−	3.04311i	0.828857	−	0.369031i
$69$	4.55927	+	14.0320i	0.548872	+	1.68925i
$70$	0.514195	−	1.58253i	0.0614581	−	0.189149i
$71$	2.72458	−	3.02595i	0.323348	−	0.359114i	−0.559453	−	0.828862i	$-0.688989\pi$
$71$	2.72458	−	3.02595i	0.323348	−	0.359114i	0.882800	+	0.469748i	$0.155655\pi$
$72$	−6.62457			−0.780713
$73$	11.0836	−	12.3096i	1.29724	−	1.44073i	0.466028	−	0.884770i	$-0.345684\pi$
$73$	11.0836	−	12.3096i	1.29724	−	1.44073i	0.831210	−	0.555959i	$-0.187649\pi$
$74$	−0.797944	+	1.38208i	−0.0927591	+	0.160663i
$75$	−7.40079	−	12.8185i	−0.854569	−	1.48016i
$76$	−5.02761	−	1.06865i	−0.576707	−	0.122583i
$77$	−3.79774	+	1.69086i	−0.432792	+	0.192692i
$78$	−6.25448	+	1.32943i	−0.708180	+	0.150528i
$79$	−9.18923	−	1.95323i	−1.03387	−	0.219756i	−0.340429	−	0.940270i	$-0.610572\pi$
$79$	−9.18923	−	1.95323i	−1.03387	−	0.219756i	−0.693440	+	0.720514i	$0.743906\pi$
$80$	0.437085	+	0.194603i	0.0488676	+	0.0217572i
$81$	−12.1443	−	8.82336i	−1.34937	−	0.980374i
$82$	3.30843	−	5.73037i	0.365355	−	0.632813i
$83$	0.654654	+	6.22862i	0.0718576	+	0.683680i	0.969856	+	0.243680i	$0.0783548\pi$
$83$	0.654654	+	6.22862i	0.0718576	+	0.683680i	−0.897998	+	0.440000i	$0.854979\pi$
$84$	3.33414	−	10.2614i	0.363784	−	1.11961i
$85$	−2.89599	−	2.10406i	−0.314114	−	0.228217i
$86$	−0.476690	+	4.53540i	−0.0514028	+	0.489065i
$87$	−0.771820	−	0.343636i	−0.0827478	−	0.0368417i
$88$	−0.369374	−	1.13682i	−0.0393754	−	0.121185i
$89$	1.85050	−	1.34447i	0.196153	−	0.142513i	−0.485374	−	0.874307i	$-0.661316\pi$
$89$	1.85050	−	1.34447i	0.196153	−	0.142513i	0.681526	+	0.731794i	$0.261316\pi$
$90$	1.58476	+	2.74488i	0.167048	+	0.289336i
$91$	0.749274	−	7.12887i	0.0785453	−	0.747309i
$92$	0.497115	−	4.72973i	0.0518278	−	0.493109i
$93$	−12.9436	−	22.4189i	−1.34219	−	2.32473i
$94$	−7.43290	+	5.40032i	−0.766645	+	0.557000i
$95$	0.759933	+	2.33883i	0.0779675	+	0.239959i
$96$	2.83414	+	1.26184i	0.289258	+	0.128786i
$97$	−1.07950	+	10.2708i	−0.109607	+	1.04284i	0.792071	+	0.610429i	$0.209003\pi$
$97$	−1.07950	+	10.2708i	−0.109607	+	1.04284i	−0.901678	+	0.432409i	$0.857664\pi$
$98$	4.12228	+	2.99501i	0.416413	+	0.302542i
$99$	2.44695	−	7.53092i	0.245927	−	0.756886i
$100$	0.498714	+	4.74495i	0.0498714	+	0.474495i
$101$	−4.15162	+	7.19082i	−0.413102	+	0.715513i	−0.995227	−	0.0975858i	$-0.968888\pi$
$101$	−4.15162	+	7.19082i	−0.413102	+	0.715513i	0.582125	+	0.813099i	$0.302221\pi$
$102$	−18.7781	−	13.6431i	−1.85931	−	1.35087i
$103$	5.84106	+	2.60061i	0.575536	+	0.256245i	0.673798	−	0.738915i	$-0.264662\pi$
$103$	5.84106	+	2.60061i	0.575536	+	0.256245i	−0.0982620	+	0.995161i	$0.531328\pi$
$104$	2.01605	+	0.428524i	0.197689	+	0.0420202i
$105$	−5.04941	+	1.07329i	−0.492772	+	0.104742i
$106$	11.3305	−	5.04465i	1.10051	−	0.489979i
$107$	−3.62393	−	0.770290i	−0.350338	−	0.0744667i	0.0293814	−	0.999568i	$-0.490646\pi$
$107$	−3.62393	−	0.770290i	−0.350338	−	0.0744667i	−0.379720	+	0.925102i	$0.623980\pi$
$108$	5.62234	+	9.73818i	0.541010	+	0.937056i
$109$	2.61563	−	4.53041i	0.250532	−	0.433935i	−0.713140	−	0.701022i	$-0.752728\pi$
$109$	2.61563	−	4.53041i	0.250532	−	0.433935i	0.963673	+	0.267087i	$0.0860610\pi$
$110$	−0.382675	+	0.425004i	−0.0364867	+	0.0405225i
$111$	4.95100			0.469928
$112$	−2.32713	+	2.58454i	−0.219893	+	0.244216i
$113$	−2.45665	+	7.56080i	−0.231103	+	0.711261i	0.766512	+	0.642230i	$0.221991\pi$
$113$	−2.45665	+	7.56080i	−0.231103	+	0.711261i	−0.997615	+	0.0690305i	$0.978009\pi$
$114$	4.92755	+	15.1654i	0.461507	+	1.42037i
$115$	−2.07868	+	0.925488i	−0.193838	+	0.0863022i
$116$	0.182224	+	0.202381i	0.0169191	+	0.0187906i
$117$	9.13617	+	10.1467i	0.844640	+	0.938067i
$118$	−2.35284	+	0.500112i	−0.216597	+	0.0460390i
$119$	21.0510	−	15.2944i	1.92974	−	1.40204i
$120$	−0.155153	−	1.47618i	−0.0141635	−	0.134757i
$121$	−9.57121			−0.870110
$122$	−4.14603	+	6.61895i	−0.375364	+	0.599251i
$123$	−20.5278			−1.85093
$124$	0.872224	+	8.29866i	0.0783280	+	0.745241i
$125$	3.78213	−	2.74787i	0.338284	−	0.245777i
$126$	−22.5358	+	4.79013i	−2.00765	+	0.426738i
$127$	−3.08435	−	3.42552i	−0.273692	−	0.303966i	0.590592	−	0.806971i	$-0.298894\pi$
$127$	−3.08435	−	3.42552i	−0.273692	−	0.303966i	−0.864284	+	0.503005i	$0.832228\pi$
$128$	−0.669131	−	0.743145i	−0.0591433	−	0.0656853i
$129$	12.9247	−	5.75447i	1.13796	−	0.506652i
$130$	−0.304729	−	0.937859i	−0.0267265	−	0.0822557i
$131$	1.47095	−	4.52712i	0.128518	−	0.395536i	−0.866008	−	0.500030i	$-0.833322\pi$
$131$	1.47095	−	4.52712i	0.128518	−	0.395536i	0.994526	+	0.104494i	$0.0333222\pi$
$132$	−2.48134	+	2.75580i	−0.215973	+	0.239862i
$133$	−17.8759			−1.55004
$134$	−5.78253	+	6.42215i	−0.499535	+	0.554789i
$135$	2.69000	−	4.65922i	0.231518	−	0.401002i
$136$	3.74088	+	6.47940i	0.320778	+	0.555604i
$137$	−10.5151	−	2.23506i	−0.898368	−	0.190954i	−0.264491	−	0.964388i	$-0.585204\pi$
$137$	−10.5151	−	2.23506i	−0.898368	−	0.190954i	−0.633877	+	0.773434i	$0.718537\pi$
$138$	−13.4785	+	6.00104i	−1.14737	+	0.510842i
$139$	8.87894	−	1.88728i	0.753102	−	0.160077i	0.184663	−	0.982802i	$-0.440881\pi$
$139$	8.87894	−	1.88728i	0.753102	−	0.160077i	0.568439	+	0.822725i	$0.307547\pi$
$140$	1.62761	+	0.345959i	0.137558	+	0.0292389i
$141$	26.0388	+	11.5932i	2.19286	+	0.976326i
$142$	3.29417	+	2.39335i	0.276440	+	0.200846i
$143$	−1.23183	+	2.13359i	−0.103011	+	0.178420i
$144$	−0.692456	−	6.58828i	−0.0577047	−	0.549023i
$145$	0.0402636	−	0.123919i	0.00334371	−	0.0102909i
$146$	13.4007	+	9.73619i	1.10905	+	0.805773i
$147$	1.65236	−	15.7212i	0.136284	−	1.29666i
$148$	−1.45792	−	0.649106i	−0.119840	−	0.0533562i
$149$	−3.58134	−	11.0222i	−0.293394	−	0.902975i	−0.983756	−	0.179511i	$-0.942549\pi$
$149$	−3.58134	−	11.0222i	−0.293394	−	0.902975i	0.690362	−	0.723465i	$-0.257451\pi$
$150$	11.9747	−	8.70015i	0.977732	−	0.710364i
$151$	0.146336	+	0.253461i	0.0119086	+	0.0206263i	0.871918	−	0.489651i	$-0.162876\pi$
$151$	0.146336	+	0.253461i	0.0119086	+	0.0206263i	−0.860010	+	0.510278i	$0.829543\pi$
$152$	0.537269	−	5.11178i	0.0435783	−	0.414620i
$153$	−5.18079	+	49.2920i	−0.418842	+	3.98502i
$154$	−2.07857	−	3.60019i	−0.167496	−	0.290111i
$155$	3.22988	−	2.34665i	0.259430	−	0.188487i
$156$	−1.97592	−	6.08125i	−0.158200	−	0.486890i
$157$	−3.47226	−	1.54595i	−0.277117	−	0.123380i	0.263473	−	0.964667i	$-0.415132\pi$
$157$	−3.47226	−	1.54595i	−0.277117	−	0.123380i	−0.540589	+	0.841287i	$0.681799\pi$
$158$	0.981995	−	9.34306i	0.0781233	−	0.743294i
$159$	−31.1290	−	22.6166i	−2.46869	−	1.79361i
$160$	−0.147849	+	0.455032i	−0.0116885	+	0.0359734i
$161$	−1.72889	−	16.4493i	−0.136256	−	1.29639i
$162$	7.50560	−	13.0001i	0.589696	−	1.02138i
$163$	−2.40094	−	1.74438i	−0.188056	−	0.136631i	0.489774	−	0.871850i	$-0.337079\pi$
$163$	−2.40094	−	1.74438i	−0.188056	−	0.136631i	−0.677830	+	0.735219i	$0.737079\pi$
$164$	6.04480	+	2.69132i	0.472020	+	0.210157i
$165$	1.73546	+	0.368883i	0.135105	+	0.0287175i
$166$	−6.12607	+	1.30214i	−0.475475	+	0.101065i
$167$	−2.79414	+	1.24403i	−0.216217	+	0.0962660i	−0.511987	−	0.858993i	$-0.671090\pi$
$167$	−2.79414	+	1.24403i	−0.216217	+	0.0962660i	0.295770	+	0.955259i	$0.404424\pi$
$168$	10.5537	+	2.24326i	0.814237	+	0.173071i
$169$	4.37596	+	7.57939i	0.336613	+	0.583030i
$170$	1.78982	−	3.10006i	0.137273	−	0.237764i
$171$	22.7838	−	25.3040i	1.74232	−	1.93504i
$172$	−4.56038			−0.347726
$173$	−9.93486	+	11.0338i	−0.755334	+	0.838883i	−0.991127	−	0.132920i	$-0.957565\pi$
$173$	−9.93486	+	11.0338i	−0.755334	+	0.838883i	0.235793	+	0.971803i	$0.424231\pi$
$174$	0.261077	−	0.803512i	0.0197922	−	0.0609141i
$175$	5.12755	+	15.7810i	0.387607	+	1.19293i
$176$	1.09198	−	0.486181i	0.0823110	−	0.0366472i
$177$	4.99332	+	5.54565i	0.375321	+	0.416836i
$178$	1.53053	+	1.69983i	0.114718	+	0.127407i
$179$	−20.4363	+	4.34387i	−1.52748	+	0.324676i	−0.893639	−	0.448787i	$-0.851856\pi$
$179$	−20.4363	+	4.34387i	−1.52748	+	0.324676i	−0.633841	+	0.773463i	$0.718523\pi$
$180$	−2.56419	+	1.86300i	−0.191124	+	0.138859i
$181$	−1.82052	−	17.3211i	−0.135318	−	1.28747i	−0.825736	−	0.564057i	$-0.809240\pi$
$181$	−1.82052	−	17.3211i	−0.135318	−	1.28747i	0.690418	−	0.723411i	$-0.257427\pi$
$182$	7.16814			0.531338
$183$	24.2144	+	0.872042i	1.78998	+	0.0644632i
$184$	4.75579			0.350601
$185$	0.0798127	+	0.759367i	0.00586795	+	0.0558298i
$186$	20.9431	−	15.2161i	1.53563	−	1.11570i
$187$	−8.74768	+	1.85938i	−0.639693	+	0.135971i
$188$	−6.14768	−	6.82769i	−0.448366	−	0.497961i
$189$	26.1679	+	29.0624i	1.90343	+	2.11398i
