LMFDB - Embedded newform 690.2.i.e.47.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.12
Character	$\chi$	$=$	690.47
Dual form			690.2.i.e.323.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.00790 - 1.40859i) q^{3} -1.00000i q^{4} +(0.318132 - 2.21332i) q^{5} +(-1.70872 - 0.283328i) q^{6} +(-2.49652 - 2.49652i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.968258 + 2.83945i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.00790 - 1.40859i) q^{3} -1.00000i q^{4} +(0.318132 - 2.21332i) q^{5} +(-1.70872 - 0.283328i) q^{6} +(-2.49652 - 2.49652i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.968258 + 2.83945i) q^{9} +(-1.34010 - 1.79001i) q^{10} -0.391175i q^{11} +(-1.40859 + 1.00790i) q^{12} +(-0.323514 + 0.323514i) q^{13} -3.53061 q^{14} +(-3.43831 + 1.78270i) q^{15} -1.00000 q^{16} +(3.34201 - 3.34201i) q^{17} +(1.32313 + 2.69246i) q^{18} +7.09192i q^{19} +(-2.21332 - 0.318132i) q^{20} +(-1.00032 + 6.03283i) q^{21} +(-0.276603 - 0.276603i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-0.283328 + 1.70872i) q^{24} +(-4.79758 - 1.40826i) q^{25} +0.457518i q^{26} +(4.97554 - 1.49802i) q^{27} +(-2.49652 + 2.49652i) q^{28} +5.19650 q^{29} +(-1.17069 + 3.69181i) q^{30} -3.88859 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.551006 + 0.394267i) q^{33} -4.72632i q^{34} +(-6.31982 + 4.73138i) q^{35} +(2.83945 + 0.968258i) q^{36} +(-0.830991 - 0.830991i) q^{37} +(5.01475 + 5.01475i) q^{38} +(0.781770 + 0.129628i) q^{39} +(-1.79001 + 1.34010i) q^{40} -9.20789i q^{41} +(3.55852 + 4.97319i) q^{42} +(4.32271 - 4.32271i) q^{43} -0.391175 q^{44} +(5.97658 + 3.04638i) q^{45} -1.00000 q^{46} +(-7.82278 + 7.82278i) q^{47} +(1.00790 + 1.40859i) q^{48} +5.46521i q^{49} +(-4.38819 + 2.39662i) q^{50} +(-8.07595 - 1.33910i) q^{51} +(0.323514 + 0.323514i) q^{52} +(1.05090 + 1.05090i) q^{53} +(2.45898 - 4.57749i) q^{54} +(-0.865797 - 0.124445i) q^{55} +3.53061i q^{56} +(9.98962 - 7.14798i) q^{57} +(3.67448 - 3.67448i) q^{58} -10.5913 q^{59} +(1.78270 + 3.43831i) q^{60} +1.98438 q^{61} +(-2.74965 + 2.74965i) q^{62} +(9.50601 - 4.67147i) q^{63} +1.00000i q^{64} +(0.613120 + 0.818961i) q^{65} +(-0.110831 + 0.668409i) q^{66} +(-6.39385 - 6.39385i) q^{67} +(-3.34201 - 3.34201i) q^{68} +(-0.283328 + 1.70872i) q^{69} +(-1.12320 + 7.81438i) q^{70} -9.11312i q^{71} +(2.69246 - 1.32313i) q^{72} +(5.64130 - 5.64130i) q^{73} -1.17520 q^{74} +(2.85185 + 8.17722i) q^{75} +7.09192 q^{76} +(-0.976577 + 0.976577i) q^{77} +(0.644456 - 0.461134i) q^{78} +8.35272i q^{79} +(-0.318132 + 2.21332i) q^{80} +(-7.12495 - 5.49864i) q^{81} +(-6.51096 - 6.51096i) q^{82} +(-4.16531 - 4.16531i) q^{83} +(6.03283 + 1.00032i) q^{84} +(-6.33374 - 8.46014i) q^{85} -6.11324i q^{86} +(-5.23758 - 7.31975i) q^{87} +(-0.276603 + 0.276603i) q^{88} -1.17975 q^{89} +(6.38020 - 2.07196i) q^{90} +1.61532 q^{91} +(-0.707107 + 0.707107i) q^{92} +(3.91932 + 5.47743i) q^{93} +11.0631i q^{94} +(15.6967 + 2.25617i) q^{95} +(1.70872 + 0.283328i) q^{96} +(-3.27380 - 3.27380i) q^{97} +(3.86449 + 3.86449i) q^{98} +(1.11072 + 0.378759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.00790	−	1.40859i	−0.581914	−	0.813250i
$3$	−1.00790	−	1.40859i	−0.581914	−	0.813250i
$4$		−	1.00000i		−	0.500000i
$5$	0.318132	−	2.21332i	0.142273	−	0.989827i
$5$	0.318132	−	2.21332i	0.142273	−	0.989827i
$6$	−1.70872	−	0.283328i	−0.697582	−	0.115668i
$7$	−2.49652	−	2.49652i	−0.943595	−	0.943595i	0.0548966	−	0.998492i	$-0.482517\pi$
$7$	−2.49652	−	2.49652i	−0.943595	−	0.943595i	−0.998492	+	0.0548966i	$0.982517\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.968258	+	2.83945i	−0.322753	+	0.946483i
$10$	−1.34010	−	1.79001i	−0.423777	−	0.566050i
$11$		−	0.391175i		−	0.117944i	−0.998260	−	0.0589719i	$-0.981218\pi$
$11$		−	0.391175i		−	0.117944i	0.998260	−	0.0589719i	$-0.0187822\pi$
$12$	−1.40859	+	1.00790i	−0.406625	+	0.290957i
$13$	−0.323514	+	0.323514i	−0.0897266	+	0.0897266i	−0.750545	−	0.660819i	$-0.770209\pi$
$13$	−0.323514	+	0.323514i	−0.0897266	+	0.0897266i	0.660819	+	0.750545i	$0.270209\pi$
$14$	−3.53061			−0.943595
$15$	−3.43831	+	1.78270i	−0.887768	+	0.460291i
$16$	−1.00000			−0.250000
$17$	3.34201	−	3.34201i	0.810557	−	0.810557i	−0.174161	−	0.984717i	$-0.555721\pi$
$17$	3.34201	−	3.34201i	0.810557	−	0.810557i	0.984717	+	0.174161i	$0.0557212\pi$
$18$	1.32313	+	2.69246i	0.311865	+	0.634618i
$19$			7.09192i			1.62700i	0.581566	+	0.813499i	$0.302440\pi$
$19$			7.09192i			1.62700i	−0.581566	+	0.813499i	$0.697560\pi$
$20$	−2.21332	−	0.318132i	−0.494914	−	0.0711364i
$21$	−1.00032	+	6.03283i	−0.218288	+	1.31647i
$22$	−0.276603	−	0.276603i	−0.0589719	−	0.0589719i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$	−0.283328	+	1.70872i	−0.0578341	+	0.348791i
$25$	−4.79758	−	1.40826i	−0.959517	−	0.281651i
$26$			0.457518i			0.0897266i
$27$	4.97554	−	1.49802i	0.957542	−	0.288293i
$28$	−2.49652	+	2.49652i	−0.471798	+	0.471798i
$29$	5.19650			0.964966			0.482483	−	0.875905i	$-0.339735\pi$
$29$	5.19650			0.964966			0.482483	+	0.875905i	$0.339735\pi$
$30$	−1.17069	+	3.69181i	−0.213739	+	0.674030i
$31$	−3.88859			−0.698411			−0.349205	−	0.937046i	$-0.613548\pi$
$31$	−3.88859			−0.698411			−0.349205	+	0.937046i	$0.613548\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.551006	+	0.394267i	−0.0959179	+	0.0686332i
$34$		−	4.72632i		−	0.810557i
$35$	−6.31982	+	4.73138i	−1.06824	+	0.799749i
$36$	2.83945	+	0.968258i	0.473242	+	0.161376i
$37$	−0.830991	−	0.830991i	−0.136614	−	0.136614i	0.635493	−	0.772107i	$-0.280797\pi$
$37$	−0.830991	−	0.830991i	−0.136614	−	0.136614i	−0.772107	+	0.635493i	$0.780797\pi$
$38$	5.01475	+	5.01475i	0.813499	+	0.813499i
$39$	0.781770	+	0.129628i	0.125183	+	0.0207571i
$40$	−1.79001	+	1.34010i	−0.283025	+	0.211889i
$41$		−	9.20789i		−	1.43803i	−0.694994	−	0.719016i	$-0.744593\pi$
$41$		−	9.20789i		−	1.43803i	0.694994	−	0.719016i	$-0.255407\pi$
$42$	3.55852	+	4.97319i	0.549091	+	0.767379i
$43$	4.32271	−	4.32271i	0.659207	−	0.659207i	−0.295985	−	0.955192i	$-0.595648\pi$
$43$	4.32271	−	4.32271i	0.659207	−	0.659207i	0.955192	+	0.295985i	$0.0956479\pi$
$44$	−0.391175			−0.0589719
$45$	5.97658	+	3.04638i	0.890936	+	0.454128i
$46$	−1.00000			−0.147442
$47$	−7.82278	+	7.82278i	−1.14107	+	1.14107i	−0.152815	+	0.988255i	$0.548834\pi$
$47$	−7.82278	+	7.82278i	−1.14107	+	1.14107i	−0.988255	+	0.152815i	$0.951166\pi$
$48$	1.00790	+	1.40859i	0.145478	+	0.203313i
$49$			5.46521i			0.780745i
$50$	−4.38819	+	2.39662i	−0.620584	+	0.338933i
$51$	−8.07595	−	1.33910i	−1.13086	−	0.187511i
$52$	0.323514	+	0.323514i	0.0448633	+	0.0448633i
$53$	1.05090	+	1.05090i	0.144352	+	0.144352i	0.775589	−	0.631238i	$-0.217453\pi$
$53$	1.05090	+	1.05090i	0.144352	+	0.144352i	−0.631238	+	0.775589i	$0.717453\pi$
$54$	2.45898	−	4.57749i	0.334625	−	0.622918i
$55$	−0.865797	−	0.124445i	−0.116744	−	0.0167802i
$56$			3.53061i			0.471798i
$57$	9.98962	−	7.14798i	1.32316	−	0.946773i
$58$	3.67448	−	3.67448i	0.482483	−	0.482483i
$59$	−10.5913			−1.37887			−0.689435	−	0.724348i	$-0.742141\pi$
$59$	−10.5913			−1.37887			−0.689435	+	0.724348i	$0.742141\pi$
$60$	1.78270	+	3.43831i	0.230145	+	0.443884i
$61$	1.98438			0.254074			0.127037	−	0.991898i	$-0.459453\pi$
$61$	1.98438			0.254074			0.127037	+	0.991898i	$0.459453\pi$
$62$	−2.74965	+	2.74965i	−0.349205	+	0.349205i
$63$	9.50601	−	4.67147i	1.19765	−	0.588550i
$64$			1.00000i			0.125000i
$65$	0.613120	+	0.818961i	0.0760482	+	0.101580i
$66$	−0.110831	+	0.668409i	−0.0136424	+	0.0822755i
$67$	−6.39385	−	6.39385i	−0.781133	−	0.781133i	0.198889	−	0.980022i	$-0.436267\pi$
$67$	−6.39385	−	6.39385i	−0.781133	−	0.781133i	−0.980022	+	0.198889i	$0.936267\pi$
$68$	−3.34201	−	3.34201i	−0.405278	−	0.405278i
$69$	−0.283328	+	1.70872i	−0.0341087	+	0.205706i
$70$	−1.12320	+	7.81438i	−0.134248	+	0.933997i
$71$		−	9.11312i		−	1.08153i	−0.841174	−	0.540764i	$-0.818135\pi$
$71$		−	9.11312i		−	1.08153i	0.841174	−	0.540764i	$-0.181865\pi$
$72$	2.69246	−	1.32313i	0.317309	−	0.155933i
$73$	5.64130	−	5.64130i	0.660265	−	0.660265i	−0.295178	−	0.955442i	$-0.595379\pi$
$73$	5.64130	−	5.64130i	0.660265	−	0.660265i	0.955442	+	0.295178i	$0.0953789\pi$
$74$	−1.17520			−0.136614
$75$	2.85185	+	8.17722i	0.329303	+	0.944224i
$76$	7.09192			0.813499
$77$	−0.976577	+	0.976577i	−0.111291	+	0.111291i
$78$	0.644456	−	0.461134i	0.0729702	−	0.0522132i
$79$			8.35272i			0.939754i	0.882732	+	0.469877i	$0.155702\pi$
$79$			8.35272i			0.939754i	−0.882732	+	0.469877i	$0.844298\pi$
