LMFDB - Embedded newform 570.2.k.b.533.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (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:	$4.55147291521$
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			533.3
Character	$\chi$	$=$	570.533
Dual form			570.2.k.b.77.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.32879 + 1.11099i) q^{3} +1.00000i q^{4} +(-1.28568 - 1.82949i) q^{5} +(1.72519 + 0.154007i) q^{6} +(1.30605 - 1.30605i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.531382 - 2.95256i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.32879 + 1.11099i) q^{3} +1.00000i q^{4} +(-1.28568 - 1.82949i) q^{5} +(1.72519 + 0.154007i) q^{6} +(1.30605 - 1.30605i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.531382 - 2.95256i) q^{9} +(-0.384532 + 2.20276i) q^{10} +5.15114i q^{11} +(-1.11099 - 1.32879i) q^{12} +(0.342145 + 0.342145i) q^{13} -1.84704 q^{14} +(3.74095 + 1.00263i) q^{15} -1.00000 q^{16} +(-4.25002 - 4.25002i) q^{17} +(-2.46352 + 1.71203i) q^{18} +1.00000i q^{19} +(1.82949 - 1.28568i) q^{20} +(-0.284456 + 3.18649i) q^{21} +(3.64241 - 3.64241i) q^{22} +(3.32373 - 3.32373i) q^{23} +(-0.154007 + 1.72519i) q^{24} +(-1.69406 + 4.70427i) q^{25} -0.483866i q^{26} +(2.57419 + 4.51371i) q^{27} +(1.30605 + 1.30605i) q^{28} -8.73926 q^{29} +(-1.93629 - 3.35422i) q^{30} -10.0988 q^{31} +(0.707107 + 0.707107i) q^{32} +(-5.72289 - 6.84480i) q^{33} +6.01044i q^{34} +(-4.06858 - 0.710245i) q^{35} +(2.95256 + 0.531382i) q^{36} +(0.317424 - 0.317424i) q^{37} +(0.707107 - 0.707107i) q^{38} +(-0.834762 - 0.0745186i) q^{39} +(-2.20276 - 0.384532i) q^{40} -8.89223i q^{41} +(2.45433 - 2.05205i) q^{42} +(-8.84777 - 8.84777i) q^{43} -5.15114 q^{44} +(-6.08487 + 2.82389i) q^{45} -4.70047 q^{46} +(-2.14509 - 2.14509i) q^{47} +(1.32879 - 1.11099i) q^{48} +3.58845i q^{49} +(4.52430 - 2.12854i) q^{50} +(10.3691 + 0.925647i) q^{51} +(-0.342145 + 0.342145i) q^{52} +(-8.17583 + 8.17583i) q^{53} +(1.37145 - 5.01190i) q^{54} +(9.42396 - 6.62272i) q^{55} -1.84704i q^{56} +(-1.11099 - 1.32879i) q^{57} +(6.17959 + 6.17959i) q^{58} +1.27397 q^{59} +(-1.00263 + 3.74095i) q^{60} -6.26456 q^{61} +(7.14093 + 7.14093i) q^{62} +(-3.16219 - 4.55022i) q^{63} -1.00000i q^{64} +(0.186062 - 1.06584i) q^{65} +(-0.793310 + 8.88670i) q^{66} +(-1.50061 + 1.50061i) q^{67} +(4.25002 - 4.25002i) q^{68} +(-0.723903 + 8.10920i) q^{69} +(2.37470 + 3.37914i) q^{70} +11.7068i q^{71} +(-1.71203 - 2.46352i) q^{72} +(-2.73639 - 2.73639i) q^{73} -0.448905 q^{74} +(-2.97537 - 8.13309i) q^{75} -1.00000 q^{76} +(6.72767 + 6.72767i) q^{77} +(0.537573 + 0.642958i) q^{78} +5.23062i q^{79} +(1.28568 + 1.82949i) q^{80} +(-8.43527 - 3.13788i) q^{81} +(-6.28776 + 6.28776i) q^{82} +(9.88555 - 9.88555i) q^{83} +(-3.18649 - 0.284456i) q^{84} +(-2.31120 + 13.2395i) q^{85} +12.5126i q^{86} +(11.6127 - 9.70927i) q^{87} +(3.64241 + 3.64241i) q^{88} +16.2880 q^{89} +(6.29945 + 2.30586i) q^{90} +0.893720 q^{91} +(3.32373 + 3.32373i) q^{92} +(13.4192 - 11.2197i) q^{93} +3.03362i q^{94} +(1.82949 - 1.28568i) q^{95} +(-1.72519 - 0.154007i) q^{96} +(4.02586 - 4.02586i) q^{97} +(2.53742 - 2.53742i) q^{98} +(15.2091 + 2.73722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.32879	+	1.11099i	−0.767179	+	0.641433i
$3$	−1.32879	+	1.11099i	−0.767179	+	0.641433i
$4$			1.00000i			0.500000i
$5$	−1.28568	−	1.82949i	−0.574973	−	0.818172i
$5$	−1.28568	−	1.82949i	−0.574973	−	0.818172i
$6$	1.72519	+	0.154007i	0.704306	+	0.0628729i
$7$	1.30605	−	1.30605i	0.493642	−	0.493642i	−0.415810	−	0.909452i	$-0.636502\pi$
$7$	1.30605	−	1.30605i	0.493642	−	0.493642i	0.909452	+	0.415810i	$0.136502\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.531382	−	2.95256i	0.177127	−	0.984188i
$10$	−0.384532	+	2.20276i	−0.121600	+	0.696573i
$11$			5.15114i			1.55313i	0.630038	+	0.776564i	$0.283039\pi$
$11$			5.15114i			1.55313i	−0.630038	+	0.776564i	$0.716961\pi$
$12$	−1.11099	−	1.32879i	−0.320717	−	0.383589i
$13$	0.342145	+	0.342145i	0.0948940	+	0.0948940i	0.752960	−	0.658066i	$-0.228625\pi$
$13$	0.342145	+	0.342145i	0.0948940	+	0.0948940i	−0.658066	+	0.752960i	$0.728625\pi$
$14$	−1.84704			−0.493642
$15$	3.74095	+	1.00263i	0.965910	+	0.258878i
$16$	−1.00000			−0.250000
$17$	−4.25002	−	4.25002i	−1.03078	−	1.03078i	−0.999511	−	0.0312704i	$-0.990045\pi$
$17$	−4.25002	−	4.25002i	−1.03078	−	1.03078i	−0.0312704	−	0.999511i	$-0.509955\pi$
$18$	−2.46352	+	1.71203i	−0.580658	+	0.403530i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	1.82949	−	1.28568i	0.409086	−	0.287487i
$21$	−0.284456	+	3.18649i	−0.0620734	+	0.695350i
$22$	3.64241	−	3.64241i	0.776564	−	0.776564i
$23$	3.32373	−	3.32373i	0.693046	−	0.693046i	−0.269855	−	0.962901i	$-0.586976\pi$
$23$	3.32373	−	3.32373i	0.693046	−	0.693046i	0.962901	+	0.269855i	$0.0869757\pi$
$24$	−0.154007	+	1.72519i	−0.0314365	+	0.352153i
$25$	−1.69406	+	4.70427i	−0.338812	+	0.940854i
$26$		−	0.483866i		−	0.0948940i
$27$	2.57419	+	4.51371i	0.495402	+	0.868664i
$28$	1.30605	+	1.30605i	0.246821	+	0.246821i
$29$	−8.73926			−1.62284			−0.811420	−	0.584463i	$-0.801305\pi$
$29$	−8.73926			−1.62284			−0.811420	+	0.584463i	$0.801305\pi$
$30$	−1.93629	−	3.35422i	−0.353516	−	0.612394i
$31$	−10.0988			−1.81380			−0.906899	−	0.421348i	$-0.861557\pi$
$31$	−10.0988			−1.81380			−0.906899	+	0.421348i	$0.861557\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−5.72289	−	6.84480i	−0.996228	−	1.19153i
$34$			6.01044i			1.03078i
$35$	−4.06858	−	0.710245i	−0.687715	−	0.120053i
$36$	2.95256	+	0.531382i	0.492094	+	0.0885636i
$37$	0.317424	−	0.317424i	0.0521842	−	0.0521842i	−0.680533	−	0.732717i	$-0.738252\pi$
$37$	0.317424	−	0.317424i	0.0521842	−	0.0521842i	0.732717	+	0.680533i	$0.238252\pi$
$38$	0.707107	−	0.707107i	0.114708	−	0.114708i
$39$	−0.834762	−	0.0745186i	−0.133669	−	0.0119325i
$40$	−2.20276	−	0.384532i	−0.348286	−	0.0607998i
$41$		−	8.89223i		−	1.38873i	−0.719622	−	0.694366i	$-0.755685\pi$
$41$		−	8.89223i		−	1.38873i	0.719622	−	0.694366i	$-0.244315\pi$
$42$	2.45433	−	2.05205i	0.378712	−	0.316638i
$43$	−8.84777	−	8.84777i	−1.34927	−	1.34927i	−0.886452	−	0.462820i	$-0.846838\pi$
$43$	−8.84777	−	8.84777i	−1.34927	−	1.34927i	−0.462820	−	0.886452i	$-0.653162\pi$
$44$	−5.15114			−0.776564
$45$	−6.08487	+	2.82389i	−0.907079	+	0.420961i
$46$	−4.70047			−0.693046
$47$	−2.14509	−	2.14509i	−0.312894	−	0.312894i	0.533136	−	0.846030i	$-0.321014\pi$
$47$	−2.14509	−	2.14509i	−0.312894	−	0.312894i	−0.846030	+	0.533136i	$0.821014\pi$
$48$	1.32879	−	1.11099i	0.191795	−	0.160358i
$49$			3.58845i			0.512636i
$50$	4.52430	−	2.12854i	0.639833	−	0.301021i
$51$	10.3691	+	0.925647i	1.45197	+	0.129617i
$52$	−0.342145	+	0.342145i	−0.0474470	+	0.0474470i
$53$	−8.17583	+	8.17583i	−1.12304	+	1.12304i	−0.131754	+	0.991283i	$0.542061\pi$
$53$	−8.17583	+	8.17583i	−1.12304	+	1.12304i	−0.991283	+	0.131754i	$0.957939\pi$
$54$	1.37145	−	5.01190i	0.186631	−	0.682033i
$55$	9.42396	−	6.62272i	1.27073	−	0.893007i
$56$		−	1.84704i		−	0.246821i
$57$	−1.11099	−	1.32879i	−0.147155	−	0.176003i
$58$	6.17959	+	6.17959i	0.811420	+	0.811420i
$59$	1.27397			0.165856			0.0829282	−	0.996556i	$-0.473573\pi$
$59$	1.27397			0.165856			0.0829282	+	0.996556i	$0.473573\pi$
$60$	−1.00263	+	3.74095i	−0.129439	+	0.482955i
$61$	−6.26456			−0.802094			−0.401047	−	0.916057i	$-0.631354\pi$
$61$	−6.26456			−0.802094			−0.401047	+	0.916057i	$0.631354\pi$
$62$	7.14093	+	7.14093i	0.906899	+	0.906899i
$63$	−3.16219	−	4.55022i	−0.398399	−	0.573274i
$64$		−	1.00000i		−	0.125000i
$65$	0.186062	−	1.06584i	0.0230781	−	0.132201i
$66$	−0.793310	+	8.88670i	−0.0976498	+	1.09388i
$67$	−1.50061	+	1.50061i	−0.183328	+	0.183328i	−0.792804	−	0.609476i	$-0.791380\pi$
$67$	−1.50061	+	1.50061i	−0.183328	+	0.183328i	0.609476	+	0.792804i	$0.291380\pi$
$68$	4.25002	−	4.25002i	0.515391	−	0.515391i
$69$	−0.723903	+	8.10920i	−0.0871477	+	0.976233i
$70$	2.37470	+	3.37914i	0.283831	+	0.403884i
$71$			11.7068i			1.38935i	0.719325	+	0.694674i	$0.244451\pi$
$71$			11.7068i			1.38935i	−0.719325	+	0.694674i	$0.755549\pi$
$72$	−1.71203	−	2.46352i	−0.201765	−	0.290329i
$73$	−2.73639	−	2.73639i	−0.320270	−	0.320270i	0.528601	−	0.848871i	$-0.322717\pi$
$73$	−2.73639	−	2.73639i	−0.320270	−	0.320270i	−0.848871	+	0.528601i	$0.822717\pi$
$74$	−0.448905			−0.0521842
$75$	−2.97537	−	8.13309i	−0.343566	−	0.939129i
$76$	−1.00000			−0.114708
$77$	6.72767	+	6.72767i	0.766689	+	0.766689i
$78$	0.537573	+	0.642958i	0.0608682	+	0.0728007i
$79$			5.23062i			0.588491i	0.955730	+	0.294246i	$0.0950683\pi$
