LMFDB - Embedded newform 231.2.be.a.149.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(2,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 10, 3]))

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

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

chi := DirichletCharacter("231.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.be (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			149.19
Character	$\chi$	$=$	231.149
Dual form			231.2.be.a.200.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.988032 + 0.210013i) q^{2} +(-1.20257 + 1.24653i) q^{3} +(-0.894989 - 0.398475i) q^{4} +(-1.24323 + 1.11941i) q^{5} +(-1.44996 + 0.979053i) q^{6} +(-0.513908 + 2.59536i) q^{7} +(-2.43498 - 1.76911i) q^{8} +(-0.107655 - 2.99807i) q^{9} +O(q^{10})$	\(q+(0.988032 + 0.210013i) q^{2} +(-1.20257 + 1.24653i) q^{3} +(-0.894989 - 0.398475i) q^{4} +(-1.24323 + 1.11941i) q^{5} +(-1.44996 + 0.979053i) q^{6} +(-0.513908 + 2.59536i) q^{7} +(-2.43498 - 1.76911i) q^{8} +(-0.107655 - 2.99807i) q^{9} +(-1.46344 + 0.844920i) q^{10} +(-3.18831 + 0.913606i) q^{11} +(1.57299 - 0.636433i) q^{12} +(-0.659160 + 0.214174i) q^{13} +(-1.05282 + 2.45637i) q^{14} +(0.0996973 - 2.89589i) q^{15} +(-0.723222 - 0.803220i) q^{16} +(-0.217864 + 0.0463083i) q^{17} +(0.523266 - 2.98480i) q^{18} +(3.31894 + 7.45446i) q^{19} +(1.55874 - 0.506464i) q^{20} +(-2.61718 - 3.76170i) q^{21} +(-3.34202 + 0.233087i) q^{22} +(0.226106 + 0.130542i) q^{23} +(5.13348 - 0.907780i) q^{24} +(-0.230098 + 2.18923i) q^{25} +(-0.696250 + 0.0731788i) q^{26} +(3.86663 + 3.47119i) q^{27} +(1.49413 - 2.11804i) q^{28} +(-0.136493 + 0.0991679i) q^{29} +(0.706678 - 2.84030i) q^{30} +(3.60716 - 4.00616i) q^{31} +(2.46392 + 4.26763i) q^{32} +(2.69533 - 5.07299i) q^{33} -0.224982 q^{34} +(-2.26637 - 3.80191i) q^{35} +(-1.09830 + 2.72613i) q^{36} +(-0.585798 - 5.57350i) q^{37} +(1.71369 + 8.06227i) q^{38} +(0.525712 - 1.07922i) q^{39} +(5.00761 - 0.526321i) q^{40} +(-3.49306 - 2.53786i) q^{41} +(-1.79585 - 4.26632i) q^{42} -4.60809i q^{43} +(3.21755 + 0.452793i) q^{44} +(3.48991 + 3.60678i) q^{45} +(0.195984 + 0.176465i) q^{46} +(2.88287 + 6.47504i) q^{47} +(1.87096 + 0.0644118i) q^{48} +(-6.47180 - 2.66755i) q^{49} +(-0.687111 + 2.11471i) q^{50} +(0.204271 - 0.327262i) q^{51} +(0.675283 + 0.0709751i) q^{52} +(8.41687 + 7.57859i) q^{53} +(3.09136 + 4.24169i) q^{54} +(2.94111 - 4.70486i) q^{55} +(5.84285 - 5.41048i) q^{56} +(-13.2834 - 4.82736i) q^{57} +(-0.155686 + 0.0693158i) q^{58} +(-4.62977 + 10.3986i) q^{59} +(-1.24317 + 2.55206i) q^{60} +(-8.79542 + 7.91943i) q^{61} +(4.40534 - 3.20067i) q^{62} +(7.83639 + 1.26133i) q^{63} +(2.20617 + 6.78989i) q^{64} +(0.579740 - 1.00414i) q^{65} +(3.72846 - 4.44622i) q^{66} +(-1.21210 - 2.09942i) q^{67} +(0.213438 + 0.0453677i) q^{68} +(-0.434632 + 0.124861i) q^{69} +(-1.44080 - 4.23238i) q^{70} +(-9.62898 - 3.12864i) q^{71} +(-5.04179 + 7.49068i) q^{72} +(4.69964 - 10.5556i) q^{73} +(0.591718 - 5.62982i) q^{74} +(-2.45223 - 2.91953i) q^{75} -7.99417i q^{76} +(-0.732640 - 8.74433i) q^{77} +(0.746070 - 0.955897i) q^{78} +(-1.11709 + 5.25548i) q^{79} +(1.79827 + 0.189005i) q^{80} +(-8.97682 + 0.645512i) q^{81} +(-2.91827 - 3.24107i) q^{82} +(-1.31998 + 4.06249i) q^{83} +(0.843400 + 4.40956i) q^{84} +(0.219017 - 0.301451i) q^{85} +(0.967757 - 4.55294i) q^{86} +(0.0405268 - 0.289398i) q^{87} +(9.37974 + 3.41588i) q^{88} +(-0.945459 - 0.545861i) q^{89} +(2.69067 + 4.29655i) q^{90} +(-0.217111 - 1.82082i) q^{91} +(-0.150344 - 0.206931i) q^{92} +(0.655921 + 9.31411i) q^{93} +(1.48853 + 7.00299i) q^{94} +(-12.4708 - 5.55237i) q^{95} +(-8.28274 - 2.06078i) q^{96} +(1.06820 + 3.28757i) q^{97} +(-5.83412 - 3.99479i) q^{98} +(3.08229 + 9.46042i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	0.988032	+	0.210013i	0.698644	+	0.148501i	0.543523	−	0.839394i	$-0.317090\pi$
$2$	0.988032	+	0.210013i	0.698644	+	0.148501i	0.155121	+	0.987895i	$0.450423\pi$
$3$	−1.20257	+	1.24653i	−0.694304	+	0.719682i
$3$	−1.20257	+	1.24653i	−0.694304	+	0.719682i
$4$	−0.894989	−	0.398475i	−0.447494	−	0.199237i
$5$	−1.24323	+	1.11941i	−0.555990	+	0.500616i	−0.898545	−	0.438882i	$-0.855375\pi$
$5$	−1.24323	+	1.11941i	−0.555990	+	0.500616i	0.342554	+	0.939498i	$0.388708\pi$
$6$	−1.44996	+	0.979053i	−0.591945	+	0.399697i
$7$	−0.513908	+	2.59536i	−0.194239	+	0.980954i
$7$	−0.513908	+	2.59536i	−0.194239	+	0.980954i
$8$	−2.43498	−	1.76911i	−0.860895	−	0.625477i
$9$	−0.107655	−	2.99807i	−0.0358849	−	0.999356i
$10$	−1.46344	+	0.844920i	−0.462782	+	0.267187i
$11$	−3.18831	+	0.913606i	−0.961312	+	0.275463i
$11$	−3.18831	+	0.913606i	−0.961312	+	0.275463i
$12$	1.57299	−	0.636433i	0.454085	−	0.183723i
$13$	−0.659160	+	0.214174i	−0.182818	+	0.0594012i	−0.398995	−	0.916953i	$-0.630641\pi$
$13$	−0.659160	+	0.214174i	−0.182818	+	0.0594012i	0.216177	+	0.976354i	$0.430641\pi$
$14$	−1.05282	+	2.45637i	−0.281377	+	0.656493i
$15$	0.0996973	−	2.89589i	0.0257417	−	0.747716i
$16$	−0.723222	−	0.803220i	−0.180806	−	0.200805i
$17$	−0.217864	+	0.0463083i	−0.0528397	+	0.0112314i	−0.234256	−	0.972175i	$-0.575265\pi$
$17$	−0.217864	+	0.0463083i	−0.0528397	+	0.0112314i	0.181416	+	0.983406i	$0.441932\pi$
$18$	0.523266	−	2.98480i	0.123335	−	0.703523i
$19$	3.31894	+	7.45446i	0.761417	+	1.71017i	0.702259	+	0.711922i	$0.252175\pi$
$19$	3.31894	+	7.45446i	0.761417	+	1.71017i	0.0591581	+	0.998249i	$0.481158\pi$
$20$	1.55874	−	0.506464i	0.348544	−	0.113249i
$21$	−2.61718	−	3.76170i	−0.571114	−	0.820870i
$22$	−3.34202	+	0.233087i	−0.712522	+	0.0496943i
$23$	0.226106	+	0.130542i	0.0471463	+	0.0272199i	0.523388	−	0.852095i	$-0.324668\pi$
$23$	0.226106	+	0.130542i	0.0471463	+	0.0272199i	−0.476242	+	0.879314i	$0.658001\pi$
$24$	5.13348	−	0.907780i	1.04787	−	0.185300i
$25$	−0.230098	+	2.18923i	−0.0460195	+	0.437847i
$26$	−0.696250	+	0.0731788i	−0.136546	+	0.0143516i
$27$	3.86663	+	3.47119i	0.744134	+	0.668031i
$28$	1.49413	−	2.11804i	0.282364	−	0.400272i
$29$	−0.136493	+	0.0991679i	−0.0253461	+	0.0184150i	−0.600386	−	0.799710i	$-0.704986\pi$
$29$	−0.136493	+	0.0991679i	−0.0253461	+	0.0184150i	0.575040	+	0.818125i	$0.304986\pi$
$30$	0.706678	−	2.84030i	0.129021	−	0.518565i
$31$	3.60716	−	4.00616i	0.647866	−	0.719528i	−0.326324	−	0.945258i	$-0.605810\pi$
$31$	3.60716	−	4.00616i	0.647866	−	0.719528i	0.974190	+	0.225730i	$0.0724767\pi$
$32$	2.46392	+	4.26763i	0.435563	+	0.754418i
$33$	2.69533	−	5.07299i	0.469197	−	0.883094i
$34$	−0.224982			−0.0385840
$35$	−2.26637	−	3.80191i	−0.383086	−	0.642640i
$36$	−1.09830	+	2.72613i	−0.183051	+	0.454356i
$37$	−0.585798	−	5.57350i	−0.0963046	−	0.916277i	−0.930866	−	0.365362i	$-0.880945\pi$
$37$	−0.585798	−	5.57350i	−0.0963046	−	0.916277i	0.834561	−	0.550915i	$-0.185721\pi$
$38$	1.71369	+	8.06227i	0.277997	+	1.30787i
$39$	0.525712	−	1.07922i	0.0841812	−	0.172813i
$40$	5.00761	−	0.526321i	0.791773	−	0.0832187i
$41$	−3.49306	−	2.53786i	−0.545524	−	0.396347i	0.280608	−	0.959822i	$-0.409464\pi$
$41$	−3.49306	−	2.53786i	−0.545524	−	0.396347i	−0.826133	+	0.563476i	$0.809464\pi$
$42$	−1.79585	−	4.26632i	−0.277105	−	0.658308i
$43$		−	4.60809i		−	0.702727i	−0.936239	−	0.351363i	$-0.885718\pi$
$43$		−	4.60809i		−	0.702727i	0.936239	−	0.351363i	$-0.114282\pi$
$44$	3.21755	+	0.452793i	0.485064	+	0.0682612i
$45$	3.48991	+	3.60678i	0.520245	+	0.537668i
$46$	0.195984	+	0.176465i	0.0288963	+	0.0260183i
$47$	2.88287	+	6.47504i	0.420510	+	0.944482i	0.992274	+	0.124063i	$0.0395926\pi$
$47$	2.88287	+	6.47504i	0.420510	+	0.944482i	−0.571764	+	0.820418i	$0.693741\pi$
$48$	1.87096	+	0.0644118i	0.270050	+	0.00929705i
$49$	−6.47180	−	2.66755i	−0.924542	−	0.381079i
$50$	−0.687111	+	2.11471i	−0.0971721	+	0.299065i
$51$	0.204271	−	0.327262i	0.0286037	−	0.0458258i
$52$	0.675283	+	0.0709751i	0.0936449	+	0.00984248i
$53$	8.41687	+	7.57859i	1.15615	+	1.04100i	0.998568	+	0.0534924i	$0.0170353\pi$
$53$	8.41687	+	7.57859i	1.15615	+	1.04100i	0.157578	+	0.987507i	$0.449631\pi$
$54$	3.09136	+	4.24169i	0.420681	+	0.577221i
$55$	2.94111	−	4.70486i	0.396579	−	0.634403i
$56$	5.84285	−	5.41048i	0.780783	−	0.723006i
$57$	−13.2834	−	4.82736i	−1.75943	−	0.639399i
$58$	−0.155686	+	0.0693158i	−0.0204426	+	0.00910161i
$59$	−4.62977	+	10.3986i	−0.602745	+	1.35379i	0.312126	+	0.950041i	$0.398959\pi$
$59$	−4.62977	+	10.3986i	−0.602745	+	1.35379i	−0.914871	+	0.403746i	$0.867708\pi$
$60$	−1.24317	+	2.55206i	−0.160492	+	0.329470i
$61$	−8.79542	+	7.91943i	−1.12614	+	1.01398i	−0.126379	+	0.991982i	$0.540336\pi$
$61$	−8.79542	+	7.91943i	−1.12614	+	1.01398i	−0.999758	+	0.0219968i	$0.992998\pi$
$62$	4.40534	−	3.20067i	0.559479	−	0.406485i
$63$	7.83639	+	1.26133i	0.987293	+	0.158912i
$64$	2.20617	+	6.78989i	0.275771	+	0.848736i
$65$	0.579740	−	1.00414i	0.0719079	−	0.124548i
$66$	3.72846	−	4.44622i	0.458942	−	0.547292i
$67$	−1.21210	−	2.09942i	−0.148082	−	0.256485i	0.782437	−	0.622730i	$-0.213977\pi$
$67$	−1.21210	−	2.09942i	−0.148082	−	0.256485i	−0.930519	+	0.366245i	$0.880643\pi$
$68$	0.213438	+	0.0453677i	0.0258832	+	0.00550164i
$69$	−0.434632	+	0.124861i	−0.0523235	+	0.0150314i
$70$	−1.44080	−	4.23238i	−0.172208	−	0.505866i
$71$	−9.62898	−	3.12864i	−1.14275	−	0.371302i	−0.324342	−	0.945940i	$-0.605143\pi$
$71$	−9.62898	−	3.12864i	−1.14275	−	0.371302i	−0.818407	+	0.574638i	$0.805143\pi$
$72$	−5.04179	+	7.49068i	−0.594181	+	0.882785i
$73$	4.69964	−	10.5556i	0.550052	−	1.23544i	−0.398019	−	0.917377i	$-0.630302\pi$
$73$	4.69964	−	10.5556i	0.550052	−	1.23544i	0.948071	−	0.318059i	$-0.103031\pi$
