LMFDB - Embedded newform 650.2.ba.b.187.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(73,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([11, 5]))

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

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

chi := DirichletCharacter("650.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.ba (of order $20$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			187.2
Character	$\chi$	$=$	650.187
Dual form			650.2.ba.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-2.34666 - 1.19569i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.373709 + 2.20462i) q^{5} +(-1.19569 - 2.34666i) q^{6} -2.39032i q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.31381 + 3.18469i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-2.34666 - 1.19569i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.373709 + 2.20462i) q^{5} +(-1.19569 - 2.34666i) q^{6} -2.39032i q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.31381 + 3.18469i) q^{9} +(-0.993505 + 2.00323i) q^{10} +(-0.643101 - 4.06038i) q^{11} +(0.412005 - 2.60130i) q^{12} +(1.87888 + 3.07731i) q^{13} +(1.40499 - 1.93381i) q^{14} +(1.75906 - 5.62034i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.87967 + 5.65166i) q^{17} +3.93650i q^{18} +(3.21929 - 1.64031i) q^{19} +(-1.98123 + 1.03668i) q^{20} +(-2.85806 + 5.60927i) q^{21} +(1.86635 - 3.66292i) q^{22} +(0.596712 + 3.76749i) q^{23} +(1.86232 - 1.86232i) q^{24} +(-4.72068 + 1.64777i) q^{25} +(-0.288754 + 3.59397i) q^{26} +(-0.385841 - 2.43611i) q^{27} +(2.27333 - 0.738648i) q^{28} +(7.59035 - 2.46625i) q^{29} +(4.72666 - 3.51300i) q^{30} +(3.11882 + 6.12103i) q^{31} -1.00000 q^{32} +(-3.34580 + 10.2973i) q^{33} +(-0.992265 + 6.26492i) q^{34} +(5.26973 - 0.893283i) q^{35} +(-2.31381 + 3.18469i) q^{36} +(0.632128 + 0.870050i) q^{37} +(3.56861 + 0.565213i) q^{38} +(-0.729599 - 9.46795i) q^{39} +(-2.21220 - 0.325846i) q^{40} +(1.22407 - 7.72850i) q^{41} +(-5.60927 + 2.85806i) q^{42} +(1.10367 + 1.10367i) q^{43} +(3.66292 - 1.86635i) q^{44} +(-6.15634 + 6.29123i) q^{45} +(-1.73173 + 3.39870i) q^{46} +(2.14234 - 0.696089i) q^{47} +(2.60130 - 0.412005i) q^{48} +1.28639 q^{49} +(-4.78765 - 1.44167i) q^{50} -16.7057i q^{51} +(-2.34609 + 2.73786i) q^{52} +(11.6715 + 5.94693i) q^{53} +(1.11976 - 2.19764i) q^{54} +(8.71126 - 2.93519i) q^{55} +(2.27333 + 0.738648i) q^{56} -9.51590 q^{57} +(7.59035 + 2.46625i) q^{58} +(-1.08707 + 6.86351i) q^{59} +(5.88884 - 0.0638150i) q^{60} +(-0.0389707 - 0.0283138i) q^{61} +(-1.07467 + 6.78521i) q^{62} +(7.61242 - 5.53075i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-6.08214 + 5.29222i) q^{65} +(-8.75941 + 6.36408i) q^{66} +(-3.32786 + 10.2421i) q^{67} +(-4.48519 + 4.48519i) q^{68} +(3.10445 - 9.55452i) q^{69} +(4.78836 + 2.37479i) q^{70} +(-11.6150 - 5.91814i) q^{71} +(-3.74383 + 1.21644i) q^{72} +(-13.0854 - 9.50711i) q^{73} +1.07544i q^{74} +(13.0481 + 1.77768i) q^{75} +(2.55485 + 2.55485i) q^{76} +(-9.70559 + 1.53721i) q^{77} +(4.97487 - 8.08858i) q^{78} +(-6.22131 + 2.02143i) q^{79} +(-1.59818 - 1.56391i) q^{80} +(1.64196 - 5.05342i) q^{81} +(5.53299 - 5.53299i) q^{82} +(8.86923 + 2.88179i) q^{83} +(-6.21792 - 0.984822i) q^{84} +(-11.3836 + 8.46064i) q^{85} +(0.244167 + 1.54161i) q^{86} +(-20.7609 - 3.28820i) q^{87} +(4.06038 + 0.643101i) q^{88} +(8.60376 - 1.36270i) q^{89} +(-8.67847 + 1.47111i) q^{90} +(7.35574 - 4.49111i) q^{91} +(-3.39870 + 1.73173i) q^{92} -18.0931i q^{93} +(2.14234 + 0.696089i) q^{94} +(4.81934 + 6.48431i) q^{95} +(2.34666 + 1.19569i) q^{96} +(-3.74588 - 11.5286i) q^{97} +(1.04071 + 0.756122i) q^{98} +(11.4431 - 11.4431i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9}+O(q^{10}) $ 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9	$ 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9} + 6 q^{13} + 8 q^{15} - 36 q^{16} - 6 q^{17} - 20 q^{19} - 6 q^{21} + 12 q^{23} + 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} + 12 q^{30} - 6 q^{31} - 144 q^{32} - 54 q^{33} + 6 q^{34} + 40 q^{35} + 20 q^{36} - 60 q^{37} + 20 q^{39} + 52 q^{41} + 6 q^{42} - 12 q^{43} - 6 q^{45} + 28 q^{46} + 50 q^{47} - 160 q^{49} - 22 q^{50} + 6 q^{52} + 20 q^{53} - 6 q^{54} - 32 q^{55} - 28 q^{57} + 20 q^{58} - 16 q^{59} - 12 q^{60} + 12 q^{61} + 6 q^{62} - 70 q^{63} - 36 q^{64} + 44 q^{65} - 16 q^{66} - 8 q^{67} - 6 q^{68} + 26 q^{69} + 10 q^{70} + 72 q^{71} - 52 q^{73} + 32 q^{75} - 56 q^{77} - 50 q^{78} - 20 q^{79} + 124 q^{81} - 22 q^{82} + 70 q^{83} - 6 q^{84} - 18 q^{85} - 8 q^{86} + 8 q^{87} + 28 q^{89} - 14 q^{90} - 26 q^{91} + 12 q^{92} + 50 q^{94} - 46 q^{95} + 28 q^{97} - 20 q^{98} + 40 q^{99}+O(q^{100}) $ 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9 + 6 * q^13 + 8 * q^15 - 36 * q^16 - 6 * q^17 - 20 * q^19 - 6 * q^21 + 12 * q^23 + 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 + 12 * q^30 - 6 * q^31 - 144 * q^32 - 54 * q^33 + 6 * q^34 + 40 * q^35 + 20 * q^36 - 60 * q^37 + 20 * q^39 + 52 * q^41 + 6 * q^42 - 12 * q^43 - 6 * q^45 + 28 * q^46 + 50 * q^47 - 160 * q^49 - 22 * q^50 + 6 * q^52 + 20 * q^53 - 6 * q^54 - 32 * q^55 - 28 * q^57 + 20 * q^58 - 16 * q^59 - 12 * q^60 + 12 * q^61 + 6 * q^62 - 70 * q^63 - 36 * q^64 + 44 * q^65 - 16 * q^66 - 8 * q^67 - 6 * q^68 + 26 * q^69 + 10 * q^70 + 72 * q^71 - 52 * q^73 + 32 * q^75 - 56 * q^77 - 50 * q^78 - 20 * q^79 + 124 * q^81 - 22 * q^82 + 70 * q^83 - 6 * q^84 - 18 * q^85 - 8 * q^86 + 8 * q^87 + 28 * q^89 - 14 * q^90 - 26 * q^91 + 12 * q^92 + 50 * q^94 - 46 * q^95 + 28 * q^97 - 20 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−2.34666	−	1.19569i	−1.35485	−	0.690329i	−0.382519	−	0.923948i	$-0.624943\pi$
$3$	−2.34666	−	1.19569i	−1.35485	−	0.690329i	−0.972328	+	0.233618i	$0.924943\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.373709	+	2.20462i	0.167128	+	0.985935i
$5$	0.373709	+	2.20462i	0.167128	+	0.985935i
$6$	−1.19569	−	2.34666i	−0.488136	−	0.958022i
$7$		−	2.39032i		−	0.903454i	−0.892156	−	0.451727i	$-0.850808\pi$
$7$		−	2.39032i		−	0.903454i	0.892156	−	0.451727i	$-0.149192\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	2.31381	+	3.18469i	0.771272	+	1.06156i
$10$	−0.993505	+	2.00323i	−0.314174	+	0.633478i
$11$	−0.643101	−	4.06038i	−0.193902	−	1.22425i	−0.872084	−	0.489357i	$-0.837232\pi$
$11$	−0.643101	−	4.06038i	−0.193902	−	1.22425i	0.678181	−	0.734895i	$-0.262768\pi$
$12$	0.412005	−	2.60130i	0.118936	−	0.750930i
$13$	1.87888	+	3.07731i	0.521106	+	0.853492i
$13$	1.87888	+	3.07731i	0.521106	+	0.853492i
$14$	1.40499	−	1.93381i	0.375500	−	0.516831i
$15$	1.75906	−	5.62034i	0.454187	−	1.45116i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.87967	+	5.65166i	0.698422	+	1.37073i	0.918568	+	0.395263i	$0.129347\pi$
$17$	2.87967	+	5.65166i	0.698422	+	1.37073i	−0.220146	+	0.975467i	$0.570653\pi$
$18$			3.93650i			0.927841i
$19$	3.21929	−	1.64031i	0.738557	−	0.376313i	−0.0438857	−	0.999037i	$-0.513974\pi$
$19$	3.21929	−	1.64031i	0.738557	−	0.376313i	0.782442	+	0.622723i	$0.213974\pi$
$20$	−1.98123	+	1.03668i	−0.443017	+	0.231809i
$21$	−2.85806	+	5.60927i	−0.623681	+	1.22404i
$22$	1.86635	−	3.66292i	0.397908	−	0.780938i
$23$	0.596712	+	3.76749i	0.124423	+	0.785576i	0.968438	+	0.249256i	$0.0801861\pi$
$23$	0.596712	+	3.76749i	0.124423	+	0.785576i	−0.844015	+	0.536320i	$0.819814\pi$
$24$	1.86232	−	1.86232i	0.380145	−	0.380145i
$25$	−4.72068	+	1.64777i	−0.944137	+	0.329554i
$26$	−0.288754	+	3.59397i	−0.0566293	+	0.704836i
$27$	−0.385841	−	2.43611i	−0.0742552	−	0.468829i
$28$	2.27333	−	0.738648i	0.429618	−	0.139591i
$29$	7.59035	−	2.46625i	1.40949	−	0.457972i	0.497245	−	0.867610i	$-0.334345\pi$
$29$	7.59035	−	2.46625i	1.40949	−	0.457972i	0.912248	+	0.409639i	$0.134345\pi$
$30$	4.72666	−	3.51300i	0.862966	−	0.641383i
$31$	3.11882	+	6.12103i	0.560156	+	1.09937i	0.981320	+	0.192384i	$0.0616219\pi$
$31$	3.11882	+	6.12103i	0.560156	+	1.09937i	−0.421163	+	0.906985i	$0.638378\pi$
$32$	−1.00000			−0.176777
$33$	−3.34580	+	10.2973i	−0.582428	+	1.79253i
$34$	−0.992265	+	6.26492i	−0.170172	+	1.07442i
$35$	5.26973	−	0.893283i	0.890747	−	0.150992i
$36$	−2.31381	+	3.18469i	−0.385636	+	0.530782i
$37$	0.632128	+	0.870050i	0.103921	+	0.143035i	0.857810	−	0.513966i	$-0.171824\pi$
$37$	0.632128	+	0.870050i	0.103921	+	0.143035i	−0.753889	+	0.657002i	$0.771824\pi$
$38$	3.56861	+	0.565213i	0.578906	+	0.0916897i
$39$	−0.729599	−	9.46795i	−0.116829	−	1.51609i
$40$	−2.21220	−	0.325846i	−0.349779	−	0.0515208i
$41$	1.22407	−	7.72850i	0.191168	−	1.20699i	−0.686287	−	0.727331i	$-0.740761\pi$
$41$	1.22407	−	7.72850i	0.191168	−	1.20699i	0.877455	−	0.479658i	$-0.159239\pi$
$42$	−5.60927	+	2.85806i	−0.865529	+	0.441009i
$43$	1.10367	+	1.10367i	0.168308	+	0.168308i	0.786235	−	0.617927i	$-0.212027\pi$
$43$	1.10367	+	1.10367i	0.168308	+	0.168308i	−0.617927	+	0.786235i	$0.712027\pi$
$44$	3.66292	−	1.86635i	0.552206	−	0.281363i
$45$	−6.15634	+	6.29123i	−0.917733	+	0.937841i
$46$	−1.73173	+	3.39870i	−0.255329	+	0.501111i
$47$	2.14234	−	0.696089i	0.312493	−	0.101535i	−0.148572	−	0.988902i	$-0.547468\pi$
$47$	2.14234	−	0.696089i	0.312493	−	0.101535i	0.461065	+	0.887367i	$0.347468\pi$
$48$	2.60130	−	0.412005i	0.375465	−	0.0594678i
$49$	1.28639			0.183770
$50$	−4.78765	−	1.44167i	−0.677076	−	0.203883i
$51$		−	16.7057i		−	2.33927i
$52$	−2.34609	+	2.73786i	−0.325344	+	0.379673i
$53$	11.6715	+	5.94693i	1.60321	+	0.816874i	0.999811	+	0.0194309i	$0.00618545\pi$
$53$	11.6715	+	5.94693i	1.60321	+	0.816874i	0.603394	+	0.797443i	$0.293815\pi$
$54$	1.11976	−	2.19764i	0.152379	−	0.299061i
$55$	8.71126	−	2.93519i	1.17463	−	0.395782i
$56$	2.27333	+	0.738648i	0.303786	+	0.0987060i
$57$	−9.51590			−1.26041
