LMFDB - Embedded newform 804.2.j.a.499.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.13
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.699111 - 1.22933i) q^{2} -1.00000 q^{3} +(-1.02249 + 1.71887i) q^{4} +3.18642i q^{5} +(0.699111 + 1.22933i) q^{6} +(-2.40111 + 4.15884i) q^{7} +(2.82789 + 0.0552894i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.699111 - 1.22933i) q^{2} -1.00000 q^{3} +(-1.02249 + 1.71887i) q^{4} +3.18642i q^{5} +(0.699111 + 1.22933i) q^{6} +(-2.40111 + 4.15884i) q^{7} +(2.82789 + 0.0552894i) q^{8} +1.00000 q^{9} +(3.91715 - 2.22766i) q^{10} +(2.46827 - 4.27516i) q^{11} +(1.02249 - 1.71887i) q^{12} +(-1.30002 + 0.750569i) q^{13} +(6.79121 + 0.0442545i) q^{14} -3.18642i q^{15} +(-1.90904 - 3.51505i) q^{16} +(3.33782 + 5.78127i) q^{17} +(-0.699111 - 1.22933i) q^{18} +(3.66111 - 2.11374i) q^{19} +(-5.47705 - 3.25808i) q^{20} +(2.40111 - 4.15884i) q^{21} +(-6.98116 - 0.0454922i) q^{22} +(-6.42813 + 3.71128i) q^{23} +(-2.82789 - 0.0552894i) q^{24} -5.15329 q^{25} +(1.83156 + 1.07342i) q^{26} -1.00000 q^{27} +(-4.69341 - 8.37956i) q^{28} +(-2.65582 + 4.60001i) q^{29} +(-3.91715 + 2.22766i) q^{30} +(-0.397098 + 0.687793i) q^{31} +(-2.98651 + 4.80424i) q^{32} +(-2.46827 + 4.27516i) q^{33} +(4.77356 - 8.14501i) q^{34} +(-13.2518 - 7.65094i) q^{35} +(-1.02249 + 1.71887i) q^{36} +(-0.704760 - 1.22068i) q^{37} +(-5.15800 - 3.02296i) q^{38} +(1.30002 - 0.750569i) q^{39} +(-0.176175 + 9.01084i) q^{40} +(-4.56779 - 2.63721i) q^{41} +(-6.79121 - 0.0442545i) q^{42} -9.35287 q^{43} +(4.82468 + 8.61393i) q^{44} +3.18642i q^{45} +(9.05635 + 5.30767i) q^{46} +(4.15926 + 2.40135i) q^{47} +(1.90904 + 3.51505i) q^{48} +(-8.03064 - 13.9095i) q^{49} +(3.60272 + 6.33507i) q^{50} +(-3.33782 - 5.78127i) q^{51} +(0.0391266 - 3.00202i) q^{52} -5.57183i q^{53} +(0.699111 + 1.22933i) q^{54} +(13.6225 + 7.86494i) q^{55} +(-7.02000 + 11.6280i) q^{56} +(-3.66111 + 2.11374i) q^{57} +(7.51163 + 0.0489490i) q^{58} +5.46021i q^{59} +(5.47705 + 3.25808i) q^{60} +(7.29427 - 4.21135i) q^{61} +(1.12314 + 0.00731885i) q^{62} +(-2.40111 + 4.15884i) q^{63} +(7.99389 + 0.312704i) q^{64} +(-2.39163 - 4.14243i) q^{65} +(6.98116 + 0.0454922i) q^{66} +(-6.99166 - 4.25637i) q^{67} +(-13.3501 - 0.173998i) q^{68} +(6.42813 - 3.71128i) q^{69} +(-0.141013 + 21.6397i) q^{70} +(-5.08416 - 2.93534i) q^{71} +(2.82789 + 0.0552894i) q^{72} +(0.0425283 + 0.0736612i) q^{73} +(-1.00791 + 1.71977i) q^{74} +5.15329 q^{75} +(-0.110188 + 8.45425i) q^{76} +(11.8531 + 20.5303i) q^{77} +(-1.83156 - 1.07342i) q^{78} +(1.33783 - 2.31720i) q^{79} +(11.2004 - 6.08300i) q^{80} +1.00000 q^{81} +(-0.0486061 + 7.45901i) q^{82} +(2.66441 - 1.53830i) q^{83} +(4.69341 + 8.37956i) q^{84} +(-18.4216 + 10.6357i) q^{85} +(6.53870 + 11.4977i) q^{86} +(2.65582 - 4.60001i) q^{87} +(7.21635 - 11.9532i) q^{88} -8.37066 q^{89} +(3.91715 - 2.22766i) q^{90} -7.20879i q^{91} +(0.193466 - 14.8439i) q^{92} +(0.397098 - 0.687793i) q^{93} +(0.0442589 - 6.79190i) q^{94} +(6.73528 + 11.6658i) q^{95} +(2.98651 - 4.80424i) q^{96} +(12.2482 - 7.07150i) q^{97} +(-11.4850 + 19.5965i) q^{98} +(2.46827 - 4.27516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.699111	−	1.22933i	−0.494346	−	0.869265i
$2$	−0.699111	−	1.22933i	−0.494346	−	0.869265i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.02249	+	1.71887i	−0.511244	+	0.859436i
$5$			3.18642i			1.42501i	0.701666	+	0.712506i	$0.252440\pi$
$5$			3.18642i			1.42501i	−0.701666	+	0.712506i	$0.747560\pi$
$6$	0.699111	+	1.22933i	0.285411	+	0.501870i
$7$	−2.40111	+	4.15884i	−0.907533	+	1.57189i	−0.0900536	+	0.995937i	$0.528704\pi$
$7$	−2.40111	+	4.15884i	−0.907533	+	1.57189i	−0.817480	+	0.575957i	$0.804629\pi$
$8$	2.82789	+	0.0552894i	0.999809	+	0.0195478i
$9$	1.00000			0.333333
$10$	3.91715	−	2.22766i	1.23871	−	0.704449i
$11$	2.46827	−	4.27516i	0.744210	−	1.28901i	−0.206353	−	0.978478i	$-0.566159\pi$
$11$	2.46827	−	4.27516i	0.744210	−	1.28901i	0.950563	−	0.310532i	$-0.100507\pi$
$12$	1.02249	−	1.71887i	0.295167	−	0.496195i
$13$	−1.30002	+	0.750569i	−0.360562	+	0.208170i	−0.669327	−	0.742968i	$-0.733418\pi$
$13$	−1.30002	+	0.750569i	−0.360562	+	0.208170i	0.308765	+	0.951138i	$0.400084\pi$
$14$	6.79121	+	0.0442545i	1.81503	+	0.0118275i
$15$		−	3.18642i		−	0.822731i
$16$	−1.90904	−	3.51505i	−0.477259	−	0.878762i
$17$	3.33782	+	5.78127i	0.809539	+	1.40216i	0.913183	+	0.407549i	$0.133616\pi$
$17$	3.33782	+	5.78127i	0.809539	+	1.40216i	−0.103644	+	0.994614i	$0.533050\pi$
$18$	−0.699111	−	1.22933i	−0.164782	−	0.289755i
$19$	3.66111	−	2.11374i	0.839916	−	0.484926i	−0.0173195	−	0.999850i	$-0.505513\pi$
$19$	3.66111	−	2.11374i	0.839916	−	0.484926i	0.857236	+	0.514924i	$0.172180\pi$
$20$	−5.47705	−	3.25808i	−1.22471	−	0.728528i
$21$	2.40111	−	4.15884i	0.523965	−	0.907533i
$22$	−6.98116	−	0.0454922i	−1.48839	−	0.00969898i
$23$	−6.42813	+	3.71128i	−1.34036	+	0.773856i	−0.986860	−	0.161580i	$-0.948341\pi$
$23$	−6.42813	+	3.71128i	−1.34036	+	0.773856i	−0.353498	+	0.935435i	$0.615008\pi$
$24$	−2.82789	−	0.0552894i	−0.577240	−	0.0112859i
$25$	−5.15329			−1.03066
$26$	1.83156	+	1.07342i	0.359198	+	0.210516i
$27$	−1.00000			−0.192450
$28$	−4.69341	−	8.37956i	−0.886971	−	1.58359i
$29$	−2.65582	+	4.60001i	−0.493173	+	0.854201i	−0.999969	−	0.00786524i	$-0.997496\pi$
$29$	−2.65582	+	4.60001i	−0.493173	+	0.854201i	0.506796	+	0.862066i	$0.330830\pi$
$30$	−3.91715	+	2.22766i	−0.715171	+	0.406714i
$31$	−0.397098	+	0.687793i	−0.0713209	+	0.123531i	−0.899480	−	0.436961i	$-0.856055\pi$
$31$	−0.397098	+	0.687793i	−0.0713209	+	0.123531i	0.828160	+	0.560492i	$0.189388\pi$
$32$	−2.98651	+	4.80424i	−0.527946	+	0.849278i
$33$	−2.46827	+	4.27516i	−0.429670	+	0.744210i
$34$	4.77356	−	8.14501i	0.818659	−	1.39686i
$35$	−13.2518	−	7.65094i	−2.23997	−	1.29325i
$36$	−1.02249	+	1.71887i	−0.170415	+	0.286479i
$37$	−0.704760	−	1.22068i	−0.115862	−	0.200678i	0.802262	−	0.596972i	$-0.203630\pi$
$37$	−0.704760	−	1.22068i	−0.115862	−	0.200678i	−0.918124	+	0.396293i	$0.870296\pi$
$38$	−5.15800	−	3.02296i	−0.836738	−	0.490389i
$39$	1.30002	−	0.750569i	0.208170	−	0.120187i
$40$	−0.176175	+	9.01084i	−0.0278558	+	1.42474i
$41$	−4.56779	−	2.63721i	−0.713368	−	0.411863i	0.0989386	−	0.995094i	$-0.468455\pi$
$41$	−4.56779	−	2.63721i	−0.713368	−	0.411863i	−0.812307	+	0.583230i	$0.801789\pi$
$42$	−6.79121	−	0.0442545i	−1.04791	−	0.00682861i
$43$	−9.35287			−1.42630			−0.713150	−	0.701012i	$-0.752732\pi$
$43$	−9.35287			−1.42630			−0.713150	+	0.701012i	$0.752732\pi$
$44$	4.82468	+	8.61393i	0.727348	+	1.29860i
$45$			3.18642i			0.475004i
$46$	9.05635	+	5.30767i	1.33529	+	0.782573i
$47$	4.15926	+	2.40135i	0.606690	+	0.350273i	0.771669	−	0.636024i	$-0.219422\pi$
$47$	4.15926	+	2.40135i	0.606690	+	0.350273i	−0.164979	+	0.986297i	$0.552756\pi$
$48$	1.90904	+	3.51505i	0.275546	+	0.507354i
$49$	−8.03064	−	13.9095i	−1.14723	−	1.98707i
$50$	3.60272	+	6.33507i	0.509502	+	0.895915i
$51$	−3.33782	−	5.78127i	−0.467388	−	0.809539i
$52$	0.0391266	−	3.00202i	0.00542588	−	0.416305i
$53$		−	5.57183i		−	0.765349i	−0.923883	−	0.382675i	$-0.875003\pi$
$53$		−	5.57183i		−	0.765349i	0.923883	−	0.382675i	$-0.124997\pi$
$54$	0.699111	+	1.22933i	0.0951370	+	0.167290i
$55$	13.6225	+	7.86494i	1.83685	+	1.06051i
$56$	−7.02000	+	11.6280i	−0.938087	+	1.55385i
$57$	−3.66111	+	2.11374i	−0.484926	+	0.279972i
$58$	7.51163	+	0.0489490i	0.986325	+	0.00642732i
$59$			5.46021i			0.710859i	0.934703	+	0.355429i	$0.115665\pi$
$59$			5.46021i			0.710859i	−0.934703	+	0.355429i	$0.884335\pi$
$60$	5.47705	+	3.25808i	0.707084	+	0.420616i
$61$	7.29427	−	4.21135i	0.933935	−	0.539208i	0.0458812	−	0.998947i	$-0.485390\pi$
$61$	7.29427	−	4.21135i	0.933935	−	0.539208i	0.888054	+	0.459739i	$0.152057\pi$
$62$	1.12314	+	0.00731885i	0.142639	+	0.000929495i
$63$	−2.40111	+	4.15884i	−0.302511	+	0.523965i
$64$	7.99389	+	0.312704i	0.999236	+	0.0390881i
$65$	−2.39163	−	4.14243i	−0.296645	−	0.513805i
$66$	6.98116	+	0.0454922i	0.859322	+	0.00559971i
$67$	−6.99166	−	4.25637i	−0.854168	−	0.519998i
$67$	−6.99166	−	4.25637i	−0.854168	−	0.519998i
$68$	−13.3501	−	0.173998i	−1.61894	−	0.0211003i
$69$	6.42813	−	3.71128i	0.773856	−	0.446786i
$70$	−0.141013	+	21.6397i	−0.0168543	+	2.58644i
$71$	−5.08416	−	2.93534i	−0.603378	−	0.348361i	0.166991	−	0.985958i	$-0.446595\pi$
$71$	−5.08416	−	2.93534i	−0.603378	−	0.348361i	−0.770369	+	0.637598i	$0.779928\pi$
$72$	2.82789	+	0.0552894i	0.333270	+	0.00651592i
$73$	0.0425283	+	0.0736612i	0.00497756	+	0.00862139i	0.868503	−	0.495683i	$-0.165082\pi$
$73$	0.0425283	+	0.0736612i	0.00497756	+	0.00862139i	−0.863526	+	0.504305i	$0.831749\pi$
$74$	−1.00791	+	1.71977i	−0.117167	+	0.199919i
$75$	5.15329			0.595050
$76$	−0.110188	+	8.45425i	−0.0126394	+	0.969769i
$77$	11.8531	+	20.5303i	1.35079	+	2.33964i
$78$	−1.83156	−	1.07342i	−0.207383	−	0.121541i
