LMFDB - Embedded newform 65.2.t.a.28.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(7,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 11]))

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

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

chi := DirichletCharacter("65.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.t (of order $12$, degree $4$, 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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			28.4
Root			$0.274809i$ of defining polynomial
Character	$\chi$	$=$	65.28
Dual form			65.2.t.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.237991 + 0.137404i) q^{2} +(0.611610 - 2.28256i) q^{3} +(-0.962240 + 1.66665i) q^{4} +(1.45395 - 1.69883i) q^{5} +(0.168076 + 0.627267i) q^{6} +(-0.193052 + 0.334376i) q^{7} -1.07848i q^{8} +(-2.23793 - 1.29207i) q^{9} +(-0.112600 + 0.604086i) q^{10} +(-1.12873 + 4.21249i) q^{11} +(3.21571 + 3.21571i) q^{12} +(-1.35750 + 3.34024i) q^{13} -0.106105i q^{14} +(-2.98844 - 4.35775i) q^{15} +(-1.77629 - 3.07663i) q^{16} +(1.90527 - 0.510514i) q^{17} +0.710144 q^{18} +(-4.83947 + 1.29673i) q^{19} +(1.43231 + 4.05791i) q^{20} +(0.645159 + 0.645159i) q^{21} +(-0.310185 - 1.15763i) q^{22} +(0.322241 + 0.0863441i) q^{23} +(-2.46170 - 0.659609i) q^{24} +(-0.772064 - 4.94003i) q^{25} +(-0.135891 - 0.981474i) q^{26} +(0.694880 - 0.694880i) q^{27} +(-0.371524 - 0.643499i) q^{28} +(7.07031 - 4.08205i) q^{29} +(1.30999 + 0.626482i) q^{30} +(-2.54187 + 2.54187i) q^{31} +(2.71347 + 1.56662i) q^{32} +(8.92491 + 5.15280i) q^{33} +(-0.383290 + 0.383290i) q^{34} +(0.287361 + 0.814128i) q^{35} +(4.30685 - 2.48656i) q^{36} +(-2.41251 - 4.17859i) q^{37} +(0.973575 - 0.973575i) q^{38} +(6.79403 + 5.14149i) q^{39} +(-1.83216 - 1.56806i) q^{40} +(4.49768 + 1.20515i) q^{41} +(-0.242190 - 0.0648946i) q^{42} +(-1.76471 - 6.58600i) q^{43} +(-5.93462 - 5.93462i) q^{44} +(-5.44885 + 1.92327i) q^{45} +(-0.0885545 + 0.0237281i) q^{46} -9.83310 q^{47} +(-8.10898 + 2.17280i) q^{48} +(3.42546 + 5.93307i) q^{49} +(0.862526 + 1.06960i) q^{50} -4.66112i q^{51} +(-4.26077 - 5.47658i) q^{52} +(-7.17155 - 7.17155i) q^{53} +(-0.0698958 + 0.260855i) q^{54} +(5.51519 + 8.04227i) q^{55} +(0.360618 + 0.208203i) q^{56} +11.8395i q^{57} +(-1.12178 + 1.94298i) q^{58} +(-0.628209 - 2.34451i) q^{59} +(10.1384 - 0.787474i) q^{60} +(-5.32338 + 9.22037i) q^{61} +(0.255679 - 0.954209i) q^{62} +(0.864073 - 0.498873i) q^{63} +6.24413 q^{64} +(3.70078 + 7.16270i) q^{65} -2.83207 q^{66} +(5.52170 - 3.18796i) q^{67} +(-0.982475 + 3.66665i) q^{68} +(0.394171 - 0.682724i) q^{69} +(-0.180254 - 0.154271i) q^{70} +(-1.12684 - 4.20542i) q^{71} +(-1.39347 + 2.41357i) q^{72} +6.08593i q^{73} +(1.14831 + 0.662979i) q^{74} +(-11.7481 - 1.25909i) q^{75} +(2.49554 - 9.31346i) q^{76} +(-1.19065 - 1.19065i) q^{77} +(-2.32338 - 0.290100i) q^{78} +3.34944i q^{79} +(-7.80932 - 1.45564i) q^{80} +(-5.03732 - 8.72489i) q^{81} +(-1.23600 + 0.331185i) q^{82} +5.18834 q^{83} +(-1.69605 + 0.454456i) q^{84} +(1.90288 - 3.97899i) q^{85} +(1.32493 + 1.32493i) q^{86} +(-4.99324 - 18.6350i) q^{87} +(4.54309 + 1.21732i) q^{88} +(4.82829 + 1.29374i) q^{89} +(1.03251 - 1.20642i) q^{90} +(-0.854827 - 1.09875i) q^{91} +(-0.453978 + 0.453978i) q^{92} +(4.24734 + 7.35661i) q^{93} +(2.34019 - 1.35111i) q^{94} +(-4.83341 + 10.1068i) q^{95} +(5.23549 - 5.23549i) q^{96} +(12.7722 + 7.37402i) q^{97} +(-1.63046 - 0.941346i) q^{98} +(7.96886 - 7.96886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9} - 2 q^{10} - 16 q^{11} - 24 q^{12} - 4 q^{13} - 20 q^{15} - 2 q^{16} + 4 q^{17} - 20 q^{19} + 4 q^{21} + 16 q^{22} - 10 q^{23} + 32 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9 - 2 * q^10 - 16 * q^11 - 24 * q^12 - 4 * q^13 - 20 * q^15 - 2 * q^16 + 4 * q^17 - 20 * q^19 + 4 * q^21 + 16 * q^22 - 10 * q^23 + 32 * q^24 + 18 * q^25 - 24 * q^26 + 4 * q^27 + 18 * q^28 - 26 * q^30 + 48 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 + 36 * q^36 - 4 * q^37 - 8 * q^38 + 4 * q^39 - 16 * q^40 + 10 * q^41 + 40 * q^42 + 10 * q^43 - 36 * q^44 + 4 * q^46 - 40 * q^47 - 56 * q^48 + 18 * q^49 + 36 * q^50 - 30 * q^52 - 10 * q^53 - 48 * q^54 - 10 * q^55 - 16 * q^59 + 28 * q^60 - 16 * q^61 - 44 * q^62 - 36 * q^63 + 20 * q^64 - 14 * q^65 - 32 * q^66 + 18 * q^67 + 22 * q^68 - 16 * q^69 - 12 * q^70 - 16 * q^71 + 4 * q^72 + 18 * q^74 - 38 * q^75 - 64 * q^76 - 28 * q^77 + 68 * q^78 - 2 * q^80 - 14 * q^81 + 56 * q^82 + 48 * q^83 - 40 * q^84 - 26 * q^85 + 60 * q^86 - 34 * q^87 + 82 * q^88 - 6 * q^89 + 46 * q^90 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 48 * q^94 - 26 * q^95 + 56 * q^96 + 66 * q^97 - 30 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.237991	+	0.137404i	−0.168285	+	0.0971595i	−0.581777	−	0.813348i	$-0.697642\pi$
$2$	−0.237991	+	0.137404i	−0.168285	+	0.0971595i	0.413492	+	0.910508i	$0.364309\pi$
$3$	0.611610	−	2.28256i	0.353113	−	1.31784i	−0.529729	−	0.848167i	$-0.677707\pi$
$3$	0.611610	−	2.28256i	0.353113	−	1.31784i	0.882842	−	0.469669i	$-0.155627\pi$
$4$	−0.962240	+	1.66665i	−0.481120	+	0.833324i
$5$	1.45395	−	1.69883i	0.650226	−	0.759741i
$5$	1.45395	−	1.69883i	0.650226	−	0.759741i
$6$	0.168076	+	0.627267i	0.0686166	+	0.256081i
$7$	−0.193052	+	0.334376i	−0.0729667	+	0.126382i	−0.900200	−	0.435476i	$-0.856580\pi$
$7$	−0.193052	+	0.334376i	−0.0729667	+	0.126382i	0.827234	+	0.561858i	$0.189913\pi$
$8$		−	1.07848i		−	0.381301i
$9$	−2.23793	−	1.29207i	−0.745977	−	0.430690i
$10$	−0.112600	+	0.604086i	−0.0356073	+	0.191029i
$11$	−1.12873	+	4.21249i	−0.340326	+	1.27011i	0.557653	+	0.830074i	$0.311702\pi$
$11$	−1.12873	+	4.21249i	−0.340326	+	1.27011i	−0.897979	+	0.440039i	$0.854965\pi$
$12$	3.21571	+	3.21571i	0.928295	+	0.928295i
$13$	−1.35750	+	3.34024i	−0.376502	+	0.926416i
$13$	−1.35750	+	3.34024i	−0.376502	+	0.926416i
$14$		−	0.106105i		−	0.0283576i
$15$	−2.98844	−	4.35775i	−0.771611	−	1.12517i
$16$	−1.77629	−	3.07663i	−0.444073	−	0.769157i
$17$	1.90527	−	0.510514i	0.462095	−	0.123818i	−0.0202583	−	0.999795i	$-0.506449\pi$
$17$	1.90527	−	0.510514i	0.462095	−	0.123818i	0.482353	+	0.875977i	$0.339782\pi$
$18$	0.710144			0.167383
$19$	−4.83947	+	1.29673i	−1.11025	+	0.297491i	−0.766932	−	0.641728i	$-0.778218\pi$
$19$	−4.83947	+	1.29673i	−1.11025	+	0.297491i	−0.343318	+	0.939219i	$0.611551\pi$
$20$	1.43231	+	4.05791i	0.320274	+	0.907376i
$21$	0.645159	+	0.645159i	0.140785	+	0.140785i
$22$	−0.310185	−	1.15763i	−0.0661318	−	0.246807i
$23$	0.322241	+	0.0863441i	0.0671918	+	0.0180040i	0.292258	−	0.956339i	$-0.405593\pi$
$23$	0.322241	+	0.0863441i	0.0671918	+	0.0180040i	−0.225067	+	0.974343i	$0.572260\pi$
$24$	−2.46170	−	0.659609i	−0.502492	−	0.134642i
$25$	−0.772064	−	4.94003i	−0.154413	−	0.988006i
$26$	−0.135891	−	0.981474i	−0.0266504	−	0.192483i
$27$	0.694880	−	0.694880i	0.133730	−	0.133730i
$28$	−0.371524	−	0.643499i	−0.0702115	−	0.121610i
$29$	7.07031	−	4.08205i	1.31292	−	0.758017i	0.330345	−	0.943860i	$-0.392835\pi$
$29$	7.07031	−	4.08205i	1.31292	−	0.758017i	0.982579	+	0.185843i	$0.0595016\pi$
$30$	1.30999	+	0.626482i	0.239171	+	0.114379i
$31$	−2.54187	+	2.54187i	−0.456534	+	0.456534i	−0.897516	−	0.440982i	$-0.854630\pi$
$31$	−2.54187	+	2.54187i	−0.456534	+	0.456534i	0.440982	+	0.897516i	$0.354630\pi$
$32$	2.71347	+	1.56662i	0.479678	+	0.276942i
$33$	8.92491	+	5.15280i	1.55363	+	0.896987i
$34$	−0.383290	+	0.383290i	−0.0657336	+	0.0657336i
$35$	0.287361	+	0.814128i	0.0485728	+	0.137613i
$36$	4.30685	−	2.48656i	0.717809	−	0.414427i
$37$	−2.41251	−	4.17859i	−0.396614	−	0.686956i	0.596691	−	0.802471i	$-0.296482\pi$
$37$	−2.41251	−	4.17859i	−0.396614	−	0.686956i	−0.993306	+	0.115514i	$0.963148\pi$
$38$	0.973575	−	0.973575i	0.157935	−	0.157935i
$39$	6.79403	+	5.14149i	1.08792	+	0.823297i
$40$	−1.83216	−	1.56806i	−0.289690	−	0.247931i
$41$	4.49768	+	1.20515i	0.702419	+	0.188213i	0.592314	−	0.805707i	$-0.298214\pi$
$41$	4.49768	+	1.20515i	0.702419	+	0.188213i	0.110105	+	0.993920i	$0.464881\pi$
$42$	−0.242190	−	0.0648946i	−0.0373707	−	0.0100135i
$43$	−1.76471	−	6.58600i	−0.269116	−	1.00436i	−0.959682	−	0.281087i	$-0.909305\pi$
$43$	−1.76471	−	6.58600i	−0.269116	−	1.00436i	0.690566	−	0.723269i	$-0.257362\pi$
$44$	−5.93462	−	5.93462i	−0.894678	−	0.894678i
$45$	−5.44885	+	1.92327i	−0.812267	+	0.286704i
$46$	−0.0885545	+	0.0237281i	−0.0130566	+	0.00349852i
$47$	−9.83310			−1.43430			−0.717152	−	0.696917i	$-0.754555\pi$
$47$	−9.83310			−1.43430			−0.717152	+	0.696917i	$0.754555\pi$
$48$	−8.10898	+	2.17280i	−1.17043	+	0.313616i
$49$	3.42546	+	5.93307i	0.489352	+	0.847582i
$50$	0.862526	+	1.06960i	0.121980	+	0.151264i
$51$		−	4.66112i		−	0.652687i
$52$	−4.26077	−	5.47658i	−0.590862	−	0.759466i
$53$	−7.17155	−	7.17155i	−0.985088	−	0.985088i	0.0148021	−	0.999890i	$-0.495288\pi$
$53$	−7.17155	−	7.17155i	−0.985088	−	0.985088i	−0.999890	+	0.0148021i	$0.995288\pi$
$54$	−0.0698958	+	0.260855i	−0.00951161	+	0.0354978i
$55$	5.51519	+	8.04227i	0.743668	+	1.08442i
$56$	0.360618	+	0.208203i	0.0481896	+	0.0278223i
$57$			11.8395i			1.56818i
$58$	−1.12178	+	1.94298i	−0.147297	+	0.255126i
$59$	−0.628209	−	2.34451i	−0.0817858	−	0.305229i	0.912900	−	0.408183i	$-0.133837\pi$
$59$	−0.628209	−	2.34451i	−0.0817858	−	0.305229i	−0.994686	+	0.102954i	$0.967171\pi$
$60$	10.1384	−	0.787474i	1.30887	−	0.101662i
$61$	−5.32338	+	9.22037i	−0.681589	+	1.18055i	0.292906	+	0.956141i	$0.405378\pi$
$61$	−5.32338	+	9.22037i	−0.681589	+	1.18055i	−0.974496	+	0.224406i	$0.927956\pi$
$62$	0.255679	−	0.954209i	0.0324713	−	0.121185i
$63$	0.864073	−	0.498873i	0.108863	−	0.0628521i
$64$	6.24413			0.780516
