LMFDB - Embedded newform 224.2.x.b.27.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(27,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4]))

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

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

chi := DirichletCharacter("224.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.x (of order $8$, degree $4$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			27.12
Character	$\chi$	$=$	224.27
Dual form			224.2.x.b.83.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.522376 - 1.31420i) q^{2} +(0.167131 + 0.403490i) q^{3} +(-1.45425 + 1.37301i) q^{4} +(0.883342 - 2.13258i) q^{5} +(0.442962 - 0.430417i) q^{6} +(-2.48955 - 0.895629i) q^{7} +(2.56408 + 1.19394i) q^{8} +(1.98645 - 1.98645i) q^{9} +O(q^{10})$	\(q+(-0.522376 - 1.31420i) q^{2} +(0.167131 + 0.403490i) q^{3} +(-1.45425 + 1.37301i) q^{4} +(0.883342 - 2.13258i) q^{5} +(0.442962 - 0.430417i) q^{6} +(-2.48955 - 0.895629i) q^{7} +(2.56408 + 1.19394i) q^{8} +(1.98645 - 1.98645i) q^{9} +(-3.26407 - 0.0468829i) q^{10} +(0.0226972 + 0.00940149i) q^{11} +(-0.797048 - 0.357302i) q^{12} +(-2.06204 - 4.97820i) q^{13} +(0.123443 + 3.73962i) q^{14} +1.00811 q^{15} +(0.229671 - 3.99340i) q^{16} -1.21121 q^{17} +(-3.64826 - 1.57292i) q^{18} +(1.70228 - 0.705105i) q^{19} +(1.64346 + 4.31414i) q^{20} +(-0.0547034 - 1.15420i) q^{21} +(0.000498978 - 0.0347398i) q^{22} +(-1.89294 - 1.89294i) q^{23} +(-0.0532077 + 1.23413i) q^{24} +(-0.232058 - 0.232058i) q^{25} +(-5.46520 + 5.31043i) q^{26} +(2.34398 + 0.970909i) q^{27} +(4.85013 - 2.11572i) q^{28} +(2.01467 + 4.86384i) q^{29} +(-0.526611 - 1.32486i) q^{30} -0.187704 q^{31} +(-5.36811 + 1.78422i) q^{32} +0.0107294i q^{33} +(0.632709 + 1.59178i) q^{34} +(-4.10912 + 4.51801i) q^{35} +(-0.161368 + 5.61621i) q^{36} +(2.35207 + 0.974258i) q^{37} +(-1.81588 - 1.86880i) q^{38} +(1.66403 - 1.66403i) q^{39} +(4.81114 - 4.41343i) q^{40} +(-1.89007 - 1.89007i) q^{41} +(-1.48827 + 0.674815i) q^{42} +(5.31052 + 2.19969i) q^{43} +(-0.0459157 + 0.0174915i) q^{44} +(-2.48154 - 5.99097i) q^{45} +(-1.49888 + 3.47653i) q^{46} +10.7802i q^{47} +(1.64968 - 0.574752i) q^{48} +(5.39570 + 4.45942i) q^{49} +(-0.183749 + 0.426191i) q^{50} +(-0.202432 - 0.488713i) q^{51} +(9.83385 + 4.40833i) q^{52} +(2.89250 - 6.98312i) q^{53} +(0.0515304 - 3.58764i) q^{54} +(0.0400988 - 0.0400988i) q^{55} +(-5.31406 - 5.26884i) q^{56} +(0.569007 + 0.569007i) q^{57} +(5.33964 - 5.18843i) q^{58} +(13.1854 + 5.46159i) q^{59} +(-1.46604 + 1.38415i) q^{60} +(10.3612 - 4.29176i) q^{61} +(0.0980521 + 0.246681i) q^{62} +(-6.72448 + 3.16624i) q^{63} +(5.14899 + 6.12273i) q^{64} -12.4379 q^{65} +(0.0141006 - 0.00560477i) q^{66} +(-0.900161 + 0.372859i) q^{67} +(1.76141 - 1.66301i) q^{68} +(0.447414 - 1.08015i) q^{69} +(8.08407 + 3.04011i) q^{70} +(3.87314 - 3.87314i) q^{71} +(7.46512 - 2.72170i) q^{72} +(-2.87435 - 2.87435i) q^{73} +(0.0517081 - 3.60002i) q^{74} +(0.0548489 - 0.132417i) q^{75} +(-1.50741 + 3.36264i) q^{76} +(-0.0480855 - 0.0437337i) q^{77} +(-3.05611 - 1.31762i) q^{78} -11.2913 q^{79} +(-8.31336 - 4.01733i) q^{80} -7.31974i q^{81} +(-1.49660 + 3.47126i) q^{82} +(-7.36131 + 3.04916i) q^{83} +(1.66428 + 1.60338i) q^{84} +(-1.06992 + 2.58301i) q^{85} +(0.116747 - 8.12815i) q^{86} +(-1.62580 + 1.62580i) q^{87} +(0.0469726 + 0.0512054i) q^{88} +(-9.46502 + 9.46502i) q^{89} +(-6.57704 + 6.39078i) q^{90} +(0.674922 + 14.2403i) q^{91} +(5.35184 + 0.153772i) q^{92} +(-0.0313712 - 0.0757369i) q^{93} +(14.1674 - 5.63132i) q^{94} -4.25308i q^{95} +(-1.61709 - 1.86778i) q^{96} +18.3664i q^{97} +(3.04200 - 9.42052i) q^{98} +(0.0637624 - 0.0264113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9	$ 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{11} - 20 q^{14} - 16 q^{15} + 16 q^{16} - 16 q^{18} - 4 q^{21} + 32 q^{22} - 48 q^{23} - 8 q^{25} - 24 q^{28} - 8 q^{29} + 16 q^{30} - 8 q^{32} + 20 q^{35} + 32 q^{36} - 8 q^{37} - 8 q^{39} + 16 q^{42} + 32 q^{43} - 144 q^{44} - 8 q^{46} + 16 q^{50} - 32 q^{51} - 32 q^{53} + 64 q^{56} - 8 q^{57} - 72 q^{58} - 88 q^{60} + 112 q^{64} - 16 q^{65} - 64 q^{67} - 40 q^{70} + 56 q^{71} - 8 q^{72} - 168 q^{74} + 52 q^{77} + 192 q^{78} - 16 q^{79} - 24 q^{84} - 48 q^{85} - 8 q^{86} - 96 q^{88} - 52 q^{91} - 8 q^{92} - 32 q^{93} + 88 q^{98} + 16 q^{99}+O(q^{100}) $ 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^11 - 20 * q^14 - 16 * q^15 + 16 * q^16 - 16 * q^18 - 4 * q^21 + 32 * q^22 - 48 * q^23 - 8 * q^25 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 8 * q^32 + 20 * q^35 + 32 * q^36 - 8 * q^37 - 8 * q^39 + 16 * q^42 + 32 * q^43 - 144 * q^44 - 8 * q^46 + 16 * q^50 - 32 * q^51 - 32 * q^53 + 64 * q^56 - 8 * q^57 - 72 * q^58 - 88 * q^60 + 112 * q^64 - 16 * q^65 - 64 * q^67 - 40 * q^70 + 56 * q^71 - 8 * q^72 - 168 * q^74 + 52 * q^77 + 192 * q^78 - 16 * q^79 - 24 * q^84 - 48 * q^85 - 8 * q^86 - 96 * q^88 - 52 * q^91 - 8 * q^92 - 32 * q^93 + 88 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−0.522376	−	1.31420i	−0.369375	−	0.929280i
$2$	−0.522376	−	1.31420i	−0.369375	−	0.929280i
$3$	0.167131	+	0.403490i	0.0964932	+	0.232955i	0.964754	−	0.263152i	$-0.0847622\pi$
$3$	0.167131	+	0.403490i	0.0964932	+	0.232955i	−0.868261	+	0.496108i	$0.834762\pi$
$4$	−1.45425	+	1.37301i	−0.727124	+	0.686506i
$5$	0.883342	−	2.13258i	0.395043	−	0.953717i	−0.593781	−	0.804627i	$-0.702365\pi$
$5$	0.883342	−	2.13258i	0.395043	−	0.953717i	0.988824	−	0.149091i	$-0.0476346\pi$
$6$	0.442962	−	0.430417i	0.180839	−	0.175717i
$7$	−2.48955	−	0.895629i	−0.940961	−	0.338516i
$7$	−2.48955	−	0.895629i	−0.940961	−	0.338516i
$8$	2.56408	+	1.19394i	0.906539	+	0.422123i
$9$	1.98645	−	1.98645i	0.662150	−	0.662150i
$10$	−3.26407	−	0.0468829i	−1.03219	−	0.0148257i
$11$	0.0226972	+	0.00940149i	0.00684347	+	0.00283466i	0.386103	−	0.922456i	$-0.373821\pi$
$11$	0.0226972	+	0.00940149i	0.00684347	+	0.00283466i	−0.379259	+	0.925291i	$0.623821\pi$
$12$	−0.797048	−	0.357302i	−0.230088	−	0.103144i
$13$	−2.06204	−	4.97820i	−0.571907	−	1.38071i	−0.899930	−	0.436035i	$-0.856382\pi$
$13$	−2.06204	−	4.97820i	−0.571907	−	1.38071i	0.328023	−	0.944670i	$-0.393618\pi$
$14$	0.123443	+	3.73962i	0.0329915	+	0.999456i
$15$	1.00811			0.260292
$16$	0.229671	−	3.99340i	0.0574177	−	0.998350i
$17$	−1.21121			−0.293763			−0.146881	−	0.989154i	$-0.546924\pi$
$17$	−1.21121			−0.293763			−0.146881	+	0.989154i	$0.546924\pi$
$18$	−3.64826	−	1.57292i	−0.859904	−	0.370741i
$19$	1.70228	−	0.705105i	0.390529	−	0.161762i	−0.178774	−	0.983890i	$-0.557213\pi$
$19$	1.70228	−	0.705105i	0.390529	−	0.161762i	0.569303	+	0.822128i	$0.307213\pi$
$20$	1.64346	+	4.31414i	0.367488	+	0.964670i
$21$	−0.0547034	−	1.15420i	−0.0119373	−	0.251866i
$22$	0.000498978	−	0.0347398i	0.000106383	−	0.00740655i
$23$	−1.89294	−	1.89294i	−0.394706	−	0.394706i	0.481655	−	0.876361i	$-0.340036\pi$
$23$	−1.89294	−	1.89294i	−0.394706	−	0.394706i	−0.876361	+	0.481655i	$0.840036\pi$
$24$	−0.0532077	+	1.23413i	−0.0108610	+	0.251915i
$25$	−0.232058	−	0.232058i	−0.0464115	−	0.0464115i
$26$	−5.46520	+	5.31043i	−1.07181	+	1.04146i
$27$	2.34398	+	0.970909i	0.451099	+	0.186852i
$28$	4.85013	−	2.11572i	0.916588	−	0.399833i
$29$	2.01467	+	4.86384i	0.374114	+	0.903192i	0.993044	+	0.117745i	$0.0375666\pi$
$29$	2.01467	+	4.86384i	0.374114	+	0.903192i	−0.618930	+	0.785447i	$0.712433\pi$
$30$	−0.526611	−	1.32486i	−0.0961456	−	0.241885i
$31$	−0.187704			−0.0337127			−0.0168563	−	0.999858i	$-0.505366\pi$
$31$	−0.187704			−0.0337127			−0.0168563	+	0.999858i	$0.505366\pi$
$32$	−5.36811	+	1.78422i	−0.948956	+	0.315409i
$33$			0.0107294i			0.00186775i
$34$	0.632709	+	1.59178i	0.108509	+	0.272988i
$35$	−4.10912	+	4.51801i	−0.694568	+	0.763682i
$36$	−0.161368	+	5.61621i	−0.0268947	+	0.936035i
$37$	2.35207	+	0.974258i	0.386677	+	0.160167i	0.567549	−	0.823340i	$-0.307892\pi$
$37$	2.35207	+	0.974258i	0.386677	+	0.160167i	−0.180872	+	0.983507i	$0.557892\pi$
$38$	−1.81588	−	1.86880i	−0.294574	−	0.303160i
$39$	1.66403	−	1.66403i	0.266457	−	0.266457i
$40$	4.81114	−	4.41343i	0.760708	−	0.697825i
$41$	−1.89007	−	1.89007i	−0.295179	−	0.295179i	0.543943	−	0.839122i	$-0.316931\pi$
$41$	−1.89007	−	1.89007i	−0.295179	−	0.295179i	−0.839122	+	0.543943i	$0.816931\pi$
$42$	−1.48827	+	0.674815i	−0.229645	+	0.104126i
$43$	5.31052	+	2.19969i	0.809847	+	0.335450i	0.748893	−	0.662691i	$-0.230586\pi$
$43$	5.31052	+	2.19969i	0.809847	+	0.335450i	0.0609539	+	0.998141i	$0.480586\pi$
$44$	−0.0459157	+	0.0174915i	−0.00692206	+	0.00263694i
$45$	−2.48154	−	5.99097i	−0.369926	−	0.893081i
$46$	−1.49888	+	3.47653i	−0.220998	+	0.512587i
$47$			10.7802i			1.57246i	0.617937	+	0.786228i	$0.287969\pi$
$47$			10.7802i			1.57246i	−0.617937	+	0.786228i	$0.712031\pi$
$48$	1.64968	−	0.574752i	0.238111	−	0.0829583i
$49$	5.39570	+	4.45942i	0.770814	+	0.637060i
$50$	−0.183749	+	0.426191i	−0.0259860	+	0.0602726i
$51$	−0.202432	−	0.488713i	−0.0283461	−	0.0684336i
$52$	9.83385	+	4.40833i	1.36371	+	0.611326i
$53$	2.89250	−	6.98312i	0.397316	−	0.959206i	−0.590984	−	0.806683i	$-0.701260\pi$
$53$	2.89250	−	6.98312i	0.397316	−	0.959206i	0.988300	−	0.152522i	$-0.0487396\pi$
$54$	0.0515304	−	3.58764i	0.00701240	−	0.488216i
$55$	0.0400988	−	0.0400988i	0.00540692	−	0.00540692i
$56$	−5.31406	−	5.26884i	−0.710122	−	0.704079i
$57$	0.569007	+	0.569007i	0.0753668	+	0.0753668i
$58$	5.33964	−	5.18843i	0.701130	−	0.681274i
$59$	13.1854	+	5.46159i	1.71660	+	0.711039i	0.999907	+	0.0136491i	$0.00434479\pi$
$59$	13.1854	+	5.46159i	1.71660	+	0.711039i	0.716692	+	0.697390i	$0.245655\pi$