$79$			5.23062i			0.588491i	−0.955730	+	0.294246i	$0.904932\pi$
$80$	1.28568	+	1.82949i	0.143743	+	0.204543i
$81$	−8.43527	−	3.13788i	−0.937252	−	0.348653i
$82$	−6.28776	+	6.28776i	−0.694366	+	0.694366i
$83$	9.88555	−	9.88555i	1.08508	−	1.08508i	0.0890537	−	0.996027i	$-0.471616\pi$
$83$	9.88555	−	9.88555i	1.08508	−	1.08508i	0.996027	−	0.0890537i	$-0.0283843\pi$
$84$	−3.18649	−	0.284456i	−0.347675	−	0.0310367i
$85$	−2.31120	+	13.2395i	−0.250685	+	1.43603i
$86$			12.5126i			1.34927i
$87$	11.6127	−	9.70927i	1.24501	−	1.04094i
$88$	3.64241	+	3.64241i	0.388282	+	0.388282i
$89$	16.2880			1.72653			0.863264	−	0.504753i	$-0.168416\pi$
$89$	16.2880			1.72653			0.863264	+	0.504753i	$0.168416\pi$
$90$	6.29945	+	2.30586i	0.664020	+	0.243059i
$91$	0.893720			0.0936873
$92$	3.32373	+	3.32373i	0.346523	+	0.346523i
$93$	13.4192	−	11.2197i	1.39151	−	1.16343i
$94$			3.03362i			0.312894i
$95$	1.82949	−	1.28568i	0.187702	−	0.131908i
$96$	−1.72519	−	0.154007i	−0.176077	−	0.0157182i
$97$	4.02586	−	4.02586i	0.408765	−	0.408765i	−0.472543	−	0.881308i	$-0.656664\pi$
$97$	4.02586	−	4.02586i	0.408765	−	0.408765i	0.881308	+	0.472543i	$0.156664\pi$
$98$	2.53742	−	2.53742i	0.256318	−	0.256318i
$99$	15.2091	+	2.73722i	1.52857	+	0.275101i
$100$	−4.70427	−	1.69406i	−0.470427	−	0.169406i
$101$			3.68192i			0.366365i	0.983079	+	0.183183i	$0.0586400\pi$
$101$			3.68192i			0.366365i	−0.983079	+	0.183183i	$0.941360\pi$
$102$	−6.67756	−	7.98663i	−0.661177	−	0.790794i
$103$	−5.58428	−	5.58428i	−0.550235	−	0.550235i	0.376273	−	0.926509i	$-0.377205\pi$
$103$	−5.58428	−	5.58428i	−0.550235	−	0.550235i	−0.926509	+	0.376273i	$0.877205\pi$
$104$	0.483866			0.0474470
$105$	6.19537	−	3.57640i	0.604606	−	0.349021i
$106$	11.5624			1.12304
$107$	−2.07440	−	2.07440i	−0.200540	−	0.200540i	0.599691	−	0.800231i	$-0.295290\pi$
$107$	−2.07440	−	2.07440i	−0.200540	−	0.200540i	−0.800231	+	0.599691i	$0.795290\pi$
$108$	−4.51371	+	2.57419i	−0.434332	+	0.247701i
$109$			4.47191i			0.428331i	0.976797	+	0.214165i	$0.0687032\pi$
$109$			4.47191i			0.428331i	−0.976797	+	0.214165i	$0.931297\pi$
$110$	−11.3467	−	1.98078i	−1.08187	−	0.188860i
$111$	−0.0691344	+	0.774447i	−0.00656195	+	0.0735073i
$112$	−1.30605	+	1.30605i	−0.123410	+	0.123410i
$113$	−6.24110	+	6.24110i	−0.587114	+	0.587114i	−0.936849	−	0.349735i	$-0.886272\pi$
$113$	−6.24110	+	6.24110i	−0.587114	+	0.587114i	0.349735	+	0.936849i	$0.386272\pi$
$114$	−0.154007	+	1.72519i	−0.0144240	+	0.161579i
$115$	−10.3540	−	1.80748i	−0.965514	−	0.168548i
$116$		−	8.73926i		−	0.811420i
$117$	1.19202	−	0.828396i	0.110202	−	0.0765852i
$118$	−0.900830	−	0.900830i	−0.0829282	−	0.0829282i
$119$	−11.1015			−1.01767
$120$	3.35422	−	1.93629i	0.306197	−	0.176758i
$121$	−15.5343			−1.41221
$122$	4.42971	+	4.42971i	0.401047	+	0.401047i
$123$	9.87922	+	11.8159i	0.890779	+	1.06541i
$124$		−	10.0988i		−	0.906899i
$125$	10.7844	−	2.94892i	0.964588	−	0.263760i
$126$	−0.981482	+	5.45350i	−0.0874374	+	0.485836i
$127$	1.82261	−	1.82261i	0.161730	−	0.161730i	−0.621603	−	0.783333i	$-0.713518\pi$
$127$	1.82261	−	1.82261i	0.161730	−	0.161730i	0.783333	+	0.621603i	$0.213518\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	21.5867	+	1.92703i	1.90060	+	0.169665i
$130$	−0.885228	+	0.622097i	−0.0776397	+	0.0545615i
$131$		−	11.4188i		−	0.997666i	−0.866698	−	0.498833i	$-0.833762\pi$
$131$		−	11.4188i		−	0.997666i	0.866698	−	0.498833i	$-0.166238\pi$
$132$	6.84480	−	5.72289i	0.595764	−	0.498114i
$133$	1.30605	+	1.30605i	0.113249	+	0.113249i
$134$	2.12218			0.183328
$135$	4.94820	−	10.5126i	0.425873	−	0.904783i
$136$	−6.01044			−0.515391
$137$	−11.0007	−	11.0007i	−0.939857	−	0.939857i	0.0584339	−	0.998291i	$-0.481389\pi$
$137$	−11.0007	−	11.0007i	−0.939857	−	0.939857i	−0.998291	+	0.0584339i	$0.981389\pi$
$138$	6.24595	−	5.22220i	0.531690	−	0.444543i
$139$			1.23352i			0.104626i	0.998631	+	0.0523128i	$0.0166593\pi$
$139$			1.23352i			0.104626i	−0.998631	+	0.0523128i	$0.983341\pi$
$140$	0.710245	−	4.06858i	0.0600266	−	0.343857i
$141$	5.23357	+	0.467198i	0.440746	+	0.0393452i
$142$	8.27799	−	8.27799i	0.694674	−	0.694674i
$143$	−1.76244	+	1.76244i	−0.147383	+	0.147383i
$144$	−0.531382	+	2.95256i	−0.0442818	+	0.246047i
$145$	11.2359	+	15.9884i	0.933090	+	1.32776i
$146$			3.86983i			0.320270i
$147$	−3.98675	−	4.76831i	−0.328821	−	0.393283i
$148$	0.317424	+	0.317424i	0.0260921	+	0.0260921i
$149$	−0.607952			−0.0498053			−0.0249027	−	0.999690i	$-0.507928\pi$
$149$	−0.607952			−0.0498053			−0.0249027	+	0.999690i	$0.507928\pi$
$150$	−3.64706	+	7.85487i	−0.297781	+	0.641347i
$151$	2.49294			0.202873			0.101436	−	0.994842i	$-0.467656\pi$
$151$	2.49294			0.202873			0.101436	+	0.994842i	$0.467656\pi$
$152$	0.707107	+	0.707107i	0.0573539	+	0.0573539i
$153$	−14.8068	+	10.2901i	−1.19706	+	0.831903i
$154$		−	9.51436i		−	0.766689i
$155$	12.9838	+	18.4756i	1.04288	+	1.48400i
$156$	0.0745186	−	0.834762i	0.00596627	−	0.0668344i
$157$	0.0444358	−	0.0444358i	0.00354636	−	0.00354636i	−0.705331	−	0.708878i	$-0.749202\pi$
$157$	0.0444358	−	0.0444358i	0.00354636	−	0.00354636i	0.708878	+	0.705331i	$0.249202\pi$
$158$	3.69861	−	3.69861i	0.294246	−	0.294246i
$159$	1.78068	−	19.9473i	0.141217	−	1.58192i
$160$	0.384532	−	2.20276i	0.0303999	−	0.174143i
$161$		−	8.68195i		−	0.684233i
$162$	3.74582	+	8.18345i	0.294300	+	0.642952i
$163$	8.99735	+	8.99735i	0.704727	+	0.704727i	0.965421	−	0.260694i	$-0.0839515\pi$
$163$	8.99735	+	8.99735i	0.704727	+	0.704727i	−0.260694	+	0.965421i	$0.583952\pi$
$164$	8.89223			0.694366
$165$	−5.16469	+	19.2702i	−0.402070	+	1.50018i
$166$	−13.9803			−1.08508
$167$	1.17503	+	1.17503i	0.0909264	+	0.0909264i	0.751107	−	0.660181i	$-0.229520\pi$
$167$	1.17503	+	1.17503i	0.0909264	+	0.0909264i	−0.660181	+	0.751107i	$0.729520\pi$
$168$	2.05205	+	2.45433i	0.158319	+	0.189356i
$169$		−	12.7659i		−	0.981990i
$170$	10.9960	−	7.72749i	0.843357	−	0.592672i
$171$	2.95256	+	0.531382i	0.225788	+	0.0406358i
$172$	8.84777	−	8.84777i	0.674636	−	0.674636i
$173$	−13.5995	+	13.5995i	−1.03395	+	1.03395i	−0.0345455	+	0.999403i	$0.510998\pi$
$173$	−13.5995	+	13.5995i	−1.03395	+	1.03395i	−0.999403	+	0.0345455i	$0.989002\pi$
$174$	−15.0769	−	1.34590i	−1.14298	−	0.102033i
$175$	3.93150	+	8.35656i	0.297193	+	0.631697i
$176$		−	5.15114i		−	0.388282i
$177$	−1.69284	+	1.41537i	−0.127241	+	0.106386i
$178$	−11.5174	−	11.5174i	−0.863264	−	0.863264i
$179$	17.9786			1.34378			0.671892	−	0.740649i	$-0.265482\pi$
$179$	17.9786			1.34378			0.671892	+	0.740649i	$0.265482\pi$
$180$	−2.82389	−	6.08487i	−0.210481	−	0.453539i
$181$	4.58187			0.340568			0.170284	−	0.985395i	$-0.445531\pi$
$181$	4.58187			0.340568			0.170284	+	0.985395i	$0.445531\pi$
$182$	−0.631955	−	0.631955i	−0.0468437	−	0.0468437i
$183$	8.32430	−	6.95989i	0.615350	−	0.514490i
$184$		−	4.70047i		−	0.346523i
$185$	−0.988829	−	0.172618i	−0.0727002	−	0.0126911i
$186$	−17.4223	−	1.55528i	−1.27747	−	0.114039i
$187$	21.8925	−	21.8925i	1.60094	−	1.60094i
$188$	2.14509	−	2.14509i	0.156447	−	0.156447i
$189$	9.25717	+	2.53312i	0.673360	+	0.184257i
$190$	−2.20276	−	0.384532i	−0.159805	−	0.0278969i
$191$		−	12.3225i		−	0.891626i	−0.895126	−	0.445813i	$-0.852915\pi$
$191$		−	12.3225i		−	0.891626i	0.895126	−	0.445813i	$-0.147085\pi$
$192$	1.11099	+	1.32879i	0.0801791	+	0.0958974i
$193$	−11.8604	−	11.8604i	−0.853728	−	0.853728i	0.136862	−	0.990590i	$-0.456298\pi$
$193$	−11.8604	−	11.8604i	−0.853728	−	0.853728i	−0.990590	+	0.136862i	$0.956298\pi$
$194$	−5.69343			−0.408765
$195$	0.936905	+	1.62299i	0.0670931	+	0.116225i
$196$	−3.58845			−0.256318
$197$	−3.56808	−	3.56808i	−0.254215	−	0.254215i	0.568481	−	0.822696i	$-0.307531\pi$
$197$	−3.56808	−	3.56808i	−0.254215	−	0.254215i	−0.822696	+	0.568481i	$0.807531\pi$
$198$	−8.81894	−	12.6900i	−0.626735	−	0.901836i
$199$			3.23189i			0.229102i	0.993417	+	0.114551i	$0.0365430\pi$
$199$			3.23189i			0.229102i	−0.993417	+	0.114551i	$0.963457\pi$
$200$	2.12854	+	4.52430i	0.150511	+	0.319916i
$201$	0.326830	−	3.66116i	0.0230528	−	0.258239i
$202$	2.60351	−	2.60351i	0.183183	−	0.183183i
$203$	−11.4139	+	11.4139i	−0.801102	+	0.801102i
$204$	−0.925647	+	10.3691i	−0.0648083	+	0.725986i
$205$	−16.2682	+	11.4326i	−1.13622	+	0.798484i
$206$			7.89736i			0.550235i
$207$	−8.04736	−	11.5797i	−0.559330	−	0.804845i
$208$	−0.342145	−	0.342145i	−0.0237235	−	0.0237235i
$209$	−5.15114			−0.356312
$210$	−6.90969	−	1.85189i	−0.476814	−	0.127793i
$211$	13.2442			0.911766			0.455883	−	0.890040i	$-0.349324\pi$