$65$	3.70078	+	7.16270i	0.459025	+	0.888424i
$66$	−2.83207			−0.348603
$67$	5.52170	−	3.18796i	0.674583	−	0.389471i	−0.123228	−	0.992378i	$-0.539325\pi$
$67$	5.52170	−	3.18796i	0.674583	−	0.389471i	0.797811	+	0.602908i	$0.205991\pi$
$68$	−0.982475	+	3.66665i	−0.119143	+	0.444646i
$69$	0.394171	−	0.682724i	0.0474526	−	0.0821903i
$70$	−0.180254	−	0.154271i	−0.0215445	−	0.0184389i
$71$	−1.12684	−	4.20542i	−0.133731	−	0.499091i	0.866269	−	0.499578i	$-0.166512\pi$
$71$	−1.12684	−	4.20542i	−0.133731	−	0.499091i	−1.00000		0.000486883i	$0.999845\pi$
$72$	−1.39347	+	2.41357i	−0.164222	+	0.284442i
$73$			6.08593i			0.712304i	0.934428	+	0.356152i	$0.115912\pi$
$73$			6.08593i			0.712304i	−0.934428	+	0.356152i	$0.884088\pi$
$74$	1.14831	+	0.662979i	0.133489	+	0.0770697i
$75$	−11.7481	−	1.25909i	−1.35656	−	0.145387i
$76$	2.49554	−	9.31346i	0.286258	−	1.06833i
$77$	−1.19065	−	1.19065i	−0.135687	−	0.135687i
$78$	−2.32338	−	0.290100i	−0.263071	−	0.0328474i
$79$			3.34944i			0.376842i	0.982088	+	0.188421i	$0.0603369\pi$
$79$			3.34944i			0.376842i	−0.982088	+	0.188421i	$0.939663\pi$
$80$	−7.80932	−	1.45564i	−0.873108	−	0.162745i
$81$	−5.03732	−	8.72489i	−0.559702	−	0.969433i
$82$	−1.23600	+	0.331185i	−0.136493	+	0.0365733i
$83$	5.18834			0.569494			0.284747	−	0.958603i	$-0.408090\pi$
$83$	5.18834			0.569494			0.284747	+	0.958603i	$0.408090\pi$
$84$	−1.69605	+	0.454456i	−0.185054	+	0.0495852i
$85$	1.90288	−	3.97899i	0.206396	−	0.431582i
$86$	1.32493	+	1.32493i	0.142871	+	0.142871i
$87$	−4.99324	−	18.6350i	−0.535332	−	1.99788i
$88$	4.54309	+	1.21732i	0.484295	+	0.129766i
$89$	4.82829	+	1.29374i	0.511798	+	0.137136i	0.505470	−	0.862844i	$-0.331319\pi$
$89$	4.82829	+	1.29374i	0.511798	+	0.137136i	0.00632782	+	0.999980i	$0.497986\pi$
$90$	1.03251	−	1.20642i	0.108836	−	0.127167i
$91$	−0.854827	−	1.09875i	−0.0896102	−	0.115181i
$92$	−0.453978	+	0.453978i	−0.0473305	+	0.0473305i
$93$	4.24734	+	7.35661i	0.440429	+	0.762845i
$94$	2.34019	−	1.35111i	0.241372	−	0.139356i
$95$	−4.83341	+	10.1068i	−0.495898	+	1.03694i
$96$	5.23549	−	5.23549i	0.534345	−	0.534345i
$97$	12.7722	+	7.37402i	1.29682	+	0.748718i	0.979853	−	0.199719i	$-0.0640030\pi$
$97$	12.7722	+	7.37402i	1.29682	+	0.748718i	0.316965	+	0.948437i	$0.397336\pi$
$98$	−1.63046	−	0.941346i	−0.164701	−	0.0950903i
$99$	7.96886	−	7.96886i	0.800900	−	0.800900i
$100$	8.97621	+	3.46674i	0.897621	+	0.346674i
$101$	4.57218	−	2.63975i	0.454949	−	0.262665i	−0.254969	−	0.966949i	$-0.582065\pi$
$101$	4.57218	−	2.63975i	0.454949	−	0.262665i	0.709918	+	0.704284i	$0.248732\pi$
$102$	0.640458	+	1.10930i	0.0634147	+	0.109838i
$103$	−1.21001	+	1.21001i	−0.119226	+	0.119226i	−0.764203	−	0.644976i	$-0.776867\pi$
$103$	−1.21001	+	1.21001i	−0.119226	+	0.119226i	0.644976	+	0.764203i	$0.276867\pi$
$104$	3.60238	+	1.46404i	0.353243	+	0.143560i
$105$	2.03405	−	0.157989i	0.198503	−	0.0154181i
$106$	2.69217	+	0.721364i	0.261487	+	0.0700651i
$107$	−3.91480	−	1.04897i	−0.378458	−	0.101408i	0.0645749	−	0.997913i	$-0.479431\pi$
$107$	−3.91480	−	1.04897i	−0.378458	−	0.101408i	−0.443033	+	0.896505i	$0.646098\pi$
$108$	0.489479	+	1.82676i	0.0471002	+	0.175780i
$109$	−5.02898	−	5.02898i	−0.481689	−	0.481689i	0.423982	−	0.905671i	$-0.360632\pi$
$109$	−5.02898	−	5.02898i	−0.481689	−	0.481689i	−0.905671	+	0.423982i	$0.860632\pi$
$110$	−2.41761	−	1.15618i	−0.230510	−	0.110237i
$111$	−11.0134	+	2.95103i	−1.04535	+	0.280099i
$112$	1.37167			0.129610
$113$	3.83891	−	1.02863i	0.361134	−	0.0967655i	−0.0736896	−	0.997281i	$-0.523477\pi$
$113$	3.83891	−	1.02863i	0.361134	−	0.0967655i	0.434824	+	0.900516i	$0.356811\pi$
$114$	−1.62679	−	2.81769i	−0.152363	−	0.263901i
$115$	0.615206	−	0.421893i	0.0573682	−	0.0393417i
$116$			15.7116i			1.45879i
$117$	7.35381	−	5.72124i	0.679860	−	0.528929i
$118$	0.471653	+	0.471653i	0.0434192	+	0.0434192i
$119$	−0.197111	+	0.735630i	−0.0180692	+	0.0674351i
$120$	−4.69975	+	3.22297i	−0.429026	+	0.294216i
$121$	−6.94473	−	4.00954i	−0.631339	−	0.364504i
$122$		−	2.92582i		−	0.264892i
$123$	5.50165	−	9.52914i	0.496067	−	0.859213i
$124$	−1.79052	−	6.68231i	−0.160793	−	0.600089i
$125$	−9.51483	−	5.87095i	−0.851032	−	0.525113i
$126$	−0.137095	+	0.237455i	−0.0122134	+	0.0211542i
$127$	−2.95156	+	11.0154i	−0.261908	+	0.977455i	0.702207	+	0.711972i	$0.252198\pi$
$127$	−2.95156	+	11.0154i	−0.261908	+	0.977455i	−0.964116	+	0.265483i	$0.914469\pi$
$128$	−6.91298	+	3.99121i	−0.611027	+	0.352777i
$129$	−16.1123			−1.41860
$130$	−1.86494	−	1.19616i	−0.163566	−	0.104910i
$131$	20.8627			1.82279			0.911393	−	0.411536i	$-0.135008\pi$
$131$	20.8627			1.82279			0.911393	+	0.411536i	$0.135008\pi$
$132$	−17.1758	+	9.91645i	−1.49496	+	0.863117i
$133$	0.500673	−	1.86854i	0.0434138	−	0.162023i
$134$	−0.876078	+	1.51741i	−0.0756816	+	0.131084i
$135$	−0.170165	−	2.19080i	−0.0146454	−	0.188554i
$136$	−0.550580	−	2.05479i	−0.0472119	−	0.176197i
$137$	0.121975	−	0.211266i	0.0104210	−	0.0180497i	−0.860768	−	0.508998i	$-0.830016\pi$
$137$	0.121975	−	0.211266i	0.0104210	−	0.0180497i	0.871189	+	0.490948i	$0.163349\pi$
$138$			0.216643i			0.0184419i
$139$	10.1187	+	5.84202i	0.858255	+	0.495514i	0.863428	−	0.504473i	$-0.168313\pi$
$139$	10.1187	+	5.84202i	0.858255	+	0.495514i	−0.00517263	+	0.999987i	$0.501647\pi$
$140$	−1.63337	−	0.304457i	−0.138045	−	0.0257313i
$141$	−6.01402	+	22.4446i	−0.506472	+	1.89018i
$142$	0.846020	+	0.846020i	0.0709965	+	0.0709965i
$143$	−12.5385	−	9.48868i	−1.04852	−	0.793483i
$144$			9.18038i			0.765032i
$145$	3.34516	−	17.9464i	0.277800	−	1.49036i
$146$	−0.836233	−	1.44840i	−0.0692071	−	0.119870i
$147$	15.6376	−	4.19009i	1.28977	−	0.345593i
$148$	9.28566			0.763277
$149$	−2.44620	+	0.655457i	−0.200400	+	0.0536971i	−0.357623	−	0.933866i	$-0.616413\pi$
$149$	−2.44620	+	0.655457i	−0.200400	+	0.0536971i	0.157223	+	0.987563i	$0.449746\pi$
$150$	2.96895	−	1.31459i	0.242414	−	0.107336i
$151$	2.58498	+	2.58498i	0.210362	+	0.210362i	0.804421	−	0.594059i	$-0.202475\pi$
$151$	2.58498	+	2.58498i	0.210362	+	0.210362i	−0.594059	+	0.804421i	$0.702475\pi$
$152$	1.39850	+	5.21928i	0.113433	+	0.423339i
$153$	−4.92348	−	1.31924i	−0.398039	−	0.106654i
$154$	0.446964	+	0.119764i	0.0360174	+	0.00965083i
$155$	0.622463	+	8.01398i	0.0499974	+	0.643698i
$156$	−15.1066	+	6.37592i	−1.20949	+	0.510482i
$157$	−2.21767	+	2.21767i	−0.176990	+	0.176990i	−0.790042	−	0.613053i	$-0.789941\pi$
$157$	−2.21767	+	2.21767i	−0.176990	+	0.176990i	0.613053	+	0.790042i	$0.289941\pi$
$158$	−0.460228	−	0.797137i	−0.0366137	−	0.0634169i
$159$	−20.7557	+	11.9833i	−1.64603	+	0.950337i
$160$	6.60667	−	2.33194i	0.522303	−	0.184356i
$161$	−0.0910805	+	0.0910805i	−0.00717815	+	0.00717815i
$162$	2.39768	+	1.38430i	0.188379	+	0.108761i
$163$	−12.8283	−	7.40642i	−1.00479	−	0.580116i	−0.0951279	−	0.995465i	$-0.530326\pi$
$163$	−12.8283	−	7.40642i	−1.00479	−	0.580116i	−0.909662	+	0.415349i	$0.863659\pi$
$164$	−6.33641	+	6.33641i	−0.494790	+	0.494790i
$165$	21.7301	−	7.67002i	1.69169	−	0.597110i
$166$	−1.23478	+	0.712900i	−0.0958374	+	0.0553318i
$167$	−1.73406	−	3.00348i	−0.134186	−	0.232417i	0.791100	−	0.611686i	$-0.209509\pi$
$167$	−1.73406	−	3.00348i	−0.134186	−	0.232417i	−0.925286	+	0.379270i	$0.876175\pi$
$168$	0.695792	−	0.695792i	0.0536815	−	0.0536815i
$169$	−9.31440	−	9.06873i	−0.716492	−	0.697595i
$170$	0.0938613	+	1.20843i	0.00719883	+	0.0926823i
$171$	12.5059	+	3.35094i	0.956348	+	0.256253i
$172$	12.6746	+	3.39616i	0.966432	+	0.258955i
$173$	−1.01194	−	3.77661i	−0.0769362	−	0.287130i	0.916729	−	0.399509i	$-0.130819\pi$
$173$	−1.01194	−	3.77661i	−0.0769362	−	0.287130i	−0.993665	+	0.112379i	$0.964153\pi$
$174$	3.74888	+	3.74888i	0.284202	+	0.284202i
$175$	1.80087	+	0.695523i	0.136133	+	0.0525766i
$176$	14.9652	−	4.00992i	1.12805	−	0.302259i
$177$	−5.73569			−0.431121
$178$	−1.32686	+	0.355530i	−0.0994521	+	0.0266481i
$179$	−3.24880	−	5.62708i	−0.242827	−	0.420588i	0.718692	−	0.695329i	$-0.244741\pi$
$179$	−3.24880	−	5.62708i	−0.242827	−	0.420588i	−0.961518	+	0.274741i	$0.911408\pi$
$180$	2.03769	−	10.9320i	0.151881	−	0.814820i
$181$		−	11.9845i		−	0.890802i	−0.895331	−	0.445401i	$-0.853061\pi$
$181$		−	11.9845i		−	0.890802i	0.895331	−	0.445401i	$-0.146939\pi$
$182$	0.354415	+	0.144037i	0.0262710	+	0.0106767i
$183$	17.7902	+	17.7902i	1.31509	+	1.31509i
$184$	0.0931205	−	0.347530i	0.00686493	−	0.0256203i
$185$	−10.6064	−	1.97701i	−0.779798	−	0.145352i
$186$	−2.02166	−	1.16721i	−0.148235	−	0.0855837i
$187$			8.60214i			0.629051i
$188$	9.46180	−	16.3883i	0.690073	−	1.19524i
$189$	0.0982030	+	0.366499i	0.00714322	+	0.0266588i
$190$	−0.238412	−	3.06947i	−0.0172963	−	0.222683i
$191$	2.59646	−	4.49719i	0.187873	−	0.325405i	−0.756668	−	0.653799i	$-0.773174\pi$
$191$	2.59646	−	4.49719i	0.187873	−	0.325405i	0.944541	+	0.328394i	$0.106507\pi$
$192$	3.81897	−	14.2526i	0.275610	−	1.02859i
$193$	5.77996	−	3.33706i	0.416051	−	0.240207i	−0.277335	−	0.960773i	$-0.589451\pi$
$193$	5.77996	−	3.33706i	0.416051	−	0.240207i	0.693386	+	0.720566i	$0.256118\pi$
$194$	−4.05289			−0.290980
$195$	18.6127	−	4.06646i	1.33288	−	0.291205i
$196$	−13.1845			−0.941748
$197$	−16.9716	+	9.79857i	−1.20918	+	0.698119i	−0.962580	−	0.270999i	$-0.912646\pi$
$197$	−16.9716	+	9.79857i	−1.20918	+	0.698119i	−0.246598	+	0.969118i	$0.579313\pi$
$198$	−0.801563	+	2.99147i	−0.0569646	+	0.212595i
$199$	−7.35302	+	12.7358i	−0.521242	+	0.902817i	0.478453	+	0.878113i	$0.341198\pi$
$199$	−7.35302	+	12.7358i	−0.521242	+	0.902817i	−0.999695	+	0.0247042i	$0.992136\pi$
$200$	−5.32773	+	0.832657i	−0.376727	+	0.0588777i
$201$	−3.89957	−	14.5534i	−0.275054	−	1.02652i
