LMFDB - Embedded newform 380.2.bb.a.219.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			219.12
Character	$\chi$	$=$	380.219
Dual form			380.2.bb.a.59.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05231 + 0.944795i) q^{2} +(-0.108582 - 0.129403i) q^{3} +(0.214726 - 1.98844i) q^{4} +(2.23516 - 0.0637665i) q^{5} +(0.236522 + 0.0335848i) q^{6} +(0.176277 - 0.305321i) q^{7} +(1.65271 + 2.29533i) q^{8} +(0.515989 - 2.92632i) q^{9} +O(q^{10})$	\(q+(-1.05231 + 0.944795i) q^{2} +(-0.108582 - 0.129403i) q^{3} +(0.214726 - 1.98844i) q^{4} +(2.23516 - 0.0637665i) q^{5} +(0.236522 + 0.0335848i) q^{6} +(0.176277 - 0.305321i) q^{7} +(1.65271 + 2.29533i) q^{8} +(0.515989 - 2.92632i) q^{9} +(-2.29184 + 2.17887i) q^{10} +(0.465827 - 0.268946i) q^{11} +(-0.280626 + 0.188123i) q^{12} +(-2.90974 - 2.44156i) q^{13} +(0.102967 + 0.487839i) q^{14} +(-0.250950 - 0.282313i) q^{15} +(-3.90779 - 0.853938i) q^{16} +(-1.16250 + 0.204980i) q^{17} +(2.22179 + 3.56691i) q^{18} +(1.57208 - 4.06553i) q^{19} +(0.353150 - 4.45817i) q^{20} +(-0.0586501 + 0.0103416i) q^{21} +(-0.236098 + 0.723126i) q^{22} +(5.38963 - 1.96166i) q^{23} +(0.117569 - 0.463098i) q^{24} +(4.99187 - 0.285056i) q^{25} +(5.36874 - 0.179820i) q^{26} +(-0.873580 + 0.504362i) q^{27} +(-0.569262 - 0.416077i) q^{28} +(2.19146 + 0.386413i) q^{29} +(0.530806 + 0.0599852i) q^{30} +(-3.30786 + 5.72938i) q^{31} +(4.91901 - 2.79345i) q^{32} +(-0.0853830 - 0.0310769i) q^{33} +(1.02965 - 1.31403i) q^{34} +(0.374538 - 0.693682i) q^{35} +(-5.70802 - 1.65437i) q^{36} +0.773573 q^{37} +(2.18677 + 5.76351i) q^{38} +0.641641i q^{39} +(3.84043 + 5.02505i) q^{40} +(-2.78057 - 3.31376i) q^{41} +(0.0519476 - 0.0662949i) q^{42} +(10.6401 + 3.87268i) q^{43} +(-0.434757 - 0.984019i) q^{44} +(0.966717 - 6.57370i) q^{45} +(-3.81820 + 7.15637i) q^{46} +(0.460262 - 2.61027i) q^{47} +(0.313814 + 0.598403i) q^{48} +(3.43785 + 5.95454i) q^{49} +(-4.98369 + 5.01626i) q^{50} +(0.152752 + 0.128174i) q^{51} +(-5.47970 + 5.26158i) q^{52} +(4.14817 - 1.50981i) q^{53} +(0.442761 - 1.35610i) q^{54} +(1.02405 - 0.630840i) q^{55} +(0.992149 - 0.0999921i) q^{56} +(-0.696793 + 0.238012i) q^{57} +(-2.67118 + 1.66385i) q^{58} +(0.583091 + 3.30687i) q^{59} +(-0.615247 + 0.438379i) q^{60} +(-6.49253 + 2.36309i) q^{61} +(-1.93219 - 9.15436i) q^{62} +(-0.802511 - 0.673386i) q^{63} +(-2.53711 + 7.58703i) q^{64} +(-6.65943 - 5.27174i) q^{65} +(0.119211 - 0.0479668i) q^{66} +(-6.98470 - 1.23159i) q^{67} +(0.157972 + 2.35557i) q^{68} +(-0.839063 - 0.484433i) q^{69} +(0.261255 + 1.08383i) q^{70} +(6.72322 + 2.44705i) q^{71} +(7.56966 - 3.65199i) q^{72} +(-7.32925 - 8.73466i) q^{73} +(-0.814041 + 0.730868i) q^{74} +(-0.578915 - 0.615012i) q^{75} +(-7.74650 - 3.99897i) q^{76} -0.189636i q^{77} +(-0.606219 - 0.675207i) q^{78} +(-5.66076 + 4.74994i) q^{79} +(-8.78897 - 1.65950i) q^{80} +(-8.21667 - 2.99062i) q^{81} +(6.05686 + 0.860040i) q^{82} +(-0.764089 + 1.32344i) q^{83} +(0.00796996 + 0.118843i) q^{84} +(-2.58530 + 0.532291i) q^{85} +(-14.8556 + 5.97744i) q^{86} +(-0.187950 - 0.325540i) q^{87} +(1.38720 + 0.624740i) q^{88} +(3.25011 - 3.87334i) q^{89} +(5.19350 + 7.83093i) q^{90} +(-1.25838 + 0.458014i) q^{91} +(-2.74336 - 11.1382i) q^{92} +(1.10058 - 0.194061i) q^{93} +(1.98183 + 3.18168i) q^{94} +(3.25461 - 9.18736i) q^{95} +(-0.895598 - 0.333217i) q^{96} +(2.09122 + 11.8599i) q^{97} +(-9.24351 - 3.01797i) q^{98} +(-0.546659 - 1.50193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.05231	+	0.944795i	−0.744098	+	0.668071i
$2$	−1.05231	+	0.944795i	−0.744098	+	0.668071i
$3$	−0.108582	−	0.129403i	−0.0626900	−	0.0747110i	0.733788	−	0.679378i	$-0.237750\pi$
$3$	−0.108582	−	0.129403i	−0.0626900	−	0.0747110i	−0.796478	+	0.604667i	$0.793306\pi$
$4$	0.214726	−	1.98844i	0.107363	−	0.994220i
$5$	2.23516	−	0.0637665i	0.999593	−	0.0285172i
$5$	2.23516	−	0.0637665i	0.999593	−	0.0285172i
$6$	0.236522	+	0.0335848i	0.0965597	+	0.0137109i
$7$	0.176277	−	0.305321i	0.0666265	−	0.115401i	−0.830788	−	0.556589i	$-0.812110\pi$
$7$	0.176277	−	0.305321i	0.0666265	−	0.115401i	0.897414	+	0.441189i	$0.145443\pi$
$8$	1.65271	+	2.29533i	0.584321	+	0.811523i
$9$	0.515989	−	2.92632i	0.171996	−	0.975440i
$10$	−2.29184	+	2.17887i	−0.724744	+	0.689019i
$11$	0.465827	−	0.268946i	0.140452	−	0.0810901i	−0.428127	−	0.903718i	$-0.640827\pi$
$11$	0.465827	−	0.268946i	0.140452	−	0.0810901i	0.568579	+	0.822628i	$0.307493\pi$
$12$	−0.280626	+	0.188123i	−0.0810097	+	0.0543064i
$13$	−2.90974	−	2.44156i	−0.807018	−	0.677168i	0.142876	−	0.989741i	$-0.454365\pi$
$13$	−2.90974	−	2.44156i	−0.807018	−	0.677168i	−0.949894	+	0.312572i	$0.898809\pi$
$14$	0.102967	+	0.487839i	0.0275191	+	0.130381i
$15$	−0.250950	−	0.282313i	−0.0647950	−	0.0728929i
$16$	−3.90779	−	0.853938i	−0.976946	−	0.213484i
$17$	−1.16250	+	0.204980i	−0.281947	+	0.0497149i	−0.312833	−	0.949808i	$-0.601278\pi$
$17$	−1.16250	+	0.204980i	−0.281947	+	0.0497149i	0.0308862	+	0.999523i	$0.490167\pi$
$18$	2.22179	+	3.56691i	0.523681	+	0.840729i
$19$	1.57208	−	4.06553i	0.360661	−	0.932697i
$19$	1.57208	−	4.06553i	0.360661	−	0.932697i
$20$	0.353150	−	4.45817i	0.0789667	−	0.996877i
$21$	−0.0586501	+	0.0103416i	−0.0127985	+	0.00225672i
$22$	−0.236098	+	0.723126i	−0.0503362	+	0.154171i
$23$	5.38963	−	1.96166i	1.12381	−	0.409035i	0.287772	−	0.957699i	$-0.407086\pi$
$23$	5.38963	−	1.96166i	1.12381	−	0.409035i	0.836043	+	0.548664i	$0.184863\pi$
$24$	0.117569	−	0.463098i	0.0239986	−	0.0945295i
$25$	4.99187	−	0.285056i	0.998374	−	0.0570113i
$26$	5.36874	−	0.179820i	1.05290	−	0.0352656i
$27$	−0.873580	+	0.504362i	−0.168121	+	0.0970644i
$28$	−0.569262	−	0.416077i	−0.107580	−	0.0786312i
$29$	2.19146	+	0.386413i	0.406944	+	0.0717552i	0.373373	−	0.927681i	$-0.378201\pi$
$29$	2.19146	+	0.386413i	0.406944	+	0.0717552i	0.0335705	+	0.999436i	$0.489312\pi$
$30$	0.530806	+	0.0599852i	0.0969114	+	0.0109517i
$31$	−3.30786	+	5.72938i	−0.594110	+	1.02903i	0.399562	+	0.916706i	$0.369162\pi$
$31$	−3.30786	+	5.72938i	−0.594110	+	1.02903i	−0.993672	+	0.112322i	$0.964171\pi$
$32$	4.91901	−	2.79345i	0.869566	−	0.493816i
$33$	−0.0853830	−	0.0310769i	−0.0148633	−	0.00540979i
$34$	1.02965	−	1.31403i	0.176583	−	0.225353i
$35$	0.374538	−	0.693682i	0.0633085	−	0.117254i
$36$	−5.70802	−	1.65437i	−0.951336	−	0.275728i
$37$	0.773573			0.127175			0.0635873	−	0.997976i	$-0.479746\pi$
$37$	0.773573			0.127175			0.0635873	+	0.997976i	$0.479746\pi$
$38$	2.18677	+	5.76351i	0.354741	+	0.934965i
$39$			0.641641i			0.102745i
$40$	3.84043	+	5.02505i	0.607226	+	0.794529i
$41$	−2.78057	−	3.31376i	−0.434253	−	0.517522i	0.503891	−	0.863767i	$-0.331901\pi$
$41$	−2.78057	−	3.31376i	−0.434253	−	0.517522i	−0.938144	+	0.346245i	$0.887457\pi$
$42$	0.0519476	−	0.0662949i	0.00801569	−	0.0102295i
$43$	10.6401	+	3.87268i	1.62260	+	0.590578i	0.983875	−	0.178858i	$-0.0572402\pi$
$43$	10.6401	+	3.87268i	1.62260	+	0.590578i	0.638724	+	0.769436i	$0.279462\pi$
$44$	−0.434757	−	0.984019i	−0.0655421	−	0.148346i
$45$	0.966717	−	6.57370i	0.144110	−	0.979949i
$46$	−3.81820	+	7.15637i	−0.562963	+	1.05515i
$47$	0.460262	−	2.61027i	0.0671361	−	0.380748i	−0.932664	−	0.360747i	$-0.882522\pi$
$47$	0.460262	−	2.61027i	0.0671361	−	0.380748i	0.999800	−	0.0200010i	$-0.00636694\pi$
$48$	0.313814	+	0.598403i	0.0452951	+	0.0863720i
$49$	3.43785	+	5.95454i	0.491122	+	0.850648i
$50$	−4.98369	+	5.01626i	−0.704800	+	0.709406i
$51$	0.152752	+	0.128174i	0.0213895	+	0.0179479i
$52$	−5.47970	+	5.26158i	−0.759898	+	0.729650i
$53$	4.14817	−	1.50981i	0.569796	−	0.207389i	−0.0410244	−	0.999158i	$-0.513062\pi$
$53$	4.14817	−	1.50981i	0.569796	−	0.207389i	0.610820	+	0.791770i	$0.290840\pi$
$54$	0.442761	−	1.35610i	0.0602522	−	0.184542i
$55$	1.02405	−	0.630840i	0.138083	−	0.0850625i
$56$	0.992149	−	0.0999921i	0.132581	−	0.0133620i
$57$	−0.696793	+	0.238012i	−0.0922925	+	0.0315254i
$58$	−2.67118	+	1.66385i	−0.350743	+	0.218474i
$59$	0.583091	+	3.30687i	0.0759120	+	0.430518i	0.998950	+	0.0458100i	$0.0145869\pi$
$59$	0.583091	+	3.30687i	0.0759120	+	0.430518i	−0.923038	+	0.384708i	$0.874302\pi$
$60$	−0.615247	+	0.438379i	−0.0794281	+	0.0565945i
$61$	−6.49253	+	2.36309i	−0.831283	+	0.302562i	−0.722386	−	0.691491i	$-0.756954\pi$
$61$	−6.49253	+	2.36309i	−0.831283	+	0.302562i	−0.108898	+	0.994053i	$0.534732\pi$
$62$	−1.93219	−	9.15436i	−0.245388	−	1.16260i
$63$	−0.802511	−	0.673386i	−0.101107	−	0.0848387i
$64$	−2.53711	+	7.58703i	−0.317138	+	0.948379i
$65$	−6.65943	−	5.27174i	−0.826000	−	0.653879i
$66$	0.119211	−	0.0479668i	0.0146738	−	0.00590431i
$67$	−6.98470	−	1.23159i	−0.853317	−	0.150463i	−0.270153	−	0.962817i	$-0.587074\pi$
$67$	−6.98470	−	1.23159i	−0.853317	−	0.150463i	−0.583164	+	0.812355i	$0.698185\pi$
$68$	0.157972	+	2.35557i	0.0191569	+	0.285655i
$69$	−0.839063	−	0.484433i	−0.101011	−	0.0583189i
$70$	0.261255	+	1.08383i	0.0312260	+	0.129543i
$71$	6.72322	+	2.44705i	0.797899	+	0.290412i	0.708616	−	0.705595i	$-0.249320\pi$
$71$	6.72322	+	2.44705i	0.797899	+	0.290412i	0.0892837	+	0.996006i	$0.471542\pi$
$72$	7.56966	−	3.65199i	0.892093	−	0.430391i
$73$	−7.32925	−	8.73466i	−0.857823	−	1.02231i	−0.999475	−	0.0323977i	$-0.989686\pi$
$73$	−7.32925	−	8.73466i	−0.857823	−	1.02231i	0.141652	−	0.989917i	$-0.454759\pi$
$74$	−0.814041	+	0.730868i	−0.0946304	+	0.0849617i
$75$	−0.578915	−	0.615012i	−0.0668474	−	0.0710154i
$76$	−7.74650	−	3.99897i	−0.888585	−	0.458713i
$77$		−	0.189636i		−	0.0216110i
