LMFDB - Embedded newform 625.2.d.n.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, degree $4$, 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.2
Root			$-1.51514i$ of defining polynomial
Character	$\chi$	$=$	625.251
Dual form			625.2.d.n.376.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.855434 + 0.621509i) q^{2} +(-0.212419 + 0.653760i) q^{3} +(-0.272540 + 0.838792i) q^{4} +(-0.224607 - 0.691269i) q^{6} +1.01199 q^{7} +(-0.941671 - 2.89816i) q^{8} +(2.04477 + 1.48561i) q^{9} +O(q^{10})$	\(q+(-0.855434 + 0.621509i) q^{2} +(-0.212419 + 0.653760i) q^{3} +(-0.272540 + 0.838792i) q^{4} +(-0.224607 - 0.691269i) q^{6} +1.01199 q^{7} +(-0.941671 - 2.89816i) q^{8} +(2.04477 + 1.48561i) q^{9} +(-4.14276 + 3.00989i) q^{11} +(-0.490476 - 0.356351i) q^{12} +(-4.92309 - 3.57684i) q^{13} +(-0.865695 + 0.628964i) q^{14} +(1.17974 + 0.857128i) q^{16} +(0.986752 + 3.03691i) q^{17} -2.67249 q^{18} +(1.05953 + 3.26090i) q^{19} +(-0.214967 + 0.661601i) q^{21} +(1.67318 - 5.14953i) q^{22} +(-2.36165 + 1.71584i) q^{23} +2.09473 q^{24} +6.43442 q^{26} +(-3.07395 + 2.23335i) q^{27} +(-0.275809 + 0.848853i) q^{28} +(-0.479737 + 1.47648i) q^{29} +(-2.47121 - 7.60559i) q^{31} +4.55272 q^{32} +(-1.08774 - 3.34773i) q^{33} +(-2.73157 - 1.98460i) q^{34} +(-1.80340 + 1.31025i) q^{36} +(-6.80161 - 4.94166i) q^{37} +(-2.93304 - 2.13098i) q^{38} +(3.38415 - 2.45873i) q^{39} +(1.50764 + 1.09537i) q^{41} +(-0.227301 - 0.699561i) q^{42} -5.22402 q^{43} +(-1.39561 - 4.29523i) q^{44} +(0.953826 - 2.93558i) q^{46} +(-1.48353 + 4.56584i) q^{47} +(-0.810954 + 0.589193i) q^{48} -5.97587 q^{49} -2.19501 q^{51} +(4.34196 - 3.15462i) q^{52} +(3.10560 - 9.55806i) q^{53} +(1.24151 - 3.82097i) q^{54} +(-0.952966 - 2.93293i) q^{56} -2.35691 q^{57} +(-0.507262 - 1.56119i) q^{58} +(-2.34170 - 1.70135i) q^{59} +(1.86855 - 1.35758i) q^{61} +(6.84090 + 4.97020i) q^{62} +(2.06930 + 1.50343i) q^{63} +(-6.25402 + 4.54382i) q^{64} +(3.01114 + 2.18772i) q^{66} +(1.43660 + 4.42142i) q^{67} -2.81626 q^{68} +(-0.620086 - 1.90843i) q^{69} +(-2.39090 + 7.35843i) q^{71} +(2.38005 - 7.32504i) q^{72} +(0.481802 - 0.350050i) q^{73} +8.88962 q^{74} -3.02398 q^{76} +(-4.19245 + 3.04600i) q^{77} +(-1.36680 + 4.20656i) q^{78} +(3.41751 - 10.5180i) q^{79} +(1.53599 + 4.72729i) q^{81} -1.97047 q^{82} +(4.41810 + 13.5975i) q^{83} +(-0.496359 - 0.360626i) q^{84} +(4.46880 - 3.24678i) q^{86} +(-0.863357 - 0.627265i) q^{87} +(12.6243 + 9.17208i) q^{88} +(5.17223 - 3.75785i) q^{89} +(-4.98214 - 3.61974i) q^{91} +(-0.795588 - 2.44857i) q^{92} +5.49716 q^{93} +(-1.56865 - 4.82780i) q^{94} +(-0.967086 + 2.97639i) q^{96} +(-4.35197 + 13.3940i) q^{97} +(5.11196 - 3.71406i) q^{98} -12.9425 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9	$ 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9} + 2 q^{11} - 25 q^{12} - 5 q^{13} + 9 q^{14} - 14 q^{16} + 10 q^{17} - 10 q^{18} + 7 q^{21} + 40 q^{22} - 15 q^{23} + 10 q^{24} + 22 q^{26} - 20 q^{27} - 30 q^{28} - 10 q^{29} + 17 q^{31} + 60 q^{32} - 5 q^{33} - q^{34} - 4 q^{36} + 15 q^{37} + 15 q^{38} - 9 q^{39} + 12 q^{41} + 45 q^{42} + 49 q^{44} - 33 q^{46} - 25 q^{47} + 20 q^{48} - 8 q^{49} - 28 q^{51} - 20 q^{52} - 30 q^{54} - 35 q^{56} - 20 q^{57} - 5 q^{58} + 20 q^{59} - 23 q^{61} - 15 q^{62} - 10 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{68} + 6 q^{69} + 22 q^{71} - 5 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 40 q^{77} + 25 q^{78} + 75 q^{79} + 11 q^{81} - 90 q^{82} - 25 q^{83} - 31 q^{84} + 17 q^{86} + 20 q^{87} + 5 q^{89} + 22 q^{91} - 60 q^{92} - 80 q^{93} - 51 q^{94} - 28 q^{96} - 40 q^{97} - 15 q^{98} - 44 q^{99}+O(q^{100}) $ 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9 + 2 * q^11 - 25 * q^12 - 5 * q^13 + 9 * q^14 - 14 * q^16 + 10 * q^17 - 10 * q^18 + 7 * q^21 + 40 * q^22 - 15 * q^23 + 10 * q^24 + 22 * q^26 - 20 * q^27 - 30 * q^28 - 10 * q^29 + 17 * q^31 + 60 * q^32 - 5 * q^33 - q^34 - 4 * q^36 + 15 * q^37 + 15 * q^38 - 9 * q^39 + 12 * q^41 + 45 * q^42 + 49 * q^44 - 33 * q^46 - 25 * q^47 + 20 * q^48 - 8 * q^49 - 28 * q^51 - 20 * q^52 - 30 * q^54 - 35 * q^56 - 20 * q^57 - 5 * q^58 + 20 * q^59 - 23 * q^61 - 15 * q^62 - 10 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^68 + 6 * q^69 + 22 * q^71 - 5 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 40 * q^77 + 25 * q^78 + 75 * q^79 + 11 * q^81 - 90 * q^82 - 25 * q^83 - 31 * q^84 + 17 * q^86 + 20 * q^87 + 5 * q^89 + 22 * q^91 - 60 * q^92 - 80 * q^93 - 51 * q^94 - 28 * q^96 - 40 * q^97 - 15 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.855434	+	0.621509i	−0.604883	+	0.439474i	−0.847609	−	0.530622i	$-0.821959\pi$
$2$	−0.855434	+	0.621509i	−0.604883	+	0.439474i	0.242725	+	0.970095i	$0.421959\pi$
$3$	−0.212419	+	0.653760i	−0.122640	+	0.377448i	−0.993464	−	0.114148i	$-0.963586\pi$
$3$	−0.212419	+	0.653760i	−0.122640	+	0.377448i	0.870823	+	0.491596i	$0.163586\pi$
$4$	−0.272540	+	0.838792i	−0.136270	+	0.419396i
$5$		0			0
$5$		0			0
$6$	−0.224607	−	0.691269i	−0.0916954	−	0.282209i
$7$	1.01199			0.382498			0.191249	−	0.981542i	$-0.438746\pi$
$7$	1.01199			0.382498			0.191249	+	0.981542i	$0.438746\pi$
$8$	−0.941671	−	2.89816i	−0.332931	−	1.02466i
$9$	2.04477	+	1.48561i	0.681590	+	0.495204i
$10$		0			0
$11$	−4.14276	+	3.00989i	−1.24909	+	0.907517i	−0.998169	−	0.0604903i	$-0.980734\pi$
$11$	−4.14276	+	3.00989i	−1.24909	+	0.907517i	−0.250921	+	0.968007i	$0.580734\pi$
$12$	−0.490476	−	0.356351i	−0.141588	−	0.102870i
$13$	−4.92309	−	3.57684i	−1.36542	−	0.992036i	−0.998079	−	0.0619496i	$-0.980268\pi$
$13$	−4.92309	−	3.57684i	−1.36542	−	0.992036i	−0.367341	−	0.930086i	$-0.619732\pi$
$14$	−0.865695	+	0.628964i	−0.231367	+	0.168098i
$15$		0			0
$16$	1.17974	+	0.857128i	0.294934	+	0.214282i
$17$	0.986752	+	3.03691i	0.239322	+	0.736559i	0.996519	+	0.0833711i	$0.0265687\pi$
$17$	0.986752	+	3.03691i	0.239322	+	0.736559i	−0.757196	+	0.653188i	$0.773431\pi$
$18$	−2.67249			−0.629912
$19$	1.05953	+	3.26090i	0.243073	+	0.748102i	0.995947	+	0.0899377i	$0.0286668\pi$
$19$	1.05953	+	3.26090i	0.243073	+	0.748102i	−0.752874	+	0.658164i	$0.771333\pi$
$20$		0			0
$21$	−0.214967	+	0.661601i	−0.0469097	+	0.144373i
$22$	1.67318	−	5.14953i	0.356724	−	1.09788i
$23$	−2.36165	+	1.71584i	−0.492438	+	0.357777i	−0.806121	−	0.591751i	$-0.798437\pi$
$23$	−2.36165	+	1.71584i	−0.492438	+	0.357777i	0.313683	+	0.949528i	$0.398437\pi$
$24$	2.09473			0.427585
$25$		0			0
$26$	6.43442			1.26189
$27$	−3.07395	+	2.23335i	−0.591581	+	0.429809i
$28$	−0.275809	+	0.848853i	−0.0521230	+	0.160418i
$29$	−0.479737	+	1.47648i	−0.0890849	+	0.274175i	−0.985667	−	0.168702i	$-0.946042\pi$
$29$	−0.479737	+	1.47648i	−0.0890849	+	0.274175i	0.896582	+	0.442878i	$0.146042\pi$
$30$		0			0
$31$	−2.47121	−	7.60559i	−0.443842	−	1.36600i	−0.883749	−	0.467961i	$-0.844989\pi$
$31$	−2.47121	−	7.60559i	−0.443842	−	1.36600i	0.439907	−	0.898043i	$-0.355011\pi$
$32$	4.55272			0.804815
$33$	−1.08774	−	3.34773i	−0.189352	−	0.582765i
$34$	−2.73157	−	1.98460i	−0.468460	−	0.340356i
$35$		0			0
$36$	−1.80340	+	1.31025i	−0.300567	+	0.218375i
$37$	−6.80161	−	4.94166i	−1.11818	−	0.812404i	−0.134246	−	0.990948i	$-0.542861\pi$
$37$	−6.80161	−	4.94166i	−1.11818	−	0.812404i	−0.983932	+	0.178544i	$0.942861\pi$
$38$	−2.93304	−	2.13098i	−0.475802	−	0.345690i
$39$	3.38415	−	2.45873i	0.541898	−	0.393712i
$40$		0			0
$41$	1.50764	+	1.09537i	0.235454	+	0.171067i	0.699256	−	0.714872i	$-0.253515\pi$
$41$	1.50764	+	1.09537i	0.235454	+	0.171067i	−0.463802	+	0.885939i	$0.653515\pi$
$42$	−0.227301	−	0.699561i	−0.0350733	−	0.107945i
$43$	−5.22402			−0.796655			−0.398328	−	0.917243i	$-0.630409\pi$
$43$	−5.22402			−0.796655			−0.398328	+	0.917243i	$0.630409\pi$
$44$	−1.39561	−	4.29523i	−0.210396	−	0.647531i
$45$		0			0
$46$	0.953826	−	2.93558i	0.140634	−	0.432827i
$47$	−1.48353	+	4.56584i	−0.216395	+	0.665996i	0.782656	+	0.622454i	$0.213864\pi$
$47$	−1.48353	+	4.56584i	−0.216395	+	0.665996i	−0.999052	+	0.0435419i	$0.986136\pi$
$48$	−0.810954	+	0.589193i	−0.117051	+	0.0850426i
$49$	−5.97587			−0.853695
$50$		0			0
$51$	−2.19501			−0.307363
$52$	4.34196	−	3.15462i	0.602122	−	0.437467i
$53$	3.10560	−	9.55806i	0.426587	−	1.31290i	−0.474879	−	0.880051i	$-0.657508\pi$
$53$	3.10560	−	9.55806i	0.426587	−	1.31290i	0.901466	−	0.432849i	$-0.142492\pi$
$54$	1.24151	−	3.82097i	0.168948	−	0.519969i
$55$		0			0
$56$	−0.952966	−	2.93293i	−0.127345	−	0.391929i
$57$	−2.35691			−0.312180
$58$	−0.507262	−	1.56119i	−0.0666068	−	0.204995i
