LMFDB - Embedded newform 1000.2.d.c.501.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(501,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1000.501");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.d (of order $2$, degree $1$, 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			501.18
Character	$\chi$	$=$	1000.501
Dual form			1000.2.d.c.501.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.493756 + 1.32522i) q^{2} +1.83526i q^{3} +(-1.51241 - 1.30867i) q^{4} +(-2.43212 - 0.906170i) q^{6} +1.31564 q^{7} +(2.48104 - 1.35811i) q^{8} -0.368171 q^{9} +O(q^{10})$	\(q+(-0.493756 + 1.32522i) q^{2} +1.83526i q^{3} +(-1.51241 - 1.30867i) q^{4} +(-2.43212 - 0.906170i) q^{6} +1.31564 q^{7} +(2.48104 - 1.35811i) q^{8} -0.368171 q^{9} -6.60274i q^{11} +(2.40175 - 2.77566i) q^{12} +2.96705i q^{13} +(-0.649606 + 1.74351i) q^{14} +(0.574768 + 3.95849i) q^{16} +2.69502 q^{17} +(0.181787 - 0.487907i) q^{18} +4.97013i q^{19} +2.41454i q^{21} +(8.75007 + 3.26014i) q^{22} +3.73739 q^{23} +(2.49248 + 4.55334i) q^{24} +(-3.93199 - 1.46500i) q^{26} +4.83008i q^{27} +(-1.98979 - 1.72174i) q^{28} +5.52846i q^{29} +8.36121 q^{31} +(-5.52966 - 1.19283i) q^{32} +12.1177 q^{33} +(-1.33068 + 3.57149i) q^{34} +(0.556826 + 0.481814i) q^{36} -7.19517i q^{37} +(-6.58651 - 2.45403i) q^{38} -5.44530 q^{39} -3.77169 q^{41} +(-3.19980 - 1.19220i) q^{42} +3.07951i q^{43} +(-8.64080 + 9.98605i) q^{44} +(-1.84536 + 4.95287i) q^{46} +8.77645 q^{47} +(-7.26485 + 1.05485i) q^{48} -5.26908 q^{49} +4.94606i q^{51} +(3.88289 - 4.48739i) q^{52} -0.0464228i q^{53} +(-6.40092 - 2.38488i) q^{54} +(3.26416 - 1.78679i) q^{56} -9.12147 q^{57} +(-7.32642 - 2.72971i) q^{58} -1.02084i q^{59} -5.23191i q^{61} +(-4.12840 + 11.0804i) q^{62} -0.484382 q^{63} +(4.31107 - 6.73904i) q^{64} +(-5.98320 + 16.0586i) q^{66} +10.8187i q^{67} +(-4.07598 - 3.52689i) q^{68} +6.85908i q^{69} +9.35643 q^{71} +(-0.913446 + 0.500017i) q^{72} -12.4143 q^{73} +(9.53518 + 3.55266i) q^{74} +(6.50426 - 7.51688i) q^{76} -8.68684i q^{77} +(2.68865 - 7.21621i) q^{78} +1.43842 q^{79} -9.96896 q^{81} +(1.86230 - 4.99832i) q^{82} +13.0280i q^{83} +(3.15984 - 3.65178i) q^{84} +(-4.08102 - 1.52053i) q^{86} -10.1462 q^{87} +(-8.96725 - 16.3816i) q^{88} +3.94185 q^{89} +3.90357i q^{91} +(-5.65247 - 4.89101i) q^{92} +15.3450i q^{93} +(-4.33343 + 11.6307i) q^{94} +(2.18916 - 10.1484i) q^{96} -1.00691 q^{97} +(2.60164 - 6.98269i) q^{98} +2.43094i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−0.493756	+	1.32522i	−0.349138	+	0.937071i
$2$	−0.493756	+	1.32522i	−0.349138	+	0.937071i
$3$			1.83526i			1.05959i	0.848127	+	0.529793i	$0.177730\pi$
$3$			1.83526i			1.05959i	−0.848127	+	0.529793i	$0.822270\pi$
$4$	−1.51241	−	1.30867i	−0.756205	−	0.654335i
$5$		0			0
$5$		0			0
$6$	−2.43212	−	0.906170i	−0.992908	−	0.369942i
$7$	1.31564			0.497266			0.248633	−	0.968598i	$-0.420019\pi$
$7$	1.31564			0.497266			0.248633	+	0.968598i	$0.420019\pi$
$8$	2.48104	−	1.35811i	0.877178	−	0.480165i
$9$	−0.368171			−0.122724
$10$		0			0
$11$		−	6.60274i		−	1.99080i	−0.0958055	−	0.995400i	$-0.530543\pi$
$11$		−	6.60274i		−	1.99080i	0.0958055	−	0.995400i	$-0.469457\pi$
$12$	2.40175	−	2.77566i	0.693324	−	0.801265i
$13$			2.96705i			0.822911i	0.911430	+	0.411456i	$0.134979\pi$
$13$			2.96705i			0.822911i	−0.911430	+	0.411456i	$0.865021\pi$
$14$	−0.649606	+	1.74351i	−0.173615	+	0.465974i
$15$		0			0
$16$	0.574768	+	3.95849i	0.143692	+	0.989622i
$17$	2.69502			0.653639			0.326819	−	0.945087i	$-0.394023\pi$
$17$	2.69502			0.653639			0.326819	+	0.945087i	$0.394023\pi$
$18$	0.181787	−	0.487907i	0.0428475	−	0.115001i
$19$			4.97013i			1.14023i	0.821566	+	0.570113i	$0.193101\pi$
$19$			4.97013i			1.14023i	−0.821566	+	0.570113i	$0.806899\pi$
$20$		0			0
$21$			2.41454i			0.526897i
$22$	8.75007	+	3.26014i	1.86552	+	0.695064i
$23$	3.73739			0.779301			0.389650	−	0.920963i	$-0.372596\pi$
$23$	3.73739			0.779301			0.389650	+	0.920963i	$0.372596\pi$
$24$	2.49248	+	4.55334i	0.508776	+	0.929446i
$25$		0			0
$26$	−3.93199	−	1.46500i	−0.771126	−	0.287310i
$27$			4.83008i			0.929550i
$28$	−1.98979	−	1.72174i	−0.376035	−	0.325379i
$29$			5.52846i			1.02661i	0.858206	+	0.513305i	$0.171579\pi$
$29$			5.52846i			1.02661i	−0.858206	+	0.513305i	$0.828421\pi$
$30$		0			0
$31$	8.36121			1.50172			0.750859	−	0.660462i	$-0.229640\pi$
$31$	8.36121			1.50172			0.750859	+	0.660462i	$0.229640\pi$
$32$	−5.52966	−	1.19283i	−0.977515	−	0.210865i
$33$	12.1177			2.10943
$34$	−1.33068	+	3.57149i	−0.228210	+	0.612506i
$35$		0			0
$36$	0.556826	+	0.481814i	0.0928043	+	0.0803024i
$37$		−	7.19517i		−	1.18288i	−0.806349	−	0.591439i	$-0.798560\pi$
$37$		−	7.19517i		−	1.18288i	0.806349	−	0.591439i	$-0.201440\pi$
$38$	−6.58651	−	2.45403i	−1.06847	−	0.398097i
$39$	−5.44530			−0.871945
$40$		0			0
$41$	−3.77169			−0.589040			−0.294520	−	0.955645i	$-0.595160\pi$
$41$	−3.77169			−0.589040			−0.294520	+	0.955645i	$0.595160\pi$
$42$	−3.19980	−	1.19220i	−0.493740	−	0.183960i
$43$			3.07951i			0.469621i	0.972041	+	0.234810i	$0.0754469\pi$
$43$			3.07951i			0.469621i	−0.972041	+	0.234810i	$0.924553\pi$
$44$	−8.64080	+	9.98605i	−1.30265	+	1.50545i
$45$		0			0
$46$	−1.84536	+	4.95287i	−0.272084	+	0.730260i
$47$	8.77645			1.28018			0.640088	−	0.768301i	$-0.278898\pi$
$47$	8.77645			1.28018			0.640088	+	0.768301i	$0.278898\pi$
$48$	−7.26485	+	1.05485i	−1.04859	+	0.152254i
$49$	−5.26908			−0.752726
$50$		0			0
$51$			4.94606i			0.692587i
$52$	3.88289	−	4.48739i	0.538459	−	0.622289i
$53$		−	0.0464228i		−	0.00637666i	−0.999995	−	0.00318833i	$-0.998985\pi$
$53$		−	0.0464228i		−	0.00637666i	0.999995	−	0.00318833i	$-0.00101488\pi$
$54$	−6.40092	−	2.38488i	−0.871055	−	0.324541i
$55$		0			0
$56$	3.26416	−	1.78679i	0.436191	−	0.238770i
$57$	−9.12147			−1.20817
$58$	−7.32642	−	2.72971i	−0.962006	−	0.358429i
$59$		−	1.02084i		−	0.132902i	−0.997790	−	0.0664510i	$-0.978832\pi$
$59$		−	1.02084i		−	0.132902i	0.997790	−	0.0664510i	$-0.0211676\pi$
$60$		0			0
$61$		−	5.23191i		−	0.669877i	−0.942240	−	0.334938i	$-0.891284\pi$
$61$		−	5.23191i		−	0.669877i	0.942240	−	0.334938i	$-0.108716\pi$
$62$	−4.12840	+	11.0804i	−0.524307	+	1.40722i
$63$	−0.484382			−0.0610264
$64$	4.31107	−	6.73904i	0.538884	−	0.842380i
$65$		0			0
$66$	−5.98320	+	16.0586i	−0.736481	+	1.97668i
$67$			10.8187i			1.32172i	0.750511	+	0.660858i	$0.229807\pi$
$67$			10.8187i			1.32172i	−0.750511	+	0.660858i	$0.770193\pi$
$68$	−4.07598	−	3.52689i	−0.494285	−	0.427699i
$69$			6.85908i			0.825737i
$70$		0			0
$71$	9.35643			1.11040			0.555202	−	0.831715i	$-0.312641\pi$
$71$	9.35643			1.11040			0.555202	+	0.831715i	$0.312641\pi$
$72$	−0.913446	+	0.500017i	−0.107651	+	0.0589276i
$73$	−12.4143			−1.45298			−0.726490	−	0.687177i	$-0.758850\pi$
$73$	−12.4143			−1.45298			−0.726490	+	0.687177i	$0.758850\pi$
$74$	9.53518	+	3.55266i	1.10844	+	0.412988i
$75$		0			0
$76$	6.50426	−	7.51688i	0.746090	−	0.862245i
$77$		−	8.68684i		−	0.989958i
$78$	2.68865	−	7.21621i	0.304429	−	0.817075i