$202$	−0.725425	+	1.25647i	−0.0510408	+	0.0884052i
$203$			3.15219i			0.221240i
$204$	7.76844	+	4.48511i	0.543900	+	0.314021i
$205$	8.58674	−	5.88858i	0.599724	−	0.411276i
$206$	0.121712	−	0.454234i	0.00848005	−	0.0316480i
$207$	−0.609590	−	0.609590i	−0.0423694	−	0.0423694i
$208$	12.6880	−	1.75673i	0.879754	−	0.121807i
$209$		−	21.8499i		−	1.51139i
$210$	−0.462377	+	0.317087i	−0.0319070	+	0.0218811i
$211$	10.7072	+	18.5453i	0.737111	+	1.27671i	0.953791	+	0.300471i	$0.0971440\pi$
$211$	10.7072	+	18.5453i	0.737111	+	1.27671i	−0.216679	+	0.976243i	$0.569523\pi$
$212$	18.8532	−	5.05170i	1.29484	−	0.346952i
$213$	−10.2883			−0.704943
$214$	1.07582	−	0.288265i	0.0735416	−	0.0197054i
$215$	−13.7543	−	6.57776i	−0.938037	−	0.448599i
$216$	−0.749414	−	0.749414i	−0.0509912	−	0.0509912i
$217$	−0.359227	−	1.34065i	−0.0243859	−	0.0910095i
$218$	1.88786	+	0.505850i	0.127862	+	0.0342605i
$219$	13.8915	+	3.72221i	0.938700	+	0.251524i
$220$	−18.7106	+	1.45329i	−1.26147	+	0.0979809i
$221$	−0.881153	+	7.05707i	−0.0592728	+	0.474710i
$222$	2.21561	−	2.21561i	0.148702	−	0.148702i
$223$	13.6678	+	23.6733i	0.915264	+	1.58528i	0.806515	+	0.591214i	$0.201351\pi$
$223$	13.6678	+	23.6733i	0.915264	+	1.58528i	0.108749	+	0.994069i	$0.465315\pi$
$224$	−1.04768	+	0.604878i	−0.0700010	+	0.0404151i
$225$	−4.65504	+	12.0530i	−0.310336	+	0.803534i
$226$	−0.772287	+	0.772287i	−0.0513718	+	0.0513718i
$227$	5.99928	+	3.46369i	0.398186	+	0.229893i	0.685701	−	0.727883i	$-0.259496\pi$
$227$	5.99928	+	3.46369i	0.398186	+	0.229893i	−0.287515	+	0.957776i	$0.592829\pi$
$228$	−19.7322	−	11.3924i	−1.30680	−	0.754481i
$229$	4.56825	−	4.56825i	0.301879	−	0.301879i	−0.539870	−	0.841749i	$-0.681527\pi$
$229$	4.56825	−	4.56825i	0.301879	−	0.301879i	0.841749	+	0.539870i	$0.181527\pi$
$230$	−0.0884436	+	0.184939i	−0.00583180	+	0.0121945i
$231$	−3.44594	+	1.98951i	−0.226726	+	0.130900i
$232$	−4.40241	−	7.62520i	−0.289032	−	0.500619i
$233$	5.49074	−	5.49074i	0.359711	−	0.359711i	−0.503996	−	0.863706i	$-0.668137\pi$
$233$	5.49074	−	5.49074i	0.359711	−	0.359711i	0.863706	+	0.503996i	$0.168137\pi$
$234$	−0.964019	+	2.37205i	−0.0630199	+	0.155066i
$235$	−14.2968	+	16.7048i	−0.932622	+	1.08970i
$236$	4.51196	+	1.20898i	0.293703	+	0.0786976i
$237$	7.64529	+	2.04855i	0.496615	+	0.133068i
$238$	−0.0541679	−	0.202157i	−0.00351119	−	0.0131039i
$239$	8.33949	+	8.33949i	0.539437	+	0.539437i	0.923363	−	0.383927i	$-0.125429\pi$
$239$	8.33949	+	8.33949i	0.539437	+	0.539437i	−0.383927	+	0.923363i	$0.625429\pi$
$240$	−8.09883	+	16.9349i	−0.522777	+	1.09315i
$241$	−1.40952	+	0.377680i	−0.0907952	+	0.0243285i	−0.303931	−	0.952694i	$-0.598299\pi$
$241$	−1.40952	+	0.377680i	−0.0907952	+	0.0243285i	0.213135	+	0.977023i	$0.431632\pi$
$242$	2.20371			0.141660
$243$	−20.1483	+	5.39872i	−1.29251	+	0.346328i
$244$	−10.2447	−	17.7444i	−0.655853	−	1.13597i
$245$	15.0597	+	2.80710i	0.962132	+	0.179339i
$246$			3.02380i			0.192791i
$247$	2.23817	−	17.9253i	0.142412	−	1.14056i
$248$	2.74136	+	2.74136i	0.174077	+	0.174077i
$249$	3.17324	−	11.8427i	0.201096	−	0.750500i
$250$	3.07114	+	0.0898555i	0.194236	+	0.00568296i
$251$	−11.2668	−	6.50488i	−0.711153	−	0.410585i	0.100335	−	0.994954i	$-0.468009\pi$
$251$	−11.2668	−	6.50488i	−0.711153	−	0.410585i	−0.811488	+	0.584369i	$0.801342\pi$
$252$			1.92014i			0.120958i
$253$	−0.727447	+	1.25997i	−0.0457342	+	0.0792139i
$254$	−0.811113	−	3.02712i	−0.0508938	−	0.189938i
$255$	−7.91846	−	6.77703i	−0.495873	−	0.424394i
$256$	−5.14731	+	8.91540i	−0.321707	+	0.557212i
$257$	−7.62518	+	28.4576i	−0.475646	+	1.77513i	0.143276	+	0.989683i	$0.454236\pi$
$257$	−7.62518	+	28.4576i	−0.475646	+	1.77513i	−0.618922	+	0.785452i	$0.712430\pi$
$258$	3.83458	−	2.21389i	0.238730	−	0.137831i
$259$	1.86296			0.115759
$260$	−15.4987	−	0.724344i	−0.961191	−	0.0449219i
$261$	−21.0972			−1.30588
$262$	−4.96515	+	2.86663i	−0.306748	+	0.177101i
$263$	−1.30768	+	4.88034i	−0.0806351	+	0.300934i	−0.994452	−	0.105192i	$-0.966454\pi$
$263$	−1.30768	+	4.88034i	−0.0806351	+	0.300934i	0.913817	+	0.406127i	$0.133121\pi$
$264$	5.55719	−	9.62534i	0.342022	−	0.592399i
$265$	−22.6103	+	1.75619i	−1.38894	+	0.107882i
$266$	0.137589	+	0.513490i	0.00843614	+	0.0314841i
$267$	5.90606	−	10.2296i	0.361445	−	0.626041i
$268$			12.2703i			0.749529i
$269$	7.49111	+	4.32499i	0.456741	+	0.263699i	0.710673	−	0.703523i	$-0.248391\pi$
$269$	7.49111	+	4.32499i	0.456741	+	0.263699i	−0.253932	+	0.967222i	$0.581724\pi$
$270$	0.341524	+	0.498011i	0.0207845	+	0.0303080i
$271$	5.96047	−	22.2448i	0.362073	−	1.35127i	−0.509273	−	0.860605i	$-0.670086\pi$
$271$	5.96047	−	22.2448i	0.362073	−	1.35127i	0.871346	−	0.490669i	$-0.163248\pi$
$272$	−4.95497	−	4.95497i	−0.300439	−	0.300439i
$273$	−3.03079	+	1.27918i	−0.183432	+	0.0774198i
$274$			0.0670394i			0.00405000i
$275$	21.6813	+	2.32366i	1.30743	+	0.140122i
$276$	0.758574	+	1.31389i	0.0456608	+	0.0790868i
$277$	−20.9037	+	5.60114i	−1.25598	+	0.336540i	−0.824645	−	0.565650i	$-0.808625\pi$
$277$	−20.9037	+	5.60114i	−1.25598	+	0.336540i	−0.431338	+	0.902190i	$0.641958\pi$
$278$	−3.21087			−0.192575
$279$	8.97282	−	2.40426i	0.537189	−	0.143939i
$280$	0.878021	−	0.309913i	0.0524718	−	0.0185208i
$281$	8.17717	+	8.17717i	0.487809	+	0.487809i	0.907614	−	0.419805i	$-0.137902\pi$
$281$	8.17717	+	8.17717i	0.487809	+	0.487809i	−0.419805	+	0.907614i	$0.637902\pi$
$282$	−1.65270	−	6.16797i	−0.0984171	−	0.367298i
$283$	−4.34603	−	1.16452i	−0.258345	−	0.0692233i	0.127322	−	0.991861i	$-0.459362\pi$
$283$	−4.34603	−	1.16452i	−0.258345	−	0.0692233i	−0.385667	+	0.922638i	$0.626029\pi$
$284$	8.09325	+	2.16858i	0.480246	+	0.128681i
$285$	20.1133	+	17.2140i	1.19141	+	1.01967i
$286$	4.28783	+	0.535383i	0.253545	+	0.0316579i
$287$	−1.27126	+	1.27126i	−0.0750400	+	0.0750400i
$288$	−4.04837	−	7.01198i	−0.238552	−	0.413185i
$289$	−11.3530	+	6.55467i	−0.667825	+	0.385569i
$290$	1.66979	+	4.73072i	0.0980534	+	0.277797i
$291$	24.6432	−	24.6432i	1.44461	−	1.44461i
$292$	−10.1431	−	5.85613i	−0.593580	−	0.342704i
$293$	11.3497	+	6.55274i	0.663056	+	0.382815i	0.793440	−	0.608648i	$-0.208288\pi$
$293$	11.3497	+	6.55274i	0.663056	+	0.382815i	−0.130385	+	0.991463i	$0.541621\pi$
$294$	−3.14588	+	3.14588i	−0.183472	+	0.183472i
$295$	−4.89631	−	2.34157i	−0.285074	−	0.136332i
$296$	−4.50653	+	2.60185i	−0.261937	+	0.151229i
$297$	2.14284	+	3.71150i	0.124340	+	0.215363i
$298$	0.492111	−	0.492111i	0.0285072	−	0.0285072i
$299$	−0.725851	+	0.959149i	−0.0419770	+	0.0554690i
$300$	13.4030	−	18.3684i	0.773821	−	1.06050i
$301$	2.54288	+	0.681363i	0.146569	+	0.0392731i
$302$	−0.970388	−	0.260015i	−0.0558396	−	0.0149622i
$303$	−3.22899	−	12.0508i	−0.185501	−	0.692298i
$304$	12.5859	+	12.5859i	0.721849	+	0.721849i
$305$	7.92394	+	22.4495i	0.453723	+	1.28545i
$306$	1.35301	−	0.362539i	0.0773466	−	0.0207250i
$307$	7.75447			0.442571			0.221285	−	0.975209i	$-0.428975\pi$
$307$	7.75447			0.442571			0.221285	+	0.975209i	$0.428975\pi$
$308$	3.13008	−	0.838703i	0.178353	−	0.0477896i
$309$	2.02187	+	3.50198i	0.115020	+	0.199221i
$310$	−1.24930	−	1.82173i	−0.0709552	−	0.103467i
$311$		−	11.6030i		−	0.657947i	−0.944339	−	0.328974i	$-0.893297\pi$
$311$		−	11.6030i		−	0.657947i	0.944339	−	0.328974i	$-0.106703\pi$
$312$	5.54500	−	7.32724i	0.313924	−	0.414823i
$313$	−10.1565	−	10.1565i	−0.574078	−	0.574078i	0.359188	−	0.933265i	$-0.383054\pi$
$313$	−10.1565	−	10.1565i	−0.574078	−	0.574078i	−0.933265	+	0.359188i	$0.883054\pi$
$314$	0.223069	−	0.832505i	0.0125885	−	0.0469810i
$315$	0.408817	−	2.19325i	0.0230342	−	0.123576i
$316$	−5.58234	−	3.22297i	−0.314031	−	0.181306i
$317$		−	21.7686i		−	1.22265i	−0.791381	−	0.611323i	$-0.790638\pi$
$317$		−	21.7686i		−	1.22265i	0.791381	−	0.611323i	$-0.209362\pi$
$318$	3.29311	−	5.70384i	0.184669	−	0.319855i
$319$	9.21508	+	34.3911i	0.515945	+	1.92553i
$320$	9.07864	−	10.6077i	0.507512	−	0.592990i
$321$	−4.78866	+	8.29420i	−0.267277	+	0.462937i
$322$	0.00916151	−	0.0341912i	0.000510551	−	0.00190540i
$323$	−8.55848	+	4.94124i	−0.476206	+	0.274938i
$324$	19.3884			1.07714
$325$	17.5490	+	4.12720i	0.973441	+	0.228936i
$326$	4.07070			0.225455
$327$	−14.5547	+	8.40318i	−0.804878	+	0.464697i
$328$	1.29973	−	4.85066i	0.0717656	−	0.267833i
$329$	1.89830	−	3.28795i	0.104657	−	0.181270i
$330$	−4.11768	+	4.81121i	−0.226671	+	0.264848i
$331$	−5.07792	−	18.9511i	−0.279108	−	1.04164i	−0.953038	−	0.302850i	$-0.902062\pi$
$331$	−5.07792	−	18.9511i	−0.279108	−	1.04164i	0.673931	−	0.738795i	$-0.264605\pi$
$332$	−4.99243	+	8.64714i	−0.273995	+	0.474573i
$333$			12.4685i			0.683272i
$334$	0.825383	+	0.476535i	0.0451630	+	0.0260748i
$335$	2.61247	−	14.0156i	0.142734	−	0.765753i
$336$	0.838924	−	3.13091i	0.0457671	−	0.170805i
$337$	−9.35946	−	9.35946i	−0.509842	−	0.509842i	0.404636	−	0.914478i	$-0.367398\pi$
$337$	−9.35946	−	9.35946i	−0.509842	−	0.509842i	−0.914478	+	0.404636i	$0.867398\pi$
$338$	3.46283	+	0.878441i	0.188353	+	0.0477809i
$339$		−	9.39165i		−	0.510084i
$340$	4.80055	+	7.00018i	0.260346	+	0.379638i
$341$	−7.83852	−	13.5767i	−0.424480	−	0.735220i
$342$	−3.43672	+	0.920867i	−0.185837	+	0.0497948i
$343$	−5.34789			−0.288759
$344$	−7.10288	+	1.90321i	−0.382962	+	0.102614i
$345$	−0.586730	−	1.66228i	−0.0315885	−	0.0894940i
$346$	0.759754	+	0.759754i	0.0408446	+	0.0408446i
$347$	−7.15698	−	26.7102i	−0.384207	−	1.43388i	−0.839414	−	0.543493i	$-0.817101\pi$
$347$	−7.15698	−	26.7102i	−0.384207	−	1.43388i	0.455207	−	0.890386i	$-0.349565\pi$
$348$	35.8627	+	9.60939i	1.92244	+	0.515118i
$349$	−28.5113	−	7.63958i	−1.52618	−	0.408938i	−0.604406	−	0.796676i	$-0.706590\pi$