$79$	1.33783	−	2.31720i	0.150518	−	0.260705i	−0.780900	−	0.624656i	$-0.785239\pi$
$79$	1.33783	−	2.31720i	0.150518	−	0.260705i	0.931418	+	0.363951i	$0.118573\pi$
$80$	11.2004	−	6.08300i	1.25225	−	0.680100i
$81$	1.00000			0.111111
$82$	−0.0486061	+	7.45901i	−0.00536764	+	0.823709i
$83$	2.66441	−	1.53830i	0.292457	−	0.168850i	−0.346592	−	0.938016i	$-0.612661\pi$
$83$	2.66441	−	1.53830i	0.292457	−	0.168850i	0.639049	+	0.769166i	$0.279328\pi$
$84$	4.69341	+	8.37956i	0.512093	+	0.914285i
$85$	−18.4216	+	10.6357i	−1.99810	+	1.15360i
$86$	6.53870	+	11.4977i	0.705086	+	1.23983i
$87$	2.65582	−	4.60001i	0.284734	−	0.493173i
$88$	7.21635	−	11.9532i	0.769265	−	1.27422i
$89$	−8.37066			−0.887288			−0.443644	−	0.896203i	$-0.646314\pi$
$89$	−8.37066			−0.887288			−0.443644	+	0.896203i	$0.646314\pi$
$90$	3.91715	−	2.22766i	0.412904	−	0.234816i
$91$		−	7.20879i		−	0.755687i
$92$	0.193466	−	14.8439i	0.0201702	−	1.54758i
$93$	0.397098	−	0.687793i	0.0411771	−	0.0713209i
$94$	0.0442589	−	6.79190i	0.00456496	−	0.700531i
$95$	6.73528	+	11.6658i	0.691025	+	1.19689i
$96$	2.98651	−	4.80424i	0.304810	−	0.490331i
$97$	12.2482	−	7.07150i	1.24362	−	0.718002i	0.273788	−	0.961790i	$-0.411723\pi$
$97$	12.2482	−	7.07150i	1.24362	−	0.718002i	0.969829	+	0.243788i	$0.0783900\pi$
$98$	−11.4850	+	19.5965i	−1.16016	+	1.97955i
$99$	2.46827	−	4.27516i	0.248070	−	0.429670i
$100$	5.26917	−	8.85784i	0.526917	−	0.885784i
$101$	2.62304	+	1.51442i	0.261003	+	0.150690i	0.624792	−	0.780791i	$-0.285184\pi$
$101$	2.62304	+	1.51442i	0.261003	+	0.150690i	−0.363789	+	0.931481i	$0.618517\pi$
$102$	−4.77356	+	8.14501i	−0.472653	+	0.806476i
$103$	−17.1845	−	9.92149i	−1.69324	−	0.977594i	−0.951871	−	0.306498i	$-0.900843\pi$
$103$	−17.1845	−	9.92149i	−1.69324	−	0.977594i	−0.741371	−	0.671096i	$-0.765824\pi$
$104$	−3.71782	+	2.05065i	−0.364562	+	0.201082i
$105$	13.2518	+	7.65094i	1.29325	+	0.746656i
$106$	−6.84960	+	3.89533i	−0.665292	+	0.378347i
$107$			7.96862i			0.770355i	0.922842	+	0.385178i	$0.125860\pi$
$107$			7.96862i			0.770355i	−0.922842	+	0.385178i	$0.874140\pi$
$108$	1.02249	−	1.71887i	0.0983889	−	0.165398i
$109$			0.0519742i			0.00497823i	0.999997	+	0.00248911i	$0.000792310\pi$
$109$			0.0519742i			0.00497823i	−0.999997	+	0.00248911i	$0.999208\pi$
$110$	0.144958	−	22.2449i	0.0138212	−	2.12097i
$111$	0.704760	+	1.22068i	0.0668928	+	0.115862i
$112$	19.2023	+	0.500629i	1.81445	+	0.0473050i
$113$	4.26288	+	2.46117i	0.401018	+	0.231528i	0.686923	−	0.726730i	$-0.258961\pi$
$113$	4.26288	+	2.46117i	0.401018	+	0.231528i	−0.285905	+	0.958258i	$0.592294\pi$
$114$	5.15800	+	3.02296i	0.483091	+	0.283126i
$115$	−11.8257	−	20.4827i	−1.10275	−	1.91002i
$116$	−5.19129	−	9.26847i	−0.481999	−	0.860555i
$117$	−1.30002	+	0.750569i	−0.120187	+	0.0693901i
$118$	6.71238	−	3.81729i	0.617925	−	0.351410i
$119$	−32.0578			−2.93874
$120$	0.176175	−	9.01084i	0.0160825	−	0.822574i
$121$	−6.68468	−	11.5782i	−0.607698	−	1.05256i
$122$	−10.2766	−	6.02284i	−0.930402	−	0.545282i
$123$	4.56779	+	2.63721i	0.411863	+	0.237789i
$124$	−0.776201	−	1.38582i	−0.0697049	−	0.124450i
$125$		−	0.488439i		−	0.0436873i
$126$	6.79121	+	0.0442545i	0.605009	+	0.00394250i
$127$	−1.52572	−	0.880873i	−0.135385	−	0.0781648i	0.430777	−	0.902458i	$-0.358239\pi$
$127$	−1.52572	−	0.880873i	−0.135385	−	0.0781648i	−0.566163	+	0.824293i	$0.691573\pi$
$128$	−5.20420	−	10.0457i	−0.459990	−	0.887924i
$129$	9.35287			0.823474
$130$	−3.42038	+	5.83611i	−0.299987	+	0.511861i
$131$			18.8890i			1.65034i	0.564884	+	0.825170i	$0.308921\pi$
$131$			18.8890i			1.65034i	−0.564884	+	0.825170i	$0.691079\pi$
$132$	−4.82468	−	8.61393i	−0.419935	−	0.749747i
$133$			20.3013i			1.76035i
$134$	−0.344515	+	11.5707i	−0.0297615	+	0.999557i
$135$		−	3.18642i		−	0.274244i
$136$	9.11932	+	16.5333i	0.781975	+	1.41772i
$137$		−	4.03905i		−	0.345080i	−0.985003	−	0.172540i	$-0.944803\pi$
$137$		−	4.03905i		−	0.345080i	0.985003	−	0.172540i	$-0.0551974\pi$
$138$	−9.05635	−	5.30767i	−0.770928	−	0.451819i
$139$	11.8276			1.00321			0.501604	−	0.865097i	$-0.332743\pi$
$139$	11.8276			1.00321			0.501604	+	0.865097i	$0.332743\pi$
$140$	26.7008	−	14.9552i	2.25663	−	1.26394i
$141$	−4.15926	−	2.40135i	−0.350273	−	0.202230i
$142$	−0.0541008	+	8.30222i	−0.00454004	+	0.696707i
$143$			7.41042i			0.619690i
$144$	−1.90904	−	3.51505i	−0.159086	−	0.292921i
$145$	−14.6576	−	8.46256i	−1.21725	−	0.702777i
$146$	0.0608217	−	0.103779i	0.00503364	−	0.00858878i
$147$	8.03064	+	13.9095i	0.662356	+	1.14723i
$148$	2.81880	+	0.0367386i	0.231704	+	0.00301989i
$149$	6.94608			0.569045			0.284523	−	0.958669i	$-0.408165\pi$
$149$	6.94608			0.569045			0.284523	+	0.958669i	$0.408165\pi$
$150$	−3.60272	−	6.33507i	−0.294161	−	0.517257i
$151$	−9.07534	+	5.23965i	−0.738541	+	0.426397i	−0.821539	−	0.570153i	$-0.806884\pi$
$151$	−9.07534	+	5.23965i	−0.738541	+	0.426397i	0.0829977	+	0.996550i	$0.473551\pi$
$152$	10.4701	−	5.77500i	0.849235	−	0.468415i
$153$	3.33782	+	5.78127i	0.269846	+	0.467388i
$154$	16.9517	−	28.9243i	1.36601	−	2.33079i
$155$	−2.19160	−	1.26532i	−0.176034	−	0.101633i
$156$	−0.0391266	+	3.00202i	−0.00313263	+	0.240354i
$157$	−2.56044	−	4.43481i	−0.204345	−	0.353936i	0.745579	−	0.666418i	$-0.232173\pi$
$157$	−2.56044	−	4.43481i	−0.204345	−	0.353936i	−0.949924	+	0.312481i	$0.898840\pi$
$158$	−3.78388	−	0.0246574i	−0.301030	−	0.00196164i
$159$			5.57183i			0.441875i
$160$	−15.3083	−	9.51630i	−1.21023	−	0.752329i
$161$		−	35.6447i		−	2.80920i
$162$	−0.699111	−	1.22933i	−0.0549273	−	0.0965850i
$163$	11.1484	+	6.43651i	0.873208	+	0.504147i	0.868413	−	0.495842i	$-0.165140\pi$
$163$	11.1484	+	6.43651i	0.873208	+	0.504147i	0.00479475	+	0.999989i	$0.498474\pi$
$164$	9.20353	−	5.15492i	0.718675	−	0.402532i
$165$	−13.6225	−	7.86494i	−1.06051	−	0.612285i
$166$	−3.75379	−	2.19999i	−0.291351	−	0.170752i
$167$	0.417022	+	0.240768i	0.0322701	+	0.0186312i	0.516048	−	0.856559i	$-0.327403\pi$
$167$	0.417022	+	0.240768i	0.0322701	+	0.0186312i	−0.483778	+	0.875191i	$0.660736\pi$
$168$	7.02000	−	11.6280i	0.541605	−	0.897118i
$169$	−5.37329	+	9.30681i	−0.413330	+	0.715909i
$170$	25.9535	+	15.2106i	1.99054	+	1.16660i
$171$	3.66111	−	2.11374i	0.279972	−	0.161642i
$172$	9.56320	−	16.0764i	0.729187	−	1.22581i
$173$	7.30608	+	12.6545i	0.555471	+	0.962103i	0.997867	+	0.0652837i	$0.0207952\pi$
$173$	7.30608	+	12.6545i	0.555471	+	0.962103i	−0.442396	+	0.896820i	$0.645871\pi$
$174$	−7.51163	−	0.0489490i	−0.569455	−	0.00371081i
$175$	12.3736	−	21.4317i	0.935356	−	1.62008i
$176$	−19.7394	−	0.514631i	−1.48791	−	0.0387918i
$177$		−	5.46021i		−	0.410414i
$178$	5.85202	+	10.2903i	0.438627	+	0.771288i
$179$	10.7114			0.800610			0.400305	−	0.916382i	$-0.368904\pi$
$179$	10.7114			0.800610			0.400305	+	0.916382i	$0.368904\pi$
$180$	−5.47705	−	3.25808i	−0.408235	−	0.242843i
$181$	2.99527	−	5.18797i	0.222637	−	0.385619i	−0.732971	−	0.680260i	$-0.761867\pi$
$181$	2.99527	−	5.18797i	0.222637	−	0.385619i	0.955608	+	0.294641i	$0.0952002\pi$
$182$	−8.86196	+	5.03974i	−0.656892	+	0.373571i
$183$	−7.29427	+	4.21135i	−0.539208	+	0.311312i
$184$	−18.3832	+	10.1397i	−1.35523	+	0.747507i
$185$	3.88960	−	2.24566i	0.285969	−	0.165104i
$186$	−1.12314	−	0.00731885i	−0.0823525	−	0.000536644i
$187$	32.9545			2.40987
$188$	−8.38040	+	4.69388i	−0.611204	+	0.342336i
$189$	2.40111	−	4.15884i	0.174655	−	0.302511i
$190$	9.63242	−	16.4356i	0.698809	−	1.19236i
$191$	9.06987	+	15.7095i	0.656273	+	1.13670i	0.981573	+	0.191087i	$0.0612013\pi$
$191$	9.06987	+	15.7095i	0.656273	+	1.13670i	−0.325300	+	0.945611i	$0.605465\pi$
$192$	−7.99389	−	0.312704i	−0.576909	−	0.0225675i
$193$	−8.74131			−0.629213			−0.314607	−	0.949222i	$-0.601873\pi$
$193$	−8.74131			−0.629213			−0.314607	+	0.949222i	$0.601873\pi$
$194$	−17.2560	−	10.1133i	−1.23891	−	0.726091i
$195$	2.39163	+	4.14243i	0.171268	+	0.296645i
$196$	32.1198	+	0.418631i	2.29427	+	0.0299022i
$197$	11.9922	+	6.92368i	0.854406	+	0.493292i	0.862135	−	0.506678i	$-0.169127\pi$
$197$	11.9922	+	6.92368i	0.854406	+	0.493292i	−0.00772872	+	0.999970i	$0.502460\pi$
$198$	−6.98116	−	0.0454922i	−0.496130	−	0.00323299i
$199$	−11.8573	+	6.84583i	−0.840543	+	0.485288i	−0.857449	−	0.514569i	$-0.827952\pi$
$199$	−11.8573	+	6.84583i	−0.840543	+	0.485288i	0.0169055	+	0.999857i	$0.494619\pi$
$200$	−14.5729	−	0.284922i	−1.03046	−	0.0201470i
$201$	6.99166	+	4.25637i	0.493154	+	0.300221i
$202$	0.0279120	−	4.28332i	0.00196388	−	0.301374i
$203$	−12.7538	−	22.0902i	−0.895142	−	1.55043i
$204$	13.3501	+	0.173998i	0.934696	+	0.0121823i
$205$	8.40327	−	14.5549i	0.586910	−	1.01656i
$206$	−0.182862	+	28.0616i	−0.0127406	+	1.95515i
$207$	−6.42813	+	3.71128i	−0.446786	+	0.257952i
$208$	5.12008	+	3.13678i	0.355014	+	0.217497i
$209$		−	20.8691i		−	1.44355i
$210$	0.141013	−	21.6397i	0.00973085	−	1.49328i
$211$	−7.13792	+	4.12108i	−0.491395	+	0.283707i	−0.725153	−	0.688588i	$-0.758231\pi$
