LMFDB - Embedded newform 210.2.t.e.59.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [210,2,Mod(59,210)] 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("210.59"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(210, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.4
Root			$1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	210.59
Dual form			210.2.t.e.89.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.72286 + 0.178197i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.792893 - 2.09077i) q^{5} +(-0.707107 - 1.58114i) q^{6} +(1.41421 + 2.23607i) q^{7} +1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +(-2.20711 + 0.358719i) q^{10} +(-4.05781 - 2.34278i) q^{11} +(-1.01575 + 1.40294i) q^{12} +1.04456 q^{13} +(1.22938 - 2.34278i) q^{14} +(1.73861 - 3.46081i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.73861 + 1.58114i) q^{17} +(-0.936492 - 2.85008i) q^{18} +(-1.23861 + 0.715113i) q^{19} +(1.41421 + 1.73205i) q^{20} +(2.03803 + 4.10444i) q^{21} +4.68556i q^{22} +(-2.23861 - 3.87739i) q^{23} +(1.72286 + 0.178197i) q^{24} +(-3.74264 - 3.31552i) q^{25} +(-0.522278 - 0.904612i) q^{26} +(4.94975 + 1.58114i) q^{27} +(-2.64360 + 0.106711i) q^{28} +6.92163i q^{29} +(-3.86646 + 0.224724i) q^{30} +(-5.73861 - 3.31319i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.57357 - 4.75937i) q^{33} -3.16228i q^{34} +(5.79642 - 1.18383i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(2.30615 - 1.33146i) q^{37} +(1.23861 + 0.715113i) q^{38} +(1.79962 + 0.186137i) q^{39} +(0.792893 - 2.09077i) q^{40} -1.04456 q^{41} +(2.53553 - 3.81721i) q^{42} +6.92163i q^{43} +(4.05781 - 2.34278i) q^{44} +(3.61209 - 5.65268i) q^{45} +(-2.23861 + 3.87739i) q^{46} +(-9.71584 + 5.60944i) q^{47} +(-0.707107 - 1.58114i) q^{48} +(-3.00000 + 6.32456i) q^{49} +(-1.00000 + 4.89898i) q^{50} +(4.43649 + 3.21209i) q^{51} +(-0.522278 + 0.904612i) q^{52} +(-2.50000 + 4.33013i) q^{53} +(-1.10557 - 5.07718i) q^{54} +(-8.11562 + 6.62638i) q^{55} +(1.41421 + 2.23607i) q^{56} +(-2.26139 + 1.01132i) q^{57} +(5.99430 - 3.46081i) q^{58} +(-5.28720 + 9.15769i) q^{59} +(2.12785 + 3.23609i) q^{60} +(3.00000 - 1.73205i) q^{61} +6.62638i q^{62} +(2.77984 + 7.43455i) q^{63} +1.00000 q^{64} +(0.828222 - 2.18393i) q^{65} +(-0.834952 + 8.07256i) q^{66} +(12.3583 + 7.13505i) q^{67} +(-2.73861 + 1.58114i) q^{68} +(-3.16588 - 7.07912i) q^{69} +(-3.92344 - 4.42793i) q^{70} -6.92163i q^{71} +(2.93649 + 0.614017i) q^{72} +(1.75166 - 3.03397i) q^{73} +(-2.30615 - 1.33146i) q^{74} +(-5.85723 - 6.37909i) q^{75} -1.43023i q^{76} +(-0.500000 - 12.3867i) q^{77} +(-0.738613 - 1.65159i) q^{78} +(-5.73861 - 9.93957i) q^{79} +(-2.20711 + 0.358719i) q^{80} +(8.24597 + 3.60611i) q^{81} +(0.522278 + 0.904612i) q^{82} -4.06775i q^{83} +(-4.57357 - 0.287233i) q^{84} +(5.47723 - 4.47214i) q^{85} +(5.99430 - 3.46081i) q^{86} +(-1.23341 + 11.9250i) q^{87} +(-4.05781 - 2.34278i) q^{88} +(-2.45877 - 4.25871i) q^{89} +(-6.70141 - 0.301824i) q^{90} +(1.47723 + 2.33570i) q^{91} +4.47723 q^{92} +(-9.29642 - 6.73076i) q^{93} +(9.71584 + 5.60944i) q^{94} +(0.513050 + 3.15666i) q^{95} +(-1.01575 + 1.40294i) q^{96} -11.9886 q^{97} +(6.97723 - 0.564201i) q^{98} +(-10.4772 - 9.37112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 12 q^{5} + 8 q^{8} + 8 q^{9} - 12 q^{10} - 8 q^{15} - 4 q^{16} + 8 q^{18} + 12 q^{19} + 4 q^{21} + 4 q^{23} + 4 q^{25} + 4 q^{30} - 24 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{35}+ \cdots - 40 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 12 * q^5 + 8 * q^8 + 8 * q^9 - 12 * q^10 - 8 * q^15 - 4 * q^16 + 8 * q^18 + 12 * q^19 + 4 * q^21 + 4 * q^23 + 4 * q^25 + 4 * q^30 - 24 * q^31 - 4 * q^32 - 12 * q^33 - 8 * q^35 - 16 * q^36 - 12 * q^38 - 8 * q^39 + 12 * q^40 - 8 * q^42 + 24 * q^45 + 4 * q^46 - 12 * q^47 - 24 * q^49 - 8 * q^50 + 20 * q^51 - 20 * q^53 - 40 * q^57 + 4 * q^60 + 24 * q^61 + 20 * q^63 + 8 * q^64 + 16 * q^65 + 12 * q^66 - 8 * q^70 + 8 * q^72 - 24 * q^75 - 4 * q^77 + 16 * q^78 - 24 * q^79 - 12 * q^80 + 4 * q^81 + 4 * q^84 + 12 * q^87 - 32 * q^91 - 8 * q^92 - 20 * q^93 + 12 * q^94 + 12 * q^95 + 12 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.72286	+	0.178197i	0.994694	+	0.102882i
$3$	1.72286	+	0.178197i	0.994694	+	0.102882i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.792893	−	2.09077i	0.354593	−	0.935021i
$5$	0.792893	−	2.09077i	0.354593	−	0.935021i
$6$	−0.707107	−	1.58114i	−0.288675	−	0.645497i
$7$	1.41421	+	2.23607i	0.534522	+	0.845154i
$7$	1.41421	+	2.23607i	0.534522	+	0.845154i
$8$	1.00000			0.353553
$9$	2.93649	+	0.614017i	0.978831	+	0.204672i
$10$	−2.20711	+	0.358719i	−0.697948	+	0.113437i
$11$	−4.05781	−	2.34278i	−1.22348	−	0.706374i	−0.257819	−	0.966193i	$-0.583004\pi$
$11$	−4.05781	−	2.34278i	−1.22348	−	0.706374i	−0.965657	+	0.259819i	$0.916337\pi$
$12$	−1.01575	+	1.40294i	−0.293223	+	0.404994i
$13$	1.04456			0.289708			0.144854	−	0.989453i	$-0.453729\pi$
$13$	1.04456			0.289708			0.144854	+	0.989453i	$0.453729\pi$
$14$	1.22938	−	2.34278i	0.328567	−	0.626134i
$15$	1.73861	−	3.46081i	0.448908	−	0.893578i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.73861	+	1.58114i	0.664211	+	0.383482i	0.793880	−	0.608075i	$-0.208058\pi$
$17$	2.73861	+	1.58114i	0.664211	+	0.383482i	−0.129668	+	0.991557i	$0.541391\pi$
$18$	−0.936492	−	2.85008i	−0.220733	−	0.671771i
$19$	−1.23861	+	0.715113i	−0.284157	+	0.164058i	−0.635304	−	0.772262i	$-0.719125\pi$
$19$	−1.23861	+	0.715113i	−0.284157	+	0.164058i	0.351147	+	0.936320i	$0.385792\pi$
$20$	1.41421	+	1.73205i	0.316228	+	0.387298i
$21$	2.03803	+	4.10444i	0.444735	+	0.895662i
$22$			4.68556i			0.998964i
$23$	−2.23861	−	3.87739i	−0.466783	−	0.808492i	0.532497	−	0.846432i	$-0.321254\pi$
$23$	−2.23861	−	3.87739i	−0.466783	−	0.808492i	−0.999280	+	0.0379400i	$0.987920\pi$
$24$	1.72286	+	0.178197i	0.351677	+	0.0363743i
$25$	−3.74264	−	3.31552i	−0.748528	−	0.663103i
$26$	−0.522278	−	0.904612i	−0.102427	−	0.177409i
$27$	4.94975	+	1.58114i	0.952579	+	0.304290i
$28$	−2.64360	+	0.106711i	−0.499593	+	0.0201665i
$29$			6.92163i			1.28531i	0.766154	+	0.642657i	$0.222168\pi$
$29$			6.92163i			1.28531i	−0.766154	+	0.642657i	$0.777832\pi$
$30$	−3.86646	+	0.224724i	−0.705915	+	0.0410287i
$31$	−5.73861	−	3.31319i	−1.03069	−	0.595066i	−0.113504	−	0.993537i	$-0.536208\pi$
$31$	−5.73861	−	3.31319i	−1.03069	−	0.595066i	−0.917181	+	0.398471i	$0.869541\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−6.57357	−	4.75937i	−1.14431	−	0.828500i
$34$		−	3.16228i		−	0.542326i
$35$	5.79642	−	1.18383i	0.979775	−	0.200104i
$36$	−2.00000	+	2.23607i	−0.333333	+	0.372678i
$37$	2.30615	−	1.33146i	0.379129	−	0.218890i	−0.298310	−	0.954469i	$-0.596423\pi$
$37$	2.30615	−	1.33146i	0.379129	−	0.218890i	0.677439	+	0.735579i	$0.263090\pi$
$38$	1.23861	+	0.715113i	0.200930	+	0.116007i
$39$	1.79962	+	0.186137i	0.288170	+	0.0298057i
$40$	0.792893	−	2.09077i	0.125367	−	0.330580i
$41$	−1.04456			−0.163132			−0.0815661	−	0.996668i	$-0.525992\pi$
$41$	−1.04456			−0.163132			−0.0815661	+	0.996668i	$0.525992\pi$
$42$	2.53553	−	3.81721i	0.391241	−	0.589008i
$43$			6.92163i			1.05554i	0.849388	+	0.527769i	$0.176971\pi$
$43$			6.92163i			1.05554i	−0.849388	+	0.527769i	$0.823029\pi$
$44$	4.05781	−	2.34278i	0.611738	−	0.353187i
$45$	3.61209	−	5.65268i	0.538459	−	0.842652i
$46$	−2.23861	+	3.87739i	−0.330065	+	0.571690i
$47$	−9.71584	+	5.60944i	−1.41720	+	0.818221i	−0.996052	−	0.0887705i	$-0.971706\pi$
$47$	−9.71584	+	5.60944i	−1.41720	+	0.818221i	−0.421149	+	0.906992i	$0.638373\pi$
$48$	−0.707107	−	1.58114i	−0.102062	−	0.228218i
$49$	−3.00000	+	6.32456i	−0.428571	+	0.903508i
$50$	−1.00000	+	4.89898i	−0.141421	+	0.692820i
$51$	4.43649	+	3.21209i	0.621233	+	0.449783i
$52$	−0.522278	+	0.904612i	−0.0724269	+	0.125447i
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	−0.985062	−	0.172200i	$-0.944912\pi$
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	0.641661	+	0.766989i	$0.278246\pi$
$54$	−1.10557	−	5.07718i	−0.150449	−	0.690916i
$55$	−8.11562	+	6.62638i	−1.09431	+	0.893501i
$56$	1.41421	+	2.23607i	0.188982	+	0.298807i
$57$	−2.26139	+	1.01132i	−0.299528	+	0.133953i
$58$	5.99430	−	3.46081i	0.787091	−	0.454427i
$59$	−5.28720	+	9.15769i	−0.688334	+	1.19223i	0.284042	+	0.958812i	$0.408324\pi$
$59$	−5.28720	+	9.15769i	−0.688334	+	1.19223i	−0.972376	+	0.233418i	$0.925009\pi$
$60$	2.12785	+	3.23609i	0.274704	+	0.417777i
$61$	3.00000	−	1.73205i	0.384111	−	0.221766i	−0.295495	−	0.955344i	$-0.595484\pi$
$61$	3.00000	−	1.73205i	0.384111	−	0.221766i	0.679605	+	0.733578i	$0.262151\pi$
$62$			6.62638i			0.841551i
$63$	2.77984	+	7.43455i	0.350227	+	0.936665i
$64$	1.00000			0.125000
$65$	0.828222	−	2.18393i	0.102728	−	0.270883i
$66$	−0.834952	+	8.07256i	−0.102776	+	0.993663i
$67$	12.3583	+	7.13505i	1.50980	+	0.871685i	0.999935	+	0.0114319i	$0.00363898\pi$
$67$	12.3583	+	7.13505i	1.50980	+	0.871685i	0.509868	+	0.860253i	$0.329694\pi$
$68$	−2.73861	+	1.58114i	−0.332106	+	0.191741i
$69$	−3.16588	−	7.07912i	−0.381127	−	0.852225i
$70$	−3.92344	−	4.42793i	−0.468941	−	0.529239i
$71$		−	6.92163i		−	0.821446i	−0.911760	−	0.410723i	$-0.865276\pi$
