LMFDB - Embedded newform 71.2.g.a.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, 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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			16.5
Character	$\chi$	$=$	71.16
Dual form			71.2.g.a.40.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.13757 + 0.387912i) q^{2} +(-1.78691 + 0.493156i) q^{3} +(2.54627 + 0.955632i) q^{4} +(-0.00692986 + 0.0213279i) q^{5} +(-4.01095 + 0.360992i) q^{6} +(-1.29201 - 2.40095i) q^{7} +(1.34221 + 0.801931i) q^{8} +(0.374497 - 0.223752i) q^{9} +O(q^{10})$	\(q+(2.13757 + 0.387912i) q^{2} +(-1.78691 + 0.493156i) q^{3} +(2.54627 + 0.955632i) q^{4} +(-0.00692986 + 0.0213279i) q^{5} +(-4.01095 + 0.360992i) q^{6} +(-1.29201 - 2.40095i) q^{7} +(1.34221 + 0.801931i) q^{8} +(0.374497 - 0.223752i) q^{9} +(-0.0230864 + 0.0429018i) q^{10} +(1.10135 - 2.57674i) q^{11} +(-5.02123 - 0.451919i) q^{12} +(2.16765 + 5.07147i) q^{13} +(-1.83040 - 5.63340i) q^{14} +(0.00186505 - 0.0415285i) q^{15} +(-1.53826 - 1.34394i) q^{16} +(-4.52281 + 3.28601i) q^{17} +(0.887311 - 0.333013i) q^{18} +(-0.0803815 - 1.78983i) q^{19} +(-0.0380269 + 0.0476843i) q^{20} +(3.49275 + 3.65313i) q^{21} +(3.35377 - 5.08075i) q^{22} +(6.37911 + 3.07202i) q^{23} +(-2.79388 - 0.771061i) q^{24} +(4.04468 + 2.93863i) q^{25} +(2.66622 + 11.6815i) q^{26} +(3.28425 - 3.43505i) q^{27} +(-0.995377 - 7.34817i) q^{28} +(-3.03565 - 4.59881i) q^{29} +(0.0200961 - 0.0880468i) q^{30} +(-4.13294 + 3.61084i) q^{31} +(-4.71650 - 5.91431i) q^{32} +(-0.697282 + 5.14755i) q^{33} +(-10.9425 + 5.26964i) q^{34} +(0.0601608 - 0.0109176i) q^{35} +(1.16740 - 0.211851i) q^{36} +(5.61345 - 2.70330i) q^{37} +(0.522477 - 3.85708i) q^{38} +(-6.37442 - 7.99326i) q^{39} +(-0.0264048 + 0.0230692i) q^{40} +(0.145743 - 0.638544i) q^{41} +(6.04891 + 9.16370i) q^{42} +(0.361507 + 2.66876i) q^{43} +(5.26676 - 5.50860i) q^{44} +(0.00217694 + 0.00953781i) q^{45} +(12.4441 + 9.04119i) q^{46} +(-6.66098 - 1.83831i) q^{47} +(3.41151 + 1.64290i) q^{48} +(-0.239016 + 0.362093i) q^{49} +(7.50586 + 7.85052i) q^{50} +(6.46133 - 8.10225i) q^{51} +(0.672969 + 14.9848i) q^{52} +(-6.99687 + 2.62597i) q^{53} +(8.35281 - 6.06867i) q^{54} +(0.0473243 + 0.0413460i) q^{55} +(0.191257 - 4.25868i) q^{56} +(1.02630 + 3.15863i) q^{57} +(-4.70499 - 11.0079i) q^{58} +(-5.38067 - 0.484269i) q^{59} +(0.0444349 - 0.103961i) q^{60} +(7.05785 - 13.1157i) q^{61} +(-10.2351 + 6.11521i) q^{62} +(-1.02107 - 0.610061i) q^{63} +(-5.85174 - 10.8744i) q^{64} +(-0.123185 + 0.0110869i) q^{65} +(-3.48729 + 10.7328i) q^{66} +(3.55888 + 1.33567i) q^{67} +(-14.6565 + 4.04494i) q^{68} +(-12.9139 - 2.34352i) q^{69} +0.132833 q^{70} +(-8.03904 + 2.52464i) q^{71} +0.682085 q^{72} +(4.85109 + 0.880343i) q^{73} +(13.0478 - 3.60097i) q^{74} +(-8.67668 - 3.25641i) q^{75} +(1.50575 - 4.63422i) q^{76} +(-7.60960 + 0.684876i) q^{77} +(-10.5251 - 19.5589i) q^{78} +(0.736717 + 0.440168i) q^{79} +(0.0393234 - 0.0234946i) q^{80} +(-4.79481 + 8.91025i) q^{81} +(0.559236 - 1.30840i) q^{82} +(-8.32249 - 0.749038i) q^{83} +(5.40244 + 12.6396i) q^{84} +(-0.0387413 - 0.119234i) q^{85} +(-0.262494 + 5.84489i) q^{86} +(7.69236 + 6.72061i) q^{87} +(3.54461 - 2.57531i) q^{88} +(11.1385 - 4.18034i) q^{89} +(0.000953540 + 0.0212322i) q^{90} +(9.37574 - 11.7568i) q^{91} +(13.3072 + 13.9183i) q^{92} +(5.60448 - 8.49042i) q^{93} +(-13.5252 - 6.51340i) q^{94} +(0.0387304 + 0.0106889i) q^{95} +(11.3446 + 8.24236i) q^{96} +(2.49858 + 10.9470i) q^{97} +(-0.651374 + 0.681284i) q^{98} +(-0.164097 - 1.21141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{12}{35}\right)$

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 $

$2$	2.13757	+	0.387912i	1.51149	+	0.274295i	0.870084	−	0.492904i	$-0.164065\pi$
$2$	2.13757	+	0.387912i	1.51149	+	0.274295i	0.641409	+	0.767199i	$0.278350\pi$
$3$	−1.78691	+	0.493156i	−1.03167	+	0.284724i	−0.740578	−	0.671971i	$-0.765448\pi$
$3$	−1.78691	+	0.493156i	−1.03167	+	0.284724i	−0.291095	+	0.956694i	$0.594020\pi$
$4$	2.54627	+	0.955632i	1.27314	+	0.477816i
$5$	−0.00692986	+	0.0213279i	−0.00309913	+	0.00953813i	−0.952594	−	0.304244i	$-0.901596\pi$
$5$	−0.00692986	+	0.0213279i	−0.00309913	+	0.00953813i	0.949495	+	0.313782i	$0.101596\pi$
$6$	−4.01095	+	0.360992i	−1.63746	+	0.147374i
$7$	−1.29201	−	2.40095i	−0.488333	−	0.907475i	−0.998866	−	0.0476168i	$-0.984837\pi$
$7$	−1.29201	−	2.40095i	−0.488333	−	0.907475i	0.510532	−	0.859859i	$-0.329448\pi$
$8$	1.34221	+	0.801931i	0.474541	+	0.283525i
$9$	0.374497	−	0.223752i	0.124832	−	0.0745838i
$10$	−0.0230864	+	0.0429018i	−0.00730057	+	0.0135667i
$11$	1.10135	−	2.57674i	0.332070	−	0.776917i	−0.667410	−	0.744690i	$-0.732597\pi$
$11$	1.10135	−	2.57674i	0.332070	−	0.776917i	0.999481	−	0.0322270i	$-0.0102599\pi$
$12$	−5.02123	−	0.451919i	−1.44951	−	0.130458i
$13$	2.16765	+	5.07147i	0.601198	+	1.40657i	0.892984	+	0.450088i	$0.148608\pi$
$13$	2.16765	+	5.07147i	0.601198	+	1.40657i	−0.291786	+	0.956484i	$0.594250\pi$
$14$	−1.83040	−	5.63340i	−0.489196	−	1.50559i
$15$	0.00186505	−	0.0415285i	0.000481554	−	0.0107226i
$16$	−1.53826	−	1.34394i	−0.384566	−	0.335985i
$17$	−4.52281	+	3.28601i	−1.09694	+	0.796975i	−0.980558	−	0.196230i	$-0.937130\pi$
$17$	−4.52281	+	3.28601i	−1.09694	+	0.796975i	−0.116384	+	0.993204i	$0.537130\pi$
$18$	0.887311	−	0.333013i	0.209141	−	0.0784920i
$19$	−0.0803815	−	1.78983i	−0.0184408	−	0.410616i	−0.986889	−	0.161401i	$-0.948399\pi$
$19$	−0.0803815	−	1.78983i	−0.0184408	−	0.410616i	0.968448	−	0.249215i	$-0.0801726\pi$
$20$	−0.0380269	+	0.0476843i	−0.00850308	+	0.0106625i
$21$	3.49275	+	3.65313i	0.762180	+	0.797178i
$22$	3.35377	−	5.08075i	0.715027	−	1.08322i
$23$	6.37911	+	3.07202i	1.33014	+	0.640559i	0.957772	−	0.287528i	$-0.0928333\pi$
$23$	6.37911	+	3.07202i	1.33014	+	0.640559i	0.372363	+	0.928087i	$0.378548\pi$
$24$	−2.79388	−	0.771061i	−0.570298	−	0.157392i
$25$	4.04468	+	2.93863i	0.808936	+	0.587726i
$26$	2.66622	+	11.6815i	0.522889	+	2.29093i
$27$	3.28425	−	3.43505i	0.632053	−	0.661076i
$28$	−0.995377	−	7.34817i	−0.188109	−	1.38867i
$29$	−3.03565	−	4.59881i	−0.563706	−	0.853978i	0.435220	−	0.900324i	$-0.356671\pi$
$29$	−3.03565	−	4.59881i	−0.563706	−	0.853978i	−0.998925	+	0.0463464i	$0.985242\pi$
$30$	0.0200961	−	0.0880468i	0.00366903	−	0.0160751i
$31$	−4.13294	+	3.61084i	−0.742297	+	0.648525i	−0.943632	−	0.330997i	$-0.892615\pi$
$31$	−4.13294	+	3.61084i	−0.742297	+	0.648525i	0.201335	+	0.979523i	$0.435472\pi$
$32$	−4.71650	−	5.91431i	−0.833768	−	1.04551i
$33$	−0.697282	+	5.14755i	−0.121381	+	0.896073i
$34$	−10.9425	+	5.26964i	−1.87663	+	0.903735i
$35$	0.0601608	−	0.0109176i	0.0101690	−	0.00184541i
$36$	1.16740	−	0.211851i	0.194566	−	0.0353085i
$37$	5.61345	−	2.70330i	0.922846	−	0.444419i	0.0887597	−	0.996053i	$-0.471710\pi$
$37$	5.61345	−	2.70330i	0.922846	−	0.444419i	0.834086	+	0.551634i	$0.185995\pi$
$38$	0.522477	−	3.85708i	0.0847569	−	0.625701i
$39$	−6.37442	−	7.99326i	−1.02072	−	1.27995i
$40$	−0.0264048	+	0.0230692i	−0.00417497	+	0.00364756i
$41$	0.145743	−	0.638544i	0.0227613	−	0.0997238i	−0.962271	−	0.272092i	$-0.912285\pi$
$41$	0.145743	−	0.638544i	0.0227613	−	0.0997238i	0.985033	+	0.172368i	$0.0551418\pi$
$42$	6.04891	+	9.16370i	0.933367	+	1.41399i
$43$	0.361507	+	2.66876i	0.0551294	+	0.406981i	0.997396	+	0.0721181i	$0.0229758\pi$
$43$	0.361507	+	2.66876i	0.0551294	+	0.406981i	−0.942267	+	0.334863i	$0.891310\pi$
$44$	5.26676	−	5.50860i	0.793994	−	0.830453i
$45$	0.00217694	+	0.00953781i	0.000324519	+	0.00142181i
$46$	12.4441	+	9.04119i	1.83479	+	1.33305i
$47$	−6.66098	−	1.83831i	−0.971604	−	0.268146i	−0.256019	−	0.966672i	$-0.582411\pi$
$47$	−6.66098	−	1.83831i	−0.971604	−	0.268146i	−0.715585	+	0.698526i	$0.753840\pi$
$48$	3.41151	+	1.64290i	0.492409	+	0.237132i
$49$	−0.239016	+	0.362093i	−0.0341451	+	0.0517276i
$50$	7.50586	+	7.85052i	1.06149	+	1.11023i
$51$	6.46133	−	8.10225i	0.904767	−	1.13454i
$52$	0.672969	+	14.9848i	0.0933240	+	2.07802i
$53$	−6.99687	+	2.62597i	−0.961093	+	0.360704i	−0.782105	−	0.623147i	$-0.785854\pi$
$53$	−6.99687	+	2.62597i	−0.961093	+	0.360704i	−0.178988	+	0.983851i	$0.557282\pi$
$54$	8.35281	−	6.06867i	1.13667	−	0.825842i
$55$	0.0473243	+	0.0413460i	0.00638121	+	0.00557510i
$56$	0.191257	−	4.25868i	0.0255578	−	0.569089i
$57$	1.02630	+	3.15863i	0.135937	+	0.418371i
$58$	−4.70499	−	11.0079i	−0.617795	−	1.44540i
$59$	−5.38067	−	0.484269i	−0.700503	−	0.0630464i	−0.266338	−	0.963880i	$-0.585814\pi$
$59$	−5.38067	−	0.484269i	−0.700503	−	0.0630464i	−0.434165	+	0.900833i	$0.642957\pi$
$60$	0.0444349	−	0.103961i	0.00573652	−	0.0134213i
$61$	7.05785	−	13.1157i	0.903665	−	1.67929i	0.186419	−	0.982470i	$-0.440312\pi$
$61$	7.05785	−	13.1157i	0.903665	−	1.67929i	0.717246	−	0.696820i	$-0.245402\pi$
$62$	−10.2351	+	6.11521i	−1.29986	+	0.776632i
$63$	−1.02107	−	0.610061i	−0.128643	−	0.0768605i
$64$	−5.85174	−	10.8744i	−0.731467	−	1.35929i
$65$	−0.123185	+	0.0110869i	−0.0152793	+	0.00137516i
$66$	−3.48729	+	10.7328i	−0.429255	+	1.32111i
$67$	3.55888	+	1.33567i	0.434787	+	0.163178i	0.559164	−	0.829057i	$-0.311122\pi$
$67$	3.55888	+	1.33567i	0.434787	+	0.163178i	−0.124378	+	0.992235i	$0.539693\pi$
$68$	−14.6565	+	4.04494i	−1.77736	+	0.490521i
$69$	−12.9139	−	2.34352i	−1.55465	−	0.282127i
$70$	0.132833			0.0158766
$71$	−8.03904	+	2.52464i	−0.954059	+	0.299620i
$71$	−8.03904	+	2.52464i	−0.954059	+	0.299620i
$72$	0.682085			0.0803845
$73$	4.85109	+	0.880343i	0.567777	+	0.103036i	0.454852	−	0.890567i	$-0.349692\pi$
