LMFDB - Embedded newform 725.2.p.b.149.7

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			149.7
Character	$\chi$	$=$	725.149
Dual form			725.2.p.b.399.7

$q$-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	$-0.698679\pi$
$2$	0.416060	−	1.82288i	0.294199	−	1.28897i	0.878621	−	0.477519i	$-0.158464\pi$
$3$	−0.896481	+	0.431723i	−0.517584	+	0.249255i	−0.674391	−	0.738374i	$-0.735594\pi$
$3$	−0.896481	+	0.431723i	−0.517584	+	0.249255i	0.156808	+	0.987629i	$0.449880\pi$
$4$	−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	0.962008	−	0.273023i	$-0.0880234\pi$
$7$	0.393550	+	0.817215i	0.148748	+	0.308878i	−0.813260	+	0.581901i	$0.802309\pi$
$8$	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	−0.788707	−	0.614769i	$-0.789249\pi$
$13$	−1.31550	+	1.04908i	−0.364855	+	0.290962i	0.423852	+	0.905731i	$0.360678\pi$
$14$	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	$-0.602551\pi$
$17$	−2.61099			−0.633259			−0.316630	+	0.948549i	$0.602551\pi$
$18$	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	−0.489555	−	0.871972i	$-0.662841\pi$
$23$	−2.64871	+	0.604551i	−0.552294	+	0.126058i	−0.0627391	+	0.998030i	$0.519984\pi$
$24$	−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	$-0.514115\pi$
$37$	5.71479	−	7.16612i	0.939506	−	1.17810i	0.983833	−	0.179086i	$-0.0573139\pi$
$38$	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	$0.0837664\pi$
$43$	1.36716	+	5.98990i	0.208489	+	0.913451i	−0.757084	+	0.653318i	$0.773376\pi$
$44$	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	0.953550	−	0.301234i	$-0.0973986\pi$
$47$	3.06916	+	3.84861i	0.447684	+	0.561378i	−0.505867	+	0.862612i	$0.668827\pi$
$48$	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	0.549978	−	0.835179i	$-0.314636\pi$
$53$	4.97319	+	1.13510i	0.683120	+	0.155918i	0.133142	+	0.991097i	$0.457493\pi$
$54$	−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	−0.0493756	−	0.998780i	$-0.515723\pi$
$67$	−8.46449	−	6.75020i	−1.03410	−	0.824668i	−0.984726	+	0.174112i	$0.944295\pi$
$68$	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	0.926470	−	0.376368i	$-0.122827\pi$
$73$	−0.611330	−	2.67841i	−0.0715507	−	0.313484i	−0.998021	+	0.0628841i	$0.979970\pi$
$74$	−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	−0.935118	−	0.354337i	$-0.884707\pi$
$83$	−0.683737	+	1.41979i	−0.0750498	+	0.155843i	0.860068	+	0.510179i	$0.170421\pi$
$84$	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	−0.527595	−	0.849496i	$-0.676906\pi$
$97$	−14.9772	−	7.21266i	−1.52071	−	0.732334i	−0.993113	+	0.117161i	$0.962621\pi$
$98$	−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	−0.909360	−	0.416010i	$-0.863428\pi$
$103$	−7.16645	+	5.71506i	−0.706132	+	0.563121i	0.203228	+	0.979131i	$0.434857\pi$
$104$			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	0.287350	−	0.957826i	$-0.407226\pi$
$107$	−6.02564	−	4.80528i	−0.582520	−	0.464544i	−0.869870	+	0.493281i	$0.835797\pi$
$108$	−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	−0.411432	−	0.911440i	$-0.634971\pi$
$113$	0.474497	−	0.228506i	0.0446370	−	0.0214960i	0.456069	+	0.889944i	$0.349257\pi$
$114$	−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	0.854292	−	0.519794i	$-0.173991\pi$
$127$	1.77417	+	2.22474i	0.157432	+	0.197413i	−0.696860	+	0.717208i	$0.745420\pi$
$128$	−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	$0.531855\pi$
$137$	−12.2633	+	15.3777i	−1.04773	+	1.31381i	−0.947818	+	0.318812i	$0.896716\pi$
$138$	−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	$-0.276625\pi$
$157$	16.1776			1.29111			0.645556	+	0.763713i	$0.276625\pi$
$158$	−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	0.990593	−	0.136842i	$-0.0436953\pi$
$163$	8.12953	+	10.1941i	0.636754	+	0.798464i	−0.353839	+	0.935306i	$0.615124\pi$
$164$	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	0.925411	−	0.378965i	$-0.123720\pi$
$167$	0.673791	+	1.39914i	0.0521395	+	0.108269i	−0.873271	+	0.487234i	$0.838006\pi$
$168$	−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	$-0.728663\pi$
$173$		−	19.8052i		−	1.50576i	0.658157	−	0.752881i	$-0.271337\pi$
