LMFDB - Embedded newform 288.2.bf.a.275.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			275.6
Character	$\chi$	$=$	288.275
Dual form			288.2.bf.a.155.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35242 - 0.413466i) q^{2} +(0.986415 + 1.42372i) q^{3} +(1.65809 + 1.11836i) q^{4} +(-1.47515 - 0.194207i) q^{5} +(-0.745388 - 2.33332i) q^{6} +(-0.772924 + 2.88459i) q^{7} +(-1.78004 - 2.19806i) q^{8} +(-1.05397 + 2.80876i) q^{9} +O(q^{10})$	\(q+(-1.35242 - 0.413466i) q^{2} +(0.986415 + 1.42372i) q^{3} +(1.65809 + 1.11836i) q^{4} +(-1.47515 - 0.194207i) q^{5} +(-0.745388 - 2.33332i) q^{6} +(-0.772924 + 2.88459i) q^{7} +(-1.78004 - 2.19806i) q^{8} +(-1.05397 + 2.80876i) q^{9} +(1.91472 + 0.872572i) q^{10} +(0.930918 - 1.21320i) q^{11} +(0.0433298 + 3.46383i) q^{12} +(-4.09955 + 3.14570i) q^{13} +(2.23800 - 3.58161i) q^{14} +(-1.17861 - 2.29177i) q^{15} +(1.49854 + 3.70869i) q^{16} +0.887001 q^{17} +(2.58674 - 3.36285i) q^{18} +(1.18314 - 2.85635i) q^{19} +(-2.22873 - 1.97176i) q^{20} +(-4.86928 + 1.74497i) q^{21} +(-1.76061 + 1.25585i) q^{22} +(-4.57200 + 1.22506i) q^{23} +(1.37358 - 4.70248i) q^{24} +(-2.69129 - 0.721129i) q^{25} +(6.84496 - 2.55928i) q^{26} +(-5.03855 + 1.27004i) q^{27} +(-4.50759 + 3.91851i) q^{28} +(0.945074 + 7.17855i) q^{29} +(0.646410 + 3.58675i) q^{30} +(7.16956 + 4.13935i) q^{31} +(-0.493237 - 5.63531i) q^{32} +(2.64552 + 0.128655i) q^{33} +(-1.19960 - 0.366745i) q^{34} +(1.70038 - 4.10509i) q^{35} +(-4.88879 + 3.47846i) q^{36} +(6.13689 - 2.54198i) q^{37} +(-2.78111 + 3.37380i) q^{38} +(-8.52246 - 2.73366i) q^{39} +(2.19894 + 3.58816i) q^{40} +(2.37130 + 8.84981i) q^{41} +(7.30681 - 0.346659i) q^{42} +(0.438670 + 0.336603i) q^{43} +(2.90034 - 0.970487i) q^{44} +(2.10024 - 3.93865i) q^{45} +(6.68979 + 0.233563i) q^{46} +(-6.71629 + 3.87765i) q^{47} +(-3.80197 + 5.79181i) q^{48} +(-1.66127 - 0.959138i) q^{49} +(3.34160 + 2.08803i) q^{50} +(0.874950 + 1.26284i) q^{51} +(-10.3155 + 0.631075i) q^{52} +(1.92282 - 0.796456i) q^{53} +(7.33937 + 0.365641i) q^{54} +(-1.60885 + 1.60885i) q^{55} +(7.71634 - 3.43574i) q^{56} +(5.23371 - 1.13308i) q^{57} +(1.68995 - 10.0992i) q^{58} +(1.77908 - 13.5135i) q^{59} +(0.608781 - 5.11807i) q^{60} +(3.56050 - 0.468748i) q^{61} +(-7.98480 - 8.56252i) q^{62} +(-7.28749 - 5.21124i) q^{63} +(-1.66294 + 7.82526i) q^{64} +(6.65835 - 3.84420i) q^{65} +(-3.52467 - 1.26783i) q^{66} +(10.8486 - 8.32441i) q^{67} +(1.47073 + 0.991987i) q^{68} +(-6.25403 - 5.30084i) q^{69} +(-3.99695 + 4.84876i) q^{70} +(4.27235 - 4.27235i) q^{71} +(8.04994 - 2.68300i) q^{72} +(2.09233 + 2.09233i) q^{73} +(-9.35069 + 0.900439i) q^{74} +(-1.62804 - 4.54298i) q^{75} +(5.15618 - 3.41291i) q^{76} +(2.78004 + 3.62302i) q^{77} +(10.3957 + 7.22081i) q^{78} +(-3.53518 - 6.12311i) q^{79} +(-1.49031 - 5.76189i) q^{80} +(-6.77828 - 5.92072i) q^{81} +(0.452097 - 12.9491i) q^{82} +(0.307069 + 2.33242i) q^{83} +(-10.0252 - 2.55229i) q^{84} +(-1.30846 - 0.172261i) q^{85} +(-0.454093 - 0.636605i) q^{86} +(-9.28803 + 8.42655i) q^{87} +(-4.32374 + 0.113318i) q^{88} +(4.22741 + 4.22741i) q^{89} +(-4.46891 + 4.45833i) q^{90} +(-5.90541 - 14.2569i) q^{91} +(-8.95085 - 3.08188i) q^{92} +(1.17888 + 14.2906i) q^{93} +(10.6865 - 2.46727i) q^{94} +(-2.30002 + 3.98376i) q^{95} +(7.53658 - 6.26098i) q^{96} +(3.95899 + 6.85717i) q^{97} +(1.85017 + 1.98404i) q^{98} +(2.42642 + 3.89340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.35242	−	0.413466i	−0.956307	−	0.292365i
$2$	−1.35242	−	0.413466i	−0.956307	−	0.292365i
$3$	0.986415	+	1.42372i	0.569507	+	0.821987i
$3$	0.986415	+	1.42372i	0.569507	+	0.821987i
$4$	1.65809	+	1.11836i	0.829046	+	0.559181i
$5$	−1.47515	−	0.194207i	−0.659705	−	0.0868519i	−0.206762	−	0.978391i	$-0.566293\pi$
$5$	−1.47515	−	0.194207i	−0.659705	−	0.0868519i	−0.452943	+	0.891539i	$0.649626\pi$
$6$	−0.745388	−	2.33332i	−0.304303	−	0.952575i
$7$	−0.772924	+	2.88459i	−0.292138	+	1.09027i	0.651326	+	0.758798i	$0.274213\pi$
$7$	−0.772924	+	2.88459i	−0.292138	+	1.09027i	−0.943464	+	0.331475i	$0.892454\pi$
$8$	−1.78004	−	2.19806i	−0.629338	−	0.777132i
$9$	−1.05397	+	2.80876i	−0.351324	+	0.936254i
$10$	1.91472	+	0.872572i	0.605488	+	0.275932i
$11$	0.930918	−	1.21320i	0.280682	−	0.365792i	−0.631642	−	0.775260i	$-0.717619\pi$
$11$	0.930918	−	1.21320i	0.280682	−	0.365792i	0.912325	+	0.409468i	$0.134286\pi$
$12$	0.0433298	+	3.46383i	0.0125082	+	0.999922i
$13$	−4.09955	+	3.14570i	−1.13701	+	0.872459i	−0.993116	−	0.117134i	$-0.962629\pi$
$13$	−4.09955	+	3.14570i	−1.13701	+	0.872459i	−0.143895	+	0.989593i	$0.545963\pi$
$14$	2.23800	−	3.58161i	0.598131	−	0.957225i
$15$	−1.17861	−	2.29177i	−0.304316	−	0.591732i
$16$	1.49854	+	3.70869i	0.374634	+	0.927173i
$17$	0.887001			0.215129			0.107565	−	0.994198i	$-0.465695\pi$
$17$	0.887001			0.215129			0.107565	+	0.994198i	$0.465695\pi$
$18$	2.58674	−	3.36285i	0.609701	−	0.792631i
$19$	1.18314	−	2.85635i	0.271431	−	0.655291i	−0.728114	−	0.685456i	$-0.759603\pi$
$19$	1.18314	−	2.85635i	0.271431	−	0.655291i	0.999545	+	0.0301642i	$0.00960303\pi$
$20$	−2.22873	−	1.97176i	−0.498360	−	0.440899i
$21$	−4.86928	+	1.74497i	−1.06256	+	0.380784i
$22$	−1.76061	+	1.25585i	−0.375363	+	0.267748i
$23$	−4.57200	+	1.22506i	−0.953327	+	0.255443i	−0.701774	−	0.712400i	$-0.747608\pi$
$23$	−4.57200	+	1.22506i	−0.953327	+	0.255443i	−0.251554	+	0.967843i	$0.580941\pi$
$24$	1.37358	−	4.70248i	0.280380	−	0.959889i
$25$	−2.69129	−	0.721129i	−0.538258	−	0.144226i
$26$	6.84496	−	2.55928i	1.34241	−	0.501917i
$27$	−5.03855	+	1.27004i	−0.969670	+	0.244419i
$28$	−4.50759	+	3.91851i	−0.851855	+	0.740528i
$29$	0.945074	+	7.17855i	0.175496	+	1.33302i	0.821727	+	0.569881i	$0.193011\pi$
$29$	0.945074	+	7.17855i	0.175496	+	1.33302i	−0.646231	+	0.763142i	$0.723656\pi$
$30$	0.646410	+	3.58675i	0.118018	+	0.654848i
$31$	7.16956	+	4.13935i	1.28769	+	0.743449i	0.978242	−	0.207467i	$-0.0665219\pi$
$31$	7.16956	+	4.13935i	1.28769	+	0.743449i	0.309449	+	0.950916i	$0.399855\pi$
$32$	−0.493237	−	5.63531i	−0.0871928	−	0.996191i
$33$	2.64552	+	0.128655i	0.460527	+	0.0223959i
$34$	−1.19960	−	0.366745i	−0.205730	−	0.0628962i
$35$	1.70038	−	4.10509i	0.287417	−	0.693886i
$36$	−4.88879	+	3.47846i	−0.814799	+	0.579744i
$37$	6.13689	−	2.54198i	1.00890	−	0.417899i	0.183845	−	0.982955i	$-0.441145\pi$
$37$	6.13689	−	2.54198i	1.00890	−	0.417899i	0.825053	+	0.565056i	$0.191145\pi$
$38$	−2.78111	+	3.37380i	−0.451155	+	0.547303i
$39$	−8.52246	−	2.73366i	−1.36469	−	0.437736i
$40$	2.19894	+	3.58816i	0.347682	+	0.567337i
$41$	2.37130	+	8.84981i	0.370335	+	1.38211i	0.860043	+	0.510221i	$0.170437\pi$
$41$	2.37130	+	8.84981i	0.370335	+	1.38211i	−0.489708	+	0.871886i	$0.662897\pi$
$42$	7.30681	−	0.346659i	1.12747	−	0.0534906i
$43$	0.438670	+	0.336603i	0.0668965	+	0.0513315i	0.641668	−	0.766982i	$-0.278243\pi$
$43$	0.438670	+	0.336603i	0.0668965	+	0.0513315i	−0.574772	+	0.818314i	$0.694909\pi$
$44$	2.90034	−	0.970487i	0.437242	−	0.146306i
$45$	2.10024	−	3.93865i	0.313086	−	0.587139i
$46$	6.68979	+	0.233563i	0.986356	+	0.0344370i
$47$	−6.71629	+	3.87765i	−0.979672	+	0.565614i	−0.902171	−	0.431378i	$-0.858027\pi$
$47$	−6.71629	+	3.87765i	−0.979672	+	0.565614i	−0.0775008	+	0.996992i	$0.524694\pi$
$48$	−3.80197	+	5.79181i	−0.548767	+	0.835975i
$49$	−1.66127	−	0.959138i	−0.237325	−	0.137020i
$50$	3.34160	+	2.08803i	0.472573	+	0.295292i
$51$	0.874950	+	1.26284i	0.122518	+	0.176833i
$52$	−10.3155	+	0.631075i	−1.43050	+	0.0875143i
$53$	1.92282	−	0.796456i	0.264119	−	0.109402i	−0.246694	−	0.969093i	$-0.579344\pi$
$53$	1.92282	−	0.796456i	0.264119	−	0.109402i	0.510813	+	0.859692i	$0.329344\pi$
$54$	7.33937	+	0.365641i	0.998761	+	0.0497574i
$55$	−1.60885	+	1.60885i	−0.216937	+	0.216937i
$56$	7.71634	−	3.43574i	1.03114	−	0.459120i
$57$	5.23371	−	1.13308i	0.693222	−	0.150081i
$58$	1.68995	−	10.0992i	0.221901	−	1.32609i
$59$	1.77908	−	13.5135i	0.231617	−	1.75930i	−0.341548	−	0.939864i	$-0.610951\pi$
$59$	1.77908	−	13.5135i	0.231617	−	1.75930i	0.573165	−	0.819440i	$-0.305716\pi$
$60$	0.608781	−	5.11807i	0.0785933	−	0.660740i
$61$	3.56050	−	0.468748i	0.455875	−	0.0600171i	0.100908	−	0.994896i	$-0.467825\pi$
$61$	3.56050	−	0.468748i	0.455875	−	0.0600171i	0.354967	+	0.934879i	$0.384492\pi$
$62$	−7.98480	−	8.56252i	−1.01407	−	1.08744i
$63$	−7.28749	−	5.21124i	−0.918137	−	0.656554i
$64$	−1.66294	+	7.82526i	−0.207868	+	0.978157i
$65$	6.65835	−	3.84420i	0.825867	−	0.476815i
$66$	−3.52467	−	1.26783i	−0.433857	−	0.156059i
$67$	10.8486	−	8.32441i	1.32537	−	1.01699i	0.327983	−	0.944684i	$-0.393631\pi$
$67$	10.8486	−	8.32441i	1.32537	−	1.01699i	0.997383	−	0.0723048i	$-0.0230354\pi$
$68$	1.47073	+	0.991987i	0.178352	+	0.120296i
$69$	−6.25403	−	5.30084i	−0.752897	−	0.638146i
$70$	−3.99695	+	4.84876i	−0.477727	+	0.579538i
$71$	4.27235	−	4.27235i	0.507035	−	0.507035i	−0.406580	−	0.913615i	$-0.633279\pi$
$71$	4.27235	−	4.27235i	0.507035	−	0.507035i	0.913615	+	0.406580i	$0.133279\pi$
$72$	8.04994	−	2.68300i	0.948694	−	0.316195i
$73$	2.09233	+	2.09233i	0.244888	+	0.244888i	0.818869	−	0.573981i	$-0.194602\pi$
$73$	2.09233	+	2.09233i	0.244888	+	0.244888i	−0.573981	+	0.818869i	$0.694602\pi$
$74$	−9.35069	+	0.900439i	−1.08700	+	0.104674i
$75$	−1.62804	−	4.54298i	−0.187990	−	0.524578i
$76$	5.15618	−	3.41291i	0.591455	−	0.391488i
$77$	2.78004	+	3.62302i	0.316815	+	0.412882i
