LMFDB - Embedded newform 570.2.k.b.77.3

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			77.3
Character	$\chi$	$=$	570.77
Dual form			570.2.k.b.533.3

$q$-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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

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	0.909452	−	0.415810i	$-0.136502\pi$
$7$	1.30605	+	1.30605i	0.493642	+	0.493642i	−0.415810	+	0.909452i	$0.636502\pi$
$8$	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	$-0.716961\pi$
$11$		−	5.15114i		−	1.55313i	0.630038	−	0.776564i	$-0.283039\pi$
$12$	−1.11099	+	1.32879i	−0.320717	+	0.383589i
$13$	0.342145	−	0.342145i	0.0948940	−	0.0948940i	−0.658066	−	0.752960i	$-0.728625\pi$
$13$	0.342145	−	0.342145i	0.0948940	−	0.0948940i	0.752960	+	0.658066i	$0.228625\pi$
$14$	−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	−0.0312704	+	0.999511i	$0.509955\pi$
$17$	−4.25002	+	4.25002i	−1.03078	+	1.03078i	−0.999511	+	0.0312704i	$0.990045\pi$
$18$	−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	0.962901	−	0.269855i	$-0.0869757\pi$
$23$	3.32373	+	3.32373i	0.693046	+	0.693046i	−0.269855	+	0.962901i	$0.586976\pi$
$24$	−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	0.732717	−	0.680533i	$-0.238252\pi$
$37$	0.317424	+	0.317424i	0.0521842	+	0.0521842i	−0.680533	+	0.732717i	$0.738252\pi$
$38$	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	$0.244315\pi$
$41$			8.89223i			1.38873i	−0.719622	+	0.694366i	$0.755685\pi$
$42$	2.45433	+	2.05205i	0.378712	+	0.316638i
$43$	−8.84777	+	8.84777i	−1.34927	+	1.34927i	−0.462820	+	0.886452i	$0.653162\pi$
$43$	−8.84777	+	8.84777i	−1.34927	+	1.34927i	−0.886452	+	0.462820i	$0.846838\pi$
$44$	−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	−0.846030	−	0.533136i	$-0.821014\pi$
$47$	−2.14509	+	2.14509i	−0.312894	+	0.312894i	0.533136	+	0.846030i	$0.321014\pi$
$48$	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	−0.991283	−	0.131754i	$-0.957939\pi$
$53$	−8.17583	−	8.17583i	−1.12304	−	1.12304i	−0.131754	−	0.991283i	$-0.542061\pi$
$54$	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	0.609476	−	0.792804i	$-0.291380\pi$
$67$	−1.50061	−	1.50061i	−0.183328	−	0.183328i	−0.792804	+	0.609476i	$0.791380\pi$
$68$	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	$-0.755549\pi$
$71$		−	11.7068i		−	1.38935i	0.719325	−	0.694674i	$-0.244451\pi$
$72$	−1.71203	+	2.46352i	−0.201765	+	0.290329i
$73$	−2.73639	+	2.73639i	−0.320270	+	0.320270i	−0.848871	−	0.528601i	$-0.822717\pi$
$73$	−2.73639	+	2.73639i	−0.320270	+	0.320270i	0.528601	+	0.848871i	$0.322717\pi$
$74$	−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	$-0.904932\pi$
$79$		−	5.23062i		−	0.588491i	0.955730	−	0.294246i	$-0.0950683\pi$
$80$	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	0.996027	+	0.0890537i	$0.0283843\pi$
$83$	9.88555	+	9.88555i	1.08508	+	1.08508i	0.0890537	+	0.996027i	$0.471616\pi$
$84$	−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	0.881308	−	0.472543i	$-0.156664\pi$
$97$	4.02586	+	4.02586i	0.408765	+	0.408765i	−0.472543	+	0.881308i	$0.656664\pi$
$98$	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	$-0.941360\pi$
$101$		−	3.68192i		−	0.366365i	0.983079	−	0.183183i	$-0.0586400\pi$
$102$	−6.67756	+	7.98663i	−0.661177	+	0.790794i