$79$	1.43842			0.161835			0.0809174	−	0.996721i	$-0.474215\pi$
$79$	1.43842			0.161835			0.0809174	+	0.996721i	$0.474215\pi$
$80$		0			0
$81$	−9.96896			−1.10766
$82$	1.86230	−	4.99832i	0.205656	−	0.551972i
$83$			13.0280i			1.43001i	0.699120	+	0.715005i	$0.253575\pi$
$83$			13.0280i			1.43001i	−0.699120	+	0.715005i	$0.746425\pi$
$84$	3.15984	−	3.65178i	0.344767	−	0.398442i
$85$		0			0
$86$	−4.08102	−	1.52053i	−0.440068	−	0.163962i
$87$	−10.1462			−1.08778
$88$	−8.96725	−	16.3816i	−0.955912	−	1.74629i
$89$	3.94185			0.417835			0.208917	−	0.977933i	$-0.433006\pi$
$89$	3.94185			0.417835			0.208917	+	0.977933i	$0.433006\pi$
$90$		0			0
$91$			3.90357i			0.409206i
$92$	−5.65247	−	4.89101i	−0.589311	−	0.509924i
$93$			15.3450i			1.59120i
$94$	−4.33343	+	11.6307i	−0.446959	+	1.19962i
$95$		0			0
$96$	2.18916	−	10.1484i	0.223430	−	1.03576i
$97$	−1.00691			−0.102236			−0.0511181	−	0.998693i	$-0.516278\pi$
$97$	−1.00691			−0.102236			−0.0511181	+	0.998693i	$0.516278\pi$
$98$	2.60164	−	6.98269i	0.262806	−	0.705358i
$99$			2.43094i			0.244318i
$100$		0			0
$101$			2.50175i			0.248933i	0.992224	+	0.124466i	$0.0397219\pi$
$101$			2.50175i			0.248933i	−0.992224	+	0.124466i	$0.960278\pi$
$102$	−6.55461	−	2.44215i	−0.649003	−	0.241809i
$103$	5.34336			0.526497			0.263248	−	0.964728i	$-0.415206\pi$
$103$	5.34336			0.526497			0.263248	+	0.964728i	$0.415206\pi$
$104$	4.02958	+	7.36135i	0.395133	+	0.721840i
$105$		0			0
$106$	0.0615203	+	0.0229215i	0.00597538	+	0.00222633i
$107$			0.971619i			0.0939299i	0.998897	+	0.0469650i	$0.0149549\pi$
$107$			0.971619i			0.0939299i	−0.998897	+	0.0469650i	$0.985045\pi$
$108$	6.32098	−	7.30507i	0.608237	−	0.702930i
$109$		−	18.8454i		−	1.80506i	−0.430626	−	0.902531i	$-0.641707\pi$
$109$		−	18.8454i		−	1.80506i	0.430626	−	0.902531i	$-0.358293\pi$
$110$		0			0
$111$	13.2050			1.25336
$112$	0.756189	+	5.20796i	0.0714532	+	0.492106i
$113$	12.3812			1.16472			0.582361	−	0.812930i	$-0.302129\pi$
$113$	12.3812			1.16472			0.582361	+	0.812930i	$0.302129\pi$
$114$	4.50378	−	12.0879i	0.421818	−	1.13214i
$115$		0			0
$116$	7.23493	−	8.36130i	0.671746	−	0.776327i
$117$		−	1.09238i		−	0.100991i
$118$	1.35284	+	0.504045i	0.124539	+	0.0464011i
$119$	3.54568			0.325032
$120$		0			0
$121$	−32.5961			−2.96329
$122$	6.93342	+	2.58328i	0.627722	+	0.233880i
$123$		−	6.92203i		−	0.624139i
$124$	−12.6456	−	10.9421i	−1.13561	−	0.982627i
$125$		0			0
$126$	0.239166	−	0.641912i	0.0213066	−	0.0571860i
$127$	−11.8083			−1.04782			−0.523909	−	0.851774i	$-0.675527\pi$
$127$	−11.8083			−1.04782			−0.523909	+	0.851774i	$0.675527\pi$
$128$	6.80209	+	9.04055i	0.601225	+	0.799080i
$129$	−5.65169			−0.497604
$130$		0			0
$131$		−	12.6735i		−	1.10729i	−0.832752	−	0.553646i	$-0.813236\pi$
$131$		−	12.6735i		−	1.10729i	0.832752	−	0.553646i	$-0.186764\pi$
$132$	−18.3270	−	15.8581i	−1.59516	−	1.38027i
$133$			6.53892i			0.566996i
$134$	−14.3372	−	5.34180i	−1.23854	−	0.461461i
$135$		0			0
$136$	6.68644	−	3.66014i	0.573358	−	0.313854i
$137$	−4.33562			−0.370417			−0.185209	−	0.982699i	$-0.559296\pi$
$137$	−4.33562			−0.370417			−0.185209	+	0.982699i	$0.559296\pi$
$138$	−9.08979	−	3.38671i	−0.773774	−	0.288296i
$139$			3.48791i			0.295841i	0.988999	+	0.147920i	$0.0472579\pi$
$139$			3.48791i			0.295841i	−0.988999	+	0.147920i	$0.952742\pi$
$140$		0			0
$141$			16.1070i			1.35646i
$142$	−4.61980	+	12.3993i	−0.387685	+	1.04053i
$143$	19.5906			1.63825
$144$	−0.211613	−	1.45740i	−0.0176344	−	0.121450i
$145$		0			0
$146$	6.12962	−	16.4516i	0.507291	−	1.36155i
$147$		−	9.67013i		−	0.797579i
$148$	−9.41610	+	10.8820i	−0.773999	+	0.894499i
$149$			9.11838i			0.747007i	0.927629	+	0.373503i	$0.121844\pi$
$149$			9.11838i			0.747007i	−0.927629	+	0.373503i	$0.878156\pi$
$150$		0			0
$151$	−10.5180			−0.855944			−0.427972	−	0.903792i	$-0.640772\pi$
$151$	−10.5180			−0.855944			−0.427972	+	0.903792i	$0.640772\pi$
$152$	6.74999	+	12.3311i	0.547496	+	1.00018i
$153$	−0.992229			−0.0802170
$154$	11.5120	+	4.28918i	0.927661	+	0.345632i
$155$		0			0
$156$	8.23552	+	7.12610i	0.659370	+	0.570544i
$157$			5.59017i			0.446144i	0.974802	+	0.223072i	$0.0716085\pi$
$157$			5.59017i			0.446144i	−0.974802	+	0.223072i	$0.928392\pi$
$158$	−0.710228	+	1.90622i	−0.0565027	+	0.151651i
$159$	0.0851977			0.00675662
$160$		0			0
$161$	4.91708			0.387520
$162$	4.92224	−	13.2111i	0.386727	−	1.03796i
$163$			5.48367i			0.429514i	0.976667	+	0.214757i	$0.0688960\pi$
$163$			5.48367i			0.429514i	−0.976667	+	0.214757i	$0.931104\pi$
$164$	5.70435	+	4.93590i	0.445435	+	0.385429i
$165$		0			0
$166$	−17.2650	−	6.43266i	−1.34002	−	0.499271i
$167$	19.4503			1.50511			0.752556	−	0.658528i	$-0.228821\pi$
$167$	19.4503			1.50511			0.752556	+	0.658528i	$0.228821\pi$
$168$	3.27922	+	5.99057i	0.252997	+	0.462182i
$169$	4.19663			0.322817
$170$		0			0
$171$		−	1.82986i		−	0.139933i
$172$	4.03006	−	4.65748i	0.307289	−	0.355129i
$173$		−	11.9677i		−	0.909885i	−0.890521	−	0.454942i	$-0.849660\pi$
$173$		−	11.9677i		−	0.909885i	0.890521	−	0.454942i	$-0.150340\pi$
$174$	5.00972	−	13.4459i	0.379786	−	1.01933i
$175$		0			0
$176$	26.1369	−	3.79504i	1.97014	−	0.286062i
$177$	1.87350			0.140821
$178$	−1.94631	+	5.22381i	−0.145882	+	0.391541i
$179$		−	11.0142i		−	0.823244i	−0.911355	−	0.411622i	$-0.864962\pi$
$179$		−	11.0142i		−	0.823244i	0.911355	−	0.411622i	$-0.135038\pi$
$180$		0			0
$181$			18.6306i			1.38480i	0.721511	+	0.692402i	$0.243448\pi$
$181$			18.6306i			1.38480i	−0.721511	+	0.692402i	$0.756552\pi$
$182$	−5.17309	−	1.92741i	−0.383455	−	0.142869i
$183$	9.60190			0.709793
$184$	9.27261	−	5.07580i	0.683586	−	0.374193i
$185$		0			0
$186$	−20.3355	−	7.57668i	−1.49107	−	0.555549i
$187$		−	17.7945i		−	1.30126i
$188$	−13.2736	−	11.4855i	−0.968076	−	0.837664i
$189$			6.35466i			0.462234i
$190$		0			0
$191$	10.6266			0.768912			0.384456	−	0.923143i	$-0.374389\pi$
$191$	10.6266			0.768912			0.384456	+	0.923143i	$0.374389\pi$
$192$	12.3679	+	7.91192i	0.892575	+	0.570994i
$193$	17.9777			1.29406			0.647031	−	0.762464i	$-0.276011\pi$
$193$	17.9777			1.29406			0.647031	+	0.762464i	$0.276011\pi$
$194$	0.497168	−	1.33438i	0.0356945	−	0.0958026i
$195$		0			0
$196$	7.96902	+	6.89549i	0.569215	+	0.492535i
$197$			23.6813i			1.68722i	0.536956	+	0.843610i	$0.319574\pi$
$197$			23.6813i			1.68722i	−0.536956	+	0.843610i	$0.680426\pi$
$198$	−3.22152	−	1.20029i	−0.228944	−	0.0853009i
$199$	17.9303			1.27104			0.635522	−	0.772082i	$-0.280785\pi$
$199$	17.9303			1.27104			0.635522	+	0.772082i	$0.280785\pi$
$200$		0			0
$201$	−19.8551			−1.40047
$202$	−3.31536	−	1.23525i	−0.233268	−	0.0869120i
$203$			7.27348i			0.510498i
$204$	6.47276	−	7.48047i	0.453184	−	0.523738i
$205$		0			0
$206$	−2.63831	+	7.08112i	−0.183820	+	0.493365i
$207$	−1.37600			−0.0956387
$208$	−11.7450	+	1.70536i	−0.814371	+	0.118246i
$209$	32.8165			2.26996
$210$		0			0
$211$		−	15.0943i		−	1.03913i	−0.854430	−	0.519566i	$-0.826094\pi$
$211$		−	15.0943i		−	1.03913i	0.854430	−	0.519566i	$-0.173906\pi$
$212$	−0.0607521	+	0.0702103i	−0.00417247	+	0.00482206i