$78$	−0.606219	−	0.675207i	−0.0686408	−	0.0764521i
$79$	−5.66076	+	4.74994i	−0.636885	+	0.534410i	−0.903060	−	0.429515i	$-0.858685\pi$
$79$	−5.66076	+	4.74994i	−0.636885	+	0.534410i	0.266175	+	0.963925i	$0.414240\pi$
$80$	−8.78897	−	1.65950i	−0.982637	−	0.185538i
$81$	−8.21667	−	2.99062i	−0.912963	−	0.332291i
$82$	6.05686	+	0.860040i	0.668868	+	0.0949756i
$83$	−0.764089	+	1.32344i	−0.0838696	+	0.145266i	−0.904909	−	0.425605i	$-0.860061\pi$
$83$	−0.764089	+	1.32344i	−0.0838696	+	0.145266i	0.821039	+	0.570872i	$0.193395\pi$
$84$	0.00796996	+	0.118843i	0.000869594	+	0.0129668i
$85$	−2.58530	+	0.532291i	−0.280415	+	0.0577350i
$86$	−14.8556	+	5.97744i	−1.60192	+	0.644564i
$87$	−0.187950	−	0.325540i	−0.0201504	−	0.0349015i
$88$	1.38720	+	0.624740i	0.147876	+	0.0665975i
$89$	3.25011	−	3.87334i	0.344511	−	0.410573i	−0.565770	−	0.824563i	$-0.691421\pi$
$89$	3.25011	−	3.87334i	0.344511	−	0.410573i	0.910281	+	0.413991i	$0.135865\pi$
$90$	5.19350	+	7.83093i	0.547443	+	0.825453i
$91$	−1.25838	+	0.458014i	−0.131914	+	0.0480129i
$92$	−2.74336	−	11.1382i	−0.286015	−	1.16123i
$93$	1.10058	−	0.194061i	0.114124	−	0.0201232i
$94$	1.98183	+	3.18168i	0.204411	+	0.328165i
$95$	3.25461	−	9.18736i	0.333916	−	0.942603i
$96$	−0.895598	−	0.333217i	−0.0914066	−	0.0340088i
$97$	2.09122	+	11.8599i	0.212331	+	1.20419i	0.885478	+	0.464680i	$0.153831\pi$
$97$	2.09122	+	11.8599i	0.212331	+	1.20419i	−0.673147	+	0.739508i	$0.735058\pi$
$98$	−9.24351	−	3.01797i	−0.933736	−	0.304861i
$99$	−0.546659	−	1.50193i	−0.0549413	−	0.150950i
$100$	0.505064	−	9.98724i	0.0505064	−	0.998724i
$101$	−6.10589	−	5.12345i	−0.607559	−	0.509803i	0.286306	−	0.958138i	$-0.407573\pi$
$101$	−6.10589	−	5.12345i	−0.607559	−	0.509803i	−0.893865	+	0.448336i	$0.852017\pi$
$102$	−0.281841	+	0.00943994i	−0.0279064	+	0.000934694i
$103$	−8.62565	+	4.98002i	−0.849911	+	0.490696i	−0.860621	−	0.509246i	$-0.829924\pi$
$103$	−8.62565	+	4.98002i	−0.849911	+	0.490696i	0.0107099	+	0.999943i	$0.496591\pi$
$104$	0.795244	−	10.7140i	0.0779801	−	1.05060i
$105$	−0.130433	+	0.0268550i	−0.0127289	+	0.00262078i
$106$	−2.93872	+	5.50797i	−0.285433	+	0.534981i
$107$	−9.83620	−	5.67893i	−0.950901	−	0.549003i	−0.0575406	−	0.998343i	$-0.518326\pi$
$107$	−9.83620	−	5.67893i	−0.950901	−	0.549003i	−0.893361	+	0.449340i	$0.851659\pi$
$108$	0.815313	+	1.84536i	0.0784535	+	0.177570i
$109$	−1.80107	+	4.94840i	−0.172511	+	0.473971i	−0.995574	−	0.0939794i	$-0.970041\pi$
$109$	−1.80107	+	4.94840i	−0.172511	+	0.473971i	0.823063	+	0.567950i	$0.192263\pi$
$110$	−0.481605	+	1.63136i	−0.0459192	+	0.155544i
$111$	−0.0839963	−	0.100103i	−0.00797257	−	0.00950134i
$112$	−0.949579	+	1.04260i	−0.0897268	+	0.0985164i
$113$	15.1869			1.42867			0.714333	−	0.699806i	$-0.246730\pi$
$113$	15.1869			1.42867			0.714333	+	0.699806i	$0.246730\pi$
$114$	0.508372	−	0.908790i	0.0476134	−	0.0851159i
$115$	11.9216	−	4.72831i	1.11169	−	0.440917i
$116$	1.23892	−	4.27461i	0.115031	−	0.396888i
$117$	−8.64620	+	7.25502i	−0.799341	+	0.670727i
$118$	−3.73791	−	2.92897i	−0.344103	−	0.269633i
$119$	−0.142337	+	0.391069i	−0.0130480	+	0.0358492i
$120$	0.233255	−	1.04259i	0.0212931	−	0.0951754i
$121$	−5.35534	+	9.27572i	−0.486849	+	0.843247i
$122$	4.59954	−	8.62082i	0.416423	−	0.780492i
$123$	−0.126890	+	0.719631i	−0.0114413	+	0.0648869i
$124$	10.6823	+	7.80773i	0.959295	+	0.701155i
$125$	11.1394	−	0.955460i	0.996342	−	0.0854589i
$126$	1.48070	−	0.0495946i	0.131912	−	0.00441824i
$127$	−10.1362	+	12.0799i	−0.899446	+	1.07192i	0.0976092	+	0.995225i	$0.468880\pi$
$127$	−10.1362	+	12.0799i	−0.899446	+	1.07192i	−0.997055	+	0.0766927i	$0.975564\pi$
$128$	−4.49836	−	10.3810i	−0.397603	−	0.917558i
$129$	−0.654188	−	1.79737i	−0.0575980	−	0.158249i
$130$	11.9885	−	0.744272i	1.05146	−	0.0652770i
$131$	−16.1902	+	2.85477i	−1.41455	+	0.249423i	−0.828107	−	0.560571i	$-0.810582\pi$
$131$	−16.1902	+	2.85477i	−1.41455	+	0.249423i	−0.586439	+	0.809993i	$0.699471\pi$
$132$	−0.0801284	+	0.163106i	−0.00697428	+	0.0141965i
$133$	−0.964171	−	1.19665i	−0.0836042	−	0.103763i
$134$	8.51369	−	5.30309i	0.735471	−	0.458117i
$135$	−1.92043	+	1.18303i	−0.165284	+	0.101819i
$136$	−2.39177	−	2.32955i	−0.205092	−	0.199757i
$137$	7.03395	+	19.3256i	0.600950	+	1.65110i	0.749353	+	0.662171i	$0.230365\pi$
$137$	7.03395	+	19.3256i	0.600950	+	1.65110i	−0.148402	+	0.988927i	$0.547413\pi$
$138$	1.34065	−	0.282967i	0.114123	−	0.0240877i
$139$	5.01188	−	5.97293i	0.425102	−	0.506617i	−0.510400	−	0.859937i	$-0.670503\pi$
$139$	5.01188	−	5.97293i	0.425102	−	0.506617i	0.935503	+	0.353320i	$0.114947\pi$
$140$	−1.29892	−	0.893698i	−0.109779	−	0.0755313i
$141$	−0.387754	+	0.223870i	−0.0326548	+	0.0188532i
$142$	−9.38689	+	3.77700i	−0.787731	+	0.316959i
$143$	−2.01209	−	0.354785i	−0.168259	−	0.0296686i
$144$	−4.51527	+	10.9948i	−0.376273	+	0.916235i
$145$	4.92290	+	0.723954i	0.408825	+	0.0601211i
$146$	15.9651	+	2.26696i	1.32128	+	0.187615i
$147$	0.397246	−	1.09143i	0.0327643	−	0.0900193i
$148$	0.166106	−	1.53820i	0.0136538	−	0.126440i
$149$	0.955499	−	0.801759i	0.0782775	−	0.0656826i	−0.602809	−	0.797885i	$-0.705952\pi$
$149$	0.955499	−	0.801759i	0.0782775	−	0.0656826i	0.681087	+	0.732203i	$0.261508\pi$
$150$	1.19026	+	0.100229i	0.0971843	+	0.00818365i
$151$	22.9818			1.87023			0.935117	−	0.354338i	$-0.115294\pi$
$151$	22.9818			1.87023			0.935117	+	0.354338i	$0.115294\pi$
$152$	11.9299	−	3.11069i	0.967646	−	0.252310i
$153$			3.50761i			0.283574i
$154$	0.179167	+	0.199556i	0.0144377	+	0.0160807i
$155$	−7.02825	+	13.0170i	−0.564523	+	1.04555i
$156$	1.27586	+	0.137777i	0.102151	+	0.0110310i
$157$	−4.71179	+	12.9455i	−0.376041	+	1.03317i	0.596941	+	0.802285i	$0.296383\pi$
$157$	−4.71179	+	12.9455i	−0.376041	+	1.03317i	−0.972982	+	0.230880i	$0.925839\pi$
$158$	1.46917	−	10.3467i	0.116881	−	0.823137i
$159$	−0.645792	−	0.372848i	−0.0512147	−	0.0295688i
$160$	10.8166	−	6.55746i	0.855130	−	0.518413i
$161$	0.351131	−	1.99136i	0.0276730	−	0.156941i
$162$	11.4720	−	4.61599i	0.901328	−	0.362667i
$163$	−6.76334	−	11.7144i	−0.529746	−	0.917546i	−0.999398	−	0.0346948i	$-0.988954\pi$
$163$	−6.76334	−	11.7144i	−0.529746	−	0.917546i	0.469652	−	0.882851i	$-0.344379\pi$
$164$	−7.18627	+	4.81746i	−0.561154	+	0.376180i
$165$	−0.192826	−	0.0640171i	−0.0150115	−	0.00498373i
$166$	−0.446319	−	2.11458i	−0.0346411	−	0.164123i
$167$	4.76621	+	13.0951i	0.368820	+	1.01333i	0.975811	+	0.218616i	$0.0701544\pi$
$167$	4.76621	+	13.0951i	0.368820	+	1.01333i	−0.606991	+	0.794709i	$0.707623\pi$
$168$	−0.120669	−	0.117530i	−0.00930982	−	0.00906763i
$169$	0.247942	+	1.40615i	0.0190725	+	0.108165i
$170$	2.21764	−	3.00271i	0.170085	−	0.230297i
$171$	−11.0859	−	6.69819i	−0.847758	−	0.512224i
$172$	9.98529	−	20.3256i	0.761371	−	1.54981i
$173$	1.22760	+	6.96205i	0.0933325	+	0.529315i	0.995246	+	0.0973973i	$0.0310517\pi$
$173$	1.22760	+	6.96205i	0.0933325	+	0.529315i	−0.901913	+	0.431918i	$0.857837\pi$
$174$	0.505351	+	0.164995i	0.0383105	+	0.0125082i
$175$	0.792919	−	1.57437i	0.0599390	−	0.119011i
$176$	−2.05002	+	0.653194i	−0.154526	+	0.0492363i
$177$	0.364607	−	0.434522i	0.0274055	−	0.0326606i
$178$	0.239369	+	7.14665i	0.0179415	+	0.535664i
$179$	−8.98666	−	15.5654i	−0.671695	−	1.16341i	−0.977423	−	0.211291i	$-0.932233\pi$
$179$	−8.98666	−	15.5654i	−0.671695	−	1.16341i	0.305729	−	0.952119i	$-0.401100\pi$
$180$	−12.8638	−	3.33380i	−0.958812	−	0.248487i
$181$	5.47047	+	0.964591i	0.406616	+	0.0716975i	0.373216	−	0.927745i	$-0.378255\pi$
$181$	5.47047	+	0.964591i	0.406616	+	0.0716975i	0.0334007	+	0.999442i	$0.489366\pi$
$182$	0.891484	−	1.67089i	0.0660812	−	0.123854i
$183$	1.01076	+	0.583565i	0.0747179	+	0.0431384i
$184$	13.4102	+	9.12893i	0.988610	+	0.672993i
$185$	1.72906	−	0.0493280i	0.127123	−	0.00362667i
$186$	−0.974802	+	1.24403i	−0.0714760	+	0.0912168i
$187$	−0.486395	+	0.408134i	−0.0355687	+	0.0298457i
$188$	−5.09154	−	1.47570i	−0.371339	−	0.107626i
$189$			0.355630i			0.0258683i
$190$	5.25530	+	12.7429i	0.381259	+	0.924468i
$191$			8.81735i			0.638001i	0.947755	+	0.319001i	$0.103347\pi$
$191$			8.81735i			0.638001i	−0.947755	+	0.319001i	$0.896653\pi$
$192$	1.25727	−	0.495507i	0.0907357	−	0.0357602i
$193$	−14.7524	+	12.3787i	−1.06190	+	0.891041i	−0.994294	−	0.106671i	$-0.965981\pi$
$193$	−14.7524	+	12.3787i	−1.06190	+	0.891041i	−0.0676066	+	0.997712i	$0.521536\pi$
$194$	−13.4058	−	10.5045i	−0.962478	−	0.754182i
$195$	0.0409152	+	1.43417i	0.00293000	+	0.102703i
$196$	12.5784	−	5.55737i	0.898459	−	0.396955i
$197$	18.2159	+	10.5170i	1.29783	+	0.749304i	0.980029	−	0.198853i	$-0.0637217\pi$
$197$	18.2159	+	10.5170i	1.29783	+	0.749304i	0.317803	+	0.948157i	$0.397055\pi$
$198$	1.99428	+	1.06402i	0.141727	+	0.0756169i
$199$	17.2506	+	3.04175i	1.22286	+	0.215624i	0.747557	−	0.664197i	$-0.231226\pi$
$199$	17.2506	+	3.04175i	1.22286	+	0.215624i	0.475305	+	0.879821i	$0.342338\pi$
$200$	8.90440	+	10.9869i	0.629636	+	0.776890i
$201$	0.599042	+	1.03757i	0.0422532	+	0.0731846i
$202$	11.2659	−	0.377340i	0.792667	−	0.0265495i
$203$	0.504285	−	0.600983i	0.0353938	−	0.0421807i
$204$	0.287666	−	0.276215i	0.0201406	−	0.0193389i
$205$	−6.42633	−	7.22947i	−0.448835	−	0.504928i
$206$	4.37179	−	13.3900i	0.304597	−	0.932927i
$207$	−2.95947	−	16.7840i	−0.205697	−	1.16657i
$208$	9.28571	+	12.0259i	0.643848	+	0.833843i
$209$	−0.361088	−	2.31664i	−0.0249769	−	0.160245i
$210$	0.111884	−	0.151492i	0.00772071	−	0.0104540i
$211$	−1.82576	−	10.3544i	−0.125691	−	0.712827i	−0.980895	−	0.194537i	$-0.937680\pi$
