LMFDB - Embedded newform 637.2.bl.a.53.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.18
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.a.625.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.726317 + 0.495195i) q^{2} +(-1.98880 - 1.84534i) q^{3} +(-0.448363 - 1.14241i) q^{4} +(1.60817 - 0.496054i) q^{5} +(-0.530699 - 2.32514i) q^{6} +(0.921177 - 2.48021i) q^{7} +(0.631282 - 2.76583i) q^{8} +(0.325867 + 4.34840i) q^{9} +O(q^{10})$	\(q+(0.726317 + 0.495195i) q^{2} +(-1.98880 - 1.84534i) q^{3} +(-0.448363 - 1.14241i) q^{4} +(1.60817 - 0.496054i) q^{5} +(-0.530699 - 2.32514i) q^{6} +(0.921177 - 2.48021i) q^{7} +(0.631282 - 2.76583i) q^{8} +(0.325867 + 4.34840i) q^{9} +(1.41368 + 0.436064i) q^{10} +(0.132963 - 1.77427i) q^{11} +(-1.21643 + 3.09941i) q^{12} +(0.900969 - 0.433884i) q^{13} +(1.89725 - 1.34526i) q^{14} +(-4.11371 - 1.98106i) q^{15} +(0.0288670 - 0.0267846i) q^{16} +(0.740180 - 0.111564i) q^{17} +(-1.91662 + 3.31969i) q^{18} +(2.18476 + 3.78411i) q^{19} +(-1.28774 - 1.61477i) q^{20} +(-6.40886 + 3.23276i) q^{21} +(0.975185 - 1.22284i) q^{22} +(-1.63390 - 0.246271i) q^{23} +(-6.35938 + 4.33575i) q^{24} +(-1.79106 + 1.22112i) q^{25} +(0.869246 + 0.131018i) q^{26} +(2.30152 - 2.88601i) q^{27} +(-3.24644 + 0.0596713i) q^{28} +(-3.15294 - 3.95366i) q^{29} +(-2.00685 - 3.47597i) q^{30} +(4.92075 - 8.52300i) q^{31} +(-5.57631 + 0.840494i) q^{32} +(-3.53857 + 3.28331i) q^{33} +(0.592852 + 0.285502i) q^{34} +(0.251090 - 4.44554i) q^{35} +(4.82155 - 2.32194i) q^{36} +(-3.33672 + 8.50181i) q^{37} +(-0.287045 + 3.83035i) q^{38} +(-2.59251 - 0.799683i) q^{39} +(-0.356793 - 4.76107i) q^{40} +(-1.25718 + 5.50806i) q^{41} +(-6.25571 - 0.825625i) q^{42} +(-1.31477 - 5.76036i) q^{43} +(-2.08656 + 0.643620i) q^{44} +(2.68109 + 6.83131i) q^{45} +(-1.06478 - 0.987970i) q^{46} +(4.17079 + 2.84360i) q^{47} -0.106837 q^{48} +(-5.30287 - 4.56942i) q^{49} -1.90557 q^{50} +(-1.67794 - 1.14400i) q^{51} +(-0.899634 - 0.834739i) q^{52} +(0.0842258 + 0.214604i) q^{53} +(3.10077 - 0.956460i) q^{54} +(-0.666308 - 2.91929i) q^{55} +(-6.27831 - 4.11353i) q^{56} +(2.63792 - 11.5575i) q^{57} +(-0.332202 - 4.43293i) q^{58} +(10.4802 + 3.23270i) q^{59} +(-0.418746 + 5.58778i) q^{60} +(4.18436 - 10.6616i) q^{61} +(7.79457 - 3.75367i) q^{62} +(11.0851 + 3.19743i) q^{63} +(-4.53734 - 2.18507i) q^{64} +(1.23368 - 1.14469i) q^{65} +(-4.19600 + 0.632446i) q^{66} +(-2.33816 + 4.04982i) q^{67} +(-0.459321 - 0.795568i) q^{68} +(2.79505 + 3.50488i) q^{69} +(2.38378 - 3.10454i) q^{70} +(0.535413 - 0.671387i) q^{71} +(12.2326 + 1.84377i) q^{72} +(-10.8258 + 7.38088i) q^{73} +(-6.63357 + 4.52269i) q^{74} +(5.81545 + 0.876537i) q^{75} +(3.34345 - 4.19255i) q^{76} +(-4.27808 - 1.96420i) q^{77} +(-1.48699 - 1.86462i) q^{78} +(-0.397337 - 0.688208i) q^{79} +(0.0331363 - 0.0573937i) q^{80} +(3.03275 - 0.457114i) q^{81} +(-3.64067 + 3.37805i) q^{82} +(12.6148 + 6.07496i) q^{83} +(6.56663 + 5.87209i) q^{84} +(1.13499 - 0.546583i) q^{85} +(1.89756 - 4.83492i) q^{86} +(-1.02527 + 13.6813i) q^{87} +(-4.82340 - 1.48782i) q^{88} +(-0.103215 - 1.37731i) q^{89} +(-1.43551 + 6.28936i) q^{90} +(-0.246170 - 2.63427i) q^{91} +(0.451238 + 1.97700i) q^{92} +(-25.5142 + 7.87009i) q^{93} +(1.62118 + 4.13071i) q^{94} +(5.39058 + 5.00173i) q^{95} +(12.6412 + 8.61860i) q^{96} +14.2208 q^{97} +(-1.58881 - 5.94480i) q^{98} +7.75858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	0.726317	+	0.495195i	0.513584	+	0.350156i	0.792214	−	0.610243i	$-0.208928\pi$
$2$	0.726317	+	0.495195i	0.513584	+	0.350156i	−0.278631	+	0.960398i	$0.589880\pi$
$3$	−1.98880	−	1.84534i	−1.14823	−	1.06541i	−0.997039	−	0.0769017i	$-0.975497\pi$
$3$	−1.98880	−	1.84534i	−1.14823	−	1.06541i	−0.151195	−	0.988504i	$-0.548312\pi$
$4$	−0.448363	−	1.14241i	−0.224181	−	0.571205i
$5$	1.60817	−	0.496054i	0.719194	−	0.221842i	0.0865091	−	0.996251i	$-0.472429\pi$
$5$	1.60817	−	0.496054i	0.719194	−	0.221842i	0.632685	+	0.774409i	$0.281953\pi$
$6$	−0.530699	−	2.32514i	−0.216657	−	0.949236i
$7$	0.921177	−	2.48021i	0.348172	−	0.937431i
$7$	0.921177	−	2.48021i	0.348172	−	0.937431i
$8$	0.631282	−	2.76583i	0.223192	−	0.977868i
$9$	0.325867	+	4.34840i	0.108622	+	1.44947i
$10$	1.41368	+	0.436064i	0.447046	+	0.137895i
$11$	0.132963	−	1.77427i	0.0400900	−	0.534964i	−0.940616	−	0.339473i	$-0.889751\pi$
$11$	0.132963	−	1.77427i	0.0400900	−	0.534964i	0.980706	−	0.195490i	$-0.0626298\pi$
$12$	−1.21643	+	3.09941i	−0.351152	+	0.894721i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$14$	1.89725	−	1.34526i	0.507062	−	0.359535i
$15$	−4.11371	−	1.98106i	−1.06216	−	0.511507i
$16$	0.0288670	−	0.0267846i	0.00721674	−	0.00669615i
$17$	0.740180	−	0.111564i	0.179520	−	0.0270583i	−0.0586670	−	0.998278i	$-0.518685\pi$
$17$	0.740180	−	0.111564i	0.179520	−	0.0270583i	0.238187	+	0.971219i	$0.423447\pi$
$18$	−1.91662	+	3.31969i	−0.451752	+	0.782458i
$19$	2.18476	+	3.78411i	0.501218	+	0.868135i	0.999999	+	0.00140722i	$0.000447931\pi$
$19$	2.18476	+	3.78411i	0.501218	+	0.868135i	−0.498781	+	0.866728i	$0.666219\pi$
$20$	−1.28774	−	1.61477i	−0.287947	−	0.361075i
$21$	−6.40886	+	3.23276i	−1.39853	+	0.705445i
$22$	0.975185	−	1.22284i	0.207910	−	0.260711i
$23$	−1.63390	−	0.246271i	−0.340692	−	0.0513510i	−0.0235319	−	0.999723i	$-0.507491\pi$
$23$	−1.63390	−	0.246271i	−0.340692	−	0.0513510i	−0.317160	+	0.948372i	$0.602729\pi$
$24$	−6.35938	+	4.33575i	−1.29810	+	0.885032i
$25$	−1.79106	+	1.22112i	−0.358212	+	0.244225i
$26$	0.869246	+	0.131018i	0.170473	+	0.0256947i
$27$	2.30152	−	2.88601i	0.442927	−	0.555413i
$28$	−3.24644	+	0.0596713i	−0.613519	+	0.0112768i
$29$	−3.15294	−	3.95366i	−0.585486	−	0.734176i	0.397552	−	0.917580i	$-0.369860\pi$
$29$	−3.15294	−	3.95366i	−0.585486	−	0.734176i	−0.983038	+	0.183404i	$0.941288\pi$
$30$	−2.00685	−	3.47597i	−0.366399	−	0.634622i
$31$	4.92075	−	8.52300i	0.883793	−	1.53078i	0.0367030	−	0.999326i	$-0.488314\pi$
$31$	4.92075	−	8.52300i	0.883793	−	1.53078i	0.847090	−	0.531449i	$-0.178352\pi$
$32$	−5.57631	+	0.840494i	−0.985762	+	0.148580i
$33$	−3.53857	+	3.28331i	−0.615986	+	0.571551i
$34$	0.592852	+	0.285502i	0.101673	+	0.0489632i
$35$	0.251090	−	4.44554i	0.0424420	−	0.751434i
$36$	4.82155	−	2.32194i	0.803592	−	0.386989i
$37$	−3.33672	+	8.50181i	−0.548553	+	1.39769i	0.340656	+	0.940188i	$0.389351\pi$
$37$	−3.33672	+	8.50181i	−0.548553	+	1.39769i	−0.889209	+	0.457502i	$0.848744\pi$
$38$	−0.287045	+	3.83035i	−0.0465649	+	0.621365i
$39$	−2.59251	−	0.799683i	−0.415134	−	0.128052i
$40$	−0.356793	−	4.76107i	−0.0564139	−	0.752791i
$41$	−1.25718	+	5.50806i	−0.196338	+	0.860214i	0.776755	+	0.629803i	$0.216864\pi$
$41$	−1.25718	+	5.50806i	−0.196338	+	0.860214i	−0.973093	+	0.230411i	$0.925993\pi$
$42$	−6.25571	−	0.825625i	−0.965277	−	0.127397i
$43$	−1.31477	−	5.76036i	−0.200500	−	0.878447i	−0.970633	−	0.240564i	$-0.922668\pi$
$43$	−1.31477	−	5.76036i	−0.200500	−	0.878447i	0.770133	−	0.637883i	$-0.220190\pi$
$44$	−2.08656	+	0.643620i	−0.314561	+	0.0970293i
$45$	2.68109	+	6.83131i	0.399673	+	1.01835i
$46$	−1.06478	−	0.987970i	−0.156993	−	0.145668i
$47$	4.17079	+	2.84360i	0.608372	+	0.414781i	0.827941	−	0.560816i	$-0.189512\pi$
$47$	4.17079	+	2.84360i	0.608372	+	0.414781i	−0.219568	+	0.975597i	$0.570465\pi$
$48$	−0.106837			−0.0154206
$49$	−5.30287	−	4.56942i	−0.757552	−	0.652775i
$50$	−1.90557			−0.269489
$51$	−1.67794	−	1.14400i	−0.234959	−	0.160192i
$52$	−0.899634	−	0.834739i	−0.124757	−	0.115757i
$53$	0.0842258	+	0.214604i	0.0115693	+	0.0294781i	0.936542	−	0.350556i	$-0.114007\pi$
$53$	0.0842258	+	0.214604i	0.0115693	+	0.0294781i	−0.924972	+	0.380034i	$0.875912\pi$
$54$	3.10077	−	0.956460i	0.421961	−	0.130158i
$55$	−0.666308	−	2.91929i	−0.0898450	−	0.393636i
$56$	−6.27831	−	4.11353i	−0.838974	−	0.549694i
$57$	2.63792	−	11.5575i	0.349400	−	1.53082i
$58$	−0.332202	−	4.43293i	−0.0436203	−	0.582072i
$59$	10.4802	+	3.23270i	1.36440	+	0.420862i	0.888597	−	0.458689i	$-0.151681\pi$
$59$	10.4802	+	3.23270i	1.36440	+	0.420862i	0.475805	+	0.879551i	$0.342157\pi$
$60$	−0.418746	+	5.58778i	−0.0540599	+	0.721379i
$61$	4.18436	−	10.6616i	0.535752	−	1.36507i	−0.365108	−	0.930965i	$-0.618968\pi$
$61$	4.18436	−	10.6616i	0.535752	−	1.36507i	0.900860	−	0.434109i	$-0.142937\pi$
$62$	7.79457	−	3.75367i	0.989912	−	0.476716i
$63$	11.0851	+	3.19743i	1.39659	+	0.402838i
$64$	−4.53734	−	2.18507i	−0.567167	−	0.273133i
$65$	1.23368	−	1.14469i	0.153019	−	0.141981i
$66$	−4.19600	+	0.632446i	−0.516492	+	0.0778487i
$67$	−2.33816	+	4.04982i	−0.285652	+	0.494764i	−0.972767	−	0.231785i	$-0.925544\pi$
$67$	−2.33816	+	4.04982i	−0.285652	+	0.494764i	0.687115	+	0.726549i	$0.258877\pi$
$68$	−0.459321	−	0.795568i	−0.0557009	−	0.0964768i
$69$	2.79505	+	3.50488i	0.336484	+	0.421938i
$70$	2.38378	−	3.10454i	0.284916	−	0.371063i
$71$	0.535413	−	0.671387i	0.0635418	−	0.0796789i	−0.749045	−	0.662519i	$-0.769487\pi$
$71$	0.535413	−	0.671387i	0.0635418	−	0.0796789i	0.812587	+	0.582840i	$0.198059\pi$
$72$	12.2326	+	1.84377i	1.44163	+	0.217291i
$73$	−10.8258	+	7.38088i	−1.26706	+	0.863867i	−0.995142	−	0.0984540i	$-0.968610\pi$
$73$	−10.8258	+	7.38088i	−1.26706	+	0.863867i	−0.271918	+	0.962320i	$0.587658\pi$
$74$	−6.63357	+	4.52269i	−0.771137	+	0.525752i
$75$	5.81545	+	0.876537i	0.671510	+	0.101214i
$76$	3.34345	−	4.19255i	0.383520	−	0.480918i
