LMFDB - Embedded newform 672.2.ch.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(11,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 12, 16]))

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

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

chi := DirichletCharacter("672.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.ch (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$124$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	672.11
Dual form			672.2.ch.a.611.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40999 + 0.109279i) q^{2} +(1.70442 - 0.308130i) q^{3} +(1.97612 - 0.308164i) q^{4} +(-0.270326 - 2.05333i) q^{5} +(-2.36954 + 0.620717i) q^{6} +(-2.18436 - 1.49283i) q^{7} +(-2.75262 + 0.650455i) q^{8} +(2.81011 - 1.05037i) q^{9} +O(q^{10})$	\(q+(-1.40999 + 0.109279i) q^{2} +(1.70442 - 0.308130i) q^{3} +(1.97612 - 0.308164i) q^{4} +(-0.270326 - 2.05333i) q^{5} +(-2.36954 + 0.620717i) q^{6} +(-2.18436 - 1.49283i) q^{7} +(-2.75262 + 0.650455i) q^{8} +(2.81011 - 1.05037i) q^{9} +(0.605541 + 2.86562i) q^{10} +(-1.54111 + 1.18253i) q^{11} +(3.27318 - 1.13414i) q^{12} +(-0.208388 - 0.503093i) q^{13} +(3.24306 + 1.86617i) q^{14} +(-1.09344 - 3.41644i) q^{15} +(3.81007 - 1.21794i) q^{16} +(1.41189 - 2.44546i) q^{17} +(-3.84743 + 1.78809i) q^{18} +(-3.29179 - 2.52588i) q^{19} +(-1.16696 - 3.97431i) q^{20} +(-4.18307 - 1.87135i) q^{21} +(2.04371 - 1.83576i) q^{22} +(0.143808 + 0.0385332i) q^{23} +(-4.49120 + 1.95681i) q^{24} +(0.686548 - 0.183960i) q^{25} +(0.348801 + 0.686581i) q^{26} +(4.46597 - 2.65615i) q^{27} +(-4.77660 - 2.27687i) q^{28} +(-1.56796 - 3.78538i) q^{29} +(1.91508 + 4.69764i) q^{30} +(-6.74344 - 3.89333i) q^{31} +(-5.23905 + 2.13363i) q^{32} +(-2.26232 + 2.49040i) q^{33} +(-1.72350 + 3.60235i) q^{34} +(-2.47479 + 4.88877i) q^{35} +(5.22942 - 2.94162i) q^{36} +(-2.70043 + 0.355519i) q^{37} +(4.91740 + 3.20173i) q^{38} +(-0.510199 - 0.793272i) q^{39} +(2.07970 + 5.47620i) q^{40} +(0.114119 + 0.114119i) q^{41} +(6.10256 + 2.18145i) q^{42} +(0.651652 - 1.57323i) q^{43} +(-2.68099 + 2.81173i) q^{44} +(-2.91640 - 5.48614i) q^{45} +(-0.206978 - 0.0386160i) q^{46} +(1.19950 - 0.692533i) q^{47} +(6.11869 - 3.24987i) q^{48} +(2.54290 + 6.52178i) q^{49} +(-0.947919 + 0.334406i) q^{50} +(1.65293 - 4.60314i) q^{51} +(-0.566833 - 0.929952i) q^{52} +(7.59158 + 9.89354i) q^{53} +(-6.00669 + 4.23317i) q^{54} +(2.84473 + 2.84473i) q^{55} +(6.98374 + 2.68837i) q^{56} +(-6.38890 - 3.29087i) q^{57} +(2.62446 + 5.16599i) q^{58} +(3.94519 + 5.14147i) q^{59} +(-3.21359 - 6.41433i) q^{60} +(-10.3214 - 7.91987i) q^{61} +(9.93361 + 4.75261i) q^{62} +(-7.70633 - 1.90064i) q^{63} +(7.15382 - 3.58091i) q^{64} +(-0.976682 + 0.563887i) q^{65} +(2.91769 - 3.75864i) q^{66} +(6.65290 + 0.875872i) q^{67} +(2.03645 - 5.26761i) q^{68} +(0.256982 + 0.0213653i) q^{69} +(2.95517 - 7.16353i) q^{70} +(-6.45823 - 6.45823i) q^{71} +(-7.05195 + 4.71911i) q^{72} +(-1.63657 - 6.10775i) q^{73} +(3.76872 - 0.796377i) q^{74} +(1.11348 - 0.525091i) q^{75} +(-7.28335 - 3.97702i) q^{76} +(5.13166 - 0.282468i) q^{77} +(0.806061 + 1.06275i) q^{78} +(-3.55198 - 6.15220i) q^{79} +(-3.53078 - 7.49409i) q^{80} +(6.79345 - 5.90330i) q^{81} +(-0.173376 - 0.148435i) q^{82} +(-0.571369 - 1.37941i) q^{83} +(-8.84291 - 2.40893i) q^{84} +(-5.40300 - 2.23800i) q^{85} +(-0.746899 + 2.28944i) q^{86} +(-3.83885 - 5.96876i) q^{87} +(3.47289 - 4.25748i) q^{88} +(-11.4120 - 3.05783i) q^{89} +(4.71160 + 7.41668i) q^{90} +(-0.295838 + 1.41003i) q^{91} +(0.296055 + 0.0318297i) q^{92} +(-12.6933 - 4.55802i) q^{93} +(-1.61560 + 1.10754i) q^{94} +(-4.29661 + 7.44194i) q^{95} +(-8.27211 + 5.25092i) q^{96} +14.3964 q^{97} +(-4.29815 - 8.91773i) q^{98} +(-3.08859 + 4.94177i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9	$ 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} + 24 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 44 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} - 36 q^{30} - 8 q^{33} + 64 q^{36} - 8 q^{37} - 4 q^{39} - 72 q^{40} - 68 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 20 q^{51} + 16 q^{52} - 92 q^{54} - 32 q^{55} - 16 q^{57} + 24 q^{58} - 20 q^{60} - 8 q^{61} - 128 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 16 q^{75} - 32 q^{76} + 136 q^{78} - 16 q^{79} - 48 q^{82} + 124 q^{84} + 48 q^{85} - 4 q^{87} - 8 q^{88} + 128 q^{90} - 64 q^{91} - 28 q^{93} - 64 q^{94} - 72 q^{96} - 64 q^{97} - 16 q^{99}+O(q^{100}) $ 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 - 32 * q^13 - 32 * q^15 + 24 * q^16 - 4 * q^18 - 8 * q^19 - 8 * q^21 - 32 * q^22 - 44 * q^24 - 8 * q^25 - 16 * q^27 - 16 * q^28 - 36 * q^30 - 8 * q^33 + 64 * q^36 - 8 * q^37 - 4 * q^39 - 72 * q^40 - 68 * q^42 - 32 * q^43 - 4 * q^45 - 8 * q^46 - 16 * q^48 + 20 * q^51 + 16 * q^52 - 92 * q^54 - 32 * q^55 - 16 * q^57 + 24 * q^58 - 20 * q^60 - 8 * q^61 - 128 * q^64 - 20 * q^66 - 72 * q^67 - 16 * q^69 - 16 * q^70 - 4 * q^72 - 8 * q^73 + 16 * q^75 - 32 * q^76 + 136 * q^78 - 16 * q^79 - 48 * q^82 + 124 * q^84 + 48 * q^85 - 4 * q^87 - 8 * q^88 + 128 * q^90 - 64 * q^91 - 28 * q^93 - 64 * q^94 - 72 * q^96 - 64 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.40999	+	0.109279i	−0.997010	+	0.0772720i
$2$	−1.40999	+	0.109279i	−0.997010	+	0.0772720i
$3$	1.70442	−	0.308130i	0.984049	−	0.177899i
$3$	1.70442	−	0.308130i	0.984049	−	0.177899i
$4$	1.97612	−	0.308164i	0.988058	−	0.154082i
$5$	−0.270326	−	2.05333i	−0.120893	−	0.918276i	−0.939170	−	0.343452i	$-0.888404\pi$
$5$	−0.270326	−	2.05333i	−0.120893	−	0.918276i	0.818277	−	0.574824i	$-0.194930\pi$
$6$	−2.36954	+	0.620717i	−0.967360	+	0.253407i
$7$	−2.18436	−	1.49283i	−0.825612	−	0.564238i
$7$	−2.18436	−	1.49283i	−0.825612	−	0.564238i
$8$	−2.75262	+	0.650455i	−0.973198	+	0.229970i
$9$	2.81011	−	1.05037i	0.936704	−	0.350123i
$10$	0.605541	+	2.86562i	0.191489	+	0.906189i
$11$	−1.54111	+	1.18253i	−0.464661	+	0.356547i	−0.814404	−	0.580299i	$-0.802936\pi$
$11$	−1.54111	+	1.18253i	−0.464661	+	0.356547i	0.349743	+	0.936846i	$0.386269\pi$
$12$	3.27318	−	1.13414i	0.944886	−	0.327399i
$13$	−0.208388	−	0.503093i	−0.0577964	−	0.139533i	0.892343	−	0.451357i	$-0.149060\pi$
$13$	−0.208388	−	0.503093i	−0.0577964	−	0.139533i	−0.950140	+	0.311824i	$0.899060\pi$
$14$	3.24306	+	1.86617i	0.866744	+	0.498754i
$15$	−1.09344	−	3.41644i	−0.282325	−	0.882122i
$16$	3.81007	−	1.21794i	0.952518	−	0.304484i
$17$	1.41189	−	2.44546i	0.342433	−	0.593111i	−0.642451	−	0.766327i	$-0.722082\pi$
$17$	1.41189	−	2.44546i	0.342433	−	0.593111i	0.984884	+	0.173215i	$0.0554157\pi$
$18$	−3.84743	+	1.78809i	−0.906848	+	0.421457i
$19$	−3.29179	−	2.52588i	−0.755189	−	0.579477i	0.157795	−	0.987472i	$-0.449561\pi$
$19$	−3.29179	−	2.52588i	−0.755189	−	0.579477i	−0.912984	+	0.407995i	$0.866228\pi$
$20$	−1.16696	−	3.97431i	−0.260939	−	0.888683i
$21$	−4.18307	−	1.87135i	−0.912820	−	0.408362i
$22$	2.04371	−	1.83576i	0.435720	−	0.391386i
$23$	0.143808	+	0.0385332i	0.0299860	+	0.00803472i	0.273781	−	0.961792i	$-0.411726\pi$
$23$	0.143808	+	0.0385332i	0.0299860	+	0.00803472i	−0.243795	+	0.969827i	$0.578392\pi$
$24$	−4.49120	+	1.95681i	−0.916762	+	0.399433i
$25$	0.686548	−	0.183960i	0.137310	−	0.0367920i
$26$	0.348801	+	0.686581i	0.0684055	+	0.134650i
$27$	4.46597	−	2.65615i	0.859476	−	0.511176i
$28$	−4.77660	−	2.27687i	−0.902692	−	0.430288i
$29$	−1.56796	−	3.78538i	−0.291162	−	0.702928i	0.708835	−	0.705375i	$-0.249221\pi$
$29$	−1.56796	−	3.78538i	−0.291162	−	0.702928i	−0.999997	+	0.00244675i	$0.999221\pi$
$30$	1.91508	+	4.69764i	0.349645	+	0.857669i
$31$	−6.74344	−	3.89333i	−1.21116	−	0.699262i	−0.248146	−	0.968723i	$-0.579821\pi$
$31$	−6.74344	−	3.89333i	−1.21116	−	0.699262i	−0.963011	+	0.269461i	$0.913155\pi$
$32$	−5.23905	+	2.13363i	−0.926141	+	0.377176i
$33$	−2.26232	+	2.49040i	−0.393820	+	0.433522i
$34$	−1.72350	+	3.60235i	−0.295578	+	0.617798i
$35$	−2.47479	+	4.88877i	−0.418315	+	0.826353i
$36$	5.22942	−	2.94162i	0.871570	−	0.490271i
$37$	−2.70043	+	0.355519i	−0.443948	+	0.0584469i	−0.349187	−	0.937053i	$-0.613542\pi$
$37$	−2.70043	+	0.355519i	−0.443948	+	0.0584469i	−0.0947615	+	0.995500i	$0.530209\pi$
$38$	4.91740	+	3.20173i	0.797708	+	0.519389i
$39$	−0.510199	−	0.793272i	−0.0816972	−	0.127025i
$40$	2.07970	+	5.47620i	0.328830	+	0.865862i
$41$	0.114119	+	0.114119i	0.0178223	+	0.0178223i	0.715962	−	0.698139i	$-0.245988\pi$
$41$	0.114119	+	0.114119i	0.0178223	+	0.0178223i	−0.698139	+	0.715962i	$0.745988\pi$
$42$	6.10256	+	2.18145i	0.941646	+	0.336605i
$43$	0.651652	−	1.57323i	0.0993760	−	0.239915i	−0.866371	−	0.499401i	$-0.833553\pi$
$43$	0.651652	−	1.57323i	0.0993760	−	0.239915i	0.965747	+	0.259487i	$0.0835533\pi$
$44$	−2.68099	+	2.81173i	−0.404174	+	0.423885i
$45$	−2.91640	−	5.48614i	−0.434751	−	0.817826i
$46$	−0.206978	−	0.0386160i	−0.0305172	−	0.00569362i
$47$	1.19950	−	0.692533i	0.174965	−	0.101016i	−0.409960	−	0.912104i	$-0.634457\pi$
$47$	1.19950	−	0.692533i	0.174965	−	0.101016i	0.584925	+	0.811087i	$0.301124\pi$
$48$	6.11869	−	3.24987i	0.883156	−	0.469079i
$49$	2.54290	+	6.52178i	0.363271	+	0.931683i
$50$	−0.947919	+	0.334406i	−0.134056	+	0.0472922i
$51$	1.65293	−	4.60314i	0.231457	−	0.644569i
$52$	−0.566833	−	0.929952i	−0.0786056	−	0.128961i
$53$	7.59158	+	9.89354i	1.04278	+	1.35898i	0.930906	+	0.365260i	$0.119020\pi$
$53$	7.59158	+	9.89354i	1.04278	+	1.35898i	0.111878	+	0.993722i	$0.464313\pi$
$54$	−6.00669	+	4.23317i	−0.817406	+	0.576061i
$55$	2.84473	+	2.84473i	0.383583	+	0.383583i
$56$	6.98374	+	2.68837i	0.933242	+	0.359248i
$57$	−6.38890	−	3.29087i	−0.846231	−	0.435886i
$58$	2.62446	+	5.16599i	0.344608	+	0.678327i
$59$	3.94519	+	5.14147i	0.513619	+	0.669362i	0.976114	−	0.217260i	$-0.0697121\pi$
$59$	3.94519	+	5.14147i	0.513619	+	0.669362i	−0.462494	+	0.886622i	$0.653045\pi$
