LMFDB - Embedded newform 570.2.k.b.533.16

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			533.16
Character	$\chi$	$=$	570.533
Dual form			570.2.k.b.77.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.11099 - 1.32879i) q^{3} +1.00000i q^{4} +(1.28568 + 1.82949i) q^{5} +(1.72519 - 0.154007i) q^{6} +(1.30605 - 1.30605i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.531382 - 2.95256i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.11099 - 1.32879i) 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} +(1.32879 + 1.11099i) q^{12} +(0.342145 + 0.342145i) q^{13} +1.84704 q^{14} +(3.85939 + 0.324151i) q^{15} -1.00000 q^{16} +(4.25002 + 4.25002i) q^{17} +(1.71203 - 2.46352i) 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} +(-4.51371 - 2.57419i) q^{27} +(1.30605 + 1.30605i) q^{28} +8.73926 q^{29} +(2.49979 + 2.95821i) q^{30} -10.0988 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-6.84480 - 5.72289i) 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} +(2.05205 - 2.45433i) q^{42} +(-8.84777 - 8.84777i) q^{43} +5.15114 q^{44} +(4.71850 - 4.76821i) q^{45} -4.70047 q^{46} +(2.14509 + 2.14509i) q^{47} +(-1.11099 + 1.32879i) 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} +(1.32879 + 1.11099i) q^{57} +(6.17959 + 6.17959i) q^{58} -1.27397 q^{59} +(-0.324151 + 3.85939i) q^{60} -6.26456 q^{61} +(-7.14093 - 7.14093i) q^{62} +(-4.55022 - 3.16219i) 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} +(2.46352 + 1.71203i) q^{72} +(-2.73639 - 2.73639i) q^{73} +0.448905 q^{74} +(4.36891 + 7.47747i) q^{75} -1.00000 q^{76} +(-6.72767 - 6.72767i) q^{77} +(0.642958 + 0.537573i) 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} +(9.70927 - 11.6127i) q^{87} +(3.64241 + 3.64241i) q^{88} -16.2880 q^{89} +(6.70811 - 0.0351501i) q^{90} +0.893720 q^{91} +(-3.32373 - 3.32373i) q^{92} +(-11.2197 + 13.4192i) 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
$3$	1.11099	−	1.32879i	0.641433	−	0.767179i
$3$	1.11099	−	1.32879i	0.641433	−	0.767179i
$4$			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	$-0.716961\pi$
$11$		−	5.15114i		−	1.55313i	0.630038	−	0.776564i	$-0.283039\pi$
$12$	1.32879	+	1.11099i	0.383589	+	0.320717i
$13$	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
$15$	3.85939	+	0.324151i	0.996491	+	0.0836954i
$16$	−1.00000			−0.250000
$17$	4.25002	+	4.25002i	1.03078	+	1.03078i	0.999511	+	0.0312704i	$0.00995530\pi$
$17$	4.25002	+	4.25002i	1.03078	+	1.03078i	0.0312704	+	0.999511i	$0.490045\pi$
$18$	1.71203	−	2.46352i	0.403530	−	0.580658i
$19$			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	$-0.913024\pi$
$23$	−3.32373	+	3.32373i	−0.693046	+	0.693046i	0.269855	+	0.962901i	$0.413024\pi$
$24$	0.154007	+	1.72519i	0.0314365	+	0.352153i
$25$	−1.69406	+	4.70427i	−0.338812	+	0.940854i
$26$			0.483866i			0.0948940i
$27$	−4.51371	−	2.57419i	−0.868664	−	0.495402i
$28$	1.30605	+	1.30605i	0.246821	+	0.246821i
$29$	8.73926			1.62284			0.811420	−	0.584463i	$-0.198695\pi$
$29$	8.73926			1.62284			0.811420	+	0.584463i	$0.198695\pi$
$30$	2.49979	+	2.95821i	0.456398	+	0.540093i
$31$	−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
$33$	−6.84480	−	5.72289i	−1.19153	−	0.996228i
$34$			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	$0.244315\pi$
$41$			8.89223i			1.38873i	−0.719622	+	0.694366i	$0.755685\pi$
$42$	2.05205	−	2.45433i	0.316638	−	0.378712i
$43$	−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
$45$	4.71850	−	4.76821i	0.703392	−	0.710802i
$46$	−4.70047			−0.693046
$47$	2.14509	+	2.14509i	0.312894	+	0.312894i	0.846030	−	0.533136i	$-0.178986\pi$
$47$	2.14509	+	2.14509i	0.312894	+	0.312894i	−0.533136	+	0.846030i	$0.678986\pi$
$48$	−1.11099	+	1.32879i	−0.160358	+	0.191795i
$49$			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	$-0.457939\pi$
$53$	8.17583	−	8.17583i	1.12304	−	1.12304i	0.991283	−	0.131754i	$-0.0420607\pi$
$54$	−1.37145	−	5.01190i	−0.186631	−	0.682033i
$55$	9.42396	−	6.62272i	1.27073	−	0.893007i
$56$			1.84704i			0.246821i
$57$	1.32879	+	1.11099i	0.176003	+	0.147155i
$58$	6.17959	+	6.17959i	0.811420	+	0.811420i
$59$	−1.27397			−0.165856			−0.0829282	−	0.996556i	$-0.526427\pi$
$59$	−1.27397			−0.165856			−0.0829282	+	0.996556i	$0.526427\pi$
$60$	−0.324151	+	3.85939i	−0.0418477	+	0.498246i
$61$	−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
$63$	−4.55022	−	3.16219i	−0.573274	−	0.398399i
$64$		−	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	$-0.755549\pi$
$71$		−	11.7068i		−	1.38935i	0.719325	−	0.694674i	$-0.244451\pi$
$72$	2.46352	+	1.71203i	0.290329	+	0.201765i
$73$	−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
$75$	4.36891	+	7.47747i	0.504478	+	0.863424i
$76$	−1.00000			−0.114708
$77$	−6.72767	−	6.72767i	−0.766689	−	0.766689i
