LMFDB - Embedded newform 420.2.i.a.139.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(139,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))

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

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

chi := DirichletCharacter("420.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.i (of order $2$, degree $1$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.3
Character	$\chi$	$=$	420.139
Dual form			420.2.i.a.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36843 + 0.356944i) q^{2} -1.00000i q^{3} +(1.74518 - 0.976904i) q^{4} +(1.65234 + 1.50657i) q^{5} +(0.356944 + 1.36843i) q^{6} +(-2.07310 + 1.64386i) q^{7} +(-2.03945 + 1.95975i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.36843 + 0.356944i) q^{2} -1.00000i q^{3} +(1.74518 - 0.976904i) q^{4} +(1.65234 + 1.50657i) q^{5} +(0.356944 + 1.36843i) q^{6} +(-2.07310 + 1.64386i) q^{7} +(-2.03945 + 1.95975i) q^{8} -1.00000 q^{9} +(-2.79887 - 1.47184i) q^{10} +4.97024i q^{11} +(-0.976904 - 1.74518i) q^{12} -5.35119 q^{13} +(2.25011 - 2.98948i) q^{14} +(1.50657 - 1.65234i) q^{15} +(2.09132 - 3.40975i) q^{16} -3.34087 q^{17} +(1.36843 - 0.356944i) q^{18} -2.12411 q^{19} +(4.35541 + 1.01507i) q^{20} +(1.64386 + 2.07310i) q^{21} +(-1.77410 - 6.80140i) q^{22} +6.71438 q^{23} +(1.95975 + 2.03945i) q^{24} +(0.460466 + 4.97875i) q^{25} +(7.32271 - 1.91008i) q^{26} +1.00000i q^{27} +(-2.01203 + 4.89405i) q^{28} -1.42645 q^{29} +(-1.47184 + 2.79887i) q^{30} -5.76942 q^{31} +(-1.64472 + 5.41248i) q^{32} +4.97024 q^{33} +(4.57174 - 1.19250i) q^{34} +(-5.90206 - 0.407054i) q^{35} +(-1.74518 + 0.976904i) q^{36} -0.864770i q^{37} +(2.90669 - 0.758191i) q^{38} +5.35119i q^{39} +(-6.32239 + 0.165596i) q^{40} +1.68563i q^{41} +(-2.98948 - 2.25011i) q^{42} +5.29678 q^{43} +(4.85545 + 8.67397i) q^{44} +(-1.65234 - 1.50657i) q^{45} +(-9.18813 + 2.39666i) q^{46} +8.84199i q^{47} +(-3.40975 - 2.09132i) q^{48} +(1.59545 - 6.81576i) q^{49} +(-2.40725 - 6.64869i) q^{50} +3.34087i q^{51} +(-9.33880 + 5.22760i) q^{52} +10.1805i q^{53} +(-0.356944 - 1.36843i) q^{54} +(-7.48803 + 8.21253i) q^{55} +(1.00642 - 7.41533i) q^{56} +2.12411i q^{57} +(1.95199 - 0.509164i) q^{58} +4.51007 q^{59} +(1.01507 - 4.35541i) q^{60} -3.54820i q^{61} +(7.89503 - 2.05936i) q^{62} +(2.07310 - 1.64386i) q^{63} +(0.318730 - 7.99365i) q^{64} +(-8.84199 - 8.06197i) q^{65} +(-6.80140 + 1.77410i) q^{66} +0.310390 q^{67} +(-5.83043 + 3.26371i) q^{68} -6.71438i q^{69} +(8.22183 - 1.54968i) q^{70} -4.74826i q^{71} +(2.03945 - 1.95975i) q^{72} +12.2187 q^{73} +(0.308675 + 1.18337i) q^{74} +(4.97875 - 0.460466i) q^{75} +(-3.70697 + 2.07506i) q^{76} +(-8.17037 - 10.3038i) q^{77} +(-1.91008 - 7.32271i) q^{78} +9.38349i q^{79} +(8.59261 - 2.48335i) q^{80} +1.00000 q^{81} +(-0.601678 - 2.30667i) q^{82} -6.05979i q^{83} +(4.89405 + 2.01203i) q^{84} +(-5.52026 - 5.03327i) q^{85} +(-7.24825 + 1.89065i) q^{86} +1.42645i q^{87} +(-9.74044 - 10.1366i) q^{88} -3.30075i q^{89} +(2.79887 + 1.47184i) q^{90} +(11.0935 - 8.79661i) q^{91} +(11.7178 - 6.55930i) q^{92} +5.76942i q^{93} +(-3.15610 - 12.0996i) q^{94} +(-3.50976 - 3.20014i) q^{95} +(5.41248 + 1.64472i) q^{96} +5.32789 q^{97} +(0.249591 + 9.89635i) q^{98} -4.97024i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{9}+O(q^{10}) $ 48 * q - 48 * q^9	$ 48 q - 48 q^{9} + 20 q^{14} - 16 q^{16} + 8 q^{25} - 16 q^{30} - 40 q^{44} + 16 q^{46} - 16 q^{49} + 48 q^{50} + 28 q^{56} - 32 q^{60} - 112 q^{74} + 48 q^{81} - 28 q^{84} + 56 q^{85} + 8 q^{86}+O(q^{100}) $ 48 * q - 48 * q^9 + 20 * q^14 - 16 * q^16 + 8 * q^25 - 16 * q^30 - 40 * q^44 + 16 * q^46 - 16 * q^49 + 48 * q^50 + 28 * q^56 - 32 * q^60 - 112 * q^74 + 48 * q^81 - 28 * q^84 + 56 * q^85 + 8 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−1.36843	+	0.356944i	−0.967624	+	0.252398i
$2$	−1.36843	+	0.356944i	−0.967624	+	0.252398i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.74518	−	0.976904i	0.872591	−	0.488452i
$5$	1.65234	+	1.50657i	0.738950	+	0.673761i
$5$	1.65234	+	1.50657i	0.738950	+	0.673761i
$6$	0.356944	+	1.36843i	0.145722	+	0.558658i
$7$	−2.07310	+	1.64386i	−0.783556	+	0.621321i
$7$	−2.07310	+	1.64386i	−0.783556	+	0.621321i
$8$	−2.03945	+	1.95975i	−0.721055	+	0.692878i
$9$	−1.00000			−0.333333
$10$	−2.79887	−	1.47184i	−0.885081	−	0.465437i
$11$			4.97024i			1.49858i	0.662240	+	0.749292i	$0.269606\pi$
$11$			4.97024i			1.49858i	−0.662240	+	0.749292i	$0.730394\pi$
$12$	−0.976904	−	1.74518i	−0.282008	−	0.503791i
$13$	−5.35119			−1.48415			−0.742077	−	0.670315i	$-0.766159\pi$
$13$	−5.35119			−1.48415			−0.742077	+	0.670315i	$0.766159\pi$
$14$	2.25011	−	2.98948i	0.601368	−	0.798972i
$15$	1.50657	−	1.65234i	0.388996	−	0.426633i
$16$	2.09132	−	3.40975i	0.522829	−	0.852437i
$17$	−3.34087			−0.810280			−0.405140	−	0.914255i	$-0.632777\pi$
$17$	−3.34087			−0.810280			−0.405140	+	0.914255i	$0.632777\pi$
$18$	1.36843	−	0.356944i	0.322541	−	0.0841326i
$19$	−2.12411			−0.487305			−0.243653	−	0.969863i	$-0.578346\pi$
$19$	−2.12411			−0.487305			−0.243653	+	0.969863i	$0.578346\pi$
$20$	4.35541	+	1.01507i	0.973900	+	0.226976i
$21$	1.64386	+	2.07310i	0.358720	+	0.452386i
$22$	−1.77410	−	6.80140i	−0.378239	−	1.45006i
$23$	6.71438			1.40004			0.700022	−	0.714121i	$-0.253173\pi$
$23$	6.71438			1.40004			0.700022	+	0.714121i	$0.253173\pi$
$24$	1.95975	+	2.03945i	0.400033	+	0.416301i
$25$	0.460466	+	4.97875i	0.0920932	+	0.995750i
$26$	7.32271	−	1.91008i	1.43610	−	0.374597i
$27$			1.00000i			0.192450i
$28$	−2.01203	+	4.89405i	−0.380239	+	0.924888i
$29$	−1.42645			−0.264885			−0.132443	−	0.991191i	$-0.542282\pi$
$29$	−1.42645			−0.264885			−0.132443	+	0.991191i	$0.542282\pi$
$30$	−1.47184	+	2.79887i	−0.268720	+	0.511002i
$31$	−5.76942			−1.03622			−0.518109	−	0.855315i	$-0.673364\pi$
$31$	−5.76942			−1.03622			−0.518109	+	0.855315i	$0.673364\pi$
$32$	−1.64472	+	5.41248i	−0.290749	+	0.956799i
$33$	4.97024			0.865207
$34$	4.57174	−	1.19250i	0.784046	−	0.204513i
$35$	−5.90206	−	0.407054i	−0.997630	−	0.0688047i
$36$	−1.74518	+	0.976904i	−0.290864	+	0.162817i
$37$		−	0.864770i		−	0.142167i	−0.997470	−	0.0710836i	$-0.977354\pi$
$37$		−	0.864770i		−	0.142167i	0.997470	−	0.0710836i	$-0.0226457\pi$
$38$	2.90669	−	0.758191i	0.471528	−	0.122995i
$39$			5.35119i			0.856876i
$40$	−6.32239	+	0.165596i	−0.999657	+	0.0261831i
$41$			1.68563i			0.263252i	0.991299	+	0.131626i	$0.0420198\pi$
$41$			1.68563i			0.263252i	−0.991299	+	0.131626i	$0.957980\pi$
$42$	−2.98948	−	2.25011i	−0.461287	−	0.347200i
$43$	5.29678			0.807751			0.403876	−	0.914814i	$-0.367663\pi$
$43$	5.29678			0.807751			0.403876	+	0.914814i	$0.367663\pi$
$44$	4.85545	+	8.67397i	0.731986	+	1.30765i
$45$	−1.65234	−	1.50657i	−0.246317	−	0.224587i
$46$	−9.18813	+	2.39666i	−1.35472	+	0.353368i
$47$			8.84199i			1.28974i	0.764293	+	0.644869i	$0.223088\pi$
$47$			8.84199i			1.28974i	−0.764293	+	0.644869i	$0.776912\pi$
$48$	−3.40975	−	2.09132i	−0.492155	−	0.301856i
$49$	1.59545	−	6.81576i	0.227921	−	0.973680i
$50$	−2.40725	−	6.64869i	−0.340437	−	0.940267i
$51$			3.34087i			0.467815i
$52$	−9.33880	+	5.22760i	−1.29506	+	0.724938i
$53$			10.1805i			1.39839i	0.714930	+	0.699197i	$0.246459\pi$
$53$			10.1805i			1.39839i	−0.714930	+	0.699197i	$0.753541\pi$
$54$	−0.356944	−	1.36843i	−0.0485740	−	0.186219i
$55$	−7.48803	+	8.21253i	−1.00969	+	1.10738i
$56$	1.00642	−	7.41533i	0.134488	−	0.990915i
$57$			2.12411i			0.281346i
$58$	1.95199	−	0.509164i	0.256309	−	0.0668565i
$59$	4.51007			0.587162			0.293581	−	0.955934i	$-0.405153\pi$
$59$	4.51007			0.587162			0.293581	+	0.955934i	$0.405153\pi$
$60$	1.01507	−	4.35541i	0.131045	−	0.562282i
$61$		−	3.54820i		−	0.454300i	−0.973860	−	0.227150i	$-0.927059\pi$
$61$		−	3.54820i		−	0.454300i	0.973860	−	0.227150i	$-0.0729408\pi$
$62$	7.89503	−	2.05936i	1.00267	−	0.261539i
$63$	2.07310	−	1.64386i	0.261185	−	0.207107i
$64$	0.318730	−	7.99365i	0.0398412	−	0.999206i
$65$	−8.84199	−	8.06197i	−1.09671	−	0.999964i
$66$	−6.80140	+	1.77410i	−0.837195	+	0.218376i
$67$	0.310390			0.0379202			0.0189601	−	0.999820i	$-0.493964\pi$
$67$	0.310390			0.0379202			0.0189601	+	0.999820i	$0.493964\pi$
$68$	−5.83043	+	3.26371i	−0.707043	+	0.395783i
$69$		−	6.71438i		−	0.808316i