$60$	−3.21359	−	6.41433i	−0.414873	−	0.828086i
$61$	−10.3214	−	7.91987i	−1.32152	−	1.01403i	−0.997691	−	0.0679179i	$-0.978364\pi$
$61$	−10.3214	−	7.91987i	−1.32152	−	1.01403i	−0.323825	−	0.946117i	$-0.604969\pi$
$62$	9.93361	+	4.75261i	1.26157	+	0.603583i
$63$	−7.70633	−	1.90064i	−0.970907	−	0.239458i
$64$	7.15382	−	3.58091i	0.894227	−	0.447613i
$65$	−0.976682	+	0.563887i	−0.121142	+	0.0699416i
$66$	2.91769	−	3.75864i	0.359143	−	0.462657i
$67$	6.65290	+	0.875872i	0.812782	+	0.107005i	0.525448	−	0.850826i	$-0.323898\pi$
$67$	6.65290	+	0.875872i	0.812782	+	0.107005i	0.287334	+	0.957831i	$0.407231\pi$
$68$	2.03645	−	5.26761i	0.246956	−	0.638791i
$69$	0.256982	+	0.0213653i	0.0309371	+	0.00257208i
$70$	2.95517	−	7.16353i	0.353210	−	0.856206i
$71$	−6.45823	−	6.45823i	−0.766450	−	0.766450i	0.211029	−	0.977480i	$-0.432318\pi$
$71$	−6.45823	−	6.45823i	−0.766450	−	0.766450i	−0.977480	+	0.211029i	$0.932318\pi$
$72$	−7.05195	+	4.71911i	−0.831080	+	0.556153i
$73$	−1.63657	−	6.10775i	−0.191546	−	0.714858i	−0.993134	−	0.116982i	$-0.962678\pi$
$73$	−1.63657	−	6.10775i	−0.191546	−	0.714858i	0.801588	−	0.597876i	$-0.203989\pi$
$74$	3.76872	−	0.796377i	0.438105	−	0.0925769i
$75$	1.11348	−	0.525091i	0.128574	−	0.0606323i
$76$	−7.28335	−	3.97702i	−0.835457	−	0.456196i
$77$	5.13166	−	0.282468i	0.584807	−	0.0321902i
$78$	0.806061	+	1.06275i	0.0912684	+	0.120332i
$79$	−3.55198	−	6.15220i	−0.399629	−	0.692177i	0.594051	−	0.804427i	$-0.297528\pi$
$79$	−3.55198	−	6.15220i	−0.399629	−	0.692177i	−0.993680	+	0.112250i	$0.964194\pi$
$80$	−3.53078	−	7.49409i	−0.394753	−	0.837864i
$81$	6.79345	−	5.90330i	0.754828	−	0.655922i
$82$	−0.173376	−	0.148435i	−0.0191462	−	0.0163919i
$83$	−0.571369	−	1.37941i	−0.0627159	−	0.151410i	0.889415	−	0.457101i	$-0.151112\pi$
$83$	−0.571369	−	1.37941i	−0.0627159	−	0.151410i	−0.952131	+	0.305692i	$0.901112\pi$
$84$	−8.84291	−	2.40893i	−0.964840	−	0.262836i
$85$	−5.40300	−	2.23800i	−0.586038	−	0.242745i
$86$	−0.746899	+	2.28944i	−0.0805402	+	0.246876i
$87$	−3.83885	−	5.96876i	−0.411568	−	0.639918i
$88$	3.47289	−	4.25748i	0.370212	−	0.453849i
$89$	−11.4120	−	3.05783i	−1.20967	−	0.324129i	−0.403036	−	0.915184i	$-0.632045\pi$
$89$	−11.4120	−	3.05783i	−1.20967	−	0.324129i	−0.806631	+	0.591055i	$0.798712\pi$
$90$	4.71160	+	7.41668i	0.496646	+	0.781786i
$91$	−0.295838	+	1.41003i	−0.0310123	+	0.147811i
$92$	0.296055	+	0.0318297i	0.0308659	+	0.00331847i
$93$	−12.6933	−	4.55802i	−1.31624	−	0.472644i
$94$	−1.61560	+	1.10754i	−0.166637	+	0.114234i
$95$	−4.29661	+	7.44194i	−0.440823	+	0.763527i
$96$	−8.27211	+	5.25092i	−0.844269	+	0.535920i
$97$	14.3964			1.46173			0.730866	−	0.682521i	$-0.239116\pi$
$97$	14.3964			1.46173			0.730866	+	0.682521i	$0.239116\pi$
$98$	−4.29815	−	8.91773i	−0.434178	−	0.900827i
$99$	−3.08859	+	4.94177i	−0.310414	+	0.496667i
$100$	1.30001	−	0.575095i	0.130001	−	0.0575095i
$101$	12.2356	−	9.38871i	1.21749	−	0.934212i	0.218357	−	0.975869i	$-0.429930\pi$
$101$	12.2356	−	9.38871i	1.21749	−	0.934212i	0.999132	+	0.0416572i	$0.0132637\pi$
$102$	−1.82758	+	6.67099i	−0.180958	+	0.660527i
$103$	9.26030	+	2.48129i	0.912445	+	0.244489i	0.684353	−	0.729151i	$-0.260085\pi$
$103$	9.26030	+	2.48129i	0.912445	+	0.244489i	0.228092	+	0.973640i	$0.426751\pi$
$104$	0.900851	+	1.24928i	0.0883357	+	0.122501i
$105$	−2.71170	+	9.09508i	−0.264635	+	0.887589i
$106$	−11.7852	−	13.1201i	−1.14468	−	1.27434i
$107$	2.01878	+	15.3342i	0.195163	+	1.48241i	0.756048	+	0.654517i	$0.227128\pi$
$107$	2.01878	+	15.3342i	0.195163	+	1.48241i	−0.560884	+	0.827894i	$0.689539\pi$
$108$	8.00674	−	6.62511i	0.770449	−	0.637502i
$109$	17.1689	+	2.26033i	1.64448	+	0.216501i	0.895174	−	0.445718i	$-0.147051\pi$
$109$	17.1689	+	2.26033i	1.64448	+	0.216501i	0.749311	+	0.662218i	$0.230385\pi$
$110$	−4.32189	−	3.70015i	−0.412076	−	0.352796i
$111$	−4.49313	+	1.43804i	−0.426469	+	0.136493i
$112$	−10.1408	−	3.02738i	−0.958211	−	0.286061i
$113$	11.8819			1.11776			0.558878	−	0.829250i	$-0.311232\pi$
$113$	11.8819			1.11776			0.558878	+	0.829250i	$0.311232\pi$
$114$	9.36788	+	3.94190i	0.877383	+	0.369193i
$115$	0.0402463	−	0.305701i	0.00375299	−	0.0285068i
$116$	−4.26498	−	6.99717i	−0.395994	−	0.649671i
$117$	−1.11403	−	1.19486i	−0.102992	−	0.110465i
$118$	−6.12451	−	6.81826i	−0.563807	−	0.627672i
$119$	−6.73474	+	3.23407i	−0.617373	+	0.296466i
$120$	5.23207	+	8.69293i	0.477620	+	0.793552i
$121$	−1.87038	+	6.98037i	−0.170035	+	0.634579i
$122$	15.4185	+	10.0390i	1.39592	+	0.908887i
$123$	0.229670	+	0.159343i	0.0207086	+	0.0143675i
$124$	−14.5256	−	5.61558i	−1.30444	−	0.504294i
$125$	−4.52610	−	10.9270i	−0.404826	−	0.977338i
$126$	11.0735	+	1.83773i	0.986507	+	0.163718i
$127$		−	4.51012i		−	0.400209i	−0.979775	−	0.200104i	$-0.935872\pi$
$127$		−	4.51012i		−	0.400209i	0.979775	−	0.200104i	$-0.0641281\pi$
$128$	−9.69546	+	5.83079i	−0.856965	+	0.515374i
$129$	0.625931	−	2.88224i	0.0551102	−	0.253767i
$130$	1.31549	−	0.901804i	0.115376	−	0.0790934i
$131$	−1.69412	−	1.29994i	−0.148016	−	0.113577i	0.532099	−	0.846682i	$-0.321403\pi$
$131$	−1.69412	−	1.29994i	−0.148016	−	0.113577i	−0.680115	+	0.733106i	$0.738070\pi$
$132$	−3.70316	+	5.61848i	−0.322319	+	0.489026i
$133$	3.41976	+	10.4315i	0.296531	+	0.904529i
$134$	−9.47621	−	0.507942i	−0.818620	−	0.0438795i
$135$	−6.66122	−	8.45207i	−0.573306	−	0.727438i
$136$	−2.29573	+	7.64979i	−0.196857	+	0.655964i
$137$	14.6160	−	3.91635i	1.24873	−	0.334596i	0.426884	−	0.904306i	$-0.359611\pi$
$137$	14.6160	−	3.91635i	1.24873	−	0.334596i	0.821846	+	0.569710i	$0.192945\pi$
$138$	−0.364676	−	0.00204194i	−0.0310433	−	0.000173821i
$139$	−3.50642	+	8.46525i	−0.297411	+	0.718013i	0.702569	+	0.711616i	$0.252036\pi$
$139$	−3.50642	+	8.46525i	−0.297411	+	0.718013i	−0.999980	+	0.00639725i	$0.997964\pi$
$140$	−3.38392	+	10.4234i	−0.285994	+	0.880939i
$141$	1.83107	−	1.54997i	0.154204	−	0.130531i
$142$	9.81175	+	8.40025i	0.823384	+	0.704934i
$143$	0.916071	+	0.528894i	0.0766057	+	0.0442283i
$144$	9.42744	−	7.42451i	0.785620	−	0.618709i
$145$	−7.34877	+	4.24282i	−0.610282	+	0.352347i
$146$	2.97499	+	8.43300i	0.246212	+	0.697920i
$147$	6.34373	+	10.3323i	0.523222	+	0.852196i
$148$	−5.22681	+	1.53472i	−0.429641	+	0.126153i
$149$	18.9842	−	2.49932i	1.55525	−	0.204753i	0.696655	−	0.717406i	$-0.254671\pi$
$149$	18.9842	−	2.49932i	1.55525	−	0.204753i	0.858595	+	0.512654i	$0.171338\pi$
$150$	−1.51261	+	0.862052i	−0.123504	+	0.0703862i
$151$	8.15595	−	2.18538i	0.663722	−	0.177844i	0.0887967	−	0.996050i	$-0.471698\pi$
$151$	8.15595	−	2.18538i	0.663722	−	0.177844i	0.574925	+	0.818206i	$0.305031\pi$
$152$	10.7040	+	4.81162i	0.868211	+	0.390274i
$153$	1.39893	−	8.35502i	0.113097	−	0.675463i
$154$	−7.20470	+	0.959059i	−0.580571	+	0.0772832i
$155$	−6.17135	+	14.8990i	−0.495695	+	1.19671i
$156$	−1.25267	−	1.41037i	−0.100294	−	0.112920i
$157$	−2.76173	+	20.9774i	−0.220410	+	1.67418i	0.421060	+	0.907033i	$0.361658\pi$
$157$	−2.76173	+	20.9774i	−0.220410	+	1.67418i	−0.641470	+	0.767148i	$0.721675\pi$
$158$	5.68054	+	8.28636i	0.451920	+	0.659227i
$159$	15.9878	+	14.5236i	1.26791	+	1.15179i
$160$	5.79730	+	10.1807i	0.458317	+	0.804856i
$161$	−0.256605	−	0.298852i	−0.0202233	−	0.0235528i
$162$	−8.93356	+	9.06595i	−0.701887	+	0.712288i
$163$	−10.7633	+	14.0270i	−0.843047	+	1.09868i	0.150870	+	0.988554i	$0.451792\pi$
$163$	−10.7633	+	14.0270i	−0.843047	+	1.09868i	−0.993918	+	0.110127i	$0.964874\pi$
$164$	0.260679	+	0.190344i	0.0203556	+	0.0148634i
$165$	5.72516	+	3.97207i	0.445703	+	0.309225i
$166$	0.956363	+	1.88251i	0.0742281	+	0.146111i
$167$	14.5081	+	14.5081i	1.12267	+	1.12267i	0.991339	+	0.131328i	$0.0419240\pi$
$167$	14.5081	+	14.5081i	1.12267	+	1.12267i	0.131328	+	0.991339i	$0.458076\pi$
$168$	12.7316	+	2.43021i	0.982266	+	0.187495i
$169$	8.98271	−	8.98271i	0.690978	−	0.690978i
$170$	7.86272	+	2.56511i	0.603043	+	0.196735i
$171$	−11.9034	−	3.64041i	−0.910276	−	0.278389i
$172$	0.802928	−	3.30969i	0.0612227	−	0.252362i
$173$	−11.3467	−	8.70663i	−0.862674	−	0.661953i	0.0795888	−	0.996828i	$-0.474639\pi$
$173$	−11.3467	−	8.70663i	−0.862674	−	0.661953i	−0.942263	+	0.334875i	$0.891306\pi$
$174$	6.06498	+	7.99635i	0.459785	+	0.606202i
$175$	−1.77429	−	0.623065i	−0.134124	−	0.0470993i
$176$	−4.43147	+	6.38250i	−0.334035	+	0.481099i
$177$	8.30850	+	7.54760i	0.624505	+	0.567312i
$178$	16.4249	+	3.06440i	1.23110	+	0.229687i
$179$	−20.2994	−	2.67247i	−1.51725	−	0.199750i	−0.674590	−	0.738193i	$-0.735679\pi$
$179$	−20.2994	−	2.67247i	−1.51725	−	0.199750i	−0.842662	+	0.538443i	$0.819013\pi$
$180$	−7.45377	−	9.94252i	−0.555571	−	0.741072i
$181$	7.92947	+	3.28449i	0.589393	+	0.244135i	0.657389	−	0.753551i	$-0.271661\pi$
$181$	7.92947	+	3.28449i	0.589393	+	0.244135i	−0.0679965	+	0.997686i	$0.521661\pi$
$182$	0.263041	−	2.02044i	0.0194979	−	0.149765i
$183$	−20.0323	−	10.3185i	−1.48083	−	0.762763i
$184$	−0.420912	−	0.0125267i	−0.0310301	−	0.000923480i
$185$	1.45999	+	5.44877i	0.107341	+	0.400601i
$186$	18.3955	+	5.03962i	1.34882	+	0.369523i
$187$	0.715968	+	5.43832i	0.0523567	+	0.397689i
$188$	2.15694	−	1.73817i	0.157311	−	0.126769i
$189$	−13.7205	−	0.864940i	−0.998019	−	0.0629151i
$190$	5.24490	−	10.9626i	0.380505	−	0.795307i
$191$	2.67412	+	4.63172i	0.193493	+	0.335139i	0.946405	−	0.322981i	$-0.104685\pi$
$191$	2.67412	+	4.63172i	0.193493	+	0.335139i	−0.752913	+	0.658120i	$0.771352\pi$
$192$	11.0897	−	8.30769i	0.800333	−	0.599556i
$193$	−1.67229	+	2.89649i	−0.120374	+	0.208494i	−0.919915	−	0.392117i	$-0.871743\pi$
$193$	−1.67229	+	2.89649i	−0.120374	+	0.208494i	0.799541	+	0.600611i	$0.205076\pi$
$194$	−20.2987	+	1.57323i	−1.45736	+	0.112951i
$195$	−1.49093	+	1.26205i	−0.106768	+	0.0903771i
$196$	7.03484	+	12.1042i	0.502489	+	0.864584i
$197$	6.12671	+	2.53777i	0.436510	+	0.180808i	0.590107	−	0.807325i	$-0.299086\pi$