$213$			17.1715i			1.17657i
$214$	−1.28761	−	0.479743i	−0.0880190	−	0.0327945i
$215$		0			0
$216$	6.55979	+	11.9836i	0.446337	+	0.815381i
$217$	11.0004			0.746754
$218$	24.9743	+	9.30503i	1.69147	+	0.630216i
$219$		−	22.7834i		−	1.53956i
$220$		0			0
$221$			7.99626i			0.537886i
$222$	−6.52005	+	17.4995i	−0.437597	+	1.17449i
$223$	−21.0583			−1.41017			−0.705083	−	0.709125i	$-0.749090\pi$
$223$	−21.0583			−1.41017			−0.705083	+	0.709125i	$0.749090\pi$
$224$	−7.27506	−	1.56934i	−0.486085	−	0.104856i
$225$		0			0
$226$	−6.11327	+	16.4077i	−0.406649	+	1.09143i
$227$			6.94442i			0.460917i	0.973082	+	0.230459i	$0.0740226\pi$
$227$			6.94442i			0.460917i	−0.973082	+	0.230459i	$0.925977\pi$
$228$	13.7954	+	11.9370i	0.913623	+	0.790547i
$229$		−	19.8805i		−	1.31374i	−0.754003	−	0.656871i	$-0.771879\pi$
$229$		−	19.8805i		−	1.31374i	0.754003	−	0.656871i	$-0.228121\pi$
$230$		0			0
$231$	15.9426			1.04895
$232$	7.50826	+	13.7163i	0.492942	+	0.900520i
$233$	−9.43816			−0.618315			−0.309157	−	0.951011i	$-0.600047\pi$
$233$	−9.43816			−0.618315			−0.309157	+	0.951011i	$0.600047\pi$
$234$	1.44764	+	0.539370i	0.0946355	+	0.0352597i
$235$		0			0
$236$	−1.33594	+	1.54393i	−0.0869624	+	0.100501i
$237$			2.63987i			0.171478i
$238$	−1.75070	+	4.69881i	−0.113481	+	0.304579i
$239$	−21.3865			−1.38338			−0.691688	−	0.722197i	$-0.743132\pi$
$239$	−21.3865			−1.38338			−0.691688	+	0.722197i	$0.743132\pi$
$240$		0			0
$241$	11.4117			0.735094			0.367547	−	0.930005i	$-0.380198\pi$
$241$	11.4117			0.735094			0.367547	+	0.930005i	$0.380198\pi$
$242$	16.0945	−	43.1970i	1.03460	−	2.77681i
$243$		−	3.80536i		−	0.244114i
$244$	−6.84684	+	7.91279i	−0.438324	+	0.506564i
$245$		0			0
$246$	9.17321	+	3.41779i	0.584862	+	0.217911i
$247$	−14.7466			−0.938305
$248$	20.7445	−	11.3555i	1.31727	−	0.721072i
$249$	−23.9097			−1.51522
$250$		0			0
$251$			2.76130i			0.174292i	0.996196	+	0.0871459i	$0.0277746\pi$
$251$			2.76130i			0.174292i	−0.996196	+	0.0871459i	$0.972225\pi$
$252$	0.732584	+	0.633896i	0.0461484	+	0.0399317i
$253$		−	24.6770i		−	1.55143i
$254$	5.83043	−	15.6486i	0.365834	−	0.981881i
$255$		0			0
$256$	−15.3393	+	4.55043i	−0.958705	+	0.284402i
$257$	12.1685			0.759052			0.379526	−	0.925181i	$-0.376087\pi$
$257$	12.1685			0.759052			0.379526	+	0.925181i	$0.376087\pi$
$258$	2.79056	−	7.48973i	0.173732	−	0.466290i
$259$		−	9.46627i		−	0.588206i
$260$		0			0
$261$		−	2.03542i		−	0.125989i
$262$	16.7952	+	6.25763i	1.03761	+	0.386598i
$263$	−22.4088			−1.38179			−0.690894	−	0.722956i	$-0.742783\pi$
$263$	−22.4088			−1.38179			−0.690894	+	0.722956i	$0.742783\pi$
$264$	30.0645	−	16.4572i	1.85034	−	1.01287i
$265$		0			0
$266$	−8.66550	−	3.22863i	−0.531316	−	0.197960i
$267$			7.23430i			0.442732i
$268$	14.1581	−	16.3623i	0.864844	−	0.999488i
$269$		−	29.7546i		−	1.81417i	−0.420946	−	0.907086i	$-0.638302\pi$
$269$		−	29.7546i		−	1.81417i	0.420946	−	0.907086i	$-0.361698\pi$
$270$		0			0
$271$	15.1173			0.918308			0.459154	−	0.888357i	$-0.348153\pi$
$271$	15.1173			0.918308			0.459154	+	0.888357i	$0.348153\pi$
$272$	1.54901	+	10.6682i	0.0939227	+	0.646856i
$273$	−7.16407			−0.433589
$274$	2.14074	−	5.74565i	0.129327	−	0.347107i
$275$		0			0
$276$	8.97627	−	10.3737i	0.540308	−	0.624426i
$277$		−	9.51304i		−	0.571583i	−0.958292	−	0.285792i	$-0.907743\pi$
$277$		−	9.51304i		−	0.571583i	0.958292	−	0.285792i	$-0.0922565\pi$
$278$	−4.62224	−	1.72218i	−0.277224	−	0.103289i
$279$	−3.07836			−0.184296
$280$		0			0
$281$	−17.5890			−1.04927			−0.524637	−	0.851326i	$-0.675799\pi$
$281$	−17.5890			−1.04927			−0.524637	+	0.851326i	$0.675799\pi$
$282$	−21.3454	−	7.95295i	−1.27110	−	0.473591i
$283$		−	15.3245i		−	0.910944i	−0.890250	−	0.455472i	$-0.849471\pi$
$283$		−	15.3245i		−	0.910944i	0.890250	−	0.455472i	$-0.150529\pi$
$284$	−14.1508	−	12.2445i	−0.839693	−	0.726576i
$285$		0			0
$286$	−9.67299	+	25.9619i	−0.571976	+	1.53516i
$287$	−4.96220			−0.292909
$288$	2.03586	+	0.439167i	0.119964	+	0.0258782i
$289$	−9.73686			−0.572756
$290$		0			0
$291$		−	1.84794i		−	0.108328i
$292$	18.7755	+	16.2462i	1.09875	+	0.950735i
$293$		−	3.18687i		−	0.186179i	−0.995658	−	0.0930894i	$-0.970326\pi$
$293$		−	3.18687i		−	0.186179i	0.995658	−	0.0930894i	$-0.0296742\pi$
$294$	12.8150	+	4.77468i	0.747388	+	0.278465i
$295$		0			0
$296$	−9.77184	−	17.8515i	−0.567977	−	1.03760i
$297$	31.8918			1.85055
$298$	−12.0838	−	4.50225i	−0.699999	−	0.260809i
$299$			11.0890i			0.641295i
$300$		0			0
$301$			4.05153i			0.233526i
$302$	5.19334	−	13.9387i	0.298843	−	0.802081i
$303$	−4.59135			−0.263766
$304$	−19.6742	+	2.85667i	−1.12839	+	0.163841i
$305$		0			0
$306$	0.489919	−	1.31492i	0.0280068	−	0.0751690i
$307$		−	28.0569i		−	1.60129i	−0.599138	−	0.800645i	$-0.704490\pi$
$307$		−	28.0569i		−	1.60129i	0.599138	−	0.800645i	$-0.295510\pi$
$308$	−11.3682	+	13.1381i	−0.647764	+	0.748611i
$309$			9.80644i			0.557869i
$310$		0			0
$311$	27.7970			1.57622			0.788112	−	0.615532i	$-0.211059\pi$
$311$	27.7970			1.57622			0.788112	+	0.615532i	$0.211059\pi$
$312$	−13.5100	+	7.39532i	−0.764852	+	0.418677i
$313$	−21.6443			−1.22341			−0.611703	−	0.791088i	$-0.709515\pi$
$313$	−21.6443			−1.22341			−0.611703	+	0.791088i	$0.709515\pi$
$314$	−7.40819	−	2.76018i	−0.418069	−	0.155766i
$315$		0			0
$316$	−2.17548	−	1.88242i	−0.122380	−	0.105894i
$317$			16.0032i			0.898827i	0.893324	+	0.449414i	$0.148367\pi$
$317$			16.0032i			0.898827i	−0.893324	+	0.449414i	$0.851633\pi$
$318$	−0.0420669	+	0.112906i	−0.00235899	+	0.00633143i
$319$	36.5030			2.04377
$320$		0			0
$321$	−1.78317			−0.0995269
$322$	−2.42784	+	6.51620i	−0.135298	+	0.363134i
$323$			13.3946i			0.745296i
$324$	15.0772	+	13.0461i	0.837620	+	0.724782i
$325$		0			0
$326$	−7.26706	−	2.70759i	−0.402485	−	0.149960i
$327$	34.5862			1.91262
$328$	−9.35771	+	5.12238i	−0.516693	+	0.282836i
$329$	11.5467			0.636589
$330$		0			0
$331$			5.39927i			0.296771i	0.988930	+	0.148385i	$0.0474076\pi$
$331$			5.39927i			0.296771i	−0.988930	+	0.148385i	$0.952592\pi$
$332$	17.0494	−	19.7037i	0.935705	−	1.08138i
$333$			2.64905i			0.145167i
$334$	−9.60372	+	25.7760i	−0.525492	+	1.41040i
$335$		0			0
$336$	−9.55794	+	1.38780i	−0.521429	+	0.0757108i
$337$	−26.3679			−1.43635			−0.718176	−	0.695861i	$-0.755023\pi$
$337$	−26.3679			−1.43635			−0.718176	+	0.695861i	$0.755023\pi$
$338$	−2.07211	+	5.56145i	−0.112708	+	0.302503i
$339$			22.7226i			1.23412i
$340$		0			0
$341$		−	55.2069i		−	2.98962i
$342$	2.42496	+	0.903504i	0.131127	+	0.0488559i
$343$	−16.1417			−0.871571
$344$	4.18231	+	7.64037i	0.225495	+	0.411941i
$345$		0			0
$346$	15.8598	+	5.90911i	0.852627	+	0.317676i
$347$		−	8.70069i		−	0.467077i	−0.972348	−	0.233539i	$-0.924969\pi$
$347$		−	8.70069i		−	0.467077i	0.972348	−	0.233539i	$-0.0750306\pi$
$348$	15.3451	+	13.2780i	0.822586	+	0.711773i
$349$			14.7757i			0.790923i	0.918483	+	0.395462i	$0.129415\pi$
$349$			14.7757i			0.790923i	−0.918483	+	0.395462i	$0.870585\pi$
$350$		0			0
$351$	−14.3311			−0.764937
