LMFDB - Embedded newform 825.2.cb.a.169.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(169,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("825.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.cb (of order $10$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.16
Character	$\chi$	$=$	825.169
Dual form			825.2.cb.a.454.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41304 - 0.459125i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.167853 + 0.121952i) q^{4} +(1.85059 + 1.25512i) q^{5} -1.48576 q^{6} +(1.08303 - 0.351897i) q^{7} +(1.56542 + 2.15462i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-2.03870 - 2.62318i) q^{10} +(2.38514 - 2.30458i) q^{11} +(0.197323 + 0.0641141i) q^{12} +(0.944395 + 1.29985i) q^{13} -1.69193 q^{14} +(2.14787 + 0.621823i) q^{15} +(-1.35099 - 4.15793i) q^{16} +0.334780i q^{17} +(-1.41304 + 0.459125i) q^{18} +(-1.89006 + 1.37321i) q^{19} +(0.157563 + 0.436359i) q^{20} +(0.921279 - 0.669348i) q^{21} +(-4.42839 + 2.16139i) q^{22} +(-0.809321 + 0.262964i) q^{23} +(2.15462 + 1.56542i) q^{24} +(1.84937 + 4.64541i) q^{25} +(-0.737676 - 2.27033i) q^{26} +(0.587785 - 0.809017i) q^{27} +(0.224704 + 0.0730108i) q^{28} +(4.38760 + 3.18778i) q^{29} +(-2.74953 - 1.86480i) q^{30} +(1.10692 + 3.40675i) q^{31} +1.16909i q^{32} +(1.55625 - 2.92884i) q^{33} +(0.153706 - 0.473057i) q^{34} +(2.44591 + 0.708109i) q^{35} +0.207478 q^{36} -3.52650i q^{37} +(3.30120 - 1.07263i) q^{38} +(1.29985 + 0.944395i) q^{39} +(0.192658 + 5.95210i) q^{40} +(-3.12877 - 2.27318i) q^{41} +(-1.60912 + 0.522834i) q^{42} +10.1739i q^{43} +(0.681402 - 0.0959571i) q^{44} +(2.23490 - 0.0723392i) q^{45} +1.26434 q^{46} +(12.8598 - 4.17842i) q^{47} +(-2.56974 - 3.53695i) q^{48} +(-4.61400 + 3.35227i) q^{49} +(-0.480407 - 7.41324i) q^{50} +(0.103453 + 0.318395i) q^{51} +0.333354i q^{52} -7.48023i q^{53} +(-1.20200 + 0.873307i) q^{54} +(7.30644 - 1.27120i) q^{55} +(2.45360 + 1.78264i) q^{56} +(-1.37321 + 1.89006i) q^{57} +(-4.73627 - 6.51892i) q^{58} +1.60356 q^{59} +(0.284693 + 0.366312i) q^{60} +(-10.8237 - 7.86389i) q^{61} -5.32208i q^{62} +(0.669348 - 0.921279i) q^{63} +(-2.16523 + 6.66389i) q^{64} +(0.116227 + 3.59081i) q^{65} +(-3.54375 + 3.42405i) q^{66} +(4.82355 - 6.63904i) q^{67} +(-0.0408272 + 0.0561938i) q^{68} +(-0.688449 + 0.500188i) q^{69} +(-3.13106 - 2.12356i) q^{70} +(3.00001 - 9.23308i) q^{71} +(2.53291 + 0.822991i) q^{72} +(9.41599 + 12.9600i) q^{73} +(-1.61910 + 4.98309i) q^{74} +(3.19436 + 3.84656i) q^{75} -0.484718 q^{76} +(1.77220 - 3.33525i) q^{77} +(-1.40314 - 1.93126i) q^{78} -3.20383 q^{79} +(2.71855 - 9.39028i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.37740 + 4.64859i) q^{82} -7.65826i q^{83} +0.236268 q^{84} +(-0.420188 + 0.619540i) q^{85} +(4.67108 - 14.3761i) q^{86} +(5.15794 + 1.67592i) q^{87} +(8.69925 + 1.53143i) q^{88} +(-0.641628 - 1.97473i) q^{89} +(-3.19121 - 0.923878i) q^{90} +(1.48022 + 1.07544i) q^{91} +(-0.167916 - 0.0545592i) q^{92} +(2.10548 + 2.89795i) q^{93} -20.0899 q^{94} +(-5.22126 + 0.169002i) q^{95} +(0.361268 + 1.11187i) q^{96} -8.64882i q^{97} +(8.05888 - 2.61849i) q^{98} +(0.575022 - 3.26640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 60 q^{4} + 6 q^{5} - 16 q^{6} + 10 q^{7} + 60 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} - 64 q^{16} - 24 q^{19} - 44 q^{20} + 8 q^{21} - 40 q^{22} + 40 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{26} + 30 q^{28}+ \cdots - 4 q^{99}+O(q^{100}) $ 240 * q + 60 * q^4 + 6 * q^5 - 16 * q^6 + 10 * q^7 + 60 * q^9 + 8 * q^10 + 4 * q^11 - 20 * q^12 - 64 * q^16 - 24 * q^19 - 44 * q^20 + 8 * q^21 - 40 * q^22 + 40 * q^23 - 12 * q^24 + 4 * q^25 + 40 * q^26 + 30 * q^28 + 4 * q^30 - 2 * q^31 + 30 * q^35 + 240 * q^36 - 16 * q^39 + 68 * q^40 - 6 * q^41 - 10 * q^42 + 26 * q^44 + 4 * q^45 - 48 * q^46 - 40 * q^47 + 40 * q^48 + 58 * q^49 - 78 * q^50 + 16 * q^51 - 4 * q^54 - 10 * q^55 - 40 * q^57 + 60 * q^58 - 24 * q^59 + 8 * q^60 + 28 * q^61 - 10 * q^63 + 44 * q^64 + 60 * q^65 + 8 * q^66 - 40 * q^67 - 250 * q^68 + 2 * q^69 - 44 * q^70 - 16 * q^71 + 22 * q^74 + 20 * q^75 - 168 * q^76 - 30 * q^77 + 172 * q^79 - 118 * q^80 - 60 * q^81 + 40 * q^82 + 96 * q^84 + 40 * q^85 - 72 * q^86 - 40 * q^87 - 100 * q^88 + 2 * q^90 - 30 * q^91 + 100 * q^92 + 56 * q^94 - 122 * q^95 + 28 * q^96 - 140 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−1.41304	−	0.459125i	−0.999170	−	0.324650i	−0.236636	−	0.971598i	$-0.576045\pi$
$2$	−1.41304	−	0.459125i	−0.999170	−	0.324650i	−0.762534	+	0.646948i	$0.776045\pi$
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	0.167853	+	0.121952i	0.0839265	+	0.0609762i
$5$	1.85059	+	1.25512i	0.827609	+	0.561305i
$5$	1.85059	+	1.25512i	0.827609	+	0.561305i
$6$	−1.48576			−0.606558
$7$	1.08303	−	0.351897i	0.409346	−	0.133005i	−0.0971033	−	0.995274i	$-0.530958\pi$
$7$	1.08303	−	0.351897i	0.409346	−	0.133005i	0.506449	+	0.862270i	$0.330958\pi$
$8$	1.56542	+	2.15462i	0.553460	+	0.761773i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	−2.03870	−	2.62318i	−0.644695	−	0.829523i
$11$	2.38514	−	2.30458i	0.719148	−	0.694857i
$11$	2.38514	−	2.30458i	0.719148	−	0.694857i
$12$	0.197323	+	0.0641141i	0.0569622	+	0.0185082i
$13$	0.944395	+	1.29985i	0.261928	+	0.360513i	0.919644	−	0.392753i	$-0.128477\pi$
$13$	0.944395	+	1.29985i	0.261928	+	0.360513i	−0.657716	+	0.753266i	$0.728477\pi$
$14$	−1.69193			−0.452186
$15$	2.14787	+	0.621823i	0.554577	+	0.160554i
$16$	−1.35099	−	4.15793i	−0.337748	−	1.03948i
$17$			0.334780i			0.0811960i	0.999176	+	0.0405980i	$0.0129263\pi$
$17$			0.334780i			0.0811960i	−0.999176	+	0.0405980i	$0.987074\pi$
$18$	−1.41304	+	0.459125i	−0.333057	+	0.108217i
$19$	−1.89006	+	1.37321i	−0.433609	+	0.315035i	−0.783090	−	0.621908i	$-0.786358\pi$
$19$	−1.89006	+	1.37321i	−0.433609	+	0.315035i	0.349481	+	0.936943i	$0.386358\pi$
$20$	0.157563	+	0.436359i	0.0352321	+	0.0975728i
$21$	0.921279	−	0.669348i	0.201039	−	0.146064i
$22$	−4.42839	+	2.16139i	−0.944136	+	0.460809i
$23$	−0.809321	+	0.262964i	−0.168755	+	0.0548318i	−0.392176	−	0.919890i	$-0.628278\pi$
$23$	−0.809321	+	0.262964i	−0.168755	+	0.0548318i	0.223421	+	0.974722i	$0.428278\pi$
$24$	2.15462	+	1.56542i	0.439810	+	0.319540i
$25$	1.84937	+	4.64541i	0.369873	+	0.929082i
$26$	−0.737676	−	2.27033i	−0.144670	−	0.445249i
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	0.224704	+	0.0730108i	0.0424651	+	0.0137977i
$29$	4.38760	+	3.18778i	0.814758	+	0.591956i	0.915206	−	0.402986i	$-0.132028\pi$
$29$	4.38760	+	3.18778i	0.814758	+	0.591956i	−0.100448	+	0.994942i	$0.532028\pi$
$30$	−2.74953	−	1.86480i	−0.501993	−	0.340464i
$31$	1.10692	+	3.40675i	0.198808	+	0.611870i	0.999911	+	0.0133424i	$0.00424714\pi$
$31$	1.10692	+	3.40675i	0.198808	+	0.611870i	−0.801103	+	0.598527i	$0.795753\pi$
$32$			1.16909i			0.206668i
$33$	1.55625	−	2.92884i	0.270909	−	0.509845i
$34$	0.153706	−	0.473057i	0.0263603	−	0.0811287i
$35$	2.44591	+	0.708109i	0.413435	+	0.119692i
$36$	0.207478			0.0345796
$37$		−	3.52650i		−	0.579754i	−0.957064	−	0.289877i	$-0.906386\pi$
$37$		−	3.52650i		−	0.579754i	0.957064	−	0.289877i	$-0.0936143\pi$
$38$	3.30120	−	1.07263i	0.535526	−	0.174003i
$39$	1.29985	+	0.944395i	0.208142	+	0.151224i
$40$	0.192658	+	5.95210i	0.0304619	+	0.941110i
$41$	−3.12877	−	2.27318i	−0.488632	−	0.355012i	0.316026	−	0.948750i	$-0.397651\pi$
$41$	−3.12877	−	2.27318i	−0.488632	−	0.355012i	−0.804658	+	0.593739i	$0.797651\pi$
$42$	−1.60912	+	0.522834i	−0.248292	+	0.0806750i
$43$			10.1739i			1.55150i	0.631039	+	0.775751i	$0.282629\pi$
$43$			10.1739i			1.55150i	−0.631039	+	0.775751i	$0.717371\pi$
$44$	0.681402	−	0.0959571i	0.102725	−	0.0144661i
$45$	2.23490	−	0.0723392i	0.333159	−	0.0107837i
$46$	1.26434			0.186416
$47$	12.8598	−	4.17842i	1.87580	−	0.609485i	0.886680	−	0.462384i	$-0.153006\pi$
$47$	12.8598	−	4.17842i	1.87580	−	0.609485i	0.989122	−	0.147101i	$-0.0469942\pi$
$48$	−2.56974	−	3.53695i	−0.370910	−	0.510514i
$49$	−4.61400	+	3.35227i	−0.659143	+	0.478895i
$50$	−0.480407	−	7.41324i	−0.0679399	−	1.04839i
$51$	0.103453	+	0.318395i	0.0144863	+	0.0445842i
$52$			0.333354i			0.0462279i
$53$		−	7.48023i		−	1.02749i	−0.857943	−	0.513744i	$-0.828258\pi$
$53$		−	7.48023i		−	1.02749i	0.857943	−	0.513744i	$-0.171742\pi$
$54$	−1.20200	+	0.873307i	−0.163572	+	0.118842i
$55$	7.30644	−	1.27120i	0.985200	−	0.171409i
$56$	2.45360	+	1.78264i	0.327876	+	0.238216i
$57$	−1.37321	+	1.89006i	−0.181886	+	0.250344i
$58$	−4.73627	−	6.51892i	−0.621903	−	0.855976i
$59$	1.60356			0.208766			0.104383	−	0.994537i	$-0.466713\pi$
$59$	1.60356			0.208766			0.104383	+	0.994537i	$0.466713\pi$
$60$	0.284693	+	0.366312i	0.0367537	+	0.0472907i
$61$	−10.8237	−	7.86389i	−1.38583	−	1.00687i	−0.996308	−	0.0858520i	$-0.972639\pi$
$61$	−10.8237	−	7.86389i	−1.38583	−	1.00687i	−0.389526	−	0.921015i	$-0.627361\pi$
$62$		−	5.32208i		−	0.675905i
$63$	0.669348	−	0.921279i	0.0843299	−	0.116070i
$64$	−2.16523	+	6.66389i	−0.270654	+	0.832987i
$65$	0.116227	+	3.59081i	0.0144162	+	0.445385i
$66$	−3.54375	+	3.42405i	−0.436205	+	0.421471i
$67$	4.82355	−	6.63904i	0.589290	−	0.811088i	−0.405385	−	0.914146i	$-0.632863\pi$
$67$	4.82355	−	6.63904i	0.589290	−	0.811088i	0.994675	+	0.103058i	$0.0328627\pi$
$68$	−0.0408272	+	0.0561938i	−0.00495102	+	0.00681450i