$78$	10.3957	+	7.22081i	1.17708	+	0.817596i
$79$	−3.53518	−	6.12311i	−0.397739	−	0.688904i	0.595708	−	0.803201i	$-0.296872\pi$
$79$	−3.53518	−	6.12311i	−0.397739	−	0.688904i	−0.993447	+	0.114297i	$0.963538\pi$
$80$	−1.49031	−	5.76189i	−0.166622	−	0.644199i
$81$	−6.77828	−	5.92072i	−0.753143	−	0.657857i
$82$	0.452097	−	12.9491i	0.0499258	−	1.42999i
$83$	0.307069	+	2.33242i	0.0337051	+	0.256016i	0.999999	−	0.00142567i	$-0.000453805\pi$
$83$	0.307069	+	2.33242i	0.0337051	+	0.256016i	−0.966294	+	0.257442i	$0.917120\pi$
$84$	−10.0252	−	2.55229i	−1.09384	−	0.278477i
$85$	−1.30846	−	0.172261i	−0.141922	−	0.0186844i
$86$	−0.454093	−	0.636605i	−0.0489661	−	0.0686468i
$87$	−9.28803	+	8.42655i	−0.995781	+	0.903421i
$88$	−4.32374	+	0.113318i	−0.460913	+	0.0120797i
$89$	4.22741	+	4.22741i	0.448105	+	0.448105i	0.894724	−	0.446619i	$-0.147372\pi$
$89$	4.22741	+	4.22741i	0.448105	+	0.448105i	−0.446619	+	0.894724i	$0.647372\pi$
$90$	−4.46891	+	4.45833i	−0.471065	+	0.469950i
$91$	−5.90541	−	14.2569i	−0.619055	−	1.49453i
$92$	−8.95085	−	3.08188i	−0.933191	−	0.321308i
$93$	1.17888	+	14.2906i	0.122244	+	1.48186i
$94$	10.6865	−	2.46727i	1.10223	−	0.254479i
$95$	−2.30002	+	3.98376i	−0.235978	+	0.408725i
$96$	7.53658	−	6.26098i	0.769199	−	0.639009i
$97$	3.95899	+	6.85717i	0.401975	+	0.696241i	0.993964	−	0.109705i	$-0.0349906\pi$
$97$	3.95899	+	6.85717i	0.401975	+	0.696241i	−0.591989	+	0.805946i	$0.701657\pi$
$98$	1.85017	+	1.98404i	0.186896	+	0.200418i
$99$	2.42642	+	3.89340i	0.243864	+	0.391302i
$100$	−3.65592	−	4.20553i	−0.365592	−	0.420553i
$101$	6.91226	−	9.00823i	0.687795	−	0.896352i	−0.310738	−	0.950496i	$-0.600576\pi$
$101$	6.91226	−	9.00823i	0.687795	−	0.896352i	0.998533	+	0.0541433i	$0.0172428\pi$
$102$	−0.661160	−	2.06966i	−0.0654646	−	0.204927i
$103$	12.9283	−	3.46414i	1.27387	−	0.341332i	0.442356	−	0.896840i	$-0.354143\pi$
$103$	12.9283	−	3.46414i	1.27387	−	0.341332i	0.831511	+	0.555508i	$0.187476\pi$
$104$	14.2118	+	3.41161i	1.39358	+	0.334536i
$105$	7.52179	−	1.62844i	0.734051	−	0.158920i
$106$	−2.92977	+	0.282126i	−0.284564	+	0.0274025i
$107$	1.93352	+	4.66793i	0.186920	+	0.451266i	0.989364	−	0.145462i	$-0.0464670\pi$
$107$	1.93352	+	4.66793i	0.186920	+	0.451266i	−0.802443	+	0.596728i	$0.796467\pi$
$108$	−9.77474	−	3.52908i	−0.940575	−	0.339586i
$109$	−10.0048	−	4.14414i	−0.958290	−	0.396937i	−0.151950	−	0.988388i	$-0.548555\pi$
$109$	−10.0048	−	4.14414i	−0.958290	−	0.396937i	−0.806341	+	0.591451i	$0.798555\pi$
$110$	2.84105	−	1.51064i	0.270883	−	0.144034i
$111$	9.67259	+	6.22978i	0.918082	+	0.591304i
$112$	−11.8563	+	1.45613i	−1.12032	+	0.137591i
$113$	−7.18958	+	12.4527i	−0.676339	+	1.17145i	0.299737	+	0.954022i	$0.403101\pi$
$113$	−7.18958	+	12.4527i	−0.676339	+	1.17145i	−0.976076	+	0.217431i	$0.930232\pi$
$114$	−7.54668	−	0.631556i	−0.706812	−	0.0591506i
$115$	6.98228	−	0.919234i	0.651101	−	0.0857191i
$116$	−6.46119	+	12.9596i	−0.599907	+	1.20327i
$117$	−4.51470	−	14.8301i	−0.417384	−	1.37105i
$118$	−7.99343	+	17.5403i	−0.735855	+	1.61472i
$119$	−0.685584	+	2.55863i	−0.0628474	+	0.234550i
$120$	−2.93948	+	6.67008i	−0.268336	+	0.608893i
$121$	2.24177	+	8.36641i	0.203798	+	0.760583i
$122$	−5.00911	−	0.838199i	−0.453503	−	0.0758870i
$123$	−10.2606	+	12.1057i	−0.925166	+	1.09153i
$124$	7.25851	+	14.8816i	0.651833	+	1.33641i
$125$	10.7031	+	4.43336i	0.957313	+	0.396532i
$126$	7.70109	+	10.0609i	0.686068	+	0.896298i
$127$		−	4.41029i		−	0.391350i	−0.980669	−	0.195675i	$-0.937310\pi$
$127$		−	4.41029i		−	0.391350i	0.980669	−	0.195675i	$-0.0626898\pi$
$128$	5.48448	−	9.89548i	0.484764	−	0.874645i
$129$	−0.0465193	+	0.956574i	−0.00409579	+	0.0842217i
$130$	−10.5944	+	2.44598i	−0.929186	+	0.214527i
$131$	0.849749	+	1.10741i	0.0742429	+	0.0967553i	0.828998	−	0.559251i	$-0.188911\pi$
$131$	0.849749	+	1.10741i	0.0742429	+	0.0967553i	−0.754755	+	0.656006i	$0.772245\pi$
$132$	4.24264	+	3.17197i	0.369274	+	0.276085i
$133$	7.32492	+	5.62061i	0.635151	+	0.487369i
$134$	−18.1137	+	6.77260i	−1.56479	+	0.585063i
$135$	7.67925	−	0.894973i	0.660925	−	0.0770270i
$136$	−1.57889	−	1.94968i	−0.135389	−	0.167184i
$137$	8.93662	+	2.39456i	0.763507	+	0.204581i	0.619501	−	0.784996i	$-0.287335\pi$
$137$	8.93662	+	2.39456i	0.763507	+	0.204581i	0.144006	+	0.989577i	$0.454002\pi$
$138$	6.26638	+	9.75480i	0.533430	+	0.830384i
$139$	−1.87801	+	14.2649i	−0.159290	+	1.20993i	0.705836	+	0.708376i	$0.250572\pi$
$139$	−1.87801	+	14.2649i	−0.159290	+	1.20993i	−0.865126	+	0.501555i	$0.832762\pi$
$140$	7.41036	−	4.90497i	0.626290	−	0.414545i
$141$	−12.1458	−	5.73716i	−1.02286	−	0.483156i
$142$	−7.54449	+	4.01155i	−0.633120	+	0.336642i
$143$			7.90194i			0.660794i
$144$	−11.9962	+	0.300174i	−0.999687	+	0.0250145i
$145$		−	10.7730i		−	0.894645i
$146$	−1.96460	−	3.69481i	−0.162592	−	0.305785i
$147$	−0.273160	−	3.31130i	−0.0225299	−	0.273112i
$148$	13.0184	+	2.64842i	1.07010	+	0.217699i
$149$	−1.22133	+	9.27695i	−0.100056	+	0.759997i	0.865704	+	0.500557i	$0.166871\pi$
$149$	−1.22133	+	9.27695i	−0.100056	+	0.759997i	−0.965759	+	0.259440i	$0.916462\pi$
$150$	0.323429	+	6.81717i	0.0264078	+	0.556619i
$151$	0.0398073	+	0.0106663i	0.00323948	+	0.000868015i	0.260438	−	0.965490i	$-0.416133\pi$
$151$	0.0398073	+	0.0106663i	0.00323948	+	0.000868015i	−0.257199	+	0.966358i	$0.582800\pi$
$152$	−8.38446	+	2.48379i	−0.680069	+	0.201462i
$153$	−0.934874	+	2.49137i	−0.0755801	+	0.201416i
$154$	−2.26180	−	6.04931i	−0.182261	−	0.487467i
$155$	−9.77226	−	7.49852i	−0.784927	−	0.602296i
$156$	−11.0738	−	14.0638i	−0.886613	−	1.12601i
$157$	−13.4747	−	17.5606i	−1.07540	−	1.40148i	−0.909679	−	0.415311i	$-0.863673\pi$
$157$	−13.4747	−	17.5606i	−1.07540	−	1.40148i	−0.165718	−	0.986173i	$-0.552994\pi$
$158$	2.24936	+	9.74271i	0.178949	+	0.775088i
$159$	3.03063	+	1.95192i	0.240344	+	0.154797i
$160$	−0.366818	+	8.40870i	−0.0289995	+	0.664766i
$161$		−	14.1352i		−	1.11401i
$162$	6.71909	+	10.8099i	0.527901	+	0.849306i
$163$	−10.1647	−	4.21034i	−0.796157	−	0.329779i	−0.0527408	−	0.998608i	$-0.516796\pi$
$163$	−10.1647	−	4.21034i	−0.796157	−	0.329779i	−0.743416	+	0.668829i	$0.766796\pi$
$164$	−5.96545	+	17.3258i	−0.465823	+	1.35291i
$165$	−3.87755	−	0.703563i	−0.301867	−	0.0547723i
$166$	0.549089	−	3.28137i	0.0426176	−	0.254684i
$167$	0.924054	+	3.44862i	0.0715054	+	0.266862i	0.992418	−	0.122907i	$-0.0392216\pi$
$167$	0.924054	+	3.44862i	0.0715054	+	0.266862i	−0.920913	+	0.389769i	$0.872555\pi$
$168$	12.5031	+	7.59686i	0.964631	+	0.586111i
$169$	3.54627	−	13.2349i	0.272790	−	1.01807i
$170$	1.69836	+	0.773972i	0.130258	+	0.0593610i
$171$	6.77581	+	6.33367i	0.518159	+	0.484348i
$172$	0.350911	+	1.04871i	0.0267567	+	0.0799634i
$173$	−21.9988	+	2.89620i	−1.67254	+	0.220194i	−0.906382	−	0.422459i	$-0.861167\pi$
$173$	−21.9988	+	2.89620i	−1.67254	+	0.220194i	−0.766157	+	0.642653i	$0.777834\pi$
$174$	16.0454	−	7.55597i	1.21640	−	0.572817i
$175$	4.16032	−	7.20589i	0.314491	−	0.544714i
$176$	5.89438	+	1.63447i	0.444306	+	0.123203i
$177$	20.9944	−	10.7970i	1.57803	−	0.811550i
$178$	−3.96936	−	7.46514i	−0.297516	−	0.559536i
$179$	14.3471	+	5.94276i	1.07235	+	0.444182i	0.847820	−	0.530284i	$-0.177915\pi$
$179$	14.3471	+	5.94276i	1.07235	+	0.444182i	0.224531	+	0.974467i	$0.427915\pi$
$180$	7.88723	−	4.18180i	0.587879	−	0.311693i
$181$	−4.31265	−	10.4117i	−0.320557	−	0.773893i	−0.999222	−	0.0394449i	$-0.987441\pi$
$181$	−4.31265	−	10.4117i	−0.320557	−	0.773893i	0.678665	−	0.734448i	$-0.262559\pi$
$182$	2.09185	+	21.7230i	0.155059	+	1.61022i
$183$	4.17950	+	4.60678i	0.308957	+	0.340543i
$184$	10.8311	+	7.86887i	0.798478	+	0.580101i
$185$	−9.54648	+	2.55797i	−0.701871	+	0.188066i
$186$	4.31433	−	19.8143i	0.316342	−	1.45286i
$187$	0.825725	−	1.07611i	0.0603830	−	0.0786926i
$188$	−15.4728	−	1.08174i	−1.12847	−	0.0788937i
$189$	0.230874	−	15.5158i	0.0167936	−	1.12861i
$190$	4.75775	−	4.43674i	0.345164	−	0.321875i
$191$	−8.28293	−	14.3465i	−0.599332	−	1.03807i	−0.992920	−	0.118786i	$-0.962100\pi$
$191$	−8.28293	−	14.3465i	−0.599332	−	1.03807i	0.393588	−	0.919287i	$-0.371234\pi$
$192$	−12.7813	+	5.35137i	−0.922414	+	0.386202i
$193$	−9.24911	+	16.0199i	−0.665765	+	1.15314i	0.313312	+	0.949650i	$0.398561\pi$
$193$	−9.24911	+	16.0199i	−0.665765	+	1.15314i	−0.979077	+	0.203489i	$0.934772\pi$
$194$	−2.51902	−	10.9107i	−0.180855	−	0.783343i
$195$	12.0410	+	5.68767i	0.862272	+	0.407303i
$196$	−1.68188	−	3.44824i	−0.120135	−	0.246303i
$197$	3.15402	+	7.61448i	0.224715	+	0.542509i	0.995519	−	0.0945630i	$-0.0301454\pi$
$197$	3.15402	+	7.61448i	0.224715	+	0.542509i	−0.770804	+	0.637072i	$0.780145\pi$
$198$	−1.67175	−	6.26876i	−0.118806	−	0.445502i
$199$	14.2498	+	14.2498i	1.01014	+	1.01014i	0.999948	+	0.0101931i	$0.00324463\pi$
$199$	14.2498	+	14.2498i	1.01014	+	1.01014i	0.0101931	+	0.999948i	$0.496755\pi$
$200$	3.20551	+	7.19925i	0.226664	+	0.509064i
$201$	22.5529	+	7.23405i	1.59076	+	0.510251i
$202$	−13.0729	+	9.32495i	−0.919805	+	0.656101i
$203$	−21.4376	−	2.82232i	−1.50463	−	0.198088i
$204$	0.0384336	+	3.07242i	0.00269089	+	0.215112i
$205$	−1.77932	−	13.5153i	−0.124273	−	0.943948i
$206$	−18.9169	−	0.660451i	−1.31800	−	0.0460158i
$207$	1.37785	−	14.1328i	0.0957671	−	0.982300i
$208$	−17.8097	−	10.4900i	−1.23488	−	0.727353i
$209$	−2.36391	−	4.09440i	−0.163515	−	0.283216i
$210$	−10.8459	−	0.907659i	−0.748441	−	0.0626344i
