LMFDB - Embedded newform 357.2.p.a.16.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(16,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("357.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.p (of order $6$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			16.9
Character	$\chi$	$=$	357.16
Dual form			357.2.p.a.67.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.427664 + 0.740736i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.634207 + 1.09848i) q^{4} +(3.01361 + 1.73991i) q^{5} -0.855328i q^{6} +(2.30724 + 1.29485i) q^{7} -2.79557 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.427664 + 0.740736i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.634207 + 1.09848i) q^{4} +(3.01361 + 1.73991i) q^{5} -0.855328i q^{6} +(2.30724 + 1.29485i) q^{7} -2.79557 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.57762 + 1.48819i) q^{10} +(4.73290 - 2.73254i) q^{11} +(-1.09848 - 0.634207i) q^{12} -1.39065 q^{13} +(-1.94587 + 1.15529i) q^{14} -3.47982 q^{15} +(-0.0728520 + 0.126183i) q^{16} +(1.58813 - 3.80497i) q^{17} +(0.427664 + 0.740736i) q^{18} +(-0.0543544 + 0.0941445i) q^{19} +4.41385i q^{20} +(-2.64555 + 0.0322424i) q^{21} +4.67444i q^{22} +(-6.77780 - 3.91317i) q^{23} +(2.42103 - 1.39778i) q^{24} +(3.55456 + 6.15668i) q^{25} +(0.594733 - 1.03011i) q^{26} +1.00000i q^{27} +(0.0408967 + 3.35566i) q^{28} +0.259414i q^{29} +(1.48819 - 2.57762i) q^{30} +(-4.32717 + 2.49830i) q^{31} +(-2.85788 - 4.94999i) q^{32} +(-2.73254 + 4.73290i) q^{33} +(2.13929 + 2.80364i) q^{34} +(4.70019 + 7.91657i) q^{35} +1.26841 q^{36} +(0.259119 + 0.149603i) q^{37} +(-0.0464908 - 0.0805244i) q^{38} +(1.20434 - 0.695327i) q^{39} +(-8.42474 - 4.86403i) q^{40} +4.70410i q^{41} +(1.10753 - 1.97345i) q^{42} -9.73333 q^{43} +(6.00328 + 3.46599i) q^{44} +(3.01361 - 1.73991i) q^{45} +(5.79724 - 3.34704i) q^{46} +(2.55039 - 4.41741i) q^{47} -0.145704i q^{48} +(3.64670 + 5.97508i) q^{49} -6.08063 q^{50} +(0.527124 + 4.08927i) q^{51} +(-0.881963 - 1.52760i) q^{52} +(-5.04594 - 8.73983i) q^{53} +(-0.740736 - 0.427664i) q^{54} +19.0175 q^{55} +(-6.45004 - 3.61985i) q^{56} -0.108709i q^{57} +(-0.192157 - 0.110942i) q^{58} +(-3.27208 - 5.66740i) q^{59} +(-2.20693 - 3.82251i) q^{60} +(-2.39543 - 1.38300i) q^{61} -4.27372i q^{62} +(2.27500 - 1.35070i) q^{63} +4.59744 q^{64} +(-4.19089 - 2.41961i) q^{65} +(-2.33722 - 4.04818i) q^{66} +(-1.35489 - 2.34674i) q^{67} +(5.18689 - 0.668611i) q^{68} +7.82633 q^{69} +(-7.87419 + 0.0959658i) q^{70} -14.8468i q^{71} +(-1.39778 + 2.42103i) q^{72} +(10.2030 - 5.89072i) q^{73} +(-0.221632 + 0.127959i) q^{74} +(-6.15668 - 3.55456i) q^{75} -0.137888 q^{76} +(14.4582 - 0.176207i) q^{77} +1.18947i q^{78} +(0.707868 + 0.408688i) q^{79} +(-0.439095 + 0.253512i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.48450 - 2.01177i) q^{82} -0.882937 q^{83} +(-1.71325 - 2.88564i) q^{84} +(11.4063 - 8.70350i) q^{85} +(4.16259 - 7.20983i) q^{86} +(-0.129707 - 0.224659i) q^{87} +(-13.2311 + 7.63900i) q^{88} +(-6.35909 + 11.0143i) q^{89} +2.97638i q^{90} +(-3.20857 - 1.80070i) q^{91} -9.92703i q^{92} +(2.49830 - 4.32717i) q^{93} +(2.18142 + 3.77833i) q^{94} +(-0.327606 + 0.189143i) q^{95} +(4.94999 + 2.85788i) q^{96} +16.7772i q^{97} +(-5.98552 + 0.145917i) q^{98} -5.46508i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) $ 48 * q - 24 * q^4 + 24 * q^9	$ 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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 $

$2$	−0.427664	+	0.740736i	−0.302404	+	0.523779i	−0.976680	−	0.214700i	$-0.931123\pi$
$2$	−0.427664	+	0.740736i	−0.302404	+	0.523779i	0.674276	+	0.738479i	$0.264456\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.634207	+	1.09848i	0.317104	+	0.549240i
$5$	3.01361	+	1.73991i	1.34773	+	0.778111i	0.987927	−	0.154919i	$-0.0495116\pi$
$5$	3.01361	+	1.73991i	1.34773	+	0.778111i	0.359800	+	0.933029i	$0.382845\pi$
$6$		−	0.855328i		−	0.349186i
$7$	2.30724	+	1.29485i	0.872054	+	0.489409i
$7$	2.30724	+	1.29485i	0.872054	+	0.489409i
$8$	−2.79557			−0.988382
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.57762	+	1.48819i	−0.815116	+	0.470608i
$11$	4.73290	−	2.73254i	1.42702	−	0.823892i	0.430138	−	0.902763i	$-0.358465\pi$
$11$	4.73290	−	2.73254i	1.42702	−	0.823892i	0.996885	+	0.0788708i	$0.0251315\pi$
$12$	−1.09848	−	0.634207i	−0.317104	−	0.183080i
$13$	−1.39065			−0.385698			−0.192849	−	0.981228i	$-0.561773\pi$
$13$	−1.39065			−0.385698			−0.192849	+	0.981228i	$0.561773\pi$
$14$	−1.94587	+	1.15529i	−0.520055	+	0.308765i
$15$	−3.47982			−0.898485
$16$	−0.0728520	+	0.126183i	−0.0182130	+	0.0315459i
$17$	1.58813	−	3.80497i	0.385179	−	0.922842i
$17$	1.58813	−	3.80497i	0.385179	−	0.922842i
$18$	0.427664	+	0.740736i	0.100801	+	0.174593i
$19$	−0.0543544	+	0.0941445i	−0.0124697	+	0.0215982i	−0.872193	−	0.489162i	$-0.837303\pi$
$19$	−0.0543544	+	0.0941445i	−0.0124697	+	0.0215982i	0.859723	+	0.510760i	$0.170636\pi$
$20$			4.41385i			0.986967i
$21$	−2.64555	+	0.0322424i	−0.577307	+	0.00703587i
$22$			4.67444i			0.996593i
$23$	−6.77780	−	3.91317i	−1.41327	−	0.815952i	−0.417575	−	0.908643i	$-0.637120\pi$
$23$	−6.77780	−	3.91317i	−1.41327	−	0.815952i	−0.995695	+	0.0926911i	$0.970453\pi$
$24$	2.42103	−	1.39778i	0.494191	−	0.285321i
$25$	3.55456	+	6.15668i	0.710913	+	1.23134i
$26$	0.594733	−	1.03011i	0.116637	−	0.202021i
$27$			1.00000i			0.192450i
$28$	0.0408967	+	3.35566i	0.00772876	+	0.634160i
$29$			0.259414i			0.0481720i	0.999710	+	0.0240860i	$0.00766756\pi$
$29$			0.259414i			0.0481720i	−0.999710	+	0.0240860i	$0.992332\pi$
$30$	1.48819	−	2.57762i	0.271705	−	0.470608i
$31$	−4.32717	+	2.49830i	−0.777183	+	0.448707i	−0.835431	−	0.549595i	$-0.814782\pi$
$31$	−4.32717	+	2.49830i	−0.777183	+	0.448707i	0.0582477	+	0.998302i	$0.481449\pi$
$32$	−2.85788	−	4.94999i	−0.505206	−	0.875043i
$33$	−2.73254	+	4.73290i	−0.475674	+	0.823892i
$34$	2.13929	+	2.80364i	0.366886	+	0.480820i
$35$	4.70019	+	7.91657i	0.794477	+	1.33814i
$36$	1.26841			0.211402
$37$	0.259119	+	0.149603i	0.0425989	+	0.0245945i	0.521148	−	0.853466i	$-0.325504\pi$
$37$	0.259119	+	0.149603i	0.0425989	+	0.0245945i	−0.478549	+	0.878061i	$0.658837\pi$
$38$	−0.0464908	−	0.0805244i	−0.00754180	−	0.0130628i
$39$	1.20434	−	0.695327i	0.192849	−	0.111341i
$40$	−8.42474	−	4.86403i	−1.33207	−	0.769070i
$41$			4.70410i			0.734657i	0.930091	+	0.367329i	$0.119728\pi$
$41$			4.70410i			0.734657i	−0.930091	+	0.367329i	$0.880272\pi$
$42$	1.10753	−	1.97345i	0.170895	−	0.304509i
$43$	−9.73333			−1.48432			−0.742160	−	0.670223i	$-0.766198\pi$
$43$	−9.73333			−1.48432			−0.742160	+	0.670223i	$0.766198\pi$
$44$	6.00328	+	3.46599i	0.905028	+	0.522518i
$45$	3.01361	−	1.73991i	0.449242	−	0.259370i
$46$	5.79724	−	3.34704i	0.854757	−	0.493494i
$47$	2.55039	−	4.41741i	0.372013	−	0.644345i	−0.617862	−	0.786286i	$-0.712001\pi$
$47$	2.55039	−	4.41741i	0.372013	−	0.644345i	0.989875	+	0.141941i	$0.0453344\pi$
$48$		−	0.145704i		−	0.0210306i
$49$	3.64670	+	5.97508i	0.520958	+	0.853583i
$50$	−6.08063			−0.859931
$51$	0.527124	+	4.08927i	0.0738121	+	0.572613i
$52$	−0.881963	−	1.52760i	−0.122306	−	0.211841i
$53$	−5.04594	−	8.73983i	−0.693114	−	1.20051i	−0.970812	−	0.239840i	$-0.922905\pi$
$53$	−5.04594	−	8.73983i	−0.693114	−	1.20051i	0.277699	−	0.960668i	$-0.410428\pi$
$54$	−0.740736	−	0.427664i	−0.100801	−	0.0581977i
$55$	19.0175			2.56432
$56$	−6.45004	−	3.61985i	−0.861923	−	0.483723i
$57$		−	0.108709i		−	0.0143988i
$58$	−0.192157	−	0.110942i	−0.0252315	−	0.0145674i
$59$	−3.27208	−	5.66740i	−0.425988	−	0.737833i	0.570524	−	0.821281i	$-0.306740\pi$
$59$	−3.27208	−	5.66740i	−0.425988	−	0.737833i	−0.996512	+	0.0834480i	$0.973407\pi$
$60$	−2.20693	−	3.82251i	−0.284913	−	0.493483i
$61$	−2.39543	−	1.38300i	−0.306704	−	0.177075i	0.338747	−	0.940878i	$-0.389997\pi$
$61$	−2.39543	−	1.38300i	−0.306704	−	0.177075i	−0.645450	+	0.763802i	$0.723330\pi$
$62$		−	4.27372i		−	0.542763i
$63$	2.27500	−	1.35070i	0.286623	−	0.170172i
$64$	4.59744			0.574680
$65$	−4.19089	−	2.41961i	−0.519816	−	0.300116i
$66$	−2.33722	−	4.04818i	−0.287692	−	0.498297i
$67$	−1.35489	−	2.34674i	−0.165526	−	0.286700i	0.771316	−	0.636453i	$-0.219599\pi$
$67$	−1.35489	−	2.34674i	−0.165526	−	0.286700i	−0.936842	+	0.349753i	$0.886266\pi$
$68$	5.18689	−	0.668611i	0.629003	−	0.0810810i
$69$	7.82633			0.942180
$70$	−7.87419	+	0.0959658i	−0.941145	+	0.0114701i
$71$		−	14.8468i		−	1.76199i	−0.473125	−	0.880995i	$-0.656874\pi$
$71$		−	14.8468i		−	1.76199i	0.473125	−	0.880995i	$-0.343126\pi$
$72$	−1.39778	+	2.42103i	−0.164730	+	0.285321i
$73$	10.2030	−	5.89072i	1.19417	−	0.689457i	0.234923	−	0.972014i	$-0.424516\pi$
