LMFDB - Embedded newform 770.2.m.f.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(43,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0, 2]))

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

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

chi := DirichletCharacter("770.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.m (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.1
Character	$\chi$	$=$	770.197
Dual form			770.2.m.f.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-2.29790 + 2.29790i) q^{3} -1.00000i q^{4} +(2.01966 + 0.959678i) q^{5} -3.24972i q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -7.56071i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.29790 + 2.29790i) q^{3} -1.00000i q^{4} +(2.01966 + 0.959678i) q^{5} -3.24972i q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -7.56071i q^{9} +(-2.10671 + 0.749519i) q^{10} +(1.71546 + 2.83852i) q^{11} +(2.29790 + 2.29790i) q^{12} +(3.57405 + 3.57405i) q^{13} -1.00000i q^{14} +(-6.84622 + 2.43573i) q^{15} -1.00000 q^{16} +(-2.70200 + 2.70200i) q^{17} +(5.34623 + 5.34623i) q^{18} -6.45132 q^{19} +(0.959678 - 2.01966i) q^{20} -3.24972i q^{21} +(-3.22015 - 0.794119i) q^{22} +(-3.60265 + 3.60265i) q^{23} -3.24972 q^{24} +(3.15804 + 3.87644i) q^{25} -5.05447 q^{26} +(10.4801 + 10.4801i) q^{27} +(0.707107 + 0.707107i) q^{28} -0.0794899 q^{29} +(3.11869 - 6.56333i) q^{30} +7.10488 q^{31} +(0.707107 - 0.707107i) q^{32} +(-10.4646 - 2.58067i) q^{33} -3.82121i q^{34} +(-2.10671 + 0.749519i) q^{35} -7.56071 q^{36} +(-6.54200 - 6.54200i) q^{37} +(4.56177 - 4.56177i) q^{38} -16.4256 q^{39} +(0.749519 + 2.10671i) q^{40} +2.31017i q^{41} +(2.29790 + 2.29790i) q^{42} +(-1.39491 - 1.39491i) q^{43} +(2.83852 - 1.71546i) q^{44} +(7.25585 - 15.2700i) q^{45} -5.09491i q^{46} +(3.51179 + 3.51179i) q^{47} +(2.29790 - 2.29790i) q^{48} -1.00000i q^{49} +(-4.97413 - 0.507989i) q^{50} -12.4179i q^{51} +(3.57405 - 3.57405i) q^{52} +(6.36944 - 6.36944i) q^{53} -14.8211 q^{54} +(0.740587 + 7.37913i) q^{55} -1.00000 q^{56} +(14.8245 - 14.8245i) q^{57} +(0.0562078 - 0.0562078i) q^{58} +2.39138i q^{59} +(2.43573 + 6.84622i) q^{60} -3.28768i q^{61} +(-5.02391 + 5.02391i) q^{62} +(5.34623 + 5.34623i) q^{63} +1.00000i q^{64} +(3.78842 + 10.6483i) q^{65} +(9.22440 - 5.57478i) q^{66} +(-4.69856 - 4.69856i) q^{67} +(2.70200 + 2.70200i) q^{68} -16.5571i q^{69} +(0.959678 - 2.01966i) q^{70} -5.70658 q^{71} +(5.34623 - 5.34623i) q^{72} +(-5.28606 - 5.28606i) q^{73} +9.25178 q^{74} +(-16.1645 - 1.65082i) q^{75} +6.45132i q^{76} +(-3.22015 - 0.794119i) q^{77} +(11.6147 - 11.6147i) q^{78} -11.0590 q^{79} +(-2.01966 - 0.959678i) q^{80} -25.4822 q^{81} +(-1.63354 - 1.63354i) q^{82} +(-0.760395 - 0.760395i) q^{83} -3.24972 q^{84} +(-8.05018 + 2.86407i) q^{85} +1.97270 q^{86} +(0.182660 - 0.182660i) q^{87} +(-0.794119 + 3.22015i) q^{88} -6.82098i q^{89} +(5.66690 + 15.9282i) q^{90} -5.05447 q^{91} +(3.60265 + 3.60265i) q^{92} +(-16.3263 + 16.3263i) q^{93} -4.96642 q^{94} +(-13.0295 - 6.19119i) q^{95} +3.24972i q^{96} +(8.02852 + 8.02852i) q^{97} +(0.707107 + 0.707107i) q^{98} +(21.4612 - 12.9701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{3}+O(q^{10}) $ 36 * q - 4 * q^3	$ 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) $ 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−2.29790	+	2.29790i	−1.32669	+	1.32669i	−0.418459	+	0.908236i	$0.637430\pi$
$3$	−2.29790	+	2.29790i	−1.32669	+	1.32669i	−0.908236	+	0.418459i	$0.862570\pi$
$4$		−	1.00000i		−	0.500000i
$5$	2.01966	+	0.959678i	0.903219	+	0.429181i
$5$	2.01966	+	0.959678i	0.903219	+	0.429181i
$6$		−	3.24972i		−	1.32669i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	7.56071i		−	2.52024i
$10$	−2.10671	+	0.749519i	−0.666200	+	0.237019i
$11$	1.71546	+	2.83852i	0.517232	+	0.855845i
$11$	1.71546	+	2.83852i	0.517232	+	0.855845i
$12$	2.29790	+	2.29790i	0.663347	+	0.663347i
$13$	3.57405	+	3.57405i	0.991264	+	0.991264i	0.999962	−	0.00869848i	$-0.00276885\pi$
$13$	3.57405	+	3.57405i	0.991264	+	0.991264i	−0.00869848	+	0.999962i	$0.502769\pi$
$14$		−	1.00000i		−	0.267261i
$15$	−6.84622	+	2.43573i	−1.76769	+	0.628903i
$16$	−1.00000			−0.250000
$17$	−2.70200	+	2.70200i	−0.655332	+	0.655332i	−0.954272	−	0.298940i	$-0.903367\pi$
$17$	−2.70200	+	2.70200i	−0.655332	+	0.655332i	0.298940	+	0.954272i	$0.403367\pi$
$18$	5.34623	+	5.34623i	1.26012	+	1.26012i
$19$	−6.45132			−1.48004			−0.740018	−	0.672588i	$-0.765183\pi$
$19$	−6.45132			−1.48004			−0.740018	+	0.672588i	$0.765183\pi$
$20$	0.959678	−	2.01966i	0.214590	−	0.451609i
$21$		−	3.24972i		−	0.709148i
$22$	−3.22015	−	0.794119i	−0.686539	−	0.169307i
$23$	−3.60265	+	3.60265i	−0.751204	+	0.751204i	−0.974704	−	0.223500i	$-0.928252\pi$
$23$	−3.60265	+	3.60265i	−0.751204	+	0.751204i	0.223500	+	0.974704i	$0.428252\pi$
$24$	−3.24972			−0.663347
$25$	3.15804	+	3.87644i	0.631607	+	0.775288i
$26$	−5.05447			−0.991264
$27$	10.4801	+	10.4801i	2.01689	+	2.01689i
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$	−0.0794899			−0.0147609			−0.00738045	−	0.999973i	$-0.502349\pi$
$29$	−0.0794899			−0.0147609			−0.00738045	+	0.999973i	$0.502349\pi$
$30$	3.11869	−	6.56333i	0.569392	−	1.19830i
$31$	7.10488			1.27607			0.638037	−	0.770006i	$-0.279747\pi$
$31$	7.10488			1.27607			0.638037	+	0.770006i	$0.279747\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−10.4646	−	2.58067i	−1.82165	−	0.449237i
$34$		−	3.82121i		−	0.655332i
$35$	−2.10671	+	0.749519i	−0.356099	+	0.126692i
$36$	−7.56071			−1.26012
$37$	−6.54200	−	6.54200i	−1.07550	−	1.07550i	−0.996907	−	0.0785906i	$-0.974958\pi$
$37$	−6.54200	−	6.54200i	−1.07550	−	1.07550i	−0.0785906	−	0.996907i	$-0.525042\pi$
$38$	4.56177	−	4.56177i	0.740018	−	0.740018i
$39$	−16.4256			−2.63021
$40$	0.749519	+	2.10671i	0.118509	+	0.333100i
$41$			2.31017i			0.360789i	0.983594	+	0.180394i	$0.0577374\pi$
$41$			2.31017i			0.360789i	−0.983594	+	0.180394i	$0.942263\pi$
$42$	2.29790	+	2.29790i	0.354574	+	0.354574i
$43$	−1.39491	−	1.39491i	−0.212722	−	0.212722i	0.592701	−	0.805423i	$-0.298062\pi$
$43$	−1.39491	−	1.39491i	−0.212722	−	0.212722i	−0.805423	+	0.592701i	$0.798062\pi$
$44$	2.83852	−	1.71546i	0.427923	−	0.258616i
$45$	7.25585	−	15.2700i	1.08164	−	2.27632i
$46$		−	5.09491i		−	0.751204i
$47$	3.51179	+	3.51179i	0.512247	+	0.512247i	0.915214	−	0.402967i	$-0.132021\pi$
$47$	3.51179	+	3.51179i	0.512247	+	0.512247i	−0.402967	+	0.915214i	$0.632021\pi$
$48$	2.29790	−	2.29790i	0.331674	−	0.331674i
$49$		−	1.00000i		−	0.142857i
$50$	−4.97413	−	0.507989i	−0.703448	−	0.0718405i
$51$		−	12.4179i		−	1.73885i
$52$	3.57405	−	3.57405i	0.495632	−	0.495632i
$53$	6.36944	−	6.36944i	0.874910	−	0.874910i	−0.118093	−	0.993003i	$-0.537678\pi$
$53$	6.36944	−	6.36944i	0.874910	−	0.874910i	0.993003	+	0.118093i	$0.0376780\pi$
$54$	−14.8211			−2.01689
$55$	0.740587	+	7.37913i	0.0998608	+	0.995001i
$56$	−1.00000			−0.133631
$57$	14.8245	−	14.8245i	1.96355	−	1.96355i
$58$	0.0562078	−	0.0562078i	0.00738045	−	0.00738045i
$59$			2.39138i			0.311332i	0.987810	+	0.155666i	$0.0497523\pi$
$59$			2.39138i			0.311332i	−0.987810	+	0.155666i	$0.950248\pi$
$60$	2.43573	+	6.84622i	0.314452	+	0.883844i
$61$		−	3.28768i		−	0.420944i	−0.977600	−	0.210472i	$-0.932500\pi$
$61$		−	3.28768i		−	0.420944i	0.977600	−	0.210472i	$-0.0675001\pi$
$62$	−5.02391	+	5.02391i	−0.638037	+	0.638037i
$63$	5.34623	+	5.34623i	0.673562	+	0.673562i
$64$			1.00000i			0.125000i
$65$	3.78842	+	10.6483i	0.469896	+	1.32076i
$66$	9.22440	−	5.57478i	1.13545	−	0.686209i
$67$	−4.69856	−	4.69856i	−0.574020	−	0.574020i	0.359229	−	0.933249i	$-0.383040\pi$
$67$	−4.69856	−	4.69856i	−0.574020	−	0.574020i	−0.933249	+	0.359229i	$0.883040\pi$
$68$	2.70200	+	2.70200i	0.327666	+	0.327666i
$69$		−	16.5571i		−	1.99324i
$70$	0.959678	−	2.01966i	0.114703	−	0.241395i
$71$	−5.70658			−0.677247			−0.338624	−	0.940922i	$-0.609961\pi$
$71$	−5.70658			−0.677247			−0.338624	+	0.940922i	$0.609961\pi$
$72$	5.34623	−	5.34623i	0.630059	−	0.630059i
$73$	−5.28606	−	5.28606i	−0.618686	−	0.618686i	0.326508	−	0.945194i	$-0.394128\pi$
$73$	−5.28606	−	5.28606i	−0.618686	−	0.618686i	−0.945194	+	0.326508i	$0.894128\pi$
$74$	9.25178			1.07550
$75$	−16.1645	−	1.65082i	−1.86652	−	0.190621i
