LMFDB - Embedded newform 192.2.s.a.11.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(11,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8]))

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

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

chi := DirichletCharacter("192.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			11.23
Character	$\chi$	$=$	192.11
Dual form			192.2.s.a.35.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01373 + 0.986078i) q^{2} +(0.422356 + 1.67977i) q^{3} +(0.0553009 + 1.99924i) q^{4} +(1.22014 - 0.815271i) q^{5} +(-1.22823 + 2.11931i) q^{6} +(0.731141 - 1.76513i) q^{7} +(-1.91534 + 2.08122i) q^{8} +(-2.64323 + 1.41892i) q^{9} +O(q^{10})$	\(q+(1.01373 + 0.986078i) q^{2} +(0.422356 + 1.67977i) q^{3} +(0.0553009 + 1.99924i) q^{4} +(1.22014 - 0.815271i) q^{5} +(-1.22823 + 2.11931i) q^{6} +(0.731141 - 1.76513i) q^{7} +(-1.91534 + 2.08122i) q^{8} +(-2.64323 + 1.41892i) q^{9} +(2.04081 + 0.376687i) q^{10} +(1.20236 - 6.04466i) q^{11} +(-3.33489 + 0.937281i) q^{12} +(-3.02825 + 4.53210i) q^{13} +(2.48173 - 1.06840i) q^{14} +(1.88480 + 1.70521i) q^{15} +(-3.99388 + 0.221119i) q^{16} +(-3.03900 - 3.03900i) q^{17} +(-4.07869 - 1.16803i) q^{18} +(2.32633 - 3.48160i) q^{19} +(1.69739 + 2.39426i) q^{20} +(3.27381 + 0.482633i) q^{21} +(7.17937 - 4.94204i) q^{22} +(1.64886 + 3.98070i) q^{23} +(-4.30492 - 2.33831i) q^{24} +(-1.08934 + 2.62991i) q^{25} +(-7.53884 + 1.60824i) q^{26} +(-3.49984 - 3.84072i) q^{27} +(3.56934 + 1.36411i) q^{28} +(1.06679 - 0.212197i) q^{29} +(0.229203 + 3.58718i) q^{30} +5.57545 q^{31} +(-4.26676 - 3.71413i) q^{32} +(10.6614 - 0.533317i) q^{33} +(-0.0840376 - 6.07741i) q^{34} +(-0.546965 - 2.74978i) q^{35} +(-2.98292 - 5.20597i) q^{36} +(4.53654 - 3.03122i) q^{37} +(5.79140 - 1.23546i) q^{38} +(-8.89188 - 3.17260i) q^{39} +(-0.640227 + 4.10090i) q^{40} +(1.77481 - 0.735151i) q^{41} +(2.84285 + 3.71749i) q^{42} +(0.201937 - 1.01521i) q^{43} +(12.1512 + 2.06952i) q^{44} +(-2.06831 + 3.88623i) q^{45} +(-2.25378 + 5.66127i) q^{46} +(-7.29047 + 7.29047i) q^{47} +(-2.05827 - 6.61540i) q^{48} +(2.36863 + 2.36863i) q^{49} +(-3.69760 + 1.59184i) q^{50} +(3.82127 - 6.38834i) q^{51} +(-9.22821 - 5.80356i) q^{52} +(-9.51158 - 1.89197i) q^{53} +(0.239360 - 7.34457i) q^{54} +(-3.46099 - 8.35557i) q^{55} +(2.27323 + 4.90249i) q^{56} +(6.83081 + 2.43722i) q^{57} +(1.29068 + 0.836823i) q^{58} +(0.917273 + 1.37280i) q^{59} +(-3.30489 + 3.86245i) q^{60} +(-6.16153 + 1.22560i) q^{61} +(5.65200 + 5.49782i) q^{62} +(0.572001 + 5.70307i) q^{63} +(-0.662934 - 7.97249i) q^{64} +7.99864i q^{65} +(11.3337 + 9.97237i) q^{66} +(-0.485448 - 2.44051i) q^{67} +(5.90761 - 6.24373i) q^{68} +(-5.99025 + 4.45098i) q^{69} +(2.15702 - 3.32689i) q^{70} +(3.68483 + 1.52631i) q^{71} +(2.10961 - 8.21885i) q^{72} +(-2.00609 + 0.830949i) q^{73} +(7.58785 + 1.40054i) q^{74} +(-4.87773 - 0.719087i) q^{75} +(7.08918 + 4.45834i) q^{76} +(-9.79052 - 6.54181i) q^{77} +(-5.88554 - 11.9842i) q^{78} +(-1.55705 + 1.55705i) q^{79} +(-4.69282 + 3.52589i) q^{80} +(4.97334 - 7.50106i) q^{81} +(2.52410 + 1.00486i) q^{82} +(-12.4656 - 8.32922i) q^{83} +(-0.783852 + 6.57180i) q^{84} +(-6.18560 - 1.23039i) q^{85} +(1.20578 - 0.830021i) q^{86} +(0.807004 + 1.70233i) q^{87} +(10.2773 + 14.0800i) q^{88} +(2.73428 + 1.13258i) q^{89} +(-5.92883 + 1.90008i) q^{90} +(5.78567 + 8.65887i) q^{91} +(-7.86718 + 3.51660i) q^{92} +(2.35482 + 9.36545i) q^{93} +(-14.5796 + 0.201604i) q^{94} -6.14462i q^{95} +(4.43677 - 8.73585i) q^{96} +8.88438i q^{97} +(0.0655000 + 4.73681i) q^{98} +(5.39877 + 17.6835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$	1.01373	+	0.986078i	0.716816	+	0.697262i
$2$	1.01373	+	0.986078i	0.716816	+	0.697262i
$3$	0.422356	+	1.67977i	0.243847	+	0.969814i
$3$	0.422356	+	1.67977i	0.243847	+	0.969814i
$4$	0.0553009	+	1.99924i	0.0276504	+	0.999618i
$5$	1.22014	−	0.815271i	0.545663	−	0.364600i	−0.251978	−	0.967733i	$-0.581081\pi$
$5$	1.22014	−	0.815271i	0.545663	−	0.364600i	0.797641	+	0.603133i	$0.206081\pi$
$6$	−1.22823	+	2.11931i	−0.501421	+	0.865203i
$7$	0.731141	−	1.76513i	0.276345	−	0.667156i	−0.723384	−	0.690446i	$-0.757414\pi$
$7$	0.731141	−	1.76513i	0.276345	−	0.667156i	0.999729	+	0.0232901i	$0.00741415\pi$
$8$	−1.91534	+	2.08122i	−0.677175	+	0.735822i
$9$	−2.64323	+	1.41892i	−0.881077	+	0.472973i
$10$	2.04081	+	0.376687i	0.645362	+	0.119119i
$11$	1.20236	−	6.04466i	0.362525	−	1.82253i	−0.181412	−	0.983407i	$-0.558067\pi$
$11$	1.20236	−	6.04466i	0.362525	−	1.82253i	0.543936	−	0.839127i	$-0.316933\pi$
$12$	−3.33489	+	0.937281i	−0.962700	+	0.270570i
$13$	−3.02825	+	4.53210i	−0.839887	+	1.25698i	0.124430	+	0.992228i	$0.460290\pi$
$13$	−3.02825	+	4.53210i	−0.839887	+	1.25698i	−0.964317	+	0.264751i	$0.914710\pi$
$14$	2.48173	−	1.06840i	0.663272	−	0.285543i
$15$	1.88480	+	1.70521i	0.486653	+	0.440284i
$16$	−3.99388	+	0.221119i	−0.998471	+	0.0552797i
$17$	−3.03900	−	3.03900i	−0.737065	−	0.737065i	0.234944	−	0.972009i	$-0.424509\pi$
$17$	−3.03900	−	3.03900i	−0.737065	−	0.737065i	−0.972009	+	0.234944i	$0.924509\pi$
$18$	−4.07869	−	1.16803i	−0.961356	−	0.275307i
$19$	2.32633	−	3.48160i	0.533696	−	0.798733i	−0.462431	−	0.886655i	$-0.653023\pi$
$19$	2.32633	−	3.48160i	0.533696	−	0.798733i	0.996127	+	0.0879221i	$0.0280227\pi$
$20$	1.69739	+	2.39426i	0.379549	+	0.535373i
$21$	3.27381	+	0.482633i	0.714403	+	0.105319i
$22$	7.17937	−	4.94204i	1.53065	−	1.05365i
$23$	1.64886	+	3.98070i	0.343811	+	0.830034i	0.997323	+	0.0731180i	$0.0232950\pi$
$23$	1.64886	+	3.98070i	0.343811	+	0.830034i	−0.653512	+	0.756916i	$0.726705\pi$
$24$	−4.30492	−	2.33831i	−0.878737	−	0.477306i
$25$	−1.08934	+	2.62991i	−0.217869	+	0.525982i
$26$	−7.53884	+	1.60824i	−1.47849	+	0.315402i
$27$	−3.49984	−	3.84072i	−0.673544	−	0.739147i
$28$	3.56934	+	1.36411i	0.674542	+	0.257792i
$29$	1.06679	−	0.212197i	0.198097	−	0.0394040i	−0.0950443	−	0.995473i	$-0.530299\pi$
$29$	1.06679	−	0.212197i	0.198097	−	0.0394040i	0.293142	+	0.956069i	$0.405299\pi$
$30$	0.229203	+	3.58718i	0.0418466	+	0.654927i
$31$	5.57545			1.00138			0.500690	−	0.865627i	$-0.333080\pi$
$31$	5.57545			1.00138			0.500690	+	0.865627i	$0.333080\pi$
$32$	−4.26676	−	3.71413i	−0.754264	−	0.656571i
$33$	10.6614	−	0.533317i	1.85592	−	0.0928386i
$34$	−0.0840376	−	6.07741i	−0.0144123	−	1.04227i
$35$	−0.546965	−	2.74978i	−0.0924540	−	0.464798i
$36$	−2.98292	−	5.20597i	−0.497154	−	0.867662i
$37$	4.53654	−	3.03122i	0.745803	−	0.498330i	−0.123662	−	0.992324i	$-0.539464\pi$
$37$	4.53654	−	3.03122i	0.745803	−	0.498330i	0.869465	+	0.493995i	$0.164464\pi$
$38$	5.79140	−	1.23546i	0.939489	−	0.200418i
$39$	−8.89188	−	3.17260i	−1.42384	−	0.508023i
$40$	−0.640227	+	4.10090i	−0.101229	+	0.648409i
$41$	1.77481	−	0.735151i	0.277179	−	0.114811i	−0.239764	−	0.970831i	$-0.577070\pi$
$41$	1.77481	−	0.735151i	0.277179	−	0.114811i	0.516943	+	0.856020i	$0.327070\pi$
$42$	2.84285	+	3.71749i	0.438661	+	0.573621i
$43$	0.201937	−	1.01521i	0.0307951	−	0.154818i	−0.962328	−	0.271891i	$-0.912351\pi$
$43$	0.201937	−	1.01521i	0.0307951	−	0.154818i	0.993123	+	0.117073i	$0.0373511\pi$
$44$	12.1512	+	2.06952i	1.83186	+	0.311992i
$45$	−2.06831	+	3.88623i	−0.308325	+	0.579324i
$46$	−2.25378	+	5.66127i	−0.332302	+	0.834709i
$47$	−7.29047	+	7.29047i	−1.06342	+	1.06342i	−0.0655774	+	0.997847i	$0.520889\pi$
$47$	−7.29047	+	7.29047i	−1.06342	+	1.06342i	−0.997847	+	0.0655774i	$0.979111\pi$
$48$	−2.05827	−	6.61540i	−0.297085	−	0.954851i
$49$	2.36863	+	2.36863i	0.338376	+	0.338376i
$50$	−3.69760	+	1.59184i	−0.522920	+	0.225121i
$51$	3.82127	−	6.38834i	0.535084	−	0.894546i
$52$	−9.22821	−	5.80356i	−1.27972	−	0.804810i
$53$	−9.51158	−	1.89197i	−1.30652	−	0.259882i	−0.507740	−	0.861510i	$-0.669519\pi$
$53$	−9.51158	−	1.89197i	−1.30652	−	0.259882i	−0.798776	+	0.601628i	$0.794519\pi$
$54$	0.239360	−	7.34457i	0.0325728	−	0.999469i
$55$	−3.46099	−	8.35557i	−0.466680	−	1.12667i
$56$	2.27323	+	4.90249i	0.303774	+	0.655123i
$57$	6.83081	+	2.43722i	0.904763	+	0.322817i
$58$	1.29068	+	0.836823i	0.169474	+	0.109880i
$59$	0.917273	+	1.37280i	0.119419	+	0.178723i	0.886363	−	0.462991i	$-0.153224\pi$
$59$	0.917273	+	1.37280i	0.119419	+	0.178723i	−0.766944	+	0.641714i	$0.778224\pi$
$60$	−3.30489	+	3.86245i	−0.426660	+	0.498640i
$61$	−6.16153	+	1.22560i	−0.788903	+	0.156923i	−0.573069	−	0.819507i	$-0.694247\pi$
$61$	−6.16153	+	1.22560i	−0.788903	+	0.156923i	−0.215834	+	0.976430i	$0.569247\pi$
$62$	5.65200	+	5.49782i	0.717805	+	0.698224i
$63$	0.572001	+	5.70307i	0.0720653	+	0.718520i
$64$	−0.662934	−	7.97249i	−0.0828668	−	0.996561i
$65$			7.99864i			0.992110i
$66$	11.3337	+	9.97237i	1.39509	+	1.22751i
$67$	−0.485448	−	2.44051i	−0.0593069	−	0.298156i	0.939736	−	0.341902i	$-0.111071\pi$
$67$	−0.485448	−	2.44051i	−0.0593069	−	0.298156i	−0.999043	+	0.0437455i	$0.986071\pi$
$68$	5.90761	−	6.24373i	0.716403	−	0.757163i
$69$	−5.99025	+	4.45098i	−0.721141	+	0.535835i
$70$	2.15702	−	3.32689i	0.257813	−	0.397639i
$71$	3.68483	+	1.52631i	0.437309	+	0.181139i	0.590466	−	0.807063i	$-0.298944\pi$
$71$	3.68483	+	1.52631i	0.437309	+	0.181139i	−0.153157	+	0.988202i	$0.548944\pi$
$72$	2.10961	−	8.21885i	0.248620	−	0.968601i
$73$	−2.00609	+	0.830949i	−0.234795	+	0.0972553i	−0.496979	−	0.867763i	$-0.665557\pi$
