LMFDB - Embedded newform 441.2.bh.a.41.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(20,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([7, 39]))

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

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

chi := DirichletCharacter("441.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bh (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			41.42
Character	$\chi$	$=$	441.41
Dual form			441.2.bh.a.398.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52873 + 0.599983i) q^{2} +(1.14417 - 1.30034i) q^{3} +(0.510936 + 0.474079i) q^{4} +(0.0481771 - 0.642879i) q^{5} +(2.52930 - 1.30139i) q^{6} +(1.24367 + 2.33523i) q^{7} +(-0.928450 - 1.92795i) q^{8} +(-0.381764 - 2.97561i) q^{9} +O(q^{10})$	\(q+(1.52873 + 0.599983i) q^{2} +(1.14417 - 1.30034i) q^{3} +(0.510936 + 0.474079i) q^{4} +(0.0481771 - 0.642879i) q^{5} +(2.52930 - 1.30139i) q^{6} +(1.24367 + 2.33523i) q^{7} +(-0.928450 - 1.92795i) q^{8} +(-0.381764 - 2.97561i) q^{9} +(0.459366 - 0.953884i) q^{10} +(2.85570 + 1.12078i) q^{11} +(1.20106 - 0.121964i) q^{12} +(-0.424627 - 2.81722i) q^{13} +(0.500141 + 4.31611i) q^{14} +(-0.780838 - 0.798208i) q^{15} +(-0.366789 - 4.89447i) q^{16} +(0.255080 + 1.11758i) q^{17} +(1.20170 - 4.77796i) q^{18} +2.78250i q^{19} +(0.329391 - 0.305630i) q^{20} +(4.45955 + 1.05470i) q^{21} +(3.69315 + 3.42674i) q^{22} +(-5.92497 + 6.38559i) q^{23} +(-3.56929 - 0.998593i) q^{24} +(4.53318 + 0.683267i) q^{25} +(1.04114 - 4.56154i) q^{26} +(-4.30610 - 2.90817i) q^{27} +(-0.471647 + 1.78275i) q^{28} +(-0.853937 - 0.920325i) q^{29} +(-0.714781 - 1.68873i) q^{30} +(-4.77494 - 2.75681i) q^{31} +(1.11440 - 3.61281i) q^{32} +(4.72480 - 2.43102i) q^{33} +(-0.280579 + 1.86152i) q^{34} +(1.56119 - 0.687025i) q^{35} +(1.21562 - 1.70133i) q^{36} +(2.37473 + 10.4044i) q^{37} +(-1.66945 + 4.25370i) q^{38} +(-4.14918 - 2.67121i) q^{39} +(-1.28417 + 0.503998i) q^{40} +(0.285247 - 3.80636i) q^{41} +(6.18466 + 4.28800i) q^{42} +(0.109879 + 1.46623i) q^{43} +(0.927742 + 1.92648i) q^{44} +(-1.93135 + 0.102071i) q^{45} +(-12.8889 + 6.20698i) q^{46} +(1.74574 - 4.44807i) q^{47} +(-6.78413 - 5.12314i) q^{48} +(-3.90657 + 5.80850i) q^{49} +(6.52007 + 3.76436i) q^{50} +(1.74509 + 0.947007i) q^{51} +(1.11863 - 1.64072i) q^{52} +(-1.35105 - 0.308368i) q^{53} +(-4.83802 - 7.02940i) q^{54} +(0.858106 - 1.78188i) q^{55} +(3.34751 - 4.56587i) q^{56} +(3.61820 + 3.18365i) q^{57} +(-0.753260 - 1.91928i) q^{58} +(-7.97062 + 5.43427i) q^{59} +(-0.0205446 - 0.778012i) q^{60} +(2.11544 + 2.27990i) q^{61} +(-5.64555 - 7.07930i) q^{62} +(6.47394 - 4.59218i) q^{63} +(-2.24917 + 2.82037i) q^{64} +(-1.83159 + 0.137258i) q^{65} +(8.68151 - 0.881582i) q^{66} +(-2.45560 + 4.25322i) q^{67} +(-0.399492 + 0.691940i) q^{68} +(1.52429 + 15.0107i) q^{69} +(2.79884 - 0.113592i) q^{70} +(-6.56623 - 1.49870i) q^{71} +(-5.38237 + 3.49873i) q^{72} +(-0.705605 - 0.562701i) q^{73} +(-2.61212 + 17.3303i) q^{74} +(6.07520 - 5.11290i) q^{75} +(-1.31913 + 1.42168i) q^{76} +(0.934275 + 8.06260i) q^{77} +(-4.74030 - 6.57299i) q^{78} +(6.63674 + 11.4952i) q^{79} -3.16422 q^{80} +(-8.70851 + 2.27196i) q^{81} +(2.71981 - 5.64775i) q^{82} +(-5.86303 - 0.883709i) q^{83} +(1.77854 + 2.65306i) q^{84} +(0.730758 - 0.110144i) q^{85} +(-0.711740 + 2.30740i) q^{86} +(-2.17378 + 0.0574019i) q^{87} +(-0.490572 - 6.54623i) q^{88} +(4.79110 - 6.00784i) q^{89} +(-3.01376 - 1.00274i) q^{90} +(6.05074 - 4.49529i) q^{91} +(-6.05456 + 0.453726i) q^{92} +(-9.04811 + 3.05478i) q^{93} +(5.33754 - 5.75249i) q^{94} +(1.78881 + 0.134053i) q^{95} +(-3.42281 - 5.58276i) q^{96} +(11.1315 - 6.42677i) q^{97} +(-9.45710 + 6.53577i) q^{98} +(2.24480 - 8.92533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 15 q^{2} - 14 q^{3} - 57 q^{4} - 21 q^{5} + 14 q^{6} - 5 q^{7} - 20 q^{9}+O(q^{10}) $ 648 * q - 15 * q^2 - 14 * q^3 - 57 * q^4 - 21 * q^5 + 14 * q^6 - 5 * q^7 - 20 * q^9	$ 648 q - 15 q^{2} - 14 q^{3} - 57 q^{4} - 21 q^{5} + 14 q^{6} - 5 q^{7} - 20 q^{9} - 28 q^{10} - 15 q^{11} + 21 q^{12} - 7 q^{13} - 114 q^{14} - 10 q^{15} + 39 q^{16} - 18 q^{18} - 21 q^{20} + 10 q^{21} + 3 q^{22} + 30 q^{23} - 14 q^{24} + 41 q^{25} + 7 q^{27} - 20 q^{28} + 75 q^{29} - 70 q^{30} - 39 q^{32} - 14 q^{33} - 7 q^{34} - 128 q^{36} - 10 q^{37} + 21 q^{38} - 36 q^{39} - 7 q^{40} - 21 q^{41} + 104 q^{42} + 3 q^{43} - 35 q^{45} - 72 q^{46} - 147 q^{47} - 13 q^{49} - 18 q^{50} + 22 q^{51} - 35 q^{52} - 14 q^{54} - 112 q^{55} - 63 q^{56} - 16 q^{57} + 33 q^{58} - 21 q^{59} - 90 q^{60} - 56 q^{61} - 38 q^{63} + 52 q^{64} + 27 q^{65} - 42 q^{66} - 26 q^{67} - 182 q^{69} - 25 q^{70} + 24 q^{72} - 28 q^{73} + 33 q^{74} - 14 q^{75} + 21 q^{76} + 3 q^{77} + 90 q^{78} - 2 q^{79} + 56 q^{81} - 28 q^{82} - 21 q^{83} + 116 q^{84} + 5 q^{85} - 123 q^{86} - 70 q^{87} - 41 q^{88} - 224 q^{90} - 4 q^{91} - 225 q^{92} + 112 q^{93} - 7 q^{94} - 12 q^{95} - 371 q^{96} + 224 q^{99}+O(q^{100}) $ 648 * q - 15 * q^2 - 14 * q^3 - 57 * q^4 - 21 * q^5 + 14 * q^6 - 5 * q^7 - 20 * q^9 - 28 * q^10 - 15 * q^11 + 21 * q^12 - 7 * q^13 - 114 * q^14 - 10 * q^15 + 39 * q^16 - 18 * q^18 - 21 * q^20 + 10 * q^21 + 3 * q^22 + 30 * q^23 - 14 * q^24 + 41 * q^25 + 7 * q^27 - 20 * q^28 + 75 * q^29 - 70 * q^30 - 39 * q^32 - 14 * q^33 - 7 * q^34 - 128 * q^36 - 10 * q^37 + 21 * q^38 - 36 * q^39 - 7 * q^40 - 21 * q^41 + 104 * q^42 + 3 * q^43 - 35 * q^45 - 72 * q^46 - 147 * q^47 - 13 * q^49 - 18 * q^50 + 22 * q^51 - 35 * q^52 - 14 * q^54 - 112 * q^55 - 63 * q^56 - 16 * q^57 + 33 * q^58 - 21 * q^59 - 90 * q^60 - 56 * q^61 - 38 * q^63 + 52 * q^64 + 27 * q^65 - 42 * q^66 - 26 * q^67 - 182 * q^69 - 25 * q^70 + 24 * q^72 - 28 * q^73 + 33 * q^74 - 14 * q^75 + 21 * q^76 + 3 * q^77 + 90 * q^78 - 2 * q^79 + 56 * q^81 - 28 * q^82 - 21 * q^83 + 116 * q^84 + 5 * q^85 - 123 * q^86 - 70 * q^87 - 41 * q^88 - 224 * q^90 - 4 * q^91 - 225 * q^92 + 112 * q^93 - 7 * q^94 - 12 * q^95 - 371 * q^96 + 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.52873	+	0.599983i	1.08098	+	0.424252i	0.837938	−	0.545765i	$-0.183761\pi$
$2$	1.52873	+	0.599983i	1.08098	+	0.424252i	0.243038	+	0.970017i	$0.421856\pi$
$3$	1.14417	−	1.30034i	0.660585	−	0.750751i
$3$	1.14417	−	1.30034i	0.660585	−	0.750751i
$4$	0.510936	+	0.474079i	0.255468	+	0.237040i
$5$	0.0481771	−	0.642879i	0.0215455	−	0.287504i	−0.976015	−	0.217702i	$-0.930144\pi$
$5$	0.0481771	−	0.642879i	0.0215455	−	0.287504i	0.997561	−	0.0698026i	$-0.0222369\pi$
$6$	2.52930	−	1.30139i	1.03258	−	0.531290i
$7$	1.24367	+	2.33523i	0.470063	+	0.882633i
$7$	1.24367	+	2.33523i	0.470063	+	0.882633i
$8$	−0.928450	−	1.92795i	−0.328257	−	0.681632i
$9$	−0.381764	−	2.97561i	−0.127255	−	0.991870i
$10$	0.459366	−	0.953884i	0.145264	−	0.301645i
$11$	2.85570	+	1.12078i	0.861027	+	0.337928i	0.754435	−	0.656375i	$-0.227911\pi$
$11$	2.85570	+	1.12078i	0.861027	+	0.337928i	0.106592	+	0.994303i	$0.466006\pi$
$12$	1.20106	−	0.121964i	0.346716	−	0.0352080i
$13$	−0.424627	−	2.81722i	−0.117770	−	0.781355i	−0.967267	−	0.253761i	$-0.918332\pi$
$13$	−0.424627	−	2.81722i	−0.117770	−	0.781355i	0.849497	−	0.527594i	$-0.176906\pi$
$14$	0.500141	+	4.31611i	0.133668	+	1.15353i
$15$	−0.780838	−	0.798208i	−0.201612	−	0.206096i
$16$	−0.366789	−	4.89447i	−0.0916974	−	1.22362i
$17$	0.255080	+	1.11758i	0.0618660	+	0.271053i	0.996395	−	0.0848340i	$-0.0270360\pi$
$17$	0.255080	+	1.11758i	0.0618660	+	0.271053i	−0.934529	+	0.355887i	$0.884179\pi$
$18$	1.20170	−	4.77796i	0.283244	−	1.12618i
$19$			2.78250i			0.638350i	0.947696	+	0.319175i	$0.103406\pi$
$19$			2.78250i			0.638350i	−0.947696	+	0.319175i	$0.896594\pi$
$20$	0.329391	−	0.305630i	0.0736541	−	0.0683410i
$21$	4.45955	+	1.05470i	0.973154	+	0.230154i
$22$	3.69315	+	3.42674i	0.787383	+	0.730584i
$23$	−5.92497	+	6.38559i	−1.23544	+	1.33149i	−0.310882	+	0.950448i	$0.600624\pi$
$23$	−5.92497	+	6.38559i	−1.23544	+	1.33149i	−0.924559	+	0.381040i	$0.875566\pi$
$24$	−3.56929	−	0.998593i	−0.728578	−	0.203837i
$25$	4.53318	+	0.683267i	0.906636	+	0.136653i
$26$	1.04114	−	4.56154i	0.204184	−	0.894591i
$27$	−4.30610	−	2.90817i	−0.828710	−	0.559678i
$28$	−0.471647	+	1.78275i	−0.0891329	+	0.336908i
$29$	−0.853937	−	0.920325i	−0.158572	−	0.170900i	0.648768	−	0.760986i	$-0.275284\pi$
$29$	−0.853937	−	0.920325i	−0.158572	−	0.170900i	−0.807341	+	0.590086i	$0.799094\pi$
$30$	−0.714781	−	1.68873i	−0.130501	−	0.308319i
$31$	−4.77494	−	2.75681i	−0.857604	−	0.495138i	0.00560541	−	0.999984i	$-0.498216\pi$
$31$	−4.77494	−	2.75681i	−0.857604	−	0.495138i	−0.863209	+	0.504847i	$0.831549\pi$
$32$	1.11440	−	3.61281i	0.197000	−	0.638660i
$33$	4.72480	−	2.43102i	0.822481	−	0.423187i
$34$	−0.280579	+	1.86152i	−0.0481190	+	0.319248i
$35$	1.56119	−	0.687025i	0.263888	−	0.116128i
$36$	1.21562	−	1.70133i	0.202603	−	0.283555i
$37$	2.37473	+	10.4044i	0.390403	+	1.71047i	0.663239	+	0.748408i	$0.269181\pi$
$37$	2.37473	+	10.4044i	0.390403	+	1.71047i	−0.272836	+	0.962061i	$0.587962\pi$
$38$	−1.66945	+	4.25370i	−0.270821	+	0.690041i
$39$	−4.14918	−	2.67121i	−0.664401	−	0.427735i
$40$	−1.28417	+	0.503998i	−0.203045	+	0.0796892i
$41$	0.285247	−	3.80636i	0.0445481	−	0.594453i	−0.929604	−	0.368560i	$-0.879851\pi$
$41$	0.285247	−	3.80636i	0.0445481	−	0.594453i	0.974152	−	0.225893i	$-0.0725300\pi$
$42$	6.18466	+	4.28800i	0.954313	+	0.661653i
$43$	0.109879	+	1.46623i	0.0167564	+	0.223599i	0.999295	+	0.0375404i	$0.0119523\pi$
$43$	0.109879	+	1.46623i	0.0167564	+	0.223599i	−0.982539	+	0.186058i	$0.940429\pi$
$44$	0.927742	+	1.92648i	0.139862	+	0.290427i
$45$	−1.93135	+	0.102071i	−0.287909	+	0.0152159i
$46$	−12.8889	+	6.20698i	−1.90037	+	0.915169i
$47$	1.74574	−	4.44807i	0.254642	−	0.648818i	−0.745195	−	0.666847i	$-0.767644\pi$
$47$	1.74574	−	4.44807i	0.254642	−	0.648818i	0.999837	+	0.0180283i	$0.00573890\pi$
$48$	−6.78413	−	5.12314i	−0.979205	−	0.739461i
$49$	−3.90657	+	5.80850i	−0.558081	+	0.829786i
$50$	6.52007	+	3.76436i	0.922077	+	0.532361i