$211$	13.2442			0.911766			0.455883	+	0.890040i	$0.349324\pi$
$212$	−8.17583	−	8.17583i	−0.561518	−	0.561518i
$213$	−13.0062	−	15.5560i	−0.891173	−	1.06588i
$214$			2.93365i			0.200540i
$215$	−4.81150	+	27.5623i	−0.328142	+	1.87973i
$216$	5.01190	+	1.37145i	0.341017	+	0.0933153i
$217$	−13.1896	+	13.1896i	−0.895366	+	0.895366i
$218$	3.16212	−	3.16212i	0.214165	−	0.214165i
$219$	6.67620	+	0.595980i	0.451136	+	0.0402726i
$220$	6.62272	+	9.42396i	0.446504	+	0.635363i
$221$		−	2.90825i		−	0.195630i
$222$	0.596502	−	0.498731i	0.0400346	−	0.0334727i
$223$	3.93298	+	3.93298i	0.263372	+	0.263372i	0.826423	−	0.563050i	$-0.190372\pi$
$223$	3.93298	+	3.93298i	0.263372	+	0.263372i	−0.563050	+	0.826423i	$0.690372\pi$
$224$	1.84704			0.123410
$225$	12.9895	+	7.50158i	0.865965	+	0.500105i
$226$	8.82625			0.587114
$227$	4.90875	+	4.90875i	0.325805	+	0.325805i	0.850989	−	0.525184i	$-0.176003\pi$
$227$	4.90875	+	4.90875i	0.325805	+	0.325805i	−0.525184	+	0.850989i	$0.676003\pi$
$228$	1.32879	−	1.11099i	0.0880015	−	0.0735774i
$229$		−	0.309162i		−	0.0204300i	−0.999948	−	0.0102150i	$-0.996748\pi$
$229$		−	0.309162i		−	0.0204300i	0.999948	−	0.0102150i	$-0.00325159\pi$
$230$	6.04329	+	8.59945i	0.398483	+	0.567031i
$231$	−16.4141	−	1.46527i	−1.07997	−	0.0964080i
$232$	−6.17959	+	6.17959i	−0.405710	+	0.405710i
$233$	1.09776	−	1.09776i	0.0719169	−	0.0719169i	−0.670233	−	0.742150i	$-0.733806\pi$
$233$	1.09776	−	1.09776i	0.0719169	−	0.0719169i	0.742150	+	0.670233i	$0.233806\pi$
$234$	−1.42865	−	0.257118i	−0.0933935	−	0.0168083i
$235$	−1.16652	+	6.68233i	−0.0760956	+	0.435907i
$236$			1.27397i			0.0829282i
$237$	−5.81119	−	6.95041i	−0.377478	−	0.451478i
$238$	7.84995	+	7.84995i	0.508837	+	0.508837i
$239$	−24.4016			−1.57841			−0.789205	−	0.614130i	$-0.789507\pi$
$239$	−24.4016			−1.57841			−0.789205	+	0.614130i	$0.789507\pi$
$240$	−3.74095	−	1.00263i	−0.241478	−	0.0647194i
$241$	−15.4813			−0.997235			−0.498618	−	0.866822i	$-0.666159\pi$
$241$	−15.4813			−0.997235			−0.498618	+	0.866822i	$0.666159\pi$
$242$	10.9844	+	10.9844i	0.706104	+	0.706104i
$243$	14.6949	−	5.20195i	0.942677	−	0.333705i
$244$		−	6.26456i		−	0.401047i
$245$	6.56503	−	4.61359i	0.419424	−	0.294752i
$246$	1.36946	−	15.3408i	0.0873137	−	0.978093i
$247$	−0.342145	+	0.342145i	−0.0217702	+	0.0217702i
$248$	−7.14093	+	7.14093i	−0.453449	+	0.453449i
$249$	−2.15306	+	24.1187i	−0.136444	+	1.52846i
$250$	−9.71094	−	5.54054i	−0.614174	−	0.350414i
$251$		−	10.3840i		−	0.655435i	−0.944776	−	0.327718i	$-0.893721\pi$
$251$		−	10.3840i		−	0.655435i	0.944776	−	0.327718i	$-0.106279\pi$
$252$	4.55022	−	3.16219i	0.286637	−	0.199199i
$253$	17.1210	+	17.1210i	1.07639	+	1.07639i
$254$	−2.57755			−0.161730
$255$	−11.6379	−	20.1603i	−0.728796	−	1.26249i
$256$	1.00000			0.0625000
$257$	10.1303	+	10.1303i	0.631914	+	0.631914i	0.948548	−	0.316634i	$-0.102553\pi$
$257$	10.1303	+	10.1303i	0.631914	+	0.631914i	−0.316634	+	0.948548i	$0.602553\pi$
$258$	−13.9015	−	16.6267i	−0.865468	−	1.03513i
$259$		−	0.829145i		−	0.0515206i
$260$	1.06584	+	0.186062i	0.0661006	+	0.0115391i
$261$	−4.64388	+	25.8032i	−0.287449	+	1.59718i
$262$	−8.07432	+	8.07432i	−0.498833	+	0.498833i
$263$	−18.8740	+	18.8740i	−1.16382	+	1.16382i	−0.180189	+	0.983632i	$0.557671\pi$
$263$	−18.8740	+	18.8740i	−1.16382	+	1.16382i	−0.983632	+	0.180189i	$0.942329\pi$
$264$	−8.88670	−	0.793310i	−0.546939	−	0.0488249i
$265$	25.4691	+	4.44609i	1.56455	+	0.273121i
$266$		−	1.84704i		−	0.113249i
$267$	−21.6434	+	18.0959i	−1.32456	+	1.10745i
$268$	−1.50061	−	1.50061i	−0.0916642	−	0.0916642i
$269$	−6.51981			−0.397520			−0.198760	−	0.980048i	$-0.563691\pi$
$269$	−6.51981			−0.397520			−0.198760	+	0.980048i	$0.563691\pi$
$270$	−10.9325	+	3.93464i	−0.665328	+	0.239455i
$271$	14.4070			0.875160			0.437580	−	0.899179i	$-0.355836\pi$
$271$	14.4070			0.875160			0.437580	+	0.899179i	$0.355836\pi$
$272$	4.25002	+	4.25002i	0.257695	+	0.257695i
$273$	−1.18757	+	0.992918i	−0.0718749	+	0.0600941i
$274$			15.5574i			0.939857i
$275$	−24.2324	−	8.72634i	−1.46127	−	0.526218i
$276$	−8.10920	−	0.723903i	−0.488117	−	0.0435739i
$277$	13.9724	−	13.9724i	0.839520	−	0.839520i	−0.149276	−	0.988796i	$-0.547694\pi$
$277$	13.9724	−	13.9724i	0.839520	−	0.839520i	0.988796	+	0.149276i	$0.0476942\pi$
$278$	0.872229	−	0.872229i	0.0523128	−	0.0523128i
$279$	−5.36632	+	29.8173i	−0.321273	+	1.78512i
$280$	−3.37914	+	2.37470i	−0.201942	+	0.141915i
$281$		−	24.2309i		−	1.44549i	−0.691113	−	0.722747i	$-0.742879\pi$
$281$		−	24.2309i		−	1.44549i	0.691113	−	0.722747i	$-0.257121\pi$
$282$	−3.37034	−	4.03105i	−0.200701	−	0.240046i
$283$	9.26434	+	9.26434i	0.550708	+	0.550708i	0.926645	−	0.375937i	$-0.122679\pi$
$283$	9.26434	+	9.26434i	0.550708	+	0.550708i	−0.375937	+	0.926645i	$0.622679\pi$
$284$	−11.7068			−0.694674
$285$	−1.00263	+	3.74095i	−0.0593906	+	0.221595i
$286$	2.49247			0.147383
$287$	−11.6137	−	11.6137i	−0.685537	−	0.685537i
$288$	2.46352	−	1.71203i	0.145164	−	0.100883i
$289$			19.1253i			1.12502i
$290$	3.36052	−	19.2505i	0.197337	−	1.13043i
$291$	−0.876826	+	9.82225i	−0.0514005	+	0.575791i
$292$	2.73639	−	2.73639i	0.160135	−	0.160135i
$293$	−9.00595	+	9.00595i	−0.526133	+	0.526133i	−0.919417	−	0.393284i	$-0.871339\pi$
$293$	−9.00595	+	9.00595i	−0.526133	+	0.526133i	0.393284	+	0.919417i	$0.371339\pi$
$294$	−0.552645	+	6.19076i	−0.0322309	+	0.361052i
$295$	−1.63791	−	2.33071i	−0.0953629	−	0.135699i
$296$		−	0.448905i		−	0.0260921i
$297$	−23.2508	+	13.2600i	−1.34915	+	0.769424i
$298$	0.429887	+	0.429887i	0.0249027	+	0.0249027i
$299$	2.27440			0.131532
$300$	8.13309	−	2.97537i	0.469564	−	0.171783i
$301$	−23.1113			−1.33211
$302$	−1.76278	−	1.76278i	−0.101436	−	0.101436i
$303$	−4.09060	−	4.89252i	−0.234999	−	0.281068i
$304$		−	1.00000i		−	0.0573539i
$305$	8.05421	+	11.4609i	0.461183	+	0.656251i
$306$	17.7462	+	3.19384i	1.01448	+	0.182579i
$307$	4.39219	−	4.39219i	0.250675	−	0.250675i	−0.570572	−	0.821247i	$-0.693279\pi$
$307$	4.39219	−	4.39219i	0.250675	−	0.250675i	0.821247	+	0.570572i	$0.193279\pi$
$308$	−6.72767	+	6.72767i	−0.383345	+	0.383345i
$309$	13.6245	+	1.21625i	0.775068	+	0.0691898i
$310$	3.88331	−	22.2452i	0.220557	−	1.26344i
$311$		−	16.1534i		−	0.915975i	−0.888959	−	0.457988i	$-0.848570\pi$
$311$		−	16.1534i		−	0.915975i	0.888959	−	0.457988i	$-0.151430\pi$
$312$	−0.642958	+	0.537573i	−0.0364003	+	0.0304341i
$313$	−0.493189	−	0.493189i	−0.0278767	−	0.0278767i	0.693031	−	0.720908i	$-0.256275\pi$
$313$	−0.493189	−	0.493189i	−0.0278767	−	0.0278767i	−0.720908	+	0.693031i	$0.756275\pi$
$314$	−0.0628417			−0.00354636
$315$	−4.25901	+	11.6353i	−0.239968	+	0.655576i
$316$	−5.23062			−0.294246
$317$	16.9755	+	16.9755i	0.953441	+	0.953441i	0.998963	−	0.0455227i	$-0.0144953\pi$
$317$	16.9755	+	16.9755i	0.953441	+	0.953441i	−0.0455227	+	0.998963i	$0.514495\pi$
$318$	−15.3640	+	12.8457i	−0.861570	+	0.720352i
$319$		−	45.0172i		−	2.52048i
$320$	−1.82949	+	1.28568i	−0.102272	+	0.0718716i
$321$	5.06110	+	0.451801i	0.282483	+	0.0252171i
$322$	−6.13906	+	6.13906i	−0.342117	+	0.342117i
$323$	4.25002	−	4.25002i	0.236477	−	0.236477i
$324$	3.13788	−	8.43527i	0.174326	−	0.468626i
$325$	−2.18916	+	1.02993i	−0.121433	+	0.0571302i
$326$		−	12.7242i		−	0.704727i
$327$	−4.96826	−	5.94224i	−0.274746	−	0.328607i
$328$	−6.28776	−	6.28776i	−0.347183	−	0.347183i
$329$	−5.60322			−0.308915
$330$	17.2781	−	9.97410i	0.951126	−	0.549056i
$331$	14.7118			0.808635			0.404318	−	0.914619i	$-0.367509\pi$
$331$	14.7118			0.808635			0.404318	+	0.914619i	$0.367509\pi$
$332$	9.88555	+	9.88555i	0.542540	+	0.542540i
$333$	−0.768541	−	1.10589i	−0.0421158	−	0.0606023i
$334$		−	1.66174i		−	0.0909264i
$335$	4.67464	+	0.816045i	0.255403	+	0.0445853i
$336$	0.284456	−	3.18649i	0.0155184	−	0.173837i
$337$	13.8928	−	13.8928i	0.756787	−	0.756787i	−0.218949	−	0.975736i	$-0.570263\pi$
$337$	13.8928	−	13.8928i	0.756787	−	0.756787i	0.975736	+	0.218949i	$0.0702629\pi$
$338$	−9.02684	+	9.02684i	−0.490995	+	0.490995i
$339$	1.35930	−	15.2270i	0.0738271	−	0.827015i
$340$	−13.2395	−	2.31120i	−0.718014	−	0.125343i
$341$		−	52.0204i		−	2.81706i
$342$	−1.71203	−	2.46352i	−0.0925762	−	0.133212i
$343$	13.8291	+	13.8291i	0.746700	+	0.746700i
$344$	−12.5126			−0.674636
$345$	15.7664	−	9.10146i	0.848835	−	0.490006i
$346$	19.2326			1.03395
$347$	−21.0082	−	21.0082i	−1.12778	−	1.12778i	−0.990537	−	0.137245i	$-0.956175\pi$
$347$	−21.0082	−	21.0082i	−1.12778	−	1.12778i	−0.137245	−	0.990537i	$-0.543825\pi$
$348$	9.70927	+	11.6127i	0.520472	+	0.622504i
