LMFDB - Embedded newform 570.2.k.b.77.11

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			77.11
Character	$\chi$	$=$	570.77
Dual form			570.2.k.b.533.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.63290 - 0.577604i) q^{3} -1.00000i q^{4} +(-2.23603 + 0.0135681i) q^{5} +(-1.56306 + 0.746209i) q^{6} +(3.38538 + 3.38538i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.33275 + 1.88634i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.63290 - 0.577604i) q^{3} -1.00000i q^{4} +(-2.23603 + 0.0135681i) q^{5} +(-1.56306 + 0.746209i) q^{6} +(3.38538 + 3.38538i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.33275 + 1.88634i) q^{9} +(-1.57152 + 1.59070i) q^{10} +1.22574i q^{11} +(-0.577604 + 1.63290i) q^{12} +(3.51689 - 3.51689i) q^{13} +4.78765 q^{14} +(3.65905 + 1.26938i) q^{15} -1.00000 q^{16} +(-0.826034 + 0.826034i) q^{17} +(2.98335 - 0.315656i) q^{18} -1.00000i q^{19} +(0.0135681 + 2.23603i) q^{20} +(-3.57259 - 7.48341i) q^{21} +(0.866730 + 0.866730i) q^{22} +(1.04719 + 1.04719i) q^{23} +(0.746209 + 1.56306i) q^{24} +(4.99963 - 0.0606771i) q^{25} -4.97363i q^{26} +(-2.71959 - 4.42762i) q^{27} +(3.38538 - 3.38538i) q^{28} +8.14348 q^{29} +(3.48493 - 1.68975i) q^{30} +7.41990 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.707993 - 2.00152i) q^{33} +1.16819i q^{34} +(-7.61574 - 7.52387i) q^{35} +(1.88634 - 2.33275i) q^{36} +(-5.83375 - 5.83375i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(-7.77411 + 3.71137i) q^{39} +(1.59070 + 1.57152i) q^{40} +3.53572i q^{41} +(-7.81778 - 2.76537i) q^{42} +(-2.68748 + 2.68748i) q^{43} +1.22574 q^{44} +(-5.24168 - 4.18626i) q^{45} +1.48094 q^{46} +(6.84848 - 6.84848i) q^{47} +(1.63290 + 0.577604i) q^{48} +15.9216i q^{49} +(3.49237 - 3.57818i) q^{50} +(1.82595 - 0.871713i) q^{51} +(-3.51689 - 3.51689i) q^{52} +(3.40629 + 3.40629i) q^{53} +(-5.05384 - 1.20776i) q^{54} +(-0.0166309 - 2.74079i) q^{55} -4.78765i q^{56} +(-0.577604 + 1.63290i) q^{57} +(5.75831 - 5.75831i) q^{58} +9.91906 q^{59} +(1.26938 - 3.65905i) q^{60} -10.5422 q^{61} +(5.24666 - 5.24666i) q^{62} +(1.51125 + 14.2832i) q^{63} +1.00000i q^{64} +(-7.81614 + 7.91158i) q^{65} +(-0.914660 - 1.91591i) q^{66} +(6.00309 + 6.00309i) q^{67} +(0.826034 + 0.826034i) q^{68} +(-1.10509 - 2.31481i) q^{69} +(-10.7053 + 0.0649592i) q^{70} +8.35839i q^{71} +(-0.315656 - 2.98335i) q^{72} +(-3.99393 + 3.99393i) q^{73} -8.25017 q^{74} +(-8.19896 - 2.78873i) q^{75} -1.00000 q^{76} +(-4.14960 + 4.14960i) q^{77} +(-2.87279 + 8.12146i) q^{78} +6.75057i q^{79} +(2.23603 - 0.0135681i) q^{80} +(1.88342 + 8.80072i) q^{81} +(2.50013 + 2.50013i) q^{82} +(-0.717790 - 0.717790i) q^{83} +(-7.48341 + 3.57259i) q^{84} +(1.83583 - 1.85824i) q^{85} +3.80067i q^{86} +(-13.2975 - 4.70370i) q^{87} +(0.866730 - 0.866730i) q^{88} +0.384471 q^{89} +(-6.66656 + 0.746293i) q^{90} +23.8120 q^{91} +(1.04719 - 1.04719i) q^{92} +(-12.1160 - 4.28576i) q^{93} -9.68521i q^{94} +(0.0135681 + 2.23603i) q^{95} +(1.56306 - 0.746209i) q^{96} +(-12.5444 - 12.5444i) q^{97} +(11.2583 + 11.2583i) q^{98} +(-2.31217 + 2.85934i) 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
$3$	−1.63290	−	0.577604i	−0.942757	−	0.333480i
$3$	−1.63290	−	0.577604i	−0.942757	−	0.333480i
$4$		−	1.00000i		−	0.500000i
$5$	−2.23603	+	0.0135681i	−0.999982	+	0.00606782i
$5$	−2.23603	+	0.0135681i	−0.999982	+	0.00606782i
$6$	−1.56306	+	0.746209i	−0.638119	+	0.304639i
$7$	3.38538	+	3.38538i	1.27955	+	1.27955i	0.940917	+	0.338638i	$0.109966\pi$
$7$	3.38538	+	3.38538i	1.27955	+	1.27955i	0.338638	+	0.940917i	$0.390034\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.33275	+	1.88634i	0.777582	+	0.628781i
$10$	−1.57152	+	1.59070i	−0.496957	+	0.503025i
$11$			1.22574i			0.369575i	0.982779	+	0.184787i	$0.0591597\pi$
$11$			1.22574i			0.369575i	−0.982779	+	0.184787i	$0.940840\pi$
$12$	−0.577604	+	1.63290i	−0.166740	+	0.471379i
$13$	3.51689	−	3.51689i	0.975410	−	0.975410i	−0.0242950	−	0.999705i	$-0.507734\pi$
$13$	3.51689	−	3.51689i	0.975410	−	0.975410i	0.999705	+	0.0242950i	$0.00773410\pi$
$14$	4.78765			1.27955
$15$	3.65905	+	1.26938i	0.944763	+	0.327753i
$16$	−1.00000			−0.250000
$17$	−0.826034	+	0.826034i	−0.200343	+	0.200343i	−0.800147	−	0.599804i	$-0.795245\pi$
$17$	−0.826034	+	0.826034i	−0.200343	+	0.200343i	0.599804	+	0.800147i	$0.295245\pi$
$18$	2.98335	−	0.315656i	0.703182	−	0.0744008i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	0.0135681	+	2.23603i	0.00303391	+	0.499991i
$21$	−3.57259	−	7.48341i	−0.779604	−	1.63301i
$22$	0.866730	+	0.866730i	0.184787	+	0.184787i
$23$	1.04719	+	1.04719i	0.218353	+	0.218353i	0.807804	−	0.589451i	$-0.200656\pi$
$23$	1.04719	+	1.04719i	0.218353	+	0.218353i	−0.589451	+	0.807804i	$0.700656\pi$
$24$	0.746209	+	1.56306i	0.152319	+	0.319059i
$25$	4.99963	−	0.0606771i	0.999926	−	0.0121354i
$26$		−	4.97363i		−	0.975410i
$27$	−2.71959	−	4.42762i	−0.523386	−	0.852096i
$28$	3.38538	−	3.38538i	0.639777	−	0.639777i
$29$	8.14348			1.51221			0.756103	−	0.654453i	$-0.227101\pi$
$29$	8.14348			1.51221			0.756103	+	0.654453i	$0.227101\pi$
$30$	3.48493	−	1.68975i	0.636258	−	0.308505i
$31$	7.41990			1.33265			0.666327	−	0.745660i	$-0.267866\pi$
$31$	7.41990			1.33265			0.666327	+	0.745660i	$0.267866\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.707993	−	2.00152i	0.123246	−	0.348419i
$34$			1.16819i			0.200343i
$35$	−7.61574	−	7.52387i	−1.28730	−	1.27177i
$36$	1.88634	−	2.33275i	0.314390	−	0.388791i
$37$	−5.83375	−	5.83375i	−0.959063	−	0.959063i	0.0401316	−	0.999194i	$-0.487222\pi$
$37$	−5.83375	−	5.83375i	−0.959063	−	0.959063i	−0.999194	+	0.0401316i	$0.987222\pi$
$38$	−0.707107	−	0.707107i	−0.114708	−	0.114708i
$39$	−7.77411	+	3.71137i	−1.24485	+	0.594295i
$40$	1.59070	+	1.57152i	0.251512	+	0.248478i
$41$			3.53572i			0.552187i	0.961131	+	0.276093i	$0.0890399\pi$
$41$			3.53572i			0.552187i	−0.961131	+	0.276093i	$0.910960\pi$
$42$	−7.81778	−	2.76537i	−1.20631	−	0.426706i
$43$	−2.68748	+	2.68748i	−0.409836	+	0.409836i	−0.881681	−	0.471845i	$-0.843588\pi$
$43$	−2.68748	+	2.68748i	−0.409836	+	0.409836i	0.471845	+	0.881681i	$0.343588\pi$
$44$	1.22574			0.184787
$45$	−5.24168	−	4.18626i	−0.781383	−	0.624051i
$46$	1.48094			0.218353
$47$	6.84848	−	6.84848i	0.998953	−	0.998953i	−0.00104620	−	0.999999i	$-0.500333\pi$
$47$	6.84848	−	6.84848i	0.998953	−	0.998953i	0.999999	+	0.00104620i	$0.000333015\pi$
$48$	1.63290	+	0.577604i	0.235689	+	0.0833699i
$49$			15.9216i			2.27452i
$50$	3.49237	−	3.57818i	0.493895	−	0.506031i
$51$	1.82595	−	0.871713i	0.255685	−	0.122064i
$52$	−3.51689	−	3.51689i	−0.487705	−	0.487705i
$53$	3.40629	+	3.40629i	0.467890	+	0.467890i	0.901230	−	0.433340i	$-0.142665\pi$
$53$	3.40629	+	3.40629i	0.467890	+	0.467890i	−0.433340	+	0.901230i	$0.642665\pi$
$54$	−5.05384	−	1.20776i	−0.687741	−	0.164355i
$55$	−0.0166309	−	2.74079i	−0.00224251	−	0.369568i
$56$		−	4.78765i		−	0.639777i
$57$	−0.577604	+	1.63290i	−0.0765055	+	0.216283i
$58$	5.75831	−	5.75831i	0.756103	−	0.756103i
$59$	9.91906			1.29135			0.645676	−	0.763612i	$-0.276576\pi$
$59$	9.91906			1.29135			0.645676	+	0.763612i	$0.276576\pi$
$60$	1.26938	−	3.65905i	0.163877	−	0.472382i
$61$	−10.5422			−1.34979			−0.674894	−	0.737915i	$-0.735811\pi$
$61$	−10.5422			−1.34979			−0.674894	+	0.737915i	$0.735811\pi$
$62$	5.24666	−	5.24666i	0.666327	−	0.666327i
$63$	1.51125	+	14.2832i	0.190400	+	1.79952i
$64$			1.00000i			0.125000i
$65$	−7.81614	+	7.91158i	−0.969473	+	0.981310i
$66$	−0.914660	−	1.91591i	−0.112587	−	0.235833i
$67$	6.00309	+	6.00309i	0.733394	+	0.733394i	0.971291	−	0.237896i	$-0.0764579\pi$
$67$	6.00309	+	6.00309i	0.733394	+	0.733394i	−0.237896	+	0.971291i	$0.576458\pi$
$68$	0.826034	+	0.826034i	0.100171	+	0.100171i
$69$	−1.10509	−	2.31481i	−0.133038	−	0.278671i
$70$	−10.7053	+	0.0649592i	−1.27953	+	0.00776411i
$71$			8.35839i			0.991958i	0.868334	+	0.495979i	$0.165191\pi$
$71$			8.35839i			0.991958i	−0.868334	+	0.495979i	$0.834809\pi$
$72$	−0.315656	−	2.98335i	−0.0372004	−	0.351591i
$73$	−3.99393	+	3.99393i	−0.467454	+	0.467454i	−0.901089	−	0.433635i	$-0.857231\pi$
$73$	−3.99393	+	3.99393i	−0.467454	+	0.467454i	0.433635	+	0.901089i	$0.357231\pi$
$74$	−8.25017			−0.959063
$75$	−8.19896	−	2.78873i	−0.946735	−	0.322014i
$76$	−1.00000			−0.114708
$77$	−4.14960	+	4.14960i	−0.472891	+	0.472891i
$78$	−2.87279	+	8.12146i	−0.325279	+	0.919575i
$79$			6.75057i			0.759498i	0.925090	+	0.379749i	$0.123990\pi$
$79$			6.75057i			0.759498i	−0.925090	+	0.379749i	$0.876010\pi$