$60$	−1.46604	+	1.38415i	−0.189265	+	0.178692i
$61$	10.3612	−	4.29176i	1.32662	−	0.549503i	0.396930	−	0.917849i	$-0.370076\pi$
$61$	10.3612	−	4.29176i	1.32662	−	0.549503i	0.929689	+	0.368346i	$0.120076\pi$
$62$	0.0980521	+	0.246681i	0.0124526	+	0.0313285i
$63$	−6.72448	+	3.16624i	−0.847205	+	0.398908i
$64$	5.14899	+	6.12273i	0.643624	+	0.765342i
$65$	−12.4379			−1.54273
$66$	0.0141006	−	0.00560477i	0.00173566	−	0.000689900i
$67$	−0.900161	+	0.372859i	−0.109972	+	0.0455519i	−0.436991	−	0.899466i	$-0.643956\pi$
$67$	−0.900161	+	0.372859i	−0.109972	+	0.0455519i	0.327019	+	0.945018i	$0.393956\pi$
$68$	1.76141	−	1.66301i	0.213602	−	0.201670i
$69$	0.447414	−	1.08015i	0.0538624	−	0.130035i
$70$	8.08407	+	3.04011i	0.966231	+	0.363363i
$71$	3.87314	−	3.87314i	0.459657	−	0.459657i	−0.438886	−	0.898543i	$-0.644627\pi$
$71$	3.87314	−	3.87314i	0.459657	−	0.459657i	0.898543	+	0.438886i	$0.144627\pi$
$72$	7.46512	−	2.72170i	0.879773	−	0.320755i
$73$	−2.87435	−	2.87435i	−0.336417	−	0.336417i	0.518600	−	0.855017i	$-0.326454\pi$
$73$	−2.87435	−	2.87435i	−0.336417	−	0.336417i	−0.855017	+	0.518600i	$0.826454\pi$
$74$	0.0517081	−	3.60002i	0.00601095	−	0.418493i
$75$	0.0548489	−	0.132417i	0.00633341	−	0.0152902i
$76$	−1.50741	+	3.36264i	−0.172912	+	0.385722i
$77$	−0.0480855	−	0.0437337i	−0.00547986	−	0.00498392i
$78$	−3.05611	−	1.31762i	−0.346036	−	0.149191i
$79$	−11.2913			−1.27038			−0.635188	−	0.772358i	$-0.719077\pi$
$79$	−11.2913			−1.27038			−0.635188	+	0.772358i	$0.719077\pi$
$80$	−8.31336	−	4.01733i	−0.929462	−	0.449151i
$81$		−	7.31974i		−	0.813305i
$82$	−1.49660	+	3.47126i	−0.165272	+	0.383336i
$83$	−7.36131	+	3.04916i	−0.808009	+	0.334688i	−0.748159	−	0.663519i	$-0.769062\pi$
$83$	−7.36131	+	3.04916i	−0.808009	+	0.334688i	−0.0598498	+	0.998207i	$0.519062\pi$
$84$	1.66428	+	1.60338i	0.181588	+	0.174943i
$85$	−1.06992	+	2.58301i	−0.116049	+	0.280167i
$86$	0.116747	−	8.12815i	0.0125892	−	0.876481i
$87$	−1.62580	+	1.62580i	−0.174304	+	0.174304i
$88$	0.0469726	+	0.0512054i	0.00500729	+	0.00545851i
$89$	−9.46502	+	9.46502i	−1.00329	+	1.00329i	−0.00329557	+	0.999995i	$0.501049\pi$
$89$	−9.46502	+	9.46502i	−1.00329	+	1.00329i	−0.999995	+	0.00329557i	$0.998951\pi$
$90$	−6.57704	+	6.39078i	−0.693281	+	0.673647i
$91$	0.674922	+	14.2403i	0.0707511	+	1.49279i
$92$	5.35184	+	0.153772i	0.557968	+	0.0160318i
$93$	−0.0313712	−	0.0757369i	−0.00325305	−	0.00785355i
$94$	14.1674	−	5.63132i	1.46125	−	0.580826i
$95$		−	4.25308i		−	0.436357i
$96$	−1.61709	−	1.86778i	−0.165044	−	0.190629i
$97$			18.3664i			1.86482i	0.361399	+	0.932411i	$0.382299\pi$
$97$			18.3664i			1.86482i	−0.361399	+	0.932411i	$0.617701\pi$
$98$	3.04200	−	9.42052i	0.307288	−	0.951617i
$99$	0.0637624	−	0.0264113i	0.00640836	−	0.00265443i
$100$	0.656087	+	0.0188511i	0.0656087	+	0.00188511i
$101$	−4.24883	+	10.2576i	−0.422774	+	1.02067i	0.558751	+	0.829335i	$0.311281\pi$
$101$	−4.24883	+	10.2576i	−0.422774	+	1.02067i	−0.981525	+	0.191332i	$0.938719\pi$
$102$	−0.536522	+	0.521328i	−0.0531236	+	0.0516192i
$103$	−12.6505	−	12.6505i	−1.24649	−	1.24649i	−0.957261	−	0.289225i	$-0.906602\pi$
$103$	−12.6505	−	12.6505i	−1.24649	−	1.24649i	−0.289225	−	0.957261i	$-0.593398\pi$
$104$	0.656468	−	15.2265i	0.0643720	−	1.49308i
$105$	−2.50973	−	0.902891i	−0.244925	−	0.0881132i
$106$	−10.6882	−	0.153518i	−1.03813	−	0.0149110i
$107$	−5.64429	−	2.33794i	−0.545654	−	0.226017i	0.0927897	−	0.995686i	$-0.470422\pi$
$107$	−5.64429	−	2.33794i	−0.545654	−	0.226017i	−0.638444	+	0.769668i	$0.720422\pi$
$108$	−4.74180	+	1.80638i	−0.456280	+	0.173819i
$109$	16.0118	−	6.63232i	1.53366	−	0.635261i	0.553386	−	0.832925i	$-0.313336\pi$
$109$	16.0118	−	6.63232i	1.53366	−	0.635261i	0.980270	+	0.197664i	$0.0633355\pi$
$110$	−0.0736445	−	0.0317512i	−0.00702173	−	0.00302736i
$111$			1.11186i			0.105534i
$112$	−4.14838	+	9.73606i	−0.391985	+	0.919971i
$113$			9.71297i			0.913720i	0.889539	+	0.456860i	$0.151026\pi$
$113$			9.71297i			0.913720i	−0.889539	+	0.456860i	$0.848974\pi$
$114$	0.450554	−	1.04502i	0.0421982	−	0.0978755i
$115$	−5.70896	+	2.36473i	−0.532364	+	0.220512i
$116$	−9.60794	−	4.30706i	−0.892074	−	0.399900i
$117$	−13.9851	−	5.79281i	−1.29292	−	0.535545i
$118$	0.289871	−	20.1813i	0.0266848	−	1.85784i
$119$	3.01538	+	1.08480i	0.276419	+	0.0994433i
$120$	2.58487	+	1.20363i	0.235965	+	0.109875i
$121$	−7.77775	−	7.77775i	−0.707068	−	0.707068i
$122$	−11.0527	−	11.3748i	−1.00066	−	1.02983i
$123$	0.446735	−	1.07851i	0.0402808	−	0.0972464i
$124$	0.272968	−	0.257720i	0.0245133	−	0.0231440i
$125$	9.96302	−	4.12682i	0.891119	−	0.369114i
$126$	7.67378	+	7.18335i	0.683634	+	0.639944i
$127$		−	16.9587i		−	1.50484i	−0.658684	−	0.752419i	$-0.728887\pi$
$127$		−	16.9587i		−	1.50484i	0.658684	−	0.752419i	$-0.271113\pi$
$128$	5.35679	−	9.96518i	0.473478	−	0.880806i
$129$			2.51038i			0.221027i
$130$	6.49725	+	16.3459i	0.569847	+	1.43363i
$131$	0.732500	+	1.76841i	0.0639988	+	0.154507i	0.952643	−	0.304090i	$-0.0983523\pi$
$131$	0.732500	+	1.76841i	0.0639988	+	0.154507i	−0.888645	+	0.458597i	$0.848352\pi$
$132$	−0.0147316	−	0.0156032i	−0.00128222	−	0.00135808i
$133$	−4.86941	+	0.230787i	−0.422231	+	0.0200117i
$134$	0.960233	+	0.988219i	0.0829515	+	0.0853691i
$135$	4.14108	−	4.14108i	0.356407	−	0.356407i
$136$	−3.10565	−	1.44612i	−0.266307	−	0.124004i
$137$	8.94224	−	8.94224i	0.763987	−	0.763987i	−0.213053	−	0.977041i	$-0.568341\pi$
$137$	8.94224	−	8.94224i	0.763987	−	0.763987i	0.977041	+	0.213053i	$0.0683408\pi$
$138$	−1.65326	−	0.0237462i	−0.140735	−	0.00202141i
$139$	5.33005	−	12.8679i	0.452089	−	1.09144i	−0.519438	−	0.854508i	$-0.673859\pi$
$139$	5.33005	−	12.8679i	0.452089	−	1.09144i	0.971527	−	0.236930i	$-0.0761414\pi$
$140$	−0.227602	−	12.2122i	−0.0192359	−	1.03212i
$141$	−4.34971	+	1.80171i	−0.366312	+	0.151731i
$142$	−7.11332	−	3.06685i	−0.596937	−	0.257364i
$143$		−	0.132378i		−	0.0110700i
$144$	−7.47646	−	8.38892i	−0.623038	−	0.699076i
$145$	12.1521			1.00918
$146$	−2.27598	+	5.27897i	−0.188362	+	0.436890i
$147$	−0.897545	+	2.92242i	−0.0740283	+	0.241037i
$148$	−4.75815	+	1.81261i	−0.391118	+	0.148995i
$149$	−6.86653	+	16.5773i	−0.562528	+	1.35806i	0.345210	+	0.938525i	$0.387808\pi$
$149$	−6.86653	+	16.5773i	−0.562528	+	1.35806i	−0.907738	+	0.419537i	$0.862192\pi$
$150$	−0.202674	−	0.00291107i	−0.0165483	−	0.000237688i
$151$	8.73933	+	8.73933i	0.711196	+	0.711196i	0.966785	−	0.255589i	$-0.0822695\pi$
$151$	8.73933	+	8.73933i	0.711196	+	0.711196i	−0.255589	+	0.966785i	$0.582269\pi$
$152$	5.20662	+	0.224476i	0.422313	+	0.0182074i
$153$	−2.40602	+	2.40602i	−0.194515	+	0.194515i
$154$	−0.0323562	+	0.0860395i	−0.00260734	+	0.00693326i
$155$	−0.165807	+	0.400294i	−0.0133179	+	0.0321524i
$156$	−0.135176	+	4.70463i	−0.0108228	+	0.376672i
$157$	3.33915	−	1.38312i	0.266493	−	0.110385i	−0.245436	−	0.969413i	$-0.578931\pi$
$157$	3.33915	−	1.38312i	0.266493	−	0.110385i	0.511929	+	0.859028i	$0.328931\pi$
$158$	5.89832	+	14.8391i	0.469246	+	1.18054i
$159$	3.30105			0.261790
$160$	−0.936884	+	13.0240i	−0.0740672	+	1.02964i
$161$	3.01720	+	6.40795i	0.237788	+	0.505017i
$162$	−9.61961	+	3.82366i	−0.755788	+	0.300415i
$163$	18.1360	−	7.51216i	1.42052	−	0.588398i	0.465528	−	0.885033i	$-0.345865\pi$
$163$	18.1360	−	7.51216i	1.42052	−	0.588398i	0.954991	+	0.296635i	$0.0958646\pi$
$164$	5.34372	+	0.153539i	0.417274	+	0.0119894i
$165$	0.0228812	+	0.00947772i	0.00178130	+	0.000737840i
$166$	7.85257	+	8.08144i	0.609478	+	0.627241i
$167$	2.57753	+	2.57753i	0.199455	+	0.199455i	0.799766	−	0.600311i	$-0.204957\pi$
$167$	2.57753	+	2.57753i	0.199455	+	0.199455i	−0.600311	+	0.799766i	$0.704957\pi$
$168$	1.23778	−	3.02476i	0.0954970	−	0.233365i
$169$	−11.3381	+	11.3381i	−0.872163	+	0.872163i
$170$	3.95349	+	0.0567852i	0.303219	+	0.00435523i
$171$	1.98083	−	4.78214i	0.151478	−	0.365699i
$172$	−10.7430	+	4.09252i	−0.819147	+	0.312052i
$173$	−0.718205	−	1.73390i	−0.0546041	−	0.131826i	0.894223	−	0.447621i	$-0.147729\pi$
$173$	−0.718205	−	1.73390i	−0.0546041	−	0.131826i	−0.948827	+	0.315795i	$0.897729\pi$
$174$	2.98590	+	1.28735i	0.226361	+	0.0975936i
$175$	0.369881	+	0.785556i	0.0279604	+	0.0593824i
$176$	0.0427568	−	0.0884798i	0.00322292	−	0.00666942i
$177$			6.23300i			0.468501i
$178$	17.3832	+	7.49464i	1.30293	+	0.561747i
$179$	−0.872905	−	2.10738i	−0.0652440	−	0.157513i	0.887895	−	0.460047i	$-0.152167\pi$
$179$	−0.872905	−	2.10738i	−0.0652440	−	0.157513i	−0.953139	+	0.302534i	$0.902167\pi$
$180$	11.8345	+	5.30516i	0.882088	+	0.395424i
$181$	9.17797	+	3.80164i	0.682193	+	0.282574i	0.696743	−	0.717321i	$-0.254632\pi$
$181$	9.17797	+	3.80164i	0.682193	+	0.282574i	−0.0145503	+	0.999894i	$0.504632\pi$
$182$	18.3620	−	8.32577i	1.36109	−	0.617147i
$183$	3.46337	+	3.46337i	0.256019	+	0.256019i
$184$	−2.59358	−	7.11372i	−0.191202	−	0.524431i
$185$	4.15536	−	4.15536i	0.305508	−	0.305508i
$186$	−0.0831459	+	0.0807912i	−0.00609655	+	0.00592390i
$187$	−0.0274912	−	0.0113872i	−0.00201035	−	0.000832716i
$188$	−14.8014	−	15.6771i	−1.07950	−	1.14337i
$189$	−4.96588	−	4.51646i	−0.361215	−	0.328524i
$190$	−5.58940	+	2.22171i	−0.405498	+	0.161180i
$191$			22.7943i			1.64934i	0.565617	+	0.824668i	$0.308638\pi$
$191$			22.7943i			1.64934i	−0.565617	+	0.824668i	$0.691362\pi$
$192$	−1.60991	+	3.10087i	−0.116185	+	0.223786i
$193$	11.7224			0.843796			0.421898	−	0.906643i	$-0.361364\pi$
$193$	11.7224			0.843796			0.421898	+	0.906643i	$0.361364\pi$
$194$	24.1371	−	9.59415i	1.73294	−	0.688820i
$195$	−2.07876	−	5.01857i	−0.148863	−	0.359387i
$196$	−13.9695	+	0.923259i	−0.997823	+	0.0659471i