$51$	1.74509	+	0.947007i	0.244361	+	0.132607i
$52$	1.11863	−	1.64072i	0.155126	−	0.227527i
$53$	−1.35105	−	0.308368i	−0.185581	−	0.0423576i	0.128720	−	0.991681i	$-0.458913\pi$
$53$	−1.35105	−	0.308368i	−0.185581	−	0.0423576i	−0.314301	+	0.949323i	$0.601770\pi$
$54$	−4.83802	−	7.02940i	−0.658371	−	0.956581i
$55$	0.858106	−	1.78188i	0.115707	−	0.240268i
$56$	3.34751	−	4.56587i	0.447330	−	0.610140i
$57$	3.61820	+	3.18365i	0.479242	+	0.421685i
$58$	−0.753260	−	1.91928i	−0.0989079	−	0.252013i
$59$	−7.97062	+	5.43427i	−1.03769	+	0.707482i	−0.957245	−	0.289277i	$-0.906585\pi$
$59$	−7.97062	+	5.43427i	−1.03769	+	0.707482i	−0.0804404	+	0.996759i	$0.525633\pi$
$60$	−0.0205446	−	0.778012i	−0.00265229	−	0.100441i
$61$	2.11544	+	2.27990i	0.270854	+	0.291911i	0.853802	−	0.520598i	$-0.174291\pi$
$61$	2.11544	+	2.27990i	0.270854	+	0.291911i	−0.582947	+	0.812510i	$0.698101\pi$
$62$	−5.64555	−	7.07930i	−0.716986	−	0.899072i
$63$	6.47394	−	4.59218i	0.815639	−	0.578561i
$64$	−2.24917	+	2.82037i	−0.281146	+	0.352546i
$65$	−1.83159	+	0.137258i	−0.227180	+	0.0170248i
$66$	8.68151	−	0.881582i	1.06862	−	0.108515i
$67$	−2.45560	+	4.25322i	−0.299999	+	0.519614i	−0.976135	−	0.217163i	$-0.930320\pi$
$67$	−2.45560	+	4.25322i	−0.299999	+	0.519614i	0.676136	+	0.736777i	$0.263653\pi$
$68$	−0.399492	+	0.691940i	−0.0484455	+	0.0839100i
$69$	1.52429	+	15.0107i	0.183503	+	1.80707i
$70$	2.79884	−	0.113592i	0.334525	−	0.0135769i
$71$	−6.56623	−	1.49870i	−0.779269	−	0.177863i	−0.185657	−	0.982615i	$-0.559441\pi$
$71$	−6.56623	−	1.49870i	−0.779269	−	0.177863i	−0.593612	+	0.804752i	$0.702298\pi$
$72$	−5.38237	+	3.49873i	−0.634318	+	0.412329i
$73$	−0.705605	−	0.562701i	−0.0825848	−	0.0658592i	0.581327	−	0.813670i	$-0.302534\pi$
$73$	−0.705605	−	0.562701i	−0.0825848	−	0.0658592i	−0.663912	+	0.747811i	$0.731105\pi$
$74$	−2.61212	+	17.3303i	−0.303653	+	2.01460i
$75$	6.07520	−	5.11290i	0.701503	−	0.590387i
$76$	−1.31913	+	1.42168i	−0.151314	+	0.163078i
$77$	0.934275	+	8.06260i	0.106471	+	0.918818i
$78$	−4.74030	−	6.57299i	−0.536734	−	0.744245i
$79$	6.63674	+	11.4952i	0.746691	+	1.29331i	0.949400	+	0.314068i	$0.101692\pi$
$79$	6.63674	+	11.4952i	0.746691	+	1.29331i	−0.202709	+	0.979239i	$0.564975\pi$
$80$	−3.16422			−0.353771
$81$	−8.70851	+	2.27196i	−0.967613	+	0.252440i
$82$	2.71981	−	5.64775i	0.300353	−	0.623690i
$83$	−5.86303	−	0.883709i	−0.643551	−	0.0969997i	−0.180845	−	0.983512i	$-0.557883\pi$
$83$	−5.86303	−	0.883709i	−0.643551	−	0.0969997i	−0.462706	+	0.886512i	$0.653121\pi$
$84$	1.77854	+	2.65306i	0.194054	+	0.289473i
$85$	0.730758	−	0.110144i	0.0792618	−	0.0119468i
$86$	−0.711740	+	2.30740i	−0.0767489	+	0.248814i
$87$	−2.17378	+	0.0574019i	−0.233054	+	0.00615413i
$88$	−0.490572	−	6.54623i	−0.0522952	−	0.697831i
$89$	4.79110	−	6.00784i	0.507855	−	0.636830i	−0.460126	−	0.887854i	$-0.652196\pi$
$89$	4.79110	−	6.00784i	0.507855	−	0.636830i	0.967981	+	0.251023i	$0.0807671\pi$
$90$	−3.01376	−	1.00274i	−0.317678	−	0.105698i
$91$	6.05074	−	4.49529i	0.634290	−	0.471234i
$92$	−6.05456	+	0.453726i	−0.631231	+	0.0473042i
$93$	−9.04811	+	3.05478i	−0.938245	+	0.316766i
$94$	5.33754	−	5.75249i	0.550525	−	0.593325i
$95$	1.78881	+	0.134053i	0.183528	+	0.0137536i
$96$	−3.42281	−	5.58276i	−0.349339	−	0.569788i
$97$	11.1315	−	6.42677i	1.13023	−	0.652539i	0.186238	−	0.982505i	$-0.440370\pi$
$97$	11.1315	−	6.42677i	1.13023	−	0.652539i	0.943993	+	0.329965i	$0.107037\pi$
$98$	−9.45710	+	6.53577i	−0.955311	+	0.660212i
$99$	2.24480	−	8.92533i	0.225611	−	0.897030i
$100$	1.99224	+	2.49819i	0.199224	+	0.249819i
$101$	−12.5736	−	8.57256i	−1.25112	−	0.853002i	−0.257559	−	0.966263i	$-0.582918\pi$
$101$	−12.5736	−	8.57256i	−1.25112	−	0.853002i	−0.993565	+	0.113261i	$0.963870\pi$
$102$	2.09958	+	2.49474i	0.207889	+	0.247016i
$103$	13.9860	+	1.04810i	1.37808	+	0.103273i	0.743060	−	0.669225i	$-0.233374\pi$
$103$	13.9860	+	1.04810i	1.37808	+	0.103273i	0.635018	+	0.772498i	$0.280993\pi$
$104$	−5.03720	+	3.43430i	−0.493938	+	0.336761i
$105$	0.892891	−	2.81614i	0.0871373	−	0.274827i
$106$	−1.88038	−	1.28202i	−0.182638	−	0.124521i
$107$	−5.83450	−	4.65286i	−0.564043	−	0.449809i	0.299492	−	0.954099i	$-0.403183\pi$
$107$	−5.83450	−	4.65286i	−0.564043	−	0.449809i	−0.863534	+	0.504290i	$0.831754\pi$
$108$	−0.821439	−	3.52732i	−0.0790430	−	0.339417i
$109$	−6.76887	−	8.48790i	−0.648341	−	0.812993i	0.343678	−	0.939088i	$-0.388327\pi$
$109$	−6.76887	−	8.48790i	−0.648341	−	0.812993i	−0.992018	+	0.126094i	$0.959756\pi$
$110$	2.38091	−	2.20916i	0.227011	−	0.210635i
$111$	16.2463	+	8.81639i	1.54203	+	0.836814i
$112$	10.9735	−	6.94364i	1.03690	−	0.656112i
$113$	15.7859	−	6.19550i	1.48501	−	0.582823i	0.522157	−	0.852850i	$-0.325128\pi$
$113$	15.7859	−	6.19550i	1.48501	−	0.582823i	0.962853	+	0.270026i	$0.0870324\pi$
$114$	3.62112	+	7.03780i	0.339149	+	0.659150i
$115$	3.81972	+	4.11668i	0.356191	+	0.383882i
$116$		−	0.875061i		−	0.0812473i
$117$	−8.22083	+	2.33904i	−0.760016	+	0.216244i
$118$	−15.4454	+	3.52531i	−1.42186	+	0.324531i
$119$	−2.29257	+	1.98557i	−0.210159	+	0.182017i
$120$	−0.813933	+	2.24651i	−0.0743016	+	0.205077i
$121$	−1.16468	−	1.08067i	−0.105880	−	0.0982425i
$122$	1.86604	+	4.75458i	0.168943	+	0.430460i
$123$	−4.62318	−	4.72603i	−0.416858	−	0.426131i
$124$	−1.13274	−	3.67225i	−0.101723	−	0.329778i
$125$	1.37493	−	6.02396i	0.122977	−	0.538800i
$126$	12.6521	−	3.13596i	1.12714	−	0.279374i
$127$	1.55697	+	6.82153i	0.138159	+	0.605313i	0.995839	+	0.0911297i	$0.0290478\pi$
$127$	1.55697	+	6.82153i	0.138159	+	0.605313i	−0.857680	+	0.514183i	$0.828095\pi$
$128$	−11.6790	+	6.74290i	−1.03229	+	0.595994i
$129$	2.03232	+	1.53474i	0.178936	+	0.135126i
$130$	−2.88236	−	0.889089i	−0.252799	−	0.0779783i
$131$	14.5264	−	9.90396i	1.26918	−	0.865313i	0.273844	−	0.961774i	$-0.411705\pi$
$131$	14.5264	−	9.90396i	1.26918	−	0.865313i	0.995337	+	0.0964612i	$0.0307524\pi$
$132$	3.56656	+	0.997832i	0.310430	+	0.0868501i
$133$	−6.49778	+	3.46052i	−0.563429	+	0.300065i
$134$	−6.30581	+	5.02872i	−0.544739	+	0.434415i
$135$	−2.07706	+	2.62820i	−0.178765	+	0.226199i
$136$	1.91780	−	1.52940i	0.164450	−	0.131145i
$137$	−5.42967	+	0.406898i	−0.463888	+	0.0347636i	−0.304625	−	0.952472i	$-0.598531\pi$
$137$	−5.42967	+	0.406898i	−0.463888	+	0.0347636i	−0.159264	+	0.987236i	$0.550912\pi$
$138$	−6.67591	+	23.8618i	−0.568291	+	2.03125i
$139$	2.38133	+	0.178456i	0.201981	+	0.0151364i	0.175337	−	0.984509i	$-0.443899\pi$
$139$	2.38133	+	0.178456i	0.201981	+	0.0151364i	0.0266449	+	0.999645i	$0.491518\pi$
$140$	1.12337	+	0.389100i	0.0949421	+	0.0328849i
$141$	−3.78659	−	7.35939i	−0.318888	−	0.619773i
$142$	−9.13881	−	6.23074i	−0.766912	−	0.522872i
$143$	1.94487	−	8.52105i	0.162638	−	0.712566i
$144$	−14.4240	+	2.95995i	−1.20200	+	0.246663i
$145$	−0.632798	+	0.504639i	−0.0525510	+	0.0419080i
$146$	−0.741069	−	1.28357i	−0.0613313	−	0.106229i
$147$	3.08326	+	11.7258i	0.254303	+	0.967125i
$148$	−3.71916	+	6.44178i	−0.305713	+	0.529511i
$149$	−2.68386	−	17.8062i	−0.219870	−	1.45874i	−0.777620	−	0.628735i	$-0.783573\pi$
$149$	−2.68386	−	17.8062i	−0.219870	−	1.45874i	0.557750	−	0.830009i	$-0.311665\pi$
$150$	12.3550	−	4.17124i	1.00878	−	0.340580i
$151$	9.17394	−	2.82979i	0.746565	−	0.230285i	0.101947	−	0.994790i	$-0.467493\pi$
$151$	9.17394	−	2.82979i	0.746565	−	0.230285i	0.644618	+	0.764505i	$0.277017\pi$
$152$	5.36452	−	2.58342i	0.435120	−	0.209543i
$153$	3.22810	−	1.18567i	0.260976	−	0.0958558i
$154$	−3.40916	+	12.8861i	−0.274718	+	1.03839i
$155$	−2.00234	+	2.93689i	−0.160832	+	0.235897i
$156$	−0.853602	−	3.33186i	−0.0683428	−	0.266762i
$157$	−11.7625	−	17.2524i	−0.938748	−	1.37689i	−0.926226	−	0.376968i	$-0.876967\pi$
$157$	−11.7625	−	17.2524i	−0.938748	−	1.37689i	−0.0125213	−	0.999922i	$-0.503986\pi$
$158$	3.24888	+	21.5549i	0.258467	+	1.71482i
$159$	−1.94681	+	1.40400i	−0.154392	+	0.111344i
$160$	−2.26891	−	0.890481i	−0.179373	−	0.0703987i
$161$	−22.2805	−	5.89457i	−1.75595	−	0.464557i
$162$	−14.6761	−	1.75174i	−1.15306	−	0.137630i
$163$	15.8504	+	7.63314i	1.24150	+	0.597873i	0.935219	−	0.354069i	$-0.115202\pi$
$163$	15.8504	+	7.63314i	1.24150	+	0.597873i	0.306277	+	0.951942i	$0.400916\pi$
$164$	1.95026	−	1.80957i	0.152290	−	0.141304i
$165$	−1.33523	−	3.15459i	−0.103947	−	0.245585i
$166$	−8.43278	−	4.86867i	−0.654511	−	0.377882i
$167$	−12.7855	−	3.94381i	−0.989374	−	0.305181i	−0.242503	−	0.970151i	$-0.577968\pi$
$167$	−12.7855	−	3.94381i	−0.989374	−	0.305181i	−0.746871	+	0.664969i	$0.768445\pi$
$168$	−2.10707	−	9.57702i	−0.162564	−	0.738883i
$169$	4.66605	−	1.43928i	0.358927	−	0.110714i
$170$	1.18322	+	0.270061i	0.0907486	+	0.0207128i
$171$	8.27965	−	1.06226i	0.633160	−	0.0812329i
$172$	−0.638970	+	0.801243i	−0.0487210	+	0.0610942i
$173$	−0.429415	+	0.132457i	−0.0326478	+	0.0100705i	−0.311036	−	0.950398i	$-0.600676\pi$
$173$	−0.429415	+	0.132457i	−0.0326478	+	0.0100705i	0.278388	+	0.960469i	$0.410200\pi$
$174$	−3.35757	−	1.21648i	−0.254536	−	0.0922210i
$175$	4.04220	+	11.4358i	0.305561	+	0.864463i
$176$	4.43818	−	14.3882i	0.334540	−	1.08455i
$177$	−2.05332	+	16.5822i	−0.154337	+	1.24640i
$178$	10.9289	−	6.30980i	0.819156	−	0.472940i
$179$	7.21493	−	1.64676i	0.539269	−	0.123085i	0.0557932	−	0.998442i	$-0.482231\pi$
$179$	7.21493	−	1.64676i	0.539269	−	0.123085i	0.483476	+	0.875358i	$0.339374\pi$
$180$	−1.03519	−	0.863461i	−0.0771582	−	0.0643586i
$181$	4.57595	+	3.64920i	0.340127	+	0.271243i	0.778625	−	0.627490i	$-0.215918\pi$
$181$	4.57595	+	3.64920i	0.340127	+	0.271243i	−0.438497	+	0.898733i	$0.644489\pi$
$182$	11.9471	−	3.24175i	0.885575	−	0.240294i
$183$	5.38506	−	0.142200i	0.398075	−	0.0105118i
$184$	17.8121	+	5.49431i	1.31313	+	0.405046i
$185$	6.80316	−	1.02541i	0.500178	−	0.0753898i
$186$	−15.6649	−	0.758768i	−1.14861	−	0.0556356i
$187$	−0.524128	+	3.47736i	−0.0383280	+	0.254290i
$188$	3.00070	−	1.44506i	0.218849	−	0.105392i
$189$	1.43587	−	13.6725i	0.104444	−	0.994531i
$190$	2.65419	+	1.27819i	0.192555	+	0.0927295i
$191$	−14.0114	+	20.5509i	−1.01383	+	1.48701i	−0.146541	+	0.989205i	$0.546814\pi$
