LMFDB - Embedded newform 920.2.bb.a.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(11,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 9]))

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

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

chi := DirichletCharacter("920.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bb (of order $22$, degree $10$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.a.251.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.296367 + 1.38281i) q^{2} +(0.323664 - 2.25113i) q^{3} +(-1.82433 - 0.819638i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(3.01696 + 1.11473i) q^{6} +(-2.70611 - 3.12302i) q^{7} +(1.67408 - 2.27980i) q^{8} +(-2.08435 - 0.612020i) q^{9} +(-0.105221 - 1.41029i) q^{10} +(0.776978 - 1.20900i) q^{11} +(-2.43558 + 3.84152i) q^{12} +(1.25599 + 1.08833i) q^{13} +(5.12054 - 2.81648i) q^{14} +(0.323664 + 2.25113i) q^{15} +(2.65639 + 2.99059i) q^{16} +(-1.82880 + 0.835186i) q^{17} +(1.46404 - 2.70088i) q^{18} +(-2.51849 - 1.15016i) q^{19} +(1.98135 + 0.272463i) q^{20} +(-7.90618 + 5.08100i) q^{21} +(1.44155 + 1.43272i) q^{22} +(4.53402 + 1.56289i) q^{23} +(-4.59028 - 4.50645i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-1.87718 + 1.41426i) q^{26} +(0.781946 - 1.71222i) q^{27} +(2.37710 + 7.91545i) q^{28} +(-9.29457 + 4.24469i) q^{29} +(-3.20881 - 0.219594i) q^{30} +(-9.38546 + 1.34943i) q^{31} +(-4.92268 + 2.78697i) q^{32} +(-2.47014 - 2.14039i) q^{33} +(-0.612908 - 2.77641i) q^{34} +(3.47635 + 2.23411i) q^{35} +(3.30091 + 2.82494i) q^{36} +(-6.53193 - 1.91795i) q^{37} +(2.33684 - 3.14173i) q^{38} +(2.85648 - 2.47515i) q^{39} +(-0.963973 + 2.65909i) q^{40} +(3.55718 - 1.04448i) q^{41} +(-4.68293 - 12.4386i) q^{42} +(3.42696 + 0.492722i) q^{43} +(-2.40841 + 1.56878i) q^{44} +2.17234 q^{45} +(-3.50492 + 5.80651i) q^{46} +5.79646i q^{47} +(7.59198 - 5.01192i) q^{48} +(-1.43400 + 9.97370i) q^{49} +(0.498285 + 1.32352i) q^{50} +(1.28819 + 4.38719i) q^{51} +(-1.39932 - 3.01493i) q^{52} +(2.24737 + 2.59360i) q^{53} +(2.13594 + 1.58873i) q^{54} +(-0.404890 + 1.37893i) q^{55} +(-11.6501 + 0.941205i) q^{56} +(-3.40429 + 5.29718i) q^{57} +(-3.11500 - 14.1106i) q^{58} +(-2.36937 + 2.73440i) q^{59} +(1.25464 - 4.37210i) q^{60} +(0.780548 + 5.42883i) q^{61} +(0.915538 - 13.3782i) q^{62} +(3.72912 + 8.16564i) q^{63} +(-2.39493 - 7.63311i) q^{64} +(-1.51173 - 0.690386i) q^{65} +(3.69182 - 2.78140i) q^{66} +(-6.86024 - 10.6747i) q^{67} +(4.02089 - 0.0247011i) q^{68} +(4.98577 - 9.70082i) q^{69} +(-4.11963 + 4.14502i) q^{70} +(-1.89226 - 2.94442i) q^{71} +(-4.88464 + 3.72732i) q^{72} +(-4.95810 + 10.8567i) q^{73} +(4.58801 - 8.46401i) q^{74} +(-0.944769 - 2.06876i) q^{75} +(3.65185 + 4.16252i) q^{76} +(-5.87832 + 0.845175i) q^{77} +(2.57611 + 4.68353i) q^{78} +(-2.88977 + 3.33497i) q^{79} +(-3.39133 - 2.12106i) q^{80} +(-9.08382 - 5.83782i) q^{81} +(0.390092 + 5.22846i) q^{82} +(3.29376 - 11.2175i) q^{83} +(18.5881 - 2.78922i) q^{84} +(1.51942 - 1.31659i) q^{85} +(-1.69698 + 4.59281i) q^{86} +(6.54703 + 22.2971i) q^{87} +(-1.45555 - 3.79531i) q^{88} +(-2.54677 - 0.366170i) q^{89} +(-0.643810 + 3.00394i) q^{90} -6.86762i q^{91} +(-6.99057 - 6.56749i) q^{92} +21.5646i q^{93} +(-8.01541 - 1.71788i) q^{94} +(2.74051 + 0.394026i) q^{95} +(4.68053 + 11.9836i) q^{96} +(4.29177 + 14.6164i) q^{97} +(-13.3667 - 4.93882i) q^{98} +(-2.35942 + 2.04445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) $ 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.296367	+	1.38281i	−0.209563	+	0.977795i
$2$	−0.296367	+	1.38281i	−0.209563	+	0.977795i
$3$	0.323664	−	2.25113i	0.186867	−	1.29969i	−0.653191	−	0.757193i	$-0.726570\pi$
$3$	0.323664	−	2.25113i	0.186867	−	1.29969i	0.840058	−	0.542497i	$-0.182521\pi$
$4$	−1.82433	−	0.819638i	−0.912167	−	0.409819i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	3.01696	+	1.11473i	1.23167	+	0.455085i
$7$	−2.70611	−	3.12302i	−1.02281	−	1.18039i	−0.983453	−	0.181164i	$-0.942013\pi$
$7$	−2.70611	−	3.12302i	−1.02281	−	1.18039i	−0.0393603	−	0.999225i	$-0.512532\pi$
$8$	1.67408	−	2.27980i	0.591876	−	0.806029i
$9$	−2.08435	−	0.612020i	−0.694782	−	0.204007i
$10$	−0.105221	−	1.41029i	−0.0332738	−	0.445974i
$11$	0.776978	−	1.20900i	0.234268	−	0.364528i	−0.704138	−	0.710063i	$-0.748666\pi$
$11$	0.776978	−	1.20900i	0.234268	−	0.364528i	0.938406	+	0.345536i	$0.112303\pi$
$12$	−2.43558	+	3.84152i	−0.703092	+	1.10895i
$13$	1.25599	+	1.08833i	0.348350	+	0.301847i	0.811407	−	0.584481i	$-0.198702\pi$
$13$	1.25599	+	1.08833i	0.348350	+	0.301847i	−0.463057	+	0.886329i	$0.653247\pi$
$14$	5.12054	−	2.81648i	1.36852	−	0.752736i
$15$	0.323664	+	2.25113i	0.0835696	+	0.581239i
$16$	2.65639	+	2.99059i	0.664096	+	0.747647i
$17$	−1.82880	+	0.835186i	−0.443550	+	0.202562i	−0.624654	−	0.780902i	$-0.714760\pi$
$17$	−1.82880	+	0.835186i	−0.443550	+	0.202562i	0.181105	+	0.983464i	$0.442033\pi$
$18$	1.46404	−	2.70088i	0.345077	−	0.636603i
$19$	−2.51849	−	1.15016i	−0.577781	−	0.263864i	0.105018	−	0.994470i	$-0.466510\pi$
$19$	−2.51849	−	1.15016i	−0.577781	−	0.263864i	−0.682799	+	0.730607i	$0.739237\pi$
$20$	1.98135	+	0.272463i	0.443044	+	0.0609246i
$21$	−7.90618	+	5.08100i	−1.72527	+	1.10876i
$22$	1.44155	+	1.43272i	0.307340	+	0.305457i
$23$	4.53402	+	1.56289i	0.945409	+	0.325885i
$23$	4.53402	+	1.56289i	0.945409	+	0.325885i
$24$	−4.59028	−	4.50645i	−0.936986	−	0.919875i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−1.87718	+	1.41426i	−0.368146	+	0.277359i
$27$	0.781946	−	1.71222i	0.150486	−	0.329517i
$28$	2.37710	+	7.91545i	0.449230	+	1.49588i
$29$	−9.29457	+	4.24469i	−1.72596	+	0.788219i	−0.731649	+	0.681681i	$0.761249\pi$
$29$	−9.29457	+	4.24469i	−1.72596	+	0.788219i	−0.994309	+	0.106537i	$0.966024\pi$
$30$	−3.20881	−	0.219594i	−0.585846	−	0.0400923i
$31$	−9.38546	+	1.34943i	−1.68568	+	0.242364i	−0.917461	−	0.397825i	$-0.869765\pi$
$31$	−9.38546	+	1.34943i	−1.68568	+	0.242364i	−0.768217	+	0.640189i	$0.778856\pi$
$32$	−4.92268	+	2.78697i	−0.870216	+	0.492671i
$33$	−2.47014	−	2.14039i	−0.429996	−	0.372594i
$34$	−0.612908	−	2.77641i	−0.105113	−	0.476150i
$35$	3.47635	+	2.23411i	0.587610	+	0.377634i
$36$	3.30091	+	2.82494i	0.550152	+	0.470823i
$37$	−6.53193	−	1.91795i	−1.07384	−	0.315309i	−0.303430	−	0.952854i	$-0.598132\pi$
$37$	−6.53193	−	1.91795i	−1.07384	−	0.315309i	−0.770413	+	0.637545i	$0.779950\pi$
$38$	2.33684	−	3.14173i	0.379086	−	0.509655i
$39$	2.85648	−	2.47515i	0.457403	−	0.396342i
$40$	−0.963973	+	2.65909i	−0.152417	+	0.420439i
$41$	3.55718	−	1.04448i	0.555538	−	0.163121i	0.00810045	−	0.999967i	$-0.497422\pi$
$41$	3.55718	−	1.04448i	0.555538	−	0.163121i	0.547438	+	0.836846i	$0.315603\pi$
$42$	−4.68293	−	12.4386i	−0.722591	−	1.91932i
$43$	3.42696	+	0.492722i	0.522606	+	0.0751394i	0.398569	−	0.917138i	$-0.369507\pi$
$43$	3.42696	+	0.492722i	0.522606	+	0.0751394i	0.124037	+	0.992278i	$0.460416\pi$
$44$	−2.40841	+	1.56878i	−0.363082	+	0.236503i
$45$	2.17234			0.323834
$46$	−3.50492	+	5.80651i	−0.516772	+	0.856123i
$47$			5.79646i			0.845500i	0.906246	+	0.422750i	$0.138935\pi$
$47$			5.79646i			0.845500i	−0.906246	+	0.422750i	$0.861065\pi$
$48$	7.59198	−	5.01192i	1.09581	−	0.723409i
$49$	−1.43400	+	9.97370i	−0.204857	+	1.42481i
$50$	0.498285	+	1.32352i	0.0704681	+	0.187174i
$51$	1.28819	+	4.38719i	0.180383	+	0.614329i
$52$	−1.39932	−	3.01493i	−0.194051	−	0.418096i
$53$	2.24737	+	2.59360i	0.308699	+	0.356258i	0.888807	−	0.458282i	$-0.151535\pi$
$53$	2.24737	+	2.59360i	0.308699	+	0.356258i	−0.580108	+	0.814540i	$0.696989\pi$
$54$	2.13594	+	1.58873i	0.290664	+	0.216199i
$55$	−0.404890	+	1.37893i	−0.0545953	+	0.185935i
$56$	−11.6501	+	0.941205i	−1.55681	+	0.125774i
$57$	−3.40429	+	5.29718i	−0.450909	+	0.701629i
$58$	−3.11500	−	14.1106i	−0.409020	−	1.85281i
$59$	−2.36937	+	2.73440i	−0.308466	+	0.355988i	−0.888723	−	0.458445i	$-0.848407\pi$
$59$	−2.36937	+	2.73440i	−0.308466	+	0.355988i	0.580257	+	0.814433i	$0.302952\pi$
$60$	1.25464	−	4.37210i	0.161974	−	0.564435i
$61$	0.780548	+	5.42883i	0.0999389	+	0.695090i	0.976770	+	0.214291i	$0.0687442\pi$
$61$	0.780548	+	5.42883i	0.0999389	+	0.695090i	−0.876831	+	0.480799i	$0.840347\pi$
$62$	0.915538	−	13.3782i	0.116273	−	1.69904i
$63$	3.72912	+	8.16564i	0.469825	+	1.02877i
$64$	−2.39493	−	7.63311i	−0.299367	−	0.954138i
$65$	−1.51173	−	0.690386i	−0.187508	−	0.0856318i
$66$	3.69182	−	2.78140i	0.454432	−	0.342366i
$67$	−6.86024	−	10.6747i	−0.838111	−	1.30413i	−0.950583	−	0.310472i	$-0.899513\pi$
$67$	−6.86024	−	10.6747i	−0.838111	−	1.30413i	0.112471	−	0.993655i	$-0.464123\pi$
$68$	4.02089	−	0.0247011i	0.487605	−	0.00299545i
$69$	4.98577	−	9.70082i	0.600216	−	1.16784i
$70$	−4.11963	+	4.14502i	−0.492390	+	0.495424i
$71$	−1.89226	−	2.94442i	−0.224570	−	0.349438i	0.710625	−	0.703571i	$-0.248412\pi$
$71$	−1.89226	−	2.94442i	−0.224570	−	0.349438i	−0.935195	+	0.354133i	$0.884776\pi$
$72$	−4.88464	+	3.72732i	−0.575660	+	0.439269i
$73$	−4.95810	+	10.8567i	−0.580302	+	1.27068i	0.360826	+	0.932633i	$0.382495\pi$
$73$	−4.95810	+	10.8567i	−0.580302	+	1.27068i	−0.941128	+	0.338051i	$0.890232\pi$
$74$	4.58801	−	8.46401i	0.533345	−	0.983921i
$75$	−0.944769	−	2.06876i	−0.109093	−	0.238879i