$70$	8.22183	−	1.54968i	0.982697	−	0.185223i
$71$		−	4.74826i		−	0.563514i	−0.959486	−	0.281757i	$-0.909083\pi$
$71$		−	4.74826i		−	0.563514i	0.959486	−	0.281757i	$-0.0909173\pi$
$72$	2.03945	−	1.95975i	0.240352	−	0.230959i
$73$	12.2187			1.43009			0.715047	−	0.699077i	$-0.246405\pi$
$73$	12.2187			1.43009			0.715047	+	0.699077i	$0.246405\pi$
$74$	0.308675	+	1.18337i	0.0358827	+	0.137564i
$75$	4.97875	−	0.460466i	0.574897	−	0.0531701i
$76$	−3.70697	+	2.07506i	−0.425218	+	0.238025i
$77$	−8.17037	−	10.3038i	−0.931101	−	1.17422i
$78$	−1.91008	−	7.32271i	−0.216274	−	0.829134i
$79$			9.38349i			1.05573i	0.849330	+	0.527863i	$0.177006\pi$
$79$			9.38349i			1.05573i	−0.849330	+	0.527863i	$0.822994\pi$
$80$	8.59261	−	2.48335i	0.960683	−	0.277647i
$81$	1.00000			0.111111
$82$	−0.601678	−	2.30667i	−0.0664442	−	0.254729i
$83$		−	6.05979i		−	0.665149i	−0.943077	−	0.332574i	$-0.892083\pi$
$83$		−	6.05979i		−	0.665149i	0.943077	−	0.332574i	$-0.107917\pi$
$84$	4.89405	+	2.01203i	0.533985	+	0.219531i
$85$	−5.52026	−	5.03327i	−0.598756	−	0.545935i
$86$	−7.24825	+	1.89065i	−0.781599	+	0.203875i
$87$			1.42645i			0.152932i
$88$	−9.74044	−	10.1366i	−1.03833	−	1.08056i
$89$		−	3.30075i		−	0.349879i	−0.984579	−	0.174940i	$-0.944027\pi$
$89$		−	3.30075i		−	0.349879i	0.984579	−	0.174940i	$-0.0559730\pi$
$90$	2.79887	+	1.47184i	0.295027	+	0.155146i
$91$	11.0935	−	8.79661i	1.16292	−	0.922135i
$92$	11.7178	−	6.55930i	1.22167	−	0.683854i
$93$			5.76942i			0.598261i
$94$	−3.15610	−	12.0996i	−0.325527	−	1.24798i
$95$	−3.50976	−	3.20014i	−0.360094	−	0.328327i
$96$	5.41248	+	1.64472i	0.552408	+	0.167864i
$97$	5.32789			0.540965			0.270483	−	0.962725i	$-0.412817\pi$
$97$	5.32789			0.540965			0.270483	+	0.962725i	$0.412817\pi$
$98$	0.249591	+	9.89635i	0.0252125	+	0.999682i
$99$		−	4.97024i		−	0.499528i
$100$	5.66736	+	8.23899i	0.566736	+	0.823899i
$101$			13.3387i			1.32725i	0.748067	+	0.663624i	$0.230982\pi$
$101$			13.3387i			1.32725i	−0.748067	+	0.663624i	$0.769018\pi$
$102$	−1.19250	−	4.57174i	−0.118076	−	0.452669i
$103$		−	4.36679i		−	0.430272i	−0.976584	−	0.215136i	$-0.930980\pi$
$103$		−	4.36679i		−	0.430272i	0.976584	−	0.215136i	$-0.0690195\pi$
$104$	10.9135	−	10.4870i	1.07016	−	1.02834i
$105$	−0.407054	+	5.90206i	−0.0397244	+	0.575982i
$106$	−3.63386	−	13.9312i	−0.352951	−	1.35312i
$107$	11.6355			1.12485			0.562423	−	0.826850i	$-0.309869\pi$
$107$	11.6355			1.12485			0.562423	+	0.826850i	$0.309869\pi$
$108$	0.976904	+	1.74518i	0.0940026	+	0.167930i
$109$	20.5529			1.96861			0.984305	−	0.176478i	$-0.0564703\pi$
$109$	20.5529			1.96861			0.984305	+	0.176478i	$0.0564703\pi$
$110$	7.31541	−	13.9111i	0.697497	−	1.32637i
$111$	−0.864770			−0.0820803
$112$	1.26965	+	10.5066i	0.119971	+	0.992777i
$113$		−	17.0252i		−	1.60159i	−0.598937	−	0.800796i	$-0.704410\pi$
$113$		−	17.0252i		−	1.60159i	0.598937	−	0.800796i	$-0.295590\pi$
$114$	−0.758191	−	2.90669i	−0.0710111	−	0.272237i
$115$	11.0944	+	10.1157i	1.03456	+	0.943295i
$116$	−2.48942	+	1.39351i	−0.231137	+	0.129384i
$117$	5.35119			0.494718
$118$	−6.17171	+	1.60985i	−0.568152	+	0.148198i
$119$	6.92594	−	5.49192i	0.634900	−	0.503444i
$120$	0.165596	+	6.32239i	0.0151168	+	0.577152i
$121$	−13.7033			−1.24575
$122$	1.26651	+	4.85545i	0.114664	+	0.439591i
$123$	1.68563			0.151989
$124$	−10.0687	+	5.63617i	−0.904195	+	0.506143i
$125$	−6.74001	+	8.92033i	−0.602845	+	0.797858i
$126$	−2.25011	+	2.98948i	−0.200456	+	0.266324i
$127$	−19.8108			−1.75793			−0.878964	−	0.476888i	$-0.841765\pi$
$127$	−19.8108			−1.75793			−0.878964	+	0.476888i	$0.841765\pi$
$128$	2.41713	+	11.0525i	0.213646	+	0.976911i
$129$		−	5.29678i		−	0.466355i
$130$	14.9773	+	7.87611i	1.31360	+	0.690780i
$131$	−18.0138			−1.57388			−0.786938	−	0.617032i	$-0.788335\pi$
$131$	−18.0138			−1.57388			−0.786938	+	0.617032i	$0.788335\pi$
$132$	8.67397	−	4.85545i	0.754972	−	0.422612i
$133$	4.40349	−	3.49175i	0.381831	−	0.302773i
$134$	−0.424746	+	0.110792i	−0.0366925	+	0.00957098i
$135$	−1.50657	+	1.65234i	−0.129665	+	0.142211i
$136$	6.81355	−	6.54728i	0.584257	−	0.561425i
$137$			3.66018i			0.312710i	0.987701	+	0.156355i	$0.0499744\pi$
$137$			3.66018i			0.312710i	−0.987701	+	0.156355i	$0.950026\pi$
$138$	2.39666	+	9.18813i	0.204017	+	0.782146i
$139$	0.740858			0.0628387			0.0314194	−	0.999506i	$-0.489997\pi$
$139$	0.740858			0.0628387			0.0314194	+	0.999506i	$0.489997\pi$
$140$	−10.6978	+	5.05536i	−0.904131	+	0.427256i
$141$	8.84199			0.744630
$142$	1.69486	+	6.49764i	0.142230	+	0.545270i
$143$		−	26.5967i		−	2.22413i
$144$	−2.09132	+	3.40975i	−0.174276	+	0.284146i
$145$	−2.35699	−	2.14906i	−0.195737	−	0.178469i
$146$	−16.7204	+	4.36140i	−1.38379	+	0.360952i
$147$	−6.81576	−	1.59545i	−0.562154	−	0.131590i
$148$	−0.844797	−	1.50918i	−0.0694419	−	0.124054i
$149$	−9.14899			−0.749514			−0.374757	−	0.927123i	$-0.622274\pi$
$149$	−9.14899			−0.749514			−0.374757	+	0.927123i	$0.622274\pi$
$150$	−6.64869	+	2.40725i	−0.542864	+	0.196551i
$151$		−	9.54599i		−	0.776841i	−0.921482	−	0.388421i	$-0.873021\pi$
$151$		−	9.54599i		−	0.776841i	0.921482	−	0.388421i	$-0.126979\pi$
$152$	4.33203	−	4.16274i	0.351374	−	0.337643i
$153$	3.34087			0.270093
$154$	14.8584	+	11.1836i	1.19733	+	0.901199i
$155$	−9.53305	−	8.69206i	−0.765713	−	0.698163i
$156$	5.22760	+	9.33880i	0.418543	+	0.747702i
$157$	−5.51368			−0.440040			−0.220020	−	0.975495i	$-0.570612\pi$
$157$	−5.51368			−0.440040			−0.220020	+	0.975495i	$0.570612\pi$
$158$	−3.34938	−	12.8406i	−0.266463	−	1.02154i
$159$	10.1805			0.807363
$160$	−10.8719	+	6.46536i	−0.859502	+	0.511132i
$161$	−13.9195	+	11.0375i	−1.09701	+	0.869876i
$162$	−1.36843	+	0.356944i	−0.107514	+	0.0280442i
$163$	6.67293			0.522665			0.261332	−	0.965249i	$-0.415838\pi$
$163$	6.67293			0.522665			0.261332	+	0.965249i	$0.415838\pi$
$164$	1.64670	+	2.94174i	0.128586	+	0.229711i
$165$	8.21253	+	7.48803i	0.639345	+	0.582943i
$166$	2.16301	+	8.29238i	0.167882	+	0.643614i
$167$		−	0.444207i		−	0.0343737i	−0.999852	−	0.0171869i	$-0.994529\pi$
$167$		−	0.444207i		−	0.0343737i	0.999852	−	0.0171869i	$-0.00547102\pi$
$168$	−7.41533	−	1.00642i	−0.572105	−	0.0776468i
$169$	15.6352			1.20271
$170$	9.35067	+	4.91724i	0.717163	+	0.377135i
$171$	2.12411			0.162435
$172$	9.24384	−	5.17444i	0.704836	−	0.394548i
$173$	−18.4717			−1.40437			−0.702187	−	0.711992i	$-0.747793\pi$
$173$	−18.4717			−1.40437			−0.702187	+	0.711992i	$0.747793\pi$
$174$	−0.509164	−	1.95199i	−0.0385996	−	0.147980i
$175$	−9.13896	−	9.56449i	−0.690841	−	0.723007i
$176$	16.9473	+	10.3943i	1.27745	+	0.783503i
$177$		−	4.51007i		−	0.338998i
$178$	1.17819	+	4.51684i	0.0883087	+	0.338551i
$179$			5.94123i			0.444069i	0.975039	+	0.222034i	$0.0712697\pi$
$179$			5.94123i			0.444069i	−0.975039	+	0.222034i	$0.928730\pi$
$180$	−4.35541	−	1.01507i	−0.324633	−	0.0756586i
$181$		−	8.08638i		−	0.601056i	−0.953773	−	0.300528i	$-0.902837\pi$
$181$		−	8.08638i		−	0.601056i	0.953773	−	0.300528i	$-0.0971629\pi$
$182$	−12.0408	+	15.9973i	−0.892522	+	1.18580i
$183$	−3.54820			−0.262290
$184$	−13.6936	+	13.1585i	−1.00951	+	0.970059i
$185$	1.30284	−	1.42890i	0.0957867	−	0.105054i
$186$	−2.05936	−	7.89503i	−0.151000	−	0.578891i
$187$		−	16.6049i		−	1.21427i
$188$	8.63778	+	15.4309i	0.629975	+	1.12541i
$189$	−1.64386	−	2.07310i	−0.119573	−	0.150795i
$190$	5.94512	+	3.12636i	0.431305	+	0.226810i
$191$			0.655244i			0.0474118i	0.999719	+	0.0237059i	$0.00754653\pi$
$191$			0.655244i			0.0474118i	−0.999719	+	0.0237059i	$0.992453\pi$
$192$	−7.99365	−	0.318730i	−0.576892	−	0.0230023i
$193$			5.96835i			0.429611i	0.976657	+	0.214806i	$0.0689118\pi$
$193$			5.96835i			0.429611i	−0.976657	+	0.214806i	$0.931088\pi$
$194$	−7.29083	+	1.90176i	−0.523451	+	0.136538i
$195$	−8.06197	+	8.84199i	−0.577329	+	0.633188i
$196$	−3.87399	−	13.4533i	−0.276714	−	0.960952i
$197$			18.7547i			1.33622i	0.744064	+	0.668109i	$0.232896\pi$
$197$			18.7547i			1.33622i	−0.744064	+	0.668109i	$0.767104\pi$
$198$	1.77410	+	6.80140i	0.126080	+	0.483355i
$199$	2.45854			0.174282			0.0871408	−	0.996196i	$-0.472227\pi$
$199$	2.45854			0.174282			0.0871408	+	0.996196i	$0.472227\pi$
$200$	−10.6962	−	9.25153i	−0.756337	−	0.654182i
$201$		−	0.310390i		−	0.0218932i
$202$	−4.76116	−	18.2530i	−0.334994	−	1.28428i
$203$	2.95717	−	2.34489i	0.207553	−	0.164579i