$73$	10.2030	−	5.89072i	1.19417	−	0.689457i	0.959250	+	0.282557i	$0.0911827\pi$
$74$	−0.221632	+	0.127959i	−0.0257642	+	0.0148750i
$75$	−6.15668	−	3.55456i	−0.710913	−	0.410446i
$76$	−0.137888			−0.0158168
$77$	14.4582	−	0.176207i	1.64766	−	0.0200807i
$78$			1.18947i			0.134680i
$79$	0.707868	+	0.408688i	0.0796414	+	0.0459810i	0.539292	−	0.842119i	$-0.318692\pi$
$79$	0.707868	+	0.408688i	0.0796414	+	0.0459810i	−0.459650	+	0.888100i	$0.652025\pi$
$80$	−0.439095	+	0.253512i	−0.0490923	+	0.0283435i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.48450	−	2.01177i	−0.384798	−	0.222163i
$83$	−0.882937			−0.0969149			−0.0484574	−	0.998825i	$-0.515431\pi$
$83$	−0.882937			−0.0969149			−0.0484574	+	0.998825i	$0.515431\pi$
$84$	−1.71325	−	2.88564i	−0.186931	−	0.314849i
$85$	11.4063	−	8.70350i	1.23719	−	0.944027i
$86$	4.16259	−	7.20983i	0.448864	−	0.777455i
$87$	−0.129707	−	0.224659i	−0.0139061	−	0.0240860i
$88$	−13.2311	+	7.63900i	−1.41044	+	0.814320i
$89$	−6.35909	+	11.0143i	−0.674062	+	1.16751i	0.302680	+	0.953092i	$0.402119\pi$
$89$	−6.35909	+	11.0143i	−0.674062	+	1.16751i	−0.976742	+	0.214417i	$0.931215\pi$
$90$			2.97638i			0.313738i
$91$	−3.20857	−	1.80070i	−0.336350	−	0.188764i
$92$		−	9.92703i		−	1.03496i
$93$	2.49830	−	4.32717i	0.259061	−	0.448707i
$94$	2.18142	+	3.77833i	0.224996	+	0.389705i
$95$	−0.327606	+	0.189143i	−0.0336116	+	0.0194057i
$96$	4.94999	+	2.85788i	0.505206	+	0.291681i
$97$			16.7772i			1.70346i	0.523978	+	0.851732i	$0.324448\pi$
$97$			16.7772i			1.70346i	−0.523978	+	0.851732i	$0.675552\pi$
$98$	−5.98552	+	0.145917i	−0.604628	+	0.0147399i
$99$		−	5.46508i		−	0.549261i
$100$	−4.50866	+	7.80923i	−0.450866	+	0.780923i
$101$	9.46267	+	16.3898i	0.941571	+	1.63085i	0.762475	+	0.647018i	$0.223984\pi$
$101$	9.46267	+	16.3898i	0.941571	+	1.63085i	0.179096	+	0.983832i	$0.442683\pi$
$102$	−3.25450	−	1.35837i	−0.322244	−	0.134499i
$103$	−4.70651	+	8.15191i	−0.463746	+	0.803231i	−0.999144	−	0.0413684i	$-0.986828\pi$
$103$	−4.70651	+	8.15191i	−0.463746	+	0.803231i	0.535398	+	0.844600i	$0.320162\pi$
$104$	3.88767			0.381217
$105$	−8.02877	−	4.50586i	−0.783528	−	0.439727i
$106$	8.63187			0.838402
$107$	−3.87911	−	2.23960i	−0.375008	−	0.216511i	0.300636	−	0.953739i	$-0.402801\pi$
$107$	−3.87911	−	2.23960i	−0.375008	−	0.216511i	−0.675644	+	0.737228i	$0.736134\pi$
$108$	−1.09848	+	0.634207i	−0.105701	+	0.0610266i
$109$	13.1929	−	7.61691i	1.26365	−	0.729568i	0.289870	−	0.957066i	$-0.406388\pi$
$109$	13.1929	−	7.61691i	1.26365	−	0.729568i	0.973779	+	0.227498i	$0.0730546\pi$
$110$	−8.13309	+	14.0869i	−0.775460	+	1.34314i
$111$	−0.299205			−0.0283993
$112$	−0.331476	+	0.196803i	−0.0313216	+	0.0185961i
$113$			8.69076i			0.817558i	0.912633	+	0.408779i	$0.134045\pi$
$113$			8.69076i			0.817558i	−0.912633	+	0.408779i	$0.865955\pi$
$114$	0.0805244	+	0.0464908i	0.00754180	+	0.00435426i
$115$	−13.6171	−	23.5855i	−1.26980	−	2.19936i
$116$	−0.284961	+	0.164522i	−0.0264580	+	0.0152755i
$117$	−0.695327	+	1.20434i	−0.0642830	+	0.111341i
$118$	5.59739			0.515282
$119$	8.59109	−	6.72258i	0.787544	−	0.616258i
$120$	9.72806			0.888046
$121$	9.43356	−	16.3394i	0.857597	−	1.48540i
$122$	2.04888	−	1.18292i	0.185497	−	0.107097i
$123$	−2.35205	−	4.07387i	−0.212077	−	0.367329i
$124$	−5.48865	−	3.16887i	−0.492895	−	0.284573i
$125$			7.33937i			0.656454i
$126$	0.0275778	+	2.26282i	0.00245683	+	0.201588i
$127$	−6.66613			−0.591523			−0.295762	−	0.955262i	$-0.595573\pi$
$127$	−6.66613			−0.591523			−0.295762	+	0.955262i	$0.595573\pi$
$128$	3.74960	−	6.49449i	0.331421	−	0.574038i
$129$	8.42931	−	4.86667i	0.742160	−	0.428486i
$130$	3.58458	−	2.06956i	0.314389	−	0.181512i
$131$	10.3060	+	5.95015i	0.900436	+	0.519867i	0.877342	−	0.479867i	$-0.159315\pi$
$131$	10.3060	+	5.95015i	0.900436	+	0.519867i	0.0230942	+	0.999733i	$0.492648\pi$
$132$	−6.93199			−0.603352
$133$	−0.247312	+	0.146833i	−0.0214447	+	0.0127320i
$134$	2.31775			0.200223
$135$	−1.73991	+	3.01361i	−0.149747	+	0.259370i
$136$	−4.43973	+	10.6371i	−0.380704	+	0.912120i
$137$	3.60456	+	6.24327i	0.307958	+	0.533399i	0.977916	−	0.209001i	$-0.0670210\pi$
$137$	3.60456	+	6.24327i	0.307958	+	0.533399i	−0.669958	+	0.742399i	$0.733688\pi$
$138$	−3.34704	+	5.79724i	−0.284919	+	0.493494i
$139$		−	2.91833i		−	0.247530i	−0.992312	−	0.123765i	$-0.960503\pi$
$139$		−	2.91833i		−	0.247530i	0.992312	−	0.123765i	$-0.0394968\pi$
$140$	−5.71529	+	10.1838i	−0.483031	+	0.860689i
$141$			5.10078i			0.429564i
$142$	10.9976	+	6.34944i	0.922894	+	0.532833i
$143$	−6.58183	+	3.80002i	−0.550400	+	0.317774i
$144$	0.0728520	+	0.126183i	0.00607100	+	0.0105153i
$145$	−0.451357	+	0.781774i	−0.0374832	+	0.0649228i
$146$			10.0770i			0.833978i
$147$	−6.14568	−	3.35122i	−0.506887	−	0.276404i
$148$			0.379516i			0.0311960i
$149$	−5.17365	+	8.96103i	−0.423842	+	0.734116i	−0.996312	−	0.0858098i	$-0.972652\pi$
$149$	−5.17365	+	8.96103i	−0.423842	+	0.734116i	0.572469	+	0.819926i	$0.305986\pi$
$150$	5.26598	−	3.04032i	0.429966	−	0.248241i
$151$	−5.14458	−	8.91068i	−0.418660	−	0.725141i	0.577145	−	0.816642i	$-0.304167\pi$
$151$	−5.14458	−	8.91068i	−0.418660	−	0.725141i	−0.995805	+	0.0915011i	$0.970834\pi$
$152$	0.151951	−	0.263187i	0.0123249	−	0.0213473i
$153$	−2.50114	−	3.27785i	−0.202205	−	0.264999i
$154$	−6.05272	+	10.7850i	−0.487742	+	0.869083i
$155$	−17.3872			−1.39658
$156$	1.52760	+	0.881963i	0.122306	+	0.0706136i
$157$	−0.277210	−	0.480143i	−0.0221238	−	0.0383196i	0.854752	−	0.519037i	$-0.173709\pi$
$157$	−0.277210	−	0.480143i	−0.0221238	−	0.0383196i	−0.876875	+	0.480718i	$0.840376\pi$
$158$	−0.605459	+	0.349562i	−0.0481677	+	0.0278097i
$159$	8.73983	+	5.04594i	0.693114	+	0.400169i
$160$		−	19.8898i		−	1.57243i
$161$	−10.5710	−	17.8049i	−0.833114	−	1.40322i
$162$	0.855328			0.0672009
$163$	−3.76387	−	2.17307i	−0.294809	−	0.170208i	0.345300	−	0.938493i	$-0.387777\pi$
$163$	−3.76387	−	2.17307i	−0.294809	−	0.170208i	−0.640109	+	0.768284i	$0.721111\pi$
$164$	−5.16736	+	2.98338i	−0.403503	+	0.232963i
$165$	−16.4696	+	9.50874i	−1.28216	+	0.740255i
$166$	0.377600	−	0.654023i	0.0293075	−	0.0507620i
$167$			7.54869i			0.584135i	0.956398	+	0.292067i	$0.0943432\pi$
$167$			7.54869i			0.584135i	−0.956398	+	0.292067i	$0.905657\pi$
$168$	7.39582	−	0.0901358i	0.570600	−	0.00695413i
$169$	−11.0661			−0.851237
$170$	1.56892	+	12.1712i	0.120331	+	0.933492i
$171$	0.0543544	+	0.0941445i	0.00415658	+	0.00719941i
$172$	−6.17295	−	10.6919i	−0.470683	−	0.815247i
$173$	8.76674	+	5.06148i	0.666523	+	0.384817i	0.794758	−	0.606927i	$-0.207598\pi$
$173$	8.76674	+	5.06148i	0.666523	+	0.384817i	−0.128235	+	0.991744i	$0.540931\pi$
$174$	0.221884			0.0168210
$175$	0.229215	+	18.8076i	0.0173271	+	1.42172i
$176$			0.796285i			0.0600222i
$177$	5.66740	+	3.27208i	0.425988	+	0.245944i
$178$	−5.43910	−	9.42080i	−0.407678	−	0.706119i
$179$	0.673502	+	1.16654i	0.0503399	+	0.0871913i	0.890097	−	0.455770i	$-0.150636\pi$
$179$	0.673502	+	1.16654i	0.0503399	+	0.0871913i	−0.839757	+	0.542962i	$0.817303\pi$
$180$	3.82251	+	2.20693i	0.284913	+	0.164494i
$181$			7.20428i			0.535490i	0.963490	+	0.267745i	$0.0862785\pi$
$181$			7.20428i			0.535490i	−0.963490	+	0.267745i	$0.913722\pi$
$182$	2.70603	−	1.60661i	0.200584	−	0.119090i
$183$	2.76601			0.204469
$184$	18.9478	+	10.9395i	1.39685	+	0.806472i
$185$	0.520590	+	0.901688i	0.0382745	+	0.0662934i
$186$	2.13686	+	3.70115i	0.156682	+	0.271382i
$187$	−2.88077	−	22.3482i	−0.210663	−	1.63426i
$188$	6.46991			0.471867
$189$	−1.29485	+	2.30724i	−0.0941868	+	0.167827i
$190$		−	0.323559i		−	0.0234734i
$191$	4.45236	−	7.71172i	0.322162	−	0.558000i	−0.658772	−	0.752342i	$-0.728924\pi$
$191$	4.45236	−	7.71172i	0.322162	−	0.558000i	0.980934	+	0.194342i	$0.0622572\pi$
$192$	−3.98150	+	2.29872i	−0.287340	+	0.165896i
$193$	12.3264	−	7.11667i	0.887276	−	0.512269i	0.0142252	−	0.999899i	$-0.495472\pi$
$193$	12.3264	−	7.11667i	0.887276	−	0.512269i	0.873050	+	0.487630i	$0.162138\pi$
$194$	−12.4274	−	7.17499i	−0.892239	−	0.515134i
$195$	4.83922			0.346544
$196$	−4.25073	+	7.79526i	−0.303624	+	0.556805i
$197$			9.45415i			0.673580i	0.941580	+	0.336790i	$0.109341\pi$
$197$			9.45415i			0.673580i	−0.941580	+	0.336790i	$0.890659\pi$
$198$	4.04818	+	2.33722i	0.287692	+	0.166099i
$199$	8.09420	−	4.67319i	0.573782	−	0.331273i	−0.184876	−	0.982762i	$-0.559188\pi$
$199$	8.09420	−	4.67319i	0.573782	−	0.331273i	0.758659	+	0.651488i	$0.225855\pi$
$200$	−9.93701	−	17.2114i	−0.702653	−	1.21703i
$201$	2.34674	+	1.35489i	0.165526	+	0.0955667i
$202$	−16.1874			−1.13894
$203$	−0.335904	+	0.598531i	−0.0235758	+	0.0420086i
$204$	−4.15767	+	3.17248i	−0.291095	+	0.222118i
$205$	−8.18471	+	14.1763i	−0.571645	+	0.990118i