$191$	−14.0114	+	20.5509i	−1.01383	+	1.48701i	−0.867287	+	0.497808i	$0.834138\pi$
$192$	1.09401	+	6.15165i	0.0789534	+	0.443957i
$193$	−0.0725428	+	0.968016i	−0.00522174	+	0.0696793i	−0.999206	−	0.0398448i	$-0.987314\pi$
$193$	−0.0725428	+	0.968016i	−0.00522174	+	0.0696793i	0.993984	+	0.109524i	$0.0349327\pi$
$194$	20.8730	−	3.14610i	1.49859	−	0.225877i
$195$	−1.91716	+	2.53873i	−0.137291	+	0.181802i
$196$	−4.74970	+	1.11575i	−0.339264	+	0.0796964i
$197$			9.89619i			0.705075i	0.935798	+	0.352537i	$0.114681\pi$
$197$			9.89619i			0.705075i	−0.935798	+	0.352537i	$0.885319\pi$
$198$	8.78675	−	12.2976i	0.624447	−	0.873952i
$199$	−11.0687	−	22.9844i	−0.784638	−	1.62932i	−0.777125	−	0.629346i	$-0.783323\pi$
$199$	−11.0687	−	22.9844i	−0.784638	−	1.62932i	−0.00751350	−	0.999972i	$-0.502392\pi$
$200$	−2.89153	−	9.37411i	−0.204462	−	0.662850i
$201$	2.72102	+	8.05951i	0.191926	+	0.568474i
$202$	−14.0783	−	20.6491i	−0.990547	−	1.45287i
$203$	1.08715	−	3.13872i	0.0763031	−	0.220295i
$204$	0.442671	+	1.31117i	0.0309932	+	0.0918002i
$205$	−2.43329	−	0.366759i	−0.169948	−	0.0256155i
$206$	20.7519	+	9.99360i	1.44586	+	0.696287i
$207$	21.2630	+	15.1926i	1.47788	+	1.05596i
$208$	−13.6330	+	3.11165i	−0.945280	+	0.215754i
$209$	−3.11858	+	7.94600i	−0.215716	+	0.549636i
$210$	3.05463	−	3.76940i	0.210789	−	0.260114i
$211$	−1.48074	−	3.77286i	−0.101938	−	0.259734i	0.870801	−	0.491635i	$-0.163601\pi$
$211$	−1.48074	−	3.77286i	−0.101938	−	0.259734i	−0.972739	+	0.231901i	$0.925505\pi$
$212$	−0.544109	−	0.798061i	−0.0373695	−	0.0548110i
$213$	−9.46169	+	6.82357i	−0.648304	+	0.467543i
$214$	−6.12775	−	10.6136i	−0.418884	−	0.725529i
$215$	0.947905			0.0646466
$216$	−1.60880	+	11.0020i	−0.109465	+	0.748594i
$217$	0.499333	−	14.5791i	0.0338969	−	0.989695i
$218$	−5.25520	−	17.0369i	−0.355927	−	1.15389i
$219$	−1.53903	+	0.273701i	−0.103998	+	0.0184950i
$220$	1.28319	−	0.503614i	0.0865125	−	0.0339537i
$221$	3.04015	−	1.19317i	0.204503	−	0.0802613i
$222$	19.5465	+	23.2254i	1.31188	+	1.55879i
$223$	−3.71233	−	12.0351i	−0.248596	−	0.805929i	−0.990750	−	0.135700i	$-0.956672\pi$
$223$	−3.71233	−	12.0351i	−0.248596	−	0.805929i	0.742154	−	0.670230i	$-0.233804\pi$
$224$	9.82267	−	1.89076i	0.656305	−	0.126331i
$225$	0.302533	−	13.7498i	0.0201689	−	0.916655i
$226$	27.8495			1.85252
$227$	9.20020	+	15.9352i	0.610639	+	1.05766i	0.991133	+	0.132874i	$0.0424205\pi$
$227$	9.20020	+	15.9352i	0.610639	+	1.05766i	−0.380494	+	0.924783i	$0.624246\pi$
$228$	0.339366	+	3.34195i	0.0224750	+	0.221326i
$229$	12.0971	+	17.7432i	0.799398	+	1.17250i	0.981919	+	0.189300i	$0.0606218\pi$
$229$	12.0971	+	17.7432i	0.799398	+	1.17250i	−0.182521	+	0.983202i	$0.558426\pi$
$230$	3.36939	+	8.58506i	0.222171	+	0.566082i
$231$	11.5531	+	8.01008i	0.760136	+	0.527025i
$232$	−0.981500	+	2.50082i	−0.0644386	+	0.164187i
$233$	10.7990	−	2.46481i	0.707469	−	0.161475i	0.146377	−	0.989229i	$-0.453239\pi$
$233$	10.7990	−	2.46481i	0.707469	−	0.161475i	0.561092	+	0.827754i	$0.310382\pi$
$234$	−13.9708	−	1.35660i	−0.913301	−	0.0886838i
$235$	−2.77547	−	1.33660i	−0.181052	−	0.0871899i
$236$	−6.64875	−	1.00214i	−0.432797	−	0.0652336i
$237$	22.5411	+	4.52238i	1.46420	+	0.293760i
$238$	−4.69602	+	1.65990i	−0.304398	+	0.107596i
$239$	−7.73198	−	11.3407i	−0.500140	−	0.733571i	0.490294	−	0.871557i	$-0.336889\pi$
$239$	−7.73198	−	11.3407i	−0.500140	−	0.733571i	−0.990434	+	0.137986i	$0.955937\pi$
$240$	−3.62040	+	4.11456i	−0.233696	+	0.265594i
$241$	6.09683	+	19.7654i	0.392731	+	1.27320i	0.909007	+	0.416781i	$0.136842\pi$
$241$	6.09683	+	19.7654i	0.392731	+	1.27320i	−0.516276	+	0.856422i	$0.672682\pi$
$242$	−1.13210	−	2.35084i	−0.0727744	−	0.151118i
$243$	−7.00968	+	13.9235i	−0.449671	+	0.893194i
$244$			2.16777i			0.138777i
$245$	3.54596	+	2.79129i	0.226543	+	0.178329i
$246$	−4.23207	−	9.99865i	−0.269827	−	0.637491i
$247$	7.83891	−	1.18153i	0.498778	−	0.0751787i
$248$	−0.881694	+	11.7654i	−0.0559876	+	0.747103i
$249$	−7.85741	+	6.61281i	−0.497943	+	0.419070i
$250$	5.71617	−	8.38408i	0.361522	−	0.530256i
$251$	5.06089	+	2.43720i	0.319441	+	0.153834i	0.586732	−	0.809781i	$-0.300414\pi$
$251$	5.06089	+	2.43720i	0.319441	+	0.153834i	−0.267291	+	0.963616i	$0.586129\pi$
$252$	5.48483	+	0.722848i	0.345512	+	0.0455352i
$253$	−24.0768	+	11.5948i	−1.51369	+	0.728957i
$254$	−1.71261	+	11.3624i	−0.107459	+	0.712943i
$255$	0.692884	−	1.07626i	0.0433901	−	0.0673977i
$256$	−14.7655	+	2.22555i	−0.922847	+	0.139097i
$257$	−13.6245	−	4.20261i	−0.849875	−	0.262152i	−0.160930	−	0.986966i	$-0.551449\pi$
$257$	−13.6245	−	4.20261i	−0.849875	−	0.262152i	−0.688944	+	0.724814i	$0.741926\pi$
$258$	2.18606	+	3.56556i	0.136098	+	0.221982i
$259$	−21.3432	+	18.4851i	−1.32620	+	1.14861i
$260$	−1.00090	−	0.798187i	−0.0620729	−	0.0495015i
$261$	−2.41253	+	2.89233i	−0.149332	+	0.179031i
$262$	28.1492	−	6.42488i	1.73906	−	0.396930i
$263$	25.1439	−	14.5168i	1.55044	−	0.895146i	0.552333	−	0.833624i	$-0.313738\pi$
$263$	25.1439	−	14.5168i	1.55044	−	0.895146i	0.998106	−	0.0615222i	$-0.0195955\pi$
$264$	−9.07362	−	6.85207i	−0.558443	−	0.421716i
$265$	−0.263333	+	0.853705i	−0.0161764	+	0.0524427i
$266$	−12.0096	+	1.39165i	−0.736356	+	0.0853272i
$267$	−2.33042	−	13.1040i	−0.142619	−	0.801953i
$268$	−3.27102	+	1.00898i	−0.199809	+	0.0616330i
$269$	1.86936	−	2.34410i	0.113977	−	0.142923i	−0.721570	−	0.692341i	$-0.756579\pi$
$269$	1.86936	−	2.34410i	0.113977	−	0.142923i	0.835547	+	0.549419i	$0.185151\pi$
$270$	−4.75214	+	2.77161i	−0.289206	+	0.168675i
$271$	16.1036	+	3.67555i	0.978227	+	0.223274i	0.681604	−	0.731721i	$-0.261283\pi$
$271$	16.1036	+	3.67555i	0.978227	+	0.223274i	0.296622	+	0.954995i	$0.404140\pi$
$272$	5.37639	−	1.65840i	0.325992	−	0.100555i
$273$	1.07766	−	13.0114i	0.0652231	−	0.787484i
$274$	−8.54464	−	2.63567i	−0.516201	−	0.159227i
$275$	12.1796	+	7.03191i	0.734459	+	0.424040i
$276$	−6.33743	+	8.39211i	−0.381468	+	0.505146i
$277$	−8.07754	+	7.49486i	−0.485332	+	0.450323i	−0.884490	−	0.466560i	$-0.845493\pi$
$277$	−8.07754	+	7.49486i	−0.485332	+	0.450323i	0.399157	+	0.916882i	$0.369303\pi$
$278$	3.53334	+	1.70157i	0.211916	+	0.102053i
$279$	−6.38030	+	15.2608i	−0.381978	+	0.913640i
$280$	−2.77403	−	2.37201i	−0.165780	−	0.141755i
$281$	−6.33448	−	2.48610i	−0.377884	−	0.148308i	0.168794	−	0.985651i	$-0.446013\pi$
$281$	−6.33448	−	2.48610i	−0.377884	−	0.148308i	−0.546678	+	0.837343i	$0.684108\pi$
$282$	−1.37316	−	13.5224i	−0.0817706	−	0.805248i
$283$	−4.55792	−	30.2399i	−0.270941	−	1.79757i	−0.547744	−	0.836646i	$-0.684513\pi$
$283$	−4.55792	−	30.2399i	−0.270941	−	1.79757i	0.276803	−	0.960927i	$-0.410725\pi$
$284$	−2.64442	−	3.87866i	−0.156918	−	0.230156i
$285$	2.22102	−	2.17269i	0.131562	−	0.128699i
$286$	8.08567	−	11.8595i	0.478116	−	0.701267i
$287$	9.24346	−	4.06774i	0.545624	−	0.240111i
$288$	−11.1757	−	1.93679i	−0.658537	−	0.114127i
$289$	14.1326	−	6.80588i	0.831327	−	0.400346i
$290$	−1.27015	+	0.391790i	−0.0745859	+	0.0230067i
$291$	4.37930	−	21.8280i	0.256719	−	1.27958i
$292$	−0.0937539	−	0.622017i	−0.00548653	−	0.0364008i
$293$	0.743927	−	1.28852i	0.0434607	−	0.0752762i	−0.843477	−	0.537166i	$-0.819495\pi$
$293$	0.743927	−	1.28852i	0.0434607	−	0.0752762i	0.886937	+	0.461889i	$0.152828\pi$
$294$	−2.32178	+	19.7754i	−0.135409	+	1.15333i
$295$	3.10958	+	5.38595i	0.181047	+	0.313582i
$296$	17.8543	−	14.2383i	1.03776	−	0.827584i
$297$	−9.03753	−	13.1311i	−0.524411	−	0.761942i
$298$	6.58054	−	28.8312i	0.381200	−	1.67015i
$299$	20.5055	+	13.9804i	1.18586	+	0.808508i
$300$	5.52796	+	0.267759i	0.319157	+	0.0154591i
$301$	−3.28734	+	2.08010i	−0.189479	+	0.119895i
$302$	15.7223	+	1.17822i	0.904718	+	0.0677992i
$303$	−25.5336	+	6.54155i	−1.46687	+	0.375802i
$304$	13.6189	−	1.02059i	0.781096	−	0.0585350i
$305$	1.56762	−	1.25013i	0.0897615	−	0.0715824i
$306$	5.64628	+	0.124233i	0.322776	+	0.00710195i
$307$	−18.1139	+	14.4453i	−1.03381	+	0.824439i	−0.984683	−	0.174353i	$-0.944217\pi$
$307$	−18.1139	+	14.4453i	−1.03381	+	0.824439i	−0.0491310	+	0.998792i	$0.515645\pi$
$308$	−3.34495	+	4.56239i	−0.190596	+	0.259966i
$309$	17.3652	−	16.9873i	0.987870	−	0.966373i
$310$	−4.82312	+	3.28835i	−0.273935	+	0.186766i
$311$	2.63709	+	0.813436i	0.149536	+	0.0461257i	0.368619	−	0.929580i	$-0.379831\pi$
$311$	2.63709	+	0.813436i	0.149536	+	0.0461257i	−0.219084	+	0.975706i	$0.570307\pi$
$312$	−1.29764	+	10.4795i	−0.0734642	+	0.593284i
$313$	−22.8582	+	13.1972i	−1.29202	+	0.745948i	−0.979012	−	0.203803i	$-0.934670\pi$
$313$	−22.8582	+	13.1972i	−1.29202	+	0.745948i	−0.313008	+	0.949751i	$0.601337\pi$
$314$	−7.63053	−	33.4315i	−0.430616	−	1.88665i
$315$	−2.64032	−	4.38320i	−0.148765	−	0.246965i
$316$	−2.05867	+	9.01963i	−0.115809	+	0.507394i
$317$	−6.97120	−	22.6001i	−0.391541	−	1.26935i	−0.910130	−	0.414322i	$-0.864019\pi$
$317$	−6.97120	−	22.6001i	−0.391541	−	1.26935i	0.518589	−	0.855024i	$-0.326458\pi$
$318$	−3.81852	+	0.978283i	−0.214132	+	0.0548594i
$319$	−1.40711	−	3.58525i	−0.0787829	−	0.200735i
$320$	1.70480	+	1.58182i	0.0953011	+	0.0884265i
$321$	−12.7259	+	2.26318i	−0.710293	+	0.126318i
$322$	−30.5243	−	22.3791i	−1.70105	−	1.24714i
$323$	−3.10967	+	0.709761i	−0.173027	+	0.0394922i
$324$	−5.52658	−	2.96770i	−0.307032	−	0.164872i
$325$		−	13.0611i		−	0.724499i
$326$	19.6512	+	21.1790i	1.08838	+	1.17299i
$327$	−18.7819	−	0.909743i	−1.03864	−	0.0503089i
$328$	−7.60329	+	2.98407i	−0.419822	+	0.164768i
$329$	12.5584	−	1.45524i	0.692366	−	0.0802298i
$330$	−0.148500	−	5.62364i	−0.00817468	−	0.309571i
$331$	6.34929	−	5.89128i	0.348988	−	0.323814i	−0.486127	−	0.873888i	$-0.661591\pi$
$331$	6.34929	−	5.89128i	0.348988	−	0.323814i	0.835116	+	0.550074i	$0.185400\pi$
$332$	−2.57668	−	3.23106i	−0.141414	−	0.177327i
$333$	30.0528	−	11.0383i	1.64688	−	0.604894i
$334$	−17.1794	−	13.7001i	−0.940016	−	0.749638i
$335$	2.61601	+	1.78356i	0.142928	+	0.0974464i
$336$	3.52646	−	22.2140i	0.192384	−	1.21187i
$337$	1.30790	−	0.891711i	0.0712459	−	0.0485746i	−0.527173	−	0.849758i	$-0.676748\pi$