$211$	−1.82576	−	10.3544i	−0.125691	−	0.712827i	0.855205	−	0.518291i	$-0.173431\pi$
$212$	−2.11145	−	8.57259i	−0.145015	−	0.588768i
$213$	−0.413366	−	1.13571i	−0.0283233	−	0.0778177i
$214$	15.7162	−	3.31718i	1.07434	−	0.226757i
$215$	24.0292	+	7.97757i	1.63878	+	0.544066i
$216$	−2.60145	−	1.17159i	−0.177006	−	0.0797169i
$217$	1.16620	+	2.01992i	0.0791669	+	0.137121i
$218$	−2.77993	−	6.90891i	−0.188281	−	0.467930i
$219$	−0.334467	+	1.89686i	−0.0226012	+	0.128178i
$220$	−1.03450	−	2.17172i	−0.0697459	−	0.146417i
$221$	3.88304	+	2.24188i	0.261202	+	0.150805i
$222$	0.182967	+	0.0259803i	0.0122799	+	0.00174368i
$223$	3.62008	−	9.94608i	0.242418	−	0.666039i	−0.757495	−	0.652842i	$-0.773577\pi$
$223$	3.62008	−	9.94608i	0.242418	−	0.666039i	0.999913	−	0.0131976i	$-0.00420103\pi$
$224$	0.0142115	−	1.99430i	0.000949547	−	0.133250i
$225$	1.74158	−	14.7549i	0.116106	−	0.983660i
$226$	−15.9814	+	14.3485i	−1.06307	+	0.954450i
$227$		−	1.80739i		−	0.119961i	−0.998200	−	0.0599803i	$-0.980896\pi$
$227$		−	1.80739i		−	0.119961i	0.998200	−	0.0599803i	$-0.0191038\pi$
$228$	0.323653	+	1.43664i	0.0214344	+	0.0951437i
$229$	0.747250			0.0493797			0.0246898	−	0.999695i	$-0.492140\pi$
$229$	0.747250			0.0493797			0.0246898	+	0.999695i	$0.492140\pi$
$230$	−8.07795	+	16.2391i	−0.532645	+	1.07077i
$231$	−0.0245395	+	0.0205911i	−0.00161458	+	0.00135479i
$232$	2.73490	+	5.66876i	0.179555	+	0.372172i
$233$	4.01918	−	11.0426i	0.263306	−	0.723426i	−0.735634	−	0.677380i	$-0.763116\pi$
$233$	4.01918	−	11.0426i	0.263306	−	0.723426i	0.998939	−	0.0460466i	$-0.0146623\pi$
$234$	2.24400	−	15.8034i	0.146695	−	1.03310i
$235$	0.862310	−	5.86372i	0.0562509	−	0.382507i
$236$	6.70072	−	0.449371i	0.436180	−	0.0292516i
$237$	1.22931	+	0.216761i	0.0798526	+	0.0140802i
$238$	−0.219696	−	0.546006i	−0.0142408	−	0.0353923i
$239$	−8.67765	+	5.01004i	−0.561311	+	0.324073i	−0.753671	−	0.657251i	$-0.771719\pi$
$239$	−8.67765	+	5.01004i	−0.561311	+	0.324073i	0.192361	+	0.981324i	$0.438386\pi$
$240$	0.739581	+	1.31751i	0.0477398	+	0.0850451i
$241$	11.6615	−	13.8976i	0.751181	−	0.895223i	−0.246075	−	0.969251i	$-0.579141\pi$
$241$	11.6615	−	13.8976i	0.751181	−	0.895223i	0.997256	+	0.0740278i	$0.0235854\pi$
$242$	−3.12816	−	14.8207i	−0.201086	−	0.952707i
$243$	1.54020	+	4.23166i	0.0988038	+	0.271461i
$244$	3.30475	+	13.4174i	0.211565	+	0.858962i
$245$	8.06385	+	13.0901i	0.515180	+	0.836297i
$246$	−0.546375	−	0.877162i	−0.0348356	−	0.0559258i
$247$	−14.5006	+	7.99131i	−0.922652	+	0.508475i
$248$	−18.6178	+	1.87636i	−1.18223	+	0.119149i
$249$	0.254224	−	0.0448265i	0.0161108	−	0.00284077i
$250$	−10.8195	+	11.5299i	−0.684283	+	0.729217i
$251$	−6.31812	−	17.3589i	−0.398796	−	1.09568i	−0.962871	−	0.269961i	$-0.912989\pi$
$251$	−6.31812	−	17.3589i	−0.398796	−	1.09568i	0.564075	−	0.825724i	$-0.309233\pi$
$252$	−1.51131	+	1.45115i	−0.0952035	+	0.0914139i
$253$	1.98305	−	2.36331i	0.124674	−	0.148580i
$254$	−0.746529	−	22.2885i	−0.0468414	−	1.39850i
$255$	0.349597	+	0.276748i	0.0218926	+	0.0173307i
$256$	14.5416	+	6.67401i	0.908849	+	0.417126i
$257$	1.52649	−	8.65713i	0.0952196	−	0.540017i	−0.899460	−	0.437003i	$-0.856040\pi$
$257$	1.52649	−	8.65713i	0.0952196	−	0.540017i	0.994680	−	0.103015i	$-0.0328488\pi$
$258$	2.38655	+	1.27332i	0.148580	+	0.0792734i
$259$	0.136363	−	0.236188i	0.00847321	−	0.0146760i
$260$	−11.9125	+	12.1099i	−0.738781	+	0.751024i
$261$	2.26154	−	6.21353i	0.139986	−	0.384608i
$262$	14.3400	−	18.3005i	0.885928	−	1.13061i
$263$	−19.8411	+	16.6487i	−1.22345	+	1.02660i	−0.224818	+	0.974401i	$0.572179\pi$
$263$	−19.8411	+	16.6487i	−1.22345	+	1.02660i	−0.998637	+	0.0521999i	$0.983377\pi$
$264$	−0.0697815	−	0.247343i	−0.00429475	−	0.0152229i
$265$	9.17555	−	3.63918i	0.563650	−	0.223553i
$266$	2.14520	+	0.348308i	0.131531	+	0.0213562i
$267$	−0.854127			−0.0522717
$268$	−3.94874	+	13.6242i	−0.241208	+	0.832230i
$269$	−4.22376	−	5.03368i	−0.257527	−	0.306909i	0.621753	−	0.783213i	$-0.286421\pi$
$269$	−4.22376	−	5.03368i	−0.257527	−	0.306909i	−0.879281	+	0.476304i	$0.841976\pi$
$270$	0.903168	−	3.05933i	0.0549651	−	0.186185i
$271$	−5.55145	+	15.2525i	−0.337226	+	0.926522i	0.648951	+	0.760830i	$0.275208\pi$
$271$	−5.55145	+	15.2525i	−0.337226	+	0.926522i	−0.986178	+	0.165692i	$0.947014\pi$
$272$	4.71783	+	0.191684i	0.286061	+	0.0116226i
$273$	0.195906	+	0.113107i	0.0118568	+	0.00684553i
$274$	−25.6606	−	13.6910i	−1.55022	−	0.827101i
$275$	2.24868	−	1.47533i	0.135601	−	0.0889656i
$276$	−1.14343	+	1.56441i	−0.0688267	+	0.0941662i
$277$	−14.9324	+	8.62125i	−0.897203	+	0.518000i	−0.876292	−	0.481781i	$-0.839990\pi$
$277$	−14.9324	+	8.62125i	−0.897203	+	0.518000i	−0.0209114	+	0.999781i	$0.506657\pi$
$278$	0.369123	+	11.0206i	0.0221385	+	0.660971i
$279$	15.0592	+	12.6362i	0.901571	+	0.756508i
$280$	2.21123	−	0.286764i	0.132146	−	0.0171374i
$281$	8.80831	+	24.2006i	0.525460	+	1.44369i	0.864364	+	0.502867i	$0.167722\pi$
$281$	8.80831	+	24.2006i	0.525460	+	1.44369i	−0.338904	+	0.940821i	$0.610056\pi$
$282$	0.196528	−	0.601929i	0.0117030	−	0.0358444i
$283$	−4.11288	−	23.3253i	−0.244486	−	1.38655i	−0.821684	−	0.569943i	$-0.806965\pi$
$283$	−4.11288	−	23.3253i	−0.244486	−	1.38655i	0.577199	−	0.816604i	$-0.304146\pi$
$284$	6.30946	−	12.8433i	0.374398	−	0.762108i
$285$	−1.54227	+	0.576426i	−0.0913560	+	0.0341445i
$286$	2.45254	−	1.52766i	0.145022	−	0.0903326i
$287$	−1.50191	+	0.264828i	−0.0886551	+	0.0156323i
$288$	−5.63636	−	15.8360i	−0.332126	−	0.933145i
$289$	−14.6654	+	5.33777i	−0.862670	+	0.313986i
$290$	−5.86442	+	3.88930i	−0.344371	+	0.228388i
$291$	1.30764	−	1.55838i	0.0766551	−	0.0913540i
$292$	−18.9421	+	12.6982i	−1.10850	+	0.743107i
$293$	−7.68269	−	13.3068i	−0.448828	−	0.777392i	0.549482	−	0.835505i	$-0.314825\pi$
$293$	−7.68269	−	13.3068i	−0.448828	−	0.777392i	−0.998310	+	0.0581131i	$0.981492\pi$
$294$	0.613146	+	1.52384i	0.0357594	+	0.0888720i
$295$	1.51417	+	7.35421i	0.0881583	+	0.428178i
$296$	1.27849	+	1.77561i	0.0743108	+	0.103205i
$297$	−0.271292	+	0.469891i	−0.0157419	+	0.0272658i
$298$	−0.247986	+	1.74645i	−0.0143655	+	0.101169i
$299$	−20.4720	−	7.45118i	−1.18392	−	0.430913i
$300$	−1.34722	+	1.01908i	−0.0777819	+	0.0588366i
$301$	3.05802	−	2.56598i	0.176261	−	0.147901i
$302$	−24.1841	+	21.7131i	−1.39164	+	1.24945i
$303$			1.34644i			0.0773508i
$304$	−9.61508	+	14.5448i	−0.551462	+	0.834200i
$305$	−14.3612	+	5.69588i	−0.822317	+	0.326145i
$306$	−3.31397	−	3.69111i	−0.189447	−	0.211006i
$307$	2.89483	+	3.44993i	0.165217	+	0.196898i	0.842300	−	0.539008i	$-0.181201\pi$
$307$	2.89483	+	3.44993i	0.165217	+	0.196898i	−0.677084	+	0.735906i	$0.736756\pi$
$308$	−0.377080	−	0.0407197i	−0.0214861	−	0.00232022i
$309$	1.58102	+	0.575446i	0.0899413	+	0.0327360i
$310$	−4.90248	−	20.3382i	−0.278442	−	1.15513i
$311$	27.8935	+	16.1043i	1.58170	+	0.913194i	0.994612	+	0.103669i	$0.0330582\pi$
$311$	27.8935	+	16.1043i	1.58170	+	0.913194i	0.587086	+	0.809525i	$0.300275\pi$
$312$	−1.47278	+	1.06045i	−0.0833797	+	0.0600359i
$313$	−11.1710	−	1.96975i	−0.631422	−	0.111337i	−0.151228	−	0.988499i	$-0.548323\pi$
$313$	−11.1710	−	1.96975i	−0.631422	−	0.111337i	−0.480194	+	0.877162i	$0.659434\pi$
$314$	−7.27259	−	18.0744i	−0.410416	−	1.02000i
$315$	−1.83668	−	1.45395i	−0.103485	−	0.0819209i
$316$	8.22946	+	12.2760i	0.462943	+	0.690579i
$317$	6.45464	+	5.41608i	0.362528	+	0.304197i	0.805798	−	0.592191i	$-0.201737\pi$
$317$	6.45464	+	5.41608i	0.362528	+	0.304197i	−0.443269	+	0.896389i	$0.646181\pi$
$318$	1.03184	−	0.217788i	0.0578628	−	0.0122129i
$319$	1.12477	−	0.409381i	0.0629748	−	0.0229210i
$320$	−5.18704	+	17.1200i	−0.289964	+	0.957038i
$321$	0.333164	+	1.88947i	0.0185954	+	0.105460i
$322$	1.51193	+	2.42728i	0.0842566	+	0.135267i
$323$	−0.994192	+	5.04842i	−0.0553183	+	0.280902i
$324$	−7.71100	+	15.6962i	−0.428389	+	0.872010i
$325$	−15.2210	−	11.3585i	−0.844311	−	0.630058i
$326$	18.1849	+	5.93730i	1.00717	+	0.328836i
$327$	0.835903	−	0.304244i	0.0462256	−	0.0168247i
$328$	3.01070	−	11.8590i	0.166238	−	0.654805i
$329$	−0.715838	−	0.600660i	−0.0394654	−	0.0331154i
$330$	0.263397	−	0.114815i	0.0144995	−	0.00632036i
$331$	−13.0871	−	22.6674i	−0.719330	−	1.24592i	−0.961266	−	0.275623i	$-0.911116\pi$
$331$	−13.0871	−	22.6674i	−0.719330	−	1.24592i	0.241936	−	0.970292i	$-0.422218\pi$
$332$	2.46751	+	1.80352i	0.135422	+	0.0989811i
$333$	0.399156	−	2.26372i	0.0218736	−	0.124051i
$334$	−17.3877	−	9.27700i	−0.951412	−	0.507615i
$335$	−15.6904	−	2.30741i	−0.857260	−	0.126067i
$336$	0.238023	+	0.00967081i	0.0129852	+	0.000527586i
$337$	−16.5722	−	6.03180i	−0.902746	−	0.328573i	−0.151394	−	0.988474i	$-0.548376\pi$
$337$	−16.5722	−	6.03180i	−0.902746	−	0.328573i	−0.751353	+	0.659901i	$0.770598\pi$
$338$	−1.58944	−	1.24546i	−0.0864540	−	0.0677439i
$339$	−1.64903	−	1.96524i	−0.0895631	−	0.106737i
$340$	0.503299	+	5.25500i	0.0272952	+	0.284993i
$341$			3.55854i			0.192706i
$342$	17.9942	−	3.42528i	0.973017	−	0.185218i
$343$	4.89194			0.264140
$344$	8.69590	+	30.8230i	0.468851	+	1.66186i
$345$	−1.90633	−	1.02928i	−0.102633	−	0.0554146i
$346$	−7.86953	−	6.16643i	−0.423068	−	0.331509i
$347$	6.32576	+	2.30239i	0.339585	+	0.123599i	0.506183	−	0.862426i	$-0.331056\pi$
$347$	6.32576	+	2.30239i	0.339585	+	0.123599i	−0.166598	+	0.986025i	$0.553278\pi$
$348$	−0.687673	+	0.303826i	−0.0368632	+	0.0162868i
$349$	2.63674	−	4.56697i	0.141142	−	0.244464i	−0.786785	−	0.617227i	$-0.788256\pi$