$206$	−4.02561	−	6.97255i	−0.280477	−	0.485801i
$207$	−6.77780	+	3.91317i	−0.471090	+	0.271984i
$208$	0.101312	−	0.175478i	0.00702472	−	0.0121672i
$209$			0.594102i			0.0410949i
$210$	6.77126	−	4.02020i	0.467262	−	0.277420i
$211$			27.4341i			1.88864i	0.329029	+	0.944320i	$0.393279\pi$
$211$			27.4341i			1.88864i	−0.329029	+	0.944320i	$0.606721\pi$
$212$	6.40035	−	11.0857i	0.439578	−	0.761371i
$213$	7.42340	+	12.8577i	0.508643	+	0.880995i
$214$	3.31791	−	1.91560i	0.226808	−	0.130947i
$215$	−29.3325	−	16.9351i	−2.00046	−	1.15496i
$216$		−	2.79557i		−	0.190214i
$217$	−13.2188	+	0.161102i	−0.897347	+	0.0109363i
$218$			13.0299i			0.882497i
$219$	−5.89072	+	10.2030i	−0.398058	+	0.689457i
$220$	12.0610	+	20.8903i	0.813154	+	1.40842i
$221$	−2.20854	+	5.29140i	−0.148563	+	0.355938i
$222$	0.127959	−	0.221632i	0.00858806	−	0.0148750i
$223$	11.0700			0.741299			0.370650	−	0.928773i	$-0.379135\pi$
$223$	11.0700			0.741299			0.370650	+	0.928773i	$0.379135\pi$
$224$	−0.184290	−	15.1213i	−0.0123134	−	1.01034i
$225$	7.10913			0.473942
$226$	−6.43756	−	3.71673i	−0.428220	−	0.247233i
$227$	−6.87739	+	3.97066i	−0.456468	+	0.263542i	−0.710558	−	0.703639i	$-0.751557\pi$
$227$	−6.87739	+	3.97066i	−0.456468	+	0.263542i	0.254090	+	0.967181i	$0.418224\pi$
$228$	0.119414	−	0.0689438i	0.00790840	−	0.00456592i
$229$	−5.58167	+	9.66774i	−0.368847	+	0.638862i	−0.989386	−	0.145314i	$-0.953581\pi$
$229$	−5.58167	+	9.66774i	−0.368847	+	0.638862i	0.620538	+	0.784176i	$0.286914\pi$
$230$	23.2942			1.53597
$231$	−12.4330	+	7.38169i	−0.818034	+	0.485679i
$232$		−	0.725210i		−	0.0476124i
$233$	−9.06026	−	5.23094i	−0.593557	−	0.342690i	0.172946	−	0.984931i	$-0.444672\pi$
$233$	−9.06026	−	5.23094i	−0.593557	−	0.342690i	−0.766503	+	0.642241i	$0.778005\pi$
$234$	−0.594733	−	1.03011i	−0.0388789	−	0.0673402i
$235$	15.3718	−	8.87490i	1.00274	−	0.578935i
$236$	4.15035	−	7.18861i	0.270165	−	0.467939i
$237$	−0.817376			−0.0530943
$238$	1.30556	+	9.23873i	0.0846267	+	0.598858i
$239$	30.6461			1.98233			0.991165	−	0.132631i	$-0.0423426\pi$
$239$	30.6461			1.98233			0.991165	+	0.132631i	$0.0423426\pi$
$240$	0.253512	−	0.439095i	0.0163641	−	0.0283435i
$241$	17.1623	−	9.90864i	1.10552	−	0.638272i	0.167854	−	0.985812i	$-0.446316\pi$
$241$	17.1623	−	9.90864i	1.10552	−	0.638272i	0.937665	+	0.347540i	$0.112983\pi$
$242$	8.06879	+	13.9756i	0.518681	+	0.898383i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		−	3.50844i		−	0.224605i
$245$	0.593650	+	24.3515i	0.0379269	+	1.55576i
$246$	4.02355			0.256532
$247$	0.0755881	−	0.130922i	0.00480956	−	0.00833040i
$248$	12.0969	−	6.98415i	0.768154	−	0.443494i
$249$	0.764646	−	0.441468i	0.0484574	−	0.0279769i
$250$	−5.43653	−	3.13878i	−0.343837	−	0.198514i
$251$	−21.5984			−1.36328			−0.681641	−	0.731687i	$-0.738733\pi$
$251$	−21.5984			−1.36328			−0.681641	+	0.731687i	$0.738733\pi$
$252$	2.92654	+	1.64241i	0.184354	+	0.103462i
$253$	−42.7716			−2.68902
$254$	2.85086	−	4.93784i	0.178879	−	0.309828i
$255$	−5.52641	+	13.2406i	−0.346077	+	0.829160i
$256$	7.80457	+	13.5179i	0.487786	+	0.844870i
$257$	−1.40842	+	2.43945i	−0.0878548	+	0.152169i	−0.906604	−	0.421982i	$-0.861334\pi$
$257$	−1.40842	+	2.43945i	−0.0878548	+	0.152169i	0.818749	+	0.574151i	$0.194668\pi$
$258$			8.32519i			0.518304i
$259$	0.404136	+	0.680691i	0.0251118	+	0.0422961i
$260$		−	6.13814i		−	0.380671i
$261$	0.224659	+	0.129707i	0.0139061	+	0.00802867i
$262$	−8.81497	+	5.08933i	−0.544591	+	0.314420i
$263$	8.63092	+	14.9492i	0.532205	+	0.921807i	0.999293	+	0.0375959i	$0.0119700\pi$
$263$	8.63092	+	14.9492i	0.532205	+	0.921807i	−0.467088	+	0.884211i	$0.654697\pi$
$264$	7.63900	−	13.2311i	0.470148	−	0.814320i
$265$		−	35.1179i		−	2.15728i
$266$	−0.00299795	−	0.245988i	−0.000183816	−	0.0150825i
$267$		−	12.7182i		−	0.778339i
$268$	1.71856	−	2.97664i	0.104978	−	0.181827i
$269$	15.1040	−	8.72031i	0.920908	−	0.531687i	0.0369837	−	0.999316i	$-0.488225\pi$
$269$	15.1040	−	8.72031i	0.920908	−	0.531687i	0.883925	+	0.467629i	$0.154892\pi$
$270$	−1.48819	−	2.57762i	−0.0905685	−	0.156869i
$271$	11.3811	−	19.7126i	0.691351	−	1.19745i	−0.280045	−	0.959987i	$-0.590349\pi$
$271$	11.3811	−	19.7126i	0.691351	−	1.19745i	0.971395	−	0.237468i	$-0.0763174\pi$
$272$	0.364426	+	0.477596i	0.0220966	+	0.0289585i
$273$	3.67905	−	0.0448380i	0.222666	−	0.00271372i
$274$	−6.16615			−0.372511
$275$	33.6468	+	19.4260i	2.02898	+	1.17143i
$276$	4.96352	+	8.59706i	0.298769	+	0.517482i
$277$	11.1093	−	6.41397i	0.667494	−	0.385378i	−0.127632	−	0.991822i	$-0.540738\pi$
$277$	11.1093	−	6.41397i	0.667494	−	0.385378i	0.795126	+	0.606444i	$0.207404\pi$
$278$	2.16171	+	1.24807i	0.129651	+	0.0748540i
$279$			4.99659i			0.299138i
$280$	−13.1397	−	22.1313i	−0.785247	−	1.32260i
$281$	−15.7661			−0.940526			−0.470263	−	0.882526i	$-0.655841\pi$
$281$	−15.7661			−0.940526			−0.470263	+	0.882526i	$0.655841\pi$
$282$	−3.77833	−	2.18142i	−0.224996	−	0.129902i
$283$	−17.6013	+	10.1621i	−1.04629	+	0.604074i	−0.921607	−	0.388123i	$-0.873123\pi$
$283$	−17.6013	+	10.1621i	−1.04629	+	0.604074i	−0.124679	+	0.992197i	$0.539790\pi$
$284$	16.3089	−	9.41595i	0.967755	−	0.558734i
$285$	0.189143	−	0.327606i	0.0112039	−	0.0194057i
$286$		−	6.50053i		−	0.384384i
$287$	−6.09113	+	10.8535i	−0.359548	+	0.640661i
$288$	−5.71576			−0.336804
$289$	−11.9557	−	12.0856i	−0.703274	−	0.710918i
$290$	−0.386058	−	0.668673i	−0.0226701	−	0.0392658i
$291$	−8.38859	−	14.5295i	−0.491748	−	0.851732i
$292$	12.9417	+	7.47187i	0.757354	+	0.437258i
$293$	−4.27480			−0.249736			−0.124868	−	0.992173i	$-0.539851\pi$
$293$	−4.27480			−0.249736			−0.124868	+	0.992173i	$0.539851\pi$
$294$	5.11065	−	3.11913i	0.298059	−	0.181911i
$295$		−	22.7724i		−	1.32586i
$296$	−0.724385	−	0.418224i	−0.0421040	−	0.0243088i
$297$	2.73254	+	4.73290i	0.158558	+	0.274631i
$298$	−4.42517	−	7.66462i	−0.256343	−	0.443999i
$299$	9.42558	+	5.44186i	0.545095	+	0.314711i
$300$		−	9.01732i		−	0.520615i
$301$	−22.4571	−	12.6033i	−1.29441	−	0.726439i
$302$	8.80061			0.506418
$303$	−16.3898	−	9.46267i	−0.941571	−	0.543616i
$304$	−0.00791965	−	0.0137172i	−0.000454223	−	0.000786738i
$305$	−4.81260	−	8.33566i	−0.275569	−	0.477299i
$306$	3.49767	−	0.450863i	0.199948	−	0.0257741i
$307$	16.5490			0.944499			0.472250	−	0.881465i	$-0.343442\pi$
$307$	16.5490			0.944499			0.472250	+	0.881465i	$0.343442\pi$
$308$	9.36304	+	15.7703i	0.533509	+	0.898594i
$309$		−	9.41301i		−	0.535488i
$310$	7.43589	−	12.8793i	0.422330	−	0.731497i
$311$	−19.3132	+	11.1505i	−1.09515	+	0.632286i	−0.934943	−	0.354797i	$-0.884550\pi$
$311$	−19.3132	+	11.1505i	−1.09515	+	0.632286i	−0.160209	+	0.987083i	$0.551217\pi$
$312$	−3.36682	+	1.94383i	−0.190608	+	0.110048i
$313$	−11.3586	−	6.55791i	−0.642027	−	0.370675i	0.143368	−	0.989670i	$-0.454207\pi$
$313$	−11.3586	−	6.55791i	−0.642027	−	0.370675i	−0.785395	+	0.618995i	$0.787540\pi$
$314$	0.474212			0.0267613
$315$	9.20605	−	0.112198i	0.518702	−	0.00632162i
$316$			1.03677i			0.0583229i
$317$	−17.1903	−	9.92484i	−0.965505	−	0.557434i	−0.0676418	−	0.997710i	$-0.521548\pi$
$317$	−17.1903	−	9.92484i	−0.965505	−	0.557434i	−0.897863	+	0.440275i	$0.854881\pi$
$318$	−7.47542	+	4.31594i	−0.419201	+	0.242026i
$319$	0.708861	+	1.22778i	0.0396886	+	0.0687426i
$320$	13.8549	+	7.99912i	0.774511	+	0.447164i
$321$	4.47921			0.250005
$322$	17.7096	−	0.215833i	0.986915	−	0.0120279i
$323$	0.271895	+	0.356331i	0.0151287	+	0.0198268i
$324$	0.634207	−	1.09848i	0.0352337	−	0.0610266i
$325$	−4.94317	−	8.56182i	−0.274198	−	0.474924i
$326$	3.21934	−	1.85869i	0.178303	−	0.102943i
$327$	−7.61691	+	13.1929i	−0.421216	+	0.729568i
$328$		−	13.1506i		−	0.726122i
$329$	11.6043	−	6.88963i	0.639764	−	0.379838i
$330$		−	16.2662i		−	0.895424i
$331$	−2.56331	+	4.43978i	−0.140892	+	0.244032i	−0.927833	−	0.372996i	$-0.878330\pi$
$331$	−2.56331	+	4.43978i	−0.140892	+	0.244032i	0.786941	+	0.617029i	$0.211664\pi$
$332$	−0.559965	−	0.969888i	−0.0307321	−	0.0532295i
$333$	0.259119	−	0.149603i	0.0141996	−	0.00819817i
$334$	−5.59158	−	3.22830i	−0.305958	−	0.176645i
$335$		−	9.42955i		−	0.515192i
$336$	0.188666	−	0.336174i	0.0102926	−	0.0183398i
$337$			10.0077i			0.545155i	0.962134	+	0.272577i	$0.0878761\pi$
$337$			10.0077i			0.545155i	−0.962134	+	0.272577i	$0.912124\pi$
$338$	4.73256	−	8.19704i	0.257417	−	0.445860i
$339$	−4.34538	−	7.52642i	−0.236009	−	0.408779i
$340$	16.7946	+	7.00978i	0.910814	+	0.380159i
$341$	−13.6534	+	23.6484i	−0.739373	+	1.28063i
$342$	−0.0929816			−0.00502787
$343$	0.676957	+	18.5079i	0.0365522	+	0.999332i
$344$	27.2102			1.46707
$345$	23.5855	+	13.6171i	1.26980	+	0.733120i
$346$	−7.49843	+	4.32922i	−0.403118	+	0.232740i
$347$	−14.3874	+	8.30654i	−0.772354	+	0.445919i	−0.833714	−	0.552197i	$-0.813790\pi$