$80$	2.23603	−	0.0135681i	0.249995	−	0.00151695i
$81$	1.88342	+	8.80072i	0.209269	+	0.977858i
$82$	2.50013	+	2.50013i	0.276093	+	0.276093i
$83$	−0.717790	−	0.717790i	−0.0787877	−	0.0787877i	0.666615	−	0.745402i	$-0.267743\pi$
$83$	−0.717790	−	0.717790i	−0.0787877	−	0.0787877i	−0.745402	+	0.666615i	$0.767743\pi$
$84$	−7.48341	+	3.57259i	−0.816507	+	0.389802i
$85$	1.83583	−	1.85824i	0.199123	−	0.201555i
$86$			3.80067i			0.409836i
$87$	−13.2975	−	4.70370i	−1.42564	−	0.504290i
$88$	0.866730	−	0.866730i	0.0923937	−	0.0923937i
$89$	0.384471			0.0407539			0.0203769	−	0.999792i	$-0.493513\pi$
$89$	0.384471			0.0407539			0.0203769	+	0.999792i	$0.493513\pi$
$90$	−6.66656	+	0.746293i	−0.702717	+	0.0786662i
$91$	23.8120			2.49618
$92$	1.04719	−	1.04719i	0.109177	−	0.109177i
$93$	−12.1160	−	4.28576i	−1.25637	−	0.444413i
$94$		−	9.68521i		−	0.998953i
$95$	0.0135681	+	2.23603i	0.00139205	+	0.229412i
$96$	1.56306	−	0.746209i	0.159530	−	0.0761597i
$97$	−12.5444	−	12.5444i	−1.27369	−	1.27369i	−0.944137	−	0.329554i	$-0.893101\pi$
$97$	−12.5444	−	12.5444i	−1.27369	−	1.27369i	−0.329554	−	0.944137i	$-0.606899\pi$
$98$	11.2583	+	11.2583i	1.13726	+	1.13726i
$99$	−2.31217	+	2.85934i	−0.232382	+	0.287375i
$100$	−0.0606771	−	4.99963i	−0.00606771	−	0.499963i
$101$			1.19949i			0.119354i	0.998218	+	0.0596768i	$0.0190070\pi$
$101$			1.19949i			0.119354i	−0.998218	+	0.0596768i	$0.980993\pi$
$102$	0.674750	−	1.90754i	0.0668102	−	0.188875i
$103$	13.1711	−	13.1711i	1.29778	−	1.29778i	0.367931	−	0.929853i	$-0.380066\pi$
$103$	13.1711	−	13.1711i	1.29778	−	1.29778i	0.929853	−	0.367931i	$-0.119934\pi$
$104$	−4.97363			−0.487705
$105$	8.08995	+	16.6846i	0.789498	+	1.62825i
$106$	4.81722			0.467890
$107$	−9.98389	+	9.98389i	−0.965179	+	0.965179i	−0.999414	−	0.0342348i	$-0.989101\pi$
$107$	−9.98389	+	9.98389i	−0.965179	+	0.965179i	0.0342348	+	0.999414i	$0.489101\pi$
$108$	−4.42762	+	2.71959i	−0.426048	+	0.261693i
$109$			8.95394i			0.857632i	0.903392	+	0.428816i	$0.141069\pi$
$109$			8.95394i			0.857632i	−0.903392	+	0.428816i	$0.858931\pi$
$110$	−1.94979	−	1.92627i	−0.185905	−	0.183663i
$111$	6.15635	+	12.8956i	0.584335	+	1.22399i
$112$	−3.38538	−	3.38538i	−0.319889	−	0.319889i
$113$	−13.3747	−	13.3747i	−1.25818	−	1.25818i	−0.951959	−	0.306225i	$-0.900934\pi$
$113$	−13.3747	−	13.3747i	−1.25818	−	1.25818i	−0.306225	−	0.951959i	$-0.599066\pi$
$114$	0.746209	+	1.56306i	0.0698889	+	0.146394i
$115$	−2.35574	−	2.32733i	−0.219674	−	0.217024i
$116$		−	8.14348i		−	0.756103i
$117$	14.8381	−	1.56996i	1.37178	−	0.145142i
$118$	7.01383	−	7.01383i	0.645676	−	0.645676i
$119$	−5.59288			−0.512699
$120$	−1.68975	−	3.48493i	−0.154253	−	0.318129i
$121$	9.49756			0.863414
$122$	−7.45445	+	7.45445i	−0.674894	+	0.674894i
$123$	2.04225	−	5.77349i	0.184143	−	0.520578i
$124$		−	7.41990i		−	0.666327i
$125$	−11.1785	+	0.203511i	−0.999834	+	0.0182026i
$126$	11.1684	+	9.03116i	0.994959	+	0.804560i
$127$	−6.46428	−	6.46428i	−0.573612	−	0.573612i	0.359524	−	0.933136i	$-0.382939\pi$
$127$	−6.46428	−	6.46428i	−0.573612	−	0.573612i	−0.933136	+	0.359524i	$0.882939\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	5.94069	−	2.83609i	0.523048	−	0.249704i
$130$	0.0674826	+	11.1212i	0.00591861	+	0.975392i
$131$		−	4.64733i		−	0.406039i	−0.979175	−	0.203020i	$-0.934924\pi$
$131$		−	4.64733i		−	0.406039i	0.979175	−	0.203020i	$-0.0650755\pi$
$132$	−2.00152	−	0.707993i	−0.174210	−	0.0616229i
$133$	3.38538	−	3.38538i	0.293550	−	0.293550i
$134$	8.48965			0.733394
$135$	6.14116	+	9.86338i	0.528547	+	0.848904i
$136$	1.16819			0.100171
$137$	0.825480	−	0.825480i	0.0705255	−	0.0705255i	−0.670964	−	0.741490i	$-0.734120\pi$
$137$	0.825480	−	0.825480i	0.0705255	−	0.0705255i	0.741490	+	0.670964i	$0.234120\pi$
$138$	−2.41824	−	0.855399i	−0.205854	−	0.0728164i
$139$		−	3.47441i		−	0.294695i	−0.989085	−	0.147348i	$-0.952926\pi$
$139$		−	3.47441i		−	0.294695i	0.989085	−	0.147348i	$-0.0470736\pi$
$140$	−7.52387	+	7.61574i	−0.635883	+	0.643648i
$141$	−15.1386	+	7.22720i	−1.27490	+	0.608640i
$142$	5.91027	+	5.91027i	0.495979	+	0.495979i
$143$	4.31080	+	4.31080i	0.360487	+	0.360487i
$144$	−2.33275	−	1.88634i	−0.194396	−	0.157195i
$145$	−18.2090	+	0.110491i	−1.51218	+	0.00917579i
$146$			5.64827i			0.467454i
$147$	9.19640	−	25.9985i	0.758506	−	2.14432i
$148$	−5.83375	+	5.83375i	−0.479531	+	0.479531i
$149$	1.10597			0.0906042			0.0453021	−	0.998973i	$-0.485575\pi$
$149$	1.10597			0.0906042			0.0453021	+	0.998973i	$0.485575\pi$
$150$	−7.76947	+	3.82561i	−0.634375	+	0.312360i
$151$	3.28699			0.267491			0.133746	−	0.991016i	$-0.457299\pi$
$151$	3.28699			0.267491			0.133746	+	0.991016i	$0.457299\pi$
$152$	−0.707107	+	0.707107i	−0.0573539	+	0.0573539i
$153$	−3.48511	+	0.368745i	−0.281755	+	0.0298113i
$154$			5.86842i			0.472891i
$155$	−16.5911	+	0.100674i	−1.33263	+	0.00808630i
$156$	3.71137	+	7.77411i	0.297148	+	0.622427i
$157$	−12.0134	−	12.0134i	−0.958773	−	0.958773i	0.0404098	−	0.999183i	$-0.487134\pi$
$157$	−12.0134	−	12.0134i	−0.958773	−	0.958773i	−0.999183	+	0.0404098i	$0.987134\pi$
$158$	4.77337	+	4.77337i	0.379749	+	0.379749i
$159$	−3.59466	−	7.52963i	−0.285075	−	0.597138i
$160$	1.57152	−	1.59070i	0.124239	−	0.125756i
$161$			7.09025i			0.558790i
$162$	7.55483	+	4.89127i	0.593564	+	0.384295i
$163$	3.82552	−	3.82552i	0.299638	−	0.299638i	−0.541234	−	0.840872i	$-0.682043\pi$
$163$	3.82552	−	3.82552i	0.299638	−	0.299638i	0.840872	+	0.541234i	$0.182043\pi$
$164$	3.53572			0.276093
$165$	−1.55593	+	4.48505i	−0.121129	+	0.349161i
$166$	−1.01511			−0.0787877
$167$	−14.1056	+	14.1056i	−1.09152	+	1.09152i	−0.0961553	+	0.995366i	$0.530655\pi$
$167$	−14.1056	+	14.1056i	−1.09152	+	1.09152i	−0.995366	+	0.0961553i	$0.969345\pi$
$168$	−2.76537	+	7.81778i	−0.213353	+	0.603155i
$169$		−	11.7370i		−	0.902849i
$170$	−0.0158500	−	2.61210i	−0.00121564	−	0.200339i
$171$	1.88634	−	2.33275i	0.144252	−	0.178390i
$172$	2.68748	+	2.68748i	0.204918	+	0.204918i
$173$	−6.57463	−	6.57463i	−0.499860	−	0.499860i	0.411535	−	0.911394i	$-0.364993\pi$
$173$	−6.57463	−	6.57463i	−0.499860	−	0.499860i	−0.911394	+	0.411535i	$0.864993\pi$
$174$	−12.7288	+	6.07674i	−0.964966	+	0.460676i
$175$	17.1311	+	16.7203i	1.29499	+	1.26393i
$176$		−	1.22574i		−	0.0923937i
$177$	−16.1969	−	5.72929i	−1.21743	−	0.430639i
$178$	0.271862	−	0.271862i	0.0203769	−	0.0203769i
$179$	11.2885			0.843741			0.421870	−	0.906656i	$-0.361374\pi$
$179$	11.2885			0.843741			0.421870	+	0.906656i	$0.361374\pi$
$180$	−4.18626	+	5.24168i	−0.312026	+	0.390692i
$181$	−9.96083			−0.740383			−0.370191	−	0.928956i	$-0.620708\pi$
$181$	−9.96083			−0.740383			−0.370191	+	0.928956i	$0.620708\pi$
$182$	16.8377	−	16.8377i	1.24809	−	1.24809i
$183$	17.2144	+	6.08920i	1.27252	+	0.450127i
$184$		−	1.48094i		−	0.109177i
$185$	13.1236	+	12.9653i	0.964865	+	0.953226i
$186$	−11.5978	+	5.53680i	−0.850391	+	0.405978i
$187$	−1.01250	−	1.01250i	−0.0740416	−	0.0740416i
$188$	−6.84848	−	6.84848i	−0.499477	−	0.499477i
$189$	5.78233	−	24.1961i	0.420602	−	1.76000i
$190$	1.59070	+	1.57152i	0.115402	+	0.114010i
$191$		−	10.1454i		−	0.734095i	−0.930202	−	0.367048i	$-0.880369\pi$
$191$		−	10.1454i		−	0.734095i	0.930202	−	0.367048i	$-0.119631\pi$
$192$	0.577604	−	1.63290i	0.0416850	−	0.117845i
$193$	1.33016	−	1.33016i	0.0957468	−	0.0957468i	−0.657611	−	0.753358i	$-0.728433\pi$
$193$	1.33016	−	1.33016i	0.0957468	−	0.0957468i	0.753358	+	0.657611i	$0.228433\pi$
$194$	−17.7405			−1.27369
$195$	17.3328	−	8.40421i	1.24123	−	0.601838i
$196$	15.9216			1.13726
$197$	−3.67465	+	3.67465i	−0.261808	+	0.261808i	−0.825788	−	0.563980i	$-0.809269\pi$
$197$	−3.67465	+	3.67465i	−0.261808	+	0.261808i	0.563980	+	0.825788i	$0.309269\pi$
$198$	0.386912	+	3.65681i	0.0274966	+	0.259878i
$199$		−	0.894086i		−	0.0633801i	−0.999498	−	0.0316900i	$-0.989911\pi$
$199$		−	0.894086i		−	0.0633801i	0.999498	−	0.0316900i	$-0.0100889\pi$
$200$	−3.57818	−	3.49237i	−0.253015	−	0.246948i
$201$	−6.33506	−	13.2699i	−0.446841	−	0.935985i
$202$	0.848167	+	0.848167i	0.0596768	+	0.0596768i
$203$	27.5688	+	27.5688i	1.93495	+	1.93495i
$204$	−0.871713	−	1.82595i	−0.0610321	−	0.127842i
$205$	−0.0479729	−	7.90597i	−0.00335057	−	0.552177i
$206$		−	18.6267i		−	1.29778i
$207$	0.467469	+	4.41817i	0.0324913	+	0.307084i
$208$	−3.51689	+	3.51689i	−0.243852	+	0.243852i
$209$	1.22574			0.0847863
$210$	17.5183	+	6.07737i	1.20888	+	0.419378i
$211$	−0.656325			−0.0451833			−0.0225916	−	0.999745i	$-0.507192\pi$
$211$	−0.656325			−0.0451833			−0.0225916	+	0.999745i	$0.507192\pi$