$197$	−17.8929	−	7.41146i	−1.27481	−	0.528045i	−0.360389	−	0.932802i	$-0.617356\pi$
$197$	−17.8929	−	7.41146i	−1.27481	−	0.528045i	−0.914424	+	0.404757i	$0.867356\pi$
$198$	−0.0680176	−	0.0700000i	−0.00483380	−	0.00497469i
$199$	−14.6615	−	14.6615i	−1.03932	−	1.03932i	−0.999194	−	0.0401297i	$-0.987223\pi$
$199$	−14.6615	−	14.6615i	−1.03932	−	1.03932i	−0.0401297	−	0.999194i	$-0.512777\pi$
$200$	−0.317950	−	0.872078i	−0.0224825	−	0.0616652i
$201$	−0.300890	−	0.300890i	−0.0212231	−	0.0212231i
$202$	15.7000	+	0.225504i	1.10465	+	0.0158664i
$203$	−0.659417	−	13.9131i	−0.0462820	−	0.976512i
$204$	0.965396	+	0.432769i	0.0675912	+	0.0302999i
$205$	−5.70030	+	2.36114i	−0.398126	+	0.164909i
$206$	−10.0169	+	23.2335i	−0.697914	+	1.61876i
$207$	−7.52047			−0.522709
$208$	−20.3536	+	7.09120i	−1.41126	+	0.491686i
$209$	0.0452659			0.00313111
$210$	0.124444	+	3.76994i	0.00858744	+	0.260151i
$211$	−7.17951	−	17.3329i	−0.494258	−	1.19324i	−0.952534	−	0.304434i	$-0.901533\pi$
$211$	−7.17951	−	17.3329i	−0.494258	−	1.19324i	0.458276	−	0.888810i	$-0.348467\pi$
$212$	5.38150	+	14.1266i	0.369603	+	0.970221i
$213$	2.21010	+	0.915453i	0.151433	+	0.0627258i
$214$	−0.124085	+	8.63902i	−0.00848226	+	0.590551i
$215$	9.38202	−	9.38202i	0.639848	−	0.639848i
$216$	4.85094	+	5.28807i	0.330065	+	0.359808i
$217$	0.467299	+	0.168113i	0.0317223	+	0.0114123i
$218$	−17.0804	−	17.5782i	−1.15683	−	1.19055i
$219$	0.679380	−	1.64017i	0.0459082	−	0.110832i
$220$	−0.00325740	+	0.113370i	−0.000219614	+	0.00764339i
$221$	2.49757	+	6.02967i	0.168005	+	0.405600i
$222$	1.46121	−	0.580811i	0.0980702	−	0.0389815i
$223$	6.12615			0.410237			0.205119	−	0.978737i	$-0.434242\pi$
$223$	6.12615			0.410237			0.205119	+	0.978737i	$0.434242\pi$
$224$	14.9622	+	0.365925i	0.999701	+	0.0244494i
$225$	−0.921941			−0.0614627
$226$	12.7648	−	5.07382i	0.849102	−	0.337506i
$227$	−2.38899	−	5.76753i	−0.158563	−	0.382804i	0.824554	−	0.565783i	$-0.191426\pi$
$227$	−2.38899	−	5.76753i	−0.158563	−	0.382804i	−0.983117	+	0.182979i	$0.941426\pi$
$228$	−1.60873	−	0.0462229i	−0.106541	−	0.00306119i
$229$	−6.39511	+	15.4392i	−0.422601	+	1.02025i	0.558976	+	0.829184i	$0.311194\pi$
$229$	−6.39511	+	15.4392i	−0.422601	+	1.02025i	−0.981577	+	0.191065i	$0.938806\pi$
$230$	6.08995	+	6.26745i	0.401560	+	0.413263i
$231$	0.00960955	−	0.0267113i	0.000632262	−	0.00175748i
$232$	−0.641387	+	14.8767i	−0.0421091	+	0.976700i
$233$	3.09584	−	3.09584i	0.202815	−	0.202815i	−0.598390	−	0.801205i	$-0.704193\pi$
$233$	3.09584	−	3.09584i	0.202815	−	0.202815i	0.801205	+	0.598390i	$0.204193\pi$
$234$	−0.307450	+	21.4052i	−0.0200986	+	1.39930i
$235$	22.9896	+	9.52262i	1.49968	+	0.621187i
$236$	−26.6737	+	10.1613i	−1.73631	+	0.661443i
$237$	−1.88714	−	4.55595i	−0.122583	−	0.295941i
$238$	−0.149516	−	4.52948i	−0.00969167	−	0.293603i
$239$	18.4414			1.19288			0.596439	−	0.802659i	$-0.296582\pi$
$239$	18.4414			1.19288			0.596439	+	0.802659i	$0.296582\pi$
$240$	0.231533	−	4.02578i	0.0149454	−	0.259863i
$241$	16.0892			1.03640			0.518198	−	0.855261i	$-0.326603\pi$
$241$	16.0892			1.03640			0.518198	+	0.855261i	$0.326603\pi$
$242$	−6.15862	+	14.2844i	−0.395891	+	0.918238i
$243$	9.98539	−	4.13608i	0.640563	−	0.265330i
$244$	−9.17514	+	20.4674i	−0.587378	+	1.31029i
$245$	14.2763	−	7.56754i	0.912080	−	0.483473i
$246$	−1.65075	−	0.0237102i	−0.105248	−	0.00151171i
$247$	−7.02032	−	7.02032i	−0.446692	−	0.446692i
$248$	−0.481288	−	0.224108i	−0.0305618	−	0.0142309i
$249$	−2.46061	−	2.46061i	−0.155935	−	0.155935i
$250$	−10.6279	−	10.9377i	−0.672168	−	0.691758i
$251$	−0.238196	−	0.0986640i	−0.0150348	−	0.00622761i	0.375153	−	0.926963i	$-0.377590\pi$
$251$	−0.238196	−	0.0986640i	−0.0150348	−	0.00622761i	−0.390188	+	0.920735i	$0.627590\pi$
$252$	5.43177	−	13.8373i	0.342169	−	0.871667i
$253$	−0.0251680	−	0.0607610i	−0.00158230	−	0.00382001i
$254$	−22.2871	+	8.85880i	−1.39842	+	0.555850i
$255$	−1.22104			−0.0764642
$256$	−15.8945	−	1.83433i	−0.993406	−	0.114646i
$257$		−	4.69418i		−	0.292815i	−0.989224	−	0.146408i	$-0.953229\pi$
$257$		−	4.69418i		−	0.292815i	0.989224	−	0.146408i	$-0.0467711\pi$
$258$	3.29914	−	1.31136i	0.205396	−	0.0816418i
$259$	−4.98301	−	4.53204i	−0.309629	−	0.281607i
$260$	18.0878	−	17.0774i	1.12176	−	1.05909i
$261$	13.6638	+	5.65973i	0.845768	+	0.350328i
$262$	1.94141	−	1.88643i	0.119941	−	0.116544i
$263$	−10.7215	+	10.7215i	−0.661117	+	0.661117i	−0.955643	−	0.294526i	$-0.904838\pi$
$263$	−10.7215	+	10.7215i	−0.661117	+	0.661117i	0.294526	+	0.955643i	$0.404838\pi$
$264$	−0.0128103	+	0.0275110i	−0.000788419	+	0.00169318i
$265$	−12.3370	−	12.3370i	−0.757854	−	0.757854i
$266$	2.84696	+	6.27882i	0.174558	+	0.384979i
$267$	−5.40094	−	2.23714i	−0.330532	−	0.136911i
$268$	0.797116	−	1.77816i	0.0486916	−	0.108618i
$269$	6.12387	+	14.7843i	0.373379	+	0.901416i	0.993173	+	0.116651i	$0.0372160\pi$
$269$	6.12387	+	14.7843i	0.373379	+	0.901416i	−0.619794	+	0.784764i	$0.712784\pi$
$270$	−7.60540	−	3.27901i	−0.462850	−	0.199554i
$271$			3.70138i			0.224843i	0.993661	+	0.112421i	$0.0358607\pi$
$271$			3.70138i			0.224843i	−0.993661	+	0.112421i	$0.964139\pi$
$272$	−0.278181	+	4.83687i	−0.0168672	+	0.293278i
$273$	−5.63302	+	2.65232i	−0.340926	+	0.160526i
$274$	−16.4231	−	7.08069i	−0.992156	−	0.427760i
$275$	−0.00308537	−	0.00744875i	−0.000186055	−	0.000449176i
$276$	0.832414	+	2.18512i	0.0501054	+	0.131529i
$277$	1.96367	−	4.74071i	0.117985	−	0.284842i	−0.853843	−	0.520530i	$-0.825734\pi$
$277$	1.96367	−	4.74071i	0.117985	−	0.284842i	0.971829	+	0.235688i	$0.0757344\pi$
$278$	−19.6953	−	0.282889i	−1.18124	−	0.0169666i
$279$	−0.372865	+	0.372865i	−0.0223228	+	0.0223228i
$280$	−15.9304	+	6.67846i	−0.952021	+	0.399114i
$281$	11.3747	+	11.3747i	0.678557	+	0.678557i	0.959674	−	0.281117i	$-0.0907048\pi$
$281$	11.3747	+	11.3747i	0.678557	+	0.678557i	−0.281117	+	0.959674i	$0.590705\pi$
$282$	4.63999	+	4.77522i	0.276307	+	0.284360i
$283$	−21.0703	−	8.72759i	−1.25250	−	0.518801i	−0.344898	−	0.938640i	$-0.612087\pi$
$283$	−21.0703	−	8.72759i	−1.25250	−	0.518801i	−0.907599	+	0.419839i	$0.862087\pi$
$284$	−0.314632	+	10.9504i	−0.0186700	+	0.649786i
$285$	1.71608	−	0.710823i	0.101652	−	0.0421055i
$286$	−0.173971	+	0.0691508i	−0.0102871	+	0.00408897i
$287$	3.01262	+	6.39822i	0.177829	+	0.377675i
$288$	−7.11920	+	14.2077i	−0.419503	+	0.837199i
$289$	−15.5330			−0.913703
$290$	−6.34799	−	15.9704i	−0.372767	−	0.937812i
$291$	−7.41065	+	3.06959i	−0.434420	+	0.179943i
$292$	8.12654	+	0.233496i	0.475570	+	0.0136643i
$293$	−3.96236	+	9.56598i	−0.231483	+	0.558850i	−0.996352	−	0.0853357i	$-0.972804\pi$
$293$	−3.96236	+	9.56598i	−0.231483	+	0.558850i	0.764869	+	0.644186i	$0.222804\pi$
$294$	4.30950	−	0.347047i	0.251335	−	0.0202402i
$295$	23.2945	−	23.2945i	1.35626	−	1.35626i
$296$	4.86767	+	5.30631i	0.282928	+	0.308423i
$297$	0.0440739	+	0.0440739i	0.00255742	+	0.00255742i
$298$	25.3728	+	0.364437i	1.46980	+	0.0211113i
$299$	−5.52013	+	13.3268i	−0.319237	+	0.770707i
$300$	0.102046	+	0.267875i	0.00589165	+	0.0154658i
$301$	−11.2507	−	10.2325i	−0.648479	−	0.589791i
$302$	6.92002	−	16.0504i	0.398202	−	0.923599i
$303$	−4.84895			−0.278565
$304$	−2.42481	−	6.95981i	−0.139072	−	0.399172i
$305$		−	25.8872i		−	1.48230i
$306$	4.41883	+	1.90514i	0.252608	+	0.108910i
$307$	−22.2734	+	9.22595i	−1.27121	+	0.526553i	−0.913332	−	0.407215i	$-0.866500\pi$
$307$	−22.2734	+	9.22595i	−1.27121	+	0.526553i	−0.357879	+	0.933768i	$0.616500\pi$
$308$	0.129975	−	0.00242239i	0.00740603	−	0.000138028i
$309$	2.99005	−	7.21862i	0.170098	−	0.410653i
$310$	0.612680	+	0.00880011i	0.0347979	+	0.000499813i
$311$	18.5499	−	18.5499i	1.05187	−	1.05187i	0.0532917	−	0.998579i	$-0.483029\pi$
$311$	18.5499	−	18.5499i	1.05187	−	1.05187i	0.998579	−	0.0532917i	$-0.0169713\pi$
$312$	6.25345	−	2.27994i	0.354032	−	0.129076i
$313$	5.76565	−	5.76565i	0.325894	−	0.325894i	−0.525129	−	0.851023i	$-0.675983\pi$
$313$	5.76565	−	5.76565i	0.325894	−	0.325894i	0.851023	+	0.525129i	$0.175983\pi$
$314$	−3.56199	−	3.66580i	−0.201015	−	0.206873i
$315$	0.812228	+	17.1373i	0.0457639	+	0.965580i
$316$	16.4204	−	15.5032i	0.923720	−	0.872121i
$317$	8.97014	+	21.6558i	0.503813	+	1.21631i	0.947391	+	0.320077i	$0.103709\pi$
$317$	8.97014	+	21.6558i	0.503813	+	1.21631i	−0.443578	+	0.896236i	$0.646291\pi$
$318$	−1.72439	−	4.33824i	−0.0966989	−	0.243277i
$319$			0.129336i			0.00724145i
$320$	17.6055	−	5.57216i	0.984179	−	0.311493i
$321$		−	2.66816i		−	0.148922i
$322$	6.84522	−	7.31256i	0.381469	−	0.407513i
$323$	−2.06182	+	0.854034i	−0.114723	+	0.0475197i
$324$	10.0501	+	10.6447i	0.558339	+	0.591373i
$325$	−0.676718	+	1.63374i	−0.0375376	+	0.0906237i
$326$	−19.3463	−	19.9101i	−1.07149	−	1.10272i
$327$	5.35215	+	5.35215i	0.295975	+	0.295975i
$328$	−2.58965	−	7.10293i	−0.142989	−	0.392193i
$329$	9.65507	−	26.8378i	0.532301	−	1.47962i
$330$	0.000503024	−	0.0350215i	2.76906e−5	−	0.00192787i
$331$	9.58530	+	3.97036i	0.526856	+	0.218231i	0.630225	−	0.776412i	$-0.282962\pi$
$331$	9.58530	+	3.97036i	0.526856	+	0.218231i	−0.103370	+	0.994643i	$0.532962\pi$
$332$	6.51864	−	14.5414i	0.357757	−	0.798063i
$333$	6.60757	−	2.73695i	0.362093	−	0.149984i
$334$	2.04095	−	4.73382i	0.111676	−	0.259023i
$335$			2.24902i			0.122877i
$336$	−4.62173	−	0.0466325i	−0.252136	−	0.00254401i
$337$			19.1782i			1.04470i	0.852730	+	0.522352i	$0.174945\pi$
$337$			19.1782i			1.04470i	−0.852730	+	0.522352i	$0.825055\pi$
$338$	20.8233	+	8.97780i	1.13264	+	0.488328i
$339$	−3.91909	+	1.62334i	−0.212856	+	0.0881678i
$340$	−1.99058	−	5.22534i	−0.107954	−	0.283384i