$347$	−14.3874	+	8.30654i	−0.772354	+	0.445919i	0.0613599	+	0.998116i	$0.480456\pi$
$348$	0.164522	−	0.284961i	0.00881933	−	0.0152755i
$349$	5.97100			0.319621			0.159810	−	0.987148i	$-0.448912\pi$
$349$	5.97100			0.319621			0.159810	+	0.987148i	$0.448912\pi$
$350$	−14.0295	−	7.87354i	−0.749907	−	0.420858i
$351$		−	1.39065i		−	0.0742276i
$352$	−27.0521	−	15.6185i	−1.44188	−	0.832471i
$353$	−16.0712	−	27.8361i	−0.855382	−	1.48157i	−0.876290	−	0.481784i	$-0.839989\pi$
$353$	−16.0712	−	27.8361i	−0.855382	−	1.48157i	0.0209075	−	0.999781i	$-0.493344\pi$
$354$	−4.84749	+	2.79870i	−0.257641	+	0.148749i
$355$	25.8321	−	44.7425i	1.37102	−	2.37468i
$356$	−16.1319			−0.854990
$357$	−4.07881	+	10.1175i	−0.215874	+	0.535474i
$358$	−1.15213			−0.0608920
$359$	7.94847	−	13.7672i	0.419504	−	0.726603i	−0.576385	−	0.817178i	$-0.695537\pi$
$359$	7.94847	−	13.7672i	0.419504	−	0.726603i	0.995890	+	0.0905754i	$0.0288706\pi$
$360$	−8.42474	+	4.86403i	−0.444023	+	0.256357i
$361$	9.49409	+	16.4442i	0.499689	+	0.865487i
$362$	−5.33647	−	3.08101i	−0.280479	−	0.161934i
$363$			18.8671i			0.990267i
$364$	−0.0568732	−	4.66656i	−0.00298097	−	0.244594i
$365$	40.9973			2.14589
$366$	−1.18292	+	2.04888i	−0.0618323	+	0.107097i
$367$	−17.7893	+	10.2707i	−0.928596	+	0.536125i	−0.886367	−	0.462983i	$-0.846779\pi$
$367$	−17.7893	+	10.2707i	−0.928596	+	0.536125i	−0.0422285	+	0.999108i	$0.513446\pi$
$368$	0.987554	−	0.570164i	0.0514798	−	0.0297219i
$369$	4.07387	+	2.35205i	0.212077	+	0.122443i
$370$	−0.890549			−0.0462975
$371$	−0.325387	−	26.6986i	−0.0168932	−	1.38612i
$372$	6.33775			0.328597
$373$	8.38366	−	14.5209i	0.434089	−	0.751865i	−0.563131	−	0.826367i	$-0.690404\pi$
$373$	8.38366	−	14.5209i	0.434089	−	0.751865i	0.997221	+	0.0745024i	$0.0237368\pi$
$374$	17.7861	+	7.42363i	0.919698	+	0.383867i
$375$	−3.66969	−	6.35608i	−0.189502	−	0.328227i
$376$	−7.12979	+	12.3492i	−0.367691	+	0.636859i
$377$		−	0.360756i		−	0.0185799i
$378$	−1.15529	−	1.94587i	−0.0594218	−	0.100085i
$379$			8.44464i			0.433772i	0.976197	+	0.216886i	$0.0695900\pi$
$379$			8.44464i			0.433772i	−0.976197	+	0.216886i	$0.930410\pi$
$380$	−0.415540	−	0.239912i	−0.0213167	−	0.0123072i
$381$	5.77304	−	3.33306i	0.295762	−	0.170758i
$382$	3.80823	+	6.59604i	0.194846	+	0.337483i
$383$	8.26164	−	14.3096i	0.422150	−	0.731186i	−0.573999	−	0.818856i	$-0.694609\pi$
$383$	8.26164	−	14.3096i	0.422150	−	0.731186i	0.996150	+	0.0876701i	$0.0279421\pi$
$384$			7.49920i			0.382692i
$385$	43.8779	+	24.6249i	2.23622	+	1.25500i
$386$			12.1742i			0.619649i
$387$	−4.86667	+	8.42931i	−0.247387	+	0.428486i
$388$	−18.4294	+	10.6402i	−0.935610	+	0.540175i
$389$	−5.32338	−	9.22037i	−0.269906	−	0.467491i	0.698931	−	0.715189i	$-0.253659\pi$
$389$	−5.32338	−	9.22037i	−0.269906	−	0.467491i	−0.968837	+	0.247698i	$0.920326\pi$
$390$	−2.06956	+	3.58458i	−0.104796	+	0.181512i
$391$	−25.6536	+	19.5747i	−1.29736	+	0.989937i
$392$	−10.1946	−	16.7037i	−0.514905	−	0.843665i
$393$	−11.9003			−0.600290
$394$	−7.00303	−	4.04320i	−0.352807	−	0.203693i
$395$	1.42216	+	2.46325i	0.0715566	+	0.123940i
$396$	6.00328	−	3.46599i	0.301676	−	0.174173i
$397$	16.9769	+	9.80160i	0.852045	+	0.491928i	0.861340	−	0.508029i	$-0.169626\pi$
$397$	16.9769	+	9.80160i	0.852045	+	0.491928i	−0.00929557	+	0.999957i	$0.502959\pi$
$398$			7.99421i			0.400714i
$399$	0.140762	−	0.250817i	0.00704691	−	0.0125566i
$400$	−1.03583			−0.0517914
$401$	−4.28816	−	2.47577i	−0.214141	−	0.123634i	0.389094	−	0.921198i	$-0.372788\pi$
$401$	−4.28816	−	2.47577i	−0.214141	−	0.123634i	−0.603234	+	0.797564i	$0.706122\pi$
$402$	−2.00723	+	1.15888i	−0.100112	+	0.0577995i
$403$	6.01760	−	3.47427i	0.299758	−	0.173065i
$404$	−12.0026	+	20.7891i	−0.597151	+	1.03430i
$405$		−	3.47982i		−	0.172913i
$406$	−0.299699	−	0.504786i	−0.0148738	−	0.0250521i
$407$	1.63518			0.0810529
$408$	−1.47361	−	11.4318i	−0.0729545	−	0.565960i
$409$	5.73531	+	9.93385i	0.283593	+	0.491197i	0.972267	−	0.233874i	$-0.0751402\pi$
$409$	5.73531	+	9.93385i	0.283593	+	0.491197i	−0.688674	+	0.725071i	$0.741807\pi$
$410$	−7.00061	−	12.1254i	−0.345735	−	0.598831i
$411$	−6.24327	−	3.60456i	−0.307958	−	0.177800i
$412$	−11.9396			−0.588222
$413$	−0.210999	−	17.3129i	−0.0103826	−	0.851913i
$414$		−	6.69408i		−	0.328996i
$415$	−2.66083	−	1.53623i	−0.130615	−	0.0754105i
$416$	3.97432	+	6.88372i	0.194857	+	0.337502i
$417$	1.45917	+	2.52735i	0.0714557	+	0.123765i
$418$	−0.440073	−	0.254076i	−0.0215247	−	0.0124273i
$419$		−	19.5720i		−	0.956153i	−0.878318	−	0.478076i	$-0.841334\pi$
$419$		−	19.5720i		−	0.956153i	0.878318	−	0.478076i	$-0.158666\pi$
$420$	−0.142313	−	11.6771i	−0.00694417	−	0.569783i
$421$	−11.3303			−0.552207			−0.276103	−	0.961128i	$-0.589043\pi$
$421$	−11.3303			−0.552207			−0.276103	+	0.961128i	$0.589043\pi$
$422$	−20.3214	−	11.7326i	−0.989230	−	0.571132i
$423$	−2.55039	−	4.41741i	−0.124004	−	0.214782i
$424$	14.1063	+	24.4328i	0.685061	+	1.18656i
$425$	29.0711	−	3.74739i	1.41016	−	0.181775i
$426$	−12.6989			−0.615263
$427$	−3.73605	−	6.29265i	−0.180800	−	0.304523i
$428$		−	5.68149i		−	0.274625i
$429$	3.80002	−	6.58183i	0.183467	−	0.317774i
$430$	25.0889	−	14.4851i	1.20989	−	0.698532i
$431$	−18.0780	+	10.4374i	−0.870788	+	0.502750i	−0.867610	−	0.497245i	$-0.834345\pi$
$431$	−18.0780	+	10.4374i	−0.870788	+	0.502750i	−0.00317797	+	0.999995i	$0.501012\pi$
$432$	−0.126183	−	0.0728520i	−0.00607100	−	0.00350510i
$433$	−17.8246			−0.856598			−0.428299	−	0.903637i	$-0.640887\pi$
$433$	−17.8246			−0.856598			−0.428299	+	0.903637i	$0.640887\pi$
$434$	5.53385	−	9.86050i	0.265633	−	0.473319i
$435$		−	0.902715i		−	0.0432819i
$436$	16.7340	+	9.66140i	0.801415	+	0.462697i
$437$	0.736806	−	0.425395i	0.0352462	−	0.0203494i
$438$	−5.03850	−	8.72693i	−0.240749	−	0.416989i
$439$	9.79975	+	5.65789i	0.467717	+	0.270036i	0.715283	−	0.698834i	$-0.246298\pi$
$439$	9.79975	+	5.65789i	0.467717	+	0.270036i	−0.247567	+	0.968871i	$0.579631\pi$
$440$	−53.1646			−2.53452
$441$	6.99792	−	0.170598i	0.333234	−	0.00812372i
$442$	−2.97502	−	3.89889i	−0.141507	−	0.185451i
$443$	−16.1484	+	27.9699i	−0.767234	+	1.32889i	0.171823	+	0.985128i	$0.445034\pi$
$443$	−16.1484	+	27.9699i	−0.767234	+	1.32889i	−0.939057	+	0.343761i	$0.888299\pi$
$444$	−0.189758	−	0.328671i	−0.00900552	−	0.0155980i
$445$	−38.3276	+	22.1285i	−1.81690	+	1.04899i
$446$	−4.73422	+	8.19991i	−0.224172	+	0.388277i
$447$		−	10.3473i		−	0.489411i
$448$	10.6074	+	5.95301i	0.501152	+	0.281253i
$449$		−	20.6764i		−	0.975779i	−0.872905	−	0.487890i	$-0.837767\pi$
$449$		−	20.6764i		−	0.975779i	0.872905	−	0.487890i	$-0.162233\pi$
$450$	−3.04032	+	5.26598i	−0.143322	+	0.248241i
$451$	12.8542	+	22.2641i	0.605279	+	1.04837i
$452$	−9.54662	+	5.51175i	−0.449035	+	0.259251i
$453$	8.91068	+	5.14458i	0.418660	+	0.241714i
$454$		−	6.79244i		−	0.318785i
$455$	−6.53634	−	11.0092i	−0.306428	−	0.516120i
$456$			0.303902i			0.0142315i
$457$	−9.13954	+	15.8301i	−0.427530	+	0.740503i	−0.996653	−	0.0817492i	$-0.973949\pi$
$457$	−9.13954	+	15.8301i	−0.427530	+	0.740503i	0.569123	+	0.822252i	$0.307283\pi$
$458$	−4.77416	−	8.26909i	−0.223082	−	0.386389i
$459$	3.80497	+	1.58813i	0.177601	+	0.0741277i
$460$	17.2721	−	29.9162i	0.805317	−	1.39485i
$461$	−7.89112			−0.367526			−0.183763	−	0.982971i	$-0.558828\pi$
$461$	−7.89112			−0.367526			−0.183763	+	0.982971i	$0.558828\pi$
$462$	−0.150715	−	12.3665i	−0.00701190	−	0.575341i
$463$	24.5467			1.14078			0.570391	−	0.821374i	$-0.306792\pi$
$463$	24.5467			1.14078			0.570391	+	0.821374i	$0.306792\pi$
$464$	−0.0327338	−	0.0188989i	−0.00151963	−	0.000877358i
$465$	15.0578	−	8.69361i	0.698288	−	0.403157i
$466$	7.74949	−	4.47417i	0.358988	−	0.207262i
$467$	−2.15358	+	3.73012i	−0.0996560	+	0.172609i	−0.911542	−	0.411206i	$-0.865108\pi$
$467$	−2.15358	+	3.73012i	−0.0996560	+	0.172609i	0.811886	+	0.583816i	$0.198441\pi$
$468$	−1.76393			−0.0815375
$469$	−0.0873700	−	7.16888i	−0.00403437	−	0.331028i
$470$			15.1819i			0.700289i
$471$	0.480143	+	0.277210i	0.0221238	+	0.0127732i
$472$	9.14730	+	15.8436i	0.421039	+	0.729260i
$473$	−46.0669	+	26.5967i	−2.11816	+	1.22292i
$474$	0.349562	−	0.605459i	0.0160559	−	0.0278097i
$475$	−0.772824			−0.0354596
$476$	12.8332	+	5.17362i	0.588207	+	0.237133i
$477$	−10.0919			−0.462076
$478$	−13.1062	+	22.7007i	−0.599465	+	1.03830i
$479$	19.7124	−	11.3810i	0.900683	−	0.520010i	0.0232615	−	0.999729i	$-0.492595\pi$
$479$	19.7124	−	11.3810i	0.900683	−	0.520010i	0.877422	+	0.479720i	$0.159262\pi$
$480$	9.94489	+	17.2251i	0.453920	+	0.786213i
$481$	−0.360345	−	0.208045i	−0.0164303	−	0.00948606i
$482$			16.9503i			0.772064i
$483$	18.0572	+	10.1340i	0.821632	+	0.461111i
