LMFDB - Embedded newform 380.2.bb.a.59.7

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			59.7
Character	$\chi$	$=$	380.59
Dual form			380.2.bb.a.219.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31199 + 0.527904i) q^{2} +(-0.108582 + 0.129403i) q^{3} +(1.44263 - 1.38521i) q^{4} +(1.67124 - 1.48558i) q^{5} +(0.0741462 - 0.227097i) q^{6} +(0.176277 + 0.305321i) q^{7} +(-1.16146 + 2.57895i) q^{8} +(0.515989 + 2.92632i) q^{9} +O(q^{10})$	\(q+(-1.31199 + 0.527904i) q^{2} +(-0.108582 + 0.129403i) q^{3} +(1.44263 - 1.38521i) q^{4} +(1.67124 - 1.48558i) q^{5} +(0.0741462 - 0.227097i) q^{6} +(0.176277 + 0.305321i) q^{7} +(-1.16146 + 2.57895i) q^{8} +(0.515989 + 2.92632i) q^{9} +(-1.40841 + 2.83132i) q^{10} +(-0.465827 - 0.268946i) q^{11} +(0.0226063 + 0.337091i) q^{12} +(2.90974 - 2.44156i) q^{13} +(-0.392454 - 0.307521i) q^{14} +(0.0107717 + 0.377572i) q^{15} +(0.162385 - 3.99670i) 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} +(0.753138 + 0.106941i) q^{22} +(5.38963 + 1.96166i) q^{23} +(-0.207611 - 0.430325i) q^{24} +(0.586103 - 4.96553i) q^{25} +(-2.52864 + 4.73937i) q^{26} +(-0.873580 - 0.504362i) q^{27} +(0.677238 + 0.196286i) q^{28} +(2.19146 - 0.386413i) q^{29} +(-0.213454 - 0.489684i) q^{30} +(3.30786 + 5.72938i) q^{31} +(1.89683 + 5.32936i) q^{32} +(0.0853830 - 0.0310769i) q^{33} +(-1.63340 + 0.344757i) q^{34} +(0.748181 + 0.248392i) q^{35} +(4.79795 + 3.50686i) q^{36} -0.773573 q^{37} +(4.20877 + 4.50403i) q^{38} +0.641641i q^{39} +(1.89016 + 6.03550i) q^{40} +(-2.78057 + 3.31376i) q^{41} +(0.0824077 - 0.0173936i) q^{42} +(10.6401 - 3.87268i) q^{43} +(-1.04456 + 0.257279i) q^{44} +(5.20963 + 4.12405i) q^{45} +(-8.10670 + 0.271525i) q^{46} +(0.460262 + 2.61027i) q^{47} +(0.499554 + 0.454984i) q^{48} +(3.43785 - 5.95454i) q^{49} +(1.85236 + 6.82413i) q^{50} +(-0.152752 + 0.128174i) q^{51} +(0.815614 - 7.55289i) q^{52} +(-4.14817 - 1.50981i) q^{53} +(1.41238 + 0.200551i) q^{54} +(-1.17805 + 0.242551i) 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} +(0.538556 + 0.529777i) q^{60} +(-6.49253 - 2.36309i) q^{61} +(-7.36445 - 5.77066i) q^{62} +(-0.802511 + 0.673386i) q^{63} +(-5.30201 - 5.99072i) q^{64} +(1.23575 - 8.40310i) q^{65} +(-0.0956160 + 0.0858466i) q^{66} +(-6.98470 + 1.23159i) q^{67} +(1.96100 - 1.31459i) q^{68} +(-0.839063 + 0.484433i) q^{69} +(-1.11273 + 0.0690808i) q^{70} +(-6.72322 + 2.44705i) q^{71} +(-8.14615 - 2.06810i) q^{72} +(7.32925 - 8.73466i) q^{73} +(1.01492 - 0.408373i) q^{74} +(0.578915 + 0.615012i) q^{75} +(-7.89956 - 3.68741i) q^{76} -0.189636i q^{77} +(-0.338725 - 0.841826i) q^{78} +(5.66076 + 4.74994i) q^{79} +(-5.66604 - 6.92069i) q^{80} +(-8.21667 + 2.99062i) q^{81} +(1.89874 - 5.81550i) q^{82} +(-0.764089 - 1.32344i) q^{83} +(-0.0989359 + 0.0663236i) q^{84} +(2.24733 - 1.38441i) q^{85} +(-11.9153 + 10.6979i) q^{86} +(-0.187950 + 0.325540i) q^{87} +(1.23464 - 0.888977i) q^{88} +(3.25011 + 3.87334i) q^{89} +(-9.01208 - 2.66052i) q^{90} +(1.25838 + 0.458014i) q^{91} +(10.4926 - 4.63580i) q^{92} +(-1.10058 - 0.194061i) q^{93} +(-1.98183 - 3.18168i) q^{94} +(-8.66701 - 4.45904i) q^{95} +(-0.895598 - 0.333217i) q^{96} +(-2.09122 + 11.8599i) q^{97} +(-1.36700 + 9.62715i) 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.31199	+	0.527904i	−0.927717	+	0.373285i
$2$	−1.31199	+	0.527904i	−0.927717	+	0.373285i
$3$	−0.108582	+	0.129403i	−0.0626900	+	0.0747110i	−0.796478	−	0.604667i	$-0.793306\pi$
$3$	−0.108582	+	0.129403i	−0.0626900	+	0.0747110i	0.733788	+	0.679378i	$0.237750\pi$
$4$	1.44263	−	1.38521i	0.721317	−	0.692605i
$5$	1.67124	−	1.48558i	0.747402	−	0.664372i
$5$	1.67124	−	1.48558i	0.747402	−	0.664372i
$6$	0.0741462	−	0.227097i	0.0302701	−	0.0927118i
$7$	0.176277	+	0.305321i	0.0666265	+	0.115401i	0.897414	−	0.441189i	$-0.145443\pi$
$7$	0.176277	+	0.305321i	0.0666265	+	0.115401i	−0.830788	+	0.556589i	$0.812110\pi$
$8$	−1.16146	+	2.57895i	−0.410639	+	0.911798i
$9$	0.515989	+	2.92632i	0.171996	+	0.975440i
$10$	−1.40841	+	2.83132i	−0.445378	+	0.895343i
$11$	−0.465827	−	0.268946i	−0.140452	−	0.0810901i	0.428127	−	0.903718i	$-0.359173\pi$
$11$	−0.465827	−	0.268946i	−0.140452	−	0.0810901i	−0.568579	+	0.822628i	$0.692507\pi$
$12$	0.0226063	+	0.337091i	0.00652589	+	0.0973097i
$13$	2.90974	−	2.44156i	0.807018	−	0.677168i	−0.142876	−	0.989741i	$-0.545635\pi$
$13$	2.90974	−	2.44156i	0.807018	−	0.677168i	0.949894	+	0.312572i	$0.101191\pi$
$14$	−0.392454	−	0.307521i	−0.104888	−	0.0821884i
$15$	0.0107717	+	0.377572i	0.00278124	+	0.0974886i
$16$	0.162385	−	3.99670i	0.0405962	−	0.999176i
$17$	1.16250	+	0.204980i	0.281947	+	0.0497149i	0.312833	−	0.949808i	$-0.398722\pi$
$17$	1.16250	+	0.204980i	0.281947	+	0.0497149i	−0.0308862	+	0.999523i	$0.509833\pi$
$18$	−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
$22$	0.753138	+	0.106941i	0.160570	+	0.0228000i
$23$	5.38963	+	1.96166i	1.12381	+	0.409035i	0.836043	−	0.548664i	$-0.184863\pi$
$23$	5.38963	+	1.96166i	1.12381	+	0.409035i	0.287772	+	0.957699i	$0.407086\pi$
$24$	−0.207611	−	0.430325i	−0.0423784	−	0.0878398i
$25$	0.586103	−	4.96553i	0.117221	−	0.993106i
$26$	−2.52864	+	4.73937i	−0.495907	+	0.929468i
$27$	−0.873580	−	0.504362i	−0.168121	−	0.0970644i
$28$	0.677238	+	0.196286i	0.127986	+	0.0370945i
$29$	2.19146	−	0.386413i	0.406944	−	0.0717552i	0.0335705	−	0.999436i	$-0.489312\pi$
$29$	2.19146	−	0.386413i	0.406944	−	0.0717552i	0.373373	+	0.927681i	$0.378201\pi$
$30$	−0.213454	−	0.489684i	−0.0389712	−	0.0894036i
$31$	3.30786	+	5.72938i	0.594110	+	1.02903i	0.993672	+	0.112322i	$0.0358288\pi$
$31$	3.30786	+	5.72938i	0.594110	+	1.02903i	−0.399562	+	0.916706i	$0.630838\pi$
$32$	1.89683	+	5.32936i	0.335315	+	0.942106i
$33$	0.0853830	−	0.0310769i	0.0148633	−	0.00540979i
$34$	−1.63340	+	0.344757i	−0.280125	+	0.0591253i
$35$	0.748181	+	0.248392i	0.126466	+	0.0419859i
$36$	4.79795	+	3.50686i	0.799659	+	0.584476i
$37$	−0.773573			−0.127175			−0.0635873	−	0.997976i	$-0.520254\pi$
$37$	−0.773573			−0.127175			−0.0635873	+	0.997976i	$0.520254\pi$
$38$	4.20877	+	4.50403i	0.682753	+	0.730650i
$39$			0.641641i			0.102745i
$40$	1.89016	+	6.03550i	0.298860	+	0.954297i
$41$	−2.78057	+	3.31376i	−0.434253	+	0.517522i	−0.938144	−	0.346245i	$-0.887457\pi$
$41$	−2.78057	+	3.31376i	−0.434253	+	0.517522i	0.503891	+	0.863767i	$0.331901\pi$
$42$	0.0824077	−	0.0173936i	0.0127158	−	0.00268389i
$43$	10.6401	−	3.87268i	1.62260	−	0.590578i	0.638724	−	0.769436i	$-0.279462\pi$
$43$	10.6401	−	3.87268i	1.62260	−	0.590578i	0.983875	+	0.178858i	$0.0572402\pi$
$44$	−1.04456	+	0.257279i	−0.157474	+	0.0387863i
$45$	5.20963	+	4.12405i	0.776606	+	0.614777i
$46$	−8.10670	+	0.271525i	−1.19527	+	0.0400342i
$47$	0.460262	+	2.61027i	0.0671361	+	0.380748i	0.999800	+	0.0200010i	$0.00636694\pi$
$47$	0.460262	+	2.61027i	0.0671361	+	0.380748i	−0.932664	+	0.360747i	$0.882522\pi$
$48$	0.499554	+	0.454984i	0.0721044	+	0.0656713i
$49$	3.43785	−	5.95454i	0.491122	−	0.850648i
$50$	1.85236	+	6.82413i	0.261964	+	0.965078i
$51$	−0.152752	+	0.128174i	−0.0213895	+	0.0179479i
$52$	0.815614	−	7.55289i	0.113105	−	1.04740i
$53$	−4.14817	−	1.50981i	−0.569796	−	0.207389i	0.0410244	−	0.999158i	$-0.486938\pi$
$53$	−4.14817	−	1.50981i	−0.569796	−	0.207389i	−0.610820	+	0.791770i	$0.709160\pi$
$54$	1.41238	+	0.200551i	0.192201	+	0.0272915i
$55$	−1.17805	+	0.242551i	−0.158848	+	0.0327055i
$56$	−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	0.923038	+	0.384708i	$0.125698\pi$
$59$	−0.583091	+	3.30687i	−0.0759120	+	0.430518i	−0.998950	+	0.0458100i	$0.985413\pi$
$60$	0.538556	+	0.529777i	0.0695273	+	0.0683939i
$61$	−6.49253	−	2.36309i	−0.831283	−	0.302562i	−0.108898	−	0.994053i	$-0.534732\pi$
$61$	−6.49253	−	2.36309i	−0.831283	−	0.302562i	−0.722386	+	0.691491i	$0.756954\pi$
$62$	−7.36445	−	5.77066i	−0.935286	−	0.732874i
$63$	−0.802511	+	0.673386i	−0.101107	+	0.0848387i
$64$	−5.30201	−	5.99072i	−0.662751	−	0.748839i
$65$	1.23575	−	8.40310i	0.153276	−	1.04228i
$66$	−0.0956160	+	0.0858466i	−0.0117695	+	0.0105670i
$67$	−6.98470	+	1.23159i	−0.853317	+	0.150463i	−0.583164	−	0.812355i	$-0.698185\pi$
$67$	−6.98470	+	1.23159i	−0.853317	+	0.150463i	−0.270153	+	0.962817i	$0.587074\pi$
$68$	1.96100	−	1.31459i	0.237806	−	0.159418i
$69$	−0.839063	+	0.484433i	−0.101011	+	0.0583189i
$70$	−1.11273	+	0.0690808i	−0.132997	+	0.00825673i
$71$	−6.72322	+	2.44705i	−0.797899	+	0.290412i	−0.708616	−	0.705595i	$-0.750680\pi$
$71$	−6.72322	+	2.44705i	−0.797899	+	0.290412i	−0.0892837	+	0.996006i	$0.528458\pi$
$72$	−8.14615	−	2.06810i	−0.960033	−	0.243728i
$73$	7.32925	−	8.73466i	0.857823	−	1.02231i	−0.141652	−	0.989917i	$-0.545241\pi$
$73$	7.32925	−	8.73466i	0.857823	−	1.02231i	0.999475	−	0.0323977i	$-0.0103143\pi$
$74$	1.01492	−	0.408373i	0.117982	−	0.0474724i
$75$	0.578915	+	0.615012i	0.0668474	+	0.0710154i
$76$	−7.89956	−	3.68741i	−0.906141	−	0.422975i
$77$		−	0.189636i		−	0.0216110i
$78$	−0.338725	−	0.841826i	−0.0383530	−	0.0953180i
$79$	5.66076	+	4.74994i	0.636885	+	0.534410i	0.903060	−	0.429515i	$-0.141315\pi$