$352$	−7.87597	+	36.5109i	−0.419791	+	1.94604i
$353$	−17.4259			−0.927485			−0.463743	−	0.885970i	$-0.653494\pi$
$353$	−17.4259			−0.927485			−0.463743	+	0.885970i	$0.653494\pi$
$354$	−0.925053	+	2.48280i	−0.0491660	+	0.131959i
$355$		0			0
$356$	−5.96169	−	5.15857i	−0.315969	−	0.273404i
$357$			6.50725i			0.344400i
$358$	14.5963	+	5.43835i	0.771438	+	0.287426i
$359$	−12.3632			−0.652506			−0.326253	−	0.945282i	$-0.605786\pi$
$359$	−12.3632			−0.652506			−0.326253	+	0.945282i	$0.605786\pi$
$360$		0			0
$361$	−5.70221			−0.300116
$362$	−24.6897	−	9.19899i	−1.29766	−	0.483488i
$363$		−	59.8223i		−	3.13986i
$364$	5.10849	−	5.90381i	0.267758	−	0.309443i
$365$		0			0
$366$	−4.74099	+	12.7246i	−0.247816	+	0.665126i
$367$	4.15969			0.217134			0.108567	−	0.994089i	$-0.465374\pi$
$367$	4.15969			0.217134			0.108567	+	0.994089i	$0.465374\pi$
$368$	2.14814	+	14.7944i	0.111979	+	0.771213i
$369$	1.38863			0.0722891
$370$		0			0
$371$		−	0.0610758i		−	0.00317090i
$372$	20.0815	−	23.2079i	1.04118	−	1.20327i
$373$		−	33.9114i		−	1.75586i	−0.478786	−	0.877932i	$-0.658923\pi$
$373$		−	33.9114i		−	1.75586i	0.478786	−	0.877932i	$-0.341077\pi$
$374$	23.5816	+	8.78615i	1.21938	+	0.454321i
$375$		0			0
$376$	21.7747	−	11.9194i	1.12294	−	0.614696i
$377$	−16.4032			−0.844808
$378$	−8.42132	−	3.13765i	−0.433146	−	0.161383i
$379$			8.17397i			0.419869i	0.977715	+	0.209934i	$0.0673250\pi$
$379$			8.17397i			0.419869i	−0.977715	+	0.209934i	$0.932675\pi$
$380$		0			0
$381$		−	21.6713i		−	1.11025i
$382$	−5.24693	+	14.0825i	−0.268457	+	0.720525i
$383$	3.27290			0.167238			0.0836188	−	0.996498i	$-0.473352\pi$
$383$	3.27290			0.167238			0.0836188	+	0.996498i	$0.473352\pi$
$384$	−16.5917	+	12.4836i	−0.846694	+	0.637050i
$385$		0			0
$386$	−8.87659	+	23.8244i	−0.451806	+	1.21263i
$387$		−	1.13379i		−	0.0576336i
$388$	1.52286	+	1.31771i	0.0773115	+	0.0668967i
$389$			2.07560i			0.105237i	0.998615	+	0.0526186i	$0.0167568\pi$
$389$			2.07560i			0.105237i	−0.998615	+	0.0526186i	$0.983243\pi$
$390$		0			0
$391$	10.0724			0.509381
$392$	−13.0728	+	7.15600i	−0.660275	+	0.361433i
$393$	23.2592			1.17327
$394$	−31.3829	−	11.6928i	−1.58105	−	0.589073i
$395$		0			0
$396$	3.18129	−	3.67657i	0.159866	−	0.184755i
$397$			6.23114i			0.312732i	0.987699	+	0.156366i	$0.0499779\pi$
$397$			6.23114i			0.312732i	−0.987699	+	0.156366i	$0.950022\pi$
$398$	−8.85319	+	23.7616i	−0.443770	+	1.19106i
$399$	−12.0006			−0.600781
$400$		0			0
$401$	20.9959			1.04849			0.524243	−	0.851569i	$-0.324348\pi$
$401$	20.9959			1.04849			0.524243	+	0.851569i	$0.324348\pi$
$402$	9.80358	−	26.3124i	0.488958	−	1.31234i
$403$			24.8081i			1.23578i
$404$	3.27396	−	3.78366i	0.162885	−	0.188244i
$405$		0			0
$406$	−9.63895	−	3.59132i	−0.478373	−	0.178234i
$407$	−47.5078			−2.35488
$408$	6.71730	+	12.2713i	0.332556	+	0.607522i
$409$	6.61521			0.327101			0.163551	−	0.986535i	$-0.447705\pi$
$409$	6.61521			0.327101			0.163551	+	0.986535i	$0.447705\pi$
$410$		0			0
$411$		−	7.95698i		−	0.392489i
$412$	−8.08135	−	6.99269i	−0.398139	−	0.344505i
$413$		−	1.34306i		−	0.0660876i
$414$	0.679409	−	1.82350i	0.0333911	−	0.0896203i
$415$		0			0
$416$	3.53920	−	16.4068i	0.173523	−	0.804408i
$417$	−6.40121			−0.313469
$418$	−16.2033	+	43.4890i	−0.792531	+	2.12712i
$419$		−	17.6296i		−	0.861262i	−0.902528	−	0.430631i	$-0.858291\pi$
$419$		−	17.6296i		−	0.861262i	0.902528	−	0.430631i	$-0.141709\pi$
$420$		0			0
$421$			18.0508i			0.879742i	0.898061	+	0.439871i	$0.144976\pi$
$421$			18.0508i			0.879742i	−0.898061	+	0.439871i	$0.855024\pi$
$422$	20.0032	+	7.45289i	0.973741	+	0.362801i
$423$	−3.23124			−0.157108
$424$	−0.0630473	−	0.115177i	−0.00306185	−	0.00559347i
$425$		0			0
$426$	−22.7560	−	8.47852i	−1.10253	−	0.410785i
$427$		−	6.88332i		−	0.333107i
$428$	1.27153	−	1.46949i	0.0614616	−	0.0710303i
$429$			35.9539i			1.73587i
$430$		0			0
$431$	4.44104			0.213917			0.106959	−	0.994263i	$-0.465889\pi$
$431$	4.44104			0.213917			0.106959	+	0.994263i	$0.465889\pi$
$432$	−19.1198	+	2.77618i	−0.919904	+	0.133569i
$433$	−24.5345			−1.17905			−0.589526	−	0.807749i	$-0.700685\pi$
$433$	−24.5345			−1.17905			−0.589526	+	0.807749i	$0.700685\pi$
$434$	−5.43150	+	14.5779i	−0.260720	+	0.699761i
$435$		0			0
$436$	−24.6624	+	28.5020i	−1.18111	+	1.36500i
$437$			18.5753i			0.888579i
$438$	30.1930	+	11.2494i	1.44268	+	0.537518i
$439$	−26.1063			−1.24598			−0.622992	−	0.782228i	$-0.714083\pi$
$439$	−26.1063			−1.24598			−0.622992	+	0.782228i	$0.714083\pi$
$440$		0			0
$441$	1.93993			0.0923774
$442$	−10.5968	−	3.94820i	−0.504038	−	0.187797i
$443$		−	29.4964i		−	1.40141i	−0.713449	−	0.700707i	$-0.752868\pi$
$443$		−	29.4964i		−	1.40141i	0.713449	−	0.700707i	$-0.247132\pi$
$444$	−19.9714	−	17.2810i	−0.947799	−	0.820119i
$445$		0			0
$446$	10.3976	−	27.9068i	0.492343	−	1.32143i
$447$	−16.7346			−0.791518
$448$	5.67183	−	8.86617i	0.267969	−	0.418887i
$449$	−18.7321			−0.884021			−0.442010	−	0.897010i	$-0.645735\pi$
$449$	−18.7321			−0.884021			−0.442010	+	0.897010i	$0.645735\pi$
$450$		0			0
$451$			24.9035i			1.17266i
$452$	−18.7254	−	16.2028i	−0.880768	−	0.762118i
$453$		−	19.3033i		−	0.906947i
$454$	−9.20288	−	3.42885i	−0.431912	−	0.160924i
$455$		0			0
$456$	−22.6307	+	12.3880i	−1.05978	+	0.580120i
$457$	0.111216			0.00520245			0.00260123	−	0.999997i	$-0.499172\pi$
$457$	0.111216			0.00520245			0.00260123	+	0.999997i	$0.499172\pi$
$458$	26.3461	+	9.81613i	1.23107	+	0.458678i
$459$			13.0172i			0.607590i
$460$		0			0
$461$		−	3.71668i		−	0.173103i	−0.996247	−	0.0865516i	$-0.972415\pi$
$461$		−	3.71668i		−	0.173103i	0.996247	−	0.0865516i	$-0.0275847\pi$
$462$	−7.87175	+	21.1274i	−0.366227	+	0.982937i
$463$	11.9601			0.555831			0.277915	−	0.960606i	$-0.410356\pi$
$463$	11.9601			0.555831			0.277915	+	0.960606i	$0.410356\pi$
$464$	−21.8844	+	3.17758i	−1.01596	+	0.147516i
$465$		0			0
$466$	4.66015	−	12.5076i	0.215877	−	0.579405i
$467$			17.1232i			0.792365i	0.918172	+	0.396183i	$0.129665\pi$
$467$			17.1232i			0.792365i	−0.918172	+	0.396183i	$0.870335\pi$
$468$	−1.42957	+	1.65213i	−0.0660817	+	0.0763697i
$469$			14.2336i			0.657244i
$470$		0			0
$471$	−10.2594			−0.472728
$472$	−1.38641	−	2.53274i	−0.0638148	−	0.116579i
$473$	20.3332			0.934921
$474$	−3.49841	−	1.30345i	−0.160687	−	0.0598695i
$475$		0			0
$476$	−5.36253	−	4.64013i	−0.245791	−	0.212680i
$477$			0.0170915i			0.000782567i
$478$	10.5597	−	28.3417i	0.482989	−	1.29632i
$479$	7.70565			0.352080			0.176040	−	0.984383i	$-0.443671\pi$
$479$	7.70565			0.352080			0.176040	+	0.984383i	$0.443671\pi$
$480$		0			0
$481$	21.3484			0.973404
$482$	−5.63461	+	15.1230i	−0.256649	+	0.688835i
$483$			9.02410i			0.410611i
$484$	49.2987	+	42.6576i	2.24085	+	1.93898i
$485$		0			0
$486$	5.04294	+	1.87892i	0.228752	+	0.0852296i
$487$	−0.471068			−0.0213461			−0.0106731	−	0.999943i	$-0.503397\pi$
$487$	−0.471068			−0.0213461			−0.0106731	+	0.999943i	$0.503397\pi$
$488$	−7.10551	−	12.9805i	−0.321651	−	0.587601i
$489$	−10.0639			−0.455107
$490$		0			0