$74$	0.591718	−	5.62982i	0.0687858	−	0.654453i
$75$	−2.45223	−	2.91953i	−0.283159	−	0.337118i
$76$		−	7.99417i		−	0.916994i
$77$	−0.732640	−	8.74433i	−0.0834921	−	0.996508i
$78$	0.746070	−	0.955897i	0.0844757	−	0.108234i
$79$	−1.11709	+	5.25548i	−0.125682	+	0.591288i	0.869558	+	0.493832i	$0.164404\pi$
$79$	−1.11709	+	5.25548i	−0.125682	+	0.591288i	−0.995240	+	0.0974566i	$0.968929\pi$
$80$	1.79827	+	0.189005i	0.201052	+	0.0211315i
$81$	−8.97682	+	0.645512i	−0.997425	+	0.0717236i
$82$	−2.91827	−	3.24107i	−0.322269	−	0.357916i
$83$	−1.31998	+	4.06249i	−0.144887	+	0.445917i	−0.996996	−	0.0774472i	$-0.975323\pi$
$83$	−1.31998	+	4.06249i	−0.144887	+	0.445917i	0.852109	+	0.523364i	$0.175323\pi$
$84$	0.843400	+	4.40956i	0.0920225	+	0.481122i
$85$	0.219017	−	0.301451i	0.0237557	−	0.0326969i
$86$	0.967757	−	4.55294i	0.104356	−	0.490956i
$87$	0.0405268	−	0.289398i	0.00434493	−	0.0310267i
$88$	9.37974	+	3.41588i	0.999884	+	0.364134i
$89$	−0.945459	−	0.545861i	−0.100218	−	0.0578611i	0.449053	−	0.893505i	$-0.351761\pi$
$89$	−0.945459	−	0.545861i	−0.100218	−	0.0578611i	−0.549272	+	0.835644i	$0.685095\pi$
$90$	2.69067	+	4.29655i	0.283622	+	0.452896i
$91$	−0.217111	−	1.82082i	−0.0227594	−	0.190874i
$92$	−0.150344	−	0.206931i	−0.0156745	−	0.0215741i
$93$	0.655921	+	9.31411i	0.0680158	+	0.965828i
$94$	1.48853	+	7.00299i	0.153530	+	0.722303i
$95$	−12.4708	−	5.55237i	−1.27948	−	0.569661i
$96$	−8.28274	−	2.06078i	−0.845354	−	0.210328i
$97$	1.06820	+	3.28757i	0.108459	+	0.333802i	0.990527	−	0.137320i	$-0.0438489\pi$
$97$	1.06820	+	3.28757i	0.108459	+	0.333802i	−0.882068	+	0.471123i	$0.843849\pi$
$98$	−5.83412	−	3.99479i	−0.589335	−	0.403535i
$99$	3.08229	+	9.46042i	0.309782	+	0.950808i
$100$	1.07829	−	1.86765i	0.107829	−	0.186765i
$101$	−2.59240	+	2.87916i	−0.257954	+	0.286487i	−0.858186	−	0.513339i	$-0.828408\pi$
$101$	−2.59240	+	2.87916i	−0.257954	+	0.286487i	0.600232	+	0.799826i	$0.295075\pi$
$102$	0.270556	−	0.280445i	0.0267890	−	0.0277682i
$103$	−0.646124	−	6.14746i	−0.0636645	−	0.605727i	−0.979117	−	0.203300i	$-0.934833\pi$
$103$	−0.646124	−	6.14746i	−0.0636645	−	0.605727i	0.915452	−	0.402427i	$-0.131833\pi$
$104$	1.98394	+	0.644620i	0.194541	+	0.0632102i
$105$	7.46465	+	1.74697i	0.728475	+	0.170487i
$106$	6.72454	+	9.25554i	0.653145	+	0.898977i
$107$	16.9570	−	7.54973i	1.63929	−	0.729860i	0.640032	−	0.768348i	$-0.278921\pi$
$107$	16.9570	−	7.54973i	1.63929	−	0.729860i	0.999259	+	0.0384883i	$0.0122542\pi$
$108$	−2.07741	−	4.64743i	−0.199899	−	0.447199i
$109$	−6.28539	+	3.62887i	−0.602032	+	0.347583i	−0.769840	−	0.638236i	$-0.779664\pi$
$109$	−6.28539	+	3.62887i	−0.602032	+	0.347583i	0.167809	+	0.985820i	$0.446331\pi$
$110$	3.89399	−	4.03088i	0.371277	−	0.384329i
$111$	7.65197	+	5.97230i	0.726293	+	0.566866i
$112$	2.45632	−	1.46424i	0.232100	−	0.138358i
$113$	−2.65450	+	3.65360i	−0.249714	+	0.343702i	−0.915411	−	0.402520i	$-0.868134\pi$
$113$	−2.65450	+	3.65360i	−0.249714	+	0.343702i	0.665697	+	0.746222i	$0.268134\pi$
$114$	−12.1107	−	7.55928i	−1.13427	−	0.707991i
$115$	−0.427232	+	0.0908110i	−0.0398396	+	0.00846817i
$116$	0.161675	−	0.0343652i	0.0150112	−	0.00319073i
$117$	0.713070	+	1.95315i	0.0659233	+	0.180569i
$118$	−6.75821	+	9.30187i	−0.622143	+	0.856307i
$119$	−0.00822498	−	0.589233i	−0.000753983	−	0.0540149i
$120$	−5.36593	+	6.87505i	−0.489840	+	0.627604i
$121$	9.33065	−	5.82572i	0.848241	−	0.529611i
$122$	−10.3533	+	5.97750i	−0.937347	+	0.541177i
$123$	7.36415	−	1.30224i	0.664003	−	0.117419i
$124$	−4.82472	+	2.14811i	−0.433273	+	0.192906i
$125$	−7.08122	−	9.74646i	−0.633363	−	0.871750i
$126$	7.47771	+	2.89198i	0.666168	+	0.257638i
$127$	9.87874	+	3.20980i	0.876596	+	0.284823i	0.712543	−	0.701628i	$-0.247543\pi$
$127$	9.87874	+	3.20980i	0.876596	+	0.284823i	0.164053	+	0.986452i	$0.447543\pi$
$128$	−0.276396	−	2.62973i	−0.0244302	−	0.232437i
$129$	5.74410	+	5.54154i	0.505740	+	0.487906i
$130$	0.783683	−	0.870369i	0.0687336	−	0.0763364i
$131$	−4.05987	+	7.03190i	−0.354712	+	0.614380i	−0.987069	−	0.160298i	$-0.948755\pi$
$131$	−4.05987	+	7.03190i	−0.354712	+	0.614380i	0.632356	+	0.774678i	$0.282088\pi$
$132$	−4.43375	+	3.46625i	−0.385908	+	0.301698i
$133$	−21.0526	+	4.78294i	−1.82550	+	0.414733i
$134$	−0.756691	−	2.32885i	−0.0653681	−	0.201182i
$135$	−8.69281	+	0.0128569i	−0.748158	+	0.00110655i
$136$	0.612418	+	0.272666i	0.0525144	+	0.0233809i
$137$	−4.67042	−	21.9726i	−0.399021	−	1.87725i	−0.474755	−	0.880118i	$-0.657463\pi$
$137$	−4.67042	−	21.9726i	−0.399021	−	1.87725i	0.0757344	−	0.997128i	$-0.475870\pi$
$138$	−0.455653	+	0.0320881i	−0.0387877	+	0.00273152i
$139$	6.80052	+	9.36011i	0.576812	+	0.793914i	0.993341	−	0.115208i	$-0.0367536\pi$
$139$	6.80052	+	9.36011i	0.576812	+	0.793914i	−0.416529	+	0.909122i	$0.636754\pi$
$140$	0.513410	+	4.30576i	0.0433911	+	0.363903i
$141$	−11.5382	−	4.19311i	−0.971688	−	0.353123i
$142$	−8.85668	−	5.11341i	−0.743236	−	0.429108i
$143$	1.90593	−	1.28507i	0.159382	−	0.107463i
$144$	−2.33025	+	2.25474i	−0.194187	+	0.187895i
$145$	0.0586827	−	0.276080i	0.00487333	−	0.0229272i
$146$	6.86020	−	9.44226i	0.567754	−	0.781447i
$147$	11.1080	−	4.85935i	0.916169	−	0.400792i
$148$	−1.69661	+	5.22164i	−0.139461	+	0.429216i
$149$	7.82096	+	8.68606i	0.640718	+	0.711589i	0.972796	−	0.231662i	$-0.0744165\pi$
$149$	7.82096	+	8.68606i	0.640718	+	0.711589i	−0.332078	+	0.943252i	$0.607750\pi$
$150$	−1.80974	−	3.39958i	−0.147765	−	0.277575i
$151$	6.64783	+	0.698716i	0.540993	+	0.0568607i	0.371084	−	0.928599i	$-0.378986\pi$
$151$	6.64783	+	0.698716i	0.540993	+	0.0568607i	0.169909	+	0.985460i	$0.445653\pi$
$152$	5.10625	−	24.0230i	0.414172	−	1.94852i
$153$	0.162290	+	0.648184i	0.0131203	+	0.0524026i
$154$	1.11255	−	8.79354i	0.0896517	−	0.708604i
$155$			9.01849i			0.724383i
$156$	−0.900547	+	0.756406i	−0.0721015	+	0.0605609i
$157$	−0.998917	+	9.50406i	−0.0797223	+	0.758507i	0.879509	+	0.475883i	$0.157871\pi$
$157$	−0.998917	+	9.50406i	−0.0797223	+	0.758507i	−0.959231	+	0.282624i	$0.908795\pi$
$158$	−2.20744	+	4.95798i	−0.175614	+	0.394436i
$159$	−19.5688	+	1.37808i	−1.55190	+	0.109289i
$160$	−7.84046	−	2.54752i	−0.619842	−	0.201399i
$161$	−0.455001	+	0.519739i	−0.0358591	+	0.0409612i
$162$	−9.00495	−	1.24746i	−0.707496	−	0.0980097i
$163$	1.17081	+	0.248863i	0.0917048	+	0.0194924i	0.253536	−	0.967326i	$-0.418407\pi$
$163$	1.17081	+	0.248863i	0.0917048	+	0.0194924i	−0.161831	+	0.986819i	$0.551740\pi$
$164$	2.11498	+	3.66325i	0.165152	+	0.286052i
$165$	2.32784	+	9.32408i	0.181222	+	0.725879i
$166$	−2.15736	+	3.73666i	−0.167444	+	0.290021i
$167$	6.31398	+	19.4324i	0.488590	+	1.50373i	0.826713	+	0.562624i	$0.190208\pi$
$167$	6.31398	+	19.4324i	0.488590	+	1.50373i	−0.338122	+	0.941102i	$0.609792\pi$
$168$	−0.282118	+	13.7897i	−0.0217659	+	1.06390i
$169$	−10.1286	+	7.35886i	−0.779123	+	0.566066i
$170$	0.279704	−	0.251847i	0.0214523	−	0.0193158i
$171$	21.9917	−	10.7529i	1.68175	−	0.822296i
$172$	−1.83621	+	4.12419i	−0.140009	+	0.314466i
$173$	−12.8068	+	5.70194i	−0.973680	+	0.433510i	−0.831009	−	0.556260i	$-0.812236\pi$
$173$	−12.8068	+	5.70194i	−0.973680	+	0.433510i	−0.142672	+	0.989770i	$0.545569\pi$
$174$	0.100819	−	0.277424i	0.00764307	−	0.0210314i
$175$	−5.56360	−	1.72225i	−0.420569	−	0.130190i
$176$	3.03968	+	1.90017i	0.229125	+	0.143231i
$177$	−7.39455	−	18.2762i	−0.555808	−	1.37372i
$178$	−0.819506	−	0.737886i	−0.0614246	−	0.0553069i
$179$	12.5732	+	1.32150i	0.939767	+	0.0987735i	0.562009	−	0.827131i	$-0.310029\pi$
$179$	12.5732	+	1.32150i	0.939767	+	0.0987735i	0.377758	+	0.925904i	$0.376695\pi$
$180$	−1.68622	−	4.61867i	−0.125683	−	0.344256i
$181$	6.46032	−	19.8828i	0.480192	−	1.47788i	−0.358633	−	0.933479i	$-0.616757\pi$
$181$	6.46032	−	19.8828i	0.480192	−	1.47788i	0.838825	−	0.544401i	$-0.183243\pi$
$182$	0.167883	−	1.84463i	0.0124443	−	0.136733i
$183$	0.705322	−	20.4874i	0.0521389	−	1.51447i
$184$	−0.319618	−	0.717874i	−0.0235626	−	0.0529224i
$185$	6.96732	+	6.27340i	0.512247	+	0.461230i
$186$	−1.30801	+	9.34039i	−0.0959080	+	0.684871i
$187$	0.652309	−	0.346687i	0.0477016	−	0.0253523i
$188$		−	6.94384i		−	0.506432i
$189$	−10.9961	+	8.25143i	−0.799847	+	0.600203i
$190$	−11.1555	−	8.10495i	−0.809305	−	0.587995i
$191$	1.51196	−	0.158914i	0.109402	−	0.0114986i	−0.0496694	−	0.998766i	$-0.515817\pi$
$191$	1.51196	−	0.158914i	0.109402	−	0.0114986i	0.159071	+	0.987267i	$0.449150\pi$
$192$	−11.1168	−	5.41526i	−0.802289	−	0.390813i
$193$	−0.483334	−	2.27391i	−0.0347911	−	0.163679i	0.957322	−	0.289022i	$-0.0933302\pi$
$193$	−0.483334	−	2.27391i	−0.0347911	−	0.163679i	−0.992113	+	0.125343i	$0.959997\pi$
$194$	0.364981	+	3.47256i	0.0262041	+	0.249315i
$195$	0.554508	+	1.93021i	0.0397091	+	0.138225i
$196$	4.72923	+	4.96628i	0.337802	+	0.354734i
$197$	22.1508			1.57818			0.789090	−	0.614278i	$-0.210553\pi$
$197$	22.1508			1.57818			0.789090	+	0.614278i	$0.210553\pi$
$198$	1.05859	+	9.99452i	0.0752310	+	0.710279i
$199$	−4.92178	−	8.52477i	−0.348896	−	0.604305i	0.637158	−	0.770733i	$-0.280110\pi$
$199$	−4.92178	−	8.52477i	−0.348896	−	0.604305i	−0.986054	+	0.166428i	$0.946777\pi$
$200$	4.43329	−	4.92366i	0.313481	−	0.348156i
$201$	4.07462	+	1.01378i	0.287402	+	0.0715068i
$202$	−3.16604	+	2.30026i	−0.222762	+	0.161846i
$203$	−0.187232	−	0.405211i	−0.0131411	−	0.0284403i
$204$	−0.313226	+	0.211498i	−0.0219302	+	0.0148079i
$205$	7.18359	−	0.755026i	0.501724	−	0.0527333i
$206$	0.652653	−	6.20958i	0.0454725	−	0.432642i
$207$	0.367033	−	0.691933i	0.0255105	−	0.0480927i
