LMFDB - Embedded newform 880.2.t.b.197.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(197,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.197"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.t (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [272] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$136$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.15
Character	$\chi$	$=$	880.197
Dual form			880.2.t.b.813.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31339 - 0.524410i) q^{2} +1.92611i q^{3} +(1.44999 + 1.37751i) q^{4} +(2.10484 - 0.754755i) q^{5} +(1.01007 - 2.52973i) q^{6} +(1.16754 + 1.16754i) q^{7} +(-1.18202 - 2.56960i) q^{8} -0.709896 q^{9} +(-3.16028 - 0.112510i) q^{10} +(1.53212 + 2.94153i) q^{11} +(-2.65323 + 2.79284i) q^{12} +2.52290 q^{13} +(-0.921165 - 2.14570i) q^{14} +(1.45374 + 4.05415i) q^{15} +(0.204932 + 3.99475i) q^{16} +(-2.19950 + 2.19950i) q^{17} +(0.932370 + 0.372276i) q^{18} +(2.30934 - 2.30934i) q^{19} +(4.09167 + 1.80505i) q^{20} +(-2.24881 + 2.24881i) q^{21} +(-0.469704 - 4.66684i) q^{22} +(-1.97618 - 1.97618i) q^{23} +(4.94932 - 2.27670i) q^{24} +(3.86069 - 3.17728i) q^{25} +(-3.31355 - 1.32303i) q^{26} +4.41099i q^{27} +(0.0846213 + 3.30121i) q^{28} +(3.82037 - 3.82037i) q^{29} +(0.216706 - 6.08704i) q^{30} +2.31803 q^{31} +(1.82573 - 5.35413i) q^{32} +(-5.66571 + 2.95103i) q^{33} +(4.04225 - 1.73536i) q^{34} +(3.33869 + 1.57627i) q^{35} +(-1.02934 - 0.977889i) q^{36} -8.59901i q^{37} +(-4.24411 + 1.82203i) q^{38} +4.85937i q^{39} +(-4.42738 - 4.51645i) q^{40} -3.14094 q^{41} +(4.13286 - 1.77426i) q^{42} +5.10977i q^{43} +(-1.83043 + 6.37570i) q^{44} +(-1.49422 + 0.535798i) q^{45} +(1.55917 + 3.63183i) q^{46} +(1.26877 + 1.26877i) q^{47} +(-7.69432 + 0.394722i) q^{48} -4.27370i q^{49} +(-6.73679 + 2.14842i) q^{50} +(-4.23648 - 4.23648i) q^{51} +(3.65817 + 3.47532i) q^{52} -13.1317 q^{53} +(2.31317 - 5.79335i) q^{54} +(5.44500 + 5.03507i) q^{55} +(1.62005 - 4.38016i) q^{56} +(4.44805 + 4.44805i) q^{57} +(-7.02109 + 3.01420i) q^{58} +(-4.19138 + 4.19138i) q^{59} +(-3.47672 + 7.88101i) q^{60} +(4.99416 + 4.99416i) q^{61} +(-3.04448 - 1.21560i) q^{62} +(-0.828831 - 0.828831i) q^{63} +(-5.20565 + 6.07463i) q^{64} +(5.31029 - 1.90417i) q^{65} +(8.98884 - 0.904700i) q^{66} +2.49840 q^{67} +(-6.21909 + 0.159416i) q^{68} +(3.80634 - 3.80634i) q^{69} +(-3.55839 - 3.82110i) q^{70} +4.17809i q^{71} +(0.839112 + 1.82415i) q^{72} +(-11.7939 + 11.7939i) q^{73} +(-4.50940 + 11.2939i) q^{74} +(6.11978 + 7.43611i) q^{75} +(6.52967 - 0.167377i) q^{76} +(-1.64554 + 5.22316i) q^{77} +(2.54830 - 6.38225i) q^{78} +12.8208 q^{79} +(3.44641 + 8.25362i) q^{80} -10.6257 q^{81} +(4.12528 + 1.64714i) q^{82} -0.425481 q^{83} +(-6.35850 + 0.162990i) q^{84} +(-2.96951 + 6.28968i) q^{85} +(2.67961 - 6.71112i) q^{86} +(7.35846 + 7.35846i) q^{87} +(5.74755 - 7.41388i) q^{88} +9.82399 q^{89} +(2.24347 + 0.0798702i) q^{90} +(2.94558 + 2.94558i) q^{91} +(-0.143230 - 5.58765i) q^{92} +4.46478i q^{93} +(-1.00103 - 2.33174i) q^{94} +(3.11781 - 6.60379i) q^{95} +(10.3126 + 3.51655i) q^{96} +(-0.539801 - 0.539801i) q^{97} +(-2.24117 + 5.61304i) q^{98} +(-1.08765 - 2.08818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 16 q^{4} - 4 q^{5} - 280 q^{9} - 4 q^{11} - 8 q^{12} - 8 q^{15} - 40 q^{16} - 4 q^{20} - 12 q^{22} - 24 q^{23} - 40 q^{25} + 72 q^{26} + 16 q^{31} - 4 q^{33} - 32 q^{34} - 72 q^{36} - 24 q^{42}+ \cdots - 20 q^{99}+O(q^{100}) $ 272 * q - 16 * q^4 - 4 * q^5 - 280 * q^9 - 4 * q^11 - 8 * q^12 - 8 * q^15 - 40 * q^16 - 4 * q^20 - 12 * q^22 - 24 * q^23 - 40 * q^25 + 72 * q^26 + 16 * q^31 - 4 * q^33 - 32 * q^34 - 72 * q^36 - 24 * q^42 - 40 * q^44 - 12 * q^45 - 8 * q^47 + 8 * q^48 - 56 * q^53 + 40 * q^55 - 56 * q^56 + 72 * q^58 + 8 * q^59 + 44 * q^60 - 64 * q^64 + 12 * q^66 - 8 * q^67 + 88 * q^70 - 24 * q^75 - 32 * q^77 - 32 * q^78 + 104 * q^80 + 192 * q^81 - 8 * q^82 - 56 * q^88 + 24 * q^89 - 24 * q^91 + 48 * q^92 - 40 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.31339	−	0.524410i	−0.928707	−	0.370814i
$2$	−1.31339	−	0.524410i	−0.928707	−	0.370814i
$3$			1.92611i			1.11204i	0.831169	+	0.556020i	$0.187672\pi$
$3$			1.92611i			1.11204i	−0.831169	+	0.556020i	$0.812328\pi$
$4$	1.44999	+	1.37751i	0.724994	+	0.688755i
$5$	2.10484	−	0.754755i	0.941312	−	0.337537i
$5$	2.10484	−	0.754755i	0.941312	−	0.337537i
$6$	1.01007	−	2.52973i	0.412360	−	1.03276i
$7$	1.16754	+	1.16754i	0.441288	+	0.441288i	0.892445	−	0.451157i	$-0.148988\pi$
$7$	1.16754	+	1.16754i	0.441288	+	0.441288i	−0.451157	+	0.892445i	$0.648988\pi$
$8$	−1.18202	−	2.56960i	−0.417907	−	0.908490i
$9$	−0.709896			−0.236632
$10$	−3.16028	−	0.112510i	−0.999367	−	0.0355787i
$11$	1.53212	+	2.94153i	0.461952	+	0.886905i
$11$	1.53212	+	2.94153i	0.461952	+	0.886905i
$12$	−2.65323	+	2.79284i	−0.765923	+	0.806222i
$13$	2.52290			0.699726			0.349863	−	0.936801i	$-0.386228\pi$
$13$	2.52290			0.699726			0.349863	+	0.936801i	$0.386228\pi$
$14$	−0.921165	−	2.14570i	−0.246192	−	0.573463i
$15$	1.45374	+	4.05415i	0.375354	+	1.04678i
$16$	0.204932	+	3.99475i	0.0512331	+	0.998687i
$17$	−2.19950	+	2.19950i	−0.533458	+	0.533458i	−0.921600	−	0.388142i	$-0.873117\pi$
$17$	−2.19950	+	2.19950i	−0.533458	+	0.533458i	0.388142	+	0.921600i	$0.373117\pi$
$18$	0.932370	+	0.372276i	0.219762	+	0.0877464i
$19$	2.30934	−	2.30934i	0.529800	−	0.529800i	−0.390713	−	0.920513i	$-0.627771\pi$
$19$	2.30934	−	2.30934i	0.529800	−	0.529800i	0.920513	+	0.390713i	$0.127771\pi$
$20$	4.09167	+	1.80505i	0.914926	+	0.403621i
$21$	−2.24881	+	2.24881i	−0.490730	+	0.490730i
$22$	−0.469704	−	4.66684i	−0.100141	−	0.994973i
$23$	−1.97618	−	1.97618i	−0.412062	−	0.412062i	0.470394	−	0.882456i	$-0.344112\pi$
$23$	−1.97618	−	1.97618i	−0.412062	−	0.412062i	−0.882456	+	0.470394i	$0.844112\pi$
$24$	4.94932	−	2.27670i	1.01028	−	0.464730i
$25$	3.86069	−	3.17728i	0.772138	−	0.635455i
$26$	−3.31355	−	1.32303i	−0.649840	−	0.259468i
$27$			4.41099i			0.848895i
$28$	0.0846213	+	3.30121i	0.0159919	+	0.623871i
$29$	3.82037	−	3.82037i	0.709426	−	0.709426i	−0.256989	−	0.966414i	$-0.582730\pi$
$29$	3.82037	−	3.82037i	0.709426	−	0.709426i	0.966414	+	0.256989i	$0.0827303\pi$
$30$	0.216706	−	6.08704i	0.0395649	−	1.11134i
$31$	2.31803			0.416330			0.208165	−	0.978094i	$-0.433251\pi$
$31$	2.31803			0.416330			0.208165	+	0.978094i	$0.433251\pi$
$32$	1.82573	−	5.35413i	0.322746	−	0.946485i
$33$	−5.66571	+	2.95103i	−0.986274	+	0.513709i
$34$	4.04225	−	1.73536i	0.693239	−	0.297612i
$35$	3.33869	+	1.57627i	0.564341	+	0.266439i
$36$	−1.02934	−	0.977889i	−0.171557	−	0.162981i
$37$		−	8.59901i		−	1.41367i	−0.707379	−	0.706834i	$-0.750123\pi$
$37$		−	8.59901i		−	1.41367i	0.707379	−	0.706834i	$-0.249877\pi$
$38$	−4.24411	+	1.82203i	−0.688486	+	0.295572i
$39$			4.85937i			0.778123i
$40$	−4.42738	−	4.51645i	−0.700030	−	0.714113i
$41$	−3.14094			−0.490533			−0.245266	−	0.969456i	$-0.578875\pi$
$41$	−3.14094			−0.490533			−0.245266	+	0.969456i	$0.578875\pi$
$42$	4.13286	−	1.77426i	0.637714	−	0.273775i
$43$			5.10977i			0.779233i	0.920977	+	0.389616i	$0.127392\pi$
$43$			5.10977i			0.779233i	−0.920977	+	0.389616i	$0.872608\pi$
$44$	−1.83043	+	6.37570i	−0.275948	+	0.961173i
$45$	−1.49422	+	0.535798i	−0.222745	+	0.0798720i
$46$	1.55917	+	3.63183i	0.229887	+	0.535484i
$47$	1.26877	+	1.26877i	0.185068	+	0.185068i	0.793560	−	0.608492i	$-0.208225\pi$
$47$	1.26877	+	1.26877i	0.185068	+	0.185068i	−0.608492	+	0.793560i	$0.708225\pi$
$48$	−7.69432	+	0.394722i	−1.11058	+	0.0569732i
$49$		−	4.27370i		−	0.610529i
$50$	−6.73679	+	2.14842i	−0.952725	+	0.303833i
$51$	−4.23648	−	4.23648i	−0.593226	−	0.593226i
$52$	3.65817	+	3.47532i	0.507297	+	0.481940i
$53$	−13.1317			−1.80378			−0.901888	−	0.431970i	$-0.857818\pi$
$53$	−13.1317			−1.80378			−0.901888	+	0.431970i	$0.857818\pi$
$54$	2.31317	−	5.79335i	0.314782	−	0.788375i
$55$	5.44500	+	5.03507i	0.734204	+	0.678929i
$56$	1.62005	−	4.38016i	0.216488	−	0.585323i
$57$	4.44805	+	4.44805i	0.589158	+	0.589158i
$58$	−7.02109	+	3.01420i	−0.921914	+	0.395784i
$59$	−4.19138	+	4.19138i	−0.545671	+	0.545671i	−0.925186	−	0.379514i	$-0.876091\pi$
$59$	−4.19138	+	4.19138i	−0.545671	+	0.545671i	0.379514	+	0.925186i	$0.376091\pi$
$60$	−3.47672	+	7.88101i	−0.448843	+	1.01743i
$61$	4.99416	+	4.99416i	0.639437	+	0.639437i	0.950417	−	0.310980i	$-0.100657\pi$
$61$	4.99416	+	4.99416i	0.639437	+	0.639437i	−0.310980	+	0.950417i	$0.600657\pi$
$62$	−3.04448	−	1.21560i	−0.386649	−	0.154381i
$63$	−0.828831	−	0.828831i	−0.104423	−	0.104423i
$64$	−5.20565	+	6.07463i	−0.650707	+	0.759329i
$65$	5.31029	−	1.90417i	0.658660	−	0.236183i
$66$	8.98884	−	0.904700i	1.10645	−	0.111361i
$67$	2.49840			0.305228			0.152614	−	0.988286i	$-0.451231\pi$
$67$	2.49840			0.305228			0.152614	+	0.988286i	$0.451231\pi$
$68$	−6.21909	+	0.159416i	−0.754175	+	0.0193321i
$69$	3.80634	−	3.80634i	0.458230	−	0.458230i