$73$	4.85109	+	0.880343i	0.567777	+	0.103036i	0.112925	+	0.993603i	$0.463978\pi$
$74$	13.0478	−	3.60097i	1.51678	−	0.418604i
$75$	−8.67668	−	3.25641i	−1.00190	−	0.376018i
$76$	1.50575	−	4.63422i	0.172721	−	0.531581i
$77$	−7.60960	+	0.684876i	−0.867194	+	0.0780489i
$78$	−10.5251	−	19.5589i	−1.19173	−	2.21461i
$79$	0.736717	+	0.440168i	0.0828871	+	0.0495227i	0.553745	−	0.832686i	$-0.313198\pi$
$79$	0.736717	+	0.440168i	0.0828871	+	0.0495227i	−0.470858	+	0.882209i	$0.656055\pi$
$80$	0.0393234	−	0.0234946i	0.00439649	−	0.00262678i
$81$	−4.79481	+	8.91025i	−0.532756	+	0.990027i
$82$	0.559236	−	1.30840i	0.0617573	−	0.144488i
$83$	−8.32249	−	0.749038i	−0.913512	−	0.0822176i	−0.377099	−	0.926173i	$-0.623078\pi$
$83$	−8.32249	−	0.749038i	−0.913512	−	0.0822176i	−0.536413	+	0.843956i	$0.680221\pi$
$84$	5.40244	+	12.6396i	0.589454	+	1.37910i
$85$	−0.0387413	−	0.119234i	−0.00420209	−	0.0129327i
$86$	−0.262494	+	5.84489i	−0.0283055	+	0.630271i
$87$	7.69236	+	6.72061i	0.824708	+	0.720525i
$88$	3.54461	−	2.57531i	0.377857	−	0.274529i
$89$	11.1385	−	4.18034i	1.18068	−	0.443115i	0.317618	−	0.948219i	$-0.397117\pi$
$89$	11.1385	−	4.18034i	1.18068	−	0.443115i	0.863059	+	0.505103i	$0.168546\pi$
$90$	0.000953540		0.0212322i	0.000100512		0.00223807i
$91$	9.37574	−	11.7568i	0.982844	−	1.23245i
$92$	13.3072	+	13.9183i	1.38737	+	1.45108i
$93$	5.60448	−	8.49042i	0.581157	−	0.880415i
$94$	−13.5252	−	6.51340i	−1.39502	−	0.671806i
$95$	0.0387304	+	0.0106889i	0.00397366	+	0.00109666i
$96$	11.3446	+	8.24236i	1.15786	+	0.841233i
$97$	2.49858	+	10.9470i	0.253693	+	1.11150i	0.927862	+	0.372923i	$0.121645\pi$
$97$	2.49858	+	10.9470i	0.253693	+	1.11150i	−0.674169	+	0.738577i	$0.735498\pi$
$98$	−0.651374	+	0.681284i	−0.0657987	+	0.0688201i
$99$	−0.164097	−	1.21141i	−0.0164924	−	0.121751i
$100$	7.49060	+	11.3478i	0.749060	+	1.13478i
$101$	1.23725	−	5.42073i	0.123111	−	0.539383i	−0.875328	−	0.483529i	$-0.839355\pi$
$101$	1.23725	−	5.42073i	0.123111	−	0.539383i	0.998439	−	0.0558538i	$-0.0177881\pi$
$102$	16.9545	−	14.8127i	1.67875	−	1.46668i
$103$	8.33829	+	10.4559i	0.821596	+	1.03025i	0.998937	+	0.0460994i	$0.0146791\pi$
$103$	8.33829	+	10.4559i	0.821596	+	1.03025i	−0.177341	+	0.984150i	$0.556749\pi$
$104$	−1.15753	+	8.54526i	−0.113506	+	0.837931i
$105$	−0.102118	+	0.0491773i	−0.00996568	+	0.00479922i
$106$	−15.9750	+	2.89903i	−1.55162	+	0.281578i
$107$	−4.09907	+	0.743871i	−0.396272	+	0.0719128i	−0.373035	−	0.927817i	$-0.621683\pi$
$107$	−4.09907	+	0.743871i	−0.396272	+	0.0719128i	−0.0232369	+	0.999730i	$0.507397\pi$
$108$	11.6452	−	5.60805i	1.12056	−	0.539635i
$109$	−0.110319	+	0.814408i	−0.0105666	+	0.0780061i	−0.995465	−	0.0951262i	$-0.969675\pi$
$109$	−0.110319	+	0.814408i	−0.0105666	+	0.0780061i	0.984899	+	0.173132i	$0.0553888\pi$
$110$	0.0851206	+	0.106738i	0.00811593	+	0.0101771i
$111$	−8.69759	+	7.59885i	−0.825538	+	0.721251i
$112$	−1.23929	+	5.42968i	−0.117102	+	0.513057i
$113$	−2.74888	−	4.16437i	−0.258593	−	0.391751i	0.681965	−	0.731385i	$-0.261126\pi$
$113$	−2.74888	−	4.16437i	−0.258593	−	0.391751i	−0.940558	+	0.339633i	$0.889697\pi$
$114$	0.968521	+	7.14991i	0.0907103	+	0.669651i
$115$	−0.109726	+	0.114764i	−0.0102320	+	0.0107018i
$116$	−3.33482	−	14.6108i	−0.309630	−	1.35658i
$117$	1.94653	+	1.41423i	0.179956	+	0.130746i
$118$	−11.3137	−	3.12239i	−1.04151	−	0.287439i
$119$	13.7331	+	6.61350i	1.25891	+	0.606258i
$120$	0.0358063	−	0.0542442i	0.00326865	−	0.00495180i
$121$	2.17506	+	2.27494i	0.197733	+	0.206812i
$122$	20.1744	−	25.2979i	1.82650	−	2.29036i
$123$	0.0544712	+	1.21289i	0.00491150	+	0.109363i
$124$	−13.9742	+	5.24461i	−1.25492	+	0.470980i
$125$	−0.181417	+	0.131807i	−0.0162264	+	0.0117892i
$126$	−1.94596	−	1.70014i	−0.173360	−	0.151460i
$127$	0.335942	−	7.48033i	0.0298100	−	0.663772i	−0.927347	−	0.374202i	$-0.877917\pi$
$127$	0.335942	−	7.48033i	0.0298100	−	0.663772i	0.957157	−	0.289569i	$-0.0935120\pi$
$128$	−3.61499	−	11.1258i	−0.319523	−	0.983391i
$129$	−1.96209	−	4.59054i	−0.172753	−	0.404175i
$130$	−0.267618	−	0.0240861i	−0.0234717	−	0.00211249i
$131$	−0.750833	+	1.75666i	−0.0656006	+	0.153480i	−0.949120	−	0.314914i	$-0.898024\pi$
$131$	−0.750833	+	1.75666i	−0.0656006	+	0.153480i	0.883520	+	0.468394i	$0.155167\pi$
$132$	−6.69463	+	12.4407i	−0.582693	+	1.08282i
$133$	−4.19345	+	2.50547i	−0.363618	+	0.217252i
$134$	7.08925	+	4.23563i	0.612418	+	0.365902i
$135$	0.0505031	+	0.0938505i	0.00434662	+	0.00807737i
$136$	−8.70569	+	0.783526i	−0.746507	+	0.0671868i
$137$	−4.04155	+	12.4386i	−0.345293	+	1.06270i	0.616134	+	0.787642i	$0.288698\pi$
$137$	−4.04155	+	12.4386i	−0.345293	+	1.06270i	−0.961427	+	0.275061i	$0.911302\pi$
$138$	−26.6952	−	10.0189i	−2.27245	−	0.852865i
$139$	−0.993716	+	0.274248i	−0.0842859	+	0.0232614i	−0.307925	−	0.951410i	$-0.599635\pi$
$139$	−0.993716	+	0.274248i	−0.0842859	+	0.0232614i	0.223640	+	0.974672i	$0.428206\pi$
$140$	0.163619	+	0.0296924i	0.0138283	+	0.00250947i
$141$	12.8091			1.07872
$142$	−18.1634	+	2.27817i	−1.52424	+	0.191180i
$143$	15.4552			1.29243
$144$	−0.876784	−	0.159113i	−0.0730653	−	0.0132594i
$145$	0.119120	−	0.0328749i	0.00989235	−	0.00273012i
$146$	10.0281	+	3.76359i	0.829928	+	0.311477i
$147$	0.248531	−	0.764900i	0.0204985	−	0.0630879i
$148$	16.8767	−	1.51893i	1.38726	−	0.124856i
$149$	10.0523	+	18.6803i	0.823519	+	1.53035i	0.847595	+	0.530644i	$0.178050\pi$
$149$	10.0523	+	18.6803i	0.823519	+	1.53035i	−0.0240765	+	0.999710i	$0.507665\pi$
$150$	−17.2838	−	10.3266i	−1.41122	−	0.843164i
$151$	−19.4540	+	11.6232i	−1.58315	+	0.945886i	−0.593103	+	0.805126i	$0.702098\pi$
$151$	−19.4540	+	11.6232i	−1.58315	+	0.945886i	−0.990044	+	0.140760i	$0.955045\pi$
$152$	1.32743	−	2.46678i	0.107669	−	0.200083i
$153$	−0.958527	+	2.24259i	−0.0774923	+	0.181302i
$154$	−16.5317	−	1.48788i	−1.33217	−	0.119897i
$155$	−0.0483709	−	0.113169i	−0.00388525	−	0.00908999i
$156$	−8.59238	−	26.4446i	−0.687941	−	2.11726i
$157$	0.879305	−	19.5793i	0.0701762	−	1.56259i	−0.587456	−	0.809256i	$-0.699871\pi$
$157$	0.879305	−	19.5793i	0.0701762	−	1.56259i	0.657633	−	0.753339i	$-0.271558\pi$
$158$	1.40404	+	1.22667i	0.111699	+	0.0975888i
$159$	11.2078	−	8.14291i	0.888833	−	0.645775i
$160$	0.158825	−	0.0596078i	0.0125562	−	0.00471241i
$161$	−0.866091	−	19.2850i	−0.0682575	−	1.51987i
$162$	−13.7056	+	17.1863i	−1.07682	+	1.35029i
$163$	5.71813	+	5.98070i	0.447879	+	0.468444i	0.907732	−	0.419551i	$-0.137812\pi$
$163$	5.71813	+	5.98070i	0.447879	+	0.468444i	−0.459853	+	0.887995i	$0.652098\pi$
$164$	0.981316	−	1.48663i	0.0766279	−	0.116086i
$165$	−0.104954	−	0.0505433i	−0.00817068	−	0.00393479i
$166$	−17.4994	−	4.82952i	−1.35821	−	0.374843i
$167$	−2.73838	−	1.98955i	−0.211903	−	0.153956i	0.476772	−	0.879027i	$-0.341807\pi$
$167$	−2.73838	−	1.98955i	−0.211903	−	0.153956i	−0.688674	+	0.725071i	$0.741807\pi$
$168$	1.75843	+	7.70419i	0.135666	+	0.594391i
$169$	−12.0373	+	12.5900i	−0.925943	+	0.968461i
$170$	−0.0365603	−	0.269899i	−0.00280404	−	0.0207003i
$171$	−0.430580	−	0.652301i	−0.0329273	−	0.0498827i
$172$	−1.62985	+	7.14085i	−0.124275	+	0.544484i
$173$	−0.163684	+	0.143006i	−0.0124447	+	0.0108726i	−0.664139	−	0.747609i	$-0.731202\pi$
$173$	−0.163684	+	0.143006i	−0.0124447	+	0.0108726i	0.651694	+	0.758482i	$0.274059\pi$
$174$	13.8360	+	17.3498i	1.04890	+	1.31528i
$175$	1.82976	−	13.5078i	0.138317	−	1.02110i
$176$	−5.15716	+	2.48356i	−0.388736	+	0.187205i
$177$	9.85359	−	1.78816i	0.740641	−	0.134407i
$178$	25.4309	−	4.61503i	1.90613	−	0.345911i
$179$	16.5547	−	7.97232i	1.23736	−	0.595879i	0.303262	−	0.952907i	$-0.401924\pi$
$179$	16.5547	−	7.97232i	1.23736	−	0.595879i	0.934094	+	0.357028i	$0.116210\pi$
$180$	−0.00357155	+	0.0263662i	−0.000266207	+	0.00196522i
$181$	−1.07893	−	1.35294i	−0.0801964	−	0.100563i	0.740115	−	0.672481i	$-0.234771\pi$
$181$	−1.07893	−	1.35294i	−0.0801964	−	0.100563i	−0.820311	+	0.571918i	$0.806200\pi$
$182$	24.6019	−	21.4941i	1.82362	−	1.59325i
$183$	−6.14366	+	26.9172i	−0.454153	+	1.98977i
$184$	6.09853	+	9.23888i	0.449589	+	0.681099i
$185$	0.0187552	+	0.138457i	0.00137891	+	0.0101795i
$186$	15.2735	−	15.9748i	1.11991	−	1.17133i
$187$	3.48600	+	15.2732i	0.254922	+	1.11688i
$188$	−15.2039	−	11.0463i	−1.10886	−	0.805634i
$189$	−12.4907	−	3.44721i	−0.908563	−	0.250747i
$190$	0.0786427	+	0.0378723i	0.00570534	+	0.00274755i
$191$	9.61454	−	14.5654i	0.695684	−	1.05392i	−0.299327	−	0.954150i	$-0.596762\pi$
$191$	9.61454	−	14.5654i	0.695684	−	1.05392i	0.995011	−	0.0997651i	$-0.0318091\pi$
$192$	15.8193	+	16.5457i	1.14166	+	1.19408i
$193$	−13.9736	+	17.5223i	−1.00584	+	1.26128i	−0.0408041	+	0.999167i	$0.512992\pi$
$193$	−13.9736	+	17.5223i	−1.00584	+	1.26128i	−0.965036	+	0.262117i	$0.915579\pi$
$194$	1.09442	+	24.3693i	0.0785751	+	1.74961i
$195$	0.214653	−	0.0805608i	0.0153717	−	0.00576908i
$196$	−0.954627	+	0.693577i	−0.0681877	+	0.0495412i
$197$	−4.44961	−	3.88751i	−0.317022	−	0.276974i	0.484688	−	0.874687i	$-0.338933\pi$
$197$	−4.44961	−	3.88751i	−0.317022	−	0.276974i	−0.801710	+	0.597714i	$0.796076\pi$
$198$	0.119153	−	2.65314i	0.00846780	−	0.188550i
$199$	−6.33452	−	19.4956i	−0.449042	−	1.38201i	−0.877989	−	0.478680i	$-0.841115\pi$
$199$	−6.33452	−	19.4956i	−0.449042	−	1.38201i	0.428947	−	0.903330i	$-0.358885\pi$
$200$	3.07221	+	7.18780i	0.217238	+	0.508254i
$201$	−7.01809	−	0.631640i	−0.495018	−	0.0445524i
$202$	4.74747	−	11.1073i	0.334031	−	0.781504i
$203$	−7.11945	+	13.2302i	−0.499688	+	0.928575i
$204$	24.1951	−	14.4559i	1.69399	−	1.01211i
$205$	0.0126088	+	0.00753342i	0.000880639	+	0.000526157i