$73$	−2.00609	+	0.830949i	−0.234795	+	0.0972553i	0.262184	+	0.965018i	$0.415557\pi$
$74$	7.58785	+	1.40054i	0.882070	+	0.162810i
$75$	−4.87773	−	0.719087i	−0.563231	−	0.0830330i
$76$	7.08918	+	4.45834i	0.813185	+	0.511407i
$77$	−9.79052	−	6.54181i	−1.11573	−	0.745509i
$78$	−5.88554	−	11.9842i	−0.666406	−	1.35695i
$79$	−1.55705	+	1.55705i	−0.175182	+	0.175182i	−0.789252	−	0.614070i	$-0.789531\pi$
$79$	−1.55705	+	1.55705i	−0.175182	+	0.175182i	0.614070	+	0.789252i	$0.289531\pi$
$80$	−4.69282	+	3.52589i	−0.524673	+	0.394207i
$81$	4.97334	−	7.50106i	0.552594	−	0.833451i
$82$	2.52410	+	1.00486i	0.278740	+	0.110968i
$83$	−12.4656	−	8.32922i	−1.36827	−	0.914250i	−0.368391	−	0.929671i	$-0.620091\pi$
$83$	−12.4656	−	8.32922i	−1.36827	−	0.914250i	−0.999881	+	0.0154204i	$0.995091\pi$
$84$	−0.783852	+	6.57180i	−0.0855253	+	0.717042i
$85$	−6.18560	−	1.23039i	−0.670922	−	0.133455i
$86$	1.20578	−	0.830021i	0.130023	−	0.0895035i
$87$	0.807004	+	1.70233i	0.0865200	+	0.182509i
$88$	10.2773	+	14.0800i	1.09557	+	1.50093i
$89$	2.73428	+	1.13258i	0.289833	+	0.120053i	0.522863	−	0.852417i	$-0.324864\pi$
$89$	2.73428	+	1.13258i	0.289833	+	0.120053i	−0.233030	+	0.972470i	$0.574864\pi$
$90$	−5.92883	+	1.90008i	−0.624953	+	0.200286i
$91$	5.78567	+	8.65887i	0.606503	+	0.907696i
$92$	−7.86718	+	3.51660i	−0.820210	+	0.366631i
$93$	2.35482	+	9.36545i	0.244184	+	0.971152i
$94$	−14.5796	+	0.201604i	−1.50377	+	0.0207939i
$95$		−	6.14462i		−	0.630425i
$96$	4.43677	−	8.73585i	0.452826	−	0.891599i
$97$			8.88438i			0.902073i	0.892506	+	0.451036i	$0.148946\pi$
$97$			8.88438i			0.902073i	−0.892506	+	0.451036i	$0.851054\pi$
$98$	0.0655000	+	4.73681i	0.00661650	+	0.478490i
$99$	5.39877	+	17.6835i	0.542597	+	1.77726i
$100$	−5.31805	−	2.03242i	−0.531805	−	0.203242i
$101$	6.30265	+	9.43259i	0.627137	+	0.938577i	0.999943	+	0.0106680i	$0.00339579\pi$
$101$	6.30265	+	9.43259i	0.627137	+	0.938577i	−0.372806	+	0.927909i	$0.621604\pi$
$102$	10.1731	−	2.70799i	1.00729	−	0.268131i
$103$	5.30739	+	2.19839i	0.522953	+	0.216614i	0.628513	−	0.777799i	$-0.283664\pi$
$103$	5.30739	+	2.19839i	0.522953	+	0.216614i	−0.105561	+	0.994413i	$0.533664\pi$
$104$	−3.63215	−	14.9830i	−0.356162	−	1.46920i
$105$	4.38797	−	2.08016i	0.428223	−	0.203003i
$106$	−7.77655	−	11.2971i	−0.755326	−	1.09727i
$107$	−10.1892	−	2.02675i	−0.985026	−	0.195934i	−0.323804	−	0.946124i	$-0.604962\pi$
$107$	−10.1892	−	2.02675i	−0.985026	−	0.195934i	−0.661222	+	0.750190i	$0.729962\pi$
$108$	7.48496	−	7.20939i	0.720241	−	0.693724i
$109$	3.67885	+	2.45813i	0.352370	+	0.235446i	0.719139	−	0.694866i	$-0.244536\pi$
$109$	3.67885	+	2.45813i	0.352370	+	0.235446i	−0.366770	+	0.930312i	$0.619536\pi$
$110$	4.73073	−	11.8831i	0.451057	−	1.13301i
$111$	7.00778	+	6.34008i	0.665149	+	0.601774i
$112$	−2.52979	+	7.21139i	−0.239042	+	0.681412i
$113$	1.64187	−	1.64187i	0.154454	−	0.154454i	−0.625650	−	0.780104i	$-0.715166\pi$
$113$	1.64187	−	1.64187i	0.154454	−	0.154454i	0.780104	+	0.625650i	$0.215166\pi$
$114$	4.52132	+	9.20639i	0.423460	+	0.862258i
$115$	5.25719	+	3.51274i	0.490236	+	0.327565i
$116$	0.483226	+	2.12102i	0.0448664	+	0.196932i
$117$	1.57369	−	16.2762i	0.145488	−	1.50474i
$118$	−0.423816	+	2.29615i	−0.0390154	+	0.211378i
$119$	−7.58615	+	3.14229i	−0.695421	+	0.288053i
$120$	−7.15895	+	0.656606i	−0.653520	+	0.0599397i
$121$	−24.9296	−	10.3262i	−2.26633	−	0.938743i
$122$	−7.45467	−	4.83331i	−0.674915	−	0.437588i
$123$	1.98449	+	2.67078i	0.178935	+	0.240816i
$124$	0.308327	+	11.1466i	0.0276886	+	1.00100i
$125$	2.24636	+	11.2932i	0.200921	+	1.01010i
$126$	−5.04382	+	6.34542i	−0.449339	+	0.565295i
$127$			9.25174i			0.820959i	0.911870	+	0.410480i	$0.134639\pi$
$127$			9.25174i			0.820959i	−0.911870	+	0.410480i	$0.865361\pi$
$128$	7.18945	−	8.73566i	0.635464	−	0.772131i
$129$	1.79060	−	0.0895712i	0.157654	−	0.00788630i
$130$	−7.88728	+	8.10847i	−0.691761	+	0.711160i
$131$	4.86814	−	0.968334i	0.425331	−	0.0846037i	0.0222168	−	0.999753i	$-0.492928\pi$
$131$	4.86814	−	0.968334i	0.425331	−	0.0846037i	0.403115	+	0.915149i	$0.367928\pi$
$132$	1.65581	+	21.2852i	0.144120	+	1.85264i
$133$	−4.44460	−	6.65181i	−0.385395	−	0.576785i
$134$	1.91442	−	2.95271i	0.165381	−	0.255076i
$135$	−7.40151	−	1.83290i	−0.637021	−	0.157751i
$136$	12.1455	−	0.504097i	1.04147	−	0.0432260i
$137$	0.353772	+	0.854081i	0.0302248	+	0.0729691i	0.938271	−	0.345900i	$-0.112426\pi$
$137$	0.353772	+	0.854081i	0.0302248	+	0.0729691i	−0.908046	+	0.418869i	$0.862426\pi$
$138$	−10.4615	−	1.39476i	−0.890543	−	0.118730i
$139$	−8.09542	−	1.61028i	−0.686645	−	0.136582i	−0.160575	−	0.987024i	$-0.551335\pi$
$139$	−8.09542	−	1.61028i	−0.686645	−	0.136582i	−0.526070	+	0.850442i	$0.676335\pi$
$140$	5.46721	−	1.24558i	0.462064	−	0.105271i
$141$	−15.3255	−	9.16712i	−1.29064	−	0.772011i
$142$	2.23037	+	5.18079i	0.187168	+	0.434763i
$143$	23.7540	+	23.7540i	1.98641	+	1.98641i
$144$	10.2430	−	6.25146i	0.853584	−	0.520955i
$145$	1.12863	−	1.12863i	0.0937275	−	0.0937275i
$146$	−2.85302	−	1.13580i	−0.236117	−	0.0939996i
$147$	−2.97834	+	4.97915i	−0.245650	+	0.410674i
$148$	6.31100	+	8.90199i	0.518761	+	0.731739i
$149$	2.95971	−	14.8794i	0.242469	−	1.21897i	−0.647184	−	0.762334i	$-0.724053\pi$
$149$	2.95971	−	14.8794i	0.242469	−	1.21897i	0.889653	−	0.456638i	$-0.150947\pi$
$150$	−4.23563	−	5.53878i	−0.345838	−	0.452239i
$151$	0.629307	−	0.260667i	0.0512122	−	0.0212128i	−0.356930	−	0.934131i	$-0.616177\pi$
$151$	0.629307	−	0.260667i	0.0512122	−	0.0212128i	0.408143	+	0.912918i	$0.366177\pi$
$152$	2.79025	+	11.5100i	0.226319	+	0.933588i
$153$	12.3449	+	3.72068i	0.998022	+	0.300799i
$154$	−3.47421	−	16.2859i	−0.279960	−	1.31235i
$155$	6.80282	−	4.54550i	0.546415	−	0.365103i
$156$	5.85105	−	17.9524i	0.468459	−	1.43734i
$157$	−0.458624	−	2.30566i	−0.0366022	−	0.184012i	0.958159	−	0.286236i	$-0.0924041\pi$
$157$	−0.458624	−	2.30566i	−0.0366022	−	0.184012i	−0.994761	+	0.102224i	$0.967404\pi$
$158$	−3.11381	+	0.0430573i	−0.247721	+	0.00342546i
$159$	−0.839202	−	16.7763i	−0.0665530	−	1.33045i
$160$	−8.23406	−	1.05318i	−0.650960	−	0.0832612i
$161$	8.23201			0.648773
$162$	12.4383	−	2.69995i	0.977242	−	0.212128i
$163$	16.9624	−	3.37404i	1.32860	−	0.264275i	0.520773	−	0.853695i	$-0.325644\pi$
$163$	16.9624	−	3.37404i	1.32860	−	0.264275i	0.807827	+	0.589420i	$0.200644\pi$
$164$	1.56789	+	3.50761i	0.122432	+	0.273899i
$165$	12.5736	−	9.34268i	0.978857	−	0.727327i
$166$	−4.42346	−	20.7356i	−0.343327	−	1.60939i
$167$	1.37271	−	3.31401i	0.106223	−	0.256446i	−0.861827	−	0.507203i	$-0.830680\pi$
$167$	1.37271	−	3.31401i	0.106223	−	0.256446i	0.968050	+	0.250757i	$0.0806796\pi$
$168$	−7.27492	+	5.88910i	−0.561272	+	0.454354i
$169$	−6.39475	−	15.4383i	−0.491904	−	1.18756i
$170$	−5.05727	−	7.34677i	−0.387875	−	0.563471i
$171$	−1.20892	+	12.5035i	−0.0924487	+	0.956169i
$172$	2.04081	+	0.347578i	0.155610	+	0.0265026i
$173$	0.782577	−	1.17121i	0.0594982	−	0.0890453i	−0.800528	−	0.599296i	$-0.795447\pi$
$173$	0.782577	−	1.17121i	0.0594982	−	0.0890453i	0.860026	+	0.510251i	$0.170447\pi$
$174$	−0.860543	+	2.52147i	−0.0652376	+	0.191152i
$175$	3.84567	+	3.84567i	0.290705	+	0.290705i
$176$	−3.46549	+	24.4075i	−0.261221	+	1.83979i
$177$	−1.91856	+	2.12061i	−0.144208	+	0.159395i
$178$	1.65502	+	3.84434i	0.124049	+	0.288145i
$179$	10.8187	−	16.1914i	0.808631	−	1.21020i	−0.165943	−	0.986135i	$-0.553067\pi$
$179$	10.8187	−	16.1914i	0.808631	−	1.21020i	0.974574	−	0.224066i	$-0.0719332\pi$
$180$	−7.88386	−	3.92012i	−0.587628	−	0.292188i
$181$	0.283124	−	1.42336i	0.0210444	−	0.105798i	−0.968835	−	0.247705i	$-0.920324\pi$
$181$	0.283124	−	1.42336i	0.0210444	−	0.105798i	0.989880	+	0.141908i	$0.0453236\pi$
$182$	−2.67320	+	14.4829i	−0.198151	+	1.07354i
$183$	−4.66109	−	9.83229i	−0.344557	−	0.726824i
$184$	−11.4428	−	4.19277i	−0.843578	−	0.309095i
$185$	3.06395	−	7.39702i	0.225266	−	0.543840i
$186$	−6.84790	+	11.8161i	−0.502113	+	0.866397i
$187$	−22.0237	+	14.7157i	−1.61053	+	1.07612i
$188$	−14.9785	−	14.1722i	−1.09242	−	1.03361i
$189$	−9.33824	+	3.36955i	−0.679257	+	0.245099i
$190$	6.05907	−	6.22899i	0.439571	−	0.451899i
$191$	−17.8204			−1.28944			−0.644721	−	0.764418i	$-0.723026\pi$
$191$	−17.8204			−1.28944			−0.644721	+	0.764418i	$0.723026\pi$
$192$	13.1119	−	4.48080i	0.946271	−	0.323374i
$193$	16.8508			1.21295			0.606473	−	0.795104i	$-0.292584\pi$
$193$	16.8508			1.21295			0.606473	+	0.795104i	$0.292584\pi$
$194$	−8.76069	+	9.00638i	−0.628981	+	0.646620i
$195$	−13.4359	+	3.37827i	−0.962161	+	0.241923i
$196$	−4.60447	+	4.86644i	−0.328890	+	0.347603i
$197$	8.74380	−	5.84242i	0.622970	−	0.416255i	−0.203628	−	0.979048i	$-0.565273\pi$
$197$	8.74380	−	5.84242i	0.622970	−	0.416255i	0.826598	+	0.562793i	$0.190273\pi$
$198$	−11.9644	+	23.2499i	−0.850272	+	1.65230i
$199$	3.50455	−	8.46074i	0.248431	−	0.599766i	−0.749640	−	0.661846i	$-0.769773\pi$
$199$	3.50455	−	8.46074i	0.248431	−	0.599766i	0.998071	+	0.0620797i	$0.0197733\pi$
$200$	−3.38695	−	7.30434i	−0.239494	−	0.516495i
$201$	3.89446	−	1.84620i	0.274694	−	0.130221i
$202$	−2.91207	+	15.7770i	−0.204893	+	1.11007i
$203$	0.405415	−	2.03816i	0.0284546	−	0.143051i
$204$	12.9831	+	7.28633i	0.909000	+	0.510145i
$205$	1.56617	−	2.34394i	0.109386	−	0.163708i
$206$	3.21248	+	7.46208i	0.223824	+	0.519908i
$207$	−10.0066	−	8.18232i	−0.695508	−	0.568711i
$208$	11.0924	−	18.7703i	0.769117	−	1.30149i