$80$	−0.318132	+	2.21332i	−0.0355682	+	0.247457i
$81$	−7.12495	−	5.49864i	−0.791662	−	0.610960i
$82$	−6.51096	−	6.51096i	−0.719016	−	0.719016i
$83$	−4.16531	−	4.16531i	−0.457202	−	0.457202i	0.440534	−	0.897736i	$-0.354789\pi$
$83$	−4.16531	−	4.16531i	−0.457202	−	0.457202i	−0.897736	+	0.440534i	$0.854789\pi$
$84$	6.03283	+	1.00032i	0.658235	+	0.109144i
$85$	−6.33374	−	8.46014i	−0.686991	−	0.917631i
$86$		−	6.11324i		−	0.659207i
$87$	−5.23758	−	7.31975i	−0.561527	−	0.784759i
$88$	−0.276603	+	0.276603i	−0.0294860	+	0.0294860i
$89$	−1.17975			−0.125053			−0.0625266	−	0.998043i	$-0.519916\pi$
$89$	−1.17975			−0.125053			−0.0625266	+	0.998043i	$0.519916\pi$
$90$	6.38020	−	2.07196i	0.672532	−	0.218404i
$91$	1.61532			0.169331
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$	3.91932	+	5.47743i	0.406415	+	0.567983i
$94$			11.0631i			1.14107i
$95$	15.6967	+	2.25617i	1.61045	+	0.231478i
$96$	1.70872	+	0.283328i	0.174396	+	0.0289171i
$97$	−3.27380	−	3.27380i	−0.332404	−	0.332404i	0.521095	−	0.853499i	$-0.325524\pi$
$97$	−3.27380	−	3.27380i	−0.332404	−	0.332404i	−0.853499	+	0.521095i	$0.825524\pi$
$98$	3.86449	+	3.86449i	0.390372	+	0.390372i
$99$	1.11072	+	0.378759i	0.111632	+	0.0380667i
$100$	−1.40826	+	4.79758i	−0.140826	+	0.479758i
$101$			6.26052i			0.622945i	0.950255	+	0.311473i	$0.100822\pi$
$101$			6.26052i			0.622945i	−0.950255	+	0.311473i	$0.899178\pi$
$102$	−6.65745	+	4.76367i	−0.659185	+	0.471674i
$103$	0.462360	−	0.462360i	0.0455577	−	0.0455577i	−0.683961	−	0.729519i	$-0.739744\pi$
$103$	0.462360	−	0.462360i	0.0455577	−	0.0455577i	0.729519	+	0.683961i	$0.239744\pi$
$104$	0.457518			0.0448633
$105$	13.0344	+	4.13327i	1.27202	+	0.403366i
$106$	1.48619			0.144352
$107$	11.8842	−	11.8842i	1.14889	−	1.14889i	0.162120	−	0.986771i	$-0.448167\pi$
$107$	11.8842	−	11.8842i	1.14889	−	1.14889i	0.986771	−	0.162120i	$-0.0518330\pi$
$108$	−1.49802	−	4.97554i	−0.144147	−	0.478771i
$109$		−	1.31614i		−	0.126064i	−0.998012	−	0.0630318i	$-0.979923\pi$
$109$		−	1.31614i		−	0.126064i	0.998012	−	0.0630318i	$-0.0200769\pi$
$110$	−0.700207	+	0.524215i	−0.0667621	+	0.0499819i
$111$	−0.332967	+	2.00809i	−0.0316038	+	0.190599i
$112$	2.49652	+	2.49652i	0.235899	+	0.235899i
$113$	−3.70049	−	3.70049i	−0.348113	−	0.348113i	0.511294	−	0.859406i	$-0.329167\pi$
$113$	−3.70049	−	3.70049i	−0.348113	−	0.348113i	−0.859406	+	0.511294i	$0.829167\pi$
$114$	2.00934	−	12.1181i	0.188192	−	1.13497i
$115$	−1.79001	+	1.34010i	−0.166919	+	0.124965i
$116$		−	5.19650i		−	0.482483i
$117$	−0.605357	−	1.23185i	−0.0559653	−	0.113884i
$118$	−7.48918	+	7.48918i	−0.689435	+	0.689435i
$119$	−16.6868			−1.52968
$120$	3.69181	+	1.17069i	0.337015	+	0.106869i
$121$	10.8470			0.986089
$122$	1.40317	−	1.40317i	0.127037	−	0.127037i
$123$	−12.9702	+	9.28068i	−1.16948	+	0.836810i
$124$			3.88859i			0.349205i
$125$	−4.64319	+	10.1706i	−0.415299	+	0.909685i
$126$	3.41854	−	10.0250i	0.304548	−	0.893097i
$127$	14.8287	+	14.8287i	1.31583	+	1.31583i	0.917042	+	0.398791i	$0.130570\pi$
$127$	14.8287	+	14.8287i	1.31583	+	1.31583i	0.398791	+	0.917042i	$0.369430\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−10.4458	−	1.73205i	−0.919702	−	0.152499i
$130$	1.01263	+	0.145551i	0.0888139	+	0.0127657i
$131$		−	20.0644i		−	1.75303i	−0.481373	−	0.876516i	$-0.659862\pi$
$131$		−	20.0644i		−	1.75303i	0.481373	−	0.876516i	$-0.340138\pi$
$132$	0.394267	+	0.551006i	0.0343166	+	0.0479589i
$133$	17.7051	−	17.7051i	1.53523	−	1.53523i
$134$	−9.04227			−0.781133
$135$	−1.73271	−	11.4890i	−0.149128	−	0.988818i
$136$	−4.72632			−0.405278
$137$	3.91319	−	3.91319i	0.334326	−	0.334326i	−0.519900	−	0.854227i	$-0.674031\pi$
$137$	3.91319	−	3.91319i	0.334326	−	0.334326i	0.854227	+	0.519900i	$0.174031\pi$
$138$	1.00790	+	1.40859i	0.0857985	+	0.119907i
$139$		−	16.9351i		−	1.43642i	−0.695827	−	0.718210i	$-0.744962\pi$
$139$		−	16.9351i		−	1.43642i	0.695827	−	0.718210i	$-0.255038\pi$
$140$	4.73138	+	6.31982i	0.399874	+	0.534122i
$141$	18.9037	+	3.13448i	1.59198	+	0.263971i
$142$	−6.44395	−	6.44395i	−0.540764	−	0.540764i
$143$	0.126551	+	0.126551i	0.0105827	+	0.0105827i
$144$	0.968258	−	2.83945i	0.0806881	−	0.236621i
$145$	1.65317	−	11.5015i	0.137289	−	0.955150i
$146$		−	7.97801i		−	0.660265i
$147$	7.69825	−	5.50841i	0.634941	−	0.454326i
$148$	−0.830991	+	0.830991i	−0.0683070	+	0.0683070i
$149$	14.6077			1.19671			0.598356	−	0.801231i	$-0.295821\pi$
$149$	14.6077			1.19671			0.598356	+	0.801231i	$0.295821\pi$
$150$	7.79873	+	3.76561i	0.636764	+	0.307461i
$151$	14.1289			1.14980			0.574898	−	0.818225i	$-0.305042\pi$
$151$	14.1289			1.14980			0.574898	+	0.818225i	$0.305042\pi$
$152$	5.01475	−	5.01475i	0.406750	−	0.406750i
$153$	6.25354	+	12.7254i	0.505569	+	1.02879i
$154$			1.38109i			0.111291i
$155$	−1.23708	+	8.60669i	−0.0993649	+	0.691306i
$156$	0.129628	−	0.781770i	0.0103785	−	0.0625917i
$157$	−2.51780	−	2.51780i	−0.200943	−	0.200943i	0.599461	−	0.800404i	$-0.295382\pi$
$157$	−2.51780	−	2.51780i	−0.200943	−	0.200943i	−0.800404	+	0.599461i	$0.795382\pi$
$158$	5.90627	+	5.90627i	0.469877	+	0.469877i
$159$	0.421081	−	2.53949i	0.0333939	−	0.201395i
$160$	1.34010	+	1.79001i	0.105944	+	0.141513i
$161$			3.53061i			0.278251i
$162$	−8.92623	+	1.14998i	−0.701311	+	0.0903509i
$163$	11.9727	−	11.9727i	0.937775	−	0.937775i	−0.0603995	−	0.998174i	$-0.519237\pi$
$163$	11.9727	−	11.9727i	0.937775	−	0.937775i	0.998174	+	0.0603995i	$0.0192375\pi$
$164$	−9.20789			−0.719016
$165$	0.697348	+	1.34498i	0.0542885	+	0.104707i
$166$	−5.89064			−0.457202
$167$	−1.09273	+	1.09273i	−0.0845583	+	0.0845583i	−0.748121	−	0.663563i	$-0.769044\pi$
$167$	−1.09273	+	1.09273i	−0.0845583	+	0.0845583i	0.663563	+	0.748121i	$0.269044\pi$
$168$	4.97319	−	3.55852i	0.383690	−	0.274546i
$169$			12.7907i			0.983898i
$170$	−10.4609	−	1.50359i	−0.802311	−	0.115320i
$171$	−20.1372	−	6.86681i	−1.53993	−	0.525118i
$172$	−4.32271	−	4.32271i	−0.329604	−	0.329604i
$173$	−13.4058	−	13.4058i	−1.01922	−	1.01922i	−0.999812	−	0.0194133i	$-0.993820\pi$
$173$	−13.4058	−	13.4058i	−1.01922	−	1.01922i	−0.0194133	−	0.999812i	$-0.506180\pi$
$174$	−8.87937	−	1.47232i	−0.673143	−	0.111616i
$175$	8.46152	+	15.4930i	0.639631	+	1.17116i
$176$			0.391175i			0.0294860i
$177$	10.6750	+	14.9188i	0.802383	+	1.12137i
$178$	−0.834209	+	0.834209i	−0.0625266	+	0.0625266i
$179$	−21.1186			−1.57848			−0.789241	−	0.614084i	$-0.789526\pi$
$179$	−21.1186			−1.57848			−0.789241	+	0.614084i	$0.789526\pi$
$180$	3.04638	−	5.97658i	0.227064	−	0.445468i
$181$	17.4734			1.29879			0.649395	−	0.760451i	$-0.275022\pi$
$181$	17.4734			1.29879			0.649395	+	0.760451i	$0.275022\pi$
$182$	1.14220	−	1.14220i	0.0846656	−	0.0846656i
$183$	−2.00007	−	2.79519i	−0.147849	−	0.206626i
$184$			1.00000i			0.0737210i
$185$	−2.10362	+	1.57489i	−0.154661	+	0.115788i
$186$	6.64451	+	1.10175i	0.487199	+	0.0807840i
$187$	−1.30731	−	1.30731i	−0.0956002	−	0.0956002i
$188$	7.82278	+	7.82278i	0.570535	+	0.570535i
$189$	−16.1613	−	8.68169i	−1.17556	−	0.631500i
$190$	12.6946	−	9.50390i	0.920963	−	0.689485i
$191$			3.23619i			0.234162i	0.993122	+	0.117081i	$0.0373538\pi$
$191$			3.23619i			0.234162i	−0.993122	+	0.117081i	$0.962646\pi$
$192$	1.40859	−	1.00790i	0.101656	−	0.0727392i
$193$	−7.53284	+	7.53284i	−0.542226	+	0.542226i	−0.924181	−	0.381955i	$-0.875251\pi$
$193$	−7.53284	+	7.53284i	−0.542226	+	0.542226i	0.381955	+	0.924181i	$0.375251\pi$
$194$	−4.62985			−0.332404
$195$	0.535614	−	1.68907i	0.0383561	−	0.120957i
$196$	5.46521			0.390372
$197$	−5.97320	+	5.97320i	−0.425573	+	0.425573i	−0.887117	−	0.461544i	$-0.847296\pi$
$197$	−5.97320	+	5.97320i	−0.425573	+	0.425573i	0.461544	+	0.887117i	$0.347296\pi$
$198$	1.05322	−	0.517577i	0.0748493	−	0.0367826i
$199$			16.5402i			1.17250i	0.810130	+	0.586251i	$0.199397\pi$
$199$			16.5402i			1.17250i	−0.810130	+	0.586251i	$0.800603\pi$
$200$	2.39662	+	4.38819i	0.169466	+	0.310292i
$201$	−2.56193	+	15.4507i	−0.180705	+	1.08981i
$202$	4.42686	+	4.42686i	0.311473	+	0.311473i
$203$	−12.9732	−	12.9732i	−0.910538	−	0.910538i
$204$	−1.33910	+	8.07595i	−0.0937557	+	0.565430i
$205$	−20.3800	−	2.92932i	−1.42340	−	0.204593i
$206$		−	0.653876i		−	0.0455577i
$207$	2.69246	−	1.32313i	0.187139	−	0.0919641i
$208$	0.323514	−	0.323514i	0.0224317	−	0.0224317i
$209$	2.77419			0.191894
$210$	12.1393	−	6.29402i	0.837694	−	0.434328i
$211$	−12.5787			−0.865952			−0.432976	−	0.901405i	$-0.642537\pi$
$211$	−12.5787			−0.865952			−0.432976	+	0.901405i	$0.642537\pi$
$212$	1.05090	−	1.05090i	0.0721759	−	0.0721759i