$206$	13.7677	+	25.5847i	0.959244	+	1.78257i
$207$	3.07632	−	0.276874i	0.213819	−	0.0192441i
$208$	3.48133	−	10.7144i	0.241387	−	0.742913i
$209$	−4.70047	−	1.76411i	−0.325138	−	0.122026i
$210$	−0.237361	+	0.0655074i	−0.0163794	+	0.00452044i
$211$	−15.2119	−	2.76056i	−1.04723	−	0.190045i	−0.372444	−	0.928055i	$-0.621480\pi$
$211$	−15.2119	−	2.76056i	−1.04723	−	0.190045i	−0.674790	+	0.738010i	$0.735766\pi$
$212$	−20.3254			−1.39595
$213$	13.1200	−	8.47581i	0.898967	−	0.580753i
$214$	−9.05062			−0.618687
$215$	−0.0594242	−	0.0107839i	−0.00405269	−	0.000735456i
$216$	7.16281	−	1.97681i	0.487367	−	0.134505i
$217$	14.0092	+	5.25776i	0.951009	+	0.356920i
$218$	−0.551734	+	1.69806i	−0.0373681	+	0.115007i
$219$	−9.10260	+	0.819249i	−0.615097	+	0.0553597i
$220$	0.0809890	+	0.150503i	0.00546028	+	0.0101469i
$221$	−26.4688	−	15.8143i	−1.78048	−	1.06379i
$222$	−21.5394	+	12.8692i	−1.44563	+	0.863724i
$223$	−5.08412	+	9.44788i	−0.340458	+	0.632677i	−0.992043	−	0.125899i	$-0.959819\pi$
$223$	−5.08412	+	9.44788i	−0.340458	+	0.632677i	0.651585	+	0.758576i	$0.274104\pi$
$224$	−8.10622	+	18.9654i	−0.541620	+	1.26718i
$225$	2.17224	+	0.195505i	0.144816	+	0.0130337i
$226$	−4.26052	−	9.96797i	−0.283405	−	0.663060i
$227$	1.83830	+	5.65770i	0.122012	+	0.375515i	0.993345	−	0.115178i	$-0.0367438\pi$
$227$	1.83830	+	5.65770i	0.122012	+	0.375515i	−0.871333	+	0.490693i	$0.836744\pi$
$228$	−0.405246	+	9.02349i	−0.0268380	+	0.597595i
$229$	−2.08875	−	1.82488i	−0.138028	−	0.120592i	0.586156	−	0.810198i	$-0.300641\pi$
$229$	−2.08875	−	1.82488i	−0.138028	−	0.120592i	−0.724184	+	0.689607i	$0.757783\pi$
$230$	−0.279066	+	0.202753i	−0.0184010	+	0.0133691i
$231$	13.2599	−	4.97653i	0.872438	−	0.327432i
$232$	−0.386538	−	8.60693i	−0.0253774	−	0.565073i
$233$	9.20042	−	11.5370i	0.602740	−	0.755812i	−0.383063	−	0.923722i	$-0.625131\pi$
$233$	9.20042	−	11.5370i	0.602740	−	0.755812i	0.985802	+	0.167911i	$0.0537021\pi$
$234$	3.61224	+	3.77811i	0.236140	+	0.246983i
$235$	0.0853670	−	0.129326i	0.00556873	−	0.00843627i
$236$	−13.2379	−	6.37502i	−0.861712	−	0.414978i
$237$	−1.53352	−	0.423224i	−0.0996127	−	0.0274913i
$238$	26.7900	+	19.4641i	1.73654	+	1.26167i
$239$	−1.84353	−	8.07702i	−0.119248	−	0.522459i	−0.998902	−	0.0468453i	$-0.985083\pi$
$239$	−1.84353	−	8.07702i	−0.119248	−	0.522459i	0.879654	−	0.475614i	$-0.157774\pi$
$240$	−0.0586808	+	0.0613753i	−0.00378783	+	0.00396176i
$241$	1.70546	+	12.5902i	0.109859	+	0.811009i	0.959113	+	0.283025i	$0.0913378\pi$
$241$	1.70546	+	12.5902i	0.109859	+	0.811009i	−0.849254	+	0.527985i	$0.822948\pi$
$242$	3.76688	+	5.70658i	0.242144	+	0.366833i
$243$	1.00119	−	4.38648i	0.0642261	−	0.281393i
$244$	30.5050	−	26.6514i	1.95288	−	1.70618i
$245$	−0.00606635	−	0.00760696i	−0.000387565	−	0.000485991i
$246$	−0.354061	+	2.61378i	−0.0225741	+	0.166649i
$247$	8.90284	−	4.28738i	0.566474	−	0.272799i
$248$	−8.44289	+	1.53216i	−0.536124	+	0.0972922i
$249$	15.2409	−	2.76582i	0.965855	−	0.175277i
$250$	−0.438921	+	0.211373i	−0.0277598	+	0.0133684i
$251$	−1.98899	+	14.6833i	−0.125544	+	0.926802i	0.813151	+	0.582053i	$0.197750\pi$
$251$	−1.98899	+	14.6833i	−0.125544	+	0.926802i	−0.938695	+	0.344749i	$0.887964\pi$
$252$	−2.01693	−	2.52915i	−0.127055	−	0.159321i
$253$	14.9414	−	13.0539i	0.939360	−	0.820694i
$254$	3.61981	−	15.8594i	0.227127	−	0.995109i
$255$	0.128028	+	0.193954i	0.00801742	+	0.0121459i
$256$	−0.0962166	−	0.710299i	−0.00601354	−	0.0443937i
$257$	−17.2157	+	18.0062i	−1.07388	+	1.12319i	−0.0819240	+	0.996639i	$0.526106\pi$
$257$	−17.2157	+	18.0062i	−1.07388	+	1.12319i	−0.991960	+	0.126555i	$0.959608\pi$
$258$	−2.41339	−	10.5737i	−0.150251	−	0.658293i
$259$	−13.7431	−	9.98496i	−0.853956	−	0.620435i
$260$	−0.324258	−	0.0894896i	−0.0201096	−	0.00554991i
$261$	−2.16583	−	1.04301i	−0.134062	−	0.0645607i
$262$	−2.28639	+	3.46373i	−0.141254	+	0.213990i
$263$	−4.37945	−	4.58054i	−0.270048	−	0.282448i	0.573840	−	0.818968i	$-0.305453\pi$
$263$	−4.37945	−	4.58054i	−0.270048	−	0.282448i	−0.843888	+	0.536519i	$0.819739\pi$
$264$	−5.06387	+	6.34989i	−0.311660	+	0.390809i
$265$	−0.00751912	−	0.167426i	−0.000461896	−	0.0102849i
$266$	−9.93571	+	3.72894i	−0.609198	+	0.228636i
$267$	−17.8419	+	12.9629i	−1.09191	+	0.793317i
$268$	7.78547	+	6.80196i	0.475573	+	0.415496i
$269$	0.945356	−	21.0500i	0.0576394	−	1.28344i	−0.736806	−	0.676104i	$-0.763667\pi$
$269$	0.945356	−	21.0500i	0.0576394	−	1.28344i	0.794445	−	0.607336i	$-0.207762\pi$
$270$	0.0715483	+	0.220203i	0.00435429	+	0.0134011i
$271$	−2.00826	−	4.69856i	−0.121993	−	0.285417i	0.847390	−	0.530971i	$-0.178173\pi$
$271$	−2.00826	−	4.69856i	−0.121993	−	0.285417i	−0.969383	+	0.245554i	$0.921030\pi$
$272$	11.3735	+	1.02363i	0.689618	+	0.0620667i
$273$	−10.9557	+	25.6320i	−0.663067	+	1.55132i
$274$	−13.4642	+	25.0207i	−0.813402	+	1.51155i
$275$	12.0267	−	7.18563i	0.725238	−	0.433310i
$276$	−30.6427	−	18.3081i	−1.84447	−	1.10202i
$277$	−9.42968	−	17.5233i	−0.566575	−	1.05287i	−0.989201	−	0.146568i	$-0.953177\pi$
$277$	−9.42968	−	17.5233i	−0.566575	−	1.05287i	0.422626	−	0.906304i	$-0.361108\pi$
$278$	−2.23052	+	0.200751i	−0.133778	+	0.0120402i
$279$	−0.739842	+	2.27700i	−0.0442932	+	0.136320i
$280$	0.0895033	+	0.0335911i	0.00534884	+	0.00200745i
$281$	−4.44125	+	1.22571i	−0.264943	+	0.0731195i	−0.395984	−	0.918257i	$-0.629596\pi$
$281$	−4.44125	+	1.22571i	−0.264943	+	0.0731195i	0.131041	+	0.991377i	$0.458168\pi$
$282$	27.3805	+	4.96882i	1.63048	+	0.295889i
$283$	13.2852			0.789722			0.394861	−	0.918741i	$-0.370793\pi$
$283$	13.2852			0.789722			0.394861	+	0.918741i	$0.370793\pi$
$284$	−22.8822	−	1.25393i	−1.35781	−	0.0744073i
$285$	−0.0744791			−0.00441176
$286$	33.0366	+	5.99527i	1.95350	+	0.354508i
$287$	−1.72142	+	0.475081i	−0.101612	+	0.0280431i
$288$	−3.08965	−	1.15957i	−0.182059	−	0.0683281i
$289$	4.40462	−	13.5560i	0.259095	−	0.797413i
$290$	0.267380	−	0.0240646i	0.0157011	−	0.00141312i
$291$	−9.86332	−	18.3291i	−0.578198	−	1.07447i
$292$	11.5109	+	6.87745i	0.673625	+	0.402472i
$293$	20.0294	−	11.9670i	1.17013	−	0.699121i	0.209735	−	0.977758i	$-0.432740\pi$
$293$	20.0294	−	11.9670i	1.17013	−	0.699121i	0.960396	+	0.278638i	$0.0898829\pi$
$294$	0.827968	−	1.53862i	0.0482880	−	0.0897342i
$295$	0.0476157	−	0.111403i	0.00277229	−	0.00648610i
$296$	9.70227	+	0.873220i	0.563933	+	0.0507549i
$297$	−5.23413	−	12.2459i	−0.303715	−	0.710577i
$298$	14.2412	+	43.8300i	0.824973	+	2.53901i
$299$	−1.75196	+	39.0105i	−0.101319	+	2.25603i
$300$	−18.9813	−	16.5834i	−1.09588	−	0.957444i
$301$	5.94049	−	4.31602i	0.342404	−	0.248771i
$302$	−46.0932	+	17.2991i	−2.65237	+	0.995450i
$303$	0.462417	+	10.2965i	0.0265651	+	0.591519i
$304$	−2.28178	+	2.86126i	−0.130869	+	0.164105i
$305$	0.230820	+	0.241419i	0.0132167	+	0.0138236i
$306$	−2.91885	+	4.42187i	−0.166859	+	0.252781i
$307$	8.25632	+	3.97604i	0.471213	+	0.226924i	0.654392	−	0.756155i	$-0.272925\pi$
$307$	8.25632	+	3.97604i	0.471213	+	0.226924i	−0.183179	+	0.983080i	$0.558639\pi$
$308$	−20.0306	−	5.52809i	−1.14135	−	0.314992i
$309$	−20.0561	−	14.5716i	−1.14095	−	0.828952i
$310$	−0.0594966	−	0.260672i	−0.00337918	−	0.0148052i
$311$	−3.39711	+	3.55310i	−0.192632	+	0.201478i	−0.812056	−	0.583579i	$-0.801652\pi$
$311$	−3.39711	+	3.55310i	−0.192632	+	0.201478i	0.619424	+	0.785057i	$0.287366\pi$
$312$	−2.14573	−	15.8404i	−0.121478	−	0.896789i
$313$	−14.0849	−	21.3376i	−0.796123	−	1.20607i	−0.975000	−	0.222203i	$-0.928675\pi$
$313$	−14.0849	−	21.3376i	−0.796123	−	1.20607i	0.178877	−	0.983871i	$-0.442753\pi$
$314$	9.47461	−	41.5110i	0.534683	−	2.34260i
$315$	0.0200872	−	0.0175497i	0.00113179	−	0.000988811i
$316$	1.45524	+	1.82482i	0.0818638	+	0.102654i
$317$	1.48724	−	10.9793i	0.0835320	−	0.616658i	−0.899996	−	0.435899i	$-0.856430\pi$
$317$	1.48724	−	10.9793i	0.0835320	−	0.616658i	0.983527	−	0.180759i	$-0.0578553\pi$
$318$	27.1161	−	13.0584i	1.52060	−	0.732281i
$319$	−15.1933	+	2.75717i	−0.850660	+	0.154372i
$320$	0.272479	−	0.0494476i	0.0152320	−	0.00276421i
$321$	6.95782	−	3.35071i	0.388348	−	0.187018i
$322$	5.62956	−	41.5591i	0.313723	−	2.31600i
$323$	6.24496	+	7.83093i	0.347479	+	0.435725i
$324$	−20.7238	+	18.1058i	−1.15132	+	1.00588i
$325$	−6.13573	+	26.8824i	−0.340349	+	1.49117i
$326$	9.90294	+	15.0023i	0.548473	+	0.830901i
$327$	−0.204500	−	1.50968i	−0.0113089	−	0.0834854i
$328$	0.707686	−	0.740181i	0.0390754	−	0.0408697i
$329$	4.19234	+	18.3678i	0.231131	+	1.01265i
$330$	−0.204741	−	0.148753i	−0.0112706	−	0.00818859i
$331$	27.9928	+	7.72551i	1.53862	+	0.424633i	0.929615	−	0.368532i	$-0.120140\pi$
$331$	27.9928	+	7.72551i	1.53862	+	0.424633i	0.609007	+	0.793165i	$0.291568\pi$
$332$	−20.4755	−	9.86049i	−1.12374	−	0.541165i
$333$	1.49735	−	2.26840i	0.0820545	−	0.124307i
$334$	−5.08172	−	5.31507i	−0.278060	−	0.290828i
$335$	−0.0531496	+	0.0666475i	−0.00290387	+	0.00364134i
$336$	−0.463181	−	10.3135i	−0.0252686	−	0.562648i
$337$	6.47277	−	2.42927i	0.352594	−	0.132331i	−0.168792	−	0.985652i	$-0.553987\pi$
$337$	6.47277	−	2.42927i	0.352594	−	0.132331i	0.521386	+	0.853321i	$0.325415\pi$
$338$	−30.6143	+	22.2426i	−1.66520	+	1.20984i
$339$	6.96568	+	6.08573i	0.378324	+	0.330532i
$340$	0.0152974	−	0.340624i	0.000829619	−	0.0184729i
$341$	4.75238	+	14.6263i	0.257356	+	0.792059i
$342$	−0.667361	−	1.56137i	−0.0360868	−	0.0844292i
$343$	−17.8306	−	1.60478i	−0.962760	−	0.0866500i
$344$	−1.65494	+	3.87192i	−0.0892283	+	0.208760i
$345$	0.139474	−	0.259186i	0.00750901	−	0.0139541i
$346$	−0.405361	+	0.242192i	−0.0217923	+	0.0130203i