$71$		−	6.92163i		−	0.821446i	0.911760	−	0.410723i	$-0.134724\pi$
$72$	2.93649	+	0.614017i	0.346069	+	0.0723626i
$73$	1.75166	−	3.03397i	0.205017	−	0.355099i	−0.745121	−	0.666929i	$-0.767608\pi$
$73$	1.75166	−	3.03397i	0.205017	−	0.355099i	0.950138	+	0.311830i	$0.100942\pi$
$74$	−2.30615	−	1.33146i	−0.268084	−	0.154779i
$75$	−5.85723	−	6.37909i	−0.676335	−	0.736594i
$76$		−	1.43023i		−	0.164058i
$77$	−0.500000	−	12.3867i	−0.0569803	−	1.41160i
$78$	−0.738613	−	1.65159i	−0.0836314	−	0.187006i
$79$	−5.73861	−	9.93957i	−0.645644	−	1.11829i	−0.984152	−	0.177325i	$-0.943256\pi$
$79$	−5.73861	−	9.93957i	−0.645644	−	1.11829i	0.338508	−	0.940964i	$-0.390078\pi$
$80$	−2.20711	+	0.358719i	−0.246762	+	0.0401061i
$81$	8.24597	+	3.60611i	0.916219	+	0.400679i
$82$	0.522278	+	0.904612i	0.0576760	+	0.0998977i
$83$		−	4.06775i		−	0.446494i	−0.974762	−	0.223247i	$-0.928334\pi$
$83$		−	4.06775i		−	0.446494i	0.974762	−	0.223247i	$-0.0716656\pi$
$84$	−4.57357	−	0.287233i	−0.499017	−	0.0313397i
$85$	5.47723	−	4.47214i	0.594089	−	0.485071i
$86$	5.99430	−	3.46081i	0.646382	−	0.373189i
$87$	−1.23341	+	11.9250i	−0.132236	+	1.27849i
$88$	−4.05781	−	2.34278i	−0.432564	−	0.249741i
$89$	−2.45877	−	4.25871i	−0.260629	−	0.451423i	0.705780	−	0.708431i	$-0.250597\pi$
$89$	−2.45877	−	4.25871i	−0.260629	−	0.451423i	−0.966409	+	0.257008i	$0.917263\pi$
$90$	−6.70141	−	0.301824i	−0.706391	−	0.0318150i
$91$	1.47723	+	2.33570i	0.154855	+	0.244848i
$92$	4.47723			0.466783
$93$	−9.29642	−	6.73076i	−0.963994	−	0.697948i
$94$	9.71584	+	5.60944i	1.00211	+	0.578570i
$95$	0.513050	+	3.15666i	0.0526378	+	0.323867i
$96$	−1.01575	+	1.40294i	−0.103670	+	0.143187i
$97$	−11.9886			−1.21726			−0.608629	−	0.793455i	$-0.708280\pi$
$97$	−11.9886			−1.21726			−0.608629	+	0.793455i	$0.708280\pi$
$98$	6.97723	−	0.564201i	0.704806	−	0.0569930i
$99$	−10.4772	−	9.37112i	−1.05300	−	0.941833i
$100$	4.74264	−	1.58346i	0.474264	−	0.158346i
$101$	5.65685	−	9.79796i	0.562878	−	0.974933i	−0.434366	−	0.900737i	$-0.643027\pi$
$101$	5.65685	−	9.79796i	0.562878	−	0.974933i	0.997244	−	0.0741967i	$-0.0236393\pi$
$102$	0.563508	−	5.44816i	0.0557956	−	0.539448i
$103$	−2.45877	−	4.25871i	−0.242270	−	0.419624i	0.719091	−	0.694916i	$-0.244559\pi$
$103$	−2.45877	−	4.25871i	−0.242270	−	0.419624i	−0.961360	+	0.275293i	$0.911225\pi$
$104$	1.04456			0.102427
$105$	10.1974	−	1.00667i	0.995163	−	0.0982411i
$106$	5.00000			0.485643
$107$	2.73861	+	4.74342i	0.264752	+	0.458563i	0.967499	−	0.252877i	$-0.0813767\pi$
$107$	2.73861	+	4.74342i	0.264752	+	0.458563i	−0.702747	+	0.711440i	$0.748043\pi$
$108$	−3.84418	+	3.49604i	−0.369906	+	0.336406i
$109$	10.2158	−	17.6944i	0.978500	−	1.69481i	0.310634	−	0.950529i	$-0.399459\pi$
$109$	10.2158	−	17.6944i	0.978500	−	1.69481i	0.667866	−	0.744282i	$-0.267208\pi$
$110$	9.79642	+	3.71515i	0.934052	+	0.354225i
$111$	4.21043	−	1.88296i	0.399637	−	0.178723i
$112$	1.22938	−	2.34278i	0.116166	−	0.221372i
$113$	17.4772			1.64412			0.822060	−	0.569402i	$-0.192825\pi$
$113$	17.4772			1.64412			0.822060	+	0.569402i	$0.192825\pi$
$114$	2.00653	+	1.45276i	0.187928	+	0.136063i
$115$	−9.88171	+	1.60607i	−0.921475	+	0.149767i
$116$	−5.99430	−	3.46081i	−0.556557	−	0.321328i
$117$	3.06733	+	0.641375i	0.283575	+	0.0592951i
$118$	10.5744			0.973452
$119$	0.337449	+	8.35979i	0.0309339	+	0.766341i
$120$	1.73861	−	3.46081i	0.158713	−	0.315928i
$121$	5.47723	+	9.48683i	0.497930	+	0.862439i
$122$	−3.00000	−	1.73205i	−0.271607	−	0.156813i
$123$	−1.79962	−	0.186137i	−0.162267	−	0.0167834i
$124$	5.73861	−	3.31319i	0.515343	−	0.297533i
$125$	−9.89949	+	5.19615i	−0.885438	+	0.464758i
$126$	5.04858	−	6.12469i	0.449764	−	0.545631i
$127$		−	8.73085i		−	0.774738i	−0.921925	−	0.387369i	$-0.873384\pi$
$127$		−	8.73085i		−	0.774738i	0.921925	−	0.387369i	$-0.126616\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.23341	+	11.9250i	−0.108596	+	1.04994i
$130$	−2.30545	+	0.374703i	−0.202201	+	0.0328636i
$131$	−6.88624	−	11.9273i	−0.601654	−	1.04209i	−0.992571	−	0.121669i	$-0.961175\pi$
$131$	−6.88624	−	11.9273i	−0.601654	−	1.04209i	0.390917	−	0.920426i	$-0.372158\pi$
$132$	7.40852	−	3.31319i	0.644829	−	0.288376i
$133$	−3.35071	−	1.75830i	−0.290543	−	0.152464i
$134$		−	14.2701i		−	1.23275i
$135$	7.23042	−	9.09511i	0.622295	−	0.782782i
$136$	2.73861	+	1.58114i	0.234834	+	0.135582i
$137$	1.73861	−	3.01137i	0.148540	−	0.257278i	−0.782148	−	0.623092i	$-0.785876\pi$
$137$	1.73861	−	3.01137i	0.148540	−	0.257278i	0.930688	+	0.365814i	$0.119209\pi$
$138$	−4.54776	+	6.28129i	−0.387131	+	0.534699i
$139$			20.1810i			1.71173i	0.517202	+	0.855863i	$0.326974\pi$
$139$			20.1810i			1.71173i	−0.517202	+	0.855863i	$0.673026\pi$
$140$	−1.87298	+	5.61177i	−0.158296	+	0.474281i
$141$	−17.7386	+	7.93295i	−1.49386	+	0.668075i
$142$	−5.99430	+	3.46081i	−0.503031	+	0.290425i
$143$	−4.23861	−	2.44716i	−0.354451	−	0.204642i
$144$	−0.936492	−	2.85008i	−0.0780410	−	0.237507i
$145$	14.4715	+	5.48811i	1.20180	+	0.455763i
$146$	−3.50333			−0.289937
$147$	−6.29560	+	10.3617i	−0.519252	+	0.854621i
$148$			2.66291i			0.218890i
$149$	−2.12132	+	1.22474i	−0.173785	+	0.100335i	−0.584370	−	0.811488i	$-0.698658\pi$
$149$	−2.12132	+	1.22474i	−0.173785	+	0.100335i	0.410584	+	0.911823i	$0.365325\pi$
$150$	−2.59584	+	8.26206i	−0.211950	+	0.674594i
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	−0.822464	−	0.568818i	$-0.807401\pi$
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	0.903842	+	0.427865i	$0.140734\pi$
$152$	−1.23861	+	0.715113i	−0.100465	+	0.0580034i
$153$	7.07107	+	6.32456i	0.571662	+	0.511310i
$154$	−10.4772	+	6.62638i	−0.844279	+	0.533969i
$155$	−11.4772	+	9.37112i	−0.921873	+	0.752706i
$156$	−1.06101	+	1.46545i	−0.0849489	+	0.117330i
$157$	7.22369	−	12.5118i	0.576513	−	0.998550i	−0.419362	−	0.907819i	$-0.637746\pi$
$157$	7.22369	−	12.5118i	0.576513	−	0.998550i	0.995875	−	0.0907311i	$-0.0289204\pi$
$158$	−5.73861	+	9.93957i	−0.456540	+	0.790750i
$159$	−5.07877	+	7.01471i	−0.402772	+	0.556303i
$160$	1.41421	+	1.73205i	0.111803	+	0.136931i
$161$	5.50423	−	10.4891i	0.433794	−	0.826661i
$162$	−1.00000	−	8.94427i	−0.0785674	−	0.702728i
$163$	12.7279	−	7.34847i	0.996928	−	0.575577i	0.0895899	−	0.995979i	$-0.471444\pi$
$163$	12.7279	−	7.34847i	0.996928	−	0.575577i	0.907338	+	0.420402i	$0.138111\pi$
$164$	0.522278	−	0.904612i	0.0407831	−	0.0706383i
$165$	−15.1629	+	9.97014i	−1.18043	+	0.776175i
$166$	−3.52277	+	2.03387i	−0.273420	+	0.157859i
$167$		−	4.29068i		−	0.332023i	−0.986124	−	0.166011i	$-0.946911\pi$
$167$		−	4.29068i		−	0.332023i	0.986124	−	0.166011i	$-0.0530889\pi$
$168$	2.03803	+	4.10444i	0.157238	+	0.316664i
$169$	−11.9089			−0.916069
$170$	−6.61160	−	2.50735i	−0.507086	−	0.192305i
$171$	−4.07627	+	1.33940i	−0.311720	+	0.102426i
$172$	−5.99430	−	3.46081i	−0.457061	−	0.263885i
$173$	0.977226	−	0.564201i	0.0742971	−	0.0428954i	−0.462391	−	0.886676i	$-0.653008\pi$
$173$	0.977226	−	0.564201i	0.0742971	−	0.0428954i	0.536688	+	0.843781i	$0.319675\pi$
$174$	10.9441	−	4.89433i	0.829666	−	0.371038i
$175$	2.12082	−	13.0576i	0.160319	−	0.987065i
$176$			4.68556i			0.353187i
$177$	−10.7410	+	14.8353i	−0.807341	+	1.11509i
$178$	−2.45877	+	4.25871i	−0.184293	+	0.319204i
$179$	16.7857	+	9.69125i	1.25462	+	0.724358i	0.972024	−	0.234880i	$-0.0754697\pi$
$179$	16.7857	+	9.69125i	1.25462	+	0.724358i	0.282600	+	0.959238i	$0.408803\pi$
$180$	3.08932	+	5.95450i	0.230264	+	0.443823i
$181$			3.16228i			0.235050i	0.993070	+	0.117525i	$0.0374961\pi$
$181$			3.16228i			0.235050i	−0.993070	+	0.117525i	$0.962504\pi$
$182$	1.28416	−	2.44716i	0.0951884	−	0.181396i
$183$	5.47723	−	2.44949i	0.404888	−	0.181071i
$184$	−2.23861	−	3.87739i	−0.165033	−	0.285845i
$185$	−0.955238	−	5.87733i	−0.0702305	−	0.432110i
$186$	−1.18080	+	11.4163i	−0.0865805	+	0.837085i
$187$	−7.40852	−	12.8319i	−0.541764	−	0.938364i
$188$		−	11.2189i		−	0.818221i
$189$	3.46447	+	13.3040i	0.252003	+	0.967726i
$190$	2.47723	−	2.02265i	0.179717	−	0.146738i
$191$	−14.1099	+	8.14637i	−1.02096	+	0.589451i	−0.914381	−	0.404854i	$-0.867322\pi$
$191$	−14.1099	+	8.14637i	−1.02096	+	0.589451i	−0.106577	+	0.994304i	$0.533989\pi$
$192$	1.72286	+	0.178197i	0.124337	+	0.0128603i
$193$	6.36396	+	3.67423i	0.458088	+	0.264477i	0.711240	−	0.702949i	$-0.248134\pi$
$193$	6.36396	+	3.67423i	0.458088	+	0.264477i	−0.253152	+	0.967427i	$0.581467\pi$
$194$	5.99430	+	10.3824i	0.430366	+	0.745416i
$195$	1.81608	−	3.61501i	0.130052	−	0.258877i
$196$	−3.97723	−	5.76035i	−0.284088	−	0.411454i
$197$	9.00000			0.641223			0.320612	−	0.947211i	$-0.396112\pi$
$197$	9.00000			0.641223			0.320612	+	0.947211i	$0.396112\pi$
$198$	−2.87701	+	13.7591i	−0.204460	+	0.977817i
$199$	13.4317	+	7.75478i	0.952146	+	0.549722i	0.893747	−	0.448571i	$-0.148067\pi$
$199$	13.4317	+	7.75478i	0.952146	+	0.549722i	0.0583993	+	0.998293i	$0.481400\pi$
$200$	−3.74264	−	3.31552i	−0.264645	−	0.234442i
$201$	20.0201	+	14.4949i	1.41211	+	1.02239i
$202$	−11.3137			−0.796030
$203$	−15.4772	+	9.78866i	−1.08629	+	0.687029i
$204$	−5.00000	+	2.23607i	−0.350070	+	0.156556i
$205$	−0.828222	+	2.18393i	−0.0578455	+	0.152532i
$206$	−2.45877	+	4.25871i	−0.171311	+	0.296719i
$207$	−4.19288	−	12.7605i	−0.291426	−	0.886914i