$213$	−12.8367	+	9.18516i	−0.879554	+	0.629357i
$214$		−	16.8068i		−	1.14889i
$215$	−8.19236	−	10.9427i	−0.558714	−	0.746289i
$216$	−4.57749	−	2.45898i	−0.311459	−	0.167312i
$217$	9.70793	+	9.70793i	0.659017	+	0.659017i
$218$	−0.930653	−	0.930653i	−0.0630318	−	0.0630318i
$219$	−13.6322	−	2.26040i	−0.921178	−	0.152743i
$220$	−0.124445	+	0.865797i	−0.00839011	+	0.0583720i
$221$			2.16237i			0.145457i
$222$	1.18449	+	1.65537i	0.0794976	+	0.111101i
$223$	13.8055	−	13.8055i	0.924485	−	0.924485i	−0.0728577	−	0.997342i	$-0.523212\pi$
$223$	13.8055	−	13.8055i	0.924485	−	0.924485i	0.997342	+	0.0728577i	$0.0232119\pi$
$224$	3.53061			0.235899
$225$	8.64397	−	12.2589i	0.576265	−	0.817263i
$226$	−5.23328			−0.348113
$227$	6.12215	−	6.12215i	0.406342	−	0.406342i	−0.474119	−	0.880461i	$-0.657233\pi$
$227$	6.12215	−	6.12215i	0.406342	−	0.406342i	0.880461	+	0.474119i	$0.157233\pi$
$228$	−7.14798	−	9.98962i	−0.473387	−	0.661579i
$229$		−	2.16016i		−	0.142747i	−0.997450	−	0.0713737i	$-0.977262\pi$
$229$		−	2.16016i		−	0.142747i	0.997450	−	0.0713737i	$-0.0227383\pi$
$230$	−0.318132	+	2.21332i	−0.0209770	+	0.145942i
$231$	2.35989	+	0.391301i	0.155270	+	0.0257457i
$232$	−3.67448	−	3.67448i	−0.241242	−	0.241242i
$233$	9.23376	+	9.23376i	0.604924	+	0.604924i	0.941615	−	0.336692i	$-0.109308\pi$
$233$	9.23376	+	9.23376i	0.604924	+	0.604924i	−0.336692	+	0.941615i	$0.609308\pi$
$234$	−1.29910	−	0.442995i	−0.0849248	−	0.0289595i
$235$	14.8257	+	19.8030i	0.967119	+	1.29181i
$236$			10.5913i			0.689435i
$237$	11.7656	−	8.41874i	0.764256	−	0.546856i
$238$	−11.7993	+	11.7993i	−0.764838	+	0.764838i
$239$	−22.0332			−1.42521			−0.712606	−	0.701564i	$-0.752485\pi$
$239$	−22.0332			−1.42521			−0.712606	+	0.701564i	$0.752485\pi$
$240$	3.43831	−	1.78270i	0.221942	−	0.115073i
$241$	−2.81804			−0.181526			−0.0907630	−	0.995873i	$-0.528931\pi$
$241$	−2.81804			−0.181526			−0.0907630	+	0.995873i	$0.528931\pi$
$242$	7.66997	−	7.66997i	0.493045	−	0.493045i
$243$	−0.564060	+	15.5782i	−0.0361845	+	0.999345i
$244$		−	1.98438i		−	0.127037i
$245$	12.0963	+	1.73866i	0.772803	+	0.111079i
$246$	−2.60886	+	15.7337i	−0.166335	+	1.00315i
$247$	−2.29434	−	2.29434i	−0.145985	−	0.145985i
$248$	2.74965	+	2.74965i	0.174603	+	0.174603i
$249$	−1.66898	+	10.0655i	−0.105768	+	0.637872i
$250$	3.90846	+	10.4749i	0.247193	+	0.662492i
$251$			13.8933i			0.876936i	0.898747	+	0.438468i	$0.144479\pi$
$251$			13.8933i			0.876936i	−0.898747	+	0.438468i	$0.855521\pi$
$252$	−4.67147	−	9.50601i	−0.294275	−	0.598823i
$253$	−0.276603	+	0.276603i	−0.0173899	+	0.0173899i
$254$	20.9709			1.31583
$255$	−5.53307	+	17.4487i	−0.346495	+	1.09268i
$256$	1.00000			0.0625000
$257$	8.45334	−	8.45334i	0.527305	−	0.527305i	−0.392463	−	0.919768i	$-0.628377\pi$
$257$	8.45334	−	8.45334i	0.527305	−	0.527305i	0.919768	+	0.392463i	$0.128377\pi$
$258$	−8.61105	+	6.16156i	−0.536101	+	0.383602i
$259$			4.14917i			0.257817i
$260$	0.818961	−	0.613120i	0.0507898	−	0.0380241i
$261$	−5.03155	+	14.7552i	−0.311445	+	0.913325i
$262$	−14.1877	−	14.1877i	−0.876516	−	0.876516i
$263$	16.4266	+	16.4266i	1.01291	+	1.01291i	0.999916	+	0.0129934i	$0.00413606\pi$
$263$	16.4266	+	16.4266i	1.01291	+	1.01291i	0.0129934	+	0.999916i	$0.495864\pi$
$264$	0.668409	+	0.110831i	0.0411378	+	0.00682118i
$265$	2.66030	−	1.99165i	0.163421	−	0.122346i
$266$		−	25.0388i		−	1.53523i
$267$	1.18907	+	1.66178i	0.0727702	+	0.101700i
$268$	−6.39385	+	6.39385i	−0.390566	+	0.390566i
$269$	4.14372			0.252647			0.126323	−	0.991989i	$-0.459682\pi$
$269$	4.14372			0.252647			0.126323	+	0.991989i	$0.459682\pi$
$270$	−9.34918	−	6.89875i	−0.568973	−	0.419845i
$271$	15.2033			0.923534			0.461767	−	0.887001i	$-0.347216\pi$
$271$	15.2033			0.923534			0.461767	+	0.887001i	$0.347216\pi$
$272$	−3.34201	+	3.34201i	−0.202639	+	0.202639i
$273$	−1.62809	−	2.27532i	−0.0985362	−	0.137709i
$274$		−	5.53409i		−	0.334326i
$275$	−0.550875	+	1.87670i	−0.0332190	+	0.113169i
$276$	1.70872	+	0.283328i	0.102853	+	0.0170544i
$277$	−9.06239	−	9.06239i	−0.544506	−	0.544506i	0.380340	−	0.924847i	$-0.375807\pi$
$277$	−9.06239	−	9.06239i	−0.544506	−	0.544506i	−0.924847	+	0.380340i	$0.875807\pi$
$278$	−11.9750	−	11.9750i	−0.718210	−	0.718210i
$279$	3.76515	−	11.0414i	0.225414	−	0.661034i
$280$	7.81438	+	1.12320i	0.466998	+	0.0671240i
$281$			8.70916i			0.519545i	0.965670	+	0.259773i	$0.0836476\pi$
$281$			8.70916i			0.519545i	−0.965670	+	0.259773i	$0.916352\pi$
$282$	15.5834	−	11.1505i	0.927976	−	0.664004i
$283$	−22.7584	+	22.7584i	−1.35284	+	1.35284i	−0.470379	+	0.882464i	$0.655883\pi$
$283$	−22.7584	+	22.7584i	−1.35284	+	1.35284i	−0.882464	+	0.470379i	$0.844117\pi$
$284$	−9.11312			−0.540764
$285$	−12.6428	−	24.3842i	−0.748893	−	1.44440i
$286$	0.178970			0.0105827
$287$	−22.9877	+	22.9877i	−1.35692	+	1.35692i
$288$	−1.32313	−	2.69246i	−0.0779664	−	0.158654i
$289$		−	5.33807i		−	0.314004i
$290$	−6.96384	−	9.30178i	−0.408931	−	0.546219i
$291$	−1.31177	+	7.91111i	−0.0768971	+	0.463758i
$292$	−5.64130	−	5.64130i	−0.330132	−	0.330132i
$293$	18.7508	+	18.7508i	1.09544	+	1.09544i	0.994937	+	0.100499i	$0.0320439\pi$
$293$	18.7508	+	18.7508i	1.09544	+	1.09544i	0.100499	+	0.994937i	$0.467956\pi$
$294$	1.54845	−	9.33852i	0.0903074	−	0.544634i
$295$	−3.36943	+	23.4419i	−0.196176	+	1.36484i
$296$			1.17520i			0.0683070i
$297$	−0.585987	−	1.94631i	−0.0340024	−	0.112936i
$298$	10.3292	−	10.3292i	0.598356	−	0.598356i
$299$	0.457518			0.0264589
$300$	8.17722	−	2.85185i	0.472112	−	0.164652i
$301$	−21.5835			−1.24405
$302$	9.99067	−	9.99067i	0.574898	−	0.574898i
$303$	8.81852	−	6.31001i	0.506611	−	0.362501i
$304$		−	7.09192i		−	0.406750i
$305$	0.631296	−	4.39208i	0.0361479	−	0.251490i
$306$	13.4201	+	4.57629i	0.767178	+	0.261609i
$307$	−22.2579	−	22.2579i	−1.27032	−	1.27032i	−0.945918	−	0.324407i	$-0.894835\pi$
$307$	−22.2579	−	22.2579i	−1.27032	−	1.27032i	−0.324407	−	0.945918i	$-0.605165\pi$
$308$	0.976577	+	0.976577i	0.0556456	+	0.0556456i
$309$	−1.11729	−	0.185261i	−0.0635604	−	0.0105392i
$310$	5.21110	+	6.96060i	0.295971	+	0.395336i
$311$		−	7.36643i		−	0.417712i	−0.977946	−	0.208856i	$-0.933026\pi$
$311$		−	7.36643i		−	0.417712i	0.977946	−	0.208856i	$-0.0669740\pi$
$312$	−0.461134	−	0.644456i	−0.0261066	−	0.0364851i
$313$	12.8470	−	12.8470i	0.726158	−	0.726158i	−0.243694	−	0.969852i	$-0.578359\pi$
$313$	12.8470	−	12.8470i	0.726158	−	0.726158i	0.969852	+	0.243694i	$0.0783594\pi$
$314$	−3.56071			−0.200943
$315$	−7.31529	−	22.5260i	−0.412170	−	1.26920i
$316$	8.35272			0.469877
$317$	−14.6817	+	14.6817i	−0.824609	+	0.824609i	−0.986765	−	0.162156i	$-0.948155\pi$
$317$	−14.6817	+	14.6817i	−0.824609	+	0.824609i	0.162156	+	0.986765i	$0.448155\pi$
$318$	−1.49794	−	2.09344i	−0.0840003	−	0.117394i
$319$		−	2.03274i		−	0.113812i
$320$	2.21332	+	0.318132i	0.123728	+	0.0177841i
$321$	−28.7182	−	4.76185i	−1.60289	−	0.265780i
$322$	2.49652	+	2.49652i	0.139126	+	0.139126i
$323$	23.7013	+	23.7013i	1.31877	+	1.31877i
$324$	−5.49864	+	7.12495i	−0.305480	+	0.395831i
$325$	2.00768	−	1.09649i	0.111366	−	0.0608226i
$326$		−	16.9320i		−	0.937775i
$327$	−1.85391	+	1.32655i	−0.102521	+	0.0733581i
$328$	−6.51096	+	6.51096i	−0.359508	+	0.359508i
$329$	39.0594			2.15342
$330$	1.44415	+	0.457947i	0.0794976	+	0.0252092i
$331$	19.6920			1.08237			0.541185	−	0.840904i	$-0.317976\pi$
$331$	19.6920			1.08237			0.541185	+	0.840904i	$0.317976\pi$
$332$	−4.16531	+	4.16531i	−0.228601	+	0.228601i
$333$	3.16417	−	1.55494i	0.173396	−	0.0852104i
$334$			1.54536i			0.0845583i
$335$	−16.1857	+	12.1176i	−0.884321	+	0.662053i
$336$	1.00032	−	6.03283i	0.0545720	−	0.329118i
$337$	13.8778	+	13.8778i	0.755973	+	0.755973i	0.975587	−	0.219614i	$-0.0704798\pi$
$337$	13.8778	+	13.8778i	0.755973	+	0.755973i	−0.219614	+	0.975587i	$0.570480\pi$
$338$	9.04437	+	9.04437i	0.491949	+	0.491949i
$339$	−1.48274	+	8.94221i	−0.0805312	+	0.485674i
$340$	−8.46014	+	6.33374i	−0.458816	+	0.343495i
$341$			1.52112i			0.0823733i
$342$	−19.0947	+	9.38356i	−1.03252	+	0.507405i
$343$	−3.83162	+	3.83162i	−0.206888	+	0.206888i
$344$	−6.11324			−0.329604
$345$	3.69181	+	1.17069i	0.198760	+	0.0630281i
$346$	−18.9587			−1.01922
$347$	16.4622	−	16.4622i	0.883736	−	0.883736i	−0.110176	−	0.993912i	$-0.535141\pi$
$347$	16.4622	−	16.4622i	0.883736	−	0.883736i	0.993912	+	0.110176i	$0.0351414\pi$
$348$	−7.31975	+	5.23758i	−0.392380	+	0.280764i
$349$		−	36.9783i		−	1.97940i	−0.143141	−	0.989702i	$-0.545720\pi$
$349$		−	36.9783i		−	1.97940i	0.143141	−	0.989702i	$-0.454280\pi$