$208$	0.648748	+	0.374555i	0.0449826	+	0.0259707i
$209$	−17.3923	−	20.7349i	−1.20305	−	1.43426i
$210$	7.00843	+	3.29374i	0.483627	+	0.227289i
$211$	11.0997	−	3.60651i	0.764134	−	0.248282i	0.0990822	−	0.995079i	$-0.468409\pi$
$211$	11.0997	−	3.60651i	0.764134	−	0.248282i	0.665052	+	0.746797i	$0.268409\pi$
$212$	−4.51313	−	10.1367i	−0.309963	−	0.696189i
$213$	15.4794	−	8.24036i	1.06063	−	0.564620i
$214$	18.3396	−	3.89819i	1.25367	−	0.266475i
$215$	5.15835	+	5.72892i	0.351796	+	0.390709i
$216$	−3.27423	−	15.2928i	−0.222783	−	1.04054i
$217$	8.54368	+	11.4207i	0.579983	+	0.775287i
$218$	−6.97228	+	2.26543i	−0.472222	+	0.153434i
$219$	7.50615	+	18.5520i	0.507218	+	1.25363i
$220$	−4.50703	+	3.03884i	−0.303864	+	0.204878i
$221$	0.133689	−	0.0771853i	0.00899288	−	0.00519204i
$222$	6.30613	+	7.50784i	0.423240	+	0.503893i
$223$	13.6979	+	9.95211i	0.917280	+	0.666443i	0.942845	−	0.333230i	$-0.108139\pi$
$223$	13.6979	+	9.95211i	0.917280	+	0.666443i	−0.0255656	+	0.999673i	$0.508139\pi$
$224$	−12.3423	+	4.20159i	−0.824652	+	0.280730i
$225$	6.58824	+	0.454167i	0.439216	+	0.0302778i
$226$	−3.39003	+	3.05240i	−0.225501	+	0.203042i
$227$	−7.21130	−	3.21068i	−0.478631	−	0.213100i	0.153217	−	0.988193i	$-0.451037\pi$
$227$	−7.21130	−	3.21068i	−0.478631	−	0.213100i	−0.631848	+	0.775092i	$0.717703\pi$
$228$	9.96494	+	9.61354i	0.659944	+	0.636672i
$229$	24.3174	+	5.16881i	1.60694	+	0.341565i	0.922046	−	0.387081i	$-0.126517\pi$
$229$	24.3174	+	5.16881i	1.60694	+	0.341565i	0.684890	+	0.728646i	$0.259850\pi$
$230$	−0.441191			−0.0290912
$231$	11.7811	+	9.60240i	0.775138	+	0.631792i
$232$	0.507796			0.0333385
$233$	9.71007	+	2.06394i	0.636128	+	0.135213i	0.514677	−	0.857384i	$-0.327912\pi$
$233$	9.71007	+	2.06394i	0.636128	+	0.135213i	0.121451	+	0.992597i	$0.461245\pi$
$234$	0.294350	+	2.07953i	0.0192422	+	0.135943i
$235$	−10.8323	−	4.82286i	−0.706622	−	0.314609i
$236$	8.28718	−	7.46181i	0.539450	−	0.485723i
$237$	−5.20772	−	7.71256i	−0.338278	−	0.500985i
$238$	0.115620	−	0.583908i	0.00749452	−	0.0378492i
$239$	21.2204	+	15.4175i	1.37263	+	0.997275i	0.997526	+	0.0702919i	$0.0223931\pi$
$239$	21.2204	+	15.4175i	1.37263	+	0.997275i	0.375104	+	0.926983i	$0.377607\pi$
$240$	−2.39814	+	2.01429i	−0.154799	+	0.130022i
$241$	−0.0765792	+	0.0442130i	−0.00493290	+	0.00284801i	−0.502464	−	0.864598i	$-0.667573\pi$
$241$	−0.0765792	+	0.0442130i	−0.00493290	+	0.00284801i	0.497532	+	0.867446i	$0.334240\pi$
$242$	10.4425	−	3.79645i	0.671266	−	0.244045i
$243$	9.99060	−	11.9661i	0.640897	−	0.767627i
$244$	11.0275	−	3.58305i	0.705963	−	0.229381i
$245$	11.0320	−	3.92821i	0.704811	−	0.250964i
$246$	7.54951	+	0.259908i	0.481339	+	0.0165711i
$247$	−3.78426	−	4.20285i	−0.240787	−	0.267421i
$248$	−15.8707	+	3.37343i	−1.00779	+	0.214213i
$249$	−3.47663	−	6.53082i	−0.220323	−	0.413874i
$250$	−4.94959	−	11.1170i	−0.313040	−	0.703098i
$251$	−26.3571	+	8.56394i	−1.66365	+	0.540551i	−0.981631	−	0.190787i	$-0.938896\pi$
$251$	−26.3571	+	8.56394i	−1.66365	+	0.540551i	−0.682015	+	0.731338i	$0.738896\pi$
$252$	−6.51088	−	4.25148i	−0.410147	−	0.267818i
$253$	−0.840159	−	0.209637i	−0.0528203	−	0.0131798i
$254$	9.08642	+	5.24604i	0.570132	+	0.329166i
$255$	0.112383	+	0.635526i	0.00703773	+	0.0397982i
$256$	1.77171	−	16.8567i	0.110732	−	1.05354i
$257$	3.32519	−	0.349491i	0.207420	−	0.0218007i	−0.000248797	−	1.00000i	$-0.500079\pi$
$257$	3.32519	−	0.349491i	0.207420	−	0.0218007i	0.207668	+	0.978199i	$0.433413\pi$
$258$	4.51156	+	6.68156i	0.280878	+	0.415976i
$259$	14.7663	+	1.34391i	0.917532	+	0.0835063i
$260$	−0.918984	+	0.667681i	−0.0569930	+	0.0414078i
$261$	0.312006	+	0.398539i	0.0193127	+	0.0246689i
$262$	−5.48807	+	6.09512i	−0.339054	+	0.376558i
$263$	3.99556	+	6.92052i	0.246377	+	0.426738i	0.962518	−	0.271218i	$-0.0874265\pi$
$263$	3.99556	+	6.92052i	0.246377	+	0.426738i	−0.716141	+	0.697956i	$0.754093\pi$
$264$	−15.5378	+	7.58426i	−0.956283	+	0.466779i
$265$	−18.9477			−1.16395
$266$	−21.8052	+	0.304374i	−1.33696	+	0.0186624i
$267$	1.81741	−	0.522103i	0.111224	−	0.0319522i
$268$	0.248251	+	2.36195i	0.0151644	+	0.144279i
$269$	1.93311	+	9.09455i	0.117864	+	0.554504i	0.996964	+	0.0778673i	$0.0248111\pi$
$269$	1.93311	+	9.09455i	0.117864	+	0.554504i	−0.879100	+	0.476637i	$0.841856\pi$
$270$	−8.59148	−	1.81290i	−0.522861	−	0.110329i
$271$	1.57779	−	0.165833i	0.0958442	−	0.0100736i	−0.0564849	−	0.998403i	$-0.517989\pi$
$271$	1.57779	−	0.165833i	0.0958442	−	0.0100736i	0.152329	+	0.988330i	$0.451323\pi$
$272$	0.194760	+	0.141501i	0.0118090	+	0.00857976i
$273$	2.53079	+	1.91903i	0.153171	+	0.116145i
$274$		−	22.6905i		−	1.37078i
$275$	−1.26647	−	7.19017i	−0.0763713	−	0.433584i
$276$	0.438744	+	0.0614409i	0.0264093	+	0.00369831i
$277$	−4.16219	−	3.74765i	−0.250082	−	0.225175i	0.534550	−	0.845137i	$-0.320481\pi$
$277$	−4.16219	−	3.74765i	−0.250082	−	0.225175i	−0.784632	+	0.619962i	$0.787148\pi$
$278$	4.75339	+	10.6763i	0.285089	+	0.640321i
$279$	−12.3991	−	10.3832i	−0.742313	−	0.621628i
$280$	−1.20746	+	13.2670i	−0.0721594	+	0.792857i
$281$	7.82986	−	24.0978i	0.467090	−	1.43756i	−0.389244	−	0.921135i	$-0.627264\pi$
$281$	7.82986	−	24.0978i	0.467090	−	1.43756i	0.856334	−	0.516422i	$-0.172736\pi$
$282$	−10.5195	−	6.56608i	−0.626425	−	0.391005i
$283$	−20.6977	−	2.17542i	−1.23035	−	0.129315i	−0.533045	−	0.846087i	$-0.678952\pi$
$283$	−20.6977	−	2.17542i	−1.23035	−	0.129315i	−0.697308	+	0.716772i	$0.745619\pi$
$284$	7.37114	+	6.63700i	0.437397	+	0.393834i
$285$	21.9182	−	8.86810i	1.29832	−	0.525301i
$286$	2.15300	−	0.869415i	0.127310	−	0.0514096i
$287$	8.38177	−	7.76153i	0.494760	−	0.458148i
$288$	12.5294	−	7.84642i	0.738302	−	0.462355i
$289$	−15.4850	+	6.89435i	−0.910880	+	0.405550i
$290$	0.115961	−	0.260452i	0.00680945	−	0.0152943i
$291$	−5.38263	−	2.62200i	−0.315535	−	0.153704i
$292$	−8.41225	+	7.57443i	−0.492290	+	0.443260i
$293$	9.97394	−	7.24649i	0.582684	−	0.423345i	−0.257007	−	0.966410i	$-0.582736\pi$
$293$	9.97394	−	7.24649i	0.582684	−	0.423345i	0.839691	+	0.543065i	$0.182736\pi$
$294$	11.9955	−	2.46838i	0.699594	−	0.143959i
$295$	−5.88447	−	18.1105i	−0.342607	−	1.05444i
$296$	−8.43375	+	14.6077i	−0.490202	+	0.849054i
$297$	−15.4993	−	7.53465i	−0.899362	−	0.437205i
$298$	5.90318	+	10.2246i	0.341962	+	0.592295i
$299$	−0.176998	−	0.0376222i	−0.0102361	−	0.00217575i
$300$	1.03136	+	3.59009i	0.0595455	+	0.207274i
$301$	11.9596	+	2.36813i	0.689343	+	0.136497i
$302$	6.42154	+	2.08648i	0.369518	+	0.120064i
$303$	−0.471398	−	6.69388i	−0.0270811	−	0.384553i
$304$	3.58724	−	8.05707i	0.205742	−	0.462105i
$305$	2.06965	−	19.6914i	0.118508	−	1.12752i
$306$	0.0242203	+	0.674510i	0.00138458	+	0.0385592i
$307$		−	0.617255i		−	0.0352286i	−0.999845	−	0.0176143i	$-0.994393\pi$
$307$		−	0.617255i		−	0.0352286i	0.999845	−	0.0176143i	$-0.00560710\pi$
$308$	−2.82869	+	8.11801i	−0.161179	+	0.462567i
$309$	8.43997	+	6.58733i	0.480133	+	0.374740i
$310$	−1.89400	+	8.91056i	−0.107572	+	0.506086i
$311$	−22.2874	−	2.34250i	−1.26381	−	0.132831i	−0.551186	−	0.834382i	$-0.685825\pi$
$311$	−22.2874	−	2.34250i	−1.26381	−	0.132831i	−0.712619	+	0.701551i	$0.752491\pi$
$312$	−3.18936	+	1.69783i	−0.180562	+	0.0961206i
$313$	−10.0881	−	11.2040i	−0.570212	−	0.633285i	0.387205	−	0.921994i	$-0.373441\pi$
$313$	−10.0881	−	11.2040i	−0.570212	−	0.633285i	−0.957417	+	0.288709i	$0.906774\pi$
$314$	−2.98294	+	9.18053i	−0.168337	+	0.518087i
$315$	−11.1544	+	7.20402i	−0.628479	+	0.405901i
$316$	3.09396	−	4.25847i	0.174049	−	0.239558i
$317$	−4.44254	+	20.9005i	−0.249518	+	1.17389i	0.657717	+	0.753265i	$0.271522\pi$
$317$	−4.44254	+	20.9005i	−0.249518	+	1.17389i	−0.907235	+	0.420624i	$0.861811\pi$
$318$	−19.6240	−	2.74811i	−1.10046	−	0.154106i
$319$	0.344581	−	0.440879i	0.0192928	−	0.0246845i
$320$	−10.3435	−	5.97180i	−0.578217	−	0.333834i
$321$	−10.9810	+	30.2164i	−0.612899	+	1.68651i
$322$	−0.558708	+	0.417963i	−0.0311356	+	0.0232922i
$323$	−1.06828	−	1.47036i	−0.0594407	−	0.0818130i
$324$	8.29137	+	2.99931i	0.460632	+	0.166628i
$325$	−0.317206	−	1.49233i	−0.0175954	−	0.0827798i
$326$	1.10453	+	0.491769i	0.0611743	+	0.0272366i
$327$	3.03513	−	12.1989i	0.167843	−	0.674600i
$328$	4.01576	+	12.3592i	0.221733	+	0.682425i
$329$	−18.2866	+	4.15452i	−1.00817	+	0.229046i
$330$	0.341803	+	9.70137i	0.0188157	+	0.534043i
$331$	−14.2285	+	24.6444i	−0.782066	+	1.35458i	0.148670	+	0.988887i	$0.452501\pi$
$331$	−14.2285	+	24.6444i	−0.782066	+	1.35458i	−0.930736	+	0.365692i	$0.880832\pi$
$332$	2.80017	−	3.10991i	0.153679	−	0.170678i
$333$	−16.6467	+	2.35627i	−0.912231	+	0.129123i
$334$	2.15736	+	20.5259i	0.118045	+	1.12313i
$335$	3.85704	+	1.25323i	0.210733	+	0.0684712i
$336$	−1.12867	+	4.82271i	−0.0615742	+	0.263101i
$337$	0.0525208	+	0.0722887i	0.00286099	+	0.00393781i	0.810445	−	0.585815i	$-0.199225\pi$
$337$	0.0525208	+	0.0722887i	0.00286099	+	0.00393781i	−0.807584	+	0.589752i	$0.799225\pi$
$338$	−11.5528	+	5.14365i	−0.628391	+	0.279778i
$339$	−1.36209	−	7.70260i	−0.0739787	−	0.418348i
$340$	−0.316138	+	0.182523i	−0.0171450	+	0.00989867i
$341$	−7.84070	+	16.0684i	−0.424598	+	0.870153i
$342$	23.9867	−	6.00569i	1.29705	−	0.324751i
$343$	10.2492	−	15.4258i	0.553403	−	0.832913i
$344$	−8.15224	+	11.2206i	−0.439539	+	0.604974i
$345$	0.400578	−	0.641763i	0.0215664	−	0.0345513i
$346$	−13.8510	+	2.94412i	−0.744633	+	0.158277i
$347$	−31.3512	+	6.66389i	−1.68302	+	0.357737i	−0.947497	−	0.319765i	$-0.896396\pi$
$347$	−31.3512	+	6.66389i	−1.68302	+	0.357737i	−0.735521	+	0.677502i	$0.763063\pi$