$337$	1.30790	−	0.891711i	0.0712459	−	0.0485746i	0.598419	+	0.801183i	$0.295796\pi$
$338$	7.99668	+	0.599268i	0.434962	+	0.0325959i
$339$	10.0054	−	27.6157i	0.543420	−	1.49988i
$340$	0.425587	+	0.290160i	0.0230807	+	0.0157362i
$341$	−10.5460	−	13.2243i	−0.571099	−	0.716135i
$342$	13.2947	+	3.34374i	0.718894	+	0.180809i
$343$	−18.4227	−	1.89886i	−0.994730	−	0.102529i
$344$	2.72481	−	1.57317i	0.146912	−	0.0848195i
$345$	9.72347	−	0.256763i	0.523494	−	0.0138236i
$346$	−0.735932	−	0.0551505i	−0.0395639	−	0.00296491i
$347$	3.03003	−	3.26559i	0.162660	−	0.175306i	−0.646462	−	0.762946i	$-0.723752\pi$
$347$	3.03003	−	3.26559i	0.162660	−	0.175306i	0.809123	+	0.587640i	$0.199943\pi$
$348$	−1.13788	−	1.00122i	−0.0609965	−	0.0536708i
$349$	−22.3017	+	1.67128i	−1.19378	+	0.0894617i	−0.656756	−	0.754103i	$-0.728072\pi$
$349$	−22.3017	+	1.67128i	−1.19378	+	0.0894617i	−0.537028	+	0.843565i	$0.680453\pi$
$350$	−0.681828	+	19.9075i	−0.0364452	+	1.06410i
$351$	−6.36447	+	13.3661i	−0.339710	+	0.713430i
$352$	7.23157	−	9.06810i	0.385444	−	0.483331i
$353$	0.125992	+	1.68124i	0.00670586	+	0.0894835i	0.999553	−	0.0299131i	$-0.00952306\pi$
$353$	0.125992	+	1.68124i	0.00670586	+	0.0894835i	−0.992847	+	0.119397i	$0.961904\pi$
$354$	−13.0880	+	24.1178i	−0.695620	+	1.28185i
$355$	−1.27983	+	4.14909i	−0.0679261	+	0.220211i
$356$	5.29614	−	0.798264i	0.280695	−	0.0423079i
$357$	−0.0411636	+	5.25294i	−0.00217861	+	0.278015i
$358$	12.0177	+	1.81138i	0.635156	+	0.0957344i
$359$	−10.1194	+	21.0131i	−0.534080	+	1.10903i	0.443071	+	0.896486i	$0.353889\pi$
$359$	−10.1194	+	21.0131i	−0.534080	+	1.10903i	−0.977152	+	0.212543i	$0.931825\pi$
$360$	1.98995	+	3.62877i	0.104880	+	0.191253i
$361$	11.2577			0.592509
$362$	4.80594	+	8.32413i	0.252594	+	0.437507i
$363$	−2.73783	+	0.278018i	−0.143699	+	0.0145922i
$364$	5.22267	+	0.571728i	0.273742	+	0.0299667i
$365$	−0.395743	+	0.426509i	−0.0207141	+	0.0223245i
$366$	8.31763	+	3.01356i	0.434769	+	0.157521i
$367$	−2.02816	+	13.4560i	−0.105869	+	0.702396i	0.871428	+	0.490523i	$0.163194\pi$
$367$	−2.02816	+	13.4560i	−0.105869	+	0.702396i	−0.977297	+	0.211873i	$0.932044\pi$
$368$	33.4273	+	26.6574i	1.74252	+	1.38961i
$369$	−11.4351	+	0.604344i	−0.595289	+	0.0314609i
$370$	11.0154	+	2.51420i	0.572665	+	0.130707i
$371$	−0.960150	−	3.53852i	−0.0498485	−	0.183711i
$372$	−6.07121	−	2.72872i	−0.314778	−	0.141478i
$373$	−6.55224	+	11.3488i	−0.339262	+	0.587619i	−0.984294	−	0.176536i	$-0.943511\pi$
$373$	−6.55224	+	11.3488i	−0.339262	+	0.587619i	0.645032	+	0.764156i	$0.276844\pi$
$374$	−2.88761	+	5.00149i	−0.149315	+	0.258621i
$375$	−6.26004	−	8.68029i	−0.323267	−	0.448248i
$376$	−10.1965	+	0.764121i	−0.525843	+	0.0394065i
$377$	−2.23015	+	2.79652i	−0.114859	+	0.144028i
$378$	10.3983	−	20.0401i	0.534833	−	1.03075i
$379$	6.53491	+	8.19452i	0.335676	+	0.420924i	0.920809	−	0.390013i	$-0.127529\pi$
$379$	6.53491	+	8.19452i	0.335676	+	0.420924i	−0.585134	+	0.810937i	$0.698958\pi$
$380$	0.850417	+	0.916532i	0.0436255	+	0.0470171i
$381$	10.6517	+	5.78038i	0.545705	+	0.296138i
$382$	−33.7498	+	23.0103i	−1.72679	+	1.17731i
$383$	7.50025	+	19.1103i	0.383245	+	0.976492i	0.984176	+	0.177191i	$0.0567012\pi$
$383$	7.50025	+	19.1103i	0.383245	+	0.976492i	−0.600932	+	0.799300i	$0.705204\pi$
$384$	−4.59472	+	22.9017i	−0.234473	+	1.16870i
$385$	5.22829	−	0.212193i	0.266458	−	0.0108144i
$386$	−0.691691	+	1.43631i	−0.0352062	+	0.0731063i
$387$	4.32099	−	0.886712i	0.219648	−	0.0450741i
$388$	8.73428	+	1.99354i	0.443416	+	0.101207i
$389$	−6.91793	+	10.1467i	−0.350753	+	0.514460i	−0.960554	−	0.278095i	$-0.910297\pi$
$389$	−6.91793	+	10.1467i	−0.350753	+	0.514460i	0.609801	+	0.792555i	$0.291249\pi$
$390$	−4.45402	+	2.73077i	−0.225538	+	0.138278i
$391$	−8.64775	−	4.99278i	−0.437336	−	0.252496i
$392$	14.8255	+	2.13875i	0.748803	+	0.108023i
$393$	3.74217	−	30.2211i	0.188767	−	1.52445i
$394$	−5.93755	+	15.1286i	−0.299129	+	0.762169i
$395$	7.70974	−	3.71282i	0.387919	−	0.186812i
$396$	5.37827	−	3.49606i	0.270268	−	0.175684i
$397$	−11.8503	−	24.6074i	−0.594750	−	1.23501i	−0.953448	−	0.301558i	$-0.902493\pi$
$397$	−11.8503	−	24.6074i	−0.594750	−	1.23501i	0.358698	−	0.933454i	$-0.383221\pi$
$398$	−3.13082	−	41.7779i	−0.156934	−	2.09414i
$399$	−2.93470	+	12.4087i	−0.146919	+	0.621213i
$400$	1.68150	−	22.4381i	0.0840752	−	1.12191i
$401$	17.2739	−	6.77950i	0.862617	−	0.338552i	0.107550	−	0.994200i	$-0.465699\pi$
$401$	17.2739	−	6.77950i	0.862617	−	0.338552i	0.755067	+	0.655647i	$0.227604\pi$
$402$	−0.675865	+	13.9534i	−0.0337091	+	0.695932i
$403$	−5.73896	+	14.6226i	−0.285878	+	0.728406i
$404$	−2.36025	−	10.3409i	−0.117427	−	0.514481i
$405$	1.04104	+	5.70798i	0.0517299	+	0.283632i
$406$	3.54514	−	4.14598i	0.175942	−	0.205762i
$407$	−4.87950	+	32.3733i	−0.241868	+	1.60469i
$408$	0.205553	−	4.24368i	0.0101764	−	0.210094i
$409$	−2.86573	+	9.29047i	−0.141701	+	0.459384i	−0.998407	−	0.0564212i	$-0.982031\pi$
$409$	−2.86573	+	9.29047i	−0.141701	+	0.459384i	0.856706	+	0.515805i	$0.172507\pi$
$410$	−3.49979	−	2.02060i	−0.172842	−	0.0997906i
$411$	−5.68335	+	7.52597i	−0.280339	+	0.371229i
$412$	6.64905	+	7.16597i	0.327575	+	0.353042i
$413$	−22.6031	−	11.8548i	−1.11222	−	0.583334i
$414$	23.3901	+	35.9828i	1.14956	+	1.76846i
$415$	−0.850582	+	3.72664i	−0.0417534	+	0.182934i
$416$	−10.6513	−	1.60542i	−0.522221	−	0.0787122i
$417$	2.95669	−	2.89235i	0.144790	−	0.141639i
$418$	−9.53493	+	10.2762i	−0.466369	+	0.502626i
$419$	−17.8432	−	16.5561i	−0.871697	−	0.808817i	0.111041	−	0.993816i	$-0.464581\pi$
$419$	−17.8432	−	16.5561i	−0.871697	−	0.808817i	−0.982739	+	0.184999i	$0.940772\pi$
$420$	1.79128	−	1.01557i	0.0874057	−	0.0495546i
$421$	−21.7179	+	20.1513i	−1.05847	+	0.982112i	−0.999869	−	0.0161694i	$-0.994853\pi$
$421$	−21.7179	+	20.1513i	−1.05847	+	0.982112i	−0.0585962	+	0.998282i	$0.518662\pi$
$422$		−	6.65610i		−	0.324014i
$423$	−13.9022	−	3.49653i	−0.675948	−	0.170007i
$424$	0.659865	+	2.89106i	0.0320459	+	0.140402i
$425$	0.392720	+	5.24048i	0.0190497	+	0.254201i
$426$	−18.5584	+	4.75455i	−0.899157	+	0.230359i
$427$	−2.69318	+	7.77547i	−0.130332	+	0.376282i
$428$	−0.775232	−	5.14333i	−0.0374723	−	0.248612i
$429$	−8.85499	−	12.2785i	−0.427523	−	0.592811i
$430$	1.44909	+	0.568727i	0.0698814	+	0.0274264i
$431$	−14.6908	+	30.5057i	−0.707630	+	1.46941i	0.167677	+	0.985842i	$0.446373\pi$
$431$	−14.6908	+	30.5057i	−0.707630	+	1.46941i	−0.875307	+	0.483567i	$0.839341\pi$
$432$	−12.6545	+	22.1428i	−0.608841	+	1.06534i
$433$	−0.0617456	−	0.128216i	−0.00296731	−	0.00616167i	0.899480	−	0.436962i	$-0.143946\pi$
$433$	−0.0617456	−	0.128216i	−0.00296731	−	0.00616167i	−0.902447	+	0.430800i	$0.858231\pi$
$434$	9.51057	−	21.9880i	0.456522	−	1.05546i
$435$	−0.0678240	+	1.40024i	−0.00325191	+	0.0671365i
$436$	0.565476	−	7.54576i	0.0270814	−	0.361376i
$437$	−17.7679	−	16.4862i	−0.849956	−	0.788644i
$438$	−2.51698	−	0.504977i	−0.120266	−	0.0241287i
$439$	−13.6869	−	5.37173i	−0.653242	−	0.256379i	0.0154925	−	0.999880i	$-0.495068\pi$
$439$	−13.6869	−	5.37173i	−0.653242	−	0.256379i	−0.668734	+	0.743501i	$0.733164\pi$
$440$	−4.23207			−0.201756
$441$	18.7752	+	9.40695i	0.894059	+	0.447950i
$442$	5.36345			0.255113
$443$	−15.7663	−	6.18782i	−0.749080	−	0.293992i	−0.0400759	−	0.999197i	$-0.512760\pi$
$443$	−15.7663	−	6.18782i	−0.749080	−	0.293992i	−0.709004	+	0.705204i	$0.750855\pi$
$444$	4.12115	+	12.2066i	0.195581	+	0.579302i
$445$	−3.63150	−	3.36954i	−0.172149	−	0.159731i
$446$	1.54569	−	20.6258i	0.0731904	−	0.976658i
$447$	−26.2249	−	16.8834i	−1.24040	−	0.798557i
$448$	−9.38342	−	1.74471i	−0.443325	−	0.0824299i
$449$	−1.77406	−	3.68387i	−0.0837230	−	0.173853i	0.854904	−	0.518786i	$-0.173616\pi$
$449$	−1.77406	−	3.68387i	−0.0837230	−	0.173853i	−0.938627	+	0.344933i	$0.887902\pi$
$450$	8.71215	−	20.8383i	0.410695	−	0.982326i
$451$	5.08067	−	10.5501i	0.239239	−	0.496786i
$452$	11.0027	+	4.31825i	0.517525	+	0.203113i
$453$	6.81684	−	15.1670i	0.320283	−	0.712607i
$454$	4.50378	+	29.8806i	0.211373	+	1.40237i
$455$	−2.59842	−	4.10647i	−0.121816	−	0.192514i
$456$	2.77859	−	9.93155i	0.130119	−	0.465088i
$457$	−1.16005	−	15.4798i	−0.0542649	−	0.724115i	−0.956288	−	0.292427i	$-0.905537\pi$
$457$	−1.16005	−	15.4798i	−0.0542649	−	0.724115i	0.902023	−	0.431688i	$-0.142082\pi$
$458$	7.84760	+	34.3826i	0.366694	+	1.60659i
$459$	2.15171	−	5.55423i	0.100433	−	0.259249i
$460$			3.91421i			0.182501i
$461$	−7.82527	+	7.26079i	−0.364459	+	0.338169i	−0.841051	−	0.540956i	$-0.818062\pi$
$461$	−7.82527	+	7.26079i	−0.364459	+	0.338169i	0.476592	+	0.879125i	$0.341872\pi$
$462$	12.8556	+	19.1769i	0.598098	+	0.892190i
$463$	9.24393	+	8.57712i	0.429602	+	0.398612i	0.865118	−	0.501569i	$-0.167244\pi$
$463$	9.24393	+	8.57712i	0.429602	+	0.398612i	−0.435516	+	0.900181i	$0.643434\pi$
$464$	−4.19128	+	4.51713i	−0.194575	+	0.209702i
$465$	1.52794	+	5.96401i	0.0708567	+	0.276575i
$466$	17.9877	+	2.71121i	0.833263	+	0.125594i
$467$	3.30402	−	14.4759i	0.152892	−	0.669863i	−0.839144	−	0.543909i	$-0.816944\pi$
$467$	3.30402	−	14.4759i	0.152892	−	0.669863i	0.992036	−	0.125954i	$-0.0401992\pi$
$468$	−5.30921	−	2.70223i	−0.245418	−	0.124911i
$469$	−12.9862	−	0.444775i	−0.599647	−	0.0205378i
$470$	−3.44101	−	3.70853i	−0.158722	−	0.171062i
$471$	−35.8922	−	4.44440i	−1.65382	−	0.204787i
$472$	17.8773	+	10.3215i	0.822870	+	0.475084i
$473$	−1.32955	+	4.31028i	−0.0611326	+	0.198187i
$474$	31.7460	+	20.4378i	1.45814	+	0.938739i
$475$	−1.90119	+	12.6136i	−0.0872327	+	0.578751i
$476$	−2.11267	−	0.0723587i	−0.0968342	−	0.00331656i
$477$	−0.401802	+	4.13792i	−0.0183973	+	0.189462i
$478$	−5.01587	−	21.9760i	−0.229421	−	1.00516i
$479$	−8.03422	+	20.4709i	−0.367093	+	0.935337i	0.621321	+	0.783556i	$0.286596\pi$
$479$	−8.03422	+	20.4709i	−0.367093	+	0.935337i	−0.988414	+	0.151781i	$0.951499\pi$
$480$	−3.75394	+	1.93149i	−0.171343	+	0.0881601i
$481$	28.3030	−	11.1081i	1.29051	−	0.506486i
$482$	−2.53851	+	33.8740i	−0.115626	+	1.54292i