$76$			6.45132i			0.740018i
$77$	−3.22015	−	0.794119i	−0.366970	−	0.0904983i
$78$	11.6147	−	11.6147i	1.31510	−	1.31510i
$79$	−11.0590			−1.24424			−0.622120	−	0.782922i	$-0.713728\pi$
$79$	−11.0590			−1.24424			−0.622120	+	0.782922i	$0.713728\pi$
$80$	−2.01966	−	0.959678i	−0.225805	−	0.107295i
$81$	−25.4822			−2.83136
$82$	−1.63354	−	1.63354i	−0.180394	−	0.180394i
$83$	−0.760395	−	0.760395i	−0.0834642	−	0.0834642i	0.664142	−	0.747606i	$-0.268797\pi$
$83$	−0.760395	−	0.760395i	−0.0834642	−	0.0834642i	−0.747606	+	0.664142i	$0.768797\pi$
$84$	−3.24972			−0.354574
$85$	−8.05018	+	2.86407i	−0.873164	+	0.310652i
$86$	1.97270			0.212722
$87$	0.182660	−	0.182660i	0.0195832	−	0.0195832i
$88$	−0.794119	+	3.22015i	−0.0846534	+	0.343269i
$89$		−	6.82098i		−	0.723023i	−0.932368	−	0.361511i	$-0.882261\pi$
$89$		−	6.82098i		−	0.723023i	0.932368	−	0.361511i	$-0.117739\pi$
$90$	5.66690	+	15.9282i	0.597343	+	1.67898i
$91$	−5.05447			−0.529853
$92$	3.60265	+	3.60265i	0.375602	+	0.375602i
$93$	−16.3263	+	16.3263i	−1.69296	+	1.69296i
$94$	−4.96642			−0.512247
$95$	−13.0295	−	6.19119i	−1.33680	−	0.635203i
$96$			3.24972i			0.331674i
$97$	8.02852	+	8.02852i	0.815173	+	0.815173i	0.985404	−	0.170231i	$-0.0544514\pi$
$97$	8.02852	+	8.02852i	0.815173	+	0.815173i	−0.170231	+	0.985404i	$0.554451\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$	21.4612	−	12.9701i	2.15693	−	1.30355i
$100$	3.87644	−	3.15804i	0.387644	−	0.315804i
$101$			6.49902i			0.646677i	0.946283	+	0.323338i	$0.104805\pi$
$101$			6.49902i			0.646677i	−0.946283	+	0.323338i	$0.895195\pi$
$102$	8.78077	+	8.78077i	0.869426	+	0.869426i
$103$	−6.78722	+	6.78722i	−0.668765	+	0.668765i	−0.957430	−	0.288665i	$-0.906788\pi$
$103$	−6.78722	+	6.78722i	−0.668765	+	0.668765i	0.288665	+	0.957430i	$0.406788\pi$
$104$			5.05447i			0.495632i
$105$	3.11869	−	6.56333i	0.304353	−	0.640516i
$106$			9.00775i			0.874910i
$107$	8.84807	−	8.84807i	0.855375	−	0.855375i	−0.135414	−	0.990789i	$-0.543236\pi$
$107$	8.84807	−	8.84807i	0.855375	−	0.855375i	0.990789	+	0.135414i	$0.0432364\pi$
$108$	10.4801	−	10.4801i	1.00844	−	1.00844i
$109$	4.65853			0.446206			0.223103	−	0.974795i	$-0.428381\pi$
$109$	4.65853			0.446206			0.223103	+	0.974795i	$0.428381\pi$
$110$	−5.74151	−	4.69416i	−0.547431	−	0.447570i
$111$	30.0657			2.85371
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	−2.71369	+	2.71369i	−0.255283	+	0.255283i	−0.823132	−	0.567850i	$-0.807775\pi$
$113$	−2.71369	+	2.71369i	−0.255283	+	0.255283i	0.567850	+	0.823132i	$0.307775\pi$
$114$			20.9650i			1.96355i
$115$	−10.7335	+	3.81873i	−1.00090	+	0.356099i
$116$			0.0794899i			0.00738045i
$117$	27.0224	−	27.0224i	2.49822	−	2.49822i
$118$	−1.69096	−	1.69096i	−0.155666	−	0.155666i
$119$		−	3.82121i		−	0.350290i
$120$	−6.56333	−	3.11869i	−0.599148	−	0.284696i
$121$	−5.11437	+	9.73875i	−0.464943	+	0.885341i
$122$	2.32474	+	2.32474i	0.210472	+	0.210472i
$123$	−5.30856	−	5.30856i	−0.478656	−	0.478656i
$124$		−	7.10488i		−	0.638037i
$125$	2.65802	+	10.8598i	0.237741	+	0.971329i
$126$	−7.56071			−0.673562
$127$	−14.1885	+	14.1885i	−1.25902	+	1.25902i	−0.307463	+	0.951560i	$0.599480\pi$
$127$	−14.1885	+	14.1885i	−1.25902	+	1.25902i	−0.951560	+	0.307463i	$0.900520\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	6.41074			0.564434
$130$	−10.2083	−	4.85067i	−0.895328	−	0.425431i
$131$		−	15.3921i		−	1.34482i	−0.740181	−	0.672408i	$-0.765260\pi$
$131$		−	15.3921i		−	1.34482i	0.740181	−	0.672408i	$-0.234740\pi$
$132$	−2.58067	+	10.4646i	−0.224618	+	0.910827i
$133$	4.56177	−	4.56177i	0.395556	−	0.395556i
$134$	6.64477			0.574020
$135$	11.1087	+	31.2236i	0.956081	+	2.68730i
$136$	−3.82121			−0.327666
$137$	3.29290	+	3.29290i	0.281332	+	0.281332i	0.833640	−	0.552308i	$-0.186253\pi$
$137$	3.29290	+	3.29290i	0.281332	+	0.281332i	−0.552308	+	0.833640i	$0.686253\pi$
$138$	11.7076	+	11.7076i	0.996618	+	0.996618i
$139$	16.5906			1.40720			0.703598	−	0.710599i	$-0.251576\pi$
$139$	16.5906			1.40720			0.703598	+	0.710599i	$0.251576\pi$
$140$	0.749519	+	2.10671i	0.0633459	+	0.178049i
$141$	−16.1395			−1.35919
$142$	4.03516	−	4.03516i	0.338624	−	0.338624i
$143$	−4.01385	+	16.2762i	−0.335655	+	1.36108i
$144$			7.56071i			0.630059i
$145$	−0.160542	−	0.0762847i	−0.0133323	−	0.00633510i
$146$	7.47562			0.618686
$147$	2.29790	+	2.29790i	0.189528	+	0.189528i
$148$	−6.54200	+	6.54200i	−0.537749	+	0.537749i
$149$	3.14131			0.257346			0.128673	−	0.991687i	$-0.458928\pi$
$149$	3.14131			0.257346			0.128673	+	0.991687i	$0.458928\pi$
$150$	12.5974	−	10.2628i	1.02857	−	0.837950i
$151$			21.3879i			1.74052i	0.492592	+	0.870260i	$0.336049\pi$
$151$			21.3879i			1.74052i	−0.492592	+	0.870260i	$0.663951\pi$
$152$	−4.56177	−	4.56177i	−0.370009	−	0.370009i
$153$	20.4291	+	20.4291i	1.65159	+	1.65159i
$154$	2.83852	−	1.71546i	0.228734	−	0.138236i
$155$	14.3494	+	6.81840i	1.15257	+	0.547667i
$156$			16.4256i			1.31510i
$157$	−7.66397	−	7.66397i	−0.611652	−	0.611652i	0.331725	−	0.943376i	$-0.392369\pi$
$157$	−7.66397	−	7.66397i	−0.611652	−	0.611652i	−0.943376	+	0.331725i	$0.892369\pi$
$158$	7.81992	−	7.81992i	0.622120	−	0.622120i
$159$			29.2727i			2.32148i
$160$	2.10671	−	0.749519i	0.166550	−	0.0592547i
$161$		−	5.09491i		−	0.401535i
$162$	18.0186	−	18.0186i	1.41568	−	1.41568i
$163$	0.0831077	−	0.0831077i	0.00650950	−	0.00650950i	−0.703845	−	0.710354i	$-0.748535\pi$
$163$	0.0831077	−	0.0831077i	0.00650950	−	0.00650950i	0.710354	+	0.703845i	$0.248535\pi$
$164$	2.31017			0.180394
$165$	−18.6583	−	15.2547i	−1.45255	−	1.18758i
$166$	1.07536			0.0834642
$167$	11.6730	−	11.6730i	0.903285	−	0.903285i	−0.0924337	−	0.995719i	$-0.529465\pi$
$167$	11.6730	−	11.6730i	0.903285	−	0.903285i	0.995719	+	0.0924337i	$0.0294646\pi$
$168$	2.29790	−	2.29790i	0.177287	−	0.177287i
$169$			12.5477i			0.965207i
$170$	3.66713	−	7.71754i	0.281256	−	0.591908i
$171$			48.7766i			3.73004i
$172$	−1.39491	+	1.39491i	−0.106361	+	0.106361i
$173$	8.38395	+	8.38395i	0.637420	+	0.637420i	0.949918	−	0.312498i	$-0.101166\pi$
$173$	8.38395	+	8.38395i	0.637420	+	0.637420i	−0.312498	+	0.949918i	$0.601166\pi$
$174$			0.258320i			0.0195832i
$175$	−4.97413	−	0.507989i	−0.376009	−	0.0384003i
$176$	−1.71546	−	2.83852i	−0.129308	−	0.213961i
$177$	−5.49517	−	5.49517i	−0.413042	−	0.413042i
$178$	4.82316	+	4.82316i	0.361511	+	0.361511i
$179$		−	7.32841i		−	0.547751i	−0.961765	−	0.273875i	$-0.911694\pi$
$179$		−	7.32841i		−	0.547751i	0.961765	−	0.273875i	$-0.0883056\pi$
$180$	−15.2700	−	7.25585i	−1.13816	−	0.540819i
$181$	−13.9234			−1.03492			−0.517460	−	0.855707i	$-0.673122\pi$
$181$	−13.9234			−1.03492			−0.517460	+	0.855707i	$0.673122\pi$
$182$	3.57405	−	3.57405i	0.264926	−	0.264926i
$183$	7.55476	+	7.55476i	0.558464	+	0.558464i
$184$	−5.09491			−0.375602
$185$	−6.93439	−	19.4908i	−0.509826	−	1.43299i
$186$		−	23.0889i		−	1.69296i
$187$	−12.3049	−	3.03450i	−0.899822	−	0.221904i
$188$	3.51179	−	3.51179i	0.256124	−	0.256124i
$189$	−14.8211			−1.07807
$190$	13.5911	−	4.83539i	0.985999	−	0.350796i
$191$	17.3756			1.25726			0.628628	−	0.777706i	$-0.283617\pi$
$191$	17.3756			1.25726			0.628628	+	0.777706i	$0.283617\pi$
$192$	−2.29790	−	2.29790i	−0.165837	−	0.165837i
$193$	6.14589	+	6.14589i	0.442391	+	0.442391i	0.892815	−	0.450424i	$-0.148727\pi$
$193$	6.14589	+	6.14589i	0.442391	+	0.442391i	−0.450424	+	0.892815i	$0.648727\pi$
$194$	−11.3540			−0.815173
$195$	−33.1742	−	15.7633i	−2.37565	−	1.12884i
$196$	−1.00000			−0.0714286
$197$	−18.0676	+	18.0676i	−1.28726	+	1.28726i	−0.350819	+	0.936443i	$0.614097\pi$
$197$	−18.0676	+	18.0676i	−1.28726	+	1.28726i	−0.936443	+	0.350819i	$0.885903\pi$
$198$	−6.00411	+	24.3466i	−0.426693	+	1.73024i
$199$		−	4.51944i		−	0.320374i	−0.987087	−	0.160187i	$-0.948790\pi$
$199$		−	4.51944i		−	0.320374i	0.987087	−	0.160187i	$-0.0512098\pi$
$200$	−0.507989	+	4.97413i	−0.0359202	+	0.351724i
$201$	21.5937			1.52310
$202$	−4.59550	−	4.59550i	−0.323338	−	0.323338i
$203$	0.0562078	−	0.0562078i	0.00394502	−	0.00394502i
$204$	−12.4179			−0.869426
$205$	−2.21702	+	4.66576i	−0.154844	+	0.325871i
$206$		−	9.59858i		−	0.668765i
$207$	27.2386	+	27.2386i	1.89321	+	1.89321i
$208$	−3.57405	−	3.57405i	−0.247816	−	0.247816i