$69$	−0.688449	+	0.500188i	−0.0828796	+	0.0602155i
$70$	−3.13106	−	2.12356i	−0.374234	−	0.253814i
$71$	3.00001	−	9.23308i	0.356036	−	1.09576i	−0.599371	−	0.800471i	$-0.704583\pi$
$71$	3.00001	−	9.23308i	0.356036	−	1.09576i	0.955407	−	0.295293i	$-0.0954174\pi$
$72$	2.53291	+	0.822991i	0.298506	+	0.0969904i
$73$	9.41599	+	12.9600i	1.10206	+	1.51685i	0.832627	+	0.553834i	$0.186836\pi$
$73$	9.41599	+	12.9600i	1.10206	+	1.51685i	0.269432	+	0.963019i	$0.413164\pi$
$74$	−1.61910	+	4.98309i	−0.188217	+	0.579273i
$75$	3.19436	+	3.84656i	0.368853	+	0.444163i
$76$	−0.484718			−0.0556009
$77$	1.77220	−	3.33525i	0.201961	−	0.380087i
$78$	−1.40314	−	1.93126i	−0.158875	−	0.218672i
$79$	−3.20383			−0.360459			−0.180229	−	0.983625i	$-0.557684\pi$
$79$	−3.20383			−0.360459			−0.180229	+	0.983625i	$0.557684\pi$
$80$	2.71855	−	9.39028i	0.303943	−	1.04987i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	3.37740	+	4.64859i	0.372972	+	0.513351i
$83$		−	7.65826i		−	0.840604i	−0.907384	−	0.420302i	$-0.861924\pi$
$83$		−	7.65826i		−	0.840604i	0.907384	−	0.420302i	$-0.138076\pi$
$84$	0.236268			0.0257789
$85$	−0.420188	+	0.619540i	−0.0455757	+	0.0671986i
$86$	4.67108	−	14.3761i	0.503695	−	1.55022i
$87$	5.15794	+	1.67592i	0.552989	+	0.179677i
$88$	8.69925	+	1.53143i	0.927343	+	0.163251i
$89$	−0.641628	−	1.97473i	−0.0680124	−	0.209321i	0.911274	−	0.411801i	$-0.135100\pi$
$89$	−0.641628	−	1.97473i	−0.0680124	−	0.209321i	−0.979286	+	0.202480i	$0.935100\pi$
$90$	−3.19121	−	0.923878i	−0.336383	−	0.0973853i
$91$	1.48022	+	1.07544i	0.155169	+	0.112737i
$92$	−0.167916	−	0.0545592i	−0.0175065	−	0.00568819i
$93$	2.10548	+	2.89795i	0.218329	+	0.300503i
$94$	−20.0899			−2.07211
$95$	−5.22126	+	0.169002i	−0.535690	+	0.0173392i
$96$	0.361268	+	1.11187i	0.0368718	+	0.113480i
$97$		−	8.64882i		−	0.878155i	−0.898449	−	0.439077i	$-0.855305\pi$
$97$		−	8.64882i		−	0.878155i	0.898449	−	0.439077i	$-0.144695\pi$
$98$	8.05888	−	2.61849i	0.814070	−	0.264507i
$99$	0.575022	−	3.26640i	0.0577919	−	0.328285i
$100$	−0.256097	+	1.00528i	−0.0256097	+	0.100528i
$101$	5.16305	+	3.75118i	0.513743	+	0.373256i	0.814242	−	0.580526i	$-0.197153\pi$
$101$	5.16305	+	3.75118i	0.513743	+	0.373256i	−0.300499	+	0.953782i	$0.597153\pi$
$102$		−	0.497402i		−	0.0492501i
$103$	3.47870	−	4.78801i	0.342766	−	0.471777i	−0.602481	−	0.798133i	$-0.705821\pi$
$103$	3.47870	−	4.78801i	0.342766	−	0.471777i	0.945247	+	0.326356i	$0.105821\pi$
$104$	−1.32230	+	4.06962i	−0.129662	+	0.399059i
$105$	2.54502	−	0.0823772i	0.248368	−	0.00803920i
$106$	−3.43436	+	10.5699i	−0.333574	+	1.02664i
$107$	11.7035	+	3.80271i	1.13142	+	0.367622i	0.814117	−	0.580701i	$-0.197222\pi$
$107$	11.7035	+	3.80271i	1.13142	+	0.367622i	0.317307	+	0.948323i	$0.397222\pi$
$108$	0.197323	−	0.0641141i	0.0189874	−	0.00616939i
$109$	−2.05837	+	6.33502i	−0.197156	+	0.606785i	0.802788	+	0.596264i	$0.203349\pi$
$109$	−2.05837	+	6.33502i	−0.197156	+	0.606785i	−0.999945	+	0.0105207i	$0.996651\pi$
$110$	−10.9079	−	1.55830i	−1.04003	−	0.148578i
$111$	−1.08975	−	3.35390i	−0.103434	−	0.318338i
$112$	−2.92633	−	4.02775i	−0.276512	−	0.380586i
$113$	3.60880	−	4.96709i	0.339487	−	0.467264i	−0.604804	−	0.796374i	$-0.706749\pi$
$113$	3.60880	−	4.96709i	0.339487	−	0.467264i	0.944292	+	0.329110i	$0.106749\pi$
$114$	2.80817	−	2.04025i	0.263009	−	0.191087i
$115$	−1.82777	−	0.529152i	−0.170441	−	0.0493437i
$116$	0.347715	+	1.07016i	0.0322845	+	0.0993616i
$117$	1.52806	+	0.496498i	0.141269	+	0.0459012i
$118$	−2.26590	−	0.736236i	−0.208593	−	0.0677760i
$119$	0.117808	+	0.362576i	0.0107994	+	0.0332373i
$120$	2.02253	+	5.60125i	0.184631	+	0.511322i
$121$	0.377813	−	10.9935i	0.0343466	−	0.999410i
$122$	11.6838	+	16.0814i	1.05780	+	1.45594i
$123$	−3.67809	−	1.19508i	−0.331642	−	0.107757i
$124$	−0.229661	+	0.706824i	−0.0206242	+	0.0634746i
$125$	−2.40811	+	10.9179i	−0.215388	+	0.976529i
$126$	−1.36880	+	0.994489i	−0.121942	+	0.0885962i
$127$	−8.37340	+	11.5250i	−0.743019	+	1.02268i	0.255420	+	0.966830i	$0.417786\pi$
$127$	−8.37340	+	11.5250i	−0.743019	+	1.02268i	−0.998439	+	0.0558481i	$0.982214\pi$
$128$	7.49346	−	10.3139i	0.662335	−	0.911625i
$129$	3.14390	+	9.67594i	0.276805	+	0.851919i
$130$	1.48440	−	5.12732i	0.130190	−	0.449696i
$131$	−7.08937	−	5.15073i	−0.619402	−	0.450022i	0.233311	−	0.972402i	$-0.425044\pi$
$131$	−7.08937	−	5.15073i	−0.619402	−	0.450022i	−0.852712	+	0.522381i	$0.825044\pi$
$132$	0.618400	−	0.301825i	0.0538248	−	0.0262705i
$133$	−1.56376	+	2.15233i	−0.135595	+	0.186631i
$134$	−9.86401	+	7.16662i	−0.852121	+	0.619102i
$135$	2.10316	−	0.759420i	0.181011	−	0.0653605i
$136$	−0.721323	+	0.524072i	−0.0618529	+	0.0449388i
$137$	−6.84710	+	2.22476i	−0.584987	+	0.190074i	−0.586534	−	0.809925i	$-0.699508\pi$
$137$	−6.84710	+	2.22476i	−0.584987	+	0.190074i	0.00154619	+	0.999999i	$0.499508\pi$
$138$	1.20245	−	0.390701i	0.102360	−	0.0332587i
$139$	5.03733	−	3.65983i	0.427260	−	0.310423i	−0.353292	−	0.935513i	$-0.614938\pi$
$139$	5.03733	−	3.65983i	0.427260	−	0.310423i	0.780552	+	0.625090i	$0.214938\pi$
$140$	0.324198	+	0.417143i	0.0273997	+	0.0352550i
$141$	10.9392	−	7.94782i	0.921250	−	0.669327i
$142$	−8.47827	+	11.6693i	−0.711480	+	0.979269i
$143$	5.24812	+	0.923889i	0.438870	+	0.0772594i
$144$	−3.53695	−	2.56974i	−0.294746	−	0.214145i
$145$	4.11862	+	11.4062i	0.342033	+	0.947236i
$146$	−7.35492	−	22.6361i	−0.608698	−	1.87338i
$147$	−3.35227	+	4.61400i	−0.276490	+	0.380556i
$148$	0.430065	−	0.591934i	0.0353512	−	0.0486567i
$149$	−9.56831	+	6.95178i	−0.783867	+	0.569512i	−0.906137	−	0.422984i	$-0.860982\pi$
$149$	−9.56831	+	6.95178i	−0.783867	+	0.569512i	0.122270	+	0.992497i	$0.460982\pi$
$150$	−2.74771	−	6.90196i	−0.224350	−	0.563542i
$151$	0.561166	−	1.72709i	0.0456670	−	0.140549i	−0.925623	−	0.378447i	$-0.876458\pi$
$151$	0.561166	−	1.72709i	0.0456670	−	0.140549i	0.971290	+	0.237898i	$0.0764584\pi$
$152$	−5.91748	−	1.92270i	−0.479971	−	0.155952i
$153$	0.196779	+	0.270843i	0.0159086	+	0.0218963i
$154$	−4.03549	+	3.89918i	−0.325189	+	0.314205i
$155$	−2.22741	+	7.69380i	−0.178910	+	0.617981i
$156$	0.103012	+	0.317039i	0.00824758	+	0.0253834i
$157$	3.13986	+	1.02020i	0.250588	+	0.0814210i	0.431618	−	0.902057i	$-0.357943\pi$
$157$	3.13986	+	1.02020i	0.250588	+	0.0814210i	−0.181030	+	0.983478i	$0.557943\pi$
$158$	4.52714	+	1.47096i	0.360160	+	0.117023i
$159$	−2.31152	−	7.11412i	−0.183315	−	0.564186i
$160$	−1.46734	+	2.16351i	−0.116004	+	0.171040i
$161$	−0.783981	+	0.569595i	−0.0617863	+	0.0448904i
$162$	−0.873307	+	1.20200i	−0.0686135	+	0.0944383i
$163$	−0.343477	−	0.472756i	−0.0269032	−	0.0370291i	0.795353	−	0.606146i	$-0.207285\pi$
$163$	−0.343477	−	0.472756i	−0.0269032	−	0.0370291i	−0.822257	+	0.569117i	$0.807285\pi$
$164$	−0.247953	−	0.763121i	−0.0193619	−	0.0595898i
$165$	6.55601	−	3.46680i	0.510385	−	0.269890i
$166$	−3.51610	+	10.8214i	−0.272902	+	0.839906i
$167$	−6.15976	+	2.00143i	−0.476656	+	0.154875i	−0.537485	−	0.843273i	$-0.680626\pi$
$167$	−6.15976	+	2.00143i	−0.476656	+	0.154875i	0.0608289	+	0.998148i	$0.480626\pi$
$168$	2.88438	+	0.937192i	0.222535	+	0.0723059i
$169$	3.21950	−	9.90860i	0.247654	−	0.762200i
$170$	0.878188	−	0.682517i	0.0673539	−	0.0523466i
$171$	−0.721938	+	2.22190i	−0.0552080	+	0.169913i
$172$	−1.24073	+	1.70772i	−0.0946047	+	0.130212i
$173$			9.90987i			0.753434i	0.926328	+	0.376717i	$0.122947\pi$
$173$			9.90987i			0.753434i	−0.926328	+	0.376717i	$0.877053\pi$
$174$	−6.51892	−	4.73627i	−0.494198	−	0.359056i
$175$	3.63762	+	4.38032i	0.274978	+	0.331121i
$176$	−12.8046	−	6.80379i	−0.965183	−	0.512855i
$177$	1.52508	−	0.495529i	0.114632	−	0.0372462i
$178$			3.08496i			0.231227i
$179$	6.74480	+	20.7583i	0.504130	+	1.55155i	0.802229	+	0.597017i	$0.203647\pi$
$179$	6.74480	+	20.7583i	0.504130	+	1.55155i	−0.298099	+	0.954535i	$0.596353\pi$
$180$	0.383956	+	0.260409i	0.0286184	+	0.0194097i
$181$	−18.0079			−1.33851			−0.669257	−	0.743031i	$-0.733388\pi$
$181$	−18.0079			−1.33851			−0.669257	+	0.743031i	$0.733388\pi$
$182$	−1.59785	−	2.19925i	−0.118440	−	0.163019i
$183$	−12.7240	−	4.13429i	−0.940588	−	0.305615i
$184$	−1.83352	−	1.33213i	−0.135169	−	0.0982057i
$185$	4.42617	−	6.52611i	0.325419	−	0.479809i
$186$	−1.64461	−	5.06160i	−0.120589	−	0.371135i
$187$	0.771527	+	0.798498i	0.0564197	+	0.0583919i
$188$	2.66813	+	0.866928i	0.194593	+	0.0632272i
$189$	0.351897	−	1.08303i	0.0255967	−	0.0787787i
$190$	7.45544	+	2.15840i	0.540874	+	0.156587i
$191$	−9.65493			−0.698607			−0.349303	−	0.937010i	$-0.613582\pi$
$191$	−9.65493			−0.698607			−0.349303	+	0.937010i	$0.613582\pi$
$192$			7.00683i			0.505675i
$193$	−13.5014	−	18.5831i	−0.971855	−	1.33764i	−0.941104	−	0.338117i	$-0.890210\pi$
$193$	−13.5014	−	18.5831i	−0.971855	−	1.33764i	−0.0307508	−	0.999527i	$-0.509790\pi$
$194$	−3.97089	+	12.2211i	−0.285093	+	0.877426i
$195$	1.22016	+	3.37915i	0.0873775	+	0.241986i
$196$	−1.18329			−0.0845208
$197$	−0.215950	−	0.297229i	−0.0153858	−	0.0211767i	0.801255	−	0.598323i	$-0.204166\pi$
$197$	−0.215950	−	0.297229i	−0.0153858	−	0.0211767i	−0.816641	+	0.577147i	$0.804166\pi$
$198$	−2.31221	+	4.35154i	−0.164322	+	0.309251i
$199$	−22.7175			−1.61040			−0.805199	−	0.593004i	$-0.797942\pi$
$199$	−22.7175			−1.61040			−0.805199	+	0.593004i	$0.797942\pi$