$58$	7.59035	+	2.46625i	0.996662	+	0.323835i
$59$	−1.08707	+	6.86351i	−0.141525	+	0.893553i	0.810100	+	0.586292i	$0.199413\pi$
$59$	−1.08707	+	6.86351i	−0.141525	+	0.893553i	−0.951625	+	0.307262i	$0.900587\pi$
$60$	5.88884	−	0.0638150i	0.760246	−	0.00823848i
$61$	−0.0389707	−	0.0283138i	−0.00498968	−	0.00362522i	0.585288	−	0.810826i	$-0.300982\pi$
$61$	−0.0389707	−	0.0283138i	−0.00498968	−	0.00362522i	−0.590277	+	0.807201i	$0.700982\pi$
$62$	−1.07467	+	6.78521i	−0.136483	+	0.861723i
$63$	7.61242	−	5.53075i	0.959075	−	0.696809i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−6.08214	+	5.29222i	−0.754396	+	0.656419i
$66$	−8.75941	+	6.36408i	−1.07821	+	0.783364i
$67$	−3.32786	+	10.2421i	−0.406563	+	1.25127i	0.513020	+	0.858377i	$0.328527\pi$
$67$	−3.32786	+	10.2421i	−0.406563	+	1.25127i	−0.919583	+	0.392896i	$0.871473\pi$
$68$	−4.48519	+	4.48519i	−0.543909	+	0.543909i
$69$	3.10445	−	9.55452i	0.373732	−	1.15023i
$70$	4.78836	+	2.37479i	0.572319	+	0.283842i
$71$	−11.6150	−	5.91814i	−1.37845	−	0.702354i	−0.401505	−	0.915857i	$-0.631513\pi$
$71$	−11.6150	−	5.91814i	−1.37845	−	0.702354i	−0.976943	+	0.213502i	$0.931513\pi$
$72$	−3.74383	+	1.21644i	−0.441215	+	0.143359i
$73$	−13.0854	−	9.50711i	−1.53153	−	1.11272i	−0.955379	−	0.295382i	$-0.904553\pi$
$73$	−13.0854	−	9.50711i	−1.53153	−	1.11272i	−0.576153	−	0.817342i	$-0.695447\pi$
$74$			1.07544i			0.125017i
$75$	13.0481	+	1.77768i	1.50666	+	0.205269i
$76$	2.55485	+	2.55485i	0.293061	+	0.293061i
$77$	−9.70559	+	1.53721i	−1.10605	+	0.175182i
$78$	4.97487	−	8.08858i	0.563293	−	0.915852i
$79$	−6.22131	+	2.02143i	−0.699952	+	0.227428i	−0.637309	−	0.770608i	$-0.719953\pi$
$79$	−6.22131	+	2.02143i	−0.699952	+	0.227428i	−0.0626422	+	0.998036i	$0.519953\pi$
$80$	−1.59818	−	1.56391i	−0.178682	−	0.174851i
$81$	1.64196	−	5.05342i	0.182440	−	0.561491i
$82$	5.53299	−	5.53299i	0.611017	−	0.611017i
$83$	8.86923	+	2.88179i	0.973524	+	0.316317i	0.752238	−	0.658892i	$-0.228974\pi$
$83$	8.86923	+	2.88179i	0.973524	+	0.316317i	0.221286	+	0.975209i	$0.428974\pi$
$84$	−6.21792	−	0.984822i	−0.678431	−	0.107453i
$85$	−11.3836	+	8.46064i	−1.23473	+	0.917686i
$86$	0.244167	+	1.54161i	0.0263292	+	0.166236i
$87$	−20.7609	−	3.28820i	−2.22580	−	0.352532i
$88$	4.06038	+	0.643101i	0.432838	+	0.0685548i
$89$	8.60376	−	1.36270i	0.911997	−	0.144446i	0.317234	−	0.948347i	$-0.397246\pi$
$89$	8.60376	−	1.36270i	0.911997	−	0.144446i	0.594763	+	0.803901i	$0.297246\pi$
$90$	−8.67847	+	1.47111i	−0.914791	+	0.155068i
$91$	7.35574	−	4.49111i	0.771091	−	0.470796i
$92$	−3.39870	+	1.73173i	−0.354339	+	0.180545i
$93$		−	18.0931i		−	1.87617i
$94$	2.14234	+	0.696089i	0.220966	+	0.0717961i
$95$	4.81934	+	6.48431i	0.494454	+	0.665277i
$96$	2.34666	+	1.19569i	0.239505	+	0.122034i
$97$	−3.74588	−	11.5286i	−0.380337	−	1.17056i	−0.939807	−	0.341705i	$-0.888996\pi$
$97$	−3.74588	−	11.5286i	−0.380337	−	1.17056i	0.559471	−	0.828850i	$-0.311004\pi$
$98$	1.04071	+	0.756122i	0.105128	+	0.0763799i
$99$	11.4431	−	11.4431i	1.15007	−	1.15007i
$100$	−3.02590	−	3.98045i	−0.302590	−	0.398045i
$101$		−	8.37930i		−	0.833772i	−0.908959	−	0.416886i	$-0.863121\pi$
$101$		−	8.37930i		−	0.833772i	0.908959	−	0.416886i	$-0.136879\pi$
$102$	9.81938	−	13.5152i	0.972264	−	1.33821i
$103$	1.75567	−	3.44571i	0.172992	−	0.339515i	−0.788190	−	0.615432i	$-0.788981\pi$
$103$	1.75567	−	3.44571i	0.172992	−	0.339515i	0.961182	+	0.275917i	$0.0889814\pi$
$104$	−3.50730	+	0.835976i	−0.343919	+	0.0819742i
$105$	−13.4344	−	4.20471i	−1.31106	−	0.410337i
$106$	5.94693	+	11.6715i	0.577617	+	1.13364i
$107$	−5.21716	−	5.21716i	−0.504362	−	0.504362i	0.408428	−	0.912790i	$-0.366077\pi$
$107$	−5.21716	−	5.21716i	−0.504362	−	0.504362i	−0.912790	+	0.408428i	$0.866077\pi$
$108$	2.19764	−	1.11976i	0.211468	−	0.107749i
$109$	−4.74678	−	0.751816i	−0.454659	−	0.0720109i	−0.0750951	−	0.997176i	$-0.523926\pi$
$109$	−4.74678	−	0.751816i	−0.454659	−	0.0720109i	−0.379564	+	0.925165i	$0.623926\pi$
$110$	8.77282	+	2.74573i	0.836456	+	0.261795i
$111$	−0.443087	−	2.79754i	−0.0420559	−	0.265531i
$112$	1.40499	+	1.93381i	0.132759	+	0.182727i
$113$	0.341353	−	2.15522i	0.0321118	−	0.202746i	−0.966416	−	0.256981i	$-0.917272\pi$
$113$	0.341353	−	2.15522i	0.0321118	−	0.202746i	0.998528	+	0.0542355i	$0.0172722\pi$
$114$	−7.69852	−	5.59330i	−0.721033	−	0.523861i
$115$	−8.08288	+	2.72347i	−0.753733	+	0.253965i
$116$	4.69109	+	6.45674i	0.435557	+	0.599493i
$117$	−5.45291	+	13.1040i	−0.504122	+	1.21146i
$118$	−4.91373	+	4.91373i	−0.452346	+	0.452346i
$119$	13.5093	−	6.88331i	1.23839	−	0.630992i
$120$	4.80168	+	3.40974i	0.438331	+	0.311266i
$121$	−5.61150	+	1.82329i	−0.510136	+	0.165753i
$122$	−0.0148855	−	0.0458127i	−0.00134767	−	0.00414769i
$123$	−12.1133	+	16.6726i	−1.09222	+	1.50332i
$124$	−4.85767	+	4.85767i	−0.436232	+	0.436232i
$125$	−5.39687	−	9.79152i	−0.482711	−	0.875780i
$126$	9.40947			0.838262
$127$	−17.3733	+	2.75165i	−1.54163	+	0.244170i	−0.868625	−	0.495470i	$-0.834996\pi$
$127$	−17.3733	+	2.75165i	−1.54163	+	0.244170i	−0.673003	+	0.739640i	$0.734996\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−1.27030	−	3.90959i	−0.111844	−	0.344220i
$130$	−8.03124	+	0.706507i	−0.704387	+	0.0619648i
$131$	−1.07632	+	3.31257i	−0.0940384	+	0.289421i	−0.987002	−	0.160709i	$-0.948622\pi$
$131$	−1.07632	+	3.31257i	−0.0940384	+	0.289421i	0.892963	+	0.450129i	$0.148622\pi$
$132$	−10.8272			−0.942389
$133$	−3.92086	−	7.69513i	−0.339982	−	0.667252i
$134$	−8.71246	+	6.32997i	−0.752642	+	0.546826i
$135$	5.22649	−	1.76103i	0.449825	−	0.151565i
$136$	−6.26492	+	0.992265i	−0.537212	+	0.0850861i
$137$	−9.11378	−	12.5440i	−0.778642	−	1.07171i	−0.995430	−	0.0954907i	$-0.969558\pi$
$137$	−9.11378	−	12.5440i	−0.778642	−	1.07171i	0.216788	−	0.976219i	$-0.430442\pi$
$138$	8.12756	−	5.90502i	0.691864	−	0.502668i
$139$	−1.47120	+	2.02493i	−0.124786	+	0.171753i	−0.866839	−	0.498588i	$-0.833852\pi$
$139$	−1.47120	+	2.02493i	−0.124786	+	0.171753i	0.742053	+	0.670341i	$0.233852\pi$
$140$	2.47800	+	4.73577i	0.209429	+	0.400246i
$141$	−5.85966	−	0.928079i	−0.493473	−	0.0781584i
$142$	−5.91814	−	11.6150i	−0.496640	−	0.974710i
$143$	11.2867	−	9.60797i	0.943845	−	0.803459i
$144$	−3.74383	−	1.21644i	−0.311986	−	0.101370i
$145$	8.27373	+	15.8122i	0.687096	+	1.31313i
$146$	−4.99819	−	15.3828i	−0.413653	−	1.27309i
$147$	−3.01873	−	1.53812i	−0.248981	−	0.126862i
$148$	−0.632128	+	0.870050i	−0.0519606	+	0.0715176i
$149$	14.1601	+	14.1601i	1.16004	+	1.16004i	0.984466	+	0.175573i	$0.0561779\pi$
$149$	14.1601	+	14.1601i	1.16004	+	1.16004i	0.175573	+	0.984466i	$0.443822\pi$
$150$	9.51122	+	9.10764i	0.776588	+	0.743636i
$151$	−2.57334	−	2.57334i	−0.209416	−	0.209416i	0.594603	−	0.804019i	$-0.297309\pi$
$151$	−2.57334	−	2.57334i	−0.209416	−	0.209416i	−0.804019	+	0.594603i	$0.797309\pi$
$152$	0.565213	+	3.56861i	0.0458448	+	0.289453i
$153$	−11.3358	+	22.2478i	−0.916445	+	1.79862i
$154$	−8.75554	−	4.46117i	−0.705542	−	0.359491i
$155$	−12.3290	+	9.16329i	−0.990289	+	0.736013i
$156$	8.77910	−	3.61965i	0.702891	−	0.289804i
$157$	11.0223	+	11.0223i	0.879674	+	0.879674i	0.993501	−	0.113827i	$-0.0363109\pi$
$157$	11.0223	+	11.0223i	0.879674	+	0.879674i	−0.113827	+	0.993501i	$0.536311\pi$
$158$	−6.22131	−	2.02143i	−0.494941	−	0.160816i
$159$	−20.2785	−	27.9109i	−1.60819	−	2.21348i
$160$	−0.373709	−	2.20462i	−0.0295443	−	0.174290i
$161$	9.00549	−	1.42633i	0.709732	−	0.112411i
$162$	4.29870	−	3.12319i	0.337738	−	0.245381i
$163$	−5.29635	+	3.84802i	−0.414842	+	0.301401i	−0.775559	−	0.631275i	$-0.782532\pi$
$163$	−5.29635	+	3.84802i	−0.414842	+	0.301401i	0.360717	+	0.932675i	$0.382532\pi$
$164$	7.72850	−	1.22407i	0.603494	−	0.0955841i
$165$	−23.9520	−	3.52801i	−1.86466	−	0.274655i
$166$	5.48148	+	7.54461i	0.425446	+	0.585576i
$167$	15.2648	+	4.95984i	1.18123	+	0.383804i	0.832822	−	0.553541i	$-0.186724\pi$
$167$	15.2648	+	4.95984i	1.18123	+	0.383804i	0.348404	+	0.937344i	$0.386724\pi$
$168$	−4.45154	−	4.45154i	−0.343444	−	0.343444i
$169$	−5.93965	+	11.5638i	−0.456896	+	0.889520i
$170$	−14.1826	+	0.153691i	−1.08775	+	0.0117875i
$171$	12.6727	+	6.45708i	0.969108	+	0.493785i
$172$	−0.708601	+	1.39071i	−0.0540303	+	0.106040i
$173$	3.02404	+	19.0930i	0.229914	+	1.45162i	0.784830	+	0.619711i	$0.212750\pi$
$173$	3.02404	+	19.0930i	0.229914	+	1.45162i	−0.554917	+	0.831906i	$0.687250\pi$
$174$	−14.8631	−	14.8631i	−1.12677	−	1.12677i
$175$	3.93870	+	11.2839i	0.297737	+	0.852984i
$176$	2.90691	+	2.90691i	0.219117	+	0.219117i
$177$	10.7576	−	14.8066i	0.808591	−	1.11293i
$178$	7.76156	+	3.95471i	0.581754	+	0.296418i
$179$	0.558806	+	1.71983i	0.0417671	+	0.128546i	0.969766	−	0.244038i	$-0.0784720\pi$
$179$	0.558806	+	1.71983i	0.0417671	+	0.128546i	−0.927999	+	0.372583i	$0.878472\pi$
$180$	−7.88573	−	3.91093i	−0.587767	−	0.291503i
$181$	0.413091	+	0.134221i	0.0307048	+	0.00997660i	0.324329	−	0.945944i	$-0.394861\pi$
$181$	0.413091	+	0.134221i	0.0307048	+	0.00997660i	−0.293624	+	0.955921i	$0.594861\pi$
$182$	8.59072	+	0.690213i	0.636787	+	0.0511620i
$183$	0.0575966	+	0.113040i	0.00425766	+	0.00835613i
$184$	−3.76749	−	0.596712i	−0.277743	−	0.0439902i
$185$	−1.68190	+	1.71875i	−0.123655	+	0.126365i
$186$	10.6349	−	14.6376i	0.779787	−	1.07328i
$187$	21.0960	−	15.3271i	1.54269	−	1.12083i
$188$	1.32404	+	1.82239i	0.0965656	+	0.132911i
$189$	−5.82306	+	0.922283i	−0.423566	+	0.0670862i
$190$	0.0875451	+	8.07866i	0.00635119	+	0.586087i
$191$	6.27879	−	4.56181i	0.454317	−	0.330081i	−0.336981	−	0.941512i	$-0.609406\pi$
$191$	6.27879	−	4.56181i	0.454317	−	0.330081i	0.791298	+	0.611431i	$0.209406\pi$
$192$	1.19569	+	2.34666i	0.0862911	+	0.169356i
$193$	−7.33734			−0.528153			−0.264077	−	0.964502i	$-0.585067\pi$
