LMFDB - Embedded newform 725.2.p.b.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(149,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("725.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.p (of order $14$, degree $6$, not 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			149.2
Character	$\chi$	$=$	725.149
Dual form			725.2.p.b.399.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.416060 + 1.82288i) q^{2} +(0.896481 - 0.431723i) q^{3} +(-1.34784 - 0.649083i) q^{4} +(0.413987 + 1.81380i) q^{6} +(-0.393550 - 0.817215i) q^{7} +(-0.587568 + 0.736786i) q^{8} +(-1.25318 + 1.57143i) q^{9} +O(q^{10})$	\(q+(-0.416060 + 1.82288i) q^{2} +(0.896481 - 0.431723i) q^{3} +(-1.34784 - 0.649083i) q^{4} +(0.413987 + 1.81380i) q^{6} +(-0.393550 - 0.817215i) q^{7} +(-0.587568 + 0.736786i) q^{8} +(-1.25318 + 1.57143i) q^{9} +(-4.84001 + 3.85978i) q^{11} -1.48853 q^{12} +(1.31550 - 1.04908i) q^{13} +(1.65342 - 0.377383i) q^{14} +(-2.96407 - 3.71683i) q^{16} +2.61099 q^{17} +(-2.34313 - 2.93819i) q^{18} +(-0.943542 + 1.95929i) q^{19} +(-0.705621 - 0.562714i) q^{21} +(-5.02216 - 10.4286i) q^{22} +(2.64871 - 0.604551i) q^{23} +(-0.208656 + 0.914181i) q^{24} +(1.36501 + 2.83448i) q^{26} +(-1.10926 + 4.86000i) q^{27} +1.35692i q^{28} +(-3.35329 + 4.21372i) q^{29} +(-6.14573 - 1.40272i) q^{31} +(6.31043 - 3.03894i) q^{32} +(-2.67262 + 5.54976i) q^{33} +(-1.08633 + 4.75952i) q^{34} +(2.70907 - 1.30462i) q^{36} +(-5.71479 + 7.16612i) q^{37} +(-3.17897 - 2.53514i) q^{38} +(0.726413 - 1.50841i) q^{39} +9.46763i q^{41} +(1.31934 - 1.05214i) q^{42} +(-1.36716 - 5.98990i) q^{43} +(9.02885 - 2.06078i) q^{44} +5.07980i q^{46} +(-3.06916 - 3.84861i) q^{47} +(-4.26187 - 2.05241i) q^{48} +(3.85147 - 4.82959i) q^{49} +(2.34071 - 1.12723i) q^{51} +(-2.45402 + 0.560114i) q^{52} +(-4.97319 - 1.13510i) q^{53} +(-8.39766 - 4.04410i) q^{54} +(0.833350 + 0.190207i) q^{56} +2.16381i q^{57} +(-6.28592 - 7.86580i) q^{58} +9.00832 q^{59} +(0.934156 + 1.93979i) q^{61} +(5.11398 - 10.6193i) q^{62} +(1.77739 + 0.405677i) q^{63} +(0.798372 + 3.49790i) q^{64} +(-9.00455 - 7.18089i) q^{66} +(8.46449 + 6.75020i) q^{67} +(-3.51919 - 1.69475i) q^{68} +(2.11352 - 1.68548i) q^{69} +(2.92119 + 3.66306i) q^{71} +(-0.421485 - 1.84665i) q^{72} +(0.611330 + 2.67841i) q^{73} +(-10.6853 - 13.3989i) q^{74} +(2.54348 - 2.02836i) q^{76} +(5.05905 + 2.43631i) q^{77} +(2.44742 + 1.95175i) q^{78} +(-4.33260 - 3.45513i) q^{79} +(-0.238022 - 1.04284i) q^{81} +(-17.2583 - 3.93910i) q^{82} +(0.683737 - 1.41979i) q^{83} +(0.585812 + 1.21645i) q^{84} +11.4877 q^{86} +(-1.18701 + 5.22521i) q^{87} -5.83393i q^{88} +(7.82729 + 1.78653i) q^{89} +(-1.37504 - 0.662184i) q^{91} +(-3.96243 - 0.904398i) q^{92} +(-6.11512 + 1.39574i) q^{93} +(8.29250 - 3.99346i) q^{94} +(4.34520 - 5.44871i) q^{96} +(14.9772 + 7.21266i) q^{97} +(7.20131 + 9.03015i) q^{98} -12.4427i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{6} + 8 q^{9}+O(q^{10}) $ 48 * q + 8 * q^6 + 8 * q^9	$ 48 q + 8 q^{6} + 8 q^{9} - 28 q^{11} + 84 q^{14} - 20 q^{16} + 98 q^{21} - 76 q^{24} - 14 q^{29} + 14 q^{31} - 40 q^{34} - 56 q^{36} - 14 q^{39} + 42 q^{44} + 4 q^{49} + 12 q^{51} - 214 q^{54} - 84 q^{56} + 132 q^{59} + 112 q^{61} - 66 q^{64} - 140 q^{66} + 56 q^{69} + 106 q^{71} - 66 q^{74} - 84 q^{76} + 112 q^{79} - 58 q^{81} - 28 q^{84} + 60 q^{86} - 28 q^{89} - 62 q^{91} + 76 q^{94} - 2 q^{96}+O(q^{100}) $ 48 * q + 8 * q^6 + 8 * q^9 - 28 * q^11 + 84 * q^14 - 20 * q^16 + 98 * q^21 - 76 * q^24 - 14 * q^29 + 14 * q^31 - 40 * q^34 - 56 * q^36 - 14 * q^39 + 42 * q^44 + 4 * q^49 + 12 * q^51 - 214 * q^54 - 84 * q^56 + 132 * q^59 + 112 * q^61 - 66 * q^64 - 140 * q^66 + 56 * q^69 + 106 * q^71 - 66 * q^74 - 84 * q^76 + 112 * q^79 - 58 * q^81 - 28 * q^84 + 60 * q^86 - 28 * q^89 - 62 * q^91 + 76 * q^94 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$-1$

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 $

$2$	−0.416060	+	1.82288i	−0.294199	+	1.28897i	0.584423	+	0.811449i	$0.301321\pi$
$2$	−0.416060	+	1.82288i	−0.294199	+	1.28897i	−0.878621	+	0.477519i	$0.841536\pi$
$3$	0.896481	−	0.431723i	0.517584	−	0.249255i	−0.156808	−	0.987629i	$-0.550120\pi$
$3$	0.896481	−	0.431723i	0.517584	−	0.249255i	0.674391	+	0.738374i	$0.264406\pi$
$4$	−1.34784	−	0.649083i	−0.673918	−	0.324542i
$5$		0			0
$5$		0			0
$6$	0.413987	+	1.81380i	0.169010	+	0.740479i
$7$	−0.393550	−	0.817215i	−0.148748	−	0.308878i	0.813260	−	0.581901i	$-0.197691\pi$
$7$	−0.393550	−	0.817215i	−0.148748	−	0.308878i	−0.962008	+	0.273023i	$0.911977\pi$
$8$	−0.587568	+	0.736786i	−0.207736	+	0.260493i
$9$	−1.25318	+	1.57143i	−0.417725	+	0.523811i
$10$		0			0
$11$	−4.84001	+	3.85978i	−1.45932	+	1.16377i	−0.505713	+	0.862702i	$0.668770\pi$
$11$	−4.84001	+	3.85978i	−1.45932	+	1.16377i	−0.953604	+	0.301064i	$0.902658\pi$
$12$	−1.48853			−0.429703
$13$	1.31550	−	1.04908i	0.364855	−	0.290962i	−0.423852	−	0.905731i	$-0.639322\pi$
$13$	1.31550	−	1.04908i	0.364855	−	0.290962i	0.788707	+	0.614769i	$0.210751\pi$
$14$	1.65342	−	0.377383i	0.441896	−	0.100860i
$15$		0			0
$16$	−2.96407	−	3.71683i	−0.741017	−	0.929207i
$17$	2.61099			0.633259			0.316630	−	0.948549i	$-0.397449\pi$
$17$	2.61099			0.633259			0.316630	+	0.948549i	$0.397449\pi$
$18$	−2.34313	−	2.93819i	−0.552281	−	0.692539i
$19$	−0.943542	+	1.95929i	−0.216463	+	0.449491i	−0.980719	−	0.195422i	$-0.937392\pi$
$19$	−0.943542	+	1.95929i	−0.216463	+	0.449491i	0.764256	+	0.644913i	$0.223107\pi$
$20$		0			0
$21$	−0.705621	−	0.562714i	−0.153979	−	0.122794i
$22$	−5.02216	−	10.4286i	−1.07073	−	2.22339i
$23$	2.64871	−	0.604551i	0.552294	−	0.126058i	0.0627391	−	0.998030i	$-0.480016\pi$
$23$	2.64871	−	0.604551i	0.552294	−	0.126058i	0.489555	+	0.871972i	$0.337159\pi$
$24$	−0.208656	+	0.914181i	−0.0425917	+	0.186606i
$25$		0			0
$26$	1.36501	+	2.83448i	0.267701	+	0.555887i
$27$	−1.10926	+	4.86000i	−0.213478	+	0.935307i
$28$			1.35692i			0.256434i
$29$	−3.35329	+	4.21372i	−0.622691	+	0.782468i
$29$	−3.35329	+	4.21372i	−0.622691	+	0.782468i
$30$		0			0
$31$	−6.14573	−	1.40272i	−1.10381	−	0.251936i	−0.368470	−	0.929640i	$-0.620118\pi$
$31$	−6.14573	−	1.40272i	−1.10381	−	0.251936i	−0.735336	+	0.677703i	$0.762975\pi$
$32$	6.31043	−	3.03894i	1.11554	−	0.537214i
$33$	−2.67262	+	5.54976i	−0.465244	+	0.966088i
$34$	−1.08633	+	4.75952i	−0.186304	+	0.816251i
$35$		0			0
$36$	2.70907	−	1.30462i	0.451511	−	0.217436i
$37$	−5.71479	+	7.16612i	−0.939506	+	1.17810i	0.0443280	+	0.999017i	$0.485885\pi$
$37$	−5.71479	+	7.16612i	−0.939506	+	1.17810i	−0.983833	+	0.179086i	$0.942686\pi$
$38$	−3.17897	−	2.53514i	−0.515696	−	0.411254i
$39$	0.726413	−	1.50841i	0.116319	−	0.241539i
$40$		0			0
$41$			9.46763i			1.47860i	0.673378	+	0.739298i	$0.264843\pi$
$41$			9.46763i			1.47860i	−0.673378	+	0.739298i	$0.735157\pi$
$42$	1.31934	−	1.05214i	0.203578	−	0.162348i
$43$	−1.36716	−	5.98990i	−0.208489	−	0.913451i	−0.965573	−	0.260133i	$-0.916234\pi$
$43$	−1.36716	−	5.98990i	−0.208489	−	0.913451i	0.757084	−	0.653318i	$-0.226624\pi$
$44$	9.02885	−	2.06078i	1.36115	−	0.310674i
$45$		0			0
$46$			5.07980i			0.748976i
$47$	−3.06916	−	3.84861i	−0.447684	−	0.561378i	0.505867	−	0.862612i	$-0.331173\pi$
$47$	−3.06916	−	3.84861i	−0.447684	−	0.561378i	−0.953550	+	0.301234i	$0.902601\pi$
$48$	−4.26187	−	2.05241i	−0.615148	−	0.296240i
$49$	3.85147	−	4.82959i	0.550210	−	0.689941i
$50$		0			0
$51$	2.34071	−	1.12723i	0.327765	−	0.157843i
$52$	−2.45402	+	0.560114i	−0.340311	+	0.0776739i
$53$	−4.97319	−	1.13510i	−0.683120	−	0.155918i	−0.133142	−	0.991097i	$-0.542507\pi$
$53$	−4.97319	−	1.13510i	−0.683120	−	0.155918i	−0.549978	+	0.835179i	$0.685364\pi$
$54$	−8.39766	−	4.04410i	−1.14278	−	0.550332i
$55$		0			0
$56$	0.833350	+	0.190207i	0.111361	+	0.0254175i
$57$			2.16381i			0.286604i
$58$	−6.28592	−	7.86580i	−0.825381	−	1.03283i
$59$	9.00832			1.17278			0.586391	−	0.810028i	$-0.300548\pi$
$59$	9.00832			1.17278			0.586391	+	0.810028i	$0.300548\pi$
$60$		0			0
$61$	0.934156	+	1.93979i	0.119606	+	0.248365i	0.952173	−	0.305560i	$-0.0988437\pi$
$61$	0.934156	+	1.93979i	0.119606	+	0.248365i	−0.832566	+	0.553925i	$0.813129\pi$
$62$	5.11398	−	10.6193i	0.649476	−	1.34865i
$63$	1.77739	+	0.405677i	0.223930	+	0.0511105i
$64$	0.798372	+	3.49790i	0.0997965	+	0.437237i
$65$		0			0
$66$	−9.00455	−	7.18089i	−1.10838	−	0.883906i
$67$	8.46449	+	6.75020i	1.03410	+	0.824668i	0.984726	−	0.174112i	$-0.0557054\pi$