$208$	−0.522278	−	0.904612i	−0.0362135	−	0.0627236i
$209$	6.70141			0.463546
$210$	−5.97049	−	8.32786i	−0.412003	−	0.574677i
$211$	24.4772			1.68508			0.842541	−	0.538632i	$-0.181059\pi$
$211$	24.4772			1.68508			0.842541	+	0.538632i	$0.181059\pi$
$212$	−2.50000	−	4.33013i	−0.171701	−	0.297394i
$213$	1.23341	−	11.9250i	0.0845121	−	0.817087i
$214$	2.73861	−	4.74342i	0.187208	−	0.324253i
$215$	14.4715	+	5.48811i	0.986950	+	0.374286i
$216$	4.94975	+	1.58114i	0.336788	+	0.107583i
$217$	−0.707107	−	17.5175i	−0.0480015	−	1.18916i
$218$	−20.4317			−1.38381
$219$	3.55851	−	4.91496i	0.240462	−	0.332122i
$220$	−1.68080	−	10.3415i	−0.113320	−	0.697226i
$221$	2.86064	+	1.65159i	0.192427	+	0.111098i
$222$	−3.73591	−	2.70486i	−0.250738	−	0.181538i
$223$	−21.8881			−1.46574			−0.732868	−	0.680371i	$-0.761819\pi$
$223$	−21.8881			−1.46574			−0.732868	+	0.680371i	$0.761819\pi$
$224$	−2.64360	+	0.106711i	−0.176633	+	0.00712992i
$225$	−8.95445	−	12.0340i	−0.596963	−	0.802268i
$226$	−8.73861	−	15.1357i	−0.581284	−	1.00681i
$227$	9.00000	+	5.19615i	0.597351	+	0.344881i	0.767999	−	0.640451i	$-0.221253\pi$
$227$	9.00000	+	5.19615i	0.597351	+	0.344881i	−0.170648	+	0.985332i	$0.554586\pi$
$228$	0.254862	−	2.46408i	0.0168787	−	0.163188i
$229$	−11.7386	+	6.77729i	−0.775709	+	0.447856i	−0.834908	−	0.550390i	$-0.814479\pi$
$229$	−11.7386	+	6.77729i	−0.775709	+	0.447856i	0.0591982	+	0.998246i	$0.481146\pi$
$230$	6.33175	+	7.75478i	0.417503	+	0.511335i
$231$	1.34585	−	21.4297i	0.0885503	−	1.40997i
$232$			6.92163i			0.454427i
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	0.924072	−	0.382219i	$-0.124840\pi$
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	−0.793047	+	0.609160i	$0.791507\pi$
$234$	−0.978218	−	2.97707i	−0.0639481	−	0.194617i
$235$	4.02443	+	24.7613i	0.262525	+	1.61525i
$236$	−5.28720	−	9.15769i	−0.344167	−	0.596115i
$237$	−8.11562	−	18.1471i	−0.527166	−	1.17878i
$238$	7.07107	−	4.47214i	0.458349	−	0.289886i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−3.86646	+	0.224724i	−0.249579	+	0.0145058i
$241$	−18.4545	−	10.6547i	−1.18876	−	0.686328i	−0.230732	−	0.973017i	$-0.574112\pi$
$241$	−18.4545	−	10.6547i	−1.18876	−	0.686328i	−0.958024	+	0.286689i	$0.907445\pi$
$242$	5.47723	−	9.48683i	0.352089	−	0.609837i
$243$	13.5640	+	7.68223i	0.870134	+	0.492815i
$244$			3.46410i			0.221766i
$245$	10.8445	+	11.2870i	0.692830	+	0.721100i
$246$	0.738613	+	1.65159i	0.0470922	+	0.105301i
$247$	−1.29380	+	0.746976i	−0.0823226	+	0.0475290i
$248$	−5.73861	−	3.31319i	−0.364402	−	0.210388i
$249$	0.724861	−	7.00816i	0.0459362	−	0.444124i
$250$	9.44975	+	5.97514i	0.597655	+	0.377901i
$251$	−8.85494			−0.558919			−0.279459	−	0.960158i	$-0.590155\pi$
$251$	−8.85494			−0.558919			−0.279459	+	0.960158i	$0.590155\pi$
$252$	−7.82843	−	1.30986i	−0.493145	−	0.0825133i
$253$			20.9783i			1.31889i
$254$	−7.56114	+	4.36543i	−0.474428	+	0.273911i
$255$	10.2334	−	6.72884i	0.640841	−	0.421376i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.52277	+	5.49798i	−0.594014	+	0.342954i	−0.766683	−	0.642026i	$-0.778094\pi$
$257$	−9.52277	+	5.49798i	−0.594014	+	0.342954i	0.172669	+	0.984980i	$0.444761\pi$
$258$	10.9441	−	4.89433i	0.681347	−	0.304708i
$259$	6.23861	+	3.27374i	0.387649	+	0.203421i
$260$	1.47723	+	1.80922i	0.0916136	+	0.112203i
$261$	−4.24999	+	20.3253i	−0.263068	+	1.25810i
$262$	−6.88624	+	11.9273i	−0.425433	+	0.736872i
$263$	1.00000	−	1.73205i	0.0616626	−	0.106803i	−0.833546	−	0.552450i	$-0.813693\pi$
$263$	1.00000	−	1.73205i	0.0616626	−	0.106803i	0.895209	+	0.445647i	$0.147026\pi$
$264$	−6.57357	−	4.75937i	−0.404575	−	0.292919i
$265$	7.07107	+	8.66025i	0.434372	+	0.531995i
$266$	0.152621	+	3.78095i	0.00935778	+	0.231825i
$267$	−3.47723	−	7.77531i	−0.212803	−	0.475841i
$268$	−12.3583	+	7.13505i	−0.754901	+	0.435842i
$269$	8.79052	−	15.2256i	0.535968	−	0.928323i	−0.463148	−	0.886281i	$-0.653280\pi$
$269$	8.79052	−	15.2256i	0.535968	−	0.928323i	0.999116	−	0.0420423i	$-0.0133864\pi$
$270$	−11.4918	−	1.71417i	−0.699369	−	0.104321i
$271$	−5.47723	+	3.16228i	−0.332718	+	0.192095i	−0.657047	−	0.753850i	$-0.728195\pi$
$271$	−5.47723	+	3.16228i	−0.332718	+	0.192095i	0.324329	+	0.945944i	$0.394861\pi$
$272$		−	3.16228i		−	0.191741i
$273$	2.12884	+	4.28732i	0.128843	+	0.259480i
$274$	−3.47723			−0.210067
$275$	7.41941	+	22.2219i	0.447407	+	1.34003i
$276$	7.71363	+	0.797828i	0.464306	+	0.0480236i
$277$	−8.48528	−	4.89898i	−0.509831	−	0.294351i	0.222933	−	0.974834i	$-0.428437\pi$
$277$	−8.48528	−	4.89898i	−0.509831	−	0.294351i	−0.732764	+	0.680483i	$0.761770\pi$
$278$	17.4772	−	10.0905i	1.04821	−	0.605187i
$279$	−14.8170	−	13.2528i	−0.887073	−	0.793422i
$280$	5.79642	−	1.18383i	0.346403	−	0.0707475i
$281$		−	1.80922i		−	0.107929i	−0.998543	−	0.0539646i	$-0.982814\pi$
$281$		−	1.80922i		−	0.107929i	0.998543	−	0.0539646i	$-0.0171858\pi$
$282$	15.7394	+	11.3956i	0.937270	+	0.678599i
$283$	4.61230	−	7.98873i	0.274173	−	0.474881i	−0.695753	−	0.718281i	$-0.744929\pi$
$283$	4.61230	−	7.98873i	0.274173	−	0.474881i	0.969926	+	0.243400i	$0.0782627\pi$
$284$	5.99430	+	3.46081i	0.355696	+	0.205361i
$285$	0.321406	+	5.52991i	0.0190384	+	0.327564i
$286$			4.89433i			0.289408i
$287$	−1.47723	−	2.33570i	−0.0871979	−	0.137872i
$288$	−2.00000	+	2.23607i	−0.117851	+	0.131762i
$289$	−3.50000	−	6.06218i	−0.205882	−	0.356599i
$290$	−2.48292	−	15.2768i	−0.145802	−	0.897083i
$291$	−20.6547	−	2.13633i	−1.21080	−	0.125234i
$292$	1.75166	+	3.03397i	0.102508	+	0.177550i
$293$			8.05661i			0.470672i	0.971914	+	0.235336i	$0.0756190\pi$
$293$			8.05661i			0.470672i	−0.971914	+	0.235336i	$0.924381\pi$
$294$	12.1213	+	0.271281i	0.706930	+	0.0158214i
$295$	14.9545	+	18.3154i	0.870682	+	1.06636i
$296$	2.30615	−	1.33146i	0.134042	−	0.0773893i
$297$	−16.3809	−	18.0121i	−0.950515	−	1.04517i
$298$	2.12132	+	1.22474i	0.122885	+	0.0709476i
$299$	−2.33836	−	4.05015i	−0.135231	−	0.234226i
$300$	8.45307	−	1.88296i	0.488038	−	0.108713i
$301$	−15.4772	+	9.78866i	−0.892092	+	0.564209i
$302$	−2.00000			−0.115087
$303$	11.4919	−	15.8725i	0.660194	−	0.911850i
$304$	1.23861	+	0.715113i	0.0710393	+	0.0410146i
$305$	−1.24264	−	7.64564i	−0.0711534	−	0.437788i
$306$	1.94169	−	9.28600i	0.110999	−	0.530845i
$307$	11.9886			0.684226			0.342113	−	0.939659i	$-0.388857\pi$
$307$	11.9886			0.684226			0.342113	+	0.939659i	$0.388857\pi$
$308$	10.9772	+	5.76035i	0.625485	+	0.328227i
$309$	−3.47723	−	7.77531i	−0.197812	−	0.442322i
$310$	13.8542	+	5.25401i	0.786868	+	0.298408i
$311$	8.79052	−	15.2256i	0.498465	−	0.863366i	−0.501534	−	0.865138i	$-0.667231\pi$
$311$	8.79052	−	15.2256i	0.498465	−	0.863366i	0.999998	+	0.00177176i	$0.000563970\pi$
$312$	1.79962	+	0.186137i	0.101884	+	0.0105379i
$313$	11.6190	+	20.1246i	0.656742	+	1.13751i	0.981454	+	0.191697i	$0.0613992\pi$
$313$	11.6190	+	20.1246i	0.656742	+	1.13751i	−0.324712	+	0.945813i	$0.605267\pi$
$314$	−14.4474			−0.815313
$315$	17.7480	+	0.0827879i	0.999989	+	0.00466457i
$316$	11.4772			0.645644
$317$	4.95445	+	8.58136i	0.278270	+	0.481977i	0.970955	−	0.239263i	$-0.0769058\pi$
$317$	4.95445	+	8.58136i	0.278270	+	0.481977i	−0.692685	+	0.721240i	$0.743572\pi$
$318$	8.61430	+	0.890985i	0.483066	+	0.0499640i
$319$	16.2158	−	28.0867i	0.907913	−	1.57255i
$320$	0.792893	−	2.09077i	0.0443241	−	0.116878i
$321$	3.87298	+	8.66025i	0.216169	+	0.483368i
$322$	−11.8360	+	0.477769i	−0.659594	+	0.0266250i
$323$	−4.52277			−0.251654
$324$	−7.24597	+	5.33816i	−0.402554	+	0.296565i
$325$	−3.90940	−	3.46324i	−0.216854	−	0.192106i
$326$	−12.7279	−	7.34847i	−0.704934	−	0.406994i
$327$	20.7535	−	28.6645i	1.14767	−	1.58515i
$328$	−1.04456			−0.0576760
$329$	−26.2834	−	13.7923i	−1.44905	−	0.760396i
$330$	16.2158	+	8.14637i	0.892653	+	0.448443i
$331$	−10.7158	−	18.5604i	−0.588996	−	1.02017i	−0.994364	−	0.106017i	$-0.966190\pi$
$331$	−10.7158	−	18.5604i	−0.588996	−	1.02017i	0.405369	−	0.914153i	$-0.367143\pi$
$332$	3.52277	+	2.03387i	0.193337	+	0.111623i
$333$	7.58952	−	2.49379i	0.415903	−	0.136659i
$334$	−3.71584	+	2.14534i	−0.203322	+	0.117388i
$335$	24.7165	−	20.1810i	1.35041	−	1.10260i
$336$	2.53553	−	3.81721i	0.138325	−	0.208246i
$337$			17.1464i			0.934025i	0.884251	+	0.467013i	$0.154670\pi$
$337$			17.1464i			0.934025i	−0.884251	+	0.467013i	$0.845330\pi$
$338$	5.95445	+	10.3134i	0.323879	+	0.560976i
$339$	30.1108	+	3.11439i	1.63539	+	0.169150i
$340$	1.13437	+	6.97948i	0.0615199	+	0.378516i
$341$	15.5241	+	26.8886i	0.840679	+	1.45610i
$342$	3.19808	+	2.86045i	0.172933	+	0.154676i
$343$	−18.3848	+	2.23607i	−0.992685	+	0.120736i
$344$			6.92163i			0.373189i
$345$	−17.3110	+	1.00614i	−0.931993	+	0.0541687i
$346$	−0.977226	−	0.564201i	−0.0525360	−	0.0303317i
$347$	8.73861	−	15.1357i	0.469113	−	0.812528i	−0.530263	−	0.847833i	$-0.677907\pi$
$347$	8.73861	−	15.1357i	0.469113	−	0.812528i	0.999377	+	0.0353049i	$0.0112402\pi$
$348$	−9.71064	−	7.03066i	−0.520545	−	0.376883i
$349$		−	11.7436i		−	0.628623i	−0.949320	−	0.314311i	$-0.898226\pi$
$349$		−	11.7436i		−	0.628623i	0.949320	−	0.314311i	$-0.101774\pi$
$350$	−12.3687	+	4.69214i	−0.661133	+	0.250805i
$351$	5.17029	+	1.65159i	0.275970	+	0.0881553i