$103$	−5.58428	+	5.58428i	−0.550235	+	0.550235i	−0.926509	−	0.376273i	$-0.877205\pi$
$103$	−5.58428	+	5.58428i	−0.550235	+	0.550235i	0.376273	+	0.926509i	$0.377205\pi$
$104$	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	−0.800231	−	0.599691i	$-0.795290\pi$
$107$	−2.07440	+	2.07440i	−0.200540	+	0.200540i	0.599691	+	0.800231i	$0.295290\pi$
$108$	−4.51371	−	2.57419i	−0.434332	−	0.247701i
$109$		−	4.47191i		−	0.428331i	−0.976797	−	0.214165i	$-0.931297\pi$
$109$		−	4.47191i		−	0.428331i	0.976797	−	0.214165i	$-0.0687032\pi$
$110$	−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	0.349735	−	0.936849i	$-0.386272\pi$
$113$	−6.24110	−	6.24110i	−0.587114	−	0.587114i	−0.936849	+	0.349735i	$0.886272\pi$
$114$	−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	0.783333	−	0.621603i	$-0.213518\pi$
$127$	1.82261	+	1.82261i	0.161730	+	0.161730i	−0.621603	+	0.783333i	$0.713518\pi$
$128$	−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	$0.166238\pi$
$131$			11.4188i			0.997666i	−0.866698	+	0.498833i	$0.833762\pi$
$132$	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	−0.998291	−	0.0584339i	$-0.981389\pi$
$137$	−11.0007	+	11.0007i	−0.939857	+	0.939857i	0.0584339	+	0.998291i	$0.481389\pi$
$138$	6.24595	+	5.22220i	0.531690	+	0.444543i
$139$		−	1.23352i		−	0.104626i	−0.998631	−	0.0523128i	$-0.983341\pi$
$139$		−	1.23352i		−	0.104626i	0.998631	−	0.0523128i	$-0.0166593\pi$
$140$	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	0.708878	−	0.705331i	$-0.249202\pi$
$157$	0.0444358	+	0.0444358i	0.00354636	+	0.00354636i	−0.705331	+	0.708878i	$0.749202\pi$
$158$	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	−0.260694	−	0.965421i	$-0.583952\pi$
$163$	8.99735	−	8.99735i	0.704727	−	0.704727i	0.965421	+	0.260694i	$0.0839515\pi$
$164$	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	−0.660181	−	0.751107i	$-0.729520\pi$
$167$	1.17503	−	1.17503i	0.0909264	−	0.0909264i	0.751107	+	0.660181i	$0.229520\pi$
$168$	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	−0.999403	−	0.0345455i	$-0.989002\pi$
$173$	−13.5995	−	13.5995i	−1.03395	−	1.03395i	−0.0345455	−	0.999403i	$-0.510998\pi$
$174$	−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	$0.147085\pi$
$191$			12.3225i			0.891626i	−0.895126	+	0.445813i	$0.852915\pi$
$192$	1.11099	−	1.32879i	0.0801791	−	0.0958974i
$193$	−11.8604	+	11.8604i	−0.853728	+	0.853728i	−0.990590	−	0.136862i	$-0.956298\pi$
$193$	−11.8604	+	11.8604i	−0.853728	+	0.853728i	0.136862	+	0.990590i	$0.456298\pi$
$194$	−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	−0.822696	−	0.568481i	$-0.807531\pi$
$197$	−3.56808	+	3.56808i	−0.254215	+	0.254215i	0.568481	+	0.822696i	$0.307531\pi$
$198$	−8.81894	+	12.6900i	−0.626735	+	0.901836i
$199$		−	3.23189i		−	0.229102i	−0.993417	−	0.114551i	$-0.963457\pi$
$199$		−	3.23189i		−	0.229102i	0.993417	−	0.114551i	$-0.0365430\pi$
$200$	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	−0.563050	−	0.826423i	$-0.690372\pi$
$223$	3.93298	−	3.93298i	0.263372	−	0.263372i	0.826423	+	0.563050i	$0.190372\pi$
$224$	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	−0.525184	−	0.850989i	$-0.676003\pi$
$227$	4.90875	−	4.90875i	0.325805	−	0.325805i	0.850989	+	0.525184i	$0.176003\pi$
$228$	1.32879	+	1.11099i	0.0880015	+	0.0735774i