$341$	−0.00426036	−	0.00176470i	−0.000230712	−	9.55639e-5i
$342$	−7.31942	−	0.105131i	−0.395789	−	0.00568484i
$343$	−9.43886	−	15.9345i	−0.509650	−	0.860382i
$344$	10.9903	+	11.9806i	0.592556	+	0.645953i
$345$	−1.90829	−	1.90829i	−0.102739	−	0.102739i
$346$	−1.90352	+	1.84961i	−0.102334	+	0.0994358i
$347$	2.67951	−	6.46890i	0.143843	−	0.347269i	−0.835495	−	0.549499i	$-0.814819\pi$
$347$	2.67951	−	6.46890i	0.143843	−	0.347269i	0.979338	+	0.202230i	$0.0648188\pi$
$348$	0.132071	−	4.59655i	0.00707973	−	0.246401i
$349$	−15.3115	+	6.34224i	−0.819607	+	0.339493i	−0.752780	−	0.658272i	$-0.771288\pi$
$349$	−15.3115	+	6.34224i	−0.819607	+	0.339493i	−0.0668273	+	0.997765i	$0.521288\pi$
$350$	0.839161	−	0.896453i	0.0448551	−	0.0479174i
$351$		−	13.6709i		−	0.729697i
$352$	−0.138615	−	0.00997134i	−0.00738822	−	0.000531474i
$353$		−	20.1998i		−	1.07513i	−0.843224	−	0.537563i	$-0.819345\pi$
$353$		−	20.1998i		−	1.07513i	0.843224	−	0.537563i	$-0.180655\pi$
$354$	8.19142	−	3.25597i	0.435369	−	0.173053i
$355$	−4.83846	−	11.6811i	−0.256799	−	0.619968i
$356$	0.768885	−	26.7601i	0.0407508	−	1.41828i
$357$	0.0662575	+	1.39798i	0.00350672	+	0.0739889i
$358$	−2.31353	+	2.24802i	−0.122274	+	0.118811i
$359$	−20.9054	+	20.9054i	−1.10335	+	1.10335i	−0.109343	+	0.994004i	$0.534875\pi$
$359$	−20.9054	+	20.9054i	−1.10335	+	1.10335i	−0.994004	+	0.109343i	$0.965125\pi$
$360$	0.790020	−	18.3241i	0.0416377	−	0.965767i
$361$	−11.0345	+	11.0345i	−0.580761	+	0.580761i
$362$	0.201770	−	14.0476i	0.0106048	−	0.738324i
$363$	1.83834	−	4.43815i	0.0964879	−	0.232942i
$364$	−20.5336	−	19.7822i	−1.07625	−	1.03687i
$365$	−8.66882	+	3.59074i	−0.453747	+	0.187948i
$366$	2.74238	−	6.36074i	0.143347	−	0.332481i
$367$			27.7632i			1.44923i	0.689155	+	0.724614i	$0.257982\pi$
$367$			27.7632i			1.44923i	−0.689155	+	0.724614i	$0.742018\pi$
$368$	−7.99403	+	7.12453i	−0.416718	+	0.371392i
$369$	−7.50905			−0.390906
$370$	−7.63164	−	3.29032i	−0.396750	−	0.171055i
$371$	−13.4553	+	14.7942i	−0.698565	+	0.768077i
$372$	0.149609	+	0.0670670i	0.00775688	+	0.00347726i
$373$	−2.53886	+	6.12934i	−0.131457	+	0.317365i	−0.975879	−	0.218314i	$-0.929944\pi$
$373$	−2.53886	+	6.12934i	−0.131457	+	0.317365i	0.844422	+	0.535679i	$0.179944\pi$
$374$	−0.000604370		0.0420774i	−3.12512e−5		0.00217577i
$375$	3.33026	+	3.33026i	0.171974	+	0.171974i
$376$	−12.8710	+	27.6413i	−0.663770	+	1.42549i
$377$	20.0588	−	20.0588i	1.03308	−	1.03308i
$378$	−3.34148	+	8.88545i	−0.171867	+	0.457018i
$379$	5.39673	−	13.0289i	0.277211	−	0.669247i	−0.722545	−	0.691324i	$-0.757028\pi$
$379$	5.39673	−	13.0289i	0.277211	−	0.669247i	0.999756	+	0.0220767i	$0.00702779\pi$
$380$	5.83954	+	6.18503i	0.299562	+	0.317286i
$381$	6.84266	−	2.83432i	0.350560	−	0.145207i
$382$	29.9563	−	11.9072i	1.53270	−	0.609224i
$383$	21.1949			1.08301			0.541505	−	0.840697i	$-0.317855\pi$
$383$	21.1949			1.08301			0.541505	+	0.840697i	$0.317855\pi$
$384$	4.91614	+	0.495922i	0.250876	+	0.0253074i
$385$	−0.135742	+	0.0639143i	−0.00691803	+	0.00325737i
$386$	−6.12349	−	15.4056i	−0.311678	−	0.784123i
$387$	14.9186	−	6.17951i	0.758357	−	0.314122i
$388$	−25.2173	−	26.7092i	−1.28021	−	1.35596i
$389$	−28.8928	−	11.9678i	−1.46492	−	0.606790i	−0.499226	−	0.866472i	$-0.666382\pi$
$389$	−28.8928	−	11.9678i	−1.46492	−	0.606790i	−0.965694	+	0.259682i	$0.916382\pi$
$390$	−5.50951	+	5.35349i	−0.278985	+	0.271084i
$391$	2.29276	+	2.29276i	0.115950	+	0.115950i
$392$	8.51069	+	17.8765i	0.429855	+	0.902898i
$393$	−0.591114	+	0.591114i	−0.0298177	+	0.0298177i
$394$	−0.393359	+	27.3864i	−0.0198171	+	1.37971i
$395$	−9.97412	+	24.0797i	−0.501853	+	1.21158i
$396$	−0.0564633	+	0.125955i	−0.00283739	+	0.00632948i
$397$	3.42735	+	8.27436i	0.172014	+	0.415278i	0.986251	−	0.165254i	$-0.0528444\pi$
$397$	3.42735	+	8.27436i	0.172014	+	0.415278i	−0.814237	+	0.580532i	$0.802844\pi$
$398$	−11.6093	+	26.9269i	−0.581923	+	1.34972i
$399$	−0.906950	−	1.92619i	−0.0454043	−	0.0964300i
$400$	−0.979996	+	0.873402i	−0.0489998	+	0.0436701i
$401$			1.46000i			0.0729088i	0.999335	+	0.0364544i	$0.0116064\pi$
$401$			1.46000i			0.0729088i	−0.999335	+	0.0364544i	$0.988394\pi$
$402$	−0.238252	+	0.552607i	−0.0118829	+	0.0275615i
$403$	0.387054	+	0.934430i	0.0192805	+	0.0465473i
$404$	−7.90494	−	20.7508i	−0.393286	−	1.03239i
$405$	−15.6099	−	6.46584i	−0.775663	−	0.321290i
$406$	−17.9402	+	8.13450i	−0.890358	+	0.403708i
$407$	0.0442259	+	0.0442259i	0.00219219	+	0.00219219i
$408$	0.0644459	−	1.49479i	0.00319055	−	0.0740032i
$409$	−19.4063	+	19.4063i	−0.959579	+	0.959579i	−0.999214	−	0.0396351i	$-0.987380\pi$
$409$	−19.4063	+	19.4063i	−0.959579	+	0.959579i	0.0396351	+	0.999214i	$0.487380\pi$
$410$	6.08071	+	6.25793i	0.300305	+	0.309057i
$411$	5.10264	+	2.11358i	0.251694	+	0.104255i
$412$	35.7661	+	1.02765i	1.76207	+	0.0506288i
$413$	−27.9342	−	25.4062i	−1.37455	−	1.25016i
$414$	3.92851	+	9.88340i	0.193076	+	0.485743i
$415$			18.3920i			0.902829i
$416$	19.9515	+	23.0444i	0.978201	+	1.12984i
$417$	6.08288			0.297880
$418$	−0.0236458	−	0.0594885i	−0.00115656	−	0.00290968i
$419$	7.96959	+	19.2403i	0.389340	+	0.939950i	0.990080	+	0.140506i	$0.0448728\pi$
$419$	7.96959	+	19.2403i	0.389340	+	0.939950i	−0.600740	+	0.799445i	$0.705127\pi$
$420$	4.88946	−	2.13287i	0.238581	−	0.104073i
$421$	−14.5397	−	6.02253i	−0.708620	−	0.293520i	−0.000886861	−	1.00000i	$-0.500282\pi$
$421$	−14.5397	−	6.02253i	−0.708620	−	0.293520i	−0.707734	+	0.706479i	$0.750282\pi$
$422$	−19.0285	+	18.4896i	−0.926291	+	0.900059i
$423$	21.4143	+	21.4143i	1.04120	+	1.04120i
$424$	15.7541	−	14.4518i	0.765085	−	0.701841i
$425$	0.281071	+	0.281071i	0.0136340	+	0.0136340i
$426$	0.0485871	−	3.38272i	0.00235405	−	0.163893i
$427$	−29.6386	+	1.40473i	−1.43431	+	0.0679795i
$428$	11.4182	−	4.34974i	0.551920	−	0.210253i
$429$	0.0534131	−	0.0221244i	0.00257881	−	0.00106818i
$430$	−17.2308	−	7.42892i	−0.830942	−	0.358254i
$431$	−21.7201			−1.04622			−0.523111	−	0.852265i	$-0.675229\pi$
$431$	−21.7201			−1.04622			−0.523111	+	0.852265i	$0.675229\pi$
$432$	4.41557	−	9.13747i	0.212444	−	0.439627i
$433$	11.6173			0.558290			0.279145	−	0.960249i	$-0.409949\pi$
$433$	11.6173			0.558290			0.279145	+	0.960249i	$0.409949\pi$
$434$	−0.0231707	−	0.701943i	−0.00111223	−	0.0336943i
$435$	2.03100	+	4.90327i	0.0973791	+	0.235094i
$436$	−14.1789	+	31.6295i	−0.679047	+	1.51478i
$437$	−4.55703	−	1.88759i	−0.217992	−	0.0902954i
$438$	−2.51040	−	0.0360577i	−0.119952	−	0.00172290i
$439$	−17.1141	+	17.1141i	−0.816811	+	0.816811i	−0.985645	−	0.168833i	$-0.946000\pi$
$439$	−17.1141	+	17.1141i	−0.816811	+	0.816811i	0.168833	+	0.985645i	$0.446000\pi$
$440$	0.150692	−	0.0549407i	0.00718397	−	0.00261920i
$441$	19.5767	−	1.85986i	0.932223	−	0.0885648i
$442$	6.61953	−	6.43206i	0.314859	−	0.305942i
$443$	6.51762	−	15.7349i	0.309662	−	0.747589i	−0.690054	−	0.723757i	$-0.742413\pi$
$443$	6.51762	−	15.7349i	0.309662	−	0.747589i	0.999716	−	0.0238316i	$-0.00758655\pi$
$444$	−1.52661	−	1.61693i	−0.0724495	−	0.0767359i
$445$	11.8240	+	28.5457i	0.560513	+	1.35320i
$446$	−3.20015	−	8.05099i	−0.151531	−	0.381225i
$447$	−7.83638			−0.370648
$448$	−7.33497	−	19.8544i	−0.346545	−	0.938033i
$449$	7.70962			0.363840			0.181920	−	0.983313i	$-0.441769\pi$
$449$	7.70962			0.363840			0.181920	+	0.983313i	$0.441769\pi$
$450$	0.481599	+	1.21162i	0.0227028	+	0.0571161i
$451$	−0.0251298	−	0.0606688i	−0.00118332	−	0.00285678i
$452$	−13.3360	−	14.1251i	−0.627274	−	0.664387i
$453$	−2.06562	+	4.98685i	−0.0970513	+	0.234303i
$454$	−6.33174	+	6.15243i	−0.297163	+	0.288748i
$455$	30.9647	+	11.1397i	1.45165	+	0.522239i
$456$	0.779615	+	2.13834i	0.0365088	+	0.100137i
$457$	13.8268	−	13.8268i	0.646788	−	0.646788i	−0.305427	−	0.952215i	$-0.598799\pi$
$457$	13.8268	−	13.8268i	0.646788	−	0.646788i	0.952215	+	0.305427i	$0.0987992\pi$
$458$	23.6308	+	0.339417i	1.10420	+	0.0158599i
$459$	−2.83906	−	1.17598i	−0.132516	−	0.0548900i
$460$	5.05544	−	11.2774i	0.235711	−	0.525811i
$461$	12.4410	+	30.0351i	0.579433	+	1.39888i	0.893322	+	0.449416i	$0.148368\pi$
$461$	12.4410	+	30.0351i	0.579433	+	1.39888i	−0.313889	+	0.949460i	$0.601632\pi$
$462$	−0.0401238	+	0.00132447i	−0.00186673	+	6.16197e-5i
$463$	5.60549			0.260509			0.130255	−	0.991481i	$-0.458421\pi$
$463$	5.60549			0.260509			0.130255	+	0.991481i	$0.458421\pi$
$464$	19.8860	−	6.92829i	0.923183	−	0.321638i
$465$	−0.189226			−0.00877516
$466$	−5.68575	−	2.45136i	−0.263387	−	0.113557i
$467$	−20.3070	+	8.41144i	−0.939697	+	0.389235i	−0.799349	−	0.600867i	$-0.794822\pi$
$467$	−20.3070	+	8.41144i	−0.939697	+	0.389235i	−0.140348	+	0.990102i	$0.544822\pi$
$468$	28.2914	−	10.7775i	1.30777	−	0.498191i
$469$	2.57494	−	0.122040i	0.118899	−	0.00563527i
$470$	0.505407	−	35.1874i	0.0233127	−	1.62307i
$471$	1.11615	+	1.11615i	0.0514296	+	0.0514296i
$472$	27.2877	+	29.7466i	1.25602	+	1.36920i
$473$	0.0998536	+	0.0998536i	0.00459128	+	0.00459128i
$474$	−5.00164	+	4.85999i	−0.229733	+	0.223227i
$475$	−0.558651	−	0.231401i	−0.0256327	−	0.0106174i
$476$	−5.87455	+	2.56259i	−0.269259	+	0.117456i
$477$	−8.12580	−	19.6174i	−0.372055	−	0.898220i
$478$	−9.63336	−	24.2357i	−0.440620	−	1.10852i
$479$	11.7110			0.535089			0.267544	−	0.963546i	$-0.413788\pi$
$479$	11.7110			0.535089			0.267544	+	0.963546i	$0.413788\pi$
$480$	−5.41163	+	1.79869i	−0.247006	+	0.0820986i
$481$		−	13.7180i		−	0.625488i
$482$	−8.40461	−	21.1444i	−0.382819	−	0.963103i
$483$	−2.08128	+	2.28838i	−0.0947014	+	0.104125i
$484$	21.9897	+	0.631821i	0.999533	+	0.0287191i
$485$	39.1677	+	16.2238i	1.77851	+	0.736685i
$486$	−10.6518	−	10.9622i	−0.483174	−	0.497256i