$77$	−4.27808	−	1.96420i	−0.487533	−	0.223841i
$78$	−1.48699	−	1.86462i	−0.168368	−	0.211127i
$79$	−0.397337	−	0.688208i	−0.0447039	−	0.0774295i	0.842808	−	0.538215i	$-0.180901\pi$
$79$	−0.397337	−	0.688208i	−0.0447039	−	0.0774295i	−0.887512	+	0.460785i	$0.847568\pi$
$80$	0.0331363	−	0.0573937i	0.00370475	−	0.00641681i
$81$	3.03275	−	0.457114i	0.336973	−	0.0507905i
$82$	−3.64067	+	3.37805i	−0.402045	+	0.373043i
$83$	12.6148	+	6.07496i	1.38465	+	0.666814i	0.969986	−	0.243160i	$-0.0781840\pi$
$83$	12.6148	+	6.07496i	1.38465	+	0.666814i	0.414666	+	0.909973i	$0.363898\pi$
$84$	6.56663	+	5.87209i	0.716478	+	0.640698i
$85$	1.13499	−	0.546583i	0.123107	−	0.0592853i
$86$	1.89756	−	4.83492i	0.204620	−	0.521362i
$87$	−1.02527	+	13.6813i	−0.109920	+	1.46679i
$88$	−4.82340	−	1.48782i	−0.514176	−	0.158602i
$89$	−0.103215	−	1.37731i	−0.0109407	−	0.145994i	0.989058	−	0.147527i	$-0.0471312\pi$
$89$	−0.103215	−	1.37731i	−0.0109407	−	0.145994i	−0.999999	+	0.00153254i	$0.999512\pi$
$90$	−1.43551	+	6.28936i	−0.151316	+	0.662957i
$91$	−0.246170	−	2.63427i	−0.0258056	−	0.276147i
$92$	0.451238	+	1.97700i	0.0470448	+	0.206117i
$93$	−25.5142	+	7.87009i	−2.64570	+	0.816090i
$94$	1.62118	+	4.13071i	0.167212	+	0.426050i
$95$	5.39058	+	5.00173i	0.553062	+	0.513167i
$96$	12.6412	+	8.61860i	1.29018	+	0.879632i
$97$	14.2208			1.44390			0.721951	−	0.691944i	$-0.243245\pi$
$97$	14.2208			1.44390			0.721951	+	0.691944i	$0.243245\pi$
$98$	−1.58881	−	5.94480i	−0.160494	−	0.600516i
$99$	7.75858			0.779766
$100$	2.19807	+	1.49862i	0.219807	+	0.149862i
$101$	1.36886	+	1.27011i	0.136206	+	0.126381i	0.745334	−	0.666691i	$-0.232290\pi$
$101$	1.36886	+	1.27011i	0.136206	+	0.126381i	−0.609128	+	0.793072i	$0.708480\pi$
$102$	−0.652215	−	1.66182i	−0.0645789	−	0.164544i
$103$	−5.14672	+	1.58755i	−0.507122	+	0.156426i	−0.537750	−	0.843105i	$-0.680725\pi$
$103$	−5.14672	+	1.58755i	−0.507122	+	0.156426i	0.0306281	+	0.999531i	$0.490249\pi$
$104$	−0.631282	−	2.76583i	−0.0619023	−	0.271212i
$105$	−8.70289	+	8.37795i	−0.849315	+	0.817604i
$106$	−0.0450960	+	0.197579i	−0.00438011	+	0.0191905i
$107$	−0.970346	−	12.9484i	−0.0938069	−	1.25177i	−0.823232	−	0.567705i	$-0.807831\pi$
$107$	−0.970346	−	12.9484i	−0.0938069	−	1.25177i	0.729425	−	0.684061i	$-0.239788\pi$
$108$	−4.32892	−	1.33530i	−0.416551	−	0.128489i
$109$	−0.129907	+	1.73349i	−0.0124429	+	0.166038i	0.987521	+	0.157490i	$0.0503401\pi$
$109$	−0.129907	+	1.73349i	−0.0124429	+	0.166038i	−0.999963	+	0.00854849i	$0.997279\pi$
$110$	0.961664	−	2.45028i	0.0916911	−	0.233625i
$111$	22.3248	−	10.7510i	2.11897	−	1.02044i
$112$	−0.0398399	−	0.0962694i	−0.00376451	−	0.00909661i
$113$	8.35837	+	4.02518i	0.786290	+	0.378657i	0.783542	−	0.621339i	$-0.213411\pi$
$113$	8.35837	+	4.02518i	0.786290	+	0.378657i	0.00274777	+	0.999996i	$0.499125\pi$
$114$	7.63916	−	7.08810i	0.715473	−	0.663862i
$115$	−2.74975	+	0.414458i	−0.256416	+	0.0386484i
$116$	−3.10304	+	5.37462i	−0.288110	+	0.499021i
$117$	2.18030	+	3.77638i	0.201568	+	0.349127i
$118$	6.01111	+	7.53770i	0.553368	+	0.693901i
$119$	0.405134	−	1.93857i	0.0371386	−	0.177708i
$120$	−8.07618	+	10.1272i	−0.737251	+	0.924484i
$121$	7.74677	+	1.16764i	0.704252	+	0.106149i
$122$	8.31872	−	5.67161i	0.753142	−	0.513483i
$123$	12.6645	−	8.63451i	1.14192	−	0.778547i
$124$	−11.9430	−	1.80012i	−1.07252	−	0.161656i
$125$	−7.52105	+	9.43110i	−0.672703	+	0.843543i
$126$	6.46796	+	7.81164i	0.576212	+	0.695916i
$127$	−4.96623	−	6.22745i	−0.440682	−	0.552597i	0.511041	−	0.859556i	$-0.329260\pi$
$127$	−4.96623	−	6.22745i	−0.440682	−	0.552597i	−0.951723	+	0.306959i	$0.900689\pi$
$128$	3.42578	+	5.93363i	0.302799	+	0.524464i
$129$	−8.01500	+	13.8824i	−0.705682	+	1.22228i
$130$	1.46289	−	0.220495i	0.128304	−	0.0193387i
$131$	11.8756	−	11.0190i	1.03758	−	0.962733i	0.0382471	−	0.999268i	$-0.487823\pi$
$131$	11.8756	−	11.0190i	1.03758	−	0.962733i	0.999332	+	0.0365353i	$0.0116321\pi$
$132$	5.33745	+	2.57038i	0.464566	+	0.223723i
$133$	11.3979	−	1.93282i	0.988327	−	0.167597i
$134$	−3.70370	+	1.78361i	−0.319951	+	0.154080i
$135$	2.26961	−	5.78286i	0.195337	−	0.497709i
$136$	0.158695	−	2.11764i	0.0136080	−	0.181586i
$137$	6.13463	+	1.89228i	0.524117	+	0.161669i	0.545513	−	0.838102i	$-0.316335\pi$
$137$	6.13463	+	1.89228i	0.524117	+	0.161669i	−0.0213958	+	0.999771i	$0.506811\pi$
$138$	0.294494	+	3.92975i	0.0250690	+	0.334523i
$139$	0.142468	−	0.624195i	0.0120840	−	0.0529435i	−0.968526	−	0.248911i	$-0.919927\pi$
$139$	0.142468	−	0.624195i	0.0120840	−	0.0529435i	0.980610	+	0.195967i	$0.0627846\pi$
$140$	−5.19121	+	1.70637i	−0.438738	+	0.144215i
$141$	−3.04747	−	13.3519i	−0.256644	−	1.12443i
$142$	0.721347	−	0.222506i	0.0605341	−	0.0186723i
$143$	−0.650033	−	1.65626i	−0.0543585	−	0.138503i
$144$	0.125877	+	0.116797i	0.0104898	+	0.00973307i
$145$	−7.03168	−	4.79412i	−0.583949	−	0.398130i
$146$	−11.5179			−0.953229
$147$	2.11422	+	18.8732i	0.174378	+	1.55664i
$148$	11.2086			0.921343
$149$	4.19858	+	2.86254i	0.343961	+	0.234508i	0.722962	−	0.690888i	$-0.242780\pi$
$149$	4.19858	+	2.86254i	0.343961	+	0.234508i	−0.379001	+	0.925396i	$0.623732\pi$
$150$	3.78980	+	3.51642i	0.309436	+	0.287115i
$151$	−6.23498	−	15.8865i	−0.507396	−	1.29282i	−0.923532	−	0.383521i	$-0.874711\pi$
$151$	−6.23498	−	15.8865i	−0.507396	−	1.29282i	0.416137	−	0.909302i	$-0.363384\pi$
$152$	11.8454	−	3.65383i	0.960790	−	0.296364i
$153$	0.726326	+	3.18224i	0.0587200	+	0.257269i
$154$	−2.13459	−	3.54512i	−0.172010	−	0.285674i
$155$	3.68553	−	16.1474i	0.296029	−	1.29699i
$156$	0.248819	+	3.32026i	0.0199214	+	0.265833i
$157$	7.32388	+	2.25912i	0.584509	+	0.180297i	0.572886	−	0.819635i	$-0.305824\pi$
$157$	7.32388	+	2.25912i	0.584509	+	0.180297i	0.0116234	+	0.999932i	$0.496300\pi$
$158$	0.0522042	−	0.696617i	0.00415314	−	0.0554199i
$159$	0.228508	−	0.582229i	0.0181219	−	0.0461737i
$160$	−8.55071	+	4.11781i	−0.675993	+	0.325541i
$161$	−2.11592	+	3.82556i	−0.166758	+	0.301496i
$162$	2.42910	+	1.16979i	0.190848	+	0.0919077i
$163$	2.43849	−	2.26259i	0.190997	−	0.177220i	−0.578877	−	0.815415i	$-0.696509\pi$
$163$	2.43849	−	2.26259i	0.190997	−	0.177220i	0.769875	+	0.638195i	$0.220319\pi$
$164$	6.85613	−	1.03340i	0.535374	−	0.0806947i
$165$	−4.06191	+	7.03544i	−0.316219	+	0.547708i
$166$	6.15405	+	10.6591i	0.477647	+	0.827309i
$167$	−14.8478	−	18.6185i	−1.14896	−	1.44074i	−0.878327	−	0.478061i	$-0.841340\pi$
$167$	−14.8478	−	18.6185i	−1.14896	−	1.44074i	−0.270629	−	0.962684i	$-0.587232\pi$
$168$	4.89545	+	19.7666i	0.377692	+	1.52502i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	1.09503	+	0.165049i	0.0839849	+	0.0126587i
$171$	−15.7429	+	10.7333i	−1.20389	+	0.820798i
$172$	−5.99121	+	4.08473i	−0.456825	+	0.311458i
$173$	−19.8024	−	2.98473i	−1.50555	−	0.226925i	−0.656131	−	0.754647i	$-0.727808\pi$
$173$	−19.8024	−	2.98473i	−1.50555	−	0.226925i	−0.849417	+	0.527723i	$0.823046\pi$
$174$	−7.51956	+	9.42923i	−0.570057	+	0.714828i
$175$	1.37876	+	5.56707i	0.104224	+	0.420831i
$176$	−0.0436850	−	0.0547792i	−0.00329288	−	0.00412914i
$177$	−14.8775	−	25.7686i	−1.11826	−	1.93689i
$178$	0.607068	−	1.05147i	0.0455017	−	0.0788112i
$179$	14.9341	−	2.25095i	1.11623	−	0.168244i	0.435081	−	0.900391i	$-0.356720\pi$
$179$	14.9341	−	2.25095i	1.11623	−	0.168244i	0.681146	+	0.732147i	$0.261482\pi$
$180$	6.60205	−	6.12581i	0.492088	−	0.456591i
$181$	−8.87100	−	4.27205i	−0.659376	−	0.317539i	0.0741032	−	0.997251i	$-0.476391\pi$
$181$	−8.87100	−	4.27205i	−0.659376	−	0.317539i	−0.733479	+	0.679712i	$0.762105\pi$
$182$	1.12568	−	2.03522i	0.0834410	−	0.150861i
$183$	−27.9960	+	13.4822i	−2.06953	+	0.996631i
$184$	−1.71260	+	4.36362i	−0.126254	+	0.321691i
$185$	−1.14864	+	15.3275i	−0.0844497	+	1.12690i
$186$	−22.4286	−	6.91831i	−1.64455	−	0.507275i
$187$	−0.0995285	−	1.32812i	−0.00727824	−	0.0971214i
$188$	1.37853	−	6.03972i	0.100539	−	0.440492i
$189$	−5.03780	−	8.36676i	−0.366446	−	0.608592i
$190$	1.43844	+	6.30223i	0.104356	+	0.457212i
$191$	−9.99791	+	3.08395i	−0.723424	+	0.223147i	−0.634534	−	0.772895i	$-0.718808\pi$
$191$	−9.99791	+	3.08395i	−0.723424	+	0.223147i	−0.0888895	+	0.996041i	$0.528332\pi$
$192$	4.99167	+	12.7186i	0.360243	+	0.917884i
$193$	−16.4714	−	15.2833i	−1.18564	−	1.10011i	−0.992911	−	0.118861i	$-0.962076\pi$
$193$	−16.4714	−	15.2833i	−1.18564	−	1.10011i	−0.192729	−	0.981252i	$-0.561734\pi$
$194$	10.3288	+	7.04206i	0.741565	+	0.505591i
$195$	−4.56587			−0.326969
$196$	−2.84255	+	8.10681i	−0.203039	+	0.579058i
$197$	9.66263			0.688434			0.344217	−	0.938890i	$-0.388144\pi$
$197$	9.66263			0.688434			0.344217	+	0.938890i	$0.388144\pi$
$198$	5.63519	+	3.84201i	0.400476	+	0.273040i
$199$	3.60550	+	3.34542i	0.255587	+	0.237150i	0.797551	−	0.603252i	$-0.206129\pi$
$199$	3.60550	+	3.34542i	0.255587	+	0.237150i	−0.541964	+	0.840402i	$0.682319\pi$
$200$	2.24676	+	5.72464i	0.158870	+	0.404793i
$201$	12.1234	−	3.73958i	0.855120	−	0.263770i
$202$	0.365271	+	1.60036i	0.0257004	+	0.112601i
$203$	−12.7103	+	4.17792i	−0.892089	+	0.293233i
$204$	−0.554592	+	2.42983i	−0.0388292	+	0.170122i
$205$	0.710541	+	9.48151i	0.0496263	+	0.662217i
$206$	−4.52430	−	1.39556i	−0.315223	−	0.0972334i
$207$	0.538449	−	7.18511i	0.0374248	−	0.499399i
$208$	0.0143868	−	0.0366570i	0.000997546	−	0.00254171i
$209$	7.00455	−	3.37321i	0.484515	−	0.233330i
$210$	−10.4698	+	1.77542i	−0.722484	+	0.122516i