$212$	3.40629	−	3.40629i	0.233945	−	0.233945i
$213$	4.82784	−	13.6484i	0.330798	−	0.935176i
$214$			14.1194i			0.965179i
$215$	5.97281	−	6.04574i	0.407342	−	0.412316i
$216$	−1.20776	+	5.05384i	−0.0821775	+	0.343870i
$217$	25.1192	+	25.1192i	1.70520	+	1.70520i
$218$	6.33139	+	6.33139i	0.428816	+	0.428816i
$219$	8.82861	−	4.21479i	0.596582	−	0.284809i
$220$	−2.74079	+	0.0166309i	−0.184784	+	0.00112126i
$221$			5.81014i			0.390832i
$222$	13.4717	+	4.76533i	0.904163	+	0.319828i
$223$	−5.81309	+	5.81309i	−0.389273	+	0.389273i	−0.874428	−	0.485155i	$-0.838763\pi$
$223$	−5.81309	+	5.81309i	−0.389273	+	0.389273i	0.485155	+	0.874428i	$0.338763\pi$
$224$	−4.78765			−0.319889
$225$	11.7773	+	9.28948i	0.785156	+	0.619298i
$226$	−18.9147			−1.25818
$227$	11.1211	−	11.1211i	0.738133	−	0.738133i	−0.234083	−	0.972217i	$-0.575209\pi$
$227$	11.1211	−	11.1211i	0.738133	−	0.738133i	0.972217	+	0.234083i	$0.0752088\pi$
$228$	1.63290	+	0.577604i	0.108142	+	0.0382528i
$229$			15.9766i			1.05576i	0.849318	+	0.527881i	$0.177013\pi$
$229$			15.9766i			1.05576i	−0.849318	+	0.527881i	$0.822987\pi$
$230$	−3.31143	+	0.0200935i	−0.218349	+	0.00132493i
$231$	9.17273	−	4.37907i	0.603521	−	0.288122i
$232$	−5.75831	−	5.75831i	−0.378051	−	0.378051i
$233$	−10.3048	−	10.3048i	−0.675090	−	0.675090i	0.283795	−	0.958885i	$-0.408407\pi$
$233$	−10.3048	−	10.3048i	−0.675090	−	0.675090i	−0.958885	+	0.283795i	$0.908407\pi$
$234$	9.38198	−	11.6022i	0.613319	−	0.758462i
$235$	−15.2205	+	15.4063i	−0.992873	+	1.00500i
$236$		−	9.91906i		−	0.645676i
$237$	3.89915	−	11.0230i	0.253277	−	0.716022i
$238$	−3.95477	+	3.95477i	−0.256349	+	0.256349i
$239$	−16.1045			−1.04172			−0.520858	−	0.853644i	$-0.674388\pi$
$239$	−16.1045			−1.04172			−0.520858	+	0.853644i	$0.674388\pi$
$240$	−3.65905	−	1.26938i	−0.236191	−	0.0819383i
$241$	−19.9193			−1.28312			−0.641559	−	0.767074i	$-0.721712\pi$
$241$	−19.9193			−1.28312			−0.641559	+	0.767074i	$0.721712\pi$
$242$	6.71579	−	6.71579i	0.431707	−	0.431707i
$243$	2.00789	−	15.4586i	0.128806	−	0.991670i
$244$			10.5422i			0.674894i
$245$	−0.216026	−	35.6012i	−0.0138014	−	2.27448i
$246$	−2.63839	−	5.52656i	−0.168218	−	0.352361i
$247$	−3.51689	−	3.51689i	−0.223774	−	0.223774i
$248$	−5.24666	−	5.24666i	−0.333163	−	0.333163i
$249$	0.757484	+	1.58668i	0.0480036	+	0.100552i
$250$	−7.76048	+	8.04829i	−0.490816	+	0.509018i
$251$		−	17.8998i		−	1.12982i	−0.825151	−	0.564912i	$-0.808910\pi$
$251$		−	17.8998i		−	1.12982i	0.825151	−	0.564912i	$-0.191090\pi$
$252$	14.2832	−	1.51125i	0.899759	−	0.0951998i
$253$	−1.28358	+	1.28358i	−0.0806979	+	0.0806979i
$254$	−9.14187			−0.573612
$255$	−4.07106	+	1.97395i	−0.254939	+	0.123613i
$256$	1.00000			0.0625000
$257$	−14.5464	+	14.5464i	−0.907378	+	0.907378i	−0.996060	−	0.0886822i	$-0.971734\pi$
$257$	−14.5464	+	14.5464i	−0.907378	+	0.907378i	0.0886822	+	0.996060i	$0.471734\pi$
$258$	2.19528	−	6.20612i	0.136672	−	0.386376i
$259$		−	39.4990i		−	2.45435i
$260$	7.91158	+	7.81614i	0.490655	+	0.484737i
$261$	18.9967	+	15.3614i	1.17586	+	0.950846i
$262$	−3.28616	−	3.28616i	−0.203020	−	0.203020i
$263$	6.05674	+	6.05674i	0.373475	+	0.373475i	0.868741	−	0.495266i	$-0.164930\pi$
$263$	6.05674	+	6.05674i	0.373475	+	0.373475i	−0.495266	+	0.868741i	$0.664930\pi$
$264$	−1.91591	+	0.914660i	−0.117916	+	0.0562934i
$265$	−7.66277	−	7.57034i	−0.470720	−	0.465042i
$266$		−	4.78765i		−	0.293550i
$267$	−0.627804	−	0.222072i	−0.0384210	−	0.0135906i
$268$	6.00309	−	6.00309i	0.366697	−	0.366697i
$269$	−9.51326			−0.580034			−0.290017	−	0.957022i	$-0.593661\pi$
$269$	−9.51326			−0.580034			−0.290017	+	0.957022i	$0.593661\pi$
$270$	11.3169	+	2.63201i	0.688725	+	0.160179i
$271$	0.405502			0.0246325			0.0123162	−	0.999924i	$-0.496080\pi$
$271$	0.405502			0.0246325			0.0123162	+	0.999924i	$0.496080\pi$
$272$	0.826034	−	0.826034i	0.0500857	−	0.0500857i
$273$	−38.8828	−	13.7539i	−2.35329	−	0.832426i
$274$		−	1.16740i		−	0.0705255i
$275$	0.0743744	+	6.12825i	0.00448494	+	0.369548i
$276$	−2.31481	+	1.10509i	−0.139335	+	0.0665189i
$277$	3.15621	+	3.15621i	0.189639	+	0.189639i	0.795540	−	0.605901i	$-0.207187\pi$
$277$	3.15621	+	3.15621i	0.189639	+	0.189639i	−0.605901	+	0.795540i	$0.707187\pi$
$278$	−2.45678	−	2.45678i	−0.147348	−	0.147348i
$279$	17.3088	+	13.9965i	1.03625	+	0.837947i
$280$	0.0649592	+	10.7053i	0.00388205	+	0.639765i
$281$		−	11.9223i		−	0.711227i	−0.934633	−	0.355613i	$-0.884272\pi$
$281$		−	11.9223i		−	0.711227i	0.934633	−	0.355613i	$-0.115728\pi$
$282$	−5.59422	+	15.8150i	−0.333131	+	0.941770i
$283$	11.1386	−	11.1386i	0.662120	−	0.662120i	−0.293759	−	0.955879i	$-0.594906\pi$
$283$	11.1386	−	11.1386i	0.662120	−	0.662120i	0.955879	+	0.293759i	$0.0949063\pi$
$284$	8.35839			0.495979
$285$	1.26938	−	3.65905i	0.0751917	−	0.216744i
$286$	6.09639			0.360487
$287$	−11.9698	+	11.9698i	−0.706553	+	0.706553i
$288$	−2.98335	+	0.315656i	−0.175795	+	0.0186002i
$289$			15.6353i			0.919726i
$290$	−12.7976	+	12.9539i	−0.751501	+	0.760677i
$291$	13.2381	+	27.7295i	0.776031	+	1.62553i
$292$	3.99393	+	3.99393i	0.233727	+	0.233727i
$293$	3.32969	+	3.32969i	0.194522	+	0.194522i	0.797647	−	0.603125i	$-0.206078\pi$
$293$	3.32969	+	3.32969i	0.194522	+	0.194522i	−0.603125	+	0.797647i	$0.706078\pi$
$294$	−11.8809	−	24.8866i	−0.692907	−	1.45141i
$295$	−22.1793	+	0.134582i	−1.29133	+	0.00783569i
$296$			8.25017i			0.479531i
$297$	5.42712	−	3.33352i	0.314913	−	0.193430i
$298$	0.782036	−	0.782036i	0.0453021	−	0.0453021i
$299$	7.36568			0.425968
$300$	−2.78873	+	8.19896i	−0.161007	+	0.473367i
$301$	−18.1963			−1.04882
$302$	2.32425	−	2.32425i	0.133746	−	0.133746i
$303$	0.692830	−	1.95865i	0.0398020	−	0.112522i
$304$			1.00000i			0.0573539i
$305$	23.5726	−	0.143037i	1.34976	−	0.00819027i
$306$	−2.20360	+	2.72509i	−0.125972	+	0.155783i
$307$	−1.69015	−	1.69015i	−0.0964621	−	0.0964621i	0.657229	−	0.753691i	$-0.271728\pi$
$307$	−1.69015	−	1.69015i	−0.0964621	−	0.0964621i	−0.753691	+	0.657229i	$0.771728\pi$
$308$	4.14960	+	4.14960i	0.236446	+	0.236446i
$309$	−29.1147	+	13.8994i	−1.65628	+	0.790711i
$310$	−11.6605	+	11.8029i	−0.662271	+	0.670358i
$311$		−	14.3337i		−	0.812790i	−0.913697	−	0.406395i	$-0.866786\pi$
$311$		−	14.3337i		−	0.812790i	0.913697	−	0.406395i	$-0.133214\pi$
$312$	8.12146	+	2.87279i	0.459787	+	0.162640i
$313$	1.56414	−	1.56414i	0.0884102	−	0.0884102i	−0.661519	−	0.749929i	$-0.730088\pi$
$313$	1.56414	−	1.56414i	0.0884102	−	0.0884102i	0.749929	+	0.661519i	$0.230088\pi$
$314$	−16.9895			−0.958773
$315$	−3.57299	−	31.9172i	−0.201315	−	1.79833i
$316$	6.75057			0.379749
$317$	21.5987	−	21.5987i	1.21311	−	1.21311i	0.243107	−	0.969999i	$-0.421833\pi$
$317$	21.5987	−	21.5987i	1.21311	−	1.21311i	0.969999	−	0.243107i	$-0.0781666\pi$
$318$	−7.86606	−	2.78245i	−0.441107	−	0.156032i
$319$			9.98179i			0.558873i
$320$	−0.0135681	−	2.23603i	−0.000758477	−	0.124998i
$321$	22.0695	−	10.5360i	1.23180	−	0.588062i
$322$	5.01356	+	5.01356i	0.279395	+	0.279395i
$323$	0.826034	+	0.826034i	0.0459618	+	0.0459618i
$324$	8.80072	−	1.88342i	0.488929	−	0.104635i
$325$	17.3698	−	17.7966i	0.963501	−	0.987175i
$326$		−	5.41010i		−	0.299638i
$327$	5.17183	−	14.6209i	0.286003	−	0.808538i
$328$	2.50013	−	2.50013i	0.138047	−	0.138047i
$329$	46.3694			2.55643
$330$	2.07120	+	4.27162i	0.114016	+	0.235145i
$331$	−6.37126			−0.350196			−0.175098	−	0.984551i	$-0.556024\pi$
$331$	−6.37126			−0.350196			−0.175098	+	0.984551i	$0.556024\pi$
$332$	−0.717790	+	0.717790i	−0.0393939	+	0.0393939i
$333$	−2.60421	−	24.6131i	−0.142710	−	1.34879i
$334$			19.9483i			1.09152i
$335$	−13.5045	−	13.3416i	−0.737831	−	0.728931i
$336$	3.57259	+	7.48341i	0.194901	+	0.408254i
$337$	1.13280	+	1.13280i	0.0617073	+	0.0617073i	0.737287	−	0.675580i	$-0.236107\pi$
$337$	1.13280	+	1.13280i	0.0617073	+	0.0617073i	−0.675580	+	0.737287i	$0.736107\pi$
$338$	−8.29934	−	8.29934i	−0.451424	−	0.451424i
$339$	14.1143	+	29.5648i	0.766583	+	1.60574i
$340$	−1.85824	−	1.83583i	−0.100777	−	0.0995617i
$341$			9.09487i			0.492515i
$342$	−0.315656	−	2.98335i	−0.0170687	−	0.161321i
$343$	−30.2032	+	30.2032i	−1.63082	+	1.63082i
$344$	3.80067			0.204918
$345$	2.50243	+	5.16099i	0.134726	+	0.277858i
$346$	−9.29793			−0.499860
$347$	−22.1434	+	22.1434i	−1.18872	+	1.18872i	−0.211296	+	0.977422i	$0.567768\pi$
$347$	−22.1434	+	22.1434i	−1.18872	+	1.18872i	−0.977422	+	0.211296i	$0.932232\pi$
$348$	−4.70370	+	13.2975i	−0.252145	+	0.712821i
$349$		−	19.6754i		−	1.05320i	−0.850113	−	0.526600i	$-0.823467\pi$
$349$		−	19.6754i		−	1.05320i	0.850113	−	0.526600i	$-0.176533\pi$
