LMFDB - Embedded newform 880.2.w.a.221.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(221,880)] 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("880.221"); 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, 3, 0, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [72] 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:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			221.17
Character	$\chi$	$=$	880.221
Dual form			880.2.w.a.661.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0993049 - 1.41072i) q^{2} +(1.33671 + 1.33671i) q^{3} +(-1.98028 + 0.280183i) q^{4} +(0.707107 - 0.707107i) q^{5} +(1.75298 - 2.01847i) q^{6} -1.42871i q^{7} +(0.591912 + 2.76580i) q^{8} +0.573579i q^{9} +(-1.06775 - 0.927312i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-3.02158 - 2.27253i) q^{12} +(3.58990 + 3.58990i) q^{13} +(-2.01552 + 0.141878i) q^{14} +1.89039 q^{15} +(3.84299 - 1.10968i) q^{16} +7.03926 q^{17} +(0.809161 - 0.0569592i) q^{18} +(-2.88589 - 2.88589i) q^{19} +(-1.20215 + 1.59839i) q^{20} +(1.90977 - 1.90977i) q^{21} +(1.06775 + 0.927312i) q^{22} -1.01049i q^{23} +(-2.90585 + 4.48828i) q^{24} -1.00000i q^{25} +(4.70786 - 5.42085i) q^{26} +(3.24342 - 3.24342i) q^{27} +(0.400302 + 2.82925i) q^{28} +(-3.51938 - 3.51938i) q^{29} +(-0.187725 - 2.66682i) q^{30} +4.92667 q^{31} +(-1.94708 - 5.31120i) q^{32} -1.89039 q^{33} +(-0.699033 - 9.93045i) q^{34} +(-1.01025 - 1.01025i) q^{35} +(-0.160707 - 1.13585i) q^{36} +(-5.46590 + 5.46590i) q^{37} +(-3.78460 + 4.35777i) q^{38} +9.59731i q^{39} +(2.37426 + 1.53717i) q^{40} +11.8151i q^{41} +(-2.88381 - 2.50451i) q^{42} +(7.86103 - 7.86103i) q^{43} +(1.20215 - 1.59839i) q^{44} +(0.405582 + 0.405582i) q^{45} +(-1.42552 + 0.100347i) q^{46} -0.953653 q^{47} +(6.62028 + 3.65364i) q^{48} +4.95878 q^{49} +(-1.41072 + 0.0993049i) q^{50} +(9.40944 + 9.40944i) q^{51} +(-8.11483 - 6.10317i) q^{52} +(5.05070 - 5.05070i) q^{53} +(-4.89765 - 4.25348i) q^{54} +1.00000i q^{55} +(3.95154 - 0.845673i) q^{56} -7.71518i q^{57} +(-4.61538 + 5.31436i) q^{58} +(6.05778 - 6.05778i) q^{59} +(-3.74350 + 0.529656i) q^{60} +(-5.61774 - 5.61774i) q^{61} +(-0.489242 - 6.95016i) q^{62} +0.819480 q^{63} +(-7.29928 + 3.27422i) q^{64} +5.07689 q^{65} +(0.187725 + 2.66682i) q^{66} +(5.90717 + 5.90717i) q^{67} +(-13.9397 + 1.97228i) q^{68} +(1.35073 - 1.35073i) q^{69} +(-1.32486 + 1.52551i) q^{70} -13.8850i q^{71} +(-1.58640 + 0.339508i) q^{72} +11.0651i q^{73} +(8.25366 + 7.16808i) q^{74} +(1.33671 - 1.33671i) q^{75} +(6.52343 + 4.90628i) q^{76} +(1.01025 + 1.01025i) q^{77} +(13.5391 - 0.953059i) q^{78} -4.21273 q^{79} +(1.93274 - 3.50207i) q^{80} +10.3917 q^{81} +(16.6678 - 1.17329i) q^{82} +(-6.16621 - 6.16621i) q^{83} +(-3.24680 + 4.31697i) q^{84} +(4.97751 - 4.97751i) q^{85} +(-11.8704 - 10.3091i) q^{86} -9.40877i q^{87} +(-2.37426 - 1.53717i) q^{88} +15.1986i q^{89} +(0.531887 - 0.612439i) q^{90} +(5.12895 - 5.12895i) q^{91} +(0.283122 + 2.00105i) q^{92} +(6.58552 + 6.58552i) q^{93} +(0.0947024 + 1.34534i) q^{94} -4.08126 q^{95} +(4.49685 - 9.70221i) q^{96} -16.1082 q^{97} +(-0.492430 - 6.99546i) q^{98} +(-0.405582 - 0.405582i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) $ 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Character values

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

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.0993049	−	1.41072i	−0.0702191	−	0.997532i
$2$	−0.0993049	−	1.41072i	−0.0702191	−	0.997532i
$3$	1.33671	+	1.33671i	0.771749	+	0.771749i	0.978412	−	0.206663i	$-0.0662604\pi$
$3$	1.33671	+	1.33671i	0.771749	+	0.771749i	−0.206663	+	0.978412i	$0.566260\pi$
$4$	−1.98028	+	0.280183i	−0.990139	+	0.140092i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	1.75298	−	2.01847i	0.715652	−	0.824036i
$7$		−	1.42871i		−	0.540003i	−0.962860	−	0.270002i	$-0.912976\pi$
$7$		−	1.42871i		−	0.540003i	0.962860	−	0.270002i	$-0.0870242\pi$
$8$	0.591912	+	2.76580i	0.209272	+	0.977857i
$9$			0.573579i			0.191193i
$10$	−1.06775	−	0.927312i	−0.337652	−	0.293242i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	−3.02158	−	2.27253i	−0.872254	−	0.656023i
$13$	3.58990	+	3.58990i	0.995660	+	0.995660i	0.999991	−	0.00433069i	$-0.00137851\pi$
$13$	3.58990	+	3.58990i	0.995660	+	0.995660i	−0.00433069	+	0.999991i	$0.501379\pi$
$14$	−2.01552	+	0.141878i	−0.538670	+	0.0379186i
$15$	1.89039			0.488097
$16$	3.84299	−	1.10968i	0.960749	−	0.277420i
$17$	7.03926			1.70727			0.853636	−	0.520870i	$-0.174393\pi$
$17$	7.03926			1.70727			0.853636	+	0.520870i	$0.174393\pi$
$18$	0.809161	−	0.0569592i	0.190721	−	0.0134254i
$19$	−2.88589	−	2.88589i	−0.662068	−	0.662068i	0.293800	−	0.955867i	$-0.405080\pi$
$19$	−2.88589	−	2.88589i	−0.662068	−	0.662068i	−0.955867	+	0.293800i	$0.905080\pi$
$20$	−1.20215	+	1.59839i	−0.268808	+	0.357410i
$21$	1.90977	−	1.90977i	0.416747	−	0.416747i
$22$	1.06775	+	0.927312i	0.227645	+	0.197704i
$23$		−	1.01049i		−	0.210702i	−0.994435	−	0.105351i	$-0.966403\pi$
$23$		−	1.01049i		−	0.210702i	0.994435	−	0.105351i	$-0.0335965\pi$
$24$	−2.90585	+	4.48828i	−0.593155	+	0.916166i
$25$		−	1.00000i		−	0.200000i
$26$	4.70786	−	5.42085i	0.923288	−	1.06312i
$27$	3.24342	−	3.24342i	0.624196	−	0.624196i
$28$	0.400302	+	2.82925i	0.0756499	+	0.534678i
$29$	−3.51938	−	3.51938i	−0.653533	−	0.653533i	0.300309	−	0.953842i	$-0.402910\pi$
$29$	−3.51938	−	3.51938i	−0.653533	−	0.653533i	−0.953842	+	0.300309i	$0.902910\pi$
$30$	−0.187725	−	2.66682i	−0.0342737	−	0.486892i
$31$	4.92667			0.884856			0.442428	−	0.896804i	$-0.354117\pi$
$31$	4.92667			0.884856			0.442428	+	0.896804i	$0.354117\pi$
$32$	−1.94708	−	5.31120i	−0.344198	−	0.938897i
$33$	−1.89039			−0.329075
$34$	−0.699033	−	9.93045i	−0.119883	−	1.70306i
$35$	−1.01025	−	1.01025i	−0.170764	−	0.170764i
$36$	−0.160707	−	1.13585i	−0.0267845	−	0.189308i
$37$	−5.46590	+	5.46590i	−0.898588	+	0.898588i	−0.995311	−	0.0967232i	$-0.969164\pi$
$37$	−5.46590	+	5.46590i	−0.898588	+	0.898588i	0.0967232	+	0.995311i	$0.469164\pi$
$38$	−3.78460	+	4.35777i	−0.613943	+	0.706923i
$39$			9.59731i			1.53680i
$40$	2.37426	+	1.53717i	0.375403	+	0.243048i
$41$			11.8151i			1.84520i	0.385756	+	0.922601i	$0.373941\pi$
$41$			11.8151i			1.84520i	−0.385756	+	0.922601i	$0.626059\pi$
$42$	−2.88381	−	2.50451i	−0.444982	−	0.386455i
$43$	7.86103	−	7.86103i	1.19880	−	1.19880i	0.224268	−	0.974527i	$-0.428001\pi$
$43$	7.86103	−	7.86103i	1.19880	−	1.19880i	0.974527	−	0.224268i	$-0.0719991\pi$
$44$	1.20215	−	1.59839i	0.181231	−	0.240966i
$45$	0.405582	+	0.405582i	0.0604605	+	0.0604605i
$46$	−1.42552	+	0.100347i	−0.210182	+	0.0147953i
$47$	−0.953653			−0.139105			−0.0695523	−	0.997578i	$-0.522157\pi$
$47$	−0.953653			−0.139105			−0.0695523	+	0.997578i	$0.522157\pi$
$48$	6.62028	+	3.65364i	0.955556	+	0.527358i
$49$	4.95878			0.708396
$50$	−1.41072	+	0.0993049i	−0.199506	+	0.0140438i
$51$	9.40944	+	9.40944i	1.31759	+	1.31759i
$52$	−8.11483	−	6.10317i	−1.12532	−	0.846358i
$53$	5.05070	−	5.05070i	0.693767	−	0.693767i	−0.269292	−	0.963059i	$-0.586790\pi$
$53$	5.05070	−	5.05070i	0.693767	−	0.693767i	0.963059	+	0.269292i	$0.0867896\pi$
$54$	−4.89765	−	4.25348i	−0.666486	−	0.578825i
$55$			1.00000i			0.134840i
$56$	3.95154	−	0.845673i	0.528046	−	0.113008i
$57$		−	7.71518i		−	1.02190i
$58$	−4.61538	+	5.31436i	−0.606029	+	0.697810i
$59$	6.05778	−	6.05778i	0.788656	−	0.788656i	−0.192618	−	0.981274i	$-0.561698\pi$
$59$	6.05778	−	6.05778i	0.788656	−	0.788656i	0.981274	+	0.192618i	$0.0616978\pi$
$60$	−3.74350	+	0.529656i	−0.483284	+	0.0683783i
$61$	−5.61774	−	5.61774i	−0.719278	−	0.719278i	0.249180	−	0.968457i	$-0.419839\pi$
$61$	−5.61774	−	5.61774i	−0.719278	−	0.719278i	−0.968457	+	0.249180i	$0.919839\pi$
$62$	−0.489242	−	6.95016i	−0.0621338	−	0.882671i
$63$	0.819480			0.103245
$64$	−7.29928	+	3.27422i	−0.912410	+	0.409277i
$65$	5.07689			0.629711
$66$	0.187725	+	2.66682i	0.0231074	+	0.328263i
$67$	5.90717	+	5.90717i	0.721676	+	0.721676i	0.968947	−	0.247270i	$-0.0795336\pi$
$67$	5.90717	+	5.90717i	0.721676	+	0.721676i	−0.247270	+	0.968947i	$0.579534\pi$
$68$	−13.9397	+	1.97228i	−1.69044	+	0.239174i
$69$	1.35073	−	1.35073i	0.162609	−	0.162609i
$70$	−1.32486	+	1.52551i	−0.158352	+	0.182333i
$71$		−	13.8850i		−	1.64784i	−0.566705	−	0.823921i	$-0.691782\pi$
$71$		−	13.8850i		−	1.64784i	0.566705	−	0.823921i	$-0.308218\pi$
$72$	−1.58640	+	0.339508i	−0.186959	+	0.0400114i
$73$			11.0651i			1.29508i	0.762033	+	0.647538i	$0.224201\pi$
$73$			11.0651i			1.29508i	−0.762033	+	0.647538i	$0.775799\pi$