$349$			18.0913i			0.968404i	0.874956	+	0.484202i	$0.160890\pi$
$349$			18.0913i			0.968404i	−0.874956	+	0.484202i	$0.839110\pi$
$350$	3.12899	−	8.68897i	0.167252	−	0.464445i
$351$	−0.663598	+	2.42509i	−0.0354202	+	0.129442i
$352$	−3.64241	+	3.64241i	−0.194141	+	0.194141i
$353$	−8.95609	+	8.95609i	−0.476685	+	0.476685i	−0.904070	−	0.427385i	$-0.859435\pi$
$353$	−8.95609	+	8.95609i	−0.476685	+	0.476685i	0.427385	+	0.904070i	$0.359435\pi$
$354$	2.19783	+	0.196199i	0.116814	+	0.0104279i
$355$	21.4175	−	15.0512i	1.13673	−	0.798837i
$356$			16.2880i			0.863264i
$357$	14.7516	−	12.3337i	0.780738	−	0.652769i
$358$	−12.7128	−	12.7128i	−0.671892	−	0.671892i
$359$	13.9018			0.733708			0.366854	−	0.930278i	$-0.380435\pi$
$359$	13.9018			0.733708			0.366854	+	0.930278i	$0.380435\pi$
$360$	−2.30586	+	6.29945i	−0.121529	+	0.332010i
$361$	−1.00000			−0.0526316
$362$	−3.23987	−	3.23987i	−0.170284	−	0.170284i
$363$	20.6419	−	17.2585i	1.08342	−	0.905837i
$364$			0.893720i			0.0468437i
$365$	−1.48807	+	8.52430i	−0.0778893	+	0.446182i
$366$	−10.8076	−	0.964784i	−0.564920	−	0.0504300i
$367$	2.43869	−	2.43869i	0.127299	−	0.127299i	−0.640587	−	0.767886i	$-0.721309\pi$
$367$	2.43869	−	2.43869i	0.127299	−	0.127299i	0.767886	+	0.640587i	$0.221309\pi$
$368$	−3.32373	+	3.32373i	−0.173262	+	0.173262i
$369$	−26.2549	−	4.72517i	−1.36677	−	0.245982i
$370$	0.577148	+	0.821267i	0.0300045	+	0.0426957i
$371$			21.3561i			1.10876i
$372$	11.2197	+	13.4192i	0.581715	+	0.695754i
$373$	−21.0831	−	21.0831i	−1.09164	−	1.09164i	−0.995354	−	0.0962879i	$-0.969303\pi$
$373$	−21.0831	−	21.0831i	−1.09164	−	1.09164i	−0.0962879	−	0.995354i	$-0.530697\pi$
$374$	−30.9606			−1.60094
$375$	−11.0540	+	15.8999i	−0.570828	+	0.821070i
$376$	−3.03362			−0.156447
$377$	−2.99010	−	2.99010i	−0.153998	−	0.153998i
$378$	−4.75462	−	8.33699i	−0.244551	−	0.428809i
$379$		−	2.25390i		−	0.115775i	−0.998323	−	0.0578874i	$-0.981564\pi$
$379$		−	2.25390i		−	0.115775i	0.998323	−	0.0578874i	$-0.0184364\pi$
$380$	1.28568	+	1.82949i	0.0659539	+	0.0938508i
$381$	−0.396960	+	4.44677i	−0.0203369	+	0.227815i
$382$	−8.71334	+	8.71334i	−0.445813	+	0.445813i
$383$	−4.29081	+	4.29081i	−0.219250	+	0.219250i	−0.808182	−	0.588932i	$-0.799548\pi$
$383$	−4.29081	+	4.29081i	−0.219250	+	0.219250i	0.588932	+	0.808182i	$0.299548\pi$
$384$	0.154007	−	1.72519i	0.00785912	−	0.0880383i
$385$	3.65857	−	20.9578i	0.186458	−	1.06811i
$386$			16.7731i			0.853728i
$387$	−30.8252	+	21.4221i	−1.56693	+	1.08894i
$388$	4.02586	+	4.02586i	0.204382	+	0.204382i
$389$	21.0267			1.06609			0.533047	−	0.846086i	$-0.321047\pi$
$389$	21.0267			1.06609			0.533047	+	0.846086i	$0.321047\pi$
$390$	0.485139	−	1.81012i	0.0245660	−	0.0916591i
$391$	−28.2519			−1.42876
$392$	2.53742	+	2.53742i	0.128159	+	0.128159i
$393$	12.6862	+	15.1732i	0.639936	+	0.765389i
$394$			5.04603i			0.254215i
$395$	9.56937	−	6.72490i	0.481487	−	0.338367i
$396$	−2.73722	+	15.2091i	−0.137551	+	0.764285i
$397$	7.05671	−	7.05671i	0.354166	−	0.354166i	−0.507491	−	0.861657i	$-0.669427\pi$
$397$	7.05671	−	7.05671i	0.354166	−	0.354166i	0.861657	+	0.507491i	$0.169427\pi$
$398$	2.28529	−	2.28529i	0.114551	−	0.114551i
$399$	−3.18649	−	0.284456i	−0.159524	−	0.0142406i
$400$	1.69406	−	4.70427i	0.0847029	−	0.235214i
$401$			3.58548i			0.179050i	0.995985	+	0.0895252i	$0.0285350\pi$
$401$			3.58548i			0.179050i	−0.995985	+	0.0895252i	$0.971465\pi$
$402$	−2.81994	+	2.35773i	−0.140646	+	0.117593i
$403$	−3.45526	−	3.45526i	−0.172119	−	0.172119i
$404$	−3.68192			−0.183183
$405$	5.10434	+	19.4665i	0.253637	+	0.967300i
$406$	16.1418			0.801102
$407$	1.63510	+	1.63510i	0.0810487	+	0.0810487i
$408$	7.98663	−	6.67756i	0.395397	−	0.330589i
$409$		−	16.2138i		−	0.801720i	−0.916139	−	0.400860i	$-0.868711\pi$
$409$		−	16.2138i		−	0.801720i	0.916139	−	0.400860i	$-0.131289\pi$
$410$	19.5874	+	3.41934i	0.967354	+	0.168869i
$411$	26.8395	+	2.39594i	1.32389	+	0.118183i
$412$	5.58428	−	5.58428i	0.275118	−	0.275118i
$413$	1.66387	−	1.66387i	0.0818736	−	0.0818736i
$414$	−2.49774	+	13.8784i	−0.122757	+	0.682088i
$415$	−30.7952	−	5.37586i	−1.51168	−	0.263891i
$416$			0.483866i			0.0237235i
$417$	−1.37043	−	1.63909i	−0.0671104	−	0.0802666i
$418$	3.64241	+	3.64241i	0.178156	+	0.178156i
$419$	−7.46153			−0.364520			−0.182260	−	0.983250i	$-0.558341\pi$
$419$	−7.46153			−0.364520			−0.182260	+	0.983250i	$0.558341\pi$
$420$	3.57640	+	6.19537i	0.174510	+	0.302303i
$421$	3.53068			0.172075			0.0860374	−	0.996292i	$-0.472580\pi$
$421$	3.53068			0.172075			0.0860374	+	0.996292i	$0.472580\pi$
$422$	−9.36503	−	9.36503i	−0.455883	−	0.455883i
$423$	−7.47339	+	5.19366i	−0.363369	+	0.252525i
$424$			11.5624i			0.561518i
$425$	27.1930	−	12.7935i	1.31906	−	0.620574i
$426$	−1.80293	+	20.1965i	−0.0873523	+	0.978526i
$427$	−8.18185	+	8.18185i	−0.395947	+	0.395947i
$428$	2.07440	−	2.07440i	0.100270	−	0.100270i
$429$	0.383856	−	4.29998i	0.0185328	−	0.207605i
$430$	22.8917	−	16.0872i	1.10394	−	0.775795i
$431$			36.0994i			1.73885i	0.494067	+	0.869424i	$0.335510\pi$
$431$			36.0994i			1.73885i	−0.494067	+	0.869424i	$0.664490\pi$
$432$	−2.57419	−	4.51371i	−0.123851	−	0.217166i
$433$	8.42713	+	8.42713i	0.404982	+	0.404982i	0.879984	−	0.475003i	$-0.157553\pi$
$433$	8.42713	+	8.42713i	0.404982	+	0.404982i	−0.475003	+	0.879984i	$0.657553\pi$
$434$	18.6529			0.895366
$435$	−32.6932	−	8.76224i	−1.56752	−	0.420117i
$436$	−4.47191			−0.214165
$437$	3.32373	+	3.32373i	0.158996	+	0.158996i
$438$	−4.29936	−	5.14221i	−0.205432	−	0.245704i
$439$		−	6.71446i		−	0.320464i	−0.987079	−	0.160232i	$-0.948776\pi$
$439$		−	6.71446i		−	0.320464i	0.987079	−	0.160232i	$-0.0512242\pi$
$440$	1.98078	−	11.3467i	0.0944299	−	0.540933i
$441$	10.5951	+	1.90684i	0.504530	+	0.0908017i
$442$	−2.05644	+	2.05644i	−0.0978150	+	0.0978150i
$443$	−15.5862	+	15.5862i	−0.740522	+	0.740522i	−0.972678	−	0.232157i	$-0.925422\pi$
$443$	−15.5862	+	15.5862i	−0.740522	+	0.740522i	0.232157	+	0.972678i	$0.425422\pi$
$444$	−0.774447	−	0.0691344i	−0.0367536	−	0.00328097i
$445$	−20.9412	−	29.7988i	−0.992707	−	1.41260i
$446$		−	5.56208i		−	0.263372i
$447$	0.807842	−	0.675431i	0.0382096	−	0.0319468i
$448$	−1.30605	−	1.30605i	−0.0617052	−	0.0617052i
$449$	−21.1036			−0.995941			−0.497971	−	0.867194i	$-0.665921\pi$
$449$	−21.1036			−0.995941			−0.497971	+	0.867194i	$0.665921\pi$
$450$	−3.88052	−	14.4894i	−0.182930	−	0.683035i
$451$	45.8052			2.15688
$452$	−6.24110	−	6.24110i	−0.293557	−	0.293557i
$453$	−3.31260	+	2.76964i	−0.155640	+	0.130129i
$454$		−	6.94202i		−	0.325805i
$455$	−1.14904	−	1.63505i	−0.0538677	−	0.0766524i
$456$	−1.72519	−	0.154007i	−0.0807894	−	0.00721202i
$457$	−3.24691	+	3.24691i	−0.151884	+	0.151884i	−0.778959	−	0.627075i	$-0.784252\pi$
$457$	−3.24691	+	3.24691i	−0.151884	+	0.151884i	0.627075	+	0.778959i	$0.284252\pi$
$458$	−0.218610	+	0.218610i	−0.0102150	+	0.0102150i
$459$	8.24301	−	30.1237i	0.384751	−	1.40605i
$460$	1.80748	−	10.3540i	0.0842741	−	0.482757i
$461$		−	31.5064i		−	1.46740i	−0.679473	−	0.733700i	$-0.737792\pi$
$461$		−	31.5064i		−	1.46740i	0.679473	−	0.733700i	$-0.262208\pi$
$462$	10.5704	+	12.6426i	0.491780	+	0.588188i
$463$	−8.81741	−	8.81741i	−0.409780	−	0.409780i	0.471882	−	0.881662i	$-0.343575\pi$
$463$	−8.81741	−	8.81741i	−0.409780	−	0.409780i	−0.881662	+	0.471882i	$0.843575\pi$
$464$	8.73926			0.405710
$465$	−37.7791	−	10.1254i	−1.75197	−	0.469552i
$466$	−1.55247			−0.0719169
$467$	−4.04048	−	4.04048i	−0.186971	−	0.186971i	0.607414	−	0.794385i	$-0.292207\pi$
$467$	−4.04048	−	4.04048i	−0.186971	−	0.186971i	−0.794385	+	0.607414i	$0.792207\pi$
$468$	0.828396	+	1.19202i	0.0382926	+	0.0551009i
$469$			3.91975i			0.180997i
$470$	5.54998	−	3.90026i	0.256001	−	0.179906i
$471$	−0.00967804	+	0.108414i	−0.000445941	+	0.00499545i
$472$	0.900830	−	0.900830i	0.0414641	−	0.0414641i
$473$	45.5761	−	45.5761i	2.09559	−	2.09559i
$474$	−0.805551	+	9.02382i	−0.0370002	+	0.414478i
$475$	−4.70427	−	1.69406i	−0.215847	−	0.0777287i
$476$		−	11.1015i		−	0.508837i
$477$	19.7952	+	28.4841i	0.906358	+	1.30420i
$478$	17.2546	+	17.2546i	0.789205	+	0.789205i
$479$	25.6778			1.17325			0.586624	−	0.809859i	$-0.300457\pi$
$479$	25.6778			1.17325			0.586624	+	0.809859i	$0.300457\pi$
$480$	1.93629	+	3.35422i	0.0883790	+	0.153098i
$481$	0.217210			0.00990393
$482$	10.9469	+	10.9469i	0.498618	+	0.498618i
$483$	9.64560	+	11.5365i	0.438890	+	0.524929i
$484$		−	15.5343i		−	0.706104i
$485$	−12.5412	−	2.18930i	−0.569469	−	0.0994112i
$486$	−14.0692	−	6.71252i	−0.638191	−	0.304486i