$190$	−2.24659	+	1.00024i	−0.162985	+	0.0725654i
$191$	6.03524	+	18.5746i	0.436695	+	1.34401i	0.891340	+	0.453336i	$0.149766\pi$
$191$	6.03524	+	18.5746i	0.436695	+	1.34401i	−0.454645	+	0.890673i	$0.650234\pi$
$192$	−0.958679	+	2.95051i	−0.0691867	+	0.212935i
$193$	−3.44630	+	3.82751i	−0.248070	+	0.275510i	−0.854301	−	0.519779i	$-0.826014\pi$
$193$	−3.44630	+	3.82751i	−0.248070	+	0.275510i	0.606230	+	0.795289i	$0.292681\pi$
$194$	−10.3273			−0.741460
$195$	−2.04707	+	2.27350i	−0.146594	+	0.162809i
$196$	−2.54771	+	4.41276i	−0.181979	+	0.315197i
$197$	−1.72174	−	2.98213i	−0.122669	−	0.212468i	0.798151	−	0.602458i	$-0.205812\pi$
$197$	−1.72174	−	2.98213i	−0.122669	−	0.212468i	−0.920819	+	0.389990i	$0.872479\pi$
$198$	7.74544	+	1.64634i	0.550445	+	0.117001i
$199$	−12.6613	+	5.63718i	−0.897536	+	0.399609i	−0.803046	−	0.595917i	$-0.796789\pi$
$199$	−12.6613	+	5.63718i	−0.897536	+	0.399609i	−0.0944901	+	0.995526i	$0.530122\pi$
$200$	−4.66683	+	0.991965i	−0.329995	+	0.0701425i
$201$	26.2242	+	5.57412i	1.84971	+	0.393168i
$202$	−7.58539	−	3.37723i	−0.533706	−	0.237621i
$203$	0.766237	+	0.556704i	0.0537793	+	0.0390730i
$204$	11.6055	−	20.1014i	0.812549	−	1.40738i
$205$	−0.330919	−	3.14849i	−0.0231124	−	0.219900i
$206$	−1.97580	+	6.08089i	−0.137661	+	0.423676i
$207$	25.4881	+	18.5182i	1.77155	+	1.28710i
$208$	−0.215442	+	2.04979i	−0.0149382	+	0.142128i
$209$	5.61270	+	2.49894i	0.388239	+	0.172855i
$210$	−1.59521	−	4.90956i	−0.110080	−	0.338792i
$211$	5.47490	−	3.97775i	0.376908	−	0.273840i	−0.383162	−	0.923681i	$-0.625165\pi$
$211$	5.47490	−	3.97775i	0.376908	−	0.273840i	0.760070	+	0.649842i	$0.225165\pi$
$212$	6.20137	+	10.7411i	0.425912	+	0.737700i
$213$	1.32042	−	12.5630i	0.0904739	−	0.860802i
$214$	0.387266	−	3.68459i	0.0264730	−	0.251874i
$215$	1.09095	+	1.88959i	0.0744025	+	0.128869i
$216$	−9.09713	+	6.60946i	−0.618982	+	0.449716i
$217$	8.96781	+	27.6001i	0.608774	+	1.87361i
$218$	4.77900	+	2.12775i	0.323675	+	0.144109i
$219$	5.37150	−	51.1064i	0.362972	−	3.45345i
$220$	−0.462676	−	0.336154i	−0.0311936	−	0.0226635i
$221$	4.76521	−	14.6658i	0.320543	−	0.986530i
$222$	0.517520	+	4.92388i	0.0347337	+	0.330469i
$223$	−2.68722	+	4.65440i	−0.179949	+	0.311681i	−0.941863	−	0.335997i	$-0.890927\pi$
$223$	−2.68722	+	4.65440i	−0.179949	+	0.311681i	0.761914	+	0.647679i	$0.224260\pi$
$224$	−2.81364	−	2.04423i	−0.187994	−	0.136586i
$225$	−28.8739	−	12.8555i	−1.92493	−	0.857032i
$226$	−7.77617	−	1.65288i	−0.517263	−	0.109948i
$227$	11.3501	−	2.41254i	0.753333	−	0.160126i	0.184789	−	0.982778i	$-0.440840\pi$
$227$	11.3501	−	2.41254i	0.753333	−	0.160126i	0.568545	+	0.822652i	$0.307507\pi$
$228$	−14.5673	+	6.48577i	−0.964742	+	0.429531i
$229$	−10.4968	−	2.23117i	−0.693650	−	0.147440i	−0.152422	−	0.988316i	$-0.548707\pi$
$229$	−10.4968	−	2.23117i	−0.693650	−	0.147440i	−0.541228	+	0.840876i	$0.682041\pi$
$230$	−1.13770	−	1.97055i	−0.0750177	−	0.129934i
$231$	−6.44845	+	11.1690i	−0.424277	+	0.734869i
$232$	−0.182224	+	0.202381i	−0.0119636	+	0.0132869i
$233$	−21.9190			−1.43596			−0.717980	−	0.696064i	$-0.754933\pi$
$233$	−21.9190			−1.43596			−0.717980	+	0.696064i	$0.754933\pi$
$234$	−9.13617	+	10.1467i	−0.597250	+	0.663314i
$235$	−1.35837	+	4.18064i	−0.0886103	+	0.272715i
$236$	−0.743311	−	2.28768i	−0.0483854	−	0.148915i
$237$	−26.6254	+	11.8544i	−1.72950	+	0.770024i
$238$	17.4111	+	19.3369i	1.12859	+	1.25343i
$239$	−9.20352	−	10.2215i	−0.595326	−	0.661177i	0.367901	−	0.929865i	$-0.380077\pi$
$239$	−9.20352	−	10.2215i	−0.595326	−	0.661177i	−0.963227	+	0.268688i	$0.913410\pi$
$240$	1.45188	−	0.308606i	0.0937184	−	0.0199205i
$241$	−22.8994	+	16.6374i	−1.47508	+	1.07171i	−0.495979	+	0.868334i	$0.665191\pi$
$241$	−22.8994	+	16.6374i	−1.47508	+	1.07171i	−0.979101	+	0.203374i	$0.934809\pi$
$242$	−1.00046	−	9.51878i	−0.0643123	−	0.611890i
$243$	−12.8360			−0.823427
$244$	−7.01607	−	3.43145i	−0.449158	−	0.219676i
$245$	2.43790			0.155751
$246$	−2.14574	−	20.4154i	−0.136807	−	1.30164i
$247$	−8.57060	+	6.22690i	−0.545334	+	0.396208i
$248$	−8.16202	+	1.73489i	−0.518289	+	0.110166i
$249$	13.0011	+	14.4391i	0.823909	+	0.915044i
$250$	3.12816	+	3.47418i	0.197842	+	0.219726i
$251$	19.6328	−	8.74108i	1.23921	−	0.551732i	0.320720	−	0.947174i	$-0.396075\pi$
$251$	19.6328	−	8.74108i	1.23921	−	0.551732i	0.918491	+	0.395442i	$0.129409\pi$
$252$	−7.11951	−	21.9116i	−0.448487	−	1.38030i
$253$	−1.75666	+	5.40646i	−0.110441	+	0.339901i
$254$	3.08435	−	3.42552i	0.193529	−	0.214936i
$255$	−11.1053			−0.695441
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	6.55378	−	11.3515i	0.408813	−	0.708086i	−0.585944	−	0.810352i	$-0.699276\pi$
$257$	6.55378	−	11.3515i	0.408813	−	0.708086i	0.994757	+	0.102266i	$0.0326094\pi$
$258$	7.07395	+	12.2524i	0.440405	+	0.762803i
$259$	−5.42896	−	1.15396i	−0.337339	−	0.0717037i
$260$	0.900869	−	0.401093i	0.0558695	−	0.0248747i
$261$	−1.76464	+	0.375087i	−0.109229	+	0.0232173i
$262$	4.65608	+	0.989680i	0.287653	+	0.0611426i
$263$	−4.41076	−	1.96380i	−0.271979	−	0.121093i	0.266215	−	0.963914i	$-0.414227\pi$
$263$	−4.41076	−	1.96380i	−0.271979	−	0.121093i	−0.538194	+	0.842821i	$0.680893\pi$
$264$	−3.00008	−	2.17968i	−0.184642	−	0.134150i
$265$	2.96704	−	5.13906i	0.182264	−	0.315690i
$266$	−1.86854	−	17.7780i	−0.114568	−	1.09004i
$267$	2.19283	−	6.74883i	0.134199	−	0.413021i
$268$	−6.99141	−	5.07956i	−0.427068	−	0.310283i
$269$	−1.73870	+	16.5427i	−0.106011	+	1.00862i	0.804167	+	0.594404i	$0.202612\pi$
$269$	−1.73870	+	16.5427i	−0.106011	+	1.00862i	−0.910177	+	0.414219i	$0.864055\pi$
$270$	4.91488	+	2.18824i	0.299110	+	0.133172i
$271$	3.99516	+	12.2958i	0.242689	+	0.746919i	0.996008	+	0.0892638i	$0.0284514\pi$
$271$	3.99516	+	12.2958i	0.242689	+	0.746919i	−0.753319	+	0.657655i	$0.771549\pi$
$272$	−6.05288	+	4.39767i	−0.367009	+	0.266648i
$273$	−11.1190	−	19.2587i	−0.672954	−	1.16559i
$274$	1.12369	−	10.6911i	0.0678843	−	0.645876i
$275$	0.596123	−	5.67173i	0.0359476	−	0.342018i
$276$	−7.37705	−	12.7774i	−0.444046	−	0.769111i
$277$	18.7013	−	13.5873i	1.12365	−	0.816380i	0.138892	−	0.990308i	$-0.455646\pi$
$277$	18.7013	−	13.5873i	1.12365	−	0.816380i	0.984758	+	0.173928i	$0.0556459\pi$
$278$	2.80504	+	8.63303i	0.168235	+	0.517774i
$279$	−50.4988	−	22.4835i	−3.02329	−	1.34605i
$280$	−0.173932	+	1.65486i	−0.0103944	+	0.0988966i
$281$	11.2842	+	8.19845i	0.673159	+	0.489078i	0.871081	−	0.491139i	$-0.163419\pi$
$281$	11.2842	+	8.19845i	0.673159	+	0.489078i	−0.197922	+	0.980218i	$0.563419\pi$
$282$	−8.80792	+	27.1080i	−0.524504	+	1.61426i
$283$	0.604079	+	5.74743i	0.0359088	+	0.341649i	0.997696	+	0.0678497i	$0.0216138\pi$
$283$	0.604079	+	5.74743i	0.0359088	+	0.341649i	−0.961787	+	0.273800i	$0.911719\pi$
$284$	−2.03591	+	3.52629i	−0.120809	+	0.209247i
$285$	6.17222	+	4.48438i	0.365611	+	0.265632i
$286$	−2.25066	−	1.00206i	−0.133084	−	0.0592530i
$287$	22.5095	+	4.78455i	1.32870	+	0.282423i
$288$	6.47981	−	1.37733i	0.381826	−	0.0811597i
$289$	35.6071	−	15.8533i	2.09453	−	0.932547i
$290$	0.127449	+	0.0270900i	0.00748404	+	0.00159078i
$291$	16.0195	+	27.7466i	0.939080	+	1.62653i
$292$	−8.28210	+	14.3450i	−0.484673	+	0.839478i
$293$	3.80827	−	4.22951i	0.222482	−	0.247091i	−0.621563	−	0.783364i	$-0.713502\pi$
$293$	3.80827	−	4.22951i	0.222482	−	0.247091i	0.844044	+	0.536274i	$0.180169\pi$
$294$	15.8078			0.921927
$295$	−0.770077	+	0.855258i	−0.0448356	+	0.0497950i
$296$	0.493156	−	1.51778i	0.0286641	−	0.0882191i
$297$	−4.15349	−	12.7831i	−0.241010	−	0.741753i
$298$	10.5875	−	4.71385i	0.613317	−	0.273066i
$299$	−6.55887	−	7.28436i	−0.379309	−	0.421266i
$300$	9.90419	+	10.9997i	0.571819	+	0.635069i
$301$	−15.5137	+	3.29754i	−0.894196	+	0.190067i
$302$	−0.236776	+	0.172028i	−0.0136249	+	0.00989909i
$303$	2.69261	+	25.6184i	0.154686	+	1.47174i
$304$	5.13993			0.294795
$305$	0.256599	+	3.72798i	0.0146928	+	0.213464i
$306$	−49.5635			−2.83335
$307$	0.661982	+	6.29834i	0.0377813	+	0.359465i	0.997037	+	0.0769253i	$0.0245103\pi$
$307$	0.661982	+	6.29834i	0.0377813	+	0.359465i	−0.959256	+	0.282540i	$0.908823\pi$
$308$	3.36320	−	2.44351i	0.191636	−	0.139232i
$309$	19.4024	−	4.12411i	1.10377	−	0.234613i
$310$	2.67141	+	2.96690i	0.151726	+	0.168508i
$311$	−1.22529	−	1.36082i	−0.0694795	−	0.0771649i	0.707403	−	0.706811i	$-0.249867\pi$
$311$	−1.22529	−	1.36082i	−0.0694795	−	0.0771649i	−0.776882	+	0.629646i	$0.783200\pi$
$312$	5.84140	−	2.60076i	0.330704	−	0.147239i