$74$	8.25366	+	7.16808i	0.959468	+	0.833272i
$75$	1.33671	−	1.33671i	0.154350	−	0.154350i
$76$	6.52343	+	4.90628i	0.748289	+	0.562789i
$77$	1.01025	+	1.01025i	0.115129	+	0.115129i
$78$	13.5391	−	0.953059i	1.53301	−	0.107913i
$79$	−4.21273			−0.473969			−0.236985	−	0.971513i	$-0.576159\pi$
$79$	−4.21273			−0.473969			−0.236985	+	0.971513i	$0.576159\pi$
$80$	1.93274	−	3.50207i	0.216087	−	0.391543i
$81$	10.3917			1.15464
$82$	16.6678	−	1.17329i	1.84065	−	0.129568i
$83$	−6.16621	−	6.16621i	−0.676829	−	0.676829i	0.282452	−	0.959281i	$-0.408852\pi$
$83$	−6.16621	−	6.16621i	−0.676829	−	0.676829i	−0.959281	+	0.282452i	$0.908852\pi$
$84$	−3.24680	+	4.31697i	−0.354254	+	0.471020i
$85$	4.97751	−	4.97751i	0.539887	−	0.539887i
$86$	−11.8704	−	10.3091i	−1.28001	−	1.11166i
$87$		−	9.40877i		−	1.00873i
$88$	−2.37426	−	1.53717i	−0.253097	−	0.163863i
$89$			15.1986i			1.61104i	0.592566	+	0.805522i	$0.298115\pi$
$89$			15.1986i			1.61104i	−0.592566	+	0.805522i	$0.701885\pi$
$90$	0.531887	−	0.612439i	0.0560658	−	0.0645568i
$91$	5.12895	−	5.12895i	0.537660	−	0.537660i
$92$	0.283122	+	2.00105i	0.0295175	+	0.208624i
$93$	6.58552	+	6.58552i	0.682886	+	0.682886i
$94$	0.0947024	+	1.34534i	0.00976781	+	0.138761i
$95$	−4.08126			−0.418728
$96$	4.49685	−	9.70221i	0.458958	−	0.990227i
$97$	−16.1082			−1.63554			−0.817771	−	0.575544i	$-0.804790\pi$
$97$	−16.1082			−1.63554			−0.817771	+	0.575544i	$0.804790\pi$
$98$	−0.492430	−	6.99546i	−0.0497430	−	0.706648i
$99$	−0.405582	−	0.405582i	−0.0407625	−	0.0407625i
$100$	0.280183	+	1.98028i	0.0280183	+	0.198028i
$101$	−9.76117	+	9.76117i	−0.971273	+	0.971273i	−0.999599	−	0.0283257i	$-0.990982\pi$
$101$	−9.76117	+	9.76117i	−0.971273	+	0.971273i	0.0283257	+	0.999599i	$0.490982\pi$
$102$	12.3397	−	14.2085i	1.22181	−	1.40685i
$103$			6.79143i			0.669180i	0.942364	+	0.334590i	$0.108598\pi$
$103$			6.79143i			0.669180i	−0.942364	+	0.334590i	$0.891402\pi$
$104$	−7.80404	+	12.0539i	−0.765249	+	1.18198i
$105$		−	2.70083i		−	0.263574i
$106$	−7.62669	−	6.62358i	−0.740770	−	0.643339i
$107$	−11.9442	+	11.9442i	−1.15469	+	1.15469i	−0.169086	+	0.985601i	$0.554081\pi$
$107$	−11.9442	+	11.9442i	−1.15469	+	1.15469i	−0.985601	+	0.169086i	$0.945919\pi$
$108$	−5.51411	+	7.33162i	−0.530596	+	0.705485i
$109$	−1.18584	−	1.18584i	−0.113583	−	0.113583i	0.648031	−	0.761614i	$-0.275593\pi$
$109$	−1.18584	−	1.18584i	−0.113583	−	0.113583i	−0.761614	+	0.648031i	$0.775593\pi$
$110$	1.41072	−	0.0993049i	0.134507	−	0.00946835i
$111$	−14.6126			−1.38697
$112$	−1.58542	−	5.49054i	−0.149808	−	0.518807i
$113$	6.37217			0.599444			0.299722	−	0.954027i	$-0.403106\pi$
$113$	6.37217			0.599444			0.299722	+	0.954027i	$0.403106\pi$
$114$	−10.8840	+	0.766154i	−1.01938	+	0.0717569i
$115$	−0.714524	−	0.714524i	−0.0666297	−	0.0666297i
$116$	7.95542	+	5.98328i	0.738642	+	0.555534i
$117$	−2.05909	+	2.05909i	−0.190363	+	0.190363i
$118$	−9.14742	−	7.94428i	−0.842088	−	0.731330i
$119$		−	10.0571i		−	0.921932i
$120$	1.11895	+	5.22844i	0.102145	+	0.477289i
$121$		−	1.00000i		−	0.0909091i
$122$	−7.36720	+	8.48294i	−0.666995	+	0.768009i
$123$	−15.7933	+	15.7933i	−1.42403	+	1.42403i
$124$	−9.75617	+	1.38037i	−0.876130	+	0.123961i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−0.0813784	−	1.15606i	−0.00724976	−	0.102990i
$127$	−21.2563			−1.88619			−0.943095	−	0.332522i	$-0.892100\pi$
$127$	−21.2563			−1.88619			−0.943095	+	0.332522i	$0.892100\pi$
$128$	5.34387	+	9.97211i	0.472336	+	0.881419i
$129$	21.0158			1.85034
$130$	−0.504160	−	7.16208i	−0.0442177	−	0.628156i
$131$	−5.47248	−	5.47248i	−0.478132	−	0.478132i	0.426402	−	0.904534i	$-0.359781\pi$
$131$	−5.47248	−	5.47248i	−0.478132	−	0.478132i	−0.904534	+	0.426402i	$0.859781\pi$
$132$	3.74350	−	0.529656i	0.325830	−	0.0461006i
$133$	−4.12311	+	4.12311i	−0.357519	+	0.357519i
$134$	7.74677	−	8.92000i	0.669219	−	0.770570i
$135$		−	4.58689i		−	0.394776i
$136$	4.16662	+	19.4692i	0.357285	+	1.66947i
$137$		−	0.966806i		−	0.0825998i	−0.999147	−	0.0412999i	$-0.986850\pi$
$137$		−	0.966806i		−	0.0825998i	0.999147	−	0.0412999i	$-0.0131499\pi$
$138$	−2.03964	−	1.77137i	−0.173626	−	0.150789i
$139$	−6.45591	+	6.45591i	−0.547583	+	0.547583i	−0.925741	−	0.378158i	$-0.876558\pi$
$139$	−6.45591	+	6.45591i	−0.547583	+	0.547583i	0.378158	+	0.925741i	$0.376558\pi$
$140$	2.28364	+	1.71753i	0.193003	+	0.145157i
$141$	−1.27476	−	1.27476i	−0.107354	−	0.107354i
$142$	−19.5878	+	1.37884i	−1.64377	+	0.115710i
$143$	−5.07689			−0.424551
$144$	0.636490	+	2.20426i	0.0530408	+	0.183688i
$145$	−4.97716			−0.413330
$146$	15.6098	−	1.09882i	1.29188	−	0.0909391i
$147$	6.62844	+	6.62844i	0.546704	+	0.546704i
$148$	9.29254	−	12.3554i	0.763842	−	1.01561i
$149$	5.56300	−	5.56300i	0.455738	−	0.455738i	−0.441515	−	0.897254i	$-0.645559\pi$
$149$	5.56300	−	5.56300i	0.455738	−	0.455738i	0.897254	+	0.441515i	$0.145559\pi$
$150$	−2.01847	−	1.75298i	−0.164807	−	0.143130i
$151$			16.7222i			1.36083i	0.732827	+	0.680415i	$0.238200\pi$
$151$			16.7222i			1.36083i	−0.732827	+	0.680415i	$0.761800\pi$
$152$	6.27359	−	9.68997i	0.508855	−	0.785960i
$153$			4.03757i			0.326418i
$154$	1.32486	−	1.52551i	0.106761	−	0.122929i
$155$	3.48368	−	3.48368i	0.279816	−	0.279816i
$156$	−2.68900	−	19.0053i	−0.215293	−	1.52164i
$157$	−4.78498	−	4.78498i	−0.381883	−	0.381883i	0.489897	−	0.871780i	$-0.337034\pi$
$157$	−4.78498	−	4.78498i	−0.381883	−	0.381883i	−0.871780	+	0.489897i	$0.837034\pi$
$158$	0.418345	+	5.94299i	0.0332817	+	0.472799i
$159$	13.5026			1.07083
$160$	−5.13238	−	2.37879i	−0.405750	−	0.188060i
$161$	−1.44370			−0.113780
$162$	−1.03195	−	14.6599i	−0.0810777	−	1.15179i
$163$	−5.99344	−	5.99344i	−0.469443	−	0.469443i	0.432291	−	0.901734i	$-0.357705\pi$
$163$	−5.99344	−	5.99344i	−0.469443	−	0.469443i	−0.901734	+	0.432291i	$0.857705\pi$
$164$	−3.31038	−	23.3971i	−0.258497	−	1.82701i
$165$	−1.33671	+	1.33671i	−0.104063	+	0.104063i
$166$	−8.08647	+	9.31114i	−0.627632	+	0.722685i
$167$		−	7.34023i		−	0.568004i	−0.958824	−	0.284002i	$-0.908338\pi$
$167$		−	7.34023i		−	0.568004i	0.958824	−	0.284002i	$-0.0916623\pi$
$168$	6.41247	+	4.15163i	0.494733	+	0.320305i
$169$			12.7748i			0.982677i
$170$	−7.51618	−	6.52759i	−0.576464	−	0.500644i
$171$	1.65528	−	1.65528i	0.126583	−	0.126583i
$172$	−13.3645	+	17.7695i	−1.01903	+	1.35491i
$173$	−16.4161	−	16.4161i	−1.24809	−	1.24809i	−0.956563	−	0.291527i	$-0.905837\pi$
$173$	−16.4161	−	16.4161i	−1.24809	−	1.24809i	−0.291527	−	0.956563i	$-0.594163\pi$
$174$	−13.2732	+	0.934337i	−1.00624	+	0.0708319i
$175$	−1.42871			−0.108001
$176$	−1.93274	+	3.50207i	−0.145686	+	0.263978i
$177$	16.1950			1.21729
$178$	21.4410	−	1.50929i	1.60707	−	0.113126i
$179$	8.76739	+	8.76739i	0.655306	+	0.655306i	0.954266	−	0.298960i	$-0.0966397\pi$
$179$	8.76739	+	8.76739i	0.655306	+	0.655306i	−0.298960	+	0.954266i	$0.596640\pi$
$180$	−0.916801	−	0.689527i	−0.0683343	−	0.0513943i
$181$	−13.7785	+	13.7785i	−1.02415	+	1.02415i	−0.0244488	+	0.999701i	$0.507783\pi$
$181$	−13.7785	+	13.7785i	−1.02415	+	1.02415i	−0.999701	+	0.0244488i	$0.992217\pi$
$182$	−7.74485	−	6.72619i	−0.574086	−	0.498578i
$183$		−	15.0186i		−	1.11020i
$184$	2.79481	−	0.598121i	0.206036	−	0.0440941i
$185$			7.72995i			0.568317i
$186$	8.63637	−	9.94431i	0.633249	−	0.729153i
$187$	−4.97751	+	4.97751i	−0.363992	+	0.363992i
$188$	1.88850	−	0.267198i	0.137733	−	0.0194874i
$189$	−4.63392	−	4.63392i	−0.337068	−	0.337068i
$190$	0.405289	+	5.75752i	0.0294027	+	0.417695i
$191$	17.5745			1.27164			0.635822	−	0.771835i	$-0.280661\pi$
$191$	17.5745			1.27164			0.635822	+	0.771835i	$0.280661\pi$
$192$	−14.1337	−	5.38033i	−1.02001	−	0.388292i
$193$	10.4953			0.755465			0.377733	−	0.925915i	$-0.376704\pi$
$193$	10.4953			0.755465			0.377733	+	0.925915i	$0.376704\pi$
$194$	1.59962	+	22.7242i	0.114846	+	1.63150i
$195$	6.78632	+	6.78632i	0.485979	+	0.485979i
$196$	−9.81975	+	1.38937i	−0.701411	+	0.0992404i
$197$	9.25514	−	9.25514i	0.659402	−	0.659402i	−0.295837	−	0.955238i	$-0.595598\pi$
$197$	9.25514	−	9.25514i	0.659402	−	0.659402i	0.955238	+	0.295837i	$0.0955985\pi$
$198$	−0.531887	+	0.612439i	−0.0377996	+	0.0435242i
$199$			10.0374i			0.711533i	0.934575	+	0.355766i	$0.115780\pi$
$199$			10.0374i			0.711533i	−0.934575	+	0.355766i	$0.884220\pi$
$200$	2.76580	−	0.591912i	0.195571	−	0.0418545i
$201$			15.7923i			1.11391i
$202$	14.7396	+	12.8010i	1.03708	+	0.900674i
$203$	−5.02819	+	5.02819i	−0.352910	+	0.352910i
$204$	−21.2697	−	15.9969i	−1.48917	−	1.12001i
$205$	8.35451	+	8.35451i	0.583504	+	0.583504i
$206$	9.58083	−	0.674422i	0.667528	−	0.0469892i