$487$	−10.1276	+	10.1276i	−0.458925	+	0.458925i	−0.898303	−	0.439377i	$-0.855199\pi$
$487$	−10.1276	+	10.1276i	−0.458925	+	0.458925i	0.439377	+	0.898303i	$0.355199\pi$
$488$	−4.42971	+	4.42971i	−0.200524	+	0.200524i
$489$	−21.9516	−	1.95961i	−0.992687	−	0.0886165i
$490$	−7.90448	−	1.37987i	−0.357088	−	0.0623363i
$491$			19.2496i			0.868723i	0.900739	+	0.434361i	$0.143026\pi$
$491$			19.2496i			0.868723i	−0.900739	+	0.434361i	$0.856974\pi$
$492$	−11.8159	+	9.87922i	−0.532703	+	0.445390i
$493$	37.1420	+	37.1420i	1.67279	+	1.67279i
$494$	0.483866			0.0217702
$495$	−14.5463	−	31.3440i	−0.653807	−	1.40881i
$496$	10.0988			0.453449
$497$	15.2898	+	15.2898i	0.685840	+	0.685840i
$498$	18.5769	−	15.5320i	0.832451	−	0.696007i
$499$			19.5782i			0.876439i	0.898868	+	0.438220i	$0.144391\pi$
$499$			19.5782i			0.876439i	−0.898868	+	0.438220i	$0.855609\pi$
$500$	2.94892	+	10.7844i	0.131880	+	0.482294i
$501$	−2.86682	−	0.255919i	−0.128080	−	0.0114336i
$502$	−7.34263	+	7.34263i	−0.327718	+	0.327718i
$503$	18.0640	−	18.0640i	0.805434	−	0.805434i	−0.178505	−	0.983939i	$-0.557126\pi$
$503$	18.0640	−	18.0640i	0.805434	−	0.805434i	0.983939	+	0.178505i	$0.0571262\pi$
$504$	−5.45350	−	0.981482i	−0.242918	−	0.0437187i
$505$	6.73604	−	4.73377i	0.299750	−	0.210650i
$506$		−	24.2128i		−	1.07639i
$507$	14.1828	+	16.9632i	0.629881	+	0.753362i
$508$	1.82261	+	1.82261i	0.0808651	+	0.0808651i
$509$	−24.2848			−1.07640			−0.538202	−	0.842816i	$-0.680896\pi$
$509$	−24.2848			−1.07640			−0.538202	+	0.842816i	$0.680896\pi$
$510$	−6.02624	+	22.4848i	−0.266846	+	0.995642i
$511$	−7.14773			−0.316197
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−4.51371	+	2.57419i	−0.199285	+	0.113653i
$514$		−	14.3265i		−	0.631914i
$515$	−3.03678	+	17.3960i	−0.133817	+	0.766558i
$516$	−1.92703	+	21.5867i	−0.0848327	+	0.950301i
$517$	11.0497	−	11.0497i	0.485965	−	0.485965i
$518$	−0.586294	+	0.586294i	−0.0257603	+	0.0257603i
$519$	2.96194	−	33.1798i	0.130015	−	1.45643i
$520$	−0.622097	−	0.885228i	−0.0272808	−	0.0388198i
$521$		−	19.1374i		−	0.838425i	−0.907888	−	0.419213i	$-0.862306\pi$
$521$		−	19.1374i		−	0.838425i	0.907888	−	0.419213i	$-0.137694\pi$
$522$	21.5294	−	14.9619i	0.942315	−	0.654865i
$523$	−3.69849	−	3.69849i	−0.161724	−	0.161724i	0.621606	−	0.783330i	$-0.286480\pi$
$523$	−3.69849	−	3.69849i	−0.161724	−	0.161724i	−0.783330	+	0.621606i	$0.786480\pi$
$524$	11.4188			0.498833
$525$	−14.5082	−	6.73627i	−0.633192	−	0.293995i
$526$	26.6919			1.16382
$527$	42.9201	+	42.9201i	1.86963	+	1.86963i
$528$	5.72289	+	6.84480i	0.249057	+	0.297882i
$529$			0.905600i			0.0393739i
$530$	−14.8655	−	21.1532i	−0.645716	−	0.918837i
$531$	0.676962	−	3.76147i	0.0293777	−	0.163234i
$532$	−1.30605	+	1.30605i	−0.0566246	+	0.0566246i
$533$	3.04243	−	3.04243i	0.131782	−	0.131782i
$534$	28.0999	+	2.50846i	1.21600	+	0.108552i
$535$	−1.12808	+	6.46211i	−0.0487711	+	0.279381i
$536$			2.12218i			0.0916642i
$537$	−23.8899	+	19.9741i	−1.03092	+	0.861948i
$538$	4.61020	+	4.61020i	0.198760	+	0.198760i
$539$	−18.4846			−0.796189
$540$	10.5126	+	4.94820i	0.452391	+	0.212937i
$541$	−15.7000			−0.674995			−0.337498	−	0.941326i	$-0.609581\pi$
$541$	−15.7000			−0.674995			−0.337498	+	0.941326i	$0.609581\pi$
$542$	−10.1873	−	10.1873i	−0.437580	−	0.437580i
$543$	−6.08836	+	5.09044i	−0.261277	+	0.218452i
$544$		−	6.01044i		−	0.257695i
$545$	8.18130	−	5.74944i	0.350449	−	0.246279i
$546$	1.54184	+	0.137639i	0.0659845	+	0.00589040i
$547$	6.76457	−	6.76457i	0.289232	−	0.289232i	−0.547545	−	0.836777i	$-0.684437\pi$
$547$	6.76457	−	6.76457i	0.289232	−	0.289232i	0.836777	+	0.547545i	$0.184437\pi$
$548$	11.0007	−	11.0007i	0.469929	−	0.469929i
$549$	−3.32887	+	18.4965i	−0.142073	+	0.789412i
$550$	10.9644	+	23.3053i	0.467525	+	0.993743i
$551$		−	8.73926i		−	0.372305i
$552$	5.22220	+	6.24595i	0.222271	+	0.265845i
$553$	6.83147	+	6.83147i	0.290504	+	0.290504i
$554$	−19.7600			−0.839520
$555$	1.50573	−	0.869210i	0.0639146	−	0.0368959i
$556$	−1.23352			−0.0523128
$557$	7.92409	+	7.92409i	0.335754	+	0.335754i	0.854767	−	0.519012i	$-0.173700\pi$
$557$	7.92409	+	7.92409i	0.335754	+	0.335754i	−0.519012	+	0.854767i	$0.673700\pi$
$558$	24.8786	−	17.2895i	1.05320	−	0.731922i
$559$		−	6.05445i		−	0.256076i
$560$	4.06858	+	0.710245i	0.171929	+	0.0300133i
$561$	−4.76814	+	53.4130i	−0.201311	+	2.25510i
$562$	−17.1338	+	17.1338i	−0.722747	+	0.722747i
$563$	−2.50755	+	2.50755i	−0.105681	+	0.105681i	−0.757970	−	0.652289i	$-0.773809\pi$
$563$	−2.50755	+	2.50755i	−0.105681	+	0.105681i	0.652289	+	0.757970i	$0.273809\pi$
$564$	−0.467198	+	5.23357i	−0.0196726	+	0.220373i
$565$	19.4421	+	3.39397i	0.817935	+	0.142786i
$566$		−	13.1018i		−	0.550708i
$567$	−15.1151	+	6.91868i	−0.634776	+	0.290557i
$568$	8.27799	+	8.27799i	0.347337	+	0.347337i
$569$	19.7316			0.827190			0.413595	−	0.910461i	$-0.364273\pi$
$569$	19.7316			0.827190			0.413595	+	0.910461i	$0.364273\pi$
$570$	3.35422	−	1.93629i	0.140493	−	0.0811022i
$571$	11.2502			0.470807			0.235403	−	0.971898i	$-0.424359\pi$
$571$	11.2502			0.470807			0.235403	+	0.971898i	$0.424359\pi$
$572$	−1.76244	−	1.76244i	−0.0736913	−	0.0736913i
$573$	13.6903	+	16.3741i	0.571919	+	0.684037i
$574$			16.4243i			0.685537i
$575$	10.0051	+	21.2663i	0.417243	+	0.886868i
$576$	−2.95256	−	0.531382i	−0.123023	−	0.0221409i
$577$	22.9715	−	22.9715i	0.956315	−	0.956315i	−0.0427697	−	0.999085i	$-0.513618\pi$
$577$	22.9715	−	22.9715i	0.956315	−	0.956315i	0.999085	+	0.0427697i	$0.0136182\pi$
$578$	13.5237	−	13.5237i	0.562510	−	0.562510i
$579$	28.9368	+	2.58317i	1.20257	+	0.107353i
$580$	−15.9884	+	11.2359i	−0.663881	+	0.466545i
$581$		−	25.8221i		−	1.07128i
$582$	7.56539	−	6.32537i	0.313596	−	0.262195i
$583$	−42.1149	−	42.1149i	−1.74422	−	1.74422i
$584$	−3.86983			−0.160135
$585$	−3.04809	−	1.11573i	−0.126023	−	0.0461297i
$586$	12.7363			0.526133
$587$	−20.3746	−	20.3746i	−0.840951	−	0.840951i	0.148032	−	0.988983i	$-0.452706\pi$
$587$	−20.3746	−	20.3746i	−0.840951	−	0.840951i	−0.988983	+	0.148032i	$0.952706\pi$
$588$	4.76831	−	3.98675i	0.196642	−	0.164411i
$589$		−	10.0988i		−	0.416114i
$590$	−0.489880	+	2.80624i	−0.0201681	+	0.115531i
$591$	8.70536	+	0.777122i	0.358091	+	0.0319665i
$592$	−0.317424	+	0.317424i	−0.0130460	+	0.0130460i
$593$	7.81504	−	7.81504i	0.320925	−	0.320925i	−0.528197	−	0.849122i	$-0.677132\pi$
$593$	7.81504	−	7.81504i	0.320925	−	0.320925i	0.849122	+	0.528197i	$0.177132\pi$
$594$	25.8170	+	7.06453i	1.05928	+	0.289861i
$595$	14.2730	+	20.3101i	0.585135	+	0.832632i
$596$		−	0.607952i		−	0.0249027i
$597$	−3.59061	−	4.29451i	−0.146954	−	0.175762i
$598$	−1.60824	−	1.60824i	−0.0657659	−	0.0657659i
$599$	6.25932			0.255749			0.127874	−	0.991790i	$-0.459185\pi$
$599$	6.25932			0.255749			0.127874	+	0.991790i	$0.459185\pi$
$600$	−7.85487	−	3.64706i	−0.320674	−	0.148891i
$601$	−13.5081			−0.551009			−0.275504	−	0.961300i	$-0.588845\pi$
$601$	−13.5081			−0.551009			−0.275504	+	0.961300i	$0.588845\pi$
$602$	16.3422	+	16.3422i	0.666057	+	0.666057i
$603$	3.63324	+	5.22803i	0.147957	+	0.212902i
$604$			2.49294i			0.101436i
$605$	19.9721	+	28.4198i	0.811982	+	1.15543i
$606$	−0.567041	+	6.35202i	−0.0230345	+	0.258033i
$607$	−19.7516	+	19.7516i	−0.801691	+	0.801691i	−0.983360	−	0.181669i	$-0.941850\pi$
$607$	−19.7516	+	19.7516i	−0.801691	+	0.801691i	0.181669	+	0.983360i	$0.441850\pi$
$608$	−0.707107	+	0.707107i	−0.0286770	+	0.0286770i
$609$	2.48594	−	27.8476i	0.100735	−	1.12844i
$610$	2.40892	−	13.7993i	0.0975343	−	0.558717i
$611$		−	1.46787i		−	0.0593836i
$612$	−10.2901	−	14.8068i	−0.415952	−	0.598531i
$613$	−8.37167	−	8.37167i	−0.338129	−	0.338129i	0.517534	−	0.855663i	$-0.326850\pi$
$613$	−8.37167	−	8.37167i	−0.338129	−	0.338129i	−0.855663	+	0.517534i	$0.826850\pi$
$614$	−6.21149			−0.250675
$615$	8.91561	−	33.2654i	0.359512	−	1.34139i
$616$	9.51436			0.383345
$617$	−18.8481	−	18.8481i	−0.758795	−	0.758795i	0.217308	−	0.976103i	$-0.430272\pi$
$617$	−18.8481	−	18.8481i	−0.758795	−	0.758795i	−0.976103	+	0.217308i	$0.930272\pi$
$618$	−8.77393	−	10.4940i	−0.352939	−	0.422129i
$619$			19.7510i			0.793860i	0.917849	+	0.396930i	$0.129924\pi$
$619$			19.7510i			0.793860i	−0.917849	+	0.396930i	$0.870076\pi$
$620$	−18.4756	+	12.9838i	−0.741999	+	0.521442i
$621$	23.5583	+	6.44645i	0.945361	+	0.258687i
$622$	−11.4222	+	11.4222i	−0.457988	+	0.457988i
$623$	21.2730	−	21.2730i	0.852286	−	0.852286i
$624$	0.834762	+	0.0745186i	0.0334172	+	0.00298313i
$625$	−19.2603	−	15.9386i	−0.770413	−	0.637545i
$626$			0.697474i			0.0278767i