$67$	8.46449	+	6.75020i	1.03410	+	0.824668i	0.0493756	+	0.998780i	$0.484277\pi$
$68$	−3.51919	−	1.69475i	−0.426765	−	0.205519i
$69$	2.11352	−	1.68548i	0.254438	−	0.202907i
$70$		0			0
$71$	2.92119	+	3.66306i	0.346682	+	0.434725i	0.924350	−	0.381547i	$-0.124608\pi$
$71$	2.92119	+	3.66306i	0.346682	+	0.434725i	−0.577668	+	0.816272i	$0.696037\pi$
$72$	−0.421485	−	1.84665i	−0.0496724	−	0.217629i
$73$	0.611330	+	2.67841i	0.0715507	+	0.313484i	0.998021	−	0.0628841i	$-0.0200299\pi$
$73$	0.611330	+	2.67841i	0.0715507	+	0.313484i	−0.926470	+	0.376368i	$0.877173\pi$
$74$	−10.6853	−	13.3989i	−1.24214	−	1.55759i
$75$		0			0
$76$	2.54348	−	2.02836i	0.291757	−	0.232668i
$77$	5.05905	+	2.43631i	0.576533	+	0.277643i
$78$	2.44742	+	1.95175i	0.277115	+	0.220992i
$79$	−4.33260	−	3.45513i	−0.487455	−	0.388733i	0.348692	−	0.937237i	$-0.386626\pi$
$79$	−4.33260	−	3.45513i	−0.487455	−	0.388733i	−0.836148	+	0.548505i	$0.815197\pi$
$80$		0			0
$81$	−0.238022	−	1.04284i	−0.0264468	−	0.115871i
$82$	−17.2583	−	3.93910i	−1.90586	−	0.435001i
$83$	0.683737	−	1.41979i	0.0750498	−	0.155843i	−0.860068	−	0.510179i	$-0.829579\pi$
$83$	0.683737	−	1.41979i	0.0750498	−	0.155843i	0.935118	+	0.354337i	$0.115293\pi$
$84$	0.585812	+	1.21645i	0.0639174	+	0.132726i
$85$		0			0
$86$	11.4877			1.23875
$87$	−1.18701	+	5.22521i	−0.127261	+	0.560201i
$88$		−	5.83393i		−	0.621899i
$89$	7.82729	+	1.78653i	0.829691	+	0.189372i	0.616216	−	0.787577i	$-0.288665\pi$
$89$	7.82729	+	1.78653i	0.829691	+	0.189372i	0.213475	+	0.976949i	$0.431522\pi$
$90$		0			0
$91$	−1.37504	−	0.662184i	−0.144143	−	0.0694157i
$92$	−3.96243	−	0.904398i	−0.413112	−	0.0942901i
$93$	−6.11512	+	1.39574i	−0.634108	+	0.144731i
$94$	8.29250	−	3.99346i	0.855306	−	0.411894i
$95$		0			0
$96$	4.34520	−	5.44871i	0.443480	−	0.556106i
$97$	14.9772	+	7.21266i	1.52071	+	0.732334i	0.993113	−	0.117161i	$-0.0373795\pi$
$97$	14.9772	+	7.21266i	1.52071	+	0.732334i	0.527595	+	0.849496i	$0.323094\pi$
$98$	7.20131	+	9.03015i	0.727442	+	0.912183i
$99$		−	12.4427i		−	1.25054i
$100$		0			0
$101$	−0.556601	+	0.127041i	−0.0553839	+	0.0126410i	−0.250123	−	0.968214i	$-0.580471\pi$
$101$	−0.556601	+	0.127041i	−0.0553839	+	0.0126410i	0.194739	+	0.980855i	$0.437614\pi$
$102$	1.08092	+	4.73581i	0.107027	+	0.468915i
$103$	7.16645	−	5.71506i	0.706132	−	0.563121i	−0.203228	−	0.979131i	$-0.565143\pi$
$103$	7.16645	−	5.71506i	0.706132	−	0.563121i	0.909360	+	0.416010i	$0.136572\pi$
$104$			1.58565i			0.155486i
$105$		0			0
$106$	4.13829	−	8.59324i	0.401946	−	0.834649i
$107$	6.02564	+	4.80528i	0.582520	+	0.464544i	0.869870	−	0.493281i	$-0.164203\pi$
$107$	6.02564	+	4.80528i	0.582520	+	0.464544i	−0.287350	+	0.957826i	$0.592774\pi$
$108$	4.64965	−	5.83048i	0.447413	−	0.561038i
$109$	−1.72516	+	0.830794i	−0.165241	+	0.0795756i	−0.514676	−	0.857385i	$-0.672088\pi$
$109$	−1.72516	+	0.830794i	−0.165241	+	0.0795756i	0.349435	+	0.936960i	$0.386373\pi$
$110$		0			0
$111$	−2.02943	+	8.89149i	−0.192625	+	0.843943i
$112$	−1.87094	+	3.88504i	−0.176787	+	0.367102i
$113$	−0.474497	+	0.228506i	−0.0446370	+	0.0214960i	−0.456069	−	0.889944i	$-0.650743\pi$
$113$	−0.474497	+	0.228506i	−0.0446370	+	0.0214960i	0.411432	+	0.911440i	$0.365029\pi$
$114$	−3.94436	−	0.900274i	−0.369423	−	0.0843184i
$115$		0			0
$116$	7.25474	−	3.50283i	0.673586	−	0.325230i
$117$			3.38190i			0.312657i
$118$	−3.74800	+	16.4210i	−0.345031	+	1.51168i
$119$	−1.02756	−	2.13374i	−0.0941960	−	0.195600i
$120$		0			0
$121$	6.08006	−	26.6385i	0.552732	−	2.42168i
$122$	−3.92467	+	0.895780i	−0.355323	+	0.0811001i
$123$	4.08739	+	8.48756i	0.368548	+	0.765297i
$124$	7.37295	+	5.87973i	0.662110	+	0.528015i
$125$		0			0
$126$	−1.47900	+	3.07117i	−0.131760	+	0.273602i
$127$	−1.77417	−	2.22474i	−0.157432	−	0.197413i	0.696860	−	0.717208i	$-0.254580\pi$
$127$	−1.77417	−	2.22474i	−0.157432	−	0.197413i	−0.854292	+	0.519794i	$0.826009\pi$
$128$	7.29969			0.645207
$129$	−3.81160	−	4.77960i	−0.335593	−	0.420820i
$130$		0			0
$131$	−18.7153	+	4.27165i	−1.63516	+	0.373216i	−0.938797	−	0.344470i	$-0.888059\pi$
$131$	−18.7153	+	4.27165i	−1.63516	+	0.373216i	−0.696367	+	0.717686i	$0.745201\pi$
$132$	7.20451	−	5.74540i	0.627072	−	0.500073i
$133$	1.97249			0.171036
$134$	−15.8265	+	12.6212i	−1.36720	+	1.09031i
$135$		0			0
$136$	−1.53414	+	1.92374i	−0.131551	+	0.164960i
$137$	12.2633	−	15.3777i	1.04773	−	1.31381i	0.0999090	−	0.994997i	$-0.468145\pi$
$137$	12.2633	−	15.3777i	1.04773	−	1.31381i	0.947818	−	0.318812i	$-0.103284\pi$
$138$	2.19306	+	4.55394i	0.186686	+	0.387657i
$139$	2.45586	+	10.7598i	0.208303	+	0.912636i	0.965696	+	0.259676i	$0.0836158\pi$
$139$	2.45586	+	10.7598i	0.208303	+	0.912636i	−0.757393	+	0.652960i	$0.773527\pi$
$140$		0			0
$141$	−4.41298	−	2.12518i	−0.371640	−	0.178972i
$142$	−7.89270	+	3.80092i	−0.662341	+	0.318966i
$143$	−2.31783	+	10.1551i	−0.193827	+	0.849211i
$144$	9.55524			0.796270
$145$		0			0
$146$	−5.13676			−0.425121
$147$	1.36773	−	5.99240i	0.112808	−	0.494245i
$148$	12.3540	−	5.94938i	1.01549	−	0.489036i
$149$	14.6501	+	7.05510i	1.20018	+	0.577976i	0.923727	−	0.383051i	$-0.125127\pi$
$149$	14.6501	+	7.05510i	1.20018	+	0.577976i	0.276453	+	0.961027i	$0.410841\pi$
$150$		0			0
$151$	−2.45134	−	10.7400i	−0.199487	−	0.874009i	−0.971243	−	0.238090i	$-0.923479\pi$
$151$	−2.45134	−	10.7400i	−0.199487	−	0.874009i	0.771756	−	0.635919i	$-0.219379\pi$
$152$	−0.889180	−	1.84640i	−0.0721220	−	0.149763i
$153$	−3.27203	+	4.10300i	−0.264528	+	0.331708i
$154$	−6.54596	+	8.20838i	−0.527489	+	0.661450i
$155$		0			0
$156$	−1.95817	+	1.56159i	−0.156779	+	0.125027i
$157$	−16.1776			−1.29111			−0.645556	−	0.763713i	$-0.723375\pi$
$157$	−16.1776			−1.29111			−0.645556	+	0.763713i	$0.723375\pi$
$158$	8.10090	−	6.46025i	0.644473	−	0.513950i
$159$	−4.94842	+	1.12944i	−0.392435	+	0.0895707i
$160$		0			0
$161$	−1.53645	−	1.92664i	−0.121089	−	0.151841i
$162$	2.00000			0.157135
$163$	−8.12953	−	10.1941i	−0.636754	−	0.798464i	0.353839	−	0.935306i	$-0.384876\pi$
$163$	−8.12953	−	10.1941i	−0.636754	−	0.798464i	−0.990593	+	0.136842i	$0.956305\pi$
$164$	6.14528	−	12.7608i	0.479866	−	0.996452i
$165$		0			0
$166$	2.30363	+	1.83709i	0.178797	+	0.142586i
$167$	−0.673791	−	1.39914i	−0.0521395	−	0.108269i	0.873271	−	0.487234i	$-0.161994\pi$
$167$	−0.673791	−	1.39914i	−0.0521395	−	0.108269i	−0.925411	+	0.378965i	$0.876280\pi$
$168$	0.829199	−	0.189259i	0.0639741	−	0.0146017i
$169$	−2.26279	+	9.91393i	−0.174061	+	0.762610i
$170$		0			0
$171$	−1.89646	−	3.93804i	−0.145026	−	0.301149i
$172$	−2.04524	+	8.96080i	−0.155948	+	0.683254i
$173$			19.8052i			1.50576i	0.658157	+	0.752881i	$0.271337\pi$
$173$			19.8052i			1.50576i	−0.658157	+	0.752881i	$0.728663\pi$
$174$	−9.03105	−	4.33777i	−0.684642	−	0.328845i
$175$		0			0
$176$	28.6922	+	6.54881i	2.16276	+	0.493635i
$177$	8.07579	−	3.88909i	0.607013	−	0.292322i
$178$	−6.51324	+	13.5249i	−0.488188	+	1.01373i
$179$	−3.48214	+	15.2563i	−0.260267	+	1.14031i	0.660695	+	0.750655i	$0.270262\pi$
$179$	−3.48214	+	15.2563i	−0.260267	+	1.14031i	−0.920962	+	0.389652i	$0.872595\pi$
$180$		0			0
$181$	13.6897	−	6.59260i	1.01754	−	0.490024i	0.150688	−	0.988581i	$-0.451851\pi$
$181$	13.6897	−	6.59260i	1.01754	−	0.490024i	0.866857	+	0.498558i	$0.166137\pi$
$182$	1.77918	−	2.23102i	0.131881	−	0.165374i
$183$	1.67491	+	1.33569i	0.123813	+	0.0987372i
$184$	−1.11087	+	2.30675i	−0.0818945	+	0.170056i
$185$		0			0
$186$		−	11.7278i		−	0.859925i
$187$	−12.6372	+	10.0779i	−0.924126	+	0.736965i
$188$	1.63866	+	7.17944i	0.119512	+	0.523614i
$189$	4.40822	−	1.00615i	0.320651	−	0.0731864i
$190$		0			0
$191$			26.7264i			1.93386i	0.255049	+	0.966928i	$0.417908\pi$
$191$			26.7264i			1.93386i	−0.255049	+	0.966928i	$0.582092\pi$
$192$	2.22585	+	2.79112i	0.160637	+	0.201432i
$193$	22.4069	+	10.7906i	1.61288	+	0.776724i	0.999910	−	0.0133799i	$-0.00425907\pi$
$193$	22.4069	+	10.7906i	1.61288	+	0.776724i	0.612973	+	0.790104i	$0.289973\pi$
$194$	−19.3792	+	24.3008i	−1.39135	+	1.74469i
$195$		0			0
$196$	−8.32596	+	4.00957i	−0.594711	+	0.286398i
$197$	−2.84500	+	0.649353i	−0.202698	+	0.0462645i	−0.322664	−	0.946513i	$-0.604579\pi$
$197$	−2.84500	+	0.649353i	−0.202698	+	0.0462645i	0.119966	+	0.992778i	$0.461721\pi$
$198$	22.6815	+	5.17691i	1.61191	+	0.367907i
$199$	−7.73240	−	3.72373i	−0.548135	−	0.263968i	0.139255	−	0.990257i	$-0.455529\pi$