$78$	0.642958	+	0.537573i	0.0728007	+	0.0608682i
$79$			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	$0.528384\pi$
$83$	−9.88555	+	9.88555i	−1.08508	+	1.08508i	−0.996027	+	0.0890537i	$0.971616\pi$
$84$	3.18649	−	0.284456i	0.347675	−	0.0310367i
$85$	−2.31120	+	13.2395i	−0.250685	+	1.43603i
$86$		−	12.5126i		−	1.34927i
$87$	9.70927	−	11.6127i	1.04094	−	1.24501i
$88$	3.64241	+	3.64241i	0.388282	+	0.388282i
$89$	−16.2880			−1.72653			−0.863264	−	0.504753i	$-0.831584\pi$
$89$	−16.2880			−1.72653			−0.863264	+	0.504753i	$0.831584\pi$
$90$	6.70811	−	0.0351501i	0.707097	−	0.00370514i
$91$	0.893720			0.0936873
$92$	−3.32373	−	3.32373i	−0.346523	−	0.346523i
$93$	−11.2197	+	13.4192i	−1.16343	+	1.39151i
$94$			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	$-0.941360\pi$
$101$		−	3.68192i		−	0.366365i	0.983079	−	0.183183i	$-0.0586400\pi$
$102$	7.98663	+	6.67756i	0.790794	+	0.661177i
$103$	−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
$105$	5.46393	−	4.61722i	0.533225	−	0.450594i
$106$	11.5624			1.12304
$107$	2.07440	+	2.07440i	0.200540	+	0.200540i	0.800231	−	0.599691i	$-0.204710\pi$
$107$	2.07440	+	2.07440i	0.200540	+	0.200540i	−0.599691	+	0.800231i	$0.704710\pi$
$108$	2.57419	−	4.51371i	0.247701	−	0.434332i
$109$			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	−0.349735	−	0.936849i	$-0.613728\pi$
$113$	6.24110	−	6.24110i	0.587114	−	0.587114i	0.936849	+	0.349735i	$0.113728\pi$
$114$	0.154007	+	1.72519i	0.0144240	+	0.161579i
$115$	−10.3540	−	1.80748i	−0.965514	−	0.168548i
$116$			8.73926i			0.811420i
$117$	0.828396	−	1.19202i	0.0765852	−	0.110202i
$118$	−0.900830	−	0.900830i	−0.0829282	−	0.0829282i
$119$	11.1015			1.01767
$120$	−2.95821	+	2.49979i	−0.270047	+	0.228199i
$121$	−15.5343			−1.41221
$122$	−4.42971	−	4.42971i	−0.401047	−	0.401047i
$123$	11.8159	+	9.87922i	1.06541	+	0.890779i
$124$		−	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	$0.166238\pi$
$131$			11.4188i			0.997666i	−0.866698	+	0.498833i	$0.833762\pi$
$132$	5.72289	−	6.84480i	0.498114	−	0.595764i
$133$	1.30605	+	1.30605i	0.113249	+	0.113249i
$134$	−2.12218			−0.183328
$135$	−1.09373	−	11.5674i	−0.0941337	−	0.995560i
$136$	−6.01044			−0.515391
$137$	11.0007	+	11.0007i	0.939857	+	0.939857i	0.998291	−	0.0584339i	$-0.0186107\pi$
$137$	11.0007	+	11.0007i	0.939857	+	0.939857i	−0.0584339	+	0.998291i	$0.518611\pi$
$138$	−5.22220	+	6.24595i	−0.444543	+	0.531690i
$139$			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
$147$	4.76831	+	3.98675i	0.393283	+	0.328821i
$148$	0.317424	+	0.317424i	0.0260921	+	0.0260921i
$149$	0.607952			0.0498053			0.0249027	−	0.999690i	$-0.492072\pi$
$149$	0.607952			0.0498053			0.0249027	+	0.999690i	$0.492072\pi$
$150$	−2.19808	+	8.37666i	−0.179473	+	0.683951i
$151$	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
$153$	10.2901	−	14.8068i	0.831903	−	1.19706i
$154$		−	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
$162$	−8.18345	−	3.74582i	−0.642952	−	0.294300i
$163$	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
$165$	1.66975	−	19.8803i	0.129990	−	1.54768i
$166$	−13.9803			−1.08508
$167$	−1.17503	−	1.17503i	−0.0909264	−	0.0909264i	0.660181	−	0.751107i	$-0.270480\pi$
$167$	−1.17503	−	1.17503i	−0.0909264	−	0.0909264i	−0.751107	+	0.660181i	$0.770480\pi$
$168$	2.45433	+	2.05205i	0.189356	+	0.158319i
$169$		−	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	$-0.489002\pi$
$173$	13.5995	−	13.5995i	1.03395	−	1.03395i	0.999403	−	0.0345455i	$-0.0109984\pi$
$174$	15.0769	−	1.34590i	1.14298	−	0.102033i
$175$	3.93150	+	8.35656i	0.297193	+	0.631697i
$176$			5.15114i			0.388282i
$177$	−1.41537	+	1.69284i	−0.106386	+	0.127241i
$178$	−11.5174	−	11.5174i	−0.863264	−	0.863264i
$179$	−17.9786			−1.34378			−0.671892	−	0.740649i	$-0.734518\pi$
$179$	−17.9786			−1.34378			−0.671892	+	0.740649i	$0.734518\pi$
$180$	4.76821	+	4.71850i	0.355401	+	0.351696i
$181$	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
$183$	−6.95989	+	8.32430i	−0.514490	+	0.615350i
$184$		−	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	$0.852915\pi$
$192$	−1.32879	−	1.11099i	−0.0958974	−	0.0801791i
$193$	−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
$195$	1.20957	+	1.43138i	0.0866189	+	0.102503i
$196$	−3.58845			−0.256318
$197$	3.56808	+	3.56808i	0.254215	+	0.254215i	0.822696	−	0.568481i	$-0.192469\pi$
$197$	3.56808	+	3.56808i	0.254215	+	0.254215i	−0.568481	+	0.822696i	$0.692469\pi$
$198$	−12.6900	−	8.81894i	−0.901836	−	0.626735i
$199$			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
$207$	11.5797	+	8.04736i	0.804845	+	0.559330i
$208$	−0.342145	−	0.342145i	−0.0237235	−	0.0237235i
$209$	5.15114			0.356312
$210$	7.12845	+	0.598720i	0.491910	+	0.0413156i