$59$	−2.34170	−	1.70135i	−0.304864	−	0.221496i	0.424826	−	0.905275i	$-0.360335\pi$
$59$	−2.34170	−	1.70135i	−0.304864	−	0.221496i	−0.729689	+	0.683779i	$0.760335\pi$
$60$		0			0
$61$	1.86855	−	1.35758i	0.239244	−	0.173821i	−0.461702	−	0.887035i	$-0.652761\pi$
$61$	1.86855	−	1.35758i	0.239244	−	0.173821i	0.700946	+	0.713214i	$0.252761\pi$
$62$	6.84090	+	4.97020i	0.868795	+	0.631217i
$63$	2.06930	+	1.50343i	0.260707	+	0.189415i
$64$	−6.25402	+	4.54382i	−0.781753	+	0.567977i
$65$		0			0
$66$	3.01114	+	2.18772i	0.370646	+	0.269290i
$67$	1.43660	+	4.42142i	0.175509	+	0.540162i	0.999656	−	0.0262139i	$-0.00834510\pi$
$67$	1.43660	+	4.42142i	0.175509	+	0.540162i	−0.824147	+	0.566376i	$0.808345\pi$
$68$	−2.81626			−0.341522
$69$	−0.620086	−	1.90843i	−0.0746496	−	0.229748i
$70$		0			0
$71$	−2.39090	+	7.35843i	−0.283747	+	0.873285i	0.703024	+	0.711166i	$0.251833\pi$
$71$	−2.39090	+	7.35843i	−0.283747	+	0.873285i	−0.986771	+	0.162118i	$0.948167\pi$
$72$	2.38005	−	7.32504i	0.280492	−	0.863264i
$73$	0.481802	−	0.350050i	0.0563907	−	0.0409702i	−0.559233	−	0.829011i	$-0.688904\pi$
$73$	0.481802	−	0.350050i	0.0563907	−	0.0409702i	0.615624	+	0.788040i	$0.288904\pi$
$74$	8.88962			1.03340
$75$		0			0
$76$	−3.02398			−0.346875
$77$	−4.19245	+	3.04600i	−0.477775	+	0.347124i
$78$	−1.36680	+	4.20656i	−0.154759	+	0.476300i
$79$	3.41751	−	10.5180i	0.384500	−	1.18337i	−0.552342	−	0.833618i	$-0.686266\pi$
$79$	3.41751	−	10.5180i	0.384500	−	1.18337i	0.936842	−	0.349752i	$-0.113734\pi$
$80$		0			0
$81$	1.53599	+	4.72729i	0.170665	+	0.525254i
$82$	−1.97047			−0.217602
$83$	4.41810	+	13.5975i	0.484950	+	1.49252i	0.832054	+	0.554695i	$0.187165\pi$
$83$	4.41810	+	13.5975i	0.484950	+	1.49252i	−0.347104	+	0.937827i	$0.612835\pi$
$84$	−0.496359	−	0.360626i	−0.0541572	−	0.0393475i
$85$		0			0
$86$	4.46880	−	3.24678i	0.481883	−	0.350109i
$87$	−0.863357	−	0.627265i	−0.0925616	−	0.0672499i
$88$	12.6243	+	9.17208i	1.34575	+	0.977747i
$89$	5.17223	−	3.75785i	0.548256	−	0.398331i	−0.278886	−	0.960324i	$-0.589965\pi$
$89$	5.17223	−	3.75785i	0.548256	−	0.398331i	0.827142	+	0.561993i	$0.189965\pi$
$90$		0			0
$91$	−4.98214	−	3.61974i	−0.522271	−	0.379452i
$92$	−0.795588	−	2.44857i	−0.0829458	−	0.255281i
$93$	5.49716			0.570029
$94$	−1.56865	−	4.82780i	−0.161794	−	0.497950i
$95$		0			0
$96$	−0.967086	+	2.97639i	−0.0987028	+	0.303776i
$97$	−4.35197	+	13.3940i	−0.441876	+	1.35995i	0.443998	+	0.896028i	$0.353560\pi$
$97$	−4.35197	+	13.3940i	−0.441876	+	1.35995i	−0.885874	+	0.463926i	$0.846440\pi$
$98$	5.11196	−	3.71406i	0.516386	−	0.375176i
$99$	−12.9425			−1.30077
$100$		0			0
$101$	−10.5130			−1.04608			−0.523040	−	0.852308i	$-0.675202\pi$
$101$	−10.5130			−1.04608			−0.523040	+	0.852308i	$0.675202\pi$
$102$	1.87769	−	1.36422i	0.185919	−	0.135078i
$103$	−0.951061	+	2.92706i	−0.0937108	+	0.288412i	−0.986916	−	0.161238i	$-0.948451\pi$
$103$	−0.951061	+	2.92706i	−0.0937108	+	0.288412i	0.893205	+	0.449650i	$0.148451\pi$
$104$	−5.73033	+	17.6361i	−0.561905	+	1.72937i
$105$		0			0
$106$	3.28378	+	10.1064i	0.318949	+	0.981625i
$107$	−5.24731			−0.507277			−0.253638	−	0.967299i	$-0.581627\pi$
$107$	−5.24731			−0.507277			−0.253638	+	0.967299i	$0.581627\pi$
$108$	−1.03555	−	3.18708i	−0.0996454	−	0.306677i
$109$	5.27403	+	3.83181i	0.505160	+	0.367021i	0.810985	−	0.585067i	$-0.198932\pi$
$109$	5.27403	+	3.83181i	0.505160	+	0.367021i	−0.305824	+	0.952088i	$0.598932\pi$
$110$		0			0
$111$	4.67545	−	3.39692i	0.443774	−	0.322421i
$112$	1.19389	+	0.867409i	0.112812	+	0.0819624i
$113$	−0.311920	−	0.226623i	−0.0293430	−	0.0213189i	0.573017	−	0.819543i	$-0.305773\pi$
$113$	−0.311920	−	0.226623i	−0.0293430	−	0.0213189i	−0.602360	+	0.798224i	$0.705773\pi$
$114$	2.01618	−	1.46484i	0.188833	−	0.137195i
$115$		0			0
$116$	−1.10771	−	0.804799i	−0.102848	−	0.0747237i
$117$	−4.75280	−	14.6276i	−0.439397	−	1.35232i
$118$	3.06058			0.281749
$119$	0.998587	+	3.07334i	0.0915403	+	0.281732i
$120$		0			0
$121$	4.70384	−	14.4769i	0.427622	−	1.31608i
$122$	−0.754674	+	2.32265i	−0.0683250	+	0.210283i
$123$	−1.03636	+	0.752958i	−0.0934452	+	0.0678919i
$124$	7.05301			0.633379
$125$		0			0
$126$	−2.70455			−0.240940
$127$	3.75646	−	2.72923i	0.333332	−	0.242180i	−0.408511	−	0.912753i	$-0.633952\pi$
$127$	3.75646	−	2.72923i	0.333332	−	0.242180i	0.741843	+	0.670574i	$0.233952\pi$
$128$	−0.287853	+	0.885921i	−0.0254429	+	0.0783051i
$129$	1.10968	−	3.41525i	0.0977021	−	0.300696i
$130$		0			0
$131$	5.01265	+	15.4273i	0.437957	+	1.34789i	0.890026	+	0.455910i	$0.150686\pi$
$131$	5.01265	+	15.4273i	0.437957	+	1.34789i	−0.452069	+	0.891983i	$0.649314\pi$
$132$	3.10450			0.270212
$133$	1.07224	+	3.30001i	0.0929750	+	0.286148i
$134$	−3.97687	−	2.88937i	−0.343549	−	0.249603i
$135$		0			0
$136$	7.87227	−	5.71954i	0.675041	−	0.490446i
$137$	15.5171	+	11.2738i	1.32571	+	0.963186i	0.999842	+	0.0177718i	$0.00565724\pi$
$137$	15.5171	+	11.2738i	1.32571	+	0.963186i	0.325870	+	0.945415i	$0.394343\pi$
$138$	1.71655	+	1.24715i	0.146122	+	0.106164i
$139$	−2.90247	+	2.10877i	−0.246184	+	0.178863i	−0.704034	−	0.710166i	$-0.748620\pi$
$139$	−2.90247	+	2.10877i	−0.246184	+	0.178863i	0.457850	+	0.889030i	$0.348620\pi$
$140$		0			0
$141$	−2.66983	−	1.93974i	−0.224840	−	0.163356i
$142$	−2.52808	−	7.78062i	−0.212151	−	0.652935i
$143$	31.1611			2.60582
$144$	1.13893	+	3.50526i	0.0949107	+	0.292105i
$145$		0			0
$146$	−0.194591	+	0.598889i	−0.0161044	+	0.0495644i
$147$	1.26939	−	3.90678i	0.104698	−	0.322226i
$148$	5.99874	−	4.35834i	0.493093	−	0.358253i
$149$	1.60192			0.131234			0.0656170	−	0.997845i	$-0.479098\pi$
$149$	1.60192			0.131234			0.0656170	+	0.997845i	$0.479098\pi$
$150$		0			0
$151$	6.74218			0.548671			0.274336	−	0.961634i	$-0.411542\pi$
$151$	6.74218			0.548671			0.274336	+	0.961634i	$0.411542\pi$
$152$	8.45290	−	6.14139i	0.685621	−	0.498132i
$153$	−2.49399	+	7.67572i	−0.201627	+	0.620545i
$154$	1.69325	−	5.21130i	0.136446	−	0.419938i
$155$		0			0
$156$	1.14005	+	3.50870i	0.0912768	+	0.280921i
$157$	−14.2612			−1.13817			−0.569083	−	0.822280i	$-0.692702\pi$
$157$	−14.2612			−1.13817			−0.569083	+	0.822280i	$0.692702\pi$
$158$	3.61359	+	11.1215i	0.287482	+	0.884778i
$159$	5.58898	+	4.06063i	0.443235	+	0.322029i
$160$		0			0
$161$	−2.38998	+	1.73642i	−0.188357	+	0.136849i
$162$	−4.25199	−	3.08925i	−0.334068	−	0.242715i
$163$	8.18244	+	5.94489i	0.640899	+	0.465640i	0.860159	−	0.510026i	$-0.170364\pi$
$163$	8.18244	+	5.94489i	0.640899	+	0.465640i	−0.219260	+	0.975666i	$0.570364\pi$
$164$	−1.32968	+	0.966066i	−0.103830	+	0.0754371i
$165$		0			0
$166$	−12.2304	−	8.88589i	−0.949262	−	0.689679i
$167$	5.16556	+	15.8980i	0.399723	+	1.23022i	0.925222	+	0.379426i	$0.123879\pi$
$167$	5.16556	+	15.8980i	0.399723	+	1.23022i	−0.525499	+	0.850794i	$0.676121\pi$
$168$	2.11986			0.163551
$169$	7.42586	+	22.8545i	0.571220	+	1.75804i
$170$		0			0
$171$	−2.67794	+	8.24185i	−0.204787	+	0.630270i
$172$	1.42375	−	4.38186i	0.108560	−	0.334114i
$173$	−5.21223	+	3.78691i	−0.396279	+	0.287913i	−0.768024	−	0.640422i	$-0.778760\pi$
$173$	−5.21223	+	3.78691i	−0.396279	+	0.287913i	0.371745	+	0.928335i	$0.378760\pi$
$174$	1.12840			0.0855435
$175$		0			0
$176$	−7.46723			−0.562864
$177$	1.60969	−	1.16951i	0.120992	−	0.0879059i
$178$	−2.08897	+	6.42918i	−0.156575	+	0.481888i
$179$	−4.76944	+	14.6788i	−0.356485	+	1.09715i	0.598659	+	0.801004i	$0.295700\pi$
$179$	−4.76944	+	14.6788i	−0.356485	+	1.09715i	−0.955144	+	0.296143i	$0.904300\pi$
$180$		0			0
$181$	0.394905	+	1.21539i	0.0293531	+	0.0903395i	0.964660	−	0.263499i	$-0.0848764\pi$
$181$	0.394905	+	1.21539i	0.0293531	+	0.0903395i	−0.935307	+	0.353838i	$0.884876\pi$
$182$	6.51160			0.482672
$183$	0.490617	+	1.50996i	0.0362674	+	0.111620i
$184$	7.19668	+	5.22869i	0.530546	+	0.385464i
$185$		0			0
$186$	−4.70246	+	3.41654i	−0.344801	+	0.250513i
$187$	−13.2287	−	9.61118i	−0.967375	−	0.702839i
$188$	−3.42547	−	2.48875i	−0.249828	−	0.181511i
$189$	−3.11082	+	2.26014i	−0.226279	+	0.164401i
$190$		0			0
$191$	−4.72153	−	3.43039i	−0.341638	−	0.248214i	0.403715	−	0.914885i	$-0.367719\pi$
$191$	−4.72153	−	3.43039i	−0.341638	−	0.248214i	−0.745352	+	0.666671i	$0.767719\pi$
$192$	−1.64209	−	5.05382i	−0.118507	−	0.364728i
$193$	−4.17773			−0.300719			−0.150360	−	0.988631i	$-0.548043\pi$
$193$	−4.17773			−0.300719			−0.150360	+	0.988631i	$0.548043\pi$
$194$	−4.60167	−	14.1625i	−0.330380	−	1.01681i
$195$		0			0
$196$	1.62866	−	5.01251i	0.116333	−	0.358036i
$197$	−5.40330	+	16.6296i	−0.384969	+	1.18481i	0.551534	+	0.834153i	$0.314043\pi$