$209$	−18.2480	−	18.2480i	−1.26224	−	1.26224i
$210$	6.49943	+	2.21816i	0.448503	+	0.153068i
$211$	13.3997	−	20.0541i	0.922473	−	1.38058i	−0.00227390	−	0.999997i	$-0.500724\pi$
$211$	13.3997	−	20.0541i	0.922473	−	1.38058i	0.924747	−	0.380582i	$-0.124276\pi$
$212$	3.25650	−	19.1205i	0.223657	−	1.31320i
$213$	−1.00753	+	6.83430i	−0.0690348	+	0.468279i
$214$	−8.33055	−	12.1019i	−0.569465	−	0.827270i
$215$	−0.581277	−	1.40333i	−0.0396428	−	0.0957061i
$216$	14.6968	+	0.0723763i	0.999988	+	0.00492458i
$217$	4.07643	−	9.84138i	0.276726	−	0.668077i
$218$	1.30546	+	6.11951i	0.0884167	+	0.414466i
$219$	−2.24308	−	3.01881i	−0.151574	−	0.203992i
$220$	16.5134	−	7.38141i	1.11333	−	0.497654i
$221$	22.9759	−	4.57019i	1.54553	−	0.307424i
$222$	0.852191	+	13.3374i	0.0571953	+	0.895144i
$223$	−8.95365			−0.599581			−0.299790	−	0.954005i	$-0.596917\pi$
$223$	−8.95365			−0.599581			−0.299790	+	0.954005i	$0.596917\pi$
$224$	−9.67552	+	4.81584i	−0.646473	+	0.321772i
$225$	−0.852239	−	8.49715i	−0.0568159	−	0.566477i
$226$	3.28342	−	0.0454028i	0.218410	−	0.00302015i
$227$	1.88826	+	9.49292i	0.125328	+	0.630067i	0.991477	+	0.130281i	$0.0415880\pi$
$227$	1.88826	+	9.49292i	0.125328	+	0.630067i	−0.866149	+	0.499786i	$0.833412\pi$
$228$	−4.49482	+	13.7912i	−0.297677	+	0.913343i
$229$	−20.2187	+	13.5097i	−1.33609	+	0.892746i	−0.998815	−	0.0486611i	$-0.984505\pi$
$229$	−20.2187	+	13.5097i	−1.33609	+	0.892746i	−0.337273	+	0.941407i	$0.609505\pi$
$230$	1.86554	+	8.74498i	0.123010	+	0.576627i
$231$	6.85364	−	19.2088i	0.450936	−	1.26384i
$232$	−1.60163	+	2.62664i	−0.105152	+	0.172448i
$233$	−25.6460	+	10.6229i	−1.68012	+	0.695930i	−0.999332	−	0.0365481i	$-0.988364\pi$
$233$	−25.6460	+	10.6229i	−1.68012	+	0.695930i	−0.680791	+	0.732478i	$0.738364\pi$
$234$	17.6449	−	14.9479i	1.15349	−	0.977178i
$235$	−2.95168	+	14.8391i	−0.192546	+	0.967996i
$236$	−2.69382	+	1.90976i	−0.175352	+	0.124315i
$237$	−3.27312	−	1.95786i	−0.212612	−	0.127176i
$238$	−10.7889	−	4.29510i	−0.699338	−	0.278410i
$239$	10.4800	−	10.4800i	0.677895	−	0.677895i	−0.281629	−	0.959524i	$-0.590875\pi$
$239$	10.4800	−	10.4800i	0.677895	−	0.677895i	0.959524	+	0.281629i	$0.0908746\pi$
$240$	−7.90472	−	6.39366i	−0.510247	−	0.412709i
$241$	13.0003	+	13.0003i	0.837422	+	0.837422i	0.988519	−	0.151097i	$-0.0482807\pi$
$241$	13.0003	+	13.0003i	0.837422	+	0.837422i	−0.151097	+	0.988519i	$0.548281\pi$
$242$	−15.0895	−	35.0505i	−0.969989	−	2.25313i
$243$	14.7005	+	5.18594i	0.943040	+	0.332678i
$244$	−2.79101	−	12.2506i	−0.178676	−	0.784262i
$245$	4.82114	+	0.958984i	0.308011	+	0.0612672i
$246$	−0.621858	+	4.66430i	−0.0396482	+	0.297385i
$247$	8.73424	+	21.0863i	0.555747	+	1.34169i
$248$	−10.6789	+	11.6037i	−0.678110	+	0.736837i
$249$	8.72624	−	24.4571i	0.553003	−	1.54991i
$250$	−8.85879	+	13.6634i	−0.560279	+	0.864148i
$251$	7.00936	+	10.4902i	0.442427	+	0.662138i	0.983929	−	0.178561i	$-0.0571442\pi$
$251$	7.00936	+	10.4902i	0.442427	+	0.662138i	−0.541502	+	0.840699i	$0.682144\pi$
$252$	−11.3702	+	1.45895i	−0.716252	+	0.0919052i
$253$	26.0445	−	5.18058i	1.63741	−	0.325700i
$254$	−9.12294	+	9.37878i	−0.572424	+	0.588477i
$255$	−0.545752	−	10.9100i	−0.0341763	−	0.683212i
$256$	15.9022	−	1.76625i	0.993888	−	0.110390i
$257$			26.0879i			1.62732i	0.581343	+	0.813658i	$0.302527\pi$
$257$			26.0879i			1.62732i	−0.581343	+	0.813658i	$0.697473\pi$
$258$	1.90351	+	1.67487i	0.118507	+	0.104273i
$259$	−2.03365	−	10.2238i	−0.126365	−	0.635278i
$260$	−15.9912	+	0.442332i	−0.991730	+	0.0274323i
$261$	−2.51867	+	2.07457i	−0.155902	+	0.128413i
$262$	5.88984	+	3.81874i	0.363875	+	0.235922i
$263$	24.1339	+	9.99659i	1.48816	+	0.616416i	0.970916	−	0.239421i	$-0.0769577\pi$
$263$	24.1339	+	9.99659i	1.48816	+	0.616416i	0.517245	+	0.855838i	$0.326958\pi$
$264$	−19.3104	+	23.2103i	−1.18847	+	1.42849i
$265$	−13.1479	+	5.44605i	−0.807670	+	0.334548i
$266$	2.05358	−	11.1259i	0.125913	−	0.682170i
$267$	−0.747624	+	5.07130i	−0.0457538	+	0.310359i
$268$	4.85231	−	1.10549i	0.296402	−	0.0675284i
$269$	20.5077	+	13.7028i	1.25037	+	0.835474i	0.991458	−	0.130426i	$-0.0416345\pi$
$269$	20.5077	+	13.7028i	1.25037	+	0.835474i	0.258917	+	0.965900i	$0.416635\pi$
$270$	−5.69576	−	9.15654i	−0.346633	−	0.557249i
$271$	−10.2897	+	10.2897i	−0.625057	+	0.625057i	−0.946820	−	0.321763i	$-0.895724\pi$
$271$	−10.2897	+	10.2897i	−0.625057	+	0.625057i	0.321763	+	0.946820i	$0.395724\pi$
$272$	12.8094	+	11.4654i	0.776682	+	0.695193i
$273$	−12.1013	+	13.3757i	−0.732402	+	0.809534i
$274$	−0.483561	+	1.21466i	−0.0292130	+	0.0733800i
$275$	14.5871	+	9.74681i	0.879638	+	0.587755i
$276$	−9.22982	−	11.7298i	−0.555570	−	0.706049i
$277$	12.2914	+	2.44491i	0.738517	+	0.146900i	0.549994	−	0.835169i	$-0.314630\pi$
$277$	12.2914	+	2.44491i	0.738517	+	0.146900i	0.188523	+	0.982069i	$0.439630\pi$
$278$	−6.61872	−	9.61510i	−0.396964	−	0.576676i
$279$	−14.7372	+	7.91110i	−0.882293	+	0.473625i
$280$	6.77052	+	4.12841i	0.404616	+	0.246720i
$281$	−19.9649	−	8.26972i	−1.19100	−	0.493330i	−0.302923	−	0.953015i	$-0.597962\pi$
$281$	−19.9649	−	8.26972i	−1.19100	−	0.493330i	−0.888082	+	0.459685i	$0.847962\pi$
$282$	−6.49641	−	24.4051i	−0.386855	−	1.45330i
$283$	−6.09348	−	9.11953i	−0.362220	−	0.542100i	0.604940	−	0.796271i	$-0.293197\pi$
$283$	−6.09348	−	9.11953i	−0.362220	−	0.542100i	−0.967159	+	0.254172i	$0.918197\pi$
$284$	−2.84767	+	7.45125i	−0.168978	+	0.442150i
$285$	10.3215	−	2.59522i	0.611394	−	0.153727i
$286$	0.656871	+	47.5034i	0.0388416	+	2.80894i
$287$		−	3.67027i		−	0.216649i
$288$	16.5481	+	3.76310i	0.975105	+	0.221743i
$289$			1.47098i			0.0865284i
$290$	2.25704	−	0.0312101i	0.132538	−	0.00183272i
$291$	−14.9237	+	3.75237i	−0.874842	+	0.219968i
$292$	−1.77220	−	3.96469i	−0.103710	−	0.232016i
$293$	18.2602	+	27.3284i	1.06677	+	1.59654i	0.765994	+	0.642847i	$0.222247\pi$
$293$	18.2602	+	27.3284i	1.06677	+	1.59654i	0.300780	+	0.953693i	$0.402753\pi$
$294$	−7.92907	+	2.11064i	−0.462433	+	0.123095i
$295$	2.23840	+	0.927176i	0.130325	+	0.0539822i
$296$	−2.38040	+	15.2474i	−0.138358	+	0.886235i
$297$	−27.4239	+	16.5374i	−1.59130	+	0.959597i
$298$	17.6726	−	12.1653i	1.02375	−	0.704714i
$299$	−23.0341	−	4.58178i	−1.33210	−	0.264971i
$300$	1.16788	−	9.79149i	0.0674276	−	0.565312i
$301$	−1.64433	−	1.09870i	−0.0947775	−	0.0633283i
$302$	0.894986	+	0.356299i	0.0515007	+	0.0205027i
$303$	−13.1826	+	14.5709i	−0.757319	+	0.837076i
$304$	−8.52124	+	14.4195i	−0.488727	+	0.827014i
$305$	−6.51872	+	6.51872i	−0.373261	+	0.373261i
$306$	8.84548	+	15.9448i	0.505662	+	0.911501i
$307$	−13.8568	−	9.25879i	−0.790847	−	0.528427i	0.0932987	−	0.995638i	$-0.470259\pi$
$307$	−13.8568	−	9.25879i	−0.790847	−	0.528427i	−0.884146	+	0.467211i	$0.845259\pi$
$308$	12.5372	−	19.9353i	0.714373	−	1.13592i
$309$	−1.45118	+	9.84368i	−0.0825547	+	0.559987i
$310$	11.3784	+	2.10020i	0.646252	+	0.119283i
$311$	−16.2016	+	6.71094i	−0.918711	+	0.380542i	−0.791385	−	0.611318i	$-0.790639\pi$
$311$	−16.2016	+	6.71094i	−0.918711	+	0.380542i	−0.127326	+	0.991861i	$0.540639\pi$
$312$	23.6339	−	12.4293i	1.33800	−	0.703672i
$313$	16.3151	+	6.75794i	0.922185	+	0.381982i	0.792708	−	0.609601i	$-0.208670\pi$
$313$	16.3151	+	6.75794i	0.922185	+	0.381982i	0.129477	+	0.991582i	$0.458670\pi$
$314$	1.80864	−	2.78956i	0.102067	−	0.157424i
$315$	5.34747	+	6.49221i	0.301296	+	0.365794i
$316$	−3.19902	−	3.02681i	−0.179959	−	0.170271i
$317$	−2.95858	−	14.8738i	−0.166170	−	0.835395i	−0.970479	−	0.241184i	$-0.922464\pi$
$317$	−2.95858	−	14.8738i	−0.166170	−	0.835395i	0.804309	−	0.594211i	$-0.202536\pi$
$318$	15.6920	−	17.8342i	0.879966	−	1.00009i
$319$		−	6.70350i		−	0.375324i
$320$	−7.30860	−	9.18707i	−0.408563	−	0.513573i
$321$	−0.898986	−	17.9715i	−0.0501765	−	1.00307i
$322$	8.34504	+	8.11740i	0.465051	+	0.452365i
$323$	−17.6503	+	3.51085i	−0.982087	+	0.195349i
$324$	15.2714	+	9.52807i	0.848412	+	0.529337i
$325$	−8.62022	−	12.9011i	−0.478164	−	0.715622i
$326$	20.5224	+	13.3059i	1.13663	+	0.736946i
$327$	−2.57530	+	7.21781i	−0.142414	+	0.399146i
$328$	−1.86936	+	5.10184i	−0.103218	+	0.281702i
$329$	7.53827	+	18.1990i	0.415598	+	1.00334i
$330$	21.9589	+	2.92762i	1.20880	+	0.161160i
$331$	23.6184	+	4.69798i	1.29818	+	0.258225i	0.795345	−	0.606157i	$-0.207290\pi$
$331$	23.6184	+	4.69798i	1.29818	+	0.258225i	0.502837	+	0.864381i	$0.332290\pi$
$332$	15.9627	−	25.3822i	0.876067	−	1.39303i
$333$	−7.69008	+	14.4492i	−0.421414	+	0.791811i
$334$	4.65942	−	2.00592i	0.254952	−	0.109759i
$335$	−2.58199	−	2.58199i	−0.141069	−	0.141069i
$336$	−13.1819	−	1.20368i	−0.719133	−	0.0656660i
$337$	2.35157	−	2.35157i	0.128098	−	0.128098i	−0.640151	−	0.768249i	$-0.721128\pi$
$337$	2.35157	−	2.35157i	0.128098	−	0.128098i	0.768249	+	0.640151i	$0.221128\pi$
$338$	8.74081	−	21.9560i	0.475437	−	1.19425i
$339$	3.45141	+	2.06450i	0.187455	+	0.112128i
$340$	2.11777	−	12.4345i	0.114852	−	0.674356i
$341$	6.70368	−	33.7017i	0.363025	−	1.82505i
$342$	−13.5550	+	11.4831i	−0.732970	+	0.620937i
$343$	18.2687	−	7.56712i	0.986414	−	0.408586i
$344$	1.72609	+	2.36474i	0.0930644	+	0.127498i
$345$	−3.68018	+	10.3145i	−0.198134	+	0.555313i
$346$	1.94822	−	0.415609i	0.104737	−	0.0223433i
$347$	13.9283	−	9.30661i	0.747712	−	0.499605i	−0.122387	−	0.992482i	$-0.539055\pi$
$347$	13.9283	−	9.30661i	0.747712	−	0.499605i	0.870099	+	0.492878i	$0.164055\pi$
