LMFDB - Embedded newform 288.2.bf.a.11.30

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			11.30
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.716655 - 1.21918i) q^{2} +(-0.325939 + 1.70111i) q^{3} +(-0.972810 - 1.74747i) q^{4} +(-0.471581 - 3.58202i) q^{5} +(1.84037 + 1.61649i) q^{6} +(-0.240641 - 0.898083i) q^{7} +(-2.82765 - 0.0662985i) q^{8} +(-2.78753 - 1.10892i) q^{9} +O(q^{10})$	\(q+(0.716655 - 1.21918i) q^{2} +(-0.325939 + 1.70111i) q^{3} +(-0.972810 - 1.74747i) q^{4} +(-0.471581 - 3.58202i) q^{5} +(1.84037 + 1.61649i) q^{6} +(-0.240641 - 0.898083i) q^{7} +(-2.82765 - 0.0662985i) q^{8} +(-2.78753 - 1.10892i) q^{9} +(-4.70509 - 1.99213i) q^{10} +(-3.26867 + 2.50814i) q^{11} +(3.28970 - 1.08529i) q^{12} +(3.99957 - 5.21234i) q^{13} +(-1.26738 - 0.350231i) q^{14} +(6.24710 + 0.365310i) q^{15} +(-2.10728 + 3.39991i) q^{16} +0.549959 q^{17} +(-3.34967 + 2.60379i) q^{18} +(5.33432 - 2.20955i) q^{19} +(-5.80070 + 4.30870i) q^{20} +(1.60617 - 0.116635i) q^{21} +(0.715368 + 5.78257i) q^{22} +(-3.35871 - 0.899962i) q^{23} +(1.03442 - 4.78852i) q^{24} +(-7.77883 + 2.08433i) q^{25} +(-3.48848 - 8.61165i) q^{26} +(2.79495 - 4.38044i) q^{27} +(-1.33527 + 1.29418i) q^{28} +(5.25943 + 0.692417i) q^{29} +(4.92240 - 7.35455i) q^{30} +(0.693328 - 0.400293i) q^{31} +(2.63491 + 5.00572i) q^{32} +(-3.20122 - 6.37785i) q^{33} +(0.394131 - 0.670500i) q^{34} +(-3.10347 + 1.28550i) q^{35} +(0.773942 + 5.94988i) q^{36} +(-0.929033 + 2.24288i) q^{37} +(1.12903 - 8.08700i) q^{38} +(7.56312 + 8.50259i) q^{39} +(1.09598 + 10.1600i) q^{40} +(-0.841025 + 3.13875i) q^{41} +(1.00887 - 2.04180i) q^{42} +(4.28519 + 5.58457i) q^{43} +(7.56268 + 3.27195i) q^{44} +(-2.65761 + 10.5079i) q^{45} +(-3.50425 + 3.44991i) q^{46} +(1.79295 + 1.03516i) q^{47} +(-5.09676 - 4.69287i) q^{48} +(5.31353 - 3.06777i) q^{49} +(-3.03356 + 10.9776i) q^{50} +(-0.179253 + 0.935539i) q^{51} +(-12.9992 - 1.91849i) q^{52} +(1.71670 - 4.14448i) q^{53} +(-3.33754 - 6.54682i) q^{54} +(10.5256 + 10.5256i) q^{55} +(0.620906 + 2.55542i) q^{56} +(2.02001 + 9.79443i) q^{57} +(4.61338 - 5.91598i) q^{58} +(2.13608 - 0.281220i) q^{59} +(-5.43888 - 11.2720i) q^{60} +(-1.27923 + 9.71668i) q^{61} +(0.00884700 - 1.13217i) q^{62} +(-0.325106 + 2.77028i) q^{63} +(7.99121 + 0.374938i) q^{64} +(-20.5568 - 11.8685i) q^{65} +(-10.0699 - 0.667851i) q^{66} +(6.45600 - 8.41363i) q^{67} +(-0.535006 - 0.961035i) q^{68} +(2.62567 - 5.42018i) q^{69} +(-0.656860 + 4.70495i) q^{70} +(-10.4157 - 10.4157i) q^{71} +(7.80863 + 3.32043i) q^{72} +(-8.18821 + 8.18821i) q^{73} +(2.06869 + 2.74004i) q^{74} +(-1.01024 - 13.9120i) q^{75} +(-9.05040 - 7.17208i) q^{76} +(3.03909 + 2.33198i) q^{77} +(15.7864 - 3.12739i) q^{78} +(-0.656058 + 1.13633i) q^{79} +(13.1723 + 5.94498i) q^{80} +(6.54061 + 6.18226i) q^{81} +(3.22398 + 3.27476i) q^{82} +(7.51437 + 0.989285i) q^{83} +(-1.76631 - 2.69326i) q^{84} +(-0.259351 - 1.96996i) q^{85} +(9.87961 - 1.22222i) q^{86} +(-2.89213 + 8.72117i) q^{87} +(9.40894 - 6.87543i) q^{88} +(-3.96066 + 3.96066i) q^{89} +(10.9065 + 10.7707i) q^{90} +(-5.64357 - 2.33764i) q^{91} +(1.69473 + 6.74472i) q^{92} +(0.454958 + 1.30990i) q^{93} +(2.54697 - 1.44408i) q^{94} +(-10.4302 - 18.0657i) q^{95} +(-9.37409 + 2.85071i) q^{96} +(6.94041 - 12.0211i) q^{97} +(0.0678017 - 8.67670i) q^{98} +(11.8928 - 3.36682i) 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.716655	−	1.21918i	0.506752	−	0.862092i
$2$	0.716655	−	1.21918i	0.506752	−	0.862092i
$3$	−0.325939	+	1.70111i	−0.188181	+	0.982134i
$3$	−0.325939	+	1.70111i	−0.188181	+	0.982134i
$4$	−0.972810	−	1.74747i	−0.486405	−	0.873733i
$5$	−0.471581	−	3.58202i	−0.210898	−	1.60193i	−0.689761	−	0.724037i	$-0.742284\pi$
$5$	−0.471581	−	3.58202i	−0.210898	−	1.60193i	0.478863	−	0.877889i	$-0.341049\pi$
$6$	1.84037	+	1.61649i	0.751329	+	0.659928i
$7$	−0.240641	−	0.898083i	−0.0909536	−	0.339443i	0.905421	−	0.424514i	$-0.139555\pi$
$7$	−0.240641	−	0.898083i	−0.0909536	−	0.339443i	−0.996375	+	0.0850707i	$0.972888\pi$
$8$	−2.82765	−	0.0662985i	−0.999725	−	0.0234401i
$9$	−2.78753	−	1.10892i	−0.929176	−	0.369638i
$10$	−4.70509	−	1.99213i	−1.48788	−	0.629966i
$11$	−3.26867	+	2.50814i	−0.985541	+	0.756232i	−0.969864	−	0.243645i	$-0.921657\pi$
$11$	−3.26867	+	2.50814i	−0.985541	+	0.756232i	−0.0156761	+	0.999877i	$0.504990\pi$
$12$	3.28970	−	1.08529i	0.949656	−	0.313295i
$13$	3.99957	−	5.21234i	1.10928	−	1.44564i	0.227624	−	0.973749i	$-0.426904\pi$
$13$	3.99957	−	5.21234i	1.10928	−	1.44564i	0.881656	−	0.471893i	$-0.156429\pi$
$14$	−1.26738	−	0.350231i	−0.338722	−	0.0936032i
$15$	6.24710	+	0.365310i	1.61299	+	0.0943227i
$16$	−2.10728	+	3.39991i	−0.526820	+	0.849977i
$17$	0.549959			0.133385			0.0666923	−	0.997774i	$-0.478755\pi$
$17$	0.549959			0.133385			0.0666923	+	0.997774i	$0.478755\pi$
$18$	−3.34967	+	2.60379i	−0.789524	+	0.613720i
$19$	5.33432	−	2.20955i	1.22378	−	0.506905i	0.325169	−	0.945656i	$-0.394579\pi$
$19$	5.33432	−	2.20955i	1.22378	−	0.506905i	0.898609	+	0.438751i	$0.144579\pi$
$20$	−5.80070	+	4.30870i	−1.29708	+	0.963454i
$21$	1.60617	−	0.116635i	0.350495	−	0.0254518i
$22$	0.715368	+	5.78257i	0.152517	+	1.23285i
$23$	−3.35871	−	0.899962i	−0.700338	−	0.187655i	−0.108956	−	0.994047i	$-0.534751\pi$
$23$	−3.35871	−	0.899962i	−0.700338	−	0.187655i	−0.591382	+	0.806391i	$0.701418\pi$
$24$	1.03442	−	4.78852i	0.211151	−	0.977453i
$25$	−7.77883	+	2.08433i	−1.55577	+	0.416866i
$26$	−3.48848	−	8.61165i	−0.684146	−	1.68888i
$27$	2.79495	−	4.38044i	0.537888	−	0.843016i
$28$	−1.33527	+	1.29418i	−0.252343	+	0.244576i
$29$	5.25943	+	0.692417i	0.976652	+	0.128579i	0.601922	−	0.798555i	$-0.294402\pi$
$29$	5.25943	+	0.692417i	0.976652	+	0.128579i	0.374730	+	0.927134i	$0.377735\pi$
$30$	4.92240	−	7.35455i	0.898703	−	1.34275i
$31$	0.693328	−	0.400293i	0.124525	−	0.0718948i	−0.436443	−	0.899732i	$-0.643762\pi$
$31$	0.693328	−	0.400293i	0.124525	−	0.0718948i	0.560969	+	0.827837i	$0.310429\pi$
$32$	2.63491	+	5.00572i	0.465791	+	0.884895i
$33$	−3.20122	−	6.37785i	−0.557261	−	1.11024i
$34$	0.394131	−	0.670500i	0.0675929	−	0.114990i
$35$	−3.10347	+	1.28550i	−0.524582	+	0.217289i
$36$	0.773942	+	5.94988i	0.128990	+	0.991646i
$37$	−0.929033	+	2.24288i	−0.152732	+	0.368728i	−0.981663	−	0.190622i	$-0.938949\pi$
$37$	−0.929033	+	2.24288i	−0.152732	+	0.368728i	0.828931	+	0.559350i	$0.188949\pi$
$38$	1.12903	−	8.08700i	0.183153	−	1.31188i
$39$	7.56312	+	8.50259i	1.21107	+	1.36150i
$40$	1.09598	+	10.1600i	0.173290	+	1.60643i
$41$	−0.841025	+	3.13875i	−0.131346	+	0.490190i	−0.999986	−	0.00525338i	$-0.998328\pi$
$41$	−0.841025	+	3.13875i	−0.131346	+	0.490190i	0.868640	+	0.495444i	$0.164994\pi$
$42$	1.00887	−	2.04180i	0.155672	−	0.315056i
$43$	4.28519	+	5.58457i	0.653485	+	0.851639i	0.996136	−	0.0878242i	$-0.0279914\pi$
$43$	4.28519	+	5.58457i	0.653485	+	0.851639i	−0.342651	+	0.939463i	$0.611325\pi$
$44$	7.56268	+	3.27195i	1.14012	+	0.493265i
$45$	−2.65761	+	10.5079i	−0.396173	+	1.56643i
$46$	−3.50425	+	3.44991i	−0.516674	+	0.508662i
$47$	1.79295	+	1.03516i	0.261528	+	0.150993i	0.625032	−	0.780599i	$-0.285086\pi$
$47$	1.79295	+	1.03516i	0.261528	+	0.150993i	−0.363503	+	0.931593i	$0.618419\pi$
$48$	−5.09676	−	4.69287i	−0.735654	−	0.677358i
$49$	5.31353	−	3.06777i	0.759076	−	0.438253i
$50$	−3.03356	+	10.9776i	−0.429010	+	1.55246i
$51$	−0.179253	+	0.935539i	−0.0251005	+	0.131002i
$52$	−12.9992	−	1.91849i	−1.80266	−	0.266047i
$53$	1.71670	−	4.14448i	0.235807	−	0.569288i	−0.761034	−	0.648712i	$-0.775308\pi$
$53$	1.71670	−	4.14448i	0.235807	−	0.569288i	0.996841	+	0.0794240i	$0.0253081\pi$
$54$	−3.33754	−	6.54682i	−0.454182	−	0.890909i
$55$	10.5256	+	10.5256i	1.41928	+	1.41928i
$56$	0.620906	+	2.55542i	0.0829720	+	0.341482i
$57$	2.02001	+	9.79443i	0.267557	+	1.29730i
$58$	4.61338	−	5.91598i	0.605767	−	0.776806i
$59$	2.13608	−	0.281220i	0.278094	−	0.0366118i	0.00981088	−	0.999952i	$-0.496877\pi$
$59$	2.13608	−	0.281220i	0.278094	−	0.0366118i	0.268283	+	0.963340i	$0.413544\pi$
$60$	−5.43888	−	11.2720i	−0.702156	−	1.45521i
$61$	−1.27923	+	9.71668i	−0.163788	+	1.24409i	0.690130	+	0.723686i	$0.257553\pi$
$61$	−1.27923	+	9.71668i	−0.163788	+	1.24409i	−0.853918	+	0.520408i	$0.825780\pi$
$62$	0.00884700	−	1.13217i	0.00112357	−	0.143785i
$63$	−0.325106	+	2.77028i	−0.0409595	+	0.349022i
$64$	7.99121	+	0.374938i	0.998901	+	0.0468673i
$65$	−20.5568	−	11.8685i	−2.54976	−	1.47210i
$66$	−10.0699	−	0.667851i	−1.23952	−	0.0822068i
$67$	6.45600	−	8.41363i	0.788726	−	1.02789i	−0.210013	−	0.977699i	$-0.567351\pi$
$67$	6.45600	−	8.41363i	0.788726	−	1.02789i	0.998740	−	0.0501898i	$-0.0159826\pi$
$68$	−0.535006	−	0.961035i	−0.0648790	−	0.116543i
$69$	2.62567	−	5.42018i	0.316093	−	0.652513i
$70$	−0.656860	+	4.70495i	−0.0785097	+	0.562349i
$71$	−10.4157	−	10.4157i	−1.23612	−	1.23612i	−0.961576	−	0.274540i	$-0.911474\pi$
$71$	−10.4157	−	10.4157i	−1.23612	−	1.23612i	−0.274540	−	0.961576i	$-0.588526\pi$
$72$	7.80863	+	3.32043i	0.920256	+	0.391317i
$73$	−8.18821	+	8.18821i	−0.958358	+	0.958358i	−0.999167	−	0.0408093i	$-0.987006\pi$
$73$	−8.18821	+	8.18821i	−0.958358	+	0.958358i	0.0408093	+	0.999167i	$0.487006\pi$
$74$	2.06869	+	2.74004i	0.240480	+	0.318523i
$75$	−1.01024	−	13.9120i	−0.116653	−	1.60642i
$76$	−9.05040	−	7.17208i	−1.03815	−	0.822694i
$77$	3.03909	+	2.33198i	0.346336	+	0.265753i