$350$	16.9384	+	4.97200i	0.905396	+	0.265765i
$351$	−1.12503	+	2.09428i	−0.0600495	+	0.111785i
$352$	0.276603	+	0.276603i	0.0147430	+	0.0147430i
$353$	−4.86250	−	4.86250i	−0.258805	−	0.258805i	0.565763	−	0.824568i	$-0.308582\pi$
$353$	−4.86250	−	4.86250i	−0.258805	−	0.258805i	−0.824568	+	0.565763i	$0.808582\pi$
$354$	18.0976	+	3.00081i	0.961874	+	0.159491i
$355$	−20.1703	−	2.89918i	−1.07053	−	0.153872i
$356$			1.17975i			0.0625266i
$357$	16.8187	+	23.5049i	0.890139	+	1.24401i
$358$	−14.9331	+	14.9331i	−0.789241	+	0.789241i
$359$	26.5958			1.40367			0.701837	−	0.712338i	$-0.252363\pi$
$359$	26.5958			1.40367			0.701837	+	0.712338i	$0.252363\pi$
$360$	−2.07196	−	6.38020i	−0.109202	−	0.336266i
$361$	−31.2954			−1.64712
$362$	12.3556	−	12.3556i	0.649395	−	0.649395i
$363$	−10.9327	−	15.2790i	−0.573819	−	0.801938i
$364$		−	1.61532i		−	0.0846656i
$365$	−10.6913	−	14.2807i	−0.559610	−	0.747486i
$366$	−3.39076	−	0.562232i	−0.177238	−	0.0293883i
$367$	17.5306	+	17.5306i	0.915090	+	0.915090i	0.996667	−	0.0815769i	$-0.0259956\pi$
$367$	17.5306	+	17.5306i	0.915090	+	0.915090i	−0.0815769	+	0.996667i	$0.525996\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$	26.1454	+	8.91561i	1.36107	+	0.464128i
$370$	−0.373868	+	2.60109i	−0.0194365	+	0.135224i
$371$		−	5.24717i		−	0.272420i
$372$	5.47743	−	3.91932i	0.283991	−	0.203207i
$373$	−15.2026	+	15.2026i	−0.787161	+	0.787161i	−0.981028	−	0.193867i	$-0.937897\pi$
$373$	−15.2026	+	15.2026i	−0.787161	+	0.787161i	0.193867	+	0.981028i	$0.437897\pi$
$374$	−1.84882			−0.0956002
$375$	19.0061	−	3.71062i	0.981470	−	0.191616i
$376$	11.0631			0.570535
$377$	−1.68114	+	1.68114i	−0.0865832	+	0.0865832i
$378$	−17.5667	+	5.28891i	−0.903532	+	0.272032i
$379$			24.6155i			1.26442i	0.774799	+	0.632208i	$0.217851\pi$
$379$			24.6155i			1.26442i	−0.774799	+	0.632208i	$0.782149\pi$
$380$	2.25617	−	15.6967i	0.115739	−	0.805224i
$381$	5.94166	−	35.8334i	0.304400	−	1.83580i
$382$	2.28833	+	2.28833i	0.117081	+	0.117081i
$383$	1.16468	+	1.16468i	0.0595121	+	0.0595121i	0.736236	−	0.676724i	$-0.236601\pi$
$383$	1.16468	+	1.16468i	0.0595121	+	0.0595121i	−0.676724	+	0.736236i	$0.736601\pi$
$384$	0.283328	−	1.70872i	0.0144585	−	0.0871978i
$385$	1.85080	+	2.47216i	0.0943254	+	0.125993i
$386$			10.6531i			0.542226i
$387$	8.08862	+	16.4596i	0.411168	+	0.836689i
$388$	−3.27380	+	3.27380i	−0.166202	+	0.166202i
$389$	5.08293			0.257715			0.128857	−	0.991663i	$-0.458869\pi$
$389$	5.08293			0.257715			0.128857	+	0.991663i	$0.458869\pi$
$390$	−0.815616	−	1.57309i	−0.0413003	−	0.0796565i
$391$	−4.72632			−0.239020
$392$	3.86449	−	3.86449i	0.195186	−	0.195186i
$393$	−28.2625	+	20.2230i	−1.42565	+	1.02011i
$394$			8.44738i			0.425573i
$395$	18.4873	+	2.65727i	0.930195	+	0.133702i
$396$	0.378759	−	1.11072i	0.0190333	−	0.0558159i
$397$	−2.47590	−	2.47590i	−0.124262	−	0.124262i	0.642241	−	0.766503i	$-0.278005\pi$
$397$	−2.47590	−	2.47590i	−0.124262	−	0.124262i	−0.766503	+	0.642241i	$0.778005\pi$
$398$	11.6957	+	11.6957i	0.586251	+	0.586251i
$399$	−42.7843	−	7.09421i	−2.14190	−	0.355155i
$400$	4.79758	+	1.40826i	0.239879	+	0.0704128i
$401$		−	26.0071i		−	1.29873i	−0.760475	−	0.649367i	$-0.775034\pi$
$401$		−	26.0071i		−	1.29873i	0.760475	−	0.649367i	$-0.224966\pi$
$402$	9.11374	+	12.7369i	0.454552	+	0.635257i
$403$	1.25801	−	1.25801i	0.0626661	−	0.0626661i
$404$	6.26052			0.311473
$405$	−14.4369	+	14.0205i	−0.717377	+	0.696685i
$406$	−18.3468			−0.910538
$407$	−0.325063	+	0.325063i	−0.0161128	+	0.0161128i
$408$	4.76367	+	6.65745i	0.235837	+	0.329593i
$409$		−	1.04874i		−	0.0518569i	−0.999664	−	0.0259284i	$-0.991746\pi$
$409$		−	1.04874i		−	0.0518569i	0.999664	−	0.0259284i	$-0.00825421\pi$
$410$	−16.4822	+	12.3395i	−0.813998	+	0.609405i
$411$	−9.45621	−	1.56796i	−0.466440	−	0.0773419i
$412$	−0.462360	−	0.462360i	−0.0227788	−	0.0227788i
$413$	26.4414	+	26.4414i	1.30109	+	1.30109i
$414$	0.968258	−	2.83945i	0.0475873	−	0.139551i
$415$	−10.5443	+	7.89405i	−0.517599	+	0.387504i
$416$		−	0.457518i		−	0.0224317i
$417$	−23.8547	+	17.0690i	−1.16817	+	0.835873i
$418$	1.96165	−	1.96165i	0.0959472	−	0.0959472i
$419$	−15.2582			−0.745413			−0.372706	−	0.927949i	$-0.621570\pi$
$419$	−15.2582			−0.745413			−0.372706	+	0.927949i	$0.621570\pi$
$420$	4.13327	−	13.0344i	0.201683	−	0.636011i
$421$	−3.29001			−0.160345			−0.0801727	−	0.996781i	$-0.525547\pi$
$421$	−3.29001			−0.160345			−0.0801727	+	0.996781i	$0.525547\pi$
$422$	−8.89447	+	8.89447i	−0.432976	+	0.432976i
$423$	−14.6379	−	29.7869i	−0.711721	−	1.44829i
$424$		−	1.48619i		−	0.0721759i
$425$	−20.7400	+	11.3272i	−1.00604	+	0.549448i
$426$	−2.58201	+	15.5718i	−0.125099	+	0.754455i
$427$	−4.95405	−	4.95405i	−0.239743	−	0.239743i
$428$	−11.8842	−	11.8842i	−0.574445	−	0.574445i
$429$	0.0507072	−	0.305809i	0.00244817	−	0.0147646i
$430$	−13.5306	−	1.94482i	−0.652501	−	0.0937873i
$431$		−	13.0209i		−	0.627196i	−0.949556	−	0.313598i	$-0.898466\pi$
$431$		−	13.0209i		−	0.627196i	0.949556	−	0.313598i	$-0.101534\pi$
$432$	−4.97554	+	1.49802i	−0.239386	+	0.0720733i
$433$	−2.97532	+	2.97532i	−0.142985	+	0.142985i	−0.774976	−	0.631991i	$-0.782238\pi$
$433$	−2.97532	+	2.97532i	−0.142985	+	0.142985i	0.631991	+	0.774976i	$0.282238\pi$
$434$	13.7291			0.659017
$435$	−17.8672	+	9.26380i	−0.856666	+	0.444165i
$436$	−1.31614			−0.0630318
$437$	5.01475	−	5.01475i	0.239888	−	0.239888i
$438$	−11.2378	+	8.04107i	−0.536960	+	0.384217i
$439$			27.1103i			1.29390i	0.762530	+	0.646952i	$0.223957\pi$
$439$			27.1103i			1.29390i	−0.762530	+	0.646952i	$0.776043\pi$
$440$	0.524215	+	0.700207i	0.0249910	+	0.0333811i
$441$	−15.5182	−	5.29173i	−0.738962	−	0.251987i
$442$	1.52903	+	1.52903i	0.0727285	+	0.0727285i
$443$	−4.53631	−	4.53631i	−0.215526	−	0.215526i	0.591084	−	0.806610i	$-0.298700\pi$
$443$	−4.53631	−	4.53631i	−0.215526	−	0.215526i	−0.806610	+	0.591084i	$0.798700\pi$
$444$	2.00809	+	0.332967i	0.0952996	+	0.0158019i
$445$	−0.375316	+	2.61116i	−0.0177917	+	0.123781i
$446$		−	19.5239i		−	0.924485i
$447$	−14.7232	−	20.5763i	−0.696383	−	0.973226i
$448$	2.49652	−	2.49652i	0.117949	−	0.117949i
$449$	34.7433			1.63964			0.819819	−	0.572623i	$-0.194074\pi$
$449$	34.7433			1.63964			0.819819	+	0.572623i	$0.194074\pi$
$450$	−2.55617	−	14.7806i	−0.120499	−	0.696764i
$451$	−3.60190			−0.169607
$452$	−3.70049	+	3.70049i	−0.174056	+	0.174056i
$453$	−14.2406	−	19.9019i	−0.669083	−	0.935073i
$454$		−	8.65803i		−	0.406342i
$455$	0.513884	−	3.57522i	0.0240913	−	0.167609i
$456$	−12.1181	−	2.00934i	−0.567483	−	0.0940961i
$457$	7.54987	+	7.54987i	0.353168	+	0.353168i	0.861287	−	0.508119i	$-0.169659\pi$
$457$	7.54987	+	7.54987i	0.353168	+	0.353168i	−0.508119	+	0.861287i	$0.669659\pi$
$458$	−1.52746	−	1.52746i	−0.0713737	−	0.0713737i
$459$	11.6219	−	21.6347i	0.542464	−	1.00982i
$460$	1.34010	+	1.79001i	0.0624826	+	0.0834595i
$461$			17.2715i			0.804413i	0.915549	+	0.402207i	$0.131757\pi$
$461$			17.2715i			0.804413i	−0.915549	+	0.402207i	$0.868243\pi$
$462$	1.94539	−	1.39201i	0.0905077	−	0.0647619i
$463$	24.1703	−	24.1703i	1.12329	−	1.12329i	0.132048	−	0.991243i	$-0.457845\pi$
$463$	24.1703	−	24.1703i	1.12329	−	1.12329i	0.991243	−	0.132048i	$-0.0421553\pi$
$464$	−5.19650			−0.241242
$465$	13.3702	−	6.93218i	0.620027	−	0.321472i
$466$	13.0585			0.604924
$467$	−11.9797	+	11.9797i	−0.554355	+	0.554355i	−0.927695	−	0.373340i	$-0.878213\pi$
$467$	−11.9797	+	11.9797i	−0.554355	+	0.554355i	0.373340	+	0.927695i	$0.378213\pi$
$468$	−1.23185	+	0.605357i	−0.0569421	+	0.0279826i
$469$			31.9247i			1.47415i
$470$	24.4862	+	3.51952i	1.12946	+	0.162343i
$471$	−1.00885	+	6.08426i	−0.0464854	+	0.280348i
$472$	7.48918	+	7.48918i	0.344717	+	0.344717i
$473$	−1.69094	−	1.69094i	−0.0777494	−	0.0777494i
$474$	2.36656	−	14.2725i	0.108700	−	0.655556i
$475$	9.98724	−	34.0241i	0.458246	−	1.56113i
$476$			16.6868i			0.764838i
$477$	−4.00151	+	1.96643i	−0.183217	+	0.0900367i
$478$	−15.5799	+	15.5799i	−0.712606	+	0.712606i
$479$	−25.6825			−1.17346			−0.586731	−	0.809782i	$-0.699585\pi$
$479$	−25.6825			−1.17346			−0.586731	+	0.809782i	$0.699585\pi$
$480$	1.17069	−	3.69181i	0.0534347	−	0.168507i
$481$	0.537674			0.0245158
$482$	−1.99266	+	1.99266i	−0.0907630	+	0.0907630i
$483$	4.97319	−	3.55852i	0.226288	−	0.161918i
$484$		−	10.8470i		−	0.493045i
$485$	−8.28746	+	6.20446i	−0.376314	+	0.281730i
$486$	10.6166	+	11.4143i	0.481580	+	0.517765i
$487$	−17.0755	−	17.0755i	−0.773766	−	0.773766i	0.204996	−	0.978763i	$-0.434282\pi$