$79$	5.66076	+	4.74994i	0.636885	+	0.534410i	−0.266175	+	0.963925i	$0.585760\pi$
$80$	−5.66604	−	6.92069i	−0.633482	−	0.773757i
$81$	−8.21667	+	2.99062i	−0.912963	+	0.332291i
$82$	1.89874	−	5.81550i	0.209680	−	0.642214i
$83$	−0.764089	−	1.32344i	−0.0838696	−	0.145266i	0.821039	−	0.570872i	$-0.193395\pi$
$83$	−0.764089	−	1.32344i	−0.0838696	−	0.145266i	−0.904909	+	0.425605i	$0.860061\pi$
$84$	−0.0989359	+	0.0663236i	−0.0107948	+	0.00723650i
$85$	2.24733	−	1.38441i	0.243757	−	0.150161i
$86$	−11.9153	+	10.6979i	−1.28486	+	1.15358i
$87$	−0.187950	+	0.325540i	−0.0201504	+	0.0349015i
$88$	1.23464	−	0.888977i	0.131613	−	0.0947653i
$89$	3.25011	+	3.87334i	0.344511	+	0.410573i	0.910281	−	0.413991i	$-0.135865\pi$
$89$	3.25011	+	3.87334i	0.344511	+	0.410573i	−0.565770	+	0.824563i	$0.691421\pi$
$90$	−9.01208	−	2.66052i	−0.949957	−	0.280444i
$91$	1.25838	+	0.458014i	0.131914	+	0.0480129i
$92$	10.4926	−	4.63580i	1.09393	−	0.483316i
$93$	−1.10058	−	0.194061i	−0.114124	−	0.0201232i
$94$	−1.98183	−	3.18168i	−0.204411	−	0.328165i
$95$	−8.66701	−	4.45904i	−0.889216	−	0.457487i
$96$	−0.895598	−	0.333217i	−0.0914066	−	0.0340088i
$97$	−2.09122	+	11.8599i	−0.212331	+	1.20419i	0.673147	+	0.739508i	$0.264942\pi$
$97$	−2.09122	+	11.8599i	−0.212331	+	1.20419i	−0.885478	+	0.464680i	$0.846169\pi$
$98$	−1.36700	+	9.62715i	−0.138088	+	0.972489i
$99$	0.546659	−	1.50193i	0.0549413	−	0.150950i
$100$	−6.03277	−	7.97532i	−0.603277	−	0.797532i
$101$	−6.10589	+	5.12345i	−0.607559	+	0.509803i	−0.893865	−	0.448336i	$-0.852017\pi$
$101$	−6.10589	+	5.12345i	−0.607559	+	0.509803i	0.286306	+	0.958138i	$0.407573\pi$
$102$	0.132745	−	0.248801i	0.0131437	−	0.0246350i
$103$	−8.62565	−	4.98002i	−0.849911	−	0.490696i	0.0107099	−	0.999943i	$-0.496591\pi$
$103$	−8.62565	−	4.98002i	−0.849911	−	0.490696i	−0.860621	+	0.509246i	$0.829924\pi$
$104$	2.91713	+	10.3399i	0.286048	+	1.01391i
$105$	−0.113382	+	0.0698461i	−0.0110649	+	0.00681629i
$106$	6.23940	−	0.208982i	0.606024	−	0.0202981i
$107$	−9.83620	+	5.67893i	−0.950901	+	0.549003i	−0.893361	−	0.449340i	$-0.851659\pi$
$107$	−9.83620	+	5.67893i	−0.950901	+	0.549003i	−0.0575406	+	0.998343i	$0.518326\pi$
$108$	−1.95890	+	0.482483i	−0.188496	+	0.0464269i
$109$	−1.80107	−	4.94840i	−0.172511	−	0.473971i	0.823063	−	0.567950i	$-0.192263\pi$
$109$	−1.80107	−	4.94840i	−0.172511	−	0.473971i	−0.995574	+	0.0939794i	$0.970041\pi$
$110$	1.41755	−	0.940122i	0.135158	−	0.0896371i
$111$	0.0839963	−	0.100103i	0.00797257	−	0.00950134i
$112$	1.24890	−	0.654948i	0.118010	−	0.0618868i
$113$	−15.1869			−1.42867			−0.714333	−	0.699806i	$-0.753270\pi$
$113$	−15.1869			−1.42867			−0.714333	+	0.699806i	$0.753270\pi$
$114$	−1.03983	+	0.0555712i	−0.0973893	+	0.00520472i
$115$	11.9216	−	4.72831i	1.11169	−	0.440917i
$116$	2.62621	−	3.59309i	0.243837	−	0.333610i
$117$	8.64620	+	7.25502i	0.799341	+	0.670727i
$118$	−0.980704	−	4.64640i	−0.0902811	−	0.427736i
$119$	0.142337	+	0.391069i	0.0130480	+	0.0358492i
$120$	−0.986251	−	0.410756i	−0.0900320	−	0.0374967i
$121$	−5.35534	−	9.27572i	−0.486849	−	0.843247i
$122$	9.76562	−	0.327089i	0.884138	−	0.0296132i
$123$	−0.126890	−	0.719631i	−0.0114413	−	0.0648869i
$124$	12.7084	+	3.68332i	1.14125	+	0.330772i
$125$	−6.39717	−	9.16931i	−0.572180	−	0.820128i
$126$	0.697402	−	1.30713i	0.0621295	−	0.116448i
$127$	−10.1362	−	12.0799i	−0.899446	−	1.07192i	−0.997055	−	0.0766927i	$-0.975564\pi$
$127$	−10.1362	−	12.0799i	−0.899446	−	1.07192i	0.0976092	−	0.995225i	$-0.468880\pi$
$128$	10.1187	+	5.06080i	0.894376	+	0.447316i
$129$	−0.654188	+	1.79737i	−0.0575980	+	0.158249i
$130$	2.81475	+	11.6771i	0.246870	+	1.02415i
$131$	16.1902	+	2.85477i	1.41455	+	0.249423i	0.828107	−	0.560571i	$-0.189418\pi$
$131$	16.1902	+	2.85477i	1.41455	+	0.249423i	0.586439	+	0.809993i	$0.300529\pi$
$132$	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
$135$	−2.20923	+	0.454862i	−0.190141	+	0.0391483i
$136$	−1.87883	+	2.75995i	−0.161108	+	0.236664i
$137$	−7.03395	+	19.3256i	−0.600950	+	1.65110i	0.148402	+	0.988927i	$0.452587\pi$
$137$	−7.03395	+	19.3256i	−0.600950	+	1.65110i	−0.749353	+	0.662171i	$0.769635\pi$
$138$	0.845107	−	1.07852i	0.0719403	−	0.0918094i
$139$	−5.01188	−	5.97293i	−0.425102	−	0.506617i	0.510400	−	0.859937i	$-0.329497\pi$
$139$	−5.01188	−	5.97293i	−0.425102	−	0.506617i	−0.935503	+	0.353320i	$0.885053\pi$
$140$	1.42343	−	0.678050i	0.120301	−	0.0573057i
$141$	−0.387754	−	0.223870i	−0.0326548	−	0.0188532i
$142$	7.52899	−	6.75972i	0.631818	−	0.567263i
$143$	−2.01209	+	0.354785i	−0.168259	+	0.0296686i
$144$	11.7794	−	1.58707i	0.981619	−	0.132256i
$145$	3.08841	−	3.90138i	0.256479	−	0.323992i
$146$	−5.00483	+	15.3289i	−0.414203	+	1.26863i
$147$	0.397246	+	1.09143i	0.0327643	+	0.0900193i
$148$	−1.11598	+	1.07156i	−0.0917332	+	0.0880818i
$149$	0.955499	+	0.801759i	0.0782775	+	0.0656826i	0.681087	−	0.732203i	$-0.261508\pi$
$149$	0.955499	+	0.801759i	0.0782775	+	0.0656826i	−0.602809	+	0.797885i	$0.705952\pi$
$150$	−1.08420	−	0.501277i	−0.0885244	−	0.0409291i
$151$	−22.9818			−1.87023			−0.935117	−	0.354338i	$-0.884706\pi$
$151$	−22.9818			−1.87023			−0.935117	+	0.354338i	$0.884706\pi$
$152$	12.3107	+	0.667631i	0.998533	+	0.0541520i
$153$			3.50761i			0.283574i
$154$	0.100110	+	0.248800i	0.00806707	+	0.0200489i
$155$	14.0397	+	4.66110i	1.12770	+	0.374388i
$156$	0.888807	+	0.925652i	0.0711615	+	0.0741115i
$157$	4.71179	+	12.9455i	0.376041	+	1.03317i	0.972982	+	0.230880i	$0.0741605\pi$
$157$	4.71179	+	12.9455i	0.376041	+	1.03317i	−0.596941	+	0.802285i	$0.703617\pi$
$158$	−9.93437	−	3.24353i	−0.790336	−	0.258041i
$159$	0.645792	−	0.372848i	0.0512147	−	0.0295688i
$160$	11.0872	+	6.08875i	0.876524	+	0.481358i
$161$	0.351131	+	1.99136i	0.0276730	+	0.156941i
$162$	9.20142	−	8.26128i	0.722932	−	0.649068i
$163$	−6.76334	+	11.7144i	−0.529746	+	0.917546i	0.469652	+	0.882851i	$0.344379\pi$
$163$	−6.76334	+	11.7144i	−0.529746	+	0.917546i	−0.999398	+	0.0346948i	$0.988954\pi$
$164$	0.578903	+	8.63222i	0.0452048	+	0.674063i
$165$	0.0965285	−	0.178780i	0.00751473	−	0.0139180i
$166$	1.70113	+	1.33297i	0.132033	+	0.103459i
$167$	4.76621	−	13.0951i	0.368820	−	1.01333i	−0.606991	−	0.794709i	$-0.707623\pi$
$167$	4.76621	−	13.0951i	0.368820	−	1.01333i	0.975811	−	0.218616i	$-0.0701544\pi$
$168$	0.0947904	−	0.139245i	0.00731324	−	0.0107430i
$169$	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	0.901913	+	0.431918i	$0.142163\pi$
$173$	−1.22760	+	6.96205i	−0.0933325	+	0.529315i	−0.995246	+	0.0973973i	$0.968948\pi$
$174$	0.0747351	−	0.526324i	0.00566566	−	0.0399005i
$175$	1.61940	−	0.696360i	0.122415	−	0.0526399i
$176$	−1.15054	+	1.81810i	−0.0867251	+	0.137044i
$177$	−0.364607	−	0.434522i	−0.0274055	−	0.0326606i
$178$	−6.30887	−	3.36603i	−0.472870	−	0.252294i
$179$	8.98666	−	15.5654i	0.671695	−	1.16341i	−0.305729	−	0.952119i	$-0.598900\pi$
$179$	8.98666	−	15.5654i	0.671695	−	1.16341i	0.977423	−	0.211291i	$-0.0677667\pi$
$180$	13.2283	−	1.26694i	0.985976	−	0.0944320i
$181$	5.47047	−	0.964591i	0.406616	−	0.0716975i	0.0334007	−	0.999442i	$-0.489366\pi$
$181$	5.47047	−	0.964591i	0.406616	−	0.0716975i	0.373216	+	0.927745i	$0.378255\pi$
$182$	−1.89277	+	0.0633964i	−0.140302	+	0.00469925i
$183$	1.01076	−	0.583565i	0.0747179	−	0.0431384i
$184$	−11.3189	+	11.6212i	−0.834439	+	0.856726i
$185$	−1.29283	+	1.14920i	−0.0950506	+	0.0844912i
$186$	1.54639	−	0.326393i	0.113387	−	0.0239323i
$187$	−0.486395	−	0.408134i	−0.0355687	−	0.0298457i
$188$	4.27977	+	3.12811i	0.312134	+	0.228141i
$189$		−	0.355630i		−	0.0258683i
$190$	13.7250	+	1.27486i	0.995714	+	0.0924878i
$191$			8.81735i			0.638001i	0.947755	+	0.319001i	$0.103347\pi$
$191$			8.81735i			0.638001i	−0.947755	+	0.319001i	$0.896653\pi$
$192$	1.35092	−	0.0356124i	0.0974944	−	0.00257010i
$193$	14.7524	+	12.3787i	1.06190	+	0.891041i	0.994294	−	0.106671i	$-0.0340193\pi$
$193$	14.7524	+	12.3787i	1.06190	+	0.891041i	0.0676066	+	0.997712i	$0.478464\pi$
$194$	−3.51723	−	16.6640i	−0.252522	−	1.19641i
$195$	0.953209	+	1.07234i	0.0682607	+	0.0767917i
$196$	−3.28872	−	13.3524i	−0.234909	−	0.953740i
$197$	−18.2159	+	10.5170i	−1.29783	+	0.749304i	−0.980029	−	0.198853i	$-0.936278\pi$
$197$	−18.2159	+	10.5170i	−1.29783	+	0.749304i	−0.317803	+	0.948157i	$0.602945\pi$
$198$	0.0756663	+	2.25911i	0.00537737	+	0.160548i
$199$	−17.2506	+	3.04175i	−1.22286	+	0.215624i	−0.747557	−	0.664197i	$-0.768774\pi$
$199$	−17.2506	+	3.04175i	−1.22286	+	0.215624i	−0.475305	+	0.879821i	$0.657662\pi$
$200$	12.1251	+	7.27881i	0.857377	+	0.514689i
$201$	0.599042	−	1.03757i	0.0422532	−	0.0731846i
$202$	5.30617	−	9.94524i	0.373341	−	0.699745i
$203$	0.504285	+	0.600983i	0.0353938	+	0.0421807i
$204$	−0.0428170	+	0.396501i	−0.00299779	+	0.0277606i
$205$	0.275841	+	9.66886i	0.0192656	+	0.675303i
$206$	13.9457	+	1.98022i	0.971646	+	0.137968i
$207$	−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	−0.855205	−	0.518291i	$-0.826569\pi$
$211$	1.82576	−	10.3544i	0.125691	−	0.712827i	0.980895	−	0.194537i	$-0.0623203\pi$
$212$	−8.07570	+	3.56799i	−0.554642	+	0.245050i