$76$	3.65185	+	4.16252i	0.418896	+	0.477473i
$77$	−5.87832	+	0.845175i	−0.669897	+	0.0963166i
$78$	2.57611	+	4.68353i	0.291687	+	0.530305i
$79$	−2.88977	+	3.33497i	−0.325124	+	0.375213i	−0.894656	−	0.446756i	$-0.852579\pi$
$79$	−2.88977	+	3.33497i	−0.325124	+	0.375213i	0.569532	+	0.821969i	$0.307125\pi$
$80$	−3.39133	−	2.12106i	−0.379162	−	0.237141i
$81$	−9.08382	−	5.83782i	−1.00931	−	0.648646i
$82$	0.390092	+	5.22846i	0.0430784	+	0.577386i
$83$	3.29376	−	11.2175i	0.361538	−	1.23128i	−0.555174	−	0.831734i	$-0.687348\pi$
$83$	3.29376	−	11.2175i	0.361538	−	1.23128i	0.916711	−	0.399550i	$-0.130834\pi$
$84$	18.5881	−	2.78922i	2.02813	−	0.304329i
$85$	1.51942	−	1.31659i	0.164805	−	0.142804i
$86$	−1.69698	+	4.59281i	−0.182990	+	0.495255i
$87$	6.54703	+	22.2971i	0.701915	+	2.39050i
$88$	−1.45555	−	3.79531i	−0.155163	−	0.404582i
$89$	−2.54677	−	0.366170i	−0.269957	−	0.0388139i	0.00600697	−	0.999982i	$-0.498088\pi$
$89$	−2.54677	−	0.366170i	−0.269957	−	0.0388139i	−0.275964	+	0.961168i	$0.588997\pi$
$90$	−0.643810	+	3.00394i	−0.0678635	+	0.316643i
$91$		−	6.86762i		−	0.719922i
$92$	−6.99057	−	6.56749i	−0.728817	−	0.684709i
$93$			21.5646i			2.23615i
$94$	−8.01541	−	1.71788i	−0.826726	−	0.177185i
$95$	2.74051	+	0.394026i	0.281170	+	0.0404262i
$96$	4.68053	+	11.9836i	0.477705	+	1.22307i
$97$	4.29177	+	14.6164i	0.435763	+	1.48407i	0.826165	+	0.563429i	$0.190518\pi$
$97$	4.29177	+	14.6164i	0.435763	+	1.48407i	−0.390402	+	0.920645i	$0.627664\pi$
$98$	−13.3667	−	4.93882i	−1.35025	−	0.498897i
$99$	−2.35942	+	2.04445i	−0.237131	+	0.205475i
$100$	−1.97786	+	0.296785i	−0.197786	+	0.0296785i
$101$	5.03231	−	17.1385i	0.500733	−	1.70534i	−0.189611	−	0.981859i	$-0.560723\pi$
$101$	5.03231	−	17.1385i	0.500733	−	1.70534i	0.690344	−	0.723481i	$-0.257459\pi$
$102$	−6.44843	+	0.481113i	−0.638490	+	0.0476373i
$103$	2.67543	+	1.71939i	0.263618	+	0.169417i	0.665772	−	0.746155i	$-0.268102\pi$
$103$	2.67543	+	1.71939i	0.263618	+	0.169417i	−0.402155	+	0.915572i	$0.631739\pi$
$104$	4.58379	−	1.04147i	0.449478	−	0.102124i
$105$	6.15445	−	7.10261i	0.600612	−	0.693144i
$106$	−4.25250	+	2.33903i	−0.413039	+	0.227186i
$107$	10.6553	−	1.53199i	1.03008	−	0.148103i	0.393510	−	0.919320i	$-0.371261\pi$
$107$	10.6553	−	1.53199i	1.03008	−	0.148103i	0.636572	+	0.771217i	$0.280352\pi$
$108$	−2.82993	+	2.48275i	−0.272310	+	0.238903i
$109$	−5.50718	−	12.0590i	−0.527492	−	1.15505i	−0.966524	−	0.256575i	$-0.917406\pi$
$109$	−5.50718	−	12.0590i	−0.527492	−	1.15505i	0.439032	−	0.898471i	$-0.355321\pi$
$110$	−1.78680	−	0.968555i	−0.170365	−	0.0923481i
$111$	−6.43170	+	14.0835i	−0.610470	+	1.33674i
$112$	2.15119	−	16.3888i	0.203268	−	1.54860i
$113$	−6.69257	−	10.4138i	−0.629584	−	0.979653i	−0.998735	−	0.0502830i	$-0.983988\pi$
$113$	−6.69257	−	10.4138i	−0.629584	−	0.979653i	0.369151	−	0.929370i	$-0.379649\pi$
$114$	−6.31608	−	6.27740i	−0.591555	−	0.587932i
$115$	−4.79068	−	0.222200i	−0.446733	−	0.0207203i
$116$	20.4355	−	0.125539i	1.89739	−	0.0116560i
$117$	−1.95185	−	3.03714i	−0.180449	−	0.280784i
$118$	−3.07896	−	4.08678i	−0.283441	−	0.376218i
$119$	7.55724	+	3.45127i	0.692771	+	0.316378i
$120$	5.67395	+	3.03068i	0.517959	+	0.276662i
$121$	3.71158	+	8.12722i	0.337416	+	0.738838i
$122$	−7.73837	−	0.529574i	−0.700599	−	0.0479454i
$123$	−1.19994	−	8.34573i	−0.108195	−	0.752509i
$124$	18.2283	+	5.23088i	1.63695	+	0.469747i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−12.3967	+	2.73665i	−1.10439	+	0.243800i
$127$	5.70304	−	8.87411i	0.506063	−	0.787450i	−0.490399	−	0.871498i	$-0.663149\pi$
$127$	5.70304	−	8.87411i	0.506063	−	0.787450i	0.996462	+	0.0840487i	$0.0267851\pi$
$128$	11.2649	−	1.04954i	0.995688	−	0.0927671i
$129$	2.21836	−	7.55505i	0.195316	−	0.665185i
$130$	1.40270	−	1.88584i	0.123025	−	0.165399i
$131$	−0.586735	−	0.677128i	−0.0512633	−	0.0591610i	0.729539	−	0.683939i	$-0.239735\pi$
$131$	−0.586735	−	0.677128i	−0.0512633	−	0.0591610i	−0.780802	+	0.624778i	$0.785189\pi$
$132$	2.75201	+	5.92940i	0.239532	+	0.516088i
$133$	3.22335	+	10.9777i	0.279500	+	0.951890i
$134$	16.7943	−	6.32278i	1.45081	−	0.546205i
$135$	−0.267883	+	1.86316i	−0.0230557	+	0.160356i
$136$	−1.15750	+	5.56746i	−0.0992550	+	0.477406i
$137$		−	1.60015i		−	0.136710i	−0.997661	−	0.0683551i	$-0.978225\pi$
$137$		−	1.60015i		−	0.136710i	0.997661	−	0.0683551i	$-0.0217751\pi$
$138$	11.9368	+	9.76938i	1.01613	+	0.831625i
$139$	−6.63212			−0.562529			−0.281265	−	0.959630i	$-0.590754\pi$
$139$	−6.63212			−0.562529			−0.281265	+	0.959630i	$0.590754\pi$
$140$	−4.51085	−	6.92512i	−0.381237	−	0.585279i
$141$	13.0486	+	1.87610i	1.09889	+	0.157996i
$142$	4.63238	−	1.74401i	0.388741	−	0.146354i
$143$	2.29167	−	0.672894i	0.191639	−	0.0562702i
$144$	−3.70653	−	7.85918i	−0.308878	−	0.654932i
$145$	7.72221	−	6.69133i	0.641294	−	0.555685i
$146$	−13.5434	−	10.0737i	−1.12086	−	0.833705i
$147$	21.9879	+	6.45624i	1.81354	+	0.532502i
$148$	10.3444	+	8.85280i	0.850304	+	0.727695i
$149$	−16.3386	−	10.5002i	−1.33851	−	0.860207i	−0.341683	−	0.939815i	$-0.610997\pi$
$149$	−16.3386	−	10.5002i	−1.33851	−	0.860207i	−0.996826	+	0.0796079i	$0.974633\pi$
$150$	3.14070	−	0.693327i	0.256437	−	0.0566099i
$151$	9.38766	+	8.13445i	0.763957	+	0.661972i	0.947037	−	0.321126i	$-0.104061\pi$
$151$	9.38766	+	8.13445i	0.763957	+	0.661972i	−0.183080	+	0.983098i	$0.558607\pi$
$152$	−6.83826	+	3.81619i	−0.554656	+	0.309534i
$153$	4.32301	−	0.621555i	0.349494	−	0.0502497i
$154$	0.573421	−	8.37909i	0.0462076	−	0.675206i
$155$	8.62511	−	3.93895i	0.692785	−	0.316384i
$156$	−7.23991	+	2.17423i	−0.579656	+	0.174077i
$157$	9.67886	−	21.1937i	0.772457	−	1.69144i	0.0512896	−	0.998684i	$-0.483667\pi$
$157$	9.67886	−	21.1937i	0.772457	−	1.69144i	0.721167	−	0.692761i	$-0.243606\pi$
$158$	−3.75520	−	4.98437i	−0.298748	−	0.396535i
$159$	6.56591	−	4.21966i	0.520711	−	0.334641i
$160$	3.93810	−	4.06096i	0.311334	−	0.321047i
$161$	−7.38863	−	18.3892i	−0.582306	−	1.44927i
$162$	10.7647	−	10.8311i	0.845758	−	0.850969i
$163$	−4.75266	+	3.05435i	−0.372257	+	0.239235i	−0.713371	−	0.700787i	$-0.752832\pi$
$163$	−4.75266	+	3.05435i	−0.372257	+	0.239235i	0.341113	+	0.940022i	$0.389196\pi$
$164$	−7.34558	−	1.01012i	−0.573593	−	0.0788769i
$165$	2.97310	+	1.35777i	0.231455	+	0.105702i
$166$	14.5356	+	7.87916i	1.12818	+	0.611541i
$167$	3.24779	−	1.48322i	0.251322	−	0.114775i	−0.285771	−	0.958298i	$-0.592250\pi$
$167$	3.24779	−	1.48322i	0.251322	−	0.114775i	0.537093	+	0.843523i	$0.319522\pi$
$168$	−1.65193	+	26.5305i	−0.127449	+	2.04687i
$169$	−1.45702	−	10.1338i	−0.112079	−	0.779524i
$170$	1.37029	+	2.49127i	0.105096	+	0.191072i
$171$	4.54549	+	3.93869i	0.347602	+	0.301199i
$172$	−5.84806	−	3.70775i	−0.445910	−	0.282714i
$173$	8.30961	−	12.9300i	0.631768	−	0.983050i	−0.366839	−	0.930285i	$-0.619560\pi$
$173$	8.30961	−	12.9300i	0.631768	−	0.983050i	0.998607	−	0.0527658i	$-0.0168037\pi$
$174$	−32.7730	+	2.44518i	−2.48452	+	0.185368i
$175$	−3.96495	−	1.16422i	−0.299722	−	0.0880064i
$176$	5.67958	−	0.887953i	0.428114	−	0.0669320i
$177$	5.38861	+	6.21878i	0.405033	+	0.467432i
$178$	1.26112	−	3.41318i	0.0945250	−	0.255829i
$179$	−14.8664	+	4.36518i	−1.11117	+	0.326269i	−0.785281	−	0.619139i	$-0.787482\pi$
$179$	−14.8664	+	4.36518i	−1.11117	+	0.326269i	−0.325889	+	0.945408i	$0.605664\pi$
$180$	−3.96308	−	1.78054i	−0.295390	−	0.132713i
$181$	−0.825489	+	5.74140i	−0.0613581	+	0.426755i	0.935870	+	0.352346i	$0.114616\pi$
$181$	−0.825489	+	5.74140i	−0.0613581	+	0.426755i	−0.997228	+	0.0744087i	$0.976293\pi$
$182$	9.49662	+	2.03533i	0.703936	+	0.150869i
$183$	12.4736			0.922077
$184$	11.1534	−	7.72025i	0.822238	−	0.569144i
$185$	6.80769			0.500511
$186$	−29.8198	−	6.39104i	−2.18650	−	0.468614i
$187$	−0.411198	+	2.85994i	−0.0300698	+	0.209140i
$188$	4.75100	−	10.5747i	0.346502	−	0.771237i
$189$	−7.46333	+	2.19143i	−0.542877	+	0.159403i
$190$	−1.35706	+	3.67283i	−0.0984514	+	0.266455i
$191$	−15.7544	−	18.1815i	−1.13995	−	1.31557i	−0.942099	−	0.335336i	$-0.891150\pi$
$191$	−15.7544	−	18.1815i	−1.13995	−	1.31557i	−0.197848	−	0.980233i	$-0.563395\pi$
$192$	−17.9583	+	2.92074i	−1.29603	+	0.210787i
$193$	−15.1983	−	4.46261i	−1.09399	−	0.321226i	−0.315531	−	0.948915i	$-0.602183\pi$
$193$	−15.1983	−	4.46261i	−1.09399	−	0.321226i	−0.778464	+	0.627690i	$0.784001\pi$
$194$	−21.4837	+	1.60288i	−1.54244	+	0.115080i
$195$	−2.04344	+	3.17966i	−0.146334	+	0.227700i
$196$	10.7909	−	17.0200i	0.770780	−	1.21571i
$197$	5.88945	+	5.10324i	0.419606	+	0.363591i	0.838924	−	0.544249i	$-0.183185\pi$
$197$	5.88945	+	5.10324i	0.419606	+	0.363591i	−0.419318	+	0.907839i	$0.637731\pi$
$198$	−2.12784	−	3.86855i	−0.151219	−	0.274926i
$199$	1.59369	+	11.0844i	0.112974	+	0.785750i	0.965000	+	0.262250i	$0.0844646\pi$
$199$	1.59369	+	11.0844i	0.112974	+	0.785750i	−0.852026	+	0.523499i	$0.824626\pi$
$200$	0.175773	−	2.82296i	0.0124290	−	0.199613i
$201$	−26.2506	+	11.9883i	−1.85158	+	0.845587i
$202$	22.2078	+	12.0380i	1.56254	+	0.846991i
$203$	38.4083	+	17.5405i	2.69574	+	1.23110i
$204$	1.24581	−	9.05955i	0.0872243	−	0.634295i
$205$	−3.11882	+	2.00435i	−0.217828	+	0.139990i
$206$	−3.17051	+	3.19004i	−0.220900	+	0.222261i
$207$	−8.49396	−	6.03252i	−0.590371	−	0.419289i
$208$	0.0816727	+	6.64717i	0.00566298	+	0.460899i