$350$	23.9365	−	0.290501i	1.27946	−	0.0155279i
$351$	−25.1360	−	6.00695i	−1.34166	−	0.320627i
$352$	−0.866730	−	0.866730i	−0.0461969	−	0.0461969i
$353$	24.9047	+	24.9047i	1.32554	+	1.32554i	0.909214	+	0.416330i	$0.136684\pi$
$353$	24.9047	+	24.9047i	1.32554	+	1.32554i	0.416330	+	0.909214i	$0.363316\pi$
$354$	−15.5041	+	7.40169i	−0.824035	+	0.393396i
$355$	−0.113407	−	18.6896i	−0.00601902	−	0.991940i
$356$		−	0.384471i		−	0.0203769i
$357$	9.13264	+	3.23047i	0.483350	+	0.170975i
$358$	7.98216	−	7.98216i	0.421870	−	0.421870i
$359$	−20.9304			−1.10466			−0.552331	−	0.833625i	$-0.686261\pi$
$359$	−20.9304			−1.10466			−0.552331	+	0.833625i	$0.686261\pi$
$360$	0.746293	+	6.66656i	0.0393331	+	0.351359i
$361$	−1.00000			−0.0526316
$362$	−7.04337	+	7.04337i	−0.370191	+	0.370191i
$363$	−15.5086	−	5.48583i	−0.813990	−	0.287931i
$364$		−	23.8120i		−	1.24809i
$365$	8.87634	−	8.98472i	0.464609	−	0.470282i
$366$	16.4781	−	7.86667i	0.861325	−	0.411198i
$367$	26.3718	+	26.3718i	1.37660	+	1.37660i	0.850298	+	0.526301i	$0.176422\pi$
$367$	26.3718	+	26.3718i	1.37660	+	1.37660i	0.526301	+	0.850298i	$0.323578\pi$
$368$	−1.04719	−	1.04719i	−0.0545883	−	0.0545883i
$369$	−6.66958	+	8.24795i	−0.347205	+	0.429371i
$370$	18.4476	−	0.111939i	0.959045	−	0.00581942i
$371$			23.0632i			1.19738i
$372$	−4.28576	+	12.1160i	−0.222206	+	0.628184i
$373$	−6.66242	+	6.66242i	−0.344967	+	0.344967i	−0.858231	−	0.513264i	$-0.828436\pi$
$373$	−6.66242	+	6.66242i	−0.344967	+	0.344967i	0.513264	+	0.858231i	$0.328436\pi$
$374$	−1.43190			−0.0740416
$375$	18.3709	+	6.12442i	0.948671	+	0.316264i
$376$	−9.68521			−0.499477
$377$	28.6397	−	28.6397i	1.47502	−	1.47502i
$378$	−13.0205	−	21.1979i	−0.669701	−	1.09030i
$379$			0.205871i			0.0105749i	0.999986	+	0.00528745i	$0.00168305\pi$
$379$			0.205871i			0.0105749i	−0.999986	+	0.00528745i	$0.998317\pi$
$380$	2.23603	−	0.0135681i	0.114706	−	0.000696027i
$381$	6.82175	+	14.2893i	0.349489	+	0.732065i
$382$	−7.17388	−	7.17388i	−0.367048	−	0.367048i
$383$	−8.26926	−	8.26926i	−0.422539	−	0.422539i	0.463538	−	0.886077i	$-0.346580\pi$
$383$	−8.26926	−	8.26926i	−0.422539	−	0.422539i	−0.886077	+	0.463538i	$0.846580\pi$
$384$	−0.746209	−	1.56306i	−0.0380798	−	0.0797648i
$385$	9.22232	−	9.33493i	0.470013	−	0.475752i
$386$		−	1.88113i		−	0.0957468i
$387$	−11.3387	+	1.19970i	−0.576379	+	0.0609843i
$388$	−12.5444	+	12.5444i	−0.636846	+	0.636846i
$389$	−25.3999			−1.28782			−0.643912	−	0.765099i	$-0.722690\pi$
$389$	−25.3999			−1.28782			−0.643912	+	0.765099i	$0.722690\pi$
$390$	6.31344	−	18.1988i	0.319694	−	0.921532i
$391$	−1.73002			−0.0874910
$392$	11.2583	−	11.2583i	0.568630	−	0.568630i
$393$	−2.68432	+	7.58865i	−0.135406	+	0.382797i
$394$			5.19674i			0.261808i
$395$	−0.0915921	−	15.0944i	−0.00460850	−	0.759484i
$396$	2.85934	+	2.31217i	0.143687	+	0.116191i
$397$	14.4297	+	14.4297i	0.724206	+	0.724206i	0.969459	−	0.245253i	$-0.0788711\pi$
$397$	14.4297	+	14.4297i	0.724206	+	0.724206i	−0.245253	+	0.969459i	$0.578871\pi$
$398$	−0.632214	−	0.632214i	−0.0316900	−	0.0316900i
$399$	−7.48341	+	3.57259i	−0.374639	+	0.178853i
$400$	−4.99963	+	0.0606771i	−0.249982	+	0.00303385i
$401$		−	8.03063i		−	0.401030i	−0.979691	−	0.200515i	$-0.935738\pi$
$401$		−	8.03063i		−	0.401030i	0.979691	−	0.200515i	$-0.0642616\pi$
$402$	−13.8628	−	4.90366i	−0.691413	−	0.244572i
$403$	26.0950	−	26.0950i	1.29988	−	1.29988i
$404$	1.19949			0.0596768
$405$	−4.33079	−	19.6531i	−0.215199	−	0.976570i
$406$	38.9882			1.93495
$407$	7.15067	−	7.15067i	0.354445	−	0.354445i
$408$	−1.90754	−	0.674750i	−0.0944373	−	0.0334051i
$409$		−	13.8653i		−	0.685596i	−0.939409	−	0.342798i	$-0.888625\pi$
$409$		−	13.8653i		−	0.685596i	0.939409	−	0.342798i	$-0.111375\pi$
$410$	−5.62429	−	5.55644i	−0.277764	−	0.274413i
$411$	−1.82473	+	0.871129i	−0.0900073	+	0.0429696i
$412$	−13.1711	−	13.1711i	−0.648892	−	0.648892i
$413$	33.5798	+	33.5798i	1.65235	+	1.65235i
$414$	3.45467	+	2.79357i	0.169788	+	0.137296i
$415$	1.61474	+	1.59526i	0.0792643	+	0.0783082i
$416$			4.97363i			0.243852i
$417$	−2.00683	+	5.67337i	−0.0982749	+	0.277826i
$418$	0.866730	−	0.866730i	0.0423931	−	0.0423931i
$419$	17.7272			0.866028			0.433014	−	0.901387i	$-0.357450\pi$
$419$	17.7272			0.866028			0.433014	+	0.901387i	$0.357450\pi$
$420$	16.6846	−	8.08995i	0.814127	−	0.394749i
$421$	2.65269			0.129284			0.0646420	−	0.997909i	$-0.479409\pi$
$421$	2.65269			0.129284			0.0646420	+	0.997909i	$0.479409\pi$
$422$	−0.464092	+	0.464092i	−0.0225916	+	0.0225916i
$423$	28.8943	−	3.05719i	1.40489	−	0.148646i
$424$		−	4.81722i		−	0.233945i
$425$	−4.07974	+	4.17999i	−0.197897	+	0.202759i
$426$	−6.23711	−	13.0647i	−0.302189	−	0.632987i
$427$	−35.6893	−	35.6893i	−1.72713	−	1.72713i
$428$	9.98389	+	9.98389i	0.482590	+	0.482590i
$429$	−4.54918	−	9.52905i	−0.219637	−	0.460067i
$430$	−0.0515677	−	8.49839i	−0.00248681	−	0.409829i
$431$		−	17.0087i		−	0.819280i	−0.912247	−	0.409640i	$-0.865654\pi$
$431$		−	17.0087i		−	0.819280i	0.912247	−	0.409640i	$-0.134346\pi$
$432$	2.71959	+	4.42762i	0.130846	+	0.213024i
$433$	13.8732	−	13.8732i	0.666705	−	0.666705i	−0.290247	−	0.956952i	$-0.593738\pi$
$433$	13.8732	−	13.8732i	0.666705	−	0.666705i	0.956952	+	0.290247i	$0.0937375\pi$
$434$	35.5239			1.70520
$435$	29.7974	+	10.3372i	1.42868	+	0.495630i
$436$	8.95394			0.428816
$437$	1.04719	−	1.04719i	0.0500937	−	0.0500937i
$438$	3.26246	−	9.22308i	0.155887	−	0.440696i
$439$			7.44257i			0.355214i	0.984101	+	0.177607i	$0.0568357\pi$
$439$			7.44257i			0.355214i	−0.984101	+	0.177607i	$0.943164\pi$
$440$	−1.92627	+	1.94979i	−0.0918314	+	0.0929526i
$441$	−30.0337	+	37.1412i	−1.43017	+	1.76863i
$442$	4.10839	+	4.10839i	0.195416	+	0.195416i
$443$	−14.0091	−	14.0091i	−0.665593	−	0.665593i	0.291100	−	0.956693i	$-0.405979\pi$
$443$	−14.0091	−	14.0091i	−0.665593	−	0.665593i	−0.956693	+	0.291100i	$0.905979\pi$
$444$	12.8956	−	6.15635i	0.611996	−	0.292168i
$445$	−0.859688	+	0.00521653i	−0.0407531	+	0.000247287i
$446$			8.22095i			0.389273i
$447$	−1.80593	−	0.638810i	−0.0854178	−	0.0302147i
$448$	−3.38538	+	3.38538i	−0.159944	+	0.159944i
$449$	17.0757			0.805851			0.402926	−	0.915233i	$-0.367993\pi$
$449$	17.0757			0.805851			0.402926	+	0.915233i	$0.367993\pi$
$450$	14.8965	−	1.75918i	0.702227	−	0.0829287i
$451$	−4.33388			−0.204074
$452$	−13.3747	+	13.3747i	−0.629092	+	0.629092i
$453$	−5.36734	−	1.89858i	−0.252179	−	0.0892030i
$454$		−	15.7276i		−	0.738133i
$455$	−53.2444	+	0.323083i	−2.49613	+	0.0151464i
$456$	1.56306	−	0.746209i	0.0731972	−	0.0349445i
$457$	−4.57545	−	4.57545i	−0.214030	−	0.214030i	0.591947	−	0.805977i	$-0.298360\pi$
$457$	−4.57545	−	4.57545i	−0.214030	−	0.214030i	−0.805977	+	0.591947i	$0.798360\pi$
$458$	11.2971	+	11.2971i	0.527881	+	0.527881i
$459$	5.90384	+	1.41089i	0.275568	+	0.0658547i
$460$	−2.32733	+	2.35574i	−0.108512	+	0.109837i
$461$		−	0.120191i		−	0.00559787i	−0.999996	−	0.00279893i	$-0.999109\pi$
$461$		−	0.120191i		−	0.00559787i	0.999996	−	0.00279893i	$-0.000890930\pi$
$462$	3.38963	−	9.58257i	0.157700	−	0.445822i
$463$	−5.82164	+	5.82164i	−0.270555	+	0.270555i	−0.829323	−	0.558769i	$-0.811274\pi$
$463$	−5.82164	+	5.82164i	−0.270555	+	0.270555i	0.558769	+	0.829323i	$0.311274\pi$
$464$	−8.14348			−0.378051
$465$	27.1498	+	9.41869i	1.25904	+	0.436781i
$466$	−14.5732			−0.675090
$467$	−1.26700	+	1.26700i	−0.0586298	+	0.0586298i	−0.735814	−	0.677184i	$-0.763200\pi$
$467$	−1.26700	+	1.26700i	−0.0586298	+	0.0586298i	0.677184	+	0.735814i	$0.263200\pi$
$468$	−1.56996	−	14.8381i	−0.0725712	−	0.685890i
$469$			40.6455i			1.87684i
$470$	0.131410	+	21.6564i	0.00606147	+	0.998935i
$471$	12.6777	+	26.5557i	0.584159	+	1.22362i
$472$	−7.01383	−	7.01383i	−0.322838	−	0.322838i
$473$	−3.29415	−	3.29415i	−0.151465	−	0.151465i
$474$	−5.03734	−	10.5516i	−0.231373	−	0.484650i
$475$	−0.0606771	−	4.99963i	−0.00278406	−	0.229399i
$476$			5.59288i			0.256349i
$477$	1.52058	+	14.3714i	0.0696227	+	0.658023i
$478$	−11.3876	+	11.3876i	−0.520858	+	0.520858i
$479$	−4.76857			−0.217881			−0.108941	−	0.994048i	$-0.534746\pi$
$479$	−4.76857			−0.217881			−0.108941	+	0.994048i	$0.534746\pi$
$480$	−3.48493	+	1.68975i	−0.159065	+	0.0771263i
$481$	−41.0333			−1.87096
$482$	−14.0851	+	14.0851i	−0.641559	+	0.641559i
$483$	4.09536	−	11.5777i	0.186345	−	0.526803i
$484$		−	9.49756i		−	0.431707i
$485$	28.2198	+	27.8794i	1.28140	+	1.26594i
$486$	−9.51109	−	12.3507i	−0.431432	−	0.560238i
$487$	18.6777	+	18.6777i	0.846368	+	0.846368i	0.989678	−	0.143310i	$-0.0457747\pi$