$213$	0.413366	−	1.13571i	0.0283233	−	0.0778177i
$214$	9.90706	−	12.6433i	0.677233	−	0.864277i
$215$	12.0290	−	22.2789i	0.820371	−	1.51941i
$216$	2.31536	−	1.66713i	0.157540	−	0.113434i
$217$	−1.16620	+	2.01992i	−0.0791669	+	0.137121i
$218$	4.97527	+	5.54146i	0.336968	+	0.375315i
$219$	0.334467	+	1.89686i	0.0226012	+	0.128178i
$220$	−1.36351	+	1.98176i	−0.0919280	+	0.133610i
$221$	3.88304	−	2.24188i	0.261202	−	0.150805i
$222$	−0.0573575	+	0.175676i	−0.00384958	+	0.0117906i
$223$	3.62008	+	9.94608i	0.242418	+	0.666039i	0.999913	+	0.0131976i	$0.00420103\pi$
$223$	3.62008	+	9.94608i	0.242418	+	0.666039i	−0.757495	+	0.652842i	$0.773577\pi$
$224$	−1.29280	+	1.51859i	−0.0863787	+	0.101465i
$225$	14.8332	−	0.847035i	0.988877	−	0.0564690i
$226$	19.9251	−	8.01725i	1.32540	−	0.533300i
$227$			1.80739i			0.119961i	0.998200	+	0.0599803i	$0.0191038\pi$
$227$			1.80739i			0.119961i	−0.998200	+	0.0599803i	$0.980896\pi$
$228$	1.33491	−	0.621841i	0.0884068	−	0.0411824i
$229$	0.747250			0.0493797			0.0246898	−	0.999695i	$-0.492140\pi$
$229$	0.747250			0.0493797			0.0246898	+	0.999695i	$0.492140\pi$
$230$	−13.1449	+	12.4969i	−0.866749	+	0.824024i
$231$	0.0245395	+	0.0205911i	0.00161458	+	0.00135479i
$232$	−1.54875	+	6.10048i	−0.101681	+	0.400516i
$233$	−4.01918	−	11.0426i	−0.263306	−	0.723426i	−0.998939	−	0.0460466i	$-0.985338\pi$
$233$	−4.01918	−	11.0426i	−0.263306	−	0.723426i	0.735634	−	0.677380i	$-0.236884\pi$
$234$	−15.1737	−	4.95415i	−0.991935	−	0.323863i
$235$	4.64698	+	3.67864i	0.303136	+	0.239968i
$236$	3.73953	+	5.57831i	0.243423	+	0.363117i
$237$	−1.22931	+	0.216761i	−0.0798526	+	0.0140802i
$238$	−0.393192	−	0.437938i	−0.0254869	−	0.0283873i
$239$	8.67765	+	5.01004i	0.561311	+	0.324073i	0.753671	−	0.657251i	$-0.228281\pi$
$239$	8.67765	+	5.01004i	0.561311	+	0.324073i	−0.192361	+	0.981324i	$0.561614\pi$
$240$	1.51079	+	0.0182607i	0.0975211	+	0.00117872i
$241$	11.6615	+	13.8976i	0.751181	+	0.895223i	0.997256	−	0.0740278i	$-0.0235854\pi$
$241$	11.6615	+	13.8976i	0.751181	+	0.895223i	−0.246075	+	0.969251i	$0.579141\pi$
$242$	11.9228	+	9.34254i	0.766429	+	0.600561i
$243$	1.54020	−	4.23166i	0.0988038	−	0.271461i
$244$	−12.6397	+	5.58445i	−0.809175	+	0.357508i
$245$	−3.10045	−	15.0587i	−0.198081	−	0.962064i
$246$	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
$250$	13.2335	+	8.65294i	0.836963	+	0.547260i
$251$	6.31812	−	17.3589i	0.398796	−	1.09568i	−0.564075	−	0.825724i	$-0.690767\pi$
$251$	6.31812	−	17.3589i	0.398796	−	1.09568i	0.962871	−	0.269961i	$-0.0870107\pi$
$252$	−0.224947	+	2.08310i	−0.0141703	+	0.131223i
$253$	−1.98305	−	2.36331i	−0.124674	−	0.148580i
$254$	19.6757	+	10.4977i	1.23456	+	0.658687i
$255$	−0.0648725	+	0.441134i	−0.00406247	+	0.0276249i
$256$	−15.9473	−	1.29801i	−0.996704	−	0.0811254i
$257$	−1.52649	−	8.65713i	−0.0952196	−	0.540017i	−0.994680	−	0.103015i	$-0.967151\pi$
$257$	−1.52649	−	8.65713i	−0.0952196	−	0.540017i	0.899460	−	0.437003i	$-0.143960\pi$
$258$	−0.0905499	−	2.70347i	−0.00563739	−	0.168311i
$259$	−0.136363	−	0.236188i	−0.00847321	−	0.0146760i
$260$	−9.85734	−	13.8344i	−0.611326	−	0.857971i
$261$	2.26154	+	6.21353i	0.139986	+	0.384608i
$262$	−22.7484	+	4.80146i	−1.40540	+	0.296635i
$263$	−19.8411	−	16.6487i	−1.22345	−	1.02660i	−0.998637	−	0.0521999i	$-0.983377\pi$
$263$	−19.8411	−	16.6487i	−1.22345	−	1.02660i	−0.224818	−	0.974401i	$-0.572179\pi$
$264$	−0.0190233	+	0.256293i	−0.00117080	+	0.0157738i
$265$	−9.17555	+	3.63918i	−0.563650	+	0.223553i
$266$	−0.633265	+	2.07898i	−0.0388279	+	0.127471i
$267$	−0.854127			−0.0522717
$268$	−8.37035	+	11.4520i	−0.511300	+	0.699543i
$269$	−4.22376	+	5.03368i	−0.257527	+	0.306909i	−0.879281	−	0.476304i	$-0.841976\pi$
$269$	−4.22376	+	5.03368i	−0.257527	+	0.306909i	0.621753	+	0.783213i	$0.286421\pi$
$270$	2.65837	−	1.76304i	0.161783	−	0.107295i
$271$	5.55145	+	15.2525i	0.337226	+	0.926522i	0.986178	+	0.165692i	$0.0529857\pi$
$271$	5.55145	+	15.2525i	0.337226	+	0.926522i	−0.648951	+	0.760830i	$0.724792\pi$
$272$	1.00802	−	4.61287i	0.0611199	−	0.279697i
$273$	−0.195906	+	0.113107i	−0.0118568	+	0.00684553i
$274$	−0.973609	−	29.0682i	−0.0588179	−	1.75608i
$275$	−1.60848	+	2.15545i	−0.0969950	+	0.129978i
$276$	−0.539419	+	1.86114i	−0.0324692	+	0.112027i
$277$	14.9324	+	8.62125i	0.897203	+	0.518000i	0.876292	−	0.481781i	$-0.160010\pi$
$277$	14.9324	+	8.62125i	0.897203	+	0.518000i	0.0209114	+	0.999781i	$0.493343\pi$
$278$	9.72867	+	5.19062i	0.583487	+	0.311313i
$279$	−15.0592	+	12.6362i	−0.901571	+	0.756508i
$280$	−1.50958	+	1.64103i	−0.0902144	+	0.0980702i
$281$	8.80831	−	24.2006i	0.525460	−	1.44369i	−0.338904	−	0.940821i	$-0.610056\pi$
$281$	8.80831	−	24.2006i	0.525460	−	1.44369i	0.864364	−	0.502867i	$-0.167722\pi$
$282$	0.626911	+	0.0890179i	0.0373320	+	0.00530094i
$283$	−4.11288	+	23.3253i	−0.244486	+	1.38655i	0.577199	+	0.816604i	$0.304146\pi$
$283$	−4.11288	+	23.3253i	−0.244486	+	1.38655i	−0.821684	+	0.569943i	$0.806965\pi$
$284$	−6.30946	+	12.8433i	−0.374398	+	0.762108i
$285$	1.51810	−	0.637367i	0.0899243	−	0.0377543i
$286$	2.45254	−	1.52766i	0.145022	−	0.0903326i
$287$	−1.50191	−	0.264828i	−0.0886551	−	0.0156323i
$288$	−14.6167	+	8.30063i	−0.861295	+	0.489119i
$289$	−14.6654	−	5.33777i	−0.862670	−	0.313986i
$290$	−1.99241	+	6.74896i	−0.116998	+	0.396312i
$291$	−1.30764	−	1.55838i	−0.0766551	−	0.0913540i
$292$	−1.52592	−	22.7535i	−0.0892975	−	1.33155i
$293$	7.68269	−	13.3068i	0.448828	−	0.777392i	−0.549482	−	0.835505i	$-0.685175\pi$
$293$	7.68269	−	13.3068i	0.448828	−	0.777392i	0.998310	+	0.0581131i	$0.0185084\pi$
$294$	−1.09735	−	1.22223i	−0.0639989	−	0.0712820i
$295$	3.93814	+	6.39282i	0.229287	+	0.372204i
$296$	0.898476	−	1.99501i	0.0522228	−	0.115958i
$297$	0.271292	+	0.469891i	0.0157419	+	0.0272658i
$298$	−1.67686	−	0.547487i	−0.0971377	−	0.0317151i
$299$	20.4720	−	7.45118i	1.18392	−	0.430913i
$300$	1.68708	+	0.0853175i	0.0974038	+	0.00492581i
$301$	3.05802	+	2.56598i	0.176261	+	0.147901i
$302$	30.1519	−	12.1322i	1.73505	−	0.698130i
$303$		−	1.34644i		−	0.0773508i
$304$	−16.5040	+	5.62297i	−0.946570	+	0.322499i
$305$	−14.3612	+	5.69588i	−0.822317	+	0.326145i
$306$	−1.85168	−	4.60195i	−0.105854	−	0.263076i
$307$	2.89483	−	3.44993i	0.165217	−	0.196898i	−0.677084	−	0.735906i	$-0.736756\pi$
$307$	2.89483	−	3.44993i	0.165217	−	0.196898i	0.842300	+	0.539008i	$0.181201\pi$
$308$	−0.262686	−	0.273575i	−0.0149679	−	0.0155884i
$309$	1.58102	−	0.575446i	0.0899413	−	0.0327360i
$310$	−20.8806	+	1.29631i	−1.18594	+	0.0736253i
$311$	−27.8935	+	16.1043i	−1.58170	+	0.913194i	−0.587086	+	0.809525i	$0.699725\pi$
$311$	−27.8935	+	16.1043i	−1.58170	+	0.913194i	−0.994612	+	0.103669i	$0.966942\pi$
$312$	−1.65476	−	0.745241i	−0.0936824	−	0.0421910i
$313$	11.1710	−	1.96975i	0.631422	−	0.111337i	0.151228	−	0.988499i	$-0.451677\pi$
$313$	11.1710	−	1.96975i	0.631422	−	0.111337i	0.480194	+	0.877162i	$0.340566\pi$
$314$	−13.0158	−	14.4970i	−0.734525	−	0.818114i
$315$	−0.340820	+	2.31759i	−0.0192031	+	0.130581i
$316$	14.7461	−	0.988916i	0.829531	−	0.0556309i
$317$	−6.45464	+	5.41608i	−0.362528	+	0.304197i	−0.805798	−	0.592191i	$-0.798263\pi$
$317$	−6.45464	+	5.41608i	−0.362528	+	0.304197i	0.443269	+	0.896389i	$0.353819\pi$
$318$	−0.650445	+	0.830090i	−0.0364751	+	0.0465491i
$319$	−1.12477	−	0.409381i	−0.0629748	−	0.0229210i
$320$	−17.7606	−	2.13537i	−0.992850	−	0.119371i
$321$	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
$325$	−10.4183	−	15.8794i	−0.577901	−	0.880832i
$326$	2.68932	−	18.9396i	0.148948	−	1.04897i
$327$	0.835903	+	0.304244i	0.0462256	+	0.0168247i
$328$	−5.31650	−	11.0198i	−0.293555	−	0.608466i
$329$	−0.715838	+	0.600660i	−0.0394654	+	0.0331154i
$330$	−0.0322655	+	0.285516i	−0.00177616	+	0.0157171i
$331$	13.0871	−	22.6674i	0.719330	−	1.24592i	−0.241936	−	0.970292i	$-0.577782\pi$
$331$	13.0871	−	22.6674i	0.719330	−	1.24592i	0.961266	−	0.275623i	$-0.0888842\pi$
$332$	−2.93554	−	0.850816i	−0.161109	−	0.0466946i
$333$	−0.399156	−	2.26372i	−0.0218736	−	0.124051i
$334$	0.659719	+	19.6967i	0.0360982	+	1.07775i
$335$	−9.84350	+	12.4346i	−0.537808	+	0.679376i
$336$	−0.0508562	+	0.232728i	−0.00277443	+	0.0126963i
$337$	16.5722	−	6.03180i	0.902746	−	0.328573i	0.151394	−	0.988474i	$-0.451624\pi$
$337$	16.5722	−	6.03180i	0.902746	−	0.328573i	0.751353	+	0.659901i	$0.229402\pi$
$338$	0.417016	+	1.97575i	0.0226827	+	0.107466i
$339$	1.64903	−	1.96524i	0.0895631	−	0.106737i
$340$	1.32437	−	5.11023i	0.0718241	−	0.277141i
$341$		−	3.55854i		−	0.192706i
$342$	−11.0086	+	14.6402i	−0.595274	+	0.791654i
$343$	4.89194			0.264140
$344$	−2.37061	+	31.9383i	−0.127815	+	1.72200i
$345$	−0.682613	+	2.05610i	−0.0367507	+	0.110697i
$346$	−2.06470	−	9.78219i	−0.110999	−	0.525894i
$347$	6.32576	−	2.30239i	0.339585	−	0.123599i	−0.166598	−	0.986025i	$-0.553278\pi$
$347$	6.32576	−	2.30239i	0.339585	−	0.123599i	0.506183	+	0.862426i	$0.331056\pi$
$348$	0.179797	+	0.729985i	0.00963814	+	0.0391313i
$349$	2.63674	+	4.56697i	0.141142	+	0.244464i	0.927927	−	0.372763i	$-0.121589\pi$