$348$	−3.35873	+	1.70753i	−0.180047	+	0.0915333i
$349$	3.29594	+	16.5698i	0.176427	+	0.886960i	0.963008	+	0.269473i	$0.0868494\pi$
$349$	3.29594	+	16.5698i	0.176427	+	0.886960i	−0.786581	+	0.617488i	$0.788151\pi$
$350$	0.106345	+	7.69060i	0.00568436	+	0.411080i
$351$	28.0049	−	4.23093i	1.49479	−	0.225830i
$352$	−27.5808	+	21.3254i	−1.47006	+	1.13665i
$353$	−6.83488			−0.363784			−0.181892	−	0.983319i	$-0.558222\pi$
$353$	−6.83488			−0.363784			−0.181892	+	0.983319i	$0.558222\pi$
$354$	−4.03599	+	0.257880i	−0.214511	+	0.0137062i
$355$	5.74036	−	1.14183i	0.304667	−	0.0606020i
$356$	−2.11308	+	5.52910i	−0.111993	+	0.293042i
$357$	−8.48236	−	11.4158i	−0.448934	−	0.604188i
$358$	26.9333	−	5.74559i	1.42347	−	0.303664i
$359$	−2.92186	+	7.05399i	−0.154210	+	0.372296i	−0.982037	−	0.188687i	$-0.939577\pi$
$359$	−2.92186	+	7.05399i	−0.154210	+	0.372296i	0.827827	+	0.560983i	$0.189577\pi$
$360$	−4.12657	−	11.7480i	−0.217489	−	0.619176i
$361$	0.561272	+	1.35503i	0.0295406	+	0.0713174i
$362$	1.69056	−	1.16372i	0.0888536	−	0.0611639i
$363$	6.81640	−	46.2372i	0.357768	−	2.42682i
$364$	−16.9912	+	12.0458i	−0.890579	+	0.631369i
$365$	−1.77026	+	2.64938i	−0.0926596	+	0.138675i
$366$	4.97032	−	14.5635i	0.259803	−	0.761246i
$367$	−19.5981	−	19.5981i	−1.02301	−	1.02301i	−0.999729	−	0.0232824i	$-0.992588\pi$
$367$	−19.5981	−	19.5981i	−1.02301	−	1.02301i	−0.0232824	−	0.999729i	$-0.507412\pi$
$368$	−7.46557	−	15.5339i	−0.389170	−	0.809759i
$369$	−3.64812	+	4.46149i	−0.189914	+	0.232256i
$370$	10.4001	−	4.47730i	0.540673	−	0.232764i
$371$	−10.2939	+	15.4059i	−0.534432	+	0.799833i
$372$	−18.5935	+	5.22576i	−0.964028	+	0.270943i
$373$	−2.16853	+	10.9019i	−0.112282	+	0.564481i	0.883156	+	0.469079i	$0.155414\pi$
$373$	−2.16853	+	10.9019i	−0.112282	+	0.564481i	−0.995439	+	0.0954028i	$0.969586\pi$
$374$	−36.8369	−	6.79924i	−1.90479	−	0.351580i
$375$	−18.0212	+	8.54312i	−0.930612	+	0.441165i
$376$	−1.20932	−	29.1368i	−0.0623657	−	1.50262i
$377$	−2.26880	+	5.47737i	−0.116849	+	0.282099i
$378$	−12.7891	−	5.79241i	−0.657801	−	0.297930i
$379$	9.42890	−	6.30019i	0.484330	−	0.323619i	−0.289320	−	0.957233i	$-0.593429\pi$
$379$	9.42890	−	6.30019i	0.484330	−	0.323619i	0.773650	+	0.633614i	$0.218429\pi$
$380$	12.2845	−	0.339803i	0.630184	−	0.0174315i
$381$	−15.5408	+	3.90753i	−0.796178	+	0.200189i
$382$	−18.0651	−	17.5723i	−0.924293	−	0.899079i
$383$	−6.88819			−0.351970			−0.175985	−	0.984393i	$-0.556311\pi$
$383$	−6.88819			−0.351970			−0.175985	+	0.984393i	$0.556311\pi$
$384$	17.7104	+	8.38705i	0.903779	+	0.428000i
$385$	−17.2791			−0.880626
$386$	17.0822	+	16.6162i	0.869459	+	0.845742i
$387$	0.906729	+	2.96996i	0.0460916	+	0.150972i
$388$	−17.7620	+	0.491314i	−0.901728	+	0.0249427i
$389$	−20.8076	+	13.9032i	−1.05499	+	0.704920i	−0.956947	−	0.290262i	$-0.906257\pi$
$389$	−20.8076	+	13.9032i	−1.05499	+	0.704920i	−0.0980403	+	0.995182i	$0.531257\pi$
$390$	−16.9516	−	9.82414i	−0.858377	−	0.497465i
$391$	7.08646	−	17.1082i	0.358378	−	0.865200i
$392$	−9.46638	+	0.392900i	−0.478124	+	0.0198444i
$393$	3.68266	+	7.76836i	0.185766	+	0.391862i
$394$	14.6249	+	2.69943i	0.736794	+	0.135995i
$395$	−0.630401	+	3.16924i	−0.0317189	+	0.159462i
$396$	−35.0549	+	11.7713i	−1.76157	+	0.591531i
$397$	9.95342	−	14.8963i	0.499548	−	0.747626i	−0.492928	−	0.870070i	$-0.664073\pi$
$397$	9.95342	−	14.8963i	0.499548	−	0.747626i	0.992475	+	0.122444i	$0.0390733\pi$
$398$	11.8956	−	5.12115i	0.596274	−	0.256700i
$399$	9.29628	−	10.2753i	0.465396	−	0.514409i
$400$	3.76919	−	10.7444i	0.188460	−	0.537222i
$401$	−11.7473	−	11.7473i	−0.586634	−	0.586634i	0.350084	−	0.936718i	$-0.386153\pi$
$401$	−11.7473	−	11.7473i	−0.586634	−	0.586634i	−0.936718	+	0.350084i	$0.886153\pi$
$402$	5.76843	+	1.96869i	0.287703	+	0.0981891i
$403$	−16.8839	+	25.2685i	−0.841045	+	1.25871i
$404$	−18.5094	+	13.1221i	−0.920878	+	0.652850i
$405$	−0.0472253	−	13.2070i	−0.00234664	−	0.656259i
$406$	2.42077	−	1.66638i	0.120141	−	0.0827008i
$407$	−12.8682	−	31.0665i	−0.637851	−	1.53991i
$408$	5.97650	+	20.1887i	0.295881	+	0.999491i
$409$	−1.20658	+	2.91293i	−0.0596614	+	0.144035i	−0.950899	−	0.309501i	$-0.899838\pi$
$409$	−1.20658	+	2.91293i	−0.0596614	+	0.144035i	0.891238	+	0.453537i	$0.149838\pi$
$410$	3.89898	−	0.831758i	0.192557	−	0.0410776i
$411$	−1.28524	+	0.954981i	−0.0633962	+	0.0471057i
$412$	−4.10160	+	10.7323i	−0.202071	+	0.528742i
$413$	3.09382	−	0.615398i	0.152237	−	0.0302818i
$414$	−2.07561	−	18.1620i	−0.102011	−	0.892613i
$415$	−22.0003			−1.07995
$416$	29.7536	−	8.09010i	1.45879	−	0.396650i
$417$	−0.714255	−	14.2785i	−0.0349772	−	0.699222i
$418$	−0.504613	−	36.4925i	−0.0246814	−	1.78491i
$419$	2.16695	+	10.8940i	0.105862	+	0.532206i	0.996927	+	0.0783304i	$0.0249589\pi$
$419$	2.16695	+	10.8940i	0.105862	+	0.532206i	−0.891065	+	0.453875i	$0.850041\pi$
$420$	4.40139	+	8.65756i	0.214766	+	0.422446i
$421$	−3.42035	+	2.28541i	−0.166698	+	0.111384i	−0.636121	−	0.771590i	$-0.719462\pi$
$421$	−3.42035	+	2.28541i	−0.166698	+	0.111384i	0.469423	+	0.882973i	$0.344462\pi$
$422$	33.3586	−	7.11628i	1.62387	−	0.346415i
$423$	8.92582	−	29.6150i	0.433988	−	1.43993i
$424$	22.1555	−	16.1719i	1.07597	−	0.785377i
$425$	11.3028	−	4.68177i	0.548266	−	0.227099i
$426$	−7.76052	+	5.93464i	−0.375998	+	0.287534i
$427$	−2.34159	+	11.7720i	−0.113318	+	0.569686i
$428$	3.48849	−	20.4827i	0.168622	−	0.990067i
$429$	−29.8685	+	49.9338i	−1.44207	+	2.41083i
$430$	0.794531	−	1.99578i	0.0383157	−	0.0962451i
$431$	11.6107	−	11.6107i	0.559267	−	0.559267i	−0.369832	−	0.929099i	$-0.620585\pi$
$431$	11.6107	−	11.6107i	0.559267	−	0.559267i	0.929099	+	0.369832i	$0.120585\pi$
$432$	14.8272	+	14.5655i	0.713374	+	0.700784i
$433$	−9.98974	−	9.98974i	−0.480076	−	0.480076i	0.425080	−	0.905156i	$-0.360246\pi$
$433$	−9.98974	−	9.98974i	−0.480076	−	0.480076i	−0.905156	+	0.425080i	$0.860246\pi$
$434$	13.8368	−	5.95683i	0.664187	−	0.285937i
$435$	2.37252	+	1.41915i	0.113753	+	0.0680430i
$436$	−4.71093	+	7.49082i	−0.225613	+	0.358745i
$437$	17.6950	+	3.51976i	0.846467	+	0.168373i
$438$	0.702893	−	5.27211i	0.0335855	−	0.251911i
$439$	−9.32951	−	22.5234i	−0.445273	−	1.07499i	−0.974072	−	0.226238i	$-0.927357\pi$
$439$	−9.32951	−	22.5234i	−0.445273	−	1.07499i	0.528799	−	0.848747i	$-0.322643\pi$
$440$	24.0187	+	8.80070i	1.14505	+	0.419557i
$441$	−9.62174	−	2.89995i	−0.458178	−	0.138093i
$442$	27.7979	+	18.0231i	1.32221	+	0.857270i
$443$	12.5241	+	18.7436i	0.595036	+	0.890535i	0.999714	−	0.0239248i	$-0.00761624\pi$
$443$	12.5241	+	18.7436i	0.595036	+	0.890535i	−0.404678	+	0.914459i	$0.632616\pi$
$444$	−12.2878	+	14.3608i	−0.583152	+	0.681534i
$445$	4.25956	−	0.847279i	0.201922	−	0.0401649i
$446$	−9.07660	−	8.82900i	−0.429789	−	0.418065i
$447$	26.2441	−	1.31281i	1.24130	−	0.0620936i
$448$	−14.5572	−	4.65884i	−0.687761	−	0.220110i
$449$		−	5.72540i		−	0.270198i	−0.990832	−	0.135099i	$-0.956865\pi$
$449$		−	5.72540i		−	0.270198i	0.990832	−	0.135099i	$-0.0431353\pi$
$450$	7.51491	−	9.45420i	0.354256	−	0.445675i
$451$	−2.30978	−	11.6121i	−0.108763	−	0.546790i
$452$	3.37328	+	3.19169i	0.158666	+	0.150124i
$453$	0.703652	+	0.946994i	0.0330604	+	0.0444937i
$454$	−7.44657	+	11.4852i	−0.349485	+	0.539029i
$455$	14.1186	+	5.84813i	0.661892	+	0.274165i
$456$	−18.1557	+	9.54830i	−0.850219	+	0.447140i
$457$	20.0259	−	8.29501i	0.936773	−	0.388024i	0.138529	−	0.990358i	$-0.455763\pi$
$457$	20.0259	−	8.29501i	0.936773	−	0.388024i	0.798244	+	0.602334i	$0.205763\pi$
$458$	−33.8179	−	6.24200i	−1.58021	−	0.291670i
$459$	−1.03596	+	22.3079i	−0.0483542	+	1.04124i
$460$	−6.73207	+	10.7046i	−0.313885	+	0.499106i
$461$	−18.8490	−	12.5945i	−0.877887	−	0.586586i	0.0329013	−	0.999459i	$-0.489525\pi$
$461$	−18.8490	−	12.5945i	−0.877887	−	0.586586i	−0.910789	+	0.412873i	$0.864525\pi$
$462$	25.8891	−	12.7143i	1.20447	−	0.591522i
$463$	11.4676	−	11.4676i	0.532946	−	0.532946i	−0.388502	−	0.921448i	$-0.627007\pi$
$463$	11.4676	−	11.4676i	0.532946	−	0.532946i	0.921448	+	0.388502i	$0.127007\pi$
$464$	−4.21370	+	1.08338i	−0.195616	+	0.0502945i
$465$	10.5086	+	9.50733i	0.487324	+	0.440892i
$466$	−36.4731	−	14.5201i	−1.68958	−	0.672633i
$467$	3.07835	+	2.05689i	0.142449	+	0.0951813i	0.624753	−	0.780823i	$-0.285200\pi$
$467$	3.07835	+	2.05689i	0.142449	+	0.0951813i	−0.482304	+	0.876004i	$0.660200\pi$
$468$	32.6271	+	2.24609i	1.50819	+	0.103826i
$469$	−4.66275	−	0.927479i	−0.215306	−	0.0428270i
$470$	−17.6247	+	12.1323i	−0.812968	+	0.559620i
$471$	3.67927	−	1.74419i	0.169532	−	0.0803680i
$472$	−4.61398	−	0.720328i	−0.212375	−	0.0331558i
$473$	−5.89378	−	2.44128i	−0.270996	−	0.112250i
$474$	−1.38746	−	5.21229i	−0.0637282	−	0.239408i
$475$	6.62212	+	9.91070i	0.303844	+	0.454734i
$476$	−6.70169	−	14.9927i	−0.307172	−	0.687191i
$477$	27.8259	−	8.49524i	1.27406	−	0.388970i
$478$	20.9580	−	0.289804i	0.958597	−	0.0132553i
$479$		−	7.79696i		−	0.356252i	−0.984008	−	0.178126i	$-0.942997\pi$
$479$		−	7.79696i		−	0.356252i	0.984008	−	0.178126i	$-0.0570035\pi$
$480$	−1.70861	−	14.2761i	−0.0779868	−	0.651613i
$481$			29.7394i			1.35600i
$482$	0.359498	+	25.9981i	0.0163747	+	1.18418i
$483$	3.47684	+	13.8279i	0.158202	+	0.629189i
$484$	19.2658	−	50.4112i	0.875719	−	2.29142i
$485$	7.24318	+	10.8402i	0.328896	+	0.492227i
$486$	9.78866	+	19.7530i	0.444023	+	0.896016i