$487$	18.6777	+	18.6777i	0.846368	+	0.846368i	−0.143310	+	0.989678i	$0.545775\pi$
$488$	7.45445	+	7.45445i	0.337447	+	0.337447i
$489$	−8.45634	+	4.03707i	−0.382409	+	0.182563i
$490$	−25.3266	−	25.0211i	−1.14414	−	1.13034i
$491$			42.9796i			1.93964i	0.243814	+	0.969822i	$0.421601\pi$
$491$			42.9796i			1.93964i	−0.243814	+	0.969822i	$0.578399\pi$
$492$	−5.77349	−	2.04225i	−0.260289	−	0.0920716i
$493$	−6.72679	+	6.72679i	−0.302959	+	0.302959i
$494$	−4.97363			−0.223774
$495$	5.13127	−	6.42494i	0.230634	−	0.288780i
$496$	−7.41990			−0.333163
$497$	−28.2963	+	28.2963i	−1.26926	+	1.26926i
$498$	1.65757	+	0.586331i	0.0742777	+	0.0262741i
$499$			20.8455i			0.933173i	0.884475	+	0.466587i	$0.154516\pi$
$499$			20.8455i			0.933173i	−0.884475	+	0.466587i	$0.845484\pi$
$500$	0.203511	+	11.1785i	0.00910128	+	0.499917i
$501$	31.1805	−	14.8856i	1.39304	−	0.665040i
$502$	−12.6570	−	12.6570i	−0.564912	−	0.564912i
$503$	−15.7847	−	15.7847i	−0.703804	−	0.703804i	0.261421	−	0.965225i	$-0.415809\pi$
$503$	−15.7847	−	15.7847i	−0.703804	−	0.703804i	−0.965225	+	0.261421i	$0.915809\pi$
$504$	9.03116	−	11.1684i	0.402280	−	0.497480i
$505$	−0.0162747	−	2.68209i	−0.000724216	−	0.119351i
$506$			1.81525i			0.0806979i
$507$	−6.77936	+	19.1654i	−0.301082	+	0.851167i
$508$	−6.46428	+	6.46428i	−0.286806	+	0.286806i
$509$	4.31039			0.191055			0.0955274	−	0.995427i	$-0.469546\pi$
$509$	4.31039			0.191055			0.0955274	+	0.995427i	$0.469546\pi$
$510$	−1.48288	+	4.27446i	−0.0656629	+	0.189276i
$511$	−27.0420			−1.19627
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−4.42762	+	2.71959i	−0.195484	+	0.120073i
$514$			20.5717i			0.907378i
$515$	−29.2722	+	29.6296i	−1.28989	+	1.30563i
$516$	−2.83609	−	5.94069i	−0.124852	−	0.261524i
$517$	8.39446	+	8.39446i	0.369188	+	0.369188i
$518$	−27.9300	−	27.9300i	−1.22717	−	1.22717i
$519$	6.93820	+	14.5333i	0.304553	+	0.637939i
$520$	11.1212	−	0.0674826i	0.487696	−	0.00295931i
$521$		−	11.7874i		−	0.516417i	−0.966089	−	0.258208i	$-0.916868\pi$
$521$		−	11.7874i		−	0.516417i	0.966089	−	0.258208i	$-0.0831321\pi$
$522$	24.2948	−	2.57053i	1.06336	−	0.112509i
$523$	−9.59018	+	9.59018i	−0.419349	+	0.419349i	−0.884979	−	0.465630i	$-0.845828\pi$
$523$	−9.59018	+	9.59018i	−0.419349	+	0.419349i	0.465630	+	0.884979i	$0.345828\pi$
$524$	−4.64733			−0.203020
$525$	−18.3157	−	37.1975i	−0.799364	−	1.62343i
$526$	8.56553			0.373475
$527$	−6.12909	+	6.12909i	−0.266987	+	0.266987i
$528$	−0.707993	+	2.00152i	−0.0308114	+	0.0871048i
$529$		−	20.8068i		−	0.904644i
$530$	−10.7714	+	0.0653603i	−0.467881	+	0.00283907i
$531$	23.1387	+	18.7107i	1.00413	+	0.811977i
$532$	−3.38538	−	3.38538i	−0.146775	−	0.146775i
$533$	12.4347	+	12.4347i	0.538609	+	0.538609i
$534$	−0.600953	+	0.286896i	−0.0260058	+	0.0124152i
$535$	22.1888	−	22.4597i	0.959305	−	0.971018i
$536$		−	8.48965i		−	0.366697i
$537$	−18.4330	−	6.52027i	−0.795443	−	0.281370i
$538$	−6.72689	+	6.72689i	−0.290017	+	0.290017i
$539$	−19.5158			−0.840605
$540$	9.86338	−	6.14116i	0.424452	−	0.264273i
$541$	−29.8151			−1.28185			−0.640925	−	0.767603i	$-0.721449\pi$
$541$	−29.8151			−1.28185			−0.640925	+	0.767603i	$0.721449\pi$
$542$	0.286733	−	0.286733i	0.0123162	−	0.0123162i
$543$	16.2651	+	5.75341i	0.698001	+	0.246903i
$544$		−	1.16819i		−	0.0500857i
$545$	−0.121488	−	20.0212i	−0.00520395	−	0.857616i
$546$	−37.2198	+	17.7688i	−1.59286	+	0.760433i
$547$	−9.70052	−	9.70052i	−0.414764	−	0.414764i	0.468630	−	0.883395i	$-0.344748\pi$
$547$	−9.70052	−	9.70052i	−0.414764	−	0.414764i	−0.883395	+	0.468630i	$0.844748\pi$
$548$	−0.825480	−	0.825480i	−0.0352628	−	0.0352628i
$549$	−24.5922	−	19.8862i	−1.04957	−	0.848721i
$550$	4.38592	+	4.28074i	0.187016	+	0.182531i
$551$		−	8.14348i		−	0.346924i
$552$	−0.855399	+	2.41824i	−0.0364082	+	0.102927i
$553$	−22.8533	+	22.8533i	−0.971819	+	0.971819i
$554$	4.46356			0.189639
$555$	−13.9407	−	28.7513i	−0.591752	−	1.22042i
$556$	−3.47441			−0.147348
$557$	−19.7758	+	19.7758i	−0.837928	+	0.837928i	−0.988586	−	0.150658i	$-0.951861\pi$
$557$	−19.7758	+	19.7758i	−0.837928	+	0.837928i	0.150658	+	0.988586i	$0.451861\pi$
$558$	22.1361	−	2.34213i	0.937097	−	0.0991504i
$559$			18.9031i			0.799517i
$560$	7.61574	+	7.52387i	0.321824	+	0.317942i
$561$	1.06849	+	2.23815i	0.0451119	+	0.0944946i
$562$	−8.43036	−	8.43036i	−0.355613	−	0.355613i
$563$	−26.3822	−	26.3822i	−1.11188	−	1.11188i	−0.992896	−	0.118981i	$-0.962037\pi$
$563$	−26.3822	−	26.3822i	−1.11188	−	1.11188i	−0.118981	−	0.992896i	$-0.537963\pi$
$564$	7.22720	+	15.1386i	0.304320	+	0.637451i
$565$	30.0876	+	29.7247i	1.26580	+	1.25053i
$566$		−	15.7523i		−	0.662120i
$567$	−23.4177	+	36.1699i	−0.983452	+	1.51899i
$568$	5.91027	−	5.91027i	0.247990	−	0.247990i
$569$	21.7175			0.910445			0.455222	−	0.890378i	$-0.349560\pi$
$569$	21.7175			0.910445			0.455222	+	0.890378i	$0.349560\pi$
$570$	−1.68975	−	3.48493i	−0.0707759	−	0.145968i
$571$	−15.2769			−0.639319			−0.319660	−	0.947532i	$-0.603569\pi$
$571$	−15.2769			−0.639319			−0.319660	+	0.947532i	$0.603569\pi$
$572$	4.31080	−	4.31080i	0.180243	−	0.180243i
$573$	−5.86002	+	16.5665i	−0.244806	+	0.692073i
$574$			16.9278i			0.706553i
$575$	5.29908	+	5.17200i	0.220987	+	0.215687i
$576$	−1.88634	+	2.33275i	−0.0785976	+	0.0971978i
$577$	7.00181	+	7.00181i	0.291489	+	0.291489i	0.837668	−	0.546179i	$-0.183918\pi$
$577$	7.00181	+	7.00181i	0.291489	+	0.291489i	−0.546179	+	0.837668i	$0.683918\pi$
$578$	11.0559	+	11.0559i	0.459863	+	0.459863i
$579$	−2.94032	+	1.40371i	−0.122196	+	0.0583364i
$580$	0.110491	+	18.2090i	0.00458790	+	0.756089i
$581$		−	4.85999i		−	0.201626i
$582$	28.9685	+	10.2470i	1.20078	+	0.424750i
$583$	−4.17523	+	4.17523i	−0.172920	+	0.172920i
$584$	5.64827			0.233727
$585$	−33.1570	+	3.71179i	−1.37087	+	0.153464i
$586$	4.70889			0.194522
$587$	5.53868	−	5.53868i	0.228606	−	0.228606i	−0.583504	−	0.812110i	$-0.698319\pi$
$587$	5.53868	−	5.53868i	0.228606	−	0.228606i	0.812110	+	0.583504i	$0.198319\pi$
$588$	−25.9985	−	9.19640i	−1.07216	−	0.379253i
$589$		−	7.41990i		−	0.305732i
$590$	−15.5880	+	15.7783i	−0.641746	+	0.649582i
$591$	8.12283	−	3.87785i	0.334129	−	0.159514i
$592$	5.83375	+	5.83375i	0.239766	+	0.239766i
$593$	−31.4864	−	31.4864i	−1.29299	−	1.29299i	−0.932929	−	0.360061i	$-0.882756\pi$
$593$	−31.4864	−	31.4864i	−1.29299	−	1.29299i	−0.360061	−	0.932929i	$-0.617244\pi$
$594$	1.48040	−	6.19470i	0.0607415	−	0.254172i
$595$	12.5058	−	0.0758846i	0.512689	−	0.00311096i
$596$		−	1.10597i		−	0.0453021i
$597$	−0.516428	+	1.45996i	−0.0211360	+	0.0597520i
$598$	5.20832	−	5.20832i	0.212984	−	0.212984i
$599$	31.3766			1.28201			0.641007	−	0.767535i	$-0.278517\pi$
$599$	31.3766			1.28201			0.641007	+	0.767535i	$0.278517\pi$
$600$	3.82561	+	7.76947i	0.156180	+	0.317187i
$601$	−36.3695			−1.48354			−0.741771	−	0.670654i	$-0.766014\pi$
$601$	−36.3695			−1.48354			−0.741771	+	0.670654i	$0.766014\pi$
$602$	−12.8667	+	12.8667i	−0.524408	+	0.524408i
$603$	2.67981	+	25.3276i	0.109130	+	1.03142i
$604$		−	3.28699i		−	0.133746i
$605$	−21.2368	+	0.128863i	−0.863399	+	0.00523904i
$606$	−0.895070	−	1.87488i	−0.0363597	−	0.0761618i
$607$	8.74748	+	8.74748i	0.355049	+	0.355049i	0.861984	−	0.506935i	$-0.169222\pi$
$607$	8.74748	+	8.74748i	0.355049	+	0.355049i	−0.506935	+	0.861984i	$0.669222\pi$
$608$	0.707107	+	0.707107i	0.0286770	+	0.0286770i
$609$	−29.0933	−	60.9410i	−1.17892	−	2.46945i
$610$	16.5672	−	16.7695i	0.670786	−	0.678977i
$611$		−	48.1707i		−	1.94878i
$612$	0.368745	+	3.48511i	0.0149056	+	0.140877i
$613$	−1.37399	+	1.37399i	−0.0554951	+	0.0554951i	−0.734310	−	0.678815i	$-0.762494\pi$
$613$	−1.37399	+	1.37399i	−0.0554951	+	0.0554951i	0.678815	+	0.734310i	$0.262494\pi$
$614$	−2.39024			−0.0964621
$615$	−4.48818	+	12.9374i	−0.180981	+	0.521686i
$616$	5.86842			0.236446
$617$	−11.8837	+	11.8837i	−0.478419	+	0.478419i	−0.904626	−	0.426207i	$-0.859850\pi$
$617$	−11.8837	+	11.8837i	−0.478419	+	0.478419i	0.426207	+	0.904626i	$0.359850\pi$
$618$	−10.7589	+	30.4156i	−0.432785	+	1.22350i
$619$			4.06759i			0.163490i	0.996653	+	0.0817450i	$0.0260493\pi$
$619$			4.06759i			0.163490i	−0.996653	+	0.0817450i	$0.973951\pi$
$620$	0.100674	+	16.5911i	0.00404315	+	0.666314i
$621$	1.78862	−	7.48446i	0.0717750	−	0.300341i
$622$	−10.1355	−	10.1355i	−0.406395	−	0.406395i
$623$	1.30158	+	1.30158i	0.0521468	+	0.0521468i
$624$	7.77411	−	3.71137i	0.311214	−	0.148574i
$625$	24.9926	−	0.606726i	0.999705	−	0.0242690i
$626$		−	2.21202i		−	0.0884102i
$627$	−2.00152	−	0.707993i	−0.0799329	−	0.0282745i