$200$	−7.11405	+	11.2567i	−0.503039	+	0.795969i
$201$	2.53589	−	7.80466i	0.178868	−	0.550498i
$202$	−5.57334	−	7.67105i	−0.392139	−	0.539733i
$203$	5.87367	+	1.90847i	0.412251	+	0.133948i
$204$	−0.0214641	+	0.0660598i	−0.00150279	+	0.00462511i
$205$	−2.93696	−	8.13370i	−0.205126	−	0.568082i
$206$	−7.11383	+	5.16850i	−0.495644	+	0.360107i
$207$	−0.500188	+	0.688449i	−0.0347654	+	0.0478505i
$208$	4.12881	−	5.68282i	0.286281	−	0.394032i
$209$	−1.34339	+	7.63109i	−0.0929243	+	0.527853i
$210$	−3.63403	−	1.05208i	−0.250772	−	0.0726003i
$211$	0.731974	−	2.25278i	0.0503911	−	0.155088i	−0.922694	−	0.385532i	$-0.874018\pi$
$211$	0.731974	−	2.25278i	0.0503911	−	0.155088i	0.973086	+	0.230444i	$0.0740179\pi$
$212$	0.912231	−	1.25558i	0.0626523	−	0.0862335i
$213$		−	9.70823i		−	0.665197i
$214$	−14.7916	−	10.7468i	−1.01114	−	0.734633i
$215$	−12.7694	+	18.8277i	−0.870866	+	1.28404i
$216$	2.66325			0.181212
$217$	2.39765	+	3.30008i	0.162763	+	0.224024i
$218$	5.81713	−	8.00659i	0.393985	−	0.542274i
$219$	12.9600	+	9.41599i	0.875756	+	0.636274i
$220$	1.38143	+	0.677662i	0.0931362	+	0.0456880i
$221$	−0.435163	+	0.316164i	−0.0292722	+	0.0212675i
$222$			5.23953i			0.351654i
$223$			17.1956i			1.15150i	0.817625	+	0.575751i	$0.195290\pi$
$223$			17.1956i			1.15150i	−0.817625	+	0.575751i	$0.804710\pi$
$224$	0.411399	+	1.26616i	0.0274878	+	0.0845986i
$225$	4.22667	+	2.67119i	0.281778	+	0.178079i
$226$	−7.37989	+	5.36181i	−0.490903	+	0.356662i
$227$	7.93701	+	10.9244i	0.526798	+	0.725075i	0.986638	−	0.162927i	$-0.0520934\pi$
$227$	7.93701	+	10.9244i	0.526798	+	0.725075i	−0.459840	+	0.888002i	$0.652093\pi$
$228$	−0.460994	+	0.149786i	−0.0305301	+	0.00991982i
$229$	−26.5252			−1.75283			−0.876416	−	0.481554i	$-0.840073\pi$
$229$	−26.5252			−1.75283			−0.876416	+	0.481554i	$0.840073\pi$
$230$	2.33977	+	1.58689i	0.154280	+	0.104636i
$231$	0.654814	−	3.71965i	0.0430836	−	0.244735i
$232$			14.4438i			0.948284i
$233$	−11.2407	+	3.65234i	−0.736405	+	0.239273i	−0.653121	−	0.757253i	$-0.726541\pi$
$233$	−11.2407	+	3.65234i	−0.736405	+	0.239273i	−0.0832840	+	0.996526i	$0.526541\pi$
$234$	−1.93126	−	1.40314i	−0.126250	−	0.0917263i
$235$	29.0427	+	8.40806i	1.89454	+	0.548482i
$236$	0.269163	+	0.195558i	0.0175210	+	0.0127298i
$237$	−3.04702	+	0.990037i	−0.197925	+	0.0643098i
$238$		−	0.566423i		−	0.0367157i
$239$	−3.25985			−0.210862			−0.105431	−	0.994427i	$-0.533622\pi$
$239$	−3.25985			−0.210862			−0.105431	+	0.994427i	$0.533622\pi$
$240$	−0.316261	−	9.77077i	−0.0204145	−	0.630700i
$241$	−7.45439	+	22.9423i	−0.480180	+	1.47784i	0.358663	+	0.933467i	$0.383233\pi$
$241$	−7.45439	+	22.9423i	−0.480180	+	1.47784i	−0.838843	+	0.544374i	$0.816767\pi$
$242$	−5.58126	+	15.3608i	−0.358777	+	0.987430i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.857773	−	2.63995i	−0.0549133	−	0.169006i
$245$	−12.7461	+	0.412567i	−0.814319	+	0.0263579i
$246$	4.64859	+	3.37740i	0.296384	+	0.215335i
$247$	−3.56992	−	1.15994i	−0.227149	−	0.0738051i
$248$	−5.60744	+	7.71798i	−0.356073	+	0.490092i
$249$	−2.36653	−	7.28344i	−0.149973	−	0.461569i
$250$	8.41544	−	14.3218i	0.532239	−	0.905793i
$251$	−11.8220	−	8.58921i	−0.746200	−	0.542146i	0.148447	−	0.988920i	$-0.452573\pi$
$251$	−11.8220	−	8.58921i	−0.746200	−	0.542146i	−0.894647	+	0.446774i	$0.852573\pi$
$252$	0.224704	−	0.0730108i	0.0141550	−	0.00459925i
$253$	−1.32432	+	2.49235i	−0.0832595	+	0.156693i
$254$	17.1234	−	12.4409i	1.07442	−	0.780608i
$255$	−0.208174	+	0.719063i	−0.0130363	+	0.0450295i
$256$	−3.98662	+	2.89645i	−0.249164	+	0.181028i
$257$	1.12199	−	0.364556i	0.0699877	−	0.0227404i	−0.273814	−	0.961783i	$-0.588285\pi$
$257$	1.12199	−	0.364556i	0.0699877	−	0.0227404i	0.343802	+	0.939042i	$0.388285\pi$
$258$		−	15.1159i		−	0.941077i
$259$	−1.24097	−	3.81930i	−0.0771099	−	0.237320i
$260$	−0.418399	+	0.616902i	−0.0259480	+	0.0382587i
$261$	5.42338			0.335699
$262$	7.65274	+	10.5331i	0.472788	+	0.650737i
$263$	16.4735	+	5.35256i	1.01580	+	0.330053i	0.769161	−	0.639055i	$-0.220674\pi$
$263$	16.4735	+	5.35256i	1.01580	+	0.330053i	0.246637	+	0.969108i	$0.420674\pi$
$264$	8.74671	−	1.23174i	0.538323	−	0.0758082i
$265$	9.38855	−	13.8428i	0.576734	−	0.850358i
$266$	3.19784	−	2.32337i	0.196072	−	0.142455i
$267$	−1.22045	−	1.67980i	−0.0746903	−	0.102802i
$268$	1.61929	−	0.526140i	0.0989141	−	0.0321391i
$269$	−20.4757			−1.24842			−0.624212	−	0.781255i	$-0.714580\pi$
$269$	−20.4757			−1.24842			−0.624212	+	0.781255i	$0.714580\pi$
$270$	−3.32052	+	0.107479i	−0.202080	+	0.00654094i
$271$	−7.33051	−	5.32593i	−0.445297	−	0.323527i	0.342439	−	0.939540i	$-0.388747\pi$
$271$	−7.33051	−	5.32593i	−0.445297	−	0.323527i	−0.787736	+	0.616013i	$0.788747\pi$
$272$	1.39199	−	0.452286i	0.0844019	−	0.0274238i
$273$	1.74010	+	0.565393i	0.105316	+	0.0342192i
$274$	10.6967			0.646210
$275$	15.1167	+	6.81795i	0.911573	+	0.411138i
$276$	−0.176557			−0.0106275
$277$	−17.6687	−	5.74092i	−1.06161	−	0.344939i	−0.274397	−	0.961617i	$-0.588478\pi$
$277$	−17.6687	−	5.74092i	−1.06161	−	0.344939i	−0.787216	+	0.616678i	$0.788478\pi$
$278$	−8.79826	+	2.85873i	−0.527685	+	0.171455i
$279$	2.89795	+	2.10548i	0.173496	+	0.126052i
$280$	2.30318	+	6.37850i	0.137641	+	0.381188i
$281$	−25.5737			−1.52560			−0.762800	−	0.646635i	$-0.776176\pi$
$281$	−25.5737			−1.52560			−0.762800	+	0.646635i	$0.776176\pi$
$282$	−19.1066	+	6.20812i	−1.13778	+	0.369688i
$283$	−7.08969	−	9.75812i	−0.421438	−	0.580060i	0.544523	−	0.838746i	$-0.316711\pi$
$283$	−7.08969	−	9.75812i	−0.421438	−	0.580060i	−0.965962	+	0.258686i	$0.916711\pi$
$284$	1.62956	−	1.18394i	0.0966964	−	0.0702540i
$285$	−4.91349	+	1.77419i	−0.291050	+	0.105094i
$286$	−6.99163	−	3.71503i	−0.413423	−	0.219674i
$287$	−4.18847	−	1.36092i	−0.247238	−	0.0803324i
$288$	0.687173	+	0.945813i	0.0404921	+	0.0557326i
$289$	16.8879			0.993407
$290$	−0.582897	−	18.0084i	−0.0342289	−	1.05749i
$291$	−2.67263	−	8.22552i	−0.156672	−	0.482188i
$292$			3.32368i			0.194504i
$293$	−11.8281	+	3.84318i	−0.691005	+	0.224521i	−0.633407	−	0.773819i	$-0.718344\pi$
$293$	−11.8281	+	3.84318i	−0.691005	+	0.224521i	−0.0575979	+	0.998340i	$0.518344\pi$
$294$	6.85529	−	4.98066i	0.399809	−	0.290478i
$295$	2.96754	+	2.01266i	0.172777	+	0.117182i
$296$	7.59827	−	5.52047i	0.441640	−	0.320871i
$297$	−0.462493	−	3.28422i	−0.0268366	−	0.190570i
$298$	16.7121	−	5.43010i	0.968108	−	0.314557i
$299$	−1.10613	−	0.803652i	−0.0639692	−	0.0464764i
$300$	0.0670862	+	1.03522i	0.00387322	+	0.0597683i
$301$	3.58016	+	11.0186i	0.206357	+	0.635101i
$302$	−1.58590	+	2.18280i	−0.0912582	+	0.125606i
$303$	6.06953	+	1.97211i	0.348685	+	0.113295i
$304$	8.26316	+	6.00354i	0.473925	+	0.344326i
$305$	−10.1602	−	28.1378i	−0.581769	−	1.61117i
$306$	−0.153706	−	0.473057i	−0.00878677	−	0.0270429i
$307$		−	14.7273i		−	0.840533i	−0.907401	−	0.420266i	$-0.861937\pi$
$307$		−	14.7273i		−	0.840533i	0.907401	−	0.420266i	$-0.138063\pi$
$308$	0.704211	−	0.343708i	0.0401261	−	0.0195846i
$309$	1.82886	−	5.62865i	0.104040	−	0.320203i
$310$	6.67983	−	9.84899i	0.379389	−	0.559385i
$311$	14.6914			0.833075			0.416538	−	0.909119i	$-0.363243\pi$
$311$	14.6914			0.833075			0.416538	+	0.909119i	$0.363243\pi$
$312$			4.27905i			0.242254i
$313$	18.3410	−	5.95934i	1.03669	−	0.336842i	0.259259	−	0.965808i	$-0.416522\pi$
$313$	18.3410	−	5.95934i	1.03669	−	0.336842i	0.777433	+	0.628966i	$0.216522\pi$
$314$	−3.96835	−	2.88317i	−0.223947	−	0.162707i
$315$	2.39500	−	0.864799i	0.134943	−	0.0487259i
$316$	−0.537772	−	0.390714i	−0.0302520	−	0.0219794i
$317$	26.6977	−	8.67462i	1.49949	−	0.487215i	0.559624	−	0.828747i	$-0.310946\pi$
$317$	26.6977	−	8.67462i	1.49949	−	0.487215i	0.939870	+	0.341532i	$0.110946\pi$
$318$			11.1138i			0.623231i
$319$	17.8116	−	2.50828i	0.997256	−	0.140436i
$320$	−12.3709	+	9.61452i	−0.691555	+	0.537468i
$321$	12.3058			0.686844
$322$	1.36931	−	0.444916i	0.0763087	−	0.0247942i
$323$	−0.459722	−	0.632753i	−0.0255796	−	0.0352073i
$324$	0.167853	−	0.121952i	0.00932517	−	0.00677513i
$325$	−4.29179	+	6.79100i	−0.238066	+	0.376697i
$326$	0.268293	+	0.825722i	0.0148594	+	0.0457325i
$327$			6.66103i			0.368356i
$328$		−	10.2998i		−	0.568711i
$329$	12.4572	−	9.05068i	0.686788	−	0.498980i
$330$	−10.8556	+	1.88870i	−0.597581	+	0.103970i
$331$	8.11726	+	5.89754i	0.446165	+	0.324158i	0.788080	−	0.615573i	$-0.211075\pi$
$331$	8.11726	+	5.89754i	0.446165	+	0.324158i	−0.341915	+	0.939731i	$0.611075\pi$
$332$	0.933943	−	1.28546i	0.0512568	−	0.0705489i
$333$	−2.07283	−	2.85300i	−0.113590	−	0.156344i
$334$	9.62289			0.526541
$335$	17.2592	−	6.23203i	0.942969	−	0.340492i
$336$	−4.02775	−	2.92633i	−0.219732	−	0.159644i
$337$		−	8.50999i		−	0.463569i	−0.972767	−	0.231784i	$-0.925544\pi$
$337$		−	8.50999i		−	0.463569i	0.972767	−	0.231784i	$-0.0744564\pi$
$338$	−9.09856	+	12.5231i	−0.494896	+	0.681166i
$339$	1.89726	−	5.83916i	0.103045	−	0.317140i
$340$	−0.146084	+	0.0527488i	−0.00792252	+	0.00286071i
$341$	10.4913	+	5.57459i	0.568135	+	0.301881i
$342$	2.04025	−	2.80817i	0.110324	−	0.151848i
$343$	−8.50287	+	11.7032i	−0.459112	+	0.631914i
$344$	−21.9208	+	15.9264i	−1.18189	+	0.858695i
$345$	−1.90183	+	0.0615585i	−0.102391	+	0.00331420i
$346$	4.54987	−	14.0030i	0.244602	−	0.752808i
$347$	−10.5614	−	3.43162i	−0.566968	−	0.184219i	0.0114862	−	0.999934i	$-0.496344\pi$