$349$	2.63674	−	4.56697i	0.141142	−	0.244464i	0.927927	+	0.372763i	$0.121589\pi$
$350$	0.653059	+	2.40588i	0.0349075	+	0.128600i
$351$	3.77332	+	0.665339i	0.201405	+	0.0355132i
$352$	1.54012	−	2.62421i	0.0820889	−	0.139871i
$353$	24.1899	−	13.9660i	1.28750	−	0.743337i	0.309290	−	0.950968i	$-0.399909\pi$
$353$	24.1899	−	13.9660i	1.28750	−	0.743337i	0.978207	+	0.207631i	$0.0665752\pi$
$354$	0.0268531	+	0.801731i	0.00142723	+	0.0426115i
$355$	15.1835	+	5.04083i	0.805857	+	0.267540i
$356$	−7.00401	−	7.29436i	−0.371212	−	0.386600i
$357$	0.0660608	−	0.0240442i	0.00349631	−	0.00127255i
$358$	24.1629	+	7.88908i	1.27705	+	0.416951i
$359$	4.12396	−	0.727165i	0.217654	−	0.0383783i	−0.0637576	−	0.997965i	$-0.520308\pi$
$359$	4.12396	−	0.727165i	0.217654	−	0.0383783i	0.281412	+	0.959587i	$0.409197\pi$
$360$	16.6865	−	8.64547i	0.879457	−	0.455656i
$361$	−14.0571	−	12.7827i	−0.739848	−	0.672774i
$362$	−6.66798	+	4.15342i	−0.350461	+	0.218299i
$363$	1.78180	−	0.314180i	0.0935203	−	0.0164902i
$364$	0.640526	+	2.60057i	0.0335727	+	0.136307i
$365$	−16.9390	−	19.0560i	−0.886628	−	0.997436i
$366$	−1.61499	+	0.340872i	−0.0844169	+	0.0178177i
$367$	4.01358	+	3.36779i	0.209507	+	0.175797i	0.741503	−	0.670950i	$-0.234113\pi$
$367$	4.01358	+	3.36779i	0.209507	+	0.175797i	−0.531996	+	0.846747i	$0.678558\pi$
$368$	−22.7366	+	3.06335i	−1.18523	+	0.159688i
$369$	−11.1319	+	6.42699i	−0.579502	+	0.334576i
$370$	−1.77291	+	1.68551i	−0.0921690	+	0.0876257i
$371$	0.270251	−	1.53267i	0.0140307	−	0.0795723i
$372$	−0.149557	−	2.23010i	−0.00775418	−	0.115625i
$373$	8.38038	−	14.5152i	0.433920	−	0.751571i	−0.563287	−	0.826261i	$-0.690464\pi$
$373$	8.38038	−	14.5152i	0.433920	−	0.751571i	0.997207	+	0.0746904i	$0.0237968\pi$
$374$	0.126237	−	0.889028i	0.00652756	−	0.0459706i
$375$	−1.33318	−	1.33773i	−0.0688453	−	0.0690803i
$376$	6.75213	−	3.25757i	0.348214	−	0.167996i
$377$	−5.43313	−	6.47495i	−0.279820	−	0.333477i
$378$	−0.335997	−	0.374234i	−0.0172818	−	0.0192485i
$379$	7.16672			0.368130			0.184065	−	0.982914i	$-0.441074\pi$
$379$	7.16672			0.368130			0.184065	+	0.982914i	$0.441074\pi$
$380$	−17.5697	−	8.44436i	−0.901304	−	0.433186i
$381$	2.66379			0.136470
$382$	−8.33059	−	9.27861i	−0.426230	−	0.474735i
$383$	21.4278	+	25.5367i	1.09491	+	1.30486i	0.948898	+	0.315582i	$0.102200\pi$
$383$	21.4278	+	25.5367i	1.09491	+	1.30486i	0.146013	+	0.989283i	$0.453356\pi$
$384$	−0.854890	+	1.70929i	−0.0436259	+	0.0872269i
$385$	−0.0120924	−	0.423866i	−0.000616286	−	0.0216022i
$386$	3.82878	−	26.9643i	0.194880	−	1.37245i
$387$	16.8229	−	29.1381i	0.855155	−	1.48117i
$388$	24.0317	−	1.61164i	1.22002	−	0.0818186i
$389$	1.25719	−	7.12991i	0.0637423	−	0.361501i	−0.936207	−	0.351449i	$-0.885689\pi$
$389$	1.25719	−	7.12991i	0.0637423	−	0.361501i	0.999949	−	0.0100520i	$-0.00319969\pi$
$390$	−1.39805	−	1.47054i	−0.0707930	−	0.0744636i
$391$	−5.86333	+	3.38519i	−0.296521	+	0.171197i
$392$	−7.98587	+	17.7321i	−0.403347	+	0.895608i
$393$	2.12739	+	1.78509i	0.107312	+	0.0900458i
$394$	−29.1053	+	6.14317i	−1.46630	+	0.309489i
$395$	−12.3498	+	10.9778i	−0.621386	+	0.552355i
$396$	−3.10389	+	0.764495i	−0.155976	+	0.0384173i
$397$	1.69283	−	0.298492i	0.0849608	−	0.0149809i	−0.131006	−	0.991382i	$-0.541821\pi$
$397$	1.69283	−	0.298492i	0.0849608	−	0.0149809i	0.215967	+	0.976401i	$0.430710\pi$
$398$	−21.0269	+	13.0974i	−1.05398	+	0.656514i
$399$	−0.0501588	+	0.254702i	−0.00251108	+	0.0127510i
$400$	−19.7506	−	3.14881i	−0.987529	−	0.157440i
$401$	14.9749	−	2.64047i	0.747809	−	0.131859i	0.213259	−	0.976996i	$-0.431592\pi$
$401$	14.9749	−	2.64047i	0.747809	−	0.131859i	0.534550	+	0.845137i	$0.320481\pi$
$402$	−1.61067	−	0.525878i	−0.0803330	−	0.0262284i
$403$	23.6137	−	8.59468i	1.17628	−	0.428132i
$404$	−11.4988	+	11.0411i	−0.572085	+	0.549313i
$405$	−18.5563	−	6.16057i	−0.922068	−	0.306121i
$406$	0.0371403	+	1.10887i	0.00184324	+	0.0550322i
$407$	0.360352	−	0.208049i	0.0178620	−	0.0103126i
$408$	−0.0417476	+	0.562450i	−0.00206682	+	0.0278454i
$409$	−7.87743	−	1.38900i	−0.389514	−	0.0686818i	−0.0245384	−	0.999699i	$-0.507812\pi$
$409$	−7.87743	−	1.38900i	−0.389514	−	0.0686818i	−0.364976	+	0.931017i	$0.618923\pi$
$410$	13.5929	+	1.53610i	0.671305	+	0.0758627i
$411$	1.73703	−	3.00863i	0.0856816	−	0.148405i
$412$	8.05033	+	18.2209i	0.396611	+	0.897681i
$413$	1.11244	+	0.404897i	0.0547398	+	0.0199237i
$414$	18.9717	+	14.8659i	0.932408	+	0.730619i
$415$	−1.62347	+	3.00682i	−0.0796929	+	0.147599i
$416$	−21.1334	−	3.88187i	−1.03615	−	0.190324i
$417$	−1.31712			−0.0644995
$418$	2.56873	+	2.09668i	0.125641	+	0.102552i
$419$			29.5028i			1.44131i	0.693296	+	0.720653i	$0.256158\pi$
$419$			29.5028i			1.44131i	−0.693296	+	0.720653i	$0.743842\pi$
$420$	0.0253923	+	0.265124i	0.00123902	+	0.0129367i
$421$	15.3524	+	18.2962i	0.748229	+	0.891704i	0.997043	−	0.0768469i	$-0.0244853\pi$
$421$	15.3524	+	18.2962i	0.748229	+	0.891704i	−0.248814	+	0.968551i	$0.580041\pi$
$422$	11.7041	+	9.17111i	0.569745	+	0.446443i
$423$	−7.40101	−	2.69375i	−0.359849	−	0.130974i
$424$	10.3212	+	7.02616i	0.501244	+	0.341221i
$425$	−5.74461	+	1.35461i	−0.278654	+	0.0657082i
$426$	1.50801	+	0.804580i	0.0730631	+	0.0389820i
$427$	−0.422985	+	2.39887i	−0.0204697	+	0.116089i
$428$	−13.4043	+	18.3393i	−0.647921	+	0.886463i
$429$	0.172566	+	0.298894i	0.00833158	+	0.0144307i
$430$	−32.8235	+	14.3078i	−1.58289	+	0.689984i
$431$	11.0099	+	9.23838i	0.530327	+	0.444997i	0.868214	−	0.496189i	$-0.165268\pi$
$431$	11.0099	+	9.23838i	0.530327	+	0.444997i	−0.337887	+	0.941187i	$0.609712\pi$
$432$	3.84446	−	1.22495i	0.184967	−	0.0589356i
$433$	−24.8805	+	9.05575i	−1.19568	+	0.435191i	−0.861714	−	0.507394i	$-0.830609\pi$
$433$	−24.8805	+	9.05575i	−1.19568	+	0.435191i	−0.333965	+	0.942586i	$0.608387\pi$
$434$	−3.13562	−	1.02377i	−0.150515	−	0.0491424i
$435$	−0.440857	−	0.715648i	−0.0211375	−	0.0343127i
$436$	9.45286	+	4.64387i	0.452710	+	0.222401i
$437$	0.497733	−	24.9956i	0.0238098	−	1.19570i
$438$	−1.44018	−	2.31209i	−0.0688143	−	0.110476i
$439$	5.33260	+	30.2427i	0.254511	+	1.44341i	0.797324	+	0.603552i	$0.206248\pi$
$439$	5.33260	+	30.2427i	0.254511	+	1.44341i	−0.542813	+	0.839854i	$0.682641\pi$
$440$	3.14044	+	1.30794i	0.149715	+	0.0623534i
$441$	19.1988	−	6.98778i	0.914228	−	0.332752i
$442$	−6.20429	+	1.30952i	−0.295108	+	0.0622877i
$443$	24.3577	+	20.4385i	1.15727	+	0.971064i	0.999864	−	0.0164704i	$-0.00524292\pi$
$443$	24.3577	+	20.4385i	1.15727	+	0.971064i	0.157404	+	0.987534i	$0.449687\pi$
$444$	−0.217085	+	0.145527i	−0.0103024	+	0.00690640i
$445$	7.01753	−	8.86477i	0.332663	−	0.420230i
$446$	5.58755	+	13.8866i	0.264578	+	0.657551i
$447$	−0.207500	−	0.0365879i	−0.00981443	−	0.00173055i
$448$	1.86925	+	2.11205i	0.0883137	+	0.0997852i
$449$	21.7050	+	12.5314i	1.02432	+	0.591391i	0.915352	−	0.402654i	$-0.131912\pi$
$449$	21.7050	+	12.5314i	1.02432	+	0.591391i	0.108968	+	0.994045i	$0.465245\pi$
$450$	12.1077	+	17.1722i	0.570760	+	0.809506i
$451$	−2.18649	−	0.795817i	−0.102958	−	0.0374735i
$452$	3.26102	−	30.1983i	0.153386	−	1.42041i
$453$	−2.49542	−	2.97392i	−0.117245	−	0.139727i
$454$	1.70761	+	1.90194i	0.0801422	+	0.0892624i
$455$	−2.78348	+	1.10398i	−0.130492	+	0.0517552i
$456$	−1.69791	−	1.20601i	−0.0795121	−	0.0564765i
$457$		−	28.0718i		−	1.31314i	−0.754264	−	0.656571i	$-0.772006\pi$
$457$		−	28.0718i		−	1.31314i	0.754264	−	0.656571i	$-0.227994\pi$
$458$	−0.786341	+	0.705998i	−0.0367433	+	0.0329891i
$459$	0.912151	−	0.765386i	0.0425756	−	0.0357251i
$460$	−6.84208	−	24.7206i	−0.319014	−	1.15261i
$461$	8.10603	+	2.95035i	0.377535	+	0.137412i	0.523816	−	0.851831i	$-0.324508\pi$
$461$	8.10603	+	2.95035i	0.377535	+	0.137412i	−0.146280	+	0.989243i	$0.546730\pi$
$462$	0.00636889	−	0.0448531i	0.000296307	−	0.00208675i
$463$	19.5043	−	33.7824i	0.906440	−	1.57000i	0.0874686	−	0.996167i	$-0.472122\pi$
$463$	19.5043	−	33.7824i	0.906440	−	1.57000i	0.818972	−	0.573834i	$-0.194544\pi$
$464$	−8.23378	−	3.38139i	−0.382244	−	0.156977i
$465$	2.44759	−	0.503937i	0.113504	−	0.0233695i
$466$	6.20357	+	15.4176i	0.287375	+	0.714206i
$467$	5.82760	+	10.0937i	0.269669	+	0.467081i	0.968776	−	0.247936i	$-0.0797523\pi$
$467$	5.82760	+	10.0937i	0.269669	+	0.467081i	−0.699107	+	0.715017i	$0.746419\pi$
$468$	12.5696	+	18.7503i	0.581031	+	0.866732i
$469$	−1.60727	+	1.91547i	−0.0742170	+	0.0884484i
$470$	4.63260	+	6.98518i	0.213686	+	0.322202i
$471$	2.18681	−	0.795933i	0.100763	−	0.0366747i
$472$	−6.62670	+	6.80369i	−0.305018	+	0.313165i
$473$	5.99799	−	1.05761i	0.275788	−	0.0486288i
$474$	−1.49842	+	0.933349i	−0.0688246	+	0.0428701i
$475$	6.68873	−	20.7427i	0.306900	−	0.951742i
$476$	0.747053	+	0.367002i	0.0342411	+	0.0168215i
$477$	−2.27778	−	12.9179i	−0.104292	−	0.591472i
$478$	4.39814	−	13.4707i	0.201166	−	0.616137i
$479$	−5.89779	−	16.2040i	−0.269477	−	0.740382i	−0.998440	−	0.0558292i	$-0.982220\pi$
$479$	−5.89779	−	16.2040i	−0.269477	−	0.740382i	0.728963	−	0.684553i	$-0.240002\pi$
$480$	−2.02305	−	0.687684i	−0.0923392	−	0.0313884i
$481$	−2.25090	−	1.88873i	−0.102632	−	0.0861186i
$482$	0.858862	+	25.6423i	0.0391201	+	1.16798i
$483$	−0.295815	+	0.170789i	−0.0134601	+	0.00777117i
$484$	17.2943	+	12.6405i	0.786103	+	0.574568i
$485$	5.43047	+	26.3754i	0.246585	+	1.19764i
$486$	−5.61882	−	2.99786i	−0.254875	−	0.135986i
$487$	−26.0280	−	15.0273i	−1.17944	−	0.680950i	−0.223555	−	0.974691i	$-0.571766\pi$
$487$	−26.0280	−	15.0273i	−1.17944	−	0.680950i	−0.955885	+	0.293741i	$0.905100\pi$