$197$	−5.40330	+	16.6296i	−0.384969	+	1.18481i	−0.936503	+	0.350660i	$0.885957\pi$
$198$	11.0715	−	8.04391i	0.786817	−	0.571656i
$199$	5.89046			0.417564			0.208782	−	0.977962i	$-0.433050\pi$
$199$	5.89046			0.417564			0.208782	+	0.977962i	$0.433050\pi$
$200$		0			0
$201$	−3.19571			−0.225408
$202$	8.99316	−	6.53392i	0.632757	−	0.459725i
$203$	−0.485491	+	1.49419i	−0.0340748	+	0.104871i
$204$	0.598229	−	1.84116i	0.0418844	−	0.128907i
$205$		0			0
$206$	−1.00563	−	3.09500i	−0.0700654	−	0.215639i
$207$	−7.37811			−0.512814
$208$	−2.74214	−	8.43944i	−0.190133	−	0.585170i
$209$	−14.2044	−	10.3201i	−0.982536	−	0.713854i
$210$		0			0
$211$	9.68981	−	7.04006i	0.667074	−	0.484658i	−0.201970	−	0.979392i	$-0.564734\pi$
$211$	9.68981	−	7.04006i	0.667074	−	0.484658i	0.869045	+	0.494734i	$0.164734\pi$
$212$	7.17082	+	5.20991i	0.492494	+	0.357818i
$213$	−4.30277	−	3.12615i	−0.294821	−	0.214200i
$214$	4.48873	−	3.26125i	0.306843	−	0.222935i
$215$		0			0
$216$	9.36727	+	6.80572i	0.637362	+	0.463071i
$217$	−2.50085	−	7.69682i	−0.169769	−	0.522494i
$218$	−6.89309			−0.466859
$219$	0.126504	+	0.389340i	0.00854836	+	0.0263092i
$220$		0			0
$221$	6.00466	−	18.4804i	0.403917	−	1.24313i
$222$	−1.88833	+	5.81168i	−0.126736	+	0.390054i
$223$	1.03324	−	0.750694i	0.0691910	−	0.0502702i	−0.552652	−	0.833412i	$-0.686384\pi$
$223$	1.03324	−	0.750694i	0.0691910	−	0.0502702i	0.621843	+	0.783142i	$0.286384\pi$
$224$	4.60733			0.307840
$225$		0			0
$226$	0.407676			0.0271182
$227$	−22.7642	+	16.5392i	−1.51092	+	1.09774i	−0.545147	+	0.838340i	$0.683526\pi$
$227$	−22.7642	+	16.5392i	−1.51092	+	1.09774i	−0.965769	+	0.259405i	$0.916474\pi$
$228$	0.642353	−	1.97696i	0.0425408	−	0.130927i
$229$	3.48637	−	10.7299i	0.230386	−	0.709055i	−0.767314	−	0.641271i	$-0.778407\pi$
$229$	3.48637	−	10.7299i	0.230386	−	0.709055i	0.997700	−	0.0677835i	$-0.0215927\pi$
$230$		0			0
$231$	−1.10079	−	3.38789i	−0.0724267	−	0.222907i
$232$	4.73083			0.310594
$233$	−4.16306	−	12.8126i	−0.272731	−	0.839380i	−0.989811	−	0.142389i	$-0.954522\pi$
$233$	−4.16306	−	12.8126i	−0.272731	−	0.839380i	0.717080	−	0.696991i	$-0.245478\pi$
$234$	13.1569	+	9.55906i	0.860095	+	0.624895i
$235$		0			0
$236$	2.06528	−	1.50052i	0.134439	−	0.0976753i
$237$	6.15031	+	4.46846i	0.399506	+	0.290258i
$238$	−2.76433	−	2.00841i	−0.179185	−	0.130186i
$239$	−1.53916	+	1.11827i	−0.0995600	+	0.0723346i	−0.636451	−	0.771317i	$-0.719598\pi$
$239$	−1.53916	+	1.11827i	−0.0995600	+	0.0723346i	0.536891	+	0.843651i	$0.319598\pi$
$240$		0			0
$241$	15.8312	+	11.5021i	1.01978	+	0.740913i	0.966238	−	0.257653i	$-0.0829491\pi$
$241$	15.8312	+	11.5021i	1.01978	+	0.740913i	0.0535415	+	0.998566i	$0.482949\pi$
$242$	4.97372	+	15.3075i	0.319723	+	0.984006i
$243$	−14.8156			−0.950422
$244$	0.629475	+	1.93732i	0.0402980	+	0.124025i
$245$		0			0
$246$	0.418565	−	1.28821i	0.0266868	−	0.0821334i
$247$	6.44754	−	19.8435i	0.410247	−	1.26261i
$248$	−19.7152	+	14.3239i	−1.25192	+	0.909570i
$249$	−9.82800			−0.622824
$250$		0			0
$251$	20.7096			1.30718			0.653590	−	0.756849i	$-0.273262\pi$
$251$	20.7096			1.30718			0.653590	+	0.756849i	$0.273262\pi$
$252$	−1.82503	+	1.32596i	−0.114966	+	0.0835279i
$253$	4.61926	−	14.2166i	0.290411	−	0.893792i
$254$	−1.51716	+	4.66935i	−0.0951953	+	0.292981i
$255$		0			0
$256$	−5.08202	−	15.6408i	−0.317626	−	0.977553i
$257$	15.0730			0.940225			0.470113	−	0.882606i	$-0.344213\pi$
$257$	15.0730			0.940225			0.470113	+	0.882606i	$0.344213\pi$
$258$	1.17335	+	3.61120i	0.0730496	+	0.224824i
$259$	−6.88320	−	5.00093i	−0.427701	−	0.310743i
$260$		0			0
$261$	−3.17443	+	2.30636i	−0.196492	+	0.142760i
$262$	−13.8762	−	10.0817i	−0.857276	−	0.622848i
$263$	−4.04773	−	2.94085i	−0.249594	−	0.181340i	0.455953	−	0.890004i	$-0.349298\pi$
$263$	−4.04773	−	2.94085i	−0.249594	−	0.181340i	−0.705547	+	0.708663i	$0.749298\pi$
$264$	−8.67798	+	6.30492i	−0.534093	+	0.388041i
$265$		0			0
$266$	−2.96822	−	2.15654i	−0.181993	−	0.132226i
$267$	1.35805	+	4.17964i	0.0831111	+	0.255790i
$268$	−4.10018			−0.250458
$269$	−8.55371	−	26.3256i	−0.521529	−	1.60510i	−0.771079	−	0.636740i	$-0.780283\pi$
$269$	−8.55371	−	26.3256i	−0.521529	−	1.60510i	0.249550	−	0.968362i	$-0.419717\pi$
$270$		0			0
$271$	−8.15582	+	25.1010i	−0.495431	+	1.52478i	0.320854	+	0.947129i	$0.396030\pi$
$271$	−8.15582	+	25.1010i	−0.495431	+	1.52478i	−0.816285	+	0.577650i	$0.803970\pi$
$272$	−1.43891	+	4.42852i	−0.0872470	+	0.268519i
$273$	3.42474	−	2.48822i	0.207275	−	0.150594i
$274$	−20.2806			−1.22520
$275$		0			0
$276$	1.76977			0.106528
$277$	5.76244	−	4.18666i	0.346231	−	0.251552i	−0.401055	−	0.916054i	$-0.631356\pi$
$277$	5.76244	−	4.18666i	0.346231	−	0.251552i	0.747286	+	0.664502i	$0.231356\pi$
$278$	1.17225	−	3.60782i	0.0703070	−	0.216383i
$279$	6.24591	−	19.2229i	0.373933	−	1.15085i
$280$		0			0
$281$	−3.19112	−	9.82125i	−0.190366	−	0.585886i	0.809633	−	0.586936i	$-0.199666\pi$
$281$	−3.19112	−	9.82125i	−0.190366	−	0.585886i	−0.999999	+	0.00104949i	$0.999666\pi$
$282$	3.48943			0.207793
$283$	1.40908	+	4.33670i	0.0837610	+	0.257790i	0.984162	−	0.177271i	$-0.0567269\pi$
$283$	1.40908	+	4.33670i	0.0837610	+	0.257790i	−0.900401	+	0.435061i	$0.856727\pi$
$284$	−5.52058	−	4.01093i	−0.327586	−	0.238005i
$285$		0			0
$286$	−26.6563	+	19.3669i	−1.57622	+	1.14519i
$287$	1.52572	+	1.10850i	0.0900607	+	0.0654329i
$288$	9.30927	+	6.76358i	0.548554	+	0.398548i
$289$	5.50415	−	3.99900i	0.323774	−	0.235235i
$290$		0			0
$291$	−7.83201	−	5.69029i	−0.459120	−	0.333571i
$292$	0.162309	+	0.499534i	0.00949839	+	0.0292330i
$293$	−20.8237			−1.21653			−0.608267	−	0.793733i	$-0.708135\pi$
$293$	−20.8237			−1.21653			−0.608267	+	0.793733i	$0.708135\pi$
$294$	1.34222	+	4.13093i	0.0782799	+	0.240921i
$295$		0			0
$296$	−7.91687	+	24.3656i	−0.460159	+	1.41622i
$297$	6.01248	−	18.5045i	0.348879	−	1.07374i
$298$	−1.37033	+	0.995606i	−0.0793813	+	0.0576739i
$299$	17.7639			1.02731
$300$		0			0
$301$	−5.28668			−0.304719
$302$	−5.76749	+	4.19033i	−0.331882	+	0.241126i
$303$	2.23316	−	6.87296i	0.128292	−	0.394841i
$304$	−1.54504	+	4.75515i	−0.0886143	+	0.272727i
$305$		0			0
$306$	−2.63708	−	8.11611i	−0.150752	−	0.463967i
$307$	9.44200			0.538884			0.269442	−	0.963017i	$-0.413161\pi$
$307$	9.44200			0.538884			0.269442	+	0.963017i	$0.413161\pi$
$308$	−1.41235	−	4.34675i	−0.0804759	−	0.247679i
$309$	−1.71157	−	1.24353i	−0.0973679	−	0.0707419i
$310$		0			0
$311$	−10.8250	+	7.86479i	−0.613827	+	0.445971i	−0.850760	−	0.525555i	$-0.823858\pi$
$311$	−10.8250	+	7.86479i	−0.613827	+	0.445971i	0.236933	+	0.971526i	$0.423858\pi$
$312$	−10.3126	−	7.49251i	−0.583834	−	0.424180i
$313$	−19.4121	−	14.1037i	−1.09724	−	0.797191i	−0.116632	−	0.993175i	$-0.537210\pi$
$313$	−19.4121	−	14.1037i	−1.09724	−	0.797191i	−0.980607	+	0.195984i	$0.937210\pi$
$314$	12.1995	−	8.86345i	0.688457	−	0.500194i
$315$		0			0
$316$	7.89103	+	5.73317i	0.443905	+	0.322516i
$317$	4.49979	+	13.8489i	0.252733	+	0.777833i	0.994268	+	0.106918i	$0.0340984\pi$
$317$	4.49979	+	13.8489i	0.252733	+	0.777833i	−0.741534	+	0.670915i	$0.765902\pi$
$318$	−7.30473			−0.409629
$319$	−2.45661	−	7.56066i	−0.137544	−	0.423316i
$320$		0			0
$321$	1.11463	−	3.43048i	0.0622126	−	0.191471i
$322$	0.965267	−	2.97079i	0.0537922	−	0.165555i
$323$	−8.85757	+	6.43540i	−0.492848	+	0.358075i
$324$	−4.38383			−0.243546
$325$		0			0
$326$	−10.6944			−0.592305
$327$	−3.62539	+	2.63400i	−0.200484	+	0.145660i
$328$	1.75485	−	5.40086i	0.0968952	−	0.298213i
$329$	−1.50132	+	4.62060i	−0.0827707	+	0.254742i
$330$		0			0
$331$	−7.54769	−	23.2294i	−0.414859	−	1.27680i	−0.912377	−	0.409350i	$-0.865755\pi$
$331$	−7.54769	−	23.2294i	−0.414859	−	1.27680i	0.497519	−	0.867453i	$-0.334245\pi$
$332$	−12.6096			−0.692042
$333$	−6.56635	−	20.2091i	−0.359834	−	1.10745i
$334$	−14.2995	−	10.3892i	−0.782435	−	0.568472i
$335$		0			0
$336$	−0.820681	+	0.596260i	−0.0447718	+	0.0325286i
$337$	6.93506	+	5.03862i	0.377777	+	0.274471i	0.760428	−	0.649422i	$-0.224989\pi$
$337$	6.93506	+	5.03862i	0.377777	+	0.274471i	−0.382651	+	0.923893i	$0.624989\pi$
$338$	−20.5566	−	14.9352i	−1.11813	−	0.812370i
$339$	0.214415	−	0.155782i	0.0116454	−	0.00846090i
$340$		0			0
$341$	33.1296	+	24.0701i	1.79407	+	1.30347i
$342$	−2.83159	−	8.71473i	−0.153115	−	0.471238i
$343$	−13.1315			−0.709035
$344$	4.91930	+	15.1401i	0.265231	+	0.816297i
$345$		0			0
$346$	2.10512	−	6.47890i	0.113172	−	0.348308i
$347$	3.33973	−	10.2786i	0.179286	−	0.551785i	−0.820517	−	0.571622i	$-0.806314\pi$