$483$	−33.1576	+	22.2279i	−1.50872	+	1.01140i
$484$	−0.0827561	−	1.10430i	−0.00376164	−	0.0501956i
$485$	−3.59535	−	7.46583i	−0.163257	−	0.339006i
$486$	−19.0698	+	17.0796i	−0.865023	+	0.774748i
$487$	19.2653	−	9.27770i	0.872996	−	0.420413i	0.0569347	−	0.998378i	$-0.481867\pi$
$487$	19.2653	−	9.27770i	0.872996	−	0.420413i	0.816062	+	0.577965i	$0.196153\pi$
$488$	2.43145	−	6.19523i	0.110066	−	0.280445i
$489$	28.0611	−	11.8773i	1.26897	−	0.537109i
$490$	3.74609	+	6.39465i	0.169231	+	0.288881i
$491$	0.995052	+	0.574494i	0.0449061	+	0.0259265i	0.522285	−	0.852771i	$-0.325080\pi$
$491$	0.995052	+	0.574494i	0.0449061	+	0.0259265i	−0.477379	+	0.878698i	$0.658413\pi$
$492$	−0.121640	−	4.60645i	−0.00548396	−	0.207675i
$493$	0.810714	−	1.18910i	0.0365127	−	0.0535543i
$494$	12.6925	+	2.89698i	0.571062	+	0.130341i
$495$	−5.62976	−	1.87313i	−0.253039	−	0.0841911i
$496$	−11.7417	+	24.3819i	−0.527219	+	1.09478i
$497$	−4.66642	−	17.1975i	−0.209318	−	0.771415i
$498$	−15.9794	+	5.39491i	−0.716056	+	0.241752i
$499$	−5.83924	−	14.8782i	−0.261400	−	0.666038i	0.738566	−	0.674181i	$-0.235503\pi$
$499$	−5.83924	−	14.8782i	−0.261400	−	0.666038i	−0.999967	+	0.00814324i	$0.997408\pi$
$500$	3.55834	−	2.42603i	0.159134	−	0.108495i
$501$	−19.7571	+	12.1131i	−0.882681	+	0.541175i
$502$	6.27446	+	6.76226i	0.280043	+	0.301815i
$503$	23.3181	+	29.2400i	1.03970	+	1.30375i	0.951502	+	0.307644i	$0.0995406\pi$
$503$	23.3181	+	29.2400i	1.03970	+	1.30375i	0.0882016	+	0.996103i	$0.471888\pi$
$504$	−14.8642	−	8.21779i	−0.662105	−	0.366050i
$505$	−6.11688	+	7.67033i	−0.272198	+	0.341325i
$506$	−43.7636	+	3.27963i	−1.94553	+	0.145797i
$507$	3.46718	−	7.71422i	0.153983	−	0.342601i
$508$	−2.43843	+	4.22349i	−0.108188	+	0.187387i
$509$	−10.7031	+	18.5383i	−0.474405	+	0.821694i	−0.999570	−	0.0293065i	$-0.990670\pi$
$509$	−10.7031	+	18.5383i	−0.474405	+	0.821694i	0.525165	+	0.851000i	$0.324003\pi$
$510$	1.70497	−	1.22959i	0.0754973	−	0.0544470i
$511$	0.436495	−	2.34756i	0.0193094	−	0.103850i
$512$	2.38751	+	0.544934i	0.105514	+	0.0240829i
$513$	8.09200	−	11.9817i	0.357271	−	0.529007i
$514$	−18.3067	−	14.5991i	−0.807476	−	0.643941i
$515$	1.34761	−	8.94079i	0.0593827	−	0.393978i
$516$	0.310799	+	1.74763i	0.0136822	+	0.0769353i
$517$	9.97063	−	10.7458i	0.438508	−	0.472599i
$518$	−43.7188	+	15.4533i	−1.92089	+	0.678977i
$519$	−0.319083	+	0.709938i	−0.0140062	+	0.0311628i
$520$	1.96516	+	3.40377i	0.0861782	+	0.149265i
$521$	−25.8835			−1.13398			−0.566988	−	0.823726i	$-0.691892\pi$
$521$	−25.8835			−1.13398			−0.566988	+	0.823726i	$0.691892\pi$
$522$	−5.42345	+	2.97412i	−0.237378	+	0.130174i
$523$	3.92027	−	8.14053i	0.171422	−	0.355961i	−0.797504	−	0.603314i	$-0.793847\pi$
$523$	3.92027	−	8.14053i	0.171422	−	0.355961i	0.968925	+	0.247353i	$0.0795609\pi$
$524$	12.1173	+	1.82640i	0.529348	+	0.0797864i
$525$	19.4953	+	7.82820i	0.850846	+	0.341651i
$526$	47.1481	−	7.10643i	2.05575	−	0.309855i
$527$	1.86296	−	6.03958i	0.0811519	−	0.263088i
$528$	−13.6316	−	22.2337i	−0.593237	−	0.967597i
$529$	−3.95181	−	52.7332i	−0.171818	−	2.29275i
$530$	−0.914774	+	1.14709i	−0.0397353	+	0.0498264i
$531$	19.2132	+	21.6428i	0.833781	+	0.939219i
$532$	−4.96051	−	1.31236i	−0.215065	−	0.0568980i
$533$	−10.8445	+	0.812679i	−0.469725	+	0.0352011i
$534$	4.29960	−	21.4307i	0.186062	−	0.927399i
$535$	−3.27232	+	3.52672i	−0.141475	+	0.152473i
$536$	10.4799	+	0.785360i	0.452662	+	0.0339224i
$537$	6.11374	−	11.2660i	0.263827	−	0.486165i
$538$	4.26417	−	2.46192i	0.183842	−	0.106141i
$539$	−17.6661	+	12.2090i	−0.760931	+	0.525877i
$540$	−2.30722	+	0.358149i	−0.0992869	+	0.0154123i
$541$	−5.60954	−	7.03414i	−0.241173	−	0.302421i	0.646483	−	0.762928i	$-0.276239\pi$
$541$	−5.60954	−	7.03414i	−0.241173	−	0.302421i	−0.887656	+	0.460507i	$0.847668\pi$
$542$	22.4129	+	15.2808i	0.962715	+	0.656368i
$543$	9.98084	−	1.77499i	0.428319	−	0.0761722i
$544$	4.32186	+	0.323879i	0.185298	+	0.0138862i
$545$	−5.78280	+	3.94265i	−0.247708	+	0.168884i
$546$	9.45406	−	19.2443i	0.404596	−	0.823581i
$547$	19.1352	+	13.0462i	0.818163	+	0.557814i	0.898510	−	0.438953i	$-0.144651\pi$
$547$	19.1352	+	13.0462i	0.818163	+	0.557814i	−0.0803473	+	0.996767i	$0.525603\pi$
$548$	−2.96712	−	2.36620i	−0.126749	−	0.101079i
$549$	5.97650	−	7.16510i	0.255071	−	0.305799i
$550$	14.4003	+	18.0575i	0.614033	+	0.769973i
$551$	2.56081	−	2.37608i	0.109094	−	0.101224i
$552$	27.5245	−	16.8754i	1.17152	−	0.718264i
$553$	−18.5899	+	29.7945i	−0.790523	+	1.26699i
$554$	−16.8452	+	6.61124i	−0.715683	+	0.280885i
$555$	6.45057	−	10.0197i	0.273812	−	0.425311i
$556$	1.13210	+	1.22012i	0.0480119	+	0.0517445i
$557$		−	38.9043i		−	1.64843i	−0.566279	−	0.824214i	$-0.691618\pi$
$557$		−	38.9043i		−	1.64843i	0.566279	−	0.824214i	$-0.308382\pi$
$558$	−18.9100	+	19.5016i	−0.800523	+	0.825568i
$559$	4.08404	−	0.932156i	0.172737	−	0.0394260i
$560$	−3.93525	−	7.38917i	−0.166295	−	0.312250i
$561$	3.92206	+	4.66023i	0.165590	+	0.196755i
$562$	−8.19210	−	7.60116i	−0.345563	−	0.320636i
$563$	7.29710	+	18.5927i	0.307536	+	0.783589i	0.998175	+	0.0603892i	$0.0192342\pi$
$563$	7.29710	+	18.5927i	0.307536	+	0.783589i	−0.690639	+	0.723200i	$0.742671\pi$
$564$	1.55423	−	5.55532i	0.0654450	−	0.233921i
$565$	−3.22244	−	10.4469i	−0.135569	−	0.439504i
$566$	11.1756	−	48.9633i	0.469743	−	2.05808i
$567$	−16.1361	−	17.5108i	−0.677651	−	0.735384i
$568$	3.20701	+	14.0508i	0.134563	+	0.589559i
$569$	−17.9286	+	10.3511i	−0.751607	+	0.433941i	−0.826274	−	0.563268i	$-0.809544\pi$
$569$	−17.9286	+	10.3511i	−0.751607	+	0.433941i	0.0746672	+	0.997209i	$0.476211\pi$
$570$	4.69891	−	1.98888i	0.196816	−	0.0833050i
$571$	17.5528	+	5.41431i	0.734561	+	0.226582i	0.639394	−	0.768879i	$-0.279185\pi$
$571$	17.5528	+	5.41431i	0.734561	+	0.226582i	0.0951669	+	0.995461i	$0.469662\pi$
$572$	5.03336	−	3.43168i	0.210455	−	0.143486i
$573$	10.6918	+	41.7332i	0.446657	+	1.74343i
$574$	16.5713	−	0.672558i	0.691674	−	0.0280720i
$575$	−31.2220	+	24.8987i	−1.30205	+	1.03835i
$576$	9.25097	+	5.61594i	0.385457	+	0.233997i
$577$	0.228360	−	0.182111i	0.00950674	−	0.00758137i	−0.618725	−	0.785608i	$-0.712350\pi$
$577$	0.228360	−	0.182111i	0.00950674	−	0.00758137i	0.628232	+	0.778026i	$0.283779\pi$
$578$	25.6883	−	1.92507i	1.06849	−	0.0800724i
$579$	1.17575	+	1.20190i	0.0488624	+	0.0499493i
$580$	−0.562558	−	0.0421579i	−0.0233590	−	0.00175051i
$581$	−5.22801	−	14.7905i	−0.216894	−	0.613615i
$582$	19.7912	−	30.7416i	0.820372	−	1.27428i
$583$	−3.51258	−	2.39484i	−0.145476	−	0.0991841i
$584$	−0.429739	+	1.88281i	−0.0177827	+	0.0779112i
$585$	1.10766	+	5.39769i	0.0457961	+	0.223167i
$586$	1.91036	−	1.52346i	0.0789160	−	0.0629334i
$587$	−10.9257	−	18.9238i	−0.450951	−	0.781070i	0.547494	−	0.836809i	$-0.315582\pi$
$587$	−10.9257	−	18.9238i	−0.450951	−	0.781070i	−0.998445	+	0.0557393i	$0.982248\pi$
$588$	−3.98359	+	7.45282i	−0.164281	+	0.307349i
$589$	7.67083	−	13.2863i	0.316071	−	0.547451i
$590$	1.52223	+	10.0994i	0.0626694	+	0.415784i
$591$	12.8684	+	11.3229i	0.529336	+	0.465762i
$592$	50.0528	−	15.4392i	2.05716	−	0.634549i
$593$	30.3591	−	14.6202i	1.24670	−	0.600379i	0.310074	−	0.950712i	$-0.399646\pi$
$593$	30.3591	−	14.6202i	1.24670	−	0.600379i	0.936625	+	0.350334i	$0.113932\pi$
$594$	−5.93753	−	25.4962i	−0.243620	−	1.04612i
$595$	1.16603	+	1.56950i	0.0478027	+	0.0643433i
$596$	7.07029	−	10.3702i	0.289610	−	0.424780i
$597$	−42.5519	−	11.9049i	−1.74153	−	0.487235i
$598$	22.9594	+	33.6752i	0.938879	+	1.37708i
$599$	−5.35750	−	35.5447i	−0.218901	−	1.45232i	−0.780630	−	0.624994i	$-0.785101\pi$
$599$	−5.35750	−	35.5447i	−0.218901	−	1.45232i	0.561728	−	0.827322i	$-0.310137\pi$
$600$	−15.4979	−	6.96558i	−0.632700	−	0.284369i
$601$	−1.17533	−	0.461283i	−0.0479427	−	0.0188161i	0.341249	−	0.939973i	$-0.389150\pi$
$601$	−1.17533	−	0.461283i	−0.0479427	−	0.0188161i	−0.389191	+	0.921157i	$0.627245\pi$
$602$	−6.27348	+	1.20758i	−0.255688	+	0.0492171i
$603$	13.5934	+	5.68318i	0.553566	+	0.231437i
$604$	6.02884	+	2.90334i	0.245310	+	0.118135i
$605$	−0.750850	+	0.696687i	−0.0305264	+	0.0283243i
$606$	−42.9588	−	5.31943i	−1.74508	−	0.216087i
$607$	−16.6121	−	9.59099i	−0.674263	−	0.389286i	0.123427	−	0.992354i	$-0.460612\pi$
$607$	−16.6121	−	9.59099i	−0.674263	−	0.389286i	−0.797690	+	0.603068i	$0.793945\pi$
$608$	10.0526	+	3.10083i	0.407689	+	0.125755i
$609$	−2.83751	−	5.00488i	−0.114982	−	0.202808i
$610$	3.14652	−	0.970574i	0.127399	−	0.0392974i
$611$	−13.2725	−	3.02936i	−0.536947	−	0.122555i
$612$	2.21145	+	0.924574i	0.0893927	+	0.0373737i
$613$	−23.6281	+	29.6287i	−0.954332	+	1.19669i	0.0260652	+	0.999660i	$0.491702\pi$
$613$	−23.6281	+	29.6287i	−0.954332	+	1.19669i	−0.980397	+	0.197034i	$0.936869\pi$
$614$	−36.3582	+	11.2150i	−1.46730	+	0.452602i
$615$	−3.26100	+	2.74446i	−0.131496	+	0.110667i
$616$	14.6768	−	9.28695i	0.591346	−	0.374182i
$617$	−0.201273	+	0.652509i	−0.00810293	+	0.0262690i	−0.959534	−	0.281593i	$-0.909137\pi$
$617$	−0.201273	+	0.652509i	−0.00810293	+	0.0262690i	0.951431	+	0.307862i	$0.0996135\pi$
$618$	36.7387	−	15.5502i	1.47785	−	0.625521i
$619$	−32.7010	+	18.8799i	−1.31436	+	0.758848i	−0.982816	−	0.184590i	$-0.940904\pi$
$619$	−32.7010	+	18.8799i	−1.31436	+	0.758848i	−0.331548	+	0.943438i	$0.607571\pi$
$620$	−2.41539	+	0.551296i	−0.0970042	+	0.0221406i
$621$	44.0839	−	10.2662i	1.76903	−	0.411969i
$622$	3.54336	+	2.82574i	0.142076	+	0.113302i
$623$	19.9882	+	3.71652i	0.800811	+	0.148899i
$624$	−11.5523	+	21.2878i	−0.462460	+	0.852194i
$625$	18.0971	+	5.58223i	0.723885	+	0.223289i
$626$	−42.8621	+	6.46042i	−1.71311	+	0.258210i
$627$	6.76433	+	13.1468i	0.270141	+	0.525031i
$628$	2.16913	−	14.3912i	0.0865575	−	0.574272i
$629$	−11.0220	+	5.30790i	−0.439475	+	0.211640i
$630$	−1.40650	−	8.28488i	−0.0560363	−	0.330078i
$631$	28.9070	+	13.9209i	1.15077	+	0.554181i	0.909265	−	0.416219i	$-0.136645\pi$
$631$	28.9070	+	13.9209i	1.15077	+	0.554181i	0.241504	+	0.970400i	$0.422359\pi$
$632$	16.0002	−	23.4680i	0.636453	−	0.933506i