$487$	2.21908	+	0.919173i	0.100556	+	0.0416517i	0.432394	−	0.901685i	$-0.357669\pi$
$487$	2.21908	+	0.919173i	0.100556	+	0.0416517i	−0.331838	+	0.943336i	$0.607669\pi$
$488$	9.25068	−	15.1709i	0.418759	−	0.686756i
$489$	12.8318	+	27.0679i	0.580273	+	1.22405i
$490$	3.94170	+	5.72617i	0.178068	+	0.258682i
$491$	−22.8188	−	4.53895i	−1.02980	−	0.204840i	−0.348856	−	0.937176i	$-0.613430\pi$
$491$	−22.8188	−	4.53895i	−1.02980	−	0.204840i	−0.680943	+	0.732336i	$0.738430\pi$
$492$	−5.22976	+	4.11515i	−0.235776	+	0.185525i
$493$	−3.88682	−	2.59709i	−0.175054	−	0.116967i
$494$	−11.9386	+	29.9885i	−0.537143	+	1.34925i
$495$	21.0041	+	17.1748i	0.944063	+	0.771952i
$496$	−22.2677	+	1.23284i	−0.999848	+	0.0553560i
$497$	5.38826	−	5.38826i	0.241696	−	0.241696i
$498$	32.9627	−	16.1882i	1.47709	−	0.725410i
$499$	−15.6396	−	10.4501i	−0.700125	−	0.467809i	0.153869	−	0.988091i	$-0.450827\pi$
$499$	−15.6396	−	10.4501i	−0.700125	−	0.467809i	−0.853994	+	0.520283i	$0.825827\pi$
$500$	−22.4536	+	5.11553i	−1.00416	+	0.228774i
$501$	6.14653	+	0.906136i	0.274607	+	0.0404832i
$502$	−3.23860	+	17.5461i	−0.144546	+	0.783119i
$503$	1.20108	−	0.497504i	0.0535535	−	0.0221826i	−0.355746	−	0.934583i	$-0.615773\pi$
$503$	1.20108	−	0.497504i	0.0535535	−	0.0221826i	0.409299	+	0.912400i	$0.365773\pi$
$504$	−12.9649	−	9.73288i	−0.577503	−	0.433537i
$505$	15.3802	+	6.37070i	0.684411	+	0.283492i
$506$	31.5106	+	20.4302i	1.40082	+	0.908234i
$507$	23.2319	−	17.2621i	1.03176	−	0.766639i
$508$	−18.4964	+	0.511630i	−0.820645	+	0.0226999i
$509$	−1.37602	−	6.91774i	−0.0609912	−	0.306623i	0.938233	−	0.346004i	$-0.112462\pi$
$509$	−1.37602	−	6.91774i	−0.0609912	−	0.306623i	−0.999224	+	0.0393805i	$0.987462\pi$
$510$	10.2049	−	11.5980i	0.451880	−	0.513567i
$511$			4.14855i			0.183521i
$512$	17.8622	+	13.8903i	0.789406	+	0.613871i
$513$	−21.5136	+	3.25023i	−0.949849	+	0.143501i
$514$	−25.7247	+	26.4461i	−1.13467	+	1.16649i
$515$	8.26804	−	1.64461i	0.364333	−	0.0724704i
$516$	0.278096	+	3.57488i	0.0122425	+	0.157375i
$517$	35.3027	+	52.8342i	1.55261	+	2.32365i
$518$	8.01993	−	12.3696i	0.352375	−	0.543487i
$519$	2.29788	+	0.819879i	0.100866	+	0.0359887i
$520$	−16.6469	−	15.3201i	−0.730016	−	0.671832i
$521$	0.0798364	+	0.192742i	0.00349770	+	0.00844419i	0.925619	−	0.378457i	$-0.123545\pi$
$521$	0.0798364	+	0.192742i	0.00349770	+	0.00844419i	−0.922121	+	0.386902i	$0.873545\pi$
$522$	−4.59894	−	0.380553i	−0.201290	−	0.0166564i
$523$	−42.2898	−	8.41196i	−1.84920	−	0.367829i	−0.859519	−	0.511104i	$-0.829237\pi$
$523$	−42.2898	−	8.41196i	−1.84920	−	0.367829i	−0.989683	+	0.143275i	$0.954237\pi$
$524$	2.20514	+	9.67901i	0.0963320	+	0.422830i
$525$	−4.83559	+	8.08407i	−0.211042	+	0.352818i
$526$	14.6079	+	33.9318i	0.636933	+	1.47950i
$527$	−16.9438	−	16.9438i	−0.738081	−	0.738081i
$528$	−42.4626	+	4.48745i	−1.84795	+	0.195291i
$529$	3.13619	−	3.13619i	0.136356	−	0.136356i
$530$	−18.6987	−	7.44405i	−0.812219	−	0.323349i
$531$	−4.37245	−	2.32708i	−0.189748	−	0.100987i
$532$	13.0527	−	9.25365i	0.565908	−	0.401196i
$533$	−2.04280	+	10.2699i	−0.0884836	+	0.444837i
$534$	−5.75859	+	4.40372i	−0.249198	+	0.190568i
$535$	−14.0846	+	5.83402i	−0.608929	+	0.252227i
$536$	6.00904	+	3.66409i	0.259551	+	0.158265i
$537$	31.7671	+	11.3344i	1.37085	+	0.489117i
$538$	7.27724	+	34.1131i	0.313744	+	1.47072i
$539$	17.1655	−	11.4696i	0.739371	−	0.494032i
$540$	3.25509	−	14.8987i	0.140077	−	0.641139i
$541$	−4.58368	−	23.0437i	−0.197068	−	0.990727i	−0.945029	−	0.326985i	$-0.893967\pi$
$541$	−4.58368	−	23.0437i	−0.197068	−	0.990727i	0.747962	−	0.663742i	$-0.231033\pi$
$542$	−20.5775	+	0.284543i	−0.883879	+	0.0122222i
$543$	2.51049	−	0.125582i	0.107736	−	0.00538925i
$544$	1.67947	+	24.2539i	0.0720065	+	1.03988i
$545$	6.49274			0.278119
$546$	−25.4569	+	1.62657i	−1.08945	+	0.0696108i
$547$	−30.4755	+	6.06195i	−1.30304	+	0.259190i	−0.797345	−	0.603524i	$-0.793763\pi$
$547$	−30.4755	+	6.06195i	−1.30304	+	0.259190i	−0.505692	+	0.862714i	$0.668763\pi$
$548$	−1.68795	+	0.754505i	−0.0721055	+	0.0322309i
$549$	14.5473	−	11.9823i	0.620864	−	0.511391i
$550$	5.17632	+	24.2647i	0.220719	+	1.03465i
$551$	1.74291	−	4.20776i	0.0742505	−	0.179257i
$552$	2.20992	−	20.9922i	0.0940604	−	0.893485i
$553$	1.60998	+	3.88683i	0.0684632	+	0.165285i
$554$	10.0493	+	14.5987i	0.426953	+	0.620241i
$555$	13.7193	+	2.02254i	0.582354	+	0.0858520i
$556$	2.77164	−	16.2737i	0.117544	−	0.690159i
$557$	20.6916	−	30.9671i	0.876730	−	1.31212i	−0.0724461	−	0.997372i	$-0.523081\pi$
$557$	20.6916	−	30.9671i	0.876730	−	1.31212i	0.949176	−	0.314746i	$-0.101919\pi$
$558$	−22.7405	−	6.51229i	−0.962682	−	0.275687i
$559$	3.98951	+	3.98951i	0.168738	+	0.168738i
$560$	2.79254	+	10.8614i	0.118007	+	0.458976i
$561$	−34.0208	−	30.7793i	−1.43636	−	1.29950i
$562$	−12.0844	−	28.0702i	−0.509751	−	1.18407i
$563$	−4.88739	+	7.31450i	−0.205979	+	0.308269i	−0.920048	−	0.391806i	$-0.871850\pi$
$563$	−4.88739	+	7.31450i	−0.205979	+	0.308269i	0.714069	+	0.700076i	$0.246850\pi$
$564$	17.4797	−	31.1462i	0.736029	−	1.31149i
$565$	0.664741	−	3.34188i	0.0279658	−	0.140594i
$566$	2.81542	−	15.2534i	0.118341	−	0.641148i
$567$	−9.60413	−	14.2629i	−0.403335	−	0.598986i
$568$	−10.2343	+	4.74554i	−0.429421	+	0.199118i
$569$	13.0636	−	31.5384i	0.547656	−	1.32216i	−0.371562	−	0.928408i	$-0.621178\pi$
$569$	13.0636	−	31.5384i	0.547656	−	1.32216i	0.919218	−	0.393750i	$-0.128822\pi$
$570$	13.0223	+	7.54698i	0.545446	+	0.316108i
$571$	16.2774	−	10.8762i	0.681189	−	0.455156i	−0.166226	−	0.986088i	$-0.553158\pi$
$571$	16.2774	−	10.8762i	0.681189	−	0.455156i	0.847414	+	0.530932i	$0.178158\pi$
$572$	−46.1762	+	48.8034i	−1.93072	+	2.04057i
$573$	−7.52657	−	29.9342i	−0.314427	−	1.25052i
$574$	3.61918	−	3.72067i	0.151061	−	0.155298i
$575$	−12.2651			−0.511489
$576$	13.0646	+	20.1325i	0.544358	+	0.838853i
$577$	19.0173			0.791701			0.395851	−	0.918315i	$-0.370450\pi$
$577$	19.0173			0.791701			0.395851	+	0.918315i	$0.370450\pi$
$578$	−1.45050	+	1.49118i	−0.0603330	+	0.0620249i
$579$	7.11703	+	28.3054i	0.295774	+	1.17633i
$580$	2.31881	+	2.19398i	0.0962833	+	0.0911001i
$581$	−23.8162	+	15.9135i	−0.988063	+	0.660203i
$582$	−18.8287	−	10.9120i	−0.780476	−	0.452318i
$583$	−22.8727	+	55.2195i	−0.947288	+	2.28696i
$584$	2.11296	−	5.76666i	0.0874349	−	0.238626i
$585$	−11.3494	−	21.1423i	−0.469241	−	0.874125i
$586$	−8.43694	+	45.7096i	−0.348527	+	1.88825i
$587$	1.00936	−	5.07440i	0.0416608	−	0.209443i	−0.954348	−	0.298697i	$-0.903448\pi$
$587$	1.00936	−	5.07440i	0.0416608	−	0.209443i	0.996009	+	0.0892536i	$0.0284482\pi$
$588$	−10.1192	−	5.67906i	−0.417309	−	0.234200i
$589$	12.9703	−	19.4115i	0.534433	−	0.799835i
$590$	1.35487	+	3.14714i	0.0557790	+	0.129566i
$591$	13.5069	+	12.2200i	0.555599	+	0.502662i
$592$	−17.4482	+	13.1095i	−0.717115	+	0.538796i
$593$	13.3965	+	13.3965i	0.550128	+	0.550128i	0.926478	−	0.376350i	$-0.122821\pi$
$593$	13.3965	+	13.3965i	0.550128	+	0.550128i	−0.376350	+	0.926478i	$0.622821\pi$
$594$	−44.1076	−	10.2777i	−1.80976	−	0.421697i
$595$	−6.69434	+	10.0188i	−0.274441	+	0.410730i
$596$	29.9112	+	5.09430i	1.22521	+	0.208671i
$597$	15.6922	+	2.31339i	0.642241	+	0.0946807i
$598$	−18.8324	−	27.3581i	−0.770116	−	1.11876i
$599$	3.16761	+	7.64730i	0.129425	+	0.312460i	0.975287	−	0.220942i	$-0.0709132\pi$
$599$	3.16761	+	7.64730i	0.129425	+	0.312460i	−0.845862	+	0.533402i	$0.820913\pi$
$600$	10.8391	−	8.77432i	0.442504	−	0.358210i
$601$	−1.82628	+	4.40903i	−0.0744955	+	0.179848i	−0.956741	−	0.290942i	$-0.906031\pi$
$601$	−1.82628	+	4.40903i	−0.0744955	+	0.179848i	0.882245	+	0.470790i	$0.156031\pi$
$602$	−0.583497	−	2.73523i	−0.0237816	−	0.111479i
$603$	4.74604	+	5.76203i	0.193274	+	0.234648i
$604$	0.555937	+	1.24372i	0.0226207	+	0.0506061i
$605$	−38.8362	+	7.72500i	−1.57892	+	0.314066i
$606$	−27.7316	+	1.77191i	−1.12652	+	0.0719791i
$607$	−23.5474			−0.955758			−0.477879	−	0.878426i	$-0.658594\pi$
$607$	−23.5474			−0.955758			−0.477879	+	0.878426i	$0.658594\pi$
$608$	−22.8570	+	6.21488i	−0.926973	+	0.252047i
$609$	3.59486	−	0.179826i	0.145671	−	0.00728691i
$610$	−13.0362	+	0.180263i	−0.527820	+	0.00729863i
$611$	−10.9638	−	55.1186i	−0.443547	−	2.22986i
$612$	−6.75584	+	24.8860i	−0.273088	+	1.00596i
$613$	1.44177	−	0.963361i	0.0582326	−	0.0389098i	−0.526113	−	0.850415i	$-0.676351\pi$
$613$	1.44177	−	0.963361i	0.0582326	−	0.0389098i	0.584346	+	0.811505i	$0.301351\pi$
$614$	−4.91714	−	23.0498i	−0.198440	−	0.930213i
$615$	4.59875	+	1.64082i	0.185440	+	0.0661644i
$616$	32.3671	−	7.84639i	1.30411	−	0.316140i
$617$	0.759206	−	0.314474i	0.0305645	−	0.0126602i	−0.367349	−	0.930083i	$-0.619734\pi$
$617$	0.759206	−	0.314474i	0.0305645	−	0.0126602i	0.397913	+	0.917423i	$0.369734\pi$
$618$	−11.1777	+	8.54787i	−0.449635	+	0.343846i
$619$	3.54466	−	17.8202i	0.142472	−	0.716255i	−0.841827	−	0.539747i	$-0.818520\pi$
$619$	3.54466	−	17.8202i	0.142472	−	0.716255i	0.984299	−	0.176508i	$-0.0564800\pi$
$620$	9.46372	+	13.3491i	0.380072	+	0.536111i
$621$	9.51804	−	20.2646i	0.381946	−	0.813192i
$622$	−23.0416	−	9.17299i	−0.923884	−	0.367803i
$623$	3.99829	−	3.99829i	0.160188	−	0.160188i
$624$	36.2146	+	10.7048i	1.44975	+	0.428536i
$625$	1.88368	+	1.88368i	0.0753470	+	0.0753470i
$626$	9.87528	+	22.9387i	0.394696	+	0.916815i
$627$	22.9452	−	38.3595i	0.916344	−	1.53193i
$628$	4.58419	−	1.04440i	0.182929	−	0.0416762i