$347$	16.3640	+	9.77704i	0.878466	+	0.524859i	0.879910	−	0.475140i	$-0.157603\pi$
$347$	16.3640	+	9.77704i	0.878466	+	0.524859i	−0.00144432	+	0.999999i	$0.500460\pi$
$348$	13.1644	+	24.4636i	0.705687	+	1.31139i
$349$	6.39009	−	0.575118i	0.342054	−	0.0307854i	0.0827190	−	0.996573i	$-0.473640\pi$
$349$	6.39009	−	0.575118i	0.342054	−	0.0307854i	0.259335	+	0.965788i	$0.416497\pi$
$350$	9.15109	−	28.1642i	0.489147	−	1.50544i
$351$	24.5398	+	9.20996i	1.30984	+	0.491591i
$352$	−20.4342	+	5.63948i	−1.08915	+	0.300585i
$353$	−9.85580	−	1.78856i	−0.524571	−	0.0951956i	−0.0901896	−	0.995925i	$-0.528747\pi$
$353$	−9.85580	−	1.78856i	−0.524571	−	0.0951956i	−0.434381	+	0.900729i	$0.643033\pi$
$354$	21.7564			1.15634
$355$	0.00186403	−	0.188951i	9.89325e−5	−	0.0100285i
$356$	32.3565			1.71489
$357$	−27.8012	−	5.04518i	−1.47140	−	0.267019i
$358$	38.4794	−	10.6196i	2.03370	−	0.561266i
$359$	8.55977	+	3.21254i	0.451767	+	0.169551i	0.566878	−	0.823802i	$-0.308151\pi$
$359$	8.55977	+	3.21254i	0.451767	+	0.169551i	−0.115111	+	0.993353i	$0.536722\pi$
$360$	−0.00472675	+	0.0145475i	−0.000249122	+	0.000766718i
$361$	15.7265	−	1.41541i	0.827709	−	0.0744952i
$362$	−1.78147	−	3.31053i	−0.0936322	−	0.173998i
$363$	−5.00854	−	2.99246i	−0.262880	−	0.157064i
$364$	35.1084	−	20.9763i	1.84018	−	1.09946i
$365$	−0.0523932	+	0.0973629i	−0.00274239	+	0.00509621i
$366$	−23.5740	+	55.1542i	−1.23223	+	2.88295i
$367$	20.8171	+	1.87357i	1.08664	+	0.0977996i	0.618448	−	0.785826i	$-0.287762\pi$
$367$	20.8171	+	1.87357i	1.08664	+	0.0977996i	0.468195	+	0.883625i	$0.344905\pi$
$368$	−5.68414	−	13.2987i	−0.296306	−	0.693243i
$369$	−0.0882947	−	0.271743i	−0.00459644	−	0.0141464i
$370$	−0.0136184	+	0.303237i	−0.000707986	+	0.0157645i
$371$	15.3448	+	13.4064i	0.796664	+	0.696025i
$372$	22.3842	−	16.2631i	1.16057	−	0.843203i
$373$	−20.5347	+	7.70682i	−1.06325	+	0.399044i	−0.820856	−	0.571135i	$-0.806503\pi$
$373$	−20.5347	+	7.70682i	−1.06325	+	0.399044i	−0.242392	+	0.970178i	$0.577932\pi$
$374$	1.52693	+	33.9998i	0.0789557	+	1.75809i
$375$	0.259174	−	0.324994i	0.0133837	−	0.0167826i
$376$	−7.46620	−	7.80904i	−0.385040	−	0.402720i
$377$	16.7425	−	25.3638i	0.862283	−	1.30630i
$378$	−25.3625	−	12.2139i	−1.30451	−	0.628217i
$379$	35.4335	+	9.77904i	1.82010	+	0.502315i	0.997773	−	0.0667019i	$-0.0212476\pi$
$379$	35.4335	+	9.77904i	1.82010	+	0.502315i	0.822326	+	0.569017i	$0.192676\pi$
$380$	0.0884035	+	0.0642289i	0.00453500	+	0.00329487i
$381$	3.08867	+	13.5323i	0.158237	+	0.693283i
$382$	26.2019	−	27.4050i	1.34060	−	1.40216i
$383$	0.0563940	+	0.416317i	0.00288160	+	0.0212728i	0.992333	−	0.123589i	$-0.0394405\pi$
$383$	0.0563940	+	0.416317i	0.00288160	+	0.0212728i	−0.989452	+	0.144862i	$0.953726\pi$
$384$	11.9464	+	18.0980i	0.609638	+	0.923562i
$385$	0.0381265	−	0.167043i	0.00194310	−	0.00851330i
$386$	−36.6667	+	32.0347i	−1.86628	+	1.63052i
$387$	0.732522	+	0.918553i	0.0372362	+	0.0466927i
$388$	−4.09924	+	30.2618i	−0.208107	+	1.53631i
$389$	8.64694	−	4.16415i	0.438417	−	0.211131i	−0.201637	−	0.979460i	$-0.564626\pi$
$389$	8.64694	−	4.16415i	0.438417	−	0.211131i	0.640054	+	0.768330i	$0.278912\pi$
$390$	0.490088	−	0.0889378i	0.0248166	−	0.00450354i
$391$	−38.9461	+	7.06768i	−1.96959	+	0.357428i
$392$	−0.611182	+	0.294330i	−0.0308694	+	0.0148659i
$393$	0.475363	−	3.50927i	0.0239789	−	0.177019i
$394$	−8.00336	−	10.0359i	−0.403203	−	0.505601i
$395$	−0.0144932	+	0.0126623i	−0.000729232	+	0.000637111i
$396$	0.739829	−	3.24140i	0.0371778	−	0.162887i
$397$	4.57787	+	6.93517i	0.229757	+	0.348066i	0.931104	−	0.364753i	$-0.118847\pi$
$397$	4.57787	+	6.93517i	0.229757	+	0.348066i	−0.701348	+	0.712819i	$0.747418\pi$
$398$	−5.97790	−	44.1306i	−0.299645	−	2.21207i
$399$	6.25773	−	6.54507i	0.313278	−	0.327664i
$400$	−2.27244	−	9.95620i	−0.113622	−	0.497810i
$401$	2.19960	+	1.59810i	0.109843	+	0.0798055i	0.641351	−	0.767248i	$-0.278374\pi$
$401$	2.19960	+	1.59810i	0.109843	+	0.0798055i	−0.531508	+	0.847053i	$0.678374\pi$
$402$	−14.7567	−	4.07258i	−0.735996	−	0.203122i
$403$	−27.2710	−	13.1330i	−1.35846	−	0.654202i
$404$	8.33059	−	12.6203i	0.414462	−	0.627883i
$405$	−0.156810	−	0.164010i	−0.00779193	−	0.00814972i
$406$	−20.3505	+	25.5187i	−1.00998	+	1.26647i
$407$	−0.783308	−	17.4417i	−0.0388271	−	0.864553i
$408$	15.1699	−	5.69335i	0.751021	−	0.281863i
$409$	−9.91792	+	7.20579i	−0.490410	+	0.356304i	−0.805342	−	0.592811i	$-0.798018\pi$
$409$	−9.91792	+	7.20579i	−0.490410	+	0.356304i	0.314932	+	0.949114i	$0.398018\pi$
$410$	0.0240300	+	0.0209944i	0.00118676	+	0.00103684i
$411$	1.08771	−	24.2198i	0.0536529	−	1.19467i
$412$	11.2396	+	34.5919i	0.553734	+	1.70422i
$413$	5.78916	+	13.5444i	0.284866	+	0.666477i
$414$	6.68327	+	0.601505i	0.328465	+	0.0295624i
$415$	0.0736491	−	0.172311i	0.00361529	−	0.00845839i
$416$	19.7705	−	36.7397i	0.969328	−	1.80131i
$417$	1.64043	−	0.980113i	0.0803324	−	0.0479964i
$418$	−9.36327	−	5.59429i	−0.457972	−	0.273626i
$419$	−2.95586	−	5.49290i	−0.144403	−	0.268346i	0.798112	−	0.602509i	$-0.205832\pi$
$419$	−2.95586	−	5.49290i	−0.144403	−	0.268346i	−0.942515	+	0.334163i	$0.891546\pi$
$420$	−0.307015	+	0.0276319i	−0.0149808	+	0.00134830i
$421$	−2.44924	+	7.53797i	−0.119368	+	0.367378i	−0.992833	−	0.119509i	$-0.961868\pi$
$421$	−2.44924	+	7.53797i	−0.119368	+	0.367378i	0.873465	+	0.486888i	$0.161868\pi$
$422$	−31.4458	−	11.8018i	−1.53076	−	0.574503i
$423$	−2.90584	+	0.801962i	−0.141287	+	0.0389927i
$424$	−11.4971	−	2.08641i	−0.558347	−	0.101325i
$425$	−27.9497			−1.35576
$426$	31.3328	−	13.0283i	1.51808	−	0.631221i
$427$	−40.6089			−1.96520
$428$	−11.1482	−	2.02310i	−0.538869	−	0.0977904i
$429$	−27.6171	+	7.62183i	−1.33336	+	0.367985i
$430$	−0.122840	−	0.0461027i	−0.00592388	−	0.00222327i
$431$	1.29684	−	3.99127i	0.0624668	−	0.192253i	−0.914953	−	0.403561i	$-0.867772\pi$
$431$	1.29684	−	3.99127i	0.0624668	−	0.192253i	0.977420	+	0.211308i	$0.0677723\pi$
$432$	−9.66854	+	0.870184i	−0.465178	+	0.0418668i
$433$	9.83756	+	18.2812i	0.472763	+	0.878541i	0.999592	+	0.0285693i	$0.00909514\pi$
$433$	9.83756	+	18.2812i	0.472763	+	0.878541i	−0.526829	+	0.849971i	$0.676619\pi$
$434$	27.9062	+	16.6732i	1.33954	+	0.800339i
$435$	−0.196644	+	0.117489i	−0.00942834	+	0.00563317i
$436$	−1.05918	+	1.96828i	−0.0507253	+	0.0942635i
$437$	4.98563	−	11.6645i	0.238495	−	0.557987i
$438$	−19.7753	−	1.77981i	−0.944899	−	0.0850424i
$439$	−10.6493	−	24.9152i	−0.508262	−	1.18914i	−0.955572	−	0.294759i	$-0.904761\pi$
$439$	−10.6493	−	24.9152i	−0.508262	−	1.18914i	0.447310	−	0.894379i	$-0.352382\pi$
$440$	0.0303623	+	0.0934457i	0.00144747	+	0.00445485i
$441$	−0.00849173	+	0.189083i	−0.000404368	+	0.00900395i
$442$	−50.4443	−	44.0719i	−2.39939	−	2.09628i
$443$	−29.0365	+	21.0963i	−1.37957	+	1.00231i	−0.382646	+	0.923895i	$0.624987\pi$
$443$	−29.0365	+	21.0963i	−1.37957	+	1.00231i	−0.996921	+	0.0784186i	$0.975013\pi$
$444$	−29.4081	+	11.0371i	−1.39565	+	0.523796i
$445$	0.0119699	+	0.266530i	0.000567426	+	0.0126347i
$446$	−14.5326	+	18.2233i	−0.688140	+	0.862900i
$447$	−27.1749	−	28.4227i	−1.28533	−	1.34435i
$448$	−18.5483	+	28.0995i	−0.876326	+	1.32758i
$449$	14.8808	+	7.16619i	0.702266	+	0.338193i	0.750710	−	0.660632i	$-0.229712\pi$
$449$	14.8808	+	7.16619i	0.702266	+	0.338193i	−0.0484435	+	0.998826i	$0.515426\pi$
$450$	4.56749	+	1.26055i	0.215313	+	0.0594227i
$451$	−1.48485	−	1.07881i	−0.0699188	−	0.0507990i
$452$	−3.01978	−	13.2305i	−0.142039	−	0.622312i
$453$	29.0305	−	30.3636i	1.36397	−	1.42660i
$454$	1.73481	+	12.8068i	0.0814184	+	0.601055i
$455$	0.185776	+	0.281438i	0.00870929	+	0.0131940i
$456$	−1.15549	+	5.06255i	−0.0541110	+	0.237076i
$457$	9.55801	−	8.35059i	0.447105	−	0.390624i	−0.404728	−	0.914437i	$-0.632634\pi$
$457$	9.55801	−	8.35059i	0.447105	−	0.390624i	0.851833	+	0.523813i	$0.175491\pi$
$458$	−3.75695	−	4.71107i	−0.175551	−	0.220134i
$459$	−3.56639	+	26.3281i	−0.166465	+	1.22889i
$460$	−0.389065	+	0.187364i	−0.0181402	+	0.00873588i
$461$	2.59254	−	0.470476i	0.120747	−	0.0219123i	−0.117847	−	0.993032i	$-0.537599\pi$
$461$	2.59254	−	0.470476i	0.120747	−	0.0219123i	0.238594	+	0.971119i	$0.423314\pi$
$462$	30.2745	−	5.49401i	1.40850	−	0.255604i
$463$	26.0499	−	12.5450i	1.21064	−	0.583015i	0.283951	−	0.958839i	$-0.408355\pi$
$463$	26.0499	−	12.5450i	1.21064	−	0.583015i	0.926691	+	0.375824i	$0.122640\pi$
$464$	−1.51090	+	11.1539i	−0.0701418	+	0.517808i
$465$	0.142245	+	0.178369i	0.00659644	+	0.00827167i
$466$	24.1419	−	21.0921i	1.11835	−	0.977075i
$467$	3.85643	−	16.8961i	0.178455	−	0.781860i	−0.803890	−	0.594778i	$-0.797240\pi$
$467$	3.85643	−	16.8961i	0.178455	−	0.781860i	0.982344	−	0.187082i	$-0.0599030\pi$
$468$	3.60490	+	5.46119i	0.166637	+	0.252444i
$469$	−1.39122	−	10.2704i	−0.0642406	−	0.474243i
$470$	0.232645	−	0.243328i	0.0107311	−	0.0112239i
$471$	8.08438	+	35.4200i	0.372509	+	1.63207i
$472$	−6.83361	−	4.96491i	−0.314543	−	0.228529i
$473$	7.27484	+	2.00773i	0.334498	+	0.0923155i
$474$	−3.11383	−	1.49954i	−0.143023	−	0.0688763i
$475$	4.93454	−	7.47551i	0.226412	−	0.343000i
$476$	28.6481	+	29.9635i	1.31308	+	1.37338i
$477$	−2.03274	+	2.54898i	−0.0930728	+	0.116710i
$478$	−0.807498	−	17.9803i	−0.0369341	−	0.822402i
$479$	1.51355	−	0.568045i	0.0691558	−	0.0259546i	−0.316557	−	0.948573i	$-0.602527\pi$
$479$	1.51355	−	0.568045i	0.0691558	−	0.0259546i	0.385713	+	0.922619i	$0.373955\pi$
$480$	−0.254409	+	0.184839i	−0.0116121	+	0.00843671i
$481$	25.8777	+	22.6086i	1.17992	+	1.03087i
$482$	−1.23836	+	27.5741i	−0.0564056	+	1.25597i
$483$	11.0581	+	34.0334i	0.503163	+	1.54858i