$78$	15.7864	−	3.12739i	1.78745	−	0.354108i
$79$	−0.656058	+	1.13633i	−0.0738123	+	0.127847i	−0.900569	−	0.434713i	$-0.856850\pi$
$79$	−0.656058	+	1.13633i	−0.0738123	+	0.127847i	0.826757	+	0.562559i	$0.190183\pi$
$80$	13.1723	+	5.94498i	1.47271	+	0.664669i
$81$	6.54061	+	6.18226i	0.726735	+	0.686918i
$82$	3.22398	+	3.27476i	0.356029	+	0.361637i
$83$	7.51437	+	0.989285i	0.824809	+	0.108588i	0.531103	−	0.847308i	$-0.321778\pi$
$83$	7.51437	+	0.989285i	0.824809	+	0.108588i	0.293706	+	0.955896i	$0.405111\pi$
$84$	−1.76631	−	2.69326i	−0.192721	−	0.293859i
$85$	−0.259351	−	1.96996i	−0.0281305	−	0.213672i
$86$	9.87961	−	1.22222i	1.06535	−	0.131795i
$87$	−2.89213	+	8.72117i	−0.310069	+	0.935007i
$88$	9.40894	−	6.87543i	1.00300	−	0.732923i
$89$	−3.96066	+	3.96066i	−0.419829	+	0.419829i	−0.885145	−	0.465315i	$-0.845941\pi$
$89$	−3.96066	+	3.96066i	−0.419829	+	0.419829i	0.465315	+	0.885145i	$0.345941\pi$
$90$	10.9065	+	10.7707i	1.14964	+	1.13533i
$91$	−5.64357	−	2.33764i	−0.591607	−	0.245051i
$92$	1.69473	+	6.74472i	0.176688	+	0.703186i
$93$	0.454958	+	1.30990i	0.0471770	+	0.135830i
$94$	2.54697	−	1.44408i	0.262700	−	0.148945i
$95$	−10.4302	−	18.0657i	−1.07012	−	1.85350i
$96$	−9.37409	+	2.85071i	−0.956739	+	0.290949i
$97$	6.94041	−	12.0211i	0.704692	−	1.22056i	−0.262110	−	0.965038i	$-0.584418\pi$
$97$	6.94041	−	12.0211i	0.704692	−	1.22056i	0.966803	−	0.255525i	$-0.0822482\pi$
$98$	0.0678017	−	8.67670i	0.00684901	−	0.876479i
$99$	11.8928	−	3.36682i	1.19527	−	0.338379i
$100$	11.2096	+	11.5656i	1.12096	+	1.15656i
$101$	7.72444	−	5.92717i	0.768611	−	0.589776i	−0.148265	−	0.988948i	$-0.547369\pi$
$101$	7.72444	−	5.92717i	0.768611	−	0.589776i	0.916876	+	0.399172i	$0.130702\pi$
$102$	1.01213	+	0.889002i	0.100216	+	0.0880243i
$103$	−3.72001	−	0.996774i	−0.366544	−	0.0982151i	0.0708458	−	0.997487i	$-0.477430\pi$
$103$	−3.72001	−	0.996774i	−0.366544	−	0.0982151i	−0.437389	+	0.899272i	$0.644097\pi$
$104$	−11.6549	+	14.4735i	−1.14286	+	1.41924i
$105$	−1.17523	−	5.69832i	−0.114690	−	0.556099i
$106$	−3.82259	−	5.06313i	−0.371283	−	0.491775i
$107$	2.04382	+	0.846577i	0.197583	+	0.0818417i	0.479281	−	0.877662i	$-0.340897\pi$
$107$	2.04382	+	0.846577i	0.197583	+	0.0818417i	−0.281698	+	0.959503i	$0.590897\pi$
$108$	−10.3736	−	0.622741i	−0.998203	−	0.0599232i
$109$	−6.40876	−	15.4721i	−0.613848	−	1.48196i	−0.858741	−	0.512409i	$-0.828753\pi$
$109$	−6.40876	−	15.4721i	−0.613848	−	1.48196i	0.244894	−	0.969550i	$-0.421247\pi$
$110$	20.3759	−	5.28941i	1.94277	−	0.504326i
$111$	−3.51258	−	2.31143i	−0.333399	−	0.219391i
$112$	3.56050	+	1.07436i	0.336435	+	0.101517i
$113$	1.03767	+	1.79730i	0.0976160	+	0.169076i	0.910697	−	0.413074i	$-0.135545\pi$
$113$	1.03767	+	1.79730i	0.0976160	+	0.169076i	−0.813081	+	0.582150i	$0.802212\pi$
$114$	13.3889	+	4.55647i	1.25398	+	0.426752i
$115$	−1.63978	+	12.4553i	−0.152910	+	1.16147i
$116$	−3.90645	−	9.86427i	−0.362705	−	0.915875i
$117$	−16.9289	+	10.0943i	−1.56508	+	0.933223i
$118$	1.18797	−	2.80581i	0.109362	−	0.258296i
$119$	−0.132342	−	0.493909i	−0.0121318	−	0.0452766i
$120$	−17.6404	−	1.44714i	−1.61034	−	0.132105i
$121$	1.54643	−	5.77135i	0.140585	−	0.524669i
$122$	10.9296	+	8.52312i	0.989523	+	0.771647i
$123$	−5.06522	−	2.45372i	−0.456716	−	0.221244i
$124$	−1.37398	−	0.822158i	−0.123387	−	0.0738320i
$125$	4.22142	+	10.1914i	0.377576	+	0.911548i
$126$	3.14449	+	2.38170i	0.280133	+	0.212179i
$127$			17.5362i			1.55609i	0.628209	+	0.778044i	$0.283788\pi$
$127$			17.5362i			1.55609i	−0.628209	+	0.778044i	$0.716212\pi$
$128$	6.18406	−	9.47404i	0.546599	−	0.837395i
$129$	−10.8967	+	5.46933i	−0.959397	+	0.481548i
$130$	−29.2020	+	16.5569i	−2.56118	+	1.45213i
$131$	−6.45725	−	4.95482i	−0.564172	−	0.432905i	0.286894	−	0.957962i	$-0.407377\pi$
$131$	−6.45725	−	4.95482i	−0.564172	−	0.432905i	−0.851067	+	0.525058i	$0.824044\pi$
$132$	−8.03091	+	11.7985i	−0.699001	+	1.02692i
$133$	−3.26801	−	4.25896i	−0.283373	−	0.369298i
$134$	−5.63102	−	13.9007i	−0.486446	−	1.20084i
$135$	−17.0089	−	7.94582i	−1.46389	−	0.683867i
$136$	−1.55509	−	0.0364615i	−0.133348	−	0.00312655i
$137$	1.61484	−	0.432694i	0.137965	−	0.0369675i	−0.189176	−	0.981943i	$-0.560582\pi$
$137$	1.61484	−	0.432694i	0.137965	−	0.0369675i	0.327141	+	0.944976i	$0.393915\pi$
$138$	−4.72649	−	7.08557i	−0.402346	−	0.603164i
$139$	−12.5789	+	1.65605i	−1.06693	+	0.140464i	−0.643486	−	0.765458i	$-0.722512\pi$
$139$	−12.5789	+	1.65605i	−1.06693	+	0.140464i	−0.423444	+	0.905922i	$0.639179\pi$
$140$	5.26545	+	4.17266i	0.445012	+	0.352654i
$141$	−2.34531	+	2.71260i	−0.197511	+	0.228442i
$142$	−20.1631	+	5.23417i	−1.69205	+	0.439241i
$143$			27.0689i			2.26361i
$144$	9.64431	−	7.14054i	0.803693	−	0.595045i
$145$		−	19.1659i		−	1.59164i
$146$	4.11480	+	15.8510i	0.340543	+	1.31184i
$147$	3.48671	+	10.0388i	0.287579	+	0.827986i
$148$	4.82314	−	0.558446i	0.396460	−	0.0459040i
$149$	6.86184	−	0.903379i	0.562144	−	0.0740077i	0.155901	−	0.987773i	$-0.450172\pi$
$149$	6.86184	−	0.903379i	0.562144	−	0.0740077i	0.406243	+	0.913765i	$0.366839\pi$
$150$	−17.6852	−	8.73843i	−1.44399	−	0.713489i
$151$	8.60778	−	2.30645i	0.700491	−	0.187696i	0.109041	−	0.994037i	$-0.465222\pi$
$151$	8.60778	−	2.30645i	0.700491	−	0.187696i	0.591451	+	0.806341i	$0.298556\pi$
$152$	−15.2301	+	5.89417i	−1.23532	+	0.478081i
$153$	−1.53303	−	0.609858i	−0.123938	−	0.0493041i
$154$	5.02108	−	2.03398i	0.404610	−	0.163903i
$155$	−1.76082	−	2.29474i	−0.141432	−	0.184318i
$156$	7.50052	−	21.4877i	0.600522	−	1.72039i
$157$	3.28311	+	2.51922i	0.262021	+	0.201056i	0.731414	−	0.681933i	$-0.238861\pi$
$157$	3.28311	+	2.51922i	0.262021	+	0.201056i	−0.469393	+	0.882989i	$0.655527\pi$
$158$	0.915221	+	1.61421i	0.0728110	+	0.128420i
$159$	6.49066	+	4.27114i	0.514743	+	0.338723i
$160$	16.6880	−	11.7989i	1.31930	−	0.932785i
$161$			3.23296i			0.254793i
$162$	12.2247	−	3.54365i	0.960461	−	0.278415i
$163$	−2.87542	−	6.94187i	−0.225220	−	0.543730i	0.770364	−	0.637605i	$-0.220075\pi$
$163$	−2.87542	−	6.94187i	−0.225220	−	0.543730i	−0.995584	+	0.0938750i	$0.970075\pi$
$164$	6.30302	−	1.58374i	0.492183	−	0.123670i
$165$	−21.3359	+	14.4745i	−1.66100	+	1.12684i
$166$	6.59133	−	8.45241i	0.511586	−	0.656034i
$167$	−0.878020	+	3.27681i	−0.0679432	+	0.253568i	−0.991541	−	0.129796i	$-0.958568\pi$
$167$	−0.878020	+	3.27681i	−0.0679432	+	0.253568i	0.923597	+	0.383364i	$0.125234\pi$
$168$	−4.54942	+	0.223315i	−0.350995	+	0.0172292i
$169$	−7.80727	−	29.1371i	−0.600559	−	2.24132i
$170$	−2.58761	−	1.09559i	−0.198461	−	0.0840278i
$171$	−17.3198	+	0.243865i	−1.32448	+	0.0186488i
$172$	5.59017	−	12.9210i	0.426247	−	0.985213i
$173$	0.379027	−	2.87900i	0.0288169	−	0.218886i	−0.970977	−	0.239172i	$-0.923124\pi$
$173$	0.379027	−	2.87900i	0.0288169	−	0.218886i	0.999794	+	0.0202855i	$0.00645751\pi$
$174$	8.56003	+	9.77611i	0.648934	+	0.741125i
$175$	3.74380	+	6.48446i	0.283005	+	0.490179i
$176$	−1.63943	−	16.3985i	−0.123577	−	1.23608i
$177$	−0.217847	+	3.72536i	−0.0163744	+	0.280015i
$178$	1.99034	+	7.66720i	0.149182	+	0.574681i
$179$	−1.11992	−	2.70373i	−0.0837067	−	0.202086i	0.876484	−	0.481431i	$-0.159883\pi$
$179$	−1.11992	−	2.70373i	−0.0837067	−	0.202086i	−0.960191	+	0.279345i	$0.909883\pi$
$180$	20.9476	−	5.57813i	1.56134	−	0.415769i
$181$	10.9516	+	4.53629i	0.814023	+	0.337179i	0.750558	−	0.660805i	$-0.229785\pi$
$181$	10.9516	+	4.53629i	0.814023	+	0.337179i	0.0634653	+	0.997984i	$0.479785\pi$
$182$	−6.89450	+	5.20525i	−0.511055	+	0.385839i
$183$	−16.1122	−	5.34315i	−1.19105	−	0.394977i
$184$	9.43758	+	2.76746i	0.695747	+	0.204020i
$185$	8.47217	+	2.27011i	0.622886	+	0.166902i
$186$	1.92305	+	0.384067i	0.141005	+	0.0281612i
$187$	−1.79763	+	1.37937i	−0.131456	+	0.100870i
$188$	0.0647078	−	4.14013i	0.00471930	−	0.301950i
$189$	−4.60658	−	1.45598i	−0.335079	−	0.105907i
$190$	−29.5002	−	0.230521i	−2.14017	−	0.0167238i
$191$	−7.34276	+	12.7180i	−0.531304	+	0.920245i	0.468029	+	0.883713i	$0.344964\pi$
$191$	−7.34276	+	12.7180i	−0.531304	+	0.920245i	−0.999332	+	0.0365318i	$0.988369\pi$
$192$	−3.24246	+	13.4717i	−0.234004	+	0.972236i
$193$	12.3177	+	21.3348i	0.886645	+	1.53572i	0.843816	+	0.536633i	$0.180304\pi$
$193$	12.3177	+	21.3348i	0.886645	+	1.53572i	0.0428295	+	0.999082i	$0.486363\pi$
$194$	−9.68208	−	17.0766i	−0.695133	−	1.22603i
$195$	26.8898	−	31.1009i	1.92562	−	2.22718i
$196$	−10.5299	−	6.30086i	−0.752135	−	0.450062i
$197$	18.0668	+	7.48351i	1.28721	+	0.533178i	0.918151	−	0.396230i	$-0.129682\pi$
$197$	18.0668	+	7.48351i	1.28721	+	0.533178i	0.369055	+	0.929408i	$0.379682\pi$
$198$	4.41828	−	16.9124i	0.313993	−	1.20191i
$199$	−1.37901	+	1.37901i	−0.0977557	+	0.0977557i	−0.754293	−	0.656538i	$-0.772020\pi$
$199$	−1.37901	+	1.37901i	−0.0977557	+	0.0977557i	0.656538	+	0.754293i	$0.272020\pi$
$200$	22.1340	−	5.37803i	1.56511	−	0.380284i
$201$	12.2082	+	13.7247i	0.861101	+	0.968065i
$202$	−1.69054	−	13.6652i	−0.118946	−	0.961483i
$203$	−0.643785	−	4.89003i	−0.0451848	−	0.343213i
$204$	1.80920	−	0.596863i	0.126670	−	0.0417888i
$205$	11.6397	+	1.53239i	0.812949	+	0.107027i
$206$	−3.88121	+	3.82103i	−0.270417	+	0.266224i
$207$	8.36450	+	6.23319i	0.581373	+	0.433237i
$208$	9.29325	+	24.5820i	0.644371	+	1.70446i
$209$	−11.8943	+	20.6015i	−0.822745	+	1.42504i
$210$	−7.78952	−	2.65092i	−0.537528	−	0.182931i
$211$	−9.41129	−	7.22154i	−0.647900	−	0.497151i	0.231748	−	0.972776i	$-0.425555\pi$