$633$	−6.60020	−	2.39132i	−0.262335	−	0.0950464i
$634$	2.90256	−	38.7320i	0.115276	−	1.53824i
$635$	4.46043	−	0.672302i	0.177007	−	0.0266795i
$636$	−1.66030	−	0.205589i	−0.0658352	−	0.00815214i
$637$	18.0226	+	8.53920i	0.714083	+	0.338336i
$638$		−	6.32512i		−	0.250414i
$639$	−1.95280	+	20.1107i	−0.0772515	+	0.795567i
$640$	3.77221	+	7.83307i	0.149110	+	0.309629i
$641$	−3.55031	−	11.5098i	−0.140229	−	0.454610i	0.858030	−	0.513600i	$-0.171688\pi$
$641$	−3.55031	−	11.5098i	−0.140229	−	0.454610i	−0.998259	+	0.0589895i	$0.981212\pi$
$642$	−20.8124	−	4.17555i	−0.821400	−	0.164796i
$643$	−3.19635	−	4.68819i	−0.126052	−	0.184884i	0.758025	−	0.652225i	$-0.226164\pi$
$643$	−3.19635	−	4.68819i	−0.126052	−	0.184884i	−0.884077	+	0.467341i	$0.845212\pi$
$644$	−8.58942	−	13.5745i	−0.338471	−	0.534909i
$645$	1.08456	−	1.23260i	0.0427046	−	0.0485335i
$646$	−5.17969	−	0.780713i	−0.203792	−	0.0307167i
$647$	36.6568	+	17.6530i	1.44113	+	0.694010i	0.981030	−	0.193858i	$-0.0621000\pi$
$647$	36.6568	+	17.6530i	1.44113	+	0.694010i	0.460098	+	0.887868i	$0.347814\pi$
$648$	12.4656	+	14.6802i	0.489697	+	0.576691i
$649$	−28.8523	+	6.58536i	−1.13255	+	0.258498i
$650$	7.83643	−	19.9669i	0.307370	−	0.783166i
$651$	−18.3865	−	17.3302i	−0.720623	−	0.679226i
$652$	4.47981	+	11.4144i	0.175443	+	0.447021i
$653$	16.4822	+	24.1750i	0.644999	+	0.946040i	0.999938	+	0.0111505i	$0.00354937\pi$
$653$	16.4822	+	24.1750i	0.644999	+	0.946040i	−0.354939	+	0.934890i	$0.615498\pi$
$654$	−28.1666	−	12.6596i	−1.10140	−	0.495028i
$655$	−5.66721	−	9.81589i	−0.221436	−	0.383539i
$656$	−18.7347			−0.731467
$657$	−1.40500	+	2.31442i	−0.0548144	+	0.0902942i
$658$	20.0715	+	5.31015i	0.782469	+	0.207011i
$659$	3.14692	+	10.2021i	0.122587	+	0.397417i	0.995978	−	0.0896036i	$-0.0285600\pi$
$659$	3.14692	+	10.2021i	0.122587	+	0.397417i	−0.873391	+	0.487020i	$0.838084\pi$
$660$	0.813312	−	2.24480i	0.0316581	−	0.0873786i
$661$	20.3227	−	7.97608i	0.790462	−	0.310233i	0.0644548	−	0.997921i	$-0.479469\pi$
$661$	20.3227	−	7.97608i	0.790462	−	0.310233i	0.726007	+	0.687687i	$0.241374\pi$
$662$	13.2410	−	5.19672i	0.514627	−	0.201976i
$663$	1.92691	−	5.31841i	0.0748351	−	0.206550i
$664$	3.73979	+	12.1241i	0.145132	+	0.470506i
$665$	1.91165	+	4.34400i	0.0741306	+	0.168453i
$666$	52.5654	+	1.15658i	2.03687	+	0.0448166i
$667$	10.9364			0.423458
$668$	−4.66291	−	8.07639i	−0.180413	−	0.312485i
$669$	−19.8972	−	8.94286i	−0.769271	−	0.345751i
$670$	2.92906	+	4.29615i	0.113160	+	0.165975i
$671$	3.48580	+	8.88166i	0.134568	+	0.342873i
$672$	8.78015	−	14.9361i	0.338702	−	0.576174i
$673$	13.4132	−	34.1764i	0.517042	−	1.31740i	−0.399232	−	0.916850i	$-0.630723\pi$
$673$	13.4132	−	34.1764i	0.517042	−	1.31740i	0.916274	−	0.400552i	$-0.131182\pi$
$674$	2.53444	−	0.578469i	0.0976229	−	0.0222818i
$675$	−17.5333	−	16.1255i	−0.674857	−	0.620671i
$676$	3.06639	+	1.47669i	0.117938	+	0.0567959i
$677$	33.6607	+	5.07354i	1.29369	+	0.194992i	0.759574	−	0.650421i	$-0.225408\pi$
$677$	33.6607	+	5.07354i	1.29369	+	0.194992i	0.534113	+	0.845413i	$0.320646\pi$
$678$	31.8645	−	36.2138i	1.22375	−	1.39078i
$679$	28.8519	+	18.0018i	1.10723	+	0.690845i
$680$	−0.890824	−	1.30660i	−0.0341615	−	0.0501058i
$681$	31.2477	+	6.26917i	1.19742	+	0.240235i
$682$	−8.18768	−	26.5438i	−0.313522	−	1.01641i
$683$	0.751972	+	1.56149i	0.0287734	+	0.0597486i	0.914860	−	0.403771i	$-0.132301\pi$
$683$	0.751972	+	1.56149i	0.0287734	+	0.0597486i	−0.886087	+	0.463519i	$0.846586\pi$
$684$	4.73396	+	3.38246i	0.181008	+	0.129332i
$685$			3.51023i			0.134119i
$686$	−27.0240	−	13.9561i	−1.03178	−	0.532847i
$687$	36.9132	+	4.57083i	1.40833	+	0.174388i
$688$	7.13613	−	1.07560i	0.272062	−	0.0410068i
$689$	−0.295048	+	3.93714i	−0.0112404	+	0.149993i
$690$	15.0186	+	5.44139i	0.571749	+	0.207150i
$691$	18.7025	−	27.4316i	0.711478	−	1.04355i	−0.284903	−	0.958556i	$-0.591961\pi$
$691$	18.7025	−	27.4316i	0.711478	−	1.04355i	0.996382	−	0.0849909i	$-0.0270861\pi$
$692$	−0.282199	−	0.135900i	−0.0107276	−	0.00516613i
$693$	23.6345	−	5.85804i	0.897799	−	0.222529i
$694$	6.59140	−	3.17425i	0.250206	−	0.120493i
$695$	0.229451	−	1.52231i	0.00870357	−	0.0577444i
$696$	2.12891	+	4.13764i	0.0806963	+	0.156837i
$697$	4.32667	−	0.652140i	0.163884	−	0.0247016i
$698$	−35.0961	−	10.8257i	−1.32841	−	0.409759i
$699$	9.15082	−	16.8626i	0.346116	−	0.637801i
$700$	−3.35616	+	7.75927i	−0.126851	+	0.293273i
$701$	−23.9075	−	19.0656i	−0.902974	−	0.720098i	0.0575359	−	0.998343i	$-0.481676\pi$
$701$	−23.9075	−	19.0656i	−0.902974	−	0.720098i	−0.960510	+	0.278246i	$0.910247\pi$
$702$	−17.7490	+	16.6146i	−0.669893	+	0.627079i
$703$	−28.9502	+	6.60769i	−1.09188	+	0.249214i
$704$	−9.58397	+	5.53331i	−0.361210	+	0.208544i
$705$	−4.91363	+	2.07976i	−0.185058	+	0.0783284i
$706$	−0.816109	+	2.64576i	−0.0307147	+	0.0995745i
$707$	4.38142	−	40.0237i	0.164780	−	1.50525i
$708$	−8.91040	+	7.49902i	−0.334873	+	0.281830i
$709$	1.31030	−	0.404173i	0.0492093	−	0.0151791i	−0.270053	−	0.962846i	$-0.587041\pi$
$709$	1.31030	−	0.404173i	0.0492093	−	0.0151791i	0.319262	+	0.947666i	$0.396565\pi$
$710$	−4.44589	+	5.57497i	−0.166851	+	0.209225i
$711$	31.6715	−	24.1368i	1.18777	−	0.905200i
$712$	−16.0311	−	3.65899i	−0.600791	−	0.137127i
$713$	45.8952	−	14.1568i	1.71879	−	0.530176i
$714$	−3.21460	+	8.00563i	−0.120303	+	0.299603i
$715$	−5.38431	−	1.66084i	−0.201362	−	0.0621118i
$716$	4.46706	+	2.57906i	0.166942	+	0.0963840i
$717$	−23.5935	−	2.92149i	−0.881114	−	0.109105i
$718$	−28.0773	+	26.0519i	−1.04784	+	0.972250i
$719$	1.24045	+	0.597369i	0.0462610	+	0.0222781i	0.456871	−	0.889533i	$-0.348970\pi$
$719$	1.24045	+	0.597369i	0.0462610	+	0.0222781i	−0.410610	+	0.911811i	$0.634684\pi$
$720$	1.20798	+	9.41549i	0.0450189	+	0.350895i
$721$	14.9464	+	33.9639i	0.556632	+	1.26488i
$722$	17.2100	+	6.75441i	0.640488	+	0.251373i
$723$	32.6776	+	14.6870i	1.21529	+	0.546216i
$724$	0.608008	+	4.03387i	0.0225964	+	0.149917i
$725$	−3.24222	−	4.75547i	−0.120413	−	0.176614i
$726$	−4.35220	−	1.21763i	−0.161525	−	0.0451906i
$727$	24.6232	−	36.1157i	0.913226	−	1.33946i	−0.0272620	−	0.999628i	$-0.508679\pi$
$727$	24.6232	−	36.1157i	0.913226	−	1.33946i	0.940488	−	0.339828i	$-0.110369\pi$
$728$	−14.2845	−	7.49186i	−0.529419	−	0.277667i
$729$	10.0851	+	25.0458i	0.373521	+	0.927622i
$730$	−0.860883	+	0.414579i	−0.0318627	+	0.0153443i
$731$	−1.61061	+	0.496806i	−0.0595704	+	0.0183750i
$732$	2.81883	+	2.48029i	0.104187	+	0.0916742i
$733$	6.60262	+	43.8055i	0.243873	+	1.61799i	0.690541	+	0.723293i	$0.257372\pi$
$733$	6.60262	+	43.8055i	0.243873	+	1.61799i	−0.446668	+	0.894700i	$0.647389\pi$
$734$	−11.1739	+	19.3537i	−0.412435	+	0.714358i
$735$	7.68679	−	1.41725i	0.283532	−	0.0522760i
$736$	16.4671	+	28.5219i	0.606986	+	1.05133i
$737$	−11.7794	+	9.39375i	−0.433900	+	0.346023i
$738$	−17.8438	−	5.93700i	−0.656841	−	0.218544i
$739$	11.2783	−	49.4134i	0.414878	−	1.81770i	−0.145371	−	0.989377i	$-0.546438\pi$
$739$	11.2783	−	49.4134i	0.414878	−	1.81770i	0.560249	−	0.828324i	$-0.310705\pi$
$740$	3.96211	+	2.70132i	0.145650	+	0.0993024i
$741$	7.43264	−	11.5451i	0.273045	−	0.424120i
$742$	0.655237	−	5.98551i	0.0240545	−	0.219735i
$743$	−8.38087	−	0.628059i	−0.307464	−	0.0230413i	−0.0798953	−	0.996803i	$-0.525459\pi$
$743$	−8.38087	−	0.628059i	−0.307464	−	0.0230413i	−0.227569	+	0.973762i	$0.573078\pi$
$744$	14.2902	+	14.6081i	0.523904	+	0.535558i
$745$	−11.5766	+	0.867543i	−0.424132	+	0.0317843i
$746$	−16.8257	+	13.4181i	−0.616033	+	0.491270i
$747$	−0.391284	+	17.7835i	−0.0143163	+	0.650663i
$748$	−1.91634	+	1.52823i	−0.0700684	+	0.0558777i
$749$	3.60929	−	19.4115i	0.131881	−	0.709281i
$750$	−4.36190	−	17.0258i	−0.159274	−	0.621693i
$751$	4.80950	−	3.27906i	0.175501	−	0.119655i	−0.472384	−	0.881393i	$-0.656606\pi$
$751$	4.80950	−	3.27906i	0.175501	−	0.119655i	0.647885	+	0.761739i	$0.275654\pi$
$752$	−22.4113	−	6.91296i	−0.817255	−	0.252090i
$753$	8.95968	−	3.79231i	0.326509	−	0.138200i
$754$	−5.08716	+	2.93707i	−0.185264	+	0.106962i
$755$	−1.37724	−	6.03407i	−0.0501228	−	0.219602i
$756$	7.21550	−	6.30507i	0.262425	−	0.229313i
$757$	−0.319428	+	1.39950i	−0.0116098	+	0.0508659i	−0.980401	−	0.197012i	$-0.936876\pi$
$757$	−0.319428	+	1.39950i	−0.0116098	+	0.0508659i	0.968791	+	0.247878i	$0.0797333\pi$
$758$	5.07355	+	16.4480i	0.184280	+	0.597420i
$759$	−12.4707	+	44.5744i	−0.452659	+	1.61795i
$760$	−1.40238	−	3.57320i	−0.0508696	−	0.129614i
$761$	15.7635	+	14.6264i	0.571428	+	0.530208i	0.912096	−	0.409976i	$-0.134463\pi$
$761$	15.7635	+	14.6264i	0.571428	+	0.530208i	−0.340668	+	0.940184i	$0.610653\pi$
$762$	12.8155	+	15.2275i	0.464257	+	0.551635i
$763$	11.4029	−	26.3630i	0.412814	−	0.954405i
$764$	−16.9017	+	3.85770i	−0.611482	+	0.139567i
$765$	−0.606722	−	2.13240i	−0.0219361	−	0.0770971i
$766$			33.7146i			1.21816i
$767$	18.6941	+	20.1474i	0.675003	+	0.727481i
$768$	−14.0003	+	21.7466i	−0.505192	+	0.784713i
$769$	−12.8813	+	5.05552i	−0.464510	+	0.182307i	−0.586042	−	0.810281i	$-0.699315\pi$
$769$	−12.8813	+	5.05552i	−0.464510	+	0.182307i	0.121532	+	0.992588i	$0.461219\pi$
$770$	8.11996	+	2.81249i	0.292623	+	0.101355i
$771$	−21.0536	+	12.9080i	−0.758225	+	0.464871i
$772$	−0.495981	+	0.460203i	−0.0178507	+	0.0165631i
$773$	23.7915	+	29.8336i	0.855720	+	1.07304i	0.996549	+	0.0830046i	$0.0264516\pi$
$773$	23.7915	+	29.8336i	0.855720	+	1.07304i	−0.140830	+	0.990034i	$0.544977\pi$
$774$	7.13765	+	1.23698i	0.256558	+	0.0444622i
$775$	−19.7620	−	15.7597i	−0.709872	−	0.566104i
$776$	−22.7255	−	15.4940i	−0.815798	−	0.556202i
$777$	−0.383222	+	48.9035i	−0.0137480	+	1.75440i
$778$	−16.6635	+	11.3610i	−0.597416	+	0.407311i
$779$	10.5912	+	0.793701i	0.379469	+	0.0284373i
$780$	−2.18311	+	0.388244i	−0.0781677	+	0.0139013i
$781$	−17.0715	−	11.6391i	−0.610866	−	0.416482i
$782$	−10.2245	−	12.8211i	−0.365627	−	0.458482i
$783$	1.00068	+	6.44641i	0.0357612	+	0.230376i
$784$	29.8624	+	16.9901i	1.06651	+	0.606788i
$785$	−11.6579	+	6.73068i	−0.416088	+	0.240228i
$786$	23.8529	−	43.9547i	0.850805	−	1.56781i