$174$	−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	−0.612973	−	0.790104i	$-0.710027\pi$
$193$	−22.4069	−	10.7906i	−1.61288	−	0.776724i	−0.999910	+	0.0133799i	$0.995741\pi$
$194$	−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	−0.119966	−	0.992778i	$-0.538279\pi$
$197$	2.84500	−	0.649353i	0.202698	−	0.0462645i	0.322664	+	0.946513i	$0.395421\pi$
$198$	−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	0.545195	−	0.838309i	$-0.316455\pi$
$223$	−2.25159	−	1.79559i	−0.150778	−	0.120241i	−0.695973	+	0.718068i	$0.745027\pi$
$224$	−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	−0.0871217	−	0.996198i	$-0.527767\pi$
$227$	−9.00751	−	2.05591i	−0.597850	−	0.136455i	−0.510728	+	0.859742i	$0.670624\pi$
$228$	−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	$0.170394\pi$
$233$			15.5728i			1.02021i	−0.860112	+	0.510106i	$0.829606\pi$
$234$	−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	$-0.617467\pi$
$257$	9.51266	−	19.7532i	0.593383	−	1.23217i	0.954097	−	0.299497i	$-0.0968188\pi$
$258$	−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	$0.421261\pi$
$263$	−6.42899	+	28.1673i	−0.396429	+	1.73687i	−0.641280	+	0.767307i	$0.721596\pi$
$264$	−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	−0.323971	−	0.946067i	$-0.605018\pi$
$277$	8.75914	−	6.98518i	0.526286	−	0.419699i	0.850257	+	0.526368i	$0.176447\pi$
$278$	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	$-0.997578\pi$
$283$	−6.43379	−	13.3599i	−0.382449	−	0.794163i	0.617522	−	0.786553i	$-0.288137\pi$
$284$	−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	−0.421727	−	0.906723i	$-0.638576\pi$
$293$	0.414842	−	0.199777i	0.0242353	−	0.0116711i	0.445962	+	0.895052i	$0.352862\pi$
$294$	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	$-0.454344\pi$
$307$	5.00905			0.285882			0.142941	+	0.989731i	$0.454344\pi$
$308$	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	0.331912	−	0.943310i	$-0.392306\pi$
$313$	18.4038	−	4.20054i	1.04024	−	0.237428i	0.708330	+	0.705882i	$0.249449\pi$
$314$	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	$-0.732481\pi$
$317$	4.57837	−	20.0592i	0.257147	−	1.12663i	0.924286	−	0.381701i	$-0.124662\pi$
$318$			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	0.936925	−	0.349531i	$-0.113659\pi$
$337$	7.11671	+	8.92407i	0.387672	+	0.486125i	−0.549253	+	0.835656i	$0.685088\pi$
$338$	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	$0.291641\pi$
$347$			29.5553i			1.58661i	−0.608824	+	0.793305i	$0.708359\pi$
$348$	−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	−0.649254	−	0.760572i	$-0.724919\pi$
$353$	−29.3889	−	6.70782i	−1.56421	−	0.357021i	−0.914957	+	0.403550i	$0.867776\pi$
$354$	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	0.825190	−	0.564856i	$-0.191068\pi$
$367$	17.2045	+	8.28523i	0.898065	+	0.432485i	0.0728755	+	0.997341i	$0.476782\pi$
$368$	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	−0.998040	−	0.0625740i	$-0.980069\pi$
$373$	−6.31252	+	13.1081i	−0.326850	+	0.678711i	0.671190	+	0.741285i	$0.265783\pi$
$374$	−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	0.740475	−	0.672084i	$-0.234601\pi$
$383$	33.2545	−	7.59012i	1.69923	−	0.387837i	0.958751	+	0.284247i	$0.0917436\pi$
$384$	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	0.949174	−	0.314751i	$-0.101921\pi$
$397$	17.0064	+	13.5621i	0.853526	+	0.680664i	−0.0956482	+	0.995415i	$0.530492\pi$
$398$	−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	$-0.715856\pi$
$433$	5.73819	−	25.1406i	0.275760	−	1.20818i	0.903098	−	0.429435i	$-0.141287\pi$
$434$	−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	$0.524994\pi$
$443$	−21.7402	+	27.2614i	−1.03291	+	1.29523i	−0.954469	+	0.298310i	$0.903577\pi$
$444$	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	$0.0386811\pi$
$457$	10.0156	+	20.7975i	0.468508	+	0.972867i	−0.524117	+	0.851646i	$0.675605\pi$
$458$	−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	$0.235746\pi$
$463$			29.0375i			1.34949i	−0.738053	+	0.674743i	$0.764254\pi$