$211$	−0.761275	−	0.366611i	−0.0524084	−	0.0252385i	0.407496	−	0.913207i	$-0.366402\pi$
$211$	−0.761275	−	0.366611i	−0.0524084	−	0.0252385i	−0.459904	+	0.887968i	$0.652116\pi$
$212$	0.207402	−	0.192441i	0.0142444	−	0.0132169i
$213$	−2.30376	+	0.347236i	−0.157851	+	0.0237922i
$214$	5.70719	−	9.88514i	0.390135	−	0.675734i
$215$	−4.97181	−	8.61143i	−0.339075	−	0.587295i
$216$	−6.52930	−	8.18748i	−0.444263	−	0.557088i
$217$	−16.6059	−	20.0557i	−1.12728	−	1.36147i
$218$	−0.952770	+	1.19474i	−0.0645297	+	0.0809177i
$219$	35.1505	+	5.29808i	2.37525	+	0.358011i
$220$	−3.03627	+	2.07010i	−0.204706	+	0.139566i
$221$	0.618473	−	0.421668i	0.0416030	−	0.0283644i
$222$	21.5387	+	3.24644i	1.44558	+	0.217887i
$223$	−12.4331	+	15.5906i	−0.832582	+	1.04403i	0.165743	+	0.986169i	$0.446998\pi$
$223$	−12.4331	+	15.5906i	−0.832582	+	1.04403i	−0.998325	+	0.0578560i	$0.981574\pi$
$224$	−3.05217	+	14.6047i	−0.203932	+	0.975815i
$225$	−5.89358	−	7.39032i	−0.392906	−	0.492688i
$226$	4.07758	+	7.06258i	0.271237	+	0.469796i
$227$	11.2357	−	19.4608i	0.745741	−	1.29166i	−0.204107	−	0.978949i	$-0.565429\pi$
$227$	11.2357	−	19.4608i	0.745741	−	1.29166i	0.949848	−	0.312712i	$-0.101238\pi$
$228$	−14.3861	+	2.16836i	−0.952743	+	0.143603i
$229$	10.9505	−	10.1606i	0.723632	−	0.671432i	−0.229733	−	0.973254i	$-0.573785\pi$
$229$	10.9505	−	10.1606i	0.723632	−	0.671432i	0.953364	+	0.301822i	$0.0975947\pi$
$230$	−2.20243	−	1.06063i	−0.145224	−	0.0699361i
$231$	4.88365	+	11.8009i	0.321321	+	0.776442i
$232$	−12.9255	+	6.22461i	−0.848603	+	0.408666i
$233$	−0.172665	+	0.439944i	−0.0113117	+	0.0288217i	−0.936418	−	0.350886i	$-0.885880\pi$
$233$	−0.172665	+	0.439944i	−0.0113117	+	0.0288217i	0.925106	+	0.379708i	$0.123976\pi$
$234$	−0.286459	+	3.82252i	−0.0187264	+	0.249886i
$235$	8.11791	+	2.50404i	0.529554	+	0.163346i
$236$	−1.00585	−	13.4221i	−0.0654750	−	0.873703i
$237$	−0.479752	+	2.10193i	−0.0311632	+	0.136535i
$238$	1.25423	−	1.20740i	0.0812994	−	0.0782639i
$239$	−2.47138	−	10.8278i	−0.159860	−	0.700393i	−0.989791	−	0.142527i	$-0.954477\pi$
$239$	−2.47138	−	10.8278i	−0.159860	−	0.700393i	0.829931	−	0.557866i	$-0.188380\pi$
$240$	−0.171812	+	0.0529970i	−0.0110904	+	0.00342094i
$241$	4.36394	+	11.1191i	0.281106	+	0.716246i	0.999782	+	0.0209009i	$0.00665344\pi$
$241$	4.36394	+	11.1191i	0.281106	+	0.716246i	−0.718676	+	0.695346i	$0.755251\pi$
$242$	5.04841	+	4.68424i	0.324524	+	0.301114i
$243$	−16.0249	−	10.9256i	−1.02800	−	0.700875i
$244$	−14.0560			−0.899843
$245$	−10.7946	−	4.71789i	−0.689640	−	0.301415i
$246$	13.4742			0.859084
$247$	3.61027	+	2.46144i	0.229716	+	0.156618i
$248$	−20.4668	−	18.9904i	−1.29964	−	1.20589i
$249$	−13.8779	−	35.3604i	−0.879479	−	2.24087i
$250$	−10.1329	+	3.12559i	−0.640861	+	0.197679i
$251$	3.70580	+	16.2362i	0.233908	+	1.02482i	0.946364	+	0.323101i	$0.104725\pi$
$251$	3.70580	+	16.2362i	0.233908	+	1.02482i	−0.712457	+	0.701716i	$0.752418\pi$
$252$	−1.31738	−	14.0974i	−0.0829873	−	0.888050i
$253$	−0.654201	+	2.86624i	−0.0411293	+	0.180199i
$254$	−0.523255	−	6.98236i	−0.0328320	−	0.438112i
$255$	−3.26590	−	1.00740i	−0.204519	−	0.0630856i
$256$	−1.20279	+	16.0501i	−0.0751743	+	1.00313i
$257$	−4.15062	+	10.5756i	−0.258909	+	0.659689i	−0.999930	−	0.0117922i	$-0.996246\pi$
$257$	−4.15062	+	10.5756i	−0.258909	+	0.659689i	0.741022	+	0.671481i	$0.234342\pi$
$258$	−12.6959	+	6.11404i	−0.790414	+	0.380643i
$259$	18.0126	+	16.1074i	1.11925	+	1.00087i
$260$	−1.86084	−	0.896132i	−0.115404	−	0.0555758i
$261$	16.1646	−	14.9986i	1.00057	−	0.928390i
$262$	14.0820	−	2.12252i	0.869991	−	0.131130i
$263$	2.98367	−	5.16786i	0.183981	−	0.318664i	−0.759252	−	0.650797i	$-0.774435\pi$
$263$	2.98367	−	5.16786i	0.183981	−	0.318664i	0.943233	+	0.332133i	$0.107768\pi$
$264$	6.84725	+	11.8598i	0.421419	+	0.729919i
$265$	0.241904	+	0.303338i	0.0148601	+	0.0186339i
$266$	9.23565	+	4.24036i	0.566274	+	0.259993i
$267$	−2.33632	+	2.92965i	−0.142980	+	0.179292i
$268$	5.67490	+	0.855354i	0.346650	+	0.0522491i
$269$	16.9389	−	11.5488i	1.03278	−	0.704141i	0.0766471	−	0.997058i	$-0.475579\pi$
$269$	16.9389	−	11.5488i	1.03278	−	0.704141i	0.956138	+	0.292918i	$0.0946261\pi$
$270$	4.51210	−	3.07630i	0.274597	−	0.187217i
$271$	3.04046	+	0.458275i	0.184695	+	0.0278382i	0.240738	−	0.970590i	$-0.422610\pi$
$271$	3.04046	+	0.458275i	0.184695	+	0.0278382i	−0.0560436	+	0.998428i	$0.517849\pi$
$272$	0.0183785	−	0.0230460i	0.00111436	−	0.00139737i
$273$	−4.37154	+	5.69331i	−0.264578	+	0.344575i
$274$	3.51864	+	4.41224i	0.212569	+	0.266553i
$275$	1.92846	+	3.34020i	0.116291	+	0.201421i
$276$	2.75082	−	4.76455i	0.165580	−	0.286792i
$277$	2.62499	−	0.395653i	0.157720	−	0.0237725i	−0.0697074	−	0.997567i	$-0.522207\pi$
$277$	2.62499	−	0.395653i	0.157720	−	0.0237725i	0.227428	+	0.973795i	$0.426968\pi$
$278$	0.412575	−	0.382814i	0.0247446	−	0.0229597i
$279$	38.6649	+	18.6200i	2.31481	+	1.11475i
$280$	−12.1371	−	3.50087i	−0.725331	−	0.209217i
$281$	15.4730	−	7.45142i	0.923044	−	0.444515i	0.0888871	−	0.996042i	$-0.471669\pi$
$281$	15.4730	−	7.45142i	0.923044	−	0.444515i	0.834157	+	0.551527i	$0.185955\pi$
$282$	4.39834	−	11.2068i	0.261917	−	0.667354i
$283$	−0.938574	+	12.5244i	−0.0557924	+	0.744498i	0.897223	+	0.441577i	$0.145581\pi$
$283$	−0.938574	+	12.5244i	−0.0557924	+	0.744498i	−0.953016	+	0.302921i	$0.902038\pi$
$284$	−1.00706	−	0.310636i	−0.0597579	−	0.0184329i
$285$	−1.49092	−	19.8949i	−0.0883142	−	1.17847i
$286$	0.348039	−	1.52486i	0.0205800	−	0.0901669i
$287$	12.5030	+	8.19196i	0.738032	+	0.483556i
$288$	−5.47194	−	23.9741i	−0.322437	−	1.41269i
$289$	−15.7093	+	4.84568i	−0.924078	+	0.285040i
$290$	−2.73321	−	6.96410i	−0.160500	−	0.408946i
$291$	−28.2823	−	26.2421i	−1.65794	−	1.53834i
$292$	13.2859	+	9.05815i	0.777496	+	0.530088i
$293$	−3.48707			−0.203717			−0.101858	−	0.994799i	$-0.532479\pi$
$293$	−3.48707			−0.203717			−0.101858	+	0.994799i	$0.532479\pi$
$294$	−7.81034	+	14.7549i	−0.455508	+	0.860524i
$295$	18.4575			1.07464
$296$	21.4082	+	14.5958i	1.24432	+	0.848366i
$297$	−4.81455	−	4.46725i	−0.279369	−	0.259216i
$298$	1.63198	+	4.15823i	0.0945383	+	0.240880i
$299$	−1.57895	+	0.487041i	−0.0913129	+	0.0281663i
$300$	−1.60607	−	7.03663i	−0.0927262	−	0.406260i
$301$	−15.4980	−	2.04542i	−0.893292	−	0.117896i
$302$	3.33832	−	14.6262i	0.192099	−	0.841640i
$303$	−0.378595	−	5.05201i	−0.0217497	−	0.290230i
$304$	0.164423	+	0.0507179i	0.00943033	+	0.00290887i
$305$	1.44043	−	19.2213i	0.0824790	−	1.10061i
$306$	−1.04829	+	2.67099i	−0.0599266	+	0.152690i
$307$	26.7090	−	12.8624i	1.52436	−	0.734093i	0.530811	−	0.847490i	$-0.321887\pi$
$307$	26.7090	−	12.8624i	1.52436	−	0.734093i	0.993550	+	0.113397i	$0.0361732\pi$
$308$	−0.325784	+	5.76800i	−0.0185633	+	0.328662i
$309$	13.1654	+	6.34011i	0.748952	+	0.360676i
$310$	10.6730	−	9.90306i	0.606183	−	0.562456i
$311$	13.3189	−	2.00751i	0.755248	−	0.113835i	0.239878	−	0.970803i	$-0.422893\pi$
$311$	13.3189	−	2.00751i	0.755248	−	0.113835i	0.515370	+	0.856968i	$0.327654\pi$
$312$	−3.84839	+	6.66561i	−0.217872	+	0.377366i
$313$	−2.69445	−	4.66692i	−0.152299	−	0.263790i	0.779773	−	0.626062i	$-0.215334\pi$
$313$	−2.69445	−	4.66692i	−0.152299	−	0.263790i	−0.932072	+	0.362272i	$0.882001\pi$
$314$	4.20076	+	5.26758i	0.237062	+	0.297267i
$315$	19.4128	−	0.356819i	1.09379	−	0.0201044i
$316$	−0.608065	+	0.762489i	−0.0342063	+	0.0428934i
$317$	19.4781	+	2.93585i	1.09400	+	0.164894i	0.671161	−	0.741312i	$-0.265796\pi$
$317$	19.4781	+	2.93585i	1.09400	+	0.164894i	0.422838	+	0.906205i	$0.361034\pi$
$318$	0.454286	−	0.309727i	0.0254751	−	0.0173686i
$319$	−7.43410	+	5.06848i	−0.416229	+	0.283780i
$320$	−8.38071	−	1.26319i	−0.468496	−	0.0706144i
$321$	−21.9643	+	27.5423i	−1.22593	+	1.53726i
$322$	−3.43122	+	1.73078i	−0.191215	+	0.0964524i
$323$	2.03929	+	2.55718i	0.113469	+	0.142286i
$324$	−1.88199	−	3.25970i	−0.104555	−	0.181094i
$325$	−1.08386	+	1.87731i	−0.0601219	+	0.104134i
$326$	2.89154	−	0.435830i	0.160148	−	0.0241384i
$327$	3.45723	−	3.20784i	0.191185	−	0.177394i
$328$	14.4407	+	6.95428i	0.797355	+	0.383986i
$329$	10.8947	−	7.72497i	0.600647	−	0.425892i
$330$	−6.43415	+	3.09852i	−0.354188	+	0.170568i
$331$	−8.33749	+	21.2436i	−0.458270	+	1.16765i	0.495898	+	0.868381i	$0.334839\pi$
$331$	−8.33749	+	21.2436i	−0.458270	+	1.16765i	−0.954168	+	0.299272i	$0.903256\pi$
$332$	1.28409	−	17.1350i	0.0704738	−	0.940408i
$333$	−38.0566	−	11.7389i	−2.08549	−	0.643288i
$334$	−1.56440	−	20.8755i	−0.0856003	−	1.14226i
$335$	−1.75123	+	7.67264i	−0.0956800	+	0.419201i
$336$	−0.0984160	+	0.264979i	−0.00536903	+	0.0144558i
$337$	−2.28970	−	10.0318i	−0.124728	−	0.546469i	−0.998220	−	0.0596312i	$-0.981008\pi$
$337$	−2.28970	−	10.0318i	−0.124728	−	0.546469i	0.873493	−	0.486838i	$-0.161850\pi$
$338$	0.840010	−	0.259109i	0.0456905	−	0.0140937i
$339$	−9.19532	−	23.4293i	−0.499421	−	1.27250i
$340$	−1.13331	−	1.05156i	−0.0614624	−	0.0570288i
$341$	−14.4678	−	9.86401i	−0.783478	−	0.534166i
$342$	−16.7494			−0.905705
$343$	−16.2180	+	8.94296i	−0.875690	+	0.482875i
$344$	−16.7622			−0.903755
$345$	6.23352	+	4.24994i	0.335601	+	0.228809i
$346$	−12.9048	−	11.9739i	−0.693766	−	0.643721i
$347$	9.51607	+	24.2465i	0.510849	+	1.30162i	0.920985	+	0.389598i	$0.127386\pi$
$347$	9.51607	+	24.2465i	0.510849	+	1.30162i	−0.410136	+	0.912024i	$0.634519\pi$