$487$	−17.0755	−	17.0755i	−0.773766	−	0.773766i	−0.978763	+	0.204996i	$0.934282\pi$
$488$	−1.40317	−	1.40317i	−0.0635186	−	0.0635186i
$489$	−28.9320	−	4.79730i	−1.30835	−	0.216942i
$490$	9.78278	−	7.32394i	0.441941	−	0.330862i
$491$		−	5.69263i		−	0.256905i	−0.991716	−	0.128452i	$-0.958999\pi$
$491$		−	5.69263i		−	0.256905i	0.991716	−	0.128452i	$-0.0410009\pi$
$492$	9.28068	+	12.9702i	0.418405	+	0.584740i
$493$	17.3668	−	17.3668i	0.782160	−	0.782160i
$494$	−3.24468			−0.145985
$495$	1.19167	−	2.33789i	0.0535616	−	0.105080i
$496$	3.88859			0.174603
$497$	−22.7511	+	22.7511i	−1.02053	+	1.02053i
$498$	5.93720	+	8.29750i	0.266052	+	0.371820i
$499$		−	20.0610i		−	0.898053i	−0.893518	−	0.449027i	$-0.851771\pi$
$499$		−	20.0610i		−	0.898053i	0.893518	−	0.449027i	$-0.148229\pi$
$500$	10.1706	+	4.64319i	0.454842	+	0.207650i
$501$	2.64059	+	0.437844i	0.117973	+	0.0195614i
$502$	9.82403	+	9.82403i	0.438468	+	0.438468i
$503$	−14.6107	−	14.6107i	−0.651457	−	0.651457i	0.301887	−	0.953344i	$-0.402384\pi$
$503$	−14.6107	−	14.6107i	−0.651457	−	0.651457i	−0.953344	+	0.301887i	$0.902384\pi$
$504$	−10.0250	−	3.41854i	−0.446549	−	0.152274i
$505$	13.8566	+	1.99167i	0.616608	+	0.0886282i
$506$			0.391175i			0.0173899i
$507$	18.0168	−	12.8918i	0.800156	−	0.572544i
$508$	14.8287	−	14.8287i	0.657916	−	0.657916i
$509$	36.2578			1.60710			0.803550	−	0.595237i	$-0.202942\pi$
$509$	36.2578			1.60710			0.803550	+	0.595237i	$0.202942\pi$
$510$	8.42560	+	16.2505i	0.373092	+	0.719586i
$511$	−28.1672			−1.24605
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	10.6238	+	35.2861i	0.469053	+	1.55792i
$514$		−	11.9548i		−	0.527305i
$515$	−0.876260	−	1.17044i	−0.0386126	−	0.0515759i
$516$	−1.73205	+	10.4458i	−0.0762494	+	0.459851i
$517$	3.06008	+	3.06008i	0.134582	+	0.134582i
$518$	2.93391	+	2.93391i	0.128908	+	0.128908i
$519$	−5.37153	+	32.3951i	−0.235784	+	1.42199i
$520$	0.145551	−	1.01263i	0.00638283	−	0.0444069i
$521$			32.3134i			1.41568i	0.706375	+	0.707838i	$0.250329\pi$
$521$			32.3134i			1.41568i	−0.706375	+	0.707838i	$0.749671\pi$
$522$	6.87566	+	13.9914i	0.300940	+	0.612385i
$523$	20.5874	−	20.5874i	0.900225	−	0.900225i	−0.0952304	−	0.995455i	$-0.530359\pi$
$523$	20.5874	−	20.5874i	0.900225	−	0.900225i	0.995455	+	0.0952304i	$0.0303588\pi$
$524$	−20.0644			−0.876516
$525$	13.2949	−	27.5343i	0.580237	−	1.20169i
$526$	23.2308			1.01291
$527$	−12.9957	+	12.9957i	−0.566102	+	0.566102i
$528$	0.551006	−	0.394267i	0.0239795	−	0.0171583i
$529$			1.00000i			0.0434783i
$530$	0.472805	−	3.28942i	0.0205374	−	0.142883i
$531$	10.2551	−	30.0735i	0.445033	−	1.30508i
$532$	−17.7051	−	17.7051i	−0.767614	−	0.767614i
$533$	2.97888	+	2.97888i	0.129030	+	0.129030i
$534$	2.01586	+	0.334256i	0.0872349	+	0.0144647i
$535$	−22.5228	−	30.0843i	−0.973748	−	1.30066i
$536$			9.04227i			0.390566i
$537$	21.2856	+	29.7475i	0.918540	+	1.28370i
$538$	2.93005	−	2.93005i	0.126323	−	0.126323i
$539$	2.13786			0.0920840
$540$	−11.4890	+	1.73271i	−0.494409	+	0.0745641i
$541$	−35.3989			−1.52192			−0.760959	−	0.648800i	$-0.775271\pi$
$541$	−35.3989			−1.52192			−0.760959	+	0.648800i	$0.775271\pi$
$542$	10.7503	−	10.7503i	0.461767	−	0.461767i
$543$	−17.6115	−	24.6129i	−0.755784	−	1.05624i
$544$			4.72632i			0.202639i
$545$	−2.91305	−	0.418707i	−0.124781	−	0.0179354i
$546$	−2.76013	−	0.457665i	−0.118122	−	0.0195863i
$547$	3.54099	+	3.54099i	0.151402	+	0.151402i	0.778744	−	0.627342i	$-0.215857\pi$
$547$	3.54099	+	3.54099i	0.151402	+	0.151402i	−0.627342	+	0.778744i	$0.715857\pi$
$548$	−3.91319	−	3.91319i	−0.167163	−	0.167163i
$549$	−1.92140	+	5.63456i	−0.0820031	+	0.240477i
$550$	0.937498	+	1.71655i	0.0399750	+	0.0731941i
$551$			36.8532i			1.57000i
$552$	1.40859	−	1.00790i	0.0599536	−	0.0428993i
$553$	20.8527	−	20.8527i	0.886748	−	0.886748i
$554$	−12.8162			−0.544506
$555$	4.33861	+	1.37580i	0.184164	+	0.0583994i
$556$	−16.9351			−0.718210
$557$	−0.936148	+	0.936148i	−0.0396658	+	0.0396658i	−0.726662	−	0.686996i	$-0.758929\pi$
$557$	−0.936148	+	0.936148i	−0.0396658	+	0.0396658i	0.686996	+	0.726662i	$0.258929\pi$
$558$	−5.14512	−	10.4698i	−0.217810	−	0.443224i
$559$			2.79691i			0.118297i
$560$	6.31982	−	4.73138i	0.267061	−	0.199937i
$561$	−0.523823	+	3.15911i	−0.0221158	+	0.133378i
$562$	6.15831	+	6.15831i	0.259773	+	0.259773i
$563$	−22.3491	−	22.3491i	−0.941900	−	0.941900i	0.0565022	−	0.998402i	$-0.482005\pi$
$563$	−22.3491	−	22.3491i	−0.941900	−	0.941900i	−0.998402	+	0.0565022i	$0.982005\pi$
$564$	3.13448	−	18.9037i	0.131986	−	0.795990i
$565$	−9.36761	+	7.01313i	−0.394098	+	0.295044i
$566$			32.1852i			1.35284i
$567$	4.06013	+	31.5150i	0.170509	+	1.32351i
$568$	−6.44395	+	6.44395i	−0.270382	+	0.270382i
$569$	29.5184			1.23747			0.618737	−	0.785598i	$-0.287645\pi$
$569$	29.5184			1.23747			0.618737	+	0.785598i	$0.287645\pi$
$570$	−26.1820	−	8.30248i	−1.09665	−	0.347753i
$571$	27.2195			1.13910			0.569549	−	0.821957i	$-0.307118\pi$
$571$	27.2195			1.13910			0.569549	+	0.821957i	$0.307118\pi$
$572$	0.126551	−	0.126551i	0.00529135	−	0.00529135i
$573$	4.55847	−	3.26177i	0.190433	−	0.136262i
$574$			32.5095i			1.35692i
$575$	2.39662	+	4.38819i	0.0999458	+	0.183000i
$576$	−2.83945	−	0.968258i	−0.118310	−	0.0403441i
$577$	−19.3742	−	19.3742i	−0.806560	−	0.806560i	0.177552	−	0.984111i	$-0.443182\pi$
$577$	−19.3742	−	19.3742i	−0.806560	−	0.806560i	−0.984111	+	0.177552i	$0.943182\pi$
$578$	−3.77458	−	3.77458i	−0.157002	−	0.157002i
$579$	18.2031	+	3.01831i	0.756494	+	0.125437i
$580$	−11.5015	−	1.65317i	−0.477575	−	0.0686443i
$581$			20.7976i			0.862828i
$582$	4.66644	+	6.52156i	0.193430	+	0.270327i
$583$	0.411085	−	0.411085i	0.0170254	−	0.0170254i
$584$	−7.97801			−0.330132
$585$	−2.91906	+	0.947960i	−0.120688	+	0.0391933i
$586$	26.5177			1.09544
$587$	8.50047	−	8.50047i	0.350852	−	0.350852i	−0.509575	−	0.860427i	$-0.670197\pi$
$587$	8.50047	−	8.50047i	0.350852	−	0.350852i	0.860427	+	0.509575i	$0.170197\pi$
$588$	−5.50841	−	7.69825i	−0.227163	−	0.317471i
$589$		−	27.5776i		−	1.13631i
$590$	14.1934	+	18.9585i	0.584333	+	0.780509i
$591$	14.4342	+	2.39338i	0.593744	+	0.0984506i
$592$	0.830991	+	0.830991i	0.0341535	+	0.0341535i
$593$	−17.9882	−	17.9882i	−0.738685	−	0.738685i	0.233638	−	0.972324i	$-0.424937\pi$
$593$	−17.9882	−	17.9882i	−0.738685	−	0.738685i	−0.972324	+	0.233638i	$0.924937\pi$
$594$	−1.79060	−	0.961892i	−0.0734693	−	0.0394669i
$595$	−5.30860	+	36.9332i	−0.217631	+	1.51411i
$596$		−	14.6077i		−	0.598356i
$597$	23.2983	−	16.6709i	0.953537	−	0.682295i
$598$	0.323514	−	0.323514i	0.0132295	−	0.0132295i
$599$	36.9679			1.51047			0.755234	−	0.655455i	$-0.227523\pi$
$599$	36.9679			1.51047			0.755234	+	0.655455i	$0.227523\pi$
$600$	3.76561	−	7.79873i	0.153730	−	0.318382i
$601$	40.8104			1.66469			0.832345	−	0.554259i	$-0.186998\pi$
$601$	40.8104			1.66469			0.832345	+	0.554259i	$0.186998\pi$
$602$	−15.2618	+	15.2618i	−0.622025	+	0.622025i
$603$	24.3459	−	11.9641i	0.991442	−	0.487217i
$604$		−	14.1289i		−	0.574898i
$605$	3.45077	−	24.0079i	0.140294	−	0.976058i
$606$	1.77378	−	10.6975i	0.0720550	−	0.434556i
$607$	−1.50520	−	1.50520i	−0.0610943	−	0.0610943i	0.675899	−	0.736994i	$-0.263755\pi$
$607$	−1.50520	−	1.50520i	−0.0610943	−	0.0610943i	−0.736994	+	0.675899i	$0.763755\pi$
$608$	−5.01475	−	5.01475i	−0.203375	−	0.203375i
$609$	−5.19818	+	31.3496i	−0.210641	+	1.27035i
$610$	−2.65928	−	3.55206i	−0.107671	−	0.143819i
$611$		−	5.06156i		−	0.204769i
$612$	12.7254	−	6.25354i	0.514394	−	0.252785i
$613$	−5.16544	+	5.16544i	−0.208630	+	0.208630i	−0.803685	−	0.595055i	$-0.797130\pi$
$613$	−5.16544	+	5.16544i	−0.208630	+	0.208630i	0.595055	+	0.803685i	$0.297130\pi$
$614$	−31.4774			−1.27032
$615$	16.4149	+	31.6596i	0.661913	+	1.27664i
$616$	1.38109			0.0556456
$617$	−6.24729	+	6.24729i	−0.251507	+	0.251507i	−0.821588	−	0.570082i	$-0.806912\pi$
$617$	−6.24729	+	6.24729i	−0.251507	+	0.251507i	0.570082	+	0.821588i	$0.306912\pi$
$618$	−0.921043	+	0.659044i	−0.0370498	+	0.0265106i
$619$		−	4.23939i		−	0.170396i	−0.996364	−	0.0851978i	$-0.972848\pi$
$619$		−	4.23939i		−	0.170396i	0.996364	−	0.0851978i	$-0.0271522\pi$
$620$	8.60669	+	1.23708i	0.345653	+	0.0496825i
$621$	−4.57749	−	2.45898i	−0.183688	−	0.0986754i
$622$	−5.20885	−	5.20885i	−0.208856	−	0.208856i
$623$	2.94527	+	2.94527i	0.118000	+	0.118000i
$624$	−0.781770	−	0.129628i	−0.0312958	−	0.00518926i
$625$	21.0336	+	13.5125i	0.841345	+	0.540498i
$626$		−	18.1685i		−	0.726158i
$627$	−2.79611	−	3.90769i	−0.111666	−	0.156058i