$484$	3.36430	+	7.87117i	0.152923	+	0.357780i
$485$	−0.250792	−	0.0225717i	−0.0113879	−	0.00102493i
$486$	3.84168	−	8.98806i	0.174262	−	0.407706i
$487$	−1.27124	+	2.36236i	−0.0576054	+	0.107049i	−0.907770	−	0.419468i	$-0.862217\pi$
$487$	−1.27124	+	2.36236i	−0.0576054	+	0.107049i	0.850165	+	0.526517i	$0.176502\pi$
$488$	19.9909	−	11.9440i	0.904948	−	0.540681i
$489$	−13.1672	−	7.86703i	−0.595441	−	0.355760i
$490$	−0.0100164	−	0.0186136i	−0.000452496	−	0.000840879i
$491$	15.9920	−	1.43931i	0.721709	−	0.0649550i	0.277306	−	0.960782i	$-0.410558\pi$
$491$	15.9920	−	1.43931i	0.721709	−	0.0649550i	0.444404	+	0.895827i	$0.353416\pi$
$492$	−1.02038	+	3.14041i	−0.0460024	+	0.141581i
$493$	28.8414	+	10.8244i	1.29895	+	0.487505i
$494$	20.6936	−	5.71107i	0.931049	−	0.256953i
$495$	0.0269741	+	0.00489507i	0.00121239	+	0.000220017i
$496$	11.2103			0.503357
$497$	16.4481	+	16.0395i	0.737796	+	0.719470i
$498$	33.6515			1.50796
$499$	−7.91562	−	1.43647i	−0.354352	−	0.0643054i	−0.00153769	−	0.999999i	$-0.500489\pi$
$499$	−7.91562	−	1.43647i	−0.354352	−	0.0643054i	−0.352814	+	0.935693i	$0.614775\pi$
$500$	−0.587896	+	0.162249i	−0.0262915	+	0.00725599i
$501$	5.87441	+	2.20470i	0.262449	+	0.0984988i
$502$	−9.94744	+	30.6151i	−0.443976	+	1.36642i
$503$	−0.839086	+	0.0755191i	−0.0374130	+	0.00336723i	−0.108330	−	0.994115i	$-0.534550\pi$
$503$	−0.839086	+	0.0755191i	−0.0374130	+	0.00336723i	0.0709170	+	0.997482i	$0.477407\pi$
$504$	−0.881260	−	1.63766i	−0.0392544	−	0.0729470i
$505$	0.107039	+	0.0639528i	0.00476317	+	0.00284586i
$506$	37.0022	−	22.1078i	1.64495	−	0.982811i
$507$	15.3007	−	28.4334i	0.679527	−	1.26277i
$508$	8.00384	−	18.7259i	0.355113	−	0.830828i
$509$	12.8752	+	1.15879i	0.570685	+	0.0513626i	0.371224	−	0.928543i	$-0.378938\pi$
$509$	12.8752	+	1.15879i	0.570685	+	0.0513626i	0.199461	+	0.979906i	$0.436081\pi$
$510$	0.198432	+	0.464255i	0.00878672	+	0.0205575i
$511$	−4.15398	−	12.7846i	−0.183761	−	0.565560i
$512$	−0.979825	+	21.8175i	−0.0433026	+	0.964207i
$513$	−6.41216	−	5.60213i	−0.283104	−	0.247340i
$514$	−43.7845	+	31.8113i	−1.93125	+	1.40314i
$515$	−0.280785	+	0.105381i	−0.0123729	+	0.00464362i
$516$	−0.609152	−	13.5638i	−0.0268164	−	0.597114i
$517$	−12.0730	+	15.1390i	−0.530968	+	0.665812i
$518$	−25.5036	−	26.6747i	−1.12057	−	1.17202i
$519$	0.221964	−	0.336261i	0.00974314	−	0.0147602i
$520$	−0.174231	−	0.0839052i	−0.00764053	−	0.00367949i
$521$	−28.9710	−	7.99550i	−1.26924	−	0.350289i	−0.434373	−	0.900733i	$-0.643030\pi$
$521$	−28.9710	−	7.99550i	−1.26924	−	0.350289i	−0.834872	+	0.550444i	$0.814458\pi$
$522$	−4.22503	−	3.06966i	−0.184924	−	0.134356i
$523$	−1.08980	−	4.77473i	−0.0476537	−	0.208785i	0.945496	−	0.325634i	$-0.105578\pi$
$523$	−1.08980	−	4.77473i	−0.0476537	−	0.208785i	−0.993150	+	0.116849i	$0.962721\pi$
$524$	−3.59055	+	3.75542i	−0.156854	+	0.164056i
$525$	3.39185	+	25.0396i	0.148032	+	1.09282i
$526$	−7.58454	−	11.4901i	−0.330702	−	0.500992i
$527$	6.82722	−	29.9120i	0.297398	−	1.30299i
$528$	7.99060	−	6.98118i	0.347746	−	0.303817i
$529$	16.9154	+	21.2113i	0.735454	+	0.922230i
$530$	0.0488740	−	0.360802i	0.00212295	−	0.0156722i
$531$	−2.12340	+	1.02258i	−0.0921477	+	0.0443760i
$532$	−13.0720	+	2.37221i	−0.566742	+	0.102849i
$533$	3.55428	−	0.645006i	0.153953	−	0.0279383i
$534$	−43.1668	+	20.7881i	−1.86801	+	0.899587i
$535$	0.0125407	−	0.0925795i	0.000542184	−	0.00400256i
$536$	3.70564	+	4.64672i	0.160059	+	0.200708i
$537$	−25.6501	+	22.4099i	−1.10689	+	0.967056i
$538$	10.1863	−	44.6292i	0.439163	−	1.92410i
$539$	0.669781	+	1.01467i	0.0288495	+	0.0437051i
$540$	0.0389081	+	0.287231i	0.00167434	+	0.0123605i
$541$	−0.550272	+	0.575539i	−0.0236580	+	0.0247444i	−0.734518	−	0.678589i	$-0.762592\pi$
$541$	−0.550272	+	0.575539i	−0.0236580	+	0.0247444i	0.710860	+	0.703334i	$0.248306\pi$
$542$	−2.47017	−	10.8225i	−0.106103	−	0.464868i
$543$	2.59516	+	1.88550i	0.111369	+	0.0809144i
$544$	40.7663	+	11.2508i	1.74784	+	0.482373i
$545$	−0.0166051	−	0.00799660i	−0.000711285	−	0.000342537i
$546$	−33.3615	+	50.5405i	−1.42774	+	2.16294i
$547$	−25.4185	−	26.5857i	−1.08682	−	1.13672i	−0.989949	−	0.141424i	$-0.954832\pi$
$547$	−25.4185	−	26.5857i	−1.08682	−	1.13672i	−0.0968679	−	0.995297i	$-0.530882\pi$
$548$	−22.1776	+	27.8099i	−0.947381	+	1.18798i
$549$	−0.291511	−	6.49099i	−0.0124414	−	0.277029i
$550$	28.4954	−	10.6945i	1.21505	−	0.456015i
$551$	−7.98709	+	5.80296i	−0.340262	+	0.247215i
$552$	−15.4537	−	13.5015i	−0.657754	−	0.574663i
$553$	0.104978	−	2.33752i	0.00446413	−	0.0994016i
$554$	−13.3591	−	41.1152i	−0.567575	−	1.74682i
$555$	−0.101795	−	0.238160i	−0.00432094	−	0.0101093i
$556$	−2.79235	−	0.251316i	−0.118422	−	0.0106582i
$557$	1.02593	−	2.40028i	0.0434700	−	0.101703i	−0.896386	−	0.443275i	$-0.853816\pi$
$557$	1.02593	−	2.40028i	0.0434700	−	0.101703i	0.939856	+	0.341572i	$0.110959\pi$
$558$	−2.46474	+	4.58026i	−0.104341	+	0.193898i
$559$	−12.7509	+	7.61830i	−0.539305	+	0.322220i
$560$	−0.107216	−	0.0640584i	−0.00453069	−	0.00270696i
$561$	−13.7612	−	25.5726i	−0.580999	−	1.07968i
$562$	−9.96896	+	0.897223i	−0.420515	+	0.0378470i
$563$	5.15164	−	15.8551i	0.217116	−	0.668214i	−0.781881	−	0.623428i	$-0.785739\pi$
$563$	5.15164	−	15.8551i	0.217116	−	0.668214i	0.998997	−	0.0447858i	$-0.0142605\pi$
$564$	32.6156	+	12.2408i	1.37336	+	0.515432i
$565$	0.107867	−	0.0297693i	0.00453799	−	0.00125240i
$566$	28.3980	+	5.15349i	1.19366	+	0.216617i
$567$	27.5880			1.15859
$568$	−12.8146	−	3.05816i	−0.537690	−	0.128318i
$569$	19.8172			0.830779			0.415389	−	0.909644i	$-0.363645\pi$
$569$	19.8172			0.830779			0.415389	+	0.909644i	$0.363645\pi$
$570$	−0.159204	−	0.0288913i	−0.00666834	−	0.00121013i
$571$	−29.7712	+	8.21633i	−1.24589	+	0.343843i	−0.825967	−	0.563719i	$-0.809370\pi$
$571$	−29.7712	+	8.21633i	−1.24589	+	0.343843i	−0.419919	+	0.907562i	$0.637941\pi$
$572$	39.3532	+	14.7695i	1.64544	+	0.617544i
$573$	−9.99730	+	30.7685i	−0.417643	+	1.28537i
$574$	−3.86394	+	0.347761i	−0.161278	+	0.0145153i
$575$	16.7739	+	31.1711i	0.699520	+	1.29993i
$576$	−4.62461	−	2.76308i	−0.192692	−	0.115128i
$577$	−32.4448	+	19.3849i	−1.35069	+	0.807002i	−0.991974	−	0.126443i	$-0.959644\pi$
$577$	−32.4448	+	19.3849i	−1.35069	+	0.807002i	−0.358720	+	0.933445i	$0.616787\pi$
$578$	14.6737	−	27.2684i	0.610347	−	1.13421i
$579$	16.3283	−	38.2019i	0.678581	−	1.58762i
$580$	0.334727	+	0.0301260i	0.0138988	+	0.00125091i
$581$	8.95432	+	20.9497i	0.371488	+	0.869139i
$582$	−13.9735	−	43.0059i	−0.579219	−	1.78265i
$583$	−0.939574	+	20.9212i	−0.0389132	+	0.866469i
$584$	5.80518	+	5.07184i	0.240220	+	0.209874i
$585$	−0.0436518	+	0.0317149i	−0.00180478	+	0.00131125i
$586$	47.4565	−	17.8107i	1.96041	−	0.735754i
$587$	−1.68696	−	37.5631i	−0.0696283	−	1.55039i	−0.664938	−	0.746898i	$-0.731542\pi$
$587$	−1.68696	−	37.5631i	−0.0696283	−	1.55039i	0.595310	−	0.803496i	$-0.297029\pi$
$588$	1.36379	−	1.71014i	0.0562418	−	0.0705250i
$589$	6.79500	+	7.10702i	0.279983	+	0.292840i
$590$	0.144996	−	0.219660i	0.00596941	−	0.00904327i
$591$	9.86820	+	4.75228i	0.405924	+	0.195483i
$592$	−12.2680	−	3.38576i	−0.504213	−	0.139154i
$593$	11.3064	+	8.21459i	0.464299	+	0.337333i	0.795215	−	0.606327i	$-0.207358\pi$
$593$	11.3064	+	8.21459i	0.464299	+	0.337333i	−0.330916	+	0.943660i	$0.607358\pi$
$594$	−6.43802	−	28.2068i	−0.264155	−	1.15734i
$595$	−0.236220	+	0.247067i	−0.00968409	+	0.0101288i
$596$	7.74442	+	57.1716i	0.317224	+	2.34184i
$597$	20.9336	+	31.7131i	0.856755	+	1.29793i
$598$	−18.8776	+	82.7081i	−0.771962	+	3.38219i
$599$	−5.65590	+	4.94141i	−0.231094	+	0.201901i	−0.765695	−	0.643204i	$-0.777605\pi$
$599$	−5.65590	+	4.94141i	−0.231094	+	0.201901i	0.534601	+	0.845105i	$0.320462\pi$
$600$	−9.03447	−	11.3289i	−0.368831	−	0.462499i
$601$	5.07932	−	37.4970i	0.207190	−	1.52954i	−0.526573	−	0.850130i	$-0.676523\pi$
$601$	5.07932	−	37.4970i	0.207190	−	1.52954i	0.733763	−	0.679406i	$-0.237762\pi$
$602$	14.3725	−	6.92141i	0.585778	−	0.282096i
$603$	1.63165	−	0.296101i	0.0664459	−	0.0120581i
$604$	−60.6428	+	11.0051i	−2.46752	+	0.447789i
$605$	−0.0635925	+	0.0306245i	−0.00258540	+	0.00124506i
$606$	−3.00569	+	22.1889i	−0.122098	+	0.901363i
$607$	−19.3501	−	24.2642i	−0.785396	−	0.984855i	−0.999967	−	0.00814673i	$-0.997407\pi$
$607$	−19.3501	−	24.2642i	−0.785396	−	0.984855i	0.214571	−	0.976708i	$-0.431165\pi$
$608$	−10.2065	+	8.91715i	−0.413928	+	0.361638i
$609$	6.19729	−	27.1521i	0.251127	−	1.10026i
$610$	0.399746	+	0.605589i	0.0161852	+	0.0245196i
$611$	−5.11572	−	37.7658i	−0.206960	−	1.52784i
$612$	−4.58376	+	4.79424i	−0.185287	+	0.193795i
$613$	−2.23651	−	9.79880i	−0.0903319	−	0.395770i	0.909468	−	0.415774i	$-0.136489\pi$
$613$	−2.23651	−	9.79880i	−0.0903319	−	0.395770i	−0.999800	+	0.0200041i	$0.993632\pi$
$614$	16.1061	+	11.7018i	0.649991	+	0.472246i
$615$	−0.0262460	−	0.00724343i	−0.00105834	−	0.000292083i
$616$	−10.7629	−	5.18313i	−0.433648	−	0.208834i
$617$	−23.6726	+	35.8624i	−0.953022	+	1.44377i	−0.0577070	+	0.998334i	$0.518379\pi$
$617$	−23.6726	+	35.8624i	−0.953022	+	1.44377i	−0.895315	+	0.445433i	$0.853050\pi$
$618$	−37.2190	−	38.9280i	−1.49717	−	1.56591i
$619$	−5.60687	+	7.03079i	−0.225359	+	0.282591i	−0.881637	−	0.471928i	$-0.843558\pi$
$619$	−5.60687	+	7.03079i	−0.225359	+	0.282591i	0.656278	+	0.754519i	$0.272130\pi$
$620$	−0.0150173	−	0.334385i	−0.000603107	−	0.0134292i
$621$	31.5031	−	11.8233i	1.26417	−	0.474453i
$622$	−8.63986	+	6.27722i	−0.346427	+	0.251694i
$623$	−24.4278	−	21.3419i	−0.978680	−	0.855047i
$624$	−0.936940	+	20.8626i	−0.0375076	+	0.835172i