$349$	−28.5113	−	7.63958i	−1.52618	−	0.408938i	−0.921769	+	0.387739i	$0.873256\pi$
$350$	−0.524160	+	0.0819196i	−0.0280175	+	0.00437878i
$351$	1.37777	+	3.26436i	0.0735398	+	0.174239i
$352$	−9.66215	+	9.66215i	−0.514994	+	0.514994i
$353$	−7.81777	−	13.5408i	−0.416098	−	0.720702i	0.579445	−	0.815011i	$-0.303269\pi$
$353$	−7.81777	−	13.5408i	−0.416098	−	0.720702i	−0.995543	+	0.0943088i	$0.969936\pi$
$354$	1.36504	−	0.788109i	0.0725513	−	0.0418875i
$355$	−8.78267	−	4.20015i	−0.466136	−	0.222921i
$356$	−6.80218	+	6.80218i	−0.360515	+	0.360515i
$357$	1.55856	+	0.899837i	0.0824879	+	0.0476244i
$358$	1.54637	+	0.892798i	0.0817282	+	0.0471858i
$359$	14.0592	−	14.0592i	0.742017	−	0.742017i	−0.230949	−	0.972966i	$-0.574183\pi$
$359$	14.0592	−	14.0592i	0.742017	−	0.742017i	0.972966	+	0.230949i	$0.0741830\pi$
$360$	2.07421	+	5.87648i	0.109320	+	0.309718i
$361$	5.28447	−	3.05099i	0.278130	−	0.160578i
$362$	1.64672	+	2.85221i	0.0865499	+	0.149909i
$363$	−13.3995	+	13.3995i	−0.703290	+	0.703290i
$364$	2.65378	−	0.367432i	0.139096	−	0.0192587i
$365$	10.3390	+	8.84863i	0.541167	+	0.463159i
$366$	−6.67836	−	1.78946i	−0.349084	−	0.0935367i
$367$	21.2746	+	5.70052i	1.11053	+	0.297565i	0.767045	−	0.641594i	$-0.221727\pi$
$367$	21.2746	+	5.70052i	1.11053	+	0.297565i	0.343483	+	0.939159i	$0.388393\pi$
$368$	−0.306745	−	1.14479i	−0.0159902	−	0.0596761i
$369$	−8.50836	−	8.50836i	−0.442928	−	0.442928i
$370$	2.79588	−	0.986854i	0.145351	−	0.0513041i
$371$	3.78247	−	1.01351i	0.196376	−	0.0526188i
$372$	−16.3479			−0.847597
$373$	1.12584	−	0.301668i	0.0582937	−	0.0156198i	−0.229554	−	0.973296i	$-0.573727\pi$
$373$	1.12584	−	0.301668i	0.0582937	−	0.0156198i	0.287848	+	0.957676i	$0.407060\pi$
$374$	−1.18197	−	2.04723i	−0.0611183	−	0.105860i
$375$	−19.2201	+	18.1274i	−0.992524	+	0.936096i
$376$			10.6048i			0.546901i
$377$	4.03708	+	29.1579i	0.207920	+	1.50171i
$378$	−0.0737299	−	0.0737299i	−0.00379226	−	0.00379226i
$379$	6.82640	−	25.4765i	0.350649	−	1.30864i	−0.535224	−	0.844710i	$-0.679773\pi$
$379$	6.82640	−	25.4765i	0.350649	−	1.30864i	0.885873	−	0.463928i	$-0.153560\pi$
$380$	−12.1936	−	17.7808i	−0.625520	−	0.912136i
$381$	23.3380	+	13.4742i	1.19564	+	0.690304i
$382$			1.42706i			0.0730146i
$383$	−16.4001	+	28.4058i	−0.838004	+	1.45147i	0.0535563	+	0.998565i	$0.482944\pi$
$383$	−16.4001	+	28.4058i	−0.838004	+	1.45147i	−0.891561	+	0.452901i	$0.850389\pi$
$384$	4.88213	+	18.2204i	0.249140	+	0.929804i
$385$	−3.75386	+	0.291570i	−0.191314	+	0.0148598i
$386$	−0.917054	+	1.58838i	−0.0466768	+	0.0808466i
$387$	−4.56027	+	17.0192i	−0.231812	+	0.865132i
$388$	−24.5798	+	14.1912i	−1.24785	+	0.720447i
$389$	9.36826			0.474989			0.237495	−	0.971389i	$-0.423674\pi$
$389$	9.36826			0.474989			0.237495	+	0.971389i	$0.423674\pi$
$390$	−3.87091	+	3.52525i	−0.196011	+	0.178508i
$391$	0.658034			0.0332782
$392$	6.39871	−	3.69430i	0.323184	−	0.186590i
$393$	12.7599	−	47.6205i	0.643650	−	2.40213i
$394$	2.69273	−	4.66395i	0.135658	−	0.234966i
$395$	5.69014	+	4.86992i	0.286302	+	0.245032i
$396$	5.61333	+	20.9492i	0.282080	+	1.05274i
$397$	5.82600	−	10.0909i	0.292399	−	0.506449i	−0.681978	−	0.731373i	$-0.738880\pi$
$397$	5.82600	−	10.0909i	0.292399	−	0.506449i	0.974376	+	0.224924i	$0.0722133\pi$
$398$		−	4.04135i		−	0.202574i
$399$	−3.95883	−	2.28563i	−0.198189	−	0.114425i
$400$	−13.8272	+	11.1503i	−0.691362	+	0.557515i
$401$	−5.33600	+	19.9142i	−0.266467	+	0.994469i	0.694879	+	0.719126i	$0.255458\pi$
$401$	−5.33600	+	19.9142i	−0.266467	+	0.994469i	−0.961346	+	0.275342i	$0.911209\pi$
$402$	2.92776	+	2.92776i	0.146024	+	0.146024i
$403$	−5.03988	−	11.9411i	−0.251054	−	0.594827i
$404$			10.1603i			0.505493i
$405$	−22.1461	−	4.12799i	−1.10045	−	0.205121i
$406$	−0.433124	−	0.750193i	−0.0214956	−	0.0372314i
$407$	20.3253	−	5.44616i	1.00749	−	0.269956i
$408$	−5.02693			−0.248870
$409$	4.40250	−	1.17965i	0.217689	−	0.0583297i	−0.148326	−	0.988939i	$-0.547388\pi$
$409$	4.40250	−	1.17965i	0.217689	−	0.0583297i	0.366015	+	0.930609i	$0.380722\pi$
$410$	−1.23445	+	2.58129i	−0.0609653	+	0.127481i
$411$	−0.407627	−	0.407627i	−0.0201067	−	0.0201067i
$412$	−0.852344	−	3.18099i	−0.0419920	−	0.156716i
$413$	0.905223	+	0.242554i	0.0445431	+	0.0119353i
$414$	0.228837	+	0.0613168i	0.0112467	+	0.00301355i
$415$	7.54358	−	8.81412i	0.370300	−	0.432668i
$416$	−8.91642	+	6.93695i	−0.437163	+	0.340112i
$417$	19.5234	−	19.5234i	0.956067	−	0.956067i
$418$	3.00227	+	5.20008i	0.146846	+	0.254344i
$419$	0.564687	−	0.326022i	0.0275868	−	0.0159272i	−0.486143	−	0.873879i	$-0.661597\pi$
$419$	0.564687	−	0.326022i	0.0275868	−	0.0159272i	0.513730	+	0.857952i	$0.328263\pi$
$420$	−1.69393	+	3.54206i	−0.0826553	+	0.172835i
$421$	−5.58095	+	5.58095i	−0.271999	+	0.271999i	−0.829904	−	0.557906i	$-0.811605\pi$
$421$	−5.58095	+	5.58095i	−0.271999	+	0.271999i	0.557906	+	0.829904i	$0.311605\pi$
$422$	−5.09642	−	2.94242i	−0.248090	−	0.143235i
$423$	22.0058	+	12.7051i	1.06996	+	0.617741i
$424$	−7.73438	+	7.73438i	−0.375615	+	0.375615i
$425$	−3.99295	−	9.01792i	−0.193686	−	0.437434i
$426$	2.44853	−	1.41366i	0.118631	−	0.0684919i
$427$	−2.05538	−	3.56002i	−0.0994667	−	0.172281i
$428$	5.51524	−	5.51524i	0.266589	−	0.266589i
$429$	−29.3271	+	22.8164i	−1.41593	+	1.10159i
$430$	4.17722	−	0.324454i	0.201443	−	0.0156466i
$431$	−34.5325	−	9.25295i	−1.66337	−	0.445699i	−0.700060	−	0.714084i	$-0.746843\pi$
$431$	−34.5325	−	9.25295i	−1.66337	−	0.445699i	−0.963312	+	0.268385i	$0.913510\pi$
$432$	−3.37220	−	0.903577i	−0.162245	−	0.0434734i
$433$	6.82761	+	25.4810i	0.328114	+	1.22454i	0.911144	+	0.412087i	$0.135200\pi$
$433$	6.82761	+	25.4810i	0.328114	+	1.22454i	−0.583031	+	0.812450i	$0.698133\pi$
$434$	0.269705	+	0.269705i	0.0129462	+	0.0129462i
$435$	−38.9177	−	18.6117i	−1.86596	−	0.892363i
$436$	13.2206	−	3.54246i	0.633154	−	0.169653i
$437$	−1.67144			−0.0799558
$438$	−3.81750	+	1.02290i	−0.182407	+	0.0488759i
$439$	−0.864675	−	1.49766i	−0.0412687	−	0.0714794i	0.844653	−	0.535314i	$-0.179807\pi$
$439$	−0.864675	−	1.49766i	−0.0412687	−	0.0714794i	−0.885922	+	0.463834i	$0.846473\pi$
$440$	8.67343	−	5.94803i	0.413490	−	0.283561i
$441$		−	17.7038i		−	0.843036i
$442$	−0.759965	−	1.80059i	−0.0361478	−	0.0856455i
$443$	2.86737	+	2.86737i	0.136233	+	0.136233i	0.771935	−	0.635702i	$-0.219289\pi$
$443$	2.86737	+	2.86737i	0.136233	+	0.136233i	−0.635702	+	0.771935i	$0.719289\pi$
$444$	5.67920	−	21.1951i	0.269523	−	1.00587i
$445$	9.21793	−	6.32143i	0.436972	−	0.299665i
$446$	−6.50564	−	3.75603i	−0.308051	−	0.177853i
$447$			5.98448i			0.283056i
$448$	−1.20544	+	2.08788i	−0.0569517	+	0.0986432i
$449$	−5.22508	−	19.5003i	−0.246587	−	0.920274i	−0.972579	−	0.232571i	$-0.925286\pi$
$449$	−5.22508	−	19.5003i	−0.246587	−	0.920274i	0.725993	−	0.687702i	$-0.241381\pi$
$450$	−0.548277	−	3.50813i	−0.0258460	−	0.165375i
$451$	−10.1534	+	17.5861i	−0.478103	+	0.828098i
$452$	−1.97958	+	7.38790i	−0.0931117	+	0.347497i
$453$	7.48135	−	4.31936i	0.351505	−	0.202941i
$454$	−1.90370			−0.0893452
$455$	−3.10947	−	0.145323i	−0.145774	−	0.00681286i
$456$	12.7686			0.597946
$457$	12.8012	−	7.39079i	0.598816	−	0.345727i	−0.169759	−	0.985486i	$-0.554299\pi$
$457$	12.8012	−	7.39079i	0.598816	−	0.345727i	0.768576	+	0.639759i	$0.220966\pi$
$458$	−0.459507	+	1.71490i	−0.0214713	+	0.0801321i
$459$	0.969184	−	1.67868i	0.0452377	−	0.0783539i
$460$	0.111172	+	1.43129i	0.00518341	+	0.0667344i
$461$	−1.57205	−	5.86696i	−0.0732175	−	0.273252i	0.919606	−	0.392843i	$-0.128508\pi$
$461$	−1.57205	−	5.86696i	−0.0732175	−	0.273252i	−0.992823	+	0.119591i	$0.961842\pi$
$462$	0.546735	−	0.946973i	0.0254364	−	0.0440572i
$463$		−	36.0148i		−	1.67375i	−0.547396	−	0.836874i	$-0.684381\pi$
$463$		−	36.0148i		−	1.67375i	0.547396	−	0.836874i	$-0.315619\pi$
$464$	−25.1179	−	14.5018i	−1.16607	−	0.673230i
$465$	18.6731	+	3.48062i	0.865943	+	0.161410i
$466$	−0.552297	+	2.06120i	−0.0255847	+	0.0954833i
$467$	7.68952	+	7.68952i	0.355829	+	0.355829i	0.862273	−	0.506444i	$-0.169040\pi$
$467$	7.68952	+	7.68952i	0.355829	+	0.355829i	−0.506444	+	0.862273i	$0.669040\pi$
$468$	2.45917	+	17.7614i	0.113675	+	0.821022i
$469$			2.46176i			0.113674i
$470$	1.10721	−	5.94004i	0.0510717	−	0.273993i
$471$	3.70562	+	6.41832i	0.170746	+	0.295741i
$472$	−2.52851	+	0.677511i	−0.116384	+	0.0311850i
$473$	29.7353			1.36723
$474$	−2.10099	+	0.562959i	−0.0965018	+	0.0258576i
$475$	10.1423	+	22.9060i	0.465360	+	1.05100i
$476$	−1.03637	−	1.03637i	−0.0475019	−	0.0475019i
$477$	6.78329	+	25.3156i	0.310586	+	1.15912i
$478$	−3.13061	−	0.838843i	−0.143191	−	0.0383678i
$479$	−8.87096	−	2.37697i	−0.405324	−	0.108606i	0.0503960	−	0.998729i	$-0.483952\pi$
$479$	−8.87096	−	2.37697i	−0.405324	−	0.108606i	−0.455720	+	0.890123i	$0.650618\pi$
$480$	−1.28208	−	16.5064i	−0.0585189	−	0.753408i
$481$	17.2325	−	2.38594i	0.785733	−	0.108789i
$482$	0.283559	−	0.283559i	0.0129157	−	0.0129157i
$483$	0.152191	+	0.263602i	0.00692492	+	0.0119943i
$484$	13.3650	−	7.71629i	0.607500	−	0.350740i
$485$	31.0973	−	10.9763i	1.41206	−	0.498410i
$486$	4.05331	−	4.05331i	0.183862	−	0.183862i
$487$	22.2840	+	12.8657i	1.00978	+	0.582998i	0.911128	−	0.412123i	$-0.135213\pi$
$487$	22.2840	+	12.8657i	1.00978	+	0.582998i	0.0986549	+	0.995122i	$0.468546\pi$
$488$	9.94399	+	5.74117i	0.450143	+	0.259890i
$489$	−24.7515	+	24.7515i	−1.11930	+	1.11930i
$490$	−3.96980	+	1.40121i	−0.179337	+	0.0633001i
$491$	11.4291	−	6.59859i	0.515788	−	0.297790i	−0.219422	−	0.975630i	$-0.570417\pi$
$491$	11.4291	−	6.59859i	0.515788	−	0.297790i	0.735210	+	0.677840i	$0.237084\pi$
$492$	10.5878	+	18.3386i	0.477336	+	0.826769i
$493$	11.3869	−	11.3869i	0.512839	−	0.512839i