$629$	−22.9984	−	4.57467i	−0.917006	−	0.182404i
$630$	−0.980925	+	11.8544i	−0.0390810	+	0.472289i
$631$	15.6060	+	37.6763i	0.621266	+	1.49987i	0.850217	+	0.526432i	$0.176470\pi$
$631$	15.6060	+	37.6763i	0.621266	+	1.49987i	−0.228951	+	0.973438i	$0.573530\pi$
$632$	−0.258278	−	6.22286i	−0.0102738	−	0.247532i
$633$	39.3456	+	14.0384i	1.56385	+	0.557977i
$634$	11.6675	−	17.9954i	0.463376	−	0.714689i
$635$	7.54267	+	11.2884i	0.299322	+	0.447967i
$636$	33.4934	−	2.60551i	1.32810	−	0.103315i
$637$	−17.9077	+	3.56206i	−0.709529	+	0.141134i
$638$	6.61017	−	6.79554i	0.261699	−	0.269038i
$639$	−11.9056	+	1.19409i	−0.470977	+	0.0472375i
$640$	1.65020	−	16.5201i	0.0652301	−	0.653013i
$641$			18.0363i			0.712391i	0.934412	+	0.356195i	$0.115926\pi$
$641$			18.0363i			0.712391i	−0.934412	+	0.356195i	$0.884074\pi$
$642$	16.8099	−	19.1047i	0.663435	−	0.754002i
$643$	3.54089	+	17.8012i	0.139639	+	0.702012i	0.985644	+	0.168837i	$0.0540013\pi$
$643$	3.54089	+	17.8012i	0.139639	+	0.702012i	−0.846005	+	0.533175i	$0.820999\pi$
$644$	0.455237	+	16.4577i	0.0179389	+	0.648525i
$645$	2.11176	−	1.56911i	0.0831503	−	0.0617838i
$646$	−21.3546	−	13.8455i	−0.840185	−	0.544743i
$647$	−6.62347	−	2.74353i	−0.260395	−	0.107859i	0.248667	−	0.968589i	$-0.420008\pi$
$647$	−6.62347	−	2.74353i	−0.260395	−	0.107859i	−0.509062	+	0.860730i	$0.670008\pi$
$648$	6.08569	+	24.7177i	0.239068	+	0.971003i
$649$	9.40097	−	3.89401i	0.369020	−	0.152853i
$650$	3.98287	−	21.5784i	0.156221	−	0.846375i
$651$	18.2529	+	2.69089i	0.715389	+	0.105464i
$652$	7.68353	+	33.7253i	0.300910	+	1.32078i
$653$	6.41718	+	4.28782i	0.251124	+	0.167795i	0.674761	−	0.738037i	$-0.264247\pi$
$653$	6.41718	+	4.28782i	0.251124	+	0.167795i	−0.423637	+	0.905832i	$0.639247\pi$
$654$	−9.72798	+	4.77747i	−0.380394	+	0.186814i
$655$	5.15035	−	5.15035i	0.201241	−	0.201241i
$656$	−6.92584	+	3.32855i	−0.270409	+	0.129958i
$657$	4.12351	−	5.04287i	0.160873	−	0.196741i
$658$	−10.3038	+	25.8822i	−0.401686	+	1.00899i
$659$	−15.7559	−	10.5277i	−0.613762	−	0.410103i	0.209464	−	0.977816i	$-0.432828\pi$
$659$	−15.7559	−	10.5277i	−0.613762	−	0.410103i	−0.823226	+	0.567714i	$0.807828\pi$
$660$	19.3736	+	24.6210i	0.754115	+	0.958371i
$661$	−32.9062	−	6.54545i	−1.27990	−	0.254589i	−0.492113	−	0.870532i	$-0.663775\pi$
$661$	−32.9062	−	6.54545i	−1.27990	−	0.254589i	−0.787791	+	0.615943i	$0.788775\pi$
$662$	19.3101	+	28.0520i	0.750508	+	1.09027i
$663$	17.3809	+	36.6639i	0.675016	+	1.42391i
$664$	41.2107	−	9.99024i	1.59929	−	0.387696i
$665$	−10.8460	−	4.49258i	−0.420592	−	0.174215i
$666$	−22.0437	+	7.06459i	−0.854176	+	0.273747i
$667$	2.60368	+	3.89668i	0.100815	+	0.150880i
$668$	6.70139	+	2.56110i	0.259285	+	0.0990918i
$669$	−3.78163	−	15.0400i	−0.146206	−	0.581482i
$670$	−0.0714001	−	5.16349i	−0.00275842	−	0.199483i
$671$			38.7180i			1.49469i
$672$	−12.1760	−	14.2186i	−0.469699	−	0.548495i
$673$		−	44.2110i		−	1.70421i	−0.523372	−	0.852104i	$-0.675326\pi$
$673$		−	44.2110i		−	1.70421i	0.523372	−	0.852104i	$-0.324674\pi$
$674$	4.70269	−	0.0650282i	0.181141	−	0.00250479i
$675$	13.9133	−	5.02038i	0.535523	−	0.193235i
$676$	30.5112	−	13.6384i	1.17351	−	0.524553i
$677$	−20.1648	−	30.1787i	−0.774994	−	1.15986i	−0.983335	−	0.181805i	$-0.941806\pi$
$677$	−20.1648	−	30.1787i	−0.774994	−	1.15986i	0.208340	−	0.978056i	$-0.433194\pi$
$678$	1.46304	+	5.49621i	0.0561877	+	0.211081i
$679$	15.6821	+	6.49573i	0.601823	+	0.249283i
$680$	14.4082	−	10.5170i	0.552531	−	0.403307i
$681$	−15.1484	+	7.18122i	−0.580487	+	0.275185i
$682$	40.0282	−	27.5541i	1.53276	−	1.05510i
$683$	−30.6641	−	6.09947i	−1.17333	−	0.233390i	−0.430323	−	0.902675i	$-0.641600\pi$
$683$	−30.6641	−	6.09947i	−1.17333	−	0.233390i	−0.743006	+	0.669285i	$0.766600\pi$
$684$	−25.0644	−	1.72546i	−0.958360	−	0.0659748i
$685$	1.12796	+	0.753678i	0.0430971	+	0.0287966i
$686$	25.9813	+	10.3433i	0.991969	+	0.394908i
$687$	−31.2326	−	28.2568i	−1.19160	−	1.07806i
$688$	−0.582032	+	4.09927i	−0.0221898	+	0.156283i
$689$	37.3781	−	37.3781i	1.42399	−	1.42399i
$690$	−13.9016	+	6.82716i	−0.529225	+	0.259906i
$691$	16.7843	+	11.2149i	0.638506	+	0.426636i	0.832238	−	0.554419i	$-0.187059\pi$
$691$	16.7843	+	11.2149i	0.638506	+	0.426636i	−0.193732	+	0.981054i	$0.562059\pi$
$692$	2.38480	+	1.49979i	0.0906564	+	0.0570133i
$693$	35.1609	+	3.39958i	1.33565	+	0.129140i
$694$	23.2966	+	4.30001i	0.884327	+	0.163226i
$695$	−11.1903	+	4.63519i	−0.424474	+	0.175823i
$696$	−5.08861	−	1.58099i	−0.192883	−	0.0599272i
$697$	−7.62777	−	3.15953i	−0.288922	−	0.119676i
$698$	−12.9979	+	20.0474i	−0.491978	+	0.758804i
$699$	−28.6757	−	38.5926i	−1.08462	−	1.45971i
$700$	−7.47573	+	7.90107i	−0.282556	+	0.298632i
$701$	6.99714	+	35.1770i	0.264279	+	1.32862i	0.853689	+	0.520784i	$0.174360\pi$
$701$	6.99714	+	35.1770i	0.264279	+	1.32862i	−0.589410	+	0.807834i	$0.700640\pi$
$702$	32.5615	+	23.3260i	1.22895	+	0.880384i
$703$		−	22.8460i		−	0.861655i
$704$	−48.9881	−	5.57857i	−1.84631	−	0.210250i
$705$	−26.1729	+	1.30925i	−0.985728	+	0.0493091i
$706$	−6.92873	−	6.73973i	−0.260766	−	0.253653i
$707$	21.2579	−	4.22845i	0.799484	−	0.159027i
$708$	−4.34570	−	3.71838i	−0.163321	−	0.139745i
$709$	−24.9901	−	37.4003i	−0.938523	−	1.40460i	−0.914365	−	0.404890i	$-0.867310\pi$
$709$	−24.9901	−	37.4003i	−0.938523	−	1.40460i	−0.0241575	−	0.999708i	$-0.507690\pi$
$710$	6.94511	+	4.50293i	0.260645	+	0.168992i
$711$	1.90632	−	6.32498i	0.0714926	−	0.237205i
$712$	−7.59422	+	3.52136i	−0.284605	+	0.131969i
$713$	9.19314	+	22.1942i	0.344286	+	0.831179i
$714$	2.65803	−	19.9368i	0.0994744	−	0.746117i
$715$	48.3491	+	9.61723i	1.80815	+	0.359664i
$716$	32.9687	+	20.7338i	1.23210	+	0.774859i
$717$	22.0302	+	13.1777i	0.822735	+	0.492129i
$718$	−9.91777	+	4.26967i	−0.370128	+	0.159343i
$719$	34.1557	+	34.1557i	1.27379	+	1.27379i	0.944082	+	0.329712i	$0.106952\pi$
$719$	34.1557	+	34.1557i	1.27379	+	1.27379i	0.329712	+	0.944082i	$0.393048\pi$
$720$	7.40126	−	15.9785i	0.275829	−	0.595483i
$721$	7.76090	−	7.76090i	0.289031	−	0.289031i
$722$	−0.767187	+	1.92709i	−0.0285517	+	0.0717190i
$723$	−16.3467	+	27.3282i	−0.607940	+	1.01635i
$724$	2.86129	+	0.487318i	0.106339	+	0.0181110i
$725$	−0.604039	+	3.03671i	−0.0224334	+	0.112780i
$726$	52.5035	−	40.1506i	1.94859	−	1.49013i
$727$	16.2600	−	6.73511i	0.603050	−	0.249791i	−0.0602039	−	0.998186i	$-0.519175\pi$
$727$	16.2600	−	6.73511i	0.603050	−	0.249791i	0.663254	+	0.748395i	$0.269175\pi$
$728$	−29.1025	−	4.54345i	−1.07861	−	0.168391i
$729$	−2.50230	+	26.8838i	−0.0926779	+	0.995696i
$730$	−4.40706	+	0.940145i	−0.163113	+	0.0347963i
$731$	−3.69890	+	2.47152i	−0.136809	+	0.0914126i
$732$	19.3993	−	9.86234i	0.717019	−	0.364523i
$733$	−8.22139	−	41.3317i	−0.303664	−	1.52662i	−0.767702	−	0.640807i	$-0.778600\pi$
$733$	−8.22139	−	41.3317i	−0.303664	−	1.52662i	0.464038	−	0.885815i	$-0.346400\pi$
$734$	−0.541947	−	39.1924i	−0.0200036	−	1.44662i
$735$	0.425366	+	8.50342i	0.0156899	+	0.313653i
$736$	7.74953	−	23.1088i	0.285652	−	0.851802i
$737$	−15.3358			−0.564900
$738$	−8.09759	+	0.925419i	−0.298076	+	0.0340652i
$739$	−39.0931	+	7.77610i	−1.43806	+	0.286049i	−0.851713	−	0.524009i	$-0.824436\pi$
$739$	−39.0931	+	7.77610i	−1.43806	+	0.286049i	−0.586350	+	0.810058i	$0.699436\pi$
$740$	14.9578	+	5.71649i	0.549861	+	0.210142i
$741$	−31.7312	+	23.5774i	−1.16567	+	0.866138i
$742$	−25.6266	+	5.46685i	−0.940783	+	0.200694i
$743$	−5.33812	+	12.8874i	−0.195837	+	0.472791i	−0.991042	−	0.133548i	$-0.957363\pi$
$743$	−5.33812	+	12.8874i	−0.195837	+	0.472791i	0.795206	+	0.606340i	$0.207363\pi$
$744$	−24.0018	−	13.0371i	−0.879949	−	0.477964i
$745$	−8.51953	−	20.5680i	−0.312131	−	0.753552i
$746$	−12.9485	+	8.91330i	−0.474077	+	0.326339i
$747$	44.7678	+	4.32844i	1.63797	+	0.158369i
$748$	−30.6381	−	43.2167i	−1.12024	−	1.58016i
$749$	−11.0272	+	16.5034i	−0.402925	+	0.603021i
$750$	−26.6929	−	9.10990i	−0.974685	−	0.332646i
$751$	−21.3648	−	21.3648i	−0.779614	−	0.779614i	0.200151	−	0.979765i	$-0.435857\pi$
$751$	−21.3648	−	21.3648i	−0.779614	−	0.779614i	−0.979765	+	0.200151i	$0.935857\pi$
$752$	27.5052	−	30.7294i	1.00301	−	1.12058i
$753$	−14.6607	+	16.2047i	−0.534266	+	0.590532i
$754$	−7.70107	+	3.31537i	−0.280456	+	0.120738i
$755$	0.555327	−	0.831106i	0.0202104	−	0.0302470i
$756$	−7.25295	−	18.4830i	−0.263787	−	0.672221i
$757$	−9.93649	+	49.9541i	−0.361148	+	1.81561i	0.190676	+	0.981653i	$0.438932\pi$
$757$	−9.93649	+	49.9541i	−0.361148	+	1.81561i	−0.551824	+	0.833960i	$0.686068\pi$
$758$	15.7708	+	2.91093i	0.572823	+	0.105730i
$759$	19.7022	+	41.5607i	0.715145	+	1.50856i
$760$	12.7883	+	11.7690i	0.463880	+	0.426908i
$761$	−4.15271	+	10.0255i	−0.150535	+	0.363425i	−0.981101	−	0.193496i	$-0.938017\pi$
$761$	−4.15271	+	10.0255i	−0.150535	+	0.363425i	0.830566	+	0.556921i	$0.188017\pi$
$762$	−19.6073	−	11.3632i	−0.710297	−	0.411646i
$763$	7.02867	−	4.69641i	0.254455	−	0.170021i
$764$	−0.985486	−	35.6273i	−0.0356536	−	1.28895i
$765$	18.0958	−	5.52465i	0.654255	−	0.199744i
$766$	−6.98277	−	6.79229i	−0.252298	−	0.245416i
$767$	−8.99939			−0.324949
$768$	9.68327	+	25.9660i	0.349415	+	0.936968i
$769$	−20.1862			−0.727933			−0.363967	−	0.931412i	$-0.618578\pi$
$769$	−20.1862			−0.727933			−0.363967	+	0.931412i	$0.618578\pi$
$770$	−17.5164	−	17.0386i	−0.631247	−	0.614028i
$771$	−43.8215	+	11.0184i	−1.57819	+	0.396817i