$70$	−3.55839	−	3.82110i	−0.425308	−	0.456709i
$71$			4.17809i			0.495848i	0.968779	+	0.247924i	$0.0797483\pi$
$71$			4.17809i			0.495848i	−0.968779	+	0.247924i	$0.920252\pi$
$72$	0.839112	+	1.82415i	0.0988902	+	0.214978i
$73$	−11.7939	+	11.7939i	−1.38038	+	1.38038i	−0.536433	+	0.843943i	$0.680229\pi$
$73$	−11.7939	+	11.7939i	−1.38038	+	1.38038i	−0.843943	+	0.536433i	$0.819771\pi$
$74$	−4.50940	+	11.2939i	−0.524208	+	1.31288i
$75$	6.11978	+	7.43611i	0.706651	+	0.858648i
$76$	6.52967	−	0.167377i	0.749004	−	0.0191995i
$77$	−1.64554	+	5.22316i	−0.187527	+	0.595235i
$78$	2.54830	−	6.38225i	0.288539	−	0.722648i
$79$	12.8208			1.44246			0.721228	−	0.692698i	$-0.243578\pi$
$79$	12.8208			1.44246			0.721228	+	0.692698i	$0.243578\pi$
$80$	3.44641	+	8.25362i	0.385320	+	0.922783i
$81$	−10.6257			−1.18064
$82$	4.12528	+	1.64714i	0.455561	+	0.181896i
$83$	−0.425481			−0.0467026			−0.0233513	−	0.999727i	$-0.507434\pi$
$83$	−0.425481			−0.0467026			−0.0233513	+	0.999727i	$0.507434\pi$
$84$	−6.35850	+	0.162990i	−0.693769	+	0.0177836i
$85$	−2.96951	+	6.28968i	−0.322089	+	0.682212i
$86$	2.67961	−	6.71112i	0.288950	−	0.723679i
$87$	7.35846	+	7.35846i	0.788910	+	0.788910i
$88$	5.74755	−	7.41388i	0.612691	−	0.790323i
$89$	9.82399			1.04134			0.520671	−	0.853758i	$-0.325682\pi$
$89$	9.82399			1.04134			0.520671	+	0.853758i	$0.325682\pi$
$90$	2.24347	+	0.0798702i	0.236482	+	0.00841906i
$91$	2.94558	+	2.94558i	0.308781	+	0.308781i
$92$	−0.143230	−	5.58765i	−0.0149328	−	0.582553i
$93$			4.46478i			0.462976i
$94$	−1.00103	−	2.33174i	−0.103248	−	0.240500i
$95$	3.11781	−	6.60379i	0.319880	−	0.677534i
$96$	10.3126	+	3.51655i	1.05253	+	0.358907i
$97$	−0.539801	−	0.539801i	−0.0548085	−	0.0548085i	0.679171	−	0.733980i	$-0.262339\pi$
$97$	−0.539801	−	0.539801i	−0.0548085	−	0.0548085i	−0.733980	+	0.679171i	$0.762339\pi$
$98$	−2.24117	+	5.61304i	−0.226393	+	0.567003i
$99$	−1.08765	−	2.08818i	−0.109313	−	0.209870i
$100$	9.97468	+	0.711124i	0.997468	+	0.0711124i
$101$	−7.86447	+	7.86447i	−0.782544	+	0.782544i	−0.980259	−	0.197716i	$-0.936648\pi$
$101$	−7.86447	+	7.86447i	−0.782544	+	0.782544i	0.197716	+	0.980259i	$0.436648\pi$
$102$	3.34250	+	7.78580i	0.330957	+	0.770910i
$103$	−2.02658	−	2.02658i	−0.199685	−	0.199685i	0.600180	−	0.799865i	$-0.295096\pi$
$103$	−2.02658	−	2.02658i	−0.199685	−	0.199685i	−0.799865	+	0.600180i	$0.795096\pi$
$104$	−2.98212	−	6.48283i	−0.292421	−	0.635693i
$105$	−3.03608	+	6.43068i	−0.296291	+	0.627570i
$106$	17.2470	+	6.88639i	1.67518	+	0.668865i
$107$	−8.92968			−0.863265			−0.431633	−	0.902050i	$-0.642062\pi$
$107$	−8.92968			−0.863265			−0.431633	+	0.902050i	$0.642062\pi$
$108$	−6.07618	+	6.39588i	−0.584681	+	0.615444i
$109$	11.8945	−	11.8945i	1.13929	−	1.13929i	0.150714	−	0.988577i	$-0.451843\pi$
$109$	11.8945	−	11.8945i	1.13929	−	1.13929i	0.988577	−	0.150714i	$-0.0481571\pi$
$110$	−4.51097	−	9.46843i	−0.430104	−	0.902779i
$111$	16.5626			1.57205
$112$	−4.42476	+	4.90329i	−0.418100	+	0.463317i
$113$	1.59620	−	1.59620i	0.150158	−	0.150158i	−0.628031	−	0.778189i	$-0.716139\pi$
$113$	1.59620	−	1.59620i	0.150158	−	0.150158i	0.778189	+	0.628031i	$0.216139\pi$
$114$	−3.50942	−	8.17462i	−0.328688	−	0.765624i
$115$	−5.65108	−	2.66801i	−0.526966	−	0.248793i
$116$	10.8021	−	0.276894i	1.00295	−	0.0257090i
$117$	−1.79099			−0.165577
$118$	7.70292	−	3.30692i	0.709112	−	0.304426i
$119$	−5.13601			−0.470817
$120$	8.69917	−	8.52762i	0.794122	−	0.778461i
$121$	−6.30521	+	9.01356i	−0.573201	+	0.819415i
$122$	−3.94030	−	9.17827i	−0.356738	−	0.830962i
$123$		−	6.04980i		−	0.545492i
$124$	3.36111	+	3.19311i	0.301837	+	0.286749i
$125$	5.72806	−	9.60153i	0.512333	−	0.858787i
$126$	0.653932	+	1.52323i	0.0582569	+	0.135700i
$127$	−9.03165	+	9.03165i	−0.801429	+	0.801429i	−0.983319	−	0.181890i	$-0.941779\pi$
$127$	−9.03165	+	9.03165i	−0.801429	+	0.801429i	0.181890	+	0.983319i	$0.441779\pi$
$128$	10.0227	−	5.24847i	0.885886	−	0.463903i
$129$	−9.84197			−0.866537
$130$	−7.97305	−	0.283851i	−0.699283	−	0.0248953i
$131$	−10.1008	−	10.1008i	−0.882513	−	0.882513i	0.111277	−	0.993789i	$-0.464506\pi$
$131$	−10.1008	−	10.1008i	−0.882513	−	0.882513i	−0.993789	+	0.111277i	$0.964506\pi$
$132$	−12.2803	−	3.52561i	−1.06886	−	0.306865i
$133$	5.39250			0.467589
$134$	−3.28137	−	1.31019i	−0.283468	−	0.113183i
$135$	3.32922	+	9.28442i	0.286534	+	0.799076i
$136$	8.25169	+	3.05198i	0.707577	+	0.261705i
$137$	8.74818	−	8.74818i	0.747407	−	0.747407i	−0.226584	−	0.973992i	$-0.572756\pi$
$137$	8.74818	−	8.74818i	0.747407	−	0.747407i	0.973992	+	0.226584i	$0.0727558\pi$
$138$	−6.99530	+	3.00313i	−0.595479	+	0.255643i
$139$	−3.72219	−	3.72219i	−0.315712	−	0.315712i	0.531405	−	0.847118i	$-0.321664\pi$
$139$	−3.72219	−	3.72219i	−0.315712	−	0.315712i	−0.847118	+	0.531405i	$0.821664\pi$
$140$	2.66972	+	6.88466i	0.225633	+	0.581860i
$141$	−2.44378	+	2.44378i	−0.205803	+	0.205803i
$142$	2.19103	−	5.48746i	0.183867	−	0.460498i
$143$	3.86538	+	7.42118i	0.323239	+	0.620590i
$144$	−0.145481	−	2.83585i	−0.0121234	−	0.236321i
$145$	5.15782	−	10.9247i	0.428334	−	0.907249i
$146$	21.6749	−	9.30519i	1.79383	−	0.770103i
$147$	8.23162			0.678933
$148$	11.8452	−	12.4685i	0.973671	−	1.02490i
$149$	−4.20817	−	4.20817i	−0.344747	−	0.344747i	0.513401	−	0.858149i	$-0.328385\pi$
$149$	−4.20817	−	4.20817i	−0.344747	−	0.344747i	−0.858149	+	0.513401i	$0.828385\pi$
$150$	−4.13809	−	12.9758i	−0.337874	−	1.05947i
$151$	−6.65639			−0.541689			−0.270845	−	0.962623i	$-0.587303\pi$
$151$	−6.65639			−0.541689			−0.270845	+	0.962623i	$0.587303\pi$
$152$	−8.66377	−	3.20439i	−0.702725	−	0.259910i
$153$	1.56142	−	1.56142i	0.126233	−	0.126233i
$154$	4.90032	−	5.99711i	0.394879	−	0.483261i
$155$	4.87907	−	1.74954i	0.391897	−	0.140527i
$156$	−6.69384	+	7.04604i	−0.535936	+	0.564134i
$157$	−2.07551			−0.165644			−0.0828218	−	0.996564i	$-0.526393\pi$
$157$	−2.07551			−0.165644			−0.0828218	+	0.996564i	$0.526393\pi$
$158$	−16.8387	−	6.72337i	−1.33962	−	0.534882i
$159$		−	25.2931i		−	2.00587i
$160$	−0.198195	−	12.6476i	−0.0156687	−	0.999877i
$161$		−	4.61454i		−	0.363677i
$162$	13.9557	+	5.57224i	1.09647	+	0.437797i
$163$			0.953667i			0.0746969i	0.999302	+	0.0373485i	$0.0118912\pi$
$163$			0.953667i			0.0746969i	−0.999302	+	0.0373485i	$0.988109\pi$
$164$	−4.55433	−	4.32668i	−0.355633	−	0.337857i
$165$	−9.69810	+	10.4877i	−0.754996	+	0.816464i
$166$	0.558823	+	0.223127i	0.0433731	+	0.0173180i
$167$	16.5881	+	16.5881i	1.28363	+	1.28363i	0.938587	+	0.345042i	$0.112135\pi$
$167$	16.5881	+	16.5881i	1.28363	+	1.28363i	0.345042	+	0.938587i	$0.387865\pi$
$168$	8.43667	+	3.12039i	0.650903	+	0.240743i
$169$	−6.63499			−0.510384
$170$	7.19850	−	6.70357i	0.552100	−	0.514140i
$171$	−1.63939	+	1.63939i	−0.125368	+	0.125368i
$172$	−7.03876	+	7.40911i	−0.536700	+	0.564939i
$173$	−12.6184			−0.959360			−0.479680	−	0.877444i	$-0.659247\pi$
$173$	−12.6184			−0.959360			−0.479680	+	0.877444i	$0.659247\pi$
$174$	−5.80568	−	13.5234i	−0.440127	−	1.02520i
$175$	8.21710	+	0.797911i	0.621154	+	0.0603164i
$176$	−11.4367	+	6.72325i	−0.862073	+	0.506784i
$177$	−8.07306	−	8.07306i	−0.606808	−	0.606808i
$178$	−12.9027	−	5.15180i	−0.967101	−	0.386144i
$179$	−14.3226	−	14.3226i	−1.07052	−	1.07052i	−0.997317	−	0.0732011i	$-0.976679\pi$
$179$	−14.3226	−	14.3226i	−1.07052	−	1.07052i	−0.0732011	−	0.997317i	$-0.523321\pi$
$180$	−2.90466	−	1.28140i	−0.216501	−	0.0955097i
$181$	4.64602	+	4.64602i	0.345336	+	0.345336i	0.858369	−	0.513033i	$-0.171478\pi$
$181$	4.64602	+	4.64602i	0.345336	+	0.345336i	−0.513033	+	0.858369i	$0.671478\pi$
$182$	−2.32401	−	5.41339i	−0.172267	−	0.401267i
$183$	−9.61930	+	9.61930i	−0.711079	+	0.711079i
$184$	−2.74210	+	7.41388i	−0.202151	+	0.546558i
$185$	−6.49015	−	18.0995i	−0.477165	−	1.33070i
$186$	2.34137	−	5.86399i	0.171678	−	0.429969i
$187$	−9.83981	−	3.10000i	−0.719558	−	0.226695i
$188$	0.0919580	+	3.58743i	0.00670673	+	0.261640i
$189$	−5.15000	+	5.15000i	−0.374608	+	0.374608i
$190$	−7.55799	+	7.03834i	−0.548314	+	0.510615i
$191$	1.31643			0.0952537			0.0476268	−	0.998865i	$-0.484834\pi$
$191$	1.31643			0.0952537			0.0476268	+	0.998865i	$0.484834\pi$
$192$	−11.7004	−	10.0267i	−0.844404	−	0.723612i
$193$	14.1691	+	14.1691i	1.01992	+	1.01992i	0.999798	+	0.0201181i	$0.00640421\pi$
$193$	14.1691	+	14.1691i	1.01992	+	1.01992i	0.0201181	+	0.999798i	$0.493596\pi$
$194$	0.425893	+	0.992047i	0.0305773	+	0.0712248i
$195$	3.66764	+	10.2282i	0.262645	+	0.732456i
$196$	5.88707	−	6.19682i	0.420505	−	0.442630i
$197$	−18.7432			−1.33540			−0.667698	−	0.744432i	$-0.732720\pi$
$197$	−18.7432			−1.33540			−0.667698	+	0.744432i	$0.732720\pi$
$198$	0.333441	+	3.31297i	0.0236966	+	0.235442i
$199$	11.7667			0.834119			0.417059	−	0.908879i	$-0.363061\pi$
$199$	11.7667			0.834119			0.417059	+	0.908879i	$0.363061\pi$
$200$	−12.7277	−	6.16481i	−0.899987	−	0.435918i
$201$			4.81219i			0.339426i
$202$	14.4533	−	6.20491i	1.01693	−	0.436576i
$203$	8.92087			0.626123