$484$	23.9313			1.08779
$485$	−29.1907	+	50.5599i	−1.32548	+	2.29580i
$486$	−0.740736	+	0.427664i	−0.0336004	+	0.0193992i
$487$	32.3009	−	18.6489i	1.46369	−	0.845064i	0.464514	−	0.885566i	$-0.346229\pi$
$487$	32.3009	−	18.6489i	1.46369	−	0.845064i	0.999179	+	0.0405022i	$0.0128958\pi$
$488$	6.69659	+	3.86628i	0.303140	+	0.175018i
$489$	4.34614			0.196539
$490$	−18.2919	−	9.97451i	−0.826343	−	0.450603i
$491$	−18.6183			−0.840234			−0.420117	−	0.907470i	$-0.638011\pi$
$491$	−18.6183			−0.840234			−0.420117	+	0.907470i	$0.638011\pi$
$492$	2.98338	−	5.16736i	0.134501	−	0.232963i
$493$	0.987065	+	0.411985i	0.0444552	+	0.0185549i
$494$	0.0646526	+	0.111982i	0.00290886	+	0.00503829i
$495$	9.50874	−	16.4696i	0.427386	−	0.740255i
$496$		−	0.728024i		−	0.0326892i
$497$	19.2244	−	34.2551i	0.862334	−	1.53655i
$498$			0.755200i			0.0338413i
$499$	0.0100555	+	0.00580553i	0.000450145	+	0.000259891i	0.500225	−	0.865895i	$-0.333251\pi$
$499$	0.0100555	+	0.00580553i	0.000450145	+	0.000259891i	−0.499775	+	0.866155i	$0.666584\pi$
$500$	−8.06215	+	4.65468i	−0.360550	+	0.208164i
$501$	−3.77434	−	6.53735i	−0.168625	−	0.292067i
$502$	9.23687	−	15.9987i	0.412262	−	0.714058i
$503$		−	5.38545i		−	0.240125i	−0.992766	−	0.120063i	$-0.961690\pi$
$503$		−	5.38545i		−	0.240125i	0.992766	−	0.120063i	$-0.0383096\pi$
$504$	−6.35990	+	3.77597i	−0.283293	+	0.168195i
$505$			65.8568i			2.93059i
$506$	18.2918	−	31.6824i	0.813172	−	1.40845i
$507$	9.58351	−	5.53304i	0.425618	−	0.245731i
$508$	−4.22771	−	7.32260i	−0.187574	−	0.324888i
$509$	4.05364	−	7.02111i	0.179674	−	0.311205i	−0.762095	−	0.647466i	$-0.775829\pi$
$509$	4.05364	−	7.02111i	0.179674	−	0.311205i	0.941769	+	0.336261i	$0.109162\pi$
$510$	−7.44435	−	9.75614i	−0.329641	−	0.432009i
$511$	31.1684	−	0.379862i	1.37881	−	0.0168041i
$512$	1.64746			0.0728081
$513$	−0.0941445	−	0.0543544i	−0.00415658	−	0.00239980i
$514$	−1.20466	−	2.08653i	−0.0531353	−	0.0920330i
$515$	−28.3672	+	16.3778i	−1.25001	+	0.721691i
$516$	10.6919	+	6.17295i	0.470683	+	0.271749i
$517$		−	27.8762i		−	1.22599i
$518$	−0.677046	+	0.00825143i	−0.0297477	+	0.000362547i
$519$	−10.1230			−0.444348
$520$	11.7159	+	6.76418i	0.513777	+	0.296629i
$521$	−9.90655	+	5.71955i	−0.434014	+	0.250578i	−0.701055	−	0.713107i	$-0.747287\pi$
$521$	−9.90655	+	5.71955i	−0.434014	+	0.250578i	0.267041	+	0.963685i	$0.413954\pi$
$522$	−0.192157	+	0.110942i	−0.00841050	+	0.00485581i
$523$	−19.0835	+	33.0535i	−0.834461	+	1.44533i	0.0600072	+	0.998198i	$0.480888\pi$
$523$	−19.0835	+	33.0535i	−0.834461	+	1.44533i	−0.894468	+	0.447131i	$0.852446\pi$
$524$			15.0945i			0.659407i
$525$	−9.60230	−	16.1732i	−0.419079	−	0.705858i
$526$	−14.7645			−0.643764
$527$	2.63382	+	20.4324i	0.114731	+	0.890050i
$528$	−0.398142	−	0.689603i	−0.0173269	−	0.0300111i
$529$	19.1257	+	33.1268i	0.831554	+	1.44029i
$530$	26.0131	+	15.0187i	1.12994	+	0.652369i
$531$	−6.54415			−0.283992
$532$	−0.318140	−	0.178545i	−0.0137931	−	0.00774089i
$533$		−	6.54178i		−	0.283356i
$534$	9.42080	+	5.43910i	0.407678	+	0.235373i
$535$	−7.79342	−	13.4986i	−0.336939	−	0.583595i
$536$	3.78769	+	6.56047i	0.163603	+	0.283369i
$537$	−1.16654	−	0.673502i	−0.0503399	−	0.0290638i
$538$			14.9174i			0.643137i
$539$	33.5866	+	18.3147i	1.44668	+	0.788869i
$540$	−4.41385			−0.189942
$541$	7.88022	+	4.54965i	0.338797	+	0.195605i	0.659740	−	0.751494i	$-0.270666\pi$
$541$	7.88022	+	4.54965i	0.338797	+	0.195605i	−0.320943	+	0.947099i	$0.604000\pi$
$542$	9.73454	+	16.8607i	0.418134	+	0.724230i
$543$	−3.60214	−	6.23909i	−0.154583	−	0.267745i
$544$	−23.3733	+	3.01291i	−1.00212	+	0.129177i
$545$	53.0109			2.27074
$546$	−1.54018	+	2.74438i	−0.0659138	+	0.117449i
$547$		−	6.27347i		−	0.268234i	−0.990965	−	0.134117i	$-0.957180\pi$
$547$		−	6.27347i		−	0.268234i	0.990965	−	0.134117i	$-0.0428198\pi$
$548$	−4.57207	+	7.91906i	−0.195309	+	0.338285i
$549$	−2.39543	+	1.38300i	−0.102235	+	0.0590251i
$550$	−28.7790	+	16.6156i	−1.22714	+	0.708491i
$551$	−0.0244224	−	0.0141003i	−0.00104043	−	0.000600693i
$552$	−21.8790			−0.931233
$553$	1.10403	+	1.85953i	0.0469481	+	0.0790751i
$554$			10.9721i			0.466159i
$555$	−0.901688	−	0.520590i	−0.0382745	−	0.0220978i
$556$	3.20573	−	1.85083i	0.135953	−	0.0784926i
$557$	15.4218	+	26.7114i	0.653444	+	1.13180i	0.982282	+	0.187411i	$0.0600097\pi$
$557$	15.4218	+	26.7114i	0.653444	+	1.13180i	−0.328838	+	0.944386i	$0.606657\pi$
$558$	−3.70115	−	2.13686i	−0.156682	−	0.0904605i
$559$	13.5357			0.572499
$560$	−1.34136	+	0.0163477i	−0.0566828	+	0.000690815i
$561$	13.6689	+	17.9137i	0.577103	+	0.756318i
$562$	6.74258	−	11.6785i	0.284419	−	0.492628i
$563$	0.552275	+	0.956569i	0.0232756	+	0.0403146i	0.877429	−	0.479707i	$-0.159257\pi$
$563$	0.552275	+	0.956569i	0.0232756	+	0.0403146i	−0.854153	+	0.520022i	$0.825924\pi$
$564$	−5.60311	+	3.23495i	−0.235933	+	0.136216i
$565$	−15.1211	+	26.1906i	−0.636151	+	1.10185i
$566$		−	17.3838i		−	0.730697i
$567$	−0.0322424	−	2.64555i	−0.00135405	−	0.111103i
$568$			41.5052i			1.74152i
$569$	−4.48955	+	7.77614i	−0.188212	+	0.325993i	−0.944654	−	0.328068i	$-0.893603\pi$
$569$	−4.48955	+	7.77614i	−0.188212	+	0.325993i	0.756442	+	0.654060i	$0.226936\pi$
$570$	0.161779	+	0.280210i	0.00677619	+	0.0117367i
$571$	−19.0666	+	11.0081i	−0.797913	+	0.460675i	−0.842741	−	0.538320i	$-0.819059\pi$
$571$	−19.0666	+	11.0081i	−0.797913	+	0.460675i	0.0448280	+	0.998995i	$0.485726\pi$
$572$	−8.34849	−	4.82000i	−0.349068	−	0.201534i
$573$			8.90472i			0.372000i
$574$	−5.43461	−	9.15356i	−0.226836	−	0.382062i
$575$		−	55.6384i		−	2.32028i
$576$	2.29872	−	3.98150i	0.0957799	−	0.165896i
$577$	−16.2300	−	28.1112i	−0.675665	−	1.17029i	−0.976274	−	0.216539i	$-0.930523\pi$
$577$	−16.2300	−	28.1112i	−0.675665	−	1.17029i	0.300609	−	0.953747i	$-0.402810\pi$
$578$	14.0653	−	3.68741i	0.585037	−	0.153376i
$579$	−7.11667	+	12.3264i	−0.295759	+	0.512269i
$580$	−1.14502			−0.0475442
$581$	−2.03715	−	1.14327i	−0.0845151	−	0.0474310i
$582$	14.3500			0.594826
$583$	−47.7639	−	27.5765i	−1.97818	−	1.14210i
$584$	−28.5232	+	16.4679i	−1.18030	+	0.681446i
$585$	−4.19089	+	2.41961i	−0.173272	+	0.100039i
$586$	1.82818	−	3.16649i	0.0755212	−	0.130807i
$587$	−48.2383			−1.99101			−0.995504	−	0.0947218i	$-0.969804\pi$
$587$	−48.2383			−1.99101			−0.995504	+	0.0947218i	$0.969804\pi$
$588$	−0.216389	−	8.87626i	−0.00892374	−	0.366051i
$589$		−	0.543173i		−	0.0223810i
$590$	16.8684	+	9.73895i	0.694459	+	0.400946i
$591$	−4.72708	−	8.18753i	−0.194446	−	0.336790i
$592$	−0.0377547	+	0.0217977i	−0.00155171	+	0.000895880i
$593$	5.37424	−	9.30846i	0.220694	−	0.382253i	−0.734325	−	0.678798i	$-0.762501\pi$
$593$	5.37424	−	9.30846i	0.220694	−	0.382253i	0.955019	+	0.296545i	$0.0958346\pi$
$594$	−4.67444			−0.191794
$595$	37.5869	−	5.31153i	1.54091	−	0.217752i
$596$	−13.1247			−0.537608
$597$	−4.67319	+	8.09420i	−0.191261	+	0.331273i
$598$	−8.06196	+	4.65458i	−0.329678	+	0.190340i
$599$	−6.19579	−	10.7314i	−0.253153	−	0.438474i	0.711239	−	0.702950i	$-0.248134\pi$
$599$	−6.19579	−	10.7314i	−0.253153	−	0.438474i	−0.964392	+	0.264476i	$0.914801\pi$
$600$	17.2114	+	9.93701i	0.702653	+	0.405677i
$601$			5.22221i			0.213018i	0.994312	+	0.106509i	$0.0339674\pi$
$601$			5.22221i			0.213018i	−0.994312	+	0.106509i	$0.966033\pi$
$602$	18.9398	−	11.2448i	0.771928	−	0.458305i
$603$	−2.70978			−0.110351
$604$	6.52546	−	11.3024i	0.265517	−	0.459890i
$605$	56.8582	−	32.8271i	2.31161	−	1.33461i
$606$	14.0187	−	8.09369i	0.569470	−	0.328784i
$607$	10.6423	+	6.14432i	0.431957	+	0.249390i	0.700180	−	0.713966i	$-0.253103\pi$
$607$	10.6423	+	6.14432i	0.431957	+	0.249390i	−0.268223	+	0.963357i	$0.586436\pi$
$608$	0.621352			0.0251992
$609$	−0.00836415	−	0.686295i	−0.000338932	−	0.0278101i
$610$	8.23270			0.333332
$611$	−3.54671	+	6.14309i	−0.143485	+	0.248523i
$612$	2.01441	−	4.82628i	0.0814278	−	0.195091i
$613$	−3.31113	−	5.73505i	−0.133735	−	0.231636i	0.791378	−	0.611327i	$-0.209364\pi$
$613$	−3.31113	−	5.73505i	−0.133735	−	0.231636i	−0.925114	+	0.379690i	$0.876031\pi$
$614$	−7.07739	+	12.2584i	−0.285620	+	0.494709i
$615$		−	16.3694i		−	0.660079i
$616$	−40.4188	+	0.492599i	−1.62852	+	0.0198474i
$617$		−	13.2526i		−	0.533528i	−0.963762	−	0.266764i	$-0.914046\pi$
$617$		−	13.2526i		−	0.533528i	0.963762	−	0.266764i	$-0.0859544\pi$
$618$	6.97255	+	4.02561i	0.280477	+	0.161934i
$619$	−2.16791	+	1.25165i	−0.0871358	+	0.0503079i	−0.542935	−	0.839775i	$-0.682687\pi$
$619$	−2.16791	+	1.25165i	−0.0871358	+	0.0503079i	0.455799	+	0.890083i	$0.349354\pi$
$620$	−11.0271	−	19.0995i	−0.442859	−	0.767054i
$621$	3.91317	−	6.77780i	0.157030	−	0.271984i
$622$		−	19.0747i		−	0.764824i
$623$	−28.9338	+	17.1784i	−1.15921	+	0.688240i