$347$	3.33973	−	10.2786i	0.179286	−	0.551785i	0.999803	+	0.0198363i	$0.00631450\pi$
$348$	0.761445	−	0.553222i	0.0408177	−	0.0296558i
$349$	−8.13956			−0.435701			−0.217850	−	0.975982i	$-0.569904\pi$
$349$	−8.13956			−0.435701			−0.217850	+	0.975982i	$0.569904\pi$
$350$		0			0
$351$	23.1217			1.23414
$352$	−18.8608	+	13.7032i	−1.00529	+	0.730384i
$353$	6.54069	−	20.1302i	0.348126	−	1.07142i	−0.611764	−	0.791041i	$-0.709540\pi$
$353$	6.54069	−	20.1302i	0.348126	−	1.07142i	0.959889	−	0.280380i	$-0.0904604\pi$
$354$	−0.650126	+	2.00088i	−0.0345538	+	0.106346i
$355$		0			0
$356$	1.74241	+	5.36259i	0.0923476	+	0.284217i
$357$	−2.22134			−0.117566
$358$	−5.04309	−	15.5210i	−0.266535	−	0.820312i
$359$	4.30870	+	3.13045i	0.227405	+	0.165219i	0.695653	−	0.718378i	$-0.255115\pi$
$359$	4.30870	+	3.13045i	0.227405	+	0.165219i	−0.468249	+	0.883597i	$0.655115\pi$
$360$		0			0
$361$	5.86045	−	4.25787i	0.308445	−	0.224098i
$362$	−1.09319	−	0.794252i	−0.0574570	−	0.0417449i
$363$	8.46525	+	6.15036i	0.444310	+	0.322810i
$364$	4.39404	−	3.19246i	0.230310	−	0.167330i
$365$		0			0
$366$	−1.35815	−	0.986751i	−0.0709914	−	0.0515783i
$367$	−5.26169	−	16.1938i	−0.274658	−	0.845310i	−0.989310	−	0.145830i	$-0.953415\pi$
$367$	−5.26169	−	16.1938i	−0.274658	−	0.845310i	0.714652	−	0.699480i	$-0.246585\pi$
$368$	−4.25682			−0.221902
$369$	1.45549	+	4.47954i	0.0757699	+	0.233196i
$370$		0			0
$371$	3.14285	−	9.67270i	0.163169	−	0.502182i
$372$	−1.49820	+	4.61097i	−0.0776779	+	0.239068i
$373$	5.54283	−	4.02710i	0.286997	−	0.208515i	−0.434967	−	0.900447i	$-0.643240\pi$
$373$	5.54283	−	4.02710i	0.286997	−	0.208515i	0.721963	+	0.691931i	$0.243240\pi$
$374$	17.2897			0.894028
$375$		0			0
$376$	14.6295			0.754461
$377$	7.64291	−	5.55290i	0.393630	−	0.285989i
$378$	1.25640	−	3.86680i	0.0646223	−	0.198887i
$379$	−2.28307	+	7.02655i	−0.117273	+	0.360930i	−0.992414	−	0.122938i	$-0.960768\pi$
$379$	−2.28307	+	7.02655i	−0.117273	+	0.360930i	0.875141	+	0.483868i	$0.160768\pi$
$380$		0			0
$381$	0.986314	+	3.03556i	0.0505304	+	0.155517i
$382$	6.17097			0.315734
$383$	6.24312	+	19.2143i	0.319008	+	0.981807i	0.974073	+	0.226234i	$0.0726415\pi$
$383$	6.24312	+	19.2143i	0.319008	+	0.981807i	−0.655064	+	0.755573i	$0.727359\pi$
$384$	−0.518034	−	0.376374i	−0.0264358	−	0.0192067i
$385$		0			0
$386$	3.57377	−	2.59650i	0.181900	−	0.132158i
$387$	−10.6819	−	7.76087i	−0.542992	−	0.394507i
$388$	−10.0487	−	7.30080i	−0.510145	−	0.370642i
$389$	−7.11958	+	5.17268i	−0.360977	+	0.262265i	−0.753460	−	0.657494i	$-0.771616\pi$
$389$	−7.11958	+	5.17268i	−0.360977	+	0.262265i	0.392482	+	0.919760i	$0.371616\pi$
$390$		0			0
$391$	−7.54121	−	5.47901i	−0.381375	−	0.277085i
$392$	5.62730	+	17.3190i	0.284222	+	0.874744i
$393$	−11.1506			−0.562471
$394$	−5.71331	−	17.5838i	−0.287833	−	0.885857i
$395$		0			0
$396$	3.52736	−	10.8561i	0.177257	−	0.545540i
$397$	1.88286	−	5.79484i	0.0944979	−	0.290835i	−0.892625	−	0.450801i	$-0.851138\pi$
$397$	1.88286	−	5.79484i	0.0944979	−	0.290835i	0.987123	+	0.159966i	$0.0511385\pi$
$398$	−5.03890	+	3.66098i	−0.252577	+	0.183508i
$399$	−2.38518			−0.119408
$400$		0			0
$401$	−1.71924			−0.0858547			−0.0429274	−	0.999078i	$-0.513668\pi$
$401$	−1.71924			−0.0858547			−0.0429274	+	0.999078i	$0.513668\pi$
$402$	2.73372	−	1.98616i	0.136345	−	0.0990607i
$403$	−15.0380	+	46.2821i	−0.749095	+	2.30548i
$404$	2.86521	−	8.81821i	0.142549	−	0.438722i
$405$		0			0
$406$	−0.513346	−	1.57992i	−0.0254770	−	0.0784100i
$407$	43.0514			2.13398
$408$	2.06698	+	6.36151i	0.102331	+	0.314942i
$409$	22.4433	+	16.3060i	1.10975	+	0.806280i	0.982624	−	0.185607i	$-0.0594250\pi$
$409$	22.4433	+	16.3060i	1.10975	+	0.806280i	0.127125	+	0.991887i	$0.459425\pi$
$410$		0			0
$411$	−10.6665	+	7.74965i	−0.526139	+	0.382262i
$412$	−2.19600	−	1.59548i	−0.108189	−	0.0786039i
$413$	−2.36979	−	1.72175i	−0.116610	−	0.0847220i
$414$	6.31149	−	4.58556i	0.310193	−	0.225368i
$415$		0			0
$416$	−22.4135	−	16.2843i	−1.09891	−	0.798406i
$417$	−0.762086	−	2.34546i	−0.0373195	−	0.114858i
$418$	18.5649			0.908039
$419$	5.05366	+	15.5536i	0.246887	+	0.759841i	0.995320	+	0.0966306i	$0.0308065\pi$
$419$	5.05366	+	15.5536i	0.246887	+	0.759841i	−0.748433	+	0.663210i	$0.769193\pi$
$420$		0			0
$421$	−3.07336	+	9.45883i	−0.149786	+	0.460995i	−0.997595	−	0.0693064i	$-0.977921\pi$
$421$	−3.07336	+	9.45883i	−0.149786	+	0.460995i	0.847809	+	0.530302i	$0.177921\pi$
$422$	−3.91353	+	12.0446i	−0.190508	+	0.586323i
$423$	−9.81655	+	7.13214i	−0.477297	+	0.346777i
$424$	−30.6253			−1.48729
$425$		0			0
$426$	5.62367			0.272467
$427$	1.89097	−	1.37387i	0.0915103	−	0.0664861i
$428$	1.43010	−	4.40141i	0.0691267	−	0.212750i
$429$	−6.61922	+	20.3719i	−0.319579	+	0.983563i
$430$		0			0
$431$	−6.34417	−	19.5254i	−0.305588	−	0.940503i	−0.979457	−	0.201652i	$-0.935369\pi$
$431$	−6.34417	−	19.5254i	−0.305588	−	0.940503i	0.673869	−	0.738851i	$-0.264631\pi$
$432$	−5.54071			−0.266578
$433$	−8.01802	−	24.6769i	−0.385321	−	1.18590i	−0.936247	−	0.351343i	$-0.885725\pi$
$433$	−8.01802	−	24.6769i	−0.385321	−	1.18590i	0.550925	−	0.834555i	$-0.314275\pi$
$434$	6.92295	+	5.02982i	0.332312	+	0.241439i
$435$		0			0
$436$	−4.65147	+	3.37949i	−0.222765	+	0.161848i
$437$	−8.09742	−	5.88312i	−0.387352	−	0.281428i
$438$	−0.350194	−	0.254431i	−0.0167329	−	0.0121572i
$439$	−20.3293	+	14.7701i	−0.970263	+	0.704938i	−0.955512	−	0.294954i	$-0.904696\pi$
$439$	−20.3293	+	14.7701i	−0.970263	+	0.704938i	−0.0147517	+	0.999891i	$0.504696\pi$
$440$		0			0
$441$	−12.2193	−	8.87783i	−0.581871	−	0.422754i
$442$	6.34917	+	19.5407i	0.301999	+	0.929459i
$443$	27.0262			1.28405			0.642027	−	0.766682i	$-0.278094\pi$
$443$	27.0262			1.28405			0.642027	+	0.766682i	$0.278094\pi$
$444$	1.57506	+	4.84753i	0.0747489	+	0.230054i
$445$		0			0
$446$	−0.417307	+	1.28434i	−0.0197601	+	0.0608152i
$447$	−0.340278	+	1.04727i	−0.0160946	+	0.0495341i
$448$	−6.32904	+	4.59832i	−0.299019	+	0.217250i
$449$	37.9871			1.79272			0.896361	−	0.443325i	$-0.146201\pi$
$449$	37.9871			1.79272			0.896361	+	0.443325i	$0.146201\pi$
$450$		0			0
$451$	−9.54273			−0.449350
$452$	0.275101	−	0.199872i	0.0129396	−	0.00940120i
$453$	−1.43217	+	4.40777i	−0.0672892	+	0.207095i
$454$	9.19405	−	28.2964i	0.431498	−	1.32802i
$455$		0			0
$456$	2.21943	+	6.83071i	0.103934	+	0.319877i
$457$	−29.9832			−1.40256			−0.701278	−	0.712888i	$-0.747387\pi$
$457$	−29.9832			−1.40256			−0.701278	+	0.712888i	$0.747387\pi$
$458$	3.68640	+	11.3456i	0.172254	+	0.530144i
$459$	−9.81571	−	7.13153i	−0.458158	−	0.332871i
$460$		0			0
$461$	1.72615	−	1.25412i	0.0803948	−	0.0584102i	−0.546862	−	0.837223i	$-0.684178\pi$
$461$	1.72615	−	1.25412i	0.0803948	−	0.0584102i	0.627257	+	0.778813i	$0.284178\pi$
$462$	3.04726	+	2.21396i	0.141771	+	0.103003i
$463$	17.7825	+	12.9197i	0.826422	+	0.600431i	0.918545	−	0.395317i	$-0.129365\pi$
$463$	17.7825	+	12.9197i	0.826422	+	0.600431i	−0.0921226	+	0.995748i	$0.529365\pi$
$464$	−1.83149	+	1.33066i	−0.0850250	+	0.0617743i
$465$		0			0
$466$	11.5244	+	8.37294i	0.533856	+	0.387869i
$467$	1.64117	+	5.05100i	0.0759442	+	0.233732i	0.981821	−	0.189809i	$-0.0607869\pi$
$467$	1.64117	+	5.05100i	0.0759442	+	0.233732i	−0.905877	+	0.423541i	$0.860787\pi$
$468$	13.5649			0.627036
$469$	1.45384	+	4.47445i	0.0671319	+	0.206611i
$470$		0			0
$471$	3.02935	−	9.32338i	0.139585	−	0.429599i
$472$	−2.72567	+	8.38875i	−0.125459	+	0.386123i
$473$	21.6419	−	15.7237i	0.995094	−	0.722978i
$474$	−8.03838			−0.369215
$475$		0			0
$476$	−2.85005			−0.130632
$477$	20.5498	−	14.9303i	0.940912	−	0.683612i
$478$	0.621638	−	1.91321i	0.0284331	−	0.0875080i
$479$	−6.51646	+	20.0556i	−0.297745	+	0.916364i	0.684541	+	0.728975i	$0.260003\pi$
$479$	−6.51646	+	20.0556i	−0.297745	+	0.916364i	−0.982286	+	0.187390i	$0.939997\pi$
$480$		0			0
$481$	15.8095	+	48.6565i	0.720849	+	2.21855i
$482$	−20.6912			−0.942459
$483$	−0.627524	−	1.93132i	−0.0285533	−	0.0878781i
$484$	10.8612	+	7.89109i	0.493689	+	0.358686i
$485$		0			0
$486$	12.6738	−	9.20804i	0.574894	−	0.417685i
$487$	21.5296	+	15.6422i	0.975600	+	0.708815i	0.956721	−	0.291007i	$-0.0939904\pi$
$487$	21.5296	+	15.6422i	0.975600	+	0.708815i	0.0188787	+	0.999822i	$0.493990\pi$
$488$	−5.69406	−	4.13698i	−0.257758	−	0.187272i
$489$	−5.62464	+	4.08654i	−0.254355	+	0.184800i
$490$		0			0
$491$	−1.45678	−	1.05842i	−0.0657438	−	0.0477657i	0.554428	−	0.832232i	$-0.312937\pi$
$491$	−1.45678	−	1.05842i	−0.0657438	−	0.0477657i	−0.620172	+	0.784466i	$0.712937\pi$