$211$	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
$213$	−15.5560	−	13.0062i	−1.06588	−	0.891173i
$214$			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
$222$	0.498731	−	0.596502i	0.0334727	−	0.0400346i
$223$	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
$225$	14.7899	+	2.50205i	0.985990	+	0.166804i
$226$	8.82625			0.587114
$227$	−4.90875	−	4.90875i	−0.325805	−	0.325805i	0.525184	−	0.850989i	$-0.323997\pi$
$227$	−4.90875	−	4.90875i	−0.325805	−	0.325805i	−0.850989	+	0.525184i	$0.823997\pi$
$228$	−1.11099	+	1.32879i	−0.0735774	+	0.0880015i
$229$		−	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	−0.742150	−	0.670233i	$-0.766194\pi$
$233$	−1.09776	+	1.09776i	−0.0719169	+	0.0719169i	0.670233	+	0.742150i	$0.266194\pi$
$234$	1.42865	−	0.257118i	0.0933935	−	0.0168083i
$235$	−1.16652	+	6.68233i	−0.0760956	+	0.435907i
$236$		−	1.27397i		−	0.0829282i
$237$	6.95041	+	5.81119i	0.451478	+	0.377478i
$238$	7.84995	+	7.84995i	0.508837	+	0.508837i
$239$	24.4016			1.57841			0.789205	−	0.614130i	$-0.210493\pi$
$239$	24.4016			1.57841			0.789205	+	0.614130i	$0.210493\pi$
$240$	−3.85939	−	0.324151i	−0.249123	−	0.0209239i
$241$	−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
$243$	−5.20195	+	14.6949i	−0.333705	+	0.942677i
$244$		−	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	$0.893721\pi$
$252$	3.16219	−	4.55022i	0.199199	−	0.286637i
$253$	17.1210	+	17.1210i	1.07639	+	1.07639i
$254$	2.57755			0.161730
$255$	15.0249	+	17.7802i	0.940893	+	1.11344i
$256$	1.00000			0.0625000
$257$	−10.1303	−	10.1303i	−0.631914	−	0.631914i	0.316634	−	0.948548i	$-0.397447\pi$
$257$	−10.1303	−	10.1303i	−0.631914	−	0.631914i	−0.948548	+	0.316634i	$0.897447\pi$
$258$	−16.6267	−	13.9015i	−1.03513	−	0.865468i
$259$		−	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	$-0.442329\pi$
$263$	18.8740	−	18.8740i	1.16382	−	1.16382i	0.983632	−	0.180189i	$-0.0576710\pi$
$264$	8.88670	−	0.793310i	0.546939	−	0.0488249i
$265$	25.4691	+	4.44609i	1.56455	+	0.273121i
$266$			1.84704i			0.113249i
$267$	−18.0959	+	21.6434i	−1.10745	+	1.32456i
$268$	−1.50061	−	1.50061i	−0.0916642	−	0.0916642i
$269$	6.51981			0.397520			0.198760	−	0.980048i	$-0.436309\pi$
$269$	6.51981			0.397520			0.198760	+	0.980048i	$0.436309\pi$
$270$	7.40597	−	8.95274i	0.450713	−	0.544847i
$271$	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
$273$	0.992918	−	1.18757i	0.0600941	−	0.0718749i
$274$			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	$0.257121\pi$
$281$			24.2309i			1.44549i	−0.691113	+	0.722747i	$0.742879\pi$
$282$	4.03105	+	3.37034i	0.240046	+	0.200701i
$283$	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
$285$	−0.324151	+	3.85939i	−0.0192011	+	0.228611i
$286$	2.49247			0.147383
$287$	11.6137	+	11.6137i	0.685537	+	0.685537i
$288$	−1.71203	+	2.46352i	−0.100883	+	0.145164i
$289$			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	$-0.628661\pi$
$293$	9.00595	−	9.00595i	0.526133	−	0.526133i	0.919417	+	0.393284i	$0.128661\pi$
$294$	0.552645	+	6.19076i	0.0322309	+	0.361052i
$295$	−1.63791	−	2.33071i	−0.0953629	−	0.135699i
$296$			0.448905i			0.0260921i
$297$	−13.2600	+	23.2508i	−0.769424	+	1.34915i
$298$	0.429887	+	0.429887i	0.0249027	+	0.0249027i
$299$	−2.27440			−0.131532
$300$	−7.47747	+	4.36891i	−0.431712	+	0.252239i
$301$	−23.1113			−1.33211
$302$	1.76278	+	1.76278i	0.101436	+	0.101436i
$303$	−4.89252	−	4.09060i	−0.281068	−	0.234999i
$304$		−	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	$0.151430\pi$
$311$			16.1534i			0.915975i	−0.888959	+	0.457988i	$0.848570\pi$
$312$	−0.537573	+	0.642958i	−0.0304341	+	0.0364003i
$313$	−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
$315$	−0.0649235	−	12.3901i	−0.00365803	−	0.698105i
$316$	−5.23062			−0.294246
$317$	−16.9755	−	16.9755i	−0.953441	−	0.953441i	0.0455227	−	0.998963i	$-0.485505\pi$
$317$	−16.9755	−	16.9755i	−0.953441	−	0.953441i	−0.998963	+	0.0455227i	$0.985505\pi$
$318$	12.8457	−	15.3640i	0.720352	−	0.861570i
$319$		−	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
$327$	5.94224	+	4.96826i	0.328607	+	0.274746i
$328$	−6.28776	−	6.28776i	−0.347183	−	0.347183i
$329$	5.60322			0.308915
$330$	15.2382	−	12.8768i	0.838834	−	0.708845i
$331$	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
$333$	−1.10589	−	0.768541i	−0.0606023	−	0.0421158i
$334$		−	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
$342$	2.46352	+	1.71203i	0.133212	+	0.0925762i
$343$	13.8291	+	13.8291i	0.746700	+	0.746700i
$344$	12.5126			0.674636
$345$	−13.9050	+	11.7502i	−0.748619	+	0.632610i
$346$	19.2326			1.03395
$347$	21.0082	+	21.0082i	1.12778	+	1.12778i	0.990537	+	0.137245i	$0.0438246\pi$
$347$	21.0082	+	21.0082i	1.12778	+	1.12778i	0.137245	+	0.990537i	$0.456175\pi$