$313$	1.40063	+	4.31071i	0.0791685	+	0.243656i	0.982806	−	0.184643i	$-0.0591130\pi$
$313$	1.40063	+	4.31071i	0.0791685	+	0.243656i	−0.903637	+	0.428299i	$0.859113\pi$
$314$	1.17453	−	3.61484i	0.0662827	−	0.203997i
$315$	−7.37589	+	8.19175i	−0.415584	+	0.461553i
$316$	9.39452			0.528483
$317$	−4.89756	+	5.43929i	−0.275074	+	0.305501i	−0.864814	−	0.502092i	$-0.832564\pi$
$317$	−4.89756	+	5.43929i	−0.275074	+	0.305501i	0.589740	+	0.807594i	$0.299230\pi$
$318$	19.2388	−	33.3226i	1.07886	−	1.86864i
$319$	−0.162761	−	0.281910i	−0.00911285	−	0.0157839i
$320$	−0.467993	−	0.0994751i	−0.0261616	−	0.00556083i
$321$	−10.5002	+	4.67497i	−0.586062	+	0.260932i
$322$	16.1785	−	3.43884i	0.901590	−	0.191639i
$323$	−37.6154	−	7.99541i	−2.09298	−	0.444876i
$324$	13.7134	+	6.10561i	0.761857	+	0.339200i
$325$	7.95556	+	5.78005i	0.441295	+	0.320620i
$326$	1.48386	−	2.57012i	0.0821834	−	0.142346i
$327$	−1.69642	−	16.1403i	−0.0938120	−	0.892562i
$328$	−2.04472	+	6.29301i	−0.112901	+	0.347473i
$329$	−25.8505	−	18.7815i	−1.42518	−	1.03546i
$330$	−0.185458	+	1.76451i	−0.0102091	+	0.0971332i
$331$	−19.8443	−	8.83524i	−1.09074	−	0.485629i	−0.219063	−	0.975711i	$-0.570300\pi$
$331$	−19.8443	−	8.83524i	−1.09074	−	0.485629i	−0.871676	+	0.490082i	$0.836967\pi$
$332$	−1.93535	−	5.95640i	−0.106216	−	0.326900i
$333$	8.55298	−	6.21410i	0.468700	−	0.340531i
$334$	−1.52928	−	2.64880i	−0.0836787	−	0.144936i
$335$	−0.432192	+	4.11204i	−0.0236132	+	0.224665i
$336$	−1.12781	+	10.7304i	−0.0615270	+	0.585391i
$337$	6.23019	+	10.7910i	0.339380	+	0.587824i	0.984316	−	0.176413i	$-0.0564493\pi$
$337$	6.23019	+	10.7910i	0.339380	+	0.587824i	−0.644936	+	0.764237i	$0.723116\pi$
$338$	−7.08046	+	5.14425i	−0.385126	+	0.279811i
$339$	7.62140	+	23.4562i	0.413937	+	1.27397i
$340$	3.27016	+	1.45597i	0.177350	+	0.0789611i
$341$	1.04259	−	9.91955i	0.0564592	−	0.537174i
$342$	27.5469	+	20.0140i	1.48957	+	1.08223i
$343$	2.04688	−	6.29966i	0.110521	−	0.340149i
$344$	−0.476690	−	4.53540i	−0.0257014	−	0.244532i
$345$	−3.52954	+	6.11335i	−0.190024	+	0.329131i
$346$	−12.0118	−	8.72709i	−0.645759	−	0.469171i
$347$	3.52155	+	1.56790i	0.189047	+	0.0841691i	0.499077	−	0.866558i	$-0.333672\pi$
$347$	3.52155	+	1.56790i	0.189047	+	0.0841691i	−0.310030	+	0.950727i	$0.600339\pi$
$348$	0.826400	+	0.175657i	0.0442997	+	0.00941619i
$349$	30.9336	−	6.57515i	1.65584	−	0.351960i	0.717202	−	0.696865i	$-0.245422\pi$
$349$	30.9336	−	6.57515i	1.65584	−	0.351960i	0.938637	+	0.344906i	$0.112089\pi$
$350$	−15.1586	+	6.74902i	−0.810259	+	0.360751i
$351$	22.6698	+	4.81861i	1.21002	+	0.257198i
$352$	0.597660	+	1.03518i	0.0318554	+	0.0551752i
$353$	0.695053	−	1.20387i	0.0369940	−	0.0640754i	−0.846936	−	0.531695i	$-0.821555\pi$
$353$	0.695053	−	1.20387i	0.0369940	−	0.0640754i	0.883930	+	0.467620i	$0.154888\pi$
$354$	−4.99332	+	5.54565i	−0.265392	+	0.294748i
$355$	1.94815			0.103397
$356$	−1.53053	+	1.69983i	−0.0811180	+	0.0900907i
$357$	24.9452	−	76.7735i	1.32024	−	4.06329i
$358$	−6.45624	−	19.8703i	−0.341223	−	1.05018i
$359$	20.1264	−	8.96085i	1.06223	−	0.472936i	0.200181	−	0.979759i	$-0.435847\pi$
$359$	20.1264	−	8.96085i	1.06223	−	0.472936i	0.862050	+	0.506823i	$0.169180\pi$
$360$	−2.12082	−	2.35541i	−0.111777	−	0.124141i
$361$	4.96423	+	5.51334i	0.261275	+	0.290176i
$362$	17.0359	−	3.62110i	0.895388	−	0.190321i
$363$	−24.0223	+	17.4532i	−1.26085	+	0.916058i
$364$	0.749274	+	7.12887i	0.0392726	+	0.373654i
$365$	7.92512			0.414820
$366$	1.66383	+	24.1729i	0.0869699	+	1.26354i
$367$	19.2239			1.00348			0.501739	−	0.865019i	$-0.332694\pi$
$367$	19.2239			1.00348			0.501739	+	0.865019i	$0.332694\pi$
$368$	0.497115	+	4.72973i	0.0259139	+	0.246554i
$369$	−35.4623	+	25.7649i	−1.84609	+	1.34127i
$370$	−0.746865	+	0.158751i	−0.0388277	+	0.00825307i
$371$	28.8628	+	32.0554i	1.49848	+	1.66423i
$372$	17.3219	+	19.2379i	0.898098	+	0.997438i
$373$	−24.0629	+	10.7135i	−1.24593	+	0.554724i	−0.920463	−	0.390829i	$-0.872188\pi$
$373$	−24.0629	+	10.7135i	−1.24593	+	0.554724i	−0.325467	+	0.945553i	$0.605522\pi$
$374$	−2.76357	−	8.50540i	−0.142901	−	0.439804i
$375$	4.48179	−	13.7935i	0.231439	−	0.712295i
$376$	6.14768	−	6.82769i	0.317043	−	0.352111i
$377$	0.561295			0.0289082
$378$	−26.1679	+	29.0624i	−1.34593	+	1.49481i
$379$	−1.84537	+	3.19628i	−0.0947904	+	0.164182i	−0.909521	−	0.415658i	$-0.863551\pi$
$379$	−1.84537	+	3.19628i	−0.0947904	+	0.164182i	0.814731	+	0.579840i	$0.196885\pi$
$380$	−1.22960	−	2.12973i	−0.0630770	−	0.109253i
$381$	−13.9877	−	2.97319i	−0.716614	−	0.152321i
$382$	−17.8420	+	7.94375i	−0.912874	+	0.406438i
$383$	18.7002	−	3.97484i	0.955533	−	0.203105i	0.296344	−	0.955081i	$-0.404233\pi$
$383$	18.7002	−	3.97484i	0.955533	−	0.203105i	0.659190	+	0.751977i	$0.270899\pi$
$384$	−3.03456	−	0.645015i	−0.154856	−	0.0329158i
$385$	−1.81702	−	0.808990i	−0.0926040	−	0.0412300i
$386$	−4.16677	−	3.02734i	−0.212083	−	0.154087i
$387$	15.1053	−	26.1631i	0.767844	−	1.32995i
$388$	−1.07950	−	10.2708i	−0.0548033	−	0.521419i
$389$	0.571702	−	1.75952i	0.0289864	−	0.0892111i	−0.935517	−	0.353282i	$-0.885065\pi$
$389$	0.571702	−	1.75952i	0.0289864	−	0.0892111i	0.964503	+	0.264071i	$0.0850655\pi$
$390$	−2.47502	−	1.79821i	−0.125328	−	0.0910559i
$391$	3.71930	−	35.3868i	0.188093	−	1.78959i
$392$	−4.65489	−	2.07249i	−0.235108	−	0.104677i
$393$	−4.56340	−	14.0447i	−0.230193	−	0.708462i
$394$	2.78583	−	2.02402i	0.140348	−	0.101969i
$395$	−2.24740	−	3.89261i	−0.113079	−	0.195858i
$396$	−0.827707	+	7.87510i	−0.0415938	+	0.395739i
$397$	0.732638	−	6.97058i	0.0367700	−	0.349843i	−0.960633	−	0.277821i	$-0.910388\pi$
$397$	0.732638	−	6.97058i	0.0367700	−	0.349843i	0.997403	−	0.0720228i	$-0.0229454\pi$
$398$	−6.92976	−	12.0027i	−0.347358	−	0.601641i
$399$	−44.8659	+	32.5970i	−2.24610	+	1.63189i
$400$	−1.47435	−	4.53757i	−0.0737173	−	0.226879i
$401$	32.5353	+	14.4856i	1.62473	+	0.723378i	0.998420	−	0.0561932i	$-0.0178963\pi$
$401$	32.5353	+	14.4856i	1.62473	+	0.723378i	0.626314	+	0.779571i	$0.284563\pi$
$402$	−2.80241	+	26.6632i	−0.139772	+	1.32984i
$403$	13.9138	+	10.1090i	0.693098	+	0.503565i
$404$	2.56584	−	7.89685i	0.127655	−	0.392883i
$405$	−0.750733	−	7.14275i	−0.0373042	−	0.354926i
$406$	−0.473561	+	0.820231i	−0.0235024	+	0.0407074i
$407$	1.54328	+	1.12126i	0.0764974	+	0.0555786i
$408$	21.2043	+	9.44078i	1.04977	+	0.467388i
$409$	18.8550	+	4.00775i	0.932319	+	0.198170i	0.648942	−	0.760838i	$-0.275212\pi$
$409$	18.8550	+	4.00775i	0.932319	+	0.198170i	0.283377	+	0.959009i	$0.408545\pi$
$410$	3.09665	−	0.658213i	0.152933	−	0.0325068i
$411$	−30.4671	+	13.5648i	−1.50283	+	0.669103i
$412$	−6.25411	−	1.32935i	−0.308118	−	0.0654925i
$413$	−4.18281	−	7.24485i	−0.205823	−	0.356496i
$414$	−15.7525	+	27.2842i	−0.774194	+	1.34094i
$415$	−2.00504	+	2.22683i	−0.0984237	+	0.109311i
$416$	−2.06108			−0.101053
$417$	18.8434	−	20.9277i	0.922763	−	1.02483i
$418$	−1.89856	+	5.84317i	−0.0928616	+	0.285799i
$419$	−3.34023	−	10.2802i	−0.163181	−	0.502219i	0.835717	−	0.549161i	$-0.185053\pi$
$419$	−3.34023	−	10.2802i	−0.163181	−	0.502219i	−0.998898	+	0.0469416i	$0.985053\pi$
$420$	4.71592	−	2.09966i	0.230113	−	0.102453i
$421$	−5.20902	−	5.78520i	−0.253872	−	0.281953i	0.602714	−	0.797957i	$-0.294086\pi$
$421$	−5.20902	−	5.78520i	−0.253872	−	0.281953i	−0.856586	+	0.516004i	$0.827419\pi$
$422$	4.52824	+	5.02912i	0.220431	+	0.244814i
$423$	59.5337	−	12.6543i	2.89463	−	0.615272i
$424$	−10.0340	+	7.29014i	−0.487295	+	0.354041i
$425$	3.73126	+	35.5006i	0.180993	+	1.72203i
$426$	12.6322			0.612032
$427$	−26.3488	−	6.60004i	−1.27511	−	0.319398i
$428$	3.70489			0.179083
$429$	0.798924	+	7.60125i	0.0385724	+	0.366992i
$430$	−1.76520	+	1.28249i	−0.0851256	+	0.0618473i
$431$	16.5129	−	3.50993i	0.795399	−	0.169067i	0.207749	−	0.978182i	$-0.433386\pi$
$431$	16.5129	−	3.50993i	0.795399	−	0.169067i	0.587650	+	0.809115i	$0.300053\pi$
$432$	−7.52416	−	8.35642i	−0.362006	−	0.402049i
$433$	−8.89147	−	9.87498i	−0.427297	−	0.474561i	0.490597	−	0.871386i	$-0.336779\pi$
$433$	−8.89147	−	9.87498i	−0.427297	−	0.474561i	−0.917894	+	0.396825i	$0.870112\pi$
$434$	−26.5115	+	11.8037i	−1.27259	+	0.566594i
$435$	−0.124912	−	0.384439i	−0.00598906	−	0.0184324i
$436$	−1.61655	+	4.97523i	−0.0774188	+	0.238270i
$437$	−16.3565	+	18.1658i	−0.782438	+	0.868986i
$438$	51.3879			2.45541
$439$	−16.9189	+	18.7903i	−0.807494	+	0.896813i	−0.996365	−	0.0851890i	$-0.972851\pi$
$439$	−16.9189	+	18.7903i	−0.807494	+	0.896813i	0.188871	+	0.982002i	$0.439517\pi$