$492$	−0.349126	−	1.07450i	−0.0157398	−	0.0484422i
$493$	−4.95731			−0.223266
$494$	6.81747	+	20.9820i	0.306732	+	0.944025i
$495$		0			0
$496$	3.60359	−	11.0907i	0.161806	−	0.497988i
$497$	−2.41958	+	7.44669i	−0.108533	+	0.334030i
$498$	8.40721	−	6.10819i	0.376736	−	0.273715i
$499$	28.6962			1.28462			0.642309	−	0.766446i	$-0.277977\pi$
$499$	28.6962			1.28462			0.642309	+	0.766446i	$0.277977\pi$
$500$		0			0
$501$	−11.4907			−0.513367
$502$	−17.7157	+	12.8712i	−0.790692	+	0.574471i
$503$	−7.31837	+	22.5236i	−0.326310	+	1.00428i	0.644536	+	0.764574i	$0.277051\pi$
$503$	−7.31837	+	22.5236i	−0.326310	+	1.00428i	−0.970846	+	0.239704i	$0.922949\pi$
$504$	2.40860	−	7.41290i	0.107287	−	0.330197i
$505$		0			0
$506$	4.88429	+	15.0323i	0.217133	+	0.668268i
$507$	−16.5187			−0.733622
$508$	1.26547	+	3.89471i	0.0561461	+	0.172800i
$509$	−14.3161	−	10.4012i	−0.634550	−	0.461027i	0.223424	−	0.974721i	$-0.428277\pi$
$509$	−14.3161	−	10.4012i	−0.634550	−	0.461027i	−0.857973	+	0.513694i	$0.828277\pi$
$510$		0			0
$511$	0.487581	−	0.354248i	0.0215693	−	0.0156710i
$512$	12.5610	+	9.12613i	0.555125	+	0.403322i
$513$	−10.5397	−	7.65753i	−0.465338	−	0.338088i
$514$	−12.8939	+	9.36798i	−0.568727	+	0.413204i
$515$		0			0
$516$	2.56225	+	1.86159i	0.112797	+	0.0819517i
$517$	−7.59677	−	23.3805i	−0.334106	−	1.02827i
$518$	8.99625			0.395273
$519$	−1.36855	−	4.21196i	−0.0600726	−	0.184884i
$520$		0			0
$521$	7.09984	−	21.8511i	0.311050	−	0.957312i	−0.666301	−	0.745683i	$-0.732123\pi$
$521$	7.09984	−	21.8511i	0.311050	−	0.957312i	0.977350	−	0.211629i	$-0.0678768\pi$
$522$	1.28209	−	3.94587i	0.0561157	−	0.172706i
$523$	23.4431	−	17.0324i	1.02510	−	0.744775i	0.0577743	−	0.998330i	$-0.481600\pi$
$523$	23.4431	−	17.0324i	1.02510	−	0.744775i	0.967321	+	0.253554i	$0.0815996\pi$
$524$	−14.3065			−0.624982
$525$		0			0
$526$	5.29033			0.230669
$527$	20.6590	−	15.0097i	0.899921	−	0.653831i
$528$	1.58618	−	4.88177i	0.0690298	−	0.212452i
$529$	−4.47410	+	13.7699i	−0.194526	+	0.598690i
$530$		0			0
$531$	−2.26070	−	6.95773i	−0.0981062	−	0.301940i
$532$	−3.06025			−0.132679
$533$	−3.50431	−	10.7852i	−0.151789	−	0.467158i
$534$	−3.75940	−	2.73137i	−0.162685	−	0.118198i
$535$		0			0
$536$	11.4612	−	8.32703i	0.495048	−	0.359673i
$537$	−8.58330	−	6.23613i	−0.370397	−	0.269109i
$538$	23.6788	+	17.2036i	1.02086	+	0.741701i
$539$	24.7566	−	17.9867i	1.06634	−	0.774743i
$540$		0			0
$541$	−19.7809	−	14.3717i	−0.850447	−	0.617886i	0.0748225	−	0.997197i	$-0.476161\pi$
$541$	−19.7809	−	14.3717i	−0.850447	−	0.617886i	−0.925269	+	0.379311i	$0.876161\pi$
$542$	−8.62376	−	26.5412i	−0.370422	−	1.14004i
$543$	−0.878460			−0.0376983
$544$	4.49241	+	13.8262i	0.192610	+	0.592794i
$545$		0			0
$546$	−1.38319	+	4.25702i	−0.0591951	+	0.182184i
$547$	−2.00964	+	6.18504i	−0.0859261	+	0.264453i	−0.984783	−	0.173789i	$-0.944399\pi$
$547$	−2.00964	+	6.18504i	−0.0859261	+	0.264453i	0.898857	+	0.438242i	$0.144399\pi$
$548$	−13.6854	+	9.94303i	−0.584611	+	0.424745i
$549$	5.83761			0.249143
$550$		0			0
$551$	−5.32295			−0.226765
$552$	−4.94702	+	3.59422i	−0.210559	+	0.152980i
$553$	3.45850	−	10.6442i	0.147071	−	0.452637i
$554$	−2.32734	+	7.16282i	−0.0988793	+	0.304319i
$555$		0			0
$556$	−0.977778	−	3.00929i	−0.0414670	−	0.127622i
$557$	3.12305			0.132328			0.0661640	−	0.997809i	$-0.478924\pi$
$557$	3.12305			0.132328			0.0661640	+	0.997809i	$0.478924\pi$
$558$	6.60427	+	20.3259i	0.279581	+	0.860462i
$559$	25.7183	+	18.6855i	1.08777	+	0.790310i
$560$		0			0
$561$	9.09342	−	6.60676i	0.383925	−	0.278938i
$562$	8.83379	+	6.41812i	0.372631	+	0.270732i
$563$	29.5495	+	21.4690i	1.24536	+	0.904810i	0.997944	−	0.0640981i	$-0.0204171\pi$
$563$	29.5495	+	21.4690i	1.24536	+	0.904810i	0.247421	+	0.968908i	$0.420417\pi$
$564$	2.35468	−	1.71077i	0.0991498	−	0.0720366i
$565$		0			0
$566$	−3.90067	−	2.83400i	−0.163957	−	0.119122i
$567$	1.55441	+	4.78399i	0.0652792	+	0.200909i
$568$	23.5774			0.989285
$569$	−11.6708	−	35.9191i	−0.489267	−	1.50581i	−0.825705	−	0.564102i	$-0.809222\pi$
$569$	−11.6708	−	35.9191i	−0.489267	−	1.50581i	0.336439	−	0.941705i	$-0.390778\pi$
$570$		0			0
$571$	−12.7429	+	39.2187i	−0.533275	+	1.64125i	0.214072	+	0.976818i	$0.431327\pi$
$571$	−12.7429	+	39.2187i	−0.533275	+	1.64125i	−0.747347	+	0.664434i	$0.768673\pi$
$572$	−8.49265	+	26.1377i	−0.355096	+	1.09287i
$573$	3.24559	−	2.35806i	0.135587	−	0.0985094i
$574$	−1.99410			−0.0832322
$575$		0			0
$576$	−19.5384			−0.814100
$577$	3.45392	−	2.50942i	0.143789	−	0.104469i	−0.513565	−	0.858050i	$-0.671676\pi$
$577$	3.45392	−	2.50942i	0.143789	−	0.104469i	0.657354	+	0.753582i	$0.271676\pi$
$578$	−2.22302	+	6.84176i	−0.0924656	+	0.284580i
$579$	0.887430	−	2.73123i	0.0368803	−	0.113506i
$580$		0			0
$581$	4.47109	+	13.7606i	0.185492	+	0.570886i
$582$	10.2363			0.424310
$583$	15.9030	+	48.9443i	0.658634	+	2.02707i
$584$	−1.46820	−	1.06671i	−0.0607546	−	0.0441408i
$585$		0			0
$586$	17.8133	−	12.9421i	0.735861	−	0.534634i
$587$	−9.24955	−	6.72019i	−0.381770	−	0.277372i	0.380305	−	0.924861i	$-0.375819\pi$
$587$	−9.24955	−	6.72019i	−0.381770	−	0.277372i	−0.762075	+	0.647489i	$0.775819\pi$
$588$	2.93102	+	2.12951i	0.120873	+	0.0878195i
$589$	22.1828	−	16.1167i	0.914024	−	0.664078i
$590$		0			0
$591$	−9.72402	−	7.06492i	−0.399993	−	0.290612i
$592$	−3.78847	−	11.6597i	−0.155705	−	0.479211i
$593$	30.9375			1.27045			0.635225	−	0.772327i	$-0.280908\pi$
$593$	30.9375			1.27045			0.635225	+	0.772327i	$0.280908\pi$
$594$	6.35744	+	19.5662i	0.260849	+	0.802811i
$595$		0			0
$596$	−0.436586	+	1.34367i	−0.0178833	+	0.0550390i
$597$	−1.25125	+	3.85094i	−0.0512102	+	0.157609i
$598$	−15.1958	+	11.0404i	−0.621404	+	0.451477i
$599$	−46.1912			−1.88732			−0.943660	−	0.330916i	$-0.892642\pi$
$599$	−46.1912			−1.88732			−0.943660	+	0.330916i	$0.892642\pi$
$600$		0			0
$601$	−38.0963			−1.55398			−0.776990	−	0.629513i	$-0.783254\pi$
$601$	−38.0963			−1.55398			−0.776990	+	0.629513i	$0.783254\pi$
$602$	4.52240	−	3.28572i	0.184319	−	0.133916i
$603$	−3.63098	+	11.1750i	−0.147865	+	0.455082i
$604$	−1.83752	+	5.65529i	−0.0747674	+	0.230111i
$605$		0			0
$606$	2.36129	+	7.26730i	0.0959208	+	0.295214i
$607$	38.6361			1.56819			0.784095	−	0.620641i	$-0.213127\pi$
$607$	38.6361			1.56819			0.784095	+	0.620641i	$0.213127\pi$
$608$	4.82375	+	14.8460i	0.195629	+	0.602084i
$609$	−0.873712	−	0.634789i	−0.0354046	−	0.0257230i
$610$		0			0
$611$	23.6348	−	17.1717i	0.956162	−	0.694692i
$612$	−5.75862	−	4.18388i	−0.232778	−	0.169123i
$613$	8.70185	+	6.32226i	0.351464	+	0.255354i	0.749483	−	0.662023i	$-0.230302\pi$
$613$	8.70185	+	6.32226i	0.351464	+	0.255354i	−0.398019	+	0.917377i	$0.630302\pi$
$614$	−8.07701	+	5.86829i	−0.325962	+	0.236825i
$615$		0			0
$616$	12.7757	+	9.28210i	0.514748	+	0.373986i
$617$	−3.33961	−	10.2783i	−0.134448	−	0.413788i	0.861056	−	0.508510i	$-0.169804\pi$
$617$	−3.33961	−	10.2783i	−0.134448	−	0.413788i	−0.995504	+	0.0947225i	$0.969804\pi$
$618$	2.23700			0.0899855
$619$	−11.4008	−	35.0881i	−0.458237	−	1.41031i	−0.867292	−	0.497799i	$-0.834142\pi$
$619$	−11.4008	−	35.0881i	−0.458237	−	1.41031i	0.409055	−	0.912510i	$-0.365858\pi$
$620$		0			0
$621$	3.42751	−	10.5488i	0.137541	−	0.423309i
$622$	4.37200	−	13.4556i	0.175301	−	0.539521i
$623$	5.23427	−	3.80292i	0.209707	−	0.152361i
$624$	6.09985			0.244189
$625$		0			0
$626$	25.3714			1.01405
$627$	9.76412	−	7.09405i	0.389941	−	0.283309i
$628$	3.88674	−	11.9622i	0.155098	−	0.477342i
$629$	8.29587	−	25.5321i	0.330778	−	1.01803i
$630$		0			0
$631$	12.1318	+	37.3378i	0.482959	+	1.48640i	0.834915	+	0.550379i	$0.185517\pi$
$631$	12.1318	+	37.3378i	0.482959	+	1.48640i	−0.351955	+	0.936017i	$0.614483\pi$
$632$	−33.7011			−1.34056
$633$	2.54420	+	7.83025i	0.101123	+	0.311225i
$634$	−12.4565	−	9.05018i	−0.494711	−	0.359429i
$635$		0			0
$636$	−4.92925	+	3.58131i	−0.195457	+	0.142008i
$637$	29.4197	+	21.3747i	1.16565	+	0.846896i
$638$	6.80049	+	4.94084i	0.269234	+	0.195610i
$639$	−15.8206	+	11.4944i	−0.625854	+	0.454710i
$640$		0			0
$641$	−6.75394	−	4.90703i	−0.266765	−	0.193816i	0.446359	−	0.894854i	$-0.352720\pi$
$641$	−6.75394	−	4.90703i	−0.266765	−	0.193816i	−0.713124	+	0.701038i	$0.752720\pi$
$642$	1.17858	+	3.62731i	0.0465150	+	0.143158i
$643$	−13.1408			−0.518223			−0.259112	−	0.965847i	$-0.583430\pi$
$643$	−13.1408			−0.518223			−0.259112	+	0.965847i	$0.583430\pi$
$644$	−0.805131	−	2.47794i	−0.0317266	−	0.0976444i
$645$		0			0
$646$	3.57740	−	11.0101i	0.140751	−	0.433187i