$193$	−7.33734			−0.528153			−0.264077	+	0.964502i	$0.585067\pi$
$194$	3.74588	−	11.5286i	0.268939	−	0.827708i
$195$	20.6006	−	5.14675i	1.47524	−	0.368566i
$196$	0.397517	+	1.22343i	0.0283941	+	0.0873880i
$197$	−4.11807	−	12.6741i	−0.293400	−	0.902993i	−0.983754	−	0.179521i	$-0.942545\pi$
$197$	−4.11807	−	12.6741i	−0.293400	−	0.902993i	0.690354	−	0.723472i	$-0.257455\pi$
$198$	15.9837	−	2.53157i	1.13591	−	0.179911i
$199$	2.64812			0.187720			0.0938601	−	0.995585i	$-0.470079\pi$
$199$	2.64812			0.187720			0.0938601	+	0.995585i	$0.470079\pi$
$200$	−0.108353	−	4.99883i	−0.00766173	−	0.353470i
$201$	20.0557	−	20.0557i	1.41462	−	1.41462i
$202$	4.92523	−	6.77900i	0.346538	−	0.476969i
$203$	−5.89513	−	18.1433i	−0.413757	−	1.27341i
$204$	15.8881	−	5.16236i	1.11239	−	0.361437i
$205$	17.4958	−	0.189595i	1.22196	−	0.0132419i
$206$	3.44571	−	1.75567i	0.240074	−	0.122324i
$207$	−10.6176	+	10.6176i	−0.737976	+	0.737976i
$208$	−3.32884	−	1.38522i	−0.230813	−	0.0960477i
$209$	−8.73062	−	12.0167i	−0.603910	−	0.831211i
$210$	−8.39718	−	11.2982i	−0.579460	−	0.779651i
$211$	1.16131	+	0.843738i	0.0799476	+	0.0580853i	0.627041	−	0.778986i	$-0.284266\pi$
$211$	1.16131	+	0.843738i	0.0799476	+	0.0580853i	−0.547094	+	0.837071i	$0.684266\pi$
$212$	−2.04917	+	12.9380i	−0.140738	+	0.888583i
$213$	20.1803	+	27.7758i	1.38273	+	1.90317i
$214$	−1.15420	−	7.28734i	−0.0788996	−	0.498152i
$215$	−2.02072	+	2.84563i	−0.137812	+	0.194070i
$216$	2.43611	+	0.385841i	0.165756	+	0.0262532i
$217$	14.6312	−	7.45496i	0.993230	−	0.506076i
$218$	−3.39832	−	3.39832i	−0.230163	−	0.230163i
$219$	19.3396	+	37.9560i	1.30685	+	2.56483i
$220$	5.48346	+	7.37787i	0.369695	+	0.497416i
$221$	−11.9814	+	19.4804i	−0.805955	+	1.31039i
$222$	1.28589	−	2.52370i	0.0863032	−	0.169379i
$223$	15.1243	−	20.8169i	1.01280	−	1.39400i	0.0956710	−	0.995413i	$-0.469500\pi$
$223$	15.1243	−	20.8169i	1.01280	−	1.39400i	0.917130	−	0.398588i	$-0.130500\pi$
$224$			2.39032i			0.159710i
$225$	−16.1704	−	11.2213i	−1.07803	−	0.748086i
$226$	1.54296	−	1.54296i	0.102636	−	0.102636i
$227$	−1.52463	−	1.10771i	−0.101193	−	0.0735211i	0.536038	−	0.844194i	$-0.319920\pi$
$227$	−1.52463	−	1.10771i	−0.101193	−	0.0735211i	−0.637231	+	0.770673i	$0.719920\pi$
$228$	−2.94057	−	9.05016i	−0.194744	−	0.599361i
$229$	20.0332	+	10.2074i	1.32383	+	0.674525i	0.965825	−	0.259194i	$-0.0834569\pi$
$229$	20.0332	+	10.2074i	1.32383	+	0.674525i	0.358005	+	0.933720i	$0.383457\pi$
$230$	−8.14000	−	2.54767i	−0.536736	−	0.167988i
$231$	24.6138	+	7.99751i	1.61947	+	0.526197i
$232$			7.98097i			0.523976i
$233$	−11.3419	+	5.77898i	−0.743032	+	0.378594i	−0.784159	−	0.620560i	$-0.786905\pi$
$233$	−11.3419	+	5.77898i	−0.743032	+	0.378594i	0.0411269	+	0.999154i	$0.486905\pi$
$234$	−12.1138	+	7.39619i	−0.791905	+	0.483504i
$235$	2.33522	+	4.46291i	0.152333	+	0.291128i
$236$	−6.86351	+	1.08707i	−0.446777	+	0.0707625i
$237$	17.0163	+	2.69512i	1.10533	+	0.175067i
$238$	14.9751	+	2.37183i	0.970693	+	0.153743i
$239$	2.02845	+	12.8071i	0.131209	+	0.828422i	0.962241	+	0.272198i	$0.0877505\pi$
$239$	2.02845	+	12.8071i	0.131209	+	0.828422i	−0.831032	+	0.556225i	$0.812249\pi$
$240$	1.88044	+	5.58090i	0.121382	+	0.360245i
$241$	−2.33393	−	0.369657i	−0.150341	−	0.0238117i	0.0808101	−	0.996730i	$-0.474249\pi$
$241$	−2.33393	−	0.369657i	−0.150341	−	0.0238117i	−0.231151	+	0.972918i	$0.574249\pi$
$242$	−5.61150	−	1.82329i	−0.360721	−	0.117205i
$243$	−15.1276	+	15.1276i	−0.970436	+	0.970436i
$244$	0.0148855	−	0.0458127i	0.000952944	−	0.00293286i
$245$	0.480737	+	2.83600i	0.0307131	+	0.181186i
$246$	−19.5998	+	6.36836i	−1.24964	+	0.406032i
$247$	11.0964	+	6.82482i	0.706047	+	0.434253i
$248$	−6.78521	+	1.07467i	−0.430861	+	0.0682417i
$249$	−17.3674	−	17.3674i	−1.10061	−	1.10061i
$250$	1.38915	−	11.0937i	0.0878574	−	0.701627i
$251$		−	27.2453i		−	1.71971i	−0.510542	−	0.859853i	$-0.670555\pi$
$251$		−	27.2453i		−	1.71971i	0.510542	−	0.859853i	$-0.329445\pi$
$252$	7.61242	+	5.53075i	0.479537	+	0.348404i
$253$	14.9137	−	4.84576i	0.937617	−	0.304650i
$254$	−15.6726	−	7.98561i	−0.983389	−	0.501062i
$255$	36.8298	−	6.24309i	2.30637	−	0.390957i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	5.47434	−	5.47434i	0.341480	−	0.341480i	−0.515444	−	0.856924i	$-0.672373\pi$
$257$	5.47434	−	5.47434i	0.341480	−	0.341480i	0.856924	+	0.515444i	$0.172373\pi$
$258$	1.27030	−	3.90959i	0.0790856	−	0.243401i
$259$	2.07969	−	1.51099i	0.129226	−	0.0938881i
$260$	−6.91269	−	4.14907i	−0.428707	−	0.257314i
$261$	25.4169	+	18.4665i	1.57327	+	1.14305i
$262$	−2.81784	+	2.04728i	−0.174087	+	0.126481i
$263$	3.40870	−	21.5217i	0.210189	−	1.32708i	−0.626507	−	0.779416i	$-0.715516\pi$
$263$	3.40870	−	21.5217i	0.210189	−	1.32708i	0.836697	−	0.547667i	$-0.184484\pi$
$264$	−8.75941	−	6.36408i	−0.539104	−	0.391682i
$265$	−8.74896	+	27.9537i	−0.537445	+	1.71718i
$266$	1.35104	−	8.53011i	0.0828374	−	0.523015i
$267$	−21.8195	−	7.08958i	−1.33533	−	0.433876i
$268$	−10.7692			−0.657833
$269$	2.71559	+	0.882349i	0.165573	+	0.0537978i	0.390630	−	0.920548i	$-0.372257\pi$
$269$	2.71559	+	0.882349i	0.165573	+	0.0537978i	−0.225058	+	0.974345i	$0.572257\pi$
$270$	5.26343	+	1.64735i	0.320322	+	0.100255i
$271$	−3.40823	+	6.68902i	−0.207035	+	0.406329i	−0.971052	−	0.238867i	$-0.923224\pi$
$271$	−3.40823	+	6.68902i	−0.207035	+	0.406329i	0.764017	+	0.645196i	$0.223224\pi$
$272$	−5.65166	−	2.87967i	−0.342682	−	0.174605i
$273$	−22.6314	+	1.74397i	−1.36971	+	0.105550i
$274$		−	15.5053i		−	0.936708i
$275$	9.72646	+	18.1081i	0.586528	+	1.09196i
$276$	10.0462			0.604711
$277$	−17.5638	+	2.78183i	−1.05530	+	0.167144i	−0.659892	−	0.751360i	$-0.729398\pi$
$277$	−17.5638	+	2.78183i	−1.05530	+	0.167144i	−0.395412	+	0.918504i	$0.629398\pi$
$278$	−2.38045	+	0.773456i	−0.142770	+	0.0463888i
$279$	−12.2772	+	24.0954i	−0.735018	+	1.44255i
$280$	−0.778875	+	5.28785i	−0.0465467	+	0.316010i
$281$	−2.80556	+	1.42950i	−0.167366	+	0.0852771i	−0.535667	−	0.844430i	$-0.679940\pi$
$281$	−2.80556	+	1.42950i	−0.167366	+	0.0852771i	0.368301	+	0.929707i	$0.379940\pi$
$282$	−4.19506	−	4.19506i	−0.249812	−	0.249812i
$283$	3.80116	−	1.93679i	0.225955	−	0.115130i	−0.337348	−	0.941380i	$-0.609530\pi$
$283$	3.80116	−	1.93679i	0.225955	−	0.115130i	0.563304	+	0.826250i	$0.309530\pi$
$284$	2.03925	−	12.8753i	0.121007	−	0.764011i
$285$	−3.55618	−	20.9789i	−0.210650	−	1.24268i
$286$	14.7786	−	1.13884i	0.873876	−	0.0673407i
$287$	−18.4735	−	2.92592i	−1.09046	−	0.172712i
$288$	−2.31381	−	3.18469i	−0.136343	−	0.187660i
$289$	−13.6565	+	18.7965i	−0.803322	+	1.10568i
$290$	−2.60057	+	17.6555i	−0.152710	+	1.03677i
$291$	−4.99429	+	31.5327i	−0.292771	+	1.84848i
$292$	4.99819	−	15.3828i	0.292497	−	0.900212i
$293$	−27.7158			−1.61918			−0.809588	−	0.586998i	$-0.800310\pi$
$293$	−27.7158			−1.61918			−0.809588	+	0.586998i	$0.800310\pi$
$294$	−1.53812	−	3.01873i	−0.0897050	−	0.176056i
$295$	−15.5377	+	0.168376i	−0.904639	+	0.00980320i
$296$	−1.02280	+	0.332329i	−0.0594493	+	0.0193163i
$297$	−9.64339	+	3.13333i	−0.559566	+	0.181814i
$298$	3.13266	+	19.7788i	0.181470	+	1.14576i
$299$	−10.4726	+	8.91492i	−0.605645	+	0.515563i
$300$	2.34140	+	12.9588i	0.135181	+	0.748176i
$301$	2.63812	−	2.63812i	0.152059	−	0.152059i
$302$	−0.569305	−	3.59445i	−0.0327598	−	0.206837i
$303$	−10.0190	+	19.6634i	−0.575577	+	1.12963i
$304$	−1.64031	+	3.21929i	−0.0940783	+	0.184639i
$305$	0.0478575	−	0.0964965i	0.00274031	−	0.00552538i
$306$	−22.2478	+	11.3358i	−1.27182	+	0.648024i
$307$			16.3298i			0.931989i	0.884788	+	0.465994i	$0.154303\pi$
$307$			16.3298i			0.931989i	−0.884788	+	0.465994i	$0.845697\pi$
$308$	−4.46117	−	8.75554i	−0.254199	−	0.498893i
$309$	−8.23996	+	5.98668i	−0.468755	+	0.340570i
$310$	−15.3604	+	0.166455i	−0.872413	+	0.00945399i
$311$	2.37455	−	3.26829i	0.134649	−	0.185328i	−0.736368	−	0.676581i	$-0.763461\pi$
$311$	2.37455	−	3.26829i	0.134649	−	0.185328i	0.871017	+	0.491253i	$0.163461\pi$
$312$	9.23002	+	2.23187i	0.522547	+	0.126355i
$313$	−4.15008	+	26.2026i	−0.234576	+	1.48106i	0.536276	+	0.844043i	$0.319831\pi$
$313$	−4.15008	+	26.2026i	−0.234576	+	1.48106i	−0.770852	+	0.637014i	$0.780169\pi$
$314$	2.43848	+	15.3959i	0.137611	+	0.868843i
$315$	15.0380	+	14.7156i	0.847296	+	0.829130i
$316$	−3.84498	−	5.29216i	−0.216297	−	0.297707i
$317$	8.41322	−	25.8932i	0.472533	−	1.45431i	−0.376723	−	0.926326i	$-0.622949\pi$
$317$	8.41322	−	25.8932i	0.472533	−	1.45431i	0.849256	−	0.527982i	$-0.177051\pi$
$318$		−	34.4998i		−	1.93465i
$319$	−14.8953	−	29.2337i	−0.833976	−	1.63677i
$320$	0.993505	−	2.00323i	0.0555386	−	0.111984i
$321$	6.00484	+	18.4810i	0.335158	+	1.03151i
$322$	8.12397	+	4.13937i	0.452731	+	0.230678i
$323$	18.5410	+	13.4708i	1.03165	+	0.749536i
$324$	5.31348			0.295194
$325$	−13.9403	−	11.4310i	−0.773268	−	0.634080i
$326$	−6.54665			−0.362585
$327$	10.2402	+	7.43992i	0.566283	+	0.411428i
$328$	6.97198	+	3.55240i	0.384963	+	0.196149i
$329$	−1.66387	−	5.12087i	−0.0917323	−	0.282323i
$330$	−17.3038	−	16.9328i	−0.952545	−	0.932122i
$331$	−9.53866	−	18.7207i	−0.524292	−	1.02898i	−0.989602	−	0.143834i	$-0.954057\pi$
$331$	−9.53866	−	18.7207i	−0.524292	−	1.02898i	0.465309	−	0.885148i	$-0.345943\pi$
$332$			9.32566i			0.511812i
$333$	−1.30821	+	4.02627i	−0.0716897	+	0.220638i
$334$	9.43417	+	12.9850i	0.516215	+	0.710509i
$335$	−23.8236	−	3.50910i	−1.30162	−	0.191722i
$336$	−0.984822	−	6.21792i	−0.0537264	−	0.339215i
$337$	−1.01457	+	6.40572i	−0.0552669	+	0.348942i	0.944523	+	0.328445i	$0.106525\pi$
$337$	−1.01457	+	6.40572i	−0.0552669	+	0.348942i	−0.999790	+	0.0204963i	$0.993475\pi$
$338$	−11.6023	+	5.86404i	−0.631081	+	0.318962i
$339$	−3.37800	+	4.64942i	−0.183468	+	0.252522i