$229$			0.309162i			0.0204300i	0.999948	+	0.0102150i	$0.00325159\pi$
$229$			0.309162i			0.0204300i	−0.999948	+	0.0102150i	$0.996748\pi$
$230$	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	0.742150	−	0.670233i	$-0.233806\pi$
$233$	1.09776	+	1.09776i	0.0719169	+	0.0719169i	−0.670233	+	0.742150i	$0.733806\pi$
$234$	−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	$0.106279\pi$
$251$			10.3840i			0.655435i	−0.944776	+	0.327718i	$0.893721\pi$
$252$	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	−0.316634	−	0.948548i	$-0.602553\pi$
$257$	10.1303	−	10.1303i	0.631914	−	0.631914i	0.948548	+	0.316634i	$0.102553\pi$
$258$	−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	−0.983632	−	0.180189i	$-0.942329\pi$
$263$	−18.8740	−	18.8740i	−1.16382	−	1.16382i	−0.180189	−	0.983632i	$-0.557671\pi$
$264$	−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	0.988796	−	0.149276i	$-0.0476942\pi$
$277$	13.9724	+	13.9724i	0.839520	+	0.839520i	−0.149276	+	0.988796i	$0.547694\pi$
$278$	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	$0.257121\pi$
$281$			24.2309i			1.44549i	−0.691113	+	0.722747i	$0.742879\pi$
$282$	−3.37034	+	4.03105i	−0.200701	+	0.240046i
$283$	9.26434	−	9.26434i	0.550708	−	0.550708i	−0.375937	−	0.926645i	$-0.622679\pi$
$283$	9.26434	−	9.26434i	0.550708	−	0.550708i	0.926645	+	0.375937i	$0.122679\pi$
$284$	−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	0.393284	−	0.919417i	$-0.371339\pi$
$293$	−9.00595	−	9.00595i	−0.526133	−	0.526133i	−0.919417	+	0.393284i	$0.871339\pi$
$294$	−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	0.821247	−	0.570572i	$-0.193279\pi$
$307$	4.39219	+	4.39219i	0.250675	+	0.250675i	−0.570572	+	0.821247i	$0.693279\pi$
$308$	−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	$0.151430\pi$
$311$			16.1534i			0.915975i	−0.888959	+	0.457988i	$0.848570\pi$
$312$	−0.642958	−	0.537573i	−0.0364003	−	0.0304341i
$313$	−0.493189	+	0.493189i	−0.0278767	+	0.0278767i	−0.720908	−	0.693031i	$-0.756275\pi$
$313$	−0.493189	+	0.493189i	−0.0278767	+	0.0278767i	0.693031	+	0.720908i	$0.256275\pi$
$314$	−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	−0.0455227	−	0.998963i	$-0.514495\pi$
$317$	16.9755	−	16.9755i	0.953441	−	0.953441i	0.998963	+	0.0455227i	$0.0144953\pi$
$318$	−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	0.975736	−	0.218949i	$-0.0702629\pi$
$337$	13.8928	+	13.8928i	0.756787	+	0.756787i	−0.218949	+	0.975736i	$0.570263\pi$
$338$	−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	−0.137245	+	0.990537i	$0.543825\pi$
$347$	−21.0082	+	21.0082i	−1.12778	+	1.12778i	−0.990537	+	0.137245i	$0.956175\pi$
$348$	9.70927	−	11.6127i	0.520472	−	0.622504i
$349$		−	18.0913i		−	0.968404i	−0.874956	−	0.484202i	$-0.839110\pi$
$349$		−	18.0913i		−	0.968404i	0.874956	−	0.484202i	$-0.160890\pi$
$350$	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	0.427385	−	0.904070i	$-0.359435\pi$
$353$	−8.95609	−	8.95609i	−0.476685	−	0.476685i	−0.904070	+	0.427385i	$0.859435\pi$
$354$	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	0.767886	−	0.640587i	$-0.221309\pi$
$367$	2.43869	+	2.43869i	0.127299	+	0.127299i	−0.640587	+	0.767886i	$0.721309\pi$
$368$	−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	−0.0962879	+	0.995354i	$0.530697\pi$