$204$	−0.307053	−	11.9786i	−0.0214980	−	0.838673i
$205$	−6.61118	+	2.37064i	−0.461745	+	0.165573i
$206$	1.59894	+	3.72446i	0.111403	+	0.259495i
$207$	1.40288	+	1.40288i	0.0975071	+	0.0975071i
$208$	0.517023	+	10.0783i	0.0358491	+	0.698807i
$209$	10.3312	+	3.25481i	0.714624	+	0.225140i
$210$	7.35986	−	6.85384i	0.507879	−	0.472960i
$211$	2.43578	+	2.43578i	0.167686	+	0.167686i	0.785961	−	0.618276i	$-0.212168\pi$
$211$	2.43578	+	2.43578i	0.167686	+	0.167686i	−0.618276	+	0.785961i	$0.712168\pi$
$212$	−19.0408	−	18.0890i	−1.30773	−	1.24236i
$213$	−8.04745			−0.551402
$214$	11.7282	+	4.68282i	0.801721	+	0.320111i
$215$	3.85663	+	10.7552i	0.263020	+	0.733501i
$216$	11.3345	−	5.21388i	0.771213	−	0.354760i
$217$	2.70639	+	2.70639i	0.183722	+	0.183722i
$218$	−21.8598	+	9.38456i	−1.48053	+	0.635603i
$219$	−22.7164	−	22.7164i	−1.53503	−	1.53503i
$220$	0.959328	+	14.8013i	0.0646779	+	0.997906i
$221$	−5.54912	+	5.54912i	−0.373274	+	0.373274i
$222$	−21.7532	−	8.68561i	−1.45998	−	0.582940i
$223$	−1.84607	+	1.84607i	−0.123622	+	0.123622i	−0.766211	−	0.642589i	$-0.777860\pi$
$223$	−1.84607	+	1.84607i	−0.123622	+	0.123622i	0.642589	+	0.766211i	$0.277860\pi$
$224$	8.38277	−	4.11955i	0.560097	−	0.275249i
$225$	−2.74069	+	2.25554i	−0.182712	+	0.150369i
$226$	−2.93350	+	1.25937i	−0.195134	+	0.0837722i
$227$		−	22.1850i		−	1.47247i	−0.676726	−	0.736235i	$-0.736602\pi$
$227$		−	22.1850i		−	1.47247i	0.676726	−	0.736235i	$-0.263398\pi$
$228$	0.322387	+	12.5768i	0.0213506	+	0.832922i
$229$	−4.40704	+	4.40704i	−0.291225	+	0.291225i	−0.837564	−	0.546339i	$-0.816021\pi$
$229$	−4.40704	+	4.40704i	−0.291225	+	0.291225i	0.546339	+	0.837564i	$0.316021\pi$
$230$	6.02294	+	6.46762i	0.397141	+	0.426462i
$231$	−10.0604	−	3.16949i	−0.661925	−	0.208537i
$232$	−14.3326	−	5.30106i	−0.940980	−	0.348032i
$233$	20.1225	−	20.1225i	1.31827	−	1.31827i	0.403127	−	0.915144i	$-0.367923\pi$
$233$	20.1225	−	20.1225i	1.31827	−	1.31827i	0.915144	−	0.403127i	$-0.132077\pi$
$234$	2.35227	+	0.939215i	0.153773	+	0.0613984i
$235$	3.62815	+	1.71294i	0.236675	+	0.111740i
$236$	−11.8511	+	0.303784i	−0.771443	+	0.0197747i
$237$			24.6943i			1.60407i
$238$	6.74558	+	2.69337i	0.437251	+	0.174586i
$239$	−3.88954			−0.251594			−0.125797	−	0.992056i	$-0.540149\pi$
$239$	−3.88954			−0.251594			−0.125797	+	0.992056i	$0.540149\pi$
$240$	−15.8974	+	6.63815i	−1.02617	+	0.428491i
$241$		−	9.84415i		−	0.634118i	−0.948406	−	0.317059i	$-0.897305\pi$
$241$		−	9.84415i		−	0.634118i	0.948406	−	0.317059i	$-0.102695\pi$
$242$	13.0080	−	8.53181i	0.836186	−	0.548445i
$243$		−	7.23335i		−	0.464020i
$244$	0.361968	+	14.1210i	0.0231727	+	0.904004i
$245$	−3.22560	−	8.99546i	−0.206076	−	0.574699i
$246$	−3.17257	+	7.94575i	−0.202276	+	0.506602i
$247$	5.82624	−	5.82624i	0.370715	−	0.370715i
$248$	−2.73996	−	5.95640i	−0.173987	−	0.378232i
$249$		−	0.819523i		−	0.0519352i
$250$	−12.5583	+	9.60670i	−0.794258	+	0.607581i
$251$	−4.97338	−	4.97338i	−0.313917	−	0.313917i	0.532508	−	0.846425i	$-0.321250\pi$
$251$	−4.97338	−	4.97338i	−0.313917	−	0.313917i	−0.846425	+	0.532508i	$0.821250\pi$
$252$	−0.0600723	−	2.34352i	−0.00378420	−	0.147628i
$253$	2.78525	−	8.84075i	0.175107	−	0.555813i
$254$	16.5984	−	7.12579i	1.04147	−	0.447112i
$255$	−12.1146	−	5.71960i	−0.758646	−	0.358175i
$256$	−15.9160	+	1.63731i	−0.994750	+	0.102332i
$257$	−21.8560	−	21.8560i	−1.36334	−	1.36334i	−0.869623	−	0.493716i	$-0.835638\pi$
$257$	−21.8560	−	21.8560i	−1.36334	−	1.36334i	−0.493716	−	0.869623i	$-0.664362\pi$
$258$	12.9264	+	5.16123i	0.804760	+	0.321324i
$259$	10.0397	−	10.0397i	0.623835	−	0.623835i
$260$	10.3229	+	4.55395i	0.640197	+	0.282424i
$261$	−2.71207	+	2.71207i	−0.167873	+	0.167873i
$262$	7.96935	+	18.5633i	0.492348	+	1.14684i
$263$	18.8172	−	18.8172i	1.16032	−	1.16032i	0.175910	−	0.984406i	$-0.443713\pi$
$263$	18.8172	−	18.8172i	1.16032	−	1.16032i	0.984406	−	0.175910i	$-0.0562869\pi$
$264$	14.2799	+	11.0704i	0.878870	+	0.681337i
$265$	−27.6401	+	9.91121i	−1.69792	+	0.608841i
$266$	−7.08246	−	2.82788i	−0.434253	−	0.173388i
$267$			18.9221i			1.15801i
$268$	3.62265	+	3.44157i	0.221289	+	0.210227i
$269$	0.221171	+	0.221171i	0.0134850	+	0.0134850i	0.713817	−	0.700332i	$-0.246965\pi$
$269$	0.221171	+	0.221171i	0.0134850	+	0.0134850i	−0.700332	+	0.713817i	$0.746965\pi$
$270$	0.496279	−	13.9399i	0.0302026	−	0.848358i
$271$		−	18.3793i		−	1.11646i	−0.829686	−	0.558231i	$-0.811480\pi$
$271$		−	18.3793i		−	1.11646i	0.829686	−	0.558231i	$-0.188520\pi$
$272$	−9.23720	−	8.33570i	−0.560088	−	0.505426i
$273$	−5.67351	+	5.67351i	−0.343376	+	0.343376i
$274$	−16.0774	+	6.90214i	−0.971272	+	0.416974i
$275$	15.2611	+	6.48837i	0.920279	+	0.391263i
$276$	10.7624	−	0.275877i	0.647822	−	0.0166059i
$277$	8.12732			0.488323			0.244162	−	0.969735i	$-0.421487\pi$
$277$	8.12732			0.488323			0.244162	+	0.969735i	$0.421487\pi$
$278$	2.93674	+	6.84065i	0.176134	+	0.410275i
$279$	−1.64556			−0.0985170
$280$	0.103992	−	10.4423i	0.00621473	−	0.624045i
$281$	11.0616			0.659880			0.329940	−	0.944002i	$-0.392971\pi$
$281$	11.0616			0.659880			0.329940	+	0.944002i	$0.392971\pi$
$282$	4.49118	−	1.92810i	0.267446	−	0.114816i
$283$			5.16155i			0.306822i	0.988162	+	0.153411i	$0.0490259\pi$
$283$			5.16155i			0.306822i	−0.988162	+	0.153411i	$0.950974\pi$
$284$	−5.75536	+	6.05818i	−0.341518	+	0.359487i
$285$	12.7196	+	6.00523i	0.753445	+	0.355719i
$286$	−1.18501	−	11.7740i	−0.0700713	−	0.696208i
$287$	−3.66717	−	3.66717i	−0.216466	−	0.216466i
$288$	−1.29608	+	3.80088i	−0.0763721	+	0.223969i
$289$			7.32438i			0.430846i
$290$	−12.5033	+	11.6436i	−0.734217	+	0.683736i
$291$	1.03972	−	1.03972i	0.0609493	−	0.0609493i
$292$	−33.3473	+	0.854805i	−1.95151	+	0.0500237i
$293$		−	8.55351i		−	0.499701i	−0.968284	−	0.249851i	$-0.919618\pi$
$293$		−	8.55351i		−	0.499701i	0.968284	−	0.249851i	$-0.0803815\pi$
$294$	−10.8113	−	4.31674i	−0.630530	−	0.251758i
$295$	−5.65871	+	11.9856i	−0.329463	+	0.697831i
$296$	−22.0960	+	10.1642i	−1.28430	+	0.590782i
$297$	−12.9751	+	6.75817i	−0.752890	+	0.392149i
$298$	3.32017	+	7.73378i	0.192332	+	0.448006i
$299$	−4.98570	−	4.98570i	−0.288331	−	0.288331i
$300$	−1.36970	+	19.2123i	−0.0790798	+	1.10922i
$301$	−5.96586	+	5.96586i	−0.343866	+	0.343866i
$302$	8.74243	+	3.49068i	0.503070	+	0.200866i
$303$	−15.1478	−	15.1478i	−0.870220	−	0.870220i
$304$	9.69850	+	8.75198i	0.556247	+	0.501961i
$305$	14.2813	+	6.74253i	0.817743	+	0.386076i
$306$	−2.86957	+	1.23193i	−0.164043	+	0.0704246i
$307$		−	17.4628i		−	0.996656i	−0.866989	−	0.498328i	$-0.833948\pi$
$307$		−	17.4628i		−	0.996656i	0.866989	−	0.498328i	$-0.166052\pi$
$308$	−9.58098	+	5.30677i	−0.545927	+	0.302382i
$309$	3.90342	−	3.90342i	0.222058	−	0.222058i
$310$	−7.32561	−	0.260801i	−0.416067	−	0.0148125i
$311$		−	29.7088i		−	1.68463i	−0.538985	−	0.842316i	$-0.681192\pi$
$311$		−	29.7088i		−	1.68463i	0.538985	−	0.842316i	$-0.318808\pi$
$312$	12.4866	−	5.74388i	0.706916	−	0.325183i
$313$	−1.32224	−	1.32224i	−0.0747377	−	0.0747377i	0.668750	−	0.743488i	$-0.266830\pi$
$313$	−1.32224	−	1.32224i	−0.0747377	−	0.0747377i	−0.743488	+	0.668750i	$0.766830\pi$
$314$	2.72595	+	1.08842i	0.153834	+	0.0614230i
$315$	−2.37012	−	1.11899i	−0.133541	−	0.0630480i
$316$	18.5900	+	17.6608i	1.04577	+	0.993498i
$317$	21.8207			1.22557			0.612785	−	0.790250i	$-0.290049\pi$
$317$	21.8207			1.22557			0.612785	+	0.790250i	$0.290049\pi$
$318$	−13.2639	+	33.2197i	−0.743804	+	1.86287i
$319$	17.0910	+	5.38448i	0.956914	+	0.301473i
$320$	−6.37220	+	16.7151i	−0.356217	+	0.934403i
$321$		−	17.1995i		−	0.959985i
$322$	−2.41991	+	6.06069i	−0.134856	+	0.337749i
$323$			10.1588i			0.565251i
$324$	−15.4072	−	14.6371i	−0.855955	−	0.813170i
$325$	9.74012	−	8.01594i	0.540285	−	0.444644i
$326$	0.500112	−	1.25254i	0.0276987	−	0.0693716i
$327$	22.9102	+	22.9102i	1.26694	+	1.26694i
$328$	3.71266	+	8.07096i	0.204997	+	0.445644i
$329$			2.96267i			0.163337i
$330$	18.2372	−	8.68862i	1.00393	−	0.478293i
$331$	−18.6749	−	18.6749i	−1.02647	−	1.02647i	−0.999640	−	0.0268265i	$-0.991460\pi$
$331$	−18.6749	−	18.6749i	−1.02647	−	1.02647i	−0.0268265	−	0.999640i	$-0.508540\pi$
$332$	−0.616943	−	0.586104i	−0.0338591	−	0.0321667i
$333$			6.10440i			0.334519i
$334$	−13.0877	−	30.4857i	−0.716128	−	1.66810i
$335$	5.25873	−	1.88568i	0.287315	−	0.103026i
$336$	−9.44427	−	8.52256i	−0.515227	−	0.464944i
$337$	14.4833	−	14.4833i	0.788957	−	0.788957i	−0.192367	−	0.981323i	$-0.561616\pi$
$337$	14.4833	−	14.4833i	0.788957	−	0.788957i	0.981323	+	0.192367i	$0.0616163\pi$
$338$	8.71433	+	3.47946i	0.473997	+	0.189257i
$339$	3.07446	+	3.07446i	0.166982	+	0.166982i
$340$	−12.9699	+	5.02944i	−0.703389	+	0.272759i
$341$	3.55150	+	6.81855i	0.192324	+	0.369245i
$342$	3.01288	−	1.29345i	0.162918	−	0.0699417i
$343$	13.1625	−	13.1625i	0.710708	−	0.710708i
$344$	13.1300	−	6.03985i	0.707925	−	0.325647i
$345$	5.13888	−	10.8846i	0.276668	−	0.586007i
$346$	16.5729	+	6.61722i	0.890964	+	0.355744i