$211$	−7.13792	+	4.12108i	−0.491395	+	0.283707i	0.233758	+	0.972295i	$0.424898\pi$
$212$	9.57726	+	5.69713i	0.657769	+	0.391280i
$213$	5.08416	+	2.93534i	0.348361	+	0.201126i
$214$	9.79603	−	5.57095i	0.669643	−	0.380822i
$215$		−	29.8022i		−	2.03249i
$216$	−2.82789	−	0.0552894i	−0.192413	−	0.00376197i
$217$	−1.90695	−	3.30293i	−0.129452	−	0.224218i
$218$	0.0638933	−	0.0363357i	0.00432740	−	0.00246097i
$219$	−0.0425283	−	0.0736612i	−0.00287380	−	0.00497756i
$220$	−27.4476	+	15.3735i	−1.85052	+	1.03648i
$221$	−8.67848	−	5.01052i	−0.583778	−	0.337044i
$222$	1.00791	−	1.71977i	0.0676464	−	0.115423i
$223$			11.7095i			0.784126i	0.919938	+	0.392063i	$0.128239\pi$
$223$			11.7095i			0.784126i	−0.919938	+	0.392063i	$0.871761\pi$
$224$	−12.8091	−	23.9559i	−0.855846	−	1.60062i
$225$	−5.15329			−0.343553
$226$	0.0453615	−	6.96110i	0.00301740	−	0.463046i
$227$	−21.4107	−	12.3615i	−1.42108	−	0.820461i	−0.424689	−	0.905339i	$-0.639617\pi$
$227$	−21.4107	−	12.3615i	−1.42108	−	0.820461i	−0.996391	+	0.0848777i	$0.972950\pi$
$228$	0.110188	−	8.45425i	0.00729736	−	0.559897i
$229$	−6.18629	+	3.57165i	−0.408801	+	0.236022i	−0.690275	−	0.723547i	$-0.742510\pi$
$229$	−6.18629	+	3.57165i	−0.408801	+	0.236022i	0.281473	+	0.959569i	$0.409177\pi$
$230$	−16.9125	+	28.8574i	−1.11518	+	1.90280i
$231$	−11.8531	−	20.5303i	−0.779880	−	1.35079i
$232$	−7.76468	+	12.8615i	−0.509777	+	0.844397i
$233$	12.4280	+	7.17529i	0.814183	+	0.470069i	0.848407	−	0.529345i	$-0.177562\pi$
$233$	12.4280	+	7.17529i	0.814183	+	0.470069i	−0.0342232	+	0.999414i	$0.510896\pi$
$234$	1.83156	+	1.07342i	0.119733	+	0.0701718i
$235$	−7.65171	+	13.2532i	−0.499143	+	0.864541i
$236$	−9.38540	−	5.58300i	−0.610937	−	0.363422i
$237$	−1.33783	+	2.31720i	−0.0869016	+	0.150518i
$238$	22.4120	+	39.4095i	1.45275	+	2.55454i
$239$	13.5434	−	23.4579i	0.876050	−	1.51736i	0.0204093	−	0.999792i	$-0.493503\pi$
$239$	13.5434	−	23.4579i	0.876050	−	1.51736i	0.855640	−	0.517571i	$-0.173164\pi$
$240$	−11.2004	+	6.08300i	−0.722985	+	0.392656i
$241$	−13.8862			−0.894486			−0.447243	−	0.894412i	$-0.647594\pi$
$241$	−13.8862			−0.894486			−0.447243	+	0.894412i	$0.647594\pi$
$242$	−9.56006	+	16.3121i	−0.614544	+	1.04858i
$243$	−1.00000			−0.0641500
$244$	−0.219534	+	16.8440i	−0.0140542	+	1.07832i
$245$	44.3215	−	25.5890i	2.83159	−	1.63482i
$246$	0.0486061	−	7.45901i	0.00309901	−	0.475569i
$247$	−3.17302	+	5.49583i	−0.201894	+	0.349691i
$248$	−1.16098	+	1.92305i	−0.0737220	+	0.122114i
$249$	−2.66441	+	1.53830i	−0.168850	+	0.0974858i
$250$	−0.600451	+	0.341473i	−0.0379758	+	0.0215966i
$251$	2.31310	+	4.00640i	0.146001	+	0.252882i	0.929746	−	0.368201i	$-0.120026\pi$
$251$	2.31310	+	4.00640i	0.146001	+	0.252882i	−0.783745	+	0.621083i	$0.786693\pi$
$252$	−4.69341	−	8.37956i	−0.295657	−	0.527863i
$253$			36.6417i			2.30365i
$254$	−0.0162352	+	2.49143i	−0.00101869	+	0.156326i
$255$	18.4216	−	10.6357i	1.15360	−	0.666033i
$256$	−8.71115	+	13.4207i	−0.544447	+	0.838795i
$257$	14.5163	−	25.1430i	0.905504	−	1.56838i	0.0852657	−	0.996358i	$-0.472826\pi$
$257$	14.5163	−	25.1430i	0.905504	−	1.56838i	0.820239	−	0.572021i	$-0.193841\pi$
$258$	−6.53870	−	11.4977i	−0.407081	−	0.715818i
$259$	6.76882			0.420594
$260$	9.56571	+	0.124674i	0.593240	+	0.00773194i
$261$	−2.65582	+	4.60001i	−0.164391	+	0.284734i
$262$	23.2208	−	13.2055i	1.43458	−	0.815839i
$263$			18.2753i			1.12690i	0.826150	+	0.563450i	$0.190526\pi$
$263$			18.2753i			1.12690i	−0.826150	+	0.563450i	$0.809474\pi$
$264$	−7.21635	+	11.9532i	−0.444136	+	0.735669i
$265$	17.7542			1.09063
$266$	24.9569	−	14.1929i	1.53021	−	0.870220i
$267$	8.37066			0.512276
$268$	14.4650	−	7.66569i	0.883593	−	0.468256i
$269$	−30.4479			−1.85644			−0.928221	−	0.372029i	$-0.878662\pi$
$269$	−30.4479			−1.85644			−0.928221	+	0.372029i	$0.878662\pi$
$270$	−3.91715	+	2.22766i	−0.238390	+	0.135571i
$271$	−3.90668			−0.237314			−0.118657	−	0.992935i	$-0.537859\pi$
$271$	−3.90668			−0.237314			−0.118657	+	0.992935i	$0.537859\pi$
$272$	13.9494	−	22.7692i	0.845808	−	1.38059i
$273$			7.20879i			0.436296i
$274$	−4.96532	+	2.82375i	−0.299966	+	0.170589i
$275$	−12.7197	+	22.0311i	−0.767026	+	1.32853i
$276$	−0.193466	+	14.8439i	−0.0116453	+	0.893496i
$277$	−9.87146			−0.593119			−0.296559	−	0.955014i	$-0.595839\pi$
$277$	−9.87146			−0.593119			−0.296559	+	0.955014i	$0.595839\pi$
$278$	−8.26884	−	14.5400i	−0.495932	−	0.872054i
$279$	−0.397098	+	0.687793i	−0.0237736	+	0.0411771i
$280$	−37.0516	−	22.3687i	−2.21426	−	1.33678i
$281$	−9.02229	+	5.20902i	−0.538224	+	0.310744i	−0.744359	−	0.667780i	$-0.767245\pi$
$281$	−9.02229	+	5.20902i	−0.538224	+	0.310744i	0.206135	+	0.978524i	$0.433912\pi$
$282$	−0.0442589	+	6.79190i	−0.00263558	+	0.404452i
$283$			20.9096i			1.24295i	0.783435	+	0.621473i	$0.213465\pi$
$283$			20.9096i			1.24295i	−0.783435	+	0.621473i	$0.786535\pi$
$284$	10.2440	−	5.73766i	0.607867	−	0.340468i
$285$	−6.73528	−	11.6658i	−0.398963	−	0.691025i
$286$	9.10982	−	5.18070i	0.538675	−	0.306341i
$287$	21.9355	−	12.6645i	1.29481	−	0.747560i
$288$	−2.98651	+	4.80424i	−0.175982	+	0.283093i
$289$	−13.7820	+	23.8712i	−0.810708	+	1.40419i
$290$	−0.155972	+	23.9352i	−0.00915900	+	1.40552i
$291$	−12.2482	+	7.07150i	−0.718002	+	0.414539i
$292$	−0.170099	−	0.00221697i	−0.00995428	−	0.000129738i
$293$	−11.1507			−0.651434			−0.325717	−	0.945467i	$-0.605606\pi$
$293$	−11.1507			−0.651434			−0.325717	+	0.945467i	$0.605606\pi$
$294$	11.4850	−	19.5965i	0.669818	−	1.14289i
$295$	−17.3985			−1.01298
$296$	−1.92549	−	3.49091i	−0.111917	−	0.202905i
$297$	−2.46827	+	4.27516i	−0.143223	+	0.248070i
$298$	−4.85608	−	8.53901i	−0.281305	−	0.494651i
$299$	5.57115	−	9.64951i	0.322188	−	0.558046i
$300$	−5.26917	+	8.85784i	−0.304216	+	0.511408i
$301$	22.4573	−	38.8971i	1.29441	−	2.24199i
$302$	12.7859	+	7.49346i	0.735747	+	0.431200i
$303$	−2.62304	−	1.51442i	−0.150690	−	0.0870009i
$304$	−14.4191	−	8.83377i	−0.826993	−	0.506651i
$305$	13.4191	+	23.2426i	0.768377	+	1.33087i
$306$	4.77356	−	8.14501i	0.272886	−	0.465619i
$307$	19.3296	−	11.1599i	1.10320	−	0.636932i	0.166139	−	0.986102i	$-0.446870\pi$
$307$	19.3296	−	11.1599i	1.10320	−	0.636932i	0.937059	+	0.349170i	$0.113537\pi$
$308$	−47.4086	−	0.617895i	−2.70135	−	0.0352078i
$309$	17.1845	+	9.92149i	0.977594	+	0.564414i
$310$	−0.0233209	+	3.57879i	−0.00132454	+	0.203262i
$311$	26.8528			1.52268			0.761342	−	0.648351i	$-0.224541\pi$
$311$	26.8528			1.52268			0.761342	+	0.648351i	$0.224541\pi$
$312$	3.71782	−	2.05065i	0.210480	−	0.116095i
$313$			26.2539i			1.48396i	0.670422	+	0.741980i	$0.266113\pi$
$313$			26.2539i			1.48396i	−0.670422	+	0.741980i	$0.733887\pi$
$314$	−3.66180	+	6.24804i	−0.206647	+	0.352597i
$315$	−13.2518	−	7.65094i	−0.746656	−	0.431082i
$316$	2.61504	+	4.66887i	0.147108	+	0.262644i
$317$	12.6695	+	21.9443i	0.711592	+	1.23251i	0.964259	+	0.264960i	$0.0853587\pi$
$317$	12.6695	+	21.9443i	0.711592	+	1.23251i	−0.252668	+	0.967553i	$0.581308\pi$
$318$	6.84960	−	3.89533i	0.384106	−	0.218439i
$319$	13.1105	+	22.7081i	0.734049	+	1.27141i
$320$	−0.996408	+	25.4719i	−0.0557009	+	1.42392i
$321$		−	7.96862i		−	0.444765i
$322$	−43.8190	+	24.9196i	−2.44194	+	1.38872i
$323$	24.4402	+	14.1106i	1.35989	+	0.785133i
$324$	−1.02249	+	1.71887i	−0.0568049	+	0.0954929i
$325$	6.69940	−	3.86790i	0.371616	−	0.214552i
$326$	0.118630	−	18.2048i	0.00657033	−	1.00827i
$327$		−	0.0519742i		−	0.00287418i
$328$	−12.7714	−	7.71029i	−0.705181	−	0.425729i
$329$	−19.9737	+	11.5318i	−1.10118	+	0.635769i
$330$	−0.144958	+	22.2449i	−0.00797965	+	1.22454i
$331$	11.2686	−	19.5178i	0.619379	−	1.07280i	−0.370220	−	0.928944i	$-0.620718\pi$
$331$	11.2686	−	19.5178i	0.619379	−	1.07280i	0.989599	−	0.143852i	$-0.0459490\pi$
$332$	−0.0801903	+	6.15267i	−0.00440102	+	0.337672i
$333$	−0.704760	−	1.22068i	−0.0386206	−	0.0668928i
$334$	0.00443756	−	0.680980i	0.000242812	−	0.0372616i
$335$	13.5626	−	22.2784i	0.741003	−	1.21720i
$336$	−19.2023	−	0.500629i	−1.04757	−	0.0273115i
$337$	19.3137	−	11.1508i	1.05209	−	0.607422i	0.128853	−	0.991664i	$-0.458870\pi$
$337$	19.3137	−	11.1508i	1.05209	−	0.607422i	0.923233	+	0.384241i	$0.125537\pi$
$338$	15.1976	+	0.0990343i	0.826643	+	0.00538676i
$339$	−4.26288	−	2.46117i	−0.231528	−	0.133673i
$340$	0.554430	−	42.5392i	0.0300682	−	2.30701i
$341$	1.96029	+	3.39531i	0.106155	+	0.183867i
$342$	−5.15800	−	3.02296i	−0.278913	−	0.163463i
$343$	43.5142			2.34955
$344$	−26.4489	−	0.517115i	−1.42603	−	0.0278810i
$345$	11.8257	+	20.4827i	0.636675	+	1.10275i
$346$	10.4487	−	17.8285i	0.561728	−	0.958463i
$347$	−13.9078	+	24.0890i	−0.746608	+	1.29316i	0.202832	+	0.979214i	$0.434986\pi$
$347$	−13.9078	+	24.0890i	−0.746608	+	1.29316i	−0.949440	+	0.313949i	$0.898348\pi$
$348$	5.19129	+	9.26847i	0.278282	+	0.496842i
$349$	8.68364			0.464825			0.232412	−	0.972617i	$-0.425338\pi$