$647$	8.05918	−	24.8036i	0.316839	−	0.975130i	−0.658152	−	0.752885i	$-0.728661\pi$
$647$	8.05918	−	24.8036i	0.316839	−	0.975130i	0.974991	−	0.222245i	$-0.0713385\pi$
$648$	12.2541	−	8.90310i	0.481385	−	0.349747i
$649$	14.8220			0.581814
$650$		0			0
$651$	5.56310			0.218035
$652$	−7.21657	+	5.24315i	−0.282623	+	0.205338i
$653$	7.11650	−	21.9023i	0.278490	−	0.857104i	−0.709785	−	0.704419i	$-0.751208\pi$
$653$	7.11650	−	21.9023i	0.278490	−	0.857104i	0.988275	−	0.152686i	$-0.0487922\pi$
$654$	1.46423	−	4.50642i	0.0572558	−	0.176215i
$655$		0			0
$656$	0.839749	+	2.58448i	0.0327867	+	0.100907i
$657$	1.50521			0.0587240
$658$	−1.58746	−	4.88571i	−0.0618858	−	0.190465i
$659$	−28.1198	−	20.4303i	−1.09539	−	0.795850i	−0.115092	−	0.993355i	$-0.536716\pi$
$659$	−28.1198	−	20.4303i	−1.09539	−	0.795850i	−0.980302	+	0.197505i	$0.936716\pi$
$660$		0			0
$661$	−14.5650	+	10.5821i	−0.566513	+	0.411596i	−0.833837	−	0.552011i	$-0.813861\pi$
$661$	−14.5650	+	10.5821i	−0.566513	+	0.411596i	0.267324	+	0.963607i	$0.413861\pi$
$662$	20.8938	+	15.1803i	0.812062	+	0.589998i
$663$	10.8063	+	7.85120i	0.419680	+	0.304916i
$664$	35.2474	−	25.6088i	1.36787	−	0.993813i
$665$		0			0
$666$	18.1772	+	13.2065i	0.704354	+	0.511743i
$667$	−1.40043	−	4.31008i	−0.0542248	−	0.166887i
$668$	−14.7429			−0.570420
$669$	0.271293	+	0.834954i	0.0104888	+	0.0322812i
$670$		0			0
$671$	−3.65479	+	11.2483i	−0.141092	+	0.434236i
$672$	−0.978686	+	3.01209i	−0.0377536	+	0.116194i
$673$	−12.0238	+	8.73578i	−0.463482	+	0.336740i	−0.794896	−	0.606746i	$-0.792474\pi$
$673$	−12.0238	+	8.73578i	−0.463482	+	0.336740i	0.331414	+	0.943486i	$0.392474\pi$
$674$	−9.06404			−0.349134
$675$		0			0
$676$	−21.1940			−0.815153
$677$	18.7075	−	13.5918i	0.718989	−	0.522376i	−0.167072	−	0.985945i	$-0.553431\pi$
$677$	18.7075	−	13.5918i	0.718989	−	0.522376i	0.886061	+	0.463568i	$0.153431\pi$
$678$	−0.0865982	+	0.266522i	−0.00332578	+	0.0102357i
$679$	−4.40417	+	13.5546i	−0.169017	+	0.520180i
$680$		0			0
$681$	−5.97709	−	18.3956i	−0.229043	−	0.704921i
$682$	−43.3000			−1.65804
$683$	−6.06747	−	18.6737i	−0.232165	−	0.714531i	−0.997485	−	0.0708804i	$-0.977419\pi$
$683$	−6.06747	−	18.6737i	−0.232165	−	0.714531i	0.765320	−	0.643650i	$-0.222581\pi$
$684$	−6.18335	−	4.49247i	−0.236426	−	0.171774i
$685$		0			0
$686$	11.2331	−	8.16136i	0.428883	−	0.311602i
$687$	6.27423	+	4.55850i	0.239377	+	0.173918i
$688$	−6.16296	−	4.47765i	−0.234961	−	0.170709i
$689$	−49.4768	+	35.9470i	−1.88491	+	1.36947i
$690$		0			0
$691$	4.75525	+	3.45489i	0.180898	+	0.131430i	0.674549	−	0.738230i	$-0.264338\pi$
$691$	4.75525	+	3.45489i	0.180898	+	0.131430i	−0.493651	+	0.869660i	$0.664338\pi$
$692$	−1.75589	−	5.40406i	−0.0667488	−	0.205432i
$693$	−13.0978			−0.497544
$694$	3.53134	+	10.8684i	0.134048	+	0.412557i
$695$		0			0
$696$	−1.00492	+	3.09283i	−0.0380914	+	0.117233i
$697$	−1.83886	+	5.65942i	−0.0696517	+	0.214366i
$698$	6.96286	−	5.05882i	0.263548	−	0.191479i
$699$	9.26066			0.350270
$700$		0			0
$701$	−50.0581			−1.89067			−0.945334	−	0.326103i	$-0.894264\pi$
$701$	−50.0581			−1.89067			−0.945334	+	0.326103i	$0.894264\pi$
$702$	−19.7791	+	14.3703i	−0.746513	+	0.542373i
$703$	8.90775	−	27.4152i	0.335962	−	1.03398i
$704$	12.2325	−	37.6479i	0.461031	−	1.41891i
$705$		0			0
$706$	6.91596	+	21.2851i	0.260285	+	0.801076i
$707$	−10.6391			−0.400124
$708$	0.542271	+	1.66894i	0.0203798	+	0.0627225i
$709$	−11.1245	−	8.08239i	−0.417788	−	0.303541i	0.358959	−	0.933353i	$-0.383132\pi$
$709$	−11.1245	−	8.08239i	−0.417788	−	0.303541i	−0.776747	+	0.629813i	$0.783132\pi$
$710$		0			0
$711$	22.6137	−	16.4298i	0.848082	−	0.616167i
$712$	−15.7614	−	11.4513i	−0.590683	−	0.429157i
$713$	18.8861	+	13.7215i	0.707290	+	0.513876i
$714$	1.90021	−	1.38058i	0.0711137	−	0.0516671i
$715$		0			0
$716$	−11.0126	−	8.00114i	−0.411561	−	0.299017i
$717$	−0.404129	−	1.24378i	−0.0150925	−	0.0464499i
$718$	−5.63142			−0.210163
$719$	−3.24466	−	9.98605i	−0.121006	−	0.372417i	0.872147	−	0.489245i	$-0.162727\pi$
$719$	−3.24466	−	9.98605i	−0.121006	−	0.372417i	−0.993152	+	0.116828i	$0.962727\pi$
$720$		0			0
$721$	−0.962468	+	2.96217i	−0.0358442	+	0.110317i
$722$	−2.36693	+	7.28466i	−0.0880879	+	0.271107i
$723$	−10.8824	+	7.90656i	−0.404722	+	0.294048i
$724$	−1.12709			−0.0418880
$725$		0			0
$726$	−11.0640			−0.410623
$727$	4.90560	−	3.56413i	0.181939	−	0.132186i	−0.493088	−	0.869979i	$-0.664132\pi$
$727$	4.90560	−	3.56413i	0.181939	−	0.132186i	0.675027	+	0.737793i	$0.264132\pi$
$728$	−5.79906	+	17.8477i	−0.214927	+	0.661479i
$729$	−1.46085	+	4.49602i	−0.0541054	+	0.166519i
$730$		0			0
$731$	−5.15481	−	15.8649i	−0.190657	−	0.586783i
$732$	−1.40026			−0.0517550
$733$	0.723317	+	2.22614i	0.0267163	+	0.0822243i	0.963526	−	0.267616i	$-0.0862358\pi$
$733$	0.723317	+	2.22614i	0.0267163	+	0.0822243i	−0.936809	+	0.349840i	$0.886236\pi$
$734$	14.5656	+	10.5826i	0.537628	+	0.390609i
$735$		0			0
$736$	−10.7519	+	7.81174i	−0.396322	+	0.287945i
$737$	−19.2595	−	13.9928i	−0.709433	−	0.515433i
$738$	−4.02916	−	2.92735i	−0.148315	−	0.107757i
$739$	33.6027	−	24.4138i	1.23610	−	0.898076i	0.238764	−	0.971078i	$-0.423258\pi$
$739$	33.6027	−	24.4138i	1.23610	−	0.898076i	0.997332	+	0.0730014i	$0.0232578\pi$
$740$		0			0
$741$	11.6033	+	8.43028i	0.426257	+	0.309694i
$742$	3.32317	+	10.2277i	0.121997	+	0.375470i
$743$	−0.813821			−0.0298562			−0.0149281	−	0.999889i	$-0.504752\pi$
$743$	−0.813821			−0.0298562			−0.0149281	+	0.999889i	$0.504752\pi$
$744$	−5.17651	−	15.9317i	−0.189780	−	0.584083i
$745$		0			0
$746$	−2.23864	+	6.88984i	−0.0819626	+	0.252255i
$747$	−11.1666	+	34.3674i	−0.408566	+	1.25744i
$748$	11.6671	−	8.47666i	0.426592	−	0.309937i
$749$	−5.31025			−0.194032
$750$		0			0
$751$	31.8919			1.16375			0.581877	−	0.813277i	$-0.302319\pi$
$751$	31.8919			1.16375			0.581877	+	0.813277i	$0.302319\pi$
$752$	−5.66368	+	4.11490i	−0.206533	+	0.150055i
$753$	−4.39913	+	13.5391i	−0.160313	+	0.493393i
$754$	−3.08683	+	9.50028i	−0.112416	+	0.345980i
$755$		0			0
$756$	−1.04797	−	3.22531i	−0.0381142	−	0.117303i
$757$	26.7040			0.970572			0.485286	−	0.874355i	$-0.338715\pi$
$757$	26.7040			0.970572			0.485286	+	0.874355i	$0.338715\pi$
$758$	−2.41406	−	7.42970i	−0.0876825	−	0.269859i
$759$	8.31304	+	6.03978i	0.301744	+	0.219230i
$760$		0			0
$761$	−34.8399	+	25.3126i	−1.26294	+	0.917582i	−0.998898	−	0.0469277i	$-0.985057\pi$
$761$	−34.8399	+	25.3126i	−1.26294	+	0.917582i	−0.264046	+	0.964510i	$0.585057\pi$
$762$	−2.73036	−	1.98372i	−0.0989104	−	0.0718626i
$763$	5.33729	+	3.87777i	0.193223	+	0.140385i
$764$	4.16419	−	3.02546i	0.150655	−	0.109457i
$765$		0			0
$766$	−17.2825	−	12.5565i	−0.624441	−	0.453683i
$767$	5.44298	+	16.7518i	0.196535	+	0.604872i
$768$	11.3049			0.407929
$769$	−0.325574	−	1.00201i	−0.0117405	−	0.0361335i	0.945015	−	0.327028i	$-0.106047\pi$
$769$	−0.325574	−	1.00201i	−0.0117405	−	0.0361335i	−0.956755	+	0.290894i	$0.906047\pi$
$770$		0			0
$771$	−3.20179	+	9.85409i	−0.115310	+	0.354886i
$772$	1.13860	−	3.50424i	0.0409790	−	0.126121i
$773$	10.7032	−	7.77632i	0.384967	−	0.279695i	−0.378423	−	0.925633i	$-0.623534\pi$
$773$	10.7032	−	7.77632i	0.384967	−	0.279695i	0.763390	+	0.645938i	$0.223534\pi$
$774$	13.9611			0.501823
$775$		0			0
$776$	42.9161			1.54060
$777$	4.73153	−	3.43766i	0.169743	−	0.123325i
$778$	2.87547	−	8.84978i	0.103090	−	0.317280i
$779$	−1.97449	+	6.07684i	−0.0707433	+	0.217725i
$780$		0			0
$781$	−12.2432	−	37.6806i	−0.438095	−	1.34832i
$782$	9.85627			0.352459
$783$	−1.82281	−	5.61004i	−0.0651420	−	0.200486i
$784$	−7.04994	−	5.12208i	−0.251784	−	0.182932i
$785$		0			0
$786$	9.53857	−	6.93018i	0.340230	−	0.247191i
$787$	−27.2135	−	19.7718i	−0.970057	−	0.704788i	−0.0145925	−	0.999894i	$-0.504645\pi$
$787$	−27.2135	−	19.7718i	−0.970057	−	0.704788i	−0.955465	+	0.295106i	$0.904645\pi$
$788$	−12.4762	−	9.06449i	−0.444446	−	0.322909i
$789$	2.78242	−	2.02155i	0.0990569	−	0.0719690i
$790$		0			0
$791$	−0.315662	−	0.229342i	−0.0112236	−	0.00815445i
$792$	12.1876	+	37.5096i	0.433068	+	1.33285i
$793$	−14.0549			−0.499105
$794$	1.99089	+	6.12732i	0.0706539	+	0.217450i
$795$		0			0
$796$	−1.60539	+	4.94087i	−0.0569014	+	0.175125i
$797$	2.13142	−	6.55982i	0.0754986	−	0.232361i	−0.906184	−	0.422883i	$-0.861018\pi$
$797$	2.13142	−	6.55982i	0.0754986	−	0.232361i	0.981683	+	0.190522i	$0.0610181\pi$
$798$	2.04037	−	1.48241i	0.0722281	−	0.0524768i
$799$	−15.3299			−0.542333
$800$		0			0
$801$	16.1587			0.570941
$802$	1.47070	−	1.06852i	0.0519321	−	0.0377309i