$347$	−10.5614	−	3.43162i	−0.566968	−	0.184219i	−0.578454	+	0.815715i	$0.696344\pi$
$348$	0.661393	+	0.910330i	0.0354544	+	0.0487988i
$349$	10.2585	−	31.5725i	0.549126	−	1.69004i	−0.161845	−	0.986816i	$-0.551744\pi$
$349$	10.2585	−	31.5725i	0.549126	−	1.69004i	0.710971	−	0.703221i	$-0.248256\pi$
$350$	−3.12899	−	7.85969i	−0.167252	−	0.420118i
$351$	1.60670			0.0857593
$352$	2.69426	+	2.78845i	0.143605	+	0.148625i
$353$	−10.4098	−	14.3278i	−0.554056	−	0.762592i	0.436500	−	0.899704i	$-0.356218\pi$
$353$	−10.4098	−	14.3278i	−0.554056	−	0.762592i	−0.990556	+	0.137112i	$0.956218\pi$
$354$	−2.38251			−0.126629
$355$	17.1404	−	13.3213i	0.909717	−	0.707020i
$356$	0.133123	−	0.409712i	0.00705553	−	0.0217147i
$357$	0.224084	+	0.308425i	0.0118598	+	0.0163236i
$358$		−	32.4291i		−	1.71393i
$359$	−5.63206			−0.297249			−0.148624	−	0.988894i	$-0.547485\pi$
$359$	−5.63206			−0.297249			−0.148624	+	0.988894i	$0.547485\pi$
$360$	3.65442	+	4.70211i	0.192605	+	0.247823i
$361$	−4.18470	+	12.8792i	−0.220248	+	0.677852i
$362$	25.4458	+	8.26786i	1.33740	+	0.434549i
$363$	−3.03786	−	10.5722i	−0.159446	−	0.554897i
$364$	0.117306	+	0.361032i	0.00614853	+	0.0189232i
$365$	1.15883	+	35.8018i	0.0606562	+	1.87395i
$366$	16.0814	+	11.6838i	0.840589	+	0.610724i
$367$	1.76001	+	0.571863i	0.0918719	+	0.0298510i	0.354592	−	0.935021i	$-0.384620\pi$
$367$	1.76001	+	0.571863i	0.0918719	+	0.0298510i	−0.262720	+	0.964872i	$0.584620\pi$
$368$	2.18677	+	3.00984i	0.113994	+	0.156899i
$369$	−3.86737			−0.201327
$370$	−9.25066	+	7.18949i	−0.480919	+	0.373764i
$371$	−2.63227	−	8.10129i	−0.136661	−	0.420598i
$372$			0.743198i			0.0385330i
$373$	13.4960	−	4.38512i	0.698798	−	0.227053i	0.0619910	−	0.998077i	$-0.480255\pi$
$373$	13.4960	−	4.38512i	0.698798	−	0.227053i	0.636807	+	0.771024i	$0.280255\pi$
$374$	−0.723589	−	1.48254i	−0.0374159	−	0.0766601i
$375$	1.08357	+	11.1277i	0.0559555	+	0.574632i
$376$	29.1340	+	21.1671i	1.50247	+	1.09161i
$377$			8.71374i			0.448780i
$378$	−0.994489	+	1.36880i	−0.0511510	+	0.0704033i
$379$	−3.51892	+	10.8301i	−0.180755	+	0.556306i	−0.999849	−	0.0173523i	$-0.994476\pi$
$379$	−3.51892	+	10.8301i	−0.180755	+	0.556306i	0.819095	+	0.573658i	$0.194476\pi$
$380$	−0.897014	−	0.608377i	−0.0460158	−	0.0312091i
$381$	−4.40216	+	13.5484i	−0.225529	+	0.694108i
$382$	13.6428	+	4.43282i	0.698027	+	0.226803i
$383$	−13.4176	+	4.35964i	−0.685608	+	0.222767i	−0.631049	−	0.775743i	$-0.717375\pi$
$383$	−13.4176	+	4.35964i	−0.685608	+	0.222767i	−0.0545588	+	0.998511i	$0.517375\pi$
$384$	3.93955	−	12.1247i	0.201039	−	0.618735i
$385$	7.46574	−	3.94786i	0.380490	−	0.201202i
$386$	10.5461	+	32.4576i	0.536782	+	1.65205i
$387$	5.98006	+	8.23084i	0.303983	+	0.418397i
$388$	1.05474	−	1.45173i	0.0535465	−	0.0737004i
$389$	12.0646	−	8.76541i	0.611697	−	0.444424i	−0.238314	−	0.971188i	$-0.576595\pi$
$389$	12.0646	−	8.76541i	0.611697	−	0.444424i	0.850012	+	0.526764i	$0.176595\pi$
$390$	−0.172686	−	5.33508i	−0.00874429	−	0.270152i
$391$	−0.0880351	−	0.270944i	−0.00445213	−	0.0137022i
$392$	−14.4457	−	4.69370i	−0.729619	−	0.237068i
$393$	−8.33406	−	2.70790i	−0.420398	−	0.136595i
$394$	0.168680	+	0.519144i	0.00849799	+	0.0261541i
$395$	−5.92897	−	4.02117i	−0.298319	−	0.202327i
$396$	0.494864	−	0.478149i	0.0248678	−	0.0240279i
$397$	5.16665	+	7.11129i	0.259307	+	0.356905i	0.918744	−	0.394855i	$-0.129205\pi$
$397$	5.16665	+	7.11129i	0.259307	+	0.356905i	−0.659437	+	0.751760i	$0.729205\pi$
$398$	32.1007	+	10.4301i	1.60906	+	0.522816i
$399$	−0.822116	+	2.53021i	−0.0411573	+	0.126669i
$400$	16.8168	−	13.9655i	0.840841	−	0.698273i
$401$	14.3838	−	10.4504i	0.718291	−	0.521869i	−0.167547	−	0.985864i	$-0.553584\pi$
$401$	14.3838	−	10.4504i	0.718291	−	0.521869i	0.885838	+	0.463995i	$0.153584\pi$
$402$	−7.16662	+	9.86401i	−0.357439	+	0.491972i
$403$	−3.38288	+	4.65614i	−0.168513	+	0.231939i
$404$	0.409169	+	1.25929i	0.0203569	+	0.0626521i
$405$	1.76555	−	1.37216i	0.0877309	−	0.0681834i
$406$	−7.42350	−	5.39349i	−0.368422	−	0.267674i
$407$	−8.12711	−	8.41121i	−0.402846	−	0.416928i
$408$	−0.524072	+	0.721323i	−0.0259454	+	0.0357108i
$409$	8.65156	−	6.28573i	0.427792	−	0.310809i	−0.352973	−	0.935633i	$-0.614829\pi$
$409$	8.65156	−	6.28573i	0.427792	−	0.310809i	0.780766	+	0.624824i	$0.214829\pi$
$410$	0.415660	+	12.8417i	0.0205280	+	0.634205i
$411$	−5.82449	+	4.23174i	−0.287301	+	0.208736i
$412$	1.16782	−	0.379447i	0.0575343	−	0.0186940i
$413$	1.73670	−	0.564290i	0.0854576	−	0.0277669i
$414$	1.02287	−	0.743158i	0.0502713	−	0.0365242i
$415$	9.61201	−	14.1723i	0.471835	−	0.695691i
$416$	−1.51964	+	1.10408i	−0.0745064	+	0.0541321i
$417$	3.65983	−	5.03733i	0.179223	−	0.246679i
$418$	5.40188	−	10.1662i	0.264215	−	0.497248i
$419$	7.73548	+	5.62016i	0.377903	+	0.274563i	0.760480	−	0.649361i	$-0.224963\pi$
$419$	7.73548	+	5.62016i	0.377903	+	0.274563i	−0.382577	+	0.923923i	$0.624963\pi$
$420$	0.437235	+	0.296544i	0.0213349	+	0.0144698i
$421$	7.69125	+	23.6712i	0.374849	+	1.15367i	0.943581	+	0.331143i	$0.107434\pi$
$421$	7.69125	+	23.6712i	0.374849	+	1.15367i	−0.568732	+	0.822523i	$0.692566\pi$
$422$	−2.06862	+	2.84721i	−0.100699	+	0.138600i
$423$	7.94782	−	10.9392i	0.386436	−	0.531884i
$424$	16.1170	−	11.7097i	0.782712	−	0.568674i
$425$	−1.55519	+	0.619131i	−0.0754378	+	0.0300323i
$426$	−4.45729	+	13.7181i	−0.215956	+	0.664645i
$427$	−14.4897	−	4.70798i	−0.701204	−	0.227835i
$428$	1.50072	+	2.06557i	0.0725402	+	0.0998431i
$429$	5.27676	−	0.743088i	0.254764	−	0.0358766i
$430$	26.6879	−	20.7415i	1.28701	−	1.00025i
$431$	−1.26233	−	3.88505i	−0.0608043	−	0.187136i	0.916040	−	0.401086i	$-0.131367\pi$
$431$	−1.26233	−	3.88505i	−0.0608043	−	0.187136i	−0.976845	+	0.213950i	$0.931367\pi$
$432$	−4.15793	−	1.35099i	−0.200049	−	0.0649997i
$433$	−26.9318	−	8.75066i	−1.29426	−	0.420530i	−0.420678	−	0.907210i	$-0.638208\pi$
$433$	−26.9318	−	8.75066i	−1.29426	−	0.420530i	−0.873580	+	0.486680i	$0.838208\pi$
$434$	−1.87282	−	5.76396i	−0.0898985	−	0.276679i
$435$	7.44176	+	9.57524i	0.356805	+	0.459098i
$436$	−1.11807	+	0.812329i	−0.0535460	+	0.0389035i
$437$	1.16856	−	1.60838i	0.0558997	−	0.0769394i
$438$	−13.9899	−	19.2554i	−0.668463	−	0.920060i
$439$	7.67554	+	23.6229i	0.366334	+	1.12746i	0.949142	+	0.314849i	$0.101954\pi$
$439$	7.67554	+	23.6229i	0.366334	+	1.12746i	−0.582808	+	0.812610i	$0.698046\pi$
$440$	14.1766	+	13.7526i	0.675844	+	0.655630i
$441$	−1.76239	+	5.42408i	−0.0839234	+	0.258290i
$442$	0.760061	−	0.246959i	0.0361524	−	0.0117466i
$443$	−18.8108	−	6.11200i	−0.893727	−	0.290390i	−0.174082	−	0.984731i	$-0.555696\pi$
$443$	−18.8108	−	6.11200i	−0.893727	−	0.290390i	−0.719646	+	0.694342i	$0.755696\pi$
$444$	0.226099	−	0.695860i	0.0107302	−	0.0330241i
$445$	1.29112	−	4.45973i	0.0612051	−	0.211411i
$446$	7.89492	−	24.2981i	0.373835	−	1.15055i
$447$	−6.95178	+	9.56831i	−0.328808	+	0.452566i
$448$			7.97912i			0.376978i
$449$	10.4666	+	7.60441i	0.493948	+	0.358874i	0.806701	−	0.590960i	$-0.201251\pi$
$449$	10.4666	+	7.60441i	0.493948	+	0.358874i	−0.312752	+	0.949835i	$0.601251\pi$
$450$	−4.74605	−	5.71506i	−0.223731	−	0.269411i
$451$	−12.7013	+	1.78863i	−0.598081	+	0.0842235i
$452$	1.21150	−	0.393639i	0.0569840	−	0.0185152i
$453$		−	1.81597i		−	0.0853217i
$454$	−6.19967	−	19.0806i	−0.290965	−	0.895498i
$455$	1.38947	+	3.84805i	0.0651395	+	0.180399i
$456$	−6.22200			−0.291372
$457$	−22.3917	−	30.8195i	−1.04744	−	1.44167i	−0.891009	−	0.453986i	$-0.850002\pi$
$457$	−22.3917	−	30.8195i	−1.04744	−	1.44167i	−0.156429	−	0.987689i	$-0.549998\pi$
$458$	37.4811	+	12.1784i	1.75138	+	0.569057i
$459$	0.270843	+	0.196779i	0.0126418	+	0.00918484i
$460$	−0.242265	−	0.311721i	−0.0112957	−	0.0145341i
$461$	−3.22683	−	9.93117i	−0.150289	−	0.462541i	0.847365	−	0.531012i	$-0.178188\pi$
$461$	−3.22683	−	9.93117i	−0.150289	−	0.462541i	−0.997653	+	0.0684710i	$0.978188\pi$
$462$	−2.63306	+	4.95538i	−0.122501	+	0.230545i
$463$	−13.0716	−	4.24723i	−0.607490	−	0.197386i	−0.0109121	−	0.999940i	$-0.503473\pi$
$463$	−13.0716	−	4.24723i	−0.607490	−	0.197386i	−0.596578	+	0.802555i	$0.703473\pi$
$464$	7.32695	−	22.5500i	0.340145	−	1.04686i
$465$	0.259124	+	8.00555i	0.0120166	+	0.371248i
$466$	17.5605			0.813474
$467$			19.6140i			0.907626i	0.891097	+	0.453813i	$0.149937\pi$
$467$			19.6140i			0.907626i	−0.891097	+	0.453813i	$0.850063\pi$
$468$	0.195941	+	0.269689i	0.00905737	+	0.0124664i
$469$	2.88778	−	8.88766i	0.133345	−	0.410394i
$470$	−37.1782	−	25.2151i	−1.71490	−	1.16309i
$471$	3.30144			0.152123
$472$	2.51025	+	3.45507i	0.115544	+	0.159032i
$473$	23.4465	+	24.2662i	1.07807	+	1.11576i
$474$	4.76011			0.218639
$475$	−9.87452	−	6.24053i	−0.453074	−	0.286335i
$476$	−0.0244425	+	0.0752264i	−0.00112032	+	0.00344800i
$477$	−4.39677	−	6.05163i	−0.201314	−	0.277085i
$478$	4.60630	+	1.49668i	0.210687	+	0.0684564i
$479$	8.31169	−	25.5807i	0.379771	−	1.16881i	−0.560433	−	0.828200i	$-0.689365\pi$
$479$	8.31169	−	25.5807i	0.379771	−	1.16881i	0.940203	−	0.340614i	$-0.110635\pi$
$480$	−0.726966	+	2.51105i	−0.0331813	+	0.114613i
$481$	4.58392	−	3.33041i	0.209009	−	0.151854i
$482$	21.0667	−	28.9958i	0.959562	−	1.32072i
$483$	−0.569595	+	0.783981i	−0.0259175	+	0.0356723i
$484$	1.40410	−	1.79922i	0.0638228	−	0.0817826i
$485$	10.8553	−	16.0054i	0.492913	−	0.726769i