$207$	0.579595			0.0402847
$208$	17.7796	+	9.81233i	1.23280	+	0.680363i
$209$	4.08126			0.282307
$210$	−3.81012	+	0.268205i	−0.262923	+	0.0185079i
$211$	−6.51309	−	6.51309i	−0.448380	−	0.448380i	0.446436	−	0.894816i	$-0.352693\pi$
$211$	−6.51309	−	6.51309i	−0.448380	−	0.448380i	−0.894816	+	0.446436i	$0.852693\pi$
$212$	−8.58666	+	11.4169i	−0.589734	+	0.784116i
$213$	18.5601	−	18.5601i	1.27172	−	1.27172i
$214$	18.0360	+	15.6638i	1.23292	+	1.07076i
$215$		−	11.1172i		−	0.758185i
$216$	10.8905	+	7.05082i	0.741002	+	0.479748i
$217$		−	7.03880i		−	0.477825i
$218$	−1.55513	+	1.79065i	−0.105327	+	0.121278i
$219$	−14.7909	+	14.7909i	−0.999473	+	0.999473i
$220$	−0.280183	−	1.98028i	−0.0188899	−	0.133510i
$221$	25.2703	+	25.2703i	1.69986	+	1.69986i
$222$	1.45110	+	20.6144i	0.0973918	+	1.38355i
$223$	−17.8888			−1.19792			−0.598960	−	0.800779i	$-0.704419\pi$
$223$	−17.8888			−1.19792			−0.598960	+	0.800779i	$0.704419\pi$
$224$	−7.58819	+	2.78182i	−0.507007	+	0.185868i
$225$	0.573579			0.0382386
$226$	−0.632788	−	8.98937i	−0.0420924	−	0.597964i
$227$	−10.6686	−	10.6686i	−0.708103	−	0.708103i	0.258033	−	0.966136i	$-0.416926\pi$
$227$	−10.6686	−	10.6686i	−0.708103	−	0.708103i	−0.966136	+	0.258033i	$0.916926\pi$
$228$	2.16166	+	15.2782i	0.143160	+	1.01182i
$229$	−0.845816	+	0.845816i	−0.0558931	+	0.0558931i	−0.734501	−	0.678608i	$-0.762584\pi$
$229$	−0.845816	+	0.845816i	−0.0558931	+	0.0558931i	0.678608	+	0.734501i	$0.262584\pi$
$230$	−0.937039	+	1.07895i	−0.0617866	+	0.0711439i
$231$			2.70083i			0.177701i
$232$	7.65074	−	11.8171i	0.502295	−	0.775828i
$233$		−	0.932626i		−	0.0610984i	−0.999533	−	0.0305492i	$-0.990274\pi$
$233$		−	0.932626i		−	0.0610984i	0.999533	−	0.0305492i	$-0.00972562\pi$
$234$	3.10929	+	2.70033i	0.203260	+	0.176526i
$235$	−0.674335	+	0.674335i	−0.0439887	+	0.0439887i
$236$	−10.2988	+	13.6934i	−0.670394	+	0.891363i
$237$	−5.63119	−	5.63119i	−0.365785	−	0.365785i
$238$	−14.1878	+	0.998718i	−0.919656	+	0.0647373i
$239$	5.19593			0.336097			0.168049	−	0.985779i	$-0.446253\pi$
$239$	5.19593			0.336097			0.168049	+	0.985779i	$0.446253\pi$
$240$	7.26476	−	2.09773i	0.468938	−	0.135408i
$241$	−14.5725			−0.938696			−0.469348	−	0.883013i	$-0.655511\pi$
$241$	−14.5725			−0.938696			−0.469348	+	0.883013i	$0.655511\pi$
$242$	−1.41072	+	0.0993049i	−0.0906847	+	0.00638356i
$243$	4.16048	+	4.16048i	0.266895	+	0.266895i
$244$	12.6987	+	9.55068i	0.812949	+	0.611420i
$245$	3.50638	−	3.50638i	0.224015	−	0.224015i
$246$	23.8483	+	20.7116i	1.52051	+	1.32052i
$247$		−	20.7201i		−	1.31839i
$248$	2.91615	+	13.6262i	0.185176	+	0.865263i
$249$		−	16.4848i		−	1.04468i
$250$	−0.927312	+	1.06775i	−0.0586484	+	0.0675305i
$251$	2.42557	−	2.42557i	0.153101	−	0.153101i	−0.626401	−	0.779501i	$-0.715473\pi$
$251$	2.42557	−	2.42557i	0.153101	−	0.153101i	0.779501	+	0.626401i	$0.215473\pi$
$252$	−1.62280	+	0.229605i	−0.102227	+	0.0144637i
$253$	0.714524	+	0.714524i	0.0449217	+	0.0449217i
$254$	2.11085	+	29.9867i	0.132447	+	1.88153i
$255$	13.3070			0.833314
$256$	13.5372	−	8.52900i	0.846076	−	0.533062i
$257$	25.4727			1.58894			0.794472	−	0.607300i	$-0.207747\pi$
$257$	25.4727			1.58894			0.794472	+	0.607300i	$0.207747\pi$
$258$	−2.08697	−	29.6475i	−0.129929	−	1.84577i
$259$	7.80921	+	7.80921i	0.485241	+	0.485241i
$260$	−10.0536	+	1.42246i	−0.623501	+	0.0882172i
$261$	2.01864	−	2.01864i	0.124951	−	0.124951i
$262$	−7.17670	+	8.26359i	−0.443378	+	0.510526i
$263$			9.82593i			0.605893i	0.953008	+	0.302946i	$0.0979703\pi$
$263$			9.82593i			0.605893i	−0.953008	+	0.302946i	$0.902030\pi$
$264$	−1.11895	−	5.22844i	−0.0688663	−	0.321788i
$265$		−	7.14277i		−	0.438777i
$266$	6.22600	+	5.40711i	0.381741	+	0.331531i
$267$	−20.3160	+	20.3160i	−1.24332	+	1.24332i
$268$	−13.3529	−	10.0428i	−0.815660	−	0.613459i
$269$	−4.41505	−	4.41505i	−0.269190	−	0.269190i	0.559584	−	0.828774i	$-0.310961\pi$
$269$	−4.41505	−	4.41505i	−0.269190	−	0.269190i	−0.828774	+	0.559584i	$0.810961\pi$
$270$	−6.47082	+	0.455500i	−0.393802	+	0.0277208i
$271$	−5.58606			−0.339329			−0.169665	−	0.985502i	$-0.554268\pi$
$271$	−5.58606			−0.339329			−0.169665	+	0.985502i	$0.554268\pi$
$272$	27.0518	−	7.81133i	1.64026	−	0.473632i
$273$	13.7118			0.829876
$274$	−1.36389	+	0.0960085i	−0.0823959	+	0.00580008i
$275$	0.707107	+	0.707107i	0.0426401	+	0.0426401i
$276$	−2.29637	+	3.05327i	−0.138225	+	0.183785i
$277$	−7.87695	+	7.87695i	−0.473280	+	0.473280i	−0.902974	−	0.429694i	$-0.858621\pi$
$277$	−7.87695	+	7.87695i	−0.473280	+	0.473280i	0.429694	+	0.902974i	$0.358621\pi$
$278$	9.74860	+	8.46639i	0.584682	+	0.507781i
$279$			2.82583i			0.169178i
$280$	2.19618	−	3.39214i	0.131247	−	0.202719i
$281$			28.1360i			1.67845i	0.543783	+	0.839226i	$0.316991\pi$
$281$			28.1360i			1.67845i	−0.543783	+	0.839226i	$0.683009\pi$
$282$	−1.67174	+	1.92492i	−0.0995505	+	0.114627i
$283$	−21.2133	+	21.2133i	−1.26100	+	1.26100i	−0.310390	+	0.950609i	$0.600460\pi$
$283$	−21.2133	+	21.2133i	−1.26100	+	1.26100i	−0.950609	+	0.310390i	$0.899540\pi$
$284$	3.89033	+	27.4961i	0.230849	+	1.63159i
$285$	−5.45545	−	5.45545i	−0.323153	−	0.323153i
$286$	0.504160	+	7.16208i	0.0298116	+	0.423503i
$287$	16.8803			0.996415
$288$	3.04639	−	1.11680i	0.179510	−	0.0658083i
$289$	32.5512			1.91478
$290$	0.494256	+	7.02139i	0.0290237	+	0.412310i
$291$	−21.5320	−	21.5320i	−1.26223	−	1.26223i
$292$	−3.10026	−	21.9120i	−0.181429	−	1.28230i
$293$	−0.682013	+	0.682013i	−0.0398436	+	0.0398436i	−0.726748	−	0.686904i	$-0.758969\pi$
$293$	−0.682013	+	0.682013i	−0.0398436	+	0.0398436i	0.686904	+	0.726748i	$0.258969\pi$
$294$	8.69265	−	10.0091i	0.506966	−	0.583744i
$295$		−	8.56700i		−	0.498790i
$296$	−18.3529	−	11.8822i	−1.06674	−	0.690641i
$297$			4.58689i			0.266158i
$298$	−8.40028	−	7.29541i	−0.486615	−	0.422612i
$299$	3.62756	−	3.62756i	0.209787	−	0.209787i
$300$	−2.27253	+	3.02158i	−0.131205	+	0.174451i
$301$	−11.2312	−	11.2312i	−0.647354	−	0.647354i
$302$	23.5903	−	1.66059i	1.35747	−	0.0955563i
$303$	−26.0957			−1.49916
$304$	−14.2929	−	7.88803i	−0.819751	−	0.452410i
$305$	−7.94468			−0.454911
$306$	5.69589	−	0.400950i	0.325613	−	0.0229208i
$307$	−7.91390	−	7.91390i	−0.451670	−	0.451670i	0.444238	−	0.895909i	$-0.353474\pi$
$307$	−7.91390	−	7.91390i	−0.451670	−	0.451670i	−0.895909	+	0.444238i	$0.853474\pi$
$308$	−2.28364	−	1.71753i	−0.130122	−	0.0978651i
$309$	−9.07817	+	9.07817i	−0.516439	+	0.516439i
$310$	−5.26045	−	4.56856i	−0.298774	−	0.259477i
$311$		−	12.2669i		−	0.695591i	−0.937570	−	0.347796i	$-0.886930\pi$
$311$		−	12.2669i		−	0.695591i	0.937570	−	0.347796i	$-0.113070\pi$
$312$	−26.5442	+	5.68076i	−1.50277	+	0.321610i
$313$		−	0.938677i		−	0.0530572i	−0.999648	−	0.0265286i	$-0.991555\pi$
$313$		−	0.938677i		−	0.0530572i	0.999648	−	0.0265286i	$-0.00844530\pi$
$314$	−6.27510	+	7.22545i	−0.354125	+	0.407755i
$315$	0.579460	−	0.579460i	0.0326489	−	0.0326489i
$316$	8.34237	−	1.18034i	0.469295	−	0.0663991i
$317$	6.10309	+	6.10309i	0.342783	+	0.342783i	0.857413	−	0.514629i	$-0.172070\pi$
$317$	6.10309	+	6.10309i	0.342783	+	0.342783i	−0.514629	+	0.857413i	$0.672070\pi$
$318$	−1.34088	−	19.0485i	−0.0751926	−	1.06818i
$319$	4.97716			0.278667
$320$	−2.84615	+	7.47659i	−0.159105	+	0.417954i
$321$	−31.9318			−1.78226
$322$	0.143366	+	2.03666i	0.00798950	+	0.113499i
$323$	−20.3145	−	20.3145i	−1.13033	−	1.13033i
$324$	−20.5785	+	2.91159i	−1.14325	+	0.161755i
$325$	3.58990	−	3.58990i	0.199132	−	0.199132i
$326$	−7.85991	+	9.05026i	−0.435320	+	0.501248i
$327$		−	3.17024i		−	0.175315i
$328$	−32.6781	+	6.99347i	−1.80434	+	0.386150i
$329$			1.36250i			0.0751169i
$330$	2.01847	+	1.75298i	0.111113	+	0.0964986i
$331$	−2.59671	+	2.59671i	−0.142728	+	0.142728i	−0.774861	−	0.632132i	$-0.782180\pi$
$331$	−2.59671	+	2.59671i	−0.142728	+	0.142728i	0.632132	+	0.774861i	$0.282180\pi$
$332$	13.9385	+	10.4831i	0.764973	+	0.575336i
$333$	−3.13512	−	3.13512i	−0.171804	−	0.171804i
$334$	−10.3550	+	0.728921i	−0.566602	+	0.0398848i
$335$	8.35401			0.456428
$336$	5.22001	−	9.45849i	0.284775	−	0.516003i
$337$	−1.30654			−0.0711718			−0.0355859	−	0.999367i	$-0.511330\pi$
$337$	−1.30654			−0.0711718			−0.0355859	+	0.999367i	$0.511330\pi$
$338$	18.0217	−	1.26860i	0.980252	−	0.0690028i
$339$	8.51774	+	8.51774i	0.462620	+	0.462620i
$340$	−8.46223	+	11.2515i	−0.458929	+	0.610196i
$341$	−3.48368	+	3.48368i	−0.188652	+	0.188652i
$342$	−2.49952	−	2.17077i	−0.135159	−	0.117382i
$343$		−	17.0857i		−	0.922540i
$344$	26.3951	+	17.0890i	1.42313	+	0.921376i
$345$		−	1.91022i		−	0.102843i