$440$	0.285950	−	0.495279i	0.0136321	−	0.0236115i
$441$	−16.8775	−	29.2326i	−0.803689	−	1.39203i
$442$	15.0836	+	3.20611i	0.717453	+	0.152499i
$443$	24.3923	−	10.8602i	1.15892	−	0.515982i	0.265013	−	0.964245i	$-0.414624\pi$
$443$	24.3923	−	10.8602i	1.15892	−	0.515982i	0.893902	+	0.448262i	$0.147957\pi$
$444$	−4.84281	+	1.02937i	−0.229829	+	0.0488518i
$445$	1.07046	+	0.227534i	0.0507447	+	0.0107861i
$446$	−4.90979	−	2.18598i	−0.232485	−	0.103509i
$447$	−29.0878	−	21.1335i	−1.37581	−	0.999582i
$448$	1.73892	−	3.01190i	0.0821564	−	0.142299i
$449$	0.675809	+	6.42989i	0.0318934	+	0.303446i	0.998827	+	0.0484179i	$0.0154179\pi$
$449$	0.675809	+	6.42989i	0.0318934	+	0.303446i	−0.966934	+	0.255028i	$0.917915\pi$
$450$	9.76691	−	30.0595i	0.460417	−	1.41702i
$451$	−6.39873	−	4.64895i	−0.301304	−	0.218911i
$452$	0.830991	−	7.90635i	0.0390865	−	0.371883i
$453$	0.829471	+	0.369304i	0.0389719	+	0.0173514i
$454$	3.58573	+	11.0358i	0.168287	+	0.517934i
$455$	2.77459	−	2.01586i	0.130075	−	0.0945050i
$456$	−7.97294	−	13.8095i	−0.373367	−	0.646690i
$457$	−0.729252	+	6.93837i	−0.0341130	+	0.324563i	0.964136	+	0.265409i	$0.0855070\pi$
$457$	−0.729252	+	6.93837i	−0.0341130	+	0.324563i	−0.998249	+	0.0591542i	$0.981160\pi$
$458$	1.12173	−	10.6725i	0.0524150	−	0.498695i
$459$	42.0650	+	72.8587i	1.96343	+	3.40076i
$460$	1.84084	−	1.33745i	0.0858295	−	0.0623588i
$461$	5.11146	+	15.7315i	0.238064	+	0.732687i	0.996700	+	0.0811719i	$0.0258663\pi$
$461$	5.11146	+	15.7315i	0.238064	+	0.732687i	−0.758636	+	0.651515i	$0.774134\pi$
$462$	−11.7819	−	5.24564i	−0.548144	−	0.244049i
$463$	2.28934	−	21.7816i	0.106395	−	1.01228i	−0.802896	−	0.596119i	$-0.796709\pi$
$463$	2.28934	−	21.7816i	0.106395	−	1.01228i	0.909291	−	0.416160i	$-0.136625\pi$
$464$	−0.220319	−	0.160071i	−0.0102281	−	0.00743113i
$465$	3.82738	−	11.7795i	0.177491	−	0.546260i
$466$	−2.29116	−	21.7989i	−0.106136	−	1.00982i
$467$	−9.52732	+	16.5018i	−0.440872	+	0.763613i	−0.997754	−	0.0669787i	$-0.978664\pi$
$467$	−9.52732	+	16.5018i	−0.440872	+	0.763613i	0.556882	+	0.830591i	$0.311997\pi$
$468$	−11.0462	−	8.02550i	−0.510609	−	0.370979i
$469$	−27.4567	−	12.2245i	−1.26783	−	0.564475i
$470$	−4.29972	−	0.913934i	−0.198331	−	0.0421566i
$471$	−11.5339	+	2.45161i	−0.531456	+	0.112964i
$472$	2.19745	−	0.978366i	0.101146	−	0.0450329i
$473$	5.33200	+	1.13335i	0.245165	+	0.0521115i
$474$	−14.5725	−	25.2404i	−0.669339	−	1.15933i
$475$	12.2615	−	21.2376i	0.562598	−	0.974448i
$476$	−17.4111	+	19.3369i	−0.798035	+	0.886308i
$477$	−82.1627			−3.76197
$478$	9.20352	−	10.2215i	0.420959	−	0.467523i
$479$	9.39204	−	28.9057i	0.429133	−	1.32074i	−0.469847	−	0.882748i	$-0.655691\pi$
$479$	9.39204	−	28.9057i	0.429133	−	1.32074i	0.898980	−	0.437989i	$-0.144309\pi$
$480$	0.458679	+	1.41167i	0.0209357	+	0.0644335i
$481$	−3.00489	+	1.33786i	−0.137011	+	0.0610013i
$482$	−18.9399	−	21.0349i	−0.862688	−	0.958112i
$483$	−34.3348	−	38.1326i	−1.56229	−	1.73509i
$484$	9.36206	−	1.98997i	0.425548	−	0.0904530i
$485$	−3.99743	+	2.90431i	−0.181514	+	0.131878i
$486$	−1.34172	−	12.7656i	−0.0608618	−	0.579061i
$487$	−3.84885			−0.174408			−0.0872041	−	0.996190i	$-0.527793\pi$
$487$	−3.84885			−0.174408			−0.0872041	+	0.996190i	$0.527793\pi$
$488$	2.67927	−	7.33631i	0.121285	−	0.332099i
$489$	−9.20691			−0.416351
$490$	0.254829	+	2.42454i	0.0115120	+	0.109530i
$491$	2.13095	−	1.54822i	0.0961683	−	0.0698704i	−0.538662	−	0.842522i	$-0.681070\pi$
$491$	2.13095	−	1.54822i	0.0961683	−	0.0698704i	0.634830	+	0.772652i	$0.281070\pi$
$492$	20.0792	−	4.26797i	0.905241	−	0.192415i
$493$	1.36336	+	1.51416i	0.0614026	+	0.0681945i
$494$	−7.08866	−	7.87276i	−0.318934	−	0.354212i
$495$	3.46105	−	1.54096i	0.155562	−	0.0692609i
$496$	−2.57855	−	7.93597i	−0.115780	−	0.356335i
$497$	−4.37603	+	13.4680i	−0.196292	+	0.604125i
$498$	−13.0011	+	14.4391i	−0.582592	+	0.647034i
$499$	0.874165			0.0391330			0.0195665	−	0.999809i	$-0.493771\pi$
$499$	0.874165			0.0391330			0.0195665	+	0.999809i	$0.493771\pi$
$500$	−3.12816	+	3.47418i	−0.139896	+	0.155370i
$501$	−4.74437	+	8.21749i	−0.211963	+	0.367130i
$502$	10.7454	+	18.6115i	0.479590	+	0.830674i
$503$	−26.6222	−	5.65872i	−1.18703	−	0.252310i	−0.428249	−	0.903661i	$-0.640869\pi$
$503$	−26.6222	−	5.65872i	−1.18703	−	0.252310i	−0.758777	+	0.651351i	$0.774203\pi$
$504$	21.0474	−	9.37090i	0.937525	−	0.417413i
$505$	−3.88586	+	0.825966i	−0.172919	+	0.0367550i
$506$	−5.56046	−	1.18191i	−0.247193	−	0.0525424i
$507$	24.8042	+	11.0435i	1.10159	+	0.490460i
$508$	3.72916	+	2.70939i	0.165455	+	0.120210i
$509$	−16.0083	+	27.7272i	−0.709555	+	1.22899i	0.255467	+	0.966818i	$0.417771\pi$
$509$	−16.0083	+	27.7272i	−0.709555	+	1.22899i	−0.965022	+	0.262168i	$0.915563\pi$
$510$	−1.16082	−	11.0445i	−0.0514020	−	0.489057i
$511$	−17.8018	+	54.7882i	−0.787504	+	2.42369i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	6.04142	−	57.4803i	0.266735	−	2.53782i
$514$	11.9743	+	5.33132i	0.528166	+	0.235155i
$515$	0.945320	+	2.90940i	0.0416558	+	0.128203i
$516$	−11.4459	+	8.31592i	−0.503877	+	0.366088i
$517$	5.49104	+	9.51077i	0.241496	+	0.418283i
$518$	0.580159	−	5.51985i	0.0254907	−	0.242528i
$519$	−4.81478	+	45.8095i	−0.211345	+	2.01082i
$520$	0.493062	+	0.854008i	0.0216222	+	0.0374507i
$521$	0.972649	−	0.706671i	0.0426125	−	0.0309598i	−0.566275	−	0.824216i	$-0.691616\pi$
$521$	0.972649	−	0.706671i	0.0426125	−	0.0309598i	0.608888	+	0.793256i	$0.291616\pi$
$522$	−0.557488	−	1.71577i	−0.0244006	−	0.0750972i
$523$	−26.8166	−	11.9395i	−1.17261	−	0.522078i	−0.274385	−	0.961620i	$-0.588474\pi$
$523$	−26.8166	−	11.9395i	−1.17261	−	0.522078i	−0.898222	+	0.439541i	$0.855141\pi$
$524$	−0.497566	+	4.73402i	−0.0217363	+	0.206807i
$525$	41.6463	+	30.2578i	1.81759	+	1.32056i
$526$	1.49199	−	4.59187i	0.0650538	−	0.200215i
$527$	6.52578	+	62.0886i	0.284267	+	2.70462i
$528$	1.85415	−	3.21148i	0.0806915	−	0.139762i
$529$	0.309448	+	0.224827i	0.0134543	+	0.00977509i
$530$	5.42104	+	2.41360i	0.235475	+	0.104840i
$531$	15.5866	+	3.31302i	0.676399	+	0.143773i
$532$	17.4853	−	3.71661i	0.758083	−	0.161135i
$533$	12.4589	−	5.54704i	0.539653	−	0.240269i
$534$	6.94107	+	1.47537i	0.300369	+	0.0638455i
$535$	−0.886300	−	1.53512i	−0.0383181	−	0.0663689i
$536$	4.32093	−	7.48407i	0.186636	−	0.323263i
$537$	−43.3710	+	48.1683i	−1.87160	+	2.07862i
$538$	−16.6338			−0.717133
$539$	4.07544	−	4.52624i	0.175542	−	0.194959i
$540$	−1.66251	+	5.11669i	−0.0715431	+	0.220187i
$541$	0.169758	+	0.522461i	0.00729846	+	0.0224624i	0.954639	−	0.297764i	$-0.0962409\pi$
$541$	0.169758	+	0.522461i	0.00729846	+	0.0224624i	−0.947341	+	0.320227i	$0.896241\pi$
$542$	−11.8109	+	5.25854i	−0.507320	+	0.225873i
$543$	−36.1545	−	40.1537i	−1.55154	−	1.72316i
$544$	−5.00628	−	5.56004i	−0.214642	−	0.238385i
$545$	2.44820	−	0.520381i	0.104869	−	0.0222907i
$546$	17.9910	−	13.0712i	0.769942	−	0.559396i
$547$	−4.14455	−	39.4328i	−0.177208	−	1.68602i	−0.616245	−	0.787555i	$-0.711347\pi$
$547$	−4.14455	−	39.4328i	−0.177208	−	1.68602i	0.439036	−	0.898469i	$-0.355320\pi$
$548$	10.7500			0.459219
$549$	42.9256	−	28.8856i	1.83202	−	1.23281i
$550$	5.70298			0.243176
$551$	−0.146315	−	1.39209i	−0.00623321	−	0.0593050i
$552$	11.9363	−	8.67225i	0.508044	−	0.369115i
$553$	31.9587	−	6.79304i	1.35902	−	0.288869i
$554$	15.4677	+	17.1786i	0.657158	+	0.729847i
$555$	1.58504	+	1.76036i	0.0672810	+	0.0747232i
$556$	−8.29253	+	3.69207i	−0.351681	+	0.156579i
$557$	−7.54879	−	23.2328i	−0.319852	−	0.984405i	−0.973711	−	0.227788i	$-0.926851\pi$
$557$	−7.54879	−	23.2328i	−0.319852	−	0.984405i	0.653858	−	0.756617i	$-0.273149\pi$
$558$	17.0818	−	52.5724i	0.723130	−	2.22557i
$559$	−6.28938	+	6.98506i	−0.266012	+	0.295437i
$560$	−1.66397			−0.0703156
$561$	−18.5648	+	20.6183i	−0.783806	+	0.870504i
$562$	−6.97402	+	12.0793i	−0.294181	+	0.509537i
$563$	21.1178	+	36.5770i	0.890007	+	1.54154i	0.839865	+	0.542796i	$0.182634\pi$
$563$	21.1178	+	36.5770i	0.890007	+	1.54154i	0.0501429	+	0.998742i	$0.484032\pi$
$564$	−27.8802	−	5.92612i	−1.17397	−	0.249534i
$565$	−3.47478	+	1.54707i	−0.146185	+	0.0650858i
$566$	−5.65280	+	1.20154i	−0.237605	+	0.0505045i
$567$	51.0658	+	10.8544i	2.14456	+	0.455841i
$568$	−3.71979	−	1.65616i	−0.156079	−	0.0694908i
$569$	1.55147	+	1.12721i	0.0650412	+	0.0472552i	0.619831	−	0.784735i	$-0.287201\pi$
$569$	1.55147	+	1.12721i	0.0650412	+	0.0472552i	−0.554790	+	0.831991i	$0.687201\pi$
$570$	−3.81464	+	6.60715i	−0.159778	+	0.276743i