$491$		−	42.9128i		−	1.93663i	−0.249735	−	0.968314i	$-0.580343\pi$
$491$		−	42.9128i		−	1.93663i	0.249735	−	0.968314i	$-0.419657\pi$
$492$	−9.05865	+	10.4689i	−0.408396	+	0.471977i
$493$			14.8993i			0.671032i
$494$	7.28123	−	19.5425i	0.327598	−	0.879258i
$495$		0			0
$496$	4.80576	+	33.0978i	0.215785	+	1.48613i
$497$	12.3097			0.552167
$498$	11.8056	−	31.6857i	0.529021	−	1.41987i
$499$		−	20.7158i		−	0.927365i	−0.886001	−	0.463683i	$-0.846528\pi$
$499$		−	20.7158i		−	0.927365i	0.886001	−	0.463683i	$-0.153472\pi$
$500$		0			0
$501$			35.6964i			1.59480i
$502$	−3.65933	−	1.36341i	−0.163324	−	0.0608519i
$503$	6.72612			0.299903			0.149951	−	0.988693i	$-0.452088\pi$
$503$	6.72612			0.299903			0.149951	+	0.988693i	$0.452088\pi$
$504$	−1.20177	+	0.657844i	−0.0535310	+	0.0293027i
$505$		0			0
$506$	32.7025	+	12.1844i	1.45380	+	0.541664i
$507$			7.70189i			0.342053i
$508$	17.8590	+	15.4532i	0.792366	+	0.685624i
$509$		−	28.6335i		−	1.26916i	−0.772858	−	0.634579i	$-0.781174\pi$
$509$		−	28.6335i		−	1.26916i	0.772858	−	0.634579i	$-0.218826\pi$
$510$		0			0
$511$	−16.3327			−0.722518
$512$	1.54355	−	22.5747i	0.0682160	−	0.997671i
$513$	−24.0062			−1.05990
$514$	−6.00828	+	16.1260i	−0.265014	+	0.711286i
$515$		0			0
$516$	8.54767	+	7.39620i	0.376290	+	0.325599i
$517$		−	57.9486i		−	2.54858i
$518$	12.5449	+	4.67403i	0.551191	+	0.205365i
$519$	21.9637			0.964102
$520$		0			0
$521$	−23.0885			−1.01152			−0.505762	−	0.862673i	$-0.668789\pi$
$521$	−23.0885			−1.01152			−0.505762	+	0.862673i	$0.668789\pi$
$522$	2.69738	+	1.00500i	0.118061	+	0.0439877i
$523$			11.3256i			0.495236i	0.968858	+	0.247618i	$0.0796478\pi$
$523$			11.3256i			0.495236i	−0.968858	+	0.247618i	$0.920352\pi$
$524$	−16.5855	+	19.1676i	−0.724539	+	0.837339i
$525$		0			0
$526$	11.0645	−	29.6966i	0.482435	−	1.29483i
$527$	22.5337			0.981581
$528$	6.96488	+	47.9679i	0.303108	+	2.08753i
$529$	−9.03188			−0.392690
$530$		0			0
$531$			0.375844i			0.0163102i
$532$	8.55728	−	9.88952i	0.371005	−	0.428765i
$533$		−	11.1908i		−	0.484727i
$534$	−9.58703	−	3.57198i	−0.414872	−	0.154575i
$535$		0			0
$536$	14.6930	+	26.8416i	0.634641	+	1.15938i
$537$	20.2140			0.872298
$538$	39.4314	+	14.6915i	1.70001	+	0.633397i
$539$			34.7904i			1.49853i
$540$		0			0
$541$			28.1159i			1.20880i	0.796683	+	0.604398i	$0.206586\pi$
$541$			28.1159i			1.20880i	−0.796683	+	0.604398i	$0.793414\pi$
$542$	−7.46424	+	20.0337i	−0.320616	+	0.860520i
$543$	−34.1920			−1.46732
$544$	−14.9026	−	3.21471i	−0.638942	−	0.137830i
$545$		0			0
$546$	3.53730	−	9.49395i	0.151382	−	0.406304i
$547$		−	25.7268i		−	1.10000i	−0.835166	−	0.549998i	$-0.814628\pi$
$547$		−	25.7268i		−	1.10000i	0.835166	−	0.549998i	$-0.185372\pi$
$548$	6.55724	+	5.67389i	0.280111	+	0.242377i
$549$			1.92624i			0.0822098i
$550$		0			0
$551$	−27.4772			−1.17057
$552$	9.31540	+	17.0176i	0.396490	+	0.724318i
$553$	1.89245			0.0804750
$554$	12.6069	+	4.69712i	0.535614	+	0.199562i
$555$		0			0
$556$	4.56452	−	5.27515i	0.193579	−	0.223716i
$557$		−	11.3682i		−	0.481685i	−0.970564	−	0.240842i	$-0.922576\pi$
$557$		−	11.3682i		−	0.481685i	0.970564	−	0.240842i	$-0.0774237\pi$
$558$	1.51996	−	4.07950i	0.0643449	−	0.172699i
$559$	−9.13705			−0.386456
$560$		0			0
$561$	32.6575			1.37880
$562$	8.68470	−	23.3093i	0.366342	−	0.983245i
$563$		−	6.10463i		−	0.257279i	−0.991691	−	0.128640i	$-0.958939\pi$
$563$		−	6.10463i		−	0.257279i	0.991691	−	0.128640i	$-0.0410611\pi$
$564$	21.0788	−	24.3605i	0.887578	−	1.02576i
$565$		0			0
$566$	20.3083	+	7.56654i	0.853619	+	0.318045i
$567$	−13.1156			−0.550803
$568$	23.2136	−	12.7071i	0.974023	−	0.533177i
$569$	20.0788			0.841749			0.420875	−	0.907119i	$-0.361723\pi$
$569$	20.0788			0.841749			0.420875	+	0.907119i	$0.361723\pi$
$570$		0			0
$571$			12.1145i			0.506975i	0.967339	+	0.253487i	$0.0815776\pi$
$571$			12.1145i			0.506975i	−0.967339	+	0.253487i	$0.918422\pi$
$572$	−29.6291	−	25.6377i	−1.23885	−	1.07196i
$573$			19.5025i			0.814729i
$574$	2.45012	−	6.57600i	0.102266	−	0.274477i
$575$		0			0
$576$	−1.58721	+	2.48112i	−0.0661338	+	0.103380i
$577$	−37.1530			−1.54670			−0.773351	−	0.633979i	$-0.781421\pi$
$577$	−37.1530			−1.54670			−0.773351	+	0.633979i	$0.781421\pi$
$578$	4.80763	−	12.9035i	0.199971	−	0.536714i
$579$			32.9937i			1.37117i
$580$		0			0
$581$			17.1402i			0.711095i
$582$	2.44892	+	0.912431i	0.101511	+	0.0378215i
$583$	−0.306517			−0.0126946
$584$	−30.8002	+	16.8599i	−1.27452	+	0.697670i
$585$		0			0
$586$	4.22330	+	1.57353i	0.174463	+	0.0650021i
$587$			14.6112i			0.603071i	0.953455	+	0.301535i	$0.0974991\pi$
$587$			14.6112i			0.603071i	−0.953455	+	0.301535i	$0.902501\pi$
$588$	−12.6550	+	14.6252i	−0.521884	+	0.603133i
$589$			41.5563i			1.71230i
$590$		0			0
$591$	−43.4612			−1.78776
$592$	28.4820	−	4.13555i	1.17060	−	0.169970i
$593$	−43.9414			−1.80446			−0.902229	−	0.431257i	$-0.858070\pi$
$593$	−43.9414			−1.80446			−0.902229	+	0.431257i	$0.858070\pi$
$594$	−15.7468	+	42.2636i	−0.646097	+	1.73410i
$595$		0			0
$596$	11.9329	−	13.7907i	0.488792	−	0.564890i
$597$			32.9067i			1.34678i
$598$	−14.6954	−	5.47528i	−0.600939	−	0.223901i
$599$	−19.8918			−0.812756			−0.406378	−	0.913705i	$-0.633208\pi$
$599$	−19.8918			−0.812756			−0.406378	+	0.913705i	$0.633208\pi$
$600$		0			0
$601$	−7.20689			−0.293975			−0.146988	−	0.989138i	$-0.546958\pi$
$601$	−7.20689			−0.293975			−0.146988	+	0.989138i	$0.546958\pi$
$602$	−5.36917	−	2.00047i	−0.218831	−	0.0815330i
$603$		−	3.98314i		−	0.162206i
$604$	15.9076	+	13.7646i	0.647269	+	0.560074i
$605$		0			0
$606$	2.26701	−	6.08454i	0.0920908	−	0.247168i
$607$	6.17988			0.250834			0.125417	−	0.992104i	$-0.459973\pi$
$607$	6.17988			0.250834			0.125417	+	0.992104i	$0.459973\pi$
$608$	5.92854	−	27.4831i	0.240434	−	1.11459i
$609$	−13.3487			−0.540917
$610$		0			0
$611$			26.0401i			1.05347i
$612$	1.50066	+	1.29850i	0.0606605	+	0.0524888i
$613$			14.3999i			0.581605i	0.956783	+	0.290803i	$0.0939223\pi$
$613$			14.3999i			0.581605i	−0.956783	+	0.290803i	$0.906078\pi$
$614$	37.1815	+	13.8533i	1.50052	+	0.559072i
$615$		0			0
$616$	−11.7977	−	21.5524i	−0.475343	−	0.868369i
$617$	−38.5229			−1.55087			−0.775437	−	0.631425i	$-0.782470\pi$
$617$	−38.5229			−1.55087			−0.775437	+	0.631425i	$0.782470\pi$
$618$	−12.9957	−	4.84199i	−0.522763	−	0.194773i
$619$		−	4.77140i		−	0.191779i	−0.995392	−	0.0958894i	$-0.969430\pi$
$619$		−	4.77140i		−	0.191779i	0.995392	−	0.0958894i	$-0.0305695\pi$
$620$		0			0
$621$			18.0519i			0.724399i
$622$	−13.7249	+	36.8371i	−0.550320	+	1.47703i
$623$	5.18606			0.207775
$624$	−3.12978	−	21.5552i	−0.125292	−	0.862897i
$625$		0			0
$626$	10.6870	−	28.6834i	0.427138	−	1.14642i
$627$			60.2267i			2.40522i
$628$	7.31568	−	8.45462i	0.291927	−	0.337376i
$629$		−	19.3911i		−	0.773175i
$630$		0			0
$631$	−16.4566			−0.655127			−0.327563	−	0.944829i	$-0.606228\pi$
$631$	−16.4566			−0.655127			−0.327563	+	0.944829i	$0.606228\pi$
$632$	3.56877	−	1.95353i	0.141958	−	0.0777073i
$633$	27.7019			1.10105
$634$	−21.2077	−	7.90166i	−0.842265	−	0.313815i