$349$	8.68364			0.464825			0.232412	+	0.972617i	$0.425338\pi$
$350$	−34.9971	−	0.228056i	−1.87067	−	0.0121901i
$351$	1.30002	−	0.750569i	0.0693901	−	0.0400624i
$352$	13.1674	+	24.6260i	0.701825	+	1.31257i
$353$	−20.9381	+	12.0886i	−1.11442	+	0.643413i	−0.939971	−	0.341253i	$-0.889149\pi$
$353$	−20.9381	+	12.0886i	−1.11442	+	0.643413i	−0.174452	+	0.984666i	$0.555815\pi$
$354$	−6.71238	+	3.81729i	−0.356759	+	0.202887i
$355$	9.35323	−	16.2003i	0.496418	−	0.859821i
$356$	8.55889	−	14.3881i	0.453620	−	0.762567i
$357$	32.0578			1.69668
$358$	−7.48848	−	13.1679i	−0.395779	−	0.695943i
$359$		−	8.15691i		−	0.430505i	−0.976558	−	0.215253i	$-0.930943\pi$
$359$		−	8.15691i		−	0.430505i	0.976558	−	0.215253i	$-0.0690575\pi$
$360$	−0.176175	+	9.01084i	−0.00928526	+	0.474913i
$361$	−0.564183	+	0.977193i	−0.0296938	+	0.0514312i
$362$	−8.47174	−	0.0552055i	−0.445265	−	0.00290153i
$363$	6.68468	+	11.5782i	0.350855	+	0.607698i
$364$	12.3910	+	7.37090i	0.649464	+	0.386340i
$365$	−0.234716	+	0.135513i	−0.0122856	+	0.00709309i
$366$	10.2766	+	6.02284i	0.537168	+	0.314819i
$367$	−5.76594	+	9.98691i	−0.300980	+	0.521312i	−0.976358	−	0.216159i	$-0.930647\pi$
$367$	−5.76594	+	9.98691i	−0.300980	+	0.521312i	0.675378	+	0.737471i	$0.263980\pi$
$368$	25.3169	+	15.5102i	1.31973	+	0.808526i
$369$	−4.56779	−	2.63721i	−0.237789	−	0.137288i
$370$	−5.47991	−	3.21162i	−0.284887	−	0.166964i
$371$	23.1723	+	13.3786i	1.20305	+	0.694580i
$372$	0.776201	+	1.38582i	0.0402441	+	0.0718514i
$373$	−5.41635	−	3.12713i	−0.280448	−	0.161917i	0.353178	−	0.935556i	$-0.385101\pi$
$373$	−5.41635	−	3.12713i	−0.280448	−	0.161917i	−0.633626	+	0.773639i	$0.718434\pi$
$374$	−23.0388	−	40.5118i	−1.19131	−	2.09482i
$375$			0.488439i			0.0252229i
$376$	11.6291	+	7.02071i	0.599727	+	0.362065i
$377$		−	7.97350i		−	0.410656i
$378$	−6.79121	−	0.0442545i	−0.349302	−	0.00227620i
$379$	7.69494	+	13.3280i	0.395263	+	0.684615i	0.993135	−	0.116977i	$-0.0373203\pi$
$379$	7.69494	+	13.3280i	0.395263	+	0.684615i	−0.597872	+	0.801592i	$0.703987\pi$
$380$	−26.9388	−	0.351105i	−1.38193	−	0.0180113i
$381$	1.52572	+	0.880873i	0.0781648	+	0.0451285i
$382$	12.9712	−	22.1325i	0.663666	−	1.13240i
$383$	9.68247	+	16.7705i	0.494751	+	0.856934i	0.999982	−	0.00605055i	$-0.00192596\pi$
$383$	9.68247	+	16.7705i	0.494751	+	0.856934i	−0.505231	+	0.862984i	$0.668593\pi$
$384$	5.20420	+	10.0457i	0.265576	+	0.512643i
$385$	−65.4181	+	37.7691i	−3.33401	+	1.92489i
$386$	6.11115	+	10.7459i	0.311049	+	0.546953i
$387$	−9.35287			−0.475433
$388$	−0.368632	+	28.2836i	−0.0187144	+	1.43588i
$389$	0.503042	+	0.871295i	0.0255053	+	0.0441764i	0.878496	−	0.477749i	$-0.158547\pi$
$389$	0.503042	+	0.871295i	0.0255053	+	0.0441764i	−0.852991	+	0.521926i	$0.825214\pi$
$390$	3.42038	−	5.83611i	0.173198	−	0.295523i
$391$	−42.9118	−	24.7751i	−2.17014	−	1.25293i
$392$	−21.9407	−	39.7784i	−1.10817	−	2.00911i
$393$		−	18.8890i		−	0.952824i
$394$	0.127609	−	19.5827i	0.00642886	−	0.986563i
$395$	7.38356	+	4.26290i	0.371507	+	0.214490i
$396$	4.82468	+	8.61393i	0.242449	+	0.432866i
$397$	−27.2887			−1.36958			−0.684791	−	0.728740i	$-0.740106\pi$
$397$	−27.2887			−1.36958			−0.684791	+	0.728740i	$0.740106\pi$
$398$	16.7053	+	9.79053i	0.837363	+	0.490755i
$399$		−	20.3013i		−	1.01634i
$400$	9.83782	+	18.1141i	0.491891	+	0.905703i
$401$			11.4119i			0.569881i	0.958545	+	0.284941i	$0.0919739\pi$
$401$			11.4119i			0.569881i	−0.958545	+	0.284941i	$0.908026\pi$
$402$	0.344515	−	11.5707i	0.0171828	−	0.577095i
$403$		−	1.19220i		−	0.0593876i
$404$	−5.28512	+	2.96020i	−0.262944	+	0.147276i
$405$			3.18642i			0.158335i
$406$	−18.2398	+	31.1221i	−0.905226	+	1.54457i
$407$	−6.95814			−0.344902
$408$	−9.11932	−	16.5333i	−0.451474	−	0.818521i
$409$	−9.57579	−	5.52859i	−0.473492	−	0.273371i	0.244208	−	0.969723i	$-0.421472\pi$
$409$	−9.57579	−	5.52859i	−0.473492	−	0.273371i	−0.717701	+	0.696352i	$0.754805\pi$
$410$	−23.7675	−	0.154879i	−1.17380	−	0.00764895i
$411$			4.03905i			0.199232i
$412$	34.6247	−	19.3934i	1.70584	−	0.955444i
$413$	−22.7081	−	13.1105i	−1.11739	−	0.645128i
$414$	9.05635	+	5.30767i	0.445095	+	0.260858i
$415$	4.90167	+	8.48994i	0.240614	+	0.416755i
$416$	0.276626	−	8.48721i	0.0135627	−	0.416120i
$417$	−11.8276			−0.579202
$418$	−25.6550	+	14.5898i	−1.25483	+	0.713612i
$419$	26.0513	−	15.0407i	1.27269	−	0.734786i	0.297194	−	0.954817i	$-0.403949\pi$
$419$	26.0513	−	15.0407i	1.27269	−	0.734786i	0.975493	+	0.220031i	$0.0706158\pi$
$420$	−26.7008	+	14.9552i	−1.30287	+	0.729738i
$421$	7.85077	+	13.5979i	0.382623	+	0.662722i	0.991436	−	0.130591i	$-0.0416875\pi$
$421$	7.85077	+	13.5979i	0.382623	+	0.662722i	−0.608813	+	0.793313i	$0.708354\pi$
$422$	10.0564	+	5.89374i	0.489536	+	0.286903i
$423$	4.15926	+	2.40135i	0.202230	+	0.116758i
$424$	0.308063	−	15.7565i	0.0149609	−	0.765203i
$425$	−17.2007	−	29.7925i	−0.834358	−	1.44515i
$426$	0.0541008	−	8.30222i	0.00262119	−	0.402244i
$427$			40.4476i			1.95740i
$428$	−13.6970	−	8.14781i	−0.662071	−	0.393839i
$429$		−	7.41042i		−	0.357778i
$430$	−36.6366	+	20.8350i	−1.76678	+	1.00476i
$431$	−9.93403	−	5.73542i	−0.478506	−	0.276265i	0.241288	−	0.970454i	$-0.422430\pi$
$431$	−9.93403	−	5.73542i	−0.478506	−	0.276265i	−0.719793	+	0.694188i	$0.755764\pi$
$432$	1.90904	+	3.51505i	0.0918486	+	0.169118i
$433$	−14.6141	−	8.43745i	−0.702308	−	0.405478i	0.105898	−	0.994377i	$-0.466228\pi$
$433$	−14.6141	−	8.43745i	−0.702308	−	0.405478i	−0.808207	+	0.588899i	$0.799562\pi$
$434$	−2.72721	+	4.65338i	−0.130910	+	0.223369i
$435$	14.6576	+	8.46256i	0.702777	+	0.405749i
$436$	−0.0893370	−	0.0531430i	−0.00427847	−	0.00254509i
$437$	−15.6894	+	27.1748i	−0.750525	+	1.29995i
$438$	−0.0608217	+	0.103779i	−0.00290617	+	0.00495873i
$439$	−5.62622	+	3.24830i	−0.268525	+	0.155033i	−0.628217	−	0.778038i	$-0.716215\pi$
$439$	−5.62622	+	3.24830i	−0.268525	+	0.155033i	0.359692	+	0.933071i	$0.382882\pi$
$440$	38.0880	+	22.9943i	1.81577	+	1.09621i
$441$	−8.03064	−	13.9095i	−0.382411	−	0.662356i
$442$	−0.0923482	+	14.1716i	−0.00439256	+	0.674074i
$443$	3.84527	−	6.66020i	0.182694	−	0.316436i	−0.760103	−	0.649803i	$-0.774852\pi$
$443$	3.84527	−	6.66020i	0.182694	−	0.316436i	0.942797	+	0.333367i	$0.108185\pi$
$444$	−2.81880	−	0.0367386i	−0.133774	−	0.00174354i
$445$		−	26.6724i		−	1.26440i
$446$	14.3948	−	8.18624i	0.681614	−	0.387630i
$447$	−6.94608			−0.328539
$448$	−20.4947	+	32.4945i	−0.968282	+	1.53522i
$449$	−8.92877	+	15.4651i	−0.421375	+	0.729842i	−0.996074	−	0.0885223i	$-0.971786\pi$
$449$	−8.92877	+	15.4651i	−0.421375	+	0.729842i	0.574700	+	0.818364i	$0.305119\pi$
$450$	3.60272	+	6.33507i	0.169834	+	0.298638i
$451$	−22.5490	+	13.0187i	−1.06179	+	0.613026i
$452$	−8.58918	+	4.81082i	−0.404001	+	0.226282i
$453$	9.07534	−	5.23965i	0.426397	−	0.246180i
$454$	−0.227833	+	34.9629i	−0.0106927	+	1.64089i
$455$	22.9702			1.07686
$456$	−10.4701	+	5.77500i	−0.490306	+	0.270439i
$457$	11.6293	−	20.1425i	0.543995	−	0.942228i	−0.454674	−	0.890658i	$-0.650244\pi$
$457$	11.6293	−	20.1425i	0.543995	−	0.942228i	0.998669	−	0.0515698i	$-0.0164225\pi$
$458$	8.71563	+	5.10798i	0.407255	+	0.238680i
$459$	−3.33782	−	5.78127i	−0.155796	−	0.269846i
$460$	47.2988	+	0.616465i	2.20532	+	0.0287428i
$461$	17.3150			0.806442			0.403221	−	0.915103i	$-0.367891\pi$
$461$	17.3150			0.806442			0.403221	+	0.915103i	$0.367891\pi$
$462$	−16.9517	+	28.9243i	−0.788665	+	1.34568i
$463$	11.7013	+	20.2672i	0.543803	+	0.941895i	0.998681	+	0.0513411i	$0.0163496\pi$
$463$	11.7013	+	20.2672i	0.543803	+	0.941895i	−0.454878	+	0.890554i	$0.650317\pi$
$464$	21.2393	+	0.553736i	0.986011	+	0.0257065i
$465$	2.19160	+	1.26532i	0.101633	+	0.0586779i
$466$	0.132247	−	20.2944i	0.00612621	−	0.940118i
$467$	−6.20091	+	3.58010i	−0.286944	+	0.165667i	−0.636563	−	0.771225i	$-0.719644\pi$
$467$	−6.20091	+	3.58010i	−0.286944	+	0.165667i	0.349619	+	0.936892i	$0.386311\pi$
$468$	0.0391266	−	3.00202i	0.00180863	−	0.138768i
$469$	34.4893	−	18.8572i	1.59257	−	0.870746i
$470$	21.6419	+	0.141028i	0.998264	+	0.00650512i
$471$	2.56044	+	4.43481i	0.117979	+	0.204345i
$472$	−0.301892	+	15.4408i	−0.0138957	+	0.710723i
$473$	−23.0854	+	39.9850i	−1.06147	+	1.83851i
$474$	3.78388	+	0.0246574i	0.173800	+	0.00113255i
$475$	−18.8668	+	10.8927i	−0.865666	+	0.499792i
$476$	32.7787	−	55.1033i	1.50241	−	2.52565i
$477$		−	5.57183i		−	0.255116i
$478$	−38.3057	−	0.249616i	−1.75206	−	0.0114172i
$479$	−37.3905	+	21.5874i	−1.70841	+	0.986353i	−0.771886	+	0.635760i	$0.780687\pi$
$479$	−37.3905	+	21.5874i	−1.70841	+	0.986353i	−0.936528	+	0.350593i	$0.885980\pi$
$480$	15.3083	+	9.51630i	0.698727	+	0.434358i
$481$	1.83241	+	1.05794i	0.0835507	+	0.0482380i
$482$	9.70797	+	17.0706i	0.442186	+	0.777546i
$483$			35.6447i			1.62189i
$484$	26.7364	+	0.348467i	1.21529	+	0.0158394i
$485$	22.5328	+	39.0279i	1.02316	+	1.77217i