$204$	3.26371	+	5.83043i	0.228505	+	0.408211i
$205$	−2.53953	+	2.78524i	−0.177369	+	0.194530i
$206$	1.55870	+	5.97563i	0.108600	+	0.416342i
$207$	−6.71438			−0.466681
$208$	−11.1910	+	18.2462i	−0.775959	+	1.26515i
$209$		−	10.5574i		−	0.730267i
$210$	−1.54968	−	8.22183i	−0.106938	−	0.567360i
$211$			7.92825i			0.545804i	0.962042	+	0.272902i	$0.0879834\pi$
$211$			7.92825i			0.545804i	−0.962042	+	0.272902i	$0.912017\pi$
$212$	9.94533	+	17.7667i	0.683048	+	1.22022i
$213$	−4.74826			−0.325345
$214$	−15.9223	+	4.15322i	−1.08843	+	0.283908i
$215$	8.75209	+	7.97999i	0.596887	+	0.544231i
$216$	−1.95975	−	2.03945i	−0.133344	−	0.138767i
$217$	11.9606	−	9.48412i	0.811935	−	0.643824i
$218$	−28.1251	+	7.33624i	−1.90487	+	0.496873i
$219$		−	12.2187i		−	0.825665i
$220$	−5.04512	+	21.6474i	−0.340142	+	1.45947i
$221$	17.8776			1.20258
$222$	1.18337	−	0.308675i	0.0794229	−	0.0207169i
$223$		−	12.4786i		−	0.835630i	−0.908532	−	0.417815i	$-0.862796\pi$
$223$		−	12.4786i		−	0.835630i	0.908532	−	0.417815i	$-0.137204\pi$
$224$	−5.48768	−	13.9243i	−0.366661	−	0.930354i
$225$	−0.460466	−	4.97875i	−0.0306977	−	0.331917i
$226$	6.07703	+	23.2977i	0.404238	+	1.54974i
$227$			18.5529i			1.23140i	0.787981	+	0.615699i	$0.211126\pi$
$227$			18.5529i			1.23140i	−0.787981	+	0.615699i	$0.788874\pi$
$228$	2.07506	+	3.70697i	0.137424	+	0.245500i
$229$			29.1494i			1.92625i	0.269058	+	0.963124i	$0.413288\pi$
$229$			29.1494i			1.92625i	−0.269058	+	0.963124i	$0.586712\pi$
$230$	−18.7927	−	9.88250i	−1.23915	−	0.651633i
$231$	−10.3038	+	8.17037i	−0.677939	+	0.537571i
$232$	2.90918	−	2.79549i	0.190997	−	0.183533i
$233$		−	10.0714i		−	0.659801i	−0.944016	−	0.329900i	$-0.892985\pi$
$233$		−	10.0714i		−	0.659801i	0.944016	−	0.329900i	$-0.107015\pi$
$234$	−7.32271	+	1.91008i	−0.478700	+	0.124866i
$235$	−13.3211	+	14.6100i	−0.868974	+	0.953051i
$236$	7.87090	−	4.40591i	0.512352	−	0.286800i
$237$	9.38349			0.609523
$238$	−7.51733	+	9.98747i	−0.487276	+	0.647391i
$239$		−	8.54285i		−	0.552591i	−0.961073	−	0.276296i	$-0.910893\pi$
$239$		−	8.54285i		−	0.552591i	0.961073	−	0.276296i	$-0.0891069\pi$
$240$	−2.48335	−	8.59261i	−0.160299	−	0.554651i
$241$		−	18.4140i		−	1.18615i	−0.805146	−	0.593076i	$-0.797913\pi$
$241$		−	18.4140i		−	1.18615i	0.805146	−	0.593076i	$-0.202087\pi$
$242$	18.7519	−	4.89130i	1.20542	−	0.314425i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.46625	−	6.19225i	−0.221904	−	0.396418i
$245$	12.9047	−	8.85830i	0.824449	−	0.565936i
$246$	−2.30667	+	0.601678i	−0.147068	+	0.0383616i
$247$	11.3665			0.723236
$248$	11.7665	−	11.3066i	0.747171	−	0.717972i
$249$	−6.05979			−0.384024
$250$	6.03915	−	14.6126i	0.381950	−	0.924183i
$251$	23.7250			1.49751			0.748753	−	0.662849i	$-0.230653\pi$
$251$	23.7250			1.49751			0.748753	+	0.662849i	$0.230653\pi$
$252$	2.01203	−	4.89405i	0.126746	−	0.308296i
$253$			33.3720i			2.09808i
$254$	27.1097	−	7.07137i	1.70101	−	0.443697i
$255$	−5.03327	+	5.52026i	−0.315196	+	0.345692i
$256$	−7.25279	−	14.2617i	−0.453299	−	0.891358i
$257$	−6.43711			−0.401536			−0.200768	−	0.979639i	$-0.564344\pi$
$257$	−6.43711			−0.401536			−0.200768	+	0.979639i	$0.564344\pi$
$258$	1.89065	+	7.24825i	0.117707	+	0.451256i
$259$	1.42156	+	1.79275i	0.0883315	+	0.111396i
$260$	−23.3067	−	5.43182i	−1.44542	−	0.336867i
$261$	1.42645			0.0882951
$262$	24.6506	−	6.42994i	1.52292	−	0.397243i
$263$	−7.75540			−0.478218			−0.239109	−	0.970993i	$-0.576855\pi$
$263$	−7.75540			−0.478218			−0.239109	+	0.970993i	$0.576855\pi$
$264$	−10.1366	+	9.74044i	−0.623862	+	0.599483i
$265$	−15.3376	+	16.8216i	−0.942182	+	1.03334i
$266$	−4.77950	+	6.35000i	−0.293050	+	0.389343i
$267$	−3.30075			−0.202003
$268$	0.541688	−	0.303222i	0.0330888	−	0.0185222i
$269$			10.8864i			0.663756i	0.943322	+	0.331878i	$0.107682\pi$
$269$			10.8864i			0.663756i	−0.943322	+	0.331878i	$0.892318\pi$
$270$	1.47184	−	2.79887i	0.0895735	−	0.170334i
$271$	28.1065			1.70735			0.853675	−	0.520807i	$-0.174369\pi$
$271$	28.1065			1.70735			0.853675	+	0.520807i	$0.174369\pi$
$272$	−6.98682	+	11.3915i	−0.423638	+	0.690713i
$273$	−8.79661	−	11.0935i	−0.532395	−	0.671411i
$274$	−1.30648	−	5.00869i	−0.0789274	−	0.302586i
$275$	−24.7456	+	2.28863i	−1.49221	+	0.138009i
$276$	−6.55930	−	11.7178i	−0.394824	−	0.705329i
$277$			27.8836i			1.67536i	0.546161	+	0.837680i	$0.316089\pi$
$277$			27.8836i			1.67536i	−0.546161	+	0.837680i	$0.683911\pi$
$278$	−1.01381	+	0.264445i	−0.0608042	+	0.0158604i
$279$	5.76942			0.345406
$280$	12.8347	−	10.7364i	0.767020	−	0.641624i
$281$	15.9615			0.952180			0.476090	−	0.879396i	$-0.342054\pi$
$281$	15.9615			0.952180			0.476090	+	0.879396i	$0.342054\pi$
$282$	−12.0996	+	3.15610i	−0.720522	+	0.187943i
$283$		−	23.8111i		−	1.41542i	−0.706502	−	0.707711i	$-0.749728\pi$
$283$		−	23.8111i		−	1.41542i	0.706502	−	0.707711i	$-0.250272\pi$
$284$	−4.63859	−	8.28657i	−0.275250	−	0.491718i
$285$	−3.20014	+	3.50976i	−0.189560	+	0.207900i
$286$	9.49354	+	36.3956i	0.561365	+	2.15212i
$287$	−2.77095	−	3.49448i	−0.163564	−	0.206273i
$288$	1.64472	−	5.41248i	0.0969162	−	0.318933i
$289$	−5.83858			−0.343446
$290$	3.99245	+	2.09951i	0.234445	+	0.123288i
$291$		−	5.32789i		−	0.312326i
$292$	21.3239	−	11.9365i	1.24789	−	0.698532i
$293$	30.8384			1.80160			0.900798	−	0.434237i	$-0.142982\pi$
$293$	30.8384			1.80160			0.900798	+	0.434237i	$0.142982\pi$
$294$	9.89635	−	0.249591i	0.577167	−	0.0145565i
$295$	7.45218	+	6.79476i	0.433883	+	0.395606i
$296$	1.69474	+	1.76366i	0.0985045	+	0.102510i
$297$	−4.97024			−0.288402
$298$	12.5197	−	3.26568i	0.725248	−	0.189176i
$299$	−35.9299			−2.07788
$300$	8.23899	−	5.66736i	0.475679	−	0.327205i
$301$	−10.9807	+	8.70716i	−0.632919	+	0.501872i
$302$	3.40739	+	13.0630i	0.196073	+	0.751690i
$303$	13.3387			0.766287
$304$	−4.44220	+	7.24270i	−0.254777	+	0.415397i
$305$	5.34562	−	5.86283i	0.306089	−	0.335705i
$306$	−4.57174	+	1.19250i	−0.261349	+	0.0681710i
$307$		−	4.80160i		−	0.274042i	−0.990568	−	0.137021i	$-0.956247\pi$
$307$		−	4.80160i		−	0.274042i	0.990568	−	0.137021i	$-0.0437528\pi$
$308$	−24.3246	−	10.0003i	−1.38602	−	0.569819i
$309$	−4.36679			−0.248418
$310$	16.1479	+	8.49168i	0.917137	+	0.482295i
$311$	5.82773			0.330460			0.165230	−	0.986255i	$-0.447163\pi$
$311$	5.82773			0.330460			0.165230	+	0.986255i	$0.447163\pi$
$312$	−10.4870	−	10.9135i	−0.593710	−	0.617855i
$313$	1.05286			0.0595111			0.0297556	−	0.999557i	$-0.490527\pi$
$313$	1.05286			0.0595111			0.0297556	+	0.999557i	$0.490527\pi$
$314$	7.54507	−	1.96808i	0.425793	−	0.111065i
$315$	5.90206	+	0.407054i	0.332543	+	0.0229349i
$316$	9.16677	+	16.3759i	0.515671	+	0.921216i
$317$			2.12872i			0.119561i	0.998212	+	0.0597804i	$0.0190400\pi$
$317$			2.12872i			0.119561i	−0.998212	+	0.0597804i	$0.980960\pi$
$318$	−13.9312	+	3.63386i	−0.781223	+	0.203776i
$319$		−	7.08980i		−	0.396953i
$320$	12.5697	−	12.7280i	0.702666	−	0.711520i
$321$		−	11.6355i		−	0.649430i
$322$	15.1081	−	20.0725i	0.841941	−	1.11860i
$323$	7.09639			0.394854
$324$	1.74518	−	0.976904i	0.0969545	−	0.0542724i
$325$	−2.46404	−	26.6422i	−0.136680	−	1.47785i
$326$	−9.13142	+	2.38187i	−0.505743	+	0.131919i
$327$		−	20.5529i		−	1.13658i
$328$	−3.30343	−	3.43777i	−0.182401	−	0.189819i
$329$	−14.5350	−	18.3303i	−0.801341	−	1.01058i
$330$	−13.9111	−	7.31541i	−0.765778	−	0.402700i
$331$			3.69852i			0.203289i	0.994821	+	0.101645i	$0.0324105\pi$
$331$			3.69852i			0.203289i	−0.994821	+	0.101645i	$0.967590\pi$
$332$	−5.91984	−	10.5754i	−0.324893	−	0.580403i
$333$			0.864770i			0.0473891i
$334$	0.158557	+	0.607864i	0.00867585	+	0.0332608i
$335$	0.512871	+	0.467626i	0.0280211	+	0.0255491i
$336$	10.5066	−	1.26965i	0.573180	−	0.0692652i
$337$		−	30.0724i		−	1.63815i	−0.573687	−	0.819075i	$-0.694487\pi$
$337$		−	30.0724i		−	1.63815i	0.573687	−	0.819075i	$-0.305513\pi$
$338$	−21.3957	+	5.58091i	−1.16377	+	0.303561i
$339$	−17.0252			−0.924680
$340$	−14.5509	−	3.39121i	−0.789132	−	0.183914i
$341$		−	28.6754i		−	1.55286i
$342$	−2.90669	+	0.758191i	−0.157176	+	0.0409983i
$343$	7.89663	+	16.7524i	0.426378	+	0.904545i
$344$	−10.8025	+	10.3804i	−0.582433	+	0.559673i
$345$	10.1157	−	11.0944i	0.544611	−	0.597305i
$346$	25.2771	−	6.59335i	1.35891	−	0.354461i
$347$	13.6306			0.731729			0.365865	−	0.930668i	$-0.380773\pi$