$494$	1.93035	+	4.57360i	0.0868504	+	0.205776i
$495$	−1.95144	−	25.1241i	−0.0877108	−	1.12924i
$496$	12.3355	+	3.30529i	0.553881	+	0.148412i
$497$	1.62373	+	0.435076i	0.0728341	+	0.0195158i
$498$	0.872033	+	3.25447i	0.0390767	+	0.145836i
$499$	16.7683	+	16.7683i	0.750650	+	0.750650i	0.974601	−	0.223950i	$-0.0718954\pi$
$499$	16.7683	+	16.7683i	0.750650	+	0.750650i	−0.223950	+	0.974601i	$0.571895\pi$
$500$	18.9404	−	10.2086i	0.847039	−	0.456543i
$501$	−7.91620	+	2.12114i	−0.353670	+	0.0947655i
$502$	3.57520			0.159569
$503$	−7.28214	+	1.95124i	−0.324695	+	0.0870017i	−0.417485	−	0.908684i	$-0.637088\pi$
$503$	−7.28214	+	1.95124i	−0.324695	+	0.0870017i	0.0927898	+	0.995686i	$0.470422\pi$
$504$	−0.538025	−	0.931887i	−0.0239655	−	0.0415095i
$505$	2.16322	−	11.6054i	0.0962622	−	0.516435i
$506$		−	0.399817i		−	0.0177740i
$507$	−26.3967	+	15.7141i	−1.17232	+	0.697889i
$508$	−15.5186	−	15.5186i	−0.688528	−	0.688528i
$509$	−7.93327	+	29.6074i	−0.351636	+	1.31232i	0.533030	+	0.846097i	$0.321053\pi$
$509$	−7.93327	+	29.6074i	−0.351636	+	1.31232i	−0.884666	+	0.466226i	$0.845613\pi$
$510$	2.81572	+	0.524843i	0.124682	+	0.0232404i
$511$	−2.03499	−	1.17490i	−0.0900225	−	0.0519745i
$512$		−	18.7939i		−	0.830581i
$513$	−2.46178	+	4.26392i	−0.108690	+	0.188257i
$514$	−2.09547	−	7.82039i	−0.0924271	−	0.344942i
$515$	0.296312	+	3.81491i	0.0130571	+	0.168105i
$516$	15.5039	−	26.8535i	0.682519	−	1.18216i
$517$	11.0989	−	41.4218i	0.488131	−	1.82173i
$518$	−0.443368	+	0.255979i	−0.0194805	+	0.0112471i
$519$	−9.23923			−0.405557
$520$	7.72483	−	3.99122i	0.338756	−	0.175026i
$521$	−7.16076			−0.313719			−0.156859	−	0.987621i	$-0.550137\pi$
$521$	−7.16076			−0.313719			−0.156859	+	0.987621i	$0.550137\pi$
$522$	5.02094	−	2.89884i	0.219761	−	0.126879i
$523$	2.78390	−	10.3897i	0.121731	−	0.454308i	−0.877971	−	0.478714i	$-0.841103\pi$
$523$	2.78390	−	10.3897i	0.121731	−	0.454308i	0.999702	+	0.0244065i	$0.00776960\pi$
$524$	−20.0750	+	34.7709i	−0.876979	+	1.51897i
$525$	2.68900	−	3.68521i	0.117358	−	0.160836i
$526$	−0.359362	−	1.34116i	−0.0156689	−	0.0584773i
$527$	−3.54528	+	6.14061i	−0.154435	+	0.267489i
$528$		−	36.6115i		−	1.59331i
$529$	−19.8222	−	11.4444i	−0.861835	−	0.497581i
$530$	5.13975	−	3.52472i	0.223257	−	0.153104i
$531$	−1.62338	+	6.05854i	−0.0704487	+	0.262918i
$532$	2.63243	+	2.63243i	0.114130	+	0.114130i
$533$	−10.1311	+	13.3873i	−0.438826	+	0.579870i
$534$			3.24607i			0.140471i
$535$	−7.47394	+	5.12544i	−0.323127	+	0.221592i
$536$	−3.43815	−	5.95505i	−0.148505	−	0.257219i
$537$	−14.8311	+	3.97399i	−0.640011	+	0.171490i
$538$	−2.37709			−0.102484
$539$	−28.8594	+	7.73286i	−1.24306	+	0.333078i
$540$	3.81504	+	1.82447i	0.164173	+	0.0785129i
$541$	11.1986	+	11.1986i	0.481464	+	0.481464i	0.905599	−	0.424135i	$-0.139422\pi$
$541$	11.1986	+	11.1986i	0.481464	+	0.481464i	−0.424135	+	0.905599i	$0.639422\pi$
$542$	1.63799	+	6.11306i	0.0703576	+	0.262578i
$543$	−27.3554	−	7.32985i	−1.17393	−	0.314554i
$544$	5.96966	+	1.59957i	0.255947	+	0.0685808i
$545$	−15.8553	+	1.23152i	−0.679166	+	0.0527523i
$546$	0.545536	−	0.720878i	0.0233468	−	0.0308507i
$547$	−23.6205	+	23.6205i	−1.00994	+	1.00994i	−0.00999077	+	0.999950i	$0.503180\pi$
$547$	−23.6205	+	23.6205i	−1.00994	+	1.00994i	−0.999950	+	0.00999077i	$0.996820\pi$
$548$	0.234738	+	0.406578i	0.0100275	+	0.0173681i
$549$	23.8267	−	13.7564i	1.01690	−	0.587108i
$550$	−5.47923	+	2.42609i	−0.233635	+	0.103449i
$551$	−28.9232	+	28.9232i	−1.23217	+	1.23217i
$552$	−0.736305	−	0.425106i	−0.0313392	−	0.0180937i
$553$	−1.11997	−	0.646616i	−0.0476260	−	0.0274969i
$554$	4.20528	−	4.20528i	0.178665	−	0.178665i
$555$	−10.9996	+	23.0006i	−0.466908	+	0.976320i
$556$	−19.4732	+	11.2429i	−0.825847	+	0.476803i
$557$	−15.5732	−	26.9736i	−0.659859	−	1.14291i	−0.980652	−	0.195759i	$-0.937283\pi$
$557$	−15.5732	−	26.9736i	−0.659859	−	1.14291i	0.320793	−	0.947149i	$-0.396050\pi$
$558$	−1.80510	+	1.80510i	−0.0764159	+	0.0764159i
$559$	24.3944	+	3.04592i	1.03177	+	0.128829i
$560$	1.99433	−	2.33023i	0.0842759	−	0.0984702i
$561$	19.6349	+	5.26115i	0.828986	+	0.222126i
$562$	−3.06967	−	0.822517i	−0.129486	−	0.0346958i
$563$	−5.39509	−	20.1348i	−0.227376	−	0.848579i	−0.981439	−	0.191776i	$-0.938575\pi$
$563$	−5.39509	−	20.1348i	−0.227376	−	0.848579i	0.754063	−	0.656802i	$-0.228091\pi$
$564$	−31.6204	−	31.6204i	−1.33146	−	1.33146i
$565$	3.83410	−	8.01724i	0.161302	−	0.337288i
$566$	1.19433	−	0.320019i	0.0502013	−	0.0134514i
$567$	3.88985			0.163359
$568$	−4.53546	+	1.21527i	−0.190304	+	0.0509918i
$569$	20.8728	+	36.1527i	0.875031	+	1.51560i	0.856729	+	0.515766i	$0.172493\pi$
$569$	20.8728	+	36.1527i	0.875031	+	1.51560i	0.0183019	+	0.999833i	$0.494174\pi$
$570$	−7.15206	−	1.33313i	−0.299567	−	0.0558385i
$571$			19.2151i			0.804127i	0.915612	+	0.402064i	$0.131707\pi$
$571$			19.2151i			0.804127i	−0.915612	+	0.402064i	$0.868293\pi$
$572$	27.8793	−	11.7668i	1.16569	−	0.491996i
$573$	−8.67709	−	8.67709i	−0.362491	−	0.362491i
$574$	0.127872	−	0.477224i	0.00533727	−	0.0199190i
$575$	0.177752	−	1.65854i	0.00741278	−	0.0691660i
$576$	−13.9739	−	8.06785i	−0.582247	−	0.336160i
$577$			21.8168i			0.908243i	0.890940	+	0.454122i	$0.150047\pi$
$577$			21.8168i			0.908243i	−0.890940	+	0.454122i	$0.849953\pi$
$578$	1.80128	−	3.11991i	0.0749233	−	0.129771i
$579$	−4.08196	−	15.2341i	−0.169640	−	0.633107i
$580$	26.6914	+	22.8439i	1.10830	+	0.948542i
$581$	−1.00162	+	1.73485i	−0.0415541	+	0.0719738i
$582$	−2.47879	+	9.25095i	−0.102749	+	0.383464i
$583$	38.3048	−	22.1153i	1.58642	−	0.915922i
$584$	6.56356			0.271602
$585$	0.972630	−	20.8113i	0.0402133	−	0.860441i
$586$	−3.60150			−0.148777
$587$	5.07084	−	2.92765i	0.209296	−	0.120837i	−0.391688	−	0.920098i	$-0.628109\pi$
$587$	5.07084	−	2.92765i	0.209296	−	0.120837i	0.600984	+	0.799261i	$0.294775\pi$
$588$	−8.06375	+	30.0943i	−0.332543	+	1.24107i
$589$	9.00520	−	15.5975i	0.371053	−	0.642682i
$590$	1.48702	−	0.115500i	0.0612197	−	0.00475507i
$591$	11.9858	+	44.7316i	0.493030	+	1.84001i
$592$	−8.57065	+	14.8448i	−0.352252	+	0.610118i
$593$			45.6277i			1.87370i	0.349727	+	0.936852i	$0.386274\pi$
$593$			45.6277i			1.87370i	−0.349727	+	0.936852i	$0.613726\pi$
$594$	−1.01995	−	0.588870i	−0.0418492	−	0.0241616i
$595$	0.963122	+	1.40443i	0.0394842	+	0.0575759i
$596$	1.26141	−	4.70766i	0.0516695	−	0.192833i
$597$	24.5730	+	24.5730i	1.00571	+	1.00571i
$598$	0.0409550	−	0.328004i	0.00167477	−	0.0134131i
$599$			12.7240i			0.519888i	0.965624	+	0.259944i	$0.0837041\pi$
$599$			12.7240i			0.519888i	−0.965624	+	0.259944i	$0.916296\pi$
$600$	−1.35790	+	12.6701i	−0.0554362	+	0.517255i
$601$	12.3636	+	21.4144i	0.504321	+	0.873510i	0.999988	+	0.00499702i	$0.00159061\pi$
$601$	12.3636	+	21.4144i	0.504321	+	0.873510i	−0.495666	+	0.868513i	$0.665076\pi$
$602$	−0.698805	+	0.187244i	−0.0284812	+	0.00763151i
$603$	−16.4763			−0.670965
$604$	−6.79561	+	1.82088i	−0.276510	+	0.0740905i
$605$	−16.9088	+	5.96827i	−0.687442	+	0.242644i
$606$	2.42430	+	2.42430i	0.0984804	+	0.0984804i
$607$	1.13924	+	4.25169i	0.0462402	+	0.172571i	0.985184	−	0.171499i	$-0.0548610\pi$
$607$	1.13924	+	4.25169i	0.0462402	+	0.172571i	−0.938944	+	0.344070i	$0.888194\pi$
$608$	−15.1632	−	4.06298i	−0.614950	−	0.164775i
$609$	7.19505	+	1.92791i	0.291558	+	0.0781228i
$610$	−4.97048	−	4.25400i	−0.201249	−	0.172239i
$611$	13.3484	−	32.8449i	0.540019	−	1.32876i
$612$	6.93628	−	6.93628i	0.280382	−	0.280382i
$613$	−0.580288	−	1.00509i	−0.0234376	−	0.0405951i	0.854069	−	0.520160i	$-0.174128\pi$
$613$	−0.580288	−	1.00509i	−0.0234376	−	0.0405951i	−0.877506	+	0.479565i	$0.840794\pi$
$614$	−1.84550	+	1.06550i	−0.0744781	+	0.0430000i
$615$	−8.18929	−	23.2013i	−0.330224	−	0.935565i
$616$	−1.28409	+	1.28409i	−0.0517375	+	0.0517375i
$617$	−33.3212	−	19.2380i	−1.34146	−	0.774493i	−0.354439	−	0.935079i	$-0.615328\pi$
$617$	−33.3212	−	19.2380i	−1.34146	−	0.774493i	−0.987022	+	0.160587i	$0.948661\pi$
$618$	−0.962375	−	0.555628i	−0.0387124	−	0.0223506i
$619$	24.7229	−	24.7229i	0.993698	−	0.993698i	−0.00628240	−	0.999980i	$-0.502000\pi$
$619$	24.7229	−	24.7229i	0.993698	−	0.993698i	0.999980	+	0.00628240i	$0.00199976\pi$
$620$	−13.9554	−	6.67394i	−0.560464	−	0.268032i
$621$	0.283917	−	0.163920i	0.0113932	−	0.00657787i
$622$	1.59431	+	2.76142i	0.0639258	+	0.110723i
$623$	−1.36470	+	1.36470i	−0.0546757	+	0.0546757i
$624$	3.75027	−	30.0355i	0.150131	−	1.20238i
$625$	−23.8078	+	7.62804i	−0.952313	+	0.305122i
$626$	3.81269	+	1.02161i	0.152386	+	0.0408317i
$627$	−49.8736	−	13.3636i	−1.99176	−	0.533690i
$628$	−1.56215	−	5.83002i	−0.0623365	−	0.232643i
$629$	−6.72971	−	6.72971i	−0.268331	−	0.268331i
$630$	0.204067	+	0.578148i	0.00813024	+	0.0230340i
$631$	−7.05694	+	1.89090i	−0.280933	+	0.0752756i	−0.396534	−	0.918020i	$-0.629787\pi$
$631$	−7.05694	+	1.89090i	−0.280933	+	0.0752756i	0.115601	+	0.993296i	$0.463120\pi$
$632$	3.61231			0.143690
$633$	48.8794	−	13.0972i	1.94278	−	0.520567i
$634$	2.99110	+	5.18074i	0.118792	+	0.205753i
$635$	14.4218	+	21.0300i	0.572313	+	0.834549i
$636$		−	46.1232i		−	1.82891i
$637$	−24.4679	+	3.38773i	−0.969455	+	0.134227i
$638$	−6.91860	−	6.91860i	−0.273910	−	0.273910i
$639$	−2.91191	+	10.8674i	−0.115193	+	0.429907i
$640$	−3.27072	+	17.5470i	−0.129287	+	0.693607i
$641$	−7.19858	−	4.15610i	−0.284327	−	0.164156i	0.351054	−	0.936355i	$-0.385823\pi$
$641$	−7.19858	−	4.15610i	−0.284327	−	0.164156i	−0.635381	+	0.772199i	$0.719157\pi$
$642$		−	2.63193i		−	0.103874i
$643$	−5.57779	+	9.66101i	−0.219967	+	0.380993i	−0.954797	−	0.297257i	$-0.903928\pi$
$643$	−5.57779	+	9.66101i	−0.219967	+	0.380993i	0.734831	+	0.678250i	$0.237261\pi$