$772$	0.931864	+	33.6887i	0.0335385	+	1.21248i
$773$	31.1512	−	20.8146i	1.12043	−	0.748648i	0.149679	−	0.988735i	$-0.452176\pi$
$773$	31.1512	−	20.8146i	1.12043	−	0.748648i	0.970751	+	0.240087i	$0.0771760\pi$
$774$	−2.00943	+	3.90485i	−0.0722275	+	0.140357i
$775$	−6.07358	+	14.6629i	−0.218170	+	0.526708i
$776$	−18.4903	−	17.0166i	−0.663764	−	0.610861i
$777$	16.3147	−	7.73415i	0.585288	−	0.277461i
$778$	−34.8029	−	6.42382i	−1.24775	−	0.230305i
$779$	1.56930	−	7.88939i	0.0562259	−	0.282667i
$780$	−7.49698	−	26.6746i	−0.268435	−	0.955104i
$781$	13.6565	−	20.4384i	0.488668	−	0.731343i
$782$	24.0538	−	10.3553i	0.860162	−	0.370306i
$783$	−4.54856	−	3.35457i	−0.162552	−	0.119883i
$784$	−9.98379	−	8.93629i	−0.356564	−	0.319153i
$785$	−2.43932	−	2.43932i	−0.0870631	−	0.0870631i
$786$	−3.92698	+	11.5064i	−0.140071	+	0.410420i
$787$	18.3039	−	27.3937i	0.652462	−	0.976479i	−0.346795	−	0.937941i	$-0.612730\pi$
$787$	18.3039	−	27.3937i	0.652462	−	0.976479i	0.999257	−	0.0385378i	$-0.0122700\pi$
$788$	12.1639	+	17.1578i	0.433321	+	0.611222i
$789$	−6.59884	+	44.7615i	−0.234925	+	1.59355i
$790$	−3.76418	+	2.59113i	−0.133923	+	0.0921884i
$791$	−1.69767	−	4.09855i	−0.0603624	−	0.145728i
$792$	−47.1437	−	22.6339i	−1.67518	−	0.804260i
$793$	13.1041	−	31.6361i	0.465341	−	1.12343i
$794$	24.7790	−	5.28604i	0.879375	−	0.187594i
$795$	−14.7012	−	19.7853i	−0.521397	−	0.701711i
$796$	17.1088	+	6.53854i	0.606406	+	0.231752i
$797$	−42.7141	+	8.49637i	−1.51301	+	0.300957i	−0.880669	−	0.473731i	$-0.842907\pi$
$797$	−42.7141	+	8.49637i	−1.51301	+	0.300957i	−0.632343	+	0.774688i	$0.717907\pi$
$798$	19.5562	−	1.24954i	0.692282	−	0.0442334i
$799$	44.3114			1.56763
$800$	14.4158	−	7.17525i	0.509675	−	0.253683i
$801$	−8.83437	+	0.886060i	−0.312147	+	0.0313074i
$802$	−0.324850	−	23.4924i	−0.0114709	−	0.829547i
$803$	2.61077	+	13.1252i	0.0921321	+	0.463179i
$804$	3.90636	+	7.68384i	0.137767	+	0.270988i
$805$	10.0442	−	6.71132i	0.354011	−	0.236543i
$806$	−42.0324	+	8.96665i	−1.48053	+	0.315837i
$807$	−14.3559	+	40.2355i	−0.505353	+	1.41636i
$808$	−31.7030	−	4.94943i	−1.11531	−	0.174120i
$809$	33.6238	−	13.9275i	1.18215	−	0.489663i	0.296960	−	0.954890i	$-0.404027\pi$
$809$	33.6238	−	13.9275i	1.18215	−	0.489663i	0.885192	+	0.465227i	$0.154027\pi$
$810$	12.9752	−	13.4349i	0.455902	−	0.472053i
$811$	−2.84165	+	14.2859i	−0.0997838	+	0.501647i	0.898279	+	0.439426i	$0.144818\pi$
$811$	−2.84165	+	14.2859i	−0.0997838	+	0.501647i	−0.998062	+	0.0622206i	$0.980182\pi$
$812$	4.09718	+	0.697809i	0.143783	+	0.0244883i
$813$	−21.6303	−	12.9384i	−0.758607	−	0.453770i
$814$	17.5891	−	44.1821i	0.616498	−	1.54858i
$815$	17.9458	−	17.9458i	0.628613	−	0.628613i
$816$	−13.8491	+	26.3592i	−0.484816	+	0.922758i
$817$	−3.06477	−	3.06477i	−0.107223	−	0.107223i
$818$	−4.09552	+	1.76315i	−0.143197	+	0.0616472i
$819$	−27.5791	−	14.6780i	−0.963691	−	0.512891i
$820$	4.77270	+	3.00152i	0.166670	+	0.104818i
$821$	−54.9485	−	10.9299i	−1.91772	−	0.381458i	−0.917837	−	0.396957i	$-0.870066\pi$
$821$	−54.9485	−	10.9299i	−1.91772	−	0.381458i	−0.999880	+	0.0154997i	$0.995066\pi$
$822$	−2.24457	−	0.299253i	−0.0782885	−	0.0104376i
$823$	2.45204	+	5.91975i	0.0854727	+	0.206349i	0.960837	−	0.277115i	$-0.0893783\pi$
$823$	2.45204	+	5.91975i	0.0854727	+	0.206349i	−0.875364	+	0.483464i	$0.839378\pi$
$824$	−14.7408	+	6.83516i	−0.513520	+	0.238114i
$825$	−10.2114	+	28.6196i	−0.355516	+	0.996407i
$826$	3.74313	+	2.42690i	0.130240	+	0.0844425i
$827$	−0.518324	−	0.775726i	−0.0180239	−	0.0269746i	0.822348	−	0.568984i	$-0.192664\pi$
$827$	−0.518324	−	0.775726i	−0.0180239	−	0.0269746i	−0.840372	+	0.542010i	$0.817664\pi$
$828$	15.8050	−	20.4581i	0.549262	−	0.710967i
$829$	44.1937	−	8.79068i	1.53491	−	0.305313i	0.645980	−	0.763354i	$-0.276449\pi$
$829$	44.1937	−	8.79068i	1.53491	−	0.305313i	0.888931	+	0.458041i	$0.151449\pi$
$830$	−22.3024	−	21.6940i	−0.774126	−	0.753009i
$831$	1.08446	+	21.6793i	0.0376196	+	0.752045i
$832$	38.1397	+	21.1382i	1.32225	+	0.732836i
$833$		−	14.3965i		−	0.498810i
$834$	13.3557	−	15.1789i	0.462469	−	0.525602i
$835$	−1.02692	−	5.16268i	−0.0355380	−	0.178662i
$836$	35.4729	−	37.4912i	1.22686	−	1.29666i
$837$	−19.5131	−	21.4137i	−0.674473	−	0.740167i
$838$	−8.54561	+	13.1803i	−0.295203	+	0.455307i
$839$	−27.0571	−	11.2074i	−0.934116	−	0.386924i	−0.136878	−	0.990588i	$-0.543707\pi$
$839$	−27.0571	−	11.2074i	−0.934116	−	0.386924i	−0.797239	+	0.603664i	$0.793707\pi$
$840$	−4.07521	+	13.1165i	−0.140608	+	0.452564i
$841$	−25.6995	+	10.6451i	−0.886190	+	0.367072i
$842$	−5.72090	−	1.05595i	−0.197155	−	0.0363903i
$843$	5.45892	−	37.0291i	0.188015	−	1.27535i
$844$	40.8338	+	25.6801i	1.40556	+	0.883947i
$845$	−20.3889	−	13.6234i	−0.701399	−	0.468660i
$846$	38.2511	−	21.2201i	1.31510	−	0.729561i
$847$	−36.4541	+	36.4541i	−1.25258	+	1.25258i
$848$	38.4065	+	5.45312i	1.31888	+	0.187261i
$849$	12.7451	−	14.0873i	0.437410	−	0.483475i
$850$	16.0746	+	6.39938i	0.551354	+	0.219497i
$851$	19.5465	+	13.0606i	0.670046	+	0.447711i
$852$	−13.7191	−	1.63635i	−0.470008	−	0.0560603i
$853$	25.4179	+	5.05593i	0.870292	+	0.173112i	0.609984	−	0.792414i	$-0.291176\pi$
$853$	25.4179	+	5.05593i	0.870292	+	0.173112i	0.260308	+	0.965526i	$0.416176\pi$
$854$	−13.9818	+	9.62463i	−0.478449	+	0.329348i
$855$	8.71871	+	16.2416i	0.298174	+	0.555453i
$856$	23.7339	−	17.3240i	0.811207	−	0.592122i
$857$	13.3762	+	5.54061i	0.456923	+	0.189264i	0.599260	−	0.800555i	$-0.295462\pi$
$857$	13.3762	+	5.54061i	0.456923	+	0.189264i	−0.142337	+	0.989818i	$0.545462\pi$
$858$	−79.5172	+	21.1667i	−2.71467	+	0.722621i
$859$	19.4625	+	29.1276i	0.664051	+	0.993822i	0.998675	+	0.0514702i	$0.0163907\pi$
$859$	19.4625	+	29.1276i	0.664051	+	0.993822i	−0.334624	+	0.942352i	$0.608609\pi$
$860$	2.77344	−	1.23971i	0.0945734	−	0.0422739i
$861$	6.16520	−	1.55016i	0.210110	−	0.0528293i
$862$	23.2191	−	0.321071i	0.790847	−	0.0109357i
$863$			7.11593i			0.242229i	0.992639	+	0.121114i	$0.0386468\pi$
$863$			7.11593i			0.242229i	−0.992639	+	0.121114i	$0.961353\pi$
$864$	0.668047	+	29.3863i	0.0227274	+	0.999742i
$865$		−	2.06705i		−	0.0702818i
$866$	−0.276247	−	19.9776i	−0.00938726	−	0.678866i
$867$	−2.47091	+	0.621278i	−0.0839164	+	0.0210997i
$868$	19.9007	+	7.60551i	0.675473	+	0.258148i
$869$	7.53973	+	11.2840i	0.255768	+	0.382783i
$870$	1.00570	+	3.77812i	0.0340964	+	0.128090i
$871$	12.5307	+	5.19039i	0.424587	+	0.175870i
$872$	−12.1621	+	2.94833i	−0.411862	+	0.0998430i
$873$	−12.6062	−	23.4835i	−0.426656	−	0.794795i
$874$	14.4672	+	21.0167i	0.489361	+	0.710902i
$875$	21.5764	+	4.29182i	0.729416	+	0.145090i
$876$	5.91126	−	4.65140i	0.199723	−	0.157156i
$877$	14.4250	+	9.63850i	0.487099	+	0.325469i	0.774752	−	0.632266i	$-0.217875\pi$
$877$	14.4250	+	9.63850i	0.487099	+	0.325469i	−0.287653	+	0.957735i	$0.592875\pi$
$878$	12.7522	−	32.0323i	0.430368	−	1.08104i
$879$	−38.1930	+	42.2152i	−1.28822	+	1.42388i
$880$	15.6704	+	32.6059i	0.528248	+	1.09914i
$881$	−8.17606	+	8.17606i	−0.275458	+	0.275458i	−0.831293	−	0.555835i	$-0.812399\pi$
$881$	−8.17606	+	8.17606i	−0.275458	+	0.275458i	0.555835	+	0.831293i	$0.312399\pi$
$882$	−6.89428	−	12.4275i	−0.232142	−	0.418457i
$883$	2.72387	+	1.82003i	0.0916655	+	0.0612489i	0.600558	−	0.799581i	$-0.294945\pi$
$883$	2.72387	+	1.82003i	0.0916655	+	0.0612489i	−0.508893	+	0.860830i	$0.669945\pi$
$884$	10.4075	+	45.6815i	0.350041	+	1.53643i
$885$	−0.612037	+	4.15159i	−0.0205734	+	0.139554i
$886$	−5.78660	+	31.3507i	−0.194405	+	1.05325i
$887$	26.5174	−	10.9839i	0.890367	−	0.368802i	0.109859	−	0.993947i	$-0.464960\pi$
$887$	26.5174	−	10.9839i	0.890367	−	0.368802i	0.780509	+	0.625145i	$0.214960\pi$
$888$	−26.6174	+	2.44130i	−0.893221	+	0.0819246i
$889$	16.3305	+	6.76432i	0.547708	+	0.226868i
$890$	5.15353	+	3.34134i	0.172747	+	0.112002i
$891$	−39.3616	−	39.0811i	−1.31866	−	1.30927i
$892$	−0.495145	−	17.9005i	−0.0165787	−	0.599352i
$893$	8.42245	+	42.3425i	0.281847	+	1.41694i
$894$	27.8989	+	24.5478i	0.933080	+	0.821003i
$895$		−	28.5759i		−	0.955189i
$896$	−10.1631	−	19.0773i	−0.339524	−	0.637328i
$897$	−2.03229	−	40.6271i	−0.0678562	−	1.35650i
$898$	5.64569	−	5.80401i	0.188399	−	0.193682i
$899$	5.94781	−	1.18309i	0.198370	−	0.0394583i
$900$	16.9407	−	2.17373i	0.564689	−	0.0724575i
$901$	23.1560	+	34.6553i	0.771437	+	1.15454i
$902$	9.10889	−	14.0491i	0.303293	−	0.467785i
$903$	1.15108	−	3.22613i	0.0383054	−	0.107359i
$904$	0.272347	+	6.56183i	0.00905813	+	0.218243i
$905$	−0.814973	−	1.96752i	−0.0270906	−	0.0654026i
$906$	−0.220496	+	1.65385i	−0.00732550	+	0.0549456i
$907$	−0.257259	−	0.0511719i	−0.00854213	−	0.00169913i	0.190817	−	0.981626i	$-0.438886\pi$
$907$	−0.257259	−	0.0511719i	−0.00854213	−	0.00169913i	−0.199360	+	0.979926i	$0.563886\pi$
$908$	−18.8742	+	4.30004i	−0.626361	+	0.142702i
$909$	−30.0434	−	15.9896i	−0.996478	−	0.530340i
$910$	8.54579	+	19.8505i	0.283290	+	0.658038i
$911$	−23.5054	−	23.5054i	−0.778770	−	0.778770i	0.200852	−	0.979622i	$-0.435629\pi$
$911$	−23.5054	−	23.5054i	−0.778770	−	0.778770i	−0.979622	+	0.200852i	$0.935629\pi$
$912$	−27.8204	−	8.22354i	−0.921225	−	0.272309i
$913$	−65.3354	+	65.3354i	−2.16228	+	2.16228i
$914$	28.4804	+	11.3382i	0.942048	+	0.375035i
$915$	−13.7032	−	8.19671i	−0.453012	−	0.270975i
$916$	−28.1272	−	39.6748i	−0.929348	−	1.31089i
$917$	1.85006	−	9.30089i	0.0610944	−	0.307142i