$635$		0			0
$636$	−0.128854	−	0.111496i	−0.00510939	−	0.00442109i
$637$		−	15.6336i		−	0.619427i
$638$	−18.0236	+	48.3744i	−0.713560	+	1.91516i
$639$	−3.44477			−0.136273
$640$		0			0
$641$	37.6381			1.48662			0.743309	−	0.668949i	$-0.233255\pi$
$641$	37.6381			1.48662			0.743309	+	0.668949i	$0.233255\pi$
$642$	0.880451	−	2.36309i	0.0347486	−	0.0932638i
$643$			0.647618i			0.0255396i	0.999918	+	0.0127698i	$0.00406486\pi$
$643$			0.647618i			0.0255396i	−0.999918	+	0.0127698i	$0.995935\pi$
$644$	−7.43663	−	6.43483i	−0.293044	−	0.253568i
$645$		0			0
$646$	−17.7508	−	6.61367i	−0.698395	−	0.260211i
$647$	40.6274			1.59723			0.798613	−	0.601845i	$-0.205567\pi$
$647$	40.6274			1.59723			0.798613	+	0.601845i	$0.205567\pi$
$648$	−24.7333	+	13.5390i	−0.971618	+	0.531860i
$649$	−6.74033			−0.264581
$650$		0			0
$651$			20.1885i			0.791250i
$652$	7.17631	−	8.29356i	0.281046	−	0.324801i
$653$		−	21.7949i		−	0.852900i	−0.904511	−	0.426450i	$-0.859764\pi$
$653$		−	21.7949i		−	0.852900i	0.904511	−	0.426450i	$-0.140236\pi$
$654$	−17.0771	+	45.8342i	−0.667768	+	1.79226i
$655$		0			0
$656$	−2.16785	−	14.9302i	−0.0846403	−	0.582927i
$657$	4.57057			0.178315
$658$	−5.70124	+	15.3019i	−0.222257	+	0.596529i
$659$			10.4657i			0.407684i	0.979004	+	0.203842i	$0.0653429\pi$
$659$			10.4657i			0.407684i	−0.979004	+	0.203842i	$0.934657\pi$
$660$		0			0
$661$		−	23.8297i		−	0.926870i	−0.886131	−	0.463435i	$-0.846617\pi$
$661$		−	23.8297i		−	0.926870i	0.886131	−	0.463435i	$-0.153383\pi$
$662$	−7.15521	−	2.66592i	−0.278095	−	0.103614i
$663$	−14.6752			−0.569937
$664$	17.6935	+	32.3229i	0.686640	+	1.25437i
$665$		0			0
$666$	−3.51058	−	1.30799i	−0.136032	−	0.0506835i
$667$			20.6620i			0.800037i
$668$	−29.4169	−	25.4541i	−1.13817	−	0.984847i
$669$		−	38.6474i		−	1.49419i
$670$		0			0
$671$	−34.5449			−1.33359
$672$	2.88015	−	13.3516i	0.111104	−	0.515049i
$673$	−18.0022			−0.693935			−0.346968	−	0.937877i	$-0.612789\pi$
$673$	−18.0022			−0.693935			−0.346968	+	0.937877i	$0.612789\pi$
$674$	13.0193	−	34.9433i	0.501485	−	1.34596i
$675$		0			0
$676$	−6.34702	−	5.49200i	−0.244116	−	0.211231i
$677$		−	38.0024i		−	1.46055i	−0.683152	−	0.730276i	$-0.739391\pi$
$677$		−	38.0024i		−	1.46055i	0.683152	−	0.730276i	$-0.260609\pi$
$678$	−30.1124	−	11.2194i	−1.15646	−	0.430880i
$679$	−1.32473			−0.0508386
$680$		0			0
$681$	−12.7448			−0.488382
$682$	73.1612	+	27.2587i	2.80149	+	1.04379i
$683$		−	44.0579i		−	1.68583i	−0.538046	−	0.842915i	$-0.680837\pi$
$683$		−	44.0579i		−	1.68583i	0.538046	−	0.842915i	$-0.319163\pi$
$684$	−2.39468	+	2.76750i	−0.0915629	+	0.105818i
$685$		0			0
$686$	7.97008	−	21.3913i	0.304299	−	0.816725i
$687$	36.4859			1.39202
$688$	−12.1902	+	1.77000i	−0.464747	+	0.0674807i
$689$	0.137739			0.00524742
$690$		0			0
$691$			6.13682i			0.233456i	0.993164	+	0.116728i	$0.0372405\pi$
$691$			6.13682i			0.233456i	−0.993164	+	0.116728i	$0.962759\pi$
$692$	−15.6617	+	18.1000i	−0.595369	+	0.688059i
$693$			3.19824i			0.121491i
$694$	11.5303	+	4.29602i	0.437685	+	0.163075i
$695$		0			0
$696$	−25.1730	+	13.7796i	−0.954178	+	0.522314i
$697$	−10.1648			−0.385019
$698$	−19.5810	−	7.29557i	−0.741151	−	0.276141i
$699$		−	17.3215i		−	0.655158i
$700$		0			0
$701$		−	41.6486i		−	1.57305i	−0.617561	−	0.786523i	$-0.711879\pi$
$701$		−	41.6486i		−	1.57305i	0.617561	−	0.786523i	$-0.288121\pi$
$702$	7.07606	−	18.9918i	0.267069	−	0.716801i
$703$	35.7609			1.34875
$704$	−44.4961	−	28.4649i	−1.67701	−	1.07281i
$705$		0			0
$706$	8.60412	−	23.0931i	0.323821	−	0.869120i
$707$			3.29140i			0.123786i
$708$	−2.83350	−	2.45180i	−0.106490	−	0.0921441i
$709$			46.6032i			1.75022i	0.483925	+	0.875109i	$0.339211\pi$
$709$			46.6032i			1.75022i	−0.483925	+	0.875109i	$0.660789\pi$
$710$		0			0
$711$	−0.529584			−0.0198610
$712$	9.77986	−	5.35346i	0.366516	−	0.200629i
$713$	31.2492			1.17029
$714$	−8.62352	−	3.21299i	−0.322727	−	0.120243i
$715$		0			0
$716$	−14.4140	+	16.6581i	−0.538677	+	0.622541i
$717$		−	39.2497i		−	1.46581i
$718$	6.10442	−	16.3840i	0.227815	−	0.611445i
$719$	−33.3634			−1.24424			−0.622122	−	0.782920i	$-0.713729\pi$
$719$	−33.3634			−1.24424			−0.622122	+	0.782920i	$0.713729\pi$
$720$		0			0
$721$	7.02995			0.261809
$722$	2.81550	−	7.55667i	0.104782	−	0.281230i
$723$			20.9435i			0.778895i
$724$	24.3814	−	28.1772i	0.906126	−	1.04720i
$725$		0			0
$726$	79.2777	+	29.5376i	2.94227	+	1.09624i
$727$	−34.3672			−1.27461			−0.637305	−	0.770612i	$-0.719951\pi$
$727$	−34.3672			−1.27461			−0.637305	+	0.770612i	$0.719951\pi$
$728$	5.30149	+	9.68491i	0.196486	+	0.358946i
$729$	−22.9231			−0.849002
$730$		0			0
$731$			8.29934i			0.306962i
$732$	−14.5220	−	12.5657i	−0.536749	−	0.464442i
$733$		−	40.7127i		−	1.50376i	−0.659302	−	0.751878i	$-0.729148\pi$
$733$		−	40.7127i		−	1.50376i	0.659302	−	0.751878i	$-0.270852\pi$
$734$	−2.05387	+	5.51250i	−0.0758098	+	0.203470i
$735$		0			0
$736$	−20.6665	−	4.45809i	−0.761778	−	0.164328i
$737$	71.4331			2.63127
$738$	−0.685644	+	1.84024i	−0.0252389	+	0.0677401i
$739$		−	22.9998i		−	0.846061i	−0.906115	−	0.423030i	$-0.860966\pi$
$739$		−	22.9998i		−	0.846061i	0.906115	−	0.423030i	$-0.139034\pi$
$740$		0			0
$741$		−	27.0638i		−	0.994215i
$742$	0.0809388	+	0.0301565i	0.00297136	+	0.00110708i
$743$	14.7518			0.541192			0.270596	−	0.962693i	$-0.412779\pi$
$743$	14.7518			0.541192			0.270596	+	0.962693i	$0.412779\pi$
$744$	20.8402	+	38.0714i	0.764038	+	1.39577i
$745$		0			0
$746$	44.9400	+	16.7439i	1.64537	+	0.613039i
$747$		−	4.79654i		−	0.175496i
$748$	−23.2871	+	26.9126i	−0.851462	+	0.984022i
$749$			1.27830i			0.0467082i
$750$		0			0
$751$	−19.6790			−0.718099			−0.359049	−	0.933319i	$-0.616899\pi$
$751$	−19.6790			−0.718099			−0.359049	+	0.933319i	$0.616899\pi$
$752$	5.04442	+	34.7415i	0.183951	+	1.26689i
$753$	−5.06770			−0.184677
$754$	8.09918	−	21.7378i	0.294955	−	0.791645i
$755$		0			0
$756$	8.31616	−	9.61086i	0.302456	−	0.349544i
$757$		−	3.22189i		−	0.117102i	−0.998284	−	0.0585508i	$-0.981352\pi$
$757$		−	3.22189i		−	0.117102i	0.998284	−	0.0585508i	$-0.0186480\pi$
$758$	−10.8323	−	4.03595i	−0.393447	−	0.146592i
$759$	45.2887			1.64388
$760$		0			0
$761$	21.5082			0.779672			0.389836	−	0.920884i	$-0.372532\pi$
$761$	21.5082			0.779672			0.389836	+	0.920884i	$0.372532\pi$
$762$	28.7192	+	10.7003i	1.04039	+	0.387632i
$763$		−	24.7938i		−	0.897596i
$764$	−16.0717	−	13.9067i	−0.581455	−	0.503126i
$765$		0			0
$766$	−1.61602	+	4.33731i	−0.0583890	+	0.156713i
$767$	3.02888			0.109366
$768$	−8.35121	−	28.1515i	−0.301348	−	1.01583i
$769$	16.0974			0.580487			0.290243	−	0.956953i	$-0.406264\pi$
$769$	16.0974			0.580487			0.290243	+	0.956953i	$0.406264\pi$
$770$		0			0
$771$			22.3324i			0.804281i
$772$	−27.1896	−	23.5268i	−0.978576	−	0.846749i
$773$		−	2.13036i		−	0.0766237i	−0.999266	−	0.0383118i	$-0.987802\pi$
$773$		−	2.13036i		−	0.0766237i	0.999266	−	0.0383118i	$-0.0121980\pi$
$774$	1.50251	+	0.559814i	0.0540068	+	0.0201221i
$775$		0			0
$776$	−2.49818	+	1.36749i	−0.0896793	+	0.0490902i
$777$	17.3731			0.623255