$464$	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	−0.392899	−	0.919582i	$-0.628528\pi$
$467$	1.75238	−	0.843899i	0.0810902	−	0.0390510i	0.473989	+	0.880531i	$0.342814\pi$
$468$	−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	−0.596935	−	0.802290i	$-0.703615\pi$
$487$	−17.3600	+	3.96230i	−0.786654	+	0.179549i	−0.189719	+	0.981838i	$0.560758\pi$
$488$	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	−0.539473	−	0.842003i	$-0.681377\pi$
$503$	−34.4070	−	16.5696i	−1.53413	−	0.738800i	−0.994660	+	0.103203i	$0.967091\pi$
$504$	−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	$0.0576620\pi$
$523$			8.24028i			0.360322i	−0.983637	+	0.180161i	$0.942338\pi$
$524$	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	−0.788080	−	0.615572i	$-0.788925\pi$
$547$	4.31634	−	8.96298i	0.184553	−	0.383229i	0.972634	+	0.232343i	$0.0746392\pi$
$548$	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	−0.266214	−	0.963914i	$-0.585773\pi$
$557$	−2.07304	+	0.473158i	−0.0878375	+	0.0200483i	0.178376	+	0.983962i	$0.442916\pi$
$558$	−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	$-0.348741\pi$
$563$	21.7113			0.915023			0.457511	+	0.889204i	$0.348741\pi$
$564$	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	−0.782154	−	0.623085i	$-0.785879\pi$
$577$	−18.8004	+	9.05380i	−0.782671	+	0.376915i	−0.000517201		1.00000i	$0.500165\pi$
$578$	−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	0.665492	−	0.746405i	$-0.268222\pi$
$587$	−8.06792	−	16.7532i	−0.332999	−	0.691479i	−0.998490	+	0.0549262i	$0.982508\pi$
$588$	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	−0.232067	−	0.972700i	$-0.574549\pi$
$593$	16.1842	−	12.9065i	0.664605	−	0.530005i	0.896672	+	0.442695i	$0.145977\pi$
$594$	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	−0.997549	−	0.0699643i	$-0.977711\pi$
$607$	−1.68599	+	7.38679i	−0.0684321	+	0.299821i	0.929117	+	0.369785i	$0.120569\pi$
$608$		−	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	−0.789290	−	0.614021i	$-0.789551\pi$
$613$	4.52802	−	9.40254i	0.182885	−	0.379765i	0.972175	+	0.234256i	$0.0752654\pi$
$614$	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	$-0.416733\pi$
$617$	28.3873	−	35.5966i	1.14283	−	1.43306i	0.884213	−	0.467084i	$-0.154695\pi$
$618$	−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	0.260648	−	0.965434i	$-0.416064\pi$
$643$	1.94232	+	0.443322i	0.0765976	+	0.0174829i	−0.184050	+	0.982917i	$0.558921\pi$
$644$	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	0.933961	−	0.357374i	$-0.116328\pi$
$647$	20.1804	+	16.0933i	0.793373	+	0.632694i	−0.140588	+	0.990068i	$0.544899\pi$
$648$	−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	$-0.917751\pi$
$653$	−5.27976	−	23.1321i	−0.206613	−	0.905230i	0.760189	−	0.649702i	$-0.225106\pi$
$654$	−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	−0.306009	−	0.952029i	$-0.598994\pi$
$673$	−4.37501	+	0.998567i	−0.168644	+	0.0384919i	0.137365	+	0.990521i	$0.456137\pi$
$674$	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	0.427690	−	0.903926i	$-0.359328\pi$
$677$	−0.321803	−	0.154972i	−0.0123679	−	0.00595606i	−0.440057	+	0.897970i	$0.645042\pi$
$678$	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	−0.781054	−	0.624463i	$-0.785318\pi$
$683$	−9.04371	+	7.21212i	−0.346048	+	0.275964i	0.435006	+	0.900428i	$0.356746\pi$
$684$			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	$0.333972\pi$
$727$	−8.81272	+	38.6110i	−0.326846	+	1.43200i	−0.825106	+	0.564977i	$0.808885\pi$
$728$	−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	$0.522539\pi$
$733$	−27.8183	+	34.8830i	−1.02749	+	1.28843i	−0.956741	+	0.290939i	$0.906032\pi$
$734$	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	0.464023	−	0.885823i	$-0.346405\pi$
$743$	−13.7066	−	17.1875i	−0.502845	−	0.630548i	−0.966868	+	0.255275i	$0.917834\pi$
$744$	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	−0.999199	−	0.0400143i	$-0.987260\pi$
$757$	−43.7716	+	21.0793i	−1.59091	+	0.766140i	−0.591706	+	0.806154i	$0.701545\pi$
$758$	−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	0.912622	−	0.408805i	$-0.134055\pi$