$347$	14.1772			0.761073			0.380537	−	0.924766i	$-0.375739\pi$
$347$	14.1772			0.761073			0.380537	+	0.924766i	$0.375739\pi$
$348$	0.533329	+	20.8060i	0.0285894	+	1.11532i
$349$	−9.28589	+	9.28589i	−0.497062	+	0.497062i	−0.910522	−	0.413460i	$-0.864320\pi$
$349$	−9.28589	+	9.28589i	−0.497062	+	0.497062i	0.413460	+	0.910522i	$0.364320\pi$
$350$	−10.3738	−	5.35710i	−0.554504	−	0.286349i
$351$			11.1285i			0.593994i
$352$	18.5466	−	2.83273i	0.988536	−	0.150985i
$353$	4.56601	−	4.56601i	0.243024	−	0.243024i	−0.575076	−	0.818100i	$-0.695027\pi$
$353$	4.56601	−	4.56601i	0.243024	−	0.243024i	0.818100	+	0.575076i	$0.195027\pi$
$354$	6.36948	+	14.8367i	0.338534	+	0.788560i
$355$	3.15343	+	8.79420i	0.167367	+	0.466748i
$356$	14.2447	+	13.5326i	0.754966	+	0.717229i
$357$		−	9.89251i		−	0.523567i
$358$	11.3002	+	26.3220i	0.597235	+	1.39116i
$359$			15.9325i			0.840883i	0.907320	+	0.420441i	$0.138125\pi$
$359$			15.9325i			0.840883i	−0.907320	+	0.420441i	$0.861875\pi$
$360$	3.14298	+	3.20621i	0.165650	+	0.168982i
$361$			8.33386i			0.438624i
$362$	−3.66562	−	8.53846i	−0.192661	−	0.448772i
$363$	−17.3611	−	12.1445i	−0.911221	−	0.637423i
$364$	0.213491	+	8.32862i	0.0111900	+	0.436539i
$365$	−15.9228	+	33.7259i	−0.833437	+	1.76529i
$366$	17.6784	−	7.58944i	0.924062	−	0.396706i
$367$	18.7165	+	18.7165i	0.976996	+	0.976996i	0.999741	−	0.0227454i	$-0.00724072\pi$
$367$	18.7165	+	18.7165i	0.976996	+	0.976996i	−0.0227454	+	0.999741i	$0.507241\pi$
$368$	7.48936	−	8.29933i	0.390410	−	0.432633i
$369$	2.22974			0.116076
$370$	−0.967472	+	27.1752i	−0.0502965	+	1.41277i
$371$	−15.3318	−	15.3318i	−0.795985	−	0.795985i
$372$	−6.15027	+	6.47387i	−0.318877	+	0.335655i
$373$		−	35.3314i		−	1.82939i	−0.404145	−	0.914695i	$-0.632431\pi$
$373$		−	35.3314i		−	1.82939i	0.404145	−	0.914695i	$-0.367569\pi$
$374$	11.2978	+	9.23161i	0.584197	+	0.477355i
$375$	18.4936	+	11.0329i	0.955005	+	0.569735i
$376$	1.76051	−	4.75992i	0.0907913	−	0.245474i
$377$	9.63841	−	9.63841i	0.496403	−	0.496403i
$378$	9.46468	−	4.06325i	0.486810	−	0.208991i
$379$	6.65968	−	6.65968i	0.342085	−	0.342085i	−0.515066	−	0.857151i	$-0.672233\pi$
$379$	6.65968	−	6.65968i	0.342085	−	0.342085i	0.857151	+	0.515066i	$0.172233\pi$
$380$	13.6176	−	5.28060i	0.698566	−	0.270889i
$381$	−17.3959	−	17.3959i	−0.891221	−	0.891221i
$382$	−1.72899	−	0.690350i	−0.0884628	−	0.0353214i
$383$	−7.17356	+	7.17356i	−0.366552	+	0.366552i	−0.866218	−	0.499666i	$-0.833456\pi$
$383$	−7.17356	+	7.17356i	−0.366552	+	0.366552i	0.499666	+	0.866218i	$0.333456\pi$
$384$	10.1091	+	19.3047i	0.515879	+	0.985140i
$385$	0.478610	+	12.2359i	0.0243922	+	0.623599i
$386$	−11.1792	−	26.0400i	−0.569004	−	1.32540i
$387$		−	3.62740i		−	0.184391i
$388$	−0.0391239	−	1.52629i	−0.00198622	−	0.0774855i
$389$	3.11517	−	3.11517i	0.157945	−	0.157945i	−0.623710	−	0.781656i	$-0.714375\pi$
$389$	3.11517	−	3.11517i	0.157945	−	0.157945i	0.781656	+	0.623710i	$0.214375\pi$
$390$	0.546727	−	15.3570i	0.0276846	−	0.777630i
$391$	8.69323			0.439636
$392$	−10.9817	+	5.05161i	−0.554660	+	0.255145i
$393$	19.4553	−	19.4553i	0.981389	−	0.981389i
$394$	24.6171	+	9.82911i	1.24019	+	0.495183i
$395$	26.9858	−	9.67659i	1.35780	−	0.486882i
$396$	1.29942	−	4.52608i	0.0652981	−	0.227444i
$397$	−26.3123			−1.32057			−0.660287	−	0.751013i	$-0.729565\pi$
$397$	−26.3123			−1.32057			−0.660287	+	0.751013i	$0.729565\pi$
$398$	−15.4543	−	6.17057i	−0.774652	−	0.309303i
$399$			10.3865i			0.519977i
$400$	13.4836	+	14.7713i	0.674180	+	0.738567i
$401$	3.32684			0.166134			0.0830672	−	0.996544i	$-0.473528\pi$
$401$	3.32684			0.166134			0.0830672	+	0.996544i	$0.473528\pi$
$402$	2.52356	−	6.32028i	0.125864	−	0.315227i
$403$	5.84815			0.291317
$404$	−22.2368	+	0.570003i	−1.10632	+	0.0283587i
$405$	−22.3655	+	8.01983i	−1.11135	+	0.398509i
$406$	−11.7166	−	4.67820i	−0.581485	−	0.232175i
$407$	25.2942	−	13.1747i	1.25379	−	0.653046i
$408$	−5.87844	+	15.8937i	−0.291026	+	0.786853i
$409$		−	37.6199i		−	1.86018i	−0.367326	−	0.930092i	$-0.619727\pi$
$409$		−	37.6199i		−	1.86018i	0.367326	−	0.930092i	$-0.380273\pi$
$410$	9.92624	+	0.353387i	0.490222	+	0.0174525i
$411$	16.8499	+	16.8499i	0.831147	+	0.831147i
$412$	−0.146883	−	5.73017i	−0.00723643	−	0.282305i
$413$	−9.78720			−0.481597
$414$	−1.10685	−	2.57822i	−0.0543986	−	0.126713i
$415$	−0.895569	+	0.321134i	−0.0439617	+	0.0157639i
$416$	4.60613	−	13.5079i	0.225834	−	0.662280i
$417$	7.16935	−	7.16935i	0.351085	−	0.351085i
$418$	−11.8620	−	9.69263i	−0.580191	−	0.474082i
$419$	14.8973	+	14.8973i	0.727781	+	0.727781i	0.970177	−	0.242397i	$-0.0779335\pi$
$419$	14.8973	+	14.8973i	0.727781	+	0.727781i	−0.242397	+	0.970177i	$0.577934\pi$
$420$	−13.2606	+	5.14218i	−0.647051	+	0.250913i
$421$	5.46488	+	5.46488i	0.266342	+	0.266342i	0.827624	−	0.561282i	$-0.189692\pi$
$421$	5.46488	+	5.46488i	0.266342	+	0.266342i	−0.561282	+	0.827624i	$0.689692\pi$
$422$	−1.92178	−	4.47647i	−0.0935508	−	0.217911i
$423$	−0.900691	−	0.900691i	−0.0437931	−	0.0437931i
$424$	15.5219	+	33.7431i	0.753811	+	1.63871i
$425$	−1.50317	+	15.4800i	−0.0729143	+	0.750891i
$426$	10.5694	+	4.22017i	0.512091	+	0.204468i
$427$			11.6618i			0.564352i
$428$	−12.9479	−	12.3007i	−0.625862	−	0.594578i
$429$	−14.2940	+	7.44515i	−0.690121	+	0.359455i
$430$	0.574899	−	16.1483i	0.0277241	−	0.778739i
$431$			38.6261i			1.86055i	0.366861	+	0.930276i	$0.380432\pi$
$431$			38.6261i			1.86055i	−0.366861	+	0.930276i	$0.619568\pi$
$432$	−17.6208	+	0.903954i	−0.847781	+	0.0434915i
$433$	26.5059	−	26.5059i	1.27379	−	1.27379i	0.329711	−	0.944082i	$-0.393049\pi$
$433$	26.5059	−	26.5059i	1.27379	−	1.27379i	0.944082	−	0.329711i	$-0.106951\pi$
$434$	−2.13529	−	4.97380i	−0.102497	−	0.238750i
$435$	21.0422	+	9.93453i	1.00890	+	0.476324i
$436$	33.6318	−	0.862097i	1.61067	−	0.0412869i
$437$	−9.12737			−0.436621
$438$	17.9228	+	41.7482i	0.856385	+	1.99481i
$439$			3.11932i			0.148877i	0.997226	+	0.0744385i	$0.0237164\pi$
$439$			3.11932i			0.148877i	−0.997226	+	0.0744385i	$0.976284\pi$
$440$	6.50200	−	19.9430i	0.309971	−	0.950746i
$441$			3.03389i			0.144471i
$442$	10.1982	−	4.37814i	0.485077	−	0.208247i
$443$	−24.6030			−1.16893			−0.584463	−	0.811421i	$-0.698695\pi$
$443$	−24.6030			−1.16893			−0.584463	+	0.811421i	$0.698695\pi$
$444$	24.0156	+	22.8152i	1.13973	+	1.08276i
$445$	20.6779	−	7.41471i	0.980227	−	0.351491i
$446$	3.39271	−	1.45651i	0.160650	−	0.0689680i
$447$	8.10540	−	8.10540i	0.383372	−	0.383372i
$448$	−13.1702	+	1.01457i	−0.622232	+	0.0479337i
$449$			22.3378i			1.05418i	0.849808	+	0.527092i	$0.176718\pi$
$449$			22.3378i			1.05418i	−0.849808	+	0.527092i	$0.823282\pi$
$450$	4.78242	−	1.52515i	0.225445	−	0.0718965i
$451$	−4.81230	−	9.23918i	−0.226602	−	0.435056i
$452$	4.51326	−	0.115690i	0.212286	−	0.00544160i
$453$		−	12.8209i		−	0.602380i
$454$	−11.6340	+	29.1376i	−0.546012	+	1.36749i
$455$	8.42316	+	3.97678i	0.394884	+	0.186434i
$456$	6.17200	−	16.6874i	0.289031	−	0.781458i
$457$	−4.08141	−	4.08141i	−0.190920	−	0.190920i	0.605173	−	0.796094i	$-0.293104\pi$
$457$	−4.08141	−	4.08141i	−0.190920	−	0.190920i	−0.796094	+	0.605173i	$0.793104\pi$
$458$	8.09926	−	3.47707i	0.378453	−	0.162473i
$459$	−9.70198	−	9.70198i	−0.452850	−	0.452850i
$460$	−4.51879	−	11.6530i	−0.210690	−	0.543324i
$461$	12.9617	+	12.9617i	0.603689	+	0.603689i	0.941289	−	0.337601i	$-0.109615\pi$
$461$	12.9617	+	12.9617i	0.603689	+	0.603689i	−0.337601	+	0.941289i	$0.609615\pi$
$462$	11.5511	+	9.43855i	0.537406	+	0.439121i
$463$	0.352161	−	0.352161i	0.0163663	−	0.0163663i	−0.698876	−	0.715243i	$-0.746316\pi$
$463$	0.352161	−	0.352161i	0.0163663	−	0.0163663i	0.715243	+	0.698876i	$0.246316\pi$
$464$	16.0443	+	14.4785i	0.744840	+	0.672148i
$465$	3.36981	+	9.39763i	0.156271	+	0.435805i
$466$	−36.9812	+	15.8763i	−1.71312	+	0.735455i
$467$	−35.6703			−1.65063			−0.825313	−	0.564676i	$-0.809001\pi$
$467$	−35.6703			−1.65063			−0.825313	+	0.564676i	$0.809001\pi$
$468$	−2.59692	−	2.46711i	−0.120043	−	0.114042i
$469$	2.91698	+	2.91698i	0.134694	+	0.134694i
$470$	−3.86690	−	4.15240i	−0.178367	−	0.191536i
$471$		−	3.99766i		−	0.184202i
$472$	15.7245	+	5.81586i	0.723777	+	0.267697i
$473$	−15.0305	+	7.82878i	−0.691105	+	0.359968i
$474$	12.9499	−	32.4333i	0.594810	−	1.48971i
$475$	1.57823	−	16.2531i	0.0724143	−	0.745742i
$476$	−7.44715	−	7.07490i	−0.341340	−	0.324278i
$477$	9.32213			0.426831
$478$	5.10849	+	2.03972i	0.233657	+	0.0932944i
$479$	−39.8137			−1.81913			−0.909566	−	0.415559i	$-0.863586\pi$
$479$	−39.8137			−1.81913			−0.909566	+	0.415559i	$0.863586\pi$
$480$	24.3606	−	0.381744i	1.11190	−	0.0174242i
$481$		−	21.6944i		−	0.989180i
$482$	−5.16237	+	12.9292i	−0.235140	+	0.588910i
$483$	8.88811			0.404423
$484$	−21.5588	+	4.38406i	−0.979944	+	0.199276i
$485$	−1.54361	−	0.728777i	−0.0700919	−	0.0330920i
$486$	−3.79324	+	9.50022i	−0.172065	+	0.430939i
$487$	−24.4418	+	24.4418i	−1.10756	+	1.10756i	−0.114094	+	0.993470i	$0.536397\pi$