$347$	13.6306			0.731729			0.365865	+	0.930668i	$0.380773\pi$
$348$	1.39351	+	2.48942i	0.0746998	+	0.133447i
$349$			33.6876i			1.80326i	0.432512	+	0.901628i	$0.357627\pi$
$349$			33.6876i			1.80326i	−0.432512	+	0.901628i	$0.642373\pi$
$350$	15.9200	+	9.82619i	0.850959	+	0.525232i
$351$		−	5.35119i		−	0.285625i
$352$	−26.9013	−	8.17466i	−1.43384	−	0.435711i
$353$	17.9280			0.954209			0.477105	−	0.878847i	$-0.341686\pi$
$353$	17.9280			0.954209			0.477105	+	0.878847i	$0.341686\pi$
$354$	1.60985	+	6.17171i	0.0855623	+	0.328022i
$355$	7.15360	−	7.84574i	0.379674	−	0.416409i
$356$	−3.22452	−	5.76041i	−0.170899	−	0.305301i
$357$	−5.49192	−	6.92594i	−0.290663	−	0.366560i
$358$	−2.12069	−	8.13014i	−0.112082	−	0.429691i
$359$			9.46725i			0.499662i	0.968289	+	0.249831i	$0.0803751\pi$
$359$			9.46725i			0.499662i	−0.968289	+	0.249831i	$0.919625\pi$
$360$	6.32239	−	0.165596i	0.333219	−	0.00872769i
$361$	−14.4881			−0.762534
$362$	2.88639	+	11.0656i	0.151705	+	0.581596i
$363$			13.7033i			0.719235i
$364$	10.7668	−	26.1890i	0.564332	−	1.37268i
$365$	20.1895	+	18.4084i	1.05677	+	0.963541i
$366$	4.85545	−	1.26651i	0.253798	−	0.0662015i
$367$			27.8246i			1.45243i	0.687466	+	0.726216i	$0.258723\pi$
$367$			27.8246i			1.45243i	−0.687466	+	0.726216i	$0.741277\pi$
$368$	14.0419	−	22.8943i	0.731984	−	1.19345i
$369$		−	1.68563i		−	0.0877506i
$370$	−1.27280	+	2.42038i	−0.0661700	+	0.125830i
$371$	−16.7352	−	21.1051i	−0.868851	−	1.09572i
$372$	5.63617	+	10.0687i	0.292222	+	0.522037i
$373$		−	28.0722i		−	1.45352i	−0.686889	−	0.726762i	$-0.741024\pi$
$373$		−	28.0722i		−	1.45352i	0.686889	−	0.726762i	$-0.258976\pi$
$374$	5.92703	+	22.7226i	0.306480	+	1.17496i
$375$	8.92033	+	6.74001i	0.460644	+	0.348053i
$376$	−17.3281	−	18.0328i	−0.893630	−	0.929972i
$377$	7.63321			0.393131
$378$	2.98948	+	2.25011i	0.153762	+	0.115733i
$379$			19.7679i			1.01541i	0.861531	+	0.507705i	$0.169506\pi$
$379$			19.7679i			1.01541i	−0.861531	+	0.507705i	$0.830494\pi$
$380$	−9.25140	−	2.15612i	−0.474587	−	0.110607i
$381$			19.8108i			1.01494i
$382$	−0.233886	−	0.896654i	−0.0119666	−	0.0458768i
$383$			29.5142i			1.50811i	0.656814	+	0.754053i	$0.271904\pi$
$383$			29.5142i			1.50811i	−0.656814	+	0.754053i	$0.728096\pi$
$384$	11.0525	−	2.41713i	0.564020	−	0.123349i
$385$	2.02316	−	29.3346i	0.103110	−	1.49503i
$386$	−2.13037	−	8.16725i	−0.108433	−	0.415702i
$387$	−5.29678			−0.269250
$388$	9.29814	−	5.20484i	0.472041	−	0.264236i
$389$	−2.16003			−0.109518			−0.0547589	−	0.998500i	$-0.517439\pi$
$389$	−2.16003			−0.109518			−0.0547589	+	0.998500i	$0.517439\pi$
$390$	7.87611	−	14.9773i	0.398822	−	0.758405i
$391$	−22.4319			−1.13443
$392$	10.1034	+	17.0271i	0.510297	+	0.859998i
$393$			18.0138i			0.908678i
$394$	−6.69438	−	25.6644i	−0.337258	−	1.29296i
$395$	−14.1369	+	15.5047i	−0.711306	+	0.780128i
$396$	−4.85545	−	8.67397i	−0.243995	−	0.435883i
$397$	5.56028			0.279063			0.139531	−	0.990218i	$-0.455440\pi$
$397$	5.56028			0.279063			0.139531	+	0.990218i	$0.455440\pi$
$398$	−3.36434	+	0.877564i	−0.168639	+	0.0439883i
$399$	−3.49175	−	4.40349i	−0.174806	−	0.220450i
$400$	17.9393	+	8.84207i	0.896964	+	0.442104i
$401$	−16.1551			−0.806747			−0.403374	−	0.915035i	$-0.632162\pi$
$401$	−16.1551			−0.806747			−0.403374	+	0.915035i	$0.632162\pi$
$402$	0.110792	+	0.424746i	0.00552581	+	0.0211844i
$403$	30.8733			1.53791
$404$	13.0306	+	23.2784i	0.648297	+	1.15814i
$405$	1.65234	+	1.50657i	0.0821055	+	0.0748623i
$406$	−3.20968	+	4.26435i	−0.159294	+	0.211636i
$407$	4.29811			0.213049
$408$	−6.54728	−	6.81355i	−0.324139	−	0.337321i
$409$			4.78252i			0.236480i	0.992985	+	0.118240i	$0.0377253\pi$
$409$			4.78252i			0.236480i	−0.992985	+	0.118240i	$0.962275\pi$
$410$	2.48099	−	4.71787i	0.122527	−	0.232999i
$411$	3.66018			0.180543
$412$	−4.26593	−	7.62084i	−0.210167	−	0.375452i
$413$	−9.34981	+	7.41393i	−0.460074	+	0.364816i
$414$	9.18813	−	2.39666i	0.451572	−	0.117789i
$415$	9.12953	−	10.0128i	0.448151	−	0.491511i
$416$	8.80122	−	28.9632i	0.431515	−	1.42004i
$417$		−	0.740858i		−	0.0362800i
$418$	3.76839	+	14.4470i	0.184318	+	0.706624i
$419$	28.4752			1.39111			0.695553	−	0.718475i	$-0.255159\pi$
$419$	28.4752			1.39111			0.695553	+	0.718475i	$0.255159\pi$
$420$	5.05536	+	10.6978i	0.246676	+	0.522000i
$421$	−3.07907			−0.150065			−0.0750323	−	0.997181i	$-0.523906\pi$
$421$	−3.07907			−0.150065			−0.0750323	+	0.997181i	$0.523906\pi$
$422$	−2.82995	−	10.8492i	−0.137760	−	0.528132i
$423$		−	8.84199i		−	0.429912i
$424$	−19.9512	−	20.7626i	−0.968915	−	1.00832i
$425$	−1.53836	−	16.6334i	−0.0746213	−	0.806837i
$426$	6.49764	−	1.69486i	0.314812	−	0.0821164i
$427$	5.83274	+	7.35575i	0.282266	+	0.355970i
$428$	20.3060	−	11.3668i	0.981530	−	0.549433i
$429$	−26.5967			−1.28410
$430$	−14.8250	−	7.79602i	−0.714925	−	0.375958i
$431$			19.7785i			0.952698i	0.879256	+	0.476349i	$0.158040\pi$
$431$			19.7785i			0.952698i	−0.879256	+	0.476349i	$0.841960\pi$
$432$	3.40975	+	2.09132i	0.164052	+	0.100619i
$433$	−20.7908			−0.999144			−0.499572	−	0.866272i	$-0.666509\pi$
$433$	−20.7908			−0.999144			−0.499572	+	0.866272i	$0.666509\pi$
$434$	−12.9818	+	17.2476i	−0.623148	+	0.827910i
$435$	−2.14906	+	2.35699i	−0.103039	+	0.113009i
$436$	35.8685	−	20.0782i	1.71779	−	0.961571i
$437$	−14.2621			−0.682249
$438$	4.36140	+	16.7204i	0.208396	+	0.798933i
$439$	−16.6175			−0.793112			−0.396556	−	0.918010i	$-0.629795\pi$
$439$	−16.6175			−0.793112			−0.396556	+	0.918010i	$0.629795\pi$
$440$	−0.823053	−	31.4238i	−0.0392375	−	1.49807i
$441$	−1.59545	+	6.81576i	−0.0759738	+	0.324560i
$442$	−24.4642	+	6.38132i	−1.16364	+	0.303528i
$443$	−12.0535			−0.572679			−0.286340	−	0.958128i	$-0.592439\pi$
$443$	−12.0535			−0.572679			−0.286340	+	0.958128i	$0.592439\pi$
$444$	−1.50918	+	0.844797i	−0.0716225	+	0.0400923i
$445$	4.97283	−	5.45397i	0.235735	−	0.258543i
$446$	4.45417	+	17.0761i	0.210911	+	0.808575i
$447$			9.14899i			0.432732i
$448$	12.4797	+	17.0955i	0.589610	+	0.807688i
$449$	−25.2281			−1.19059			−0.595295	−	0.803507i	$-0.702965\pi$
$449$	−25.2281			−1.19059			−0.595295	+	0.803507i	$0.702965\pi$
$450$	2.40725	+	6.64869i	0.113479	+	0.313422i
$451$	−8.37800			−0.394505
$452$	−16.6319	−	29.7120i	−0.782301	−	1.39753i
$453$	−9.54599			−0.448510
$454$	−6.62235	−	25.3883i	−0.310802	−	1.19153i
$455$	31.5830	+	2.17823i	1.48064	+	0.102117i
$456$	−4.16274	−	4.33203i	−0.194938	−	0.202866i
$457$		−	12.8112i		−	0.599284i	−0.954052	−	0.299642i	$-0.903133\pi$
$457$		−	12.8112i		−	0.599284i	0.954052	−	0.299642i	$-0.0968672\pi$
$458$	−10.4047	−	39.8888i	−0.486181	−	1.86388i
$459$		−	3.34087i		−	0.155938i
$460$	29.2439	+	6.81554i	1.36350	+	0.317776i
$461$		−	38.2334i		−	1.78071i	−0.455269	−	0.890354i	$-0.650457\pi$
$461$		−	38.2334i		−	1.78071i	0.455269	−	0.890354i	$-0.349543\pi$
$462$	11.1836	−	14.8584i	0.520308	−	0.691277i
$463$	9.21729			0.428364			0.214182	−	0.976794i	$-0.431291\pi$
$463$	9.21729			0.428364			0.214182	+	0.976794i	$0.431291\pi$
$464$	−2.98316	+	4.86384i	−0.138490	+	0.225798i
$465$	−8.69206	+	9.53305i	−0.403085	+	0.442085i
$466$	3.59494	+	13.7820i	0.166532	+	0.638439i
$467$			26.2754i			1.21588i	0.793982	+	0.607941i	$0.208004\pi$
$467$			26.2754i			1.21588i	−0.793982	+	0.607941i	$0.791996\pi$
$468$	9.33880	−	5.22760i	0.431686	−	0.241646i
$469$	−0.643469	+	0.510238i	−0.0297126	+	0.0235606i
$470$	13.0140	−	24.7476i	0.600292	−	1.14152i
$471$			5.51368i			0.254057i
$472$	−9.19808	+	8.83864i	−0.423376	+	0.406831i
$473$			26.3262i			1.21048i
$474$	−12.8406	+	3.34938i	−0.589789	+	0.153842i
$475$	−0.978083	−	10.5754i	−0.0448775	−	0.485234i
$476$	6.72195	−	16.3504i	0.308100	−	0.749419i
$477$		−	10.1805i		−	0.466131i
$478$	3.04932	+	11.6903i	0.139473	+	0.534700i
$479$	−22.0780			−1.00877			−0.504385	−	0.863479i	$-0.668281\pi$
$479$	−22.0780			−1.00877			−0.504385	+	0.863479i	$0.668281\pi$
$480$	6.46536	+	10.8719i	0.295102	+	0.496234i
$481$			4.62755i			0.210998i
$482$	6.57278	+	25.1982i	0.299382	+	1.14775i
$483$	11.0375	+	13.9195i	0.502223	+	0.633361i
$484$	−23.9147	+	13.3868i	−1.08703	+	0.608490i
$485$	8.80350	+	8.02686i	0.399746	+	0.364481i
$486$	0.356944	+	1.36843i	0.0161913	+	0.0620731i
$487$	−9.52152			−0.431461			−0.215731	−	0.976453i	$-0.569213\pi$