$628$	−2.51780	+	2.51780i	−0.100471	+	0.100471i
$629$	−5.55436			−0.221467
$630$	−21.1010	−	10.7556i	−0.840683	−	0.428513i
$631$	11.7095			0.466148			0.233074	−	0.972459i	$-0.425122\pi$
$631$	11.7095			0.466148			0.233074	+	0.972459i	$0.425122\pi$
$632$	5.90627	−	5.90627i	0.234939	−	0.234939i
$633$	12.6781	+	17.7182i	0.503910	+	0.704236i
$634$			20.7631i			0.824609i
$635$	37.5381	−	28.1032i	1.48965	−	1.11524i
$636$	−2.53949	−	0.421081i	−0.100697	−	0.0166969i
$637$	−1.76807	−	1.76807i	−0.0700536	−	0.0700536i
$638$	−1.43737	−	1.43737i	−0.0569059	−	0.0569059i
$639$	25.8763	+	8.82385i	1.02365	+	0.349066i
$640$	1.79001	−	1.34010i	0.0707563	−	0.0529722i
$641$		−	27.6385i		−	1.09166i	−0.837897	−	0.545828i	$-0.816215\pi$
$641$		−	27.6385i		−	1.09166i	0.837897	−	0.545828i	$-0.183785\pi$
$642$	−23.6739	+	16.9397i	−0.934336	+	0.668555i
$643$	17.0111	−	17.0111i	0.670850	−	0.670850i	−0.287062	−	0.957912i	$-0.592678\pi$
$643$	17.0111	−	17.0111i	0.670850	−	0.670850i	0.957912	+	0.287062i	$0.0926785\pi$
$644$	3.53061			0.139126
$645$	−7.15673	+	22.5689i	−0.281796	+	0.888650i
$646$	33.5187			1.31877
$647$	11.3587	−	11.3587i	0.446558	−	0.446558i	−0.447651	−	0.894209i	$-0.647739\pi$
$647$	11.3587	−	11.3587i	0.446558	−	0.446558i	0.894209	+	0.447651i	$0.147739\pi$
$648$	1.14998	+	8.92623i	0.0451754	+	0.350655i
$649$			4.14305i			0.162629i
$650$	0.644302	−	2.19498i	0.0252716	−	0.0860942i
$651$	3.88984	−	23.4592i	0.152455	−	0.919437i
$652$	−11.9727	−	11.9727i	−0.468887	−	0.468887i
$653$	−21.4477	−	21.4477i	−0.839314	−	0.839314i	0.149455	−	0.988769i	$-0.452248\pi$
$653$	−21.4477	−	21.4477i	−0.839314	−	0.839314i	−0.988769	+	0.149455i	$0.952248\pi$
$654$	−0.372900	+	2.24892i	−0.0145816	+	0.0879397i
$655$	−44.4089	−	6.38312i	−1.73520	−	0.249409i
$656$			9.20789i			0.359508i
$657$	10.5560	+	21.4804i	0.411827	+	0.838032i
$658$	27.6192	−	27.6192i	1.07671	−	1.07671i
$659$	41.1073			1.60131			0.800656	−	0.599124i	$-0.204484\pi$
$659$	41.1073			1.60131			0.800656	+	0.599124i	$0.204484\pi$
$660$	1.34498	−	0.697348i	0.0523534	−	0.0271442i
$661$	1.39962			0.0544388			0.0272194	−	0.999629i	$-0.491335\pi$
$661$	1.39962			0.0544388			0.0272194	+	0.999629i	$0.491335\pi$
$662$	13.9243	−	13.9243i	0.541185	−	0.541185i
$663$	3.04590	−	2.17947i	0.118293	−	0.0846435i
$664$			5.89064i			0.228601i
$665$	−33.5546	−	44.8197i	−1.30119	−	1.73803i
$666$	1.13790	−	3.33692i	0.0440925	−	0.129303i
$667$	−3.67448	−	3.67448i	−0.142277	−	0.142277i
$668$	1.09273	+	1.09273i	0.0422792	+	0.0422792i
$669$	−33.3609	−	5.53168i	−1.28981	−	0.213867i
$670$	−2.87663	+	20.0134i	−0.111134	+	0.773187i
$671$		−	0.776242i		−	0.0299665i
$672$	−3.55852	−	4.97319i	−0.137273	−	0.191845i
$673$	−0.892398	+	0.892398i	−0.0343994	+	0.0343994i	−0.724097	−	0.689698i	$-0.757743\pi$
$673$	−0.892398	+	0.892398i	−0.0343994	+	0.0343994i	0.689698	+	0.724097i	$0.257743\pi$
$674$	19.6262			0.755973
$675$	−25.9801	+	0.180026i	−0.999976	+	0.00692919i
$676$	12.7907			0.491949
$677$	34.1799	−	34.1799i	1.31364	−	1.31364i	0.394929	−	0.918712i	$-0.370769\pi$
$677$	34.1799	−	34.1799i	1.31364	−	1.31364i	0.918712	−	0.394929i	$-0.129231\pi$
$678$	5.27465	+	7.37155i	0.202572	+	0.283103i
$679$			16.3462i			0.627309i
$680$	−1.50359	+	10.4609i	−0.0576601	+	0.401156i
$681$	−14.7942	−	2.45307i	−0.566913	−	0.0940017i
$682$	1.07559	+	1.07559i	0.0411866	+	0.0411866i
$683$	4.92447	+	4.92447i	0.188430	+	0.188430i	0.795017	−	0.606587i	$-0.207462\pi$
$683$	4.92447	+	4.92447i	0.188430	+	0.188430i	−0.606587	+	0.795017i	$0.707462\pi$
$684$	−6.86681	+	20.1372i	−0.262559	+	0.769964i
$685$	−7.41624	−	9.90606i	−0.283360	−	0.378491i
$686$			5.41873i			0.206888i
$687$	−3.04278	+	2.17724i	−0.116089	+	0.0830667i
$688$	−4.32271	+	4.32271i	−0.164802	+	0.164802i
$689$	−0.679960			−0.0259044
$690$	3.43831	−	1.78270i	0.130894	−	0.0678662i
$691$	41.2820			1.57044			0.785220	−	0.619216i	$-0.212550\pi$
$691$	41.2820			1.57044			0.785220	+	0.619216i	$0.212550\pi$
$692$	−13.4058	+	13.4058i	−0.509612	+	0.509612i
$693$	−1.82736	−	3.71852i	−0.0694158	−	0.141255i
$694$		−	23.2810i		−	0.883736i
$695$	−37.4829	−	5.38761i	−1.42181	−	0.204364i
$696$	−1.47232	+	8.87937i	−0.0558080	+	0.336572i
$697$	−30.7729	−	30.7729i	−1.16561	−	1.16561i
$698$	−26.1476	−	26.1476i	−0.989702	−	0.989702i
$699$	3.69984	−	22.3133i	0.139941	−	0.843968i
$700$	15.4930	−	8.46152i	0.585580	−	0.319815i
$701$			31.7603i			1.19957i	0.800161	+	0.599786i	$0.204748\pi$
$701$			31.7603i			1.19957i	−0.800161	+	0.599786i	$0.795252\pi$
$702$	0.685369	+	2.27640i	0.0258676	+	0.0859170i
$703$	5.89332	−	5.89332i	0.222271	−	0.222271i
$704$	0.391175			0.0147430
$705$	12.9515	−	40.8428i	0.487782	−	1.53823i
$706$	−6.87661			−0.258805
$707$	15.6295	−	15.6295i	0.587808	−	0.587808i
$708$	14.9188	−	10.6750i	0.560683	−	0.401191i
$709$		−	42.2602i		−	1.58711i	−0.608495	−	0.793557i	$-0.708227\pi$
$709$		−	42.2602i		−	1.58711i	0.608495	−	0.793557i	$-0.291773\pi$
$710$	−16.3126	+	12.2125i	−0.612200	+	0.458327i
$711$	−23.7171	−	8.08759i	−0.889462	−	0.303308i
$712$	0.834209	+	0.834209i	0.0312633	+	0.0312633i
$713$	2.74965	+	2.74965i	0.102975	+	0.102975i
$714$	28.5130	+	4.72784i	1.06707	+	0.176935i
$715$	0.320357	−	0.239838i	0.0119807	−	0.00896942i
$716$			21.1186i			0.789241i
$717$	22.2074	+	31.0358i	0.829351	+	1.15905i
$718$	18.8061	−	18.8061i	0.701837	−	0.701837i
$719$	4.96412			0.185131			0.0925653	−	0.995707i	$-0.470493\pi$
$719$	4.96412			0.185131			0.0925653	+	0.995707i	$0.470493\pi$
$720$	−5.97658	−	3.04638i	−0.222734	−	0.113532i
$721$	−2.30858			−0.0859760
$722$	−22.1292	+	22.1292i	−0.823562	+	0.823562i
$723$	2.84032	+	3.96947i	0.105632	+	0.147626i
$724$		−	17.4734i		−	0.649395i
$725$	−24.9307	−	7.31801i	−0.925901	−	0.271784i
$726$	−18.5345	−	3.07326i	−0.687878	−	0.114059i
$727$	−20.6314	−	20.6314i	−0.765176	−	0.765176i	0.212077	−	0.977253i	$-0.431977\pi$
$727$	−20.6314	−	20.6314i	−0.765176	−	0.765176i	−0.977253	+	0.212077i	$0.931977\pi$
$728$	−1.14220	−	1.14220i	−0.0423328	−	0.0423328i
$729$	22.5119	−	14.9069i	0.833774	−	0.552106i
$730$	−17.6579	−	2.53806i	−0.653548	−	0.0939378i
$731$		−	28.8931i		−	1.06865i
$732$	−2.79519	+	2.00007i	−0.103313	+	0.0739247i
$733$	−28.4876	+	28.4876i	−1.05221	+	1.05221i	−0.0536526	+	0.998560i	$0.517086\pi$
$733$	−28.4876	+	28.4876i	−1.05221	+	1.05221i	−0.998560	+	0.0536526i	$0.982914\pi$
$734$	24.7920			0.915090
$735$	−9.74283	−	18.7911i	−0.359370	−	0.693120i
$736$	1.00000			0.0368605
$737$	−2.50112	+	2.50112i	−0.0921298	+	0.0921298i
$738$	24.7918	−	12.1833i	0.912601	−	0.448472i
$739$			50.3015i			1.85037i	0.379516	+	0.925185i	$0.376090\pi$
$739$			50.3015i			1.85037i	−0.379516	+	0.925185i	$0.623910\pi$
$740$	1.57489	+	2.10362i	0.0578939	+	0.0773304i
$741$	−0.919310	+	5.54425i	−0.0337717	+	0.203673i
$742$	−3.71031	−	3.71031i	−0.136210	−	0.136210i
$743$	22.9596	+	22.9596i	0.842305	+	0.842305i	0.989158	−	0.146854i	$-0.0469146\pi$
$743$	22.9596	+	22.9596i	0.842305	+	0.842305i	−0.146854	+	0.989158i	$0.546915\pi$
$744$	1.10175	−	6.64451i	0.0403920	−	0.243599i
$745$	4.64718	−	32.3316i	0.170260	−	1.18454i
$746$			21.4997i			0.787161i
$747$	15.8603	−	7.79410i	0.580298	−	0.285171i
$748$	−1.30731	+	1.30731i	−0.0478001	+	0.0478001i
$749$	−59.3383			−2.16818
$750$	10.8155	−	16.0631i	0.394927	−	0.586543i
$751$	33.2365			1.21282			0.606409	−	0.795153i	$-0.292610\pi$
$751$	33.2365			1.21282			0.606409	+	0.795153i	$0.292610\pi$
$752$	7.82278	−	7.82278i	0.285268	−	0.285268i
$753$	19.5699	−	14.0031i	0.713168	−	0.510301i
$754$			2.37749i			0.0865832i
$755$	4.49486	−	31.2719i	0.163585	−	1.13810i
$756$	−8.68169	+	16.1613i	−0.315750	+	0.587782i
$757$	31.0850	+	31.0850i	1.12980	+	1.12980i	0.990209	+	0.139595i	$0.0445802\pi$
$757$	31.0850	+	31.0850i	1.12980	+	1.12980i	0.139595	+	0.990209i	$0.455420\pi$
$758$	17.4058	+	17.4058i	0.632208	+	0.632208i
$759$	0.668409	+	0.110831i	0.0242617	+	0.00402291i
$760$	−9.50390	−	12.6946i	−0.344743	−	0.460481i
$761$			28.3349i			1.02714i	0.858048	+	0.513570i	$0.171677\pi$
$761$			28.3349i			1.02714i	−0.858048	+	0.513570i	$0.828323\pi$
$762$	−21.1367	−	29.5395i	−0.765701	−	1.07010i
$763$	−3.28577	+	3.28577i	−0.118953	+	0.118953i
$764$	3.23619			0.117081
$765$	30.1549	−	9.79275i	1.09025	−	0.354058i
$766$	1.64710			0.0595121
$767$	3.42643	−	3.42643i	0.123721	−	0.123721i
$768$	−1.00790	−	1.40859i	−0.0363696	−	0.0508282i
$769$			12.9211i			0.465948i	0.972483	+	0.232974i	$0.0748457\pi$
$769$			12.9211i			0.465948i	−0.972483	+	0.232974i	$0.925154\pi$