$197$	6.12671	+	2.53777i	0.436510	+	0.180808i	−0.153597	+	0.988134i	$0.549086\pi$
$198$	3.81483	−	7.30535i	0.271108	−	0.519168i
$199$	1.50914	+	5.63217i	0.106980	+	0.399254i	0.998562	−	0.0536042i	$-0.0170709\pi$
$199$	1.50914	+	5.63217i	0.106980	+	0.399254i	−0.891582	+	0.452859i	$0.850404\pi$
$200$	−1.77015	+	0.952940i	−0.125168	+	0.0673830i
$201$	11.6092	−	0.557106i	0.818853	−	0.0392952i
$202$	−16.2260	+	14.5750i	−1.14166	+	1.02550i
$203$	−2.22595	+	10.6094i	−0.156231	+	0.744631i
$204$	1.84786	−	9.60572i	0.129376	−	0.672535i
$205$	0.203474	−	0.265172i	0.0142112	−	0.0185204i
$206$	−13.3280	−	2.48662i	−0.928609	−	0.173251i
$207$	0.444590	−	0.0427686i	0.0309011	−	0.00297262i
$208$	−1.40671	−	1.66302i	−0.0975375	−	0.115309i
$209$	8.05993			0.557517
$210$	2.82956	−	13.1203i	0.195258	−	0.905384i
$211$	−0.246343	+	0.102039i	−0.0169590	+	0.00702463i	−0.391147	−	0.920328i	$-0.627922\pi$
$211$	−0.246343	+	0.102039i	−0.0169590	+	0.00702463i	0.374188	+	0.927353i	$0.377922\pi$
$212$	18.0507	+	17.2113i	1.23973	+	1.18208i
$213$	−12.9975	−	9.01757i	−0.890575	−	0.617874i
$214$	−4.52216	−	21.4003i	−0.309128	−	1.46290i
$215$	−3.40651	−	0.912772i	−0.232322	−	0.0622505i
$216$	−10.5654	+	10.2163i	−0.718884	+	0.695130i
$217$	8.91805	+	18.5713i	0.605396	+	1.26070i
$218$	−24.4549	−	1.31083i	−1.65630	−	0.0887806i
$219$	−4.67139	−	9.90592i	−0.315663	−	0.669380i
$220$	6.49815	+	4.74487i	0.438105	+	0.319899i
$221$	−1.52451	−	0.200706i	−0.102550	−	0.0135009i
$222$	6.17810	−	2.51862i	0.414647	−	0.169039i
$223$		−	7.91178i		−	0.529812i	−0.964274	−	0.264906i	$-0.914659\pi$
$223$		−	7.91178i		−	0.529812i	0.964274	−	0.264906i	$-0.0853409\pi$
$224$	14.6291	+	3.16039i	0.977451	+	0.211163i
$225$	1.73605	−	1.23808i	0.115737	−	0.0825384i
$226$	−16.7533	+	1.29844i	−1.11441	+	0.0863713i
$227$	1.56930	−	11.9200i	0.104158	−	0.791158i	−0.857031	−	0.515266i	$-0.827693\pi$
$227$	1.56930	−	11.9200i	0.104158	−	0.791158i	0.961188	−	0.275893i	$-0.0889734\pi$
$228$	−13.6393	−	4.53431i	−0.903288	−	0.300292i
$229$	2.73876	−	0.360565i	0.180983	−	0.0238268i	−0.0394901	−	0.999220i	$-0.512573\pi$
$229$	2.73876	−	0.360565i	0.180983	−	0.0238268i	0.220473	+	0.975393i	$0.429240\pi$
$230$	−0.0233400	+	0.435432i	−0.00153899	+	0.0287115i
$231$	8.65948	−	2.06266i	0.569752	−	0.135713i
$232$	6.77821	+	9.39983i	0.445011	+	0.617129i
$233$	6.35634	−	23.7222i	0.416418	−	1.55409i	−0.365562	−	0.930787i	$-0.619123\pi$
$233$	6.35634	−	23.7222i	0.416418	−	1.55409i	0.781979	−	0.623305i	$-0.214210\pi$
$234$	1.70133	+	1.56300i	0.111220	+	0.102176i
$235$	−1.74626	−	2.27576i	−0.113913	−	0.148454i
$236$	9.38056	+	8.94437i	0.610622	+	0.582229i
$237$	−7.94975	−	9.39148i	−0.516392	−	0.610042i
$238$	9.14247	−	5.29595i	0.592618	−	0.343286i
$239$			0.939164i			0.0607495i	0.999539	+	0.0303747i	$0.00967007\pi$
$239$			0.939164i			0.0607495i	−0.999539	+	0.0303747i	$0.990330\pi$
$240$	−8.32710	−	11.6851i	−0.537512	−	0.754273i
$241$	0.692490	+	0.399810i	0.0446072	+	0.0257540i	0.522138	−	0.852861i	$-0.325135\pi$
$241$	0.692490	+	0.399810i	0.0446072	+	0.0257540i	−0.477531	+	0.878615i	$0.658468\pi$
$242$	1.87441	−	10.0466i	0.120491	−	0.645821i
$243$	9.75993	−	12.1550i	0.626100	−	0.779743i
$244$	−22.8368	−	12.4699i	−1.46198	−	0.798304i
$245$	12.7040	−	6.98441i	0.811626	−	0.446218i
$246$	−0.341243	−	0.199573i	−0.0217569	−	0.0127243i
$247$	−0.584783	+	2.18244i	−0.0372088	+	0.138865i
$248$	21.0945	+	6.33054i	1.33951	+	0.401990i
$249$	−1.39889	−	2.17504i	−0.0886512	−	0.137837i
$250$	7.57582	+	14.9123i	0.479137	+	0.943134i
$251$	−4.92125	+	11.8810i	−0.310627	+	0.749919i	0.689055	+	0.724709i	$0.258026\pi$
$251$	−4.92125	+	11.8810i	−0.310627	+	0.749919i	−0.999682	+	0.0252107i	$0.991974\pi$
$252$	−15.8143	−	1.38107i	−0.996208	−	0.0869994i
$253$	−0.267190	+	0.110674i	−0.0167981	+	0.00695799i
$254$	0.492862	+	6.35920i	0.0309249	+	0.399012i
$255$	−9.89859	−	2.14966i	−0.619874	−	0.134617i
$256$	13.0333	−	9.28084i	0.814579	−	0.580052i
$257$	−4.22770	+	2.44086i	−0.263717	+	0.152257i	−0.626029	−	0.779800i	$-0.715321\pi$
$257$	−4.22770	+	2.44086i	−0.263717	+	0.152257i	0.362312	+	0.932057i	$0.381987\pi$
$258$	−0.567586	+	4.13231i	−0.0353363	+	0.257267i
$259$	6.42946	+	3.25471i	0.399507	+	0.202238i
$260$	−1.75627	+	1.41528i	−0.108919	+	0.0877722i
$261$	−8.38218	−	8.99041i	−0.518844	−	0.556493i
$262$	2.53074	+	1.64777i	0.156350	+	0.101800i
$263$	2.93747	−	0.787092i	0.181132	−	0.0485342i	−0.167113	−	0.985938i	$-0.553444\pi$
$263$	2.93747	−	0.787092i	0.181132	−	0.0485342i	0.348245	+	0.937404i	$0.386778\pi$
$264$	4.60742	−	8.32665i	0.283567	−	0.512470i
$265$	18.2625	−	18.2625i	1.12186	−	1.12186i
$266$	−5.96176	−	14.3346i	−0.365539	−	0.878911i
$267$	−20.3930	−	1.69546i	−1.24803	−	0.103760i
$268$	13.4168	−	0.319361i	0.819563	−	0.0195081i
$269$	3.12682	−	23.7505i	0.190645	−	1.44810i	−0.581964	−	0.813214i	$-0.697716\pi$
$269$	3.12682	−	23.7505i	0.190645	−	1.44810i	0.772610	−	0.634881i	$-0.218951\pi$
$270$	10.3159	+	11.1894i	0.627803	+	0.680963i
$271$	11.5867	+	20.0687i	0.703840	+	1.21909i	0.967108	+	0.254365i	$0.0818664\pi$
$271$	11.5867	+	20.0687i	0.703840	+	1.21909i	−0.263268	+	0.964723i	$0.584800\pi$
$272$	2.40098	−	11.0370i	0.145581	−	0.669214i
$273$	−0.0697618	+	2.49444i	−0.00422218	+	0.150970i
$274$	−20.1804	+	7.11921i	−1.21914	+	0.430087i
$275$	−0.840504	+	1.09537i	−0.0506843	+	0.0660531i
$276$	0.514411	−	0.0369724i	0.0309639	−	0.00222548i
$277$	−22.5249	+	17.2839i	−1.35339	+	1.03849i	−0.358929	+	0.933365i	$0.616858\pi$
$277$	−22.5249	+	17.2839i	−1.35339	+	1.03849i	−0.994459	+	0.105126i	$0.966475\pi$
$278$	4.01893	−	12.3191i	0.241039	−	0.738848i
$279$	−23.0392	−	3.85759i	−1.37932	−	0.230948i
$280$	3.63222	−	15.0667i	0.217067	−	0.900405i
$281$	−9.82468	+	9.82468i	−0.586091	+	0.586091i	−0.936570	−	0.350479i	$-0.886019\pi$
$281$	−9.82468	+	9.82468i	−0.586091	+	0.586091i	0.350479	+	0.936570i	$0.386019\pi$
$282$	−2.41240	+	2.38554i	−0.143656	+	0.142057i
$283$	−16.4158	+	12.5963i	−0.975817	+	0.748771i	−0.967936	−	0.251198i	$-0.919175\pi$
$283$	−16.4158	+	12.5963i	−0.975817	+	0.748771i	−0.00788149	+	0.999969i	$0.502509\pi$
$284$	−14.7524	−	10.7720i	−0.875394	−	0.639201i
$285$	−5.03015	+	14.0081i	−0.297960	+	0.829770i
$286$	−1.34944	−	0.645625i	−0.0797942	−	0.0381766i
$287$	−0.0789166	−	0.419636i	−0.00465830	−	0.0247704i
$288$	−12.4812	+	11.4987i	−0.735462	+	0.677566i
$289$	4.51315	+	7.81700i	0.265479	+	0.459824i
$290$	9.89801	−	6.78538i	0.581231	−	0.398451i
$291$	24.5375	−	4.43596i	1.43842	−	0.260041i
$292$	−5.11624	−	11.5653i	−0.299405	−	0.676808i
$293$	−0.771836	−	0.319705i	−0.0450911	−	0.0186774i	0.360024	−	0.932943i	$-0.382769\pi$
$293$	−0.771836	−	0.319705i	−0.0450911	−	0.0186774i	−0.405115	+	0.914266i	$0.632769\pi$
$294$	−10.0737	−	13.8752i	−0.587509	−	0.809218i
$295$	9.49063	−	9.49063i	0.552566	−	0.552566i
$296$	7.20201	−	2.73512i	0.418608	−	0.158975i
$297$	−3.74154	+	9.37456i	−0.217106	+	0.543967i
$298$	−26.4944	+	5.59859i	−1.53478	+	0.324318i
$299$	−0.0105820	−	0.0803785i	−0.000611974	−	0.00464841i
$300$	2.03856	−	1.38078i	0.117696	−	0.0797192i
$301$	−3.77201	+	2.46369i	−0.217415	+	0.142005i
$302$	−11.2610	+	3.97263i	−0.647995	+	0.228599i
$303$	17.9617	−	19.7725i	1.03187	−	1.13590i
$304$	−15.6183	−	5.61459i	−0.895772	−	0.322019i
$305$	−13.4720	+	23.3341i	−0.771402	+	1.33611i
$306$	−1.05944	+	11.9333i	−0.0605640	+	0.682183i
$307$	22.6481	−	9.38115i	1.29260	−	0.535411i	0.372837	−	0.927897i	$-0.378385\pi$
$307$	22.6481	−	9.38115i	1.29260	−	0.535411i	0.919758	+	0.392486i	$0.128385\pi$
$308$	10.0537	−	2.13958i	0.572863	−	0.121914i
$309$	16.5480	+	1.37579i	0.941384	+	0.0782659i
$310$	7.07337	−	21.6817i	0.401740	−	1.23144i
$311$	−6.03086	−	22.5075i	−0.341979	−	1.27628i	−0.896102	−	0.443848i	$-0.853613\pi$
$311$	−6.03086	−	22.5075i	−0.341979	−	1.27628i	0.554124	−	0.832434i	$-0.313054\pi$
$312$	1.92037	+	1.85171i	0.108720	+	0.104833i
$313$	4.37609	−	16.3318i	0.247351	−	0.923127i	−0.724836	−	0.688922i	$-0.758084\pi$
$313$	4.37609	−	16.3318i	0.247351	−	0.923127i	0.972187	−	0.234206i	$-0.0752489\pi$
$314$	1.60160	−	29.8797i	0.0903838	−	1.68621i
$315$	−1.81942	+	16.3374i	−0.102513	+	0.920510i
$316$	−8.91500	−	11.0629i	−0.501508	−	0.622336i
$317$	−20.1616	+	26.2751i	−1.13239	+	1.47575i	−0.274737	+	0.961520i	$0.588591\pi$
$317$	−20.1616	+	26.2751i	−1.13239	+	1.47575i	−0.857650	+	0.514235i	$0.828076\pi$
$318$	−24.1296	−	18.7309i	−1.35312	−	1.05038i
$319$	6.89272	+	3.97951i	0.385918	+	0.222810i
$320$	−9.28664	−	13.7211i	−0.519139	−	0.767034i
$321$	8.16578	+	25.5139i	0.455769	+	1.42405i
$322$	0.394468	+	0.393335i	0.0219828	+	0.0219197i
$323$	−10.8246	+	4.48369i	−0.602296	+	0.249479i
$324$	11.6055	−	13.7591i	0.644748	−	0.764395i
$325$	−0.235617	−	0.307062i	−0.0130697	−	0.0170327i
$326$	13.6432	−	20.9541i	0.755629	−	1.16054i
$327$	29.9596	−	1.43770i	1.65677	−	0.0795052i
$328$	−0.388354	−	0.239896i	−0.0214432	−	0.0132460i
$329$	−3.65399	−	0.277912i	−0.201451	−	0.0153218i
$330$	−8.50646	−	4.97492i	−0.468265	−	0.273860i
$331$	−16.8506	+	2.21842i	−0.926192	+	0.121935i	−0.578508	−	0.815676i	$-0.696365\pi$
$331$	−16.8506	+	2.21842i	−0.926192	+	0.121935i	−0.347684	+	0.937612i	$0.613032\pi$
$332$	−1.55418	−	2.54979i	−0.0852965	−	0.139938i
$333$	−7.21509	+	3.83549i	−0.395385	+	0.210184i
$334$	−22.0416	−	18.8707i	−1.20606	−	1.03256i
$335$		−	13.8974i		−	0.759294i
$336$	−18.2170	−	2.03527i	−0.993817	−	0.111033i
$337$		−	13.3175i		−	0.725449i	−0.931896	−	0.362725i	$-0.881847\pi$
$337$		−	13.3175i		−	0.725449i	0.931896	−	0.362725i	$-0.118153\pi$
$338$	−11.6839	+	13.6471i	−0.635519	+	0.742305i
$339$	20.2518	−	3.66118i	1.09993	−	0.198848i
$340$	−11.3666	−	2.75753i	−0.616442	−	0.149548i
$341$	14.9963	−	1.97430i	0.812097	−	0.106915i
$342$	17.1814	+	3.83214i	0.929066	+	0.207218i
$343$	4.18131	−	18.0421i	0.225770	−	0.974181i