$199$	−7.73240	−	3.72373i	−0.548135	−	0.263968i	−0.687390	+	0.726289i	$0.741244\pi$
$200$		0			0
$201$	10.5025	+	2.39712i	0.740787	+	0.169080i
$202$		−	1.06747i		−	0.0751071i
$203$	4.76320	+	1.08205i	0.334311	+	0.0759453i
$204$	−3.88655			−0.272113
$205$		0			0
$206$	7.43617	+	15.4414i	0.518102	+	1.07585i
$207$	−2.36929	+	4.91987i	−0.164677	+	0.341955i
$208$	−7.79848	−	1.77995i	−0.540728	−	0.123418i
$209$	−2.99565	−	13.1248i	−0.207214	−	0.907862i
$210$		0			0
$211$	5.31424	+	4.23796i	0.365847	+	0.291753i	0.789108	−	0.614255i	$-0.210543\pi$
$211$	5.31424	+	4.23796i	0.365847	+	0.291753i	−0.423261	+	0.906008i	$0.639115\pi$
$212$	5.96627	+	4.75794i	0.409765	+	0.326777i
$213$	4.20022	+	2.02272i	0.287794	+	0.138594i
$214$	−11.2665	+	8.98471i	−0.770160	+	0.614182i
$215$		0			0
$216$	−2.92901	−	3.67287i	−0.199294	−	0.249907i
$217$	1.27233	+	5.57443i	0.0863711	+	0.378417i
$218$	−0.796665	−	3.49042i	−0.0539570	−	0.236401i
$219$	1.70438	+	2.13722i	0.115171	+	0.144420i
$220$		0			0
$221$	3.43477	−	2.73914i	0.231048	−	0.184254i
$222$	−15.3637	−	7.39878i	−1.03115	−	0.496574i
$223$	2.25159	+	1.79559i	0.150778	+	0.120241i	0.695973	−	0.718068i	$-0.254973\pi$
$223$	2.25159	+	1.79559i	0.150778	+	0.120241i	−0.545195	+	0.838309i	$0.683545\pi$
$224$	−4.96694	−	3.96100i	−0.331868	−	0.264656i
$225$		0			0
$226$	−0.219119	−	0.960022i	−0.0145756	−	0.0638597i
$227$	9.00751	+	2.05591i	0.597850	+	0.136455i	0.510728	−	0.859742i	$-0.329376\pi$
$227$	9.00751	+	2.05591i	0.597850	+	0.136455i	0.0871217	+	0.996198i	$0.472233\pi$
$228$	1.40449	−	2.91646i	0.0930149	−	0.193147i
$229$	−0.386375	−	0.802316i	−0.0255324	−	0.0530186i	0.887813	−	0.460205i	$-0.152224\pi$
$229$	−0.386375	−	0.802316i	−0.0255324	−	0.0530186i	−0.913345	+	0.407187i	$0.866510\pi$
$230$		0			0
$231$	5.58716			0.367608
$232$	−1.13432	−	4.94651i	−0.0744720	−	0.324754i
$233$		−	15.5728i		−	1.02021i	−0.860112	−	0.510106i	$-0.829606\pi$
$233$		−	15.5728i		−	1.02021i	0.860112	−	0.510106i	$-0.170394\pi$
$234$	−6.16479	−	1.40707i	−0.403005	−	0.0919833i
$235$		0			0
$236$	−12.1417	−	5.84715i	−0.790359	−	0.380617i
$237$	−5.37575	−	1.22698i	−0.349193	−	0.0797009i
$238$	4.31708	−	0.985345i	0.279835	−	0.0638704i
$239$	18.0421	−	8.68859i	1.16704	−	0.562018i	0.252933	−	0.967484i	$-0.418605\pi$
$239$	18.0421	−	8.68859i	1.16704	−	0.562018i	0.914110	+	0.405465i	$0.132891\pi$
$240$		0			0
$241$	1.97959	−	2.48233i	0.127517	−	0.159901i	−0.713975	−	0.700172i	$-0.753107\pi$
$241$	1.97959	−	2.48233i	0.127517	−	0.159901i	0.841491	+	0.540271i	$0.181678\pi$
$242$	46.0290	+	22.1664i	2.95885	+	1.42491i
$243$	−9.98786	−	12.5244i	−0.640721	−	0.803439i
$244$		−	3.22087i		−	0.206195i
$245$		0			0
$246$	−17.1724	+	3.91948i	−1.09487	+	0.249897i
$247$	0.814212	+	3.56729i	0.0518070	+	0.226982i
$248$	4.64454	−	3.70390i	0.294928	−	0.235198i
$249$		−	1.56800i		−	0.0993681i
$250$		0			0
$251$	11.4432	−	23.7621i	0.722289	−	1.49985i	−0.138213	−	0.990403i	$-0.544136\pi$
$251$	11.4432	−	23.7621i	0.722289	−	1.49985i	0.860502	−	0.509447i	$-0.170150\pi$
$252$	−2.13231	−	1.70046i	−0.134323	−	0.107119i
$253$	−10.4863	+	13.1495i	−0.659270	+	0.826699i
$254$	4.79358	−	2.30847i	0.300776	−	0.144846i
$255$		0			0
$256$	−4.63385	+	20.3022i	−0.289616	+	1.26889i
$257$	−9.51266	+	19.7532i	−0.593383	+	1.23217i	0.360714	+	0.932677i	$0.382533\pi$
$257$	−9.51266	+	19.7532i	−0.593383	+	1.23217i	−0.954097	+	0.299497i	$0.903181\pi$
$258$	10.2985	−	4.95948i	0.641155	−	0.308764i
$259$	8.10532	+	1.84999i	0.503640	+	0.114953i
$260$		0			0
$261$	−2.41931	−	10.5500i	−0.149751	−	0.653029i
$262$		−	35.8930i		−	2.21747i
$263$	6.42899	−	28.1673i	0.396429	−	1.73687i	−0.244851	−	0.969561i	$-0.578739\pi$
$263$	6.42899	−	28.1673i	0.396429	−	1.73687i	0.641280	−	0.767307i	$-0.278404\pi$
$264$	−2.51864	−	5.23001i	−0.155011	−	0.321885i
$265$		0			0
$266$	−0.820673	+	3.59560i	−0.0503187	+	0.220461i
$267$	7.78830	−	1.77763i	0.476636	−	0.108789i
$268$	−7.02729	−	14.5923i	−0.429260	−	0.891368i
$269$	−4.75931	−	3.79542i	−0.290180	−	0.231411i	0.467569	−	0.883956i	$-0.345130\pi$
$269$	−4.75931	−	3.79542i	−0.290180	−	0.231411i	−0.757750	+	0.652545i	$0.773701\pi$
$270$		0			0
$271$	−10.6915	+	22.2012i	−0.649465	+	1.34863i	0.272800	+	0.962071i	$0.412050\pi$
$271$	−10.6915	+	22.2012i	−0.649465	+	1.34863i	−0.922265	+	0.386558i	$0.873664\pi$
$272$	−7.73917	−	9.70461i	−0.469256	−	0.588428i
$273$	−1.51858			−0.0919084
$274$	22.9294	+	28.7526i	1.38522	+	1.73701i
$275$		0			0
$276$	−3.94269	+	0.899894i	−0.237322	+	0.0541672i
$277$	−8.75914	+	6.98518i	−0.526286	+	0.419699i	−0.850257	−	0.526368i	$-0.823553\pi$
$277$	−8.75914	+	6.98518i	−0.526286	+	0.419699i	0.323971	+	0.946067i	$0.394982\pi$
$278$	−20.6356			−1.23764
$279$	9.90596	−	7.89974i	0.593054	−	0.472945i
$280$		0			0
$281$	−10.4258	+	13.0735i	−0.621949	+	0.779899i	−0.988617	−	0.150452i	$-0.951927\pi$
$281$	−10.4258	+	13.0735i	−0.621949	+	0.779899i	0.366668	+	0.930352i	$0.380498\pi$
$282$	5.71000	−	7.16012i	0.340026	−	0.426379i
$283$	6.43379	+	13.3599i	0.382449	+	0.794163i	0.999971	+	0.00760983i	$0.00242231\pi$
$283$	6.43379	+	13.3599i	0.382449	+	0.794163i	−0.617522	+	0.786553i	$0.711863\pi$
$284$	−1.55966	−	6.83330i	−0.0925486	−	0.405482i
$285$		0			0
$286$	−17.5471	−	8.45025i	−1.03758	−	0.499674i
$287$	7.73710	−	3.72599i	0.456706	−	0.219938i
$288$	−3.13258	+	13.7247i	−0.184589	+	0.808738i
$289$	−10.1827			−0.598983
$290$		0			0
$291$	16.5407			0.969632
$292$	0.914540	−	4.00686i	0.0535194	−	0.234484i
$293$	−0.414842	+	0.199777i	−0.0242353	+	0.0116711i	−0.445962	−	0.895052i	$-0.647138\pi$
$293$	−0.414842	+	0.199777i	−0.0242353	+	0.0116711i	0.421727	+	0.906723i	$0.361424\pi$
$294$	10.3544	+	4.98639i	0.603878	+	0.290812i
$295$		0			0
$296$	−1.92207	−	8.42116i	−0.111718	−	0.489470i
$297$	−13.3897	−	27.8039i	−0.776947	−	1.61335i
$298$	−18.9559	+	23.7699i	−1.09808	+	1.37695i
$299$	2.85016	−	3.57399i	0.164829	−	0.206689i
$300$		0			0
$301$	−4.35699	+	3.47459i	−0.251133	+	0.200272i
$302$	20.5976			1.18526
$303$	−0.444136	+	0.354187i	−0.0255150	+	0.0203475i
$304$	10.0790	−	2.30048i	0.578073	−	0.131941i
$305$		0			0
$306$	−6.11790	−	7.67161i	−0.349737	−	0.438557i
$307$	−5.00905			−0.285882			−0.142941	−	0.989731i	$-0.545656\pi$
$307$	−5.00905			−0.285882			−0.142941	+	0.989731i	$0.545656\pi$
$308$	−5.23740	−	6.56750i	−0.298429	−	0.374218i
$309$	3.95727	−	8.21736i	0.225121	−	0.467469i
$310$		0			0
$311$	−17.3854	−	13.8644i	−0.985836	−	0.786178i	−0.00895418	−	0.999960i	$-0.502850\pi$
$311$	−17.3854	−	13.8644i	−0.985836	−	0.786178i	−0.976881	+	0.213782i	$0.931422\pi$
$312$	0.684560	+	1.42150i	0.0387556	+	0.0804768i
$313$	−18.4038	+	4.20054i	−1.04024	+	0.237428i	−0.708330	−	0.705882i	$-0.750551\pi$
$313$	−18.4038	+	4.20054i	−1.04024	+	0.237428i	−0.331912	+	0.943310i	$0.607694\pi$
$314$	6.73085	−	29.4898i	0.379844	−	1.66420i
$315$		0			0
$316$	3.59696	+	7.46917i	0.202345	+	0.420173i
$317$	−4.57837	+	20.0592i	−0.257147	+	1.12663i	0.667139	+	0.744933i	$0.267519\pi$
$317$	−4.57837	+	20.0592i	−0.257147	+	1.12663i	−0.924286	+	0.381701i	$0.875338\pi$
$318$		−	9.49027i		−	0.532188i
$319$	−0.0340432	−	33.3374i	−0.00190605	−	1.86654i
$320$		0			0
$321$	7.47642	+	1.70644i	0.417293	+	0.0952444i
$322$	4.15129	−	1.99916i	0.231342	−	0.111409i
$323$	−2.46358	+	5.11568i	−0.137077	+	0.284644i
$324$	−0.356077	+	1.56007i	−0.0197820	+	0.0866708i
$325$		0			0
$326$	21.9650	−	10.5778i	1.21653	−	0.585849i
$327$	−1.18790	+	1.48958i	−0.0656912	+	0.0823741i
$328$	−6.97562	−	5.56287i	−0.385164	−	0.307158i
$329$	−1.93727	+	4.02279i	−0.106805	+	0.221784i
$330$		0			0
$331$		−	0.558158i		−	0.0306791i	−0.999882	−	0.0153396i	$-0.995117\pi$
$331$		−	0.558158i		−	0.0306791i	0.999882	−	0.0153396i	$-0.00488293\pi$
$332$	−1.84313	+	1.46985i	−0.101155	+	0.0806683i
$333$	−4.09944	−	17.9608i	−0.224648	−	0.984246i
$334$	2.83080	−	0.646112i	0.154895	−	0.0353537i
$335$		0			0
$336$			4.29059i			0.234071i
$337$	−7.11671	−	8.92407i	−0.387672	−	0.486125i	0.549253	−	0.835656i	$-0.314912\pi$
$337$	−7.11671	−	8.92407i	−0.387672	−	0.486125i	−0.936925	+	0.349531i	$0.886341\pi$
$338$	−17.1304	−	8.24957i	−0.931772	−	0.448718i
$339$	−0.326727	+	0.409702i	−0.0177454	+	0.0222520i
$340$		0			0
$341$	35.1596	−	16.9320i	1.90400	−	0.916917i
$342$	7.96760	−	1.81855i	0.430839	−	0.0983361i
$343$	−11.6527	−	2.65964i	−0.629184	−	0.143607i
$344$	5.21657	+	2.51217i	0.281259	+	0.135447i
$345$		0			0