$803$	−0.942379	+	2.90035i	−0.0332558	+	0.102351i
$804$	0.870958	−	2.68053i	0.0307163	−	0.0945351i
$805$		0			0
$806$	−15.9008	−	48.9376i	−0.560081	−	1.72375i
$807$	19.0276			0.669803
$808$	9.89977	+	30.4683i	0.348273	+	1.07187i
$809$	28.5850	+	20.7682i	1.00499	+	0.730172i	0.963153	−	0.268953i	$-0.0866775\pi$
$809$	28.5850	+	20.7682i	1.00499	+	0.730172i	0.0418416	+	0.999124i	$0.486678\pi$
$810$		0			0
$811$	3.21342	−	2.33469i	0.112839	−	0.0819820i	−0.529935	−	0.848038i	$-0.677784\pi$
$811$	3.21342	−	2.33469i	0.112839	−	0.0819820i	0.642773	+	0.766056i	$0.277784\pi$
$812$	−1.12100	−	0.814453i	−0.0393393	−	0.0285817i
$813$	−14.6776	−	10.6639i	−0.514765	−	0.373999i
$814$	−36.8276	+	26.7568i	−1.29081	+	0.937826i
$815$		0			0
$816$	−2.58954	−	1.88141i	−0.0906519	−	0.0658624i
$817$	−5.53501	−	17.0350i	−0.193645	−	0.595979i
$818$	−29.3331			−1.02561
$819$	−4.80981	−	14.8031i	−0.168068	−	0.517261i
$820$		0			0
$821$	7.53253	−	23.1827i	0.262887	−	0.809083i	−0.729286	−	0.684209i	$-0.760147\pi$
$821$	7.53253	−	23.1827i	0.262887	−	0.809083i	0.992173	−	0.124874i	$-0.0398525\pi$
$822$	4.30799	−	13.2586i	0.150259	−	0.462448i
$823$	−18.0090	+	13.0843i	−0.627755	+	0.456090i	−0.855622	−	0.517602i	$-0.826825\pi$
$823$	−18.0090	+	13.0843i	−0.627755	+	0.456090i	0.227867	+	0.973692i	$0.426825\pi$
$824$	9.37870			0.326722
$825$		0			0
$826$	3.09729			0.107768
$827$	−21.5357	+	15.6466i	−0.748871	+	0.544087i	−0.895477	−	0.445108i	$-0.853165\pi$
$827$	−21.5357	+	15.6466i	−0.748871	+	0.544087i	0.146606	+	0.989195i	$0.453165\pi$
$828$	2.01083	−	6.18870i	0.0698812	−	0.215072i
$829$	−2.42064	+	7.44995i	−0.0840722	+	0.258748i	−0.984252	−	0.176771i	$-0.943435\pi$
$829$	−2.42064	+	7.44995i	−0.0840722	+	0.258748i	0.900180	+	0.435518i	$0.143435\pi$
$830$		0			0
$831$	1.51301	+	4.65658i	0.0524859	+	0.161535i
$832$	47.0416			1.63088
$833$	−5.89670	−	18.1482i	−0.204308	−	0.628797i
$834$	2.10964	+	1.53274i	0.0730508	+	0.0530745i
$835$		0			0
$836$	12.5276	−	9.10187i	0.433278	−	0.314795i
$837$	24.5823	+	17.8601i	0.849689	+	0.617335i
$838$	−13.9898	−	10.1642i	−0.483268	−	0.351115i
$839$	−4.75218	+	3.45266i	−0.164063	+	0.119199i	−0.666788	−	0.745248i	$-0.732331\pi$
$839$	−4.75218	+	3.45266i	−0.164063	+	0.119199i	0.502724	+	0.864447i	$0.332331\pi$
$840$		0			0
$841$	21.5117	+	15.6291i	0.741781	+	0.538935i
$842$	−3.24970	−	10.0015i	−0.111992	−	0.344676i
$843$	7.09859			0.244488
$844$	3.26429	+	10.0464i	0.112361	+	0.345813i
$845$		0			0
$846$	3.96472	−	12.2022i	0.136310	−	0.419519i
$847$	4.76026	−	14.6506i	0.163565	−	0.503400i
$848$	11.8563	−	8.61408i	0.407146	−	0.295809i
$849$	−3.13447			−0.107575
$850$		0			0
$851$	24.5421			0.841293
$852$	3.79486	−	2.75713i	0.130010	−	0.0944577i
$853$	−8.69717	+	26.7671i	−0.297786	+	0.916490i	0.684486	+	0.729026i	$0.260027\pi$
$853$	−8.69717	+	26.7671i	−0.297786	+	0.916490i	−0.982272	+	0.187464i	$0.939973\pi$
$854$	−0.763726	+	2.35051i	−0.0261342	+	0.0804327i
$855$		0			0
$856$	4.94124	+	15.2076i	0.168888	+	0.519784i
$857$	−36.2976			−1.23990			−0.619951	−	0.784640i	$-0.712848\pi$
$857$	−36.2976			−1.23990			−0.619951	+	0.784640i	$0.712848\pi$
$858$	−6.99900	−	21.5407i	−0.238942	−	0.735388i
$859$	−3.09368	−	2.24769i	−0.105555	−	0.0766903i	0.533756	−	0.845639i	$-0.320780\pi$
$859$	−3.09368	−	2.24769i	−0.105555	−	0.0766903i	−0.639311	+	0.768949i	$0.720780\pi$
$860$		0			0
$861$	−1.04879	+	0.761989i	−0.0357426	+	0.0259685i
$862$	17.5622	+	12.7597i	0.598171	+	0.434597i
$863$	−20.7072	−	15.0446i	−0.704881	−	0.512126i	0.176637	−	0.984276i	$-0.443478\pi$
$863$	−20.7072	−	15.0446i	−0.704881	−	0.512126i	−0.881518	+	0.472150i	$0.843478\pi$
$864$	−13.9948	+	10.1678i	−0.476114	+	0.345917i
$865$		0			0
$866$	22.1958	+	16.1262i	0.754245	+	0.547991i
$867$	1.44520	+	4.44786i	0.0490814	+	0.151057i
$868$	7.13761			0.242266
$869$	17.5002	+	53.8600i	0.593653	+	1.82708i
$870$		0			0
$871$	8.74214	−	26.9055i	0.296216	−	0.911659i
$872$	6.13881	−	18.8933i	0.207886	−	0.639808i
$873$	−28.7971	+	20.9223i	−0.974634	+	0.708113i
$874$	10.5832			0.357983
$875$		0			0
$876$	−0.361053			−0.0121988
$877$	−12.0203	+	8.73324i	−0.405896	+	0.294901i	−0.771938	−	0.635698i	$-0.780713\pi$
$877$	−12.0203	+	8.73324i	−0.405896	+	0.294901i	0.366042	+	0.930598i	$0.380713\pi$
$878$	8.21061	−	25.2697i	0.277095	−	0.852810i
$879$	4.42336	−	13.6137i	0.149196	−	0.459178i
$880$		0			0
$881$	0.653144	+	2.01017i	0.0220050	+	0.0677244i	0.961456	−	0.274959i	$-0.0886642\pi$
$881$	0.653144	+	2.01017i	0.0220050	+	0.0677244i	−0.939451	+	0.342683i	$0.888664\pi$
$882$	15.9704			0.537753
$883$	−15.7855	−	48.5827i	−0.531223	−	1.63494i	−0.751671	−	0.659538i	$-0.770752\pi$
$883$	−15.7855	−	48.5827i	−0.531223	−	1.63494i	0.220448	−	0.975399i	$-0.429248\pi$
$884$	13.8647	+	10.0733i	0.466321	+	0.338802i
$885$		0			0
$886$	−23.1192	+	16.7970i	−0.776703	+	0.564308i
$887$	−36.8749	−	26.7912i	−1.23814	−	0.899560i	−0.240666	−	0.970608i	$-0.577366\pi$
$887$	−36.8749	−	26.7912i	−1.23814	−	0.899560i	−0.997473	+	0.0710478i	$0.977366\pi$
$888$	−14.2476	−	10.3515i	−0.478117	−	0.347372i
$889$	3.80152	−	2.76196i	0.127499	−	0.0926333i
$890$		0			0
$891$	−20.5919	−	14.9609i	−0.689854	−	0.501208i
$892$	0.348077	+	1.07127i	0.0116545	+	0.0358688i
$893$	−16.4606			−0.550833
$894$	−0.359801	−	1.10735i	−0.0120336	−	0.0370355i
$895$		0			0
$896$	−0.291306	+	0.896547i	−0.00973185	+	0.0299515i
$897$	−3.77340	+	11.6133i	−0.125990	+	0.387757i
$898$	−32.4955	+	23.6093i	−1.08439	+	0.787854i
$899$	12.4150			0.414064
$900$		0			0
$901$	32.0914			1.06912
$902$	8.16318	−	5.93090i	0.271804	−	0.197477i
$903$	1.12299	−	3.45622i	0.0373709	−	0.115016i
$904$	−0.363065	+	1.11740i	−0.0120754	+	0.0371642i
$905$		0			0
$906$	−1.51434	−	4.66066i	−0.0503106	−	0.154840i
$907$	−27.5215			−0.913837			−0.456919	−	0.889508i	$-0.651047\pi$
$907$	−27.5215			−0.913837			−0.456919	+	0.889508i	$0.651047\pi$
$908$	−7.66878	−	23.6021i	−0.254497	−	0.783262i
$909$	−21.4966	−	15.6182i	−0.712999	−	0.518024i
$910$		0			0
$911$	−40.7834	+	29.6309i	−1.35121	+	0.981714i	−0.352264	+	0.935901i	$0.614588\pi$
$911$	−40.7834	+	29.6309i	−1.35121	+	0.981714i	−0.998950	+	0.0458135i	$0.985412\pi$
$912$	−2.78053	−	2.02017i	−0.0920726	−	0.0668946i
$913$	−59.2302	−	43.0333i	−1.96023	−	1.42419i
$914$	25.6487	−	18.6349i	0.848383	−	0.616386i
$915$		0			0
$916$	8.05002	+	5.84868i	0.265980	+	0.193246i
$917$	5.07277	+	15.6124i	0.167518	+	0.515567i
$918$	12.8290			0.423420
$919$	3.91040	+	12.0350i	0.128992	+	0.396997i	0.994607	−	0.103713i	$-0.0330724\pi$
$919$	3.91040	+	12.0350i	0.128992	+	0.396997i	−0.865615	+	0.500710i	$0.833072\pi$
$920$		0			0
$921$	−2.00566	+	6.17280i	−0.0660889	+	0.203401i
$922$	−0.697159	+	2.14564i	−0.0229597	+	0.0706628i
$923$	38.0905	−	27.6744i	1.25376	−	0.910913i
$924$	3.14174			0.103356
$925$		0			0
$926$	−23.2415			−0.763763
$927$	−6.29319	+	4.57227i	−0.206695	+	0.150173i
$928$	−2.18411	+	6.72200i	−0.0716969	+	0.220660i
$929$	−0.939293	+	2.89085i	−0.0308172	+	0.0948456i	−0.965282	−	0.261210i	$-0.915879\pi$
$929$	−0.939293	+	2.89085i	−0.0308172	+	0.0948456i	0.934465	+	0.356055i	$0.115879\pi$
$930$		0			0
$931$	−6.33162	−	19.4867i	−0.207510	−	0.638651i
$932$	11.8817			0.389198
$933$	−2.84225	−	8.74755i	−0.0930512	−	0.286382i
$934$	−4.54315	−	3.30079i	−0.148657	−	0.108005i
$935$		0			0
$936$	−37.9177	+	27.5488i	−1.23938	+	0.900461i
$937$	−0.0388934	−	0.0282577i	−0.00127059	−	0.000923138i	0.587150	−	0.809478i	$-0.300250\pi$
$937$	−0.0388934	−	0.0282577i	−0.00127059	−	0.000923138i	−0.588420	+	0.808555i	$0.700250\pi$
$938$	−4.02457	−	2.92402i	−0.131407	−	0.0954728i
$939$	13.3440	−	9.69496i	0.435464	−	0.316383i
$940$		0			0
$941$	1.01445	+	0.737040i	0.0330701	+	0.0240268i	0.604198	−	0.796835i	$-0.293494\pi$
$941$	1.01445	+	0.737040i	0.0330701	+	0.0240268i	−0.571127	+	0.820861i	$0.693494\pi$
$942$	3.20316	+	9.85831i	0.104365	+	0.321201i
$943$	−5.43999			−0.177150
$944$	−1.30432	−	4.01428i	−0.0424519	−	0.130654i
$945$		0			0
$946$	−8.74074	+	26.9012i	−0.284186	+	0.874635i
$947$	13.7817	−	42.4157i	0.447845	−	1.37833i	−0.431488	−	0.902119i	$-0.642011\pi$
$947$	13.7817	−	42.4157i	0.447845	−	1.37833i	0.879333	−	0.476207i	$-0.157989\pi$
$948$	−5.42432	+	3.94100i	−0.176174	+	0.127998i
$949$	−3.62403			−0.117641
$950$		0			0
$951$	−10.0097			−0.324587
$952$	7.96669	−	5.78814i	0.258202	−	0.187595i
$953$	−12.9239	+	39.7757i	−0.418647	+	1.28846i	0.490301	+	0.871553i	$0.336887\pi$
$953$	−12.9239	+	39.7757i	−0.418647	+	1.28846i	−0.908948	+	0.416909i	$0.863113\pi$