$346$	−21.5283	+	24.7887i	−1.15737	+	1.33265i
$347$	5.38414	−	5.38414i	0.289036	−	0.289036i	−0.547663	−	0.836699i	$-0.684483\pi$
$347$	5.38414	−	5.38414i	0.289036	−	0.289036i	0.836699	+	0.547663i	$0.184483\pi$
$348$	2.63618	+	18.6320i	0.141314	+	0.998779i
$349$	12.7184	+	12.7184i	0.680800	+	0.680800i	0.960181	−	0.279380i	$-0.0901290\pi$
$349$	12.7184	+	12.7184i	0.680800	+	0.680800i	−0.279380	+	0.960181i	$0.590129\pi$
$350$	0.141878	+	2.01552i	0.00758371	+	0.107734i
$351$	23.2871			1.24297
$352$	5.13238	+	2.37879i	0.273557	+	0.126790i
$353$	9.27162			0.493479			0.246739	−	0.969082i	$-0.420641\pi$
$353$	9.27162			0.493479			0.246739	+	0.969082i	$0.420641\pi$
$354$	−1.60824	−	22.8466i	−0.0854770	−	1.21428i
$355$	−9.81815	−	9.81815i	−0.521093	−	0.521093i
$356$	−4.25838	−	30.0974i	−0.225694	−	1.59516i
$357$	13.4434	−	13.4434i	0.711500	−	0.711500i
$358$	11.4977	−	13.2390i	0.607673	−	0.699703i
$359$			25.4418i			1.34277i	0.741109	+	0.671384i	$0.234300\pi$
$359$			25.4418i			1.34277i	−0.741109	+	0.671384i	$0.765700\pi$
$360$	−0.881688	+	1.36183i	−0.0464690	+	0.0717745i
$361$		−	2.34333i		−	0.123333i
$362$	20.8060	+	18.0694i	1.09354	+	0.949707i
$363$	1.33671	−	1.33671i	0.0701590	−	0.0701590i
$364$	−8.71969	+	11.5938i	−0.457036	+	0.607679i
$365$	7.82423	+	7.82423i	0.409539	+	0.409539i
$366$	−21.1870	+	1.49142i	−1.10746	+	0.0779575i
$367$	−0.187304			−0.00977718			−0.00488859	−	0.999988i	$-0.501556\pi$
$367$	−0.187304			−0.00977718			−0.00488859	+	0.999988i	$0.501556\pi$
$368$	−1.12132	−	3.88331i	−0.0584529	−	0.202431i
$369$	−6.77687			−0.352790
$370$	10.9048	−	0.767621i	0.566914	−	0.0399067i
$371$	−7.21601	−	7.21601i	−0.374636	−	0.374636i
$372$	−14.8863	−	11.1960i	−0.771819	−	0.580486i
$373$	4.30635	−	4.30635i	0.222975	−	0.222975i	−0.586775	−	0.809750i	$-0.699603\pi$
$373$	4.30635	−	4.30635i	0.222975	−	0.222975i	0.809750	+	0.586775i	$0.199603\pi$
$374$	7.51618	+	6.52759i	0.388652	+	0.337534i
$375$		−	1.89039i		−	0.0976194i
$376$	−0.564479	−	2.63761i	−0.0291108	−	0.136024i
$377$		−	25.2685i		−	1.30139i
$378$	−6.07700	+	6.99734i	−0.312567	+	0.359904i
$379$	9.01573	−	9.01573i	0.463107	−	0.463107i	−0.436566	−	0.899672i	$-0.643805\pi$
$379$	9.01573	−	9.01573i	0.463107	−	0.463107i	0.899672	+	0.436566i	$0.143805\pi$
$380$	8.08202	−	1.14350i	0.414599	−	0.0586603i
$381$	−28.4135	−	28.4135i	−1.45567	−	1.45567i
$382$	−1.74523	−	24.7927i	−0.0892938	−	1.26851i
$383$	−14.1214			−0.721572			−0.360786	−	0.932649i	$-0.617491\pi$
$383$	−14.1214			−0.721572			−0.360786	+	0.932649i	$0.617491\pi$
$384$	−6.18662	+	20.4730i	−0.315709	+	1.04476i
$385$	1.42871			0.0728140
$386$	−1.04223	−	14.8059i	−0.0530481	−	0.753600i
$387$	4.50892	+	4.50892i	0.229201	+	0.229201i
$388$	31.8987	−	4.51325i	1.61941	−	0.229126i
$389$	0.342295	−	0.342295i	0.0173551	−	0.0173551i	−0.698376	−	0.715731i	$-0.746094\pi$
$389$	0.342295	−	0.342295i	0.0173551	−	0.0173551i	0.715731	+	0.698376i	$0.246094\pi$
$390$	8.89970	−	10.2475i	0.450654	−	0.518904i
$391$		−	7.11310i		−	0.359725i
$392$	2.93516	+	13.7150i	0.148248	+	0.692711i
$393$		−	14.6302i		−	0.737996i
$394$	−13.9755	−	12.1374i	−0.704077	−	0.611471i
$395$	−2.97885	+	2.97885i	−0.149882	+	0.149882i
$396$	0.916801	+	0.689527i	0.0460710	+	0.0346500i
$397$	−19.0892	−	19.0892i	−0.958061	−	0.958061i	0.0410938	−	0.999155i	$-0.486916\pi$
$397$	−19.0892	−	19.0892i	−0.958061	−	0.958061i	−0.999155	+	0.0410938i	$0.986916\pi$
$398$	14.1600	−	0.996763i	0.709777	−	0.0499632i
$399$	−11.0228			−0.551829
$400$	−1.10968	−	3.84299i	−0.0554840	−	0.192150i
$401$	3.41043			0.170309			0.0851544	−	0.996368i	$-0.472862\pi$
$401$	3.41043			0.170309			0.0851544	+	0.996368i	$0.472862\pi$
$402$	22.2786	−	1.56826i	1.11116	−	0.0782175i
$403$	17.6863	+	17.6863i	0.881015	+	0.881015i
$404$	16.5949	−	22.0647i	0.825628	−	1.09776i
$405$	7.34807	−	7.34807i	0.365129	−	0.365129i
$406$	7.59271	+	6.59406i	0.376820	+	0.327258i
$407$		−	7.72995i		−	0.383159i
$408$	−20.4551	+	31.5942i	−1.01268	+	1.56414i
$409$			16.3015i			0.806055i	0.915188	+	0.403027i	$0.132042\pi$
$409$			16.3015i			0.806055i	−0.915188	+	0.403027i	$0.867958\pi$
$410$	10.9562	−	12.6155i	0.541090	−	0.623037i
$411$	1.29234	−	1.29234i	0.0637463	−	0.0637463i
$412$	−1.90285	−	13.4489i	−0.0937465	−	0.662581i
$413$	−8.65484	−	8.65484i	−0.425877	−	0.425877i
$414$	−0.0575566	−	0.817648i	−0.00282875	−	0.0401852i
$415$	−8.72033			−0.428064
$416$	12.0769	−	26.0565i	0.592118	−	1.27753i
$417$	−17.2593			−0.845193
$418$	−0.405289	−	5.75752i	−0.0198233	−	0.281610i
$419$	0.537588	+	0.537588i	0.0262629	+	0.0262629i	0.720116	−	0.693853i	$-0.244088\pi$
$419$	0.537588	+	0.537588i	0.0262629	+	0.0262629i	−0.693853	+	0.720116i	$0.744088\pi$
$420$	0.756727	+	5.34839i	0.0369245	+	0.260975i
$421$	−8.92988	+	8.92988i	−0.435216	+	0.435216i	−0.890398	−	0.455183i	$-0.849574\pi$
$421$	−8.92988	+	8.92988i	−0.435216	+	0.435216i	0.455183	+	0.890398i	$0.349574\pi$
$422$	−8.54138	+	9.83495i	−0.415788	+	0.478758i
$423$		−	0.546995i		−	0.0265958i
$424$	16.9588	+	10.9796i	0.823591	+	0.533219i
$425$		−	7.03926i		−	0.341454i
$426$	−28.0263	−	24.3401i	−1.35788	−	1.17928i
$427$	−8.02614	+	8.02614i	−0.388412	+	0.388412i
$428$	20.3062	−	26.9993i	0.981538	−	1.30506i
$429$	−6.78632	−	6.78632i	−0.327647	−	0.327647i
$430$	−15.6832	+	1.10399i	−0.756313	+	0.0532391i
$431$	8.16958			0.393515			0.196757	−	0.980452i	$-0.436959\pi$
$431$	8.16958			0.393515			0.196757	+	0.980452i	$0.436959\pi$
$432$	8.86528	−	16.0636i	0.426531	−	0.772860i
$433$	8.13387			0.390889			0.195444	−	0.980715i	$-0.437385\pi$
$433$	8.13387			0.390889			0.195444	+	0.980715i	$0.437385\pi$
$434$	−9.92980	+	0.698987i	−0.476645	+	0.0335525i
$435$	−6.65301	−	6.65301i	−0.318987	−	0.318987i
$436$	2.68054	+	2.01604i	0.128375	+	0.0965507i
$437$	−2.91616	+	2.91616i	−0.139499	+	0.139499i
$438$	22.3346	+	19.3970i	1.06719	+	0.926824i
$439$		−	27.8481i		−	1.32912i	−0.747235	−	0.664560i	$-0.768619\pi$
$439$		−	27.8481i		−	1.32912i	0.747235	−	0.664560i	$-0.231381\pi$
$440$	−2.76580	+	0.591912i	−0.131854	+	0.0282183i
$441$			2.84425i			0.135440i
$442$	33.1399	−	38.1588i	1.57630	−	1.81503i
$443$	2.79693	−	2.79693i	0.132886	−	0.132886i	−0.637535	−	0.770421i	$-0.720046\pi$
$443$	2.79693	−	2.79693i	0.132886	−	0.132886i	0.770421	+	0.637535i	$0.220046\pi$
$444$	28.9370	−	4.09421i	1.37329	−	0.194303i
$445$	10.7470	+	10.7470i	0.509457	+	0.509457i
$446$	1.77644	+	25.2361i	0.0841169	+	1.19496i
$447$	14.8722			0.703431
$448$	4.67792	+	10.4286i	0.221011	+	0.492704i
$449$	29.1331			1.37487			0.687437	−	0.726244i	$-0.258736\pi$
$449$	29.1331			1.37487			0.687437	+	0.726244i	$0.258736\pi$
$450$	−0.0569592	−	0.809161i	−0.00268508	−	0.0381442i
$451$	−8.35451	−	8.35451i	−0.393398	−	0.393398i
$452$	−12.6187	+	1.78538i	−0.593532	+	0.0839770i
$453$	−22.3527	+	22.3527i	−1.05022	+	1.05022i
$454$	−13.9910	+	16.1099i	−0.656632	+	0.756077i
$455$		−	7.25342i		−	0.340046i
$456$	21.3386	−	4.56670i	0.999272	−	0.213856i
$457$		−	40.8208i		−	1.90952i	−0.297380	−	0.954759i	$-0.596113\pi$
$457$		−	40.8208i		−	1.90952i	0.297380	−	0.954759i	$-0.403887\pi$
$458$	1.27721	+	1.10922i	0.0596799	+	0.0518304i
$459$	22.8313	−	22.8313i	1.06567	−	1.06567i
$460$	1.61515	+	1.21476i	0.0753069	+	0.0566384i
$461$	4.39061	+	4.39061i	0.204491	+	0.204491i	0.801921	−	0.597430i	$-0.203811\pi$
$461$	4.39061	+	4.39061i	0.204491	+	0.204491i	−0.597430	+	0.801921i	$0.703811\pi$
$462$	3.81012	−	0.268205i	0.177263	−	0.0124780i
$463$	0.572655			0.0266135			0.0133068	−	0.999911i	$-0.495764\pi$
$463$	0.572655			0.0266135			0.0133068	+	0.999911i	$0.495764\pi$
$464$	−17.4304	−	9.61958i	−0.809184	−	0.446578i
$465$	9.31333			0.431895
$466$	−1.31568	+	0.0926143i	−0.0609476	+	0.00429028i
$467$	24.2128	+	24.2128i	1.12043	+	1.12043i	0.991676	+	0.128758i	$0.0410991\pi$
$467$	24.2128	+	24.2128i	1.12043	+	1.12043i	0.128758	+	0.991676i	$0.458901\pi$
$468$	3.50065	−	4.65450i	0.161818	−	0.215154i
$469$	8.43966	−	8.43966i	0.389708	−	0.389708i
$470$	1.01826	+	0.884334i	0.0469690	+	0.0407913i
$471$		−	12.7922i		−	0.589435i
$472$	20.3403	+	13.1689i	0.936237	+	0.606149i
$473$			11.1172i			0.511168i
$474$	−7.38485	+	8.50325i	−0.339197	+	0.390567i
$475$	−2.88589	+	2.88589i	−0.132414	+	0.132414i
$476$	2.81783	+	19.9158i	0.129155	+	0.912841i
$477$	2.89697	+	2.89697i	0.132643	+	0.132643i
$478$	−0.515981	−	7.33002i	−0.0236004	−	0.335267i
$479$	−17.2646			−0.788842			−0.394421	−	0.918930i	$-0.629055\pi$
$479$	−17.2646			−0.788842			−0.394421	+	0.918930i	$0.629055\pi$
$480$	−3.68074	−	10.0403i	−0.168002	−	0.458273i