$488$	−16.1543	−	10.9970i	−0.731273	−	0.497812i
$489$	−0.781509	+	2.14718i	−0.0353411	+	0.0970987i
$490$	−20.8532	−	6.15622i	−0.942050	−	0.278109i
$491$	−12.0290	−	14.3357i	−0.542863	−	0.646959i	0.422964	−	0.906147i	$-0.360990\pi$
$491$	−12.0290	−	14.3357i	−0.542863	−	0.646959i	−0.965827	+	0.259187i	$0.916545\pi$
$492$	1.40370	+	0.406837i	0.0632835	+	0.0183416i
$493$	−2.62677			−0.118304
$494$	7.70904	−	22.1095i	0.346846	−	0.994752i
$495$	−1.31764	−	3.32220i	−0.0592236	−	0.149322i
$496$	17.8190	−	19.5645i	0.800095	−	0.878472i
$497$	1.93229	−	1.62138i	0.0866750	−	0.0727289i
$498$	−0.225171	+	0.287361i	−0.0100902	+	0.0128770i
$499$	1.26220	−	3.46788i	0.0565040	−	0.155243i	−0.908229	−	0.418473i	$-0.862565\pi$
$499$	1.26220	−	3.46788i	0.0565040	−	0.155243i	0.964733	+	0.263230i	$0.0847877\pi$
$500$	0.492048	−	22.3553i	0.0220051	−	0.999758i
$501$	1.17702	−	2.03865i	0.0525852	−	0.0910803i
$502$	23.0492	+	12.2977i	1.02874	+	0.548872i
$503$	−3.50139	+	19.8574i	−0.156119	+	0.885397i	0.801636	+	0.597813i	$0.203963\pi$
$503$	−3.50139	+	19.8574i	−0.156119	+	0.885397i	−0.957755	+	0.287585i	$0.907148\pi$
$504$	0.219329	−	2.95494i	0.00976970	−	0.131624i
$505$	−13.9743	−	11.0624i	−0.621850	−	0.492269i
$506$	0.146051	+	4.36052i	0.00649276	+	0.193849i
$507$	0.155038	−	0.184768i	0.00688550	−	0.00820582i
$508$	21.8436	+	22.7492i	0.969155	+	1.00933i
$509$	−8.80102	−	24.1806i	−0.390098	−	1.07179i	−0.966956	−	0.254942i	$-0.917944\pi$
$509$	−8.80102	−	24.1806i	−0.390098	−	1.07179i	0.576858	−	0.816844i	$-0.304278\pi$
$510$	−0.629356	+	0.0390717i	−0.0278684	+	0.00173013i
$511$	−3.95886	+	0.698053i	−0.175129	+	0.0308800i
$512$	−21.6079	+	6.71566i	−0.954942	+	0.296793i
$513$	0.677158	+	4.34447i	0.0298973	+	0.191813i
$514$	6.57287	+	10.5522i	0.289917	+	0.465439i
$515$	−18.9621	+	11.6812i	−0.835572	+	0.514734i
$516$	−3.71443	+	0.914873i	−0.163518	+	0.0402750i
$517$	−0.487619	−	1.33972i	−0.0214455	−	0.0589209i
$518$	0.0796525	+	0.377379i	0.00349973	+	0.0165811i
$519$	0.767616	−	0.914810i	0.0336946	−	0.0401557i
$520$	1.09430	−	23.9983i	0.0479883	−	1.05239i
$521$	14.1055	−	8.14382i	0.617974	−	0.356787i	−0.158106	−	0.987422i	$-0.550539\pi$
$521$	14.1055	−	8.14382i	0.617974	−	0.356787i	0.776080	+	0.630635i	$0.217205\pi$
$522$	3.49066	+	8.67527i	0.152782	+	0.379706i
$523$	3.09462	+	0.545665i	0.135318	+	0.0238603i	0.240897	−	0.970551i	$-0.422558\pi$
$523$	3.09462	+	0.545665i	0.135318	+	0.0238603i	−0.105579	+	0.994411i	$0.533669\pi$
$524$	2.20009	+	32.8063i	0.0961113	+	1.43315i
$525$	−0.289826	+	0.0683425i	−0.0126490	+	0.00298271i
$526$	5.14948	−	36.2654i	0.224528	−	1.58125i
$527$	2.67098	−	7.33844i	0.116350	−	0.319668i
$528$	0.307121	+	0.194353i	0.0133657	+	0.00845815i
$529$	7.58091	−	6.36114i	0.329605	−	0.276571i
$530$	−6.21727	+	12.4986i	−0.270061	+	0.542903i
$531$	9.97785			0.433002
$532$	−2.58650	+	1.66024i	−0.112139	+	0.0719807i
$533$			16.4311i			0.711712i
$534$	0.898809	−	0.806975i	0.0388953	−	0.0349212i
$535$	−22.3476	−	12.0661i	−0.966171	−	0.521663i
$536$	−8.71676	−	18.0677i	−0.376507	−	0.780404i
$537$	−1.03842	+	2.85302i	−0.0448109	+	0.123117i
$538$	9.20051	+	1.30642i	0.396662	+	0.0563238i
$539$	3.20289	+	1.84919i	0.137958	+	0.0796503i
$540$	1.94003	+	4.07268i	0.0834854	+	0.175260i
$541$	−1.34105	+	7.60549i	−0.0576564	+	0.326986i	−0.999970	−	0.00774564i	$-0.997534\pi$
$541$	−1.34105	+	7.60549i	−0.0576564	+	0.326986i	0.942314	+	0.334731i	$0.108646\pi$
$542$	−8.56860	−	21.2954i	−0.368053	−	0.914714i
$543$	−0.469174	−	0.812633i	−0.0201342	−	0.0348734i
$544$	−5.14574	+	4.25567i	−0.220622	+	0.182461i
$545$	−3.71014	+	11.1753i	−0.158925	+	0.478698i
$546$	−0.313018	+	0.0660678i	−0.0133959	+	0.00282744i
$547$	13.1507	+	36.1314i	0.562285	+	1.54487i	0.816278	+	0.577660i	$0.196034\pi$
$547$	13.1507	+	36.1314i	0.562285	+	1.54487i	−0.253992	+	0.967206i	$0.581744\pi$
$548$	39.9382	−	9.83687i	1.70607	−	0.420210i
$549$	3.56508	+	20.2186i	0.152154	+	0.862907i
$550$	−0.972438	+	3.67705i	−0.0414649	+	0.156790i
$551$	5.01613	−	8.30198i	0.213694	−	0.353676i
$552$	−0.274791	−	2.72656i	−0.0116959	−	0.116050i
$553$	0.452394	+	2.56565i	0.0192378	+	0.109103i
$554$	7.56829	−	23.1803i	0.321546	−	0.984838i
$555$	−0.194128	−	0.218390i	−0.00824028	−	0.00927012i
$556$	−10.8006	−	11.2484i	−0.458049	−	0.477037i
$557$	−10.8639	+	12.9471i	−0.460317	+	0.548585i	−0.945412	−	0.325877i	$-0.894341\pi$
$557$	−10.8639	+	12.9471i	−0.460317	+	0.548585i	0.485095	+	0.874461i	$0.338785\pi$
$558$	−27.7856	+	0.930648i	−1.17626	+	0.0393975i
$559$	−21.5046	−	37.2470i	−0.909546	−	1.57538i
$560$	−2.05598	+	2.39093i	−0.0868809	+	0.101035i
$561$	0.105628	+	0.0186250i	0.00445960	+	0.000786349i
$562$	−32.1337	−	17.1446i	−1.35548	−	0.723201i
$563$	−28.0438	−	16.1911i	−1.18190	−	0.682372i	−0.225449	−	0.974255i	$-0.572385\pi$
$563$	−28.0438	−	16.1911i	−1.18190	−	0.682372i	−0.956454	+	0.291883i	$0.905718\pi$
$564$	0.361891	+	0.819096i	0.0152384	+	0.0344902i
$565$	33.9452	−	0.968417i	1.42809	−	0.0407416i
$566$	26.3657	+	20.6597i	1.10823	+	0.868392i
$567$	−2.36151	+	1.98154i	−0.0991742	+	0.0832170i
$568$	5.49473	+	19.4763i	0.230554	+	0.817207i
$569$		−	24.2370i		−	1.01607i	−0.861336	−	0.508035i	$-0.830372\pi$
$569$		−	24.2370i		−	1.01607i	0.861336	−	0.508035i	$-0.169628\pi$
$570$	1.07834	−	2.06371i	0.0451668	−	0.0864391i
$571$		−	37.6440i		−	1.57535i	−0.616090	−	0.787676i	$-0.711284\pi$
$571$		−	37.6440i		−	1.57535i	0.616090	−	0.787676i	$-0.288716\pi$
$572$	−1.13751	+	3.92473i	−0.0475619	+	0.164101i
$573$	1.14099	−	0.957407i	0.0476657	−	0.0399963i
$574$	1.33028	−	1.69768i	0.0555246	−	0.0708599i
$575$	26.3451	−	11.3287i	1.09867	−	0.472440i
$576$	20.8930	+	11.3392i	0.870541	+	0.472467i
$577$	33.0145	+	19.0610i	1.37441	+	0.793518i	0.991480	−	0.130258i	$-0.0415805\pi$
$577$	33.0145	+	19.0610i	1.37441	+	0.793518i	0.382934	+	0.923776i	$0.374914\pi$
$578$	10.3895	−	19.4728i	0.432146	−	0.809961i
$579$	3.20370	+	0.564898i	0.133141	+	0.0234764i
$580$	2.49661	−	9.63344i	0.103666	−	0.400007i
$581$	0.269383	+	0.466585i	0.0111759	+	0.0193572i
$582$	0.0963069	+	2.87536i	0.00399205	+	0.119187i
$583$	1.52628	−	1.81894i	0.0632119	−	0.0753330i
$584$	7.93583	−	31.2589i	0.328387	−	1.29350i
$585$	−18.8630	+	16.7675i	−0.779889	+	0.693249i
$586$	20.6568	+	6.74436i	0.853325	+	0.278607i
$587$	−2.86570	−	16.2522i	−0.118280	−	0.670799i	−0.985074	−	0.172132i	$-0.944934\pi$
$587$	−2.86570	−	16.2522i	−0.118280	−	0.670799i	0.866794	−	0.498667i	$-0.166177\pi$
$588$	−2.08494	−	1.02426i	−0.0859813	−	0.0422397i
$589$	18.0928	+	22.4553i	0.745499	+	0.925254i
$590$	−8.54159	−	6.30835i	−0.351652	−	0.259711i
$591$	−0.616996	−	3.49916i	−0.0253798	−	0.143936i
$592$	−3.02296	−	0.660583i	−0.124243	−	0.0271498i
$593$	2.47644	+	6.80396i	0.101695	+	0.279405i	0.980097	−	0.198517i	$-0.0636124\pi$
$593$	2.47644	+	6.80396i	0.101695	+	0.279405i	−0.878402	+	0.477922i	$0.841390\pi$
$594$	−0.158467	−	0.750787i	−0.00650197	−	0.0308052i
$595$	−0.293209	+	0.883177i	−0.0120204	+	0.0362067i
$596$	−1.38908	−	2.07211i	−0.0568989	−	0.0848769i
$597$	−1.47950	−	2.56256i	−0.0605518	−	0.104879i
$598$	28.5827	−	11.5008i	1.16884	−	0.470303i
$599$	1.58315	−	8.97847i	0.0646856	−	0.366850i	−0.935232	−	0.354035i	$-0.884809\pi$
$599$	1.58315	−	8.97847i	0.0646856	−	0.366850i	0.999918	−	0.0128156i	$-0.00407945\pi$
$600$	0.454878	−	2.34524i	0.0185703	−	0.0957440i
$601$	12.0081	+	6.93289i	0.489822	+	0.282799i	0.724500	−	0.689274i	$-0.242071\pi$
$601$	12.0081	+	6.93289i	0.489822	+	0.282799i	−0.234679	+	0.972073i	$0.575404\pi$
$602$	−0.793666	+	5.58941i	−0.0323474	+	0.227808i
$603$	−7.20806	+	19.8040i	−0.293535	+	0.806481i
$604$	4.93479	−	45.6980i	0.200794	−	1.85942i
$605$	−11.3785	+	21.0742i	−0.462604	+	0.856787i
$606$	−1.27211	−	1.41687i	−0.0516758	−	0.0575566i
$607$		−	0.0255150i		−	0.00103562i	−1.00000		0.000517812i	$-0.999835\pi$
$607$		−	0.0255150i		−	0.00103562i	1.00000		0.000517812i	$-0.000164825\pi$
$608$	−3.62375	−	24.3899i	−0.146963	−	0.989142i
$609$	−0.132525			−0.00537020
$610$	9.73099	−	19.5622i	0.393996	−	0.792050i
$611$	−7.71239	+	6.47147i	−0.312010	+	0.261808i
$612$	6.97467	+	0.753174i	0.281934	+	0.0304453i
$613$	−11.9906	+	32.9440i	−0.484297	+	1.33059i	0.421479	+	0.906838i	$0.361511\pi$
$613$	−11.9906	+	32.9440i	−0.484297	+	1.33059i	−0.905776	+	0.423757i	$0.860711\pi$
$614$	−6.30574	−	0.895380i	−0.254479	−	0.0361346i
$615$	−0.237732	+	1.61658i	−0.00958627	+	0.0651868i
$616$	0.435278	−	0.313413i	0.0175378	−	0.0126278i
$617$	14.8841	+	2.62446i	0.599210	+	0.105657i	0.465022	−	0.885299i	$-0.346046\pi$
$617$	14.8841	+	2.62446i	0.599210	+	0.105657i	0.134188	+	0.990956i	$0.457158\pi$
$618$	−2.20741	+	0.888194i	−0.0887950	+	0.0357284i
$619$	−34.3479	+	19.8308i	−1.38056	+	0.797066i	−0.992225	−	0.124454i	$-0.960282\pi$
$619$	−34.3479	+	19.8308i	−1.38056	+	0.797066i	−0.388333	+	0.921519i	$0.626949\pi$
$620$	24.3744	+	16.7703i	0.978900	+	0.673513i
$621$	−3.71888	+	4.43199i	−0.149234	+	0.177850i
$622$	−44.5680	+	9.40686i	−1.78702	+	0.377181i
$623$	−0.609690	−	1.67511i	−0.0244267	−	0.0671119i
$624$	0.547921	−	2.50739i	0.0219344	−	0.100376i
$625$	24.8375	−	2.84593i	0.993499	−	0.113837i
$626$	13.6164	−	8.48150i	0.544220	−	0.338989i
$627$	−0.260573	+	0.298272i	−0.0104063	+	0.0119118i
$628$	24.7297	+	12.1488i	0.986821	+	0.484791i
$629$	−0.899278	+	0.158567i	−0.0358565	+	0.00632248i
$630$	3.30645	−	0.205271i	0.131732	−	0.00817820i
$631$	3.46482	+	9.51953i	0.137932	+	0.378966i	0.989357	−	0.145511i	$-0.0464828\pi$