$348$	16.0893	−	4.96290i	0.862478	−	0.266039i
$349$	8.21786	+	36.0048i	0.439892	+	1.92729i	0.367832	+	0.929892i	$0.380100\pi$
$349$	8.21786	+	36.0048i	0.439892	+	1.92729i	0.0720604	+	0.997400i	$0.477043\pi$
$350$	−1.75537	+	4.72622i	−0.0938285	+	0.252627i
$351$	0.821401	−	3.59879i	0.0438432	−	0.192089i
$352$	0.749820	+	10.0057i	0.0399656	+	0.533303i
$353$	6.10880	+	1.88432i	0.325139	+	0.100292i	0.453028	−	0.891497i	$-0.350344\pi$
$353$	6.10880	+	1.88432i	0.325139	+	0.100292i	−0.127889	+	0.991788i	$0.540820\pi$
$354$	1.95469	−	26.0835i	0.103890	−	1.38632i
$355$	0.527990	−	1.34530i	0.0280228	−	0.0714009i
$356$	−1.52717	+	0.735447i	−0.0809399	+	0.0389786i
$357$	−4.38305	+	3.10782i	−0.231975	+	0.164483i
$358$	11.9616	+	5.76038i	0.632188	+	0.304446i
$359$	−15.0598	+	13.9734i	−0.794825	+	0.737490i	−0.968956	−	0.247233i	$-0.920479\pi$
$359$	−15.0598	+	13.9734i	−0.794825	+	0.737490i	0.174131	+	0.984722i	$0.444288\pi$
$360$	20.5868	−	3.10295i	1.08502	−	0.163540i
$361$	−0.0463476	+	0.0802764i	−0.00243935	+	0.00422507i
$362$	−4.32766	−	7.49574i	−0.227457	−	0.393967i
$363$	−13.2521	−	16.6176i	−0.695555	−	0.872198i
$364$	−2.89905	+	1.46234i	−0.151951	+	0.0766474i
$365$	−13.7483	+	17.2399i	−0.719620	+	0.902375i
$366$	−27.0103	−	4.07115i	−1.41185	−	0.212802i
$367$	−12.1829	+	8.30614i	−0.635940	+	0.433577i	−0.837905	−	0.545816i	$-0.816220\pi$
$367$	−12.1829	+	8.30614i	−0.635940	+	0.433577i	0.201965	+	0.979393i	$0.435267\pi$
$368$	−0.0537620	+	0.0366543i	−0.00280254	+	0.00191074i
$369$	−24.3609	−	3.67182i	−1.26818	−	0.191147i
$370$	−8.42439	+	10.5639i	−0.437963	+	0.549189i
$371$	0.609849	−	0.0112094i	0.0316618	−	0.000581961i
$372$	20.4305	+	25.6190i	1.05927	+	1.32828i
$373$	8.53196	+	14.7778i	0.441768	+	0.765165i	0.997821	−	0.0659820i	$-0.0210180\pi$
$373$	8.53196	+	14.7778i	0.441768	+	0.765165i	−0.556052	+	0.831147i	$0.687685\pi$
$374$	0.585387	−	1.01392i	0.0302696	−	0.0524285i
$375$	32.3614	−	4.87770i	1.67114	−	0.251883i
$376$	10.4978	−	9.74058i	0.541385	−	0.502332i
$377$	−4.55613	−	2.19411i	−0.234652	−	0.113003i
$378$	0.484136	−	8.57162i	0.0249013	−	0.440876i
$379$	−21.5834	+	10.3940i	−1.10867	+	0.533906i	−0.896373	−	0.443300i	$-0.853808\pi$
$379$	−21.5834	+	10.3940i	−1.10867	+	0.533906i	−0.212294	+	0.977206i	$0.568093\pi$
$380$	3.29709	−	8.40085i	0.169137	−	0.430955i
$381$	−1.61491	+	21.5495i	−0.0827345	+	1.10402i
$382$	−8.78881	−	2.71099i	−0.449675	−	0.138706i
$383$	−0.395867	−	5.28248i	−0.0202279	−	0.269922i	−0.998143	−	0.0609186i	$-0.980597\pi$
$383$	−0.395867	−	5.28248i	−0.0202279	−	0.269922i	0.977915	−	0.209004i	$-0.0670220\pi$
$384$	4.13635	−	18.1225i	0.211082	−	0.924812i
$385$	−7.85423	−	1.03660i	−0.400288	−	0.0528299i
$386$	−4.39530	−	19.2571i	−0.223715	−	0.980159i
$387$	24.6199	−	7.59424i	1.25150	−	0.386037i
$388$	−6.37608	−	16.2460i	−0.323696	−	0.824764i
$389$	−5.99057	−	5.55844i	−0.303734	−	0.281824i	0.513549	−	0.858060i	$-0.328330\pi$
$389$	−5.99057	−	5.55844i	−0.303734	−	0.281824i	−0.817283	+	0.576236i	$0.804521\pi$
$390$	−3.31627	−	2.26100i	−0.167926	−	0.114490i
$391$	−1.23686			−0.0625505
$392$	−15.9858	+	11.7822i	−0.807407	+	0.595092i
$393$	−43.9520			−2.21709
$394$	7.01814	+	4.78488i	0.353569	+	0.241059i
$395$	−0.980373	−	0.909653i	−0.0493279	−	0.0457696i
$396$	−3.47866	−	8.86348i	−0.174809	−	0.445407i
$397$	−13.7103	+	4.22906i	−0.688099	+	0.212251i	−0.619037	−	0.785362i	$-0.712477\pi$
$397$	−13.7103	+	4.22906i	−0.688099	+	0.212251i	−0.0690623	+	0.997612i	$0.522001\pi$
$398$	0.962105	+	4.21526i	0.0482260	+	0.211292i
$399$	−26.2349	−	17.1891i	−1.31339	−	0.860529i
$400$	−0.0189951	+	0.0832230i	−0.000949755	+	0.00416115i
$401$	0.471128	+	6.28677i	0.0235270	+	0.313946i	0.996535	+	0.0831746i	$0.0265059\pi$
$401$	0.471128	+	6.28677i	0.0235270	+	0.313946i	−0.973008	+	0.230771i	$0.925875\pi$
$402$	10.6573	+	3.28733i	0.531536	+	0.163957i
$403$	0.735457	−	9.81399i	0.0366357	−	0.488870i
$404$	0.837246	−	2.13327i	0.0416546	−	0.106134i
$405$	4.65042	−	2.23953i	0.231081	−	0.111283i
$406$	−11.3006	−	3.25958i	−0.560840	−	0.161770i
$407$	14.6409	+	7.05068i	0.725722	+	0.349489i
$408$	−4.22337	+	3.91872i	−0.209088	+	0.194005i
$409$	−1.46821	+	0.221297i	−0.0725984	+	0.0109424i	−0.185241	−	0.982693i	$-0.559307\pi$
$409$	−1.46821	+	0.221297i	−0.0725984	+	0.0109424i	0.112643	+	0.993636i	$0.464068\pi$
$410$	−4.17912	+	7.23844i	−0.206392	+	0.357481i
$411$	−8.70866	−	15.0838i	−0.429567	−	0.744031i
$412$	4.12124	+	5.16787i	0.203039	+	0.254603i
$413$	17.6719	−	23.0151i	0.869576	−	1.13250i
$414$	3.94911	−	4.95203i	0.194088	−	0.243379i
$415$	23.3002	+	3.51194i	1.14376	+	0.172394i
$416$	−4.65941	+	3.17673i	−0.228446	+	0.155752i
$417$	−1.43519	+	0.978496i	−0.0702816	+	0.0479172i
$418$	6.75792	+	1.01859i	0.330541	+	0.0498210i
$419$	22.6114	−	28.3538i	1.10464	−	1.38517i	0.189574	−	0.981866i	$-0.439289\pi$
$419$	22.6114	−	28.3538i	1.10464	−	1.38517i	0.915065	−	0.403307i	$-0.132139\pi$
$420$	13.4731	+	6.18591i	0.657421	+	0.301842i
$421$	24.1611	+	30.2971i	1.17754	+	1.47659i	0.846026	+	0.533142i	$0.178989\pi$
$421$	24.1611	+	30.2971i	1.17754	+	1.47659i	0.331516	+	0.943449i	$0.392440\pi$
$422$	−0.371384	−	0.643256i	−0.0180787	−	0.0313132i
$423$	−11.0060	+	19.0629i	−0.535129	+	0.926870i
$424$	0.646727	−	0.0974785i	0.0314079	−	0.00473397i
$425$	−1.18947	+	1.10367i	−0.0576979	+	0.0535358i
$426$	−1.84521	−	0.888608i	−0.0894009	−	0.0430532i
$427$	−22.5884	−	20.1993i	−1.09313	−	0.977511i
$428$	−14.3573	+	6.91410i	−0.693986	+	0.334206i
$429$	−1.76357	+	4.49349i	−0.0851457	+	0.216948i
$430$	0.653223	−	8.71665i	0.0315012	−	0.420354i
$431$	33.0084	+	10.1817i	1.58996	+	0.490437i	0.958529	−	0.284996i	$-0.0919921\pi$
$431$	33.0084	+	10.1817i	1.58996	+	0.490437i	0.631430	+	0.775433i	$0.282468\pi$
$432$	−0.0108629	−	0.144955i	−0.000522642	−	0.00697417i
$433$	3.97325	−	17.4079i	0.190942	−	0.836573i	−0.785166	−	0.619286i	$-0.787422\pi$
$433$	3.97325	−	17.4079i	0.190942	−	0.836573i	0.976108	−	0.217287i	$-0.0697207\pi$
$434$	−2.12970	−	22.7900i	−0.102229	−	1.09395i
$435$	5.13784	+	22.5104i	0.246341	+	1.07929i
$436$	2.03860	−	0.628826i	0.0976314	−	0.0301153i
$437$	−2.63776	−	6.72091i	−0.126181	−	0.321505i
$438$	22.9068	+	21.2544i	1.09453	+	1.01558i
$439$	−16.4147	−	11.1914i	−0.783433	−	0.534135i	0.104272	−	0.994549i	$-0.466749\pi$
$439$	−16.4147	−	11.1914i	−0.783433	−	0.534135i	−0.887705	+	0.460413i	$0.847701\pi$
$440$	−8.49488			−0.404977
$441$	18.1416	−	24.5480i	0.863888	−	1.16895i
$442$	0.658016			0.0312986
$443$	−23.6770	−	16.1427i	−1.12493	−	0.766962i	−0.149823	−	0.988713i	$-0.547870\pi$
$443$	−23.6770	−	16.1427i	−1.12493	−	0.766962i	−0.975103	+	0.221751i	$0.928823\pi$
$444$	−22.2917	−	20.6837i	−1.05792	−	0.981604i
$445$	−0.849205	−	2.16374i	−0.0402562	−	0.102571i
$446$	−16.7508	+	5.16693i	−0.793172	+	0.244661i
$447$	−3.06778	−	13.4408i	−0.145101	−	0.635728i
$448$	−9.59912	+	9.24071i	−0.453516	+	0.436583i
$449$	1.34035	−	5.87245i	0.0632549	−	0.277138i	−0.933403	−	0.358831i	$-0.883176\pi$
$449$	1.34035	−	5.87245i	0.0632549	−	0.277138i	0.996658	+	0.0816929i	$0.0260327\pi$
$450$	−0.620964	−	8.28619i	−0.0292725	−	0.390615i
$451$	9.60564	+	2.96295i	0.452312	+	0.139520i
$452$	0.850822	−	11.3534i	0.0400193	−	0.534021i
$453$	−16.9158	+	43.1007i	−0.794772	+	2.02505i
$454$	17.7976	−	8.57087i	0.835283	−	0.402251i
$455$	−1.70262	−	4.11424i	−0.0798203	−	0.192879i
$456$	−30.3007	−	14.5920i	−1.41896	−	0.683335i
$457$	−7.71795	+	7.16121i	−0.361030	+	0.334987i	−0.839743	−	0.542985i	$-0.817294\pi$
$457$	−7.71795	+	7.16121i	−0.361030	+	0.334987i	0.478712	+	0.877972i	$0.341104\pi$
$458$	12.9850	−	1.95718i	0.606751	−	0.0914530i
$459$	1.38156	−	2.39293i	0.0644857	−	0.111693i
$460$	1.70637	+	2.95552i	0.0795598	+	0.137802i
$461$	24.2103	+	30.3588i	1.12759	+	1.41395i	0.897630	+	0.440749i	$0.145287\pi$
$461$	24.2103	+	30.3588i	1.12759	+	1.41395i	0.229957	+	0.973201i	$0.426142\pi$
$462$	−2.29667	+	10.9896i	−0.106851	+	0.511281i
$463$	−21.9664	+	27.5450i	−1.02087	+	1.28013i	−0.0614557	+	0.998110i	$0.519574\pi$
$463$	−21.9664	+	27.5450i	−1.02087	+	1.28013i	−0.959410	+	0.282015i	$0.908997\pi$
$464$	−0.196913	−	0.0296798i	−0.00914145	−	0.00137785i
$465$	−37.1271	+	25.3128i	−1.72173	+	1.17385i
$466$	−0.343268	+	0.234036i	−0.0159016	+	0.0108415i
$467$	−12.3794	−	1.86589i	−0.572849	−	0.0863431i	−0.143772	−	0.989611i	$-0.545923\pi$
$467$	−12.3794	−	1.86589i	−0.572849	−	0.0863431i	−0.429077	+	0.903268i	$0.641161\pi$
$468$	3.33662	−	4.18398i	0.154235	−	0.193405i
$469$	7.89053	+	9.52974i	0.364351	+	0.440042i
$470$	4.65619	+	5.83868i	0.214774	+	0.269318i
$471$	−10.3969	−	18.0080i	−0.479064	−	0.829763i
$472$	15.5571	−	26.9456i	0.716072	−	1.24027i
$473$	−10.3953	+	1.56684i	−0.477975	+	0.0720432i
$474$	−1.38932	+	1.28910i	−0.0638134	+	0.0592102i
$475$	−8.53391	−	4.10971i	−0.391563	−	0.188567i
$476$	−2.39629	+	0.406354i	−0.109834	+	0.0186252i
$477$	−0.905736	+	0.436180i	−0.0414708	+	0.0199713i
$478$	3.56687	−	9.08824i	0.163145	−	0.415687i
$479$	−0.362780	+	4.84096i	−0.0165758	+	0.221189i	0.982764	+	0.184864i	$0.0591844\pi$
$479$	−0.362780	+	4.84096i	−0.0165758	+	0.221189i	−0.999340	+	0.0363255i	$0.988435\pi$
$480$	24.6044	+	7.58945i	1.12303	+	0.346410i
$481$	0.682522	+	9.10762i	0.0311203	+	0.415272i
$482$	−2.33653	+	10.2370i	−0.106426	+	0.466284i
$483$	11.2676	−	3.70369i	0.512692	−	0.168524i