$481$	−39.2441			−1.78938
$482$	1.44712	+	20.5577i	0.0659144	+	0.936379i
$483$	−1.92981	−	1.92981i	−0.0878093	−	0.0878093i
$484$	0.280183	+	1.98028i	0.0127356	+	0.0900126i
$485$	−11.3902	+	11.3902i	−0.517203	+	0.517203i
$486$	5.45613	−	6.28244i	0.247495	−	0.284977i
$487$		−	12.3088i		−	0.557763i	−0.960325	−	0.278882i	$-0.910036\pi$
$487$		−	12.3088i		−	0.557763i	0.960325	−	0.278882i	$-0.0899637\pi$
$488$	12.2123	−	18.8627i	0.552826	−	0.853876i
$489$		−	16.0230i		−	0.724584i
$490$	−5.29474	−	4.59833i	−0.239192	−	0.207732i
$491$	18.9293	−	18.9293i	0.854269	−	0.854269i	−0.136387	−	0.990656i	$-0.543549\pi$
$491$	18.9293	−	18.9293i	0.854269	−	0.854269i	0.990656	+	0.136387i	$0.0435490\pi$
$492$	26.8501	−	35.7001i	1.21049	−	1.60948i
$493$	−24.7738	−	24.7738i	−1.11576	−	1.11576i
$494$	−29.2303	+	2.05761i	−1.31513	+	0.0925761i
$495$	−0.573579			−0.0257805
$496$	18.9332	−	5.46703i	0.850124	−	0.245477i
$497$	−19.8376			−0.889840
$498$	−23.2555	+	1.63702i	−1.04211	+	0.0733568i
$499$	−17.1328	−	17.1328i	−0.766967	−	0.766967i	0.210604	−	0.977571i	$-0.432457\pi$
$499$	−17.1328	−	17.1328i	−0.766967	−	0.766967i	−0.977571	+	0.210604i	$0.932457\pi$
$500$	1.59839	+	1.20215i	0.0714820	+	0.0537617i
$501$	9.81175	−	9.81175i	0.438357	−	0.438357i
$502$	−3.66268	−	3.18094i	−0.163473	−	0.141972i
$503$		−	18.8469i		−	0.840341i	−0.907445	−	0.420171i	$-0.861970\pi$
$503$		−	18.8469i		−	0.840341i	0.907445	−	0.420171i	$-0.138030\pi$
$504$	0.485060	+	2.26652i	0.0216063	+	0.100959i
$505$			13.8044i			0.614287i
$506$	0.937039	−	1.07895i	0.0416565	−	0.0479652i
$507$	−17.0762	+	17.0762i	−0.758380	+	0.758380i
$508$	42.0933	−	5.95566i	1.86759	−	0.264240i
$509$	2.15102	+	2.15102i	0.0953424	+	0.0953424i	0.753169	−	0.657827i	$-0.228524\pi$
$509$	2.15102	+	2.15102i	0.0953424	+	0.0953424i	−0.657827	+	0.753169i	$0.728524\pi$
$510$	−1.32145	−	18.7724i	−0.0585146	−	0.831257i
$511$	15.8089			0.699345
$512$	−13.3764	−	18.2503i	−0.591157	−	0.806556i
$513$	−18.7203			−0.826520
$514$	−2.52957	−	35.9350i	−0.111574	−	1.58502i
$515$	4.80227	+	4.80227i	0.211613	+	0.211613i
$516$	−41.6171	+	5.88828i	−1.83209	+	0.259217i
$517$	0.674335	−	0.674335i	0.0296572	−	0.0296572i
$518$	10.2411	−	11.7921i	0.449970	−	0.518116i
$519$		−	43.8870i		−	1.92642i
$520$	3.00507	+	14.0417i	0.131781	+	0.615767i
$521$		−	35.5181i		−	1.55608i	−0.628217	−	0.778038i	$-0.716215\pi$
$521$		−	35.5181i		−	1.55608i	0.628217	−	0.778038i	$-0.283785\pi$
$522$	−3.04821	−	2.64728i	−0.133416	−	0.115868i
$523$	−22.9918	+	22.9918i	−1.00536	+	1.00536i	−0.00537692	+	0.999986i	$0.501712\pi$
$523$	−22.9918	+	22.9918i	−1.00536	+	1.00536i	−0.999986	+	0.00537692i	$0.998288\pi$
$524$	12.3703	+	9.30372i	0.540400	+	0.406435i
$525$	−1.90977	−	1.90977i	−0.0833494	−	0.0833494i
$526$	13.8617	−	0.975763i	0.604397	−	0.0425453i
$527$	34.6801			1.51069
$528$	−7.26476	+	2.09773i	−0.316158	+	0.0912920i
$529$	21.9789			0.955605
$530$	−10.0765	+	0.709311i	−0.437694	+	0.0308105i
$531$	3.47461	+	3.47461i	0.150785	+	0.150785i
$532$	7.00967	−	9.32012i	0.303908	−	0.404078i
$533$	−42.4149	+	42.4149i	−1.83719	+	1.83719i
$534$	30.6778	+	26.6428i	1.32756	+	1.15295i
$535$			16.8916i			0.730288i
$536$	−12.8415	+	19.8346i	−0.554669	+	0.856723i
$537$			23.4389i			1.01146i
$538$	−5.78997	+	6.66685i	−0.249624	+	0.287428i
$539$	−3.50638	+	3.50638i	−0.151031	+	0.151031i
$540$	1.28517	+	9.08330i	0.0553048	+	0.390883i
$541$	−13.2804	−	13.2804i	−0.570969	−	0.570969i	0.361430	−	0.932399i	$-0.382289\pi$
$541$	−13.2804	−	13.2804i	−0.570969	−	0.570969i	−0.932399	+	0.361430i	$0.882289\pi$
$542$	0.554723	+	7.88039i	0.0238274	+	0.338492i
$543$	−36.8357			−1.58077
$544$	−13.7060	−	37.3869i	−0.587640	−	1.60295i
$545$	−1.67703			−0.0718360
$546$	−1.36165	−	19.3436i	−0.0582732	−	0.827828i
$547$	−3.57410	−	3.57410i	−0.152817	−	0.152817i	0.626558	−	0.779375i	$-0.284463\pi$
$547$	−3.57410	−	3.57410i	−0.152817	−	0.152817i	−0.779375	+	0.626558i	$0.784463\pi$
$548$	0.270883	+	1.91454i	0.0115715	+	0.0817852i
$549$	3.22222	−	3.22222i	0.137521	−	0.137521i
$550$	0.927312	−	1.06775i	0.0395407	−	0.0455290i
$551$			20.3131i			0.865366i
$552$	4.53536	+	2.93633i	0.193038	+	0.124979i
$553$			6.01879i			0.255945i
$554$	11.8944	+	10.3300i	0.505345	+	0.438878i
$555$	−10.3327	+	10.3327i	−0.438598	+	0.438598i
$556$	10.9757	−	14.5933i	0.465471	−	0.618895i
$557$	3.67437	+	3.67437i	0.155688	+	0.155688i	0.780653	−	0.624965i	$-0.214887\pi$
$557$	3.67437	+	3.67437i	0.155688	+	0.155688i	−0.624965	+	0.780653i	$0.714887\pi$
$558$	3.98647	−	0.280619i	0.168761	−	0.0118795i
$559$	56.4407			2.38719
$560$	−5.00346	−	2.76134i	−0.211435	−	0.116688i
$561$	−13.3070			−0.561820
$562$	39.6921	−	2.79404i	1.67431	−	0.117859i
$563$	20.5716	+	20.5716i	0.866992	+	0.866992i	0.992138	−	0.125147i	$-0.0399401\pi$
$563$	20.5716	+	20.5716i	0.866992	+	0.866992i	−0.125147	+	0.992138i	$0.539940\pi$
$564$	2.88154	+	2.16721i	0.121335	+	0.0912558i
$565$	4.50581	−	4.50581i	0.189561	−	0.189561i
$566$	32.0327	+	27.8195i	1.34643	+	1.16934i
$567$		−	14.8468i		−	0.623508i
$568$	38.4030	−	8.21868i	1.61135	−	0.344848i
$569$		−	20.0785i		−	0.841735i	−0.907122	−	0.420868i	$-0.861726\pi$
$569$		−	20.0785i		−	0.841735i	0.907122	−	0.420868i	$-0.138274\pi$
$570$	−7.15438	+	8.23788i	−0.299664	+	0.345047i
$571$	3.10542	−	3.10542i	0.129958	−	0.129958i	−0.639136	−	0.769094i	$-0.720708\pi$
$571$	3.10542	−	3.10542i	0.129958	−	0.129958i	0.769094	+	0.639136i	$0.220708\pi$
$572$	10.0536	−	1.42246i	0.420364	−	0.0594760i
$573$	23.4920	+	23.4920i	0.981391	+	0.981391i
$574$	−1.67630	−	23.8135i	−0.0699674	−	0.993955i
$575$	−1.01049			−0.0421403
$576$	−1.87802	−	4.18671i	−0.0782509	−	0.174446i
$577$	2.31212			0.0962550			0.0481275	−	0.998841i	$-0.484675\pi$
$577$	2.31212			0.0962550			0.0481275	+	0.998841i	$0.484675\pi$
$578$	−3.23249	−	45.9207i	−0.134454	−	1.91005i
$579$	14.0291	+	14.0291i	0.583029	+	0.583029i
$580$	9.85615	−	1.39452i	0.409254	−	0.0579041i
$581$	−8.80975	+	8.80975i	−0.365490	+	0.365490i
$582$	−28.2374	+	32.5139i	−1.17048	+	1.34774i
$583$			7.14277i			0.295823i
$584$	−30.6039	+	6.54958i	−1.26640	+	0.271024i
$585$			2.91200i			0.120396i
$586$	1.02986	+	0.894404i	0.0425431	+	0.0369475i
$587$	−8.58148	+	8.58148i	−0.354196	+	0.354196i	−0.861668	−	0.507472i	$-0.830580\pi$
$587$	−8.58148	+	8.58148i	−0.354196	+	0.354196i	0.507472	+	0.861668i	$0.330580\pi$
$588$	−14.9833	−	11.2690i	−0.617902	−	0.464724i
$589$	−14.2178	−	14.2178i	−0.585834	−	0.585834i
$590$	−12.0857	+	0.850744i	−0.497559	+	0.0350246i
$591$	24.7429			1.01779
$592$	−14.9400	+	27.0708i	−0.614031	+	1.11260i
$593$	25.5679			1.04995			0.524974	−	0.851118i	$-0.324075\pi$
$593$	25.5679			1.04995			0.524974	+	0.851118i	$0.324075\pi$
$594$	6.47082	−	0.455500i	0.265501	−	0.0186894i
$595$	−7.11144	−	7.11144i	−0.291541	−	0.291541i
$596$	−9.45761	+	12.5749i	−0.387399	+	0.515089i
$597$	−13.4171	+	13.4171i	−0.549125	+	0.549125i
$598$	−5.47771	−	4.75725i	−0.224000	−	0.194538i
$599$		−	16.4393i		−	0.671693i	−0.941917	−	0.335847i	$-0.890978\pi$
$599$		−	16.4393i		−	0.671693i	0.941917	−	0.335847i	$-0.109022\pi$
$600$	4.48828	+	2.90585i	0.183233	+	0.118631i
$601$			20.5741i			0.839236i	0.907701	+	0.419618i	$0.137836\pi$
$601$			20.5741i			0.839236i	−0.907701	+	0.419618i	$0.862164\pi$
$602$	−14.7287	+	16.9594i	−0.600299	+	0.691212i
$603$	−3.38823	+	3.38823i	−0.137979	+	0.137979i
$604$	−4.68527	−	33.1145i	−0.190641	−	1.34741i
$605$	−0.707107	−	0.707107i	−0.0287480	−	0.0287480i
$606$	2.59143	+	36.8138i	0.105270	+	1.49546i
$607$	20.3256			0.824991			0.412496	−	0.910960i	$-0.364657\pi$
$607$	20.3256			0.824991			0.412496	+	0.910960i	$0.364657\pi$
$608$	−9.70847	+	20.9466i	−0.393731	+	0.849496i
$609$	−13.4425			−0.544716
$610$	0.788945	+	11.2077i	0.0319435	+	0.453788i
$611$	−3.42352	−	3.42352i	−0.138501	−	0.138501i
$612$	−1.13126	−	7.99551i	−0.0457285	−	0.323199i
$613$	9.12629	−	9.12629i	0.368607	−	0.368607i	−0.498362	−	0.866969i	$-0.666065\pi$
$613$	9.12629	−	9.12629i	0.368607	−	0.368607i	0.866969	+	0.498362i	$0.166065\pi$
$614$	−10.3784	+	11.9502i	−0.418840	+	0.482271i
$615$			22.3351i			0.900637i
$616$	−2.19618	+	3.39214i	−0.0884865	+	0.136673i
$617$		−	26.3647i		−	1.06140i	−0.847559	−	0.530701i	$-0.821929\pi$
$617$		−	26.3647i		−	1.06140i	0.847559	−	0.530701i	$-0.178071\pi$
$618$	13.7083	+	11.9053i	0.551428	+	0.478900i
$619$	−4.45395	+	4.45395i	−0.179019	+	0.179019i	−0.790928	−	0.611909i	$-0.790402\pi$
$619$	−4.45395	+	4.45395i	−0.179019	+	0.179019i	0.611909	+	0.790928i	$0.290402\pi$
$620$	−5.92258	+	7.87472i	−0.237857	+	0.316256i