$211$	−10.2003	−	13.2933i	−0.702218	−	0.915148i	0.296993	−	0.954880i	$-0.404016\pi$
$211$	−10.2003	−	13.2933i	−0.702218	−	0.915148i	−0.999210	+	0.0397318i	$0.987350\pi$
$212$	4.07893	+	0.829805i	0.280142	+	0.0569912i
$213$	10.2970	+	1.86833i	0.705536	+	0.128016i
$214$	−0.684905	−	7.11246i	−0.0468192	−	0.486198i
$215$	−0.581731	−	0.581731i	−0.0396738	−	0.0396738i
$216$	11.7604	+	8.81433i	0.800196	+	0.599739i
$217$	−17.4819	+	17.4819i	−1.18675	+	1.18675i
$218$	11.8173	+	9.74129i	0.800369	+	0.659764i
$219$	−0.914991	+	5.04279i	−0.0618294	+	0.340760i
$220$	−4.46690	+	0.868346i	−0.301158	+	0.0585439i
$221$	−3.63631	+	2.79023i	−0.244604	+	0.187692i
$222$	−10.5056	−	12.4246i	−0.705092	−	0.833883i
$223$	−7.48891	+	4.32372i	−0.501494	+	0.289538i	−0.729330	−	0.684162i	$-0.760168\pi$
$223$	−7.48891	+	4.32372i	−0.501494	+	0.289538i	0.227836	+	0.973700i	$0.426835\pi$
$224$	16.6368	+	2.93288i	1.11159	+	0.195961i
$225$	4.86202	−	6.79914i	0.324135	−	0.453276i
$226$	14.8721	−	13.8687i	0.989279	−	0.922531i
$227$	27.1010	−	3.56791i	1.79875	−	0.236811i	0.844448	−	0.535638i	$-0.179929\pi$
$227$	27.1010	−	3.56791i	1.79875	−	0.236811i	0.954307	+	0.298828i	$0.0965955\pi$
$228$	9.94518	+	3.97443i	0.658635	+	0.263213i
$229$	1.40661	−	10.6843i	0.0929517	−	0.706038i	−0.879991	−	0.474991i	$-0.842451\pi$
$229$	1.40661	−	10.6843i	0.0929517	−	0.706038i	0.972942	−	0.231047i	$-0.0742152\pi$
$230$	−9.82306	−	1.64374i	−0.647713	−	0.108385i
$231$	−2.41591	+	7.53182i	−0.158955	+	0.495557i
$232$	14.0966	−	14.8554i	0.925489	−	0.975305i
$233$	−9.86729	+	9.86729i	−0.646428	+	0.646428i	−0.952128	−	0.305700i	$-0.901110\pi$
$233$	−9.86729	+	9.86729i	−0.646428	+	0.646428i	0.305700	+	0.952128i	$0.401110\pi$
$234$	−0.0259816	+	21.9233i	−0.00169847	+	1.43317i
$235$	10.6606	−	4.41576i	0.695419	−	0.288052i
$236$	18.0628	−	20.4169i	1.17579	−	1.32903i
$237$	5.23046	−	11.0730i	0.339755	−	0.719272i
$238$	1.98511	−	3.17689i	0.128675	−	0.205927i
$239$	6.46306	+	3.73145i	0.418060	+	0.241367i	0.694247	−	0.719737i	$-0.255737\pi$
$239$	6.46306	+	3.73145i	0.418060	+	0.241367i	−0.276187	+	0.961104i	$0.589071\pi$
$240$	6.73327	−	7.80540i	0.434631	−	0.503836i
$241$	−23.9772	+	13.8432i	−1.54450	+	0.891720i	−0.545959	+	0.837812i	$0.683835\pi$
$241$	−23.9772	+	13.8432i	−1.54450	+	0.891720i	−0.998546	+	0.0539084i	$0.982832\pi$
$242$	0.427403	−	12.2418i	0.0274745	−	0.786934i
$243$	1.74326	−	15.4907i	0.111830	−	0.993727i
$244$	6.42786	+	3.20469i	0.411502	+	0.205160i
$245$	2.26435	+	1.73750i	0.144664	+	0.111005i
$246$	18.8819	−	12.1295i	1.20387	−	0.773352i
$247$	4.13487	+	15.4315i	0.263095	+	0.981886i
$248$	−3.66354	−	23.1273i	−0.232635	−	1.46859i
$249$	−3.01782	+	2.73791i	−0.191246	+	0.173508i
$250$	−12.6420	−	10.4211i	−0.799553	−	0.659091i
$251$	1.16235	−	0.481460i	0.0733667	−	0.0303895i	−0.345698	−	0.938346i	$-0.612358\pi$
$251$	1.16235	−	0.481460i	0.0733667	−	0.0303895i	0.419065	+	0.907956i	$0.362358\pi$
$252$	−6.25528	−	16.7908i	−0.394045	−	1.05772i
$253$	−2.76991	+	6.68716i	−0.174143	+	0.420418i
$254$	−1.82351	+	5.96458i	−0.114417	+	0.374251i
$255$	−1.04543	−	2.03280i	−0.0654672	−	0.127299i
$256$	−11.5088	+	11.1152i	−0.719298	+	0.694701i
$257$	−8.14612	−	4.70317i	−0.508141	−	0.293375i	0.223928	−	0.974606i	$-0.428112\pi$
$257$	−8.14612	−	4.70317i	−0.508141	−	0.293375i	−0.732069	+	0.681230i	$0.761445\pi$
$258$	0.458425	−	1.27446i	0.0285403	−	0.0793443i
$259$	2.58923	+	19.6672i	0.160887	+	1.22206i
$260$	15.3394	+	1.07240i	0.951307	+	0.0665077i
$261$	−21.1589	−	4.91151i	−1.30970	−	0.304015i
$262$	−0.691341	−	1.84903i	−0.0427112	−	0.114234i
$263$	−14.4109	−	3.86139i	−0.888614	−	0.238103i	−0.214494	−	0.976725i	$-0.568810\pi$
$263$	−14.4109	−	3.86139i	−0.888614	−	0.238103i	−0.674120	+	0.738622i	$0.735477\pi$
$264$	−4.42634	−	6.04404i	−0.272422	−	0.371985i
$265$	−2.99111	+	0.801466i	−0.183742	+	0.0492337i
$266$	−7.58246	−	10.6300i	−0.464910	−	0.651770i
$267$	−1.84868	+	10.1886i	−0.113137	+	0.623535i
$268$	27.2976	−	1.67000i	1.66747	−	0.102012i
$269$	−5.89740	+	14.2376i	−0.359571	+	0.868081i	0.635789	+	0.771863i	$0.280675\pi$
$269$	−5.89740	+	14.2376i	−0.359571	+	0.868081i	−0.995360	+	0.0962185i	$0.969325\pi$
$270$	−10.7556	−	1.96473i	−0.654567	−	0.119570i
$271$	19.6337			1.19266			0.596332	−	0.802738i	$-0.296624\pi$
$271$	19.6337			1.19266			0.596332	+	0.802738i	$0.296624\pi$
$272$	1.32920	+	3.28961i	0.0805948	+	0.199462i
$273$	14.4727	−	22.4709i	0.875928	−	1.36000i
$274$	−11.0960	−	6.93344i	−0.670335	−	0.418865i
$275$	−3.38024	+	2.59375i	−0.203836	+	0.156409i
$276$	−4.44151	−	15.7835i	−0.267348	−	0.950057i
$277$	5.59267	−	7.28851i	0.336031	−	0.437924i	−0.594523	−	0.804079i	$-0.702659\pi$
$277$	5.59267	−	7.28851i	0.336031	−	0.437924i	0.930554	+	0.366154i	$0.119326\pi$
$278$	8.43789	−	18.5156i	0.506071	−	1.11049i
$279$	−19.1830	+	15.7748i	−1.14845	+	0.944415i
$280$	−12.0500	+	3.56966i	−0.720124	+	0.213328i
$281$	5.97185	−	22.2872i	0.356250	−	1.32954i	−0.522653	−	0.852545i	$-0.675058\pi$
$281$	5.97185	−	22.2872i	0.356250	−	1.32954i	0.878904	−	0.476999i	$-0.158276\pi$
$282$	14.0541	+	12.7809i	0.836907	+	0.761093i
$283$	15.3691	+	2.02338i	0.913596	+	0.120277i	0.572645	−	0.819804i	$-0.305917\pi$
$283$	15.3691	+	2.02338i	0.913596	+	0.120277i	0.340952	+	0.940081i	$0.389251\pi$
$284$	11.8620	−	2.30592i	0.703879	−	0.136831i
$285$	−7.94055	+	0.655041i	−0.470357	+	0.0388013i
$286$	3.26718	−	10.6868i	0.193193	−	0.631922i
$287$	−27.3609			−1.61506
$288$	16.3481	+	4.55408i	0.963321	+	0.268352i
$289$	−16.2132			−0.953719
$290$	−4.45425	+	14.5696i	−0.261562	+	0.855555i
$291$	−5.85751	+	12.4005i	−0.343373	+	0.726932i
$292$	1.12929	+	5.80925i	0.0660869	+	0.339960i
$293$	10.8989	+	1.43487i	0.636721	+	0.0838259i	0.441974	−	0.897028i	$-0.354278\pi$
$293$	10.8989	+	1.43487i	0.636721	+	0.0838259i	0.194747	+	0.980854i	$0.437612\pi$
$294$	−0.999683	+	4.59122i	−0.0583027	+	0.267765i
$295$	−5.24881	+	19.5888i	−0.305598	+	1.14051i
$296$	−16.5113	−	8.96443i	−0.959701	−	0.521047i
$297$	−3.14967	+	7.29505i	−0.182762	+	0.423302i
$298$	5.48746	−	12.0414i	0.317880	−	0.697538i
$299$	14.8895	−	19.4043i	0.861080	−	1.12218i
$300$	2.38125	−	9.35342i	0.137482	−	0.540020i
$301$	−1.31002	+	1.00521i	−0.0755083	+	0.0579396i
$302$	−0.0494262	−	0.0308844i	−0.00284416	−	0.00177720i
$303$	19.6436	+	0.955289i	1.12849	+	0.0548799i
$304$	12.3663	+	0.107551i	0.709256	+	0.00616847i
$305$	−5.34329			−0.305956
$306$	2.29444	−	2.98285i	0.131165	−	0.170518i
$307$	−8.89741	+	21.4803i	−0.507802	+	1.22594i	0.437344	+	0.899294i	$0.355919\pi$
$307$	−8.89741	+	21.4803i	−0.507802	+	1.22594i	−0.945146	+	0.326649i	$0.894081\pi$
$308$	0.557719	+	9.11640i	0.0317790	+	0.519455i
$309$	17.6847	+	14.9893i	1.00605	+	0.852711i
$310$	10.1158	+	14.1817i	0.574541	+	0.805465i
$311$	12.6179	−	3.38097i	0.715498	−	0.191717i	0.117336	−	0.993092i	$-0.462565\pi$
$311$	12.6179	−	3.38097i	0.715498	−	0.191717i	0.598162	+	0.801375i	$0.295898\pi$
$312$	9.16152	+	23.5989i	0.518669	+	1.33602i
$313$	22.2146	+	5.95237i	1.25564	+	0.336448i	0.824513	−	0.565843i	$-0.191449\pi$
$313$	22.2146	+	5.95237i	1.25564	+	0.336448i	0.431128	+	0.902291i	$0.358116\pi$
$314$	10.9628	+	29.3206i	0.618665	+	1.65466i
$315$	9.73805	+	9.10262i	0.548677	+	0.512874i
$316$	0.986197	−	14.1063i	0.0554779	−	0.793541i
$317$	1.86579	+	14.1721i	0.104793	+	0.795984i	0.960452	+	0.278444i	$0.0898187\pi$
$317$	1.86579	+	14.1721i	0.104793	+	0.795984i	−0.855659	+	0.517540i	$0.826848\pi$
$318$	−3.29163	−	3.89288i	−0.184586	−	0.218302i
$319$	9.58877	+	5.53608i	0.536868	+	0.309961i
$320$	3.97280	−	11.2204i	0.222086	−	0.627242i
$321$	−4.73859	+	7.35731i	−0.264482	+	0.410645i
$322$	−5.84443	+	19.1168i	−0.325697	+	1.06534i
$323$	1.04944	−	2.53358i	0.0583927	−	0.140972i
$324$	−4.61752	−	17.3977i	−0.256529	−	0.966537i
$325$	13.3015	−	5.50967i	0.737836	−	0.305622i
$326$	12.0061	+	9.89689i	0.664955	+	0.548138i
$327$	−3.96882	−	18.3320i	−0.219476	−	1.01376i
$328$	15.2314	−	20.9652i	0.841014	−	1.15761i
$329$	−5.99426	−	22.3709i	−0.330474	−	1.23335i
$330$	4.95319	+	2.55475i	0.272664	+	0.140634i
$331$	−8.50835	−	6.52869i	−0.467661	−	0.358849i	0.347889	−	0.937536i	$-0.386899\pi$
$331$	−8.50835	−	6.52869i	−0.467661	−	0.358849i	−0.815550	+	0.578687i	$0.803565\pi$
$332$	−2.09934	+	4.21077i	−0.115216	+	0.231096i
$333$	0.671711	+	19.9162i	0.0368095	+	1.09140i
$334$	0.176174	−	5.04605i	0.00963983	−	0.276108i
$335$	−17.6199	+	10.1729i	−0.962678	+	0.555802i
$336$	−13.7684	−	15.4437i	−0.751126	−	0.842526i
$337$	−0.938629	−	0.541918i	−0.0511304	−	0.0295201i	0.474217	−	0.880408i	$-0.342731\pi$
$337$	−0.938629	−	0.541918i	−0.0511304	−	0.0295201i	−0.525347	+	0.850888i	$0.676065\pi$
$338$	−10.2682	+	16.4329i	−0.558517	+	0.893829i
$339$	−24.8211	+	2.04757i	−1.34810	+	0.111209i
$340$	−1.97689	−	1.74895i	−0.107212	−	0.0948502i
$341$	11.6961	−	4.84469i	0.633380	−	0.262355i
$342$	−6.54500	−	11.3674i	−0.353913	−	0.614676i
$343$	−10.7309	+	10.7309i	−0.579415	+	0.579415i
$344$	−0.0409737	−	1.56339i	−0.00220915	−	0.0842923i
$345$	8.19616	+	9.03408i	0.441266	+	0.486379i
$346$	30.9492	+	5.17888i	1.66384	+	0.278418i
$347$	−0.748916	+	5.68859i	−0.0402039	+	0.305379i	0.959515	+	0.281659i	$0.0908846\pi$
$347$	−0.748916	+	5.68859i	−0.0402039	+	0.305379i	−0.999719	+	0.0237207i	$0.992449\pi$
$348$	−24.8243	+	3.58462i	−1.33072	+	0.192156i
$349$	−22.2069	+	2.92360i	−1.18871	+	0.156497i	−0.698826	−	0.715291i	$-0.746294\pi$