$487$	−24.4418	+	24.4418i	−1.10756	+	1.10756i	−0.993470	+	0.114094i	$0.963603\pi$
$488$	6.92978	−	18.7362i	0.313696	−	0.848147i
$489$	−1.83687			−0.0830659
$490$	−0.480834	+	13.5061i	−0.0217218	+	0.610143i
$491$	−23.8093	+	23.8093i	−1.07450	+	1.07450i	−0.0775079	+	0.996992i	$0.524696\pi$
$491$	−23.8093	+	23.8093i	−1.07450	+	1.07450i	−0.996992	+	0.0775079i	$0.975304\pi$
$492$	8.33366	−	8.77214i	0.375710	−	0.395478i
$493$			16.8058i			0.756897i
$494$	−10.7075	+	4.59679i	−0.481751	+	0.206819i
$495$	−3.86538	−	3.57438i	−0.173736	−	0.160656i
$496$	0.475039	+	9.25994i	0.0213299	+	0.415783i
$497$	−4.87808	+	4.87808i	−0.218812	+	0.218812i
$498$	−0.429766	+	1.07635i	−0.0192583	+	0.0482326i
$499$	−12.7789	−	12.7789i	−0.572060	−	0.572060i	0.360644	−	0.932704i	$-0.382557\pi$
$499$	−12.7789	−	12.7789i	−0.572060	−	0.572060i	−0.932704	+	0.360644i	$0.882557\pi$
$500$	21.5318	−	6.03165i	0.962932	−	0.269743i
$501$	−31.9506	+	31.9506i	−1.42745	+	1.42745i
$502$	3.92390	+	9.14009i	0.175132	+	0.407942i
$503$	9.86180	−	9.86180i	0.439716	−	0.439716i	−0.452201	−	0.891916i	$-0.649361\pi$
$503$	9.86180	−	9.86180i	0.439716	−	0.439716i	0.891916	+	0.452201i	$0.149361\pi$
$504$	−1.15007	+	3.10946i	−0.0512280	+	0.138506i
$505$	−10.6177	+	22.4892i	−0.472481	+	1.00076i
$506$	−8.29430	+	10.1507i	−0.368727	+	0.451256i
$507$		−	12.7797i		−	0.567567i
$508$	−25.5370	+	0.654598i	−1.13302	+	0.0290431i
$509$	22.5012	+	22.5012i	0.997347	+	0.997347i	0.999996	−	0.00264917i	$-0.000843259\pi$
$509$	22.5012	+	22.5012i	0.997347	+	0.997347i	−0.00264917	+	0.999996i	$0.500843\pi$
$510$	12.9118	+	13.8651i	0.571744	+	0.613957i
$511$	−27.5398			−1.21829
$512$	21.7625	+	6.19609i	0.961778	+	0.273831i
$513$	10.1865	+	10.1865i	0.449745	+	0.449745i
$514$	17.2439	+	40.1669i	0.760598	+	1.77169i
$515$	−5.79521	−	2.73606i	−0.255367	−	0.120565i
$516$	−14.2707	−	13.5574i	−0.628235	−	0.596832i
$517$	−1.78821	+	5.67602i	−0.0786455	+	0.249631i
$518$	−18.4509	+	7.92111i	−0.810687	+	0.348033i
$519$		−	24.3044i		−	1.06685i
$520$	−11.1698	−	11.3945i	−0.489829	−	0.499683i
$521$			20.4209i			0.894655i	0.894370	+	0.447328i	$0.147624\pi$
$521$			20.4209i			0.894655i	−0.894370	+	0.447328i	$0.852376\pi$
$522$	4.98424	−	2.13977i	0.218154	−	0.0936551i
$523$			39.6016i			1.73166i	0.500342	+	0.865828i	$0.333208\pi$
$523$			39.6016i			1.73166i	−0.500342	+	0.865828i	$0.666792\pi$
$524$	−0.732090	−	28.5600i	−0.0319815	−	1.24765i
$525$	−1.53686	+	15.8270i	−0.0670742	+	0.690748i
$526$	−34.5822	+	14.8464i	−1.50786	+	0.647333i
$527$	−5.09851	+	5.09851i	−0.222094	+	0.222094i
$528$	−12.9497	−	22.0283i	−0.563564	−	0.958659i
$529$		−	15.1894i		−	0.660409i
$530$	41.4997	+	1.47744i	1.80263	+	0.0641760i
$531$	2.97544	−	2.97544i	0.129123	−	0.129123i
$532$	7.81906	+	7.42822i	0.338999	+	0.322054i
$533$	−7.92427			−0.343238
$534$	9.92293	−	24.8521i	0.429407	−	1.07545i
$535$	−18.7955	+	6.73973i	−0.812602	+	0.291384i
$536$	−2.95316	−	6.41988i	−0.127557	−	0.277297i
$537$	27.5868	−	27.5868i	1.19046	−	1.19046i
$538$	−0.174499	−	0.406467i	−0.00752320	−	0.0175241i
$539$	12.5712	−	6.54783i	0.541482	−	0.282035i
$540$	−7.96205	+	18.0483i	−0.342632	+	0.776677i
$541$	14.1872	+	14.1872i	0.609956	+	0.609956i	0.942934	−	0.332978i	$-0.108054\pi$
$541$	14.1872	+	14.1872i	0.609956	+	0.609956i	−0.332978	+	0.942934i	$0.608054\pi$
$542$	−9.63828	+	24.1392i	−0.414000	+	1.03687i
$543$	−8.94874	+	8.94874i	−0.384027	+	0.384027i
$544$	7.76073	+	15.7921i	0.332738	+	0.677081i
$545$	16.0586	−	34.0136i	0.687876	−	1.45698i
$546$	10.4268	−	4.47629i	0.446225	−	0.191567i
$547$		−	19.0324i		−	0.813768i	−0.913480	−	0.406884i	$-0.866615\pi$
$547$		−	19.0324i		−	0.813768i	0.913480	−	0.406884i	$-0.133385\pi$
$548$	24.7355	−	0.634053i	1.05665	−	0.0270854i
$549$	−3.54534	−	3.54534i	−0.151311	−	0.151311i
$550$	−16.6412	−	16.5248i	−0.709584	−	0.704621i
$551$		−	17.6451i		−	0.751707i
$552$	−14.2799	−	5.28159i	−0.607795	−	0.224799i
$553$	14.9688	+	14.9688i	0.636539	+	0.636539i
$554$	−10.6743	−	4.26205i	−0.453509	−	0.181077i
$555$	34.8616	−	12.5007i	1.47979	−	0.530626i
$556$	−0.269778	−	10.5245i	−0.0114411	−	0.446338i
$557$		−	25.8327i		−	1.09457i	−0.836948	−	0.547283i	$-0.815662\pi$
$557$		−	25.8327i		−	1.09457i	0.836948	−	0.547283i	$-0.184338\pi$
$558$	2.16126	+	0.862947i	0.0914935	+	0.0365315i
$559$			12.8914i			0.545249i
$560$	−5.61261	+	13.6602i	−0.237176	+	0.577251i
$561$	5.97094	−	18.9525i	0.252093	−	0.800177i
$562$	−14.5282	−	5.80082i	−0.612836	−	0.244693i
$563$	6.45085			0.271871			0.135935	−	0.990718i	$-0.456596\pi$
$563$	6.45085			0.271871			0.135935	+	0.990718i	$0.456596\pi$
$564$	−6.90979	+	0.177121i	−0.290954	+	0.00745814i
$565$	2.15501	−	4.56449i	0.0906618	−	0.192030i
$566$	2.70677	−	6.77913i	0.113774	−	0.284948i
$567$	−12.4060	−	12.4060i	−0.521001	−	0.521001i
$568$	10.7360	−	4.93859i	0.450473	−	0.207219i
$569$		−	35.3403i		−	1.48154i	−0.671758	−	0.740771i	$-0.734460\pi$
$569$		−	35.3403i		−	1.48154i	0.671758	−	0.740771i	$-0.265540\pi$
$570$	−13.5566	−	14.5575i	−0.567824	−	0.609747i
$571$	2.39271	−	2.39271i	0.100132	−	0.100132i	−0.655266	−	0.755398i	$-0.727444\pi$
$571$	2.39271	−	2.39271i	0.100132	−	0.100132i	0.755398	+	0.655266i	$0.227444\pi$
$572$	−4.61799	+	16.0852i	−0.193088	+	0.672557i
$573$			2.53559i			0.105926i
$574$	2.89333	+	6.73953i	0.120765	+	0.281303i
$575$	−13.9083	−	1.35055i	−0.580016	−	0.0563217i
$576$	3.69547	−	4.31236i	0.153978	−	0.179682i
$577$	5.64754	+	5.64754i	0.235110	+	0.235110i	0.814822	−	0.579711i	$-0.196835\pi$
$577$	5.64754	+	5.64754i	0.235110	+	0.235110i	−0.579711	+	0.814822i	$0.696835\pi$
$578$	3.84098	−	9.61977i	0.159764	−	0.400130i
$579$	−27.2913	+	27.2913i	−1.13419	+	1.13419i
$580$	22.5277	−	8.73576i	0.935412	−	0.362733i
$581$	−0.496766	−	0.496766i	−0.0206093	−	0.0206093i
$582$	−1.91079	+	0.820316i	−0.0792048	+	0.0340032i
$583$	−20.1193	−	38.6273i	−0.833257	−	1.59978i
$584$	44.2463	+	16.3650i	1.83093	+	0.677188i
$585$	−3.76975	+	1.35176i	−0.155860	+	0.0558885i
$586$	−4.48554	+	11.2341i	−0.185296	+	0.464076i
$587$			20.5810i			0.849468i	0.905318	+	0.424734i	$0.139632\pi$
$587$			20.5810i			0.849468i	−0.905318	+	0.424734i	$0.860368\pi$
$588$	11.9358	+	11.3391i	0.492222	+	0.467618i
$589$	5.35312	−	5.35312i	0.220572	−	0.220572i
$590$	13.7175	−	12.7744i	0.564740	−	0.525912i
$591$		−	36.1014i		−	1.48501i
$592$	34.3509	−	1.76221i	1.41181	−	0.0724266i
$593$	10.9278	+	10.9278i	0.448752	+	0.448752i	0.894939	−	0.446188i	$-0.147219\pi$
$593$	10.9278	+	10.9278i	0.448752	+	0.448752i	−0.446188	+	0.894939i	$0.647219\pi$
$594$	20.5854	−	2.07186i	0.844628	−	0.0850094i
$595$	−10.8105	+	3.87643i	−0.443186	+	0.158918i
$596$	−0.305001	−	11.8986i	−0.0124933	−	0.487386i
$597$			22.6639i			0.927573i
$598$	3.93362	+	9.16273i	0.160858	+	0.374692i
$599$	−8.77558			−0.358560			−0.179280	−	0.983798i	$-0.557377\pi$
$599$	−8.77558			−0.358560			−0.179280	+	0.983798i	$0.557377\pi$
$600$	11.8741	−	24.5150i	0.484758	−	1.00082i
$601$	−20.4688			−0.834941			−0.417471	−	0.908690i	$-0.637083\pi$
$601$	−20.4688			−0.834941			−0.417471	+	0.908690i	$0.637083\pi$
$602$	10.9641	−	4.70694i	0.446861	−	0.191841i
$603$	−1.77360			−0.0722267
$604$	−9.65168	−	9.16924i	−0.392721	−	0.373091i
$605$	−6.46842	+	23.7310i	−0.262979	+	0.964802i
$606$	11.9513	+	27.8387i	0.485490	+	1.13087i
$607$	17.4127	−	17.4127i	0.706759	−	0.706759i	−0.259093	−	0.965852i	$-0.583424\pi$
$607$	17.4127	−	17.4127i	0.706759	−	0.706759i	0.965852	+	0.259093i	$0.0834237\pi$
$608$	−8.14829	−	16.5808i	−0.330457	−	0.672439i
$609$			17.1826i			0.696273i
$610$	−15.2210	−	16.3448i	−0.616282	−	0.661783i
$611$	3.20096	+	3.20096i	0.129497	+	0.129497i
$612$	4.41490	−	0.113169i	0.178462	−	0.00457458i
$613$		−	15.1403i		−	0.611510i	−0.952110	−	0.305755i	$-0.901091\pi$
$613$		−	15.1403i		−	0.611510i	0.952110	−	0.305755i	$-0.0989089\pi$
$614$	−9.15768	+	22.9355i	−0.369574	+	0.925602i
$615$	−4.56612	−	12.7338i	−0.184124	−	0.513478i
$616$	15.3665	−	1.94551i	0.619133	−	0.0783867i
$617$	3.15698	−	3.15698i	0.127095	−	0.127095i	−0.640698	−	0.767793i	$-0.721355\pi$
$617$	3.15698	−	3.15698i	0.127095	−	0.127095i	0.767793	+	0.640698i	$0.221355\pi$
$618$	−7.17371	+	3.07972i	−0.288569	+	0.123885i
$619$	−19.4545	+	19.4545i	−0.781943	+	0.781943i	−0.980158	−	0.198216i	$-0.936485\pi$
$619$	−19.4545	+	19.4545i	−0.781943	+	0.781943i	0.198216	+	0.980158i	$0.436485\pi$
$620$	9.48462	+	4.18416i	0.380911	+	0.168040i
$621$	8.71692	−	8.71692i	0.349798	−	0.349798i
$622$	−15.5796	+	39.0192i	−0.624685	+	1.56453i
$623$	11.4699	+	11.4699i	0.459532	+	0.459532i
$624$	−19.4120	+	0.995843i	−0.777101	+	0.0398656i
$625$	4.80983	−	24.5329i	0.192393	−	0.981318i
$626$	1.04323	+	2.43002i	0.0416957	+	0.0971232i
$627$	−6.26913	+	19.8990i	−0.250365	+	0.794690i
$628$	−3.00946	−	2.85903i	−0.120091	−	0.114088i
$629$	18.9135	+	18.9135i	0.754132	+	0.754132i
$630$	2.52608	+	2.71259i	0.100642	+	0.108072i
$631$			6.31248i			0.251296i	0.992075	+	0.125648i	$0.0401010\pi$