$209$	−3.34735	+	2.15121i	−0.231541	+	0.148802i
$210$	7.99759	+	10.6154i	0.551886	+	0.732533i
$211$	−3.08634	+	6.75815i	−0.212473	+	0.465250i	−0.985620	−	0.168976i	$-0.945954\pi$
$211$	−3.08634	+	6.75815i	−0.212473	+	0.465250i	0.773147	+	0.634226i	$0.218681\pi$
$212$	−1.97413	−	6.57361i	−0.135584	−	0.451478i
$213$	−7.24073	+	3.30673i	−0.496126	+	0.226573i
$214$	−1.03940	+	15.1882i	−0.0710522	+	1.03825i
$215$	−3.42696	+	0.492722i	−0.233716	+	0.0336034i
$216$	−2.59448	−	4.64907i	−0.176532	−	0.316329i
$217$	29.6124	+	25.6593i	2.01022	+	1.74186i
$218$	18.3075	−	4.04149i	1.23994	−	0.273724i
$219$	22.8351	+	14.6753i	1.54306	+	0.991662i
$220$	1.86888	−	2.18376i	0.126000	−	0.147229i
$221$	−3.20592	−	0.941343i	−0.215653	−	0.0633216i
$222$	−17.5686	−	13.0677i	−1.17913	−	0.877046i
$223$	−3.81432	+	3.30513i	−0.255426	+	0.221328i	−0.773156	−	0.634216i	$-0.781323\pi$
$223$	−3.81432	+	3.30513i	−0.255426	+	0.221328i	0.517730	+	0.855544i	$0.326777\pi$
$224$	22.0251	+	7.83178i	1.47161	+	0.523283i
$225$	−2.08435	+	0.612020i	−0.138956	+	0.0408013i
$226$	16.3838	−	6.16825i	1.08984	−	0.410306i
$227$	−8.56284	−	1.23115i	−0.568336	−	0.0817144i	−0.147844	−	0.989011i	$-0.547233\pi$
$227$	−8.56284	−	1.23115i	−0.568336	−	0.0817144i	−0.420492	+	0.907296i	$0.638142\pi$
$228$	10.5523	−	6.87354i	0.698845	−	0.455211i
$229$	7.50515			0.495954			0.247977	−	0.968766i	$-0.420234\pi$
$229$	7.50515			0.495954			0.247977	+	0.968766i	$0.420234\pi$
$230$	1.72706	−	6.55875i	0.113879	−	0.432471i
$231$			13.5064i			0.888657i
$232$	−5.88281	+	28.2956i	−0.386225	+	1.85770i
$233$	−2.78841	+	19.3938i	−0.182675	+	1.27053i	0.667731	+	0.744403i	$0.267266\pi$
$233$	−2.78841	+	19.3938i	−0.182675	+	1.27053i	−0.850405	+	0.526128i	$0.823643\pi$
$234$	4.77826	−	1.79894i	0.312364	−	0.117600i
$235$	−1.63305	−	5.56166i	−0.106528	−	0.362803i
$236$	6.56374	−	3.04643i	0.427263	−	0.198306i
$237$	6.57213	+	7.58464i	0.426906	+	0.492676i
$238$	−7.01217	+	9.42739i	−0.454532	+	0.611087i
$239$	−1.79259	+	6.10500i	−0.115953	+	0.394900i	−0.996934	−	0.0782528i	$-0.975066\pi$
$239$	−1.79259	+	6.10500i	−0.115953	+	0.394900i	0.880981	+	0.473152i	$0.156884\pi$
$240$	−5.87243	+	6.94781i	−0.379063	+	0.448479i
$241$	6.66844	−	10.3763i	0.429552	−	0.668396i	−0.557247	−	0.830347i	$-0.688142\pi$
$241$	6.66844	−	10.3763i	0.429552	−	0.668396i	0.986799	+	0.161951i	$0.0517785\pi$
$242$	−12.3384	+	2.72377i	−0.793142	+	0.175091i
$243$	−12.3838	+	14.2917i	−0.794421	+	0.916811i
$244$	3.02570	−	10.5438i	0.193700	−	0.674995i
$245$	−1.43400	−	9.97370i	−0.0916150	−	0.637196i
$246$	11.8962	+	0.814114i	0.758474	+	0.0519060i
$247$	−1.91146	−	4.18552i	−0.121624	−	0.266318i
$248$	−12.6356	+	23.6560i	−0.802359	+	1.50216i
$249$	−24.1860	−	11.0454i	−1.53273	−	0.699974i
$250$	−0.850980	−	1.12953i	−0.0538207	−	0.0714376i
$251$	−7.73171	−	12.0308i	−0.488021	−	0.759376i	0.506686	−	0.862131i	$-0.330870\pi$
$251$	−7.73171	−	12.0308i	−0.488021	−	0.759376i	−0.994707	+	0.102755i	$0.967234\pi$
$252$	−0.110291	−	17.9534i	−0.00694768	−	1.13096i
$253$	5.41237	−	4.26731i	0.340273	−	0.268283i
$254$	10.5810	+	10.5162i	0.663912	+	0.659846i
$255$	−2.47203	−	3.84655i	−0.154804	−	0.240880i
$256$	−1.88723	+	15.8883i	−0.117952	+	0.993019i
$257$	−4.27982	+	9.37149i	−0.266968	+	0.584578i	−0.994877	−	0.101096i	$-0.967765\pi$
$257$	−4.27982	+	9.37149i	−0.266968	+	0.584578i	0.727909	+	0.685674i	$0.240492\pi$
$258$	9.78975	+	5.30664i	0.609483	+	0.330377i
$259$	11.6863	+	25.5895i	0.726153	+	1.59005i
$260$	2.19204	+	2.49857i	0.135945	+	0.154955i
$261$	21.9709	−	3.15894i	1.35997	−	0.195534i
$262$	1.11023	−	0.610666i	0.0685902	−	0.0377270i
$263$	−6.21917	+	7.17730i	−0.383490	+	0.442572i	−0.914372	−	0.404874i	$-0.867315\pi$
$263$	−6.21917	+	7.17730i	−0.383490	+	0.442572i	0.530882	+	0.847446i	$0.321861\pi$
$264$	−9.01485	+	2.04824i	−0.554826	+	0.126060i
$265$	−2.88703	−	1.85538i	−0.177349	−	0.113975i
$266$	−16.1354	+	1.20385i	−0.989326	+	0.0738130i
$267$	−1.64859	+	5.61459i	−0.100892	+	0.343607i
$268$	3.76594	+	25.0972i	0.230041	+	1.53306i
$269$	−1.12161	+	0.971883i	−0.0683860	+	0.0592568i	−0.688383	−	0.725347i	$-0.741679\pi$
$269$	−1.12161	+	0.971883i	−0.0683860	+	0.0592568i	0.619997	+	0.784604i	$0.287134\pi$
$270$	−2.49701	−	0.922611i	−0.151963	−	0.0561483i
$271$	−3.09540	−	10.5420i	−0.188032	−	0.640379i	−0.998508	−	0.0546067i	$-0.982610\pi$
$271$	−3.09540	−	10.5420i	−0.188032	−	0.640379i	0.810476	−	0.585772i	$-0.199209\pi$
$272$	−7.35570	−	3.25062i	−0.446005	−	0.197098i
$273$	−15.4599	−	2.22280i	−0.935676	−	0.134530i
$274$	2.21271	+	0.474231i	0.133674	+	0.0286494i
$275$		−	1.43714i		−	0.0866630i
$276$	−17.0469	+	13.6110i	−1.02610	+	0.819287i
$277$		−	8.95461i		−	0.538030i	−0.963136	−	0.269015i	$-0.913302\pi$
$277$		−	8.95461i		−	0.538030i	0.963136	−	0.269015i	$-0.0866982\pi$
$278$	1.96554	−	9.17097i	0.117885	−	0.550038i
$279$	20.3884	+	2.93141i	1.22062	+	0.175499i
$280$	10.9130	−	4.18528i	0.652176	−	0.250119i
$281$	6.10965	+	20.8076i	0.364471	+	1.24128i	0.913970	+	0.405781i	$0.133000\pi$
$281$	6.10965	+	20.8076i	0.364471	+	1.24128i	−0.549499	+	0.835494i	$0.685181\pi$
$282$	−6.46146	+	17.4877i	−0.384774	+	1.04138i
$283$	21.1004	−	18.2836i	1.25429	−	1.08685i	0.261723	−	0.965143i	$-0.415709\pi$
$283$	21.1004	−	18.2836i	1.25429	−	1.08685i	0.992566	−	0.121704i	$-0.0388360\pi$
$284$	1.03876	+	6.92257i	0.0616391	+	0.410779i
$285$	1.77401	−	6.04171i	0.105083	−	0.357880i
$286$	0.251312	+	3.36837i	0.0148604	+	0.199176i
$287$	−12.8881	−	8.28265i	−0.760758	−	0.488909i
$288$	11.9663	−	2.79623i	0.705119	−	0.164770i
$289$	−8.48565	+	9.79296i	−0.499156	+	0.576057i
$290$	6.96424	+	12.6614i	0.408954	+	0.743505i
$291$	34.2926	−	4.93053i	2.01027	−	0.289033i
$292$	17.9438	−	15.7424i	1.05008	−	0.921257i
$293$	−11.0733	−	24.2471i	−0.646908	−	1.41653i	−0.894235	−	0.447598i	$-0.852279\pi$
$293$	−11.0733	−	24.2471i	−0.646908	−	1.41653i	0.247327	−	0.968932i	$-0.420448\pi$
$294$	−15.4443	+	28.4918i	−0.900728	+	1.66167i
$295$	1.50302	−	3.29117i	0.0875095	−	0.191619i
$296$	−15.3075	+	11.6807i	−0.889729	+	0.678925i
$297$	−1.46252	−	2.27573i	−0.0848643	−	0.132051i
$298$	19.3620	−	19.4813i	1.12161	−	1.12852i
$299$	3.99378	+	6.89748i	0.230966	+	0.398891i
$300$	0.0279421	+	4.54847i	0.00161324	+	0.262606i
$301$	−7.73494	−	12.0358i	−0.445834	−	0.693732i
$302$	−14.0306	+	10.5706i	−0.807370	+	0.608268i
$303$	−36.9521	−	16.8755i	−2.12284	−	0.969470i
$304$	−3.25044	−	10.5870i	−0.186425	−	0.607207i
$305$	−2.27841	−	4.98902i	−0.130461	−	0.285670i
$306$	−0.421703	+	6.16211i	−0.0241072	+	0.352264i
$307$	3.37692	+	23.4870i	0.192731	+	1.34047i	0.824740	+	0.565512i	$0.191321\pi$
$307$	3.37692	+	23.4870i	0.192731	+	1.34047i	−0.632009	+	0.774961i	$0.717770\pi$
$308$	11.4168	+	3.27622i	0.650530	+	0.186680i
$309$	4.73652	−	5.46623i	0.269451	−	0.310963i
$310$	2.89063	+	13.0943i	0.164177	+	0.743704i
$311$	16.8179	−	26.1692i	0.953658	−	1.48392i	0.0803416	−	0.996767i	$-0.474399\pi$
$311$	16.8179	−	26.1692i	0.953658	−	1.48392i	0.873316	−	0.487153i	$-0.161965\pi$
$312$	−0.860877	−	10.6558i	−0.0487376	−	0.603265i
$313$	1.30068	−	4.42971i	0.0735188	−	0.250382i	−0.914531	−	0.404515i	$-0.867440\pi$
$313$	1.30068	−	4.42971i	0.0735188	−	0.250382i	0.988050	+	0.154133i	$0.0492584\pi$
$314$	26.4385	+	19.6652i	1.49201	+	1.10977i
$315$	−5.87860	−	6.78426i	−0.331221	−	0.382250i
$316$	8.00536	−	3.71553i	0.450337	−	0.209015i
$317$	5.26998	+	17.9479i	0.295992	+	1.00806i	0.964441	+	0.264298i	$0.0851401\pi$
$317$	5.26998	+	17.9479i	0.295992	+	1.00806i	−0.668449	+	0.743758i	$0.733042\pi$
$318$	3.88907	+	10.3300i	0.218088	+	0.579277i
$319$	−2.08984	+	14.5352i	−0.117009	+	0.813814i
$320$	4.44841	+	6.64918i	0.248674	+	0.371701i
$321$		−	24.4822i		−	1.36646i
$322$	27.6185	−	4.76714i	1.53912	−	0.265662i
$323$	5.56641			0.309723
$324$	11.7870	+	18.0956i	0.654834	+	1.00531i
$325$	1.64500	+	0.236516i	0.0912483	+	0.0131195i
$326$	−2.81506	−	7.47724i	−0.155912	−	0.414126i
$327$	−28.9289	+	8.49430i	−1.59977	+	0.469736i
$328$	3.57379	−	9.85818i	0.197329	−	0.544327i
$329$	18.1024	−	15.6858i	0.998019	−	0.864789i
$330$	−2.75866	+	3.70884i	−0.151860	+	0.204165i
$331$	−22.7378	−	6.67642i	−1.24978	−	0.366969i	−0.411100	−	0.911590i	$-0.634855\pi$
$331$	−22.7378	−	6.67642i	−1.24978	−	0.366969i	−0.838682	+	0.544621i	$0.816673\pi$
$332$	−15.2032	+	17.7648i	−0.834387	+	0.974971i
$333$	12.4410	+	7.99534i	0.681762	+	0.438142i
$334$	1.08847	+	4.93066i	0.0595585	+	0.269794i
$335$	9.58977	+	8.30958i	0.523945	+	0.454001i
$336$	−36.1970	−	10.1471i	−1.97471	−	0.553567i
$337$	−0.883796	+	0.127071i	−0.0481435	+	0.00692198i	−0.166344	−	0.986068i	$-0.553196\pi$
$337$	−0.883796	+	0.127071i	−0.0481435	+	0.00692198i	0.118201	+	0.992990i	$0.462287\pi$
$338$	14.4450	+	0.988539i	0.785703	+	0.0537694i
$339$	−25.6091	+	11.6953i	−1.39089	+	0.635200i
$340$	−3.85106	+	1.15652i	−0.208853	+	0.0627210i
$341$	−5.66084	+	12.3955i	−0.306552	+	0.671254i
$342$	−6.79359	+	5.11825i	−0.367355	+	0.276763i
$343$	10.6941	−	6.87271i	0.577430	−	0.371091i
$344$	6.86029	−	6.98790i	0.369882	−	0.376762i
$345$	−2.05077	+	10.7125i	−0.110410	+	0.576743i
$346$	15.4171	+	15.3226i	0.828827	+	0.823751i
$347$	−6.47167	+	4.15909i	−0.347417	+	0.223272i	−0.702698	−	0.711488i	$-0.748022\pi$