$644$	−0.0641579	−	0.239440i	−0.00252817	−	0.00943528i
$645$	−23.4264	+	27.3720i	−0.922414	+	1.07777i
$646$	1.35789	−	2.35194i	0.0534257	−	0.0925360i
$647$	10.8961	−	40.6647i	0.428369	−	1.59870i	−0.328085	−	0.944648i	$-0.606403\pi$
$647$	10.8961	−	40.6647i	0.428369	−	1.59870i	0.756454	−	0.654047i	$-0.226930\pi$
$648$	−9.40963	+	5.43265i	−0.369645	+	0.213415i
$649$	10.5853			0.415509
$650$	−4.74360	+	1.42907i	−0.186059	+	0.0560526i
$651$	−3.27983			−0.128547
$652$	24.6878	−	14.2535i	0.966849	−	0.558211i
$653$	−11.0577	+	41.2678i	−0.432721	+	1.61494i	0.313742	+	0.949508i	$0.398417\pi$
$653$	−11.0577	+	41.2678i	−0.432721	+	1.61494i	−0.746463	+	0.665427i	$0.768250\pi$
$654$	2.30926	−	3.99976i	0.0902994	−	0.156403i
$655$	30.3334	−	35.4423i	1.18522	−	1.38485i
$656$	−4.28140	−	15.9784i	−0.167160	−	0.623851i
$657$	7.86345	−	13.6199i	0.306782	−	0.531363i
$658$			1.04334i			0.0406735i
$659$	15.2491	+	8.80408i	0.594021	+	0.342958i	0.766686	−	0.642023i	$-0.221904\pi$
$659$	15.2491	+	8.80408i	0.594021	+	0.342958i	−0.172665	+	0.984981i	$0.555238\pi$
$660$	−8.12635	+	43.5968i	−0.316318	+	1.69700i
$661$	7.21232	−	26.9167i	0.280527	−	1.04694i	−0.671520	−	0.740987i	$-0.734358\pi$
$661$	7.21232	−	26.9167i	0.280527	−	1.04694i	0.952047	−	0.305953i	$-0.0989751\pi$
$662$	3.81246	+	3.81246i	0.148175	+	0.148175i
$663$	15.5692	+	6.32746i	0.604659	+	0.245738i
$664$		−	5.59552i		−	0.217148i
$665$	−2.44638	−	3.56732i	−0.0948665	−	0.138335i
$666$	−1.71323	−	2.96740i	−0.0663863	−	0.114985i
$667$	2.63080	−	0.704922i	0.101865	−	0.0272947i
$668$	6.67434			0.258238
$669$	62.3951	−	16.7187i	2.41234	−	0.646383i
$670$	1.30406	+	3.69455i	0.0503800	+	0.142733i
$671$	−32.8320	−	32.8320i	−1.26747	−	1.26747i
$672$	0.739899	+	2.76134i	0.0285422	+	0.106521i
$673$	7.05459	+	1.89027i	0.271934	+	0.0728646i	0.392209	−	0.919876i	$-0.371711\pi$
$673$	7.05459	+	1.89027i	0.271934	+	0.0728646i	−0.120275	+	0.992741i	$0.538378\pi$
$674$	3.51350	+	0.941440i	0.135335	+	0.0362629i
$675$	−3.96922	−	2.89624i	−0.152775	−	0.111476i
$676$	24.0771	−	6.79753i	0.926042	−	0.261444i
$677$	3.26988	−	3.26988i	0.125672	−	0.125672i	−0.641473	−	0.767145i	$-0.721677\pi$
$677$	3.26988	−	3.26988i	0.125672	−	0.125672i	0.767145	+	0.641473i	$0.221677\pi$
$678$	1.29045	+	2.23513i	0.0495595	+	0.0858397i
$679$	−4.93138	+	2.84713i	−0.189249	+	0.109263i
$680$	−4.29126	−	2.05222i	−0.164562	−	0.0786991i
$681$	11.5753	−	11.5753i	0.443566	−	0.443566i
$682$	3.73100	+	2.15409i	0.142867	+	0.0824845i
$683$	23.4651	+	13.5476i	0.897868	+	0.518384i	0.876508	−	0.481388i	$-0.159867\pi$
$683$	23.4651	+	13.5476i	0.897868	+	0.518384i	0.0213600	+	0.999772i	$0.493200\pi$
$684$	−17.6185	+	17.6185i	−0.673660	+	0.673660i
$685$	−0.181561	−	0.514385i	−0.00693709	−	0.0196536i
$686$	1.27275	−	0.734823i	0.0485939	−	0.0280557i
$687$	−7.63332	−	13.2213i	−0.291229	−	0.504424i
$688$	−17.1280	+	17.1280i	−0.653000	+	0.653000i
$689$	33.6901	−	14.2193i	1.28349	−	0.541714i
$690$	0.368040	+	0.314988i	0.0140111	+	0.0119914i
$691$	−12.1374	−	3.25221i	−0.461729	−	0.123720i	0.0204532	−	0.999791i	$-0.493489\pi$
$691$	−12.1374	−	3.25221i	−0.461729	−	0.123720i	−0.482182	+	0.876071i	$0.660156\pi$
$692$	7.26800	+	1.94746i	0.276288	+	0.0740311i
$693$	1.12619	+	4.20299i	0.0427804	+	0.159658i
$694$	5.37339	+	5.37339i	0.203971	+	0.203971i
$695$	24.6367	−	8.69594i	0.934522	−	0.329856i
$696$	−20.0975	+	5.38511i	−0.761795	+	0.204122i
$697$	9.18452			0.347889
$698$	7.83515	−	2.09942i	0.296565	−	0.0794643i
$699$	−9.17475	−	15.8911i	−0.347021	−	0.601058i
$700$	−2.89207	+	2.33217i	−0.109310	+	0.0881476i
$701$			39.3955i			1.48795i	0.668208	+	0.743974i	$0.267062\pi$
$701$			39.3955i			1.48795i	−0.668208	+	0.743974i	$0.732938\pi$
$702$	−0.776434	−	0.587578i	−0.0293046	−	0.0221767i
$703$	17.0938	+	17.0938i	0.644705	+	0.644705i
$704$	−7.04795	+	26.3033i	−0.265630	+	0.991343i
$705$	29.3856	+	42.8501i	1.10672	+	1.61383i
$706$	3.72112	+	2.14839i	0.140046	+	0.0808557i
$707$			2.03843i			0.0766631i
$708$	5.51911	−	9.55939i	0.207421	−	0.359264i
$709$	−6.62303	−	24.7175i	−0.248733	−	0.928285i	−0.971470	−	0.237162i	$-0.923783\pi$
$709$	−6.62303	−	24.7175i	−0.248733	−	0.928285i	0.722737	−	0.691123i	$-0.242884\pi$
$710$	2.66732	−	0.207176i	0.100103	−	0.00777519i
$711$	4.32771	−	7.49582i	0.162302	−	0.281115i
$712$	1.39527	−	5.20722i	0.0522900	−	0.195149i
$713$	−1.03857	+	0.599619i	−0.0388948	+	0.0224559i
$714$	−0.494566			−0.0185087
$715$	−34.3500	+	7.50470i	−1.28462	+	0.280660i
$716$	12.5045			0.467315
$717$	24.1359	−	13.9349i	0.901371	−	0.520407i
$718$	−1.41417	+	5.27777i	−0.0527765	+	0.196965i
$719$	4.34268	−	7.52174i	0.161955	−	0.280514i	−0.773615	−	0.633656i	$-0.781554\pi$
$719$	4.34268	−	7.52174i	0.161955	−	0.280514i	0.935570	+	0.353142i	$0.114887\pi$
$720$	15.5959	+	13.3478i	0.581226	+	0.497443i
$721$	−0.171004	−	0.638194i	−0.00636851	−	0.0237676i
$722$	−0.838438	+	1.45222i	−0.0312034	+	0.0540460i
$723$			3.44830i			0.128244i
$724$	19.9740	+	11.5320i	0.742327	+	0.428583i
$725$	−25.6242	−	31.7760i	−0.951658	−	1.18013i
$726$	1.34781	−	5.03011i	0.0500220	−	0.186685i
$727$	−17.4677	−	17.4677i	−0.647841	−	0.647841i	0.304630	−	0.952471i	$-0.401467\pi$
$727$	−17.4677	−	17.4677i	−0.647841	−	0.647841i	−0.952471	+	0.304630i	$0.901467\pi$
$728$	−1.18498	+	0.921915i	−0.0439184	+	0.0341684i
$729$			19.0676i			0.706209i
$730$	−3.67643	−	0.685277i	−0.136071	−	0.0253632i
$731$	−6.72450	−	11.6472i	−0.248715	−	0.430786i
$732$	−46.7685	+	12.5316i	−1.72861	+	0.463180i
$733$	−34.2413			−1.26473			−0.632365	−	0.774670i	$-0.717916\pi$
$733$	−34.2413			−1.26473			−0.632365	+	0.774670i	$0.717916\pi$
$734$	−5.84646	+	1.56655i	−0.215797	+	0.0578225i
$735$	15.6181	−	32.6579i	0.576081	−	1.20461i
$736$	0.739121	+	0.739121i	0.0272444	+	0.0272444i
$737$	7.19670	+	26.8584i	0.265094	+	0.989344i
$738$	3.19400	+	0.855830i	0.117573	+	0.0315035i
$739$	−27.2869	−	7.31150i	−1.00376	−	0.268958i	−0.280743	−	0.959783i	$-0.590581\pi$
$739$	−27.2869	−	7.31150i	−1.00376	−	0.268958i	−0.723022	+	0.690825i	$0.757247\pi$
$740$	13.5009	−	15.7748i	0.496302	−	0.579893i
$741$	−39.5467	−	16.0720i	−1.45278	−	0.590421i
$742$	−0.760935	+	0.760935i	−0.0279348	+	0.0279348i
$743$	−15.8384	−	27.4329i	−0.581055	−	1.00642i	−0.995355	−	0.0962765i	$-0.969307\pi$
$743$	−15.8384	−	27.4329i	−0.581055	−	1.00642i	0.414299	−	0.910141i	$-0.364027\pi$
$744$	7.93397	−	4.58068i	0.290873	−	0.167936i
$745$	−2.44314	+	5.10868i	−0.0895096	+	0.187168i
$746$	−0.226489	+	0.226489i	−0.00829237	+	0.00829237i
$747$	−11.6111	−	6.70370i	−0.424830	−	0.245275i
$748$	−14.3367	−	8.27733i	−0.524203	−	0.302649i
$749$	1.10651	−	1.10651i	0.0404309	−	0.0404309i
$750$	2.08344	−	6.95510i	0.0760764	−	0.253964i
$751$	2.11351	−	1.22024i	0.0771231	−	0.0445271i	−0.460943	−	0.887430i	$-0.652489\pi$
$751$	2.11351	−	1.22024i	0.0771231	−	0.0445271i	0.538066	+	0.842903i	$0.319155\pi$
$752$	17.4665	+	30.2528i	0.636936	+	1.10321i
$753$	−21.7387	+	21.7387i	−0.792201	+	0.792201i
$754$	−4.96721	−	6.38462i	−0.180895	−	0.232514i
$755$	8.14986	−	0.633018i	0.296604	−	0.0230379i
$756$	−0.705319	−	0.188990i	−0.0256522	−	0.00687349i
$757$	−41.2367	−	11.0493i	−1.49877	−	0.401595i	−0.586084	−	0.810250i	$-0.699331\pi$
$757$	−41.2367	−	11.0493i	−1.49877	−	0.401595i	−0.912689	+	0.408655i	$0.865998\pi$
$758$	1.87595	+	7.00115i	0.0681377	+	0.254293i
$759$	2.43105	+	2.43105i	0.0882416	+	0.0882416i
$760$	10.9000	+	5.21274i	0.395385	+	0.189086i
$761$	−38.5996	+	10.3427i	−1.39923	+	0.374923i	−0.878069	−	0.478533i	$-0.841169\pi$
$761$	−38.5996	+	10.3427i	−1.39923	+	0.374923i	−0.521164	+	0.853457i	$0.674502\pi$
$762$	−7.40565			−0.268279
$763$	2.65242	−	0.710715i	0.0960242	−	0.0257296i
$764$	4.99683	+	8.65476i	0.180779	+	0.313118i
$765$	−9.39965	+	6.44605i	−0.339845	+	0.233057i
$766$		−	9.01376i		−	0.325680i
$767$	8.68401	+	1.08429i	0.313561	+	0.0391516i
$768$	17.2018	+	17.2018i	0.620716	+	0.620716i
$769$	−9.91969	+	37.0208i	−0.357713	+	1.33500i	0.519322	+	0.854579i	$0.326184\pi$
$769$	−9.91969	+	37.0208i	−0.357713	+	1.33500i	−0.877035	+	0.480426i	$0.840482\pi$
$770$	0.853322	−	0.585187i	0.0307516	−	0.0210887i
$771$	60.2925	+	34.8099i	2.17138	+	1.25365i
$772$			12.8442i			0.462274i
$773$	7.28940	−	12.6256i	0.262181	−	0.454111i	−0.704640	−	0.709565i	$-0.748891\pi$
$773$	7.28940	−	12.6256i	0.262181	−	0.454111i	0.966821	+	0.255454i	$0.0822248\pi$
$774$	−1.25320	−	4.67701i	−0.0450454	−	0.168112i
$775$	14.5194	+	10.5945i	0.521553	+	0.380564i
$776$	7.95274	−	13.7745i	0.285487	−	0.494477i
$777$	1.13940	−	4.25231i	0.0408759	−	0.152551i
$778$	−2.22956	+	1.28724i	−0.0799337	+	0.0461497i
$779$	−23.3291			−0.835853
$780$	−11.1325	+	34.9338i	−0.398609	+	1.25083i
$781$	18.9872			0.679414
$782$	−0.156606	+	0.0904167i	−0.00560023	+	0.00323329i
$783$	2.07649	−	7.74955i	0.0742075	−	0.276946i
$784$	12.1692	−	21.0777i	0.434616	−	0.752777i
$785$	0.543072	+	6.99184i	0.0193831	+	0.249549i
$786$	3.50652	+	13.0865i	0.125073	+	0.466780i
$787$	−0.473902	+	0.820823i	−0.0168928	+	0.0292592i	−0.874348	−	0.485299i	$-0.838711\pi$
$787$	−0.473902	+	0.820823i	−0.0168928	+	0.0292592i	0.857455	+	0.514558i	$0.172044\pi$
$788$		−	37.7143i		−	1.34352i
$789$	10.3399	+	5.96972i	0.368109	+	0.212528i
$790$	−2.02335	−	0.377148i	−0.0719876	−	0.0134183i
$791$	−0.397158	+	1.48222i	−0.0141213	+	0.0527015i
$792$	−8.59426	−	8.59426i	−0.305384	−	0.305384i
$793$	−23.5718	−	30.2980i	−0.837058	−	1.07591i
$794$			3.20207i			0.113637i
$795$	−9.82008	+	52.6835i	−0.348283	+	1.86849i
$796$	−14.1507	−	24.5098i	−0.501560	−	0.868727i
$797$	−4.51774	+	1.21053i	−0.160027	+	0.0428790i	−0.337943	−	0.941167i	$-0.609731\pi$