$624$			0.202624i			0.00811145i
$625$	5.00298	−	8.66541i	0.200119	−	0.346616i
$626$	9.71535	−	5.60916i	0.388303	−	0.224187i
$627$	−0.297051	−	0.514507i	−0.0118631	−	0.0205474i
$628$	0.351618	−	0.609020i	0.0140311	−	0.0243025i
$629$	0.980750	−	0.748353i	0.0391051	−	0.0298388i
$630$	−3.85398	+	6.86723i	−0.153546	+	0.273597i
$631$	12.8684			0.512282			0.256141	−	0.966639i	$-0.417549\pi$
$631$	12.8684			0.512282			0.256141	+	0.966639i	$0.417549\pi$
$632$	−1.97889	−	1.14251i	−0.0787161	−	0.0454467i
$633$	−13.7170	−	23.7586i	−0.545203	−	0.944320i
$634$	14.7034	−	8.48899i	0.583945	−	0.337141i
$635$	−20.0891	−	11.5985i	−0.797212	−	0.460271i
$636$			12.8007i			0.507581i
$637$	−5.07130	−	8.30927i	−0.200932	−	0.329225i
$638$	−1.21262			−0.0480079
$639$	−12.8577	−	7.42340i	−0.508643	−	0.293665i
$640$	22.5997	−	13.0479i	0.893330	−	0.515764i
$641$	40.5073	−	23.3869i	1.59994	−	0.923728i	0.608447	−	0.793595i	$-0.291793\pi$
$641$	40.5073	−	23.3869i	1.59994	−	0.923728i	0.991497	−	0.130133i	$-0.0415405\pi$
$642$	−1.91560	+	3.31791i	−0.0756026	+	0.130947i
$643$			28.0052i			1.10442i	0.833706	+	0.552208i	$0.186215\pi$
$643$			28.0052i			1.10442i	−0.833706	+	0.552208i	$0.813785\pi$
$644$	12.8541	−	22.9040i	0.506521	−	0.902545i
$645$	33.8702			1.33364
$646$	−0.380227	+	0.0490128i	−0.0149598	+	0.00192838i
$647$	−18.3842	−	31.8423i	−0.722756	−	1.25185i	−0.959891	−	0.280374i	$-0.909542\pi$
$647$	−18.3842	−	31.8423i	−0.722756	−	1.25185i	0.237134	−	0.971477i	$-0.423792\pi$
$648$	1.39778	+	2.42103i	0.0549101	+	0.0951071i
$649$	−30.9728	−	17.8822i	−1.21579	−	0.701936i
$650$	8.45606			0.331674
$651$	11.3672	−	6.74890i	0.445517	−	0.264510i
$652$		−	5.51271i		−	0.215894i
$653$	34.4488	+	19.8890i	1.34809	+	0.778318i	0.987978	−	0.154592i	$-0.0494064\pi$
$653$	34.4488	+	19.8890i	1.34809	+	0.778318i	0.360108	+	0.932910i	$0.382740\pi$
$654$	−6.51496	−	11.2842i	−0.254755	−	0.441249i
$655$	20.7054	+	35.8628i	0.809028	+	1.40128i
$656$	−0.593580	−	0.342704i	−0.0231754	−	0.0133803i
$657$		−	11.7814i		−	0.459638i
$658$	0.140669	+	11.5421i	0.00548383	+	0.449959i
$659$	−6.11119			−0.238058			−0.119029	−	0.992891i	$-0.537978\pi$
$659$	−6.11119			−0.238058			−0.119029	+	0.992891i	$0.537978\pi$
$660$	−20.8903	−	12.0610i	−0.813154	−	0.469475i
$661$	8.23748	+	14.2677i	0.320401	+	0.554951i	0.980571	−	0.196166i	$-0.0628490\pi$
$661$	8.23748	+	14.2677i	0.320401	+	0.554951i	−0.660170	+	0.751116i	$0.729516\pi$
$662$	−2.19247	−	3.79746i	−0.0852126	−	0.147593i
$663$	−0.733047	−	5.68676i	−0.0284692	−	0.220856i
$664$	2.46831			0.0957889
$665$	−1.00078	+	0.0121969i	−0.0388085	+	0.000472974i
$666$			0.255918i			0.00991664i
$667$	1.01513	−	1.75826i	0.0393061	−	0.0680801i
$668$	−8.29207	+	4.78743i	−0.320830	+	0.185231i
$669$	−9.58687	+	5.53498i	−0.370650	+	0.213995i
$670$	6.98481	+	4.03268i	0.269847	+	0.155796i
$671$	−15.1165			−0.583564
$672$	7.72027	+	13.0033i	0.297816	+	0.501614i
$673$		−	27.9597i		−	1.07777i	−0.842380	−	0.538884i	$-0.818846\pi$
$673$		−	27.9597i		−	1.07777i	0.842380	−	0.538884i	$-0.181154\pi$
$674$	−7.41307	−	4.27994i	−0.285541	−	0.164857i
$675$	−6.15668	+	3.55456i	−0.236971	+	0.136815i
$676$	−7.01819	−	12.1559i	−0.269930	−	0.467533i
$677$	25.5372	+	14.7439i	0.981475	+	0.566655i	0.902715	−	0.430239i	$-0.141571\pi$
$677$	25.5372	+	14.7439i	0.981475	+	0.566655i	0.0787601	+	0.996894i	$0.474904\pi$
$678$	7.43345			0.285480
$679$	−21.7240	+	38.7089i	−0.833691	+	1.48551i
$680$	−31.8871	+	24.3312i	−1.22282	+	0.933059i
$681$	3.97066	−	6.87739i	0.152156	−	0.263542i
$682$	−11.6781	−	20.2271i	−0.447178	−	0.774536i
$683$	−20.2085	+	11.6674i	−0.773256	+	0.446439i	−0.834035	−	0.551712i	$-0.813975\pi$
$683$	−20.2085	+	11.6674i	−0.773256	+	0.446439i	0.0607790	+	0.998151i	$0.480642\pi$
$684$	−0.0689438	+	0.119414i	−0.00263613	+	0.00456592i
$685$			25.0864i			0.958502i
$686$	−13.9990	−	7.41371i	−0.534483	−	0.283057i
$687$		−	11.1633i		−	0.425908i
$688$	0.709093	−	1.22819i	0.0270339	−	0.0468241i
$689$	7.01717	+	12.1541i	0.267333	+	0.463034i
$690$	−20.1733	+	11.6471i	−0.767986	+	0.443397i
$691$	3.64154	+	2.10245i	0.138531	+	0.0799808i	0.567664	−	0.823261i	$-0.307847\pi$
$691$	3.64154	+	2.10245i	0.138531	+	0.0799808i	−0.429133	+	0.903241i	$0.641181\pi$
$692$			12.8401i			0.488107i
$693$	7.07649	−	12.6093i	0.268814	−	0.478986i
$694$		−	14.2096i		−	0.539390i
$695$	5.07763	−	8.79471i	0.192605	−	0.333603i
$696$	0.362605	+	0.628050i	0.0137445	+	0.0238062i
$697$	17.8990	+	7.47074i	0.677973	+	0.282975i
$698$	−2.55358	+	4.42294i	−0.0966545	+	0.167411i
$699$	10.4619			0.395705
$700$	−20.5144	+	12.1797i	−0.775370	+	0.460349i
$701$	−11.9955			−0.453063			−0.226531	−	0.974004i	$-0.572739\pi$
$701$	−11.9955			−0.453063			−0.226531	+	0.974004i	$0.572739\pi$
$702$	1.03011	+	0.594733i	0.0388789	+	0.0224467i
$703$	−0.0281685	+	0.0162631i	−0.00106240	+	0.000613375i
$704$	21.7592	−	12.5627i	0.820081	−	0.473474i
$705$	−8.87490	+	15.3718i	−0.334248	+	0.578935i
$706$	27.4922			1.03468
$707$	0.610199	+	50.0680i	0.0229489	+	1.88300i
$708$			8.30070i			0.311959i
$709$	−42.8509	−	24.7400i	−1.60930	−	0.929129i	−0.989527	−	0.144346i	$-0.953892\pi$
$709$	−42.8509	−	24.7400i	−1.60930	−	0.929129i	−0.619771	−	0.784782i	$-0.712775\pi$
$710$	22.0949	+	38.2695i	0.829206	+	1.43623i
$711$	0.707868	−	0.408688i	0.0265471	−	0.0153270i
$712$	17.7772	−	30.7911i	0.666230	−	1.15394i
$713$	39.1050			1.46449
$714$	−5.75001	−	7.34820i	−0.215189	−	0.274999i
$715$	−26.4468			−0.989052
$716$	−0.854280	+	1.47966i	−0.0319259	+	0.0552974i
$717$	−26.5403	+	15.3230i	−0.991165	+	0.572250i
$718$	6.79855	+	11.7754i	0.253719	+	0.439455i
$719$	−8.39350	−	4.84599i	−0.313025	−	0.180725i	0.335255	−	0.942128i	$-0.391178\pi$
$719$	−8.39350	−	4.84599i	−0.313025	−	0.180725i	−0.648279	+	0.761403i	$0.724511\pi$
$720$			0.507024i			0.0188957i
$721$	−21.4146	+	12.7142i	−0.797520	+	0.473500i
$722$	−16.2411			−0.604432
$723$	−9.90864	+	17.1623i	−0.368506	+	0.638272i
$724$	−7.91375	+	4.56901i	−0.294112	+	0.169806i
$725$	−1.59713	+	0.922105i	−0.0593160	+	0.0342461i
$726$	−13.9756	−	8.06879i	−0.518681	−	0.299461i
$727$	27.2472			1.01054			0.505272	−	0.862960i	$-0.331392\pi$
$727$	27.2472			1.01054			0.505272	+	0.862960i	$0.331392\pi$
$728$	8.96977	+	5.03396i	0.332442	+	0.186571i
$729$	−1.00000			−0.0370370
$730$	−17.5330	+	30.3681i	−0.648927	+	1.12397i
$731$	−15.4578	+	37.0351i	−0.571728	+	1.36979i
$732$	1.75422	+	3.03840i	0.0648379	+	0.112303i
$733$	7.45384	−	12.9104i	0.275314	−	0.476858i	−0.694900	−	0.719106i	$-0.744551\pi$
$733$	7.45384	−	12.9104i	0.275314	−	0.476858i	0.970214	+	0.242248i	$0.0778848\pi$
$734$		−	17.5696i		−	0.648505i
$735$	−12.6899	−	20.7922i	−0.468072	−	0.766931i
$736$			44.7334i			1.64890i
$737$	−12.8251	−	7.40460i	−0.472420	−	0.272752i
$738$	−3.48450	+	2.01177i	−0.128266	+	0.0740545i
$739$	23.9688	+	41.5152i	0.881706	+	1.52716i	0.849443	+	0.527681i	$0.176938\pi$
$739$	23.9688	+	41.5152i	0.881706	+	1.52716i	0.0322633	+	0.999479i	$0.489728\pi$
$740$	−0.660323	+	1.14371i	−0.0242740	+	0.0420437i
$741$			0.151176i			0.00555360i
$742$	19.9158	+	11.1770i	0.731132	+	0.410321i
$743$		−	32.5861i		−	1.19547i	−0.801695	−	0.597734i	$-0.796068\pi$
$743$		−	32.5861i		−	1.19547i	0.801695	−	0.597734i	$-0.203932\pi$
$744$	−6.98415	+	12.0969i	−0.256051	+	0.443494i
$745$	−31.1828	+	18.0034i	−1.14245	+	0.659592i
$746$	7.17078	+	12.4202i	0.262541	+	0.454734i
$747$	−0.441468	+	0.764646i	−0.0161525	+	0.0279769i
$748$	22.7220	−	17.3379i	0.830800	−	0.633935i
$749$	−6.05007	−	10.1902i	−0.221065	−	0.372341i
$750$	6.27757			0.229224
$751$	0.565209	+	0.326323i	0.0206248	+	0.0119077i	0.510277	−	0.860010i	$-0.329543\pi$
$751$	0.565209	+	0.326323i	0.0206248	+	0.0119077i	−0.489652	+	0.871918i	$0.662876\pi$
$752$	0.371603	+	0.643635i	0.0135510	+	0.0234709i
$753$	18.7048	−	10.7992i	0.681641	−	0.393545i
$754$	0.267225	+	0.154282i	0.00973175	+	0.00561863i
$755$		−	35.8044i		−	1.30306i
$756$	−3.35566	+	0.0408967i	−0.122044	+	0.00148740i
$757$	46.1106			1.67592			0.837958	−	0.545734i	$-0.183749\pi$
$757$	46.1106			1.67592			0.837958	+	0.545734i	$0.183749\pi$
$758$	−6.25524	−	3.61147i	−0.227201	−	0.131174i
$759$	37.0413	−	21.3858i	1.34451	−	0.776255i
$760$	0.915843	−	0.528762i	0.0332211	−	0.0191802i
$761$	12.1554	−	21.0538i	0.440633	−	0.763198i	−0.557104	−	0.830443i	$-0.688087\pi$
$761$	12.1554	−	21.0538i	0.440633	−	0.763198i	0.997737	+	0.0672447i	$0.0214208\pi$
$762$			5.70172i			0.206552i
$763$	40.3019	−	0.491175i	1.45903	−	0.0177817i
$764$	11.2949			0.408634
$765$	−1.83429	−	14.2299i	−0.0663190	−	0.514484i
$766$	7.06641	+	12.2394i	0.255320	+	0.442227i
$767$	4.55033	+	7.88140i	0.164303	+	0.284581i
$768$	−13.5179	−	7.80457i	−0.487786	−	0.281623i