$487$	−24.7420	+	24.7420i	−1.12117	+	1.12117i	−0.129599	+	0.991567i	$0.541369\pi$
$487$	−24.7420	+	24.7420i	−1.12117	+	1.12117i	−0.991567	+	0.129599i	$0.958631\pi$
$488$	31.6911	+	1.36632i	1.43459	+	0.0618504i
$489$	6.06217	+	6.06217i	0.274141	+	0.274141i
$490$	−17.4029	−	14.8088i	−0.786181	−	0.668995i
$491$	−10.0084	−	4.14563i	−0.451674	−	0.187090i	0.145237	−	0.989397i	$-0.453606\pi$
$491$	−10.0084	−	4.14563i	−0.451674	−	0.187090i	−0.596911	+	0.802307i	$0.703606\pi$
$492$	0.831151	+	2.18180i	0.0374712	+	0.0983632i
$493$	−2.44019	−	5.89115i	−0.109901	−	0.265324i
$494$	−5.55886	+	12.8933i	−0.250105	+	0.580099i
$495$		−	0.159308i		−	0.00716038i
$496$	−0.0431102	+	0.749578i	−0.00193570	+	0.0336571i
$497$	−13.1113	+	6.17347i	−0.588121	+	0.276918i
$498$	−1.94837	+	4.51910i	−0.0873087	+	0.202506i
$499$	−5.33539	−	12.8808i	−0.238845	−	0.576622i	0.758319	−	0.651884i	$-0.226021\pi$
$499$	−5.33539	−	12.8808i	−0.238845	−	0.576622i	−0.997164	+	0.0752613i	$0.976021\pi$
$500$	−8.82252	+	19.6808i	−0.394555	+	0.880151i
$501$	−0.609222	+	1.47079i	−0.0272180	+	0.0657101i
$502$	−0.00523653	+	0.364577i	−0.000233718	+	0.0162719i
$503$	0.348488	−	0.348488i	0.0155383	−	0.0155383i	−0.699295	−	0.714833i	$-0.746503\pi$
$503$	0.348488	−	0.348488i	0.0155383	−	0.0155383i	0.714833	+	0.699295i	$0.246503\pi$
$504$	−21.0224	+	0.0898258i	−0.936412	+	0.00400116i
$505$	18.1219	+	18.1219i	0.806414	+	0.806414i
$506$	−0.0667050	+	0.0648159i	−0.00296540	+	0.00288142i
$507$	−6.46977	−	2.67987i	−0.287333	−	0.119017i
$508$	23.2845	+	24.6621i	1.03308	+	1.09420i
$509$	5.32191	−	2.20441i	0.235889	−	0.0977086i	−0.261608	−	0.965174i	$-0.584253\pi$
$509$	5.32191	−	2.20441i	0.235889	−	0.0977086i	0.497497	+	0.867466i	$0.334253\pi$
$510$	0.637839	+	1.60469i	0.0282440	+	0.0710567i
$511$	4.58148	+	9.73019i	0.202673	+	0.430438i
$512$	5.89222	+	21.8468i	0.260402	+	0.965500i
$513$	4.67469			0.206393
$514$	−6.16910	+	2.45213i	−0.272107	+	0.108159i
$515$	−38.1528	+	15.8034i	−1.68121	+	0.696380i
$516$	−3.44679	−	3.65071i	−0.151736	−	0.160714i
$517$	−0.101350	+	0.244681i	−0.00445737	+	0.0107610i
$518$	−3.35301	+	8.91610i	−0.147323	+	0.391751i
$519$	0.579578	−	0.579578i	0.0254406	−	0.0254406i
$520$	−31.8917	−	14.8501i	−1.39854	−	0.651222i
$521$	−5.35868	−	5.35868i	−0.234768	−	0.234768i	0.579911	−	0.814679i	$-0.303087\pi$
$521$	−5.35868	−	5.35868i	−0.234768	−	0.234768i	−0.814679	+	0.579911i	$0.803087\pi$
$522$	0.300387	−	20.9135i	0.0131476	−	0.915358i
$523$	8.65398	−	20.8926i	0.378412	−	0.913568i	−0.613852	−	0.789421i	$-0.710381\pi$
$523$	8.65398	−	20.8926i	0.378412	−	0.913568i	0.992264	−	0.124146i	$-0.0396192\pi$
$524$	−3.49329	−	1.56598i	−0.152605	−	0.0684100i
$525$	−0.255146	+	0.280534i	−0.0111355	+	0.0122435i
$526$	19.6909	+	8.48957i	0.858564	+	0.370163i
$527$	0.227350			0.00990353
$528$	0.0428468	+	0.00246423i	0.00186467	+	0.000107242i
$529$		−	15.8335i		−	0.688415i
$530$	−9.76873	+	22.6578i	−0.424326	+	0.984192i
$531$	37.0414	−	15.3430i	1.60746	−	0.665831i
$532$	6.76445	−	7.02138i	0.293276	−	0.304416i
$533$	−5.51175	+	13.3066i	−0.238741	+	0.576371i
$534$	−0.118735	+	8.26656i	−0.00513817	+	0.357729i
$535$	−9.97168	+	9.97168i	−0.431113	+	0.431113i
$536$	−2.75325	−	0.118703i	−0.118922	−	0.00512718i
$537$	0.704418	−	0.704418i	0.0303979	−	0.0303979i
$538$	16.2306	−	15.7710i	0.699751	−	0.679934i
$539$	0.0805420	+	0.151944i	0.00346919	+	0.00654469i
$540$	−0.336398	+	11.7079i	−0.0144763	+	0.503828i
$541$	−3.42486	−	8.26835i	−0.147246	−	0.355484i	0.832998	−	0.553277i	$-0.186623\pi$
$541$	−3.42486	−	8.26835i	−0.147246	−	0.355484i	−0.980244	+	0.197792i	$0.936623\pi$
$542$	4.86436	−	1.93351i	0.208942	−	0.0830514i
$543$			4.33859i			0.186187i
$544$	6.50193	−	2.16108i	0.278768	−	0.0926553i
$545$		−	40.0051i		−	1.71363i
$546$	6.42824	+	6.01741i	0.275103	+	0.257522i
$547$	−22.5646	+	9.34657i	−0.964793	+	0.399630i	−0.808771	−	0.588123i	$-0.799867\pi$
$547$	−22.5646	+	9.34657i	−0.964793	+	0.399630i	−0.156022	+	0.987754i	$0.549867\pi$
$548$	−0.726417	+	25.2820i	−0.0310310	+	1.08000i
$549$	12.0567	−	29.1074i	0.514566	−	1.24227i
$550$	−0.00817743	+	0.00794584i	−0.000348687	+	0.000338812i
$551$	6.85904	+	6.85904i	0.292205	+	0.292205i
$552$	2.43685	−	2.23541i	0.103719	−	0.0951454i
$553$	28.1103	+	10.1129i	1.19537	+	0.430042i
$554$	−7.25602	−	0.104220i	−0.308279	−	0.00442790i
$555$	2.37114	+	0.982157i	0.100649	+	0.0416903i
$556$	9.91655	+	26.0313i	0.420555	+	1.10397i
$557$	4.10506	−	1.70037i	0.173937	−	0.0720471i	−0.294016	−	0.955801i	$-0.594992\pi$
$557$	4.10506	−	1.70037i	0.173937	−	0.0720471i	0.467953	+	0.883754i	$0.344992\pi$
$558$	0.684795	+	0.295244i	0.0289897	+	0.0124987i
$559$		−	30.9727i		−	1.31001i
$560$	17.0985	+	17.4470i	0.722542	+	0.737271i
$561$		−	0.0129956i		−	0.000548674i
$562$	9.00676	−	20.8905i	0.379927	−	0.881212i
$563$	19.6680	−	8.14674i	0.828906	−	0.343344i	0.0724362	−	0.997373i	$-0.476923\pi$
$563$	19.6680	−	8.14674i	0.828906	−	0.343344i	0.756469	+	0.654029i	$0.226923\pi$
$564$	3.85179	−	8.59234i	0.162189	−	0.361803i
$565$	20.7137	+	8.57988i	0.871430	+	0.360958i
$566$	−0.463211	+	32.2496i	−0.0194702	+	1.35555i
$567$	−6.55578	+	18.2229i	−0.275317	+	0.765288i
$568$	14.5554	−	5.30672i	0.610729	−	0.222665i
$569$	−16.7614	−	16.7614i	−0.702676	−	0.702676i	0.262308	−	0.964984i	$-0.415516\pi$
$569$	−16.7614	−	16.7614i	−0.702676	−	0.702676i	−0.964984	+	0.262308i	$0.915516\pi$
$570$	−1.83060	−	1.88395i	−0.0766754	−	0.0789102i
$571$	2.56694	−	6.19714i	0.107423	−	0.259342i	−0.861023	−	0.508566i	$-0.830176\pi$
$571$	2.56694	−	6.19714i	0.107423	−	0.259342i	0.968446	+	0.249224i	$0.0801756\pi$
$572$	0.181756	+	0.192510i	0.00759961	+	0.00804924i
$573$	−9.19727	+	3.80964i	−0.384222	+	0.159150i
$574$	6.83483	−	7.30146i	0.285280	−	0.304757i
$575$			0.878543i			0.0366378i
$576$	22.3907	+	1.93429i	0.932946	+	0.0805952i
$577$		−	4.18054i		−	0.174038i	−0.996207	−	0.0870191i	$-0.972266\pi$
$577$		−	4.18054i		−	0.174038i	0.996207	−	0.0870191i	$-0.0277341\pi$
$578$	8.11404	+	20.4134i	0.337500	+	0.849087i
$579$	1.95918	+	4.72987i	0.0814206	+	0.196567i
$580$	−17.6722	+	16.6851i	−0.733799	+	0.692809i
$581$	21.0573	−	0.998014i	0.873602	−	0.0414046i
$582$	7.90521	+	8.13561i	0.327681	+	0.337232i
$583$	0.131304	−	0.131304i	0.00543804	−	0.00543804i
$584$	−3.93825	−	10.8019i	−0.162966	−	0.446985i
$585$	−24.7072	+	24.7072i	−1.02152	+	1.02152i
$586$	14.6415	+	0.210300i	0.604833	+	0.00868740i
$587$	−15.3382	+	37.0296i	−0.633074	+	1.52837i	0.202666	+	0.979248i	$0.435040\pi$
$587$	−15.3382	+	37.0296i	−0.633074	+	1.52837i	−0.835739	+	0.549127i	$0.814960\pi$
$588$	−2.70727	−	5.48226i	−0.111646	−	0.226085i
$589$	−0.319524	+	0.132351i	−0.0131658	+	0.00545344i
$590$	−42.7822	−	18.4452i	−1.76131	−	0.759377i
$591$		−	8.45828i		−	0.347927i
$592$	4.43080	−	9.16899i	0.182105	−	0.376843i
$593$	−21.7418			−0.892828			−0.446414	−	0.894826i	$-0.647299\pi$
$593$	−21.7418			−0.892828			−0.446414	+	0.894826i	$0.647299\pi$
$594$	0.0348988	−	0.0809450i	0.00143191	−	0.00332121i
$595$	4.97703	−	5.47227i	0.204038	−	0.224341i
$596$	−12.7752	−	33.5353i	−0.523291	−	1.37366i
$597$	3.46537	−	8.36615i	0.141828	−	0.342404i
$598$	20.3976	+	0.292978i	0.834122	+	0.0119807i
$599$	18.7195	+	18.7195i	0.764859	+	0.764859i	0.977196	−	0.212338i	$-0.0681076\pi$
$599$	18.7195	+	18.7195i	0.764859	+	0.764859i	−0.212338	+	0.977196i	$0.568108\pi$
$600$	0.298736	−	0.274041i	0.0121958	−	0.0111877i
$601$	−1.96477	+	1.96477i	−0.0801446	+	0.0801446i	−0.746043	−	0.665898i	$-0.768049\pi$
$601$	−1.96477	+	1.96477i	−0.0801446	+	0.0801446i	0.665898	+	0.746043i	$0.268049\pi$
$602$	−7.57046	+	20.1309i	−0.308549	+	0.820473i
$603$	−1.04746	+	2.52879i	−0.0426558	+	0.102980i
$604$	−24.7084	−	0.709934i	−1.00537	−	0.0288868i
$605$	−23.4571	+	9.71623i	−0.953665	+	0.395021i
$606$	2.53297	+	6.37249i	0.102895	+	0.258865i
$607$	−29.3907			−1.19293			−0.596465	−	0.802639i	$-0.703429\pi$
$607$	−29.3907			−1.19293			−0.596465	+	0.802639i	$0.703429\pi$
$608$	−7.87993	+	6.82232i	−0.319573	+	0.276681i
$609$	5.50361	−	2.59139i	0.223018	−	0.105008i
$610$	−34.0210	+	13.5228i	−1.37747	+	0.547524i
$611$	53.6661	−	22.2292i	2.17110	−	0.899298i
$612$	0.195451	−	6.80243i	0.00790065	−	0.274972i
$613$	−6.19487	−	2.56600i	−0.250208	−	0.103640i	0.254055	−	0.967190i	$-0.418236\pi$
$613$	−6.19487	−	2.56600i	−0.250208	−	0.103640i	−0.504263	+	0.863550i	$0.668236\pi$
$614$	23.7598	+	24.4523i	0.958869	+	0.986816i
$615$	−1.90540	−	1.90540i	−0.0768330	−	0.0768330i
$616$	−0.0710794	−	0.169548i	−0.00286387	−	0.00683129i
$617$	−13.7460	+	13.7460i	−0.553395	+	0.553395i	−0.927419	−	0.374024i	$-0.877978\pi$
$617$	−13.7460	+	13.7460i	−0.553395	+	0.553395i	0.374024	+	0.927419i	$0.377978\pi$
$618$	−11.0486	−	0.158695i	−0.444442	−	0.00638365i
$619$	9.36933	−	22.6196i	0.376585	−	0.909157i	−0.616016	−	0.787734i	$-0.711254\pi$
$619$	9.36933	−	22.6196i	0.376585	−	0.909157i	0.992601	−	0.121423i	$-0.0387457\pi$
$620$	−0.308484	−	0.809782i	−0.0123890	−	0.0325216i
$621$	−2.59915	−	6.27490i	−0.104300	−	0.251803i
$622$	−34.0684	−	14.6883i	−1.36602	−	0.588948i
$623$	32.0408	−	15.0865i	1.28369	−	0.604427i
$624$	−6.26295	−	7.02730i	−0.250718	−	0.281317i
$625$		−	26.5332i		−	1.06133i
$626$	−10.5890	−	4.56538i	−0.423223	−	0.182469i
$627$	0.00756535	+	0.0182644i	0.000302131	+	0.000729409i
$628$	−2.95691	+	6.59609i	−0.117993	+	0.263213i
$629$	−2.84886	−	1.18004i	−0.113591	−	0.0470511i
$630$	22.0976	−	10.0196i	0.880390	−	0.399189i
$631$	3.18722	+	3.18722i	0.126881	+	0.126881i	0.767696	−	0.640814i	$-0.221403\pi$
$631$	3.18722	+	3.18722i	0.126881	+	0.126881i	−0.640814	+	0.767696i	$0.721403\pi$