$209$	−11.0670	−	18.3122i	−0.765521	−	1.26668i
$210$	2.43573	+	6.84622i	0.168081	+	0.472434i
$211$		−	14.3254i		−	0.986202i	−0.869972	−	0.493101i	$-0.835863\pi$
$211$		−	14.3254i		−	0.986202i	0.869972	−	0.493101i	$-0.164137\pi$
$212$	−6.36944	−	6.36944i	−0.437455	−	0.437455i
$213$	13.1132	−	13.1132i	0.898500	−	0.898500i
$214$			12.5131i			0.855375i
$215$	−1.47858	−	4.15591i	−0.100838	−	0.283431i
$216$			14.8211i			1.00844i
$217$	−5.02391	+	5.02391i	−0.341045	+	0.341045i
$218$	−3.29408	+	3.29408i	−0.223103	+	0.223103i
$219$	24.2937			1.64162
$220$	7.37913	−	0.740587i	0.497501	−	0.0499304i
$221$	−19.3142			−1.29921
$222$	−21.2597	+	21.2597i	−1.42686	+	1.42686i
$223$	−14.0254	+	14.0254i	−0.939210	+	0.939210i	−0.998255	−	0.0590450i	$-0.981194\pi$
$223$	−14.0254	+	14.0254i	−0.939210	+	0.939210i	0.0590450	+	0.998255i	$0.481194\pi$
$224$			1.00000i			0.0668153i
$225$	29.3087	−	23.8770i	1.95391	−	1.59180i
$226$		−	3.83774i		−	0.255283i
$227$	−11.8039	+	11.8039i	−0.783455	+	0.783455i	−0.980412	−	0.196957i	$-0.936894\pi$
$227$	−11.8039	+	11.8039i	−0.783455	+	0.783455i	0.196957	+	0.980412i	$0.436894\pi$
$228$	−14.8245	−	14.8245i	−0.981777	−	0.981777i
$229$			7.29763i			0.482241i	0.970495	+	0.241121i	$0.0775149\pi$
$229$			7.29763i			0.482241i	−0.970495	+	0.241121i	$0.922485\pi$
$230$	4.88947	−	10.2900i	0.322402	−	0.678501i
$231$	9.22440	−	5.57478i	0.606921	−	0.366794i
$232$	−0.0562078	−	0.0562078i	−0.00369023	−	0.00369023i
$233$	−10.0995	−	10.0995i	−0.661640	−	0.661640i	0.294126	−	0.955767i	$-0.404971\pi$
$233$	−10.0995	−	10.0995i	−0.661640	−	0.661640i	−0.955767	+	0.294126i	$0.904971\pi$
$234$			38.2154i			2.49822i
$235$	3.72243	+	10.4628i	0.242824	+	0.682518i
$236$	2.39138			0.155666
$237$	25.4126	−	25.4126i	1.65073	−	1.65073i
$238$	2.70200	+	2.70200i	0.175145	+	0.175145i
$239$	20.4280			1.32138			0.660689	−	0.750659i	$-0.270264\pi$
$239$	20.4280			1.32138			0.660689	+	0.750659i	$0.270264\pi$
$240$	6.84622	−	2.43573i	0.441922	−	0.157226i
$241$		−	4.12911i		−	0.265979i	−0.991117	−	0.132990i	$-0.957542\pi$
$241$		−	4.12911i		−	0.265979i	0.991117	−	0.132990i	$-0.0424577\pi$
$242$	−3.26993	−	10.5027i	−0.210199	−	0.675142i
$243$	27.1154	−	27.1154i	1.73945	−	1.73945i
$244$	−3.28768			−0.210472
$245$	0.959678	−	2.01966i	0.0613116	−	0.129031i
$246$	7.50743			0.478656
$247$	−23.0574	−	23.0574i	−1.46710	−	1.46710i
$248$	5.02391	+	5.02391i	0.319019	+	0.319019i
$249$	3.49463			0.221463
$250$	−9.55853	−	5.79952i	−0.604535	−	0.366794i
$251$	5.03129			0.317572			0.158786	−	0.987313i	$-0.449242\pi$
$251$	5.03129			0.317572			0.158786	+	0.987313i	$0.449242\pi$
$252$	5.34623	−	5.34623i	0.336781	−	0.336781i
$253$	−16.4064	−	4.04597i	−1.03146	−	0.254368i
$254$		−	20.0655i		−	1.25902i
$255$	11.9172	−	25.0799i	0.746282	−	1.57056i
$256$	1.00000			0.0625000
$257$	16.2704	+	16.2704i	1.01492	+	1.01492i	0.999887	+	0.0150316i	$0.00478490\pi$
$257$	16.2704	+	16.2704i	1.01492	+	1.01492i	0.0150316	+	0.999887i	$0.495215\pi$
$258$	−4.53308	+	4.53308i	−0.282217	+	0.282217i
$259$	9.25178			0.574878
$260$	10.6483	−	3.78842i	0.660380	−	0.234948i
$261$			0.601000i			0.0372010i
$262$	10.8839	+	10.8839i	0.672408	+	0.672408i
$263$	−12.2463	−	12.2463i	−0.755141	−	0.755141i	0.220293	−	0.975434i	$-0.429299\pi$
$263$	−12.2463	−	12.2463i	−0.755141	−	0.755141i	−0.975434	+	0.220293i	$0.929299\pi$
$264$	−5.57478	−	9.22440i	−0.343104	−	0.567723i
$265$	18.9767	−	6.75148i	1.16573	−	0.414740i
$266$			6.45132i			0.395556i
$267$	15.6740	+	15.6740i	0.959230	+	0.959230i
$268$	−4.69856	+	4.69856i	−0.287010	+	0.287010i
$269$			21.6849i			1.32215i	0.750319	+	0.661075i	$0.229900\pi$
$269$			21.6849i			1.32215i	−0.750319	+	0.661075i	$0.770100\pi$
$270$	−29.9335	−	14.2234i	−1.82169	−	0.865611i
$271$			9.03319i			0.548727i	0.961626	+	0.274364i	$0.0884672\pi$
$271$			9.03319i			0.548727i	−0.961626	+	0.274364i	$0.911533\pi$
$272$	2.70200	−	2.70200i	0.163833	−	0.163833i
$273$	11.6147	−	11.6147i	0.702953	−	0.702953i
$274$	−4.65687			−0.281332
$275$	−5.58585	+	15.6140i	−0.336840	+	0.941562i
$276$	−16.5571			−0.996618
$277$	−1.70700	+	1.70700i	−0.102563	+	0.102563i	−0.756527	−	0.653963i	$-0.773105\pi$
$277$	−1.70700	+	1.70700i	−0.102563	+	0.102563i	0.653963	+	0.756527i	$0.273105\pi$
$278$	−11.7313	+	11.7313i	−0.703598	+	0.703598i
$279$		−	53.7179i		−	3.21601i
$280$	−2.01966	−	0.959678i	−0.120698	−	0.0573517i
$281$		−	4.46122i		−	0.266134i	−0.991107	−	0.133067i	$-0.957517\pi$
$281$		−	4.46122i		−	0.266134i	0.991107	−	0.133067i	$-0.0424826\pi$
$282$	11.4123	−	11.4123i	0.679595	−	0.679595i
$283$	−0.313267	−	0.313267i	−0.0186218	−	0.0186218i	0.697735	−	0.716356i	$-0.254192\pi$
$283$	−0.313267	−	0.313267i	−0.0186218	−	0.0186218i	−0.716356	+	0.697735i	$0.754192\pi$
$284$			5.70658i			0.338624i
$285$	44.1672	−	15.7137i	2.61624	−	0.930799i
$286$	−8.67076	−	14.3472i	−0.512713	−	0.848368i
$287$	−1.63354	−	1.63354i	−0.0964248	−	0.0964248i
$288$	−5.34623	−	5.34623i	−0.315030	−	0.315030i
$289$			2.39835i			0.141079i
$290$	0.167462	−	0.0595792i	0.00983371	−	0.00349861i
$291$	−36.8975			−2.16297
$292$	−5.28606	+	5.28606i	−0.309343	+	0.309343i
$293$	−9.46067	−	9.46067i	−0.552698	−	0.552698i	0.374521	−	0.927219i	$-0.377807\pi$
$293$	−9.46067	−	9.46067i	−0.552698	−	0.552698i	−0.927219	+	0.374521i	$0.877807\pi$
$294$	−3.24972			−0.189528
$295$	−2.29496	+	4.82978i	−0.133618	+	0.281201i
$296$		−	9.25178i		−	0.537749i
$297$	−11.7697	+	47.7260i	−0.682946	+	2.76934i
$298$	−2.22124	+	2.22124i	−0.128673	+	0.128673i
$299$	−25.7521			−1.48928
$300$	−1.65082	+	16.1645i	−0.0953104	+	0.933260i
$301$	1.97270			0.113705
$302$	−15.1235	−	15.1235i	−0.870260	−	0.870260i
$303$	−14.9341	−	14.9341i	−0.857943	−	0.857943i
$304$	6.45132			0.370009
$305$	3.15511	−	6.63998i	0.180661	−	0.380204i
$306$	−28.8911			−1.65159
$307$	9.95362	−	9.95362i	0.568083	−	0.568083i	−0.363508	−	0.931591i	$-0.618421\pi$
$307$	9.95362	−	9.95362i	0.568083	−	0.568083i	0.931591	+	0.363508i	$0.118421\pi$
$308$	−0.794119	+	3.22015i	−0.0452491	+	0.183485i
$309$		−	31.1927i		−	1.77449i
$310$	−14.9679	+	5.32524i	−0.850120	+	0.302454i
$311$	24.2578			1.37554			0.687768	−	0.725931i	$-0.258591\pi$
$311$	24.2578			1.37554			0.687768	+	0.725931i	$0.258591\pi$
$312$	−11.6147	−	11.6147i	−0.657552	−	0.657552i
$313$	0.798824	−	0.798824i	0.0451522	−	0.0451522i	−0.684170	−	0.729322i	$-0.739835\pi$
$313$	0.798824	−	0.798824i	0.0451522	−	0.0451522i	0.729322	+	0.684170i	$0.239835\pi$
$314$	10.8385			0.611652
$315$	5.66690	+	15.9282i	0.319293	+	0.897453i
$316$			11.0590i			0.622120i
$317$	10.3920	+	10.3920i	0.583670	+	0.583670i	0.935910	−	0.352240i	$-0.114580\pi$
$317$	10.3920	+	10.3920i	0.583670	+	0.583670i	−0.352240	+	0.935910i	$0.614580\pi$
$318$	−20.6989	−	20.6989i	−1.16074	−	1.16074i
$319$	−0.136362	−	0.225633i	−0.00763481	−	0.0126330i
$320$	−0.959678	+	2.01966i	−0.0536476	+	0.112902i
$321$			40.6640i			2.26964i
$322$	3.60265	+	3.60265i	0.200768	+	0.200768i
$323$	17.4315	−	17.4315i	0.969915	−	0.969915i
$324$			25.4822i			1.41568i
$325$	−2.56762	+	25.1416i	−0.142426	+	1.39460i
$326$			0.117532i			0.00650950i
$327$	−10.7048	+	10.7048i	−0.591979	+	0.591979i
$328$	−1.63354	+	1.63354i	−0.0901972	+	0.0901972i
$329$	−4.96642			−0.273808
$330$	23.9801	−	2.40671i	1.32006	−	0.132485i
$331$	−26.4633			−1.45455			−0.727277	−	0.686344i	$-0.759215\pi$
$331$	−26.4633			−1.45455			−0.727277	+	0.686344i	$0.759215\pi$
$332$	−0.760395	+	0.760395i	−0.0417321	+	0.0417321i
$333$	−49.4621	+	49.4621i	−2.71051	+	2.71051i
$334$			16.5081i			0.903285i
$335$	−4.98038	−	13.9986i	−0.272107	−	0.764824i
$336$			3.24972i			0.177287i
$337$	−18.8917	+	18.8917i	−1.02910	+	1.02910i	−0.0295319	+	0.999564i	$0.509402\pi$
$337$	−18.8917	+	18.8917i	−1.02910	+	1.02910i	−0.999564	+	0.0295319i	$0.990598\pi$
$338$	−8.87256	−	8.87256i	−0.482604	−	0.482604i
$339$		−	12.4716i		−	0.677364i
$340$	2.86407	+	8.05018i	0.155326	+	0.436582i
$341$	12.1882	+	20.1673i	0.660026	+	1.09212i
$342$	−34.4903	−	34.4903i	−1.86502	−	1.86502i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		−	1.97270i		−	0.106361i
$345$	15.8894	−	33.4396i	0.855459	−	1.80033i
$346$	−11.8567			−0.637420
$347$	23.9814	−	23.9814i	1.28739	−	1.28739i	0.351023	−	0.936367i	$-0.385834\pi$