$352$	4.05781	−	2.34278i	0.216282	−	0.124871i
$353$	0.522774	+	0.301824i	0.0278245	+	0.0160645i	0.513848	−	0.857881i	$-0.328220\pi$
$353$	0.522774	+	0.301824i	0.0278245	+	0.0160645i	−0.486023	+	0.873946i	$0.661553\pi$
$354$	18.2182	+	1.88433i	0.968286	+	0.100151i
$355$	−14.4715	−	5.48811i	−0.768069	−	0.291279i
$356$	4.91754			0.260629
$357$	−0.908312	+	14.4629i	−0.0480730	+	0.765457i
$358$		−	19.3825i		−	1.02440i
$359$	9.86729	−	5.69688i	0.520775	−	0.300670i	−0.216476	−	0.976288i	$-0.569456\pi$
$359$	9.86729	−	5.69688i	0.520775	−	0.300670i	0.737252	+	0.675618i	$0.236123\pi$
$360$	3.61209	−	5.65268i	0.190374	−	0.297922i
$361$	−8.47723	+	14.6830i	−0.446170	+	0.772789i
$362$	2.73861	−	1.58114i	0.143938	−	0.0831028i
$363$	7.74597	+	17.3205i	0.406558	+	0.909091i
$364$	−2.76139	+	0.111466i	−0.144736	+	0.00584238i
$365$	−4.95445	−	6.06794i	−0.259328	−	0.317610i
$366$	−4.85993	−	3.51867i	−0.254033	−	0.183924i
$367$	0.184829	−	0.320133i	0.00964798	−	0.0167108i	−0.861161	−	0.508332i	$-0.830262\pi$
$367$	0.184829	−	0.320133i	0.00964798	−	0.0167108i	0.870809	+	0.491621i	$0.163596\pi$
$368$	−2.23861	+	3.87739i	−0.116696	+	0.202123i
$369$	−3.06733	−	0.641375i	−0.159679	−	0.0333887i
$370$	−4.61230	+	3.76593i	−0.239782	+	0.195781i
$371$	−13.2180	+	0.533554i	−0.686244	+	0.0277008i
$372$	10.4772	−	4.68556i	0.543219	−	0.242935i
$373$	−20.1042	+	11.6072i	−1.04096	+	0.600997i	−0.920104	−	0.391673i	$-0.871896\pi$
$373$	−20.1042	+	11.6072i	−1.04096	+	0.600997i	−0.120853	+	0.992670i	$0.538563\pi$
$374$	−7.40852	+	12.8319i	−0.383085	+	0.663523i
$375$	−17.9814	+	7.18818i	−0.928554	+	0.371196i
$376$	−9.71584	+	5.60944i	−0.501056	+	0.289285i
$377$			7.23003i			0.372365i
$378$	9.78940	−	9.65234i	0.503513	−	0.496463i
$379$	−20.4772			−1.05184			−0.525922	−	0.850533i	$-0.676280\pi$
$379$	−20.4772			−1.05184			−0.525922	+	0.850533i	$0.676280\pi$
$380$	−2.99028	−	1.13402i	−0.153398	−	0.0581739i
$381$	1.55581	−	15.0420i	0.0797066	−	0.770627i
$382$	14.1099	+	8.14637i	0.721927	+	0.416805i
$383$	15.7158	−	9.07354i	0.803042	−	0.463636i	−0.0414919	−	0.999139i	$-0.513211\pi$
$383$	15.7158	−	9.07354i	0.803042	−	0.463636i	0.844534	+	0.535502i	$0.179878\pi$
$384$	−0.707107	−	1.58114i	−0.0360844	−	0.0806872i
$385$	−26.2943	−	8.77597i	−1.34008	−	0.447265i
$386$		−	7.34847i		−	0.374027i
$387$	−4.24999	+	20.3253i	−0.216039	+	1.03319i
$388$	5.99430	−	10.3824i	0.304315	−	0.527088i
$389$	6.36396	+	3.67423i	0.322666	+	0.186291i	0.652580	−	0.757720i	$-0.273687\pi$
$389$	6.36396	+	3.67423i	0.322666	+	0.186291i	−0.329914	+	0.944011i	$0.607020\pi$
$390$	−4.03873	+	0.234736i	−0.204509	+	0.0118863i
$391$		−	14.1582i		−	0.716012i
$392$	−3.00000	+	6.32456i	−0.151523	+	0.319438i
$393$	−9.73861	−	21.7762i	−0.491248	−	1.09846i
$394$	−4.50000	−	7.79423i	−0.226707	−	0.392668i
$395$	−25.3315	+	4.11710i	−1.27456	+	0.207154i
$396$	13.3542	−	4.38799i	0.671076	−	0.220505i
$397$	7.44073	+	12.8877i	0.373439	+	0.646816i	0.990092	−	0.140419i	$-0.0448451\pi$
$397$	7.44073	+	12.8877i	0.373439	+	0.646816i	−0.616653	+	0.787235i	$0.711512\pi$
$398$		−	15.5096i		−	0.777424i
$399$	−5.45947	−	3.62639i	−0.273315	−	0.181547i
$400$	−1.00000	+	4.89898i	−0.0500000	+	0.244949i
$401$	−0.827520	+	0.477769i	−0.0413244	+	0.0238586i	−0.520520	−	0.853850i	$-0.674262\pi$
$401$	−0.827520	+	0.477769i	−0.0413244	+	0.0238586i	0.479195	+	0.877708i	$0.340928\pi$
$402$	2.54289	−	24.5854i	0.126828	−	1.22621i
$403$	−5.99430	−	3.46081i	−0.298598	−	0.172395i
$404$	5.65685	+	9.79796i	0.281439	+	0.487467i
$405$	14.0777	−	14.3812i	0.699528	−	0.714606i
$406$	16.2158	+	8.50934i	0.804779	+	0.422312i
$407$	−12.4772			−0.618473
$408$	4.43649	+	3.21209i	0.219639	+	0.159022i
$409$	13.4317	+	7.75478i	0.664154	+	0.383449i	0.793858	−	0.608103i	$-0.208069\pi$
$409$	13.4317	+	7.75478i	0.664154	+	0.383449i	−0.129704	+	0.991553i	$0.541403\pi$
$410$	2.30545	−	0.374703i	0.113858	−	0.0185052i
$411$	3.53200	−	4.87835i	0.174221	−	0.240631i
$412$	4.91754			0.242270
$413$	−27.9545	+	1.12840i	−1.37555	+	0.0555251i
$414$	−8.95445	+	10.0114i	−0.440087	+	0.492033i
$415$	−8.50473	−	3.22529i	−0.417481	−	0.158323i
$416$	−0.522278	+	0.904612i	−0.0256068	+	0.0443523i
$417$	−3.59619	+	34.7690i	−0.176106	+	1.70264i
$418$	−3.35071	−	5.80359i	−0.163888	−	0.283863i
$419$	8.85494			0.432592			0.216296	−	0.976328i	$-0.430602\pi$
$419$	8.85494			0.432592			0.216296	+	0.976328i	$0.430602\pi$
$420$	−4.22689	+	9.33453i	−0.206251	+	0.455478i
$421$	18.9545			0.923783			0.461892	−	0.886936i	$-0.347171\pi$
$421$	18.9545			0.923783			0.461892	+	0.886936i	$0.347171\pi$
$422$	−12.2386	−	21.1979i	−0.595766	−	1.03190i
$423$	−31.9748	+	10.5064i	−1.55467	+	0.510838i
$424$	−2.50000	+	4.33013i	−0.121411	+	0.210290i
$425$	−5.00735	−	14.9975i	−0.242892	−	0.727488i
$426$	−10.9441	+	4.89433i	−0.530241	+	0.237131i
$427$	8.11562	+	4.25871i	0.392743	+	0.206094i
$428$	−5.47723			−0.264752
$429$	−6.86646	−	4.97143i	−0.331516	−	0.240023i
$430$	−2.48292	−	15.2768i	−0.119737	−	0.736711i
$431$	6.63699	+	3.83187i	0.319693	+	0.184575i	0.651256	−	0.758858i	$-0.274243\pi$
$431$	6.63699	+	3.83187i	0.319693	+	0.184575i	−0.331563	+	0.943433i	$0.607576\pi$
$432$	−1.10557	−	5.07718i	−0.0531916	−	0.244276i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$	−14.8170	+	9.37112i	−0.711240	+	0.449828i
$435$	23.9545	+	12.0340i	1.14853	+	0.576987i
$436$	10.2158	+	17.6944i	0.489250	+	0.847406i
$437$	5.54555	+	3.20172i	0.265280	+	0.153159i
$438$	−6.03574	−	0.624282i	−0.288399	−	0.0298294i
$439$	−7.69306	+	4.44159i	−0.367170	+	0.211986i	−0.672221	−	0.740350i	$-0.734660\pi$
$439$	−7.69306	+	4.44159i	−0.367170	+	0.211986i	0.305051	+	0.952336i	$0.401326\pi$
$440$	−8.11562	+	6.62638i	−0.386897	+	0.315900i
$441$	−12.6929	+	16.7300i	−0.604422	+	0.796664i
$442$		−	3.30318i		−	0.157116i
$443$	7.52277	+	13.0298i	0.357418	+	0.619066i	0.987529	−	0.157439i	$-0.0503239\pi$
$443$	7.52277	+	13.0298i	0.357418	+	0.619066i	−0.630111	+	0.776505i	$0.716991\pi$
$444$	−0.474523	+	4.58782i	−0.0225199	+	0.217728i
$445$	−10.8535	+	1.76402i	−0.514507	+	0.0836224i
$446$	10.9441	+	18.9557i	0.518216	+	0.897576i
$447$	−3.87298	+	1.73205i	−0.183186	+	0.0819232i
$448$	1.41421	+	2.23607i	0.0668153	+	0.105644i
$449$		−	25.8773i		−	1.22122i	−0.791930	−	0.610612i	$-0.790923\pi$
$449$		−	25.8773i		−	1.22122i	0.791930	−	0.610612i	$-0.209077\pi$
$450$	−5.94455	+	13.7718i	−0.280229	+	0.649209i
$451$	4.23861	+	2.44716i	0.199588	+	0.115232i
$452$	−8.73861	+	15.1357i	−0.411030	+	0.711924i
$453$	2.03151	−	2.80588i	0.0954485	−	0.131832i
$454$		−	10.3923i		−	0.487735i
$455$	6.05469	−	1.23658i	0.283848	−	0.0579717i
$456$	−2.26139	+	1.01132i	−0.105899	+	0.0473595i
$457$	9.59425	−	5.53924i	0.448800	−	0.259115i	−0.258523	−	0.966005i	$-0.583236\pi$
$457$	9.59425	−	5.53924i	0.448800	−	0.259115i	0.707323	+	0.706890i	$0.249902\pi$
$458$	11.7386	+	6.77729i	0.548509	+	0.316682i
$459$	11.0554	+	12.1564i	0.516024	+	0.567411i
$460$	3.54996	−	9.36085i	0.165518	−	0.436452i
$461$	31.7876			1.48050			0.740248	−	0.672334i	$-0.234708\pi$
$461$	31.7876			1.48050			0.740248	+	0.672334i	$0.234708\pi$
$462$	−19.2316	+	9.54931i	−0.894735	+	0.444274i
$463$		−	22.5741i		−	1.04911i	−0.851377	−	0.524554i	$-0.824232\pi$
$463$		−	22.5741i		−	1.04911i	0.851377	−	0.524554i	$-0.175768\pi$
$464$	5.99430	−	3.46081i	0.278279	−	0.160664i
$465$	−21.4436	+	14.0999i	−0.994421	+	0.653868i
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	−24.2614	+	14.0073i	−1.12268	+	0.648181i	−0.942085	−	0.335375i	$-0.891137\pi$
$467$	−24.2614	+	14.0073i	−1.12268	+	0.648181i	−0.180599	+	0.983557i	$0.557803\pi$
$468$	−2.08911	+	2.33570i	−0.0965693	+	0.107968i
$469$	1.52277	+	37.7244i	0.0703152	+	1.74195i
$470$	19.4317	−	15.8659i	0.896316	−	0.731839i
$471$	14.6750	−	20.2688i	0.676187	−	0.933938i
$472$	−5.28720	+	9.15769i	−0.243363	+	0.421517i
$473$	16.2158	−	28.0867i	0.745605	−	1.29143i
$474$	−11.6580	+	16.1019i	−0.535471	+	0.739584i
$475$	7.00665	+	1.43023i	0.321487	+	0.0656233i
$476$	−7.40852	−	3.88766i	−0.339569	−	0.178190i
$477$	−10.0000	+	11.1803i	−0.457869	+	0.511913i
$478$		0			0
$479$	−21.1810	+	36.6866i	−0.967784	+	1.67625i	−0.265844	+	0.964016i	$0.585651\pi$
$479$	−21.1810	+	36.6866i	−0.967784	+	1.67625i	−0.701940	+	0.712236i	$0.747683\pi$
$480$	2.12785	+	3.23609i	0.0971224	+	0.147707i
$481$	2.40890	−	1.39078i	0.109836	−	0.0634141i
$482$			21.3094i			0.970615i
$483$	11.3522	−	17.0905i	0.516541	−	0.777644i
$484$	−10.9545			−0.497930
$485$	−9.50569	+	25.0654i	−0.431631	+	1.13816i
$486$	−0.129018	−	15.5879i	−0.00585235	−	0.707083i
$487$	−14.7526	−	8.51743i	−0.668505	−	0.385962i	0.127005	−	0.991902i	$-0.459464\pi$
$487$	−14.7526	−	8.51743i	−0.668505	−	0.385962i	−0.795510	+	0.605941i	$0.792797\pi$
$488$	3.00000	−	1.73205i	0.135804	−	0.0784063i
$489$	23.2379	−	10.3923i	1.05085	−	0.469956i
$490$	4.35258	−	15.0351i	0.196629	−	0.679218i
$491$			13.8433i			0.624737i	0.949961	+	0.312369i	$0.101122\pi$
$491$			13.8433i			0.624737i	−0.949961	+	0.312369i	$0.898878\pi$
$492$	1.06101	−	1.46545i	0.0478341	−	0.0660677i
$493$	−10.9441	+	18.9557i	−0.492895	+	0.853720i
$494$	1.29380	+	0.746976i	0.0582108	+	0.0336080i
$495$	−27.9002	+	14.4752i	−1.25402	+	0.650611i