$346$	−36.1025	−	8.24015i	−1.94088	−	0.442993i
$347$		−	29.5553i		−	1.58661i	−0.608824	−	0.793305i	$-0.708359\pi$
$347$		−	29.5553i		−	1.58661i	0.608824	−	0.793305i	$-0.291641\pi$
$348$	4.99149	−	6.27226i	0.267572	−	0.336228i
$349$	18.7732			1.00490			0.502452	−	0.864605i	$-0.332431\pi$
$349$	18.7732			1.00490			0.502452	+	0.864605i	$0.332431\pi$
$350$		0			0
$351$	3.63928	+	7.55705i	0.194250	+	0.403365i
$352$	−18.8129	+	39.0653i	−1.00273	+	2.08219i
$353$	29.3889	+	6.70782i	1.56421	+	0.357021i	0.914957	−	0.403550i	$-0.132224\pi$
$353$	29.3889	+	6.70782i	1.56421	+	0.357021i	0.649254	+	0.760572i	$0.275081\pi$
$354$	3.72933	+	16.3393i	0.198212	+	0.868422i
$355$		0			0
$356$	−9.39030	−	7.48851i	−0.497685	−	0.396890i
$357$	−1.84237	−	1.46924i	−0.0975086	−	0.0777605i
$358$	−26.3615	−	12.6950i	−1.39325	−	0.670953i
$359$	−14.5757	+	11.6238i	−0.769278	+	0.613479i	−0.927456	−	0.373932i	$-0.878009\pi$
$359$	−14.5757	+	11.6238i	−0.769278	+	0.613479i	0.158178	+	0.987411i	$0.449438\pi$
$360$		0			0
$361$	8.89778	+	11.1575i	0.468304	+	0.587235i
$362$	6.32177	+	27.6975i	0.332265	+	1.45575i
$363$	−6.04977	−	26.5058i	−0.317531	−	1.39119i
$364$	1.42351	+	1.78503i	0.0746124	+	0.0935610i
$365$		0			0
$366$	−3.13166	+	2.49742i	−0.163695	+	0.130542i
$367$	−17.2045	−	8.28523i	−0.898065	−	0.432485i	−0.0728755	−	0.997341i	$-0.523218\pi$
$367$	−17.2045	−	8.28523i	−0.898065	−	0.432485i	−0.825190	+	0.564856i	$0.808932\pi$
$368$	−10.0980	−	8.05286i	−0.526393	−	0.419784i
$369$	−14.8777	−	11.8646i	−0.774505	−	0.617647i
$370$		0			0
$371$	1.02958	+	4.51088i	0.0534531	+	0.234193i
$372$	9.14812	+	2.08800i	0.474308	+	0.108258i
$373$	6.31252	−	13.1081i	0.326850	−	0.678711i	−0.671190	−	0.741285i	$-0.734217\pi$
$373$	6.31252	−	13.1081i	0.326850	−	0.678711i	0.998040	+	0.0625740i	$0.0199309\pi$
$374$	−13.1128	−	27.2291i	−0.678049	−	1.40798i
$375$		0			0
$376$	4.63895			0.239235
$377$	0.00925286	+	9.06103i	0.000476546	+	0.466667i
$378$			8.45425i			0.434840i
$379$	−12.5563	−	2.86590i	−0.644975	−	0.147211i	−0.112493	−	0.993653i	$-0.535884\pi$
$379$	−12.5563	−	2.86590i	−0.644975	−	0.147211i	−0.532482	+	0.846441i	$0.678741\pi$
$380$		0			0
$381$	−2.55098	−	1.22849i	−0.130690	−	0.0629372i
$382$	−48.7190	−	11.1198i	−2.49268	−	0.568938i
$383$	−33.2545	+	7.59012i	−1.69923	+	0.387837i	−0.958751	−	0.284247i	$-0.908256\pi$
$383$	−33.2545	+	7.59012i	−1.69923	+	0.387837i	−0.740475	+	0.672084i	$0.765399\pi$
$384$	6.54403	−	3.15144i	0.333949	−	0.160821i
$385$		0			0
$386$	−28.9925	+	36.3555i	−1.47568	+	1.85045i
$387$	11.1260	+	5.35800i	0.565567	+	0.272363i
$388$	−15.5052	−	19.4430i	−0.787159	−	0.987067i
$389$			12.2281i			0.619990i	0.950738	+	0.309995i	$0.100327\pi$
$389$			12.2281i			0.619990i	−0.950738	+	0.309995i	$0.899673\pi$
$390$		0			0
$391$	6.91576	−	1.57848i	0.349745	−	0.0798271i
$392$	1.29538	+	5.67542i	0.0654265	+	0.286652i
$393$	−14.9338	+	11.9093i	−0.753308	+	0.600743i
$394$		−	5.45626i		−	0.274882i
$395$		0			0
$396$	−8.07636	+	16.7707i	−0.405852	+	0.842761i
$397$	−17.0064	−	13.5621i	−0.853526	−	0.680664i	0.0956482	−	0.995415i	$-0.469508\pi$
$397$	−17.0064	−	13.5621i	−0.853526	−	0.680664i	−0.949174	+	0.314751i	$0.898079\pi$
$398$	10.0050	−	12.5459i	0.501507	−	0.628870i
$399$	1.76830	−	0.851568i	0.0885257	−	0.0426317i
$400$		0			0
$401$	−0.0921722	+	0.403833i	−0.00460286	+	0.0201665i	−0.977177	−	0.212426i	$-0.931864\pi$
$401$	−0.0921722	+	0.403833i	−0.00460286	+	0.0201665i	0.972574	+	0.232592i	$0.0747208\pi$
$402$	−8.73931	+	18.1474i	−0.435877	+	0.905108i
$403$	−9.55629	+	4.60207i	−0.476033	+	0.229245i
$404$	0.832667	+	0.190051i	0.0414267	+	0.00945538i
$405$		0			0
$406$	−3.95423	+	8.23253i	−0.196245	+	0.408574i
$407$		−	56.7419i		−	2.81259i
$408$	−0.544799	+	2.38692i	−0.0269716	+	0.118170i
$409$	2.20142	+	4.57129i	0.108853	+	0.226036i	0.948279	−	0.317439i	$-0.102823\pi$
$409$	2.20142	+	4.57129i	0.108853	+	0.226036i	−0.839426	+	0.543474i	$0.817108\pi$
$410$		0			0
$411$	4.35493	−	19.0802i	0.214813	−	0.941157i
$412$	−13.3687	+	3.05133i	−0.658631	+	0.150328i
$413$	−3.54522	−	7.36173i	−0.174449	−	0.362247i
$414$	−7.98256	−	6.36588i	−0.392321	−	0.312866i
$415$		0			0
$416$	5.11330	−	10.6179i	0.250700	−	0.520584i
$417$	6.84689	+	8.58572i	0.335293	+	0.420445i
$418$	25.1713			1.23117
$419$	−2.74481	−	3.44188i	−0.134093	−	0.168147i	0.710252	−	0.703948i	$-0.248581\pi$
$419$	−2.74481	−	3.44188i	−0.134093	−	0.168147i	−0.844344	+	0.535801i	$0.820010\pi$
$420$		0			0
$421$	−1.15385	+	0.263359i	−0.0562353	+	0.0128353i	−0.250546	−	0.968105i	$-0.580610\pi$
$421$	−1.15385	+	0.263359i	−0.0562353	+	0.0128353i	0.194311	+	0.980940i	$0.437753\pi$
$422$	−9.93632	+	7.92395i	−0.483693	+	0.385732i
$423$	9.89403			0.481064
$424$	3.75841	−	2.99723i	0.182524	−	0.145558i
$425$		0			0
$426$	−5.43471	+	6.81491i	−0.263313	+	0.330184i
$427$	1.21759	−	1.52681i	0.0589234	−	0.0738876i
$428$	−5.00254	−	10.3879i	−0.241807	−	0.502117i
$429$	2.30629	+	10.1045i	0.111349	+	0.487850i
$430$		0			0
$431$	−13.2563	−	6.38389i	−0.638532	−	0.307501i	0.0864626	−	0.996255i	$-0.472444\pi$
$431$	−13.2563	−	6.38389i	−0.638532	−	0.307501i	−0.724995	+	0.688754i	$0.758158\pi$
$432$	21.3517	−	10.2824i	1.02728	−	0.494714i
$433$	−5.73819	+	25.1406i	−0.275760	+	1.20818i	0.627338	+	0.778747i	$0.284144\pi$
$433$	−5.73819	+	25.1406i	−0.275760	+	1.20818i	−0.903098	+	0.429435i	$0.858713\pi$
$434$	−10.6909			−0.513177
$435$		0			0
$436$	2.86449			0.137184
$437$	−1.31468	+	5.76000i	−0.0628897	+	0.275538i
$438$	−4.60501	+	2.21766i	−0.220036	+	0.105964i
$439$	25.8763	+	12.4614i	1.23501	+	0.594749i	0.933453	−	0.358700i	$-0.116780\pi$
$439$	25.8763	+	12.4614i	1.23501	+	0.594749i	0.301555	+	0.953449i	$0.402494\pi$
$440$		0			0
$441$	2.76281	+	12.1046i	0.131562	+	0.576412i
$442$	3.56404	+	7.40081i	0.169524	+	0.352020i
$443$	21.7402	−	27.2614i	1.03291	−	1.29523i	0.0784412	−	0.996919i	$-0.475006\pi$
$443$	21.7402	−	27.2614i	1.03291	−	1.29523i	0.954469	−	0.298310i	$-0.0964229\pi$
$444$	8.50665	−	10.6670i	0.403708	−	0.506234i
$445$		0			0
$446$	−4.20993	+	3.35731i	−0.199346	+	0.158973i
$447$	16.1794			0.765257
$448$	2.54434	−	2.02904i	0.120209	−	0.0958631i
$449$	10.7981	−	2.46459i	0.509593	−	0.116311i	0.0400093	−	0.999199i	$-0.487261\pi$
$449$	10.7981	−	2.46459i	0.509593	−	0.116311i	0.469583	+	0.882888i	$0.344404\pi$
$450$		0			0
$451$	−36.5429	−	45.8234i	−1.72074	−	2.15774i
$452$	0.787864			0.0370580
$453$	−6.83428	−	8.56991i	−0.321102	−	0.402650i
$454$	−7.49533	+	15.5642i	−0.351773	+	0.730464i
$455$		0			0
$456$	−1.59427	−	1.27138i	−0.0746583	−	0.0595380i
$457$	−10.0156	−	20.7975i	−0.468508	−	0.972867i	−0.992626	−	0.121221i	$-0.961319\pi$
$457$	−10.0156	−	20.7975i	−0.468508	−	0.972867i	0.524117	−	0.851646i	$-0.324395\pi$
$458$	1.62328	−	0.370503i	0.0758508	−	0.0173125i
$459$	−2.89628	+	12.6894i	−0.135187	+	0.592292i
$460$		0			0
$461$	16.8149	+	34.9165i	0.783149	+	1.62623i	0.779637	+	0.626232i	$0.215404\pi$
$461$	16.8149	+	34.9165i	0.783149	+	1.62623i	0.00351214	+	0.999994i	$0.498882\pi$
$462$	−2.32459	+	10.1847i	−0.108150	+	0.473835i
$463$		−	29.0375i		−	1.34949i	−0.738053	−	0.674743i	$-0.764254\pi$
$463$		−	29.0375i		−	1.34949i	0.738053	−	0.674743i	$-0.235746\pi$
$464$	25.6011	−	0.0261431i	1.18850	−	0.00121366i
$465$		0			0
$466$	28.3874	+	6.47923i	1.31502	+	0.300145i
$467$	−1.75238	+	0.843899i	−0.0810902	+	0.0390510i	−0.473989	−	0.880531i	$-0.657186\pi$
$467$	−1.75238	+	0.843899i	−0.0810902	+	0.0390510i	0.392899	+	0.919582i	$0.371472\pi$
$468$	2.19514	−	4.55825i	0.101470	−	0.210705i
$469$	2.18517	−	9.57385i	0.100902	−	0.442079i
$470$		0			0
$471$	−14.5029	+	6.98423i	−0.668259	+	0.321817i
$472$	−5.29299	+	6.63720i	−0.243630	+	0.305502i
$473$	29.7367	+	23.7142i	1.36730	+	1.09038i
$474$	4.47327	−	9.28883i	0.205464	−	0.426650i
$475$		0			0
$476$			3.54291i			0.162389i
$477$	8.01601	−	6.39255i	0.367028	−	0.292695i
$478$	8.33166	+	36.5034i	0.381081	+	1.66963i
$479$	−31.4499	+	7.17824i	−1.43698	+	0.327982i	−0.868900	−	0.494988i	$-0.835172\pi$
$479$	−31.4499	+	7.17824i	−1.43698	+	0.327982i	−0.568084	+	0.822971i	$0.692315\pi$
$480$		0			0
$481$			15.4223i			0.703197i
$482$	3.70135	+	4.64135i	0.168592	+	0.211408i
$483$	−2.20917	−	1.06388i	−0.100521	−	0.0484083i
$484$	−25.4855	+	31.9578i	−1.15843	+	1.45263i
$485$		0			0
$486$	26.9859	−	12.9957i	1.22411	−	0.589499i
$487$	17.3600	−	3.96230i	0.786654	−	0.179549i	0.189719	−	0.981838i	$-0.439242\pi$