$571$	−3.84586	−	36.5909i	−0.160944	−	1.53128i	−0.715190	−	0.698930i	$-0.753660\pi$
$571$	−3.84586	−	36.5909i	−0.160944	−	1.53128i	0.554246	−	0.832353i	$-0.313007\pi$
$572$	0.761312	−	2.34308i	0.0318320	−	0.0979689i
$573$	49.0186	+	35.6141i	2.04778	+	1.48780i
$574$	−2.40545	+	22.8864i	−0.100402	+	0.955258i
$575$	20.7286	+	9.22896i	0.864442	+	0.384874i
$576$	2.04710	+	6.30034i	0.0852960	+	0.262514i
$577$	22.0535	−	16.0228i	0.918100	−	0.667038i	−0.0249506	−	0.999689i	$-0.507943\pi$
$577$	22.0535	−	16.0228i	0.918100	−	0.667038i	0.943050	+	0.332650i	$0.107943\pi$
$578$	19.4884	+	33.7549i	0.810611	+	1.40402i
$579$	−1.67020	+	15.8909i	−0.0694110	+	0.660401i
$580$	−0.0136196	+	0.129582i	−0.000565524	+	0.00538060i
$581$	−10.8908	−	18.8633i	−0.451825	−	0.782583i
$582$	−25.9201	+	18.8321i	−1.07442	+	0.780614i
$583$	−4.58125	−	14.0996i	−0.189736	−	0.583947i
$584$	−15.1321	−	6.73726i	−0.626172	−	0.278790i
$585$	−0.682847	+	6.49686i	−0.0282323	+	0.268612i
$586$	4.60442	+	3.34530i	0.190207	+	0.138193i
$587$	−11.7702	+	36.2249i	−0.485807	+	1.49516i	0.345001	+	0.938602i	$0.387879\pi$
$587$	−11.7702	+	36.2249i	−0.485807	+	1.49516i	−0.830808	+	0.556559i	$0.812121\pi$
$588$	1.65236	+	15.7212i	0.0681422	+	0.648330i
$589$	21.4448	−	37.1434i	0.883616	−	1.53047i
$590$	−0.931067	−	0.676460i	−0.0383314	−	0.0278494i
$591$	−9.75927	−	4.34510i	−0.401443	−	0.178734i
$592$	1.56101	+	0.331804i	0.0641573	+	0.0136370i
$593$	3.19048	−	0.678157i	0.131017	−	0.0278486i	−0.141936	−	0.989876i	$-0.545333\pi$
$593$	3.19048	−	0.678157i	0.131017	−	0.0278486i	0.272954	+	0.962027i	$0.411999\pi$
$594$	12.2790	−	5.46694i	0.503812	−	0.224311i
$595$	12.1774	+	2.58838i	0.499224	+	0.106113i
$596$	5.79472	+	10.0368i	0.237361	+	0.411122i
$597$	−21.4985	+	37.2366i	−0.879877	+	1.52399i
$598$	6.55887	−	7.28436i	0.268212	−	0.297880i
$599$	−0.0964461			−0.00394068			−0.00197034	−	0.999998i	$-0.500627\pi$
$599$	−0.0964461			−0.00394068			−0.00197034	+	0.999998i	$0.500627\pi$
$600$	−9.90419	+	10.9997i	−0.404337	+	0.449061i
$601$	4.65421	−	14.3242i	0.189849	−	0.584296i	−0.810149	−	0.586224i	$-0.800614\pi$
$601$	4.65421	−	14.3242i	0.189849	−	0.584296i	0.999998	+	0.00192842i	$0.000613834\pi$
$602$	−4.90110	−	15.0840i	−0.199754	−	0.614780i
$603$	52.2992	−	23.2851i	2.12979	−	0.948242i
$604$	−0.195835	−	0.217497i	−0.00796843	−	0.00884984i
$605$	−3.06417	−	3.40311i	−0.124576	−	0.138356i
$606$	−25.1966	+	5.35571i	−1.02354	+	0.217561i
$607$	14.2028	−	10.3190i	0.576475	−	0.418833i	−0.260977	−	0.965345i	$-0.584045\pi$
$607$	14.2028	−	10.3190i	0.576475	−	0.418833i	0.837451	+	0.546512i	$0.184045\pi$
$608$	0.537269	+	5.11178i	0.0217892	+	0.207310i
$609$	2.93830			0.119066
$610$	−3.68074	+	0.644873i	−0.149029	+	0.0261102i
$611$	−18.9364			−0.766083
$612$	−5.18079	−	49.2920i	−0.209421	−	1.99251i
$613$	−10.5911	+	7.69489i	−0.427771	+	0.310794i	−0.780757	−	0.624835i	$-0.785166\pi$
$613$	−10.5911	+	7.69489i	−0.427771	+	0.310794i	0.352986	+	0.935629i	$0.385166\pi$
$614$	−6.19464	+	1.31671i	−0.249995	+	0.0531381i
$615$	−6.57187	−	7.29880i	−0.265003	−	0.294316i
$616$	2.78167	+	3.08936i	0.112077	+	0.124474i
$617$	−8.21638	+	3.65817i	−0.330779	+	0.147272i	−0.565405	−	0.824813i	$-0.691280\pi$
$617$	−8.21638	+	3.65817i	−0.330779	+	0.147272i	0.234626	+	0.972086i	$0.424613\pi$
$618$	6.12963	+	18.8651i	0.246570	+	0.758864i
$619$	−13.1837	+	40.5752i	−0.529896	+	1.63085i	0.224529	+	0.974468i	$0.427916\pi$
$619$	−13.1837	+	40.5752i	−0.529896	+	1.63085i	−0.754425	+	0.656386i	$0.772084\pi$
$620$	−2.67141	+	2.96690i	−0.107286	+	0.119153i
$621$	53.4773			2.14597
$622$	1.22529	−	1.36082i	0.0491295	−	0.0545638i
$623$	−3.97751	+	6.88926i	−0.159356	+	0.276012i
$624$	3.19710	+	5.53754i	0.127987	+	0.221679i
$625$	−21.1463	−	4.49478i	−0.845851	−	0.179791i
$626$	−4.14069	+	1.84355i	−0.165495	+	0.0736832i
$627$	18.6439	−	3.96288i	0.744566	−	0.158262i
$628$	3.71781	+	0.790244i	0.148357	+	0.0315342i
$629$	−10.9078	−	4.85646i	−0.434922	−	0.193640i
$630$	−8.91787	−	6.47921i	−0.355296	−	0.258138i
$631$	2.61549	−	4.53016i	0.104121	−	0.180343i	−0.809258	−	0.587454i	$-0.800130\pi$
$631$	2.61549	−	4.53016i	0.104121	−	0.180343i	0.913379	+	0.407111i	$0.133464\pi$
$632$	0.981995	+	9.34306i	0.0390617	+	0.371647i
$633$	6.48771	−	19.9671i	0.257863	−	0.793622i
$634$	−5.92143	−	4.30217i	−0.235170	−	0.170861i
$635$	0.230528	−	2.19332i	0.00914821	−	0.0870394i
$636$	35.1510	+	15.6502i	1.39383	+	0.620573i
$637$	3.24532	+	9.98808i	0.128584	+	0.395742i
$638$	0.263352	−	0.191337i	0.0104262	−	0.00757509i
$639$	−13.4870	−	23.3602i	−0.533538	−	0.924115i
$640$	0.0500115	−	0.475828i	0.00197688	−	0.0188087i
$641$	3.91227	−	37.2228i	0.154525	−	1.47021i	−0.592583	−	0.805509i	$-0.701892\pi$
$641$	3.91227	−	37.2228i	0.154525	−	1.47021i	0.747109	−	0.664702i	$-0.231441\pi$
$642$	−5.74693	−	9.95397i	−0.226813	−	0.392852i
$643$	29.9909	−	21.7897i	1.18273	−	0.859300i	0.190249	−	0.981736i	$-0.439070\pi$
$643$	29.9909	−	21.7897i	1.18273	−	0.859300i	0.992476	+	0.122435i	$0.0390705\pi$
$644$	5.11111	+	15.7304i	0.201406	+	0.619864i
$645$	6.18383	+	2.75322i	0.243488	+	0.108408i
$646$	4.01972	−	38.2451i	0.158154	−	1.50473i
$647$	−14.4213	−	10.4777i	−0.566961	−	0.411921i	0.267039	−	0.963686i	$-0.413955\pi$
$647$	−14.4213	−	10.4777i	−0.566961	−	0.411921i	−0.834000	+	0.551764i	$0.813955\pi$
$648$	−4.63872	+	14.2765i	−0.182226	+	0.560834i
$649$	0.300543	+	2.85948i	0.0117974	+	0.112244i
$650$	−4.91681	+	8.51616i	−0.192853	+	0.334031i
$651$	72.8370	+	52.9192i	2.85471	+	2.07407i
$652$	2.71115	+	1.20708i	0.106177	+	0.0472729i
$653$	−46.7434	−	9.93562i	−1.82921	−	0.388811i	−0.840892	−	0.541204i	$-0.817969\pi$
$653$	−46.7434	−	9.93562i	−1.82921	−	0.388811i	−0.988320	+	0.152393i	$0.951302\pi$
$654$	15.8746	−	3.37425i	0.620745	−	0.131943i
$655$	2.08057	−	0.926327i	0.0812944	−	0.0361946i
$656$	−6.47227	−	1.37572i	−0.252700	−	0.0537129i
$657$	−54.8653	−	95.0295i	−2.14050	−	3.70745i
$658$	15.9765	−	27.6721i	0.622828	−	1.07877i
$659$	0.983863	−	1.09269i	0.0383259	−	0.0425652i	−0.723677	−	0.690139i	$-0.757549\pi$
$659$	0.983863	−	1.09269i	0.0383259	−	0.0425652i	0.762003	+	0.647574i	$0.224216\pi$
$660$	−1.77423			−0.0690619
$661$	−20.4914	+	22.7580i	−0.797023	+	0.885183i	−0.995484	−	0.0949252i	$-0.969739\pi$
$661$	−20.4914	+	22.7580i	−0.797023	+	0.885183i	0.198462	+	0.980109i	$0.436405\pi$
$662$	6.71255	−	20.6591i	0.260891	−	0.802939i
$663$	−14.7834	−	45.4985i	−0.574138	−	1.76701i
$664$	5.72147	−	2.54736i	0.222036	−	0.0988568i
$665$	−5.72288	−	6.35590i	−0.221924	−	0.246471i
$666$	7.07409	+	7.85658i	0.274115	+	0.304436i
$667$	1.26684	−	0.269275i	0.0490523	−	0.0104264i
$668$	2.47443	−	1.79778i	0.0957387	−	0.0695582i
$669$	1.74284	+	16.5820i	0.0673821	+	0.641098i
$670$	−4.13469			−0.159737
$671$	7.35039	+	5.75568i	0.283759	+	0.222196i
$672$	−10.7895			−0.416214
$673$	−1.14711	−	10.9140i	−0.0442177	−	0.420703i	−0.994130	−	0.108188i	$-0.965495\pi$
$673$	−1.14711	−	10.9140i	−0.0442177	−	0.420703i	0.949913	−	0.312515i	$-0.101171\pi$
$674$	−10.0807	+	7.32403i	−0.388293	+	0.282111i
$675$	−52.4770	+	11.1543i	−2.01984	+	0.429330i
$676$	−5.85618	−	6.50395i	−0.225238	−	0.250152i
$677$	−10.3897	−	11.5389i	−0.399307	−	0.443475i	0.509640	−	0.860388i	$-0.329779\pi$
$677$	−10.3897	−	11.5389i	−0.399307	−	0.443475i	−0.908947	+	0.416913i	$0.863112\pi$
$678$	−22.5311	+	10.0315i	−0.865302	+	0.385257i
$679$	−11.0989	−	34.1590i	−0.425938	−	1.31090i
$680$	−1.10617	+	3.40444i	−0.0424197	+	0.130554i
$681$	24.0878	−	26.7522i	0.923047	−	1.02515i
$682$	9.97419			0.381932
$683$	−4.32680	+	4.80540i	−0.165561	+	0.183874i	−0.820216	−	0.572054i	$-0.806147\pi$
$683$	−4.32680	+	4.80540i	−0.165561	+	0.183874i	0.654656	+	0.755927i	$0.272814\pi$
$684$	−17.0249	+	29.4880i	−0.650964	+	1.12750i
$685$	−2.57167	−	4.45427i	−0.0982585	−	0.170189i
$686$	6.47910	+	1.37718i	0.247373	+	0.0525808i
$687$	−30.4141	+	13.5412i	−1.16037	+	0.516630i
$688$	4.46073	−	0.948156i	0.170064	−	0.0361481i
$689$	25.0045	+	5.31486i	0.952594	+	0.202480i
$690$	−6.44879	−	2.87119i	−0.245501	−	0.109304i
$691$	4.51164	+	3.27790i	0.171631	+	0.124697i	0.670285	−	0.742104i	$-0.266172\pi$
$691$	4.51164	+	3.27790i	0.171631	+	0.124697i	−0.498654	+	0.866801i	$0.666172\pi$
$692$	7.42371	−	12.8582i	0.282207	−	0.488797i
$693$	2.87864	+	27.3884i	0.109350	+	1.04040i
$694$	−1.19120	+	3.66615i	−0.0452175	+	0.139165i
$695$	3.51358	+	2.55276i	0.133278	+	0.0968319i
$696$	−0.0883121	+	0.840234i	−0.00334746	+	0.0318490i
$697$	45.2258	+	20.1358i	1.71305	+	0.762699i