$954$	−8.29969	+	25.5438i	−0.268712	+	0.827011i
$955$		0			0
$956$	−0.518509	−	1.59581i	−0.0167698	−	0.0516121i
$957$	5.46469			0.176648
$958$	−6.89034	−	21.2063i	−0.222617	−	0.685144i
$959$	15.7032	+	11.4090i	0.507082	+	0.368417i
$960$		0			0
$961$	−26.6586	+	19.3686i	−0.859955	+	0.624794i
$962$	−43.7644	−	31.7967i	−1.41102	−	1.02517i
$963$	−10.7296	−	7.79548i	−0.345755	−	0.251206i
$964$	−13.9625	+	10.1443i	−0.449701	+	0.326727i
$965$		0			0
$966$	1.73714	+	1.26211i	0.0558915	+	0.0406076i
$967$	13.7508	+	42.3207i	0.442197	+	1.36094i	0.885529	+	0.464585i	$0.153796\pi$
$967$	13.7508	+	42.3207i	0.442197	+	1.36094i	−0.443332	+	0.896358i	$0.646204\pi$
$968$	−46.3860			−1.49090
$969$	−2.32568	−	7.15772i	−0.0747118	−	0.229939i
$970$		0			0
$971$	1.13254	−	3.48561i	0.0363451	−	0.111859i	−0.931238	−	0.364412i	$-0.881270\pi$
$971$	1.13254	−	3.48561i	0.0363451	−	0.111859i	0.967583	+	0.252553i	$0.0812702\pi$
$972$	4.03785	−	12.4272i	0.129514	−	0.398603i
$973$	−2.93728	+	2.13406i	−0.0941649	+	0.0684148i
$974$	−28.1389			−0.901629
$975$		0			0
$976$	3.36802			0.107808
$977$	−12.7464	+	9.26079i	−0.407793	+	0.296279i	−0.772708	−	0.634762i	$-0.781098\pi$
$977$	−12.7464	+	9.26079i	−0.407793	+	0.296279i	0.364915	+	0.931041i	$0.381098\pi$
$978$	2.27169	−	6.99153i	0.0726406	−	0.223565i
$979$	−10.1166	+	31.1357i	−0.323328	+	0.995103i
$980$		0			0
$981$	5.09160	+	15.6703i	0.162562	+	0.500315i
$982$	1.90400			0.0607591
$983$	8.31313	+	25.5852i	0.265148	+	0.816041i	0.991659	+	0.128887i	$0.0411404\pi$
$983$	8.31313	+	25.5852i	0.265148	+	0.816041i	−0.726512	+	0.687154i	$0.758860\pi$
$984$	3.15810	+	2.29450i	0.100677	+	0.0731459i
$985$		0			0
$986$	4.24066	−	3.08102i	0.135050	−	0.0981196i
$987$	−2.70185	−	1.96301i	−0.0860009	−	0.0624833i
$988$	14.8873	+	10.8163i	0.473630	+	0.344112i
$989$	12.3373	−	8.96357i	0.392303	−	0.285025i
$990$		0			0
$991$	−11.3812	−	8.26896i	−0.361537	−	0.262672i	0.392156	−	0.919899i	$-0.371729\pi$
$991$	−11.3812	−	8.26896i	−0.361537	−	0.262672i	−0.753693	+	0.657227i	$0.771729\pi$
$992$	−11.2507	−	34.6261i	−0.357210	−	1.09938i
$993$	16.7897			0.532806
$994$	−2.55840	−	7.87394i	−0.0811475	−	0.249746i
$995$		0			0
$996$	2.67852	−	8.24365i	0.0848723	−	0.261210i
$997$	0.191171	−	0.588365i	0.00605446	−	0.0186337i	−0.947984	−	0.318319i	$-0.896882\pi$
$997$	0.191171	−	0.588365i	0.00605446	−	0.0186337i	0.954038	+	0.299685i	$0.0968817\pi$
$998$	−24.5477	+	17.8349i	−0.777044	+	0.564555i
$999$	31.9443			1.01067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.n.251.2		16
5.2	odd	4		625.2.e.k.374.3		32
5.3	odd	4		625.2.e.k.374.6		32
5.4	even	2		625.2.d.p.251.3		16
25.2	odd	20		625.2.e.j.499.3		32
25.3	odd	20		625.2.b.d.624.6		16
25.4	even	10		625.2.a.e.1.4	✓	8
25.6	even	5		625.2.d.m.501.3		16
25.8	odd	20		625.2.e.j.124.3		32
25.9	even	10		625.2.d.p.376.3		16
25.11	even	5		625.2.d.m.126.3		16
25.12	odd	20		625.2.e.k.249.6		32
25.13	odd	20		625.2.e.k.249.3		32
25.14	even	10		625.2.d.q.126.2		16
25.16	even	5	inner	625.2.d.n.376.2		16
25.17	odd	20		625.2.e.j.124.6		32
25.19	even	10		625.2.d.q.501.2		16
25.21	even	5		625.2.a.g.1.5	yes	8
25.22	odd	20		625.2.b.d.624.11		16
25.23	odd	20		625.2.e.j.499.6		32
75.29	odd	10		5625.2.a.be.1.5		8
75.71	odd	10		5625.2.a.s.1.4		8
100.71	odd	10		10000.2.a.be.1.6		8
100.79	odd	10		10000.2.a.bn.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.4	✓	8	25.4	even	10
625.2.a.g.1.5	yes	8	25.21	even	5
625.2.b.d.624.6		16	25.3	odd	20
625.2.b.d.624.11		16	25.22	odd	20
625.2.d.m.126.3		16	25.11	even	5
625.2.d.m.501.3		16	25.6	even	5
625.2.d.n.251.2		16	1.1	even	1	trivial
625.2.d.n.376.2		16	25.16	even	5	inner
625.2.d.p.251.3		16	5.4	even	2
625.2.d.p.376.3		16	25.9	even	10
625.2.d.q.126.2		16	25.14	even	10
625.2.d.q.501.2		16	25.19	even	10
625.2.e.j.124.3		32	25.8	odd	20
625.2.e.j.124.6		32	25.17	odd	20
625.2.e.j.499.3		32	25.2	odd	20
625.2.e.j.499.6		32	25.23	odd	20
625.2.e.k.249.3		32	25.13	odd	20
625.2.e.k.249.6		32	25.12	odd	20
625.2.e.k.374.3		32	5.2	odd	4
625.2.e.k.374.6		32	5.3	odd	4
5625.2.a.s.1.4		8	75.71	odd	10
5625.2.a.be.1.5		8	75.29	odd	10
10000.2.a.be.1.6		8	100.71	odd	10
10000.2.a.bn.1.3		8	100.79	odd	10

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.855434 + 0.621509i) q^{2} +(-0.212419 + 0.653760i) q^{3} +(-0.272540 + 0.838792i) q^{4} +(-0.224607 - 0.691269i) q^{6} +1.01199 q^{7} +(-0.941671 - 2.89816i) q^{8} +(2.04477 + 1.48561i) q^{9} +O(q^{10})\)	\(q+(-0.855434 + 0.621509i) q^{2} +(-0.212419 + 0.653760i) q^{3} +(-0.272540 + 0.838792i) q^{4} +(-0.224607 - 0.691269i) q^{6} +1.01199 q^{7} +(-0.941671 - 2.89816i) q^{8} +(2.04477 + 1.48561i) q^{9} +(-4.14276 + 3.00989i) q^{11} +(-0.490476 - 0.356351i) q^{12} +(-4.92309 - 3.57684i) q^{13} +(-0.865695 + 0.628964i) q^{14} +(1.17974 + 0.857128i) q^{16} +(0.986752 + 3.03691i) q^{17} -2.67249 q^{18} +(1.05953 + 3.26090i) q^{19} +(-0.214967 + 0.661601i) q^{21} +(1.67318 - 5.14953i) q^{22} +(-2.36165 + 1.71584i) q^{23} +2.09473 q^{24} +6.43442 q^{26} +(-3.07395 + 2.23335i) q^{27} +(-0.275809 + 0.848853i) q^{28} +(-0.479737 + 1.47648i) q^{29} +(-2.47121 - 7.60559i) q^{31} +4.55272 q^{32} +(-1.08774 - 3.34773i) q^{33} +(-2.73157 - 1.98460i) q^{34} +(-1.80340 + 1.31025i) q^{36} +(-6.80161 - 4.94166i) q^{37} +(-2.93304 - 2.13098i) q^{38} +(3.38415 - 2.45873i) q^{39} +(1.50764 + 1.09537i) q^{41} +(-0.227301 - 0.699561i) q^{42} -5.22402 q^{43} +(-1.39561 - 4.29523i) q^{44} +(0.953826 - 2.93558i) q^{46} +(-1.48353 + 4.56584i) q^{47} +(-0.810954 + 0.589193i) q^{48} -5.97587 q^{49} -2.19501 q^{51} +(4.34196 - 3.15462i) q^{52} +(3.10560 - 9.55806i) q^{53} +(1.24151 - 3.82097i) q^{54} +(-0.952966 - 2.93293i) q^{56} -2.35691 q^{57} +(-0.507262 - 1.56119i) q^{58} +(-2.34170 - 1.70135i) q^{59} +(1.86855 - 1.35758i) q^{61} +(6.84090 + 4.97020i) q^{62} +(2.06930 + 1.50343i) q^{63} +(-6.25402 + 4.54382i) q^{64} +(3.01114 + 2.18772i) q^{66} +(1.43660 + 4.42142i) q^{67} -2.81626 q^{68} +(-0.620086 - 1.90843i) q^{69} +(-2.39090 + 7.35843i) q^{71} +(2.38005 - 7.32504i) q^{72} +(0.481802 - 0.350050i) q^{73} +8.88962 q^{74} -3.02398 q^{76} +(-4.19245 + 3.04600i) q^{77} +(-1.36680 + 4.20656i) q^{78} +(3.41751 - 10.5180i) q^{79} +(1.53599 + 4.72729i) q^{81} -1.97047 q^{82} +(4.41810 + 13.5975i) q^{83} +(-0.496359 - 0.360626i) q^{84} +(4.46880 - 3.24678i) q^{86} +(-0.863357 - 0.627265i) q^{87} +(12.6243 + 9.17208i) q^{88} +(5.17223 - 3.75785i) q^{89} +(-4.98214 - 3.61974i) q^{91} +(-0.795588 - 2.44857i) q^{92} +5.49716 q^{93} +(-1.56865 - 4.82780i) q^{94} +(-0.967086 + 2.97639i) q^{96} +(-4.35197 + 13.3940i) q^{97} +(5.11196 - 3.71406i) q^{98} -12.9425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9	\( 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9} + 2 q^{11} - 25 q^{12} - 5 q^{13} + 9 q^{14} - 14 q^{16} + 10 q^{17} - 10 q^{18} + 7 q^{21} + 40 q^{22} - 15 q^{23} + 10 q^{24} + 22 q^{26} - 20 q^{27} - 30 q^{28} - 10 q^{29} + 17 q^{31} + 60 q^{32} - 5 q^{33} - q^{34} - 4 q^{36} + 15 q^{37} + 15 q^{38} - 9 q^{39} + 12 q^{41} + 45 q^{42} + 49 q^{44} - 33 q^{46} - 25 q^{47} + 20 q^{48} - 8 q^{49} - 28 q^{51} - 20 q^{52} - 30 q^{54} - 35 q^{56} - 20 q^{57} - 5 q^{58} + 20 q^{59} - 23 q^{61} - 15 q^{62} - 10 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{68} + 6 q^{69} + 22 q^{71} - 5 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 40 q^{77} + 25 q^{78} + 75 q^{79} + 11 q^{81} - 90 q^{82} - 25 q^{83} - 31 q^{84} + 17 q^{86} + 20 q^{87} + 5 q^{89} + 22 q^{91} - 60 q^{92} - 80 q^{93} - 51 q^{94} - 28 q^{96} - 40 q^{97} - 15 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9 + 2 * q^11 - 25 * q^12 - 5 * q^13 + 9 * q^14 - 14 * q^16 + 10 * q^17 - 10 * q^18 + 7 * q^21 + 40 * q^22 - 15 * q^23 + 10 * q^24 + 22 * q^26 - 20 * q^27 - 30 * q^28 - 10 * q^29 + 17 * q^31 + 60 * q^32 - 5 * q^33 - q^34 - 4 * q^36 + 15 * q^37 + 15 * q^38 - 9 * q^39 + 12 * q^41 + 45 * q^42 + 49 * q^44 - 33 * q^46 - 25 * q^47 + 20 * q^48 - 8 * q^49 - 28 * q^51 - 20 * q^52 - 30 * q^54 - 35 * q^56 - 20 * q^57 - 5 * q^58 + 20 * q^59 - 23 * q^61 - 15 * q^62 - 10 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^68 + 6 * q^69 + 22 * q^71 - 5 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 40 * q^77 + 25 * q^78 + 75 * q^79 + 11 * q^81 - 90 * q^82 - 25 * q^83 - 31 * q^84 + 17 * q^86 + 20 * q^87 + 5 * q^89 + 22 * q^91 - 60 * q^92 - 80 * q^93 - 51 * q^94 - 28 * q^96 - 40 * q^97 - 15 * q^98 - 44 * q^99

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