$484$	−2.13944	−	9.37352i	−0.0972475	−	0.426069i
$485$	22.8694	−	7.05428i	1.03845	−	0.320318i
$486$	−6.22885	−	15.8709i	−0.282547	−	0.719917i
$487$	−2.51383	−	2.33249i	−0.113912	−	0.105695i	0.621160	−	0.783683i	$-0.286662\pi$
$487$	−2.51383	−	2.33249i	−0.113912	−	0.105695i	−0.735073	+	0.677988i	$0.762852\pi$
$488$	−26.8466	−	18.3037i	−1.21529	−	0.828568i
$489$	−9.02492			−0.408121
$490$	−5.50401	−	8.77210i	−0.248646	−	0.396283i
$491$	18.8015			0.848500			0.424250	−	0.905545i	$-0.360538\pi$
$491$	18.8015			0.848500			0.424250	+	0.905545i	$0.360538\pi$
$492$	−15.5424	−	10.5967i	−0.700707	−	0.477734i
$493$	−2.77483	−	2.57466i	−0.124972	−	0.115957i
$494$	1.40331	+	3.57557i	0.0631378	+	0.160872i
$495$	12.4771	−	3.84867i	0.560804	−	0.172985i
$496$	−0.0862380	−	0.377833i	−0.00387220	−	0.0169652i
$497$	−1.17197	−	1.94640i	−0.0525700	−	0.0873080i
$498$	7.43050	−	32.5552i	0.332969	−	1.45883i
$499$	1.87551	+	25.0270i	0.0839595	+	1.12036i	0.866972	+	0.498356i	$0.166063\pi$
$499$	1.87551	+	25.0270i	0.0839595	+	1.12036i	−0.783013	+	0.622006i	$0.786318\pi$
$500$	14.1463	+	4.36357i	0.632644	+	0.195145i
$501$	−4.82819	+	64.4277i	−0.215707	+	2.87842i
$502$	−5.34848	+	13.6277i	−0.238714	+	0.608234i
$503$	−37.8426	+	18.2240i	−1.68732	+	0.812569i	−0.691383	+	0.722488i	$0.742998\pi$
$503$	−37.8426	+	18.2240i	−1.68732	+	0.812569i	−0.995934	+	0.0900811i	$0.971287\pi$
$504$	15.8414	−	28.6411i	0.705631	−	1.27577i
$505$	2.83140	+	1.36353i	0.125996	+	0.0606762i
$506$	−1.89451	+	1.75784i	−0.0842211	+	0.0781457i
$507$	−2.68274	+	0.404358i	−0.119145	+	0.0179582i
$508$	−4.88763	+	8.46563i	−0.216854	+	0.375602i
$509$	−8.55921	−	14.8250i	−0.379380	−	0.657106i	0.611592	−	0.791173i	$-0.290529\pi$
$509$	−8.55921	−	14.8250i	−0.379380	−	0.657106i	−0.990972	+	0.134067i	$0.957196\pi$
$510$	−1.87322	−	2.34895i	−0.0829477	−	0.104013i
$511$	8.33367	+	33.6492i	0.368660	+	1.48855i
$512$	−0.277768	+	0.348310i	−0.0122757	+	0.0153933i
$513$	15.9492	+	2.40396i	0.704176	+	0.106138i
$514$	−8.25166	+	5.62589i	−0.363965	+	0.248147i
$515$	−7.48928	+	5.10610i	−0.330017	+	0.225002i
$516$	19.4530	+	2.93207i	0.856371	+	0.129077i
$517$	5.59988	−	7.02203i	0.246282	−	0.308828i
$518$	5.10652	+	20.6188i	0.224368	+	0.905940i
$519$	33.8751	+	42.4781i	1.48695	+	1.86458i
$520$	−2.38721	−	4.13477i	−0.104686	−	0.181322i
$521$	−0.403606	+	0.699065i	−0.0176823	+	0.0306266i	−0.874731	−	0.484609i	$-0.838962\pi$
$521$	−0.403606	+	0.699065i	−0.0176823	+	0.0306266i	0.857049	+	0.515235i	$0.172295\pi$
$522$	19.1679	−	2.88909i	0.838956	−	0.126452i
$523$	−19.0091	+	17.6379i	−0.831210	+	0.771250i	−0.975898	−	0.218227i	$-0.929973\pi$
$523$	−19.0091	+	17.6379i	−0.831210	+	0.771250i	0.144688	+	0.989477i	$0.453782\pi$
$524$	−17.9128	−	8.62635i	−0.782524	−	0.376844i
$525$	7.53105	−	13.6161i	0.328682	−	0.594254i
$526$	4.72619	−	2.27601i	0.206072	−	0.0992388i
$527$	2.69138	−	6.85753i	0.117238	−	0.298719i
$528$	−0.0142054	+	0.189558i	−0.000618213	+	0.00824947i
$529$	−19.3692	−	5.97460i	−0.842139	−	0.259765i
$530$	0.0254877	+	0.340110i	0.00110711	+	0.0147734i
$531$	−10.6419	+	46.6254i	−0.461821	+	2.02337i
$532$	−7.31849	−	12.1545i	−0.317297	−	0.526965i
$533$	1.25718	+	5.50806i	0.0544544	+	0.238580i
$534$	−3.14766	+	0.970924i	−0.136212	+	0.0420160i
$535$	−7.98357	−	20.3418i	−0.345160	−	0.879453i
$536$	9.72507	+	9.02354i	0.420059	+	0.389758i
$537$	−33.8547	−	23.0817i	−1.46094	−	0.996051i
$538$	18.0219			0.776981
$539$	−8.81249	+	8.80117i	−0.379581	+	0.379093i
$540$	−7.62401			−0.328085
$541$	−25.2533	−	17.2174i	−1.08572	−	0.740233i	−0.118193	−	0.992991i	$-0.537710\pi$
$541$	−25.2533	−	17.2174i	−1.08572	−	0.740233i	−0.967530	+	0.252757i	$0.918663\pi$
$542$	1.98140	+	1.83847i	0.0851085	+	0.0789691i
$543$	9.75928	+	24.8662i	0.418811	+	1.06711i
$544$	−4.03370	+	1.24423i	−0.172944	+	0.0533461i
$545$	0.650993	+	2.85218i	0.0278855	+	0.122174i
$546$	−5.99442	+	1.97039i	−0.256538	+	0.0843248i
$547$	−3.37144	+	14.7713i	−0.144152	+	0.631573i	0.850292	+	0.526311i	$0.176425\pi$
$547$	−3.37144	+	14.7713i	−0.144152	+	0.631573i	−0.994445	+	0.105262i	$0.966432\pi$
$548$	−0.588778	−	7.85670i	−0.0251514	−	0.335622i
$549$	47.7243	+	14.7210i	2.03682	+	0.628277i
$550$	−0.253371	+	3.38101i	−0.0108038	+	0.144167i
$551$	8.07269	−	20.5689i	0.343908	−	0.876263i
$552$	11.4584	−	5.51806i	0.487701	−	0.234864i
$553$	−2.07292	+	0.351517i	−0.0881494	+	0.0149480i
$554$	2.10250	+	1.01251i	0.0893267	+	0.0430175i
$555$	30.5689	−	28.3638i	1.29758	−	1.20398i
$556$	−0.776964	+	0.117108i	−0.0329506	+	0.00496651i
$557$	−2.63514	+	4.56420i	−0.111655	+	0.193391i	−0.916437	−	0.400178i	$-0.868948\pi$
$557$	−2.63514	+	4.56420i	−0.111655	+	0.193391i	0.804783	+	0.593569i	$0.202282\pi$
$558$	18.8624	+	32.6707i	0.798511	+	1.38306i
$559$	−3.68389	−	4.61945i	−0.155812	−	0.195382i
$560$	−0.111824	−	0.135055i	−0.00472543	−	0.00570710i
$561$	−2.25288	+	2.82502i	−0.0951166	+	0.119272i
$562$	14.9282	+	2.25007i	0.629710	+	0.0949135i
$563$	−35.5785	+	24.2570i	−1.49945	+	1.02231i	−0.512978	+	0.858402i	$0.671458\pi$
$563$	−35.5785	+	24.2570i	−1.49945	+	1.02231i	−0.986476	+	0.163908i	$0.947590\pi$
$564$	−13.8869	+	9.46794i	−0.584745	+	0.398672i
$565$	15.4384	+	2.32696i	0.649497	+	0.0978959i
$566$	−6.88372	+	8.63191i	−0.289344	+	0.362826i
$567$	1.65997	−	7.94294i	0.0697120	−	0.333572i
$568$	−1.51894	−	1.90470i	−0.0637335	−	0.0799192i
$569$	6.88994	+	11.9337i	0.288841	+	0.500288i	0.973533	−	0.228544i	$-0.0733966\pi$
$569$	6.88994	+	11.9337i	0.288841	+	0.500288i	−0.684692	+	0.728833i	$0.740063\pi$
$570$	8.76897	−	15.1883i	0.367292	−	0.636168i
$571$	20.4316	−	3.07957i	0.855037	−	0.128876i	0.293126	−	0.956074i	$-0.405304\pi$
$571$	20.4316	−	3.07957i	0.855037	−	0.128876i	0.561911	+	0.827198i	$0.310066\pi$
$572$	−1.60067	+	1.48521i	−0.0669275	+	0.0620997i
$573$	25.5748	+	12.3162i	1.06840	+	0.514515i
$574$	5.02456	+	12.1414i	0.209721	+	0.506773i
$575$	3.22714	−	1.55411i	0.134581	−	0.0648109i
$576$	8.02297	−	20.4422i	0.334291	−	0.851759i
$577$	−1.11883	+	14.9297i	−0.0465774	+	0.621532i	0.924256	+	0.381774i	$0.124687\pi$
$577$	−1.11883	+	14.9297i	−0.0465774	+	0.621532i	−0.970833	+	0.239757i	$0.922932\pi$
$578$	−13.8095	−	4.25967i	−0.574400	−	0.177179i
$579$	4.55563	+	60.7907i	0.189326	+	2.52638i
$580$	−2.32410	+	10.1826i	−0.0965032	+	0.422808i
$581$	26.6876	−	25.6912i	1.10719	−	1.06585i
$582$	−7.54696	−	33.0654i	−0.312831	−	1.37060i
$583$	0.391965	−	0.120905i	0.0162335	−	0.00500738i
$584$	13.5801	+	34.6016i	0.561950	+	1.43183i
$585$	5.37957	+	4.99151i	0.222418	+	0.206374i
$586$	−2.53272	−	1.72678i	−0.104626	−	0.0713326i
$587$	38.0386			1.57002			0.785011	−	0.619481i	$-0.212657\pi$
$587$	38.0386			1.57002			0.785011	+	0.619481i	$0.212657\pi$
$588$	20.6130	−	10.8774i	0.850068	−	0.448575i
$589$	43.0027			1.77189
$590$	13.4060	+	9.14004i	0.551915	+	0.376290i
$591$	−19.2170	−	17.8308i	−0.790483	−	0.733461i
$592$	0.131397	+	0.334794i	0.00540038	+	0.0137600i
$593$	34.7362	−	10.7147i	1.42645	−	0.440000i	0.517058	−	0.855950i	$-0.327027\pi$
$593$	34.7362	−	10.7147i	1.42645	−	0.440000i	0.909387	+	0.415950i	$0.136551\pi$
$594$	−1.28473	−	5.62878i	−0.0527132	−	0.230952i
$595$	−0.310112	−	3.31851i	−0.0127133	−	0.136046i
$596$	1.38771	−	6.07995i	0.0568428	−	0.249045i
$597$	−0.997201	−	13.3067i	−0.0408127	−	0.544608i
$598$	−1.38800	−	0.428140i	−0.0567594	−	0.0175080i
$599$	−1.16502	+	15.5460i	−0.0476012	+	0.635194i	0.921476	+	0.388436i	$0.126984\pi$
$599$	−1.16502	+	15.5460i	−0.0476012	+	0.635194i	−0.969077	+	0.246758i	$0.920635\pi$
$600$	6.09554	−	15.5312i	0.248849	−	0.634058i
$601$	−17.6463	+	8.49799i	−0.719806	+	0.346640i	−0.757666	−	0.652643i	$-0.773660\pi$
$601$	−17.6463	+	8.49799i	−0.719806	+	0.346640i	0.0378600	+	0.999283i	$0.487946\pi$
$602$	−10.2436	−	9.16017i	−0.417498	−	0.373341i
$603$	−18.3722	−	8.84757i	−0.748172	−	0.360301i
$604$	−15.3533	+	14.2458i	−0.624718	+	0.579654i
$605$	13.0373	−	1.96506i	0.530042	−	0.0798910i
$606$	2.22675	−	3.85684i	0.0904554	−	0.156673i
$607$	−4.43758	−	7.68611i	−0.180116	−	0.311970i	0.761804	−	0.647808i	$-0.224314\pi$
$607$	−4.43758	−	7.68611i	−0.180116	−	0.311970i	−0.941920	+	0.335838i	$0.890981\pi$
$608$	−15.3634	−	19.2651i	−0.623069	−	0.781304i
$609$	32.9879	+	15.1457i	1.33674	+	0.613737i
$610$	10.5645	−	13.2474i	0.427743	−	0.536373i
$611$	4.99154	+	0.752354i	0.201936	+	0.0304370i
$612$	3.30977	−	2.25656i	0.133789	−	0.0912161i
$613$	16.3732	−	11.1630i	0.661306	−	0.450871i	−0.185591	−	0.982627i	$-0.559420\pi$
$613$	16.3732	−	11.1630i	0.661306	−	0.450871i	0.846898	+	0.531756i	$0.178468\pi$
$614$	25.7685	+	3.88398i	1.03993	+	0.156745i
$615$	16.0835	−	20.1680i	0.648547	−	0.813253i
$616$	−8.13331	+	10.5925i	−0.327701	+	0.426784i
$617$	−19.1420	−	24.0033i	−0.770628	−	0.966337i	0.229348	−	0.973345i	$-0.426341\pi$
$617$	−19.1420	−	24.0033i	−0.770628	−	0.966337i	−0.999975	+	0.00700781i	$0.997769\pi$
$618$	6.42265	+	11.1244i	0.258357	+	0.447487i
$619$	4.41253	−	7.64273i	0.177355	−	0.307187i	−0.763619	−	0.645667i	$-0.776579\pi$
$619$	4.41253	−	7.64273i	0.177355	−	0.307187i	0.940974	+	0.338480i	$0.109913\pi$
$620$	−20.0994	+	3.02949i	−0.807210	+	0.121667i
$621$	−4.47119	+	4.14866i	−0.179423	+	0.166480i
$622$	10.6679	+	5.13738i	0.427743	+	0.205990i
$623$	−3.51108	−	1.01275i	−0.140669	−	0.0405749i
$624$	−0.0962570	+	0.0463549i	−0.00385336	+	0.00185568i