$496$			6.62638i			0.297533i
$497$	15.4772	−	9.78866i	0.694248	−	0.439081i
$498$	−6.43168	+	2.87633i	−0.288210	+	0.128892i
$499$	−0.954451	−	1.65316i	−0.0427271	−	0.0740055i	0.843871	−	0.536546i	$-0.180271\pi$
$499$	−0.954451	−	1.65316i	−0.0427271	−	0.0740055i	−0.886598	+	0.462541i	$0.846938\pi$
$500$	0.449747	−	11.1713i	0.0201133	−	0.499595i
$501$	0.764586	−	7.39224i	0.0341592	−	0.330261i
$502$	4.42747	+	7.66860i	0.197608	+	0.342266i
$503$			15.5096i			0.691537i	0.938320	+	0.345769i	$0.112382\pi$
$503$			15.5096i			0.691537i	−0.938320	+	0.345769i	$0.887618\pi$
$504$	2.77984	+	7.43455i	0.123824	+	0.331161i
$505$	−16.0000	−	19.5959i	−0.711991	−	0.872007i
$506$	18.1677	−	10.4891i	0.807655	−	0.466300i
$507$	−20.5174	−	2.12213i	−0.911208	−	0.0942471i
$508$	7.56114	+	4.36543i	0.335471	+	0.193684i
$509$	−12.3583	−	21.4051i	−0.547770	−	0.948766i	−0.998427	−	0.0560688i	$-0.982143\pi$
$509$	−12.3583	−	21.4051i	−0.547770	−	0.948766i	0.450656	−	0.892697i	$-0.351190\pi$
$510$	−10.9441	−	5.49798i	−0.484611	−	0.243454i
$511$	9.26139	−	0.373843i	0.409700	−	0.0165378i
$512$	1.00000			0.0441942
$513$	−7.26151	+	1.58121i	−0.320604	+	0.0698122i
$514$	9.52277	+	5.49798i	0.420032	+	0.242505i
$515$	−10.8535	+	1.76402i	−0.478264	+	0.0777319i
$516$	−9.71064	−	7.03066i	−0.427487	−	0.309508i
$517$	52.5667			2.31188
$518$	−0.284162	−	7.03967i	−0.0124853	−	0.309305i
$519$	1.78416	−	0.797901i	0.0783160	−	0.0350240i
$520$	0.828222	−	2.18393i	0.0363199	−	0.0957715i
$521$	−17.7981	+	30.8272i	−0.779748	+	1.35056i	0.152339	+	0.988328i	$0.451320\pi$
$521$	−17.7981	+	30.8272i	−0.779748	+	1.35056i	−0.932087	+	0.362235i	$0.882014\pi$
$522$	19.7272	−	6.48204i	0.863437	−	0.283711i
$523$	−8.45307	−	14.6412i	−0.369627	−	0.640213i	0.619880	−	0.784697i	$-0.287181\pi$
$523$	−8.45307	−	14.6412i	−0.369627	−	0.640213i	−0.989507	+	0.144484i	$0.953848\pi$
$524$	13.7725			0.601654
$525$	5.98072	−	22.1186i	0.261020	−	0.965333i
$526$	−2.00000			−0.0872041
$527$	−10.4772	−	18.1471i	−0.456395	−	0.790500i
$528$	−0.834952	+	8.07256i	−0.0363366	+	0.351313i
$529$	1.47723	−	2.55863i	0.0642272	−	0.111245i
$530$	3.96447	−	10.4539i	0.172205	−	0.454086i
$531$	−21.1488	+	23.6451i	−0.917779	+	1.02611i
$532$	3.19808	−	2.02265i	0.138655	−	0.0876928i
$533$	−1.09110			−0.0472607
$534$	−4.99501	+	6.89902i	−0.216155	+	0.298550i
$535$	12.0888	−	1.96479i	0.522645	−	0.0849452i
$536$	12.3583	+	7.13505i	0.533796	+	0.308187i
$537$	27.1925	+	19.6878i	1.17344	+	0.849593i
$538$	−17.5810			−0.757973
$539$	26.9905	−	18.6355i	1.16256	−	0.802689i
$540$	4.26139	+	10.8093i	0.183381	+	0.465157i
$541$	−4.26139	−	7.38094i	−0.183211	−	0.317331i	0.759761	−	0.650202i	$-0.225316\pi$
$541$	−4.26139	−	7.38094i	−0.183211	−	0.317331i	−0.942972	+	0.332871i	$0.891983\pi$
$542$	5.47723	+	3.16228i	0.235267	+	0.135831i
$543$	−0.563508	+	5.44816i	−0.0241825	+	0.233803i
$544$	−2.73861	+	1.58114i	−0.117417	+	0.0677908i
$545$	−28.8948	−	35.3887i	−1.23772	−	1.51589i
$546$	2.64851	−	3.98729i	0.113346	−	0.170640i
$547$			3.61845i			0.154714i	0.997003	+	0.0773569i	$0.0246481\pi$
$547$			3.61845i			0.154714i	−0.997003	+	0.0773569i	$0.975352\pi$
$548$	1.73861	+	3.01137i	0.0742699	+	0.128639i
$549$	9.87298	−	3.24410i	0.421369	−	0.138455i
$550$	15.5350	−	17.5364i	0.662416	−	0.747753i
$551$	−4.94975	−	8.57321i	−0.210866	−	0.365231i
$552$	−3.16588	−	7.07912i	−0.134749	−	0.301307i
$553$	14.1099	−	26.8886i	0.600015	−	1.14342i
$554$			9.79796i			0.416275i
$555$	−0.598419	−	10.2960i	−0.0254015	−	0.437042i
$556$	−17.4772	−	10.0905i	−0.741199	−	0.427932i
$557$	−13.9317	+	24.1304i	−0.590304	+	1.02244i	0.403887	+	0.914809i	$0.367659\pi$
$557$	−13.9317	+	24.1304i	−0.590304	+	1.02244i	−0.994191	+	0.107628i	$0.965674\pi$
$558$	−4.06871	+	19.4583i	−0.172242	+	0.823736i
$559$			7.23003i			0.305798i
$560$	−3.92344	−	4.42793i	−0.165796	−	0.187114i
$561$	−10.4772	−	23.4278i	−0.442349	−	0.989122i
$562$	−1.56683	+	0.904612i	−0.0660929	+	0.0381588i
$563$	9.00000	+	5.19615i	0.379305	+	0.218992i	0.677516	−	0.735508i	$-0.263057\pi$
$563$	9.00000	+	5.19615i	0.379305	+	0.218992i	−0.298211	+	0.954500i	$0.596390\pi$
$564$	1.99917	−	19.3286i	0.0841803	−	0.813879i
$565$	13.8576	−	36.5409i	0.582993	−	1.53729i
$566$	−9.22460			−0.387739
$567$	3.59805	+	23.5384i	0.151104	+	0.988518i
$568$		−	6.92163i		−	0.290425i
$569$	−6.54879	+	3.78095i	−0.274540	+	0.158505i	−0.630949	−	0.775824i	$-0.717334\pi$
$569$	−6.54879	+	3.78095i	−0.274540	+	0.158505i	0.356409	+	0.934330i	$0.384001\pi$
$570$	4.62834	−	3.04330i	0.193860	−	0.127470i
$571$	−7.47723	+	12.9509i	−0.312912	+	0.541980i	−0.978991	−	0.203901i	$-0.934638\pi$
$571$	−7.47723	+	12.9509i	−0.312912	+	0.541980i	0.666079	+	0.745881i	$0.267971\pi$
$572$	4.23861	−	2.44716i	0.177225	−	0.102321i
$573$	−25.7611	+	11.5207i	−1.07618	+	0.481284i
$574$	−1.28416	+	2.44716i	−0.0535999	+	0.102143i
$575$	−4.47723	+	21.9338i	−0.186713	+	0.914704i
$576$	2.93649	+	0.614017i	0.122354	+	0.0255840i
$577$	−0.337449	+	0.584480i	−0.0140482	+	0.0243322i	−0.872964	−	0.487785i	$-0.837805\pi$
$577$	−0.337449	+	0.584480i	−0.0140482	+	0.0243322i	0.858916	+	0.512117i	$0.171138\pi$
$578$	−3.50000	+	6.06218i	−0.145581	+	0.252153i
$579$	10.3095	+	7.46423i	0.428447	+	0.310203i
$580$	−11.9886	+	9.78866i	−0.497800	+	0.406452i
$581$	9.09576	−	5.75267i	0.377356	−	0.238661i
$582$	8.47723	+	18.9557i	0.351392	+	0.785737i
$583$	20.2891	−	11.7139i	0.840287	−	0.485140i
$584$	1.75166	−	3.03397i	0.0724843	−	0.125547i
$585$	3.77303	−	5.90454i	0.155996	−	0.244123i
$586$	6.97723	−	4.02830i	0.288227	−	0.166408i
$587$		−	21.0864i		−	0.870330i	−0.900351	−	0.435165i	$-0.856690\pi$
$587$		−	21.0864i		−	0.870330i	0.900351	−	0.435165i	$-0.143310\pi$
$588$	−5.82572	−	10.6330i	−0.240249	−	0.438498i
$589$	9.47723			0.390502
$590$	8.38437	−	22.1086i	0.345179	−	0.910198i
$591$	15.5057	+	1.60377i	0.637821	+	0.0659704i
$592$	−2.30615	−	1.33146i	−0.0947821	−	0.0547225i
$593$	−1.43168	+	0.826579i	−0.0587919	+	0.0339435i	−0.529108	−	0.848555i	$-0.677473\pi$
$593$	−1.43168	+	0.826579i	−0.0587919	+	0.0339435i	0.470316	+	0.882498i	$0.344140\pi$
$594$	−7.40852	+	23.1923i	−0.303975	+	0.951593i
$595$	17.7460	+	5.92289i	0.727514	+	0.242815i
$596$		−	2.44949i		−	0.100335i
$597$	21.7590	+	15.7539i	0.890537	+	0.644764i
$598$	−2.33836	+	4.05015i	−0.0956225	+	0.165623i
$599$	−20.4739	−	11.8206i	−0.836540	−	0.482977i	0.0195464	−	0.999809i	$-0.493778\pi$
$599$	−20.4739	−	11.8206i	−0.836540	−	0.482977i	−0.856087	+	0.516832i	$0.827111\pi$
$600$	−5.85723	−	6.37909i	−0.239120	−	0.260425i
$601$		−	4.06775i		−	0.165927i	−0.996553	−	0.0829635i	$-0.973562\pi$
$601$		−	4.06775i		−	0.165927i	0.996553	−	0.0829635i	$-0.0264385\pi$
$602$	16.2158	+	8.50934i	0.660908	+	0.346815i
$603$	31.9089	+	28.5402i	1.29943	+	1.16225i
$604$	1.00000	+	1.73205i	0.0406894	+	0.0704761i
$605$	24.1776	−	3.92957i	0.982961	−	0.159760i
$606$	−19.4919	−	2.01607i	−0.791806	−	0.0818972i
$607$	6.14692	+	10.6468i	0.249496	+	0.432140i	0.963386	−	0.268118i	$-0.0864017\pi$
$607$	6.14692	+	10.6468i	0.249496	+	0.432140i	−0.713890	+	0.700258i	$0.753068\pi$
$608$		−	1.43023i		−	0.0580034i
$609$	−28.4094	+	14.1065i	−1.15121	+	0.571624i
$610$	−6.00000	+	4.89898i	−0.242933	+	0.198354i
$611$	−10.1487	+	5.85938i	−0.410574	+	0.237045i
$612$	−9.01276	+	2.96145i	−0.364319	+	0.119709i
$613$	5.07016	+	2.92726i	0.204782	+	0.118231i	0.598884	−	0.800836i	$-0.295611\pi$
$613$	5.07016	+	2.92726i	0.204782	+	0.118231i	−0.394102	+	0.919067i	$0.628944\pi$
$614$	−5.99430	−	10.3824i	−0.241910	−	0.419001i
$615$	−1.81608	+	3.61501i	−0.0732314	+	0.145771i
$616$	−0.500000	−	12.3867i	−0.0201456	−	0.499076i
$617$	14.5228			0.584665			0.292332	−	0.956317i	$-0.405569\pi$
$617$	14.5228			0.584665			0.292332	+	0.956317i	$0.405569\pi$
$618$	−4.99501	+	6.89902i	−0.200929	+	0.277519i
$619$	26.1475	+	15.0963i	1.05096	+	0.606771i	0.922917	−	0.384998i	$-0.125798\pi$
$619$	26.1475	+	15.0963i	1.05096	+	0.606771i	0.128040	+	0.991769i	$0.459131\pi$
$620$	−2.37701	−	14.6251i	−0.0954631	−	0.587359i
$621$	−4.94987	−	22.7317i	−0.198632	−	0.912190i
$622$	−17.5810			−0.704936
$623$	6.04555	−	11.5207i	0.242210	−	0.461567i
$624$	−0.738613	−	1.65159i	−0.0295682	−	0.0661165i
$625$	3.01472	+	24.8176i	0.120589	+	0.992703i
$626$	11.6190	−	20.1246i	0.464387	−	0.804341i
$627$	11.5456	+	1.19417i	0.461086	+	0.0476906i
$628$	7.22369	+	12.5118i	0.288257	+	0.499275i
$629$	8.42087			0.335762
$630$	−8.80233	−	15.4117i	−0.350693	−	0.614015i
$631$	3.47723			0.138426			0.0692131	−	0.997602i	$-0.477951\pi$
$631$	3.47723			0.138426			0.0692131	+	0.997602i	$0.477951\pi$
$632$	−5.73861	−	9.93957i	−0.228270	−	0.395375i
$633$	42.1708	+	4.36177i	1.67614	+	0.173365i
$634$	4.95445	−	8.58136i	0.196766	−	0.340809i
$635$	−18.2542	−	6.92263i	−0.724396	−	0.274716i
$636$	−3.53553	−	7.90569i	−0.140193	−	0.313481i
$637$	−3.13367	+	6.60635i	−0.124160	+	0.261753i
$638$	−32.4317			−1.28398
$639$	4.24999	−	20.3253i	0.168127	−	0.804056i
$640$	−2.20711	+	0.358719i	−0.0872436	+	0.0141796i
$641$	13.9251	+	8.03966i	0.550008	+	0.317547i	0.749125	−	0.662428i	$-0.230474\pi$
$641$	13.9251	+	8.03966i	0.550008	+	0.317547i	−0.199117	+	0.979976i	$0.563807\pi$
$642$	5.56351	−	7.68423i	0.219574	−	0.303272i