$373$	−21.0831	+	21.0831i	−1.09164	+	1.09164i	−0.995354	+	0.0962879i	$0.969303\pi$
$374$	−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	$0.0184364\pi$
$379$			2.25390i			0.115775i	−0.998323	+	0.0578874i	$0.981564\pi$
$380$	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	0.588932	−	0.808182i	$-0.299548\pi$
$383$	−4.29081	−	4.29081i	−0.219250	−	0.219250i	−0.808182	+	0.588932i	$0.799548\pi$
$384$	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	0.861657	−	0.507491i	$-0.169427\pi$
$397$	7.05671	+	7.05671i	0.354166	+	0.354166i	−0.507491	+	0.861657i	$0.669427\pi$
$398$	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	$-0.971465\pi$
$401$		−	3.58548i		−	0.179050i	0.995985	−	0.0895252i	$-0.0285350\pi$
$402$	−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	$0.131289\pi$
$409$			16.2138i			0.801720i	−0.916139	+	0.400860i	$0.868711\pi$
$410$	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	$-0.664490\pi$
$431$		−	36.0994i		−	1.73885i	0.494067	−	0.869424i	$-0.335510\pi$
$432$	−2.57419	+	4.51371i	−0.123851	+	0.217166i
$433$	8.42713	−	8.42713i	0.404982	−	0.404982i	−0.475003	−	0.879984i	$-0.657553\pi$
$433$	8.42713	−	8.42713i	0.404982	−	0.404982i	0.879984	+	0.475003i	$0.157553\pi$
$434$	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	$0.0512242\pi$
$439$			6.71446i			0.320464i	−0.987079	+	0.160232i	$0.948776\pi$
$440$	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	0.232157	−	0.972678i	$-0.425422\pi$
$443$	−15.5862	−	15.5862i	−0.740522	−	0.740522i	−0.972678	+	0.232157i	$0.925422\pi$
$444$	−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	0.627075	−	0.778959i	$-0.284252\pi$
$457$	−3.24691	−	3.24691i	−0.151884	−	0.151884i	−0.778959	+	0.627075i	$0.784252\pi$
$458$	−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	$0.262208\pi$
$461$			31.5064i			1.46740i	−0.679473	+	0.733700i	$0.737792\pi$
$462$	10.5704	−	12.6426i	0.491780	−	0.588188i
$463$	−8.81741	+	8.81741i	−0.409780	+	0.409780i	−0.881662	−	0.471882i	$-0.843575\pi$
$463$	−8.81741	+	8.81741i	−0.409780	+	0.409780i	0.471882	+	0.881662i	$0.343575\pi$
$464$	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	−0.794385	−	0.607414i	$-0.792207\pi$
$467$	−4.04048	+	4.04048i	−0.186971	+	0.186971i	0.607414	+	0.794385i	$0.292207\pi$
$468$	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	0.439377	−	0.898303i	$-0.355199\pi$
$487$	−10.1276	−	10.1276i	−0.458925	−	0.458925i	−0.898303	+	0.439377i	$0.855199\pi$
$488$	−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	$-0.856974\pi$
$491$		−	19.2496i		−	0.868723i	0.900739	−	0.434361i	$-0.143026\pi$
$492$	−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	$-0.855609\pi$
$499$		−	19.5782i		−	0.876439i	0.898868	−	0.438220i	$-0.144391\pi$
$500$	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	0.983939	−	0.178505i	$-0.0571262\pi$
$503$	18.0640	+	18.0640i	0.805434	+	0.805434i	−0.178505	+	0.983939i	$0.557126\pi$
$504$	−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	$0.137694\pi$
$521$			19.1374i			0.838425i	−0.907888	+	0.419213i	$0.862306\pi$
$522$	21.5294	+	14.9619i	0.942315	+	0.654865i
$523$	−3.69849	+	3.69849i	−0.161724	+	0.161724i	−0.783330	−	0.621606i	$-0.786480\pi$
$523$	−3.69849	+	3.69849i	−0.161724	+	0.161724i	0.621606	+	0.783330i	$0.286480\pi$