$631$			6.31248i			0.251296i	−0.992075	+	0.125648i	$0.959899\pi$
$632$	−15.1545	−	32.9443i	−0.602813	−	1.31046i
$633$	−4.69157	+	4.69157i	−0.186473	+	0.186473i
$634$	−28.6590	−	11.4430i	−1.13820	−	0.454458i
$635$	−12.1935	+	25.8268i	−0.483883	+	1.02491i
$636$	34.8414	−	36.6746i	1.38155	−	1.45424i
$637$		−	10.7821i		−	0.427203i
$638$	−19.6235	−	16.0346i	−0.776902	−	0.634817i
$639$		−	2.96601i		−	0.117333i
$640$	17.1348	−	18.6118i	0.677311	−	0.735697i
$641$	−1.32249			−0.0522353			−0.0261176	−	0.999659i	$-0.508314\pi$
$641$	−1.32249			−0.0522353			−0.0261176	+	0.999659i	$0.508314\pi$
$642$	−9.01961	+	22.5897i	−0.355976	+	0.891545i
$643$		−	0.274996i		−	0.0108448i	−0.999985	−	0.00542240i	$-0.998274\pi$
$643$		−	0.274996i		−	0.0108448i	0.999985	−	0.00542240i	$-0.00172601\pi$
$644$	6.35657	−	6.69103i	0.250484	−	0.263663i
$645$	−20.7158	+	7.42828i	−0.815682	+	0.292488i
$646$	5.32738	−	13.3425i	0.209603	−	0.524953i
$647$	−33.8376	+	33.8376i	−1.33029	+	1.33029i	−0.425191	+	0.905104i	$0.639793\pi$
$647$	−33.8376	+	33.8376i	−1.33029	+	1.33029i	−0.905104	+	0.425191i	$0.860207\pi$
$648$	12.5598	+	27.3039i	0.493397	+	1.07260i
$649$	−18.7508	−	5.90738i	−0.736033	−	0.231885i
$650$	−16.9962	+	5.42024i	−0.666646	+	0.212599i
$651$	−5.21280	+	5.21280i	−0.204306	+	0.204306i
$652$	−1.31369	+	1.38281i	−0.0514479	+	0.0541548i
$653$		−	11.8691i		−	0.464472i	−0.972659	−	0.232236i	$-0.925396\pi$
$653$		−	11.8691i		−	0.464472i	0.972659	−	0.232236i	$-0.0746042\pi$
$654$	−18.0757	−	42.1044i	−0.706816	−	1.64641i
$655$	−28.8842	−	13.6369i	−1.12860	−	0.532839i
$656$	−0.643681	−	12.5473i	−0.0251315	−	0.489889i
$657$	8.37247	−	8.37247i	0.326641	−	0.326641i
$658$	1.55365	−	3.89114i	0.0605677	−	0.151692i
$659$	2.39683	−	2.39683i	0.0933673	−	0.0933673i	−0.658880	−	0.752248i	$-0.728970\pi$
$659$	2.39683	−	2.39683i	0.0933673	−	0.0933673i	0.752248	+	0.658880i	$0.228970\pi$
$660$	−28.5090	+	1.84777i	−1.10971	+	0.0719244i
$661$	24.5350	+	24.5350i	0.954301	+	0.954301i	0.999000	−	0.0446999i	$-0.0142332\pi$
$661$	24.5350	+	24.5350i	0.954301	+	0.954301i	−0.0446999	+	0.999000i	$0.514233\pi$
$662$	14.7341	+	34.3208i	0.572659	+	1.33392i
$663$	−10.6882	−	10.6882i	−0.415095	−	0.415095i
$664$	0.502927	+	1.09331i	0.0195174	+	0.0424288i
$665$	11.3503	−	4.07002i	0.440147	−	0.157829i
$666$	3.20121	−	8.01746i	0.124044	−	0.310670i
$667$	−15.0995			−0.584655
$668$	1.20228	+	46.9030i	0.0465176	+	1.81473i
$669$	−3.55574	−	3.55574i	−0.137473	−	0.137473i
$670$	−7.89563	−	0.281094i	−0.305035	−	0.0108596i
$671$	−7.03883	+	22.3421i	−0.271731	+	0.862509i
$672$	7.93470	+	16.1461i	0.306088	+	0.622850i
$673$	27.2290	+	27.2290i	1.04960	+	1.04960i	0.998704	+	0.0508979i	$0.0162083\pi$
$673$	27.2290	+	27.2290i	1.04960	+	1.04960i	0.0508979	+	0.998704i	$0.483792\pi$
$674$	−26.6174	+	11.4271i	−1.02527	+	0.440154i
$675$	14.0149	+	17.0295i	0.539435	+	0.655464i
$676$	−9.62066	−	9.13977i	−0.370025	−	0.351530i
$677$	−21.3070			−0.818895			−0.409447	−	0.912334i	$-0.634279\pi$
$677$	−21.3070			−0.818895			−0.409447	+	0.912334i	$0.634279\pi$
$678$	−2.42569	−	5.65024i	−0.0931580	−	0.216996i
$679$		−	1.26048i		−	0.0483727i
$680$	19.6720	+	0.195909i	0.754385	+	0.00751277i
$681$	42.7307			1.63744
$682$	−1.08879	−	10.8179i	−0.0416918	−	0.414237i
$683$	−14.6865			−0.561965			−0.280982	−	0.959713i	$-0.590660\pi$
$683$	−14.6865			−0.561965			−0.280982	+	0.959713i	$0.590660\pi$
$684$	−4.63538	+	0.118820i	−0.177238	+	0.00454321i
$685$	11.8108	−	25.0162i	0.451266	−	0.955821i
$686$	−24.1900	+	10.3849i	−0.923580	+	0.396499i
$687$	−8.48844	−	8.48844i	−0.323854	−	0.323854i
$688$	−20.4122	+	1.04716i	−0.778209	+	0.0399225i
$689$	−33.1299			−1.26215
$690$	−12.4573	+	11.6008i	−0.474243	+	0.441636i
$691$	−25.7323	+	25.7323i	−0.978904	+	0.978904i	−0.999782	−	0.0208782i	$-0.993354\pi$
$691$	−25.7323	+	25.7323i	−0.978904	+	0.978904i	0.0208782	+	0.999782i	$0.493354\pi$
$692$	−18.2965	−	17.3820i	−0.695530	−	0.660764i
$693$	1.16816	−	3.70790i	0.0443749	−	0.140852i
$694$	−18.6202	−	7.43468i	−0.706814	−	0.282217i
$695$	−10.6440	−	5.02527i	−0.403748	−	0.190619i
$696$	10.2104	−	27.6061i	0.387025	−	1.04641i
$697$	6.90851	−	6.90851i	0.261678	−	0.261678i
$698$	17.0656	−	7.32638i	0.645943	−	0.277308i
$699$	38.7582	+	38.7582i	1.46597	+	1.46597i
$700$	10.8156	+	12.4761i	0.408790	+	0.471552i
$701$	−14.0475	−	14.0475i	−0.530566	−	0.530566i	0.390175	−	0.920741i	$-0.372415\pi$
$701$	−14.0475	−	14.0475i	−0.530566	−	0.530566i	−0.920741	+	0.390175i	$0.872415\pi$
$702$	5.83588	−	14.6160i	0.220261	−	0.551646i
$703$	−19.8581	−	19.8581i	−0.748961	−	0.748961i
$704$	−25.8444	−	6.00553i	−0.974048	−	0.226342i
$705$	−3.29931	+	6.98822i	−0.124259	+	0.263192i
$706$	−8.39141	+	3.60249i	−0.315815	+	0.135582i
$707$	−18.3641			−0.690655
$708$	−0.585122	−	22.8266i	−0.0219902	−	0.857875i
$709$	7.08387	−	7.08387i	0.266040	−	0.266040i	−0.561462	−	0.827503i	$-0.689761\pi$
$709$	7.08387	−	7.08387i	0.266040	−	0.266040i	0.827503	+	0.561462i	$0.189761\pi$
$710$	0.470076	−	13.2039i	0.0176416	−	0.495534i
$711$	−9.10145			−0.341331
$712$	−11.6122	−	25.2437i	−0.435184	−	0.946048i
$713$	−4.58085	−	4.58085i	−0.171554	−	0.171554i
$714$	−5.18773	+	12.9927i	−0.194146	+	0.486241i
$715$	13.7372	+	12.7030i	0.513741	+	0.475064i
$716$	−1.03807	−	40.4970i	−0.0387947	−	1.51344i
$717$		−	7.49169i		−	0.279782i
$718$	8.35514	−	20.9255i	0.311811	−	0.780934i
$719$		−	27.1187i		−	1.01136i	−0.862722	−	0.505679i	$-0.831242\pi$
$719$		−	27.1187i		−	1.01136i	0.862722	−	0.505679i	$-0.168758\pi$
$720$	−2.44659	−	5.85921i	−0.0911790	−	0.218360i
$721$		−	4.73223i		−	0.176238i
$722$	4.37036	−	10.9456i	0.162648	−	0.407354i
$723$	18.9609			0.705164
$724$	0.336736	+	13.1366i	0.0125147	+	0.488219i
$725$	2.61089	−	26.8877i	0.0969661	−	0.998583i
$726$	16.4332	+	25.0548i	0.609893	+	0.929872i
$727$	20.3812	−	20.3812i	0.755897	−	0.755897i	−0.219676	−	0.975573i	$-0.570500\pi$
$727$	20.3812	−	20.3812i	0.755897	−	0.755897i	0.975573	+	0.219676i	$0.0705000\pi$
$728$	4.08722	−	11.0507i	0.151482	−	0.409566i
$729$	−17.9450			−0.664629
$730$	38.5990	−	35.9452i	1.42861	−	1.33039i
$731$	−11.2389	−	11.2389i	−0.415687	−	0.415687i
$732$	−27.1986	+	0.697191i	−1.00529	+	0.0257689i
$733$	−0.281716			−0.0104054			−0.00520271	−	0.999986i	$-0.501656\pi$
$733$	−0.281716			−0.0104054			−0.00520271	+	0.999986i	$0.501656\pi$
$734$	−14.7670	−	34.3973i	−0.545059	−	1.26963i
$735$	17.3262	−	6.21286i	0.639088	−	0.229165i
$736$	−14.1887	+	6.97276i	−0.523003	+	0.257019i
$737$	3.82785	+	7.34912i	0.141001	+	0.270708i
$738$	−2.92852	−	1.16930i	−0.107800	−	0.0430425i
$739$	0.146832	−	0.146832i	0.00540130	−	0.00540130i	−0.704401	−	0.709802i	$-0.748784\pi$
$739$	0.146832	−	0.146832i	0.00540130	−	0.00540130i	0.709802	+	0.704401i	$0.248784\pi$
$740$	15.5216	−	35.1843i	0.570586	−	1.29340i
$741$	11.2220	+	11.2220i	0.412249	+	0.412249i
$742$	12.0965	+	28.1767i	0.444075	+	1.03440i
$743$	−9.65350	+	9.65350i	−0.354153	+	0.354153i	−0.861652	−	0.507500i	$-0.830570\pi$
$743$	−9.65350	+	9.65350i	−0.354153	+	0.354153i	0.507500	+	0.861652i	$0.330570\pi$
$744$	11.4727	−	5.27746i	0.420609	−	0.193481i
$745$	−12.0337	−	5.68138i	−0.440880	−	0.208150i
$746$	−18.5281	+	46.4039i	−0.678363	+	1.69897i
$747$	0.302047			0.0110513
$748$	−9.99732	−	18.0494i	−0.365538	−	0.659951i
$749$	−10.4258	−	10.4258i	−0.380949	−	0.380949i
$750$	−18.5036	−	24.1887i	−0.675654	−	0.883246i
$751$	−31.1642			−1.13720			−0.568599	−	0.822615i	$-0.692514\pi$
$751$	−31.1642			−1.13720			−0.568599	+	0.822615i	$0.692514\pi$
$752$	−4.80839	+	5.32841i	−0.175344	+	0.194307i
$753$	9.57928	−	9.57928i	0.349088	−	0.349088i
$754$	−17.7135	+	7.60452i	−0.645087	+	0.276940i
$755$	−14.0106	+	5.02394i	−0.509899	+	0.182840i
$756$	−14.5616	+	0.373264i	−0.529601	+	0.0135755i
$757$		−	27.4269i		−	0.996849i	−0.866933	−	0.498424i	$-0.833912\pi$
$757$		−	27.4269i		−	0.996849i	0.866933	−	0.498424i	$-0.166088\pi$
$758$	−12.2392	+	5.25435i	−0.444546	+	0.190847i
$759$	17.0282	+	5.36470i	0.618086	+	0.194726i
$760$	−20.6544	−	0.205693i	−0.749213	−	0.00746126i
$761$	−11.6576			−0.422586			−0.211293	−	0.977423i	$-0.567767\pi$
$761$	−11.6576			−0.422586			−0.211293	+	0.977423i	$0.567767\pi$
$762$	13.7250	+	31.9703i	0.497206	+	1.15816i
$763$	27.7747			1.00551
$764$	1.90881	+	1.81340i	0.0690584	+	0.0656064i
$765$	2.10804	−	4.46502i	0.0762164	−	0.161433i
$766$	13.1836	−	5.65979i	0.476342	−	0.204497i
$767$	−10.5744	+	10.5744i	−0.381820	+	0.381820i
$768$	−3.15363	−	30.6560i	−0.113797	−	1.10620i
$769$	−12.2788			−0.442784			−0.221392	−	0.975185i	$-0.571060\pi$
$769$	−12.2788			−0.442784			−0.221392	+	0.975185i	$0.571060\pi$
$770$	5.78802	−	16.3215i	0.208586	−	0.588186i
$771$	42.0970	−	42.0970i	1.51609	−	1.51609i
$772$	1.02695	+	40.0632i	0.0369609	+	1.44190i
$773$	50.3958			1.81261			0.906305	−	0.422625i	$-0.138891\pi$
$773$	50.3958			1.81261			0.906305	+	0.422625i	$0.138891\pi$