$349$	2.63674	+	4.56697i	0.141142	+	0.244464i	−0.786785	+	0.617227i	$0.788256\pi$
$350$	−1.75702	+	1.76850i	−0.0939168	+	0.0945306i
$351$	−3.77332	+	0.665339i	−0.201405	+	0.0355132i
$352$	0.549711	−	2.99270i	0.0292997	−	0.159512i
$353$	−24.1899	−	13.9660i	−1.28750	−	0.743337i	−0.309290	−	0.950968i	$-0.600091\pi$
$353$	−24.1899	−	13.9660i	−1.28750	−	0.743337i	−0.978207	+	0.207631i	$0.933425\pi$
$354$	0.707746	+	0.377610i	0.0376163	+	0.0200698i
$355$	−7.60084	+	14.0775i	−0.403411	+	0.747156i
$356$	10.0541	+	1.08571i	0.532867	+	0.0575427i
$357$	−0.0660608	−	0.0240442i	−0.00349631	−	0.00127255i
$358$	−3.57339	+	25.1657i	−0.188859	+	1.33005i
$359$	−4.12396	−	0.727165i	−0.217654	−	0.0383783i	0.0637576	−	0.997965i	$-0.479692\pi$
$359$	−4.12396	−	0.727165i	−0.217654	−	0.0383783i	−0.281412	+	0.959587i	$0.590803\pi$
$360$	−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
$364$	2.44983	−	1.08238i	0.128406	−	0.0567321i
$365$	−0.727083	−	25.4859i	−0.0380573	−	1.33399i
$366$	−1.01805	+	1.29922i	−0.0532141	+	0.0679112i
$367$	4.01358	−	3.36779i	0.209507	−	0.175797i	−0.531996	−	0.846747i	$-0.678558\pi$
$367$	4.01358	−	3.36779i	0.209507	−	0.175797i	0.741503	+	0.670950i	$0.234113\pi$
$368$	8.71538	−	21.2222i	0.454320	−	1.10628i
$369$	−11.1319	−	6.42699i	−0.579502	−	0.334576i
$370$	1.08951	−	2.19023i	0.0566408	−	0.113865i
$371$	−0.270251	−	1.53267i	−0.0140307	−	0.0795723i
$372$	−1.85654	+	1.24457i	−0.0962573	+	0.0645279i
$373$	−8.38038	−	14.5152i	−0.433920	−	0.751571i	0.563287	−	0.826261i	$-0.309536\pi$
$373$	−8.38038	−	14.5152i	−0.433920	−	0.751571i	−0.997207	+	0.0746904i	$0.976203\pi$
$374$	0.853601	+	0.278697i	0.0441387	+	0.0144111i
$375$	1.88116	+	0.167809i	0.0971425	+	0.00866561i
$376$	−7.26635	−	1.84474i	−0.374734	−	0.0951352i
$377$	5.43313	−	6.47495i	0.279820	−	0.333477i
$378$	0.187739	+	0.466583i	0.00965623	+	0.0239984i
$379$	−7.16672			−0.368130			−0.184065	−	0.982914i	$-0.558926\pi$
$379$	−7.16672			−0.368130			−0.184065	+	0.982914i	$0.558926\pi$
$380$	−18.6800	+	5.57287i	−0.958265	+	0.285882i
$381$	2.66379			0.136470
$382$	−4.65472	−	11.5683i	−0.238156	−	0.591884i
$383$	21.4278	−	25.5367i	1.09491	−	1.30486i	0.146013	−	0.989283i	$-0.453356\pi$
$383$	21.4278	−	25.5367i	1.09491	−	1.30486i	0.948898	−	0.315582i	$-0.102200\pi$
$384$	−1.75360	+	0.759881i	−0.0894878	+	0.0387775i
$385$	−0.281719	−	0.316928i	−0.0143577	−	0.0161521i
$386$	−25.8898	−	8.45291i	−1.31776	−	0.430242i
$387$	16.8229	+	29.1381i	0.855155	+	1.48117i
$388$	13.4116	+	20.0062i	0.680869	+	1.01566i
$389$	1.25719	+	7.12991i	0.0637423	+	0.361501i	0.999949	+	0.0100520i	$0.00319969\pi$
$389$	1.25719	+	7.12991i	0.0637423	+	0.361501i	−0.936207	+	0.351449i	$0.885689\pi$
$390$	−1.81669	−	0.903692i	−0.0919917	−	0.0457602i
$391$	5.86333	+	3.38519i	0.296521	+	0.171197i
$392$	11.3635	+	15.7820i	0.573945	+	0.797113i
$393$	−2.12739	+	1.78509i	−0.107312	+	0.0900458i
$394$	18.3472	−	23.4144i	0.924317	−	1.17960i
$395$	16.5169	−	0.471208i	0.831056	−	0.0237091i
$396$	−1.29186	−	2.92398i	−0.0649187	−	0.146935i
$397$	−1.69283	−	0.298492i	−0.0849608	−	0.0149809i	0.131006	−	0.991382i	$-0.458179\pi$
$397$	−1.69283	−	0.298492i	−0.0849608	−	0.0149809i	−0.215967	+	0.976401i	$0.569290\pi$
$398$	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	0.534550	−	0.845137i	$-0.320481\pi$
$401$	14.9749	+	2.64047i	0.747809	+	0.131859i	0.213259	+	0.976996i	$0.431592\pi$
$402$	−0.238199	+	1.67752i	−0.0118803	+	0.0836671i
$403$	23.6137	+	8.59468i	1.17628	+	0.428132i
$404$	−1.71151	+	15.8492i	−0.0851507	+	0.788528i
$405$	−9.28924	+	17.2046i	−0.461586	+	0.854902i
$406$	−0.978878	−	0.522269i	−0.0485809	−	0.0259198i
$407$	0.360352	+	0.208049i	0.0178620	+	0.0103126i
$408$	−0.153139	−	0.542809i	−0.00758153	−	0.0268730i
$409$	−7.87743	+	1.38900i	−0.389514	+	0.0686818i	−0.364976	−	0.931017i	$-0.618923\pi$
$409$	−7.87743	+	1.38900i	−0.389514	+	0.0686818i	−0.0245384	+	0.999699i	$0.507812\pi$
$410$	−5.46614	−	12.5398i	−0.269953	−	0.619298i
$411$	−1.73703	−	3.00863i	−0.0856816	−	0.148405i
$412$	−19.3420	+	4.76399i	−0.952914	+	0.234705i
$413$	−1.11244	+	0.404897i	−0.0547398	+	0.0199237i
$414$	−4.97754	−	23.5827i	−0.244633	−	1.15903i
$415$	−3.24305	−	1.07668i	−0.159195	−	0.0528519i
$416$	18.5313	+	10.8758i	0.908570	+	0.533231i
$417$	1.31712			0.0644995
$418$	−0.749222	−	3.23003i	−0.0366456	−	0.157986i
$419$			29.5028i			1.44131i	0.693296	+	0.720653i	$0.256158\pi$
$419$			29.5028i			1.44131i	−0.693296	+	0.720653i	$0.743842\pi$
$420$	−0.0668169	+	0.257820i	−0.00326033	+	0.0125803i
$421$	15.3524	−	18.2962i	0.748229	−	0.891704i	−0.248814	−	0.968551i	$-0.580041\pi$
$421$	15.3524	−	18.2962i	0.748229	−	0.891704i	0.997043	+	0.0768469i	$0.0244853\pi$
$422$	3.07076	+	14.5487i	0.149482	+	0.708220i
$423$	−7.40101	+	2.69375i	−0.359849	+	0.130974i
$424$	8.71168	−	8.94436i	0.423077	−	0.434377i
$425$	1.69918	−	5.65228i	0.0824222	−	0.274176i
$426$	0.0572163	+	1.70826i	0.00277214	+	0.0827655i
$427$	−0.422985	−	2.39887i	−0.0204697	−	0.116089i
$428$	−6.32352	+	21.8178i	−0.305659	+	1.05460i
$429$	0.172566	−	0.298894i	0.00833158	−	0.0144307i
$430$	−4.02080	+	35.5798i	−0.193900	+	1.71581i
$431$	−11.0099	+	9.23838i	−0.530327	+	0.444997i	−0.868214	−	0.496189i	$-0.834732\pi$
$431$	−11.0099	+	9.23838i	−0.530327	+	0.444997i	0.337887	+	0.941187i	$0.390288\pi$
$432$	−2.15764	+	3.40954i	−0.103809	+	0.164041i
$433$	24.8805	+	9.05575i	1.19568	+	0.435191i	0.861714	−	0.507394i	$-0.169391\pi$
$433$	24.8805	+	9.05575i	1.19568	+	0.435191i	0.333965	+	0.942586i	$0.391613\pi$
$434$	0.463720	−	3.26576i	0.0222593	−	0.156761i
$435$	0.169504	+	0.823271i	0.00812712	+	0.0394728i
$436$	−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	0.542813	+	0.839854i	$0.317359\pi$
$439$	−5.33260	+	30.2427i	−0.254511	+	1.44341i	−0.797324	+	0.603552i	$0.793752\pi$
$440$	0.742734	−	3.31985i	0.0354085	−	0.158268i
$441$	19.1988	+	6.98778i	0.914228	+	0.332752i
$442$	−3.91102	+	4.99119i	−0.186028	+	0.237407i
$443$	24.3577	−	20.4385i	1.15727	−	0.971064i	0.157404	−	0.987534i	$-0.449687\pi$
$443$	24.3577	−	20.4385i	1.15727	−	0.971064i	0.999864	+	0.0164704i	$0.00524292\pi$
$444$	−0.0174876	−	0.260764i	−0.000829927	−	0.0123753i
$445$	11.1859	+	1.64498i	0.530262	+	0.0779794i
$446$	−10.0001	−	11.1381i	−0.473518	−	0.527405i
$447$	−0.207500	+	0.0365879i	−0.00981443	+	0.00173055i
$448$	0.894468	−	2.67484i	0.0422596	−	0.126374i
$449$	21.7050	−	12.5314i	1.02432	−	0.591391i	0.108968	−	0.994045i	$-0.465245\pi$
$449$	21.7050	−	12.5314i	1.02432	−	0.591391i	0.915352	+	0.402654i	$0.131912\pi$
$450$	−19.0138	+	8.94179i	−0.896319	+	0.421520i
$451$	2.18649	−	0.795817i	0.102958	−	0.0374735i
$452$	−21.9092	+	21.0371i	−1.03052	+	0.989502i
$453$	2.49542	−	2.97392i	0.117245	−	0.139727i
$454$	−0.954129	−	2.37128i	−0.0447795	−	0.111290i
$455$	2.78348	−	1.10398i	0.130492	−	0.0517552i
$456$	−1.42312	+	1.52056i	−0.0666437	+	0.0712066i
$457$		−	28.0718i		−	1.31314i	−0.754264	−	0.656571i	$-0.772006\pi$
$457$		−	28.0718i		−	1.31314i	0.754264	−	0.656571i	$-0.227994\pi$
$458$	−0.980384	+	0.394477i	−0.0458103	+	0.0184327i
$459$	−0.912151	−	0.765386i	−0.0425756	−	0.0357251i
$460$	10.6488	−	23.3351i	0.496502	−	1.08800i
$461$	8.10603	−	2.95035i	0.377535	−	0.137412i	−0.146280	−	0.989243i	$-0.546730\pi$
$461$	8.10603	−	2.95035i	0.377535	−	0.137412i	0.523816	+	0.851831i	$0.324508\pi$
$462$	−0.0430657	−	0.0140608i	−0.00200360	−	0.000654167i
$463$	19.5043	+	33.7824i	0.906440	+	1.57000i	0.818972	+	0.573834i	$0.194544\pi$
$463$	19.5043	+	33.7824i	0.906440	+	1.57000i	0.0874686	+	0.996167i	$0.472122\pi$
$464$	−1.18852	−	8.82136i	−0.0551756	−	0.409521i
$465$	−2.12762	+	1.31067i	−0.0986661	+	0.0607809i
$466$	11.1026	+	12.3661i	0.514317	+	0.572847i
$467$	5.82760	−	10.0937i	0.269669	−	0.467081i	−0.699107	−	0.715017i	$-0.746419\pi$
$467$	5.82760	−	10.0937i	0.269669	−	0.467081i	0.968776	+	0.247936i	$0.0797523\pi$
$468$	22.5230	−	1.51046i	1.04113	−	0.0698212i
$469$	−1.60727	−	1.91547i	−0.0742170	−	0.0884484i
$470$	−8.03876	−	2.37318i	−0.370800	−	0.109467i
$471$	−2.18681	−	0.795933i	−0.100763	−	0.0366747i
$472$	−7.85104	−	5.34457i	−0.361373	−	0.246004i
$473$	−5.99799	−	1.05761i	−0.275788	−	0.0486288i
$474$	1.49842	−	0.933349i	0.0688246	−	0.0428701i
$475$	−21.1089	+	5.42340i	−0.968544	+	0.248843i
$476$	0.747053	+	0.367002i	0.0342411	+	0.0168215i
$477$	2.27778	−	12.9179i	0.104292	−	0.591472i
$478$	−14.0298	−	1.99216i	−0.641709	−	0.0911191i
$479$	5.89779	−	16.2040i	0.269477	−	0.740382i	−0.728963	−	0.684553i	$-0.759998\pi$
$479$	5.89779	−	16.2040i	0.269477	−	0.740382i	0.998440	−	0.0558292i	$-0.0177802\pi$
$480$	−1.99178	+	0.773595i	−0.0909120	+	0.0353096i
$481$	−2.25090	+	1.88873i	−0.102632	+	0.0861186i
$482$	−22.6363	−	12.0774i	−1.03106	−	0.550109i
$483$	−0.295815	−	0.170789i	−0.0134601	−	0.00777117i
$484$	−20.5746	−	5.96319i	−0.935209	−	0.271054i
$485$	14.1239	+	22.9274i	0.641332	+	1.04108i
$486$	0.213188	+	6.36497i	0.00967040	+	0.288721i
$487$	−26.0280	+	15.0273i	−1.17944	+	0.680950i	−0.955885	−	0.293741i	$-0.905100\pi$