$348$	−0.151589	+	0.242859i	−0.00812601	+	0.0130186i
$349$	2.90060	−	3.99234i	0.155266	−	0.213705i	−0.724297	−	0.689488i	$-0.757835\pi$
$349$	2.90060	−	3.99234i	0.155266	−	0.213705i	0.879562	+	0.475783i	$0.157835\pi$
$350$	−5.13532	−	2.87007i	−0.274494	−	0.153411i
$351$	−3.29217	−	1.45994i	−0.175723	−	0.0779256i
$352$	−11.7547	−	11.3555i	−0.626526	−	0.605249i
$353$	12.1762	−	7.02991i	0.648071	−	0.374164i	−0.139646	−	0.990202i	$-0.544596\pi$
$353$	12.1762	−	7.02991i	0.648071	−	0.374164i	0.787717	+	0.616037i	$0.211263\pi$
$354$	−3.46782	−	19.6104i	−0.184312	−	1.04228i
$355$	15.4733	−	6.88915i	0.821237	−	0.365638i
$356$	0.628663	+	0.865280i	0.0333191	+	0.0458598i
$357$	0.744385	+	0.698341i	0.0393970	+	0.0369601i
$358$	12.1452	+	3.94622i	0.641895	+	0.208564i
$359$	0.711303	+	6.76760i	0.0375411	+	0.357180i	0.997126	+	0.0757607i	$0.0241385\pi$
$359$	0.711303	+	6.76760i	0.0375411	+	0.357180i	−0.959585	+	0.281419i	$0.909195\pi$
$360$	−2.11704	−	14.9565i	−0.111578	−	0.788276i
$361$	−31.8401	+	35.3620i	−1.67580	+	1.86116i
$362$	10.5587	−	18.2881i	0.554951	−	0.961203i
$363$	−3.95883	+	18.6367i	−0.207785	+	0.978175i
$364$	−0.531240	+	1.71613i	−0.0278445	+	0.0899496i
$365$	5.97328	+	18.3839i	0.312656	+	0.962255i
$366$	4.99949	−	20.0941i	0.261328	−	1.05033i
$367$	−3.33571	−	1.48515i	−0.174122	−	0.0775243i	0.317824	−	0.948150i	$-0.397048\pi$
$367$	−3.33571	−	1.48515i	−0.174122	−	0.0775243i	−0.491947	+	0.870625i	$0.663714\pi$
$368$	−0.0586706	−	0.276023i	−0.00305842	−	0.0143887i
$369$	−7.23262	+	10.7456i	−0.376515	+	0.559396i
$370$	5.56644	+	7.66155i	0.289385	+	0.398305i
$371$	−23.9947	+	17.9501i	−1.24574	+	0.931924i
$372$	3.12440	−	8.59739i	0.161992	−	0.445754i
$373$	19.7737	+	11.4164i	1.02384	+	0.591117i	0.915215	−	0.402965i	$-0.132020\pi$
$373$	19.7737	+	11.4164i	1.02384	+	0.591117i	0.108629	+	0.994082i	$0.465354\pi$
$374$	0.717311	−	0.205545i	0.0370913	−	0.0106285i
$375$	20.6649	+	2.89387i	1.06713	+	0.149439i
$376$	4.43536	−	20.8667i	0.228736	−	1.07612i
$377$	0.0687314	−	0.0946007i	0.00353985	−	0.00487218i
$378$	−12.5974	+	5.84336i	−0.647940	+	0.300550i
$379$	5.13507	−	15.8041i	0.263771	−	0.811803i	−0.728203	−	0.685361i	$-0.759644\pi$
$379$	5.13507	−	15.8041i	0.263771	−	0.811803i	0.991974	−	0.126442i	$-0.0403556\pi$
$380$	8.94877	+	9.93861i	0.459062	+	0.509840i
$381$	−15.8810	+	8.45410i	−0.813607	+	0.433117i
$382$	1.52724	+	0.160519i	0.0781404	+	0.00821289i
$383$	1.82043	−	8.56446i	0.0930198	−	0.437624i	−0.906850	−	0.421455i	$-0.861520\pi$
$383$	1.82043	−	8.56446i	0.0930198	−	0.437624i	0.999869	−	0.0161690i	$-0.00514698\pi$
$384$	3.61041	+	2.81790i	0.184243	+	0.143800i
$385$	10.6993	+	10.0511i	0.545289	+	0.512252i
$386$		−	2.34820i		−	0.119520i
$387$	−13.8154	+	0.496082i	−0.702274	+	0.0252173i
$388$	0.353990	−	3.36799i	0.0179711	−	0.170984i
$389$	−6.29098	+	14.1298i	−0.318965	+	0.716408i	−0.999873	−	0.0159619i	$-0.994919\pi$
$389$	−6.29098	+	14.1298i	−0.318965	+	0.716408i	0.680907	+	0.732370i	$0.261586\pi$
$390$	0.142504	+	2.02356i	0.00721595	+	0.102467i
$391$	−0.0553054	−	0.0179698i	−0.00279691	−	0.000908772i
$392$	11.0395	+	17.9448i	0.557578	+	0.906349i
$393$	−3.88317	−	13.5171i	−0.195880	−	0.681846i
$394$	21.8857	+	4.65195i	1.10259	+	0.234362i
$395$	−4.49425	−	7.78427i	−0.226130	−	0.391669i
$396$	1.01112	−	9.69518i	0.0508107	−	0.487201i
$397$	−2.78743	+	4.82796i	−0.139897	+	0.242308i	−0.927457	−	0.373929i	$-0.878010\pi$
$397$	−2.78743	+	4.82796i	−0.139897	+	0.242308i	0.787561	+	0.616237i	$0.211344\pi$
$398$	−3.07257	−	9.45638i	−0.154014	−	0.474006i
$399$	19.3552	−	31.9945i	0.968972	−	1.60173i
$400$	1.92485	−	1.39848i	0.0962423	−	0.0699241i
$401$	−8.38349	+	7.54853i	−0.418651	+	0.376955i	−0.851363	−	0.524577i	$-0.824223\pi$
$401$	−8.38349	+	7.54853i	−0.418651	+	0.376955i	0.432712	+	0.901532i	$0.357557\pi$
$402$	3.81295	+	1.85737i	0.190173	+	0.0926374i
$403$	−1.51968	+	3.41326i	−0.0757007	+	0.170027i
$404$	3.46744	−	1.54380i	0.172512	−	0.0768071i
$405$	10.4377	−	10.8513i	0.518653	−	0.539204i
$406$	−0.0998913	−	0.439683i	−0.00495752	−	0.0218211i
$407$	6.95969	+	17.2348i	0.344979	+	0.854300i
$408$	−1.07636	+	0.435495i	−0.0532877	+	0.0215602i
$409$	15.1094	+	13.6046i	0.747112	+	0.672703i	0.952005	−	0.306081i	$-0.0990180\pi$
$409$	15.1094	+	13.6046i	0.747112	+	0.672703i	−0.204893	+	0.978784i	$0.565685\pi$
$410$	7.25618	+	0.762656i	0.358357	+	0.0376649i
$411$	33.0059	+	20.6018i	1.62806	+	1.01621i
$412$	−1.87133	+	5.75937i	−0.0921939	+	0.283744i
$413$	−24.6089	−	17.3599i	−1.21093	−	0.854223i
$414$	0.507955	−	0.606571i	0.0249646	−	0.0298113i
$415$	−2.90655	−	6.52823i	−0.142677	−	0.320458i
$416$	−2.53813	−	2.28534i	−0.124442	−	0.112048i
$417$	−19.8457	−	2.77916i	−0.971849	−	0.136096i
$418$	−12.8295	−	24.1394i	−0.627512	−	1.18070i
$419$		−	11.3202i		−	0.553027i	−0.961010	−	0.276514i	$-0.910821\pi$
$419$		−	11.3202i		−	0.553027i	0.961010	−	0.276514i	$-0.0891791\pi$
$420$	−5.98465	−	4.53799i	−0.292021	−	0.221431i
$421$	2.96907	+	2.15716i	0.144704	+	0.105133i	0.657782	−	0.753208i	$-0.271495\pi$
$421$	2.96907	+	2.15716i	0.144704	+	0.105133i	−0.513078	+	0.858342i	$0.671495\pi$
$422$	11.7243	−	1.23227i	0.570728	−	0.0599860i
$423$	19.1023	−	9.34012i	0.928783	−	0.454132i
$424$	−7.08751	−	33.3441i	−0.344200	−	1.61933i
$425$	−0.0512498	−	0.487609i	−0.00248598	−	0.0236525i
$426$	17.0248	−	4.89086i	0.824853	−	0.236963i
$427$	−16.0337	−	26.8971i	−0.775927	−	1.30164i
$428$	−18.1847			−0.878989
$429$	−0.690151	+	3.92118i	−0.0333208	+	0.189316i
$430$	3.89346	+	6.74368i	0.187760	+	0.325209i
$431$	9.88442	−	10.9778i	0.476116	−	0.528780i	−0.456465	−	0.889741i	$-0.650885\pi$
$431$	9.88442	−	10.9778i	0.476116	−	0.528780i	0.932581	+	0.360961i	$0.117551\pi$
$432$	−0.00830654	−	5.61620i	−0.000399648	−	0.270209i
$433$	−13.3238	+	9.68031i	−0.640301	+	0.465206i	−0.859954	−	0.510372i	$-0.829508\pi$
$433$	−13.3238	+	9.68031i	−0.640301	+	0.465206i	0.219653	+	0.975578i	$0.429508\pi$
$434$	6.04294	+	13.0783i	0.290071	+	0.627778i
$435$	0.273571	+	0.405155i	0.0131167	+	0.0194257i
$436$	7.07137	−	0.743231i	0.338657	−	0.0355943i
$437$	−0.222690	+	2.11876i	−0.0106527	+	0.101354i
$438$	3.52015	+	19.9064i	0.168199	+	0.951164i
$439$	0.328427	+	0.189617i	0.0156750	+	0.00904995i	0.507817	−	0.861465i	$-0.330453\pi$
$439$	0.328427	+	0.189617i	0.0156750	+	0.00904995i	−0.492142	+	0.870515i	$0.663786\pi$
$440$	−15.4850	+	6.25306i	−0.738217	+	0.298103i
$441$	−7.30079	+	19.6901i	−0.347657	+	0.937622i
$442$	0.148299	−	0.0481852i	0.00705385	−	0.00229194i
$443$	−16.3860	−	36.8035i	−0.778521	−	1.74859i	−0.654169	−	0.756349i	$-0.726981\pi$
$443$	−16.3860	−	36.8035i	−0.778521	−	1.74859i	−0.124352	−	0.992238i	$-0.539685\pi$
$444$	−4.46862	−	8.39426i	−0.212071	−	0.398374i
$445$	1.78647	−	0.379725i	0.0846867	−	0.0180007i
$446$	11.4439	+	12.7097i	0.541885	+	0.601824i
$447$	−20.2326	−	0.696553i	−0.956971	−	0.0329458i
$448$	−18.7560	+	2.23642i	−0.886137	+	0.105661i
$449$	22.9740	−	7.46469i	1.08421	−	0.352280i	0.288202	−	0.957570i	$-0.406943\pi$
$449$	22.9740	−	7.46469i	1.08421	−	0.352280i	0.796006	+	0.605289i	$0.206943\pi$
$450$	6.41401	+	1.83235i	0.302359	+	0.0863776i
$451$	13.4556	+	4.90019i	0.633598	+	0.230741i
$452$	3.83161	−	2.21218i	0.180224	−	0.104052i
$453$	−8.86545	+	7.44645i	−0.416535	+	0.349865i
$454$	−6.45072	−	4.68672i	−0.302747	−	0.219959i
$455$	2.30817	+	2.02067i	0.108209	+	0.0947304i
$456$	23.8047	+	35.2544i	1.11476	+	1.65094i
$457$	24.8171	−	22.3454i	1.16089	−	1.04527i	0.162611	−	0.986690i	$-0.448008\pi$
$457$	24.8171	−	22.3454i	1.16089	−	1.04527i	0.998283	−	0.0585830i	$-0.0186582\pi$
$458$	22.9408	+	10.2139i	1.07195	+	0.477265i
$459$	−1.00314	−	0.577188i	−0.0468227	−	0.0269408i
$460$	0.418554	+	0.0889664i	0.0195152	+	0.00414808i
$461$	17.0848			0.795719			0.397859	−	0.917446i	$-0.369753\pi$
$461$	17.0848			0.795719			0.397859	+	0.917446i	$0.369753\pi$
$462$	9.62346	+	11.9617i	0.447724	+	0.556507i
$463$	−24.1597			−1.12280			−0.561399	−	0.827545i	$-0.689737\pi$
$463$	−24.1597			−1.12280			−0.561399	+	0.827545i	$0.689737\pi$
$464$	0.178368	+	0.0379133i	0.00828054	+	0.00176008i
$465$	−11.2418	−	10.8454i	−0.521325	−	0.502941i
$466$	9.16041	+	4.07848i	0.424348	+	0.188932i
$467$	−12.0935	+	10.8890i	−0.559619	+	0.503883i	−0.899698	−	0.436514i	$-0.856213\pi$
$467$	−12.0935	+	10.8890i	−0.559619	+	0.503883i	0.340079	+	0.940397i	$0.389546\pi$
$468$	0.140091	−	2.03219i	0.00647570	−	0.0939378i
$469$	6.07167	−	2.06693i	0.280364	−	0.0954421i
$470$	−9.68981	−	7.04006i	−0.446958	−	0.324734i
$471$	−10.6458	−	12.6745i	−0.490532	−	0.584009i
$472$	29.6698	−	17.1298i	1.36566	−	0.788465i
$473$	4.20998	+	14.6920i	0.193575	+	0.675539i
$474$	−3.52566	−	8.71395i	−0.161939	−	0.400245i
$475$	−17.0832	+	5.55068i	−0.783832	+	0.254683i
$476$	−0.227433	+	0.530634i	−0.0104244	+	0.0243216i
$477$	21.8150	−	26.0502i	0.998840	−	1.19276i
$478$	17.7285	+	19.6895i	0.810884	+	0.900578i
$479$	6.91474	−	1.46977i	0.315942	−	0.0671556i	−0.0472111	−	0.998885i	$-0.515033\pi$
$479$	6.91474	−	1.46977i	0.315942	−	0.0671556i	0.363154	+	0.931729i	$0.381700\pi$
$480$	12.6042	−	6.70977i	0.575302	−	0.306257i
$481$	1.57983	+	3.54836i	0.0720341	+	0.161791i
$482$	−0.0849480	+	0.0276013i	−0.00386928	+	0.00125720i
$483$	−0.100698	−	1.19219i	−0.00458190	−	0.0542467i
$484$	−10.6722	+	1.49593i	−0.485101	+	0.0679968i
$485$	−5.00816	−	2.89146i	−0.227409	−	0.131295i
$486$	12.3841	−	9.72475i	0.561753	−	0.441124i
$487$	−0.674297	+	6.41551i	−0.0305553	+	0.290714i	0.968564	+	0.248763i	$0.0800241\pi$