$486$	0.699111	+	1.22933i	0.0317123	+	0.0557634i
$487$	−11.2102	−	19.4166i	−0.507981	−	0.879849i	−0.999957	−	0.00924016i	$-0.997059\pi$
$487$	−11.2102	−	19.4166i	−0.507981	−	0.879849i	0.491976	−	0.870609i	$-0.336275\pi$
$488$	20.8602	−	11.5059i	0.944297	−	0.520848i
$489$	−11.1484	−	6.43651i	−0.504147	−	0.291069i
$490$	−62.4429	−	36.5960i	−2.82088	−	1.65324i
$491$			32.4354i			1.46379i	0.681417	+	0.731895i	$0.261364\pi$
$491$			32.4354i			1.46379i	−0.681417	+	0.731895i	$0.738636\pi$
$492$	−9.20353	+	5.15492i	−0.414927	+	0.232402i
$493$	−35.4585			−1.59697
$494$	8.97447	+	0.0584815i	0.403780	+	0.00263121i
$495$	13.6225	+	7.86494i	0.612285	+	0.353503i
$496$	3.17570	+	0.0827945i	0.142593	+	0.00371758i
$497$	24.4152	−	14.0961i	1.09517	−	0.632298i
$498$	3.75379	+	2.19999i	0.168211	+	0.0985840i
$499$	2.24126	+	3.88198i	0.100333	+	0.173781i	0.911822	−	0.410586i	$-0.134676\pi$
$499$	2.24126	+	3.88198i	0.100333	+	0.173781i	−0.811489	+	0.584368i	$0.801343\pi$
$500$	0.839564	+	0.499423i	0.0375464	+	0.0223349i
$501$	−0.417022	−	0.240768i	−0.0186312	−	0.0107567i
$502$	3.30806	−	5.64447i	0.147646	−	0.251925i
$503$	16.9395	−	29.3401i	0.755296	−	1.30821i	−0.189931	−	0.981798i	$-0.560826\pi$
$503$	16.9395	−	29.3401i	0.755296	−	1.30821i	0.945227	−	0.326414i	$-0.105840\pi$
$504$	−7.02000	+	11.6280i	−0.312696	+	0.517951i
$505$	−4.82557	+	8.35813i	−0.214735	+	0.371932i
$506$	45.0446	−	25.6166i	2.00248	−	1.13880i
$507$	5.37329	−	9.30681i	0.238636	−	0.413330i
$508$	3.07413	−	1.72183i	0.136393	−	0.0763938i
$509$	7.35225			0.325883			0.162941	−	0.986636i	$-0.447902\pi$
$509$	7.35225			0.325883			0.162941	+	0.986636i	$0.447902\pi$
$510$	−25.9535	−	15.2106i	−1.14924	−	0.673536i
$511$	−0.408460			−0.0180692
$512$	22.5885	+	1.32627i	0.998281	+	0.0586134i
$513$	−3.66111	+	2.11374i	−0.161642	+	0.0933240i
$514$	−41.0575	−	0.267548i	−1.81097	−	0.0118011i
$515$	31.6141	−	54.7572i	1.39308	−	2.41289i
$516$	−9.56320	+	16.0764i	−0.420996	+	0.707723i
$517$	20.5323	−	11.8543i	0.903010	−	0.521353i
$518$	−4.73215	−	8.32109i	−0.207919	−	0.365608i
$519$	−7.30608	−	12.6545i	−0.320701	−	0.555471i
$520$	−6.53423	−	11.8465i	−0.286545	−	0.519505i
$521$		−	30.9702i		−	1.35683i	−0.734678	−	0.678416i	$-0.762667\pi$
$521$		−	30.9702i		−	1.35683i	0.734678	−	0.678416i	$-0.237333\pi$
$522$	7.51163	+	0.0489490i	0.328775	+	0.00214244i
$523$	25.8887	−	14.9468i	1.13203	−	0.653580i	0.187588	−	0.982248i	$-0.439933\pi$
$523$	25.8887	−	14.9468i	1.13203	−	0.653580i	0.944445	+	0.328668i	$0.106600\pi$
$524$	−32.4678	−	19.3138i	−1.41836	−	0.843726i
$525$	−12.3736	+	21.4317i	−0.540028	+	0.935356i
$526$	22.4663	−	12.7764i	0.979576	−	0.557079i
$527$	−5.30176			−0.230948
$528$	19.7394	+	0.514631i	0.859048	+	0.0223965i
$529$	16.0472	−	27.7946i	0.697705	−	1.20846i
$530$	−12.4122	−	21.8257i	−0.539149	−	0.948048i
$531$			5.46021i			0.236953i
$532$	−34.8953	−	20.7578i	−1.51290	−	0.899966i
$533$	7.91764			0.342951
$534$	−5.85202	−	10.2903i	−0.253242	−	0.445304i
$535$	−25.3914			−1.09777
$536$	−19.5363	−	12.4231i	−0.843840	−	0.536595i
$537$	−10.7114			−0.462233
$538$	21.2865	+	37.4304i	0.917725	+	1.61374i
$539$	−79.2870			−3.41513
$540$	5.47705	+	3.25808i	0.235695	+	0.140205i
$541$		−	10.5943i		−	0.455482i	−0.973722	−	0.227741i	$-0.926866\pi$
$541$		−	10.5943i		−	0.455482i	0.973722	−	0.227741i	$-0.0731340\pi$
$542$	2.73120	+	4.80259i	0.117315	+	0.206289i
$543$	−2.99527	+	5.18797i	−0.128540	+	0.222637i
$544$	−37.7430	−	1.23017i	−1.61822	−	0.0527430i
$545$	−0.165612			−0.00709403
$546$	8.86196	−	5.03974i	0.379257	−	0.215681i
$547$	−10.1419	+	17.5663i	−0.433638	+	0.751082i	−0.997183	−	0.0750025i	$-0.976104\pi$
$547$	−10.1419	+	17.5663i	−0.433638	+	0.751082i	0.563546	+	0.826085i	$0.309437\pi$
$548$	6.94262	+	4.12988i	0.296574	+	0.176420i
$549$	7.29427	−	4.21135i	0.311312	−	0.179736i
$550$	35.9759	+	0.234435i	1.53402	+	0.00999633i
$551$			22.4549i			0.956609i
$552$	18.3832	−	10.1397i	0.782441	−	0.431573i
$553$	6.42456	+	11.1277i	0.273200	+	0.473197i
$554$	6.90125	+	12.1352i	0.293206	+	0.515577i
$555$	−3.88960	+	2.24566i	−0.165104	+	0.0953230i
$556$	−12.0936	+	20.3302i	−0.512884	+	0.862193i
$557$	18.4798	−	32.0080i	0.783015	−	1.35622i	−0.147162	−	0.989112i	$-0.547014\pi$
$557$	18.4798	−	32.0080i	0.783015	−	1.35622i	0.930177	−	0.367110i	$-0.119653\pi$
$558$	1.12314	+	0.00731885i	0.0475462	+	0.000309832i
$559$	12.1590	−	7.01998i	0.514269	−	0.296913i
$560$	−1.59522	+	61.1868i	−0.0674101	+	2.58561i
$561$	−32.9545			−1.39134
$562$	12.7112	+	7.44965i	0.536188	+	0.314245i
$563$	−18.3197			−0.772084			−0.386042	−	0.922481i	$-0.626158\pi$
$563$	−18.3197			−0.772084			−0.386042	+	0.922481i	$0.626158\pi$
$564$	8.38040	−	4.69388i	0.352879	−	0.197648i
$565$	−7.84234	+	13.5833i	−0.329930	+	0.571455i
$566$	25.7047	−	14.6181i	1.08045	−	0.614446i
$567$	−2.40111	+	4.15884i	−0.100837	+	0.174655i
$568$	−14.2151	−	8.58191i	−0.596453	−	0.360089i
$569$	−23.0582	+	39.9380i	−0.966651	+	1.67429i	−0.261540	+	0.965193i	$0.584230\pi$
$569$	−23.0582	+	39.9380i	−0.966651	+	1.67429i	−0.705111	+	0.709097i	$0.749103\pi$
$570$	−9.63242	+	16.4356i	−0.403458	+	0.688410i
$571$	27.5973	+	15.9333i	1.15491	+	0.666789i	0.950080	−	0.312008i	$-0.101001\pi$
$571$	27.5973	+	15.9333i	1.15491	+	0.666789i	0.204833	+	0.978797i	$0.434335\pi$
$572$	−12.7376	−	7.57706i	−0.532584	−	0.316813i
$573$	−9.06987	−	15.7095i	−0.378899	−	0.656273i
$574$	−30.9041	−	18.1120i	−1.28991	−	0.755981i
$575$	33.1260	−	19.1253i	1.38145	−	0.797580i
$576$	7.99389	+	0.312704i	0.333079	+	0.0130294i
$577$	−19.9183	−	11.4999i	−0.829212	−	0.478746i	0.0243710	−	0.999703i	$-0.492242\pi$
$577$	−19.9183	−	11.4999i	−0.829212	−	0.478746i	−0.853583	+	0.520957i	$0.825575\pi$
$578$	38.9806	+	0.254015i	1.62138	+	0.0105656i
$579$	8.74131			0.363277
$580$	29.5332	−	16.5416i	1.22630	−	0.686854i
$581$			14.7745i			0.612949i
$582$	17.2560	+	10.1133i	0.715286	+	0.419209i
$583$	−23.8205	−	13.7528i	−0.986543	−	0.569581i
$584$	0.116193	+	0.210657i	0.00480808	+	0.00871705i
$585$	−2.39163	−	4.14243i	−0.0988817	−	0.171268i
$586$	7.79561	+	13.7079i	0.322034	+	0.566269i
$587$	16.8758	+	29.2297i	0.696537	+	1.20644i	0.969660	+	0.244459i	$0.0786103\pi$
$587$	16.8758	+	29.2297i	0.696537	+	1.20644i	−0.273122	+	0.961979i	$0.588056\pi$
$588$	−32.1198	−	0.418631i	−1.32460	−	0.0172640i
$589$			3.35745i			0.138341i
$590$	12.1635	+	21.3885i	0.500763	+	0.880550i
$591$	−11.9922	−	6.92368i	−0.493292	−	0.284802i
$592$	−2.94534	+	4.80759i	−0.121053	+	0.197591i
$593$	−20.8005	+	12.0092i	−0.854173	+	0.493157i	−0.862057	−	0.506812i	$-0.830824\pi$
$593$	−20.8005	+	12.0092i	−0.854173	+	0.493157i	0.00788396	+	0.999969i	$0.497490\pi$
$594$	6.98116	+	0.0454922i	0.286441	+	0.00186657i
$595$		−	102.150i		−	4.18773i
$596$	−7.10229	+	11.9394i	−0.290921	+	0.489058i
$597$	11.8573	−	6.84583i	0.485288	−	0.280181i
$598$	−15.7572	−	0.102681i	−0.644362	−	0.00419894i
$599$	3.69632	−	6.40221i	0.151027	−	0.261587i	−0.780578	−	0.625058i	$-0.785075\pi$
$599$	3.69632	−	6.40221i	0.151027	−	0.261587i	0.931605	+	0.363471i	$0.118408\pi$
$600$	14.5729	+	0.284922i	0.594937	+	0.0116319i
$601$	19.5092	+	33.7909i	0.795796	+	1.37836i	0.922332	+	0.386397i	$0.126281\pi$
$601$	19.5092	+	33.7909i	0.795796	+	1.37836i	−0.126536	+	0.991962i	$0.540386\pi$
$602$	−63.5174	−	0.413906i	−2.58877	−	0.0168696i
$603$	−6.99166	−	4.25637i	−0.284723	−	0.173333i
$604$	0.273139	−	20.9568i	0.0111139	−	0.852721i
$605$	36.8930	−	21.3002i	1.49992	−	0.865976i
$606$	−0.0279120	+	4.28332i	−0.00113385	+	0.173998i
$607$	−2.61353	−	1.50892i	−0.106080	−	0.0612453i	0.446021	−	0.895022i	$-0.352841\pi$
$607$	−2.61353	−	1.50892i	−0.106080	−	0.0612453i	−0.552101	+	0.833777i	$0.686174\pi$
$608$	−0.779029	+	23.9016i	−0.0315938	+	0.969337i
$609$	12.7538	+	22.0902i	0.516811	+	0.895142i
$610$	19.1913	−	32.7457i	0.777033	−	1.32583i
$611$	−7.20951			−0.291666
$612$	−13.3501	−	0.173998i	−0.539647	−	0.00703344i
$613$	−19.5653	−	33.8881i	−0.790235	−	1.36873i	−0.925821	−	0.377962i	$-0.876625\pi$
$613$	−19.5653	−	33.8881i	−0.790235	−	1.36873i	0.135585	−	0.990766i	$-0.456708\pi$
$614$	−27.2328	−	15.9603i	−1.09902	−	0.644107i
$615$	−8.40327	+	14.5549i	−0.338853	+	0.586910i
$616$	32.3843	+	58.7126i	1.30480	+	2.36560i
$617$	19.4393			0.782597			0.391298	−	0.920264i	$-0.372026\pi$
$617$	19.4393			0.782597			0.391298	+	0.920264i	$0.372026\pi$
$618$	0.182862	−	28.0616i	0.00735577	−	1.12880i
$619$	28.2648	−	16.3187i	1.13606	−	0.655904i	0.190607	−	0.981666i	$-0.438954\pi$
$619$	28.2648	−	16.3187i	1.13606	−	0.655904i	0.945452	+	0.325763i	$0.105621\pi$
$620$	4.41581	−	2.47330i	0.177343	−	0.0993303i
$621$	6.42813	−	3.71128i	0.257952	−	0.148929i
$622$	−18.7731	−	33.0109i	−0.752733	−	1.32362i
$623$	20.0988	−	34.8122i	0.805243	−	1.39472i
$624$	−5.12008	−	3.13678i	−0.204967	−	0.125572i
$625$	−24.2101			−0.968403
$626$	32.2746	−	18.3544i	1.28995	−	0.733589i