$770$	3.05679	+	0.439368i	0.110159	+	0.0158337i
$771$	−20.4275	−	3.38714i	−0.735677	−	0.121985i
$772$	7.53284	+	7.53284i	0.271113	+	0.271113i
$773$	−15.8763	−	15.8763i	−0.571031	−	0.571031i	0.361385	−	0.932417i	$-0.382304\pi$
$773$	−15.8763	−	15.8763i	−0.571031	−	0.571031i	−0.932417	+	0.361385i	$0.882304\pi$
$774$	17.3582	+	5.91919i	0.623929	+	0.212761i
$775$	18.6558	+	5.47613i	0.670137	+	0.196708i
$776$			4.62985i			0.166202i
$777$	5.84448	−	4.18197i	0.209670	−	0.150027i
$778$	3.59418	−	3.59418i	0.128857	−	0.128857i
$779$	65.3017			2.33968
$780$	−1.68907	−	0.535614i	−0.0604784	−	0.0191781i
$781$	−3.56483			−0.127560
$782$	−3.34201	+	3.34201i	−0.119510	+	0.119510i
$783$	25.8554	−	7.78444i	0.923996	−	0.278193i
$784$		−	5.46521i		−	0.195186i
$785$	−6.37370	+	4.77171i	−0.227487	+	0.170310i
$786$	−5.68480	+	34.2844i	−0.202770	+	1.22288i
$787$	35.9450	+	35.9450i	1.28130	+	1.28130i	0.939927	+	0.341375i	$0.110893\pi$
$787$	35.9450	+	35.9450i	1.28130	+	1.28130i	0.341375	+	0.939927i	$0.389107\pi$
$788$	5.97320	+	5.97320i	0.212786	+	0.212786i
$789$	6.58193	−	39.6949i	0.234323	−	1.41317i
$790$	14.9514	−	11.1935i	0.531948	−	0.398247i
$791$			18.4767i			0.656955i
$792$	−0.517577	−	1.05322i	−0.0183913	−	0.0374246i
$793$	−0.641976	+	0.641976i	−0.0227972	+	0.0227972i
$794$	−3.50145			−0.124262
$795$	−5.48675	−	1.73988i	−0.194595	−	0.0617072i
$796$	16.5402			0.586251
$797$	15.7822	−	15.7822i	0.559033	−	0.559033i	−0.369999	−	0.929032i	$-0.620642\pi$
$797$	15.7822	−	15.7822i	0.559033	−	0.559033i	0.929032	+	0.369999i	$0.120642\pi$
$798$	−35.2695	+	25.2367i	−1.24853	+	0.893371i
$799$			52.2876i			1.84980i
$800$	4.38819	−	2.39662i	0.155146	−	0.0847332i
$801$	1.14230	−	3.34984i	0.0403612	−	0.118361i
$802$	−18.3898	−	18.3898i	−0.649367	−	0.649367i
$803$	−2.20674	−	2.20674i	−0.0778741	−	0.0778741i
$804$	15.4507	+	2.56193i	0.544904	+	0.0903523i
$805$	7.81438	+	1.12320i	0.275421	+	0.0395876i
$806$		−	1.77910i		−	0.0626661i
$807$	−4.17647	−	5.83681i	−0.147019	−	0.205465i
$808$	4.42686	−	4.42686i	0.155736	−	0.155736i
$809$	−14.6939			−0.516609			−0.258304	−	0.966064i	$-0.583164\pi$
$809$	−14.6939			−0.516609			−0.258304	+	0.966064i	$0.583164\pi$
$810$	−0.294444	+	20.1225i	−0.0103457	+	0.707031i
$811$	−12.5789			−0.441707			−0.220853	−	0.975307i	$-0.570884\pi$
$811$	−12.5789			−0.441707			−0.220853	+	0.975307i	$0.570884\pi$
$812$	−12.9732	+	12.9732i	−0.455269	+	0.455269i
$813$	−15.3235	−	21.4152i	−0.537417	−	0.751064i
$814$			0.459709i			0.0161128i
$815$	−22.6906	−	30.3084i	−0.794815	−	1.06166i
$816$	8.07595	+	1.33910i	0.282715	+	0.0468778i
$817$	30.6563	+	30.6563i	1.07253	+	1.07253i
$818$	−0.741572	−	0.741572i	−0.0259284	−	0.0259284i
$819$	−1.56404	+	4.58661i	−0.0546521	+	0.160269i
$820$	−2.92932	+	20.3800i	−0.102296	+	0.711702i
$821$		−	10.4853i		−	0.365940i	−0.983118	−	0.182970i	$-0.941429\pi$
$821$		−	10.4853i		−	0.365940i	0.983118	−	0.182970i	$-0.0585711\pi$
$822$	−7.79527	+	5.57783i	−0.271891	+	0.194549i
$823$	−33.1750	+	33.1750i	−1.15641	+	1.15641i	−0.171166	+	0.985242i	$0.554753\pi$
$823$	−33.1750	+	33.1750i	−1.15641	+	1.15641i	−0.985242	+	0.171166i	$0.945247\pi$
$824$	−0.653876			−0.0227788
$825$	3.19873	−	1.11557i	0.111365	−	0.0388393i
$826$	37.3937			1.30109
$827$	−26.7790	+	26.7790i	−0.931199	+	0.931199i	−0.997781	−	0.0665822i	$-0.978791\pi$
$827$	−26.7790	+	26.7790i	−0.931199	+	0.931199i	0.0665822	+	0.997781i	$0.478791\pi$
$828$	−1.32313	−	2.69246i	−0.0459820	−	0.0935693i
$829$			2.70283i			0.0938730i	0.998898	+	0.0469365i	$0.0149458\pi$
$829$			2.70283i			0.0938730i	−0.998898	+	0.0469365i	$0.985054\pi$
$830$	−1.87400	+	13.0379i	−0.0650475	+	0.452551i
$831$	−3.63118	+	21.8992i	−0.125964	+	0.759675i
$832$	−0.323514	−	0.323514i	−0.0112158	−	0.0112158i
$833$	18.2648	+	18.2648i	0.632838	+	0.632838i
$834$	−4.79820	+	28.9374i	−0.166148	+	1.00202i
$835$	2.07094	+	2.76621i	0.0716678	+	0.0957285i
$836$		−	2.77419i		−	0.0959472i
$837$	−19.3478	+	5.82516i	−0.668758	+	0.201347i
$838$	−10.7892	+	10.7892i	−0.372706	+	0.372706i
$839$	38.8686			1.34189			0.670947	−	0.741505i	$-0.265888\pi$
$839$	38.8686			1.34189			0.670947	+	0.741505i	$0.265888\pi$
$840$	−6.29402	−	12.1393i	−0.217164	−	0.418847i
$841$	−1.99637			−0.0688402
$842$	−2.32639	+	2.32639i	−0.0801727	+	0.0801727i
$843$	12.2677	−	8.77800i	0.422520	−	0.302331i
$844$			12.5787i			0.432976i
$845$	28.3099	+	4.06912i	0.973890	+	0.139982i
$846$	−31.4131	−	10.7119i	−1.08000	−	0.368283i
$847$	−27.0797	−	27.0797i	−0.930469	−	0.930469i
$848$	−1.05090	−	1.05090i	−0.0360880	−	0.0360880i
$849$	54.9954	+	9.11897i	1.88744	+	0.312962i
$850$	−6.65586	+	22.6749i	−0.228294	+	0.777743i
$851$			1.17520i			0.0402853i
$852$	9.18516	+	12.8367i	0.314678	+	0.439777i
$853$	−14.1110	+	14.1110i	−0.483153	+	0.483153i	−0.906137	−	0.422984i	$-0.860983\pi$
$853$	−14.1110	+	14.1110i	−0.483153	+	0.483153i	0.422984	+	0.906137i	$0.360983\pi$
$854$	−7.00609			−0.239743
$855$	−21.6047	+	42.3855i	−0.738866	+	1.44955i
$856$	−16.8068			−0.574445
$857$	3.79517	−	3.79517i	0.129641	−	0.129641i	−0.639309	−	0.768950i	$-0.720780\pi$
$857$	3.79517	−	3.79517i	0.129641	−	0.129641i	0.768950	+	0.639309i	$0.220780\pi$
$858$	−0.180384	−	0.252095i	−0.00615822	−	0.00860639i
$859$		−	19.4024i		−	0.662003i	−0.943630	−	0.331001i	$-0.892614\pi$
$859$		−	19.4024i		−	0.662003i	0.943630	−	0.331001i	$-0.107386\pi$
$860$	−10.9427	+	8.19236i	−0.373144	+	0.279357i
$861$	55.5496	+	9.21086i	1.89313	+	0.313905i
$862$	−9.20719	−	9.20719i	−0.313598	−	0.313598i
$863$	−2.99071	−	2.99071i	−0.101805	−	0.101805i	0.654370	−	0.756175i	$-0.272934\pi$
$863$	−2.99071	−	2.99071i	−0.101805	−	0.101805i	−0.756175	+	0.654370i	$0.772934\pi$
$864$	−2.45898	+	4.57749i	−0.0836561	+	0.155729i
$865$	−33.9362	+	25.4066i	−1.15386	+	0.863849i
$866$			4.20774i			0.142985i
$867$	−7.51915	+	5.38026i	−0.255364	+	0.182723i
$868$	9.70793	−	9.70793i	0.329509	−	0.329509i
$869$	3.26738			0.110838
$870$	−6.08352	+	19.1845i	−0.206251	+	0.650416i
$871$	4.13700			0.140177
$872$	−0.930653	+	0.930653i	−0.0315159	+	0.0315159i
$873$	12.4657	−	6.12590i	0.421899	−	0.207330i
$874$		−	7.09192i		−	0.239888i
$875$	36.9829	−	13.7993i	1.25025	−	0.466500i
$876$	−2.26040	+	13.6322i	−0.0763717	+	0.460589i
$877$	−4.54714	−	4.54714i	−0.153546	−	0.153546i	0.626154	−	0.779700i	$-0.284628\pi$
$877$	−4.54714	−	4.54714i	−0.153546	−	0.153546i	−0.779700	+	0.626154i	$0.784628\pi$
$878$	19.1699	+	19.1699i	0.646952	+	0.646952i
$879$	7.51321	−	45.3113i	0.253414	−	1.52831i
$880$	0.865797	+	0.124445i	0.0291860	+	0.00419505i
$881$			14.2676i			0.480689i	0.970688	+	0.240344i	$0.0772604\pi$
$881$			14.2676i			0.480689i	−0.970688	+	0.240344i	$0.922740\pi$
$882$	−14.7148	+	7.23120i	−0.495475	+	0.243487i
$883$	−5.46840	+	5.46840i	−0.184026	+	0.184026i	−0.793108	−	0.609081i	$-0.791538\pi$
$883$	−5.46840	+	5.46840i	−0.184026	+	0.184026i	0.609081	+	0.793108i	$0.291538\pi$
$884$	2.16237			0.0727285
$885$	36.4162	−	18.8811i	1.22412	−	0.634681i
$886$	−6.41531			−0.215526
$887$	−14.7314	+	14.7314i	−0.494632	+	0.494632i	−0.909762	−	0.415130i	$-0.863736\pi$
$887$	−14.7314	+	14.7314i	−0.494632	+	0.494632i	0.415130	+	0.909762i	$0.363736\pi$
$888$	1.65537	−	1.18449i	0.0555507	−	0.0397488i
$889$		−	74.0402i		−	2.48323i
$890$	1.58098	+	2.11176i	0.0529947	+	0.0707864i
$891$	−2.15093	+	2.78711i	−0.0720589	+	0.0933716i
$892$	−13.8055	−	13.8055i	−0.462242	−	0.462242i
$893$	−55.4786	−	55.4786i	−1.85652	−	1.85652i
$894$	−24.9605	−	4.13878i	−0.834805	−	0.138422i
$895$	−6.71851	+	46.7423i	−0.224575	+	1.56242i
$896$		−	3.53061i		−	0.117949i
$897$	−0.461134	−	0.644456i	−0.0153968	−	0.0215177i
$898$	24.5672	−	24.5672i	0.819819	−	0.819819i
$899$	−20.2071			−0.673943
$900$	−12.2589	−	8.64397i	−0.408632	−	0.288132i
$901$	7.02422			0.234011
$902$	−2.54693	+	2.54693i	−0.0848035	+	0.0848035i
$903$	21.7541	+	30.4023i	0.723930	+	1.01172i
$904$			5.23328i			0.174056i
$905$	5.55886	−	38.6743i	0.184783	−	1.28558i
$906$	−24.1424	−	4.00313i	−0.802078	−	0.132995i
$907$	−11.7666	−	11.7666i	−0.390703	−	0.390703i	0.484235	−	0.874938i	$-0.339098\pi$
$907$	−11.7666	−	11.7666i	−0.390703	−	0.390703i	−0.874938	+	0.484235i	$0.839098\pi$
$908$	−6.12215	−	6.12215i	−0.203171	−	0.203171i
$909$	−17.7764	−	6.06180i	−0.589607	−	0.201057i
$910$	−2.16469	−	2.89143i	−0.0717588	−	0.0958500i
$911$			45.2156i			1.49806i	0.662536	+	0.749030i	$0.269480\pi$
$911$			45.2156i			1.49806i	−0.662536	+	0.749030i	$0.730520\pi$
$912$	−9.98962	+	7.14798i	−0.330789	+	0.236693i