$487$	−0.674297	+	6.41551i	−0.0305553	+	0.290714i	−0.999120	+	0.0419513i	$0.986643\pi$
$488$	35.4270	−	3.72353i	1.60371	−	0.168556i
$489$	−1.71819	+	1.16017i	−0.0776993	+	0.0524646i
$490$	11.7250	−	1.56433i	0.529681	−	0.0706694i
$491$	−2.75484	+	2.00151i	−0.124324	+	0.0903267i	−0.648210	−	0.761462i	$-0.724482\pi$
$491$	−2.75484	+	2.00151i	−0.124324	+	0.0903267i	0.523886	+	0.851789i	$0.324482\pi$
$492$	−7.10974	−	1.76894i	−0.320532	−	0.0797498i
$493$	0.0251445	−	0.0279258i	0.00113245	−	0.00125772i
$494$	−2.85632	−	4.94729i	−0.128512	−	0.222589i
$495$	−14.4221	−	8.31114i	−0.648225	−	0.373558i
$496$	−5.82661			−0.261623
$497$	13.0684	−	23.3828i	0.586196	−	1.04886i
$498$	−2.06347	−	7.18280i	−0.0924662	−	0.321869i
$499$	2.76671	+	26.3235i	0.123855	+	1.17840i	0.863125	+	0.504991i	$0.168504\pi$
$499$	2.76671	+	26.3235i	0.123855	+	1.17840i	−0.739270	+	0.673409i	$0.764829\pi$
$500$	2.45389	+	11.5447i	0.109741	+	0.516293i
$501$	−31.8160	−	15.4983i	−1.42144	−	0.692413i
$502$	−27.8402	+	2.92612i	−1.24257	+	0.130599i
$503$	5.22459	+	3.79589i	0.232953	+	0.169250i	0.698138	−	0.715963i	$-0.254012\pi$
$503$	5.22459	+	3.79589i	0.232953	+	0.169250i	−0.465185	+	0.885213i	$0.654012\pi$
$504$	−16.8500	−	16.9348i	−0.750559	−	0.754335i
$505$		−	6.48142i		−	0.288420i
$506$	−0.786078	−	0.383572i	−0.0349454	−	0.0170519i
$507$	3.00733	−	21.4751i	0.133560	−	0.953743i
$508$	−7.56234	−	6.80916i	−0.335525	−	0.302108i
$509$	1.24219	+	2.79001i	0.0550591	+	0.123665i	0.938980	−	0.343972i	$-0.111772\pi$
$509$	1.24219	+	2.79001i	0.0550591	+	0.123665i	−0.883921	+	0.467636i	$0.845106\pi$
$510$	−0.0224301	+	0.651522i	−0.000993220	+	0.0288499i
$511$	24.9803	+	17.6219i	1.10506	+	0.779545i
$512$	3.65642	−	11.2533i	0.161592	−	0.497330i
$513$	−13.0427	+	40.3443i	−0.575850	+	1.78125i
$514$	3.35879	+	0.353023i	0.148150	+	0.0155712i
$515$	7.68482	+	6.91944i	0.338633	+	0.304907i
$516$	−2.93274	−	7.24850i	−0.129107	−	0.319097i
$517$	−15.1071	−	18.0106i	−0.664411	−	0.792106i
$518$	14.3073	+	4.42893i	0.628628	+	0.194596i
$519$	8.29340	−	22.8209i	0.364040	−	1.00173i
$520$	−3.18809	+	1.41943i	−0.139807	+	0.0622461i
$521$	11.8444	−	26.6030i	0.518914	−	1.16550i	−0.444083	−	0.895986i	$-0.646470\pi$
$521$	11.8444	−	26.6030i	0.518914	−	1.16550i	0.962997	−	0.269514i	$-0.0868630\pi$
$522$	0.224574	+	0.459295i	0.00982933	+	0.0201028i
$523$	−2.80884	+	2.52910i	−0.122822	+	0.110590i	−0.728253	−	0.685308i	$-0.759667\pi$
$523$	−2.80884	+	2.52910i	−0.122822	+	0.110590i	0.605431	+	0.795898i	$0.293001\pi$
$524$	6.43557	−	4.67572i	0.281139	−	0.204260i
$525$	8.83744	−	4.86405i	0.385698	−	0.212284i
$526$	2.49435	+	7.67682i	0.108759	+	0.334725i
$527$	−0.600351	+	1.03984i	−0.0261517	+	0.0452961i
$528$	−6.02405	+	1.50396i	−0.262163	+	0.0654513i
$529$	−11.4659	−	19.8596i	−0.498518	−	0.863459i
$530$	−18.7209	−	3.97925i	−0.813185	−	0.172848i
$531$	31.6742	+	12.7609i	1.37454	+	0.553776i
$532$	20.7478	+	4.10827i	0.899529	+	0.178116i
$533$	2.84603	+	0.924730i	0.123275	+	0.0400545i
$534$	1.90531	−	0.134176i	0.0824507	−	0.00580636i
$535$	−12.6302	+	28.3679i	−0.546051	+	1.22645i
$536$	−0.762678	+	7.25640i	−0.0329427	+	0.313429i
$537$	−16.7675	+	14.0837i	−0.723569	+	0.607755i
$538$			9.39168i			0.404904i
$539$	23.0712	+	2.59231i	0.993747	+	0.111659i
$540$	7.78509	+	3.45236i	0.335017	+	0.148566i
$541$	1.58889	−	7.47513i	0.0683117	−	0.321381i	−0.930702	−	0.365778i	$-0.880803\pi$
$541$	1.58889	−	7.47513i	0.0683117	−	0.321381i	0.999014	+	0.0443964i	$0.0141364\pi$
$542$	1.59374	+	0.167509i	0.0684570	+	0.00719512i
$543$	17.0155	+	31.9634i	0.730204	+	1.37168i
$544$	−0.734425	−	0.815661i	−0.0314882	−	0.0349712i
$545$	3.75200	−	11.5475i	0.160718	−	0.494639i
$546$	2.09749	+	2.42756i	0.0897641	+	0.103890i
$547$	−14.9884	+	20.6297i	−0.640856	+	0.882062i	−0.998661	−	0.0517338i	$-0.983525\pi$
$547$	−14.9884	+	20.6297i	−0.640856	+	0.882062i	0.357805	+	0.933796i	$0.383525\pi$
$548$	−4.57555	+	21.5263i	−0.195458	+	0.919557i
$549$	24.6898	+	25.5167i	1.05374	+	1.08903i
$550$	0.258710	−	7.37010i	0.0110314	−	0.314262i
$551$	−1.19225	−	0.688348i	−0.0507917	−	0.0293246i
$552$	1.27921	+	0.464881i	0.0544469	+	0.0197866i
$553$	−13.0658	−	5.60008i	−0.555614	−	0.238140i
$554$	−3.32532	−	4.57692i	−0.141279	−	0.194454i
$555$	−16.1986	+	1.14074i	−0.687594	+	0.0484219i
$556$	−2.35662	−	11.0870i	−0.0999429	−	0.470195i
$557$	6.70393	+	2.98478i	0.284055	+	0.126469i	0.543818	−	0.839203i	$-0.316978\pi$
$557$	6.70393	+	2.98478i	0.284055	+	0.126469i	−0.259764	+	0.965672i	$0.583645\pi$
$558$	−10.0701	−	12.8629i	−0.426300	−	0.544532i
$559$	0.986932	+	3.03746i	0.0417428	+	0.128471i
$560$	−1.41468	+	4.57002i	−0.0597812	+	0.193119i
$561$	−0.352293	+	1.23004i	−0.0148738	+	0.0519321i
$562$	12.7970	−	22.1651i	0.539809	−	0.934977i
$563$	4.53295	−	5.03435i	0.191041	−	0.212173i	−0.640013	−	0.768364i	$-0.721071\pi$
$563$	4.53295	−	5.03435i	0.191041	−	0.212173i	0.831054	+	0.556191i	$0.187738\pi$
$564$	8.65568	+	8.35045i	0.364470	+	0.351617i
$565$	−0.789726	−	7.51375i	−0.0332240	−	0.316106i
$566$	−19.9932	−	6.49617i	−0.840375	−	0.273055i
$567$	2.93792	−	23.6298i	0.123381	−	0.992359i
$568$	17.9114	+	24.6529i	0.751546	+	1.03441i
$569$	1.72559	−	0.768280i	0.0723403	−	0.0322080i	−0.370248	−	0.928933i	$-0.620727\pi$
$569$	1.72559	−	0.768280i	0.0723403	−	0.0322080i	0.442588	+	0.896725i	$0.354060\pi$
$570$	23.5183	−	4.15887i	0.985073	−	0.174196i
$571$	−26.2847	+	15.1755i	−1.09998	+	0.635074i	−0.936216	−	0.351426i	$-0.885697\pi$
$571$	−26.2847	+	15.1755i	−1.09998	+	0.635074i	−0.163764	+	0.986499i	$0.552364\pi$
$572$	−2.21786	+	0.390652i	−0.0927332	+	0.0163340i
$573$	−1.62015	+	2.07580i	−0.0676827	+	0.0867180i
$574$	9.91147	−	5.90836i	0.413697	−	0.246610i
$575$	−0.337813	+	0.464960i	−0.0140878	+	0.0193902i
$576$	20.1190	−	7.34521i	0.838293	−	0.306050i
$577$	−10.8950	+	2.31580i	−0.453564	+	0.0964080i	−0.429028	−	0.903291i	$-0.641144\pi$
$577$	−10.8950	+	2.31580i	−0.453564	+	0.0964080i	−0.0245354	+	0.999699i	$0.507811\pi$
$578$	−16.7475	+	3.55980i	−0.696605	+	0.148068i
$579$	3.41573	+	2.13204i	0.141953	+	0.0886046i
$580$	−0.162531	+	0.223705i	−0.00674875	+	0.00928885i
$581$	−9.86528	−	5.51358i	−0.409281	−	0.228742i
$582$	−4.76755	−	3.72104i	−0.197621	−	0.154242i
$583$	−33.7594	−	16.4732i	−1.39817	−	0.682249i
$584$	−30.1175	+	17.3884i	−1.24627	+	0.719536i
$585$	−3.07289	−	1.63000i	−0.127048	−	0.0673922i
$586$	11.3764	−	5.06511i	0.469956	−	0.209238i
$587$	11.8252	+	16.2761i	0.488080	+	0.671785i	0.980032	−	0.198838i	$-0.0637166\pi$
$587$	11.8252	+	16.2761i	0.488080	+	0.671785i	−0.491952	+	0.870622i	$0.663717\pi$
$588$	−11.8778	−	0.0771807i	−0.489833	−	0.00318288i
$589$	41.8357	+	13.5933i	1.72381	+	0.560100i
$590$	−2.01060	−	19.1296i	−0.0827752	−	0.787553i
$591$	−26.6379	+	27.6116i	−1.09574	+	1.13579i
$592$	−4.05308	+	4.50140i	−0.166581	+	0.185006i
$593$	19.9645	−	34.5794i	0.819842	−	1.42001i	−0.0859566	−	0.996299i	$-0.527395\pi$
$593$	19.9645	−	34.5794i	0.819842	−	1.42001i	0.905798	−	0.423709i	$-0.139272\pi$
$594$	−13.7315	−	10.6995i	−0.563409	−	0.439007i
$595$	0.669819	+	0.723346i	0.0274599	+	0.0296543i
$596$	−3.53850	−	10.8904i	−0.144943	−	0.446087i
$597$	16.5451	+	4.11650i	0.677147	+	0.168477i
$598$	−0.166979	−	0.0743438i	−0.00682828	−	0.00304015i
$599$	−5.62700	−	26.4729i	−0.229913	−	1.08165i	−0.929989	−	0.367587i	$-0.880184\pi$
$599$	−5.62700	−	26.4729i	−0.229913	−	1.08165i	0.700076	−	0.714068i	$-0.253149\pi$
$600$	0.806141	+	11.4473i	0.0329106	+	0.467332i
$601$	−7.00340	−	9.63936i	−0.285675	−	0.393198i	0.641928	−	0.766765i	$-0.278135\pi$
$601$	−7.00340	−	9.63936i	−0.285675	−	0.393198i	−0.927603	+	0.373567i	$0.878135\pi$
$602$	11.3192	+	4.85147i	0.461335	+	0.197731i
$603$	−6.16372	+	3.85998i	−0.251006	+	0.157190i
$604$	−5.67132	−	3.27434i	−0.230763	−	0.133231i
$605$	−5.07878	+	17.6876i	−0.206482	+	0.719101i
$606$	0.940044	−	6.71277i	0.0381867	−	0.272688i
$607$	−5.16086	+	24.2800i	−0.209473	+	0.985493i	0.740233	+	0.672350i	$0.234715\pi$
$607$	−5.16086	+	24.2800i	−0.209473	+	0.985493i	−0.949706	+	0.313143i	$0.898618\pi$
$608$	−23.6353	+	32.5312i	−0.958537	+	1.31931i
$609$	0.730266	+	0.253906i	0.0295919	+	0.0102888i
$610$	6.18032	−	19.0211i	0.250234	−	0.770140i
$611$	−3.28706	−	3.65065i	−0.132980	−	0.147689i
$612$	0.113038	−	0.644786i	0.00456928	−	0.0260639i
$613$	41.5314	+	4.36512i	1.67744	+	0.176306i	0.894890	−	0.446287i	$-0.147254\pi$
$613$	41.5314	+	4.36512i	1.67744	+	0.176306i	0.782546	+	0.622592i	$0.213921\pi$
$614$	0.129631	−	0.609868i	0.00523150	−	0.0246123i
$615$	−7.69761	+	9.86250i	−0.310397	+	0.397695i
$616$	−13.6858	+	22.5884i	−0.551415	+	0.910111i
$617$			10.6454i			0.428567i	0.976772	+	0.214283i	$0.0687416\pi$
$617$			10.6454i			0.428567i	−0.976772	+	0.214283i	$0.931258\pi$
$618$	6.95554	+	8.28100i	0.279793	+	0.333111i
$619$	1.27511	−	12.1319i	0.0512510	−	0.487621i	−0.938548	−	0.345149i	$-0.887828\pi$
$619$	1.27511	−	12.1319i	0.0512510	−	0.487621i	0.989799	−	0.142472i	$-0.0455050\pi$
$620$	3.59364	−	8.07145i	0.144324	−	0.324157i
$621$	0.421131	+	1.28961i	0.0168994	+	0.0517504i
$622$	−21.5288	−	6.99512i	−0.863225	−	0.280479i
$623$	1.90258	−	2.17328i	0.0762254	−	0.0870708i
$624$	−1.24706	+	0.358253i	−0.0499222	+	0.0143416i
$625$	8.94796	+	1.90195i	0.357918	+	0.0760779i
$626$	−7.61438	−	13.1885i	−0.304332	−	0.527118i
$627$	46.7620	+	3.25529i	1.86749	+	0.130004i
$628$	4.68115	−	8.10798i	0.186798	−	0.323544i
$629$	0.385723	+	1.18713i	0.0153798	+	0.0473341i