$524$	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	0.836777	−	0.547545i	$-0.184437\pi$
$547$	6.76457	+	6.76457i	0.289232	+	0.289232i	−0.547545	+	0.836777i	$0.684437\pi$
$548$	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	−0.519012	−	0.854767i	$-0.673700\pi$
$557$	7.92409	−	7.92409i	0.335754	−	0.335754i	0.854767	+	0.519012i	$0.173700\pi$
$558$	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	0.652289	−	0.757970i	$-0.273809\pi$
$563$	−2.50755	−	2.50755i	−0.105681	−	0.105681i	−0.757970	+	0.652289i	$0.773809\pi$
$564$	−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	0.999085	−	0.0427697i	$-0.0136182\pi$
$577$	22.9715	+	22.9715i	0.956315	+	0.956315i	−0.0427697	+	0.999085i	$0.513618\pi$
$578$	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	−0.988983	−	0.148032i	$-0.952706\pi$
$587$	−20.3746	+	20.3746i	−0.840951	+	0.840951i	0.148032	+	0.988983i	$0.452706\pi$
$588$	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	0.849122	−	0.528197i	$-0.177132\pi$
$593$	7.81504	+	7.81504i	0.320925	+	0.320925i	−0.528197	+	0.849122i	$0.677132\pi$
$594$	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	0.181669	−	0.983360i	$-0.441850\pi$
$607$	−19.7516	−	19.7516i	−0.801691	−	0.801691i	−0.983360	+	0.181669i	$0.941850\pi$
$608$	−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	−0.855663	−	0.517534i	$-0.826850\pi$
$613$	−8.37167	+	8.37167i	−0.338129	+	0.338129i	0.517534	+	0.855663i	$0.326850\pi$
$614$	−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	−0.976103	−	0.217308i	$-0.930272\pi$
$617$	−18.8481	+	18.8481i	−0.758795	+	0.758795i	0.217308	+	0.976103i	$0.430272\pi$
$618$	−8.77393	+	10.4940i	−0.352939	+	0.422129i
$619$		−	19.7510i		−	0.793860i	−0.917849	−	0.396930i	$-0.870076\pi$
$619$		−	19.7510i		−	0.793860i	0.917849	−	0.396930i	$-0.129924\pi$
$620$	−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	$-0.894779\pi$
$641$		−	16.4351i		−	0.649146i	0.945861	−	0.324573i	$-0.105221\pi$
$642$	−3.25926	+	3.89821i	−0.128633	+	0.153850i
$643$	16.1113	−	16.1113i	0.635369	−	0.635369i	−0.314041	−	0.949409i	$-0.601683\pi$
$643$	16.1113	−	16.1113i	0.635369	−	0.635369i	0.949409	+	0.314041i	$0.101683\pi$
$644$	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	0.422570	−	0.906330i	$-0.361128\pi$
$647$	33.8022	−	33.8022i	1.32890	−	1.32890i	0.906330	−	0.422570i	$-0.138872\pi$
$648$	−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	0.566453	−	0.824094i	$-0.308315\pi$
$653$	−6.58374	−	6.58374i	−0.257642	−	0.257642i	−0.824094	+	0.566453i	$0.808315\pi$
$654$	−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	−0.997385	−	0.0722701i	$-0.976976\pi$
$673$	−23.9996	+	23.9996i	−0.925115	+	0.925115i	0.0722701	+	0.997385i	$0.476976\pi$
$674$	−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	−0.970359	−	0.241668i	$-0.922305\pi$
$677$	−18.9600	+	18.9600i	−0.728691	+	0.728691i	0.241668	+	0.970359i	$0.422305\pi$
$678$	−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	0.828217	−	0.560407i	$-0.189355\pi$
$683$	6.99901	+	6.99901i	0.267810	+	0.267810i	−0.560407	+	0.828217i	$0.689355\pi$
$684$	−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	$-0.645534\pi$
$701$		−	47.5139i		−	1.79458i	0.441445	−	0.897288i	$-0.354466\pi$