$349$	−22.2069	+	2.92360i	−1.18871	+	0.156497i	−0.489883	+	0.871788i	$0.662961\pi$
$350$	−8.60590	+	8.02525i	−0.460005	+	0.428968i
$351$	16.6606	−	21.0563i	0.889279	−	1.12390i
$352$	−7.29590	−	4.64762i	−0.388873	−	0.247719i
$353$	8.87706	−	5.12517i	0.472478	−	0.272785i	−0.244798	−	0.969574i	$-0.578722\pi$
$353$	8.87706	−	5.12517i	0.472478	−	0.272785i	0.717277	+	0.696789i	$0.245388\pi$
$354$	−32.8574	+	5.92161i	−1.74635	+	0.314730i
$355$	−7.13206	+	5.47262i	−0.378531	+	0.290457i
$356$	2.28166	+	11.7372i	0.120928	+	0.622071i
$357$	−4.31906	+	1.54779i	−0.228589	+	0.0819179i
$358$	−16.9462	−	13.9691i	−0.895634	−	0.738292i
$359$	−8.16132	+	8.16132i	−0.430738	+	0.430738i	−0.888879	−	0.458141i	$-0.848515\pi$
$359$	−8.16132	+	8.16132i	−0.430738	+	0.430738i	0.458141	+	0.888879i	$0.348515\pi$
$360$	−12.3959	+	2.39447i	−0.653321	+	0.126199i
$361$	6.67611	+	6.67611i	0.351374	+	0.351374i
$362$	1.52766	+	15.8641i	0.0802920	+	0.833799i
$363$	−9.70013	+	11.4444i	−0.509125	+	0.600676i
$364$	6.15267	−	30.2436i	0.322488	−	1.58520i
$365$	−2.68014	−	3.49283i	−0.140285	−	0.182823i
$366$	−3.74769	−	7.95839i	−0.195895	−	0.415992i
$367$	−11.4007	−	19.7466i	−0.595110	−	1.03076i	−0.993531	−	0.113559i	$-0.963775\pi$
$367$	−11.4007	−	19.7466i	−0.595110	−	1.03076i	0.398421	−	0.917203i	$-0.369558\pi$
$368$	−11.3947	−	15.1203i	−0.593989	−	0.788201i
$369$	−27.3563	−	2.66704i	−1.42411	−	0.138841i
$370$	13.9685	+	0.487687i	0.726188	+	0.0253536i
$371$	0.811261	+	6.16214i	0.0421186	+	0.319922i
$372$	−14.0273	+	25.0135i	−0.727284	+	1.29689i
$373$	−12.4567	−	1.63995i	−0.644982	−	0.0849135i	−0.199063	−	0.979987i	$-0.563790\pi$
$373$	−12.4567	−	1.63995i	−0.644982	−	0.0849135i	−0.445919	+	0.895073i	$0.647123\pi$
$374$	−1.56166	+	1.11394i	−0.0807516	+	0.0576005i
$375$	4.24580	+	19.6114i	0.219252	+	1.01273i
$376$	20.4786	+	7.86046i	1.05610	+	0.405372i
$377$	−26.4559	−	26.4559i	−1.36255	−	1.36255i
$378$	−6.72749	+	20.8885i	−0.346025	+	1.07439i
$379$	−9.55960	−	23.0789i	−0.491044	−	1.18548i	−0.954190	−	0.299203i	$-0.903279\pi$
$379$	−9.55960	−	23.0789i	−0.491044	−	1.18548i	0.463146	−	0.886282i	$-0.346721\pi$
$380$	−8.26893	+	4.03318i	−0.424187	+	0.206898i
$381$	6.27903	−	4.35038i	0.321685	−	0.222877i
$382$	5.27025	+	22.8272i	0.269649	+	1.16794i
$383$	9.83238	−	17.0302i	0.502411	−	0.870202i	−0.497585	−	0.867415i	$-0.665780\pi$
$383$	9.83238	−	17.0302i	0.502411	−	0.870202i	0.999996	−	0.00278656i	$-0.000886989\pi$
$384$	19.4984	−	1.95267i	0.995023	−	0.0996466i
$385$	−3.39736	−	5.88439i	−0.173145	−	0.299896i
$386$	19.1324	−	17.8415i	0.973813	−	0.908109i
$387$	−1.40778	+	0.877348i	−0.0715617	+	0.0445981i
$388$	−1.10443	+	15.7974i	−0.0560687	+	0.801992i
$389$	12.8425	−	16.7366i	0.651138	−	0.848580i	−0.344795	−	0.938678i	$-0.612051\pi$
$389$	12.8425	−	16.7366i	0.651138	−	0.848580i	0.995933	+	0.0900982i	$0.0287181\pi$
$390$	−13.9328	−	12.6707i	−0.705516	−	0.641604i
$391$	−4.05536	+	1.08663i	−0.205089	+	0.0549533i
$392$	0.848886	+	5.35888i	0.0428752	+	0.270664i
$393$	−0.738446	+	2.30218i	−0.0372497	+	0.116129i
$394$	−1.11724	−	11.6021i	−0.0562857	−	0.584504i
$395$	4.02576	+	9.71904i	0.202558	+	0.489018i
$396$	−0.331008	+	9.16922i	−0.0166338	+	0.460771i
$397$	31.3765	+	12.9966i	1.57474	+	0.652279i	0.987570	−	0.157183i	$-0.0502411\pi$
$397$	31.3765	+	12.9966i	1.57474	+	0.652279i	0.587172	+	0.809462i	$0.300241\pi$
$398$	−13.3799	−	25.1635i	−0.670676	−	1.26133i
$399$	−0.776780	+	15.9729i	−0.0388877	+	0.799646i
$400$	−1.35855	−	11.0618i	−0.0679276	−	0.553090i
$401$	18.8692	−	32.6825i	0.942284	−	1.63208i	0.181185	−	0.983449i	$-0.442007\pi$
$401$	18.8692	−	32.6825i	0.942284	−	1.63208i	0.761099	−	0.648636i	$-0.224660\pi$
$402$	−27.5099	−	19.1083i	−1.37207	−	0.953037i
$403$	−42.4131	+	5.58379i	−2.11275	+	0.278149i
$404$	21.5356	−	7.20607i	1.07144	−	0.358515i
$405$	8.84912	+	10.0503i	0.439716	+	0.499404i
$406$	27.8258	+	12.6807i	1.38097	+	0.629333i
$407$	2.62902	−	9.81162i	0.130315	−	0.486344i
$408$	1.21836	−	4.17110i	0.0603179	−	0.206500i
$409$	−7.18937	−	26.8311i	−0.355491	−	1.32671i	−0.879865	−	0.475224i	$-0.842367\pi$
$409$	−7.18937	−	26.8311i	−0.355491	−	1.32671i	0.524374	−	0.851488i	$-0.324300\pi$
$410$	−3.18172	+	19.0141i	−0.157134	+	0.939037i
$411$	5.40602	+	15.0853i	0.266659	+	0.744103i
$412$	25.3105	+	8.71469i	1.24696	+	0.429342i
$413$	37.6057	+	15.5768i	1.85046	+	0.766485i
$414$	−7.70688	+	18.5439i	−0.378772	+	0.911381i
$415$		−	3.50029i		−	0.171823i
$416$	19.7490	+	21.5507i	0.968276	+	1.05661i
$417$	−22.1617	+	11.3973i	−1.08526	+	0.558129i
$418$	1.50410	+	6.51476i	0.0735680	+	0.318647i
$419$	−14.6384	−	19.0771i	−0.715131	−	0.931977i	0.284512	−	0.958672i	$-0.408168\pi$
$419$	−14.6384	−	19.0771i	−0.715131	−	0.931977i	−0.999644	+	0.0266950i	$0.991502\pi$
$420$	14.2930	+	5.71196i	0.697427	+	0.278715i
$421$	12.8724	+	9.87736i	0.627364	+	0.481393i	0.872838	−	0.488010i	$-0.162277\pi$
$421$	12.8724	+	9.87736i	0.627364	+	0.481393i	−0.245474	+	0.969403i	$0.578944\pi$
$422$	8.29879	+	22.1956i	0.403979	+	1.08047i
$423$	−3.81262	−	22.9514i	−0.185376	−	1.11594i
$424$	−5.17334	−	2.80874i	−0.251240	−	0.136405i
$425$	−2.38718	−	0.639642i	−0.115795	−	0.0310272i
$426$	−13.1533	−	6.78422i	−0.637281	−	0.328696i
$427$	−1.39985	+	10.6329i	−0.0677433	+	0.514561i
$428$	−2.01448	+	9.90223i	−0.0973735	+	0.478642i
$429$	−11.2502	+	7.79459i	−0.543164	+	0.376326i
$430$	0.546220	+	1.02727i	0.0263411	+	0.0495395i
$431$		−	8.55498i		−	0.412079i	−0.978544	−	0.206039i	$-0.933942\pi$
$431$		−	8.55498i		−	0.412079i	0.978544	−	0.206039i	$-0.0660575\pi$
$432$	−12.2606	−	16.7832i	−0.589890	−	0.807484i
$433$			17.4339i			0.837818i	0.908028	+	0.418909i	$0.137587\pi$
$433$			17.4339i			0.837818i	−0.908028	+	0.418909i	$0.862413\pi$
$434$	30.8710	−	16.4147i	1.48186	−	0.787931i
$435$	15.3377	−	10.6266i	0.735386	−	0.509506i
$436$	−11.9543	−	18.0604i	−0.572507	−	0.864936i
$437$	−1.91010	+	14.5086i	−0.0913724	+	0.694042i
$438$	3.32248	−	6.44167i	0.158754	−	0.307795i
$439$	27.9664	+	7.49358i	1.33476	+	0.357649i	0.854489	−	0.519469i	$-0.173870\pi$
$439$	27.9664	+	7.49358i	1.33476	+	0.357649i	0.480275	+	0.877118i	$0.340537\pi$
$440$	6.40016	+	0.672540i	0.305116	+	0.0320621i
$441$	4.44493	−	3.65522i	0.211663	−	0.174058i
$442$	6.07149	−	2.27009i	0.288791	−	0.107977i
$443$	−3.69196	−	2.83294i	−0.175410	−	0.134597i	0.517325	−	0.855789i	$-0.326928\pi$
$443$	−3.69196	−	2.83294i	−0.175410	−	0.134597i	−0.692735	+	0.721192i	$0.743595\pi$
$444$	9.07091	+	21.1470i	0.430486	+	1.00359i
$445$	−5.41506	−	7.05704i	−0.256698	−	0.334536i
$446$	11.9159	−	2.75109i	0.564233	−	0.130268i
$447$	−14.4125	+	7.41208i	−0.681690	+	0.350579i
$448$	−21.2873	−	10.8452i	−1.00573	−	0.512389i
$449$			5.58227i			0.263444i	0.991287	+	0.131722i	$0.0420506\pi$
$449$			5.58227i			0.263444i	−0.991287	+	0.131722i	$0.957949\pi$
$450$	−9.38672	+	7.18503i	−0.442494	+	0.338705i
$451$	12.9440	+	5.36159i	0.609511	+	0.252468i
$452$	−25.8476	+	12.6072i	−1.21577	+	0.592993i
$453$	0.0240806	+	0.0671961i	0.00113141	+	0.00315715i
$454$	−38.1272	−	6.38001i	−1.78940	−	0.299429i
$455$	5.94255	+	22.1779i	0.278591	+	1.03972i
$456$	−11.8068	−	9.48709i	−0.552903	−	0.444274i
$457$	6.77487	−	25.2842i	0.316915	−	1.18274i	−0.605278	−	0.796014i	$-0.706938\pi$
$457$	6.77487	−	25.2842i	0.316915	−	1.18274i	0.922193	−	0.386729i	$-0.126395\pi$
$458$	−6.31993	+	13.8681i	−0.295311	+	0.648013i
$459$	−4.46920	+	1.12653i	−0.208604	+	0.0525817i
$460$	12.6053	+	6.28453i	0.587725	+	0.293018i
$461$	−2.77700	+	0.365599i	−0.129338	+	0.0170277i	−0.194917	−	0.980820i	$-0.562444\pi$
$461$	−2.77700	+	0.365599i	−0.129338	+	0.0170277i	0.0655793	+	0.997847i	$0.479110\pi$
$462$	6.38147	−	9.18730i	0.296893	−	0.427432i
$463$	15.0241	−	26.0225i	0.698229	−	1.20937i	−0.270850	−	0.962621i	$-0.587305\pi$
$463$	15.0241	−	26.0225i	0.698229	−	1.20937i	0.969080	−	0.246747i	$-0.0793618\pi$
$464$	−25.2068	+	14.2623i	−1.17020	+	0.662111i
$465$	1.03631	−	21.3096i	0.0480578	−	0.988211i
$466$	17.4245	−	9.26496i	0.807176	−	0.429191i
$467$	35.0030	+	14.4987i	1.61975	+	0.670921i	0.994028	−	0.109127i	$-0.0348056\pi$
$467$	35.0030	+	14.4987i	1.61975	+	0.670921i	0.625719	+	0.780048i	$0.284806\pi$
$468$	9.09967	−	29.6388i	0.420632	−	1.37005i
$469$	15.6274	+	37.7279i	0.721606	+	1.74211i
$470$	−16.2434	+	1.56418i	−0.749251	+	0.0721503i
$471$	11.7097	−	36.5062i	0.539556	−	1.68212i
$472$	−32.8703	+	20.1439i	−1.51298	+	0.927200i
$473$	0.816731	−	0.218842i	0.0375533	−	0.0100624i
$474$	−11.6521	+	12.8128i	−0.535199	+	0.588512i
$475$	−5.24396	+	6.83407i	−0.240610	+	0.313568i
$476$	−3.99824	+	3.47572i	−0.183259	+	0.159309i
$477$	0.210461	+	6.24017i	0.00963635	+	0.285718i
$478$	−7.19795	−	7.71875i	−0.329227	−	0.353047i
$479$	−8.48254	−	14.6922i	−0.387577	−	0.671304i	0.604546	−	0.796570i	$-0.293355\pi$
$479$	−8.48254	−	14.6922i	−0.387577	−	0.671304i	−0.992123	+	0.125267i	$0.960021\pi$
$480$	−12.3335	+	7.77221i	−0.562944	+	0.354751i
$481$	−17.1622	+	29.7258i	−0.782528	+	1.35538i
$482$	38.1510	−	8.80814i	1.73773	−	0.401200i
$483$	20.1246	−	13.9432i	0.915702	−	0.634437i
$484$	−5.63961	+	16.3794i	−0.256346	+	0.744518i
$485$	−4.50838	−	10.8842i	−0.204715	−	0.494226i
$486$	−8.76249	+	20.2292i	−0.397475	+	0.917613i
$487$	−6.91170	−	6.91170i	−0.313199	−	0.313199i	0.532949	−	0.846148i	$-0.321084\pi$