$344$	−0.770436	+	4.75436i	−0.0415391	+	0.256338i
$345$	−0.0255990	−	0.533445i	−0.00137820	−	0.0287197i
$346$	16.9501	+	11.0363i	0.911245	+	0.593313i
$347$	−11.4484	−	14.9199i	−0.614584	−	0.800941i	0.377568	−	0.925982i	$-0.376761\pi$
$347$	−11.4484	−	14.9199i	−0.614584	−	0.800941i	−0.992152	+	0.125041i	$0.960094\pi$
$348$	−9.42537	−	10.6120i	−0.505253	−	0.568861i
$349$	0.387754	−	0.160613i	0.0207560	−	0.00859742i	−0.372281	−	0.928120i	$-0.621424\pi$
$349$	0.387754	−	0.160613i	0.0207560	−	0.00859742i	0.393037	+	0.919523i	$0.371424\pi$
$350$	2.56981	+	0.684620i	0.137362	+	0.0365945i
$351$	−2.26694	−	1.69329i	−0.121000	−	0.0903809i
$352$	5.55084	−	9.48349i	0.295861	−	0.505472i
$353$	3.79922	+	2.19348i	0.202212	+	0.116747i	0.597687	−	0.801730i	$-0.296087\pi$
$353$	3.79922	+	2.19348i	0.202212	+	0.116747i	−0.395475	+	0.918477i	$0.629420\pi$
$354$	−12.5397	−	9.73406i	−0.666475	−	0.517359i
$355$	−11.5150	+	15.0067i	−0.611154	+	0.796472i
$356$	−23.4937	−	2.52587i	−1.24516	−	0.133871i
$357$	−10.4823	+	7.58739i	−0.554784	+	0.401567i
$358$	28.9140	+	1.54984i	1.52815	+	0.0819117i
$359$	−3.08844	+	11.5262i	−0.163002	+	0.608331i	0.835285	+	0.549818i	$0.185303\pi$
$359$	−3.08844	+	11.5262i	−0.163002	+	0.608331i	−0.998287	+	0.0585137i	$0.981364\pi$
$360$	11.5962	+	13.2043i	0.611174	+	0.695926i
$361$	−0.461742	−	1.72324i	−0.0243022	−	0.0906970i
$362$	−11.5394	−	3.76456i	−0.606495	−	0.197861i
$363$	−1.03706	+	12.4738i	−0.0544317	+	0.654706i
$364$	−0.150092	+	2.87754i	−0.00786694	+	0.150824i
$365$	−12.0988	+	5.01149i	−0.633281	+	0.262314i
$366$	29.3729	+	12.3598i	1.53534	+	0.646056i
$367$	4.93207	−	8.54260i	0.257452	−	0.445920i	−0.708107	−	0.706106i	$-0.750450\pi$
$367$	4.93207	−	8.54260i	0.257452	−	0.445920i	0.965559	+	0.260186i	$0.0837837\pi$
$368$	0.594849	−	0.0283345i	0.0310086	−	0.00147704i
$369$	0.440552	+	0.200819i	0.0229342	+	0.0104542i
$370$	−2.65401	−	7.52314i	−0.137975	−	0.391109i
$371$	−1.81338	−	32.9441i	−0.0941459	−	1.71037i
$372$	−26.4881	−	5.09555i	−1.37334	−	0.264192i
$373$	1.42186	+	10.8001i	0.0736209	+	0.559206i	0.988012	+	0.154375i	$0.0493364\pi$
$373$	1.42186	+	10.8001i	0.0736209	+	0.559206i	−0.914391	+	0.404831i	$0.867330\pi$
$374$	−1.60380	−	7.58970i	−0.0829304	−	0.392454i
$375$	−11.0813	−	17.2295i	−0.572236	−	0.889730i
$376$	−2.85131	+	2.68650i	−0.147045	+	0.138546i
$377$	−1.57765	+	1.57765i	−0.0812533	+	0.0812533i
$378$	19.4402	−	0.279811i	0.999896	−	0.0143919i
$379$	14.9047	+	6.17371i	0.765601	+	0.317122i	0.731089	−	0.682282i	$-0.239012\pi$
$379$	14.9047	+	6.17371i	0.765601	+	0.317122i	0.0345117	+	0.999404i	$0.489012\pi$
$380$	−6.19726	+	16.0302i	−0.317913	+	0.822332i
$381$	−1.38970	−	7.68715i	−0.0711967	−	0.393825i
$382$	−4.27662	−	6.23843i	−0.218811	−	0.319186i
$383$	5.93872	+	10.2862i	0.303454	+	0.525598i	0.976916	−	0.213624i	$-0.0685267\pi$
$383$	5.93872	+	10.2862i	0.303454	+	0.525598i	−0.673462	+	0.739222i	$0.735193\pi$
$384$	−14.7285	+	12.9256i	−0.751611	+	0.659606i
$385$	−1.96722	−	10.4606i	−0.100259	−	0.533123i
$386$	2.04137	−	4.26675i	0.103903	−	0.217172i
$387$	0.178748	−	5.10542i	0.00908625	−	0.259523i
$388$	28.4490	−	4.43645i	1.44428	−	0.225227i
$389$	−14.1689	+	10.8722i	−0.718394	+	0.551243i	−0.901989	−	0.431759i	$-0.857893\pi$
$389$	−14.1689	+	10.8722i	−0.718394	+	0.551243i	0.183595	+	0.983002i	$0.441226\pi$
$390$	1.96427	−	1.94240i	0.0994647	−	0.0983570i
$391$	0.297272	−	0.297272i	0.0150337	−	0.0150337i
$392$	−11.2418	−	16.2979i	−0.567795	−	0.823170i
$393$	−3.28805	−	1.69364i	−0.165860	−	0.0854331i
$394$	−8.91590	−	2.90869i	−0.449177	−	0.146538i
$395$	−11.6723	+	8.95647i	−0.587297	+	0.450649i
$396$	−4.58053	+	10.7173i	−0.230180	+	0.538565i
$397$	3.29041	−	4.28815i	0.165141	−	0.215216i	−0.703451	−	0.710744i	$-0.748359\pi$
$397$	3.29041	−	4.28815i	0.165141	−	0.215216i	0.868592	+	0.495528i	$0.165025\pi$
$398$	−2.74334	−	7.77637i	−0.137511	−	0.389794i
$399$	9.04298	+	16.7260i	0.452715	+	0.837348i
$400$	2.39174	−	1.53707i	0.119587	−	0.0768535i
$401$	0.877854	+	1.52049i	0.0438379	+	0.0759295i	0.887112	−	0.461555i	$-0.152708\pi$
$401$	0.877854	+	1.52049i	0.0438379	+	0.0759295i	−0.843274	+	0.537484i	$0.819375\pi$
$402$	−16.3080	+	2.05416i	−0.813368	+	0.102452i
$403$	−0.553453	+	4.20390i	−0.0275695	+	0.209411i
$404$	21.2857	−	22.3238i	1.05900	−	1.11065i
$405$	−13.9579	−	12.3534i	−0.693572	−	0.613844i
$406$	1.97918	−	15.2023i	0.0982251	−	0.754476i
$407$	3.74124	−	3.74124i	0.185446	−	0.185446i
$408$	−1.55576	+	13.7459i	−0.0770214	+	0.680521i
$409$	31.7040	−	8.49506i	1.56766	−	0.420054i	0.632582	−	0.774493i	$-0.281995\pi$
$409$	31.7040	−	8.49506i	1.56766	−	0.420054i	0.935079	+	0.354440i	$0.115328\pi$
$410$	−0.257917	+	0.396124i	−0.0127376	+	0.0195632i
$411$	23.7051	−	11.1787i	1.16929	−	0.551407i
$412$	19.0641	+	2.04963i	0.939220	+	0.100978i
$413$	−0.942375	−	17.1203i	−0.0463713	−	0.842437i
$414$	−0.622192	+	0.108887i	−0.0305790	+	0.00535153i
$415$	−2.67792	+	1.54610i	−0.131454	+	0.0758950i
$416$	2.16517	+	2.19110i	0.106156	+	0.107428i
$417$	−3.36802	+	15.5088i	−0.164933	+	0.759469i
$418$	−11.3644	+	0.880782i	−0.555850	+	0.0430805i
$419$	17.5728	−	7.27888i	0.858486	−	0.355596i	0.0903707	−	0.995908i	$-0.471195\pi$
$419$	17.5728	−	7.27888i	0.858486	−	0.355596i	0.768115	+	0.640312i	$0.221195\pi$
$420$	−2.55586	+	18.8086i	−0.124713	+	0.917765i
$421$	−8.22963	+	19.8681i	−0.401088	+	0.968312i	0.586315	+	0.810083i	$0.300578\pi$
$421$	−8.22963	+	19.8681i	−0.401088	+	0.968312i	−0.987403	+	0.158228i	$0.949422\pi$
$422$	0.336189	−	0.170793i	0.0163654	−	0.00831408i
$423$	2.64332	−	3.20602i	0.128523	−	0.155882i
$424$	−27.3320	−	22.2952i	−1.32736	−	1.08275i
$425$	0.519461	−	1.93866i	0.0251976	−	0.0940386i
$426$	19.3117	+	11.2943i	0.935657	+	0.547210i
$427$	10.7226	+	32.7080i	0.518903	+	1.58285i
$428$	8.71479	+	29.6800i	0.421245	+	1.43464i
$429$	1.72434	+	0.619189i	0.0832519	+	0.0298947i
$430$	4.90287	+	0.914734i	0.236438	+	0.0441124i
$431$	−12.9593	−	7.48205i	−0.624227	−	0.360398i	0.154286	−	0.988026i	$-0.450692\pi$
$431$	−12.9593	−	7.48205i	−0.624227	−	0.360398i	−0.778513	+	0.627628i	$0.784026\pi$
$432$	13.7806	−	15.5594i	0.663021	−	0.748601i
$433$		−	19.3138i		−	0.928161i	−0.885793	−	0.464081i	$-0.846385\pi$
$433$		−	19.3138i		−	0.928161i	0.885793	−	0.464081i	$-0.153615\pi$
$434$	−14.6038	−	25.2107i	−0.701003	−	1.21015i
$435$	−11.2181	+	9.49593i	−0.537865	+	0.455295i
$436$	34.6243	−	0.824164i	1.65821	−	0.0394703i
$437$	−0.376055	−	0.490085i	−0.0179892	−	0.0234439i
$438$	7.66909	+	13.4567i	0.366444	+	0.642986i
$439$	8.69223	−	32.4398i	0.414857	−	1.54827i	−0.370264	−	0.928927i	$-0.620733\pi$
$439$	8.69223	−	32.4398i	0.414857	−	1.54827i	0.785121	−	0.619342i	$-0.212601\pi$
$440$	−9.68081	−	5.98008i	−0.461515	−	0.285089i
$441$	13.9961	+	15.6560i	0.666481	+	0.745522i
$442$	2.17147	+	0.116395i	0.103286	+	0.00553634i
$443$	−27.9740	+	3.68284i	−1.32908	+	0.174977i	−0.761407	−	0.648274i	$-0.775491\pi$
$443$	−27.9740	+	3.68284i	−1.32908	+	0.174977i	−0.567677	+	0.823251i	$0.692158\pi$
$444$	−8.43580	+	4.22635i	−0.400345	+	0.200574i
$445$	−3.19378	+	24.2591i	−0.151400	+	1.14999i
$446$	0.864592	+	11.1555i	0.0409396	+	0.528228i
$447$	31.5871	−	10.1095i	1.49402	−	0.478164i
$448$	−20.9722	−	2.85745i	−0.990845	−	0.135002i
$449$		−	32.0154i		−	1.51090i	−0.655205	−	0.755451i	$-0.727418\pi$
$449$		−	32.0154i		−	1.51090i	0.655205	−	0.755451i	$-0.272582\pi$
$450$	−2.31251	+	1.93538i	−0.109013	+	0.0912348i
$451$	−0.310818	−	0.0409199i	−0.0146358	−	0.00192684i
$452$	23.4800	−	3.66158i	1.10441	−	0.172226i
$453$	13.2278	−	6.23791i	0.621496	−	0.293082i
$454$	−0.910079	+	16.9785i	−0.0427121	+	0.796841i
$455$	2.97522	+	0.226287i	0.139480	+	0.0106085i
$456$	19.7268	+	4.90281i	0.923791	+	0.229595i
$457$	−4.13235	−	1.10726i	−0.193303	−	0.0517955i	0.160868	−	0.986976i	$-0.448571\pi$
$457$	−4.13235	−	1.10726i	−0.193303	−	0.0517955i	−0.354172	+	0.935180i	$0.615237\pi$
$458$	−3.82221	+	0.807681i	−0.178600	+	0.0377405i
$459$	−0.190070	−	14.6715i	−0.00887170	−	0.684808i
$460$	−0.0146746	−	0.616503i	−0.000684209	−	0.0287446i
$461$	−29.0145	+	12.0182i	−1.35134	+	0.559744i	−0.936665	−	0.350226i	$-0.886105\pi$
$461$	−29.0145	+	12.0182i	−1.35134	+	0.559744i	−0.414675	+	0.909969i	$0.636105\pi$
$462$	−11.9843	+	3.85463i	−0.557562	+	0.179333i
$463$	8.40444			0.390587			0.195294	−	0.980745i	$-0.437434\pi$
$463$	8.40444			0.390587			0.195294	+	0.980745i	$0.437434\pi$
$464$	−10.5844	−	12.5129i	−0.491367	−	0.580897i
$465$	−5.92777	+	27.2957i	−0.274894	+	1.26581i
$466$	−6.37000	+	34.1425i	−0.295085	+	1.58162i
$467$	18.2102	−	23.7321i	0.842670	−	1.09819i	−0.151295	−	0.988489i	$-0.548344\pi$
$467$	18.2102	−	23.7321i	0.842670	−	1.09819i	0.993965	−	0.109700i	$-0.0349890\pi$
$468$	−2.56966	−	2.01788i	−0.118782	−	0.0932767i
$469$	−13.2248	−	11.8449i	−0.610666	−	0.546947i
$470$	2.71089	+	3.01796i	0.125044	+	0.139208i
$471$	1.75662	+	36.6054i	0.0809409	+	1.68669i
$472$	−14.2039	−	11.5863i	−0.653787	−	0.533304i
$473$	0.856127	+	3.19511i	0.0393647	+	0.146911i
$474$	12.2353	+	12.3731i	0.561987	+	0.568316i
$475$	−2.72463	−	1.12858i	−0.125015	−	0.0517828i
$476$	−12.3120	+	8.46629i	−0.564320	+	0.388052i
$477$	31.7250	+	19.8280i	1.45259	+	0.907861i
$478$	−0.102631	−	1.32421i	−0.00469423	−	0.0605678i
$479$	−11.2739	+	19.5269i	−0.515116	+	0.892207i	0.484730	+	0.874664i	$0.338918\pi$
$479$	−11.2739	+	19.5269i	−0.515116	+	0.892207i	−0.999846	+	0.0175434i	$0.994415\pi$
$480$	13.0180	+	15.5659i	0.594189	+	0.710483i
$481$	0.741596	+	1.28448i	0.0338139	+	0.0585673i
$482$	−1.02009	−	0.488051i	−0.0464639	−	0.0222301i
$483$	−0.529449	−	0.430302i	−0.0240907	−	0.0195794i
$484$	−1.54500	+	14.3704i	−0.0702272	+	0.653200i
$485$	−3.89172	−	29.5605i	−0.176714	−	1.34227i
$486$	−12.4331	+	18.2049i	−0.563976	+	0.825792i
$487$	7.10846	+	26.5291i	0.322115	+	1.20215i	0.917181	+	0.398472i	$0.130459\pi$