$774$	−1.90225	+	4.76420i	−0.0683749	+	0.171246i
$775$	8.94919	−	7.36502i	0.321464	−	0.264559i
$776$	−0.749016	+	2.02513i	−0.0268881	+	0.0726979i
$777$	19.3375	+	19.3375i	0.693729	+	0.693729i
$778$	−5.72506	+	2.45781i	−0.205253	+	0.0881166i
$779$	−7.25352	+	7.25352i	−0.259884	+	0.259884i
$780$	−8.77141	+	19.8830i	−0.314067	+	0.711925i
$781$	−12.2900	+	6.40133i	−0.439770	+	0.229058i
$782$	−11.4176	−	4.55882i	−0.408293	−	0.163023i
$783$	16.8516	+	16.8516i	0.602228	+	0.602228i
$784$	17.0724	−	0.875820i	0.609727	−	0.0312793i
$785$	−4.36861	+	1.56650i	−0.155922	+	0.0559108i
$786$	−35.7549	+	15.3498i	−1.27534	+	0.547510i
$787$		−	42.2672i		−	1.50666i	−0.657642	−	0.753331i	$-0.728446\pi$
$787$		−	42.2672i		−	1.50666i	0.657642	−	0.753331i	$-0.271554\pi$
$788$	−27.1774	−	25.8189i	−0.968154	−	0.919761i
$789$	36.2439	+	36.2439i	1.29032	+	1.29032i
$790$	−40.5173	−	1.44247i	−1.44154	−	0.0513207i
$791$	3.72726			0.132526
$792$	−4.08016	+	5.26308i	−0.144982	+	0.187016i
$793$	12.5998	+	12.5998i	0.447430	+	0.447430i
$794$	34.5583	+	13.7984i	1.22643	+	0.489687i
$795$	−19.0901	−	53.2378i	−0.677055	−	1.88815i
$796$	17.0616	+	16.2087i	0.604731	+	0.574503i
$797$	36.4056			1.28955			0.644777	−	0.764371i	$-0.276950\pi$
$797$	36.4056			1.28955			0.644777	+	0.764371i	$0.276950\pi$
$798$	5.44681	−	13.6416i	0.192815	−	0.482907i
$799$	−5.58130			−0.197452
$800$	−9.96298	−	26.4715i	−0.352245	−	0.935908i
$801$	−6.97401			−0.246415
$802$	−4.36944	−	1.74463i	−0.154290	−	0.0616050i
$803$	−52.7620	−	16.6225i	−1.86193	−	0.586596i
$804$	−6.62884	+	6.97762i	−0.233781	+	0.246082i
$805$	−3.48285	−	9.71286i	−0.122754	−	0.342333i
$806$	−7.68090	−	3.06683i	−0.270548	−	0.108024i
$807$	−0.425999	+	0.425999i	−0.0149959	+	0.0149959i
$808$	29.5045	+	10.9125i	1.03796	+	0.383902i
$809$			12.0905i			0.425078i	0.977153	+	0.212539i	$0.0681733\pi$
$809$			12.0905i			0.425078i	−0.977153	+	0.212539i	$0.931827\pi$
$810$	33.5803	+	1.19550i	1.17989	+	0.0420056i
$811$	1.12312	−	1.12312i	0.0394380	−	0.0394380i	−0.687113	−	0.726551i	$-0.741122\pi$
$811$	1.12312	−	1.12312i	0.0394380	−	0.0394380i	0.726551	+	0.687113i	$0.241122\pi$
$812$	12.9352	+	12.2886i	0.453935	+	0.431245i
$813$	35.4005			1.24155
$814$	−40.1302	+	4.03898i	−1.40656	+	0.141566i
$815$	0.719785	+	2.00731i	0.0252130	+	0.0703131i
$816$	16.0555	−	17.7919i	0.562054	−	0.622840i
$817$	11.8002	+	11.8002i	0.412837	+	0.412837i
$818$	−19.7283	+	49.4096i	−0.689782	+	1.72757i
$819$	−2.09106	−	2.09106i	−0.0730674	−	0.0730674i
$820$	−12.8517	−	5.66956i	−0.448801	−	0.197989i
$821$	−18.3440	+	18.3440i	−0.640211	+	0.640211i	−0.950607	−	0.310396i	$-0.899538\pi$
$821$	−18.3440	+	18.3440i	−0.640211	+	0.640211i	0.310396	+	0.950607i	$0.399538\pi$
$822$	−13.2943	−	30.9668i	−0.463691	−	1.08009i
$823$	24.6386	+	24.6386i	0.858848	+	0.858848i	0.991203	−	0.132354i	$-0.0422536\pi$
$823$	24.6386	+	24.6386i	0.858848	+	0.858848i	−0.132354	+	0.991203i	$0.542254\pi$
$824$	−2.81204	+	7.60297i	−0.0979621	+	0.264862i
$825$	−12.4973	+	29.3945i	−0.435100	+	1.02339i
$826$	12.8544	+	5.13251i	0.447262	+	0.178583i
$827$	−11.3517			−0.394737			−0.197369	−	0.980329i	$-0.563240\pi$
$827$	−11.3517			−0.394737			−0.197369	+	0.980329i	$0.563240\pi$
$828$	0.101679	+	3.96665i	0.00353358	+	0.137851i
$829$	−16.8415	−	16.8415i	−0.584931	−	0.584931i	0.351323	−	0.936254i	$-0.385732\pi$
$829$	−16.8415	−	16.8415i	−0.584931	−	0.584931i	−0.936254	+	0.351323i	$0.885732\pi$
$830$	1.34464	+	0.0478708i	0.0466730	+	0.00166162i
$831$			15.6541i			0.543035i
$832$	−13.1333	+	15.3257i	−0.455316	+	0.531322i
$833$	9.40002	+	9.40002i	0.325691	+	0.325691i
$834$	−13.1758	+	5.65648i	−0.456242	+	0.195868i
$835$	47.4354	+	22.3954i	1.64157	+	0.775024i
$836$	10.4966	+	18.9508i	0.363032	+	0.655426i
$837$			10.2248i			0.353421i
$838$	−11.7537	−	27.3783i	−0.406024	−	0.945766i
$839$	−21.5470			−0.743885			−0.371943	−	0.928256i	$-0.621308\pi$
$839$	−21.5470			−0.743885			−0.371943	+	0.928256i	$0.621308\pi$
$840$	20.1129	+	0.200301i	0.693963	+	0.00691103i
$841$		−	0.190526i		−	0.00656988i
$842$	−4.31168	−	10.0434i	−0.148590	−	0.346117i
$843$			21.3059i			0.733813i
$844$	0.176541	+	6.88715i	0.00607679	+	0.237066i
$845$	−13.9656	+	5.00780i	−0.480431	+	0.172273i
$846$	0.710628	+	1.65529i	0.0244319	+	0.0569101i
$847$	−17.8853	+	3.16210i	−0.614545	+	0.108651i
$848$	−2.69111	−	52.4578i	−0.0924130	−	1.80141i
$849$	−9.94171			−0.341199
$850$	10.0921	−	19.5430i	0.346157	−	0.670320i
$851$	−16.9932	+	16.9932i	−0.582519	+	0.582519i
$852$	−11.6687	−	11.0854i	−0.399764	−	0.379781i
$853$		−	22.6705i		−	0.776222i	−0.921613	−	0.388111i	$-0.873128\pi$
$853$		−	22.6705i		−	0.776222i	0.921613	−	0.388111i	$-0.126872\pi$
$854$	6.11554	−	15.3164i	0.209270	−	0.524118i
$855$	−2.21332	+	4.68800i	−0.0756939	+	0.160326i
$856$	10.5551	+	22.9457i	0.360765	+	0.784267i
$857$	21.8230	+	21.8230i	0.745460	+	0.745460i	0.973623	−	0.228163i	$-0.0732718\pi$
$857$	21.8230	+	21.8230i	0.745460	+	0.745460i	−0.228163	+	0.973623i	$0.573272\pi$
$858$	22.6779	−	2.28247i	0.774211	−	0.0779221i
$859$	33.6873	−	33.6873i	1.14940	−	1.14940i	0.162725	−	0.986671i	$-0.447972\pi$
$859$	33.6873	−	33.6873i	1.14940	−	1.14940i	0.986671	−	0.162725i	$-0.0520284\pi$
$860$	−9.22339	+	20.9075i	−0.314515	+	0.712940i
$861$	7.06337	−	7.06337i	0.240719	−	0.240719i
$862$	20.2559	−	50.7311i	0.689918	−	1.72791i
$863$	25.4734	−	25.4734i	0.867123	−	0.867123i	−0.125030	−	0.992153i	$-0.539903\pi$
$863$	25.4734	−	25.4734i	0.867123	−	0.867123i	0.992153	+	0.125030i	$0.0399027\pi$
$864$	23.6170	+	8.05327i	0.803467	+	0.273978i
$865$	−26.5597	+	9.52381i	−0.903057	+	0.323819i
$866$	−48.7126	+	20.9126i	−1.65532	+	0.710641i
$867$	−14.1076			−0.479118
$868$	0.196154	+	7.65231i	0.00665792	+	0.259736i
$869$	19.6430	+	37.7129i	0.666345	+	1.27932i
$870$	−22.4269	−	24.0827i	−0.760342	−	0.816478i
$871$	6.30321			0.213576
$872$	−44.6238	−	16.5046i	−1.51115	−	0.558916i
$873$	0.383203	+	0.383203i	0.0129695	+	0.0129695i
$874$	11.9878	+	4.78648i	0.405493	+	0.161905i
$875$	17.8979	−	4.52243i	0.605059	−	0.152886i
$876$	−1.64645	−	64.2306i	−0.0556283	−	2.17015i
$877$		−	23.1345i		−	0.781198i	−0.920561	−	0.390599i	$-0.872268\pi$
$877$		−	23.1345i		−	0.781198i	0.920561	−	0.390599i	$-0.127732\pi$
$878$	1.63580	−	4.09688i	0.0552056	−	0.138263i
$879$	16.4750			0.555687
$880$	−18.9980	+	22.7833i	−0.640422	+	0.768023i
$881$	47.7990			1.61039			0.805195	−	0.593010i	$-0.202061\pi$
$881$	47.7990			1.61039			0.805195	+	0.593010i	$0.202061\pi$
$882$	1.59100	−	3.98468i	0.0535718	−	0.134171i
$883$		−	3.01680i		−	0.101524i	−0.998711	−	0.0507618i	$-0.983835\pi$
$883$		−	3.01680i		−	0.101524i	0.998711	−	0.0507618i	$-0.0161649\pi$
$884$	−15.6901	+	0.402191i	−0.527716	+	0.0135271i
$885$	−23.0857	−	10.8993i	−0.776016	−	0.366376i
$886$	32.3134	+	12.9021i	1.08559	+	0.433454i
$887$	41.7633	+	41.7633i	1.40227	+	1.40227i	0.792827	+	0.609447i	$0.208608\pi$
$887$	41.7633	+	41.7633i	1.40227	+	1.40227i	0.609447	+	0.792827i	$0.291392\pi$
$888$	−19.5774	−	42.5593i	−0.656973	−	1.42820i
$889$	−21.0896			−0.707322
$890$	−31.0465	−	1.10530i	−1.04068	−	0.0370496i
$891$	−16.2799	−	31.2559i	−0.545397	−	1.04711i
$892$	−5.21977	+	0.133800i	−0.174771	+	0.00447996i
$893$	5.86003			0.196098
$894$	−14.8961	+	6.39500i	−0.498200	+	0.213881i
$895$	−40.9567	−	19.3366i	−1.36903	−	0.646353i
$896$	17.8296	+	5.57405i	0.595646	+	0.186216i
$897$	9.60301	−	9.60301i	0.320635	−	0.320635i
$898$	11.7141	−	29.3382i	0.390906	−	0.979028i
$899$	8.85574	−	8.85574i	0.295355	−	0.295355i
$900$	−7.08099	−	0.504824i	−0.236033	−	0.0168275i
$901$	28.8832	−	28.8832i	0.962238	−	0.962238i
$902$	1.47531	+	14.6583i	0.0491225	+	0.488067i
$903$	−11.4909	−	11.4909i	−0.382393	−	0.382393i
$904$	−5.98834	−	2.21485i	−0.199169	−	0.0736649i
$905$	13.2857	+	6.27251i	0.441633	+	0.208505i
$906$	−6.72342	+	16.8389i	−0.223371	+	0.559434i
$907$			9.86029i			0.327405i	0.986510	+	0.163703i	$0.0523438\pi$
$907$			9.86029i			0.327405i	−0.986510	+	0.163703i	$0.947656\pi$
$908$	30.5601	−	32.1680i	1.01417	−	1.06753i
$909$	5.58295	−	5.58295i	0.185175	−	0.185175i
$910$	−8.97744	−	9.64025i	−0.297599	−	0.319571i
$911$	30.9716			1.02613			0.513067	−	0.858349i	$-0.328509\pi$
$911$	30.9716			1.02613			0.513067	+	0.858349i	$0.328509\pi$
$912$	−16.8573	+	18.6804i	−0.558200	+	0.618569i
$913$	−0.651888	−	1.25157i	−0.0215744	−	0.0414208i
$914$	3.22015	+	7.50081i	0.106513	+	0.248105i
$915$	−12.9869	+	27.5073i	−0.429332	+	0.909363i
$916$	−12.4609	+	0.319415i	−0.411719	+	0.0105538i
$917$		−	23.5862i		−	0.778885i
$918$	7.65467	+	17.8303i	0.252642	+	0.588488i
$919$		−	23.2086i		−	0.765582i	−0.923835	−	0.382791i	$-0.874963\pi$
$919$		−	23.2086i		−	0.765582i	0.923835	−	0.382791i	$-0.125037\pi$
$920$	−0.176018	+	17.6746i	−0.00580314	+	0.582715i
$921$	33.6353			1.10832
$922$	−10.2266	−	23.8211i	−0.336794	−	0.784506i
$923$			10.5409i			0.346957i
$924$	−10.2214	−	18.4540i	−0.336260	−	0.607092i
$925$	−27.3214	−	33.1981i	−0.898323	−	1.09155i