$628$	−12.0134	+	12.0134i	−0.479387	+	0.479387i
$629$	9.63775			0.384282
$630$	−25.0954	−	20.0424i	−0.999823	−	0.798507i
$631$	−5.67496			−0.225917			−0.112958	−	0.993600i	$-0.536033\pi$
$631$	−5.67496			−0.225917			−0.112958	+	0.993600i	$0.536033\pi$
$632$	4.77337	−	4.77337i	0.189875	−	0.189875i
$633$	1.07172	+	0.379096i	0.0425969	+	0.0150677i
$634$		−	30.5452i		−	1.21311i
$635$	14.5420	+	14.3666i	0.577082	+	0.570121i
$636$	−7.52963	+	3.59466i	−0.298569	+	0.142537i
$637$	55.9947	+	55.9947i	2.21859	+	2.21859i
$638$	7.05819	+	7.05819i	0.279437	+	0.279437i
$639$	−15.7668	+	19.4980i	−0.623724	+	0.771329i
$640$	−1.59070	−	1.57152i	−0.0628781	−	0.0621196i
$641$		−	1.58825i		−	0.0627323i	−0.999508	−	0.0313661i	$-0.990014\pi$
$641$		−	1.58825i		−	0.0627323i	0.999508	−	0.0313661i	$-0.00998579\pi$
$642$	8.15539	−	23.0555i	0.321868	−	0.909930i
$643$	−8.25666	+	8.25666i	−0.325611	+	0.325611i	−0.850915	−	0.525304i	$-0.823952\pi$
$643$	−8.25666	+	8.25666i	−0.325611	+	0.325611i	0.525304	+	0.850915i	$0.323952\pi$
$644$	7.09025			0.279395
$645$	−13.2451	+	6.42219i	−0.521524	+	0.252873i
$646$	1.16819			0.0459618
$647$	12.9377	−	12.9377i	0.508635	−	0.508635i	−0.405472	−	0.914107i	$-0.632893\pi$
$647$	12.9377	−	12.9377i	0.508635	−	0.508635i	0.914107	+	0.405472i	$0.132893\pi$
$648$	4.89127	−	7.55483i	0.192147	−	0.296782i
$649$			12.1582i			0.477251i
$650$	−0.301786	−	24.8663i	−0.0118370	−	0.975338i
$651$	−26.5083	−	55.5262i	−1.03894	−	2.17624i
$652$	−3.82552	−	3.82552i	−0.149819	−	0.149819i
$653$	−16.2867	−	16.2867i	−0.637350	−	0.637350i	0.312551	−	0.949901i	$-0.398816\pi$
$653$	−16.2867	−	16.2867i	−0.637350	−	0.637350i	−0.949901	+	0.312551i	$0.898816\pi$
$654$	−6.68151	−	13.9956i	−0.261268	−	0.547271i
$655$	0.0630553	+	10.3916i	0.00246377	+	0.406032i
$656$		−	3.53572i		−	0.138047i
$657$	−16.8508	+	1.78291i	−0.657410	+	0.0695579i
$658$	32.7882	−	32.7882i	1.27822	−	1.27822i
$659$	40.1270			1.56313			0.781563	−	0.623827i	$-0.214423\pi$
$659$	40.1270			1.56313			0.781563	+	0.623827i	$0.214423\pi$
$660$	4.48505	+	1.55593i	0.174580	+	0.0605647i
$661$	−17.8333			−0.693634			−0.346817	−	0.937933i	$-0.612737\pi$
$661$	−17.8333			−0.693634			−0.346817	+	0.937933i	$0.612737\pi$
$662$	−4.50516	+	4.50516i	−0.175098	+	0.175098i
$663$	3.35596	−	9.48740i	0.130335	−	0.368460i
$664$			1.01511i			0.0393939i
$665$	−7.52387	+	7.61574i	−0.291763	+	0.295326i
$666$	−19.2456	−	15.5626i	−0.745750	−	0.603040i
$667$	8.52773	+	8.52773i	0.330195	+	0.330195i
$668$	14.1056	+	14.1056i	0.545761	+	0.545761i
$669$	12.8499	−	6.13455i	0.496805	−	0.237176i
$670$	−18.9831	+	0.115188i	−0.733381	+	0.00445010i
$671$		−	12.9220i		−	0.498848i
$672$	7.81778	+	2.76537i	0.301577	+	0.106676i
$673$	15.7599	−	15.7599i	0.607498	−	0.607498i	−0.334793	−	0.942292i	$-0.608667\pi$
$673$	15.7599	−	15.7599i	0.607498	−	0.607498i	0.942292	+	0.334793i	$0.108667\pi$
$674$	1.60201			0.0617073
$675$	−13.8656	−	21.9715i	−0.533688	−	0.845682i
$676$	−11.7370			−0.451424
$677$	−28.0078	+	28.0078i	−1.07643	+	1.07643i	−0.0795985	+	0.996827i	$0.525364\pi$
$677$	−28.0078	+	28.0078i	−1.07643	+	1.07643i	−0.996827	+	0.0795985i	$0.974636\pi$
$678$	30.8858	+	10.9252i	1.18616	+	0.419579i
$679$		−	84.9352i		−	3.25951i
$680$	−2.61210	+	0.0158500i	−0.100169	+	0.000607822i
$681$	−24.5833	+	11.7361i	−0.942033	+	0.449728i
$682$	6.43105	+	6.43105i	0.246258	+	0.246258i
$683$	11.0403	+	11.0403i	0.422444	+	0.422444i	0.886045	−	0.463600i	$-0.153443\pi$
$683$	11.0403	+	11.0403i	0.422444	+	0.422444i	−0.463600	+	0.886045i	$0.653443\pi$
$684$	−2.33275	−	1.88634i	−0.0891948	−	0.0721261i
$685$	−1.83459	+	1.85700i	−0.0700963	+	0.0709521i
$686$			42.7137i			1.63082i
$687$	9.22813	−	26.0882i	0.352075	−	0.995327i
$688$	2.68748	−	2.68748i	0.102459	−	0.102459i
$689$	23.9591			0.912769
$690$	5.41885	+	1.87989i	0.206292	+	0.0715660i
$691$	−34.6717			−1.31897			−0.659486	−	0.751717i	$-0.729226\pi$
$691$	−34.6717			−1.31897			−0.659486	+	0.751717i	$0.729226\pi$
$692$	−6.57463	+	6.57463i	−0.249930	+	0.249930i
$693$	−17.5075	+	1.85240i	−0.665057	+	0.0703669i
$694$			31.3154i			1.18872i
$695$	0.0471409	+	7.76887i	0.00178816	+	0.294690i
$696$	6.07674	+	12.7288i	0.230338	+	0.482483i
$697$	−2.92063	−	2.92063i	−0.110627	−	0.110627i
$698$	−13.9126	−	13.9126i	−0.526600	−	0.526600i
$699$	10.8747	+	22.7788i	0.411317	+	0.861575i
$700$	16.7203	−	17.1311i	0.631966	−	0.647494i
$701$			2.11730i			0.0799692i	0.999200	+	0.0399846i	$0.0127309\pi$
$701$			2.11730i			0.0799692i	−0.999200	+	0.0399846i	$0.987269\pi$
$702$	−22.0214	+	13.5263i	−0.831143	+	0.510516i
$703$	−5.83375	+	5.83375i	−0.220024	+	0.220024i
$704$	−1.22574			−0.0461969
$705$	33.7523	−	16.3656i	1.27118	−	0.616364i
$706$	35.2206			1.32554
$707$	−4.06073	+	4.06073i	−0.152719	+	0.152719i
$708$	−5.72929	+	16.1969i	−0.215320	+	0.608715i
$709$		−	14.5305i		−	0.545705i	−0.962056	−	0.272852i	$-0.912033\pi$
$709$		−	14.5305i		−	0.545705i	0.962056	−	0.272852i	$-0.0879670\pi$
$710$	−13.2957	−	13.1353i	−0.498979	−	0.492960i
$711$	−12.7339	+	15.7474i	−0.477558	+	0.590572i
$712$	−0.271862	−	0.271862i	−0.0101885	−	0.0101885i
$713$	7.77001	+	7.77001i	0.290989	+	0.290989i
$714$	8.74204	−	4.17346i	0.327163	−	0.156188i
$715$	−9.69755	−	9.58057i	−0.362668	−	0.358293i
$716$		−	11.2885i		−	0.421870i
$717$	26.2971	+	9.30204i	0.982085	+	0.347391i
$718$	−14.8000	+	14.8000i	−0.552331	+	0.552331i
$719$	2.51322			0.0937272			0.0468636	−	0.998901i	$-0.485077\pi$
$719$	2.51322			0.0937272			0.0468636	+	0.998901i	$0.485077\pi$
$720$	5.24168	+	4.18626i	0.195346	+	0.156013i
$721$	89.1782			3.32117
$722$	−0.707107	+	0.707107i	−0.0263158	+	0.0263158i
$723$	32.5264	+	11.5055i	1.20967	+	0.427894i
$724$			9.96083i			0.370191i
$725$	40.7144	−	0.494122i	1.51209	−	0.0183512i
$726$	−14.8453	+	7.08717i	−0.550961	+	0.263029i
$727$	−7.64794	−	7.64794i	−0.283646	−	0.283646i	0.550915	−	0.834561i	$-0.314279\pi$
$727$	−7.64794	−	7.64794i	−0.283646	−	0.283646i	−0.834561	+	0.550915i	$0.814279\pi$
$728$	−16.8377	−	16.8377i	−0.624045	−	0.624045i
$729$	−12.2076	+	24.0826i	−0.452135	+	0.891950i
$730$	−0.0766361	−	12.6297i	−0.00283643	−	0.467446i
$731$		−	4.43990i		−	0.164215i
$732$	6.08920	−	17.2144i	0.225063	−	0.636261i
$733$	24.3729	−	24.3729i	0.900235	−	0.900235i	−0.0952214	−	0.995456i	$-0.530356\pi$
$733$	24.3729	−	24.3729i	0.900235	−	0.900235i	0.995456	+	0.0952214i	$0.0303559\pi$
$734$	37.2954			1.37660
$735$	−20.2106	+	58.2581i	−0.745481	+	2.14888i
$736$	−1.48094			−0.0545883
$737$	−7.35823	+	7.35823i	−0.271044	+	0.271044i
$738$	1.11607	+	10.5483i	0.0410831	+	0.388288i
$739$		−	30.8274i		−	1.13401i	−0.823716	−	0.567003i	$-0.808103\pi$
$739$		−	30.8274i		−	1.13401i	0.823716	−	0.567003i	$-0.191897\pi$
$740$	12.9653	−	13.1236i	0.476613	−	0.482432i
$741$	3.71137	+	7.77411i	0.136341	+	0.285589i
$742$	16.3081	+	16.3081i	0.598691	+	0.598691i
$743$	23.0214	+	23.0214i	0.844574	+	0.844574i	0.989450	−	0.144876i	$-0.0462783\pi$
$743$	23.0214	+	23.0214i	0.844574	+	0.844574i	−0.144876	+	0.989450i	$0.546278\pi$
$744$	5.53680	+	11.5978i	0.202989	+	0.425195i
$745$	−2.47297	+	0.0150058i	−0.0906026	+	0.000549770i
$746$			9.42209i			0.344967i
$747$	−0.320425	−	3.02842i	−0.0117237	−	0.110804i
$748$	−1.01250	+	1.01250i	−0.0370208	+	0.0370208i
$749$	−67.5986			−2.47000
$750$	17.3208	−	8.65959i	0.632468	−	0.316204i
$751$	43.6630			1.59329			0.796643	−	0.604450i	$-0.206607\pi$
$751$	43.6630			1.59329			0.796643	+	0.604450i	$0.206607\pi$
$752$	−6.84848	+	6.84848i	−0.249738	+	0.249738i
$753$	−10.3390	+	29.2286i	−0.376773	+	1.06515i
$754$		−	40.5027i		−	1.47502i
$755$	−7.34980	+	0.0445981i	−0.267486	+	0.00162309i
$756$	−24.1961	−	5.78233i	−0.880002	−	0.210301i
$757$	−8.25576	−	8.25576i	−0.300061	−	0.300061i	0.540977	−	0.841038i	$-0.318055\pi$
$757$	−8.25576	−	8.25576i	−0.300061	−	0.300061i	−0.841038	+	0.540977i	$0.818055\pi$
$758$	0.145573	+	0.145573i	0.00528745	+	0.00528745i
$759$	2.83736	−	1.35456i	0.102990	−	0.0491674i
$760$	1.57152	−	1.59070i	0.0570049	−	0.0577009i
$761$		−	45.4398i		−	1.64719i	−0.567176	−	0.823596i	$-0.691964\pi$
$761$		−	45.4398i		−	1.64719i	0.567176	−	0.823596i	$-0.308036\pi$
$762$	14.9278	+	5.28038i	0.540777	+	0.191288i
$763$	−30.3125	+	30.3125i	−1.09739	+	1.09739i
$764$	−10.1454			−0.367048
$765$	7.78780	−	0.871811i	0.281569	−	0.0315204i
$766$	−11.6945			−0.422539
$767$	34.8842	−	34.8842i	1.25960	−	1.25960i
$768$	−1.63290	−	0.577604i	−0.0589223	−	0.0208425i
$769$		−	14.3253i		−	0.516582i	−0.966067	−	0.258291i	$-0.916841\pi$
$769$		−	14.3253i		−	0.516582i	0.966067	−	0.258291i	$-0.0831593\pi$