$486$	−0.459125	+	1.41304i	−0.0208263	+	0.0640968i
$487$	−10.6228	+	14.6210i	−0.481364	+	0.662541i	−0.978766	−	0.204979i	$-0.934287\pi$
$487$	−10.6228	+	14.6210i	−0.481364	+	0.662541i	0.497402	+	0.867520i	$0.334287\pi$
$488$		−	35.6313i		−	1.61295i
$489$	−0.472756	−	0.343477i	−0.0213788	−	0.0155326i
$490$	18.2002	+	5.26908i	0.822201	+	0.238033i
$491$	24.4711			1.10437			0.552184	−	0.833722i	$-0.313795\pi$
$491$	24.4711			1.10437			0.552184	+	0.833722i	$0.313795\pi$
$492$	−0.471635	−	0.649150i	−0.0212629	−	0.0292659i
$493$	−1.06720	+	1.46888i	−0.0480645	+	0.0661551i
$494$	4.51189	+	3.27808i	0.202999	+	0.147488i
$495$	5.16384	−	5.32304i	0.232097	−	0.239253i
$496$	12.6696	−	9.20498i	0.568881	−	0.413316i
$497$		−	11.0554i		−	0.495901i
$498$			11.3783i			0.509875i
$499$	−9.77256	−	30.0768i	−0.437480	−	1.34642i	−0.890524	−	0.454936i	$-0.849662\pi$
$499$	−9.77256	−	30.0768i	−0.437480	−	1.34642i	0.453044	−	0.891488i	$-0.350338\pi$
$500$	−1.73567	+	1.53893i	−0.0776217	+	0.0688231i
$501$	−5.23980	+	3.80694i	−0.234097	+	0.170082i
$502$	12.7615	+	17.5647i	0.569573	+	0.783950i
$503$	21.1073	−	6.85817i	0.941128	−	0.305791i	0.202022	−	0.979381i	$-0.435249\pi$
$503$	21.1073	−	6.85817i	0.941128	−	0.305791i	0.739105	+	0.673590i	$0.235249\pi$
$504$	3.03282			0.135092
$505$	4.84653	+	13.4221i	0.215668	+	0.597276i
$506$	3.01562	−	2.91376i	0.134061	−	0.129533i
$507$		−	10.4185i		−	0.462702i
$508$	−2.81100	+	0.913350i	−0.124718	+	0.0405233i
$509$	−26.6172	−	19.3385i	−1.17979	−	0.857165i	−0.187639	−	0.982238i	$-0.560084\pi$
$509$	−26.6172	−	19.3385i	−1.17979	−	0.857165i	−0.992148	+	0.125072i	$0.960084\pi$
$510$	0.624297	−	0.920487i	0.0276443	−	0.0407598i
$511$	14.7584	+	10.7226i	0.652872	+	0.474339i
$512$	−17.2863	+	5.61665i	−0.763952	+	0.248223i
$513$			2.33624i			0.103148i
$514$	−1.75279			−0.0773123
$515$	12.4472	−	4.49448i	0.548487	−	0.198051i
$516$	−0.652290	+	2.00754i	−0.0287154	+	0.0883771i
$517$	21.0431	−	39.6027i	0.925473	−	1.74172i
$518$			5.96658i			0.262157i
$519$	3.06232	+	9.42485i	0.134421	+	0.413705i
$520$	−7.55488	+	5.87156i	−0.331303	+	0.257485i
$521$	−8.78134	−	6.38002i	−0.384718	−	0.279514i	0.378570	−	0.925573i	$-0.376416\pi$
$521$	−8.78134	−	6.38002i	−0.384718	−	0.279514i	−0.763287	+	0.646059i	$0.776416\pi$
$522$	−7.66345	−	2.49001i	−0.335420	−	0.108985i
$523$	−23.2819	+	32.0448i	−1.01805	+	1.40122i	−0.104485	+	0.994527i	$0.533319\pi$
$523$	−23.2819	+	32.0448i	−1.01805	+	1.40122i	−0.913563	+	0.406696i	$0.866681\pi$
$524$	−0.561829	−	1.72913i	−0.0245436	−	0.0755375i
$525$	4.81318	+	3.04185i	0.210064	+	0.132757i
$526$	−20.8202	−	15.1268i	−0.907803	−	0.659558i
$527$	−1.14051	+	0.370574i	−0.0496814	+	0.0161425i
$528$	−14.2804	−	2.51395i	−0.621474	−	0.109405i
$529$	−18.0215	+	13.0934i	−0.783545	+	0.569279i
$530$	−19.6220	+	15.2500i	−0.852325	+	0.662416i
$531$	1.29731	−	0.942551i	0.0562985	−	0.0409032i
$532$	−0.524963	+	0.170571i	−0.0227600	+	0.00739518i
$533$		−	6.21371i		−	0.269146i
$534$	0.953304	+	2.93397i	0.0412535	+	0.126965i
$535$	16.8856	+	21.7266i	0.730028	+	0.939321i
$536$	21.8555			0.944013
$537$	12.8294	+	17.6581i	0.553628	+	0.762004i
$538$	28.9330	+	9.40089i	1.24739	+	0.405301i
$539$	−3.27948	+	18.6290i	−0.141257	+	0.802407i
$540$	0.445635	+	0.129014i	0.0191771	+	0.00555189i
$541$	−2.58758	+	1.87999i	−0.111249	+	0.0808269i	−0.642019	−	0.766689i	$-0.721903\pi$
$541$	−2.58758	+	1.87999i	−0.111249	+	0.0808269i	0.530770	+	0.847516i	$0.321903\pi$
$542$	7.91304	+	10.8914i	0.339894	+	0.467824i
$543$	−17.1265	+	5.56474i	−0.734969	+	0.238806i
$544$	−0.391388			−0.0167806
$545$	−11.7604	+	9.14003i	−0.503760	+	0.391516i
$546$	−2.19925	−	1.59785i	−0.0941191	−	0.0683815i
$547$	14.1673	−	4.60325i	0.605752	−	0.196821i	0.00994761	−	0.999951i	$-0.496834\pi$
$547$	14.1673	−	4.60325i	0.605752	−	0.196821i	0.595804	+	0.803130i	$0.296834\pi$
$548$	−1.42062	−	0.461588i	−0.0606859	−	0.0197181i
$549$	−13.3788			−0.570995
$550$	−18.2303	−	16.5745i	−0.777341	−	0.706739i
$551$	−12.6703			−0.539773
$552$	−2.15543	−	0.700341i	−0.0917411	−	0.0298085i
$553$	−3.46983	+	1.12742i	−0.147552	+	0.0479427i
$554$	22.3308	+	16.2243i	0.948747	+	0.689305i
$555$	2.19286	−	7.57446i	0.0930817	−	0.321518i
$556$	1.29185			0.0547869
$557$	15.3542	−	4.98887i	0.650577	−	0.211385i	0.0349082	−	0.999391i	$-0.488886\pi$
$557$	15.3542	−	4.98887i	0.650577	−	0.211385i	0.615668	+	0.788005i	$0.288886\pi$
$558$	−3.12824	−	4.30565i	−0.132429	−	0.182273i
$559$	−13.2245	+	9.60816i	−0.559337	+	0.406382i
$560$	−0.360146	−	11.1266i	−0.0152189	−	0.470184i
$561$	0.980515	+	0.521001i	0.0413974	+	0.0219967i
$562$	36.1367	+	11.7415i	1.52433	+	0.495286i
$563$	−5.59789	−	7.70483i	−0.235923	−	0.324720i	0.674596	−	0.738187i	$-0.264318\pi$
$563$	−5.59789	−	7.70483i	−0.235923	−	0.324720i	−0.910519	+	0.413467i	$0.864318\pi$
$564$	2.80544			0.118130
$565$	12.9127	−	4.66258i	0.543241	−	0.196156i
$566$	5.53782	+	17.0437i	0.232772	+	0.716399i
$567$		−	1.13876i		−	0.0478235i
$568$	24.5900	−	7.98979i	1.03178	−	0.335244i
$569$	−14.6199	+	10.6220i	−0.612899	+	0.445297i	−0.850434	−	0.526082i	$-0.823661\pi$
$569$	−14.6199	+	10.6220i	−0.612899	+	0.445297i	0.237535	+	0.971379i	$0.423661\pi$
$570$	7.75753	−	0.251096i	0.324927	−	0.0105172i
$571$	−4.25376	+	3.09053i	−0.178014	+	0.129335i	−0.673224	−	0.739438i	$-0.735091\pi$
$571$	−4.25376	+	3.09053i	−0.178014	+	0.129335i	0.495210	+	0.868773i	$0.335091\pi$
$572$	0.768242	+	0.795098i	0.0321218	+	0.0332447i
$573$	−9.18239	+	2.98354i	−0.383600	+	0.124639i
$574$	5.29365	+	3.84606i	0.220953	+	0.160531i
$575$	−2.71831	−	3.27331i	−0.113361	−	0.136506i
$576$	2.16523	+	6.66389i	0.0902179	+	0.277662i
$577$	−4.56807	+	6.28741i	−0.190171	+	0.261748i	−0.893447	−	0.449169i	$-0.851720\pi$
$577$	−4.56807	+	6.28741i	−0.190171	+	0.261748i	0.703275	+	0.710918i	$0.251720\pi$
$578$	−23.8633	−	7.75366i	−0.992583	−	0.322510i
$579$	−18.5831	−	13.5014i	−0.772289	−	0.561101i
$580$	−0.699693	+	2.41684i	−0.0290532	+	0.100354i
$581$	−2.69492	−	8.29411i	−0.111804	−	0.344098i
$582$			12.8501i			0.532652i
$583$	−17.2388	−	17.8414i	−0.713958	−	0.738916i
$584$	−13.1839	+	40.5757i	−0.545552	+	1.67904i
$585$	2.20466	+	2.83671i	0.0911513	+	0.117284i
$586$	18.4781			0.763323
$587$		−	7.22521i		−	0.298216i	−0.988821	−	0.149108i	$-0.952360\pi$
$587$		−	7.22521i		−	0.298216i	0.988821	−	0.149108i	$-0.0476403\pi$
$588$	−1.12538	+	0.365657i	−0.0464097	+	0.0150794i
$589$	−6.77031	−	4.91892i	−0.278966	−	0.202680i
$590$	−3.26919	−	4.20644i	−0.134590	−	0.173176i
$591$	−0.297229	−	0.215950i	−0.0122264	−	0.00888298i
$592$	−14.6630	+	4.76428i	−0.602644	+	0.195811i
$593$		−	15.1769i		−	0.623239i	−0.950207	−	0.311619i	$-0.899129\pi$
$593$		−	15.1769i		−	0.623239i	0.950207	−	0.311619i	$-0.100871\pi$
$594$	−0.854344	+	4.85308i	−0.0350542	+	0.199124i
$595$	−0.237060	+	0.818842i	−0.00971853	+	0.0335693i
$596$	−2.45386			−0.100514
$597$	−21.6056	+	7.02008i	−0.884258	+	0.287313i
$598$	1.19403	+	1.64344i	0.0488276	+	0.0672054i
$599$	16.6965	−	12.1307i	0.682199	−	0.495647i	−0.191887	−	0.981417i	$-0.561461\pi$
$599$	16.6965	−	12.1307i	0.682199	−	0.495647i	0.874087	+	0.485770i	$0.161461\pi$
$600$	−3.28735	+	12.9041i	−0.134205	+	0.526809i
$601$	−3.85300	−	11.8583i	−0.157167	−	0.483711i	0.841207	−	0.540714i	$-0.181846\pi$
$601$	−3.85300	−	11.8583i	−0.157167	−	0.483711i	−0.998374	+	0.0570024i	$0.981846\pi$
$602$		−	17.2135i		−	0.701568i
$603$		−	8.20631i		−	0.334187i
$604$	0.304816	−	0.221462i	0.0124028	−	0.00901115i
$605$	14.4973	−	19.8703i	0.589399	−	0.807842i
$606$	−7.67105	−	5.57334i	−0.311615	−	0.226401i
$607$	−12.1196	+	16.6813i	−0.491921	+	0.677072i	−0.980741	−	0.195313i	$-0.937428\pi$
$607$	−12.1196	+	16.6813i	−0.491921	+	0.677072i	0.488820	+	0.872385i	$0.337428\pi$
$608$	−1.60540	−	2.20965i	−0.0651077	−	0.0896130i
$609$	6.17594			0.250262
$610$	1.43794	+	44.4247i	0.0582205	+	1.79870i
$611$	17.5761	+	12.7698i	0.711052	+	0.516609i
$612$			0.0694593i			0.00280773i
$613$	−21.4925	+	29.5818i	−0.868073	+	1.19480i	0.111511	+	0.993763i	$0.464431\pi$
$613$	−21.4925	+	29.5818i	−0.868073	+	1.19480i	−0.979584	+	0.201036i	$0.935569\pi$
$614$	−6.76168	+	20.8103i	−0.272879	+	0.839835i
$615$	−5.30667	−	6.82804i	−0.213985	−	0.275333i
$616$	9.96043	−	1.40266i	0.401317	−	0.0565147i
$617$	−21.5935	+	29.7209i	−0.869323	+	1.19652i	0.109942	+	0.993938i	$0.464933\pi$
$617$	−21.5935	+	29.7209i	−0.869323	+	1.19652i	−0.979265	+	0.202582i	$0.935067\pi$
$618$	−5.16850	+	7.11383i	−0.207908	+	0.286160i
$619$	−5.48353	+	3.98402i	−0.220402	+	0.160131i	−0.692507	−	0.721411i	$-0.743494\pi$
$619$	−5.48353	+	3.98402i	−0.220402	+	0.160131i	0.472106	+	0.881542i	$0.343494\pi$
$620$	−1.31215	+	1.01979i	−0.0526974	+	0.0409557i
$621$	−0.262964	+	0.809321i	−0.0105524	+	0.0324769i
$622$	−20.7596	−	6.74520i	−0.832384	−	0.270458i
$623$	−1.38980	−	1.91290i	−0.0556812	−	0.0766387i
$624$	2.17064	−	6.68055i	0.0868952	−	0.267436i
$625$	−18.1597	+	17.1821i	−0.726387	+	0.687286i
$626$	−28.6526			−1.14519
$627$	1.08050	+	7.67273i	0.0431508	+	0.306419i
$628$	0.402619	+	0.554157i	0.0160662	+	0.0221133i
$629$	1.18060			0.0470737
$630$	−3.78128	+	0.122393i	−0.150650	+	0.00487624i
$631$	−11.1154	+	34.2096i	−0.442496	+	1.36186i	0.442710	+	0.896665i	$0.354017\pi$
$631$	−11.1154	+	34.2096i	−0.442496	+	1.36186i	−0.885206	+	0.465199i	$0.845983\pi$