$340$	−11.5643	−	8.21197i	−0.627161	−	0.445356i
$341$	22.8480	−	16.6000i	1.23729	−	0.898942i
$342$	6.45708	+	12.6727i	0.349159	+	0.685263i
$343$		−	19.8071i		−	1.06948i
$344$	−1.39071	+	0.708601i	−0.0749819	+	0.0382052i
$345$	22.2242	+	3.27352i	1.19651	+	0.176240i
$346$	−8.77611	+	17.2241i	−0.471806	+	0.925972i
$347$	−2.07844	+	4.07917i	−0.111577	+	0.218982i	−0.940042	−	0.341059i	$-0.889214\pi$
$347$	−2.07844	+	4.07917i	−0.111577	+	0.218982i	0.828465	+	0.560040i	$0.189214\pi$
$348$	−3.28820	−	20.7609i	−0.176266	−	1.11290i
$349$	2.26651	−	2.26651i	0.121324	−	0.121324i	−0.643838	−	0.765162i	$-0.722659\pi$
$349$	2.26651	−	2.26651i	0.121324	−	0.121324i	0.765162	+	0.643838i	$0.222659\pi$
$350$	−3.44605	+	11.4440i	−0.184199	+	0.611707i
$351$	6.77170	−	5.76449i	0.361447	−	0.307686i
$352$	0.643101	+	4.06038i	0.0342774	+	0.216419i
$353$	−2.54672	+	0.827481i	−0.135548	+	0.0440424i	−0.376006	−	0.926617i	$-0.622703\pi$
$353$	−2.54672	+	0.827481i	−0.135548	+	0.0440424i	0.240457	+	0.970660i	$0.422703\pi$
$354$	17.4062	−	5.65561i	0.925127	−	0.300592i
$355$	8.70661	−	27.8183i	0.462099	−	1.47644i
$356$	3.95471	+	7.76156i	0.209599	+	0.411362i
$357$	−39.9320			−2.11342
$358$	−0.558806	+	1.71983i	−0.0295338	+	0.0908957i
$359$	−0.254520	+	1.60698i	−0.0134331	+	0.0848130i	−0.993494	−	0.113884i	$-0.963671\pi$
$359$	−0.254520	+	1.60698i	−0.0134331	+	0.0848130i	0.980061	+	0.198697i	$0.0636709\pi$
$360$	−4.08090	−	7.79912i	−0.215082	−	0.411050i
$361$	−3.49469	+	4.81003i	−0.183931	+	0.253160i
$362$	0.255304	+	0.351396i	0.0134185	+	0.0184690i
$363$	15.3484	+	2.43094i	0.805581	+	0.127591i
$364$	6.54434	+	5.60789i	0.343017	+	0.293934i
$365$	16.0694	−	32.4012i	0.841112	−	1.69596i
$366$	−0.0198464	+	0.125305i	−0.00103739	+	0.00654982i
$367$	−3.06840	+	1.56343i	−0.160169	+	0.0816104i	−0.532238	−	0.846595i	$-0.678649\pi$
$367$	−3.06840	+	1.56343i	−0.160169	+	0.0816104i	0.372068	+	0.928205i	$0.378649\pi$
$368$	−2.69723	−	2.69723i	−0.140603	−	0.140603i
$369$	27.4452	−	13.9840i	1.42874	−	0.727979i
$370$	−2.37094	+	0.401902i	−0.123259	+	0.0208939i
$371$	14.2150	−	27.8986i	0.738008	−	1.44842i
$372$	17.2076	−	5.59108i	0.892172	−	0.289884i
$373$	−8.49754	+	1.34588i	−0.439986	+	0.0696869i	−0.372498	−	0.928033i	$-0.621499\pi$
$373$	−8.49754	+	1.34588i	−0.439986	+	0.0696869i	−0.0674882	+	0.997720i	$0.521499\pi$
$374$	26.0761			1.34836
$375$	0.957074	+	29.4304i	0.0494231	+	1.51978i
$376$			2.25259i			0.116169i
$377$	21.8507	+	18.7241i	1.12537	+	0.964338i
$378$	−5.25306	−	2.67657i	−0.270188	−	0.137668i
$379$	−6.62479	+	13.0019i	−0.340293	+	0.667862i	−0.996211	−	0.0869700i	$-0.972282\pi$
$379$	−6.62479	+	13.0019i	−0.340293	+	0.667862i	0.655918	+	0.754832i	$0.272282\pi$
$380$	−4.67769	+	6.58723i	−0.239960	+	0.337918i
$381$	44.0593	+	14.3157i	2.25723	+	0.733418i
$382$	7.76101			0.397088
$383$	14.9747	+	4.86556i	0.765170	+	0.248619i	0.665496	−	0.746402i	$-0.268220\pi$
$383$	14.9747	+	4.86556i	0.765170	+	0.248619i	0.0996737	+	0.995020i	$0.468220\pi$
$384$	−0.412005	+	2.60130i	−0.0210250	+	0.132747i
$385$	−7.01604	−	20.8227i	−0.357571	−	1.06122i
$386$	−5.93603	−	4.31278i	−0.302136	−	0.219515i
$387$	−0.961164	+	6.06855i	−0.0488587	+	0.308482i
$388$	9.80684	−	7.12509i	0.497867	−	0.361722i
$389$	−26.2636	−	19.0816i	−1.33162	−	0.967475i	−0.999708	−	0.0241636i	$-0.992308\pi$
$389$	−26.2636	−	19.0816i	−1.33162	−	0.967475i	−0.331908	−	0.943312i	$-0.607692\pi$
$390$	19.6914	+	7.94490i	0.997112	+	0.402306i
$391$	−19.5743	+	14.2215i	−0.989913	+	0.719214i
$392$	−0.397517	+	1.22343i	−0.0200776	+	0.0617926i
$393$	6.48655	−	6.48655i	0.327203	−	0.327203i
$394$	4.11807	−	12.6741i	0.207465	−	0.638512i
$395$	−6.78143	−	12.9602i	−0.341211	−	0.652097i
$396$	14.4191	+	7.34689i	0.724586	+	0.369195i
$397$	27.7466	−	9.01541i	1.39256	−	0.452471i	0.485783	−	0.874079i	$-0.338534\pi$
$397$	27.7466	−	9.01541i	1.39256	−	0.452471i	0.906778	+	0.421609i	$0.138534\pi$
$398$	2.14237	+	1.55652i	0.107387	+	0.0780215i
$399$			22.7460i			1.13872i
$400$	2.85058	−	4.10782i	0.142529	−	0.205391i
$401$	2.64339	+	2.64339i	0.132004	+	0.132004i	0.770022	−	0.638017i	$-0.220245\pi$
$401$	2.64339	+	2.64339i	0.132004	+	0.132004i	−0.638017	+	0.770022i	$0.720245\pi$
$402$	28.0139	−	4.43696i	1.39720	−	0.221296i
$403$	−12.9764	+	21.0982i	−0.646401	+	1.05098i
$404$	7.96919	−	2.58935i	0.396482	−	0.128825i
$405$	11.7545	+	1.73138i	0.584085	+	0.0860328i
$406$	5.89513	−	18.1433i	0.292570	−	0.900438i
$407$	3.12621	−	3.12621i	0.154961	−	0.154961i
$408$	15.8881	+	5.16236i	0.786578	+	0.255575i
$409$	−20.7727	−	3.29007i	−1.02714	−	0.162683i	−0.379948	−	0.925008i	$-0.624058\pi$
$409$	−20.7727	−	3.29007i	−1.02714	−	0.162683i	−0.647195	+	0.762325i	$0.724058\pi$
$410$	14.2659	+	10.1304i	0.704541	+	0.500305i
$411$	6.38825	+	40.3339i	0.315109	+	1.98952i
$412$	3.81959	+	0.604964i	0.188178	+	0.0298045i
$413$	16.4060	+	2.59845i	0.807285	+	0.127861i
$414$	−14.8307	+	2.34896i	−0.728890	+	0.115445i
$415$	−3.03873	+	20.6302i	−0.149165	+	1.01270i
$416$	−1.87888	−	3.07731i	−0.0921195	−	0.150877i
$417$	5.87360	−	2.99275i	0.287631	−	0.146555i
$418$		−	14.8534i		−	0.726505i
$419$	−16.6844	−	5.42109i	−0.815086	−	0.264837i	−0.128335	−	0.991731i	$-0.540963\pi$
$419$	−16.6844	−	5.42109i	−0.815086	−	0.264837i	−0.686750	+	0.726893i	$0.740963\pi$
$420$	−0.152538	−	14.0762i	−0.00744309	−	0.686847i
$421$	−7.21377	−	3.67560i	−0.351578	−	0.179138i	0.269278	−	0.963062i	$-0.413215\pi$
$421$	−7.21377	−	3.67560i	−0.351578	−	0.179138i	−0.620856	+	0.783925i	$0.713215\pi$
$422$	0.443579	+	1.36520i	0.0215931	+	0.0664567i
$423$	7.17381	+	5.21208i	0.348803	+	0.253420i
$424$	−9.26256	+	9.26256i	−0.449830	+	0.449830i
$425$	−22.9066	−	21.9347i	−1.11114	−	1.06399i
$426$			34.3328i			1.66343i
$427$	−0.0676790	+	0.0931521i	−0.00327522	+	0.00450795i
$428$	3.34962	−	6.57401i	0.161910	−	0.317767i
$429$	−37.9743	+	9.05130i	−1.83342	+	0.437001i
$430$	−3.30742	+	1.11441i	−0.159498	+	0.0537416i
$431$	−17.6392	−	34.6189i	−0.849651	−	1.66753i	−0.739031	−	0.673671i	$-0.764717\pi$
$431$	−17.6392	−	34.6189i	−0.849651	−	1.66753i	−0.110619	−	0.993863i	$-0.535283\pi$
$432$	1.74406	+	1.74406i	0.0839111	+	0.0839111i
$433$	−26.2114	+	13.3554i	−1.25964	+	0.641819i	−0.950950	−	0.309344i	$-0.899891\pi$
$433$	−26.2114	+	13.3554i	−1.25964	+	0.641819i	−0.308690	+	0.951163i	$0.599891\pi$
$434$	16.2188	+	2.56880i	0.778527	+	0.123307i
$435$	−0.509305	−	46.9986i	−0.0244193	−	2.25341i
$436$	−0.751816	−	4.74678i	−0.0360055	−	0.227330i
$437$	8.10085	+	11.1499i	0.387516	+	0.533370i
$438$	−6.66396	+	42.0746i	−0.318416	+	2.01040i
$439$	11.5981	+	8.42651i	0.553547	+	0.402175i	0.829091	−	0.559113i	$-0.188858\pi$
$439$	11.5981	+	8.42651i	0.553547	+	0.402175i	−0.275545	+	0.961288i	$0.588858\pi$
$440$	0.0996092	+	9.19192i	0.00474868	+	0.438208i
$441$	2.97647	+	4.09676i	0.141737	+	0.195084i
$442$	−21.1434	+	8.71749i	−1.00569	+	0.414649i
$443$	18.1813	−	18.1813i	0.863821	−	0.863821i	−0.127959	−	0.991779i	$-0.540843\pi$
$443$	18.1813	−	18.1813i	0.863821	−	0.863821i	0.991779	+	0.127959i	$0.0408425\pi$
$444$	2.52370	−	1.28589i	0.119769	−	0.0610256i
$445$	6.21954	+	18.4588i	0.294835	+	0.875029i
$446$	24.4717	−	7.95134i	1.15877	−	0.376507i
$447$	−16.2980	−	50.1600i	−0.770867	−	2.37249i
$448$	−1.40499	+	1.93381i	−0.0663796	+	0.0913637i
$449$	13.6140	−	13.6140i	0.642483	−	0.642483i	−0.308682	−	0.951165i	$-0.599888\pi$
$449$	13.6140	−	13.6140i	0.642483	−	0.642483i	0.951165	+	0.308682i	$0.0998879\pi$
$450$	−6.48645	−	18.5830i	−0.305774	−	0.876009i
$451$	−32.1679			−1.51473
$452$	2.15522	−	0.341353i	0.101373	−	0.0160559i
$453$	2.96186	+	9.11568i	0.139161	+	0.428292i
$454$	−0.582356	−	1.79231i	−0.0273313	−	0.0841172i
$455$	12.6501	+	14.5382i	0.593045	+	0.681563i
$456$	2.94057	−	9.05016i	0.137705	−	0.423812i
$457$	−12.1698			−0.569278			−0.284639	−	0.958635i	$-0.591874\pi$
$457$	−12.1698			−0.569278			−0.284639	+	0.958635i	$0.591874\pi$
$458$	10.2074	+	20.0332i	0.476961	+	0.936090i
$459$	12.6570	−	9.19582i	0.590776	−	0.429224i
$460$	−5.08792	−	6.84568i	−0.237226	−	0.319182i
$461$	−26.6768	+	4.22519i	−1.24246	+	0.196787i	−0.742847	−	0.669461i	$-0.766525\pi$
$461$	−26.6768	+	4.22519i	−1.24246	+	0.196787i	−0.499615	+	0.866247i	$0.666525\pi$
$462$	15.2122	+	20.9377i	0.707734	+	0.974112i
$463$	−23.2027	+	16.8578i	−1.07832	+	0.783446i	−0.977389	−	0.211447i	$-0.932182\pi$
$463$	−23.2027	+	16.8578i	−1.07832	+	0.783446i	−0.100932	+	0.994893i	$0.532182\pi$
$464$	−4.69109	+	6.45674i	−0.217779	+	0.299746i
$465$	39.8884	−	6.76157i	1.84978	−	0.313560i
$466$	−12.5726	−	1.99130i	−0.582414	−	0.0922453i
$467$	5.88119	+	11.5425i	0.272149	+	0.534122i	0.986116	−	0.166057i	$-0.0531035\pi$
$467$	5.88119	+	11.5425i	0.272149	+	0.534122i	−0.713967	+	0.700179i	$0.753104\pi$
$468$	−14.1477	−	1.13668i	−0.653975	−	0.0525430i
$469$	24.4819	+	7.95464i	1.13047	+	0.367311i
$470$	−0.733998	+	4.98318i	−0.0338568	+	0.229857i
$471$	−12.6864	−	39.0448i	−0.584559	−	1.79909i
$472$	−6.19167	−	3.15481i	−0.284995	−	0.145212i
$473$	3.77156	−	5.19110i	0.173416	−	0.238687i
$474$	12.1823	+	12.1823i	0.559553	+	0.559553i
$475$	−12.4944	+	13.0481i	−0.573283	+	0.598686i
$476$	10.7210	+	10.7210i	0.491397	+	0.491397i
$477$	8.06656	+	50.9303i	0.369343	+	2.33194i
$478$	−5.88678	+	11.5535i	−0.269255	+	0.528443i
$479$	32.6065	+	16.6139i	1.48983	+	0.759107i	0.994007	−	0.109317i	$-0.0348663\pi$
$479$	32.6065	+	16.6139i	1.48983	+	0.759107i	0.495823	+	0.868423i	$0.334866\pi$
$480$	−1.75906	+	5.62034i	−0.0802897	+	0.256532i
$481$	−1.48972	+	3.57997i	−0.0679254	+	0.163232i
$482$	−1.67091	−	1.67091i	−0.0761077	−	0.0761077i
$483$	−22.8383	−	7.42062i	−1.03918	−	0.337650i
$484$	−3.46810	−	4.77343i	−0.157641	−	0.216974i