$487$	−6.91170	−	6.91170i	−0.313199	−	0.313199i	−0.846148	+	0.532949i	$0.821084\pi$
$488$	−7.36815	−	6.99180i	−0.333541	−	0.316504i
$489$	−4.03221	−	18.6248i	−0.182343	−	0.842242i
$490$	−2.34396	−	3.28606i	−0.105890	−	0.148449i
$491$	−13.3453	−	1.75695i	−0.602267	−	0.0792900i	−0.176774	−	0.984252i	$-0.556566\pi$
$491$	−13.3453	−	1.75695i	−0.602267	−	0.0792900i	−0.425493	+	0.904962i	$0.639899\pi$
$492$	−30.5515	+	8.59724i	−1.37737	+	0.387593i
$493$	0.838281	+	6.36738i	0.0377543	+	0.286772i
$494$	0.788329	−	22.5796i	0.0354686	−	1.01590i
$495$	−2.82319	−	6.21456i	−0.126893	−	0.279324i
$496$	−4.60771	+	32.7927i	−0.206892	+	1.47243i
$497$	9.02178	+	15.6262i	0.404682	+	0.700930i
$498$	5.21340	−	2.45505i	0.233618	−	0.110013i
$499$	−4.88416	−	6.36517i	−0.218645	−	0.284944i	0.671133	−	0.741337i	$-0.265808\pi$
$499$	−4.88416	−	6.36517i	−0.218645	−	0.284944i	−0.889778	+	0.456393i	$0.849141\pi$
$500$	12.7886	+	19.3208i	0.571923	+	0.864054i
$501$	−3.99837	+	4.71736i	−0.178634	+	0.210756i
$502$	−1.77105	+	0.170546i	−0.0790459	+	0.00761185i
$503$	−4.82687	−	4.82687i	−0.215219	−	0.215219i	0.591261	−	0.806480i	$-0.298630\pi$
$503$	−4.82687	−	4.82687i	−0.215219	−	0.215219i	−0.806480	+	0.591261i	$0.798630\pi$
$504$	1.51737	+	25.2945i	0.0675891	+	1.12671i
$505$	−11.9460	+	11.9460i	−0.531592	+	0.531592i
$506$	6.51100	−	7.89860i	0.289449	−	0.351136i
$507$	22.3409	−	8.00615i	0.992192	−	0.355566i
$508$	4.93230	−	7.31267i	0.218835	−	0.324447i
$509$	−4.83468	+	3.70978i	−0.214293	+	0.164433i	−0.710331	−	0.703868i	$-0.751455\pi$
$509$	−4.83468	+	3.70978i	−0.214293	+	0.164433i	0.496037	+	0.868301i	$0.334788\pi$
$510$	0.573366	+	3.18145i	0.0253891	+	0.140877i
$511$	−7.65272	+	4.41830i	−0.338536	+	0.195454i
$512$	20.1605	−	10.2740i	0.890976	−	0.454050i
$513$	−2.33363	+	15.8945i	−0.103032	+	0.701759i
$514$	9.07240	+	9.72881i	0.400166	+	0.429119i
$515$	−19.7439	+	2.59934i	−0.870022	+	0.114541i
$516$	−1.14693	+	1.53406i	−0.0504907	+	0.0675333i
$517$	−1.54796	+	11.7580i	−0.0680794	+	0.517114i
$518$	4.62997	−	27.6689i	0.203429	−	1.21570i
$519$	−25.8233	−	28.4634i	−1.13352	−	1.24940i
$520$	−20.3019	−	7.79265i	−0.890297	−	0.341730i
$521$	−15.0823	+	15.0823i	−0.660769	+	0.660769i	−0.955561	−	0.294792i	$-0.904750\pi$
$521$	−15.0823	+	15.0823i	−0.660769	+	0.660769i	0.294792	+	0.955561i	$0.404750\pi$
$522$	26.5850	+	15.3909i	1.16360	+	0.673642i
$523$	−10.9752	+	4.54608i	−0.479912	+	0.198786i	−0.609507	−	0.792781i	$-0.708632\pi$
$523$	−10.9752	+	4.54608i	−0.479912	+	0.198786i	0.129594	+	0.991567i	$0.458632\pi$
$524$	0.170473	+	2.78652i	0.00744713	+	0.121730i
$525$	14.3630	−	1.18485i	0.626852	−	0.0517111i
$526$	17.8931	+	11.1806i	0.780175	+	0.487499i
$527$	6.35941	+	3.67161i	0.277020	+	0.159938i
$528$	3.48728	+	10.0042i	0.151764	+	0.435378i
$529$	−0.516211	+	0.298035i	−0.0224440	+	0.0129580i
$530$	4.37662	+	0.152802i	0.190108	+	0.00663732i
$531$	36.0810	+	19.2398i	1.56578	+	0.834938i
$532$	5.85952	+	17.5114i	0.254042	+	0.759215i
$533$	−37.5601	−	28.8209i	−1.62691	−	1.24837i
$534$	6.71286	−	13.0150i	0.290494	−	0.563213i
$535$	−1.94568	−	7.26138i	−0.0841192	−	0.313937i
$536$	−37.6084	−	9.02810i	−1.62444	−	0.389954i
$537$	5.69133	+	26.2883i	0.245599	+	1.13442i
$538$	13.8625	−	16.8169i	0.597657	−	0.725026i
$539$	−2.71013	+	1.12257i	−0.116734	+	0.0483527i
$540$	13.7338	+	7.10423i	0.591009	+	0.305717i
$541$	−6.79072	+	16.3942i	−0.291956	+	0.704844i	−0.999999	−	0.00132530i	$-0.999578\pi$
$541$	−6.79072	+	16.3942i	−0.291956	+	0.704844i	0.708043	+	0.706169i	$0.249578\pi$
$542$	−26.5531	−	8.11788i	−1.14055	−	0.348693i
$543$	10.5693	−	16.4102i	0.453570	−	0.704231i
$544$	−0.437502	−	4.99852i	−0.0187577	−	0.214310i
$545$	13.9538	+	8.05622i	0.597715	+	0.345091i
$546$	−28.8642	+	24.4062i	−1.23527	+	1.04449i
$547$	−2.42354	−	18.4086i	−0.103623	−	0.787094i	−0.961802	−	0.273744i	$-0.911738\pi$
$547$	−2.42354	−	18.4086i	−0.103623	−	0.787094i	0.858180	−	0.513350i	$-0.171596\pi$
$548$	12.1398	+	13.9648i	0.518584	+	0.596545i
$549$	−2.43606	+	10.4946i	−0.103969	+	0.447900i
$550$	5.64394	−	2.11023i	0.240658	−	0.0899805i
$551$	21.6226	+	5.79376i	0.921154	+	0.246822i
$552$	−0.519154	+	23.1824i	−0.0220967	+	0.986710i
$553$	20.3951	−	5.46485i	0.867288	−	0.232389i
$554$	−10.5772	+	7.54476i	−0.449382	+	0.320546i
$555$	−13.0586	−	11.0683i	−0.554308	−	0.469824i
$556$	−19.0672	+	21.5522i	−0.808628	+	0.914016i
$557$	8.26441	−	19.9521i	0.350174	−	0.845396i	−0.646424	−	0.762979i	$-0.723736\pi$
$557$	8.26441	−	19.9521i	0.350174	−	0.845396i	0.996598	−	0.0824169i	$-0.0262639\pi$
$558$	32.4658	−	13.4027i	1.37439	−	0.567383i
$559$	−2.85720			−0.120847
$560$	17.7726	+	0.154570i	0.751029	+	0.00653177i
$561$	2.34658	+	0.114117i	0.0990728	+	0.00481802i
$562$	−17.2915	+	27.6726i	−0.729397	+	1.16730i
$563$	−5.37439	+	4.12391i	−0.226504	+	0.173802i	−0.715779	−	0.698327i	$-0.753928\pi$
$563$	−5.37439	+	4.12391i	−0.226504	+	0.173802i	0.489275	+	0.872129i	$0.337261\pi$
$564$	−13.7225	−	23.0961i	−0.577824	−	0.972520i
$565$	13.0241	−	16.9733i	0.547927	−	0.714073i
$566$	−19.9489	−	9.09104i	−0.838514	−	0.382125i
$567$	22.3179	−	14.9763i	0.937265	−	0.628946i
$568$	−16.9958	−	1.78595i	−0.713129	−	0.0749368i
$569$	−9.74852	+	36.3820i	−0.408679	+	1.52521i	0.388488	+	0.921454i	$0.372997\pi$
$569$	−9.74852	+	36.3820i	−0.408679	+	1.52521i	−0.797167	+	0.603758i	$0.793669\pi$
$570$	11.0098	+	2.39725i	0.461150	+	0.100410i
$571$	6.97213	+	0.917899i	0.291775	+	0.0384129i	0.274993	−	0.961446i	$-0.411325\pi$
$571$	6.97213	+	0.917899i	0.291775	+	0.0384129i	0.0167820	+	0.999859i	$0.494658\pi$
$572$	−8.83723	+	13.1021i	−0.369503	+	0.547828i
$573$	12.2550	−	25.9442i	0.511959	−	1.08383i
$574$	37.0035	+	11.3128i	1.54450	+	0.472187i
$575$	13.1880			0.549977
$576$	−20.2266	−	12.9184i	−0.842774	−	0.538267i
$577$	33.4211			1.39134			0.695669	−	0.718362i	$-0.255108\pi$
$577$	33.4211			1.39134			0.695669	+	0.718362i	$0.255108\pi$
$578$	21.9271	+	6.70362i	0.912048	+	0.278834i
$579$	−31.9314	+	2.63412i	−1.32702	+	0.109470i
$580$	12.0480	−	17.8625i	0.500268	−	0.741702i
$581$	−6.96541	−	0.917013i	−0.288974	−	0.0380441i
$582$	13.0490	−	14.3489i	0.540899	−	0.594780i
$583$	0.823726	−	3.07419i	0.0341152	−	0.127320i
$584$	0.874645	−	8.32348i	0.0361931	−	0.344428i
$585$	3.77973	+	22.7534i	0.156272	+	0.940738i
$586$	−14.1467	−	6.44688i	−0.584393	−	0.266318i
$587$	18.4887	−	24.0949i	0.763109	−	0.994503i	−0.236628	−	0.971600i	$-0.576042\pi$
$587$	18.4887	−	24.0949i	0.763109	−	0.994503i	0.999738	−	0.0229032i	$-0.00729097\pi$
$588$	3.25031	−	5.79593i	0.134040	−	0.239020i
$589$	20.3060	−	15.5814i	0.836695	−	0.642018i
$590$	15.1979	−	24.3222i	0.625689	−	1.00133i
$591$	−7.72973	+	12.0015i	−0.317959	+	0.493675i
$592$	18.6238	+	18.9506i	0.765433	+	0.778863i
$593$	−1.19902			−0.0492377			−0.0246188	−	0.999697i	$-0.507837\pi$
$593$	−1.19902			−0.0492377			−0.0246188	+	0.999697i	$0.507837\pi$
$594$	7.27594	−	8.56371i	0.298535	−	0.351373i
$595$	1.50824	−	3.64121i	0.0618318	−	0.149275i
$596$	−12.4001	+	14.0161i	−0.507926	+	0.574124i
$597$	−6.23155	+	34.3440i	−0.255040	+	1.40560i
$598$	−28.1599	+	20.0866i	−1.15154	+	0.821400i
$599$	−24.2295	+	6.49227i	−0.989990	+	0.265267i	−0.717246	−	0.696820i	$-0.754598\pi$
$599$	−24.2295	+	6.49227i	−0.989990	+	0.265267i	−0.272744	+	0.962087i	$0.587931\pi$
$600$	−7.08778	+	11.6652i	−0.289357	+	0.476230i
$601$	20.3796	+	5.46069i	0.831300	+	0.222746i	0.649281	−	0.760549i	$-0.275070\pi$
$601$	20.3796	+	5.46069i	0.831300	+	0.222746i	0.182019	+	0.983295i	$0.441737\pi$
$602$	2.18732	−	0.817825i	0.0891486	−	0.0333321i
$603$	11.9472	+	39.2448i	0.486527	+	1.59817i
$604$	0.0540754	+	0.0622048i	0.00220030	+	0.00253108i
$605$	−1.68213	−	12.7771i	−0.0683883	−	0.519461i
$606$	−26.1714	−	9.41390i	−1.06314	−	0.382414i
$607$	12.0169	+	6.93794i	0.487749	+	0.281602i	0.723640	−	0.690177i	$-0.242467\pi$
$607$	12.0169	+	6.93794i	0.487749	+	0.281602i	−0.235891	+	0.971780i	$0.575801\pi$
$608$	−16.6800	−	5.25850i	−0.676463	−	0.213260i
$609$	−17.1282	−	33.3052i	−0.694070	−	1.34960i
$610$	7.22638	+	2.20927i	0.292588	+	0.0894507i
$611$	15.3359	−	37.0241i	0.620423	−	1.49783i
$612$	−4.33636	+	3.08540i	−0.175287	+	0.124720i
$613$	22.9844	−	9.52046i	0.928332	−	0.384528i	0.133287	−	0.991078i	$-0.457447\pi$
$613$	22.9844	−	9.52046i	0.928332	−	0.384528i	0.795046	+	0.606550i	$0.207447\pi$
$614$	20.9144	−	25.3716i	0.844037	−	1.02391i
$615$	17.4869	−	15.8649i	0.705138	−	0.639736i
$616$	3.01505	−	12.5598i	0.121480	−	0.506050i
$617$	−9.77626	−	36.4855i	−0.393577	−	1.46885i	−0.824190	−	0.566314i	$-0.808369\pi$
$617$	−9.77626	−	36.4855i	−0.393577	−	1.46885i	0.430612	−	0.902537i	$-0.358298\pi$
$618$	−17.7196	−	27.5839i	−0.712786	−	1.10959i
$619$	21.7069	+	16.6563i	0.872476	+	0.669474i	0.944708	−	0.327914i	$-0.106346\pi$
$619$	21.7069	+	16.6563i	0.872476	+	0.669474i	−0.0722321	+	0.997388i	$0.523012\pi$
$620$	−7.81726	−	23.3622i	−0.313949	−	0.938247i
$621$	21.4804	−	11.9792i	0.861977	−	0.480707i
$622$	−18.4627	−	0.644595i	−0.740287	−	0.0258459i
$623$	−15.4618	+	8.92689i	−0.619465	+	0.357648i
$624$	−2.63290	−	35.7037i	−0.105400	−	1.42929i
$625$	−2.86291	−	1.65290i	−0.114516	−	0.0661160i
$626$	−27.5824	−	17.2351i	−1.10241	−	0.688853i
$627$	3.49751	−	7.40433i	0.139677	−	0.295700i
$628$	−2.70323	−	44.1866i	−0.107870	−	1.76324i
$629$	5.44342	−	2.25474i	0.217044	−	0.0899024i