$632$	−28.9519	−	13.4812i	−1.15164	−	0.536255i
$633$	5.79372	−	5.79372i	0.230280	−	0.230280i
$634$	23.7743	−	23.1010i	0.944199	−	0.917460i
$635$	−36.1657	−	14.9803i	−1.43519	−	0.594476i
$636$	−4.80054	+	4.53238i	−0.190354	+	0.179721i
$637$	11.0738	−	36.0564i	0.438759	−	1.42861i
$638$	0.169974	−	0.0675622i	0.00672934	−	0.00267481i
$639$		−	15.3876i		−	0.608724i
$640$	−16.5196	−	20.2264i	−0.652996	−	0.799520i
$641$	14.3257			0.565830			0.282915	−	0.959145i	$-0.408699\pi$
$641$	14.3257			0.565830			0.282915	+	0.959145i	$0.408699\pi$
$642$	−3.50650	+	1.39378i	−0.138390	+	0.0550082i
$643$	4.29059	+	10.3584i	0.169205	+	0.408496i	0.985622	−	0.168967i	$-0.0540430\pi$
$643$	4.29059	+	10.3584i	0.169205	+	0.408496i	−0.816417	+	0.577462i	$0.804043\pi$
$644$	−13.1859	−	5.17609i	−0.519599	−	0.203966i
$645$	5.35358	+	2.21753i	0.210797	+	0.0873150i
$646$	2.19942	+	2.26352i	0.0865349	+	0.0890570i
$647$	2.81733	+	2.81733i	0.110761	+	0.110761i	0.760315	−	0.649554i	$-0.225044\pi$
$647$	2.81733	+	2.81733i	0.110761	+	0.110761i	−0.649554	+	0.760315i	$0.725044\pi$
$648$	8.73937	−	18.7684i	0.343315	−	0.737292i
$649$	0.247926	+	0.247926i	0.00973194	+	0.00973194i
$650$	2.50057	+	0.0359164i	0.0980802	+	0.00140876i
$651$	0.0102681	+	0.216648i	0.000402437	+	0.00849109i
$652$	−16.0599	+	35.8255i	−0.628953	+	1.40303i
$653$	−17.6782	+	7.32255i	−0.691801	+	0.286553i	−0.700750	−	0.713407i	$-0.747151\pi$
$653$	−17.6782	+	7.32255i	−0.691801	+	0.286553i	0.00894921	+	0.999960i	$0.497151\pi$
$654$	4.23797	−	9.82964i	0.165718	−	0.384369i
$655$	4.41832			0.172638
$656$	−7.98190	+	7.11371i	−0.311641	+	0.277744i
$657$	−11.4195			−0.445517
$658$	−40.3139	+	1.33074i	−1.57160	+	0.0518776i
$659$	7.98324	+	19.2732i	0.310983	+	0.750779i	0.999669	+	0.0257197i	$0.00818772\pi$
$659$	7.98324	+	19.2732i	0.310983	+	0.750779i	−0.688686	+	0.725059i	$0.741812\pi$
$660$	−0.0462880	+	0.0176333i	−0.00180176	+	0.000686375i
$661$	−3.76651	−	1.56014i	−0.146500	−	0.0606824i	0.308229	−	0.951312i	$-0.400264\pi$
$661$	−3.76651	−	1.56014i	−0.146500	−	0.0606824i	−0.454729	+	0.890630i	$0.650264\pi$
$662$	0.210724	−	14.6710i	0.00819004	−	0.570206i
$663$	−2.01549	+	2.01549i	−0.0782752	+	0.0782752i
$664$	−22.5155	−	0.970726i	−0.873771	−	0.0376715i
$665$	−3.80918	+	10.5883i	−0.147714	+	0.410595i
$666$	−7.04853	−	7.25396i	−0.273125	−	0.281085i
$667$	5.39332	−	13.0206i	0.208830	−	0.504160i
$668$	−7.28734	−	0.209384i	−0.281955	−	0.00810130i
$669$	1.02387	+	2.47184i	0.0395851	+	0.0955669i
$670$	2.95567	−	1.17484i	0.114187	−	0.0453878i
$671$	0.275520			0.0106363
$672$	2.35300	+	6.09824i	0.0907688	+	0.235245i
$673$	8.24154			0.317688			0.158844	−	0.987304i	$-0.449223\pi$
$673$	8.24154			0.317688			0.158844	+	0.987304i	$0.449223\pi$
$674$	25.2040	−	10.0182i	0.970823	−	0.385888i
$675$	−0.318632	−	0.769245i	−0.0122641	−	0.0296083i
$676$	0.921045	−	32.0558i	0.0354248	−	1.23292i
$677$	15.0784	−	36.4024i	0.579509	−	1.39906i	−0.313745	−	0.949507i	$-0.601584\pi$
$677$	15.0784	−	36.4024i	0.579509	−	1.39906i	0.893254	−	0.449551i	$-0.148416\pi$
$678$	4.18063	+	4.30248i	0.160556	+	0.165236i
$679$	16.4495	−	45.7240i	0.631272	−	1.75472i
$680$	−5.82732	+	5.34561i	−0.223467	+	0.204995i
$681$	1.92787	−	1.92787i	0.0738761	−	0.0738761i
$682$	−9.36604e−5		0.00652081i	−3.58644e−6		0.000249695i
$683$	14.5549	+	6.02883i	0.556927	+	0.230687i	0.643351	−	0.765572i	$-0.277544\pi$
$683$	14.5549	+	6.02883i	0.556927	+	0.230687i	−0.0864233	+	0.996259i	$0.527544\pi$
$684$	3.68533	+	9.67411i	0.140912	+	0.369899i
$685$	−11.1710	−	26.9691i	−0.426820	−	1.03044i
$686$	−16.0105	+	20.7283i	−0.611283	+	0.791412i
$687$	−7.29838			−0.278451
$688$	10.0039	−	20.7018i	0.381396	−	0.789250i
$689$	−40.7279			−1.55161
$690$	−1.51103	+	3.50472i	−0.0575241	+	0.133423i
$691$	17.9815	−	7.44818i	0.684048	−	0.283342i	−0.0134697	−	0.999909i	$-0.504288\pi$
$691$	17.9815	−	7.44818i	0.684048	−	0.283342i	0.697518	+	0.716567i	$0.254288\pi$
$692$	3.42512	+	1.53542i	0.130203	+	0.0583677i
$693$	−0.182394	+	0.00864462i	−0.00692859	+	0.000328382i
$694$	−9.90115	−	0.142213i	−0.375842	−	0.00539834i
$695$	−22.7335	−	22.7335i	−0.862330	−	0.862330i
$696$	−6.10978	+	2.22756i	−0.231591	+	0.0844354i
$697$	2.28928	+	2.28928i	0.0867127	+	0.0867127i
$698$	16.3334	+	16.8094i	0.618226	+	0.636245i
$699$	1.76655	+	0.731730i	0.0668172	+	0.0276766i
$700$	−1.61648	−	0.634541i	−0.0610971	−	0.0239834i
$701$	−1.92894	−	4.65688i	−0.0728552	−	0.175888i	0.883257	−	0.468890i	$-0.155346\pi$
$701$	−1.92894	−	4.65688i	−0.0728552	−	0.175888i	−0.956112	+	0.293002i	$0.905346\pi$
$702$	−17.9663	+	7.14133i	−0.678093	+	0.269532i
$703$	4.69082			0.176918
$704$	0.0593050	+	0.187377i	0.00223514	+	0.00706204i
$705$			10.8676i			0.409298i
$706$	−26.5466	+	10.5519i	−0.999093	+	0.397125i
$707$	19.7646	−	21.7314i	0.743326	−	0.817292i
$708$	−8.55800	−	9.06433i	−0.321629	−	0.340658i
$709$	15.6194	+	6.46978i	0.586600	+	0.242978i	0.656187	−	0.754598i	$-0.272168\pi$
$709$	15.6194	+	6.46978i	0.586600	+	0.242978i	−0.0695869	+	0.997576i	$0.522168\pi$
$710$	−12.8238	+	12.4606i	−0.481268	+	0.467639i
$711$	−22.4297	+	22.4297i	−0.841179	+	0.841179i
$712$	−35.5698	+	12.9683i	−1.33303	+	0.486009i
$713$	0.355313	+	0.355313i	0.0133066	+	0.0133066i
$714$	1.80261	−	0.817346i	0.0674611	−	0.0305884i
$715$	−0.282305	−	0.116935i	−0.0105576	−	0.00437311i
$716$	4.16288	+	1.86614i	0.155574	+	0.0697409i
$717$	3.08214	+	7.44094i	0.115105	+	0.277887i
$718$	38.3944	+	16.5535i	1.43287	+	0.617769i
$719$		−	47.5268i		−	1.77245i	−0.463254	−	0.886226i	$-0.653318\pi$
$719$		−	47.5268i		−	1.77245i	0.463254	−	0.886226i	$-0.346682\pi$
$720$	−24.4943	+	8.53384i	−0.912848	+	0.318037i
$721$	20.1638	+	42.8240i	0.750939	+	1.59485i
$722$	20.2656	+	8.73736i	0.754209	+	0.325171i
$723$	2.68901	+	6.49184i	0.100005	+	0.241434i
$724$	−18.5667	+	7.07295i	−0.690027	+	0.262864i
$725$	0.661171	−	1.59621i	0.0245553	−	0.0592817i
$726$	−6.79293	−	0.0975689i	−0.252109	−	0.00362112i
$727$	−13.7811	+	13.7811i	−0.511111	+	0.511111i	−0.914867	−	0.403756i	$-0.867705\pi$
$727$	−13.7811	+	13.7811i	−0.511111	+	0.511111i	0.403756	+	0.914867i	$0.367705\pi$
$728$	−15.2716	+	37.3191i	−0.566002	+	1.38314i
$729$	−12.1898	−	12.1898i	−0.451473	−	0.451473i
$730$	9.24733	+	9.51685i	0.342259	+	0.352234i
$731$	−6.43218	−	2.66430i	−0.237903	−	0.0985425i
$732$	−9.79184	−	0.281344i	−0.361917	−	0.0103988i
$733$	−36.7962	+	15.2415i	−1.35910	+	0.562958i	−0.938811	−	0.344433i	$-0.888071\pi$
$733$	−36.7962	+	15.2415i	−1.35910	+	0.562958i	−0.420289	+	0.907390i	$0.638071\pi$
$734$	36.4864	−	14.5028i	1.34674	−	0.535309i
$735$	5.43945	+	4.49558i	0.200637	+	0.165822i
$736$	13.5389	+	6.78409i	0.499052	+	0.250065i
$737$	−0.0239366			−0.000881715
$738$	3.92255	+	9.86840i	0.144391	+	0.363261i
$739$	−21.6350	+	8.96153i	−0.795858	+	0.329655i	−0.743296	−	0.668962i	$-0.766739\pi$
$739$	−21.6350	+	8.96153i	−0.795858	+	0.329655i	−0.0525619	+	0.998618i	$0.516739\pi$
$740$	−0.337558	+	11.7483i	−0.0124089	+	0.431875i
$741$	1.65932	−	4.00594i	0.0609565	−	0.147162i
$742$	26.4713	+	9.95485i	0.971791	+	0.365454i
$743$	−8.61267	+	8.61267i	−0.315968	+	0.315968i	−0.847216	−	0.531248i	$-0.821723\pi$
$743$	−8.61267	+	8.61267i	−0.315968	+	0.315968i	0.531248	+	0.847216i	$0.321723\pi$
$744$	0.00998731	−	0.231651i	0.000366152	−	0.00849273i
$745$	29.2868	+	29.2868i	1.07299	+	1.07299i
$746$	9.38142	+	0.134748i	0.343478	+	0.00493348i
$747$	−8.56588	+	20.6799i	−0.313409	+	0.756637i
$748$	0.0556138	−	0.0211859i	0.00203344	−	0.000774634i
$749$	11.9578	+	10.8756i	0.436929	+	0.397386i
$750$	2.63699	−	6.11628i	0.0962891	−	0.223335i
$751$	5.39453			0.196849			0.0984246	−	0.995145i	$-0.468620\pi$
$751$	5.39453			0.196849			0.0984246	+	0.995145i	$0.468620\pi$
$752$	43.0497	+	2.47590i	1.56986	+	0.0902867i
$753$		−	0.112600i		−	0.00410336i
$754$	−36.8396	−	15.8831i	−1.34162	−	0.578428i
$755$	26.3571	−	10.9175i	0.959233	−	0.397327i
$756$	13.4228	−	0.250165i	0.488182	−	0.00909840i
$757$	−7.64418	+	18.4547i	−0.277832	+	0.670747i	−0.999775	−	0.0212062i	$-0.993249\pi$
$757$	−7.64418	+	18.4547i	−0.277832	+	0.670747i	0.721943	+	0.691953i	$0.243249\pi$
$758$	−19.9416	−	0.286428i	−0.724313	−	0.0104035i
$759$	0.0203101	−	0.0203101i	0.000737211	−	0.000737211i
$760$	5.07794	−	10.9052i	0.184196	−	0.395574i
$761$	29.0436	−	29.0436i	1.05283	−	1.05283i	0.0543056	−	0.998524i	$-0.482705\pi$
$761$	29.0436	−	29.0436i	1.05283	−	1.05283i	0.998524	−	0.0543056i	$-0.0172945\pi$
$762$	−7.29931	−	7.51205i	−0.264426	−	0.272133i
$763$	−45.8023	+	2.17081i	−1.65816	+	0.0785887i
$764$	−31.2968	−	33.1485i	−1.13228	−	1.19927i
$765$	3.00568	+	7.25635i	0.108671	+	0.262354i
$766$	−11.0717	−	27.8544i	−0.400037	−	1.00642i
$767$		−	76.9019i		−	2.77677i
$768$	−1.91633	−	6.71985i	−0.0691496	−	0.242482i
$769$			32.2311i			1.16228i	0.813802	+	0.581142i	$0.197394\pi$
$769$			32.2311i			1.16228i	−0.813802	+	0.581142i	$0.802606\pi$
$770$	0.154904	+	0.145004i	0.00558236	+	0.00522560i
$771$	1.89406	−	0.784544i	0.0682128	−	0.0282547i
$772$	−17.0473	+	16.0950i	−0.613544	+	0.579272i
$773$	0.516893	−	1.24789i	0.0185914	−	0.0448835i	−0.914311	−	0.405012i	$-0.867267\pi$
$773$	0.516893	−	1.24789i	0.0185914	−	0.0448835i	0.932903	+	0.360129i	$0.117267\pi$
$774$	−15.9143	−	16.3781i	−0.572026	−	0.588698i
$775$	0.0435582	+	0.0435582i	0.00156466	+	0.00156466i
$776$	−21.9284	+	47.0928i	−0.787185	+	1.69053i
$777$	0.995819	−	2.76804i	0.0357248	−	0.0993029i
$778$	−0.635182	+	44.2225i	−0.0227724	+	1.58546i
$779$	−4.55012	−	1.88472i	−0.163025	−	0.0675271i
$780$	9.91359	+	4.44408i	0.354963	+	0.159123i