$797$	−4.51774	+	1.21053i	−0.160027	+	0.0428790i	0.177916	+	0.984046i	$0.443064\pi$
$798$	1.25622			0.0444698
$799$	−18.7347	+	5.01994i	−0.662785	+	0.177593i
$800$	5.64419	−	14.6142i	0.199552	−	0.516688i
$801$	−9.13379	−	9.13379i	−0.322726	−	0.322726i
$802$	−1.46638	−	5.47260i	−0.0517796	−	0.193244i
$803$	−25.6369	−	6.86939i	−0.904707	−	0.242415i
$804$	28.0077	+	7.50465i	0.987756	+	0.264668i
$805$	0.0223041	+	0.287157i	0.000786117	+	0.0101210i
$806$	2.84020	+	2.14937i	0.100042	+	0.0757082i
$807$	14.4537	−	14.4537i	0.508794	−	0.508794i
$808$	−2.84692	−	4.93101i	−0.100154	−	0.173472i
$809$	21.1627	−	12.2183i	0.744040	−	0.429572i	−0.0794964	−	0.996835i	$-0.525331\pi$
$809$	21.1627	−	12.2183i	0.744040	−	0.429572i	0.823536	+	0.567263i	$0.191998\pi$
$810$	5.83779	−	2.06055i	0.205119	−	0.0724003i
$811$	−9.34795	+	9.34795i	−0.328251	+	0.328251i	−0.851921	−	0.523670i	$-0.824562\pi$
$811$	−9.34795	+	9.34795i	−0.328251	+	0.328251i	0.523670	+	0.851921i	$0.324562\pi$
$812$	−5.25359	−	3.03316i	−0.184365	−	0.106443i
$813$	−47.1295	−	27.2103i	−1.65291	−	0.954305i
$814$	−4.08893	+	4.08893i	−0.143317	+	0.143317i
$815$	−31.2340	+	11.0246i	−1.09408	+	0.386174i
$816$	−14.3405	+	8.27951i	−0.502019	+	0.289841i
$817$	17.0806	+	29.5844i	0.597573	+	1.03503i
$818$	−0.885667	+	0.885667i	−0.0309666	+	0.0309666i
$819$	0.493378	+	3.56343i	0.0172400	+	0.124516i
$820$	1.55168	+	19.9773i	0.0541871	+	0.697638i
$821$	−1.89876	−	0.508771i	−0.0662672	−	0.0177562i	0.225533	−	0.974236i	$-0.427588\pi$
$821$	−1.89876	−	0.508771i	−0.0662672	−	0.0177562i	−0.291800	+	0.956479i	$0.594254\pi$
$822$	0.153021	+	0.0410019i	0.00533723	+	0.00143011i
$823$	4.25627	+	15.8846i	0.148364	+	0.553703i	0.999583	+	0.0288913i	$0.00919767\pi$
$823$	4.25627	+	15.8846i	0.148364	+	0.553703i	−0.851218	+	0.524812i	$0.824136\pi$
$824$	1.30498	+	1.30498i	0.0454610	+	0.0454610i
$825$	18.5644	−	48.0676i	0.646329	−	1.67350i
$826$	−0.248763	+	0.0666558i	−0.00865557	+	0.00231925i
$827$	27.3262			0.950225			0.475113	−	0.879925i	$-0.342407\pi$
$827$	27.3262			0.950225			0.475113	+	0.879925i	$0.342407\pi$
$828$	1.60254	−	0.429400i	0.0556922	−	0.0149227i
$829$	7.27764	+	12.6052i	0.252763	+	0.437798i	0.964286	−	0.264865i	$-0.0853274\pi$
$829$	7.27764	+	12.6052i	0.252763	+	0.437798i	−0.711523	+	0.702663i	$0.751994\pi$
$830$	−0.584208	+	3.13420i	−0.0202782	+	0.108790i
$831$			51.1397i			1.77402i
$832$	−8.47639	+	20.8569i	−0.293866	+	0.723082i
$833$	9.55534	+	9.55534i	0.331073	+	0.331073i
$834$	−1.96380	+	7.32901i	−0.0680009	+	0.253783i
$835$	−7.62366	−	1.42103i	−0.263827	−	0.0491768i
$836$	36.4161	+	21.0248i	1.25948	+	0.727159i
$837$			3.53259i			0.122104i
$838$	−0.0895937	+	0.155181i	−0.00309496	+	0.00536063i
$839$	−6.33030	−	23.6250i	−0.218546	−	0.815625i	−0.984888	−	0.173192i	$-0.944592\pi$
$839$	−6.33030	−	23.6250i	−0.218546	−	0.815625i	0.766342	−	0.642433i	$-0.222075\pi$
$840$	−0.170388	−	2.19368i	−0.00587895	−	0.0756892i
$841$	18.8262	−	32.6080i	0.649180	−	1.12441i
$842$	0.561370	−	2.09506i	0.0193461	−	0.0722006i
$843$	23.6661	−	13.6636i	0.815104	−	0.470601i
$844$	−41.2114			−1.41856
$845$	−28.9489	+	2.63813i	−0.995873	+	0.0907544i
$846$	−6.98292			−0.240078
$847$	2.68139	−	1.54810i	0.0921335	−	0.0531933i
$848$	−9.32543	+	34.8030i	−0.320237	+	1.19514i
$849$	−5.31615	+	9.20784i	−0.182450	+	0.316012i
$850$	2.18939	+	1.59754i	0.0750954	+	0.0547951i
$851$	−0.416612	−	1.55482i	−0.0142813	−	0.0532985i
$852$	9.89982	−	17.1470i	0.339162	−	0.587446i
$853$			2.94669i			0.100893i	0.998727	+	0.0504464i	$0.0160644\pi$
$853$			2.94669i			0.100893i	−0.998727	+	0.0504464i	$0.983936\pi$
$854$	0.978324	+	0.564835i	0.0334775	+	0.0193283i
$855$	23.8756	−	16.3733i	0.816528	−	0.559955i
$856$	−1.13129	+	4.22204i	−0.0386667	+	0.144306i
$857$	−13.0632	−	13.0632i	−0.446229	−	0.446229i	0.447870	−	0.894099i	$-0.352183\pi$
$857$	−13.0632	−	13.0632i	−0.446229	−	0.446229i	−0.894099	+	0.447870i	$0.852183\pi$
$858$	3.84452	−	9.45978i	0.131250	−	0.322951i
$859$			3.08382i			0.105219i	0.998615	+	0.0526093i	$0.0167538\pi$
$859$			3.08382i			0.105219i	−0.998615	+	0.0526093i	$0.983246\pi$
$860$	24.1978	−	16.5942i	0.825137	−	0.565859i
$861$	2.12421	+	3.67923i	0.0723928	+	0.125388i
$862$	9.48982	−	2.54279i	0.323225	−	0.0866078i
$863$	50.9818			1.73544			0.867720	−	0.497053i	$-0.165585\pi$
$863$	50.9818			1.73544			0.867720	+	0.497053i	$0.165585\pi$
$864$	2.97415	−	0.796920i	0.101183	−	0.0271118i
$865$	−7.88713	−	3.77188i	−0.268170	−	0.128248i
$866$	−5.12611	−	5.12611i	−0.174192	−	0.174192i
$867$	8.01780	+	29.9228i	0.272299	+	1.01623i
$868$	2.58006	+	0.691326i	0.0875730	+	0.0234651i
$869$	−14.1095	−	3.78062i	−0.478631	−	0.128249i
$870$	11.8194	−	0.918039i	0.400715	−	0.0311244i
$871$	3.15284	+	22.7715i	0.106830	+	0.771581i
$872$	−5.42366	+	5.42366i	−0.183668	+	0.183668i
$873$	−19.0555	−	33.0051i	−0.644931	−	1.11705i
$874$	0.397788	−	0.229663i	0.0134554	−	0.00776846i
$875$	3.79996	−	2.04813i	0.128462	−	0.0692394i
$876$	−19.5706	+	19.5706i	−0.661228	+	0.661228i
$877$	−23.1824	−	13.3844i	−0.782814	−	0.451958i	0.0546128	−	0.998508i	$-0.482608\pi$
$877$	−23.1824	−	13.3844i	−0.782814	−	0.451958i	−0.837427	+	0.546550i	$0.815941\pi$
$878$	0.411570	+	0.237620i	0.0138898	+	0.00801929i
$879$	21.8986	−	21.8986i	0.738621	−	0.738621i
$880$	14.9465	−	31.2536i	0.503846	−	1.05356i
$881$	27.2630	−	15.7403i	0.918512	−	0.530303i	0.0353521	−	0.999375i	$-0.488745\pi$
$881$	27.2630	−	15.7403i	0.918512	−	0.530303i	0.883160	+	0.469072i	$0.155411\pi$
$882$	2.43257	+	4.21334i	0.0819089	+	0.141870i
$883$	27.3576	−	27.3576i	0.920657	−	0.920657i	−0.0764191	−	0.997076i	$-0.524349\pi$
$883$	27.3576	−	27.3576i	0.920657	−	0.920657i	0.997076	+	0.0764191i	$0.0243487\pi$
$884$	−10.9138	−	8.25917i	−0.367070	−	0.277786i
$885$	−8.33941	+	9.74398i	−0.280326	+	0.327540i
$886$	−1.07640	−	0.288420i	−0.0361623	−	0.00968965i
$887$	1.32670	+	0.355489i	0.0445463	+	0.0119362i	0.281023	−	0.959701i	$-0.409326\pi$
$887$	1.32670	+	0.355489i	0.0445463	+	0.0119362i	−0.236477	+	0.971637i	$0.575993\pi$
$888$	3.18263	+	11.8777i	0.106802	+	0.398591i
$889$	−3.11346	−	3.11346i	−0.104422	−	0.104422i
$890$	−1.32520	+	2.77103i	−0.0444206	+	0.0928851i
$891$	42.4393	−	11.3716i	1.42177	−	0.380962i
$892$	−52.6068			−1.76141
$893$	47.5870	−	12.7509i	1.59244	−	0.426692i
$894$	−0.822293	−	1.42425i	−0.0275016	−	0.0476341i
$895$	−14.2831	−	2.66233i	−0.477430	−	0.0889918i
$896$		−	3.08204i		−	0.102964i
$897$	1.74538	+	2.24342i	0.0582764	+	0.0749057i
$898$	3.92294	+	3.92294i	0.130910	+	0.130910i
$899$	−7.59580	+	28.3479i	−0.253334	+	0.945456i
$900$	−15.6089	−	19.3562i	−0.520296	−	0.645207i
$901$	−17.3249	−	10.0025i	−0.577176	−	0.333233i
$902$		−	5.58046i		−	0.185809i
$903$	3.11050	−	5.38754i	0.103511	−	0.179286i
$904$	−1.10936	−	4.14019i	−0.0368968	−	0.137701i
$905$	−20.3597	−	17.4249i	−0.676779	−	0.579223i
$906$	−1.18700	+	2.05594i	−0.0394354	+	0.0683040i
$907$	−6.02625	+	22.4903i	−0.200098	+	0.746777i	0.790790	+	0.612088i	$0.209670\pi$
$907$	−6.02625	+	22.4903i	−0.200098	+	0.746777i	−0.990888	+	0.134689i	$0.956996\pi$
$908$	−11.5455	+	6.66580i	−0.383151	+	0.221212i
$909$	−13.6430			−0.452508
$910$	0.759995	−	0.392669i	0.0251936	−	0.0130169i
$911$	2.89704			0.0959832			0.0479916	−	0.998848i	$-0.484718\pi$
$911$	2.89704			0.0959832			0.0479916	+	0.998848i	$0.484718\pi$
$912$	36.4256	−	21.0304i	1.20617	−	0.696385i
$913$	−5.85624	+	21.8558i	−0.193813	+	0.723322i
$914$	−2.03105	+	3.51789i	−0.0671813	+	0.116361i
$915$	56.0886	−	4.35653i	1.85423	−	0.144022i
$916$	3.21792	+	12.0094i	0.106323	+	0.396803i
$917$	−4.02759	+	6.97599i	−0.133003	+	0.230368i
$918$			0.532680i			0.0175811i
$919$	−14.3846	−	8.30494i	−0.474503	−	0.273955i	0.243620	−	0.969871i	$-0.421665\pi$
$919$	−14.3846	−	8.30494i	−0.474503	−	0.273955i	−0.718123	+	0.695916i	$0.754998\pi$
$920$	−0.455003	−	0.663488i	−0.0150010	−	0.0218745i
$921$	4.74271	−	17.7000i	0.156278	−	0.583236i
$922$	1.18028	+	1.18028i	0.0388704	+	0.0388704i
$923$	15.5768	+	1.94494i	0.512716	+	0.0640183i
$924$		−	7.65756i		−	0.251915i
$925$	−18.7798	+	15.1440i	−0.617475	+	0.497932i
$926$	4.94858	+	8.57120i	0.162621	+	0.281667i
$927$	4.27135	−	1.14451i	0.140290	−	0.0375905i
$928$	25.5801			0.839708
$929$	41.3672	−	11.0843i	1.35721	−	0.363664i	0.494420	−	0.869223i	$-0.335380\pi$
$929$	41.3672	−	11.0843i	1.35721	−	0.363664i	0.862792	+	0.505559i	$0.168714\pi$
$930$	−4.92228	+	1.73740i	−0.161408	+	0.0569717i
$931$	−24.2710	−	24.2710i	−0.795451	−	0.795451i
$932$	3.86773	+	14.4346i	0.126692	+	0.472820i
$933$	−26.4846	−	7.09653i	−0.867067	−	0.232330i
$934$	−2.88661	−	0.773465i	−0.0944528	−	0.0253086i
$935$	14.6136	+	12.5071i	0.477916	+	0.409025i
$936$	−6.17025	−	7.93095i	−0.201681	−	0.259231i
$937$	27.9881	−	27.9881i	0.914331	−	0.914331i	−0.0822783	−	0.996609i	$-0.526220\pi$
$937$	27.9881	−	27.9881i	0.914331	−	0.914331i	0.996609	+	0.0822783i	$0.0262196\pi$
$938$	−0.338257	−	0.585878i	−0.0110445	−	0.0191296i
$939$	−29.3945	+	16.9709i	−0.959254	+	0.553826i
$940$	−14.0840	−	39.9018i	−0.459371	−	1.30145i
$941$	−4.15042	+	4.15042i	−0.135300	+	0.135300i	−0.771513	−	0.636213i	$-0.780500\pi$
$941$	−4.15042	+	4.15042i	−0.135300	+	0.135300i	0.636213	+	0.771513i	$0.280500\pi$
$942$	−1.76381	−	1.01834i	−0.0574680	−	0.0331792i
$943$	1.34528	+	0.776696i	0.0438083	+	0.0252927i
$944$	−6.09729	+	6.09729i	−0.198450	+	0.198450i
$945$	0.765402	+	0.366040i	0.0248985	+	0.0119073i
$946$	−7.07675	+	4.08576i	−0.230085	+	0.132840i
$947$	12.4299	+	21.5292i	0.403918	+	0.699606i	0.994195	−	0.107595i	$-0.0343148\pi$