$630$	−12.5338	+	4.77524i	−0.499360	+	0.190250i
$631$	−25.3690	+	18.4317i	−1.00992	+	0.733753i	−0.964193	−	0.265201i	$-0.914562\pi$
$631$	−25.3690	+	18.4317i	−1.00992	+	0.733753i	−0.0457308	+	0.998954i	$0.514562\pi$
$632$	12.0176	−	10.8207i	0.478036	−	0.430426i
$633$	−8.85254	+	18.1731i	−0.351857	+	0.722317i
$634$	−8.77874	+	19.7174i	−0.348648	+	0.783077i
$635$	−15.8747	+	7.06785i	−0.629966	+	0.280479i
$636$	18.0630	+	6.56430i	0.716243	+	0.260291i
$637$	4.83727	+	0.372254i	0.191660	+	0.0147492i
$638$	0.433047	−	0.363236i	0.0171445	−	0.0143806i
$639$	−8.34328	+	29.2051i	−0.330055	+	1.15534i
$640$	3.28737	+	2.95996i	0.129945	+	0.117003i
$641$	−9.12810	−	0.959402i	−0.360538	−	0.0378941i	−0.0774722	−	0.996995i	$-0.524685\pi$
$641$	−9.12810	−	0.959402i	−0.360538	−	0.0378941i	−0.283066	+	0.959100i	$0.591352\pi$
$642$	−17.1954	+	27.5486i	−0.678648	+	1.08726i
$643$	6.07271	−	18.6899i	0.239484	−	0.737057i	−0.757010	−	0.653403i	$-0.773341\pi$
$643$	6.07271	−	18.6899i	0.239484	−	0.737057i	0.996495	−	0.0836545i	$-0.0266592\pi$
$644$	0.614324	−	0.283854i	0.0242078	−	0.0111854i
$645$	−13.3445	−	0.459414i	−0.525440	−	0.0180894i
$646$	−0.746700	−	1.67712i	−0.0293785	−	0.0659852i
$647$	−14.1416	−	12.7332i	−0.555964	−	0.500592i	0.342572	−	0.939492i	$-0.388702\pi$
$647$	−14.1416	−	12.7332i	−0.555964	−	0.500592i	−0.898536	+	0.438899i	$0.855369\pi$
$648$	23.0003	+	14.3092i	0.903539	+	0.562119i
$649$	5.26088	−	37.3839i	0.206508	−	1.46744i
$650$		−	1.54109i		−	0.0604466i
$651$	−24.5106	−	3.08425i	−0.960645	−	0.120881i
$652$	−0.948694	−	0.689267i	−0.0371537	−	0.0269938i
$653$	34.4682	−	3.62276i	1.34885	−	0.141769i	0.597602	−	0.801793i	$-0.296120\pi$
$653$	34.4682	−	3.62276i	1.34885	−	0.141769i	0.751245	+	0.660024i	$0.229454\pi$
$654$	5.56073	−	11.4155i	0.217442	−	0.446380i
$655$	−2.82423	−	13.2869i	−0.110352	−	0.519164i
$656$	0.487802	+	4.64113i	0.0190455	+	0.181206i
$657$	−32.1523	−	12.9535i	−1.25438	−	0.505364i
$658$	−18.9402	+	0.264383i	−0.738368	+	0.0103067i
$659$	−9.40653			−0.366427			−0.183213	−	0.983073i	$-0.558650\pi$
$659$	−9.40653			−0.366427			−0.183213	+	0.983073i	$0.558650\pi$
$660$	1.63202	−	9.27254i	0.0635264	−	0.360933i
$661$	−0.0540771	−	0.0936643i	−0.00210336	−	0.00364312i	0.864972	−	0.501820i	$-0.167336\pi$
$661$	−0.0540771	−	0.0936643i	−0.00210336	−	0.00364312i	−0.867075	+	0.498177i	$0.834003\pi$
$662$	−19.2338	+	21.3613i	−0.747543	+	0.830231i
$663$	−0.0645566	+	0.259467i	−0.00250717	+	0.0100769i
$664$	10.4011	−	7.55688i	0.403643	−	0.293264i
$665$	20.8193	−	29.5129i	0.807336	−	1.14446i
$666$	−16.9423	−	1.16793i	−0.656500	−	0.0452565i
$667$	−0.0438074	+	0.00460434i	−0.00169623	+	0.000178281i
$668$	2.09239	−	19.9078i	0.0809570	−	0.770255i
$669$	−28.8783	+	5.10670i	−1.11650	+	0.197436i
$670$	3.54769	+	2.04826i	0.137059	+	0.0791311i
$671$	20.8073	−	33.2851i	0.803256	−	1.28496i
$672$	9.60505	−	20.4377i	0.370523	−	0.788400i
$673$	−21.2632	+	6.90883i	−0.819636	+	0.266316i	−0.688674	−	0.725071i	$-0.741807\pi$
$673$	−21.2632	+	6.90883i	−0.819636	+	0.266316i	−0.130962	+	0.991387i	$0.541807\pi$
$674$	0.0367107	+	0.0824535i	0.00141404	+	0.00317599i
$675$	−8.48894	+	7.66624i	−0.326740	+	0.295074i
$676$	11.9973	−	2.55011i	0.461435	−	0.0980810i
$677$	−3.67010	−	4.07606i	−0.141054	−	0.156656i	0.668479	−	0.743731i	$-0.266946\pi$
$677$	−3.67010	−	4.07606i	−0.141054	−	0.156656i	−0.809532	+	0.587075i	$0.800279\pi$
$678$	0.271853	−	7.89648i	0.0104405	−	0.303262i
$679$	−9.08139	+	1.08285i	−0.348512	+	0.0415558i
$680$	−1.06660	+	0.346560i	−0.0409023	+	0.0132900i
$681$	12.6743	−	5.12801i	0.485680	−	0.196506i
$682$	−11.1214	+	14.2295i	−0.425862	+	0.544874i
$683$	−4.72303	+	2.72684i	−0.180722	+	0.104340i	−0.587632	−	0.809129i	$-0.699940\pi$
$683$	−4.72303	+	2.72684i	−0.180722	+	0.104340i	0.406910	+	0.913468i	$0.366606\pi$
$684$	−23.9671	+	0.860610i	−0.916404	+	0.0329062i
$685$	30.4028	+	22.0889i	1.16163	+	0.843974i
$686$	13.3661	−	13.0887i	0.510321	−	0.499729i
$687$	−35.6864	+	24.0964i	−1.36152	+	0.919334i
$688$	−3.70131	+	3.33267i	−0.141111	+	0.127057i
$689$	−7.17120	−	3.19282i	−0.273201	−	0.121637i
$690$	0.530562	−	0.549956i	0.0201982	−	0.0209365i
$691$	39.7493	+	8.44897i	1.51213	+	0.321414i	0.887978	−	0.459885i	$-0.152109\pi$
$691$	39.7493	+	8.44897i	1.51213	+	0.321414i	0.624156	+	0.781299i	$0.285443\pi$
$692$	13.7340			0.522088
$693$	−26.1372	+	3.13787i	−0.992871	+	0.119198i
$694$	−32.3754			−1.22896
$695$	−18.9324	−	4.02421i	−0.718148	−	0.152647i
$696$	−0.610660	+	0.632981i	−0.0231470	+	0.0239931i
$697$	0.878534	+	0.391149i	0.0332769	+	0.0148158i
$698$	3.70433	−	3.33540i	0.140211	−	0.126247i
$699$	−14.2498	+	9.62182i	−0.538976	+	0.363931i
$700$	4.29309	+	3.75835i	0.162263	+	0.142052i
$701$	5.81185	+	4.22255i	0.219510	+	0.159484i	0.692106	−	0.721796i	$-0.256683\pi$
$701$	5.81185	+	4.22255i	0.219510	+	0.159484i	−0.472596	+	0.881279i	$0.656683\pi$
$702$	−2.94616	−	2.13386i	−0.111196	−	0.0805374i
$703$	39.6032	−	22.8649i	1.49366	−	0.862366i
$704$	−13.2372	−	19.6327i	−0.498897	−	0.739935i
$705$	19.0384	−	7.70294i	0.717029	−	0.290110i
$706$	13.5068	−	4.38863i	0.508335	−	0.165168i
$707$	−6.14019	−	8.20784i	−0.230926	−	0.308688i
$708$	−0.664566	+	19.3035i	−0.0249759	+	0.725471i
$709$	−21.1905	−	23.5345i	−0.795827	−	0.883855i	0.199552	−	0.979887i	$-0.436051\pi$
$709$	−21.1905	−	23.5345i	−0.795827	−	0.883855i	−0.995378	+	0.0960322i	$0.969385\pi$
$710$	16.7349	−	3.55712i	0.628050	−	0.133496i
$711$	15.8766	+	2.78333i	0.595417	+	0.104383i
$712$	1.33648	+	3.00178i	0.0500867	+	0.112497i
$713$	1.33857	−	0.434929i	0.0501299	−	0.0162882i
$714$	0.588816	+	0.846313i	0.0220359	+	0.0316725i
$715$	−0.931003	+	3.73116i	−0.0348175	+	0.139537i
$716$	−10.7263	−	6.19284i	−0.400861	−	0.231437i
$717$	−44.7372	+	7.91113i	−1.67074	+	0.295446i
$718$	−0.718491	+	6.83598i	−0.0268138	+	0.255117i
$719$	−37.2266	+	3.91268i	−1.38832	+	0.145918i	−0.769014	−	0.639232i	$-0.779252\pi$
$719$	−37.2266	+	3.91268i	−1.38832	+	0.145918i	−0.619305	+	0.785150i	$0.712586\pi$
$720$	0.373059	−	5.41167i	0.0139031	−	0.201681i
$721$	16.2869	+	1.48230i	0.606557	+	0.0552039i
$722$	−38.8856	+	28.2520i	−1.44717	+	1.05143i
$723$	0.0369791	−	0.148627i	0.00137527	−	0.00552750i
$724$	−13.7047	+	15.2206i	−0.509332	+	0.565670i
$725$	−0.185695	−	0.321633i	−0.00689653	−	0.0119451i
$726$	−7.82540	+	17.5823i	−0.290428	+	0.652540i
$727$	45.3591			1.68227			0.841137	−	0.540822i	$-0.181887\pi$
$727$	45.3591			1.68227			0.841137	+	0.540822i	$0.181887\pi$
$728$	−2.69258	+	4.81776i	−0.0997938	+	0.178558i
$729$	2.90169	+	26.8436i	0.107470	+	0.994208i
$730$	2.04095	+	19.4183i	0.0755388	+	0.718704i
$731$	0.213393	+	1.00393i	0.00789262	+	0.0371318i
$732$	−8.79495	+	18.0549i	−0.325071	+	0.667329i
$733$	−30.0329	+	3.15658i	−1.10929	+	0.116591i	−0.641408	−	0.767200i	$-0.721649\pi$
$733$	−30.0329	+	3.15658i	−1.10929	+	0.116591i	−0.467882	+	0.883791i	$0.654983\pi$
$734$	−2.98388	−	2.16792i	−0.110137	−	0.0800193i
$735$	−8.37017	+	18.4757i	−0.308738	+	0.681485i
$736$			1.28658i			0.0474240i
$737$	5.78260	+	5.58623i	0.213005	+	0.205771i
$738$	−9.40278	+	9.09810i	−0.346121	+	0.334906i
$739$	−16.7082	−	15.0441i	−0.614622	−	0.553408i	0.301927	−	0.953331i	$-0.402370\pi$
$739$	−16.7082	−	15.0441i	−0.614622	−	0.553408i	−0.916549	+	0.399923i	$0.869037\pi$
$740$	−3.73588	−	8.39092i	−0.137334	−	0.308456i
$741$	9.78980	+	0.337035i	0.359637	+	0.0123813i
$742$	−27.4773	+	12.6961i	−1.00872	+	0.466089i
$743$	12.6450	−	38.9173i	0.463900	−	1.42774i	−0.396461	−	0.918052i	$-0.629762\pi$
$743$	12.6450	−	38.9173i	0.463900	−	1.42774i	0.860361	−	0.509686i	$-0.170238\pi$
$744$	14.8806	−	23.8401i	0.545548	−	0.874019i
$745$	−19.4465	−	2.04391i	−0.712466	−	0.0748832i
$746$	17.1395	+	15.4325i	0.627521	+	0.565023i
$747$	12.3217	+	3.52005i	0.450829	+	0.128792i
$748$	−0.721955	+	0.0503522i	−0.0263973	+	0.00184106i
$749$	10.8799	+	47.8893i	0.397545	+	1.74984i
$750$	19.8098	+	7.19912i	0.723352	+	0.262875i
$751$	2.70025	−	1.20223i	0.0985334	−	0.0438699i	−0.356878	−	0.934151i	$-0.616159\pi$
$751$	2.70025	−	1.20223i	0.0985334	−	0.0438699i	0.455411	+	0.890281i	$0.349492\pi$
$752$	3.11592	−	6.99847i	0.113626	−	0.255208i
$753$	21.0211	−	43.1536i	0.766050	−	1.57260i
$754$	0.0877762	−	0.0790340i	0.00319662	−	0.00287825i
$755$	−9.04695	+	6.57300i	−0.329252	+	0.239216i
$756$	13.1294	−	3.00328i	0.477510	−	0.109228i
$757$	−12.6344	−	38.8848i	−0.459206	−	1.41329i	−0.866125	−	0.499827i	$-0.833397\pi$
$757$	−12.6344	−	38.8848i	−0.459206	−	1.41329i	0.406919	−	0.913464i	$-0.366603\pi$
$758$	8.39267	−	14.5365i	0.304836	−	0.527991i
$759$	1.27167	−	0.795177i	0.0461586	−	0.0288631i
$760$	20.5434	+	35.5822i	0.745187	+	1.29070i
$761$	19.2530	+	4.09234i	0.697919	+	0.148347i	0.543190	−	0.839610i	$-0.317216\pi$
$761$	19.2530	+	4.09234i	0.697919	+	0.148347i	0.154729	+	0.987957i	$0.450550\pi$
$762$	−17.4664	+	5.01772i	−0.632740	+	0.181773i
$763$	−6.18812	−	18.1778i	−0.224025	−	0.658080i
$764$	−1.41651	−	0.460253i	−0.0512476	−	0.0166514i
$765$	−0.927349	−	0.624175i	−0.0335284	−	0.0225671i
$766$	3.59729	−	8.07965i	0.129975	−	0.291930i
$767$	0.824641	−	7.84593i	0.0297761	−	0.283300i
$768$	18.8817	+	22.4798i	0.681335	+	0.811171i
$769$		−	16.4140i		−	0.591902i	−0.955203	−	0.295951i	$-0.904363\pi$
$769$		−	16.4140i		−	0.591902i	0.955203	−	0.295951i	$-0.0956365\pi$
$770$	8.46043	+	12.1778i	0.304893	+	0.438858i
$771$	−3.56312	+	4.56522i	−0.128323	+	0.164412i
$772$	−0.473516	+	2.22772i	−0.0170422	+	0.0801773i