$643$	−26.0663			−1.02796			−0.513978	−	0.857803i	$-0.671829\pi$
$643$	−26.0663			−1.02796			−0.513978	+	0.857803i	$0.671829\pi$
$644$	6.33175	+	10.0114i	0.249506	+	0.394504i
$645$	23.9545	+	12.0340i	0.943206	+	0.473839i
$646$	2.26139	+	3.91684i	0.0889731	+	0.154106i
$647$	17.6703	+	10.2019i	0.694691	+	0.401080i	0.805367	−	0.592777i	$-0.201968\pi$
$647$	17.6703	+	10.2019i	0.694691	+	0.401080i	−0.110676	+	0.993857i	$0.535302\pi$
$648$	8.24597	+	3.60611i	0.323932	+	0.141661i
$649$	42.9089	−	24.7735i	1.68432	−	0.972444i
$650$	−1.04456	+	5.11726i	−0.0409709	+	0.200715i
$651$	1.90332	−	30.3062i	0.0745969	−	1.18779i
$652$			14.6969i			0.575577i
$653$	−19.9317	−	34.5227i	−0.779987	−	1.35098i	−0.931949	−	0.362590i	$-0.881892\pi$
$653$	−19.9317	−	34.5227i	−0.779987	−	1.35098i	0.151962	−	0.988386i	$-0.451441\pi$
$654$	−35.2009	−	3.64086i	−1.37646	−	0.142369i
$655$	−30.3973	+	4.94046i	−1.18772	+	0.193040i
$656$	0.522278	+	0.904612i	0.0203915	+	0.0353192i
$657$	7.00665	−	7.83368i	0.273356	−	0.305621i
$658$	1.19718	+	29.6582i	0.0466708	+	1.15620i
$659$		−	34.2929i		−	1.33586i	−0.744224	−	0.667930i	$-0.767181\pi$
$659$		−	34.2929i		−	1.33586i	0.744224	−	0.667930i	$-0.232819\pi$
$660$	−1.05296	−	18.1165i	−0.0409862	−	0.705184i
$661$	0.522774	+	0.301824i	0.0203336	+	0.0117396i	0.510132	−	0.860096i	$-0.329596\pi$
$661$	0.522774	+	0.301824i	0.0203336	+	0.0117396i	−0.489799	+	0.871836i	$0.662930\pi$
$662$	−10.7158	+	18.5604i	−0.416483	+	0.721370i
$663$	4.63416	+	3.35521i	0.179976	+	0.130306i
$664$		−	4.06775i		−	0.157859i
$665$	−6.33295	+	5.61141i	−0.245581	+	0.217601i
$666$	−5.95445	−	5.32582i	−0.230730	−	0.206371i
$667$	26.8378	−	15.4948i	1.03917	−	0.599963i
$668$	3.71584	+	2.14534i	0.143770	+	0.0830057i
$669$	−37.7101	−	3.90039i	−1.45796	−	0.150798i
$670$	−29.8355	−	11.3147i	−1.15265	−	0.437124i
$671$	−16.2312			−0.626600
$672$	−4.57357	−	0.287233i	−0.176429	−	0.0110803i
$673$		−	14.1585i		−	0.545771i	−0.962047	−	0.272885i	$-0.912022\pi$
$673$		−	14.1585i		−	0.545771i	0.962047	−	0.272885i	$-0.0879780\pi$
$674$	14.8492	−	8.57321i	0.571971	−	0.330228i
$675$	−13.2828	−	22.3286i	−0.511257	−	0.859428i
$676$	5.95445	−	10.3134i	0.229017	−	0.396670i
$677$	−28.5000	+	16.4545i	−1.09534	+	0.632397i	−0.934994	−	0.354663i	$-0.884596\pi$
$677$	−28.5000	+	16.4545i	−1.09534	+	0.632397i	−0.160350	+	0.987060i	$0.551262\pi$
$678$	−12.3583	−	27.6339i	−0.474616	−	1.06127i
$679$	−16.9545	−	26.8073i	−0.650652	−	1.02877i
$680$	5.47723	−	4.47214i	0.210042	−	0.171499i
$681$	14.5798	+	10.5560i	0.558699	+	0.404507i
$682$	15.5241	−	26.8886i	0.594450	−	1.02962i
$683$	9.47723	−	16.4150i	0.362636	−	0.628104i	−0.625758	−	0.780017i	$-0.715210\pi$
$683$	9.47723	−	16.4150i	0.362636	−	0.628104i	0.988394	+	0.151913i	$0.0485435\pi$
$684$	0.878183	−	4.19985i	0.0335782	−	0.160585i
$685$	−4.91754	−	6.02273i	−0.187890	−	0.230117i
$686$	11.1289	+	14.8036i	0.424903	+	0.565206i
$687$	−21.4317	+	9.58454i	−0.817669	+	0.365673i
$688$	5.99430	−	3.46081i	0.228531	−	0.131942i
$689$	−2.61139	+	4.52306i	−0.0994861	+	0.172315i
$690$	9.52684	+	14.4887i	0.362681	+	0.551575i
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	−0.441851	−	0.897089i	$-0.645678\pi$
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	0.555976	+	0.831198i	$0.312345\pi$
$692$			1.12840i			0.0428954i
$693$	6.13742	−	36.6805i	0.233141	−	1.39338i
$694$	−17.4772			−0.663426
$695$	42.1938	+	16.0013i	1.60050	+	0.606966i
$696$	−1.23341	+	11.9250i	−0.0467524	+	0.452016i
$697$	−2.86064	−	1.65159i	−0.108354	−	0.0625584i
$698$	−10.1703	+	5.87182i	−0.384951	+	0.222252i
$699$	2.82843	+	6.32456i	0.106981	+	0.239217i
$700$	10.2478	+	8.36551i	0.387332	+	0.316187i
$701$			51.7546i			1.95474i	0.211531	+	0.977371i	$0.432155\pi$
$701$			51.7546i			1.95474i	−0.211531	+	0.977371i	$0.567845\pi$
$702$	−1.15483	−	5.30340i	−0.0435861	−	0.200164i
$703$	−1.90428	+	3.29832i	−0.0718214	+	0.124398i
$704$	−4.05781	−	2.34278i	−0.152935	−	0.0882968i
$705$	2.52115	+	43.3773i	0.0949519	+	1.63369i
$706$		−	0.603648i		−	0.0227186i
$707$	29.9089	−	1.20730i	1.12484	−	0.0454050i
$708$	−7.47723	−	16.7196i	−0.281011	−	0.628360i
$709$	11.2158	+	19.4264i	0.421220	+	0.729574i	0.996059	−	0.0886924i	$-0.0282688\pi$
$709$	11.2158	+	19.4264i	0.421220	+	0.729574i	−0.574839	+	0.818266i	$0.694935\pi$
$710$	2.48292	+	15.2768i	0.0931824	+	0.573327i
$711$	−10.7483	−	32.7111i	−0.403094	−	1.22676i
$712$	−2.45877	−	4.25871i	−0.0921463	−	0.159602i
$713$			29.6678i			1.11107i
$714$	12.9794	−	6.44482i	0.485741	−	0.241191i
$715$	−8.47723	+	6.92163i	−0.317030	+	0.258854i
$716$	−16.7857	+	9.69125i	−0.627312	+	0.362179i
$717$		0			0
$718$	−9.86729	−	5.69688i	−0.368244	−	0.212606i
$719$	0.401865	+	0.696051i	0.0149870	+	0.0259583i	0.873422	−	0.486965i	$-0.161896\pi$
$719$	0.401865	+	0.696051i	0.0149870	+	0.0259583i	−0.858435	+	0.512923i	$0.828563\pi$
$720$	−6.70141	−	0.301824i	−0.249747	−	0.0112483i
$721$	6.04555	−	11.5207i	0.225148	−	0.429054i
$722$	16.9545			0.630979
$723$	−29.8958	−	21.6451i	−1.11184	−	0.804988i
$724$	−2.73861	−	1.58114i	−0.101780	−	0.0587626i
$725$	22.9488	−	25.9052i	0.852295	−	0.962093i
$726$	11.1270	−	15.3685i	0.412962	−	0.570377i
$727$	−15.1223			−0.560854			−0.280427	−	0.959875i	$-0.590476\pi$
$727$	−15.1223			−0.560854			−0.280427	+	0.959875i	$0.590476\pi$
$728$	1.47723	+	2.33570i	0.0547496	+	0.0865668i
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$	−2.77776	+	7.32465i	−0.102810	+	0.271097i
$731$	−10.9441	+	18.9557i	−0.404780	+	0.701100i
$732$	−0.617292	+	5.96816i	−0.0228158	+	0.220590i
$733$	1.19718	+	2.07357i	0.0442187	+	0.0765891i	0.887288	−	0.461216i	$-0.152587\pi$
$733$	1.19718	+	2.07357i	0.0442187	+	0.0765891i	−0.843069	+	0.537805i	$0.819253\pi$
$734$	−0.369657			−0.0136443
$735$	16.6723	+	21.3784i	0.614966	+	0.788554i
$736$	4.47723			0.165033
$737$	−33.4317	−	57.9054i	−1.23147	−	2.13297i
$738$	0.978218	+	2.97707i	0.0360087	+	0.109588i
$739$	−3.23861	+	5.60944i	−0.119134	+	0.206347i	−0.919425	−	0.393266i	$-0.871345\pi$
$739$	−3.23861	+	5.60944i	−0.119134	+	0.206347i	0.800291	+	0.599612i	$0.204679\pi$
$740$	5.56754	+	2.11140i	0.204667	+	0.0776168i
$741$	−2.36215	+	1.05638i	−0.0867756	+	0.0388072i
$742$	7.07107	+	11.1803i	0.259587	+	0.410443i
$743$	13.4317			0.492760			0.246380	−	0.969173i	$-0.420759\pi$
$743$	13.4317			0.492760			0.246380	+	0.969173i	$0.420759\pi$
$744$	−9.29642	−	6.73076i	−0.340823	−	0.246762i
$745$	0.878680	+	5.40629i	0.0321923	+	0.198071i
$746$	20.1042	+	11.6072i	0.736068	+	0.424969i
$747$	2.49767	−	11.9449i	0.0913848	−	0.437041i
$748$	14.8170			0.541764
$749$	−6.73362	+	12.8319i	−0.246041	+	0.468868i
$750$	15.2158	+	11.9782i	0.555604	+	0.437384i
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	9.71584	+	5.60944i	0.354300	+	0.204555i
$753$	−15.2558	−	1.57792i	−0.555953	−	0.0575027i
$754$	6.26139	−	3.61501i	0.228026	−	0.131651i
$755$	−2.82843	−	3.46410i	−0.102937	−	0.126072i
$756$	−13.2539	−	3.65170i	−0.482039	−	0.132811i
$757$		−	48.1361i		−	1.74954i	−0.484541	−	0.874768i	$-0.661014\pi$
$757$		−	48.1361i		−	1.74954i	0.484541	−	0.874768i	$-0.338986\pi$
$758$	10.2386	+	17.7338i	0.371883	+	0.644121i
$759$	−3.73827	+	36.1427i	−0.135691	+	1.31190i
$760$	0.513050	+	3.15666i	0.0186103	+	0.114504i
$761$	−0.891935	−	1.54488i	−0.0323326	−	0.0560018i	0.849406	−	0.527739i	$-0.176960\pi$
$761$	−0.891935	−	1.54488i	−0.0323326	−	0.0560018i	−0.881739	+	0.471738i	$0.843627\pi$
$762$	−13.8047	+	6.17364i	−0.500091	+	0.223648i
$763$	54.0131	−	2.18028i	1.95541	−	0.0789315i
$764$		−	16.2927i		−	0.589451i
$765$	18.8298	−	9.76928i	0.680793	−	0.353209i
$766$	−15.7158	−	9.07354i	−0.567836	−	0.327840i
$767$	−5.52277	+	9.56573i	−0.199416	+	0.345398i
$768$	−1.01575	+	1.40294i	−0.0366528	+	0.0506243i
$769$		−	16.1921i		−	0.583902i	−0.956433	−	0.291951i	$-0.905696\pi$
$769$		−	16.1921i		−	0.583902i	0.956433	−	0.291951i	$-0.0943045\pi$
$770$	5.54692	+	27.1595i	0.199897	+	0.978760i
$771$	−17.3861	+	7.77531i	−0.626146	+	0.280021i
$772$	−6.36396	+	3.67423i	−0.229044	+	0.132239i
$773$	−14.0228	−	8.09605i	−0.504364	−	0.291195i	0.226150	−	0.974093i	$-0.427386\pi$
$773$	−14.0228	−	8.09605i	−0.504364	−	0.291195i	−0.730514	+	0.682898i	$0.760719\pi$
$774$	19.7272	−	6.48204i	0.709080	−	0.232992i
$775$	10.4926	+	31.4265i	0.376907	+	1.12887i
$776$	−11.9886			−0.430366
$777$	10.1649	+	6.75190i	0.364663	+	0.242223i
$778$		−	7.34847i		−	0.263455i
$779$	1.29380	−	0.746976i	0.0463552	−	0.0267632i
$780$	2.22265	+	3.38028i	0.0795838	+	0.121033i
$781$	−16.2158	+	28.0867i	−0.580248	+	1.00502i
$782$	−12.2614	+	7.07912i	−0.438466	+	0.253149i
$783$	−10.9441	+	34.2603i	−0.391108	+	1.22436i
$784$	6.97723	−	0.564201i	0.249187	−	0.0201501i
$785$	−20.4317	−	25.0236i	−0.729238	−	0.893130i
$786$	−13.9894	+	19.3220i	−0.498987	+	0.689192i
$787$	−25.0862	+	43.4506i	−0.894226	+	1.54884i	−0.0594664	+	0.998230i	$0.518940\pi$
$787$	−25.0862	+	43.4506i	−0.894226	+	1.54884i	−0.834760	+	0.550615i	$0.814393\pi$
$788$	−4.50000	+	7.79423i	−0.160306	+	0.277658i
$789$	2.03151	−	2.80588i	0.0723235	−	0.0998921i
$790$	16.2312	+	19.8791i	0.577482	+	0.707268i
$791$	24.7165	+	39.0803i	0.878819	+	1.38953i