$947$	12.4299	+	21.5292i	0.403918	+	0.699606i	−0.590277	+	0.807201i	$0.700982\pi$
$948$	−10.7708	+	10.7708i	−0.349820	+	0.349820i
$949$	−20.3285	−	8.26164i	−0.659890	−	0.268184i
$950$	−5.56115	−	4.05783i	−0.180428	−	0.131653i
$951$	−49.6881	−	13.3139i	−1.61125	−	0.431732i
$952$	0.793363	+	0.212581i	0.0257130	+	0.00688979i
$953$	8.46463	+	31.5904i	0.274196	+	1.02331i	0.956378	+	0.292131i	$0.0943645\pi$
$953$	8.46463	+	31.5904i	0.274196	+	1.02331i	−0.682182	+	0.731182i	$0.738969\pi$
$954$	−5.09284	−	5.09284i	−0.164887	−	0.164887i
$955$	−3.86486	−	10.9496i	−0.125064	−	0.354322i
$956$	−21.9236	+	5.87441i	−0.709059	+	0.189992i
$957$	84.1358			2.71973
$958$	2.43782	−	0.653211i	0.0787622	−	0.0211043i
$959$	0.0470949	+	0.0815707i	0.00152077	+	0.00263405i
$960$	−18.6602	−	27.2103i	−0.602254	−	0.878209i
$961$			18.0777i			0.583153i
$962$	−3.77334	+	2.93565i	−0.121657	+	0.0946491i
$963$	7.40571	+	7.40571i	0.238646	+	0.238646i
$964$	0.726837	−	2.71259i	0.0234098	−	0.0873667i
$965$	2.73466	−	14.6711i	0.0880318	−	0.472280i
$966$	−0.0724402	−	0.0418234i	−0.00233072	−	0.00134564i
$967$		−	30.0090i		−	0.965023i	−0.875890	−	0.482512i	$-0.839725\pi$
$967$		−	30.0090i		−	0.965023i	0.875890	−	0.482512i	$-0.160275\pi$
$968$	−4.32422	+	7.48976i	−0.138986	+	0.240730i
$969$	6.04422	+	22.5573i	0.194168	+	0.724646i
$970$	−5.89269	+	6.88518i	−0.189203	+	0.221070i
$971$	3.13659	−	5.43273i	0.100658	−	0.174345i	−0.811298	−	0.584633i	$-0.801239\pi$
$971$	3.13659	−	5.43273i	0.100658	−	0.174345i	0.911956	+	0.410288i	$0.134572\pi$
$972$	10.3897	−	38.7750i	0.333251	−	1.24371i
$973$	−3.90686	+	2.25563i	−0.125248	+	0.0723120i
$974$	−7.07119			−0.226575
$975$	20.1537	−	37.5323i	0.645435	−	1.20200i
$976$	37.8235			1.21070
$977$	13.4772	−	7.78106i	0.431174	−	0.248938i	−0.268673	−	0.963231i	$-0.586585\pi$
$977$	13.4772	−	7.78106i	0.431174	−	0.248938i	0.699847	+	0.714293i	$0.253252\pi$
$978$	2.48968	−	9.29160i	0.0796111	−	0.297113i
$979$	−10.8997	+	18.8788i	−0.348356	+	0.603370i
$980$	−19.1695	+	22.3982i	−0.612349	+	0.715484i
$981$	4.75672	+	17.7523i	0.151870	+	0.566788i
$982$	−1.81335	+	3.14082i	−0.0578663	+	0.100227i
$983$			53.4558i			1.70498i	0.522746	+	0.852488i	$0.324907\pi$
$983$			53.4558i			1.70498i	−0.522746	+	0.852488i	$0.675093\pi$
$984$	−10.2770	−	5.93342i	−0.327619	−	0.189151i
$985$	−8.02974	+	43.0786i	−0.255849	+	1.37260i
$986$	−1.14537	+	4.27459i	−0.0364761	+	0.136131i
$987$	−6.34391	−	6.34391i	−0.201929	−	0.201929i
$988$	27.7215	+	20.9787i	0.881939	+	0.667421i
$989$		−	2.27465i		−	0.0723297i
$990$	3.91658	+	5.71117i	0.124477	+	0.181513i
$991$	11.8198	+	20.4726i	0.375470	+	0.650333i	0.990397	−	0.138251i	$-0.0441480\pi$
$991$	11.8198	+	20.4726i	0.375470	+	0.650333i	−0.614927	+	0.788584i	$0.710815\pi$
$992$	−10.8795	+	2.91514i	−0.345423	+	0.0925558i
$993$	−46.3626			−1.47127
$994$	−0.446214	+	0.119563i	−0.0141531	+	0.00379230i
$995$	10.9451	+	31.0088i	0.346983	+	0.983044i
$996$	16.6842	+	16.6842i	0.528658	+	0.528658i
$997$	13.3882	+	49.9653i	0.424007	+	1.58242i	0.766082	+	0.642743i	$0.222204\pi$
$997$	13.3882	+	49.9653i	0.424007	+	1.58242i	−0.342075	+	0.939673i	$0.611130\pi$
$998$	−6.29473	−	1.68667i	−0.199256	−	0.0533905i
$999$	−4.58002	−	1.22721i	−0.144906	−	0.0388273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.t.a.28.4	yes	20
3.2	odd	2		585.2.dp.a.28.2		20
5.2	odd	4		65.2.o.a.2.4	✓	20
5.3	odd	4		325.2.s.b.132.2		20
5.4	even	2		325.2.x.b.93.2		20
13.2	odd	12		845.2.k.d.268.6		20
13.3	even	3		845.2.f.e.408.6		20
13.4	even	6		845.2.t.e.188.4		20
13.5	odd	4		845.2.o.f.258.2		20
13.6	odd	12		845.2.o.g.488.2		20
13.7	odd	12		65.2.o.a.33.4	yes	20
13.8	odd	4		845.2.o.e.258.4		20
13.9	even	3		845.2.t.f.188.2		20
13.10	even	6		845.2.f.d.408.5		20
13.11	odd	12		845.2.k.e.268.5		20
13.12	even	2		845.2.t.g.418.2		20
15.2	even	4		585.2.cf.a.262.2		20
39.20	even	12		585.2.cf.a.163.2		20
65.2	even	12		845.2.f.d.437.6		20
65.7	even	12	inner	65.2.t.a.7.4	yes	20
65.12	odd	4		845.2.o.g.587.2		20
65.17	odd	12		845.2.o.f.357.2		20
65.22	odd	12		845.2.o.e.357.4		20
65.32	even	12		845.2.t.g.657.2		20
65.33	even	12		325.2.x.b.7.2		20
65.37	even	12		845.2.f.e.437.5		20
65.42	odd	12		845.2.k.e.577.5		20
65.47	even	4		845.2.t.f.427.2		20
65.57	even	4		845.2.t.e.427.4		20
65.59	odd	12		325.2.s.b.293.2		20
65.62	odd	12		845.2.k.d.577.6		20
195.137	odd	12		585.2.dp.a.397.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.4	✓	20	5.2	odd	4
65.2.o.a.33.4	yes	20	13.7	odd	12
65.2.t.a.7.4	yes	20	65.7	even	12	inner
65.2.t.a.28.4	yes	20	1.1	even	1	trivial
325.2.s.b.132.2		20	5.3	odd	4
325.2.s.b.293.2		20	65.59	odd	12
325.2.x.b.7.2		20	65.33	even	12
325.2.x.b.93.2		20	5.4	even	2
585.2.cf.a.163.2		20	39.20	even	12
585.2.cf.a.262.2		20	15.2	even	4
585.2.dp.a.28.2		20	3.2	odd	2
585.2.dp.a.397.2		20	195.137	odd	12
845.2.f.d.408.5		20	13.10	even	6
845.2.f.d.437.6		20	65.2	even	12
845.2.f.e.408.6		20	13.3	even	3
845.2.f.e.437.5		20	65.37	even	12
845.2.k.d.268.6		20	13.2	odd	12
845.2.k.d.577.6		20	65.62	odd	12
845.2.k.e.268.5		20	13.11	odd	12
845.2.k.e.577.5		20	65.42	odd	12
845.2.o.e.258.4		20	13.8	odd	4
845.2.o.e.357.4		20	65.22	odd	12
845.2.o.f.258.2		20	13.5	odd	4
845.2.o.f.357.2		20	65.17	odd	12
845.2.o.g.488.2		20	13.6	odd	12
845.2.o.g.587.2		20	65.12	odd	4
845.2.t.e.188.4		20	13.4	even	6
845.2.t.e.427.4		20	65.57	even	4
845.2.t.f.188.2		20	13.9	even	3
845.2.t.f.427.2		20	65.47	even	4
845.2.t.g.418.2		20	13.12	even	2
845.2.t.g.657.2		20	65.32	even	12

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.237991 + 0.137404i) q^{2} +(0.611610 - 2.28256i) q^{3} +(-0.962240 + 1.66665i) q^{4} +(1.45395 - 1.69883i) q^{5} +(0.168076 + 0.627267i) q^{6} +(-0.193052 + 0.334376i) q^{7} -1.07848i q^{8} +(-2.23793 - 1.29207i) q^{9} +(-0.112600 + 0.604086i) q^{10} +(-1.12873 + 4.21249i) q^{11} +(3.21571 + 3.21571i) q^{12} +(-1.35750 + 3.34024i) q^{13} -0.106105i q^{14} +(-2.98844 - 4.35775i) q^{15} +(-1.77629 - 3.07663i) q^{16} +(1.90527 - 0.510514i) q^{17} +0.710144 q^{18} +(-4.83947 + 1.29673i) q^{19} +(1.43231 + 4.05791i) q^{20} +(0.645159 + 0.645159i) q^{21} +(-0.310185 - 1.15763i) q^{22} +(0.322241 + 0.0863441i) q^{23} +(-2.46170 - 0.659609i) q^{24} +(-0.772064 - 4.94003i) q^{25} +(-0.135891 - 0.981474i) q^{26} +(0.694880 - 0.694880i) q^{27} +(-0.371524 - 0.643499i) q^{28} +(7.07031 - 4.08205i) q^{29} +(1.30999 + 0.626482i) q^{30} +(-2.54187 + 2.54187i) q^{31} +(2.71347 + 1.56662i) q^{32} +(8.92491 + 5.15280i) q^{33} +(-0.383290 + 0.383290i) q^{34} +(0.287361 + 0.814128i) q^{35} +(4.30685 - 2.48656i) q^{36} +(-2.41251 - 4.17859i) q^{37} +(0.973575 - 0.973575i) q^{38} +(6.79403 + 5.14149i) q^{39} +(-1.83216 - 1.56806i) q^{40} +(4.49768 + 1.20515i) q^{41} +(-0.242190 - 0.0648946i) q^{42} +(-1.76471 - 6.58600i) q^{43} +(-5.93462 - 5.93462i) q^{44} +(-5.44885 + 1.92327i) q^{45} +(-0.0885545 + 0.0237281i) q^{46} -9.83310 q^{47} +(-8.10898 + 2.17280i) q^{48} +(3.42546 + 5.93307i) q^{49} +(0.862526 + 1.06960i) q^{50} -4.66112i q^{51} +(-4.26077 - 5.47658i) q^{52} +(-7.17155 - 7.17155i) q^{53} +(-0.0698958 + 0.260855i) q^{54} +(5.51519 + 8.04227i) q^{55} +(0.360618 + 0.208203i) q^{56} +11.8395i q^{57} +(-1.12178 + 1.94298i) q^{58} +(-0.628209 - 2.34451i) q^{59} +(10.1384 - 0.787474i) q^{60} +(-5.32338 + 9.22037i) q^{61} +(0.255679 - 0.954209i) q^{62} +(0.864073 - 0.498873i) q^{63} +6.24413 q^{64} +(3.70078 + 7.16270i) q^{65} -2.83207 q^{66} +(5.52170 - 3.18796i) q^{67} +(-0.982475 + 3.66665i) q^{68} +(0.394171 - 0.682724i) q^{69} +(-0.180254 - 0.154271i) q^{70} +(-1.12684 - 4.20542i) q^{71} +(-1.39347 + 2.41357i) q^{72} +6.08593i q^{73} +(1.14831 + 0.662979i) q^{74} +(-11.7481 - 1.25909i) q^{75} +(2.49554 - 9.31346i) q^{76} +(-1.19065 - 1.19065i) q^{77} +(-2.32338 - 0.290100i) q^{78} +3.34944i q^{79} +(-7.80932 - 1.45564i) q^{80} +(-5.03732 - 8.72489i) q^{81} +(-1.23600 + 0.331185i) q^{82} +5.18834 q^{83} +(-1.69605 + 0.454456i) q^{84} +(1.90288 - 3.97899i) q^{85} +(1.32493 + 1.32493i) q^{86} +(-4.99324 - 18.6350i) q^{87} +(4.54309 + 1.21732i) q^{88} +(4.82829 + 1.29374i) q^{89} +(1.03251 - 1.20642i) q^{90} +(-0.854827 - 1.09875i) q^{91} +(-0.453978 + 0.453978i) q^{92} +(4.24734 + 7.35661i) q^{93} +(2.34019 - 1.35111i) q^{94} +(-4.83341 + 10.1068i) q^{95} +(5.23549 - 5.23549i) q^{96} +(12.7722 + 7.37402i) q^{97} +(-1.63046 - 0.941346i) q^{98} +(7.96886 - 7.96886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9} - 2 q^{10} - 16 q^{11} - 24 q^{12} - 4 q^{13} - 20 q^{15} - 2 q^{16} + 4 q^{17} - 20 q^{19} + 4 q^{21} + 16 q^{22} - 10 q^{23} + 32 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9 - 2 * q^10 - 16 * q^11 - 24 * q^12 - 4 * q^13 - 20 * q^15 - 2 * q^16 + 4 * q^17 - 20 * q^19 + 4 * q^21 + 16 * q^22 - 10 * q^23 + 32 * q^24 + 18 * q^25 - 24 * q^26 + 4 * q^27 + 18 * q^28 - 26 * q^30 + 48 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 + 36 * q^36 - 4 * q^37 - 8 * q^38 + 4 * q^39 - 16 * q^40 + 10 * q^41 + 40 * q^42 + 10 * q^43 - 36 * q^44 + 4 * q^46 - 40 * q^47 - 56 * q^48 + 18 * q^49 + 36 * q^50 - 30 * q^52 - 10 * q^53 - 48 * q^54 - 10 * q^55 - 16 * q^59 + 28 * q^60 - 16 * q^61 - 44 * q^62 - 36 * q^63 + 20 * q^64 - 14 * q^65 - 32 * q^66 + 18 * q^67 + 22 * q^68 - 16 * q^69 - 12 * q^70 - 16 * q^71 + 4 * q^72 + 18 * q^74 - 38 * q^75 - 64 * q^76 - 28 * q^77 + 68 * q^78 - 2 * q^80 - 14 * q^81 + 56 * q^82 + 48 * q^83 - 40 * q^84 - 26 * q^85 + 60 * q^86 - 34 * q^87 + 82 * q^88 - 6 * q^89 + 46 * q^90 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 48 * q^94 - 26 * q^95 + 56 * q^96 + 66 * q^97 - 30 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more