$625$	7.72309	+	23.7692i	0.308924	+	0.950770i
$626$	−21.8303	−	51.0744i	−0.872513	−	2.04135i
$627$	9.26929	+	0.834251i	0.370180	+	0.0333168i
$628$	20.9495	−	49.0138i	0.835976	−	1.95586i
$629$	−16.5055	+	30.6724i	−0.658117	+	1.22299i
$630$	0.0497456	−	0.0297216i	0.00198191	−	0.00118414i
$631$	−18.9651	−	11.3311i	−0.754987	−	0.451084i	0.0831541	−	0.996537i	$-0.473501\pi$
$631$	−18.9651	−	11.3311i	−0.754987	−	0.451084i	−0.838142	+	0.545453i	$0.816358\pi$
$632$	0.635841	+	1.18159i	0.0252924	+	0.0470012i
$633$	28.5438	−	2.56899i	1.13451	−	0.102108i
$634$	7.43809	−	22.8921i	0.295404	−	0.909161i
$635$	0.157212	+	0.0590025i	0.00623876	+	0.00234144i
$636$	36.3196	−	10.0236i	1.44017	−	0.397461i
$637$	−2.35445	−	0.427269i	−0.0932866	−	0.0169290i
$638$	−33.5463			−1.32811
$639$	−2.44570	+	2.74422i	−0.0967505	+	0.108560i
$640$	0.262341			0.0103700
$641$	−24.2498	−	4.40069i	−0.957809	−	0.173817i	−0.322925	−	0.946424i	$-0.604666\pi$
$641$	−24.2498	−	4.40069i	−0.957809	−	0.173817i	−0.634884	+	0.772608i	$0.718952\pi$
$642$	16.1726	−	4.46336i	0.638283	−	0.176155i
$643$	−19.8323	−	7.44317i	−0.782108	−	0.293530i	−0.0717982	−	0.997419i	$-0.522874\pi$
$643$	−19.8323	−	7.44317i	−0.782108	−	0.293530i	−0.710310	+	0.703889i	$0.751445\pi$
$644$	16.2241	−	49.9325i	0.639318	−	1.96762i
$645$	0.111504	−	0.0100355i	0.00439046	−	0.000395148i
$646$	10.3113	+	19.1617i	0.405694	+	0.753906i
$647$	33.1397	+	19.8001i	1.30286	+	0.778421i	0.985466	−	0.169873i	$-0.0543358\pi$
$647$	33.1397	+	19.8001i	1.30286	+	0.778421i	0.317392	+	0.948294i	$0.397193\pi$
$648$	−13.5810	+	8.11428i	−0.533513	+	0.318759i
$649$	−7.17385	+	13.3312i	−0.281598	+	0.523297i
$650$	−23.5436	+	55.0829i	−0.923455	+	2.16053i
$651$	−27.6261	−	2.48640i	−1.08275	−	0.0974496i
$652$	8.84457	+	20.6929i	0.346380	+	0.810397i
$653$	−9.88093	−	30.4104i	−0.386671	−	1.19005i	−0.935261	−	0.353959i	$-0.884835\pi$
$653$	−9.88093	−	30.4104i	−0.386671	−	1.19005i	0.548590	−	0.836091i	$-0.315165\pi$
$654$	0.148489	−	3.30637i	0.00580640	−	0.129289i
$655$	−0.0322627	−	0.0281871i	−0.00126061	−	0.00110136i
$656$	−1.08236	+	0.786378i	−0.0422589	+	0.0307029i
$657$	2.01370	−	0.755753i	0.0785618	−	0.0294847i
$658$	1.83632	+	40.8888i	0.0715872	+	1.59401i
$659$	−8.11884	+	10.1807i	−0.316265	+	0.396584i	−0.914400	−	0.404811i	$-0.867337\pi$
$659$	−8.11884	+	10.1807i	−0.316265	+	0.396584i	0.598135	+	0.801395i	$0.295909\pi$
$660$	−0.218941	−	0.228995i	−0.00852228	−	0.00891361i
$661$	−4.70217	+	7.12348i	−0.182893	+	0.277071i	−0.914441	−	0.404719i	$-0.867369\pi$
$661$	−4.70217	+	7.12348i	−0.182893	+	0.277071i	0.731548	+	0.681790i	$0.238798\pi$
$662$	56.8398	+	27.3726i	2.20914	+	1.06387i
$663$	55.0962	+	15.2056i	2.13976	+	0.590536i
$664$	−10.5698	−	7.67942i	−0.410188	−	0.298019i
$665$	−0.0243764	−	0.106800i	−0.000945278	−	0.00414153i
$666$	4.08064	−	4.26802i	0.158122	−	0.165382i
$667$	−5.23711	−	38.6619i	−0.202782	−	1.49699i
$668$	−5.07139	−	7.68283i	−0.196218	−	0.297258i
$669$	4.42559	−	19.3898i	0.171103	−	0.749652i
$670$	−0.139465	+	0.121847i	−0.00538799	+	0.00470734i
$671$	−26.0226	−	32.6313i	−1.00459	−	1.25972i
$672$	5.13216	−	37.8872i	0.197978	−	1.46153i
$673$	16.4276	−	7.91112i	0.633238	−	0.304951i	−0.0895909	−	0.995979i	$-0.528556\pi$
$673$	16.4276	−	7.91112i	0.633238	−	0.304951i	0.722828	+	0.691028i	$0.242842\pi$
$674$	14.7784	−	2.68188i	0.569241	−	0.103302i
$675$	23.3781	−	4.24249i	0.899822	−	0.163294i
$676$	−42.6815	+	20.5543i	−1.64160	+	0.790552i
$677$	−2.29202	+	16.9204i	−0.0880895	+	0.650303i	0.892042	+	0.451953i	$0.149272\pi$
$677$	−2.29202	+	16.9204i	−0.0880895	+	0.650303i	−0.980131	+	0.198350i	$0.936442\pi$
$678$	12.5289	+	15.7108i	0.481170	+	0.603368i
$679$	23.0551	−	20.1426i	0.884772	−	0.773002i
$680$	0.0436182	−	0.191104i	0.00167268	−	0.00732850i
$681$	−6.07500	−	9.20323i	−0.232795	−	0.352669i
$682$	4.48483	+	33.1083i	0.171733	+	1.26778i
$683$	−17.0100	+	17.7910i	−0.650869	+	0.680756i	−0.963067	−	0.269261i	$-0.913220\pi$
$683$	−17.0100	+	17.7910i	−0.650869	+	0.680756i	0.312198	+	0.950017i	$0.398935\pi$
$684$	−0.473015	−	2.07241i	−0.0180862	−	0.0792407i
$685$	−0.237282	−	0.172396i	−0.00906609	−	0.00658690i
$686$	−37.4916	−	10.3470i	−1.43144	−	0.395052i
$687$	4.63235	+	2.23082i	0.176735	+	0.0851112i
$688$	3.03055	−	4.59109i	0.115539	−	0.175034i
$689$	−28.4843	−	29.7922i	−1.08516	−	1.13499i
$690$	0.398676	−	0.499924i	0.0151774	−	0.0190318i
$691$	0.530041	+	11.8023i	0.0201637	+	0.448980i	0.983525	+	0.180773i	$0.0578599\pi$
$691$	0.530041	+	11.8023i	0.0201637	+	0.448980i	−0.963361	+	0.268207i	$0.913569\pi$
$692$	−0.553446	+	0.207712i	−0.0210388	+	0.00789601i
$693$	−2.69653	+	1.95914i	−0.102433	+	0.0744217i
$694$	31.1866	+	27.2469i	1.18383	+	1.03428i
$695$	0.00103717	−	0.0230944i	3.93421e−5	−	0.000876020i
$696$	4.93527	+	15.1892i	0.187071	+	0.575745i
$697$	1.43909	+	3.36693i	0.0545095	+	0.127531i
$698$	13.8824	+	1.24944i	0.525456	+	0.0472919i
$699$	−10.7508	+	25.1528i	−0.406633	+	0.951364i
$700$	17.5676	−	32.6460i	0.663992	−	1.23390i
$701$	−31.9121	+	19.0666i	−1.20530	+	0.720136i	−0.967915	−	0.251278i	$-0.919149\pi$
$701$	−31.9121	+	19.0666i	−1.20530	+	0.720136i	−0.237390	+	0.971414i	$0.576292\pi$
$702$	48.8830	+	29.2063i	1.84497	+	1.10232i
$703$	−5.28967	−	9.82985i	−0.199504	−	0.370740i
$704$	−34.4652	+	3.10193i	−1.29896	+	0.116908i
$705$	−0.0887655	+	0.273192i	−0.00334310	+	0.0102890i
$706$	−20.3737	−	7.64637i	−0.766773	−	0.287775i
$707$	−14.6135	+	4.03306i	−0.549596	+	0.151679i
$708$	26.7987	+	4.86325i	1.00716	+	0.182772i
$709$	1.54654			0.0580815			0.0290407	−	0.999578i	$-0.490755\pi$
$709$	1.54654			0.0580815			0.0290407	+	0.999578i	$0.490755\pi$
$710$	0.0772811	−	0.403174i	0.00290031	−	0.0151309i
$711$	0.374386			0.0140406
$712$	18.3025	+	3.32141i	0.685914	+	0.124475i
$713$	−37.4570	+	10.3375i	−1.40277	+	0.387141i
$714$	−57.4701	−	21.5689i	−2.15076	−	0.807195i
$715$	−0.107102	+	0.329627i	−0.00400540	+	0.0123274i
$716$	49.7713	−	4.47950i	1.86004	−	0.167407i
$717$	7.27744	+	13.5238i	0.271781	+	0.505054i
$718$	17.0509	+	10.1875i	0.636336	+	0.380193i
$719$	−24.1611	+	14.4356i	−0.901058	+	0.538357i	−0.887116	−	0.461546i	$-0.847295\pi$
$719$	−24.1611	+	14.4356i	−0.901058	+	0.538357i	−0.0139415	+	0.999903i	$0.504438\pi$
$720$	0.00946953	−	0.0175973i	0.000352909	−	0.000655814i
$721$	14.3310	−	33.5289i	0.533713	−	1.24868i
$722$	34.1655	+	3.07495i	1.27151	+	0.114438i
$723$	−9.25646	−	21.6566i	−0.344252	−	0.805417i
$724$	−1.45434	−	4.47601i	−0.0540503	−	0.166350i
$725$	1.23599	−	27.5214i	0.0459034	−	1.02212i
$726$	−9.54530	−	8.33948i	−0.354259	−	0.309507i
$727$	12.2630	−	8.90959i	0.454810	−	0.330438i	−0.336682	−	0.941618i	$-0.609305\pi$
$727$	12.2630	−	8.90959i	0.454810	−	0.330438i	0.791492	+	0.611180i	$0.209305\pi$
$728$	22.0123	−	8.26136i	0.815831	−	0.306186i
$729$	−0.987695	−	21.9927i	−0.0365813	−	0.814546i
$730$	−0.149763	+	0.187796i	−0.00554296	+	0.00695065i
$731$	−10.4046	−	10.8823i	−0.384828	−	0.402498i
$732$	−41.3663	+	62.6673i	−1.52894	+	2.31625i
$733$	−31.9292	−	15.3763i	−1.17933	−	0.567935i	−0.261614	−	0.965173i	$-0.584255\pi$
$733$	−31.9292	−	15.3763i	−1.17933	−	0.567935i	−0.917716	+	0.397237i	$0.869969\pi$
$734$	43.7713	+	12.0801i	1.61563	+	0.445885i
$735$	0.0145914	+	0.0106013i	0.000538213	+	0.000391035i
$736$	−11.9182	−	52.2172i	−0.439312	−	1.92475i
$737$	7.36126	−	7.69928i	0.271156	−	0.283607i
$738$	−0.0833239	−	0.615121i	−0.00306719	−	0.0226429i
$739$	22.8722	+	34.6500i	0.841369	+	1.27462i	0.959525	+	0.281624i	$0.0908732\pi$
$739$	22.8722	+	34.6500i	0.841369	+	1.27462i	−0.118156	+	0.992995i	$0.537698\pi$
$740$	−0.0845577	+	0.370472i	−0.00310840	+	0.0136188i
$741$	−13.7942	+	12.0516i	−0.506743	+	0.442728i
$742$	27.6002	+	34.6096i	1.01324	+	1.27056i
$743$	−5.98064	+	44.1509i	−0.219408	+	1.61974i	0.461342	+	0.887222i	$0.347368\pi$
$743$	−5.98064	+	44.1509i	−0.219408	+	1.61974i	−0.680750	+	0.732515i	$0.738346\pi$
$744$	14.3311	−	6.90149i	0.525403	−	0.253021i
$745$	−0.468074	+	0.0849429i	−0.0171489	+	0.00311207i
$746$	−46.8841	+	8.50820i	−1.71655	+	0.311507i
$747$	−3.28435	+	1.58166i	−0.120168	+	0.0578698i
$748$	−5.71922	+	42.2210i	−0.209115	+	1.54375i
$749$	7.08203	+	8.88059i	0.258772	+	0.324490i
$750$	0.680073	−	0.594162i	0.0248328	−	0.0216957i
$751$	−2.37705	+	10.4145i	−0.0867397	+	0.380032i	−0.999601	−	0.0282378i	$-0.991010\pi$
$751$	−2.37705	+	10.4145i	−0.0867397	+	0.380032i	0.912862	+	0.408269i	$0.133868\pi$
$752$	7.77576	+	11.7798i	0.283553	+	0.429564i
$753$	−3.68701	−	27.2186i	−0.134362	−	0.991902i
$754$	45.6272	−	47.7224i	1.66165	−	1.73795i
$755$	−0.113086	−	0.495461i	−0.00411562	−	0.0180317i
$756$	−28.5104	−	20.7140i	−1.03691	−	0.753361i
$757$	−5.19482	−	1.43368i	−0.188809	−	0.0521079i	0.170354	−	0.985383i	$-0.445509\pi$
$757$	−5.19482	−	1.43368i	−0.188809	−	0.0521079i	−0.359162	+	0.933275i	$0.616938\pi$
$758$	71.9484	+	34.6485i	2.61328	+	1.25849i
$759$	−20.2614	+	30.6947i	−0.735441	+	1.11415i
$760$	0.0434124	+	0.0454058i	0.00157473	+	0.00164704i
$761$	24.9670	−	31.3076i	0.905053	−	1.13490i	−0.0853030	−	0.996355i	$-0.527186\pi$
$761$	24.9670	−	31.3076i	0.905053	−	1.13490i	0.990356	−	0.138546i	$-0.0442427\pi$
$762$	1.35289	+	30.1245i	0.0490101	+	1.09130i
$763$	2.09789	−	0.787351i	0.0759487	−	0.0285040i
$764$	38.4004	−	27.8995i	1.38928	−	1.00937i
$765$	−0.0411872	−	0.0359842i	−0.00148913	−	0.00130101i
$766$	−0.0409483	+	0.911785i	−0.00147952	+	0.0329441i
$767$	−9.20745	−	28.3376i	−0.332462	−	1.02321i
$768$	0.522219	+	1.22179i	0.0188439	+	0.0440876i