$781$	0.124323	−	0.0514962i	0.00444862	−	0.00184268i
$782$	1.81546	−	4.21083i	0.0649209	−	0.150579i
$783$			13.3568i			0.477333i
$784$	19.0475	−	20.5230i	0.680268	−	0.732964i
$785$		−	8.34276i		−	0.297766i
$786$	1.08563	+	0.468059i	0.0387230	+	0.0166951i
$787$	10.0308	−	4.15488i	0.357558	−	0.148105i	−0.196671	−	0.980470i	$-0.563013\pi$
$787$	10.0308	−	4.15488i	0.357558	−	0.148105i	0.554229	+	0.832364i	$0.313013\pi$
$788$	36.1967	−	13.7890i	1.28945	−	0.491214i
$789$	−6.11793	−	2.53413i	−0.217804	−	0.0902174i
$790$	36.8558	+	0.529371i	1.31127	+	0.0188342i
$791$	8.69922	−	24.1809i	0.309309	−	0.859774i
$792$	0.195025	+	0.00840826i	0.00692993	+	0.000298774i
$793$	−42.7305	−	42.7305i	−1.51740	−	1.51740i
$794$	9.08381	−	8.82655i	0.322372	−	0.313243i
$795$	2.91596	−	7.03974i	0.103418	−	0.249674i
$796$	41.4518	+	1.19102i	1.46922	+	0.0422144i
$797$	1.40340	−	0.581309i	0.0497111	−	0.0205910i	−0.357689	−	0.933841i	$-0.616435\pi$
$797$	1.40340	−	0.581309i	0.0497111	−	0.0205910i	0.407400	+	0.913250i	$0.366435\pi$
$798$	−2.05763	+	2.19811i	−0.0728393	+	0.0778122i
$799$		−	13.0571i		−	0.461929i
$800$	1.65975	+	0.831667i	0.0586811	+	0.0294039i
$801$			37.6036i			1.32866i
$802$	1.91873	−	0.762667i	0.0677527	−	0.0269307i
$803$	−0.0382166	−	0.0922630i	−0.00134863	−	0.00325589i
$804$	0.850694	+	0.0244426i	0.0300017	+	0.000862024i
$805$	16.3307	−	0.773995i	0.575580	−	0.0272798i
$806$	1.02584	−	0.996790i	0.0361337	−	0.0351104i
$807$	−4.94184	+	4.94184i	−0.173961	+	0.173961i
$808$	−23.1413	+	21.2284i	−0.814108	+	0.746811i
$809$	−36.0909	+	36.0909i	−1.26889	+	1.26889i	−0.322227	+	0.946662i	$0.604431\pi$
$809$	−36.0909	+	36.0909i	−1.26889	+	1.26889i	−0.946662	+	0.322227i	$0.895569\pi$
$810$	−0.343171	+	23.8922i	−0.0120578	+	0.839485i
$811$	12.4831	−	30.1369i	0.438341	−	1.05825i	−0.538181	−	0.842830i	$-0.680888\pi$
$811$	12.4831	−	30.1369i	0.438341	−	1.05825i	0.976522	−	0.215419i	$-0.0691118\pi$
$812$	20.0619	+	19.3278i	0.704034	+	0.678272i
$813$	−1.49347	+	0.618616i	−0.0523783	+	0.0216958i
$814$	0.0350192	−	0.0812242i	0.00122742	−	0.00284691i
$815$		−	45.3122i		−	1.58722i
$816$	−1.99812	+	0.696148i	−0.0699482	+	0.0243700i
$817$	10.5910			0.370531
$818$	35.6411	+	15.3664i	1.24616	+	0.537273i
$819$	29.6283	+	26.9469i	1.03530	+	0.941602i
$820$	5.04777	−	11.2603i	0.176276	−	0.393226i
$821$	−0.922556	+	2.22725i	−0.0321974	+	0.0777315i	−0.939160	−	0.343479i	$-0.888395\pi$
$821$	−0.922556	+	2.22725i	−0.0321974	+	0.0777315i	0.906963	+	0.421210i	$0.138395\pi$
$822$	0.112177	−	7.80997i	0.00391262	−	0.272404i
$823$	15.3062	+	15.3062i	0.533542	+	0.533542i	0.921625	−	0.388083i	$-0.126862\pi$
$823$	15.3062	+	15.3062i	0.533542	+	0.533542i	−0.388083	+	0.921625i	$0.626862\pi$
$824$	−17.3328	−	47.5407i	−0.603817	−	1.65616i
$825$	0.00248984	−	0.00248984i	8.66849e−5	−	8.66849e-5i
$826$	−18.7966	+	49.9828i	−0.654018	+	1.73912i
$827$	−16.4450	+	39.7017i	−0.571848	+	1.38056i	0.328131	+	0.944632i	$0.393581\pi$
$827$	−16.4450	+	39.7017i	−0.571848	+	1.38056i	−0.899980	+	0.435932i	$0.856419\pi$
$828$	10.9366	−	10.3257i	0.380074	−	0.358843i
$829$	11.5465	−	4.78272i	0.401027	−	0.166111i	−0.173049	−	0.984913i	$-0.555362\pi$
$829$	11.5465	−	4.78272i	0.401027	−	0.166111i	0.574075	+	0.818803i	$0.305362\pi$
$830$	24.1708	−	9.60754i	0.838981	−	0.333483i
$831$	2.24102			0.0777402
$832$	19.8628	−	38.2581i	0.688618	−	1.32636i
$833$	−6.53535	−	5.40132i	−0.226436	−	0.187145i
$834$	−3.17755	−	7.99413i	−0.110030	−	0.276814i
$835$	7.77361	−	3.21993i	0.269017	−	0.111430i
$836$	−0.0658279	+	0.0621507i	−0.00227670	+	0.00214953i
$837$	−0.439975	−	0.182244i	−0.0152078	−	0.00629927i
$838$	21.1225	−	20.5243i	0.729664	−	0.709001i
$839$	−13.9681	−	13.9681i	−0.482234	−	0.482234i	0.423611	−	0.905844i	$-0.360763\pi$
$839$	−13.9681	−	13.9681i	−0.482234	−	0.482234i	−0.905844	+	0.423611i	$0.860763\pi$
$840$	−5.35715	−	5.31157i	−0.184839	−	0.183266i
$841$	0.908073	−	0.908073i	0.0313129	−	0.0313129i
$842$	−0.319642	+	22.2541i	−0.0110156	+	0.766926i
$843$	−2.68851	+	6.49064i	−0.0925972	+	0.223550i
$844$	34.2390	+	15.3487i	1.17856	+	0.528325i
$845$	14.1640	+	34.1948i	0.487255	+	1.17634i
$846$	16.9564	−	39.3291i	0.582973	−	1.35216i
$847$	12.3971	+	26.3291i	0.425969	+	0.904677i
$848$	−27.2221	−	13.1547i	−0.934810	−	0.451736i
$849$		−	9.96030i		−	0.341837i
$850$	0.222559	−	0.516209i	0.00763373	−	0.0177058i
$851$	−2.60811	−	6.29654i	−0.0894050	−	0.215843i
$852$	−4.47096	+	1.70320i	−0.153173	+	0.0583506i
$853$	11.5894	+	4.80049i	0.396813	+	0.164366i	0.572161	−	0.820141i	$-0.306105\pi$
$853$	11.5894	+	4.80049i	0.396813	+	0.164366i	−0.175348	+	0.984507i	$0.556105\pi$
$854$	17.3286	+	38.2173i	0.592971	+	1.30777i
$855$	−8.44853	−	8.44853i	−0.288934	−	0.288934i
$856$	−11.6810	−	12.7336i	−0.399249	−	0.435227i
$857$	−1.20270	+	1.20270i	−0.0410833	+	0.0410833i	−0.727350	−	0.686267i	$-0.759248\pi$
$857$	−1.20270	+	1.20270i	−0.0410833	+	0.0410833i	0.686267	+	0.727350i	$0.259248\pi$
$858$	−0.0569776	−	0.0586383i	−0.00194518	−	0.00200188i
$859$	37.5490	+	15.5533i	1.28116	+	0.530672i	0.916338	−	0.400407i	$-0.131131\pi$
$859$	37.5490	+	15.5533i	1.28116	+	0.530672i	0.364818	+	0.931079i	$0.381131\pi$
$860$	−0.762142	+	26.5254i	−0.0259888	+	0.904509i
$861$	−2.07812	+	2.28490i	−0.0708221	+	0.0778693i
$862$	11.3461	+	28.5446i	0.386449	+	0.972233i
$863$			21.1168i			0.718824i	0.933179	+	0.359412i	$0.117023\pi$
$863$			21.1168i			0.718824i	−0.933179	+	0.359412i	$0.882977\pi$
$864$	−14.3151	−	1.02976i	−0.487008	−	0.0350331i
$865$	−4.33210			−0.147296
$866$	−6.06858	−	15.2674i	−0.206219	−	0.518808i
$867$	−2.59604	−	6.26740i	−0.0881662	−	0.212852i
$868$	−0.910390	+	0.397129i	−0.0309006	+	0.0134794i
$869$	−0.256282	−	0.106156i	−0.00869377	−	0.00360108i
$870$	5.38294	−	5.23050i	0.182499	−	0.177330i
$871$	3.71233	+	3.71233i	0.125788	+	0.125788i
$872$	48.9742	+	2.11146i	1.65848	+	0.0715030i
$873$	36.4839	+	36.4839i	1.23479	+	1.23479i
$874$	−0.100182	+	6.97489i	−0.00338872	+	0.235929i
$875$	−28.4995	+	1.35074i	−0.963459	+	0.0456634i
$876$	1.26399	+	3.31801i	0.0427061	+	0.112105i
$877$	22.2802	−	9.22877i	0.752350	−	0.311633i	0.0266497	−	0.999645i	$-0.491516\pi$
$877$	22.2802	−	9.22877i	0.752350	−	0.311633i	0.725700	+	0.688011i	$0.241516\pi$
$878$	31.4313	+	13.5514i	1.06076	+	0.457337i
$879$	−4.52201			−0.152524
$880$	−0.150921	−	0.169340i	−0.00508755	−	0.00570846i
$881$	−32.1069			−1.08171			−0.540855	−	0.841116i	$-0.681899\pi$
$881$	−32.1069			−1.08171			−0.540855	+	0.841116i	$0.681899\pi$
$882$	−12.6706	−	24.7562i	−0.426642	−	0.833583i
$883$	11.7782	+	28.4351i	0.396368	+	0.956917i	0.988520	+	0.151091i	$0.0482786\pi$
$883$	11.7782	+	28.4351i	0.396368	+	0.956917i	−0.592152	+	0.805826i	$0.701721\pi$
$884$	−11.9109	−	5.33944i	−0.400607	−	0.179585i
$885$	13.2924	+	5.50588i	0.446818	+	0.185078i
$886$	−24.0835	−	0.345919i	−0.809101	−	0.0116214i
$887$	9.47458	−	9.47458i	0.318125	−	0.318125i	−0.529921	−	0.848047i	$-0.677779\pi$
$887$	9.47458	−	9.47458i	0.318125	−	0.318125i	0.848047	+	0.529921i	$0.177779\pi$
$888$	−1.32751	+	2.85091i	−0.0445482	+	0.0956702i
$889$	−15.1887	+	42.2194i	−0.509412	+	1.41599i
$890$	31.3382	−	30.4508i	1.05046	−	1.02071i
$891$	0.0688165	−	0.166138i	0.00230544	−	0.00556583i
$892$	−8.90893	+	8.41128i	−0.298293	+	0.281630i
$893$	7.60118	+	18.3509i	0.254364	+	0.614089i
$894$	4.09353	+	10.2986i	0.136908	+	0.344436i
$895$	−5.26522			−0.175997
$896$	−22.2611	+	20.0111i	−0.743691	+	0.668524i
$897$	−6.29981			−0.210345
$898$	−4.02732	−	10.1320i	−0.134393	−	0.338109i
$899$	−0.378162	−	0.912963i	−0.0126124	−	0.0304490i
$900$	1.34073	−	1.26584i	0.0446910	−	0.0421946i
$901$	−3.50344	+	8.45806i	−0.116717	+	0.281779i
$902$	−0.0666038	+	0.0647176i	−0.00221766	+	0.00215486i
$903$	2.24837	−	6.24971i	0.0748211	−	0.207977i
$904$	−11.5967	+	24.9048i	−0.385702	+	0.828322i
$905$	16.2146	−	16.2146i	0.538991	−	0.538991i
$906$	7.63275	+	0.109632i	0.253581	+	0.00364226i
$907$	27.9789	+	11.5892i	0.929024	+	0.384815i	0.795308	−	0.606205i	$-0.207309\pi$
$907$	27.9789	+	11.5892i	0.929024	+	0.384815i	0.133716	+	0.991020i	$0.457309\pi$
$908$	11.3931	+	5.10730i	0.378093	+	0.169492i
$909$	11.9361	+	28.8162i	0.395895	+	0.955774i
$910$	−1.53537	−	46.5130i	−0.0508970	−	1.54189i
$911$	14.5585			0.482345			0.241172	−	0.970482i	$-0.422468\pi$
$911$	14.5585			0.482345			0.241172	+	0.970482i	$0.422468\pi$
$912$	2.40296	−	2.14159i	0.0795698	−	0.0709150i
$913$	−0.195748			−0.00647831
$914$	−25.3939	−	10.9484i	−0.839955	−	0.362140i
$915$	10.4452	−	4.32656i	0.345309	−	0.143032i
$916$	−11.8981	−	31.2329i	−0.393124	−	1.03197i
$917$	−0.239753	−	5.05860i	−0.00791735	−	0.167050i
$918$	−0.0624144	+	4.34540i	−0.00205998	+	0.143420i
$919$	−14.7953	−	14.7953i	−0.488052	−	0.488052i	0.419639	−	0.907691i	$-0.362157\pi$
$919$	−14.7953	−	14.7953i	−0.488052	−	0.488052i	−0.907691	+	0.419639i	$0.862157\pi$
$920$	−17.4616	−	0.752833i	−0.575691	−	0.0248202i
$921$	−7.44517	−	7.44517i	−0.245327	−	0.245327i
$922$	32.9733	−	32.0395i	1.08592	−	1.05517i
$923$	−27.2679	−	11.2947i	−0.897533	−	0.371770i
$924$	0.0227003	+	0.0520389i	0.000746786	+	0.00171195i
$925$	−0.319731	−	0.771899i	−0.0105127	−	0.0253799i
$926$	−2.92817	−	7.36674i	−0.0962257	−	0.242086i
$927$	−50.2590			−1.65072
$928$	−19.4931	−	22.5150i	−0.639893	−	0.739090i
$929$			31.9614i			1.04862i	0.851528	+	0.524309i	$0.175676\pi$
$929$			31.9614i			1.04862i	−0.851528	+	0.524309i	$0.824324\pi$
$930$	0.0988472	+	0.248681i	0.00324133	+	0.00815458i
$931$	12.3293	+	3.78663i	0.404077	+	0.124102i
$932$	−0.251489	+	8.75275i	−0.00823778	+	0.286706i