$487$	7.10846	+	26.5291i	0.322115	+	1.20215i	−0.595066	+	0.803677i	$0.702874\pi$
$488$	33.5623	+	15.0868i	1.51929	+	0.682947i
$489$	−14.0231	+	27.2245i	−0.634145	+	1.23113i
$490$	−17.1491	+	11.2362i	−0.774719	+	0.507600i
$491$	17.4908	+	7.24491i	0.789347	+	0.326958i	0.740681	−	0.671857i	$-0.234503\pi$
$491$	17.4908	+	7.24491i	0.789347	+	0.326958i	0.0486661	+	0.998815i	$0.484503\pi$
$492$	0.502957	+	0.244104i	0.0226751	+	0.0110051i
$493$	−11.4708	−	1.51016i	−0.516618	−	0.0680140i
$494$	0.586040	−	3.14111i	0.0263672	−	0.141325i
$495$	10.9820	+	5.00599i	0.493605	+	0.225003i
$496$	−30.4348	−	6.62077i	−1.36656	−	0.297282i
$497$	4.46607	+	23.7482i	0.200331	+	1.06525i
$498$	2.21010	+	2.91390i	0.0990371	+	0.130575i
$499$	14.5284	+	11.1480i	0.650380	+	0.499054i	0.880462	−	0.474117i	$-0.157233\pi$
$499$	14.5284	+	11.1480i	0.650380	+	0.499054i	−0.230082	+	0.973171i	$0.573899\pi$
$500$	−12.3114	−	20.1982i	−0.550582	−	0.903290i
$501$	29.1982	+	20.2575i	1.30448	+	0.905038i
$502$	5.64055	−	17.2898i	0.251750	−	0.771680i
$503$	−5.57036	+	5.57036i	−0.248370	+	0.248370i	−0.820301	−	0.571931i	$-0.806194\pi$
$503$	−5.57036	+	5.57036i	−0.248370	+	0.248370i	0.571931	+	0.820301i	$0.306194\pi$
$504$	22.4489	+	0.219117i	0.999952	+	0.00976023i
$505$	−22.5857	−	22.5857i	−1.00505	−	1.00505i
$506$	0.364639	−	0.185246i	0.0162102	−	0.00823521i
$507$	12.5425	−	18.0782i	0.557032	−	0.802880i
$508$	−1.38986	−	8.91252i	−0.0616649	−	0.395429i
$509$	−6.12316	+	7.97986i	−0.271404	+	0.353701i	−0.909093	−	0.416593i	$-0.863224\pi$
$509$	−6.12316	+	7.97986i	−0.271404	+	0.353701i	0.637689	+	0.770294i	$0.279891\pi$
$510$	14.1918	+	1.94929i	0.628423	+	0.0863158i
$511$	−5.54299	+	15.7847i	−0.245208	+	0.698273i
$512$	−17.3625	+	14.5101i	−0.767322	+	0.641262i
$513$	−21.4102	−	2.53700i	−0.945281	−	0.112011i
$514$	5.69426	−	3.90358i	0.251163	−	0.172180i
$515$	2.59161	−	19.6852i	0.114200	−	0.867433i
$516$	0.348712	−	5.88852i	0.0153512	−	0.259228i
$517$	−1.02962	+	2.48572i	−0.0452825	+	0.109322i
$518$	−9.42111	−	3.88649i	−0.413940	−	0.170763i
$519$	−22.0223	−	11.3435i	−0.966674	−	0.497925i
$520$	2.32165	−	2.18745i	0.101811	−	0.0959262i
$521$	26.7081	−	7.15640i	1.17010	−	0.313528i	0.379108	−	0.925352i	$-0.376231\pi$
$521$	26.7081	−	7.15640i	1.17010	−	0.313528i	0.790993	+	0.611825i	$0.209564\pi$
$522$	12.8012	+	11.7604i	0.560294	+	0.514737i
$523$	−13.4674	+	1.77301i	−0.588887	+	0.0775284i	−0.419081	−	0.907949i	$-0.637648\pi$
$523$	−13.4674	+	1.77301i	−0.588887	+	0.0775284i	−0.169806	+	0.985477i	$0.554314\pi$
$524$	−3.74838	−	2.04677i	−0.163749	−	0.0894138i
$525$	−3.21613	−	0.515254i	−0.140363	−	0.0224875i
$526$	−4.05577	+	1.43079i	−0.176840	+	0.0623855i
$527$	−19.0420	+	10.9939i	−0.829480	+	0.478901i
$528$	−5.58646	+	12.2439i	−0.243120	+	0.532849i
$529$	−19.8994	−	11.4889i	−0.865191	−	0.499518i
$530$	−23.7541	+	27.7455i	−1.03181	+	1.20519i
$531$	16.4868	+	10.3042i	0.715468	+	0.447164i
$532$	9.97246	+	19.5601i	0.432361	+	0.848037i
$533$	0.0336313	−	0.0811931i	0.00145673	−	0.00351686i
$534$	28.9392	+	0.162039i	1.25232	+	0.00701213i
$535$	30.9404	−	8.29045i	1.33767	−	0.358427i
$536$	−18.8826	+	1.91647i	−0.815605	+	0.0827790i
$537$	−35.4223	+	1.69985i	−1.52859	+	0.0733539i
$538$	−1.81333	+	33.8296i	−0.0781781	+	1.45850i
$539$	−11.6311	−	7.04370i	−0.500987	−	0.303394i
$540$	−15.7680	−	14.6495i	−0.678545	−	0.630415i
$541$	−22.4113	−	17.1968i	−0.963536	−	0.739347i	0.00189691	−	0.999998i	$-0.499396\pi$
$541$	−22.4113	−	17.1968i	−0.963536	−	0.739347i	−0.965433	+	0.260651i	$0.916063\pi$
$542$	−18.5301	−	27.0304i	−0.795937	−	1.16106i
$543$	14.5272	+	3.15486i	0.623423	+	0.135388i
$544$	−2.17923	+	15.8243i	−0.0934338	+	0.678463i
$545$		−	35.8645i		−	1.53626i
$546$	−0.174227	−	3.52474i	−0.00745622	−	0.150845i
$547$	1.23682	+	2.98595i	0.0528826	+	0.127670i	0.948113	−	0.317934i	$-0.102989\pi$
$547$	1.23682	+	2.98595i	0.0528826	+	0.127670i	−0.895230	+	0.445604i	$0.852989\pi$
$548$	27.6760	−	12.2433i	1.18226	−	0.523007i
$549$	−37.3230	−	11.4145i	−1.59291	−	0.487158i
$550$	1.06540	−	1.63630i	0.0454287	−	0.0697721i
$551$	−4.40004	+	16.4212i	−0.187448	+	0.699565i
$552$	−0.721272	+	0.108345i	−0.0306994	+	0.00461147i
$553$	−1.42540	+	18.7412i	−0.0606141	+	0.796955i
$554$	29.8710	−	26.8316i	1.26910	−	1.13997i
$555$	4.16738	+	8.83714i	0.176895	+	0.375116i
$556$	−4.32041	+	17.8089i	−0.183226	+	0.755264i
$557$	−3.47645	+	26.4062i	−0.147302	+	1.11887i	0.744882	+	0.667196i	$0.232506\pi$
$557$	−3.47645	+	26.4062i	−0.147302	+	1.11887i	−0.892184	+	0.451672i	$0.850828\pi$
$558$	32.9065	+	2.92144i	1.39304	+	0.123674i
$559$	−0.927275			−0.0392196
$560$	−3.47490	+	21.6407i	−0.146841	+	0.914486i
$561$	2.89602	+	9.04858i	0.122270	+	0.382031i
$562$	12.7790	−	14.9263i	0.539050	−	0.629627i
$563$	37.9031	+	4.99004i	1.59743	+	0.210305i	0.876044	−	0.482231i	$-0.160173\pi$
$563$	37.9031	+	4.99004i	1.59743	+	0.210305i	0.721383	+	0.692536i	$0.243507\pi$
$564$	3.14076	−	3.62720i	0.132250	−	0.152732i
$565$	−3.21199	−	24.3975i	−0.135129	−	1.02641i
$566$	21.7695	−	19.5545i	0.915041	−	0.821935i
$567$	−23.6520	+	2.75347i	−0.993292	+	0.115635i
$568$	21.9778	+	13.5762i	0.922169	+	0.569647i
$569$	−34.1739	−	9.15687i	−1.43264	−	0.383876i	−0.542693	−	0.839931i	$-0.682595\pi$
$569$	−34.1739	−	9.15687i	−1.43264	−	0.383876i	−0.889952	+	0.456055i	$0.849262\pi$
$570$	5.56164	−	20.3009i	0.232951	−	0.850313i
$571$	−0.0425969	+	0.0326858i	−0.00178263	+	0.00136786i	−0.609652	−	0.792669i	$-0.708691\pi$
$571$	−0.0425969	+	0.0326858i	−0.00178263	+	0.00136786i	0.607870	+	0.794037i	$0.292024\pi$
$572$	1.97325	+	0.762855i	0.0825056	+	0.0318966i
$573$	5.98501	+	7.07042i	0.250027	+	0.295371i
$574$	0.157129	+	0.583057i	0.00655843	+	0.0243363i
$575$	0.105819			0.00441298
$576$	16.3418	−	17.5769i	0.680906	−	0.732370i
$577$	21.6682	−	37.5305i	0.902060	−	1.56241i	0.0772445	−	0.997012i	$-0.475388\pi$
$577$	21.6682	−	37.5305i	0.902060	−	1.56241i	0.824816	−	0.565402i	$-0.191279\pi$
$578$	−7.21771	−	10.5287i	−0.300217	−	0.437935i
$579$	−1.95779	+	5.45212i	−0.0813629	+	0.226582i
$580$	−13.2145	+	10.6489i	−0.548704	+	0.442173i
$581$	−0.811146	+	3.86609i	−0.0336520	+	0.160392i
$582$	−34.1128	+	8.93609i	−1.41402	+	0.370413i
$583$	−23.3988	−	6.26970i	−0.969081	−	0.259665i
$584$	8.47766	+	15.7478i	0.350808	+	0.651649i
$585$	−2.15230	+	2.61046i	−0.0889864	+	0.107929i
$586$	1.12321	+	0.366434i	0.0463996	+	0.0151372i
$587$	19.9201	+	8.25118i	0.822191	+	0.340563i	0.753807	−	0.657096i	$-0.228216\pi$
$587$	19.9201	+	8.25118i	0.822191	+	0.340563i	0.0683844	+	0.997659i	$0.478216\pi$
$588$	15.7200	+	18.4630i	0.648282	+	0.761400i
$589$	12.3639	+	29.8491i	0.509446	+	1.22991i
$590$	−12.3445	+	14.4188i	−0.508216	+	0.593612i
$591$	11.2245	+	2.43760i	0.461713	+	0.100270i
$592$	−9.85584	+	4.64350i	−0.405072	+	0.190847i
$593$	11.0362	+	19.1153i	0.453204	+	0.784972i	0.998583	−	0.0532178i	$-0.0169478\pi$
$593$	11.0362	+	19.1153i	0.453204	+	0.784972i	−0.545379	+	0.838189i	$0.683614\pi$
$594$	4.25108	−	13.6269i	0.174424	−	0.559117i
$595$	8.46117	+	12.9544i	0.346874	+	0.531078i
$596$	36.7449	−	10.7892i	1.50513	−	0.441943i
$597$	4.30765	+	9.13459i	0.176300	+	0.373854i
$598$	0.0237042	+	0.112176i	0.000969336	+	0.00458722i
$599$	−12.0149	−	44.8402i	−0.490915	−	1.83212i	−0.551800	−	0.833976i	$-0.686059\pi$
$599$	−12.0149	−	44.8402i	−0.490915	−	1.83212i	0.0608846	−	0.998145i	$-0.480608\pi$
$600$	−2.72345	+	2.16965i	−0.111184	+	0.0885755i
$601$	2.64178	+	2.64178i	0.107760	+	0.107760i	0.758931	−	0.651171i	$-0.225722\pi$
$601$	2.64178	+	2.64178i	0.107760	+	0.107760i	−0.651171	+	0.758931i	$0.725722\pi$
$602$	5.04925	−	3.88597i	0.205792	−	0.158380i
$603$	19.6154	−	4.52670i	0.798801	−	0.184342i
$604$	15.4436	−	6.83193i	0.628393	−	0.277987i
$605$	14.8386	+	1.95354i	0.603275	+	0.0794227i
$606$	−23.1650	+	29.8418i	−0.941014	+	1.21224i
$607$	15.0802	−	8.70656i	0.612087	−	0.353389i	−0.161695	−	0.986841i	$-0.551696\pi$
$607$	15.0802	−	8.70656i	0.612087	−	0.353389i	0.773782	+	0.633452i	$0.218363\pi$
$608$	22.6352	+	6.20974i	0.917977	+	0.251838i
$609$	−0.524903	+	18.7687i	−0.0212702	+	0.760546i
$610$	16.4453	−	34.3729i	0.665852	−	1.39172i
$611$	−0.598370	−	0.459146i	−0.0242075	−	0.0185750i
$612$	0.189728	−	16.9416i	0.00766932	−	0.684823i
$613$	−8.88220	−	11.5755i	−0.358749	−	0.467530i	0.578757	−	0.815500i	$-0.303538\pi$
$613$	−8.88220	−	11.5755i	−0.358749	−	0.467530i	−0.937506	+	0.347970i	$0.886871\pi$
$614$	−30.9083	+	15.7022i	−1.24736	+	0.633691i
$615$	0.265098	−	0.514661i	0.0106898	−	0.0207532i
$616$	−13.9418	+	4.11544i	−0.561730	+	0.165816i
$617$	−13.7201	−	13.7201i	−0.552350	−	0.552350i	0.374769	−	0.927118i	$-0.377722\pi$
$617$	−13.7201	−	13.7201i	−0.552350	−	0.552350i	−0.927118	+	0.374769i	$0.877722\pi$
$618$	−23.4828	−	0.131488i	−0.944617	−	0.00528921i
$619$	−17.8452	−	23.2564i	−0.717261	−	0.934753i	0.282438	−	0.959286i	$-0.408857\pi$
$619$	−17.8452	−	23.2564i	−0.717261	−	0.934753i	−0.999699	+	0.0245329i	$0.992190\pi$
$620$	−7.60399	+	31.3439i	−0.305383	+	1.25880i
$621$	0.744591	−	0.209887i	0.0298794	−	0.00842249i
$622$	10.9630	+	31.0762i	0.439577	+	1.24604i
$623$	20.3631	+	23.7156i	0.815830	+	0.950145i
$624$	−2.91005	−	2.40103i	−0.116495	−	0.0961182i
$625$	−18.1354	+	10.4705i	−0.725417	+	0.418820i
$626$	−4.38550	+	23.5058i	−0.175280	+	0.939480i
$627$	13.7375	−	2.48351i	0.548624	−	0.0991818i
$628$	1.00698	+	42.3049i	0.0401831	+	1.68815i
$629$	−2.94330	+	7.10575i	−0.117357	+	0.283325i
$630$	0.780013	−	23.2343i	0.0310764	−	0.925679i
$631$	−6.92790	−	6.92790i	−0.275795	−	0.275795i	0.555633	−	0.831428i	$-0.312476\pi$
$631$	−6.92790	−	6.92790i	−0.275795	−	0.275795i	−0.831428	+	0.555633i	$0.812476\pi$
$632$	13.7790	+	14.6243i	0.548098	+	0.581722i
$633$	−0.388431	+	0.249823i	−0.0154388	+	0.00992956i
$634$	25.5562	−	39.2507i	1.01497	−	1.55884i