$787$	31.1070	+	2.33115i	1.10885	+	0.0830965i	0.616538	−	0.787325i	$-0.288535\pi$
$787$	31.1070	+	2.33115i	1.10885	+	0.0830965i	0.492307	+	0.870421i	$0.336154\pi$
$788$	−4.69158	+	5.05632i	−0.167131	+	0.180124i
$789$	9.89200	−	49.3053i	0.352165	−	1.75531i
$790$	14.0137	−	1.05019i	0.498587	−	0.0373639i
$791$	34.1003	+	29.1584i	1.21247	+	1.03675i
$792$	−19.2918	+	3.95887i	−0.685503	+	0.140672i
$793$	5.52470	−	6.92776i	0.196188	−	0.246012i
$794$	−3.35191	−	44.7281i	−0.118955	−	1.58734i
$795$	0.808809	+	1.31920i	0.0286855	+	0.0467873i
$796$	5.24102	−	16.9910i	0.185763	−	0.602229i
$797$	50.8981	−	7.67165i	1.80290	−	0.271744i	0.840194	−	0.542285i	$-0.182441\pi$
$797$	50.8981	−	7.67165i	1.80290	−	0.271744i	0.962708	+	0.270541i	$0.0872027\pi$
$798$	−11.9314	+	17.2088i	−0.422366	+	0.609186i
$799$	5.41638	+	0.816388i	0.191618	+	0.0288817i
$800$	7.52030	−	15.6161i	0.265883	−	0.552111i
$801$	−19.7061	−	11.9629i	−0.696280	−	0.422687i
$802$	30.4747			1.07610
$803$	−1.38433	−	2.39773i	−0.0488520	−	0.0846142i
$804$	−2.43058	+	5.40787i	−0.0857200	+	0.190721i
$805$	−4.86291	+	14.0397i	−0.171395	+	0.494834i
$806$	−17.5467	+	18.9108i	−0.618055	+	0.666105i
$807$	−0.909270	−	5.11285i	−0.0320078	−	0.179981i
$808$	−4.85345	+	32.2005i	−0.170744	+	1.13281i
$809$	−25.8854	−	20.6430i	−0.910084	−	0.725768i	0.0519640	−	0.998649i	$-0.483452\pi$
$809$	−25.8854	−	20.6430i	−0.910084	−	0.725768i	−0.962048	+	0.272881i	$0.912023\pi$
$810$	−1.83321	+	9.35057i	−0.0644125	+	0.328546i
$811$	23.5650	+	5.37855i	0.827478	+	0.188866i	0.615228	−	0.788349i	$-0.289064\pi$
$811$	23.5650	+	5.37855i	0.827478	+	0.188866i	0.212249	+	0.977216i	$0.431921\pi$
$812$	2.04347	−	1.08829i	0.0717116	−	0.0381914i
$813$	23.2047	−	16.7348i	0.813825	−	0.586913i
$814$	−26.8829	+	46.5625i	−0.942245	+	1.63202i
$815$	5.67081	−	9.82213i	0.198640	−	0.344054i
$816$	3.99501	−	8.88862i	0.139853	−	0.311164i
$817$	−4.07980	+	0.305739i	−0.142734	+	0.0106965i
$818$	−9.95505	+	12.4832i	−0.348070	+	0.436466i
$819$	−15.6862	−	16.2885i	−0.548119	−	0.569167i
$820$	−1.06938	−	1.34096i	−0.0373444	−	0.0468284i
$821$	−8.16079	−	8.79524i	−0.284813	−	0.306956i	0.574398	−	0.818576i	$-0.305236\pi$
$821$	−8.16079	−	8.79524i	−0.284813	−	0.306956i	−0.859212	+	0.511620i	$0.829046\pi$
$822$	−13.2038	+	8.09528i	−0.460534	+	0.282355i
$823$	−2.87572	+	1.96063i	−0.100241	+	0.0683433i	−0.612403	−	0.790546i	$-0.709797\pi$
$823$	−2.87572	+	1.96063i	−0.100241	+	0.0683433i	0.512162	+	0.858889i	$0.328845\pi$
$824$	−10.9646	−	27.9373i	−0.381969	−	0.973242i
$825$	23.0794	−	7.79196i	0.803521	−	0.271281i
$826$	−27.4414	−	31.6842i	−0.954808	−	1.10243i
$827$	−3.58887	+	7.45236i	−0.124797	+	0.259144i	−0.954002	−	0.299801i	$-0.903080\pi$
$827$	−3.58887	+	7.45236i	−0.124797	+	0.259144i	0.829204	+	0.558945i	$0.188794\pi$
$828$	3.66152	+	17.8428i	0.127247	+	0.620080i
$829$	−32.9052	−	7.51039i	−1.14284	−	0.260847i	−0.391129	−	0.920336i	$-0.627916\pi$
$829$	−32.9052	−	7.51039i	−1.14284	−	0.260847i	−0.751714	+	0.659489i	$0.770773\pi$
$830$	−3.53623	+	5.18670i	−0.122744	+	0.180033i
$831$	0.503807	+	19.0789i	0.0174769	+	0.661840i
$832$	8.90065	+	5.13879i	0.308574	+	0.178155i
$833$	−7.48795	−	2.88427i	−0.259442	−	0.0999339i
$834$	6.25534	−	2.64766i	0.216605	−	0.0916810i
$835$	−3.15137	+	8.02955i	−0.109058	+	0.277874i
$836$	−5.36043	+	2.58145i	−0.185394	+	0.0892812i
$837$	12.5441	+	25.7574i	0.433587	+	0.890308i
$838$	−17.3441	−	36.0154i	−0.599142	−	1.24413i
$839$	1.93466	+	25.8162i	0.0667918	+	0.891275i	0.925485	+	0.378785i	$0.123658\pi$
$839$	1.93466	+	25.8162i	0.0667918	+	0.891275i	−0.858693	+	0.512490i	$0.828723\pi$
$840$	−6.25838	+	0.893201i	−0.215935	+	0.0308184i
$841$	2.04938	−	27.3471i	0.0706684	−	0.943004i
$842$	−45.2912	+	17.7755i	−1.56084	+	0.612584i
$843$	−10.4805	+	5.39246i	−0.360967	+	0.185726i
$844$	1.03207	−	2.62968i	0.0355254	−	0.0905172i
$845$	−0.700489	−	3.06904i	−0.0240976	−	0.105578i
$846$	−19.1549	−	13.6863i	−0.658558	−	0.470546i
$847$	1.07512	−	4.06379i	0.0369417	−	0.139634i
$848$	−1.01375	+	6.72577i	−0.0348122	+	0.230964i
$849$	−44.5371	−	28.6726i	−1.52851	−	0.984041i
$850$	−2.54383	+	8.24691i	−0.0872528	+	0.282867i
$851$	−80.5083	−	46.4815i	−2.75979	−	1.59336i
$852$	−8.06923	−	0.999184i	−0.276447	−	0.0342315i
$853$	8.59605	+	9.26434i	0.294323	+	0.317205i	0.862850	−	0.505460i	$-0.168677\pi$
$853$	8.59605	+	9.26434i	0.294323	+	0.317205i	−0.568527	+	0.822665i	$0.692487\pi$
$854$	−8.78230	+	10.2707i	−0.300524	+	0.351458i
$855$	−0.284014	−	5.37399i	−0.00971308	−	0.183787i
$856$	−3.55342	+	15.5686i	−0.121453	+	0.532122i
$857$	6.19851	+	0.934274i	0.211737	+	0.0319142i	0.254054	−	0.967190i	$-0.418236\pi$
$857$	6.19851	+	0.934274i	0.211737	+	0.0319142i	−0.0423171	+	0.999104i	$0.513474\pi$
$858$	−6.17001	−	24.0834i	−0.210641	−	0.822192i
$859$	−12.6647	+	13.6494i	−0.432116	+	0.465710i	−0.911143	−	0.412090i	$-0.864799\pi$
$859$	−12.6647	+	13.6494i	−0.432116	+	0.465710i	0.479028	+	0.877800i	$0.340989\pi$
$860$	0.484319	+	0.449382i	0.0165151	+	0.0153238i
$861$	5.28663	−	16.6738i	0.180168	−	0.568242i
$862$	−40.7612	+	37.8208i	−1.38833	+	1.28818i
$863$			43.4801i			1.48008i	0.672563	+	0.740040i	$0.265194\pi$
$863$			43.4801i			1.48008i	−0.672563	+	0.740040i	$0.734806\pi$
$864$	−15.3054	+	12.3162i	−0.520700	+	0.419007i
$865$	0.0644659	+	0.282443i	0.00219190	+	0.00960336i
$866$	−0.0174650	−	0.233054i	−0.000593485	−	0.00791951i
$867$	7.32005	−	26.1642i	0.248602	−	0.888582i
$868$	7.16679	−	7.21227i	0.243257	−	0.244800i
$869$	6.06899	+	40.2651i	0.205876	+	1.36590i
$870$	−0.943807	+	2.09990i	−0.0319980	+	0.0711934i
$871$	13.0250	+	5.11192i	0.441334	+	0.173211i
$872$	−10.0797	+	20.9306i	−0.341340	+	0.708800i
$873$	−23.3732	−	30.6695i	−0.791061	−	1.03800i
$874$	−17.2709	−	35.8635i	−0.584198	−	1.21310i
$875$	15.7773	−	4.28105i	0.533369	−	0.144726i
$876$	−0.916103	−	0.589779i	−0.0309522	−	0.0199268i
$877$	−0.442393	+	5.90332i	−0.0149385	+	0.199341i	0.984741	+	0.174026i	$0.0556778\pi$
$877$	−0.442393	+	5.90332i	−0.0149385	+	0.199341i	−0.999680	+	0.0253146i	$0.991941\pi$
$878$	−17.7007	−	16.4239i	−0.597370	−	0.554278i
$879$	−0.824336	−	2.44164i	−0.0278042	−	0.0823545i
$880$	−9.03607	−	3.54640i	−0.304606	−	0.119549i
$881$	6.50081			0.219018			0.109509	−	0.993986i	$-0.465072\pi$
$881$	6.50081			0.219018			0.109509	+	0.993986i	$0.465072\pi$
$882$	23.0583	+	25.6455i	0.776412	+	0.863529i
$883$	−52.5134			−1.76722			−0.883608	−	0.468228i	$-0.844893\pi$
$883$	−52.5134			−1.76722			−0.883608	+	0.468228i	$0.844893\pi$
$884$	2.11898	+	0.831638i	0.0712690	+	0.0279710i
$885$	10.5614	+	2.11892i	0.355019	+	0.0712267i
$886$	−20.3899	−	18.9190i	−0.685011	−	0.635597i
$887$	−3.29678	+	43.9924i	−0.110695	+	1.47712i	0.614685	+	0.788773i	$0.289283\pi$
$887$	−3.29678	+	43.9924i	−0.110695	+	1.47712i	−0.725380	+	0.688349i	$0.758336\pi$
$888$	1.91364	−	39.5076i	0.0642176	−	1.32579i
$889$	−13.9935	+	12.1196i	−0.469326	+	0.406479i
$890$	−3.52992	−	7.32995i	−0.118323	−	0.245701i
$891$	−27.4153	−	3.27229i	−0.918447	−	0.109626i
$892$	3.80882	−	7.90910i	0.127529	−	0.264816i
$893$	12.3768	+	4.85753i	0.414173	+	0.162551i
$894$	−29.9611	−	41.5447i	−1.00205	−	1.38946i
$895$	−0.711073	−	4.71766i	−0.0237686	−	0.157694i
$896$	−30.2711	−	18.8873i	−1.01129	−	0.630979i
$897$	41.6410	−	10.6682i	1.39035	−	0.356200i
$898$	−0.501800	−	6.69605i	−0.0167453	−	0.223450i
$899$	1.54033	+	6.74863i	0.0513729	+	0.225079i
$900$	6.67308	−	6.88186i	0.222436	−	0.229395i
$901$		−	1.58856i		−	0.0529227i
$902$	14.0969	−	13.0800i	0.469375	−	0.435516i
$903$	−1.05642	+	6.65464i	−0.0351555	+	0.221453i
$904$	−26.6010	−	24.6821i	−0.884736	−	0.820915i
$905$	2.56645	−	2.76597i	0.0853116	−	0.0919441i
$906$	19.5210	−	19.0963i	0.648543	−	0.634431i
$907$	20.6132	+	3.10694i	0.684451	+	0.103164i	0.482057	−	0.876140i	$-0.339890\pi$
$907$	20.6132	+	3.10694i	0.684451	+	0.103164i	0.202394	+	0.979304i	$0.435128\pi$
$908$	−2.85384	+	12.5035i	−0.0947080	+	0.414943i
$909$	−20.7084	+	40.6869i	−0.686856	+	1.34950i
$910$	−1.50848	−	7.83669i	−0.0500055	−	0.259784i
$911$	20.2238	+	21.7961i	0.670045	+	0.722137i	0.972984	−	0.230873i	$-0.0741583\pi$
$911$	20.2238	+	21.7961i	0.670045	+	0.722137i	−0.302939	+	0.953010i	$0.597968\pi$
$912$	14.2551	−	18.8769i	0.472035	−	0.625076i
$913$	−15.7526	−	9.09478i	−0.521336	−	0.300993i
$914$	7.51422	−	24.3605i	0.248548	−	0.805773i
$915$	0.168019	−	3.46879i	0.00555454	−	0.114675i
$916$	−2.23083	+	14.8006i	−0.0737087	+	0.489026i
$917$	41.1941	+	21.6053i	1.36035	+	0.713469i
$918$	6.62183	−	7.19993i	0.218553	−	0.237633i
$919$	−3.94042	−	17.2641i	−0.129982	−	0.569491i	−0.997410	−	0.0719268i	$-0.977085\pi$
$919$	−3.94042	−	17.2641i	−0.129982	−	0.569491i	0.867427	−	0.497564i	$-0.165772\pi$
$920$	4.39032	−	11.1863i	0.144744	−	0.368803i
$921$	−1.94147	+	40.0821i	−0.0639736	+	1.32075i
$922$	−16.3191	+	6.40477i	−0.537440	+	0.210930i
$923$	−1.43396	+	19.1349i	−0.0471994	+	0.629833i
$924$	2.10547	+	9.56971i	0.0692648	+	0.314820i
$925$	3.65612	+	48.7875i	0.120212	+	1.60412i
$926$	8.98537	+	18.6583i	0.295277	+	0.613150i
$927$	−2.22058	−	42.0169i	−0.0729335	−	1.38002i
$928$	−4.27658	+	2.05949i	−0.140386	+	0.0676062i
$929$	−8.02537	+	20.4483i	−0.263304	+	0.670887i	−0.999986	−	0.00535241i	$-0.998296\pi$
$929$	−8.02537	+	20.4483i	−0.263304	+	0.670887i	0.736682	+	0.676239i	$0.236392\pi$
$930$	−1.24249	+	10.0341i	−0.0407428	+	0.329032i
$931$	−16.1622	−	10.8700i	−0.529694	−	0.356251i
$932$	6.68613	+	3.86024i	0.219012	+	0.126446i
$933$	4.07502	−	2.49841i	0.133410	−	0.0817943i
$934$	13.7362	−	20.1474i	0.449463	−	0.659242i
$935$	2.21027	+	0.504481i	0.0722837	+	0.0164983i
$936$	12.1422	+	13.6776i	0.396879	+	0.447068i
$937$	−22.3745	+	46.4612i	−0.730945	+	1.51782i	0.120119	+	0.992760i	$0.461672\pi$
$937$	−22.3745	+	46.4612i	−0.730945	+	1.51782i	−0.851064	+	0.525063i	$0.824042\pi$
$938$	−19.5856	−	8.47144i	−0.639491	−	0.276602i
$939$	−8.99276	+	44.8231i	−0.293468	+	1.46275i
$940$	−0.784435	−	1.99871i	−0.0255854	−	0.0651906i