$347$	−6.47167	+	4.15909i	−0.347417	+	0.223272i	0.355281	+	0.934760i	$0.384385\pi$
$348$	6.33162	−	46.0436i	0.339411	−	2.46820i
$349$	−20.6802	−	9.44434i	−1.10699	−	0.505544i	−0.223833	−	0.974628i	$-0.571857\pi$
$349$	−20.6802	−	9.44434i	−1.10699	−	0.505544i	−0.883154	+	0.469084i	$0.844584\pi$
$350$	2.78497	−	5.13775i	0.148863	−	0.274624i
$351$	2.84557	−	1.29953i	0.151886	−	0.0693638i
$352$	−0.455367	+	8.11694i	−0.0242711	+	0.432635i
$353$	−3.26950	−	22.7399i	−0.174018	−	1.21032i	−0.870288	−	0.492542i	$-0.836068\pi$
$353$	−3.26950	−	22.7399i	−0.174018	−	1.21032i	0.696270	−	0.717780i	$-0.254841\pi$
$354$	−10.1964	+	5.60839i	−0.541933	+	0.298082i
$355$	2.64515	+	2.29204i	0.140390	+	0.121649i
$356$	4.34603	+	2.75545i	0.230339	+	0.146038i
$357$	10.2153	−	15.8953i	0.540649	−	0.841267i
$358$	−1.63030	−	21.8512i	−0.0861642	−	1.15487i
$359$	13.1342	+	3.85654i	0.693196	+	0.203541i	0.609307	−	0.792935i	$-0.291448\pi$
$359$	13.1342	+	3.85654i	0.693196	+	0.203541i	0.0838887	+	0.996475i	$0.473266\pi$
$360$	3.63667	−	4.95250i	0.191669	−	0.261019i
$361$	−7.42243	−	8.56594i	−0.390654	−	0.450839i
$362$	−7.69462	−	2.84305i	−0.404420	−	0.149428i
$363$	19.4967	−	5.72475i	1.02331	−	0.300472i
$364$	−5.62896	+	12.5288i	−0.295038	+	0.656689i
$365$	1.69857	−	11.8138i	0.0889072	−	0.618363i
$366$	−3.69677	+	17.2487i	−0.193233	+	0.901603i
$367$	11.2911			0.589391			0.294696	−	0.955591i	$-0.404782\pi$
$367$	11.2911			0.589391			0.294696	+	0.955591i	$0.404782\pi$
$368$	7.37015	+	17.7110i	0.384196	+	0.923252i
$369$	−8.05364			−0.419256
$370$	−2.01757	+	9.41375i	−0.104889	+	0.489397i
$371$	2.01823	−	14.0371i	0.104781	−	0.728771i
$372$	17.6752	−	39.3411i	0.916417	−	2.03974i
$373$	−13.1677	+	3.86638i	−0.681796	+	0.200193i	−0.604249	−	0.796795i	$-0.706527\pi$
$373$	−13.1677	+	3.86638i	−0.681796	+	0.200193i	−0.0775468	+	0.996989i	$0.524709\pi$
$374$	−3.83290	−	1.41620i	−0.198194	−	0.0732301i
$375$	1.48934	+	1.71878i	0.0769090	+	0.0887577i
$376$	13.2147	+	9.70372i	0.681498	+	0.500431i
$377$	−16.2935	−	4.78421i	−0.839159	−	0.246399i
$378$	−0.818453	−	10.9698i	−0.0420967	−	0.564228i
$379$	−2.53696	+	3.94759i	−0.130315	+	0.202774i	−0.900279	−	0.435313i	$-0.856638\pi$
$379$	−2.53696	+	3.94759i	−0.130315	+	0.202774i	0.769964	+	0.638087i	$0.220274\pi$
$380$	−4.67664	−	2.96506i	−0.239907	−	0.152104i
$381$	−18.1309	−	15.7105i	−0.928874	−	0.804874i
$382$	29.8107	−	16.3969i	1.52525	−	0.838940i
$383$	−3.14997	−	21.9085i	−0.160956	−	1.11947i	−0.896837	−	0.442361i	$-0.854141\pi$
$383$	−3.14997	−	21.9085i	−0.160956	−	1.11947i	0.735881	−	0.677111i	$-0.236768\pi$
$384$	1.28339	−	25.6985i	0.0654929	−	1.31142i
$385$	5.40209	−	2.46705i	0.275316	−	0.125733i
$386$	10.6752	−	19.6937i	0.543354	−	1.00239i
$387$	−6.84141	−	3.12437i	−0.347768	−	0.158821i
$388$	4.15057	−	30.1829i	0.210713	−	1.53231i
$389$	−15.5442	+	9.98965i	−0.788122	+	0.506495i	−0.871720	−	0.490004i	$-0.836995\pi$
$389$	−15.5442	+	9.98965i	−0.788122	+	0.506495i	0.0835978	+	0.996500i	$0.473359\pi$
$390$	−3.79126	−	3.76804i	−0.191978	−	0.190802i
$391$	−9.59713	+	0.928535i	−0.485348	+	0.0469580i
$392$	20.3374	+	19.9660i	1.02719	+	1.00843i
$393$	−1.71421	+	1.10165i	−0.0864704	+	0.0555711i
$394$	−8.80225	+	6.63157i	−0.443451	+	0.334093i
$395$	1.83314	−	4.01402i	0.0922353	−	0.201967i
$396$	5.98009	−	1.79589i	0.300511	−	0.0902468i
$397$	5.08028	−	2.32008i	0.254972	−	0.116442i	−0.283829	−	0.958875i	$-0.591605\pi$
$397$	5.08028	−	2.32008i	0.254972	−	0.116442i	0.538801	+	0.842433i	$0.318878\pi$
$398$	−15.7999	−	1.08126i	−0.791977	−	0.0541988i
$399$	25.7556	−	3.70309i	1.28939	−	0.185386i
$400$	3.85153	+	1.07969i	0.192576	+	0.0539846i
$401$	−18.1359	−	15.7149i	−0.905665	−	0.784763i	0.0714569	−	0.997444i	$-0.477235\pi$
$401$	−18.1359	−	15.7149i	−0.905665	−	0.784763i	−0.977122	+	0.212681i	$0.931781\pi$
$402$	−8.79769	−	39.8526i	−0.438789	−	1.98767i
$403$	−13.2567	−	8.51956i	−0.660363	−	0.424390i
$404$	−23.2279	+	27.1416i	−1.15563	+	1.35035i
$405$	10.3606	+	3.04214i	0.514820	+	0.151165i
$406$	−35.6382	+	47.9131i	−1.76869	+	2.37789i
$407$	−7.39397	+	6.40691i	−0.366505	+	0.317579i
$408$	12.1584	+	4.40767i	0.601932	+	0.218212i
$409$	16.9095	−	4.96506i	0.836119	−	0.245507i	0.164475	−	0.986381i	$-0.447407\pi$
$409$	16.9095	−	4.96506i	0.836119	−	0.245507i	0.671643	+	0.740875i	$0.265589\pi$
$410$	−1.84732	−	4.90677i	−0.0912325	−	0.242328i
$411$	−3.60215	−	0.517910i	−0.177681	−	0.0255466i
$412$	−3.47159	−	5.32963i	−0.171033	−	0.262572i
$413$	14.9513			0.735708
$414$	10.8592	−	9.95771i	0.533699	−	0.489395i
$415$			11.6911i			0.573894i
$416$	−9.21599	−	1.85706i	−0.451851	−	0.0910500i
$417$	−2.14658	+	14.9298i	−0.105118	+	0.731114i
$418$	−1.98268	−	5.26630i	−0.0969758	−	0.257583i
$419$	−7.41127	−	25.2405i	−0.362064	−	1.23308i	−0.916224	−	0.400667i	$-0.868778\pi$
$419$	−7.41127	−	25.2405i	−0.362064	−	1.23308i	0.554159	−	0.832411i	$-0.313040\pi$
$420$	−17.0493	+	7.91311i	−0.831922	+	0.386120i
$421$	5.68204	+	6.55742i	0.276926	+	0.319589i	0.877126	−	0.480261i	$-0.159458\pi$
$421$	5.68204	+	6.55742i	0.276926	+	0.319589i	−0.600200	+	0.799850i	$0.704912\pi$
$422$	−8.43056	−	6.27072i	−0.410393	−	0.305254i
$423$	3.54754	−	12.0818i	0.172488	−	0.587439i
$424$	9.67513	−	0.781650i	0.469866	−	0.0379603i
$425$	−1.08695	+	1.69133i	−0.0527248	+	0.0820415i
$426$	−2.42667	−	10.9926i	−0.117573	−	0.532591i
$427$	14.8421	−	17.1287i	0.718258	−	0.828914i
$428$	−20.6944	−	5.93859i	−1.00030	−	0.287052i
$429$	−0.773043	−	5.37663i	−0.0373229	−	0.259586i
$430$	0.334294	−	4.88486i	0.0161211	−	0.235569i
$431$	6.57594	+	14.3993i	0.316752	+	0.693589i	0.999306	−	0.0372453i	$-0.0118583\pi$
$431$	6.57594	+	14.3993i	0.316752	+	0.693589i	−0.682554	+	0.730835i	$0.739131\pi$
$432$	7.19770	−	2.20984i	0.346299	−	0.106321i
$433$	23.9242	+	10.9258i	1.14972	+	0.525060i	0.896804	−	0.442428i	$-0.145883\pi$
$433$	23.9242	+	10.9258i	1.14972	+	0.525060i	0.252917	+	0.967488i	$0.418610\pi$
$434$	−44.2580	+	33.3437i	−2.12445	+	1.60055i
$435$	−12.5637	−	19.5494i	−0.602381	−	0.937323i
$436$	0.162878	+	26.5136i	0.00780044	+	1.26977i
$437$	−9.62132	−	9.15095i	−0.460250	−	0.437749i
$438$	−27.0607	+	27.2274i	−1.29301	+	1.30098i
$439$	−1.30276	−	2.02714i	−0.0621774	−	0.0967500i	0.808773	−	0.588121i	$-0.200132\pi$
$439$	−1.30276	−	2.02714i	−0.0621774	−	0.0967500i	−0.870950	+	0.491371i	$0.836496\pi$
$440$	2.46586	+	3.23150i	0.117555	+	0.154056i
$441$	9.09305	−	19.9110i	0.433003	−	0.948143i
$442$	2.25183	−	4.15420i	0.107108	−	0.197595i
$443$	−9.92170	−	21.7255i	−0.471394	−	1.03221i	−0.984741	−	0.174028i	$-0.944322\pi$
$443$	−9.92170	−	21.7255i	−0.471394	−	1.03221i	0.513347	−	0.858181i	$-0.328406\pi$
$444$	23.2769	−	20.4212i	1.10467	−	0.969149i
$445$	2.54677	−	0.366170i	0.120728	−	0.0173581i
$446$	−3.43993	−	6.25402i	−0.162886	−	0.296136i
$447$	−28.9254	+	33.3817i	−1.36813	+	1.57890i
$448$	−17.3574	+	28.1354i	−0.820058	+	1.32927i
$449$	4.08053	+	2.62240i	0.192572	+	0.123758i	0.633374	−	0.773846i	$-0.281670\pi$
$449$	4.08053	+	2.62240i	0.192572	+	0.123758i	−0.440802	+	0.897604i	$0.645306\pi$
$450$	−0.228576	−	3.06364i	−0.0107752	−	0.144421i
$451$	1.50107	−	5.11217i	0.0706826	−	0.240723i
$452$	3.67390	+	24.4838i	0.172806	+	1.15162i
$453$	21.3502	−	18.5000i	1.00312	−	0.869206i
$454$	4.24019	−	11.4759i	0.199002	−	0.538592i
$455$	1.93483	+	6.58943i	0.0907063	+	0.308917i
$456$	6.37744	+	16.6290i	0.298651	+	0.778723i
$457$	−1.96294	−	0.282228i	−0.0918224	−	0.0132021i	0.0962505	−	0.995357i	$-0.469315\pi$
$457$	−1.96294	−	0.282228i	−0.0918224	−	0.0132021i	−0.188073	+	0.982155i	$0.560224\pi$
$458$	−2.22428	+	10.3782i	−0.103934	+	0.484941i
$459$			3.78438i			0.176640i
$460$	8.55768	+	4.33199i	0.399004	+	0.201980i
$461$		−	17.2088i		−	0.801494i	−0.916189	−	0.400747i	$-0.868751\pi$
$461$		−	17.2088i		−	0.801494i	0.916189	−	0.400747i	$-0.131249\pi$
$462$	−18.6768	−	4.00285i	−0.868924	−	0.186229i
$463$	−4.82705	−	0.694025i	−0.224332	−	0.0322541i	0.0292322	−	0.999573i	$-0.490694\pi$
$463$	−4.82705	−	0.694025i	−0.224332	−	0.0322541i	−0.253564	+	0.967319i	$0.581603\pi$
$464$	−37.3841	−	16.5207i	−1.73551	−	0.766954i
$465$	−6.07546	−	20.6911i	−0.281743	−	0.959528i
$466$	−25.9916	−	9.60352i	−1.20404	−	0.444875i
$467$	0.346683	−	0.300402i	0.0160426	−	0.0139010i	−0.646803	−	0.762657i	$-0.723894\pi$
$467$	0.346683	−	0.300402i	0.0160426	−	0.0139010i	0.662845	+	0.748757i	$0.269349\pi$
$468$	1.07147	+	7.14057i	0.0495288	+	0.330073i
$469$	−14.7728	+	50.3116i	−0.682146	+	2.32318i
$470$	8.17471	−	0.609910i	0.377071	−	0.0281330i
$471$	−44.5772	−	28.6480i	−2.05401	−	1.32003i
$472$	2.26736	+	9.97927i	0.104364	+	0.459333i
$473$	3.25837	−	3.76036i	0.149820	−	0.172902i
$474$	−12.4359	+	6.84018i	−0.571199	+	0.314180i
$475$	−2.74051	+	0.394026i	−0.125743	+	0.0180791i
$476$	−10.9581	−	12.4905i	−0.502265	−	0.572500i
$477$	−3.09696	−	6.78139i	−0.141800	−	0.310499i
$478$	−7.91080	−	4.28813i	−0.361832	−	0.196135i
$479$	−2.59651	+	5.68557i	−0.118638	+	0.259780i	−0.959629	−	0.281268i	$-0.909245\pi$
$479$	−2.59651	+	5.68557i	−0.118638	+	0.259780i	0.840992	+	0.541048i	$0.181972\pi$
$480$	−7.86712	−	10.1796i	−0.359083	−	0.464631i
$481$	−6.11672	−	9.51780i	−0.278898	−	0.433974i
$482$	12.3722	+	12.2964i	0.563537	+	0.560085i