$635$	−9.26076	+	1.21920i	−0.367502	+	0.0483826i
$636$	36.0693	+	23.7734i	1.43024	+	0.942677i
$637$	2.75115	−	2.63837i	0.109005	−	0.104536i
$638$	−10.1535	−	4.85783i	−0.401981	−	0.192323i
$639$	−24.9318	−	11.3648i	−0.986289	−	0.449585i
$640$	14.5935	+	18.3317i	0.576857	+	0.724626i
$641$	33.3076	+	19.2302i	1.31557	+	0.759545i	0.983013	−	0.183537i	$-0.0587548\pi$
$641$	33.3076	+	19.2302i	1.31557	+	0.759545i	0.332558	+	0.943083i	$0.392088\pi$
$642$	−14.3018	−	35.0818i	−0.564446	−	1.38457i
$643$	−18.0027	−	43.4624i	−0.709958	−	1.71399i	−0.700106	−	0.714039i	$-0.746864\pi$
$643$	−18.0027	−	43.4624i	−0.709958	−	1.71399i	−0.00985198	−	0.999951i	$-0.503136\pi$
$644$	−0.599177	−	0.511489i	−0.0236109	−	0.0201555i
$645$	−6.08738	−	0.506100i	−0.239691	−	0.0199277i
$646$	14.7725	−	7.50483i	0.581217	−	0.295274i
$647$	−4.15458	+	1.11322i	−0.163333	+	0.0437651i	−0.339559	−	0.940585i	$-0.610278\pi$
$647$	−4.15458	+	1.11322i	−0.163333	+	0.0437651i	0.176226	+	0.984350i	$0.443611\pi$
$648$	−14.8600	+	20.6684i	−0.583754	+	0.811930i
$649$	−12.1599	−	3.25823i	−0.477318	−	0.127897i
$650$	0.365772	+	0.407205i	0.0143468	+	0.0159719i
$651$	20.9225	+	28.9054i	0.820017	+	1.13289i
$652$	−16.9469	+	31.0359i	−0.663693	+	1.21546i
$653$	9.79418	+	7.51534i	0.383276	+	0.294098i	0.782372	−	0.622811i	$-0.214009\pi$
$653$	9.79418	+	7.51534i	0.383276	+	0.294098i	−0.399096	+	0.916909i	$0.630676\pi$
$654$	−42.0854	+	5.30110i	−1.64567	+	0.207289i
$655$	−2.21125	+	3.82999i	−0.0864006	+	0.149650i
$656$	0.573789	+	0.295811i	0.0224027	+	0.0115495i
$657$	−11.0143	−	15.4445i	−0.429710	−	0.602546i
$658$	5.18244	−	0.00745299i	0.202033	−	0.000290548i
$659$	11.7011	+	28.2489i	0.455809	+	1.10042i	0.970079	+	0.242791i	$0.0780630\pi$
$659$	11.7011	+	28.2489i	0.455809	+	1.10042i	−0.514270	+	0.857629i	$0.671937\pi$
$660$	12.5376	+	6.08498i	0.488027	+	0.236858i
$661$	−22.3568	+	17.1550i	−0.869578	+	0.667251i	−0.943989	−	0.329977i	$-0.892959\pi$
$661$	−22.3568	+	17.1550i	−0.869578	+	0.667251i	0.0744106	+	0.997228i	$0.476292\pi$
$662$	23.5166	−	4.96936i	0.914000	−	0.193140i
$663$	−2.66026	+	0.127661i	−0.103316	+	0.00495793i
$664$	2.47000	+	3.42533i	0.0958547	+	0.132929i
$665$	20.4949	−	9.84180i	0.794759	−	0.381649i
$666$	9.75403	−	6.19645i	0.377961	−	0.240108i
$667$	−0.0796216	−	0.604786i	−0.00308296	−	0.0234174i
$668$	33.1405	+	24.1987i	1.28224	+	0.936277i
$669$	−2.43786	−	13.4850i	−0.0942530	−	0.521361i
$670$	1.51869	+	19.5951i	0.0586722	+	0.757024i
$671$	25.2718			0.975608
$672$	25.9081	+	0.878962i	0.999425	+	0.0339067i
$673$	−43.3045			−1.66926			−0.834632	−	0.550808i	$-0.814320\pi$
$673$	−43.3045			−1.66926			−0.834632	+	0.550808i	$0.814320\pi$
$674$	1.45532	+	18.7775i	0.0560569	+	0.723280i
$675$	2.57747	−	2.64513i	0.0992070	−	0.101811i
$676$	14.9827	−	20.5190i	0.576259	−	0.789193i
$677$	4.52079	+	34.3388i	0.173748	+	1.31975i	0.826826	+	0.562458i	$0.190144\pi$
$677$	4.52079	+	34.3388i	0.173748	+	1.31975i	−0.653078	+	0.757291i	$0.726523\pi$
$678$	−28.1546	+	7.37530i	−1.08127	+	0.283247i
$679$	−31.4470	−	21.4914i	−1.20682	−	0.824765i
$680$	16.3281	+	2.64594i	0.626155	+	0.101467i
$681$	−0.998165	−	20.8003i	−0.0382498	−	0.797068i
$682$	−20.9289	+	4.42253i	−0.801407	+	0.169347i
$683$	27.5623	−	21.1493i	1.05464	−	0.809256i	0.0724952	−	0.997369i	$-0.476904\pi$
$683$	27.5623	−	21.1493i	1.05464	−	0.809256i	0.982147	+	0.188113i	$0.0602371\pi$
$684$	−24.6444	−	3.52568i	−0.942301	−	0.134808i
$685$	−11.9926	−	28.9528i	−0.458215	−	1.10623i
$686$	−3.92396	+	25.8960i	−0.149818	+	0.988714i
$687$	4.55691	−	1.45845i	0.173857	−	0.0556434i
$688$	0.566751	−	6.78777i	0.0216072	−	0.258781i
$689$	3.39537	−	5.88096i	0.129353	−	0.224047i
$690$	0.0943886	+	0.749352i	0.00359331	+	0.0285273i
$691$	−37.6736	−	28.9080i	−1.43317	−	1.09971i	−0.977832	−	0.209392i	$-0.932851\pi$
$691$	−37.6736	−	28.9080i	−1.43317	−	1.09971i	−0.455339	−	0.890318i	$-0.650482\pi$
$692$	−25.1055	−	13.7087i	−0.954367	−	0.521125i
$693$	14.1238	−	6.18390i	0.536520	−	0.234907i
$694$	17.7725	+	19.7857i	0.674637	+	0.751056i
$695$	18.3298	+	4.91146i	0.695289	+	0.186302i
$696$	14.4493	+	13.9327i	0.547699	+	0.528118i
$697$	0.440195	−	0.117950i	0.0166736	−	0.00446767i
$698$	−0.529176	+	0.268835i	−0.0200296	+	0.0101756i
$699$	3.52437	−	42.3912i	0.133304	−	1.60338i
$700$	−3.69821	−	0.684477i	−0.139779	−	0.0258708i
$701$	−6.53641	−	15.7803i	−0.246877	−	0.596014i	0.751059	−	0.660235i	$-0.229543\pi$
$701$	−6.53641	−	15.7803i	−0.246877	−	0.596014i	−0.997936	+	0.0642218i	$0.979543\pi$
$702$	3.38140	+	2.13978i	0.127623	+	0.0807607i
$703$	9.78726	+	5.65068i	0.369133	+	0.213119i
$704$	−6.79025	+	13.9782i	−0.255917	+	0.526822i
$705$	−3.67759	−	3.34079i	−0.138506	−	0.125821i
$706$	−5.59655	−	2.67760i	−0.210629	−	0.100773i
$707$	−40.7428	+	2.24266i	−1.53229	+	0.0843437i
$708$	18.7445	+	12.3546i	0.704460	+	0.464312i
$709$	17.0004	−	2.23814i	0.638462	−	0.0840551i	0.195656	−	0.980673i	$-0.437316\pi$
$709$	17.0004	−	2.23814i	0.638462	−	0.0840551i	0.442806	+	0.896618i	$0.353983\pi$
$710$	14.5961	−	22.4176i	0.547782	−	0.841316i
$711$	−16.4435	−	13.5575i	−0.616680	−	0.508446i
$712$	33.4018	+	0.994065i	1.25179	+	0.0372542i
$713$	−0.819737	−	0.819737i	−0.0306994	−	0.0306994i
$714$	13.9508	−	11.8436i	0.522095	−	0.443236i
$715$	0.838355	−	2.02397i	0.0313527	−	0.0756921i
$716$	−40.9376	+	0.974439i	−1.52991	+	0.0364165i
$717$	0.289385	+	1.60073i	0.0108073	+	0.0597805i
$718$	3.09508	−	16.5893i	0.115508	−	0.619108i
$719$	25.0198	−	14.4452i	0.933080	−	0.538714i	0.0452955	−	0.998974i	$-0.485577\pi$
$719$	25.0198	−	14.4452i	0.933080	−	0.538714i	0.887784	+	0.460260i	$0.152244\pi$
$720$	−17.7934	−	17.3506i	−0.663122	−	0.646619i
$721$	−16.5237	−	19.2441i	−0.615376	−	0.716689i
$722$	0.839363	+	2.37929i	0.0312379	+	0.0885480i
$723$	1.30349	+	0.468067i	0.0484773	+	0.0174076i
$724$	16.6817	+	4.04697i	0.619971	+	0.150404i
$725$	−1.77284	−	2.31040i	−0.0658415	−	0.0858063i
$726$	0.0991148	−	17.7012i	0.00367849	−	0.656954i
$727$	8.36387	+	8.36387i	0.310199	+	0.310199i	0.844986	−	0.534788i	$-0.179608\pi$
$727$	8.36387	+	8.36387i	0.310199	+	0.310199i	−0.534788	+	0.844986i	$0.679608\pi$
$728$	−0.102828	−	4.07369i	−0.00381107	−	0.150981i
$729$	12.8897	−	23.7246i	0.477397	−	0.878688i
$730$	16.5115	−	8.38828i	0.611118	−	0.310464i
$731$	−2.92721	−	3.81481i	−0.108267	−	0.141096i
$732$	−42.7660	−	14.2173i	−1.58068	−	0.525485i
$733$	0.666284	+	0.511258i	0.0246098	+	0.0188837i	0.620993	−	0.783816i	$-0.286729\pi$
$733$	0.666284	+	0.511258i	0.0246098	+	0.0188837i	−0.596383	+	0.802700i	$0.703396\pi$
$734$	−6.02062	+	12.5839i	−0.222225	+	0.464480i
$735$	19.5008	−	15.8189i	0.719298	−	0.583488i
$736$	−0.835631	+	0.104956i	−0.0308018	+	0.00386872i
$737$	−11.2886	+	6.51746i	−0.415820	+	0.240074i
$738$	−0.643118	−	0.235009i	−0.0236735	−	0.00865081i
$739$	−48.2747	−	6.35549i	−1.77582	−	0.233790i	−0.829834	−	0.558011i	$-0.811565\pi$
$739$	−48.2747	−	6.35549i	−1.77582	−	0.233790i	−0.945982	+	0.324221i	$0.894898\pi$
$740$	4.56423	+	10.3175i	0.167784	+	0.379278i
$741$	−0.324241	+	3.89999i	−0.0119113	+	0.143270i
$742$	6.15693	+	46.2525i	0.226028	+	1.69798i
$743$	20.3734	+	20.3734i	0.747429	+	0.747429i	0.973996	−	0.226567i	$-0.0727501\pi$
$743$	20.3734	+	20.3734i	0.747429	+	0.747429i	−0.226567	+	0.973996i	$0.572750\pi$
$744$	37.9046	+	4.29005i	1.38965	+	0.157281i
$745$	−10.2639	−	38.3053i	−0.376039	−	1.40340i
$746$	−3.18502	−	15.0725i	−0.116612	−	0.551845i
$747$	−3.05450	−	3.27614i	−0.111758	−	0.119868i
$748$	3.09073	+	10.5261i	0.113008	+	0.384873i
$749$	18.4816	−	36.5091i	0.675303	−	1.33401i
$750$	17.5073	+	23.0824i	0.639277	+	0.842851i
$751$	−17.1345	−	29.6777i	−0.625245	−	1.08296i	−0.988493	−	0.151264i	$-0.951666\pi$
$751$	−17.1345	−	29.6777i	−0.625245	−	1.08296i	0.363248	−	0.931692i	$-0.381668\pi$
$752$	3.72673	−	4.09952i	0.135900	−	0.149494i
$753$	−4.72701	+	21.7666i	−0.172262	+	0.793217i
$754$	2.05206	−	2.39687i	0.0747318	−	0.0872890i
$755$	−6.69207	−	16.1561i	−0.243549	−	0.587980i
$756$	−27.3798	+	2.51894i	−0.995795	+	0.0916129i
$757$	34.8961	+	14.4544i	1.26832	+	0.525355i	0.912453	−	0.409181i	$-0.134186\pi$
$757$	34.8961	+	14.4544i	1.26832	+	0.525355i	0.355867	+	0.934537i	$0.384186\pi$
$758$	−21.6900	−	7.07607i	−0.787816	−	0.257015i
$759$	−0.421302	+	0.270964i	−0.0152923	+	0.00983536i
$760$	6.98627	−	23.2796i	0.253419	−	0.844439i
$761$	−31.7669	−	8.51193i	−1.15155	−	0.308557i	−0.367964	−	0.929840i	$-0.619945\pi$
$761$	−31.7669	−	8.51193i	−1.15155	−	0.308557i	−0.783586	+	0.621283i	$0.786612\pi$
$762$	2.79951	+	10.6869i	0.101415	+	0.387146i
$763$	−34.1289	−	30.5677i	−1.23555	−	1.10663i
$764$	6.71170	+	8.32874i	0.242821	+	0.301323i
$765$	−17.5338	−	0.613881i	−0.633935	−	0.0221949i
$766$	−9.49757	−	13.8544i	−0.343161	−	0.500578i
$767$	1.76450	−	3.05621i	0.0637126	−	0.110353i
$768$	19.3545	−	19.8344i	0.698395	−	0.715713i
$769$	27.4369			0.989400			0.494700	−	0.869064i	$-0.335278\pi$
$769$	27.4369			0.989400			0.494700	+	0.869064i	$0.335278\pi$
$770$	3.91688	+	14.5343i	0.141155	+	0.523782i
$771$	−6.45368	+	5.46294i	−0.232424	+	0.196743i
$772$	−2.41204	+	6.23913i	−0.0868113	+	0.224551i
$773$	4.44064	−	3.40742i	0.159719	−	0.122556i	−0.525810	−	0.850602i	$-0.676238\pi$
$773$	4.44064	−	3.40742i	0.159719	−	0.122556i	0.685529	+	0.728046i	$0.259571\pi$
$774$	0.305884	+	7.21810i	0.0109948	+	0.259449i
$775$	−5.34591	−	1.43243i	−0.192031	−	0.0514545i
$776$	−39.6278	+	9.36421i	−1.42255	+	0.336155i
$777$	11.9614	+	3.56629i	0.429112	+	0.127940i
$778$	18.7899	−	16.8780i	0.673650	−	0.605106i
$779$	−0.0874047	−	0.663904i	−0.00313160	−	0.0237868i
$780$	−2.55733	+	2.95340i	−0.0915670	+	0.105749i
$781$	17.5899	+	2.31575i	0.629415	+	0.0828640i
$782$	−0.386663	+	0.451634i	−0.0138270	+	0.0161504i
$783$	−17.0570	−	12.7407i	−0.609567	−	0.455314i
$784$	17.6317	+	21.7514i	0.629705	+	0.776834i