$347$	23.9814	−	23.9814i	1.28739	−	1.28739i	0.936367	−	0.351023i	$-0.114166\pi$
$348$	−0.182660	−	0.182660i	−0.00979160	−	0.00979160i
$349$	21.2895			1.13960			0.569801	−	0.821783i	$-0.307020\pi$
$349$	21.2895			1.13960			0.569801	+	0.821783i	$0.307020\pi$
$350$	3.87644	−	3.15804i	0.207205	−	0.168804i
$351$			74.9126i			3.99854i
$352$	3.22015	+	0.794119i	0.171635	+	0.0423267i
$353$	14.3389	−	14.3389i	0.763185	−	0.763185i	−0.213712	−	0.976897i	$-0.568555\pi$
$353$	14.3389	−	14.3389i	0.763185	−	0.763185i	0.976897	+	0.213712i	$0.0685554\pi$
$354$	7.77134			0.413042
$355$	−11.5254	−	5.47648i	−0.611702	−	0.290662i
$356$	−6.82098			−0.361511
$357$	8.78077	+	8.78077i	0.464728	+	0.464728i
$358$	5.18197	+	5.18197i	0.273875	+	0.273875i
$359$	29.9453			1.58045			0.790225	−	0.612816i	$-0.209963\pi$
$359$	29.9453			1.58045			0.790225	+	0.612816i	$0.209963\pi$
$360$	15.9282	−	5.66690i	0.839490	−	0.298672i
$361$	22.6196			1.19050
$362$	9.84535	−	9.84535i	0.517460	−	0.517460i
$363$	−10.6264	−	34.1310i	−0.557740	−	1.79141i
$364$			5.05447i			0.264926i
$365$	−5.60312	−	15.7489i	−0.293281	−	0.824337i
$366$	−10.6840			−0.558464
$367$	−0.586230	−	0.586230i	−0.0306009	−	0.0306009i	0.691641	−	0.722242i	$-0.256888\pi$
$367$	−0.586230	−	0.586230i	−0.0306009	−	0.0306009i	−0.722242	+	0.691641i	$0.756888\pi$
$368$	3.60265	−	3.60265i	0.187801	−	0.187801i
$369$	17.4666			0.909273
$370$	18.6854	+	8.87873i	0.971409	+	0.461583i
$371$			9.00775i			0.467659i
$372$	16.3263	+	16.3263i	0.846480	+	0.846480i
$373$	9.62044	+	9.62044i	0.498128	+	0.498128i	0.910855	−	0.412727i	$-0.135424\pi$
$373$	9.62044	+	9.62044i	0.498128	+	0.498128i	−0.412727	+	0.910855i	$0.635424\pi$
$374$	10.8466	−	6.55515i	0.560863	−	0.338959i
$375$	−31.0626	−	18.8469i	−1.60407	−	0.973247i
$376$			4.96642i			0.256124i
$377$	−0.284101	−	0.284101i	−0.0146319	−	0.0146319i
$378$	10.4801	−	10.4801i	0.539036	−	0.539036i
$379$			21.6891i			1.11409i	0.830482	+	0.557046i	$0.188065\pi$
$379$			21.6891i			1.11409i	−0.830482	+	0.557046i	$0.811935\pi$
$380$	−6.19119	+	13.0295i	−0.317601	+	0.668398i
$381$		−	65.2074i		−	3.34068i
$382$	−12.2864	+	12.2864i	−0.628628	+	0.628628i
$383$	−9.72764	+	9.72764i	−0.497059	+	0.497059i	−0.910521	−	0.413462i	$-0.864319\pi$
$383$	−9.72764	+	9.72764i	−0.497059	+	0.497059i	0.413462	+	0.910521i	$0.364319\pi$
$384$	3.24972			0.165837
$385$	−5.74151	−	4.69416i	−0.292614	−	0.239236i
$386$	−8.69160			−0.442391
$387$	−10.5465	+	10.5465i	−0.536110	+	0.536110i
$388$	8.02852	−	8.02852i	0.407586	−	0.407586i
$389$			14.0798i			0.713873i	0.934129	+	0.356936i	$0.116179\pi$
$389$			14.0798i			0.713873i	−0.934129	+	0.356936i	$0.883821\pi$
$390$	34.6040	−	12.3113i	1.75224	−	0.623409i
$391$		−	19.4687i		−	0.984576i
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$	35.3696	+	35.3696i	1.78416	+	1.78416i
$394$		−	25.5514i		−	1.28726i
$395$	−22.3355	−	10.6131i	−1.12382	−	0.534004i
$396$	−12.9701	−	21.4612i	−0.651773	−	1.07847i
$397$	−12.3704	−	12.3704i	−0.620854	−	0.620854i	0.324896	−	0.945750i	$-0.394671\pi$
$397$	−12.3704	−	12.3704i	−0.620854	−	0.620854i	−0.945750	+	0.324896i	$0.894671\pi$
$398$	3.19572	+	3.19572i	0.160187	+	0.160187i
$399$			20.9650i			1.04956i
$400$	−3.15804	−	3.87644i	−0.157902	−	0.193822i
$401$	25.5117			1.27399			0.636997	−	0.770867i	$-0.280176\pi$
$401$	25.5117			1.27399			0.636997	+	0.770867i	$0.280176\pi$
$402$	−15.2690	+	15.2690i	−0.761550	+	0.761550i
$403$	25.3932	+	25.3932i	1.26493	+	1.26493i
$404$	6.49902			0.323338
$405$	−51.4653	−	24.4547i	−2.55733	−	1.21516i
$406$			0.0794899i			0.00394502i
$407$	7.34702	−	29.7921i	0.364178	−	1.47674i
$408$	8.78077	−	8.78077i	0.434713	−	0.434713i
$409$	28.0156			1.38528			0.692641	−	0.721283i	$-0.256447\pi$
$409$	28.0156			1.38528			0.692641	+	0.721283i	$0.256447\pi$
$410$	−1.73152	−	4.86686i	−0.0855137	−	0.240357i
$411$	−15.1335			−0.746483
$412$	6.78722	+	6.78722i	0.334382	+	0.334382i
$413$	−1.69096	−	1.69096i	−0.0832069	−	0.0832069i
$414$	−38.5212			−1.89321
$415$	−0.806004	−	2.26547i	−0.0395652	−	0.111208i
$416$	5.05447			0.247816
$417$	−38.1235	+	38.1235i	−1.86692	+	1.86692i
$418$	20.7742	+	5.12312i	1.01610	+	0.250580i
$419$			34.9279i			1.70634i	0.521633	+	0.853170i	$0.325323\pi$
$419$			34.9279i			1.70634i	−0.521633	+	0.853170i	$0.674677\pi$
$420$	−6.56333	−	3.11869i	−0.320258	−	0.152176i
$421$	21.9625			1.07039			0.535193	−	0.844730i	$-0.320239\pi$
$421$	21.9625			1.07039			0.535193	+	0.844730i	$0.320239\pi$
$422$	10.1296	+	10.1296i	0.493101	+	0.493101i
$423$	26.5516	−	26.5516i	1.29098	−	1.29098i
$424$	9.00775			0.437455
$425$	−19.0072	−	1.94113i	−0.921984	−	0.0941587i
$426$			18.5448i			0.898500i
$427$	2.32474	+	2.32474i	0.112502	+	0.112502i
$428$	−8.84807	−	8.84807i	−0.427688	−	0.427688i
$429$	−28.1776	−	46.6245i	−1.36043	−	2.25105i
$430$	3.98419	+	1.89316i	0.192135	+	0.0912963i
$431$		−	26.3244i		−	1.26800i	−0.773333	−	0.634000i	$-0.781412\pi$
$431$		−	26.3244i		−	1.26800i	0.773333	−	0.634000i	$-0.218588\pi$
$432$	−10.4801	−	10.4801i	−0.504222	−	0.504222i
$433$	−27.1028	+	27.1028i	−1.30248	+	1.30248i	−0.375765	+	0.926715i	$0.622620\pi$
$433$	−27.1028	+	27.1028i	−1.30248	+	1.30248i	−0.926715	+	0.375765i	$0.877380\pi$
$434$		−	7.10488i		−	0.341045i
$435$	0.544205	−	0.193616i	0.0260927	−	0.00928318i
$436$		−	4.65853i		−	0.223103i
$437$	23.2418	−	23.2418i	1.11181	−	1.11181i
$438$	−17.1782	+	17.1782i	−0.820808	+	0.820808i
$439$	1.30663			0.0623621			0.0311810	−	0.999514i	$-0.490073\pi$
$439$	1.30663			0.0623621			0.0311810	+	0.999514i	$0.490073\pi$
$440$	−4.69416	+	5.74151i	−0.223785	+	0.273716i
$441$	−7.56071			−0.360034
$442$	13.6572	−	13.6572i	0.649607	−	0.649607i
$443$	−7.87468	+	7.87468i	−0.374137	+	0.374137i	−0.868982	−	0.494844i	$-0.835225\pi$
$443$	−7.87468	+	7.87468i	−0.374137	+	0.374137i	0.494844	+	0.868982i	$0.335225\pi$
$444$		−	30.0657i		−	1.42686i
$445$	6.54595	−	13.7761i	0.310308	−	0.653048i
$446$		−	19.8349i		−	0.939210i
$447$	−7.21842	+	7.21842i	−0.341420	+	0.341420i
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$			39.7293i			1.87494i	0.348062	+	0.937472i	$0.386840\pi$
$449$			39.7293i			1.87494i	−0.348062	+	0.937472i	$0.613160\pi$
$450$	−3.84076	+	37.6079i	−0.181055	+	1.77286i
$451$	−6.55747	+	3.96302i	−0.308779	+	0.186611i
$452$	2.71369	+	2.71369i	0.127641	+	0.127641i
$453$	−49.1473	−	49.1473i	−2.30914	−	2.30914i
$454$		−	16.6933i		−	0.783455i
$455$	−10.2083	−	4.85067i	−0.478573	−	0.227403i
$456$	20.9650			0.981777
$457$	11.0093	−	11.0093i	0.514993	−	0.514993i	−0.401059	−	0.916052i	$-0.631358\pi$
$457$	11.0093	−	11.0093i	0.514993	−	0.514993i	0.916052	+	0.401059i	$0.131358\pi$
$458$	−5.16021	−	5.16021i	−0.241121	−	0.241121i
$459$	−56.6344			−2.64347
$460$	3.81873	+	10.7335i	0.178049	+	0.500452i
$461$			4.07599i			0.189838i	0.995485	+	0.0949189i	$0.0302592\pi$
$461$			4.07599i			0.189838i	−0.995485	+	0.0949189i	$0.969741\pi$
$462$	−2.58067	+	10.4646i	−0.120064	+	0.486857i
$463$	5.08517	−	5.08517i	0.236328	−	0.236328i	−0.579000	−	0.815328i	$-0.696557\pi$
$463$	5.08517	−	5.08517i	0.236328	−	0.236328i	0.815328	+	0.579000i	$0.196557\pi$
$464$	0.0794899			0.00369023
$465$	−48.6416	+	17.3056i	−2.25570	+	0.802527i
$466$	14.2828			0.661640
$467$	17.1753	+	17.1753i	0.794779	+	0.794779i	0.982267	−	0.187488i	$-0.0600347\pi$
$467$	17.1753	+	17.1753i	0.794779	+	0.794779i	−0.187488	+	0.982267i	$0.560035\pi$
$468$	−27.0224	−	27.0224i	−1.24911	−	1.24911i
$469$	6.64477			0.306827
$470$	−10.0305	−	4.76616i	−0.462671	−	0.219847i
$471$	35.2221			1.62295
$472$	−1.69096	+	1.69096i	−0.0778329	+	0.0778329i
$473$	1.56656	−	6.35240i	0.0720306	−	0.292084i
$474$			35.9388i			1.65073i
$475$	−20.3735	−	25.0082i	−0.934801	−	1.14745i
$476$	−3.82121			−0.175145
$477$	−48.1575	−	48.1575i	−2.20498	−	2.20498i
$478$	−14.4448	+	14.4448i	−0.660689	+	0.660689i
$479$	−20.3842			−0.931377			−0.465689	−	0.884949i	$-0.654193\pi$
$479$	−20.3842			−0.931377			−0.465689	+	0.884949i	$0.654193\pi$
$480$	−3.11869	+	6.56333i	−0.142348	+	0.299574i
$481$		−	46.7629i		−	2.13220i
$482$	2.91972	+	2.91972i	0.132990	+	0.132990i
$483$	11.7076	+	11.7076i	0.532715	+	0.532715i
$484$	9.73875	+	5.11437i	0.442670	+	0.232471i
$485$	8.51008	+	23.9197i	0.386423	+	1.08614i