$483$	−43.7879	+	10.6809i	−1.99242	+	0.485996i
$484$	−0.109772	−	17.8689i	−0.00498964	−	0.812223i
$485$	−8.23585	−	12.8152i	−0.373971	−	0.581909i
$486$	−16.0925	−	21.3600i	−0.729972	−	0.968911i
$487$	−29.4217	−	13.4364i	−1.33322	−	0.608863i	−0.383962	−	0.923349i	$-0.625441\pi$
$487$	−29.4217	−	13.4364i	−1.33322	−	0.608863i	−0.949262	+	0.314486i	$0.898168\pi$
$488$	13.6833	+	7.30879i	0.619414	+	0.330853i
$489$	5.33747	+	11.6874i	0.241369	+	0.528524i
$490$	14.2167	+	0.972919i	0.642246	+	0.0439520i
$491$	−4.11346	−	28.6097i	−0.185638	−	1.29114i	−0.843143	−	0.537689i	$-0.819297\pi$
$491$	−4.11346	−	28.6097i	−0.185638	−	1.29114i	0.657505	−	0.753450i	$-0.271612\pi$
$492$	−4.65140	+	16.2089i	−0.209701	+	0.730754i
$493$	13.4528	−	15.5254i	0.605885	−	0.699228i
$494$	6.35428	−	1.40274i	0.285893	−	0.0631125i
$495$	1.68786	−	2.62637i	0.0758638	−	0.118046i
$496$	−28.9670	−	24.4834i	−1.30066	−	1.09934i
$497$	−4.07480	+	13.8775i	−0.182780	+	0.622490i
$498$	22.4416	−	30.1712i	1.00563	−	1.35201i
$499$	9.24726	+	10.6719i	0.413964	+	0.477740i	0.923989	−	0.382420i	$-0.124909\pi$
$499$	9.24726	+	10.6719i	0.413964	+	0.477740i	−0.510025	+	0.860160i	$0.670364\pi$
$500$	1.81413	−	0.841990i	0.0811302	−	0.0376549i
$501$	−2.28772	−	7.79126i	−0.102208	−	0.348088i
$502$	18.9277	−	7.12597i	0.844785	−	0.318048i
$503$	3.92087	−	27.2703i	0.174823	−	1.21592i	−0.693697	−	0.720267i	$-0.744019\pi$
$503$	3.92087	−	27.2703i	0.174823	−	1.21592i	0.868520	−	0.495654i	$-0.165072\pi$
$504$	24.8588	+	5.16828i	1.10730	+	0.230213i
$505$			17.8620i			0.794849i
$506$	4.29684	+	8.74898i	0.191018	+	0.388940i
$507$	−23.2841			−1.03408
$508$	−17.6778	+	11.5149i	−0.784326	+	0.510891i
$509$	1.70708	+	0.245441i	0.0756649	+	0.0108790i	0.180043	−	0.983659i	$-0.442376\pi$
$509$	1.70708	+	0.245441i	0.0756649	+	0.0108790i	−0.104378	+	0.994538i	$0.533285\pi$
$510$	6.05168	−	2.27836i	0.267973	−	0.100887i
$511$	47.3229	−	13.8953i	2.09344	−	0.614690i
$512$	−21.4112	−	7.31845i	−0.946251	−	0.323433i
$513$	−3.93864	+	3.41285i	−0.173895	+	0.150681i
$514$	−11.6906	−	8.69558i	−0.515651	−	0.383545i
$515$	−3.05146	−	0.895991i	−0.134464	−	0.0394821i
$516$	−10.2394	+	11.9647i	−0.450766	+	0.526715i
$517$	7.00792	+	4.50372i	0.308208	+	0.198073i
$518$	−38.8489	+	8.57612i	−1.70692	+	0.376813i
$519$	−26.4176	−	22.8910i	−1.15960	−	1.00480i
$520$	−4.10470	+	2.29069i	−0.180003	+	0.100453i
$521$	7.77254	−	1.11752i	0.340521	−	0.0489595i	0.0300668	−	0.999548i	$-0.490428\pi$
$521$	7.77254	−	1.11752i	0.340521	−	0.0489595i	0.310454	+	0.950588i	$0.399519\pi$
$522$	−2.14323	+	31.3179i	−0.0938067	+	1.37075i
$523$	22.5379	−	10.2927i	0.985515	−	0.450070i	0.143574	−	0.989640i	$-0.454140\pi$
$523$	22.5379	−	10.2927i	0.985515	−	0.450070i	0.841941	+	0.539570i	$0.181413\pi$
$524$	0.515400	+	1.71622i	0.0225154	+	0.0749734i
$525$	−3.90411	+	8.54881i	−0.170389	+	0.373101i
$526$	−8.08170	−	10.7271i	−0.352379	−	0.467722i
$527$	16.0371	−	10.3064i	0.698588	−	0.448955i
$528$	−0.160624	−	13.0729i	−0.00699027	−	0.568923i
$529$	18.1147	+	14.1724i	0.787598	+	0.616190i
$530$	3.42126	−	3.44235i	0.148610	−	0.149526i
$531$	6.61210	−	4.24934i	0.286941	−	0.184405i
$532$	3.11730	−	22.6690i	0.135152	−	0.982826i
$533$	5.60453	+	2.55950i	0.242759	+	0.110864i
$534$	−7.27533	−	3.94367i	−0.314834	−	0.170659i
$535$	−9.79203	+	4.47187i	−0.423346	+	0.193336i
$536$	−35.8208	−	2.23040i	−1.54722	−	0.0963385i
$537$	5.01486	+	34.8791i	0.216407	+	1.50515i
$538$	−1.01152	−	1.83901i	−0.0436098	−	0.0792855i
$539$	10.9440	+	9.48305i	0.471393	+	0.408464i
$540$	2.01583	−	3.17947i	0.0867475	−	0.136822i
$541$	−15.9991	+	24.8950i	−0.687853	+	1.07032i	0.305158	+	0.952302i	$0.401291\pi$
$541$	−15.9991	+	24.8950i	−0.687853	+	1.07032i	−0.993011	+	0.118019i	$0.962346\pi$
$542$	15.4949	−	1.15607i	0.665564	−	0.0496573i
$543$	12.6575	+	3.71656i	0.543183	+	0.159493i
$544$	6.67497	−	9.20817i	0.286187	−	0.394797i
$545$	8.68152	+	10.0190i	0.371876	+	0.429167i
$546$	7.65551	−	20.7194i	0.327626	−	0.886707i
$547$	1.26036	−	0.370076i	0.0538893	−	0.0158233i	−0.254677	−	0.967026i	$-0.581969\pi$
$547$	1.26036	−	0.370076i	0.0538893	−	0.0158233i	0.308566	+	0.951203i	$0.400151\pi$
$548$	−1.31155	+	2.91921i	−0.0560264	+	0.124702i
$549$	1.69562	−	11.7933i	0.0723671	−	0.503325i
$550$	1.98730	+	0.425921i	0.0847386	+	0.0181613i
$551$	28.2903			1.20521
$552$	−13.7693	−	27.6065i	−0.586062	−	1.17501i
$553$	18.2352			0.775439
$554$	12.3825	+	2.65385i	0.526083	+	0.112751i
$555$	2.20340	−	15.3250i	0.0935292	−	0.650510i
$556$	12.0992	+	5.43594i	0.513120	+	0.230535i
$557$	39.1365	−	11.4915i	1.65827	−	0.486911i	0.687350	−	0.726327i	$-0.258774\pi$
$557$	39.1365	−	11.4915i	1.65827	−	0.486911i	0.970917	+	0.239415i	$0.0769558\pi$
$558$	−10.0960	+	27.3246i	−0.427400	+	1.15674i
$559$	3.76800	+	4.34850i	0.159369	+	0.183922i
$560$	2.55321	+	16.3310i	0.107893	+	0.690110i
$561$	6.30502	+	1.85132i	0.266198	+	0.0781628i
$562$	−30.5836	+	2.28183i	−1.29009	+	0.0962530i
$563$	−17.8713	+	27.8083i	−0.753186	+	1.17198i	0.226999	+	0.973895i	$0.427109\pi$
$563$	−17.8713	+	27.8083i	−0.753186	+	1.17198i	−0.980185	+	0.198085i	$0.936528\pi$
$564$	−22.2672	−	14.1177i	−0.937619	−	0.594465i
$565$	9.35540	+	8.10650i	0.393585	+	0.341043i
$566$	19.0293	+	34.5965i	0.799862	+	1.45420i
$567$	6.35021	+	44.1667i	0.266684	+	1.85483i
$568$	−9.88047	−	0.615212i	−0.414575	−	0.0258137i
$569$	4.54966	−	2.07776i	0.190732	−	0.0871043i	−0.317760	−	0.948171i	$-0.602931\pi$
$569$	4.54966	−	2.07776i	0.190732	−	0.0871043i	0.508492	+	0.861067i	$0.330203\pi$
$570$	7.82878	+	4.24368i	0.327912	+	0.177748i
$571$	−20.0353	−	9.14980i	−0.838450	−	0.382907i	−0.0505581	−	0.998721i	$-0.516100\pi$
$571$	−20.0353	−	9.14980i	−0.838450	−	0.382907i	−0.787892	+	0.615814i	$0.788827\pi$
$572$	−4.73229	−	0.650755i	−0.197867	−	0.0272094i
$573$	−46.0281	+	29.5805i	−1.92285	+	1.23574i
$574$	15.2729	−	15.3670i	0.637480	−	0.641408i
$575$	4.65923	−	1.13649i	0.194303	−	0.0473950i
$576$	0.320260	+	17.3758i	0.0133442	+	0.723991i
$577$	−24.7016	+	15.8748i	−1.02834	+	0.660875i	−0.942077	−	0.335397i	$-0.891130\pi$
$577$	−24.7016	+	15.8748i	−1.02834	+	0.660875i	−0.0862652	+	0.996272i	$0.527493\pi$
$578$	−11.0270	−	14.6364i	−0.458661	−	0.608792i
$579$	−14.9650	+	32.7689i	−0.621926	+	1.36183i
$580$	−19.5724	+	5.87780i	−0.812698	+	0.244062i
$581$	−43.9458	+	20.0694i	−1.82318	+	0.832618i
$582$	−3.34519	+	48.8814i	−0.138663	+	2.02620i
$583$	4.88182	−	0.701899i	0.202184	−	0.0290697i
$584$	16.4509	+	29.4785i	0.680742	+	1.21983i
$585$	2.72845	+	2.36422i	0.112808	+	0.0977483i
$586$	36.8109	−	8.12622i	1.52064	−	0.335691i
$587$	−14.9367	−	9.59925i	−0.616505	−	0.396203i	0.194787	−	0.980846i	$-0.437599\pi$
$587$	−14.9367	−	9.59925i	−0.616505	−	0.396203i	−0.811291	+	0.584642i	$0.801235\pi$
$588$	−34.8216	−	29.8005i	−1.43602	−	1.22895i
$589$	25.1892	+	7.39622i	1.03790	+	0.304756i
$590$	4.10561	+	3.05379i	0.169025	+	0.125723i
$591$	13.3942	−	11.6062i	0.550966	−	0.477415i
$592$	−11.6155	−	24.6291i	−0.477395	−	1.01225i
$593$	32.9589	−	9.67760i	1.35346	−	0.397411i	0.477006	−	0.878900i	$-0.341722\pi$
$593$	32.9589	−	9.67760i	1.35346	−	0.397411i	0.876452	+	0.481489i	$0.159904\pi$
$594$	3.58035	−	1.34794i	0.146904	−	0.0553068i
$595$	−8.22345	−	1.18235i	−0.337129	−	0.0484718i
$596$	21.2007	+	32.5475i	0.868414	+	1.33320i
$597$	25.4682			1.04234
$598$	−10.7215	+	3.47845i	−0.438436	+	0.142245i
$599$		−	8.96908i		−	0.366467i	−0.983069	−	0.183233i	$-0.941344\pi$
$599$		−	8.96908i		−	0.366467i	0.983069	−	0.183233i	$-0.0586564\pi$
$600$	−6.29796	−	1.30938i	−0.257113	−	0.0534551i
$601$	−5.48509	+	38.1496i	−0.223741	+	1.55616i	0.499964	+	0.866046i	$0.333347\pi$
$601$	−5.48509	+	38.1496i	−0.223741	+	1.55616i	−0.723705	+	0.690109i	$0.757562\pi$
$602$	18.9356	−	7.12895i	0.771758	−	0.290554i
$603$	7.76597	+	26.4485i	0.316255	+	1.07706i
$604$	−10.4589	−	22.5344i	−0.425567	−	0.916913i
$605$	−5.85093	−	6.75234i	−0.237874	−	0.274521i
$606$	34.2870	−	46.0965i	1.39281	−	1.87254i
$607$	8.75976	−	29.8330i	0.355548	−	1.21088i	−0.566583	−	0.824005i	$-0.691735\pi$
$607$	8.75976	−	29.8330i	0.355548	−	1.21088i	0.922131	−	0.386879i	$-0.126447\pi$
$608$	15.6032	−	1.35710i	0.632792	−	0.0550377i
$609$	51.9173	−	80.7849i	2.10380	−	3.27357i
$610$	7.57411	−	1.67203i	0.306667	−	0.0676985i
$611$	−6.30843	+	7.28032i	−0.255212	+	0.294530i
$612$	−8.39606	−	2.40938i	−0.339391	−	0.0973934i
$613$	1.94385	+	13.5198i	0.0785115	+	0.546060i	0.990676	+	0.136236i	$0.0435006\pi$
$613$	1.94385	+	13.5198i	0.0785115	+	0.546060i	−0.912165	+	0.409824i	$0.865590\pi$
$614$	−33.4789	−	2.29112i	−1.35110	−	0.0924621i
$615$	3.50259	+	7.66961i	0.141238	+	0.309269i
$616$	−7.91393	+	14.8163i	−0.318861	+	0.596964i
$617$	−14.4306	−	6.59022i	−0.580953	−	0.265312i	0.103188	−	0.994662i	$-0.467096\pi$
$617$	−14.4306	−	6.59022i	−0.580953	−	0.265312i	−0.684141	+	0.729350i	$0.739823\pi$
$618$	6.15502	+	8.16972i	0.247591	+	0.328634i
$619$	5.83209	+	9.07491i	0.234412	+	0.364751i	0.938453	−	0.345408i	$-0.112259\pi$
$619$	5.83209	+	9.07491i	0.234412	+	0.364751i	−0.704041	+	0.710159i	$0.748623\pi$
$620$	−18.9636	+	0.116497i	−0.761596	+	0.00467863i
$621$	6.22138	−	6.54116i	0.249655	−	0.262488i
$622$	31.2028	+	31.0117i	1.25112	+	1.24346i
$623$	5.74828	+	8.94449i	0.230300	+	0.358354i