$792$	−10.4772	−	9.37112i	−0.372292	−	0.332988i
$793$	3.13367	−	1.80922i	0.111280	−	0.0642474i
$794$	7.44073	−	12.8877i	0.264061	−	0.457368i
$795$	10.6392	+	16.1804i	0.377335	+	0.573861i
$796$	−13.4317	+	7.75478i	−0.476073	+	0.274861i
$797$			54.2183i			1.92051i	0.279121	+	0.960256i	$0.409957\pi$
$797$			54.2183i			1.92051i	−0.279121	+	0.960256i	$0.590043\pi$
$798$	−0.410809	+	6.54124i	−0.0145425	+	0.231557i
$799$	−35.4772			−1.25509
$800$	4.74264	−	1.58346i	0.167678	−	0.0559839i
$801$	−4.60523	−	14.0154i	−0.162718	−	0.495210i
$802$	0.827520	+	0.477769i	0.0292207	+	0.0168706i
$803$	−14.2158	+	8.20752i	−0.501666	+	0.289637i
$804$	−22.5630	+	10.0905i	−0.795736	+	0.355864i
$805$	−17.5661	−	19.8249i	−0.619125	−	0.698735i
$806$			6.92163i			0.243804i
$807$	17.8580	−	24.6652i	0.628631	−	0.868256i
$808$	5.65685	−	9.79796i	0.199007	−	0.344691i
$809$	7.65776	+	4.42121i	0.269233	+	0.155441i	0.628539	−	0.777778i	$-0.283653\pi$
$809$	7.65776	+	4.42121i	0.269233	+	0.155441i	−0.359306	+	0.933220i	$0.616987\pi$
$810$	−19.4933	−	5.00108i	−0.684925	−	0.175720i
$811$		−	38.3280i		−	1.34588i	−0.739697	−	0.672940i	$-0.765031\pi$
$811$		−	38.3280i		−	1.34588i	0.739697	−	0.672940i	$-0.234969\pi$
$812$	−0.738613	−	18.2980i	−0.0259202	−	0.642134i
$813$	−10.0000	+	4.47214i	−0.350715	+	0.156845i
$814$	6.23861	+	10.8056i	0.218663	+	0.378736i
$815$	−5.27208	−	32.4377i	−0.184673	−	1.13624i
$816$	0.563508	−	5.44816i	0.0197267	−	0.190724i
$817$	−4.94975	−	8.57321i	−0.173170	−	0.299939i
$818$		−	15.5096i		−	0.542279i
$819$	2.90370	+	7.76580i	0.101464	+	0.271359i
$820$	−1.47723	−	1.80922i	−0.0515870	−	0.0631809i
$821$	10.1403	−	5.85452i	0.353900	−	0.204324i	−0.312502	−	0.949917i	$-0.601167\pi$
$821$	10.1403	−	5.85452i	0.353900	−	0.204324i	0.666401	+	0.745593i	$0.267834\pi$
$822$	−5.99077	−	0.619631i	−0.208952	−	0.0216121i
$823$	−2.76401	−	1.59580i	−0.0963474	−	0.0556262i	0.451052	−	0.892498i	$-0.351049\pi$
$823$	−2.76401	−	1.59580i	−0.0963474	−	0.0556262i	−0.547400	+	0.836871i	$0.684382\pi$
$824$	−2.45877	−	4.25871i	−0.0856553	−	0.148359i
$825$	8.82273	+	39.6074i	0.307168	+	1.37895i
$826$	14.9545	+	23.6451i	0.520332	+	0.822717i
$827$	−3.90890			−0.135926			−0.0679629	−	0.997688i	$-0.521650\pi$
$827$	−3.90890			−0.135926			−0.0679629	+	0.997688i	$0.521650\pi$
$828$	13.1473	+	2.74909i	0.456901	+	0.0955375i
$829$	−43.6931	−	25.2262i	−1.51752	−	0.876142i	−0.999788	−	0.0206012i	$-0.993442\pi$
$829$	−43.6931	−	25.2262i	−1.51752	−	0.876142i	−0.517735	−	0.855541i	$-0.673225\pi$
$830$	1.45918	+	8.97796i	0.0506489	+	0.311629i
$831$	−13.7460	−	9.95231i	−0.476842	−	0.345242i
$832$	1.04456			0.0362135
$833$	−18.2158	+	12.5771i	−0.631141	+	0.435770i
$834$	31.9089	−	14.2701i	1.10491	−	0.494133i
$835$	−8.97083	−	3.40205i	−0.310448	−	0.117733i
$836$	−3.35071	+	5.80359i	−0.115887	+	0.200721i
$837$	−23.1661	−	25.4730i	−0.800737	−	0.880476i
$838$	−4.42747	−	7.66860i	−0.152944	−	0.264907i
$839$	−40.1440			−1.38593			−0.692963	−	0.720973i	$-0.743695\pi$
$839$	−40.1440			−1.38593			−0.692963	+	0.720973i	$0.743695\pi$
$840$	10.1974	−	1.00667i	0.351843	−	0.0347335i
$841$	−18.9089			−0.652031
$842$	−9.47723	−	16.4150i	−0.326607	−	0.565700i
$843$	0.322398	−	3.11704i	0.0111040	−	0.107357i
$844$	−12.2386	+	21.1979i	−0.421270	+	0.729662i
$845$	−9.44249	+	24.8988i	−0.324831	+	0.856544i
$846$	25.0862	+	22.4378i	0.862481	+	0.771426i
$847$	−13.4672	+	25.6639i	−0.462740	+	0.881821i
$848$	5.00000			0.171701
$849$	9.36991	−	12.9416i	0.321575	−	0.444154i
$850$	−10.4846	+	11.8353i	−0.359618	+	0.405946i
$851$	−10.3251	−	5.96123i	−0.353942	−	0.204348i
$852$	9.71064	+	7.03066i	0.332681	+	0.240867i
$853$	31.2891			1.07132			0.535659	−	0.844434i	$-0.320063\pi$
$853$	31.2891			1.07132			0.535659	+	0.844434i	$0.320063\pi$
$854$	−0.369657	−	9.15769i	−0.0126494	−	0.313370i
$855$	−0.431677	+	9.58454i	−0.0147630	+	0.327784i
$856$	2.73861	+	4.74342i	0.0936039	+	0.162127i
$857$	13.0455	+	7.53185i	0.445627	+	0.257283i	0.705982	−	0.708230i	$-0.250506\pi$
$857$	13.0455	+	7.53185i	0.445627	+	0.257283i	−0.260354	+	0.965513i	$0.583839\pi$
$858$	−0.872155	+	8.43224i	−0.0297749	+	0.287872i
$859$	−26.4772	+	15.2866i	−0.903391	+	0.521573i	−0.878299	−	0.478112i	$-0.841321\pi$
$859$	−26.4772	+	15.2866i	−0.903391	+	0.521573i	−0.0250924	+	0.999685i	$0.507988\pi$
$860$	−11.9886	+	9.78866i	−0.408808	+	0.333790i
$861$	−2.12884	−	4.28732i	−0.0725506	−	0.146111i
$862$		−	7.66374i		−	0.261028i
$863$	13.2386	+	22.9299i	0.450648	+	0.780545i	0.998426	−	0.0560787i	$-0.0178598\pi$
$863$	13.2386	+	22.9299i	0.450648	+	0.780545i	−0.547779	+	0.836623i	$0.684526\pi$
$864$	−3.84418	+	3.49604i	−0.130782	+	0.118938i
$865$	−0.404780	−	2.49051i	−0.0137629	−	0.0846797i
$866$		0			0
$867$	−4.94975	−	11.0680i	−0.168102	−	0.375888i
$868$	15.5241	+	8.14637i	0.526924	+	0.276506i
$869$			53.7772i			1.82427i
$870$	−1.55545	−	26.7622i	−0.0527348	−	0.907323i
$871$	12.9089	+	7.45296i	0.437401	+	0.252534i
$872$	10.2158	−	17.6944i	0.345952	−	0.599206i
$873$	−35.2044	−	7.36121i	−1.19149	−	0.249139i
$874$		−	6.40345i		−	0.216600i
$875$	−25.6190	−	14.7875i	−0.866079	−	0.499908i
$876$	2.47723	+	5.53924i	0.0836977	+	0.187154i
$877$	−48.2359	+	27.8490i	−1.62881	+	0.940394i	−0.644361	+	0.764721i	$0.722877\pi$
$877$	−48.2359	+	27.8490i	−1.62881	+	0.940394i	−0.984449	+	0.175673i	$0.943790\pi$
$878$	7.69306	+	4.44159i	0.259628	+	0.149896i
$879$	−1.43566	+	13.8804i	−0.0484237	+	0.468174i
$880$	9.79642	+	3.71515i	0.330237	+	0.125238i
$881$	−18.7544			−0.631853			−0.315926	−	0.948784i	$-0.602315\pi$
$881$	−18.7544			−0.631853			−0.315926	+	0.948784i	$0.602315\pi$
$882$	20.8350	+	2.62736i	0.701551	+	0.0884678i
$883$			24.3833i			0.820564i	0.911959	+	0.410282i	$0.134570\pi$
$883$			24.3833i			0.820564i	−0.911959	+	0.410282i	$0.865430\pi$
$884$	−2.86064	+	1.65159i	−0.0962136	+	0.0555489i
$885$	22.5007	+	34.2197i	0.756352	+	1.15028i
$886$	7.52277	−	13.0298i	0.252733	−	0.437746i
$887$	3.00000	−	1.73205i	0.100730	−	0.0581566i	−0.448789	−	0.893638i	$-0.648144\pi$
$887$	3.00000	−	1.73205i	0.100730	−	0.0581566i	0.549519	+	0.835481i	$0.314811\pi$
$888$	4.21043	−	1.88296i	0.141293	−	0.0631881i
$889$	19.5228	−	12.3473i	0.654773	−	0.414115i
$890$	6.95445	+	8.51743i	0.233114	+	0.285505i
$891$	−25.0123	−	33.9514i	−0.837942	−	1.13741i
$892$	10.9441	−	18.9557i	0.366434	−	0.634682i
$893$	8.02277	−	13.8959i	0.268472	−	0.465007i
$894$	3.43649	+	2.48808i	0.114933	+	0.0832137i
$895$	33.5715	−	27.4110i	1.12217	−	0.916248i
$896$	1.22938	−	2.34278i	0.0410709	−	0.0782667i
$897$	−3.30694	−	7.39453i	−0.110415	−	0.246896i
$898$	−22.4104	+	12.9386i	−0.747844	+	0.431768i
$899$	22.9327	−	39.7205i	0.764847	−	1.32475i
$900$	14.8990	−	1.73777i	0.496633	−	0.0579256i
$901$	−13.6931	+	7.90569i	−0.456182	+	0.263377i
$902$		−	4.89433i		−	0.162963i
$903$	−28.4094	+	14.1065i	−0.945406	+	0.469435i
$904$	17.4772			0.581284
$905$	6.61160	+	2.50735i	0.219777	+	0.0833471i
$906$	−3.44572	−	0.356394i	−0.114476	−	0.0118404i
$907$	−8.48528	−	4.89898i	−0.281749	−	0.162668i	0.352466	−	0.935825i	$-0.385343\pi$
$907$	−8.48528	−	4.89898i	−0.281749	−	0.162668i	−0.634215	+	0.773157i	$0.718677\pi$
$908$	−9.00000	+	5.19615i	−0.298675	+	0.172440i
$909$	22.6274	−	25.2982i	0.750504	−	0.839089i
$910$	−4.09826	−	4.62523i	−0.135856	−	0.153325i
$911$		−	24.0681i		−	0.797410i	−0.917079	−	0.398705i	$-0.869460\pi$
$911$		−	24.0681i		−	0.797410i	0.917079	−	0.398705i	$-0.130540\pi$
$912$	2.00653	+	1.45276i	0.0664427	+	0.0481056i
$913$	−9.52984	+	16.5062i	−0.315392	+	0.546274i
$914$	−9.59425	−	5.53924i	−0.317350	−	0.183222i
$915$	−0.778465	−	13.3938i	−0.0257353	−	0.442786i
$916$		−	13.5546i		−	0.447856i
$917$	16.9317	−	32.2659i	0.559133	−	1.06551i
$918$	5.00000	−	15.6525i	0.165025	−	0.516609i
$919$	−0.215838	−	0.373843i	−0.00711985	−	0.0123319i	0.862444	−	0.506153i	$-0.168933\pi$
$919$	−0.215838	−	0.373843i	−0.00711985	−	0.0123319i	−0.869563	+	0.493821i	$0.835600\pi$
$920$	−9.88171	+	1.60607i	−0.325790	+	0.0529505i
$921$	20.6547	+	2.13633i	0.680595	+	0.0703946i
$922$	−15.8938	−	27.5289i	−0.523434	−	0.906615i
$923$		−	7.23003i		−	0.237979i
$924$	17.8857	+	11.8804i	0.588398	+	0.390836i
$925$	−13.0455	−	2.66291i	−0.428935	−	0.0875560i
$926$	−19.5497	+	11.2871i	−0.642444	+	0.370916i
$927$	−4.60523	−	14.0154i	−0.151256	−	0.460326i
$928$	−5.99430	−	3.46081i	−0.196773	−	0.113607i
$929$	7.96300	+	13.7923i	0.261258	+	0.452512i	0.966576	−	0.256379i	$-0.0825294\pi$
$929$	7.96300	+	13.7923i	0.261258	+	0.452512i	−0.705319	+	0.708890i	$0.749196\pi$
$930$	22.9327	+	11.5207i	0.751991	+	0.377779i
$931$	−0.806936	−	9.97902i	−0.0264463	−	0.327049i
$932$	−4.00000			−0.131024
$933$	17.8580	−	24.6652i	0.584645	−	0.807502i
$934$	24.2614	+	14.0073i	0.793857	+	0.458333i
$935$	−32.7028	+	5.31516i	−1.06950	+	0.173824i
$936$	3.06733	+	0.641375i	0.100259	+	0.0209640i
$937$	−53.6757			−1.75351			−0.876754	−	0.480938i	$-0.840296\pi$
$937$	−53.6757			−1.75351			−0.876754	+	0.480938i	$0.840296\pi$
$938$	31.9089	−	20.1810i	1.04186	−	0.658932i
$939$	16.4317	+	36.7423i	0.536228	+	1.19904i
$940$	−23.4561	−	8.89538i	−0.765054	−	0.290135i
$941$	−10.2369	+	17.7309i	−0.333715	+	0.578011i	−0.983237	−	0.182331i	$-0.941636\pi$