$487$	17.3600	−	3.96230i	0.786654	−	0.179549i	0.596935	+	0.802290i	$0.296385\pi$
$488$	−1.97809	−	0.451487i	−0.0895441	−	0.0204379i
$489$	−11.6890	−	5.62912i	−0.528595	−	0.254558i
$490$		0			0
$491$	−9.15595	−	2.08979i	−0.413202	−	0.0943107i	0.0108660	−	0.999941i	$-0.496541\pi$
$491$	−9.15595	−	2.08979i	−0.413202	−	0.0943107i	−0.424068	+	0.905630i	$0.639398\pi$
$492$		−	14.0929i		−	0.635356i
$493$	−8.75543	+	11.0020i	−0.394325	+	0.495505i
$494$	−6.84150			−0.307814
$495$		0			0
$496$	13.0027	+	27.0004i	0.583838	+	1.21235i
$497$	1.84387	−	3.82884i	0.0827090	−	0.171747i
$498$	2.85828	+	0.652383i	0.128082	+	0.0292340i
$499$	5.86242	+	25.6849i	0.262438	+	1.14982i	0.918598	+	0.395194i	$0.129322\pi$
$499$	5.86242	+	25.6849i	0.262438	+	1.14982i	−0.656160	+	0.754622i	$0.727820\pi$
$500$		0			0
$501$	−1.20808	−	0.963414i	−0.0539731	−	0.0430421i
$502$	38.5543	+	30.7460i	1.72076	+	1.37226i
$503$	34.4070	+	16.5696i	1.53413	+	0.738800i	0.994660	−	0.103203i	$-0.0329091\pi$
$503$	34.4070	+	16.5696i	1.53413	+	0.738800i	0.539473	+	0.842003i	$0.318623\pi$
$504$	−1.34323	+	1.07119i	−0.0598323	+	0.0477146i
$505$		0			0
$506$	−19.6069	−	24.5863i	−0.871632	−	1.09299i
$507$	2.25152	+	9.86455i	0.0999935	+	0.438100i
$508$	0.947247	+	4.15016i	0.0420273	+	0.184134i
$509$	−19.0190	−	23.8491i	−0.843003	−	1.05709i	−0.997609	−	0.0691162i	$-0.977982\pi$
$509$	−19.0190	−	23.8491i	−0.843003	−	1.05709i	0.154605	−	0.987976i	$-0.450589\pi$
$510$		0			0
$511$	1.94825	−	1.55368i	0.0861855	−	0.0687306i
$512$	−21.9269	−	10.5594i	−0.969041	−	0.466666i
$513$	−8.47549	−	6.75898i	−0.374202	−	0.298416i
$514$	−32.0499	−	25.5589i	−1.41366	−	1.12736i
$515$		0			0
$516$	2.03506	+	8.91616i	0.0895884	+	0.392512i
$517$	29.7095	+	6.78101i	1.30662	+	0.298229i
$518$	−6.74459	+	14.0053i	−0.296340	+	0.615357i
$519$	8.55036	+	17.7550i	0.375319	+	0.779358i
$520$		0			0
$521$	0.816728			0.0357815			0.0178907	−	0.999840i	$-0.494305\pi$
$521$	0.816728			0.0357815			0.0178907	+	0.999840i	$0.494305\pi$
$522$	20.2379	−	0.0206664i	0.885790	−	0.000904543i
$523$		−	8.24028i		−	0.360322i	−0.983637	−	0.180161i	$-0.942338\pi$
$523$		−	8.24028i		−	0.360322i	0.983637	−	0.180161i	$-0.0576620\pi$
$524$	27.9978	+	6.39032i	1.22309	+	0.279162i
$525$		0			0
$526$	48.6706	+	23.4385i	2.12214	+	1.02197i
$527$	−16.0465	−	3.66250i	−0.698995	−	0.159541i
$528$	28.5493	−	6.51619i	1.24245	−	0.283581i
$529$	−14.0721	+	6.77677i	−0.611831	+	0.294642i
$530$		0			0
$531$	−11.2890	+	14.1560i	−0.489901	+	0.614316i
$532$	−2.65859	−	1.28031i	−0.115265	−	0.0555085i
$533$	9.93229	+	12.4547i	0.430215	+	0.539473i
$534$			14.9367i			0.646375i
$535$		0			0
$536$	−9.94691	+	2.27032i	−0.429641	+	0.0980628i
$537$	3.46480	+	15.1803i	0.149517	+	0.655077i
$538$	8.89875	−	7.09651i	0.383652	−	0.305952i
$539$			38.2411i			1.64716i
$540$		0			0
$541$	9.98440	−	20.7328i	0.429263	−	0.891373i	−0.568381	−	0.822766i	$-0.692430\pi$
$541$	9.98440	−	20.7328i	0.429263	−	0.891373i	0.997644	−	0.0686078i	$-0.0218557\pi$
$542$	−36.0218	−	28.7264i	−1.54727	−	1.23390i
$543$	9.42636	−	11.8203i	0.404524	−	0.507257i
$544$	16.4765	−	7.93466i	0.706423	−	0.340196i
$545$		0			0
$546$	0.631818	−	2.76818i	0.0270393	−	0.118467i
$547$	−4.31634	+	8.96298i	−0.184553	+	0.383229i	−0.972634	−	0.232343i	$-0.925361\pi$
$547$	−4.31634	+	8.96298i	−0.184553	+	0.383229i	0.788080	+	0.615572i	$0.211075\pi$
$548$	−26.5104	+	12.7667i	−1.13247	+	0.545368i
$549$	−4.21892	−	0.962940i	−0.180059	−	0.0410973i
$550$		0			0
$551$	−5.09190	−	10.5459i	−0.216922	−	0.449270i
$552$			2.54754i			0.108431i
$553$	−1.11849	+	4.90043i	−0.0475631	+	0.208388i
$554$	−9.08880	−	18.8731i	−0.386146	−	0.801841i
$555$		0			0
$556$	3.67393	−	16.0965i	0.155809	−	0.682645i
$557$	2.07304	−	0.473158i	0.0878375	−	0.0200483i	−0.178376	−	0.983962i	$-0.557084\pi$
$557$	2.07304	−	0.473158i	0.0878375	−	0.0200483i	0.266214	+	0.963914i	$0.414227\pi$
$558$	10.2788	+	21.3441i	0.435135	+	0.903568i
$559$	−8.08237	−	6.44548i	−0.341848	−	0.272615i
$560$		0			0
$561$	−6.97820	+	14.4904i	−0.294620	+	0.611784i
$562$	−19.4936	−	24.4442i	−0.822289	−	1.03112i
$563$	−21.7113			−0.915023			−0.457511	−	0.889204i	$-0.651259\pi$
$563$	−21.7113			−0.915023			−0.457511	+	0.889204i	$0.651259\pi$
$564$	4.56855	+	5.72878i	0.192371	+	0.241225i
$565$		0			0
$566$	−27.0303	+	6.16948i	−1.13617	+	0.259323i
$567$	−0.758552	+	0.604925i	−0.0318562	+	0.0254045i
$568$	−4.41529			−0.185262
$569$	−11.2385	+	8.96240i	−0.471142	+	0.375723i	−0.830086	−	0.557636i	$-0.811709\pi$
$569$	−11.2385	+	8.96240i	−0.471142	+	0.375723i	0.358943	+	0.933359i	$0.383137\pi$
$570$		0			0
$571$	−1.11508	+	1.39826i	−0.0466645	+	0.0585155i	−0.804616	−	0.593795i	$-0.797629\pi$
$571$	−1.11508	+	1.39826i	−0.0466645	+	0.0585155i	0.757952	+	0.652311i	$0.226200\pi$
$572$	9.71556	−	12.1829i	0.406228	−	0.509394i
$573$	11.5384	+	23.9597i	0.482024	+	1.00093i
$574$	3.57292	+	15.6540i	0.149131	+	0.653386i
$575$		0			0
$576$	−6.49721	−	3.12889i	−0.270717	−	0.130370i
$577$	18.8004	−	9.05380i	0.782671	−	0.376915i	0.000517201	−	1.00000i	$-0.499835\pi$
$577$	18.8004	−	9.05380i	0.782671	−	0.376915i	0.782154	+	0.623085i	$0.214121\pi$
$578$	4.23662	−	18.5618i	0.176220	−	0.772070i
$579$	24.7459			1.02840
$580$		0			0
$581$	−1.42936			−0.0592999
$582$	−6.88191	+	30.1516i	−0.285264	+	1.24982i
$583$	28.4515	−	13.7015i	1.17834	−	0.567459i
$584$	−2.33261	−	1.12333i	−0.0965243	−	0.0464836i
$585$		0			0
$586$	−0.191570	−	0.839325i	−0.00791370	−	0.0346722i
$587$	8.06792	+	16.7532i	0.332999	+	0.691479i	0.998490	−	0.0549262i	$-0.0174924\pi$
$587$	8.06792	+	16.7532i	0.332999	+	0.691479i	−0.665492	+	0.746405i	$0.731778\pi$
$588$	−5.73304	+	7.18901i	−0.236427	+	0.296470i
$589$	8.54709	−	10.7177i	0.352177	−	0.441615i
$590$		0			0
$591$	−2.27015	+	1.81039i	−0.0933815	+	0.0744693i
$592$	43.5743			1.79089
$593$	−16.1842	+	12.9065i	−0.664605	+	0.530005i	−0.896672	−	0.442695i	$-0.854023\pi$
$593$	−16.1842	+	12.9065i	−0.664605	+	0.530005i	0.232067	+	0.972700i	$0.425451\pi$
$594$	56.2540	−	12.8396i	2.30813	−	0.526816i
$595$		0			0
$596$	−15.1665	−	19.0182i	−0.621246	−	0.779017i
$597$	−8.53957			−0.349501
$598$	5.32911	+	6.68249i	0.217923	+	0.273267i
$599$	0.657551	−	1.36542i	0.0268668	−	0.0557895i	−0.887104	−	0.461570i	$-0.847286\pi$
$599$	0.657551	−	1.36542i	0.0268668	−	0.0557895i	0.913970	+	0.405781i	$0.133000\pi$
$600$		0			0
$601$	22.5208	+	17.9598i	0.918645	+	0.732595i	0.963867	−	0.266382i	$-0.0858284\pi$
$601$	22.5208	+	17.9598i	0.918645	+	0.732595i	−0.0452229	+	0.998977i	$0.514400\pi$
$602$	−4.52097	−	9.38790i	−0.184261	−	0.382622i
$603$	−21.2150	+	4.84218i	−0.863940	+	0.197189i
$604$	−3.66716	+	16.0669i	−0.149215	+	0.653752i
$605$		0			0
$606$	−0.460852	−	0.956969i	−0.0187208	−	0.0388742i
$607$	1.68599	−	7.38679i	0.0684321	−	0.299821i	−0.929117	−	0.369785i	$-0.879431\pi$
$607$	1.68599	−	7.38679i	0.0684321	−	0.299821i	0.997549	+	0.0699643i	$0.0222885\pi$
$608$			15.2313i			0.617710i
$609$	4.73727	−	1.08634i	0.191964	−	0.0440208i
$610$		0			0
$611$	−8.07499	−	1.84306i	−0.326679	−	0.0745624i
$612$	7.07335	−	3.40635i	0.285923	−	0.137693i
$613$	−4.52802	+	9.40254i	−0.182885	+	0.379765i	−0.972175	−	0.234256i	$-0.924735\pi$
$613$	−4.52802	+	9.40254i	−0.182885	+	0.379765i	0.789290	+	0.614021i	$0.210449\pi$
$614$	2.08407	−	9.13089i	0.0841060	−	0.368493i
$615$		0			0
$616$	−4.76758	+	2.29594i	−0.192091	+	0.0925062i
$617$	−28.3873	+	35.5966i	−1.14283	+	1.43306i	−0.258617	+	0.965980i	$0.583267\pi$
$617$	−28.3873	+	35.5966i	−1.14283	+	1.43306i	−0.884213	+	0.467084i	$0.845305\pi$
$618$	13.3328	+	10.6325i	0.536323	+	0.427703i
$619$	−3.70238	+	7.68808i	−0.148811	+	0.309010i	−0.962028	−	0.272951i	$-0.912000\pi$
$619$	−3.70238	+	7.68808i	−0.148811	+	0.309010i	0.813217	+	0.581961i	$0.197714\pi$
$620$		0			0
$621$			13.5433i			0.543475i
$622$	32.5064	−	25.9230i	1.30339	−	1.03942i
$623$	−1.62045	−	7.09967i	−0.0649221	−	0.284442i
$624$	−7.75964	+	1.77109i	−0.310634	+	0.0709002i
$625$		0			0
$626$		−	35.2955i		−	1.41069i
$627$	−8.35182	−	10.4729i	−0.333540	−	0.418246i
$628$	21.8047	+	10.5006i	0.870104	+	0.419020i
$629$	−14.9213	+	18.7107i	−0.594950	+	0.746044i
$630$		0			0
$631$	0.371871	−	0.179084i	0.0148040	−	0.00712921i	−0.426467	−	0.904503i	$-0.640242\pi$
$631$	0.371871	−	0.179084i	0.0148040	−	0.00712921i	0.441271	+	0.897374i	$0.354528\pi$