$485$	24.0164	−	12.5666i	1.09053	−	0.570620i
$486$	−21.1303	+	3.34671i	−0.958489	+	0.151810i
$487$	16.3223	−	11.8588i	0.739634	−	0.537375i	−0.152963	−	0.988232i	$-0.548881\pi$
$487$	16.3223	−	11.8588i	0.739634	−	0.537375i	0.892596	+	0.450857i	$0.148881\pi$
$488$	0.0389707	−	0.0283138i	0.00176412	−	0.00128171i
$489$	17.0298	−	2.69725i	0.770113	−	0.121974i
$490$	−1.27804	+	2.57695i	−0.0577358	+	0.116415i
$491$	5.77600	+	7.94999i	0.260667	+	0.358778i	0.919211	−	0.393764i	$-0.128827\pi$
$491$	5.77600	+	7.94999i	0.260667	+	0.358778i	−0.658544	+	0.752542i	$0.728827\pi$
$492$	−19.5998	−	6.36836i	−0.883627	−	0.287108i
$493$	35.7961	+	35.7961i	1.61218	+	1.61218i
$494$	4.96565	+	12.0437i	0.223415	+	0.541871i
$495$	29.5039	+	20.9512i	1.32610	+	0.941686i
$496$	−6.12103	−	3.11882i	−0.274842	−	0.140039i
$497$	−14.1462	+	27.7635i	−0.634545	+	1.24536i
$498$	−3.84222	−	24.2588i	−0.172174	−	1.08706i
$499$	−12.6863	−	12.6863i	−0.567918	−	0.567918i	0.363627	−	0.931545i	$-0.381538\pi$
$499$	−12.6863	−	12.6863i	−0.567918	−	0.567918i	−0.931545	+	0.363627i	$0.881538\pi$
$500$	7.64456	−	8.15847i	0.341875	−	0.364858i
$501$	−29.8910	−	29.8910i	−1.33543	−	1.33543i
$502$	16.0144	−	22.0419i	0.714756	−	0.983778i
$503$	−16.7894	−	8.55463i	−0.748603	−	0.381432i	0.0376875	−	0.999290i	$-0.488001\pi$
$503$	−16.7894	−	8.55463i	−0.748603	−	0.381432i	−0.786290	+	0.617857i	$0.788001\pi$
$504$	2.90769	+	8.94894i	0.129519	+	0.398617i
$505$	18.4732	−	3.13142i	0.822045	−	0.139347i
$506$	14.9137	+	4.84576i	0.662995	+	0.215420i
$507$	27.7650	−	20.0343i	1.23309	−	0.889755i
$508$	−7.98561	−	15.6726i	−0.354304	−	0.695361i
$509$	6.26560	+	0.992373i	0.277718	+	0.0439862i	0.293740	−	0.955885i	$-0.405100\pi$
$509$	6.26560	+	0.992373i	0.277718	+	0.0439862i	−0.0160218	+	0.999872i	$0.505100\pi$
$510$	33.4655	+	16.5972i	1.48188	+	0.734938i
$511$	−22.7250	+	31.2783i	−1.00529	+	1.38367i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−5.23811	−	7.20964i	−0.231268	−	0.318313i
$514$	7.64657	−	1.21110i	0.337276	−	0.0534192i
$515$	8.25258	+	2.58290i	0.363652	+	0.113816i
$516$	3.32570	−	2.41626i	0.146406	−	0.106370i
$517$	−4.20413	−	8.25107i	−0.184897	−	0.362882i
$518$	2.57064			0.112948
$519$	15.7329	−	48.4208i	0.690596	−	2.12544i
$520$	−3.15372	−	7.41984i	−0.138300	−	0.325382i
$521$	−8.58898	−	26.4342i	−0.376290	−	1.15810i	−0.942604	−	0.333913i	$-0.891631\pi$
$521$	−8.58898	−	26.4342i	−0.376290	−	1.15810i	0.566314	−	0.824190i	$-0.308369\pi$
$522$	9.70840	+	29.8794i	0.424925	+	1.30779i
$523$	19.0276	−	3.01368i	0.832019	−	0.131779i	0.274128	−	0.961693i	$-0.411611\pi$
$523$	19.0276	−	3.01368i	0.832019	−	0.131779i	0.557891	+	0.829914i	$0.311611\pi$
$524$	−3.48304			−0.152157
$525$	4.24922	−	31.1890i	0.185451	−	1.36120i
$526$	15.4078	−	15.4078i	0.671812	−	0.671812i
$527$	−25.6128	+	35.2530i	−1.11571	+	1.53565i
$528$	−3.34580	−	10.2973i	−0.145607	−	0.448132i
$529$	8.03637	−	2.61118i	0.349407	−	0.113529i
$530$	−23.5088	+	17.4725i	−1.02116	+	0.758955i
$531$	−24.3735	+	12.4189i	−1.05772	+	0.538935i
$532$	6.10689	−	6.10689i	0.264767	−	0.264767i
$533$	26.0829	−	10.7540i	1.12977	−	0.465809i
$534$	−13.4852	−	18.5608i	−0.583561	−	0.803203i
$535$	9.55215	−	13.4515i	0.412975	−	0.581561i
$536$	−8.71246	−	6.32997i	−0.376321	−	0.273413i
$537$	0.745043	−	4.70401i	0.0321510	−	0.202993i
$538$	1.67833	+	2.31002i	0.0723579	+	0.0995921i
$539$	−0.827280	−	5.22324i	−0.0356335	−	0.224981i
$540$	3.28991	+	4.42650i	0.141575	+	0.190486i
$541$	12.4093	+	1.96544i	0.533516	+	0.0845007i	0.417379	−	0.908732i	$-0.362949\pi$
$541$	12.4093	+	1.96544i	0.533516	+	0.0845007i	0.116137	+	0.993233i	$0.462949\pi$
$542$	−6.68902	+	3.40823i	−0.287318	+	0.146396i
$543$	−0.808900	−	0.808900i	−0.0347132	−	0.0347132i
$544$	−2.87967	−	5.65166i	−0.123465	−	0.242313i
$545$	−0.116448	−	10.7458i	−0.00498808	−	0.460300i
$546$	−19.3343	−	11.8915i	−0.827430	−	0.508909i
$547$	−8.02828	+	15.7564i	−0.343264	+	0.673694i	−0.996512	−	0.0834502i	$-0.973406\pi$
$547$	−8.02828	+	15.7564i	−0.343264	+	0.673694i	0.653248	+	0.757144i	$0.273406\pi$
$548$	9.11378	−	12.5440i	0.389321	−	0.535855i
$549$		−	0.189623i		−	0.00809289i
$550$	−2.77480	+	20.3668i	−0.118318	+	0.868444i
$551$	20.3901	−	20.3901i	0.868649	−	0.868649i
$552$	8.12756	+	5.90502i	0.345932	+	0.251334i
$553$	4.83184	+	14.8709i	0.205471	+	0.632374i
$554$	−15.8445	−	8.07318i	−0.673168	−	0.342996i
$555$	6.00192	−	2.02230i	0.254767	−	0.0858420i
$556$	−2.38045	−	0.773456i	−0.100954	−	0.0328018i
$557$		−	17.0736i		−	0.723431i	−0.932289	−	0.361715i	$-0.882191\pi$
$557$		−	17.0736i		−	0.723431i	0.932289	−	0.361715i	$-0.117809\pi$
$558$	−24.0954	+	12.2772i	−1.02004	+	0.519736i
$559$	−1.32268	+	5.47000i	−0.0559432	+	0.231356i
$560$	−3.73824	+	3.82015i	−0.157970	+	0.161431i
$561$	−67.8316	+	10.7435i	−2.86385	+	0.453590i
$562$	−3.10999	−	0.492574i	−0.131187	−	0.0207780i
$563$	38.8130	+	6.14737i	1.63577	+	0.259081i	0.905585	−	0.424166i	$-0.139433\pi$
$563$	38.8130	+	6.14737i	1.63577	+	0.259081i	0.730188	+	0.683247i	$0.239433\pi$
$564$	−0.928079	−	5.85966i	−0.0390792	−	0.246736i
$565$	4.87899	−	0.0528717i	0.205261	−	0.00222433i
$566$	4.21361	+	0.667371i	0.177111	+	0.0280517i
$567$	−12.0793	−	3.92479i	−0.507282	−	0.164826i
$568$	9.21772	−	9.21772i	0.386767	−	0.386767i
$569$	8.22409	−	25.3112i	0.344772	−	1.06110i	−0.616934	−	0.787015i	$-0.711625\pi$
$569$	8.22409	−	25.3112i	0.344772	−	1.06110i	0.961706	−	0.274084i	$-0.0883746\pi$
$570$	9.45409	−	19.0626i	0.395988	−	0.798443i
$571$	4.05457	−	1.31741i	0.169678	−	0.0551319i	−0.222946	−	0.974831i	$-0.571567\pi$
$571$	4.05457	−	1.31741i	0.169678	−	0.0551319i	0.392624	+	0.919699i	$0.371567\pi$
$572$	12.6255	+	7.76530i	0.527899	+	0.324683i
$573$	−20.1887	+	3.19758i	−0.843395	+	0.133581i
$574$	−13.2256	−	13.2256i	−0.552026	−	0.552026i
$575$	−9.02486	−	16.8019i	−0.376363	−	0.700687i
$576$		−	3.93650i		−	0.164021i
$577$	−35.5656	−	25.8399i	−1.48061	−	1.07573i	−0.977358	−	0.211592i	$-0.932135\pi$
$577$	−35.5656	−	25.8399i	−1.48061	−	1.07573i	−0.503256	−	0.864137i	$-0.667865\pi$
$578$	−22.0966	+	7.17963i	−0.919099	+	0.298633i
$579$	17.2183	+	8.77315i	0.715567	+	0.364600i
$580$	−12.4815	+	12.7550i	−0.518268	+	0.529623i
$581$	6.88838	−	21.2002i	0.285778	−	0.879535i
$582$	−22.5749	+	22.5749i	−0.935762	+	0.935762i
$583$	16.6409	−	51.2153i	0.689194	−	2.12112i
$584$	13.0854	−	9.50711i	0.541479	−	0.393407i
$585$	−30.9270	−	7.12452i	−1.27868	−	0.294562i
$586$	−22.4226	−	16.2910i	−0.926269	−	0.672974i
$587$	−1.30541	+	0.948433i	−0.0538799	+	0.0391460i	−0.614399	−	0.788995i	$-0.710602\pi$
$587$	−1.30541	+	0.948433i	−0.0538799	+	0.0391460i	0.560519	+	0.828141i	$0.310602\pi$
$588$	0.530000	−	3.34629i	0.0218568	−	0.137999i
$589$	20.0808	+	14.5895i	0.827414	+	0.601152i
$590$	−12.6692	−	8.99660i	−0.521583	−	0.370384i
$591$	−5.49052	+	34.6658i	−0.225850	+	1.42596i
$592$	−1.02280	−	0.332329i	−0.0420370	−	0.0136587i
$593$	−38.0656			−1.56317			−0.781583	−	0.623802i	$-0.785587\pi$
$593$	−38.0656			−1.56317			−0.781583	+	0.623802i	$0.785587\pi$
$594$	−9.64339	−	3.13333i	−0.395673	−	0.128562i
$595$	20.2236	+	27.2104i	0.829087	+	1.11552i
$596$	−9.09134	+	17.8428i	−0.372396	+	0.730868i
$597$	−6.21424	−	3.16632i	−0.254332	−	0.129589i
$598$	−13.7126	+	1.05669i	−0.560748	+	0.0432111i
$599$			24.8865i			1.01684i	0.861110	+	0.508418i	$0.169770\pi$
$599$			24.8865i			1.01684i	−0.861110	+	0.508418i	$0.830230\pi$
$600$	−5.72275	+	11.8601i	−0.233630	+	0.484187i
$601$	−2.25576			−0.0920142			−0.0460071	−	0.998941i	$-0.514650\pi$
$601$	−2.25576			−0.0920142			−0.0460071	+	0.998941i	$0.514650\pi$
$602$	3.68494	−	0.583637i	0.150187	−	0.0237873i
$603$	−40.3180	+	13.1001i	−1.64188	+	0.533478i
$604$	1.65219	−	3.24260i	0.0672266	−	0.131940i
$605$	−6.11672	−	11.6898i	−0.248680	−	0.475259i
$606$	−19.6634	+	10.0190i	−0.798772	+	0.406994i
$607$	18.9565	+	18.9565i	0.769420	+	0.769420i	0.978004	−	0.208585i	$-0.0668857\pi$
$607$	18.9565	+	18.9565i	0.769420	+	0.769420i	−0.208585	+	0.978004i	$0.566886\pi$
$608$	−3.21929	+	1.64031i	−0.130560	+	0.0665234i
$609$	−7.85983	+	49.6250i	−0.318496	+	2.01091i
$610$	0.0954368	−	0.0499374i	0.00386412	−	0.00202191i
$611$	6.16728	+	5.28478i	0.249501	+	0.213799i
$612$	−24.6618	−	3.90605i	−0.996895	−	0.157893i
$613$	22.3969	+	30.8266i	0.904601	+	1.24508i	0.968977	+	0.247151i	$0.0794943\pi$
$613$	22.3969	+	30.8266i	0.904601	+	1.24508i	−0.0643760	+	0.997926i	$0.520506\pi$
$614$	−9.59839	+	13.2111i	−0.387360	+	0.533155i
$615$	−41.2836	−	20.4746i	−1.66471	−	0.825615i
$616$	1.53721	−	9.70559i	0.0619362	−	0.391049i
$617$	−11.9832	+	36.8805i	−0.482425	+	1.48475i	0.353250	+	0.935529i	$0.385077\pi$
$617$	−11.9832	+	36.8805i	−0.482425	+	1.48475i	−0.835675	+	0.549224i	$0.814923\pi$
$618$	−10.1851			−0.409707
$619$	−13.9760	−	27.4294i	−0.561742	−	1.10248i	−0.980890	−	0.194562i	$-0.937671\pi$
$619$	−13.9760	−	27.4294i	−0.561742	−	1.10248i	0.419149	−	0.907918i	$-0.362329\pi$
$620$	−12.5247	−	8.89396i	−0.503003	−	0.357190i
$621$	8.94777	−	2.90731i	0.359062	−	0.116666i
$622$	3.84211	−	1.24838i	0.154055	−	0.0500554i
$623$	−3.25729	−	20.5657i	−0.130500	−	0.823947i
$624$	6.15538	+	7.23089i	0.246412	+	0.289467i
$625$	19.5697	−	15.5572i	0.782788	−	0.622289i
$626$	−18.7590	+	18.7590i	−0.749759	+	0.749759i
$627$	6.11969	+	38.6382i	0.244397	+	1.54306i
$628$	−7.07674	+	13.8889i	−0.282393	+	0.554227i
$629$	−3.09691	+	6.07803i	−0.123482	+	0.242347i
$630$	3.51640	+	20.7443i	0.140097	+	0.826472i
$631$	−20.8952	+	10.6466i	−0.831826	+	0.423836i	−0.817408	−	0.576060i	$-0.804590\pi$
$631$	−20.8952	+	10.6466i	−0.831826	+	0.423836i	−0.0144182	+	0.999896i	$0.504590\pi$
$632$		−	6.54147i		−	0.260206i