$211$	−9.41129	−	7.22154i	−0.647900	−	0.497151i	−0.879648	+	0.475625i	$0.842222\pi$
$212$	−8.91236	+	1.03192i	−0.612103	+	0.0708723i
$213$	21.1131	−	14.3233i	1.44665	−	0.981418i
$214$	2.49685	−	1.88508i	0.170681	−	0.128862i
$215$	17.9832	−	17.9832i	1.22644	−	1.22644i
$216$	−8.19355	+	12.2011i	−0.557501	+	0.830177i
$217$	−0.526339	−	0.526339i	−0.0357302	−	0.0357302i
$218$	−23.4562	−	3.27473i	−1.58865	−	0.221793i
$219$	−11.2602	−	16.5979i	−0.760891	−	1.12158i
$220$	8.15375	−	28.6326i	0.549726	−	1.93041i
$221$	2.19960	−	2.86657i	0.147961	−	0.192826i
$222$	−5.33536	+	2.62597i	−0.358086	+	0.176244i
$223$	6.56980	+	3.79308i	0.439946	+	0.254003i	0.703575	−	0.710621i	$-0.251586\pi$
$223$	6.56980	+	3.79308i	0.439946	+	0.254003i	−0.263628	+	0.964624i	$0.584919\pi$
$224$	3.86148	−	3.57095i	0.258006	−	0.238594i
$225$	23.9950	+	2.81593i	1.59967	+	0.187729i
$226$	2.93489	+	0.0229339i	0.195226	+	0.00152554i
$227$	−0.428504	+	3.25481i	−0.0284408	+	0.216029i	−0.999764	−	0.0217346i	$-0.993081\pi$
$227$	−0.428504	+	3.25481i	−0.0284408	+	0.216029i	0.971323	+	0.237764i	$0.0764145\pi$
$228$	15.1504	−	13.0580i	1.00336	−	0.864789i
$229$	0.197313	−	0.0259768i	0.0130388	−	0.00171659i	−0.124004	−	0.992282i	$-0.539574\pi$
$229$	0.197313	−	0.0259768i	0.0130388	−	0.00171659i	0.137043	+	0.990565i	$0.456240\pi$
$230$	14.0102	+	10.9254i	0.923804	+	0.720398i
$231$	−4.95750	+	4.40973i	−0.326179	+	0.290139i
$232$	−14.8259	−	2.30661i	−0.973370	−	0.151436i
$233$	2.23536	+	2.23536i	0.146443	+	0.146443i	0.776527	−	0.630084i	$-0.216979\pi$
$233$	2.23536	+	2.23536i	0.146443	+	0.146443i	−0.630084	+	0.776527i	$0.716979\pi$
$234$	0.174635	+	27.8736i	0.0114162	+	1.82216i
$235$	2.86244	−	6.91053i	0.186725	−	0.450794i
$236$	−2.56942	−	3.45916i	−0.167255	−	0.225172i
$237$	−1.71918	−	1.48640i	−0.111672	−	0.0965519i
$238$	−0.697009	−	0.192613i	−0.0451804	−	0.0124852i
$239$	−19.0747	+	11.0128i	−1.23384	+	0.712356i	−0.967828	−	0.251614i	$-0.919039\pi$
$239$	−19.0747	+	11.0128i	−1.23384	+	0.712356i	−0.266010	+	0.963970i	$0.585705\pi$
$240$	−14.4064	+	20.4697i	−0.929930	+	1.32132i
$241$	−11.7986	−	6.81195i	−0.760017	−	0.438796i	0.0692849	−	0.997597i	$-0.477928\pi$
$241$	−11.7986	−	6.81195i	−0.760017	−	0.438796i	−0.829302	+	0.558801i	$0.811262\pi$
$242$	−5.92807	−	6.02145i	−0.381071	−	0.387074i
$243$	−12.6485	+	9.11124i	−0.811404	+	0.584486i
$244$	18.2240	−	7.21708i	1.16667	−	0.462026i
$245$	−13.4946	−	17.5865i	−0.862136	−	1.12356i
$246$	−6.62154	+	4.41696i	−0.422174	+	0.281615i
$247$	9.81807	−	36.6415i	0.624709	−	2.33144i
$248$	−1.98703	+	1.08592i	−0.126176	+	0.0689561i
$249$	−4.13211	+	12.4603i	−0.261862	+	0.789639i
$250$	15.4505	+	2.15705i	0.977175	+	0.136424i
$251$	−11.0560	+	26.6917i	−0.697851	+	1.68476i	0.0304785	+	0.999535i	$0.490297\pi$
$251$	−11.0560	+	26.6917i	−0.697851	+	1.68476i	−0.728330	+	0.685227i	$0.759703\pi$
$252$	5.15724	−	2.12685i	0.324876	−	0.133979i
$253$	13.2357	−	5.48242i	0.832123	−	0.344677i
$254$	21.3799	+	12.5674i	1.34149	+	0.788551i
$255$	3.43565	+	0.200906i	0.215149	+	0.0125812i
$256$	−7.11874	−	14.3291i	−0.444921	−	0.895570i
$257$	15.8329	−	9.14110i	0.987626	−	0.570206i	0.0830622	−	0.996544i	$-0.473530\pi$
$257$	15.8329	−	9.14110i	0.987626	−	0.570206i	0.904564	+	0.426338i	$0.140197\pi$
$258$	−1.14103	+	17.2046i	−0.0710377	+	1.07111i
$259$	2.23786	+	0.294620i	0.139054	+	0.0183068i
$260$	−0.741898	+	47.4681i	−0.0460106	+	2.94385i
$261$	−13.8930	−	7.76240i	−0.859954	−	0.480480i
$262$	−10.6684	+	4.32166i	−0.659099	+	0.266993i
$263$	3.79496	−	1.01686i	0.234007	−	0.0627020i	−0.139910	−	0.990164i	$-0.544681\pi$
$263$	3.79496	−	1.01686i	0.234007	−	0.0627020i	0.373917	+	0.927462i	$0.378015\pi$
$264$	8.62909	+	18.2466i	0.531084	+	1.12300i
$265$	−15.6552	−	4.19478i	−0.961688	−	0.257684i
$266$	−7.53448	+	0.932099i	−0.461969	+	0.0571506i
$267$	−5.44657	−	8.02845i	−0.333325	−	0.491333i
$268$	−20.9830	−	3.09679i	−1.28174	−	0.189166i
$269$	−11.3837	+	4.71530i	−0.694079	+	0.287497i	−0.701698	−	0.712474i	$-0.747575\pi$
$269$	−11.3837	+	4.71530i	−0.694079	+	0.287497i	0.00761958	+	0.999971i	$0.497575\pi$
$270$	−21.8769	+	15.0425i	−1.33138	+	0.915457i
$271$	26.1244			1.58695			0.793473	−	0.608606i	$-0.208271\pi$
$271$	26.1244			1.58695			0.793473	+	0.608606i	$0.208271\pi$
$272$	−1.15892	+	1.86981i	−0.0702697	+	0.113374i
$273$	5.81604	−	8.83838i	0.352003	−	0.534923i
$274$	0.629748	−	2.27887i	0.0380445	−	0.137672i
$275$	20.1986	−	26.3234i	1.21802	−	1.58736i
$276$	−12.0259	+	0.684544i	−0.723872	+	0.0412047i
$277$	−9.02751	+	6.92705i	−0.542411	+	0.416206i	−0.843292	−	0.537455i	$-0.819386\pi$
$277$	−9.02751	+	6.92705i	−0.542411	+	0.416206i	0.300882	+	0.953661i	$0.402719\pi$
$278$	−6.99573	+	16.5228i	−0.419576	+	0.990972i
$279$	−2.37656	+	0.346986i	−0.142281	+	0.0207735i
$280$	8.86074	−	3.42918i	0.529531	−	0.204933i
$281$	7.78678	+	29.0607i	0.464520	+	1.73361i	0.658474	+	0.752603i	$0.271202\pi$
$281$	7.78678	+	29.0607i	0.464520	+	1.73361i	−0.193954	+	0.981011i	$0.562131\pi$
$282$	1.62637	+	4.80336i	0.0968490	+	0.286036i
$283$	2.02404	+	15.3741i	0.120317	+	0.913896i	0.940023	+	0.341112i	$0.110803\pi$
$283$	2.02404	+	15.3741i	0.120317	+	0.913896i	−0.819706	+	0.572784i	$0.805863\pi$
$284$	−8.06859	+	28.3336i	−0.478783	+	1.68129i
$285$	34.1312	−	11.8546i	2.02176	−	0.702205i
$286$	33.0019	+	19.3990i	1.95144	+	1.14709i
$287$	3.02124			0.178338
$288$	−1.79397	−	16.8755i	−0.105711	−	0.994397i
$289$	−16.6975			−0.982209
$290$	−23.3667	−	13.7353i	−1.37214	−	0.806567i
$291$	18.1871	+	15.7245i	1.06615	+	0.921789i
$292$	22.2742	+	6.34305i	1.30350	+	0.371199i
$293$	−3.43680	−	26.1051i	−0.200780	−	1.52507i	−0.734030	−	0.679117i	$-0.762363\pi$
$293$	−3.43680	−	26.1051i	−0.200780	−	1.52507i	0.533250	−	0.845958i	$-0.320970\pi$
$294$	14.7379	+	2.94342i	0.859531	+	0.171663i
$295$	−2.01467	−	7.51886i	−0.117299	−	0.437765i
$296$	2.77568	−	6.28050i	0.161333	−	0.365047i
$297$	1.85099	+	21.3283i	0.107405	+	1.23759i
$298$	3.81619	−	9.01325i	0.221066	−	0.522123i
$299$	−18.1243	+	13.9072i	−1.04815	+	0.804276i
$300$	−23.3279	+	15.2991i	−1.34684	+	0.883293i
$301$	3.98421	−	5.19233i	0.229646	−	0.299281i
$302$	3.35683	−	12.1474i	0.193164	−	0.699003i
$303$	7.56505	+	15.0720i	0.434601	+	0.865864i
$304$	−3.72865	+	22.7923i	−0.213853	+	1.30723i
$305$	35.4086			2.02749
$306$	−1.84218	+	1.43198i	−0.105310	+	0.0818608i
$307$	−22.4892	+	9.31532i	−1.28352	+	0.531653i	−0.917049	−	0.398774i	$-0.869436\pi$
$307$	−22.4892	+	9.31532i	−1.28352	+	0.531653i	−0.366476	+	0.930428i	$0.619436\pi$
$308$	1.11859	−	7.57928i	0.0637377	−	0.431869i
$309$	2.90812	−	6.00325i	0.165437	−	0.341513i
$310$	−4.05961	+	0.502218i	−0.230570	+	0.0285241i
$311$	10.4000	+	2.78666i	0.589727	+	0.158017i	0.541328	−	0.840811i	$-0.317922\pi$
$311$	10.4000	+	2.78666i	0.589727	+	0.158017i	0.0483986	+	0.998828i	$0.484588\pi$
$312$	−20.8222	−	24.5438i	−1.17882	−	1.38952i
$313$	0.873677	−	0.234101i	0.0493832	−	0.0132322i	−0.234043	−	0.972226i	$-0.575196\pi$
$313$	0.873677	−	0.234101i	0.0493832	−	0.0132322i	0.283426	+	0.958994i	$0.408529\pi$
$314$	5.42425	−	2.19730i	0.306108	−	0.124001i
$315$	10.0765	−	0.141879i	0.567747	−	0.00799396i
$316$	2.62391	+	0.0410102i	0.147607	+	0.00230700i
$317$	21.1720	+	2.78735i	1.18914	+	0.156553i	0.699020	−	0.715102i	$-0.253620\pi$
$317$	21.1720	+	2.78735i	1.18914	+	0.156553i	0.490120	+	0.871655i	$0.336953\pi$
$318$	9.85886	−	4.85236i	0.552857	−	0.272107i
$319$	−18.9280	+	10.9281i	−1.05977	+	0.611856i
$320$	−2.42547	−	28.8015i	−0.135588	−	1.61005i
$321$	−2.10628	+	3.20082i	−0.117561	+	0.178652i
$322$	3.94157	+	2.31692i	0.219655	+	0.129117i
$323$	2.93366	−	1.21516i	0.163233	−	0.0676134i
$324$	4.44052	−	17.4437i	0.246696	−	0.969093i
$325$	−20.2477	+	48.8823i	−1.12314	+	2.71150i
$326$	−10.5241	−	1.46927i	−0.582876	−	0.0813755i
$327$	28.4086	−	5.85901i	1.57100	−	0.324004i
$328$	2.58622	−	8.81952i	0.142800	−	0.486977i
$329$	0.498203	−	1.85932i	0.0274668	−	0.102507i
$330$	2.35654	+	36.3856i	0.129723	+	2.00296i
$331$	−1.74701	−	2.27675i	−0.0960245	−	0.125142i	0.742870	−	0.669436i	$-0.233464\pi$
$331$	−1.74701	−	2.27675i	−0.0960245	−	0.125142i	−0.838894	+	0.544294i	$0.816797\pi$
$332$	−5.58131	−	14.0935i	−0.306314	−	0.773481i
$333$	5.07687	−	5.22188i	0.278211	−	0.286157i
$334$	3.36580	+	3.41881i	0.184168	+	0.187069i
$335$	−33.1823	−	19.1578i	−1.81294	−	1.04670i
$336$	−2.98810	+	5.70661i	−0.163014	+	0.311321i
$337$	5.37625	−	3.10398i	0.292863	−	0.169085i	−0.346369	−	0.938098i	$-0.612586\pi$
$337$	5.37625	−	3.10398i	0.292863	−	0.169085i	0.639232	+	0.769014i	$0.279252\pi$
$338$	−41.1186	−	11.3628i	−2.23656	−	0.618054i
$339$	−3.39562	+	1.17938i	−0.184425	+	0.0640552i
$340$	−3.19015	+	2.36961i	−0.173010	+	0.128510i
$341$	−1.26227	+	3.04739i	−0.0683557	+	0.165025i
$342$	−12.1150	+	21.2907i	−0.655104	+	1.15127i
$343$	−8.63586	−	8.63586i	−0.466293	−	0.466293i
$344$	−11.7468	−	16.0753i	−0.633343	−	0.866723i
$345$	−20.6534	−	6.84912i	−1.11194	−	0.368744i
$346$	−3.23839	−	2.52535i	−0.174097	−	0.135764i
$347$	26.4586	−	3.48334i	1.42037	−	0.186995i	0.619107	−	0.785306i	$-0.287495\pi$
$347$	26.4586	−	3.48334i	1.42037	−	0.186995i	0.801264	+	0.598311i	$0.204161\pi$
$348$	18.0534	−	3.43014i	0.967766	−	0.183875i
$349$	−2.92917	+	22.2492i	−0.156795	+	1.19097i	0.714293	+	0.699846i	$0.246748\pi$