$770$	−0.0796231	−	13.1220i	−0.00286942	−	0.472882i
$771$	32.1549	−	15.3508i	1.15803	−	0.552845i
$772$	−1.33016	−	1.33016i	−0.0478734	−	0.0478734i
$773$	30.7793	+	30.7793i	1.10706	+	1.10706i	0.993536	+	0.113520i	$0.0362125\pi$
$773$	30.7793	+	30.7793i	1.10706	+	1.10706i	0.113520	+	0.993536i	$0.463788\pi$
$774$	−7.16936	+	8.86600i	−0.257697	+	0.318682i
$775$	37.0968	−	0.450218i	1.33256	−	0.0161723i
$776$			17.7405i			0.636846i
$777$	−22.8148	+	64.4980i	−0.818475	+	2.31385i
$778$	−17.9604	+	17.9604i	−0.643912	+	0.643912i
$779$	3.53572			0.126680
$780$	−8.40421	−	17.3328i	−0.300919	−	0.620613i
$781$	−10.2452			−0.366603
$782$	−1.22331	+	1.22331i	−0.0437455	+	0.0437455i
$783$	−22.1469	−	36.0562i	−0.791467	−	1.28854i
$784$		−	15.9216i		−	0.568630i
$785$	27.0253	+	26.6993i	0.964573	+	0.952938i
$786$	3.46788	+	7.26408i	0.123695	+	0.259101i
$787$	−4.68011	−	4.68011i	−0.166828	−	0.166828i	0.618756	−	0.785583i	$-0.287637\pi$
$787$	−4.68011	−	4.68011i	−0.166828	−	0.166828i	−0.785583	+	0.618756i	$0.787637\pi$
$788$	3.67465	+	3.67465i	0.130904	+	0.130904i
$789$	−6.39168	−	13.3885i	−0.227550	−	0.476642i
$790$	−10.7382	−	10.6086i	−0.382046	−	0.377438i
$791$		−	90.5568i		−	3.21983i
$792$	3.65681	−	0.386912i	0.129939	−	0.0137483i
$793$	−37.0757	+	37.0757i	−1.31660	+	1.31660i
$794$	20.4067			0.724206
$795$	8.13991	+	16.7877i	0.288693	+	0.595398i
$796$	−0.894086			−0.0316900
$797$	0.135863	−	0.135863i	0.00481251	−	0.00481251i	−0.704696	−	0.709509i	$-0.748917\pi$
$797$	0.135863	−	0.135863i	0.00481251	−	0.00481251i	0.709509	+	0.704696i	$0.248917\pi$
$798$	−2.76537	+	7.81778i	−0.0978930	+	0.276746i
$799$			11.3142i			0.400266i
$800$	−3.49237	+	3.57818i	−0.123474	+	0.126508i
$801$	0.896874	+	0.725245i	0.0316895	+	0.0256253i
$802$	−5.67851	−	5.67851i	−0.200515	−	0.200515i
$803$	−4.89552	−	4.89552i	−0.172759	−	0.172759i
$804$	−13.2699	+	6.33506i	−0.467992	+	0.223420i
$805$	−0.0962009	−	15.8540i	−0.00339064	−	0.558780i
$806$		−	36.9039i		−	1.29988i
$807$	15.5342	+	5.49490i	0.546831	+	0.193430i
$808$	0.848167	−	0.848167i	0.0298384	−	0.0298384i
$809$	19.5668			0.687933			0.343967	−	0.938982i	$-0.388229\pi$
$809$	19.5668			0.687933			0.343967	+	0.938982i	$0.388229\pi$
$810$	−16.9592	−	10.8345i	−0.595884	−	0.380686i
$811$	19.4917			0.684447			0.342223	−	0.939619i	$-0.388820\pi$
$811$	19.4917			0.684447			0.342223	+	0.939619i	$0.388820\pi$
$812$	27.5688	−	27.5688i	0.967475	−	0.967475i
$813$	−0.662146	−	0.234220i	−0.0232225	−	0.00821444i
$814$		−	10.1126i		−	0.354445i
$815$	−8.50206	+	8.60587i	−0.297814	+	0.301451i
$816$	−1.82595	+	0.871713i	−0.0639212	+	0.0305161i
$817$	2.68748	+	2.68748i	0.0940229	+	0.0940229i
$818$	−9.80426	−	9.80426i	−0.342798	−	0.342798i
$819$	55.5475	+	44.9177i	1.94099	+	1.56955i
$820$	−7.90597	+	0.0479729i	−0.276088	+	0.00167529i
$821$			1.40866i			0.0491626i	0.999698	+	0.0245813i	$0.00782525\pi$
$821$			1.40866i			0.0491626i	−0.999698	+	0.0245813i	$0.992175\pi$
$822$	−0.674298	+	1.90626i	−0.0235188	+	0.0664884i
$823$	−33.6212	+	33.6212i	−1.17196	+	1.17196i	−0.190220	+	0.981741i	$0.560920\pi$
$823$	−33.6212	+	33.6212i	−1.17196	+	1.17196i	−0.981741	+	0.190220i	$0.939080\pi$
$824$	−18.6267			−0.648892
$825$	3.41826	−	10.0498i	0.119008	−	0.349889i
$826$	47.4890			1.65235
$827$	27.8950	−	27.8950i	0.970006	−	0.970006i	−0.0295575	−	0.999563i	$-0.509410\pi$
$827$	27.8950	−	27.8950i	0.970006	−	0.970006i	0.999563	+	0.0295575i	$0.00940982\pi$
$828$	4.41817	−	0.467469i	0.153542	−	0.0162457i
$829$			17.3145i			0.601357i	0.953725	+	0.300679i	$0.0972132\pi$
$829$			17.3145i			0.601357i	−0.953725	+	0.300679i	$0.902787\pi$
$830$	2.26981	−	0.0137731i	0.0787863	−	0.000478070i
$831$	−3.33075	−	6.97684i	−0.115542	−	0.242024i
$832$	3.51689	+	3.51689i	0.121926	+	0.121926i
$833$	−13.1518	−	13.1518i	−0.455683	−	0.455683i
$834$	2.59263	+	5.43072i	0.0897756	+	0.188051i
$835$	31.3490	−	31.7318i	1.08488	−	1.09812i
$836$		−	1.22574i		−	0.0423931i
$837$	−20.1791	−	32.8525i	−0.697492	−	1.13555i
$838$	12.5350	−	12.5350i	0.433014	−	0.433014i
$839$	−24.7985			−0.856141			−0.428070	−	0.903745i	$-0.640806\pi$
$839$	−24.7985			−0.856141			−0.428070	+	0.903745i	$0.640806\pi$
$840$	6.07737	−	17.5183i	0.209689	−	0.604438i
$841$	37.3162			1.28677
$842$	1.87573	−	1.87573i	0.0646420	−	0.0646420i
$843$	−6.88639	+	19.4680i	−0.237180	+	0.670514i
$844$			0.656325i			0.0225916i
$845$	0.159249	+	26.2443i	0.00547832	+	0.902832i
$846$	18.2696	−	22.5932i	0.628123	−	0.776769i
$847$	32.1529	+	32.1529i	1.10479	+	1.10479i
$848$	−3.40629	−	3.40629i	−0.116972	−	0.116972i
$849$	−24.6219	+	11.7545i	−0.845023	+	0.403415i
$850$	0.0708823	+	5.84051i	0.00243124	+	0.200328i
$851$		−	12.2180i		−	0.418829i
$852$	−13.6484	−	4.82784i	−0.467588	−	0.165399i
$853$	26.5568	−	26.5568i	0.909288	−	0.909288i	−0.0869270	−	0.996215i	$-0.527705\pi$
$853$	26.5568	−	26.5568i	0.909288	−	0.909288i	0.996215	+	0.0869270i	$0.0277047\pi$
$854$	−50.4723			−1.72713
$855$	−4.18626	+	5.24168i	−0.143167	+	0.179262i
$856$	14.1194			0.482590
$857$	29.8963	−	29.8963i	1.02124	−	1.02124i	0.0214701	−	0.999769i	$-0.493165\pi$
$857$	29.8963	−	29.8963i	1.02124	−	1.02124i	0.999769	−	0.0214701i	$-0.00683466\pi$
$858$	−9.95481	−	3.52130i	−0.339852	−	0.120215i
$859$			54.0727i			1.84494i	0.386074	+	0.922468i	$0.373831\pi$
$859$			54.0727i			1.84494i	−0.386074	+	0.922468i	$0.626169\pi$
$860$	−6.04574	−	5.97281i	−0.206158	−	0.203671i
$861$	26.4593	−	12.6317i	0.901730	−	0.430487i
$862$	−12.0270	−	12.0270i	−0.409640	−	0.409640i
$863$	−35.2140	−	35.2140i	−1.19870	−	1.19870i	−0.974557	−	0.224142i	$-0.928042\pi$
$863$	−35.2140	−	35.2140i	−1.19870	−	1.19870i	−0.224142	−	0.974557i	$-0.571958\pi$
$864$	5.05384	+	1.20776i	0.171935	+	0.0410888i
$865$	14.7902	+	14.6118i	0.502884	+	0.496817i
$866$		−	19.6197i		−	0.666705i
$867$	9.03103	−	25.5310i	0.306710	−	0.867078i
$868$	25.1192	−	25.1192i	0.852601	−	0.852601i
$869$	−8.27445			−0.280691
$870$	28.3794	−	13.7605i	0.962153	−	0.466523i
$871$	42.2244			1.43072
$872$	6.33139	−	6.33139i	0.214408	−	0.214408i
$873$	−5.59988	−	52.9260i	−0.189527	−	1.79127i
$874$		−	1.48094i		−	0.0500937i
$875$	−38.5324	−	37.1545i	−1.30263	−	1.25605i
$876$	−4.21479	−	8.82861i	−0.142405	−	0.298291i
$877$	6.50626	+	6.50626i	0.219701	+	0.219701i	0.808372	−	0.588671i	$-0.200349\pi$
$877$	6.50626	+	6.50626i	0.219701	+	0.219701i	−0.588671	+	0.808372i	$0.700349\pi$
$878$	5.26269	+	5.26269i	0.177607	+	0.177607i
$879$	−3.51382	−	7.36030i	−0.118518	−	0.248257i
$880$	0.0166309	+	2.74079i	0.000560628	+	0.0923920i
$881$			40.0528i			1.34941i	0.738087	+	0.674706i	$0.235730\pi$
$881$			40.0528i			1.34941i	−0.738087	+	0.674706i	$0.764270\pi$
$882$	5.02576	+	47.4998i	0.169226	+	1.59940i
$883$	−14.6050	+	14.6050i	−0.491496	+	0.491496i	−0.908777	−	0.417281i	$-0.862983\pi$
$883$	−14.6050	+	14.6050i	−0.491496	+	0.491496i	0.417281	+	0.908777i	$0.362983\pi$
$884$	5.81014			0.195416
$885$	36.2944	+	12.5911i	1.22002	+	0.423244i
$886$	−19.8119			−0.665593
$887$	−38.9555	+	38.9555i	−1.30800	+	1.30800i	−0.385142	+	0.922857i	$0.625847\pi$
$887$	−38.9555	+	38.9555i	−1.30800	+	1.30800i	−0.922857	+	0.385142i	$0.874153\pi$
$888$	4.76533	−	13.4717i	0.159914	−	0.452082i
$889$		−	43.7681i		−	1.46794i
$890$	−0.604203	+	0.611580i	−0.0202529	+	0.0205002i
$891$	−10.7874	+	2.30859i	−0.361392	+	0.0773406i
$892$	5.81309	+	5.81309i	0.194637	+	0.194637i
$893$	−6.84848	−	6.84848i	−0.229176	−	0.229176i
$894$	−1.72870	+	0.825282i	−0.0578162	+	0.0276016i
$895$	−25.2413	+	0.153163i	−0.843725	+	0.00511967i
$896$			4.78765i			0.159944i
$897$	−12.0274	−	4.25444i	−0.401584	−	0.142052i
$898$	12.0743	−	12.0743i	0.402926	−	0.402926i
$899$	60.4238			2.01525
$900$	9.28948	−	11.7773i	0.309649	−	0.392578i
$901$	−5.62742			−0.187477
$902$	−3.06452	+	3.06452i	−0.102037	+	0.102037i
$903$	29.7128	+	10.5102i	0.988779	+	0.349759i
$904$			18.9147i			0.629092i
$905$	22.2727	−	0.135149i	0.740369	−	0.00449251i
$906$	−5.13778	+	2.45278i	−0.170691	+	0.0814882i
$907$	1.61743	+	1.61743i	0.0537059	+	0.0537059i	0.733450	−	0.679744i	$-0.237909\pi$
$907$	1.61743	+	1.61743i	0.0537059	+	0.0537059i	−0.679744	+	0.733450i	$0.737909\pi$
$908$	−11.1211	−	11.1211i	−0.369067	−	0.369067i
$909$	−2.26265	+	2.79811i	−0.0750473	+	0.0928073i
$910$	−37.4210	+	37.8779i	−1.24049	+	1.25564i
$911$		−	28.2902i		−	0.937298i	−0.883385	−	0.468649i	$-0.844741\pi$
$911$		−	28.2902i		−	0.937298i	0.883385	−	0.468649i	$-0.155259\pi$
$912$	0.577604	−	1.63290i	0.0191264	−	0.0540708i