$486$			38.3470i			1.73945i
$487$	−18.9134	−	18.9134i	−0.857046	−	0.857046i	0.133943	−	0.990989i	$-0.457236\pi$
$487$	−18.9134	−	18.9134i	−0.857046	−	0.857046i	−0.990989	+	0.133943i	$0.957236\pi$
$488$	2.32474	−	2.32474i	0.105236	−	0.105236i
$489$			0.381947i			0.0172722i
$490$	0.749519	+	2.10671i	0.0338598	+	0.0951714i
$491$			31.0158i			1.39972i	0.714278	+	0.699862i	$0.246755\pi$
$491$			31.0158i			1.39972i	−0.714278	+	0.699862i	$0.753245\pi$
$492$	−5.30856	+	5.30856i	−0.239328	+	0.239328i
$493$	0.214782	−	0.214782i	0.00967329	−	0.00967329i
$494$	32.6080			1.46710
$495$	55.7914	−	5.59937i	2.50764	−	0.251673i
$496$	−7.10488			−0.319019
$497$	4.03516	−	4.03516i	0.181002	−	0.181002i
$498$	−2.47107	+	2.47107i	−0.110731	+	0.110731i
$499$		−	15.8570i		−	0.709856i	−0.934894	−	0.354928i	$-0.884505\pi$
$499$		−	15.8570i		−	0.709856i	0.934894	−	0.354928i	$-0.115495\pi$
$500$	10.8598	−	2.65802i	0.485664	−	0.118870i
$501$			53.6469i			2.39677i
$502$	−3.55766	+	3.55766i	−0.158786	+	0.158786i
$503$	7.68563	+	7.68563i	0.342685	+	0.342685i	0.857376	−	0.514691i	$-0.172093\pi$
$503$	7.68563	+	7.68563i	0.342685	+	0.342685i	−0.514691	+	0.857376i	$0.672093\pi$
$504$			7.56071i			0.336781i
$505$	−6.23697	+	13.1258i	−0.277541	+	0.584091i
$506$	14.4620	−	8.74014i	0.642914	−	0.388546i
$507$	−28.8334	−	28.8334i	−1.28054	−	1.28054i
$508$	14.1885	+	14.1885i	0.629512	+	0.629512i
$509$			13.9863i			0.619930i	0.950748	+	0.309965i	$0.100317\pi$
$509$			13.9863i			0.619930i	−0.950748	+	0.309965i	$0.899683\pi$
$510$	9.30744	+	26.1609i	0.412140	+	1.15842i
$511$	7.47562			0.330702
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−67.6103	−	67.6103i	−2.98507	−	2.98507i
$514$	−23.0098			−1.01492
$515$	−20.2214	+	7.19432i	−0.891062	+	0.317020i
$516$		−	6.41074i		−	0.282217i
$517$	−3.94393	+	15.9926i	−0.173454	+	0.703355i
$518$	−6.54200	+	6.54200i	−0.287439	+	0.287439i
$519$	−38.5310			−1.69132
$520$	−4.85067	+	10.2083i	−0.212716	+	0.447664i
$521$	4.18153			0.183196			0.0915980	−	0.995796i	$-0.470803\pi$
$521$	4.18153			0.183196			0.0915980	+	0.995796i	$0.470803\pi$
$522$	−0.424971	−	0.424971i	−0.0186005	−	0.0186005i
$523$	22.3459	+	22.3459i	0.977118	+	0.977118i	0.999744	−	0.0226261i	$-0.00720272\pi$
$523$	22.3459	+	22.3459i	0.977118	+	0.977118i	−0.0226261	+	0.999744i	$0.507203\pi$
$524$	−15.3921			−0.672408
$525$	12.5974	−	10.2628i	0.549794	−	0.447903i
$526$	17.3189			0.755141
$527$	−19.1974	+	19.1974i	−0.836253	+	0.836253i
$528$	10.4646	+	2.58067i	0.455413	+	0.112309i
$529$		−	2.95813i		−	0.128614i
$530$	−8.64454	+	18.1926i	−0.375495	+	0.790235i
$531$	18.0806			0.784629
$532$	−4.56177	−	4.56177i	−0.197778	−	0.197778i
$533$	−8.25668	+	8.25668i	−0.357637	+	0.357637i
$534$	−22.1663			−0.959230
$535$	26.3614	−	9.37878i	1.13970	−	0.405480i
$536$		−	6.64477i		−	0.287010i
$537$	16.8400	+	16.8400i	0.726698	+	0.726698i
$538$	−15.3335	−	15.3335i	−0.661075	−	0.661075i
$539$	2.83852	−	1.71546i	0.122264	−	0.0738903i
$540$	31.2236	−	11.1087i	1.34365	−	0.478041i
$541$			9.61924i			0.413563i	0.978387	+	0.206782i	$0.0662990\pi$
$541$			9.61924i			0.413563i	−0.978387	+	0.206782i	$0.933701\pi$
$542$	−6.38743	−	6.38743i	−0.274364	−	0.274364i
$543$	31.9947	−	31.9947i	1.37302	−	1.37302i
$544$			3.82121i			0.163833i
$545$	9.40863	+	4.47068i	0.403021	+	0.191503i
$546$			16.4256i			0.702953i
$547$	2.87911	−	2.87911i	0.123102	−	0.123102i	−0.642872	−	0.765974i	$-0.722257\pi$
$547$	2.87911	−	2.87911i	0.123102	−	0.123102i	0.765974	+	0.642872i	$0.222257\pi$
$548$	3.29290	−	3.29290i	0.140666	−	0.140666i
$549$	−24.8572			−1.06088
$550$	−7.09100	−	14.9906i	−0.302361	−	0.639201i
$551$	0.512815			0.0218467
$552$	11.7076	−	11.7076i	0.498309	−	0.498309i
$553$	7.81992	−	7.81992i	0.332537	−	0.332537i
$554$		−	2.41406i		−	0.102563i
$555$	60.7225	+	28.8534i	2.57753	+	1.22476i
$556$		−	16.5906i		−	0.703598i
$557$	15.6968	−	15.6968i	0.665093	−	0.665093i	−0.291483	−	0.956576i	$-0.594149\pi$
$557$	15.6968	−	15.6968i	0.665093	−	0.665093i	0.956576	+	0.291483i	$0.0941486\pi$
$558$	37.9843	+	37.9843i	1.60800	+	1.60800i
$559$		−	9.97097i		−	0.421727i
$560$	2.10671	−	0.749519i	0.0890247	−	0.0316730i
$561$	35.2484	−	21.3024i	1.48819	−	0.899389i
$562$	3.15456	+	3.15456i	0.133067	+	0.133067i
$563$	17.4123	+	17.4123i	0.733842	+	0.733842i	0.971379	−	0.237537i	$-0.0763400\pi$
$563$	17.4123	+	17.4123i	0.733842	+	0.733842i	−0.237537	+	0.971379i	$0.576340\pi$
$564$			16.1395i			0.679595i
$565$	−8.08499	+	2.87646i	−0.340138	+	0.121014i
$566$	0.443027			0.0186218
$567$	18.0186	−	18.0186i	0.756712	−	0.756712i
$568$	−4.03516	−	4.03516i	−0.169312	−	0.169312i
$569$	−17.3328			−0.726627			−0.363313	−	0.931667i	$-0.618355\pi$
$569$	−17.3328			−0.726627			−0.363313	+	0.931667i	$0.618355\pi$
$570$	−20.1197	+	42.3422i	−0.842720	+	1.77352i
$571$		−	34.9732i		−	1.46358i	−0.681529	−	0.731791i	$-0.738685\pi$
$571$		−	34.9732i		−	1.46358i	0.681529	−	0.731791i	$-0.261315\pi$
$572$	16.2762	+	4.01385i	0.680541	+	0.167828i
$573$	−39.9275	+	39.9275i	−1.66800	+	1.66800i
$574$	2.31017			0.0964248
$575$	−25.3427	−	2.58816i	−1.05687	−	0.107934i
$576$	7.56071			0.315030
$577$	14.9221	+	14.9221i	0.621215	+	0.621215i	0.945842	−	0.324627i	$-0.105239\pi$
$577$	14.9221	+	14.9221i	0.621215	+	0.621215i	−0.324627	+	0.945842i	$0.605239\pi$
$578$	−1.69589	−	1.69589i	−0.0705397	−	0.0705397i
$579$	−28.2453			−1.17383
$580$	−0.0762847	+	0.160542i	−0.00316755	+	0.00666616i
$581$	1.07536			0.0446135
$582$	26.0905	−	26.0905i	1.08149	−	1.08149i
$583$	29.0063	+	7.15323i	1.20132	+	0.296256i
$584$		−	7.47562i		−	0.309343i
$585$	80.5087	−	28.6432i	3.32863	−	1.18425i
$586$	13.3794			0.552698
$587$	7.81088	+	7.81088i	0.322390	+	0.322390i	0.849683	−	0.527294i	$-0.176793\pi$
$587$	7.81088	+	7.81088i	0.322390	+	0.322390i	−0.527294	+	0.849683i	$0.676793\pi$
$588$	2.29790	−	2.29790i	0.0947639	−	0.0947639i
$589$	−45.8359			−1.88863
$590$	−1.79239	−	5.03795i	−0.0737915	−	0.207409i
$591$		−	83.0351i		−	3.41561i
$592$	6.54200	+	6.54200i	0.268874	+	0.268874i
$593$	−16.0798	−	16.0798i	−0.660319	−	0.660319i	0.295136	−	0.955455i	$-0.404635\pi$
$593$	−16.0798	−	16.0798i	−0.660319	−	0.660319i	−0.955455	+	0.295136i	$0.904635\pi$
$594$	−25.4250	−	42.0698i	−1.04320	−	1.72615i
$595$	3.66713	−	7.71754i	0.150338	−	0.316388i
$596$		−	3.14131i		−	0.128673i
$597$	10.3852	+	10.3852i	0.425039	+	0.425039i
$598$	18.2095	−	18.2095i	0.744641	−	0.744641i
$599$		−	15.0122i		−	0.613382i	−0.951809	−	0.306691i	$-0.900778\pi$
$599$		−	15.0122i		−	0.613382i	0.951809	−	0.306691i	$-0.0992218\pi$
$600$	−10.2628	−	12.5974i	−0.418975	−	0.514285i
$601$			0.920655i			0.0375543i	0.999824	+	0.0187772i	$0.00597730\pi$
$601$			0.920655i			0.0375543i	−0.999824	+	0.0187772i	$0.994023\pi$
$602$	−1.39491	+	1.39491i	−0.0568524	+	0.0568524i
$603$	−35.5244	+	35.5244i	−1.44667	+	1.44667i
$604$	21.3879			0.870260
$605$	−19.6753	+	14.7608i	−0.799916	+	0.600112i
$606$	21.1200			0.857943
$607$	−5.48371	+	5.48371i	−0.222577	+	0.222577i	−0.809583	−	0.587006i	$-0.800307\pi$
$607$	−5.48371	+	5.48371i	−0.222577	+	0.222577i	0.587006	+	0.809583i	$0.300307\pi$
$608$	−4.56177	+	4.56177i	−0.185004	+	0.185004i
$609$			0.258320i			0.0104677i
$610$	2.46418	+	6.92618i	0.0997716	+	0.280433i
$611$			25.1026i			1.01554i
$612$	20.4291	−	20.4291i	0.825796	−	0.825796i
$613$	4.46346	+	4.46346i	0.180277	+	0.180277i	0.791477	−	0.611199i	$-0.209313\pi$
$613$	4.46346	+	4.46346i	0.180277	+	0.180277i	−0.611199	+	0.791477i	$0.709313\pi$
$614$			14.0766i			0.568083i
$615$	−5.62696	−	15.8160i	−0.226901	−	0.637761i
$616$	−1.71546	−	2.83852i	−0.0691180	−	0.114367i
$617$	−12.0107	−	12.0107i	−0.483532	−	0.483532i	0.422726	−	0.906258i	$-0.361073\pi$
$617$	−12.0107	−	12.0107i	−0.483532	−	0.483532i	−0.906258	+	0.422726i	$0.861073\pi$
$618$	22.0566	+	22.0566i	0.887246	+	0.887246i
$619$		−	6.73063i		−	0.270527i	−0.990810	−	0.135263i	$-0.956812\pi$
$619$		−	6.73063i		−	0.270527i	0.990810	−	0.135263i	$-0.0431881\pi$
$620$	6.81840	−	14.3494i	0.273833	−	0.576287i
$621$	−75.5120			−3.03019
$622$	−17.1529	+	17.1529i	−0.687768	+	0.687768i
$623$	4.82316	+	4.82316i	0.193236	+	0.193236i
$624$	16.4256			0.657552
$625$	−5.05360	+	24.4839i	−0.202144	+	0.979356i
$626$			1.12971i			0.0451522i