$769$	−30.7651			−1.10942			−0.554708	−	0.832045i	$-0.687170\pi$
$769$	−30.7651			−1.10942			−0.554708	+	0.832045i	$0.687170\pi$
$770$	−37.0055	+	21.9707i	−1.33359	+	0.791770i
$771$		−	2.81684i		−	0.101446i
$772$	15.6350	+	9.02688i	0.562717	+	0.324885i
$773$	−12.6353	−	21.8850i	−0.454460	−	0.787148i	0.544197	−	0.838958i	$-0.316834\pi$
$773$	−12.6353	−	21.8850i	−0.454460	−	0.787148i	−0.998657	+	0.0518096i	$0.983501\pi$
$774$	−4.16259	−	7.20983i	−0.149621	−	0.259152i
$775$	−30.7624	−	17.7607i	−1.10502	−	0.637983i
$776$		−	46.9017i		−	1.68367i
$777$	−0.690338	−	0.387427i	−0.0247657	−	0.0138989i
$778$	9.10648			0.326483
$779$	−0.442865	−	0.255688i	−0.0158673	−	0.00916099i
$780$	3.06907	+	5.31579i	0.109890	+	0.190336i
$781$	−40.5695	−	70.2684i	−1.45169	−	2.51440i
$782$	−3.52861	−	27.3739i	−0.126183	−	0.978889i
$783$	−0.259414			−0.00927071
$784$	−1.01963	+	0.0248568i	−0.0364152	+	0.000887745i
$785$		−	1.92928i		−	0.0688591i
$786$	5.08933	−	8.81497i	0.181530	−	0.314420i
$787$	40.5270	−	23.3983i	1.44463	−	0.834059i	0.446478	−	0.894795i	$-0.352678\pi$
$787$	40.5270	−	23.3983i	1.44463	−	0.834059i	0.998154	+	0.0607359i	$0.0193448\pi$
$788$	−10.3852	+	5.99589i	−0.369957	+	0.213595i
$789$	−14.9492	−	8.63092i	−0.532205	−	0.307269i
$790$	−2.43282			−0.0865560
$791$	−11.2533	+	20.0517i	−0.400120	+	0.712955i
$792$			15.2780i			0.542880i
$793$	3.33122	+	1.92328i	0.118295	+	0.0682977i
$794$	−14.5208	+	8.38358i	−0.515323	+	0.297522i
$795$	17.5590	+	30.4130i	0.622752	+	1.07864i
$796$	10.2668	+	5.92754i	0.363897	+	0.210096i
$797$	15.8181			0.560307			0.280154	−	0.959955i	$-0.409615\pi$
$797$	15.8181			0.560307			0.280154	+	0.959955i	$0.409615\pi$
$798$	0.125590	+	0.211533i	0.00444585	+	0.00748818i
$799$	−12.7578	−	16.7196i	−0.451337	−	0.591497i
$800$	20.3170	−	35.1901i	0.718315	−	1.24416i
$801$	6.35909	+	11.0143i	0.224687	+	0.389170i
$802$	3.66778	−	2.11760i	0.129514	−	0.0747749i
$803$	32.1933	−	55.7604i	1.13608	−	1.96774i
$804$			3.43713i			0.121218i
$805$	−0.878096	−	72.0496i	−0.0309488	−	2.53941i
$806$			5.94327i			0.209343i
$807$	−8.72031	+	15.1040i	−0.306969	+	0.531687i
$808$	−26.4535	−	45.8189i	−0.930632	−	1.61190i
$809$	21.2064	−	12.2435i	0.745577	−	0.430459i	−0.0785167	−	0.996913i	$-0.525018\pi$
$809$	21.2064	−	12.2435i	0.745577	−	0.430459i	0.824093	+	0.566454i	$0.191685\pi$
$810$	2.57762	+	1.48819i	0.0905685	+	0.0522897i
$811$		−	39.4999i		−	1.38703i	−0.720443	−	0.693514i	$-0.756062\pi$
$811$		−	39.4999i		−	1.38703i	0.720443	−	0.693514i	$-0.243938\pi$
$812$	−0.870506	+	0.0106092i	−0.0305488	+	0.000372310i
$813$			22.7621i			0.798303i
$814$	−0.699308	+	1.21124i	−0.0245107	+	0.0424538i
$815$	−7.56189	−	13.0976i	−0.264882	−	0.458788i
$816$	−0.554400	−	0.231398i	−0.0194079	−	0.00810053i
$817$	0.529049	−	0.916340i	0.0185091	−	0.0320587i
$818$	−9.81114			−0.343039
$819$	−3.16373	+	1.87836i	−0.110550	+	0.0656351i
$820$	−20.7632			−0.725083
$821$	−21.6405	−	12.4941i	−0.755257	−	0.436048i	0.0723330	−	0.997381i	$-0.476956\pi$
$821$	−21.6405	−	12.4941i	−0.755257	−	0.436048i	−0.827590	+	0.561332i	$0.810289\pi$
$822$	5.34005	−	3.08308i	0.186255	−	0.107535i
$823$	40.8882	−	23.6068i	1.42527	−	0.822881i	0.428529	−	0.903528i	$-0.359032\pi$
$823$	40.8882	−	23.6068i	1.42527	−	0.822881i	0.996743	+	0.0806465i	$0.0256985\pi$
$824$	13.1573	−	22.7892i	0.458358	−	0.793899i
$825$	−38.8520			−1.35265
$826$	12.9145	+	7.24781i	0.449354	+	0.252184i
$827$			29.0749i			1.01103i	0.862817	+	0.505516i	$0.168698\pi$
$827$			29.0749i			1.01103i	−0.862817	+	0.505516i	$0.831302\pi$
$828$	−8.59706	−	4.96352i	−0.298769	−	0.172494i
$829$	−14.0438	−	24.3246i	−0.487763	−	0.844830i	0.512138	−	0.858903i	$-0.328853\pi$
$829$	−14.0438	−	24.3246i	−0.487763	−	0.844830i	−0.999901	+	0.0140734i	$0.995520\pi$
$830$	2.27588	−	1.31398i	0.0789969	−	0.0456089i
$831$	−6.41397	+	11.1093i	−0.222498	+	0.385378i
$832$	−6.39345			−0.221653
$833$	28.5265	−	4.38639i	0.988384	−	0.151979i
$834$	−2.49613			−0.0864339
$835$	−13.1340	+	22.7488i	−0.454522	+	0.787255i
$836$	−0.652609	+	0.376784i	−0.0225709	+	0.0130313i
$837$	−2.49830	−	4.32717i	−0.0863537	−	0.149569i
$838$	14.4976	+	8.37022i	0.500813	+	0.289144i
$839$		−	10.1348i		−	0.349894i	−0.984578	−	0.174947i	$-0.944025\pi$
$839$		−	10.1348i		−	0.349894i	0.984578	−	0.174947i	$-0.0559754\pi$
$840$	22.4450	+	12.5964i	0.774424	+	0.434618i
$841$	28.9327			0.997679
$842$	4.84557	−	8.39278i	0.166990	−	0.289234i
$843$	13.6538	−	7.88304i	0.470263	−	0.271506i
$844$	−30.1358	+	17.3989i	−1.03732	+	0.598894i
$845$	−33.3488	−	19.2540i	−1.14724	−	0.662357i
$846$	4.36284			0.149998
$847$	42.9227	−	25.4838i	1.47484	−	0.875635i
$848$	1.47043			0.0504948
$849$	10.1621	−	17.6013i	0.348762	−	0.604074i
$850$	−9.65686	+	23.1367i	−0.331227	+	0.793581i
$851$	−1.17084	−	2.02795i	−0.0401359	−	0.0695174i
$852$	−9.41595	+	16.3089i	−0.322585	+	0.558734i
$853$			1.18412i			0.0405436i	0.999795	+	0.0202718i	$0.00645316\pi$
$853$			1.18412i			0.0405436i	−0.999795	+	0.0202718i	$0.993547\pi$
$854$	6.25896	−	0.0762804i	0.214177	−	0.00261026i
$855$			0.378286i			0.0129371i
$856$	10.8443	+	6.26096i	0.370651	+	0.213995i
$857$	−2.52256	+	1.45640i	−0.0861689	+	0.0497496i	−0.542465	−	0.840078i	$-0.682509\pi$
$857$	−2.52256	+	1.45640i	−0.0861689	+	0.0497496i	0.456296	+	0.889828i	$0.349176\pi$
$858$	3.25026	+	5.62962i	0.110962	+	0.192192i
$859$	−17.0286	+	29.4943i	−0.581007	+	1.00633i	0.414353	+	0.910116i	$0.364008\pi$
$859$	−17.0286	+	29.4943i	−0.581007	+	1.00633i	−0.995360	+	0.0962176i	$0.969326\pi$
$860$		−	42.9615i		−	1.46497i
$861$	−0.151672	−	12.4450i	−0.00516895	−	0.424123i
$862$		−	17.8547i		−	0.608134i
$863$	−6.84651	+	11.8585i	−0.233058	+	0.403668i	−0.958707	−	0.284397i	$-0.908207\pi$
$863$	−6.84651	+	11.8585i	−0.233058	+	0.403668i	0.725649	+	0.688066i	$0.241540\pi$
$864$	4.94999	−	2.85788i	0.168402	−	0.0972270i
$865$	17.6130	+	30.5066i	0.598860	+	1.03726i
$866$	7.62295	−	13.2033i	0.259039	−	0.448668i
$867$	16.3967	+	4.48862i	0.556862	+	0.152441i
$868$	−8.56040	−	14.4184i	−0.290559	−	0.489391i
$869$	4.46703			0.151533
$870$	0.668673	+	0.386058i	0.0226701	+	0.0130886i
$871$	1.88419	+	3.26351i	0.0638432	+	0.110580i
$872$	−36.8816	+	21.2936i	−1.24897	+	0.721091i
$873$	14.5295	+	8.38859i	0.491748	+	0.283911i
$874$			0.727705i			0.0246150i
$875$	−9.50342	+	16.9337i	−0.321274	+	0.572463i
$876$	−14.9437			−0.504902
$877$	43.5401	+	25.1379i	1.47025	+	0.848847i	0.999442	−	0.0333913i	$-0.0106307\pi$
$877$	43.5401	+	25.1379i	1.47025	+	0.848847i	0.470804	+	0.882238i	$0.343964\pi$
$878$	−8.38200	+	4.83935i	−0.282879	+	0.163320i
$879$	3.70208	−	2.13740i	0.124868	−	0.0720926i
$880$	−1.38546	+	2.39969i	−0.0467039	+	0.0808936i
$881$			23.7461i			0.800027i	0.916509	+	0.400013i	$0.130995\pi$
$881$			23.7461i			0.800027i	−0.916509	+	0.400013i	$0.869005\pi$
$882$	−2.86639	+	5.25657i	−0.0965164	+	0.176998i
$883$	−20.1850			−0.679279			−0.339639	−	0.940556i	$-0.610305\pi$
$883$	−20.1850			−0.679279			−0.339639	+	0.940556i	$0.610305\pi$
$884$	−7.21317	+	0.929807i	−0.242605	+	0.0312728i
$885$	11.3862	+	19.7215i	0.382744	+	0.662932i
$886$	−13.8122	−	23.9234i	−0.464029	−	0.803722i
$887$	30.5975	+	17.6655i	1.02736	+	0.593149i	0.916229	−	0.400656i	$-0.131218\pi$
$887$	30.5975	+	17.6655i	1.02736	+	0.593149i	0.111136	+	0.993805i	$0.464551\pi$
$888$	0.836448			0.0280693
$889$	−15.3804	−	8.63167i	−0.515840	−	0.289497i
$890$		−	37.8542i		−	1.26887i
$891$	−4.73290	−	2.73254i	−0.158558	−	0.0915436i
$892$	7.02065	+	12.1601i	0.235069	+	0.407151i
$893$	0.277250	+	0.480211i	0.00927781	+	0.0160696i
$894$	7.66462	+	4.42517i	0.256343	+	0.148000i
$895$			4.68733i			0.156680i
$896$	17.0606	−	10.1292i	0.569956	−	0.338392i
$897$	−10.8837			−0.363397
$898$	15.3157	+	8.84254i	0.511093	+	0.295080i
$899$	−0.648094	−	1.12253i	−0.0216151	−	0.0374385i
$900$	4.50866	+	7.80923i	0.150289	+	0.260308i
$901$	−41.2685	+	5.31967i	−1.37485	+	0.177224i
$902$	−21.9890			−0.732155
$903$	25.7501	−	0.313826i	0.856908	−	0.0104435i
$904$		−	24.2956i		−	0.808060i
$905$	−12.5348	+	21.7109i	−0.416671	+	0.721695i
$906$	−7.62155	+	4.40030i	−0.253209	+	0.146190i
$907$	−30.2873	+	17.4864i	−1.00567	+	0.580626i	−0.909922	−	0.414780i	$-0.863859\pi$
$907$	−30.2873	+	17.4864i	−1.00567	+	0.580626i	−0.0957512	+	0.995405i	$0.530525\pi$
$908$	−8.72338	−	5.03645i	−0.289496	−	0.167140i
$909$	18.9253			0.627714
$910$	10.9503	−	0.133455i	0.362998	−	0.00442400i
$911$			43.9551i			1.45630i	0.685420	+	0.728148i	$0.259619\pi$
$911$			43.9551i			1.45630i	−0.685420	+	0.728148i	$0.740381\pi$
$912$	0.0137172	+	0.00791965i	0.000454223	+	0.000262246i
$913$	−4.17885	+	2.41266i	−0.138300	+	0.0798474i
$914$	−7.81730	−	13.5400i	−0.258573	−	0.447862i