$621$	−3.27744	−	3.27744i	−0.131519	−	0.131519i
$622$	−17.3052	+	1.21816i	−0.693874	+	0.0488438i
$623$	21.7144			0.869969
$624$	10.6499	+	36.8824i	0.426339	+	1.47648i
$625$	−1.00000			−0.0400000
$626$	−1.32421	+	0.0932152i	−0.0529262	+	0.00372563i
$627$	5.45545	+	5.45545i	0.217870	+	0.217870i
$628$	10.8162	+	8.13491i	0.431615	+	0.324618i
$629$	−38.4759	+	38.4759i	−1.53413	+	1.53413i
$630$	−0.875001	−	0.759914i	−0.0348609	−	0.0302757i
$631$			36.8576i			1.46728i	0.679541	+	0.733638i	$0.262179\pi$
$631$			36.8576i			1.46728i	−0.679541	+	0.733638i	$0.737821\pi$
$632$	−2.49357	−	11.6516i	−0.0991887	−	0.463474i
$633$		−	17.4122i		−	0.692073i
$634$	8.00370	−	9.21583i	0.317867	−	0.366007i
$635$	−15.0305	+	15.0305i	−0.596466	+	0.596466i
$636$	−26.7389	+	3.78321i	−1.06027	+	0.150014i
$637$	17.8015	+	17.8015i	0.705322	+	0.705322i
$638$	−0.494256	−	7.02139i	−0.0195678	−	0.277979i
$639$	7.96412			0.315056
$640$	10.8300	+	3.27266i	0.428095	+	0.129363i
$641$	−33.9213			−1.33981			−0.669905	−	0.742447i	$-0.733665\pi$
$641$	−33.9213			−1.33981			−0.669905	+	0.742447i	$0.733665\pi$
$642$	3.17098	+	45.0469i	0.125149	+	1.77786i
$643$	13.7750	+	13.7750i	0.543233	+	0.543233i	0.924475	−	0.381242i	$-0.124504\pi$
$643$	13.7750	+	13.7750i	0.543233	+	0.543233i	−0.381242	+	0.924475i	$0.624504\pi$
$644$	2.85893	−	0.404501i	0.112658	−	0.0159396i
$645$	14.8604	−	14.8604i	0.585128	−	0.585128i
$646$	−26.6408	+	30.6755i	−1.04817	+	1.20691i
$647$		−	34.8198i		−	1.36891i	−0.729057	−	0.684453i	$-0.760041\pi$
$647$		−	34.8198i		−	1.36891i	0.729057	−	0.684453i	$-0.239959\pi$
$648$	6.15100	+	28.7415i	0.241634	+	1.12907i
$649$			8.56700i			0.336284i
$650$	−5.42085	−	4.70786i	−0.212623	−	0.184658i
$651$	9.40882	−	9.40882i	0.368761	−	0.368761i
$652$	13.5479	+	10.1894i	0.530578	+	0.399048i
$653$	−19.6156	−	19.6156i	−0.767619	−	0.767619i	0.210068	−	0.977687i	$-0.432631\pi$
$653$	−19.6156	−	19.6156i	−0.767619	−	0.767619i	−0.977687	+	0.210068i	$0.932631\pi$
$654$	−4.47233	+	0.314820i	−0.174882	+	0.0123104i
$655$	−7.73925			−0.302397
$656$	13.1109	+	45.4052i	0.511896	+	1.77277i
$657$	−6.34673			−0.247609
$658$	1.92211	−	0.135303i	0.0749315	−	0.00527465i
$659$	20.1402	+	20.1402i	0.784549	+	0.784549i	0.980595	−	0.196046i	$-0.0628101\pi$
$659$	20.1402	+	20.1402i	0.784549	+	0.784549i	−0.196046	+	0.980595i	$0.562810\pi$
$660$	2.27253	−	3.02158i	0.0884581	−	0.117615i
$661$	−10.5583	+	10.5583i	−0.410671	+	0.410671i	−0.881972	−	0.471301i	$-0.843785\pi$
$661$	−10.5583	+	10.5583i	−0.410671	+	0.410671i	0.471301	+	0.881972i	$0.343785\pi$
$662$	3.92111	+	3.40538i	0.152398	+	0.132354i
$663$			67.5579i			2.62373i
$664$	13.4046	−	20.7043i	0.520201	−	0.803484i
$665$			5.83095i			0.226115i
$666$	−4.11146	+	4.73412i	−0.159316	+	0.183444i
$667$	−3.55630	+	3.55630i	−0.137700	+	0.137700i
$668$	2.05661	+	14.5357i	0.0795726	+	0.562403i
$669$	−23.9121	−	23.9121i	−0.924494	−	0.924494i
$670$	−0.829593	−	11.7852i	−0.0320500	−	0.455301i
$671$	7.94468			0.306701
$672$	−13.8617	−	6.42472i	−0.534726	−	0.247839i
$673$	−15.8960			−0.612745			−0.306372	−	0.951912i	$-0.599115\pi$
$673$	−15.8960			−0.612745			−0.306372	+	0.951912i	$0.599115\pi$
$674$	0.129746	+	1.84317i	0.00499762	+	0.0709961i
$675$	−3.24342	−	3.24342i	−0.124839	−	0.124839i
$676$	−3.57929	−	25.2977i	−0.137665	−	0.972987i
$677$	−23.6453	+	23.6453i	−0.908764	+	0.908764i	−0.996173	−	0.0874082i	$-0.972142\pi$
$677$	−23.6453	+	23.6453i	−0.908764	+	0.908764i	0.0874082	+	0.996173i	$0.472142\pi$
$678$	11.1703	−	12.8620i	0.428993	−	0.493963i
$679$			23.0140i			0.883197i
$680$	16.7130	+	10.8205i	0.640916	+	0.414949i
$681$		−	28.5217i		−	1.09296i
$682$	5.26045	+	4.56856i	0.201433	+	0.174939i
$683$	−20.3023	+	20.3023i	−0.776847	+	0.776847i	−0.979293	−	0.202447i	$-0.935111\pi$
$683$	−20.3023	+	20.3023i	−0.776847	+	0.776847i	0.202447	+	0.979293i	$0.435111\pi$
$684$	−2.81414	+	3.74170i	−0.107601	+	0.143068i
$685$	−0.683635	−	0.683635i	−0.0261203	−	0.0261203i
$686$	−24.1031	+	1.69669i	−0.920262	+	0.0647799i
$687$	−2.26122			−0.0862709
$688$	21.4867	−	38.9331i	0.819171	−	1.48431i
$689$	36.2630			1.38151
$690$	−2.69479	+	0.189694i	−0.102589	+	0.00722153i
$691$	−1.57642	−	1.57642i	−0.0599698	−	0.0599698i	0.676486	−	0.736456i	$-0.263502\pi$
$691$	−1.57642	−	1.57642i	−0.0599698	−	0.0599698i	−0.736456	+	0.676486i	$0.763502\pi$
$692$	37.1078	+	27.9088i	1.41063	+	1.06093i
$693$	−0.579460	+	0.579460i	−0.0220119	+	0.0220119i
$694$	−8.13019	−	7.06085i	−0.308618	−	0.268026i
$695$			9.13003i			0.346322i
$696$	26.0228	−	5.56917i	0.986391	−	0.211099i
$697$			83.1692i			3.15026i
$698$	16.6791	−	19.2051i	0.631314	−	0.726925i
$699$	1.24665	−	1.24665i	0.0471526	−	0.0471526i
$700$	2.82925	−	0.400302i	0.106936	−	0.0151300i
$701$	−27.5373	−	27.5373i	−1.04007	−	1.04007i	−0.999163	−	0.0409045i	$-0.986976\pi$
$701$	−27.5373	−	27.5373i	−1.04007	−	1.04007i	−0.0409045	−	0.999163i	$-0.513024\pi$
$702$	−2.31252	−	32.8517i	−0.0872806	−	1.23991i
$703$	31.5479			1.18985
$704$	2.84615	−	7.47659i	0.107268	−	0.281785i
$705$	−1.80278			−0.0678965
$706$	−0.920717	−	13.0797i	−0.0346517	−	0.492261i
$707$	13.9459	+	13.9459i	0.524491	+	0.524491i
$708$	−32.0705	+	4.53756i	−1.20528	+	0.170532i
$709$	22.2104	−	22.2104i	0.834129	−	0.834129i	−0.153950	−	0.988079i	$-0.549200\pi$
$709$	22.2104	−	22.2104i	0.834129	−	0.834129i	0.988079	+	0.153950i	$0.0491995\pi$
$710$	−12.8757	+	14.8257i	−0.483216	+	0.556398i
$711$		−	2.41633i		−	0.0906196i
$712$	−42.0362	+	8.99621i	−1.57537	+	0.337147i
$713$		−	4.97835i		−	0.186441i
$714$	−20.2999	−	17.6299i	−0.759705	−	0.659783i
$715$	−3.58990	+	3.58990i	−0.134255	+	0.134255i
$716$	−19.8183	−	14.9054i	−0.740646	−	0.557041i
$717$	6.94545	+	6.94545i	0.259383	+	0.259383i
$718$	35.8914	−	2.52650i	1.33945	−	0.0942881i
$719$	−19.0498			−0.710438			−0.355219	−	0.934783i	$-0.615594\pi$
$719$	−19.0498			−0.710438			−0.355219	+	0.934783i	$0.615594\pi$
$720$	2.00871	+	1.10858i	0.0748603	+	0.0413144i
$721$	9.70302			0.361359
$722$	−3.30579	+	0.232704i	−0.123029	+	0.00866034i
$723$	−19.4792	−	19.4792i	−0.724438	−	0.724438i
$724$	23.4248	−	31.1458i	0.870575	−	1.15753i
$725$	−3.51938	+	3.51938i	−0.130707	+	0.130707i
$726$	−2.01847	−	1.75298i	−0.0749123	−	0.0650593i
$727$			17.9245i			0.664785i	0.943141	+	0.332392i	$0.107856\pi$
$727$			17.9245i			0.664785i	−0.943141	+	0.332392i	$0.892144\pi$
$728$	17.2215	+	11.1497i	0.638272	+	0.413237i
$729$		−	20.0525i		−	0.742687i
$730$	10.2608	−	11.8148i	0.379771	−	0.437285i
$731$	55.3358	−	55.3358i	2.04667	−	2.04667i
$732$	4.20795	+	29.7409i	0.155530	+	1.09926i
$733$	24.2452	+	24.2452i	0.895517	+	0.895517i	0.995036	−	0.0995190i	$-0.0317304\pi$
$733$	24.2452	+	24.2452i	0.895517	+	0.895517i	−0.0995190	+	0.995036i	$0.531730\pi$
$734$	0.0186002	+	0.264234i	0.000686545	+	0.00975305i
$735$	9.37403			0.345766
$736$	−5.36691	+	1.96750i	−0.197827	+	0.0725232i
$737$	−8.35401			−0.307724
$738$	0.672976	+	9.56028i	0.0247726	+	0.351919i
$739$	−2.09811	−	2.09811i	−0.0771801	−	0.0771801i	0.667463	−	0.744643i	$-0.267380\pi$
$739$	−2.09811	−	2.09811i	−0.0771801	−	0.0771801i	−0.744643	+	0.667463i	$0.767380\pi$
$740$	−2.16580	−	15.3074i	−0.0796165	−	0.562713i
$741$	27.6967	−	27.6967i	1.01746	−	1.01746i
$742$	−9.46320	+	10.8964i	−0.347405	+	0.400018i
$743$		−	0.722747i		−	0.0265150i	−0.999912	−	0.0132575i	$-0.995780\pi$
$743$		−	0.722747i		−	0.0265150i	0.999912	−	0.0132575i	$-0.00422012\pi$
$744$	−14.3162	+	22.1123i	−0.524856	+	0.810675i
$745$		−	7.86726i		−	0.288234i
$746$	−6.50271	−	5.64743i	−0.238081	−	0.206767i
$747$	3.53681	−	3.53681i	0.129405	−	0.129405i
$748$	8.46223	−	11.2515i	0.309410	−	0.411394i
$749$	17.0648	+	17.0648i	0.623535	+	0.623535i
$750$	−2.66682	+	0.187725i	−0.0973784	+	0.00685475i
$751$	−8.46982			−0.309068			−0.154534	−	0.987987i	$-0.549388\pi$
$751$	−8.46982			−0.309068			−0.154534	+	0.987987i	$0.549388\pi$
$752$	−3.66488	+	1.05825i	−0.133645	+	0.0385904i
$753$	6.48456			0.236311
$754$	−35.6468	+	2.50928i	−1.29818	+	0.0913827i
$755$	11.8244	+	11.8244i	0.430332	+	0.430332i
$756$	10.4748	+	7.87809i	0.380964	+	0.286524i
$757$	8.42564	−	8.42564i	0.306235	−	0.306235i	−0.537212	−	0.843447i	$-0.680523\pi$
$757$	8.42564	−	8.42564i	0.306235	−	0.306235i	0.843447	+	0.537212i	$0.180523\pi$
$758$	−13.6140	−	11.8234i	−0.494483	−	0.429445i
$759$			1.91022i			0.0693366i
$760$	−2.41575	−	11.2879i	−0.0876283	−	0.409457i
$761$			21.6348i			0.784262i	0.919909	+	0.392131i	$0.128262\pi$
$761$			21.6348i			0.784262i	−0.919909	+	0.392131i	$0.871738\pi$