$769$	23.8691	+	2.14826i	0.860743	+	0.0774683i	0.511210	−	0.859456i	$-0.329197\pi$
$769$	23.8691	+	2.14826i	0.860743	+	0.0774683i	0.349533	+	0.936924i	$0.386340\pi$
$770$	0.146296	−	0.342277i	0.00527215	−	0.0123348i
$771$	21.8830	−	40.6654i	0.788096	−	1.46453i
$772$	−52.3254	+	31.2630i	−1.88323	+	1.12518i
$773$	−12.9437	−	7.73351i	−0.465553	−	0.278155i	0.260907	−	0.965364i	$-0.415978\pi$
$773$	−12.9437	−	7.73351i	−0.465553	−	0.278155i	−0.726460	+	0.687209i	$0.758836\pi$
$774$	1.20950	+	2.24763i	0.0434746	+	0.0807893i
$775$	−27.3273	+	2.45950i	−0.981626	+	0.0883479i
$776$	−5.42513	+	16.6968i	−0.194751	+	0.599381i
$777$	29.4819	+	11.0647i	1.05766	+	0.396945i
$778$	20.0988	−	5.54692i	0.720577	−	0.198867i
$779$	−1.15460	−	0.209529i	−0.0413679	−	0.00750717i
$780$	0.623553			0.0223268
$781$	−2.34846	+	23.4951i	−0.0840346	+	0.840720i
$782$	−85.9918			−3.07506
$783$	−25.7670	−	4.67602i	−0.920836	−	0.167107i
$784$	0.854301	−	0.235772i	0.0305108	−	0.00842043i
$785$	0.411491	+	0.154435i	0.0146867	+	0.00551203i
$786$	2.37741	−	7.31693i	0.0847995	−	0.260986i
$787$	24.5961	−	2.21369i	0.876756	−	0.0789095i	0.357889	−	0.933764i	$-0.383497\pi$
$787$	24.5961	−	2.21369i	0.876756	−	0.0789095i	0.518868	+	0.854855i	$0.326354\pi$
$788$	−7.61490	−	14.1509i	−0.271269	−	0.504103i
$789$	10.0846	+	6.02527i	0.359021	+	0.214505i
$790$	−0.0358921	+	0.0214446i	−0.00127699	+	0.000762963i
$791$	−6.44689	+	11.9803i	−0.229225	+	0.425972i
$792$	0.751217	−	1.75756i	0.0266933	−	0.0624521i
$793$	81.8147	+	7.36345i	2.90532	+	0.261484i
$794$	7.09529	+	16.6002i	0.251802	+	0.589121i
$795$	0.0960031	+	0.295467i	0.00340488	+	0.0104791i
$796$	2.50125	−	55.6947i	0.0886545	−	1.97405i
$797$	37.3879	+	32.6648i	1.32435	+	1.15705i	0.975532	+	0.219856i	$0.0705588\pi$
$797$	37.3879	+	32.6648i	1.32435	+	1.15705i	0.348815	+	0.937192i	$0.386584\pi$
$798$	15.9153	−	11.5631i	0.563395	−	0.409330i
$799$	36.1670	−	13.5737i	1.27950	−	0.480204i
$800$	−1.69677	−	37.7815i	−0.0599899	−	1.33578i
$801$	3.23597	−	4.05778i	0.114337	−	0.143375i
$802$	4.08188	+	4.26931i	0.144136	+	0.150755i
$803$	7.61118	−	11.5304i	0.268593	−	0.406900i
$804$	−17.2664	−	8.31504i	−0.608938	−	0.293249i
$805$	0.417311	+	0.115170i	0.0147083	+	0.00405923i
$806$	−53.1993	−	38.6515i	−1.87386	−	1.36144i
$807$	8.69165	+	38.0806i	0.305961	+	1.34050i
$808$	6.00769	−	6.28355i	0.211350	−	0.221054i
$809$	3.04877	+	22.5069i	0.107189	+	0.791301i	0.962133	+	0.272581i	$0.0878771\pi$
$809$	3.04877	+	22.5069i	0.107189	+	0.791301i	−0.854944	+	0.518720i	$0.826409\pi$
$810$	−0.271570	−	0.411412i	−0.00954201	−	0.0144555i
$811$	−6.96209	+	30.5029i	−0.244472	+	1.07110i	0.692423	+	0.721491i	$0.256543\pi$
$811$	−6.96209	+	30.5029i	−0.244472	+	1.07110i	−0.936895	+	0.349610i	$0.886314\pi$
$812$	−30.7712	+	26.8840i	−1.07986	+	0.943444i
$813$	5.90570	+	7.40551i	0.207122	+	0.259723i
$814$	5.09148	−	37.5868i	0.178456	−	1.31742i
$815$	−0.167182	+	0.0805104i	−0.00585612	+	0.00282016i
$816$	−20.8282	+	3.77976i	−0.729132	+	0.132318i
$817$	4.74757	−	0.861556i	0.166096	−	0.0301420i
$818$	−23.9955	+	11.5556i	−0.838983	+	0.404033i
$819$	0.880583	−	6.50072i	0.0307701	−	0.227154i
$820$	0.0249063	+	0.0312315i	0.000869767	+	0.00109065i
$821$	2.18535	−	1.90928i	0.0762693	−	0.0666345i	−0.618960	−	0.785423i	$-0.712446\pi$
$821$	2.18535	−	1.90928i	0.0762693	−	0.0666345i	0.695229	+	0.718788i	$0.255303\pi$
$822$	11.7202	−	51.3496i	0.408790	−	1.79102i
$823$	−11.0381	−	16.7220i	−0.384764	−	0.582892i	0.589649	−	0.807660i	$-0.299266\pi$
$823$	−11.0381	−	16.7220i	−0.384764	−	0.582892i	−0.974412	+	0.224768i	$0.927838\pi$
$824$	2.80681	+	20.7207i	0.0977797	+	0.721839i
$825$	−17.9470	+	18.7711i	−0.624835	+	0.653526i
$826$	7.12071	+	31.1979i	0.247761	+	1.08551i
$827$	25.5968	+	18.5972i	0.890089	+	0.646687i	0.935901	−	0.352263i	$-0.114588\pi$
$827$	25.5968	+	18.5972i	0.890089	+	0.646687i	−0.0458123	+	0.998950i	$0.514588\pi$
$828$	8.09775	+	2.23484i	0.281416	+	0.0776659i
$829$	−12.3967	−	5.96992i	−0.430554	−	0.207344i	0.206039	−	0.978544i	$-0.433943\pi$
$829$	−12.3967	−	5.96992i	−0.430554	−	0.207344i	−0.636593	+	0.771200i	$0.719657\pi$
$830$	0.224272	−	0.339757i	0.00778458	−	0.0117931i
$831$	25.4917	+	26.6622i	0.884297	+	0.924902i
$832$	42.4644	−	53.2487i	1.47219	−	1.84607i
$833$	−0.108821	−	2.42309i	−0.00377042	−	0.0839550i
$834$	3.88674	−	1.45872i	0.134587	−	0.0505113i
$835$	0.0614096	−	0.0446167i	0.00212517	−	0.00154402i
$836$	−10.2828	−	8.98383i	−0.355639	−	0.310712i
$837$	−1.17016	+	26.0557i	−0.0404468	+	0.900617i
$838$	−4.18759	−	12.8881i	−0.144658	−	0.445212i
$839$	14.7742	+	34.5660i	0.510063	+	1.19335i	0.954681	+	0.297631i	$0.0961965\pi$
$839$	14.7742	+	34.5660i	0.510063	+	1.19335i	−0.444618	+	0.895720i	$0.646661\pi$
$840$	−0.176500	−	0.0158853i	−0.00608983	−	0.000548094i
$841$	−0.536179	+	1.25445i	−0.0184889	+	0.0432570i
$842$	−8.15949	+	15.1629i	−0.281195	+	0.522547i
$843$	7.33164	−	4.38045i	0.252515	−	0.150871i
$844$	−36.0957	−	21.5662i	−1.24246	−	0.742338i
$845$	−0.185102	−	0.343976i	−0.00636769	−	0.0118332i
$846$	−6.52254	+	0.587039i	−0.224250	+	0.0201828i
$847$	2.65182	−	8.16146i	0.0911176	−	0.280431i
$848$	14.2922	+	5.36394i	0.490795	+	0.184198i
$849$	−23.7394	+	6.55166i	−0.814735	+	0.224853i
$850$	−59.7445	−	10.8420i	−2.04922	−	0.371878i
$851$	44.1134			1.51219
$852$	41.5068	−	9.04383i	1.42200	−	0.309837i
$853$	−23.4436			−0.802694			−0.401347	−	0.915926i	$-0.631458\pi$
$853$	−23.4436			−0.802694			−0.401347	+	0.915926i	$0.631458\pi$
$854$	−86.8046	−	15.7527i	−2.97039	−	0.539047i
$855$	0.0168961	−	0.00466302i	0.000577834	−	0.000159472i
$856$	−6.09833	−	2.28874i	−0.208437	−	0.0782275i
$857$	7.77710	−	23.9355i	0.265661	−	0.817620i	−0.725880	−	0.687822i	$-0.758567\pi$
$857$	7.77710	−	23.9355i	0.265661	−	0.817620i	0.991540	−	0.129798i	$-0.0414329\pi$
$858$	−61.9901	+	5.57921i	−2.11631	+	0.190471i
$859$	3.39836	+	6.31522i	0.115951	+	0.215472i	0.931956	−	0.362573i	$-0.118102\pi$
$859$	3.39836	+	6.31522i	0.115951	+	0.215472i	−0.816005	+	0.578045i	$0.803816\pi$
$860$	−0.141005	−	0.0842464i	−0.00480822	−	0.00287278i
$861$	2.84173	−	1.69785i	0.0968458	−	0.0578627i
$862$	4.32036	−	8.02858i	0.147152	−	0.273454i
$863$	4.77750	−	11.1775i	0.162628	−	0.380487i	−0.818319	−	0.574765i	$-0.805094\pi$
$863$	4.77750	−	11.1775i	0.162628	−	0.380487i	0.980947	+	0.194278i	$0.0622364\pi$
$864$	−35.8061	−	3.22261i	−1.21815	−	0.109635i
$865$	−0.00191572	−	0.00448205i	−6.51365e−5	−	0.000152394i
$866$	13.9370	+	42.8936i	0.473598	+	1.45758i
$867$	−1.18543	+	26.3955i	−0.0402592	+	0.896440i
$868$	30.6469	+	26.7754i	1.04022	+	0.908815i
$869$	1.94558	−	1.41355i	0.0659994	−	0.0479514i
$870$	−0.465916	+	0.174861i	−0.0157960	+	0.00592834i
$871$	0.940597	+	20.9440i	0.0318709	+	0.709661i
$872$	−0.801169	+	1.00463i	−0.0271310	+	0.0340212i
$873$	3.38512	+	3.54056i	0.114569	+	0.119830i
$874$	15.1819	−	22.9997i	0.513537	−	0.777975i
$875$	0.550855	+	0.265278i	0.0186223	+	0.00896803i
$876$	−23.9606	−	6.61271i	−0.809554	−	0.223423i
$877$	−30.0348	−	21.8216i	−1.01420	−	0.736862i	−0.0491167	−	0.998793i	$-0.515641\pi$
$877$	−30.0348	−	21.8216i	−1.01420	−	0.736862i	−0.965087	+	0.261931i	$0.915641\pi$
$878$	−13.0987	−	57.3890i	−0.442059	−	1.93679i
$879$	−29.8891	+	31.2616i	−1.00814	+	1.05443i
$880$	−0.0172307	−	0.127202i	−0.000580847	−	0.00428798i
$881$	−6.68922	−	10.1337i	−0.225366	−	0.341414i	0.704245	−	0.709957i	$-0.251286\pi$
$881$	−6.68922	−	10.1337i	−0.225366	−	0.341414i	−0.929611	+	0.368542i	$0.879857\pi$
$882$	−0.0914993	+	0.400885i	−0.00308094	+	0.0134985i
$883$	−5.85793	+	5.11792i	−0.197135	+	0.172232i	−0.750846	−	0.660477i	$-0.770354\pi$
$883$	−5.85793	+	5.11792i	−0.197135	+	0.172232i	0.553711	+	0.832709i	$0.313211\pi$
$884$	−52.2840	−	65.5620i	−1.75850	−	2.20509i
$885$	−0.0301462	+	0.222548i	−0.00101335	+	0.00748087i
$886$	−70.2512	+	33.8312i	−2.36013	+	1.13658i
$887$	−14.0935	+	2.55760i	−0.473215	+	0.0858758i	−0.409925	−	0.912119i	$-0.634445\pi$
$887$	−14.0935	+	2.55760i	−0.473215	+	0.0858758i	−0.0632900	+	0.997995i	$0.520159\pi$
$888$	−17.7677	+	3.22436i	−0.596245	+	0.108203i
$889$	−18.3940	+	8.85806i	−0.616914	+	0.297090i
$890$	−0.0778037	+	0.574370i	−0.00260799	+	0.0192529i
$891$	17.6786	+	22.1683i	0.592257	+	0.742666i
$892$	−21.9743	+	19.1983i	−0.735753	+	0.642808i
$893$	−2.75485	+	12.0698i	−0.0921877	+	0.403901i
$894$	−47.0628	−	71.2972i	−1.57402	−	2.38453i
$895$	0.0553112	+	0.408324i	0.00184885	+	0.0136488i
$896$	−22.0419	+	23.0540i	−0.736369	+	0.770182i
$897$	−16.1076	−	70.5722i	−0.537818	−	2.35634i
$898$	29.0288	+	21.0907i	0.968705	+	0.703805i
$899$	29.1517	+	8.04536i	0.972264	+	0.268328i
$900$	5.34429	+	2.57367i	0.178143	+	0.0857892i
$901$	23.0165	−	34.8685i	0.766791	−	1.16164i
$902$	−2.75549	−	2.88202i	−0.0917478	−	0.0959607i
$903$	−8.48665	+	10.6419i	−0.282418	+	0.354141i
$904$	−0.350022	−	7.79385i	−0.0116416	−	0.259220i
$905$	0.0363322	−	0.0136357i	0.00120772	−	0.000453266i
$906$	73.8333	−	53.6430i	2.45295	−	1.78217i
$907$	11.3874	+	9.94890i	0.378113	+	0.330348i	0.825925	−	0.563780i	$-0.190654\pi$
$907$	11.3874	+	9.94890i	0.378113	+	0.330348i	−0.447811	+	0.894128i	$0.647796\pi$
$908$	−0.725871	+	16.1628i	−0.0240889	+	0.536381i
$909$	−0.749552	−	2.30688i	−0.0248611	−	0.0765145i
$910$	0.287936	+	0.673659i	0.00954497	+	0.0223316i
$911$	21.8978	+	1.97084i	0.725506	+	0.0652967i	0.446235	−	0.894916i	$-0.352764\pi$
$911$	21.8978	+	1.97084i	0.725506	+	0.0652967i	0.279271	+	0.960212i	$0.409907\pi$
$912$	2.66629	−	6.23809i	0.0882896	−	0.206564i