$702$	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	$0.227486\pi$
$709$			34.9010i			1.31073i	−0.755311	+	0.655367i	$0.772514\pi$
$710$	−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	0.957586	−	0.288147i	$-0.0930393\pi$
$727$	18.0500	+	18.0500i	0.669439	+	0.669439i	−0.288147	+	0.957586i	$0.593039\pi$
$728$	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	−0.862637	−	0.505824i	$-0.831188\pi$
$733$	−9.66033	+	9.66033i	−0.356812	+	0.356812i	0.505824	+	0.862637i	$0.331188\pi$
$734$	−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	$-0.966706\pi$
$739$		−	5.67646i		−	0.208812i	0.994535	−	0.104406i	$-0.0332941\pi$
$740$	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	−0.985804	−	0.167901i	$-0.946301\pi$
$743$	−31.4477	−	31.4477i	−1.15370	−	1.15370i	−0.167901	−	0.985804i	$-0.553699\pi$
$744$	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	0.338266	−	0.941051i	$-0.390160\pi$
$757$	−16.5848	−	16.5848i	−0.602785	−	0.602785i	−0.941051	+	0.338266i	$0.890160\pi$
$758$	−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	$-0.781953\pi$
$761$		−	34.9067i		−	1.26537i	0.774411	−	0.632683i	$-0.218047\pi$
$762$	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	$0.239176\pi$
$769$			37.8613i			1.36531i	−0.730739	+	0.682657i	$0.760824\pi$
$770$	−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	0.435635	−	0.900123i	$-0.356524\pi$
$773$	−12.9141	−	12.9141i	−0.464488	−	0.464488i	−0.900123	+	0.435635i	$0.856524\pi$
$774$	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	0.472015	−	0.881590i	$-0.343527\pi$
$787$	−11.4900	−	11.4900i	−0.409575	−	0.409575i	−0.881590	+	0.472015i	$0.843527\pi$
$788$	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	−0.998198	−	0.0600027i	$-0.980889\pi$
$797$	−26.4864	+	26.4864i	−0.938196	+	0.938196i	0.0600027	+	0.998198i	$0.480889\pi$
$798$	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	$0.0660117\pi$
$821$			11.7993i			0.411797i	−0.978573	+	0.205899i	$0.933988\pi$
$822$	−17.2842	+	20.6726i	−0.602856	+	0.721039i
$823$	2.49272	−	2.49272i	0.0868909	−	0.0868909i	−0.662325	−	0.749216i	$-0.730430\pi$
$823$	2.49272	−	2.49272i	0.0868909	−	0.0868909i	0.749216	+	0.662325i	$0.230430\pi$
$824$	−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	−0.842408	−	0.538839i	$-0.818863\pi$
$827$	−8.72992	+	8.72992i	−0.303569	+	0.303569i	0.538839	+	0.842408i	$0.318863\pi$
$828$	11.5797	+	8.04736i	0.402423	+	0.279665i
$829$			3.58566i			0.124535i	0.998059	+	0.0622676i	$0.0198332\pi$
$829$			3.58566i			0.124535i	−0.998059	+	0.0622676i	$0.980167\pi$
$830$	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	−0.975148	−	0.221556i	$-0.928886\pi$
$853$	−22.0095	+	22.0095i	−0.753591	+	0.753591i	0.221556	+	0.975148i	$0.428886\pi$
$854$	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	−0.475150	−	0.879905i	$-0.657606\pi$
$857$	11.8490	−	11.8490i	0.404754	−	0.404754i	0.879905	+	0.475150i	$0.157606\pi$
$858$	−3.31197	−	2.76912i	−0.113069	−	0.0945361i
$859$		−	24.7373i		−	0.844025i	−0.906590	−	0.422013i	$-0.861324\pi$
$859$		−	24.7373i		−	0.844025i	0.906590	−	0.422013i	$-0.138676\pi$
$860$	−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	0.923456	−	0.383704i	$-0.125352\pi$
$863$	15.8562	+	15.8562i	0.539752	+	0.539752i	−0.383704	+	0.923456i	$0.625352\pi$