$631$	3.46482	+	9.51953i	0.137932	+	0.378966i	−0.851424	+	0.524478i	$0.824261\pi$
$632$	−20.2583	−	5.14305i	−0.805831	−	0.204580i
$633$	−1.14165	+	1.36056i	−0.0453765	+	0.0540776i
$634$	−11.9094	+	0.398892i	−0.472982	+	0.0158420i
$635$	−21.8858	+	27.6468i	−0.868512	+	1.09713i
$636$	−0.880055	+	1.20406i	−0.0348964	+	0.0477441i
$637$	4.53511	−	25.7199i	0.179688	−	1.01906i
$638$	−0.796824	+	1.49347i	−0.0315466	+	0.0591270i
$639$	10.6300	−	18.4117i	0.420515	−	0.728354i
$640$	−10.7165	−	22.9163i	−0.423607	−	0.905846i
$641$	−8.54858	+	23.4870i	−0.337649	+	0.927682i	0.648411	+	0.761290i	$0.275434\pi$
$641$	−8.54858	+	23.4870i	−0.337649	+	0.927682i	−0.986060	+	0.166392i	$0.946788\pi$
$642$	−2.13575	−	1.67354i	−0.0842914	−	0.0660493i
$643$	−33.0725	+	27.7511i	−1.30425	+	1.09440i	−0.314860	+	0.949138i	$0.601957\pi$
$643$	−33.0725	+	27.7511i	−1.30425	+	1.09440i	−0.989394	+	0.145260i	$0.953598\pi$
$644$	−3.88431	−	1.12580i	−0.153063	−	0.0443627i
$645$	−1.57683	−	3.97568i	−0.0620874	−	0.156542i
$646$	−3.72352	−	6.25183i	−0.146500	−	0.245975i
$647$	4.50838			0.177243			0.0886214	−	0.996065i	$-0.471754\pi$
$647$	4.50838			0.177243			0.0886214	+	0.996065i	$0.471754\pi$
$648$	−6.71529	−	23.8026i	−0.263801	−	0.935055i
$649$	1.16099	+	1.38361i	0.0455728	+	0.0543115i
$650$	26.7488	−	2.42803i	1.04917	−	0.0952352i
$651$	0.134755	−	0.370238i	0.00528148	−	0.0145108i
$652$	−24.7457	+	10.9331i	−0.969118	+	0.428173i
$653$	22.1636	+	12.7961i	0.867327	+	0.500752i	0.866459	−	0.499248i	$-0.166390\pi$
$653$	22.1636	+	12.7961i	0.867327	+	0.500752i	0.000868020		1.00000i	$0.499724\pi$
$654$	−0.592184	+	1.10992i	−0.0231562	+	0.0434012i
$655$	−36.0057	+	7.41326i	−1.40686	+	0.289660i
$656$	8.03615	+	15.3239i	0.313759	+	0.598298i
$657$	−29.3422	+	16.9407i	−1.14475	+	0.660921i
$658$	1.32079	−	0.0442383i	0.0514896	−	0.00172459i
$659$	19.1139	+	16.0385i	0.744573	+	0.624771i	0.934061	−	0.357112i	$-0.116239\pi$
$659$	19.1139	+	16.0385i	0.744573	+	0.624771i	−0.189489	+	0.981883i	$0.560683\pi$
$660$	−0.168699	+	0.369677i	−0.00656660	+	0.0143897i
$661$	−16.7028	−	45.8904i	−0.649662	−	1.78493i	−0.618986	−	0.785402i	$-0.712456\pi$
$661$	−16.7028	−	45.8904i	−0.649662	−	1.78493i	−0.0306753	−	0.999529i	$-0.509766\pi$
$662$	35.1878	+	11.4887i	1.36761	+	0.446520i
$663$	−0.131523	−	0.745906i	−0.00510794	−	0.0289686i
$664$	−4.30055	+	0.433424i	−0.166894	+	0.0168201i
$665$	−2.23138	−	2.61322i	−0.0865292	−	0.101336i
$666$	1.71872	+	2.75927i	0.0665990	+	0.106919i
$667$	12.5692	−	2.21628i	0.486680	−	0.0858148i
$668$	27.0621	−	6.66548i	1.04707	−	0.257895i
$669$	−1.68013	+	0.611518i	−0.0649576	+	0.0236426i
$670$	18.6913	−	12.3961i	0.722107	−	0.478904i
$671$	−2.38886	+	2.84693i	−0.0922208	+	0.109904i
$672$	−0.259612	+	0.214706i	−0.0100147	+	0.00828248i
$673$	−13.7919	−	23.8883i	−0.531640	−	0.920827i	−0.999318	−	0.0369281i	$-0.988243\pi$
$673$	−13.7919	−	23.8883i	−0.531640	−	0.920827i	0.467678	−	0.883899i	$-0.345091\pi$
$674$	23.1380	−	9.31001i	0.891242	−	0.358608i
$675$	−4.21702	+	2.76673i	−0.162313	+	0.106491i
$676$	2.84929	−	0.191082i	0.109588	−	0.00734930i
$677$	18.5954	−	32.2082i	0.714679	−	1.23786i	−0.248404	−	0.968657i	$-0.579906\pi$
$677$	18.5954	−	32.2082i	0.714679	−	1.23786i	0.963083	−	0.269204i	$-0.0867608\pi$
$678$	3.59204	+	0.510050i	0.137952	+	0.0195884i
$679$	3.98971	+	1.45213i	0.153111	+	0.0557278i
$680$	−5.49453	−	5.05440i	−0.210706	−	0.193827i
$681$	−0.233882	+	0.196250i	−0.00896238	+	0.00752033i
$682$	−3.36209	−	3.74470i	−0.128741	−	0.143392i
$683$		−	36.9807i		−	1.41503i	−0.706700	−	0.707513i	$-0.749817\pi$
$683$		−	36.9807i		−	1.41503i	0.706700	−	0.707513i	$-0.250183\pi$
$684$	−15.6994	+	20.6053i	−0.600281	+	0.787864i
$685$	16.9543	+	42.7473i	0.647791	+	1.63329i
$686$	−5.14786	+	4.62188i	−0.196546	+	0.176464i
$687$	−0.0811380	−	0.0966965i	−0.00309561	−	0.00368920i
$688$	−38.2722	−	24.2196i	−1.45911	−	0.923363i
$689$	−15.7564	−	5.73487i	−0.600272	−	0.218481i
$690$	2.97851	−	0.717964i	0.113390	−	0.0273324i
$691$	7.97564	+	4.60474i	0.303408	+	0.175172i	0.643973	−	0.765049i	$-0.277285\pi$
$691$	7.97564	+	4.60474i	0.303408	+	0.175172i	−0.340565	+	0.940221i	$0.610618\pi$
$692$	14.1072	−	0.946073i	0.536276	−	0.0359643i
$693$	−0.554936	−	0.0978501i	−0.0210803	−	0.00371702i
$694$	−8.83197	+	3.55371i	−0.335257	+	0.134897i
$695$	10.8215	−	13.6700i	0.410482	−	0.518534i
$696$	0.436594	−	0.969431i	0.0165491	−	0.0367462i
$697$	3.91167	+	3.28228i	0.148165	+	0.124325i
$698$	1.54017	+	7.29706i	0.0582964	+	0.276198i
$699$	−1.86536	+	0.678936i	−0.0705545	+	0.0256797i
$700$	−2.96028	−	1.91473i	−0.111888	−	0.0723700i
$701$	1.90882	+	10.8255i	0.0720952	+	0.408872i	0.999402	+	0.0345708i	$0.0110064\pi$
$701$	1.90882	+	10.8255i	0.0720952	+	0.408872i	−0.927307	+	0.374302i	$0.877882\pi$
$702$	−4.59933	+	2.86487i	−0.173590	+	0.108128i
$703$	1.21612	−	3.14499i	0.0458669	−	0.118615i
$704$	0.858646	+	4.21659i	0.0323614	+	0.158919i
$705$	−0.852416	+	0.525110i	−0.0321039	+	0.0197768i
$706$	−12.2603	+	37.5511i	−0.461422	+	1.41325i
$707$	−2.64063	+	0.961110i	−0.0993111	+	0.0361463i
$708$	−0.785729	−	0.818302i	−0.0295295	−	0.0307537i
$709$	−15.2568	−	12.8020i	−0.572982	−	0.480789i	0.309652	−	0.950850i	$-0.399788\pi$
$709$	−15.2568	−	12.8020i	−0.572982	−	0.480789i	−0.882634	+	0.470061i	$0.844232\pi$
$710$	−20.7404	+	9.04076i	−0.778372	+	0.339294i
$711$	10.9790	+	19.0161i	0.411743	+	0.713160i
$712$	14.2621	+	1.05860i	0.534494	+	0.0396726i
$713$	−6.58901	+	37.3681i	−0.246760	+	1.39945i
$714$	−0.0467999	+	0.0877160i	−0.00175144	+	0.00328269i
$715$	−4.51995	−	0.664697i	−0.169037	−	0.0248583i
$716$	−32.8804	+	14.5272i	−1.22880	+	0.542905i
$717$	1.59055	+	0.578914i	0.0594003	+	0.0216200i
$718$	−3.65267	+	4.66150i	−0.136317	+	0.173966i
$719$	−20.6011	−	24.5514i	−0.768290	−	0.915613i	0.230051	−	0.973178i	$-0.426111\pi$
$719$	−20.6011	−	24.5514i	−0.768290	−	0.915613i	−0.998342	+	0.0575658i	$0.981666\pi$
$720$	−9.39125	+	24.8631i	−0.349991	+	0.926592i
$721$			3.51146i			0.130774i
$722$	26.8695	+	0.170329i	0.999980	+	0.00633900i
$723$	−3.06462			−0.113975
$724$	3.09268	−	10.6706i	0.114939	−	0.396569i
$725$	11.0496	+	1.30424i	0.410373	+	0.0484381i
$726$	−1.57818	+	2.01405i	−0.0585717	+	0.0747485i
$727$	39.7704	+	14.4752i	1.47500	+	0.536857i	0.949454	−	0.313908i	$-0.101638\pi$
$727$	39.7704	+	14.4752i	1.47500	+	0.536857i	0.525548	+	0.850764i	$0.323860\pi$
$728$	−3.13104	−	2.13144i	−0.116044	−	0.0789966i
$729$	−12.7356	+	22.0588i	−0.471690	+	0.816992i
$730$	35.8291	+	4.04897i	1.32610	+	0.149859i
$731$	−13.1629	−	2.32098i	−0.486848	−	0.0858444i
$732$	1.37742	−	1.88454i	0.0509110	−	0.0696545i
$733$	−14.9446	+	8.62829i	−0.551993	+	0.318693i	−0.749925	−	0.661522i	$-0.769911\pi$
$733$	−14.9446	+	8.62829i	−0.551993	+	0.318693i	0.197932	+	0.980216i	$0.436577\pi$
$734$	−7.40541	+	0.248036i	−0.273339	+	0.00915518i
$735$	0.818313	−	2.46484i	0.0301839	−	0.0909170i
$736$	21.0318	−	24.7051i	0.775243	−	0.910641i
$737$	−3.58489	+	1.30479i	−0.132051	+	0.0480627i
$738$	5.64203	−	17.2805i	0.207686	−	0.636106i
$739$	41.0588	−	7.23978i	1.51037	−	0.266320i	0.643732	−	0.765251i	$-0.277385\pi$
$739$	41.0588	−	7.23978i	1.51037	−	0.266320i	0.866641	+	0.498932i	$0.166274\pi$
$740$	0.273187	−	3.44872i	0.0100426	−	0.126778i
$741$	2.60861	+	1.00871i	0.0958297	+	0.0370560i
$742$	1.16367	+	1.86818i	0.0427197	+	0.0685831i
$743$	8.97006	−	1.58166i	0.329080	−	0.0580256i	−0.00666746	−	0.999978i	$-0.502122\pi$
$743$	8.97006	−	1.58166i	0.329080	−	0.0580256i	0.335747	+	0.941952i	$0.391011\pi$
$744$	2.26437	+	2.20546i	0.0830157	+	0.0808561i
$745$	2.08457	−	1.85299i	0.0763726	−	0.0678882i
$746$	4.89514	+	23.1923i	0.179224	+	0.849131i
$747$	3.47855	+	2.91885i	0.127274	+	0.106795i
$748$	0.707108	+	1.05480i	0.0258544	+	0.0385675i
$749$	−3.46780	+	2.00213i	−0.126711	+	0.0731564i
$750$	2.66681	+	0.148129i	0.0973782	+	0.00540889i
$751$	−8.02258	+	45.4983i	−0.292748	+	1.66026i	0.383469	+	0.923554i	$0.374729\pi$
$751$	−8.02258	+	45.4983i	−0.292748	+	1.66026i	−0.676217	+	0.736702i	$0.736382\pi$
$752$	−4.02762	+	9.80736i	−0.146872	+	0.357637i
$753$	−1.56026	+	2.70245i	−0.0568591	+	0.0984829i
$754$	11.8349	+	1.68048i	0.431000	+	0.0611996i
$755$	51.3680	−	1.46547i	1.86947	−	0.0533339i
$756$	0.707149	+	0.0763629i	0.0257188	+	0.00277729i
$757$	1.50549	+	1.79418i	0.0547181	+	0.0652105i	0.792709	−	0.609600i	$-0.208670\pi$
$757$	1.50549	+	1.79418i	0.0547181	+	0.0652105i	−0.737991	+	0.674810i	$0.764225\pi$
$758$	−7.54163	+	6.77108i	−0.273924	+	0.245937i
$759$	−0.521145			−0.0189163
$760$	26.4670	−	7.71361i	0.960058	−	0.279802i
$761$	−37.7494			−1.36841			−0.684207	−	0.729288i	$-0.739851\pi$
$761$	−37.7494			−1.36841			−0.684207	+	0.729288i	$0.739851\pi$
$762$	−2.80314	+	2.51674i	−0.101547	+	0.0911718i
$763$	1.19336	+	1.42220i	0.0432027	+	0.0514870i
$764$	17.5328	+	1.89331i	0.634313	+	0.0684976i
$765$	0.223668	+	7.84007i	0.00808673	+	0.283458i
$766$	−46.6757	−	6.62770i	−1.68646	−	0.239468i
$767$	6.37730	−	11.0458i	0.230271	−	0.398841i
$768$	−0.715318	−	2.60641i	−0.0258118	−	0.0940506i
$769$	3.51096	−	19.9117i	0.126609	−	0.718033i	−0.853731	−	0.520714i	$-0.825666\pi$
$769$	3.51096	−	19.9117i	0.126609	−	0.718033i	0.980339	−	0.197318i	$-0.0632233\pi$
$770$	0.413192	+	0.434615i	0.0148904	+	0.0156624i
$771$	−1.28601	+	0.742478i	−0.0463145	+	0.0267397i
$772$	21.4466	+	31.9923i	0.771882	+	1.15143i
$773$	7.41424	+	6.22129i	0.266672	+	0.223764i	0.766312	−	0.642469i	$-0.222090\pi$