$348$	11.6127	+	9.70927i	0.622504	+	0.520472i
$349$			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	−0.427385	−	0.904070i	$-0.640565\pi$
$353$	8.95609	−	8.95609i	0.476685	−	0.476685i	0.904070	+	0.427385i	$0.140565\pi$
$354$	−2.19783	+	0.196199i	−0.116814	+	0.0104279i
$355$	21.4175	−	15.0512i	1.13673	−	0.798837i
$356$		−	16.2880i		−	0.863264i
$357$	12.3337	−	14.7516i	0.652769	−	0.780738i
$358$	−12.7128	−	12.7128i	−0.671892	−	0.671892i
$359$	−13.9018			−0.733708			−0.366854	−	0.930278i	$-0.619565\pi$
$359$	−13.9018			−0.733708			−0.366854	+	0.930278i	$0.619565\pi$
$360$	0.0351501	+	6.70811i	0.00185257	+	0.353549i
$361$	−1.00000			−0.0526316
$362$	3.23987	+	3.23987i	0.170284	+	0.170284i
$363$	−17.2585	+	20.6419i	−0.905837	+	1.08342i
$364$			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
$372$	−13.4192	−	11.2197i	−0.695754	−	0.581715i
$373$	−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
$375$	−8.06294	+	17.6065i	−0.416368	+	0.909196i
$376$	−3.03362			−0.156447
$377$	2.99010	+	2.99010i	0.153998	+	0.153998i
$378$	−8.33699	−	4.75462i	−0.428809	−	0.244551i
$379$		−	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	−0.588932	−	0.808182i	$-0.700452\pi$
$383$	4.29081	−	4.29081i	0.219250	−	0.219250i	0.808182	+	0.588932i	$0.200452\pi$
$384$	−0.154007	−	1.72519i	−0.00785912	−	0.0880383i
$385$	3.65857	−	20.9578i	0.186458	−	1.06811i
$386$		−	16.7731i		−	0.853728i
$387$	−21.4221	+	30.8252i	−1.08894	+	1.56693i
$388$	4.02586	+	4.02586i	0.204382	+	0.204382i
$389$	−21.0267			−1.06609			−0.533047	−	0.846086i	$-0.678953\pi$
$389$	−21.0267			−1.06609			−0.533047	+	0.846086i	$0.678953\pi$
$390$	−0.156846	+	1.86743i	−0.00794220	+	0.0945611i
$391$	−28.2519			−1.42876
$392$	−2.53742	−	2.53742i	−0.128159	−	0.128159i
$393$	15.1732	+	12.6862i	0.765389	+	0.639936i
$394$			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	$-0.971465\pi$
$401$		−	3.58548i		−	0.179050i	0.995985	−	0.0895252i	$-0.0285350\pi$
$402$	−2.35773	+	2.81994i	−0.117593	+	0.140646i
$403$	−3.45526	−	3.45526i	−0.172119	−	0.172119i
$404$	3.68192			0.183183
$405$	−16.5858	−	11.3979i	−0.824153	−	0.566367i
$406$	16.1418			0.801102
$407$	−1.63510	−	1.63510i	−0.0810487	−	0.0810487i
$408$	−6.67756	+	7.98663i	−0.330589	+	0.395397i
$409$		−	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
$417$	1.63909	+	1.37043i	0.0802666	+	0.0671104i
$418$	3.64241	+	3.64241i	0.178156	+	0.178156i
$419$	7.46153			0.364520			0.182260	−	0.983250i	$-0.441659\pi$
$419$	7.46153			0.364520			0.182260	+	0.983250i	$0.441659\pi$
$420$	4.61722	+	5.46393i	0.225297	+	0.266613i
$421$	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
$423$	5.19366	−	7.47339i	0.252525	−	0.363369i
$424$			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	$-0.335510\pi$
$432$	4.51371	+	2.57419i	0.217166	+	0.123851i
$433$	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
$435$	33.7283	+	2.83284i	1.61715	+	0.135824i
$436$	−4.47191			−0.214165
$437$	−3.32373	−	3.32373i	−0.158996	−	0.158996i
$438$	−5.14221	−	4.29936i	−0.245704	−	0.205432i
$439$		−	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	−0.232157	−	0.972678i	$-0.574578\pi$
$443$	15.5862	−	15.5862i	0.740522	−	0.740522i	0.972678	+	0.232157i	$0.0745782\pi$
$444$	0.774447	−	0.0691344i	0.0367536	−	0.00328097i
$445$	−20.9412	−	29.7988i	−0.992707	−	1.41260i
$446$			5.56208i			0.263372i
$447$	0.675431	−	0.807842i	0.0319468	−	0.0382096i
$448$	−1.30605	−	1.30605i	−0.0617052	−	0.0617052i
$449$	21.1036			0.995941			0.497971	−	0.867194i	$-0.334079\pi$
$449$	21.1036			0.995941			0.497971	+	0.867194i	$0.334079\pi$
$450$	8.68879	+	12.2272i	0.409593	+	0.576397i
$451$	45.8052			2.15688
$452$	6.24110	+	6.24110i	0.293557	+	0.293557i
$453$	2.76964	−	3.31260i	0.130129	−	0.155640i
$454$		−	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	$0.262208\pi$
$461$			31.5064i			1.46740i	−0.679473	+	0.733700i	$0.737792\pi$
$462$	−12.6426	−	10.5704i	−0.588188	−	0.491780i
$463$	−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
$465$	−38.9752	−	3.27354i	−1.80743	−	0.151807i
$466$	−1.55247			−0.0719169
$467$	4.04048	+	4.04048i	0.186971	+	0.186971i	0.794385	−	0.607414i	$-0.207793\pi$
$467$	4.04048	+	4.04048i	0.186971	+	0.186971i	−0.607414	+	0.794385i	$0.707793\pi$
$468$	1.19202	+	0.828396i	0.0551009	+	0.0382926i
$469$			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
$477$	−28.4841	−	19.7952i	−1.30420	−	0.906358i
$478$	17.2546	+	17.2546i	0.789205	+	0.789205i
$479$	−25.6778			−1.17325			−0.586624	−	0.809859i	$-0.699543\pi$
$479$	−25.6778			−1.17325			−0.586624	+	0.809859i	$0.699543\pi$
$480$	−2.49979	−	2.95821i	−0.114099	−	0.135023i
$481$	0.217210			0.00990393
$482$	−10.9469	−	10.9469i	−0.498618	−	0.498618i
$483$	11.5365	+	9.64560i	0.524929	+	0.438890i