$487$	−26.0280	+	15.0273i	−1.17944	+	0.680950i	−0.223555	+	0.974691i	$0.571766\pi$
$488$	13.6351	−	13.9993i	0.617233	−	0.633719i
$489$	−0.781509	−	2.14718i	−0.0353411	−	0.0970987i
$490$	12.0173	+	18.1201i	0.542887	+	0.818582i
$491$	12.0290	−	14.3357i	0.542863	−	0.646959i	−0.422964	−	0.906147i	$-0.639010\pi$
$491$	12.0290	−	14.3357i	0.542863	−	0.646959i	0.965827	+	0.259187i	$0.0834547\pi$
$492$	−1.17990	−	0.862394i	−0.0531938	−	0.0388797i
$493$	2.62677			0.118304
$494$	23.2433	+	2.82958i	1.04577	+	0.127309i
$495$	−1.31764	−	3.32220i	−0.0592236	−	0.149322i
$496$	23.4358	−	12.2902i	1.05230	−	0.551845i
$497$	−1.93229	−	1.62138i	−0.0866750	−	0.0727289i
$498$	−0.357203	+	0.0753940i	−0.0160067	+	0.00337848i
$499$	−1.26220	−	3.46788i	−0.0565040	−	0.155243i	0.908229	−	0.418473i	$-0.137435\pi$
$499$	−1.26220	−	3.46788i	−0.0565040	−	0.155243i	−0.964733	+	0.263230i	$0.915212\pi$
$500$	−21.9302	−	4.36652i	−0.980748	−	0.195277i
$501$	1.17702	+	2.03865i	0.0525852	+	0.0910803i
$502$	0.874528	+	26.1101i	0.0390321	+	1.16535i
$503$	−3.50139	−	19.8574i	−0.156119	−	0.885397i	−0.957755	−	0.287585i	$-0.907148\pi$
$503$	−3.50139	−	19.8574i	−0.156119	−	0.885397i	0.801636	−	0.597813i	$-0.203963\pi$
$504$	−0.804547	−	2.85175i	−0.0358374	−	0.127027i
$505$	−2.59313	+	17.6333i	−0.115393	+	0.784673i
$506$	3.84935	+	2.05378i	0.171124	+	0.0913016i
$507$	0.155038	+	0.184768i	0.00688550	+	0.00820582i
$508$	−31.3561	−	3.38605i	−1.39120	−	0.150232i
$509$	−8.80102	+	24.1806i	−0.390098	+	1.07179i	0.576858	+	0.816844i	$0.304278\pi$
$509$	−8.80102	+	24.1806i	−0.390098	+	1.07179i	−0.966956	+	0.254942i	$0.917944\pi$
$510$	−0.147765	−	0.613010i	−0.00654313	−	0.0271446i
$511$	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
$515$	−21.8138	+	4.49127i	−0.961230	+	0.197909i
$516$	1.54598	+	3.49913i	0.0680578	+	0.154041i
$517$	0.487619	−	1.33972i	0.0214455	−	0.0589209i
$518$	0.303592	+	0.237890i	0.0133391	+	0.0104523i
$519$	−0.767616	−	0.914810i	−0.0336946	−	0.0401557i
$520$	20.2359	+	12.9468i	0.887405	+	0.567756i
$521$	14.1055	+	8.14382i	0.617974	+	0.356787i	0.776080	−	0.630635i	$-0.217205\pi$
$521$	14.1055	+	8.14382i	0.617974	+	0.356787i	−0.158106	+	0.987422i	$0.550539\pi$
$522$	−6.24727	−	6.95821i	−0.273435	−	0.304553i
$523$	3.09462	−	0.545665i	0.135318	−	0.0238603i	−0.105579	−	0.994411i	$-0.533669\pi$
$523$	3.09462	−	0.545665i	0.135318	−	0.0238603i	0.240897	+	0.970551i	$0.422558\pi$
$524$	27.3110	−	18.3085i	1.19309	−	0.799809i
$525$	−0.0857265	+	0.285168i	−0.00374141	+	0.0124457i
$526$	34.8202	+	11.3687i	1.51823	+	0.495697i
$527$	2.67098	+	7.33844i	0.116350	+	0.319668i
$528$	−0.110340	−	0.346297i	−0.00480194	−	0.0150706i
$529$	7.58091	+	6.36114i	0.329605	+	0.276571i
$530$	10.1171	−	9.61839i	0.439458	−	0.417796i
$531$	−9.97785			−0.433002
$532$	−0.266668	−	3.06191i	−0.0115615	−	0.132751i
$533$			16.4311i			0.711712i
$534$	1.12061	−	0.450897i	0.0484933	−	0.0195122i
$535$	−8.00217	+	24.1033i	−0.345964	+	1.04208i
$536$	4.93624	−	19.4437i	0.213213	−	0.839838i
$537$	1.03842	+	2.85302i	0.0448109	+	0.123117i
$538$	2.88423	−	8.83388i	0.124348	−	0.380856i
$539$	−3.20289	+	1.84919i	−0.137958	+	0.0796503i
$540$	−2.55703	+	3.71645i	−0.110037	+	0.159931i
$541$	−1.34105	−	7.60549i	−0.0576564	−	0.326986i	0.942314	−	0.334731i	$-0.108646\pi$
$541$	−1.34105	−	7.60549i	−0.0576564	−	0.326986i	−0.999970	+	0.00774564i	$0.997534\pi$
$542$	−15.3353	−	17.0805i	−0.658707	−	0.733668i
$543$	−0.469174	+	0.812633i	−0.0201342	+	0.0348734i
$544$	1.11265	+	6.58418i	0.0477045	+	0.282294i
$545$	−10.3613	−	5.59434i	−0.443828	−	0.239635i
$546$	0.197318	−	0.251815i	0.00844442	−	0.0107767i
$547$	13.1507	−	36.1314i	0.562285	−	1.54487i	−0.253992	−	0.967206i	$-0.581744\pi$
$547$	13.1507	−	36.1314i	0.562285	−	1.54487i	0.816278	−	0.577660i	$-0.196034\pi$
$548$	16.6226	+	37.6233i	0.710083	+	1.60719i
$549$	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
$554$	−24.1424	−	3.42809i	−1.02571	−	0.145645i
$555$	−0.00833268	−	0.292079i	−0.000353703	−	0.0123981i
$556$	−15.5041	−	1.67424i	−0.657519	−	0.0710035i
$557$	10.8639	+	12.9471i	0.460317	+	0.548585i	0.945412	−	0.325877i	$-0.105659\pi$
$557$	10.8639	+	12.9471i	0.460317	+	0.548585i	−0.485095	+	0.874461i	$0.661215\pi$
$558$	13.0868	−	24.5283i	0.554009	−	1.03837i
$559$	21.5046	−	37.2470i	0.909546	−	1.57538i
$560$	1.11424	−	2.94992i	0.0470853	−	0.124657i
$561$	0.105628	−	0.0186250i	0.00445960	−	0.000786349i
$562$	1.21921	+	36.4009i	0.0514292	+	1.53548i
$563$	−28.0438	+	16.1911i	−1.18190	+	0.682372i	−0.956454	−	0.291883i	$-0.905718\pi$
$563$	−28.0438	+	16.1911i	−1.18190	+	0.682372i	−0.225449	+	0.974255i	$0.572385\pi$
$564$	−0.869494	+	0.214159i	−0.0366123	+	0.00901770i
$565$	−25.3811	+	22.5614i	−1.06779	+	0.949166i
$566$	−6.91748	−	32.7738i	−0.290763	−	1.37759i
$567$	−2.36151	−	1.98154i	−0.0991742	−	0.0832170i
$568$	1.49793	−	20.1810i	0.0628517	−	0.846777i
$569$			24.2370i			1.01607i	0.861336	+	0.508035i	$0.169628\pi$
$569$			24.2370i			1.01607i	−0.861336	+	0.508035i	$0.830372\pi$
$570$	−1.65526	+	1.63763i	−0.0693311	+	0.0685927i
$571$		−	37.6440i		−	1.57535i	−0.616090	−	0.787676i	$-0.711284\pi$
$571$		−	37.6440i		−	1.57535i	0.616090	−	0.787676i	$-0.288716\pi$
$572$	−2.41125	+	3.29899i	−0.100819	+	0.137938i
$573$	−1.14099	−	0.957407i	−0.0476657	−	0.0399963i
$574$	2.11030	−	0.445415i	0.0880822	−	0.0185913i
$575$	12.8996	−	25.6126i	0.537949	−	1.06812i
$576$	14.7950	−	18.6065i	0.616457	−	0.775272i
$577$	−33.0145	+	19.0610i	−1.37441	+	0.793518i	−0.991480	−	0.130258i	$-0.958419\pi$
$577$	−33.0145	+	19.0610i	−1.37441	+	0.793518i	−0.382934	+	0.923776i	$0.625086\pi$
$578$	22.0587	−	0.738831i	0.917520	−	0.0307313i
$579$	−3.20370	+	0.564898i	−0.133141	+	0.0234764i
$580$	−0.948783	−	9.90636i	−0.0393961	−	0.411339i
$581$	0.269383	−	0.466585i	0.0111759	−	0.0193572i
$582$	2.53828	+	1.35427i	0.105215	+	0.0561365i
$583$	1.52628	+	1.81894i	0.0632119	+	0.0753330i
$584$	14.0136	+	29.0468i	0.579889	+	1.20196i
$585$	25.2278	−	0.719720i	1.04304	−	0.0297568i
$586$	−3.05489	+	21.5141i	−0.126196	+	0.888740i
$587$	−2.86570	+	16.2522i	−0.118280	+	0.670799i	0.866794	+	0.498667i	$0.166177\pi$
$587$	−2.86570	+	16.2522i	−0.118280	+	0.670799i	−0.985074	+	0.172132i	$0.944934\pi$
$588$	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
$592$	−0.125616	+	3.09174i	−0.00516281	+	0.127070i
$593$	−2.47644	+	6.80396i	−0.101695	+	0.279405i	−0.980097	−	0.198517i	$-0.936388\pi$
$593$	−2.47644	+	6.80396i	−0.101695	+	0.279405i	0.878402	+	0.477922i	$0.158610\pi$
$594$	−0.603989	−	0.473276i	−0.0247820	−	0.0194187i
$595$	0.818844	+	0.442117i	0.0335693	+	0.0181250i
$596$	2.48904	−	0.166923i	0.101955	−	0.00683742i
$597$	1.47950	−	2.56256i	0.0605518	−	0.104879i
$598$	−22.9255	+	20.5831i	−0.937493	+	0.841706i
$599$	−1.58315	−	8.97847i	−0.0646856	−	0.366850i	−0.999918	−	0.0128156i	$-0.995921\pi$
$599$	−1.58315	−	8.97847i	−0.0646856	−	0.366850i	0.935232	−	0.354035i	$-0.115191\pi$
$600$	−2.25848	+	0.778683i	−0.0922019	+	0.0317896i
$601$	12.0081	−	6.93289i	0.489822	−	0.282799i	−0.234679	−	0.972073i	$-0.575404\pi$
$601$	12.0081	−	6.93289i	0.489822	−	0.282799i	0.724500	+	0.689274i	$0.242071\pi$
$602$	−5.36668	−	1.75220i	−0.218730	−	0.0714143i
$603$	−7.20806	−	19.8040i	−0.293535	−	0.806481i
$604$	−33.1544	+	31.8347i	−1.34903	+	1.29533i
$605$	−22.7299	−	7.54619i	−0.924101	−	0.306796i
$606$	0.710790	+	1.76651i	0.0288739	+	0.0717597i
$607$			0.0255150i			0.00103562i	1.00000		0.000517812i	$0.000164825\pi$
$607$			0.0255150i			0.00103562i	−1.00000		0.000517812i	$0.999835\pi$
$608$	18.6847	−	16.0898i	0.757764	−	0.652528i
$609$	−0.132525			−0.00537020
$610$	15.8348	−	15.0543i	0.641132	−	0.609529i
$611$	7.71239	+	6.47147i	0.312010	+	0.261808i
$612$	4.85878	+	5.06020i	0.196405	+	0.204546i
$613$	11.9906	+	32.9440i	0.484297	+	1.33059i	0.905776	+	0.423757i	$0.139289\pi$
$613$	11.9906	+	32.9440i	0.484297	+	1.33059i	−0.421479	+	0.906838i	$0.638489\pi$
$614$	−1.97676	+	6.05446i	−0.0797755	+	0.244338i
$615$	−1.28113	−	1.01417i	−0.0516603	−	0.0408953i
$616$	0.489062	+	0.220255i	0.0197049	+	0.00887432i
$617$	−14.8841	+	2.62446i	−0.599210	+	0.105657i	−0.465022	−	0.885299i	$-0.653954\pi$
$617$	−14.8841	+	2.62446i	−0.599210	+	0.105657i	−0.134188	+	0.990956i	$0.542842\pi$
$618$	−1.77051	+	1.58961i	−0.0712202	+	0.0639434i
$619$	34.3479	+	19.8308i	1.38056	+	0.797066i	0.992225	−	0.124454i	$-0.0397178\pi$
$619$	34.3479	+	19.8308i	1.38056	+	0.797066i	0.388333	+	0.921519i	$0.373051\pi$
$620$	26.7107	−	12.7237i	1.07273	−	0.510995i
$621$	−3.71888	−	4.43199i	−0.149234	−	0.177850i
$622$	28.0945	−	35.8539i	1.12649	−	1.43761i
$623$	−0.609690	+	1.67511i	−0.0244267	+	0.0671119i
$624$	2.56445	+	0.104193i	0.102660	+	0.00417104i
$625$	−24.3130	−	5.82062i	−0.972519	−	0.232825i
$626$	−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
$630$	−0.776311	−	3.22057i	−0.0309290	−	0.128311i
$631$	−3.46482	+	9.51953i	−0.137932	+	0.378966i	−0.989357	−	0.145511i	$-0.953517\pi$
$631$	−3.46482	+	9.51953i	−0.137932	+	0.378966i	0.851424	+	0.524478i	$0.175739\pi$