$627$			20.8691i			0.833432i
$628$	10.2409	+	0.133474i	0.408656	+	0.00532617i
$629$	4.70472	−	8.14881i	0.187589	−	0.324914i
$630$	−0.141013	+	21.6397i	−0.00561811	+	0.862145i
$631$	16.2202	+	28.0942i	0.645715	+	1.11841i	0.984136	+	0.177416i	$0.0567738\pi$
$631$	16.2202	+	28.0942i	0.645715	+	1.11841i	−0.338421	+	0.940995i	$0.609893\pi$
$632$	3.91136	−	6.47880i	0.155585	−	0.257713i
$633$	7.13792	−	4.12108i	0.283707	−	0.163798i
$634$	18.1193	−	30.9165i	0.719608	−	1.22785i
$635$	2.80683	−	4.86158i	0.111386	−	0.192926i
$636$	−9.57726	−	5.69713i	−0.379763	−	0.225906i
$637$	20.8800	+	12.0551i	0.827297	+	0.477640i
$638$	18.7500	−	31.9926i	0.742318	−	1.26660i
$639$	−5.08416	−	2.93534i	−0.201126	−	0.116120i
$640$	32.0099	−	16.5828i	1.26530	−	0.655492i
$641$	−5.91470	−	3.41485i	−0.233617	−	0.134879i	0.378623	−	0.925551i	$-0.376398\pi$
$641$	−5.91470	−	3.41485i	−0.233617	−	0.134879i	−0.612239	+	0.790672i	$0.709731\pi$
$642$	−9.79603	+	5.57095i	−0.386619	+	0.219868i
$643$		−	3.68576i		−	0.145352i	−0.997356	−	0.0726762i	$-0.976846\pi$
$643$		−	3.68576i		−	0.145352i	0.997356	−	0.0726762i	$-0.0231540\pi$
$644$	61.2687	+	36.4463i	2.41433	+	1.43619i
$645$			29.8022i			1.17346i
$646$	0.260070	−	39.9099i	0.0102323	−	1.57023i
$647$	4.18194	+	7.24333i	0.164409	+	0.284765i	0.936445	−	0.350814i	$-0.114095\pi$
$647$	4.18194	+	7.24333i	0.164409	+	0.284765i	−0.772036	+	0.635579i	$0.780762\pi$
$648$	2.82789	+	0.0552894i	0.111090	+	0.00217197i
$649$	23.3433	+	13.4772i	0.916304	+	0.529028i
$650$	−9.43853	−	5.53166i	−0.370210	−	0.216969i
$651$	1.90695	+	3.30293i	0.0747392	+	0.129452i
$652$	−22.4626	+	12.5814i	−0.879704	+	0.492724i
$653$	5.12267	−	2.95758i	0.200466	−	0.115739i	−0.396407	−	0.918075i	$-0.629743\pi$
$653$	5.12267	−	2.95758i	0.200466	−	0.115739i	0.596873	+	0.802336i	$0.296410\pi$
$654$	−0.0638933	+	0.0363357i	−0.00249842	+	0.00142084i
$655$	−60.1884			−2.35175
$656$	−0.549857	+	21.0905i	−0.0214683	+	0.823447i
$657$	0.0425283	+	0.0736612i	0.00165919	+	0.00287380i
$658$	28.1401	+	16.4921i	1.09702	+	0.642931i
$659$	−18.4498	−	10.6520i	−0.718703	−	0.414943i	0.0955720	−	0.995423i	$-0.469532\pi$
$659$	−18.4498	−	10.6520i	−0.718703	−	0.414943i	−0.814275	+	0.580479i	$0.802865\pi$
$660$	27.4476	−	15.3735i	1.06840	−	0.598412i
$661$			37.3045i			1.45098i	0.688235	+	0.725488i	$0.258386\pi$
$661$			37.3045i			1.45098i	−0.688235	+	0.725488i	$0.741614\pi$
$662$	−31.8718	−	0.207690i	−1.23873	−	0.00807211i
$663$	8.67848	+	5.01052i	0.337044	+	0.194593i
$664$	7.61971	−	4.20282i	0.295702	−	0.163101i
$665$	−64.6885			−2.50851
$666$	−1.00791	+	1.71977i	−0.0390557	+	0.0666397i
$667$		−	39.4260i		−	1.52658i
$668$	−0.840249	+	0.470625i	−0.0325102	+	0.0182090i
$669$		−	11.7095i		−	0.452716i
$670$	−36.8692	−	1.09777i	−1.42438	−	0.0424105i
$671$		−	41.5789i		−	1.60514i
$672$	12.8091	+	23.9559i	0.494123	+	0.924120i
$673$		−	33.7802i		−	1.30213i	−0.759022	−	0.651065i	$-0.774323\pi$
$673$		−	33.7802i		−	1.30213i	0.759022	−	0.651065i	$-0.225677\pi$
$674$	−27.2104	−	15.9472i	−1.04811	−	0.614265i
$675$	5.15329			0.198350
$676$	−10.5031	−	18.7521i	−0.403965	−	0.721235i
$677$	24.8322	+	14.3369i	0.954379	+	0.551011i	0.894438	−	0.447191i	$-0.147576\pi$
$677$	24.8322	+	14.3369i	0.954379	+	0.551011i	0.0599404	+	0.998202i	$0.480909\pi$
$678$	−0.0453615	+	6.96110i	−0.00174210	+	0.267340i
$679$			67.9178i			2.60644i
$680$	−52.6821	+	29.0580i	−2.02027	+	1.11432i
$681$	21.4107	+	12.3615i	0.820461	+	0.473694i
$682$	2.80349	−	4.78353i	0.107351	−	0.183171i
$683$	−3.11899	−	5.40225i	−0.119345	−	0.206711i	0.800163	−	0.599782i	$-0.204746\pi$
$683$	−3.11899	−	5.40225i	−0.119345	−	0.206711i	−0.919508	+	0.393071i	$0.871413\pi$
$684$	−0.110188	+	8.45425i	−0.00421313	+	0.323256i
$685$	12.8701			0.491743
$686$	−30.4213	−	53.4932i	−1.16149	−	2.04238i
$687$	6.18629	−	3.57165i	0.236022	−	0.136267i
$688$	17.8550	+	32.8758i	0.680715	+	1.25338i
$689$	4.18204	+	7.24351i	0.159323	+	0.275956i
$690$	16.9125	−	28.8574i	0.643847	−	1.09858i
$691$	−5.45141	−	3.14737i	−0.207381	−	0.119732i	0.392712	−	0.919661i	$-0.371537\pi$
$691$	−5.45141	−	3.14737i	−0.207381	−	0.119732i	−0.600094	+	0.799930i	$0.704870\pi$
$692$	−29.2218	−	0.380860i	−1.11085	−	0.0144781i
$693$	11.8531	+	20.5303i	0.450264	+	0.779880i
$694$	39.3363	+	0.256332i	1.49318	+	0.00973023i
$695$			37.6879i			1.42958i
$696$	7.76468	−	12.8615i	0.294320	−	0.487513i
$697$		−	35.2101i		−	1.33368i
$698$	−6.07083	−	10.6750i	−0.229784	−	0.404056i
$699$	−12.4280	−	7.17529i	−0.470069	−	0.271394i
$700$	24.1865	+	43.1823i	0.914163	+	1.63214i
$701$	−10.0058	−	5.77683i	−0.377912	−	0.218188i	0.298997	−	0.954254i	$-0.403348\pi$
$701$	−10.0058	−	5.77683i	−0.377912	−	0.218188i	−0.676910	+	0.736066i	$0.736681\pi$
$702$	−1.83156	−	1.07342i	−0.0691276	−	0.0405137i
$703$	−5.16041	−	2.97936i	−0.194628	−	0.112369i
$704$	21.0679	−	33.4033i	0.794026	−	1.25894i
$705$	7.65171	−	13.2532i	0.288180	−	0.499143i
$706$	29.4989	+	17.2885i	1.11021	+	0.650661i
$707$	−12.5964	+	7.27255i	−0.473737	+	0.273512i
$708$	9.38540	+	5.58300i	0.352725	+	0.209822i
$709$	−12.5632	−	21.7600i	−0.471819	−	0.817215i	0.527661	−	0.849455i	$-0.323069\pi$
$709$	−12.5632	−	21.7600i	−0.471819	−	0.817215i	−0.999480	+	0.0322401i	$0.989736\pi$
$710$	−26.4544	−	0.172388i	−0.992815	−	0.00646961i
$711$	1.33783	−	2.31720i	0.0501727	−	0.0869016i
$712$	−23.6713	−	0.462809i	−0.887118	−	0.0173445i
$713$		−	5.89497i		−	0.220768i
$714$	−22.4120	−	39.4095i	−0.838747	−	1.47486i
$715$	−23.6127			−0.883066
$716$	−10.9523	+	18.4116i	−0.409307	+	0.688073i
$717$	−13.5434	+	23.4579i	−0.505788	+	0.876050i
$718$	−10.0275	+	5.70259i	−0.374223	+	0.212819i
$719$	24.3827	−	14.0774i	0.909321	−	0.524997i	0.0291085	−	0.999576i	$-0.490733\pi$
$719$	24.3827	−	14.0774i	0.909321	−	0.524997i	0.880213	+	0.474579i	$0.157400\pi$
$720$	11.2004	−	6.08300i	0.417415	−	0.226700i
$721$	82.5238	−	47.6451i	3.07335	−	1.77440i
$722$	1.59572	+	0.0103984i	0.0593864	+	0.000386987i
$723$	13.8862			0.516432
$724$	5.85482	+	10.4531i	0.217593	+	0.388487i
$725$	13.6862	−	23.7052i	0.508292	−	0.880388i
$726$	9.56006	−	16.3121i	0.354807	−	0.605399i
$727$	4.93939	+	8.55527i	0.183192	+	0.317297i	0.942966	−	0.332890i	$-0.108024\pi$
$727$	4.93939	+	8.55527i	0.183192	+	0.317297i	−0.759774	+	0.650187i	$0.774690\pi$
$728$	0.398570	−	20.3856i	0.0147720	−	0.755542i
$729$	1.00000			0.0370370
$730$	0.330682	+	0.193804i	0.0122391	+	0.00717299i
$731$	−31.2182	−	54.0714i	−1.15465	−	1.99990i
$732$	0.219534	−	16.8440i	0.00811422	−	0.622571i
$733$	33.5042	+	19.3437i	1.23751	+	0.714475i	0.968584	−	0.248686i	$-0.0799989\pi$
$733$	33.5042	+	19.3437i	1.23751	+	0.714475i	0.268923	+	0.963162i	$0.413332\pi$
$734$	16.3082	+	0.106271i	0.601947	+	0.00392254i
$735$	−44.3215	+	25.5890i	−1.63482	+	0.943865i
$736$	1.36781	−	41.9661i	0.0504181	−	1.54689i
$737$	−35.4539	+	19.3847i	−1.30596	+	0.714043i
$738$	−0.0486061	+	7.45901i	−0.00178921	+	0.274570i
$739$	−10.1018	−	17.4968i	−0.371601	−	0.643631i	0.618211	−	0.786012i	$-0.287858\pi$
$739$	−10.1018	−	17.4968i	−0.371601	−	0.643631i	−0.989812	+	0.142381i	$0.954524\pi$
$740$	−0.117065	+	8.98189i	−0.00430338	+	0.330181i
$741$	3.17302	−	5.49583i	0.116564	−	0.201894i
$742$	0.246578	−	37.8395i	0.00905217	−	1.38913i
$743$	8.52995	−	4.92477i	0.312934	−	0.180672i	−0.335305	−	0.942110i	$-0.608839\pi$
$743$	8.52995	−	4.92477i	0.312934	−	0.180672i	0.648238	+	0.761437i	$0.275506\pi$
$744$	1.16098	−	1.92305i	0.0425634	−	0.0705023i
$745$			22.1332i			0.810896i
$746$	−0.0576357	+	8.84468i	−0.00211019	+	0.323827i
$747$	2.66441	−	1.53830i	0.0974858	−	0.0562834i
$748$	−33.6955	+	56.6445i	−1.23203	+	2.07113i
$749$	−33.1402	−	19.1335i	−1.21092	−	0.699123i
$750$	0.600451	−	0.341473i	0.0219254	−	0.0124688i
$751$		−	36.0756i		−	1.31642i	−0.752836	−	0.658208i	$-0.771315\pi$
$751$		−	36.0756i		−	1.31642i	0.752836	−	0.658208i	$-0.228685\pi$
$752$	0.500679	−	19.2043i	0.0182579	−	0.700308i
$753$	−2.31310	−	4.00640i	−0.0842939	−	0.146001i
$754$	−9.80204	+	5.57436i	−0.356969	+	0.203006i
$755$	−16.6957	−	28.9179i	−0.607620	−	1.05243i
$756$	4.69341	+	8.37956i	0.170698	+	0.304762i
$757$	−12.3267	−	7.11683i	−0.448022	−	0.258666i	0.258973	−	0.965885i	$-0.416616\pi$
$757$	−12.3267	−	7.11683i	−0.448022	−	0.258666i	−0.706994	+	0.707219i	$0.749949\pi$
$758$	11.0049	−	18.7774i	0.399715	−	0.682025i
$759$		−	36.6417i		−	1.33001i
$760$	18.4016	+	33.3621i	0.667496	+	1.21017i
$761$	15.2175			0.551632			0.275816	−	0.961210i	$-0.411052\pi$
$761$	15.2175			0.551632			0.275816	+	0.961210i	$0.411052\pi$
$762$	0.0162352	−	2.49143i	0.000588141	−	0.0902551i
$763$	−0.216152	−	0.124796i	−0.00782524	−	0.00451791i
$764$	−36.2764	−	0.472805i	−1.31243	−	0.0171055i
$765$	−18.4216	+	10.6357i	−0.666033	+	0.384534i
$766$	13.8473	−	23.6274i	0.500324	−	0.853692i
$767$	−4.09826	−	7.09840i	−0.147980	−	0.256308i