$632$	−5.01534	−	6.90302i	−0.199500	−	0.274588i
$633$		−	2.36872i		−	0.0941480i
$634$	−41.7077			−1.65642
$635$	−29.9609	+	10.8185i	−1.18896	+	0.429317i
$636$	0.479588	−	1.47602i	0.0190169	−	0.0585280i
$637$	−8.71488	−	2.83163i	−0.345296	−	0.112193i
$638$	−26.3201	−	4.63343i	−1.04202	−	0.183439i
$639$	−3.00001	−	9.23308i	−0.118679	−	0.365255i
$640$	26.8124	−	9.68157i	1.05985	−	0.382698i
$641$	−36.6321	−	26.6148i	−1.44688	−	1.05122i	−0.986547	−	0.163476i	$-0.947729\pi$
$641$	−36.6321	−	26.6148i	−1.44688	−	1.05122i	−0.460335	−	0.887745i	$-0.652271\pi$
$642$	−17.3886	−	5.64991i	−0.686274	−	0.222984i
$643$	17.8552	+	24.5756i	0.704140	+	0.969166i	0.999903	+	0.0139045i	$0.00442609\pi$
$643$	17.8552	+	24.5756i	0.704140	+	0.969166i	−0.295763	+	0.955261i	$0.595574\pi$
$644$	−0.201057			−0.00792275
$645$	−6.32635	+	21.8522i	−0.249100	+	0.860428i
$646$	0.359093	+	1.10518i	0.0141283	+	0.0434825i
$647$			0.461196i			0.0181315i	0.999959	+	0.00906574i	$0.00288576\pi$
$647$			0.461196i			0.0181315i	−0.999959	+	0.00906574i	$0.997114\pi$
$648$	2.53291	−	0.822991i	0.0995019	−	0.0323301i
$649$	3.82473	−	3.69554i	0.150134	−	0.145063i
$650$	9.18239	−	7.62548i	0.360163	−	0.299096i
$651$	3.30008	+	2.39765i	0.129340	+	0.0939712i
$652$		−	0.121241i		−	0.00474818i
$653$	−4.74471	+	6.53053i	−0.185675	+	0.255560i	−0.891700	−	0.452628i	$-0.850487\pi$
$653$	−4.74471	+	6.53053i	−0.185675	+	0.255560i	0.706025	+	0.708187i	$0.250487\pi$
$654$	3.05824	−	9.41231i	0.119587	−	0.368050i
$655$	−6.65476	−	18.4299i	−0.260023	−	0.720115i
$656$	−5.22480	+	16.0803i	−0.203994	+	0.627829i
$657$	15.2354	+	4.95028i	0.594389	+	0.193129i
$658$	−21.7579	+	7.06957i	−0.848212	+	0.275601i
$659$	−1.70781	+	5.25610i	−0.0665269	+	0.204749i	−0.978794	−	0.204847i	$-0.934330\pi$
$659$	−1.70781	+	5.25610i	−0.0665269	+	0.204749i	0.912267	+	0.409596i	$0.134330\pi$
$660$	1.52323	+	0.217608i	0.0592917	+	0.00847039i
$661$	4.67077	+	14.3752i	0.181672	+	0.559129i	0.999875	−	0.0158003i	$-0.00502959\pi$
$661$	4.67077	+	14.3752i	0.181672	+	0.559129i	−0.818203	+	0.574929i	$0.805030\pi$
$662$	−8.76231	−	12.0603i	−0.340557	−	0.468736i
$663$	−0.316164	+	0.435163i	−0.0122788	+	0.0169003i
$664$	16.5006	−	11.9884i	0.640349	−	0.465241i
$665$	−5.59530	+	2.02038i	−0.216976	+	0.0783469i
$666$	1.61910	+	4.98309i	0.0627390	+	0.193091i
$667$	−4.38925	−	1.42615i	−0.169952	−	0.0552209i
$668$	−1.27801	−	0.415251i	−0.0494478	−	0.0160666i
$669$	5.31373	+	16.3540i	0.205441	+	0.632281i
$670$	−27.2492	+	0.882003i	−1.05273	+	0.0340747i
$671$	−43.9391	+	6.18763i	−1.69625	+	0.238871i
$672$	0.782528	+	1.07706i	0.0301867	+	0.0415484i
$673$	−36.5783	−	11.8850i	−1.40999	−	0.458133i	−0.497582	−	0.867417i	$-0.665779\pi$
$673$	−36.5783	−	11.8850i	−1.40999	−	0.458133i	−0.912407	+	0.409284i	$0.865779\pi$
$674$	−3.90715	+	12.0250i	−0.150498	+	0.463184i
$675$	4.84525	+	1.23433i	0.186494	+	0.0475096i
$676$	1.74878	−	1.27056i	0.0672607	−	0.0488678i
$677$	7.19047	−	9.89683i	0.276352	−	0.380366i	−0.648169	−	0.761496i	$-0.724465\pi$
$677$	7.19047	−	9.89683i	0.276352	−	0.380366i	0.924521	+	0.381130i	$0.124465\pi$
$678$	−5.36181	+	7.37989i	−0.205919	+	0.283423i
$679$	−3.04349	−	9.36691i	−0.116799	−	0.359469i
$680$	−1.99264	+	0.0644980i	−0.0764144	+	0.00247338i
$681$	10.9244	+	7.93701i	0.418622	+	0.304147i
$682$	−12.2652	−	12.6939i	−0.469658	−	0.486075i
$683$	−5.82242	+	8.01388i	−0.222789	+	0.306642i	−0.905750	−	0.423812i	$-0.860692\pi$
$683$	−5.82242	+	8.01388i	−0.222789	+	0.306642i	0.682961	+	0.730454i	$0.260692\pi$
$684$	−0.392145	+	0.284910i	−0.0149940	+	0.0108938i
$685$	−15.4635	−	4.47679i	−0.590830	−	0.171049i
$686$	17.3881	−	12.6332i	0.663882	−	0.482338i
$687$	−25.2269	+	8.19673i	−0.962468	+	0.312725i
$688$	42.3023	−	13.7449i	1.61276	−	0.524018i
$689$	9.72316	−	7.06429i	0.370423	−	0.269128i
$690$	2.71563	+	0.786193i	0.103382	+	0.0299298i
$691$	15.3657	−	11.1638i	0.584537	−	0.424691i	−0.255820	−	0.966724i	$-0.582345\pi$
$691$	15.3657	−	11.1638i	0.584537	−	0.424691i	0.840357	+	0.542033i	$0.182345\pi$
$692$	−1.20853	+	1.66340i	−0.0459415	+	0.0632330i
$693$	−0.526670	−	3.73995i	−0.0200066	−	0.142069i
$694$	13.3482	+	9.69803i	0.506691	+	0.368132i
$695$	13.9155	−	0.450419i	0.527846	−	0.0170854i
$696$	4.46339	+	13.7369i	0.169184	+	0.520696i
$697$	0.761016	−	1.04745i	0.0288255	−	0.0396750i
$698$	−28.9914	+	39.9033i	−1.09734	+	1.51036i
$699$	−9.56194	+	6.94716i	−0.361666	+	0.262766i
$700$	0.0763952	+	1.17887i	0.00288747	+	0.0445570i
$701$	−8.29230	+	25.5211i	−0.313196	+	0.963918i	0.663295	+	0.748358i	$0.269158\pi$
$701$	−8.29230	+	25.5211i	−0.313196	+	0.963918i	−0.976491	+	0.215560i	$0.930842\pi$
$702$	−2.27033	−	0.737676i	−0.0856882	−	0.0278418i
$703$	4.84262	+	6.66530i	0.182643	+	0.251386i
$704$	10.1931	+	20.8843i	0.384167	+	0.787106i
$705$	30.2195	−	0.978145i	1.13813	−	0.0368391i
$706$	8.13116	+	25.0252i	0.306020	+	0.941834i
$707$	6.91176	+	2.24577i	0.259943	+	0.0844607i
$708$	0.316420	+	0.102811i	0.0118918	+	0.00386388i
$709$	−5.26535	−	16.2051i	−0.197744	−	0.608594i	−0.999934	−	0.0115245i	$-0.996332\pi$
$709$	−5.26535	−	16.2051i	−0.197744	−	0.608594i	0.802189	−	0.597070i	$-0.203668\pi$
$710$	−30.3362	+	10.9539i	−1.13850	+	0.411094i
$711$	−2.59195	+	1.88316i	−0.0972057	+	0.0706241i
$712$	3.25037	−	4.47375i	0.121813	−	0.167661i
$713$	−1.79170	−	2.46607i	−0.0670998	−	0.0923550i
$714$	−0.175034	−	0.538700i	−0.00655049	−	0.0201603i
$715$	8.55253	+	8.29674i	0.319847	+	0.310280i
$716$	−1.39939	+	4.30689i	−0.0522978	+	0.160956i
$717$	−3.10030	+	1.00735i	−0.115783	+	0.0376201i
$718$	7.95832	+	2.58582i	0.297002	+	0.0965018i
$719$	7.13894	−	21.9714i	0.266238	−	0.819395i	−0.725168	−	0.688572i	$-0.758238\pi$
$719$	7.13894	−	21.9714i	0.266238	−	0.819395i	0.991406	−	0.130823i	$-0.0417621\pi$
$720$	−3.32011	−	9.19482i	−0.123733	−	0.342671i
$721$	2.08264	−	6.40970i	0.0775614	−	0.238710i
$722$	11.8263	−	16.2775i	0.440129	−	0.605786i
$723$			24.1229i			0.897141i
$724$	−3.02268	−	2.19610i	−0.112337	−	0.0816175i
$725$	−6.69426	+	26.2776i	−0.248619	+	0.975926i
$726$	−0.561339	+	16.3337i	−0.0208332	+	0.606200i
$727$	11.2608	−	3.65885i	0.417639	−	0.135699i	−0.0926568	−	0.995698i	$-0.529536\pi$
$727$	11.2608	−	3.65885i	0.417639	−	0.135699i	0.510296	+	0.859999i	$0.329536\pi$
$728$			4.87283i			0.180599i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	14.8000	−	51.1215i	0.547773	−	1.89209i
$731$	−3.40601			−0.125976
$732$	−1.63158	−	2.24568i	−0.0603050	−	0.0830027i
$733$	−35.9672	−	11.6864i	−1.32848	−	0.431649i	−0.443080	−	0.896482i	$-0.646114\pi$
$733$	−35.9672	−	11.6864i	−1.32848	−	0.431649i	−0.885398	+	0.464833i	$0.846114\pi$
$734$	−2.22441	−	1.61613i	−0.0821046	−	0.0596525i
$735$	−11.9948	+	4.33114i	−0.442434	+	0.159756i
$736$	−0.307429	−	0.946168i	−0.0113320	−	0.0348762i
$737$	−3.79536	−	26.9513i	−0.139804	−	0.992764i
$738$	5.46475	+	1.77561i	0.201160	+	0.0653609i
$739$	9.71365	−	29.8955i	0.357322	−	1.09973i	−0.597328	−	0.801997i	$-0.703771\pi$
$739$	9.71365	−	29.8955i	0.357322	−	1.09973i	0.954651	−	0.297729i	$-0.0962290\pi$
$740$	1.53882	−	0.555645i	0.0565682	−	0.0204259i
$741$	−3.75364			−0.137893
$742$			12.6560i			0.464616i
$743$	29.6786	+	40.8491i	1.08880	+	1.49861i	0.849447	+	0.527675i	$0.176936\pi$
$743$	29.6786	+	40.8491i	1.08880	+	1.49861i	0.239355	+	0.970932i	$0.423064\pi$
$744$	−2.94801	+	9.07303i	−0.108079	+	0.332633i
$745$	−26.4323	+	0.855562i	−0.968405	+	0.0313454i
$746$	−21.0837			−0.771931
$747$	−4.50141	−	6.19567i	−0.164698	−	0.226688i
$748$	0.0321245	+	0.228120i	0.00117459	+	0.00834088i
$749$	14.0134			0.512039
$750$	3.57787	−	16.2214i	0.130645	−	0.592321i
$751$	8.65908	−	26.6499i	0.315974	−	0.972469i	−0.659377	−	0.751812i	$-0.729180\pi$
$751$	8.65908	−	26.6499i	0.315974	−	0.972469i	0.975352	−	0.220657i	$-0.0708201\pi$
$752$	−34.7471	−	47.8253i	−1.26710	−	1.74401i
$753$	−13.8976	−	4.51562i	−0.506458	−	0.164558i
$754$	4.00069	−	12.3129i	0.145697	−	0.448408i
$755$	3.20619	−	2.49181i	0.116685	−	0.0906862i
$756$	0.191145	−	0.138875i	0.00695187	−	0.00505083i
$757$	5.16566	−	7.10993i	0.187749	−	0.258415i	−0.704758	−	0.709448i	$-0.748944\pi$
$757$	5.16566	−	7.10993i	0.187749	−	0.258415i	0.892507	+	0.451033i	$0.148944\pi$
$758$	9.94475	−	13.6878i	0.361210	−	0.497162i
$759$	−0.489327	+	2.77961i	−0.0177614	+	0.100893i
$760$	−8.53761	−	10.9853i	−0.309691	−	0.398477i
$761$	13.2757	−	40.8585i	0.481245	−	1.48112i	−0.356101	−	0.934448i	$-0.615894\pi$
$761$	13.2757	−	40.8585i	0.481245	−	1.48112i	0.837346	−	0.546673i	$-0.184106\pi$
$762$	12.4409	−	17.1234i	0.450684	−	0.620314i
$763$			7.58534i			0.274608i
$764$	−1.62061	−	1.17744i	−0.0586316	−	0.0425983i
$765$	0.0242177	+	0.748199i	0.000875593	+	0.0270512i
$766$	20.9612			0.757360
$767$	1.51440	+	2.08439i	0.0546817	+	0.0752629i
$768$	−2.89645	+	3.98662i	−0.104517	+	0.143855i
$769$	22.8608	+	16.6093i	0.824381	+	0.598948i	0.917964	−	0.396664i	$-0.129832\pi$
$769$	22.8608	+	16.6093i	0.824381	+	0.598948i	−0.0935829	+	0.995611i	$0.529832\pi$
$770$	−12.3620	+	2.15078i	−0.445494	+	0.0775088i
$771$	0.954421	−	0.693427i	0.0343726	−	0.0249732i
$772$		−	4.76577i		−	0.171524i
$773$			40.9479i			1.47279i	0.676551	+	0.736396i	$0.263474\pi$
$773$			40.9479i			1.47279i	−0.676551	+	0.736396i	$0.736526\pi$
$774$	−4.67108	−	14.3761i	−0.167898	−	0.516738i