$633$	−1.71635	−	3.36853i	−0.0682188	−	0.133887i
$634$	22.0261	−	16.0029i	0.874767	−	0.635556i
$635$	−12.5589	−	37.2731i	−0.498385	−	1.47914i
$636$	20.2785	−	27.9109i	0.804093	−	1.10674i
$637$	2.41697	+	3.95863i	0.0957639	+	0.156846i
$638$	5.13257	−	32.4058i	0.203200	−	1.28296i
$639$	−8.02751	−	50.6837i	−0.317563	−	2.00502i
$640$	1.98123	−	1.03668i	0.0783152	−	0.0409785i
$641$	0.499503	+	0.687507i	0.0197292	+	0.0271549i	0.818768	−	0.574125i	$-0.194658\pi$
$641$	0.499503	+	0.687507i	0.0197292	+	0.0271549i	−0.799038	+	0.601280i	$0.794658\pi$
$642$	−6.00484	+	18.4810i	−0.236992	+	0.729387i
$643$		−	11.5875i		−	0.456968i	−0.973548	−	0.228484i	$-0.926623\pi$
$643$		−	11.5875i		−	0.456968i	0.973548	−	0.228484i	$-0.0733769\pi$
$644$	4.13937	+	8.12397i	0.163114	+	0.320129i
$645$	8.14443	−	4.26158i	0.320687	−	0.167800i
$646$	7.08203	+	21.7962i	0.278639	+	0.857561i
$647$	−16.9147	−	8.61846i	−0.664984	−	0.338826i	0.0887043	−	0.996058i	$-0.471727\pi$
$647$	−16.9147	−	8.61846i	−0.664984	−	0.338826i	−0.753689	+	0.657232i	$0.771727\pi$
$648$	4.29870	+	3.12319i	0.168869	+	0.122690i
$649$	28.5676			1.12138
$650$	−4.55893	−	17.4418i	−0.178816	−	0.684123i
$651$	−43.2483			−1.69503
$652$	−5.29635	−	3.84802i	−0.207421	−	0.150700i
$653$	−6.83883	−	3.48456i	−0.267624	−	0.136361i	0.315030	−	0.949082i	$-0.397986\pi$
$653$	−6.83883	−	3.48456i	−0.267624	−	0.136361i	−0.582654	+	0.812721i	$0.697986\pi$
$654$	3.91140	+	12.0380i	0.152948	+	0.470725i
$655$	−7.70518	−	1.13493i	−0.301066	−	0.0443456i
$656$	3.55240	+	6.97198i	0.138698	+	0.272210i
$657$		−	63.6707i		−	2.48403i
$658$	1.66387	−	5.12087i	0.0648645	−	0.199632i
$659$	6.98104	+	9.60857i	0.271943	+	0.374297i	0.923044	−	0.384694i	$-0.125693\pi$
$659$	6.98104	+	9.60857i	0.271943	+	0.374297i	−0.651102	+	0.758990i	$0.725693\pi$
$660$	−4.04623	−	23.8699i	−0.157499	−	0.929134i
$661$	−4.72447	−	29.8291i	−0.183761	−	1.16022i	−0.891256	−	0.453501i	$-0.850175\pi$
$661$	−4.72447	−	29.8291i	−0.183761	−	1.16022i	0.707495	−	0.706718i	$-0.249825\pi$
$662$	3.28680	−	20.7520i	0.127745	−	0.806551i
$663$	51.4087	−	31.3880i	1.99655	−	1.21901i
$664$	−5.48148	+	7.54461i	−0.212723	+	0.292788i
$665$	15.4996	−	11.5197i	0.601047	−	0.446717i
$666$	−3.42495	+	2.48837i	−0.132714	+	0.0964224i
$667$	13.8208	+	27.1249i	0.535145	+	1.05028i
$668$			16.0504i			0.621007i
$669$	−60.3822	+	30.7663i	−2.33451	+	1.18949i
$670$	−17.2111	−	16.8421i	−0.664923	−	0.650666i
$671$	−0.0899029	+	0.176444i	−0.00347066	+	0.00681156i
$672$	2.85806	−	5.60927i	0.110252	−	0.216382i
$673$	−6.19854	−	39.1360i	−0.238936	−	1.50858i	−0.757098	−	0.653301i	$-0.773384\pi$
$673$	−6.19854	−	39.1360i	−0.238936	−	1.50858i	0.518162	−	0.855282i	$-0.326616\pi$
$674$	−4.58599	+	4.58599i	−0.176646	+	0.176646i
$675$	5.83558	+	10.8643i	0.224612	+	0.418167i
$676$	−12.8332	−	2.07555i	−0.493586	−	0.0798287i
$677$	−4.46786	−	28.2090i	−0.171714	−	1.08416i	−0.911495	−	0.411312i	$-0.865071\pi$
$677$	−4.46786	−	28.2090i	−0.171714	−	1.08416i	0.739781	−	0.672848i	$-0.234929\pi$
$678$	−5.46572	+	1.77592i	−0.209910	+	0.0682038i
$679$	−27.5571	+	8.95384i	−1.05754	+	0.343617i
$680$	−4.52882	−	13.4409i	−0.173672	−	0.515436i
$681$	2.25332	+	4.42239i	0.0863475	+	0.169466i
$682$	28.2417			1.08143
$683$	−1.76028	+	5.41757i	−0.0673551	+	0.207298i	−0.979069	−	0.203528i	$-0.934759\pi$
$683$	−1.76028	+	5.41757i	−0.0673551	+	0.207298i	0.911714	+	0.410825i	$0.134759\pi$
$684$	−2.22496	+	14.0478i	−0.0850734	+	0.537133i
$685$	24.2489	−	24.7802i	0.926503	−	0.946803i
$686$	11.6423	−	16.0243i	0.444506	−	0.611810i
$687$	−34.8063	−	47.9068i	−1.32794	−	1.82776i
$688$	−1.54161	−	0.244167i	−0.0587734	−	0.00930879i
$689$	3.62878	+	47.0904i	0.138245	+	1.79400i
$690$	16.0557	+	15.7114i	0.611228	+	0.598123i
$691$	2.19148	−	13.8365i	0.0833678	−	0.526364i	−0.910295	−	0.413960i	$-0.864145\pi$
$691$	2.19148	−	13.8365i	0.0833678	−	0.526364i	0.993663	−	0.112403i	$-0.0358548\pi$
$692$	−17.2241	+	8.77611i	−0.654761	+	0.333618i
$693$	−27.3525	−	27.3525i	−1.03904	−	1.03904i
$694$	−4.07917	+	2.07844i	−0.154843	+	0.0788966i
$695$	−5.01401	−	2.48670i	−0.190192	−	0.0943259i
$696$	9.54272	−	18.7286i	0.361716	−	0.709908i
$697$	47.2038	−	15.3374i	1.78797	−	0.580947i
$698$	3.16587	−	0.501425i	0.119830	−	0.0189792i
$699$	33.5255			1.26805
$700$	−9.51452	+	7.23285i	−0.359615	+	0.273376i
$701$			6.32389i			0.238850i	0.992843	+	0.119425i	$0.0381051\pi$
$701$			6.32389i			0.238850i	−0.992843	+	0.119425i	$0.961895\pi$
$702$	8.86671	−	0.683267i	0.334652	−	0.0257882i
$703$	3.46216	+	1.76406i	0.130578	+	0.0665327i
$704$	−1.86635	+	3.66292i	−0.0703408	+	0.138052i
$705$	−0.143749	−	13.2652i	−0.00541390	−	0.499594i
$706$	−2.54672	−	0.827481i	−0.0958472	−	0.0311426i
$707$	−20.0292			−0.753275
$708$	17.4062	+	5.65561i	0.654164	+	0.212551i
$709$	−3.86033	+	24.3732i	−0.144978	+	0.915354i	0.802760	+	0.596303i	$0.203364\pi$
$709$	−3.86033	+	24.3732i	−0.144978	+	0.915354i	−0.947737	+	0.319051i	$0.896636\pi$
$710$	23.3950	−	17.3879i	0.877999	−	0.652556i
$711$	−20.8326	−	15.1357i	−0.781282	−	0.567635i
$712$	−1.36270	+	8.60376i	−0.0510694	+	0.322440i
$713$	−21.1999	+	15.4026i	−0.793942	+	0.576832i
$714$	−32.3056	−	23.4714i	−1.20901	−	0.878396i
$715$	25.3999	+	21.2924i	0.949901	+	0.796289i
$716$	−1.46297	+	1.06291i	−0.0546738	+	0.0397229i
$717$	10.5532	−	32.4793i	0.394116	−	1.21296i
$718$	−1.15047	+	1.15047i	−0.0429351	+	0.0429351i
$719$	−11.4440	+	35.2210i	−0.426790	+	1.31352i	0.474481	+	0.880266i	$0.342636\pi$
$719$	−11.4440	+	35.2210i	−0.426790	+	1.31352i	−0.901270	+	0.433257i	$0.857364\pi$
$720$	1.28269	−	8.70831i	0.0478031	−	0.324540i
$721$	−8.23632	−	4.19662i	−0.306737	−	0.156290i
$722$	−5.65453	+	1.83727i	−0.210440	+	0.0683761i
$723$	5.03495	+	3.65810i	0.187252	+	0.136046i
$724$			0.434350i			0.0161425i
$725$	−31.7678	+	24.1496i	−1.17983	+	0.896893i
$726$	10.9882	+	10.9882i	0.407811	+	0.407811i
$727$	−19.4769	+	3.08483i	−0.722356	+	0.114410i	−0.506778	−	0.862077i	$-0.669164\pi$
$727$	−19.4769	+	3.08483i	−0.722356	+	0.114410i	−0.215578	+	0.976487i	$0.569164\pi$
$728$	1.99825	+	8.38355i	0.0740600	+	0.310715i
$729$	38.4270	−	12.4857i	1.42322	−	0.462433i
$730$	32.0454	−	16.7678i	1.18605	−	0.620604i
$731$	−3.05938	+	9.41579i	−0.113155	+	0.348256i
$732$	−0.0897088	+	0.0897088i	−0.00331573	+	0.00331573i
$733$	3.51996	+	1.14371i	0.130013	+	0.0422437i	0.373301	−	0.927710i	$-0.378226\pi$
$733$	3.51996	+	1.14371i	0.130013	+	0.0422437i	−0.243288	+	0.969954i	$0.578226\pi$
$734$	−3.40135	−	0.538721i	−0.125546	−	0.0198846i
$735$	2.26284	−	7.22996i	0.0834661	−	0.266681i
$736$	−0.596712	−	3.76749i	−0.0219951	−	0.138872i
$737$	43.7270	+	6.92568i	1.61071	+	0.255111i
$738$	30.4232	+	4.81856i	1.11989	+	0.177374i
$739$	−34.6968	+	5.49543i	−1.27634	+	0.202153i	−0.757567	−	0.652758i	$-0.773612\pi$
$739$	−34.6968	+	5.49543i	−1.27634	+	0.202153i	−0.518776	+	0.854911i	$0.673612\pi$
$740$	−2.15436	−	1.06846i	−0.0791958	−	0.0392772i
$741$	−17.8792	−	29.2834i	−0.656808	−	1.07575i
$742$	27.8986	−	14.2150i	1.02419	−	0.521851i
$743$		−	40.3334i		−	1.47969i	−0.672778	−	0.739844i	$-0.734899\pi$
$743$		−	40.3334i		−	1.47969i	0.672778	−	0.739844i	$-0.265101\pi$
$744$	17.2076	+	5.59108i	0.630861	+	0.204979i
$745$	−25.9258	+	36.5093i	−0.949849	+	1.33760i
$746$	−7.66574	−	3.90589i	−0.280663	−	0.143005i
$747$	11.3441	+	34.9137i	0.415060	+	1.27742i
$748$	21.0960	+	15.3271i	0.771346	+	0.560416i
$749$	−12.4707	+	12.4707i	−0.455668	+	0.455668i
$750$	−16.5244	+	24.3722i	−0.603387	+	0.889947i
$751$			0.747832i			0.0272888i	0.999907	+	0.0136444i	$0.00434328\pi$
$751$			0.747832i			0.0272888i	−0.999907	+	0.0136444i	$0.995657\pi$
$752$	−1.32404	+	1.82239i	−0.0482828	+	0.0664556i
$753$	−32.5768	+	63.9355i	−1.18716	+	2.32994i
$754$	6.67190	+	27.9916i	0.242976	+	1.01940i
$755$	4.71156	−	6.63492i	0.171471	−	0.241470i
$756$	−2.67657	−	5.25306i	−0.0973458	−	0.191052i
$757$	2.07047	+	2.07047i	0.0752524	+	0.0752524i	0.743731	−	0.668479i	$-0.233054\pi$
$757$	2.07047	+	2.07047i	0.0752524	+	0.0752524i	−0.668479	+	0.743731i	$0.733054\pi$
$758$	−13.0019	+	6.62479i	−0.472250	+	0.240623i
$759$	−40.7915	−	6.46073i	−1.48064	−	0.234510i
$760$	−7.65621	+	2.57970i	−0.277720	+	0.0935757i
$761$	−0.582886	−	3.68020i	−0.0211296	−	0.133407i	0.974869	−	0.222781i	$-0.0715134\pi$
$761$	−0.582886	−	3.68020i	−0.0211296	−	0.133407i	−0.995998	+	0.0893738i	$0.971513\pi$
$762$	27.2302	+	37.4791i	0.986445	+	1.35772i
$763$	−1.79708	+	11.3463i	−0.0650586	+	0.410764i
$764$	6.27879	+	4.56181i	0.227159	+	0.165040i
$765$	−53.2841	−	16.6769i	−1.92649	−	0.602955i
$766$	9.25485	+	12.7382i	0.334391	+	0.460250i
$767$	−23.1636	+	9.55043i	−0.836390	+	0.344846i
$768$	−1.86232	+	1.86232i	−0.0672008	+	0.0672008i
$769$	9.74324	−	4.96443i	0.351350	−	0.179022i	−0.269404	−	0.963027i	$-0.586827\pi$
$769$	9.74324	−	4.96443i	0.351350	−	0.179022i	0.620754	+	0.784005i	$0.286827\pi$
$770$	6.56315	−	20.9698i	0.236520	−	0.755699i
$771$	−19.3920	+	6.30085i	−0.698387	+	0.226920i
$772$	−2.26736	−	6.97822i	−0.0816042	−	0.251152i
$773$	27.6786	−	38.0963i	0.995531	−	1.37023i	0.0675028	−	0.997719i	$-0.478497\pi$
$773$	27.6786	−	38.0963i	0.995531	−	1.37023i	0.928028	−	0.372511i	$-0.121503\pi$
$774$	−4.34460	+	4.34460i	−0.156163	+	0.156163i
$775$	−24.8090	−	23.7563i	−0.891166	−	0.853352i
$776$	12.1219			0.435152
$777$	−6.68700	+	1.05912i	−0.239895	+	0.0379956i
$778$	−10.0318	−	30.8747i	−0.359657	−	1.10691i
$779$	−8.73650	−	26.8882i	−0.313017	−	0.963369i
$780$	11.2608	+	18.0019i	0.403200	+	0.644570i
$781$	−16.5603	+	50.9673i	−0.592574	+	1.82375i
$782$	−24.1951			−0.865216
$783$	−8.93673	−	17.5393i	−0.319373	−	0.626804i
$784$	−1.04071	+	0.756122i	−0.0371683	+	0.0270044i
$785$	−20.1808	+	28.4190i	−0.720283	+	1.01432i