$941$	−26.4036	+	18.0017i	−0.860732	+	0.586837i	−0.911235	−	0.411887i	$-0.864870\pi$
$941$	−26.4036	+	18.0017i	−0.860732	+	0.586837i	0.0505029	+	0.998724i	$0.483918\pi$
$942$	−52.2029	−	28.3290i	−1.70086	−	0.923008i
$943$	22.6158	+	24.3740i	0.736471	+	0.793727i
$944$	29.5214	+	37.0187i	0.960840	+	1.20486i
$945$	−8.72061	−	1.58180i	−0.283682	−	0.0514558i
$946$	−4.61861	+	5.79156i	−0.150164	+	0.188300i
$947$	53.6329	−	4.01923i	1.74284	−	0.130608i	0.835086	−	0.550119i	$-0.185418\pi$
$947$	53.6329	−	4.01923i	1.74284	−	0.130608i	0.907750	+	0.419512i	$0.137799\pi$
$948$	9.37311	+	12.9969i	0.304425	+	0.422121i
$949$	−1.28563	+	2.22678i	−0.0417334	+	0.0722843i
$950$	−10.4744	+	18.1421i	−0.339833	+	0.588608i
$951$	−37.3640	−	16.7933i	−1.21161	−	0.544561i
$952$	5.95661	+	2.57644i	0.193055	+	0.0835030i
$953$	−47.6755	−	10.8816i	−1.54436	−	0.352490i	−0.636338	−	0.771410i	$-0.719552\pi$
$953$	−47.6755	−	10.8816i	−1.54436	−	0.352490i	−0.908023	+	0.418920i	$0.862409\pi$
$954$	−3.09693	+	6.08469i	−0.100267	+	0.196999i
$955$	12.5367	+	9.99771i	0.405679	+	0.323518i
$956$	1.42586	−	9.45996i	0.0461156	−	0.305957i
$957$	−6.27201	−	2.27241i	−0.202745	−	0.0734565i
$958$	−24.5643	+	26.4740i	−0.793637	+	0.855337i
$959$	−7.70292	−	12.1735i	−0.248740	−	0.393102i
$960$	4.00748	−	0.406948i	0.129341	−	0.0131342i
$961$	−0.299996	−	0.519608i	−0.00967728	−	0.0167615i
$962$	49.9323			1.60988
$963$	−11.6177	+	19.1375i	−0.374375	+	0.616697i
$964$	−6.25529	+	12.9892i	−0.201469	+	0.418356i
$965$	0.618822	+	0.0932725i	0.0199206	+	0.00300255i
$966$	−64.0253	+	14.0864i	−2.05998	+	0.453224i
$967$	−22.0617	+	3.32526i	−0.709456	+	0.106933i	−0.493850	−	0.869547i	$-0.664411\pi$
$967$	−22.0617	+	3.32526i	−0.709456	+	0.106933i	−0.215606	+	0.976480i	$0.569173\pi$
$968$	−1.00212	+	3.24879i	−0.0322093	+	0.104420i
$969$	−2.63505	+	4.85571i	−0.0846500	+	0.155988i
$970$	−1.01696	−	13.5704i	−0.0326526	−	0.435719i
$971$	−27.4828	+	34.4623i	−0.881964	+	1.10595i	0.111721	+	0.993740i	$0.464364\pi$
$971$	−27.4828	+	34.4623i	−0.881964	+	1.10595i	−0.993685	+	0.112208i	$0.964208\pi$
$972$	−10.1823	+	3.79088i	−0.326599	+	0.121593i
$973$	2.54485	+	5.78288i	0.0815841	+	0.185391i
$974$	35.0180	−	2.62424i	1.12205	−	0.0840860i
$975$	−16.9838	−	14.9441i	−0.543918	−	0.478593i
$976$	10.3830	−	11.1902i	0.332351	−	0.358189i
$977$	−11.3069	−	0.847332i	−0.361738	−	0.0271085i	−0.107379	−	0.994218i	$-0.534246\pi$
$977$	−11.3069	−	0.847332i	−0.361738	−	0.0271085i	−0.254360	+	0.967110i	$0.581865\pi$
$978$	50.0241	−	1.32096i	1.59959	−	0.0422396i
$979$	20.4154	−	11.7868i	0.652480	−	0.376709i
$980$	0.488466	+	3.10724i	0.0156035	+	0.0992570i
$981$	−22.6726	+	23.3819i	−0.723879	+	0.746527i
$982$	1.17648	+	1.47526i	0.0375430	+	0.0470774i
$983$	0.529171	+	0.360783i	0.0168779	+	0.0115072i	0.571730	−	0.820442i	$-0.306273\pi$
$983$	0.529171	+	0.360783i	0.0168779	+	0.0115072i	−0.554852	+	0.831949i	$0.687225\pi$
$984$	−4.81913	+	13.3011i	−0.153628	+	0.424025i
$985$	6.36206	+	0.476770i	0.202712	+	0.0151912i
$986$	1.95280	−	1.33140i	0.0621899	−	0.0424003i
$987$	12.4766	−	17.9952i	0.397134	−	0.572793i
$988$	4.56532	+	3.11258i	0.145242	+	0.0990244i
$989$	−10.0138	−	7.98575i	−0.318421	−	0.253932i
$990$	−7.48254	−	6.24128i	−0.237811	−	0.198361i
$991$	22.4088	+	28.0998i	0.711839	+	0.892618i	0.997845	−	0.0656094i	$-0.0208991\pi$
$991$	22.4088	+	28.0998i	0.711839	+	0.892618i	−0.286006	+	0.958228i	$0.592328\pi$
$992$	−15.2810	+	14.1787i	−0.485173	+	0.450175i
$993$	−0.396014	−	14.9968i	−0.0125671	−	0.475910i
$994$	3.18452	−	29.0902i	0.101007	−	0.922685i
$995$	−15.3094	+	6.00851i	−0.485341	+	0.190482i
$996$	−7.14963	−	0.346309i	−0.226545	−	0.0109732i
$997$	10.7732	+	11.6108i	0.341192	+	0.367717i	0.880216	−	0.474573i	$-0.157397\pi$
$997$	10.7732	+	11.6108i	0.341192	+	0.367717i	−0.539025	+	0.842290i	$0.681207\pi$
$998$		−	26.2481i		−	0.830870i
$999$	20.0319	−	51.7084i	0.633781	−	1.63598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bh.a.41.42	✓	648
9.2	odd	6	inner	441.2.bh.a.335.42	yes	648
49.6	odd	14	inner	441.2.bh.a.104.42	yes	648
441.398	even	42	inner	441.2.bh.a.398.42	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bh.a.41.42	✓	648	1.1	even	1	trivial
441.2.bh.a.104.42	yes	648	49.6	odd	14	inner
441.2.bh.a.335.42	yes	648	9.2	odd	6	inner
441.2.bh.a.398.42	yes	648	441.398	even	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bh (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.52873 + 0.599983i) q^{2} +(1.14417 - 1.30034i) q^{3} +(0.510936 + 0.474079i) q^{4} +(0.0481771 - 0.642879i) q^{5} +(2.52930 - 1.30139i) q^{6} +(1.24367 + 2.33523i) q^{7} +(-0.928450 - 1.92795i) q^{8} +(-0.381764 - 2.97561i) q^{9} +O(q^{10})\)	\(q+(1.52873 + 0.599983i) q^{2} +(1.14417 - 1.30034i) q^{3} +(0.510936 + 0.474079i) q^{4} +(0.0481771 - 0.642879i) q^{5} +(2.52930 - 1.30139i) q^{6} +(1.24367 + 2.33523i) q^{7} +(-0.928450 - 1.92795i) q^{8} +(-0.381764 - 2.97561i) q^{9} +(0.459366 - 0.953884i) q^{10} +(2.85570 + 1.12078i) q^{11} +(1.20106 - 0.121964i) q^{12} +(-0.424627 - 2.81722i) q^{13} +(0.500141 + 4.31611i) q^{14} +(-0.780838 - 0.798208i) q^{15} +(-0.366789 - 4.89447i) q^{16} +(0.255080 + 1.11758i) q^{17} +(1.20170 - 4.77796i) q^{18} +2.78250i q^{19} +(0.329391 - 0.305630i) q^{20} +(4.45955 + 1.05470i) q^{21} +(3.69315 + 3.42674i) q^{22} +(-5.92497 + 6.38559i) q^{23} +(-3.56929 - 0.998593i) q^{24} +(4.53318 + 0.683267i) q^{25} +(1.04114 - 4.56154i) q^{26} +(-4.30610 - 2.90817i) q^{27} +(-0.471647 + 1.78275i) q^{28} +(-0.853937 - 0.920325i) q^{29} +(-0.714781 - 1.68873i) q^{30} +(-4.77494 - 2.75681i) q^{31} +(1.11440 - 3.61281i) q^{32} +(4.72480 - 2.43102i) q^{33} +(-0.280579 + 1.86152i) q^{34} +(1.56119 - 0.687025i) q^{35} +(1.21562 - 1.70133i) q^{36} +(2.37473 + 10.4044i) q^{37} +(-1.66945 + 4.25370i) q^{38} +(-4.14918 - 2.67121i) q^{39} +(-1.28417 + 0.503998i) q^{40} +(0.285247 - 3.80636i) q^{41} +(6.18466 + 4.28800i) q^{42} +(0.109879 + 1.46623i) q^{43} +(0.927742 + 1.92648i) q^{44} +(-1.93135 + 0.102071i) q^{45} +(-12.8889 + 6.20698i) q^{46} +(1.74574 - 4.44807i) q^{47} +(-6.78413 - 5.12314i) q^{48} +(-3.90657 + 5.80850i) q^{49} +(6.52007 + 3.76436i) q^{50} +(1.74509 + 0.947007i) q^{51} +(1.11863 - 1.64072i) q^{52} +(-1.35105 - 0.308368i) q^{53} +(-4.83802 - 7.02940i) q^{54} +(0.858106 - 1.78188i) q^{55} +(3.34751 - 4.56587i) q^{56} +(3.61820 + 3.18365i) q^{57} +(-0.753260 - 1.91928i) q^{58} +(-7.97062 + 5.43427i) q^{59} +(-0.0205446 - 0.778012i) q^{60} +(2.11544 + 2.27990i) q^{61} +(-5.64555 - 7.07930i) q^{62} +(6.47394 - 4.59218i) q^{63} +(-2.24917 + 2.82037i) q^{64} +(-1.83159 + 0.137258i) q^{65} +(8.68151 - 0.881582i) q^{66} +(-2.45560 + 4.25322i) q^{67} +(-0.399492 + 0.691940i) q^{68} +(1.52429 + 15.0107i) q^{69} +(2.79884 - 0.113592i) q^{70} +(-6.56623 - 1.49870i) q^{71} +(-5.38237 + 3.49873i) q^{72} +(-0.705605 - 0.562701i) q^{73} +(-2.61212 + 17.3303i) q^{74} +(6.07520 - 5.11290i) q^{75} +(-1.31913 + 1.42168i) q^{76} +(0.934275 + 8.06260i) q^{77} +(-4.74030 - 6.57299i) q^{78} +(6.63674 + 11.4952i) q^{79} -3.16422 q^{80} +(-8.70851 + 2.27196i) q^{81} +(2.71981 - 5.64775i) q^{82} +(-5.86303 - 0.883709i) q^{83} +(1.77854 + 2.65306i) q^{84} +(0.730758 - 0.110144i) q^{85} +(-0.711740 + 2.30740i) q^{86} +(-2.17378 + 0.0574019i) q^{87} +(-0.490572 - 6.54623i) q^{88} +(4.79110 - 6.00784i) q^{89} +(-3.01376 - 1.00274i) q^{90} +(6.05074 - 4.49529i) q^{91} +(-6.05456 + 0.453726i) q^{92} +(-9.04811 + 3.05478i) q^{93} +(5.33754 - 5.75249i) q^{94} +(1.78881 + 0.134053i) q^{95} +(-3.42281 - 5.58276i) q^{96} +(11.1315 - 6.42677i) q^{97} +(-9.45710 + 6.53577i) q^{98} +(2.24480 - 8.92533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 15 q^{2} - 14 q^{3} - 57 q^{4} - 21 q^{5} + 14 q^{6} - 5 q^{7} - 20 q^{9}+O(q^{10}) \) 648 * q - 15 * q^2 - 14 * q^3 - 57 * q^4 - 21 * q^5 + 14 * q^6 - 5 * q^7 - 20 * q^9	\( 648 q - 15 q^{2} - 14 q^{3} - 57 q^{4} - 21 q^{5} + 14 q^{6} - 5 q^{7} - 20 q^{9} - 28 q^{10} - 15 q^{11} + 21 q^{12} - 7 q^{13} - 114 q^{14} - 10 q^{15} + 39 q^{16} - 18 q^{18} - 21 q^{20} + 10 q^{21} + 3 q^{22} + 30 q^{23} - 14 q^{24} + 41 q^{25} + 7 q^{27} - 20 q^{28} + 75 q^{29} - 70 q^{30} - 39 q^{32} - 14 q^{33} - 7 q^{34} - 128 q^{36} - 10 q^{37} + 21 q^{38} - 36 q^{39} - 7 q^{40} - 21 q^{41} + 104 q^{42} + 3 q^{43} - 35 q^{45} - 72 q^{46} - 147 q^{47} - 13 q^{49} - 18 q^{50} + 22 q^{51} - 35 q^{52} - 14 q^{54} - 112 q^{55} - 63 q^{56} - 16 q^{57} + 33 q^{58} - 21 q^{59} - 90 q^{60} - 56 q^{61} - 38 q^{63} + 52 q^{64} + 27 q^{65} - 42 q^{66} - 26 q^{67} - 182 q^{69} - 25 q^{70} + 24 q^{72} - 28 q^{73} + 33 q^{74} - 14 q^{75} + 21 q^{76} + 3 q^{77} + 90 q^{78} - 2 q^{79} + 56 q^{81} - 28 q^{82} - 21 q^{83} + 116 q^{84} + 5 q^{85} - 123 q^{86} - 70 q^{87} - 41 q^{88} - 224 q^{90} - 4 q^{91} - 225 q^{92} + 112 q^{93} - 7 q^{94} - 12 q^{95} - 371 q^{96} + 224 q^{99}+O(q^{100}) \) 648 * q - 15 * q^2 - 14 * q^3 - 57 * q^4 - 21 * q^5 + 14 * q^6 - 5 * q^7 - 20 * q^9 - 28 * q^10 - 15 * q^11 + 21 * q^12 - 7 * q^13 - 114 * q^14 - 10 * q^15 + 39 * q^16 - 18 * q^18 - 21 * q^20 + 10 * q^21 + 3 * q^22 + 30 * q^23 - 14 * q^24 + 41 * q^25 + 7 * q^27 - 20 * q^28 + 75 * q^29 - 70 * q^30 - 39 * q^32 - 14 * q^33 - 7 * q^34 - 128 * q^36 - 10 * q^37 + 21 * q^38 - 36 * q^39 - 7 * q^40 - 21 * q^41 + 104 * q^42 + 3 * q^43 - 35 * q^45 - 72 * q^46 - 147 * q^47 - 13 * q^49 - 18 * q^50 + 22 * q^51 - 35 * q^52 - 14 * q^54 - 112 * q^55 - 63 * q^56 - 16 * q^57 + 33 * q^58 - 21 * q^59 - 90 * q^60 - 56 * q^61 - 38 * q^63 + 52 * q^64 + 27 * q^65 - 42 * q^66 - 26 * q^67 - 182 * q^69 - 25 * q^70 + 24 * q^72 - 28 * q^73 + 33 * q^74 - 14 * q^75 + 21 * q^76 + 3 * q^77 + 90 * q^78 - 2 * q^79 + 56 * q^81 - 28 * q^82 - 21 * q^83 + 116 * q^84 + 5 * q^85 - 123 * q^86 - 70 * q^87 - 41 * q^88 - 224 * q^90 - 4 * q^91 - 225 * q^92 + 112 * q^93 - 7 * q^94 - 12 * q^95 - 371 * q^96 + 224 * q^99

Introduction

L-functions

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