$625$	−3.45697	+	8.80823i	−0.138279	+	0.352329i
$626$	0.354010	−	4.72394i	0.0141491	−	0.188807i
$627$	−20.1554	−	6.21710i	−0.804927	−	0.248287i
$628$	−0.702917	−	9.37978i	−0.0280495	−	0.374294i
$629$	−1.52127	+	6.66513i	−0.0606571	+	0.265756i
$630$	14.2766	+	9.35397i	0.568792	+	0.372671i
$631$	−10.9138	−	47.8167i	−0.434473	−	1.90355i	−0.428440	−	0.903570i	$-0.640937\pi$
$631$	−10.9138	−	47.8167i	−0.434473	−	1.90355i	−0.00603295	−	0.999982i	$-0.501920\pi$
$632$	−2.15430	+	0.664513i	−0.0856934	+	0.0264329i
$633$	0.837504	+	2.13393i	0.0332878	+	0.0848159i
$634$	12.6935	+	11.7778i	0.504122	+	0.467756i
$635$	−11.0757	−	7.55127i	−0.439525	−	0.299663i
$636$	−0.767599			−0.0304373
$637$	−6.76031	−	1.81608i	−0.267853	−	0.0719557i
$638$	−7.90940			−0.313136
$639$	3.09393	+	2.10941i	0.122394	+	0.0834468i
$640$	8.45264	+	7.84290i	0.334120	+	0.310018i
$641$	17.8254	+	45.4185i	0.704063	+	1.79392i	0.601001	+	0.799248i	$0.294769\pi$
$641$	17.8254	+	45.4185i	0.704063	+	1.79392i	0.103062	+	0.994675i	$0.467136\pi$
$642$	−29.5919	+	9.12788i	−1.16790	+	0.360249i
$643$	−2.93527	−	12.8603i	−0.115756	−	0.507159i	−0.999250	−	0.0387176i	$-0.987673\pi$
$643$	−2.93527	−	12.8603i	−0.115756	−	0.507159i	0.883494	−	0.468442i	$-0.155184\pi$
$644$	5.31905	+	0.702006i	0.209600	+	0.0276629i
$645$	−6.00305	+	26.3011i	−0.236370	+	1.03560i
$646$	0.214865	+	2.86717i	0.00845374	+	0.112807i
$647$	40.7120	+	12.5580i	1.60056	+	0.493706i	0.961350	−	0.275330i	$-0.0887871\pi$
$647$	40.7120	+	12.5580i	1.60056	+	0.493706i	0.639206	+	0.769036i	$0.279263\pi$
$648$	0.650225	−	8.67665i	0.0255432	−	0.340851i
$649$	7.12918	−	18.1649i	0.279845	−	0.713033i
$650$	−1.71686	+	0.826797i	−0.0673409	+	0.0324296i
$651$	−3.98364	+	70.5302i	−0.156131	+	2.76430i
$652$	−3.67814	−	1.77130i	−0.144047	−	0.0693694i
$653$	−4.10307	+	3.80709i	−0.160566	+	0.148983i	−0.756364	−	0.654151i	$-0.773026\pi$
$653$	−4.10307	+	3.80709i	−0.160566	+	0.148983i	0.595799	+	0.803134i	$0.296836\pi$
$654$	4.09956	−	0.617909i	0.160305	−	0.0241621i
$655$	13.6320	−	23.6113i	0.532647	−	0.922571i
$656$	0.111240	+	0.192674i	0.00434321	+	0.00752265i
$657$	−35.6228	−	44.6695i	−1.38978	−	1.74272i
$658$	11.7384	−	0.215759i	0.457611	−	0.00841115i
$659$	12.1103	−	15.1859i	0.471751	−	0.591557i	−0.487848	−	0.872929i	$-0.662218\pi$
$659$	12.1103	−	15.1859i	0.471751	−	0.591557i	0.959599	+	0.281371i	$0.0907893\pi$
$660$	9.85857	+	1.48594i	0.383744	+	0.0578401i
$661$	−25.0751	+	17.0959i	−0.975308	+	0.664953i	−0.942394	−	0.334505i	$-0.891431\pi$
$661$	−25.0751	+	17.0959i	−0.975308	+	0.664953i	−0.0329135	+	0.999458i	$0.510479\pi$
$662$	−16.5754	+	11.3009i	−0.644221	+	0.439222i
$663$	−2.00814	−	0.302678i	−0.0779896	−	0.0117550i
$664$	24.7658	−	31.0553i	0.961099	−	1.20518i
$665$	17.3710	−	8.76229i	0.673619	−	0.339787i
$666$	−21.8281	−	27.3716i	−0.845823	−	1.06063i
$667$	4.17792	+	7.23636i	0.161770	+	0.280193i
$668$	−14.6128	+	25.3101i	−0.565386	+	0.979278i
$669$	53.4969	−	8.06336i	2.06831	−	0.311747i
$670$	−5.07140	+	4.70557i	−0.195925	+	0.181792i
$671$	−18.3602	−	8.84179i	−0.708787	−	0.341334i
$672$	33.0207	−	23.4135i	1.27380	−	0.903194i
$673$	25.9803	−	12.5114i	1.00147	−	0.482280i	0.140030	−	0.990147i	$-0.455280\pi$
$673$	25.9803	−	12.5114i	1.00147	−	0.482280i	0.861435	+	0.507867i	$0.169566\pi$
$674$	3.30466	−	8.42014i	0.127291	−	0.324332i
$675$	−0.597977	+	7.97945i	−0.0230162	+	0.307129i
$676$	−1.17272	−	0.361737i	−0.0451047	−	0.0139130i
$677$	1.50837	+	20.1278i	0.0579714	+	0.773575i	0.948122	+	0.317908i	$0.102980\pi$
$677$	1.50837	+	20.1278i	0.0579714	+	0.773575i	−0.890150	+	0.455667i	$0.849401\pi$
$678$	4.92334	−	21.5706i	0.189080	−	0.828413i
$679$	13.0999	−	35.2705i	0.502727	−	1.35356i
$680$	−0.795255	−	3.48424i	−0.0304966	−	0.133615i
$681$	−58.2574	+	17.9700i	−2.23243	+	0.688613i
$682$	−5.62364	−	14.3288i	−0.215340	−	0.548678i
$683$	12.3964	+	11.5022i	0.474336	+	0.440120i	0.880758	−	0.473566i	$-0.157033\pi$
$683$	12.3964	+	11.5022i	0.474336	+	0.440120i	−0.406422	+	0.913685i	$0.633224\pi$
$684$	19.3204	+	13.1724i	0.738734	+	0.503660i
$685$	10.8042			0.412807
$686$	−16.2079	−	1.53564i	−0.618821	−	0.0586309i
$687$	−40.5282			−1.54625
$688$	−0.192242	−	0.131069i	−0.00732917	−	0.00499694i
$689$	0.168998	+	0.156807i	0.00643831	+	0.00597387i
$690$	2.42296	+	6.17361i	0.0922407	+	0.235025i
$691$	46.9194	−	14.4727i	1.78490	−	0.550568i	0.787095	−	0.616832i	$-0.211584\pi$
$691$	46.9194	−	14.4727i	1.78490	−	0.550568i	0.997802	+	0.0662637i	$0.0211079\pi$
$692$	5.46887	+	23.9607i	0.207895	+	0.910849i
$693$	7.14703	−	19.2429i	0.271493	−	0.730977i
$694$	−5.09508	+	22.3230i	−0.193406	+	0.847369i
$695$	−0.0805213	−	1.07448i	−0.00305435	−	0.0407574i
$696$	37.1928	+	11.4725i	1.40979	+	0.434863i
$697$	−0.316036	+	4.21721i	−0.0119707	+	0.159738i
$698$	−11.8606	+	30.2204i	−0.448931	+	1.14386i
$699$	1.15524	−	0.556335i	0.0436953	−	0.0210425i
$700$	5.74170	−	4.07118i	0.217016	−	0.153876i
$701$	22.7914	+	10.9758i	0.860820	+	0.414549i	0.811582	−	0.584238i	$-0.198607\pi$
$701$	22.7914	+	10.9758i	0.860820	+	0.414549i	0.0492375	+	0.998787i	$0.484321\pi$
$702$	2.37870	−	2.20711i	0.0897783	−	0.0833021i
$703$	−39.4618	+	5.94790i	−1.48833	+	0.224329i
$704$	−4.48021	+	7.75995i	−0.168854	+	0.292464i
$705$	−11.5241	−	19.9603i	−0.434022	−	0.751749i
$706$	3.50383	+	4.39366i	0.131868	+	0.165357i
$707$	4.41111	−	2.22505i	0.165897	−	0.0836817i
$708$	−22.7678	+	28.5500i	−0.855667	+	1.07297i
$709$	−3.80094	−	0.572900i	−0.142747	−	0.0215157i	0.0772798	−	0.997009i	$-0.475377\pi$
$709$	−3.80094	−	0.572900i	−0.142747	−	0.0215157i	−0.220027	+	0.975494i	$0.570615\pi$
$710$	1.04967	−	0.715654i	0.0393935	−	0.0268580i
$711$	2.86312	−	1.95205i	0.107376	−	0.0732074i
$712$	−3.87455	−	0.583994i	−0.145205	−	0.0218861i
$713$	−10.1390	+	12.7139i	−0.379708	+	0.476139i
$714$	−4.72246	+	0.0868014i	−0.176734	+	0.00324846i
$715$	−1.86695	−	2.34109i	−0.0698201	−	0.0875516i
$716$	−9.26741	−	16.0516i	−0.346339	−	0.599877i
$717$	−15.0659	+	26.0949i	−0.562646	+	0.974531i
$718$	−17.8578	+	2.69162i	−0.666445	+	0.100450i
$719$	15.8471	−	14.7040i	0.590998	−	0.548366i	−0.326962	−	0.945037i	$-0.606025\pi$
$719$	15.8471	−	14.7040i	0.590998	−	0.548366i	0.917961	+	0.396671i	$0.129835\pi$
$720$	0.260369	+	0.125387i	0.00970338	+	0.00467290i
$721$	−0.803580	+	14.2274i	−0.0299269	+	0.529855i
$722$	−0.0734155	+	0.0353550i	−0.00273224	+	0.00131578i
$723$	11.8395	−	30.1667i	0.440317	−	1.12191i
$724$	−0.903004	+	12.0497i	−0.0335599	+	0.447825i
$725$	10.4750	+	3.23111i	0.389032	+	0.120000i
$726$	−1.39628	−	18.6320i	−0.0518207	−	0.691499i
$727$	4.01227	−	17.5789i	0.148807	−	0.651966i	−0.844411	−	0.535696i	$-0.820049\pi$
$727$	4.01227	−	17.5789i	0.148807	−	0.651966i	0.993218	−	0.116270i	$-0.0370937\pi$
$728$	−7.44135	−	0.982107i	−0.275795	−	0.0363993i
$729$	9.66148	+	42.3297i	0.357832	+	1.56777i
$730$	−18.5227	+	5.71351i	−0.685557	+	0.211466i
$731$	−1.61581	−	4.11702i	−0.0597630	−	0.152274i
$732$	27.9546	+	25.9380i	1.03323	+	0.958698i
$733$	23.3572	+	15.9247i	0.862719	+	0.588192i	0.911815	−	0.410602i	$-0.134681\pi$
$733$	23.3572	+	15.9247i	0.862719	+	0.588192i	−0.0490953	+	0.998794i	$0.515634\pi$
$734$	−12.9618			−0.478428
$735$	12.7622	+	29.3026i	0.470739	+	1.08084i
$736$	9.31813			0.343471
$737$	6.87460	+	4.68702i	0.253229	+	0.172649i
$738$	−15.8755	−	14.7303i	−0.584385	−	0.542230i
$739$	−0.807177	−	2.05665i	−0.0296925	−	0.0756552i	0.915259	−	0.402867i	$-0.131986\pi$
$739$	−0.807177	−	2.05665i	−0.0296925	−	0.0756552i	−0.944951	+	0.327212i	$0.893891\pi$
$740$	18.0253	−	5.56008i	0.662625	−	0.204393i
$741$	−2.63792	−	11.5575i	−0.0969062	−	0.424574i
$742$	0.448495	+	0.293852i	0.0164648	+	0.0107877i
$743$	−4.95687	+	21.7175i	−0.181850	+	0.796736i	0.798899	+	0.601465i	$0.205416\pi$
$743$	−4.95687	+	21.7175i	−0.181850	+	0.796736i	−0.980749	+	0.195271i	$0.937441\pi$
$744$	5.66065	+	75.5361i	0.207530	+	2.76929i
$745$	8.17199	+	2.52072i	0.299398	+	0.0923522i
$746$	−1.12097	+	14.9584i	−0.0410418	+	0.547664i
$747$	−22.3056	+	56.8338i	−0.816119	+	2.07944i
$748$	−1.47263	+	0.709180i	−0.0538446	+	0.0259302i
$749$	−33.0085	−	9.52108i	−1.20610	−	0.347893i
$750$	25.9201	+	12.4824i	0.946467	+	0.455794i
$751$	−25.4414	+	23.6061i	−0.928369	+	0.861400i	−0.990618	−	0.136660i	$-0.956363\pi$
$751$	−25.4414	+	23.6061i	−0.928369	+	0.861400i	0.0622491	+	0.998061i	$0.480173\pi$
$752$	0.196563	−	0.0296271i	0.00716790	−	0.00108039i
$753$	22.5911	−	39.1289i	0.823265	−	1.42594i
$754$	−2.22268	−	3.84979i	−0.0809452	−	0.140201i
$755$	−17.9074	−	22.4552i	−0.651719	−	0.817229i
$756$	−7.29951	+	9.50658i	−0.265481	+	0.345751i
$757$	−12.6825	+	15.9034i	−0.460954	+	0.578018i	−0.956930	−	0.290318i	$-0.906239\pi$
$757$	−12.6825	+	15.9034i	−0.460954	+	0.578018i	0.495976	+	0.868336i	$0.334810\pi$
$758$	−20.8235	−	3.13864i	−0.756344	−	0.114000i
$759$	6.59026	−	4.49316i	0.239211	−	0.163091i
$760$	17.2369	−	11.7519i	0.625249	−	0.426287i
$761$	−11.5550	−	1.74163i	−0.418867	−	0.0631341i	−0.0637726	−	0.997964i	$-0.520313\pi$
$761$	−11.5550	−	1.74163i	−0.418867	−	0.0631341i	−0.355095	+	0.934830i	$0.615551\pi$
$762$	−11.8442	+	14.8521i	−0.429068	+	0.538035i
$763$	4.17975	+	1.91905i	0.151317	+	0.0694742i
$764$	8.00583	+	10.0390i	0.289641	+	0.363198i
$765$	2.74662	+	4.75728i	0.0993042	+	0.172000i