$773$	7.41424	+	6.22129i	0.266672	+	0.223764i	−0.499640	+	0.866233i	$0.666534\pi$
$774$	9.82657	+	46.5565i	0.353209	+	1.67344i
$775$	−14.8792	+	29.5433i	−0.534477	+	1.06123i
$776$	−23.7662	+	24.4010i	−0.853157	+	0.875944i
$777$	−0.0453702	+	0.00799998i	−0.00162765	+	0.000286998i
$778$	5.41334	+	8.69068i	0.194077	+	0.311576i
$779$	−17.8435	+	6.09501i	−0.639310	+	0.218376i
$780$	2.86054	+	0.226595i	0.102424	+	0.00811342i
$781$	3.78998	−	0.668276i	0.135616	−	0.0239128i
$782$	2.97174	−	9.10193i	0.106269	−	0.325484i
$783$	−2.10931	+	0.767725i	−0.0753805	+	0.0274363i
$784$	−8.34959	−	26.2048i	−0.298200	−	0.935884i
$785$	−9.70610	+	29.2358i	−0.346426	+	1.04347i
$786$	−3.92522	+	0.131471i	−0.140008	+	0.00468941i
$787$	−32.3581	+	18.6820i	−1.15344	+	0.665940i	−0.949724	−	0.313090i	$-0.898636\pi$
$787$	−32.3581	+	18.6820i	−1.15344	+	0.665940i	−0.203718	+	0.979030i	$0.565303\pi$
$788$	24.8238	−	33.9630i	0.884312	−	1.20988i
$789$	4.30878	+	0.759754i	0.153397	+	0.0270480i
$790$	2.62406	−	23.2201i	0.0933598	−	0.826135i
$791$	2.67711	−	4.63689i	0.0951871	−	0.164869i
$792$	2.54397	−	3.73702i	0.0903960	−	0.132789i
$793$	24.6612	+	8.97595i	0.875746	+	0.318745i
$794$	−1.49938	+	1.91349i	−0.0532108	+	0.0679070i
$795$	−1.46722	−	0.792196i	−0.0520371	−	0.0280963i
$796$	9.75248	−	33.6486i	0.345667	−	1.19264i
$797$	−49.7980			−1.76394			−0.881968	−	0.471309i	$-0.843782\pi$
$797$	−49.7980			−1.76394			−0.881968	+	0.471309i	$0.843782\pi$
$798$	−0.187858	−	0.315416i	−0.00665011	−	0.0111656i
$799$			3.12878i			0.110688i
$800$	23.7588	−	15.3467i	0.839999	−	0.542588i
$801$	−9.65760	−	11.5095i	−0.341235	−	0.406668i
$802$	−13.2635	+	16.9268i	−0.468352	+	0.597705i
$803$	−5.76331	−	2.09767i	−0.203383	−	0.0740253i
$804$	2.19178	−	0.968366i	0.0772980	−	0.0341516i
$805$	0.657851	−	4.47340i	0.0231862	−	0.157667i
$806$	−16.7288	+	31.3544i	−0.589246	+	1.10441i
$807$	−0.192749	+	1.09314i	−0.00678510	+	0.0384802i
$808$	1.66876	−	22.4826i	0.0587069	−	0.790936i
$809$	11.2064	+	19.4100i	0.393994	+	0.682418i	0.992972	−	0.118347i	$-0.0377596\pi$
$809$	11.2064	+	19.4100i	0.393994	+	0.682418i	−0.598978	+	0.800766i	$0.704426\pi$
$810$	25.3475	−	11.0490i	0.890619	−	0.388223i
$811$	−24.1580	−	20.2710i	−0.848303	−	0.711811i	0.111112	−	0.993808i	$-0.464559\pi$
$811$	−24.1580	−	20.2710i	−0.848303	−	0.711811i	−0.959415	+	0.281997i	$0.909003\pi$
$812$	−1.08674	−	1.13179i	−0.0381370	−	0.0397179i
$813$	2.57651	−	0.937772i	0.0903620	−	0.0328891i
$814$	−0.182639	+	0.559391i	−0.00640149	+	0.0196066i
$815$	−15.8641	−	25.7524i	−0.555696	−	0.902066i
$816$	−0.487468	−	0.631316i	−0.0170648	−	0.0221005i
$817$	32.4716	−	37.1695i	1.13604	−	1.30040i
$818$	9.60185	−	5.98089i	0.335721	−	0.209117i
$819$	0.690984	+	3.91876i	0.0241449	+	0.136933i
$820$	−15.7553	+	11.2260i	−0.550198	+	0.392030i
$821$	−19.1032	+	6.95301i	−0.666708	+	0.242662i	−0.653130	−	0.757246i	$-0.726544\pi$
$821$	−19.1032	+	6.95301i	−0.666708	+	0.242662i	−0.0135780	+	0.999908i	$0.504322\pi$
$822$	1.01464	+	4.80716i	0.0353895	+	0.167669i
$823$	−28.6865	−	24.0708i	−0.999947	−	0.839055i	−0.0129702	−	0.999916i	$-0.504129\pi$
$823$	−28.6865	−	24.0708i	−0.999947	−	0.839055i	−0.986977	+	0.160860i	$0.948573\pi$
$824$	−25.6865	−	11.5682i	−0.894832	−	0.402998i
$825$	−0.435079	−	0.130793i	−0.0151475	−	0.00455361i
$826$	−1.55318	+	0.624954i	−0.0540422	+	0.0217449i
$827$	21.8309	+	3.84937i	0.759134	+	0.133856i	0.539799	−	0.841794i	$-0.318500\pi$
$827$	21.8309	+	3.84937i	0.759134	+	0.133856i	0.219335	+	0.975650i	$0.429611\pi$
$828$	−34.0094	+	2.28077i	−1.18191	+	0.0792624i
$829$	−33.6577	−	19.4323i	−1.16898	−	0.674911i	−0.215541	−	0.976495i	$-0.569151\pi$
$829$	−33.6577	−	19.4323i	−1.16898	−	0.674911i	−0.953440	+	0.301584i	$0.902485\pi$
$830$	−1.13243	−	4.69796i	−0.0393073	−	0.163069i
$831$	2.73701	+	0.996192i	0.0949460	+	0.0345575i
$832$	25.9066	−	15.8818i	0.898148	−	0.550603i
$833$	−5.21706	−	6.21745i	−0.180760	−	0.215422i
$834$	1.38602	−	1.24441i	0.0479939	−	0.0430902i
$835$	11.4883	+	28.9656i	0.397568	+	1.00240i
$836$	−4.68404	+	0.220559i	−0.162001	+	0.00762818i
$837$		−	6.67343i		−	0.230668i
$838$	−27.8741	−	31.0462i	−0.962895	−	1.07247i
$839$	22.4922	−	18.8732i	0.776516	−	0.651574i	−0.165853	−	0.986150i	$-0.553038\pi$
$839$	22.4922	−	18.8732i	0.776516	−	0.651574i	0.942369	+	0.334577i	$0.108593\pi$
$840$	−0.277209	−	0.255003i	−0.00956461	−	0.00879845i
$841$	−22.5979	−	8.22497i	−0.779238	−	0.283620i
$842$	−33.4417	−	4.74854i	−1.15248	−	0.163645i
$843$	2.17521	−	3.76758i	0.0749183	−	0.129762i
$844$	−20.9812	+	1.40706i	−0.722201	+	0.0484330i
$845$	0.643856	+	3.12716i	0.0221493	+	0.107578i
$846$	10.3332	−	4.15777i	0.355263	−	0.142947i
$847$	1.88805	+	3.27020i	0.0648741	+	0.112365i
$848$	−17.4995	+	2.35774i	−0.600934	+	0.0809651i
$849$	−2.57179	+	3.06494i	−0.0882635	+	0.105188i
$850$	4.76530	−	6.85295i	0.163448	−	0.235054i
$851$	4.16927	−	1.51749i	0.142921	−	0.0520189i
$852$	−2.34706	+	0.578086i	−0.0804088	+	0.0198049i
$853$	7.15162	−	1.26102i	0.244867	−	0.0431766i	−0.0498676	−	0.998756i	$-0.515880\pi$
$853$	7.15162	−	1.26102i	0.244867	−	0.0431766i	0.294734	+	0.955579i	$0.404769\pi$
$854$	−1.82132	−	2.92399i	−0.0623244	−	0.100057i
$855$	−25.2058	−	14.2646i	−0.862021	−	0.487840i
$856$	−3.22134	−	31.9630i	−0.110103	−	1.09247i
$857$	−3.65149	−	20.7086i	−0.124732	−	0.707392i	−0.981466	−	0.191634i	$-0.938621\pi$
$857$	−3.65149	−	20.7086i	−0.124732	−	0.707392i	0.856734	−	0.515758i	$-0.172490\pi$
$858$	−0.463987	−	0.151490i	−0.0158403	−	0.00517178i
$859$	6.77073	+	18.6024i	0.231014	+	0.634707i	0.999990	−	0.00457169i	$-0.00145522\pi$
$859$	6.77073	+	18.6024i	0.231014	+	0.634707i	−0.768975	+	0.639279i	$0.779233\pi$
$860$	21.0226	−	46.0677i	0.716865	−	1.57090i
$861$	0.197351	+	0.165597i	0.00672569	+	0.00564353i
$862$	−20.3142	+	0.680402i	−0.691905	+	0.0231746i
$863$	−32.8992	+	18.9944i	−1.11990	+	0.646576i	−0.941376	−	0.337359i	$-0.890466\pi$
$863$	−32.8992	+	18.9944i	−1.11990	+	0.646576i	−0.178527	+	0.983935i	$0.557133\pi$
$864$	−2.88824	+	4.92126i	−0.0982600	+	0.167425i
$865$	3.18782	+	15.4830i	0.108389	+	0.526438i
$866$	17.6262	−	33.0364i	0.598963	−	1.12262i
$867$	2.28312	+	1.31816i	0.0775390	+	0.0447671i
$868$	4.26690	−	1.88519i	0.144828	−	0.0639876i
$869$	−1.35946	+	3.73509i	−0.0461165	+	0.126704i
$870$	1.14006	+	0.336566i	0.0386517	+	0.0114106i
$871$	17.3167	+	20.6372i	0.586753	+	0.699265i
$872$	−14.3349	+	4.04421i	−0.485440	+	0.136954i
$873$	35.7849			1.21113
$874$	23.0919	+	26.7734i	0.781096	+	0.905625i
$875$	1.67191	−	3.56953i	0.0565208	−	0.120672i
$876$	3.69997	+	1.07237i	0.125010	+	0.0362321i
$877$	30.1437	−	25.2935i	1.01788	−	0.854102i	0.0285194	−	0.999593i	$-0.490921\pi$
$877$	30.1437	−	25.2935i	1.01788	−	0.854102i	0.989360	+	0.145491i	$0.0464763\pi$
$878$	−34.1847	−	26.7866i	−1.15368	−	0.904003i
$879$	−0.887741	+	2.43905i	−0.0299428	+	0.0822670i
$880$	−4.54046	+	1.59071i	−0.153059	+	0.0536230i
$881$	−15.9604	+	27.6442i	−0.537719	+	0.931356i	0.461308	+	0.887240i	$0.347380\pi$
$881$	−15.9604	+	27.6442i	−0.537719	+	0.931356i	−0.999026	+	0.0441160i	$0.985953\pi$
$882$	−13.6011	+	25.4922i	−0.457973	+	0.858369i
$883$	−6.36734	+	36.1110i	−0.214278	+	1.21523i	0.667877	+	0.744272i	$0.267203\pi$
$883$	−6.36734	+	36.1110i	−0.214278	+	1.21523i	−0.882155	+	0.470959i	$0.843908\pi$
$884$	5.29162	−	7.23981i	0.177977	−	0.243501i
$885$	0.787246	−	0.994474i	0.0264630	−	0.0334289i
$886$	−44.9421	+	1.50529i	−1.50986	+	0.0505711i
$887$	16.6814	−	19.8802i	0.560108	−	0.667510i	−0.409462	−	0.912327i	$-0.634283\pi$
$887$	16.6814	−	19.8802i	0.560108	−	0.667510i	0.969569	+	0.244817i	$0.0787279\pi$
$888$	0.0909480	−	0.358240i	0.00305201	−	0.0120218i
$889$	1.90146	+	5.22422i	0.0637729	+	0.175215i
$890$	0.990745	+	15.9586i	0.0332099	+	0.534935i
$891$	−4.63186	+	0.816723i	−0.155173	+	0.0273612i
$892$	−18.9999	−	9.33399i	−0.636163	−	0.312525i
$893$	−9.88858	−	5.97478i	−0.330909	−	0.199938i
$894$	0.252923	−	0.157543i	0.00845902	−	0.00526904i
$895$	−21.0792	−	34.2180i	−0.704599	−	1.14378i
$896$	−3.96249	−	0.456486i	−0.132378	−	0.0152501i
$897$	1.25868	+	3.45820i	0.0420262	+	0.115466i
$898$	−34.6800	+	7.31981i	−1.15729	+	0.244265i
$899$	−9.46296	+	11.2775i	−0.315607	+	0.376126i
$900$	−28.9653	−	6.63129i	−0.965509	−	0.221043i
$901$	−4.51276	+	2.60545i	−0.150342	+	0.0868000i
$902$	3.05275	−	1.22833i	0.101646	−	0.0408991i
$903$	−0.664093	−	0.117097i	−0.0220996	−	0.00389676i
$904$	25.0996	+	34.8591i	0.834800	+	1.15940i
$905$	12.2889	+	1.80718i	0.408496	+	0.0600727i
$906$	5.43571	+	0.771840i	0.180589	+	0.0256427i
$907$	10.6876	−	29.3641i	0.354878	−	0.975018i	−0.625903	−	0.779901i	$-0.715269\pi$
$907$	10.6876	−	29.3641i	0.354878	−	0.975018i	0.980780	−	0.195117i	$-0.0625086\pi$
$908$	−3.59388	−	0.388093i	−0.119267	−	0.0128793i
$909$	−18.1434	+	15.2242i	−0.601780	+	0.504953i
$910$	1.88606	−	3.79155i	0.0625223	−	0.125689i
$911$	−21.9268			−0.726468			−0.363234	−	0.931698i	$-0.618327\pi$
$911$	−21.9268			−0.726468			−0.363234	+	0.931698i	$0.618327\pi$
$912$	2.92617	−	0.335081i	0.0968950	−	0.0110956i
$913$			0.821993i			0.0272040i
$914$	26.5221	+	29.5403i	0.877272	+	0.977106i
$915$	2.29643	+	1.23991i	0.0759177	+	0.0409901i
$916$	0.160454	−	1.48586i	0.00530154	−	0.0490942i
$917$	−1.98234	+	5.44645i	−0.0654628	+	0.179858i
$918$	−0.236736	+	1.66722i	−0.00781346	+	0.0550265i
$919$	−5.54626	−	3.20213i	−0.182954	−	0.105629i	0.405726	−	0.913995i	$-0.367019\pi$