$484$		−	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	$-0.856974\pi$
$491$		−	19.2496i		−	0.868723i	0.900739	−	0.434361i	$-0.143026\pi$
$492$	−9.87922	+	11.8159i	−0.445390	+	0.532703i
$493$	37.1420	+	37.1420i	1.67279	+	1.67279i
$494$	−0.483866			−0.0217702
$495$	−24.5617	−	24.3057i	−1.10397	−	1.09246i
$496$	10.0988			0.453449
$497$	−15.2898	−	15.2898i	−0.685840	−	0.685840i
$498$	−15.5320	+	18.5769i	−0.696007	+	0.832451i
$499$			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	−0.983939	−	0.178505i	$-0.942874\pi$
$503$	−18.0640	+	18.0640i	−0.805434	+	0.805434i	0.178505	+	0.983939i	$0.442874\pi$
$504$	5.45350	−	0.981482i	0.242918	−	0.0437187i
$505$	6.73604	−	4.73377i	0.299750	−	0.210650i
$506$			24.2128i			1.07639i
$507$	−16.9632	−	14.1828i	−0.753362	−	0.629881i
$508$	1.82261	+	1.82261i	0.0808651	+	0.0808651i
$509$	24.2848			1.07640			0.538202	−	0.842816i	$-0.319104\pi$
$509$	24.2848			1.07640			0.538202	+	0.842816i	$0.319104\pi$
$510$	−1.94829	+	23.1966i	−0.0862717	+	1.02716i
$511$	−7.14773			−0.316197
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.57419	−	4.51371i	0.113653	−	0.199285i
$514$		−	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	$0.862306\pi$
$522$	14.9619	−	21.5294i	0.654865	−	0.942315i
$523$	−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
$525$	15.4720	+	4.05995i	0.675254	+	0.177191i
$526$	26.6919			1.16382
$527$	−42.9201	−	42.9201i	−1.86963	−	1.86963i
$528$	6.84480	+	5.72289i	0.297882	+	0.249057i
$529$			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
$537$	−19.9741	+	23.8899i	−0.861948	+	1.03092i
$538$	4.61020	+	4.61020i	0.198760	+	0.198760i
$539$	18.4846			0.796189
$540$	11.5674	−	1.09373i	0.497780	−	0.0470668i
$541$	−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
$543$	5.09044	−	6.08836i	0.218452	−	0.261277i
$544$		−	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
$552$	−6.24595	−	5.22220i	−0.265845	−	0.222271i
$553$	6.83147	+	6.83147i	0.290504	+	0.290504i
$554$	19.7600			0.839520
$555$	1.32796	−	1.12217i	0.0563687	−	0.0476335i
$556$	−1.23352			−0.0523128
$557$	−7.92409	−	7.92409i	−0.335754	−	0.335754i	0.519012	−	0.854767i	$-0.326300\pi$
$557$	−7.92409	−	7.92409i	−0.335754	−	0.335754i	−0.854767	+	0.519012i	$0.826300\pi$
$558$	−17.2895	+	24.8786i	−0.731922	+	1.05320i
$559$		−	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	$-0.726191\pi$
$563$	2.50755	−	2.50755i	0.105681	−	0.105681i	0.757970	+	0.652289i	$0.226191\pi$
$564$	0.467198	+	5.23357i	0.0196726	+	0.220373i
$565$	19.4421	+	3.39397i	0.817935	+	0.142786i
$566$			13.1018i			0.550708i
$567$	−6.91868	+	15.1151i	−0.290557	+	0.634776i
$568$	8.27799	+	8.27799i	0.347337	+	0.347337i
$569$	−19.7316			−0.827190			−0.413595	−	0.910461i	$-0.635727\pi$
$569$	−19.7316			−0.827190			−0.413595	+	0.910461i	$0.635727\pi$
$570$	−2.95821	+	2.49979i	−0.123906	+	0.104705i
$571$	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
$573$	16.3741	+	13.6903i	0.684037	+	0.571919i
$574$			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
$582$	6.32537	−	7.56539i	0.262195	−	0.313596i
$583$	−42.1149	−	42.1149i	−1.74422	−	1.74422i
$584$	3.86983			0.160135
$585$	3.24583	−	0.0170079i	0.134199	−	0.000703192i
$586$	12.7363			0.526133
$587$	20.3746	+	20.3746i	0.840951	+	0.840951i	0.988983	−	0.148032i	$-0.0472939\pi$
$587$	20.3746	+	20.3746i	0.840951	+	0.840951i	−0.148032	+	0.988983i	$0.547294\pi$
$588$	−3.98675	+	4.76831i	−0.164411	+	0.196642i
$589$		−	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	$-0.822868\pi$
$593$	−7.81504	+	7.81504i	−0.320925	+	0.320925i	0.528197	+	0.849122i	$0.322868\pi$
$594$	−25.8170	+	7.06453i	−1.05928	+	0.289861i
$595$	14.2730	+	20.3101i	0.585135	+	0.832632i
$596$			0.607952i			0.0249027i
$597$	4.29451	+	3.59061i	0.175762	+	0.146954i
$598$	−1.60824	−	1.60824i	−0.0657659	−	0.0657659i
$599$	−6.25932			−0.255749			−0.127874	−	0.991790i	$-0.540815\pi$
$599$	−6.25932			−0.255749			−0.127874	+	0.991790i	$0.540815\pi$
$600$	−8.37666	−	2.19808i	−0.341976	−	0.0897364i
$601$	−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
$603$	5.22803	+	3.63324i	0.212902	+	0.147957i
$604$			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
$612$	14.8068	+	10.2901i	0.598531	+	0.415952i
$613$	−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
$615$	−2.88243	+	34.3186i	−0.116231	+	1.38386i
$616$	9.51436			0.383345
$617$	18.8481	+	18.8481i	0.758795	+	0.758795i	0.976103	−	0.217308i	$-0.0697277\pi$
$617$	18.8481	+	18.8481i	0.758795	+	0.758795i	−0.217308	+	0.976103i	$0.569728\pi$
$618$	−10.4940	−	8.77393i	−0.422129	−	0.352939i
$619$			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
$627$	5.72289	−	6.84480i	0.228550	−	0.273355i
$628$	0.0444358	+	0.0444358i	0.00177318	+	0.00177318i