$487$	−9.52152			−0.431461			−0.215731	+	0.976453i	$0.569213\pi$
$488$	6.95359	+	7.23638i	0.314774	+	0.327575i
$489$		−	6.67293i		−	0.301761i
$490$	−14.4972	+	16.7282i	−0.654916	+	0.755702i
$491$			39.6661i			1.79011i	0.445960	+	0.895053i	$0.352863\pi$
$491$			39.6661i			1.79011i	−0.445960	+	0.895053i	$0.647137\pi$
$492$	2.94174	−	1.64670i	0.132624	−	0.0742391i
$493$	4.76559			0.214631
$494$	−15.5543	+	4.05722i	−0.699820	+	0.182543i
$495$	7.48803	−	8.21253i	0.336562	−	0.369126i
$496$	−12.0657	+	19.6723i	−0.541765	+	0.883311i
$497$	7.80547	+	9.84359i	0.350123	+	0.441545i
$498$	8.29238	−	2.16301i	0.371590	−	0.0969267i
$499$		−	24.4075i		−	1.09263i	−0.837580	−	0.546315i	$-0.816030\pi$
$499$		−	24.4075i		−	1.09263i	0.837580	−	0.546315i	$-0.183970\pi$
$500$	−3.04824	+	22.1519i	−0.136322	+	0.990665i
$501$	−0.444207			−0.0198457
$502$	−32.4659	+	8.46849i	−1.44902	+	0.377967i
$503$		−	32.0458i		−	1.42885i	−0.699710	−	0.714427i	$-0.746688\pi$
$503$		−	32.0458i		−	1.42885i	0.699710	−	0.714427i	$-0.253312\pi$
$504$	−1.00642	+	7.41533i	−0.0448294	+	0.330305i
$505$	−20.0957	+	22.0400i	−0.894247	+	0.980769i
$506$	−11.9120	−	45.6672i	−0.529551	−	2.03015i
$507$		−	15.6352i		−	0.694385i
$508$	−34.5735	+	19.3533i	−1.53395	+	0.858664i
$509$			16.4283i			0.728171i	0.931365	+	0.364086i	$0.118618\pi$
$509$			16.4283i			0.728171i	−0.931365	+	0.364086i	$0.881382\pi$
$510$	4.91724	−	9.35067i	0.217739	−	0.414054i
$511$	−25.3306	+	20.0859i	−1.12056	+	0.888547i
$512$	15.0155	+	16.9273i	0.663600	+	0.748088i
$513$		−	2.12411i		−	0.0937820i
$514$	8.80871	−	2.29769i	0.388536	−	0.101347i
$515$	6.57889	−	7.21543i	0.289901	−	0.317950i
$516$	−5.17444	−	9.24384i	−0.227792	−	0.406937i
$517$	−43.9468			−1.93278
$518$	−2.58521	−	1.94583i	−0.113588	−	0.0854948i
$519$			18.4717i			0.810816i
$520$	33.8323	−	0.886138i	1.48364	−	0.0388597i
$521$			17.7569i			0.777945i	0.921249	+	0.388972i	$0.127170\pi$
$521$			17.7569i			0.777945i	−0.921249	+	0.388972i	$0.872830\pi$
$522$	−1.95199	+	0.509164i	−0.0854365	+	0.0222855i
$523$			16.1634i			0.706776i	0.935477	+	0.353388i	$0.114970\pi$
$523$			16.1634i			0.706776i	−0.935477	+	0.353388i	$0.885030\pi$
$524$	−31.4374	+	17.5978i	−1.37335	+	0.768763i
$525$	−9.56449	+	9.13896i	−0.417428	+	0.398857i
$526$	10.6127	−	2.76824i	0.462735	−	0.120701i
$527$	19.2749			0.839627
$528$	10.3943	−	16.9473i	0.452356	−	0.737535i
$529$	22.0829			0.960124
$530$	14.9840	−	28.4938i	0.650864	−	1.23769i
$531$	−4.51007			−0.195721
$532$	4.27379	−	10.3955i	0.185292	−	0.450703i
$533$		−	9.02015i		−	0.390706i
$534$	4.51684	−	1.17819i	0.195463	−	0.0509851i
$535$	19.2258	+	17.5297i	0.831204	+	0.757876i
$536$	−0.633026	+	0.608289i	−0.0273426	+	0.0262741i
$537$	5.94123			0.256383
$538$	−3.88584	−	14.8972i	−0.167530	−	0.642266i
$539$	33.8759	+	7.92976i	1.45914	+	0.341559i
$540$	−1.01507	+	4.35541i	−0.0436815	+	0.187427i
$541$	26.3275			1.13191			0.565953	−	0.824438i	$-0.308508\pi$
$541$	26.3275			1.13191			0.565953	+	0.824438i	$0.308508\pi$
$542$	−38.4617	+	10.0325i	−1.65207	+	0.430931i
$543$	−8.08638			−0.347020
$544$	5.49481	−	18.0824i	0.235588	−	0.775276i
$545$	33.9604	+	30.9645i	1.45470	+	1.32637i
$546$	15.9973	+	12.0408i	0.684620	+	0.515298i
$547$	−14.5940			−0.623993			−0.311997	−	0.950083i	$-0.600998\pi$
$547$	−14.5940			−0.623993			−0.311997	+	0.950083i	$0.600998\pi$
$548$	3.57564	+	6.38768i	0.152744	+	0.272868i
$549$			3.54820i			0.151433i
$550$	33.0456	−	11.9646i	1.40907	−	0.510173i
$551$	3.02995			0.129080
$552$	13.1585	+	13.6936i	0.560064	+	0.582840i
$553$	−15.4251	−	19.4529i	−0.655944	−	0.827220i
$554$	−9.95288	−	38.1566i	−0.422857	−	1.62112i
$555$	−1.42890	−	1.30284i	−0.0606532	−	0.0553025i
$556$	1.29293	−	0.723747i	0.0548325	−	0.0306937i
$557$			6.05252i			0.256453i	0.991745	+	0.128227i	$0.0409285\pi$
$557$			6.05252i			0.256453i	−0.991745	+	0.128227i	$0.959072\pi$
$558$	−7.89503	+	2.05936i	−0.334223	+	0.0871797i
$559$	−28.3441			−1.19883
$560$	−13.7310	+	19.2733i	−0.580242	+	0.814444i
$561$	−16.6049			−0.701060
$562$	−21.8421	+	5.69735i	−0.921352	+	0.240328i
$563$			0.927220i			0.0390776i	0.999809	+	0.0195388i	$0.00621980\pi$
$563$			0.927220i			0.0390776i	−0.999809	+	0.0195388i	$0.993780\pi$
$564$	15.4309	−	8.63778i	0.649757	−	0.363716i
$565$	25.6497	−	28.1314i	1.07909	−	1.18350i
$566$	8.49923	+	32.5837i	0.357249	+	1.36960i
$567$	−2.07310	+	1.64386i	−0.0870618	+	0.0690356i
$568$	9.30542	+	9.68384i	0.390447	+	0.406325i
$569$	34.9542			1.46536			0.732678	−	0.680575i	$-0.238270\pi$
$569$	34.9542			1.46536			0.732678	+	0.680575i	$0.238270\pi$
$570$	3.12636	−	5.94512i	0.130949	−	0.249014i
$571$			9.68270i			0.405209i	0.979261	+	0.202604i	$0.0649405\pi$
$571$			9.68270i			0.405209i	−0.979261	+	0.202604i	$0.935059\pi$
$572$	−25.9824	−	46.4160i	−1.08638	−	1.94075i
$573$	0.655244			0.0273732
$574$	5.03917	+	3.79287i	0.210331	+	0.158311i
$575$	3.09174	+	33.4292i	0.128935	+	1.39409i
$576$	−0.318730	+	7.99365i	−0.0132804	+	0.333069i
$577$	20.6719			0.860581			0.430291	−	0.902690i	$-0.358411\pi$
$577$	20.6719			0.860581			0.430291	+	0.902690i	$0.358411\pi$
$578$	7.98967	−	2.08405i	0.332327	−	0.0866850i
$579$	5.96835			0.248036
$580$	−6.21279	−	1.44794i	−0.257972	−	0.0601226i
$581$	9.96145	+	12.5625i	0.413271	+	0.521182i
$582$	1.90176	+	7.29083i	0.0788305	+	0.302214i
$583$	−50.5993			−2.09561
$584$	−24.9195	+	23.9457i	−1.03118	+	0.990880i
$585$	8.84199	+	8.06197i	0.365571	+	0.333321i
$586$	−42.2000	+	11.0076i	−1.74327	+	0.454719i
$587$			1.42834i			0.0589540i	0.999565	+	0.0294770i	$0.00938419\pi$
$587$			1.42834i			0.0589540i	−0.999565	+	0.0294770i	$0.990616\pi$
$588$	−13.4533	+	3.87399i	−0.554806	+	0.159761i
$589$	12.2549			0.504955
$590$	−12.6231	−	6.63812i	−0.519686	−	0.273287i
$591$	18.7547			0.771465
$592$	−2.94865	−	1.80851i	−0.121189	−	0.0743292i
$593$	31.4659			1.29215			0.646074	−	0.763275i	$-0.276410\pi$
$593$	31.4659			1.29215			0.646074	+	0.763275i	$0.276410\pi$
$594$	6.80140	−	1.77410i	0.279065	−	0.0727921i
$595$	19.7180	+	1.35992i	0.808360	+	0.0557511i
$596$	−15.9666	+	8.93768i	−0.654019	+	0.366102i
$597$		−	2.45854i		−	0.100622i
$598$	49.1674	−	12.8250i	2.01061	−	0.524452i
$599$		−	23.8868i		−	0.975989i	−0.872847	−	0.487995i	$-0.837729\pi$
$599$		−	23.8868i		−	0.975989i	0.872847	−	0.487995i	$-0.162271\pi$
$600$	−9.25153	+	10.6962i	−0.377692	+	0.436672i
$601$		−	24.5499i		−	1.00141i	−0.865618	−	0.500705i	$-0.833074\pi$
$601$		−	24.5499i		−	1.00141i	0.865618	−	0.500705i	$-0.166926\pi$
$602$	11.9183	−	15.8346i	0.485755	−	0.645371i
$603$	−0.310390			−0.0126401
$604$	−9.32551	−	16.6595i	−0.379450	−	0.677865i
$605$	−22.6425	−	20.6450i	−0.920547	−	0.839338i
$606$	−18.2530	+	4.76116i	−0.741477	+	0.193409i
$607$			0.852121i			0.0345865i	0.999850	+	0.0172933i	$0.00550489\pi$
$607$			0.852121i			0.0345865i	−0.999850	+	0.0172933i	$0.994495\pi$
$608$	3.49358	−	11.4967i	0.141683	−	0.466253i
$609$	−2.34489	−	2.95717i	−0.0950196	−	0.119831i
$610$	−5.22239	+	9.93094i	−0.211448	+	0.402092i
$611$		−	47.3152i		−	1.91417i
$612$	5.83043	−	3.26371i	0.235681	−	0.131928i
$613$		−	12.3240i		−	0.497761i	−0.968534	−	0.248881i	$-0.919937\pi$
$613$		−	12.3240i		−	0.497761i	0.968534	−	0.248881i	$-0.0800627\pi$
$614$	1.71391	+	6.57064i	0.0691676	+	0.265170i
$615$	2.78524	+	2.53953i	0.112312	+	0.102404i
$616$	36.8560	+	5.00214i	1.48497	+	0.201542i
$617$			6.37695i			0.256726i	0.991727	+	0.128363i	$0.0409723\pi$
$617$			6.37695i			0.256726i	−0.991727	+	0.128363i	$0.959028\pi$
$618$	5.97563	−	1.55870i	0.240375	−	0.0627001i
$619$	3.83180			0.154013			0.0770066	−	0.997031i	$-0.475464\pi$
$619$	3.83180			0.154013			0.0770066	+	0.997031i	$0.475464\pi$
$620$	−25.1282	−	5.85635i	−1.00917	−	0.235197i
$621$			6.71438i			0.269439i
$622$	−7.97482	+	2.08018i	−0.319761	+	0.0834074i
$623$	5.42598	+	6.84278i	0.217387	+	0.274150i
$624$	18.2462	+	11.1910i	0.730433	+	0.448000i
$625$	−24.5759	+	4.58509i	−0.983038	+	0.183404i
$626$	−1.44076	+	0.375812i	−0.0575844	+	0.0150205i
$627$	−10.5574			−0.421620
$628$	−9.62238	+	5.38634i	−0.383975	+	0.214938i
$629$			2.88908i			0.115195i
$630$	−8.22183	+	1.54968i	−0.327566	+	0.0617408i
$631$		−	29.4955i		−	1.17420i	−0.809515	−	0.587099i	$-0.800270\pi$
$631$		−	29.4955i		−	1.17420i	0.809515	−	0.587099i	$-0.199730\pi$
$632$	−18.3893	−	19.1372i	−0.731488	−	0.761236i