$768$	8.71115	−	13.4207i	0.314337	−	0.484279i
$769$	13.6822	+	7.89944i	0.493394	+	0.284861i	0.725981	−	0.687714i	$-0.241386\pi$
$769$	13.6822	+	7.89944i	0.493394	+	0.284861i	−0.232587	+	0.972576i	$0.574719\pi$
$770$	92.1651	+	54.0153i	3.32140	+	1.94658i
$771$	−14.5163	+	25.1430i	−0.522793	+	0.905504i
$772$	8.93788	−	15.0252i	0.321682	−	0.540769i
$773$	−1.87010	+	3.23911i	−0.0672628	+	0.116503i	−0.897696	−	0.440616i	$-0.854760\pi$
$773$	−1.87010	+	3.23911i	−0.0672628	+	0.116503i	0.830433	+	0.557119i	$0.188093\pi$
$774$	6.53870	+	11.4977i	0.235029	+	0.413277i
$775$	2.04636	−	3.54440i	0.0735074	−	0.127319i
$776$	35.0275	−	19.3202i	1.25741	−	0.693555i
$777$	−6.76882			−0.242830
$778$	0.719424	−	1.22754i	0.0257926	−	0.0440093i
$779$	−22.2976			−0.798893
$780$	−9.56571	−	0.124674i	−0.342507	−	0.00446404i
$781$	−25.0981	+	14.4904i	−0.898081	+	0.518507i
$782$	−0.456627	+	70.0732i	−0.0163290	+	2.50581i
$783$	2.65582	−	4.60001i	0.0949112	−	0.164391i
$784$	−33.5617	+	54.7818i	−1.19863	+	1.95649i
$785$	14.1312	−	8.15863i	0.504363	−	0.291194i
$786$	−23.2208	+	13.2055i	−0.828257	+	0.471025i
$787$	1.52221	+	2.63655i	0.0542610	+	0.0939828i	0.891880	−	0.452272i	$-0.149386\pi$
$787$	1.52221	+	2.63655i	0.0542610	+	0.0939828i	−0.837619	+	0.546255i	$0.816053\pi$
$788$	−24.1628	+	13.5336i	−0.860763	+	0.482115i
$789$		−	18.2753i		−	0.650616i
$790$	0.0785689	−	12.0571i	0.00279536	−	0.428971i
$791$	−20.4713	+	11.8191i	−0.727874	+	0.420238i
$792$	7.21635	−	11.9532i	0.256422	−	0.424739i
$793$	−6.32181	+	10.9497i	−0.224494	+	0.388835i
$794$	19.0778	+	33.5467i	0.677047	+	1.19053i
$795$	−17.7542			−0.629676
$796$	0.356868	−	27.3810i	0.0126488	−	0.970494i
$797$	−19.3216	+	33.4659i	−0.684405	+	1.18542i	0.289218	+	0.957263i	$0.406605\pi$
$797$	−19.3216	+	33.4659i	−0.684405	+	1.18542i	−0.973623	+	0.228161i	$0.926729\pi$
$798$	−24.9569	+	14.1929i	−0.883466	+	0.502422i
$799$			32.0610i			1.13424i
$800$	15.3904	−	24.7576i	0.544132	−	0.875315i
$801$	−8.37066			−0.295763
$802$	14.0289	−	7.97816i	0.495378	−	0.281719i
$803$	0.419885			0.0148174
$804$	−14.4650	+	7.66569i	−0.510142	+	0.270348i
$805$	113.579			4.00314
$806$	−1.46560	+	0.833478i	−0.0516235	+	0.0293580i
$807$	30.4479			1.07182
$808$	7.33394	+	4.42762i	0.258007	+	0.155763i
$809$		−	17.1937i		−	0.604498i	−0.953229	−	0.302249i	$-0.902263\pi$
$809$		−	17.1937i		−	0.604498i	0.953229	−	0.302249i	$-0.0977374\pi$
$810$	3.91715	−	2.22766i	0.137635	−	0.0782721i
$811$	5.69070	−	9.85658i	0.199827	−	0.346111i	−0.748645	−	0.662971i	$-0.769295\pi$
$811$	5.69070	−	9.85658i	0.199827	−	0.346111i	0.948472	+	0.316860i	$0.102629\pi$
$812$	51.0109	+	0.664846i	1.79013	+	0.0233315i
$813$	3.90668			0.137013
$814$	4.86451	+	8.55382i	0.170501	+	0.299811i
$815$	−20.5094	+	35.5234i	−0.718415	+	1.24433i
$816$	−13.9494	+	22.7692i	−0.488327	+	0.797083i
$817$	−34.2419	+	19.7696i	−1.19797	+	0.691650i
$818$	−0.101897	+	15.6369i	−0.00356273	+	0.546730i
$819$		−	7.20879i		−	0.251896i
$820$	16.4258	+	29.3263i	0.573612	+	1.02412i
$821$	21.5853	+	37.3868i	0.753331	+	1.30481i	0.946200	+	0.323582i	$0.104887\pi$
$821$	21.5853	+	37.3868i	0.753331	+	1.30481i	−0.192870	+	0.981224i	$0.561779\pi$
$822$	4.96532	−	2.82375i	0.173185	−	0.0984895i
$823$	−21.4130	+	12.3628i	−0.746409	+	0.430940i	−0.824395	−	0.566015i	$-0.808484\pi$
$823$	−21.4130	+	12.3628i	−0.746409	+	0.430940i	0.0779858	+	0.996954i	$0.475151\pi$
$824$	−48.0473	−	29.0070i	−1.67381	−	1.01051i
$825$	12.7197	−	22.0311i	0.442843	−	0.767026i
$826$	−0.241639	+	37.0814i	−0.00840768	+	1.29023i
$827$	−12.1087	+	6.99099i	−0.421062	+	0.243100i	−0.695532	−	0.718495i	$-0.744831\pi$
$827$	−12.1087	+	6.99099i	−0.421062	+	0.243100i	0.274469	+	0.961596i	$0.411498\pi$
$828$	0.193466	−	14.8439i	0.00672341	−	0.515860i
$829$	15.7065			0.545509			0.272754	−	0.962084i	$-0.412065\pi$
$829$	15.7065			0.545509			0.272754	+	0.962084i	$0.412065\pi$
$830$	7.01010	−	11.9612i	0.243324	−	0.415178i
$831$	9.87146			0.342437
$832$	−10.6269	+	5.59344i	−0.368423	+	0.193918i
$833$	53.6096	−	92.8545i	1.85746	−	3.21722i
$834$	8.26884	+	14.5400i	0.286326	+	0.503480i
$835$	−0.767188	+	1.32881i	−0.0265496	+	0.0459853i
$836$	35.8713	+	21.3384i	1.24064	+	0.738005i
$837$	0.397098	−	0.687793i	0.0137257	−	0.0237736i
$838$	−36.7026	−	21.5104i	−1.26787	−	0.743064i
$839$	37.5542	+	21.6819i	1.29652	+	0.748544i	0.979801	−	0.199977i	$-0.0640868\pi$
$839$	37.5542	+	21.6819i	1.29652	+	0.748544i	0.316715	+	0.948521i	$0.397420\pi$
$840$	37.0516	+	22.3687i	1.27840	+	0.771793i
$841$	0.393261	+	0.681148i	0.0135607	+	0.0234879i
$842$	11.2277	−	19.1576i	0.386933	−	0.660215i
$843$	9.02229	−	5.20902i	0.310744	−	0.179408i
$844$	0.214829	−	16.4829i	0.00739471	−	0.567366i
$845$	−29.6554	−	17.1216i	−1.02018	−	0.589000i
$846$	0.0442589	−	6.79190i	0.00152165	−	0.233510i
$847$	64.2025			2.20602
$848$	−19.5853	+	10.6368i	−0.672560	+	0.365270i
$849$		−	20.9096i		−	0.717615i
$850$	−24.5995	+	41.9736i	−0.843757	+	1.43968i
$851$	9.06057	+	5.23112i	0.310592	+	0.179321i
$852$	−10.2440	+	5.73766i	−0.350952	+	0.196569i
$853$	−23.2354	−	40.2450i	−0.795566	−	1.37796i	−0.922479	−	0.386047i	$-0.873840\pi$
$853$	−23.2354	−	40.2450i	−0.795566	−	1.37796i	0.126913	−	0.991914i	$-0.459493\pi$
$854$	49.7233	−	28.2774i	1.70150	−	0.967631i
$855$	6.73528	+	11.6658i	0.230342	+	0.398963i
$856$	−0.440580	+	22.5343i	−0.0150587	+	0.770208i
$857$		−	13.7589i		−	0.469994i	−0.971996	−	0.234997i	$-0.924492\pi$
$857$		−	13.7589i		−	0.469994i	0.971996	−	0.234997i	$-0.0755081\pi$
$858$	−9.10982	+	5.18070i	−0.311004	+	0.176866i
$859$	−13.0102	−	7.51144i	−0.443902	−	0.256287i	0.261349	−	0.965244i	$-0.415833\pi$
$859$	−13.0102	−	7.51144i	−0.443902	−	0.256287i	−0.705252	+	0.708957i	$0.749166\pi$
$860$	51.2261	+	30.4724i	1.74680	+	1.03910i
$861$	−21.9355	+	12.6645i	−0.747560	+	0.431604i
$862$	−0.105709	+	16.2219i	−0.00360045	+	0.552519i
$863$		−	16.6502i		−	0.566779i	−0.959005	−	0.283389i	$-0.908541\pi$
$863$		−	16.6502i		−	0.566779i	0.959005	−	0.283389i	$-0.0914589\pi$
$864$	2.98651	−	4.80424i	0.101603	−	0.163444i
$865$	−40.3226	+	23.2802i	−1.37101	+	0.791552i
$866$	−0.155509	+	23.8642i	−0.00528442	+	0.810939i
$867$	13.7820	−	23.8712i	0.468062	−	0.810708i
$868$	7.62715	+	0.0994077i	0.258882	+	0.00337412i
$869$	−6.60426	−	11.4389i	−0.224034	−	0.388038i
$870$	0.155972	−	23.9352i	0.00528795	−	0.811480i
$871$	12.2840	+	0.285650i	0.416228	+	0.00967888i
$872$	−0.00287362	+	0.146977i	−9.73132e−5	+	0.00497727i
$873$	12.2482	−	7.07150i	0.414539	−	0.239334i
$874$	44.3754	+	0.289169i	1.50102	+	0.00978128i
$875$	2.03134	+	1.17279i	0.0686718	+	0.0396477i
$876$	0.170099	+	0.00221697i	0.00574711	+	7.49044e-5i
$877$	5.69696	+	9.86742i	0.192373	+	0.333199i	0.946036	−	0.324061i	$-0.105048\pi$
$877$	5.69696	+	9.86742i	0.192373	+	0.333199i	−0.753663	+	0.657261i	$0.771715\pi$
$878$	7.92657	+	4.64554i	0.267509	+	0.156779i
$879$	11.1507			0.376105
$880$	1.63983	−	62.8981i	0.0552788	−	2.12030i
$881$	14.7105	+	25.4793i	0.495609	+	0.858419i	0.999987	−	0.00506324i	$-0.00161169\pi$
$881$	14.7105	+	25.4793i	0.495609	+	0.858419i	−0.504378	+	0.863483i	$0.668278\pi$
$882$	−11.4850	+	19.5965i	−0.386719	+	0.659850i
$883$	−12.9491	+	22.4285i	−0.435772	+	0.754780i	−0.997358	−	0.0726385i	$-0.976858\pi$
$883$	−12.9491	+	22.4285i	−0.435772	+	0.754780i	0.561586	+	0.827418i	$0.310191\pi$
$884$	17.4861	−	9.79399i	0.588121	−	0.329408i
$885$	17.3985			0.584845
$886$	−10.8758	−	0.0708715i	−0.365381	−	0.00238098i
$887$	9.35385	−	5.40045i	0.314072	−	0.181329i	−0.334675	−	0.942333i	$-0.608627\pi$
$887$	9.35385	−	5.40045i	0.314072	−	0.181329i	0.648747	+	0.761004i	$0.275293\pi$
$888$	1.92549	+	3.49091i	0.0646152	+	0.117147i
$889$	7.32682	−	4.23014i	0.245734	−	0.141874i
$890$	−32.7891	+	18.6470i	−1.09909	+	0.625049i
$891$	2.46827	−	4.27516i	0.0826900	−	0.143223i
$892$	−20.1271	−	11.9728i	−0.673906	−	0.400880i
$893$	20.3033			0.679425
$894$	4.85608	+	8.53901i	0.162412	+	0.285587i
$895$			34.1312i			1.14088i
$896$	54.2744	+	2.47741i	1.81318	+	0.0827644i
$897$	−5.57115	+	9.64951i	−0.186015	+	0.322188i
$898$	25.2538	+	0.164565i	0.842731	+	0.00549160i
$899$	−2.10924	−	3.65331i	−0.0703470	−	0.121845i
$900$	5.26917	−	8.85784i	0.175639	−	0.295261i
$901$	32.2122	−	18.5977i	1.07314	−	0.619580i
$902$	31.7685	+	18.6186i	1.05777	+	0.619932i
$903$	−22.4573	+	38.8971i	−0.747331	+	1.29441i
$904$	11.9189	+	7.19561i	0.396415	+	0.239323i
$905$	16.5311	+	9.54421i	0.549511	+	0.317260i
$906$	−12.7859	−	7.49346i	−0.424784	−	0.248954i
$907$	2.93560	+	1.69487i	0.0974750	+	0.0562772i	0.547945	−	0.836514i	$-0.315410\pi$
$907$	2.93560	+	1.69487i	0.0974750	+	0.0562772i	−0.450470	+	0.892792i	$0.648744\pi$
$908$	43.1400	−	24.1628i	1.43165	−	0.801872i
$909$	2.62304	+	1.51442i	0.0870009	+	0.0502300i
$910$	−16.0588	−	28.2379i	−0.532342	−	0.936079i
$911$			17.5477i			0.581382i	0.956817	+	0.290691i	$0.0938851\pi$