$775$	−13.7786	+	11.4424i	−0.494943	+	0.411024i
$776$	18.6349	−	13.5391i	0.668954	−	0.486024i
$777$	−2.36046	−	3.24889i	−0.0846810	−	0.116553i
$778$	−21.0721	+	6.84675i	−0.755472	+	0.245468i
$779$	9.03511			0.323716
$780$	−0.207287	+	0.716001i	−0.00742208	+	0.0256370i
$781$	−14.1229	−	28.9360i	−0.505358	−	1.03541i
$782$			0.423274i			0.0151363i
$783$	5.15794	−	1.67592i	0.184330	−	0.0598923i
$784$	20.1720	+	14.6558i	0.720428	+	0.523422i
$785$	4.53012	+	5.82886i	0.161687	+	0.208041i
$786$	10.5331	+	7.65274i	0.375703	+	0.272964i
$787$	−6.49565	+	2.11056i	−0.231545	+	0.0752335i	−0.422491	−	0.906367i	$-0.638844\pi$
$787$	−6.49565	+	2.11056i	−0.231545	+	0.0752335i	0.190946	+	0.981600i	$0.438844\pi$
$788$		−	0.0762263i		−	0.00271545i
$789$	17.3212			0.616652
$790$	6.53165	+	8.40422i	0.232386	+	0.299009i
$791$	2.16053	−	6.64942i	0.0768195	−	0.236426i
$792$	7.93799	−	3.87434i	0.282064	−	0.137669i
$793$		−	21.4958i		−	0.763338i
$794$	−4.03572	−	12.4207i	−0.143222	−	0.440793i
$795$	4.65137	−	16.0665i	0.164967	−	0.569821i
$796$	−3.81319	−	2.77045i	−0.135155	−	0.0981959i
$797$	27.2448	+	8.85238i	0.965061	+	0.313567i	0.748821	−	0.662773i	$-0.230620\pi$
$797$	27.2448	+	8.85238i	0.965061	+	0.313567i	0.216241	+	0.976340i	$0.430620\pi$
$798$	2.32337	−	3.19784i	0.0822463	−	0.113202i
$799$	1.39885	+	4.30522i	0.0494877	+	0.152308i
$800$	−5.43090	+	2.16208i	−0.192011	+	0.0764409i
$801$	−1.67980	−	1.22045i	−0.0593529	−	0.0431224i
$802$	−25.1229	+	8.16292i	−0.887120	+	0.288243i
$803$	52.3259	+	9.21154i	1.84654	+	0.325068i
$804$	1.37745	−	1.00078i	0.0485790	−	0.0352947i
$805$	−2.16573	+	0.0701006i	−0.0763321	+	0.00247072i
$806$	6.91790	−	5.02615i	0.243672	−	0.177038i
$807$	−19.4735	+	6.32733i	−0.685501	+	0.222733i
$808$			16.9966i			0.597937i
$809$	8.37642	+	25.7800i	0.294499	+	0.906375i	0.983389	+	0.181509i	$0.0580983\pi$
$809$	8.37642	+	25.7800i	0.294499	+	0.906375i	−0.688890	+	0.724866i	$0.741902\pi$
$810$	−3.12479	+	1.12831i	−0.109794	+	0.0396449i
$811$	40.6518			1.42748			0.713739	−	0.700411i	$-0.247000\pi$
$811$	40.6518			1.42748			0.713739	+	0.700411i	$0.247000\pi$
$812$	0.753170	+	1.03665i	0.0264311	+	0.0363793i
$813$	−8.61753	−	2.80001i	−0.302230	−	0.0982005i
$814$	7.62214	+	15.6167i	0.267156	+	0.547366i
$815$	−0.0422721	−	1.30598i	−0.00148073	−	0.0457465i
$816$	1.18410	−	0.860298i	0.0414518	−	0.0301165i
$817$	−13.9709	−	19.2292i	−0.488778	−	0.672745i
$818$	−15.1109	+	4.90984i	−0.528342	+	0.171669i
$819$	1.82965			0.0639332
$820$	0.498946	−	1.72343i	0.0174240	−	0.0601850i
$821$	−15.0989	−	10.9700i	−0.526955	−	0.382855i	0.292263	−	0.956338i	$-0.405592\pi$
$821$	−15.0989	−	10.9700i	−0.526955	−	0.382855i	−0.819218	+	0.573483i	$0.805592\pi$
$822$	10.1731	−	3.30545i	0.354829	−	0.115291i
$823$	−8.86937	−	2.88183i	−0.309167	−	0.100454i	0.150324	−	0.988637i	$-0.451968\pi$
$823$	−8.86937	−	2.88183i	−0.309167	−	0.100454i	−0.459491	+	0.888182i	$0.651968\pi$
$824$	15.7620			0.549094
$825$	16.4837	+	1.81293i	0.573890	+	0.0631182i
$826$	−2.71311			−0.0944013
$827$	27.1453	+	8.82004i	0.943934	+	0.306703i	0.740249	−	0.672333i	$-0.234708\pi$
$827$	27.1453	+	8.82004i	0.943934	+	0.306703i	0.203686	+	0.979036i	$0.434708\pi$
$828$	−0.167916	+	0.0545592i	−0.00583548	+	0.00189606i
$829$	19.3361	+	14.0485i	0.671570	+	0.487924i	0.870551	−	0.492079i	$-0.163763\pi$
$829$	19.3361	+	14.0485i	0.671570	+	0.487924i	−0.198980	+	0.980004i	$0.563763\pi$
$830$	−20.0890	+	15.6129i	−0.697300	+	0.541933i
$831$	−18.5780			−0.644464
$832$	−10.7069	+	3.47888i	−0.371194	+	0.120608i
$833$	−1.12227	−	1.54467i	−0.0388844	−	0.0535198i
$834$	−7.48425	+	5.43762i	−0.259158	+	0.188290i
$835$	−13.9112	−	4.02739i	−0.481417	−	0.139374i
$836$	−1.15612	+	1.11707i	−0.0399853	+	0.0386347i
$837$	3.40675	+	1.10692i	0.117754	+	0.0382607i
$838$	−8.35019	−	11.4931i	−0.288453	−	0.397021i
$839$	−24.9313			−0.860722			−0.430361	−	0.902657i	$-0.641614\pi$
$839$	−24.9313			−0.860722			−0.430361	+	0.902657i	$0.641614\pi$
$840$	4.16152	+	5.35459i	0.143586	+	0.184751i
$841$	0.127628	+	0.392800i	0.00440098	+	0.0135448i
$842$		−	36.9797i		−	1.27440i
$843$	−24.3220	+	7.90271i	−0.837696	+	0.272184i
$844$	0.397596	−	0.288870i	0.0136858	−	0.00994333i
$845$	18.3944	−	14.2959i	0.632787	−	0.491794i
$846$	−16.2531	+	11.8085i	−0.558792	+	0.405986i
$847$	−3.45940	−	12.0392i	−0.118866	−	0.413673i
$848$	−31.1023	+	10.1057i	−1.06806	+	0.347033i
$849$	−9.75812	−	7.08969i	−0.334898	−	0.243318i
$850$	2.48180	−	0.160831i	0.0851252	−	0.00551645i
$851$	0.927344	+	2.85407i	0.0317890	+	0.0978363i
$852$	1.18394	−	1.62956i	0.0405612	−	0.0558277i
$853$	−3.66268	−	1.19008i	−0.125408	−	0.0407475i	0.245641	−	0.969361i	$-0.421002\pi$
$853$	−3.66268	−	1.19008i	−0.125408	−	0.0407475i	−0.371049	+	0.928613i	$0.621002\pi$
$854$	18.3129	+	13.3051i	0.626655	+	0.455292i
$855$	−4.12475	+	3.20570i	−0.141063	+	0.109633i
$856$	10.1276	+	31.1695i	0.346154	+	1.06535i
$857$		−	46.7797i		−	1.59797i	−0.601354	−	0.798983i	$-0.705372\pi$
$857$		−	46.7797i		−	1.59797i	0.601354	−	0.798983i	$-0.294628\pi$
$858$	−7.79744	−	1.37268i	−0.266200	−	0.0468624i
$859$	17.2747	−	53.1662i	0.589407	−	1.81401i	0.00860323	−	0.999963i	$-0.497261\pi$
$859$	17.2747	−	53.1662i	0.589407	−	1.81401i	0.580803	−	0.814044i	$-0.302739\pi$
$860$	−4.43946	+	1.60302i	−0.151384	+	0.0546627i
$861$	−4.40402			−0.150089
$862$			6.06930i			0.206721i
$863$	30.5781	−	9.93542i	1.04089	−	0.338206i	0.261803	−	0.965121i	$-0.415683\pi$
$863$	30.5781	−	9.93542i	1.04089	−	0.338206i	0.779087	+	0.626916i	$0.215683\pi$
$864$	0.945813	+	0.687173i	0.0321772	+	0.0233781i
$865$	−12.4380	+	18.3391i	−0.422906	+	0.623548i
$866$	34.0380	+	24.7301i	1.15666	+	0.840362i
$867$	16.0614	−	5.21866i	0.545473	−	0.177235i
$868$			0.846327i			0.0287262i
$869$	−7.64158	+	7.38348i	−0.259223	+	0.250467i
$870$	−6.11928	−	16.9469i	−0.207463	−	0.574554i
$871$	13.1851			0.446759
$872$	−16.8718	+	5.48197i	−0.571350	+	0.185643i
$873$	−5.08365	−	6.99704i	−0.172055	−	0.236814i
$874$	−2.38967	+	1.73620i	−0.0808317	+	0.0587277i
$875$	1.23393	+	12.6718i	0.0417146	+	0.428386i
$876$	1.02707	+	3.16101i	0.0347016	+	0.106800i
$877$		−	25.3900i		−	0.857359i	−0.903457	−	0.428680i	$-0.858979\pi$
$877$		−	25.3900i		−	0.857359i	0.903457	−	0.428680i	$-0.141021\pi$
$878$		−	36.9041i		−	1.24545i
$879$	−10.0616	+	7.31017i	−0.339369	+	0.246566i
$880$	−15.1565	−	28.6623i	−0.510927	−	0.966205i
$881$	9.78071	+	7.10610i	0.329521	+	0.239411i	0.740227	−	0.672357i	$-0.234718\pi$
$881$	9.78071	+	7.10610i	0.329521	+	0.239411i	−0.410707	+	0.911768i	$0.634718\pi$
$882$	4.98066	−	6.85529i	0.167708	−	0.230830i
$883$	30.6203	+	42.1452i	1.03046	+	1.41830i	0.904605	+	0.426251i	$0.140166\pi$
$883$	30.6203	+	42.1452i	1.03046	+	1.41830i	0.125851	+	0.992049i	$0.459834\pi$
$884$	−0.111600			−0.00375353
$885$	3.44424	+	0.997132i	0.115777	+	0.0335182i
$886$	23.7742	+	17.2730i	0.798711	+	0.580297i
$887$		−	22.1114i		−	0.742428i	−0.928547	−	0.371214i	$-0.878942\pi$
$887$		−	22.1114i		−	0.742428i	0.928547	−	0.371214i	$-0.121058\pi$
$888$	5.52047	−	7.59827i	0.185255	−	0.254981i
$889$	−5.01301	+	15.4285i	−0.168131	+	0.517454i
$890$	−3.87198	+	5.70899i	−0.129789	+	0.191366i
$891$	−1.45474	−	2.98056i	−0.0487355	−	0.0998525i
$892$	−2.09704	+	2.88633i	−0.0702142	+	0.0966415i
$893$	−18.5680	+	25.5567i	−0.621355	+	0.855222i
$894$	14.2162	−	10.3287i	0.475461	−	0.345442i
$895$	−13.5723	+	46.8807i	−0.453671	+	1.56705i
$896$	4.48621	−	13.8071i	0.149874	−	0.461264i
$897$	−1.30034	−	0.422505i	−0.0434169	−	0.0141070i
$898$	−11.2983	−	15.5508i	−0.377030	−	0.518937i
$899$	−6.00324	+	18.4761i	−0.200219	+	0.616211i
$900$	0.383702	+	0.963819i	0.0127901	+	0.0321273i
$901$	2.50423			0.0834280
$902$	18.7686	+	3.30407i	0.624928	+	0.110013i
$903$	6.80987	+	9.37298i	0.226618	+	0.311913i
$904$	16.3515			0.543842
$905$	−33.3252	−	22.6020i	−1.10777	−	0.751315i
$906$	−0.833757	+	2.56604i	−0.0276997	+	0.0852509i
$907$	17.6290	+	24.2643i	0.585362	+	0.805681i	0.994270	−	0.106894i	$-0.0340905\pi$
$907$	17.6290	+	24.2643i	0.585362	+	0.805681i	−0.408909	+	0.912575i	$0.634091\pi$
$908$			2.80162i			0.0929751i
$909$	6.38188			0.211674
$910$	−0.196648	−	6.07539i	−0.00651883	−	0.201397i
$911$	−13.9466	+	42.9234i	−0.462073	+	1.42211i	0.400554	+	0.916273i	$0.368818\pi$
$911$	−13.9466	+	42.9234i	−0.462073	+	1.42211i	−0.862627	+	0.505841i	$0.831182\pi$
$912$	9.71393	+	3.15625i	0.321660	+	0.104514i
$913$	−17.6491	−	18.2661i	−0.584100	−	0.604518i
$914$	17.4903	+	53.8297i	0.578529	+	1.78053i
$915$	−18.3580	−	23.6210i	−0.606895	−	0.780887i
$916$	−4.45233	−	3.23481i	−0.147109	−	0.106881i
$917$	−9.49052	−	3.08366i	−0.313405	−	0.101831i
$918$	−0.292365	−	0.402407i	−0.00964950	−	0.0132814i
$919$	19.0384			0.628019			0.314009	−	0.949420i	$-0.398328\pi$
$919$	19.0384			0.628019			0.314009	+	0.949420i	$0.398328\pi$
$920$	−1.72111	−	4.76650i	−0.0567434	−	0.157147i
$921$	−4.55099	−	14.0065i	−0.149960	−	0.461530i
$922$			15.5147i			0.510948i
$923$	14.8348	−	4.82012i	0.488293	−	0.158656i
$924$	0.563533	−	0.544499i	0.0185389	−	0.0179127i
$925$	16.3821	−	6.52180i	0.538639	−	0.214435i
$926$	16.5207	+	12.0030i	0.542905	+	0.394444i
$927$		−	5.91831i		−	0.194383i
$928$	−3.72680	+	5.12950i	−0.122338	+	0.168384i