$627$	67.5105	+	16.6487i	2.69611	+	0.664886i
$628$	−7.66397	+	7.66397i	−0.305826	+	0.305826i
$629$	35.3530			1.40962
$630$	−15.2700	−	7.25585i	−0.608373	−	0.289080i
$631$	41.5771			1.65516			0.827580	−	0.561348i	$-0.189717\pi$
$631$	41.5771			1.65516			0.827580	+	0.561348i	$0.189717\pi$
$632$	−7.81992	−	7.81992i	−0.311060	−	0.311060i
$633$	32.9184	+	32.9184i	1.30839	+	1.30839i
$634$	−14.6964			−0.583670
$635$	−42.2722	+	15.0395i	−1.67752	+	0.596824i
$636$	29.2727			1.16074
$637$	3.57405	−	3.57405i	0.141609	−	0.141609i
$638$	0.255969	+	0.0631245i	0.0101339	+	0.00249912i
$639$			43.1458i			1.70682i
$640$	−0.749519	−	2.10671i	−0.0296273	−	0.0832750i
$641$	9.34833			0.369237			0.184619	−	0.982810i	$-0.440895\pi$
$641$	9.34833			0.369237			0.184619	+	0.982810i	$0.440895\pi$
$642$	−28.7538	−	28.7538i	−1.13482	−	1.13482i
$643$	18.7050	−	18.7050i	0.737652	−	0.737652i	−0.234471	−	0.972123i	$-0.575336\pi$
$643$	18.7050	−	18.7050i	0.737652	−	0.737652i	0.972123	+	0.234471i	$0.0753359\pi$
$644$	−5.09491			−0.200768
$645$	12.9475	+	6.15225i	0.509808	+	0.242244i
$646$			24.6519i			0.969915i
$647$	14.1584	+	14.1584i	0.556624	+	0.556624i	0.928345	−	0.371721i	$-0.121232\pi$
$647$	14.1584	+	14.1584i	0.556624	+	0.556624i	−0.371721	+	0.928345i	$0.621232\pi$
$648$	−18.0186	−	18.0186i	−0.707839	−	0.707839i
$649$	−6.78799	+	4.10233i	−0.266452	+	0.161031i
$650$	−15.9622	−	19.5934i	−0.626090	−	0.768515i
$651$		−	23.0889i		−	0.904926i
$652$	−0.0831077	−	0.0831077i	−0.00325475	−	0.00325475i
$653$	6.26722	−	6.26722i	0.245255	−	0.245255i	−0.573765	−	0.819020i	$-0.694518\pi$
$653$	6.26722	−	6.26722i	0.245255	−	0.245255i	0.819020	+	0.573765i	$0.194518\pi$
$654$		−	15.1389i		−	0.591979i
$655$	14.7715	−	31.0868i	0.577169	−	1.21466i
$656$		−	2.31017i		−	0.0901972i
$657$	−39.9664	+	39.9664i	−1.55924	+	1.55924i
$658$	3.51179	−	3.51179i	0.136904	−	0.136904i
$659$	23.3618			0.910048			0.455024	−	0.890479i	$-0.349631\pi$
$659$	23.3618			0.910048			0.455024	+	0.890479i	$0.349631\pi$
$660$	−15.2547	+	18.6583i	−0.593789	+	0.726274i
$661$	−8.90710			−0.346446			−0.173223	−	0.984883i	$-0.555418\pi$
$661$	−8.90710			−0.346446			−0.173223	+	0.984883i	$0.555418\pi$
$662$	18.7124	−	18.7124i	0.727277	−	0.727277i
$663$	44.3822	−	44.3822i	1.72366	−	1.72366i
$664$		−	1.07536i		−	0.0417321i
$665$	13.5911	−	4.83539i	0.527039	−	0.187508i
$666$		−	69.9500i		−	2.71051i
$667$	0.286374	−	0.286374i	0.0110884	−	0.0110884i
$668$	−11.6730	−	11.6730i	−0.451643	−	0.451643i
$669$		−	64.4580i		−	2.49209i
$670$	13.4202	+	6.37683i	0.518466	+	0.246359i
$671$	9.33213	−	5.63989i	0.360263	−	0.217726i
$672$	−2.29790	−	2.29790i	−0.0886435	−	0.0886435i
$673$	19.8561	+	19.8561i	0.765397	+	0.765397i	0.977292	−	0.211895i	$-0.0679636\pi$
$673$	19.8561	+	19.8561i	0.765397	+	0.765397i	−0.211895	+	0.977292i	$0.567964\pi$
$674$		−	26.7169i		−	1.02910i
$675$	−7.52893	+	73.7218i	−0.289789	+	2.83755i
$676$	12.5477			0.482604
$677$	−11.5453	+	11.5453i	−0.443722	+	0.443722i	−0.893261	−	0.449539i	$-0.851588\pi$
$677$	−11.5453	+	11.5453i	−0.443722	+	0.443722i	0.449539	+	0.893261i	$0.351588\pi$
$678$	8.81875	+	8.81875i	0.338682	+	0.338682i
$679$	−11.3540			−0.435728
$680$	−7.71754	−	3.66713i	−0.295954	−	0.140628i
$681$		−	54.2486i		−	2.07881i
$682$	−22.8788	−	5.64212i	−0.876074	−	0.216048i
$683$	6.27944	−	6.27944i	0.240276	−	0.240276i	−0.576688	−	0.816964i	$-0.695655\pi$
$683$	6.27944	−	6.27944i	0.240276	−	0.240276i	0.816964	+	0.576688i	$0.195655\pi$
$684$	48.7766			1.86502
$685$	3.49041	+	9.81067i	0.133362	+	0.374846i
$686$	−1.00000			−0.0381802
$687$	−16.7692	−	16.7692i	−0.639787	−	0.639787i
$688$	1.39491	+	1.39491i	0.0531805	+	0.0531805i
$689$	45.5294			1.73453
$690$	12.4098	+	34.8809i	0.472434	+	1.32789i
$691$	−11.5212			−0.438288			−0.219144	−	0.975693i	$-0.570326\pi$
$691$	−11.5212			−0.438288			−0.219144	+	0.975693i	$0.570326\pi$
$692$	8.38395	−	8.38395i	0.318710	−	0.318710i
$693$	−6.00411	+	24.3466i	−0.228077	+	0.924852i
$694$			33.9148i			1.28739i
$695$	33.5073	+	15.9216i	1.27100	+	0.603941i
$696$	0.258320			0.00979160
$697$	−6.24210	−	6.24210i	−0.236436	−	0.236436i
$698$	−15.0540	+	15.0540i	−0.569801	+	0.569801i
$699$	46.4153			1.75559
$700$	−0.507989	+	4.97413i	−0.0192002	+	0.188004i
$701$		−	12.6198i		−	0.476643i	−0.971186	−	0.238321i	$-0.923403\pi$
$701$		−	12.6198i		−	0.476643i	0.971186	−	0.238321i	$-0.0765972\pi$
$702$	−52.9712	−	52.9712i	−1.99927	−	1.99927i
$703$	42.2045	+	42.2045i	1.59177	+	1.59177i
$704$	−2.83852	+	1.71546i	−0.106981	+	0.0646540i
$705$	−32.5963	−	15.4887i	−1.22765	−	0.583339i
$706$			20.2783i			0.763185i
$707$	−4.59550	−	4.59550i	−0.172832	−	0.172832i
$708$	−5.49517	+	5.49517i	−0.206521	+	0.206521i
$709$		−	8.98525i		−	0.337448i	−0.985663	−	0.168724i	$-0.946035\pi$
$709$		−	8.98525i		−	0.337448i	0.985663	−	0.168724i	$-0.0539647\pi$
$710$	12.0221	−	4.27720i	0.451182	−	0.160520i
$711$			83.6142i			3.13578i
$712$	4.82316	−	4.82316i	0.180756	−	0.180756i
$713$	−25.5964	+	25.5964i	−0.958592	+	0.958592i
$714$	−12.4179			−0.464728
$715$	−23.7265	+	29.0203i	−0.887320	+	1.08530i
$716$	−7.32841			−0.273875
$717$	−46.9416	+	46.9416i	−1.75307	+	1.75307i
$718$	−21.1745	+	21.1745i	−0.790225	+	0.790225i
$719$			44.6615i			1.66559i	0.553580	+	0.832796i	$0.313261\pi$
$719$			44.6615i			1.66559i	−0.553580	+	0.832796i	$0.686739\pi$
$720$	−7.25585	+	15.2700i	−0.270409	+	0.569081i
$721$		−	9.59858i		−	0.357470i
$722$	−15.9945	+	15.9945i	−0.595252	+	0.595252i
$723$	9.48828	+	9.48828i	0.352873	+	0.352873i
$724$			13.9234i			0.517460i
$725$	−0.251032	−	0.308138i	−0.00932310	−	0.0114440i
$726$	31.6483	+	16.6203i	1.17458	+	0.616837i
$727$	−3.19139	−	3.19139i	−0.118362	−	0.118362i	0.645445	−	0.763807i	$-0.276672\pi$
$727$	−3.19139	−	3.19139i	−0.118362	−	0.118362i	−0.763807	+	0.645445i	$0.776672\pi$
$728$	−3.57405	−	3.57405i	−0.132463	−	0.132463i
$729$			48.1705i			1.78409i
$730$	15.0982	+	7.17418i	0.558809	+	0.265528i
$731$	7.53811			0.278807
$732$	7.55476	−	7.55476i	0.279232	−	0.279232i
$733$	−4.37467	−	4.37467i	−0.161582	−	0.161582i	0.621685	−	0.783267i	$-0.286448\pi$
$733$	−4.37467	−	4.37467i	−0.161582	−	0.161582i	−0.783267	+	0.621685i	$0.786448\pi$
$734$	0.829054			0.0306009
$735$	2.43573	+	6.84622i	0.0898433	+	0.252527i
$736$			5.09491i			0.187801i
$737$	5.27674	−	21.3972i	0.194371	−	0.788174i
$738$	−12.3507	+	12.3507i	−0.454636	+	0.454636i
$739$	−42.5629			−1.56570			−0.782850	−	0.622210i	$-0.786235\pi$
$739$	−42.5629			−1.56570			−0.782850	+	0.622210i	$0.786235\pi$
$740$	−19.4908	+	6.93439i	−0.716496	+	0.254913i
$741$	105.967			3.89280
$742$	−6.36944	−	6.36944i	−0.233830	−	0.233830i
$743$	−7.14244	−	7.14244i	−0.262031	−	0.262031i	0.563848	−	0.825879i	$-0.309320\pi$
$743$	−7.14244	−	7.14244i	−0.262031	−	0.262031i	−0.825879	+	0.563848i	$0.809320\pi$
$744$	−23.0889			−0.846480
$745$	6.34437	+	3.01464i	0.232440	+	0.110448i
$746$	−13.6054			−0.498128
$747$	−5.74912	+	5.74912i	−0.210349	+	0.210349i
$748$	−3.03450	+	12.3049i	−0.110952	+	0.449911i
$749$			12.5131i			0.457217i
$750$	35.2913	−	8.63783i	1.28866	−	0.315409i
$751$	−41.7014			−1.52171			−0.760853	−	0.648924i	$-0.775219\pi$
$751$	−41.7014			−1.52171			−0.760853	+	0.648924i	$0.775219\pi$
$752$	−3.51179	−	3.51179i	−0.128062	−	0.128062i
$753$	−11.5614	+	11.5614i	−0.421321	+	0.421321i
$754$	0.401779			0.0146319
$755$	−20.5255	+	43.1962i	−0.746998	+	1.57207i
$756$			14.8211i			0.539036i
$757$	10.9235	+	10.9235i	0.397021	+	0.397021i	0.877181	−	0.480160i	$-0.159421\pi$
$757$	10.9235	+	10.9235i	0.397021	+	0.397021i	−0.480160	+	0.877181i	$0.659421\pi$
$758$	−15.3365	−	15.3365i	−0.557046	−	0.557046i
$759$	46.9975	−	28.4030i	1.70590	−	1.03096i
$760$	−4.83539	−	13.5911i	−0.175398	−	0.492999i
$761$			17.2014i			0.623551i	0.950156	+	0.311776i	$0.100924\pi$
$761$			17.2014i			0.623551i	−0.950156	+	0.311776i	$0.899076\pi$
$762$	46.1086	+	46.1086i	1.67034	+	1.67034i
$763$	−3.29408	+	3.29408i	−0.119254	+	0.119254i
$764$		−	17.3756i		−	0.628628i
$765$	21.6544	+	60.8651i	0.782917	+	2.20058i
$766$		−	13.7570i		−	0.497059i
$767$	−8.54693	+	8.54693i	−0.308612	+	0.308612i
$768$	−2.29790	+	2.29790i	−0.0829184	+	0.0829184i
$769$	−39.9914			−1.44213			−0.721064	−	0.692869i	$-0.756347\pi$