$941$	−10.2369	+	17.7309i	−0.333715	+	0.578011i	0.649522	+	0.760343i	$0.274969\pi$
$942$	−24.8908	−	2.57448i	−0.810986	−	0.0838811i
$943$	2.33836	+	4.05015i	0.0761474	+	0.131891i
$944$	10.5744			0.344167
$945$	30.5626	+	3.30528i	0.994203	+	0.107521i
$946$	−32.4317			−1.05444
$947$	−16.4317	−	28.4605i	−0.533958	−	0.924842i	−0.999213	−	0.0396654i	$-0.987371\pi$
$947$	−16.4317	−	28.4605i	−0.533958	−	0.924842i	0.465255	−	0.885177i	$-0.345963\pi$
$948$	19.7737	+	2.04521i	0.642218	+	0.0664252i
$949$	1.82971	−	3.16915i	0.0593949	−	0.102875i
$950$	−2.26471	−	6.78305i	−0.0734770	−	0.220071i
$951$	7.00665	+	15.6674i	0.227206	+	0.508049i
$952$	0.337449	+	8.35979i	0.0109368	+	0.270942i
$953$	46.9545			1.52100			0.760502	−	0.649336i	$-0.224953\pi$
$953$	46.9545			1.52100			0.760502	+	0.649336i	$0.224953\pi$
$954$	14.6825	+	3.07008i	0.475362	+	0.0993976i
$955$	5.84452	+	35.9598i	0.189124	+	1.16363i
$956$		0			0
$957$	32.9426	−	45.4998i	1.06488	−	1.47080i
$958$	42.3620			1.36865
$959$	9.19239	−	0.371058i	0.296838	−	0.0119821i
$960$	1.73861	−	3.46081i	0.0561135	−	0.111697i
$961$	6.45445	+	11.1794i	0.208208	+	0.360627i
$962$	−2.40890	−	1.39078i	−0.0776661	−	0.0448406i
$963$	5.12938	+	15.6106i	0.165292	+	0.503043i
$964$	18.4545	−	10.6547i	0.594378	−	0.343164i
$965$	12.7279	−	10.3923i	0.409726	−	0.334540i
$966$	−20.4769	−	1.28601i	−0.658833	−	0.0413766i
$967$			7.23690i			0.232723i	0.993207	+	0.116361i	$0.0371231\pi$
$967$			7.23690i			0.232723i	−0.993207	+	0.116361i	$0.962877\pi$
$968$	5.47723	+	9.48683i	0.176045	+	0.304918i
$969$	−7.79211	−	0.805945i	−0.250319	−	0.0258907i
$970$	26.4601	−	4.30055i	0.849584	−	0.138082i
$971$	−18.8748	−	32.6922i	−0.605723	−	1.04914i	−0.991937	−	0.126733i	$-0.959551\pi$
$971$	−18.8748	−	32.6922i	−0.605723	−	1.04914i	0.386214	−	0.922409i	$-0.373783\pi$
$972$	−13.4350	+	7.90569i	−0.430929	+	0.253575i
$973$	−45.1260	+	28.5402i	−1.44667	+	0.914956i
$974$			17.0349i			0.545832i
$975$	−6.11821	−	6.66332i	−0.195939	−	0.213397i
$976$	−3.00000	−	1.73205i	−0.0960277	−	0.0554416i
$977$	−1.95445	+	3.38521i	−0.0625284	+	0.108302i	−0.895595	−	0.444870i	$-0.853250\pi$
$977$	−1.95445	+	3.38521i	−0.0625284	+	0.108302i	0.833067	+	0.553173i	$0.186583\pi$
$978$	−20.6190	−	14.9285i	−0.659321	−	0.477359i
$979$			23.0414i			0.736407i
$980$	−15.1971	+	3.74812i	−0.485453	+	0.119729i
$981$	40.8634	−	45.6866i	1.30467	−	1.45866i
$982$	11.9886	−	6.92163i	0.382572	−	0.220878i
$983$	−45.7158	−	26.3941i	−1.45811	−	0.841840i	−0.459190	−	0.888338i	$-0.651860\pi$
$983$	−45.7158	−	26.3941i	−1.45811	−	0.841840i	−0.998918	+	0.0464984i	$0.985194\pi$
$984$	−1.79962	−	0.186137i	−0.0573699	−	0.00593382i
$985$	7.13604	−	18.8169i	0.227373	−	0.599557i
$986$	21.8881			0.697059
$987$	−42.8248	−	28.4459i	−1.36313	−	0.905442i
$988$		−	1.49395i		−	0.0475290i
$989$	26.8378	−	15.4948i	0.853394	−	0.492707i
$990$	26.4860	+	16.9247i	0.841779	+	0.537901i
$991$	−5.26139	+	9.11299i	−0.167133	+	0.289484i	−0.937411	−	0.348225i	$-0.886784\pi$
$991$	−5.26139	+	9.11299i	−0.167133	+	0.289484i	0.770277	+	0.637709i	$0.220118\pi$
$992$	5.73861	−	3.31319i	0.182201	−	0.105194i
$993$	−15.1545	−	33.8865i	−0.480913	−	1.07535i
$994$	−16.2158	−	8.50934i	−0.514335	−	0.269900i
$995$	26.8634	−	21.9338i	0.851626	−	0.695349i
$996$	5.70682	+	4.13183i	0.180827	+	0.130922i
$997$	7.74597	−	13.4164i	0.245317	−	0.424902i	−0.716904	−	0.697172i	$-0.754441\pi$
$997$	7.74597	−	13.4164i	0.245317	−	0.424902i	0.962221	+	0.272270i	$0.0877745\pi$
$998$	−0.954451	+	1.65316i	−0.0302126	+	0.0523298i
$999$	13.5201	−	2.94403i	0.427756	−	0.0931449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.t.e.59.4	yes	8
3.2	odd	2		210.2.t.f.59.2	yes	8
5.2	odd	4		1050.2.s.i.101.7		16
5.3	odd	4		1050.2.s.i.101.2		16
5.4	even	2		210.2.t.f.59.1	yes	8
7.3	odd	6		1470.2.d.f.1469.7		8
7.4	even	3		1470.2.d.f.1469.2		8
7.5	odd	6	inner	210.2.t.e.89.3	yes	8
15.2	even	4		1050.2.s.i.101.1		16
15.8	even	4		1050.2.s.i.101.8		16
15.14	odd	2	inner	210.2.t.e.59.3	✓	8
21.5	even	6		210.2.t.f.89.1	yes	8
21.11	odd	6		1470.2.d.e.1469.3		8
21.17	even	6		1470.2.d.e.1469.6		8
35.4	even	6		1470.2.d.e.1469.7		8
35.12	even	12		1050.2.s.i.551.1		16
35.19	odd	6		210.2.t.f.89.2	yes	8
35.24	odd	6		1470.2.d.e.1469.2		8
35.33	even	12		1050.2.s.i.551.8		16
105.47	odd	12		1050.2.s.i.551.7		16
105.59	even	6		1470.2.d.f.1469.3		8
105.68	odd	12		1050.2.s.i.551.2		16
105.74	odd	6		1470.2.d.f.1469.6		8
105.89	even	6	inner	210.2.t.e.89.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.3	✓	8	15.14	odd	2	inner
210.2.t.e.59.4	yes	8	1.1	even	1	trivial
210.2.t.e.89.3	yes	8	7.5	odd	6	inner
210.2.t.e.89.4	yes	8	105.89	even	6	inner
210.2.t.f.59.1	yes	8	5.4	even	2
210.2.t.f.59.2	yes	8	3.2	odd	2
210.2.t.f.89.1	yes	8	21.5	even	6
210.2.t.f.89.2	yes	8	35.19	odd	6
1050.2.s.i.101.1		16	15.2	even	4
1050.2.s.i.101.2		16	5.3	odd	4
1050.2.s.i.101.7		16	5.2	odd	4
1050.2.s.i.101.8		16	15.8	even	4
1050.2.s.i.551.1		16	35.12	even	12
1050.2.s.i.551.2		16	105.68	odd	12
1050.2.s.i.551.7		16	105.47	odd	12
1050.2.s.i.551.8		16	35.33	even	12
1470.2.d.e.1469.2		8	35.24	odd	6
1470.2.d.e.1469.3		8	21.11	odd	6
1470.2.d.e.1469.6		8	21.17	even	6
1470.2.d.e.1469.7		8	35.4	even	6
1470.2.d.f.1469.2		8	7.4	even	3
1470.2.d.f.1469.3		8	105.59	even	6
1470.2.d.f.1469.6		8	105.74	odd	6
1470.2.d.f.1469.7		8	7.3	odd	6

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.72286 + 0.178197i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.792893 - 2.09077i) q^{5} +(-0.707107 - 1.58114i) q^{6} +(1.41421 + 2.23607i) q^{7} +1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +(-2.20711 + 0.358719i) q^{10} +(-4.05781 - 2.34278i) q^{11} +(-1.01575 + 1.40294i) q^{12} +1.04456 q^{13} +(1.22938 - 2.34278i) q^{14} +(1.73861 - 3.46081i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.73861 + 1.58114i) q^{17} +(-0.936492 - 2.85008i) q^{18} +(-1.23861 + 0.715113i) q^{19} +(1.41421 + 1.73205i) q^{20} +(2.03803 + 4.10444i) q^{21} +4.68556i q^{22} +(-2.23861 - 3.87739i) q^{23} +(1.72286 + 0.178197i) q^{24} +(-3.74264 - 3.31552i) q^{25} +(-0.522278 - 0.904612i) q^{26} +(4.94975 + 1.58114i) q^{27} +(-2.64360 + 0.106711i) q^{28} +6.92163i q^{29} +(-3.86646 + 0.224724i) q^{30} +(-5.73861 - 3.31319i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.57357 - 4.75937i) q^{33} -3.16228i q^{34} +(5.79642 - 1.18383i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(2.30615 - 1.33146i) q^{37} +(1.23861 + 0.715113i) q^{38} +(1.79962 + 0.186137i) q^{39} +(0.792893 - 2.09077i) q^{40} -1.04456 q^{41} +(2.53553 - 3.81721i) q^{42} +6.92163i q^{43} +(4.05781 - 2.34278i) q^{44} +(3.61209 - 5.65268i) q^{45} +(-2.23861 + 3.87739i) q^{46} +(-9.71584 + 5.60944i) q^{47} +(-0.707107 - 1.58114i) q^{48} +(-3.00000 + 6.32456i) q^{49} +(-1.00000 + 4.89898i) q^{50} +(4.43649 + 3.21209i) q^{51} +(-0.522278 + 0.904612i) q^{52} +(-2.50000 + 4.33013i) q^{53} +(-1.10557 - 5.07718i) q^{54} +(-8.11562 + 6.62638i) q^{55} +(1.41421 + 2.23607i) q^{56} +(-2.26139 + 1.01132i) q^{57} +(5.99430 - 3.46081i) q^{58} +(-5.28720 + 9.15769i) q^{59} +(2.12785 + 3.23609i) q^{60} +(3.00000 - 1.73205i) q^{61} +6.62638i q^{62} +(2.77984 + 7.43455i) q^{63} +1.00000 q^{64} +(0.828222 - 2.18393i) q^{65} +(-0.834952 + 8.07256i) q^{66} +(12.3583 + 7.13505i) q^{67} +(-2.73861 + 1.58114i) q^{68} +(-3.16588 - 7.07912i) q^{69} +(-3.92344 - 4.42793i) q^{70} -6.92163i q^{71} +(2.93649 + 0.614017i) q^{72} +(1.75166 - 3.03397i) q^{73} +(-2.30615 - 1.33146i) q^{74} +(-5.85723 - 6.37909i) q^{75} -1.43023i q^{76} +(-0.500000 - 12.3867i) q^{77} +(-0.738613 - 1.65159i) q^{78} +(-5.73861 - 9.93957i) q^{79} +(-2.20711 + 0.358719i) q^{80} +(8.24597 + 3.60611i) q^{81} +(0.522278 + 0.904612i) q^{82} -4.06775i q^{83} +(-4.57357 - 0.287233i) q^{84} +(5.47723 - 4.47214i) q^{85} +(5.99430 - 3.46081i) q^{86} +(-1.23341 + 11.9250i) q^{87} +(-4.05781 - 2.34278i) q^{88} +(-2.45877 - 4.25871i) q^{89} +(-6.70141 - 0.301824i) q^{90} +(1.47723 + 2.33570i) q^{91} +4.47723 q^{92} +(-9.29642 - 6.73076i) q^{93} +(9.71584 + 5.60944i) q^{94} +(0.513050 + 3.15666i) q^{95} +(-1.01575 + 1.40294i) q^{96} -11.9886 q^{97} +(6.97723 - 0.564201i) q^{98} +(-10.4772 - 9.37112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 12 q^{5} + 8 q^{8} + 8 q^{9} - 12 q^{10} - 8 q^{15} - 4 q^{16} + 8 q^{18} + 12 q^{19} + 4 q^{21} + 4 q^{23} + 4 q^{25} + 4 q^{30} - 24 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{35}+ \cdots - 40 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 12 * q^5 + 8 * q^8 + 8 * q^9 - 12 * q^10 - 8 * q^15 - 4 * q^16 + 8 * q^18 + 12 * q^19 + 4 * q^21 + 4 * q^23 + 4 * q^25 + 4 * q^30 - 24 * q^31 - 4 * q^32 - 12 * q^33 - 8 * q^35 - 16 * q^36 - 12 * q^38 - 8 * q^39 + 12 * q^40 - 8 * q^42 + 24 * q^45 + 4 * q^46 - 12 * q^47 - 24 * q^49 - 8 * q^50 + 20 * q^51 - 20 * q^53 - 40 * q^57 + 4 * q^60 + 24 * q^61 + 20 * q^63 + 8 * q^64 + 16 * q^65 + 12 * q^66 - 8 * q^70 + 8 * q^72 - 24 * q^75 - 4 * q^77 + 16 * q^78 - 24 * q^79 - 12 * q^80 + 4 * q^81 + 4 * q^84 + 12 * q^87 - 32 * q^91 - 8 * q^92 - 20 * q^93 + 12 * q^94 + 12 * q^95 + 12 * q^98 - 40 * q^99

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