$632$	−18.8246	+	9.08196i	−0.748803	+	0.361261i
$633$	1.14165	+	1.36056i	0.0453765	+	0.0540776i
$634$	5.60924	−	10.5133i	0.222771	−	0.417535i
$635$	−34.8858	−	5.13024i	−1.38440	−	0.203588i
$636$	0.415169	−	1.43244i	0.0164625	−	0.0568000i
$637$	−4.53511	−	25.7199i	−0.179688	−	1.01906i
$638$	1.69180	−	0.0566648i	0.0669788	−	0.00224338i
$639$	−10.6300	−	18.4117i	−0.420515	−	0.728354i
$640$	24.4290	−	6.57433i	0.965643	−	0.259873i
$641$	−8.54858	−	23.4870i	−0.337649	−	0.927682i	−0.986060	−	0.166392i	$-0.946788\pi$
$641$	−8.54858	−	23.4870i	−0.337649	−	0.927682i	0.648411	−	0.761290i	$-0.275434\pi$
$642$	0.560350	+	2.65484i	0.0221153	+	0.104778i
$643$	−33.0725	−	27.7511i	−1.30425	−	1.09440i	−0.989394	−	0.145260i	$-0.953598\pi$
$643$	−33.0725	−	27.7511i	−1.30425	−	1.09440i	−0.314860	−	0.949138i	$-0.601957\pi$
$644$	3.26501	+	2.38642i	0.128659	+	0.0940380i
$645$	1.57683	+	3.97568i	0.0620874	+	0.156542i
$646$	3.96945	+	6.09864i	0.156176	+	0.239948i
$647$	4.50838			0.177243			0.0886214	−	0.996065i	$-0.471754\pi$
$647$	4.50838			0.177243			0.0886214	+	0.996065i	$0.471754\pi$
$648$	1.83067	−	24.6639i	0.0719155	−	0.968890i
$649$	1.16099	−	1.38361i	0.0455728	−	0.0543115i
$650$	22.0515	+	15.3338i	0.864929	+	0.601441i
$651$	−0.134755	−	0.370238i	−0.00528148	−	0.0145108i
$652$	6.46995	+	26.2683i	0.253383	+	1.02875i
$653$	−22.1636	+	12.7961i	−0.867327	+	0.500752i	−0.866459	−	0.499248i	$-0.833610\pi$
$653$	−22.1636	+	12.7961i	−0.867327	+	0.500752i	−0.000868020		1.00000i	$0.500276\pi$
$654$	−1.25731	+	0.0421122i	−0.0491647	+	0.00164672i
$655$	31.2988	−	19.2808i	1.22294	−	0.753365i
$656$	12.7926	+	11.6512i	0.499467	+	0.454904i
$657$	29.3422	+	16.9407i	1.14475	+	0.660921i
$658$	0.622081	−	1.16595i	0.0242513	−	0.0454536i
$659$	−19.1139	+	16.0385i	−0.744573	+	0.624771i	−0.934061	−	0.357112i	$-0.883761\pi$
$659$	−19.1139	+	16.0385i	−0.744573	+	0.624771i	0.189489	+	0.981883i	$0.439317\pi$
$660$	−0.108393	−	0.391627i	−0.00421919	−	0.0152440i
$661$	−16.7028	+	45.8904i	−0.649662	+	1.78493i	−0.0306753	+	0.999529i	$0.509766\pi$
$661$	−16.7028	+	45.8904i	−0.649662	+	1.78493i	−0.618986	+	0.785402i	$0.712456\pi$
$662$	−5.20384	+	36.6482i	−0.202253	+	1.42437i
$663$	−0.131523	+	0.745906i	−0.00510794	+	0.0289686i
$664$	4.30055	−	0.433424i	0.166894	−	0.0168201i
$665$	−0.166358	−	3.43225i	−0.00645110	−	0.133097i
$666$	1.71872	+	2.75927i	0.0665990	+	0.106919i
$667$	12.5692	+	2.21628i	0.486680	+	0.0858148i
$668$	−11.2635	−	25.4936i	−0.435798	−	0.986376i
$669$	−1.68013	−	0.611518i	−0.0649576	−	0.0236426i
$670$	6.35028	−	21.5105i	0.245333	−	0.831024i
$671$	2.38886	+	2.84693i	0.0922208	+	0.109904i
$672$	−0.0561352	−	0.332184i	−0.00216546	−	0.0128143i
$673$	13.7919	−	23.8883i	0.531640	−	0.920827i	−0.467678	−	0.883899i	$-0.654909\pi$
$673$	13.7919	−	23.8883i	0.531640	−	0.920827i	0.999318	−	0.0369281i	$-0.0117573\pi$
$674$	−18.5584	+	16.6622i	−0.714842	+	0.641804i
$675$	−3.01643	+	4.04218i	−0.116102	+	0.155584i
$676$	−1.59013	−	2.37201i	−0.0611587	−	0.0912313i
$677$	−18.5954	−	32.2082i	−0.714679	−	1.23786i	−0.963083	−	0.269204i	$-0.913239\pi$
$677$	−18.5954	−	32.2082i	−0.714679	−	1.23786i	0.248404	−	0.968657i	$-0.420094\pi$
$678$	−1.12605	+	3.44890i	−0.0432458	+	0.132454i
$679$	−3.98971	+	1.45213i	−0.153111	+	0.0557278i
$680$	0.960150	+	7.40371i	0.0368201	+	0.283919i
$681$	−0.233882	−	0.196250i	−0.00896238	−	0.00752033i
$682$	1.87857	+	4.66877i	0.0719341	+	0.178776i
$683$			36.9807i			1.41503i	0.706700	+	0.707513i	$0.250183\pi$
$683$			36.9807i			1.41503i	−0.706700	+	0.707513i	$0.749817\pi$
$684$	6.71446	−	25.0193i	0.256734	−	0.956637i
$685$	16.9543	+	42.7473i	0.647791	+	1.63329i
$686$	−6.41818	+	2.58248i	−0.245047	+	0.0985995i
$687$	−0.0811380	+	0.0966965i	−0.00309561	+	0.00368920i
$688$	−13.7502	−	43.1542i	−0.524220	−	1.64524i
$689$	−15.7564	+	5.73487i	−0.600272	+	0.218481i
$690$	−0.189843	−	3.05794i	−0.00722720	−	0.116414i
$691$	−7.97564	+	4.60474i	−0.303408	+	0.175172i	−0.643973	−	0.765049i	$-0.722715\pi$
$691$	−7.97564	+	4.60474i	−0.303408	+	0.175172i	0.340565	+	0.940221i	$0.389382\pi$
$692$	7.87293	+	11.7442i	0.299284	+	0.446446i
$693$	0.554936	−	0.0978501i	0.0210803	−	0.00371702i
$694$	−7.08390	+	6.36011i	−0.268901	+	0.241426i
$695$	−17.2493	−	2.53666i	−0.654304	−	0.0962209i
$696$	−0.621254	−	0.862817i	−0.0235486	−	0.0327050i
$697$	−3.91167	+	3.28228i	−0.148165	+	0.124325i
$698$	−5.87030	−	4.59987i	−0.222194	−	0.174108i
$699$	1.86536	+	0.678936i	0.0705545	+	0.0256797i
$700$	1.37159	−	3.24780i	0.0518413	−	0.122755i
$701$	1.90882	−	10.8255i	0.0720952	−	0.408872i	−0.927307	−	0.374302i	$-0.877882\pi$
$701$	1.90882	−	10.8255i	0.0720952	−	0.408872i	0.999402	−	0.0345708i	$-0.0110064\pi$
$702$	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
$705$	−0.980608	+	0.201899i	−0.0369318	+	0.00760395i
$706$	39.1096	+	5.55335i	1.47191	+	0.209003i
$707$	−2.64063	−	0.961110i	−0.0993111	−	0.0361463i
$708$	−1.12790	−	0.121798i	−0.0423890	−	0.00457746i
$709$	−15.2568	+	12.8020i	−0.572982	+	0.480789i	−0.882634	−	0.470061i	$-0.844232\pi$
$709$	−15.2568	+	12.8020i	−0.572982	+	0.480789i	0.309652	+	0.950850i	$0.399788\pi$
$710$	2.54065	−	22.4821i	0.0953488	−	0.843736i
$711$	−10.9790	+	19.0161i	−0.411743	+	0.713160i
$712$	−13.7640	+	3.88317i	−0.515829	+	0.145528i
$713$	6.58901	+	37.3681i	0.246760	+	1.39945i
$714$	0.0993642	−	0.00332810i	0.00371861	−	0.000124551i
$715$	−2.83562	+	3.58205i	−0.106046	+	0.133961i
$716$	−8.59683	−	34.9035i	−0.321279	−	1.30441i
$717$	−1.59055	+	0.578914i	−0.0594003	+	0.0216200i
$718$	5.79446	−	1.22302i	0.216247	−	0.0456428i
$719$	20.6011	−	24.5514i	0.768290	−	0.915613i	−0.230051	−	0.973178i	$-0.573889\pi$
$719$	20.6011	−	24.5514i	0.768290	−	0.915613i	0.998342	+	0.0575658i	$0.0183339\pi$
$720$	17.3286	−	20.1517i	0.645797	−	0.751008i
$721$		−	3.51146i		−	0.130774i
$722$	11.6947	−	24.1916i	0.435233	−	0.900318i
$723$	−3.06462			−0.113975
$724$	6.55572	−	8.96930i	0.243641	−	0.333341i
$725$	−0.634326	−	11.1082i	−0.0235583	−	0.412549i
$726$	−2.50356	+	0.528420i	−0.0929159	+	0.0196115i
$727$	39.7704	−	14.4752i	1.47500	−	0.536857i	0.525548	−	0.850764i	$-0.323860\pi$
$727$	39.7704	−	14.4752i	1.47500	−	0.536857i	0.949454	+	0.313908i	$0.101638\pi$
$728$	−2.64276	+	2.71335i	−0.0979472	+	0.100563i
$729$	−12.7356	−	22.0588i	−0.471690	−	0.816992i
$730$	14.4081	+	33.0534i	0.533266	+	1.22336i
$731$	13.1629	−	2.32098i	0.486848	−	0.0858444i
$732$	0.649803	−	2.24199i	0.0240174	−	0.0828664i
$733$	14.9446	+	8.62829i	0.551993	+	0.318693i	0.749925	−	0.661522i	$-0.230089\pi$
$733$	14.9446	+	8.62829i	0.551993	+	0.318693i	−0.197932	+	0.980216i	$0.563423\pi$
$734$	−3.48790	+	6.53729i	−0.128741	+	0.241296i
$735$	2.28530	+	1.23390i	0.0842944	+	0.0455129i
$736$	−0.231199	+	32.4442i	−0.00852212	+	1.19591i
$737$	3.58489	+	1.30479i	0.132051	+	0.0480627i
$738$	17.9977	+	2.55558i	0.662506	+	0.0940722i
$739$	−41.0588	−	7.23978i	−1.51037	−	0.266320i	−0.643732	−	0.765251i	$-0.722615\pi$
$739$	−41.0588	−	7.23978i	−1.51037	−	0.266320i	−0.866641	+	0.498932i	$0.833726\pi$
$740$	−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	0.335747	−	0.941952i	$-0.391011\pi$
$743$	8.97006	+	1.58166i	0.329080	+	0.0580256i	−0.00666746	+	0.999978i	$0.502122\pi$
$744$	1.77875	−	2.61294i	0.0652122	−	0.0957950i
$745$	2.78795	−	0.0795369i	0.102142	−	0.00291401i
$746$	18.6576	+	14.6198i	0.683104	+	0.535269i
$747$	3.47855	−	2.91885i	0.127274	−	0.106795i
$748$	−1.26704	+	0.0849717i	−0.0463276	+	0.00310687i
$749$	−3.46780	−	2.00213i	−0.126711	−	0.0731564i
$750$	−2.55665	+	0.772908i	−0.0933555	+	0.0282226i
$751$	8.02258	+	45.4983i	0.292748	+	1.66026i	0.676217	+	0.736702i	$0.263618\pi$
$751$	8.02258	+	45.4983i	0.292748	+	1.66026i	−0.383469	+	0.923554i	$0.625271\pi$
$752$	10.5072	−	1.41566i	0.383159	−	0.0516238i
$753$	1.56026	+	2.70245i	0.0568591	+	0.0984829i
$754$	−3.71006	+	11.3632i	−0.135112	+	0.413825i
$755$	−38.4082	+	34.1413i	−1.39782	+	1.24253i
$756$	−0.492622	−	0.513044i	−0.0179165	−	0.0186592i
$757$	−1.50549	+	1.79418i	−0.0547181	+	0.0652105i	−0.792709	−	0.609600i	$-0.791330\pi$
$757$	−1.50549	+	1.79418i	−0.0547181	+	0.0652105i	0.737991	+	0.674810i	$0.235775\pi$
$758$	9.40266	−	3.78334i	0.341520	−	0.137417i
$759$	0.521145			0.0189163
$760$	21.5660	−	17.1728i	0.782283	−	0.622923i
$761$	−37.7494			−1.36841			−0.684207	−	0.729288i	$-0.739851\pi$
$761$	−37.7494			−1.36841			−0.684207	+	0.729288i	$0.739851\pi$
$762$	−3.49487	+	1.40623i	−0.126606	+	0.0509423i
$763$	1.19336	−	1.42220i	0.0432027	−	0.0514870i
$764$	12.2139	+	12.7202i	0.441883	+	0.460201i
$765$	5.21084	+	5.86207i	0.188398	+	0.211944i
$766$	−14.6322	+	44.8157i	−0.528682	+	1.61926i
$767$	6.37730	+	11.0458i	0.230271	+	0.398841i
$768$	1.89956	−	1.92269i	0.0685443	−	0.0693790i
$769$	3.51096	+	19.9117i	0.126609	+	0.718033i	0.980339	+	0.197318i	$0.0632233\pi$
$769$	3.51096	+	19.9117i	0.126609	+	0.718033i	−0.853731	+	0.520714i	$0.825666\pi$
$770$	0.536920	+	0.267085i	0.0193493	+	0.00962507i