$633$	7.92825			0.315120
$634$	−0.759834	−	2.91299i	−0.0301769	−	0.115690i
$635$	−32.7343	−	29.8465i	−1.29902	−	1.18442i
$636$	17.7667	−	9.94533i	0.704497	−	0.394358i
$637$	−8.53755	+	36.4724i	−0.338270	+	1.44509i
$638$	2.53067	+	9.70188i	0.100190	+	0.384101i
$639$			4.74826i			0.187838i
$640$	−12.6575	+	21.9041i	−0.500331	+	0.865834i
$641$	19.5479			0.772097			0.386048	−	0.922479i	$-0.373840\pi$
$641$	19.5479			0.772097			0.386048	+	0.922479i	$0.373840\pi$
$642$	4.15322	+	15.9223i	0.163915	+	0.628403i
$643$		−	0.187616i		−	0.00739886i	−0.999993	−	0.00369943i	$-0.998822\pi$
$643$		−	0.187616i		−	0.00739886i	0.999993	−	0.00369943i	$-0.00117757\pi$
$644$	−13.5096	+	32.8605i	−0.532351	+	1.29488i
$645$	7.97999	−	8.75209i	0.314212	−	0.344613i
$646$	−9.71089	+	2.53302i	−0.382070	+	0.0996602i
$647$		−	8.90032i		−	0.349908i	−0.984577	−	0.174954i	$-0.944022\pi$
$647$		−	8.90032i		−	0.349908i	0.984577	−	0.174954i	$-0.0559776\pi$
$648$	−2.03945	+	1.95975i	−0.0801172	+	0.0769864i
$649$			22.4161i			0.879911i
$650$	12.8817	+	35.5784i	0.505260	+	1.39550i
$651$	−9.48412	−	11.9606i	−0.371712	−	0.468771i
$652$	11.6455	−	6.51882i	0.456072	−	0.255297i
$653$			0.815877i			0.0319277i	0.999873	+	0.0159639i	$0.00508167\pi$
$653$			0.815877i			0.0319277i	−0.999873	+	0.0159639i	$0.994918\pi$
$654$	7.33624	+	28.1251i	0.286869	+	1.09978i
$655$	−29.7650	−	27.1392i	−1.16302	−	1.06042i
$656$	5.74759	+	3.52520i	0.224406	+	0.137636i
$657$	−12.2187			−0.476698
$658$	26.4330	+	19.8955i	1.03046	+	0.775606i
$659$		−	20.2997i		−	0.790764i	−0.918517	−	0.395382i	$-0.870612\pi$
$659$		−	20.2997i		−	0.790764i	0.918517	−	0.395382i	$-0.129388\pi$
$660$	21.6474	+	5.04512i	0.842626	+	0.196381i
$661$			42.2140i			1.64193i	0.570976	+	0.820966i	$0.306565\pi$
$661$			42.2140i			1.64193i	−0.570976	+	0.820966i	$0.693435\pi$
$662$	−1.32017	−	5.06116i	−0.0513097	−	0.196707i
$663$		−	17.8776i		−	0.694310i
$664$	11.8757	+	12.3587i	0.460867	+	0.479609i
$665$	12.5367	+	0.864630i	0.486150	+	0.0335289i
$666$	−0.308675	−	1.18337i	−0.0119609	−	0.0458548i
$667$	−9.57773			−0.370851
$668$	−0.433947	−	0.775221i	−0.0167899	−	0.0299942i
$669$	−12.4786			−0.482451
$670$	−0.868743	−	0.456846i	−0.0335625	−	0.0176495i
$671$	17.6354			0.680806
$672$	−13.9243	+	5.48768i	−0.537140	+	0.211692i
$673$			3.34701i			0.129018i	0.997917	+	0.0645088i	$0.0205481\pi$
$673$			3.34701i			0.129018i	−0.997917	+	0.0645088i	$0.979452\pi$
$674$	10.7342	+	41.1519i	0.413465	+	1.58511i
$675$	−4.97875	+	0.460466i	−0.191632	+	0.0177234i
$676$	27.2863	−	15.2741i	1.04947	−	0.587466i
$677$	15.6248			0.600510			0.300255	−	0.953859i	$-0.402928\pi$
$677$	15.6248			0.600510			0.300255	+	0.953859i	$0.402928\pi$
$678$	23.2977	−	6.07703i	0.894742	−	0.233387i
$679$	−11.0452	+	8.75831i	−0.423877	+	0.336113i
$680$	21.1223	−	0.553236i	0.810002	−	0.0212156i
$681$	18.5529			0.710948
$682$	10.2355	+	39.2402i	0.391938	+	1.50258i
$683$	−24.4951			−0.937280			−0.468640	−	0.883389i	$-0.655256\pi$
$683$	−24.4951			−0.937280			−0.468640	+	0.883389i	$0.655256\pi$
$684$	3.70697	−	2.07506i	0.141739	−	0.0793418i
$685$	−5.51433	+	6.04787i	−0.210692	+	0.231077i
$686$	−16.7856	−	20.1058i	−0.640879	−	0.767642i
$687$	29.1494			1.11212
$688$	11.0772	−	18.0607i	0.422316	−	0.688557i
$689$		−	54.4775i		−	2.07543i
$690$	−9.88250	+	18.7927i	−0.376220	+	0.715425i
$691$	34.1035			1.29736			0.648679	−	0.761062i	$-0.275322\pi$
$691$	34.1035			1.29736			0.648679	+	0.761062i	$0.275322\pi$
$692$	−32.2364	+	18.0450i	−1.22544	+	0.685970i
$693$	8.17037	+	10.3038i	0.310367	+	0.391408i
$694$	−18.6525	+	4.86537i	−0.708038	+	0.184687i
$695$	1.22415	+	1.11616i	0.0464347	+	0.0423383i
$696$	−2.79549	−	2.90918i	−0.105963	−	0.110272i
$697$		−	5.63149i		−	0.213308i
$698$	−12.0246	−	46.0990i	−0.455138	−	1.74487i
$699$	−10.0714			−0.380936
$700$	−25.2927	−	7.76388i	−0.955975	−	0.293447i
$701$	9.46222			0.357383			0.178692	−	0.983905i	$-0.442814\pi$
$701$	9.46222			0.357383			0.178692	+	0.983905i	$0.442814\pi$
$702$	1.91008	+	7.32271i	0.0720912	+	0.276378i
$703$			1.83687i			0.0692789i
$704$	39.7303	+	1.58416i	1.49739	+	0.0597054i
$705$	14.6100	+	13.3211i	0.550244	+	0.501703i
$706$	−24.5331	+	6.39928i	−0.923315	+	0.240840i
$707$	−21.9269	−	27.6523i	−0.824646	−	1.03997i
$708$	−4.40591	−	7.87090i	−0.165584	−	0.295806i
$709$	11.2667			0.423129			0.211565	−	0.977364i	$-0.432144\pi$
$709$	11.2667			0.423129			0.211565	+	0.977364i	$0.432144\pi$
$710$	−6.98869	+	13.2898i	−0.262281	+	0.498756i
$711$		−	9.38349i		−	0.351908i
$712$	6.46866	+	6.73173i	0.242423	+	0.252282i
$713$	−38.7381			−1.45075
$714$	9.98747	+	7.51733i	0.373772	+	0.281329i
$715$	40.0699	−	43.9468i	1.49853	−	1.64352i
$716$	5.80402	+	10.3685i	0.216906	+	0.387490i
$717$	−8.54285			−0.319039
$718$	−3.37928	−	12.9552i	−0.126114	−	0.483485i
$719$	−9.40558			−0.350769			−0.175384	−	0.984500i	$-0.556117\pi$
$719$	−9.40558			−0.350769			−0.175384	+	0.984500i	$0.556117\pi$
$720$	−8.59261	+	2.48335i	−0.320228	+	0.0925489i
$721$	7.17839	+	9.05277i	0.267337	+	0.337143i
$722$	19.8259	−	5.17146i	0.737845	−	0.192462i
$723$	−18.4140			−0.684825
$724$	−7.89962	−	14.1122i	−0.293587	−	0.524476i
$725$	−0.656833	−	7.10195i	−0.0243942	−	0.263760i
$726$	−4.89130	−	18.7519i	−0.181533	−	0.695949i
$727$			10.4781i			0.388611i	0.980941	+	0.194305i	$0.0622452\pi$
$727$			10.4781i			0.388611i	−0.980941	+	0.194305i	$0.937755\pi$
$728$	−5.38553	+	39.6808i	−0.199601	+	1.47067i
$729$	−1.00000			−0.0370370
$730$	−34.1986	−	17.9840i	−1.26575	−	0.665619i
$731$	−17.6959			−0.654505
$732$	−6.19225	+	3.46625i	−0.228872	+	0.128116i
$733$	−32.5203			−1.20117			−0.600583	−	0.799562i	$-0.705065\pi$
$733$	−32.5203			−1.20117			−0.600583	+	0.799562i	$0.705065\pi$
$734$	−9.93184	−	38.0759i	−0.366591	−	1.40541i
$735$	−8.85830	−	12.9047i	−0.326743	−	0.475996i
$736$	−11.0433	+	36.3414i	−0.407061	+	1.33956i
$737$			1.54271i			0.0568266i
$738$	0.601678	+	2.30667i	0.0221481	+	0.0849096i
$739$			43.8880i			1.61445i	0.590246	+	0.807223i	$0.299031\pi$
$739$			43.8880i			1.61445i	−0.590246	+	0.807223i	$0.700969\pi$
$740$	0.877799	−	3.76643i	0.0322685	−	0.138457i
$741$		−	11.3665i		−	0.417560i
$742$	30.4343	+	22.9072i	1.11728	+	0.840948i
$743$	−12.0535			−0.442200			−0.221100	−	0.975251i	$-0.570965\pi$
$743$	−12.0535			−0.442200			−0.221100	+	0.975251i	$0.570965\pi$
$744$	−11.3066	−	11.7665i	−0.414522	−	0.431379i
$745$	−15.1173	−	13.7836i	−0.553853	−	0.504993i
$746$	10.0202	+	38.4148i	0.366866	+	1.40646i
$747$			6.05979i			0.221716i
$748$	−16.2214	−	28.9786i	−0.593114	−	1.05956i
$749$	−24.1215	+	19.1271i	−0.881380	+	0.698890i
$750$	−14.6126	−	6.03915i	−0.533577	−	0.220519i
$751$		−	0.257771i		−	0.00940621i	−0.999989	−	0.00470311i	$-0.998503\pi$
$751$		−	0.257771i		−	0.00940621i	0.999989	−	0.00470311i	$-0.00149705\pi$
$752$	30.1490	+	18.4914i	1.09942	+	0.674312i
$753$		−	23.7250i		−	0.864585i
$754$	−10.4455	+	2.72463i	−0.380402	+	0.0992253i
$755$	14.3817	−	15.7732i	0.523405	−	0.574047i
$756$	−4.89405	−	2.01203i	−0.177995	−	0.0731770i
$757$		−	33.6819i		−	1.22419i	−0.790785	−	0.612094i	$-0.790327\pi$
$757$		−	33.6819i		−	1.22419i	0.790785	−	0.612094i	$-0.209673\pi$
$758$	−7.05605	−	27.0510i	−0.256287	−	0.982535i
$759$	33.3720			1.21133
$760$	13.4295	−	0.351746i	0.487138	−	0.0127592i
$761$			12.2430i			0.443808i	0.975069	+	0.221904i	$0.0712272\pi$
$761$			12.2430i			0.443808i	−0.975069	+	0.221904i	$0.928773\pi$
$762$	−7.07137	−	27.1097i	−0.256169	−	0.982080i
$763$	−42.6081	+	33.7861i	−1.54252	+	1.22314i
$764$	0.640111	+	1.14352i	0.0231584	+	0.0413711i
$765$	5.52026	+	5.03327i	0.199585	+	0.181978i
$766$	−10.5349	−	40.3880i	−0.380642	−	1.45928i
$767$	−24.1343			−0.871438
$768$	−14.2617	+	7.25279i	−0.514626	+	0.261712i
$769$			24.7942i			0.894101i	0.894509	+	0.447051i	$0.147526\pi$
$769$			24.7942i			0.894101i	−0.894509	+	0.447051i	$0.852474\pi$
$770$	7.70229	+	40.8644i	0.277571	+	1.47265i
$771$			6.43711i			0.231827i
$772$	5.83051	+	10.4159i	0.209845	+	0.374875i
$773$	7.24022			0.260413			0.130206	−	0.991487i	$-0.458436\pi$
$773$	7.24022			0.260413			0.130206	+	0.991487i	$0.458436\pi$
$774$	7.24825	−	1.89065i	0.260533	−	0.0679582i
$775$	−2.65662	−	28.7245i	−0.0954287	−	1.03181i
$776$	−10.8660	+	10.4414i	−0.390066	+	0.374823i