$769$	−39.9914			−1.44213			−0.721064	+	0.692869i	$0.756347\pi$
$770$	7.37913	−	0.740587i	0.265925	−	0.0266889i
$771$	−74.7755			−2.69297
$772$	6.14589	−	6.14589i	0.221195	−	0.221195i
$773$	−8.12830	+	8.12830i	−0.292355	+	0.292355i	−0.838010	−	0.545655i	$-0.816281\pi$
$773$	−8.12830	+	8.12830i	−0.292355	+	0.292355i	0.545655	+	0.838010i	$0.316281\pi$
$774$		−	14.9150i		−	0.536110i
$775$	22.4375	+	27.5417i	0.805978	+	0.989326i
$776$			11.3540i			0.407586i
$777$	−21.2597	+	21.2597i	−0.762687	+	0.762687i
$778$	−9.95590	−	9.95590i	−0.356936	−	0.356936i
$779$		−	14.9037i		−	0.533980i
$780$	−15.7633	+	33.1742i	−0.564418	+	1.18783i
$781$	−9.78944	−	16.1982i	−0.350294	−	0.579619i
$782$	13.7665	+	13.7665i	0.492288	+	0.492288i
$783$	−0.833059	−	0.833059i	−0.0297711	−	0.0297711i
$784$			1.00000i			0.0357143i
$785$	−8.12366	−	22.8335i	−0.289946	−	0.814964i
$786$	−50.0202			−1.78416
$787$	−22.8118	+	22.8118i	−0.813152	+	0.813152i	−0.985105	−	0.171953i	$-0.944992\pi$
$787$	−22.8118	+	22.8118i	−0.813152	+	0.813152i	0.171953	+	0.985105i	$0.444992\pi$
$788$	18.0676	+	18.0676i	0.643631	+	0.643631i
$789$	56.2817			2.00368
$790$	23.2982	−	8.28896i	0.828912	−	0.294908i
$791$		−	3.83774i		−	0.136454i
$792$	24.3466	+	6.00411i	0.865120	+	0.213347i
$793$	11.7503	−	11.7503i	0.417266	−	0.417266i
$794$	17.4944			0.620854
$795$	−28.0924	+	59.1209i	−0.996333	+	2.09680i
$796$	−4.51944			−0.160187
$797$	9.53711	+	9.53711i	0.337822	+	0.337822i	0.855547	−	0.517725i	$-0.173221\pi$
$797$	9.53711	+	9.53711i	0.337822	+	0.337822i	−0.517725	+	0.855547i	$0.673221\pi$
$798$	−14.8245	−	14.8245i	−0.524782	−	0.524782i
$799$	−18.9777			−0.671384
$800$	4.97413	+	0.507989i	0.175862	+	0.0179601i
$801$	−51.5715			−1.82219
$802$	−18.0395	+	18.0395i	−0.636997	+	0.636997i
$803$	5.93653	−	24.0726i	0.209496	−	0.849504i
$804$		−	21.5937i		−	0.761550i
$805$	4.88947	−	10.2900i	0.172331	−	0.362674i
$806$	−35.9114			−1.26493
$807$	−49.8298	−	49.8298i	−1.75409	−	1.75409i
$808$	−4.59550	+	4.59550i	−0.161669	+	0.161669i
$809$	11.5913			0.407530			0.203765	−	0.979020i	$-0.434682\pi$
$809$	11.5913			0.407530			0.203765	+	0.979020i	$0.434682\pi$
$810$	53.6836	−	19.0994i	1.88625	−	0.671085i
$811$		−	44.2907i		−	1.55526i	−0.628725	−	0.777628i	$-0.716423\pi$
$811$		−	44.2907i		−	1.55526i	0.628725	−	0.777628i	$-0.283577\pi$
$812$	−0.0562078	−	0.0562078i	−0.00197251	−	0.00197251i
$813$	−20.7574	−	20.7574i	−0.727994	−	0.727994i
$814$	15.8711	+	26.2613i	0.556282	+	0.920460i
$815$	0.247606	−	0.0880926i	0.00867326	−	0.00308575i
$816$			12.4179i			0.434713i
$817$	8.99903	+	8.99903i	0.314836	+	0.314836i
$818$	−19.8100	+	19.8100i	−0.692641	+	0.692641i
$819$			38.2154i			1.33535i
$820$	4.66576	+	2.21702i	0.162935	+	0.0774218i
$821$		−	41.2588i		−	1.43994i	−0.694005	−	0.719970i	$-0.744155\pi$
$821$		−	41.2588i		−	1.43994i	0.694005	−	0.719970i	$-0.255845\pi$
$822$	10.7010	−	10.7010i	0.373241	−	0.373241i
$823$	17.6503	−	17.6503i	0.615251	−	0.615251i	−0.329059	−	0.944310i	$-0.606731\pi$
$823$	17.6503	−	17.6503i	0.615251	−	0.615251i	0.944310	+	0.329059i	$0.106731\pi$
$824$	−9.59858			−0.334382
$825$	−23.0438	−	48.7153i	−0.802282	−	1.69605i
$826$	2.39138			0.0832069
$827$	0.350025	−	0.350025i	0.0121716	−	0.0121716i	−0.700995	−	0.713166i	$-0.747260\pi$
$827$	0.350025	−	0.350025i	0.0121716	−	0.0121716i	0.713166	+	0.700995i	$0.247260\pi$
$828$	27.2386	−	27.2386i	0.946606	−	0.946606i
$829$		−	10.3031i		−	0.357842i	−0.983863	−	0.178921i	$-0.942739\pi$
$829$		−	10.3031i		−	0.357842i	0.983863	−	0.178921i	$-0.0572607\pi$
$830$	2.17186	+	1.03200i	0.0753864	+	0.0358212i
$831$		−	7.84502i		−	0.272141i
$832$	−3.57405	+	3.57405i	−0.123908	+	0.123908i
$833$	2.70200	+	2.70200i	0.0936189	+	0.0936189i
$834$		−	53.9148i		−	1.86692i
$835$	34.7778	−	12.3732i	1.20354	−	0.428191i
$836$	−18.3122	+	11.0670i	−0.633341	+	0.382761i
$837$	74.4596	+	74.4596i	2.57370	+	2.57370i
$838$	−24.6978	−	24.6978i	−0.853170	−	0.853170i
$839$		−	11.2740i		−	0.389221i	−0.980881	−	0.194611i	$-0.937656\pi$
$839$		−	11.2740i		−	0.389221i	0.980881	−	0.194611i	$-0.0623443\pi$
$840$	6.84622	−	2.43573i	0.236217	−	0.0840407i
$841$	−28.9937			−0.999782
$842$	−15.5298	+	15.5298i	−0.535193	+	0.535193i
$843$	10.2514	+	10.2514i	0.353079	+	0.353079i
$844$	−14.3254			−0.493101
$845$	−12.0417	+	25.3421i	−0.414249	+	0.871793i
$846$			37.5497i			1.29098i
$847$	−3.26993	−	10.5027i	−0.112356	−	0.360878i
$848$	−6.36944	+	6.36944i	−0.218727	+	0.218727i
$849$	1.43972			0.0494109
$850$	14.8127	−	12.0675i	0.508071	−	0.413913i
$851$	47.1370			1.61584
$852$	−13.1132	−	13.1132i	−0.449250	−	0.449250i
$853$	−7.94049	−	7.94049i	−0.271877	−	0.271877i	0.557978	−	0.829856i	$-0.311577\pi$
$853$	−7.94049	−	7.94049i	−0.271877	−	0.271877i	−0.829856	+	0.557978i	$0.811577\pi$
$854$	−3.28768			−0.112502
$855$	−46.8098	+	98.5120i	−1.60086	+	3.36904i
$856$	12.5131			0.427688
$857$	−0.930596	+	0.930596i	−0.0317886	+	0.0317886i	−0.722822	−	0.691034i	$-0.757156\pi$
$857$	−0.930596	+	0.930596i	−0.0317886	+	0.0317886i	0.691034	+	0.722822i	$0.257156\pi$
$858$	52.8931	+	13.0439i	1.80574	+	0.445312i
$859$			37.3252i			1.27352i	0.771062	+	0.636761i	$0.219726\pi$
$859$			37.3252i			1.27352i	−0.771062	+	0.636761i	$0.780274\pi$
$860$	−4.15591	+	1.47858i	−0.141715	+	0.0504191i
$861$	7.50743			0.255853
$862$	18.6141	+	18.6141i	0.634000	+	0.634000i
$863$	9.92446	−	9.92446i	0.337833	−	0.337833i	−0.517718	−	0.855551i	$-0.673219\pi$
$863$	9.92446	−	9.92446i	0.337833	−	0.337833i	0.855551	+	0.517718i	$0.173219\pi$
$864$	14.8211			0.504222
$865$	8.88682	+	24.9786i	0.302161	+	0.849298i
$866$		−	38.3292i		−	1.30248i
$867$	−5.51117	−	5.51117i	−0.187169	−	0.187169i
$868$	5.02391	+	5.02391i	0.170523	+	0.170523i
$869$	−18.9714	−	31.3913i	−0.643560	−	1.06488i
$870$	−0.247904	+	0.521719i	−0.00840474	+	0.0176879i
$871$		−	33.5858i		−	1.13801i
$872$	3.29408	+	3.29408i	0.111551	+	0.111551i
$873$	60.7013	−	60.7013i	2.05443	−	2.05443i
$874$			32.8689i			1.11181i
$875$	−9.55853	−	5.79952i	−0.323137	−	0.196060i
$876$		−	24.2937i		−	0.820808i
$877$	23.0466	−	23.0466i	0.778228	−	0.778228i	−0.201301	−	0.979529i	$-0.564517\pi$
$877$	23.0466	−	23.0466i	0.778228	−	0.778228i	0.979529	+	0.201301i	$0.0645171\pi$
$878$	−0.923927	+	0.923927i	−0.0311810	+	0.0311810i
$879$	43.4794			1.46652
$880$	−0.740587	−	7.37913i	−0.0249652	−	0.248750i
$881$	15.1403			0.510089			0.255044	−	0.966929i	$-0.417910\pi$
$881$	15.1403			0.510089			0.255044	+	0.966929i	$0.417910\pi$
$882$	5.34623	−	5.34623i	0.180017	−	0.180017i
$883$	22.6943	−	22.6943i	0.763725	−	0.763725i	−0.213269	−	0.976994i	$-0.568411\pi$
$883$	22.6943	−	22.6943i	0.763725	−	0.763725i	0.976994	+	0.213269i	$0.0684111\pi$
$884$			19.3142i			0.649607i
$885$	−5.82477	−	16.3719i	−0.195797	−	0.550337i
$886$		−	11.1365i		−	0.374137i
$887$	33.7735	−	33.7735i	1.13400	−	1.13400i	0.144498	−	0.989505i	$-0.453843\pi$
$887$	33.7735	−	33.7735i	1.13400	−	1.13400i	0.989505	−	0.144498i	$-0.0461567\pi$
$888$	21.2597	+	21.2597i	0.713428	+	0.713428i
$889$		−	20.0655i		−	0.672976i
$890$	5.11246	+	14.3698i	0.171370	+	0.481678i
$891$	−43.7138	−	72.3317i	−1.46447	−	2.42320i
$892$	14.0254	+	14.0254i	0.469605	+	0.469605i
$893$	−22.6557	−	22.6557i	−0.758144	−	0.758144i
$894$		−	10.2084i		−	0.341420i
$895$	7.03291	−	14.8009i	0.235084	−	0.494739i
$896$	1.00000			0.0334077
$897$	59.1758	−	59.1758i	1.97582	−	1.97582i
$898$	−28.0929	−	28.0929i	−0.937472	−	0.937472i
$899$	−0.564766			−0.0188360
$900$	−23.8770	−	29.3087i	−0.795900	−	0.976955i
$901$			34.4205i			1.14671i
$902$	1.83455	−	7.43911i	0.0610840	−	0.247695i
$903$	−4.53308	+	4.53308i	−0.150851	+	0.150851i
$904$	−3.83774			−0.127641
$905$	−28.1206	−	13.3620i	−0.934759	−	0.444168i
$906$	69.5047			2.30914
$907$	−20.4129	−	20.4129i	−0.677799	−	0.677799i	0.281703	−	0.959502i	$-0.409101\pi$
$907$	−20.4129	−	20.4129i	−0.677799	−	0.677799i	−0.959502	+	0.281703i	$0.909101\pi$
$908$	11.8039	+	11.8039i	0.391728	+	0.391728i
$909$	49.1372			1.62978
$910$	10.6483	−	3.78842i	0.352988	−	0.125585i
$911$	−48.6204			−1.61086			−0.805432	−	0.592688i	$-0.798067\pi$
$911$	−48.6204			−1.61086			−0.805432	+	0.592688i	$0.798067\pi$
$912$	−14.8245	+	14.8245i	−0.490889	+	0.490889i
$913$	0.853965	−	3.46282i	0.0282621	−	0.114603i