$762$	−37.2619	+	42.9051i	−1.34986	+	1.55429i
$763$	−1.69422	+	1.69422i	−0.0613350	+	0.0613350i
$764$	−34.8023	+	4.92407i	−1.25910	+	0.178147i
$765$	2.85499	+	2.85499i	0.103223	+	0.103223i
$766$	1.40233	+	19.9214i	0.0506681	+	0.719790i
$767$	43.4937			1.57047
$768$	29.4961	+	6.69453i	1.06435	+	0.241568i
$769$	−15.9389			−0.574771			−0.287386	−	0.957815i	$-0.592786\pi$
$769$	−15.9389			−0.574771			−0.287386	+	0.957815i	$0.592786\pi$
$770$	−0.141878	−	2.01552i	−0.00511294	−	0.0726343i
$771$	34.0496	+	34.0496i	1.22627	+	1.22627i
$772$	−20.7835	+	2.94059i	−0.748015	+	0.105834i
$773$	−7.75241	+	7.75241i	−0.278835	+	0.278835i	−0.832644	−	0.553809i	$-0.813174\pi$
$773$	−7.75241	+	7.75241i	−0.278835	+	0.278835i	0.553809	+	0.832644i	$0.313174\pi$
$774$	5.91308	−	6.80859i	0.212541	−	0.244730i
$775$		−	4.92667i		−	0.176971i
$776$	−9.53464	−	44.5521i	−0.342274	−	1.59933i
$777$			20.8773i			0.748968i
$778$	−0.516875	−	0.448892i	−0.0185309	−	0.0160936i
$779$	34.0969	−	34.0969i	1.22165	−	1.22165i
$780$	−15.3402	−	11.5374i	−0.549268	−	0.413105i
$781$	9.81815	+	9.81815i	0.351321	+	0.351321i
$782$	−10.0346	+	0.706365i	−0.358837	+	0.0252596i
$783$	−22.8296			−0.815865
$784$	19.0565	−	5.50266i	0.680591	−	0.196524i
$785$	−6.76698			−0.241524
$786$	−20.6392	+	1.45285i	−0.736175	+	0.0518215i
$787$	17.9121	+	17.9121i	0.638499	+	0.638499i	0.950185	−	0.311686i	$-0.100894\pi$
$787$	17.9121	+	17.9121i	0.638499	+	0.638499i	−0.311686	+	0.950185i	$0.600894\pi$
$788$	−15.7346	+	20.9209i	−0.560522	+	0.745276i
$789$	−13.1344	+	13.1344i	−0.467597	+	0.467597i
$790$	4.49815	+	3.90652i	0.160037	+	0.138988i
$791$		−	9.10401i		−	0.323701i
$792$	0.881688	−	1.36183i	0.0313294	−	0.0483904i
$793$		−	40.3343i		−	1.43231i
$794$	−25.0340	+	28.8253i	−0.888422	+	1.02297i
$795$	9.54780	−	9.54780i	0.338625	−	0.338625i
$796$	−2.81231	−	19.8768i	−0.0996798	−	0.704516i
$797$	−3.50691	−	3.50691i	−0.124221	−	0.124221i	0.642263	−	0.766484i	$-0.277996\pi$
$797$	−3.50691	−	3.50691i	−0.124221	−	0.124221i	−0.766484	+	0.642263i	$0.777996\pi$
$798$	1.09462	+	15.5501i	0.0387490	+	0.550467i
$799$	−6.71301			−0.237489
$800$	−5.31120	+	1.94708i	−0.187779	+	0.0688397i
$801$	−8.71757			−0.308020
$802$	−0.338672	−	4.81117i	−0.0119589	−	0.169888i
$803$	−7.82423	−	7.82423i	−0.276111	−	0.276111i
$804$	−4.42475	−	31.2732i	−0.156049	−	1.10292i
$805$	−1.02085	+	1.02085i	−0.0359803	+	0.0359803i
$806$	23.1941	−	26.7067i	0.816976	−	0.940705i
$807$		−	11.8033i		−	0.415495i
$808$	−32.7752	−	21.2197i	−1.15303	−	0.746506i
$809$		−	33.3505i		−	1.17254i	−0.810115	−	0.586271i	$-0.800595\pi$
$809$		−	33.3505i		−	1.17254i	0.810115	−	0.586271i	$-0.199405\pi$
$810$	−11.0958	−	9.63639i	−0.389866	−	0.338588i
$811$	−35.9928	+	35.9928i	−1.26388	+	1.26388i	−0.314682	+	0.949197i	$0.601898\pi$
$811$	−35.9928	+	35.9928i	−1.26388	+	1.26388i	−0.949197	+	0.314682i	$0.898102\pi$
$812$	8.54840	−	11.3660i	0.299990	−	0.398869i
$813$	−7.46694	−	7.46694i	−0.261877	−	0.261877i
$814$	−10.9048	+	0.767621i	−0.382213	+	0.0269051i
$815$	−8.47601			−0.296902
$816$	46.6019	+	25.7190i	1.63139	+	0.900343i
$817$	−45.3721			−1.58737
$818$	22.9968	−	1.61881i	0.804065	−	0.0566005i
$819$	2.94185	+	2.94185i	0.102797	+	0.102797i
$820$	−18.8850	−	14.2034i	−0.659494	−	0.496006i
$821$	19.7504	−	19.7504i	0.689294	−	0.689294i	−0.272782	−	0.962076i	$-0.587944\pi$
$821$	19.7504	−	19.7504i	0.689294	−	0.689294i	0.962076	+	0.272782i	$0.0879438\pi$
$822$	−1.95146	−	1.69479i	−0.0680651	−	0.0591127i
$823$			51.1432i			1.78274i	0.453277	+	0.891370i	$0.350255\pi$
$823$			51.1432i			1.78274i	−0.453277	+	0.891370i	$0.649745\pi$
$824$	−18.7837	+	4.01993i	−0.654362	+	0.140041i
$825$			1.89039i			0.0658150i
$826$	−11.3501	+	13.0690i	−0.394921	+	0.454730i
$827$	15.2386	−	15.2386i	0.529898	−	0.529898i	−0.390644	−	0.920542i	$-0.627748\pi$
$827$	15.2386	−	15.2386i	0.529898	−	0.529898i	0.920542	+	0.390644i	$0.127748\pi$
$828$	−1.14776	+	0.162393i	−0.0398874	+	0.00564354i
$829$	−10.1521	−	10.1521i	−0.352596	−	0.352596i	0.508478	−	0.861075i	$-0.330208\pi$
$829$	−10.1521	−	10.1521i	−0.352596	−	0.352596i	−0.861075	+	0.508478i	$0.830208\pi$
$830$	0.865971	+	12.3020i	0.0300583	+	0.427008i
$831$	−21.0584			−0.730507
$832$	−37.9578	−	14.4496i	−1.31595	−	0.500949i
$833$	34.9061			1.20943
$834$	1.71394	+	24.3481i	0.0593487	+	0.843107i
$835$	−5.19033	−	5.19033i	−0.179619	−	0.179619i
$836$	−8.08202	+	1.14350i	−0.279523	+	0.0395488i
$837$	15.9792	−	15.9792i	0.552323	−	0.552323i
$838$	0.705003	−	0.811773i	0.0243539	−	0.0280422i
$839$			24.0258i			0.829462i	0.909944	+	0.414731i	$0.136124\pi$
$839$			24.0258i			0.829462i	−0.909944	+	0.414731i	$0.863876\pi$
$840$	7.46995	−	1.59865i	0.257738	−	0.0551588i
$841$		−	4.22790i		−	0.145790i
$842$	13.4844	+	11.7108i	0.464702	+	0.403581i
$843$	−37.6096	+	37.6096i	−1.29534	+	1.29534i
$844$	14.7226	+	11.0729i	0.506772	+	0.381144i
$845$	9.03315	+	9.03315i	0.310750	+	0.310750i
$846$	−0.771659	+	0.0543193i	−0.0265302	+	0.00186754i
$847$	−1.42871			−0.0490912
$848$	13.8051	−	25.0145i	0.474071	−	0.859000i
$849$	−56.7120			−1.94635
$850$	−9.93045	+	0.699033i	−0.340611	+	0.0239766i
$851$	5.52323	+	5.52323i	0.189334	+	0.189334i
$852$	−31.5540	+	41.9545i	−1.08102	+	1.43734i
$853$	10.0206	−	10.0206i	0.343098	−	0.343098i	−0.514433	−	0.857531i	$-0.671997\pi$
$853$	10.0206	−	10.0206i	0.343098	−	0.343098i	0.857531	+	0.514433i	$0.171997\pi$
$854$	12.1197	+	10.5256i	0.414727	+	0.360180i
$855$		−	2.34092i		−	0.0800579i
$856$	−40.1051	−	25.9653i	−1.37076	−	0.887475i
$857$		−	30.8843i		−	1.05499i	−0.849559	−	0.527494i	$-0.823132\pi$
$857$		−	30.8843i		−	1.05499i	0.849559	−	0.527494i	$-0.176868\pi$
$858$	−8.89970	+	10.2475i	−0.303831	+	0.349845i
$859$	11.1283	−	11.1283i	0.379693	−	0.379693i	−0.491298	−	0.870991i	$-0.663478\pi$
$859$	11.1283	−	11.1283i	0.379693	−	0.379693i	0.870991	+	0.491298i	$0.163478\pi$
$860$	3.11485	+	22.0151i	0.106215	+	0.750708i
$861$	22.5641	+	22.5641i	0.768982	+	0.768982i
$862$	−0.811279	−	11.5250i	−0.0276323	−	0.392544i
$863$	−22.1807			−0.755039			−0.377519	−	0.926002i	$-0.623223\pi$
$863$	−22.1807			−0.755039			−0.377519	+	0.926002i	$0.623223\pi$
$864$	−23.5416	−	10.9113i	−0.800903	−	0.371208i
$865$	−23.2158			−0.789361
$866$	−0.807733	−	11.4746i	−0.0274479	−	0.389924i
$867$	43.5115	+	43.5115i	1.47773	+	1.47773i
$868$	1.97215	+	13.9388i	0.0669393	+	0.473113i
$869$	2.97885	−	2.97885i	0.101051	−	0.101051i
$870$	−8.72487	+	10.0462i	−0.295801	+	0.340599i
$871$			42.4124i			1.43709i
$872$	2.57788	−	3.98170i	0.0872980	−	0.134837i
$873$		−	9.23933i		−	0.312704i
$874$	4.40348	+	3.82430i	0.148950	+	0.129359i
$875$	−1.01025	+	1.01025i	−0.0341528	+	0.0341528i
$876$	25.1458	−	33.4341i	0.849599	−	1.12963i
$877$	2.42404	+	2.42404i	0.0818540	+	0.0818540i	0.746848	−	0.664994i	$-0.231566\pi$
$877$	2.42404	+	2.42404i	0.0818540	+	0.0818540i	−0.664994	+	0.746848i	$0.731566\pi$
$878$	−39.2860	+	2.76546i	−1.32584	+	0.0933296i
$879$	−1.82331			−0.0614986
$880$	1.10968	+	3.84299i	0.0374073	+	0.129547i
$881$	−6.92390			−0.233272			−0.116636	−	0.993175i	$-0.537211\pi$
$881$	−6.92390			−0.233272			−0.116636	+	0.993175i	$0.537211\pi$
$882$	4.01245	−	0.282448i	0.135106	−	0.00951051i
$883$	−24.9442	−	24.9442i	−0.839440	−	0.839440i	0.149345	−	0.988785i	$-0.452284\pi$
$883$	−24.9442	−	24.9442i	−0.839440	−	0.839440i	−0.988785	+	0.149345i	$0.952284\pi$
$884$	−57.1224	−	42.9618i	−1.92124	−	1.44496i
$885$	11.4516	−	11.4516i	0.384940	−	0.384940i
$886$	−4.22345	−	3.66795i	−0.141890	−	0.123227i
$887$		−	36.4317i		−	1.22326i	−0.791145	−	0.611628i	$-0.790515\pi$
$887$		−	36.4317i		−	1.22326i	0.791145	−	0.611628i	$-0.209485\pi$
$888$	−8.64939	−	40.4156i	−0.290254	−	1.35626i
$889$			30.3692i			1.01855i
$890$	14.0938	−	16.2283i	0.472426	−	0.543973i
$891$	−7.34807	+	7.34807i	−0.246170	+	0.246170i
$892$	35.4247	−	5.01213i	1.18611	−	0.167819i
$893$	2.75213	+	2.75213i	0.0920966	+	0.0920966i
$894$	−1.47688	−	20.9806i	−0.0493943	−	0.701695i
$895$	12.3990			0.414452
$896$	14.2473	−	7.63486i	0.475969	−	0.255063i
$897$	9.69798			0.323806
$898$	−2.89305	−	41.0987i	−0.0965425	−	1.37148i
$899$	−17.3388	−	17.3388i	−0.578282	−	0.578282i
$900$	−1.13585	+	0.160707i	−0.0378615	+	0.00535691i
$901$	35.5532	−	35.5532i	1.18445	−	1.18445i
$902$	−10.9562	+	12.6155i	−0.364803	+	0.420051i
$903$		−	30.0256i		−	0.999189i
$904$	3.77177	+	17.6241i	0.125447	+	0.586170i
$905$			19.4858i			0.647729i
$906$	33.7531	+	29.3137i	1.12137	+	0.973881i
$907$	4.98652	−	4.98652i	0.165575	−	0.165575i	−0.619456	−	0.785031i	$-0.712647\pi$