$630$	−9.40634	−	16.3369i	−0.374757	−	0.650879i
$631$	11.8848	−	11.8848i	0.473126	−	0.473126i	−0.429799	−	0.902925i	$-0.641416\pi$
$631$	11.8848	−	11.8848i	0.473126	−	0.473126i	0.902925	+	0.429799i	$0.141416\pi$
$632$	−7.16623	+	18.6699i	−0.285057	+	0.742649i
$633$	8.86423	−	27.6351i	0.352322	−	1.09840i
$634$	3.33634	−	19.9381i	0.132503	−	0.791843i
$635$	−0.856508	+	6.50583i	−0.0339895	+	0.258176i
$636$	2.84210	+	6.62580i	0.112697	+	0.262730i
$637$	9.82764	−	1.29383i	0.389385	−	0.0512635i
$638$	−10.6791	−	11.4517i	−0.422789	−	0.453379i
$639$	7.49707	+	16.5030i	0.296580	+	0.652847i
$640$	−10.0122	+	13.5322i	−0.395766	+	0.534905i
$641$	1.53181	−	0.884392i	0.0605029	−	0.0349314i	−0.469443	−	0.882963i	$-0.655545\pi$
$641$	1.53181	−	0.884392i	0.0605029	−	0.0349314i	0.529946	+	0.848031i	$0.322212\pi$
$642$	9.45057	−	7.99095i	0.372984	−	0.315378i
$643$	−36.7205	+	28.1767i	−1.44812	+	1.11118i	−0.475240	+	0.879856i	$0.657639\pi$
$643$	−36.7205	+	28.1767i	−1.44812	+	1.11118i	−0.972877	+	0.231323i	$0.925695\pi$
$644$	15.8083	−	23.4375i	0.622933	−	0.923567i
$645$	0.254396	−	1.40205i	0.0100168	−	0.0552058i
$646$	−2.46684	+	2.99257i	−0.0970566	+	0.117741i
$647$	26.9970	−	26.9970i	1.06136	−	1.06136i	0.0633732	−	0.997990i	$-0.479814\pi$
$647$	26.9970	−	26.9970i	1.06136	−	1.06136i	0.997990	−	0.0633732i	$-0.0201858\pi$
$648$	−0.948504	+	25.4382i	−0.0372607	+	0.999306i
$649$	−14.7383	−	14.7383i	−0.578529	−	0.578529i
$650$	−20.2673	+	1.95168i	−0.794951	+	0.0765510i
$651$	−42.1337	−	7.64496i	−1.65135	−	0.299629i
$652$	−12.1452	−	18.3489i	−0.475645	−	0.718597i
$653$	20.7715	+	27.0700i	0.812853	+	1.05933i	0.997074	+	0.0764461i	$0.0243573\pi$
$653$	20.7715	+	27.0700i	0.812853	+	1.05933i	−0.184220	+	0.982885i	$0.558976\pi$
$654$	−2.21213	+	26.4335i	−0.0865011	+	1.03363i
$655$	−1.03844	−	1.79863i	−0.0405751	−	0.0702781i
$656$	−29.2677	+	22.0562i	−1.14271	+	0.861149i
$657$	−8.08210	+	3.67159i	−0.315313	+	0.143242i
$658$	−1.14283	+	32.7333i	−0.0445521	+	1.27608i
$659$	4.69832	+	35.6872i	0.183020	+	1.39018i	0.798486	+	0.602014i	$0.205635\pi$
$659$	4.69832	+	35.6872i	0.183020	+	1.39018i	−0.615465	+	0.788164i	$0.711032\pi$
$660$	−5.64250	−	5.50307i	−0.219634	−	0.214207i
$661$	−16.4099	−	2.16041i	−0.638272	−	0.0840301i	−0.195557	−	0.980692i	$-0.562651\pi$
$661$	−16.4099	−	2.16041i	−0.638272	−	0.0840301i	−0.442715	+	0.896662i	$0.645985\pi$
$662$	8.80749	+	12.3475i	0.342313	+	0.479897i
$663$	−7.55943	−	2.42476i	−0.293584	−	0.0941699i
$664$	4.58020	−	4.82674i	0.177746	−	0.187314i
$665$	−9.71377	−	9.71377i	−0.376684	−	0.376684i
$666$	7.32625	−	27.2129i	0.283886	−	1.05448i
$667$	−13.1150	−	31.6625i	−0.507817	−	1.22598i
$668$	−2.32463	+	6.75155i	−0.0899427	+	0.261225i
$669$	−13.5430	−	6.39715i	−0.523601	−	0.247328i
$670$	28.0357	−	6.47277i	1.08311	−	0.250065i
$671$	2.74585	−	4.75595i	0.106002	−	0.183601i
$672$	12.2352	+	26.5792i	0.471982	+	1.02532i
$673$	−19.6237	−	33.9893i	−0.756440	−	1.31019i	−0.944655	−	0.328064i	$-0.893604\pi$
$673$	−19.6237	−	33.9893i	−0.756440	−	1.31019i	0.188216	−	0.982128i	$-0.439730\pi$
$674$	1.04536	+	1.12099i	0.0402657	+	0.0431790i
$675$	14.4761	+	0.215402i	0.557184	+	0.00829084i
$676$	20.6814	−	17.9786i	0.795438	−	0.691484i
$677$	−0.974083	+	1.26945i	−0.0374370	+	0.0487889i	−0.811697	−	0.584079i	$-0.801456\pi$
$677$	−0.974083	+	1.26945i	−0.0374370	+	0.0487889i	0.774260	+	0.632868i	$0.218122\pi$
$678$	34.4152	+	7.49351i	1.32171	+	0.287786i
$679$	−22.8401	+	6.12000i	−0.876524	+	0.234864i
$680$	1.95046	+	3.18270i	0.0747966	+	0.122051i
$681$	31.8125	+	35.0648i	1.21906	+	1.34369i
$682$	−17.8212	+	1.71612i	−0.682409	+	0.0657136i
$683$	−9.02449	−	21.7870i	−0.345312	−	0.833658i	−0.997160	−	0.0753081i	$-0.976006\pi$
$683$	−9.02449	−	21.7870i	−0.345312	−	0.833658i	0.651848	−	0.758350i	$-0.273994\pi$
$684$	4.15158	+	18.0796i	0.158740	+	0.691291i
$685$	−12.7178	−	5.26788i	−0.485921	−	0.201275i
$686$	18.9496	−	10.0759i	0.723499	−	0.384698i
$687$	16.5990	−	8.53652i	0.633290	−	0.325688i
$688$	−0.590994	+	2.13130i	−0.0225314	+	0.0812552i
$689$	−5.37727	+	9.31371i	−0.204858	+	0.354824i
$690$	−7.34938	−	15.6067i	−0.279786	−	0.594138i
$691$	−2.07908	+	0.273716i	−0.0790919	+	0.0104126i	−0.169968	−	0.985450i	$-0.554367\pi$
$691$	−2.07908	+	0.273716i	−0.0790919	+	0.0104126i	0.0908764	+	0.995862i	$0.471033\pi$
$692$	−39.7151	−	19.8005i	−1.50974	−	0.752701i
$693$	−13.1063	+	3.98991i	−0.497867	+	0.151564i
$694$	3.36489	−	7.38372i	0.127729	−	0.280282i
$695$	5.54067	−	20.6780i	0.210169	−	0.784363i
$696$	35.0551	+	5.41609i	1.32876	+	0.205296i
$697$	2.10334	+	7.84978i	0.0796698	+	0.297332i
$698$	31.2420	+	5.22787i	1.18253	+	0.197878i
$699$	−23.7815	−	4.31505i	−0.899500	−	0.163210i
$700$	14.9570	−	7.29528i	0.565321	−	0.275736i
$701$	−3.96149	−	1.64090i	−0.149623	−	0.0619761i	0.306615	−	0.951834i	$-0.400804\pi$
$701$	−3.96149	−	1.64090i	−0.149623	−	0.0619761i	−0.456238	+	0.889858i	$0.650804\pi$
$702$	−31.2383	+	21.5885i	−1.17901	+	0.814804i
$703$		−	20.5366i		−	0.774553i
$704$	7.94550	+	9.30215i	0.299457	+	0.350588i
$705$	16.8026	+	10.8219i	0.632821	+	0.407578i
$706$	−14.1246	+	3.26104i	−0.531587	+	0.122731i
$707$	20.6424	+	26.9017i	0.776338	+	1.01174i
$708$	46.8855	+	5.57690i	1.76206	+	0.209593i
$709$	16.9639	+	13.0169i	0.637093	+	0.488859i	0.876081	−	0.482164i	$-0.160149\pi$
$709$	16.9639	+	13.0169i	0.637093	+	0.488859i	−0.238988	+	0.971023i	$0.576816\pi$
$710$	11.9083	−	4.45243i	0.446911	−	0.167097i
$711$	20.9243	−	3.47589i	0.784724	−	0.130356i
$712$	1.76716	−	16.8171i	0.0662273	−	0.630246i
$713$	−37.8502	−	10.1419i	−1.41750	−	0.379818i
$714$	6.48115	−	0.307487i	0.242551	−	0.0115074i
$715$	1.53461	−	11.6565i	0.0573912	−	0.435929i
$716$	17.1426	+	25.8989i	0.640650	+	0.967886i
$717$	1.06271	+	12.8824i	0.0396875	+	0.481100i
$718$	14.4120	−	7.66312i	0.537850	−	0.285985i
$719$			39.9888i			1.49133i	0.666322	+	0.745665i	$0.267868\pi$
$719$			39.9888i			1.49133i	−0.666322	+	0.745665i	$0.732132\pi$
$720$	17.7545	+	1.88695i	0.661672	+	0.0703225i
$721$			39.9705i			1.48858i
$722$	−6.26858	−	11.7893i	−0.233292	−	0.438751i
$723$	−43.3603	−	20.4817i	−1.61259	−	0.761722i
$724$	4.49323	−	22.0866i	0.166990	−	0.820842i
$725$	2.63319	−	20.0011i	0.0977943	−	0.742821i
$726$	17.8506	−	11.4670i	0.662496	−	0.425581i
$727$	9.74231	+	2.61045i	0.361322	+	0.0968160i	0.434913	−	0.900472i	$-0.356779\pi$
$727$	9.74231	+	2.61045i	0.361322	+	0.0968160i	−0.0735906	+	0.997289i	$0.523446\pi$
$728$	−20.8257	+	38.3583i	−0.771853	+	1.42165i
$729$	23.7740	−	12.7983i	0.880519	−	0.474012i
$730$	2.18052	+	5.83193i	0.0807046	+	0.215849i
$731$	0.389100	+	0.298567i	0.0143914	+	0.0110429i
$732$	1.77794	+	12.3127i	0.0657146	+	0.455089i
$733$	7.39247	+	9.63405i	0.273047	+	0.355842i	0.909669	−	0.415334i	$-0.136335\pi$
$733$	7.39247	+	9.63405i	0.273047	+	0.355842i	−0.636622	+	0.771176i	$0.719669\pi$
$734$	7.25400	+	31.4195i	0.267750	+	1.15971i
$735$	−0.240126	+	4.93770i	−0.00885718	+	0.182130i
$736$	9.15869	+	25.1604i	0.337594	+	0.927424i
$737$		−	20.9108i		−	0.770259i
$738$	35.8945	+	14.9179i	1.32130	+	0.549134i
$739$	−26.5558	−	10.9998i	−0.976871	−	0.404633i	−0.163605	−	0.986526i	$-0.552312\pi$
$739$	−26.5558	−	10.9998i	−0.976871	−	0.404633i	−0.813266	+	0.581893i	$0.802312\pi$
$740$	−18.6897	−	6.43506i	−0.687046	−	0.236557i
$741$	−17.8915	+	21.1088i	−0.657262	+	0.775452i
$742$	1.45067	−	8.66924i	0.0532556	−	0.318258i
$743$	2.31816	+	8.65148i	0.0850449	+	0.317392i	0.995323	−	0.0966060i	$-0.0307987\pi$
$743$	2.31816	+	8.65148i	0.0850449	+	0.317392i	−0.910278	+	0.413998i	$0.864132\pi$
$744$	29.3131	−	28.0290i	1.07467	−	1.02759i
$745$	3.60329	−	13.4477i	0.132014	−	0.492684i
$746$	16.1686	+	7.36832i	0.591975	+	0.269773i
$747$	−6.87485	−	1.59582i	−0.251537	−	0.0583880i
$748$	2.57260	−	0.860823i	0.0940636	−	0.0314748i
$749$	−14.9595	+	1.96946i	−0.546609	+	0.0719625i
$750$	2.36652	−	28.2783i	0.0864129	−	1.03258i
$751$	−20.8879	+	36.1789i	−0.762210	+	1.32019i	0.179500	+	0.983758i	$0.442552\pi$
$751$	−20.8879	+	36.1789i	−0.762210	+	1.32019i	−0.941709	+	0.336428i	$0.890781\pi$
$752$	−24.4456	−	19.0978i	−0.891440	−	0.696427i
$753$	1.83202	+	1.17994i	0.0667626	+	0.0429994i
$754$	24.8410	+	46.7182i	0.904654	+	1.70138i
$755$	−0.0566502	−	0.0234653i	−0.00206171	−	0.000853989i
$756$	17.7351	−	25.4684i	0.645019	−	0.926278i
$757$	2.81730	+	6.80156i	0.102396	+	0.247207i	0.966772	−	0.255640i	$-0.0822861\pi$
$757$	2.81730	+	6.80156i	0.102396	+	0.247207i	−0.864376	+	0.502847i	$0.832286\pi$
$758$	3.38627	+	35.1650i	0.122995	+	1.27725i
$759$	−12.2529	+	2.65272i	−0.444754	+	0.0962878i
$760$	12.8507	−	2.03564i	0.466143	−	0.0738404i
$761$	19.4967	−	5.22413i	0.706756	−	0.189375i	0.112501	−	0.993652i	$-0.464114\pi$
$761$	19.4967	−	5.22413i	0.706756	−	0.189375i	0.594255	+	0.804277i	$0.297447\pi$
$762$	−10.2906	+	3.28738i	−0.372790	+	0.119089i
$763$	19.6871	−	25.6568i	0.712722	−	0.928838i
$764$	2.31066	−	33.0511i	0.0835968	−	1.19575i
$765$	1.86292	−	3.49358i	0.0673539	−	0.126311i
$766$	−20.3389	+	18.9666i	−0.734876	+	0.685293i
$767$	35.2158	+	60.9956i	1.27157	+	2.20242i
$768$	−27.1774	−	5.42109i	−0.980680	−	0.195617i
$769$	14.2959	−	24.7613i	0.515525	−	0.892915i	−0.484313	−	0.874895i	$-0.660930\pi$
$769$	14.2959	−	24.7613i	0.515525	−	0.892915i	0.999838	−	0.0180202i	$-0.00573630\pi$
$770$	2.16166	+	9.36288i	0.0779010	+	0.337415i
$771$	−1.33945	−	16.2371i	−0.0482391	−	0.584764i