$933$	10.5850	+	4.38445i	0.346537	+	0.143540i
$934$	21.6622	+	22.2936i	0.708809	+	0.729468i
$935$	−0.0485683	+	0.0485683i	−0.00158835	+	0.00158835i
$936$	−28.9425	−	31.5506i	−0.946017	−	1.03126i
$937$	35.6404	+	35.6404i	1.16432	+	1.16432i	0.983520	+	0.180801i	$0.0578688\pi$
$937$	35.6404	+	35.6404i	1.16432	+	1.16432i	0.180801	+	0.983520i	$0.442131\pi$
$938$	−1.50547	−	3.32023i	−0.0491553	−	0.108409i
$939$	3.29000	+	1.36276i	0.107365	+	0.0444721i
$940$	−46.5073	+	17.7168i	−1.51690	+	0.577859i
$941$	−11.9139	−	28.7628i	−0.388384	−	0.937641i	−0.990283	−	0.139069i	$-0.955589\pi$
$941$	−11.9139	−	28.7628i	−0.388384	−	0.937641i	0.601899	−	0.798572i	$-0.294411\pi$
$942$	0.883797	−	2.04990i	0.0287957	−	0.0667893i
$943$			7.15559i			0.233018i
$944$	24.8386	−	51.4004i	0.808429	−	1.67294i
$945$	−14.0183	+	6.60054i	−0.456015	+	0.214716i
$946$	0.0790666	−	0.183389i	0.00257068	−	0.00596249i
$947$	−8.71814	−	21.0475i	−0.283301	−	0.683950i	0.716607	−	0.697477i	$-0.245694\pi$
$947$	−8.71814	−	21.0475i	−0.283301	−	0.683950i	−0.999909	+	0.0135269i	$0.995694\pi$
$948$	8.99974	+	4.03442i	0.292298	+	0.131032i
$949$	−8.38208	+	20.2361i	−0.272094	+	0.656893i
$950$	−0.0122815	+	0.855057i	−0.000398463	+	0.0277417i
$951$	−7.23873	+	7.23873i	−0.234732	+	0.234732i
$952$	6.43647	+	6.38170i	0.208607	+	0.206832i
$953$	19.3646	+	19.3646i	0.627280	+	0.627280i	0.947383	−	0.320103i	$-0.103718\pi$
$953$	19.3646	+	19.3646i	0.627280	+	0.627280i	−0.320103	+	0.947383i	$0.603718\pi$
$954$	−21.5365	+	20.9266i	−0.697270	+	0.677524i
$955$	48.6106	+	20.1352i	1.57300	+	0.651558i
$956$	−26.8184	+	25.3203i	−0.867369	+	0.818918i
$957$	−0.0521860	+	0.0216161i	−0.00168693	+	0.000698751i
$958$	−6.11753	−	15.3906i	−0.197649	−	0.497247i
$959$	−30.2711	+	14.2532i	−0.977504	+	0.460260i
$960$	5.19074	+	6.17238i	0.167531	+	0.199213i
$961$	−30.9648			−0.998863
$962$	−18.0282	+	7.16596i	−0.581254	+	0.231040i
$963$	−15.8563	+	6.56789i	−0.510962	+	0.211647i
$964$	−23.3977	+	22.0907i	−0.753588	+	0.711493i
$965$	10.3549	−	24.9989i	0.333336	−	0.804743i
$966$	4.09460	+	1.53982i	0.131741	+	0.0495430i
$967$	−6.70480	+	6.70480i	−0.215612	+	0.215612i	−0.806646	−	0.591034i	$-0.798720\pi$
$967$	−6.70480	+	6.70480i	−0.215612	+	0.215612i	0.591034	+	0.806646i	$0.298720\pi$
$968$	−10.6566	−	29.2290i	−0.342515	−	0.939454i
$969$	−0.689189	−	0.689189i	−0.0221399	−	0.0221399i
$970$	0.861068	−	59.9491i	0.0276472	−	1.92485i
$971$	−0.711576	+	1.71790i	−0.0228355	+	0.0551299i	−0.934886	−	0.354948i	$-0.884499\pi$
$971$	−0.711576	+	1.71790i	−0.0228355	+	0.0551299i	0.912050	+	0.410078i	$0.134499\pi$
$972$	−8.84233	+	19.7250i	−0.283618	+	0.632678i
$973$	−24.7942	+	27.2614i	−0.794867	+	0.873962i
$974$	45.4405	+	19.5913i	1.45601	+	0.627746i
$975$	−0.772300			−0.0247334
$976$	−14.7590	−	42.3622i	−0.472425	−	1.35598i
$977$		−	48.8034i		−	1.56136i	−0.624931	−	0.780680i	$-0.714873\pi$
$977$		−	48.8034i		−	1.56136i	0.624931	−	0.780680i	$-0.285127\pi$
$978$	4.80018	−	11.1336i	0.153493	−	0.356015i
$979$	−0.303815	+	0.125844i	−0.00970997	+	0.00402200i
$980$	−10.3710	+	30.6066i	−0.331288	+	0.977693i
$981$	18.6319	−	44.9815i	0.594872	−	1.43615i
$982$	−0.220027	+	15.3187i	−0.00702134	+	0.488838i
$983$	−35.1643	+	35.1643i	−1.12157	+	1.12157i	−0.130061	+	0.991506i	$0.541517\pi$
$983$	−35.1643	+	35.1643i	−1.12157	+	1.12157i	−0.991506	+	0.130061i	$0.958483\pi$
$984$	2.43315	−	2.23202i	0.0775660	−	0.0711542i
$985$	−31.6110	+	31.6110i	−1.00721	+	1.00721i
$986$	−6.46746	+	6.28430i	−0.205966	+	0.200133i
$987$	12.4425	−	0.589714i	0.396048	−	0.0187708i
$988$	19.8483	+	0.570291i	0.631457	+	0.0181434i
$989$	−5.88863	−	14.2164i	−0.187247	−	0.452055i
$990$	−0.209363	+	0.0832189i	−0.00665400	+	0.00264487i
$991$			5.43352i			0.172601i	0.996269	+	0.0863007i	$0.0275046\pi$
$991$			5.43352i			0.172601i	−0.996269	+	0.0863007i	$0.972495\pi$
$992$	1.00762	−	0.334906i	0.0319918	−	0.0106333i
$993$			4.53115i			0.143792i
$994$	14.9622	+	14.0060i	0.474572	+	0.444242i
$995$	−44.2178	+	18.3156i	−1.40180	+	0.580644i
$996$	6.95679	+	0.199886i	0.220434	+	0.00633363i
$997$	3.96327	−	9.56817i	0.125518	−	0.303027i	−0.848612	−	0.529016i	$-0.822561\pi$
$997$	3.96327	−	9.56817i	0.125518	−	0.303027i	0.974130	+	0.225989i	$0.0725613\pi$
$998$	−14.1408	+	13.7404i	−0.447620	+	0.434944i
$999$	4.56728	+	4.56728i	0.144502	+	0.144502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.x.b.27.12	yes	112
4.3	odd	2		896.2.x.b.783.13		112
7.6	odd	2	inner	224.2.x.b.27.11	✓	112
28.27	even	2		896.2.x.b.783.16		112
32.13	even	8		896.2.x.b.111.16		112
32.19	odd	8	inner	224.2.x.b.83.11	yes	112
224.13	odd	8		896.2.x.b.111.13		112
224.83	even	8	inner	224.2.x.b.83.12	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.x.b.27.11	✓	112	7.6	odd	2	inner
224.2.x.b.27.12	yes	112	1.1	even	1	trivial
224.2.x.b.83.11	yes	112	32.19	odd	8	inner
224.2.x.b.83.12	yes	112	224.83	even	8	inner
896.2.x.b.111.13		112	224.13	odd	8
896.2.x.b.111.16		112	32.13	even	8
896.2.x.b.783.13		112	4.3	odd	2
896.2.x.b.783.16		112	28.27	even	2

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.522376 - 1.31420i) q^{2} +(0.167131 + 0.403490i) q^{3} +(-1.45425 + 1.37301i) q^{4} +(0.883342 - 2.13258i) q^{5} +(0.442962 - 0.430417i) q^{6} +(-2.48955 - 0.895629i) q^{7} +(2.56408 + 1.19394i) q^{8} +(1.98645 - 1.98645i) q^{9} +O(q^{10})\)	\(q+(-0.522376 - 1.31420i) q^{2} +(0.167131 + 0.403490i) q^{3} +(-1.45425 + 1.37301i) q^{4} +(0.883342 - 2.13258i) q^{5} +(0.442962 - 0.430417i) q^{6} +(-2.48955 - 0.895629i) q^{7} +(2.56408 + 1.19394i) q^{8} +(1.98645 - 1.98645i) q^{9} +(-3.26407 - 0.0468829i) q^{10} +(0.0226972 + 0.00940149i) q^{11} +(-0.797048 - 0.357302i) q^{12} +(-2.06204 - 4.97820i) q^{13} +(0.123443 + 3.73962i) q^{14} +1.00811 q^{15} +(0.229671 - 3.99340i) q^{16} -1.21121 q^{17} +(-3.64826 - 1.57292i) q^{18} +(1.70228 - 0.705105i) q^{19} +(1.64346 + 4.31414i) q^{20} +(-0.0547034 - 1.15420i) q^{21} +(0.000498978 - 0.0347398i) q^{22} +(-1.89294 - 1.89294i) q^{23} +(-0.0532077 + 1.23413i) q^{24} +(-0.232058 - 0.232058i) q^{25} +(-5.46520 + 5.31043i) q^{26} +(2.34398 + 0.970909i) q^{27} +(4.85013 - 2.11572i) q^{28} +(2.01467 + 4.86384i) q^{29} +(-0.526611 - 1.32486i) q^{30} -0.187704 q^{31} +(-5.36811 + 1.78422i) q^{32} +0.0107294i q^{33} +(0.632709 + 1.59178i) q^{34} +(-4.10912 + 4.51801i) q^{35} +(-0.161368 + 5.61621i) q^{36} +(2.35207 + 0.974258i) q^{37} +(-1.81588 - 1.86880i) q^{38} +(1.66403 - 1.66403i) q^{39} +(4.81114 - 4.41343i) q^{40} +(-1.89007 - 1.89007i) q^{41} +(-1.48827 + 0.674815i) q^{42} +(5.31052 + 2.19969i) q^{43} +(-0.0459157 + 0.0174915i) q^{44} +(-2.48154 - 5.99097i) q^{45} +(-1.49888 + 3.47653i) q^{46} +10.7802i q^{47} +(1.64968 - 0.574752i) q^{48} +(5.39570 + 4.45942i) q^{49} +(-0.183749 + 0.426191i) q^{50} +(-0.202432 - 0.488713i) q^{51} +(9.83385 + 4.40833i) q^{52} +(2.89250 - 6.98312i) q^{53} +(0.0515304 - 3.58764i) q^{54} +(0.0400988 - 0.0400988i) q^{55} +(-5.31406 - 5.26884i) q^{56} +(0.569007 + 0.569007i) q^{57} +(5.33964 - 5.18843i) q^{58} +(13.1854 + 5.46159i) q^{59} +(-1.46604 + 1.38415i) q^{60} +(10.3612 - 4.29176i) q^{61} +(0.0980521 + 0.246681i) q^{62} +(-6.72448 + 3.16624i) q^{63} +(5.14899 + 6.12273i) q^{64} -12.4379 q^{65} +(0.0141006 - 0.00560477i) q^{66} +(-0.900161 + 0.372859i) q^{67} +(1.76141 - 1.66301i) q^{68} +(0.447414 - 1.08015i) q^{69} +(8.08407 + 3.04011i) q^{70} +(3.87314 - 3.87314i) q^{71} +(7.46512 - 2.72170i) q^{72} +(-2.87435 - 2.87435i) q^{73} +(0.0517081 - 3.60002i) q^{74} +(0.0548489 - 0.132417i) q^{75} +(-1.50741 + 3.36264i) q^{76} +(-0.0480855 - 0.0437337i) q^{77} +(-3.05611 - 1.31762i) q^{78} -11.2913 q^{79} +(-8.31336 - 4.01733i) q^{80} -7.31974i q^{81} +(-1.49660 + 3.47126i) q^{82} +(-7.36131 + 3.04916i) q^{83} +(1.66428 + 1.60338i) q^{84} +(-1.06992 + 2.58301i) q^{85} +(0.116747 - 8.12815i) q^{86} +(-1.62580 + 1.62580i) q^{87} +(0.0469726 + 0.0512054i) q^{88} +(-9.46502 + 9.46502i) q^{89} +(-6.57704 + 6.39078i) q^{90} +(0.674922 + 14.2403i) q^{91} +(5.35184 + 0.153772i) q^{92} +(-0.0313712 - 0.0757369i) q^{93} +(14.1674 - 5.63132i) q^{94} -4.25308i q^{95} +(-1.61709 - 1.86778i) q^{96} +18.3664i q^{97} +(3.04200 - 9.42052i) q^{98} +(0.0637624 - 0.0264113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9	\( 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{11} - 20 q^{14} - 16 q^{15} + 16 q^{16} - 16 q^{18} - 4 q^{21} + 32 q^{22} - 48 q^{23} - 8 q^{25} - 24 q^{28} - 8 q^{29} + 16 q^{30} - 8 q^{32} + 20 q^{35} + 32 q^{36} - 8 q^{37} - 8 q^{39} + 16 q^{42} + 32 q^{43} - 144 q^{44} - 8 q^{46} + 16 q^{50} - 32 q^{51} - 32 q^{53} + 64 q^{56} - 8 q^{57} - 72 q^{58} - 88 q^{60} + 112 q^{64} - 16 q^{65} - 64 q^{67} - 40 q^{70} + 56 q^{71} - 8 q^{72} - 168 q^{74} + 52 q^{77} + 192 q^{78} - 16 q^{79} - 24 q^{84} - 48 q^{85} - 8 q^{86} - 96 q^{88} - 52 q^{91} - 8 q^{92} - 32 q^{93} + 88 q^{98} + 16 q^{99}+O(q^{100}) \) 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^11 - 20 * q^14 - 16 * q^15 + 16 * q^16 - 16 * q^18 - 4 * q^21 + 32 * q^22 - 48 * q^23 - 8 * q^25 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 8 * q^32 + 20 * q^35 + 32 * q^36 - 8 * q^37 - 8 * q^39 + 16 * q^42 + 32 * q^43 - 144 * q^44 - 8 * q^46 + 16 * q^50 - 32 * q^51 - 32 * q^53 + 64 * q^56 - 8 * q^57 - 72 * q^58 - 88 * q^60 + 112 * q^64 - 16 * q^65 - 64 * q^67 - 40 * q^70 + 56 * q^71 - 8 * q^72 - 168 * q^74 + 52 * q^77 + 192 * q^78 - 16 * q^79 - 24 * q^84 - 48 * q^85 - 8 * q^86 - 96 * q^88 - 52 * q^91 - 8 * q^92 - 32 * q^93 + 88 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more