$785$	43.8201			1.56401
$786$	4.82118	+	2.02870i	0.171966	+	0.0723613i
$787$	−6.91875	+	52.5531i	−0.246627	+	1.87332i	0.201701	+	0.979447i	$0.435353\pi$
$787$	−6.91875	+	52.5531i	−0.246627	+	1.87332i	−0.448328	+	0.893869i	$0.647980\pi$
$788$	12.8891	+	3.12689i	0.459157	+	0.111391i
$789$	4.76416	−	2.24666i	0.169609	−	0.0799832i
$790$	15.4790	−	13.9040i	0.550719	−	0.494683i
$791$	−25.9544	−	17.7377i	−0.922833	−	0.630680i
$792$	5.28730	−	15.6118i	0.187876	−	0.554741i
$793$	−1.83358	+	6.84301i	−0.0651123	+	0.243002i
$794$	−4.17083	+	6.40580i	−0.148017	+	0.227333i
$795$	25.4998	−	36.7542i	0.904383	−	1.30354i
$796$	4.71786	+	10.6648i	0.167220	+	0.378003i
$797$	−4.03350	−	9.73774i	−0.142874	−	0.344928i	0.836203	−	0.548421i	$-0.184771\pi$
$797$	−4.03350	−	9.73774i	−0.142874	−	0.344928i	−0.979077	+	0.203492i	$0.934771\pi$
$798$	−14.5783	−	22.5952i	−0.516065	−	0.799863i
$799$		−	3.91112i		−	0.138365i
$800$	−3.20435	+	2.42861i	−0.113291	+	0.0858645i
$801$	−35.2808	+	3.39393i	−1.24658	+	0.119919i
$802$	−1.40392	−	2.04793i	−0.0495741	−	0.0723151i
$803$	9.74474	+	7.47740i	0.343884	+	0.263872i
$804$	22.7695	−	4.67845i	0.803019	−	0.164996i
$805$	−0.544273	+	0.607682i	−0.0191831	+	0.0214180i
$806$	0.320963	−	5.98791i	0.0113054	−	0.210915i
$807$	−1.98884	−	41.4444i	−0.0700105	−	1.45891i
$808$	−27.5730	+	33.8023i	−0.970016	+	1.18916i
$809$	−18.0788	+	4.84419i	−0.635615	+	0.170313i	−0.562217	−	0.826990i	$-0.690051\pi$
$809$	−18.0788	+	4.84419i	−0.635615	+	0.170313i	−0.0733988	+	0.997303i	$0.523385\pi$
$810$	21.0303	+	15.8928i	0.738931	+	0.558415i
$811$	12.4057	−	29.9500i	0.435623	−	1.05169i	−0.541821	−	0.840494i	$-0.682265\pi$
$811$	12.4057	−	29.9500i	0.435623	−	1.05169i	0.977444	−	0.211193i	$-0.0677350\pi$
$812$	−1.12932	+	21.6513i	−0.0396315	+	0.759811i
$813$	25.9324	+	30.6354i	0.909488	+	1.07443i
$814$	−4.86625	+	5.68393i	−0.170562	+	0.199222i
$815$	31.7117	+	18.3087i	1.11081	+	0.641327i
$816$	0.691458	−	19.5515i	0.0242059	−	0.684438i
$817$	−6.11889	+	3.53274i	−0.214073	+	0.123595i
$818$	−43.7738	+	15.4425i	−1.53052	+	0.539934i
$819$	0.649707	+	4.27307i	0.0227026	+	0.149313i
$820$	0.320371	−	0.586714i	0.0111878	−	0.0204889i
$821$	13.2497	−	1.74435i	0.462417	−	0.0608783i	0.104281	−	0.994548i	$-0.466746\pi$
$821$	13.2497	−	1.74435i	0.462417	−	0.0608783i	0.358136	+	0.933670i	$0.383413\pi$
$822$	−32.2022	+	18.3523i	−1.12318	+	0.640111i
$823$	−8.69352	+	2.32942i	−0.303037	+	0.0811985i	−0.407133	−	0.913369i	$-0.633472\pi$
$823$	−8.69352	+	2.32942i	−0.303037	+	0.0811985i	0.104096	+	0.994567i	$0.466805\pi$
$824$	−27.1040	−	0.806639i	−0.944214	−	0.0281006i
$825$	−1.09506	+	2.12595i	−0.0381250	+	0.0740161i
$826$	3.19963	+	24.0364i	0.111329	+	0.836335i
$827$	1.43694	−	3.46908i	0.0499673	−	0.120632i	−0.896925	−	0.442183i	$-0.854204\pi$
$827$	1.43694	−	3.46908i	0.0499673	−	0.120632i	0.946892	+	0.321551i	$0.104204\pi$
$828$	0.865382	−	0.221522i	0.0300741	−	0.00769843i
$829$	−2.83368	+	21.5239i	−0.0984177	+	0.747556i	0.869079	+	0.494673i	$0.164712\pi$
$829$	−2.83368	+	21.5239i	−0.0984177	+	0.747556i	−0.967497	+	0.252883i	$0.918621\pi$
$830$	3.60687	−	2.47262i	0.125196	−	0.0858258i
$831$	−33.0662	+	36.3997i	−1.14705	+	1.26269i
$832$	−3.29230	−	2.85281i	−0.114140	−	0.0989036i
$833$	19.5391	+	2.98946i	0.676988	+	0.103579i
$834$	3.05408	−	22.2352i	0.105754	−	0.769943i
$835$	25.8679	−	33.7117i	0.895195	−	1.16664i
$836$	15.9274	−	2.48378i	0.550859	−	0.0859033i
$837$	−40.4572	+	0.524124i	−1.39841	+	0.0181164i
$838$	−23.9819	+	12.1834i	−0.828441	+	0.420870i
$839$	−36.9698	−	36.9698i	−1.27634	−	1.27634i	−0.942701	−	0.333639i	$-0.891723\pi$
$839$	−36.9698	−	36.9698i	−1.27634	−	1.27634i	−0.333639	−	0.942701i	$-0.608277\pi$
$840$	1.54834	−	26.7991i	0.0534229	−	0.924658i
$841$	8.63547	−	8.63547i	0.297775	−	0.297775i
$842$	9.43249	−	28.9130i	0.325065	−	0.996409i
$843$	−13.7181	+	19.7727i	−0.472477	+	0.681007i
$844$	−0.455358	+	0.277554i	−0.0156741	+	0.00955381i
$845$	−20.8727	−	16.0162i	−0.718043	−	0.550974i
$846$	−3.37669	+	4.80929i	−0.116093	+	0.165347i
$847$	14.5061	−	12.4555i	0.498437	−	0.427976i
$848$	40.9741	+	28.4490i	1.40706	+	0.976943i
$849$	−24.0981	+	26.5276i	−0.827046	+	0.910424i
$850$	−0.520578	+	2.79024i	−0.0178557	+	0.0957045i
$851$	−0.402043	−	0.0529299i	−0.0137818	−	0.00181441i
$852$	−28.4635	−	13.8144i	−0.975143	−	0.473274i
$853$	9.39172	+	3.89018i	0.321566	+	0.133197i	0.537627	−	0.843183i	$-0.319321\pi$
$853$	9.39172	+	3.89018i	0.321566	+	0.133197i	−0.216061	+	0.976380i	$0.569321\pi$
$854$	−18.6930	−	44.9460i	−0.639662	−	1.53802i
$855$	−4.25717	+	25.4257i	−0.145592	+	0.869541i
$856$	−15.5311	−	40.8960i	−0.530843	−	1.39780i
$857$	10.6144	+	39.6133i	0.362580	+	1.35317i	0.870672	+	0.491863i	$0.163684\pi$
$857$	10.6144	+	39.6133i	0.362580	+	1.35317i	−0.508093	+	0.861302i	$0.669649\pi$
$858$	−2.49896	−	0.684613i	−0.0853130	−	0.0233723i
$859$	0.317317	+	2.41026i	0.0108267	+	0.0822371i	0.996005	−	0.0892954i	$-0.0284615\pi$
$859$	0.317317	+	2.41026i	0.0108267	+	0.0822371i	−0.985178	+	0.171532i	$0.945128\pi$
$860$	−7.01294	−	0.753979i	−0.239139	−	0.0257105i
$861$	−0.263810	−	0.690921i	−0.00899062	−	0.0235465i
$862$	19.0900	+	9.13340i	0.650210	+	0.311085i
$863$	−13.4226	−	23.2487i	−0.456912	−	0.791395i	0.541884	−	0.840453i	$-0.317711\pi$
$863$	−13.4226	−	23.2487i	−0.456912	−	0.791395i	−0.998796	+	0.0490583i	$0.984378\pi$
$864$	−17.7302	+	23.4444i	−0.603192	+	0.797596i
$865$	−14.8103	+	25.6521i	−0.503564	+	0.872199i
$866$	2.11059	+	27.2321i	0.0717209	+	0.925386i
$867$	10.1010	+	11.9328i	0.343047	+	0.405260i
$868$	23.3461	+	33.9508i	0.792418	+	1.15236i
$869$	12.7491	+	5.28087i	0.432485	+	0.179141i
$870$	14.7796	−	14.6150i	0.501076	−	0.495496i
$871$	−0.945739	−	3.52955i	−0.0320452	−	0.119594i
$872$	−48.7297	+	4.94578i	−1.65020	+	0.167485i
$873$	40.4555	−	15.1215i	1.36921	−	0.511786i
$874$	0.583788	+	0.649917i	0.0197469	+	0.0219838i
$875$	−6.42549	+	30.6252i	−0.217221	+	1.03532i
$876$	−12.2838	−	18.1357i	−0.415033	−	0.612748i
$877$	−3.65828	+	4.76757i	−0.123531	+	0.160989i	−0.851025	−	0.525125i	$-0.824018\pi$
$877$	−3.65828	+	4.76757i	−0.123531	+	0.160989i	0.727494	+	0.686115i	$0.240685\pi$
$878$	−8.71092	+	46.6896i	−0.293979	+	1.57570i
$879$	−1.41405	−	0.307086i	−0.0476946	−	0.0103578i
$880$	14.3033	+	7.37392i	0.482164	+	0.248575i
$881$	−14.8140			−0.499095			−0.249548	−	0.968363i	$-0.580282\pi$
$881$	−14.8140			−0.499095			−0.249548	+	0.968363i	$0.580282\pi$
$882$	−21.4452	−	20.5452i	−0.722096	−	0.691792i
$883$	−28.7946	+	11.9271i	−0.969015	+	0.401379i	−0.810345	−	0.585953i	$-0.800721\pi$
$883$	−28.7946	+	11.9271i	−0.969015	+	0.401379i	−0.158670	+	0.987332i	$0.550721\pi$
$884$	−3.07447	+	0.0731816i	−0.103405	+	0.00246136i
$885$	13.2517	−	19.1004i	0.445451	−	0.642053i
$886$	39.0404	−	8.24973i	1.31159	−	0.277155i
$887$	2.46729	+	0.661109i	0.0828436	+	0.0221979i	0.300003	−	0.953938i	$-0.403012\pi$
$887$	2.46729	+	0.661109i	0.0828436	+	0.0221979i	−0.217159	+	0.976136i	$0.569679\pi$
$888$	11.4325	−	6.88095i	0.383650	−	0.230910i
$889$	−6.73286	+	9.85175i	−0.225813	+	0.330417i
$890$	1.85216	−	34.5540i	0.0620845	−	1.15825i
$891$	−3.48859	+	17.1311i	−0.116872	+	0.573913i
$892$	−2.43812	−	15.6346i	−0.0816344	−	0.523485i
$893$	−5.69777	−	0.750126i	−0.190669	−	0.0251020i
$894$	−43.4325	+	17.7061i	−1.45260	+	0.592180i
$895$			42.4039i			1.41741i
$896$	29.8828	+	1.73713i	0.998315	+	0.0580333i
$897$	−0.0428033	−	0.133738i	−0.00142916	−	0.00446539i
$898$	3.49862	+	45.1413i	0.116750	+	1.50638i
$899$	−4.16431	+	31.6311i	−0.138887	+	1.05495i
$900$	3.04911	−	2.98157i	0.101637	−	0.0993856i
$901$	34.9127	−	4.59635i	1.16311	−	0.153126i
$902$	0.442720	+	0.0237306i	0.0147410	+	0.000790142i
$903$	−5.66996	+	5.36145i	−0.188684	+	0.178418i
$904$	−32.7064	+	7.72865i	−1.08780	+	0.257051i
$905$	4.60061	−	17.1697i	0.152929	−	0.570740i
$906$	−17.9693	+	10.2409i	−0.596991	+	0.340230i
$907$	−3.91191	−	5.09810i	−0.129893	−	0.169280i	0.723879	−	0.689927i	$-0.242357\pi$
$907$	−3.91191	−	5.09810i	−0.129893	−	0.169280i	−0.853772	+	0.520647i	$0.825691\pi$
$908$	−0.572199	−	24.0389i	−0.0189891	−	0.797759i
$909$	24.5218	−	39.2352i	0.813338	−	1.30135i
$910$	−4.21974	+	0.00606852i	−0.139883	+	0.000201169i
$911$			47.0721i			1.55957i	0.626047	+	0.779785i	$0.284672\pi$
$911$			47.0721i			1.55957i	−0.626047	+	0.779785i	$0.715328\pi$
$912$	−28.3502	−	4.75716i	−0.938770	−	0.157525i
$913$	2.51173	+	1.45015i	0.0831263	+	0.0479930i
$914$	5.94756	+	1.10964i	0.196728	+	0.0367037i
$915$	−15.7720	+	43.9223i	−0.521405	+	1.45203i
$916$	5.30100	−	1.55651i	0.175150	−	0.0514284i
$917$	1.75998	+	5.36859i	0.0581196	+	0.177287i
$918$	1.87129	+	20.6659i	0.0617617	+	0.682075i
$919$	−7.00229	+	26.1329i	−0.230984	+	0.862045i	0.748934	+	0.662645i	$0.230566\pi$
$919$	−7.00229	+	26.1329i	−0.230984	+	0.862045i	−0.979918	+	0.199400i	$0.936101\pi$
$920$	0.0880620	+	0.867657i	0.00290332	+	0.0286058i
$921$	35.7113	−	22.9680i	1.17673	−	0.756822i
$922$	39.5967	−	20.1162i	1.30405	−	0.662491i
$923$	−1.90327	+	4.59490i	−0.0626469	+	0.151243i
$924$	16.4765	−	6.74460i	0.542037	−	0.221881i
$925$	−1.78857	+	0.740852i	−0.0588080	+	0.0243591i
$926$	−11.8501	+	0.918430i	−0.389419	+	0.0301815i
$927$	28.6287	−	2.75402i	0.940291	−	0.0904539i
$928$	16.2912	+	16.4864i	0.534785	+	0.541191i
$929$	−5.95992	+	3.44096i	−0.195539	+	0.112894i	−0.594573	−	0.804042i	$-0.702679\pi$
$929$	−5.95992	+	3.44096i	−0.195539	+	0.112894i	0.399034	+	0.916936i	$0.369345\pi$
$930$	5.37522	−	39.1343i	0.176260	−	1.28326i
$931$	8.10255	−	27.8914i	0.265550	−	0.914104i
$932$	5.25055	−	48.8366i	0.171987	−	1.59970i
$933$	−17.2144	−	36.5040i	−0.563573	−	1.19509i
$934$	−23.0828	+	35.4518i	−0.755291	+	1.16002i
$935$	10.9731	−	2.94023i	0.358859	−	0.0961559i
$936$	3.84369	+	2.56438i	0.125635	+	0.0838193i