$929$	4.79898	−	14.7697i	0.157449	−	0.484579i	−0.840951	−	0.541111i	$-0.818004\pi$
$929$	4.79898	−	14.7697i	0.157449	−	0.484579i	0.998401	+	0.0565312i	$0.0180041\pi$
$930$	3.30939	−	11.4311i	0.108519	−	0.374841i
$931$	4.11737	−	12.6720i	0.134941	−	0.415307i
$932$	−2.33220	−	0.757779i	−0.0763938	−	0.0248219i
$933$	13.9724	−	4.53990i	0.457436	−	0.148630i
$934$	9.00526	−	27.7153i	0.294661	−	0.906873i
$935$	0.425573	+	2.44605i	0.0139177	+	0.0799943i
$936$	1.32230	+	4.06962i	0.0432207	+	0.133020i
$937$	−5.34348	−	7.35467i	−0.174564	−	0.240267i	0.712766	−	0.701402i	$-0.247442\pi$
$937$	−5.34348	−	7.35467i	−0.174564	−	0.240267i	−0.887330	+	0.461135i	$0.847442\pi$
$938$	−8.16109	+	11.2328i	−0.266469	+	0.366763i
$939$	15.6018	−	11.3353i	0.509144	−	0.369915i
$940$	3.84952	+	4.95314i	0.125558	+	0.161554i
$941$	−0.860081	−	2.64706i	−0.0280378	−	0.0862916i	0.936058	−	0.351845i	$-0.114445\pi$
$941$	−0.860081	−	2.64706i	−0.0280378	−	0.0862916i	−0.964096	+	0.265553i	$0.914445\pi$
$942$	−4.66507	−	1.51577i	−0.151996	−	0.0493866i
$943$	3.12994	+	1.01698i	0.101925	+	0.0331174i
$944$	−2.16641	−	6.66751i	−0.0705105	−	0.217009i
$945$	2.01054	−	1.56257i	0.0654030	−	0.0508304i
$946$	−21.9897	−	45.0539i	−0.714947	−	1.46483i
$947$	16.7615	+	23.0702i	0.544674	+	0.749679i	0.989278	−	0.146048i	$-0.0466554\pi$
$947$	16.7615	+	23.0702i	0.544674	+	0.749679i	−0.444603	+	0.895727i	$0.646655\pi$
$948$	−0.632189	−	0.205411i	−0.0205325	−	0.00667142i
$949$	−7.95362	+	24.4787i	−0.258185	+	0.794613i
$950$	11.0879	+	13.3518i	0.359740	+	0.433188i
$951$	22.7104	−	16.5001i	0.736437	−	0.535053i
$952$	−0.596793	+	0.821416i	−0.0193422	+	0.0266222i
$953$	−8.53054	+	11.7413i	−0.276331	+	0.380338i	−0.924514	−	0.381147i	$-0.875529\pi$
$953$	−8.53054	+	11.7413i	−0.276331	+	0.380338i	0.648183	+	0.761485i	$0.275529\pi$
$954$	3.43436	+	10.5699i	0.111191	+	0.342212i
$955$	−17.8673	−	12.1181i	−0.578173	−	0.392131i
$956$	−0.547176	−	0.397546i	−0.0176969	−	0.0128576i
$957$	16.1647	−	7.88959i	0.522531	−	0.255034i
$958$	−23.4895	+	32.3305i	−0.758911	+	1.04455i
$959$	−6.63272	+	4.81895i	−0.214182	+	0.155612i
$960$	−8.79439	+	12.9668i	−0.283838	+	0.418501i
$961$	14.6989	−	10.6794i	0.474157	−	0.344496i
$962$	−8.00633	+	2.60142i	−0.258135	+	0.0838730i
$963$	11.7035	−	3.80271i	0.377141	−	0.122541i
$964$	−4.04910	+	2.94185i	−0.130413	+	0.0947505i
$965$	−1.66163	−	51.3357i	−0.0534899	−	1.65255i
$966$	1.16481	−	0.846281i	0.0374770	−	0.0272286i
$967$	18.8965	−	26.0088i	0.607670	−	0.836386i	−0.388714	−	0.921359i	$-0.627080\pi$
$967$	18.8965	−	26.0088i	0.607670	−	0.836386i	0.996383	+	0.0849731i	$0.0270804\pi$
$968$	24.2783	−	16.3954i	0.780333	−	0.526969i
$969$	−0.632753	−	0.459722i	−0.0203270	−	0.0147684i
$970$	−22.6874	+	17.6324i	−0.728449	+	0.566142i
$971$	−16.7009	−	51.4001i	−0.535958	−	1.64951i	−0.741570	−	0.670876i	$-0.765918\pi$
$971$	−16.7009	−	51.4001i	−0.535958	−	1.64951i	0.205612	−	0.978634i	$-0.434082\pi$
$972$	0.121952	−	0.167853i	0.00391162	−	0.00538389i
$973$	4.16768	−	5.73632i	0.133610	−	0.183898i
$974$	21.7233	−	15.7829i	0.696059	−	0.505716i
$975$	−1.98321	+	7.78486i	−0.0635134	+	0.249315i
$976$	−18.0747	+	55.6283i	−0.578558	+	1.78062i
$977$	54.9031	+	17.8391i	1.75651	+	0.570723i	0.996829	−	0.0795765i	$-0.0253568\pi$
$977$	54.9031	+	17.8391i	1.75651	+	0.570723i	0.759677	+	0.650300i	$0.225357\pi$
$978$	0.510324	+	0.702401i	0.0163184	+	0.0224603i
$979$	−6.08129	−	3.23132i	−0.194359	−	0.103274i
$980$	−2.18979	−	1.48517i	−0.0699501	−	0.0474419i
$981$	2.05837	+	6.33502i	0.0657188	+	0.202262i
$982$	−34.5787	−	11.2353i	−1.10345	−	0.358533i
$983$	−6.65373	−	2.16193i	−0.212221	−	0.0689548i	0.200977	−	0.979596i	$-0.435588\pi$
$983$	−6.65373	−	2.16193i	−0.212221	−	0.0689548i	−0.413198	+	0.910641i	$0.635588\pi$
$984$	−3.18281	−	9.79569i	−0.101464	−	0.312275i
$985$	−0.0265771	−	0.821091i	−0.000846817	−	0.0261621i
$986$	2.18240	−	1.58561i	0.0695019	−	0.0504961i
$987$	9.05068	−	12.4572i	0.288086	−	0.396517i
$988$	−0.457765	−	0.630059i	−0.0145634	−	0.0200449i
$989$	−2.67537	−	8.23393i	−0.0850717	−	0.261824i
$990$	−9.74065	+	5.15083i	−0.309578	+	0.163704i
$991$	−7.38517	+	22.7292i	−0.234598	+	0.722018i	0.762577	+	0.646898i	$0.223934\pi$
$991$	−7.38517	+	22.7292i	−0.234598	+	0.722018i	−0.997175	+	0.0751198i	$0.976066\pi$
$992$	−3.98279	+	1.29409i	−0.126454	+	0.0410873i
$993$	9.54241	+	3.10052i	0.302819	+	0.0983920i
$994$	−5.07579	+	15.6217i	−0.160994	+	0.495490i
$995$	−42.0407	−	28.5131i	−1.33278	−	0.903925i
$996$	0.491003	−	1.51115i	0.0155580	−	0.0478827i
$997$	−5.40154	+	7.43458i	−0.171068	+	0.235455i	−0.885940	−	0.463801i	$-0.846485\pi$
$997$	−5.40154	+	7.43458i	−0.171068	+	0.235455i	0.714871	+	0.699256i	$0.246485\pi$
$998$			46.9866i			1.48733i
$999$	−2.85300	−	2.07283i	−0.0902650	−	0.0655813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.cb.a.169.16	yes	240
11.3	even	5		825.2.by.a.619.16	yes	240
25.4	even	10		825.2.by.a.4.16	✓	240
275.179	even	10	inner	825.2.cb.a.454.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.by.a.4.16	✓	240	25.4	even	10
825.2.by.a.619.16	yes	240	11.3	even	5
825.2.cb.a.169.16	yes	240	1.1	even	1	trivial
825.2.cb.a.454.16	yes	240	275.179	even	10	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.cb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41304 - 0.459125i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.167853 + 0.121952i) q^{4} +(1.85059 + 1.25512i) q^{5} -1.48576 q^{6} +(1.08303 - 0.351897i) q^{7} +(1.56542 + 2.15462i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-2.03870 - 2.62318i) q^{10} +(2.38514 - 2.30458i) q^{11} +(0.197323 + 0.0641141i) q^{12} +(0.944395 + 1.29985i) q^{13} -1.69193 q^{14} +(2.14787 + 0.621823i) q^{15} +(-1.35099 - 4.15793i) q^{16} +0.334780i q^{17} +(-1.41304 + 0.459125i) q^{18} +(-1.89006 + 1.37321i) q^{19} +(0.157563 + 0.436359i) q^{20} +(0.921279 - 0.669348i) q^{21} +(-4.42839 + 2.16139i) q^{22} +(-0.809321 + 0.262964i) q^{23} +(2.15462 + 1.56542i) q^{24} +(1.84937 + 4.64541i) q^{25} +(-0.737676 - 2.27033i) q^{26} +(0.587785 - 0.809017i) q^{27} +(0.224704 + 0.0730108i) q^{28} +(4.38760 + 3.18778i) q^{29} +(-2.74953 - 1.86480i) q^{30} +(1.10692 + 3.40675i) q^{31} +1.16909i q^{32} +(1.55625 - 2.92884i) q^{33} +(0.153706 - 0.473057i) q^{34} +(2.44591 + 0.708109i) q^{35} +0.207478 q^{36} -3.52650i q^{37} +(3.30120 - 1.07263i) q^{38} +(1.29985 + 0.944395i) q^{39} +(0.192658 + 5.95210i) q^{40} +(-3.12877 - 2.27318i) q^{41} +(-1.60912 + 0.522834i) q^{42} +10.1739i q^{43} +(0.681402 - 0.0959571i) q^{44} +(2.23490 - 0.0723392i) q^{45} +1.26434 q^{46} +(12.8598 - 4.17842i) q^{47} +(-2.56974 - 3.53695i) q^{48} +(-4.61400 + 3.35227i) q^{49} +(-0.480407 - 7.41324i) q^{50} +(0.103453 + 0.318395i) q^{51} +0.333354i q^{52} -7.48023i q^{53} +(-1.20200 + 0.873307i) q^{54} +(7.30644 - 1.27120i) q^{55} +(2.45360 + 1.78264i) q^{56} +(-1.37321 + 1.89006i) q^{57} +(-4.73627 - 6.51892i) q^{58} +1.60356 q^{59} +(0.284693 + 0.366312i) q^{60} +(-10.8237 - 7.86389i) q^{61} -5.32208i q^{62} +(0.669348 - 0.921279i) q^{63} +(-2.16523 + 6.66389i) q^{64} +(0.116227 + 3.59081i) q^{65} +(-3.54375 + 3.42405i) q^{66} +(4.82355 - 6.63904i) q^{67} +(-0.0408272 + 0.0561938i) q^{68} +(-0.688449 + 0.500188i) q^{69} +(-3.13106 - 2.12356i) q^{70} +(3.00001 - 9.23308i) q^{71} +(2.53291 + 0.822991i) q^{72} +(9.41599 + 12.9600i) q^{73} +(-1.61910 + 4.98309i) q^{74} +(3.19436 + 3.84656i) q^{75} -0.484718 q^{76} +(1.77220 - 3.33525i) q^{77} +(-1.40314 - 1.93126i) q^{78} -3.20383 q^{79} +(2.71855 - 9.39028i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.37740 + 4.64859i) q^{82} -7.65826i q^{83} +0.236268 q^{84} +(-0.420188 + 0.619540i) q^{85} +(4.67108 - 14.3761i) q^{86} +(5.15794 + 1.67592i) q^{87} +(8.69925 + 1.53143i) q^{88} +(-0.641628 - 1.97473i) q^{89} +(-3.19121 - 0.923878i) q^{90} +(1.48022 + 1.07544i) q^{91} +(-0.167916 - 0.0545592i) q^{92} +(2.10548 + 2.89795i) q^{93} -20.0899 q^{94} +(-5.22126 + 0.169002i) q^{95} +(0.361268 + 1.11187i) q^{96} -8.64882i q^{97} +(8.05888 - 2.61849i) q^{98} +(0.575022 - 3.26640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 60 q^{4} + 6 q^{5} - 16 q^{6} + 10 q^{7} + 60 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} - 64 q^{16} - 24 q^{19} - 44 q^{20} + 8 q^{21} - 40 q^{22} + 40 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{26} + 30 q^{28}+ \cdots - 4 q^{99}+O(q^{100}) \) 240 * q + 60 * q^4 + 6 * q^5 - 16 * q^6 + 10 * q^7 + 60 * q^9 + 8 * q^10 + 4 * q^11 - 20 * q^12 - 64 * q^16 - 24 * q^19 - 44 * q^20 + 8 * q^21 - 40 * q^22 + 40 * q^23 - 12 * q^24 + 4 * q^25 + 40 * q^26 + 30 * q^28 + 4 * q^30 - 2 * q^31 + 30 * q^35 + 240 * q^36 - 16 * q^39 + 68 * q^40 - 6 * q^41 - 10 * q^42 + 26 * q^44 + 4 * q^45 - 48 * q^46 - 40 * q^47 + 40 * q^48 + 58 * q^49 - 78 * q^50 + 16 * q^51 - 4 * q^54 - 10 * q^55 - 40 * q^57 + 60 * q^58 - 24 * q^59 + 8 * q^60 + 28 * q^61 - 10 * q^63 + 44 * q^64 + 60 * q^65 + 8 * q^66 - 40 * q^67 - 250 * q^68 + 2 * q^69 - 44 * q^70 - 16 * q^71 + 22 * q^74 + 20 * q^75 - 168 * q^76 - 30 * q^77 + 172 * q^79 - 118 * q^80 - 60 * q^81 + 40 * q^82 + 96 * q^84 + 40 * q^85 - 72 * q^86 - 40 * q^87 - 100 * q^88 + 2 * q^90 - 30 * q^91 + 100 * q^92 + 56 * q^94 - 122 * q^95 + 28 * q^96 - 140 * q^98 - 4 * q^99

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