$777$	1.79275	−	1.42156i	0.0643146	−	0.0509982i
$778$	2.95584	−	0.771009i	0.105972	−	0.0276420i
$779$		−	3.58048i		−	0.128284i
$780$	−5.43182	+	23.3067i	−0.194490	+	0.834512i
$781$	23.6000			0.844473
$782$	30.6964	−	8.00693i	1.09770	−	0.286327i
$783$		−	1.42645i		−	0.0509772i
$784$	−19.9034	−	19.6940i	−0.710837	−	0.703357i
$785$	−9.11049	−	8.30678i	−0.325167	−	0.296482i
$786$	−6.42994	−	24.6506i	−0.229348	−	0.879258i
$787$		−	39.7991i		−	1.41868i	−0.704865	−	0.709342i	$-0.748992\pi$
$787$		−	39.7991i		−	1.41868i	0.704865	−	0.709342i	$-0.251008\pi$
$788$	18.3215	+	32.7304i	0.652678	+	1.16597i
$789$			7.75540i			0.276099i
$790$	13.8110	−	26.2632i	0.491374	−	0.934402i
$791$	27.9870	+	35.2948i	0.995103	+	1.25494i
$792$	9.74044	+	10.1366i	0.346112	+	0.360187i
$793$			18.9871i			0.674251i
$794$	−7.60884	+	1.98471i	−0.270028	+	0.0704348i
$795$	16.8216	+	15.3376i	0.596600	+	0.543969i
$796$	4.29061	−	2.40176i	0.152077	−	0.0851282i
$797$	16.6424			0.589504			0.294752	−	0.955574i	$-0.404763\pi$
$797$	16.6424			0.589504			0.294752	+	0.955574i	$0.404763\pi$
$798$	6.35000	+	4.77950i	0.224788	+	0.169192i
$799$		−	29.5400i		−	1.04505i
$800$	−27.7047	−	5.69640i	−0.979509	−	0.201398i
$801$			3.30075i			0.116626i
$802$	22.1071	−	5.76647i	0.780627	−	0.203621i
$803$			60.7300i			2.14311i
$804$	−0.303222	−	0.541688i	−0.0106938	−	0.0191038i
$805$	−39.6286	−	2.73312i	−1.39673	−	0.0963297i
$806$	−42.2478	+	11.0200i	−1.48811	+	0.388164i
$807$	10.8864			0.383219
$808$	−26.1405	−	27.2036i	−0.919620	−	0.957019i
$809$	12.4176			0.436578			0.218289	−	0.975884i	$-0.429952\pi$
$809$	12.4176			0.436578			0.218289	+	0.975884i	$0.429952\pi$
$810$	−2.79887	−	1.47184i	−0.0983423	−	0.0517153i
$811$	−10.2518			−0.359990			−0.179995	−	0.983668i	$-0.557608\pi$
$811$	−10.2518			−0.359990			−0.179995	+	0.983668i	$0.557608\pi$
$812$	2.87007	−	6.98113i	0.100720	−	0.244989i
$813$		−	28.1065i		−	0.985738i
$814$	−5.88165	+	1.53419i	−0.206152	+	0.0537732i
$815$	11.0260	+	10.0533i	0.386223	+	0.352151i
$816$	11.3915	+	6.98682i	0.398783	+	0.244588i
$817$	−11.2510			−0.393621
$818$	−1.70709	−	6.54452i	−0.0596871	−	0.228824i
$819$	−11.0935	+	8.79661i	−0.387639	+	0.307378i
$820$	−1.71103	+	7.34164i	−0.0597518	+	0.256381i
$821$	−12.0609			−0.420927			−0.210463	−	0.977602i	$-0.567497\pi$
$821$	−12.0609			−0.420927			−0.210463	+	0.977602i	$0.567497\pi$
$822$	−5.00869	+	1.30648i	−0.174698	+	0.0455687i
$823$	−36.5239			−1.27314			−0.636572	−	0.771217i	$-0.719648\pi$
$823$	−36.5239			−1.27314			−0.636572	+	0.771217i	$0.719648\pi$
$824$	8.55783	+	8.90585i	0.298126	+	0.310250i
$825$	2.28863	+	24.7456i	0.0796797	+	0.861531i
$826$	10.1482	−	13.4828i	0.353100	−	0.469126i
$827$	20.6441			0.717866			0.358933	−	0.933363i	$-0.383141\pi$
$827$	20.6441			0.717866			0.358933	+	0.933363i	$0.383141\pi$
$828$	−11.7178	+	6.55930i	−0.407222	+	0.227951i
$829$			6.65641i			0.231187i	0.993297	+	0.115593i	$0.0368770\pi$
$829$			6.65641i			0.231187i	−0.993297	+	0.115593i	$0.963123\pi$
$830$	−8.91906	+	16.9606i	−0.309585	+	0.588710i
$831$	27.8836			0.967270
$832$	−1.70558	+	42.7755i	−0.0591305	+	1.48297i
$833$	−5.33019	+	22.7706i	−0.184680	+	0.788953i
$834$	0.264445	+	1.01381i	0.00915698	+	0.0351053i
$835$	0.669230	−	0.733981i	0.0231597	−	0.0254005i
$836$	−10.3135	−	18.4245i	−0.356701	−	0.637225i
$837$		−	5.76942i		−	0.199420i
$838$	−38.9663	+	10.1641i	−1.34607	+	0.351112i
$839$	27.4161			0.946510			0.473255	−	0.880926i	$-0.343079\pi$
$839$	27.4161			0.946510			0.473255	+	0.880926i	$0.343079\pi$
$840$	−10.7364	−	12.8347i	−0.370442	−	0.442839i
$841$	−26.9652			−0.929836
$842$	4.21348	−	1.09906i	0.145206	−	0.0378760i
$843$		−	15.9615i		−	0.549742i
$844$	7.74514	+	13.8362i	0.266599	+	0.476263i
$845$	25.8347	+	23.5556i	0.888742	+	0.810339i
$846$	3.15610	+	12.0996i	0.108509	+	0.415993i
$847$	28.4082	−	22.5262i	0.976116	−	0.774011i
$848$	34.7128	+	21.2906i	1.19204	+	0.731121i
$849$	−23.8111			−0.817194
$850$	8.04232	+	22.2124i	0.275849	+	0.761880i
$851$		−	5.80639i		−	0.199041i
$852$	−8.28657	+	4.63859i	−0.283893	+	0.158916i
$853$	42.4973			1.45508			0.727540	−	0.686066i	$-0.240664\pi$
$853$	42.4973			1.45508			0.727540	+	0.686066i	$0.240664\pi$
$854$	−10.6073	−	7.98384i	−0.362973	−	0.273201i
$855$	3.50976	+	3.20014i	0.120031	+	0.109442i
$856$	−23.7300	+	22.8027i	−0.811075	+	0.779380i
$857$	5.55801			0.189858			0.0949290	−	0.995484i	$-0.469738\pi$
$857$	5.55801			0.189858			0.0949290	+	0.995484i	$0.469738\pi$
$858$	36.3956	−	9.49354i	1.24253	−	0.324104i
$859$	15.7169			0.536255			0.268127	−	0.963383i	$-0.413595\pi$
$859$	15.7169			0.536255			0.268127	+	0.963383i	$0.413595\pi$
$860$	23.0697	+	5.37658i	0.786669	+	0.183340i
$861$	−3.49448	+	2.77095i	−0.119092	+	0.0944336i
$862$	−7.05983	−	27.0654i	−0.240459	−	0.921853i
$863$	3.42599			0.116622			0.0583111	−	0.998298i	$-0.481428\pi$
$863$	3.42599			0.116622			0.0583111	+	0.998298i	$0.481428\pi$
$864$	−5.41248	−	1.64472i	−0.184136	−	0.0559546i
$865$	−30.5215	−	27.8289i	−1.03776	−	0.946212i
$866$	28.4507	−	7.42117i	0.966795	−	0.252182i
$867$			5.83858i			0.198289i
$868$	11.6083	−	28.2358i	0.394010	−	0.958386i
$869$	−46.6382			−1.58209
$870$	2.09951	−	3.99245i	0.0711801	−	0.135357i
$871$	−1.66096			−0.0562794
$872$	−41.9166	+	40.2786i	−1.41948	+	1.36401i
$873$	−5.32789			−0.180322
$874$	19.5166	−	5.09078i	0.660160	−	0.172198i
$875$	−0.691076	−	29.5723i	−0.0233626	−	0.999727i
$876$	−11.9365	−	21.3239i	−0.403298	−	0.720468i
$877$		−	1.66334i		−	0.0561669i	−0.999606	−	0.0280835i	$-0.991060\pi$
$877$		−	1.66334i		−	0.0561669i	0.999606	−	0.0280835i	$-0.00894042\pi$
$878$	22.7399	−	5.93154i	0.767434	−	0.200180i
$879$		−	30.8384i		−	1.04015i
$880$	12.3428	+	42.7073i	0.416076	+	1.43966i
$881$		−	25.3983i		−	0.855692i	−0.903852	−	0.427846i	$-0.859273\pi$
$881$		−	25.3983i		−	0.855692i	0.903852	−	0.427846i	$-0.140727\pi$
$882$	−0.249591	−	9.89635i	−0.00840418	−	0.333227i
$883$	26.2881			0.884664			0.442332	−	0.896851i	$-0.354151\pi$
$883$	26.2881			0.884664			0.442332	+	0.896851i	$0.354151\pi$
$884$	31.1997	−	17.4647i	1.04936	−	0.587402i
$885$	6.79476	−	7.45218i	0.228403	−	0.250502i
$886$	16.4943	−	4.30243i	0.554138	−	0.144543i
$887$		−	22.9901i		−	0.771933i	−0.922513	−	0.385966i	$-0.873868\pi$
$887$		−	22.9901i		−	0.771933i	0.922513	−	0.385966i	$-0.126132\pi$
$888$	1.76366	−	1.69474i	0.0591844	−	0.0568716i
$889$	41.0698	−	32.5663i	1.37744	−	1.09224i
$890$	−4.85819	+	9.23838i	−0.162847	+	0.309671i
$891$			4.97024i			0.166509i
$892$	−12.1904	−	21.7775i	−0.408165	−	0.729163i
$893$		−	18.7814i		−	0.628496i
$894$	−3.26568	−	12.5197i	−0.109221	−	0.418722i
$895$	−8.95091	+	9.81695i	−0.299196	+	0.328144i
$896$	−23.1797	−	18.9394i	−0.774379	−	0.632722i
$897$			35.9299i			1.19966i
$898$	34.5228	−	9.00504i	1.15204	−	0.300502i
$899$	8.22980			0.274479
$900$	−5.66736	−	8.23899i	−0.188912	−	0.274633i
$901$		−	34.0116i		−	1.13309i
$902$	11.4647	−	2.99048i	0.381732	−	0.0995721i
$903$	8.70716	+	10.9807i	0.289756	+	0.365416i
$904$	33.3651	+	34.7220i	1.10971	+	1.15484i
$905$	12.1827	−	13.3615i	0.404968	−	0.444150i
$906$	13.0630	−	3.40739i	0.433988	−	0.113203i
$907$	32.8403			1.09045			0.545223	−	0.838291i	$-0.316445\pi$
$907$	32.8403			1.09045			0.545223	+	0.838291i	$0.316445\pi$
$908$	18.1244	+	32.3782i	0.601479	+	1.07451i
$909$		−	13.3387i		−	0.442416i
$910$	−43.9966	+	8.29265i	−1.45847	+	0.274899i
$911$		−	23.1034i		−	0.765449i	−0.923863	−	0.382724i	$-0.874986\pi$
$911$		−	23.1034i		−	0.765449i	0.923863	−	0.382724i	$-0.125014\pi$
$912$	7.24270	+	4.44220i	0.239830	+	0.147096i
$913$	30.1186			0.996781
$914$	4.57289	+	17.5312i	0.151258	+	0.579881i
$915$	−5.86283	−	5.34562i	−0.193819	−	0.176721i
$916$	28.4762	+	50.8710i	0.940880	+	1.68083i
$917$	37.3444	−	29.6122i	1.23322	−	0.977882i
$918$	1.19250	+	4.57174i	0.0393585	+	0.150890i
$919$		−	29.6580i		−	0.978327i	−0.872192	−	0.489164i	$-0.837302\pi$
$919$		−	29.6580i		−	0.978327i	0.872192	−	0.489164i	$-0.162698\pi$
$920$	−42.4509	+	1.11188i	−1.39956	+	0.0366575i
$921$	−4.80160			−0.158218
$922$	13.6472	+	52.3196i	0.449447	+	1.72306i
$923$			25.4088i			0.836342i
$924$	−10.0003	+	24.3246i	−0.328985	+	0.800220i
$925$	4.30547	−	0.398197i	0.141563	−	0.0130926i
$926$	−12.6132	+	3.29006i	−0.414495	+	0.108118i