$766$	2.32833	−	4.03279i	0.0841261	−	0.145711i
$767$	10.8449	−	1.63461i	0.391588	−	0.0590223i
$768$	32.0099	−	29.7009i	1.15506	−	1.07174i
$769$	18.0265	+	8.68112i	0.650053	+	0.313049i	0.729693	−	0.683774i	$-0.239663\pi$
$769$	18.0265	+	8.68112i	0.650053	+	0.313049i	−0.0796400	+	0.996824i	$0.525377\pi$
$770$	−5.19134	−	4.64227i	−0.187083	−	0.167296i
$771$	27.7703	−	13.3735i	1.00012	−	0.481634i
$772$	−10.0746	+	25.6696i	−0.362592	+	0.923869i
$773$	2.72266	−	36.3314i	0.0979274	−	1.30675i	−0.704373	−	0.709830i	$-0.748772\pi$
$773$	2.72266	−	36.3314i	0.0979274	−	1.30675i	0.802301	−	0.596920i	$-0.203609\pi$
$774$	21.6425	+	6.67583i	0.777924	+	0.239958i
$775$	1.59427	+	21.2741i	0.0572679	+	0.764186i
$776$	8.97733	−	39.3323i	0.322268	−	1.41195i
$777$	−6.09976	−	65.2737i	−0.218828	−	2.34168i
$778$	−1.59855	−	7.00369i	−0.0573106	−	0.251094i
$779$	−23.5898	+	7.27648i	−0.845191	+	0.260707i
$780$	2.04717	+	5.21610i	0.0733004	+	0.186766i
$781$	−1.12003	−	1.03924i	−0.0400779	−	0.0371869i
$782$	−0.898350	−	0.612485i	−0.0321249	−	0.0219024i
$783$	−18.6668			−0.667098
$784$	−0.275468	+	0.0101299i	−0.00983814	+	0.000361783i
$785$	12.8987			0.460373
$786$	−31.9231	−	21.7648i	−1.13866	−	0.776325i
$787$	13.7518	+	12.7598i	0.490200	+	0.454839i	0.886127	−	0.463443i	$-0.153386\pi$
$787$	13.7518	+	12.7598i	0.490200	+	0.454839i	−0.395927	+	0.918282i	$0.629577\pi$
$788$	−4.33237	−	11.0387i	−0.154334	−	0.393237i
$789$	−15.4704	+	4.77197i	−0.550759	+	0.169887i
$790$	−0.261606	−	1.14617i	−0.00930754	−	0.0407790i
$791$	17.6828	−	17.0226i	0.628729	−	0.605254i
$792$	4.89785	−	21.4589i	0.174038	−	0.762509i
$793$	−0.855905	−	11.4213i	−0.0303941	−	0.405581i
$794$	−12.0522	−	3.71762i	−0.427717	−	0.131933i
$795$	0.0786622	−	1.04967i	0.00278986	−	0.0372281i
$796$	2.20526	−	5.61892i	0.0781635	−	0.199157i
$797$	−20.6013	+	9.92108i	−0.729736	+	0.351423i	−0.761580	−	0.648070i	$-0.775576\pi$
$797$	−20.6013	+	9.92108i	−0.729736	+	0.351423i	0.0318441	+	0.999493i	$0.489862\pi$
$798$	−10.5430	−	25.4761i	−0.373217	−	0.901844i
$799$	3.40438	+	1.63946i	0.120438	+	0.0580000i
$800$	8.96116	−	8.31475i	0.316825	−	0.293971i
$801$	5.95544	−	0.897638i	0.210425	−	0.0317165i
$802$	−2.77099	+	4.79949i	−0.0978469	+	0.169476i
$803$	11.6563	+	20.1892i	0.411341	+	0.712463i
$804$	−9.70783	−	12.1732i	−0.342369	−	0.429317i
$805$	−1.50506	+	7.20174i	−0.0530466	+	0.253828i
$806$	5.39401	−	6.76388i	0.189996	−	0.238247i
$807$	−54.9995	−	8.28984i	−1.93607	−	0.291816i
$808$	4.37705	−	2.98422i	0.153984	−	0.104985i
$809$	−37.4659	+	25.5438i	−1.31723	+	0.898073i	−0.998756	−	0.0498576i	$-0.984123\pi$
$809$	−37.4659	+	25.5438i	−1.31723	+	0.898073i	−0.318475	+	0.947931i	$0.603171\pi$
$810$	4.48669	+	0.676259i	0.157646	+	0.0237613i
$811$	−24.7714	+	31.0623i	−0.869840	+	1.09075i	0.125284	+	0.992121i	$0.460016\pi$
$811$	−24.7714	+	31.0623i	−0.869840	+	1.09075i	−0.995125	+	0.0986245i	$0.968556\pi$
$812$	10.4717	+	12.6472i	0.367486	+	0.443828i
$813$	−5.20119	−	6.52208i	−0.182414	−	0.228739i
$814$	7.14247	+	12.3711i	0.250343	+	0.433608i
$815$	2.79914	−	4.84825i	0.0980495	−	0.169827i
$816$	−0.0790788	+	0.0119192i	−0.00276831	+	0.000417256i
$817$	18.9254	−	17.5602i	0.662117	−	0.614355i
$818$	−1.17597	−	0.566319i	−0.0411169	−	0.0198009i
$819$	11.3747	−	1.92887i	0.397463	−	0.0674002i
$820$	10.5132	−	5.06289i	0.367137	−	0.176804i
$821$	8.35236	−	21.2815i	0.291499	−	0.742728i	−0.707840	−	0.706373i	$-0.750330\pi$
$821$	8.35236	−	21.2815i	0.291499	−	0.742728i	0.999339	−	0.0363548i	$-0.0115746\pi$
$822$	1.14419	−	15.2681i	0.0399082	−	0.532538i
$823$	−7.93264	−	2.44690i	−0.276514	−	0.0852934i	0.153396	−	0.988165i	$-0.450979\pi$
$823$	−7.93264	−	2.44690i	−0.276514	−	0.0852934i	−0.429911	+	0.902871i	$0.641455\pi$
$824$	1.14187	+	15.2371i	0.0397788	+	0.530811i
$825$	2.32846	−	10.2016i	0.0810665	−	0.355176i
$826$	24.2324	−	7.96526i	0.843151	−	0.277147i
$827$	−8.87476	−	38.8829i	−0.308606	−	1.35209i	−0.856761	−	0.515713i	$-0.827527\pi$
$827$	−8.87476	−	38.8829i	−0.308606	−	1.35209i	0.548155	−	0.836376i	$-0.315330\pi$
$828$	−8.44976	+	2.60641i	−0.293649	+	0.0905789i
$829$	−11.3802	−	28.9963i	−0.395251	−	1.00708i	−0.980551	−	0.196266i	$-0.937118\pi$
$829$	−11.3802	−	28.9963i	−0.395251	−	1.00708i	0.585300	−	0.810817i	$-0.300977\pi$
$830$	15.1842	+	14.0889i	0.527053	+	0.489034i
$831$	−5.95069	−	4.05711i	−0.206427	−	0.140740i
$832$	−5.03607			−0.174594
$833$	−4.43486	−	2.79058i	−0.153659	−	0.0966880i
$834$	−1.52695			−0.0528740
$835$	−33.1135	−	22.5764i	−1.14594	−	0.781289i
$836$	−6.99417	−	6.48964i	−0.241898	−	0.224449i
$837$	−13.2722	−	33.8171i	−0.458756	−	1.16889i
$838$	30.4637	−	9.39681i	1.05235	−	0.324607i
$839$	−3.71633	−	16.2823i	−0.128302	−	0.562127i	−0.997686	−	0.0679903i	$-0.978341\pi$
$839$	−3.71633	−	16.2823i	−0.128302	−	0.562127i	0.869384	−	0.494137i	$-0.164516\pi$
$840$	17.6780	+	29.3596i	0.609949	+	1.01300i
$841$	0.762707	−	3.34164i	0.0263003	−	0.115229i
$842$	2.54568	+	33.9698i	0.0877301	+	1.17068i
$843$	−44.5232	−	13.7336i	−1.53346	−	0.473010i
$844$	−0.0774924	+	1.03406i	−0.00266740	+	0.0355939i
$845$	0.614845	−	1.56660i	0.0211513	−	0.0538927i
$846$	−17.4337	+	8.39562i	−0.599382	+	0.288647i
$847$	10.0321	−	18.1380i	0.344708	−	0.623229i
$848$	0.00817942	+	0.00393900i	0.000280882	+	0.000135266i
$849$	24.9784	−	23.1765i	0.857255	−	0.795417i
$850$	−1.41047	+	0.212594i	−0.0483786	+	0.00729190i
$851$	7.54561	−	13.0694i	0.258660	−	0.448013i
$852$	1.42961	+	2.47615i	0.0489776	+	0.0848317i
$853$	18.7514	+	23.5135i	0.642035	+	0.805086i	0.991256	−	0.131954i	$-0.0421252\pi$
$853$	18.7514	+	23.5135i	0.642035	+	0.805086i	−0.349221	+	0.937040i	$0.613554\pi$
$854$	−6.40376	−	25.8567i	−0.219132	−	0.884799i
$855$	−19.9929	+	25.0703i	−0.683743	+	0.857387i
$856$	−36.4255	−	5.49027i	−1.24500	−	0.187653i
$857$	31.2725	−	21.3212i	1.06825	−	0.728319i	0.104336	−	0.994542i	$-0.466728\pi$
$857$	31.2725	−	21.3212i	1.06825	−	0.728319i	0.963911	+	0.266223i	$0.0857758\pi$
$858$	−3.50606	+	2.39039i	−0.119695	+	0.0816066i
$859$	27.4226	+	4.13330i	0.935648	+	0.141026i	0.599131	−	0.800651i	$-0.295513\pi$
$859$	27.4226	+	4.13330i	0.935648	+	0.141026i	0.336517	+	0.941677i	$0.390751\pi$
$860$	−7.60861	+	9.54090i	−0.259452	+	0.325342i
$861$	−9.74913	−	39.3645i	−0.332250	−	1.34154i
$862$	18.9326	+	23.7408i	0.644848	+	0.808614i
$863$	−17.4368	−	30.2014i	−0.593556	−	1.02807i	−0.993749	−	0.111638i	$-0.964390\pi$
$863$	−17.4368	−	30.2014i	−0.593556	−	1.02807i	0.400193	−	0.916431i	$-0.368943\pi$
$864$	−10.4083	+	18.0277i	−0.354097	+	0.613315i
$865$	−33.3261	+	5.02311i	−1.13312	+	0.170791i
$866$	11.5062	−	10.6762i	0.390995	−	0.362791i
$867$	40.1846	+	19.3519i	1.36474	+	0.657225i
$868$	−15.4663	+	27.9630i	−0.524962	+	0.949126i
$869$	−1.27390	+	0.613478i	−0.0432141	+	0.0208108i
$870$	−7.41531	+	18.8939i	−0.251402	+	0.640563i
$871$	−0.349462	+	4.66325i	−0.0118411	+	0.158008i
$872$	4.71253	+	1.45362i	0.159586	+	0.0492259i
$873$	4.63409	+	61.8377i	0.156840	+	2.09289i
$874$	1.41231	−	6.18772i	0.0477720	−	0.209303i
$875$	16.4629	+	27.3415i	0.556546	+	0.924311i
$876$	−9.70759	−	42.5317i	−0.327989	−	1.43701i
$877$	−55.4916	+	17.1169i	−1.87382	+	0.577997i	−0.878939	+	0.476934i	$0.841748\pi$
$877$	−55.4916	+	17.1169i	−1.87382	+	0.577997i	−0.994880	+	0.101062i	$0.967776\pi$
$878$	−6.38040	−	16.2570i	−0.215328	−	0.548647i
$879$	6.93509	+	6.43482i	0.233915	+	0.217041i
$880$	−0.0974263	−	0.0664241i	−0.00328424	−	0.00223916i
$881$	10.6001			0.357126			0.178563	−	0.983928i	$-0.442855\pi$
$881$	10.6001			0.357126			0.178563	+	0.983928i	$0.442855\pi$
$882$	25.3326	−	8.84599i	0.852994	−	0.297860i
$883$	−21.2838			−0.716257			−0.358128	−	0.933672i	$-0.616585\pi$
$883$	−21.2838			−0.716257			−0.358128	+	0.933672i	$0.616585\pi$
$884$	−0.759018	−	0.517490i	−0.0255285	−	0.0174051i
$885$	−36.7082	−	34.0602i	−1.23393	−	1.14492i
$886$	−9.20322	−	23.4494i	−0.309188	−	0.787799i
$887$	−44.4956	+	13.7251i	−1.49402	+	0.460843i	−0.930819	−	0.365480i	$-0.880905\pi$
$887$	−44.4956	+	13.7251i	−1.49402	+	0.460843i	−0.563196	+	0.826323i	$0.690429\pi$
$888$	−15.6423	−	68.5334i	−0.524922	−	2.29983i
$889$	−20.0202	+	6.58069i	−0.671455	+	0.220709i
$890$	0.454680	−	1.99208i	0.0152409	−	0.0667748i
$891$	−0.407800	−	5.44171i	−0.0136618	−	0.182304i
$892$	23.3854	+	7.21345i	0.783002	+	0.241524i
$893$	−1.64832	+	21.9953i	−0.0551590	+	0.736045i
$894$	4.42764	−	11.2814i	0.148082	−	0.377308i
$895$	22.8999	−	11.0280i	0.765461	−	0.368626i
$896$	17.8724	−	3.03073i	0.597075	−	0.101250i
$897$	4.03896	+	1.94506i	0.134857	+	0.0649437i
$898$	3.88152	−	3.60153i	0.129528	−	0.120185i
$899$	−49.2118	+	7.41749i	−1.64131	+	0.247387i
$900$	−5.80031	+	10.0464i	−0.193344	+	0.334881i
$901$	0.0862843	+	0.149449i	0.00287455	+	0.00497886i
$902$	5.50951	+	6.90871i	0.183447	+	0.230035i
$903$	27.0480	+	32.6670i	0.900101	+	1.08709i
$904$	16.4095	−	20.5768i	0.545770	−	0.684374i
$905$	−16.3852	−	2.46967i	−0.544663	−	0.0820948i
$906$	−33.6294	+	22.9282i	−1.11726	+	0.761737i
$907$	−38.5353	+	26.2729i	−1.27954	+	0.872378i	−0.996239	−	0.0866518i	$-0.972383\pi$
$907$	−38.5353	+	26.2729i	−1.27954	+	0.872378i	−0.283305	+	0.959030i	$0.591431\pi$
$908$	−27.2699	−	4.11028i	−0.904984	−	0.136404i
$909$	−5.07690	+	6.36623i	−0.168390	+	0.211154i
$910$	0.800705	−	3.83138i	0.0265431	−	0.127009i
$911$	7.69582	+	9.65025i	0.254974	+	0.319727i	0.892800	−	0.450453i	$-0.148738\pi$