$914$			15.5695i			0.514993i
$915$	8.00790	+	22.5082i	0.264733	+	0.744097i
$916$	7.29763			0.241121
$917$	10.8839	+	10.8839i	0.359417	+	0.359417i
$918$	40.0465	−	40.0465i	1.32173	−	1.32173i
$919$	−11.2244			−0.370260			−0.185130	−	0.982714i	$-0.559271\pi$
$919$	−11.2244			−0.370260			−0.185130	+	0.982714i	$0.559271\pi$
$920$	−10.2900	−	4.88947i	−0.339251	−	0.161201i
$921$			45.7449i			1.50735i
$922$	−2.88216	−	2.88216i	−0.0949189	−	0.0949189i
$923$	−20.3956	−	20.3956i	−0.671330	−	0.671330i
$924$	−5.57478	−	9.22440i	−0.183397	−	0.303461i
$925$	4.69980	−	46.0195i	0.154529	−	1.51311i
$926$			7.19151i			0.236328i
$927$	51.3162	+	51.3162i	1.68544	+	1.68544i
$928$	−0.0562078	+	0.0562078i	−0.00184511	+	0.00184511i
$929$			20.5532i			0.674329i	0.941446	+	0.337165i	$0.109468\pi$
$929$			20.5532i			0.674329i	−0.941446	+	0.337165i	$0.890532\pi$
$930$	22.1579	−	46.6317i	0.726586	−	1.52911i
$931$			6.45132i			0.211434i
$932$	−10.0995	+	10.0995i	−0.330820	+	0.330820i
$933$	−55.7421	+	55.7421i	−1.82492	+	1.82492i
$934$	−24.2896			−0.794779
$935$	−21.9395	−	17.9374i	−0.717498	−	0.586614i
$936$	38.2154			1.24911
$937$	18.0852	−	18.0852i	0.590819	−	0.590819i	−0.347034	−	0.937853i	$-0.612811\pi$
$937$	18.0852	−	18.0852i	0.590819	−	0.590819i	0.937853	+	0.347034i	$0.112811\pi$
$938$	−4.69856	+	4.69856i	−0.153413	+	0.153413i
$939$			3.67124i			0.119806i
$940$	10.4628	−	3.72243i	0.341259	−	0.121412i
$941$			47.1395i			1.53670i	0.640028	+	0.768351i	$0.278923\pi$
$941$			47.1395i			1.53670i	−0.640028	+	0.768351i	$0.721077\pi$
$942$	−24.9058	+	24.9058i	−0.811475	+	0.811475i
$943$	−8.32274	−	8.32274i	−0.271026	−	0.271026i
$944$		−	2.39138i		−	0.0778329i
$945$	−29.9335	−	14.2234i	−0.973735	−	0.462688i
$946$	3.38410	+	5.59955i	0.110027	+	0.182057i
$947$	−28.4245	−	28.4245i	−0.923673	−	0.923673i	0.0736138	−	0.997287i	$-0.476547\pi$
$947$	−28.4245	−	28.4245i	−0.923673	−	0.923673i	−0.997287	+	0.0736138i	$0.976547\pi$
$948$	−25.4126	−	25.4126i	−0.825363	−	0.825363i
$949$		−	37.7853i		−	1.22656i
$950$	32.0897	+	3.27720i	1.04113	+	0.106326i
$951$	−47.7594			−1.54870
$952$	2.70200	−	2.70200i	0.0875724	−	0.0875724i
$953$	0.839435	+	0.839435i	0.0271920	+	0.0271920i	0.720572	−	0.693380i	$-0.243879\pi$
$953$	0.839435	+	0.839435i	0.0271920	+	0.0271920i	−0.693380	+	0.720572i	$0.743879\pi$
$954$	68.1050			2.20498
$955$	35.0928	+	16.6750i	1.13558	+	0.539591i
$956$		−	20.4280i		−	0.660689i
$957$	0.831830	+	0.205137i	0.0268893	+	0.00663114i
$958$	14.4138	−	14.4138i	0.465689	−	0.465689i
$959$	−4.65687			−0.150378
$960$	−2.43573	−	6.84622i	−0.0786129	−	0.220961i
$961$	19.4793			0.628365
$962$	33.0663	+	33.0663i	1.06610	+	1.06610i
$963$	−66.8977	−	66.8977i	−2.15575	−	2.15575i
$964$	−4.12911			−0.132990
$965$	6.51452	+	18.3107i	0.209710	+	0.589441i
$966$	−16.5571			−0.532715
$967$	27.0196	−	27.0196i	0.868892	−	0.868892i	−0.123458	−	0.992350i	$-0.539398\pi$
$967$	27.0196	−	27.0196i	0.868892	−	0.868892i	0.992350	+	0.123458i	$0.0393983\pi$
$968$	−10.5027	+	3.26993i	−0.337571	+	0.105100i
$969$			80.1118i			2.57356i
$970$	−22.9313	−	10.8962i	−0.736279	−	0.349857i
$971$	−38.7911			−1.24487			−0.622433	−	0.782673i	$-0.713856\pi$
$971$	−38.7911			−1.24487			−0.622433	+	0.782673i	$0.713856\pi$
$972$	−27.1154	−	27.1154i	−0.869727	−	0.869727i
$973$	−11.7313	+	11.7313i	−0.376089	+	0.376089i
$974$	26.7475			0.857046
$975$	−51.8728	−	63.6731i	−1.66126	−	2.03917i
$976$			3.28768i			0.105236i
$977$	−3.27123	−	3.27123i	−0.104656	−	0.104656i	0.652840	−	0.757496i	$-0.273577\pi$
$977$	−3.27123	−	3.27123i	−0.104656	−	0.104656i	−0.757496	+	0.652840i	$0.773577\pi$
$978$	−0.270077	−	0.270077i	−0.00863612	−	0.00863612i
$979$	19.3615	−	11.7011i	0.618796	−	0.373970i
$980$	−2.01966	−	0.959678i	−0.0645156	−	0.0306558i
$981$		−	35.2218i		−	1.12454i
$982$	−21.9315	−	21.9315i	−0.699862	−	0.699862i
$983$	−42.9838	+	42.9838i	−1.37097	+	1.37097i	−0.511965	+	0.859006i	$0.671082\pi$
$983$	−42.9838	+	42.9838i	−1.37097	+	1.37097i	−0.859006	+	0.511965i	$0.828918\pi$
$984$		−	7.50743i		−	0.239328i
$985$	−53.8294	+	19.1513i	−1.71515	+	0.610211i
$986$			0.303748i			0.00967329i
$987$	11.4123	−	11.4123i	0.363259	−	0.363259i
$988$	−23.0574	+	23.0574i	−0.733552	+	0.733552i
$989$	10.0507			0.319595
$990$	−35.4912	+	43.4099i	−1.12798	+	1.37966i
$991$	31.7959			1.01003			0.505016	−	0.863110i	$-0.331487\pi$
$991$	31.7959			1.01003			0.505016	+	0.863110i	$0.331487\pi$
$992$	5.02391	−	5.02391i	0.159509	−	0.159509i
$993$	60.8101	−	60.8101i	1.92975	−	1.92975i
$994$			5.70658i			0.181002i
$995$	4.33720	−	9.12772i	0.137499	−	0.289368i
$996$		−	3.49463i		−	0.110731i
$997$	−16.5413	+	16.5413i	−0.523867	+	0.523867i	−0.918737	−	0.394870i	$-0.870790\pi$
$997$	−16.5413	+	16.5413i	−0.523867	+	0.523867i	0.394870	+	0.918737i	$0.370790\pi$
$998$	11.2126	+	11.2126i	0.354928	+	0.354928i
$999$		−	137.121i		−	4.33832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.f.197.1	yes	36
5.3	odd	4	inner	770.2.m.f.43.10	yes	36
11.10	odd	2	inner	770.2.m.f.197.10	yes	36
55.43	even	4	inner	770.2.m.f.43.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.f.43.1	✓	36	55.43	even	4	inner
770.2.m.f.43.10	yes	36	5.3	odd	4	inner
770.2.m.f.197.1	yes	36	1.1	even	1	trivial
770.2.m.f.197.10	yes	36	11.10	odd	2	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.29790 + 2.29790i) q^{3} -1.00000i q^{4} +(2.01966 + 0.959678i) q^{5} -3.24972i q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -7.56071i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.29790 + 2.29790i) q^{3} -1.00000i q^{4} +(2.01966 + 0.959678i) q^{5} -3.24972i q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -7.56071i q^{9} +(-2.10671 + 0.749519i) q^{10} +(1.71546 + 2.83852i) q^{11} +(2.29790 + 2.29790i) q^{12} +(3.57405 + 3.57405i) q^{13} -1.00000i q^{14} +(-6.84622 + 2.43573i) q^{15} -1.00000 q^{16} +(-2.70200 + 2.70200i) q^{17} +(5.34623 + 5.34623i) q^{18} -6.45132 q^{19} +(0.959678 - 2.01966i) q^{20} -3.24972i q^{21} +(-3.22015 - 0.794119i) q^{22} +(-3.60265 + 3.60265i) q^{23} -3.24972 q^{24} +(3.15804 + 3.87644i) q^{25} -5.05447 q^{26} +(10.4801 + 10.4801i) q^{27} +(0.707107 + 0.707107i) q^{28} -0.0794899 q^{29} +(3.11869 - 6.56333i) q^{30} +7.10488 q^{31} +(0.707107 - 0.707107i) q^{32} +(-10.4646 - 2.58067i) q^{33} -3.82121i q^{34} +(-2.10671 + 0.749519i) q^{35} -7.56071 q^{36} +(-6.54200 - 6.54200i) q^{37} +(4.56177 - 4.56177i) q^{38} -16.4256 q^{39} +(0.749519 + 2.10671i) q^{40} +2.31017i q^{41} +(2.29790 + 2.29790i) q^{42} +(-1.39491 - 1.39491i) q^{43} +(2.83852 - 1.71546i) q^{44} +(7.25585 - 15.2700i) q^{45} -5.09491i q^{46} +(3.51179 + 3.51179i) q^{47} +(2.29790 - 2.29790i) q^{48} -1.00000i q^{49} +(-4.97413 - 0.507989i) q^{50} -12.4179i q^{51} +(3.57405 - 3.57405i) q^{52} +(6.36944 - 6.36944i) q^{53} -14.8211 q^{54} +(0.740587 + 7.37913i) q^{55} -1.00000 q^{56} +(14.8245 - 14.8245i) q^{57} +(0.0562078 - 0.0562078i) q^{58} +2.39138i q^{59} +(2.43573 + 6.84622i) q^{60} -3.28768i q^{61} +(-5.02391 + 5.02391i) q^{62} +(5.34623 + 5.34623i) q^{63} +1.00000i q^{64} +(3.78842 + 10.6483i) q^{65} +(9.22440 - 5.57478i) q^{66} +(-4.69856 - 4.69856i) q^{67} +(2.70200 + 2.70200i) q^{68} -16.5571i q^{69} +(0.959678 - 2.01966i) q^{70} -5.70658 q^{71} +(5.34623 - 5.34623i) q^{72} +(-5.28606 - 5.28606i) q^{73} +9.25178 q^{74} +(-16.1645 - 1.65082i) q^{75} +6.45132i q^{76} +(-3.22015 - 0.794119i) q^{77} +(11.6147 - 11.6147i) q^{78} -11.0590 q^{79} +(-2.01966 - 0.959678i) q^{80} -25.4822 q^{81} +(-1.63354 - 1.63354i) q^{82} +(-0.760395 - 0.760395i) q^{83} -3.24972 q^{84} +(-8.05018 + 2.86407i) q^{85} +1.97270 q^{86} +(0.182660 - 0.182660i) q^{87} +(-0.794119 + 3.22015i) q^{88} -6.82098i q^{89} +(5.66690 + 15.9282i) q^{90} -5.05447 q^{91} +(3.60265 + 3.60265i) q^{92} +(-16.3263 + 16.3263i) q^{93} -4.96642 q^{94} +(-13.0295 - 6.19119i) q^{95} +3.24972i q^{96} +(8.02852 + 8.02852i) q^{97} +(0.707107 + 0.707107i) q^{98} +(21.4612 - 12.9701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{3}+O(q^{10}) \) 36 * q - 4 * q^3	\( 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) \) 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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