$773$	11.4636	+	1.20488i	0.412318	+	0.0433364i	0.308417	−	0.951251i	$-0.400201\pi$
$773$	11.4636	+	1.20488i	0.412318	+	0.0433364i	0.103901	+	0.994588i	$0.466867\pi$
$774$	−13.7542	−	2.41126i	−0.494385	−	0.0866708i
$775$	7.94042	+	8.81873i	0.285228	+	0.316778i
$776$	3.21506	−	9.89493i	0.115414	−	0.355207i
$777$	−19.4327	+	16.7904i	−0.697144	+	0.602353i
$778$	−9.18312	+	12.6395i	−0.329231	+	0.453147i
$779$	7.32510	−	34.4619i	0.262449	−	1.23472i
$780$	0.272860	−	1.94847i	0.00976996	−	0.0697665i
$781$	33.5585	+	1.17799i	1.20082	+	0.0421519i
$782$	−0.0508696	−	0.0293696i	−0.00181909	−	0.00105025i
$783$	−0.871998	−	0.0903469i	−0.0311627	−	0.00322874i
$784$	2.53792	+	7.12751i	0.0906399	+	0.254554i
$785$	−9.39707	−	12.9340i	−0.335396	−	0.461633i
$786$	−0.997941	−	14.1708i	−0.0355954	−	0.505457i
$787$	5.10313	+	24.0083i	0.181907	+	0.855805i	0.970540	+	0.240940i	$0.0774558\pi$
$787$	5.10313	+	24.0083i	0.181907	+	0.855805i	−0.788633	+	0.614864i	$0.789211\pi$
$788$	−19.8247	−	8.82654i	−0.706227	−	0.314432i
$789$	−13.4316	−	3.34183i	−0.478176	−	0.118972i
$790$	−2.80567	−	8.63496i	−0.0998212	−	0.307218i
$791$	−8.11824	−	8.76699i	−0.288651	−	0.311718i
$792$	9.23125	−	28.4888i	0.328018	−	1.01231i
$793$	4.10145	−	7.10392i	0.145647	−	0.252267i
$794$	−3.76800	+	4.18479i	−0.133721	+	0.148513i
$795$	22.7859	−	23.6188i	0.808133	−	0.837672i
$796$	1.00803	+	9.59078i	0.0357287	+	0.339936i
$797$	26.4365	+	8.58975i	0.936430	+	0.304265i	0.737190	−	0.675686i	$-0.236152\pi$
$797$	26.4365	+	8.58975i	0.936430	+	0.304265i	0.199241	+	0.979951i	$0.436152\pi$
$798$	25.8428	−	27.5467i	0.914826	−	0.975144i
$799$	−0.927921	−	1.27717i	−0.0328275	−	0.0451832i
$800$	−9.90978	+	4.41212i	−0.350363	+	0.155992i
$801$	−1.53474	+	2.89331i	−0.0542275	+	0.102230i
$802$	−9.86844	+	5.69755i	−0.348467	+	0.201187i
$803$	−5.34028	+	37.9481i	−0.188454	+	1.33916i
$804$	−3.24277	−	2.53096i	−0.114364	−	0.0892600i
$805$	−0.0161293	−	1.15549i	−0.000568481	−	0.0407257i
$806$	−2.21832	+	3.05326i	−0.0781371	+	0.107546i
$807$	−13.6613	−	8.52716i	−0.480900	−	0.300170i
$808$	11.4060	−	2.42442i	0.401262	−	0.0852908i
$809$	21.4400	−	4.55722i	0.753791	−	0.160223i	0.185038	−	0.982731i	$-0.440759\pi$
$809$	21.4400	−	4.55722i	0.753791	−	0.160223i	0.568753	+	0.822508i	$0.307426\pi$
$810$	12.5917	−	8.52937i	0.442426	−	0.299691i
$811$	2.01069	−	2.76748i	0.0706048	−	0.0971792i	−0.772254	−	0.635314i	$-0.780871\pi$
$811$	2.01069	−	2.76748i	0.0706048	−	0.0971792i	0.842859	+	0.538135i	$0.180871\pi$
$812$	0.00610372	+	0.437267i	0.000214198	+	0.0153451i
$813$	−1.69069	+	2.16619i	−0.0592952	+	0.0759715i
$814$	3.25686	+	18.4902i	0.114153	+	0.648081i
$815$	−1.73417	+	1.00122i	−0.0607452	+	0.0350713i
$816$	−0.410597	+	0.0726080i	−0.0143738	+	0.00254179i
$817$	34.3508	−	15.2940i	1.20178	−	0.535068i
$818$	12.0715	+	16.6149i	0.422068	+	0.580927i
$819$	−5.43558	+	0.846934i	−0.189934	+	0.0295943i
$820$	−6.73009	−	2.18674i	−0.235025	−	0.0763642i
$821$	2.78915	+	26.5370i	0.0973421	+	0.926148i	0.928805	+	0.370568i	$0.120837\pi$
$821$	2.78915	+	26.5370i	0.0973421	+	0.926148i	−0.831463	+	0.555580i	$0.812496\pi$
$822$	28.2843	+	27.2869i	0.986527	+	0.951739i
$823$	23.0503	−	25.6000i	0.803484	−	0.892360i	−0.192554	−	0.981286i	$-0.561677\pi$
$823$	23.0503	−	25.6000i	0.803484	−	0.892360i	0.996038	+	0.0889268i	$0.0283437\pi$
$824$	−9.30226	+	16.1120i	−0.324060	+	0.561288i
$825$	10.4858	+	7.06799i	0.365067	+	0.246076i
$826$	−20.6686	−	22.3203i	−0.719153	−	0.776622i
$827$	−3.60035	−	11.0807i	−0.125196	−	0.385315i	0.868741	−	0.495268i	$-0.164930\pi$
$827$	−3.60035	−	11.0807i	−0.125196	−	0.385315i	−0.993937	+	0.109953i	$0.964930\pi$
$828$	−0.604208	+	0.473019i	−0.0209977	+	0.0164386i
$829$	19.6456	+	8.74678i	0.682320	+	0.303788i	0.718470	−	0.695558i	$-0.244843\pi$
$829$	19.6456	+	8.74678i	0.682320	+	0.303788i	−0.0361502	+	0.999346i	$0.511509\pi$
$830$	−1.50076	−	7.06051i	−0.0520921	−	0.245074i
$831$	9.67687	−	0.681467i	0.335687	−	0.0236398i
$832$	−2.90843	−	4.00312i	−0.100832	−	0.138783i
$833$	1.53350	+	0.281465i	0.0531326	+	0.00975217i
$834$	−19.0245	−	6.91375i	−0.658766	−	0.239403i
$835$	−29.6026	−	17.0911i	−1.02444	−	0.591461i
$836$	7.30353	+	25.4879i	0.252598	+	0.881517i
$837$	27.8537	−	2.96920i	0.962765	−	0.102631i
$838$	2.37738	−	11.1847i	0.0821253	−	0.386369i
$839$	12.5380	−	17.2571i	0.432860	−	0.595781i	−0.535747	−	0.844379i	$-0.679970\pi$
$839$	12.5380	−	17.2571i	0.432860	−	0.595781i	0.968607	+	0.248598i	$0.0799698\pi$
$840$	−15.0857	−	17.4597i	−0.520505	−	0.602415i
$841$	−8.95270	+	27.5536i	−0.308714	+	0.950123i
$842$	2.48051	+	2.75489i	0.0854840	+	0.0949396i
$843$	20.6226	+	38.7395i	0.710281	+	1.33426i
$844$	−11.3712	−	1.19516i	−0.391413	−	0.0411392i
$845$	4.35461	−	20.4868i	0.149803	−	0.704769i
$846$	20.8352	−	5.21662i	0.716328	−	0.179351i
$847$	10.3248	+	27.2103i	0.354763	+	0.934956i
$848$		−	12.2416i		−	0.420378i
$849$	27.6022	−	23.1842i	0.947304	−	0.795679i
$850$	0.0517677	−	0.492537i	0.00177562	−	0.0168939i
$851$	0.595124	−	1.33667i	0.0204006	−	0.0458205i
$852$	−17.1375	+	1.20686i	−0.587121	+	0.0413464i
$853$	−3.24637	−	1.05481i	−0.111154	−	0.0361160i	0.252912	−	0.967489i	$-0.418612\pi$
$853$	−3.24637	−	1.05481i	−0.111154	−	0.0361160i	−0.364066	+	0.931373i	$0.618612\pi$
$854$	−10.1931	−	29.9425i	−0.348801	−	1.02461i
$855$	−15.3038	+	37.9861i	−0.523380	+	1.29910i
$856$	−54.6462	−	11.6154i	−1.86777	−	0.397006i
$857$	11.1625	+	19.3340i	0.381303	+	0.660436i	0.991249	−	0.132007i	$-0.0421421\pi$
$857$	11.1625	+	19.3340i	0.381303	+	0.660436i	−0.609946	+	0.792443i	$0.708809\pi$
$858$	−1.50539	+	3.72931i	−0.0513931	+	0.127317i
$859$	−7.88941	+	13.6649i	−0.269183	+	0.466239i	−0.968651	−	0.248425i	$-0.920087\pi$
$859$	−7.88941	+	13.6649i	−0.269183	+	0.466239i	0.699468	+	0.714664i	$0.253420\pi$
$860$	−2.33383	−	7.18279i	−0.0795830	−	0.244931i
$861$	−0.404708	+	19.7819i	−0.0137924	+	0.674164i
$862$	12.0716	−	8.77053i	0.411160	−	0.298725i
$863$	−11.5398	+	10.3905i	−0.392819	+	0.353695i	−0.841747	−	0.539872i	$-0.818473\pi$
$863$	−11.5398	+	10.3905i	−0.392819	+	0.353695i	0.448928	+	0.893568i	$0.351806\pi$
$864$	−5.28669	+	25.0541i	−0.179857	+	0.852357i
$865$	9.53897	−	21.4249i	0.324335	−	0.728468i
$866$	−15.1973	+	6.76629i	−0.516426	+	0.229928i
$867$	10.0277	−	27.5933i	0.340560	−	0.937118i
$868$	−3.09565	−	13.6258i	−0.105073	−	0.462491i
$869$	−1.23982	−	17.7767i	−0.0420581	−	0.603033i
$870$	0.185210	+	0.457760i	0.00627919	+	0.0155195i
$871$	1.24861	+	1.12425i	0.0423076	+	0.0380939i
$872$	21.7247	+	2.28336i	0.735691	+	0.0773242i
$873$	9.74137	−	3.55645i	0.329695	−	0.120368i
$874$	−0.664991	+	2.04663i	−0.0224937	+	0.0692284i
$875$	28.9347	−	13.3695i	0.978171	−	0.451973i
$876$	0.674596	−	19.5949i	0.0227925	−	0.662049i
$877$	−12.0231	−	27.0042i	−0.405990	−	0.911868i	−0.994632	−	0.103475i	$-0.967004\pi$
$877$	−12.0231	−	27.0042i	−0.405990	−	0.911868i	0.588642	−	0.808394i	$-0.299663\pi$
$878$	0.284674	+	0.256322i	0.00960729	+	0.00865045i
$879$	−2.96141	+	21.1472i	−0.0998860	+	0.713277i
$880$	−5.90611	+	1.04030i	−0.199095	+	0.0350685i
$881$			42.4150i			1.42900i	0.699637	+	0.714498i	$0.253345\pi$
$881$			42.4150i			1.42900i	−0.699637	+	0.714498i	$0.746655\pi$
$882$	−11.3486	+	17.9212i	−0.382126	+	0.603437i
$883$	−9.50181	−	6.90347i	−0.319761	−	0.232320i	0.416312	−	0.909222i	$-0.363322\pi$
$883$	−9.50181	−	6.90347i	−0.319761	−	0.232320i	−0.736074	+	0.676901i	$0.763322\pi$
$884$	−0.150406	+	0.0158083i	−0.00505871	+	0.000531692i
$885$	29.6517	+	14.4440i	0.996732	+	0.485531i
$886$	−8.46066	−	39.8043i	−0.284242	−	1.33725i
$887$	2.97665	+	28.3210i	0.0999462	+	0.950925i	0.923477	+	0.383654i	$0.125334\pi$
$887$	2.97665	+	28.3210i	0.0999462	+	0.950925i	−0.823531	+	0.567271i	$0.807999\pi$
$888$	−8.06669	−	28.0796i	−0.270700	−	0.942291i
$889$	−13.4073	+	23.9894i	−0.449668	+	0.804577i
$890$	1.84483			0.0618390
$891$	28.0311	−	10.2594i	0.939079	−	0.343702i
$892$	−8.29381	−	14.3653i	−0.277697	−	0.480986i
$893$	−38.6998	+	42.9805i	−1.29504	+	1.43829i
$894$	−19.8442	−	4.93733i	−0.663690	−	0.165129i
$895$	−17.1107	+	12.4317i	−0.571949	+	0.415545i
$896$	6.96714	+	0.634093i	0.232756	+	0.0211835i
$897$	0.259750	−	0.175390i	0.00867280	−	0.00585610i
$898$	24.2667	−	2.55053i	0.809790	−	0.0851123i
$899$	−0.0950696	+	0.904527i	−0.00317075	+	0.0301677i
$900$	−5.71543	−	3.03172i	−0.190514	−	0.101057i
$901$	−2.18468	−	1.26133i	−0.0727823	−	0.0420209i
$902$	12.2654	+	7.66739i	0.408394	+	0.255296i
$903$	−17.3342	+	12.0602i	−0.576848	+	0.401337i
$904$	12.9273	−	4.20033i	0.429955	−	0.139701i
$905$	14.2254	+	31.9507i	0.472868	+	1.06208i
$906$	−10.3232	+	5.49547i	−0.342965	+	0.182575i
$907$	42.3426	−	9.00020i	1.40596	−	0.298847i	0.558413	−	0.829563i	$-0.311410\pi$
$907$	42.3426	−	9.00020i	1.40596	−	0.298847i	0.847550	+	0.530716i	$0.178077\pi$
$908$	5.17466	+	5.74704i	0.171727	+	0.190722i
$909$	8.91099	+	7.46225i	0.295559	+	0.247507i
$910$	1.85618	+	2.48123i	0.0615318	+	0.0822520i
$911$	−39.8311	+	12.9419i	−1.31966	+	0.428785i	−0.882379	−	0.470539i	$-0.844060\pi$
$911$	−39.8311	+	12.9419i	−1.31966	+	0.428785i	−0.437284	+	0.899323i	$0.644060\pi$
$912$	5.72945	+	14.1608i	0.189721	+	0.468910i
$913$	0.496999	−	14.1584i	0.0164483	−	0.468576i
$914$	29.2129	−	16.8661i	0.966276	−	0.557880i
$915$	22.0569	+	26.2601i	0.729179	+	0.868133i
$916$	−19.7041	−	14.3159i	−0.651042	−	0.473010i
$917$	−16.1639	−	14.1506i	−0.533780	−	0.467293i
$918$	−0.869921	−	0.780954i	−0.0287117	−	0.0257753i
$919$	−26.8490	+	24.1750i	−0.885667	+	0.797458i	−0.980189	−	0.198065i	$-0.936534\pi$