$627$	6.84480	−	5.72289i	0.273355	−	0.228550i
$628$	0.0444358	+	0.0444358i	0.00177318	+	0.00177318i
$629$	−2.69812			−0.107581
$630$	11.2390	−	5.21584i	0.447772	−	0.207804i
$631$	16.2630			0.647418			0.323709	−	0.946157i	$-0.395070\pi$
$631$	16.2630			0.647418			0.323709	+	0.946157i	$0.395070\pi$
$632$	3.69861	+	3.69861i	0.147123	+	0.147123i
$633$	−17.5987	+	14.7142i	−0.699487	+	0.584837i
$634$		−	24.0070i		−	0.953441i
$635$	−5.67772	−	0.991151i	−0.225314	−	0.0393326i
$636$	19.9473	+	1.78068i	0.790961	+	0.0706086i
$637$	−1.22777	+	1.22777i	−0.0486460	+	0.0486460i
$638$	−31.8320	+	31.8320i	−1.26024	+	1.26024i
$639$	34.5652	+	6.22080i	1.36738	+	0.246091i
$640$	2.20276	+	0.384532i	0.0870716	+	0.0151999i
$641$			16.4351i			0.649146i	0.945861	+	0.324573i	$0.105221\pi$
$641$			16.4351i			0.649146i	−0.945861	+	0.324573i	$0.894779\pi$
$642$	−3.25926	−	3.89821i	−0.128633	−	0.153850i
$643$	16.1113	+	16.1113i	0.635369	+	0.635369i	0.949409	−	0.314041i	$-0.101683\pi$
$643$	16.1113	+	16.1113i	0.635369	+	0.635369i	−0.314041	+	0.949409i	$0.601683\pi$
$644$	8.68195			0.342117
$645$	−24.2281	−	41.9701i	−0.953979	−	1.65257i
$646$	−6.01044			−0.236477
$647$	33.8022	+	33.8022i	1.32890	+	1.32890i	0.906330	+	0.422570i	$0.138872\pi$
$647$	33.8022	+	33.8022i	1.32890	+	1.32890i	0.422570	+	0.906330i	$0.361128\pi$
$648$	−8.18345	+	3.74582i	−0.321476	+	0.147150i
$649$			6.56239i			0.257596i
$650$	2.27624	+	0.819698i	0.0892814	+	0.0321512i
$651$	2.87267	−	32.1797i	0.112589	−	1.26122i
$652$	−8.99735	+	8.99735i	−0.352363	+	0.352363i
$653$	−6.58374	+	6.58374i	−0.257642	+	0.257642i	−0.824094	−	0.566453i	$-0.808315\pi$
$653$	−6.58374	+	6.58374i	−0.257642	+	0.257642i	0.566453	+	0.824094i	$0.308315\pi$
$654$	−0.688703	+	7.71489i	−0.0269304	+	0.301676i
$655$	−20.8906	+	14.6809i	−0.816263	+	0.573631i
$656$			8.89223i			0.347183i
$657$	−9.53342	+	6.62529i	−0.371934	+	0.258477i
$658$	3.96207	+	3.96207i	0.154458	+	0.154458i
$659$	0.843524			0.0328590			0.0164295	−	0.999865i	$-0.494770\pi$
$659$	0.843524			0.0328590			0.0164295	+	0.999865i	$0.494770\pi$
$660$	−19.2702	−	5.16469i	−0.750091	−	0.201035i
$661$	20.3317			0.790813			0.395406	−	0.918506i	$-0.370604\pi$
$661$	20.3317			0.790813			0.395406	+	0.918506i	$0.370604\pi$
$662$	−10.4028	−	10.4028i	−0.404318	−	0.404318i
$663$	3.23105	+	3.86446i	0.125484	+	0.150083i
$664$		−	13.9803i		−	0.542540i
$665$	0.710245	−	4.06858i	0.0275421	−	0.157773i
$666$	−0.238540	+	1.32542i	−0.00924324	+	0.0513590i
$667$	−29.0470	+	29.0470i	−1.12470	+	1.12470i
$668$	−1.17503	+	1.17503i	−0.0454632	+	0.0454632i
$669$	−9.59564	−	0.856597i	−0.370989	−	0.0331180i
$670$	−2.72844	−	3.88250i	−0.105409	−	0.149994i
$671$		−	32.2696i		−	1.24576i
$672$	−2.45433	+	2.05205i	−0.0946779	+	0.0791595i
$673$	−23.9996	−	23.9996i	−0.925115	−	0.925115i	0.0722701	−	0.997385i	$-0.476976\pi$
$673$	−23.9996	−	23.9996i	−0.925115	−	0.925115i	−0.997385	+	0.0722701i	$0.976976\pi$
$674$	−19.6473			−0.756787
$675$	−25.5945	+	4.46318i	−0.985134	+	0.171788i
$676$	12.7659			0.490995
$677$	−18.9600	−	18.9600i	−0.728691	−	0.728691i	0.241668	−	0.970359i	$-0.422305\pi$
$677$	−18.9600	−	18.9600i	−0.728691	−	0.728691i	−0.970359	+	0.241668i	$0.922305\pi$
$678$	−11.7283	+	9.80592i	−0.450421	+	0.376594i
$679$		−	10.5160i		−	0.403567i
$680$	7.72749	+	10.9960i	0.296336	+	0.421678i
$681$	−11.9763	−	1.06912i	−0.458933	−	0.0409686i
$682$	−36.7840	+	36.7840i	−1.40853	+	1.40853i
$683$	6.99901	−	6.99901i	0.267810	−	0.267810i	−0.560407	−	0.828217i	$-0.689355\pi$
$683$	6.99901	−	6.99901i	0.267810	−	0.267810i	0.828217	+	0.560407i	$0.189355\pi$
$684$	−0.531382	+	2.95256i	−0.0203179	+	0.112894i
$685$	−5.98231	+	34.2692i	−0.228572	+	1.30936i
$686$		−	19.5573i		−	0.746700i
$687$	0.343477	+	0.410812i	0.0131045	+	0.0156735i
$688$	8.84777	+	8.84777i	0.337318	+	0.337318i
$689$	−5.59464			−0.213139
$690$	−17.5842	−	4.71283i	−0.669420	−	0.179414i
$691$	−44.2770			−1.68438			−0.842189	−	0.539183i	$-0.818733\pi$
$691$	−44.2770			−1.68438			−0.842189	+	0.539183i	$0.818733\pi$
$692$	−13.5995	−	13.5995i	−0.516974	−	0.516974i
$693$	23.4388	−	16.2889i	0.890368	−	0.618765i
$694$			29.7101i			1.12778i
$695$	2.25671	−	1.58591i	0.0856018	−	0.0601570i
$696$	1.34590	−	15.0769i	0.0510164	−	0.571488i
$697$	−37.7922	+	37.7922i	−1.43148	+	1.43148i
$698$	12.7925	−	12.7925i	0.484202	−	0.484202i
$699$	−0.239091	+	2.67831i	−0.00904325	+	0.101303i
$700$	−8.35656	+	3.93150i	−0.315848	+	0.148597i
$701$			47.5139i			1.79458i	0.441445	+	0.897288i	$0.354466\pi$
$701$			47.5139i			1.79458i	−0.441445	+	0.897288i	$0.645534\pi$
$702$	2.18403	−	1.24556i	0.0824310	−	0.0470107i
$703$	0.317424	+	0.317424i	0.0119719	+	0.0119719i
$704$	5.15114			0.194141
$705$	−5.87396	−	10.1754i	−0.221226	−	0.383229i
$706$	12.6658			0.476685
$707$	4.80879	+	4.80879i	0.180853	+	0.180853i
$708$	−1.41537	−	1.69284i	−0.0531929	−	0.0636207i
$709$		−	34.9010i		−	1.31073i	−0.755311	−	0.655367i	$-0.772514\pi$
$709$		−	34.9010i		−	1.31073i	0.755311	−	0.655367i	$-0.227486\pi$
$710$	−25.7873	−	4.50165i	−0.967781	−	0.168944i
$711$	15.4437	+	2.77946i	0.579186	+	0.104238i
$712$	11.5174	−	11.5174i	0.431632	−	0.431632i
$713$	−33.5657	+	33.5657i	−1.25705	+	1.25705i
$714$	−19.1522	−	1.70971i	−0.716754	−	0.0639841i
$715$	5.49029	+	0.958432i	0.205325	+	0.0358433i
$716$			17.9786i			0.671892i
$717$	32.4247	−	27.1101i	1.21092	−	1.01244i
$718$	−9.83005	−	9.83005i	−0.366854	−	0.366854i
$719$	31.1460			1.16155			0.580775	−	0.814064i	$-0.302750\pi$
$719$	31.1460			1.16155			0.580775	+	0.814064i	$0.302750\pi$
$720$	6.08487	−	2.82389i	0.226770	−	0.105240i
$721$	−14.5867			−0.543238
$722$	0.707107	+	0.707107i	0.0263158	+	0.0263158i
$723$	20.5714	−	17.1996i	0.765058	−	0.639660i
$724$			4.58187i			0.170284i
$725$	14.8048	−	41.1119i	0.549837	−	1.52686i
$726$	−26.7996	−	2.39238i	−0.994627	−	0.0887897i
$727$	18.0500	−	18.0500i	0.669439	−	0.669439i	−0.288147	−	0.957586i	$-0.593039\pi$
$727$	18.0500	−	18.0500i	0.669439	−	0.669439i	0.957586	+	0.288147i	$0.0930393\pi$
$728$	0.631955	−	0.631955i	0.0234218	−	0.0234218i
$729$	−13.7471	+	23.2383i	−0.509153	+	0.860676i
$730$	7.07982	−	4.97536i	0.262036	−	0.184146i
$731$			75.2064i			2.78161i
$732$	6.95989	+	8.32430i	0.257245	+	0.307675i
$733$	−9.66033	−	9.66033i	−0.356812	−	0.356812i	0.505824	−	0.862637i	$-0.331188\pi$
$733$	−9.66033	−	9.66033i	−0.356812	−	0.356812i	−0.862637	+	0.505824i	$0.831188\pi$
$734$	−3.44883			−0.127299
$735$	−3.59788	+	13.4242i	−0.132710	+	0.495160i
$736$	4.70047			0.173262
$737$	−7.72984	−	7.72984i	−0.284732	−	0.284732i
$738$	15.2238	+	21.9062i	0.560396	+	0.806378i
$739$			5.67646i			0.208812i	0.994535	+	0.104406i	$0.0332941\pi$
$739$			5.67646i			0.208812i	−0.994535	+	0.104406i	$0.966706\pi$
$740$	0.172618	−	0.988829i	0.00634557	−	0.0363501i
$741$	0.0745186	−	0.834762i	0.00273751	−	0.0306657i
$742$	15.1011	−	15.1011i	0.554378	−	0.554378i
$743$	−31.4477	+	31.4477i	−1.15370	+	1.15370i	−0.167901	+	0.985804i	$0.553699\pi$
$743$	−31.4477	+	31.4477i	−1.15370	+	1.15370i	−0.985804	+	0.167901i	$0.946301\pi$
$744$	1.55528	−	17.4223i	0.0570194	−	0.638734i
$745$	0.781631	+	1.11224i	0.0286367	+	0.0407494i
$746$			29.8160i			1.09164i
$747$	−23.9347	−	34.4407i	−0.875726	−	1.26012i
$748$	21.8925	+	21.8925i	0.800468	+	0.800468i
$749$	−5.41856			−0.197990
$750$	19.0593	−	3.42658i	0.695949	−	0.125121i
$751$	35.7096			1.30306			0.651532	−	0.758622i	$-0.274127\pi$
$751$	35.7096			1.30306			0.651532	+	0.758622i	$0.274127\pi$
$752$	2.14509	+	2.14509i	0.0782235	+	0.0782235i
$753$	11.5366	+	13.7983i	0.420418	+	0.502836i
$754$			4.22864i			0.153998i
$755$	−3.20512	−	4.56081i	−0.116646	−	0.165985i
$756$	−2.53312	+	9.25717i	−0.0921286	+	0.336680i
$757$	−16.5848	+	16.5848i	−0.602785	+	0.602785i	−0.941051	−	0.338266i	$-0.890160\pi$
$757$	−16.5848	+	16.5848i	−0.602785	+	0.602785i	0.338266	+	0.941051i	$0.390160\pi$
$758$	−1.59375	+	1.59375i	−0.0578874	+	0.0578874i
$759$	−41.7717	−	3.72893i	−1.51622	−	0.135352i
$760$	0.384532	−	2.20276i	0.0139484	−	0.0799024i
$761$			34.9067i			1.26537i	0.774411	+	0.632683i	$0.218047\pi$
$761$			34.9067i			1.26537i	−0.774411	+	0.632683i	$0.781953\pi$
$762$	3.42504	−	2.86365i	0.124076	−	0.103739i
$763$	5.84055	+	5.84055i	0.211442	+	0.211442i
$764$	12.3225			0.445813
$765$	37.8624	+	13.8592i	1.36892	+	0.501081i
$766$	6.06812			0.219250
$767$	0.435882	+	0.435882i	0.0157388	+	0.0157388i
$768$	−1.32879	+	1.11099i	−0.0479487	+	0.0400896i
$769$		−	37.8613i		−	1.36531i	−0.730739	−	0.682657i	$-0.760824\pi$