$786$	9.06043	−	1.43503i	0.323175	−	0.0511859i
$787$	10.3326	+	14.2216i	0.368318	+	0.506947i	0.952443	−	0.304717i	$-0.0985620\pi$
$787$	10.3326	+	14.2216i	0.368318	+	0.506947i	−0.584125	+	0.811664i	$0.698562\pi$
$788$	10.7812	−	7.83303i	0.384066	−	0.279040i
$789$	−33.7322	+	46.4284i	−1.20090	+	1.65289i
$790$	2.13151	−	14.4710i	0.0758358	−	0.514856i
$791$	−5.15165	−	0.815941i	−0.183171	−	0.0290115i
$792$	7.34689	+	14.4191i	0.261060	+	0.512360i
$793$	0.0139094	−	0.173123i	0.000493937	−	0.00614777i
$794$	27.7466	+	9.01541i	0.984689	+	0.319945i
$795$	53.9546	−	55.1368i	1.91357	−	1.95550i
$796$	0.818313	+	2.51851i	0.0290044	+	0.0892662i
$797$	−19.2989	−	9.83327i	−0.683601	−	0.348312i	0.0774569	−	0.996996i	$-0.475320\pi$
$797$	−19.2989	−	9.83327i	−0.683601	−	0.348312i	−0.761058	+	0.648683i	$0.775320\pi$
$798$	−13.3698	+	18.4019i	−0.473284	+	0.651420i
$799$	10.1033	+	10.1033i	0.357429	+	0.357429i
$800$	4.72068	−	1.64777i	0.166901	−	0.0582575i
$801$	24.2473	+	24.2473i	0.856736	+	0.856736i
$802$	0.584801	+	3.69229i	0.0206500	+	0.130379i
$803$	−30.1873	+	59.2458i	−1.06529	+	2.09074i
$804$	25.2717	+	12.8766i	0.891263	+	0.454121i
$805$	6.50995	+	19.3206i	0.229446	+	0.680963i
$806$	−22.8994	+	9.44147i	−0.806596	+	0.332562i
$807$	−5.31757	−	5.31757i	−0.187187	−	0.187187i
$808$	7.96919	+	2.58935i	0.280355	+	0.0910929i
$809$	15.0629	+	20.7323i	0.529584	+	0.728910i	0.987067	−	0.160308i	$-0.0512489\pi$
$809$	15.0629	+	20.7323i	0.529584	+	0.728910i	−0.457483	+	0.889218i	$0.651249\pi$
$810$	8.49190	+	8.30983i	0.298375	+	0.291978i
$811$	41.7625	−	6.61453i	1.46648	−	0.232267i	0.628432	−	0.777865i	$-0.283697\pi$
$811$	41.7625	−	6.61453i	1.46648	−	0.232267i	0.838047	+	0.545597i	$0.183697\pi$
$812$	15.4336	−	11.2132i	0.541615	−	0.393506i
$813$	15.9959	−	11.6217i	0.561002	−	0.407591i
$814$	4.36670	−	0.691617i	0.153053	−	0.0242412i
$815$	−10.4627	−	10.2384i	−0.366493	−	0.358635i
$816$	9.81938	+	13.5152i	0.343747	+	0.473127i
$817$	5.36341	+	1.74268i	0.187642	+	0.0609686i
$818$	−14.8716	−	14.8716i	−0.519973	−	0.519973i
$819$	31.3226	+	13.0342i	1.09450	+	0.455451i
$820$	5.58683	+	16.5809i	0.195100	+	0.579032i
$821$	10.5400	+	5.37041i	0.367849	+	0.187429i	0.628137	−	0.778102i	$-0.283818\pi$
$821$	10.5400	+	5.37041i	0.367849	+	0.187429i	−0.260288	+	0.965531i	$0.583818\pi$
$822$	−18.5394	+	36.3857i	−0.646637	+	1.26910i
$823$	−4.11330	−	25.9703i	−0.143381	−	0.905269i	−0.949557	−	0.313594i	$-0.898467\pi$
$823$	−4.11330	−	25.9703i	−0.143381	−	0.905269i	0.806176	−	0.591675i	$-0.201533\pi$
$824$	2.73453	+	2.73453i	0.0952618	+	0.0952618i
$825$	−1.17316	−	54.1234i	−0.0408443	−	1.88433i
$826$	11.7454	+	11.7454i	0.408674	+	0.408674i
$827$	24.3219	−	33.4762i	0.845756	−	1.16408i	−0.139026	−	0.990289i	$-0.544397\pi$
$827$	24.3219	−	33.4762i	0.845756	−	1.16408i	0.984782	−	0.173794i	$-0.0556028\pi$
$828$	−13.3790	−	6.81693i	−0.464952	−	0.236905i
$829$	−7.62958	−	23.4814i	−0.264986	−	0.815544i	−0.991697	−	0.128600i	$-0.958952\pi$
$829$	−7.62958	−	23.4814i	−0.264986	−	0.815544i	0.726710	−	0.686944i	$-0.241048\pi$
$830$	−14.5845	+	14.9041i	−0.506236	+	0.517328i
$831$	44.5425	+	14.4727i	1.54516	+	0.502053i
$832$	0.288754	−	3.59397i	0.0100107	−	0.124598i
$833$	3.70438	+	7.27026i	0.128349	+	0.251899i
$834$	6.51093	+	1.03123i	0.225455	+	0.0357086i
$835$	−5.22995	+	35.5066i	−0.180990	+	1.22876i
$836$	8.73062	−	12.0167i	0.301955	−	0.415605i
$837$	13.7081	−	9.95952i	0.473821	−	0.344251i
$838$	−10.3115	−	14.1926i	−0.356205	−	0.490275i
$839$	34.9326	−	5.53278i	1.20601	−	0.191013i	0.479107	−	0.877757i	$-0.340961\pi$
$839$	34.9326	−	5.53278i	1.20601	−	0.191013i	0.726899	+	0.686744i	$0.240961\pi$
$840$	8.15037	−	11.4775i	0.281214	−	0.396012i
$841$	28.0695	−	20.3937i	0.967914	−	0.703231i
$842$	−3.67560	−	7.21377i	−0.126670	−	0.248603i
$843$	8.29295			0.285624
$844$	−0.443579	+	1.36520i	−0.0152686	+	0.0469920i
$845$	−27.7134	−	8.77318i	−0.953369	−	0.301807i
$846$	2.74015	+	8.43332i	0.0942084	+	0.289944i
$847$	4.35823	+	13.4133i	0.149751	+	0.460885i
$848$	−12.9380	+	2.04917i	−0.444292	+	0.0703689i
$849$	−11.2358			−0.385613
$850$	−5.63899	−	31.2097i	−0.193416	−	1.07048i
$851$	−2.90071	+	2.90071i	−0.0994349	+	0.0994349i
$852$	−20.1803	+	27.7758i	−0.691365	+	0.951583i
$853$	−10.7326	−	33.0314i	−0.367476	−	1.13097i	−0.948416	−	0.317028i	$-0.897315\pi$
$853$	−10.7326	−	33.0314i	−0.367476	−	1.13097i	0.580941	−	0.813946i	$-0.302685\pi$
$854$	−0.109507	+	0.0355810i	−0.00374725	+	0.00121756i
$855$	−9.49948	+	30.3516i	−0.324875	+	1.03800i
$856$	6.57401	−	3.34962i	0.224695	−	0.114488i
$857$	32.7464	−	32.7464i	1.11860	−	1.11860i	0.126647	−	0.991948i	$-0.459578\pi$
$857$	32.7464	−	32.7464i	1.11860	−	1.11860i	0.991948	−	0.126647i	$-0.0404216\pi$
$858$	−36.0421	−	14.9981i	−1.23046	−	0.512026i
$859$	−14.6878	−	20.2161i	−0.501142	−	0.689763i	0.481252	−	0.876582i	$-0.340182\pi$
$859$	−14.6878	−	20.2161i	−0.501142	−	0.689763i	−0.982394	+	0.186819i	$0.940182\pi$
$860$	−3.33079	−	1.04247i	−0.113579	−	0.0355481i
$861$	39.8527	+	28.9547i	1.35818	+	0.986774i
$862$	6.07806	−	38.3753i	0.207019	−	1.30707i
$863$	−22.7765	−	31.3491i	−0.775320	−	1.06714i	−0.995783	−	0.0917409i	$-0.970757\pi$
$863$	−22.7765	−	31.3491i	−0.775320	−	1.06714i	0.220463	−	0.975395i	$-0.429243\pi$
$864$	0.385841	+	2.43611i	0.0131266	+	0.0828780i
$865$	−40.9628	+	13.8021i	−1.39278	+	0.469285i
$866$	−29.0556	−	4.60195i	−0.987349	−	0.156381i
$867$	54.5219	−	27.7803i	1.85166	−	0.943468i
$868$	11.6114	+	11.6114i	0.394116	+	0.394116i
$869$	12.2087	+	23.9609i	0.414151	+	0.812818i
$870$	27.2131	−	38.3220i	0.922609	−	1.29924i
$871$	−37.7708	+	9.00279i	−1.27981	+	0.305048i
$872$	2.18186	−	4.28213i	0.0738870	−	0.145011i
$873$	28.0479	−	38.6046i	0.949277	−	1.30657i
$874$			13.7820i			0.466183i
$875$	−23.4048	+	12.9002i	−0.791227	+	0.436107i
$876$	−30.1221	+	30.1221i	−1.01773	+	1.01773i
$877$	−1.33561	−	0.970377i	−0.0451003	−	0.0327673i	0.565007	−	0.825086i	$-0.308874\pi$
$877$	−1.33561	−	0.970377i	−0.0451003	−	0.0327673i	−0.610107	+	0.792319i	$0.708874\pi$
$878$	4.43008	+	13.6344i	0.149508	+	0.460138i
$879$	65.0398	+	33.1394i	2.19374	+	1.11777i
$880$	−5.32229	+	7.49497i	−0.179414	+	0.252655i
$881$	19.1460	+	6.22092i	0.645046	+	0.209588i	0.613229	−	0.789905i	$-0.289870\pi$
$881$	19.1460	+	6.22092i	0.645046	+	0.209588i	0.0318177	+	0.999494i	$0.489870\pi$
$882$			5.06388i			0.170510i
$883$	32.0718	−	16.3414i	1.07930	−	0.549932i	0.178402	−	0.983958i	$-0.442907\pi$
$883$	32.0718	−	16.3414i	1.07930	−	0.549932i	0.900901	+	0.434025i	$0.142907\pi$
$884$	−22.2294	−	5.37519i	−0.747656	−	0.180787i
$885$	36.6630	+	18.1831i	1.23241	+	0.611217i
$886$	25.3957	−	4.02229i	0.853186	−	0.135131i
$887$	−12.3713	−	1.95942i	−0.415387	−	0.0657908i	−0.0547566	−	0.998500i	$-0.517438\pi$
$887$	−12.3713	−	1.95942i	−0.415387	−	0.0657908i	−0.360630	+	0.932709i	$0.617438\pi$
$888$	2.79754	+	0.443087i	0.0938793	+	0.0148690i
$889$	6.57732	+	41.5276i	0.220596	+	1.39279i
$890$	−5.81807	+	18.5892i	−0.195022	+	0.623111i
$891$	−21.5748	−	3.41711i	−0.722782	−	0.114477i
$892$	24.4717	+	7.95134i	0.819373	+	0.266231i
$893$	5.75503	−	5.75503i	0.192585	−	0.192585i
$894$	16.2980	−	50.1600i	0.545085	−	1.67760i
$895$	−3.58273	+	1.87467i	−0.119758	+	0.0626633i
$896$	−2.27333	+	0.738648i	−0.0759465	+	0.0246765i
$897$	35.2351	−	8.39840i	1.17646	−	0.280414i
$898$	19.0160	−	3.01184i	0.634573	−	0.100507i
$899$	38.7689	+	38.7689i	1.29302	+	1.29302i
$900$	5.67514	−	18.8466i	0.189171	−	0.628219i
$901$			83.0886i			2.76808i
$902$	−26.0243	−	18.9078i	−0.866516	−	0.629561i
$903$	−9.34516	+	3.03643i	−0.310987	+	0.101046i
$904$	1.94425	+	0.990644i	0.0646647	+	0.0329483i
$905$	−0.141531	+	0.960868i	−0.00470465	+	0.0319403i
$906$	−2.96186	+	9.11568i	−0.0984014	+	0.302848i
$907$	26.4978	−	26.4978i	0.879844	−	0.879844i	−0.113674	−	0.993518i	$-0.536262\pi$
$907$	26.4978	−	26.4978i	0.879844	−	0.879844i	0.993518	+	0.113674i	$0.0362620\pi$
$908$	0.582356	−	1.79231i	0.0193262	−	0.0594798i
$909$	26.6855	−	19.3882i	0.885103	−	0.643065i
$910$	1.68878	+	19.1972i	0.0559823	+	0.636381i
$911$	36.4110	+	26.4542i	1.20635	+	0.876465i	0.994894	−	0.100922i	$-0.0321792\pi$
$911$	36.4110	+	26.4542i	1.20635	+	0.876465i	0.211457	+	0.977387i	$0.432179\pi$
$912$	7.69852	−	5.59330i	0.254924	−	0.185213i
$913$	5.99734	−	37.8657i	0.198483	−	1.25317i
$914$	−9.84556	−	7.15322i	−0.325662	−	0.236607i
$915$	−0.227685	+	0.169222i	−0.00752703	+	0.00559432i
$916$	−3.51724	+	22.2070i	−0.116213	+	0.733739i
$917$	7.91809	+	2.57274i	0.261478	+	0.0849594i
$918$	15.6449			0.516357
$919$	7.01647	+	2.27979i	0.231452	+	0.0752033i	0.422447	−	0.906388i	$-0.361171\pi$
$919$	7.01647	+	2.27979i	0.231452	+	0.0752033i	−0.190995	+	0.981591i	$0.561171\pi$
$920$	−0.0924240	−	8.52888i	−0.00304713	−	0.281189i
$921$	19.5253	−	38.3205i	0.643379	−	1.26270i
$922$	−24.0655	−	12.2620i	−0.792555	−	0.403827i
$923$	−3.61121	−	46.8624i	−0.118864	−	1.54250i
$924$			25.8805i			0.851405i
$925$	−4.41772	−	3.06563i	−0.145254	−	0.100797i
$926$	−28.6801			−0.942487
$927$	15.0358	−	2.38144i	0.493841	−	0.0782167i
$928$	−7.59035	+	2.46625i	−0.249165	+	0.0809588i
$929$	3.63557	−	7.13520i	0.119279	−	0.234098i	−0.823645	−	0.567105i	$-0.808063\pi$
$929$	3.63557	−	7.13520i	0.119279	−	0.234098i	0.942924	+	0.333007i	$0.108063\pi$
$930$	36.2448	+	17.9756i	1.18851	+	0.589443i
$931$	4.14127	−	2.11008i	0.135725	−	0.0691552i
$932$	−9.00097	−	9.00097i	−0.294837	−	0.294837i
$933$	−9.48013	+	4.83037i	−0.310366	+	0.158139i
$934$	−2.02652	+	12.7949i	−0.0663097	+	0.418663i
$935$	41.6743	+	40.7807i	1.36289	+	1.33367i
$936$	−10.7776	−	9.23537i	−0.352276	−	0.301868i
$937$	−15.1306	−	2.39645i	−0.494295	−	0.0782886i	−0.0956897	−	0.995411i	$-0.530506\pi$