$624$	14.9901	+	1.96759i	0.600084	+	0.0787667i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	5.73998	+	3.11142i	0.229416	+	0.124357i
$627$	3.75924	+	8.23159i	0.150130	+	0.328738i
$628$	−35.0287	+	30.7313i	−1.39780	+	1.22631i
$629$	13.5474	−	1.94783i	0.540172	−	0.0776650i
$630$	11.1236	−	6.11836i	0.443174	−	0.243761i
$631$	6.13799	−	7.08361i	0.244349	−	0.281994i	−0.620306	−	0.784360i	$-0.712991\pi$
$631$	6.13799	−	7.08361i	0.244349	−	0.281994i	0.864655	+	0.502366i	$0.167537\pi$
$632$	2.76535	+	12.1711i	0.110000	+	0.484139i
$633$	14.2145	+	9.13513i	0.564977	+	0.363089i
$634$	−26.3804	+	1.96823i	−1.04770	+	0.0781683i
$635$	−2.97190	+	10.1214i	−0.117936	+	0.401655i
$636$	−15.4370	+	2.31639i	−0.612117	+	0.0918507i
$637$	−12.6557	+	10.9662i	−0.501438	+	0.434499i
$638$	−19.4800	−	7.19760i	−0.771222	−	0.284956i
$639$	2.14209	+	7.29529i	0.0847398	+	0.288597i
$640$	−10.5129	+	4.18072i	−0.415560	+	0.165258i
$641$	11.5422	+	1.65952i	0.455889	+	0.0655469i	0.366434	−	0.930444i	$-0.380579\pi$
$641$	11.5422	+	1.65952i	0.455889	+	0.0655469i	0.0894546	+	0.995991i	$0.471488\pi$
$642$	33.8543	+	7.25571i	1.33612	+	0.286360i
$643$		−	27.0860i		−	1.06817i	−0.845431	−	0.534085i	$-0.820656\pi$
$643$		−	27.0860i		−	1.06817i	0.845431	−	0.534085i	$-0.179344\pi$
$644$	−1.59316	+	39.6040i	−0.0627792	+	1.56062i
$645$			7.87400i			0.310038i
$646$	−1.64970	+	7.69729i	−0.0649065	+	0.302846i
$647$	19.0677	+	2.74152i	0.749627	+	0.107780i	0.506531	−	0.862222i	$-0.330928\pi$
$647$	19.0677	+	2.74152i	0.749627	+	0.107780i	0.243097	+	0.970002i	$0.421837\pi$
$648$	−28.5160	+	10.9363i	−1.12022	+	0.429618i
$649$	1.46494	+	4.98914i	0.0575041	+	0.195841i
$650$	−0.814581	+	2.20463i	−0.0319505	+	0.0864728i
$651$	67.3467	−	58.3563i	2.63953	−	2.28716i
$652$	11.1739	−	1.67669i	0.437604	−	0.0656642i
$653$	−8.34151	+	28.4086i	−0.326429	+	1.11171i	0.618866	+	0.785496i	$0.287592\pi$
$653$	−8.34151	+	28.4086i	−0.326429	+	1.11171i	−0.945295	+	0.326217i	$0.894226\pi$
$654$	−3.17244	−	42.5207i	−0.124052	−	1.66269i
$655$	0.753737	+	0.484398i	0.0294510	+	0.0189270i
$656$	12.5729	+	7.86351i	0.490888	+	0.307018i
$657$	16.9789	−	19.5947i	0.662411	−	0.764463i
$658$	16.3256	+	29.6810i	0.636438	+	1.15709i
$659$	22.1912	−	3.19061i	0.864446	−	0.124289i	0.304193	−	0.952610i	$-0.401613\pi$
$659$	22.1912	−	3.19061i	0.864446	−	0.124289i	0.560253	+	0.828322i	$0.310704\pi$
$660$	−4.31104	−	4.91389i	−0.167807	−	0.191273i
$661$	6.74902	+	14.7783i	0.262506	+	0.574809i	0.994288	−	0.106730i	$-0.0340382\pi$
$661$	6.74902	+	14.7783i	0.262506	+	0.574809i	−0.731782	+	0.681539i	$0.761311\pi$
$662$	15.9710	−	29.4634i	0.620729	−	1.14513i
$663$	−3.15672	+	6.91226i	−0.122597	+	0.268450i
$664$	−20.0597	−	26.2881i	−0.778466	−	1.02018i
$665$	−6.18557	−	9.62493i	−0.239866	−	0.373239i
$666$	−14.7431	+	14.8340i	−0.571285	+	0.574805i
$667$	−48.7758	+	4.71912i	−1.88861	+	0.182725i
$668$	−7.14076	+	0.0438670i	−0.276284	+	0.00169726i
$669$	6.20572	+	9.65629i	0.239927	+	0.373334i
$670$	−14.3327	+	10.7982i	−0.553720	+	0.417169i
$671$	7.16993	+	3.27440i	0.276792	+	0.126407i
$672$	24.7591	−	47.0464i	0.955101	−	1.81485i
$673$	9.87008	+	21.6125i	0.380464	+	0.833099i	0.998883	+	0.0472511i	$0.0150461\pi$
$673$	9.87008	+	21.6125i	0.380464	+	0.833099i	−0.618419	+	0.785848i	$0.712227\pi$
$674$	0.0862130	−	1.25978i	0.00332080	−	0.0485250i
$675$	−0.267883	−	1.86316i	−0.0103108	−	0.0717132i
$676$	−5.64797	+	19.6817i	−0.217230	+	0.756988i
$677$	20.9107	−	24.1323i	0.803665	−	0.927479i	−0.194911	−	0.980821i	$-0.562442\pi$
$677$	20.9107	−	24.1323i	0.803665	−	0.927479i	0.998576	+	0.0533420i	$0.0169873\pi$
$678$	−8.58267	−	38.8786i	−0.329616	−	1.49312i
$679$	34.0333	−	52.9569i	1.30608	−	2.03230i
$680$	−0.457919	−	5.66804i	−0.0175604	−	0.217360i
$681$	−5.54296	+	18.8776i	−0.212407	+	0.723391i
$682$	−15.4630	−	11.5015i	−0.592107	−	0.440415i
$683$	3.20938	+	3.70382i	0.122804	+	0.141723i	0.813822	−	0.581114i	$-0.197383\pi$
$683$	3.20938	+	3.70382i	0.122804	+	0.141723i	−0.691018	+	0.722837i	$0.742838\pi$
$684$	−5.06418	−	10.9111i	−0.193634	−	0.417198i
$685$	0.450815	+	1.53533i	0.0172247	+	0.0586621i
$686$	6.33427	+	16.8248i	0.241844	+	0.642375i
$687$	2.42914	−	16.8951i	0.0926776	−	0.644587i
$688$	7.62979	+	11.5575i	0.290883	+	0.440624i
$689$			5.70341i			0.217283i
$690$	−14.2056	−	6.01067i	−0.540799	−	0.228822i
$691$	−27.2683			−1.03734			−0.518668	−	0.854976i	$-0.673572\pi$
$691$	−27.2683			−1.03734			−0.518668	+	0.854976i	$0.673572\pi$
$692$	−25.7574	+	16.7778i	−0.979151	+	0.637795i
$693$	12.7697	+	1.83601i	0.485082	+	0.0697442i
$694$	−3.83325	−	10.1817i	−0.145508	−	0.386492i
$695$	6.36347	−	1.86848i	0.241380	−	0.0708756i
$696$	61.7931	+	22.4012i	2.34226	+	0.849116i
$697$	−5.63304	+	4.88106i	−0.213367	+	0.184883i
$698$	19.1887	−	25.7978i	0.726301	−	0.976463i
$699$	42.7555	+	12.5541i	1.61716	+	0.474841i
$700$	6.27916	+	5.37375i	0.237330	+	0.203109i
$701$	−3.36885	−	2.16503i	−0.127240	−	0.0817720i	0.475473	−	0.879730i	$-0.342277\pi$
$701$	−3.36885	−	2.16503i	−0.127240	−	0.0817720i	−0.602712	+	0.797958i	$0.705913\pi$
$702$	0.953671	+	4.32003i	0.0359940	+	0.163049i
$703$	14.2447	+	12.3431i	0.537247	+	0.465527i
$704$	−11.0892	−	3.03528i	−0.417942	−	0.114396i
$705$	−13.0486	+	1.87610i	−0.491438	+	0.0706581i
$706$	32.4139	+	2.21824i	1.21991	+	0.0834846i
$707$	−67.1417	+	30.6626i	−2.52512	+	1.15318i
$708$	−4.73346	−	15.7618i	−0.177894	−	0.592367i
$709$	−4.26151	+	9.33141i	−0.160044	+	0.350448i	−0.972618	−	0.232411i	$-0.925339\pi$
$709$	−4.26151	+	9.33141i	−0.160044	+	0.350448i	0.812573	+	0.582859i	$0.198066\pi$
$710$	−3.95339	+	2.97846i	−0.148368	+	0.111780i
$711$	8.06434	−	5.18264i	0.302436	−	0.194364i
$712$	−5.09828	+	5.19311i	−0.191066	+	0.194620i
$713$	−44.6629	−	8.55012i	−1.67264	−	0.320205i
$714$	18.9527	+	18.8366i	0.709286	+	0.704943i
$715$	−2.00926	+	1.29127i	−0.0751421	+	0.0482909i
$716$	30.6992	+	4.22156i	1.14728	+	0.157767i
$717$	13.1630	+	6.01132i	0.491579	+	0.224497i
$718$	−9.22541	+	17.0191i	−0.344289	+	0.635149i
$719$	38.6231	−	17.6386i	1.44040	−	0.657808i	0.466445	−	0.884550i	$-0.345535\pi$
$719$	38.6231	−	17.6386i	1.44040	−	0.657808i	0.973955	+	0.226742i	$0.0728074\pi$
$720$	5.77058	+	6.49658i	0.215057	+	0.242113i
$721$	−1.87031	−	13.0083i	−0.0696539	−	0.484453i
$722$	14.0448	−	7.72516i	0.522695	−	0.287501i
$723$	−21.2001	−	18.3700i	−0.788439	−	0.683186i
$724$	6.21184	−	9.79762i	0.230861	−	0.364126i
$725$	−5.52424	+	8.59588i	−0.205165	+	0.319243i
$726$	2.13807	+	28.6569i	0.0793514	+	1.06356i
$727$	−46.9241	−	13.7782i	−1.74032	−	0.511004i	−0.751450	−	0.659790i	$-0.770645\pi$
$727$	−46.9241	−	13.7782i	−1.74032	−	0.511004i	−0.988869	+	0.148786i	$0.952463\pi$
$728$	−15.6568	−	11.4969i	−0.580278	−	0.426104i
$729$	6.95074	+	8.02158i	0.257435	+	0.297096i
$730$	15.8329	+	5.85002i	0.586001	+	0.216519i
$731$	−6.67874	+	1.96105i	−0.247022	+	0.0725322i
$732$	−22.7561	−	10.2239i	−0.841088	−	0.377885i
$733$	−5.25588	+	36.5555i	−0.194130	+	1.35021i	0.626801	+	0.779180i	$0.284364\pi$
$733$	−5.25588	+	36.5555i	−0.194130	+	1.35021i	−0.820931	+	0.571027i	$0.806545\pi$
$734$	−3.34631	+	15.6135i	−0.123515	+	0.576304i
$735$	−22.9162			−0.845277
$736$	−26.6753	+	4.94257i	−0.983264	+	0.182185i
$737$	−18.2360			−0.671733
$738$	2.38683	−	11.1367i	0.0878605	−	0.409946i
$739$	−4.98182	+	34.6493i	−0.183259	+	1.27460i	0.665732	+	0.746191i	$0.268119\pi$
$739$	−4.98182	+	34.6493i	−0.183259	+	1.27460i	−0.848992	+	0.528406i	$0.822790\pi$
$740$	−12.4195	−	5.57984i	−0.456550	−	0.205119i
$741$	−10.0408	+	2.94825i	−0.368859	+	0.108307i
$742$	18.8125	+	6.95097i	0.690630	+	0.255178i
$743$	3.92237	+	4.52666i	0.143898	+	0.166067i	0.823123	−	0.567863i	$-0.192230\pi$
$743$	3.92237	+	4.52666i	0.143898	+	0.166067i	−0.679225	+	0.733930i	$0.737684\pi$
$744$	49.1630	+	36.1009i	1.80240	+	1.32352i
$745$	18.6350	+	5.47173i	0.682733	+	0.200469i
$746$	−1.44401	−	19.3543i	−0.0528690	−	0.708610i
$747$	−13.7307	+	21.3654i	−0.502380	+	0.781719i
$748$	3.09428	−	4.88046i	0.113138	−	0.178447i
$749$	−33.6187	−	29.1308i	−1.22840	−	1.06442i
$750$	−2.81814	+	1.55008i	−0.102904	+	0.0566009i
$751$	4.60600	+	32.0354i	0.168075	+	1.16899i	0.882857	+	0.469642i	$0.155617\pi$
$751$	4.60600	+	32.0354i	0.168075	+	1.16899i	−0.714782	+	0.699348i	$0.753474\pi$
$752$	−17.3348	+	15.3976i	−0.632136	+	0.561494i
$753$	−29.5853	+	13.5112i	−1.07815	+	0.492374i
$754$	11.4445	−	21.1130i	0.416785	−	0.768890i
$755$	−11.2991	−	5.16014i	−0.411218	−	0.187797i
$756$	15.4118	+	2.11933i	0.560521	+	0.0770793i
$757$	−17.5754	+	11.2950i	−0.638787	+	0.410524i	−0.819554	−	0.573002i	$-0.805779\pi$
$757$	−17.5754	+	11.2950i	−0.638787	+	0.410524i	0.180766	+	0.983526i	$0.442142\pi$
$758$	−4.70690	−	4.67807i	−0.170962	−	0.169915i
$759$	−7.85448	−	13.5651i	−0.285100	−	0.492383i
$760$	5.48612	−	5.58817i	0.199002	−	0.202704i
$761$	2.81191	−	1.80710i	0.101932	−	0.0655075i	−0.488682	−	0.872462i	$-0.662522\pi$
$761$	2.81191	−	1.80710i	0.101932	−	0.0655075i	0.590614	+	0.806955i	$0.298886\pi$
$762$	27.0981	−	20.4155i	0.981659	−	0.739577i
$763$	−22.7576	+	49.8321i	−0.823879	+	1.80404i
$764$	13.8390	+	46.0821i	0.500676	+	1.66719i
$765$	−3.97278	+	1.81431i	−0.143636	+	0.0655965i