$772$	−33.2519	+	16.2187i	−1.19676	+	0.583722i
$773$	5.06485	+	12.2276i	0.182170	+	0.439797i	0.988413	−	0.151787i	$-0.0485027\pi$
$773$	5.06485	+	12.2276i	0.182170	+	0.439797i	−0.806243	+	0.591584i	$0.798503\pi$
$774$	2.26667	−	0.604475i	0.0814738	−	0.0217274i
$775$	−16.3104	−	16.3104i	−0.585885	−	0.585885i
$776$	8.02534	−	20.9081i	0.288093	−	0.750558i
$777$	−25.4465	+	23.0863i	−0.912889	+	0.828217i
$778$	−24.2884	+	17.3251i	−0.870783	+	0.621133i
$779$	28.0837	+	3.69729i	1.00620	+	0.132469i
$780$	13.6042	+	22.8968i	0.487107	+	0.819838i
$781$	−1.20599	−	9.16040i	−0.0431537	−	0.327785i
$782$	5.93385	+	0.207170i	0.212194	+	0.00740840i
$783$	−13.8788	−	34.9692i	−0.495989	−	1.24970i
$784$	1.06766	−	7.59846i	0.0381308	−	0.271374i
$785$	16.4668	+	28.5213i	0.587724	+	1.01797i
$786$	1.95056	−	2.80819i	0.0695743	−	0.100165i
$787$	−5.29897	−	6.90575i	−0.188888	−	0.246163i	0.689304	−	0.724472i	$-0.257917\pi$
$787$	−5.29897	−	6.90575i	−0.188888	−	0.246163i	−0.878192	+	0.478309i	$0.841250\pi$
$788$	−3.28608	+	16.1528i	−0.117062	+	0.575421i
$789$	−8.71758	−	24.3261i	−0.310354	−	0.866031i
$790$	−1.42603	−	14.8088i	−0.0507360	−	0.526872i
$791$	−30.3640	−	30.3640i	−1.07962	−	1.07962i
$792$	4.23883	−	12.2638i	0.150620	−	0.435775i
$793$	−13.1219	+	13.1219i	−0.465973	+	0.465973i
$794$	−37.0606	−	30.5500i	−1.31523	−	1.08418i
$795$	−4.09154	−	3.46794i	−0.145112	−	0.122995i
$796$	7.69105	+	39.5639i	0.272602	+	1.40230i
$797$	−15.4076	+	11.8227i	−0.545766	+	0.418781i	−0.844500	−	0.535555i	$-0.820102\pi$
$797$	−15.4076	+	11.8227i	−0.545766	+	0.418781i	0.298734	+	0.954336i	$0.403436\pi$
$798$	7.65479	−	21.2809i	0.270977	−	0.753337i
$799$	−5.95736	+	3.43948i	−0.210756	+	0.121680i
$800$	−2.73634	+	15.5219i	−0.0967442	+	0.548783i
$801$	−16.3294	+	7.41822i	−0.576970	+	0.262110i
$802$	−39.0323	+	36.3987i	−1.37828	+	1.28528i
$803$	4.48619	−	0.590618i	0.158314	−	0.0208424i
$804$	29.3044	+	37.2170i	1.03349	+	1.31254i
$805$	−2.74515	+	20.8515i	−0.0967540	+	0.734919i
$806$	59.6692	+	9.98474i	2.10176	+	0.351697i
$807$	−26.0877	+	5.64790i	−0.918329	+	0.198816i
$808$	−32.1047	+	0.841408i	−1.12944	+	0.0296006i
$809$	−33.3949	+	33.3949i	−1.17410	+	1.17410i	−0.192880	+	0.981222i	$0.561783\pi$
$809$	−33.3949	+	33.3949i	−1.17410	+	1.17410i	−0.981222	+	0.192880i	$0.938217\pi$
$810$	−7.81228	−	17.2511i	−0.274496	−	0.606141i
$811$	−16.1929	+	6.70732i	−0.568610	+	0.235526i	−0.648418	−	0.761284i	$-0.724569\pi$
$811$	−16.1929	+	6.70732i	−0.568610	+	0.235526i	0.0798085	+	0.996810i	$0.474569\pi$
$812$	−32.3892	−	28.6547i	−1.13664	−	1.00558i
$813$	19.3670	+	27.9530i	0.679230	+	0.980354i
$814$	−7.61231	+	12.1824i	−0.266811	+	0.426995i
$815$	14.1767	+	8.18490i	0.496587	+	0.286705i
$816$	−3.37235	+	5.13734i	−0.118056	+	0.179843i
$817$	1.48046	−	0.854746i	0.0517949	−	0.0299038i
$818$	−1.37068	+	39.2595i	−0.0479247	+	1.37268i
$819$	46.2684	−	1.56049i	1.61675	−	0.0545278i
$820$	12.1647	−	24.3995i	0.424809	−	0.852067i
$821$	9.11642	+	6.99528i	0.318165	+	0.244137i	0.755480	−	0.655172i	$-0.227404\pi$
$821$	9.11642	+	6.99528i	0.318165	+	0.244137i	−0.437315	+	0.899309i	$0.644070\pi$
$822$	−1.07397	−	22.6369i	−0.0374589	−	0.789552i
$823$	−7.41498	−	27.6731i	−0.258470	−	0.964623i	−0.966127	−	0.258067i	$-0.916914\pi$
$823$	−7.41498	−	27.6731i	−0.258470	−	0.964623i	0.707657	−	0.706556i	$-0.249752\pi$
$824$	−30.6273	−	22.2510i	−1.06695	−	0.775150i
$825$	−7.02710	−	2.25401i	−0.244652	−	0.0784746i
$826$	−44.4184	−	36.6151i	−1.54551	−	1.27400i
$827$	−43.8958	+	18.1822i	−1.52641	+	0.632258i	−0.978863	−	0.204519i	$-0.934437\pi$
$827$	−43.8958	+	18.1822i	−1.52641	+	0.632258i	−0.547544	+	0.836777i	$0.684437\pi$
$828$	18.0902	−	21.8926i	0.628678	−	0.760820i
$829$	14.6830	−	35.4478i	0.509960	−	1.23115i	−0.433946	−	0.900939i	$-0.642879\pi$
$829$	14.6830	−	35.4478i	0.509960	−	1.23115i	0.943906	−	0.330214i	$-0.107121\pi$
$830$	−1.44725	+	4.73387i	−0.0502348	+	0.164315i
$831$	15.8935	+	0.772919i	0.551340	+	0.0268123i
$832$	−17.7986	−	37.3112i	−0.617054	−	1.29353i
$833$	−1.47355	−	0.850756i	−0.0510556	−	0.0294769i
$834$	34.6844	−	6.25087i	1.20102	−	0.216450i
$835$	−0.693370	−	5.26667i	−0.0239951	−	0.182261i
$836$	0.659451	−	9.43260i	0.0228076	−	0.326233i
$837$	−41.3813	−	11.7507i	−1.43035	−	0.406164i
$838$	11.9095	+	31.8528i	0.411408	+	1.10034i
$839$	21.3247	+	5.71392i	0.736209	+	0.197267i	0.607392	−	0.794402i	$-0.292216\pi$
$839$	21.3247	+	5.71392i	0.736209	+	0.197267i	0.128816	+	0.991668i	$0.458882\pi$
$840$	−16.9685	−	13.6347i	−0.585468	−	0.470440i
$841$	−22.6266	+	6.06277i	−0.780226	+	0.209061i
$842$	−13.3250	−	18.6807i	−0.459210	−	0.643779i
$843$	37.6216	−	13.4822i	1.29576	−	0.464352i
$844$	−2.04634	−	33.4491i	−0.0704378	−	1.15137i
$845$	−7.80156	+	18.8346i	−0.268382	+	0.647931i
$846$	−4.33336	+	32.6164i	−0.148984	+	1.12137i
$847$	−25.8664			−0.888780
$848$	5.83522	+	5.93761i	0.200382	+	0.203898i
$849$	12.2795	+	23.8772i	0.421433	+	0.819463i
$850$	2.96400	+	1.85208i	0.101664	+	0.0635259i
$851$	−24.9437	+	19.1400i	−0.855060	+	0.656111i
$852$	14.9838	+	14.6136i	0.513337	+	0.500653i
$853$	14.3333	−	18.6795i	0.490763	−	0.639575i	−0.480666	−	0.876904i	$-0.659605\pi$
$853$	14.3333	−	18.6795i	0.490763	−	0.639575i	0.971429	+	0.237329i	$0.0762718\pi$
$854$	6.28952	−	13.8014i	0.215223	−	0.472273i
$855$	−8.76527	−	10.6590i	−0.299766	−	0.364530i
$856$	6.81866	−	12.5591i	0.233057	−	0.429261i
$857$	0.225217	−	0.840522i	0.00769327	−	0.0287117i	−0.961973	−	0.273146i	$-0.911936\pi$
$857$	0.225217	−	0.840522i	0.00769327	−	0.0287117i	0.969666	+	0.244435i	$0.0786024\pi$
$858$	18.4378	−	5.89001i	0.629456	−	0.201082i
$859$	19.2278	+	2.53139i	0.656045	+	0.0863700i	0.451198	−	0.892424i	$-0.350997\pi$
$859$	19.2278	+	2.53139i	0.656045	+	0.0863700i	0.204847	+	0.978794i	$0.434330\pi$
$860$	−0.313978	−	1.61515i	−0.0107066	−	0.0550762i
$861$	−26.9892	−	38.9543i	−0.919789	−	1.32756i
$862$	−3.53719	+	11.5699i	−0.120477	+	0.394074i
$863$	−15.9450			−0.542774			−0.271387	−	0.962470i	$-0.587482\pi$
$863$	−15.9450			−0.542774			−0.271387	+	0.962470i	$0.587482\pi$
$864$	9.64226	+	27.7674i	0.328036	+	0.944665i
$865$	33.0139			1.12251
$866$	7.20831	−	23.5780i	0.244948	−	0.801212i
$867$	−15.9930	−	23.0831i	−0.543150	−	0.783945i
$868$	−48.5375	+	9.43549i	−1.64747	+	0.320261i
$869$	−10.7195	−	1.41125i	−0.363634	−	0.0478733i
$870$	−25.1368	+	8.03003i	−0.852216	+	0.272243i
$871$	−18.2883	+	68.2527i	−0.619674	+	2.31265i
$872$	8.69991	+	29.3680i	0.294616	+	0.994525i
$873$	−23.4328	+	3.89259i	−0.793081	+	0.131744i
$874$	8.58209	−	18.8320i	0.290293	−	0.637003i
$875$	−21.0611	+	27.4474i	−0.711995	+	0.927890i
$876$	−7.15680	+	7.33813i	−0.241806	+	0.247932i
$877$	40.7542	−	31.2718i	1.37617	−	1.05597i	0.385067	−	0.922889i	$-0.374178\pi$
$877$	40.7542	−	31.2718i	1.37617	−	1.05597i	0.991105	−	0.133085i	$-0.0424882\pi$
$878$	−34.7241	−	21.6976i	−1.17188	−	0.732260i
$879$	8.70799	+	16.9324i	0.293713	+	0.571116i
$880$	−8.37765	−	3.55581i	−0.282411	−	0.119866i
$881$	31.9946			1.07792			0.538962	−	0.842330i	$-0.318817\pi$
$881$	31.9946			1.07792			0.538962	+	0.842330i	$0.318817\pi$
$882$	−7.52273	+	3.10558i	−0.253303	+	0.104570i
$883$	4.92948	−	11.9008i	0.165890	−	0.400495i	−0.818972	−	0.573834i	$-0.805456\pi$
$883$	4.92948	−	11.9008i	0.165890	−	0.400495i	0.984862	+	0.173339i	$0.0554556\pi$
$884$	−9.14982	+	0.559764i	−0.307742	+	0.0188269i
$885$	−33.0666	+	11.8499i	−1.11152	+	0.398329i
$886$	3.82176	+	5.35783i	0.128395	+	0.180000i
$887$	50.1970	−	13.4503i	1.68545	−	0.451615i	0.716242	−	0.697852i	$-0.245861\pi$
$887$	50.1970	−	13.4503i	1.68545	−	0.451615i	0.969210	+	0.246237i	$0.0791941\pi$
$888$	−3.52413	−	32.3502i	−0.118262	−	1.08560i
$889$	12.7219	+	3.40882i	0.426678	+	0.114328i
$890$	4.40560	+	11.7830i	0.147676	+	0.394969i
$891$	−13.4930	+	2.71169i	−0.452033	+	0.0908449i
$892$	−17.2528	−	1.20617i	−0.577666	−	0.0403857i
$893$	3.12963	+	23.7719i	0.104729	+	0.795495i
$894$	22.5565	−	4.06516i	0.754402	−	0.135959i
$895$	−20.0099	−	11.5527i	−0.668858	−	0.386165i
$896$	24.3053	+	23.4689i	0.811984	+	0.784042i
$897$	42.3136	+	2.05776i	1.41281	+	0.0687064i
$898$	2.30808	−	7.54959i	0.0770216	−	0.251933i
$899$	−22.9388	+	55.3791i	−0.765050	+	1.84699i
$900$	15.6656	−	5.83610i	0.522186	−	0.194537i
$901$	1.70554	−	0.706457i	0.0568197	−	0.0235355i
$902$	−15.2890	−	12.6031i	−0.509067	−	0.419636i
$903$	−2.72337	−	0.873548i	−0.0906281	−	0.0290699i
$904$	40.1696	−	6.36315i	1.33602	−	0.211635i
$905$	4.33978	+	16.1963i	0.144259	+	0.538383i
$906$	−0.00478389	−	0.100834i	−0.000158934	−	0.00334998i
$907$	15.4132	+	11.8270i	0.511787	+	0.392708i	0.832119	−	0.554597i	$-0.187128\pi$
$907$	15.4132	+	11.8270i	0.511787	+	0.392708i	−0.320332	+	0.947305i	$0.603794\pi$
$908$	48.9261	+	24.3928i	1.62367	+	0.809502i
$909$	18.0166	+	28.9093i	0.597574	+	0.958861i
$910$	1.13297	−	32.4509i	0.0375576	−	1.07574i
$911$	−22.5244	+	13.0045i	−0.746266	+	0.430857i	−0.824343	−	0.566090i	$-0.808455\pi$
$911$	−22.5244	+	13.0045i	−0.746266	+	0.430857i	0.0780768	+	0.996947i	$0.475122\pi$
$912$	12.0452	+	17.7123i	0.398855	+	0.586512i
$913$	3.11553	+	1.79875i	0.103109	+	0.0595301i
$914$	−19.6166	+	31.3937i	−0.648861	+	1.03841i
$915$	−5.27070	−	7.60736i	−0.174244	−	0.251492i
$916$	14.2812	−	16.1424i	0.471864	−	0.533361i
$917$	−3.85123	+	1.59523i	−0.127179	+	0.0526792i