$918$	−23.0475	+	21.5927i	−0.760682	+	0.712665i
$919$	−15.2209	+	6.30470i	−0.502091	+	0.207973i	−0.619330	−	0.785131i	$-0.712596\pi$
$919$	−15.2209	+	6.30470i	−0.502091	+	0.207973i	0.117239	+	0.993104i	$0.462596\pi$
$920$	−17.3801	+	4.21326i	−0.573005	+	0.138907i
$921$	9.70013	−	27.1866i	0.319630	−	0.895830i
$922$	−6.68867	−	31.3541i	−0.220280	−	1.03259i
$923$	−18.0760	+	12.0780i	−0.594978	+	0.397552i
$924$	38.7818	+	12.6398i	1.27583	+	0.415818i
$925$	3.02998	+	15.2328i	0.0996252	+	0.500850i
$926$	22.9331	−	0.317116i	0.753628	−	0.0104211i
$927$	−17.1480	+	1.71989i	−0.563214	+	0.0564887i
$928$	−5.33985	−	3.05678i	−0.175289	−	0.100344i
$929$	40.1544			1.31742			0.658711	−	0.752396i	$-0.271102\pi$
$929$	40.1544			1.31742			0.658711	+	0.752396i	$0.271102\pi$
$930$	1.27791	+	20.0002i	0.0419043	+	0.655831i
$931$	13.7568	−	2.73641i	0.450862	−	0.0896821i
$932$	−22.6559	−	50.6849i	−0.742120	−	1.66024i
$933$	−18.1157	−	24.3806i	−0.593080	−	0.798184i
$934$	1.09237	+	5.12062i	0.0357433	+	0.167552i
$935$	−14.8746	+	35.9105i	−0.486452	+	1.17440i
$936$	30.8602	+	34.4498i	1.00870	+	1.12603i
$937$	10.1105	+	24.4088i	0.330294	+	0.797401i	0.998569	+	0.0534862i	$0.0170333\pi$
$937$	10.1105	+	24.4088i	0.330294	+	0.797401i	−0.668274	+	0.743915i	$0.732967\pi$
$938$	−3.81221	−	5.53805i	−0.124473	−	0.180824i
$939$	−4.46098	+	30.2598i	−0.145579	+	0.987493i
$940$	−29.8301	−	5.08049i	−0.972950	−	0.165707i
$941$	6.35358	−	9.50880i	0.207121	−	0.309978i	−0.713336	−	0.700822i	$-0.752817\pi$
$941$	6.35358	−	9.50880i	0.207121	−	0.309978i	0.920457	+	0.390844i	$0.127817\pi$
$942$	5.44969	+	1.85990i	0.177561	+	0.0605989i
$943$	5.85284	+	5.85284i	0.190595	+	0.190595i
$944$	−3.96703	−	5.27996i	−0.129116	−	0.171848i
$945$	−8.64686	+	11.7245i	−0.281282	+	0.381399i
$946$	−3.56741	−	8.28653i	−0.115987	−	0.269418i
$947$	−24.7245	+	37.0029i	−0.803440	+	1.20243i	0.172633	+	0.984986i	$0.444773\pi$
$947$	−24.7245	+	37.0029i	−0.803440	+	1.20243i	−0.976072	+	0.217446i	$0.930227\pi$
$948$	3.73321	−	6.65200i	0.121249	−	0.216047i
$949$	2.30900	−	11.6081i	0.0749533	−	0.376816i
$950$	−3.05968	+	16.5767i	−0.0992690	+	0.537819i
$951$	23.7349	−	11.2518i	0.769657	−	0.364863i
$952$	7.99029	−	21.8070i	0.258967	−	0.706769i
$953$	−11.0789	+	26.7468i	−0.358881	+	0.866415i	0.636577	+	0.771213i	$0.280350\pi$
$953$	−11.0789	+	26.7468i	−0.358881	+	0.866415i	−0.995458	+	0.0952017i	$0.969650\pi$
$954$	36.5849	+	18.8266i	1.18448	+	0.609533i
$955$	−21.7434	+	14.5285i	−0.703600	+	0.470131i
$956$	21.5315	+	20.3724i	0.696380	+	0.658892i
$957$	11.2603	−	2.83126i	0.363994	−	0.0915216i
$958$	7.68841	−	7.90402i	0.248401	−	0.255367i
$959$	1.76622			0.0570343
$960$	12.3453	−	16.1570i	0.398443	−	0.521464i
$961$	0.0855908			0.00276099
$962$	−29.3254	+	30.1477i	−0.945488	+	0.972002i
$963$	29.8082	−	9.10044i	0.960555	−	0.293258i
$964$	−25.2717	+	26.7095i	−0.813946	+	0.860257i
$965$	20.5603	−	13.7380i	0.661860	−	0.442240i
$966$	−10.1108	+	17.4462i	−0.325308	+	0.561321i
$967$	23.0878	−	55.7388i	0.742452	−	1.79244i	0.146851	−	0.989159i	$-0.453086\pi$
$967$	23.0878	−	55.7388i	0.742452	−	1.79244i	0.595602	−	0.803280i	$-0.296914\pi$
$968$	69.2397	−	32.1057i	2.22545	−	1.03192i
$969$	−13.3521	−	28.1655i	−0.428931	−	0.904806i
$970$	−3.34663	+	18.1314i	−0.107454	+	0.582163i
$971$	1.78267	−	8.96207i	0.0572085	−	0.287607i	−0.941581	−	0.336785i	$-0.890660\pi$
$971$	1.78267	−	8.96207i	0.0572085	−	0.287607i	0.998790	+	0.0491786i	$0.0156604\pi$
$972$	−9.55496	+	29.6766i	−0.306475	+	0.951879i
$973$	−8.76124	+	13.1121i	−0.280872	+	0.420355i
$974$	1.34317	+	3.11998i	0.0430381	+	0.0999706i
$975$	18.0300	−	19.9288i	0.577421	−	0.638232i
$976$	24.3374	−	6.25735i	0.779022	−	0.200293i
$977$	19.6065	+	19.6065i	0.627266	+	0.627266i	0.947379	−	0.320113i	$-0.103721\pi$
$977$	19.6065	+	19.6065i	0.627266	+	0.627266i	−0.320113	+	0.947379i	$0.603721\pi$
$978$	−13.6831	+	40.0927i	−0.437536	+	1.28202i
$979$	10.1336	−	15.1660i	0.323872	−	0.484709i
$980$	−1.65062	+	9.69162i	−0.0527271	+	0.309587i
$981$	−13.2119	−	1.27741i	−0.421824	−	0.0407847i
$982$	−18.6564	−	27.1024i	−0.595350	−	0.864873i
$983$	−10.8230	−	26.1291i	−0.345201	−	0.833388i	−0.997173	−	0.0751452i	$-0.976058\pi$
$983$	−10.8230	−	26.1291i	−0.345201	−	0.833388i	0.651972	−	0.758243i	$-0.273942\pi$
$984$	−9.35943	−	0.985301i	−0.298368	−	0.0314102i
$985$	5.90550	−	14.2571i	0.188165	−	0.454270i
$986$	−1.37926	−	6.46546i	−0.0439245	−	0.205902i
$987$	−27.3862	+	20.3490i	−0.871713	+	0.647715i
$988$	−41.6735	+	18.6279i	−1.32581	+	0.592632i
$989$	4.37421	−	0.870084i	0.139092	−	0.0276671i
$990$	4.35675	+	38.1223i	0.138466	+	1.21161i
$991$	−23.9320			−0.760226			−0.380113	−	0.924940i	$-0.624115\pi$
$991$	−23.9320			−0.760226			−0.380113	+	0.924940i	$0.624115\pi$
$992$	−23.7891	−	20.7079i	−0.755305	−	0.657477i
$993$	2.08384	+	41.6576i	0.0661285	+	1.32196i
$994$	10.7755	−	0.149002i	0.341778	−	0.00472606i
$995$	−2.62175	−	13.1804i	−0.0831151	−	0.417848i
$996$	49.3781	+	16.0933i	1.56460	+	0.509936i
$997$	−19.7503	+	13.1967i	−0.625497	+	0.417944i	−0.827519	−	0.561437i	$-0.810249\pi$
$997$	−19.7503	+	13.1967i	−0.625497	+	0.417944i	0.202022	+	0.979381i	$0.435249\pi$
$998$	−5.54979	−	26.0154i	−0.175676	−	0.823503i
$999$	−27.5192	−	6.81483i	−0.870670	−	0.215612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.11.23	yes	240
3.2	odd	2	inner	192.2.s.a.11.8	✓	240
4.3	odd	2		768.2.s.a.719.14		240
12.11	even	2		768.2.s.a.719.15		240
64.29	even	16		768.2.s.a.47.15		240
64.35	odd	16	inner	192.2.s.a.35.8	yes	240
192.29	odd	16		768.2.s.a.47.14		240
192.35	even	16	inner	192.2.s.a.35.23	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.11.8	✓	240	3.2	odd	2	inner
192.2.s.a.11.23	yes	240	1.1	even	1	trivial
192.2.s.a.35.8	yes	240	64.35	odd	16	inner
192.2.s.a.35.23	yes	240	192.35	even	16	inner
768.2.s.a.47.14		240	192.29	odd	16
768.2.s.a.47.15		240	64.29	even	16
768.2.s.a.719.14		240	4.3	odd	2
768.2.s.a.719.15		240	12.11	even	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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.01373 + 0.986078i) q^{2} +(0.422356 + 1.67977i) q^{3} +(0.0553009 + 1.99924i) q^{4} +(1.22014 - 0.815271i) q^{5} +(-1.22823 + 2.11931i) q^{6} +(0.731141 - 1.76513i) q^{7} +(-1.91534 + 2.08122i) q^{8} +(-2.64323 + 1.41892i) q^{9} +O(q^{10})\)	\(q+(1.01373 + 0.986078i) q^{2} +(0.422356 + 1.67977i) q^{3} +(0.0553009 + 1.99924i) q^{4} +(1.22014 - 0.815271i) q^{5} +(-1.22823 + 2.11931i) q^{6} +(0.731141 - 1.76513i) q^{7} +(-1.91534 + 2.08122i) q^{8} +(-2.64323 + 1.41892i) q^{9} +(2.04081 + 0.376687i) q^{10} +(1.20236 - 6.04466i) q^{11} +(-3.33489 + 0.937281i) q^{12} +(-3.02825 + 4.53210i) q^{13} +(2.48173 - 1.06840i) q^{14} +(1.88480 + 1.70521i) q^{15} +(-3.99388 + 0.221119i) q^{16} +(-3.03900 - 3.03900i) q^{17} +(-4.07869 - 1.16803i) q^{18} +(2.32633 - 3.48160i) q^{19} +(1.69739 + 2.39426i) q^{20} +(3.27381 + 0.482633i) q^{21} +(7.17937 - 4.94204i) q^{22} +(1.64886 + 3.98070i) q^{23} +(-4.30492 - 2.33831i) q^{24} +(-1.08934 + 2.62991i) q^{25} +(-7.53884 + 1.60824i) q^{26} +(-3.49984 - 3.84072i) q^{27} +(3.56934 + 1.36411i) q^{28} +(1.06679 - 0.212197i) q^{29} +(0.229203 + 3.58718i) q^{30} +5.57545 q^{31} +(-4.26676 - 3.71413i) q^{32} +(10.6614 - 0.533317i) q^{33} +(-0.0840376 - 6.07741i) q^{34} +(-0.546965 - 2.74978i) q^{35} +(-2.98292 - 5.20597i) q^{36} +(4.53654 - 3.03122i) q^{37} +(5.79140 - 1.23546i) q^{38} +(-8.89188 - 3.17260i) q^{39} +(-0.640227 + 4.10090i) q^{40} +(1.77481 - 0.735151i) q^{41} +(2.84285 + 3.71749i) q^{42} +(0.201937 - 1.01521i) q^{43} +(12.1512 + 2.06952i) q^{44} +(-2.06831 + 3.88623i) q^{45} +(-2.25378 + 5.66127i) q^{46} +(-7.29047 + 7.29047i) q^{47} +(-2.05827 - 6.61540i) q^{48} +(2.36863 + 2.36863i) q^{49} +(-3.69760 + 1.59184i) q^{50} +(3.82127 - 6.38834i) q^{51} +(-9.22821 - 5.80356i) q^{52} +(-9.51158 - 1.89197i) q^{53} +(0.239360 - 7.34457i) q^{54} +(-3.46099 - 8.35557i) q^{55} +(2.27323 + 4.90249i) q^{56} +(6.83081 + 2.43722i) q^{57} +(1.29068 + 0.836823i) q^{58} +(0.917273 + 1.37280i) q^{59} +(-3.30489 + 3.86245i) q^{60} +(-6.16153 + 1.22560i) q^{61} +(5.65200 + 5.49782i) q^{62} +(0.572001 + 5.70307i) q^{63} +(-0.662934 - 7.97249i) q^{64} +7.99864i q^{65} +(11.3337 + 9.97237i) q^{66} +(-0.485448 - 2.44051i) q^{67} +(5.90761 - 6.24373i) q^{68} +(-5.99025 + 4.45098i) q^{69} +(2.15702 - 3.32689i) q^{70} +(3.68483 + 1.52631i) q^{71} +(2.10961 - 8.21885i) q^{72} +(-2.00609 + 0.830949i) q^{73} +(7.58785 + 1.40054i) q^{74} +(-4.87773 - 0.719087i) q^{75} +(7.08918 + 4.45834i) q^{76} +(-9.79052 - 6.54181i) q^{77} +(-5.88554 - 11.9842i) q^{78} +(-1.55705 + 1.55705i) q^{79} +(-4.69282 + 3.52589i) q^{80} +(4.97334 - 7.50106i) q^{81} +(2.52410 + 1.00486i) q^{82} +(-12.4656 - 8.32922i) q^{83} +(-0.783852 + 6.57180i) q^{84} +(-6.18560 - 1.23039i) q^{85} +(1.20578 - 0.830021i) q^{86} +(0.807004 + 1.70233i) q^{87} +(10.2773 + 14.0800i) q^{88} +(2.73428 + 1.13258i) q^{89} +(-5.92883 + 1.90008i) q^{90} +(5.78567 + 8.65887i) q^{91} +(-7.86718 + 3.51660i) q^{92} +(2.35482 + 9.36545i) q^{93} +(-14.5796 + 0.201604i) q^{94} -6.14462i q^{95} +(4.43677 - 8.73585i) q^{96} +8.88438i q^{97} +(0.0655000 + 4.73681i) q^{98} +(5.39877 + 17.6835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

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