$919$	−5.54626	−	3.20213i	−0.182954	−	0.105629i	−0.588680	+	0.808366i	$0.700352\pi$
$920$	30.5559	+	19.5495i	1.00740	+	0.644527i
$921$	0.132104	−	0.749201i	0.00435299	−	0.0246870i
$922$	−11.3176	+	4.55384i	−0.372724	+	0.149973i
$923$	−13.5882	−	23.5355i	−0.447261	−	0.774679i
$924$	0.0356749	+	0.0532168i	0.00117362	+	0.00175070i
$925$	3.86157	−	0.220512i	0.126968	−	0.00725039i
$926$	11.3928	+	53.9772i	0.374392	+	1.77380i
$927$	10.1224	+	27.8111i	0.332463	+	0.913436i
$928$	11.8592	−	4.22095i	0.389298	−	0.138560i
$929$	−7.46019	−	42.3088i	−0.244761	−	1.38811i	−0.821048	−	0.570860i	$-0.806610\pi$
$929$	−7.46019	−	42.3088i	−0.244761	−	1.38811i	0.576287	−	0.817247i	$-0.304501\pi$
$930$	−2.09951	+	2.84277i	−0.0688456	+	0.0932180i
$931$	29.6129	−	4.61568i	0.970525	−	0.151273i
$932$	−21.0946	−	10.3630i	−0.690975	−	0.339453i
$933$	−0.944788	−	5.35816i	−0.0309310	−	0.175418i
$934$	−15.6689	−	5.11585i	−0.512703	−	0.167396i
$935$	−1.06114	+	0.943260i	−0.0347031	+	0.0308479i
$936$	−30.9423	−	7.85546i	−1.01138	−	0.256764i
$937$	−15.6006	+	18.5921i	−0.509649	+	0.607376i	−0.958101	−	0.286431i	$-0.907531\pi$
$937$	−15.6006	+	18.5921i	−0.509649	+	0.607376i	0.448452	+	0.893807i	$0.351976\pi$
$938$	−0.118375	−	3.53422i	−0.00386508	−	0.115396i
$939$	0.958079	+	1.65944i	0.0312657	+	0.0541538i
$940$	−11.4745	−	2.97374i	−0.374257	−	0.0969928i
$941$	−46.9057	−	8.27073i	−1.52908	−	0.269618i	−0.655086	−	0.755554i	$-0.727368\pi$
$941$	−46.9057	−	8.27073i	−1.52908	−	0.269618i	−0.873994	+	0.485936i	$0.838479\pi$
$942$	−1.54921	+	2.90366i	−0.0504761	+	0.0946062i
$943$	−21.4867	−	12.4054i	−0.699704	−	0.403975i
$944$	0.545270	−	13.4205i	0.0177470	−	0.436799i
$945$	0.0226773	+	0.794889i	0.000737692	+	0.0258578i
$946$	−5.31254	+	6.77980i	−0.172726	+	0.220430i
$947$	−6.91093	+	5.79896i	−0.224575	+	0.188441i	−0.748132	−	0.663550i	$-0.769049\pi$
$947$	−6.91093	+	5.79896i	−0.224575	+	0.188441i	0.523557	+	0.851991i	$0.324605\pi$
$948$	0.694982	−	2.39787i	0.0225720	−	0.0778793i
$949$			43.3104i			1.40592i
$950$	12.5590	+	28.1473i	0.407468	+	0.913220i
$951$		−	1.42334i		−	0.0461550i
$952$	−1.13287	+	0.319611i	−0.0367167	+	0.0103587i
$953$	1.42806	−	1.19829i	0.0462596	−	0.0388164i	−0.619365	−	0.785103i	$-0.712610\pi$
$953$	1.42806	−	1.19829i	0.0462596	−	0.0388164i	0.665624	+	0.746287i	$0.268165\pi$
$954$	14.6017	+	11.4417i	0.472749	+	0.370438i
$955$	0.562251	+	19.7082i	0.0181940	+	0.637742i
$956$	8.09886	+	18.3308i	0.261936	+	0.592860i
$957$	−0.175105	−	0.101097i	−0.00566033	−	0.00326800i
$958$	21.5158	+	11.4795i	0.695145	+	0.370887i
$959$	7.14044	+	1.25905i	0.230577	+	0.0406569i
$960$	2.77860	−	1.18771i	0.0896791	−	0.0383331i
$961$	−6.38390	−	11.0572i	−0.205932	−	0.356685i
$962$	4.15311	−	0.139104i	0.133902	−	0.00448489i
$963$	−21.6938	+	25.8536i	−0.699072	+	0.833121i
$964$	−25.1305	−	26.1723i	−0.809400	−	0.842953i
$965$	−32.1846	+	28.6091i	−1.03606	+	0.920961i
$966$	0.149930	−	0.459208i	0.00482391	−	0.0147748i
$967$	−1.32962	−	7.54063i	−0.0427576	−	0.242490i	0.955937	−	0.293572i	$-0.0948442\pi$
$967$	−1.32962	−	7.54063i	−0.0427576	−	0.242490i	−0.998694	+	0.0510819i	$0.983733\pi$
$968$	−30.1417	+	3.03778i	−0.968790	+	0.0976379i
$969$	0.761233	−	0.419517i	0.0244543	−	0.0134768i
$970$	−30.6339	−	22.6245i	−0.983594	−	0.726428i
$971$	−3.33371	−	18.9064i	−0.106984	−	0.606735i	−0.990409	−	0.138164i	$-0.955880\pi$
$971$	−3.33371	−	18.9064i	−0.106984	−	0.606735i	0.883426	−	0.468571i	$-0.155231\pi$
$972$	8.74512	−	2.15395i	0.280500	−	0.0690879i
$973$	−0.940180	−	2.58312i	−0.0301408	−	0.0828112i
$974$	41.5873	−	8.77772i	1.33254	−	0.281256i
$975$	0.182904	+	3.20299i	0.00585761	+	0.102578i
$976$	27.3894	−	3.69022i	0.876712	−	0.118121i
$977$	−19.3160	−	33.4564i	−0.617975	−	1.07036i	−0.989855	−	0.142083i	$-0.954620\pi$
$977$	−19.3160	−	33.4564i	−0.617975	−	1.07036i	0.371880	−	0.928281i	$-0.378713\pi$
$978$	−1.20625	−	2.99787i	−0.0385716	−	0.0958613i
$979$	0.472276	−	2.67841i	0.0150940	−	0.0856023i
$980$	27.7604	−	13.2237i	0.886774	−	0.422415i
$981$	13.5513	+	7.82384i	0.432659	+	0.249796i
$982$	26.2026	+	3.72062i	0.836158	+	0.118730i
$983$	−6.94718	+	19.0872i	−0.221581	+	0.608788i	−0.999816	−	0.0191849i	$-0.993893\pi$
$983$	−6.94718	+	19.0872i	−0.221581	+	0.608788i	0.778235	+	0.627973i	$0.216115\pi$
$984$	−1.86150	+	0.898085i	−0.0593426	+	0.0286299i
$985$	41.3862	+	22.3456i	1.31867	+	0.711988i
$986$	2.76419	−	2.48176i	0.0880297	−	0.0790354i
$987$			0.157853i			0.00502451i
$988$	12.7766	+	30.5495i	0.406478	+	0.971911i
$989$	64.9430			2.06507
$990$	4.52537	+	2.25109i	0.143826	+	0.0715445i
$991$	−22.7223	+	19.0662i	−0.721796	+	0.605659i	−0.927882	−	0.372875i	$-0.878372\pi$
$991$	−22.7223	+	19.0662i	−0.721796	+	0.605659i	0.206085	+	0.978534i	$0.433928\pi$
$992$	−0.266681	+	37.4232i	−0.00846712	+	1.18819i
$993$	−1.51222	+	4.15479i	−0.0479888	+	0.131848i
$994$	−0.501498	+	3.53182i	−0.0159066	+	0.112022i
$995$	38.7518	+	5.69878i	1.22851	+	0.180663i
$996$	−0.0345465	−	0.515134i	−0.00109465	−	0.0163227i
$997$	−4.72799	−	0.833672i	−0.149737	−	0.0264027i	0.0982772	−	0.995159i	$-0.468667\pi$
$997$	−4.72799	−	0.833672i	−0.149737	−	0.0264027i	−0.248014	+	0.968756i	$0.579778\pi$
$998$	1.94820	+	4.84181i	0.0616691	+	0.153265i
$999$	−0.675778	+	0.390161i	−0.0213807	+	0.0123441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.219.12	yes	336
4.3	odd	2	inner	380.2.bb.a.219.50	yes	336
5.4	even	2	inner	380.2.bb.a.219.45	yes	336
19.2	odd	18	inner	380.2.bb.a.59.7	✓	336
20.19	odd	2	inner	380.2.bb.a.219.7	yes	336
76.59	even	18	inner	380.2.bb.a.59.45	yes	336
95.59	odd	18	inner	380.2.bb.a.59.50	yes	336
380.59	even	18	inner	380.2.bb.a.59.12	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.7	✓	336	19.2	odd	18	inner
380.2.bb.a.59.12	yes	336	380.59	even	18	inner
380.2.bb.a.59.45	yes	336	76.59	even	18	inner
380.2.bb.a.59.50	yes	336	95.59	odd	18	inner
380.2.bb.a.219.7	yes	336	20.19	odd	2	inner
380.2.bb.a.219.12	yes	336	1.1	even	1	trivial
380.2.bb.a.219.45	yes	336	5.4	even	2	inner
380.2.bb.a.219.50	yes	336	4.3	odd	2	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05231 + 0.944795i) q^{2} +(-0.108582 - 0.129403i) q^{3} +(0.214726 - 1.98844i) q^{4} +(2.23516 - 0.0637665i) q^{5} +(0.236522 + 0.0335848i) q^{6} +(0.176277 - 0.305321i) q^{7} +(1.65271 + 2.29533i) q^{8} +(0.515989 - 2.92632i) q^{9} +O(q^{10})\)	\(q+(-1.05231 + 0.944795i) q^{2} +(-0.108582 - 0.129403i) q^{3} +(0.214726 - 1.98844i) q^{4} +(2.23516 - 0.0637665i) q^{5} +(0.236522 + 0.0335848i) q^{6} +(0.176277 - 0.305321i) q^{7} +(1.65271 + 2.29533i) q^{8} +(0.515989 - 2.92632i) q^{9} +(-2.29184 + 2.17887i) q^{10} +(0.465827 - 0.268946i) q^{11} +(-0.280626 + 0.188123i) q^{12} +(-2.90974 - 2.44156i) q^{13} +(0.102967 + 0.487839i) q^{14} +(-0.250950 - 0.282313i) q^{15} +(-3.90779 - 0.853938i) q^{16} +(-1.16250 + 0.204980i) q^{17} +(2.22179 + 3.56691i) q^{18} +(1.57208 - 4.06553i) q^{19} +(0.353150 - 4.45817i) q^{20} +(-0.0586501 + 0.0103416i) q^{21} +(-0.236098 + 0.723126i) q^{22} +(5.38963 - 1.96166i) q^{23} +(0.117569 - 0.463098i) q^{24} +(4.99187 - 0.285056i) q^{25} +(5.36874 - 0.179820i) q^{26} +(-0.873580 + 0.504362i) q^{27} +(-0.569262 - 0.416077i) q^{28} +(2.19146 + 0.386413i) q^{29} +(0.530806 + 0.0599852i) q^{30} +(-3.30786 + 5.72938i) q^{31} +(4.91901 - 2.79345i) q^{32} +(-0.0853830 - 0.0310769i) q^{33} +(1.02965 - 1.31403i) q^{34} +(0.374538 - 0.693682i) q^{35} +(-5.70802 - 1.65437i) q^{36} +0.773573 q^{37} +(2.18677 + 5.76351i) q^{38} +0.641641i q^{39} +(3.84043 + 5.02505i) q^{40} +(-2.78057 - 3.31376i) q^{41} +(0.0519476 - 0.0662949i) q^{42} +(10.6401 + 3.87268i) q^{43} +(-0.434757 - 0.984019i) q^{44} +(0.966717 - 6.57370i) q^{45} +(-3.81820 + 7.15637i) q^{46} +(0.460262 - 2.61027i) q^{47} +(0.313814 + 0.598403i) q^{48} +(3.43785 + 5.95454i) q^{49} +(-4.98369 + 5.01626i) q^{50} +(0.152752 + 0.128174i) q^{51} +(-5.47970 + 5.26158i) q^{52} +(4.14817 - 1.50981i) q^{53} +(0.442761 - 1.35610i) q^{54} +(1.02405 - 0.630840i) q^{55} +(0.992149 - 0.0999921i) q^{56} +(-0.696793 + 0.238012i) q^{57} +(-2.67118 + 1.66385i) q^{58} +(0.583091 + 3.30687i) q^{59} +(-0.615247 + 0.438379i) q^{60} +(-6.49253 + 2.36309i) q^{61} +(-1.93219 - 9.15436i) q^{62} +(-0.802511 - 0.673386i) q^{63} +(-2.53711 + 7.58703i) q^{64} +(-6.65943 - 5.27174i) q^{65} +(0.119211 - 0.0479668i) q^{66} +(-6.98470 - 1.23159i) q^{67} +(0.157972 + 2.35557i) q^{68} +(-0.839063 - 0.484433i) q^{69} +(0.261255 + 1.08383i) q^{70} +(6.72322 + 2.44705i) q^{71} +(7.56966 - 3.65199i) q^{72} +(-7.32925 - 8.73466i) q^{73} +(-0.814041 + 0.730868i) q^{74} +(-0.578915 - 0.615012i) q^{75} +(-7.74650 - 3.99897i) q^{76} -0.189636i q^{77} +(-0.606219 - 0.675207i) q^{78} +(-5.66076 + 4.74994i) q^{79} +(-8.78897 - 1.65950i) q^{80} +(-8.21667 - 2.99062i) q^{81} +(6.05686 + 0.860040i) q^{82} +(-0.764089 + 1.32344i) q^{83} +(0.00796996 + 0.118843i) q^{84} +(-2.58530 + 0.532291i) q^{85} +(-14.8556 + 5.97744i) q^{86} +(-0.187950 - 0.325540i) q^{87} +(1.38720 + 0.624740i) q^{88} +(3.25011 - 3.87334i) q^{89} +(5.19350 + 7.83093i) q^{90} +(-1.25838 + 0.458014i) q^{91} +(-2.74336 - 11.1382i) q^{92} +(1.10058 - 0.194061i) q^{93} +(1.98183 + 3.18168i) q^{94} +(3.25461 - 9.18736i) q^{95} +(-0.895598 - 0.333217i) q^{96} +(2.09122 + 11.8599i) q^{97} +(-9.24351 - 3.01797i) q^{98} +(-0.546659 - 1.50193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

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