$911$	7.69582	+	9.65025i	0.254974	+	0.319727i	−0.637826	+	0.770180i	$0.720166\pi$
$912$	−0.233414	−	0.404284i	−0.00772910	−	0.0133872i
$913$	12.4559	−	21.5743i	0.412232	−	0.714006i
$914$	−9.15187	+	1.37942i	−0.302717	+	0.0456272i
$915$	−38.3344	+	35.5691i	−1.26730	+	1.17588i
$916$	−16.5174	−	7.95436i	−0.545750	−	0.262819i
$917$	−16.3898	−	39.6045i	−0.541239	−	1.30786i
$918$	2.18842	−	1.05389i	0.0722286	−	0.0347835i
$919$	9.80159	−	24.9741i	0.323325	−	0.823818i	−0.673117	−	0.739536i	$-0.735045\pi$
$919$	9.80159	−	24.9741i	0.323325	−	0.823818i	0.996442	−	0.0842822i	$-0.0268597\pi$
$920$	−0.589549	+	7.86698i	−0.0194368	+	0.259367i
$921$	−76.8541	−	23.7064i	−2.53243	−	0.781151i
$922$	2.55087	+	34.0389i	0.0840083	+	1.12101i
$923$	0.191087	−	0.837205i	0.00628969	−	0.0275569i
$924$	11.2918	−	10.8702i	0.371474	−	0.357604i
$925$	−4.40551	−	19.3018i	−0.144852	−	0.634640i
$926$	−29.5947	+	9.12877i	−0.972543	+	0.299990i
$927$	−8.58047	−	21.8627i	−0.281819	−	0.718064i
$928$	20.9048	+	19.3968i	0.686233	+	0.636731i
$929$	−8.11123	−	5.53014i	−0.266121	−	0.181438i	0.422907	−	0.906173i	$-0.361010\pi$
$929$	−8.11123	−	5.53014i	−0.266121	−	0.181438i	−0.689028	+	0.724735i	$0.741962\pi$
$930$	−39.5008			−1.29528
$931$	5.70573	−	30.0497i	0.186998	−	0.984840i
$932$	0.580013			0.0189990
$933$	−30.1932	−	20.5854i	−0.988482	−	0.673936i
$934$	−8.06738	−	7.48543i	−0.263973	−	0.244931i
$935$	−0.818876	−	2.08646i	−0.0267801	−	0.0682346i
$936$	11.8212	−	3.64636i	0.386389	−	0.119185i
$937$	13.1567	+	57.6432i	0.429810	+	1.88312i	0.467785	+	0.883842i	$0.345052\pi$
$937$	13.1567	+	57.6432i	0.429810	+	1.88312i	−0.0379748	+	0.999279i	$0.512091\pi$
$938$	1.01195	+	10.8290i	0.0330415	+	0.353578i
$939$	−3.25332	+	14.2537i	−0.106168	+	0.465153i
$940$	−0.779125	−	10.3967i	−0.0254123	−	0.339103i
$941$	35.4384	+	10.9313i	1.15526	+	0.356350i	0.812437	−	0.583050i	$-0.198141\pi$
$941$	35.4384	+	10.9313i	1.15526	+	0.356350i	0.342823	+	0.939400i	$0.388617\pi$
$942$	1.36600	−	18.2280i	0.0445066	−	0.593900i
$943$	3.41058	−	8.69002i	0.111064	−	0.282986i
$944$	0.389117	−	0.187389i	0.0126647	−	0.00609899i
$945$	−12.2520	−	10.9561i	−0.398557	−	0.356403i
$946$	−8.32616	−	4.00967i	−0.270707	−	0.130365i
$947$	24.4368	−	22.6741i	0.794091	−	0.736808i	−0.174718	−	0.984619i	$-0.555901\pi$
$947$	24.4368	−	22.6741i	0.794091	−	0.736808i	0.968809	+	0.247810i	$0.0797109\pi$
$948$	2.61637	−	0.394354i	0.0849757	−	0.0128080i
$949$	−6.55123	+	11.3471i	−0.212662	+	0.368341i
$950$	−4.16322	−	7.21091i	−0.135073	−	0.233953i
$951$	−33.3204	−	41.7824i	−1.08049	−	1.35489i
$952$	−5.10600	−	2.34432i	−0.165486	−	0.0759798i
$953$	−12.5687	+	15.7606i	−0.407139	+	0.510537i	−0.942555	−	0.334052i	$-0.891584\pi$
$953$	−12.5687	+	15.7606i	−0.407139	+	0.510537i	0.535415	+	0.844589i	$0.320155\pi$
$954$	−0.873846	−	0.131711i	−0.0282918	−	0.00426430i
$955$	−14.5485	+	9.91901i	−0.470779	+	0.320972i
$956$	−11.2617	+	7.67812i	−0.364230	+	0.248328i
$957$	24.1380	+	3.63822i	0.780270	+	0.117607i
$958$	−2.66071	+	3.33643i	−0.0859637	+	0.107795i
$959$	10.3443	−	13.4720i	0.334036	−	0.435035i
$960$	14.3366	+	17.9775i	0.462710	+	0.580220i
$961$	−32.9276	−	57.0323i	−1.06218	−	1.83975i
$962$	−4.01432	+	6.95300i	−0.129427	+	0.224174i
$963$	55.9885	−	8.43891i	1.80420	−	0.271940i
$964$	10.7460	−	9.97082i	0.346105	−	0.321138i
$965$	−34.0702	−	16.4073i	−1.09676	−	0.528170i
$966$	10.0179	+	2.88959i	0.322320	+	0.0929710i
$967$	−36.8013	+	17.7226i	−1.18345	+	0.569919i	−0.918914	−	0.394457i	$-0.870933\pi$
$967$	−36.8013	+	17.7226i	−1.18345	+	0.569919i	−0.264535	+	0.964376i	$0.585218\pi$
$968$	8.11989	−	20.6891i	0.260983	−	0.664974i
$969$	0.663133	−	8.84890i	0.0213029	−	0.284268i
$970$	20.1037	+	6.20117i	0.645491	+	0.199108i
$971$	3.65558	+	48.7803i	0.117313	+	1.56543i	0.676531	+	0.736414i	$0.263482\pi$
$971$	3.65558	+	48.7803i	0.117313	+	1.56543i	−0.559218	+	0.829021i	$0.688899\pi$
$972$	−5.29652	+	23.2056i	−0.169886	+	0.744320i
$973$	−1.41689	−	0.928345i	−0.0454235	−	0.0297614i
$974$	−0.670799	−	2.93896i	−0.0214938	−	0.0941705i
$975$	5.61985	−	1.73349i	0.179979	−	0.0555163i
$976$	−0.164776	−	0.419843i	−0.00527436	−	0.0134389i
$977$	21.0030	+	19.4879i	0.671945	+	0.623474i	0.940501	−	0.339790i	$-0.110356\pi$
$977$	21.0030	+	19.4879i	0.671945	+	0.623474i	−0.268556	+	0.963264i	$0.586547\pi$
$978$	−6.55495	−	4.46909i	−0.209604	−	0.142906i
$979$	−2.45744			−0.0785402
$980$	−0.549876	+	14.4472i	−0.0175652	+	0.461498i
$981$	−7.58024			−0.242019
$982$	13.6559	+	9.31040i	0.435776	+	0.297107i
$983$	3.89209	+	3.61133i	0.124138	+	0.115184i	0.739799	−	0.672828i	$-0.234920\pi$
$983$	3.89209	+	3.61133i	0.124138	+	0.115184i	−0.615661	+	0.788011i	$0.711111\pi$
$984$	−15.8867	−	40.4787i	−0.506449	−	1.29041i
$985$	15.5391	−	4.79319i	0.495118	−	0.152724i
$986$	−0.740445	−	3.24410i	−0.0235806	−	0.103313i
$987$	−35.9227	−	4.74106i	−1.14343	−	0.150909i
$988$	1.19326	−	5.22802i	0.0379627	−	0.166326i
$989$	0.729586	+	9.73565i	0.0231995	+	0.309576i
$990$	10.9682	+	3.38323i	0.348591	+	0.107526i
$991$	0.258945	−	3.45537i	0.00822564	−	0.109764i	−0.991580	−	0.129499i	$-0.958663\pi$
$991$	0.258945	−	3.45537i	0.00822564	−	0.109764i	0.999805	+	0.0197350i	$0.00628226\pi$
$992$	−20.2761	+	51.6627i	−0.643768	+	1.64029i
$993$	55.7832	−	26.8638i	1.77023	−	0.852496i
$994$	0.112627	−	1.99406i	0.00357231	−	0.0632477i
$995$	7.45776	+	3.59147i	0.236427	+	0.113857i
$996$	−34.1737	+	31.7086i	−1.08284	+	1.00473i
$997$	4.76089	−	0.717589i	0.150779	−	0.0227263i	−0.0732190	−	0.997316i	$-0.523327\pi$
$997$	4.76089	−	0.717589i	0.150779	−	0.0227263i	0.223998	+	0.974590i	$0.428089\pi$
$998$	−11.0310	+	19.1063i	−0.349181	+	0.604799i
$999$	16.8568	+	29.1968i	0.533326	+	0.923747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.53.18	✓	324
49.37	even	21	inner	637.2.bl.a.625.18	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.18	✓	324	1.1	even	1	trivial
637.2.bl.a.625.18	yes	324	49.37	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.726317 + 0.495195i) q^{2} +(-1.98880 - 1.84534i) q^{3} +(-0.448363 - 1.14241i) q^{4} +(1.60817 - 0.496054i) q^{5} +(-0.530699 - 2.32514i) q^{6} +(0.921177 - 2.48021i) q^{7} +(0.631282 - 2.76583i) q^{8} +(0.325867 + 4.34840i) q^{9} +O(q^{10})\)	\(q+(0.726317 + 0.495195i) q^{2} +(-1.98880 - 1.84534i) q^{3} +(-0.448363 - 1.14241i) q^{4} +(1.60817 - 0.496054i) q^{5} +(-0.530699 - 2.32514i) q^{6} +(0.921177 - 2.48021i) q^{7} +(0.631282 - 2.76583i) q^{8} +(0.325867 + 4.34840i) q^{9} +(1.41368 + 0.436064i) q^{10} +(0.132963 - 1.77427i) q^{11} +(-1.21643 + 3.09941i) q^{12} +(0.900969 - 0.433884i) q^{13} +(1.89725 - 1.34526i) q^{14} +(-4.11371 - 1.98106i) q^{15} +(0.0288670 - 0.0267846i) q^{16} +(0.740180 - 0.111564i) q^{17} +(-1.91662 + 3.31969i) q^{18} +(2.18476 + 3.78411i) q^{19} +(-1.28774 - 1.61477i) q^{20} +(-6.40886 + 3.23276i) q^{21} +(0.975185 - 1.22284i) q^{22} +(-1.63390 - 0.246271i) q^{23} +(-6.35938 + 4.33575i) q^{24} +(-1.79106 + 1.22112i) q^{25} +(0.869246 + 0.131018i) q^{26} +(2.30152 - 2.88601i) q^{27} +(-3.24644 + 0.0596713i) q^{28} +(-3.15294 - 3.95366i) q^{29} +(-2.00685 - 3.47597i) q^{30} +(4.92075 - 8.52300i) q^{31} +(-5.57631 + 0.840494i) q^{32} +(-3.53857 + 3.28331i) q^{33} +(0.592852 + 0.285502i) q^{34} +(0.251090 - 4.44554i) q^{35} +(4.82155 - 2.32194i) q^{36} +(-3.33672 + 8.50181i) q^{37} +(-0.287045 + 3.83035i) q^{38} +(-2.59251 - 0.799683i) q^{39} +(-0.356793 - 4.76107i) q^{40} +(-1.25718 + 5.50806i) q^{41} +(-6.25571 - 0.825625i) q^{42} +(-1.31477 - 5.76036i) q^{43} +(-2.08656 + 0.643620i) q^{44} +(2.68109 + 6.83131i) q^{45} +(-1.06478 - 0.987970i) q^{46} +(4.17079 + 2.84360i) q^{47} -0.106837 q^{48} +(-5.30287 - 4.56942i) q^{49} -1.90557 q^{50} +(-1.67794 - 1.14400i) q^{51} +(-0.899634 - 0.834739i) q^{52} +(0.0842258 + 0.214604i) q^{53} +(3.10077 - 0.956460i) q^{54} +(-0.666308 - 2.91929i) q^{55} +(-6.27831 - 4.11353i) q^{56} +(2.63792 - 11.5575i) q^{57} +(-0.332202 - 4.43293i) q^{58} +(10.4802 + 3.23270i) q^{59} +(-0.418746 + 5.58778i) q^{60} +(4.18436 - 10.6616i) q^{61} +(7.79457 - 3.75367i) q^{62} +(11.0851 + 3.19743i) q^{63} +(-4.53734 - 2.18507i) q^{64} +(1.23368 - 1.14469i) q^{65} +(-4.19600 + 0.632446i) q^{66} +(-2.33816 + 4.04982i) q^{67} +(-0.459321 - 0.795568i) q^{68} +(2.79505 + 3.50488i) q^{69} +(2.38378 - 3.10454i) q^{70} +(0.535413 - 0.671387i) q^{71} +(12.2326 + 1.84377i) q^{72} +(-10.8258 + 7.38088i) q^{73} +(-6.63357 + 4.52269i) q^{74} +(5.81545 + 0.876537i) q^{75} +(3.34345 - 4.19255i) q^{76} +(-4.27808 - 1.96420i) q^{77} +(-1.48699 - 1.86462i) q^{78} +(-0.397337 - 0.688208i) q^{79} +(0.0331363 - 0.0573937i) q^{80} +(3.03275 - 0.457114i) q^{81} +(-3.64067 + 3.37805i) q^{82} +(12.6148 + 6.07496i) q^{83} +(6.56663 + 5.87209i) q^{84} +(1.13499 - 0.546583i) q^{85} +(1.89756 - 4.83492i) q^{86} +(-1.02527 + 13.6813i) q^{87} +(-4.82340 - 1.48782i) q^{88} +(-0.103215 - 1.37731i) q^{89} +(-1.43551 + 6.28936i) q^{90} +(-0.246170 - 2.63427i) q^{91} +(0.451238 + 1.97700i) q^{92} +(-25.5142 + 7.87009i) q^{93} +(1.62118 + 4.13071i) q^{94} +(5.39058 + 5.00173i) q^{95} +(12.6412 + 8.61860i) q^{96} +14.2208 q^{97} +(-1.58881 - 5.94480i) q^{98} +7.75858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

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