$769$		−	37.8613i		−	1.36531i	0.730739	−	0.682657i	$-0.239176\pi$
$770$	−17.4064	+	12.2324i	−0.627284	+	0.440826i
$771$	−24.7159	−	2.20637i	−0.890121	−	0.0794605i
$772$	11.8604	−	11.8604i	0.426864	−	0.426864i
$773$	−12.9141	+	12.9141i	−0.464488	+	0.464488i	−0.900123	−	0.435635i	$-0.856524\pi$
$773$	−12.9141	+	12.9141i	−0.464488	+	0.464488i	0.435635	+	0.900123i	$0.356524\pi$
$774$	36.9444	+	6.64899i	1.32794	+	0.238993i
$775$	17.1080	−	47.5075i	0.614536	−	1.70652i
$776$		−	5.69343i		−	0.204382i
$777$	0.921176	+	1.10176i	0.0330470	+	0.0395255i
$778$	−14.8681	−	14.8681i	−0.533047	−	0.533047i
$779$	8.89223			0.318597
$780$	−1.62299	+	0.936905i	−0.0581125	+	0.0335466i
$781$	−60.3037			−2.15783
$782$	19.9771	+	19.9771i	0.714379	+	0.714379i
$783$	−22.4965	−	39.4465i	−0.803959	−	1.40970i
$784$		−	3.58845i		−	0.128159i
$785$	−0.138425	−	0.0241646i	−0.00494060	−	0.000862473i
$786$	1.75857	−	19.6996i	0.0627262	−	0.702662i
$787$	−11.4900	+	11.4900i	−0.409575	+	0.409575i	−0.881590	−	0.472015i	$-0.843527\pi$
$787$	−11.4900	+	11.4900i	−0.409575	+	0.409575i	0.472015	+	0.881590i	$0.343527\pi$
$788$	3.56808	−	3.56808i	0.127108	−	0.127108i
$789$	4.11073	−	46.0486i	0.146346	−	1.63937i
$790$	−11.5218	−	2.01134i	−0.409927	−	0.0715603i
$791$			16.3024i			0.579648i
$792$	12.6900	−	8.81894i	0.450918	−	0.313367i
$793$	−2.14339	−	2.14339i	−0.0761140	−	0.0761140i
$794$	−9.97969			−0.354166
$795$	−38.7827	+	22.3881i	−1.37548	+	0.794023i
$796$	−3.23189			−0.114551
$797$	−26.4864	−	26.4864i	−0.938196	−	0.938196i	0.0600027	−	0.998198i	$-0.480889\pi$
$797$	−26.4864	−	26.4864i	−0.938196	−	0.938196i	−0.998198	+	0.0600027i	$0.980889\pi$
$798$	2.05205	+	2.45433i	0.0726418	+	0.0868824i
$799$			18.2334i			0.645051i
$800$	−4.52430	+	2.12854i	−0.159958	+	0.0752553i
$801$	8.65516	−	48.0914i	0.305815	−	1.69923i
$802$	2.53532	−	2.53532i	0.0895252	−	0.0895252i
$803$	14.0955	−	14.0955i	0.497420	−	0.497420i
$804$	3.66116	+	0.326830i	0.129119	+	0.0115264i
$805$	−15.8835	+	11.1622i	−0.559821	+	0.393416i
$806$			4.88647i			0.172119i
$807$	8.66348	−	7.24347i	0.304969	−	0.254982i
$808$	2.60351	+	2.60351i	0.0915913	+	0.0915913i
$809$	3.31684			0.116614			0.0583069	−	0.998299i	$-0.481430\pi$
$809$	3.31684			0.116614			0.0583069	+	0.998299i	$0.481430\pi$
$810$	10.1556	−	17.3742i	0.356832	−	0.610468i
$811$	−31.1363			−1.09334			−0.546671	−	0.837347i	$-0.684105\pi$
$811$	−31.1363			−1.09334			−0.546671	+	0.837347i	$0.684105\pi$
$812$	−11.4139	−	11.4139i	−0.400551	−	0.400551i
$813$	−19.1439	+	16.0061i	−0.671405	+	0.561357i
$814$		−	2.31238i		−	0.0810487i
$815$	4.89285	−	28.0283i	0.171389	−	0.981787i
$816$	−10.3691	−	0.925647i	−0.362993	−	0.0324041i
$817$	8.84777	−	8.84777i	0.309544	−	0.309544i
$818$	−11.4649	+	11.4649i	−0.400860	+	0.400860i
$819$	0.474906	−	2.63877i	0.0165946	−	0.0922059i
$820$	−11.4326	−	16.2682i	−0.399242	−	0.568111i
$821$		−	11.7993i		−	0.411797i	−0.978573	−	0.205899i	$-0.933988\pi$
$821$		−	11.7993i		−	0.411797i	0.978573	−	0.205899i	$-0.0660117\pi$
$822$	−17.2842	−	20.6726i	−0.602856	−	0.721039i
$823$	2.49272	+	2.49272i	0.0868909	+	0.0868909i	0.749216	−	0.662325i	$-0.230430\pi$
$823$	2.49272	+	2.49272i	0.0868909	+	0.0868909i	−0.662325	+	0.749216i	$0.730430\pi$
$824$	−7.89736			−0.275118
$825$	41.8947	−	15.3265i	1.45859	−	0.533602i
$826$	−2.35307			−0.0818736
$827$	−8.72992	−	8.72992i	−0.303569	−	0.303569i	0.538839	−	0.842408i	$-0.318863\pi$
$827$	−8.72992	−	8.72992i	−0.303569	−	0.303569i	−0.842408	+	0.538839i	$0.818863\pi$
$828$	11.5797	−	8.04736i	0.402423	−	0.279665i
$829$		−	3.58566i		−	0.124535i	−0.998059	−	0.0622676i	$-0.980167\pi$
$829$		−	3.58566i		−	0.124535i	0.998059	−	0.0622676i	$-0.0198332\pi$
$830$	17.9742	+	25.5768i	0.623892	+	0.887783i
$831$	−3.04316	+	34.0897i	−0.105566	+	1.18256i
$832$	0.342145	−	0.342145i	0.0118618	−	0.0118618i
$833$	15.2510	−	15.2510i	0.528415	−	0.528415i
$834$	−0.189970	+	2.12805i	−0.00657812	+	0.0736885i
$835$	0.638992	−	3.66041i	0.0221132	−	0.126674i
$836$		−	5.15114i		−	0.178156i
$837$	−25.9962	−	45.5830i	−0.898560	−	1.57558i
$838$	5.27610	+	5.27610i	0.182260	+	0.182260i
$839$	−35.9702			−1.24183			−0.620914	−	0.783879i	$-0.713238\pi$
$839$	−35.9702			−1.24183			−0.620914	+	0.783879i	$0.713238\pi$
$840$	1.85189	−	6.90969i	0.0638964	−	0.238407i
$841$	47.3747			1.63361
$842$	−2.49657	−	2.49657i	−0.0860374	−	0.0860374i
$843$	26.9204	+	32.1978i	0.927188	+	1.10895i
$844$			13.2442i			0.455883i
$845$	−23.3550	+	16.4128i	−0.803437	+	0.564618i
$846$	8.95696	+	1.61201i	0.307947	+	0.0554221i
$847$	−20.2886	+	20.2886i	−0.697125	+	0.697125i
$848$	8.17583	−	8.17583i	0.280759	−	0.280759i
$849$	−22.6030	−	2.01776i	−0.775734	−	0.0692492i
$850$	−28.2747	−	10.1820i	−0.969815	−	0.349241i
$851$		−	2.11007i		−	0.0723321i
$852$	15.5560	−	13.0062i	0.532939	−	0.445587i
$853$	−22.0095	−	22.0095i	−0.753591	−	0.753591i	0.221556	−	0.975148i	$-0.428886\pi$
$853$	−22.0095	−	22.0095i	−0.753591	−	0.753591i	−0.975148	+	0.221556i	$0.928886\pi$
$854$	11.5709			0.395947
$855$	−2.82389	−	6.08487i	−0.0965751	−	0.208098i
$856$	−2.93365			−0.100270
$857$	11.8490	+	11.8490i	0.404754	+	0.404754i	0.879905	−	0.475150i	$-0.157606\pi$
$857$	11.8490	+	11.8490i	0.404754	+	0.404754i	−0.475150	+	0.879905i	$0.657606\pi$
$858$	−3.31197	+	2.76912i	−0.113069	+	0.0945361i
$859$			24.7373i			0.844025i	0.906590	+	0.422013i	$0.138676\pi$
$859$			24.7373i			0.844025i	−0.906590	+	0.422013i	$0.861324\pi$
$860$	−27.5623	−	4.81150i	−0.939866	−	0.164071i
$861$	28.3350	+	2.52945i	0.965655	+	0.0862034i
$862$	25.5261	−	25.5261i	0.869424	−	0.869424i
$863$	15.8562	−	15.8562i	0.539752	−	0.539752i	−0.383704	−	0.923456i	$-0.625352\pi$
$863$	15.8562	−	15.8562i	0.539752	−	0.539752i	0.923456	+	0.383704i	$0.125352\pi$
$864$	−1.37145	+	5.01190i	−0.0466576	+	0.170508i
$865$	42.3646	+	7.39553i	1.44044	+	0.251455i
$866$		−	11.9178i		−	0.404982i
$867$	−21.2482	−	25.4136i	−0.721625	−	0.863092i
$868$	−13.1896	−	13.1896i	−0.447683	−	0.447683i
$869$	−26.9437			−0.914002
$870$	16.9217	+	29.3134i	0.573700	+	0.993818i
$871$	−1.02685			−0.0347935
$872$	3.16212	+	3.16212i	0.107083	+	0.107083i
$873$	−9.74735	−	14.0259i	−0.329898	−	0.474705i
$874$		−	4.70047i		−	0.158996i
$875$	10.2336	−	17.9365i	0.345958	−	0.606364i
$876$	−0.595980	+	6.67620i	−0.0201363	+	0.225568i
$877$	−4.84768	+	4.84768i	−0.163694	+	0.163694i	−0.784201	−	0.620507i	$-0.786927\pi$
$877$	−4.84768	+	4.84768i	−0.163694	+	0.163694i	0.620507	+	0.784201i	$0.286927\pi$
$878$	−4.74784	+	4.74784i	−0.160232	+	0.160232i
$879$	1.96148	−	21.9726i	0.0661591	−	0.741117i
$880$	−9.42396	+	6.62272i	−0.317682	+	0.223252i
$881$		−	41.5364i		−	1.39940i	−0.714439	−	0.699698i	$-0.753318\pi$
$881$		−	41.5364i		−	1.39940i	0.714439	−	0.699698i	$-0.246682\pi$
$882$	−6.14355	−	8.84022i	−0.206864	−	0.297666i
$883$	39.1569	+	39.1569i	1.31773	+	1.31773i	0.915566	+	0.402167i	$0.131743\pi$
$883$	39.1569	+	39.1569i	1.31773	+	1.31773i	0.402167	+	0.915566i	$0.368257\pi$
$884$	2.90825			0.0978150
$885$	4.76585	+	1.27732i	0.160202	+	0.0429365i
$886$	22.0422			0.740522
$887$	−21.3528	−	21.3528i	−0.716958	−	0.716958i	0.251023	−	0.967981i	$-0.419233\pi$
$887$	−21.3528	−	21.3528i	−0.716958	−	0.716958i	−0.967981	+	0.251023i	$0.919233\pi$
$888$	0.498731	+	0.596502i	0.0167363	+	0.0200173i
$889$		−	4.76084i		−	0.159674i
$890$	−6.26326	+	35.8786i	−0.209945	+	1.20265i
$891$	16.1637	−	43.4513i	0.541503	−	1.45567i
$892$	−3.93298	+	3.93298i	−0.131686	+	0.131686i
$893$	2.14509	−	2.14509i	0.0717828	−	0.0717828i
$894$	−1.04883	−	0.0936286i	−0.0350782	−	0.00313141i
$895$	−23.1147	−	32.8917i	−0.772640	−	1.09945i
$896$			1.84704i			0.0617052i
$897$	−3.02221	+	2.52684i	−0.100908	+	0.0843689i
$898$	14.9225	+	14.9225i	0.497971	+	0.497971i
$899$	88.2560			2.94350
$900$	−7.50158	+	12.9895i	−0.250053	+	0.432982i
$901$	69.4949			2.31521
$902$	−32.3891	−	32.3891i	−1.07844	−	1.07844i
$903$	30.7102	−	25.6766i	1.02197	−	0.854462i
$904$			8.82625i			0.293557i
$905$	−5.89082	−	8.38249i	−0.195817	−	0.278643i
$906$	4.30080	+	0.383929i	0.142884	+	0.0127552i
$907$	−10.8871	+	10.8871i	−0.361499	+	0.361499i	−0.864364	−	0.502866i	$-0.832279\pi$
$907$	−10.8871	+	10.8871i	−0.361499	+	0.361499i	0.502866	+	0.864364i	$0.332279\pi$
$908$	−4.90875	+	4.90875i	−0.162903	+	0.162903i
$909$	10.8711	+	1.95651i	0.360572	+	0.0648932i
$910$	−0.343664	+	1.96865i	−0.0113923	+	0.0652600i
$911$			17.7253i			0.587264i	0.955919	+	0.293632i	$0.0948640\pi$
$911$			17.7253i			0.587264i	−0.955919	+	0.293632i	$0.905136\pi$
$912$	1.11099	+	1.32879i	0.0367887	+	0.0440007i