$864$	−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	0.620507	−	0.784201i	$-0.286927\pi$
$877$	−4.84768	−	4.84768i	−0.163694	−	0.163694i	−0.784201	+	0.620507i	$0.786927\pi$
$878$	−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	$0.246682\pi$
$881$			41.5364i			1.39940i	−0.714439	+	0.699698i	$0.753318\pi$
$882$	−6.14355	+	8.84022i	−0.206864	+	0.297666i
$883$	39.1569	−	39.1569i	1.31773	−	1.31773i	0.402167	−	0.915566i	$-0.368257\pi$
$883$	39.1569	−	39.1569i	1.31773	−	1.31773i	0.915566	−	0.402167i	$-0.131743\pi$
$884$	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	−0.967981	−	0.251023i	$-0.919233\pi$
$887$	−21.3528	+	21.3528i	−0.716958	+	0.716958i	0.251023	+	0.967981i	$0.419233\pi$
$888$	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	0.502866	−	0.864364i	$-0.332279\pi$
$907$	−10.8871	−	10.8871i	−0.361499	−	0.361499i	−0.864364	+	0.502866i	$0.832279\pi$
$908$	−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	$-0.905136\pi$
$911$		−	17.7253i		−	0.587264i	0.955919	−	0.293632i	$-0.0948640\pi$
$912$	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	$-0.758928\pi$
$919$		−	41.6528i		−	1.37400i	0.726658	−	0.686999i	$-0.241072\pi$
$920$	−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	1.00000		0.000123448i	$3.92947e-5\pi$
$937$	30.6142	+	30.6142i	1.00012	+	1.00012i	0.000123448		1.00000i	$0.499961\pi$
$938$	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	$0.0326220\pi$
$941$			6.27661i			0.204611i	−0.994753	+	0.102306i	$0.967378\pi$
$942$	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	−0.565452	−	0.824781i	$-0.691298\pi$
$947$	7.98043	−	7.98043i	0.259329	−	0.259329i	0.824781	+	0.565452i	$0.191298\pi$
$948$	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	0.477812	−	0.878462i	$-0.341430\pi$
$953$	−12.3683	−	12.3683i	−0.400650	−	0.400650i	−0.878462	+	0.477812i	$0.841430\pi$
$954$	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	0.361307	−	0.932447i	$-0.382331\pi$
$967$	−17.7605	−	17.7605i	−0.571140	−	0.571140i	−0.932447	+	0.361307i	$0.882331\pi$
$968$	−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	$0.117713\pi$
$971$			22.5253i			0.722872i	−0.932397	+	0.361436i	$0.882287\pi$
$972$	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	0.0279276	−	0.999610i	$-0.491109\pi$
$977$	32.1177	−	32.1177i	1.02754	−	1.02754i	0.999610	−	0.0279276i	$-0.00889078\pi$
$978$	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	0.670697	−	0.741731i	$-0.265995\pi$
$983$	−2.22712	−	2.22712i	−0.0710340	−	0.0710340i	−0.741731	+	0.670697i	$0.765995\pi$
$984$	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	0.513533	−	0.858070i	$-0.328337\pi$
$997$	−10.8789	−	10.8789i	−0.344538	−	0.344538i	−0.858070	+	0.513533i	$0.828337\pi$
$998$	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.77.3	✓	36
3.2	odd	2	inner	570.2.k.b.77.16	yes	36
5.3	odd	4	inner	570.2.k.b.533.16	yes	36
15.8	even	4	inner	570.2.k.b.533.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.3	✓	36	1.1	even	1	trivial
570.2.k.b.77.16	yes	36	3.2	odd	2	inner
570.2.k.b.533.3	yes	36	15.8	even	4	inner
570.2.k.b.533.16	yes	36	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
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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