$349$	−2.92917	+	22.2492i	−0.156795	+	1.19097i	−0.871088	+	0.491127i	$0.836585\pi$
$350$	10.5888	+	0.0827429i	0.565993	+	0.00442280i
$351$	−11.6538	−	32.0881i	−0.622031	−	1.71273i
$352$	−21.1677	−	9.75332i	−1.12824	−	0.519854i
$353$	−4.46134	−	2.57576i	−0.237453	−	0.137094i	0.376552	−	0.926395i	$-0.377109\pi$
$353$	−4.46134	−	2.57576i	−0.237453	−	0.137094i	−0.614006	+	0.789302i	$0.710443\pi$
$354$	4.38577	+	2.93540i	0.233101	+	0.156015i
$355$	−32.3973	+	42.2210i	−1.71947	+	2.24086i
$356$	10.7741	+	3.06815i	0.571026	+	0.162612i
$357$	0.883327	−	0.0641443i	0.0467506	−	0.00339488i
$358$	−4.09893	−	0.572253i	−0.216635	−	0.0302445i
$359$	−4.98029	−	4.98029i	−0.262849	−	0.262849i	0.563361	−	0.826211i	$-0.309508\pi$
$359$	−4.98029	−	4.98029i	−0.262849	−	0.262849i	−0.826211	+	0.563361i	$0.809508\pi$
$360$	8.21144	−	29.5365i	0.432781	−	1.55671i
$361$	10.1379	−	10.1379i	0.533572	−	0.533572i
$362$	13.3791	−	10.1010i	0.703188	−	0.530897i
$363$	9.31364	+	4.51175i	0.488840	+	0.236806i
$364$	1.40517	+	12.1360i	0.0736508	+	0.636101i
$365$	33.1917	+	25.4689i	1.73733	+	1.33310i
$366$	−18.0611	+	15.8145i	−0.944071	+	0.826635i
$367$	−3.97447	+	6.88398i	−0.207465	+	0.359341i	−0.950915	−	0.309451i	$-0.899855\pi$
$367$	−3.97447	+	6.88398i	−0.207465	+	0.359341i	0.743450	+	0.668792i	$0.233188\pi$
$368$	10.1375	−	9.52281i	0.528455	−	0.496411i
$369$	5.82499	−	7.81672i	0.303237	−	0.406922i
$370$	8.83930	−	8.70223i	0.459533	−	0.452407i
$371$	−4.13519	−	0.544408i	−0.214688	−	0.0282643i
$372$	1.84641	−	2.06930i	0.0957320	−	0.107288i
$373$	2.67880	+	20.3475i	0.138703	+	1.05356i	0.909273	+	0.416200i	$0.136638\pi$
$373$	2.67880	+	20.3475i	0.138703	+	1.05356i	−0.770570	+	0.637356i	$0.780028\pi$
$374$	0.393423	+	3.18018i	0.0203434	+	0.164443i
$375$	−18.7126	+	3.85931i	−0.966315	+	0.199294i
$376$	−5.00120	−	3.04594i	−0.257917	−	0.157082i
$377$	24.6446	−	24.6446i	1.26926	−	1.26926i
$378$	−5.07644	+	4.57282i	−0.261104	+	0.235200i
$379$	21.7726	+	9.01851i	1.11838	+	0.463250i	0.863817	−	0.503806i	$-0.168067\pi$
$379$	21.7726	+	9.01851i	1.11838	+	0.463250i	0.254567	+	0.967055i	$0.418067\pi$
$380$	−21.4225	+	35.8009i	−1.09895	+	1.83655i
$381$	−29.8310	−	5.71575i	−1.52829	−	0.292827i
$382$	10.2434	+	18.0666i	0.524097	+	0.924368i
$383$	2.88324	+	4.99391i	0.147326	+	0.255177i	0.930239	−	0.366955i	$-0.119600\pi$
$383$	2.88324	+	4.99391i	0.147326	+	0.255177i	−0.782912	+	0.622132i	$0.786267\pi$
$384$	14.1007	+	13.6077i	0.719574	+	0.694415i
$385$	6.92000	−	11.9858i	0.352676	−	0.610852i
$386$	34.8386	+	0.272237i	1.77324	+	0.0138565i
$387$	−5.75227	−	20.3190i	−0.292404	−	1.03288i
$388$	−27.7583	−	0.433845i	−1.40921	−	0.0220252i
$389$	−0.369999	+	0.283910i	−0.0187597	+	0.0143948i	−0.618099	−	0.786100i	$-0.712097\pi$
$389$	−0.369999	+	0.283910i	−0.0187597	+	0.0143948i	0.599339	+	0.800495i	$0.295430\pi$
$390$	−18.6469	−	55.0722i	−0.944224	−	2.78869i
$391$	−1.84715	−	0.494943i	−0.0934144	−	0.0250303i
$392$	−15.2282	+	8.32230i	−0.769140	+	0.420340i
$393$	10.5333	−	9.36949i	0.531337	−	0.472628i
$394$	22.0714	−	16.6636i	1.11194	−	0.839501i
$395$	4.37972	+	1.81414i	0.220368	+	0.0912793i
$396$	−17.4529	−	17.5070i	−0.877039	−	0.879761i
$397$	2.40248	+	5.80011i	0.120577	+	0.291099i	0.972631	−	0.232355i	$-0.0746431\pi$
$397$	2.40248	+	5.80011i	0.120577	+	0.291099i	−0.852054	+	0.523454i	$0.824643\pi$
$398$	0.692991	+	2.66955i	0.0347365	+	0.133812i
$399$	8.31011	−	4.17108i	0.416026	−	0.208815i
$400$	9.30564	−	30.8396i	0.465282	−	1.54198i
$401$	−0.782860	−	1.35595i	−0.0390941	−	0.0677131i	0.845816	−	0.533474i	$-0.179114\pi$
$401$	−0.782860	−	1.35595i	−0.0390941	−	0.0677131i	−0.884910	+	0.465761i	$0.845781\pi$
$402$	25.4820	−	5.04817i	1.27093	−	0.251780i
$403$	0.686549	−	5.21486i	0.0341994	−	0.259771i
$404$	−17.8720	−	7.73219i	−0.889163	−	0.384691i
$405$	19.0605	−	26.3440i	0.947126	−	1.30905i
$406$	−6.42321	−	2.71957i	−0.318778	−	0.134970i
$407$	−2.58876	−	9.66139i	−0.128320	−	0.478897i
$408$	0.568891	−	2.63349i	0.0281643	−	0.130377i
$409$	−1.14618	+	4.27760i	−0.0566749	+	0.211513i	−0.988456	−	0.151506i	$-0.951588\pi$
$409$	−1.14618	+	4.27760i	−0.0566749	+	0.211513i	0.931781	+	0.363020i	$0.118254\pi$
$410$	10.2099	−	13.0927i	0.504230	−	0.646601i
$411$	0.209720	+	2.88804i	0.0103447	+	0.142456i
$412$	1.87704	+	7.47027i	0.0924749	+	0.368034i
$413$	−0.766587	−	1.85070i	−0.0377213	−	0.0910672i
$414$	13.5939	−	5.73080i	0.668102	−	0.281653i
$415$		−	27.3831i		−	1.34418i
$416$	36.6300	+	6.28666i	1.79593	+	0.308229i
$417$	1.28285	−	21.9378i	0.0628216	−	1.07430i
$418$	16.5929	+	29.2655i	0.811584	+	1.43142i
$419$	6.19324	+	4.75224i	0.302560	+	0.232162i	0.748871	−	0.662715i	$-0.230596\pi$
$419$	6.19324	+	4.75224i	0.302560	+	0.232162i	−0.446312	+	0.894878i	$0.647263\pi$
$420$	−8.81435	+	7.59706i	−0.430096	+	0.370698i
$421$	−15.0641	−	19.6320i	−0.734182	−	0.956804i	0.265792	−	0.964030i	$-0.414366\pi$
$421$	−15.0641	−	19.6320i	−0.734182	−	0.956804i	−0.999974	+	0.00722631i	$0.997700\pi$
$422$	−15.5490	+	6.29872i	−0.756914	+	0.306617i
$423$	−3.84999	−	4.87376i	−0.187193	−	0.236970i
$424$	−5.12900	+	11.6053i	−0.249086	+	0.563604i
$425$	−4.27804	+	1.14630i	−0.207515	+	0.0556036i
$426$	−2.33193	−	36.0056i	−0.112982	−	1.74448i
$427$	9.03422	−	1.18938i	0.437196	−	0.0575580i
$428$	−0.508882	−	4.39506i	−0.0245977	−	0.212443i
$429$	−46.0470	−	8.82281i	−2.22317	−	0.425969i
$430$	−9.03704	−	34.8126i	−0.435805	−	1.67881i
$431$		−	36.3187i		−	1.74941i	−0.484653	−	0.874706i	$-0.661054\pi$
$431$		−	36.3187i		−	1.74941i	0.484653	−	0.874706i	$-0.338946\pi$
$432$	9.00335	+	18.7334i	0.433174	+	0.901310i
$433$			21.8733i			1.05117i	0.850742	+	0.525583i	$0.176153\pi$
$433$			21.8733i			1.05117i	−0.850742	+	0.525583i	$0.823847\pi$
$434$	−1.01891	+	0.264500i	−0.0489091	+	0.0126964i
$435$	32.6032	+	6.24692i	1.56321	+	0.299517i
$436$	−20.8025	+	26.2505i	−0.996259	+	1.25717i
$437$	−19.9049	+	2.62053i	−0.952182	+	0.125357i
$438$	−28.3055	+	1.83323i	−1.35249	+	0.0875949i
$439$	8.27013	−	2.21598i	0.394712	−	0.105763i	−0.0560032	−	0.998431i	$-0.517836\pi$
$439$	8.27013	−	2.21598i	0.394712	−	0.105763i	0.450715	+	0.892668i	$0.351169\pi$
$440$	−29.0650	−	30.4606i	−1.38562	−	1.45215i
$441$	−18.2135	+	2.65923i	−0.867310	+	0.126630i
$442$	−1.91852	−	4.73605i	−0.0912547	−	0.225271i
$443$	−11.1433	−	14.5223i	−0.529436	−	0.689974i	0.449700	−	0.893179i	$-0.351531\pi$
$443$	−11.1433	−	14.5223i	−0.529436	−	0.689974i	−0.979136	+	0.203205i	$0.934864\pi$
$444$	−0.622074	+	8.38669i	−0.0295223	+	0.398015i
$445$	16.0549	+	12.3194i	0.761077	+	0.583995i
$446$	9.33274	−	5.29146i	0.441918	−	0.250558i
$447$	−0.699801	+	11.9672i	−0.0330995	+	0.566028i
$448$	−1.58628	−	7.26699i	−0.0749449	−	0.343333i
$449$			17.1755i			0.810562i	0.914192	+	0.405281i	$0.132826\pi$
$449$			17.1755i			0.810562i	−0.914192	+	0.405281i	$0.867174\pi$
$450$	20.6293	−	27.2363i	0.972475	−	1.28393i
$451$	−5.12338	−	12.3689i	−0.241251	−	0.582430i
$452$	2.13127	−	3.56173i	0.100246	−	0.167530i
$453$	1.11790	+	15.3945i	0.0525234	+	0.723297i
$454$	3.66112	+	2.85500i	0.171825	+	0.133992i
$455$	−5.71207	+	21.3177i	−0.267786	+	0.999391i
$456$	−5.06253	−	27.8292i	−0.237075	−	1.30322i
$457$	5.20097	+	19.4103i	0.243291	+	0.907975i	0.974235	+	0.225537i	$0.0724135\pi$
$457$	5.20097	+	19.4103i	0.243291	+	0.907975i	−0.730944	+	0.682438i	$0.760920\pi$
$458$	0.109735	−	0.259177i	0.00512758	−	0.0121105i
$459$	1.53711	−	2.40906i	0.0717460	−	0.112445i
$460$	23.3605	−	9.25123i	1.08919	−	0.431341i
$461$	2.62602	−	19.9466i	0.122306	−	0.929004i	−0.814747	−	0.579817i	$-0.803124\pi$
$461$	2.62602	−	19.9466i	0.122306	−	0.929004i	0.937053	−	0.349188i	$-0.113542\pi$
$462$	1.82345	+	9.20435i	0.0848346	+	0.428225i
$463$	0.711495	+	1.23235i	0.0330660	+	0.0572720i	0.882085	−	0.471091i	$-0.156140\pi$
$463$	0.711495	+	1.23235i	0.0330660	+	0.0572720i	−0.849019	+	0.528363i	$0.822806\pi$
$464$	−13.4373	+	16.4225i	−0.623809	+	0.762394i
$465$	4.47752	−	2.24739i	0.207640	−	0.104220i
$466$	4.32729	−	1.12333i	0.200458	−	0.0520372i
$467$	13.1521	+	31.7520i	0.608608	+	1.46931i	0.864515	+	0.502607i	$0.167626\pi$
$467$	13.1521	+	31.7520i	0.608608	+	1.46931i	−0.255907	+	0.966701i	$0.582374\pi$
$468$	34.1082	+	19.7629i	1.57665	+	0.913539i
$469$	−9.10971	−	3.77337i	−0.420647	−	0.174238i
$470$	−6.37382	−	8.44230i	−0.294002	−	0.389414i
$471$	−5.35556	+	4.76381i	−0.246771	+	0.219505i
$472$	−6.05873	+	0.653574i	−0.278876	+	0.0300832i
$473$	−28.0137	−	7.50626i	−1.28807	−	0.345138i
$474$	−3.04425	+	1.03075i	−0.139827	+	0.0473441i
$475$	−36.8894	+	28.3062i	−1.69260	+	1.29878i
$476$	−0.734345	+	0.711744i	−0.0336587	+	0.0326227i
$477$	−9.38122	+	9.64917i	−0.429536	+	0.441805i
$478$	−0.243396	+	31.1478i	−0.0111327	+	1.42467i
$479$	15.9164	−	27.5679i	0.727237	−	1.25961i	−0.230809	−	0.972999i	$-0.574137\pi$
$479$	15.9164	−	27.5679i	0.727237	−	1.25961i	0.958047	−	0.286613i	$-0.0925293\pi$
$480$	14.6319	+	32.2338i	0.667853	+	1.47126i
$481$	7.97494	+	13.8130i	0.363626	+	0.629819i
$482$	−16.7606	+	9.50287i	−0.763422	+	0.432844i
$483$	−5.49961	−	1.05375i	−0.250241	−	0.0479473i
$484$	−11.5896	+	2.91210i	−0.526801	+	0.132368i
$485$	−46.3329	−	19.1917i	−2.10387	−	0.871451i
$486$	2.04362	+	21.9505i	0.0927006	+	0.995694i
$487$	0.00768501	−	0.00768501i	0.000348241	−	0.000348241i	−0.706933	−	0.707281i	$-0.749922\pi$
$487$	0.00768501	−	0.00768501i	0.000348241	−	0.000348241i	0.707281	+	0.706933i	$0.249922\pi$