$771$	1.28601	+	0.742478i	0.0463145	+	0.0267397i
$772$	38.4295	−	2.57720i	1.38311	−	0.0927553i
$773$	−7.41424	+	6.22129i	−0.266672	+	0.223764i	−0.766312	−	0.642469i	$-0.777910\pi$
$773$	−7.41424	+	6.22129i	−0.266672	+	0.223764i	0.499640	+	0.866233i	$0.333466\pi$
$774$	−37.4536	−	29.3480i	−1.34624	−	1.05489i
$775$	30.3882	−	13.0673i	1.09158	−	0.469390i
$776$	−28.1572	−	19.1680i	−1.01079	−	0.688090i
$777$	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
$782$	−9.47969	−	1.34606i	−0.338993	−	0.0481351i
$783$	−2.10931	−	0.767725i	−0.0753805	−	0.0274363i
$784$	−23.2403	−	14.7070i	−0.830009	−	0.525250i
$785$	27.1062	+	14.6354i	0.967460	+	0.522359i
$786$	1.84875	−	3.46507i	0.0659428	−	0.123595i
$787$	−32.3581	−	18.6820i	−1.15344	−	0.665940i	−0.203718	−	0.979030i	$-0.565303\pi$
$787$	−32.3581	−	18.6820i	−1.15344	−	0.665940i	−0.949724	+	0.313090i	$0.898636\pi$
$788$	−11.7107	+	40.4051i	−0.417177	+	1.43937i
$789$	4.30878	−	0.759754i	0.153397	−	0.0270480i
$790$	−21.4213	+	9.33757i	−0.762134	+	0.332216i
$791$	−2.67711	−	4.63689i	−0.0951871	−	0.164869i
$792$	3.23849	+	3.15425i	0.115075	+	0.112081i
$793$	−24.6612	+	8.97595i	−0.875746	+	0.318745i
$794$	2.37855	−	0.502035i	0.0844117	−	0.0178166i
$795$	0.525380	−	1.58250i	0.0186333	−	0.0561254i
$796$	−20.6728	+	28.2838i	−0.732730	+	1.00249i
$797$	49.7980			1.76394			0.881968	−	0.471309i	$-0.156218\pi$
$797$	49.7980			1.76394			0.881968	+	0.471309i	$0.156218\pi$
$798$	−0.200266	−	0.307687i	−0.00708934	−	0.0108920i
$799$			3.12878i			0.110688i
$800$	27.5748	−	6.29521i	0.974917	−	0.222569i
$801$	−9.65760	+	11.5095i	−0.341235	+	0.406668i
$802$	−21.0408	+	4.44102i	−0.742976	+	0.156818i
$803$	−5.76331	+	2.09767i	−0.203383	+	0.0740253i
$804$	−0.573056	−	2.32663i	−0.0202101	−	0.0820541i
$805$	3.54516	+	2.80642i	0.124950	+	0.0989132i
$806$	−35.5181	+	1.18964i	−1.25107	+	0.0419033i
$807$	−0.192749	−	1.09314i	−0.00678510	−	0.0384802i
$808$	−6.12139	−	21.6975i	−0.215350	−	0.763316i
$809$	11.2064	−	19.4100i	0.393994	−	0.682418i	−0.598978	−	0.800766i	$-0.704426\pi$
$809$	11.2064	−	19.4100i	0.393994	−	0.682418i	0.992972	+	0.118347i	$0.0377596\pi$
$810$	3.10501	−	27.4761i	0.109099	−	0.965410i
$811$	24.1580	−	20.2710i	0.848303	−	0.711811i	−0.111112	−	0.993808i	$-0.535441\pi$
$811$	24.1580	−	20.2710i	0.848303	−	0.711811i	0.959415	+	0.281997i	$0.0909968\pi$
$812$	1.55999	+	0.168458i	0.0547448	+	0.00591172i
$813$	−2.57651	−	0.937772i	−0.0903620	−	0.0328891i
$814$	−0.582607	−	0.0827270i	−0.0204204	−	0.00289958i
$815$	6.09957	+	29.6252i	0.213659	+	1.03772i
$816$	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
$820$	13.7913	+	13.5665i	0.481615	+	0.473764i
$821$	−19.1032	−	6.95301i	−0.666708	−	0.242662i	−0.0135780	−	0.999908i	$-0.504322\pi$
$821$	−19.1032	−	6.95301i	−0.666708	−	0.242662i	−0.653130	+	0.757246i	$0.726544\pi$
$822$	3.86724	+	3.03031i	0.134886	+	0.105694i
$823$	−28.6865	+	24.0708i	−0.999947	+	0.839055i	−0.986977	−	0.160860i	$-0.948573\pi$
$823$	−28.6865	+	24.0708i	−0.999947	+	0.839055i	−0.0129702	+	0.999916i	$0.504129\pi$
$824$	22.8616	−	16.4611i	0.796422	−	0.573448i
$825$	−0.104270	−	0.442186i	−0.00363021	−	0.0153949i
$826$	1.24577	−	1.11848i	0.0433458	−	0.0389171i
$827$	21.8309	−	3.84937i	0.759134	−	0.133856i	0.219335	−	0.975650i	$-0.429611\pi$
$827$	21.8309	−	3.84937i	0.759134	−	0.133856i	0.539799	+	0.841794i	$0.318500\pi$
$828$	18.9799	+	28.3126i	0.659597	+	0.983931i
$829$	−33.6577	+	19.4323i	−1.16898	+	0.674911i	−0.953440	−	0.301584i	$-0.902485\pi$
$829$	−33.6577	+	19.4323i	−1.16898	+	0.674911i	−0.215541	+	0.976495i	$0.569151\pi$
$830$	4.82324	−	0.299436i	0.167417	−	0.0103936i
$831$	−2.73701	+	0.996192i	−0.0949460	+	0.0345575i
$832$	−30.0542	−	4.48624i	−1.04194	−	0.155532i
$833$	5.21706	−	6.21745i	0.180760	−	0.215422i
$834$	−1.72804	+	0.695312i	−0.0598373	+	0.0240767i
$835$	−11.4883	−	28.9656i	−0.397568	−	1.00240i
$836$	2.68812	+	3.84225i	0.0929705	+	0.132887i
$837$		−	6.67343i		−	0.230668i
$838$	−15.5747	−	38.7074i	−0.538018	−	1.33712i
$839$	−22.4922	−	18.8732i	−0.776516	−	0.651574i	0.165853	−	0.986150i	$-0.446962\pi$
$839$	−22.4922	−	18.8732i	−0.776516	−	0.651574i	−0.942369	+	0.334577i	$0.891407\pi$
$840$	−0.0484413	−	0.373530i	−0.00167138	−	0.0128880i
$841$	−22.5979	+	8.22497i	−0.779238	+	0.283620i
$842$	−10.4835	+	32.1091i	−0.361285	+	1.10655i
$843$	2.17521	+	3.76758i	0.0749183	+	0.129762i
$844$	−11.7091	−	17.4667i	−0.403045	−	0.601228i
$845$	−1.67458	−	2.71836i	−0.0576073	−	0.0935144i
$846$	8.28801	−	7.44119i	0.284948	−	0.255834i
$847$	1.88805	−	3.27020i	0.0648741	−	0.112365i
$848$	−6.70787	+	16.3338i	−0.230349	+	0.560907i
$849$	−2.57179	−	3.06494i	−0.0882635	−	0.105188i
$850$	0.754561	+	8.31274i	0.0258812	+	0.285125i
$851$	−4.16927	−	1.51749i	−0.142921	−	0.0520189i
$852$	−0.976866	−	2.21102i	−0.0334669	−	0.0757482i
$853$	−7.15162	−	1.26102i	−0.244867	−	0.0431766i	0.0498676	−	0.998756i	$-0.484120\pi$
$853$	−7.15162	−	1.26102i	−0.244867	−	0.0431766i	−0.294734	+	0.955579i	$0.595231\pi$
$854$	1.82132	+	2.92399i	0.0623244	+	0.100057i
$855$	8.57649	−	27.6633i	0.293310	−	0.946064i
$856$	−3.22134	−	31.9630i	−0.110103	−	1.09247i
$857$	3.65149	−	20.7086i	0.124732	−	0.707392i	−0.856734	−	0.515758i	$-0.827510\pi$
$857$	3.65149	−	20.7086i	0.124732	−	0.707392i	0.981466	−	0.191634i	$-0.0613787\pi$
$858$	−0.0686180	+	0.483244i	−0.00234258	+	0.0164977i
$859$	−6.77073	+	18.6024i	−0.231014	+	0.634707i	−0.999990	−	0.00457169i	$-0.998545\pi$
$859$	−6.77073	+	18.6024i	−0.231014	+	0.634707i	0.768975	+	0.639279i	$0.220767\pi$
$860$	−13.5075	−	48.8030i	−0.460602	−	1.66417i
$861$	0.197351	−	0.165597i	0.00672569	−	0.00564353i
$862$	9.56786	−	17.9328i	0.325883	−	0.610794i
$863$	−32.8992	−	18.9944i	−1.11990	−	0.646576i	−0.178527	−	0.983935i	$-0.557133\pi$
$863$	−32.8992	−	18.9944i	−1.11990	−	0.646576i	−0.941376	+	0.337359i	$0.890466\pi$
$864$	1.03089	−	5.61231i	0.0350716	−	0.190935i
$865$	8.29107	+	13.4590i	0.281905	+	0.457619i
$866$	−37.4235	+	1.25346i	−1.27170	+	0.0425943i
$867$	2.28312	−	1.31816i	0.0775390	−	0.0447671i
$868$	1.11561	+	4.52944i	0.0378664	+	0.153739i
$869$	−1.35946	−	3.73509i	−0.0461165	−	0.126704i
$870$	−0.656996	−	0.990641i	−0.0222743	−	0.0335859i
$871$	−17.3167	+	20.6372i	−0.586753	+	0.699265i
$872$	14.8536	+	1.10250i	0.503006	+	0.0373354i
$873$	−35.7849			−1.21113
$874$	13.8483	+	32.5312i	0.468426	+	1.10038i
$875$	1.67191	−	3.56953i	0.0565208	−	0.120672i
$876$	3.11006	+	2.27316i	0.105079	+	0.0768030i
$877$	−30.1437	−	25.2935i	−1.01788	−	0.854102i	−0.0285194	−	0.999593i	$-0.509079\pi$
$877$	−30.1437	−	25.2935i	−1.01788	−	0.854102i	−0.989360	+	0.145491i	$0.953524\pi$
$878$	−8.96893	−	42.4932i	−0.302687	−	1.43408i
$879$	0.887741	+	2.43905i	0.0299428	+	0.0822670i
$880$	0.778105	+	4.74770i	0.0262299	+	0.160045i
$881$	−15.9604	−	27.6442i	−0.537719	−	0.931356i	−0.999026	−	0.0441160i	$-0.985953\pi$
$881$	−15.9604	−	27.6442i	−0.537719	−	0.931356i	0.461308	−	0.887240i	$-0.347380\pi$
$882$	−28.8775	+	0.967220i	−0.972355	+	0.0325680i
$883$	−6.36734	−	36.1110i	−0.214278	−	1.21523i	−0.882155	−	0.470959i	$-0.843908\pi$
$883$	−6.36734	−	36.1110i	−0.214278	−	1.21523i	0.667877	−	0.744272i	$-0.267203\pi$
$884$	2.49634	−	8.61304i	0.0839610	−	0.289688i
$885$	−1.25486	−	0.184538i	−0.0421818	−	0.00620318i
$886$	−21.1674	+	39.6737i	−0.711134	+	1.33286i
$887$	16.6814	+	19.8802i	0.560108	+	0.667510i	0.969569	−	0.244817i	$-0.0787279\pi$
$887$	16.6814	+	19.8802i	0.560108	+	0.667510i	−0.409462	+	0.912327i	$0.634283\pi$
$888$	0.160602	+	0.332888i	0.00538946	+	0.0111710i
$889$	1.90146	−	5.22422i	0.0637729	−	0.175215i
$890$	−15.5442	+	3.74688i	−0.521041	+	0.125596i
$891$	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
$895$	−8.10469	−	39.3639i	−0.270910	−	1.31579i
$896$	0.238529	+	3.98156i	0.00796869	+	0.133015i
$897$	−1.25868	+	3.45820i	−0.0420262	+	0.115466i
$898$	−21.8613	+	27.8992i	−0.729521	+	0.931007i
$899$	9.46296	+	11.2775i	0.315607	+	0.376126i
$900$	20.2255	−	21.7690i	0.674183	−	0.725634i
$901$	−4.51276	−	2.60545i	−0.150342	−	0.0868000i
$902$	−2.44854	+	2.19836i	−0.0815273	+	0.0731974i
$903$	−0.664093	+	0.117097i	−0.0220996	+	0.00389676i
$904$	17.6390	−	39.1664i	0.586666	−	1.30266i
$905$	7.70950	−	9.73888i	0.256272	−	0.323731i
$906$	−1.70401	+	5.21910i	−0.0566121	+	0.173393i
$907$	10.6876	+	29.3641i	0.354878	+	0.975018i	0.980780	+	0.195117i	$0.0625086\pi$
$907$	10.6876	+	29.3641i	0.354878	+	0.975018i	−0.625903	+	0.779901i	$0.715269\pi$
$908$	2.50361	+	2.60740i	0.0830854	+	0.0865296i
$909$	−18.1434	−	15.2242i	−0.601780	−	0.504953i
$910$	−3.06910	+	2.91782i	−0.101740	+	0.0967247i
$911$	21.9268			0.726468			0.363234	−	0.931698i	$-0.381673\pi$
$911$	21.9268			0.726468			0.363234	+	0.931698i	$0.381673\pi$
$912$	1.06441	−	2.74623i	0.0352462	−	0.0909366i
$913$			0.821993i			0.0272040i
$914$	14.8192	+	36.8299i	0.490176	+	1.21822i
$915$	0.822300	−	2.47685i	0.0271844	−	0.0818822i
$916$	1.07801	−	1.03510i	0.0356184	−	0.0342006i
$917$	1.98234	+	5.44645i	0.0654628	+	0.179858i
$918$	1.60078	+	0.522650i	0.0528337	+	0.0172500i