$913$	−11.0961	+	20.6200i	−0.367226	+	0.682421i
$914$	23.6702	−	14.1423i	0.782942	−	0.467786i
$915$	−0.531512	−	0.317564i	−0.0175712	−	0.0104983i
$916$	−3.57460	−	6.64272i	−0.118108	−	0.219482i
$917$	5.18775	−	0.466906i	0.171314	−	0.0154186i
$918$	−17.8364	+	54.8949i	−0.588690	+	1.81180i
$919$	−39.3912	−	14.7838i	−1.29940	−	0.487671i	−0.396699	−	0.917949i	$-0.629844\pi$
$919$	−39.3912	−	14.7838i	−1.29940	−	0.487671i	−0.902697	+	0.430277i	$0.858416\pi$
$920$	−0.239308	+	0.0660448i	−0.00788975	+	0.00217743i
$921$	−16.7141	−	3.03316i	−0.550749	−	0.0999461i
$922$	5.72424			0.188518
$923$	−30.2295	−	35.2972i	−0.995015	−	1.16182i
$924$	38.5191			1.26718
$925$	30.6486	+	5.56190i	1.00772	+	0.182874i
$926$	60.5499	−	16.7107i	1.98979	−	0.549148i
$927$	5.46218	+	2.04999i	0.179402	+	0.0673306i
$928$	−12.8811	+	39.6441i	−0.422844	+	1.30138i
$929$	12.0942	−	1.08849i	0.396797	−	0.0357124i	0.110556	−	0.993870i	$-0.464737\pi$
$929$	12.0942	−	1.08849i	0.396797	−	0.0357124i	0.286241	+	0.958158i	$0.407594\pi$
$930$	0.234867	+	0.436456i	0.00770158	+	0.0143119i
$931$	0.667299	+	0.398693i	0.0218698	+	0.0130666i
$932$	34.4519	−	20.5840i	1.12851	−	0.674252i
$933$	4.31810	−	8.02437i	0.141368	−	0.262706i
$934$	14.7976	−	34.6208i	0.484193	−	1.13283i
$935$	−0.349902	−	0.0314918i	−0.0114430	−	0.00102989i
$936$	1.47852	+	3.45917i	0.0483270	+	0.113067i
$937$	10.7048	+	32.9459i	0.349709	+	1.07629i	0.959014	+	0.283358i	$0.0914486\pi$
$937$	10.7048	+	32.9459i	0.349709	+	1.07629i	−0.609305	+	0.792936i	$0.708551\pi$
$938$	1.01018	−	22.4934i	0.0329836	−	0.734436i
$939$	35.6911	+	31.1824i	1.16474	+	1.01760i
$940$	0.340955	−	0.247719i	0.0111207	−	0.00807969i
$941$	9.56977	−	3.59159i	0.311965	−	0.117083i	−0.190481	−	0.981691i	$-0.561005\pi$
$941$	9.56977	−	3.59159i	0.311965	−	0.117083i	0.502447	+	0.864608i	$0.332433\pi$
$942$	3.54111	+	78.8488i	0.115375	+	2.56903i
$943$	2.89133	−	3.62561i	0.0941547	−	0.118066i
$944$	7.62606	+	7.97623i	0.248207	+	0.259604i
$945$	0.160080	−	0.242511i	0.00520741	−	0.00788889i
$946$	14.7717	+	7.11367i	0.480269	+	0.231285i
$947$	−50.4308	−	13.9180i	−1.63878	−	0.452275i	−0.679256	−	0.733901i	$-0.737698\pi$
$947$	−50.4308	−	13.9180i	−1.63878	−	0.452275i	−0.959524	+	0.281626i	$0.909126\pi$
$948$	−3.50031	−	2.54312i	−0.113685	−	0.0825967i
$949$	6.05083	+	26.5104i	0.196418	+	0.860564i
$950$	13.4478	−	14.0653i	0.436304	−	0.456338i
$951$	2.75692	+	20.3524i	0.0893993	+	0.659972i
$952$	13.1290	+	19.8896i	0.425514	+	0.644627i
$953$	13.3332	−	58.4165i	0.431904	−	1.89230i	−0.0191827	−	0.999816i	$-0.506106\pi$
$953$	13.3332	−	58.4165i	0.431904	−	1.89230i	0.451087	−	0.892480i	$-0.351036\pi$
$954$	−5.33391	+	4.66010i	−0.172692	+	0.150876i
$955$	0.244022	+	0.305994i	0.00789637	+	0.00990174i
$956$	3.02454	−	22.3280i	0.0978205	−	0.722140i
$957$	25.7893	−	12.4195i	0.833650	−	0.401464i
$958$	3.45567	−	0.627112i	0.111648	−	0.0202611i
$959$	35.0863	−	6.36722i	1.13299	−	0.205608i
$960$	−0.462510	+	0.222733i	−0.0149274	+	0.00718868i
$961$	−0.118220	+	0.872735i	−0.00381355	+	0.0281527i
$962$	46.5452	+	58.3659i	1.50068	+	1.88179i
$963$	−1.36865	+	1.19575i	−0.0441040	+	0.0385325i
$964$	−7.68906	+	33.6880i	−0.247648	+	1.08502i
$965$	−0.276879	−	0.419454i	−0.00891306	−	0.0135027i
$966$	10.4356	+	77.0386i	0.335759	+	2.47868i
$967$	−15.3663	+	16.0719i	−0.494148	+	0.516839i	−0.922094	−	0.386966i	$-0.873523\pi$
$967$	−15.3663	+	16.0719i	−0.494148	+	0.516839i	0.427946	+	0.903804i	$0.359237\pi$
$968$	1.09504	+	4.79768i	0.0351959	+	0.154203i
$969$	−15.0210	−	10.9134i	−0.482545	−	0.350590i
$970$	−0.527330	−	0.145534i	−0.0169315	−	0.00467281i
$971$	31.7234	+	15.2772i	1.01805	+	0.490268i	0.867026	−	0.498262i	$-0.166028\pi$
$971$	31.7234	+	15.2772i	1.01805	+	0.490268i	0.151025	+	0.988530i	$0.451743\pi$
$972$	6.74116	−	10.2124i	0.216223	−	0.327563i
$973$	1.94235	+	2.03154i	0.0622688	+	0.0651280i
$974$	−3.63376	+	4.55659i	−0.116433	+	0.146002i
$975$	−2.29321	−	51.0622i	−0.0734414	−	1.63530i
$976$	−28.4835	+	10.6900i	−0.911735	+	0.342180i
$977$	6.39085	−	4.64323i	0.204462	−	0.148550i	−0.480843	−	0.876807i	$-0.659669\pi$
$977$	6.39085	−	4.64323i	0.204462	−	0.148550i	0.685304	+	0.728257i	$0.259669\pi$
$978$	−25.0941	−	21.9241i	−0.802422	−	0.701055i
$979$	1.49573	−	33.3050i	0.0478038	−	1.06443i
$980$	−0.00817712	−	0.0251666i	−0.000261209	−	0.000803917i
$981$	0.140911	+	0.329677i	0.00449894	+	0.0105258i
$982$	34.7424	+	3.12687i	1.10868	+	0.0997826i
$983$	−18.2375	+	42.6688i	−0.581687	+	1.36092i	0.327624	+	0.944808i	$0.393752\pi$
$983$	−18.2375	+	42.6688i	−0.581687	+	1.36092i	−0.909311	+	0.416116i	$0.863391\pi$
$984$	−0.899546	+	1.67164i	−0.0286765	+	0.0532898i
$985$	0.113748	−	0.0679611i	0.00362430	−	0.00216542i
$986$	57.4517	+	34.3258i	1.82963	+	1.09316i
$987$	−16.5495	−	30.7542i	−0.526777	−	0.978916i
$988$	26.7662	−	2.40900i	0.851546	−	0.0766406i
$989$	−5.89236	+	18.1348i	−0.187366	+	0.576654i
$990$	0.0557602	+	0.0209271i	0.00177217	+	0.000665108i
$991$	−4.07156	+	1.12368i	−0.129337	+	0.0356949i	−0.330106	−	0.943944i	$-0.607085\pi$
$991$	−4.07156	+	1.12368i	−0.129337	+	0.0356949i	0.200769	+	0.979639i	$0.435656\pi$
$992$	40.8486	+	7.41293i	1.29694	+	0.235361i
$993$	−53.8304			−1.70826
$994$	28.9370	+	40.6660i	0.917826	+	1.28985i
$995$	0.459699			0.0145734
$996$	41.4507	+	7.52219i	1.31341	+	0.238350i
$997$	−42.4741	+	11.7221i	−1.34517	+	0.371243i	−0.863163	−	0.504926i	$-0.831520\pi$
$997$	−42.4741	+	11.7221i	−1.34517	+	0.371243i	−0.482005	+	0.876169i	$0.660091\pi$
$998$	−16.3630	−	6.14113i	−0.517961	−	0.194394i
$999$	9.15000	−	28.1608i	0.289493	−	0.890968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.16.5	✓	120
3.2	odd	2		639.2.v.a.442.1		120
71.18	even	35		5041.2.a.s.1.54		60
71.40	even	35	inner	71.2.g.a.40.5	yes	120
71.53	odd	70		5041.2.a.t.1.54		60
213.182	odd	70		639.2.v.a.253.1		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.16.5	✓	120	1.1	even	1	trivial
71.2.g.a.40.5	yes	120	71.40	even	35	inner
639.2.v.a.253.1		120	213.182	odd	70
639.2.v.a.442.1		120	3.2	odd	2
5041.2.a.s.1.54		60	71.18	even	35
5041.2.a.t.1.54		60	71.53	odd	70

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(2.13757 + 0.387912i) q^{2} +(-1.78691 + 0.493156i) q^{3} +(2.54627 + 0.955632i) q^{4} +(-0.00692986 + 0.0213279i) q^{5} +(-4.01095 + 0.360992i) q^{6} +(-1.29201 - 2.40095i) q^{7} +(1.34221 + 0.801931i) q^{8} +(0.374497 - 0.223752i) q^{9} +O(q^{10})\)	\(q+(2.13757 + 0.387912i) q^{2} +(-1.78691 + 0.493156i) q^{3} +(2.54627 + 0.955632i) q^{4} +(-0.00692986 + 0.0213279i) q^{5} +(-4.01095 + 0.360992i) q^{6} +(-1.29201 - 2.40095i) q^{7} +(1.34221 + 0.801931i) q^{8} +(0.374497 - 0.223752i) q^{9} +(-0.0230864 + 0.0429018i) q^{10} +(1.10135 - 2.57674i) q^{11} +(-5.02123 - 0.451919i) q^{12} +(2.16765 + 5.07147i) q^{13} +(-1.83040 - 5.63340i) q^{14} +(0.00186505 - 0.0415285i) q^{15} +(-1.53826 - 1.34394i) q^{16} +(-4.52281 + 3.28601i) q^{17} +(0.887311 - 0.333013i) q^{18} +(-0.0803815 - 1.78983i) q^{19} +(-0.0380269 + 0.0476843i) q^{20} +(3.49275 + 3.65313i) q^{21} +(3.35377 - 5.08075i) q^{22} +(6.37911 + 3.07202i) q^{23} +(-2.79388 - 0.771061i) q^{24} +(4.04468 + 2.93863i) q^{25} +(2.66622 + 11.6815i) q^{26} +(3.28425 - 3.43505i) q^{27} +(-0.995377 - 7.34817i) q^{28} +(-3.03565 - 4.59881i) q^{29} +(0.0200961 - 0.0880468i) q^{30} +(-4.13294 + 3.61084i) q^{31} +(-4.71650 - 5.91431i) q^{32} +(-0.697282 + 5.14755i) q^{33} +(-10.9425 + 5.26964i) q^{34} +(0.0601608 - 0.0109176i) q^{35} +(1.16740 - 0.211851i) q^{36} +(5.61345 - 2.70330i) q^{37} +(0.522477 - 3.85708i) q^{38} +(-6.37442 - 7.99326i) q^{39} +(-0.0264048 + 0.0230692i) q^{40} +(0.145743 - 0.638544i) q^{41} +(6.04891 + 9.16370i) q^{42} +(0.361507 + 2.66876i) q^{43} +(5.26676 - 5.50860i) q^{44} +(0.00217694 + 0.00953781i) q^{45} +(12.4441 + 9.04119i) q^{46} +(-6.66098 - 1.83831i) q^{47} +(3.41151 + 1.64290i) q^{48} +(-0.239016 + 0.362093i) q^{49} +(7.50586 + 7.85052i) q^{50} +(6.46133 - 8.10225i) q^{51} +(0.672969 + 14.9848i) q^{52} +(-6.99687 + 2.62597i) q^{53} +(8.35281 - 6.06867i) q^{54} +(0.0473243 + 0.0413460i) q^{55} +(0.191257 - 4.25868i) q^{56} +(1.02630 + 3.15863i) q^{57} +(-4.70499 - 11.0079i) q^{58} +(-5.38067 - 0.484269i) q^{59} +(0.0444349 - 0.103961i) q^{60} +(7.05785 - 13.1157i) q^{61} +(-10.2351 + 6.11521i) q^{62} +(-1.02107 - 0.610061i) q^{63} +(-5.85174 - 10.8744i) q^{64} +(-0.123185 + 0.0110869i) q^{65} +(-3.48729 + 10.7328i) q^{66} +(3.55888 + 1.33567i) q^{67} +(-14.6565 + 4.04494i) q^{68} +(-12.9139 - 2.34352i) q^{69} +0.132833 q^{70} +(-8.03904 + 2.52464i) q^{71} +0.682085 q^{72} +(4.85109 + 0.880343i) q^{73} +(13.0478 - 3.60097i) q^{74} +(-8.67668 - 3.25641i) q^{75} +(1.50575 - 4.63422i) q^{76} +(-7.60960 + 0.684876i) q^{77} +(-10.5251 - 19.5589i) q^{78} +(0.736717 + 0.440168i) q^{79} +(0.0393234 - 0.0234946i) q^{80} +(-4.79481 + 8.91025i) q^{81} +(0.559236 - 1.30840i) q^{82} +(-8.32249 - 0.749038i) q^{83} +(5.40244 + 12.6396i) q^{84} +(-0.0387413 - 0.119234i) q^{85} +(-0.262494 + 5.84489i) q^{86} +(7.69236 + 6.72061i) q^{87} +(3.54461 - 2.57531i) q^{88} +(11.1385 - 4.18034i) q^{89} +(0.000953540 + 0.0212322i) q^{90} +(9.37574 - 11.7568i) q^{91} +(13.3072 + 13.9183i) q^{92} +(5.60448 - 8.49042i) q^{93} +(-13.5252 - 6.51340i) q^{94} +(0.0387304 + 0.0106889i) q^{95} +(11.3446 + 8.24236i) q^{96} +(2.49858 + 10.9470i) q^{97} +(-0.651374 + 0.681284i) q^{98} +(-0.164097 - 1.21141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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