$778$	−2.75063	−	1.02484i	−0.0986147	−	0.0367423i
$779$		−	18.7458i		−	0.671639i
$780$		0			0
$781$		−	61.7781i		−	2.21059i
$782$	−4.97329	+	13.3481i	−0.177844	+	0.477326i
$783$	−26.7029			−0.954285
$784$	−3.02850	−	20.8576i	−0.108161	−	0.744915i
$785$		0			0
$786$	−11.4844	+	30.8235i	−0.409634	+	1.09944i
$787$			11.4913i			0.409619i	0.978802	+	0.204810i	$0.0656575\pi$
$787$			11.4913i			0.409619i	−0.978802	+	0.204810i	$0.934342\pi$
$788$	30.9910	−	35.8158i	1.10401	−	1.27588i
$789$		−	41.1260i		−	1.46412i
$790$		0			0
$791$	16.2892			0.579177
$792$	3.30148	+	6.03124i	0.117313	+	0.214311i
$793$	15.5233			0.551249
$794$	−8.25762	−	3.07666i	−0.293052	−	0.109187i
$795$		0			0
$796$	−27.1180	−	23.4648i	−0.961170	−	0.831689i
$797$			14.3363i			0.507818i	0.967228	+	0.253909i	$0.0817164\pi$
$797$			14.3363i			0.507818i	−0.967228	+	0.253909i	$0.918284\pi$
$798$	5.92537	−	15.9034i	0.209756	−	0.562975i
$799$	23.6527			0.836773
$800$		0			0
$801$	−1.45127			−0.0512782
$802$	−10.3669	+	27.8242i	−0.366066	+	0.982506i
$803$			81.9681i			2.89259i
$804$	30.0291	+	25.9838i	1.05904	+	0.916377i
$805$		0			0
$806$	−32.8762	−	12.2492i	−1.15801	−	0.431458i
$807$	54.6074			1.92227
$808$	3.39765	+	6.20692i	0.119529	+	0.218359i
$809$	43.6620			1.53508			0.767538	−	0.641004i	$-0.221482\pi$
$809$	43.6620			1.53508			0.767538	+	0.641004i	$0.221482\pi$
$810$		0			0
$811$			18.8353i			0.661396i	0.943737	+	0.330698i	$0.107284\pi$
$811$			18.8353i			0.661396i	−0.943737	+	0.330698i	$0.892716\pi$
$812$	9.51858	−	11.0005i	0.334037	−	0.386041i
$813$			27.7441i			0.973027i
$814$	23.4573	−	62.9583i	0.822177	−	2.20669i
$815$		0			0
$816$	−19.5789	+	2.84284i	−0.685399	+	0.0995192i
$817$	−15.3056			−0.535474
$818$	−3.26630	+	8.76661i	−0.114204	+	0.306517i
$819$		−	1.43718i		−	0.0502193i
$820$		0			0
$821$			1.64016i			0.0572421i	0.999590	+	0.0286210i	$0.00911160\pi$
$821$			1.64016i			0.0572421i	−0.999590	+	0.0286210i	$0.990888\pi$
$822$	10.5447	+	3.92881i	0.367790	+	0.137033i
$823$	43.7219			1.52405			0.762024	−	0.647549i	$-0.224206\pi$
$823$	43.7219			1.52405			0.762024	+	0.647549i	$0.224206\pi$
$824$	13.2571	−	7.25687i	0.461831	−	0.252805i
$825$		0			0
$826$	1.77985	+	0.663144i	0.0619288	+	0.0230737i
$827$			32.2651i			1.12197i	0.827827	+	0.560983i	$0.189577\pi$
$827$			32.2651i			1.12197i	−0.827827	+	0.560983i	$0.810423\pi$
$828$	2.08108	+	1.80073i	0.0723225	+	0.0625797i
$829$			6.83658i			0.237444i	0.992928	+	0.118722i	$0.0378798\pi$
$829$			6.83658i			0.237444i	−0.992928	+	0.118722i	$0.962120\pi$
$830$		0			0
$831$	17.4589			0.605642
$832$	19.9951	+	12.7912i	0.693204	+	0.443453i
$833$	−14.2003			−0.492011
$834$	3.16064	−	8.48301i	0.109444	−	0.293743i
$835$		0			0
$836$	−49.6320	−	42.9459i	−1.71656	−	1.48532i
$837$			40.3854i			1.39592i
$838$	23.3631	+	8.70471i	0.807064	+	0.300699i
$839$	12.3983			0.428037			0.214018	−	0.976830i	$-0.431345\pi$
$839$	12.3983			0.428037			0.214018	+	0.976830i	$0.431345\pi$
$840$		0			0
$841$	−1.56388			−0.0539268
$842$	−23.9212	−	8.91269i	−0.824381	−	0.307151i
$843$		−	32.2804i		−	1.11180i
$844$	−19.7534	+	22.8287i	−0.679941	+	0.785797i
$845$		0			0
$846$	1.59544	−	4.28209i	0.0548524	−	0.147221i
$847$	−42.8849			−1.47354
$848$	0.183764	−	0.0266823i	0.00631048	−	0.000916275i
$849$	28.1243			0.965224
$850$		0			0
$851$		−	26.8912i		−	0.921818i
$852$	22.4718	−	25.9703i	0.769870	−	0.889728i
$853$			10.2780i			0.351911i	0.984398	+	0.175955i	$0.0563015\pi$
$853$			10.2780i			0.351911i	−0.984398	+	0.175955i	$0.943699\pi$
$854$	9.12190	+	3.39868i	0.312145	+	0.116300i
$855$		0			0
$856$	1.31957	+	2.41062i	0.0451018	+	0.0823933i
$857$	−11.1493			−0.380852			−0.190426	−	0.981702i	$-0.560987\pi$
$857$	−11.1493			−0.380852			−0.190426	+	0.981702i	$0.560987\pi$
$858$	−47.6467	−	17.7524i	−1.62663	−	0.606058i
$859$		−	30.3826i		−	1.03664i	−0.855186	−	0.518321i	$-0.826557\pi$
$859$		−	30.3826i		−	1.03664i	0.855186	−	0.518321i	$-0.173443\pi$
$860$		0			0
$861$		−	9.10692i		−	0.310363i
$862$	−2.19279	+	5.88535i	−0.0746867	+	0.200456i
$863$	−46.2899			−1.57573			−0.787863	−	0.615851i	$-0.788812\pi$
$863$	−46.2899			−1.57573			−0.787863	+	0.615851i	$0.788812\pi$
$864$	5.76149	−	26.7087i	0.196010	−	0.908649i
$865$		0			0
$866$	12.1140	−	32.5136i	0.411652	−	1.10486i
$867$		−	17.8696i		−	0.606885i
$868$	−16.6371	−	14.3958i	−0.564699	−	0.488627i
$869$		−	9.49750i		−	0.322181i
$870$		0			0
$871$	−32.0996			−1.08765
$872$	−25.5941	−	46.7561i	−0.866727	−	1.58336i
$873$	0.370715			0.0125468
$874$	−24.6164	−	9.17169i	−0.832662	−	0.310237i
$875$		0			0
$876$	−29.8159	+	34.4578i	−1.00739	+	1.16422i
$877$		−	39.8781i		−	1.34659i	−0.739376	−	0.673293i	$-0.764879\pi$
$877$		−	39.8781i		−	1.34659i	0.739376	−	0.673293i	$-0.235121\pi$
$878$	12.8901	−	34.5965i	0.435021	−	1.16758i
$879$	5.84872			0.197273
$880$		0			0
$881$	38.6037			1.30059			0.650297	−	0.759680i	$-0.274645\pi$
$881$	38.6037			1.30059			0.650297	+	0.759680i	$0.274645\pi$
$882$	−0.957850	+	2.57083i	−0.0322525	+	0.0865642i
$883$			57.2207i			1.92563i	0.270164	+	0.962814i	$0.412922\pi$
$883$			57.2207i			1.92563i	−0.270164	+	0.962814i	$0.587078\pi$
$884$	10.4645	−	12.0936i	0.351958	−	0.406752i
$885$		0			0
$886$	39.0891	+	14.5640i	1.31323	+	0.489287i
$887$	11.8099			0.396537			0.198269	−	0.980148i	$-0.436468\pi$
$887$	11.8099			0.396537			0.198269	+	0.980148i	$0.436468\pi$
$888$	32.7621	−	17.9338i	1.09942	−	0.601820i
$889$	−15.5355			−0.521045
$890$		0			0
$891$			65.8224i			2.20513i
$892$	31.8487	+	27.5583i	1.06637	+	0.922721i
$893$			43.6201i			1.45969i
$894$	8.26280	−	22.1770i	0.276349	−	0.741709i
$895$		0			0
$896$	8.94912	+	11.8941i	0.298969	+	0.397355i
$897$	−20.3512			−0.679508
$898$	9.24907	−	24.8241i	0.308645	−	0.828390i
$899$			46.2246i			1.54168i
$900$		0			0
$901$		−	0.125110i		−	0.00416803i
$902$	−33.0026	−	12.2963i	−1.09887	−	0.409421i
$903$	−7.43561			−0.247441
$904$	30.7181	−	16.8150i	1.02167	−	0.559258i
$905$		0			0
$906$	25.5811	+	9.53111i	0.849874	+	0.316650i
$907$		−	36.7370i		−	1.21983i	−0.792466	−	0.609917i	$-0.791203\pi$
$907$		−	36.7370i		−	1.21983i	0.792466	−	0.609917i	$-0.208797\pi$
$908$	9.08795	−	10.5028i	0.301594	−	0.348548i
$909$		−	0.921071i		−	0.0305500i
$910$		0			0
$911$	−16.4318			−0.544409			−0.272205	−	0.962239i	$-0.587753\pi$
$911$	−16.4318			−0.544409			−0.272205	+	0.962239i	$0.587753\pi$
$912$	−5.24273	−	36.1073i	−0.173604	−	1.19563i
$913$	86.0205			2.84686
$914$	−0.0549134	+	0.147385i	−0.00181637	+	0.00487507i
$915$		0			0
$916$	−26.0171	+	30.0675i	−0.859628	+	0.993459i
$917$		−	16.6738i		−	0.550618i
$918$	−17.2506	−	6.42731i	−0.569355	−	0.212133i
$919$	−30.9480			−1.02088			−0.510440	−	0.859913i	$-0.670518\pi$
$919$	−30.9480			−1.02088			−0.510440	+	0.859913i	$0.670518\pi$
$920$		0			0
$921$	51.4916			1.69671
$922$	4.92542	+	1.83513i	0.162210	+	0.0604369i
$923$			27.7610i			0.913764i
$924$	−24.1117	−	20.8636i	−0.793218	−	0.686362i
$925$		0			0
$926$	−5.90535	+	15.8497i	−0.194062	+	0.520853i
$927$	−1.96727			−0.0646136