$913$	50.9219	+	50.9219i	1.68527	+	1.68527i
$914$	4.59183			0.151884
$915$	−23.4354	−	6.28103i	−0.774751	−	0.207644i
$916$	0.309162			0.0102150
$917$	−14.9136	−	14.9136i	−0.492490	−	0.492490i
$918$	−27.1294	+	15.4720i	−0.895402	+	0.510652i
$919$			41.6528i			1.37400i	0.726658	+	0.686999i	$0.241072\pi$
$919$			41.6528i			1.37400i	−0.726658	+	0.686999i	$0.758928\pi$
$920$	−8.59945	+	6.04329i	−0.283516	+	0.199241i
$921$	−0.956611	+	10.7160i	−0.0315214	+	0.353104i
$922$	−22.2784	+	22.2784i	−0.733700	+	0.733700i
$923$	−4.00544	+	4.00544i	−0.131841	+	0.131841i
$924$	1.46527	−	16.4141i	0.0482040	−	0.539984i
$925$	0.955514	+	2.03098i	0.0314171	+	0.0667783i
$926$			12.4697i			0.409780i
$927$	−19.4553	+	13.5206i	−0.638996	+	0.444073i
$928$	−6.17959	−	6.17959i	−0.202855	−	0.202855i
$929$	5.97512			0.196037			0.0980187	−	0.995185i	$-0.468750\pi$
$929$	5.97512			0.196037			0.0980187	+	0.995185i	$0.468750\pi$
$930$	19.5542	+	33.8736i	0.641207	+	1.11076i
$931$	−3.58845			−0.117607
$932$	1.09776	+	1.09776i	0.0359584	+	0.0359584i
$933$	17.9463	+	21.4645i	0.587537	+	0.702717i
$934$			5.71410i			0.186971i
$935$	−68.1987	−	11.9053i	−2.23034	−	0.389346i
$936$	0.257118	−	1.42865i	0.00840416	−	0.0466968i
$937$	30.6142	−	30.6142i	1.00012	−	1.00012i	0.000123448	−	1.00000i	$-0.499961\pi$
$937$	30.6142	−	30.6142i	1.00012	−	1.00012i	1.00000		0.000123448i	$-3.92947e-5\pi$
$938$	2.77168	−	2.77168i	0.0904985	−	0.0904985i
$939$	1.20328	+	0.107416i	0.0392674	+	0.00350538i
$940$	−6.68233	−	1.16652i	−0.217954	−	0.0380478i
$941$		−	6.27661i		−	0.204611i	−0.994753	−	0.102306i	$-0.967378\pi$
$941$		−	6.27661i		−	0.204611i	0.994753	−	0.102306i	$-0.0326220\pi$
$942$	0.0835037	−	0.0698168i	0.00272070	−	0.00227476i
$943$	−29.5554	−	29.5554i	−0.962456	−	0.962456i
$944$	−1.27397			−0.0414641
$945$	−7.26744	−	20.1927i	−0.236410	−	0.656867i
$946$	−64.4544			−2.09559
$947$	7.98043	+	7.98043i	0.259329	+	0.259329i	0.824781	−	0.565452i	$-0.191298\pi$
$947$	7.98043	+	7.98043i	0.259329	+	0.259329i	−0.565452	+	0.824781i	$0.691298\pi$
$948$	6.95041	−	5.81119i	0.225739	−	0.188739i
$949$		−	1.87248i		−	0.0607833i
$950$	2.12854	+	4.52430i	0.0690590	+	0.146788i
$951$	−41.4167	−	3.69724i	−1.34303	−	0.119891i
$952$	−7.84995	+	7.84995i	−0.254418	+	0.254418i
$953$	−12.3683	+	12.3683i	−0.400650	+	0.400650i	−0.878462	−	0.477812i	$-0.841430\pi$
$953$	−12.3683	+	12.3683i	−0.400650	+	0.400650i	0.477812	+	0.878462i	$0.341430\pi$
$954$	6.14403	−	34.1386i	0.198920	−	1.10528i
$955$	−22.5439	+	15.8428i	−0.729504	+	0.512661i
$956$		−	24.4016i		−	0.789205i
$957$	50.0139	+	59.8185i	1.61672	+	1.93366i
$958$	−18.1569	−	18.1569i	−0.586624	−	0.586624i
$959$	−28.7351			−0.927906
$960$	1.00263	−	3.74095i	0.0323597	−	0.120739i
$961$	70.9857			2.28986
$962$	−0.153591	−	0.153591i	−0.00495197	−	0.00495197i
$963$	−7.22710	+	5.02250i	−0.232890	+	0.161848i
$964$		−	15.4813i		−	0.498618i
$965$	−6.44978	+	36.9470i	−0.207626	+	1.18937i
$966$	1.33708	−	14.9780i	0.0430198	−	0.481910i
$967$	−17.7605	+	17.7605i	−0.571140	+	0.571140i	−0.932447	−	0.361307i	$-0.882331\pi$
$967$	−17.7605	+	17.7605i	−0.571140	+	0.571140i	0.361307	+	0.932447i	$0.382331\pi$
$968$	−10.9844	+	10.9844i	−0.353052	+	0.353052i
$969$	−0.925647	+	10.3691i	−0.0297361	+	0.333105i
$970$	7.31993	+	10.4161i	0.235029	+	0.334440i
$971$		−	22.5253i		−	0.722872i	−0.932397	−	0.361436i	$-0.882287\pi$
$971$		−	22.5253i		−	0.722872i	0.932397	−	0.361436i	$-0.117713\pi$
$972$	5.20195	+	14.6949i	0.166853	+	0.471339i
$973$	1.61104	+	1.61104i	0.0516476	+	0.0516476i
$974$	14.3226			0.458925
$975$	1.76469	−	3.80071i	0.0565154	−	0.121720i
$976$	6.26456			0.200524
$977$	32.1177	+	32.1177i	1.02754	+	1.02754i	0.999610	+	0.0279276i	$0.00889078\pi$
$977$	32.1177	+	32.1177i	1.02754	+	1.02754i	0.0279276	+	0.999610i	$0.491109\pi$
$978$	14.1365	+	16.9078i	0.452035	+	0.540652i
$979$			83.9020i			2.68152i
$980$	4.61359	+	6.56503i	0.147376	+	0.209712i
$981$	13.2036	+	2.37629i	0.421558	+	0.0758691i
$982$	13.6115	−	13.6115i	0.434361	−	0.434361i
$983$	−2.22712	+	2.22712i	−0.0710340	+	0.0710340i	−0.741731	−	0.670697i	$-0.765995\pi$
$983$	−2.22712	+	2.22712i	−0.0710340	+	0.0710340i	0.670697	+	0.741731i	$0.265995\pi$
$984$	15.3408	+	1.36946i	0.489047	+	0.0436569i
$985$	−1.94036	+	11.1152i	−0.0618250	+	0.354159i
$986$		−	52.5268i		−	1.67279i
$987$	7.44551	−	6.22514i	0.236993	−	0.198148i
$988$	−0.342145	−	0.342145i	−0.0108851	−	0.0108851i
$989$	−58.8153			−1.87022
$990$	−11.8778	+	32.4494i	−0.377502	+	1.03131i
$991$	−11.1667			−0.354723			−0.177361	−	0.984146i	$-0.556756\pi$
$991$	−11.1667			−0.354723			−0.177361	+	0.984146i	$0.556756\pi$
$992$	−7.14093	−	7.14093i	−0.226725	−	0.226725i
$993$	−19.5490	+	16.3448i	−0.620368	+	0.518685i
$994$		−	21.6230i		−	0.685840i
$995$	5.91270	−	4.15517i	0.187445	−	0.131728i
$996$	−24.1187	−	2.15306i	−0.764229	−	0.0682222i
$997$	−10.8789	+	10.8789i	−0.344538	+	0.344538i	−0.858070	−	0.513533i	$-0.828337\pi$
$997$	−10.8789	+	10.8789i	−0.344538	+	0.344538i	0.513533	+	0.858070i	$0.328337\pi$
$998$	13.8439	−	13.8439i	0.438220	−	0.438220i
$999$	2.24987	+	0.615651i	0.0711827	+	0.0194783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.b.533.3	yes	36
3.2	odd	2	inner	570.2.k.b.533.16	yes	36
5.2	odd	4	inner	570.2.k.b.77.16	yes	36
15.2	even	4	inner	570.2.k.b.77.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.3	✓	36	15.2	even	4	inner
570.2.k.b.77.16	yes	36	5.2	odd	4	inner
570.2.k.b.533.3	yes	36	1.1	even	1	trivial
570.2.k.b.533.16	yes	36	3.2	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.32879 + 1.11099i) q^{3} +1.00000i q^{4} +(-1.28568 - 1.82949i) q^{5} +(1.72519 + 0.154007i) q^{6} +(1.30605 - 1.30605i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.531382 - 2.95256i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.32879 + 1.11099i) q^{3} +1.00000i q^{4} +(-1.28568 - 1.82949i) q^{5} +(1.72519 + 0.154007i) q^{6} +(1.30605 - 1.30605i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.531382 - 2.95256i) q^{9} +(-0.384532 + 2.20276i) q^{10} +5.15114i q^{11} +(-1.11099 - 1.32879i) q^{12} +(0.342145 + 0.342145i) q^{13} -1.84704 q^{14} +(3.74095 + 1.00263i) q^{15} -1.00000 q^{16} +(-4.25002 - 4.25002i) q^{17} +(-2.46352 + 1.71203i) q^{18} +1.00000i q^{19} +(1.82949 - 1.28568i) q^{20} +(-0.284456 + 3.18649i) q^{21} +(3.64241 - 3.64241i) q^{22} +(3.32373 - 3.32373i) q^{23} +(-0.154007 + 1.72519i) q^{24} +(-1.69406 + 4.70427i) q^{25} -0.483866i q^{26} +(2.57419 + 4.51371i) q^{27} +(1.30605 + 1.30605i) q^{28} -8.73926 q^{29} +(-1.93629 - 3.35422i) q^{30} -10.0988 q^{31} +(0.707107 + 0.707107i) q^{32} +(-5.72289 - 6.84480i) q^{33} +6.01044i q^{34} +(-4.06858 - 0.710245i) q^{35} +(2.95256 + 0.531382i) q^{36} +(0.317424 - 0.317424i) q^{37} +(0.707107 - 0.707107i) q^{38} +(-0.834762 - 0.0745186i) q^{39} +(-2.20276 - 0.384532i) q^{40} -8.89223i q^{41} +(2.45433 - 2.05205i) q^{42} +(-8.84777 - 8.84777i) q^{43} -5.15114 q^{44} +(-6.08487 + 2.82389i) q^{45} -4.70047 q^{46} +(-2.14509 - 2.14509i) q^{47} +(1.32879 - 1.11099i) q^{48} +3.58845i q^{49} +(4.52430 - 2.12854i) q^{50} +(10.3691 + 0.925647i) q^{51} +(-0.342145 + 0.342145i) q^{52} +(-8.17583 + 8.17583i) q^{53} +(1.37145 - 5.01190i) q^{54} +(9.42396 - 6.62272i) q^{55} -1.84704i q^{56} +(-1.11099 - 1.32879i) q^{57} +(6.17959 + 6.17959i) q^{58} +1.27397 q^{59} +(-1.00263 + 3.74095i) q^{60} -6.26456 q^{61} +(7.14093 + 7.14093i) q^{62} +(-3.16219 - 4.55022i) q^{63} -1.00000i q^{64} +(0.186062 - 1.06584i) q^{65} +(-0.793310 + 8.88670i) q^{66} +(-1.50061 + 1.50061i) q^{67} +(4.25002 - 4.25002i) q^{68} +(-0.723903 + 8.10920i) q^{69} +(2.37470 + 3.37914i) q^{70} +11.7068i q^{71} +(-1.71203 - 2.46352i) q^{72} +(-2.73639 - 2.73639i) q^{73} -0.448905 q^{74} +(-2.97537 - 8.13309i) q^{75} -1.00000 q^{76} +(6.72767 + 6.72767i) q^{77} +(0.537573 + 0.642958i) q^{78} +5.23062i q^{79} +(1.28568 + 1.82949i) q^{80} +(-8.43527 - 3.13788i) q^{81} +(-6.28776 + 6.28776i) q^{82} +(9.88555 - 9.88555i) q^{83} +(-3.18649 - 0.284456i) q^{84} +(-2.31120 + 13.2395i) q^{85} +12.5126i q^{86} +(11.6127 - 9.70927i) q^{87} +(3.64241 + 3.64241i) q^{88} +16.2880 q^{89} +(6.29945 + 2.30586i) q^{90} +0.893720 q^{91} +(3.32373 + 3.32373i) q^{92} +(13.4192 - 11.2197i) q^{93} +3.03362i q^{94} +(1.82949 - 1.28568i) q^{95} +(-1.72519 - 0.154007i) q^{96} +(4.02586 - 4.02586i) q^{97} +(2.53742 - 2.53742i) q^{98} +(15.2091 + 2.73722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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