$766$	31.2289	+	2.13714i	1.12834	+	0.0772181i
$767$	−5.95183	+	0.855744i	−0.214908	+	0.0308991i
$768$	35.1558	+	9.39087i	1.26858	+	0.338864i
$769$	7.57998	+	6.56809i	0.273341	+	0.236851i	0.780734	−	0.624863i	$-0.214845\pi$
$769$	7.57998	+	6.56809i	0.273341	+	0.236851i	−0.507393	+	0.861715i	$0.669391\pi$
$770$	1.81047	+	8.20123i	0.0652447	+	0.295552i
$771$	19.7112	+	12.6676i	0.709882	+	0.456214i
$772$	24.0690	+	20.5984i	0.866261	+	0.741351i
$773$	−5.38343	−	1.58072i	−0.193629	−	0.0568545i	0.183480	−	0.983023i	$-0.441264\pi$
$773$	−5.38343	−	1.58072i	−0.193629	−	0.0568545i	−0.377109	+	0.926169i	$0.623082\pi$
$774$	6.34798	−	8.53442i	0.228173	−	0.306763i
$775$	−7.16600	+	6.20937i	−0.257410	+	0.223047i
$776$	40.5072	+	14.6847i	1.45412	+	0.527149i
$777$	61.3877	−	18.0251i	2.20227	−	0.646645i
$778$	−9.20702	−	24.4553i	−0.330088	−	0.876765i
$779$	−10.1600	−	1.46079i	−0.364021	−	0.0523383i
$780$	6.33409	−	4.12587i	0.226797	−	0.147730i
$781$	−5.03005			−0.179989
$782$	1.56028	−	13.5462i	0.0557956	−	0.484412i
$783$			19.2335i			0.687348i
$784$	−33.6365	+	22.2055i	−1.20130	+	0.793053i
$785$	−3.31583	+	23.0621i	−0.118347	+	0.823122i
$786$	−1.01535	−	2.69692i	−0.0362162	−	0.0961960i
$787$	−15.6092	−	53.1599i	−0.556407	−	1.89495i	−0.429599	−	0.903020i	$-0.641345\pi$
$787$	−15.6092	−	53.1599i	−0.556407	−	1.89495i	−0.126808	−	0.991927i	$-0.540473\pi$
$788$	−6.56151	−	14.1372i	−0.233744	−	0.503618i
$789$	14.1441	+	16.3232i	0.503544	+	0.581121i
$790$	5.00735	+	3.72451i	0.178153	+	0.132512i
$791$	−14.4118	+	49.0820i	−0.512424	+	1.74516i
$792$	0.711076	+	8.80158i	0.0252670	+	0.312750i
$793$	−4.92797	+	7.66807i	−0.174997	+	0.272301i
$794$	1.70261	+	7.71266i	0.0604235	+	0.273712i
$795$	−5.11113	+	5.89856i	−0.181273	+	0.209200i
$796$	6.17775	−	21.5278i	0.218964	−	0.763033i
$797$	3.02522	+	21.0409i	0.107159	+	0.745306i	0.970572	+	0.240810i	$0.0774129\pi$
$797$	3.02522	+	21.0409i	0.107159	+	0.745306i	−0.863413	+	0.504497i	$0.831678\pi$
$798$	−2.51242	+	36.7126i	−0.0889386	+	1.29961i
$799$	−4.84112	−	10.6006i	−0.171266	−	0.375021i
$800$	−2.63448	+	5.00595i	−0.0931428	+	0.176987i
$801$	5.08425	+	2.32190i	0.179643	+	0.0820402i
$802$	27.1056	−	20.4212i	0.957131	−	0.721097i
$803$	9.27346	+	14.4298i	0.327253	+	0.509216i
$804$	57.7159	−	0.354560i	2.03548	−	0.0125044i
$805$	12.2702	+	15.5627i	0.432467	+	0.548512i
$806$	15.7098	−	15.8066i	0.553354	−	0.556764i
$807$	1.82481	+	2.83946i	0.0642364	+	0.0999537i
$808$	−30.6477	−	40.1637i	−1.07818	−	1.41296i
$809$	−16.4081	+	35.9288i	−0.576879	+	1.26319i	0.366174	+	0.930547i	$0.380668\pi$
$809$	−16.4081	+	35.9288i	−0.576879	+	1.26319i	−0.943053	+	0.332643i	$0.892060\pi$
$810$	−7.27723	+	13.4251i	−0.255696	+	0.471710i
$811$	18.0468	+	39.5169i	0.633708	+	1.38763i	0.905117	+	0.425163i	$0.139783\pi$
$811$	18.0468	+	39.5169i	0.633708	+	1.38763i	−0.271409	+	0.962464i	$0.587490\pi$
$812$	−55.6928	−	63.4807i	−1.95443	−	2.22774i
$813$	−24.7332	+	3.55610i	−0.867431	+	0.124718i
$814$	−6.66822	−	12.1233i	−0.233721	−	0.424920i
$815$	3.69963	−	4.26961i	0.129593	−	0.149558i
$816$	−9.69833	+	15.5065i	−0.339510	+	0.542837i
$817$	−8.06404	−	5.18244i	−0.282125	−	0.181311i
$818$	1.85435	+	24.8541i	0.0648357	+	0.869002i
$819$	−4.20312	+	14.3145i	−0.146869	+	0.500189i
$820$	7.33261	−	1.10029i	0.256066	−	0.0384237i
$821$	16.8167	−	14.5718i	0.586908	−	0.508559i	−0.310023	−	0.950729i	$-0.600337\pi$
$821$	16.8167	−	14.5718i	0.586908	−	0.508559i	0.896931	+	0.442170i	$0.145791\pi$
$822$	1.78373	−	4.82760i	0.0622147	−	0.168382i
$823$	−8.22343	−	28.0064i	−0.286651	−	0.976242i	−0.969379	−	0.245570i	$-0.921025\pi$
$823$	−8.22343	−	28.0064i	−0.286651	−	0.976242i	0.682728	−	0.730672i	$-0.260793\pi$
$824$	8.39874	−	3.22103i	0.292584	−	0.112210i
$825$	−3.23519	−	0.465151i	−0.112635	−	0.0161945i
$826$	−4.43108	+	20.6749i	−0.154177	+	0.719371i
$827$		−	23.4225i		−	0.814479i	−0.913321	−	0.407240i	$-0.866491\pi$
$827$		−	23.4225i		−	0.814479i	0.913321	−	0.407240i	$-0.133509\pi$
$828$	10.5513	+	17.9673i	0.366684	+	0.624407i
$829$			28.0637i			0.974691i	0.873209	+	0.487346i	$0.162035\pi$
$829$			28.0637i			0.974691i	−0.873209	+	0.487346i	$0.837965\pi$
$830$	−16.1666	−	3.46485i	−0.561151	−	0.120267i
$831$	−20.1580	−	2.89828i	−0.699273	−	0.100540i
$832$	5.29928	−	12.1936i	0.183720	−	0.422737i
$833$	−5.70739	−	19.4376i	−0.197749	−	0.673472i
$834$	−20.0089	−	7.39299i	−0.692850	−	0.255998i
$835$	−2.69836	+	2.33814i	−0.0933807	+	0.0809148i
$836$	7.86990	−	1.18091i	0.272186	−	0.0408426i
$837$	−5.02840	+	17.1252i	−0.173807	+	0.591932i
$838$	37.0993	−	2.76795i	1.28157	−	0.0956174i
$839$	10.2857	+	6.61024i	0.355103	+	0.228211i	0.706014	−	0.708198i	$-0.250492\pi$
$839$	10.2857	+	6.61024i	0.355103	+	0.228211i	−0.350911	+	0.936409i	$0.614128\pi$
$840$	−5.88948	−	25.9212i	−0.203206	−	0.894366i
$841$	49.3807	−	56.9883i	1.70278	−	1.96511i
$842$	−10.7516	+	5.91378i	−0.370526	+	0.203802i
$843$	48.8180	−	7.01897i	1.68138	−	0.241746i
$844$	11.1698	−	9.79944i	0.384479	−	0.337311i
$845$	4.25303	+	9.31284i	0.146309	+	0.320371i
$846$	15.6555	+	8.48624i	0.538248	+	0.291763i
$847$	15.3375	−	33.5844i	0.527003	−	1.15398i
$848$	−1.78651	+	13.6105i	−0.0613491	+	0.467388i
$849$	−34.3293	−	53.4175i	−1.17818	−	1.83328i
$850$	−2.01665	−	2.00430i	−0.0691706	−	0.0687469i
$851$	−26.6184	−	18.9047i	−0.912466	−	0.648045i
$852$	15.9198	−	0.0977984i	0.545404	−	0.00335052i
$853$	−21.8430	−	33.9884i	−0.747891	−	1.16374i	−0.981510	−	0.191413i	$-0.938693\pi$
$853$	−21.8430	−	33.9884i	−0.747891	−	1.16374i	0.233619	−	0.972328i	$-0.424943\pi$
$854$	19.2870	+	25.6001i	0.659988	+	0.876019i
$855$	−5.47102	−	2.49853i	−0.187105	−	0.0854479i
$856$	14.3451	−	26.8565i	0.490305	−	0.917935i
$857$	19.8083	+	43.3742i	0.676640	+	1.48164i	0.866164	+	0.499760i	$0.166578\pi$
$857$	19.8083	+	43.3742i	0.676640	+	1.48164i	−0.189524	+	0.981876i	$0.560694\pi$
$858$	7.66397	+	0.524482i	0.261644	+	0.0179055i
$859$	−3.93593	−	27.3750i	−0.134292	−	0.934023i	−0.939870	−	0.341533i	$-0.889054\pi$
$859$	−3.93593	−	27.3750i	−0.134292	−	0.934023i	0.805578	−	0.592490i	$-0.201855\pi$
$860$	6.65576	+	1.90998i	0.226960	+	0.0651296i
$861$	−22.8167	+	26.3319i	−0.777591	+	0.897388i
$862$	−21.8604	+	4.82581i	−0.744568	+	0.164368i
$863$	17.9172	−	27.8798i	0.609910	−	0.949038i	−0.389696	−	0.920944i	$-0.627420\pi$
$863$	17.9172	−	27.8798i	0.609910	−	0.949038i	0.999605	−	0.0280941i	$-0.00894381\pi$
$864$	0.922639	+	10.6080i	0.0313888	+	0.360891i
$865$	−4.33021	+	14.7473i	−0.147232	+	0.501425i
$866$	−22.1986	+	29.8445i	−0.754340	+	1.01416i
$867$	19.2987	+	22.2719i	0.655419	+	0.756394i
$868$	−32.9915	−	71.0825i	−1.11980	−	2.41270i
$869$	1.78670	+	6.08493i	0.0606095	+	0.206417i
$870$	30.7566	−	11.5794i	1.04275	−	0.392577i
$871$	3.00117	−	20.8736i	0.101691	−	0.707274i
$872$	−36.7116	−	7.63252i	−1.24321	−	0.258470i
$873$		−	33.0924i		−	1.12001i
$874$	15.5055	−	10.5924i	0.524481	−	0.358294i
$875$	4.13234			0.139699
$876$	−29.6305	−	45.4891i	−1.00112	−	1.53693i
$877$	−9.09376	−	1.30748i	−0.307074	−	0.0441506i	−0.0129448	−	0.999916i	$-0.504121\pi$
$877$	−9.09376	−	1.30748i	−0.307074	−	0.0441506i	−0.294129	+	0.955766i	$0.595030\pi$
$878$	3.18924	−	1.20070i	0.107632	−	0.0405216i
$879$	−58.1674	+	17.0795i	−1.96194	+	0.576077i
$880$	−5.19935	+	2.45211i	−0.175270	+	0.0826605i
$881$	−29.6767	+	25.7150i	−0.999833	+	0.866361i	−0.991035	−	0.133601i	$-0.957346\pi$
$881$	−29.6767	+	25.7150i	−0.999833	+	0.866361i	−0.00879811	+	0.999961i	$0.502801\pi$
$882$	24.8383	+	18.4749i	0.836349	+	0.622084i
$883$	46.7851	+	13.7373i	1.57444	+	0.462298i	0.948291	−	0.317403i	$-0.102811\pi$
$883$	46.7851	+	13.7373i	1.57444	+	0.462298i	0.626152	+	0.779701i	$0.284629\pi$
$884$	5.07710	+	4.34502i	0.170761	+	0.146139i
$885$	−6.92237	−	4.44873i	−0.232693	−	0.149543i
$886$	32.9827	−	7.28112i	1.10808	−	0.244614i
$887$	−30.8429	−	26.7256i	−1.03560	−	0.897357i	−0.0408010	−	0.999167i	$-0.512991\pi$
$887$	−30.8429	−	26.7256i	−1.03560	−	0.897357i	−0.994804	+	0.101811i	$0.967536\pi$
$888$	21.3402	+	38.2397i	0.716131	+	1.28324i
$889$	−43.1470	+	6.20361i	−1.44711	+	0.208062i
$890$	−0.248433	+	3.63022i	−0.00832751	+	0.121685i
$891$	−14.1159	+	6.44650i	−0.472899	+	0.215966i
$892$	9.66761	−	2.90329i	0.323696	−	0.0972094i
$893$	6.66682	−	14.5983i	0.223097	−	0.488514i
$894$	−37.5881	−	49.8917i	−1.25713	−	1.66863i
$895$	13.0344	−	8.37672i	0.435693	−	0.280003i
$896$	−33.7618	−	32.3404i	−1.12790	−	1.08042i
$897$	16.8197	−	6.75804i	0.561595	−	0.225645i
$898$	−4.83561	+	4.86541i	−0.161366	+	0.162361i
$899$	81.5059	−	52.3807i	2.71837	−	1.74699i
$900$	4.30418	+	0.591883i	0.143473	+	0.0197294i
$901$	−6.27612	−	2.86621i	−0.209088	−	0.0954873i
$902$	6.62430	+	3.59077i	0.220565	+	0.119560i
$903$	−29.5977	+	13.5168i	−0.984948	+	0.449811i
$904$	−34.9453	−	2.17589i	−1.16226	−	0.0723689i
$905$	−0.825489	−	5.74140i	−0.0274402	−	0.190851i
$906$	19.2545	+	35.0060i	0.639689	+	1.16300i
$907$	−9.64719	−	8.35934i	−0.320330	−	0.277567i	0.479821	−	0.877367i	$-0.340702\pi$
$907$	−9.64719	−	8.35934i	−0.320330	−	0.277567i	−0.800151	+	0.599799i	$0.795247\pi$
$908$	14.6124	+	9.26447i	0.484929	+	0.307452i
$909$	−20.9781	+	32.6426i	−0.695801	+	1.08269i
$910$	−9.68536	+	0.722619i	−0.321067	+	0.0239546i