$928$	6.59454	−	30.5705i	0.216476	−	1.00353i
$929$	11.4537			0.375784			0.187892	−	0.982190i	$-0.439835\pi$
$929$	11.4537			0.375784			0.187892	+	0.982190i	$0.439835\pi$
$930$		0			0
$931$		−	26.1880i		−	0.858278i
$932$	14.2744	+	12.3514i	0.467573	+	0.404585i
$933$			51.0147i			1.67015i
$934$	−22.6919	−	8.45466i	−0.742502	−	0.276645i
$935$		0			0
$936$	−1.48358	−	2.71024i	−0.0484922	−	0.0885869i
$937$	−29.7274			−0.971151			−0.485575	−	0.874195i	$-0.661390\pi$
$937$	−29.7274			−0.971151			−0.485575	+	0.874195i	$0.661390\pi$
$938$	−18.8626	−	7.02790i	−0.615885	−	0.229469i
$939$		−	39.7228i		−	1.29630i
$940$		0			0
$941$			22.9601i			0.748477i	0.927332	+	0.374239i	$0.122096\pi$
$941$			22.9601i			0.748477i	−0.927332	+	0.374239i	$0.877904\pi$
$942$	5.06564	−	13.5959i	0.165047	−	0.442980i
$943$	−14.0963			−0.459039
$944$	4.04098	−	0.586746i	0.131523	−	0.0190969i
$945$		0			0
$946$	−10.0396	+	26.9459i	−0.326417	+	0.876087i
$947$		−	35.4333i		−	1.15143i	−0.817651	−	0.575714i	$-0.804724\pi$
$947$		−	35.4333i		−	1.15143i	0.817651	−	0.575714i	$-0.195276\pi$
$948$	3.45472	−	3.99257i	0.112204	−	0.129672i
$949$		−	36.8337i		−	1.19567i
$950$		0			0
$951$	−29.3699			−0.952385
$952$	8.79697	−	4.81543i	0.285111	−	0.156069i
$953$	1.35496			0.0438914			0.0219457	−	0.999759i	$-0.493014\pi$
$953$	1.35496			0.0438914			0.0219457	+	0.999759i	$0.493014\pi$
$954$	−0.0226500	−	0.00843904i	−0.000733321	−	0.000273224i
$955$		0			0
$956$	32.3451	+	27.9878i	1.04612	+	0.905190i
$957$			66.9924i			2.16556i
$958$	−3.80471	+	10.2117i	−0.122925	+	0.329924i
$959$	−5.70413			−0.184196
$960$		0			0
$961$	38.9099			1.25516
$962$	−10.5409	+	28.2913i	−0.339853	+	0.912149i
$963$		−	0.357722i		−	0.0115274i
$964$	−17.2592	−	14.9342i	−0.555882	−	0.480997i
$965$		0			0
$966$	−11.9589	−	4.45570i	−0.384772	−	0.143360i
$967$	−19.6245			−0.631080			−0.315540	−	0.948912i	$-0.602186\pi$
$967$	−19.6245			−0.631080			−0.315540	+	0.948912i	$0.602186\pi$
$968$	−80.8722	+	44.2692i	−2.59933	+	1.42286i
$969$	−24.5826			−0.789706
$970$		0			0
$971$		−	1.55749i		−	0.0499822i	−0.999688	−	0.0249911i	$-0.992044\pi$
$971$		−	1.55749i		−	0.0499822i	0.999688	−	0.0249911i	$-0.00795575\pi$
$972$	−4.97997	+	5.75527i	−0.159732	+	0.184600i
$973$			4.58884i			0.147112i
$974$	0.232592	−	0.624268i	0.00745274	−	0.0200028i
$975$		0			0
$976$	20.7104	−	3.00713i	0.662925	−	0.0962560i
$977$	49.4288			1.58137			0.790683	−	0.612226i	$-0.209726\pi$
$977$	49.4288			1.58137			0.790683	+	0.612226i	$0.209726\pi$
$978$	4.96913	−	13.3369i	0.158895	−	0.426468i
$979$		−	26.0270i		−	0.831825i
$980$		0			0
$981$			6.93833i			0.221524i
$982$	56.8689	+	21.1885i	1.81476	+	0.676151i
$983$	−18.1091			−0.577591			−0.288795	−	0.957391i	$-0.593255\pi$
$983$	−18.1091			−0.577591			−0.288795	+	0.957391i	$0.593255\pi$
$984$	−9.40089	−	17.1738i	−0.299689	−	0.547481i
$985$		0			0
$986$	−19.7449	−	7.35663i	−0.628804	−	0.234283i
$987$			21.1911i			0.674521i
$988$	22.3029	+	19.2984i	0.709551	+	0.613965i
$989$			11.5093i			0.365976i
$990$		0			0
$991$	4.82935			0.153409			0.0767046	−	0.997054i	$-0.475560\pi$
$991$	4.82935			0.153409			0.0767046	+	0.997054i	$0.475560\pi$
$992$	−46.2347	−	9.97355i	−1.46795	−	0.316660i
$993$	−9.90905			−0.314454
$994$	−6.07800	+	16.3131i	−0.192782	+	0.517419i
$995$		0			0
$996$	36.1613	+	31.2900i	1.14582	+	0.991460i
$997$			18.3807i			0.582122i	0.956705	+	0.291061i	$0.0940082\pi$
$997$			18.3807i			0.582122i	−0.956705	+	0.291061i	$0.905992\pi$
$998$	27.4529	+	10.2285i	0.869008	+	0.323779i
$999$	34.7533			1.09955

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.d.c.501.18	yes	40
4.3	odd	2		4000.2.d.c.2001.25		40
5.2	odd	4		1000.2.f.c.749.1		20
5.3	odd	4		1000.2.f.d.749.20		20
5.4	even	2	inner	1000.2.d.c.501.23	yes	40
8.3	odd	2		4000.2.d.c.2001.26		40
8.5	even	2	inner	1000.2.d.c.501.17	✓	40
20.3	even	4		4000.2.f.d.3249.16		20
20.7	even	4		4000.2.f.c.3249.5		20
20.19	odd	2		4000.2.d.c.2001.16		40
40.3	even	4		4000.2.f.c.3249.6		20
40.13	odd	4		1000.2.f.c.749.2		20
40.19	odd	2		4000.2.d.c.2001.15		40
40.27	even	4		4000.2.f.d.3249.15		20
40.29	even	2	inner	1000.2.d.c.501.24	yes	40
40.37	odd	4		1000.2.f.d.749.19		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1000.2.d.c.501.17	✓	40	8.5	even	2	inner
1000.2.d.c.501.18	yes	40	1.1	even	1	trivial
1000.2.d.c.501.23	yes	40	5.4	even	2	inner
1000.2.d.c.501.24	yes	40	40.29	even	2	inner
1000.2.f.c.749.1		20	5.2	odd	4
1000.2.f.c.749.2		20	40.13	odd	4
1000.2.f.d.749.19		20	40.37	odd	4
1000.2.f.d.749.20		20	5.3	odd	4
4000.2.d.c.2001.15		40	40.19	odd	2
4000.2.d.c.2001.16		40	20.19	odd	2
4000.2.d.c.2001.25		40	4.3	odd	2
4000.2.d.c.2001.26		40	8.3	odd	2
4000.2.f.c.3249.5		20	20.7	even	4
4000.2.f.c.3249.6		20	40.3	even	4
4000.2.f.d.3249.15		20	40.27	even	4
4000.2.f.d.3249.16		20	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.493756 + 1.32522i) q^{2} +1.83526i q^{3} +(-1.51241 - 1.30867i) q^{4} +(-2.43212 - 0.906170i) q^{6} +1.31564 q^{7} +(2.48104 - 1.35811i) q^{8} -0.368171 q^{9} +O(q^{10})\)	\(q+(-0.493756 + 1.32522i) q^{2} +1.83526i q^{3} +(-1.51241 - 1.30867i) q^{4} +(-2.43212 - 0.906170i) q^{6} +1.31564 q^{7} +(2.48104 - 1.35811i) q^{8} -0.368171 q^{9} -6.60274i q^{11} +(2.40175 - 2.77566i) q^{12} +2.96705i q^{13} +(-0.649606 + 1.74351i) q^{14} +(0.574768 + 3.95849i) q^{16} +2.69502 q^{17} +(0.181787 - 0.487907i) q^{18} +4.97013i q^{19} +2.41454i q^{21} +(8.75007 + 3.26014i) q^{22} +3.73739 q^{23} +(2.49248 + 4.55334i) q^{24} +(-3.93199 - 1.46500i) q^{26} +4.83008i q^{27} +(-1.98979 - 1.72174i) q^{28} +5.52846i q^{29} +8.36121 q^{31} +(-5.52966 - 1.19283i) q^{32} +12.1177 q^{33} +(-1.33068 + 3.57149i) q^{34} +(0.556826 + 0.481814i) q^{36} -7.19517i q^{37} +(-6.58651 - 2.45403i) q^{38} -5.44530 q^{39} -3.77169 q^{41} +(-3.19980 - 1.19220i) q^{42} +3.07951i q^{43} +(-8.64080 + 9.98605i) q^{44} +(-1.84536 + 4.95287i) q^{46} +8.77645 q^{47} +(-7.26485 + 1.05485i) q^{48} -5.26908 q^{49} +4.94606i q^{51} +(3.88289 - 4.48739i) q^{52} -0.0464228i q^{53} +(-6.40092 - 2.38488i) q^{54} +(3.26416 - 1.78679i) q^{56} -9.12147 q^{57} +(-7.32642 - 2.72971i) q^{58} -1.02084i q^{59} -5.23191i q^{61} +(-4.12840 + 11.0804i) q^{62} -0.484382 q^{63} +(4.31107 - 6.73904i) q^{64} +(-5.98320 + 16.0586i) q^{66} +10.8187i q^{67} +(-4.07598 - 3.52689i) q^{68} +6.85908i q^{69} +9.35643 q^{71} +(-0.913446 + 0.500017i) q^{72} -12.4143 q^{73} +(9.53518 + 3.55266i) q^{74} +(6.50426 - 7.51688i) q^{76} -8.68684i q^{77} +(2.68865 - 7.21621i) q^{78} +1.43842 q^{79} -9.96896 q^{81} +(1.86230 - 4.99832i) q^{82} +13.0280i q^{83} +(3.15984 - 3.65178i) q^{84} +(-4.08102 - 1.52053i) q^{86} -10.1462 q^{87} +(-8.96725 - 16.3816i) q^{88} +3.94185 q^{89} +3.90357i q^{91} +(-5.65247 - 4.89101i) q^{92} +15.3450i q^{93} +(-4.33343 + 11.6307i) q^{94} +(2.18916 - 10.1484i) q^{96} -1.00691 q^{97} +(2.60164 - 6.98269i) q^{98} +2.43094i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Introduction

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