$918$	6.51002	+	0.324324i	0.214863	+	0.0107043i
$919$	4.32952	−	4.32952i	0.142818	−	0.142818i	−0.632083	−	0.774901i	$-0.717800\pi$
$919$	4.32952	−	4.32952i	0.142818	−	0.142818i	0.774901	+	0.632083i	$0.217800\pi$
$920$	−14.4492	−	13.7112i	−0.476377	−	0.452045i
$921$	−39.3585	+	8.52099i	−1.29691	+	0.280776i
$922$	3.90684	+	0.653752i	0.128665	+	0.0215302i
$923$	−4.07520	+	30.9542i	−0.134137	+	1.01887i
$924$	−12.4291	+	9.78659i	−0.408887	+	0.321955i
$925$	−18.3492	+	2.41572i	−0.603319	+	0.0794285i
$926$	−31.0784	+	28.9815i	−1.02130	+	0.952390i
$927$	−3.89617	+	39.9637i	−0.127967	+	1.31258i
$928$	39.9872	−	8.86651i	1.31264	−	0.291057i
$929$	3.33393	−	1.92484i	0.109383	−	0.0631521i	−0.444311	−	0.895873i	$-0.646551\pi$
$929$	3.33393	−	1.92484i	0.109383	−	0.0631521i	0.553693	+	0.832721i	$0.313218\pi$
$930$	−10.2123	+	28.3912i	−0.334876	+	0.930983i
$931$	−4.70515	+	3.61039i	−0.154205	+	0.118326i
$932$	−27.3961	+	5.32568i	−0.897388	+	0.174448i
$933$	17.2601	+	14.6294i	0.565070	+	0.478946i
$934$	−41.3441	−	34.0810i	−1.35282	−	1.11516i
$935$	−1.42705	+	1.42705i	−0.0466696	+	0.0466696i
$936$	−24.5612	+	36.3218i	−0.802809	+	1.18721i
$937$	2.37836	+	2.37836i	0.0776976	+	0.0776976i	0.744888	−	0.667190i	$-0.232503\pi$
$937$	2.37836	+	2.37836i	0.0776976	+	0.0776976i	−0.667190	+	0.744888i	$0.732503\pi$
$938$	−5.53564	−	57.4854i	−0.180745	−	1.87696i
$939$	13.4382	+	37.4989i	0.438540	+	1.22373i
$940$	22.6146	+	4.60065i	0.737608	+	0.150057i
$941$	−7.23169	−	9.42452i	−0.235746	−	0.307231i	0.660466	−	0.750856i	$-0.270359\pi$
$941$	−7.23169	−	9.42452i	−0.235746	−	0.307231i	−0.896212	+	0.443625i	$0.853692\pi$
$942$	−30.9306	+	44.5302i	−1.00777	+	1.45087i
$943$	−21.6831	−	37.5563i	−0.706100	−	1.22300i
$944$	52.7833	−	13.6524i	1.71795	−	0.444347i
$945$	−3.35384	+	22.8432i	−0.109101	+	0.743091i
$946$	−1.19505	−	0.0417231i	−0.0388544	−	0.00135654i
$947$	−1.73453	−	13.1751i	−0.0563646	−	0.428132i	−0.996242	−	0.0866184i	$-0.972394\pi$
$947$	−1.73453	−	13.1751i	−0.0563646	−	0.428132i	0.939877	−	0.341513i	$-0.110939\pi$
$948$	21.0562	−	12.5106i	0.683875	−	0.406325i
$949$	−15.1594	−	1.99578i	−0.492096	−	0.0647856i
$950$	9.91771	−	7.07434i	0.321773	−	0.229522i
$951$	−18.3367	+	16.6359i	−0.594608	+	0.539457i
$952$	6.84440	−	3.04751i	0.221828	−	0.0987702i
$953$	13.3322	+	13.3322i	0.431872	+	0.431872i	0.889265	−	0.457393i	$-0.151217\pi$
$953$	13.3322	+	13.3322i	0.431872	+	0.431872i	−0.457393	+	0.889265i	$0.651217\pi$
$954$	2.29547	−	8.52637i	0.0743185	−	0.276051i
$955$	9.43236	+	22.7717i	0.305224	+	0.736876i
$956$	6.54323	+	13.4151i	0.211623	+	0.433876i
$957$	1.57666	+	19.1126i	0.0509662	+	0.617823i
$958$	5.39726	+	23.3773i	0.174377	+	0.755286i
$959$	−13.8146	+	23.9277i	−0.446098	+	0.772665i
$960$	19.8936	−	5.41184i	0.642064	−	0.174666i
$961$	18.7684	+	32.5079i	0.605433	+	1.04864i
$962$	35.5011	−	33.1058i	1.14460	−	1.06737i
$963$	−15.1490	+	0.510927i	−0.488169	+	0.0164644i
$964$	−55.2381	−	3.86180i	−1.77910	−	0.124380i
$965$	16.7550	−	21.8355i	0.539361	−	0.702909i
$966$	−32.9820	+	10.5362i	−1.06118	+	0.338997i
$967$	22.6822	−	6.07767i	0.729409	−	0.195445i	0.125043	−	0.992151i	$-0.460093\pi$
$967$	22.6822	−	6.07767i	0.729409	−	0.195445i	0.604366	+	0.796707i	$0.293426\pi$
$968$	14.3994	−	19.8201i	0.462816	−	0.637041i
$969$	4.64231	−	1.00505i	0.149132	−	0.0322867i
$970$	1.59699	+	16.5841i	0.0512763	+	0.532483i
$971$	6.76556	+	16.3335i	0.217117	+	0.524167i	0.994485	−	0.104879i	$-0.0334456\pi$
$971$	6.76556	+	16.3335i	0.217117	+	0.524167i	−0.777368	+	0.629046i	$0.783446\pi$
$972$	20.2147	−	23.7354i	0.648385	−	0.761312i
$973$	−39.6967	−	16.4429i	−1.27262	−	0.527136i
$974$	6.48978	+	12.2053i	0.207946	+	0.391083i
$975$	20.9651	+	13.5029i	0.671420	+	0.432438i
$976$	7.07398	+	12.5024i	0.226433	+	0.400190i
$977$	−2.93995	+	5.09214i	−0.0940573	+	0.162912i	−0.909215	−	0.416327i	$-0.863317\pi$
$977$	−2.93995	+	5.09214i	−0.0940573	+	0.162912i	0.815157	+	0.579239i	$0.196650\pi$
$978$	−2.24746	+	26.8557i	−0.0718660	+	0.858752i
$979$	9.06405	−	1.19331i	0.289688	−	0.0381382i
$980$	1.81135	+	5.41330i	0.0578616	+	0.172921i
$981$	22.1847	−	23.7334i	0.708304	−	0.757750i
$982$	17.3221	+	7.89398i	0.552771	+	0.251907i
$983$	−1.89555	+	7.07430i	−0.0604588	+	0.225635i	−0.989544	−	0.144230i	$-0.953929\pi$
$983$	−1.89555	+	7.07430i	−0.0604588	+	0.225635i	0.929085	+	0.369865i	$0.120596\pi$
$984$	44.8732	+	1.00490i	1.43050	+	0.0320352i
$985$	−3.17386	−	11.8450i	−0.101128	−	0.377413i
$986$	1.49898	−	8.95798i	0.0477374	−	0.285280i
$987$	25.9371	−	30.6011i	0.825587	−	0.974045i
$988$	−10.4020	+	30.2112i	−0.330933	+	0.961146i
$989$	−2.41796	−	1.00155i	−0.0768865	−	0.0318475i
$990$	1.24864	+	9.57201i	0.0396844	+	0.304218i
$991$		−	5.41075i		−	0.171878i	−0.996300	−	0.0859391i	$-0.972611\pi$
$991$		−	5.41075i		−	0.171878i	0.996300	−	0.0859391i	$-0.0273890\pi$
$992$	19.7902	−	42.4444i	0.628340	−	1.34761i
$993$	0.902279	−	18.5535i	0.0286329	−	0.588778i
$994$	−5.74036	−	24.8634i	−0.182073	−	0.788619i
$995$	−18.2531	−	23.7879i	−0.578663	−	0.754128i
$996$	−8.06579	+	1.16470i	−0.255574	+	0.0369048i
$997$	−35.0868	−	26.9230i	−1.11121	−	0.852661i	−0.121056	−	0.992646i	$-0.538628\pi$
$997$	−35.0868	−	26.9230i	−1.11121	−	0.852661i	−0.990154	+	0.139985i	$0.955295\pi$
$998$	3.97367	+	10.6278i	0.125784	+	0.336418i
$999$	−27.6926	+	20.6020i	−0.876155	+	0.651818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.275.6	yes	368
3.2	odd	2		864.2.bn.a.179.41		368
9.2	odd	6	inner	288.2.bf.a.83.22	yes	368
9.7	even	3		864.2.bn.a.467.25		368
32.27	odd	8	inner	288.2.bf.a.59.22	✓	368
96.59	even	8		864.2.bn.a.827.25		368
288.155	even	24	inner	288.2.bf.a.155.6	yes	368
288.187	odd	24		864.2.bn.a.251.41		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.59.22	✓	368	32.27	odd	8	inner
288.2.bf.a.83.22	yes	368	9.2	odd	6	inner
288.2.bf.a.155.6	yes	368	288.155	even	24	inner
288.2.bf.a.275.6	yes	368	1.1	even	1	trivial
864.2.bn.a.179.41		368	3.2	odd	2
864.2.bn.a.251.41		368	288.187	odd	24
864.2.bn.a.467.25		368	9.7	even	3
864.2.bn.a.827.25		368	96.59	even	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35242 - 0.413466i) q^{2} +(0.986415 + 1.42372i) q^{3} +(1.65809 + 1.11836i) q^{4} +(-1.47515 - 0.194207i) q^{5} +(-0.745388 - 2.33332i) q^{6} +(-0.772924 + 2.88459i) q^{7} +(-1.78004 - 2.19806i) q^{8} +(-1.05397 + 2.80876i) q^{9} +O(q^{10})\)	\(q+(-1.35242 - 0.413466i) q^{2} +(0.986415 + 1.42372i) q^{3} +(1.65809 + 1.11836i) q^{4} +(-1.47515 - 0.194207i) q^{5} +(-0.745388 - 2.33332i) q^{6} +(-0.772924 + 2.88459i) q^{7} +(-1.78004 - 2.19806i) q^{8} +(-1.05397 + 2.80876i) q^{9} +(1.91472 + 0.872572i) q^{10} +(0.930918 - 1.21320i) q^{11} +(0.0433298 + 3.46383i) q^{12} +(-4.09955 + 3.14570i) q^{13} +(2.23800 - 3.58161i) q^{14} +(-1.17861 - 2.29177i) q^{15} +(1.49854 + 3.70869i) q^{16} +0.887001 q^{17} +(2.58674 - 3.36285i) q^{18} +(1.18314 - 2.85635i) q^{19} +(-2.22873 - 1.97176i) q^{20} +(-4.86928 + 1.74497i) q^{21} +(-1.76061 + 1.25585i) q^{22} +(-4.57200 + 1.22506i) q^{23} +(1.37358 - 4.70248i) q^{24} +(-2.69129 - 0.721129i) q^{25} +(6.84496 - 2.55928i) q^{26} +(-5.03855 + 1.27004i) q^{27} +(-4.50759 + 3.91851i) q^{28} +(0.945074 + 7.17855i) q^{29} +(0.646410 + 3.58675i) q^{30} +(7.16956 + 4.13935i) q^{31} +(-0.493237 - 5.63531i) q^{32} +(2.64552 + 0.128655i) q^{33} +(-1.19960 - 0.366745i) q^{34} +(1.70038 - 4.10509i) q^{35} +(-4.88879 + 3.47846i) q^{36} +(6.13689 - 2.54198i) q^{37} +(-2.78111 + 3.37380i) q^{38} +(-8.52246 - 2.73366i) q^{39} +(2.19894 + 3.58816i) q^{40} +(2.37130 + 8.84981i) q^{41} +(7.30681 - 0.346659i) q^{42} +(0.438670 + 0.336603i) q^{43} +(2.90034 - 0.970487i) q^{44} +(2.10024 - 3.93865i) q^{45} +(6.68979 + 0.233563i) q^{46} +(-6.71629 + 3.87765i) q^{47} +(-3.80197 + 5.79181i) q^{48} +(-1.66127 - 0.959138i) q^{49} +(3.34160 + 2.08803i) q^{50} +(0.874950 + 1.26284i) q^{51} +(-10.3155 + 0.631075i) q^{52} +(1.92282 - 0.796456i) q^{53} +(7.33937 + 0.365641i) q^{54} +(-1.60885 + 1.60885i) q^{55} +(7.71634 - 3.43574i) q^{56} +(5.23371 - 1.13308i) q^{57} +(1.68995 - 10.0992i) q^{58} +(1.77908 - 13.5135i) q^{59} +(0.608781 - 5.11807i) q^{60} +(3.56050 - 0.468748i) q^{61} +(-7.98480 - 8.56252i) q^{62} +(-7.28749 - 5.21124i) q^{63} +(-1.66294 + 7.82526i) q^{64} +(6.65835 - 3.84420i) q^{65} +(-3.52467 - 1.26783i) q^{66} +(10.8486 - 8.32441i) q^{67} +(1.47073 + 0.991987i) q^{68} +(-6.25403 - 5.30084i) q^{69} +(-3.99695 + 4.84876i) q^{70} +(4.27235 - 4.27235i) q^{71} +(8.04994 - 2.68300i) q^{72} +(2.09233 + 2.09233i) q^{73} +(-9.35069 + 0.900439i) q^{74} +(-1.62804 - 4.54298i) q^{75} +(5.15618 - 3.41291i) q^{76} +(2.78004 + 3.62302i) q^{77} +(10.3957 + 7.22081i) q^{78} +(-3.53518 - 6.12311i) q^{79} +(-1.49031 - 5.76189i) q^{80} +(-6.77828 - 5.92072i) q^{81} +(0.452097 - 12.9491i) q^{82} +(0.307069 + 2.33242i) q^{83} +(-10.0252 - 2.55229i) q^{84} +(-1.30846 - 0.172261i) q^{85} +(-0.454093 - 0.636605i) q^{86} +(-9.28803 + 8.42655i) q^{87} +(-4.32374 + 0.113318i) q^{88} +(4.22741 + 4.22741i) q^{89} +(-4.46891 + 4.45833i) q^{90} +(-5.90541 - 14.2569i) q^{91} +(-8.95085 - 3.08188i) q^{92} +(1.17888 + 14.2906i) q^{93} +(10.6865 - 2.46727i) q^{94} +(-2.30002 + 3.98376i) q^{95} +(7.53658 - 6.26098i) q^{96} +(3.95899 + 6.85717i) q^{97} +(1.85017 + 1.98404i) q^{98} +(2.42642 + 3.89340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more