$632$	5.09139	−	1.16208i	0.202525	−	0.0462249i
$633$	6.59374	+	1.50498i	0.262077	+	0.0598175i
$634$	−34.6605	−	16.6916i	−1.37654	−	0.662909i
$635$		0			0
$636$	7.40276	+	1.68963i	0.293538	+	0.0669982i
$637$		−	10.3938i		−	0.411819i
$638$	60.7841	+	13.8083i	2.40647	+	0.546675i
$639$	−9.41702			−0.372532
$640$		0			0
$641$	−4.48586	−	9.31498i	−0.177181	−	0.367919i	0.793398	−	0.608703i	$-0.208310\pi$
$641$	−4.48586	−	9.31498i	−0.177181	−	0.367919i	−0.970579	+	0.240784i	$0.922596\pi$
$642$	−6.22127	+	12.9186i	−0.245534	+	0.509857i
$643$	−1.94232	−	0.443322i	−0.0765976	−	0.0174829i	0.184050	−	0.982917i	$-0.441079\pi$
$643$	−1.94232	−	0.443322i	−0.0765976	−	0.0174829i	−0.260648	+	0.965434i	$0.583936\pi$
$644$	0.820326	+	3.59408i	0.0323254	+	0.141627i
$645$		0			0
$646$	−8.30026	−	6.61924i	−0.326569	−	0.260430i
$647$	−20.1804	−	16.0933i	−0.793373	−	0.632694i	0.140588	−	0.990068i	$-0.455101\pi$
$647$	−20.1804	−	16.0933i	−0.793373	−	0.632694i	−0.933961	+	0.357374i	$0.883672\pi$
$648$	0.908205	+	0.437368i	0.0356777	+	0.0171815i
$649$	−43.6003	+	34.7701i	−1.71146	+	1.36485i
$650$		0			0
$651$	3.54722	+	4.44808i	0.139027	+	0.174334i
$652$	4.34044	+	19.0167i	0.169985	+	0.744752i
$653$	5.27976	+	23.1321i	0.206613	+	0.905230i	0.966802	+	0.255528i	$0.0822492\pi$
$653$	5.27976	+	23.1321i	0.206613	+	0.905230i	−0.760189	+	0.649702i	$0.774894\pi$
$654$	−2.22109	−	2.78515i	−0.0868514	−	0.108908i
$655$		0			0
$656$	35.1896	−	28.0627i	1.37392	−	1.09567i
$657$	−4.97504	−	2.39586i	−0.194095	−	0.0934712i
$658$	−6.52703	−	5.20513i	−0.254450	−	0.202917i
$659$	17.9434	+	14.3094i	0.698977	+	0.557415i	0.907217	−	0.420662i	$-0.138202\pi$
$659$	17.9434	+	14.3094i	0.698977	+	0.557415i	−0.208241	+	0.978078i	$0.566774\pi$
$660$		0			0
$661$	3.18309	+	13.9460i	0.123808	+	0.542438i	0.998347	+	0.0574819i	$0.0183072\pi$
$661$	3.18309	+	13.9460i	0.123808	+	0.542438i	−0.874539	+	0.484956i	$0.838836\pi$
$662$	1.01745	+	0.232227i	0.0395445	+	0.00902576i
$663$	1.89666	−	3.93845i	0.0736601	−	0.152957i
$664$	0.644343	+	1.33799i	0.0250054	+	0.0519242i
$665$		0			0
$666$	34.4459			1.33475
$667$	−6.33450	+	13.1881i	−0.245273	+	0.510647i
$668$			2.32316i			0.0898858i
$669$	2.79371	+	0.637645i	0.108011	+	0.0246528i
$670$		0			0
$671$	−12.0085	−	5.78298i	−0.463583	−	0.223250i
$672$	−6.16282	−	1.40662i	−0.237736	−	0.0542617i
$673$	4.37501	−	0.998567i	0.168644	−	0.0384919i	−0.137365	−	0.990521i	$-0.543863\pi$
$673$	4.37501	−	0.998567i	0.168644	−	0.0384919i	0.306009	+	0.952029i	$0.401006\pi$
$674$	19.2285	−	9.25994i	0.740653	−	0.356679i
$675$		0			0
$676$	9.48484	−	11.8936i	0.364801	−	0.457447i
$677$	0.321803	+	0.154972i	0.0123679	+	0.00595606i	0.440057	−	0.897970i	$-0.354958\pi$
$677$	0.321803	+	0.154972i	0.0123679	+	0.00595606i	−0.427690	+	0.903926i	$0.640672\pi$
$678$	−0.610899	−	0.766043i	−0.0234614	−	0.0294197i
$679$		−	15.0782i		−	0.578647i
$680$		0			0
$681$	8.96265	−	2.04567i	0.343449	−	0.0783901i
$682$	16.2364	+	71.1362i	0.621723	+	2.72395i
$683$	9.04371	−	7.21212i	0.346048	−	0.275964i	−0.435006	−	0.900428i	$-0.643254\pi$
$683$	9.04371	−	7.21212i	0.346048	−	0.275964i	0.781054	+	0.624463i	$0.214682\pi$
$684$			6.53879i			0.250017i
$685$		0			0
$686$	9.69640	−	20.1348i	0.370210	−	0.768750i
$687$	−0.692756	−	0.552455i	−0.0264303	−	0.0210775i
$688$	−18.2111	+	22.8360i	−0.694291	+	0.870613i
$689$	−7.73305	+	3.72404i	−0.294606	+	0.141875i
$690$		0			0
$691$	4.52219	−	19.8130i	0.172032	−	0.753722i	−0.813128	−	0.582085i	$-0.802237\pi$
$691$	4.52219	−	19.8130i	0.172032	−	0.753722i	0.985160	−	0.171637i	$-0.0549057\pi$
$692$	12.8552	−	26.6942i	0.488683	−	1.01476i
$693$	−10.1684	+	4.89683i	−0.386265	+	0.186015i
$694$	53.8756	+	12.2968i	2.04509	+	0.466779i
$695$		0			0
$696$	−3.15242	−	3.94474i	−0.119492	−	0.149525i
$697$			24.7199i			0.936334i
$698$	−7.81076	+	34.2212i	−0.295642	+	1.29529i
$699$	−6.72315	−	13.9608i	−0.254293	−	0.528045i
$700$		0			0
$701$	−0.417521	+	1.82928i	−0.0157695	+	0.0690909i	−0.982200	−	0.187836i	$-0.939853\pi$
$701$	−0.417521	+	1.82928i	−0.0157695	+	0.0690909i	0.966431	+	0.256927i	$0.0827099\pi$
$702$	−15.2897	+	3.48978i	−0.577073	+	0.131713i
$703$	−8.64833	−	17.9584i	−0.326178	−	0.677315i
$704$	−17.3652	−	13.8483i	−0.654476	−	0.521927i
$705$		0			0
$706$	−24.4550	+	50.7814i	−0.920378	+	1.91118i
$707$	0.322870	+	0.404866i	0.0121428	+	0.0152266i
$708$	−13.4092			−0.503948
$709$	−16.2249	−	20.3453i	−0.609338	−	0.764086i	0.377463	−	0.926025i	$-0.376797\pi$
$709$	−16.2249	−	20.3453i	−0.609338	−	0.764086i	−0.986801	+	0.161939i	$0.948225\pi$
$710$		0			0
$711$	10.8590	−	2.47850i	0.407245	−	0.0929509i
$712$	−5.91535	+	4.71734i	−0.221687	+	0.176790i
$713$	−17.1263			−0.641384
$714$	3.44478	−	2.74712i	0.128918	−	0.102808i
$715$		0			0
$716$	14.5959	−	18.3027i	0.545476	−	0.684005i
$717$	12.4233	−	15.5783i	0.463956	−	0.581783i
$718$	−15.1243	−	31.4060i	−0.564434	−	1.17206i
$719$	−3.44773	−	15.1055i	−0.128579	−	0.563340i	−0.997642	−	0.0686382i	$-0.978135\pi$
$719$	−3.44773	−	15.1055i	−0.128579	−	0.563340i	0.869063	−	0.494701i	$-0.164723\pi$
$720$		0			0
$721$	−7.49079	−	3.60737i	−0.278972	−	0.134346i
$722$	−24.0407	+	11.5774i	−0.894702	+	0.430866i
$723$	0.702989	−	3.08000i	0.0261444	−	0.114546i
$724$	−22.7306			−0.844775
$725$		0			0
$726$	50.8338			1.88662
$727$	8.81272	−	38.6110i	0.326846	−	1.43200i	−0.498261	−	0.867027i	$-0.666028\pi$
$727$	8.81272	−	38.6110i	0.326846	−	1.43200i	0.825106	−	0.564977i	$-0.191115\pi$
$728$	1.29582	−	0.624032i	0.0480262	−	0.0231282i
$729$	−11.4698	−	5.52356i	−0.424807	−	0.204576i
$730$		0			0
$731$	−3.56963	−	15.6396i	−0.132028	−	0.578451i
$732$	−1.39052	−	2.88745i	−0.0513952	−	0.106723i
$733$	27.8183	−	34.8830i	1.02749	−	1.28843i	0.0707500	−	0.997494i	$-0.477461\pi$
$733$	27.8183	−	34.8830i	1.02749	−	1.28843i	0.956741	−	0.290939i	$-0.0939678\pi$
$734$	22.2610	−	27.9144i	0.821670	−	1.03034i
$735$		0			0
$736$	14.8773	−	11.8642i	0.548384	−	0.437322i
$737$	−67.0224			−2.46880
$738$	27.8177	−	22.1839i	1.02399	−	0.816601i
$739$	−23.0599	+	5.26327i	−0.848272	+	0.193613i	−0.624496	−	0.781028i	$-0.714696\pi$
$739$	−23.0599	+	5.26327i	−0.848272	+	0.193613i	−0.223776	+	0.974641i	$0.571838\pi$
$740$		0			0
$741$	2.27001	+	2.84650i	0.0833908	+	0.104569i
$742$	−8.65115			−0.317594
$743$	13.7066	+	17.1875i	0.502845	+	0.630548i	0.966868	−	0.255275i	$-0.0821660\pi$
$743$	13.7066	+	17.1875i	0.502845	+	0.630548i	−0.464023	+	0.885823i	$0.653595\pi$
$744$	2.56469	−	5.32562i	0.0940259	−	0.195247i
$745$		0			0
$746$	21.2680	+	16.9607i	0.778678	+	0.620975i
$747$	1.37427	+	2.85370i	0.0502818	+	0.104411i
$748$	23.5743	−	5.38067i	0.861961	−	0.196737i
$749$	1.55556	−	6.81536i	0.0568390	−	0.249028i
$750$		0			0
$751$	−8.45565	−	17.5583i	−0.308551	−	0.640713i	0.687815	−	0.725886i	$-0.258570\pi$
$751$	−8.45565	−	17.5583i	−0.308551	−	0.640713i	−0.996366	+	0.0851729i	$0.972856\pi$
$752$	−5.20740	+	22.8151i	−0.189894	+	0.831981i
$753$		−	26.2426i		−	0.956332i
$754$	−16.5210	−	3.75306i	−0.601659	−	0.136678i
$755$		0			0
$756$	−6.59462	−	1.50518i	−0.239844	−	0.0547429i
$757$	43.7716	−	21.0793i	1.59091	−	0.766140i	0.591706	−	0.806154i	$-0.298455\pi$
$757$	43.7716	−	21.0793i	1.59091	−	0.766140i	0.999199	+	0.0400143i	$0.0127404\pi$
$758$	10.4484	−	21.6962i	0.379501	−	0.788043i
$759$	−3.72389	+	16.3154i	−0.135169	+	0.592212i
$760$		0			0
$761$	23.1596	−	11.1531i	0.839534	−	0.404298i	0.0358518	−	0.999357i	$-0.488586\pi$
$761$	23.1596	−	11.1531i	0.839534	−	0.404298i	0.803682	+	0.595059i	$0.202871\pi$
$762$	3.30074	−	4.13899i	0.119573	−	0.149940i
$763$	1.35788	+	1.08287i	0.0491584	+	0.0392025i
$764$	17.3477	−	36.0228i	0.627617	−	1.30326i
$765$		0			0
$766$		−	63.7768i		−	2.30435i
$767$	11.8505	−	9.45043i	0.427895	−	0.341235i
$768$	4.61077	+	20.2011i	0.166377	+	0.728944i
$769$	49.1355	−	11.2148i	1.77187	−	0.404418i	0.793053	−	0.609153i	$-0.208491\pi$
$769$	49.1355	−	11.2148i	1.77187	−	0.404418i	0.978817	+	0.204735i	$0.0656334\pi$
$770$		0			0
$771$			21.8152i			0.785657i
$772$	−23.1968	−	29.0879i	−0.834872	−	1.04690i
$773$	−32.3074	−	15.5584i	−1.16201	−	0.559597i	−0.249393	−	0.968402i	$-0.580231\pi$
$773$	−32.3074	−	15.5584i	−1.16201	−	0.559597i	−0.912622	+	0.408805i	$0.865945\pi$
$774$	−14.3961	+	18.0521i	−0.517456	+	0.648869i
$775$		0			0
$776$	−14.1143	+	6.79710i	−0.506675	+	0.244002i
$777$	8.06495	−	1.84077i	0.289328	−	0.0660373i