$915$	8.33566	+	4.81260i	0.275569	+	0.159100i
$916$	−14.1598			−0.467851
$917$	16.0737	+	27.0731i	0.530801	+	0.894033i
$918$	−2.80364	+	2.13929i	−0.0925338	+	0.0706072i
$919$	30.1274	−	52.1821i	0.993810	−	1.72133i	0.400699	−	0.916210i	$-0.368767\pi$
$919$	30.1274	−	52.1821i	0.993810	−	1.72133i	0.593111	−	0.805121i	$-0.297900\pi$
$920$	38.0675	+	65.9348i	1.25505	+	2.17381i
$921$	−14.3318	+	8.27448i	−0.472250	+	0.272653i
$922$	3.37475	−	5.84523i	0.111141	−	0.192502i
$923$			20.6468i			0.679596i
$924$	−15.9938	−	8.97592i	−0.526156	−	0.295286i
$925$			2.12709i			0.0699382i
$926$	−10.4977	+	18.1826i	−0.344977	+	0.597517i
$927$	4.70651	+	8.15191i	0.154582	+	0.267744i
$928$	1.28410	−	0.741375i	0.0421526	−	0.0243368i
$929$	−12.7974	−	7.38857i	−0.419869	−	0.242411i	0.275153	−	0.961401i	$-0.411272\pi$
$929$	−12.7974	−	7.38857i	−0.419869	−	0.242411i	−0.695021	+	0.718989i	$0.744605\pi$
$930$			14.8718i			0.487665i
$931$	−0.760735	+	0.0185455i	−0.0249321	+	0.000607804i
$932$		−	13.2700i		−	0.434673i
$933$	11.1505	−	19.3132i	0.365051	−	0.632286i
$934$	−1.84202	−	3.19047i	−0.0602727	−	0.104395i
$935$	30.2023	−	72.3611i	0.987721	−	2.36646i
$936$	1.94383	−	3.36682i	0.0635362	−	0.110048i
$937$	−39.4105			−1.28749			−0.643743	−	0.765242i	$-0.722619\pi$
$937$	−39.4105			−1.28749			−0.643743	+	0.765242i	$0.722619\pi$
$938$	5.34761	+	3.00115i	0.174606	+	0.0979912i
$939$	13.1158			0.428018
$940$	19.4978	+	11.2570i	0.635948	+	0.367164i
$941$	22.3698	−	12.9152i	0.729234	−	0.421024i	−0.0889076	−	0.996040i	$-0.528338\pi$
$941$	22.3698	−	12.9152i	0.729234	−	0.421024i	0.818142	+	0.575016i	$0.195004\pi$
$942$	−0.410679	+	0.237106i	−0.0133807	+	0.00772532i
$943$	18.4079	−	31.8835i	0.599445	−	1.03827i
$944$	0.953510			0.0310341
$945$	−7.91657	+	4.70019i	−0.257526	+	0.152897i
$946$		−	45.4978i		−	1.47926i
$947$	22.5513	+	13.0200i	0.732820	+	0.423094i	0.819453	−	0.573147i	$-0.194277\pi$
$947$	22.5513	+	13.0200i	0.732820	+	0.423094i	−0.0866331	+	0.996240i	$0.527611\pi$
$948$	−0.518386	−	0.897870i	−0.0168364	−	0.0291615i
$949$	−14.1889	+	8.19196i	−0.460591	+	0.265922i
$950$	0.330509	−	0.572458i	0.0107231	−	0.0185730i
$951$	19.8497			0.643670
$952$	−24.0170	+	18.7934i	−0.778394	+	0.609098i
$953$	−19.3107			−0.625534			−0.312767	−	0.949830i	$-0.601256\pi$
$953$	−19.3107			−0.625534			−0.312767	+	0.949830i	$0.601256\pi$
$954$	4.31594	−	7.47542i	0.139734	−	0.242026i
$955$	26.8354	−	15.4934i	0.868372	−	0.501355i
$956$	19.4360	+	33.6641i	0.628604	+	1.08877i
$957$	−1.22778	−	0.708861i	−0.0396886	−	0.0229142i
$958$			19.4689i			0.629012i
$959$	0.232439	+	19.0721i	0.00750585	+	0.615870i
$960$	−15.9982			−0.516341
$961$	−3.01704	+	5.22567i	−0.0973240	+	0.168570i
$962$	0.308213	−	0.177947i	0.00993720	−	0.00573724i
$963$	−3.87911	+	2.23960i	−0.125003	+	0.0721703i
$964$	21.7689	+	12.5683i	0.701128	+	0.404797i
$965$	49.5294			1.59441
$966$	−15.2290	+	9.04169i	−0.489985	+	0.290912i
$967$	8.43124			0.271130			0.135565	−	0.990768i	$-0.456715\pi$
$967$	8.43124			0.271130			0.135565	+	0.990768i	$0.456715\pi$
$968$	−26.3721	+	45.6779i	−0.847633	+	1.46814i
$969$	−0.413634	−	0.172644i	−0.0132878	−	0.00554612i
$970$	−24.9677	−	43.2453i	−0.801663	−	1.38852i
$971$	29.2394	−	50.6442i	0.938338	−	1.62525i	0.169768	−	0.985484i	$-0.445698\pi$
$971$	29.2394	−	50.6442i	0.938338	−	1.62525i	0.768570	−	0.639766i	$-0.220969\pi$
$972$			1.26841i			0.0406844i
$973$	3.77882	−	6.73329i	0.121143	−	0.215859i
$974$			31.9019i			1.02220i
$975$	8.56182	+	4.94317i	0.274198	+	0.158308i
$976$	0.349024	−	0.201509i	0.0111720	−	0.00645015i
$977$	10.5375	+	18.2514i	0.337124	+	0.583915i	0.983890	−	0.178773i	$-0.0572126\pi$
$977$	10.5375	+	18.2514i	0.337124	+	0.583915i	−0.646767	+	0.762688i	$0.723879\pi$
$978$	−1.85869	+	3.21934i	−0.0594343	+	0.102943i
$979$			69.5059i			2.22142i
$980$	−26.3731	+	16.0960i	−0.842458	+	0.514168i
$981$		−	15.2338i		−	0.486379i
$982$	7.96239	−	13.7913i	0.254090	−	0.440097i
$983$	27.4558	−	15.8516i	0.875705	−	0.505588i	0.00646480	−	0.999979i	$-0.497942\pi$
$983$	27.4558	−	15.8516i	0.875705	−	0.505588i	0.869240	+	0.494391i	$0.164609\pi$
$984$	6.57531	+	11.3888i	0.209613	+	0.363061i
$985$	−16.4494	+	28.4911i	−0.524120	+	0.907803i
$986$	−0.727304	+	0.554963i	−0.0231621	+	0.0176736i
$987$	−6.60477	+	11.7687i	−0.210232	+	0.374603i
$988$	0.191754			0.00610051
$989$	65.9706	+	38.0881i	2.09774	+	1.21113i
$990$	8.13309	+	14.0869i	0.258487	+	0.447712i
$991$	−0.617932	+	0.356763i	−0.0196293	+	0.0113330i	−0.509783	−	0.860303i	$-0.670274\pi$
$991$	−0.617932	+	0.356763i	−0.0196293	+	0.0113330i	0.490153	+	0.871636i	$0.336941\pi$
$992$	24.7331	+	14.2796i	0.785276	+	0.453379i
$993$		−	5.12661i		−	0.162688i
$994$	17.1524	+	28.8899i	0.544040	+	0.916332i
$995$	32.5237			1.03107
$996$	0.969888	+	0.559965i	0.0307321	+	0.0177432i
$997$	−29.5045	+	17.0344i	−0.934417	+	0.539486i	−0.888206	−	0.459446i	$-0.848048\pi$
$997$	−29.5045	+	17.0344i	−0.934417	+	0.539486i	−0.0462114	+	0.998932i	$0.514715\pi$
$998$	−0.00860073	+	0.00496563i	−0.000272251	+	0.000157184i
$999$	−0.149603	+	0.259119i	−0.00473322	+	0.00819817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.p.a.16.9	✓	48
7.4	even	3	inner	357.2.p.a.67.10	yes	48
17.16	even	2	inner	357.2.p.a.16.10	yes	48
119.67	even	6	inner	357.2.p.a.67.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.p.a.16.9	✓	48	1.1	even	1	trivial
357.2.p.a.16.10	yes	48	17.16	even	2	inner
357.2.p.a.67.9	yes	48	119.67	even	6	inner
357.2.p.a.67.10	yes	48	7.4	even	3	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.427664 + 0.740736i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.634207 + 1.09848i) q^{4} +(3.01361 + 1.73991i) q^{5} -0.855328i q^{6} +(2.30724 + 1.29485i) q^{7} -2.79557 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.427664 + 0.740736i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.634207 + 1.09848i) q^{4} +(3.01361 + 1.73991i) q^{5} -0.855328i q^{6} +(2.30724 + 1.29485i) q^{7} -2.79557 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.57762 + 1.48819i) q^{10} +(4.73290 - 2.73254i) q^{11} +(-1.09848 - 0.634207i) q^{12} -1.39065 q^{13} +(-1.94587 + 1.15529i) q^{14} -3.47982 q^{15} +(-0.0728520 + 0.126183i) q^{16} +(1.58813 - 3.80497i) q^{17} +(0.427664 + 0.740736i) q^{18} +(-0.0543544 + 0.0941445i) q^{19} +4.41385i q^{20} +(-2.64555 + 0.0322424i) q^{21} +4.67444i q^{22} +(-6.77780 - 3.91317i) q^{23} +(2.42103 - 1.39778i) q^{24} +(3.55456 + 6.15668i) q^{25} +(0.594733 - 1.03011i) q^{26} +1.00000i q^{27} +(0.0408967 + 3.35566i) q^{28} +0.259414i q^{29} +(1.48819 - 2.57762i) q^{30} +(-4.32717 + 2.49830i) q^{31} +(-2.85788 - 4.94999i) q^{32} +(-2.73254 + 4.73290i) q^{33} +(2.13929 + 2.80364i) q^{34} +(4.70019 + 7.91657i) q^{35} +1.26841 q^{36} +(0.259119 + 0.149603i) q^{37} +(-0.0464908 - 0.0805244i) q^{38} +(1.20434 - 0.695327i) q^{39} +(-8.42474 - 4.86403i) q^{40} +4.70410i q^{41} +(1.10753 - 1.97345i) q^{42} -9.73333 q^{43} +(6.00328 + 3.46599i) q^{44} +(3.01361 - 1.73991i) q^{45} +(5.79724 - 3.34704i) q^{46} +(2.55039 - 4.41741i) q^{47} -0.145704i q^{48} +(3.64670 + 5.97508i) q^{49} -6.08063 q^{50} +(0.527124 + 4.08927i) q^{51} +(-0.881963 - 1.52760i) q^{52} +(-5.04594 - 8.73983i) q^{53} +(-0.740736 - 0.427664i) q^{54} +19.0175 q^{55} +(-6.45004 - 3.61985i) q^{56} -0.108709i q^{57} +(-0.192157 - 0.110942i) q^{58} +(-3.27208 - 5.66740i) q^{59} +(-2.20693 - 3.82251i) q^{60} +(-2.39543 - 1.38300i) q^{61} -4.27372i q^{62} +(2.27500 - 1.35070i) q^{63} +4.59744 q^{64} +(-4.19089 - 2.41961i) q^{65} +(-2.33722 - 4.04818i) q^{66} +(-1.35489 - 2.34674i) q^{67} +(5.18689 - 0.668611i) q^{68} +7.82633 q^{69} +(-7.87419 + 0.0959658i) q^{70} -14.8468i q^{71} +(-1.39778 + 2.42103i) q^{72} +(10.2030 - 5.89072i) q^{73} +(-0.221632 + 0.127959i) q^{74} +(-6.15668 - 3.55456i) q^{75} -0.137888 q^{76} +(14.4582 - 0.176207i) q^{77} +1.18947i q^{78} +(0.707868 + 0.408688i) q^{79} +(-0.439095 + 0.253512i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.48450 - 2.01177i) q^{82} -0.882937 q^{83} +(-1.71325 - 2.88564i) q^{84} +(11.4063 - 8.70350i) q^{85} +(4.16259 - 7.20983i) q^{86} +(-0.129707 - 0.224659i) q^{87} +(-13.2311 + 7.63900i) q^{88} +(-6.35909 + 11.0143i) q^{89} +2.97638i q^{90} +(-3.20857 - 1.80070i) q^{91} -9.92703i q^{92} +(2.49830 - 4.32717i) q^{93} +(2.18142 + 3.77833i) q^{94} +(-0.327606 + 0.189143i) q^{95} +(4.94999 + 2.85788i) q^{96} +16.7772i q^{97} +(-5.98552 + 0.145917i) q^{98} -5.46508i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) \) 48 * q - 24 * q^4 + 24 * q^9	\( 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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