$913$	0.879825	−	0.879825i	0.0291180	−	0.0291180i
$914$	−6.47066			−0.214030
$915$	−38.5744	−	13.3821i	−1.27523	−	0.442397i
$916$	15.9766			0.527881
$917$	15.7330	−	15.7330i	0.519550	−	0.519550i
$918$	5.17229	−	3.17700i	0.170711	−	0.104857i
$919$		−	32.0879i		−	1.05848i	−0.848472	−	0.529241i	$-0.822477\pi$
$919$		−	32.0879i		−	1.05848i	0.848472	−	0.529241i	$-0.177523\pi$
$920$	0.0200935	+	3.31143i	0.000662464	+	0.109175i
$921$	1.78362	+	3.73609i	0.0587722	+	0.123109i
$922$	−0.0849881	−	0.0849881i	−0.00279893	−	0.00279893i
$923$	29.3955	+	29.3955i	0.967566	+	0.967566i
$924$	−4.37907	−	9.17273i	−0.144061	−	0.301761i
$925$	−29.5206	−	28.8126i	−0.970631	−	0.947354i
$926$			8.23304i			0.270555i
$927$	55.5699	−	5.87963i	1.82516	−	0.193112i
$928$	−5.75831	+	5.75831i	−0.189026	+	0.189026i
$929$	−46.3379			−1.52030			−0.760149	−	0.649749i	$-0.774874\pi$
$929$	−46.3379			−1.52030			−0.760149	+	0.649749i	$0.774874\pi$
$930$	25.8578	−	12.5378i	0.847912	−	0.411130i
$931$	15.9216			0.521811
$932$	−10.3048	+	10.3048i	−0.337545	+	0.337545i
$933$	−8.27921	+	23.4056i	−0.271049	+	0.766264i
$934$			1.79181i			0.0586298i
$935$	2.27772	+	2.25025i	0.0744895	+	0.0735910i
$936$	−11.6022	−	9.38198i	−0.379231	−	0.306660i
$937$	−35.8203	−	35.8203i	−1.17020	−	1.17020i	−0.982162	−	0.188037i	$-0.939788\pi$
$937$	−35.8203	−	35.8203i	−1.17020	−	1.17020i	−0.188037	−	0.982162i	$-0.560212\pi$
$938$	28.7407	+	28.7407i	0.938418	+	0.938418i
$939$	−3.45754	+	1.65063i	−0.112832	+	0.0538664i
$940$	15.4063	+	15.2205i	0.502498	+	0.496437i
$941$			36.8148i			1.20013i	0.799951	+	0.600065i	$0.204859\pi$
$941$			36.8148i			1.20013i	−0.799951	+	0.600065i	$0.795141\pi$
$942$	27.7422	+	9.81321i	0.903891	+	0.319732i
$943$	−3.70256	+	3.70256i	−0.120572	+	0.120572i
$944$	−9.91906			−0.322838
$945$	−12.6011	+	54.1815i	−0.409915	+	1.76252i
$946$	−4.65863			−0.151465
$947$	14.0227	−	14.0227i	0.455676	−	0.455676i	−0.441557	−	0.897233i	$-0.645574\pi$
$947$	14.0227	−	14.0227i	0.455676	−	0.455676i	0.897233	+	0.441557i	$0.145574\pi$
$948$	−11.0230	−	3.89915i	−0.358011	−	0.126639i
$949$			28.0924i			0.911919i
$950$	−3.57818	−	3.49237i	−0.116091	−	0.113307i
$951$	−47.7442	+	22.7931i	−1.54821	+	0.739118i
$952$	3.95477	+	3.95477i	0.128175	+	0.128175i
$953$	2.01500	+	2.01500i	0.0652723	+	0.0652723i	0.738989	−	0.673717i	$-0.235303\pi$
$953$	2.01500	+	2.01500i	0.0652723	+	0.0652723i	−0.673717	+	0.738989i	$0.735303\pi$
$954$	11.2374	+	9.08693i	0.363823	+	0.294200i
$955$	0.137653	+	22.6854i	0.00445436	+	0.734082i
$956$			16.1045i			0.520858i
$957$	5.76552	−	16.2993i	0.186373	−	0.526882i
$958$	−3.37189	+	3.37189i	−0.108941	+	0.108941i
$959$	5.58913			0.180482
$960$	−1.26938	+	3.65905i	−0.0409691	+	0.118095i
$961$	24.0549			0.775965
$962$	−29.0149	+	29.0149i	−0.935479	+	0.935479i
$963$	−42.1229	+	4.45685i	−1.35739	+	0.143620i
$964$			19.9193i			0.641559i
$965$	−2.95622	+	2.99231i	−0.0951640	+	0.0963260i
$966$	−5.29081	−	11.0825i	−0.170229	−	0.356574i
$967$	3.86264	+	3.86264i	0.124214	+	0.124214i	0.766481	−	0.642267i	$-0.222006\pi$
$967$	3.86264	+	3.86264i	0.124214	+	0.124214i	−0.642267	+	0.766481i	$0.722006\pi$
$968$	−6.71579	−	6.71579i	−0.215854	−	0.215854i
$969$	−0.871713	−	1.82595i	−0.0280035	−	0.0586581i
$970$	39.6682	−	0.240704i	1.27367	−	0.00772853i
$971$			4.62291i			0.148356i	0.997245	+	0.0741781i	$0.0236333\pi$
$971$			4.62291i			0.148356i	−0.997245	+	0.0741781i	$0.976367\pi$
$972$	−15.4586	−	2.00789i	−0.495835	−	0.0644030i
$973$	11.7622	−	11.7622i	0.377079	−	0.377079i
$974$	26.4143			0.846368
$975$	−38.6425	+	19.0272i	−1.23755	+	0.609358i
$976$	10.5422			0.337447
$977$	40.0087	−	40.0087i	1.27999	−	1.27999i	0.339323	−	0.940670i	$-0.389802\pi$
$977$	40.0087	−	40.0087i	1.27999	−	1.27999i	0.940670	−	0.339323i	$-0.110198\pi$
$978$	−3.12490	+	8.83418i	−0.0999232	+	0.282486i
$979$			0.471262i			0.0150616i
$980$	−35.6012	+	0.216026i	−1.13724	+	0.00690069i
$981$	−16.8902	+	20.8873i	−0.539262	+	0.666879i
$982$	30.3912	+	30.3912i	0.969822	+	0.969822i
$983$	−12.9031	−	12.9031i	−0.411545	−	0.411545i	0.470731	−	0.882277i	$-0.343990\pi$
$983$	−12.9031	−	12.9031i	−0.411545	−	0.411545i	−0.882277	+	0.470731i	$0.843990\pi$
$984$	−5.52656	+	2.63839i	−0.176180	+	0.0841088i
$985$	8.16675	−	8.26647i	0.260214	−	0.263392i
$986$			9.51312i			0.302959i
$987$	−75.7168	−	26.7832i	−2.41009	−	0.852518i
$988$	−3.51689	+	3.51689i	−0.111887	+	0.111887i
$989$	−5.62858			−0.178978
$990$	−0.914762	−	8.17148i	−0.0290730	−	0.259707i
$991$	16.7867			0.533248			0.266624	−	0.963801i	$-0.414092\pi$
$991$	16.7867			0.533248			0.266624	+	0.963801i	$0.414092\pi$
$992$	−5.24666	+	5.24666i	−0.166582	+	0.166582i
$993$	10.4036	+	3.68006i	0.330150	+	0.116783i
$994$			40.0171i			1.26926i
$995$	0.0121310	+	1.99920i	0.000384579	+	0.0633789i
$996$	1.58668	−	0.757484i	0.0502759	−	0.0240018i
$997$	10.3397	+	10.3397i	0.327460	+	0.327460i	0.851620	−	0.524160i	$-0.175620\pi$
$997$	10.3397	+	10.3397i	0.327460	+	0.327460i	−0.524160	+	0.851620i	$0.675620\pi$
$998$	14.7400	+	14.7400i	0.466587	+	0.466587i
$999$	−9.96421	+	41.6951i	−0.315254	+	1.31917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.b.77.11	yes	36
3.2	odd	2	inner	570.2.k.b.77.6	✓	36
5.3	odd	4	inner	570.2.k.b.533.6	yes	36
15.8	even	4	inner	570.2.k.b.533.11	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.6	✓	36	3.2	odd	2	inner
570.2.k.b.77.11	yes	36	1.1	even	1	trivial
570.2.k.b.533.6	yes	36	5.3	odd	4	inner
570.2.k.b.533.11	yes	36	15.8	even	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.63290 - 0.577604i) q^{3} -1.00000i q^{4} +(-2.23603 + 0.0135681i) q^{5} +(-1.56306 + 0.746209i) q^{6} +(3.38538 + 3.38538i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.33275 + 1.88634i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.63290 - 0.577604i) q^{3} -1.00000i q^{4} +(-2.23603 + 0.0135681i) q^{5} +(-1.56306 + 0.746209i) q^{6} +(3.38538 + 3.38538i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.33275 + 1.88634i) q^{9} +(-1.57152 + 1.59070i) q^{10} +1.22574i q^{11} +(-0.577604 + 1.63290i) q^{12} +(3.51689 - 3.51689i) q^{13} +4.78765 q^{14} +(3.65905 + 1.26938i) q^{15} -1.00000 q^{16} +(-0.826034 + 0.826034i) q^{17} +(2.98335 - 0.315656i) q^{18} -1.00000i q^{19} +(0.0135681 + 2.23603i) q^{20} +(-3.57259 - 7.48341i) q^{21} +(0.866730 + 0.866730i) q^{22} +(1.04719 + 1.04719i) q^{23} +(0.746209 + 1.56306i) q^{24} +(4.99963 - 0.0606771i) q^{25} -4.97363i q^{26} +(-2.71959 - 4.42762i) q^{27} +(3.38538 - 3.38538i) q^{28} +8.14348 q^{29} +(3.48493 - 1.68975i) q^{30} +7.41990 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.707993 - 2.00152i) q^{33} +1.16819i q^{34} +(-7.61574 - 7.52387i) q^{35} +(1.88634 - 2.33275i) q^{36} +(-5.83375 - 5.83375i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(-7.77411 + 3.71137i) q^{39} +(1.59070 + 1.57152i) q^{40} +3.53572i q^{41} +(-7.81778 - 2.76537i) q^{42} +(-2.68748 + 2.68748i) q^{43} +1.22574 q^{44} +(-5.24168 - 4.18626i) q^{45} +1.48094 q^{46} +(6.84848 - 6.84848i) q^{47} +(1.63290 + 0.577604i) q^{48} +15.9216i q^{49} +(3.49237 - 3.57818i) q^{50} +(1.82595 - 0.871713i) q^{51} +(-3.51689 - 3.51689i) q^{52} +(3.40629 + 3.40629i) q^{53} +(-5.05384 - 1.20776i) q^{54} +(-0.0166309 - 2.74079i) q^{55} -4.78765i q^{56} +(-0.577604 + 1.63290i) q^{57} +(5.75831 - 5.75831i) q^{58} +9.91906 q^{59} +(1.26938 - 3.65905i) q^{60} -10.5422 q^{61} +(5.24666 - 5.24666i) q^{62} +(1.51125 + 14.2832i) q^{63} +1.00000i q^{64} +(-7.81614 + 7.91158i) q^{65} +(-0.914660 - 1.91591i) q^{66} +(6.00309 + 6.00309i) q^{67} +(0.826034 + 0.826034i) q^{68} +(-1.10509 - 2.31481i) q^{69} +(-10.7053 + 0.0649592i) q^{70} +8.35839i q^{71} +(-0.315656 - 2.98335i) q^{72} +(-3.99393 + 3.99393i) q^{73} -8.25017 q^{74} +(-8.19896 - 2.78873i) q^{75} -1.00000 q^{76} +(-4.14960 + 4.14960i) q^{77} +(-2.87279 + 8.12146i) q^{78} +6.75057i q^{79} +(2.23603 - 0.0135681i) q^{80} +(1.88342 + 8.80072i) q^{81} +(2.50013 + 2.50013i) q^{82} +(-0.717790 - 0.717790i) q^{83} +(-7.48341 + 3.57259i) q^{84} +(1.83583 - 1.85824i) q^{85} +3.80067i q^{86} +(-13.2975 - 4.70370i) q^{87} +(0.866730 - 0.866730i) q^{88} +0.384471 q^{89} +(-6.66656 + 0.746293i) q^{90} +23.8120 q^{91} +(1.04719 - 1.04719i) q^{92} +(-12.1160 - 4.28576i) q^{93} -9.68521i q^{94} +(0.0135681 + 2.23603i) q^{95} +(1.56306 - 0.746209i) q^{96} +(-12.5444 - 12.5444i) q^{97} +(11.2583 + 11.2583i) q^{98} +(-2.31217 + 2.85934i) 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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