$937$	−26.6142	+	26.6142i	−0.869449	+	0.869449i	−0.992411	−	0.122962i	$-0.960761\pi$
$937$	−26.6142	+	26.6142i	−0.869449	+	0.869449i	0.122962	+	0.992411i	$0.460761\pi$
$938$	19.9412	+	15.2559i	0.651104	+	0.498124i
$939$	2.42639	−	29.1847i	0.0791822	−	0.952406i
$940$	−4.15211	−	3.95904i	−0.135427	−	0.129130i
$941$	−4.80877	+	36.5262i	−0.156761	+	1.19072i	0.714405	+	0.699732i	$0.246697\pi$
$941$	−4.80877	+	36.5262i	−0.156761	+	1.19072i	−0.871166	+	0.490988i	$0.836636\pi$
$942$	−6.47701	−	51.4211i	−0.211033	−	1.67539i
$943$	0.0120138	+	0.0208085i	0.000391223	+	0.000677618i
$944$	21.2934	+	14.7844i	0.693041	+	0.481190i
$945$	1.93300	+	28.4065i	0.0628804	+	0.924063i
$946$	−1.55628	−	4.41150i	−0.0505992	−	0.143430i
$947$	34.4949	−	44.9546i	1.12093	−	1.46083i	0.250781	−	0.968044i	$-0.419313\pi$
$947$	34.4949	−	44.9546i	1.12093	−	1.46083i	0.870152	−	0.492784i	$-0.164021\pi$
$948$	−18.6037	−	16.1088i	−0.604221	−	0.523191i
$949$	−2.73172	+	2.09613i	−0.0886755	+	0.0680431i
$950$	3.96502	+	1.29354i	0.128642	+	0.0419678i
$951$	−26.2677	+	50.9962i	−0.851788	+	1.65366i
$952$	16.4346	−	13.2828i	0.532647	−	0.430498i
$953$	13.2065	−	13.2065i	0.427800	−	0.427800i	−0.460078	−	0.887878i	$-0.652179\pi$
$953$	13.2065	−	13.2065i	0.427800	−	0.427800i	0.887878	+	0.460078i	$0.152179\pi$
$954$	−46.8986	−	24.4903i	−1.51840	−	0.792902i
$955$	8.78755	−	6.74292i	0.284358	−	0.218196i
$956$	0.289417	+	1.85590i	0.00936040	+	0.0600240i
$957$	12.9743	+	4.65892i	0.419400	+	0.150601i
$958$	13.7621	−	28.7646i	0.444633	−	0.929344i
$959$	−37.7731	−	13.2645i	−1.21976	−	0.428334i
$960$	−20.0563	−	20.5251i	−0.647313	−	0.662445i
$961$	14.8160	+	25.6620i	0.477935	+	0.827807i
$962$	−1.18601	−	1.73006i	−0.0382384	−	0.0557793i
$963$	21.7795	+	40.9703i	0.701836	+	1.32025i
$964$	1.49165	+	0.576670i	0.0480428	+	0.0185733i
$965$	6.39950	+	2.65076i	0.206007	+	0.0853310i
$966$	0.793538	+	0.548861i	0.0255317	+	0.0176593i
$967$	36.7938	−	36.7938i	1.18321	−	1.18321i	0.204299	−	0.978909i	$-0.434509\pi$
$967$	36.7938	−	36.7938i	1.18321	−	1.18321i	0.978909	−	0.204299i	$-0.0654914\pi$
$968$	0.608040	−	20.4309i	0.0195432	−	0.656674i
$969$	−17.0681	+	10.9775i	−0.548306	+	0.352647i
$970$	8.71761	+	41.2546i	0.279906	+	1.32461i
$971$	4.60066	+	34.9455i	0.147642	+	1.12145i	0.891469	+	0.453081i	$0.149675\pi$
$971$	4.60066	+	34.9455i	0.147642	+	1.12145i	−0.743827	+	0.668372i	$0.766991\pi$
$972$	15.5410	−	27.0273i	0.498479	−	0.866902i
$973$	20.2965	−	13.2567i	0.650676	−	0.424990i
$974$	−12.9219	−	36.6289i	−0.414044	−	1.17366i
$975$	−0.496206	−	0.450763i	−0.0158913	−	0.0144360i
$976$	−48.9710	−	17.6045i	−1.56752	−	0.563506i
$977$	−27.1093	+	46.9547i	−0.867304	+	1.50221i	−0.00256301	+	0.999997i	$0.500816\pi$
$977$	−27.1093	+	46.9547i	−0.867304	+	1.50221i	−0.864741	+	0.502218i	$0.832517\pi$
$978$	16.7973	−	39.9185i	0.537117	−	1.27645i
$979$	21.2030	−	8.78259i	0.677652	−	0.280693i
$980$	22.9521	−	17.7169i	0.733179	−	0.565946i
$981$	50.6208	−	11.6819i	1.61620	−	0.372974i
$982$	−25.4534	−	8.30384i	−0.812252	−	0.264986i
$983$	4.84018	+	18.0638i	0.154378	+	0.576146i	0.999158	+	0.0410319i	$0.0130645\pi$
$983$	4.84018	+	18.0638i	0.154378	+	0.576146i	−0.844780	+	0.535114i	$0.820269\pi$
$984$	−0.735838	−	0.289220i	−0.0234577	−	0.00922001i
$985$	3.55466	−	13.2662i	0.113261	−	0.422696i
$986$	16.3387	+	0.875782i	0.520329	+	0.0278906i
$987$	−6.31357	+	0.652225i	−0.200963	+	0.0207605i
$988$	−0.483050	+	4.49296i	−0.0153679	+	0.142940i
$989$	0.154334	−	0.201132i	0.00490754	−	0.00639563i
$990$	−16.0315	−	5.85827i	−0.509515	−	0.186188i
$991$	29.9105	+	17.2688i	0.950137	+	0.548562i	0.893124	−	0.449811i	$-0.148509\pi$
$991$	29.9105	+	17.2688i	0.950137	+	0.548562i	0.0570137	+	0.998373i	$0.481842\pi$
$992$	43.6361	+	6.00931i	1.38545	+	0.190796i
$993$	−28.0369	+	8.97330i	−0.889726	+	0.284759i
$994$	−8.89227	−	32.9965i	−0.282046	−	1.04659i
$995$	11.1567	−	4.62128i	0.353693	−	0.146504i
$996$	−3.43464	−	3.86704i	−0.108831	−	0.122532i
$997$	−1.80764	−	2.35576i	−0.0572486	−	0.0746078i	0.763852	−	0.645392i	$-0.223306\pi$
$997$	−1.80764	−	2.35576i	−0.0572486	−	0.0746078i	−0.821100	+	0.570784i	$0.806639\pi$
$998$	−21.7031	−	14.1309i	−0.686998	−	0.447306i
$999$	−11.1157	+	8.76049i	−0.351686	+	0.277170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.ch.a.11.4	✓	992
3.2	odd	2	inner	672.2.ch.a.11.121	yes	992
7.2	even	3	inner	672.2.ch.a.107.86	yes	992
21.2	odd	6	inner	672.2.ch.a.107.39	yes	992
32.3	odd	8	inner	672.2.ch.a.515.39	yes	992
96.35	even	8	inner	672.2.ch.a.515.86	yes	992
224.163	odd	24	inner	672.2.ch.a.611.121	yes	992
672.611	even	24	inner	672.2.ch.a.611.4	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.ch.a.11.4	✓	992	1.1	even	1	trivial
672.2.ch.a.11.121	yes	992	3.2	odd	2	inner
672.2.ch.a.107.39	yes	992	21.2	odd	6	inner
672.2.ch.a.107.86	yes	992	7.2	even	3	inner
672.2.ch.a.515.39	yes	992	32.3	odd	8	inner
672.2.ch.a.515.86	yes	992	96.35	even	8	inner
672.2.ch.a.611.4	yes	992	672.611	even	24	inner
672.2.ch.a.611.121	yes	992	224.163	odd	24	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.ch (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40999 + 0.109279i) q^{2} +(1.70442 - 0.308130i) q^{3} +(1.97612 - 0.308164i) q^{4} +(-0.270326 - 2.05333i) q^{5} +(-2.36954 + 0.620717i) q^{6} +(-2.18436 - 1.49283i) q^{7} +(-2.75262 + 0.650455i) q^{8} +(2.81011 - 1.05037i) q^{9} +O(q^{10})\)	\(q+(-1.40999 + 0.109279i) q^{2} +(1.70442 - 0.308130i) q^{3} +(1.97612 - 0.308164i) q^{4} +(-0.270326 - 2.05333i) q^{5} +(-2.36954 + 0.620717i) q^{6} +(-2.18436 - 1.49283i) q^{7} +(-2.75262 + 0.650455i) q^{8} +(2.81011 - 1.05037i) q^{9} +(0.605541 + 2.86562i) q^{10} +(-1.54111 + 1.18253i) q^{11} +(3.27318 - 1.13414i) q^{12} +(-0.208388 - 0.503093i) q^{13} +(3.24306 + 1.86617i) q^{14} +(-1.09344 - 3.41644i) q^{15} +(3.81007 - 1.21794i) q^{16} +(1.41189 - 2.44546i) q^{17} +(-3.84743 + 1.78809i) q^{18} +(-3.29179 - 2.52588i) q^{19} +(-1.16696 - 3.97431i) q^{20} +(-4.18307 - 1.87135i) q^{21} +(2.04371 - 1.83576i) q^{22} +(0.143808 + 0.0385332i) q^{23} +(-4.49120 + 1.95681i) q^{24} +(0.686548 - 0.183960i) q^{25} +(0.348801 + 0.686581i) q^{26} +(4.46597 - 2.65615i) q^{27} +(-4.77660 - 2.27687i) q^{28} +(-1.56796 - 3.78538i) q^{29} +(1.91508 + 4.69764i) q^{30} +(-6.74344 - 3.89333i) q^{31} +(-5.23905 + 2.13363i) q^{32} +(-2.26232 + 2.49040i) q^{33} +(-1.72350 + 3.60235i) q^{34} +(-2.47479 + 4.88877i) q^{35} +(5.22942 - 2.94162i) q^{36} +(-2.70043 + 0.355519i) q^{37} +(4.91740 + 3.20173i) q^{38} +(-0.510199 - 0.793272i) q^{39} +(2.07970 + 5.47620i) q^{40} +(0.114119 + 0.114119i) q^{41} +(6.10256 + 2.18145i) q^{42} +(0.651652 - 1.57323i) q^{43} +(-2.68099 + 2.81173i) q^{44} +(-2.91640 - 5.48614i) q^{45} +(-0.206978 - 0.0386160i) q^{46} +(1.19950 - 0.692533i) q^{47} +(6.11869 - 3.24987i) q^{48} +(2.54290 + 6.52178i) q^{49} +(-0.947919 + 0.334406i) q^{50} +(1.65293 - 4.60314i) q^{51} +(-0.566833 - 0.929952i) q^{52} +(7.59158 + 9.89354i) q^{53} +(-6.00669 + 4.23317i) q^{54} +(2.84473 + 2.84473i) q^{55} +(6.98374 + 2.68837i) q^{56} +(-6.38890 - 3.29087i) q^{57} +(2.62446 + 5.16599i) q^{58} +(3.94519 + 5.14147i) q^{59} +(-3.21359 - 6.41433i) q^{60} +(-10.3214 - 7.91987i) q^{61} +(9.93361 + 4.75261i) q^{62} +(-7.70633 - 1.90064i) q^{63} +(7.15382 - 3.58091i) q^{64} +(-0.976682 + 0.563887i) q^{65} +(2.91769 - 3.75864i) q^{66} +(6.65290 + 0.875872i) q^{67} +(2.03645 - 5.26761i) q^{68} +(0.256982 + 0.0213653i) q^{69} +(2.95517 - 7.16353i) q^{70} +(-6.45823 - 6.45823i) q^{71} +(-7.05195 + 4.71911i) q^{72} +(-1.63657 - 6.10775i) q^{73} +(3.76872 - 0.796377i) q^{74} +(1.11348 - 0.525091i) q^{75} +(-7.28335 - 3.97702i) q^{76} +(5.13166 - 0.282468i) q^{77} +(0.806061 + 1.06275i) q^{78} +(-3.55198 - 6.15220i) q^{79} +(-3.53078 - 7.49409i) q^{80} +(6.79345 - 5.90330i) q^{81} +(-0.173376 - 0.148435i) q^{82} +(-0.571369 - 1.37941i) q^{83} +(-8.84291 - 2.40893i) q^{84} +(-5.40300 - 2.23800i) q^{85} +(-0.746899 + 2.28944i) q^{86} +(-3.83885 - 5.96876i) q^{87} +(3.47289 - 4.25748i) q^{88} +(-11.4120 - 3.05783i) q^{89} +(4.71160 + 7.41668i) q^{90} +(-0.295838 + 1.41003i) q^{91} +(0.296055 + 0.0318297i) q^{92} +(-12.6933 - 4.55802i) q^{93} +(-1.61560 + 1.10754i) q^{94} +(-4.29661 + 7.44194i) q^{95} +(-8.27211 + 5.25092i) q^{96} +14.3964 q^{97} +(-4.29815 - 8.91773i) q^{98} +(-3.08859 + 4.94177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9	\( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} + 24 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 44 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} - 36 q^{30} - 8 q^{33} + 64 q^{36} - 8 q^{37} - 4 q^{39} - 72 q^{40} - 68 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 20 q^{51} + 16 q^{52} - 92 q^{54} - 32 q^{55} - 16 q^{57} + 24 q^{58} - 20 q^{60} - 8 q^{61} - 128 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 16 q^{75} - 32 q^{76} + 136 q^{78} - 16 q^{79} - 48 q^{82} + 124 q^{84} + 48 q^{85} - 4 q^{87} - 8 q^{88} + 128 q^{90} - 64 q^{91} - 28 q^{93} - 64 q^{94} - 72 q^{96} - 64 q^{97} - 16 q^{99}+O(q^{100}) \) 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 - 32 * q^13 - 32 * q^15 + 24 * q^16 - 4 * q^18 - 8 * q^19 - 8 * q^21 - 32 * q^22 - 44 * q^24 - 8 * q^25 - 16 * q^27 - 16 * q^28 - 36 * q^30 - 8 * q^33 + 64 * q^36 - 8 * q^37 - 4 * q^39 - 72 * q^40 - 68 * q^42 - 32 * q^43 - 4 * q^45 - 8 * q^46 - 16 * q^48 + 20 * q^51 + 16 * q^52 - 92 * q^54 - 32 * q^55 - 16 * q^57 + 24 * q^58 - 20 * q^60 - 8 * q^61 - 128 * q^64 - 20 * q^66 - 72 * q^67 - 16 * q^69 - 16 * q^70 - 4 * q^72 - 8 * q^73 + 16 * q^75 - 32 * q^76 + 136 * q^78 - 16 * q^79 - 48 * q^82 + 124 * q^84 + 48 * q^85 - 4 * q^87 - 8 * q^88 + 128 * q^90 - 64 * q^91 - 28 * q^93 - 64 * q^94 - 72 * q^96 - 64 * q^97 - 16 * q^99

Introduction

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