$919$	−26.8490	+	24.1750i	−0.885667	+	0.797458i	0.0945220	+	0.995523i	$0.469868\pi$
$920$	1.20096	+	0.534700i	0.0395943	+	0.0176285i
$921$	0.769425	+	0.742292i	0.0253534	+	0.0244594i
$922$	16.8803	+	3.58803i	0.555924	+	0.118165i
$923$	7.01711			0.230971
$924$	−6.71762	−	13.2885i	−0.220994	−	0.437160i
$925$	12.3365			0.405621
$926$	−23.8706	−	5.07385i	−0.784437	−	0.166737i
$927$	−18.3609	+	2.59893i	−0.603052	+	0.0853599i
$928$	−0.759519	−	0.338160i	−0.0249324	−	0.0111006i
$929$	−30.1662	+	27.1618i	−0.989721	+	0.891149i	−0.994059	−	0.108842i	$-0.965286\pi$
$929$	−30.1662	+	27.1618i	−0.989721	+	0.891149i	0.00433808	+	0.999991i	$0.498619\pi$
$930$	−8.82958	−	13.0765i	−0.289533	−	0.428795i
$931$	−1.59433	−	57.0972i	−0.0522520	−	1.87129i
$932$	−7.86797	−	5.71642i	−0.257724	−	0.187247i
$933$	29.7222	−	24.9649i	0.973061	−	0.817313i
$934$	−14.2356	+	8.21891i	−0.465802	+	0.268931i
$935$	−0.422886	+	1.16121i	−0.0138299	+	0.0379758i
$936$	1.71904	−	6.01737i	0.0561884	−	0.196684i
$937$	−3.07412	+	0.998842i	−0.100427	+	0.0326307i	−0.358800	−	0.933415i	$-0.616814\pi$
$937$	−3.07412	+	0.998842i	−0.100427	+	0.0326307i	0.258372	+	0.966045i	$0.416814\pi$
$938$	6.43309	−	0.767068i	0.210048	−	0.0250457i
$939$	26.0976	+	0.898468i	0.851664	+	0.0293204i
$940$	7.77301	+	8.63281i	0.253528	+	0.281571i
$941$	49.2351	−	10.4652i	1.60502	−	0.341157i	0.683639	−	0.729820i	$-0.260396\pi$
$941$	49.2351	−	10.4652i	1.60502	−	0.341157i	0.921380	+	0.388663i	$0.127063\pi$
$942$	−7.85659	−	14.7585i	−0.255981	−	0.480859i
$943$	−0.458503	−	1.02982i	−0.0149309	−	0.0335354i
$944$	11.7007	−	3.80180i	0.380827	−	0.123738i
$945$	4.43394	−	22.5676i	0.144236	−	0.734124i
$946$	1.07408	+	15.4003i	0.0349215	+	0.500708i
$947$	−47.4819	−	27.4137i	−1.54295	−	0.890825i	−0.998650	−	0.0519374i	$-0.983460\pi$
$947$	−47.4819	−	27.4137i	−1.54295	−	0.890825i	−0.544304	−	0.838888i	$-0.683206\pi$
$948$	1.58759	+	8.97780i	0.0515626	+	0.291585i
$949$	−0.837086	+	7.96435i	−0.0271730	+	0.258534i
$950$	−18.0445	+	1.89655i	−0.585441	+	0.0615323i
$951$	−20.7106	−	30.6720i	−0.671586	−	0.994609i
$952$	−1.02239	+	1.44932i	−0.0331359	+	0.0469727i
$953$	13.7411	−	9.98346i	0.445116	−	0.323396i	−0.342548	−	0.939500i	$-0.611290\pi$
$953$	13.7411	−	9.98346i	0.445116	−	0.323396i	0.787665	+	0.616104i	$0.211290\pi$
$954$	27.0248	−	21.1570i	0.874960	−	0.684984i
$955$	−1.70183	+	1.89007i	−0.0550699	+	0.0611614i
$956$	−12.8485	−	22.2543i	−0.415550	−	0.719754i
$957$	0.135184	+	0.959717i	0.00436988	+	0.0310232i
$958$	7.14066			0.230704
$959$	59.4270	−	0.829529i	1.91900	−	0.0267869i
$960$	19.8827	−	5.71189i	0.641712	−	0.184350i
$961$	0.202685	+	1.92842i	0.00653822	+	0.0622070i
$962$	0.815724	+	3.83768i	0.0263000	+	0.123732i
$963$	−24.4601	−	50.0254i	−0.788215	−	1.61204i
$964$	0.0861553	−	0.00905528i	0.00277487	−	0.000291651i
$965$	3.14633	+	2.28594i	0.101284	+	0.0735871i
$966$	0.150883	−	1.19907i	0.00485459	−	0.0385795i
$967$			30.0795i			0.967292i	0.875264	+	0.483646i	$0.160688\pi$
$967$			30.0795i			0.967292i	−0.875264	+	0.483646i	$0.839312\pi$
$968$	−33.0263	−	2.32148i	−1.06151	−	0.0746153i
$969$	3.11752	+	0.436572i	0.100149	+	0.0140247i
$970$	−4.34098	−	3.90864i	−0.139381	−	0.125499i
$971$	−21.9849	−	49.3788i	−0.705528	−	1.58464i	−0.807509	−	0.589855i	$-0.799185\pi$
$971$	−21.9849	−	49.3788i	−0.705528	−	1.58464i	0.101981	−	0.994786i	$-0.467482\pi$
$972$	−13.7097	+	6.72854i	−0.439738	+	0.215818i
$973$	−27.7877	+	12.8396i	−0.890833	+	0.411617i
$974$	−2.01357	+	6.19712i	−0.0645188	+	0.198568i
$975$	2.24170	+	1.39923i	0.0717917	+	0.0448112i
$976$	12.7221	+	1.33714i	0.407224	+	0.0428010i
$977$	31.7605	+	28.5973i	1.01611	+	0.914909i	0.996390	−	0.0848970i	$-0.0270561\pi$
$977$	31.7605	+	28.5973i	1.01611	+	0.914909i	0.0197192	+	0.999806i	$0.493723\pi$
$978$	−1.94128	+	0.785441i	−0.0620752	+	0.0251156i
$979$	3.51312	+	0.876596i	0.112280	+	0.0280161i
$980$	−11.4388	−	0.880280i	−0.365400	−	0.0281195i
$981$	11.5563	+	18.4534i	0.368963	+	0.589171i
$982$	−3.14221	+	1.39900i	−0.100272	+	0.0446439i
$983$	3.03111	−	6.80798i	0.0966773	−	0.217141i	−0.858732	−	0.512424i	$-0.828747\pi$
$983$	3.03111	−	6.80798i	0.0966773	−	0.217141i	0.955410	+	0.295284i	$0.0954141\pi$
$984$	−20.2354	−	9.85710i	−0.645080	−	0.314233i
$985$	−27.5386	+	24.7959i	−0.877453	+	0.790062i
$986$	0.0307084	−	0.0223109i	0.000977954	−	0.000710525i
$987$	16.8122	−	27.7908i	0.535138	−	0.884592i
$988$	1.71214	+	5.26943i	0.0544705	+	0.167643i
$989$	0.601550	−	1.04191i	0.0191282	−	0.0331309i
$990$	−12.5041	−	11.2405i	−0.397405	−	0.357247i
$991$	6.71506	+	11.6308i	0.213311	+	0.369465i	0.952749	−	0.303759i	$-0.0982419\pi$
$991$	6.71506	+	11.6308i	0.213311	+	0.369465i	−0.739438	+	0.673225i	$0.764909\pi$
$992$	25.9846	+	5.52319i	0.825011	+	0.175361i
$993$	−13.6092	−	47.3727i	−0.431875	−	1.50333i
$994$	17.8227	−	20.3585i	0.565300	−	0.645731i
$995$	15.6616	+	5.08877i	0.496507	+	0.161325i
$996$	0.509178	+	7.23036i	0.0161339	+	0.229103i
$997$	21.7774	−	48.9129i	0.689698	−	1.54909i	−0.139555	−	0.990214i	$-0.544567\pi$
$997$	21.7774	−	48.9129i	0.689698	−	1.54909i	0.829253	−	0.558873i	$-0.188766\pi$
$998$	−2.79467	+	26.5895i	−0.0884636	+	0.841675i
$999$	17.0816	−	23.5841i	0.540438	−	0.746167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.be.a.149.19	yes	224
3.2	odd	2	inner	231.2.be.a.149.10	yes	224
7.4	even	3	inner	231.2.be.a.116.10	yes	224
11.2	odd	10	inner	231.2.be.a.2.19	yes	224
21.11	odd	6	inner	231.2.be.a.116.19	yes	224
33.2	even	10	inner	231.2.be.a.2.10	✓	224
77.46	odd	30	inner	231.2.be.a.200.10	yes	224
231.200	even	30	inner	231.2.be.a.200.19	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.be.a.2.10	✓	224	33.2	even	10	inner
231.2.be.a.2.19	yes	224	11.2	odd	10	inner
231.2.be.a.116.10	yes	224	7.4	even	3	inner
231.2.be.a.116.19	yes	224	21.11	odd	6	inner
231.2.be.a.149.10	yes	224	3.2	odd	2	inner
231.2.be.a.149.19	yes	224	1.1	even	1	trivial
231.2.be.a.200.10	yes	224	77.46	odd	30	inner
231.2.be.a.200.19	yes	224	231.200	even	30	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.be (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.988032 + 0.210013i) q^{2} +(-1.20257 + 1.24653i) q^{3} +(-0.894989 - 0.398475i) q^{4} +(-1.24323 + 1.11941i) q^{5} +(-1.44996 + 0.979053i) q^{6} +(-0.513908 + 2.59536i) q^{7} +(-2.43498 - 1.76911i) q^{8} +(-0.107655 - 2.99807i) q^{9} +O(q^{10})\)	\(q+(0.988032 + 0.210013i) q^{2} +(-1.20257 + 1.24653i) q^{3} +(-0.894989 - 0.398475i) q^{4} +(-1.24323 + 1.11941i) q^{5} +(-1.44996 + 0.979053i) q^{6} +(-0.513908 + 2.59536i) q^{7} +(-2.43498 - 1.76911i) q^{8} +(-0.107655 - 2.99807i) q^{9} +(-1.46344 + 0.844920i) q^{10} +(-3.18831 + 0.913606i) q^{11} +(1.57299 - 0.636433i) q^{12} +(-0.659160 + 0.214174i) q^{13} +(-1.05282 + 2.45637i) q^{14} +(0.0996973 - 2.89589i) q^{15} +(-0.723222 - 0.803220i) q^{16} +(-0.217864 + 0.0463083i) q^{17} +(0.523266 - 2.98480i) q^{18} +(3.31894 + 7.45446i) q^{19} +(1.55874 - 0.506464i) q^{20} +(-2.61718 - 3.76170i) q^{21} +(-3.34202 + 0.233087i) q^{22} +(0.226106 + 0.130542i) q^{23} +(5.13348 - 0.907780i) q^{24} +(-0.230098 + 2.18923i) q^{25} +(-0.696250 + 0.0731788i) q^{26} +(3.86663 + 3.47119i) q^{27} +(1.49413 - 2.11804i) q^{28} +(-0.136493 + 0.0991679i) q^{29} +(0.706678 - 2.84030i) q^{30} +(3.60716 - 4.00616i) q^{31} +(2.46392 + 4.26763i) q^{32} +(2.69533 - 5.07299i) q^{33} -0.224982 q^{34} +(-2.26637 - 3.80191i) q^{35} +(-1.09830 + 2.72613i) q^{36} +(-0.585798 - 5.57350i) q^{37} +(1.71369 + 8.06227i) q^{38} +(0.525712 - 1.07922i) q^{39} +(5.00761 - 0.526321i) q^{40} +(-3.49306 - 2.53786i) q^{41} +(-1.79585 - 4.26632i) q^{42} -4.60809i q^{43} +(3.21755 + 0.452793i) q^{44} +(3.48991 + 3.60678i) q^{45} +(0.195984 + 0.176465i) q^{46} +(2.88287 + 6.47504i) q^{47} +(1.87096 + 0.0644118i) q^{48} +(-6.47180 - 2.66755i) q^{49} +(-0.687111 + 2.11471i) q^{50} +(0.204271 - 0.327262i) q^{51} +(0.675283 + 0.0709751i) q^{52} +(8.41687 + 7.57859i) q^{53} +(3.09136 + 4.24169i) q^{54} +(2.94111 - 4.70486i) q^{55} +(5.84285 - 5.41048i) q^{56} +(-13.2834 - 4.82736i) q^{57} +(-0.155686 + 0.0693158i) q^{58} +(-4.62977 + 10.3986i) q^{59} +(-1.24317 + 2.55206i) q^{60} +(-8.79542 + 7.91943i) q^{61} +(4.40534 - 3.20067i) q^{62} +(7.83639 + 1.26133i) q^{63} +(2.20617 + 6.78989i) q^{64} +(0.579740 - 1.00414i) q^{65} +(3.72846 - 4.44622i) q^{66} +(-1.21210 - 2.09942i) q^{67} +(0.213438 + 0.0453677i) q^{68} +(-0.434632 + 0.124861i) q^{69} +(-1.44080 - 4.23238i) q^{70} +(-9.62898 - 3.12864i) q^{71} +(-5.04179 + 7.49068i) q^{72} +(4.69964 - 10.5556i) q^{73} +(0.591718 - 5.62982i) q^{74} +(-2.45223 - 2.91953i) q^{75} -7.99417i q^{76} +(-0.732640 - 8.74433i) q^{77} +(0.746070 - 0.955897i) q^{78} +(-1.11709 + 5.25548i) q^{79} +(1.79827 + 0.189005i) q^{80} +(-8.97682 + 0.645512i) q^{81} +(-2.91827 - 3.24107i) q^{82} +(-1.31998 + 4.06249i) q^{83} +(0.843400 + 4.40956i) q^{84} +(0.219017 - 0.301451i) q^{85} +(0.967757 - 4.55294i) q^{86} +(0.0405268 - 0.289398i) q^{87} +(9.37974 + 3.41588i) q^{88} +(-0.945459 - 0.545861i) q^{89} +(2.69067 + 4.29655i) q^{90} +(-0.217111 - 1.82082i) q^{91} +(-0.150344 - 0.206931i) q^{92} +(0.655921 + 9.31411i) q^{93} +(1.48853 + 7.00299i) q^{94} +(-12.4708 - 5.55237i) q^{95} +(-8.28274 - 2.06078i) q^{96} +(1.06820 + 3.28757i) q^{97} +(-5.83412 - 3.99479i) q^{98} +(3.08229 + 9.46042i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Introduction

L-functions

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