$937$	−15.1306	−	2.39645i	−0.494295	−	0.0782886i	−0.398605	+	0.917123i	$0.630506\pi$
$938$	15.1306	+	20.8255i	0.494033	+	0.679978i
$939$	41.0689	−	56.5264i	1.34023	−	1.84467i
$940$	−3.52286	+	3.60005i	−0.114903	+	0.117421i
$941$	−2.50158	+	15.7943i	−0.0815490	+	0.514880i	0.912773	+	0.408467i	$0.133937\pi$
$941$	−2.50158	+	15.7943i	−0.0815490	+	0.514880i	−0.994322	+	0.106413i	$0.966063\pi$
$942$	12.6864	−	39.0448i	0.413346	−	1.27215i
$943$	29.8475			0.971967
$944$	−3.15481	−	6.19167i	−0.102680	−	0.201522i
$945$	−4.20941	−	12.4930i	−0.136932	−	0.406396i
$946$	6.10251	−	1.98282i	0.198410	−	0.0644672i
$947$	−26.8217	+	8.71489i	−0.871587	+	0.283196i	−0.710460	−	0.703738i	$-0.751513\pi$
$947$	−26.8217	+	8.71489i	−0.871587	+	0.283196i	−0.161127	+	0.986934i	$0.551513\pi$
$948$	2.69512	+	17.0163i	0.0875334	+	0.552664i
$949$	4.67044	−	58.1306i	0.151609	−	1.88700i
$950$	−17.7776	+	3.21207i	−0.576783	+	0.104213i
$951$	−50.7031	+	50.7031i	−1.64416	+	1.64416i
$952$	2.37183	+	14.9751i	0.0768714	+	0.485347i
$953$	−6.78829	+	13.3228i	−0.219894	+	0.431567i	−0.974430	−	0.224692i	$-0.927862\pi$
$953$	−6.78829	+	13.3228i	−0.219894	+	0.431567i	0.754535	+	0.656259i	$0.227862\pi$
$954$	−23.4101	+	45.9449i	−0.757929	+	1.48752i
$955$	12.4035	+	12.1375i	0.401368	+	0.392762i
$956$	−11.5535	+	5.88678i	−0.373665	+	0.190392i
$957$			86.4117i			2.79329i
$958$	16.6139	+	32.6065i	0.536769	+	1.05347i
$959$	−29.9842	+	21.7848i	−0.968240	+	0.703468i
$960$	−4.72666	+	3.51300i	−0.152552	+	0.113382i
$961$	−9.51860	+	13.1012i	−0.307052	+	0.422620i
$962$	−3.30946	+	2.02062i	−0.106701	+	0.0651474i
$963$	4.54351	−	28.6866i	0.146413	−	0.924413i
$964$	−0.369657	−	2.33393i	−0.0119059	−	0.0751707i
$965$	−2.74203	−	16.1760i	−0.0882691	−	0.520725i
$966$	−14.1149	−	19.4274i	−0.454138	−	0.625067i
$967$	6.20519	−	19.0976i	0.199545	−	0.614137i	−0.800348	−	0.599536i	$-0.795352\pi$
$967$	6.20519	−	19.0976i	0.199545	−	0.614137i	0.999893	−	0.0146017i	$-0.00464804\pi$
$968$		−	5.90028i		−	0.189642i
$969$	−27.4026	−	53.7807i	−0.880299	−	1.72768i
$970$	26.8161	+	3.94988i	0.861013	+	0.126823i
$971$	15.0351	+	46.2733i	0.482500	+	1.48498i	0.835569	+	0.549385i	$0.185138\pi$
$971$	15.0351	+	46.2733i	0.482500	+	1.48498i	−0.353069	+	0.935597i	$0.614862\pi$
$972$	−19.0619	−	9.71252i	−0.611411	−	0.311529i
$973$	4.84023	+	3.51663i	0.155171	+	0.112738i
$974$	20.1755			0.646464
$975$	19.0452	+	43.4930i	0.609936	+	1.39289i
$976$	0.0481704			0.00154190
$977$	23.5067	+	17.0786i	0.752045	+	0.546393i	0.896460	−	0.443124i	$-0.146130\pi$
$977$	23.5067	+	17.0786i	0.752045	+	0.546393i	−0.144415	+	0.989517i	$0.546130\pi$
$978$	15.3628	+	7.82773i	0.491248	+	0.250303i
$979$	−11.0662	−	34.0582i	−0.353677	−	1.08850i
$980$	−2.54864	+	1.33358i	−0.0814134	+	0.0425997i
$981$	−8.58887	−	16.8566i	−0.274221	−	0.538190i
$982$			9.82672i			0.313583i
$983$	0.997251	−	3.06922i	0.0318074	−	0.0978930i	−0.933892	−	0.357554i	$-0.883611\pi$
$983$	0.997251	−	3.06922i	0.0318074	−	0.0978930i	0.965700	+	0.259661i	$0.0836108\pi$
$984$	−12.1133	−	16.6726i	−0.386159	−	0.531503i
$985$	26.4026	−	13.8152i	0.841257	−	0.440189i
$986$	7.91924	+	50.0001i	0.252200	+	1.59233i
$987$	−2.21840	+	14.0064i	−0.0706125	+	0.445830i
$988$	−3.06181	+	12.6623i	−0.0974092	+	0.402841i
$989$	−3.49950	+	4.81665i	−0.111278	+	0.153161i
$990$	11.5544	+	34.2918i	0.367222	+	1.08987i
$991$	−17.4494	+	12.6778i	−0.554299	+	0.402722i	−0.829368	−	0.558702i	$-0.811299\pi$
$991$	−17.4494	+	12.6778i	−0.554299	+	0.402722i	0.275069	+	0.961425i	$0.411299\pi$
$992$	−3.11882	−	6.12103i	−0.0990226	−	0.194343i
$993$			55.3364i			1.75605i
$994$	−27.7635	+	14.1462i	−0.880606	+	0.448691i
$995$	0.989626	+	5.83809i	0.0313733	+	0.185080i
$996$	11.1505	−	21.8842i	0.353319	−	0.693427i
$997$	10.5407	−	20.6874i	0.333829	−	0.655176i	−0.661686	−	0.749781i	$-0.730159\pi$
$997$	10.5407	−	20.6874i	0.333829	−	0.655176i	0.995515	+	0.0946052i	$0.0301589\pi$
$998$	−2.80662	−	17.7203i	−0.0888419	−	0.560926i
$999$	1.87563	−	1.87563i	0.0593424	−	0.0593424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.ba.b.187.2	yes	144
13.8	odd	4		650.2.bd.b.437.2	yes	144
25.23	odd	20		650.2.bd.b.473.2	yes	144
325.73	even	20	inner	650.2.ba.b.73.2	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.ba.b.73.2	✓	144	325.73	even	20	inner
650.2.ba.b.187.2	yes	144	1.1	even	1	trivial
650.2.bd.b.437.2	yes	144	13.8	odd	4
650.2.bd.b.473.2	yes	144	25.23	odd	20

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.ba (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-2.34666 - 1.19569i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.373709 + 2.20462i) q^{5} +(-1.19569 - 2.34666i) q^{6} -2.39032i q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.31381 + 3.18469i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-2.34666 - 1.19569i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.373709 + 2.20462i) q^{5} +(-1.19569 - 2.34666i) q^{6} -2.39032i q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.31381 + 3.18469i) q^{9} +(-0.993505 + 2.00323i) q^{10} +(-0.643101 - 4.06038i) q^{11} +(0.412005 - 2.60130i) q^{12} +(1.87888 + 3.07731i) q^{13} +(1.40499 - 1.93381i) q^{14} +(1.75906 - 5.62034i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.87967 + 5.65166i) q^{17} +3.93650i q^{18} +(3.21929 - 1.64031i) q^{19} +(-1.98123 + 1.03668i) q^{20} +(-2.85806 + 5.60927i) q^{21} +(1.86635 - 3.66292i) q^{22} +(0.596712 + 3.76749i) q^{23} +(1.86232 - 1.86232i) q^{24} +(-4.72068 + 1.64777i) q^{25} +(-0.288754 + 3.59397i) q^{26} +(-0.385841 - 2.43611i) q^{27} +(2.27333 - 0.738648i) q^{28} +(7.59035 - 2.46625i) q^{29} +(4.72666 - 3.51300i) q^{30} +(3.11882 + 6.12103i) q^{31} -1.00000 q^{32} +(-3.34580 + 10.2973i) q^{33} +(-0.992265 + 6.26492i) q^{34} +(5.26973 - 0.893283i) q^{35} +(-2.31381 + 3.18469i) q^{36} +(0.632128 + 0.870050i) q^{37} +(3.56861 + 0.565213i) q^{38} +(-0.729599 - 9.46795i) q^{39} +(-2.21220 - 0.325846i) q^{40} +(1.22407 - 7.72850i) q^{41} +(-5.60927 + 2.85806i) q^{42} +(1.10367 + 1.10367i) q^{43} +(3.66292 - 1.86635i) q^{44} +(-6.15634 + 6.29123i) q^{45} +(-1.73173 + 3.39870i) q^{46} +(2.14234 - 0.696089i) q^{47} +(2.60130 - 0.412005i) q^{48} +1.28639 q^{49} +(-4.78765 - 1.44167i) q^{50} -16.7057i q^{51} +(-2.34609 + 2.73786i) q^{52} +(11.6715 + 5.94693i) q^{53} +(1.11976 - 2.19764i) q^{54} +(8.71126 - 2.93519i) q^{55} +(2.27333 + 0.738648i) q^{56} -9.51590 q^{57} +(7.59035 + 2.46625i) q^{58} +(-1.08707 + 6.86351i) q^{59} +(5.88884 - 0.0638150i) q^{60} +(-0.0389707 - 0.0283138i) q^{61} +(-1.07467 + 6.78521i) q^{62} +(7.61242 - 5.53075i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-6.08214 + 5.29222i) q^{65} +(-8.75941 + 6.36408i) q^{66} +(-3.32786 + 10.2421i) q^{67} +(-4.48519 + 4.48519i) q^{68} +(3.10445 - 9.55452i) q^{69} +(4.78836 + 2.37479i) q^{70} +(-11.6150 - 5.91814i) q^{71} +(-3.74383 + 1.21644i) q^{72} +(-13.0854 - 9.50711i) q^{73} +1.07544i q^{74} +(13.0481 + 1.77768i) q^{75} +(2.55485 + 2.55485i) q^{76} +(-9.70559 + 1.53721i) q^{77} +(4.97487 - 8.08858i) q^{78} +(-6.22131 + 2.02143i) q^{79} +(-1.59818 - 1.56391i) q^{80} +(1.64196 - 5.05342i) q^{81} +(5.53299 - 5.53299i) q^{82} +(8.86923 + 2.88179i) q^{83} +(-6.21792 - 0.984822i) q^{84} +(-11.3836 + 8.46064i) q^{85} +(0.244167 + 1.54161i) q^{86} +(-20.7609 - 3.28820i) q^{87} +(4.06038 + 0.643101i) q^{88} +(8.60376 - 1.36270i) q^{89} +(-8.67847 + 1.47111i) q^{90} +(7.35574 - 4.49111i) q^{91} +(-3.39870 + 1.73173i) q^{92} -18.0931i q^{93} +(2.14234 + 0.696089i) q^{94} +(4.81934 + 6.48431i) q^{95} +(2.34666 + 1.19569i) q^{96} +(-3.74588 - 11.5286i) q^{97} +(1.04071 + 0.756122i) q^{98} +(11.4431 - 11.4431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9}+O(q^{10}) \) 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9	\( 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9} + 6 q^{13} + 8 q^{15} - 36 q^{16} - 6 q^{17} - 20 q^{19} - 6 q^{21} + 12 q^{23} + 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} + 12 q^{30} - 6 q^{31} - 144 q^{32} - 54 q^{33} + 6 q^{34} + 40 q^{35} + 20 q^{36} - 60 q^{37} + 20 q^{39} + 52 q^{41} + 6 q^{42} - 12 q^{43} - 6 q^{45} + 28 q^{46} + 50 q^{47} - 160 q^{49} - 22 q^{50} + 6 q^{52} + 20 q^{53} - 6 q^{54} - 32 q^{55} - 28 q^{57} + 20 q^{58} - 16 q^{59} - 12 q^{60} + 12 q^{61} + 6 q^{62} - 70 q^{63} - 36 q^{64} + 44 q^{65} - 16 q^{66} - 8 q^{67} - 6 q^{68} + 26 q^{69} + 10 q^{70} + 72 q^{71} - 52 q^{73} + 32 q^{75} - 56 q^{77} - 50 q^{78} - 20 q^{79} + 124 q^{81} - 22 q^{82} + 70 q^{83} - 6 q^{84} - 18 q^{85} - 8 q^{86} + 8 q^{87} + 28 q^{89} - 14 q^{90} - 26 q^{91} + 12 q^{92} + 50 q^{94} - 46 q^{95} + 28 q^{97} - 20 q^{98} + 40 q^{99}+O(q^{100}) \) 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9 + 6 * q^13 + 8 * q^15 - 36 * q^16 - 6 * q^17 - 20 * q^19 - 6 * q^21 + 12 * q^23 + 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 + 12 * q^30 - 6 * q^31 - 144 * q^32 - 54 * q^33 + 6 * q^34 + 40 * q^35 + 20 * q^36 - 60 * q^37 + 20 * q^39 + 52 * q^41 + 6 * q^42 - 12 * q^43 - 6 * q^45 + 28 * q^46 + 50 * q^47 - 160 * q^49 - 22 * q^50 + 6 * q^52 + 20 * q^53 - 6 * q^54 - 32 * q^55 - 28 * q^57 + 20 * q^58 - 16 * q^59 - 12 * q^60 + 12 * q^61 + 6 * q^62 - 70 * q^63 - 36 * q^64 + 44 * q^65 - 16 * q^66 - 8 * q^67 - 6 * q^68 + 26 * q^69 + 10 * q^70 + 72 * q^71 - 52 * q^73 + 32 * q^75 - 56 * q^77 - 50 * q^78 - 20 * q^79 + 124 * q^81 - 22 * q^82 + 70 * q^83 - 6 * q^84 - 18 * q^85 - 8 * q^86 + 8 * q^87 + 28 * q^89 - 14 * q^90 - 26 * q^91 + 12 * q^92 + 50 * q^94 - 46 * q^95 + 28 * q^97 - 20 * q^98 + 40 * q^99

Introduction

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