$629$	2.69812			0.107581
$630$	8.71524	−	8.80706i	0.347224	−	0.350882i
$631$	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
$633$	14.7142	−	17.5987i	0.584837	−	0.699487i
$634$		−	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	$-0.105221\pi$
$642$	3.89821	+	3.25926i	0.153850	+	0.128633i
$643$	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
$645$	−31.2790	−	37.0151i	−1.23161	−	1.45747i
$646$	−6.01044			−0.236477
$647$	−33.8022	−	33.8022i	−1.32890	−	1.32890i	−0.906330	−	0.422570i	$-0.861128\pi$
$647$	−33.8022	−	33.8022i	−1.32890	−	1.32890i	−0.422570	−	0.906330i	$-0.638872\pi$
$648$	3.74582	−	8.18345i	0.147150	−	0.321476i
$649$			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	$-0.691685\pi$
$653$	6.58374	−	6.58374i	0.257642	−	0.257642i	0.824094	+	0.566453i	$0.191685\pi$
$654$	0.688703	+	7.71489i	0.0269304	+	0.301676i
$655$	−20.8906	+	14.6809i	−0.816263	+	0.573631i
$656$		−	8.89223i		−	0.347183i
$657$	−6.62529	+	9.53342i	−0.258477	+	0.371934i
$658$	3.96207	+	3.96207i	0.154458	+	0.154458i
$659$	−0.843524			−0.0328590			−0.0164295	−	0.999865i	$-0.505230\pi$
$659$	−0.843524			−0.0328590			−0.0164295	+	0.999865i	$0.505230\pi$
$660$	19.8803	+	1.66975i	0.773840	+	0.0649949i
$661$	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
$663$	3.86446	+	3.23105i	0.150083	+	0.125484i
$664$		−	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
$672$	−2.05205	+	2.45433i	−0.0791595	+	0.0946779i
$673$	−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
$675$	19.7562	−	16.8729i	0.760415	−	0.649438i
$676$	12.7659			0.490995
$677$	18.9600	+	18.9600i	0.728691	+	0.728691i	0.970359	−	0.241668i	$-0.0776946\pi$
$677$	18.9600	+	18.9600i	0.728691	+	0.728691i	−0.241668	+	0.970359i	$0.577695\pi$
$678$	9.80592	−	11.7283i	0.376594	−	0.450421i
$679$		−	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	$-0.810645\pi$
$683$	−6.99901	+	6.99901i	−0.267810	+	0.267810i	0.560407	+	0.828217i	$0.310645\pi$
$684$	0.531382	+	2.95256i	0.0203179	+	0.112894i
$685$	−5.98231	+	34.2692i	−0.228572	+	1.30936i
$686$			19.5573i			0.746700i
$687$	−0.410812	−	0.343477i	−0.0156735	−	0.0131045i
$688$	8.84777	+	8.84777i	0.337318	+	0.337318i
$689$	5.59464			0.213139
$690$	−18.1410	−	1.52366i	−0.690615	−	0.0580048i
$691$	−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
$693$	−16.2889	+	23.4388i	−0.618765	+	0.890368i
$694$			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	$-0.354466\pi$
$702$	1.24556	−	2.18403i	0.0470107	−	0.0824310i
$703$	0.317424	+	0.317424i	0.0119719	+	0.0119719i
$704$	−5.15114			−0.194141
$705$	7.58343	+	8.97410i	0.285609	+	0.337984i
$706$	12.6658			0.476685
$707$	−4.80879	−	4.80879i	−0.180853	−	0.180853i
$708$	−1.69284	−	1.41537i	−0.0636207	−	0.0531929i
$709$		−	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
$717$	27.1101	−	32.4247i	1.01244	−	1.21092i
$718$	−9.83005	−	9.83005i	−0.366854	−	0.366854i
$719$	−31.1460			−1.16155			−0.580775	−	0.814064i	$-0.697250\pi$
$719$	−31.1460			−1.16155			−0.580775	+	0.814064i	$0.697250\pi$
$720$	−4.71850	+	4.76821i	−0.175848	+	0.177701i
$721$	−14.5867			−0.543238
$722$	−0.707107	−	0.707107i	−0.0263158	−	0.0263158i
$723$	−17.1996	+	20.5714i	−0.639660	+	0.765058i
$724$			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
$732$	−8.32430	−	6.95989i	−0.307675	−	0.257245i
$733$	−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
$735$	−1.16320	+	13.8492i	−0.0429053	+	0.510837i
$736$	4.70047			0.173262
$737$	7.72984	+	7.72984i	0.284732	+	0.284732i
$738$	21.9062	+	15.2238i	0.806378	+	0.560396i
$739$			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	$-0.446301\pi$
$743$	31.4477	−	31.4477i	1.15370	−	1.15370i	0.985804	−	0.167901i	$-0.0536988\pi$
$744$	−1.55528	−	17.4223i	−0.0570194	−	0.638734i
$745$	0.781631	+	1.11224i	0.0286367	+	0.0407494i
$746$		−	29.8160i		−	1.09164i
$747$	34.4407	+	23.9347i	1.26012	+	0.875726i
$748$	21.8925	+	21.8925i	0.800468	+	0.800468i
$749$	5.41856			0.197990
$750$	−18.1510	+	6.74832i	−0.662782	+	0.246414i
$751$	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
$753$	13.7983	+	11.5366i	0.502836	+	0.420418i
$754$			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	$-0.781953\pi$
$761$		−	34.9067i		−	1.26537i	0.774411	−	0.632683i	$-0.218047\pi$
$762$	2.86365	−	3.42504i	0.103739	−	0.124076i
$763$	5.84055	+	5.84055i	0.211442	+	0.211442i
$764$	−12.3225			−0.445813
$765$	40.3187	−	0.211267i	1.45772	−	0.00763838i
$766$	6.06812			0.219250
$767$	−0.435882	−	0.435882i	−0.0157388	−	0.0157388i
$768$	1.11099	−	1.32879i	0.0400896	−	0.0479487i
$769$		−	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	−0.435635	−	0.900123i	$-0.643476\pi$
$773$	12.9141	−	12.9141i	0.464488	−	0.464488i	0.900123	+	0.435635i	$0.143476\pi$