$488$	4.26140	−	27.3906i	0.192905	−	1.23991i
$489$	12.7461	−	2.62876i	0.576398	−	0.118877i
$490$	−31.1121	+	3.84890i	−1.40550	+	0.173876i
$491$	4.55724	+	34.6156i	0.205665	+	1.56218i	0.713455	+	0.700701i	$0.247129\pi$
$491$	4.55724	+	34.6156i	0.205665	+	1.56218i	−0.507790	+	0.861481i	$0.669537\pi$
$492$	0.639715	+	11.2383i	0.0288406	+	0.506662i
$493$	2.89247	+	0.380801i	0.130270	+	0.0171504i
$494$	−37.6365	−	38.2294i	−1.69335	−	1.72002i
$495$	−17.6685	−	41.0125i	−0.794138	−	1.84338i
$496$	−0.100077	+	3.20078i	−0.00449360	+	0.143719i
$497$	−6.84772	+	11.8606i	−0.307162	+	0.532020i
$498$	12.2301	+	13.9675i	0.548043	+	0.625900i
$499$	−12.7920	−	9.81562i	−0.572647	−	0.439407i	0.281409	−	0.959588i	$-0.409198\pi$
$499$	−12.7920	−	9.81562i	−0.572647	−	0.439407i	−0.854056	+	0.520180i	$0.825865\pi$
$500$	13.7025	−	17.2911i	0.612795	−	0.773282i
$501$	−5.28803	−	2.56165i	−0.236252	−	0.114446i
$502$	24.6186	+	32.6080i	1.09878	+	1.45537i
$503$	−13.0937	+	13.0937i	−0.583819	+	0.583819i	−0.935951	−	0.352132i	$-0.885457\pi$
$503$	−13.0937	+	13.0937i	−0.583819	+	0.583819i	0.352132	+	0.935951i	$0.385457\pi$
$504$	1.10295	−	7.81183i	0.0491293	−	0.347967i
$505$	−24.8739	−	24.8739i	−1.10688	−	1.10688i
$506$	2.80139	−	20.0658i	0.124537	−	0.892032i
$507$	52.1100	−	3.78406i	2.31429	−	0.168056i
$508$	30.6440	−	17.0594i	1.35961	−	0.756890i
$509$	−16.1892	+	21.0982i	−0.717576	+	0.935163i	−0.999707	−	0.0242130i	$-0.992292\pi$
$509$	−16.1892	+	21.0982i	−0.717576	+	0.935163i	0.282131	+	0.959376i	$0.408959\pi$
$510$	2.70712	−	4.04470i	0.119873	−	0.179102i
$511$	9.32411	+	5.38328i	0.412474	+	0.238142i
$512$	−22.5715	−	1.59000i	−0.997528	−	0.0702687i
$513$	5.23036	−	29.5423i	0.230926	−	1.30432i
$514$	0.202030	−	25.8541i	0.00891117	−	1.14038i
$515$	−1.81617	+	13.7952i	−0.0800301	+	0.607889i
$516$	20.1579	+	13.7209i	0.887400	+	0.604030i
$517$	−8.45688	+	1.11337i	−0.371933	+	0.0489659i
$518$	1.96297	−	2.51722i	0.0862479	−	0.110600i
$519$	4.77394	+	1.58314i	0.209553	+	0.0694923i
$520$	57.3406	+	34.9228i	2.51455	+	1.53146i
$521$	−25.5790	−	25.5790i	−1.12063	−	1.12063i	−0.991646	−	0.128989i	$-0.958827\pi$
$521$	−25.5790	−	25.5790i	−1.12063	−	1.12063i	−0.128989	−	0.991646i	$-0.541173\pi$
$522$	−19.4203	+	11.3751i	−0.850001	+	0.497875i
$523$	8.15738	−	19.6936i	0.356697	−	0.861143i	−0.639063	−	0.769154i	$-0.720678\pi$
$523$	8.15738	−	19.6936i	0.356697	−	0.861143i	0.995760	−	0.0919887i	$-0.0293224\pi$
$524$	−2.37671	+	16.1039i	−0.103827	+	0.703503i
$525$	−12.2510	+	4.25507i	−0.534678	+	0.185706i
$526$	1.47994	−	5.35548i	0.0645286	−	0.233510i
$527$	0.381302	−	0.220145i	0.0166098	−	0.00958966i
$528$	28.4300	+	2.55607i	1.23726	+	0.111239i
$529$	−9.44761	−	5.45458i	−0.410766	−	0.237156i
$530$	−16.3336	+	16.0803i	−0.709484	+	0.698482i
$531$	−6.26623	−	1.58482i	−0.271931	−	0.0687755i
$532$	−4.26323	+	9.85390i	−0.184834	+	0.427221i
$533$	12.9965	+	16.9373i	0.562940	+	0.733637i
$534$	−13.6915	+	0.886737i	−0.592487	+	0.0383729i
$535$	2.06863	−	7.72022i	0.0894346	−	0.333774i
$536$	−18.8131	+	23.3628i	−0.812604	+	1.00912i
$537$	4.96435	−	1.02385i	0.214228	−	0.0441825i
$538$	−2.40941	+	17.2581i	−0.103877	+	0.744049i
$539$	−9.67379	+	23.3546i	−0.416680	+	1.00595i
$540$	2.66134	+	37.4522i	0.114526	+	1.61169i
$541$	−33.8136	+	14.0061i	−1.45376	+	0.602168i	−0.963091	−	0.269177i	$-0.913248\pi$
$541$	−33.8136	+	14.0061i	−1.45376	+	0.602168i	−0.490671	+	0.871345i	$0.663248\pi$
$542$	18.7222	−	31.8504i	0.804188	−	1.36809i
$543$	−11.2863	+	17.1512i	−0.484339	+	0.736029i
$544$	1.44909	+	2.75294i	0.0621294	+	0.118031i
$545$	−52.3991	+	30.2526i	−2.24453	+	1.29588i
$546$	−6.60750	−	13.4249i	−0.282775	−	0.574532i
$547$	10.7509	+	1.41539i	0.459677	+	0.0605177i	0.356809	−	0.934177i	$-0.383865\pi$
$547$	10.7509	+	1.41539i	0.459677	+	0.0605177i	0.102868	+	0.994695i	$0.467198\pi$
$548$	−2.32705	−	2.40094i	−0.0994065	−	0.102563i
$549$	14.3408	−	25.6670i	0.612053	−	1.09544i
$550$	−17.6175	−	43.4906i	−0.751213	−	1.85444i
$551$	29.5854	−	7.92740i	1.26038	−	0.337718i
$552$	−7.78382	+	15.1523i	−0.331301	+	0.644925i
$553$	1.17839	+	0.315748i	0.0501102	+	0.0134270i
$554$	1.97573	+	15.9705i	0.0839405	+	0.678521i
$555$	−6.62311	+	13.6721i	−0.281135	+	0.580350i
$556$	15.1308	+	20.3702i	0.641688	+	0.863890i
$557$	34.4084	−	14.2524i	1.45793	−	0.603894i	0.493860	−	0.869542i	$-0.335586\pi$
$557$	34.4084	−	14.2524i	1.45793	−	0.603894i	0.964070	+	0.265647i	$0.0855857\pi$
$558$	−1.28014	+	3.14613i	−0.0541925	+	0.133186i
$559$	46.2475			1.95606
$560$	2.16930	−	13.2604i	0.0916697	−	0.560354i
$561$	−1.76054	−	3.50756i	−0.0743301	−	0.148089i
$562$	41.0107	+	11.3330i	1.72993	+	0.478053i
$563$	−1.45318	+	1.89382i	−0.0612441	+	0.0798149i	−0.822971	−	0.568083i	$-0.807685\pi$
$563$	−1.45318	+	1.89382i	−0.0612441	+	0.0798149i	0.761727	+	0.647898i	$0.224352\pi$
$564$	7.02171	+	1.45951i	0.295667	+	0.0614563i
$565$	5.94862	−	4.56454i	0.250260	−	0.192031i
$566$	20.1944	+	8.55026i	0.848833	+	0.359394i
$567$	3.97825	−	7.36172i	0.167071	−	0.309163i
$568$	28.7614	+	30.1425i	1.20680	+	1.26475i
$569$	4.85765	+	18.1290i	0.203643	+	0.760007i	0.989859	+	0.142055i	$0.0453708\pi$
$569$	4.85765	+	18.1290i	0.203643	+	0.760007i	−0.786216	+	0.617952i	$0.787963\pi$
$570$	10.0074	−	50.1078i	0.419165	−	2.09879i
$571$	−3.95191	−	30.0178i	−0.165382	−	1.25620i	−0.849797	−	0.527111i	$-0.823275\pi$
$571$	−3.95191	−	30.0178i	−0.165382	−	1.25620i	0.684414	−	0.729093i	$-0.260058\pi$
$572$	47.3019	−	26.3329i	1.97779	−	1.10103i
$573$	−19.2414	−	16.6361i	−0.803823	−	0.694984i
$574$	2.16519	−	3.68344i	0.0903732	−	0.153744i
$575$	28.0026			1.16779
$576$	−21.8599	−	9.90672i	−0.910831	−	0.412780i
$577$	37.3353			1.55429			0.777144	−	0.629323i	$-0.216668\pi$
$577$	37.3353			1.55429			0.777144	+	0.629323i	$0.216668\pi$
$578$	−11.9664	+	20.3573i	−0.497736	+	0.846754i
$579$	−40.3076	+	13.9998i	−1.67513	+	0.581812i
$580$	−33.4918	+	18.6448i	−1.39067	+	0.774183i
$581$	−0.919802	−	6.98659i	−0.0381598	−	0.289852i
$582$	32.2050	−	10.9043i	1.33494	−	0.451998i
$583$	4.78360	+	17.8526i	0.198116	+	0.739381i
$584$	23.6963	−	22.6105i	0.980558	−	0.935630i
$585$	44.1415	+	55.8794i	1.82503	+	2.31033i
$586$	−34.2898	−	14.5183i	−1.41650	−	0.599744i
$587$	−13.8497	+	10.6272i	−0.571636	+	0.438632i	−0.853701	−	0.520763i	$-0.825647\pi$
$587$	−13.8497	+	10.6272i	−0.571636	+	0.438632i	0.282065	+	0.959395i	$0.408981\pi$
$588$	14.1505	−	15.8588i	0.583559	−	0.654004i
$589$	2.81397	−	3.66724i	0.115948	−	0.151106i
$590$	−10.6107	−	2.93218i	−0.436835	−	0.120716i
$591$	−18.6189	+	28.2944i	−0.765881	+	1.16388i
$592$	−5.66787	−	7.88501i	−0.232948	−	0.324072i
$593$	0.900061			0.0369611			0.0184805	−	0.999829i	$-0.494117\pi$
$593$	0.900061			0.0369611			0.0184805	+	0.999829i	$0.494117\pi$
$594$	27.3296	+	13.0284i	1.12135	+	0.534560i
$595$	−1.70678	+	0.706971i	−0.0699711	+	0.0289830i
$596$	−8.25390	−	11.1120i	−0.338093	−	0.455166i
$597$	−1.89637	−	2.79532i	−0.0776134	−	0.114405i
$598$	3.96661	+	32.0635i	0.162207	+	1.31117i
$599$	3.69510	+	0.990100i	0.150978	+	0.0404544i	0.333516	−	0.942744i	$-0.391765\pi$
$599$	3.69510	+	0.990100i	0.150978	+	0.0404544i	−0.182539	+	0.983199i	$0.558431\pi$
$600$	1.93427	+	39.4052i	0.0789661	+	1.60871i
$601$	6.88826	−	1.84570i	0.280978	−	0.0752878i	−0.115578	−	0.993298i	$-0.536872\pi$
$601$	6.88826	−	1.84570i	0.280978	−	0.0752878i	0.396556	+	0.918011i	$0.370205\pi$
$602$	−3.47509	−	8.57859i	−0.141634	−	0.349637i
$603$	−27.3263	+	16.2941i	−1.11281	+	0.663545i
$604$	−12.4042	−	12.7981i	−0.504719	−	0.520746i
$605$	−21.4024	−	2.81767i	−0.870129	−	0.114555i
$606$	23.7970	+	1.57825i	0.966689	+	0.0641121i
$607$	−13.4293	+	7.75342i	−0.545079	+	0.314702i	−0.747135	−	0.664672i	$-0.768571\pi$
$607$	−13.4293	+	7.75342i	−0.545079	+	0.314702i	0.202056	+	0.979374i	$0.435238\pi$
$608$	25.1159	+	20.8802i	1.01858	+	0.846803i
$609$	8.52830	+	0.498707i	0.345584	+	0.0202086i
$610$	25.3757	−	43.1695i	1.02743	−	1.74788i
$611$	12.5666	−	5.20526i	0.508391	−	0.210582i
$612$	0.425637	+	3.27219i	0.0172053	+	0.132270i
$613$	0.279501	−	0.674775i	0.0112889	−	0.0272539i	−0.918135	−	0.396269i	$-0.870305\pi$
$613$	0.279501	−	0.674775i	0.0112889	−	0.0272539i	0.929424	+	0.369015i	$0.120305\pi$
$614$	−4.75991	+	34.0943i	−0.192094	+	1.37593i
$615$	−6.40058	+	19.3008i	−0.258096	+	0.778285i
$616$	−8.43887	−	6.79550i	−0.340012	−	0.273798i
$617$	7.32021	−	27.3194i	0.294701	−	1.09984i	−0.646754	−	0.762698i	$-0.723874\pi$
$617$	7.32021	−	27.3194i	0.294701	−	1.09984i	0.941455	−	0.337139i	$-0.109459\pi$
$618$	−5.23493	−	7.84778i	−0.210580	−	0.315684i
$619$	−4.63455	−	6.03986i	−0.186278	−	0.242763i	0.690874	−	0.722975i	$-0.257226\pi$
$619$	−4.63455	−	6.03986i	−0.186278	−	0.242763i	−0.877152	+	0.480213i	$0.840559\pi$
$620$	−2.29704	+	5.30932i	−0.0922515	+	0.213227i
$621$	−13.3296	+	12.1973i	−0.534900	+	0.489459i
$622$	10.8506	−	10.6824i	0.435070	−	0.428324i
$623$	4.51010	+	2.60391i	0.180693	+	0.104323i
$624$	−44.8456	+	7.79657i	−1.79526	+	0.312112i
$625$	−0.356444	+	0.205793i	−0.0142577	+	0.00823171i
$626$	0.340714	−	1.23294i	0.0136177	−	0.0492782i
$627$	−31.1685	−	26.9483i	−1.24475	−	1.07621i
$628$	1.20841	−	8.18786i	0.0482208	−	0.326731i
$629$	−0.510930	+	1.23350i	−0.0203721	+	0.0491827i
$630$	7.04840	−	12.3868i	0.280815	−	0.493501i