$778$	−22.2903	−	5.08762i	−0.799147	−	0.182400i
$779$	−18.5498	−	8.93311i	−0.664615	−	0.320062i
$780$		0			0
$781$	−28.2772	−	6.45408i	−1.01184	−	0.230945i
$782$			13.2633i			0.474296i
$783$	−16.7590	−	20.9711i	−0.598917	−	0.749447i
$784$	−29.3668			−1.04881
$785$		0			0
$786$	−15.4958	−	32.1774i	−0.552717	−	1.14773i
$787$	−12.8278	+	26.6373i	−0.457263	+	0.949517i	0.537103	+	0.843517i	$0.319519\pi$
$787$	−12.8278	+	26.6373i	−0.457263	+	0.949517i	−0.994366	+	0.106000i	$0.966196\pi$
$788$	4.25608	+	0.971423i	0.151617	+	0.0346055i
$789$	−6.39697	−	28.0270i	−0.227738	−	0.997786i
$790$		0			0
$791$	0.373477	+	0.297838i	0.0132793	+	0.0105899i
$792$	9.16762	+	7.31094i	0.325757	+	0.259783i
$793$	3.26388	+	1.57180i	0.115904	+	0.0558163i
$794$	31.7978	−	25.3579i	1.12846	−	0.899918i
$795$		0			0
$796$	8.00500	+	10.0379i	0.283730	+	0.355786i
$797$	10.1540	+	44.4877i	0.359674	+	1.57584i	0.754005	+	0.656868i	$0.228119\pi$
$797$	10.1540	+	44.4877i	0.359674	+	1.57584i	−0.394331	+	0.918969i	$0.629024\pi$
$798$	0.816585	+	3.57769i	0.0289068	+	0.126649i
$799$	−8.01357	−	10.0487i	−0.283500	−	0.355497i
$800$		0			0
$801$	−12.6164	+	10.0612i	−0.445778	+	0.355496i
$802$	−0.697788	−	0.336037i	−0.0246398	−	0.0118659i
$803$	−13.2969	−	10.6039i	−0.469238	−	0.374204i
$804$	−12.5997	−	10.0479i	−0.444356	−	0.354362i
$805$		0			0
$806$	−4.41301	−	19.3347i	−0.155442	−	0.681035i
$807$	−5.90520	−	1.34782i	−0.207873	−	0.0474456i
$808$	0.233439	−	0.484741i	0.00821236	−	0.0170531i
$809$	9.34232	+	19.3995i	0.328458	+	0.682051i	0.998164	−	0.0605761i	$-0.0192938\pi$
$809$	9.34232	+	19.3995i	0.328458	+	0.682051i	−0.669705	+	0.742627i	$0.733579\pi$
$810$		0			0
$811$	12.1600			0.426994			0.213497	−	0.976944i	$-0.431515\pi$
$811$	12.1600			0.426994			0.213497	+	0.976944i	$0.431515\pi$
$812$	−5.71767	−	4.55015i	−0.200651	−	0.159679i
$813$			24.5188i			0.859911i
$814$	103.433	+	23.6080i	3.62534	+	0.827460i
$815$		0			0
$816$	−11.1277	−	5.35883i	−0.389548	−	0.187596i
$817$	13.0259	+	2.97307i	0.455718	+	0.104015i
$818$	−9.24882	+	2.11098i	−0.323377	+	0.0738088i
$819$	2.76374	−	1.33095i	0.0965730	−	0.0465071i
$820$		0			0
$821$	−8.32730	+	10.4421i	−0.290625	+	0.364432i	−0.905614	−	0.424104i	$-0.860589\pi$
$821$	−8.32730	+	10.4421i	−0.290625	+	0.364432i	0.614989	+	0.788536i	$0.289161\pi$
$822$	32.9689	+	15.8770i	1.14992	+	0.553774i
$823$	0.991896	+	1.24380i	0.0345753	+	0.0433561i	0.798819	−	0.601572i	$-0.205459\pi$
$823$	0.991896	+	1.24380i	0.0345753	+	0.0433561i	−0.764243	+	0.644928i	$0.776887\pi$
$824$			8.63813i			0.300923i
$825$		0			0
$826$	14.8946	−	3.39959i	0.518248	−	0.118287i
$827$	4.93266	+	21.6114i	0.171525	+	0.751502i	0.985371	+	0.170421i	$0.0545128\pi$
$827$	4.93266	+	21.6114i	0.171525	+	0.751502i	−0.813846	+	0.581081i	$0.802630\pi$
$828$	6.38682	−	5.09332i	0.221957	−	0.177005i
$829$		−	0.0463194i		−	0.00160874i	−1.00000		0.000804369i	$-0.999744\pi$
$829$		−	0.0463194i		−	0.00160874i	1.00000		0.000804369i	$-0.000256039\pi$
$830$		0			0
$831$	−4.83674	+	10.0436i	−0.167785	+	0.348409i
$832$	4.71983	+	3.76394i	0.163631	+	0.130491i
$833$	10.0562	−	12.6100i	0.348425	−	0.436912i
$834$	−18.4994	+	8.90886i	−0.640583	+	0.308488i
$835$		0			0
$836$	−4.48145	+	19.6345i	−0.154994	+	0.679074i
$837$	13.6345	−	28.3122i	0.471276	−	0.978614i
$838$	7.41614	−	3.57142i	0.256186	−	0.123373i
$839$	−29.3303	−	6.69444i	−1.01259	−	0.231118i	−0.316134	−	0.948714i	$-0.602385\pi$
$839$	−29.3303	−	6.69444i	−1.01259	−	0.231118i	−0.696459	+	0.717597i	$0.745242\pi$
$840$		0			0
$841$	−6.51084	−	28.2597i	−0.224512	−	0.974471i
$842$		−	2.21290i		−	0.0762617i
$843$	−3.70238	+	16.2212i	−0.127517	+	0.558687i
$844$	−4.41193	−	9.16146i	−0.151865	−	0.315350i
$845$		0			0
$846$	−4.11651	+	18.0356i	−0.141528	+	0.620077i
$847$	−24.1622	+	5.51486i	−0.830222	+	0.189493i
$848$	10.5219	+	21.8490i	0.361324	+	0.750297i
$849$	11.5355	+	9.19928i	0.395899	+	0.315719i
$850$		0			0
$851$	−10.8045	+	22.4358i	−0.370375	+	0.769091i
$852$	−4.34829	−	5.45259i	−0.148970	−	0.186803i
$853$	23.2348			0.795546			0.397773	−	0.917484i	$-0.369783\pi$
$853$	23.2348			0.795546			0.397773	+	0.917484i	$0.369783\pi$
$854$	2.27660	+	2.85477i	0.0779036	+	0.0976881i
$855$		0			0
$856$	−7.08094	+	1.61618i	−0.242021	+	0.0552398i
$857$	2.17025	−	1.73071i	0.0741342	−	0.0591201i	−0.585722	−	0.810512i	$-0.699189\pi$
$857$	2.17025	−	1.73071i	0.0741342	−	0.0591201i	0.659856	+	0.751392i	$0.270617\pi$
$858$	−19.3788			−0.661582
$859$	43.7827	−	34.9156i	1.49385	−	1.19130i	0.562699	−	0.826662i	$-0.309763\pi$
$859$	43.7827	−	34.9156i	1.49385	−	1.19130i	0.931148	−	0.364641i	$-0.118808\pi$
$860$		0			0
$861$	5.32757	−	6.68056i	0.181563	−	0.227673i
$862$	17.1524	−	21.5085i	0.584214	−	0.732582i
$863$	−11.0847	−	23.0176i	−0.377327	−	0.783529i	−0.999999	−	0.00104561i	$-0.999667\pi$
$863$	−11.0847	−	23.0176i	−0.377327	−	0.783529i	0.622672	−	0.782483i	$-0.286047\pi$
$864$	7.76933	+	34.0396i	0.264318	+	1.15805i
$865$		0			0
$866$	−43.4409	−	20.9200i	−1.47618	−	0.710891i
$867$	−9.12861	+	4.39611i	−0.310024	+	0.149300i
$868$	1.90338	−	8.33926i	0.0646050	−	0.283053i
$869$	34.3058			1.16375
$870$		0			0
$871$	18.2165			0.617244
$872$	0.401531	−	1.75922i	0.0135976	−	0.0595748i
$873$	−30.1033	+	14.4970i	−1.01884	+	0.490649i
$874$	−9.95277	−	4.79300i	−0.336658	−	0.162126i
$875$		0			0
$876$	−0.909985	−	3.98690i	−0.0307455	−	0.134705i
$877$	−13.6829	−	28.4129i	−0.462040	−	0.959436i	−0.993657	−	0.112451i	$-0.964130\pi$
$877$	−13.6829	−	28.4129i	−0.462040	−	0.959436i	0.531617	−	0.846985i	$-0.321584\pi$
$878$	−33.4816	+	41.9846i	−1.12995	+	1.41691i
$879$	−0.285650	+	0.358193i	−0.00963472	+	0.0120816i
$880$		0			0
$881$	−5.15686	+	4.11246i	−0.173739	+	0.138552i	−0.706499	−	0.707714i	$-0.749726\pi$
$881$	−5.15686	+	4.11246i	−0.173739	+	0.138552i	0.532760	+	0.846267i	$0.321155\pi$
$882$	−23.2148			−0.781682
$883$	−36.0942	+	28.7842i	−1.21467	+	0.968665i	−0.999968	−	0.00801501i	$-0.997449\pi$
$883$	−36.0942	+	28.7842i	−1.21467	+	0.968665i	−0.214700	+	0.976680i	$0.568877\pi$
$884$	−6.40743	+	1.46246i	−0.215505	+	0.0491877i
$885$		0			0
$886$	40.6489	+	50.9722i	1.36563	+	1.71244i
$887$	39.8468			1.33793			0.668963	−	0.743296i	$-0.266739\pi$
$887$	39.8468			1.33793			0.668963	+	0.743296i	$0.266739\pi$
$888$	−5.35871	−	6.71961i	−0.179826	−	0.225495i
$889$	−1.11986	+	2.32542i	−0.0375590	+	0.0779922i
$890$		0			0
$891$	5.17716	+	4.12865i	0.173441	+	0.138315i
$892$	−1.86929	−	3.88163i	−0.0625886	−	0.129967i
$893$	10.4364	−	2.38204i	0.349241	−	0.0797120i
$894$	−6.73158	+	29.4930i	−0.225138	+	0.986393i
$895$		0			0
$896$	−2.87279	−	5.96541i	−0.0959733	−	0.199291i
$897$	1.01214	−	4.43450i	0.0337945	−	0.148063i
$898$			20.7090i			0.691067i
$899$	26.5191	−	21.1926i	0.884462	−	0.706814i
$900$		0			0
$901$	−12.9850	−	2.96373i	−0.432592	−	0.0987363i
$902$	98.7345	−	47.5480i	3.28750	−	1.58318i
$903$	−2.40591	+	4.99591i	−0.0800635	+	0.166254i
$904$	0.110439	−	0.483866i	0.00367315	−	0.0160931i
$905$		0			0
$906$	18.4654	−	8.89245i	0.613471	−	0.295432i
$907$	20.3791	−	25.5546i	0.676677	−	0.848526i	−0.318367	−	0.947968i	$-0.603134\pi$
$907$	20.3791	−	25.5546i	0.676677	−	0.848526i	0.995043	+	0.0994419i	$0.0317058\pi$
$908$	−10.8062	−	8.61765i	−0.358616	−	0.285987i
$909$	0.497883	−	1.03387i	0.0165138	−	0.0342912i
$910$		0			0
$911$		−	9.43844i		−	0.312709i	−0.987701	−	0.156355i	$-0.950026\pi$
$911$		−	9.43844i		−	0.312709i	0.987701	−	0.156355i	$-0.0499743\pi$
$912$	8.04251	−	6.41369i	0.266314	−	0.212378i
$913$	2.17080	+	9.51088i	0.0718429	+	0.314764i
$914$	42.0784	−	9.60412i	1.39183	−	0.317676i
$915$		0			0
$916$			1.33218i			0.0440165i
$917$	10.8563	+	13.6133i	0.358506	+	0.449552i
$918$	−21.9262	−	10.5591i	−0.723674	−	0.348503i
$919$	−2.07810	+	2.60585i	−0.0685501	+	0.0859591i	−0.814924	−	0.579567i	$-0.803222\pi$
$919$	−2.07810	+	2.60585i	−0.0685501	+	0.0859591i	0.746374	+	0.665527i	$0.231793\pi$
$920$		0			0
$921$	−4.49052	+	2.16252i	−0.147968	+	0.0712575i
$922$	−70.6446	+	16.1242i	−2.32655	+	0.531021i
$923$	7.68568	+	1.75421i	0.252977	+	0.0577404i
$924$	−7.53057	−	3.62653i	−0.247738	−	0.119304i
$925$		0			0
$926$	52.9317	+	12.0813i	1.73944	+	0.397017i
$927$			18.4236i			0.605109i
$928$	−8.35547	+	36.7808i	−0.274282	+	1.20739i
$929$	−20.1497			−0.661091			−0.330546	−	0.943790i	$-0.607233\pi$
$929$	−20.1497			−0.661091			−0.330546	+	0.943790i	$0.607233\pi$
$930$		0			0