$913$	−1.62937	+	1.62937i	−0.0539242	+	0.0539242i
$914$	10.6771			0.353168
$915$	−6.82293	+	3.53756i	−0.225559	+	0.116948i
$916$	−2.16016			−0.0713737
$917$	−50.0911	+	50.0911i	−1.65415	+	1.65415i
$918$	−7.08009	−	23.5160i	−0.233678	−	0.776142i
$919$			2.13246i			0.0703434i	0.999381	+	0.0351717i	$0.0111978\pi$
$919$			2.13246i			0.0703434i	−0.999381	+	0.0351717i	$0.988802\pi$
$920$	2.21332	+	0.318132i	0.0729710	+	0.0104885i
$921$	−8.91844	+	53.7861i	−0.293873	+	1.77231i
$922$	12.2128	+	12.2128i	0.402207	+	0.402207i
$923$	2.94822	+	2.94822i	0.0970419	+	0.0970419i
$924$	0.391301	−	2.35989i	0.0128729	−	0.0776348i
$925$	2.81650	+	5.15700i	0.0926060	+	0.169561i
$926$		−	34.1820i		−	1.12329i
$927$	0.865164	+	1.76053i	0.0284157	+	0.0578234i
$928$	−3.67448	+	3.67448i	−0.120621	+	0.120621i
$929$	−33.1441			−1.08742			−0.543712	−	0.839272i	$-0.682982\pi$
$929$	−33.1441			−1.08742			−0.543712	+	0.839272i	$0.682982\pi$
$930$	4.55235	−	14.3559i	0.149277	−	0.470750i
$931$	−38.7589			−1.27027
$932$	9.23376	−	9.23376i	0.302462	−	0.302462i
$933$	−10.3763	+	7.42465i	−0.339704	+	0.243072i
$934$			16.9419i			0.554355i
$935$	−3.30940	+	2.47761i	−0.108229	+	0.0810263i
$936$	−0.442995	+	1.29910i	−0.0144797	+	0.0424624i
$937$	−32.8133	−	32.8133i	−1.07196	−	1.07196i	−0.997201	−	0.0747615i	$-0.976180\pi$
$937$	−32.8133	−	32.8133i	−1.07196	−	1.07196i	−0.0747615	−	0.997201i	$-0.523820\pi$
$938$	22.5742	+	22.5742i	0.737073	+	0.737073i
$939$	−31.0448	−	5.14764i	−1.01311	−	0.167987i
$940$	19.8030	−	14.8257i	0.645903	−	0.483560i
$941$		−	19.7775i		−	0.644727i	−0.946616	−	0.322363i	$-0.895523\pi$
$941$		−	19.7775i		−	0.644727i	0.946616	−	0.322363i	$-0.104477\pi$
$942$	3.58886	+	5.01559i	0.116931	+	0.163417i
$943$	−6.51096	+	6.51096i	−0.212026	+	0.212026i
$944$	10.5913			0.344717
$945$	−24.3568	+	33.0083i	−0.792327	+	1.07376i
$946$	−2.39135			−0.0777494
$947$	2.50419	−	2.50419i	0.0813751	−	0.0813751i	−0.665248	−	0.746623i	$-0.731674\pi$
$947$	2.50419	−	2.50419i	0.0813751	−	0.0813751i	0.746623	+	0.665248i	$0.231674\pi$
$948$	−8.41874	−	11.7656i	−0.273428	−	0.382128i
$949$			3.65008i			0.118487i
$950$	−16.9966	−	31.1207i	−0.551443	−	1.00969i
$951$	35.4784	+	5.88278i	1.15047	+	0.190762i
$952$	11.7993	+	11.7993i	0.382419	+	0.382419i
$953$	−16.4000	−	16.4000i	−0.531247	−	0.531247i	0.389696	−	0.920943i	$-0.372580\pi$
$953$	−16.4000	−	16.4000i	−0.531247	−	0.531247i	−0.920943	+	0.389696i	$0.872580\pi$
$954$	−1.43902	+	4.21997i	−0.0465899	+	0.136627i
$955$	7.16273	+	1.02953i	0.231780	+	0.0333150i
$956$			22.0332i			0.712606i
$957$	−2.86331	+	2.04881i	−0.0925575	+	0.0662287i
$958$	−18.1602	+	18.1602i	−0.586731	+	0.586731i
$959$	−19.5387			−0.630938
$960$	−1.78270	−	3.43831i	−0.0575364	−	0.110971i
$961$	−15.8789			−0.512222
$962$	0.380193	−	0.380193i	0.0122579	−	0.0122579i
$963$	22.2377	+	45.2516i	0.716599	+	1.45821i
$964$			2.81804i			0.0907630i
$965$	14.2762	+	19.0690i	0.459566	+	0.613854i
$966$	1.00032	−	6.03283i	0.0321848	−	0.194103i
$967$	−33.0956	−	33.0956i	−1.06428	−	1.06428i	−0.997787	−	0.0664955i	$-0.978818\pi$
$967$	−33.0956	−	33.0956i	−1.06428	−	1.06428i	−0.0664955	−	0.997787i	$-0.521182\pi$
$968$	−7.66997	−	7.66997i	−0.246522	−	0.246522i
$969$	9.49679	−	57.2740i	0.305081	−	1.83991i
$970$	−1.47290	+	10.2473i	−0.0472920	+	0.329022i
$971$		−	24.8727i		−	0.798202i	−0.916907	−	0.399101i	$-0.869322\pi$
$971$		−	24.8727i		−	0.798202i	0.916907	−	0.399101i	$-0.130678\pi$
$972$	15.5782	+	0.564060i	0.499673	+	0.0180922i
$973$	−42.2789	+	42.2789i	−1.35540	+	1.35540i
$974$	−24.1485			−0.773766
$975$	−3.56806	−	1.72283i	−0.114269	−	0.0551748i
$976$	−1.98438			−0.0635186
$977$	−13.6286	+	13.6286i	−0.436017	+	0.436017i	−0.890669	−	0.454652i	$-0.849764\pi$
$977$	−13.6286	+	13.6286i	−0.436017	+	0.436017i	0.454652	+	0.890669i	$0.349764\pi$
$978$	−23.8502	+	17.0658i	−0.762646	+	0.545704i
$979$			0.461489i			0.0147493i
$980$	1.73866	−	12.0963i	0.0555394	−	0.386401i
$981$	3.73712	+	1.27436i	0.119317	+	0.0406873i
$982$	−4.02529	−	4.02529i	−0.128452	−	0.128452i
$983$	1.52150	+	1.52150i	0.0485282	+	0.0485282i	0.730954	−	0.682426i	$-0.239075\pi$
$983$	1.52150	+	1.52150i	0.0485282	+	0.0485282i	−0.682426	+	0.730954i	$0.739075\pi$
$984$	15.7337	+	2.60886i	0.501573	+	0.0831673i
$985$	11.3203	+	15.1209i	0.360696	+	0.481791i
$986$		−	24.5603i		−	0.782160i
$987$	−39.3682	−	55.0188i	−1.25310	−	1.75127i
$988$	−2.29434	+	2.29434i	−0.0729926	+	0.0729926i
$989$	−6.11324			−0.194390
$990$	−0.810501	−	2.49578i	−0.0257594	−	0.0793210i
$991$	24.3406			0.773204			0.386602	−	0.922247i	$-0.373649\pi$
$991$	24.3406			0.773204			0.386602	+	0.922247i	$0.373649\pi$
$992$	2.74965	−	2.74965i	0.0873014	−	0.0873014i
$993$	−19.8476	−	27.7380i	−0.629846	−	0.880238i
$994$			32.1749i			1.02053i
$995$	36.6087	+	5.26195i	1.16057	+	0.166815i
$996$	10.0655	+	1.66898i	0.318936	+	0.0528838i
$997$	17.7102	+	17.7102i	0.560887	+	0.560887i	0.929559	−	0.368672i	$-0.120188\pi$
$997$	17.7102	+	17.7102i	0.560887	+	0.560887i	−0.368672	+	0.929559i	$0.620188\pi$
$998$	−14.1853	−	14.1853i	−0.449027	−	0.449027i
$999$	−5.37946	−	2.88979i	−0.170199	−	0.0914288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.e.47.12	yes	32
3.2	odd	2	inner	690.2.i.e.47.7	✓	32
5.3	odd	4	inner	690.2.i.e.323.7	yes	32
15.8	even	4	inner	690.2.i.e.323.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.e.47.7	✓	32	3.2	odd	2	inner
690.2.i.e.47.12	yes	32	1.1	even	1	trivial
690.2.i.e.323.7	yes	32	5.3	odd	4	inner
690.2.i.e.323.12	yes	32	15.8	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.00790 - 1.40859i) q^{3} -1.00000i q^{4} +(0.318132 - 2.21332i) q^{5} +(-1.70872 - 0.283328i) q^{6} +(-2.49652 - 2.49652i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.968258 + 2.83945i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.00790 - 1.40859i) q^{3} -1.00000i q^{4} +(0.318132 - 2.21332i) q^{5} +(-1.70872 - 0.283328i) q^{6} +(-2.49652 - 2.49652i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.968258 + 2.83945i) q^{9} +(-1.34010 - 1.79001i) q^{10} -0.391175i q^{11} +(-1.40859 + 1.00790i) q^{12} +(-0.323514 + 0.323514i) q^{13} -3.53061 q^{14} +(-3.43831 + 1.78270i) q^{15} -1.00000 q^{16} +(3.34201 - 3.34201i) q^{17} +(1.32313 + 2.69246i) q^{18} +7.09192i q^{19} +(-2.21332 - 0.318132i) q^{20} +(-1.00032 + 6.03283i) q^{21} +(-0.276603 - 0.276603i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-0.283328 + 1.70872i) q^{24} +(-4.79758 - 1.40826i) q^{25} +0.457518i q^{26} +(4.97554 - 1.49802i) q^{27} +(-2.49652 + 2.49652i) q^{28} +5.19650 q^{29} +(-1.17069 + 3.69181i) q^{30} -3.88859 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.551006 + 0.394267i) q^{33} -4.72632i q^{34} +(-6.31982 + 4.73138i) q^{35} +(2.83945 + 0.968258i) q^{36} +(-0.830991 - 0.830991i) q^{37} +(5.01475 + 5.01475i) q^{38} +(0.781770 + 0.129628i) q^{39} +(-1.79001 + 1.34010i) q^{40} -9.20789i q^{41} +(3.55852 + 4.97319i) q^{42} +(4.32271 - 4.32271i) q^{43} -0.391175 q^{44} +(5.97658 + 3.04638i) q^{45} -1.00000 q^{46} +(-7.82278 + 7.82278i) q^{47} +(1.00790 + 1.40859i) q^{48} +5.46521i q^{49} +(-4.38819 + 2.39662i) q^{50} +(-8.07595 - 1.33910i) q^{51} +(0.323514 + 0.323514i) q^{52} +(1.05090 + 1.05090i) q^{53} +(2.45898 - 4.57749i) q^{54} +(-0.865797 - 0.124445i) q^{55} +3.53061i q^{56} +(9.98962 - 7.14798i) q^{57} +(3.67448 - 3.67448i) q^{58} -10.5913 q^{59} +(1.78270 + 3.43831i) q^{60} +1.98438 q^{61} +(-2.74965 + 2.74965i) q^{62} +(9.50601 - 4.67147i) q^{63} +1.00000i q^{64} +(0.613120 + 0.818961i) q^{65} +(-0.110831 + 0.668409i) q^{66} +(-6.39385 - 6.39385i) q^{67} +(-3.34201 - 3.34201i) q^{68} +(-0.283328 + 1.70872i) q^{69} +(-1.12320 + 7.81438i) q^{70} -9.11312i q^{71} +(2.69246 - 1.32313i) q^{72} +(5.64130 - 5.64130i) q^{73} -1.17520 q^{74} +(2.85185 + 8.17722i) q^{75} +7.09192 q^{76} +(-0.976577 + 0.976577i) q^{77} +(0.644456 - 0.461134i) q^{78} +8.35272i q^{79} +(-0.318132 + 2.21332i) q^{80} +(-7.12495 - 5.49864i) q^{81} +(-6.51096 - 6.51096i) q^{82} +(-4.16531 - 4.16531i) q^{83} +(6.03283 + 1.00032i) q^{84} +(-6.33374 - 8.46014i) q^{85} -6.11324i q^{86} +(-5.23758 - 7.31975i) q^{87} +(-0.276603 + 0.276603i) q^{88} -1.17975 q^{89} +(6.38020 - 2.07196i) q^{90} +1.61532 q^{91} +(-0.707107 + 0.707107i) q^{92} +(3.91932 + 5.47743i) q^{93} +11.0631i q^{94} +(15.6967 + 2.25617i) q^{95} +(1.70872 + 0.283328i) q^{96} +(-3.27380 - 3.27380i) q^{97} +(3.86449 + 3.86449i) q^{98} +(1.11072 + 0.378759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more