$631$	−22.9070	−	22.9070i	−0.911912	−	0.911912i	0.0845110	−	0.996423i	$-0.473067\pi$
$631$	−22.9070	−	22.9070i	−0.911912	−	0.911912i	−0.996423	+	0.0845110i	$0.973067\pi$
$632$	1.93044	−	3.16964i	0.0767887	−	0.126081i
$633$	15.3521	−	13.6558i	0.610192	−	0.542770i
$634$	18.5713	−	23.8150i	0.737562	−	0.945815i
$635$	62.8151	−	8.26976i	2.49274	−	0.328175i
$636$	1.14949	−	15.4972i	0.0455802	−	0.614504i
$637$	5.26158	−	39.9657i	0.208471	−	1.58350i
$638$	−0.241525	+	30.9084i	−0.00956207	+	1.22367i
$639$	17.4839	+	40.5842i	0.691653	+	1.60548i
$640$	−36.8525	−	17.6836i	−1.45672	−	0.699007i
$641$	−26.2204	−	15.1384i	−1.03565	−	0.597930i	−0.117048	−	0.993126i	$-0.537343\pi$
$641$	−26.2204	−	15.1384i	−1.03565	−	0.597930i	−0.918597	+	0.395196i	$0.870677\pi$
$642$	2.39291	+	4.86182i	0.0944405	+	0.191881i
$643$	−20.2192	+	26.3502i	−0.797368	+	1.03915i	0.200859	+	0.979620i	$0.435627\pi$
$643$	−20.2192	+	26.3502i	−0.797368	+	1.03915i	−0.998227	+	0.0595298i	$0.981040\pi$
$644$	5.64950	−	3.14506i	0.222621	−	0.123933i
$645$	24.7299	+	36.4528i	0.973739	+	1.43533i
$646$	0.620920	−	4.44752i	0.0244298	−	0.174985i
$647$	5.86709	+	5.86709i	0.230659	+	0.230659i	0.812968	−	0.582309i	$-0.197850\pi$
$647$	5.86709	+	5.86709i	0.230659	+	0.230659i	−0.582309	+	0.812968i	$0.697850\pi$
$648$	−18.0847	−	17.9149i	−0.710434	−	0.703764i
$649$	−6.27680	+	6.27680i	−0.246386	+	0.246386i
$650$	45.0858	+	59.7174i	1.76841	+	2.34231i
$651$	1.06691	−	0.723804i	0.0418156	−	0.0283681i
$652$	−9.33346	+	11.7778i	−0.365526	+	0.461255i
$653$	4.61523	+	3.54139i	0.180608	+	0.138585i	0.695109	−	0.718904i	$-0.255356\pi$
$653$	4.61523	+	3.54139i	0.180608	+	0.138585i	−0.514501	+	0.857490i	$0.672023\pi$
$654$	13.2160	−	38.8341i	0.516785	−	1.51853i
$655$	−14.7031	+	25.4666i	−0.574499	+	0.995061i
$656$	−8.89918	−	9.47363i	−0.347455	−	0.369883i
$657$	31.9049	−	13.7448i	1.24473	−	0.536237i
$658$	−1.90981	−	1.93989i	−0.0744520	−	0.0756248i
$659$	36.9578	+	4.86559i	1.43967	+	0.189536i	0.809591	−	0.586994i	$-0.199689\pi$
$659$	36.9578	+	4.86559i	1.43967	+	0.189536i	0.630080	+	0.776530i	$0.283022\pi$
$660$	46.0495	+	23.2029i	1.79248	+	0.903172i
$661$	−3.76189	−	28.5744i	−0.146321	−	1.11141i	−0.894228	−	0.447612i	$-0.852275\pi$
$661$	−3.76189	−	28.5744i	−0.146321	−	1.11141i	0.747907	−	0.663803i	$-0.231059\pi$
$662$	−4.02778	+	0.498281i	−0.156544	+	0.0193662i
$663$	4.15941	+	4.67608i	0.161538	+	0.181604i
$664$	−21.1824	−	3.29554i	−0.822037	−	0.127892i
$665$	−13.7145	+	13.7145i	−0.531826	+	0.531826i
$666$	−2.72806	−	9.93193i	−0.105710	−	0.384854i
$667$	−17.0417	−	7.05892i	−0.659859	−	0.273322i
$668$	6.58027	−	1.65341i	0.254598	−	0.0639723i
$669$	−8.59379	+	9.93962i	−0.332255	+	0.384288i
$670$	−47.1371	+	26.7257i	−1.82107	+	1.03250i
$671$	−20.1894	−	34.9691i	−0.779403	−	1.34997i
$672$	4.81595	+	7.73271i	0.185779	+	0.298296i
$673$	−2.87781	+	4.98451i	−0.110931	+	0.192139i	−0.916146	−	0.400845i	$-0.868717\pi$
$673$	−2.87781	+	4.98451i	−0.110931	+	0.192139i	0.805215	+	0.592983i	$0.202050\pi$
$674$	0.0686020	−	8.77911i	0.00264245	−	0.338159i
$675$	−12.6111	+	39.9003i	−0.485403	+	1.53576i
$676$	−43.3212	+	41.9878i	−1.66620	+	1.61492i
$677$	2.13040	−	1.63471i	0.0818778	−	0.0628271i	−0.567011	−	0.823710i	$-0.691900\pi$
$677$	2.13040	−	1.63471i	0.0818778	−	0.0628271i	0.648889	+	0.760883i	$0.275234\pi$
$678$	−0.995610	+	4.98509i	−0.0382362	+	0.191451i
$679$	−12.4661	−	3.34029i	−0.478406	−	0.128189i
$680$	0.602747	+	5.58756i	0.0231143	+	0.214273i
$681$	−5.39711	−	1.78980i	−0.206818	−	0.0685854i
$682$	2.81071	+	3.72286i	0.107628	+	0.142556i
$683$	−23.6840	−	9.81022i	−0.906242	−	0.375378i	−0.119625	−	0.992819i	$-0.538169\pi$
$683$	−23.6840	−	9.81022i	−0.906242	−	0.375378i	−0.786617	+	0.617441i	$0.788169\pi$
$684$	17.2750	+	30.0285i	0.660526	+	1.14817i
$685$	−2.31144	−	5.58032i	−0.0883157	−	0.213213i
$686$	−16.7176	+	4.33975i	−0.638282	+	0.165692i
$687$	−0.0201229	+	0.344118i	−0.000767736	+	0.0131289i
$688$	−28.0171	+	2.80100i	−1.06814	+	0.106787i
$689$	−14.7364	−	25.5241i	−0.561410	−	0.972391i
$690$	−23.1517	+	20.2718i	−0.881370	+	0.771734i
$691$	−1.33160	+	10.1145i	−0.0506564	+	0.384774i	0.947271	+	0.320432i	$0.103828\pi$
$691$	−1.33160	+	10.1145i	−0.0506564	+	0.384774i	−0.997928	+	0.0643417i	$0.979505\pi$
$692$	−5.39967	+	2.13838i	−0.205265	+	0.0812890i
$693$	−5.88558	−	9.87054i	−0.223575	−	0.374951i
$694$	14.7149	−	34.7542i	0.558568	−	1.31925i
$695$	11.8640	+	44.2769i	0.450026	+	1.67952i
$696$	8.75614	−	24.4687i	0.331901	−	0.927482i
$697$	−0.462529	+	1.72618i	−0.0175196	+	0.0653839i
$698$	25.0266	+	19.5162i	0.947273	+	0.738699i
$699$	−4.53118	+	3.07399i	−0.171385	+	0.116269i
$700$	7.68936	−	12.8503i	0.290631	−	0.485696i
$701$	−13.6335	−	32.9141i	−0.514929	−	1.24315i	−0.940984	−	0.338451i	$-0.890097\pi$
$701$	−13.6335	−	32.9141i	−0.514929	−	1.24315i	0.426055	−	0.904697i	$-0.359903\pi$
$702$	−47.4729	−	8.78804i	−1.79175	−	0.331683i
$703$			14.0170i			0.528662i
$704$	−27.0610	+	18.8175i	−1.01990	+	0.709211i
$705$	10.8226	+	7.12173i	0.407602	+	0.268220i
$706$	−6.33756	+	3.59326i	−0.238517	+	0.135234i
$707$	−7.18191	−	5.51087i	−0.270103	−	0.207258i
$708$	6.72187	−	3.24339i	0.252623	−	0.121894i
$709$	10.4540	+	13.6239i	0.392607	+	0.511655i	0.947277	−	0.320415i	$-0.103822\pi$
$709$	10.4540	+	13.6239i	0.392607	+	0.511655i	−0.554671	+	0.832070i	$0.687156\pi$
$710$	28.2574	+	69.7562i	1.06048	+	2.61790i
$711$	3.08887	−	2.44003i	0.115842	−	0.0915081i
$712$	11.4620	−	10.9368i	0.429555	−	0.409873i
$713$	−2.68893	+	0.720497i	−0.100701	+	0.0269828i
$714$	0.554838	−	1.12291i	0.0207643	−	0.0420237i
$715$	96.9611	−	12.7652i	3.62614	−	0.477390i
$716$	−3.63520	+	4.58723i	−0.135854	+	0.171433i
$717$	−12.5167	−	36.0375i	−0.467445	−	1.34585i
$718$	−9.64103	+	2.50273i	−0.359800	+	0.0934010i
$719$		−	16.7467i		−	0.624547i	−0.949992	−	0.312273i	$-0.898909\pi$
$719$		−	16.7467i		−	0.624547i	0.949992	−	0.312273i	$-0.101091\pi$
$720$	−30.1256	−	31.1787i	−1.12272	−	1.16196i
$721$			3.58074i			0.133354i
$722$	−5.09455	−	19.6253i	−0.189600	−	0.730377i
$723$	15.4335	−	17.8505i	0.573978	−	0.663866i
$724$	−2.72678	−	23.5504i	−0.101340	−	0.875245i
$725$	−42.3554	+	5.57620i	−1.57304	+	0.207095i
$726$	12.1753	−	8.12166i	0.451869	−	0.301423i
$727$	24.7853	−	6.64120i	0.919236	−	0.246308i	0.231977	−	0.972721i	$-0.425481\pi$
$727$	24.7853	−	6.64120i	0.919236	−	0.246308i	0.687259	+	0.726413i	$0.258814\pi$
$728$	15.8030	+	6.98419i	0.585700	+	0.258851i
$729$	−11.3765	−	24.4862i	−0.421353	−	0.906897i
$730$	54.8383	−	22.2143i	2.02965	−	0.822189i
$731$	2.35668	+	3.07128i	0.0871649	+	0.113596i
$732$	6.33710	+	33.3533i	0.234226	+	1.23277i
$733$	−31.5199	−	24.1861i	−1.16422	−	0.893334i	−0.168491	−	0.985703i	$-0.553889\pi$
$733$	−31.5199	−	24.1861i	−1.16422	−	0.893334i	−0.995725	+	0.0923690i	$0.970556\pi$
$734$	5.54450	+	9.77904i	0.204651	+	0.360951i
$735$	34.3149	−	17.2236i	1.26572	−	0.635301i
$736$	−4.34493	−	19.1841i	−0.160156	−	0.707134i
$737$			43.6939i			1.60949i
$738$	−5.35550	−	12.7036i	−0.197139	−	0.467626i
$739$	0.564827	+	1.36361i	0.0207775	+	0.0501613i	0.933928	−	0.357462i	$-0.116358\pi$
$739$	0.564827	+	1.36361i	0.0207775	+	0.0501613i	−0.913150	+	0.407623i	$0.866358\pi$
$740$	−4.27487	−	17.0132i	−0.157147	−	0.625418i
$741$	59.1310	+	28.6445i	2.17223	+	1.05228i
$742$	−3.62724	+	4.65140i	−0.133160	+	0.170758i
$743$	1.05031	−	3.91983i	0.0385323	−	0.143805i	−0.943980	−	0.330003i	$-0.892950\pi$
$743$	1.05031	−	3.91983i	0.0385323	−	0.143805i	0.982512	+	0.186199i	$0.0596168\pi$
$744$	−1.19962	−	3.73409i	−0.0439802	−	0.136898i
$745$	−6.47184	−	24.1532i	−0.237110	−	0.884906i
$746$	26.7271	+	11.3162i	0.978550	+	0.414316i
$747$	−19.8495	−	11.0905i	−0.726254	−	0.405779i
$748$	4.15917	+	1.79944i	0.152074	+	0.0657940i
$749$	0.268471	−	2.03924i	0.00980971	−	0.0745122i
$750$	−8.70530	+	25.5799i	−0.317873	+	0.934045i
$751$	−5.65276	−	9.79086i	−0.206272	−	0.357274i	0.744265	−	0.667884i	$-0.232800\pi$
$751$	−5.65276	−	9.79086i	−0.206272	−	0.357274i	−0.950537	+	0.310610i	$0.899467\pi$
$752$	−7.29769	+	3.91449i	−0.266119	+	0.142747i
$753$	−41.8017	−	27.5074i	−1.52334	−	1.00242i
$754$	−12.3845	−	47.7079i	−0.451019	−	1.73742i
$755$	−12.3210	−	29.7455i	−0.448407	−	1.08255i
$756$	1.93704	+	9.46624i	0.0704496	+	0.344284i
$757$	−41.6073	−	17.2343i	−1.51224	−	0.626391i	−0.536224	−	0.844076i	$-0.680150\pi$
$757$	−41.6073	−	17.2343i	−1.51224	−	0.626391i	−0.976019	+	0.217685i	$0.930150\pi$
$758$	26.5987	−	20.0816i	0.966107	−	0.729397i
$759$	5.01213	+	24.3023i	0.181929	+	0.882118i
$760$	28.2953	+	51.7749i	1.02638	+	1.87807i
$761$	38.4314	+	10.2977i	1.39314	+	0.373290i	0.875875	−	0.482538i	$-0.160285\pi$
$761$	38.4314	+	10.2977i	1.39314	+	0.373290i	0.517261	+	0.855828i	$0.326952\pi$
$762$	−28.3471	+	32.2732i	−1.02691	+	1.16913i
$763$	−12.3530	+	9.47881i	−0.447210	+	0.343156i
$764$	29.3675	+	0.458996i	1.06248	+	0.0166059i
$765$	−1.46158	+	5.77892i	−0.0528434	+	0.208937i
$766$	8.15477	+	0.0637233i	0.294644	+	0.00230242i
$767$	7.07758	−	12.2587i	0.255557	−	0.442637i
$768$	26.6956	−	7.43931i	0.963296	−	0.268443i
$769$	13.5904	+	23.5392i	0.490082	+	0.848846i	0.999935	−	0.0114151i	$-0.00363361\pi$
$769$	13.5904	+	23.5392i	0.490082	+	0.848846i	−0.509853	+	0.860261i	$0.670300\pi$
$770$	−9.65360	−	17.0264i	−0.347892	−	0.613589i
$771$	10.3894	+	29.9128i	0.374166	+	1.07728i
$772$	25.2992	−	42.2795i	0.910537	−	1.52167i