$931$	5.82852	+	12.1030i	0.191022	+	0.396661i
$932$	−10.1081	+	20.9896i	−0.331101	+	0.687539i
$933$	−21.5713	−	4.92350i	−0.706211	−	0.161188i
$934$	−0.809232	−	3.54548i	−0.0264789	−	0.116012i
$935$		0			0
$936$	−2.49174	−	1.98710i	−0.0814451	−	0.0649503i
$937$	38.5465	+	30.7398i	1.25926	+	1.00423i	0.999254	+	0.0386184i	$0.0122957\pi$
$937$	38.5465	+	30.7398i	1.25926	+	1.00423i	0.260005	+	0.965607i	$0.416276\pi$
$938$	16.5428	+	7.96659i	0.540141	+	0.260118i
$939$	−14.6852	+	11.7110i	−0.479232	+	0.382175i
$940$		0			0
$941$	20.3245	+	25.4862i	0.662561	+	0.830825i	0.993619	−	0.112785i	$-0.0359772\pi$
$941$	20.3245	+	25.4862i	0.662561	+	0.830825i	−0.331058	+	0.943610i	$0.607406\pi$
$942$	−6.69732	−	29.3429i	−0.218210	−	0.956043i
$943$	5.72366	+	25.0770i	0.186388	+	0.816620i
$944$	−26.7013	−	33.4823i	−0.869053	−	1.08976i
$945$		0			0
$946$	−55.6004	+	44.3398i	−1.80772	+	1.44161i
$947$	−27.6766	−	13.3284i	−0.899370	−	0.433114i	−0.0737085	−	0.997280i	$-0.523483\pi$
$947$	−27.6766	−	13.3284i	−0.899370	−	0.433114i	−0.825661	+	0.564166i	$0.809198\pi$
$948$	6.44922	+	5.14308i	0.209461	+	0.167039i
$949$	3.61407	+	2.88212i	0.117318	+	0.0935577i
$950$		0			0
$951$	4.55557	+	19.9592i	0.147724	+	0.647223i
$952$	2.17587	+	0.496629i	0.0705204	+	0.0160958i
$953$	2.71318	−	5.63398i	0.0878886	−	0.182503i	−0.852392	−	0.522904i	$-0.824849\pi$
$953$	2.71318	−	5.63398i	0.0878886	−	0.182503i	0.940280	+	0.340401i	$0.110563\pi$
$954$	8.31770	+	17.2719i	0.269295	+	0.559198i
$955$		0			0
$956$	−29.9573			−0.968890
$957$	−14.4230	−	29.8716i	−0.466230	−	0.965613i
$958$		−	60.3159i		−	1.94872i
$959$	−17.3932	−	3.96987i	−0.561654	−	0.128194i
$960$		0			0
$961$	7.87232	+	3.79111i	0.253946	+	0.122294i
$962$	−28.1130	−	6.41660i	−0.906398	−	0.206880i
$963$	−15.1024	+	3.44701i	−0.486667	+	0.111078i
$964$	−4.27940	+	2.06085i	−0.137830	+	0.0663756i
$965$		0			0
$966$	2.85847	−	3.58441i	0.0919698	−	0.115327i
$967$	17.1208	+	8.24494i	0.550567	+	0.265139i	0.688419	−	0.725314i	$-0.258305\pi$
$967$	17.1208	+	8.24494i	0.550567	+	0.265139i	−0.137851	+	0.990453i	$0.544020\pi$
$968$	16.0544	+	20.1316i	0.516008	+	0.647054i
$969$			5.64970i			0.181494i
$970$		0			0
$971$	−33.2040	+	7.57859i	−1.06557	+	0.243208i	−0.719137	−	0.694868i	$-0.755463\pi$
$971$	−33.2040	+	7.57859i	−1.06557	+	0.243208i	−0.346428	+	0.938076i	$0.612606\pi$
$972$	5.33262	+	23.3638i	0.171044	+	0.749393i
$973$	7.82658	−	6.24149i	0.250909	−	0.200093i
$974$			33.2936i			1.06680i
$975$		0			0
$976$	4.44097	−	9.22178i	0.142152	−	0.295182i
$977$	−10.2342	−	8.16151i	−0.327421	−	0.261110i	0.445957	−	0.895054i	$-0.352863\pi$
$977$	−10.2342	−	8.16151i	−0.327421	−	0.261110i	−0.773379	+	0.633944i	$0.781435\pi$
$978$	15.1245	−	18.9655i	0.483629	−	0.606451i
$979$	−44.7797	+	21.5648i	−1.43117	+	0.689214i
$980$		0			0
$981$	0.856394	−	3.75211i	0.0273425	−	0.119796i
$982$	7.61884	−	15.8207i	0.243127	−	0.504858i
$983$	3.25905	−	1.56948i	0.103948	−	0.0500585i	−0.381187	−	0.924498i	$-0.624485\pi$
$983$	3.25905	−	1.56948i	0.103948	−	0.0500585i	0.485135	+	0.874439i	$0.338770\pi$
$984$	−8.65513	−	1.97548i	−0.275916	−	0.0629759i
$985$		0			0
$986$	−16.4125	−	20.5376i	−0.522680	−	0.654049i
$987$			4.44272i			0.141413i
$988$	1.21805	−	5.33662i	0.0387513	−	0.169780i
$989$	−7.24239	−	15.0390i	−0.230295	−	0.478212i
$990$		0			0
$991$	−5.60364	+	24.5511i	−0.178005	+	0.779893i	0.804544	+	0.593893i	$0.202410\pi$
$991$	−5.60364	+	24.5511i	−0.178005	+	0.779893i	−0.982550	+	0.186000i	$0.940448\pi$
$992$	−43.0450	+	9.82473i	−1.36668	+	0.311936i
$993$	−0.240969	−	0.500378i	−0.00764693	−	0.0158790i
$994$	6.21235	+	4.95418i	0.197044	+	0.157137i
$995$		0			0
$996$	−1.01776	+	2.11341i	−0.0322491	+	0.0669660i
$997$	14.2464	+	17.8644i	0.451188	+	0.565772i	0.954453	−	0.298360i	$-0.0964396\pi$
$997$	14.2464	+	17.8644i	0.451188	+	0.565772i	−0.503265	+	0.864132i	$0.667868\pi$
$998$	−49.2596			−1.55928
$999$	−28.4881	−	35.7230i	−0.901324	−	1.13022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.p.b.149.2		48
5.2	odd	4		725.2.q.b.526.1		24
5.3	odd	4		145.2.m.a.91.4	yes	24
5.4	even	2	inner	725.2.p.b.149.7		48
29.22	even	14	inner	725.2.p.b.399.7		48
145.22	odd	28		725.2.q.b.51.1		24
145.43	even	28		4205.2.a.y.1.5		24
145.73	even	28		4205.2.a.y.1.20		24
145.109	even	14	inner	725.2.p.b.399.2		48
145.138	odd	28		145.2.m.a.51.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.m.a.51.4	✓	24	145.138	odd	28
145.2.m.a.91.4	yes	24	5.3	odd	4
725.2.p.b.149.2		48	1.1	even	1	trivial
725.2.p.b.149.7		48	5.4	even	2	inner
725.2.p.b.399.2		48	145.109	even	14	inner
725.2.p.b.399.7		48	29.22	even	14	inner
725.2.q.b.51.1		24	145.22	odd	28
725.2.q.b.526.1		24	5.2	odd	4
4205.2.a.y.1.5		24	145.43	even	28
4205.2.a.y.1.20		24	145.73	even	28

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.p (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.416060 + 1.82288i) q^{2} +(0.896481 - 0.431723i) q^{3} +(-1.34784 - 0.649083i) q^{4} +(0.413987 + 1.81380i) q^{6} +(-0.393550 - 0.817215i) q^{7} +(-0.587568 + 0.736786i) q^{8} +(-1.25318 + 1.57143i) q^{9} +O(q^{10})\)	\(q+(-0.416060 + 1.82288i) q^{2} +(0.896481 - 0.431723i) q^{3} +(-1.34784 - 0.649083i) q^{4} +(0.413987 + 1.81380i) q^{6} +(-0.393550 - 0.817215i) q^{7} +(-0.587568 + 0.736786i) q^{8} +(-1.25318 + 1.57143i) q^{9} +(-4.84001 + 3.85978i) q^{11} -1.48853 q^{12} +(1.31550 - 1.04908i) q^{13} +(1.65342 - 0.377383i) q^{14} +(-2.96407 - 3.71683i) q^{16} +2.61099 q^{17} +(-2.34313 - 2.93819i) q^{18} +(-0.943542 + 1.95929i) q^{19} +(-0.705621 - 0.562714i) q^{21} +(-5.02216 - 10.4286i) q^{22} +(2.64871 - 0.604551i) q^{23} +(-0.208656 + 0.914181i) q^{24} +(1.36501 + 2.83448i) q^{26} +(-1.10926 + 4.86000i) q^{27} +1.35692i q^{28} +(-3.35329 + 4.21372i) q^{29} +(-6.14573 - 1.40272i) q^{31} +(6.31043 - 3.03894i) q^{32} +(-2.67262 + 5.54976i) q^{33} +(-1.08633 + 4.75952i) q^{34} +(2.70907 - 1.30462i) q^{36} +(-5.71479 + 7.16612i) q^{37} +(-3.17897 - 2.53514i) q^{38} +(0.726413 - 1.50841i) q^{39} +9.46763i q^{41} +(1.31934 - 1.05214i) q^{42} +(-1.36716 - 5.98990i) q^{43} +(9.02885 - 2.06078i) q^{44} +5.07980i q^{46} +(-3.06916 - 3.84861i) q^{47} +(-4.26187 - 2.05241i) q^{48} +(3.85147 - 4.82959i) q^{49} +(2.34071 - 1.12723i) q^{51} +(-2.45402 + 0.560114i) q^{52} +(-4.97319 - 1.13510i) q^{53} +(-8.39766 - 4.04410i) q^{54} +(0.833350 + 0.190207i) q^{56} +2.16381i q^{57} +(-6.28592 - 7.86580i) q^{58} +9.00832 q^{59} +(0.934156 + 1.93979i) q^{61} +(5.11398 - 10.6193i) q^{62} +(1.77739 + 0.405677i) q^{63} +(0.798372 + 3.49790i) q^{64} +(-9.00455 - 7.18089i) q^{66} +(8.46449 + 6.75020i) q^{67} +(-3.51919 - 1.69475i) q^{68} +(2.11352 - 1.68548i) q^{69} +(2.92119 + 3.66306i) q^{71} +(-0.421485 - 1.84665i) q^{72} +(0.611330 + 2.67841i) q^{73} +(-10.6853 - 13.3989i) q^{74} +(2.54348 - 2.02836i) q^{76} +(5.05905 + 2.43631i) q^{77} +(2.44742 + 1.95175i) q^{78} +(-4.33260 - 3.45513i) q^{79} +(-0.238022 - 1.04284i) q^{81} +(-17.2583 - 3.93910i) q^{82} +(0.683737 - 1.41979i) q^{83} +(0.585812 + 1.21645i) q^{84} +11.4877 q^{86} +(-1.18701 + 5.22521i) q^{87} -5.83393i q^{88} +(7.82729 + 1.78653i) q^{89} +(-1.37504 - 0.662184i) q^{91} +(-3.96243 - 0.904398i) q^{92} +(-6.11512 + 1.39574i) q^{93} +(8.29250 - 3.99346i) q^{94} +(4.34520 - 5.44871i) q^{96} +(14.9772 + 7.21266i) q^{97} +(7.20131 + 9.03015i) q^{98} -12.4427i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{6} + 8 q^{9}+O(q^{10}) \) 48 * q + 8 * q^6 + 8 * q^9	\( 48 q + 8 q^{6} + 8 q^{9} - 28 q^{11} + 84 q^{14} - 20 q^{16} + 98 q^{21} - 76 q^{24} - 14 q^{29} + 14 q^{31} - 40 q^{34} - 56 q^{36} - 14 q^{39} + 42 q^{44} + 4 q^{49} + 12 q^{51} - 214 q^{54} - 84 q^{56} + 132 q^{59} + 112 q^{61} - 66 q^{64} - 140 q^{66} + 56 q^{69} + 106 q^{71} - 66 q^{74} - 84 q^{76} + 112 q^{79} - 58 q^{81} - 28 q^{84} + 60 q^{86} - 28 q^{89} - 62 q^{91} + 76 q^{94} - 2 q^{96}+O(q^{100}) \) 48 * q + 8 * q^6 + 8 * q^9 - 28 * q^11 + 84 * q^14 - 20 * q^16 + 98 * q^21 - 76 * q^24 - 14 * q^29 + 14 * q^31 - 40 * q^34 - 56 * q^36 - 14 * q^39 + 42 * q^44 + 4 * q^49 + 12 * q^51 - 214 * q^54 - 84 * q^56 + 132 * q^59 + 112 * q^61 - 66 * q^64 - 140 * q^66 + 56 * q^69 + 106 * q^71 - 66 * q^74 - 84 * q^76 + 112 * q^79 - 58 * q^81 - 28 * q^84 + 60 * q^86 - 28 * q^89 - 62 * q^91 + 76 * q^94 - 2 * q^96

Introduction

L-functions

Modular forms

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