$698$	9.77257	+	30.0769i	0.369897	+	1.13843i
$699$	−55.0134	+	39.9696i	−2.08080	+	1.51179i
$700$	−8.29655	−	14.3701i	−0.313580	−	0.543137i
$701$	0.367748	−	3.49889i	0.0138897	−	0.132151i	−0.985380	−	0.170373i	$-0.945503\pi$
$701$	0.367748	−	3.49889i	0.0138897	−	0.132151i	0.999269	+	0.0382219i	$0.0121694\pi$
$702$	−2.42258	+	23.0493i	−0.0914342	+	0.869939i
$703$	4.10138	+	7.10380i	0.154686	+	0.267925i
$704$	−0.967034	+	0.702592i	−0.0364465	+	0.0264799i
$705$	4.21414	+	12.9698i	0.158714	+	0.488471i
$706$	1.26993	+	0.565407i	0.0477943	+	0.0212794i
$707$	3.01851	−	28.7192i	0.113523	−	1.08010i
$708$	−6.03721	−	4.38629i	−0.226892	−	0.164847i
$709$	4.50431	−	13.8629i	0.169163	−	0.520630i	−0.830156	−	0.557531i	$-0.811749\pi$
$709$	4.50431	−	13.8629i	0.169163	−	0.520630i	0.999319	+	0.0369011i	$0.0117486\pi$
$710$	0.203638	+	1.93748i	0.00764238	+	0.0727124i
$711$	−31.1173	+	53.8968i	−1.16699	+	2.02129i
$712$	−1.85050	−	1.34447i	−0.0693504	−	0.0503860i
$713$	36.2532	+	16.1409i	1.35769	+	0.604483i
$714$	78.9604	+	16.7836i	2.95502	+	0.628109i
$715$	−1.15298	+	0.245072i	−0.0431188	+	0.00916519i
$716$	19.0866	−	8.49789i	0.713298	−	0.317581i
$717$	−41.7386	−	8.87182i	−1.55876	−	0.331324i
$718$	11.0155	+	19.0795i	0.411097	+	0.712040i
$719$	23.8717	−	41.3469i	0.890263	−	1.54198i	0.0507030	−	0.998714i	$-0.483854\pi$
$719$	23.8717	−	41.3469i	0.890263	−	1.54198i	0.839560	−	0.543267i	$-0.182813\pi$
$720$	2.12082	−	2.35541i	0.0790383	−	0.0877809i
$721$	−22.2368			−0.828140
$722$	−4.96423	+	5.51334i	−0.184750	+	0.205185i
$723$	−27.1356	+	83.5148i	−1.00918	+	3.10595i
$724$	5.38200	+	16.5641i	0.200020	+	0.615599i
$725$	−1.18698	+	0.528477i	−0.0440833	+	0.0196271i
$726$	−19.8687	−	22.0664i	−0.737395	−	0.818960i
$727$	13.7595	+	15.2815i	0.510313	+	0.566760i	0.942150	−	0.335192i	$-0.108801\pi$
$727$	13.7595	+	15.2815i	0.510313	+	0.566760i	−0.431837	+	0.901952i	$0.642135\pi$
$728$	−7.01150	+	1.49034i	−0.259863	+	0.0552357i
$729$	4.21658	−	3.06352i	0.156170	−	0.113464i
$730$	0.828400	+	7.88170i	0.0306605	+	0.291715i
$731$	−34.1197			−1.26196
$732$	−23.8666	+	4.18148i	−0.882134	+	0.154552i
$733$	27.8301			1.02793			0.513964	−	0.857812i	$-0.328176\pi$
$733$	27.8301			1.02793			0.513964	+	0.857812i	$0.328176\pi$
$734$	2.00944	+	19.1186i	0.0741698	+	0.705679i
$735$	6.11876	−	4.44554i	0.225694	−	0.163976i
$736$	−4.65186	+	0.988784i	−0.171470	+	0.0364470i
$737$	6.91198	+	7.67653i	0.254606	+	0.282769i
$738$	−29.3306	−	32.5749i	−1.07967	−	1.19910i
$739$	−3.40607	+	1.51648i	−0.125294	+	0.0557846i	−0.468426	−	0.883503i	$-0.655179\pi$
$739$	−3.40607	+	1.51648i	−0.125294	+	0.0557846i	0.343132	+	0.939287i	$0.388512\pi$
$740$	−0.235950	−	0.726179i	−0.00867369	−	0.0266949i
$741$	−10.1561	+	31.2572i	−0.373093	+	1.14826i
$742$	−28.8628	+	32.0554i	−1.05959	+	1.17679i
$743$	9.97868			0.366082			0.183041	−	0.983105i	$-0.441406\pi$
$743$	9.97868			0.366082			0.183041	+	0.983105i	$0.441406\pi$
$744$	−17.3219	+	19.2379i	−0.635051	+	0.705295i
$745$	2.77248	−	4.80207i	0.101576	−	0.175934i
$746$	−13.1701	−	22.8112i	−0.482190	−	0.835178i
$747$	40.5826	+	8.62609i	1.48484	+	0.315612i
$748$	8.16993	−	3.63749i	0.298722	−	0.133000i
$749$	12.6035	−	2.67895i	0.460521	−	0.0978867i
$750$	14.1864	+	3.01542i	0.518015	+	0.110108i
$751$	−37.2257	−	16.5740i	−1.35839	−	0.604792i	−0.407180	−	0.913348i	$-0.633488\pi$
$751$	−37.2257	−	16.5740i	−1.35839	−	0.604792i	−0.951206	+	0.308556i	$0.900154\pi$
$752$	7.43290	+	5.40032i	0.271050	+	0.196929i
$753$	33.3359	−	57.7395i	1.21483	−	2.10414i
$754$	0.0586713	+	0.558220i	0.00213668	+	0.0203292i
$755$	−0.0432711	+	0.133175i	−0.00157480	+	0.00484673i
$756$	−31.6384	−	22.9867i	−1.15068	−	0.836017i
$757$	−0.508587	+	4.83889i	−0.0184849	+	0.175872i	−0.999869	−	0.0161829i	$-0.994849\pi$
$757$	−0.508587	+	4.83889i	−0.0184849	+	0.175872i	0.981384	+	0.192055i	$0.0615153\pi$
$758$	−3.37166	−	1.50116i	−0.122464	−	0.0545246i
$759$	5.44979	+	16.7727i	0.197815	+	0.608811i
$760$	1.98953	−	1.44548i	0.0721679	−	0.0524330i
$761$	−5.32916	−	9.23037i	−0.193182	−	0.334601i	0.753121	−	0.657882i	$-0.228547\pi$
$761$	−5.32916	−	9.23037i	−0.193182	−	0.334601i	−0.946303	+	0.323281i	$0.895214\pi$
$762$	1.49478	−	14.2219i	0.0541503	−	0.515205i
$763$	−1.90174	+	18.0939i	−0.0688478	+	0.655043i
$764$	−9.76523	−	16.9139i	−0.353294	−	0.611923i
$765$	−19.1847	+	13.9385i	−0.693624	+	0.503947i
$766$	5.90777	+	18.1822i	0.213456	+	0.656951i
$767$	−4.52912	−	2.01650i	−0.163537	−	0.0728114i
$768$	0.324284	−	3.08535i	0.0117016	−	0.111333i
$769$	18.9670	+	13.7803i	0.683968	+	0.496932i	0.874672	−	0.484716i	$-0.161077\pi$
$769$	18.9670	+	13.7803i	0.683968	+	0.496932i	−0.190703	+	0.981648i	$0.561077\pi$
$770$	0.614628	−	1.89163i	0.0221497	−	0.0681696i
$771$	−4.25057	−	40.4414i	−0.153080	−	1.45646i
$772$	2.57521	−	4.46039i	0.0926838	−	0.160533i
$773$	−29.4618	−	21.4052i	−1.05967	−	0.769892i	−0.0856392	−	0.996326i	$-0.527293\pi$
$773$	−29.4618	−	21.4052i	−1.05967	−	0.769892i	−0.974027	+	0.226434i	$0.927293\pi$
$774$	27.5987	+	12.2877i	0.992015	+	0.441674i
$775$	−38.9417	−	8.27732i	−1.39883	−	0.297330i
$776$	10.1017	−	2.14717i	0.362628	−	0.0770791i
$777$	−15.7302	+	7.00352i	−0.564317	+	0.251250i
$778$	1.80964	+	0.384651i	0.0648787	+	0.0137904i
$779$	−17.0051	−	29.4537i	−0.609271	−	1.05529i
$780$	1.52965	−	2.64943i	0.0547702	−	0.0948648i
$781$	3.25674	−	3.61698i	0.116535	−	0.129426i
$782$	35.5817			1.27240
$783$	−2.04905	+	2.27570i	−0.0732272	+	0.0813270i
$784$	1.57457	−	4.84603i	0.0562346	−	0.173072i
$785$	−0.561953	−	1.72951i	−0.0200570	−	0.0617290i
$786$	13.4908	−	6.00647i	0.481200	−	0.214244i
$787$	30.1284	+	33.4610i	1.07396	+	1.19276i	0.980374	+	0.197144i	$0.0631667\pi$
$787$	30.1284	+	33.4610i	1.07396	+	1.19276i	0.0935872	+	0.995611i	$0.470167\pi$
$788$	2.30413	+	2.55900i	0.0820813	+	0.0911605i
$789$	−14.6514	+	3.11424i	−0.521602	+	0.110870i
$790$	3.63637	−	2.64198i	0.129376	−	0.0939973i
$791$	−2.89006	−	27.4971i	−0.102759	−	0.977683i
$792$	−7.91848			−0.281371
$793$	−14.9320	+	6.01397i	−0.530251	+	0.213562i
$794$	7.00898			0.248739
$795$	−1.92432	−	18.3087i	−0.0682487	−	0.649343i
$796$	11.2126	−	8.14642i	0.397420	−	0.288742i
$797$	15.4342	−	3.28064i	0.546707	−	0.116206i	0.0737255	−	0.997279i	$-0.476511\pi$
$797$	15.4342	−	3.28064i	0.546707	−	0.116206i	0.472981	+	0.881072i	$0.343178\pi$
$798$	−37.1082	−	41.2128i	−1.31362	−	1.45892i
$799$	−45.9955	−	51.0832i	−1.62720	−	1.80719i
$800$	4.35860	−	1.94058i	0.154100	−	0.0686097i
$801$	−4.68243	−	14.4110i	−0.165446	−	0.509189i
$802$	−11.0054	+	33.8712i	−0.388615	+	1.19603i
$803$	13.2485	−	14.7139i	0.467528	−	0.519242i
$804$	−26.8101			−0.945518
$805$	5.29516	−	5.88087i	0.186630	−	0.207273i
$806$	−8.59923	+	14.8943i	−0.302895	+	0.524629i
$807$	25.8019	+	44.6902i	0.908269	+	1.57317i
$808$	8.12180	+	1.72634i	0.285724	+	0.0607325i
$809$	−27.0967	+	12.0642i	−0.952668	+	0.424155i	−0.823404	−	0.567455i	$-0.807928\pi$
$809$	−27.0967	+	12.0642i	−0.952668	+	0.424155i	−0.129263	+	0.991610i	$0.541261\pi$
$810$	7.02515	−	1.49324i	0.246838	−	0.0524671i
$811$	−35.1309	−	7.46731i	−1.23361	−	0.262213i	−0.455443	−	0.890265i	$-0.650519\pi$
$811$	−35.1309	−	7.46731i	−1.23361	−	0.262213i	−0.778171	+	0.628052i	$0.783852\pi$
$812$	−0.865238	−	0.385229i	−0.0303639	−	0.0135189i
$813$	32.4489	+	23.5755i	1.13803	+	0.826829i
$814$	−0.953798	+	1.65203i	−0.0334306	+	0.0579035i
$815$	−0.148420	−	1.41212i	−0.00519893	−	0.0494645i
$816$	−7.17261	+	22.0750i	−0.251092	+	0.772780i
$817$	18.9634	+	13.7777i	0.663446	+	0.482021i
$818$	−2.01491	+	19.1706i	−0.0704498	+	0.670285i
$819$	−43.3805	−	19.3142i	−1.51584	−	0.674893i
$820$	0.978295	+	3.01088i	0.0341635	+	0.105145i
$821$	31.4489	−	22.8489i	1.09757	−	0.797433i	0.116911	−	0.993142i	$-0.462701\pi$
$821$	31.4489	−	22.8489i	1.09757	−	0.797433i	0.980662	+	0.195709i	$0.0627009\pi$
$822$	−16.6752	−	28.8823i	−0.581614	−	1.00738i
$823$	2.88016	−	27.4029i	0.100396	−	0.955206i	−0.822137	−	0.569289i	$-0.807218\pi$
$823$	2.88016	−	27.4029i	0.100396	−	0.955206i	0.922534	−	0.385917i	$-0.126115\pi$
$824$	0.668337	−	6.35881i	0.0232826	−	0.221519i
$825$	−8.84631	−	15.3223i	−0.307989	−	0.533453i
$826$	6.76793	−	4.91719i	0.235487	−	0.171091i
$827$	2.49963	+	7.69307i	0.0869207	+	0.267514i	0.985064	−	0.172188i	$-0.0550838\pi$
$827$	2.49963	+	7.69307i	0.0869207	+	0.267514i	−0.898143	+	0.439703i	$0.855084\pi$
$828$	−28.7813	−	12.8143i	−1.00022	−	0.445326i