$773$	0.765917	+	0.317253i	0.0275481	+	0.0114108i	0.396415	−	0.918071i	$-0.370254\pi$
$773$	0.765917	+	0.317253i	0.0275481	+	0.0114108i	−0.368867	+	0.929482i	$0.620254\pi$
$774$	−28.8950	−	7.54869i	−1.03861	−	0.271332i
$775$	−4.55894	+	4.55894i	−0.163762	+	0.163762i
$776$	−20.4220	+	33.5315i	−0.733109	+	1.20371i
$777$	−1.23059	+	3.71081i	−0.0441470	+	0.133125i
$778$	0.0809765	+	0.654562i	0.00290315	+	0.0234672i
$779$	2.44892	+	18.6014i	0.0877416	+	0.666464i
$780$	−80.5065	−	16.7338i	−2.88259	−	0.599165i
$781$	60.1694	+	7.92146i	2.15303	+	0.283452i
$782$	−1.92720	+	1.89731i	−0.0689164	+	0.0678477i
$783$	17.7329	−	21.1034i	0.633723	−	0.754173i
$784$	−0.766972	+	24.5302i	−0.0273919	+	0.876078i
$785$	7.47564	−	12.9482i	0.266817	−	0.462141i
$786$	−3.87434	−	19.5568i	−0.138193	−	0.697567i
$787$	−3.38908	−	2.60053i	−0.120808	−	0.0926989i	0.546591	−	0.837400i	$-0.315925\pi$
$787$	−3.38908	−	2.60053i	−0.120808	−	0.0926989i	−0.667398	+	0.744701i	$0.732592\pi$
$788$	−4.49838	−	38.8512i	−0.160248	−	1.38402i
$789$	0.492854	+	6.78706i	0.0175461	+	0.241626i
$790$	5.35052	−	4.03957i	0.190363	−	0.143721i
$791$	1.36442	−	1.36442i	0.0485132	−	0.0485132i
$792$	−33.8519	+	8.73173i	−1.20288	+	0.310268i
$793$	45.5302	+	45.5302i	1.61683	+	1.61683i
$794$	8.79315	+	1.22761i	0.312057	+	0.0435664i
$795$	12.2384	−	25.2638i	0.434052	−	0.896016i
$796$	3.75130	+	1.06826i	0.132961	+	0.0378635i
$797$	15.3574	−	20.0141i	0.543986	−	0.708937i	−0.437769	−	0.899088i	$-0.644231\pi$
$797$	15.3574	−	20.0141i	0.543986	−	0.708937i	0.981755	+	0.190151i	$0.0608978\pi$
$798$	0.870186	−	13.1208i	0.0308043	−	0.464470i
$799$	0.986048	+	0.569295i	0.0348839	+	0.0201402i
$800$	−30.9301	−	33.4466i	−1.09354	−	1.18252i
$801$	15.4325	−	6.64842i	0.545280	−	0.234910i
$802$	−2.21419	−	0.0173022i	−0.0781859	−	0.000610963i
$803$	6.22739	−	47.3017i	0.219760	−	1.66924i
$804$	12.1072	−	34.6850i	0.426986	−	1.22324i
$805$	11.5805	−	1.52461i	0.408160	−	0.0537353i
$806$	−5.86584	−	4.57428i	−0.206615	−	0.161122i
$807$	−4.31082	−	20.9019i	−0.151748	−	0.735780i
$808$	−22.2350	+	16.2479i	−0.782224	+	0.571597i
$809$	17.2801	+	17.2801i	0.607535	+	0.607535i	0.942301	−	0.334766i	$-0.108657\pi$
$809$	17.2801	+	17.2801i	0.607535	+	0.607535i	−0.334766	+	0.942301i	$0.608657\pi$
$810$	−18.4583	−	42.1179i	−0.648560	−	1.47987i
$811$	6.13280	−	14.8059i	0.215352	−	0.519905i	−0.778878	−	0.627175i	$-0.784211\pi$
$811$	6.13280	−	14.8059i	0.215352	−	0.519905i	0.994230	+	0.107270i	$0.0342110\pi$
$812$	−7.91888	+	5.88206i	−0.277898	+	0.206420i
$813$	−8.51498	+	44.4404i	−0.298633	+	1.55859i
$814$	−13.6342	−	3.76771i	−0.477880	−	0.132058i
$815$	−23.5099	+	13.5735i	−0.823516	+	0.475457i
$816$	−2.80301	−	2.58089i	−0.0981249	−	0.0903492i
$817$	35.1980	+	20.3216i	1.23142	+	0.710961i
$818$	4.39375	+	4.46296i	0.153624	+	0.156044i
$819$	13.1393	+	12.7745i	0.459126	+	0.446376i
$820$	−8.64538	−	21.8306i	−0.301910	−	0.762359i
$821$	21.9275	+	28.5765i	0.765275	+	0.997326i	0.999683	+	0.0251874i	$0.00801825\pi$
$821$	21.9275	+	28.5765i	0.765275	+	0.997326i	−0.234408	+	0.972138i	$0.575315\pi$
$822$	3.67134	+	1.81404i	0.128053	+	0.0632720i
$823$	−4.79009	+	17.8769i	−0.166972	+	0.623148i	0.830808	+	0.556559i	$0.187879\pi$
$823$	−4.79009	+	17.8769i	−0.166972	+	0.623148i	−0.997780	+	0.0665897i	$0.978788\pi$
$824$	10.4528	+	3.06516i	0.364141	+	0.106780i
$825$	38.1953	+	42.9398i	1.32979	+	1.49497i
$826$	−2.80572	−	0.391708i	−0.0976236	−	0.0136293i
$827$	3.56966	−	8.61791i	0.124129	−	0.299674i	−0.849584	−	0.527454i	$-0.823147\pi$
$827$	3.56966	−	8.61791i	0.124129	−	0.299674i	0.973713	+	0.227780i	$0.0731467\pi$
$828$	2.75522	−	20.6804i	0.0957505	−	0.718693i
$829$	−6.99775	+	2.89856i	−0.243042	+	0.100671i	−0.500880	−	0.865517i	$-0.666990\pi$
$829$	−6.99775	+	2.89856i	−0.243042	+	0.100671i	0.257838	+	0.966188i	$0.416990\pi$
$830$	−33.3850	−	19.6243i	−1.15881	−	0.681168i
$831$	−8.84123	−	17.6146i	−0.306699	−	0.611042i
$832$	33.9157	−	40.1533i	1.17581	−	1.39206i
$833$	2.92223	−	1.68715i	0.101249	−	0.0584562i
$834$	−25.8269	−	17.2859i	−0.894311	−	0.598562i
$835$	12.1517	+	1.59980i	0.420526	+	0.0553632i
$836$	47.5713	+	0.743512i	1.64529	+	0.0257149i
$837$	0.184355	−	4.15588i	0.00637225	−	0.143648i
$838$	10.2323	−	4.14497i	0.353468	−	0.143186i
$839$	7.01642	−	1.88004i	0.242234	−	0.0649063i	−0.135659	−	0.990756i	$-0.543315\pi$
$839$	7.01642	−	1.88004i	0.242234	−	0.0649063i	0.377893	+	0.925849i	$0.376649\pi$
$840$	2.94534	+	16.1908i	0.101624	+	0.558635i
$841$	−0.829666	−	0.222308i	−0.0286092	−	0.00766580i
$842$	−34.7308	+	4.29658i	−1.19690	+	0.148070i
$843$	−51.9733	+	3.77413i	−1.79006	+	0.129988i
$844$	−3.46400	+	23.4711i	−0.119236	+	0.807909i
$845$	−100.688	+	41.7063i	−3.46377	+	1.43474i
$846$	−8.70112	+	1.20103i	−0.299151	+	0.0412922i
$847$	−5.55529			−0.190882
$848$	10.4733	+	14.5702i	0.359654	+	0.500342i
$849$	−26.8127	−	1.56792i	−0.920210	−	0.0538109i
$850$	−1.66833	+	6.03721i	−0.0572234	+	0.207074i
$851$	5.13886	−	6.69709i	0.176158	−	0.229573i
$852$	−45.5686	−	22.9606i	−1.56115	−	0.786616i
$853$	19.8078	−	15.1991i	0.678207	−	0.520406i	−0.211246	−	0.977433i	$-0.567752\pi$
$853$	19.8078	−	15.1991i	0.678207	−	0.520406i	0.889453	+	0.457026i	$0.151086\pi$
$854$	5.02435	−	11.8667i	0.171930	−	0.406071i
$855$	9.04121	+	61.9247i	0.309203	+	2.11778i
$856$	−5.72308	−	2.52933i	−0.195611	−	0.0864506i
$857$	−5.37911	−	20.0751i	−0.183747	−	0.685752i	−0.994895	−	0.100912i	$-0.967824\pi$
$857$	−5.37911	−	20.0751i	−0.183747	−	0.685752i	0.811149	−	0.584840i	$-0.198843\pi$
$858$	−43.7564	+	49.8168i	−1.49382	+	1.70072i
$859$	−4.71942	−	35.8476i	−0.161025	−	1.22310i	−0.860876	−	0.508815i	$-0.830084\pi$
$859$	−4.71942	−	35.8476i	−0.161025	−	1.22310i	0.699851	−	0.714289i	$-0.253250\pi$
$860$	−48.9193	−	13.9308i	−1.66813	−	0.475037i
$861$	−0.984741	+	5.13945i	−0.0335599	+	0.175152i
$862$	−44.2792	−	26.0280i	−1.50815	−	0.886518i
$863$	19.0329			0.647889			0.323944	−	0.946076i	$-0.394991\pi$
$863$	19.0329			0.647889			0.323944	+	0.946076i	$0.394991\pi$
$864$	29.2917	+	2.44865i	0.996524	+	0.0833047i
$865$	−10.4914			−0.356717
$866$	26.6676	+	15.6756i	0.906201	+	0.532680i
$867$	5.44239	−	28.4043i	0.184833	−	0.964661i
$868$	−0.407732	+	1.43179i	−0.0138393	+	0.0485981i
$869$	−0.705625	−	5.35976i	−0.0239367	−	0.181817i
$870$	30.9814	−	35.2724i	1.05037	−	1.19585i
$871$	−18.0334	−	67.3017i	−0.611040	−	2.28043i
$872$	17.0959	+	44.1746i	0.578942	+	1.49594i
$873$	−32.6770	+	25.8129i	−1.10595	+	0.873636i
$874$	−11.0701	+	26.1458i	−0.374451	+	0.884394i
$875$	8.13689	−	6.24366i	0.275077	−	0.211074i
$876$	−18.0502	+	35.8233i	−0.609861	+	1.21036i
$877$	−7.38836	+	9.62870i	−0.249487	+	0.325138i	−0.901262	−	0.433275i	$-0.857358\pi$
$877$	−7.38836	+	9.62870i	−0.249487	+	0.325138i	0.651775	+	0.758413i	$0.274025\pi$
$878$	3.22516	−	11.6709i	0.108844	−	0.393873i
$879$	45.5277	+	2.66231i	1.53561	+	0.0897975i
$880$	−57.9666	+	13.6057i	−1.95406	+	0.458649i
$881$	−52.9872			−1.78518			−0.892592	−	0.450866i	$-0.851115\pi$
$881$	−52.9872			−1.78518			−0.892592	+	0.450866i	$0.851115\pi$
$882$	−9.81072	+	24.1113i	−0.330344	+	0.811871i
$883$	30.5063	−	12.6361i	1.02662	−	0.425240i	0.195128	−	0.980778i	$-0.437488\pi$
$883$	30.5063	−	12.6361i	1.02662	−	0.425240i	0.831491	+	0.555538i	$0.187488\pi$
$884$	−7.14903	−	1.05509i	−0.240448	−	0.0354866i
$885$	13.4470	−	0.976480i	0.452017	−	0.0328240i
$886$	−25.6912	+	3.17829i	−0.863114	+	0.106777i
$887$	13.4356	+	3.60006i	0.451123	+	0.120878i	0.477225	−	0.878781i	$-0.341643\pi$
$887$	13.4356	+	3.60006i	0.451123	+	0.120878i	−0.0261017	+	0.999659i	$0.508309\pi$
$888$	9.77910	+	6.76879i	0.328165	+	0.227146i
$889$	15.7490	−	4.21993i	0.528204	−	0.141532i
$890$	26.5254	−	10.7451i	0.889135	−	0.360178i
$891$	−36.8851	−	3.80301i	−1.23570	−	0.127406i
$892$	0.237105	−	15.1705i	0.00793887	−	0.507944i
$893$	11.8514	+	1.56027i	0.396592	+	0.0522123i
$894$	14.0886	+	9.42952i	0.471195	+	0.315370i
$895$	−9.15666	+	5.28660i	−0.306073	+	0.176712i
$896$	−9.99661	−	3.27396i	−0.333963	−	0.109375i
$897$	−17.7503	−	35.3642i	−0.592665	−	1.18078i
$898$	20.9401	+	12.3089i	0.698779	+	0.410754i
$899$	3.92368	−	1.62524i	0.130862	−	0.0542049i
$900$	−18.4219	−	44.6699i	−0.614062	−	1.48900i
$901$	0.944114	−	2.27929i	0.0314530	−	0.0759343i
$902$	−18.7517	−	2.61793i	−0.624363	−	0.0871675i
$903$	7.53409	+	8.46996i	0.250719	+	0.281863i
$904$	−2.81502	−	5.15094i	−0.0936261	−	0.171318i
$905$	11.0845	−	41.3679i	0.368461	−	1.37512i
$906$	19.5699	+	9.66964i	0.650165	+	0.321252i
$907$	−20.3401	−	26.5078i	−0.675383	−	0.880176i	0.322408	−	0.946601i	$-0.395508\pi$
$907$	−20.3401	−	26.5078i	−0.675383	−	0.880176i	−0.997791	+	0.0664243i	$0.978841\pi$
$908$	6.10453	−	2.41752i	0.202586	−	0.0802281i
$909$	−28.1048	+	7.95640i	−0.932178	+	0.263897i
$910$	21.8966	+	22.2415i	0.725866	+	0.737299i
$911$	2.77440	+	1.60180i	0.0919201	+	0.0530701i	0.545255	−	0.838270i	$-0.316433\pi$
$911$	2.77440	+	1.60180i	0.0919201	+	0.0530701i	−0.453335	+	0.891340i	$0.649766\pi$
$912$	−37.5569	−	13.7718i	−1.24363	−	0.456029i
$913$	−27.0432	+	15.6134i	−0.895001	+	0.516729i
$914$	27.3920	+	7.56955i	0.906046	+	0.250379i
$915$	−11.5410	+	60.2338i	−0.381535	+	1.99127i
$916$	−0.237342	−	0.319528i	−0.00784199	−	0.0105575i
$917$	−2.89596	+	6.99147i	−0.0956331	+	0.230879i
$918$	−1.83551	−	3.60048i	−0.0605809	−	0.118834i