$926$	−0.647201	+	0.277848i	−0.0212683	+	0.00913064i
$927$	1.43866	+	1.43866i	0.0472519	+	0.0472519i
$928$	−13.4798	−	27.4298i	−0.442497	−	0.900426i
$929$		−	12.3579i		−	0.405448i	−0.979236	−	0.202724i	$-0.935021\pi$
$929$		−	12.3579i		−	0.405448i	0.979236	−	0.202724i	$-0.0649795\pi$
$930$	0.502331	−	14.1099i	0.0164721	−	0.462683i
$931$	−9.86945	−	9.86945i	−0.323458	−	0.323458i
$932$	56.8964	−	1.45845i	1.86370	−	0.0477730i
$933$	57.2224			1.87338
$934$	46.8491	+	18.7059i	1.53295	+	0.612075i
$935$	−23.0509	+	0.901643i	−0.753846	+	0.0294869i
$936$	2.11699	+	4.60213i	0.0691960	+	0.150425i
$937$	−14.4472	−	14.4472i	−0.471969	−	0.471969i	0.430582	−	0.902551i	$-0.358308\pi$
$937$	−14.4472	−	14.4472i	−0.471969	−	0.471969i	−0.902551	+	0.430582i	$0.858308\pi$
$938$	−2.30144	−	5.36083i	−0.0751447	−	0.175037i
$939$	2.54679	−	2.54679i	0.0831113	−	0.0831113i
$940$	2.90119	+	7.48156i	0.0946264	+	0.244022i
$941$	17.8821	+	17.8821i	0.582941	+	0.582941i	0.935710	−	0.352769i	$-0.114760\pi$
$941$	17.8821	+	17.8821i	0.582941	+	0.582941i	−0.352769	+	0.935710i	$0.614760\pi$
$942$	−2.09641	+	5.25048i	−0.0683048	+	0.171070i
$943$	6.20707	+	6.20707i	0.202130	+	0.202130i
$944$	−17.6025	−	15.8846i	−0.572911	−	0.516998i
$945$	−6.95293	+	14.7269i	−0.226179	+	0.479067i
$946$	23.8465	−	2.40008i	0.775316	−	0.0780332i
$947$	−23.0147			−0.747878			−0.373939	−	0.927453i	$-0.621993\pi$
$947$	−23.0147			−0.747878			−0.373939	+	0.927453i	$0.621993\pi$
$948$	−34.0166	+	35.8065i	−1.10481	+	1.16294i
$949$	−29.7549	+	29.7549i	−0.965885	+	0.965885i
$950$	−10.5961	+	20.5190i	−0.343783	+	0.665724i
$951$			42.0290i			1.36288i
$952$	6.07087	+	13.1975i	0.196758	+	0.427732i
$953$	−20.8666	+	20.8666i	−0.675934	+	0.675934i	−0.959078	−	0.283144i	$-0.908623\pi$
$953$	−20.8666	+	20.8666i	−0.675934	+	0.675934i	0.283144	+	0.959078i	$0.408623\pi$
$954$	−12.2436	−	4.88862i	−0.396401	−	0.158275i
$955$	2.77088	−	0.993584i	0.0896634	−	0.0321516i
$956$	−5.63979	−	5.35789i	−0.182404	−	0.173286i
$957$	−10.3711	+	32.9192i	−0.335250	+	1.06413i
$958$	52.2909	+	20.8787i	1.68944	+	0.674560i
$959$	20.4277			0.659644
$960$	−32.1951	−	12.2735i	−1.03909	−	0.396127i
$961$	−25.6267			−0.826669
$962$	−11.3768	+	28.4932i	−0.366802	+	0.918658i
$963$	6.33915			0.204276
$964$	13.5604	−	14.2739i	0.436752	−	0.459732i
$965$	40.5179	+	19.1295i	1.30432	+	0.615800i
$966$	−11.6736	−	4.66101i	−0.375590	−	0.149966i
$967$	16.6958	+	16.6958i	0.536901	+	0.536901i	0.922617	−	0.385717i	$-0.126046\pi$
$967$	16.6958	+	16.6958i	0.536901	+	0.536901i	−0.385717	+	0.922617i	$0.626046\pi$
$968$	30.6141	+	5.54764i	0.983975	+	0.178308i
$969$	−19.5670			−0.628582
$970$	1.64519	+	1.76665i	0.0528238	+	0.0567239i
$971$	−24.5096	−	24.5096i	−0.786552	−	0.786552i	0.194375	−	0.980927i	$-0.437732\pi$
$971$	−24.5096	−	24.5096i	−0.786552	−	0.786552i	−0.980927	+	0.194375i	$0.937732\pi$
$972$	9.96402	−	10.4883i	0.319596	−	0.336412i
$973$		−	8.69161i		−	0.278640i
$974$	44.9192	−	19.2841i	1.43930	−	0.617903i
$975$	15.4396	+	18.7605i	0.494462	+	0.600818i
$976$	−18.9270	+	20.9739i	−0.605837	+	0.671358i
$977$	24.8010	+	24.8010i	0.793455	+	0.793455i	0.982054	−	0.188599i	$-0.0603946\pi$
$977$	24.8010	+	24.8010i	0.793455	+	0.793455i	−0.188599	+	0.982054i	$0.560395\pi$
$978$	2.41252	+	0.963271i	0.0771439	+	0.0308020i
$979$	15.0515	+	28.8976i	0.481049	+	0.923571i
$980$	7.71425	−	17.4866i	0.246423	−	0.558589i
$981$	−8.44389	+	8.44389i	−0.269593	+	0.269593i
$982$	43.7568	−	18.7851i	1.39633	−	0.599456i
$983$	−12.3629	−	12.3629i	−0.394314	−	0.394314i	0.481908	−	0.876222i	$-0.339944\pi$
$983$	−12.3629	−	12.3629i	−0.394314	−	0.394314i	−0.876222	+	0.481908i	$0.839944\pi$
$984$	−15.5455	+	7.15099i	−0.495574	+	0.227965i
$985$	−39.4514	+	14.1465i	−1.25702	+	0.450745i
$986$	8.81315	−	22.0726i	0.280668	−	0.702936i
$987$	−5.70642			−0.181637
$988$	16.4737	−	0.422276i	0.524097	−	0.0134344i
$989$	10.0978	−	10.0978i	0.321092	−	0.321092i
$990$	3.20232	+	6.72160i	0.101776	+	0.213626i
$991$	−22.7423			−0.722433			−0.361216	−	0.932482i	$-0.617638\pi$
$991$	−22.7423			−0.722433			−0.361216	+	0.932482i	$0.617638\pi$
$992$	4.23209	−	12.4110i	0.134369	−	0.394050i
$993$	35.9699	−	35.9699i	1.14147	−	1.14147i
$994$	8.96494	−	3.84871i	0.284351	−	0.122074i
$995$	24.7670	−	8.88097i	0.785166	−	0.281546i
$996$	1.12890	−	1.18830i	0.0357706	−	0.0376527i
$997$	4.69363			0.148649			0.0743244	−	0.997234i	$-0.476320\pi$
$997$	4.69363			0.148649			0.0743244	+	0.997234i	$0.476320\pi$
$998$	10.0823	+	23.4850i	0.319149	+	0.743404i
$999$	37.9301			1.20006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.t.b.197.15	✓	272
5.3	odd	4		880.2.bl.b.373.54	yes	272
11.10	odd	2	inner	880.2.t.b.197.122	yes	272
16.13	even	4		880.2.bl.b.637.83	yes	272
55.43	even	4		880.2.bl.b.373.83	yes	272
80.13	odd	4	inner	880.2.t.b.813.122	yes	272
176.109	odd	4		880.2.bl.b.637.54	yes	272
880.813	even	4	inner	880.2.t.b.813.15	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.t.b.197.15	✓	272	1.1	even	1	trivial
880.2.t.b.197.122	yes	272	11.10	odd	2	inner
880.2.t.b.813.15	yes	272	880.813	even	4	inner
880.2.t.b.813.122	yes	272	80.13	odd	4	inner
880.2.bl.b.373.54	yes	272	5.3	odd	4
880.2.bl.b.373.83	yes	272	55.43	even	4
880.2.bl.b.637.54	yes	272	176.109	odd	4
880.2.bl.b.637.83	yes	272	16.13	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31339 - 0.524410i) q^{2} +1.92611i q^{3} +(1.44999 + 1.37751i) q^{4} +(2.10484 - 0.754755i) q^{5} +(1.01007 - 2.52973i) q^{6} +(1.16754 + 1.16754i) q^{7} +(-1.18202 - 2.56960i) q^{8} -0.709896 q^{9} +(-3.16028 - 0.112510i) q^{10} +(1.53212 + 2.94153i) q^{11} +(-2.65323 + 2.79284i) q^{12} +2.52290 q^{13} +(-0.921165 - 2.14570i) q^{14} +(1.45374 + 4.05415i) q^{15} +(0.204932 + 3.99475i) q^{16} +(-2.19950 + 2.19950i) q^{17} +(0.932370 + 0.372276i) q^{18} +(2.30934 - 2.30934i) q^{19} +(4.09167 + 1.80505i) q^{20} +(-2.24881 + 2.24881i) q^{21} +(-0.469704 - 4.66684i) q^{22} +(-1.97618 - 1.97618i) q^{23} +(4.94932 - 2.27670i) q^{24} +(3.86069 - 3.17728i) q^{25} +(-3.31355 - 1.32303i) q^{26} +4.41099i q^{27} +(0.0846213 + 3.30121i) q^{28} +(3.82037 - 3.82037i) q^{29} +(0.216706 - 6.08704i) q^{30} +2.31803 q^{31} +(1.82573 - 5.35413i) q^{32} +(-5.66571 + 2.95103i) q^{33} +(4.04225 - 1.73536i) q^{34} +(3.33869 + 1.57627i) q^{35} +(-1.02934 - 0.977889i) q^{36} -8.59901i q^{37} +(-4.24411 + 1.82203i) q^{38} +4.85937i q^{39} +(-4.42738 - 4.51645i) q^{40} -3.14094 q^{41} +(4.13286 - 1.77426i) q^{42} +5.10977i q^{43} +(-1.83043 + 6.37570i) q^{44} +(-1.49422 + 0.535798i) q^{45} +(1.55917 + 3.63183i) q^{46} +(1.26877 + 1.26877i) q^{47} +(-7.69432 + 0.394722i) q^{48} -4.27370i q^{49} +(-6.73679 + 2.14842i) q^{50} +(-4.23648 - 4.23648i) q^{51} +(3.65817 + 3.47532i) q^{52} -13.1317 q^{53} +(2.31317 - 5.79335i) q^{54} +(5.44500 + 5.03507i) q^{55} +(1.62005 - 4.38016i) q^{56} +(4.44805 + 4.44805i) q^{57} +(-7.02109 + 3.01420i) q^{58} +(-4.19138 + 4.19138i) q^{59} +(-3.47672 + 7.88101i) q^{60} +(4.99416 + 4.99416i) q^{61} +(-3.04448 - 1.21560i) q^{62} +(-0.828831 - 0.828831i) q^{63} +(-5.20565 + 6.07463i) q^{64} +(5.31029 - 1.90417i) q^{65} +(8.98884 - 0.904700i) q^{66} +2.49840 q^{67} +(-6.21909 + 0.159416i) q^{68} +(3.80634 - 3.80634i) q^{69} +(-3.55839 - 3.82110i) q^{70} +4.17809i q^{71} +(0.839112 + 1.82415i) q^{72} +(-11.7939 + 11.7939i) q^{73} +(-4.50940 + 11.2939i) q^{74} +(6.11978 + 7.43611i) q^{75} +(6.52967 - 0.167377i) q^{76} +(-1.64554 + 5.22316i) q^{77} +(2.54830 - 6.38225i) q^{78} +12.8208 q^{79} +(3.44641 + 8.25362i) q^{80} -10.6257 q^{81} +(4.12528 + 1.64714i) q^{82} -0.425481 q^{83} +(-6.35850 + 0.162990i) q^{84} +(-2.96951 + 6.28968i) q^{85} +(2.67961 - 6.71112i) q^{86} +(7.35846 + 7.35846i) q^{87} +(5.74755 - 7.41388i) q^{88} +9.82399 q^{89} +(2.24347 + 0.0798702i) q^{90} +(2.94558 + 2.94558i) q^{91} +(-0.143230 - 5.58765i) q^{92} +4.46478i q^{93} +(-1.00103 - 2.33174i) q^{94} +(3.11781 - 6.60379i) q^{95} +(10.3126 + 3.51655i) q^{96} +(-0.539801 - 0.539801i) q^{97} +(-2.24117 + 5.61304i) q^{98} +(-1.08765 - 2.08818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 16 q^{4} - 4 q^{5} - 280 q^{9} - 4 q^{11} - 8 q^{12} - 8 q^{15} - 40 q^{16} - 4 q^{20} - 12 q^{22} - 24 q^{23} - 40 q^{25} + 72 q^{26} + 16 q^{31} - 4 q^{33} - 32 q^{34} - 72 q^{36} - 24 q^{42}+ \cdots - 20 q^{99}+O(q^{100}) \) 272 * q - 16 * q^4 - 4 * q^5 - 280 * q^9 - 4 * q^11 - 8 * q^12 - 8 * q^15 - 40 * q^16 - 4 * q^20 - 12 * q^22 - 24 * q^23 - 40 * q^25 + 72 * q^26 + 16 * q^31 - 4 * q^33 - 32 * q^34 - 72 * q^36 - 24 * q^42 - 40 * q^44 - 12 * q^45 - 8 * q^47 + 8 * q^48 - 56 * q^53 + 40 * q^55 - 56 * q^56 + 72 * q^58 + 8 * q^59 + 44 * q^60 - 64 * q^64 + 12 * q^66 - 8 * q^67 + 88 * q^70 - 24 * q^75 - 32 * q^77 - 32 * q^78 + 104 * q^80 + 192 * q^81 - 8 * q^82 - 56 * q^88 + 24 * q^89 - 24 * q^91 + 48 * q^92 - 40 * q^97 - 20 * q^99

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