$773$	32.3074	+	15.5584i	1.16201	+	0.559597i	0.249393	+	0.968402i	$0.419769\pi$
$774$	−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	$-0.680481\pi$
$787$	12.8278	−	26.6373i	0.457263	−	0.949517i	0.994366	−	0.106000i	$-0.0338045\pi$
$788$	−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	$-0.771881\pi$
$797$	−10.1540	−	44.4877i	−0.359674	−	1.57584i	0.394331	−	0.918969i	$-0.370976\pi$
$798$	−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	0.764243	−	0.644928i	$-0.223113\pi$
$823$	−0.991896	−	1.24380i	−0.0345753	−	0.0433561i	−0.798819	+	0.601572i	$0.794541\pi$
$824$			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	$-0.945487\pi$
$827$	−4.93266	−	21.6114i	−0.171525	−	0.751502i	0.813846	−	0.581081i	$-0.197370\pi$
$828$	−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	$-0.630217\pi$
$853$	−23.2348			−0.795546			−0.397773	+	0.917484i	$0.630217\pi$
$854$	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	−0.659856	−	0.751392i	$-0.729383\pi$
$857$	−2.17025	+	1.73071i	−0.0741342	+	0.0591201i	0.585722	+	0.810512i	$0.300811\pi$
$858$	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	$0.000332827\pi$
$863$	11.0847	+	23.0176i	0.377327	+	0.783529i	−0.622672	+	0.782483i	$0.713953\pi$
$864$	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	$0.0358702\pi$
$877$	13.6829	+	28.4129i	0.462040	+	0.959436i	−0.531617	+	0.846985i	$0.678416\pi$
$878$	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	0.214700	−	0.976680i	$-0.431123\pi$
$883$	36.0942	−	28.7842i	1.21467	−	0.968665i	0.999968	+	0.00801501i	$0.00255128\pi$
$884$	−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	$-0.733261\pi$
$887$	−39.8468			−1.33793			−0.668963	+	0.743296i	$0.733261\pi$
$888$	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	−0.995043	−	0.0994419i	$-0.968294\pi$
$907$	−20.3791	+	25.5546i	−0.676677	+	0.848526i	0.318367	+	0.947968i	$0.396866\pi$
$908$	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	$-0.987704\pi$
$937$	−38.5465	−	30.7398i	−1.25926	−	1.00423i	−0.260005	−	0.965607i	$-0.583724\pi$
$938$	−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	0.825661	−	0.564166i	$-0.190802\pi$
$947$	27.6766	+	13.3284i	0.899370	+	0.433114i	0.0737085	+	0.997280i	$0.476517\pi$
$948$	−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	−0.940280	−	0.340401i	$-0.889437\pi$
$953$	−2.71318	+	5.63398i	−0.0878886	+	0.182503i	0.852392	+	0.522904i	$0.175151\pi$
$954$	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	0.137851	−	0.990453i	$-0.455980\pi$
$967$	−17.1208	−	8.24494i	−0.550567	−	0.265139i	−0.688419	+	0.725314i	$0.741695\pi$
$968$	−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	0.773379	−	0.633944i	$-0.218565\pi$
$977$	10.2342	+	8.16151i	0.327421	+	0.261110i	−0.445957	+	0.895054i	$0.647137\pi$
$978$	−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	−0.485135	−	0.874439i	$-0.661230\pi$
$983$	−3.25905	+	1.56948i	−0.103948	+	0.0500585i	0.381187	+	0.924498i	$0.375515\pi$
$984$	−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	0.503265	−	0.864132i	$-0.332132\pi$
$997$	−14.2464	−	17.8644i	−0.451188	−	0.565772i	−0.954453	+	0.298360i	$0.903560\pi$
$998$	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.149.7		48
5.2	odd	4		145.2.m.a.91.4	yes	24
5.3	odd	4		725.2.q.b.526.1		24
5.4	even	2	inner	725.2.p.b.149.2		48
29.22	even	14	inner	725.2.p.b.399.2		48
145.22	odd	28		145.2.m.a.51.4	✓	24
145.72	even	28		4205.2.a.y.1.5		24
145.102	even	28		4205.2.a.y.1.20		24
145.109	even	14	inner	725.2.p.b.399.7		48
145.138	odd	28		725.2.q.b.51.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.m.a.51.4	✓	24	145.22	odd	28
145.2.m.a.91.4	yes	24	5.2	odd	4
725.2.p.b.149.2		48	5.4	even	2	inner
725.2.p.b.149.7		48	1.1	even	1	trivial
725.2.p.b.399.2		48	29.22	even	14	inner
725.2.p.b.399.7		48	145.109	even	14	inner
725.2.q.b.51.1		24	145.138	odd	28
725.2.q.b.526.1		24	5.3	odd	4
4205.2.a.y.1.5		24	145.72	even	28
4205.2.a.y.1.20		24	145.102	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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