$919$	−38.5062	−	38.5062i	−1.27020	−	1.27020i	−0.945982	−	0.324220i	$-0.894898\pi$
$919$	−38.5062	−	38.5062i	−1.27020	−	1.27020i	−0.324220	−	0.945982i	$-0.605102\pi$
$920$	5.46249	−	35.1106i	0.180093	−	1.15756i
$921$	−8.51625	−	41.2927i	−0.280620	−	1.36064i
$922$	−22.4366	−	17.4964i	−0.738909	−	0.576214i
$923$	−95.9484	+	12.6318i	−3.15818	+	0.415782i
$924$	12.5286	+	4.37323i	0.412160	+	0.143869i
$925$	2.55188	−	19.3834i	0.0839052	−	0.637323i
$926$	2.01235	+	0.0157250i	0.0661300	+	0.000516755i
$927$	9.26429	+	6.90371i	0.304279	+	0.226748i
$928$	10.3921	+	28.1517i	0.341137	+	0.924125i
$929$	5.33687	+	3.08124i	0.175097	+	0.101092i	0.584987	−	0.811043i	$-0.301100\pi$
$929$	5.33687	+	3.08124i	0.175097	+	0.101092i	−0.409890	+	0.912135i	$0.634433\pi$
$930$	0.468860	−	7.06952i	0.0153745	−	0.231819i
$931$	21.5657	−	28.1050i	0.706788	−	0.921104i
$932$	1.73164	−	6.08080i	0.0567216	−	0.199183i
$933$	−8.13016	+	16.7831i	−0.266169	+	0.549455i
$934$	48.1370	+	6.72043i	1.57509	+	0.219899i
$935$	5.78867	+	5.78867i	0.189310	+	0.189310i
$936$	48.5383	−	27.4209i	1.58653	−	0.896281i
$937$	6.77290	−	6.77290i	0.221261	−	0.221261i	−0.587768	−	0.809029i	$-0.699993\pi$
$937$	6.77290	−	6.77290i	0.221261	−	0.221261i	0.809029	+	0.587768i	$0.199993\pi$
$938$	−11.1289	+	8.40219i	−0.363373	+	0.274341i
$939$	0.113465	+	1.56252i	0.00370279	+	0.0509909i
$940$	−14.8605	+	1.72062i	−0.484697	+	0.0561206i
$941$	34.7292	+	26.6486i	1.13214	+	0.868720i	0.992592	−	0.121495i	$-0.0387689\pi$
$941$	34.7292	+	26.6486i	1.13214	+	0.868720i	0.139546	+	0.990216i	$0.455436\pi$
$942$	1.96986	+	9.94341i	0.0641816	+	0.323974i
$943$	5.64951	−	9.78524i	0.183973	−	0.318651i
$944$	−3.54520	+	7.85509i	−0.115386	+	0.255661i
$945$	−3.04298	+	17.1875i	−0.0989881	+	0.559108i
$946$	−29.2277	+	28.7744i	−0.950274	+	0.935538i
$947$	19.6750	+	2.59026i	0.639351	+	0.0841722i	0.443231	−	0.896408i	$-0.353832\pi$
$947$	19.6750	+	2.59026i	0.639351	+	0.0841722i	0.196121	+	0.980580i	$0.437166\pi$
$948$	−0.924999	+	4.45019i	−0.0300426	+	0.144535i
$949$	9.93041	+	75.4290i	0.322355	+	2.44853i
$950$	8.07346	+	65.2606i	0.261938	+	2.11733i
$951$	−11.6424	+	35.1074i	−0.377530	+	1.13844i
$952$	0.341473	+	1.40538i	0.0110672	+	0.0455485i
$953$	15.0077	−	15.0077i	0.486147	−	0.486147i	−0.420941	−	0.907088i	$-0.638300\pi$
$953$	15.0077	−	15.0077i	0.486147	−	0.486147i	0.907088	+	0.420941i	$0.138300\pi$
$954$	5.04099	+	18.3525i	0.163208	+	0.594185i
$955$	49.0189	+	20.3043i	1.58622	+	0.657032i
$956$	37.8005	+	22.6190i	1.22255	+	0.731551i
$957$	−12.4205	−	35.7605i	−0.401497	−	1.15597i
$958$	−22.2038	−	39.1617i	−0.717372	−	1.26526i
$959$	−0.777190	−	1.34613i	−0.0250968	−	0.0434689i
$960$	49.7849	+	5.26154i	1.60680	+	0.169816i
$961$	−15.1795	+	26.2917i	−0.489662	+	0.848120i
$962$	22.5558	+	0.176257i	0.727230	+	0.00568274i
$963$	−4.75842	−	4.62628i	−0.153338	−	0.149080i
$964$	−0.425815	+	27.2445i	−0.0137146	+	0.877485i
$965$	70.6130	−	54.1832i	2.27311	−	1.74422i
$966$	−5.22604	+	5.94986i	−0.168145	+	0.191433i
$967$	14.6253	+	3.91885i	0.470319	+	0.126022i	0.486191	−	0.873852i	$-0.338386\pi$
$967$	14.6253	+	3.91885i	0.470319	+	0.126022i	−0.0158720	+	0.999874i	$0.505052\pi$
$968$	−4.75539	+	16.2168i	−0.152844	+	0.521229i
$969$	1.11092	+	5.38654i	0.0356880	+	0.173041i
$970$	−56.6029	+	42.7344i	−1.81741	+	1.37212i
$971$	23.8551	+	9.88110i	0.765546	+	0.317099i	0.731067	−	0.682306i	$-0.239023\pi$
$971$	23.8551	+	9.88110i	0.765546	+	0.317099i	0.0344790	+	0.999405i	$0.489023\pi$
$972$	28.2262	+	13.2394i	0.905356	+	0.424653i
$973$	4.51426	+	10.8984i	0.144721	+	0.349387i
$974$	−0.00386192	−	0.0148769i	−0.000123744	−	0.000476687i
$975$	−76.5544	−	50.3762i	−2.45170	−	1.61333i
$976$	−30.3401	−	24.8250i	−0.971164	−	0.794629i
$977$	12.5249	+	21.6937i	0.400706	+	0.694043i	0.993811	−	0.111082i	$-0.0354315\pi$
$977$	12.5249	+	21.6937i	0.400706	+	0.694043i	−0.593105	+	0.805125i	$0.702098\pi$
$978$	5.92961	−	17.4237i	0.189608	−	0.557149i
$979$	3.01221	−	22.8800i	0.0962705	−	0.731247i
$980$	−17.6041	+	40.6896i	−0.562343	+	1.29978i
$981$	0.707326	+	50.2357i	0.0225832	+	1.60390i
$982$	45.4687	+	19.2514i	1.45097	+	0.614336i
$983$	10.5938	+	39.5367i	0.337891	+	1.26103i	0.900701	+	0.434440i	$0.143054\pi$
$983$	10.5938	+	39.5367i	0.337891	+	1.26103i	−0.562810	+	0.826586i	$0.690280\pi$
$984$	14.1600	+	7.27406i	0.451404	+	0.231889i
$985$	18.2861	−	68.2447i	0.582644	−	2.17446i
$986$	2.53717	−	3.25355i	0.0808000	−	0.103614i
$987$	3.00051	+	1.45352i	0.0955074	+	0.0462661i
$988$	−73.5810	+	18.4885i	−2.34092	+	0.588198i
$989$	−9.36679	−	22.6134i	−0.297847	−	0.719065i
$990$	−62.6639	−	7.85078i	−1.99159	−	0.249514i
$991$		−	46.6429i		−	1.48166i	−0.671692	−	0.740830i	$-0.734432\pi$
$991$		−	46.6429i		−	1.48166i	0.671692	−	0.740830i	$-0.265568\pi$
$992$	3.83061	+	2.41587i	0.121622	+	0.0767039i
$993$	4.44242	−	2.22977i	0.140976	−	0.0707596i
$994$	9.55277	+	16.8486i	0.302996	+	0.534404i
$995$	5.58997	+	4.28933i	0.177214	+	0.135981i
$996$	25.7937	−	4.90078i	0.817305	−	0.155287i
$997$	2.01947	+	2.63183i	0.0639574	+	0.0833509i	0.824237	−	0.566245i	$-0.191605\pi$
$997$	2.01947	+	2.63183i	0.0639574	+	0.0833509i	−0.760279	+	0.649596i	$0.774938\pi$
$998$	−21.1345	+	8.56132i	−0.669000	+	0.271004i
$999$	7.22823	+	10.3383i	0.228691	+	0.327090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.30	✓	368
3.2	odd	2		864.2.bn.a.683.17		368
9.4	even	3		864.2.bn.a.395.33		368
9.5	odd	6	inner	288.2.bf.a.203.14	yes	368
32.3	odd	8	inner	288.2.bf.a.227.14	yes	368
96.35	even	8		864.2.bn.a.35.33		368
288.67	odd	24		864.2.bn.a.611.17		368
288.131	even	24	inner	288.2.bf.a.131.30	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.30	✓	368	1.1	even	1	trivial
288.2.bf.a.131.30	yes	368	288.131	even	24	inner
288.2.bf.a.203.14	yes	368	9.5	odd	6	inner
288.2.bf.a.227.14	yes	368	32.3	odd	8	inner
864.2.bn.a.35.33		368	96.35	even	8
864.2.bn.a.395.33		368	9.4	even	3
864.2.bn.a.611.17		368	288.67	odd	24
864.2.bn.a.683.17		368	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.716655 - 1.21918i) q^{2} +(-0.325939 + 1.70111i) q^{3} +(-0.972810 - 1.74747i) q^{4} +(-0.471581 - 3.58202i) q^{5} +(1.84037 + 1.61649i) q^{6} +(-0.240641 - 0.898083i) q^{7} +(-2.82765 - 0.0662985i) q^{8} +(-2.78753 - 1.10892i) q^{9} +O(q^{10})\)	\(q+(0.716655 - 1.21918i) q^{2} +(-0.325939 + 1.70111i) q^{3} +(-0.972810 - 1.74747i) q^{4} +(-0.471581 - 3.58202i) q^{5} +(1.84037 + 1.61649i) q^{6} +(-0.240641 - 0.898083i) q^{7} +(-2.82765 - 0.0662985i) q^{8} +(-2.78753 - 1.10892i) q^{9} +(-4.70509 - 1.99213i) q^{10} +(-3.26867 + 2.50814i) q^{11} +(3.28970 - 1.08529i) q^{12} +(3.99957 - 5.21234i) q^{13} +(-1.26738 - 0.350231i) q^{14} +(6.24710 + 0.365310i) q^{15} +(-2.10728 + 3.39991i) q^{16} +0.549959 q^{17} +(-3.34967 + 2.60379i) q^{18} +(5.33432 - 2.20955i) q^{19} +(-5.80070 + 4.30870i) q^{20} +(1.60617 - 0.116635i) q^{21} +(0.715368 + 5.78257i) q^{22} +(-3.35871 - 0.899962i) q^{23} +(1.03442 - 4.78852i) q^{24} +(-7.77883 + 2.08433i) q^{25} +(-3.48848 - 8.61165i) q^{26} +(2.79495 - 4.38044i) q^{27} +(-1.33527 + 1.29418i) q^{28} +(5.25943 + 0.692417i) q^{29} +(4.92240 - 7.35455i) q^{30} +(0.693328 - 0.400293i) q^{31} +(2.63491 + 5.00572i) q^{32} +(-3.20122 - 6.37785i) q^{33} +(0.394131 - 0.670500i) q^{34} +(-3.10347 + 1.28550i) q^{35} +(0.773942 + 5.94988i) q^{36} +(-0.929033 + 2.24288i) q^{37} +(1.12903 - 8.08700i) q^{38} +(7.56312 + 8.50259i) q^{39} +(1.09598 + 10.1600i) q^{40} +(-0.841025 + 3.13875i) q^{41} +(1.00887 - 2.04180i) q^{42} +(4.28519 + 5.58457i) q^{43} +(7.56268 + 3.27195i) q^{44} +(-2.65761 + 10.5079i) q^{45} +(-3.50425 + 3.44991i) q^{46} +(1.79295 + 1.03516i) q^{47} +(-5.09676 - 4.69287i) q^{48} +(5.31353 - 3.06777i) q^{49} +(-3.03356 + 10.9776i) q^{50} +(-0.179253 + 0.935539i) q^{51} +(-12.9992 - 1.91849i) q^{52} +(1.71670 - 4.14448i) q^{53} +(-3.33754 - 6.54682i) q^{54} +(10.5256 + 10.5256i) q^{55} +(0.620906 + 2.55542i) q^{56} +(2.02001 + 9.79443i) q^{57} +(4.61338 - 5.91598i) q^{58} +(2.13608 - 0.281220i) q^{59} +(-5.43888 - 11.2720i) q^{60} +(-1.27923 + 9.71668i) q^{61} +(0.00884700 - 1.13217i) q^{62} +(-0.325106 + 2.77028i) q^{63} +(7.99121 + 0.374938i) q^{64} +(-20.5568 - 11.8685i) q^{65} +(-10.0699 - 0.667851i) q^{66} +(6.45600 - 8.41363i) q^{67} +(-0.535006 - 0.961035i) q^{68} +(2.62567 - 5.42018i) q^{69} +(-0.656860 + 4.70495i) q^{70} +(-10.4157 - 10.4157i) q^{71} +(7.80863 + 3.32043i) q^{72} +(-8.18821 + 8.18821i) q^{73} +(2.06869 + 2.74004i) q^{74} +(-1.01024 - 13.9120i) q^{75} +(-9.05040 - 7.17208i) q^{76} +(3.03909 + 2.33198i) q^{77} +(15.7864 - 3.12739i) q^{78} +(-0.656058 + 1.13633i) q^{79} +(13.1723 + 5.94498i) q^{80} +(6.54061 + 6.18226i) q^{81} +(3.22398 + 3.27476i) q^{82} +(7.51437 + 0.989285i) q^{83} +(-1.76631 - 2.69326i) q^{84} +(-0.259351 - 1.96996i) q^{85} +(9.87961 - 1.22222i) q^{86} +(-2.89213 + 8.72117i) q^{87} +(9.40894 - 6.87543i) q^{88} +(-3.96066 + 3.96066i) q^{89} +(10.9065 + 10.7707i) q^{90} +(-5.64357 - 2.33764i) q^{91} +(1.69473 + 6.74472i) q^{92} +(0.454958 + 1.30990i) q^{93} +(2.54697 - 1.44408i) q^{94} +(-10.4302 - 18.0657i) q^{95} +(-9.37409 + 2.85071i) q^{96} +(6.94041 - 12.0211i) q^{97} +(0.0678017 - 8.67670i) q^{98} +(11.8928 - 3.36682i) 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

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