$911$			17.5477i			0.581382i	−0.956817	+	0.290691i	$0.906115\pi$
$912$	14.4191	+	8.83377i	0.477464	+	0.292515i
$913$		−	15.1877i		−	0.502640i
$914$	−32.8919	−	0.214338i	−1.08797	−	0.00708966i
$915$	−13.4191	−	23.2426i	−0.443623	−	0.768377i
$916$	0.186188	−	14.2854i	0.00615181	−	0.472003i
$917$	−78.5564	−	45.3545i	−2.59416	−	1.49774i
$918$	−4.77356	+	8.14501i	−0.157551	+	0.268825i
$919$	−15.8363	−	27.4293i	−0.522392	−	0.904810i	−0.999661	−	0.0260522i	$-0.991706\pi$
$919$	−15.8363	−	27.4293i	−0.522392	−	0.904810i	0.477268	−	0.878758i	$-0.341627\pi$
$920$	−32.3093	−	58.5767i	−1.06521	−	1.93122i
$921$	−19.3296	+	11.1599i	−0.636932	+	0.367733i
$922$	−12.1051	−	21.2858i	−0.398661	−	0.701012i
$923$	8.81270			0.290074
$924$	47.4086	+	0.617895i	1.55963	+	0.0203273i
$925$	3.63183	+	6.29051i	0.119414	+	0.206831i
$926$	16.7345	−	28.5537i	0.549929	−	0.938331i
$927$	−17.1845	−	9.92149i	−0.564414	−	0.325865i
$928$	−14.1679	−	26.4972i	−0.465085	−	0.869813i
$929$		−	9.72747i		−	0.319148i	−0.987186	−	0.159574i	$-0.948988\pi$
$929$		−	9.72747i		−	0.319148i	0.987186	−	0.159574i	$-0.0510121\pi$
$930$	0.0233209	−	3.57879i	0.000764724	−	0.117353i
$931$	−58.8021	−	33.9494i	−1.92716	−	1.11265i
$932$	−25.0408	+	14.0254i	−0.820240	+	0.459418i
$933$	−26.8528			−0.879122
$934$	8.73624	+	5.12006i	0.285858	+	0.167534i
$935$			105.007i			3.43409i
$936$	−3.71782	+	2.05065i	−0.121521	+	0.0670275i
$937$			28.3754i			0.926982i	0.886102	+	0.463491i	$0.153403\pi$
$937$			28.3754i			0.926982i	−0.886102	+	0.463491i	$0.846597\pi$
$938$	−47.2935	−	29.2153i	−1.54419	−	0.953913i
$939$		−	26.2539i		−	0.856764i
$940$	−14.9567	−	26.7035i	−0.487833	−	0.870972i
$941$		−	5.91463i		−	0.192812i	−0.995342	−	0.0964058i	$-0.969265\pi$
$941$		−	5.91463i		−	0.192812i	0.995342	−	0.0964058i	$-0.0307346\pi$
$942$	3.66180	−	6.24804i	0.119308	−	0.203572i
$943$	39.1498			1.27489
$944$	19.1929	−	10.4237i	0.624676	−	0.339264i
$945$	13.2518	+	7.65094i	0.431082	+	0.248885i
$946$	65.2939	+	0.425483i	2.12289	+	0.0138336i
$947$			45.8907i			1.49125i	0.666367	+	0.745624i	$0.267848\pi$
$947$			45.8907i			1.49125i	−0.666367	+	0.745624i	$0.732152\pi$
$948$	−2.61504	−	4.66887i	−0.0849326	−	0.151638i
$949$	−0.110576	−	0.0638409i	−0.00358944	−	0.00207236i
$950$	26.5807	+	15.5782i	0.862391	+	0.505423i
$951$	−12.6695	−	21.9443i	−0.410838	−	0.711592i
$952$	−90.6559	−	1.77246i	−2.93817	−	0.0574457i
$953$	−7.14016			−0.231293			−0.115646	−	0.993290i	$-0.536894\pi$
$953$	−7.14016			−0.231293			−0.115646	+	0.993290i	$0.536894\pi$
$954$	−6.84960	+	3.89533i	−0.221764	+	0.126116i
$955$	−50.0570	+	28.9004i	−1.61981	+	0.935196i
$956$	26.4731	+	47.2647i	0.856201	+	1.52865i
$957$	−13.1105	−	22.7081i	−0.423803	−	0.734049i
$958$	52.6781	+	30.8731i	1.70195	+	0.997465i
$959$	16.7978	+	9.69821i	0.542429	+	0.313171i
$960$	0.996408	−	25.4719i	0.0321589	−	0.822102i
$961$	15.1846	+	26.3005i	0.489827	+	0.848405i
$962$	0.0194988	−	2.99225i	0.000628665	−	0.0964739i
$963$			7.96862i			0.256785i
$964$	14.1984	−	23.8685i	0.457300	−	0.768753i
$965$		−	27.8535i		−	0.896636i
$966$	43.8190	−	24.9196i	1.40985	−	0.801776i
$967$	2.28035	+	1.31656i	0.0733312	+	0.0423378i	0.536217	−	0.844080i	$-0.319853\pi$
$967$	2.28035	+	1.31656i	0.0733312	+	0.0423378i	−0.462886	+	0.886418i	$0.653186\pi$
$968$	−18.2634	−	33.1114i	−0.587006	−	1.06424i
$969$	−24.4402	−	14.1106i	−0.785133	−	0.453297i
$970$	32.2252	−	54.9850i	1.03469	−	1.76546i
$971$	23.4808	+	13.5566i	0.753533	+	0.435053i	0.826969	−	0.562247i	$-0.190063\pi$
$971$	23.4808	+	13.5566i	0.753533	+	0.435053i	−0.0734359	+	0.997300i	$0.523396\pi$
$972$	1.02249	−	1.71887i	0.0327963	−	0.0551328i
$973$	−28.3995	+	49.1893i	−0.910445	+	1.57694i
$974$	−16.0322	+	27.3553i	−0.513703	+	0.876520i
$975$	−6.69940	+	3.86790i	−0.214552	+	0.123872i
$976$	−28.7281	−	17.6001i	−0.919565	−	0.563365i
$977$	12.8494	+	22.2558i	0.411088	+	0.712026i	0.995009	−	0.0997848i	$-0.0318154\pi$
$977$	12.8494	+	22.2558i	0.411088	+	0.712026i	−0.583921	+	0.811811i	$0.698482\pi$
$978$	−0.118630	+	18.2048i	−0.00379338	+	0.582126i
$979$	−20.6610	+	35.7859i	−0.660329	+	1.14372i
$980$	−1.33393	+	102.347i	−0.0426110	+	3.26937i
$981$			0.0519742i			0.00165941i
$982$	39.8737	−	22.6760i	1.27242	−	0.723619i
$983$	−28.1299			−0.897204			−0.448602	−	0.893732i	$-0.648078\pi$
$983$	−28.1299			−0.897204			−0.448602	+	0.893732i	$0.648078\pi$
$984$	12.7714	+	7.71029i	0.407136	+	0.245795i
$985$	−22.0618	+	38.2121i	−0.702946	+	1.21754i
$986$	24.7894	+	43.5901i	0.789457	+	1.38819i
$987$	19.9737	−	11.5318i	0.635769	−	0.367061i
$988$	−6.20225	−	11.0734i	−0.197320	−	0.352293i
$989$	60.1215	−	34.7111i	1.91175	−	1.10375i
$990$	0.144958	−	22.2449i	0.00460705	−	0.706990i
$991$	−58.8811			−1.87042			−0.935209	−	0.354095i	$-0.884789\pi$
$991$	−58.8811			−1.87042			−0.935209	+	0.354095i	$0.884789\pi$
$992$	−2.11839	−	3.96186i	−0.0672589	−	0.125789i
$993$	−11.2686	+	19.5178i	−0.357599	+	0.619379i
$994$	−34.3977	−	20.1595i	−1.09103	−	0.639421i
$995$	−21.8137	−	37.7824i	−0.691541	−	1.19778i
$996$	0.0801903	−	6.15267i	0.00254093	−	0.194955i
$997$	49.9353			1.58147			0.790734	−	0.612160i	$-0.209699\pi$
$997$	49.9353			1.58147			0.790734	+	0.612160i	$0.209699\pi$
$998$	3.20533	−	5.46918i	0.101463	−	0.173124i
$999$	0.704760	+	1.22068i	0.0222976	+	0.0386206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.13	✓	68
4.3	odd	2		804.2.j.b.499.24	yes	68
67.38	odd	6		804.2.j.b.775.24	yes	68
268.239	even	6	inner	804.2.j.a.775.13	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.13	✓	68	1.1	even	1	trivial
804.2.j.a.775.13	yes	68	268.239	even	6	inner
804.2.j.b.499.24	yes	68	4.3	odd	2
804.2.j.b.775.24	yes	68	67.38	odd	6

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.699111 - 1.22933i) q^{2} -1.00000 q^{3} +(-1.02249 + 1.71887i) q^{4} +3.18642i q^{5} +(0.699111 + 1.22933i) q^{6} +(-2.40111 + 4.15884i) q^{7} +(2.82789 + 0.0552894i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.699111 - 1.22933i) q^{2} -1.00000 q^{3} +(-1.02249 + 1.71887i) q^{4} +3.18642i q^{5} +(0.699111 + 1.22933i) q^{6} +(-2.40111 + 4.15884i) q^{7} +(2.82789 + 0.0552894i) q^{8} +1.00000 q^{9} +(3.91715 - 2.22766i) q^{10} +(2.46827 - 4.27516i) q^{11} +(1.02249 - 1.71887i) q^{12} +(-1.30002 + 0.750569i) q^{13} +(6.79121 + 0.0442545i) q^{14} -3.18642i q^{15} +(-1.90904 - 3.51505i) q^{16} +(3.33782 + 5.78127i) q^{17} +(-0.699111 - 1.22933i) q^{18} +(3.66111 - 2.11374i) q^{19} +(-5.47705 - 3.25808i) q^{20} +(2.40111 - 4.15884i) q^{21} +(-6.98116 - 0.0454922i) q^{22} +(-6.42813 + 3.71128i) q^{23} +(-2.82789 - 0.0552894i) q^{24} -5.15329 q^{25} +(1.83156 + 1.07342i) q^{26} -1.00000 q^{27} +(-4.69341 - 8.37956i) q^{28} +(-2.65582 + 4.60001i) q^{29} +(-3.91715 + 2.22766i) q^{30} +(-0.397098 + 0.687793i) q^{31} +(-2.98651 + 4.80424i) q^{32} +(-2.46827 + 4.27516i) q^{33} +(4.77356 - 8.14501i) q^{34} +(-13.2518 - 7.65094i) q^{35} +(-1.02249 + 1.71887i) q^{36} +(-0.704760 - 1.22068i) q^{37} +(-5.15800 - 3.02296i) q^{38} +(1.30002 - 0.750569i) q^{39} +(-0.176175 + 9.01084i) q^{40} +(-4.56779 - 2.63721i) q^{41} +(-6.79121 - 0.0442545i) q^{42} -9.35287 q^{43} +(4.82468 + 8.61393i) q^{44} +3.18642i q^{45} +(9.05635 + 5.30767i) q^{46} +(4.15926 + 2.40135i) q^{47} +(1.90904 + 3.51505i) q^{48} +(-8.03064 - 13.9095i) q^{49} +(3.60272 + 6.33507i) q^{50} +(-3.33782 - 5.78127i) q^{51} +(0.0391266 - 3.00202i) q^{52} -5.57183i q^{53} +(0.699111 + 1.22933i) q^{54} +(13.6225 + 7.86494i) q^{55} +(-7.02000 + 11.6280i) q^{56} +(-3.66111 + 2.11374i) q^{57} +(7.51163 + 0.0489490i) q^{58} +5.46021i q^{59} +(5.47705 + 3.25808i) q^{60} +(7.29427 - 4.21135i) q^{61} +(1.12314 + 0.00731885i) q^{62} +(-2.40111 + 4.15884i) q^{63} +(7.99389 + 0.312704i) q^{64} +(-2.39163 - 4.14243i) q^{65} +(6.98116 + 0.0454922i) q^{66} +(-6.99166 - 4.25637i) q^{67} +(-13.3501 - 0.173998i) q^{68} +(6.42813 - 3.71128i) q^{69} +(-0.141013 + 21.6397i) q^{70} +(-5.08416 - 2.93534i) q^{71} +(2.82789 + 0.0552894i) q^{72} +(0.0425283 + 0.0736612i) q^{73} +(-1.00791 + 1.71977i) q^{74} +5.15329 q^{75} +(-0.110188 + 8.45425i) q^{76} +(11.8531 + 20.5303i) q^{77} +(-1.83156 - 1.07342i) q^{78} +(1.33783 - 2.31720i) q^{79} +(11.2004 - 6.08300i) q^{80} +1.00000 q^{81} +(-0.0486061 + 7.45901i) q^{82} +(2.66441 - 1.53830i) q^{83} +(4.69341 + 8.37956i) q^{84} +(-18.4216 + 10.6357i) q^{85} +(6.53870 + 11.4977i) q^{86} +(2.65582 - 4.60001i) q^{87} +(7.21635 - 11.9532i) q^{88} -8.37066 q^{89} +(3.91715 - 2.22766i) q^{90} -7.20879i q^{91} +(0.193466 - 14.8439i) q^{92} +(0.397098 - 0.687793i) q^{93} +(0.0442589 - 6.79190i) q^{94} +(6.73528 + 11.6658i) q^{95} +(2.98651 - 4.80424i) q^{96} +(12.2482 - 7.07150i) q^{97} +(-11.4850 + 19.5965i) q^{98} +(2.46827 - 4.27516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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