$829$	−3.72352	+	35.4269i	−0.129323	+	1.23043i	0.716738	+	0.697343i	$0.245634\pi$
$829$	−3.72352	+	35.4269i	−0.129323	+	1.23043i	−0.846061	+	0.533086i	$0.821032\pi$
$830$	−2.42421	−	1.76129i	−0.0841456	−	0.0611354i
$831$	22.1609	−	68.2041i	0.768751	−	2.36597i
$832$	−0.215442	−	2.04979i	−0.00746911	−	0.0710638i
$833$	−19.0614	+	33.0152i	−0.660437	+	1.14391i
$834$	22.7827	+	16.5526i	0.788900	+	0.573169i
$835$	−1.33685	−	0.595205i	−0.0462637	−	0.0205979i
$836$	−6.00961	−	1.27738i	−0.207847	−	0.0441792i
$837$	−91.7793	+	19.5083i	−3.17236	+	0.674305i
$838$	9.87471	−	4.39650i	0.341116	−	0.151875i
$839$	33.9755	+	7.22171i	1.17296	+	0.249321i	0.752876	−	0.658162i	$-0.228666\pi$
$839$	33.9755	+	7.22171i	1.17296	+	0.249321i	0.420088	+	0.907483i	$0.361999\pi$
$840$	2.58111	+	4.47061i	0.0890567	+	0.154251i
$841$	14.4629	−	25.0505i	0.498721	−	0.863811i
$842$	5.20902	−	5.78520i	0.179515	−	0.199371i
$843$	43.2717			1.49036
$844$	−4.52824	+	5.02912i	−0.155869	+	0.173110i
$845$	−1.29396	+	3.98241i	−0.0445137	+	0.136999i
$846$	18.8079	+	57.8848i	0.646629	+	1.99012i
$847$	30.4094	−	13.5391i	1.04488	−	0.465210i
$848$	−8.29905	−	9.21703i	−0.284990	−	0.316514i
$849$	11.9967	+	13.3237i	0.411725	+	0.457267i
$850$	−34.9161	+	7.42165i	−1.19761	+	0.254560i
$851$	−6.14019	+	4.46111i	−0.210483	+	0.152925i
$852$	1.32042	+	12.5630i	0.0452370	+	0.430401i
$853$	−37.4016			−1.28061			−0.640303	−	0.768122i	$-0.721191\pi$
$853$	−37.4016			−1.28061			−0.640303	+	0.768122i	$0.721191\pi$
$854$	3.80969	−	26.8944i	0.130365	−	0.920306i
$855$	16.2911			0.557144
$856$	0.387266	+	3.68459i	0.0132365	+	0.125937i
$857$	6.31617	−	4.58896i	0.215756	−	0.156756i	−0.474658	−	0.880170i	$-0.657428\pi$
$857$	6.31617	−	4.58896i	0.215756	−	0.156756i	0.690414	+	0.723414i	$0.257428\pi$
$858$	−7.47610	+	1.58909i	−0.255230	+	0.0542508i
$859$	25.4993	+	28.3198i	0.870025	+	0.966261i	0.999680	−	0.0252986i	$-0.00805364\pi$
$859$	25.4993	+	28.3198i	0.870025	+	0.966261i	−0.129655	+	0.991559i	$0.541387\pi$
$860$	−1.45998	−	1.62147i	−0.0497850	−	0.0552918i
$861$	65.2204	−	29.0380i	2.22270	−	0.989611i
$862$	5.21677	+	16.0556i	0.177684	+	0.546855i
$863$	1.24960	−	3.84586i	0.0425368	−	0.130915i	−0.927533	−	0.373742i	$-0.878075\pi$
$863$	1.24960	−	3.84586i	0.0425368	−	0.130915i	0.970070	+	0.242827i	$0.0780747\pi$
$864$	7.52416	−	8.35642i	0.255977	−	0.284291i
$865$	−7.10373			−0.241534
$866$	8.89147	−	9.87498i	0.302144	−	0.335565i
$867$	60.4598	−	104.720i	2.05332	−	3.55646i
$868$	−14.5102	−	25.1324i	−0.492509	−	0.853050i
$869$	−10.9841	−	2.33474i	−0.372609	−	0.0792005i
$870$	0.369276	−	0.164412i	0.0125196	−	0.00557410i
$871$	−17.4224	+	3.70324i	−0.590335	+	0.125480i
$872$	−5.11695	−	1.08764i	−0.173282	−	0.0368322i
$873$	62.4994	+	27.8265i	2.11529	+	0.941786i
$874$	−19.7760	−	14.3681i	−0.668932	−	0.486007i
$875$	−8.12940	+	14.0805i	−0.274824	+	0.476009i
$876$	5.37150	+	51.1064i	0.181486	+	1.72672i
$877$	4.80690	−	14.7941i	0.162318	−	0.499562i	−0.836511	−	0.547950i	$-0.815408\pi$
$877$	4.80690	−	14.7941i	0.162318	−	0.499562i	0.998829	+	0.0483880i	$0.0154084\pi$
$878$	−20.4559	−	14.8621i	−0.690353	−	0.501571i
$879$	1.84562	−	17.5599i	0.0622512	−	0.592280i
$880$	0.522456	+	0.232612i	0.0176120	+	0.00784136i
$881$	−7.23845	−	22.2777i	−0.243870	−	0.750554i	−0.995820	−	0.0913343i	$-0.970887\pi$
$881$	−7.23845	−	22.2777i	−0.243870	−	0.750554i	0.751951	−	0.659219i	$-0.229113\pi$
$882$	27.3083	−	19.8407i	0.919519	−	0.668070i
$883$	2.79631	+	4.84335i	0.0941034	+	0.162992i	0.909234	−	0.416285i	$-0.136668\pi$
$883$	2.79631	+	4.84335i	0.0941034	+	0.162992i	−0.815131	+	0.579277i	$0.803335\pi$
$884$	−1.61189	+	15.3361i	−0.0542136	+	0.515808i
$885$	−0.373206	+	3.55082i	−0.0125452	+	0.119359i
$886$	13.3504	+	23.1235i	0.448515	+	0.776850i
$887$	−19.2151	+	13.9606i	−0.645179	+	0.468750i	−0.861626	−	0.507544i	$-0.830553\pi$
$887$	−19.2151	+	13.9606i	−0.645179	+	0.468750i	0.216446	+	0.976295i	$0.430553\pi$
$888$	−1.52994	−	4.70868i	−0.0513415	−	0.158013i
$889$	14.6451	+	6.52043i	0.491182	+	0.218688i
$890$	−0.114393	+	1.08838i	−0.00383448	+	0.0364826i
$891$	−14.5163	−	10.5467i	−0.486316	−	0.353329i
$892$	1.66079	−	5.11139i	0.0556074	−	0.171142i
$893$	4.93620	+	46.9648i	0.165184	+	1.57162i
$894$	17.9773	−	31.1375i	0.601249	−	1.04139i
$895$	−8.08706	−	5.87559i	−0.270321	−	0.196399i
$896$	3.17717	+	1.41457i	0.106142	+	0.0472574i
$897$	−29.7449	−	6.32248i	−0.993155	−	0.211102i
$898$	−6.32403	+	1.34421i	−0.211036	+	0.0448570i
$899$	−2.07596	+	0.924277i	−0.0692371	+	0.0308264i
$900$	30.9157	+	6.57134i	1.03052	+	0.219045i
$901$	46.3972	+	80.3622i	1.54571	+	2.67725i
$902$	3.95463	−	6.84963i	0.131675	−	0.228068i
$903$	−32.9240	+	36.5658i	−1.09564	+	1.21684i
$904$	7.94990			0.264410
$905$	5.57580	−	6.19256i	0.185346	−	0.205848i
$906$	−0.280578	+	0.863529i	−0.00932157	+	0.0286888i
$907$	11.6119	+	35.7378i	0.385567	+	1.18665i	0.936068	+	0.351819i	$0.114437\pi$
$907$	11.6119	+	35.7378i	0.385567	+	1.18665i	−0.550501	+	0.834835i	$0.685563\pi$
$908$	−10.6005	+	4.71964i	−0.351790	+	0.156627i
$909$	36.8058	+	40.8770i	1.22077	+	1.35580i
$910$	2.29484	+	2.54868i	0.0760732	+	0.0844879i
$911$	−0.451635	+	0.0959979i	−0.0149633	+	0.00318055i	−0.215387	−	0.976529i	$-0.569101\pi$
$911$	−0.451635	+	0.0959979i	−0.0149633	+	0.00318055i	0.200424	+	0.979709i	$0.435768\pi$
$912$	12.9005	−	9.37275i	0.427178	−	0.310363i
$913$	0.782522	+	7.44519i	0.0258977	+	0.246400i
$914$	−6.97659			−0.230765
$915$	7.44206	+	8.88878i	0.246027	+	0.293854i
$916$	10.7313			0.354573
$917$	1.73046	+	16.4642i	0.0571447	+	0.543696i
$918$	−68.0626	+	49.4504i	−2.24640	+	1.63211i
$919$	28.4363	−	6.04432i	0.938027	−	0.199384i	0.286562	−	0.958062i	$-0.407488\pi$
$919$	28.4363	−	6.04432i	0.938027	−	0.199384i	0.651466	+	0.758678i	$0.274154\pi$
$920$	1.52254	+	1.69095i	0.0501966	+	0.0557490i
$921$	13.1466	+	14.6008i	0.433195	+	0.481112i
$922$	−15.1110	+	6.72784i	−0.497654	+	0.221570i
$923$	2.59338	+	7.98160i	0.0853622	+	0.262718i
$924$	3.98536	−	12.2657i	0.131109	−	0.403511i
$925$	5.09484	−	5.65839i	0.167517	−	0.186047i
$926$	21.9016			0.719732
$927$	28.3419	−	31.4769i	0.930872	−	1.03384i
$928$	0.136165	−	0.235845i	0.00446983	−	0.00774198i
$929$	20.0605	+	34.7459i	0.658165	+	1.13997i	0.981090	+	0.193550i	$0.0620002\pi$
$929$	20.0605	+	34.7459i	0.658165	+	1.13997i	−0.322926	+	0.946424i	$0.604666\pi$
$930$	12.1150	+	2.57513i	0.397267	+	0.0844417i
$931$	23.9259	−	10.6525i	0.784138	−	0.349121i
$932$	21.4400	−	4.55721i	0.702291	−	0.149276i
$933$	−5.55676	−	1.18112i	−0.181920	−	0.0386683i
$934$	−17.4073	−	7.75022i	−0.569584	−	0.253595i
$935$	−3.46164	−	2.51503i	−0.113208	−	0.0822501i
$936$	6.82690	−	11.8245i	0.223144	−	0.386497i
$937$	1.74908	+	16.6414i	0.0571399	+	0.543650i	0.985223	+	0.171277i	$0.0547892\pi$
$937$	1.74908	+	16.6414i	0.0571399	+	0.543650i	−0.928083	+	0.372373i	$0.878544\pi$
$938$	9.28752	−	28.5841i	0.303248	−	0.933303i
$939$	11.3760	+	8.26517i	0.371243	+	0.269724i
$940$	0.459484	−	4.37170i	0.0149867	−	0.142589i
$941$	11.7941	+	5.25106i	0.384476	+	0.171180i	0.589867	−	0.807500i	$-0.299180\pi$
$941$	11.7941	+	5.25106i	0.384476	+	0.171180i	−0.205391	+	0.978680i	$0.565847\pi$
$942$	−3.64381	−	11.2145i	−0.118722	−	0.365388i
$943$	25.4584	−	18.4966i	0.829041	−	0.602334i
$944$	1.20270	+	2.08314i	0.0391446	+	0.0678005i
$945$	−1.95581	+	18.6083i	−0.0636226	+	0.605329i
$946$	−0.569797	+	5.42125i	−0.0185257	+	0.176260i
$947$	−24.0902	−	41.7255i	−0.782827	−	1.35590i	−0.930288	−	0.366829i	$-0.880443\pi$
$947$	−24.0902	−	41.7255i	−0.782827	−	1.35590i	0.147461	−	0.989068i	$-0.452890\pi$
$948$	23.5789	−	17.1311i	0.765806	−	0.556391i
$949$	10.5499	+	32.4693i	0.342464	+	1.05400i
$950$	22.4029	+	9.97443i	0.726847	+	0.323613i
$951$	−2.37353	+	22.5826i	−0.0769669	+	0.732291i
$952$	−21.0510	−	15.2944i	−0.682266	−	0.495695i
$953$	2.73911	−	8.43011i	0.0887285	−	0.273078i	−0.896840	−	0.442355i	$-0.854143\pi$
$953$	2.73911	−	8.43011i	0.0887285	−	0.273078i	0.985569	+	0.169277i	$0.0541432\pi$
$954$	−8.58835	−	81.7126i	−0.278058	−	2.64554i
$955$	−4.67216	+	8.09242i	−0.151188	+	0.261865i
$956$	11.1276	+	8.08466i	0.359892	+	0.261477i
$957$	−0.922572	−	0.410756i	−0.0298225	−	0.0132778i
$958$	29.7291	+	6.31912i	0.960505	+	0.204162i
$959$	36.5700	−	7.77319i	1.18091	−	0.251009i
$960$	−1.35599	+	0.603725i	−0.0437644	+	0.0194851i
$961$	−37.7844	−	8.03131i	−1.21885	−	0.259075i
$962$	−1.64463	−	2.84858i	−0.0530250	−	0.0918420i
$963$	−12.2716	+	21.2551i	−0.395448	+	0.684936i