$774$	−36.9444	+	6.64899i	−1.32794	+	0.238993i
$775$	17.1080	−	47.5075i	0.614536	−	1.70652i
$776$			5.69343i			0.204382i
$777$	−1.10176	−	0.921176i	−0.0395255	−	0.0330470i
$778$	−14.8681	−	14.8681i	−0.533047	−	0.533047i
$779$	−8.89223			−0.318597
$780$	−1.43138	+	1.20957i	−0.0512516	+	0.0433094i
$781$	−60.3037			−2.15783
$782$	−19.9771	−	19.9771i	−0.714379	−	0.714379i
$783$	−39.4465	−	22.4965i	−1.40970	−	0.803959i
$784$		−	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
$792$	8.81894	−	12.6900i	0.313367	−	0.450918i
$793$	−2.14339	−	2.14339i	−0.0761140	−	0.0761140i
$794$	9.97969			0.354166
$795$	34.2039	−	28.9035i	1.21309	−	1.02510i
$796$	−3.23189			−0.114551
$797$	26.4864	+	26.4864i	0.938196	+	0.938196i	0.998198	−	0.0600027i	$-0.0191109\pi$
$797$	26.4864	+	26.4864i	0.938196	+	0.938196i	−0.0600027	+	0.998198i	$0.519111\pi$
$798$	2.45433	+	2.05205i	0.0868824	+	0.0726418i
$799$			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
$807$	7.24347	−	8.66348i	0.254982	−	0.304969i
$808$	2.60351	+	2.60351i	0.0915913	+	0.0915913i
$809$	−3.31684			−0.116614			−0.0583069	−	0.998299i	$-0.518570\pi$
$809$	−3.31684			−0.116614			−0.0583069	+	0.998299i	$0.518570\pi$
$810$	−3.66835	−	19.7875i	−0.128893	−	0.695260i
$811$	−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
$813$	16.0061	−	19.1439i	0.561357	−	0.671405i
$814$		−	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	$0.933988\pi$
$822$	20.6726	+	17.2842i	0.721039	+	0.602856i
$823$	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
$825$	38.5175	−	22.5049i	1.34101	−	0.783520i
$826$	−2.35307			−0.0818736
$827$	8.72992	+	8.72992i	0.303569	+	0.303569i	0.842408	−	0.538839i	$-0.181137\pi$
$827$	8.72992	+	8.72992i	0.303569	+	0.303569i	−0.538839	+	0.842408i	$0.681137\pi$
$828$	−8.04736	+	11.5797i	−0.279665	+	0.402423i
$829$		−	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
$837$	45.5830	+	25.9962i	1.57558	+	0.898560i
$838$	5.27610	+	5.27610i	0.182260	+	0.182260i
$839$	35.9702			1.24183			0.620914	−	0.783879i	$-0.286762\pi$
$839$	35.9702			1.24183			0.620914	+	0.783879i	$0.286762\pi$
$840$	−0.598720	+	7.12845i	−0.0206578	+	0.245955i
$841$	47.3747			1.63361
$842$	2.49657	+	2.49657i	0.0860374	+	0.0860374i
$843$	32.1978	+	26.9204i	1.10895	+	0.927188i
$844$			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
$852$	13.0062	−	15.5560i	0.445587	−	0.532939i
$853$	−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
$855$	4.76821	+	4.71850i	0.163069	+	0.161369i
$856$	−2.93365			−0.100270
$857$	−11.8490	−	11.8490i	−0.404754	−	0.404754i	0.475150	−	0.879905i	$-0.342394\pi$
$857$	−11.8490	−	11.8490i	−0.404754	−	0.404754i	−0.879905	+	0.475150i	$0.842394\pi$
$858$	2.76912	−	3.31197i	0.0945361	−	0.113069i
$859$			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	−0.923456	−	0.383704i	$-0.874648\pi$
$863$	−15.8562	+	15.8562i	−0.539752	+	0.539752i	0.383704	+	0.923456i	$0.374648\pi$
$864$	1.37145	+	5.01190i	0.0466576	+	0.170508i
$865$	42.3646	+	7.39553i	1.44044	+	0.251455i
$866$			11.9178i			0.404982i
$867$	25.4136	+	21.2482i	0.863092	+	0.721625i
$868$	−13.1896	−	13.1896i	−0.447683	−	0.447683i
$869$	26.9437			0.914002
$870$	21.8464	+	25.8526i	0.740661	+	0.876485i
$871$	−1.02685			−0.0347935
$872$	−3.16212	−	3.16212i	−0.107083	−	0.107083i
$873$	−14.0259	−	9.74735i	−0.474705	−	0.329898i
$874$		−	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	$0.246682\pi$
$881$			41.5364i			1.39940i	−0.714439	+	0.699698i	$0.753318\pi$
$882$	8.84022	+	6.14355i	0.297666	+	0.206864i
$883$	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
$885$	−4.91674	−	0.412958i	−0.165274	−	0.0138814i
$886$	22.0422			0.740522
$887$	21.3528	+	21.3528i	0.716958	+	0.716958i	0.967981	−	0.251023i	$-0.0807670\pi$
$887$	21.3528	+	21.3528i	0.716958	+	0.716958i	−0.251023	+	0.967981i	$0.580767\pi$
$888$	0.596502	+	0.498731i	0.0200173	+	0.0167363i
$889$		−	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
$897$	−2.52684	+	3.02221i	−0.0843689	+	0.100908i
$898$	14.9225	+	14.9225i	0.497971	+	0.497971i
$899$	−88.2560			−2.94350
$900$	−2.50205	+	14.7899i	−0.0834018	+	0.492995i
$901$	69.4949			2.31521
$902$	32.3891	+	32.3891i	1.07844	+	1.07844i
$903$	−25.6766	+	30.7102i	−0.854462	+	1.02197i
$904$			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	$-0.905136\pi$
$911$		−	17.7253i		−	0.587264i	0.955919	−	0.293632i	$-0.0948640\pi$
$912$	−1.32879	−	1.11099i	−0.0440007	−	0.0367887i
$913$	50.9219	+	50.9219i	1.68527	+	1.68527i
$914$	−4.59183			−0.151884
$915$	−24.1774	−	2.03066i	−0.799280	−	0.0671317i
$916$	0.309162			0.0102150
$917$	14.9136	+	14.9136i	0.492490	+	0.492490i
$918$	15.4720	−	27.1294i	0.510652	−	0.895402i
$919$			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