$927$			4.36679i			0.143424i
$928$	2.34612	−	7.72063i	0.0770151	−	0.253442i
$929$		−	45.3687i		−	1.48850i	−0.667902	−	0.744249i	$-0.732807\pi$
$929$		−	45.3687i		−	1.48850i	0.667902	−	0.744249i	$-0.267193\pi$
$930$	8.49168	−	16.1479i	0.278453	−	0.529509i
$931$	−3.38892	+	14.4774i	−0.111067	+	0.474479i
$932$	−9.83881	−	17.5765i	−0.322281	−	0.575736i
$933$		−	5.82773i		−	0.190791i
$934$	−9.37886	−	35.9560i	−0.306886	−	1.17652i
$935$	25.0166	−	27.4370i	0.818129	−	0.897286i
$936$	−10.9135	+	10.4870i	−0.356719	+	0.342779i
$937$	2.04718			0.0668786			0.0334393	−	0.999441i	$-0.489354\pi$
$937$	2.04718			0.0668786			0.0334393	+	0.999441i	$0.489354\pi$
$938$	0.698413	−	0.927906i	0.0228040	−	0.0302972i
$939$		−	1.05286i		−	0.0343588i
$940$	−8.97522	+	38.5106i	−0.292739	+	1.25608i
$941$			12.0483i			0.392764i	0.980527	+	0.196382i	$0.0629193\pi$
$941$			12.0483i			0.392764i	−0.980527	+	0.196382i	$0.937081\pi$
$942$	−1.96808	−	7.54507i	−0.0641234	−	0.245832i
$943$			11.3180i			0.368564i
$944$	9.43200	−	15.3782i	0.306985	−	0.500519i
$945$	0.407054	−	5.90206i	0.0132415	−	0.191994i
$946$	−9.39700	−	36.0255i	−0.305523	−	1.17129i
$947$	−27.9571			−0.908484			−0.454242	−	0.890878i	$-0.650090\pi$
$947$	−27.9571			−0.908484			−0.454242	+	0.890878i	$0.650090\pi$
$948$	16.3759	−	9.16677i	0.531864	−	0.297723i
$949$	−65.3847			−2.12248
$950$	5.11328	+	14.1226i	0.165897	+	0.458197i
$951$	2.12872			0.0690284
$952$	−3.36231	+	24.7737i	−0.108973	+	0.802919i
$953$		−	4.97507i		−	0.161158i	−0.996748	−	0.0805791i	$-0.974323\pi$
$953$		−	4.97507i		−	0.161158i	0.996748	−	0.0805791i	$-0.0256770\pi$
$954$	3.63386	+	13.9312i	0.117650	+	0.451039i
$955$	−0.987174	+	1.08269i	−0.0319442	+	0.0350349i
$956$	−8.34555	−	14.9088i	−0.269914	−	0.482186i
$957$	−7.08980			−0.229181
$958$	30.2121	−	7.88062i	0.976110	−	0.254611i
$959$	−6.01682	−	7.58790i	−0.194293	−	0.245026i
$960$	−12.7280	−	12.5697i	−0.410796	−	0.405685i
$961$	2.28620			0.0737484
$962$	−1.65178	−	6.33246i	−0.0532554	−	0.204167i
$963$	−11.6355			−0.374948
$964$	−17.9887	−	32.1358i	−0.579378	−	1.03503i
$965$	−8.99177	+	9.86176i	−0.289455	+	0.317461i
$966$	−20.0725	−	15.1081i	−0.645822	−	0.486095i
$967$	−17.3575			−0.558178			−0.279089	−	0.960265i	$-0.590033\pi$
$967$	−17.3575			−0.558178			−0.279089	+	0.960265i	$0.590033\pi$
$968$	27.9471	−	26.8550i	0.898255	−	0.863153i
$969$		−	7.09639i		−	0.227969i
$970$	−14.9121	−	7.84182i	−0.478798	−	0.251786i
$971$	−7.13630			−0.229015			−0.114507	−	0.993422i	$-0.536529\pi$
$971$	−7.13630			−0.229015			−0.114507	+	0.993422i	$0.536529\pi$
$972$	−0.976904	−	1.74518i	−0.0313342	−	0.0559767i
$973$	−1.53587	+	1.21787i	−0.0492377	+	0.0390430i
$974$	13.0295	−	3.39865i	0.417492	−	0.108900i
$975$	−26.6422	+	2.46404i	−0.853235	+	0.0789125i
$976$	−12.0985	−	7.42040i	−0.387262	−	0.237521i
$977$		−	19.3382i		−	0.618684i	−0.950951	−	0.309342i	$-0.899891\pi$
$977$		−	19.3382i		−	0.618684i	0.950951	−	0.309342i	$-0.100109\pi$
$978$	2.38187	+	9.13142i	0.0761637	+	0.291991i
$979$	16.4055			0.524323
$980$	13.8673	−	28.0660i	0.442974	−	0.896534i
$981$	−20.5529			−0.656203
$982$	−14.1586	−	54.2801i	−0.451819	−	1.73215i
$983$			22.6907i			0.723720i	0.932232	+	0.361860i	$0.117858\pi$
$983$			22.6907i			0.723720i	−0.932232	+	0.361860i	$0.882142\pi$
$984$	−3.43777	+	3.30343i	−0.109592	+	0.105309i
$985$	−28.2554	+	30.9892i	−0.900291	+	0.987397i
$986$	−6.52136	+	1.70105i	−0.207682	+	0.0541725i
$987$	−18.3303	+	14.5350i	−0.583460	+	0.462654i
$988$	19.8367	−	11.1040i	0.631089	−	0.353266i
$989$	35.5646			1.13089
$990$	−7.31541	+	13.9111i	−0.232499	+	0.442122i
$991$		−	19.6232i		−	0.623351i	−0.950189	−	0.311675i	$-0.899110\pi$
$991$		−	19.6232i		−	0.623351i	0.950189	−	0.311675i	$-0.100890\pi$
$992$	9.48910	−	31.2268i	0.301279	−	0.991453i
$993$	3.69852			0.117369
$994$	−14.1948	−	10.6841i	−0.450232	−	0.338879i
$995$	4.06236	+	3.70398i	0.128785	+	0.117424i
$996$	−10.5754	+	5.91984i	−0.335096	+	0.187577i
$997$	36.2418			1.14779			0.573894	−	0.818930i	$-0.305432\pi$
$997$	36.2418			1.14779			0.573894	+	0.818930i	$0.305432\pi$
$998$	8.71212	+	33.3999i	0.275777	+	1.05725i
$999$	0.864770			0.0273601

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.i.a.139.3	yes	48
4.3	odd	2	inner	420.2.i.a.139.48	yes	48
5.4	even	2	inner	420.2.i.a.139.46	yes	48
7.6	odd	2	inner	420.2.i.a.139.4	yes	48
20.19	odd	2	inner	420.2.i.a.139.1	✓	48
28.27	even	2	inner	420.2.i.a.139.47	yes	48
35.34	odd	2	inner	420.2.i.a.139.45	yes	48
140.139	even	2	inner	420.2.i.a.139.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.i.a.139.1	✓	48	20.19	odd	2	inner
420.2.i.a.139.2	yes	48	140.139	even	2	inner
420.2.i.a.139.3	yes	48	1.1	even	1	trivial
420.2.i.a.139.4	yes	48	7.6	odd	2	inner
420.2.i.a.139.45	yes	48	35.34	odd	2	inner
420.2.i.a.139.46	yes	48	5.4	even	2	inner
420.2.i.a.139.47	yes	48	28.27	even	2	inner
420.2.i.a.139.48	yes	48	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36843 + 0.356944i) q^{2} -1.00000i q^{3} +(1.74518 - 0.976904i) q^{4} +(1.65234 + 1.50657i) q^{5} +(0.356944 + 1.36843i) q^{6} +(-2.07310 + 1.64386i) q^{7} +(-2.03945 + 1.95975i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.36843 + 0.356944i) q^{2} -1.00000i q^{3} +(1.74518 - 0.976904i) q^{4} +(1.65234 + 1.50657i) q^{5} +(0.356944 + 1.36843i) q^{6} +(-2.07310 + 1.64386i) q^{7} +(-2.03945 + 1.95975i) q^{8} -1.00000 q^{9} +(-2.79887 - 1.47184i) q^{10} +4.97024i q^{11} +(-0.976904 - 1.74518i) q^{12} -5.35119 q^{13} +(2.25011 - 2.98948i) q^{14} +(1.50657 - 1.65234i) q^{15} +(2.09132 - 3.40975i) q^{16} -3.34087 q^{17} +(1.36843 - 0.356944i) q^{18} -2.12411 q^{19} +(4.35541 + 1.01507i) q^{20} +(1.64386 + 2.07310i) q^{21} +(-1.77410 - 6.80140i) q^{22} +6.71438 q^{23} +(1.95975 + 2.03945i) q^{24} +(0.460466 + 4.97875i) q^{25} +(7.32271 - 1.91008i) q^{26} +1.00000i q^{27} +(-2.01203 + 4.89405i) q^{28} -1.42645 q^{29} +(-1.47184 + 2.79887i) q^{30} -5.76942 q^{31} +(-1.64472 + 5.41248i) q^{32} +4.97024 q^{33} +(4.57174 - 1.19250i) q^{34} +(-5.90206 - 0.407054i) q^{35} +(-1.74518 + 0.976904i) q^{36} -0.864770i q^{37} +(2.90669 - 0.758191i) q^{38} +5.35119i q^{39} +(-6.32239 + 0.165596i) q^{40} +1.68563i q^{41} +(-2.98948 - 2.25011i) q^{42} +5.29678 q^{43} +(4.85545 + 8.67397i) q^{44} +(-1.65234 - 1.50657i) q^{45} +(-9.18813 + 2.39666i) q^{46} +8.84199i q^{47} +(-3.40975 - 2.09132i) q^{48} +(1.59545 - 6.81576i) q^{49} +(-2.40725 - 6.64869i) q^{50} +3.34087i q^{51} +(-9.33880 + 5.22760i) q^{52} +10.1805i q^{53} +(-0.356944 - 1.36843i) q^{54} +(-7.48803 + 8.21253i) q^{55} +(1.00642 - 7.41533i) q^{56} +2.12411i q^{57} +(1.95199 - 0.509164i) q^{58} +4.51007 q^{59} +(1.01507 - 4.35541i) q^{60} -3.54820i q^{61} +(7.89503 - 2.05936i) q^{62} +(2.07310 - 1.64386i) q^{63} +(0.318730 - 7.99365i) q^{64} +(-8.84199 - 8.06197i) q^{65} +(-6.80140 + 1.77410i) q^{66} +0.310390 q^{67} +(-5.83043 + 3.26371i) q^{68} -6.71438i q^{69} +(8.22183 - 1.54968i) q^{70} -4.74826i q^{71} +(2.03945 - 1.95975i) q^{72} +12.2187 q^{73} +(0.308675 + 1.18337i) q^{74} +(4.97875 - 0.460466i) q^{75} +(-3.70697 + 2.07506i) q^{76} +(-8.17037 - 10.3038i) q^{77} +(-1.91008 - 7.32271i) q^{78} +9.38349i q^{79} +(8.59261 - 2.48335i) q^{80} +1.00000 q^{81} +(-0.601678 - 2.30667i) q^{82} -6.05979i q^{83} +(4.89405 + 2.01203i) q^{84} +(-5.52026 - 5.03327i) q^{85} +(-7.24825 + 1.89065i) q^{86} +1.42645i q^{87} +(-9.74044 - 10.1366i) q^{88} -3.30075i q^{89} +(2.79887 + 1.47184i) q^{90} +(11.0935 - 8.79661i) q^{91} +(11.7178 - 6.55930i) q^{92} +5.76942i q^{93} +(-3.15610 - 12.0996i) q^{94} +(-3.50976 - 3.20014i) q^{95} +(5.41248 + 1.64472i) q^{96} +5.32789 q^{97} +(0.249591 + 9.89635i) q^{98} -4.97024i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{9}+O(q^{10}) \) 48 * q - 48 * q^9	\( 48 q - 48 q^{9} + 20 q^{14} - 16 q^{16} + 8 q^{25} - 16 q^{30} - 40 q^{44} + 16 q^{46} - 16 q^{49} + 48 q^{50} + 28 q^{56} - 32 q^{60} - 112 q^{74} + 48 q^{81} - 28 q^{84} + 56 q^{85} + 8 q^{86}+O(q^{100}) \) 48 * q - 48 * q^9 + 20 * q^14 - 16 * q^16 + 8 * q^25 - 16 * q^30 - 40 * q^44 + 16 * q^46 - 16 * q^49 + 48 * q^50 + 28 * q^56 - 32 * q^60 - 112 * q^74 + 48 * q^81 - 28 * q^84 + 56 * q^85 + 8 * q^86

Introduction

L-functions

Modular forms

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