$964$	18.9399	−	21.0349i	0.610013	−	0.677488i
$965$	−2.46421			−0.0793257
$966$	34.3348	−	38.1326i	1.10470	−	1.22690i
$967$	−15.3112	+	47.1231i	−0.492376	+	1.51538i	0.328631	+	0.944458i	$0.393413\pi$
$967$	−15.3112	+	47.1231i	−0.492376	+	1.51538i	−0.821007	+	0.570918i	$0.806587\pi$
$968$	2.95767	+	9.10276i	0.0950630	+	0.292574i
$969$	−108.989	+	48.5250i	−3.50123	+	1.55885i
$970$	−3.30624	−	3.67195i	−0.106157	−	0.117899i
$971$	−11.8194	−	13.1268i	−0.379302	−	0.421258i	0.523020	−	0.852320i	$-0.324805\pi$
$971$	−11.8194	−	13.1268i	−0.379302	−	0.421258i	−0.902322	+	0.431063i	$0.858139\pi$
$972$	12.5555	−	2.66875i	0.402717	−	0.0856001i
$973$	−25.5402	+	18.5561i	−0.818782	+	0.594880i
$974$	−0.402315	−	3.82777i	−0.0128910	−	0.122650i
$975$	30.5073			0.977016
$976$	7.57619	+	1.89774i	0.242508	+	0.0607451i
$977$	−25.2554			−0.807993			−0.403997	−	0.914760i	$-0.632379\pi$
$977$	−25.2554			−0.807993			−0.403997	+	0.914760i	$0.632379\pi$
$978$	−0.962384	−	9.15647i	−0.0307736	−	0.292792i
$979$	2.21194	−	1.60707i	0.0706939	−	0.0513621i
$980$	−2.38462	+	0.506867i	−0.0761739	+	0.0161913i
$981$	−23.1887	−	25.7536i	−0.740357	−	0.822250i
$982$	1.76249	+	1.95744i	0.0562432	+	0.0624644i
$983$	−37.3010	+	16.6075i	−1.18972	+	0.529696i	−0.903550	−	0.428483i	$-0.859048\pi$
$983$	−37.3010	+	16.6075i	−1.18972	+	0.529696i	−0.286168	+	0.958180i	$0.592381\pi$
$984$	6.34344	+	19.5231i	0.202222	+	0.622374i
$985$	0.509113	−	1.56689i	0.0162217	−	0.0499252i
$986$	−1.36336	+	1.51416i	−0.0434182	+	0.0482208i
$987$	−99.1292			−3.15532
$988$	7.08866	−	7.87276i	0.225520	−	0.250466i
$989$	−10.8441	+	18.7825i	−0.344822	+	0.597250i
$990$	1.89429	+	3.28101i	0.0602046	+	0.104277i
$991$	12.4625	+	2.64898i	0.395884	+	0.0841478i	0.401552	−	0.915836i	$-0.368471\pi$
$991$	12.4625	+	2.64898i	0.395884	+	0.0841478i	−0.00566803	+	0.999984i	$0.501804\pi$
$992$	7.62296	−	3.39396i	0.242029	−	0.107758i
$993$	−65.9174	+	14.0112i	−2.09183	+	0.444631i
$994$	−13.8517	−	2.94427i	−0.439349	−	0.0933865i
$995$	−6.05779	−	2.69710i	−0.192045	−	0.0855038i
$996$	−15.7190	−	11.4205i	−0.498077	−	0.361874i
$997$	24.9795	−	43.2657i	0.791107	−	1.37024i	−0.134174	−	0.990958i	$-0.542838\pi$
$997$	24.9795	−	43.2657i	0.791107	−	1.37024i	0.925282	−	0.379281i	$-0.123828\pi$
$998$	0.0913751	+	0.869376i	0.00289243	+	0.0275196i
$999$	5.54538	−	17.0669i	0.175448	−	0.539974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.i.a.15.2	✓	16
4.3	odd	2		976.2.bw.a.625.1		16
61.22	even	15		7442.2.a.p.1.1		8
61.39	even	30		7442.2.a.r.1.1		8
61.57	even	15	inner	122.2.i.a.57.2	yes	16
244.179	odd	30		976.2.bw.a.545.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.i.a.15.2	✓	16	1.1	even	1	trivial
122.2.i.a.57.2	yes	16	61.57	even	15	inner
976.2.bw.a.545.1		16	244.179	odd	30
976.2.bw.a.625.1		16	4.3	odd	2
7442.2.a.p.1.1		8	61.22	even	15
7442.2.a.r.1.1		8	61.39	even	30

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 + 0.994522i) q^{2} +(2.50985 - 1.82351i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.320145 + 0.355557i) q^{5} +(2.07588 + 2.30549i) q^{6} +(-3.17717 + 1.41457i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.04710 - 6.30034i) q^{9} +O(q^{10})\)	\(q+(0.104528 + 0.994522i) q^{2} +(2.50985 - 1.82351i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.320145 + 0.355557i) q^{5} +(2.07588 + 2.30549i) q^{6} +(-3.17717 + 1.41457i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.04710 - 6.30034i) q^{9} +(-0.320145 + 0.355557i) q^{10} +1.19532 q^{11} +(-2.07588 + 2.30549i) q^{12} +(-1.03054 + 1.78495i) q^{13} +(-1.73892 - 3.01190i) q^{14} +(1.45188 + 0.308606i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-7.31827 + 1.55555i) q^{17} +(6.47981 + 1.37733i) q^{18} +(4.69556 + 2.09060i) q^{19} +(-0.387073 - 0.281225i) q^{20} +(-5.39475 + 9.34398i) q^{21} +(0.124945 + 1.18877i) q^{22} +(-1.46962 + 4.52302i) q^{23} +(-2.50985 - 1.82351i) q^{24} +(0.498714 - 4.74495i) q^{25} +(-1.88289 - 0.838319i) q^{26} +(-3.47480 - 10.6943i) q^{27} +(2.81364 - 2.04423i) q^{28} +(-0.136165 - 0.235845i) q^{29} +(-0.155153 + 1.47618i) q^{30} +(0.872224 - 8.29866i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00008 - 2.17968i) q^{33} +(-2.31199 - 7.11558i) q^{34} +(-1.52011 - 0.676798i) q^{35} +(-0.692456 + 6.58828i) q^{36} +(1.29110 + 0.938039i) q^{37} +(-1.58833 + 4.88837i) q^{38} +(0.668376 + 6.35918i) q^{39} +(0.239224 - 0.414349i) q^{40} +(-5.35315 - 3.88929i) q^{41} +(-9.85669 - 4.38848i) q^{42} +(4.46073 + 0.948156i) q^{43} +(-1.16920 + 0.248521i) q^{44} +(2.89550 - 1.28916i) q^{45} +(-4.65186 - 0.988784i) q^{46} +(4.59378 + 7.95667i) q^{47} +(1.55117 - 2.68671i) q^{48} +(3.40950 - 3.78663i) q^{49} +4.77109 q^{50} +(-15.5312 + 17.2492i) q^{51} +(0.636910 - 1.96021i) q^{52} +(-3.83265 - 11.7957i) q^{53} +(10.2725 - 4.57362i) q^{54} +(0.382675 + 0.425004i) q^{55} +(2.32713 + 2.58454i) q^{56} +(15.5974 - 3.31533i) q^{57} +(0.220319 - 0.160071i) q^{58} +(0.251433 + 2.39223i) q^{59} -1.48431 q^{60} +(6.14931 + 4.81518i) q^{61} +8.34437 q^{62} +(2.40826 + 22.9130i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.964574 + 0.205027i) q^{65} +(2.48134 + 2.75580i) q^{66} +(5.78253 + 6.42215i) q^{67} +(6.83493 - 3.04311i) q^{68} +(4.55927 + 14.0320i) q^{69} +(0.514195 - 1.58253i) q^{70} +(2.72458 - 3.02595i) q^{71} -6.62457 q^{72} +(11.0836 - 12.3096i) q^{73} +(-0.797944 + 1.38208i) q^{74} +(-7.40079 - 12.8185i) q^{75} +(-5.02761 - 1.06865i) q^{76} +(-3.79774 + 1.69086i) q^{77} +(-6.25448 + 1.32943i) q^{78} +(-9.18923 - 1.95323i) q^{79} +(0.437085 + 0.194603i) q^{80} +(-12.1443 - 8.82336i) q^{81} +(3.30843 - 5.73037i) q^{82} +(0.654654 + 6.22862i) q^{83} +(3.33414 - 10.2614i) q^{84} +(-2.89599 - 2.10406i) q^{85} +(-0.476690 + 4.53540i) q^{86} +(-0.771820 - 0.343636i) q^{87} +(-0.369374 - 1.13682i) q^{88} +(1.85050 - 1.34447i) q^{89} +(1.58476 + 2.74488i) q^{90} +(0.749274 - 7.12887i) q^{91} +(0.497115 - 4.72973i) q^{92} +(-12.9436 - 22.4189i) q^{93} +(-7.43290 + 5.40032i) q^{94} +(0.759933 + 2.33883i) q^{95} +(2.83414 + 1.26184i) q^{96} +(-1.07950 + 10.2708i) q^{97} +(4.12228 + 2.99501i) q^{98} +(2.44695 - 7.53092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9} - 6 q^{10} - 2 q^{11} + q^{12} - 9 q^{13} - 10 q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 24 q^{18} + 10 q^{19} - 7 q^{20} - 6 q^{21} - 11 q^{22} - 11 q^{23} - 3 q^{24} - 28 q^{25} + 4 q^{26} - 33 q^{27} + 5 q^{28} + 15 q^{29} - 12 q^{30} - 12 q^{31} + 8 q^{32} + 15 q^{33} - 11 q^{34} + 19 q^{35} + q^{36} + 16 q^{37} - 10 q^{38} + 24 q^{39} + 4 q^{40} - 20 q^{41} - 19 q^{42} - 21 q^{43} - 4 q^{44} + 17 q^{45} + 2 q^{46} - 11 q^{47} + q^{48} - 10 q^{49} + 4 q^{50} - 56 q^{51} - 2 q^{52} - 8 q^{53} + 41 q^{54} + 35 q^{55} + 10 q^{56} + 49 q^{57} - 10 q^{58} + 35 q^{59} + 6 q^{60} + 15 q^{61} + 16 q^{62} - 26 q^{63} - 4 q^{64} + 24 q^{65} + 10 q^{66} + 22 q^{67} + 12 q^{68} + 46 q^{69} + 28 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 7 q^{74} - 15 q^{75} - 20 q^{76} + 2 q^{77} + 11 q^{78} + 10 q^{79} - 4 q^{80} - 27 q^{81} + 15 q^{82} - 45 q^{83} + 17 q^{84} + 2 q^{85} + 11 q^{86} - 9 q^{87} - 8 q^{88} - 26 q^{89} + 8 q^{90} - 84 q^{91} - 47 q^{92} - 33 q^{93} - 2 q^{94} + 37 q^{95} + 9 q^{96} - 41 q^{97} - 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9 - 6 * q^10 - 2 * q^11 + q^12 - 9 * q^13 - 10 * q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 24 * q^18 + 10 * q^19 - 7 * q^20 - 6 * q^21 - 11 * q^22 - 11 * q^23 - 3 * q^24 - 28 * q^25 + 4 * q^26 - 33 * q^27 + 5 * q^28 + 15 * q^29 - 12 * q^30 - 12 * q^31 + 8 * q^32 + 15 * q^33 - 11 * q^34 + 19 * q^35 + q^36 + 16 * q^37 - 10 * q^38 + 24 * q^39 + 4 * q^40 - 20 * q^41 - 19 * q^42 - 21 * q^43 - 4 * q^44 + 17 * q^45 + 2 * q^46 - 11 * q^47 + q^48 - 10 * q^49 + 4 * q^50 - 56 * q^51 - 2 * q^52 - 8 * q^53 + 41 * q^54 + 35 * q^55 + 10 * q^56 + 49 * q^57 - 10 * q^58 + 35 * q^59 + 6 * q^60 + 15 * q^61 + 16 * q^62 - 26 * q^63 - 4 * q^64 + 24 * q^65 + 10 * q^66 + 22 * q^67 + 12 * q^68 + 46 * q^69 + 28 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 7 * q^74 - 15 * q^75 - 20 * q^76 + 2 * q^77 + 11 * q^78 + 10 * q^79 - 4 * q^80 - 27 * q^81 + 15 * q^82 - 45 * q^83 + 17 * q^84 + 2 * q^85 + 11 * q^86 - 9 * q^87 - 8 * q^88 - 26 * q^89 + 8 * q^90 - 84 * q^91 - 47 * q^92 - 33 * q^93 - 2 * q^94 + 37 * q^95 + 9 * q^96 - 41 * q^97 - 5 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more