$907$	4.98652	−	4.98652i	0.165575	−	0.165575i	0.785031	+	0.619456i	$0.212647\pi$
$908$	24.1160	+	18.1377i	0.800319	+	0.601921i
$909$	−5.59880	−	5.59880i	−0.185701	−	0.185701i
$910$	−10.2326	+	0.720300i	−0.339206	+	0.0238777i
$911$	20.7266			0.686703			0.343351	−	0.939207i	$-0.388438\pi$
$911$	20.7266			0.686703			0.343351	+	0.939207i	$0.388438\pi$
$912$	−8.56138	−	29.6494i	−0.283496	−	0.981789i
$913$	8.72033			0.288601
$914$	−57.5869	+	4.05371i	−1.90480	+	0.134085i
$915$	−10.6197	−	10.6197i	−0.351077	−	0.351077i
$916$	1.43797	−	1.91193i	0.0475118	−	0.0631721i
$917$	−7.81860	+	7.81860i	−0.258193	+	0.258193i
$918$	−34.4758	−	29.9413i	−1.13787	−	0.988211i
$919$		−	25.0426i		−	0.826078i	−0.910713	−	0.413039i	$-0.864467\pi$
$919$		−	25.0426i		−	0.826078i	0.910713	−	0.413039i	$-0.135533\pi$
$920$	1.55329	−	2.39916i	0.0512106	−	0.0790981i
$921$		−	21.1572i		−	0.697152i
$922$	5.75792	−	6.62994i	0.189627	−	0.218345i
$923$	49.8457	−	49.8457i	1.64069	−	1.64069i
$924$	−0.756727	−	5.34839i	−0.0248945	−	0.175949i
$925$	5.46590	+	5.46590i	0.179718	+	0.179718i
$926$	−0.0568674	−	0.807857i	−0.00186878	−	0.0265478i
$927$	−3.89542			−0.127942
$928$	−11.8396	+	25.5447i	−0.388655	+	0.838545i
$929$	24.3897			0.800201			0.400101	−	0.916471i	$-0.368975\pi$
$929$	24.3897			0.800201			0.400101	+	0.916471i	$0.368975\pi$
$930$	−0.924859	−	13.1385i	−0.0303273	−	0.430829i
$931$	−14.3105	−	14.3105i	−0.469006	−	0.469006i
$932$	0.261306	+	1.84686i	0.00855937	+	0.0604959i
$933$	16.3972	−	16.3972i	0.536822	−	0.536822i
$934$	31.7531	−	36.5620i	1.03899	−	1.19634i
$935$			7.03926i			0.230208i
$936$	−6.91384	−	4.47623i	−0.225986	−	0.146310i
$937$			26.1942i			0.855728i	0.903843	+	0.427864i	$0.140734\pi$
$937$			26.1942i			0.855728i	−0.903843	+	0.427864i	$0.859266\pi$
$938$	−12.7441	−	11.0679i	−0.416110	−	0.361381i
$939$	1.25474	−	1.25474i	0.0409468	−	0.0409468i
$940$	1.14643	−	1.52431i	0.0373925	−	0.0497174i
$941$	35.4044	+	35.4044i	1.15415	+	1.15415i	0.985712	+	0.168438i	$0.0538724\pi$
$941$	35.4044	+	35.4044i	1.15415	+	1.15415i	0.168438	+	0.985712i	$0.446128\pi$
$942$	−18.0463	+	1.27033i	−0.587980	+	0.0413896i
$943$	11.9390			0.388787
$944$	16.5578	−	30.0022i	0.538911	−	0.976489i
$945$	−6.55335			−0.213180
$946$	15.6832	−	1.10399i	0.509906	−	0.0358938i
$947$	9.48520	+	9.48520i	0.308227	+	0.308227i	0.844222	−	0.535994i	$-0.180063\pi$
$947$	9.48520	+	9.48520i	0.308227	+	0.308227i	−0.535994	+	0.844222i	$0.680063\pi$
$948$	12.7291	+	9.57355i	0.413421	+	0.310935i
$949$	−39.7227	+	39.7227i	−1.28945	+	1.28945i
$950$	4.35777	+	3.78460i	0.141385	+	0.122789i
$951$			16.3161i			0.529086i
$952$	27.8159	−	5.95291i	0.901518	−	0.192935i
$953$			43.6593i			1.41426i	0.707082	+	0.707131i	$0.250011\pi$
$953$			43.6593i			1.41426i	−0.707082	+	0.707131i	$0.749989\pi$
$954$	3.79914	−	4.37451i	0.123002	−	0.141630i
$955$	12.4270	−	12.4270i	0.402129	−	0.402129i
$956$	−10.2894	+	1.45581i	−0.332783	+	0.0470844i
$957$	6.65301	+	6.65301i	0.215061	+	0.215061i
$958$	1.71446	+	24.3556i	0.0553918	+	0.786894i
$959$	−1.38129			−0.0446041
$960$	−13.7985	+	6.18955i	−0.445345	+	0.199767i
$961$	−6.72794			−0.217030
$962$	3.89713	+	55.3625i	0.125648	+	1.78496i
$963$	−6.85093	−	6.85093i	−0.220768	−	0.220768i
$964$	28.8575	−	4.08296i	0.929439	−	0.131503i
$965$	7.42127	−	7.42127i	0.238899	−	0.238899i
$966$	−2.53078	+	2.91406i	−0.0814266	+	0.0937584i
$967$			36.8132i			1.18383i	0.806000	+	0.591916i	$0.201628\pi$
$967$			36.8132i			1.18383i	−0.806000	+	0.591916i	$0.798372\pi$
$968$	2.76580	−	0.591912i	0.0888961	−	0.0190248i
$969$		−	54.3091i		−	1.74466i
$970$	17.1996	+	14.9373i	0.552244	+	0.479609i
$971$	−13.1485	+	13.1485i	−0.421954	+	0.421954i	−0.885876	−	0.463922i	$-0.846442\pi$
$971$	−13.1485	+	13.1485i	−0.421954	+	0.421954i	0.463922	+	0.885876i	$0.346442\pi$
$972$	−9.40460	−	7.07320i	−0.301653	−	0.226873i
$973$	9.22365	+	9.22365i	0.295697	+	0.295697i
$974$	−17.3643	+	1.22232i	−0.556387	+	0.0391657i
$975$	9.59731			0.307360
$976$	−27.8228	−	15.3550i	−0.890587	−	0.491503i
$977$	−9.63307			−0.308189			−0.154095	−	0.988056i	$-0.549246\pi$
$977$	−9.63307			−0.308189			−0.154095	+	0.988056i	$0.549246\pi$
$978$	−22.6040	+	1.59116i	−0.722795	+	0.0508796i
$979$	−10.7470	−	10.7470i	−0.343476	−	0.343476i
$980$	−5.96118	+	7.92604i	−0.190423	+	0.253188i
$981$	0.680172	−	0.680172i	0.0217162	−	0.0217162i
$982$	−28.5838	−	24.8243i	−0.912146	−	0.792174i
$983$		−	33.8937i		−	1.08104i	−0.841331	−	0.540520i	$-0.818228\pi$
$983$		−	33.8937i		−	1.08104i	0.841331	−	0.540520i	$-0.181772\pi$
$984$	−53.0293	−	34.3328i	−1.69051	−	1.09449i
$985$		−	13.0887i		−	0.417042i
$986$	−32.4889	+	37.4092i	−1.03466	+	1.19135i
$987$	−1.82126	+	1.82126i	−0.0579714	+	0.0579714i
$988$	5.80542	+	41.0315i	0.184695	+	1.30539i
$989$	−7.94349	−	7.94349i	−0.252588	−	0.252588i
$990$	0.0569592	+	0.809161i	0.00181028	+	0.0257168i
$991$	35.7875			1.13683			0.568414	−	0.822743i	$-0.307557\pi$
$991$	35.7875			1.13683			0.568414	+	0.822743i	$0.307557\pi$
$992$	−9.59262	−	26.1665i	−0.304566	−	0.830788i
$993$	−6.94210			−0.220301
$994$	1.96997	+	27.9854i	0.0624838	+	0.887643i
$995$	7.09752	+	7.09752i	0.225006	+	0.225006i
$996$	4.61878	+	32.6446i	0.146352	+	1.03438i
$997$	−19.6867	+	19.6867i	−0.623484	+	0.623484i	−0.946420	−	0.322937i	$-0.895330\pi$
$997$	−19.6867	+	19.6867i	−0.623484	+	0.623484i	0.322937	+	0.946420i	$0.395330\pi$
$998$	−22.4682	+	25.8709i	−0.711218	+	0.818930i
$999$			35.4564i			1.12179i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.w.a.221.17	✓	72
16.5	even	4	inner	880.2.w.a.661.17	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.w.a.221.17	✓	72	1.1	even	1	trivial
880.2.w.a.661.17	yes	72	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0993049 - 1.41072i) q^{2} +(1.33671 + 1.33671i) q^{3} +(-1.98028 + 0.280183i) q^{4} +(0.707107 - 0.707107i) q^{5} +(1.75298 - 2.01847i) q^{6} -1.42871i q^{7} +(0.591912 + 2.76580i) q^{8} +0.573579i q^{9} +(-1.06775 - 0.927312i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-3.02158 - 2.27253i) q^{12} +(3.58990 + 3.58990i) q^{13} +(-2.01552 + 0.141878i) q^{14} +1.89039 q^{15} +(3.84299 - 1.10968i) q^{16} +7.03926 q^{17} +(0.809161 - 0.0569592i) q^{18} +(-2.88589 - 2.88589i) q^{19} +(-1.20215 + 1.59839i) q^{20} +(1.90977 - 1.90977i) q^{21} +(1.06775 + 0.927312i) q^{22} -1.01049i q^{23} +(-2.90585 + 4.48828i) q^{24} -1.00000i q^{25} +(4.70786 - 5.42085i) q^{26} +(3.24342 - 3.24342i) q^{27} +(0.400302 + 2.82925i) q^{28} +(-3.51938 - 3.51938i) q^{29} +(-0.187725 - 2.66682i) q^{30} +4.92667 q^{31} +(-1.94708 - 5.31120i) q^{32} -1.89039 q^{33} +(-0.699033 - 9.93045i) q^{34} +(-1.01025 - 1.01025i) q^{35} +(-0.160707 - 1.13585i) q^{36} +(-5.46590 + 5.46590i) q^{37} +(-3.78460 + 4.35777i) q^{38} +9.59731i q^{39} +(2.37426 + 1.53717i) q^{40} +11.8151i q^{41} +(-2.88381 - 2.50451i) q^{42} +(7.86103 - 7.86103i) q^{43} +(1.20215 - 1.59839i) q^{44} +(0.405582 + 0.405582i) q^{45} +(-1.42552 + 0.100347i) q^{46} -0.953653 q^{47} +(6.62028 + 3.65364i) q^{48} +4.95878 q^{49} +(-1.41072 + 0.0993049i) q^{50} +(9.40944 + 9.40944i) q^{51} +(-8.11483 - 6.10317i) q^{52} +(5.05070 - 5.05070i) q^{53} +(-4.89765 - 4.25348i) q^{54} +1.00000i q^{55} +(3.95154 - 0.845673i) q^{56} -7.71518i q^{57} +(-4.61538 + 5.31436i) q^{58} +(6.05778 - 6.05778i) q^{59} +(-3.74350 + 0.529656i) q^{60} +(-5.61774 - 5.61774i) q^{61} +(-0.489242 - 6.95016i) q^{62} +0.819480 q^{63} +(-7.29928 + 3.27422i) q^{64} +5.07689 q^{65} +(0.187725 + 2.66682i) q^{66} +(5.90717 + 5.90717i) q^{67} +(-13.9397 + 1.97228i) q^{68} +(1.35073 - 1.35073i) q^{69} +(-1.32486 + 1.52551i) q^{70} -13.8850i q^{71} +(-1.58640 + 0.339508i) q^{72} +11.0651i q^{73} +(8.25366 + 7.16808i) q^{74} +(1.33671 - 1.33671i) q^{75} +(6.52343 + 4.90628i) q^{76} +(1.01025 + 1.01025i) q^{77} +(13.5391 - 0.953059i) q^{78} -4.21273 q^{79} +(1.93274 - 3.50207i) q^{80} +10.3917 q^{81} +(16.6678 - 1.17329i) q^{82} +(-6.16621 - 6.16621i) q^{83} +(-3.24680 + 4.31697i) q^{84} +(4.97751 - 4.97751i) q^{85} +(-11.8704 - 10.3091i) q^{86} -9.40877i q^{87} +(-2.37426 - 1.53717i) q^{88} +15.1986i q^{89} +(0.531887 - 0.612439i) q^{90} +(5.12895 - 5.12895i) q^{91} +(0.283122 + 2.00105i) q^{92} +(6.58552 + 6.58552i) q^{93} +(0.0947024 + 1.34534i) q^{94} -4.08126 q^{95} +(4.49685 - 9.70221i) q^{96} -16.1082 q^{97} +(-0.492430 - 6.99546i) q^{98} +(-0.405582 - 0.405582i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) \) 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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