$911$	−47.0036	−	13.8015i	−1.55730	−	0.457264i	−0.614026	−	0.789286i	$-0.710451\pi$
$911$	−47.0036	−	13.8015i	−1.55730	−	0.457264i	−0.943272	+	0.332022i	$0.892269\pi$
$912$	−24.8848	+	3.89052i	−0.824018	+	0.128828i
$913$	−11.0028	−	12.6979i	−0.364141	−	0.420241i
$914$	0.972017	−	2.63073i	0.0321515	−	0.0870168i
$915$	−11.9684	+	3.51423i	−0.395662	+	0.116177i
$916$	−13.6919	−	6.15151i	−0.452393	−	0.203252i
$917$	−0.526914	+	3.66477i	−0.0174002	+	0.121021i
$918$	−5.23309	−	1.12157i	−0.172718	−	0.0370172i
$919$	−18.3556			−0.605496			−0.302748	−	0.953071i	$-0.597904\pi$
$919$	−18.3556			−0.605496			−0.302748	+	0.953071i	$0.597904\pi$
$920$	−8.52654	+	10.5498i	−0.281112	+	0.347816i
$921$	53.9652			1.77821
$922$	23.7965	+	5.10012i	0.783697	+	0.167963i
$923$	0.827814	−	5.75757i	0.0272478	−	0.189513i
$924$	11.0704	−	24.6402i	0.364189	−	0.810603i
$925$	−6.53193	+	1.91795i	−0.214769	+	0.0630617i
$926$	2.39028	−	6.46921i	0.0785495	−	0.212591i
$927$	−4.52422	−	5.22123i	−0.148595	−	0.171488i
$928$	33.9244	−	46.7989i	1.11362	−	1.53625i
$929$	−32.6847	−	9.59710i	−1.07235	−	0.314871i	−0.302536	−	0.953138i	$-0.597833\pi$
$929$	−32.6847	−	9.59710i	−1.07235	−	0.314871i	−0.769815	+	0.638267i	$0.779651\pi$
$930$	30.4125	−	2.26906i	0.997265	−	0.0744053i
$931$	15.0828	−	23.4693i	0.494319	−	0.769176i
$932$	20.9829	−	33.0953i	0.687318	−	1.08407i
$933$	−53.4670	−	46.3294i	−1.75043	−	1.51676i
$934$	0.312654	+	0.568426i	0.0102304	+	0.0185995i
$935$	−0.411198	−	2.85994i	−0.0134476	−	0.0935302i
$936$	−10.1916	−	0.634585i	−0.333123	−	0.0207421i
$937$	22.3714	−	10.2167i	0.730843	−	0.333765i	−0.0149992	−	0.999888i	$-0.504775\pi$
$937$	22.3714	−	10.2167i	0.730843	−	0.333765i	0.745842	+	0.666123i	$0.232047\pi$
$938$	−65.1933	−	35.3387i	−2.12864	−	1.15385i
$939$	−9.55087	−	4.36174i	−0.311681	−	0.142340i
$940$	−1.57932	+	11.4848i	−0.0515118	+	0.374594i
$941$	28.8418	−	18.5355i	0.940217	−	0.604241i	0.0217607	−	0.999763i	$-0.493073\pi$
$941$	28.8418	−	18.5355i	0.940217	−	0.604241i	0.918456	+	0.395522i	$0.129436\pi$
$942$	52.8260	−	53.1515i	1.72116	−	1.73177i
$943$	17.7607	+	0.823775i	0.578369	+	0.0268258i
$944$	−14.4714	+	0.177808i	−0.471005	+	0.00578716i
$945$	6.54361	−	4.20532i	0.212864	−	0.136799i
$946$	4.23420	+	5.62016i	0.137666	+	0.182727i
$947$	−5.32647	+	11.6633i	−0.173087	+	0.379008i	−0.976217	−	0.216796i	$-0.930439\pi$
$947$	−5.32647	+	11.6633i	−0.173087	+	0.379008i	0.803130	+	0.595804i	$0.203166\pi$
$948$	−5.77309	−	19.2237i	−0.187501	−	0.624356i
$949$	−18.0430	+	8.23996i	−0.585701	+	0.267480i
$950$	0.267332	−	3.90638i	0.00867341	−	0.126740i
$951$	42.1088	−	6.05433i	1.36547	−	0.196325i
$952$	20.5196	−	11.4513i	0.665044	−	0.371137i
$953$	42.3321	+	36.6810i	1.37127	+	1.18821i	0.961098	+	0.276207i	$0.0890776\pi$
$953$	42.3321	+	36.6810i	1.37127	+	1.18821i	0.410174	+	0.912007i	$0.365468\pi$
$954$	10.2952	−	2.27273i	0.333320	−	0.0735823i
$955$	20.2385	+	13.0065i	0.654904	+	0.420881i
$956$	8.27418	−	9.66828i	0.267606	−	0.312695i
$957$	32.0442	+	9.40901i	1.03584	+	0.304150i
$958$	−7.09255	−	5.27550i	−0.229150	−	0.170444i
$959$	−4.99730	+	4.33018i	−0.161371	+	0.139829i
$960$	16.4080	−	7.86186i	0.529565	−	0.253740i
$961$	56.5216	−	16.5962i	1.82328	−	0.535363i
$962$	14.9741	−	5.63751i	0.482785	−	0.181760i
$963$	−23.1469	−	3.32801i	−0.745897	−	0.107244i
$964$	−20.6703	+	13.4641i	−0.665745	+	0.433650i
$965$	15.8399			0.509904
$966$	−1.79234	−	63.7158i	−0.0576676	−	2.05002i
$967$			56.0740i			1.80322i	0.432552	+	0.901609i	$0.357613\pi$
$967$			56.0740i			1.80322i	−0.432552	+	0.901609i	$0.642387\pi$
$968$	24.7419	+	5.14395i	0.795233	+	0.165333i
$969$	1.80164	−	12.5307i	0.0578771	−	0.402544i
$970$	20.1619	−	7.59061i	0.647359	−	0.243720i
$971$	14.1385	+	48.1515i	0.453727	+	1.54525i	0.795788	+	0.605576i	$0.207057\pi$
$971$	14.1385	+	48.1515i	0.453727	+	1.54525i	−0.342060	+	0.939678i	$0.611125\pi$
$972$	34.3062	−	15.9225i	1.10037	−	0.510715i
$973$	17.9472	+	20.7122i	0.575362	+	0.664003i
$974$	27.2997	−	36.7025i	0.874738	−	1.17603i
$975$	1.06485	−	3.62656i	0.0341027	−	0.116143i
$976$	−14.1619	+	16.7554i	−0.453313	+	0.536326i
$977$	−1.89579	+	2.94991i	−0.0606519	+	0.0943761i	−0.870255	−	0.492602i	$-0.836046\pi$
$977$	−1.89579	+	2.94991i	−0.0606519	+	0.0943761i	0.809603	+	0.586978i	$0.199682\pi$
$978$	−17.7434	+	3.91695i	−0.567370	+	0.125250i
$979$	−2.42148	+	2.79454i	−0.0773909	+	0.0893139i
$980$	−5.55873	+	19.3707i	−0.177567	+	0.618775i
$981$	4.09850	+	28.5057i	0.130855	+	0.910118i
$982$	40.7809	+	2.79084i	1.30137	+	0.0890592i
$983$	−10.5757	−	23.1575i	−0.337311	−	0.738609i	0.662635	−	0.748942i	$-0.269438\pi$
$983$	−10.5757	−	23.1575i	−0.337311	−	0.738609i	−0.999947	+	0.0103333i	$0.996711\pi$
$984$	−21.0353	−	11.2358i	−0.670582	−	0.358184i
$985$	−7.08863	−	3.23727i	−0.225863	−	0.103148i
$986$	17.4817	+	23.2039i	0.556731	+	0.738963i
$987$	−29.4518	−	45.8279i	−0.937460	−	1.45872i
$988$	0.0565327	+	9.20250i	0.00179854	+	0.292771i
$989$	14.7678	+	7.58997i	0.469590	+	0.241347i
$990$	3.13154	+	3.11236i	0.0995269	+	0.0989174i
$991$	23.5899	+	36.7066i	0.749358	+	1.16602i	0.981148	+	0.193258i	$0.0619056\pi$
$991$	23.5899	+	36.7066i	0.749358	+	1.16602i	−0.231790	+	0.972766i	$0.574458\pi$
$992$	42.4408	−	32.7998i	1.34750	−	1.04139i
$993$	−22.3889	+	49.0248i	−0.710490	+	1.55576i
$994$	−17.9823	−	9.74750i	−0.570364	−	0.309172i
$995$	−4.65196	−	10.1864i	−0.147477	−	0.322930i
$996$	35.0702	+	39.9743i	1.11124	+	1.26663i
$997$	2.47680	−	0.356110i	0.0784410	−	0.0112781i	−0.102983	−	0.994683i	$-0.532839\pi$
$997$	2.47680	−	0.356110i	0.0784410	−	0.0112781i	0.181424	+	0.983405i	$0.441930\pi$
$998$	−17.4978	+	9.62442i	−0.553884	+	0.304656i
$999$	−8.39157	+	9.68438i	−0.265497	+	0.306400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.a.11.20	✓	480
8.3	odd	2		920.2.bb.b.11.3	yes	480
23.21	odd	22		920.2.bb.b.251.3	yes	480
184.67	even	22	inner	920.2.bb.a.251.20	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.20	✓	480	1.1	even	1	trivial
920.2.bb.a.251.20	yes	480	184.67	even	22	inner
920.2.bb.b.11.3	yes	480	8.3	odd	2
920.2.bb.b.251.3	yes	480	23.21	odd	22

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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.296367 + 1.38281i) q^{2} +(0.323664 - 2.25113i) q^{3} +(-1.82433 - 0.819638i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(3.01696 + 1.11473i) q^{6} +(-2.70611 - 3.12302i) q^{7} +(1.67408 - 2.27980i) q^{8} +(-2.08435 - 0.612020i) q^{9} +(-0.105221 - 1.41029i) q^{10} +(0.776978 - 1.20900i) q^{11} +(-2.43558 + 3.84152i) q^{12} +(1.25599 + 1.08833i) q^{13} +(5.12054 - 2.81648i) q^{14} +(0.323664 + 2.25113i) q^{15} +(2.65639 + 2.99059i) q^{16} +(-1.82880 + 0.835186i) q^{17} +(1.46404 - 2.70088i) q^{18} +(-2.51849 - 1.15016i) q^{19} +(1.98135 + 0.272463i) q^{20} +(-7.90618 + 5.08100i) q^{21} +(1.44155 + 1.43272i) q^{22} +(4.53402 + 1.56289i) q^{23} +(-4.59028 - 4.50645i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-1.87718 + 1.41426i) q^{26} +(0.781946 - 1.71222i) q^{27} +(2.37710 + 7.91545i) q^{28} +(-9.29457 + 4.24469i) q^{29} +(-3.20881 - 0.219594i) q^{30} +(-9.38546 + 1.34943i) q^{31} +(-4.92268 + 2.78697i) q^{32} +(-2.47014 - 2.14039i) q^{33} +(-0.612908 - 2.77641i) q^{34} +(3.47635 + 2.23411i) q^{35} +(3.30091 + 2.82494i) q^{36} +(-6.53193 - 1.91795i) q^{37} +(2.33684 - 3.14173i) q^{38} +(2.85648 - 2.47515i) q^{39} +(-0.963973 + 2.65909i) q^{40} +(3.55718 - 1.04448i) q^{41} +(-4.68293 - 12.4386i) q^{42} +(3.42696 + 0.492722i) q^{43} +(-2.40841 + 1.56878i) q^{44} +2.17234 q^{45} +(-3.50492 + 5.80651i) q^{46} +5.79646i q^{47} +(7.59198 - 5.01192i) q^{48} +(-1.43400 + 9.97370i) q^{49} +(0.498285 + 1.32352i) q^{50} +(1.28819 + 4.38719i) q^{51} +(-1.39932 - 3.01493i) q^{52} +(2.24737 + 2.59360i) q^{53} +(2.13594 + 1.58873i) q^{54} +(-0.404890 + 1.37893i) q^{55} +(-11.6501 + 0.941205i) q^{56} +(-3.40429 + 5.29718i) q^{57} +(-3.11500 - 14.1106i) q^{58} +(-2.36937 + 2.73440i) q^{59} +(1.25464 - 4.37210i) q^{60} +(0.780548 + 5.42883i) q^{61} +(0.915538 - 13.3782i) q^{62} +(3.72912 + 8.16564i) q^{63} +(-2.39493 - 7.63311i) q^{64} +(-1.51173 - 0.690386i) q^{65} +(3.69182 - 2.78140i) q^{66} +(-6.86024 - 10.6747i) q^{67} +(4.02089 - 0.0247011i) q^{68} +(4.98577 - 9.70082i) q^{69} +(-4.11963 + 4.14502i) q^{70} +(-1.89226 - 2.94442i) q^{71} +(-4.88464 + 3.72732i) q^{72} +(-4.95810 + 10.8567i) q^{73} +(4.58801 - 8.46401i) q^{74} +(-0.944769 - 2.06876i) q^{75} +(3.65185 + 4.16252i) q^{76} +(-5.87832 + 0.845175i) q^{77} +(2.57611 + 4.68353i) q^{78} +(-2.88977 + 3.33497i) q^{79} +(-3.39133 - 2.12106i) q^{80} +(-9.08382 - 5.83782i) q^{81} +(0.390092 + 5.22846i) q^{82} +(3.29376 - 11.2175i) q^{83} +(18.5881 - 2.78922i) q^{84} +(1.51942 - 1.31659i) q^{85} +(-1.69698 + 4.59281i) q^{86} +(6.54703 + 22.2971i) q^{87} +(-1.45555 - 3.79531i) q^{88} +(-2.54677 - 0.366170i) q^{89} +(-0.643810 + 3.00394i) q^{90} -6.86762i q^{91} +(-6.99057 - 6.56749i) q^{92} +21.5646i q^{93} +(-8.01541 - 1.71788i) q^{94} +(2.74051 + 0.394026i) q^{95} +(4.68053 + 11.9836i) q^{96} +(4.29177 + 14.6164i) q^{97} +(-13.3667 - 4.93882i) q^{98} +(-2.35942 + 2.04445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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