$919$	5.54626	−	3.20213i	0.182954	−	0.105629i	−0.405726	−	0.913995i	$-0.632981\pi$
$919$	5.54626	−	3.20213i	0.182954	−	0.105629i	0.588680	+	0.808366i	$0.299648\pi$
$920$	−1.65238	+	36.2370i	−0.0544772	+	1.19470i
$921$	0.132104	+	0.749201i	0.00435299	+	0.0246870i
$922$	−9.07752	+	8.15004i	−0.298952	+	0.268407i
$923$	−13.5882	+	23.5355i	−0.447261	+	0.774679i
$924$	0.0639245	−	0.00428697i	0.00210296	−	0.000141031i
$925$	−0.453394	+	3.84120i	−0.0149075	+	0.126298i
$926$	−43.4233	−	34.0258i	−1.42698	−	1.11816i
$927$	10.1224	−	27.8111i	0.332463	−	0.913436i
$928$	6.21616	+	10.9461i	0.204055	+	0.359324i
$929$	−7.46019	+	42.3088i	−0.244761	+	1.38811i	0.576287	+	0.817247i	$0.304501\pi$
$929$	−7.46019	+	42.3088i	−0.244761	+	1.38811i	−0.821048	+	0.570860i	$0.806610\pi$
$930$	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
$934$	−2.31724	+	16.3192i	−0.0758225	+	0.533982i
$935$	−1.41920	+	0.0404881i	−0.0464128	+	0.00132410i
$936$	−28.7526	+	13.8717i	−0.939808	+	0.453411i
$937$	15.6006	+	18.5921i	0.509649	+	0.607376i	0.958101	−	0.286431i	$-0.0924689\pi$
$937$	15.6006	+	18.5921i	0.509649	+	0.607376i	−0.448452	+	0.893807i	$0.648024\pi$
$938$	3.11991	+	1.66460i	0.101869	+	0.0543510i
$939$	−0.958079	+	1.65944i	−0.0312657	+	0.0541538i
$940$	11.7996	−	1.13011i	0.384860	−	0.0368600i
$941$	−46.9057	+	8.27073i	−1.52908	+	0.269618i	−0.873994	−	0.485936i	$-0.838479\pi$
$941$	−46.9057	+	8.27073i	−1.52908	+	0.269618i	−0.655086	+	0.755554i	$0.727368\pi$
$942$	3.28925	−	0.110170i	0.107169	−	0.00358952i
$943$	−21.4867	+	12.4054i	−0.699704	+	0.403975i
$944$	13.1219	+	2.86743i	0.427082	+	0.0933268i
$945$	−0.528317	−	0.594344i	−0.0171861	−	0.0193340i
$946$	8.42761	−	1.77879i	0.274005	−	0.0578336i
$947$	−6.91093	−	5.79896i	−0.224575	−	0.188441i	0.523557	−	0.851991i	$-0.324605\pi$
$947$	−6.91093	−	5.79896i	−0.224575	−	0.188441i	−0.748132	+	0.663550i	$0.769049\pi$
$948$	−1.47319	+	2.01557i	−0.0478470	+	0.0654625i
$949$		−	43.3104i		−	1.40592i
$950$	24.8317	−	18.2589i	0.805645	−	0.592398i
$951$		−	1.42334i		−	0.0461550i
$952$	−1.17387	−	0.0871299i	−0.0380453	−	0.00282389i
$953$	−1.42806	−	1.19829i	−0.0462596	−	0.0388164i	0.619365	−	0.785103i	$-0.287390\pi$
$953$	−1.42806	−	1.19829i	−0.0462596	−	0.0388164i	−0.665624	+	0.746287i	$0.731835\pi$
$954$	3.83101	+	18.1507i	0.124034	+	0.587649i
$955$	13.0989	+	14.7359i	0.423870	+	0.476844i
$956$	19.4586	−	4.79271i	0.629337	−	0.155007i
$957$	0.175105	−	0.101097i	0.00566033	−	0.00326800i
$958$	0.816348	+	24.3730i	0.0263750	+	0.787456i
$959$	−7.14044	+	1.25905i	−0.230577	+	0.0406569i
$960$	2.20481	−	2.06642i	0.0711600	−	0.0666934i
$961$	−6.38390	+	11.0572i	−0.205932	+	0.356685i
$962$	1.95609	−	3.66625i	0.0630668	−	0.118205i
$963$	−21.6938	−	25.8536i	−0.699072	−	0.833121i
$964$	36.0743	+	3.89556i	1.16188	+	0.125467i
$965$	43.0444	−	1.22801i	1.38565	−	0.0395310i
$966$	0.478267	+	0.0679113i	0.0153880	+	0.00218501i
$967$	−1.32962	+	7.54063i	−0.0427576	+	0.242490i	−0.998694	−	0.0510819i	$-0.983733\pi$
$967$	−1.32962	+	7.54063i	−0.0427576	+	0.242490i	0.955937	+	0.293572i	$0.0948442\pi$
$968$	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	−0.883426	−	0.468571i	$-0.844769\pi$
$971$	3.33371	−	18.9064i	0.106984	−	0.606735i	0.990409	−	0.138164i	$-0.0441200\pi$
$972$	−3.63980	−	8.23824i	−0.116747	−	0.264242i
$973$	0.940180	−	2.58312i	0.0301408	−	0.0828112i
$974$	26.2155	−	33.4559i	0.839998	−	1.07200i
$975$	3.18609	+	0.376068i	0.102036	+	0.0120438i
$976$	−10.4988	+	25.5650i	−0.336060	+	0.818315i
$977$	19.3160	−	33.4564i	0.617975	−	1.07036i	−0.371880	−	0.928281i	$-0.621287\pi$
$977$	19.3160	−	33.4564i	0.617975	−	1.07036i	0.989855	−	0.142083i	$-0.0453799\pi$
$978$	2.15884	+	2.40451i	0.0690320	+	0.0768879i
$979$	−0.472276	−	2.67841i	−0.0150940	−	0.0856023i
$980$	−25.3323	−	17.4294i	−0.809209	−	0.556761i
$981$	13.5513	−	7.82384i	0.432659	−	0.249796i
$982$	−8.21413	+	25.1584i	−0.262123	+	0.802837i
$983$	−6.94718	−	19.0872i	−0.221581	−	0.608788i	0.778235	−	0.627973i	$-0.216115\pi$
$983$	−6.94718	−	19.0872i	−0.221581	−	0.608788i	−0.999816	+	0.0191849i	$0.993893\pi$
$984$	2.00327	+	0.508579i	0.0638620	+	0.0162129i
$985$	−14.8194	+	44.6377i	−0.472187	+	1.42227i
$986$	−3.44630	+	1.38669i	−0.109753	+	0.0441611i
$987$		−	0.157853i		−	0.00502451i
$988$	−31.9887	+	8.55787i	−1.01770	+	0.272262i
$989$	64.9430			2.06507
$990$	3.48254	+	3.66310i	0.110682	+	0.116421i
$991$	22.7223	+	19.0662i	0.721796	+	0.605659i	0.927882	−	0.372875i	$-0.121628\pi$
$991$	22.7223	+	19.0662i	0.721796	+	0.605659i	−0.206085	+	0.978534i	$0.566072\pi$
$992$	−24.2595	+	28.4964i	−0.770239	+	0.904763i
$993$	1.51222	+	4.15479i	0.0479888	+	0.131848i
$994$	3.39108	+	1.10717i	0.107558	+	0.0351174i
$995$	−24.3112	+	30.7107i	−0.770716	+	0.973593i
$996$	0.428846	−	0.287485i	0.0135885	−	0.00910932i
$997$	4.72799	−	0.833672i	0.149737	−	0.0264027i	−0.0982772	−	0.995159i	$-0.531333\pi$
$997$	4.72799	−	0.833672i	0.149737	−	0.0264027i	0.248014	+	0.968756i	$0.420222\pi$
$998$	3.48670	+	3.88349i	0.110370	+	0.122930i
$999$	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.59.7	✓	336
4.3	odd	2	inner	380.2.bb.a.59.45	yes	336
5.4	even	2	inner	380.2.bb.a.59.50	yes	336
19.10	odd	18	inner	380.2.bb.a.219.12	yes	336
20.19	odd	2	inner	380.2.bb.a.59.12	yes	336
76.67	even	18	inner	380.2.bb.a.219.50	yes	336
95.29	odd	18	inner	380.2.bb.a.219.45	yes	336
380.219	even	18	inner	380.2.bb.a.219.7	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.7	✓	336	1.1	even	1	trivial
380.2.bb.a.59.12	yes	336	20.19	odd	2	inner
380.2.bb.a.59.45	yes	336	4.3	odd	2	inner
380.2.bb.a.59.50	yes	336	5.4	even	2	inner
380.2.bb.a.219.7	yes	336	380.219	even	18	inner
380.2.bb.a.219.12	yes	336	19.10	odd	18	inner
380.2.bb.a.219.45	yes	336	95.29	odd	18	inner
380.2.bb.a.219.50	yes	336	76.67	even	18	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)

\(f(q)\)	\(=\)	\(q+(-1.31199 + 0.527904i) q^{2} +(-0.108582 + 0.129403i) q^{3} +(1.44263 - 1.38521i) q^{4} +(1.67124 - 1.48558i) q^{5} +(0.0741462 - 0.227097i) q^{6} +(0.176277 + 0.305321i) q^{7} +(-1.16146 + 2.57895i) q^{8} +(0.515989 + 2.92632i) q^{9} +O(q^{10})\)	\(q+(-1.31199 + 0.527904i) q^{2} +(-0.108582 + 0.129403i) q^{3} +(1.44263 - 1.38521i) q^{4} +(1.67124 - 1.48558i) q^{5} +(0.0741462 - 0.227097i) q^{6} +(0.176277 + 0.305321i) q^{7} +(-1.16146 + 2.57895i) q^{8} +(0.515989 + 2.92632i) q^{9} +(-1.40841 + 2.83132i) q^{10} +(-0.465827 - 0.268946i) q^{11} +(0.0226063 + 0.337091i) q^{12} +(2.90974 - 2.44156i) q^{13} +(-0.392454 - 0.307521i) q^{14} +(0.0107717 + 0.377572i) q^{15} +(0.162385 - 3.99670i) 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} +(0.753138 + 0.106941i) q^{22} +(5.38963 + 1.96166i) q^{23} +(-0.207611 - 0.430325i) q^{24} +(0.586103 - 4.96553i) q^{25} +(-2.52864 + 4.73937i) q^{26} +(-0.873580 - 0.504362i) q^{27} +(0.677238 + 0.196286i) q^{28} +(2.19146 - 0.386413i) q^{29} +(-0.213454 - 0.489684i) q^{30} +(3.30786 + 5.72938i) q^{31} +(1.89683 + 5.32936i) q^{32} +(0.0853830 - 0.0310769i) q^{33} +(-1.63340 + 0.344757i) q^{34} +(0.748181 + 0.248392i) q^{35} +(4.79795 + 3.50686i) q^{36} -0.773573 q^{37} +(4.20877 + 4.50403i) q^{38} +0.641641i q^{39} +(1.89016 + 6.03550i) q^{40} +(-2.78057 + 3.31376i) q^{41} +(0.0824077 - 0.0173936i) q^{42} +(10.6401 - 3.87268i) q^{43} +(-1.04456 + 0.257279i) q^{44} +(5.20963 + 4.12405i) q^{45} +(-8.10670 + 0.271525i) q^{46} +(0.460262 + 2.61027i) q^{47} +(0.499554 + 0.454984i) q^{48} +(3.43785 - 5.95454i) q^{49} +(1.85236 + 6.82413i) q^{50} +(-0.152752 + 0.128174i) q^{51} +(0.815614 - 7.55289i) q^{52} +(-4.14817 - 1.50981i) q^{53} +(1.41238 + 0.200551i) q^{54} +(-1.17805 + 0.242551i) 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} +(0.538556 + 0.529777i) q^{60} +(-6.49253 - 2.36309i) q^{61} +(-7.36445 - 5.77066i) q^{62} +(-0.802511 + 0.673386i) q^{63} +(-5.30201 - 5.99072i) q^{64} +(1.23575 - 8.40310i) q^{65} +(-0.0956160 + 0.0858466i) q^{66} +(-6.98470 + 1.23159i) q^{67} +(1.96100 - 1.31459i) q^{68} +(-0.839063 + 0.484433i) q^{69} +(-1.11273 + 0.0690808i) q^{70} +(-6.72322 + 2.44705i) q^{71} +(-8.14615 - 2.06810i) q^{72} +(7.32925 - 8.73466i) q^{73} +(1.01492 - 0.408373i) q^{74} +(0.578915 + 0.615012i) q^{75} +(-7.89956 - 3.68741i) q^{76} -0.189636i q^{77} +(-0.338725 - 0.841826i) q^{78} +(5.66076 + 4.74994i) q^{79} +(-5.66604 - 6.92069i) q^{80} +(-8.21667 + 2.99062i) q^{81} +(1.89874 - 5.81550i) q^{82} +(-0.764089 - 1.32344i) q^{83} +(-0.0989359 + 0.0663236i) q^{84} +(2.24733 - 1.38441i) q^{85} +(-11.9153 + 10.6979i) q^{86} +(-0.187950 + 0.325540i) q^{87} +(1.23464 - 0.888977i) q^{88} +(3.25011 + 3.87334i) q^{89} +(-9.01208 - 2.66052i) q^{90} +(1.25838 + 0.458014i) q^{91} +(10.4926 - 4.63580i) q^{92} +(-1.10058 - 0.194061i) q^{93} +(-1.98183 - 3.18168i) q^{94} +(-8.66701 - 4.45904i) q^{95} +(-0.895598 - 0.333217i) q^{96} +(-2.09122 + 11.8599i) q^{97} +(-1.36700 + 9.62715i) 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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