$927$	−13.5206	+	19.4553i	−0.444073	+	0.638996i
$928$	−6.17959	−	6.17959i	−0.202855	−	0.202855i
$929$	−5.97512			−0.196037			−0.0980187	−	0.995185i	$-0.531250\pi$
$929$	−5.97512			−0.196037			−0.0980187	+	0.995185i	$0.531250\pi$
$930$	−25.2449	−	29.8744i	−0.827814	−	0.979620i
$931$	−3.58845			−0.117607
$932$	−1.09776	−	1.09776i	−0.0359584	−	0.0359584i
$933$	21.4645	+	17.9463i	0.702717	+	0.587537i
$934$			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	$0.0326220\pi$
$941$			6.27661i			0.204611i	−0.994753	+	0.102306i	$0.967378\pi$
$942$	0.0698168	−	0.0835037i	0.00227476	−	0.00272070i
$943$	−29.5554	−	29.5554i	−0.962456	−	0.962456i
$944$	1.27397			0.0414641
$945$	−16.5361	−	13.6791i	−0.537918	−	0.444981i
$946$	−64.4544			−2.09559
$947$	−7.98043	−	7.98043i	−0.259329	−	0.259329i	0.565452	−	0.824781i	$-0.308702\pi$
$947$	−7.98043	−	7.98043i	−0.259329	−	0.259329i	−0.824781	+	0.565452i	$0.808702\pi$
$948$	−5.81119	+	6.95041i	−0.188739	+	0.225739i
$949$		−	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	$-0.658570\pi$
$953$	12.3683	−	12.3683i	0.400650	−	0.400650i	0.878462	+	0.477812i	$0.158570\pi$
$954$	−6.14403	−	34.1386i	−0.198920	−	1.10528i
$955$	−22.5439	+	15.8428i	−0.729504	+	0.512661i
$956$			24.4016i			0.789205i
$957$	−59.8185	−	50.0139i	−1.93366	−	1.61672i
$958$	−18.1569	−	18.1569i	−0.586624	−	0.586624i
$959$	28.7351			0.927906
$960$	0.324151	−	3.85939i	0.0104619	−	0.124561i
$961$	70.9857			2.28986
$962$	0.153591	+	0.153591i	0.00495197	+	0.00495197i
$963$	5.02250	−	7.22710i	0.161848	−	0.232890i
$964$		−	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	$0.117713\pi$
$971$			22.5253i			0.722872i	−0.932397	+	0.361436i	$0.882287\pi$
$972$	−14.6949	−	5.20195i	−0.471339	−	0.166853i
$973$	1.61104	+	1.61104i	0.0516476	+	0.0516476i
$974$	−14.3226			−0.458925
$975$	−1.06358	+	4.05318i	−0.0340618	+	0.129806i
$976$	6.26456			0.200524
$977$	−32.1177	−	32.1177i	−1.02754	−	1.02754i	−0.999610	−	0.0279276i	$-0.991109\pi$
$977$	−32.1177	−	32.1177i	−1.02754	−	1.02754i	−0.0279276	−	0.999610i	$-0.508891\pi$
$978$	16.9078	+	14.1365i	0.540652	+	0.452035i
$979$			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	$-0.734005\pi$
$983$	2.22712	−	2.22712i	0.0710340	−	0.0710340i	0.741731	+	0.670697i	$0.234005\pi$
$984$	−15.3408	+	1.36946i	−0.489047	+	0.0436569i
$985$	−1.94036	+	11.1152i	−0.0618250	+	0.354159i
$986$			52.5268i			1.67279i
$987$	6.22514	−	7.44551i	0.198148	−	0.236993i
$988$	−0.342145	−	0.342145i	−0.0108851	−	0.0108851i
$989$	58.8153			1.87022
$990$	−0.181063	−	34.5545i	−0.00575456	−	1.09821i
$991$	−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
$993$	16.3448	−	19.5490i	0.518685	−	0.620368i
$994$		−	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.533.16	yes	36
3.2	odd	2	inner	570.2.k.b.533.3	yes	36
5.2	odd	4	inner	570.2.k.b.77.3	✓	36
15.2	even	4	inner	570.2.k.b.77.16	yes	36

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

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.11099 - 1.32879i) q^{3} +1.00000i q^{4} +(1.28568 + 1.82949i) q^{5} +(1.72519 - 0.154007i) q^{6} +(1.30605 - 1.30605i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.531382 - 2.95256i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.11099 - 1.32879i) 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} +(1.32879 + 1.11099i) q^{12} +(0.342145 + 0.342145i) q^{13} +1.84704 q^{14} +(3.85939 + 0.324151i) q^{15} -1.00000 q^{16} +(4.25002 + 4.25002i) q^{17} +(1.71203 - 2.46352i) 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} +(-4.51371 - 2.57419i) q^{27} +(1.30605 + 1.30605i) q^{28} +8.73926 q^{29} +(2.49979 + 2.95821i) q^{30} -10.0988 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-6.84480 - 5.72289i) 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} +(2.05205 - 2.45433i) q^{42} +(-8.84777 - 8.84777i) q^{43} +5.15114 q^{44} +(4.71850 - 4.76821i) q^{45} -4.70047 q^{46} +(2.14509 + 2.14509i) q^{47} +(-1.11099 + 1.32879i) 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} +(1.32879 + 1.11099i) q^{57} +(6.17959 + 6.17959i) q^{58} -1.27397 q^{59} +(-0.324151 + 3.85939i) q^{60} -6.26456 q^{61} +(-7.14093 - 7.14093i) q^{62} +(-4.55022 - 3.16219i) 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} +(2.46352 + 1.71203i) q^{72} +(-2.73639 - 2.73639i) q^{73} +0.448905 q^{74} +(4.36891 + 7.47747i) q^{75} -1.00000 q^{76} +(-6.72767 - 6.72767i) q^{77} +(0.642958 + 0.537573i) 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} +(9.70927 - 11.6127i) q^{87} +(3.64241 + 3.64241i) q^{88} -16.2880 q^{89} +(6.70811 - 0.0351501i) q^{90} +0.893720 q^{91} +(-3.32373 - 3.32373i) q^{92} +(-11.2197 + 13.4192i) 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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